LMFDB - Embedded newform 22.14.c.b.9.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,14,Mod(3,22)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 14, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("22.3");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	22.c (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$23.5908043694$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			9.5
Character	$\chi$	$=$	22.9
Dual form			22.14.c.b.5.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(19.7771 - 60.8676i) q^{2} +(697.531 - 506.786i) q^{3} +(-3313.73 - 2407.57i) q^{4} +(7802.80 + 24014.5i) q^{5} +(-17051.7 - 52479.8i) q^{6} +(9628.39 + 6995.43i) q^{7} +(-212079. + 154084. i) q^{8} +(-262955. + 809293. i) q^{9} +1.61602e6 q^{10} +(-5.75635e6 + 1.17778e6i) q^{11} -3.53155e6 q^{12} +(-7.65534e6 + 2.35607e7i) q^{13} +(616217. - 447708. i) q^{14} +(1.76129e7 + 1.27965e7i) q^{15} +(5.18444e6 + 1.59561e7i) q^{16} +(-2.05669e7 - 6.32984e7i) q^{17} +(4.40593e7 + 3.20109e7i) q^{18} +(-1.68420e8 + 1.22364e8i) q^{19} +(3.19603e7 - 9.83635e7i) q^{20} +1.02613e7 q^{21} +(-4.21552e7 + 3.73668e8i) q^{22} -1.61296e8 q^{23} +(-6.98439e7 + 2.14957e8i) q^{24} +(4.71755e8 - 3.42750e8i) q^{25} +(1.28268e9 + 9.31925e8i) q^{26} +(6.51500e8 + 2.00511e9i) q^{27} +(-1.50639e7 - 4.63620e7i) q^{28} +(3.74579e9 + 2.72147e9i) q^{29} +(1.12723e9 - 8.18979e8i) q^{30} +(-5.65131e8 + 1.73930e9i) q^{31} +1.07374e9 q^{32} +(-3.41835e9 + 3.73878e9i) q^{33} -4.25958e9 q^{34} +(-9.28637e7 + 2.85805e8i) q^{35} +(2.81979e9 - 2.04870e9i) q^{36} +(7.48615e9 + 5.43901e9i) q^{37} +(4.11717e9 + 1.26713e10i) q^{38} +(6.60041e9 + 2.03140e10i) q^{39} +(-5.35507e9 - 3.89069e9i) q^{40} +(-1.29280e10 + 9.39272e9i) q^{41} +(2.02938e8 - 6.24580e8i) q^{42} +2.18383e10 q^{43} +(2.19106e10 + 9.95596e9i) q^{44} -2.14866e10 q^{45} +(-3.18997e9 + 9.81771e9i) q^{46} +(-8.88102e10 + 6.45244e10i) q^{47} +(1.17026e10 + 8.50246e9i) q^{48} +(-2.98966e10 - 9.20122e10i) q^{49} +(-1.15324e10 - 3.54932e10i) q^{50} +(-4.64248e10 - 3.37296e10i) q^{51} +(8.20918e10 - 5.96432e10i) q^{52} +(8.34110e10 - 2.56713e11i) q^{53} +1.34931e11 q^{54} +(-7.31994e10 - 1.29046e11i) q^{55} -3.11986e9 q^{56} +(-5.54657e10 + 1.70706e11i) q^{57} +(2.39730e11 - 1.74174e11i) q^{58} +(-3.32172e11 - 2.41337e11i) q^{59} +(-2.75560e10 - 8.48086e10i) q^{60} +(-4.00698e10 - 1.23322e11i) q^{61} +(9.46901e10 + 6.87964e10i) q^{62} +(-8.19319e9 + 5.95270e9i) q^{63} +(2.12355e10 - 6.53561e10i) q^{64} -6.25533e11 q^{65} +(1.59965e11 + 2.82009e11i) q^{66} -4.98714e11 q^{67} +(-8.42420e10 + 2.59270e11i) q^{68} +(-1.12509e11 + 8.17426e10i) q^{69} +(1.55597e10 + 1.13048e10i) q^{70} +(5.76027e11 + 1.77283e12i) q^{71} +(-6.89321e10 - 2.12151e11i) q^{72} +(-4.68122e11 - 3.40110e11i) q^{73} +(4.79114e11 - 3.48097e11i) q^{74} +(1.55363e11 - 4.78158e11i) q^{75} +8.52700e11 q^{76} +(-6.36634e10 - 2.89280e10i) q^{77} +1.36700e12 q^{78} +(-5.64604e11 + 1.73767e12i) q^{79} +(-3.42725e11 + 2.49004e11i) q^{80} +(3.73030e11 + 2.71022e11i) q^{81} +(3.16035e11 + 9.72655e11i) q^{82} +(6.96377e11 + 2.14323e12i) q^{83} +(-3.40032e10 - 2.47047e10i) q^{84} +(1.35960e12 - 9.87809e11i) q^{85} +(4.31898e11 - 1.32924e12i) q^{86} +3.99201e12 q^{87} +(1.03932e12 - 1.13675e12i) q^{88} -4.65461e12 q^{89} +(-4.24942e11 + 1.30784e12i) q^{90} +(-2.38526e11 + 1.73299e11i) q^{91} +(5.34492e11 + 3.88331e11i) q^{92} +(4.87254e11 + 1.49961e12i) q^{93} +(2.17104e12 + 6.68177e12i) q^{94} +(-4.25267e12 - 3.08975e12i) q^{95} +(7.48968e11 - 5.44157e11i) q^{96} +(-1.11456e12 + 3.43027e12i) q^{97} -6.19183e12 q^{98} +(5.60493e11 - 4.96828e12i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 448 q^{2} - 1248 q^{3} - 28672 q^{4} + 71554 q^{5} + 99008 q^{6} + 361734 q^{7} - 1835008 q^{8} - 8615367 q^{9} + 2898176 q^{10} + 8699239 q^{11} - 2449408 q^{12} + 32373940 q^{13} + 23150976 q^{14}+ \cdots + 71382923151637 q^{99}+O(q^{100}) $ 28 * q - 448 * q^2 - 1248 * q^3 - 28672 * q^4 + 71554 * q^5 + 99008 * q^6 + 361734 * q^7 - 1835008 * q^8 - 8615367 * q^9 + 2898176 * q^10 + 8699239 * q^11 - 2449408 * q^12 + 32373940 * q^13 + 23150976 * q^14 - 192099788 * q^15 - 117440512 * q^16 + 288881082 * q^17 - 275612928 * q^18 - 98588517 * q^19 + 293085184 * q^20 + 1362925660 * q^21 - 44352704 * q^22 - 233099500 * q^23 + 405536768 * q^24 + 1117600307 * q^25 - 2827224960 * q^26 + 3575804241 * q^27 - 1485029376 * q^28 - 16868227562 * q^29 - 12294386432 * q^30 - 10874790260 * q^31 + 30064771072 * q^32 + 53369498501 * q^33 + 6456111488 * q^34 + 18823205444 * q^35 - 17639227392 * q^36 + 47951509642 * q^37 + 14611374592 * q^38 - 161088016778 * q^39 - 24692916224 * q^40 - 155498856970 * q^41 - 47678239360 * q^42 + 156723459918 * q^43 + 31490678784 * q^44 + 75277819092 * q^45 + 46604369920 * q^46 + 394942115908 * q^47 - 20937965568 * q^48 - 10631171627 * q^49 - 421539129152 * q^50 - 468879528009 * q^51 - 180942397440 * q^52 + 608978721416 * q^53 + 286529794304 * q^54 + 82053078738 * q^55 + 430964736 * q^56 - 655027400217 * q^57 - 1079566563968 * q^58 + 381384884765 * q^59 + 528673062912 * q^60 + 1151615204532 * q^61 - 101484696320 * q^62 + 5117893076470 * q^63 - 481036337152 * q^64 - 5194662408432 * q^65 - 2892007512576 * q^66 + 833522448542 * q^67 + 1183256911872 * q^68 - 4423665001426 * q^69 + 835597274496 * q^70 + 3476544683262 * q^71 - 2258466766848 * q^72 - 3737607886538 * q^73 + 3068896617088 * q^74 + 9622942863695 * q^75 - 1062618816512 * q^76 - 4431389843152 * q^77 - 2335610564352 * q^78 + 7224103591056 * q^79 - 1580346638336 * q^80 - 9164585352662 * q^81 + 1269347381440 * q^82 + 9607066728079 * q^83 + 260135567360 * q^84 + 25585834186966 * q^85 - 3541381155008 * q^86 - 34193079605396 * q^87 - 4585813704704 * q^88 + 19963863911122 * q^89 + 15393877925888 * q^90 - 11356103019586 * q^91 - 2505291898880 * q^92 + 6475155937894 * q^93 - 39623598881408 * q^94 - 51625880722484 * q^95 - 1340029796352 * q^96 + 4169205798475 * q^97 + 38124564609792 * q^98 + 71382923151637 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	19.7771	−	60.8676i	0.218508	−	0.672499i
$2$	19.7771	−	60.8676i	0.218508	−	0.672499i
$3$	697.531	−	506.786i	0.552428	−	0.401362i	−0.276252	−	0.961085i	$-0.589092\pi$
$3$	697.531	−	506.786i	0.552428	−	0.401362i	0.828680	+	0.559723i	$0.189092\pi$
$4$	−3313.73	−	2407.57i	−0.404508	−	0.293893i
$5$	7802.80	+	24014.5i	0.223329	+	0.687336i	0.998457	+	0.0555318i	$0.0176854\pi$
$5$	7802.80	+	24014.5i	0.223329	+	0.687336i	−0.775128	+	0.631804i	$0.782315\pi$
$6$	−17051.7	−	52479.8i	−0.149206	−	0.459208i
$7$	9628.39	+	6995.43i	0.0309326	+	0.0224738i	0.603144	−	0.797632i	$-0.293914\pi$
$7$	9628.39	+	6995.43i	0.0309326	+	0.0224738i	−0.572212	+	0.820106i	$0.693914\pi$
$8$	−212079.	+	154084.i	−0.286031	+	0.207813i
$9$	−262955.	+	809293.i	−0.164932	+	0.507609i
$10$	1.61602e6			0.511032
$11$	−5.75635e6	+	1.17778e6i	−0.979703	+	0.200453i
$11$	−5.75635e6	+	1.17778e6i	−0.979703	+	0.200453i
$12$	−3.53155e6			−0.341419
$13$	−7.65534e6	+	2.35607e7i	−0.439879	+	1.35381i	0.448125	+	0.893971i	$0.352092\pi$
$13$	−7.65534e6	+	2.35607e7i	−0.439879	+	1.35381i	−0.888004	+	0.459837i	$0.847908\pi$
$14$	616217.	−	447708.i	0.0218726	−	0.0158914i
$15$	1.76129e7	+	1.27965e7i	0.399244	+	0.290068i
$16$	5.18444e6	+	1.59561e7i	0.0772542	+	0.237764i
$17$	−2.05669e7	−	6.32984e7i	−0.206657	−	0.636026i	−0.999641	−	0.0267834i	$-0.991474\pi$
$17$	−2.05669e7	−	6.32984e7i	−0.206657	−	0.636026i	0.792984	−	0.609243i	$-0.208526\pi$
$18$	4.40593e7	+	3.20109e7i	0.305327	+	0.221833i
$19$	−1.68420e8	+	1.22364e8i	−0.821288	+	0.596701i	−0.917081	−	0.398700i	$-0.869461\pi$
$19$	−1.68420e8	+	1.22364e8i	−0.821288	+	0.596701i	0.0957928	+	0.995401i	$0.469461\pi$
$20$	3.19603e7	−	9.83635e7i	0.111665	−	0.343668i
$21$	1.02613e7			0.0261082
$22$	−4.21552e7	+	3.73668e8i	−0.0792690	+	0.702650i
$23$	−1.61296e8			−0.227192			−0.113596	−	0.993527i	$-0.536237\pi$
$23$	−1.61296e8			−0.227192			−0.113596	+	0.993527i	$0.536237\pi$
$24$	−6.98439e7	+	2.14957e8i	−0.0746028	+	0.229604i
$25$	4.71755e8	−	3.42750e8i	0.386462	−	0.280781i
$26$	1.28268e9	+	9.31925e8i	0.814317	+	0.591636i
$27$	6.51500e8	+	2.00511e9i	0.323631	+	0.996033i
$28$	−1.50639e7	−	4.63620e7i	−0.00590760	−	0.0181817i
$29$	3.74579e9	+	2.72147e9i	1.16938	+	0.849605i	0.990935	−	0.134345i	$-0.0428930\pi$
$29$	3.74579e9	+	2.72147e9i	1.16938	+	0.849605i	0.178446	+	0.983950i	$0.442893\pi$
$30$	1.12723e9	−	8.18979e8i	0.282308	−	0.205109i
$31$	−5.65131e8	+	1.73930e9i	−0.114366	+	0.351984i	−0.991814	−	0.127688i	$-0.959244\pi$
$31$	−5.65131e8	+	1.73930e9i	−0.114366	+	0.351984i	0.877448	+	0.479672i	$0.159244\pi$
$32$	1.07374e9			0.176777
$33$	−3.41835e9	+	3.73878e9i	−0.460761	+	0.503951i
$34$	−4.25958e9			−0.472883
$35$	−9.28637e7	+	2.85805e8i	−0.00853894	+	0.0262801i
$36$	2.81979e9	−	2.04870e9i	0.215899	−	0.156860i
$37$	7.48615e9	+	5.43901e9i	0.479675	+	0.348505i	0.801200	−	0.598397i	$-0.204195\pi$
$37$	7.48615e9	+	5.43901e9i	0.479675	+	0.348505i	−0.321525	+	0.946901i	$0.604195\pi$
$38$	4.11717e9	+	1.26713e10i	0.221822	+	0.682699i
$39$	6.60041e9	+	2.03140e10i	0.300366	+	0.924432i
$40$	−5.35507e9	−	3.89069e9i	−0.206717	−	0.150188i
$41$	−1.29280e10	+	9.39272e9i	−0.425045	+	0.308814i	−0.779665	−	0.626197i	$-0.784610\pi$
$41$	−1.29280e10	+	9.39272e9i	−0.425045	+	0.308814i	0.354619	+	0.935011i	$0.384610\pi$
$42$	2.02938e8	−	6.24580e8i	0.00570484	−	0.0175577i
$43$	2.18383e10			0.526834			0.263417	−	0.964682i	$-0.415151\pi$
$43$	2.18383e10			0.526834			0.263417	+	0.964682i	$0.415151\pi$
$44$	2.19106e10	+	9.95596e9i	0.455210	+	0.206843i
$45$	−2.14866e10			−0.385732
$46$	−3.18997e9	+	9.81771e9i	−0.0496433	+	0.152786i
$47$	−8.88102e10	+	6.45244e10i	−1.20178	+	0.873148i	−0.994459	−	0.105124i	$-0.966476\pi$
$47$	−8.88102e10	+	6.45244e10i	−1.20178	+	0.873148i	−0.207326	+	0.978272i	$0.566476\pi$
$48$	1.17026e10	+	8.50246e9i	0.138107	+	0.100341i
$49$	−2.98966e10	−	9.20122e10i	−0.308565	−	0.949666i
$50$	−1.15324e10	−	3.54932e10i	−0.104380	−	0.321248i
$51$	−4.64248e10	−	3.37296e10i	−0.369440	−	0.268414i
$52$	8.20918e10	−	5.96432e10i	0.575809	−	0.418350i
$53$	8.34110e10	−	2.56713e11i	0.516928	−	1.59094i	−0.262817	−	0.964846i	$-0.584652\pi$
$53$	8.34110e10	−	2.56713e11i	0.516928	−	1.59094i	0.779746	−	0.626096i	$-0.215348\pi$
$54$	1.34931e11			0.740546
$55$	−7.31994e10	−	1.29046e11i	−0.356575	−	0.628619i
$56$	−3.11986e9			−0.0135180
$57$	−5.54657e10	+	1.70706e11i	−0.214209	+	0.659268i
$58$	2.39730e11	−	1.74174e11i	0.826877	−	0.600761i
$59$	−3.32172e11	−	2.41337e11i	−1.02524	−	0.744880i	−0.0578892	−	0.998323i	$-0.518437\pi$
$59$	−3.32172e11	−	2.41337e11i	−1.02524	−	0.744880i	−0.967350	+	0.253443i	$0.918437\pi$
$60$	−2.75560e10	−	8.48086e10i	−0.0762488	−	0.234670i
$61$	−4.00698e10	−	1.23322e11i	−0.0995802	−	0.306476i	0.888840	−	0.458218i	$-0.151512\pi$
$61$	−4.00698e10	−	1.23322e11i	−0.0995802	−	0.306476i	−0.988420	+	0.151741i	$0.951512\pi$
$62$	9.46901e10	+	6.87964e10i	0.211718	+	0.153822i
$63$	−8.19319e9	+	5.95270e9i	−0.0165097	+	0.0119950i
$64$	2.12355e10	−	6.53561e10i	0.0386271	−	0.118882i
$65$	−6.25533e11			−1.02876
$66$	1.59965e11	+	2.82009e11i	0.238227	+	0.419979i
$67$	−4.98714e11			−0.673544			−0.336772	−	0.941586i	$-0.609335\pi$
$67$	−4.98714e11			−0.673544			−0.336772	+	0.941586i	$0.609335\pi$
$68$	−8.42420e10	+	2.59270e11i	−0.103329	+	0.318013i
$69$	−1.12509e11	+	8.17426e10i	−0.125507	+	0.0911863i
$70$	1.55597e10	+	1.13048e10i	0.0158075	+	0.0114848i
$71$	5.76027e11	+	1.77283e12i	0.533659	+	1.64243i	0.746529	+	0.665353i	$0.231719\pi$
$71$	5.76027e11	+	1.77283e12i	0.533659	+	1.64243i	−0.212870	+	0.977080i	$0.568281\pi$
$72$	−6.89321e10	−	2.12151e11i	−0.0583124	−	0.179467i
$73$	−4.68122e11	−	3.40110e11i	−0.362043	−	0.263040i	0.391861	−	0.920025i	$-0.371832\pi$
$73$	−4.68122e11	−	3.40110e11i	−0.362043	−	0.263040i	−0.753904	+	0.656985i	$0.771832\pi$
$74$	4.79114e11	−	3.48097e11i	0.339182	−	0.246430i
$75$	1.55363e11	−	4.78158e11i	0.100797	−	0.310222i
$76$	8.52700e11			0.507584
$77$	−6.36634e10	−	2.89280e10i	−0.0348097	−	0.0158172i
$78$	1.36700e12			0.687311
$79$	−5.64604e11	+	1.73767e12i	−0.261317	+	0.804251i	0.731202	+	0.682161i	$0.238960\pi$
$79$	−5.64604e11	+	1.73767e12i	−0.261317	+	0.804251i	−0.992519	+	0.122090i	$0.961040\pi$
$80$	−3.42725e11	+	2.49004e11i	−0.146171	+	0.106199i
$81$	3.73030e11	+	2.71022e11i	0.146754	+	0.106623i
$82$	3.16035e11	+	9.72655e11i	0.114801	+	0.353321i
$83$	6.96377e11	+	2.14323e12i	0.233796	+	0.719550i	0.997279	+	0.0737219i	$0.0234877\pi$
$83$	6.96377e11	+	2.14323e12i	0.233796	+	0.719550i	−0.763483	+	0.645828i	$0.776512\pi$
$84$	−3.40032e10	−	2.47047e10i	−0.0105610	−	0.00767300i
$85$	1.35960e12	−	9.87809e11i	0.391011	−	0.284086i
$86$	4.31898e11	−	1.32924e12i	0.115117	−	0.354295i
$87$	3.99201e12			0.986998
$88$	1.03932e12	−	1.13675e12i	0.238569	−	0.260931i
$89$	−4.65461e12			−0.992768			−0.496384	−	0.868103i	$-0.665339\pi$
$89$	−4.65461e12			−0.992768			−0.496384	+	0.868103i	$0.665339\pi$
$90$	−4.24942e11	+	1.30784e12i	−0.0842856	+	0.259404i
$91$	−2.38526e11	+	1.73299e11i	−0.0440318	+	0.0319910i
$92$	5.34492e11	+	3.88331e11i	0.0919011	+	0.0667700i
$93$	4.87254e11	+	1.49961e12i	0.0780937	+	0.240348i
$94$	2.17104e12	+	6.68177e12i	0.324591	+	0.998988i
$95$	−4.25267e12	−	3.08975e12i	−0.593552	−	0.431241i
$96$	7.48968e11	−	5.44157e11i	0.0976563	−	0.0709515i
$97$	−1.11456e12	+	3.43027e12i	−0.135859	+	0.418131i	−0.995723	−	0.0923930i	$-0.970548\pi$
$97$	−1.11456e12	+	3.43027e12i	−0.135859	+	0.418131i	0.859864	+	0.510524i	$0.170548\pi$
$98$	−6.19183e12			−0.706073
$99$	5.60493e11	−	4.96828e12i	0.0598331	−	0.530368i
$100$	−2.38847e12			−0.238847
$101$	2.03257e12	−	6.25560e12i	0.190527	−	0.586381i	−0.809473	−	0.587157i	$-0.800247\pi$
$101$	2.03257e12	−	6.25560e12i	0.190527	−	0.586381i	1.00000		0.000775988i	$0.000247005\pi$
$102$	−2.97119e12	+	2.15869e12i	−0.261234	+	0.189797i
$103$	8.86189e11	+	6.43854e11i	0.0731281	+	0.0531307i	0.623749	−	0.781625i	$-0.285609\pi$
$103$	8.86189e11	+	6.43854e11i	0.0731281	+	0.0531307i	−0.550621	+	0.834756i	$0.685609\pi$
$104$	−2.00680e12	−	6.17630e12i	−0.155521	−	0.478643i
$105$	8.00667e10	+	2.46420e11i	0.00583071	+	0.0179451i
$106$	−1.39759e13	−	1.01541e13i	−0.956953	−	0.695267i
$107$	8.81559e12	−	6.40490e12i	0.567881	−	0.412589i	−0.266454	−	0.963848i	$-0.585852\pi$
$107$	8.81559e12	−	6.40490e12i	0.567881	−	0.412589i	0.834335	+	0.551258i	$0.185852\pi$
$108$	2.66854e12	−	8.21293e12i	0.161815	−	0.498016i
$109$	−7.73588e12			−0.441812			−0.220906	−	0.975295i	$-0.570901\pi$
$109$	−7.73588e12			−0.441812			−0.220906	+	0.975295i	$0.570901\pi$
$110$	−9.30240e12	+	1.90332e12i	−0.500660	+	0.102438i
$111$	7.97824e12			0.404863
$112$	−6.17018e10	+	1.89899e11i	−0.00295380	+	0.00909086i
$113$	2.07625e13	−	1.50848e13i	0.938143	−	0.681601i	−0.00982963	−	0.999952i	$-0.503129\pi$
$113$	2.07625e13	−	1.50848e13i	0.938143	−	0.681601i	0.947973	+	0.318351i	$0.103129\pi$
$114$	9.29352e12	+	6.75213e12i	0.396551	+	0.288111i
$115$	−1.25856e12	−	3.87345e12i	−0.0507386	−	0.156157i
$116$	−5.86040e12	−	1.80365e13i	−0.223332	−	0.687345i
$117$	−1.70545e13	−	1.23908e13i	−0.614655	−	0.446573i
$118$	−2.12590e13	+	1.54456e13i	−0.724954	+	0.526710i
$119$	2.44774e11	−	7.53336e11i	0.00790150	−	0.0243183i
$120$	−5.70708e12			−0.174476
$121$	3.17484e13	−	1.35594e13i	0.919638	−	0.392768i
$122$	−8.29879e12			−0.227864
$123$	−4.25756e12	+	1.31034e13i	−0.110861	+	0.341194i
$124$	6.06017e12	−	4.40297e12i	0.149708	−	0.108769i
$125$	3.68485e13	+	2.67720e13i	0.863982	+	0.627720i
$126$	2.00289e11	+	6.16427e11i	0.00445912	+	0.0137238i
$127$	1.42386e13	+	4.38218e13i	0.301122	+	0.926757i	0.981096	+	0.193521i	$0.0619909\pi$
$127$	1.42386e13	+	4.38218e13i	0.301122	+	0.926757i	−0.679974	+	0.733236i	$0.738009\pi$
$128$	−3.55809e12	−	2.58511e12i	−0.0715077	−	0.0519534i
$129$	1.52329e13	−	1.10673e13i	0.291038	−	0.211451i
$130$	−1.23712e13	+	3.80747e13i	−0.224792	+	0.691839i
$131$	−1.65894e13			−0.286793			−0.143396	−	0.989665i	$-0.545802\pi$
$131$	−1.65894e13			−0.286793			−0.143396	+	0.989665i	$0.545802\pi$
$132$	2.03289e13	−	4.15939e12i	0.334489	−	0.0684383i
$133$	−2.47761e12			−0.0388147
$134$	−9.86312e12	+	3.03556e13i	−0.147175	+	0.452957i
$135$	−4.30683e13	+	3.12909e13i	−0.612333	+	0.444886i
$136$	1.41151e13	+	1.02552e13i	0.191285	+	0.138977i
$137$	−6.41680e12	−	1.97489e13i	−0.0829153	−	0.255187i	0.901001	−	0.433817i	$-0.142834\pi$
$137$	−6.41680e12	−	1.97489e13i	−0.0829153	−	0.255187i	−0.983916	+	0.178630i	$0.942834\pi$
$138$	2.75038e12	+	8.46479e12i	0.0338983	+	0.104328i
$139$	3.22683e13	+	2.34443e13i	0.379472	+	0.275702i	0.761128	−	0.648602i	$-0.224646\pi$
$139$	3.22683e13	+	2.34443e13i	0.379472	+	0.275702i	−0.381656	+	0.924305i	$0.624646\pi$
$140$	9.95821e11	−	7.23506e11i	0.0111776	−	0.00812101i
$141$	−2.92478e13	+	9.00155e13i	−0.313451	+	0.964702i
$142$	1.19300e14			1.22114
$143$	1.63175e13	−	1.44640e14i	0.159577	−	1.41450i
$144$	−1.42764e13			−0.133433
$145$	−3.61273e13	+	1.11188e14i	−0.322807	+	0.993499i
$146$	−2.99598e13	+	2.17671e13i	−0.256003	+	0.185997i
$147$	−6.74843e13	−	4.90302e13i	−0.551620	−	0.400775i
$148$	−1.17123e13	−	3.60468e13i	−0.0916098	−	0.281946i
$149$	5.14156e13	+	1.58241e14i	0.384932	+	1.18470i	0.936529	+	0.350589i	$0.114019\pi$
$149$	5.14156e13	+	1.58241e14i	0.384932	+	1.18470i	−0.551597	+	0.834111i	$0.685981\pi$
$150$	−2.60317e13	−	1.89131e13i	−0.186599	−	0.135572i
$151$	−1.01728e14	+	7.39100e13i	−0.698381	+	0.507403i	−0.879404	−	0.476075i	$-0.842059\pi$
$151$	−1.01728e14	+	7.39100e13i	−0.698381	+	0.507403i	0.181024	+	0.983479i	$0.442059\pi$
$152$	1.68639e13	−	5.19018e13i	0.110911	−	0.341350i
$153$	5.66352e13			0.356937
$154$	−3.01986e12	+	3.30293e12i	−0.0182432	+	0.0199533i
$155$	−4.61780e13			−0.267472
$156$	2.70353e13	−	8.32060e13i	0.150183	−	0.462216i
$157$	8.13885e13	−	5.91322e13i	0.433726	−	0.315120i	−0.349411	−	0.936970i	$-0.613618\pi$
$157$	8.13885e13	−	5.91322e13i	0.433726	−	0.315120i	0.783137	+	0.621849i	$0.213618\pi$
$158$	9.46018e13	+	6.87322e13i	0.483758	+	0.351471i
$159$	−7.19167e13	−	2.21337e14i	−0.352978	−	1.08636i
$160$	8.37819e12	+	2.57854e13i	0.0394794	+	0.121505i
$161$	−1.55302e12	−	1.12834e12i	−0.00702763	−	0.00510587i
$162$	2.38739e13	−	1.73454e13i	0.103771	−	0.0753940i
$163$	2.75847e13	−	8.48971e13i	0.115199	−	0.354547i	−0.876789	−	0.480875i	$-0.840319\pi$
$163$	2.75847e13	−	8.48971e13i	0.115199	−	0.354547i	0.991989	+	0.126328i	$0.0403192\pi$
$164$	6.54535e13			0.262692
$165$	−1.16458e14	−	5.29172e13i	−0.449285	−	0.204151i
$166$	1.44226e14			0.534983
$167$	3.53082e13	−	1.08668e14i	0.125956	−	0.387653i	−0.868118	−	0.496358i	$-0.834670\pi$
$167$	3.53082e13	−	1.08668e14i	0.125956	−	0.387653i	0.994074	+	0.108705i	$0.0346704\pi$
$168$	−2.17620e12	+	1.58110e12i	−0.00746774	+	0.00542563i
$169$	−2.51472e14	−	1.82705e14i	−0.830284	−	0.603237i
$170$	−3.32366e13	−	1.02292e14i	−0.105608	−	0.325029i
$171$	−5.47417e13	−	1.68478e14i	−0.167434	−	0.515309i
$172$	−7.23663e13	−	5.25772e13i	−0.213109	−	0.154833i
$173$	2.30222e14	−	1.67266e14i	0.652902	−	0.474361i	−0.211357	−	0.977409i	$-0.567788\pi$
$173$	2.30222e14	−	1.67266e14i	0.652902	−	0.474361i	0.864258	+	0.503048i	$0.167788\pi$
$174$	7.89503e13	−	2.42984e14i	0.215667	−	0.663754i
$175$	6.93993e12			0.0182645
$176$	−4.86362e13	−	8.57426e13i	−0.123347	−	0.217453i
$177$	−3.54007e14			−0.865338
$178$	−9.20545e13	+	2.83315e14i	−0.216928	+	0.667635i
$179$	−3.65782e14	+	2.65756e14i	−0.831147	+	0.603863i	−0.919883	−	0.392192i	$-0.871717\pi$
$179$	−3.65782e14	+	2.65756e14i	−0.831147	+	0.603863i	0.0887369	+	0.996055i	$0.471717\pi$
$180$	7.12008e13	+	5.17304e13i	0.156032	+	0.113364i
$181$	−2.87993e13	−	8.86351e13i	−0.0608795	−	0.187368i	0.915991	−	0.401198i	$-0.131406\pi$
$181$	−2.87993e13	−	8.86351e13i	−0.0608795	−	0.187368i	−0.976871	+	0.213830i	$0.931406\pi$
$182$	5.83097e12	+	1.79459e13i	0.0118926	+	0.0366016i
$183$	−9.04478e13	−	6.57142e13i	−0.178019	−	0.129338i
$184$	3.42075e13	−	2.48532e13i	0.0649839	−	0.0472135i
$185$	−7.22023e13	+	2.22216e14i	−0.132414	+	0.407529i
$186$	1.00914e14			0.178698
$187$	1.92942e14	+	3.40145e14i	0.329956	+	0.581692i
$188$	4.49640e14			0.742744
$189$	−7.75372e12	+	2.38635e13i	−0.0123739	+	0.0380831i
$190$	−2.72171e14	+	1.97744e14i	−0.419704	+	0.304933i
$191$	−7.40744e14	−	5.38182e14i	−1.10395	−	0.802070i	−0.122253	−	0.992499i	$-0.539012\pi$
$191$	−7.40744e14	−	5.38182e14i	−1.10395	−	0.802070i	−0.981701	+	0.190429i	$0.939012\pi$
$192$	−1.83092e13	−	5.63498e13i	−0.0263761	−	0.0811772i
$193$	4.41600e14	+	1.35911e15i	0.615045	+	1.89291i	0.400944	+	0.916102i	$0.368682\pi$
$193$	4.41600e14	+	1.35911e15i	0.615045	+	1.89291i	0.214101	+	0.976812i	$0.431318\pi$
$194$	1.86750e14	+	1.35681e14i	0.251506	+	0.182730i
$195$	−4.36329e14	+	3.17011e14i	−0.568315	+	0.412905i
$196$	−1.22456e14	+	3.76882e14i	−0.154283	+	0.474833i
$197$	1.60501e15			1.95636			0.978178	−	0.207767i	$-0.0666194\pi$
$197$	1.60501e15			1.95636			0.978178	+	0.207767i	$0.0666194\pi$
$198$	−2.91322e14	−	1.32374e14i	−0.343597	−	0.156127i
$199$	1.26418e15			1.44299			0.721494	−	0.692421i	$-0.243456\pi$
$199$	1.26418e15			1.44299			0.721494	+	0.692421i	$0.243456\pi$
$200$	−4.72369e13	+	1.45380e14i	−0.0521899	+	0.160624i
$201$	−3.47869e14	+	2.52741e14i	−0.372084	+	0.270335i
$202$	−3.40565e14	−	2.47435e14i	−0.352709	−	0.256258i
$203$	1.70280e13	+	5.24068e13i	0.0170781	+	0.0525610i
$204$	7.26331e13	+	2.23542e14i	0.0705568	+	0.217151i
$205$	−3.26436e14	−	2.37170e14i	−0.307184	−	0.223182i
$206$	5.67161e13	−	4.12067e13i	0.0517094	−	0.0375691i
$207$	4.24137e13	−	1.30536e14i	0.0374713	−	0.115325i
$208$	−4.15626e14			−0.355869
$209$	8.25367e14	−	9.02734e14i	0.685009	−	0.749219i
$210$	1.65825e13			0.0133421
$211$	3.33601e14	−	1.02672e15i	0.260250	−	0.800968i	−0.732500	−	0.680768i	$-0.761646\pi$
$211$	3.33601e14	−	1.02672e15i	0.260250	−	0.800968i	0.992750	−	0.120200i	$-0.0383536\pi$
$212$	−8.94456e14	+	6.49860e14i	−0.676668	+	0.491628i
$213$	1.30024e15	+	9.44681e14i	0.954019	+	0.693135i
$214$	−2.15504e14	−	6.63255e14i	−0.153379	−	0.472053i
$215$	1.70400e14	+	5.24436e14i	0.117657	+	0.362112i
$216$	−4.47125e14	−	3.24856e14i	−0.299557	−	0.217641i
$217$	−1.76084e13	+	1.27933e13i	−0.0114481	+	0.00831751i
$218$	−1.52993e14	+	4.70864e14i	−0.0965394	+	0.297118i
$219$	−4.98893e14			−0.305577
$220$	−6.81238e13	+	6.03857e14i	−0.0405090	+	0.359076i
$221$	1.64880e15			0.951961
$222$	1.57786e14	−	4.85616e14i	0.0884657	−	0.272269i
$223$	−1.95788e15	+	1.42249e15i	−1.06612	+	0.774580i	−0.975210	−	0.221280i	$-0.928977\pi$
$223$	−1.95788e15	+	1.42249e15i	−1.06612	+	0.774580i	−0.0909072	+	0.995859i	$0.528977\pi$
$224$	1.03384e13	+	7.51129e12i	0.00546816	+	0.00397285i
$225$	1.53335e14	+	4.71916e14i	0.0787870	+	0.242481i
$226$	−5.07556e14	−	1.56210e15i	−0.253384	−	0.779835i
$227$	1.38687e15	+	1.00762e15i	0.672773	+	0.488799i	0.870952	−	0.491367i	$-0.163503\pi$
$227$	1.38687e15	+	1.00762e15i	0.672773	+	0.488799i	−0.198179	+	0.980166i	$0.563503\pi$
$228$	5.94785e14	−	4.32137e14i	0.280404	−	0.203725i
$229$	6.34493e14	−	1.95277e15i	0.290734	−	0.894789i	−0.693887	−	0.720084i	$-0.744103\pi$
$229$	6.34493e14	−	1.95277e15i	0.290734	−	0.894789i	0.984621	−	0.174704i	$-0.0558969\pi$
$230$	−2.60658e14			−0.116102
$231$	−5.90675e13	+	1.20855e13i	−0.0255783	+	0.00523345i
$232$	−1.21374e15			−0.511038
$233$	6.04760e14	−	1.86126e15i	0.247611	−	0.762068i	−0.747585	−	0.664166i	$-0.768787\pi$
$233$	6.04760e14	−	1.86126e15i	0.247611	−	0.762068i	0.995196	−	0.0979022i	$-0.0312132\pi$
$234$	−1.09149e15	+	7.93013e14i	−0.434627	+	0.315775i
$235$	−2.24249e15	−	1.62926e15i	−0.868539	−	0.631031i
$236$	5.19694e14	+	1.59946e15i	0.195803	+	0.602621i
$237$	4.86799e14	+	1.49821e15i	0.178437	+	0.549174i
$238$	−4.10129e13	−	2.97976e13i	−0.0146275	−	0.0106275i
$239$	−1.13360e15	+	8.23610e14i	−0.393436	+	0.285848i	−0.766862	−	0.641812i	$-0.778183\pi$
$239$	−1.13360e15	+	8.23610e14i	−0.393436	+	0.285848i	0.373426	+	0.927660i	$0.378183\pi$
$240$	−1.12869e14	+	3.47376e14i	−0.0381244	+	0.117335i
$241$	−5.67669e15			−1.86631			−0.933156	−	0.359473i	$-0.882957\pi$
$241$	−5.67669e15			−1.86631			−0.933156	+	0.359473i	$0.882957\pi$
$242$	−1.97439e14	−	2.20061e15i	−0.0631878	−	0.704278i
$243$	−2.96376e15			−0.923425
$244$	−1.64126e14	+	5.05127e14i	−0.0497901	+	0.153238i
$245$	1.97635e15	−	1.43591e15i	0.583828	−	0.424176i
$246$	7.13372e14	+	5.18295e14i	0.205229	+	0.149107i
$247$	−1.59368e15	−	4.90484e15i	−0.446551	−	1.37434i
$248$	−1.48146e14	−	4.55946e14i	−0.0404346	−	0.124445i
$249$	1.57190e15	+	1.14205e15i	0.417956	+	0.303662i
$250$	2.35830e15	−	1.71341e15i	0.610928	−	0.443865i
$251$	1.72903e15	−	5.32141e15i	0.436439	−	1.34322i	−0.455166	−	0.890406i	$-0.650420\pi$
$251$	1.72903e15	−	5.32141e15i	0.436439	−	1.34322i	0.891605	−	0.452814i	$-0.149580\pi$
$252$	4.14816e13			0.0102036
$253$	9.28476e14	−	1.89971e14i	0.222581	−	0.0455412i
$254$	2.94893e15			0.689040
$255$	4.47757e14	−	1.37806e15i	0.101984	−	0.313874i
$256$	−2.27718e14	+	1.65447e14i	−0.0505636	+	0.0367366i
$257$	3.46874e15	+	2.52019e15i	0.750942	+	0.545591i	0.896119	−	0.443815i	$-0.146375\pi$
$257$	3.46874e15	+	2.52019e15i	0.750942	+	0.545591i	−0.145177	+	0.989406i	$0.546375\pi$
$258$	−3.72381e14	−	1.14607e15i	−0.0786066	−	0.241926i
$259$	3.40314e13	+	1.04738e14i	0.00700536	+	0.0215603i
$260$	2.07285e15	+	1.50601e15i	0.416142	+	0.302345i
$261$	−3.18744e15	+	2.31581e15i	−0.624136	+	0.453461i
$262$	−3.28091e14	+	1.00976e15i	−0.0626665	+	0.192868i
$263$	3.60930e14			0.0672529			0.0336264	−	0.999434i	$-0.489294\pi$
$263$	3.60930e14			0.0672529			0.0336264	+	0.999434i	$0.489294\pi$
$264$	1.48873e14	−	1.31963e15i	0.0270640	−	0.239898i
$265$	6.81568e15			1.20896
$266$	−4.89998e13	+	1.50806e14i	−0.00848133	+	0.0261029i
$267$	−3.24673e15	+	2.35889e15i	−0.548433	+	0.398460i
$268$	1.65261e15	+	1.20069e15i	0.272454	+	0.197949i
$269$	1.20704e15	+	3.71489e15i	0.194237	+	0.597800i	0.999985	+	0.00554099i	$0.00176376\pi$
$269$	1.20704e15	+	3.71489e15i	0.194237	+	0.597800i	−0.805748	+	0.592259i	$0.798236\pi$
$270$	1.05284e15	+	3.24031e15i	0.165386	+	0.509004i
$271$	−5.99678e15	−	4.35691e15i	−0.919639	−	0.668157i	0.0237949	−	0.999717i	$-0.492425\pi$
$271$	−5.99678e15	−	4.35691e15i	−0.919639	−	0.668157i	−0.943434	+	0.331560i	$0.892425\pi$
$272$	9.03367e14	−	6.56334e14i	0.135259	−	0.0982714i
$273$	−7.85537e13	+	2.41763e14i	−0.0114844	+	0.0353454i
$274$	−1.32897e15			−0.189731
$275$	−2.31190e15	+	2.52861e15i	−0.322335	+	0.352549i
$276$	5.69626e14			0.0775677
$277$	−3.75416e15	+	1.15541e16i	−0.499337	+	1.53680i	0.310749	+	0.950492i	$0.399420\pi$
$277$	−3.75416e15	+	1.15541e16i	−0.499337	+	1.53680i	−0.810086	+	0.586310i	$0.800580\pi$
$278$	2.06517e15	−	1.50043e15i	0.268327	−	0.194951i
$279$	−1.25900e15	−	9.14714e14i	−0.159807	−	0.116107i
$280$	−2.43437e13	−	7.49221e13i	−0.00301897	−	0.00929143i
$281$	3.97664e15	+	1.22388e16i	0.481864	+	1.48303i	0.836471	+	0.548011i	$0.184615\pi$
$281$	3.97664e15	+	1.22388e16i	0.481864	+	1.48303i	−0.354607	+	0.935015i	$0.615385\pi$
$282$	4.90059e15	+	3.56049e15i	0.580269	+	0.421590i
$283$	−7.43953e15	+	5.40513e15i	−0.860862	+	0.625453i	−0.928119	−	0.372283i	$-0.878575\pi$
$283$	−7.43953e15	+	5.40513e15i	−0.860862	+	0.625453i	0.0672574	+	0.997736i	$0.478575\pi$
$284$	2.35941e15	−	7.26151e15i	0.266829	−	0.821217i
$285$	−4.53221e15			−0.500978
$286$	−8.48118e15	−	3.85377e15i	−0.916384	−	0.416396i
$287$	−1.90182e14			−0.0200880
$288$	−2.82346e14	+	8.68972e14i	−0.0291562	+	0.0897335i
$289$	4.42928e15	−	3.21806e15i	0.447195	−	0.324906i
$290$	6.05328e15	+	4.39797e15i	0.597591	+	0.434175i
$291$	9.60971e14	+	2.95756e15i	0.0927696	+	0.285516i
$292$	7.32392e14	+	2.25407e15i	0.0691441	+	0.212804i
$293$	1.17400e16	+	8.52958e15i	1.08399	+	0.787568i	0.978375	−	0.206838i	$-0.0663174\pi$
$293$	1.17400e16	+	8.52958e15i	1.08399	+	0.787568i	0.105620	+	0.994407i	$0.466317\pi$
$294$	−4.31900e15	+	3.13793e15i	−0.390054	+	0.283391i
$295$	3.20373e15	−	9.86007e15i	0.283017	−	0.871038i
$296$	−2.42572e15			−0.209626
$297$	−6.11184e15	−	1.07748e16i	−0.516719	−	0.910944i
$298$	1.06486e16			0.880819
$299$	1.23478e15	−	3.80025e15i	0.0999369	−	0.307574i
$300$	−1.66603e15	+	1.21044e15i	−0.131945	+	0.0958640i
$301$	2.10268e14	+	1.52768e14i	0.0162963	+	0.0118400i
$302$	2.48684e15	+	7.65369e15i	0.188626	+	0.580532i
$303$	−1.75247e15	−	5.39355e15i	−0.130099	−	0.400404i
$304$	−2.82562e15	−	2.05293e15i	−0.205322	−	0.149175i
$305$	2.64887e15	−	1.92451e15i	0.188413	−	0.136890i
$306$	1.12008e15	−	3.44725e15i	0.0779936	−	0.240040i
$307$	−2.82848e16			−1.92821			−0.964105	−	0.265523i	$-0.914455\pi$
$307$	−2.82848e16			−1.92821			−0.964105	+	0.265523i	$0.914455\pi$
$308$	1.41317e14	+	2.49134e14i	0.00943227	+	0.0166285i
$309$	9.44441e14			0.0617227
$310$	−9.13266e14	+	2.81074e15i	−0.0584449	+	0.179875i
$311$	1.76093e16	−	1.27939e16i	1.10357	−	0.801791i	0.121931	−	0.992539i	$-0.461091\pi$
$311$	1.76093e16	−	1.27939e16i	1.10357	−	0.801791i	0.981639	+	0.190748i	$0.0610913\pi$
$312$	−4.52987e15	−	3.29114e15i	−0.278023	−	0.201996i
$313$	4.05274e15	+	1.24731e16i	0.243619	+	0.749782i	0.995861	+	0.0908945i	$0.0289726\pi$
$313$	4.05274e15	+	1.24731e16i	0.243619	+	0.749782i	−0.752242	+	0.658887i	$0.771027\pi$
$314$	−1.98961e15	−	6.12339e15i	−0.117145	−	0.360536i
$315$	−2.06881e14	−	1.50308e14i	−0.0119317	−	0.00866889i
$316$	6.05451e15	−	4.39886e15i	0.342069	−	0.248527i
$317$	1.05676e16	−	3.25237e16i	0.584912	−	1.80017i	−0.0147137	−	0.999892i	$-0.504684\pi$
$317$	1.05676e16	−	3.25237e16i	0.584912	−	1.80017i	0.599625	−	0.800281i	$-0.295316\pi$
$318$	−1.48945e16			−0.807701
$319$	−2.47673e16	−	1.12540e16i	−1.31595	−	0.597955i
$320$	1.73519e15			0.0903385
$321$	2.90324e15	−	8.93524e15i	0.148115	−	0.455852i
$322$	−9.93933e13	+	7.22135e13i	−0.00496929	+	0.00361040i
$323$	1.12094e16	+	8.14407e15i	0.549243	+	0.399048i
$324$	−5.83617e14	−	1.79619e15i	−0.0280276	−	0.0862600i
$325$	4.46400e15	+	1.37388e16i	0.210127	+	0.646705i
$326$	−4.62194e15	−	3.35803e15i	−0.213260	−	0.154943i
$327$	−5.39601e15	+	3.92043e15i	−0.244069	+	0.177327i
$328$	1.29448e15	−	3.98400e15i	0.0574004	−	0.176660i
$329$	−1.30647e15			−0.0567973
$330$	−5.52414e15	+	6.04195e15i	−0.235464	+	0.257535i
$331$	2.10353e16			0.879156			0.439578	−	0.898204i	$-0.355128\pi$
$331$	2.10353e16			0.879156			0.439578	+	0.898204i	$0.355128\pi$
$332$	2.85236e15	−	8.77867e15i	0.116898	−	0.359775i
$333$	−6.37027e15	+	4.62828e15i	−0.256018	+	0.186008i
$334$	−5.91604e15	−	4.29825e15i	−0.233173	−	0.169410i
$335$	−3.89137e15	−	1.19764e16i	−0.150422	−	0.462951i
$336$	5.31991e13	+	1.63730e14i	0.00201697	+	0.00620759i
$337$	2.26524e16	+	1.64579e16i	0.842403	+	0.612042i	0.923041	−	0.384702i	$-0.125696\pi$
$337$	2.26524e16	+	1.64579e16i	0.842403	+	0.612042i	−0.0806376	+	0.996743i	$0.525696\pi$
$338$	−1.60942e16	+	1.16931e16i	−0.587100	+	0.426553i
$339$	6.83770e15	−	2.10443e16i	0.244687	−	0.753071i
$340$	−6.88358e15			−0.241658
$341$	1.20459e15	−	1.06776e16i	0.0414892	−	0.367765i
$342$	−1.13375e16			−0.383130
$343$	7.12140e14	−	2.19174e15i	0.0236131	−	0.0726737i
$344$	−4.63144e15	+	3.36494e15i	−0.150691	+	0.109483i
$345$	−2.84090e15	−	2.06403e15i	−0.0907050	−	0.0659010i
$346$	−5.62797e15	−	1.73211e16i	−0.176343	−	0.542727i
$347$	1.34340e16	+	4.13457e16i	0.413109	+	1.27142i	0.913932	+	0.405868i	$0.133031\pi$
$347$	1.34340e16	+	4.13457e16i	0.413109	+	1.27142i	−0.500823	+	0.865550i	$0.666969\pi$
$348$	−1.32284e16	−	9.61103e15i	−0.399249	−	0.290071i
$349$	5.56283e15	−	4.04164e15i	0.164790	−	0.119727i	−0.502334	−	0.864674i	$-0.667525\pi$
$349$	5.56283e15	−	4.04164e15i	0.164790	−	0.119727i	0.667124	+	0.744947i	$0.267525\pi$
$350$	1.37252e14	−	4.22417e14i	0.00399094	−	0.0122828i
$351$	−5.22293e16			−1.49079
$352$	−6.18083e15	+	1.26463e15i	−0.173189	+	0.0354353i
$353$	4.43561e16			1.22016			0.610081	−	0.792339i	$-0.291137\pi$
$353$	4.43561e16			1.22016			0.610081	+	0.792339i	$0.291137\pi$
$354$	−7.00123e15	+	2.15476e16i	−0.189083	+	0.581938i
$355$	−3.80791e16	+	2.76661e16i	−1.00972	+	0.733606i
$356$	1.54241e16	+	1.12063e16i	0.401583	+	0.291767i
$357$	−2.11043e14	−	6.49523e14i	−0.00539545	−	0.0166055i
$358$	8.94184e15	+	2.75202e16i	0.224485	+	0.690894i
$359$	4.51114e16	+	3.27753e16i	1.11217	+	0.808041i	0.983004	−	0.183582i	$-0.0587692\pi$
$359$	4.51114e16	+	3.27753e16i	1.11217	+	0.808041i	0.129169	+	0.991623i	$0.458769\pi$
$360$	4.55685e15	−	3.31075e15i	0.110331	−	0.0801604i
$361$	3.97218e14	−	1.22251e15i	0.00944565	−	0.0290707i
$362$	−5.96457e15			−0.139307
$363$	1.52738e16	−	2.55478e16i	0.350391	−	0.586084i
$364$	1.20764e15			0.0272132
$365$	4.51493e15	−	1.38955e16i	0.0999419	−	0.307590i
$366$	−5.78866e15	+	4.20571e15i	−0.125878	+	0.0914560i
$367$	4.97276e16	+	3.61292e16i	1.06235	+	0.771844i	0.974522	−	0.224292i	$-0.0720069\pi$
$367$	4.97276e16	+	3.61292e16i	1.06235	+	0.771844i	0.0878296	+	0.996136i	$0.472007\pi$
$368$	−8.36231e14	−	2.57365e15i	−0.0175515	−	0.0540181i
$369$	−4.20199e15	−	1.29324e16i	−0.0866529	−	0.266690i
$370$	1.20978e16	+	8.78957e15i	0.245129	+	0.178097i
$371$	2.59893e15	−	1.88823e15i	0.0517445	−	0.0375946i
$372$	1.99579e15	−	6.14242e15i	0.0390469	−	0.120174i
$373$	−5.47949e16			−1.05350			−0.526748	−	0.850021i	$-0.676589\pi$
$373$	−5.47949e16			−1.05350			−0.526748	+	0.850021i	$0.676589\pi$
$374$	2.45196e16	−	5.01684e15i	0.463285	−	0.0947906i
$375$	3.92707e16			0.729231
$376$	8.89257e15	−	2.73685e16i	0.162295	−	0.499494i
$377$	−9.27952e16	+	6.74196e16i	−1.66459	+	1.20939i
$378$	1.29917e15	+	9.43901e14i	0.0229070	+	0.0166429i
$379$	2.00745e16	+	6.17830e16i	0.347929	+	1.07081i	0.959997	+	0.280010i	$0.0903377\pi$
$379$	2.00745e16	+	6.17830e16i	0.347929	+	1.07081i	−0.612068	+	0.790805i	$0.709662\pi$
$380$	6.65345e15	+	2.04772e16i	0.113358	+	0.348881i
$381$	3.21401e16	+	2.33512e16i	0.538313	+	0.391108i
$382$	−4.74076e16	+	3.44436e16i	−0.780613	+	0.567149i
$383$	3.36462e16	−	1.03552e17i	0.544682	−	1.67636i	−0.177061	−	0.984200i	$-0.556659\pi$
$383$	3.36462e16	−	1.03552e17i	0.544682	−	1.67636i	0.721744	−	0.692160i	$-0.243341\pi$
$384$	−3.79198e15			−0.0603549
$385$	1.97941e14	−	1.75457e15i	0.00309770	−	0.0274584i
$386$	9.14591e16			1.40737
$387$	−5.74249e15	+	1.76736e16i	−0.0868919	+	0.267426i
$388$	1.19520e16	−	8.68361e15i	0.177842	−	0.129209i
$389$	−5.05222e16	−	3.67066e16i	−0.739282	−	0.537120i	0.153204	−	0.988195i	$-0.451041\pi$
$389$	−5.05222e16	−	3.67066e16i	−0.739282	−	0.537120i	−0.892486	+	0.451075i	$0.851041\pi$
$390$	1.06664e16	+	3.28279e16i	0.153497	+	0.472414i
$391$	3.31736e15	+	1.02098e16i	0.0469509	+	0.144500i
$392$	2.05181e16	+	1.49073e16i	0.285613	+	0.207510i
$393$	−1.15716e16	+	8.40729e15i	−0.158432	+	0.115108i
$394$	3.17425e16	−	9.76933e16i	0.427480	−	1.31565i
$395$	−4.61349e16			−0.611151
$396$	−1.38188e16	+	1.51141e16i	−0.180074	+	0.196954i
$397$	−1.54469e16			−0.198017			−0.0990085	−	0.995087i	$-0.531567\pi$
$397$	−1.54469e16			−0.198017			−0.0990085	+	0.995087i	$0.531567\pi$
$398$	2.50017e16	−	7.69474e16i	0.315304	−	0.970407i
$399$	−1.72821e15	+	1.25562e15i	−0.0214423	+	0.0155788i
$400$	7.91474e15	+	5.75039e15i	0.0966155	+	0.0701952i
$401$	−3.28617e16	−	1.01138e17i	−0.394686	−	1.21472i	−0.929206	−	0.369562i	$-0.879508\pi$
$401$	−3.28617e16	−	1.01138e17i	−0.394686	−	1.21472i	0.534520	−	0.845156i	$-0.320492\pi$
$402$	8.50394e15	+	2.61724e16i	0.100496	+	0.309296i
$403$	−3.66528e16	−	2.66298e16i	−0.426211	−	0.309660i
$404$	−2.17962e16	+	1.58358e16i	−0.249403	+	0.181202i
$405$	−3.59779e15	+	1.10729e16i	−0.0405115	+	0.124682i
$406$	3.52664e15			0.0390789
$407$	−4.94989e16	−	2.24918e16i	−0.539798	−	0.245279i
$408$	1.50429e16			0.161451
$409$	2.08553e16	−	6.41860e16i	0.220300	−	0.678015i	−0.778434	−	0.627726i	$-0.783986\pi$
$409$	2.08553e16	−	6.41860e16i	0.220300	−	0.678015i	0.998735	−	0.0502887i	$-0.0160141\pi$
$410$	−2.08919e16	+	1.51789e16i	−0.217212	+	0.157814i
$411$	−1.44844e16	−	1.05235e16i	−0.148227	−	0.107693i
$412$	−1.38647e15	−	4.26712e15i	−0.0139662	−	0.0429836i
$413$	−1.51002e15	−	4.64738e15i	−0.0149730	−	0.0460821i
$414$	−7.10658e15	−	5.16324e15i	−0.0693679	−	0.0503987i
$415$	−4.60350e16	+	3.34464e16i	−0.442359	+	0.321393i
$416$	−8.21986e15	+	2.52981e16i	−0.0777603	+	0.239322i
$417$	3.43894e16			0.320287
$418$	−3.86239e16	−	6.80916e16i	−0.354169	−	0.624378i
$419$	8.43299e16			0.761361			0.380680	−	0.924707i	$-0.375690\pi$
$419$	8.43299e16			0.761361			0.380680	+	0.924707i	$0.375690\pi$
$420$	3.27953e14	−	1.00934e15i	0.00291536	−	0.00897254i
$421$	−1.33042e17	+	9.66604e16i	−1.16454	+	0.846087i	−0.990345	−	0.138625i	$-0.955732\pi$
$421$	−1.33042e17	+	9.66604e16i	−1.16454	+	0.846087i	−0.174194	+	0.984711i	$0.555732\pi$
$422$	−5.58962e16	−	4.06110e16i	−0.481783	−	0.350036i
$423$	−2.88660e16	−	8.88405e16i	−0.245005	−	0.754047i
$424$	2.18657e16	+	6.72957e16i	0.182762	+	0.562483i
$425$	−3.13981e16	−	2.28121e16i	−0.258449	−	0.187774i
$426$	8.32155e16	−	6.04596e16i	0.674593	−	0.490121i
$427$	4.76884e14	−	1.46770e15i	0.00380743	−	0.0117181i
$428$	−4.46328e16			−0.350970
$429$	−6.19196e16	−	1.09160e17i	−0.479574	−	0.845460i
$430$	3.52912e16			0.269229
$431$	−4.30571e16	+	1.32516e17i	−0.323551	+	0.995787i	0.648540	+	0.761181i	$0.275380\pi$
$431$	−4.30571e16	+	1.32516e17i	−0.323551	+	0.995787i	−0.972091	+	0.234606i	$0.924620\pi$
$432$	−2.86160e16	+	2.07908e16i	−0.211819	+	0.153896i
$433$	−2.08740e16	−	1.51659e16i	−0.152207	−	0.110585i	0.509075	−	0.860722i	$-0.329987\pi$
$433$	−2.08740e16	−	1.51659e16i	−0.152207	−	0.110585i	−0.661282	+	0.750137i	$0.729987\pi$
$434$	4.30453e14	+	1.32480e15i	0.00309202	+	0.00951625i
$435$	3.11488e16	+	9.58662e16i	0.220425	+	0.678399i
$436$	2.56346e16	+	1.86247e16i	0.178717	+	0.129845i
$437$	2.71655e16	−	1.97369e16i	0.186590	−	0.135566i
$438$	−9.86664e15	+	3.03664e16i	−0.0667710	+	0.205500i
$439$	1.40422e17			0.936299			0.468150	−	0.883649i	$-0.344921\pi$
$439$	1.40422e17			0.936299			0.468150	+	0.883649i	$0.344921\pi$
$440$	3.54080e16	+	1.60891e16i	0.232627	+	0.105703i
$441$	8.23263e16			0.532952
$442$	3.26085e16	−	1.00359e17i	0.208011	−	0.640192i
$443$	−4.91215e16	+	3.56888e16i	−0.308779	+	0.224341i	−0.731372	−	0.681978i	$-0.761120\pi$
$443$	−4.91215e16	+	3.56888e16i	−0.308779	+	0.224341i	0.422594	+	0.906319i	$0.361120\pi$
$444$	−2.64378e16	−	1.92082e16i	−0.163770	−	0.118986i
$445$	−3.63189e16	−	1.11778e17i	−0.221714	−	0.682365i
$446$	4.78621e16	+	1.47304e17i	0.287949	+	0.886214i
$447$	1.16058e17	+	8.43213e16i	0.688141	+	0.499964i
$448$	6.61658e14	−	4.80722e14i	0.00386657	−	0.00280923i
$449$	4.12047e16	−	1.26815e17i	0.237326	−	0.730416i	−0.759478	−	0.650533i	$-0.774546\pi$
$449$	4.12047e16	−	1.26815e17i	0.237326	−	0.730416i	0.996804	−	0.0798824i	$-0.0254545\pi$
$450$	3.17569e16			0.180284
$451$	6.33553e16	−	6.92941e16i	0.354516	−	0.387747i
$452$	−1.05119e17			−0.579805
$453$	−3.35022e16	+	1.03109e17i	−0.182152	+	0.560607i
$454$	8.87599e16	−	6.44879e16i	0.475723	−	0.345633i
$455$	−6.02287e15	−	4.37587e15i	−0.0318222	−	0.0231202i
$456$	−1.45400e16	−	4.47496e16i	−0.0757344	−	0.233087i
$457$	7.72527e16	+	2.37759e17i	0.396697	+	1.22091i	0.927632	+	0.373495i	$0.121841\pi$
$457$	7.72527e16	+	2.37759e17i	0.396697	+	1.22091i	−0.530936	+	0.847412i	$0.678159\pi$
$458$	−1.06312e17	−	7.72402e16i	−0.538216	−	0.391037i
$459$	1.13521e17	−	8.24778e16i	0.566622	−	0.411675i
$460$	−5.15506e15	+	1.58657e16i	−0.0253693	+	0.0780786i
$461$	−2.27685e16			−0.110479			−0.0552394	−	0.998473i	$-0.517592\pi$
$461$	−2.27685e16			−0.110479			−0.0552394	+	0.998473i	$0.517592\pi$
$462$	−4.32566e14	+	3.83432e15i	−0.00206957	+	0.0183449i
$463$	1.40724e17			0.663884			0.331942	−	0.943300i	$-0.392296\pi$
$463$	1.40724e17			0.663884			0.331942	+	0.943300i	$0.392296\pi$
$464$	−2.40042e16	+	7.38774e16i	−0.111666	+	0.343672i
$465$	−3.22106e16	+	2.34024e16i	−0.147759	+	0.107353i
$466$	−1.01330e17	−	7.36207e16i	−0.458385	−	0.333036i
$467$	3.23058e16	+	9.94270e16i	0.144119	+	0.443552i	0.996897	−	0.0787219i	$-0.0250839\pi$
$467$	3.23058e16	+	9.94270e16i	0.144119	+	0.443552i	−0.852778	+	0.522274i	$0.825084\pi$
$468$	2.66824e16	+	8.21199e16i	0.117389	+	0.361285i
$469$	−4.80181e15	−	3.48872e15i	−0.0208344	−	0.0151371i
$470$	−1.43519e17	+	1.04273e17i	−0.614150	+	0.446206i
$471$	2.68036e16	−	8.24931e16i	0.113125	−	0.348162i
$472$	1.07633e17			0.448046
$473$	−1.25709e17	+	2.57207e16i	−0.516141	+	0.105605i
$474$	1.00820e17			0.408308
$475$	−3.75127e16	+	1.15452e17i	−0.149854	+	0.461204i
$476$	−2.62482e15	+	1.90705e15i	−0.0103432	+	0.00751477i
$477$	1.85823e17	+	1.35008e17i	0.722319	+	0.524795i
$478$	2.77118e16	+	8.52883e16i	0.106263	+	0.327045i
$479$	2.39800e15	+	7.38028e15i	0.00907128	+	0.0279185i	0.955490	−	0.295024i	$-0.0953278\pi$
$479$	2.39800e15	+	7.38028e15i	0.00907128	+	0.0279185i	−0.946418	+	0.322943i	$0.895328\pi$
$480$	1.89117e16	+	1.37402e16i	0.0705770	+	0.0512772i
$481$	−1.85456e17	+	1.34742e17i	−0.682807	+	0.496088i
$482$	−1.12268e17	+	3.45526e17i	−0.407804	+	1.25509i
$483$	−1.65511e15			−0.00593156
$484$	−1.37851e17	−	3.15041e16i	−0.487433	−	0.111397i
$485$	−9.10730e16			−0.317738
$486$	−5.86145e16	+	1.80397e17i	−0.201776	+	0.621002i
$487$	3.59149e16	−	2.60937e16i	0.121993	−	0.0886334i	−0.525116	−	0.851031i	$-0.675978\pi$
$487$	3.59149e16	−	2.60937e16i	0.121993	−	0.0886334i	0.647109	+	0.762398i	$0.275978\pi$
$488$	2.75000e16	+	1.99799e16i	0.0921729	+	0.0669675i
$489$	−2.37834e16	−	7.31979e16i	−0.0786624	−	0.242098i
$490$	−4.83136e16	−	1.48694e17i	−0.157687	−	0.485310i
$491$	1.77948e17	+	1.29287e17i	0.573145	+	0.416414i	0.836246	−	0.548354i	$-0.184745\pi$
$491$	1.77948e17	+	1.29287e17i	0.573145	+	0.416414i	−0.263102	+	0.964768i	$0.584745\pi$
$492$	4.56558e16	−	3.31709e16i	0.145119	−	0.105435i
$493$	9.52257e16	−	2.93075e17i	0.298710	−	0.919334i
$494$	−3.30065e17			−1.02182
$495$	1.23684e17	−	2.53065e16i	0.377903	−	0.0773210i
$496$	−3.06822e16			−0.0925244
$497$	−6.85550e15	+	2.10990e16i	−0.0204043	+	0.0627981i
$498$	1.00602e17	−	7.30915e16i	0.295539	−	0.214722i
$499$	4.29997e17	+	3.12411e17i	1.24684	+	0.905884i	0.998034	−	0.0626690i	$-0.0199612\pi$
$499$	4.29997e17	+	3.12411e17i	1.24684	+	0.905884i	0.248808	+	0.968553i	$0.419961\pi$
$500$	−5.76507e16	−	1.77431e17i	−0.165006	−	0.507836i
$501$	−3.04426e16	−	9.36927e16i	−0.0860076	−	0.264704i
$502$	−2.89706e17	−	2.10484e17i	−0.807948	−	0.587009i
$503$	−1.58452e17	+	1.15122e17i	−0.436219	+	0.316932i	−0.784131	−	0.620596i	$-0.786891\pi$
$503$	−1.58452e17	+	1.15122e17i	−0.436219	+	0.316932i	0.347912	+	0.937527i	$0.386891\pi$
$504$	8.20385e14	−	2.52489e15i	0.00222956	−	0.00686188i
$505$	1.66085e17			0.445591
$506$	6.79946e15	−	6.02712e16i	0.0180093	−	0.159636i
$507$	−2.68002e17			−0.700789
$508$	5.83212e16	−	1.79494e17i	0.150561	−	0.463379i
$509$	4.83483e16	−	3.51271e16i	0.123230	−	0.0895316i	−0.524463	−	0.851433i	$-0.675734\pi$
$509$	4.83483e16	−	3.51271e16i	0.123230	−	0.0895316i	0.647693	+	0.761901i	$0.275734\pi$
$510$	−7.50236e16	−	5.45079e16i	−0.188796	−	0.137168i
$511$	−2.12804e15	−	6.54943e15i	−0.00528742	−	0.0162730i
$512$	5.56676e15	+	1.71327e16i	0.0136568	+	0.0420312i
$513$	−3.55080e17	−	2.57981e17i	−0.860128	−	0.624919i
$514$	2.21999e17	−	1.61292e17i	0.530996	−	0.385791i
$515$	−8.54710e15	+	2.63053e16i	−0.0201870	+	0.0621292i
$516$	−7.71231e16			−0.179871
$517$	4.35227e17	−	4.76024e17i	1.00237	−	1.09633i
$518$	7.04818e15			0.0160300
$519$	7.58190e16	−	2.33347e17i	0.170290	−	0.524100i
$520$	1.32662e17	−	9.63849e16i	0.294257	−	0.213790i
$521$	−4.14007e17	−	3.00794e17i	−0.906907	−	0.658906i	0.0333238	−	0.999445i	$-0.489391\pi$
$521$	−4.14007e17	−	3.00794e17i	−0.906907	−	0.658906i	−0.940231	+	0.340538i	$0.889391\pi$
$522$	7.79197e16	+	2.39812e17i	0.168573	+	0.518815i
$523$	−2.29876e17	−	7.07487e17i	−0.491172	−	1.51167i	−0.822839	−	0.568275i	$-0.807611\pi$
$523$	−2.29876e17	−	7.07487e17i	−0.491172	−	1.51167i	0.331667	−	0.943397i	$-0.392389\pi$
$524$	5.49730e16	+	3.99402e16i	0.116010	+	0.0842862i
$525$	4.84082e15	−	3.51706e15i	0.0100898	−	0.00733068i
$526$	7.13815e15	−	2.19690e16i	0.0146953	−	0.0452275i
$527$	1.21718e17			0.247505
$528$	−7.73784e16	−	3.51600e16i	−0.155417	−	0.0706201i
$529$	−4.78020e17			−0.948384
$530$	1.34794e17	−	4.14854e17i	0.264167	−	0.813022i
$531$	2.82659e17	−	2.05364e17i	0.547203	−	0.397566i
$532$	8.21013e15	+	5.96501e15i	0.0157009	+	0.0114074i
$533$	−1.22331e17	−	3.76497e17i	−0.231106	−	0.711270i
$534$	7.93690e16	+	2.44273e17i	0.148127	+	0.455887i
$535$	2.22597e17	+	1.61726e17i	0.410412	+	0.298182i
$536$	1.05767e17	−	7.68441e16i	0.192654	−	0.139971i
$537$	−1.20463e17	+	3.70746e17i	−0.216780	+	0.667182i
$538$	2.49988e17			0.444462
$539$	2.80465e17	+	4.94443e17i	0.492665	+	0.868539i
$540$	2.18052e17			0.378443
$541$	−2.81953e17	+	8.67761e17i	−0.483497	+	1.48805i	0.350649	+	0.936507i	$0.385961\pi$
$541$	−2.81953e17	+	8.67761e17i	−0.483497	+	1.48805i	−0.834146	+	0.551544i	$0.814039\pi$
$542$	−3.83794e17	+	2.78842e17i	−0.650283	+	0.472458i
$543$	−6.50074e16	−	4.72307e16i	−0.108834	−	0.0790725i
$544$	−2.20835e16	−	6.79662e16i	−0.0365322	−	0.112435i
$545$	−6.03615e16	−	1.85773e17i	−0.0986694	−	0.303673i
$546$	1.31620e16	+	9.56275e15i	0.0212603	+	0.0154465i
$547$	7.75169e16	−	5.63193e16i	0.123731	−	0.0898959i	−0.524199	−	0.851596i	$-0.675635\pi$
$547$	7.75169e16	−	5.63193e16i	0.123731	−	0.0898959i	0.647930	+	0.761700i	$0.275635\pi$
$548$	−2.62832e16	+	8.08914e16i	−0.0414576	+	0.127594i
$549$	1.10340e17			0.171994
$550$	1.08188e17	+	1.90729e17i	0.166656	+	0.293805i
$551$	−9.63877e17			−1.46736
$552$	1.12655e16	−	3.46718e16i	0.0169492	−	0.0521641i
$553$	−1.75920e16	+	1.27813e16i	−0.0261578	+	0.0190048i
$554$	6.29025e17	+	4.57013e17i	0.924388	+	0.671607i
$555$	6.22526e16	+	1.91594e17i	0.0904176	+	0.278277i
$556$	−5.04848e16	−	1.55376e17i	−0.0724727	−	0.223048i
$557$	−5.22099e17	−	3.79327e17i	−0.740789	−	0.538215i	0.152169	−	0.988354i	$-0.451374\pi$
$557$	−5.22099e17	−	3.79327e17i	−0.740789	−	0.538215i	−0.892958	+	0.450140i	$0.851374\pi$
$558$	−8.05757e16	+	5.85417e16i	−0.113001	+	0.0821000i
$559$	−1.67180e17	+	5.14526e17i	−0.231743	+	0.713232i
$560$	−5.04178e15			−0.00690815
$561$	3.06963e17	+	1.39481e17i	0.415746	+	0.188911i
$562$	8.23595e17			1.10262
$563$	6.41261e16	−	1.97360e17i	0.0848653	−	0.261189i	−0.899615	−	0.436684i	$-0.856153\pi$
$563$	6.41261e16	−	1.97360e17i	0.0848653	−	0.261189i	0.984480	+	0.175495i	$0.0561527\pi$
$564$	3.13638e17	−	2.27871e17i	0.410312	−	0.298109i
$565$	5.24260e17	+	3.80897e17i	0.678004	+	0.492599i
$566$	1.81865e17	+	5.59724e17i	0.232511	+	0.715595i
$567$	1.69576e15	+	5.21901e15i	0.00214326	+	0.00659626i
$568$	−3.95329e17	−	2.87223e17i	−0.493963	−	0.358885i
$569$	6.15995e16	−	4.47546e16i	0.0760934	−	0.0552851i	−0.549088	−	0.835764i	$-0.685025\pi$
$569$	6.15995e16	−	4.47546e16i	0.0760934	−	0.0552851i	0.625182	+	0.780479i	$0.285025\pi$
$570$	−8.96340e16	+	2.75865e17i	−0.109468	+	0.336907i
$571$	−1.35910e18			−1.64103			−0.820513	−	0.571628i	$-0.806312\pi$
$571$	−1.35910e18			−1.64103			−0.820513	+	0.571628i	$0.806312\pi$
$572$	−4.02303e17	+	4.40013e17i	−0.480263	+	0.525281i
$573$	−7.89435e17			−0.931775
$574$	−3.76124e15	+	1.15759e16i	−0.00438938	+	0.0135091i
$575$	−7.60923e16	+	5.52843e16i	−0.0878010	+	0.0637912i
$576$	4.73083e16	+	3.43715e16i	0.0539748	+	0.0392150i
$577$	3.35762e17	+	1.03337e18i	0.378782	+	1.16577i	0.940892	+	0.338707i	$0.109990\pi$
$577$	3.35762e17	+	1.03337e18i	0.378782	+	1.16577i	−0.562110	+	0.827062i	$0.690010\pi$
$578$	−1.08277e17	−	3.33244e17i	−0.120783	−	0.371733i
$579$	9.96806e17	+	7.24222e17i	1.09951	+	0.798842i
$580$	3.87410e17	−	2.81470e17i	0.422560	−	0.307008i
$581$	−8.28782e15	+	2.55073e16i	−0.00893914	+	0.0275118i
$582$	1.99025e17			0.212280
$583$	−1.77792e17	+	1.57597e18i	−0.187528	+	1.66227i
$584$	1.51684e17			0.158219
$585$	1.64487e17	−	5.06240e17i	0.169675	−	0.522207i
$586$	7.51358e17	−	5.45893e17i	0.766500	−	0.556895i
$587$	−1.44225e18	−	1.04786e18i	−1.45510	−	1.05719i	−0.984605	−	0.174794i	$-0.944074\pi$
$587$	−1.44225e18	−	1.04786e18i	−1.45510	−	1.05719i	−0.470499	−	0.882401i	$-0.655926\pi$
$588$	1.05581e17	+	3.24946e17i	0.105350	+	0.324234i
$589$	−1.17648e17	−	3.62084e17i	−0.116101	−	0.357323i
$590$	−5.36798e17	−	3.90007e17i	−0.523930	−	0.380657i
$591$	1.11955e18	−	8.13398e17i	1.08075	−	0.785208i
$592$	−4.79737e16	+	1.47648e17i	−0.0458049	+	0.140973i
$593$	1.27421e18			1.20334			0.601668	−	0.798746i	$-0.294503\pi$
$593$	1.27421e18			1.20334			0.601668	+	0.798746i	$0.294503\pi$
$594$	−7.76710e17	+	1.58919e17i	−0.725516	+	0.148444i
$595$	2.00009e16			0.0184795
$596$	2.10598e17	−	6.48155e17i	0.192466	−	0.592350i
$597$	8.81802e17	−	6.40667e17i	0.797146	−	0.579161i
$598$	−2.06892e17	−	1.50316e17i	−0.185006	−	0.134415i
$599$	2.33684e17	+	7.19205e17i	0.206707	+	0.636178i	0.999639	+	0.0268679i	$0.00855336\pi$
$599$	2.33684e17	+	7.19205e17i	0.206707	+	0.636178i	−0.792932	+	0.609310i	$0.791447\pi$
$600$	4.07275e16	+	1.25346e17i	0.0356373	+	0.109680i
$601$	1.26095e18	+	9.16133e17i	1.09147	+	0.793002i	0.979647	−	0.200726i	$-0.0643300\pi$
$601$	1.26095e18	+	9.16133e17i	1.09147	+	0.793002i	0.111826	+	0.993728i	$0.464330\pi$
$602$	1.34571e16	−	9.77717e15i	0.0115232	−	0.00837213i
$603$	1.31140e17	−	4.03606e17i	0.111089	−	0.341897i
$604$	5.15044e17			0.431623
$605$	5.73349e17	+	6.56621e17i	0.475345	+	0.544384i
$606$	−3.62952e17			−0.297698
$607$	−3.25772e17	+	1.00262e18i	−0.264355	+	0.813601i	0.727486	+	0.686122i	$0.240689\pi$
$607$	−3.25772e17	+	1.00262e18i	−0.264355	+	0.813601i	−0.991841	+	0.127479i	$0.959311\pi$
$608$	−1.80840e17	+	1.31388e17i	−0.145185	+	0.105483i
$609$	3.84366e16	+	2.79258e16i	0.0305304	+	0.0221816i
$610$	−6.47537e16	−	1.99291e17i	−0.0508886	−	0.156619i
$611$	−8.40369e17	−	2.58639e18i	−0.653434	−	2.01106i
$612$	−1.87674e17	−	1.36353e17i	−0.144384	−	0.104901i
$613$	−6.18950e17	+	4.49694e17i	−0.471154	+	0.342313i	−0.797891	−	0.602802i	$-0.794051\pi$
$613$	−6.18950e17	+	4.49694e17i	−0.471154	+	0.342313i	0.326737	+	0.945115i	$0.394051\pi$
$614$	−5.59392e17	+	1.72163e18i	−0.421329	+	1.29672i
$615$	−3.47894e17			−0.259274
$616$	1.79590e16	−	3.67451e15i	0.0132437	−	0.00270972i
$617$	−4.60046e17			−0.335697			−0.167849	−	0.985813i	$-0.553682\pi$
$617$	−4.60046e17			−0.335697			−0.167849	+	0.985813i	$0.553682\pi$
$618$	1.86783e16	−	5.74859e16i	0.0134869	−	0.0415084i
$619$	7.94054e17	−	5.76914e17i	0.567363	−	0.412213i	−0.266784	−	0.963756i	$-0.585961\pi$
$619$	7.94054e17	−	5.76914e17i	0.567363	−	0.412213i	0.834146	+	0.551543i	$0.185961\pi$
$620$	1.53022e17	+	1.11177e17i	0.108195	+	0.0786082i
$621$	−1.05084e17	−	3.23416e17i	−0.0735263	−	0.226291i
$622$	−4.30474e17	−	1.32486e18i	−0.298064	−	0.917347i
$623$	−4.48163e16	−	3.25610e16i	−0.0307089	−	0.0223113i
$624$	−2.89912e17	+	2.10633e17i	−0.196592	+	0.142833i
$625$	−1.35432e17	+	4.16817e17i	−0.0908869	+	0.279721i
$626$	8.39357e17			0.557460
$627$	1.18226e17	−	1.04797e18i	0.0777095	−	0.688826i
$628$	−4.12065e17			−0.268057
$629$	1.90314e17	−	5.85725e17i	0.122530	−	0.377107i
$630$	−1.32404e16	+	9.61971e15i	−0.00843699	+	0.00612983i
$631$	−1.60786e18	−	1.16818e18i	−1.01405	−	0.736749i	−0.0489936	−	0.998799i	$-0.515601\pi$
$631$	−1.60786e18	−	1.16818e18i	−1.01405	−	0.736749i	−0.965054	+	0.262050i	$0.915601\pi$
$632$	−1.48008e17	−	4.55520e17i	−0.0923896	−	0.284346i
$633$	−2.87629e17	−	8.85232e17i	−0.177709	−	0.546931i
$634$	−1.77064e18	−	1.28645e18i	−1.08281	−	0.786704i
$635$	−9.41259e17	+	6.83865e17i	−0.569744	+	0.413944i
$636$	−2.94571e17	+	9.06595e17i	−0.176489	+	0.543178i
$637$	2.39674e18			1.42140
$638$	−1.17483e18	+	1.28496e18i	−0.689670	+	0.754318i
$639$	−1.58621e18			−0.921732
$640$	3.43171e16	−	1.05617e17i	0.0197397	−	0.0607525i
$641$	−7.13554e17	+	5.18428e17i	−0.406303	+	0.295196i	−0.772103	−	0.635497i	$-0.780795\pi$
$641$	−7.13554e17	+	5.18428e17i	−0.406303	+	0.295196i	0.365801	+	0.930693i	$0.380795\pi$
$642$	−4.86449e17	−	3.53426e17i	−0.274195	−	0.199214i
$643$	−3.22819e17	−	9.93534e17i	−0.180131	−	0.554385i	0.819700	−	0.572793i	$-0.194140\pi$
$643$	−3.22819e17	−	9.93534e17i	−0.180131	−	0.554385i	−0.999831	+	0.0184081i	$0.994140\pi$
$644$	2.42975e15	+	7.47801e15i	0.00134216	+	0.00413074i
$645$	3.84636e17	+	2.79455e17i	0.210335	+	0.152818i
$646$	7.17399e17	−	5.21221e17i	0.388373	−	0.282170i
$647$	5.18258e17	−	1.59503e18i	0.277759	−	0.854854i	−0.710717	−	0.703478i	$-0.751630\pi$
$647$	5.18258e17	−	1.59503e18i	0.277759	−	0.854854i	0.988476	−	0.151376i	$-0.0483705\pi$
$648$	−1.20872e17			−0.0641340
$649$	2.19634e18	+	9.97996e17i	1.15374	+	0.524250i
$650$	9.24531e17			0.480822
$651$	−5.79898e15	+	1.78474e16i	−0.00298590	+	0.00918965i
$652$	−2.95804e17	+	2.14914e17i	−0.150798	+	0.109561i
$653$	3.71669e17	+	2.70033e17i	0.187595	+	0.136296i	0.677619	−	0.735413i	$-0.263012\pi$
$653$	3.71669e17	+	2.70033e17i	0.187595	+	0.136296i	−0.490024	+	0.871709i	$0.663012\pi$
$654$	1.31910e17	+	4.05977e17i	0.0659208	+	0.202883i
$655$	−1.29444e17	−	3.98387e17i	−0.0640491	−	0.197123i
$656$	−2.16895e17	−	1.57584e17i	−0.106261	−	0.0772034i
$657$	3.98344e17	−	2.89414e17i	0.193234	−	0.140393i
$658$	−2.58383e16	+	7.95220e16i	−0.0124107	+	0.0381961i
$659$	2.21669e18			1.05427			0.527133	−	0.849783i	$-0.323267\pi$
$659$	2.21669e18			1.05427			0.527133	+	0.849783i	$0.323267\pi$
$660$	2.58508e17	+	4.55733e17i	0.121741	+	0.214622i
$661$	−2.56479e18			−1.19603			−0.598016	−	0.801484i	$-0.704044\pi$
$661$	−2.56479e18			−1.19603			−0.598016	+	0.801484i	$0.704044\pi$
$662$	4.16016e17	−	1.28037e18i	0.192103	−	0.591231i
$663$	1.15009e18	−	8.35591e17i	0.525890	−	0.382081i
$664$	−4.77925e17	−	3.47233e17i	−0.216405	−	0.157227i
$665$	−1.93323e16	−	5.94986e16i	−0.00866846	−	0.0266788i
$666$	1.55727e17	+	4.79277e17i	0.0691481	+	0.212816i
$667$	−6.04181e17	−	4.38963e17i	−0.265674	−	0.193023i
$668$	−3.78627e17	+	2.75088e17i	−0.164879	+	0.119791i
$669$	−6.44789e17	+	1.98446e18i	−0.278066	+	0.855799i
$670$	−8.05934e17			−0.344202
$671$	3.75902e17	+	6.62692e17i	0.158993	+	0.280295i
$672$	1.10180e16			0.00461532
$673$	−8.82116e17	+	2.71487e18i	−0.365955	+	1.12629i	0.583426	+	0.812167i	$0.301712\pi$
$673$	−8.82116e17	+	2.71487e18i	−0.365955	+	1.12629i	−0.949381	+	0.314128i	$0.898288\pi$
$674$	1.44975e18	−	1.05331e18i	0.595669	−	0.432779i
$675$	9.94600e17	+	7.22619e17i	0.404738	+	0.294059i
$676$	3.93437e17	+	1.21087e18i	0.158570	+	0.488029i
$677$	−5.05840e17	−	1.55682e18i	−0.201924	−	0.621457i	−0.999826	−	0.0186699i	$-0.994057\pi$
$677$	−5.05840e17	−	1.55682e18i	−0.201924	−	0.621457i	0.797902	−	0.602787i	$-0.205943\pi$
$678$	−1.14568e18	−	8.32389e17i	−0.452973	−	0.329104i
$679$	−3.47276e16	+	2.52311e16i	−0.0135995	+	0.00988059i
$680$	−1.36137e17	+	4.18987e17i	−0.0528042	+	0.162515i
$681$	1.47804e18			0.567844
$682$	−6.26096e17	−	2.84492e17i	−0.238255	−	0.108261i
$683$	−8.81799e17			−0.332380			−0.166190	−	0.986094i	$-0.553147\pi$
$683$	−8.81799e17			−0.332380			−0.166190	+	0.986094i	$0.553147\pi$
$684$	−2.24222e17	+	6.90084e17i	−0.0837170	+	0.257654i
$685$	4.24191e17	−	3.08193e17i	0.156882	−	0.113981i
$686$	−1.19322e17	−	8.66925e16i	−0.0437133	−	0.0317596i
$687$	−5.47058e17	−	1.68367e18i	−0.198525	−	0.610996i
$688$	1.13219e17	+	3.48454e17i	0.0407002	+	0.125262i
$689$	5.40980e18	+	3.93045e18i	1.92644	+	1.39964i
$690$	−1.81817e17	+	1.32098e17i	−0.0641381	+	0.0465991i
$691$	−1.06025e18	+	3.26311e18i	−0.370510	+	1.14031i	0.575948	+	0.817486i	$0.304633\pi$
$691$	−1.06025e18	+	3.26311e18i	−0.370510	+	1.14031i	−0.946458	+	0.322827i	$0.895367\pi$
$692$	−1.16560e18			−0.403515
$693$	4.01519e16	−	4.39156e16i	0.0137702	−	0.0150610i
$694$	2.78230e18			0.945294
$695$	−3.11221e17	+	9.57839e17i	−0.104753	+	0.322397i
$696$	−8.46621e17	+	6.15106e17i	−0.282312	+	0.205111i
$697$	8.60433e17	+	6.25141e17i	0.284252	+	0.206521i
$698$	−1.35988e17	−	4.18528e17i	−0.0445082	−	0.136982i
$699$	−5.21422e17	−	1.60477e18i	−0.169078	−	0.520369i
$700$	−2.29971e16	−	1.67083e16i	−0.00738814	−	0.00536780i
$701$	2.54898e18	−	1.85194e18i	0.811334	−	0.589469i	−0.102883	−	0.994693i	$-0.532807\pi$
$701$	2.54898e18	−	1.85194e18i	0.811334	−	0.589469i	0.914217	+	0.405224i	$0.132807\pi$
$702$	−1.03294e18	+	3.17907e18i	−0.325751	+	1.00256i
$703$	−1.92636e18			−0.601905
$704$	−4.52638e16	+	4.01223e17i	−0.0140129	+	0.124212i
$705$	−2.38990e18			−0.733077
$706$	8.77234e17	−	2.69985e18i	0.266615	−	0.820558i
$707$	6.33310e16	−	4.60126e16i	0.0190717	−	0.0138564i
$708$	1.17308e18	+	8.52296e17i	0.350036	+	0.254316i
$709$	1.43496e17	+	4.41635e17i	0.0424266	+	0.130576i	0.970026	−	0.243000i	$-0.0781315\pi$
$709$	1.43496e17	+	4.41635e17i	0.0424266	+	0.130576i	−0.927600	+	0.373576i	$0.878132\pi$
$710$	9.30874e17	+	2.86494e18i	0.272717	+	0.839335i
$711$	−1.25782e18	−	9.13860e17i	−0.365146	−	0.265294i
$712$	9.87144e17	−	7.17202e17i	0.283962	−	0.206311i
$713$	9.11535e16	−	2.80542e17i	0.0259831	−	0.0799678i
$714$	−4.37087e16			−0.0123461
$715$	3.60079e18	−	7.36740e17i	1.00788	−	0.206217i
$716$	1.85193e18			0.513677
$717$	−3.73329e17	+	1.14899e18i	−0.102616	+	0.315821i
$718$	2.88713e18	−	2.09762e18i	0.786425	−	0.571371i
$719$	3.89576e18	+	2.83043e18i	1.05161	+	0.764039i	0.972518	−	0.232829i	$-0.0747981\pi$
$719$	3.89576e18	+	2.83043e18i	1.05161	+	0.764039i	0.0790913	+	0.996867i	$0.474798\pi$
$720$	−1.11396e17	−	3.42842e17i	−0.0297995	−	0.0917133i
$721$	4.02853e15	+	1.23986e16i	0.00106799	+	0.00328694i
$722$	−6.65555e16	−	4.83554e16i	−0.0174861	−	0.0127044i
$723$	−3.95967e18	+	2.87687e18i	−1.03100	+	0.749067i
$724$	−1.17962e17	+	3.63049e17i	−0.0304397	+	0.0936839i
$725$	2.69988e18			0.690474
$726$	−1.25296e18	−	1.43494e18i	−0.317577	−	0.363701i
$727$	−6.10816e18			−1.53439			−0.767197	−	0.641412i	$-0.778349\pi$
$727$	−6.10816e18			−1.53439			−0.767197	+	0.641412i	$0.778349\pi$
$728$	2.38836e16	−	7.35063e16i	0.00594630	−	0.0183008i
$729$	−2.66204e18	+	1.93409e18i	−0.656880	+	0.477251i
$730$	−7.56496e17	−	5.49626e17i	−0.185015	−	0.134422i
$731$	−4.49146e17	−	1.38233e18i	−0.108874	−	0.335080i
$732$	1.41509e17	+	4.35519e17i	0.0339986	+	0.104637i
$733$	−6.46574e18	−	4.69763e18i	−1.53972	−	1.11867i	−0.950510	−	0.310694i	$-0.899438\pi$
$733$	−6.46574e18	−	4.69763e18i	−1.53972	−	1.11867i	−0.589212	−	0.807979i	$-0.700562\pi$
$734$	3.18257e18	−	2.31227e18i	0.751196	−	0.545776i
$735$	6.50872e17	−	2.00318e18i	0.152275	−	0.468653i
$736$	−1.73190e17			−0.0401622
$737$	2.87077e18	−	5.87376e17i	0.659873	−	0.135014i
$738$	−8.70266e17			−0.198283
$739$	−1.72429e18	+	5.30682e18i	−0.389423	+	1.19852i	0.543798	+	0.839216i	$0.316986\pi$
$739$	−1.72429e18	+	5.30682e18i	−0.389423	+	1.19852i	−0.933221	+	0.359304i	$0.883014\pi$
$740$	7.74259e17	−	5.62532e17i	0.173333	−	0.125934i
$741$	−3.59735e18	−	2.61363e18i	−0.798296	−	0.579996i
$742$	−6.35330e16	−	1.95534e17i	−0.0139757	−	0.0430128i
$743$	−3.61374e17	−	1.11219e18i	−0.0788006	−	0.242523i	0.903894	−	0.427757i	$-0.140696\pi$
$743$	−3.61374e17	−	1.11219e18i	−0.0788006	−	0.242523i	−0.982695	+	0.185233i	$0.940696\pi$
$744$	−3.34403e17	−	2.42958e17i	−0.0722847	−	0.0525179i
$745$	−3.39890e18	+	2.46944e18i	−0.728320	+	0.529156i
$746$	−1.08368e18	+	3.33524e18i	−0.230197	+	0.708475i
$747$	−1.91762e18			−0.403811
$748$	1.79563e17	−	1.59167e18i	0.0374850	−	0.332271i
$749$	1.29685e17			0.0268385
$750$	7.76659e17	−	2.39031e18i	0.159343	−	0.490407i
$751$	−2.87108e18	+	2.08596e18i	−0.583963	+	0.424274i	−0.840150	−	0.542353i	$-0.817533\pi$
$751$	−2.87108e18	+	2.08596e18i	−0.583963	+	0.424274i	0.256188	+	0.966627i	$0.417533\pi$
$752$	−1.48999e18	−	1.08254e18i	−0.300446	−	0.218287i
$753$	−1.49076e18	−	4.58810e18i	−0.298017	−	0.917202i
$754$	2.26845e18	+	6.98158e18i	0.449590	+	1.38369i
$755$	−2.56868e18	−	1.86626e18i	−0.504725	−	0.366704i
$756$	8.31467e16	−	6.04096e16i	0.0161977	−	0.0117683i
$757$	1.40540e18	−	4.32537e18i	0.271441	−	0.835410i	−0.718698	−	0.695323i	$-0.755262\pi$
$757$	1.40540e18	−	4.32537e18i	0.271441	−	0.835410i	0.990139	−	0.140088i	$-0.0447385\pi$
$758$	4.15760e18			0.796146
$759$	5.51366e17	−	6.03050e17i	0.104681	−	0.114494i
$760$	1.37798e18			0.259392
$761$	1.56727e18	−	4.82355e18i	0.292511	−	0.900256i	−0.691535	−	0.722343i	$-0.743065\pi$
$761$	1.56727e18	−	4.82355e18i	0.292511	−	0.900256i	0.984046	−	0.177913i	$-0.0569347\pi$
$762$	2.05697e18	−	1.49447e18i	0.380645	−	0.276555i
$763$	−7.44840e16	−	5.41158e16i	−0.0136664	−	0.00992921i
$764$	1.15892e18	+	3.56678e18i	0.210836	+	0.648888i
$765$	4.41913e17	+	1.36007e18i	0.0797144	+	0.245336i
$766$	−5.63755e18	−	4.09592e18i	−1.00833	−	0.732596i
$767$	8.22898e18	−	5.97870e18i	1.45941	−	1.06032i
$768$	−7.49943e16	+	2.30809e17i	−0.0131880	+	0.0405886i
$769$	4.69750e18			0.819117			0.409559	−	0.912284i	$-0.365683\pi$
$769$	4.69750e18			0.819117			0.409559	+	0.912284i	$0.365683\pi$
$770$	−1.02882e17	−	4.67484e16i	−0.0177889	−	0.00808308i
$771$	3.69675e18			0.633821
$772$	1.80880e18	−	5.56690e18i	0.307523	−	0.946457i
$773$	−7.17386e18	+	5.21212e18i	−1.20945	+	0.878714i	−0.995180	−	0.0980616i	$-0.968736\pi$
$773$	−7.17386e18	+	5.21212e18i	−1.20945	+	0.878714i	−0.214266	+	0.976775i	$0.568736\pi$
$774$	9.62179e17	+	6.99064e17i	0.160857	+	0.116869i
$775$	3.29540e17	+	1.01422e18i	0.0546320	+	0.168140i
$776$	−2.92176e17	−	8.99225e17i	−0.0480334	−	0.147831i
$777$	7.68176e16	+	5.58112e16i	0.0125234	+	0.00909882i
$778$	−3.23342e18	+	2.34922e18i	−0.522751	+	0.379801i
$779$	1.02800e18	−	3.16385e18i	0.164815	−	0.507250i
$780$	2.20910e18			0.351238
$781$	−5.40382e18	−	9.52659e18i	−0.852057	−	1.50212i
$782$	6.87053e17			0.107435
$783$	−3.01647e18	+	9.28375e18i	−0.467787	+	1.43970i
$784$	1.31316e18	−	9.54065e17i	0.201959	−	0.146731i
$785$	2.05509e18	+	1.49311e18i	0.313457	+	0.227740i
$786$	2.82878e17	+	8.70610e17i	0.0427911	+	0.131697i
$787$	−8.90785e17	−	2.74155e18i	−0.133640	−	0.411302i	0.861736	−	0.507357i	$-0.169378\pi$
$787$	−8.90785e17	−	2.74155e18i	−0.133640	−	0.411302i	−0.995376	+	0.0960551i	$0.969378\pi$
$788$	−5.31859e18	−	3.86418e18i	−0.791363	−	0.574959i
$789$	2.51760e17	−	1.82914e17i	0.0371524	−	0.0269928i
$790$	−9.12414e17	+	2.80812e18i	−0.133541	+	0.410998i
$791$	3.05434e17			0.0443374
$792$	6.46665e17	+	1.14003e18i	0.0931034	+	0.164136i
$793$	3.21231e18			0.458713
$794$	−3.05494e17	+	9.40215e17i	−0.0432683	+	0.133166i
$795$	4.75415e18	−	3.45409e18i	0.667861	−	0.485230i
$796$	−4.18914e18	−	3.04359e18i	−0.583701	−	0.424083i
$797$	−3.78237e17	−	1.16409e18i	−0.0522739	−	0.160883i	0.921512	−	0.388351i	$-0.126955\pi$
$797$	−3.78237e17	−	1.16409e18i	−0.0522739	−	0.160883i	−0.973785	+	0.227468i	$0.926955\pi$
$798$	4.22475e16	+	1.30024e17i	0.00579138	+	0.0178240i
$799$	5.91084e18	+	4.29448e18i	0.803702	+	0.583924i
$800$	5.06543e17	−	3.68025e17i	0.0683175	−	0.0496355i
$801$	1.22395e18	−	3.76694e18i	0.163739	−	0.503938i
$802$	−6.80593e18			−0.903138
$803$	3.09525e18	+	1.40645e18i	0.407422	+	0.185128i
$804$	1.76124e18			0.229961
$805$	1.49786e16	−	4.60992e16i	0.00193998	−	0.00597064i
$806$	−2.34578e18	+	1.70431e18i	−0.301376	+	0.218963i
$807$	2.72460e18	+	1.97954e18i	0.347236	+	0.252282i
$808$	5.32826e17	+	1.63987e18i	0.0673614	+	0.207317i
$809$	2.72642e18	+	8.39105e18i	0.341922	+	1.05233i	0.963211	+	0.268746i	$0.0866091\pi$
$809$	2.72642e18	+	8.39105e18i	0.341922	+	1.05233i	−0.621289	+	0.783581i	$0.713391\pi$
$810$	6.02825e17	+	4.37978e17i	0.0749961	+	0.0544878i
$811$	−2.48362e18	+	1.80446e18i	−0.306514	+	0.222695i	−0.730399	−	0.683020i	$-0.760666\pi$
$811$	−2.48362e18	+	1.80446e18i	−0.306514	+	0.222695i	0.423885	+	0.905716i	$0.360666\pi$
$812$	6.97467e16	−	2.14658e17i	0.00853904	−	0.0262805i
$813$	−6.39096e18			−0.776207
$814$	−2.34796e18	+	2.56806e18i	−0.282900	+	0.309418i
$815$	2.25400e18			0.269420
$816$	2.97505e17	−	9.15627e17i	0.0352784	−	0.108576i
$817$	−3.67801e18	+	2.67223e18i	−0.432683	+	0.314362i
$818$	−3.49439e18	−	2.53883e18i	−0.407826	−	0.296303i
$819$	−7.75283e16	−	2.38607e17i	−0.00897666	−	0.0276273i
$820$	5.10720e17	+	1.57183e18i	0.0586669	+	0.180558i
$821$	1.09143e19	+	7.92967e18i	1.24384	+	0.903701i	0.997848	−	0.0655717i	$-0.0208871\pi$
$821$	1.09143e19	+	7.92967e18i	1.24384	+	0.903701i	0.245990	+	0.969272i	$0.420887\pi$
$822$	−9.27000e17	+	6.73505e17i	−0.104812	+	0.0761507i
$823$	3.59318e18	−	1.10587e19i	0.403070	−	1.24052i	−0.519426	−	0.854515i	$-0.673854\pi$
$823$	3.59318e18	−	1.10587e19i	0.403070	−	1.24052i	0.922496	−	0.386007i	$-0.126146\pi$
$824$	−2.87150e17			−0.0319582
$825$	−3.31159e17	+	2.93543e18i	−0.0365667	+	0.324131i
$826$	−3.12739e17			−0.0342619
$827$	−3.07205e18	+	9.45480e18i	−0.333920	+	1.02770i	0.633331	+	0.773881i	$0.281687\pi$
$827$	−3.07205e18	+	9.45480e18i	−0.333920	+	1.02770i	−0.967252	+	0.253820i	$0.918313\pi$
$828$	−4.54821e17	+	3.30447e17i	−0.0490505	+	0.0356373i
$829$	2.84780e18	+	2.06905e18i	0.304723	+	0.221394i	0.729629	−	0.683843i	$-0.239693\pi$
$829$	2.84780e18	+	2.06905e18i	0.304723	+	0.221394i	−0.424906	+	0.905238i	$0.639693\pi$
$830$	1.12536e18	+	3.46351e18i	0.119477	+	0.367713i
$831$	3.23682e18	+	9.96191e18i	0.340967	+	1.04939i
$832$	1.37727e18	+	1.00065e18i	0.143952	+	0.104587i
$833$	−5.20935e18	+	3.78481e18i	−0.540245	+	0.392511i
$834$	6.80121e17	−	2.09320e18i	0.0699854	−	0.215393i
$835$	2.88510e18			0.294577
$836$	−4.90844e18	+	1.00429e18i	−0.497282	+	0.101747i
$837$	−3.85566e18			−0.387600
$838$	1.66780e18	−	5.13296e18i	0.166363	−	0.512014i
$839$	−5.46379e18	+	3.96967e18i	−0.540805	+	0.392918i	−0.824384	−	0.566031i	$-0.808478\pi$
$839$	−5.46379e18	+	3.96967e18i	−0.540805	+	0.392918i	0.283579	+	0.958949i	$0.408478\pi$
$840$	−5.49499e16	−	3.99235e16i	−0.00539699	−	0.00392115i
$841$	3.45379e18	+	1.06297e19i	0.336606	+	1.03597i
$842$	3.25231e18	+	1.00096e19i	0.314531	+	0.968027i
$843$	8.97630e18	+	6.52166e18i	0.861426	+	0.625863i
$844$	−3.57736e18	+	2.59910e18i	−0.340672	+	0.247513i
$845$	2.42540e18	−	7.46461e18i	0.229200	−	0.705405i
$846$	−5.97840e18			−0.560631
$847$	4.00540e17	+	9.15383e16i	0.0372738	+	0.00851846i
$848$	4.52857e18			0.418204
$849$	−2.45006e18	+	7.54050e18i	−0.224531	+	0.691035i
$850$	−2.00948e18	+	1.45997e18i	−0.182751	+	0.132777i
$851$	−1.20749e18	−	8.77291e17i	−0.108978	−	0.0791774i
$852$	−2.03427e18	−	6.26084e18i	−0.182201	−	0.560758i
$853$	−5.31900e18	−	1.63702e19i	−0.472782	−	1.45507i	−0.848926	−	0.528512i	$-0.822750\pi$
$853$	−5.31900e18	−	1.63702e19i	−0.472782	−	1.45507i	0.376143	−	0.926561i	$-0.377250\pi$
$854$	−7.99039e16	−	5.80536e16i	−0.00704842	−	0.00512098i
$855$	3.61877e18	−	2.62919e18i	0.316798	−	0.230167i
$856$	−8.82706e17	+	2.71669e18i	−0.0766897	+	0.236026i
$857$	−1.17988e19			−1.01733			−0.508667	−	0.860964i	$-0.669861\pi$
$857$	−1.17988e19			−1.01733			−0.508667	+	0.860964i	$0.669861\pi$
$858$	−7.86893e18	+	1.61002e18i	−0.673361	+	0.137773i
$859$	2.01959e19			1.71517			0.857587	−	0.514339i	$-0.171963\pi$
$859$	2.01959e19			1.71517			0.857587	+	0.514339i	$0.171963\pi$
$860$	6.97957e17	−	2.14809e18i	0.0588287	−	0.181056i
$861$	−1.32658e17	+	9.63814e16i	−0.0110972	+	0.00806256i
$862$	7.21439e18	+	5.24156e18i	0.598967	+	0.435175i
$863$	−6.56078e18	−	2.01920e19i	−0.540611	−	1.66383i	−0.731202	−	0.682161i	$-0.761040\pi$
$863$	−6.56078e18	−	2.01920e19i	−0.540611	−	1.66383i	0.190591	−	0.981670i	$-0.438960\pi$
$864$	6.99542e17	+	2.15297e18i	0.0572104	+	0.176075i
$865$	5.81320e18	+	4.22354e18i	0.471857	+	0.342824i
$866$	−1.33594e18	+	9.70615e17i	−0.107627	+	0.0781953i
$867$	1.45869e18	−	4.48939e18i	0.116638	−	0.358974i
$868$	8.91503e16			0.00707530
$869$	1.20346e18	−	1.06676e19i	0.0947990	−	0.840309i
$870$	6.45118e18			0.504387
$871$	3.81783e18	−	1.17501e19i	0.296277	−	0.911848i
$872$	1.64062e18	−	1.19198e18i	0.126372	−	0.0918144i
$873$	−2.48301e18	−	1.80401e18i	−0.189839	−	0.137926i
$874$	−6.64083e17	−	2.04384e18i	−0.0503963	−	0.155104i
$875$	1.67510e17	+	5.15542e17i	0.0126179	+	0.0388340i
$876$	1.65320e18	+	1.20112e18i	0.123608	+	0.0898068i
$877$	6.35137e18	−	4.61454e18i	0.471379	−	0.342477i	−0.326600	−	0.945163i	$-0.605903\pi$
$877$	6.35137e18	−	4.61454e18i	0.471379	−	0.342477i	0.797978	+	0.602686i	$0.205903\pi$
$878$	2.77713e18	−	8.54713e18i	0.204589	−	0.629660i
$879$	1.25117e19			0.914929
$880$	1.67957e18	−	1.83701e18i	0.121916	−	0.133344i
$881$	−1.67103e19			−1.20404			−0.602021	−	0.798480i	$-0.705638\pi$
$881$	−1.67103e19			−1.20404			−0.602021	+	0.798480i	$0.705638\pi$
$882$	1.62817e18	−	5.01101e18i	0.116454	−	0.358409i
$883$	−1.60079e19	+	1.16304e19i	−1.13655	+	0.825752i	−0.986635	−	0.162947i	$-0.947900\pi$
$883$	−1.60079e19	+	1.16304e19i	−1.13655	+	0.825752i	−0.149916	+	0.988699i	$0.547900\pi$
$884$	−5.46370e18	−	3.96961e18i	−0.385076	−	0.279774i
$885$	−2.76224e18	−	8.50131e18i	−0.193255	−	0.594778i
$886$	1.20082e18	+	3.69573e18i	0.0833983	+	0.256673i
$887$	8.84436e18	+	6.42580e18i	0.609766	+	0.443021i	0.849332	−	0.527859i	$-0.177005\pi$
$887$	8.84436e18	+	6.42580e18i	0.609766	+	0.443021i	−0.239566	+	0.970880i	$0.577005\pi$
$888$	−1.69202e18	+	1.22932e18i	−0.115803	+	0.0841359i
$889$	−1.69458e17	+	5.21538e17i	−0.0115133	+	0.0354344i
$890$	−7.52195e18			−0.507336
$891$	−2.46649e18	−	1.12075e18i	−0.165149	−	0.0750419i
$892$	9.91263e18			0.658897
$893$	7.06194e18	−	2.17344e19i	0.466004	−	1.43421i
$894$	7.42773e18	−	5.39656e18i	0.486589	−	0.353528i
$895$	−9.23613e18	−	6.71044e18i	−0.600676	−	0.436417i
$896$	−1.61748e16	−	4.97808e16i	−0.00104433	−	0.00321410i
$897$	−1.06462e18	−	3.27656e18i	−0.0682407	−	0.210023i
$898$	−6.90403e18	−	5.01607e18i	−0.439346	−	0.319203i
$899$	−6.85031e18	+	4.97704e18i	−0.432785	+	0.314437i
$900$	6.28060e17	−	1.93297e18i	0.0393935	−	0.121241i
$901$	−1.79650e19			−1.11871
$902$	−2.96478e18	−	5.22672e18i	−0.183295	−	0.323137i
$903$	2.24089e17			0.0137547
$904$	−2.07895e18	+	6.39835e18i	−0.126692	+	0.389918i
$905$	1.90382e18	−	1.38320e18i	0.115189	−	0.0836894i
$906$	5.61343e18	+	4.07840e18i	0.337206	+	0.244994i
$907$	4.69151e18	+	1.44390e19i	0.279811	+	0.861171i	0.987906	+	0.155053i	$0.0495549\pi$
$907$	4.69151e18	+	1.44390e19i	0.279811	+	0.861171i	−0.708095	+	0.706117i	$0.750445\pi$
$908$	−2.16981e18	−	6.67799e18i	−0.128488	−	0.395446i
$909$	4.52814e18	+	3.28989e18i	0.266229	+	0.193426i
$910$	−3.85464e17	+	2.80056e17i	−0.0225017	+	0.0163484i
$911$	−5.50034e17	+	1.69283e18i	−0.0318801	+	0.0981170i	−0.965730	−	0.259547i	$-0.916427\pi$
$911$	−5.50034e17	+	1.69283e18i	−0.0318801	+	0.0981170i	0.933850	+	0.357664i	$0.116427\pi$
$912$	−3.01136e18			−0.173299
$913$	−6.53284e18	−	1.15170e19i	−0.373286	−	0.658081i
$914$	1.59997e19			0.907739
$915$	8.72350e17	−	2.68482e18i	0.0491421	−	0.151244i
$916$	−6.80397e18	+	4.94337e18i	−0.380576	+	0.276505i
$917$	−1.59729e17	−	1.16050e17i	−0.00887124	−	0.00644533i
$918$	−2.77511e18	−	8.54092e18i	−0.153039	−	0.471007i
$919$	3.64481e18	+	1.12176e19i	0.199583	+	0.614254i	0.999892	+	0.0146666i	$0.00466869\pi$
$919$	3.64481e18	+	1.12176e19i	0.199583	+	0.614254i	−0.800309	+	0.599588i	$0.795331\pi$
$920$	8.63752e17	+	6.27553e17i	0.0469644	+	0.0341216i
$921$	−1.97296e19	+	1.43344e19i	−1.06520	+	0.773910i
$922$	−4.50295e17	+	1.38587e18i	−0.0241405	+	0.0742968i
$923$	−4.61788e19			−2.45828
$924$	2.24831e17	+	1.02161e17i	0.0118847	+	0.00540029i
$925$	5.39585e18			0.283230
$926$	2.78311e18	−	8.56554e18i	0.145064	−	0.446461i
$927$	−7.54095e17	+	5.47882e17i	−0.0390308	+	0.0283575i
$928$	4.02201e18	+	2.92216e18i	0.206719	+	0.150190i
$929$	8.96110e18	+	2.75794e19i	0.457361	+	1.40761i	0.868341	+	0.495968i	$0.165187\pi$
$929$	8.96110e18	+	2.75794e19i	0.457361	+	1.40761i	−0.410980	+	0.911644i	$0.634813\pi$
$930$	7.87414e17	+	2.42341e18i	0.0399084	+	0.122825i
$931$	1.62942e19	+	1.18384e19i	0.820088	+	0.595829i
$932$	−6.48513e18	+	4.71172e18i	−0.324127	+	0.235492i
$933$	5.79927e18	−	1.78483e19i	0.287834	−	0.885863i
$934$	6.69080e18			0.329779
$935$	−6.66293e18	+	7.28749e18i	−0.326129	+	0.356699i
$936$	5.52614e18			0.268614
$937$	−3.85534e18	+	1.18655e19i	−0.186104	+	0.572768i	−0.999966	−	0.00828999i	$-0.997361\pi$
$937$	−3.85534e18	+	1.18655e19i	−0.186104	+	0.572768i	0.813862	+	0.581058i	$0.197361\pi$
$938$	−3.07316e17	+	2.23278e17i	−0.0147322	+	0.0107036i
$939$	9.14809e18	+	6.64648e18i	0.435516	+	0.316421i
$940$	3.50845e18	+	1.07979e19i	0.165876	+	0.510515i
$941$	−5.56259e18	−	1.71199e19i	−0.261183	−	0.803838i	−0.992548	−	0.121852i	$-0.961117\pi$
$941$	−5.56259e18	−	1.71199e19i	−0.261183	−	0.803838i	0.731366	−	0.681986i	$-0.238883\pi$
$942$	−4.49106e18	−	3.26295e18i	−0.209420	−	0.152153i
$943$	2.08523e18	−	1.51501e18i	0.0965669	−	0.0701599i
$944$	2.12867e18	−	6.55137e18i	0.0979017	−	0.301310i
$945$	−6.33571e17			−0.0289393
$946$	−9.20597e17	+	8.16028e18i	−0.0417616	+	0.370180i
$947$	1.56825e19			0.706548			0.353274	−	0.935520i	$-0.385068\pi$
$947$	1.56825e19			0.706548			0.353274	+	0.935520i	$0.385068\pi$
$948$	1.99393e18	−	6.13668e18i	0.0892187	−	0.274587i
$949$	1.15969e19	−	8.42563e18i	0.515360	−	0.374431i
$950$	6.28540e18	+	4.56661e18i	0.277415	+	0.201554i
$951$	−9.11132e18	−	2.80418e19i	−0.399400	−	1.22923i
$952$	6.41660e16	+	1.97483e17i	0.00279360	+	0.00859782i
$953$	1.76354e18	+	1.28129e18i	0.0762573	+	0.0554042i	0.625261	−	0.780416i	$-0.284993\pi$
$953$	1.76354e18	+	1.28129e18i	0.0762573	+	0.0554042i	−0.549003	+	0.835820i	$0.684993\pi$
$954$	1.18926e19	−	8.64051e18i	0.510757	−	0.371086i
$955$	7.14431e18	−	2.19879e19i	0.304746	−	0.937913i
$956$	5.73935e18			0.243157
$957$	−2.29794e19	+	4.70170e18i	−0.966965	+	0.197846i
$958$	4.96646e17			0.0207573
$959$	7.63685e16	−	2.35038e17i	0.00317025	−	0.00975702i
$960$	1.21035e18	−	8.79372e17i	0.0499055	−	0.0362585i
$961$	1.70484e19	+	1.23864e19i	0.698204	+	0.507275i
$962$	4.53363e18	+	1.39531e19i	0.184420	+	0.567586i
$963$	2.86534e18	+	8.81860e18i	0.115772	+	0.356311i
$964$	1.88110e19	+	1.36670e19i	0.754939	+	0.548495i
$965$	−2.91926e19	+	2.12097e19i	−1.16371	+	0.845485i
$966$	−3.27332e16	+	1.00742e17i	−0.00129609	+	0.00398897i
$967$	−2.63070e19			−1.03466			−0.517332	−	0.855785i	$-0.673075\pi$
$967$	−2.63070e19			−1.03466			−0.517332	+	0.855785i	$0.673075\pi$
$968$	−4.64387e18	+	7.76760e18i	−0.181422	+	0.303457i
$969$	1.19462e19			0.463580
$970$	−1.80116e18	+	5.54340e18i	−0.0694282	+	0.213678i
$971$	−5.43336e18	+	3.94756e18i	−0.208038	+	0.151149i	−0.686926	−	0.726728i	$-0.741040\pi$
$971$	−5.43336e18	+	3.94756e18i	−0.208038	+	0.151149i	0.478887	+	0.877876i	$0.341040\pi$
$972$	9.82110e18	+	7.13545e18i	0.373533	+	0.271388i
$973$	1.46689e17	+	4.51461e17i	0.00554195	+	0.0170564i
$974$	−8.77969e17	−	2.70211e18i	−0.0329493	−	0.101407i
$975$	1.00764e19	+	7.32093e18i	0.375643	+	0.272920i
$976$	1.76000e18	−	1.27871e18i	0.0651761	−	0.0473532i
$977$	5.14840e18	−	1.58451e19i	0.189390	−	0.582883i	−0.810606	−	0.585592i	$-0.800862\pi$
$977$	5.14840e18	−	1.58451e19i	0.189390	−	0.582883i	0.999996	+	0.00270878i	$0.000862232\pi$
$978$	−4.92575e18			−0.179999
$979$	2.67935e19	−	5.48210e18i	0.972618	−	0.199003i
$980$	−1.00061e19			−0.360826
$981$	2.03419e18	−	6.26059e18i	0.0728690	−	0.224268i
$982$	1.13887e19	−	8.27437e18i	0.405274	−	0.294449i
$983$	5.36905e17	+	3.90084e17i	0.0189801	+	0.0137899i	0.597235	−	0.802066i	$-0.296266\pi$
$983$	5.36905e17	+	3.90084e17i	0.0189801	+	0.0137899i	−0.578255	+	0.815856i	$0.696266\pi$
$984$	−1.11609e18	−	3.43499e18i	−0.0391952	−	0.120630i
$985$	1.25236e19	+	3.85436e19i	0.436911	+	1.34467i
$986$	−1.59555e19	−	1.15923e19i	−0.552980	−	0.401764i
$987$	−9.11307e17	+	6.62103e17i	−0.0313764	+	0.0227963i
$988$	−6.52771e18	+	2.00902e19i	−0.223275	+	0.687171i
$989$	−3.52243e18			−0.119692
$990$	9.05771e17	−	8.02886e18i	0.0305766	−	0.271035i
$991$	2.59159e19			0.869135			0.434567	−	0.900639i	$-0.356901\pi$
$991$	2.59159e19			0.869135			0.434567	+	0.900639i	$0.356901\pi$
$992$	−6.06805e17	+	1.86755e18i	−0.0202173	+	0.0622225i
$993$	1.46728e19	−	1.06604e19i	0.485670	−	0.352860i
$994$	1.14867e18	+	8.34555e17i	0.0377731	+	0.0274438i
$995$	9.86411e18	+	3.03586e19i	0.322261	+	0.991818i
$996$	−2.45929e18	−	7.56893e18i	−0.0798224	−	0.245668i
$997$	−2.26490e19	−	1.64554e19i	−0.730348	−	0.530629i	0.159326	−	0.987226i	$-0.449068\pi$
$997$	−2.26490e19	−	1.64554e19i	−0.730348	−	0.530629i	−0.889673	+	0.456597i	$0.849068\pi$
$998$	2.75198e19	−	1.99943e19i	0.881651	−	0.640557i
$999$	−6.02858e18	+	1.85541e19i	−0.191884	+	0.590559i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.14.c.b.9.5	yes	28
11.5	even	5	inner	22.14.c.b.5.5	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.14.c.b.5.5	✓	28	11.5	even	5	inner
22.14.c.b.9.5	yes	28	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	22.c (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(19.7771 - 60.8676i) q^{2} +(697.531 - 506.786i) q^{3} +(-3313.73 - 2407.57i) q^{4} +(7802.80 + 24014.5i) q^{5} +(-17051.7 - 52479.8i) q^{6} +(9628.39 + 6995.43i) q^{7} +(-212079. + 154084. i) q^{8} +(-262955. + 809293. i) q^{9} +1.61602e6 q^{10} +(-5.75635e6 + 1.17778e6i) q^{11} -3.53155e6 q^{12} +(-7.65534e6 + 2.35607e7i) q^{13} +(616217. - 447708. i) q^{14} +(1.76129e7 + 1.27965e7i) q^{15} +(5.18444e6 + 1.59561e7i) q^{16} +(-2.05669e7 - 6.32984e7i) q^{17} +(4.40593e7 + 3.20109e7i) q^{18} +(-1.68420e8 + 1.22364e8i) q^{19} +(3.19603e7 - 9.83635e7i) q^{20} +1.02613e7 q^{21} +(-4.21552e7 + 3.73668e8i) q^{22} -1.61296e8 q^{23} +(-6.98439e7 + 2.14957e8i) q^{24} +(4.71755e8 - 3.42750e8i) q^{25} +(1.28268e9 + 9.31925e8i) q^{26} +(6.51500e8 + 2.00511e9i) q^{27} +(-1.50639e7 - 4.63620e7i) q^{28} +(3.74579e9 + 2.72147e9i) q^{29} +(1.12723e9 - 8.18979e8i) q^{30} +(-5.65131e8 + 1.73930e9i) q^{31} +1.07374e9 q^{32} +(-3.41835e9 + 3.73878e9i) q^{33} -4.25958e9 q^{34} +(-9.28637e7 + 2.85805e8i) q^{35} +(2.81979e9 - 2.04870e9i) q^{36} +(7.48615e9 + 5.43901e9i) q^{37} +(4.11717e9 + 1.26713e10i) q^{38} +(6.60041e9 + 2.03140e10i) q^{39} +(-5.35507e9 - 3.89069e9i) q^{40} +(-1.29280e10 + 9.39272e9i) q^{41} +(2.02938e8 - 6.24580e8i) q^{42} +2.18383e10 q^{43} +(2.19106e10 + 9.95596e9i) q^{44} -2.14866e10 q^{45} +(-3.18997e9 + 9.81771e9i) q^{46} +(-8.88102e10 + 6.45244e10i) q^{47} +(1.17026e10 + 8.50246e9i) q^{48} +(-2.98966e10 - 9.20122e10i) q^{49} +(-1.15324e10 - 3.54932e10i) q^{50} +(-4.64248e10 - 3.37296e10i) q^{51} +(8.20918e10 - 5.96432e10i) q^{52} +(8.34110e10 - 2.56713e11i) q^{53} +1.34931e11 q^{54} +(-7.31994e10 - 1.29046e11i) q^{55} -3.11986e9 q^{56} +(-5.54657e10 + 1.70706e11i) q^{57} +(2.39730e11 - 1.74174e11i) q^{58} +(-3.32172e11 - 2.41337e11i) q^{59} +(-2.75560e10 - 8.48086e10i) q^{60} +(-4.00698e10 - 1.23322e11i) q^{61} +(9.46901e10 + 6.87964e10i) q^{62} +(-8.19319e9 + 5.95270e9i) q^{63} +(2.12355e10 - 6.53561e10i) q^{64} -6.25533e11 q^{65} +(1.59965e11 + 2.82009e11i) q^{66} -4.98714e11 q^{67} +(-8.42420e10 + 2.59270e11i) q^{68} +(-1.12509e11 + 8.17426e10i) q^{69} +(1.55597e10 + 1.13048e10i) q^{70} +(5.76027e11 + 1.77283e12i) q^{71} +(-6.89321e10 - 2.12151e11i) q^{72} +(-4.68122e11 - 3.40110e11i) q^{73} +(4.79114e11 - 3.48097e11i) q^{74} +(1.55363e11 - 4.78158e11i) q^{75} +8.52700e11 q^{76} +(-6.36634e10 - 2.89280e10i) q^{77} +1.36700e12 q^{78} +(-5.64604e11 + 1.73767e12i) q^{79} +(-3.42725e11 + 2.49004e11i) q^{80} +(3.73030e11 + 2.71022e11i) q^{81} +(3.16035e11 + 9.72655e11i) q^{82} +(6.96377e11 + 2.14323e12i) q^{83} +(-3.40032e10 - 2.47047e10i) q^{84} +(1.35960e12 - 9.87809e11i) q^{85} +(4.31898e11 - 1.32924e12i) q^{86} +3.99201e12 q^{87} +(1.03932e12 - 1.13675e12i) q^{88} -4.65461e12 q^{89} +(-4.24942e11 + 1.30784e12i) q^{90} +(-2.38526e11 + 1.73299e11i) q^{91} +(5.34492e11 + 3.88331e11i) q^{92} +(4.87254e11 + 1.49961e12i) q^{93} +(2.17104e12 + 6.68177e12i) q^{94} +(-4.25267e12 - 3.08975e12i) q^{95} +(7.48968e11 - 5.44157e11i) q^{96} +(-1.11456e12 + 3.43027e12i) q^{97} -6.19183e12 q^{98} +(5.60493e11 - 4.96828e12i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 448 q^{2} - 1248 q^{3} - 28672 q^{4} + 71554 q^{5} + 99008 q^{6} + 361734 q^{7} - 1835008 q^{8} - 8615367 q^{9} + 2898176 q^{10} + 8699239 q^{11} - 2449408 q^{12} + 32373940 q^{13} + 23150976 q^{14}+ \cdots + 71382923151637 q^{99}+O(q^{100}) \) 28 * q - 448 * q^2 - 1248 * q^3 - 28672 * q^4 + 71554 * q^5 + 99008 * q^6 + 361734 * q^7 - 1835008 * q^8 - 8615367 * q^9 + 2898176 * q^10 + 8699239 * q^11 - 2449408 * q^12 + 32373940 * q^13 + 23150976 * q^14 - 192099788 * q^15 - 117440512 * q^16 + 288881082 * q^17 - 275612928 * q^18 - 98588517 * q^19 + 293085184 * q^20 + 1362925660 * q^21 - 44352704 * q^22 - 233099500 * q^23 + 405536768 * q^24 + 1117600307 * q^25 - 2827224960 * q^26 + 3575804241 * q^27 - 1485029376 * q^28 - 16868227562 * q^29 - 12294386432 * q^30 - 10874790260 * q^31 + 30064771072 * q^32 + 53369498501 * q^33 + 6456111488 * q^34 + 18823205444 * q^35 - 17639227392 * q^36 + 47951509642 * q^37 + 14611374592 * q^38 - 161088016778 * q^39 - 24692916224 * q^40 - 155498856970 * q^41 - 47678239360 * q^42 + 156723459918 * q^43 + 31490678784 * q^44 + 75277819092 * q^45 + 46604369920 * q^46 + 394942115908 * q^47 - 20937965568 * q^48 - 10631171627 * q^49 - 421539129152 * q^50 - 468879528009 * q^51 - 180942397440 * q^52 + 608978721416 * q^53 + 286529794304 * q^54 + 82053078738 * q^55 + 430964736 * q^56 - 655027400217 * q^57 - 1079566563968 * q^58 + 381384884765 * q^59 + 528673062912 * q^60 + 1151615204532 * q^61 - 101484696320 * q^62 + 5117893076470 * q^63 - 481036337152 * q^64 - 5194662408432 * q^65 - 2892007512576 * q^66 + 833522448542 * q^67 + 1183256911872 * q^68 - 4423665001426 * q^69 + 835597274496 * q^70 + 3476544683262 * q^71 - 2258466766848 * q^72 - 3737607886538 * q^73 + 3068896617088 * q^74 + 9622942863695 * q^75 - 1062618816512 * q^76 - 4431389843152 * q^77 - 2335610564352 * q^78 + 7224103591056 * q^79 - 1580346638336 * q^80 - 9164585352662 * q^81 + 1269347381440 * q^82 + 9607066728079 * q^83 + 260135567360 * q^84 + 25585834186966 * q^85 - 3541381155008 * q^86 - 34193079605396 * q^87 - 4585813704704 * q^88 + 19963863911122 * q^89 + 15393877925888 * q^90 - 11356103019586 * q^91 - 2505291898880 * q^92 + 6475155937894 * q^93 - 39623598881408 * q^94 - 51625880722484 * q^95 - 1340029796352 * q^96 + 4169205798475 * q^97 + 38124564609792 * q^98 + 71382923151637 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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