LMFDB - Embedded newform 22.14.c.b.3.6

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			3.6
Character	$\chi$	$=$	22.3
Dual form			22.14.c.b.15.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-51.7771 + 37.6183i) q^{2} +(412.870 + 1270.68i) q^{3} +(1265.73 - 3895.53i) q^{4} +(-41240.7 - 29963.1i) q^{5} +(-69178.0 - 50260.8i) q^{6} +(25390.0 - 78142.3i) q^{7} +(81007.0 + 249314. i) q^{8} +(-154338. + 112133. i) q^{9} +3.26248e6 q^{10} +(5.35158e6 + 2.42556e6i) q^{11} +5.47256e6 q^{12} +(1.23266e6 - 895580. i) q^{13} +(1.62496e6 + 5.00111e6i) q^{14} +(2.10466e7 - 6.47747e7i) q^{15} +(-1.35731e7 - 9.86140e6i) q^{16} +(-5.78778e7 - 4.20507e7i) q^{17} +(3.77291e6 - 1.16118e7i) q^{18} +(4.23273e7 + 1.30270e8i) q^{19} +(-1.68922e8 + 1.22729e8i) q^{20} +1.09777e8 q^{21} +(-3.68334e8 + 7.57288e7i) q^{22} +6.72099e8 q^{23} +(-2.83353e8 + 2.05868e8i) q^{24} +(4.25788e8 + 1.31044e9i) q^{25} +(-3.01334e7 + 9.27410e7i) q^{26} +(1.51711e9 + 1.10224e9i) q^{27} +(-2.72269e8 - 1.97815e8i) q^{28} +(-6.42713e8 + 1.97807e9i) q^{29} +(1.34698e9 + 4.14558e9i) q^{30} +(-3.30762e9 + 2.40312e9i) q^{31} +1.07374e9 q^{32} +(-8.72606e8 + 7.80159e9i) q^{33} +4.57862e9 q^{34} +(-3.38849e9 + 2.46188e9i) q^{35} +(2.41466e8 + 7.43157e8i) q^{36} +(-5.55906e9 + 1.71090e10i) q^{37} +(-7.09212e9 - 5.15273e9i) q^{38} +(1.64693e9 + 1.19656e9i) q^{39} +(4.12943e9 - 1.27091e10i) q^{40} +(-4.12052e9 - 1.26817e10i) q^{41} +(-5.68392e9 + 4.12961e9i) q^{42} +6.18843e10 q^{43} +(1.62225e10 - 1.77771e10i) q^{44} +9.72484e9 q^{45} +(-3.47993e10 + 2.52832e10i) q^{46} +(1.03198e10 + 3.17610e10i) q^{47} +(6.92680e9 - 2.13185e10i) q^{48} +(7.29233e10 + 5.29819e10i) q^{49} +(-7.13425e10 - 5.18334e10i) q^{50} +(2.95371e10 - 9.09058e10i) q^{51} +(-1.92854e9 - 5.93543e9i) q^{52} +(-1.26563e11 + 9.19531e10i) q^{53} -1.20016e11 q^{54} +(-1.48026e11 - 2.60381e11i) q^{55} +2.15387e10 q^{56} +(-1.48056e11 + 1.07569e11i) q^{57} +(-4.11336e10 - 1.26596e11i) q^{58} +(1.46534e11 - 4.50985e11i) q^{59} +(-2.25692e11 - 1.63975e11i) q^{60} +(4.33409e11 + 3.14890e11i) q^{61} +(8.08574e10 - 2.48854e11i) q^{62} +(4.84369e9 + 1.49074e10i) q^{63} +(-5.55952e10 + 4.03923e10i) q^{64} -7.76701e10 q^{65} +(-2.48301e11 - 4.36770e11i) q^{66} +1.43735e12 q^{67} +(-2.37068e11 + 1.72240e11i) q^{68} +(2.77489e11 + 8.54024e11i) q^{69} +(8.28344e10 - 2.54938e11i) q^{70} +(-1.35929e11 - 9.87581e10i) q^{71} +(-4.04587e10 - 2.93950e10i) q^{72} +(4.80400e9 - 1.47852e10i) q^{73} +(-3.55780e11 - 1.09498e12i) q^{74} +(-1.48936e12 + 1.08208e12i) q^{75} +5.61046e11 q^{76} +(3.25415e11 - 3.56600e11i) q^{77} -1.30286e11 q^{78} +(-1.59140e12 + 1.15622e12i) q^{79} +(2.64284e11 + 8.13382e11i) q^{80} +(-8.68222e11 + 2.67211e12i) q^{81} +(6.90411e11 + 5.01613e11i) q^{82} +(2.40072e12 + 1.74423e12i) q^{83} +(1.38948e11 - 4.27639e11i) q^{84} +(1.12695e12 + 3.46840e12i) q^{85} +(-3.20419e12 + 2.32798e12i) q^{86} -2.77885e12 q^{87} +(-1.71209e11 + 1.53071e12i) q^{88} +8.39565e12 q^{89} +(-5.03524e11 + 3.65832e11i) q^{90} +(-3.86855e10 - 1.19062e11i) q^{91} +(8.50698e11 - 2.61818e12i) q^{92} +(-4.41922e12 - 3.21075e12i) q^{93} +(-1.72912e12 - 1.25628e12i) q^{94} +(2.15769e12 - 6.64069e12i) q^{95} +(4.43315e11 + 1.36438e12i) q^{96} +(-2.53556e12 + 1.84219e12i) q^{97} -5.76884e12 q^{98} +(-1.09793e12 + 2.25733e11i) 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 $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−51.7771	+	37.6183i	−0.572061	+	0.415627i
$2$	−51.7771	+	37.6183i	−0.572061	+	0.415627i
$3$	412.870	+	1270.68i	0.326983	+	1.00635i	0.970538	+	0.240950i	$0.0774588\pi$
$3$	412.870	+	1270.68i	0.326983	+	1.00635i	−0.643555	+	0.765400i	$0.722541\pi$
$4$	1265.73	−	3895.53i	0.154508	−	0.475528i
$5$	−41240.7	−	29963.1i	−1.18038	−	0.857594i	−0.188163	−	0.982138i	$-0.560253\pi$
$5$	−41240.7	−	29963.1i	−1.18038	−	0.857594i	−0.992214	+	0.124544i	$0.960253\pi$
$6$	−69178.0	−	50260.8i	−0.605320	−	0.439791i
$7$	25390.0	−	78142.3i	0.0815690	−	0.251044i	−0.901952	−	0.431836i	$-0.857866\pi$
$7$	25390.0	−	78142.3i	0.0815690	−	0.251044i	0.983521	+	0.180792i	$0.0578661\pi$
$8$	81007.0	+	249314.i	0.109254	+	0.336249i
$9$	−154338.	+	112133.i	−0.0968045	+	0.0703326i
$10$	3.26248e6			1.03169
$11$	5.35158e6	+	2.42556e6i	0.910813	+	0.412818i
$11$	5.35158e6	+	2.42556e6i	0.910813	+	0.412818i
$12$	5.47256e6			0.529069
$13$	1.23266e6	−	895580.i	0.0708291	−	0.0514603i	−0.551807	−	0.833972i	$-0.686062\pi$
$13$	1.23266e6	−	895580.i	0.0708291	−	0.0514603i	0.622636	+	0.782511i	$0.286062\pi$
$14$	1.62496e6	+	5.00111e6i	0.0576780	+	0.177515i
$15$	2.10466e7	−	6.47747e7i	0.477076	−	1.46829i
$16$	−1.35731e7	−	9.86140e6i	−0.202254	−	0.146946i
$17$	−5.78778e7	−	4.20507e7i	−0.581560	−	0.422528i	0.257726	−	0.966218i	$-0.417027\pi$
$17$	−5.78778e7	−	4.20507e7i	−0.581560	−	0.422528i	−0.839286	+	0.543690i	$0.817027\pi$
$18$	3.77291e6	−	1.16118e7i	0.0261460	−	0.0804691i
$19$	4.23273e7	+	1.30270e8i	0.206406	+	0.635252i	0.999653	+	0.0263520i	$0.00838908\pi$
$19$	4.23273e7	+	1.30270e8i	0.206406	+	0.635252i	−0.793247	+	0.608900i	$0.791611\pi$
$20$	−1.68922e8	+	1.22729e8i	−0.590189	+	0.428797i
$21$	1.09777e8			0.279309
$22$	−3.68334e8	+	7.57288e7i	−0.692620	+	0.142401i
$23$	6.72099e8			0.946678			0.473339	−	0.880880i	$-0.343049\pi$
$23$	6.72099e8			0.946678			0.473339	+	0.880880i	$0.343049\pi$
$24$	−2.83353e8	+	2.05868e8i	−0.302660	+	0.219895i
$25$	4.25788e8	+	1.31044e9i	0.348805	+	1.07351i
$26$	−3.01334e7	+	9.27410e7i	−0.0191303	+	0.0588769i
$27$	1.51711e9	+	1.10224e9i	0.753619	+	0.547537i
$28$	−2.72269e8	−	1.97815e8i	−0.106775	−	0.0775767i
$29$	−6.42713e8	+	1.97807e9i	−0.200646	+	0.617524i	0.799218	+	0.601041i	$0.205247\pi$
$29$	−6.42713e8	+	1.97807e9i	−0.200646	+	0.617524i	−0.999864	+	0.0164833i	$0.994753\pi$
$30$	1.34698e9	+	4.14558e9i	0.337344	+	1.03824i
$31$	−3.30762e9	+	2.40312e9i	−0.669367	+	0.486323i	−0.869813	−	0.493381i	$-0.835761\pi$
$31$	−3.30762e9	+	2.40312e9i	−0.669367	+	0.486323i	0.200446	+	0.979705i	$0.435761\pi$
$32$	1.07374e9			0.176777
$33$	−8.72606e8	+	7.80159e9i	−0.117619	+	1.05158i
$34$	4.57862e9			0.508302
$35$	−3.38849e9	+	2.46188e9i	−0.311576	+	0.226373i
$36$	2.41466e8	+	7.43157e8i	0.0184880	+	0.0569003i
$37$	−5.55906e9	+	1.71090e10i	−0.356197	+	1.09626i	0.599115	+	0.800663i	$0.295519\pi$
$37$	−5.55906e9	+	1.71090e10i	−0.356197	+	1.09626i	−0.955312	+	0.295599i	$0.904481\pi$
$38$	−7.09212e9	−	5.15273e9i	−0.382105	−	0.277615i
$39$	1.64693e9	+	1.19656e9i	0.0749469	+	0.0544521i
$40$	4.12943e9	−	1.27091e10i	0.159404	−	0.490597i
$41$	−4.12052e9	−	1.26817e10i	−0.135474	−	0.416947i	0.860189	−	0.509975i	$-0.170345\pi$
$41$	−4.12052e9	−	1.26817e10i	−0.135474	−	0.416947i	−0.995664	+	0.0930279i	$0.970345\pi$
$42$	−5.68392e9	+	4.12961e9i	−0.159782	+	0.116088i
$43$	6.18843e10			1.49292			0.746459	−	0.665432i	$-0.231753\pi$
$43$	6.18843e10			1.49292			0.746459	+	0.665432i	$0.231753\pi$
$44$	1.62225e10	−	1.77771e10i	0.337035	−	0.369334i
$45$	9.72484e9			0.174583
$46$	−3.47993e10	+	2.52832e10i	−0.541558	+	0.393465i
$47$	1.03198e10	+	3.17610e10i	0.139648	+	0.429792i	0.996284	−	0.0861294i	$-0.0274498\pi$
$47$	1.03198e10	+	3.17610e10i	0.139648	+	0.429792i	−0.856636	+	0.515921i	$0.827450\pi$
$48$	6.92680e9	−	2.13185e10i	0.0817457	−	0.251587i
$49$	7.29233e10	+	5.29819e10i	0.752648	+	0.546831i
$50$	−7.13425e10	−	5.18334e10i	−0.645719	−	0.469142i
$51$	2.95371e10	−	9.09058e10i	0.235051	−	0.723412i
$52$	−1.92854e9	−	5.93543e9i	−0.0135271	−	0.0416323i
$53$	−1.26563e11	+	9.19531e10i	−0.784354	+	0.569866i	−0.906283	−	0.422672i	$-0.861092\pi$
$53$	−1.26563e11	+	9.19531e10i	−0.784354	+	0.569866i	0.121929	+	0.992539i	$0.461092\pi$
$54$	−1.20016e11			−0.658688
$55$	−1.48026e11	−	2.60381e11i	−0.721073	−	1.26839i
$56$	2.15387e10			0.0933250
$57$	−1.48056e11	+	1.07569e11i	−0.571795	+	0.415433i
$58$	−4.11336e10	−	1.26596e11i	−0.141878	−	0.436655i
$59$	1.46534e11	−	4.50985e11i	0.452272	−	1.39195i	−0.422036	−	0.906579i	$-0.638684\pi$
$59$	1.46534e11	−	4.50985e11i	0.452272	−	1.39195i	0.874308	−	0.485372i	$-0.161316\pi$
$60$	−2.25692e11	−	1.63975e11i	−0.624501	−	0.453727i
$61$	4.33409e11	+	3.14890e11i	1.07710	+	0.782556i	0.977174	−	0.212439i	$-0.0681408\pi$
$61$	4.33409e11	+	3.14890e11i	1.07710	+	0.782556i	0.0999215	+	0.994995i	$0.468141\pi$
$62$	8.08574e10	−	2.48854e11i	0.180790	−	0.556414i
$63$	4.84369e9	+	1.49074e10i	0.00976030	+	0.0300391i
$64$	−5.55952e10	+	4.03923e10i	−0.101127	+	0.0734732i
$65$	−7.76701e10			−0.127737
$66$	−2.48301e11	−	4.36770e11i	−0.369780	−	0.650455i
$67$	1.43735e12			1.94122			0.970611	−	0.240652i	$-0.0773612\pi$
$67$	1.43735e12			1.94122			0.970611	+	0.240652i	$0.0773612\pi$
$68$	−2.37068e11	+	1.72240e11i	−0.290780	+	0.211264i
$69$	2.77489e11	+	8.54024e11i	0.309547	+	0.952688i
$70$	8.28344e10	−	2.54938e11i	0.0841537	−	0.258999i
$71$	−1.35929e11	−	9.87581e10i	−0.125931	−	0.0914942i	0.523037	−	0.852310i	$-0.324799\pi$
$71$	−1.35929e11	−	9.87581e10i	−0.125931	−	0.0914942i	−0.648968	+	0.760816i	$0.724799\pi$
$72$	−4.04587e10	−	2.93950e10i	−0.0342256	−	0.0248663i
$73$	4.80400e9	−	1.47852e10i	0.00371539	−	0.0114348i	−0.949182	−	0.314729i	$-0.898086\pi$
$73$	4.80400e9	−	1.47852e10i	0.00371539	−	0.0114348i	0.952897	+	0.303294i	$0.0980864\pi$
$74$	−3.55780e11	−	1.09498e12i	−0.251869	−	0.775174i
$75$	−1.48936e12	+	1.08208e12i	−0.966275	+	0.702040i
$76$	5.61046e11			0.333972
$77$	3.25415e11	−	3.56600e11i	0.177929	−	0.194981i
$78$	−1.30286e11			−0.0655060
$79$	−1.59140e12	+	1.15622e12i	−0.736551	+	0.535136i	−0.891629	−	0.452766i	$-0.850437\pi$
$79$	−1.59140e12	+	1.15622e12i	−0.736551	+	0.535136i	0.155078	+	0.987902i	$0.450437\pi$
$80$	2.64284e11	+	8.13382e11i	0.112716	+	0.346904i
$81$	−8.68222e11	+	2.67211e12i	−0.341569	+	1.05124i
$82$	6.90411e11	+	5.01613e11i	0.250794	+	0.182213i
$83$	2.40072e12	+	1.74423e12i	0.806000	+	0.585593i	0.912668	−	0.408702i	$-0.134018\pi$
$83$	2.40072e12	+	1.74423e12i	0.806000	+	0.585593i	−0.106669	+	0.994295i	$0.534018\pi$
$84$	1.38948e11	−	4.27639e11i	0.0431556	−	0.132819i
$85$	1.12695e12	+	3.46840e12i	0.324102	+	0.997484i
$86$	−3.20419e12	+	2.32798e12i	−0.854040	+	0.620497i
$87$	−2.77885e12			−0.687053
$88$	−1.71209e11	+	1.53071e12i	−0.0392998	+	0.351362i
$89$	8.39565e12			1.79069			0.895343	−	0.445377i	$-0.146930\pi$
$89$	8.39565e12			1.79069			0.895343	+	0.445377i	$0.146930\pi$
$90$	−5.03524e11	+	3.65832e11i	−0.0998720	+	0.0725613i
$91$	−3.86855e10	−	1.19062e11i	−0.00714133	−	0.0219787i
$92$	8.50698e11	−	2.61818e12i	0.146270	−	0.450172i
$93$	−4.41922e12	−	3.21075e12i	−0.708283	−	0.514597i
$94$	−1.72912e12	−	1.25628e12i	−0.258520	−	0.187826i
$95$	2.15769e12	−	6.64069e12i	0.301152	−	0.926850i
$96$	4.43315e11	+	1.36438e12i	0.0578029	+	0.177899i
$97$	−2.53556e12	+	1.84219e12i	−0.309070	+	0.224553i	−0.731497	−	0.681844i	$-0.761178\pi$
$97$	−2.53556e12	+	1.84219e12i	−0.309070	+	0.224553i	0.422427	+	0.906397i	$0.361178\pi$
$98$	−5.76884e12			−0.657838
$99$	−1.09793e12	+	2.25733e11i	−0.117205	+	0.0240972i
$100$	5.64379e12			0.564379
$101$	1.08473e13	−	7.88106e12i	1.01680	−	0.738747i	0.0511735	−	0.998690i	$-0.483704\pi$
$101$	1.08473e13	−	7.88106e12i	1.01680	−	0.738747i	0.965624	+	0.259943i	$0.0837038\pi$
$102$	1.89037e12	+	5.81797e12i	0.166206	+	0.511529i
$103$	4.97206e12	−	1.53024e13i	0.410293	−	1.26275i	−0.506100	−	0.862475i	$-0.668913\pi$
$103$	4.97206e12	−	1.53024e13i	0.410293	−	1.26275i	0.916394	−	0.400278i	$-0.131087\pi$
$104$	3.23134e11	+	2.34771e11i	0.0250419	+	0.0181940i
$105$	−4.52727e12	−	3.28926e12i	−0.329690	−	0.239534i
$106$	3.09393e12	−	9.52213e12i	0.211847	−	0.651997i
$107$	6.45953e10	+	1.98804e11i	0.00416108	+	0.0128065i	0.953116	−	0.302607i	$-0.0978569\pi$
$107$	6.45953e10	+	1.98804e11i	0.00416108	+	0.0128065i	−0.948954	+	0.315413i	$0.897857\pi$
$108$	6.21407e12	−	4.51479e12i	0.376810	−	0.273768i
$109$	−2.91672e13			−1.66580			−0.832898	−	0.553426i	$-0.813320\pi$
$109$	−2.91672e13			−1.66580			−0.832898	+	0.553426i	$0.813320\pi$
$110$	1.74594e13	+	7.91333e12i	0.939675	+	0.425899i
$111$	−2.40353e13			−1.21969
$112$	−1.11521e12	+	8.10249e11i	−0.0533876	+	0.0387884i
$113$	−7.75065e12	−	2.38541e13i	−0.350210	−	1.07784i	−0.958735	−	0.284301i	$-0.908239\pi$
$113$	−7.75065e12	−	2.38541e13i	−0.350210	−	1.07784i	0.608525	−	0.793535i	$-0.291761\pi$
$114$	3.61936e12	−	1.11392e13i	0.154436	−	0.475307i
$115$	−2.77178e13	−	2.01382e13i	−1.11744	−	0.811865i
$116$	6.89211e12	+	5.00741e12i	0.262649	+	0.190825i
$117$	−8.98219e10	+	2.76443e11i	−0.00323723	+	0.00996318i
$118$	9.37817e12	+	2.88630e13i	0.319805	+	0.984258i
$119$	−4.75546e12	+	3.45504e12i	−0.153510	+	0.111532i
$120$	1.78541e13			0.545834
$121$	2.27561e13	+	2.59611e13i	0.659162	+	0.752001i
$122$	−3.42863e13			−0.941416
$123$	1.44131e13	−	1.04717e13i	0.375297	−	0.272669i
$124$	5.17487e12	+	1.59266e13i	0.127838	+	0.393444i
$125$	2.47591e12	−	7.62006e12i	0.0580523	−	0.178667i
$126$	−8.11581e11	−	5.89648e11i	−0.0180686	−	0.0131276i
$127$	5.58226e13	+	4.05575e13i	1.18055	+	0.857723i	0.992234	−	0.124384i	$-0.0396956\pi$
$127$	5.58226e13	+	4.05575e13i	1.18055	+	0.857723i	0.188321	+	0.982108i	$0.439696\pi$
$128$	1.35907e12	−	4.18279e12i	0.0273135	−	0.0840623i
$129$	2.55502e13	+	7.86353e13i	0.488158	+	1.50240i
$130$	4.02153e12	−	2.92181e12i	0.0730734	−	0.0530910i
$131$	1.22364e13			0.211538			0.105769	−	0.994391i	$-0.466270\pi$
$131$	1.22364e13			0.211538			0.105769	+	0.994391i	$0.466270\pi$
$132$	2.92868e13	+	1.32740e13i	0.481883	+	0.218409i
$133$	1.12543e13			0.176312
$134$	−7.44216e13	+	5.40705e13i	−1.11050	+	0.806825i
$135$	−2.95399e13	−	9.09145e13i	−0.419991	−	1.29260i
$136$	5.79531e12	−	1.78361e13i	0.0785369	−	0.241712i
$137$	−6.70910e13	−	4.87445e13i	−0.866923	−	0.629857i	0.0628362	−	0.998024i	$-0.479985\pi$
$137$	−6.70910e13	−	4.87445e13i	−0.866923	−	0.629857i	−0.929760	+	0.368167i	$0.879985\pi$
$138$	−4.64945e13	−	3.37802e13i	−0.573043	−	0.416340i
$139$	−1.68089e13	+	5.17325e13i	−0.197671	+	0.608369i	0.802264	+	0.596969i	$0.203629\pi$
$139$	−1.68089e13	+	5.17325e13i	−0.197671	+	0.608369i	−0.999935	+	0.0113995i	$0.996371\pi$
$140$	5.30140e12	+	1.63160e13i	0.0595057	+	0.183140i
$141$	−3.60974e13	+	2.62263e13i	−0.386858	+	0.281069i
$142$	1.07531e13			0.110068
$143$	8.76895e12	−	1.80288e12i	0.0857558	−	0.0176312i
$144$	3.20062e12			0.0299142
$145$	8.57749e13	−	6.23191e13i	0.766422	−	0.556839i
$146$	3.07456e11	+	9.46252e11i	0.00262718	+	0.00808562i
$147$	−3.72153e13	+	1.14537e14i	−0.304200	+	0.936231i
$148$	5.96124e13	+	4.33110e13i	0.466268	+	0.338764i
$149$	−5.22578e12	−	3.79675e12i	−0.0391237	−	0.0284250i	0.568052	−	0.822993i	$-0.307697\pi$
$149$	−5.22578e12	−	3.79675e12i	−0.0391237	−	0.0284250i	−0.607175	+	0.794568i	$0.707697\pi$
$150$	3.64086e13	−	1.12054e14i	0.260982	−	0.803220i
$151$	8.92445e13	+	2.74666e14i	0.612677	+	1.88563i	0.431290	+	0.902213i	$0.358058\pi$
$151$	8.92445e13	+	2.74666e14i	0.612677	+	1.88563i	0.181386	+	0.983412i	$0.441942\pi$
$152$	−2.90493e13	+	2.11056e13i	−0.191052	+	0.138808i
$153$	1.36480e13			0.0860151
$154$	−3.43437e12	+	3.07053e13i	−0.0207474	+	0.185493i
$155$	2.08413e14			1.20717
$156$	6.74581e12	−	4.90111e12i	0.0374735	−	0.0272261i
$157$	−1.45818e13	−	4.48783e13i	−0.0777078	−	0.239160i	0.904655	−	0.426145i	$-0.140129\pi$
$157$	−1.45818e13	−	4.48783e13i	−0.0777078	−	0.239160i	−0.982363	+	0.186985i	$0.940129\pi$
$158$	3.89031e13	−	1.19731e14i	0.198936	−	0.612261i
$159$	−1.69097e14	−	1.22856e14i	−0.829955	−	0.602998i
$160$	−4.42818e13	−	3.21726e13i	−0.208663	−	0.151603i
$161$	1.70646e13	−	5.25194e13i	0.0772195	−	0.237657i
$162$	−5.55662e13	−	1.71015e14i	−0.241525	−	0.743339i
$163$	−3.86515e13	+	2.80820e13i	−0.161416	+	0.117276i	−0.665561	−	0.746343i	$-0.731808\pi$
$163$	−3.86515e13	+	2.80820e13i	−0.161416	+	0.117276i	0.504145	+	0.863619i	$0.331808\pi$
$164$	−5.46172e13			−0.219202
$165$	2.69747e14	−	2.95597e14i	1.04066	−	1.14039i
$166$	−1.89917e14			−0.704469
$167$	−3.64220e14	+	2.64621e14i	−1.29929	+	0.943991i	−0.999948	−	0.0101546i	$-0.996768\pi$
$167$	−3.64220e14	+	2.64621e14i	−1.29929	+	0.943991i	−0.299343	+	0.954145i	$0.596768\pi$
$168$	8.89269e12	+	2.73689e13i	0.0305157	+	0.0939175i
$169$	−9.28762e13	+	2.85843e14i	−0.306648	+	0.943767i
$170$	−1.88825e14	−	1.37190e14i	−0.599988	−	0.435917i
$171$	−2.11403e13	−	1.53593e13i	−0.0646600	−	0.0469782i
$172$	7.83291e13	−	2.41072e14i	0.230668	−	0.709924i
$173$	−1.70633e14	−	5.25155e14i	−0.483909	−	1.48932i	−0.833555	−	0.552437i	$-0.813698\pi$
$173$	−1.70633e14	−	5.25155e14i	−0.483909	−	1.48932i	0.349646	−	0.936882i	$-0.386302\pi$
$174$	1.43881e14	−	1.04535e14i	0.393036	−	0.285558i
$175$	1.13212e14			0.297950
$176$	−4.87179e13	−	8.56963e13i	−0.123554	−	0.217335i
$177$	6.33558e14			1.54867
$178$	−4.34703e14	+	3.15830e14i	−1.02438	+	0.744258i
$179$	−5.43996e13	−	1.67425e14i	−0.123609	−	0.380430i	0.870036	−	0.492988i	$-0.164095\pi$
$179$	−5.43996e13	−	1.67425e14i	−0.123609	−	0.380430i	−0.993645	+	0.112558i	$0.964095\pi$
$180$	1.23091e13	−	3.78834e13i	0.0269745	−	0.0830190i
$181$	−9.64836e13	−	7.00995e13i	−0.203959	−	0.148185i	0.481117	−	0.876656i	$-0.340231\pi$
$181$	−9.64836e13	−	7.00995e13i	−0.203959	−	0.148185i	−0.685076	+	0.728471i	$0.740231\pi$
$182$	6.48191e12	+	4.70939e12i	0.0132202	+	0.00960506i
$183$	−2.21184e14	+	6.80734e14i	−0.435333	+	1.33982i
$184$	5.44447e13	+	1.67563e14i	0.103428	+	0.318320i
$185$	7.41899e14	−	5.39021e14i	1.36059	−	0.988530i
$186$	3.49597e14			0.619062
$187$	−2.07741e14	−	3.65424e14i	−0.355265	−	0.624922i
$188$	1.36788e14			0.225955
$189$	1.24651e14	−	9.05644e13i	0.198928	−	0.144529i
$190$	1.38092e14	+	4.25004e14i	0.212946	+	0.655382i
$191$	−3.13039e13	+	9.63434e13i	−0.0466532	+	0.143584i	−0.971670	−	0.236343i	$-0.924051\pi$
$191$	−3.13039e13	+	9.63434e13i	−0.0466532	+	0.143584i	0.925016	+	0.379927i	$0.124051\pi$
$192$	−7.42794e13	−	5.39671e13i	−0.107006	−	0.0777448i
$193$	1.41079e13	+	1.02500e13i	0.0196490	+	0.0142758i	0.597566	−	0.801819i	$-0.296134\pi$
$193$	1.41079e13	+	1.02500e13i	0.0196490	+	0.0142758i	−0.577917	+	0.816095i	$0.696134\pi$
$194$	6.19838e13	−	1.90767e14i	0.0834770	−	0.256916i
$195$	−3.20676e13	−	9.86940e13i	−0.0417678	−	0.128548i
$196$	2.98694e14	−	2.17014e14i	0.376324	−	0.273415i
$197$	−9.94238e14			−1.21188			−0.605940	−	0.795510i	$-0.707203\pi$
$197$	−9.94238e14			−1.21188			−0.605940	+	0.795510i	$0.707203\pi$
$198$	4.83562e13	−	5.29902e13i	0.0570333	−	0.0624988i
$199$	5.33772e14			0.609272			0.304636	−	0.952469i	$-0.401465\pi$
$199$	5.33772e14			0.609272			0.304636	+	0.952469i	$0.401465\pi$
$200$	−2.92219e14	+	2.12310e14i	−0.322859	+	0.234571i
$201$	5.93437e14	+	1.82641e15i	0.634746	+	1.95355i
$202$	−2.65172e14	+	8.16116e14i	−0.274628	+	0.845217i
$203$	1.38252e14	+	1.00446e14i	0.138659	+	0.100742i
$204$	−3.16740e14	−	2.30125e14i	−0.307685	−	0.223546i
$205$	−2.10049e14	+	6.46464e14i	−0.197661	+	0.608337i
$206$	3.18212e14	+	9.79355e14i	0.290121	+	0.892901i
$207$	−1.03730e14	+	7.53644e13i	−0.0916427	+	0.0665823i
$208$	−2.55626e13			−0.0218874
$209$	−8.94594e13	+	7.99818e14i	−0.0742464	+	0.663805i
$210$	3.58145e14			0.288160
$211$	−9.34893e14	+	6.79239e14i	−0.729333	+	0.529891i	−0.889352	−	0.457223i	$-0.848844\pi$
$211$	−9.34893e14	+	6.79239e14i	−0.729333	+	0.529891i	0.160019	+	0.987114i	$0.448844\pi$
$212$	1.98011e14	+	6.09416e14i	0.149798	+	0.461032i
$213$	6.93692e13	−	2.13497e14i	0.0508979	−	0.156648i
$214$	−1.08232e13	−	7.86352e12i	−0.00770312	−	0.00559664i
$215$	−2.55215e15	−	1.85425e15i	−1.76221	−	1.28032i
$216$	−1.51908e14	+	4.67525e14i	−0.101773	+	0.313225i
$217$	1.03805e14	+	3.19480e14i	0.0674888	+	0.207709i
$218$	1.51019e15	−	1.09722e15i	0.952938	−	0.692350i
$219$	2.07707e13			0.0127223
$220$	−1.20168e15	+	2.47064e14i	−0.714567	+	0.146914i
$221$	−1.09003e14			−0.0629347
$222$	1.24448e15	−	9.04167e14i	0.697739	−	0.506937i
$223$	−1.03714e15	−	3.19198e15i	−0.564747	−	1.73811i	−0.668701	−	0.743532i	$-0.733149\pi$
$223$	−1.03714e15	−	3.19198e15i	−0.564747	−	1.73811i	0.103953	−	0.994582i	$-0.466851\pi$
$224$	2.72623e13	−	8.39047e13i	0.0144195	−	0.0443787i
$225$	−2.12659e14	−	1.54505e14i	−0.109269	−	0.0793885i
$226$	1.29865e15	+	9.43528e14i	0.648319	+	0.471031i
$227$	−4.64923e14	+	1.43088e15i	−0.225534	+	0.694123i	0.772703	+	0.634768i	$0.218904\pi$
$227$	−4.64923e14	+	1.43088e15i	−0.225534	+	0.694123i	−0.998237	+	0.0593550i	$0.981096\pi$
$228$	2.31639e14	+	7.12911e14i	0.109203	+	0.336093i
$229$	2.99182e15	−	2.17368e15i	1.37090	−	0.996015i	0.373230	−	0.927739i	$-0.378250\pi$
$229$	2.99182e15	−	2.17368e15i	1.37090	−	0.996015i	0.997666	−	0.0682760i	$-0.0217498\pi$
$230$	2.19271e15			0.976675
$231$	5.87479e14	+	2.66270e14i	0.254399	+	0.115304i
$232$	−5.45223e14			−0.229563
$233$	6.11029e14	−	4.43939e14i	0.250178	−	0.181765i	−0.455628	−	0.890170i	$-0.650585\pi$
$233$	6.11029e14	−	4.43939e14i	0.250178	−	0.181765i	0.705806	+	0.708406i	$0.250585\pi$
$234$	−5.74860e12	−	1.76924e13i	−0.00228907	−	0.00704504i
$235$	5.26063e14	−	1.61906e15i	0.203750	−	0.627077i
$236$	−1.57135e15	−	1.14165e15i	−0.592032	−	0.430137i
$237$	−2.12623e15	−	1.54479e15i	−0.779373	−	0.566248i
$238$	1.16251e14	−	3.57784e14i	0.0414617	−	0.127606i
$239$	−2.32683e14	−	7.16124e14i	−0.0807566	−	0.248543i	0.902524	−	0.430639i	$-0.141712\pi$
$239$	−2.32683e14	−	7.16124e14i	−0.0807566	−	0.248543i	−0.983281	+	0.182096i	$0.941712\pi$
$240$	−9.24435e14	+	6.71641e14i	−0.312251	+	0.226863i
$241$	3.84158e15			1.26299			0.631494	−	0.775380i	$-0.282442\pi$
$241$	3.84158e15			1.26299			0.631494	+	0.775380i	$0.282442\pi$
$242$	−2.15485e15	−	4.88147e14i	−0.689633	−	0.156225i
$243$	−7.64114e14			−0.238077
$244$	1.77524e15	−	1.28979e15i	0.538548	−	0.391278i
$245$	−1.41990e15	−	4.37002e15i	−0.419449	−	1.29093i
$246$	−3.52341e14	+	1.08439e15i	−0.101364	+	0.311967i
$247$	1.68842e14	+	1.22671e14i	0.0473098	+	0.0343726i
$248$	−8.67072e14	−	6.29964e14i	−0.236657	−	0.171941i
$249$	−1.22517e15	+	3.77070e15i	−0.325763	+	1.00260i
$250$	1.58458e14	+	4.87684e14i	0.0410492	+	0.126336i
$251$	−1.42321e15	+	1.03402e15i	−0.359245	+	0.261007i	−0.752737	−	0.658321i	$-0.771267\pi$
$251$	−1.42321e15	+	1.03402e15i	−0.359245	+	0.261007i	0.393492	+	0.919328i	$0.371267\pi$
$252$	6.42029e13			0.0157925
$253$	3.59679e15	+	1.63021e15i	0.862247	+	0.390806i
$254$	−4.41604e15			−1.03184
$255$	−3.94195e15	+	2.86399e15i	−0.897842	+	0.652320i
$256$	8.69806e13	+	2.67699e14i	0.0193136	+	0.0594410i
$257$	2.42527e15	−	7.46422e15i	0.525043	−	1.61592i	−0.239187	−	0.970974i	$-0.576881\pi$
$257$	2.42527e15	−	7.46422e15i	0.525043	−	1.61592i	0.764230	−	0.644944i	$-0.223119\pi$
$258$	−4.28104e15	−	3.11036e15i	−0.903693	−	0.656571i
$259$	1.19580e15	+	8.68796e14i	0.246155	+	0.178842i
$260$	−9.83096e13	+	3.02566e14i	−0.0197365	+	0.0607426i
$261$	−1.22611e14	−	3.77359e14i	−0.0240087	−	0.0738910i
$262$	−6.33564e14	+	4.60311e14i	−0.121013	+	0.0879211i
$263$	−4.87551e15			−0.908464			−0.454232	−	0.890883i	$-0.650086\pi$
$263$	−4.87551e15			−0.908464			−0.454232	+	0.890883i	$0.650086\pi$
$264$	−2.01573e15	+	4.14431e14i	−0.366444	+	0.0753401i
$265$	7.97473e15			1.41455
$266$	−5.82715e14	+	4.23367e14i	−0.100862	+	0.0732802i
$267$	3.46631e15	+	1.06682e16i	0.585524	+	1.80206i
$268$	1.81930e15	−	5.59922e15i	0.299935	−	0.923106i
$269$	6.40602e14	+	4.65424e14i	0.103086	+	0.0748961i	0.638134	−	0.769925i	$-0.279707\pi$
$269$	6.40602e14	+	4.65424e14i	0.103086	+	0.0748961i	−0.535048	+	0.844821i	$0.679707\pi$
$270$	4.94954e15	+	3.59605e15i	0.777500	+	0.564887i
$271$	−3.06205e15	+	9.42402e15i	−0.469582	+	1.44523i	0.383544	+	0.923522i	$0.374703\pi$
$271$	−3.06205e15	+	9.42402e15i	−0.469582	+	1.44523i	−0.853127	+	0.521704i	$0.825297\pi$
$272$	3.70900e14	+	1.14151e15i	0.0555340	+	0.170916i
$273$	1.35317e14	−	9.83139e13i	0.0197832	−	0.0143733i
$274$	5.30746e15			0.757719
$275$	−8.99909e14	+	8.04570e15i	−0.125469	+	1.12176i
$276$	3.67810e15			0.500858
$277$	−4.65084e15	+	3.37903e15i	−0.618604	+	0.449442i	−0.852434	−	0.522836i	$-0.824874\pi$
$277$	−4.65084e15	+	3.37903e15i	−0.618604	+	0.449442i	0.233830	+	0.972278i	$0.424874\pi$
$278$	−1.07577e15	−	3.31088e15i	−0.139775	−	0.430182i
$279$	2.41021e14	−	7.41785e14i	0.0305933	−	0.0941566i
$280$	−8.88272e14	−	6.45367e14i	−0.110159	−	0.0800349i
$281$	7.33753e15	+	5.33103e15i	0.889117	+	0.645981i	0.935648	−	0.352936i	$-0.114817\pi$
$281$	7.33753e15	+	5.33103e15i	0.889117	+	0.645981i	−0.0465306	+	0.998917i	$0.514817\pi$
$282$	8.82431e14	−	2.71584e15i	0.104487	−	0.321577i
$283$	−2.01050e15	−	6.18768e15i	−0.232644	−	0.716004i	−0.997425	−	0.0717144i	$-0.977153\pi$
$283$	−2.01050e15	−	6.18768e15i	−0.232644	−	0.716004i	0.764781	−	0.644290i	$-0.222847\pi$
$284$	−5.56765e14	+	4.04513e14i	−0.0629655	+	0.0457471i
$285$	9.32905e15			1.03121
$286$	−3.86210e14	+	4.23221e14i	−0.0417296	+	0.0457286i
$287$	−1.09559e15			−0.115722
$288$	−1.65719e14	+	1.20402e14i	−0.0171128	+	0.0124332i
$289$	−1.47910e15	−	4.55221e15i	−0.149335	−	0.459606i
$290$	−2.09684e15	+	6.45340e15i	−0.207004	+	0.637092i
$291$	−3.38769e15	−	2.46130e15i	−0.327039	−	0.237608i
$292$	−5.15155e13	−	3.74282e13i	−0.00486351	−	0.00353354i
$293$	3.93342e15	−	1.21058e16i	0.363187	−	1.11778i	−0.587921	−	0.808918i	$-0.700053\pi$
$293$	3.93342e15	−	1.21058e16i	0.363187	−	1.11778i	0.951108	−	0.308857i	$-0.0999466\pi$
$294$	−2.38178e15	−	7.33036e15i	−0.215102	−	0.662015i
$295$	−1.95561e16	+	1.42083e16i	−1.72758	+	1.25516i
$296$	−4.71584e15			−0.407533
$297$	5.44537e15	+	9.57857e15i	0.460374	+	0.809811i
$298$	4.13403e14			0.0341954
$299$	8.28469e14	−	6.01918e14i	0.0670523	−	0.0487163i
$300$	2.33015e15	+	7.17146e15i	0.184542	+	0.567962i
$301$	1.57124e15	−	4.83579e15i	0.121776	−	0.374787i
$302$	−1.49533e16	−	1.08642e16i	−1.13421	−	0.824048i
$303$	1.44929e16	+	1.05297e16i	1.07591	+	0.781696i
$304$	7.10135e14	−	2.18557e15i	0.0516015	−	0.158813i
$305$	−8.43900e15	−	2.59726e16i	−0.600264	−	1.84742i
$306$	−7.06654e14	+	5.13414e14i	−0.0492059	+	0.0357502i
$307$	8.96271e15			0.610998			0.305499	−	0.952192i	$-0.401177\pi$
$307$	8.96271e15			0.610998			0.305499	+	0.952192i	$0.401177\pi$
$308$	−9.77256e14	−	1.71902e15i	−0.0652272	−	0.114737i
$309$	2.14973e16			1.40493
$310$	−1.07910e16	+	7.84015e15i	−0.690577	+	0.501734i
$311$	−5.65945e14	−	1.74180e15i	−0.0354676	−	0.109158i	0.931755	−	0.363087i	$-0.118277\pi$
$311$	−5.65945e14	−	1.74180e15i	−0.0354676	−	0.109158i	−0.967223	+	0.253929i	$0.918277\pi$
$312$	−1.64907e14	+	5.07531e14i	−0.0101212	+	0.0311500i
$313$	−1.58618e16	−	1.15243e16i	−0.953484	−	0.692747i	−0.00185579	−	0.999998i	$-0.500591\pi$
$313$	−1.58618e16	−	1.15243e16i	−0.953484	−	0.692747i	−0.951628	+	0.307252i	$0.900591\pi$
$314$	2.44325e15	+	1.77512e15i	0.143855	+	0.104517i
$315$	2.46914e14	−	7.59922e14i	0.0142405	−	0.0438279i
$316$	2.48980e15	+	7.66280e15i	0.140669	+	0.432934i
$317$	−8.52618e15	+	6.19463e15i	−0.471921	+	0.342871i	−0.798190	−	0.602406i	$-0.794209\pi$
$317$	−8.52618e15	+	6.19463e15i	−0.471921	+	0.342871i	0.326268	+	0.945277i	$0.394209\pi$
$318$	1.33770e16			0.725407
$319$	−8.23744e15	+	9.02684e15i	−0.437676	+	0.479619i
$320$	3.50306e15			0.182378
$321$	−2.25947e14	+	1.64160e14i	−0.0115272	+	0.00837501i
$322$	1.09213e15	+	3.36124e15i	0.0546025	+	0.168049i
$323$	3.02814e15	−	9.31964e15i	0.148374	−	0.456649i
$324$	9.31035e15	+	6.76436e15i	0.447119	+	0.324851i
$325$	1.69846e15	+	1.23400e15i	0.0799489	+	0.0580862i
$326$	9.44869e14	−	2.90801e15i	0.0435970	−	0.134178i
$327$	−1.20422e16	−	3.70622e16i	−0.544687	−	1.67637i
$328$	2.82792e15	−	2.05461e15i	0.125397	−	0.0911063i
$329$	2.74390e15			0.119287
$330$	−2.84686e15	+	2.54526e16i	−0.121346	+	1.08490i
$331$	5.24671e15			0.219283			0.109642	−	0.993971i	$-0.465030\pi$
$331$	5.24671e15			0.219283			0.109642	+	0.993971i	$0.465030\pi$
$332$	9.83337e15	−	7.14436e15i	0.403000	−	0.292796i
$333$	−1.06051e15	−	3.26392e15i	−0.0426215	−	0.131175i
$334$	8.90366e15	−	2.74026e16i	0.350927	−	1.08004i
$335$	−5.92772e16	−	4.30674e16i	−2.29138	−	1.66478i
$336$	−1.49001e15	−	1.08255e15i	−0.0564915	−	0.0410435i
$337$	−1.40931e16	+	4.33742e16i	−0.524099	+	1.61301i	0.241991	+	0.970278i	$0.422199\pi$
$337$	−1.40931e16	+	4.33742e16i	−0.524099	+	1.61301i	−0.766090	+	0.642733i	$0.777801\pi$
$338$	−5.94407e15	−	1.82940e16i	−0.216833	−	0.667344i
$339$	2.71109e16	−	1.96972e16i	0.970167	−	0.704867i
$340$	1.49377e16			0.524409
$341$	−2.35299e16	+	4.83770e15i	−0.810431	+	0.166623i
$342$	1.67237e15			0.0565149
$343$	1.24320e16	−	9.03240e15i	0.412221	−	0.299496i
$344$	5.01306e15	+	1.54286e16i	0.163107	+	0.501992i
$345$	1.41454e16	−	4.35350e16i	0.451638	−	1.39000i
$346$	2.85903e16	+	2.07721e16i	0.895827	+	0.650856i
$347$	4.60097e14	+	3.34280e14i	0.0141484	+	0.0102794i	0.594837	−	0.803846i	$-0.297217\pi$
$347$	4.60097e14	+	3.34280e14i	0.0141484	+	0.0102794i	−0.580689	+	0.814126i	$0.697217\pi$
$348$	−3.51728e15	+	1.08251e16i	−0.106155	+	0.326713i
$349$	1.52420e16	+	4.69099e16i	0.451518	+	1.38963i	0.875174	+	0.483808i	$0.160747\pi$
$349$	1.52420e16	+	4.69099e16i	0.451518	+	1.38963i	−0.423656	+	0.905823i	$0.639253\pi$
$350$	−5.86177e15	+	4.25882e15i	−0.170446	+	0.123836i
$351$	2.85723e15			0.0815546
$352$	5.74621e15	+	2.60442e15i	0.161011	+	0.0729766i
$353$	−1.74176e16			−0.479129			−0.239565	−	0.970880i	$-0.577005\pi$
$353$	−1.74176e16			−0.479129			−0.239565	+	0.970880i	$0.577005\pi$
$354$	−3.28038e16	+	2.38333e16i	−0.885937	+	0.643671i
$355$	2.64670e15	+	8.14570e15i	0.0701811	+	0.215995i
$356$	1.06267e16	−	3.27055e16i	0.276676	−	0.851522i
$357$	−6.35365e15	−	4.61619e15i	−0.162435	−	0.118016i
$358$	9.11487e15	+	6.62234e15i	0.228829	+	0.166254i
$359$	−1.39637e16	+	4.29758e16i	−0.344260	+	1.05952i	0.617719	+	0.786399i	$0.288057\pi$
$359$	−1.39637e16	+	4.29758e16i	−0.344260	+	1.05952i	−0.961979	+	0.273124i	$0.911943\pi$
$360$	7.87780e14	+	2.42454e15i	0.0190739	+	0.0587033i
$361$	1.88429e16	−	1.36902e16i	0.448075	−	0.325545i
$362$	7.63266e15			0.178267
$363$	−2.35930e16	+	3.96343e16i	−0.541241	+	0.909239i
$364$	−5.12774e14			−0.0115549
$365$	−6.41130e14	+	4.65808e14i	−0.0141920	+	0.0103111i
$366$	−1.41558e16	−	4.35670e16i	−0.307827	−	0.947394i
$367$	−3.55909e15	+	1.09538e16i	−0.0760344	+	0.234010i	−0.981849	−	0.189665i	$-0.939260\pi$
$367$	−3.55909e15	+	1.09538e16i	−0.0760344	+	0.234010i	0.905815	+	0.423674i	$0.139260\pi$
$368$	−9.12243e15	−	6.62783e15i	−0.191470	−	0.139111i
$369$	2.05798e15	+	1.49521e15i	0.0424395	+	0.0308341i
$370$	−1.81363e16	+	5.58179e16i	−0.367484	+	1.13100i
$371$	3.97201e15	+	1.22246e16i	0.0790824	+	0.243390i
$372$	−1.81011e16	+	1.31512e16i	−0.354141	+	0.257299i
$373$	9.13771e16			1.75683			0.878415	−	0.477898i	$-0.158601\pi$
$373$	9.13771e16			1.75683			0.878415	+	0.477898i	$0.158601\pi$
$374$	2.45028e16	+	1.11057e16i	0.462968	+	0.209836i
$375$	1.07049e16			0.198783
$376$	−7.08248e15	+	5.14572e15i	−0.129260	+	0.0939129i
$377$	9.79270e14	+	3.01388e15i	0.0175664	+	0.0540639i
$378$	−3.04720e15	+	9.37832e15i	−0.0537285	+	0.165359i
$379$	1.04159e16	+	7.56757e15i	0.180526	+	0.131160i	0.674379	−	0.738386i	$-0.264412\pi$
$379$	1.04159e16	+	7.56757e15i	0.180526	+	0.131160i	−0.493852	+	0.869546i	$0.664412\pi$
$380$	−2.31379e16	−	1.68107e16i	−0.394213	−	0.286412i
$381$	−2.84882e16	+	8.76778e16i	−0.477148	+	1.46851i
$382$	−2.00345e15	−	6.16598e15i	−0.0329888	−	0.101529i
$383$	3.29802e16	−	2.39615e16i	0.533902	−	0.387903i	−0.287913	−	0.957657i	$-0.592961\pi$
$383$	3.29802e16	−	2.39615e16i	0.533902	−	0.387903i	0.821815	+	0.569754i	$0.192961\pi$
$384$	5.87612e15			0.0935271
$385$	−2.41052e16	+	4.95598e15i	−0.377238	+	0.0775595i
$386$	−1.11605e15			−0.0171738
$387$	−9.55108e15	+	6.93927e15i	−0.144521	+	0.105001i
$388$	3.96696e15	+	1.22091e16i	0.0590272	+	0.181667i
$389$	−2.10204e15	+	6.46941e15i	−0.0307587	+	0.0946656i	−0.965257	−	0.261301i	$-0.915848\pi$
$389$	−2.10204e15	+	6.46941e15i	−0.0307587	+	0.0946656i	0.934499	+	0.355967i	$0.115848\pi$
$390$	5.37306e15	+	3.90376e15i	0.0773218	+	0.0561776i
$391$	−3.88996e16	−	2.82622e16i	−0.550549	−	0.399998i
$392$	−7.30182e15	+	2.24727e16i	−0.101642	+	0.312821i
$393$	5.05203e15	+	1.55485e16i	0.0691694	+	0.212882i
$394$	5.14788e16	−	3.74015e16i	0.693270	−	0.503690i
$395$	1.00274e17			1.32834
$396$	−5.10343e14	+	4.56275e15i	−0.00665033	+	0.0594577i
$397$	−3.96884e15			−0.0508775			−0.0254388	−	0.999676i	$-0.508098\pi$
$397$	−3.96884e15			−0.0508775			−0.0254388	+	0.999676i	$0.508098\pi$
$398$	−2.76372e16	+	2.00796e16i	−0.348541	+	0.253230i
$399$	4.64656e15	+	1.43006e16i	0.0576511	+	0.177432i
$400$	7.14353e15	−	2.19855e16i	0.0872013	−	0.268378i
$401$	−9.60439e16	−	6.97800e16i	−1.15354	−	0.838093i	−0.164589	−	0.986362i	$-0.552630\pi$
$401$	−9.60439e16	−	6.97800e16i	−1.15354	−	0.838093i	−0.988947	+	0.148269i	$0.952630\pi$
$402$	−9.94329e16	−	7.22422e16i	−1.17506	−	0.853732i
$403$	−1.92498e15	+	5.92447e15i	−0.0223843	+	0.0688916i
$404$	−1.69710e16	−	5.22314e16i	−0.194191	−	0.597659i
$405$	1.15871e17	−	8.41851e16i	1.30472	−	0.947932i
$406$	−1.09369e16			−0.121192
$407$	−7.12487e16	+	7.80765e16i	−0.776986	+	0.851445i
$408$	2.50568e16			0.268927
$409$	−4.46749e16	+	3.24582e16i	−0.471913	+	0.342865i	−0.798186	−	0.602411i	$-0.794207\pi$
$409$	−4.46749e16	+	3.24582e16i	−0.471913	+	0.342865i	0.326273	+	0.945275i	$0.394207\pi$
$410$	−1.34431e16	−	4.13737e16i	−0.139767	−	0.430159i
$411$	3.42389e16	−	1.05377e17i	0.350387	−	1.07838i
$412$	−5.33177e16	−	3.87376e16i	−0.537081	−	0.390212i
$413$	−3.15205e16	−	2.29010e16i	−0.312549	−	0.227080i
$414$	2.53577e15	−	7.80430e15i	0.0247518	−	0.0761783i
$415$	−4.67450e16	−	1.43866e17i	−0.449182	−	1.38244i
$416$	1.32356e15	−	9.61621e14i	0.0125209	−	0.00909699i
$417$	−7.26754e16			−0.676867
$418$	−2.54558e16	−	4.47775e16i	−0.233422	−	0.410596i
$419$	1.96638e17			1.77532			0.887658	−	0.460503i	$-0.152331\pi$
$419$	1.96638e17			1.77532			0.887658	+	0.460503i	$0.152331\pi$
$420$	−1.85437e16	+	1.34728e16i	−0.164845	+	0.119767i
$421$	2.73179e16	+	8.40759e16i	0.239119	+	0.735932i	0.996548	+	0.0830152i	$0.0264550\pi$
$421$	2.73179e16	+	8.40759e16i	0.239119	+	0.735932i	−0.757429	+	0.652917i	$0.773545\pi$
$422$	2.28542e16	−	7.03381e16i	0.196986	−	0.606261i
$423$	−5.15418e15	−	3.74473e15i	−0.0437469	−	0.0317840i
$424$	−3.31776e16	−	2.41049e16i	−0.277311	−	0.201478i
$425$	3.04613e16	−	9.37501e16i	0.250738	−	0.771692i
$426$	4.43963e15	+	1.36638e16i	0.0359902	+	0.110767i
$427$	3.56105e16	−	2.58726e16i	0.284313	−	0.206566i
$428$	8.56206e14			0.00673277
$429$	5.91132e15	+	1.03982e16i	0.0457839	+	0.0805352i
$430$	2.01897e17			1.54022
$431$	−5.53421e15	+	4.02084e15i	−0.0415866	+	0.0302144i	−0.608384	−	0.793643i	$-0.708182\pi$
$431$	−5.53421e15	+	4.02084e15i	−0.0415866	+	0.0302144i	0.566798	+	0.823857i	$0.308182\pi$
$432$	−9.72212e15	−	2.99216e16i	−0.0719642	−	0.221483i
$433$	−5.55217e16	+	1.70878e17i	−0.404847	+	1.24599i	0.516176	+	0.856483i	$0.327355\pi$
$433$	−5.55217e16	+	1.70878e17i	−0.404847	+	1.24599i	−0.921023	+	0.389509i	$0.872645\pi$
$434$	−1.73930e16	−	1.26368e16i	−0.124937	−	0.0907722i
$435$	1.14602e17	+	8.32630e16i	0.810981	+	0.589212i
$436$	−3.69179e16	+	1.13621e17i	−0.257380	+	0.792133i
$437$	2.84481e16	+	8.75544e16i	0.195400	+	0.601379i
$438$	−1.07545e15	+	7.81357e14i	−0.00727791	+	0.00528771i
$439$	1.03769e17			0.691905			0.345953	−	0.938252i	$-0.387556\pi$
$439$	1.03769e17			0.691905			0.345953	+	0.938252i	$0.387556\pi$
$440$	5.29256e16	−	5.79975e16i	0.347715	−	0.381037i
$441$	−1.71958e16			−0.111320
$442$	5.64388e15	−	4.10052e15i	0.0360025	−	0.0261574i
$443$	5.42954e16	+	1.67104e17i	0.341302	+	1.05042i	0.963534	+	0.267587i	$0.0862263\pi$
$443$	5.42954e16	+	1.67104e17i	0.341302	+	1.05042i	−0.622231	+	0.782833i	$0.713774\pi$
$444$	−3.04223e16	+	9.36302e16i	−0.188453	+	0.579998i
$445$	−3.46243e17	−	2.51560e17i	−2.11369	−	1.53568i
$446$	1.73777e17	+	1.26256e17i	1.04548	+	0.759584i
$447$	2.66690e15	−	8.20786e15i	0.0158127	−	0.0486666i
$448$	1.74479e15	+	5.36990e15i	0.0101961	+	0.0313804i
$449$	7.08253e16	−	5.14576e16i	0.407932	−	0.296380i	−0.364832	−	0.931073i	$-0.618874\pi$
$449$	7.08253e16	−	5.14576e16i	0.407932	−	0.296380i	0.772764	+	0.634694i	$0.218874\pi$
$450$	1.68231e16			0.0955045
$451$	8.70878e15	−	7.78615e16i	0.0487315	−	0.435687i
$452$	−1.02734e17			−0.566652
$453$	−3.12167e17	+	2.26803e17i	−1.69726	+	1.23313i
$454$	−2.97550e16	−	9.15766e16i	−0.159477	−	0.490819i
$455$	−1.97204e15	+	6.06932e15i	−0.0104194	+	0.0320676i
$456$	−3.88121e16	−	2.81986e16i	−0.202160	−	0.146878i
$457$	−1.09156e17	−	7.93067e16i	−0.560523	−	0.407244i	0.271127	−	0.962544i	$-0.412604\pi$
$457$	−1.09156e17	−	7.93067e16i	−0.560523	−	0.407244i	−0.831650	+	0.555300i	$0.812604\pi$
$458$	−7.31375e16	+	2.25094e17i	−0.370267	+	1.13956i
$459$	−4.14568e16	−	1.27591e17i	−0.206925	−	0.636850i
$460$	−1.13532e17	+	8.24859e16i	−0.558718	+	0.405933i
$461$	−1.01004e17			−0.490097			−0.245048	−	0.969511i	$-0.578804\pi$
$461$	−1.01004e17			−0.490097			−0.245048	+	0.969511i	$0.578804\pi$
$462$	−4.04346e16	+	8.31327e15i	−0.193455	+	0.0397740i
$463$	−5.94484e16			−0.280455			−0.140228	−	0.990119i	$-0.544783\pi$
$463$	−5.94484e16			−0.280455			−0.140228	+	0.990119i	$0.544783\pi$
$464$	2.82301e16	−	2.05103e16i	0.131324	−	0.0954127i
$465$	8.60476e16	+	2.64827e17i	0.394725	+	1.21484i
$466$	−1.49371e16	+	4.59717e16i	−0.0675707	+	0.207961i
$467$	5.07515e16	+	3.68731e16i	0.226406	+	0.164494i	0.695206	−	0.718811i	$-0.255313\pi$
$467$	5.07515e16	+	3.68731e16i	0.226406	+	0.164494i	−0.468799	+	0.883305i	$0.655313\pi$
$468$	9.63202e14	+	6.99807e14i	0.00423760	+	0.00307879i
$469$	3.64942e16	−	1.12318e17i	0.158344	−	0.487332i
$470$	3.36681e16	+	1.03620e17i	0.144073	+	0.443410i
$471$	5.10056e16	−	3.70578e16i	0.215269	−	0.156402i
$472$	1.24307e17			0.517455
$473$	3.31179e17	+	1.50104e17i	1.35977	+	0.616303i
$474$	1.68202e17			0.681197
$475$	−1.52689e17	+	1.10935e17i	−0.609956	+	0.443159i
$476$	7.44007e15	+	2.28982e16i	0.0293178	+	0.0902310i
$477$	9.22241e15	−	2.83837e16i	0.0358488	−	0.110331i
$478$	3.89870e16	+	2.83257e16i	0.149499	+	0.108617i
$479$	2.89313e17	+	2.10198e17i	1.09443	+	0.795147i	0.980141	−	0.198301i	$-0.0635423\pi$
$479$	2.89313e17	+	2.10198e17i	1.09443	+	0.795147i	0.114285	+	0.993448i	$0.463542\pi$
$480$	2.25986e16	−	6.95513e16i	0.0843360	−	0.259560i
$481$	8.47007e15	+	2.60682e16i	0.0311849	+	0.0959772i
$482$	−1.98906e17	+	1.44514e17i	−0.722507	+	0.524932i
$483$	7.37809e16			0.264416
$484$	1.29935e17	−	5.57871e16i	0.459444	−	0.197260i
$485$	1.59766e17			0.557395
$486$	3.95636e16	−	2.87447e16i	0.136195	−	0.0989513i
$487$	−9.86667e16	−	3.03665e17i	−0.335145	−	1.03147i	−0.966651	−	0.256098i	$-0.917563\pi$
$487$	−9.86667e16	−	3.03665e17i	−0.335145	−	1.03147i	0.631506	−	0.775371i	$-0.282437\pi$
$488$	−4.33973e16	+	1.33563e17i	−0.145457	+	0.447670i
$489$	−5.16413e16	−	3.75196e16i	−0.170801	−	0.124094i
$490$	2.37911e17	+	1.72852e17i	0.776497	+	0.564158i
$491$	1.32984e17	−	4.09284e17i	0.428322	−	1.31824i	−0.471455	−	0.881890i	$-0.656271\pi$
$491$	1.32984e17	−	4.09284e17i	0.428322	−	1.31824i	0.899777	−	0.436350i	$-0.143729\pi$
$492$	−2.25498e16	−	6.94012e16i	−0.0716753	−	0.220594i
$493$	1.20378e17	−	8.74596e16i	0.377608	−	0.274349i
$494$	−1.33568e16			−0.0413503
$495$	5.20433e16	+	2.35881e16i	0.159012	+	0.0720709i
$496$	6.85926e16			0.206846
$497$	−1.11684e16	+	8.11433e15i	−0.0332411	+	0.0241511i
$498$	−7.84111e16	−	2.41325e17i	−0.230349	−	0.708942i
$499$	9.80048e16	−	3.01628e17i	0.284180	−	0.874617i	−0.702463	−	0.711720i	$-0.747916\pi$
$499$	9.80048e16	−	3.01628e17i	0.284180	−	0.874617i	0.986643	−	0.162896i	$-0.0520837\pi$
$500$	−2.65503e16	−	1.92899e16i	−0.0759915	−	0.0552110i
$501$	−4.86625e17	−	3.53554e17i	−1.37483	−	0.998873i
$502$	3.47916e16	−	1.07078e17i	0.0970287	−	0.298624i
$503$	1.22438e17	+	3.76826e17i	0.337074	+	1.03741i	0.965691	+	0.259693i	$0.0836213\pi$
$503$	1.22438e17	+	3.76826e17i	0.337074	+	1.03741i	−0.628617	+	0.777715i	$0.716379\pi$
$504$	−3.32424e15	+	2.41520e15i	−0.00903428	+	0.00656379i
$505$	−6.83493e17			−1.83375
$506$	−2.47557e17	+	5.08973e16i	−0.655687	+	0.134808i
$507$	−4.01562e17			−1.05003
$508$	2.28650e17	−	1.66124e17i	0.590277	−	0.428862i
$509$	−1.17284e17	−	3.60962e17i	−0.298932	−	0.920018i	−0.981872	−	0.189544i	$-0.939299\pi$
$509$	−1.17284e17	−	3.60962e17i	−0.298932	−	0.920018i	0.682940	−	0.730474i	$-0.260701\pi$
$510$	9.63642e16	−	2.96579e17i	0.242499	−	0.746335i
$511$	−1.03338e15	−	7.50791e14i	−0.00256757	−	0.00186545i
$512$	−1.45740e16	−	1.05886e16i	−0.0357538	−	0.0259767i
$513$	−7.93743e16	+	2.44289e17i	−0.192272	+	0.591753i
$514$	1.55217e17	+	4.77710e17i	0.371262	+	1.14263i
$515$	−6.63559e17	+	4.82104e17i	−1.56723	+	1.13866i
$516$	3.38666e17			0.789857
$517$	−2.18110e16	+	1.95003e17i	−0.0502327	+	0.449109i
$518$	−9.45974e16			−0.215147
$519$	5.96856e17	−	4.33641e17i	1.34055	−	0.973963i
$520$	−6.29182e15	−	1.93642e16i	−0.0139558	−	0.0429515i
$521$	5.17504e16	−	1.59271e17i	0.113362	−	0.348893i	−0.878240	−	0.478221i	$-0.841282\pi$
$521$	5.17504e16	−	1.59271e17i	0.113362	−	0.348893i	0.991602	+	0.129328i	$0.0412819\pi$
$522$	2.05441e16	+	1.49261e16i	0.0444455	+	0.0322916i
$523$	−3.91254e17	−	2.84263e17i	−0.835984	−	0.607378i	0.0852622	−	0.996359i	$-0.472827\pi$
$523$	−3.91254e17	−	2.84263e17i	−0.835984	−	0.607378i	−0.921246	+	0.388981i	$0.872827\pi$
$524$	1.54880e16	−	4.76671e16i	0.0326845	−	0.100593i
$525$	4.67416e16	+	1.43856e17i	0.0974246	+	0.299842i
$526$	2.52440e17	−	1.83408e17i	0.519697	−	0.377582i
$527$	2.92491e17			0.594762
$528$	8.87786e16	−	9.72863e16i	0.178315	−	0.195403i
$529$	−5.23198e16			−0.103802
$530$	−4.12908e17	+	2.99995e17i	−0.809208	+	0.587924i
$531$	2.79545e16	+	8.60352e16i	0.0541175	+	0.166557i
$532$	1.42449e16	−	4.38414e16i	0.0272418	−	0.0838415i
$533$	−1.64366e16	−	1.19419e16i	−0.0310518	−	0.0225604i
$534$	−5.80795e17	−	4.21972e17i	−1.08394	−	0.787527i
$535$	3.29283e15	−	1.01343e16i	0.00607113	−	0.0186850i
$536$	1.16435e17	+	3.58350e17i	0.212086	+	0.652735i
$537$	1.90284e17	−	1.38249e17i	0.342427	−	0.248788i
$538$	−5.06769e16			−0.0901002
$539$	2.61744e17	+	4.60416e17i	0.459780	+	0.808767i
$540$	−3.91550e17			−0.679560
$541$	3.71206e17	−	2.69697e17i	0.636550	−	0.462481i	−0.222113	−	0.975021i	$-0.571295\pi$
$541$	3.71206e17	−	2.69697e17i	0.636550	−	0.462481i	0.858663	+	0.512540i	$0.171295\pi$
$542$	−1.95971e17	−	6.03137e17i	−0.332045	−	1.02193i
$543$	4.92390e16	−	1.51542e17i	0.0824347	−	0.253708i
$544$	−6.21458e16	−	4.51516e16i	−0.102806	−	0.0746931i
$545$	1.20287e18	+	8.73939e17i	1.96627	+	1.42858i
$546$	−3.30795e15	+	1.01808e16i	−0.00534326	+	0.0164449i
$547$	−3.12508e17	−	9.61800e17i	−0.498819	−	1.53521i	−0.810919	−	0.585158i	$-0.801032\pi$
$547$	−3.12508e17	−	9.61800e17i	−0.498819	−	1.53521i	0.312100	−	0.950049i	$-0.398968\pi$
$548$	−2.74805e17	+	1.99657e17i	−0.433462	+	0.314928i
$549$	−1.02201e17			−0.159307
$550$	−2.56070e17	−	4.50436e17i	−0.394459	−	0.693866i
$551$	−2.84887e17			−0.433698
$552$	−1.90441e17	+	1.38364e17i	−0.286522	+	0.208170i
$553$	4.99441e16	+	1.53712e17i	0.0742627	+	0.228557i
$554$	1.13694e17	−	3.49913e17i	0.167079	−	0.514217i
$555$	9.91233e17	+	7.20173e17i	1.43970	+	1.04600i
$556$	1.80250e17	+	1.30959e17i	0.258755	+	0.187996i
$557$	8.78780e16	−	2.70461e17i	0.124687	−	0.383747i	−0.869157	−	0.494537i	$-0.835338\pi$
$557$	8.78780e16	−	2.70461e17i	0.124687	−	0.383747i	0.993844	+	0.110789i	$0.0353378\pi$
$558$	1.54253e16	+	4.74743e16i	0.0216328	+	0.0665788i
$559$	7.62823e16	−	5.54224e16i	0.105742	−	0.0768260i
$560$	7.02697e16			0.0962822
$561$	3.78567e17	−	4.14846e17i	0.512725	−	0.561860i
$562$	−5.80460e17			−0.777117
$563$	9.50439e17	−	6.90534e17i	1.25782	−	0.913862i	0.259174	−	0.965831i	$-0.416550\pi$
$563$	9.50439e17	−	6.90534e17i	1.25782	−	0.913862i	0.998649	+	0.0519684i	$0.0165495\pi$
$564$	5.64756e16	+	1.73814e17i	0.0738833	+	0.227389i
$565$	−3.95100e17	+	1.21599e18i	−0.510966	+	1.57259i
$566$	3.36867e17	+	2.44748e17i	0.430677	+	0.312905i
$567$	1.86761e17	+	1.35690e17i	0.236046	+	0.171497i
$568$	1.36106e16	−	4.18890e16i	0.0170064	−	0.0523403i
$569$	3.20838e17	+	9.87438e17i	0.396329	+	1.21978i	0.927922	+	0.372775i	$0.121594\pi$
$569$	3.20838e17	+	9.87438e17i	0.396329	+	1.21978i	−0.531593	+	0.847000i	$0.678406\pi$
$570$	−4.83031e17	+	3.50942e17i	−0.589913	+	0.428597i
$571$	−1.60508e18			−1.93804			−0.969019	−	0.246987i	$-0.920559\pi$
$571$	−1.60508e18			−1.93804			−0.969019	+	0.246987i	$0.920559\pi$
$572$	4.07599e15	−	3.64417e16i	0.00486585	−	0.0435035i
$573$	−1.35346e17			−0.159750
$574$	5.67267e16	−	4.12144e16i	0.0662003	−	0.0480974i
$575$	2.86171e17	+	8.80745e17i	0.330206	+	1.01627i
$576$	4.05113e15	−	1.24681e16i	0.00462201	−	0.0142251i
$577$	5.04057e17	+	3.66219e17i	0.568640	+	0.413141i	0.834611	−	0.550840i	$-0.185693\pi$
$577$	5.04057e17	+	3.66219e17i	0.568640	+	0.413141i	−0.265971	+	0.963981i	$0.585693\pi$
$578$	2.47830e17	+	1.80059e17i	0.276454	+	0.200855i
$579$	−7.19975e15	+	2.21586e16i	−0.00794158	+	0.0244417i
$580$	−1.34198e17	−	4.13018e17i	−0.146374	−	0.450492i
$581$	1.97252e17	−	1.43312e17i	0.212754	−	0.154575i
$582$	2.67995e17			0.285843
$583$	−9.00347e17	+	1.85110e17i	−0.949651	+	0.195247i
$584$	4.07531e15			0.00425086
$585$	1.19874e16	−	8.70937e15i	0.0123655	−	0.00898408i
$586$	2.51739e17	+	7.74772e17i	0.256812	+	0.790387i
$587$	−4.52768e17	+	1.39348e18i	−0.456802	+	1.40589i	0.412205	+	0.911091i	$0.364759\pi$
$587$	−4.52768e17	+	1.39348e18i	−0.456802	+	1.40589i	−0.869007	+	0.494800i	$0.835241\pi$
$588$	3.99077e17	+	2.89946e17i	0.398203	+	0.289311i
$589$	−4.53058e17	−	3.29166e17i	−0.447099	−	0.324837i
$590$	4.78064e17	−	1.47133e18i	0.466604	−	1.43606i
$591$	−4.10491e17	−	1.26336e18i	−0.396264	−	1.21958i
$592$	2.44172e17	−	1.77402e17i	0.233134	−	0.169382i
$593$	−1.77995e18			−1.68094			−0.840472	−	0.541855i	$-0.817722\pi$
$593$	−1.77995e18			−1.68094			−0.840472	+	0.541855i	$0.817722\pi$
$594$	−6.42275e17	−	2.91105e17i	−0.599941	−	0.271918i
$595$	2.99642e17			0.276849
$596$	−2.14048e16	+	1.55515e16i	−0.0195619	+	0.0142125i
$597$	2.20378e17	+	6.78255e17i	0.199221	+	0.613140i
$598$	−2.02526e16	+	6.23311e16i	−0.0181102	+	0.0557375i
$599$	6.37064e17	+	4.62854e17i	0.563519	+	0.409421i	0.832745	−	0.553656i	$-0.186768\pi$
$599$	6.37064e17	+	4.62854e17i	0.563519	+	0.409421i	−0.269226	+	0.963077i	$0.586768\pi$
$600$	−3.90426e17	−	2.83661e17i	−0.341630	−	0.248209i
$601$	−3.83004e17	+	1.17876e18i	−0.331527	+	1.02034i	0.636880	+	0.770963i	$0.280224\pi$
$601$	−3.83004e17	+	1.17876e18i	−0.331527	+	1.02034i	−0.968408	+	0.249373i	$0.919776\pi$
$602$	1.00559e17	+	3.09490e17i	0.0861085	+	0.265015i
$603$	−2.21837e17	+	1.61174e17i	−0.187919	+	0.136531i
$604$	1.18293e18			0.991332
$605$	−1.60601e17	−	1.75250e18i	−0.133149	−	1.45294i
$606$	−1.14651e18			−0.940382
$607$	1.22517e18	−	8.90141e17i	0.994194	−	0.722324i	0.0333588	−	0.999443i	$-0.489380\pi$
$607$	1.22517e18	−	8.90141e17i	0.994194	−	0.722324i	0.960836	+	0.277119i	$0.0893796\pi$
$608$	4.54486e16	+	1.39876e17i	0.0364878	+	0.112298i
$609$	−7.05550e16	+	2.17146e17i	−0.0560422	+	0.172480i
$610$	1.41399e18	+	1.02732e18i	1.11123	+	0.807353i
$611$	4.11653e16	+	2.99083e16i	0.0320083	+	0.0232554i
$612$	1.72747e16	−	5.31662e16i	0.0132901	−	0.0409026i
$613$	−2.91316e17	−	8.96577e17i	−0.221754	−	0.682487i	−0.998605	−	0.0528032i	$-0.983184\pi$
$613$	−2.91316e17	−	8.96577e17i	−0.221754	−	0.682487i	0.776851	−	0.629684i	$-0.216816\pi$
$614$	−4.64063e17	+	3.37162e17i	−0.349529	+	0.253947i
$615$	−9.08173e17			−0.676831
$616$	1.15266e17	+	5.22434e16i	0.0850016	+	0.0385262i
$617$	1.69506e18			1.23689			0.618445	−	0.785828i	$-0.287763\pi$
$617$	1.69506e18			1.23689			0.618445	+	0.785828i	$0.287763\pi$
$618$	−1.11307e18	+	8.08692e17i	−0.803706	+	0.583927i
$619$	8.13165e16	+	2.50266e17i	0.0581018	+	0.178819i	0.975895	−	0.218239i	$-0.0700312\pi$
$619$	8.13165e16	+	2.50266e17i	0.0581018	+	0.178819i	−0.917794	+	0.397058i	$0.870031\pi$
$620$	2.63796e17	−	8.11880e17i	0.186519	−	0.574045i
$621$	1.01965e18	+	7.40816e17i	0.713435	+	0.518341i
$622$	9.48264e16	+	6.88954e16i	0.0656586	+	0.0477038i
$623$	2.13166e17	−	6.56056e17i	0.146065	−	0.449540i
$624$	−1.05540e16	−	3.24820e16i	−0.00715680	−	0.0220264i
$625$	1.03032e18	−	7.48573e17i	0.691437	−	0.502359i
$626$	1.25480e18			0.833376
$627$	−1.05325e18	+	2.16546e17i	−0.692297	+	0.142335i
$628$	−1.93281e17			−0.125734
$629$	1.04119e18	−	7.56471e17i	0.670351	−	0.487038i
$630$	1.58025e16	+	4.86350e16i	0.0100696	+	0.0309910i
$631$	−8.05354e17	+	2.47863e18i	−0.507921	+	1.56322i	0.287883	+	0.957666i	$0.407049\pi$
$631$	−8.05354e17	+	2.47863e18i	−0.507921	+	1.56322i	−0.795804	+	0.605554i	$0.792951\pi$
$632$	−4.17176e17	−	3.03096e17i	−0.260410	−	0.189199i
$633$	−1.24909e18	−	9.07514e17i	−0.771735	−	0.560698i
$634$	2.08430e17	−	6.41480e17i	0.127462	−	0.392286i
$635$	−1.08693e18	−	3.34524e18i	−0.657921	−	2.02487i
$636$	−6.92621e17	+	5.03219e17i	−0.414978	+	0.301499i
$637$	1.37339e17			0.0814494
$638$	8.69365e16	−	7.77261e17i	0.0510349	−	0.456281i
$639$	3.20530e16			0.0186257
$640$	−1.81378e17	+	1.31779e17i	−0.104332	+	0.0758013i
$641$	−9.10334e17	−	2.80172e18i	−0.518351	−	1.59532i	−0.777102	−	0.629375i	$-0.783311\pi$
$641$	−9.10334e17	−	2.80172e18i	−0.518351	−	1.59532i	0.258751	−	0.965944i	$-0.416689\pi$
$642$	5.52346e15	−	1.69995e16i	0.00311339	−	0.00958204i
$643$	2.63468e17	+	1.91421e17i	0.147013	+	0.106811i	0.658861	−	0.752265i	$-0.271039\pi$
$643$	2.63468e17	+	1.91421e17i	0.147013	+	0.106811i	−0.511847	+	0.859076i	$0.671039\pi$
$644$	−1.82991e17	−	1.32951e17i	−0.101082	−	0.0734402i
$645$	1.30245e18	−	4.00854e18i	0.712236	−	2.19204i
$646$	1.93801e17	+	5.96457e17i	0.104917	+	0.322900i
$647$	−2.15174e18	+	1.56333e18i	−1.15322	+	0.837863i	−0.988906	−	0.148545i	$-0.952541\pi$
$647$	−2.15174e18	+	1.56333e18i	−1.15322	+	0.837863i	−0.164314	+	0.986408i	$0.552541\pi$
$648$	−7.36526e17			−0.390796
$649$	1.87808e18	−	2.05806e18i	0.986558	−	1.08110i
$650$	−1.34362e17			−0.0698779
$651$	−3.63100e17	+	2.63807e17i	−0.186960	+	0.135835i
$652$	6.04716e16	+	1.86112e17i	0.0308278	+	0.0948781i
$653$	−6.26479e15	+	1.92810e16i	−0.00316206	+	0.00973183i	−0.952625	−	0.304147i	$-0.901629\pi$
$653$	−6.26479e15	+	1.92810e16i	−0.00316206	+	0.00973183i	0.949463	+	0.313879i	$0.101629\pi$
$654$	2.01773e18	+	1.46596e18i	1.00834	+	0.732602i
$655$	−5.04636e17	−	3.66640e17i	−0.249695	−	0.181414i
$656$	−6.91309e16	+	2.12763e17i	−0.0338686	+	0.104237i
$657$	9.16468e14	+	2.82060e15i	0.000444572	+	0.00136825i
$658$	−1.42071e17	+	1.03221e17i	−0.0682397	+	0.0495790i
$659$	−1.81548e18			−0.863450			−0.431725	−	0.902005i	$-0.642095\pi$
$659$	−1.81548e18			−0.863450			−0.431725	+	0.902005i	$0.642095\pi$
$660$	−8.10079e17	−	1.42495e18i	−0.381497	−	0.671066i
$661$	−3.17338e18			−1.47983			−0.739917	−	0.672698i	$-0.765135\pi$
$661$	−3.17338e18			−1.47983			−0.739917	+	0.672698i	$0.765135\pi$
$662$	−2.71660e17	+	1.97372e17i	−0.125443	+	0.0911400i
$663$	−4.50042e16	−	1.38509e17i	−0.0205786	−	0.0633343i
$664$	−2.40385e17	+	7.39828e17i	−0.108847	+	0.334995i
$665$	−4.64135e17	−	3.37214e17i	−0.208115	−	0.151204i
$666$	1.77693e17	+	1.29102e17i	0.0789021	+	0.0573257i
$667$	−4.31966e17	+	1.32946e18i	−0.189947	+	0.584596i
$668$	5.69834e17	+	1.75377e18i	0.248143	+	0.763705i
$669$	3.62779e18	−	2.63574e18i	1.56449	−	1.13667i
$670$	4.68932e18			2.00274
$671$	1.55564e18	+	2.73642e18i	0.657980	+	1.15741i
$672$	1.17872e17			0.0493754
$673$	−2.46932e16	+	1.79407e16i	−0.0102442	+	0.00744287i	−0.592896	−	0.805279i	$-0.702015\pi$
$673$	−2.46932e16	+	1.79407e16i	−0.0102442	+	0.00744287i	0.582651	+	0.812722i	$0.302015\pi$
$674$	−9.01961e17	−	2.77595e18i	−0.370594	−	1.14057i
$675$	−7.98458e17	+	2.45740e18i	−0.324921	+	1.00000i
$676$	9.95955e17	+	7.23603e17i	0.401408	+	0.291640i
$677$	2.34117e18	+	1.70096e18i	0.934559	+	0.678997i	0.947105	−	0.320924i	$-0.103993\pi$
$677$	2.34117e18	+	1.70096e18i	0.934559	+	0.678997i	−0.0125455	+	0.999921i	$0.503993\pi$
$678$	−6.62749e17	+	2.03973e18i	−0.262033	+	0.806455i
$679$	7.95753e16	+	2.44908e17i	0.0311620	+	0.0959066i
$680$	−7.73429e17	+	5.61929e17i	−0.299994	+	0.217958i
$681$	−2.01015e18			−0.772276
$682$	1.03632e18	−	1.13563e18i	0.394363	−	0.432156i
$683$	−4.32833e18			−1.63150			−0.815748	−	0.578408i	$-0.803674\pi$
$683$	−4.32833e18			−1.63150			−0.815748	+	0.578408i	$0.803674\pi$
$684$	−8.65905e16	+	6.29117e16i	−0.0323300	+	0.0234891i
$685$	1.30634e18	+	4.02051e18i	0.483135	+	1.48694i
$686$	−3.03911e17	+	9.35343e17i	−0.111337	+	0.342661i
$687$	3.99729e18	+	2.90420e18i	1.45060	+	1.05392i
$688$	−8.39959e17	−	6.10266e17i	−0.301949	−	0.219379i
$689$	−7.36573e16	+	2.26694e17i	−0.0262295	+	0.0807262i
$690$	9.05303e17	+	2.78624e18i	0.319356	+	0.982877i
$691$	−1.05337e18	+	7.65315e17i	−0.368105	+	0.267444i	−0.756425	−	0.654081i	$-0.773056\pi$
$691$	−1.05337e18	+	7.65315e17i	−0.368105	+	0.267444i	0.388320	+	0.921525i	$0.373056\pi$
$692$	−2.26173e18			−0.782981
$693$	−1.02372e16	+	9.15266e16i	−0.00351088	+	0.0313893i
$694$	−3.63975e16			−0.0123662
$695$	2.24328e18	−	1.62984e18i	0.755060	−	0.548583i
$696$	−2.25106e17	−	6.92805e17i	−0.0750632	−	0.231021i
$697$	−2.94786e17	+	9.07258e17i	−0.0973854	+	0.299721i
$698$	−2.55385e18	−	1.85548e18i	−0.835864	−	0.607291i
$699$	8.16381e17	+	5.93135e17i	0.264723	+	0.192332i
$700$	1.43296e17	−	4.41019e17i	0.0460358	−	0.141684i
$701$	1.43067e18	+	4.40316e18i	0.455379	+	1.40151i	0.870690	+	0.491833i	$0.163673\pi$
$701$	1.43067e18	+	4.40316e18i	0.455379	+	1.40151i	−0.415310	+	0.909680i	$0.636327\pi$
$702$	−1.47939e17	+	1.07484e17i	−0.0466542	+	0.0338963i
$703$	−2.46410e18			−0.769924
$704$	−3.95496e17	+	8.13132e16i	−0.122439	+	0.0251732i
$705$	2.27450e18			0.697681
$706$	9.01832e17	−	6.55220e17i	0.274091	−	0.199139i
$707$	−3.40430e17	−	1.04774e18i	−0.102518	−	0.315519i
$708$	8.01916e17	−	2.46804e18i	0.239283	−	0.736438i
$709$	−7.10759e17	−	5.16396e17i	−0.210146	−	0.152680i	0.477734	−	0.878505i	$-0.341458\pi$
$709$	−7.10759e17	−	5.16396e17i	−0.210146	−	0.152680i	−0.687880	+	0.725825i	$0.741458\pi$
$710$	−4.43465e17	−	3.22196e17i	−0.129921	−	0.0943934i
$711$	1.15963e17	−	3.56896e17i	0.0336640	−	0.103607i
$712$	6.80106e17	+	2.09315e18i	0.195640	+	0.602117i
$713$	−2.22304e18	+	1.61514e18i	−0.633674	+	0.460391i
$714$	5.02626e17			0.141973
$715$	−4.15658e17	−	1.88393e17i	−0.116345	−	0.0527322i
$716$	−7.21063e17			−0.200004
$717$	8.13899e17	−	5.91332e17i	0.223715	−	0.162539i
$718$	−8.93676e17	−	2.75045e18i	−0.243428	−	0.749196i
$719$	1.39045e18	−	4.27936e18i	0.375333	−	1.15516i	−0.567921	−	0.823083i	$-0.692252\pi$
$719$	1.39045e18	−	4.27936e18i	0.375333	−	1.15516i	0.943254	−	0.332073i	$-0.107748\pi$
$720$	−1.31996e17	−	9.59006e16i	−0.0353101	−	0.0256543i
$721$	−1.06953e18	−	7.77057e17i	−0.283539	−	0.206003i
$722$	−4.60630e17	+	1.41767e18i	−0.121021	+	0.372464i
$723$	1.58607e18	+	4.88143e18i	0.412976	+	1.27101i
$724$	−3.95197e17	+	2.87127e17i	−0.101980	+	0.0740924i
$725$	−2.86580e18			−0.732906
$726$	−2.69395e17	−	2.93968e18i	−0.0682812	−	0.745095i
$727$	−2.71558e18			−0.682163			−0.341081	−	0.940034i	$-0.610793\pi$
$727$	−2.71558e18			−0.682163			−0.341081	+	0.940034i	$0.610793\pi$
$728$	2.65499e16	−	1.92896e16i	0.00661012	−	0.00480253i
$729$	1.06875e18	+	3.28926e18i	0.263721	+	0.811651i
$730$	1.56730e16	−	4.82364e16i	0.00383312	−	0.0117971i
$731$	−3.58173e18	−	2.60228e18i	−0.868220	−	0.630799i
$732$	2.37186e18	+	1.72326e18i	0.569858	+	0.414026i
$733$	5.25622e17	−	1.61770e18i	0.125169	−	0.385231i	−0.868763	−	0.495229i	$-0.835084\pi$
$733$	5.25622e17	−	1.61770e18i	0.125169	−	0.385231i	0.993932	+	0.109997i	$0.0350842\pi$
$734$	−2.27782e17	−	7.01041e17i	−0.0537644	−	0.165470i
$735$	4.96667e18	−	3.60849e18i	1.16198	−	0.844225i
$736$	7.21660e17			0.167351
$737$	7.69208e18	+	3.48637e18i	1.76809	+	0.801372i
$738$	−1.62804e17			−0.0370935
$739$	2.49658e18	−	1.81387e18i	0.563842	−	0.409655i	−0.269021	−	0.963134i	$-0.586700\pi$
$739$	2.49658e18	−	1.81387e18i	0.563842	−	0.409655i	0.832863	+	0.553479i	$0.186700\pi$
$740$	−1.16073e18	−	3.57235e18i	−0.259850	−	0.799737i
$741$	−8.61662e16	+	2.65192e17i	−0.0191214	+	0.0588495i
$742$	−6.65526e17	−	4.83533e17i	−0.146400	−	0.106366i
$743$	−2.69140e18	−	1.95542e18i	−0.586882	−	0.426395i	0.254317	−	0.967121i	$-0.418149\pi$
$743$	−2.69140e18	−	1.95542e18i	−0.586882	−	0.426395i	−0.841199	+	0.540726i	$0.818149\pi$
$744$	4.42497e17	−	1.36187e18i	0.0956503	−	0.294381i
$745$	1.01752e17	+	3.13161e17i	0.0218036	+	0.0671045i
$746$	−4.73124e18	+	3.43745e18i	−1.00502	+	0.730186i
$747$	−5.66108e17			−0.119211
$748$	−1.68646e18	+	3.46734e17i	−0.352060	+	0.0723828i
$749$	1.71751e16			0.00355440
$750$	−5.54269e17	+	4.02700e17i	−0.113716	+	0.0826196i
$751$	1.84399e17	+	5.67521e17i	0.0375058	+	0.115431i	0.968057	−	0.250732i	$-0.0806713\pi$
$751$	1.84399e17	+	5.67521e17i	0.0375058	+	0.115431i	−0.930551	+	0.366163i	$0.880671\pi$
$752$	1.73137e17	−	5.32861e17i	0.0349119	−	0.107448i
$753$	−1.90152e18	−	1.38153e18i	−0.380131	−	0.276181i
$754$	−1.64081e17	−	1.19212e17i	−0.0325195	−	0.0236268i
$755$	4.54935e18	−	1.40015e19i	0.893912	−	2.75118i
$756$	−1.95021e17	−	6.00213e17i	−0.0379918	−	0.116927i
$757$	4.85559e18	−	3.52779e18i	0.937819	−	0.681365i	−0.0100758	−	0.999949i	$-0.503207\pi$
$757$	4.85559e18	−	3.52779e18i	0.937819	−	0.681365i	0.947895	+	0.318584i	$0.103207\pi$
$758$	−8.23982e17			−0.157786
$759$	−5.86477e17	+	5.24344e18i	−0.111347	+	0.995508i
$760$	1.83040e18			0.344555
$761$	−5.16957e18	+	3.75591e18i	−0.964837	+	0.700995i	−0.954269	−	0.298949i	$-0.903364\pi$
$761$	−5.16957e18	+	3.75591e18i	−0.964837	+	0.700995i	−0.0105681	+	0.999944i	$0.503364\pi$
$762$	−1.82325e18	−	5.61138e18i	−0.337395	−	1.03839i
$763$	−7.40554e17	+	2.27919e18i	−0.135877	+	0.418188i
$764$	3.35686e17	+	2.43890e17i	0.0610698	+	0.0443698i
$765$	−5.62853e17	−	4.08936e17i	−0.101530	−	0.0737660i
$766$	−8.06229e17	+	2.48132e18i	−0.144202	+	0.443808i
$767$	−2.23267e17	−	6.87144e17i	−0.0395962	−	0.121865i
$768$	−3.04248e17	+	2.21049e17i	−0.0535032	+	0.0388724i
$769$	−2.11762e18			−0.369255			−0.184627	−	0.982809i	$-0.559108\pi$
$769$	−2.11762e18			−0.369255			−0.184627	+	0.982809i	$0.559108\pi$
$770$	1.06166e18	−	1.16340e18i	0.183568	−	0.201159i
$771$	1.04860e19			1.79786
$772$	5.77859e16	−	4.19839e16i	0.00982448	−	0.00713790i
$773$	1.49974e18	+	4.61574e18i	0.252843	+	0.778170i	0.994247	+	0.107111i	$0.0341602\pi$
$773$	1.49974e18	+	4.61574e18i	0.252843	+	0.778170i	−0.741404	+	0.671059i	$0.765840\pi$
$774$	2.33484e17	−	7.18590e17i	0.0390338	−	0.120134i
$775$	−4.55749e18	−	3.31121e18i	−0.755553	−	0.548941i
$776$	−6.64681e17	−	4.82919e17i	−0.109273	−	0.0793914i
$777$	−6.10256e17	+	1.87818e18i	−0.0994891	+	0.306196i
$778$	−1.34531e17	−	4.14042e17i	−0.0217497	−	0.0669387i
$779$	1.47763e18	−	1.07356e18i	0.236904	−	0.172121i
$780$	−4.25054e17			−0.0675818
$781$	−4.87891e17	−	8.58215e17i	−0.0769291	−	0.135321i
$782$	3.07728e18			0.481198
$783$	−3.15537e18	+	2.29251e18i	−0.489327	+	0.355517i
$784$	−4.67316e17	−	1.43825e18i	−0.0718715	−	0.221198i
$785$	−7.43328e17	+	2.28773e18i	−0.113378	+	0.348941i
$786$	−8.46488e17	−	6.15010e17i	−0.128049	−	0.0930327i
$787$	−1.70933e18	−	1.24190e18i	−0.256442	−	0.186316i	0.452135	−	0.891949i	$-0.350663\pi$
$787$	−1.70933e18	−	1.24190e18i	−0.256442	−	0.186316i	−0.708577	+	0.705634i	$0.750663\pi$
$788$	−1.25844e18	+	3.87308e18i	−0.187246	+	0.576284i
$789$	−2.01295e18	−	6.19522e18i	−0.297052	−	0.914232i
$790$	−5.19191e18	+	3.77214e18i	−0.759891	+	0.552093i
$791$	−2.06080e18			−0.299150
$792$	−1.45219e17	−	2.55444e17i	−0.0209078	−	0.0367775i
$793$	8.16256e17			0.116560
$794$	2.05495e17	−	1.49301e17i	0.0291051	−	0.0211461i
$795$	3.29252e18	+	1.01333e19i	0.462533	+	1.42353i
$796$	6.75613e17	−	2.07932e18i	0.0941376	−	0.289726i
$797$	−1.03086e19	−	7.48962e18i	−1.42469	−	1.03510i	−0.990975	−	0.134045i	$-0.957203\pi$
$797$	−1.03086e19	−	7.48962e18i	−1.42469	−	1.03510i	−0.433713	−	0.901051i	$-0.642797\pi$
$798$	−7.78550e17	−	5.65650e17i	−0.106725	−	0.0775406i
$799$	7.38286e17	−	2.27221e18i	0.100385	−	0.308954i
$800$	4.57186e17	+	1.40707e18i	0.0616607	+	0.189772i
$801$	−1.29577e18	+	9.41429e17i	−0.173347	+	0.125944i
$802$	7.59787e18			1.00823
$803$	6.15712e16	−	6.74717e16i	0.00810451	−	0.00888118i
$804$	7.86597e18			1.02704
$805$	−2.27740e18	+	1.65463e18i	−0.294962	+	0.214302i
$806$	−1.23198e17	−	3.79166e17i	−0.0158281	−	0.0487138i
$807$	−3.26921e17	+	1.00616e18i	−0.0416644	+	0.128230i
$808$	2.84357e18	+	2.06597e18i	0.359492	+	0.261186i
$809$	9.74157e18	+	7.07767e18i	1.22170	+	0.887615i	0.996240	−	0.0866378i	$-0.0276123\pi$
$809$	9.74157e18	+	7.07767e18i	1.22170	+	0.887615i	0.225458	+	0.974253i	$0.427612\pi$
$810$	−2.83256e18	+	8.71771e18i	−0.352392	+	1.08455i
$811$	−6.23819e17	−	1.91992e18i	−0.0769880	−	0.236945i	0.905155	−	0.425082i	$-0.139755\pi$
$811$	−6.23819e17	−	1.91992e18i	−0.0769880	−	0.236945i	−0.982143	+	0.188138i	$0.939755\pi$
$812$	5.66281e17	−	4.11427e17i	0.0693295	−	0.0503708i
$813$	−1.32392e19			−1.60795
$814$	7.51946e17	−	6.72283e18i	0.0906000	−	0.810015i
$815$	2.43544e18			0.291107
$816$	−1.29737e18	+	9.42592e17i	−0.153843	+	0.111773i
$817$	2.61940e18	+	8.06168e18i	0.308147	+	0.948379i
$818$	1.09211e18	−	3.36118e18i	0.127459	−	0.392279i
$819$	1.93214e16	+	1.40378e16i	0.00223714	+	0.00162537i
$820$	2.25245e18	+	1.63650e18i	0.258741	+	0.187986i
$821$	8.12892e17	−	2.50182e18i	0.0926408	−	0.285119i	−0.893991	−	0.448085i	$-0.852106\pi$
$821$	8.12892e17	−	2.50182e18i	0.0926408	−	0.285119i	0.986632	+	0.162966i	$0.0521061\pi$
$822$	2.19129e18	+	6.74410e18i	0.247761	+	0.762530i
$823$	−5.75000e18	+	4.17762e18i	−0.645013	+	0.468629i	−0.861569	−	0.507641i	$-0.830518\pi$
$823$	−5.75000e18	+	4.17762e18i	−0.645013	+	0.468629i	0.216556	+	0.976270i	$0.430518\pi$
$824$	4.21788e18			0.469426
$825$	−1.05951e19	+	2.17833e18i	−1.16991	+	0.240532i
$826$	2.49354e18			0.273178
$827$	−3.71897e18	+	2.70199e18i	−0.404237	+	0.293696i	−0.771265	−	0.636515i	$-0.780376\pi$
$827$	−3.71897e18	+	2.70199e18i	−0.404237	+	0.293696i	0.367027	+	0.930210i	$0.380376\pi$
$828$	1.62289e17	+	4.99475e17i	0.0175022	+	0.0538662i
$829$	4.51904e18	−	1.39082e19i	0.483551	−	1.48822i	−0.350518	−	0.936556i	$-0.613995\pi$
$829$	4.51904e18	−	1.39082e19i	0.483551	−	1.48822i	0.834069	−	0.551660i	$-0.186005\pi$
$830$	7.83232e18	+	5.69051e18i	0.831540	+	0.604149i
$831$	−6.21386e18	−	4.51464e18i	−0.654568	−	0.475572i
$832$	−3.23555e16	+	9.95799e16i	−0.00338179	+	0.0104081i
$833$	−1.99272e18	−	6.13295e18i	−0.206658	−	0.636029i
$834$	3.76292e18	−	2.73392e18i	0.387209	−	0.281324i
$835$	2.29496e19			2.34322
$836$	3.00248e18	+	1.36085e18i	0.304186	+	0.137870i
$837$	−7.66684e18			−0.770728
$838$	−1.01813e19	+	7.39717e18i	−1.01559	+	0.737869i
$839$	−2.00282e18	−	6.16405e18i	−0.198239	−	0.610117i	−0.999923	−	0.0123697i	$-0.996063\pi$
$839$	−2.00282e18	−	6.16405e18i	−0.198239	−	0.610117i	0.801684	−	0.597748i	$-0.203937\pi$
$840$	4.53316e17	−	1.39516e18i	0.0445231	−	0.137028i
$841$	4.80136e18	+	3.48839e18i	0.467940	+	0.339978i
$842$	−4.57723e18	−	3.32555e18i	−0.442664	−	0.321614i
$843$	−3.74460e18	+	1.15247e19i	−0.359357	+	1.10599i
$844$	1.46267e18	+	4.50164e18i	0.139290	+	0.428691i
$845$	1.23950e19	−	9.00552e18i	1.17133	−	0.851021i
$846$	4.07739e17			0.0382362
$847$	2.60644e18	−	1.11906e18i	0.242552	−	0.104139i
$848$	2.62463e18			0.242379
$849$	7.03250e18	−	5.10941e18i	0.644480	−	0.468242i
$850$	1.94952e18	+	6.00001e18i	0.177298	+	0.545668i
$851$	−3.73624e18	+	1.14990e19i	−0.337204	+	1.03781i
$852$	−7.43879e17	−	5.40460e17i	−0.0666262	−	0.0484067i
$853$	6.69063e18	+	4.86103e18i	0.594701	+	0.432075i	0.843994	−	0.536353i	$-0.180198\pi$
$853$	6.69063e18	+	4.86103e18i	0.594701	+	0.432075i	−0.249293	+	0.968428i	$0.580198\pi$
$854$	−8.70528e17	+	2.67921e18i	−0.0767904	+	0.236336i
$855$	4.11626e17	+	1.26686e18i	0.0360349	+	0.110904i
$856$	−4.43319e16	+	3.22090e16i	−0.00385156	+	0.00279832i
$857$	−2.70051e18			−0.232847			−0.116423	−	0.993200i	$-0.537143\pi$
$857$	−2.70051e18			−0.232847			−0.116423	+	0.993200i	$0.537143\pi$
$858$	−6.97233e17	−	3.16015e17i	−0.0596638	−	0.0270421i
$859$	1.35147e19			1.14776			0.573880	−	0.818940i	$-0.305438\pi$
$859$	1.35147e19			1.14776			0.573880	+	0.818940i	$0.305438\pi$
$860$	−1.04536e19	+	7.59499e18i	−0.881103	+	0.640159i
$861$	−4.52338e17	−	1.39215e18i	−0.0378392	−	0.116457i
$862$	1.35288e17	−	4.16375e17i	0.0112322	−	0.0345690i
$863$	−4.42309e18	−	3.21356e18i	−0.364465	−	0.264799i	0.390447	−	0.920625i	$-0.372320\pi$
$863$	−4.42309e18	−	3.21356e18i	−0.364465	−	0.264799i	−0.754912	+	0.655826i	$0.772320\pi$
$864$	1.62898e18	+	1.18353e18i	0.133222	+	0.0967917i
$865$	−8.69824e18	+	2.67704e19i	−0.706036	+	2.17296i
$866$	−3.55339e18	−	1.09362e19i	−0.286270	−	0.881049i
$867$	5.17373e18	−	3.75894e18i	0.413695	−	0.300567i
$868$	1.37593e18			0.109199
$869$	−1.13210e19	+	2.32757e18i	−0.891775	+	0.183347i
$870$	−9.06595e18			−0.708823
$871$	1.77176e18	−	1.28726e18i	0.137495	−	0.0998960i
$872$	−2.36274e18	−	7.27178e18i	−0.181995	−	0.560123i
$873$	1.84762e17	−	5.68639e17i	0.0141260	−	0.0434754i
$874$	−4.76660e18	−	3.46314e18i	−0.361730	−	0.262812i
$875$	−5.32586e17	−	3.86947e17i	−0.0401178	−	0.0291473i
$876$	2.62902e16	−	8.09128e16i	0.00196570	−	0.00604979i
$877$	−8.30879e18	−	2.55718e19i	−0.616653	−	1.89786i	−0.371876	−	0.928282i	$-0.621285\pi$
$877$	−8.30879e18	−	2.55718e19i	−0.616653	−	1.89786i	−0.244776	−	0.969580i	$-0.578715\pi$
$878$	−5.37284e18	+	3.90359e18i	−0.395812	+	0.287575i
$879$	1.70066e19			1.24363
$880$	−5.58567e17	+	4.99391e18i	−0.0405451	+	0.362496i
$881$	−9.62312e18			−0.693382			−0.346691	−	0.937979i	$-0.612695\pi$
$881$	−9.62312e18			−0.693382			−0.346691	+	0.937979i	$0.612695\pi$
$882$	8.90350e17	−	6.46877e17i	0.0636817	−	0.0462675i
$883$	−3.98518e18	−	1.22651e19i	−0.282946	−	0.870818i	−0.987007	−	0.160679i	$-0.948632\pi$
$883$	−3.98518e18	−	1.22651e19i	−0.282946	−	0.870818i	0.704061	−	0.710140i	$-0.251368\pi$
$884$	−1.37969e17	+	4.24626e17i	−0.00972395	+	0.0299272i
$885$	−2.61284e19	−	1.89834e19i	−1.82802	−	1.32813i
$886$	−9.09743e18	−	6.60967e18i	−0.631829	−	0.459051i
$887$	4.39051e17	−	1.35126e18i	0.0302699	−	0.0931612i	−0.934780	−	0.355227i	$-0.884404\pi$
$887$	4.39051e17	−	1.35126e18i	0.0302699	−	0.0931612i	0.965050	+	0.262066i	$0.0844037\pi$
$888$	−1.94703e18	−	5.99233e18i	−0.133256	−	0.410121i
$889$	4.58660e18	−	3.33236e18i	0.311623	−	0.226407i
$890$	2.73907e19			1.84743
$891$	−1.11277e19	+	1.21941e19i	−0.745076	+	0.816478i
$892$	−1.37472e19			−0.913781
$893$	−3.70070e18	+	2.68871e18i	−0.244202	+	0.177423i
$894$	1.70681e17	+	5.25303e17i	0.0111813	+	0.0344125i
$895$	−2.77309e18	+	8.53468e18i	−0.180349	+	0.555057i
$896$	−2.92346e17	−	2.12402e17i	−0.0188754	−	0.0137138i
$897$	1.10690e18	+	8.04207e17i	0.0709506	+	0.0515486i
$898$	−1.73138e18	+	5.32865e18i	−0.110179	+	0.339095i
$899$	−2.62769e18	−	8.08720e18i	−0.166011	−	0.510929i
$900$	−8.71049e17	+	6.32854e17i	−0.0546344	+	0.0396942i
$901$	1.11919e19			0.696933
$902$	2.47810e18	+	4.35905e18i	0.153206	+	0.269494i
$903$	6.79347e18			0.416986
$904$	5.31929e18	−	3.86469e18i	0.324160	−	0.235516i
$905$	1.87865e18	+	5.78190e18i	0.113666	+	0.349828i
$906$	7.63119e18	−	2.34864e19i	0.458415	−	1.41086i
$907$	−9.84383e18	−	7.15196e18i	−0.587106	−	0.426558i	0.254173	−	0.967159i	$-0.418197\pi$
$907$	−9.84383e18	−	7.15196e18i	−0.587106	−	0.426558i	−0.841279	+	0.540601i	$0.818197\pi$
$908$	4.98558e18	+	3.62224e18i	0.295228	+	0.214496i
$909$	−7.90428e17	+	2.43269e18i	−0.0464726	+	0.143028i
$910$	−1.26211e17	−	3.88437e17i	−0.00736762	−	0.0226752i
$911$	1.99612e19	−	1.45026e19i	1.15696	−	0.840577i	0.167565	−	0.985861i	$-0.446409\pi$
$911$	1.99612e19	−	1.45026e19i	1.15696	−	0.840577i	0.989390	+	0.145284i	$0.0464094\pi$
$912$	3.07036e18			0.176694
$913$	8.61694e18	+	1.51575e19i	0.492372	+	0.866097i
$914$	8.63518e18			0.489915
$915$	2.95187e19	−	2.14466e19i	1.66288	−	1.20815i
$916$	−4.68080e18	−	1.44060e19i	−0.261818	−	0.805793i
$917$	3.10681e17	−	9.56179e17i	0.0172550	−	0.0531054i
$918$	6.94626e18	+	5.04675e18i	0.383066	+	0.278314i
$919$	−9.27958e18	−	6.74201e18i	−0.508133	−	0.369180i	0.303982	−	0.952678i	$-0.401684\pi$
$919$	−9.27958e18	−	6.74201e18i	−0.508133	−	0.369180i	−0.812115	+	0.583497i	$0.801684\pi$
$920$	2.77539e18	−	8.54176e18i	0.150905	−	0.464437i
$921$	3.70043e18	+	1.13888e19i	0.199786	+	0.614878i
$922$	5.22968e18	−	3.79959e18i	0.280365	−	0.203697i
$923$	−2.56000e17			−0.0136279
$924$	1.78085e18	−	1.95152e18i	0.0941370	−	0.103158i
$925$	−2.47873e19			−1.30109
$926$	3.07807e18	−	2.23635e18i	0.160438	−	0.116565i
$927$	9.48529e17	+	2.91927e18i	0.0490945	+	0.151097i
$928$	−6.90107e17	+	2.12393e18i	−0.0354695	+	0.109164i
$929$	2.86211e19	+	2.07944e19i	1.46078	+	1.06132i	0.983160	+	0.182748i	$0.0584991\pi$
$929$	2.86211e19	+	2.07944e19i	1.46078	+	1.06132i	0.477616	+	0.878568i	$0.341501\pi$
$930$	−1.44176e19	−	1.04750e19i	−0.730726	−	0.530904i
$931$	−3.81531e18	+	1.17423e19i	−0.192024	+	0.590990i
$932$	−9.55975e17	−	2.94219e18i	−0.0477797	−	0.147051i
$933$	1.97961e18	−	1.43827e18i	0.0982538	−	0.0713855i
$934$	−4.01486e18			−0.197886
$935$	−2.38183e18	+	2.12949e19i	−0.116583	+	1.04232i
$936$	−7.61974e16			−0.00370379
$937$	−8.78080e18	+	6.37962e18i	−0.423864	+	0.307955i	−0.779191	−	0.626787i	$-0.784370\pi$
$937$	−8.78080e18	+	6.37962e18i	−0.423864	+	0.307955i	0.355327	+	0.934742i	$0.384370\pi$
$938$	2.33563e18	+	7.18833e18i	0.111966	+	0.344595i
$939$	8.09482e18	−	2.49133e19i	0.385372	−	1.18605i
$940$	−5.64122e18	−	4.09859e18i	−0.266712	−	0.193777i
$941$	7.93386e18	+	5.76429e18i	0.372522	+	0.270653i	0.758256	−	0.651957i	$-0.226052\pi$
$941$	7.93386e18	+	5.76429e18i	0.372522	+	0.270653i	−0.385734	+	0.922610i	$0.626052\pi$
$942$	−1.24687e18	+	3.83749e18i	−0.0581423	+	0.178944i
$943$	−2.76940e18	−	8.52333e18i	−0.128251	−	0.394715i
$944$	−6.43625e18	+	4.67621e18i	−0.296016	+	0.215068i
$945$	−7.85429e18			−0.358757
$946$	−2.27941e19	+	4.68643e18i	−1.03402	+	0.212593i
$947$	2.78472e19			1.25461			0.627303	−	0.778776i	$-0.284159\pi$
$947$	2.78472e19			1.25461			0.627303	+	0.778776i	$0.284159\pi$
$948$	−8.70903e18	+	6.32748e18i	−0.389687	+	0.283124i
$949$	−7.31962e15	−	2.25275e16i	−0.000325280	−	0.00100111i
$950$	3.73260e18	−	1.14878e19i	0.164743	−	0.507028i
$951$	−1.13916e19	−	8.27649e18i	−0.499358	−	0.362805i
$952$	−1.24661e18	−	9.05719e17i	−0.0542740	−	0.0394324i
$953$	−1.18145e19	+	3.63614e19i	−0.510872	+	1.57230i	0.279796	+	0.960059i	$0.409733\pi$
$953$	−1.18145e19	+	3.63614e19i	−0.510872	+	1.57230i	−0.790669	+	0.612244i	$0.790267\pi$
$954$	5.90234e17	+	1.81655e18i	0.0253489	+	0.0780160i
$955$	4.17774e18	−	3.03531e18i	0.178205	−	0.129473i
$956$	−3.08420e18			−0.130667
$957$	−1.48712e19	−	6.74025e18i	−0.625777	−	0.283628i
$958$	−2.28870e19			−0.956563
$959$	−5.51245e18	+	4.00503e18i	−0.228836	+	0.166259i
$960$	1.44631e18	+	4.45128e18i	0.0596346	+	0.183536i
$961$	−2.38012e18	+	7.32524e18i	−0.0974756	+	0.299999i
$962$	−1.41920e18	−	1.03111e18i	−0.0577304	−	0.0419436i
$963$	−3.22619e16	−	2.34397e16i	−0.00130353	−	0.000947067i
$964$	4.86242e18	−	1.49650e19i	0.195142	−	0.600587i
$965$	−2.74698e17	−	8.45432e17i	−0.0109503	−	0.0337017i
$966$	−3.82016e18	+	2.77551e18i	−0.151262	+	0.109898i
$967$	−2.25992e19			−0.888834			−0.444417	−	0.895820i	$-0.646589\pi$
$967$	−2.25992e19			−0.888834			−0.444417	+	0.895820i	$0.646589\pi$
$968$	−4.62906e18	+	7.77643e18i	−0.180844	+	0.303802i
$969$	1.30925e19			0.508065
$970$	−8.27221e18	+	6.01011e18i	−0.318864	+	0.231668i
$971$	4.92614e18	+	1.51611e19i	0.188618	+	0.580505i	0.999992	−	0.00402168i	$-0.00128015\pi$
$971$	4.92614e18	+	1.51611e19i	0.188618	+	0.580505i	−0.811374	+	0.584527i	$0.801280\pi$
$972$	−9.67165e17	+	2.97663e18i	−0.0367849	+	0.113212i
$973$	3.61572e18	+	2.62697e18i	0.136603	+	0.0992481i
$974$	1.65320e19	+	1.20112e19i	0.620430	+	0.450769i
$975$	−8.66781e17	+	2.66768e18i	−0.0323132	+	0.0994497i
$976$	−2.77743e18	−	8.54805e18i	−0.102853	−	0.316550i
$977$	−3.08264e19	+	2.23967e19i	−1.13399	+	0.823890i	−0.986270	−	0.165140i	$-0.947192\pi$
$977$	−3.08264e19	+	2.23967e19i	−1.13399	+	0.823890i	−0.147717	+	0.989030i	$0.547192\pi$
$978$	4.08526e18			0.149285
$979$	4.49300e19	+	2.03641e19i	1.63098	+	0.739228i
$980$	−1.88207e19			−0.678683
$981$	4.50159e18	−	3.27060e18i	0.161257	−	0.117160i
$982$	8.51100e18	+	2.61942e19i	0.302870	+	0.932137i
$983$	−7.98722e18	+	2.45821e19i	−0.282357	+	0.869004i	0.704822	+	0.709384i	$0.251027\pi$
$983$	−7.98722e18	+	2.45821e19i	−0.282357	+	0.869004i	−0.987179	+	0.159620i	$0.948973\pi$
$984$	3.77831e18	+	2.74511e18i	0.132687	+	0.0964031i
$985$	4.10031e19	+	2.97905e19i	1.43048	+	1.03930i
$986$	−2.94274e18	+	9.05681e18i	−0.101989	+	0.313888i
$987$	1.13287e18	+	3.48662e18i	0.0390049	+	0.120045i
$988$	6.91579e17	−	5.02461e17i	0.0236549	−	0.0171863i
$989$	4.15924e19			1.41331
$990$	−3.58199e18	+	7.36451e17i	−0.120919	+	0.0248608i
$991$	3.66135e19			1.22790			0.613950	−	0.789345i	$-0.289580\pi$
$991$	3.66135e19			1.22790			0.613950	+	0.789345i	$0.289580\pi$
$992$	−3.55153e18	+	2.58033e18i	−0.118328	+	0.0859706i
$993$	2.16621e18	+	6.66691e18i	0.0717018	+	0.220676i
$994$	2.73021e17	−	8.40273e17i	0.00897811	−	0.0276318i
$995$	−2.20131e19	−	1.59935e19i	−0.719170	−	0.522508i
$996$	1.31381e19	+	9.54540e18i	0.426430	+	0.309819i
$997$	3.47818e18	−	1.07047e19i	0.112159	−	0.345189i	−0.879185	−	0.476481i	$-0.841912\pi$
$997$	3.47818e18	−	1.07047e19i	0.112159	−	0.345189i	0.991344	+	0.131291i	$0.0419123\pi$
$998$	6.27231e18	+	1.93042e19i	0.200946	+	0.618447i
$999$	−2.72920e19	+	1.98288e19i	−0.868680	+	0.631133i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.14.c.b.3.6	✓	28
11.4	even	5	inner	22.14.c.b.15.6	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.14.c.b.3.6	✓	28	1.1	even	1	trivial
22.14.c.b.15.6	yes	28	11.4	even	5	inner

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+(-51.7771 + 37.6183i) q^{2} +(412.870 + 1270.68i) q^{3} +(1265.73 - 3895.53i) q^{4} +(-41240.7 - 29963.1i) q^{5} +(-69178.0 - 50260.8i) q^{6} +(25390.0 - 78142.3i) q^{7} +(81007.0 + 249314. i) q^{8} +(-154338. + 112133. i) q^{9} +3.26248e6 q^{10} +(5.35158e6 + 2.42556e6i) q^{11} +5.47256e6 q^{12} +(1.23266e6 - 895580. i) q^{13} +(1.62496e6 + 5.00111e6i) q^{14} +(2.10466e7 - 6.47747e7i) q^{15} +(-1.35731e7 - 9.86140e6i) q^{16} +(-5.78778e7 - 4.20507e7i) q^{17} +(3.77291e6 - 1.16118e7i) q^{18} +(4.23273e7 + 1.30270e8i) q^{19} +(-1.68922e8 + 1.22729e8i) q^{20} +1.09777e8 q^{21} +(-3.68334e8 + 7.57288e7i) q^{22} +6.72099e8 q^{23} +(-2.83353e8 + 2.05868e8i) q^{24} +(4.25788e8 + 1.31044e9i) q^{25} +(-3.01334e7 + 9.27410e7i) q^{26} +(1.51711e9 + 1.10224e9i) q^{27} +(-2.72269e8 - 1.97815e8i) q^{28} +(-6.42713e8 + 1.97807e9i) q^{29} +(1.34698e9 + 4.14558e9i) q^{30} +(-3.30762e9 + 2.40312e9i) q^{31} +1.07374e9 q^{32} +(-8.72606e8 + 7.80159e9i) q^{33} +4.57862e9 q^{34} +(-3.38849e9 + 2.46188e9i) q^{35} +(2.41466e8 + 7.43157e8i) q^{36} +(-5.55906e9 + 1.71090e10i) q^{37} +(-7.09212e9 - 5.15273e9i) q^{38} +(1.64693e9 + 1.19656e9i) q^{39} +(4.12943e9 - 1.27091e10i) q^{40} +(-4.12052e9 - 1.26817e10i) q^{41} +(-5.68392e9 + 4.12961e9i) q^{42} +6.18843e10 q^{43} +(1.62225e10 - 1.77771e10i) q^{44} +9.72484e9 q^{45} +(-3.47993e10 + 2.52832e10i) q^{46} +(1.03198e10 + 3.17610e10i) q^{47} +(6.92680e9 - 2.13185e10i) q^{48} +(7.29233e10 + 5.29819e10i) q^{49} +(-7.13425e10 - 5.18334e10i) q^{50} +(2.95371e10 - 9.09058e10i) q^{51} +(-1.92854e9 - 5.93543e9i) q^{52} +(-1.26563e11 + 9.19531e10i) q^{53} -1.20016e11 q^{54} +(-1.48026e11 - 2.60381e11i) q^{55} +2.15387e10 q^{56} +(-1.48056e11 + 1.07569e11i) q^{57} +(-4.11336e10 - 1.26596e11i) q^{58} +(1.46534e11 - 4.50985e11i) q^{59} +(-2.25692e11 - 1.63975e11i) q^{60} +(4.33409e11 + 3.14890e11i) q^{61} +(8.08574e10 - 2.48854e11i) q^{62} +(4.84369e9 + 1.49074e10i) q^{63} +(-5.55952e10 + 4.03923e10i) q^{64} -7.76701e10 q^{65} +(-2.48301e11 - 4.36770e11i) q^{66} +1.43735e12 q^{67} +(-2.37068e11 + 1.72240e11i) q^{68} +(2.77489e11 + 8.54024e11i) q^{69} +(8.28344e10 - 2.54938e11i) q^{70} +(-1.35929e11 - 9.87581e10i) q^{71} +(-4.04587e10 - 2.93950e10i) q^{72} +(4.80400e9 - 1.47852e10i) q^{73} +(-3.55780e11 - 1.09498e12i) q^{74} +(-1.48936e12 + 1.08208e12i) q^{75} +5.61046e11 q^{76} +(3.25415e11 - 3.56600e11i) q^{77} -1.30286e11 q^{78} +(-1.59140e12 + 1.15622e12i) q^{79} +(2.64284e11 + 8.13382e11i) q^{80} +(-8.68222e11 + 2.67211e12i) q^{81} +(6.90411e11 + 5.01613e11i) q^{82} +(2.40072e12 + 1.74423e12i) q^{83} +(1.38948e11 - 4.27639e11i) q^{84} +(1.12695e12 + 3.46840e12i) q^{85} +(-3.20419e12 + 2.32798e12i) q^{86} -2.77885e12 q^{87} +(-1.71209e11 + 1.53071e12i) q^{88} +8.39565e12 q^{89} +(-5.03524e11 + 3.65832e11i) q^{90} +(-3.86855e10 - 1.19062e11i) q^{91} +(8.50698e11 - 2.61818e12i) q^{92} +(-4.41922e12 - 3.21075e12i) q^{93} +(-1.72912e12 - 1.25628e12i) q^{94} +(2.15769e12 - 6.64069e12i) q^{95} +(4.43315e11 + 1.36438e12i) q^{96} +(-2.53556e12 + 1.84219e12i) q^{97} -5.76884e12 q^{98} +(-1.09793e12 + 2.25733e11i) 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

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