LMFDB - Embedded newform 22.14.c.b.9.3

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			9.3
Character	$\chi$	$=$	22.9
Dual form			22.14.c.b.5.3

$q$-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} +(-501.424 + 364.306i) q^{3} +(-3313.73 - 2407.57i) q^{4} +(17458.1 + 53730.4i) q^{5} +(12257.7 + 37725.4i) q^{6} +(-385628. - 280175. i) q^{7} +(-212079. + 154084. i) q^{8} +(-373966. + 1.15095e6i) q^{9} +3.61571e6 q^{10} +(5.87360e6 + 153242. i) q^{11} +2.53868e6 q^{12} +(6.48230e6 - 1.99505e7i) q^{13} +(-2.46802e7 + 1.79312e7i) q^{14} +(-2.83282e7 - 2.05816e7i) q^{15} +(5.18444e6 + 1.59561e7i) q^{16} +(-3.88058e7 - 1.19432e8i) q^{17} +(6.26595e7 + 4.55248e7i) q^{18} +(9.84864e7 - 7.15545e7i) q^{19} +(7.15083e7 - 2.20080e8i) q^{20} +2.95432e8 q^{21} +(1.25490e8 - 3.54482e8i) q^{22} -5.82343e8 q^{23} +(5.02076e7 - 1.54523e8i) q^{24} +(-1.59461e9 + 1.15855e9i) q^{25} +(-1.08614e9 - 7.89124e8i) q^{26} +(-5.37137e8 - 1.65314e9i) q^{27} +(6.03327e8 + 1.85685e9i) q^{28} +(-2.19265e9 - 1.59305e9i) q^{29} +(-1.81301e9 + 1.31723e9i) q^{30} +(1.11280e9 - 3.42483e9i) q^{31} +1.07374e9 q^{32} +(-3.00099e9 + 2.06295e9i) q^{33} -8.03700e9 q^{34} +(8.32161e9 - 2.56113e10i) q^{35} +(4.01021e9 - 2.91359e9i) q^{36} +(-8.13105e9 - 5.90756e9i) q^{37} +(-2.40758e9 - 7.40977e9i) q^{38} +(4.01769e9 + 1.23652e10i) q^{39} +(-1.19815e10 - 8.70508e9i) q^{40} +(-1.26905e10 + 9.22015e9i) q^{41} +(5.84279e9 - 1.79823e10i) q^{42} +2.91315e10 q^{43} +(-1.90946e10 - 1.46489e10i) q^{44} -6.83697e10 q^{45} +(-1.15170e10 + 3.54458e10i) q^{46} +(1.17541e11 - 8.53986e10i) q^{47} +(-8.41250e9 - 6.11204e9i) q^{48} +(4.02704e10 + 1.23940e11i) q^{49} +(3.89815e10 + 1.19973e11i) q^{50} +(6.29679e10 + 4.57488e10i) q^{51} +(-6.95127e10 + 5.05039e10i) q^{52} +(5.45008e10 - 1.67736e11i) q^{53} -1.11246e11 q^{54} +(9.43081e10 + 3.18267e11i) q^{55} +1.24954e11 q^{56} +(-2.33157e10 + 7.17583e10i) q^{57} +(-1.40330e11 + 1.01955e11i) q^{58} +(-4.46985e11 - 3.24754e11i) q^{59} +(4.43204e10 + 1.36404e11i) q^{60} +(1.87571e11 + 5.77285e11i) q^{61} +(-1.86453e11 - 1.35466e11i) q^{62} +(4.66678e11 - 3.39062e11i) q^{63} +(2.12355e10 - 6.53561e10i) q^{64} +1.18512e12 q^{65} +(6.62159e10 + 2.23462e11i) q^{66} +4.94624e11 q^{67} +(-1.58948e11 + 4.89193e11i) q^{68} +(2.92001e11 - 2.12151e11i) q^{69} +(-1.39432e12 - 1.01303e12i) q^{70} +(2.72872e11 + 8.39813e11i) q^{71} +(-9.80329e10 - 3.01714e11i) q^{72} +(-7.40121e11 - 5.37729e11i) q^{73} +(-5.20387e11 + 3.78084e11i) q^{74} +(3.77507e11 - 1.16185e12i) q^{75} -4.98630e11 q^{76} +(-2.22209e12 - 1.70473e12i) q^{77} +8.32097e11 q^{78} +(-1.44237e11 + 4.43915e11i) q^{79} +(-7.66817e11 + 5.57125e11i) q^{80} +(-6.89348e11 - 5.00841e11i) q^{81} +(3.10229e11 + 9.54785e11i) q^{82} +(-3.93195e11 - 1.21013e12i) q^{83} +(-9.78984e11 - 7.11274e11i) q^{84} +(5.73965e12 - 4.17010e12i) q^{85} +(5.76136e11 - 1.77317e12i) q^{86} +1.67980e12 q^{87} +(-1.26928e12 + 8.72531e11i) q^{88} -7.38624e12 q^{89} +(-1.35215e12 + 4.16150e12i) q^{90} +(-8.08937e12 + 5.87727e12i) q^{91} +(1.92973e12 + 1.40203e12i) q^{92} +(6.89704e11 + 2.12269e12i) q^{93} +(-2.87339e12 - 8.84338e12i) q^{94} +(5.56404e12 + 4.04251e12i) q^{95} +(-5.38400e11 + 3.91170e11i) q^{96} +(1.49344e12 - 4.59634e12i) q^{97} +8.34034e12 q^{98} +(-2.37290e12 + 6.70291e12i) 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
$3$	−501.424	+	364.306i	−0.397115	+	0.288521i	−0.768365	−	0.640012i	$-0.778929\pi$
$3$	−501.424	+	364.306i	−0.397115	+	0.288521i	0.371250	+	0.928533i	$0.378929\pi$
$4$	−3313.73	−	2407.57i	−0.404508	−	0.293893i
$5$	17458.1	+	53730.4i	0.499679	+	1.53785i	0.809535	+	0.587071i	$0.199719\pi$
$5$	17458.1	+	53730.4i	0.499679	+	1.53785i	−0.309856	+	0.950784i	$0.600281\pi$
$6$	12257.7	+	37725.4i	0.107257	+	0.330104i
$7$	−385628.	−	280175.i	−1.23889	−	0.900103i	−0.241362	−	0.970435i	$-0.577594\pi$
$7$	−385628.	−	280175.i	−1.23889	−	0.900103i	−0.997524	+	0.0703325i	$0.977594\pi$
$8$	−212079.	+	154084.i	−0.286031	+	0.207813i
$9$	−373966.	+	1.15095e6i	−0.234561	+	0.721904i
$10$	3.61571e6			1.14339
$11$	5.87360e6	+	153242.i	0.999660	+	0.0260811i
$11$	5.87360e6	+	153242.i	0.999660	+	0.0260811i
$12$	2.53868e6			0.245431
$13$	6.48230e6	−	1.99505e7i	0.372475	−	1.14636i	−0.572692	−	0.819771i	$-0.694101\pi$
$13$	6.48230e6	−	1.99505e7i	0.372475	−	1.14636i	0.945166	−	0.326589i	$-0.105899\pi$
$14$	−2.46802e7	+	1.79312e7i	−0.876024	+	0.636469i
$15$	−2.83282e7	−	2.05816e7i	−0.642134	−	0.466538i
$16$	5.18444e6	+	1.59561e7i	0.0772542	+	0.237764i
$17$	−3.88058e7	−	1.19432e8i	−0.389922	−	1.20006i	−0.932846	−	0.360276i	$-0.882683\pi$
$17$	−3.88058e7	−	1.19432e8i	−0.389922	−	1.20006i	0.542923	−	0.839782i	$-0.317317\pi$
$18$	6.26595e7	+	4.55248e7i	0.434226	+	0.315484i
$19$	9.84864e7	−	7.15545e7i	0.480261	−	0.348930i	−0.321165	−	0.947023i	$-0.604075\pi$
$19$	9.84864e7	−	7.15545e7i	0.480261	−	0.348930i	0.801427	+	0.598093i	$0.204075\pi$
$20$	7.15083e7	−	2.20080e8i	0.249840	−	0.768927i
$21$	2.95432e8			0.751679
$22$	1.25490e8	−	3.54482e8i	0.235973	−	0.666571i
$23$	−5.82343e8			−0.820253			−0.410126	−	0.912029i	$-0.634515\pi$
$23$	−5.82343e8			−0.820253			−0.410126	+	0.912029i	$0.634515\pi$
$24$	5.02076e7	−	1.54523e8i	0.0536286	−	0.165052i
$25$	−1.59461e9	+	1.15855e9i	−1.30630	+	0.949083i
$26$	−1.08614e9	−	7.89124e8i	−0.689537	−	0.500978i
$27$	−5.37137e8	−	1.65314e9i	−0.266822	−	0.821192i
$28$	6.03327e8	+	1.85685e9i	0.236606	+	0.728198i
$29$	−2.19265e9	−	1.59305e9i	−0.684514	−	0.497328i	0.190338	−	0.981719i	$-0.439041\pi$
$29$	−2.19265e9	−	1.59305e9i	−0.684514	−	0.497328i	−0.874852	+	0.484390i	$0.839041\pi$
$30$	−1.81301e9	+	1.31723e9i	−0.454058	+	0.329892i
$31$	1.11280e9	−	3.42483e9i	0.225198	−	0.693088i	−0.773074	−	0.634316i	$-0.781282\pi$
$31$	1.11280e9	−	3.42483e9i	0.225198	−	0.693088i	0.998271	−	0.0587714i	$-0.0187183\pi$
$32$	1.07374e9			0.176777
$33$	−3.00099e9	+	2.06295e9i	−0.404505	+	0.278066i
$34$	−8.03700e9			−0.892238
$35$	8.32161e9	−	2.56113e10i	0.765182	−	2.35499i
$36$	4.01021e9	−	2.91359e9i	0.307044	−	0.223081i
$37$	−8.13105e9	−	5.90756e9i	−0.520997	−	0.378527i	0.295982	−	0.955193i	$-0.404353\pi$
$37$	−8.13105e9	−	5.90756e9i	−0.520997	−	0.378527i	−0.816979	+	0.576667i	$0.804353\pi$
$38$	−2.40758e9	−	7.40977e9i	−0.129714	−	0.399219i
$39$	4.01769e9	+	1.23652e10i	0.182834	+	0.562704i
$40$	−1.19815e10	−	8.70508e9i	−0.462511	−	0.336034i
$41$	−1.26905e10	+	9.22015e9i	−0.417236	+	0.303140i	−0.776525	−	0.630087i	$-0.783019\pi$
$41$	−1.26905e10	+	9.22015e9i	−0.417236	+	0.303140i	0.359289	+	0.933226i	$0.383019\pi$
$42$	5.84279e9	−	1.79823e10i	0.164248	−	0.505503i
$43$	2.91315e10			0.702778			0.351389	−	0.936230i	$-0.385709\pi$
$43$	2.91315e10			0.702778			0.351389	+	0.936230i	$0.385709\pi$
$44$	−1.90946e10	−	1.46489e10i	−0.396706	−	0.304343i
$45$	−6.83697e10			−1.22739
$46$	−1.15170e10	+	3.54458e10i	−0.179232	+	0.551619i
$47$	1.17541e11	−	8.53986e10i	1.59057	−	1.15562i	0.687456	−	0.726226i	$-0.258728\pi$
$47$	1.17541e11	−	8.53986e10i	1.59057	−	1.15562i	0.903118	−	0.429393i	$-0.141272\pi$
$48$	−8.41250e9	−	6.11204e9i	−0.0992789	−	0.0721303i
$49$	4.02704e10	+	1.23940e11i	0.415634	+	1.27919i
$50$	3.89815e10	+	1.19973e11i	0.352820	+	1.08587i
$51$	6.29679e10	+	4.57488e10i	0.501087	+	0.364061i
$52$	−6.95127e10	+	5.05039e10i	−0.487576	+	0.354245i
$53$	5.45008e10	−	1.67736e11i	0.337761	−	1.03952i	−0.627584	−	0.778548i	$-0.715956\pi$
$53$	5.45008e10	−	1.67736e11i	0.337761	−	1.03952i	0.965346	−	0.260974i	$-0.0840437\pi$
$54$	−1.11246e11			−0.610553
$55$	9.43081e10	+	3.18267e11i	0.459400	+	1.55036i
$56$	1.24954e11			0.541413
$57$	−2.33157e10	+	7.17583e10i	−0.0900454	+	0.277131i
$58$	−1.40330e11	+	1.01955e11i	−0.484024	+	0.351664i
$59$	−4.46985e11	−	3.24754e11i	−1.37961	−	1.00234i	−0.996917	−	0.0784661i	$-0.974998\pi$
$59$	−4.46985e11	−	3.24754e11i	−1.37961	−	1.00234i	−0.382690	−	0.923877i	$-0.625002\pi$
$60$	4.43204e10	+	1.36404e11i	0.122637	+	0.377437i
$61$	1.87571e11	+	5.77285e11i	0.466146	+	1.43465i	0.857535	+	0.514426i	$0.171995\pi$
$61$	1.87571e11	+	5.77285e11i	0.466146	+	1.43465i	−0.391389	+	0.920226i	$0.628005\pi$
$62$	−1.86453e11	−	1.35466e11i	−0.416893	−	0.302890i
$63$	4.66678e11	−	3.39062e11i	0.940382	−	0.683227i
$64$	2.12355e10	−	6.53561e10i	0.0386271	−	0.118882i
$65$	1.18512e12			1.94905
$66$	6.62159e10	+	2.23462e11i	0.0986113	+	0.332789i
$67$	4.94624e11			0.668019			0.334009	−	0.942570i	$-0.391598\pi$
$67$	4.94624e11			0.668019			0.334009	+	0.942570i	$0.391598\pi$
$68$	−1.58948e11	+	4.89193e11i	−0.194961	+	0.600029i
$69$	2.92001e11	−	2.12151e11i	0.325735	−	0.236660i
$70$	−1.39432e12	−	1.01303e12i	−1.41653	−	1.02917i
$71$	2.72872e11	+	8.39813e11i	0.252801	+	0.778042i	0.994255	+	0.107038i	$0.0341367\pi$
$71$	2.72872e11	+	8.39813e11i	0.252801	+	0.778042i	−0.741454	+	0.671004i	$0.765863\pi$
$72$	−9.80329e10	−	3.01714e11i	−0.0829298	−	0.255232i
$73$	−7.40121e11	−	5.37729e11i	−0.572406	−	0.415877i	0.263573	−	0.964640i	$-0.415099\pi$
$73$	−7.40121e11	−	5.37729e11i	−0.572406	−	0.415877i	−0.835978	+	0.548762i	$0.815099\pi$
$74$	−5.20387e11	+	3.78084e11i	−0.368401	+	0.267659i
$75$	3.77507e11	−	1.16185e12i	0.244922	−	0.753792i
$76$	−4.98630e11			−0.296818
$77$	−2.22209e12	−	1.70473e12i	−1.21499	−	0.932108i
$78$	8.32097e11			0.418368
$79$	−1.44237e11	+	4.43915e11i	−0.0667575	+	0.205458i	−0.978871	−	0.204480i	$-0.934450\pi$
$79$	−1.44237e11	+	4.43915e11i	−0.0667575	+	0.205458i	0.912113	+	0.409938i	$0.134450\pi$
$80$	−7.66817e11	+	5.57125e11i	−0.327044	+	0.237612i
$81$	−6.89348e11	−	5.00841e11i	−0.271198	−	0.197037i
$82$	3.10229e11	+	9.54785e11i	0.112692	+	0.346829i
$83$	−3.93195e11	−	1.21013e12i	−0.132008	−	0.406279i	0.863105	−	0.505025i	$-0.168517\pi$
$83$	−3.93195e11	−	1.21013e12i	−0.132008	−	0.406279i	−0.995113	+	0.0987460i	$0.968517\pi$
$84$	−9.78984e11	−	7.11274e11i	−0.304061	−	0.220913i
$85$	5.73965e12	−	4.17010e12i	1.65068	−	1.19929i
$86$	5.76136e11	−	1.77317e12i	0.153563	−	0.472617i
$87$	1.67980e12			0.415321
$88$	−1.26928e12	+	8.72531e11i	−0.291353	+	0.200283i
$89$	−7.38624e12			−1.57539			−0.787695	−	0.616065i	$-0.788726\pi$
$89$	−7.38624e12			−1.57539			−0.787695	+	0.616065i	$0.788726\pi$
$90$	−1.35215e12	+	4.16150e12i	−0.268194	+	0.825417i
$91$	−8.08937e12	+	5.87727e12i	−1.49330	+	1.08494i
$92$	1.92973e12	+	1.40203e12i	0.331799	+	0.241066i
$93$	6.89704e11	+	2.12269e12i	0.110541	+	0.340210i
$94$	−2.87339e12	−	8.84338e12i	−0.429599	−	1.32217i
$95$	5.56404e12	+	4.04251e12i	0.776581	+	0.564219i
$96$	−5.38400e11	+	3.91170e11i	−0.0702008	+	0.0510038i
$97$	1.49344e12	−	4.59634e12i	0.182042	−	0.560268i	−0.817843	−	0.575442i	$-0.804830\pi$
$97$	1.49344e12	−	4.59634e12i	0.182042	−	0.560268i	0.999885	+	0.0151736i	$0.00483008\pi$
$98$	8.34034e12			0.951074
$99$	−2.37290e12	+	6.70291e12i	−0.253309	+	0.715541i
$100$	8.07339e12			0.807339
$101$	3.65812e12	−	1.12585e13i	0.342901	−	1.05534i	−0.619797	−	0.784762i	$-0.712785\pi$
$101$	3.65812e12	−	1.12585e13i	0.342901	−	1.05534i	0.962698	−	0.270579i	$-0.0872150\pi$
$102$	4.02994e12	−	2.92792e12i	0.354322	−	0.257430i
$103$	4.30461e12	+	3.12748e12i	0.355216	+	0.258079i	0.751054	−	0.660241i	$-0.229546\pi$
$103$	4.30461e12	+	3.12748e12i	0.355216	+	0.258079i	−0.395838	+	0.918320i	$0.629546\pi$
$104$	1.69929e12	+	5.22989e12i	0.131690	+	0.405299i
$105$	5.15768e12	+	1.58737e13i	0.375599	+	1.15597i
$106$	−9.13184e12	−	6.63467e12i	−0.625274	−	0.454288i
$107$	6.27081e12	−	4.55601e12i	0.403951	−	0.293488i	−0.367197	−	0.930143i	$-0.619683\pi$
$107$	6.27081e12	−	4.55601e12i	0.403951	−	0.293488i	0.771149	+	0.636655i	$0.219683\pi$
$108$	−2.20011e12	+	6.77126e12i	−0.133411	+	0.410596i
$109$	−1.23082e13			−0.702946			−0.351473	−	0.936198i	$-0.614319\pi$
$109$	−1.23082e13			−0.702946			−0.351473	+	0.936198i	$0.614319\pi$
$110$	2.12373e13	+	5.54081e11i	1.14300	+	0.0298209i
$111$	6.22926e12			0.316109
$112$	2.47123e12	−	7.60566e12i	0.118303	−	0.364099i
$113$	−2.91515e13	+	2.11798e13i	−1.31720	+	0.956999i	−0.317233	+	0.948348i	$0.602754\pi$
$113$	−2.91515e13	+	2.11798e13i	−1.31720	+	0.956999i	−0.999963	+	0.00865116i	$0.997246\pi$
$114$	3.90664e12	+	2.83834e12i	0.166695	+	0.121111i
$115$	−1.01666e13	−	3.12895e13i	−0.409863	−	1.26143i
$116$	3.43047e12	+	1.05579e13i	0.130730	+	0.402347i
$117$	2.05378e13	+	1.49216e13i	0.740194	+	0.537782i
$118$	−2.86071e13	+	2.07843e13i	−0.975529	+	0.708764i
$119$	−1.84972e13	+	5.69287e13i	−0.597106	+	1.83770i
$120$	9.17913e12			0.280623
$121$	3.44757e13	+	1.80017e12i	0.998640	+	0.0521445i
$122$	3.88476e13			1.06666
$123$	3.00434e12	−	9.24641e12i	0.0782287	−	0.240763i
$124$	−1.19330e13	+	8.66985e12i	−0.294788	+	0.214176i
$125$	−3.42949e13	−	2.49167e13i	−0.804107	−	0.584218i
$126$	−1.14083e13	−	3.51113e13i	−0.253988	−	0.781696i
$127$	−2.02053e12	−	6.21854e12i	−0.0427307	−	0.131512i	0.927415	−	0.374033i	$-0.122025\pi$
$127$	−2.02053e12	−	6.21854e12i	−0.0427307	−	0.131512i	−0.970146	+	0.242522i	$0.922025\pi$
$128$	−3.55809e12	−	2.58511e12i	−0.0715077	−	0.0519534i
$129$	−1.46072e13	+	1.06128e13i	−0.279084	+	0.202766i
$130$	2.34381e13	−	7.21351e13i	0.425884	−	1.31074i
$131$	−7.46859e13			−1.29114			−0.645572	−	0.763699i	$-0.723381\pi$
$131$	−7.46859e13			−1.29114			−0.645572	+	0.763699i	$0.723381\pi$
$132$	1.49112e13	+	3.89033e11i	0.245347	+	0.00640112i
$133$	−5.80269e13			−0.909062
$134$	9.78221e12	−	3.01066e13i	0.145967	−	0.449242i
$135$	7.94465e13	−	5.77213e13i	1.12955	−	0.820666i
$136$	2.66325e13	+	1.93496e13i	0.360918	+	0.262222i
$137$	−1.75485e13	−	5.40086e13i	−0.226754	−	0.697877i	−0.998109	−	0.0614718i	$-0.980421\pi$
$137$	−1.75485e13	−	5.40086e13i	−0.226754	−	0.697877i	0.771355	−	0.636405i	$-0.219579\pi$
$138$	−7.13820e12	−	2.19691e13i	−0.0879781	−	0.270769i
$139$	−1.93287e13	−	1.40431e13i	−0.227304	−	0.165146i	0.468304	−	0.883567i	$-0.344865\pi$
$139$	−1.93287e13	−	1.40431e13i	−0.227304	−	0.165146i	−0.695608	+	0.718421i	$0.744865\pi$
$140$	−8.92365e13	+	6.48341e13i	−1.00164	+	0.727731i
$141$	−2.78267e13	+	8.56418e13i	−0.298221	+	0.917829i
$142$	5.65140e13			0.578471
$143$	4.11317e13	−	1.16188e14i	0.402247	−	1.13626i
$144$	−2.03034e13			−0.189764
$145$	4.73160e13	−	1.45624e14i	0.422781	−	1.30119i
$146$	−4.73677e13	+	3.44147e13i	−0.404752	+	0.294070i
$147$	−6.53444e13	−	4.74755e13i	−0.534129	−	0.388067i
$148$	1.27213e13	+	3.91521e13i	0.0995016	+	0.306235i
$149$	2.11187e13	+	6.49966e13i	0.158109	+	0.486609i	0.998463	−	0.0554296i	$-0.0176528\pi$
$149$	2.11187e13	+	6.49966e13i	0.158109	+	0.486609i	−0.840354	+	0.542038i	$0.817653\pi$
$150$	−6.32529e13	−	4.59560e13i	−0.453406	−	0.329419i
$151$	1.15205e14	−	8.37013e13i	0.790899	−	0.574622i	−0.117331	−	0.993093i	$-0.537434\pi$
$151$	1.15205e14	−	8.37013e13i	0.790899	−	0.574622i	0.908230	+	0.418471i	$0.137434\pi$
$152$	−9.86145e12	+	3.03504e13i	−0.0648571	+	0.199610i
$153$	1.51972e14			0.957787
$154$	−1.47709e14	+	1.01539e14i	−0.892326	+	0.613405i
$155$	2.03445e14			1.17840
$156$	1.64564e13	−	5.06477e13i	0.0914168	−	0.281352i
$157$	−2.56944e14	+	1.86681e14i	−1.36928	+	0.994838i	−0.371485	+	0.928439i	$0.621151\pi$
$157$	−2.56944e14	+	1.86681e14i	−1.36928	+	0.994838i	−0.997793	+	0.0663993i	$0.978849\pi$
$158$	2.41675e13	+	1.75587e13i	0.123583	+	0.0897886i
$159$	3.37793e13	+	1.03962e14i	0.165794	+	0.510262i
$160$	1.87455e13	+	5.76926e13i	0.0883317	+	0.271857i
$161$	2.24568e14	+	1.63158e14i	1.01620	+	0.738312i
$162$	−4.41183e13	+	3.20538e13i	−0.191766	+	0.139326i
$163$	−6.27053e13	+	1.92987e14i	−0.261870	+	0.805952i	0.730528	+	0.682882i	$0.239274\pi$
$163$	−6.27053e13	+	1.92987e14i	−0.261870	+	0.805952i	−0.992398	+	0.123070i	$0.960726\pi$
$164$	6.42509e13			0.257866
$165$	−1.63235e14	−	1.25230e14i	−0.629748	−	0.483127i
$166$	−8.14340e13			−0.302067
$167$	−1.64221e14	+	5.05419e14i	−0.585829	+	1.80300i	0.0100872	+	0.999949i	$0.496789\pi$
$167$	−1.64221e14	+	5.05419e14i	−0.585829	+	1.80300i	−0.595916	+	0.803047i	$0.703211\pi$
$168$	−6.26550e13	+	4.55215e13i	−0.215003	+	0.156209i
$169$	−1.10969e14	−	8.06239e13i	−0.366386	−	0.266195i
$170$	−1.40311e14	−	4.31831e14i	−0.445833	−	1.37213i
$171$	4.55250e13	+	1.40112e14i	0.139244	+	0.428548i
$172$	−9.65341e13	−	7.01361e13i	−0.284280	−	0.206541i
$173$	4.17155e14	−	3.03081e14i	1.18304	−	0.859526i	0.190525	−	0.981682i	$-0.438981\pi$
$173$	4.17155e14	−	3.03081e14i	1.18304	−	0.859526i	0.992511	+	0.122157i	$0.0389811\pi$
$174$	3.32216e13	−	1.02246e14i	0.0907509	−	0.279303i
$175$	9.39521e14			2.47263
$176$	2.80062e13	+	9.45142e13i	0.0710268	+	0.239698i
$177$	3.42439e14			0.837060
$178$	−1.46078e14	+	4.49583e14i	−0.344236	+	1.05945i
$179$	−9.98088e13	+	7.25153e13i	−0.226790	+	0.164773i	−0.695378	−	0.718644i	$-0.744763\pi$
$179$	−9.98088e13	+	7.25153e13i	−0.226790	+	0.164773i	0.468588	+	0.883417i	$0.344763\pi$
$180$	2.26559e14	+	1.64605e14i	0.496489	+	0.360721i
$181$	−1.21799e14	−	3.74858e14i	−0.257473	−	0.792422i	−0.993332	−	0.115287i	$-0.963221\pi$
$181$	−1.21799e14	−	3.74858e14i	−0.257473	−	0.792422i	0.735859	−	0.677135i	$-0.236779\pi$
$182$	1.97751e14	+	6.08616e14i	0.403325	+	1.24131i
$183$	−3.04361e14	−	2.21131e14i	−0.599041	−	0.435229i
$184$	1.23503e14	−	8.97299e13i	0.234618	−	0.170460i
$185$	1.75463e14	−	5.40020e14i	0.321788	−	0.990360i
$186$	1.42843e14			0.252945
$187$	−2.09628e14	−	7.07442e14i	−0.358491	−	1.20982i
$188$	−5.95103e14			−0.983028
$189$	−2.56033e14	+	7.87989e14i	−0.408596	+	1.25753i
$190$	3.56099e14	−	2.58721e14i	0.549126	−	0.398963i
$191$	−3.32812e14	−	2.41802e14i	−0.496001	−	0.360366i	0.311486	−	0.950251i	$-0.399173\pi$
$191$	−3.32812e14	−	2.41802e14i	−0.496001	−	0.360366i	−0.807487	+	0.589885i	$0.799173\pi$
$192$	1.31616e13	+	4.05073e13i	0.0189606	+	0.0583547i
$193$	−1.17079e13	−	3.60332e13i	−0.0163063	−	0.0501858i	0.942572	−	0.334002i	$-0.108399\pi$
$193$	−1.17079e13	−	3.60332e13i	−0.0163063	−	0.0501858i	−0.958879	+	0.283817i	$0.908399\pi$
$194$	−2.50232e14	−	1.81805e14i	−0.337002	−	0.244846i
$195$	−5.94245e14	+	4.31744e14i	−0.773999	+	0.562343i
$196$	1.64948e14	−	5.07657e14i	0.207817	−	0.639596i
$197$	−1.33018e15			−1.62137			−0.810683	−	0.585485i	$-0.800904\pi$
$197$	−1.33018e15			−1.62137			−0.810683	+	0.585485i	$0.800904\pi$
$198$	3.61061e14	+	2.76997e14i	0.425850	+	0.326701i
$199$	3.05984e14			0.349264			0.174632	−	0.984634i	$-0.444126\pi$
$199$	3.05984e14			0.349264			0.174632	+	0.984634i	$0.444126\pi$
$200$	1.59668e14	−	4.91408e14i	0.176410	−	0.542934i
$201$	−2.48016e14	+	1.80194e14i	−0.265281	+	0.192738i
$202$	−6.12933e14	−	4.45322e14i	−0.634788	−	0.461201i
$203$	3.99213e14	+	1.22865e15i	0.400387	+	1.23227i
$204$	−9.85153e13	−	3.03199e14i	−0.0956990	−	0.294531i
$205$	−7.16954e14	−	5.20897e14i	−0.674669	−	0.490176i
$206$	2.75495e14	−	2.00159e14i	0.251175	−	0.182490i
$207$	2.17776e14	−	6.70246e14i	0.192399	−	0.592144i
$208$	3.51938e14			0.301339
$209$	5.89435e14	−	4.05191e14i	0.489199	−	0.336286i
$210$	1.06820e15			0.859462
$211$	4.09851e14	−	1.26139e15i	0.319735	−	0.984044i	−0.654026	−	0.756472i	$-0.726921\pi$
$211$	4.09851e14	−	1.26139e15i	0.319735	−	0.984044i	0.973761	−	0.227572i	$-0.0730787\pi$
$212$	−5.84438e14	+	4.24619e14i	−0.442135	+	0.321230i
$213$	−4.42773e14	−	3.21693e14i	−0.324873	−	0.236034i
$214$	−1.53295e14	−	4.71794e14i	−0.109104	−	0.335786i
$215$	5.08580e14	+	1.56525e15i	0.351164	+	1.08077i
$216$	3.68638e14	+	2.67831e14i	0.246974	+	0.179437i
$217$	−1.38868e15	+	1.00893e15i	−0.902844	+	0.655955i
$218$	−2.43420e14	+	7.49170e14i	−0.153599	+	0.472730i
$219$	5.67012e14			0.347301
$220$	4.53737e14	−	1.28170e15i	0.269809	−	0.762150i
$221$	−2.63427e15			−1.52093
$222$	1.23197e14	−	3.79160e14i	0.0690724	−	0.212583i
$223$	−3.33492e13	+	2.42296e13i	−0.0181595	+	0.0131937i	−0.596828	−	0.802369i	$-0.703573\pi$
$223$	−3.33492e13	+	2.42296e13i	−0.0181595	+	0.0131937i	0.578668	+	0.815563i	$0.303573\pi$
$224$	−4.14065e14	−	3.00836e14i	−0.219006	−	0.159117i
$225$	−7.37102e14	−	2.26857e15i	−0.378740	−	1.16564i
$226$	7.12631e14	+	2.19325e15i	0.355762	+	1.09492i
$227$	−1.07978e15	−	7.84509e14i	−0.523804	−	0.380566i	0.294231	−	0.955734i	$-0.404936\pi$
$227$	−1.07978e15	−	7.84509e14i	−0.523804	−	0.380566i	−0.818035	+	0.575169i	$0.804936\pi$
$228$	2.50025e14	−	1.81654e14i	0.117871	−	0.0856383i
$229$	−6.43487e14	+	1.98045e15i	−0.294855	+	0.907472i	0.688414	+	0.725318i	$0.258307\pi$
$229$	−6.43487e14	+	1.98045e15i	−0.294855	+	0.907472i	−0.983270	+	0.182154i	$0.941693\pi$
$230$	−2.10559e15			−0.937868
$231$	1.73525e15	+	4.52728e13i	0.751424	+	0.0196046i
$232$	7.10479e14			0.299143
$233$	3.19710e14	−	9.83967e14i	0.130901	−	0.402872i	−0.864029	−	0.503442i	$-0.832067\pi$
$233$	3.19710e14	−	9.83967e14i	0.130901	−	0.402872i	0.994930	+	0.100570i	$0.0320667\pi$
$234$	1.31442e15	−	9.54981e14i	0.523396	−	0.380269i
$235$	6.64055e15	+	4.82464e15i	2.57195	+	1.86863i
$236$	6.99323e14	+	2.15230e15i	0.263481	+	0.810912i
$237$	−8.93971e13	−	2.75136e14i	−0.0327687	−	0.100852i
$238$	3.09929e15	+	2.25177e15i	1.10538	+	0.803106i
$239$	9.00380e14	−	6.54164e14i	0.312492	−	0.227039i	−0.420473	−	0.907305i	$-0.638136\pi$
$239$	9.00380e14	−	6.54164e14i	0.312492	−	0.227039i	0.732965	+	0.680266i	$0.238136\pi$
$240$	1.81536e14	−	5.58712e14i	0.0613184	−	0.188719i
$241$	3.30381e13			0.0108619			0.00543093	−	0.999985i	$-0.498271\pi$
$241$	3.30381e13			0.0108619			0.00543093	+	0.999985i	$0.498271\pi$
$242$	7.91402e14	−	2.06285e15i	0.253278	−	0.660190i
$243$	3.29939e15			1.02800
$244$	7.68292e14	−	2.36456e15i	0.233073	−	0.717326i
$245$	−5.95628e15	+	4.32749e15i	−1.75953	+	1.27837i
$246$	−5.03390e14	−	3.65734e14i	−0.144819	−	0.105217i
$247$	−7.89128e14	−	2.42869e15i	−0.221114	−	0.680520i
$248$	2.91713e14	+	8.97799e14i	0.0796195	+	0.245043i
$249$	6.38015e14	+	4.63545e14i	0.169643	+	0.123253i
$250$	−2.19487e15	+	1.59467e15i	−0.568590	+	0.413104i
$251$	1.32229e15	−	4.06959e15i	0.333770	−	1.02724i	−0.633554	−	0.773698i	$-0.718405\pi$
$251$	1.32229e15	−	4.06959e15i	0.333770	−	1.02724i	0.967325	−	0.253541i	$-0.0815954\pi$
$252$	−2.36276e15			−0.581188
$253$	−3.42045e15	−	8.92396e13i	−0.819974	−	0.0213931i
$254$	−4.18468e14			−0.0977784
$255$	−1.35881e15	+	4.18198e15i	−0.309490	+	0.952512i
$256$	−2.27718e14	+	1.65447e14i	−0.0505636	+	0.0367366i
$257$	8.02671e14	+	5.83174e14i	0.173769	+	0.126251i	0.671270	−	0.741213i	$-0.265749\pi$
$257$	8.02671e14	+	5.83174e14i	0.173769	+	0.126251i	−0.497501	+	0.867463i	$0.665749\pi$
$258$	3.57086e14	+	1.09900e15i	0.0753780	+	0.231990i
$259$	1.48041e15	+	4.55623e15i	0.304743	+	0.937902i
$260$	−3.92716e15	−	2.85325e15i	−0.788409	−	0.572812i
$261$	2.65350e15	−	1.92788e15i	0.519583	−	0.377499i
$262$	−1.47707e15	+	4.54595e15i	−0.282126	+	0.868293i
$263$	−7.54164e15			−1.40525			−0.702624	−	0.711561i	$-0.747989\pi$
$263$	−7.54164e15			−1.40525			−0.702624	+	0.711561i	$0.747989\pi$
$264$	3.18579e14	−	8.99914e14i	0.0579151	−	0.163597i
$265$	9.96402e15			1.76741
$266$	−1.14760e15	+	3.53196e15i	−0.198637	+	0.611343i
$267$	3.70364e15	−	2.69085e15i	0.625612	−	0.454534i
$268$	−1.63905e15	−	1.19084e15i	−0.270219	−	0.196326i
$269$	−1.72316e15	−	5.30334e15i	−0.277291	−	0.853415i	−0.988604	−	0.150539i	$-0.951899\pi$
$269$	−1.72316e15	−	5.30334e15i	−0.277291	−	0.853415i	0.711313	−	0.702876i	$-0.248101\pi$
$270$	−1.94214e15	−	5.97728e15i	−0.305081	−	0.938942i
$271$	1.08618e15	+	7.89154e14i	0.166571	+	0.121021i	0.667948	−	0.744208i	$-0.267173\pi$
$271$	1.08618e15	+	7.89154e14i	0.166571	+	0.121021i	−0.501377	+	0.865229i	$0.667173\pi$
$272$	1.70448e15	−	1.23838e15i	0.255208	−	0.185419i
$273$	1.91508e15	−	5.89401e15i	0.279982	−	0.861695i
$274$	−3.63443e15			−0.518869
$275$	−9.54362e15	+	6.56050e15i	−1.33061	+	0.914691i
$276$	−1.47838e15			−0.201315
$277$	2.97984e15	−	9.17100e15i	0.396346	−	1.21983i	−0.531562	−	0.847019i	$-0.678395\pi$
$277$	2.97984e15	−	9.17100e15i	0.396346	−	1.21983i	0.927908	−	0.372808i	$-0.121605\pi$
$278$	−1.23704e15	+	8.98761e14i	−0.160728	+	0.116776i
$279$	3.52566e15	+	2.56154e15i	0.447520	+	0.325142i
$280$	2.18146e15	+	6.71384e15i	0.270533	+	0.832614i
$281$	−3.37226e15	−	1.03788e16i	−0.408630	−	1.25763i	−0.917826	−	0.396983i	$-0.870057\pi$
$281$	−3.37226e15	−	1.03788e16i	−0.408630	−	1.25763i	0.509196	−	0.860651i	$-0.329943\pi$
$282$	4.66248e15	+	3.38749e15i	0.552075	+	0.401106i
$283$	1.80631e15	−	1.31236e15i	0.209017	−	0.151860i	−0.478352	−	0.878168i	$-0.658766\pi$
$283$	1.80631e15	−	1.31236e15i	0.209017	−	0.151860i	0.687369	+	0.726309i	$0.258766\pi$
$284$	1.11768e15	−	3.43987e15i	0.126401	−	0.389021i
$285$	−4.26265e15			−0.471182
$286$	−6.25860e15	−	4.80144e15i	−0.676236	−	0.518791i
$287$	7.47705e15			0.789765
$288$	−4.01543e14	+	1.23582e15i	−0.0414649	+	0.127616i
$289$	−4.74511e15	+	3.44753e15i	−0.479083	+	0.348074i
$290$	−7.92799e15	−	5.76002e15i	−0.782665	−	0.568640i
$291$	9.25626e14	+	2.84879e15i	0.0893576	+	0.275014i
$292$	1.15794e15	+	3.56378e15i	0.109320	+	0.336452i
$293$	1.01844e16	+	7.39938e15i	0.940362	+	0.683213i	0.948508	−	0.316754i	$-0.102593\pi$
$293$	1.01844e16	+	7.39938e15i	0.940362	+	0.683213i	−0.00814615	+	0.999967i	$0.502593\pi$
$294$	−4.18204e15	+	3.03843e15i	−0.377686	+	0.274405i
$295$	9.64566e15	−	2.96863e16i	0.852097	−	2.62249i
$296$	2.63469e15			0.227684
$297$	−2.90160e15	−	9.79220e15i	−0.245313	−	0.827872i
$298$	4.37385e15			0.361792
$299$	−3.77492e15	+	1.16180e16i	−0.305524	+	0.940305i
$300$	−4.04819e15	+	2.94118e15i	−0.320607	+	0.232934i
$301$	−1.12339e16	−	8.16192e15i	−0.870661	−	0.632572i
$302$	−2.81628e15	−	8.66762e15i	−0.213614	−	0.657438i
$303$	2.26728e15	+	6.97797e15i	0.168317	+	0.518026i
$304$	1.65233e15	+	1.20049e15i	0.120065	+	0.0872326i
$305$	−2.77431e16	+	2.01566e16i	−1.97336	+	1.43373i
$306$	3.00556e15	−	9.25017e15i	0.209284	−	0.644110i
$307$	1.78233e16			1.21504			0.607519	−	0.794305i	$-0.292165\pi$
$307$	1.78233e16			1.21504			0.607519	+	0.794305i	$0.292165\pi$
$308$	3.25916e15	+	1.09989e16i	0.217533	+	0.734122i
$309$	−3.29780e15			−0.215523
$310$	4.02355e15	−	1.23832e16i	0.257489	−	0.792469i
$311$	−6.81975e14	+	4.95484e14i	−0.0427392	+	0.0310518i	−0.608950	−	0.793209i	$-0.708409\pi$
$311$	−6.81975e14	+	4.95484e14i	−0.0427392	+	0.0310518i	0.566211	+	0.824261i	$0.308409\pi$
$312$	−2.75735e15	−	2.00333e15i	−0.169234	−	0.122955i
$313$	7.43561e15	+	2.28845e16i	0.446970	+	1.37563i	0.880309	+	0.474401i	$0.157335\pi$
$313$	7.43561e15	+	2.28845e16i	0.446970	+	1.37563i	−0.433339	+	0.901231i	$0.642665\pi$
$314$	6.28122e15	+	1.93316e16i	0.369829	+	1.13822i
$315$	2.63652e16	+	1.91555e16i	1.52059	+	1.10478i
$316$	1.54672e15	−	1.12376e15i	0.0873867	−	0.0634901i
$317$	−1.61508e14	+	4.97070e14i	−0.00893940	+	0.0275126i	−0.955427	−	0.295228i	$-0.904604\pi$
$317$	−1.61508e14	+	4.97070e14i	−0.00893940	+	0.0275126i	0.946487	+	0.322741i	$0.104604\pi$
$318$	6.99597e15			0.379378
$319$	−1.26346e16	−	9.69297e15i	−0.671310	−	0.515012i
$320$	3.88234e15			0.202125
$321$	−1.48455e15	+	4.56898e15i	−0.0757379	+	0.233097i
$322$	1.43723e16	−	1.04421e16i	0.718561	−	0.522065i
$323$	−1.23677e16	−	8.98568e15i	−0.606001	−	0.440286i
$324$	1.07851e15	+	3.31931e15i	0.0517942	+	0.159406i
$325$	1.27769e16	+	3.93232e16i	0.601427	+	1.85100i
$326$	1.05065e16	+	7.63345e15i	0.484781	+	0.352214i
$327$	6.17162e15	−	4.48394e15i	0.279151	−	0.202815i
$328$	1.27070e15	−	3.91080e15i	0.0563458	−	0.173415i
$329$	−6.92537e16			−3.01071
$330$	−1.08507e16	+	7.45903e15i	−0.462507	+	0.317938i
$331$	1.67407e16			0.699667			0.349834	−	0.936812i	$-0.386238\pi$
$331$	1.67407e16			0.699667			0.349834	+	0.936812i	$0.386238\pi$
$332$	−1.61053e15	+	4.95670e15i	−0.0660041	+	0.203140i
$333$	9.84002e15	−	7.14920e15i	0.395466	−	0.287323i
$334$	2.75159e16	+	1.99914e16i	1.08450	+	0.787938i
$335$	8.63518e15	+	2.65763e16i	0.333795	+	1.02732i
$336$	1.53165e15	+	4.71394e15i	0.0580704	+	0.178722i
$337$	−1.53308e16	−	1.11385e16i	−0.570126	−	0.414221i	0.265025	−	0.964241i	$-0.414620\pi$
$337$	−1.53308e16	−	1.11385e16i	−0.570126	−	0.414221i	−0.835151	+	0.550021i	$0.814620\pi$
$338$	−7.10204e15	+	5.15993e15i	−0.259074	+	0.188229i
$339$	6.90132e15	−	2.12401e16i	0.246964	−	0.760078i
$340$	−2.90595e16			−1.02018
$341$	7.06095e15	−	1.99456e16i	0.243198	−	0.686978i
$342$	9.42861e15			0.318624
$343$	4.92395e15	−	1.51544e16i	0.163268	−	0.502488i
$344$	−6.17818e15	+	4.48871e15i	−0.201016	+	0.146047i
$345$	1.64967e16	+	1.19856e16i	0.526713	+	0.382679i
$346$	−1.01977e16	−	3.13853e16i	−0.319527	−	0.983403i
$347$	−7.11293e15	−	2.18914e16i	−0.218729	−	0.673180i	−0.998868	−	0.0475728i	$-0.984851\pi$
$347$	−7.11293e15	−	2.18914e16i	−0.218729	−	0.673180i	0.780138	−	0.625607i	$-0.215149\pi$
$348$	−5.56642e15	−	4.04424e15i	−0.168001	−	0.122060i
$349$	2.82948e16	−	2.05574e16i	0.838187	−	0.608978i	−0.0836767	−	0.996493i	$-0.526666\pi$
$349$	2.82948e16	−	2.05574e16i	0.838187	−	0.608978i	0.921864	+	0.387515i	$0.126666\pi$
$350$	1.85810e16	−	5.71864e16i	0.540289	−	1.66284i
$351$	−3.64628e16			−1.04077
$352$	6.30673e15	+	1.64543e14i	0.176717	+	0.00461054i
$353$	2.24884e16			0.618618			0.309309	−	0.950962i	$-0.399902\pi$
$353$	2.24884e16			0.618618			0.309309	+	0.950962i	$0.399902\pi$
$354$	6.77244e15	−	2.08434e16i	0.182904	−	0.562922i
$355$	−4.03597e16	+	2.93230e16i	−1.07020	+	0.777543i
$356$	2.44760e16	+	1.77829e16i	0.637259	+	0.462996i
$357$	−1.14645e16	−	3.52840e16i	−0.293097	−	0.902059i
$358$	2.43991e15	+	7.50926e15i	0.0612539	+	0.188520i
$359$	4.76481e16	+	3.46183e16i	1.17471	+	0.853478i	0.991565	−	0.129607i	$-0.0413717\pi$
$359$	4.76481e16	+	3.46183e16i	1.17471	+	0.853478i	0.183147	+	0.983086i	$0.441372\pi$
$360$	1.44998e16	−	1.05347e16i	0.351071	−	0.255068i
$361$	−8.41557e15	+	2.59005e16i	−0.200118	+	0.615901i
$362$	−2.52256e16			−0.589162
$363$	−1.79428e16	+	1.16571e16i	−0.411620	+	0.267421i
$364$	4.09560e16			0.922907
$365$	1.59713e16	−	4.91547e16i	0.353539	−	1.08808i
$366$	−1.94791e16	+	1.41524e16i	−0.423586	+	0.307753i
$367$	−2.24537e16	−	1.63136e16i	−0.479687	−	0.348513i	0.321517	−	0.946904i	$-0.395807\pi$
$367$	−2.24537e16	−	1.63136e16i	−0.479687	−	0.348513i	−0.801205	+	0.598391i	$0.795807\pi$
$368$	−3.01912e15	−	9.29191e15i	−0.0633680	−	0.195027i
$369$	−5.86612e15	−	1.80541e16i	−0.120971	−	0.372309i
$370$	−2.93996e16	−	2.13600e16i	−0.595703	−	0.432803i
$371$	−6.80125e16	+	4.94140e16i	−1.35412	+	0.983829i
$372$	2.82503e15	−	8.69454e15i	0.0552705	−	0.170105i
$373$	−7.82976e16			−1.50536			−0.752681	−	0.658386i	$-0.771240\pi$
$373$	−7.82976e16			−1.50536			−0.752681	+	0.658386i	$0.771240\pi$
$374$	−4.72061e16	−	1.23161e15i	−0.891935	−	0.0232706i
$375$	2.62735e16			0.487883
$376$	−1.17694e16	+	3.62225e16i	−0.214800	+	0.661085i
$377$	−4.59955e16	+	3.34177e16i	−0.825081	+	0.599457i
$378$	4.28994e16	+	3.11682e16i	0.756405	+	0.549561i
$379$	−4.03511e15	−	1.24188e16i	−0.0699360	−	0.215241i	0.909980	−	0.414653i	$-0.136097\pi$
$379$	−4.03511e15	−	1.24188e16i	−0.0699360	−	0.215241i	−0.979916	+	0.199412i	$0.936097\pi$
$380$	−8.70512e15	−	2.67916e16i	−0.148314	−	0.456463i
$381$	3.27859e15	+	2.38204e15i	0.0549130	+	0.0398966i
$382$	−2.13000e16	+	1.54753e16i	−0.350726	+	0.254817i
$383$	2.06618e16	−	6.35904e16i	0.334484	−	1.02944i	−0.632491	−	0.774568i	$-0.717968\pi$
$383$	2.06618e16	−	6.35904e16i	0.334484	−	1.02944i	0.966975	−	0.254869i	$-0.0820325\pi$
$384$	2.72588e15			0.0433865
$385$	5.28025e16	−	1.49155e17i	0.826343	−	2.33423i
$386$	−2.42480e15			−0.0373129
$387$	−1.08942e16	+	3.35289e16i	−0.164844	+	0.507338i
$388$	−1.60149e16	+	1.16355e16i	−0.238296	+	0.173132i
$389$	9.65637e16	+	7.01576e16i	1.41300	+	1.02660i	0.992878	+	0.119134i	$0.0380117\pi$
$389$	9.65637e16	+	7.01576e16i	1.41300	+	1.02660i	0.420119	+	0.907469i	$0.361988\pi$
$390$	1.45268e16	+	4.47089e16i	0.209050	+	0.643390i
$391$	2.25983e16	+	6.95503e16i	0.319835	+	0.984351i
$392$	−2.76377e16	−	2.00799e16i	−0.384717	−	0.279514i
$393$	3.74493e16	−	2.72085e16i	0.512734	−	0.372523i
$394$	−2.63072e16	+	8.09651e16i	−0.354281	+	1.09037i
$395$	−2.63699e16			−0.349323
$396$	2.40009e16	−	1.64987e16i	0.312758	−	0.214997i
$397$	1.04546e17			1.34020			0.670102	−	0.742269i	$-0.266250\pi$
$397$	1.04546e17			1.34020			0.670102	+	0.742269i	$0.266250\pi$
$398$	6.05148e15	−	1.86245e16i	0.0763171	−	0.234880i
$399$	2.90961e16	−	2.11395e16i	0.361003	−	0.262284i
$400$	−2.67531e16	−	1.94372e16i	−0.326575	−	0.237271i
$401$	−1.14128e16	−	3.51249e16i	−0.137073	−	0.421868i	0.858834	−	0.512255i	$-0.171190\pi$
$401$	−1.14128e16	−	3.51249e16i	−0.137073	−	0.421868i	−0.995907	+	0.0903870i	$0.971190\pi$
$402$	6.06296e15	+	1.86599e16i	0.0716498	+	0.220515i
$403$	−6.11135e16	−	4.44015e16i	−0.710647	−	0.516316i
$404$	−3.92277e16	+	2.85006e16i	−0.448863	+	0.326118i
$405$	1.48757e16	−	4.57827e16i	0.167502	−	0.515518i
$406$	8.26803e16			0.916184
$407$	−4.68533e16	−	3.59447e16i	−0.510948	−	0.391986i
$408$	−2.04033e16			−0.218983
$409$	−1.57282e16	+	4.84064e16i	−0.166141	+	0.511330i	−0.999119	−	0.0419771i	$-0.986634\pi$
$409$	−1.57282e16	+	4.84064e16i	−0.166141	+	0.511330i	0.832977	+	0.553307i	$0.186634\pi$
$410$	−4.58850e16	+	3.33374e16i	−0.477063	+	0.346607i
$411$	2.84748e16	+	2.06882e16i	0.291400	+	0.211714i
$412$	−6.73471e15	−	2.07273e16i	−0.0678402	−	0.208791i
$413$	8.13821e16	+	2.50468e17i	0.806963	+	2.48358i
$414$	−3.64893e16	−	2.65110e16i	−0.356175	−	0.258776i
$415$	5.81564e16	−	4.22531e16i	0.558837	−	0.406019i
$416$	6.96031e15	−	2.14216e16i	0.0658449	−	0.202650i
$417$	1.48079e16			0.137914
$418$	−1.30057e16	−	4.38910e16i	−0.119258	−	0.402466i
$419$	−2.12629e16			−0.191969			−0.0959847	−	0.995383i	$-0.530600\pi$
$419$	−2.12629e16			−0.191969			−0.0959847	+	0.995383i	$0.530600\pi$
$420$	2.11259e16	−	6.50187e16i	0.187799	−	0.577987i
$421$	−5.47646e16	+	3.97888e16i	−0.479365	+	0.348279i	−0.801080	−	0.598557i	$-0.795741\pi$
$421$	−5.47646e16	+	3.97888e16i	−0.479365	+	0.348279i	0.321715	+	0.946837i	$0.395741\pi$
$422$	−6.86723e16	−	4.98934e16i	−0.591903	−	0.430043i
$423$	5.43330e16	+	1.67220e17i	0.461160	+	1.41930i
$424$	1.42871e16	+	4.39711e16i	0.119417	+	0.367527i
$425$	2.00248e17	+	1.45488e17i	1.64831	+	1.19757i
$426$	−2.83375e16	+	2.05884e16i	−0.229720	+	0.166901i
$427$	8.94081e16	−	2.75170e17i	0.713832	−	2.19695i
$428$	−3.17487e16			−0.249656
$429$	2.17034e16	+	7.32438e16i	0.168096	+	0.567281i
$430$	1.05331e17			0.803549
$431$	5.44682e15	−	1.67636e16i	0.0409299	−	0.125969i	−0.928504	−	0.371323i	$-0.878904\pi$
$431$	5.44682e15	−	1.67636e16i	0.0409299	−	0.125969i	0.969434	+	0.245354i	$0.0789042\pi$
$432$	2.35929e16	−	1.71412e16i	0.174637	−	0.126881i
$433$	−7.65130e15	−	5.55899e15i	−0.0557910	−	0.0405345i	0.559540	−	0.828803i	$-0.310978\pi$
$433$	−7.65130e15	−	5.55899e15i	−0.0557910	−	0.0405345i	−0.615331	+	0.788269i	$0.710978\pi$
$434$	3.39473e16	+	1.04479e17i	0.243850	+	0.750493i
$435$	2.93262e16	+	9.02566e16i	0.207527	+	0.638703i
$436$	4.07860e16	+	2.96328e16i	0.284347	+	0.206591i
$437$	−5.73528e16	+	4.16693e16i	−0.393936	+	0.286211i
$438$	1.12138e16	−	3.45127e16i	0.0758880	−	0.233559i
$439$	−1.34634e16			−0.0897708			−0.0448854	−	0.998992i	$-0.514292\pi$
$439$	−1.34634e16			−0.0897708			−0.0448854	+	0.998992i	$0.514292\pi$
$440$	−6.90407e16	−	5.29663e16i	−0.453589	−	0.347982i
$441$	−1.57708e17			−1.02094
$442$	−5.20982e16	+	1.60342e17i	−0.332336	+	1.02283i
$443$	7.07962e16	−	5.14365e16i	0.445027	−	0.323331i	−0.342602	−	0.939480i	$-0.611308\pi$
$443$	7.07962e16	−	5.14365e16i	0.445027	−	0.323331i	0.787629	+	0.616150i	$0.211308\pi$
$444$	−2.06421e16	−	1.49974e16i	−0.127869	−	0.0929022i
$445$	−1.28950e17	−	3.96866e17i	−0.787190	−	2.42272i
$446$	8.15250e14	+	2.50908e15i	0.00490472	+	0.0150952i
$447$	−3.42680e16	−	2.48972e16i	−0.203184	−	0.147622i
$448$	−2.65001e16	+	1.92535e16i	−0.154861	+	0.112513i
$449$	2.11200e16	−	6.50006e16i	0.121644	−	0.374383i	−0.871630	−	0.490164i	$-0.836937\pi$
$449$	2.11200e16	−	6.50006e16i	0.121644	−	0.374383i	0.993275	+	0.115781i	$0.0369370\pi$
$450$	−1.52660e17			−0.866650
$451$	−7.59516e16	+	5.22108e16i	−0.425000	+	0.292155i
$452$	1.47592e17			0.814072
$453$	−2.72736e16	+	8.39397e16i	−0.148288	+	0.456382i
$454$	−6.91062e16	+	5.02086e16i	−0.370385	+	0.269101i
$455$	−4.57013e17	−	3.32040e17i	−2.41465	−	1.75435i
$456$	−6.11207e15	−	1.88110e16i	−0.0318359	−	0.0979807i
$457$	8.46297e16	+	2.60463e17i	0.434578	+	1.33749i	0.893519	+	0.449026i	$0.148229\pi$
$457$	8.46297e16	+	2.60463e17i	0.434578	+	1.33749i	−0.458941	+	0.888467i	$0.651771\pi$
$458$	1.07819e17	+	7.83351e16i	0.545845	+	0.396580i
$459$	−1.76593e17	+	1.28303e17i	−0.881439	+	0.640403i
$460$	−4.16423e16	+	1.28162e17i	−0.204932	+	0.630715i
$461$	3.51258e17			1.70439			0.852197	−	0.523221i	$-0.175270\pi$
$461$	3.51258e17			1.70439			0.852197	+	0.523221i	$0.175270\pi$
$462$	3.70739e16	−	1.04725e17i	0.177376	−	0.501047i
$463$	−7.93735e16			−0.374455			−0.187227	−	0.982317i	$-0.559950\pi$
$463$	−7.93735e16			−0.374455			−0.187227	+	0.982317i	$0.559950\pi$
$464$	1.40512e16	−	4.32452e16i	0.0653652	−	0.201173i
$465$	−1.02012e17	+	7.41162e16i	−0.467959	+	0.339992i
$466$	−5.35688e16	−	3.89200e16i	−0.242328	−	0.176062i
$467$	−6.00673e16	−	1.84868e17i	−0.267965	−	0.824712i	−0.990995	−	0.133896i	$-0.957251\pi$
$467$	−6.00673e16	−	1.84868e17i	−0.267965	−	0.824712i	0.723030	−	0.690816i	$-0.242749\pi$
$468$	−3.21320e16	−	9.88922e16i	−0.141364	−	0.435075i
$469$	−1.90741e17	−	1.38581e17i	−0.827598	−	0.601285i
$470$	4.24995e17	−	3.08777e17i	1.81864	−	1.32132i
$471$	6.08291e16	−	1.87213e17i	0.256729	−	0.790132i
$472$	1.44836e17			0.602910
$473$	1.71107e17	+	4.46418e15i	0.702539	+	0.0183292i
$474$	−1.85149e16			−0.0749828
$475$	−7.41475e16	+	2.28203e17i	−0.296202	+	0.911616i
$476$	1.98355e17	−	1.44113e17i	0.781622	−	0.567882i
$477$	1.72674e17	+	1.25455e17i	0.671210	+	0.487662i
$478$	−2.20105e16	−	6.77414e16i	−0.0844013	−	0.259760i
$479$	−1.01261e17	−	3.11650e17i	−0.383056	−	1.17892i	−0.937881	−	0.346958i	$-0.887215\pi$
$479$	−1.01261e17	−	3.11650e17i	−0.383056	−	1.17892i	0.554825	−	0.831967i	$-0.312785\pi$
$480$	−3.04172e16	−	2.20994e16i	−0.113514	−	0.0824730i
$481$	−1.70566e17	+	1.23924e17i	−0.627986	+	0.456259i
$482$	6.53398e14	−	2.01095e15i	0.00237340	−	0.00730459i
$483$	−1.72043e17			−0.616567
$484$	−1.09909e17	−	8.89680e16i	−0.388633	−	0.314586i
$485$	2.73036e17			0.952574
$486$	6.52523e16	−	2.00826e17i	0.224626	−	0.691328i
$487$	−2.90904e17	+	2.11354e17i	−0.988125	+	0.717915i	−0.959510	−	0.281676i	$-0.909110\pi$
$487$	−2.90904e17	+	2.11354e17i	−0.988125	+	0.717915i	−0.0286152	+	0.999591i	$0.509110\pi$
$488$	−1.28731e17	−	9.35282e16i	−0.431472	−	0.313483i
$489$	−3.88644e16	−	1.19612e17i	−0.128542	−	0.395611i
$490$	1.45606e17	+	4.48130e17i	0.475232	+	1.46261i
$491$	1.58162e17	+	1.14911e17i	0.509415	+	0.370112i	0.812602	−	0.582820i	$-0.198051\pi$
$491$	1.58162e17	+	1.14911e17i	0.509415	+	0.370112i	−0.303187	+	0.952931i	$0.598051\pi$
$492$	−3.22169e16	+	2.34070e16i	−0.102403	+	0.0743999i
$493$	−1.05174e17	+	3.23692e17i	−0.329915	+	1.01538i
$494$	−1.63435e17			−0.505964
$495$	−4.01576e17	−	1.04771e16i	−1.22697	−	0.0320117i
$496$	6.04161e16			0.182189
$497$	1.30068e17	−	4.00307e17i	0.387126	−	1.19145i
$498$	4.08330e16	−	2.96669e16i	0.119956	−	0.0871528i
$499$	2.89875e17	+	2.10606e17i	0.840538	+	0.610686i	0.922521	−	0.385947i	$-0.126125\pi$
$499$	2.89875e17	+	2.10606e17i	0.840538	+	0.610686i	−0.0819832	+	0.996634i	$0.526125\pi$
$500$	5.36554e16	+	1.65134e17i	0.153571	+	0.472642i
$501$	−1.01783e17	−	3.13256e17i	−0.287561	−	0.885022i
$502$	−2.21555e17	−	1.60969e17i	−0.617886	−	0.448920i
$503$	9.70042e16	−	7.04776e16i	0.267054	−	0.194026i	−0.446197	−	0.894935i	$-0.647222\pi$
$503$	9.70042e16	−	7.04776e16i	0.267054	−	0.194026i	0.713251	+	0.700909i	$0.247222\pi$
$504$	−4.67286e16	+	1.43816e17i	−0.126994	+	0.390848i
$505$	6.68789e17			1.79430
$506$	−7.30784e16	+	2.06430e17i	−0.193558	+	0.546757i
$507$	8.50144e16			0.222301
$508$	−8.27608e15	+	2.54711e16i	−0.0213654	+	0.0657558i
$509$	−5.03024e17	+	3.65468e17i	−1.28210	+	0.931502i	−0.999614	−	0.0277684i	$-0.991160\pi$
$509$	−5.03024e17	+	3.65468e17i	−1.28210	+	0.931502i	−0.282489	+	0.959271i	$0.591160\pi$
$510$	2.27674e17	+	1.65415e17i	0.572937	+	0.416263i
$511$	1.34753e17	+	4.14727e17i	0.334813	+	1.03045i
$512$	5.56676e15	+	1.71327e16i	0.0136568	+	0.0420312i
$513$	−1.71190e17	−	1.24377e17i	−0.414683	−	0.301285i
$514$	5.13709e16	−	3.73232e16i	0.122873	−	0.0892726i
$515$	−9.28909e16	+	2.85889e17i	−0.219395	+	0.675227i
$516$	7.39555e16			0.172483
$517$	7.03477e17	−	4.83585e17i	1.62017	−	1.11374i
$518$	3.06605e17			0.697327
$519$	−9.87574e16	+	3.03944e17i	−0.221810	+	0.682662i
$520$	−2.51338e17	+	1.82608e17i	−0.557489	+	0.405040i
$521$	5.80225e17	+	4.21558e17i	1.27102	+	0.923448i	0.999243	−	0.0389133i	$-0.0123896\pi$
$521$	5.80225e17	+	4.21558e17i	1.27102	+	0.923448i	0.271774	+	0.962361i	$0.412390\pi$
$522$	−6.48669e16	−	1.99640e17i	−0.140335	−	0.431906i
$523$	−1.88538e17	−	5.80260e17i	−0.402844	−	1.23983i	−0.922682	−	0.385562i	$-0.874007\pi$
$523$	−1.88538e17	−	5.80260e17i	−0.402844	−	1.23983i	0.519837	−	0.854265i	$-0.325993\pi$
$524$	2.47489e17	+	1.79811e17i	0.522279	+	0.379458i
$525$	−4.71098e17	+	3.42273e17i	−0.981920	+	0.713406i
$526$	−1.49152e17	+	4.59041e17i	−0.307058	+	0.945028i
$527$	−4.52217e17			−0.919555
$528$	−4.84751e16	−	3.71888e16i	−0.0973639	−	0.0746951i
$529$	−1.64913e17			−0.327185
$530$	1.97059e17	−	6.06486e17i	0.386193	−	1.18858i
$531$	5.40932e17	−	3.93010e17i	1.04720	−	0.760833i
$532$	1.92286e17	+	1.39704e17i	0.367723	+	0.267167i
$533$	1.01683e17	+	3.12948e17i	0.192097	+	0.591215i
$534$	−9.05384e16	−	2.78649e17i	−0.168972	−	0.520042i
$535$	3.54273e17	+	2.57394e17i	0.653188	+	0.474569i
$536$	−1.04899e17	+	7.62138e16i	−0.191074	+	0.138823i
$537$	2.36287e16	−	7.27218e16i	0.0425214	−	0.130867i
$538$	−3.56881e17			−0.634510
$539$	2.17540e17	+	7.34143e17i	0.382130	+	1.28960i
$540$	−4.02232e17			−0.698100
$541$	−5.54540e16	+	1.70670e17i	−0.0950935	+	0.292668i	−0.987278	−	0.159003i	$-0.949172\pi$
$541$	−5.54540e16	+	1.70670e17i	−0.0950935	+	0.292668i	0.892185	+	0.451671i	$0.149172\pi$
$542$	6.95153e16	−	5.05059e16i	0.117784	−	0.0855749i
$543$	1.97636e17	+	1.43591e17i	0.330877	+	0.240396i
$544$	−4.16674e16	−	1.28239e17i	−0.0689292	−	0.212142i
$545$	−2.14877e17	−	6.61324e17i	−0.351247	−	1.08103i
$546$	−3.20880e17	−	2.33133e17i	−0.518310	−	0.376575i
$547$	2.83800e17	−	2.06193e17i	0.452997	−	0.329121i	−0.337781	−	0.941225i	$-0.609676\pi$
$547$	2.83800e17	−	2.06193e17i	0.452997	−	0.329121i	0.790778	+	0.612103i	$0.209676\pi$
$548$	−7.18785e16	+	2.21219e17i	−0.113377	+	0.348939i
$549$	−7.34570e17			−1.14502
$550$	2.10577e17	+	7.10645e17i	0.324379	+	1.09470i
$551$	−3.29936e17			−0.502278
$552$	−2.92380e16	+	8.99855e16i	−0.0439890	+	0.135384i
$553$	1.79996e17	−	1.30774e17i	0.267639	−	0.194451i
$554$	−4.99285e17	−	3.62752e17i	−0.733727	−	0.533084i
$555$	1.08751e17	+	3.34701e17i	0.157953	+	0.486130i
$556$	3.02404e16	+	9.30705e16i	0.0434112	+	0.133606i
$557$	5.09309e17	+	3.70034e17i	0.722641	+	0.525029i	0.887227	−	0.461334i	$-0.152629\pi$
$557$	5.09309e17	+	3.70034e17i	0.722641	+	0.525029i	−0.164586	+	0.986363i	$0.552629\pi$
$558$	2.25642e17	−	1.63938e17i	0.316445	−	0.229910i
$559$	1.88839e17	−	5.81187e17i	0.261767	−	0.805636i
$560$	4.51798e17			0.619045
$561$	3.62838e17	+	2.78360e17i	0.491421	+	0.377006i
$562$	−6.98424e17			−0.935046
$563$	3.42691e17	−	1.05469e18i	0.453522	−	1.39580i	−0.419340	−	0.907829i	$-0.637738\pi$
$563$	3.42691e17	−	1.05469e18i	0.453522	−	1.39580i	0.872862	−	0.487968i	$-0.162262\pi$
$564$	2.98399e17	−	2.16799e17i	0.390376	−	0.283625i
$565$	−1.64693e18	−	1.19656e18i	−2.12990	−	1.54746i
$566$	−4.41568e16	−	1.35901e17i	−0.0564535	−	0.173746i
$567$	1.25509e17	+	3.86276e17i	0.158630	+	0.488212i
$568$	−1.87272e17	−	1.36061e17i	−0.233997	−	0.170008i
$569$	7.48111e17	−	5.43535e17i	0.924137	−	0.671425i	−0.0204132	−	0.999792i	$-0.506498\pi$
$569$	7.48111e17	−	5.43535e17i	0.924137	−	0.671425i	0.944550	+	0.328367i	$0.106498\pi$
$570$	−8.43028e16	+	2.59457e17i	−0.102957	+	0.316869i
$571$	−1.45652e17			−0.175866			−0.0879330	−	0.996126i	$-0.528026\pi$
$571$	−1.45652e17			−0.175866			−0.0879330	+	0.996126i	$0.528026\pi$
$572$	−4.16029e17	+	2.85988e17i	−0.496649	+	0.341408i
$573$	2.54970e17			0.300943
$574$	1.47874e17	−	4.55110e17i	0.172570	−	0.531116i
$575$	9.28607e17	−	6.74673e17i	1.07150	−	0.778489i
$576$	6.72801e16	+	4.88819e16i	0.0767610	+	0.0557701i
$577$	−4.37476e17	−	1.34641e18i	−0.493527	−	1.51892i	−0.819239	−	0.573452i	$-0.805604\pi$
$577$	−4.37476e17	−	1.34641e18i	−0.493527	−	1.51892i	0.325712	−	0.945469i	$-0.394396\pi$
$578$	1.15998e17	+	3.57006e17i	0.129396	+	0.398239i
$579$	1.89977e16	+	1.38027e16i	0.0209552	+	0.0152248i
$580$	−5.07391e17	+	3.68641e17i	−0.553428	+	0.402089i
$581$	−1.87421e17	+	5.76824e17i	−0.202150	+	0.622154i
$582$	1.91705e17			0.204472
$583$	3.45821e17	−	9.76865e17i	0.364758	−	1.03036i
$584$	2.39820e17			0.250151
$585$	−4.43192e17	+	1.36401e18i	−0.457172	+	1.40703i
$586$	6.51800e17	−	4.73560e17i	0.664936	−	0.483104i
$587$	4.09634e17	+	2.97616e17i	0.413284	+	0.300268i	0.774930	−	0.632047i	$-0.217785\pi$
$587$	4.09634e17	+	2.97616e17i	0.413284	+	0.300268i	−0.361646	+	0.932315i	$0.617785\pi$
$588$	1.02234e17	+	3.14642e17i	0.102010	+	0.313953i
$589$	−1.35467e17	−	4.16925e17i	−0.133685	−	0.411442i
$590$	−1.61617e18	−	1.17422e18i	−1.57743	−	1.14607i
$591$	6.66986e17	−	4.84593e17i	0.643870	−	0.467799i
$592$	5.21064e16	−	1.60367e17i	0.0497508	−	0.153117i
$593$	1.11813e18			1.05593			0.527965	−	0.849266i	$-0.322955\pi$
$593$	1.11813e18			1.05593			0.527965	+	0.849266i	$0.322955\pi$
$594$	−6.53413e17	−	1.70475e16i	−0.610346	−	0.0159239i
$595$	−3.38173e18			−3.12448
$596$	8.65021e16	−	2.66226e17i	0.0790543	−	0.243304i
$597$	−1.53428e17	+	1.11472e17i	−0.138698	+	0.100770i
$598$	6.32503e17	+	4.59541e17i	0.565594	+	0.410928i
$599$	4.31239e17	+	1.32722e18i	0.381455	+	1.17400i	0.939019	+	0.343865i	$0.111736\pi$
$599$	4.31239e17	+	1.32722e18i	0.381455	+	1.17400i	−0.557564	+	0.830134i	$0.688264\pi$
$600$	9.89613e16	+	3.04572e17i	0.0865929	+	0.266506i
$601$	−8.38603e17	−	6.09281e17i	−0.725893	−	0.527392i	0.162369	−	0.986730i	$-0.448087\pi$
$601$	−8.38603e17	−	6.09281e17i	−0.725893	−	0.527392i	−0.888261	+	0.459338i	$0.848087\pi$
$602$	−7.18971e17	+	5.22363e17i	−0.615650	+	0.447296i
$603$	−1.84972e17	+	5.69286e17i	−0.156691	+	0.482245i
$604$	−5.83275e17			−0.488802
$605$	5.05156e17	+	1.88382e18i	0.418809	+	1.56182i
$606$	4.69572e17			0.385151
$607$	−7.30892e17	+	2.24945e18i	−0.593098	+	1.82537i	−0.0291246	+	0.999576i	$0.509272\pi$
$607$	−7.30892e17	+	2.24945e18i	−0.593098	+	1.82537i	−0.563974	+	0.825793i	$0.690728\pi$
$608$	1.05749e17	−	7.68311e16i	0.0848990	−	0.0616828i
$609$	−6.47779e17	−	4.70639e17i	−0.514535	−	0.373831i
$610$	6.78204e17	+	2.08730e18i	0.532987	+	1.64036i
$611$	−9.41805e17	−	2.89858e18i	−0.732307	−	2.25381i
$612$	−5.03594e17	−	3.65883e17i	−0.387433	−	0.281487i
$613$	7.95285e17	−	5.77808e17i	0.605382	−	0.439836i	−0.242403	−	0.970176i	$-0.577936\pi$
$613$	7.95285e17	−	5.77808e17i	0.605382	−	0.439836i	0.847785	+	0.530340i	$0.177936\pi$
$614$	3.52494e17	−	1.08486e18i	0.265495	−	0.817111i
$615$	5.49264e17			0.409348
$616$	7.33931e17	+	1.91483e16i	0.541228	+	0.0141207i
$617$	−1.64010e18			−1.19678			−0.598392	−	0.801204i	$-0.704193\pi$
$617$	−1.64010e18			−1.19678			−0.598392	+	0.801204i	$0.704193\pi$
$618$	−6.52208e16	+	2.00729e17i	−0.0470935	+	0.144939i
$619$	1.74505e18	−	1.26785e18i	1.24686	−	0.905897i	0.248824	−	0.968549i	$-0.419956\pi$
$619$	1.74505e18	−	1.26785e18i	1.24686	−	0.905897i	0.998035	+	0.0626519i	$0.0199558\pi$
$620$	−6.74162e17	−	4.89808e17i	−0.476671	−	0.346322i
$621$	3.12798e17	+	9.62694e17i	0.218861	+	0.673585i
$622$	1.66715e16	+	5.13095e16i	0.0115435	+	0.0355271i
$623$	2.84834e18	+	2.06944e18i	1.95173	+	1.41801i
$624$	−1.76470e17	+	1.28213e17i	−0.119666	+	0.0869426i
$625$	−3.45104e15	+	1.06212e16i	−0.00231595	+	0.00712777i
$626$	1.53998e18			1.02278
$627$	−1.47944e17	+	4.17907e17i	−0.0972427	+	0.274689i
$628$	1.30089e18			0.846260
$629$	−3.90019e17	+	1.20035e18i	−0.251105	+	0.772823i
$630$	1.68738e18	−	1.22595e18i	1.07522	−	0.781195i
$631$	1.14974e18	+	8.35336e17i	0.725119	+	0.526830i	0.888015	−	0.459814i	$-0.152084\pi$
$631$	1.14974e18	+	8.35336e17i	0.725119	+	0.526830i	−0.162897	+	0.986643i	$0.552084\pi$
$632$	−3.78108e16	−	1.16370e17i	−0.0236023	−	0.0726405i
$633$	2.54023e17	+	7.81804e17i	0.156946	+	0.483029i
$634$	2.70613e16	+	1.96612e16i	0.0165489	+	0.0120235i
$635$	2.98850e17	−	2.17128e17i	0.180894	−	0.131427i
$636$	1.38360e17	−	4.25828e17i	0.0828971	−	0.255131i
$637$	2.73370e18			1.62123
$638$	−8.39864e17	+	5.77341e17i	−0.493031	+	0.338921i
$639$	−1.06863e18			−0.620969
$640$	7.67814e16	−	2.36309e17i	0.0441658	−	0.135928i
$641$	−2.39882e18	+	1.74285e18i	−1.36591	+	0.992388i	−0.367861	+	0.929881i	$0.619910\pi$
$641$	−2.39882e18	+	1.74285e18i	−1.36591	+	0.992388i	−0.998044	+	0.0625077i	$0.980090\pi$
$642$	2.48743e17	+	1.80722e17i	0.140208	+	0.101867i
$643$	4.48104e17	+	1.37912e18i	0.250039	+	0.769540i	0.994767	+	0.102172i	$0.0325792\pi$
$643$	4.48104e17	+	1.37912e18i	0.250039	+	0.769540i	−0.744728	+	0.667368i	$0.767421\pi$
$644$	−3.51343e17	−	1.08132e18i	−0.194077	−	0.597307i
$645$	−8.25243e17	−	5.99574e17i	−0.451278	−	0.327872i
$646$	−7.91535e17	+	5.75084e17i	−0.428508	+	0.311329i
$647$	−4.93014e17	+	1.51734e18i	−0.264230	+	0.813215i	0.727640	+	0.685959i	$0.240617\pi$
$647$	−4.93014e17	+	1.51734e18i	−0.264230	+	0.813215i	−0.991870	+	0.127256i	$0.959383\pi$
$648$	2.23368e17			0.118518
$649$	−2.57565e18	−	1.97597e18i	−1.35300	−	1.03798i
$650$	2.64620e18			1.37621
$651$	3.28756e17	−	1.01181e18i	0.169277	−	0.520980i
$652$	6.72419e17	−	4.88541e17i	0.342792	−	0.249053i
$653$	−1.17859e18	−	8.56294e17i	−0.594875	−	0.432202i	0.249181	−	0.968457i	$-0.419839\pi$
$653$	−1.17859e18	−	8.56294e17i	−0.594875	−	0.432202i	−0.844056	+	0.536255i	$0.819839\pi$
$654$	−1.50870e17	−	4.64331e17i	−0.0753960	−	0.232045i
$655$	−1.30387e18	−	4.01290e18i	−0.645158	−	1.98559i
$656$	−2.12910e17	−	1.54688e17i	−0.104309	−	0.0757850i
$657$	8.95678e17	−	6.50748e17i	0.434487	−	0.315674i
$658$	−1.36964e18	+	4.21531e18i	−0.657865	+	2.02470i
$659$	−1.46633e18			−0.697390			−0.348695	−	0.937236i	$-0.613375\pi$
$659$	−1.46633e18			−0.697390			−0.348695	+	0.937236i	$0.613375\pi$
$660$	2.39418e17	+	8.07976e17i	0.112751	+	0.380507i
$661$	−1.85286e18			−0.864036			−0.432018	−	0.901865i	$-0.642198\pi$
$661$	−1.85286e18			−0.864036			−0.432018	+	0.901865i	$0.642198\pi$
$662$	3.31082e17	−	1.01897e18i	0.152883	−	0.470525i
$663$	1.32089e18	−	9.59680e17i	0.603987	−	0.438822i
$664$	2.69851e17	+	1.96058e17i	0.122189	+	0.0887753i
$665$	−1.01304e18	−	3.11781e18i	−0.454239	−	1.39801i
$666$	−2.40548e17	−	7.40329e17i	−0.106812	−	0.328732i
$667$	1.27687e18	+	9.27703e17i	0.561474	+	0.407935i
$668$	1.76101e18	−	1.27945e18i	0.766860	−	0.557156i
$669$	7.89511e15	−	2.42986e16i	0.00340477	−	0.0104788i
$670$	1.78842e18			0.763805
$671$	1.01325e18	+	3.41949e18i	0.428571	+	1.44632i
$672$	3.17218e17			0.132879
$673$	−6.97940e17	+	2.14804e18i	−0.289548	+	0.891136i	0.695451	+	0.718574i	$0.255205\pi$
$673$	−6.97940e17	+	2.14804e18i	−0.289548	+	0.891136i	−0.984999	+	0.172562i	$0.944795\pi$
$674$	−9.81171e17	+	7.12863e17i	−0.403140	+	0.292898i
$675$	2.77177e18	+	2.01381e18i	1.12793	+	0.819489i
$676$	1.73615e17	+	5.34332e17i	0.0699736	+	0.215357i
$677$	7.74183e16	+	2.38269e17i	0.0309042	+	0.0951133i	0.965319	−	0.261074i	$-0.0840766\pi$
$677$	7.74183e16	+	2.38269e17i	0.0309042	+	0.0951133i	−0.934415	+	0.356187i	$0.884077\pi$
$678$	−1.15635e18	−	8.40134e17i	−0.457188	−	0.332166i
$679$	−1.86369e18	+	1.35405e18i	−0.729828	+	0.530251i
$680$	−5.74712e17	+	1.76878e18i	−0.222917	+	0.686067i
$681$	8.27230e17			0.317812
$682$	−1.07439e18	−	8.24248e17i	−0.408851	−	0.313660i
$683$	−5.32396e17			−0.200678			−0.100339	−	0.994953i	$-0.531993\pi$
$683$	−5.32396e17			−0.200678			−0.100339	+	0.994953i	$0.531993\pi$
$684$	1.86471e17	−	5.73897e17i	0.0696218	−	0.214274i
$685$	2.59554e18	−	1.88577e18i	0.959930	−	0.697430i
$686$	−8.25028e17	−	5.99418e17i	−0.302247	−	0.219595i
$687$	−3.98829e17	−	1.22747e18i	−0.144733	−	0.445443i
$688$	1.51031e17	+	4.64825e17i	0.0542926	+	0.167095i
$689$	−2.99312e18	−	2.17463e18i	−1.06586	−	0.774392i
$690$	1.05579e18	−	7.67077e17i	0.372442	−	0.270595i
$691$	−1.39430e17	+	4.29122e17i	−0.0487247	+	0.149959i	−0.972459	−	0.233075i	$-0.925121\pi$
$691$	−1.39430e17	+	4.29122e17i	−0.0487247	+	0.149959i	0.923734	+	0.383035i	$0.125121\pi$
$692$	−2.11203e18			−0.731156
$693$	2.79304e18	−	1.92000e18i	0.957881	−	0.658469i
$694$	−1.47315e18			−0.500507
$695$	4.17102e17	−	1.28371e18i	0.140392	−	0.432081i
$696$	−3.56251e17	+	2.58832e17i	−0.118794	+	0.0863092i
$697$	1.59364e18	+	1.15785e18i	0.526475	+	0.382507i
$698$	−6.91689e17	−	2.12880e18i	−0.226387	−	0.696746i
$699$	1.98154e17	+	6.09857e17i	0.0642543	+	0.197754i
$700$	−3.11332e18	−	2.26196e18i	−1.00020	−	0.726688i
$701$	−7.18462e17	+	5.21993e17i	−0.228684	+	0.166149i	−0.696227	−	0.717821i	$-0.745139\pi$
$701$	−7.18462e17	+	5.21993e17i	−0.228684	+	0.166149i	0.467543	+	0.883970i	$0.345139\pi$
$702$	−7.21127e17	+	2.21940e18i	−0.227416	+	0.699914i
$703$	−1.22351e18			−0.382294
$704$	1.34744e17	−	3.80622e17i	0.0417146	−	0.117834i
$705$	−5.08737e18			−1.56050
$706$	4.44754e17	−	1.36881e18i	0.135173	−	0.416020i
$707$	−4.56503e18	+	3.31669e18i	−1.37473	+	0.998800i
$708$	−1.13475e18	−	8.24445e17i	−0.338598	−	0.246006i
$709$	−1.12013e18	−	3.44742e18i	−0.331184	−	1.01928i	−0.968571	−	0.248736i	$-0.919985\pi$
$709$	−1.12013e18	−	3.44742e18i	−0.331184	−	1.01928i	0.637388	−	0.770543i	$-0.280015\pi$
$710$	9.86626e17	+	3.03652e18i	0.289050	+	0.889605i
$711$	−4.56984e17	−	3.32018e17i	−0.132663	−	0.0963850i
$712$	1.56647e18	−	1.13810e18i	0.450610	−	0.327387i
$713$	−6.48028e17	+	1.99443e18i	−0.184719	+	0.568507i
$714$	−2.37439e18			−0.670677
$715$	6.96090e18	+	1.81610e17i	1.94839	+	0.0508335i
$716$	5.05325e17			0.140164
$717$	−2.13156e17	+	6.56027e17i	−0.0585900	+	0.180321i
$718$	3.04948e18	−	2.21557e18i	0.830647	−	0.603500i
$719$	−4.04353e18	−	2.93780e18i	−1.09150	−	0.793020i	−0.111847	−	0.993725i	$-0.535677\pi$
$719$	−4.04353e18	−	2.93780e18i	−1.09150	−	0.793020i	−0.979652	+	0.200706i	$0.935677\pi$
$720$	−3.54459e17	−	1.09091e18i	−0.0948210	−	0.291829i
$721$	−7.83736e17	−	2.41209e18i	−0.207774	−	0.639461i
$722$	1.41006e18	+	1.02447e18i	0.370465	+	0.269159i
$723$	−1.65661e16	+	1.20360e16i	−0.00431341	+	0.00313388i
$724$	−4.98888e17	+	1.53542e18i	−0.128737	+	0.396211i
$725$	5.34204e18			1.36619
$726$	3.54682e17	+	1.32268e18i	0.0898982	+	0.335248i
$727$	6.95566e18			1.74729			0.873645	−	0.486564i	$-0.161750\pi$
$727$	6.95566e18			1.74729			0.873645	+	0.486564i	$0.161750\pi$
$728$	8.09989e17	−	2.49289e18i	0.201663	−	0.620654i
$729$	−5.55348e17	+	4.03484e17i	−0.137036	+	0.0995628i
$730$	−2.67607e18	−	1.94428e18i	−0.654483	−	0.475509i
$731$	−1.13047e18	−	3.47923e18i	−0.274029	−	0.843374i
$732$	4.76183e17	+	1.46554e18i	0.114407	+	0.352108i
$733$	4.86370e18	+	3.53369e18i	1.15822	+	0.841496i	0.989552	−	0.144177i	$-0.0460535\pi$
$733$	4.86370e18	+	3.53369e18i	1.15822	+	0.841496i	0.168668	+	0.985673i	$0.446053\pi$
$734$	−1.43704e18	+	1.04407e18i	−0.339190	+	0.246436i
$735$	1.41009e18	−	4.33982e18i	0.329898	−	1.01532i
$736$	−6.25286e17			−0.145002
$737$	2.90522e18	+	7.57973e16i	0.667791	+	0.0174227i
$738$	−1.21492e18			−0.276810
$739$	1.65805e18	−	5.10295e18i	0.374462	−	1.15248i	−0.569378	−	0.822076i	$-0.692816\pi$
$739$	1.65805e18	−	5.10295e18i	0.374462	−	1.15248i	0.943841	−	0.330401i	$-0.107184\pi$
$740$	−1.88157e18	+	1.36704e18i	−0.421225	+	0.306038i
$741$	1.28047e18	+	9.30317e17i	0.284153	+	0.206449i
$742$	1.66262e18	+	5.11703e18i	0.365737	+	1.12562i
$743$	−8.39468e17	−	2.58362e18i	−0.183053	−	0.563379i	0.816856	−	0.576841i	$-0.195715\pi$
$743$	−8.39468e17	−	2.58362e18i	−0.183053	−	0.563379i	−0.999909	+	0.0134620i	$0.995715\pi$
$744$	−4.73345e17	−	3.43905e17i	−0.102318	−	0.0743387i
$745$	−3.12360e18	+	2.26943e18i	−0.669330	+	0.486296i
$746$	−1.54850e18	+	4.76579e18i	−0.328934	+	1.01235i
$747$	1.53984e18			0.324259
$748$	−1.00857e18	+	2.84897e18i	−0.210544	+	0.594740i
$749$	−3.69468e18			−0.764619
$750$	5.19614e17	−	1.59921e18i	0.106606	−	0.328100i
$751$	−9.97283e17	+	7.24569e17i	−0.202842	+	0.147374i	−0.684569	−	0.728948i	$-0.740010\pi$
$751$	−9.97283e17	+	7.24569e17i	−0.202842	+	0.147374i	0.481727	+	0.876321i	$0.340010\pi$
$752$	1.97201e18	+	1.43275e18i	0.397643	+	0.288905i
$753$	8.19548e17	+	2.52231e18i	0.163835	+	0.504233i
$754$	1.12440e18	+	3.46054e18i	0.222847	+	0.685852i
$755$	6.50856e18	+	4.72875e18i	1.27888	+	0.929161i
$756$	2.74556e18	−	1.99477e18i	0.534859	−	0.388598i
$757$	2.20650e18	−	6.79092e18i	0.426168	−	1.31161i	−0.475703	−	0.879606i	$-0.657806\pi$
$757$	2.20650e18	−	6.79092e18i	0.426168	−	1.31161i	0.901871	−	0.432005i	$-0.142194\pi$
$758$	−8.35706e17			−0.160031
$759$	1.74761e18	−	1.20134e18i	0.331797	−	0.228084i
$760$	−1.80290e18			−0.339378
$761$	−1.20347e18	+	3.70391e18i	−0.224614	+	0.691291i	0.773717	+	0.633532i	$0.218395\pi$
$761$	−1.20347e18	+	3.70391e18i	−0.224614	+	0.691291i	−0.998331	+	0.0577587i	$0.981605\pi$
$762$	2.09830e17	−	1.52450e17i	0.0388293	−	0.0282112i
$763$	4.74638e18	+	3.44844e18i	0.870869	+	0.632723i
$764$	5.20696e17	+	1.60254e18i	0.0947278	+	0.291542i
$765$	2.65314e18	+	8.16552e18i	0.478586	+	1.47294i
$766$	−3.46197e18	−	2.51527e18i	−0.619207	−	0.449880i
$767$	−9.37648e18	+	6.81241e18i	−1.66291	+	1.20818i
$768$	5.39100e16	−	1.65918e17i	0.00948029	−	0.0291773i
$769$	−1.23890e18			−0.216030			−0.108015	−	0.994149i	$-0.534450\pi$
$769$	−1.23890e18			−0.216030			−0.108015	+	0.994149i	$0.534450\pi$
$770$	−8.03444e18	−	6.16382e18i	−1.38920	−	1.06576i
$771$	−6.14932e17			−0.105432
$772$	−4.79556e16	+	1.47592e17i	−0.00815317	+	0.0250929i
$773$	−3.91192e18	+	2.84218e18i	−0.659514	+	0.479165i	−0.866499	−	0.499179i	$-0.833635\pi$
$773$	−3.91192e18	+	2.84218e18i	−0.659514	+	0.479165i	0.206985	+	0.978344i	$0.433635\pi$
$774$	1.82537e18	+	1.32621e18i	0.305164	+	0.221715i
$775$	2.19337e18	+	6.75048e18i	0.363622	+	1.11911i
$776$	3.91497e17	+	1.20490e18i	0.0643616	+	0.198085i
$777$	−2.40218e18	−	1.74528e18i	−0.391623	−	0.284531i
$778$	6.18007e18	−	4.49009e18i	0.999140	−	0.725918i
$779$	−5.90093e17	+	1.81612e18i	−0.0946078	+	0.291173i
$780$	3.00862e18			0.478358
$781$	1.47405e18	+	4.97454e18i	0.232423	+	0.784371i
$782$	4.68029e18			0.731861
$783$	−1.45578e18	+	4.48044e18i	−0.225759	+	0.694815i
$784$	−1.76881e18	+	1.28512e18i	−0.272036	+	0.197646i
$785$	−1.45162e19	−	1.05466e19i	−2.21412	−	1.60865i
$786$	−9.15478e17	−	2.81755e18i	−0.138485	−	0.426212i
$787$	−9.37110e17	−	2.88413e18i	−0.140590	−	0.432692i	0.855827	−	0.517261i	$-0.173049\pi$
$787$	−9.37110e17	−	2.88413e18i	−0.140590	−	0.432692i	−0.996418	+	0.0845694i	$0.973049\pi$
$788$	4.40787e18	+	3.20251e18i	0.655856	+	0.476507i
$789$	3.78156e18	−	2.74746e18i	0.558046	−	0.405444i
$790$	−5.21519e17	+	1.60507e18i	−0.0763298	+	0.234919i
$791$	1.71757e19			2.49325
$792$	−5.29571e17	−	1.78717e18i	−0.0762448	−	0.257308i
$793$	1.27330e19			1.81825
$794$	2.06763e18	−	6.36350e18i	0.292845	−	0.901286i
$795$	−4.99620e18	+	3.62995e18i	−0.701865	+	0.509935i
$796$	−1.01395e18	−	7.36678e17i	−0.141280	−	0.102646i
$797$	3.05825e17	+	9.41232e17i	0.0422663	+	0.130082i	0.969963	−	0.243252i	$-0.0782143\pi$
$797$	3.05825e17	+	9.41232e17i	0.0422663	+	0.130082i	−0.927697	+	0.373335i	$0.878214\pi$
$798$	−7.11277e17	−	2.18909e18i	−0.0975035	−	0.300085i
$799$	−1.47606e19	−	1.07242e19i	−2.00701	−	1.45818i
$800$	−1.71220e18	+	1.24398e18i	−0.230924	+	0.167776i
$801$	2.76220e18	−	8.50118e18i	0.369525	−	1.13728i
$802$	−2.36368e18			−0.313657
$803$	−4.26477e18	−	3.27183e18i	−0.561365	−	0.430665i
$804$	1.25569e18			0.163952
$805$	−4.84603e18	+	1.49145e19i	−0.627643	+	1.93169i
$806$	−3.91126e18	+	2.84170e18i	−0.502504	+	0.365090i
$807$	2.79607e18	+	2.03147e18i	0.356345	+	0.258900i
$808$	9.58954e17	+	2.95136e18i	0.121234	+	0.373119i
$809$	−2.07739e18	−	6.39356e18i	−0.260527	−	0.801821i	−0.992690	−	0.120691i	$-0.961489\pi$
$809$	−2.07739e18	−	6.39356e18i	−0.260527	−	0.801821i	0.732163	−	0.681130i	$-0.238511\pi$
$810$	−2.49249e18	−	1.81090e18i	−0.310085	−	0.225290i
$811$	3.92597e18	−	2.85238e18i	0.484519	−	0.352024i	−0.318553	−	0.947905i	$-0.603197\pi$
$811$	3.92597e18	−	2.85238e18i	0.484519	−	0.352024i	0.803073	+	0.595881i	$0.203197\pi$
$812$	1.63518e18	−	5.03255e18i	0.200194	−	0.616133i
$813$	−8.32129e17			−0.101065
$814$	−3.11449e18	+	2.14097e18i	−0.375256	+	0.257959i
$815$	−1.14640e19			−1.37029
$816$	−4.03519e17	+	1.24190e18i	−0.0478495	+	0.147266i
$817$	2.86906e18	−	2.08449e18i	0.337517	−	0.245221i
$818$	2.63532e18	+	1.91467e18i	0.307565	+	0.223459i
$819$	−3.73929e18	−	1.15083e19i	−0.432956	−	1.33250i
$820$	1.12170e18	+	3.45223e18i	0.128850	+	0.396561i
$821$	6.82410e18	+	4.95800e18i	0.777705	+	0.565036i	0.904289	−	0.426920i	$-0.140401\pi$
$821$	6.82410e18	+	4.95800e18i	0.777705	+	0.565036i	−0.126584	+	0.991956i	$0.540401\pi$
$822$	1.82239e18	−	1.32404e18i	0.206051	−	0.149705i
$823$	2.96062e18	−	9.11186e18i	0.332112	−	1.02213i	−0.636016	−	0.771676i	$-0.719419\pi$
$823$	2.96062e18	−	9.11186e18i	0.332112	−	1.02213i	0.968127	−	0.250458i	$-0.0805813\pi$
$824$	−1.39481e18			−0.155235
$825$	2.39537e18	−	6.76639e18i	0.264498	−	0.747147i
$826$	1.68549e19			1.84653
$827$	−1.80337e18	+	5.55022e18i	−0.196020	+	0.603287i	0.803943	+	0.594706i	$0.202732\pi$
$827$	−1.80337e18	+	5.55022e18i	−0.196020	+	0.603287i	−0.999963	+	0.00858129i	$0.997268\pi$
$828$	−2.33532e18	+	1.69671e18i	−0.251854	+	0.182983i
$829$	7.49355e17	+	5.44438e17i	0.0801831	+	0.0582565i	0.627155	−	0.778895i	$-0.284219\pi$
$829$	7.49355e17	+	5.44438e17i	0.0801831	+	0.0582565i	−0.546972	+	0.837151i	$0.684219\pi$
$830$	−1.42168e18	−	4.37549e18i	−0.150937	−	0.464535i
$831$	1.84689e18	+	5.68413e18i	0.194551	+	0.598767i
$832$	−1.16623e18	−	8.47315e17i	−0.121894	−	0.0885612i
$833$	1.32396e19	−	9.61914e18i	1.37304	−	0.997571i
$834$	2.92857e17	−	9.01321e17i	0.0301353	−	0.0927470i
$835$	−3.00234e19			−3.06547
$836$	−2.92876e18	−	7.64113e16i	−0.296717	−	0.00774135i
$837$	−6.25945e18			−0.629246
$838$	−4.20519e17	+	1.29422e18i	−0.0419468	+	0.129099i
$839$	−5.48645e18	+	3.98614e18i	−0.543049	+	0.394548i	−0.825216	−	0.564817i	$-0.808947\pi$
$839$	−5.48645e18	+	3.98614e18i	−0.543049	+	0.394548i	0.282167	+	0.959365i	$0.408947\pi$
$840$	−3.53973e18	−	2.57176e18i	−0.347660	−	0.252590i
$841$	−9.00817e17	−	2.77243e18i	−0.0877936	−	0.270201i
$842$	1.33877e18	+	4.12030e18i	0.129472	+	0.398474i
$843$	5.47197e18	+	3.97562e18i	0.525127	+	0.381527i
$844$	−4.39503e18	+	3.19317e18i	−0.418539	+	0.304086i
$845$	2.39465e18	−	7.36997e18i	0.226294	−	0.696461i
$846$	1.12528e19			1.05525
$847$	−1.27904e19	−	1.03534e19i	−1.19026	−	0.963479i
$848$	2.95897e18			0.273255
$849$	−4.27627e17	+	1.31610e18i	−0.0391891	+	0.120612i
$850$	1.28158e19	−	9.31126e18i	1.16553	−	0.846809i
$851$	4.73506e18	+	3.44022e18i	0.427350	+	0.310488i
$852$	6.92733e17	+	2.13201e18i	0.0620452	+	0.190956i
$853$	3.71885e18	+	1.14455e19i	0.330552	+	1.01734i	0.968872	+	0.247564i	$0.0796300\pi$
$853$	3.71885e18	+	1.14455e19i	0.330552	+	1.01734i	−0.638319	+	0.769772i	$0.720370\pi$
$854$	−1.49807e19	−	1.08841e19i	−1.32147	−	0.960101i
$855$	−6.73348e18	+	4.89216e18i	−0.589467	+	0.428273i
$856$	−6.27897e17	+	1.93247e18i	−0.0545518	+	0.167893i
$857$	−9.75331e18			−0.840963			−0.420481	−	0.907301i	$-0.638139\pi$
$857$	−9.75331e18			−0.840963			−0.420481	+	0.907301i	$0.638139\pi$
$858$	4.88741e18	+	1.27512e17i	0.418226	+	0.0109115i
$859$	−1.06763e19			−0.906707			−0.453353	−	0.891331i	$-0.649772\pi$
$859$	−1.06763e19			−0.906707			−0.453353	+	0.891331i	$0.649772\pi$
$860$	2.08314e18	−	6.41126e18i	0.175582	−	0.540385i
$861$	−3.74917e18	+	2.72393e18i	−0.313628	+	0.227864i
$862$	−9.12638e17	−	6.63070e17i	−0.0757707	−	0.0550506i
$863$	−2.84113e18	−	8.74411e18i	−0.234111	−	0.720519i	−0.997238	−	0.0742706i	$-0.976337\pi$
$863$	−2.84113e18	−	8.74411e18i	−0.234111	−	0.720519i	0.763127	−	0.646248i	$-0.223663\pi$
$864$	−5.76747e17	−	1.77504e18i	−0.0471678	−	0.145168i
$865$	2.35674e19	+	1.71227e19i	1.91296	+	1.38985i
$866$	−4.89683e17	+	3.55776e17i	−0.0394502	+	0.0286622i
$867$	1.12336e18	−	3.45734e18i	0.0898244	−	0.276451i
$868$	7.03078e18			0.557989
$869$	−9.15217e17	+	2.58528e18i	−0.0720934	+	0.203647i
$870$	6.07369e18			0.474873
$871$	3.20630e18	−	9.86796e18i	0.248820	−	0.765790i
$872$	2.61031e18	−	1.89650e18i	0.201064	−	0.146082i
$873$	4.73166e18	+	3.43775e18i	0.361760	+	0.262834i
$874$	1.40204e18	+	4.31503e18i	0.106398	+	0.327461i
$875$	6.24402e18	+	1.92171e19i	0.470340	+	1.44756i
$876$	−1.87893e18	−	1.36512e18i	−0.140486	−	0.102069i
$877$	−8.73214e18	+	6.34427e18i	−0.648072	+	0.470852i	−0.862614	−	0.505863i	$-0.831174\pi$
$877$	−8.73214e18	+	6.34427e18i	−0.648072	+	0.470852i	0.214542	+	0.976715i	$0.431174\pi$
$878$	−2.66267e17	+	8.19485e17i	−0.0196156	+	0.0603707i
$879$	−7.80233e18			−0.570554
$880$	−4.58935e18	+	3.15482e18i	−0.333130	+	0.229001i
$881$	1.31967e19			0.950871			0.475435	−	0.879751i	$-0.342291\pi$
$881$	1.31967e19			0.950871			0.475435	+	0.879751i	$0.342291\pi$
$882$	−3.11900e18	+	9.59930e18i	−0.223085	+	0.686584i
$883$	2.84301e18	−	2.06556e18i	0.201852	−	0.146654i	−0.482267	−	0.876024i	$-0.660187\pi$
$883$	2.84301e18	−	2.06556e18i	0.201852	−	0.146654i	0.684120	+	0.729370i	$0.260187\pi$
$884$	8.72927e18	+	6.34219e18i	0.615231	+	0.446991i
$885$	5.97832e18	+	1.83994e19i	0.418262	+	1.28728i
$886$	−1.73067e18	−	5.32646e18i	−0.120198	−	0.369930i
$887$	1.49805e19	+	1.08840e19i	1.03282	+	0.750386i	0.968871	−	0.247567i	$-0.0796310\pi$
$887$	1.49805e19	+	1.08840e19i	1.03282	+	0.750386i	0.0639474	+	0.997953i	$0.479631\pi$
$888$	−1.32109e18	+	9.59832e17i	−0.0904169	+	0.0656917i
$889$	−9.63109e17	+	2.96414e18i	−0.0654356	+	0.201390i
$890$	−2.67065e19			−1.80128
$891$	−3.97221e18	−	3.04738e18i	−0.265967	−	0.204043i
$892$	1.68845e17			0.0112232
$893$	5.46554e18	−	1.68212e19i	0.360660	−	1.11000i
$894$	−2.19315e18	+	1.59342e18i	−0.143673	+	0.104385i
$895$	−5.63875e18	−	4.09679e18i	−0.366719	−	0.266437i
$896$	6.47818e17	+	1.99378e18i	0.0418264	+	0.128729i
$897$	−2.33967e18	−	7.20077e18i	−0.149970	−	0.461560i
$898$	−3.53874e18	−	2.57104e18i	−0.225192	−	0.163611i
$899$	−7.89590e18	+	5.73671e18i	−0.498843	+	0.362431i
$900$	−3.01917e18	+	9.29205e18i	−0.189370	+	0.582821i
$901$	−2.21480e19			−1.37919
$902$	1.67585e18	+	5.65557e18i	0.103608	+	0.349650i
$903$	8.60639e18			0.528264
$904$	2.91894e18	−	8.98357e18i	0.177881	−	0.547462i
$905$	1.80149e19	−	1.30886e19i	1.08998	−	0.791914i
$906$	4.56981e18	+	3.32016e18i	0.274514	+	0.199446i
$907$	1.21660e18	+	3.74432e18i	0.0725608	+	0.223319i	0.980759	−	0.195220i	$-0.0625422\pi$
$907$	1.21660e18	+	3.74432e18i	0.0725608	+	0.223319i	−0.908199	+	0.418539i	$0.862542\pi$
$908$	1.68936e18	+	5.19931e18i	0.100038	+	0.307884i
$909$	1.15900e19	+	8.42061e18i	0.681424	+	0.495083i
$910$	−2.92488e19	+	2.12505e19i	−1.70742	+	1.24051i
$911$	2.85024e18	−	8.77215e18i	0.165201	−	0.508436i	−0.833850	−	0.551991i	$-0.813868\pi$
$911$	2.85024e18	−	8.77215e18i	0.165201	−	0.508436i	0.999051	+	0.0435548i	$0.0138683\pi$
$912$	−1.26586e18			−0.0728483
$913$	−2.12403e18	−	7.16808e18i	−0.121367	−	0.409584i
$914$	1.75275e19			0.994421
$915$	6.56792e18	−	2.02140e19i	0.369991	−	1.13871i
$916$	6.90041e18	−	5.01344e18i	0.385971	−	0.280424i
$917$	2.88009e19	+	2.09251e19i	1.59958	+	1.16216i
$918$	4.31697e18	+	1.32863e19i	0.238068	+	0.732699i
$919$	7.34834e17	+	2.26159e18i	0.0402382	+	0.123840i	0.969158	−	0.246441i	$-0.0792612\pi$
$919$	7.34834e17	+	2.26159e18i	0.0402382	+	0.123840i	−0.928920	+	0.370282i	$0.879261\pi$
$920$	6.97735e18	+	5.06934e18i	0.379376	+	0.275633i
$921$	−8.93705e18	+	6.49314e18i	−0.482510	+	0.350564i
$922$	6.94685e18	−	2.13802e19i	0.372424	−	1.14620i
$923$	1.85235e19			0.986078
$924$	−5.64117e18	−	4.32776e18i	−0.298196	−	0.228768i
$925$	1.98100e19			1.03983
$926$	−1.56978e18	+	4.83128e18i	−0.0818213	+	0.251820i
$927$	−5.20935e18	+	3.78481e18i	−0.269628	+	0.195896i
$928$	−2.35434e18	−	1.71053e18i	−0.121006	−	0.0879160i
$929$	−3.91212e18	−	1.20403e19i	−0.199669	−	0.614517i	−0.999890	−	0.0148128i	$-0.995285\pi$
$929$	−3.91212e18	−	1.20403e19i	−0.199669	−	0.614517i	0.800221	−	0.599705i	$-0.204715\pi$
$930$	2.49377e18	+	7.67504e18i	0.126391	+	0.388993i
$931$	1.28345e19	+	9.32483e18i	0.645962	+	0.469319i
$932$	−3.42840e18	+	2.49088e18i	−0.171352	+	0.124494i
$933$	1.61451e17	−	4.96895e17i	0.00801328	−	0.0246623i
$934$	−1.24404e19			−0.613170
$935$	3.43515e19	−	2.36140e19i	1.68140	−	1.15583i
$936$	−6.65481e18			−0.323477
$937$	−2.96385e18	+	9.12179e18i	−0.143070	+	0.440324i	−0.996758	−	0.0804609i	$-0.974361\pi$
$937$	−2.96385e18	+	9.12179e18i	−0.143070	+	0.440324i	0.853688	+	0.520785i	$0.174361\pi$
$938$	−1.22074e19	+	8.86919e18i	−0.585200	+	0.425173i
$939$	−1.20653e19	−	8.76598e18i	−0.574398	−	0.417325i
$940$	−1.03894e19	−	3.19751e19i	−0.491199	−	1.51176i
$941$	2.51071e18	+	7.72718e18i	0.117887	+	0.362818i	0.992538	−	0.121935i	$-0.0389098\pi$
$941$	2.51071e18	+	7.72718e18i	0.117887	+	0.362818i	−0.874652	+	0.484752i	$0.838910\pi$
$942$	−1.01922e19	−	7.40504e18i	−0.475265	−	0.345300i
$943$	7.39019e18	−	5.36929e18i	0.342239	−	0.248651i
$944$	2.86443e18	−	8.81580e18i	0.131741	−	0.405456i
$945$	−4.68088e19			−2.13807
$946$	3.65572e18	−	1.03266e19i	0.165837	−	0.468451i
$947$	−3.93632e19			−1.77344			−0.886718	−	0.462311i	$-0.847021\pi$
$947$	−3.93632e19			−1.77344			−0.886718	+	0.462311i	$0.847021\pi$
$948$	−3.66171e17	+	1.12696e18i	−0.0163843	+	0.0504258i
$949$	−1.55256e19	+	1.12800e19i	−0.689952	+	0.501279i
$950$	1.24237e19	+	9.02637e18i	0.548338	+	0.398391i
$951$	−1.00102e17	−	3.08081e17i	−0.00438801	−	0.0135049i
$952$	−4.84894e18	−	1.49235e19i	−0.211109	−	0.649727i
$953$	−1.64810e19	−	1.19741e19i	−0.712655	−	0.517774i	0.171374	−	0.985206i	$-0.445179\pi$
$953$	−1.64810e19	−	1.19741e19i	−0.712655	−	0.517774i	−0.884029	+	0.467432i	$0.845179\pi$
$954$	1.10512e19	−	8.02914e18i	0.474617	−	0.344829i
$955$	7.18188e18	−	2.21036e19i	0.306349	−	0.942845i
$956$	−4.55856e18			−0.193131
$957$	9.86651e18	+	2.57417e17i	0.415179	+	0.0108320i
$958$	−2.09720e19			−0.876526
$959$	−8.36468e18	+	2.57438e19i	−0.347239	+	1.06869i
$960$	−1.94670e18	+	1.41436e18i	−0.0802668	+	0.0583172i
$961$	9.26305e18	+	6.73000e18i	0.379361	+	0.275622i
$962$	4.16963e18	+	1.28328e19i	0.169613	+	0.522016i
$963$	2.89866e18	+	8.92117e18i	0.117119	+	0.360455i
$964$	−1.09479e17	−	7.95415e16i	−0.00439372	−	0.00319222i
$965$	1.73168e18	−	1.25814e18i	0.0690305	−	0.0501536i
$966$	−3.40251e18	+	1.04718e19i	−0.134725	+	0.414641i
$967$	1.80292e19			0.709093			0.354547	−	0.935038i	$-0.384635\pi$
$967$	1.80292e19			0.709093			0.354547	+	0.935038i	$0.384635\pi$
$968$	−7.58896e18	+	4.93040e18i	−0.296478	+	0.192616i
$969$	9.47501e18			0.367684
$970$	5.39986e18	−	1.66191e19i	0.208145	−	0.640605i
$971$	2.83999e18	−	2.06337e18i	0.108741	−	0.0790047i	−0.532086	−	0.846690i	$-0.678592\pi$
$971$	2.83999e18	−	2.06337e18i	0.108741	−	0.0790047i	0.640827	+	0.767686i	$0.278592\pi$
$972$	−1.09333e19	−	7.94350e18i	−0.415834	−	0.302121i
$973$	3.51916e18	+	1.08309e19i	0.132955	+	0.409194i
$974$	7.11139e18	+	2.18866e19i	0.266883	+	0.821383i
$975$	−2.07323e19	−	1.50629e19i	−0.772889	−	0.561537i
$976$	−8.23875e18	+	5.98580e18i	−0.305097	+	0.221666i
$977$	9.91026e18	−	3.05006e19i	0.364561	−	1.12200i	−0.585694	−	0.810532i	$-0.699178\pi$
$977$	9.91026e18	−	3.05006e19i	0.364561	−	1.12200i	0.950255	−	0.311472i	$-0.100822\pi$
$978$	−8.04914e18			−0.294135
$979$	−4.33838e19	−	1.13188e18i	−1.57485	−	0.0410880i
$980$	3.01563e19			1.08745
$981$	4.60284e18	−	1.41661e19i	0.164883	−	0.507459i
$982$	1.01224e19	−	7.35432e18i	0.360211	−	0.261708i
$983$	−3.41072e18	−	2.47803e18i	−0.120572	−	0.0876009i	0.525865	−	0.850568i	$-0.323742\pi$
$983$	−3.41072e18	−	2.47803e18i	−0.120572	−	0.0876009i	−0.646437	+	0.762967i	$0.723742\pi$
$984$	7.87570e17	+	2.42389e18i	0.0276580	+	0.0851226i
$985$	−2.32224e19	−	7.14713e19i	−0.810163	−	2.49343i
$986$	1.76223e19	+	1.28034e19i	0.610749	+	0.443735i
$987$	3.47254e19	−	2.52295e19i	1.19560	−	0.868655i
$988$	−3.23227e18	+	9.94789e18i	−0.110557	+	0.340260i
$989$	−1.69645e19			−0.576456
$990$	−8.57973e18	+	2.42358e19i	−0.289631	+	0.818142i
$991$	4.45272e19			1.49330			0.746649	−	0.665218i	$-0.231662\pi$
$991$	4.45272e19			1.49330			0.746649	+	0.665218i	$0.231662\pi$
$992$	1.19485e18	−	3.67738e18i	0.0398097	−	0.122522i
$993$	−8.39419e18	+	6.09873e18i	−0.277849	+	0.201869i
$994$	−2.17934e19	−	1.58338e19i	−0.716659	−	0.520684i
$995$	5.34190e18	+	1.64407e19i	0.174520	+	0.537118i
$996$	−9.98196e17	−	3.07213e18i	−0.0323989	−	0.0997135i
$997$	2.53865e19	+	1.84444e19i	0.818624	+	0.594765i	0.916318	−	0.400451i	$-0.131147\pi$
$997$	2.53865e19	+	1.84444e19i	0.818624	+	0.594765i	−0.0976939	+	0.995217i	$0.531147\pi$
$998$	1.85520e19	−	1.34788e19i	0.594350	−	0.431820i
$999$	−5.39852e18	+	1.66149e19i	−0.171830	+	0.528838i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.14.c.b.9.3	yes	28
11.5	even	5	inner	22.14.c.b.5.3	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.14.c.b.5.3	✓	28	11.5	even	5	inner
22.14.c.b.9.3	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} +(-501.424 + 364.306i) q^{3} +(-3313.73 - 2407.57i) q^{4} +(17458.1 + 53730.4i) q^{5} +(12257.7 + 37725.4i) q^{6} +(-385628. - 280175. i) q^{7} +(-212079. + 154084. i) q^{8} +(-373966. + 1.15095e6i) q^{9} +3.61571e6 q^{10} +(5.87360e6 + 153242. i) q^{11} +2.53868e6 q^{12} +(6.48230e6 - 1.99505e7i) q^{13} +(-2.46802e7 + 1.79312e7i) q^{14} +(-2.83282e7 - 2.05816e7i) q^{15} +(5.18444e6 + 1.59561e7i) q^{16} +(-3.88058e7 - 1.19432e8i) q^{17} +(6.26595e7 + 4.55248e7i) q^{18} +(9.84864e7 - 7.15545e7i) q^{19} +(7.15083e7 - 2.20080e8i) q^{20} +2.95432e8 q^{21} +(1.25490e8 - 3.54482e8i) q^{22} -5.82343e8 q^{23} +(5.02076e7 - 1.54523e8i) q^{24} +(-1.59461e9 + 1.15855e9i) q^{25} +(-1.08614e9 - 7.89124e8i) q^{26} +(-5.37137e8 - 1.65314e9i) q^{27} +(6.03327e8 + 1.85685e9i) q^{28} +(-2.19265e9 - 1.59305e9i) q^{29} +(-1.81301e9 + 1.31723e9i) q^{30} +(1.11280e9 - 3.42483e9i) q^{31} +1.07374e9 q^{32} +(-3.00099e9 + 2.06295e9i) q^{33} -8.03700e9 q^{34} +(8.32161e9 - 2.56113e10i) q^{35} +(4.01021e9 - 2.91359e9i) q^{36} +(-8.13105e9 - 5.90756e9i) q^{37} +(-2.40758e9 - 7.40977e9i) q^{38} +(4.01769e9 + 1.23652e10i) q^{39} +(-1.19815e10 - 8.70508e9i) q^{40} +(-1.26905e10 + 9.22015e9i) q^{41} +(5.84279e9 - 1.79823e10i) q^{42} +2.91315e10 q^{43} +(-1.90946e10 - 1.46489e10i) q^{44} -6.83697e10 q^{45} +(-1.15170e10 + 3.54458e10i) q^{46} +(1.17541e11 - 8.53986e10i) q^{47} +(-8.41250e9 - 6.11204e9i) q^{48} +(4.02704e10 + 1.23940e11i) q^{49} +(3.89815e10 + 1.19973e11i) q^{50} +(6.29679e10 + 4.57488e10i) q^{51} +(-6.95127e10 + 5.05039e10i) q^{52} +(5.45008e10 - 1.67736e11i) q^{53} -1.11246e11 q^{54} +(9.43081e10 + 3.18267e11i) q^{55} +1.24954e11 q^{56} +(-2.33157e10 + 7.17583e10i) q^{57} +(-1.40330e11 + 1.01955e11i) q^{58} +(-4.46985e11 - 3.24754e11i) q^{59} +(4.43204e10 + 1.36404e11i) q^{60} +(1.87571e11 + 5.77285e11i) q^{61} +(-1.86453e11 - 1.35466e11i) q^{62} +(4.66678e11 - 3.39062e11i) q^{63} +(2.12355e10 - 6.53561e10i) q^{64} +1.18512e12 q^{65} +(6.62159e10 + 2.23462e11i) q^{66} +4.94624e11 q^{67} +(-1.58948e11 + 4.89193e11i) q^{68} +(2.92001e11 - 2.12151e11i) q^{69} +(-1.39432e12 - 1.01303e12i) q^{70} +(2.72872e11 + 8.39813e11i) q^{71} +(-9.80329e10 - 3.01714e11i) q^{72} +(-7.40121e11 - 5.37729e11i) q^{73} +(-5.20387e11 + 3.78084e11i) q^{74} +(3.77507e11 - 1.16185e12i) q^{75} -4.98630e11 q^{76} +(-2.22209e12 - 1.70473e12i) q^{77} +8.32097e11 q^{78} +(-1.44237e11 + 4.43915e11i) q^{79} +(-7.66817e11 + 5.57125e11i) q^{80} +(-6.89348e11 - 5.00841e11i) q^{81} +(3.10229e11 + 9.54785e11i) q^{82} +(-3.93195e11 - 1.21013e12i) q^{83} +(-9.78984e11 - 7.11274e11i) q^{84} +(5.73965e12 - 4.17010e12i) q^{85} +(5.76136e11 - 1.77317e12i) q^{86} +1.67980e12 q^{87} +(-1.26928e12 + 8.72531e11i) q^{88} -7.38624e12 q^{89} +(-1.35215e12 + 4.16150e12i) q^{90} +(-8.08937e12 + 5.87727e12i) q^{91} +(1.92973e12 + 1.40203e12i) q^{92} +(6.89704e11 + 2.12269e12i) q^{93} +(-2.87339e12 - 8.84338e12i) q^{94} +(5.56404e12 + 4.04251e12i) q^{95} +(-5.38400e11 + 3.91170e11i) q^{96} +(1.49344e12 - 4.59634e12i) q^{97} +8.34034e12 q^{98} +(-2.37290e12 + 6.70291e12i) 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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