LMFDB - Embedded newform 456.2.bj.a.173.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [456,2,Mod(29,456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(456, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 9, 17]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("456.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.bj (of order $18$, degree $6$, 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:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$456$
Relative dimension:	$76$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			173.11
Character	$\chi$	$=$	456.173
Dual form			456.2.bj.a.29.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28317 - 0.594528i) q^{2} +(0.512773 - 1.65441i) q^{3} +(1.29307 + 1.52577i) q^{4} +(-2.20694 + 0.803259i) q^{5} +(-1.64157 + 1.81804i) q^{6} +(0.552347 + 0.956693i) q^{7} +(-0.752130 - 2.72659i) q^{8} +(-2.47413 - 1.69667i) q^{9} +O(q^{10})$	\(q+(-1.28317 - 0.594528i) q^{2} +(0.512773 - 1.65441i) q^{3} +(1.29307 + 1.52577i) q^{4} +(-2.20694 + 0.803259i) q^{5} +(-1.64157 + 1.81804i) q^{6} +(0.552347 + 0.956693i) q^{7} +(-0.752130 - 2.72659i) q^{8} +(-2.47413 - 1.69667i) q^{9} +(3.30945 + 0.281363i) q^{10} +(0.221304 - 0.383309i) q^{11} +(3.18729 - 1.35690i) q^{12} +(-1.26221 + 1.05912i) q^{13} +(-0.139977 - 1.55599i) q^{14} +(0.197261 + 4.06306i) q^{15} +(-0.655919 + 3.94585i) q^{16} +(-7.21044 - 1.27139i) q^{17} +(2.16602 + 3.64806i) q^{18} +(-4.34084 - 0.396393i) q^{19} +(-4.07932 - 2.32859i) q^{20} +(1.86599 - 0.423240i) q^{21} +(-0.511860 + 0.360282i) q^{22} +(-1.25995 + 3.46169i) q^{23} +(-4.89656 - 0.153792i) q^{24} +(0.395123 - 0.331548i) q^{25} +(2.24932 - 0.608619i) q^{26} +(-4.07565 + 3.22321i) q^{27} +(-0.745463 + 2.07983i) q^{28} +(4.46539 - 0.787368i) q^{29} +(2.16248 - 5.33090i) q^{30} +(-2.69779 + 1.55757i) q^{31} +(3.18758 - 4.67326i) q^{32} +(-0.520671 - 0.562677i) q^{33} +(8.49637 + 5.91822i) q^{34} +(-1.98747 - 1.66768i) q^{35} +(-0.610510 - 5.96886i) q^{36} +0.704942 q^{37} +(5.33439 + 3.08939i) q^{38} +(1.10499 + 2.63130i) q^{39} +(3.85006 + 5.41326i) q^{40} +(1.76645 + 1.48223i) q^{41} +(-2.64602 - 0.566290i) q^{42} +(0.639362 + 1.75663i) q^{43} +(0.871003 - 0.157990i) q^{44} +(6.82311 + 1.75708i) q^{45} +(3.67481 - 3.69288i) q^{46} +(-3.26043 + 0.574902i) q^{47} +(6.19171 + 3.10849i) q^{48} +(2.88983 - 5.00533i) q^{49} +(-0.704126 + 0.190522i) q^{50} +(-5.80072 + 11.2771i) q^{51} +(-3.24811 - 0.556317i) q^{52} +(-4.05761 + 11.1482i) q^{53} +(7.14606 - 1.71285i) q^{54} +(-0.180507 + 1.02370i) q^{55} +(2.19307 - 2.22558i) q^{56} +(-2.88166 + 6.97825i) q^{57} +(-6.19798 - 1.64446i) q^{58} +(0.922560 + 0.162672i) q^{59} +(-5.94421 + 5.55481i) q^{60} +(1.91628 - 5.26494i) q^{61} +(4.38775 - 0.394723i) q^{62} +(0.256616 - 3.30413i) q^{63} +(-6.86860 + 4.10150i) q^{64} +(1.93487 - 3.35130i) q^{65} +(0.333585 + 1.03157i) q^{66} +(-0.957812 - 5.43202i) q^{67} +(-7.38378 - 12.6454i) q^{68} +(5.08098 + 3.85953i) q^{69} +(1.55878 + 3.32153i) q^{70} +(-12.9192 + 4.70222i) q^{71} +(-2.76526 + 8.02205i) q^{72} +(-10.1071 - 8.48087i) q^{73} +(-0.904564 - 0.419107i) q^{74} +(-0.345907 - 0.823703i) q^{75} +(-5.00822 - 7.13566i) q^{76} +0.488946 q^{77} +(0.146486 - 4.03337i) q^{78} +(4.00362 - 4.77133i) q^{79} +(-1.72197 - 9.23513i) q^{80} +(3.24262 + 8.39556i) q^{81} +(-1.38544 - 2.95216i) q^{82} +(2.91194 + 5.04363i) q^{83} +(3.05863 + 2.29978i) q^{84} +(16.9342 - 2.98596i) q^{85} +(0.223953 - 2.63418i) q^{86} +(0.987101 - 7.79131i) q^{87} +(-1.21158 - 0.315106i) q^{88} +(10.9032 - 9.14891i) q^{89} +(-7.71061 - 6.31117i) q^{90} +(-1.71043 - 0.622547i) q^{91} +(-6.91094 + 2.55383i) q^{92} +(1.19350 + 5.26192i) q^{93} +(4.52549 + 1.20072i) q^{94} +(9.89836 - 2.61200i) q^{95} +(-6.09697 - 7.66987i) q^{96} +(-5.14609 - 0.907395i) q^{97} +(-6.68396 + 4.70463i) q^{98} +(-1.19788 + 0.572877i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 456 q - 6 q^{4} - 6 q^{6} - 12 q^{7} - 12 q^{9}+O(q^{10}) $ 456 * q - 6 * q^4 - 6 * q^6 - 12 * q^7 - 12 * q^9	$ 456 q - 6 q^{4} - 6 q^{6} - 12 q^{7} - 12 q^{9} - 6 q^{10} - 9 q^{12} - 12 q^{15} - 6 q^{16} + 6 q^{24} - 24 q^{25} + 12 q^{28} - 6 q^{30} - 36 q^{31} + 6 q^{33} + 30 q^{34} - 66 q^{36} - 24 q^{39} - 42 q^{40} + 39 q^{42} - 18 q^{46} - 15 q^{48} - 168 q^{49} - 36 q^{52} - 45 q^{54} + 36 q^{55} - 12 q^{57} - 96 q^{58} - 18 q^{60} + 30 q^{63} - 48 q^{64} - 18 q^{66} - 78 q^{70} + 60 q^{72} - 12 q^{76} + 45 q^{78} - 24 q^{79} - 156 q^{82} - 9 q^{84} - 6 q^{87} - 90 q^{88} + 84 q^{90} - 162 q^{96} - 24 q^{97}+O(q^{100}) $ 456 * q - 6 * q^4 - 6 * q^6 - 12 * q^7 - 12 * q^9 - 6 * q^10 - 9 * q^12 - 12 * q^15 - 6 * q^16 + 6 * q^24 - 24 * q^25 + 12 * q^28 - 6 * q^30 - 36 * q^31 + 6 * q^33 + 30 * q^34 - 66 * q^36 - 24 * q^39 - 42 * q^40 + 39 * q^42 - 18 * q^46 - 15 * q^48 - 168 * q^49 - 36 * q^52 - 45 * q^54 + 36 * q^55 - 12 * q^57 - 96 * q^58 - 18 * q^60 + 30 * q^63 - 48 * q^64 - 18 * q^66 - 78 * q^70 + 60 * q^72 - 12 * q^76 + 45 * q^78 - 24 * q^79 - 156 * q^82 - 9 * q^84 - 6 * q^87 - 90 * q^88 + 84 * q^90 - 162 * q^96 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$-1$	$-1$	$1$

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 $

$2$	−1.28317	−	0.594528i	−0.907341	−	0.420394i
$2$	−1.28317	−	0.594528i	−0.907341	−	0.420394i
$3$	0.512773	−	1.65441i	0.296050	−	0.955173i
$3$	0.512773	−	1.65441i	0.296050	−	0.955173i
$4$	1.29307	+	1.52577i	0.646537	+	0.762883i
$5$	−2.20694	+	0.803259i	−0.986972	+	0.359229i	−0.784547	−	0.620069i	$-0.787105\pi$
$5$	−2.20694	+	0.803259i	−0.986972	+	0.359229i	−0.202425	+	0.979298i	$0.564882\pi$
$6$	−1.64157	+	1.81804i	−0.670167	+	0.742210i
$7$	0.552347	+	0.956693i	0.208767	+	0.361596i	0.951327	−	0.308185i	$-0.0997215\pi$
$7$	0.552347	+	0.956693i	0.208767	+	0.361596i	−0.742559	+	0.669781i	$0.766388\pi$
$8$	−0.752130	−	2.72659i	−0.265918	−	0.963996i
$9$	−2.47413	−	1.69667i	−0.824709	−	0.565557i
$10$	3.30945	+	0.281363i	1.04654	+	0.0889747i
$11$	0.221304	−	0.383309i	0.0667256	−	0.115572i	−0.830733	−	0.556672i	$-0.812078\pi$
$11$	0.221304	−	0.383309i	0.0667256	−	0.115572i	0.897458	+	0.441100i	$0.145411\pi$
$12$	3.18729	−	1.35690i	0.920092	−	0.391703i
$13$	−1.26221	+	1.05912i	−0.350075	+	0.293748i	−0.800820	−	0.598905i	$-0.795603\pi$
$13$	−1.26221	+	1.05912i	−0.350075	+	0.293748i	0.450745	+	0.892653i	$0.351158\pi$
$14$	−0.139977	−	1.55599i	−0.0374105	−	0.415856i
$15$	0.197261	+	4.06306i	0.0509325	+	1.04908i
$16$	−0.655919	+	3.94585i	−0.163980	+	0.986464i
$17$	−7.21044	−	1.27139i	−1.74879	−	0.308358i	−0.794503	−	0.607260i	$-0.792269\pi$
$17$	−7.21044	−	1.27139i	−1.74879	−	0.308358i	−0.954284	+	0.298901i	$0.903380\pi$
$18$	2.16602	+	3.64806i	0.510536	+	0.859856i
$19$	−4.34084	−	0.396393i	−0.995856	−	0.0909388i
$19$	−4.34084	−	0.396393i	−0.995856	−	0.0909388i
$20$	−4.07932	−	2.32859i	−0.912163	−	0.520689i
$21$	1.86599	−	0.423240i	0.407192	−	0.0923586i
$22$	−0.511860	+	0.360282i	−0.109129	+	0.0768123i
$23$	−1.25995	+	3.46169i	−0.262718	+	0.721812i	0.736264	+	0.676695i	$0.236588\pi$
$23$	−1.25995	+	3.46169i	−0.262718	+	0.721812i	−0.998982	+	0.0451172i	$0.985634\pi$
$24$	−4.89656	−	0.153792i	−0.999507	−	0.0313927i
$25$	0.395123	−	0.331548i	0.0790246	−	0.0663095i
$26$	2.24932	−	0.608619i	0.441127	−	0.119360i
$27$	−4.07565	+	3.22321i	−0.784359	+	0.620307i
$28$	−0.745463	+	2.07983i	−0.140879	+	0.393050i
$29$	4.46539	−	0.787368i	0.829201	−	0.146211i	0.257091	−	0.966387i	$-0.417236\pi$
$29$	4.46539	−	0.787368i	0.829201	−	0.146211i	0.572110	+	0.820177i	$0.306125\pi$
$30$	2.16248	−	5.33090i	0.394813	−	0.973284i
$31$	−2.69779	+	1.55757i	−0.484537	+	0.279748i	−0.722305	−	0.691574i	$-0.756917\pi$
$31$	−2.69779	+	1.55757i	−0.484537	+	0.279748i	0.237768	+	0.971322i	$0.423584\pi$
$32$	3.18758	−	4.67326i	0.563490	−	0.826123i
$33$	−0.520671	−	0.562677i	−0.0906373	−	0.0979496i
$34$	8.49637	+	5.91822i	1.45712	+	1.01497i
$35$	−1.98747	−	1.66768i	−0.335943	−	0.281890i
$36$	−0.610510	−	5.96886i	−0.101752	−	0.994810i
$37$	0.704942			0.115892			0.0579459	−	0.998320i	$-0.481545\pi$
$37$	0.704942			0.115892			0.0579459	+	0.998320i	$0.481545\pi$
$38$	5.33439	+	3.08939i	0.865352	+	0.501165i
$39$	1.10499	+	2.63130i	0.176940	+	0.421346i
$40$	3.85006	+	5.41326i	0.608749	+	0.855912i
$41$	1.76645	+	1.48223i	0.275874	+	0.231485i	0.770218	−	0.637781i	$-0.220147\pi$
$41$	1.76645	+	1.48223i	0.275874	+	0.231485i	−0.494344	+	0.869266i	$0.664592\pi$
$42$	−2.64602	−	0.566290i	−0.408289	−	0.0873804i
$43$	0.639362	+	1.75663i	0.0975017	+	0.267884i	0.978849	−	0.204586i	$-0.0655848\pi$
$43$	0.639362	+	1.75663i	0.0975017	+	0.267884i	−0.881347	+	0.472470i	$0.843363\pi$
$44$	0.871003	−	0.157990i	0.131309	−	0.0238179i
$45$	6.82311	+	1.75708i	1.01713	+	0.261930i
$46$	3.67481	−	3.69288i	0.541821	−	0.544485i
$47$	−3.26043	+	0.574902i	−0.475582	+	0.0838580i	−0.406301	−	0.913739i	$-0.633182\pi$
$47$	−3.26043	+	0.574902i	−0.475582	+	0.0838580i	−0.0692811	+	0.997597i	$0.522071\pi$
$48$	6.19171	+	3.10849i	0.893697	+	0.448671i
$49$	2.88983	−	5.00533i	0.412832	−	0.715047i
$50$	−0.704126	+	0.190522i	−0.0995785	+	0.0269439i
$51$	−5.80072	+	11.2771i	−0.812263	+	1.57910i
$52$	−3.24811	−	0.556317i	−0.450431	−	0.0771473i
$53$	−4.05761	+	11.1482i	−0.557355	+	1.53132i	0.266104	+	0.963944i	$0.414264\pi$
$53$	−4.05761	+	11.1482i	−0.557355	+	1.53132i	−0.823459	+	0.567376i	$0.807959\pi$
$54$	7.14606	−	1.71285i	0.972455	−	0.233090i
$55$	−0.180507	+	1.02370i	−0.0243395	+	0.138036i
$56$	2.19307	−	2.22558i	0.293062	−	0.297406i
$57$	−2.88166	+	6.97825i	−0.381685	+	0.924292i
$58$	−6.19798	−	1.64446i	−0.813835	−	0.215929i
$59$	0.922560	+	0.162672i	0.120107	+	0.0211781i	0.233379	−	0.972386i	$-0.425022\pi$
$59$	0.922560	+	0.162672i	0.120107	+	0.0211781i	−0.113272	+	0.993564i	$0.536133\pi$
$60$	−5.94421	+	5.55481i	−0.767394	+	0.717123i
$61$	1.91628	−	5.26494i	0.245355	−	0.674107i	−0.754487	−	0.656315i	$-0.772114\pi$
$61$	1.91628	−	5.26494i	0.245355	−	0.674107i	0.999842	−	0.0177916i	$-0.00566353\pi$
$62$	4.38775	−	0.394723i	0.557245	−	0.0501299i
$63$	0.256616	−	3.30413i	0.0323305	−	0.416281i
$64$	−6.86860	+	4.10150i	−0.858575	+	0.512688i
$65$	1.93487	−	3.35130i	0.239992	−	0.415678i
$66$	0.333585	+	1.03157i	0.0410615	+	0.126977i
$67$	−0.957812	−	5.43202i	−0.117015	−	0.663627i	−0.985733	−	0.168319i	$-0.946166\pi$
$67$	−0.957812	−	5.43202i	−0.117015	−	0.663627i	0.868717	−	0.495308i	$-0.164945\pi$
$68$	−7.38378	−	12.6454i	−0.895414	−	1.53348i
$69$	5.08098	+	3.85953i	0.611678	+	0.464633i
$70$	1.55878	+	3.32153i	0.186310	+	0.396999i
$71$	−12.9192	+	4.70222i	−1.53323	+	0.558051i	−0.964410	−	0.264411i	$-0.914823\pi$
$71$	−12.9192	+	4.70222i	−1.53323	+	0.558051i	−0.568821	+	0.822461i	$0.692600\pi$
$72$	−2.76526	+	8.02205i	−0.325889	+	0.945408i
$73$	−10.1071	−	8.48087i	−1.18295	−	0.992611i	−0.999955	−	0.00949666i	$-0.996977\pi$
$73$	−10.1071	−	8.48087i	−1.18295	−	0.992611i	−0.182993	−	0.983114i	$-0.558578\pi$
$74$	−0.904564	−	0.419107i	−0.105153	−	0.0487202i
$75$	−0.345907	−	0.823703i	−0.0399418	−	0.0951131i
$76$	−5.00822	−	7.13566i	−0.574482	−	0.818517i
$77$	0.488946			0.0557205
$78$	0.146486	−	4.03337i	0.0165862	−	0.456689i
$79$	4.00362	−	4.77133i	0.450442	−	0.536816i	−0.492261	−	0.870447i	$-0.663830\pi$
$79$	4.00362	−	4.77133i	0.450442	−	0.536816i	0.942704	+	0.333631i	$0.108274\pi$
$80$	−1.72197	−	9.23513i	−0.192522	−	1.03252i
$81$	3.24262	+	8.39556i	0.360291	+	0.932840i
$82$	−1.38544	−	2.95216i	−0.152996	−	0.326012i
$83$	2.91194	+	5.04363i	0.319627	+	0.553610i	0.980410	−	0.196966i	$-0.0631090\pi$
$83$	2.91194	+	5.04363i	0.319627	+	0.553610i	−0.660783	+	0.750577i	$0.729776\pi$
$84$	3.05863	+	2.29978i	0.333723	+	0.250926i
$85$	16.9342	−	2.98596i	1.83678	−	0.323873i
$86$	0.223953	−	2.63418i	0.0241495	−	0.284051i
$87$	0.987101	−	7.79131i	0.105828	−	0.835316i
$88$	−1.21158	−	0.315106i	−0.129155	−	0.0335905i
$89$	10.9032	−	9.14891i	1.15574	−	0.969783i	0.155904	−	0.987772i	$-0.450171\pi$
$89$	10.9032	−	9.14891i	1.15574	−	0.969783i	0.999838	+	0.0179894i	$0.00572651\pi$
$90$	−7.71061	−	6.31117i	−0.812770	−	0.665255i
$91$	−1.71043	−	0.622547i	−0.179302	−	0.0652607i
$92$	−6.91094	+	2.55383i	−0.720515	+	0.266255i
$93$	1.19350	+	5.26192i	0.123760	+	0.545636i
$94$	4.52549	+	1.20072i	0.466769	+	0.123844i
$95$	9.89836	−	2.61200i	1.01555	−	0.267986i
$96$	−6.09697	−	7.66987i	−0.622269	−	0.782803i
$97$	−5.14609	−	0.907395i	−0.522507	−	0.0921320i	−0.0938269	−	0.995589i	$-0.529910\pi$
$97$	−5.14609	−	0.907395i	−0.522507	−	0.0921320i	−0.428680	+	0.903457i	$0.641021\pi$
$98$	−6.68396	+	4.70463i	−0.675181	+	0.475239i
$99$	−1.19788	+	0.572877i	−0.120392	+	0.0575763i
$100$	1.01679	+	0.174149i	0.101679	+	0.0174149i
$101$	−2.17930	+	1.82865i	−0.216848	+	0.181957i	−0.744741	−	0.667354i	$-0.767427\pi$
$101$	−2.17930	+	1.82865i	−0.216848	+	0.181957i	0.527892	+	0.849311i	$0.322982\pi$
$102$	14.1479	−	11.0218i	1.40085	−	1.09132i
$103$	−16.4706	−	9.50930i	−1.62290	−	0.936979i	−0.986140	−	0.165913i	$-0.946943\pi$
$103$	−16.4706	−	9.50930i	−1.62290	−	0.936979i	−0.636755	−	0.771066i	$-0.719724\pi$
$104$	3.83714	+	2.64494i	0.376263	+	0.259358i
$105$	−3.77815	+	2.43294i	−0.368709	+	0.237430i
$106$	11.8345	−	11.8927i	1.14947	−	1.15512i
$107$	−10.4865	+	6.05441i	−1.01377	+	0.585302i	−0.912294	−	0.409536i	$-0.865691\pi$
$107$	−10.4865	+	6.05441i	−1.01377	+	0.585302i	−0.101479	+	0.994838i	$0.532357\pi$
$108$	−10.1880	−	2.05064i	−0.980339	−	0.197323i
$109$	9.22999	−	3.35944i	0.884073	−	0.321776i	0.140221	−	0.990120i	$-0.455219\pi$
$109$	9.22999	−	3.35944i	0.884073	−	0.321776i	0.743852	+	0.668344i	$0.232997\pi$
$110$	0.840242	−	1.20628i	0.0801139	−	0.115014i
$111$	0.361475	−	1.16626i	0.0343097	−	0.110697i
$112$	−4.13726	+	1.55197i	−0.390935	+	0.146647i
$113$	8.18011			0.769520			0.384760	−	0.923017i	$-0.374284\pi$
$113$	8.18011			0.769520			0.384760	+	0.923017i	$0.374284\pi$
$114$	7.84644	−	7.24109i	0.734886	−	0.678191i
$115$		−	8.65180i		−	0.806784i
$116$	6.97541	+	5.79500i	0.647651	+	0.538053i
$117$	4.91986	−	0.478845i	0.454841	−	0.0442692i
$118$	−1.08709	−	0.757224i	−0.100075	−	0.0697081i
$119$	−2.76633	−	7.60042i	−0.253589	−	0.696729i
$120$	10.9299	−	3.59380i	0.997763	−	0.328068i
$121$	5.40205	+	9.35662i	0.491095	+	0.850602i
$122$	−5.58908	+	5.61656i	−0.506011	+	0.508499i
$123$	3.35800	−	2.16239i	0.302781	−	0.194976i
$124$	−5.86492	−	2.10214i	−0.526686	−	0.188778i
$125$	5.26574	−	9.12053i	0.470982	−	0.815765i
$126$	−2.29368	+	4.08721i	−0.204337	+	0.364118i
$127$	6.40829	+	7.63711i	0.568644	+	0.677684i	0.971352	−	0.237645i	$-0.0763755\pi$
$127$	6.40829	+	7.63711i	0.568644	+	0.677684i	−0.402708	+	0.915328i	$0.631931\pi$
$128$	11.2521	−	1.17937i	0.994552	−	0.104243i
$129$	3.23403	−	0.157012i	0.284741	−	0.0138241i
$130$	−4.47522	+	3.14997i	−0.392503	+	0.276271i
$131$	3.23492	−	18.3461i	0.282636	−	1.60291i	−0.430973	−	0.902365i	$-0.641830\pi$
$131$	3.23492	−	18.3461i	0.282636	−	1.60291i	0.713609	−	0.700544i	$-0.247059\pi$
$132$	0.185247	−	1.52201i	0.0161237	−	0.132474i
$133$	−2.01842	−	4.37179i	−0.175019	−	0.379083i
$134$	−2.00045	+	7.53968i	−0.172812	+	0.651329i
$135$	6.40563	−	10.3872i	0.551309	−	0.893990i
$136$	1.95661	+	20.6162i	0.167778	+	1.76782i
$137$	5.87855	−	16.1512i	0.502238	−	1.37989i	−0.386846	−	0.922144i	$-0.626435\pi$
$137$	5.87855	−	16.1512i	0.502238	−	1.37989i	0.889084	−	0.457744i	$-0.151342\pi$
$138$	−4.22518	−	7.97324i	−0.359671	−	0.678727i
$139$	1.60730	+	1.91551i	0.136329	+	0.162471i	0.829890	−	0.557928i	$-0.188403\pi$
$139$	1.60730	+	1.91551i	0.136329	+	0.162471i	−0.693560	+	0.720399i	$0.743959\pi$
$140$	−0.0254494	−	5.18884i	−0.00215087	−	0.438537i
$141$	−0.720738	+	5.68887i	−0.0606971	+	0.479089i
$142$	19.3732	+	1.64708i	1.62577	+	0.138220i
$143$	0.126639	+	0.718206i	0.0105901	+	0.0600594i
$144$	8.31764	−	8.64967i	0.693137	−	0.720806i
$145$	−9.22236	+	5.32453i	−0.765876	+	0.442178i
$146$	7.92707	+	16.8914i	0.656049	+	1.39794i
$147$	−6.79902	−	7.34755i	−0.560774	−	0.606015i
$148$	0.911542	+	1.07558i	0.0749283	+	0.0884118i
$149$	−17.4501	−	14.6424i	−1.42957	−	1.19955i	−0.945965	−	0.324268i	$-0.894882\pi$
$149$	−17.4501	−	14.6424i	−1.42957	−	1.19955i	−0.483607	−	0.875285i	$-0.660673\pi$
$150$	−0.0458559	+	1.26261i	−0.00374412	+	0.103091i
$151$		−	0.595704i		−	0.0484777i	−0.999706	−	0.0242389i	$-0.992284\pi$
$151$		−	0.595704i		−	0.0484777i	0.999706	−	0.0242389i	$-0.00771622\pi$
$152$	2.18407	+	12.1338i	0.177152	+	0.984184i
$153$	15.6824	+	15.3793i	1.26785	+	1.24334i
$154$	−0.627403	−	0.290692i	−0.0505576	−	0.0234246i
$155$	4.70272	−	5.60448i	0.377731	−	0.450163i
$156$	−2.58592	+	5.08843i	−0.207039	+	0.407400i
$157$	−6.72477	−	18.4761i	−0.536695	−	1.47456i	−0.850965	−	0.525223i	$-0.823982\pi$
$157$	−6.72477	−	18.4761i	−0.536695	−	1.47456i	0.314270	−	0.949334i	$-0.398240\pi$
$158$	−7.97403	+	3.74219i	−0.634380	+	0.297712i
$159$	16.3630	+	12.4294i	1.29767	+	0.985717i
$160$	−3.28095	+	12.8740i	−0.259382	+	1.01778i
$161$	−4.00770	+	0.706666i	−0.315851	+	0.0556931i
$162$	0.830547	−	12.7008i	0.0652539	−	0.997869i
$163$	−17.9021	−	10.3358i	−1.40220	−	0.809562i	−0.407584	−	0.913168i	$-0.633629\pi$
$163$	−17.9021	−	10.3358i	−1.40220	−	0.809562i	−0.994618	+	0.103606i	$0.966962\pi$
$164$	0.0226193	+	4.61183i	0.00176627	+	0.360123i
$165$	1.60107	+	0.823559i	0.124643	+	0.0641140i
$166$	−0.737952	−	8.20309i	−0.0572762	−	0.636683i
$167$	4.94922	+	1.80137i	0.382982	+	0.139394i	0.526335	−	0.850278i	$-0.323566\pi$
$167$	4.94922	+	1.80137i	0.382982	+	0.139394i	−0.143352	+	0.989672i	$0.545788\pi$
$168$	−2.55747	−	4.76945i	−0.197313	−	0.367971i
$169$	−1.78598	+	10.1288i	−0.137383	+	0.779140i
$170$	−23.5048	−	6.23636i	−1.80274	−	0.478307i
$171$	10.0672	+	8.34570i	0.769861	+	0.638211i
$172$	−1.85347	+	3.24697i	−0.141325	+	0.247579i
$173$	−0.0280323	−	0.00494286i	−0.00213126	−	0.000375799i	0.172582	−	0.984995i	$-0.444789\pi$
$173$	−0.0280323	−	0.00494286i	−0.00213126	−	0.000375799i	−0.174714	+	0.984619i	$0.555900\pi$
$174$	−5.89877	+	9.41075i	−0.447185	+	0.713427i
$175$	0.535434	+	0.194882i	0.0404750	+	0.0147317i
$176$	1.36733	+	1.12465i	0.103066	+	0.0847739i
$177$	0.742190	−	1.44288i	0.0557864	−	0.108453i
$178$	−19.4301	+	5.25737i	−1.45634	+	0.394057i
$179$	−6.61136	−	3.81707i	−0.494156	−	0.285301i	0.232141	−	0.972682i	$-0.425427\pi$
$179$	−6.61136	−	3.81707i	−0.494156	−	0.285301i	−0.726297	+	0.687381i	$0.758760\pi$
$180$	6.14190	+	12.6825i	0.457790	+	0.945298i
$181$	3.06589	+	17.3875i	0.227886	+	1.29240i	0.857091	+	0.515165i	$0.172269\pi$
$181$	3.06589	+	17.3875i	0.227886	+	1.29240i	−0.629205	+	0.777239i	$0.716619\pi$
$182$	1.82466	+	1.81574i	0.135253	+	0.134591i
$183$	−7.72774	−	5.87003i	−0.571251	−	0.433925i
$184$	10.3863	+	0.831733i	0.765685	+	0.0613161i
$185$	−1.55576	+	0.566251i	−0.114382	+	0.0416316i
$186$	1.59689	−	7.46153i	0.117089	−	0.547106i
$187$	−2.08303	+	2.48246i	−0.152327	+	0.181536i
$188$	−5.09314	−	4.23126i	−0.371455	−	0.308596i
$189$	−5.33479	−	2.11882i	−0.388049	−	0.154121i
$190$	−14.2542	−	2.53319i	−1.03411	−	0.183777i
$191$			20.5872i			1.48963i	0.667268	+	0.744817i	$0.267463\pi$
$191$			20.5872i			1.48963i	−0.667268	+	0.744817i	$0.732537\pi$
$192$	3.26353	+	13.4666i	0.235525	+	0.971868i
$193$	−2.45312	+	2.92351i	−0.176579	+	0.210439i	−0.847073	−	0.531476i	$-0.821638\pi$
$193$	−2.45312	+	2.92351i	−0.176579	+	0.210439i	0.670494	+	0.741915i	$0.266082\pi$
$194$	6.06387	+	4.22384i	0.435360	+	0.303254i
$195$	−4.55227	−	4.91953i	−0.325995	−	0.352295i
$196$	11.3737	−	2.06306i	0.812408	−	0.147361i
$197$	5.76740	+	9.98943i	0.410910	+	0.711718i	0.994990	−	0.0999791i	$-0.0318776\pi$
$197$	5.76740	+	9.98943i	0.410910	+	0.711718i	−0.584079	+	0.811697i	$0.698544\pi$
$198$	1.87769	−	0.0229262i	0.133441	−	0.00162930i
$199$	1.68641	+	9.56408i	0.119546	+	0.677980i	0.984398	+	0.175953i	$0.0563008\pi$
$199$	1.68641	+	9.56408i	0.119546	+	0.677980i	−0.864852	+	0.502026i	$0.832588\pi$
$200$	−1.20118	−	0.827972i	−0.0849362	−	0.0585465i
$201$	−9.47792	−	1.20078i	−0.668521	−	0.0846967i
$202$	3.88361	−	1.05082i	0.273250	−	0.0739357i
$203$	3.21971	+	3.83710i	0.225979	+	0.269312i
$204$	−24.7069	+	5.73154i	−1.72983	+	0.401288i
$205$	−5.08907	−	1.85227i	−0.355436	−	0.129368i
$206$	15.4811	+	21.9943i	1.07862	+	1.53242i
$207$	8.99063	−	6.42694i	0.624892	−	0.446703i
$208$	−3.35123	−	5.67521i	−0.232366	−	0.393505i
$209$	−1.11259	+	1.57616i	−0.0769591	+	0.109025i
$210$	6.29447	−	0.875672i	0.434360	−	0.0604271i
$211$	−2.05042	+	11.6285i	−0.141157	+	0.800539i	0.829216	+	0.558928i	$0.188787\pi$
$211$	−2.05042	+	11.6285i	−0.141157	+	0.800539i	−0.970373	+	0.241612i	$0.922324\pi$
$212$	−22.2563	+	8.22447i	−1.52857	+	0.564859i
$213$	1.15475	+	23.7849i	0.0791221	+	1.62971i
$214$	17.0556	−	1.53433i	1.16590	−	0.104884i
$215$	−2.82206	−	3.36320i	−0.192463	−	0.229368i
$216$	11.8538	+	8.68836i	0.806548	+	0.591168i
$217$	−2.98023	−	1.72064i	−0.202311	−	0.116804i
$218$	−13.8410	−	1.17673i	−0.937429	−	0.0796985i
$219$	−19.2135	+	12.3725i	−1.29833	+	0.836057i
$220$	−1.79534	+	1.04831i	−0.121042	+	0.0706774i
$221$	10.4477	−	6.03196i	0.702786	−	0.405754i
$222$	−1.15721	+	1.28161i	−0.0776669	+	0.0860160i
$223$	2.44525	+	6.71826i	0.163746	+	0.449888i	0.994245	−	0.107132i	$-0.0341668\pi$
$223$	2.44525	+	6.71826i	0.163746	+	0.449888i	−0.830499	+	0.557020i	$0.811945\pi$
$224$	6.23152	+	0.468273i	0.416361	+	0.0312878i
$225$	−1.54011	+	0.149898i	−0.102674	+	0.00999317i
$226$	−10.4965	−	4.86330i	−0.698217	−	0.323502i
$227$			10.4564i			0.694018i	0.937862	+	0.347009i	$0.112803\pi$
$227$			10.4564i			0.694018i	−0.937862	+	0.347009i	$0.887197\pi$
$228$	−14.3734	+	4.62666i	−0.951900	+	0.306408i
$229$		−	15.4931i		−	1.02381i	−0.859042	−	0.511906i	$-0.828940\pi$
$229$		−	15.4931i		−	1.02381i	0.859042	−	0.511906i	$-0.171060\pi$
$230$	−5.14373	+	11.1018i	−0.339168	+	0.732029i
$231$	0.250718	−	0.808916i	0.0164960	−	0.0532227i
$232$	−5.50538	−	11.5831i	−0.361446	−	0.760466i
$233$	−3.05481	−	8.39303i	−0.200128	−	0.549846i	0.798513	−	0.601978i	$-0.205621\pi$
$233$	−3.05481	−	8.39303i	−0.200128	−	0.549846i	−0.998640	+	0.0521322i	$0.983398\pi$
$234$	−6.59772	−	2.31055i	−0.431307	−	0.151045i
$235$	6.73377	−	3.88774i	0.439262	−	0.253608i
$236$	0.944738	+	1.61796i	0.0614972	+	0.105320i
$237$	−5.84077	−	9.07023i	−0.379399	−	0.589175i
$238$	−0.968979	+	11.3973i	−0.0628096	+	0.738779i
$239$	20.6782	+	11.9385i	1.33756	+	0.772240i	0.986445	−	0.164093i	$-0.0524697\pi$
$239$	20.6782	+	11.9385i	1.33756	+	0.772240i	0.351114	+	0.936333i	$0.385803\pi$
$240$	−16.1616	−	1.88668i	−1.04323	−	0.121785i
$241$	−2.98050	−	3.55202i	−0.191991	−	0.228806i	0.661458	−	0.749982i	$-0.269938\pi$
$241$	−2.98050	−	3.55202i	−0.191991	−	0.228806i	−0.853449	+	0.521176i	$0.825493\pi$
$242$	−1.36900	−	15.2178i	−0.0880028	−	0.978240i
$243$	15.5524	−	1.05960i	0.997687	−	0.0679731i
$244$	10.5110	−	3.88416i	0.672895	−	0.248658i
$245$	−2.35709	+	13.3677i	−0.150589	+	0.854032i
$246$	−5.59450	+	0.778294i	−0.356692	+	0.0496222i
$247$	5.89889	−	4.09715i	0.375337	−	0.260695i
$248$	6.27594	+	6.18427i	0.398523	+	0.392702i
$249$	9.83739	−	2.23130i	0.623419	−	0.141403i
$250$	−12.1793	+	8.57260i	−0.770285	+	0.542179i
$251$	12.4963	+	4.54829i	0.788761	+	0.287085i	0.704821	−	0.709385i	$-0.251027\pi$
$251$	12.4963	+	4.54829i	0.788761	+	0.287085i	0.0839399	+	0.996471i	$0.473250\pi$
$252$	5.37315	−	3.88095i	0.338477	−	0.244477i
$253$	1.04807	+	1.24904i	0.0658914	+	0.0785263i
$254$	−3.68249	−	13.6096i	−0.231060	−	0.853945i
$255$	3.74342	−	29.5472i	0.234422	−	1.85032i
$256$	−15.1395	−	5.17632i	−0.946221	−	0.323520i
$257$	−2.40342	−	13.6305i	−0.149921	−	0.850246i	−0.963283	−	0.268488i	$-0.913476\pi$
$257$	−2.40342	−	13.6305i	−0.149921	−	0.850246i	0.813362	−	0.581758i	$-0.197635\pi$
$258$	−4.24317	−	1.72125i	−0.264169	−	0.107160i
$259$	0.389372	+	0.674413i	0.0241944	+	0.0419060i
$260$	7.61524	−	1.38132i	0.472277	−	0.0856656i
$261$	−12.3838	−	5.62824i	−0.766540	−	0.348379i
$262$	−15.0582	+	21.6180i	−0.930301	+	1.33557i
$263$	−11.2944	+	13.4601i	−0.696442	+	0.829987i	−0.992119	−	0.125301i	$-0.960010\pi$
$263$	−11.2944	+	13.4601i	−0.696442	+	0.829987i	0.295677	+	0.955288i	$0.404455\pi$
$264$	−1.14258	+	1.84286i	−0.0703209	+	0.113420i
$265$		−	27.8626i		−	1.71159i
$266$	−0.00916462	+	6.80978i	−0.000561919	+	0.417534i
$267$	−9.54514	−	22.7297i	−0.584153	−	1.39104i
$268$	7.04947	−	8.48540i	0.430615	−	0.518329i
$269$	−1.53579	+	1.83029i	−0.0936389	+	0.111594i	−0.810829	−	0.585283i	$-0.800983\pi$
$269$	−1.53579	+	1.83029i	−0.0936389	+	0.111594i	0.717190	+	0.696877i	$0.245428\pi$
$270$	−14.3950	+	9.52030i	−0.876054	+	0.579387i
$271$	−6.86776	+	2.49966i	−0.417187	+	0.151843i	−0.542080	−	0.840327i	$-0.682363\pi$
$271$	−6.86776	+	2.49966i	−0.417187	+	0.151843i	0.124894	+	0.992170i	$0.460141\pi$
$272$	9.74620	−	27.6174i	0.590950	−	1.67455i
$273$	−1.90701	+	2.51053i	−0.115418	+	0.151944i
$274$	−17.1455	+	17.2298i	−1.03580	+	1.04089i
$275$	−0.0396431	−	0.224827i	−0.00239057	−	0.0135576i
$276$	0.681334	+	12.7430i	0.0410115	+	0.767041i
$277$	−1.32389	−	0.764350i	−0.0795450	−	0.0459254i	0.459700	−	0.888074i	$-0.347957\pi$
$277$	−1.32389	−	0.764350i	−0.0795450	−	0.0459254i	−0.539245	+	0.842149i	$0.681290\pi$
$278$	−0.923626	−	3.41351i	−0.0553954	−	0.204729i
$279$	9.31735	+	0.723633i	0.557815	+	0.0433228i
$280$	−3.05225	+	6.67332i	−0.182407	+	0.398807i
$281$	20.1604	+	7.33780i	1.20267	+	0.437736i	0.864156	−	0.503225i	$-0.167853\pi$
$281$	20.1604	+	7.33780i	1.20267	+	0.437736i	0.338515	+	0.940961i	$0.390075\pi$
$282$	4.30702	−	6.87132i	0.256480	−	0.409181i
$283$	27.0111	+	4.76279i	1.60564	+	0.283118i	0.903394	−	0.428812i	$-0.141068\pi$
$283$	27.0111	+	4.76279i	1.60564	+	0.283118i	0.702250	+	0.711930i	$0.252179\pi$
$284$	−23.8800	−	13.6314i	−1.41702	−	0.808875i
$285$	0.754292	−	17.7153i	0.0446804	−	1.04936i
$286$	0.264493	−	0.996874i	0.0156398	−	0.0589464i
$287$	−0.442344	+	2.50866i	−0.0261107	+	0.148081i
$288$	−15.8155	+	6.15397i	−0.931935	+	0.362626i
$289$	34.3992	+	12.5203i	2.02348	+	0.736486i
$290$	14.9995	−	1.34936i	0.880800	−	0.0792370i
$291$	−4.13998	+	8.04845i	−0.242690	+	0.471808i
$292$	−0.129421	−	26.3875i	−0.00757378	−	1.54421i
$293$	−6.12169	−	3.53436i	−0.357633	−	0.206479i	0.310409	−	0.950603i	$-0.399534\pi$
$293$	−6.12169	−	3.53436i	−0.357633	−	0.206479i	−0.668042	+	0.744124i	$0.732867\pi$
$294$	4.35602	+	13.4704i	0.254048	+	0.785609i
$295$	−2.16670	+	0.382047i	−0.126150	+	0.0222437i
$296$	−0.530208	−	1.92209i	−0.0308177	−	0.111719i
$297$	0.333530	+	2.27554i	0.0193533	+	0.132040i
$298$	13.6863	+	29.1634i	0.792824	+	1.68939i
$299$	−2.07603	−	5.70383i	−0.120060	−	0.329861i
$300$	0.809495	−	1.59288i	0.0467362	−	0.0919651i
$301$	−1.32741	+	1.58194i	−0.0765105	+	0.0911816i
$302$	−0.354162	+	0.764392i	−0.0203798	+	0.0439858i
$303$	1.90785	+	4.54313i	0.109603	+	0.260996i
$304$	4.41135	−	16.8683i	0.253008	−	0.967464i
$305$			13.1587i			0.753463i
$306$	−10.9798	−	29.0580i	−0.627675	−	1.66113i
$307$	8.53046	+	7.15790i	0.486859	+	0.408523i	0.852899	−	0.522076i	$-0.174842\pi$
$307$	8.53046	+	7.15790i	0.486859	+	0.408523i	−0.366040	+	0.930599i	$0.619287\pi$
$308$	0.632243	+	0.746016i	0.0360254	+	0.0425082i
$309$	−24.1779	+	22.3730i	−1.37543	+	1.27275i
$310$	−9.36642	+	4.39563i	−0.531977	+	0.249655i
$311$	−8.06017	+	4.65354i	−0.457050	+	0.263878i	−0.710803	−	0.703391i	$-0.751668\pi$
$311$	−8.06017	+	4.65354i	−0.457050	+	0.263878i	0.253753	+	0.967269i	$0.418335\pi$
$312$	6.34339	−	4.99194i	0.359124	−	0.282613i
$313$	2.54897	+	14.4559i	0.144076	+	0.817096i	0.968104	+	0.250548i	$0.0806106\pi$
$313$	2.54897	+	14.4559i	0.144076	+	0.817096i	−0.824028	+	0.566549i	$0.808278\pi$
$314$	−2.35553	+	27.7062i	−0.132930	+	1.56355i
$315$	2.08774	+	7.49814i	0.117631	+	0.422472i
$316$	12.4569	−	0.0610965i	0.700756	−	0.00343695i
$317$	−17.4138	−	20.7530i	−0.978058	−	1.16560i	−0.986187	−	0.165637i	$-0.947032\pi$
$317$	−17.4138	−	20.7530i	−0.978058	−	1.16560i	0.00812895	−	0.999967i	$-0.497412\pi$
$318$	−13.6070	−	25.6774i	−0.763040	−	1.43992i
$319$	0.686401	−	1.88587i	0.0384311	−	0.105589i
$320$	11.8640	−	14.5690i	0.663218	−	0.814433i
$321$	4.63925	+	20.4536i	0.258937	+	1.14161i
$322$	5.56271	+	1.47591i	0.309998	+	0.0822494i
$323$	30.7954	+	8.37708i	1.71350	+	0.466113i
$324$	−8.61671	+	15.8036i	−0.478706	+	0.877975i
$325$	−0.147580	+	0.836968i	−0.00818627	+	0.0464266i
$326$	16.8266	+	23.9059i	0.931941	+	1.32403i
$327$	−0.824997	−	16.9928i	−0.0456224	−	0.939704i
$328$	2.71283	−	5.93122i	0.149791	−	0.327497i
$329$	−2.35089	−	2.80168i	−0.129609	−	0.154462i
$330$	−1.56482	−	2.00865i	−0.0861404	−	0.110572i
$331$	−8.70892	+	15.0843i	−0.478686	+	0.829108i	−0.999701	−	0.0244392i	$-0.992220\pi$
$331$	−8.70892	+	15.0843i	−0.478686	+	0.829108i	0.521016	+	0.853547i	$0.325553\pi$
$332$	−3.93004	+	10.9647i	−0.215689	+	0.601768i
$333$	−1.74412	−	1.19605i	−0.0955770	−	0.0655434i
$334$	−5.27975	−	5.25392i	−0.288895	−	0.287482i
$335$	6.47715	+	11.2188i	0.353885	+	0.612946i
$336$	0.446108	+	7.64053i	0.0243372	+	0.416825i
$337$	−8.05762	−	22.1381i	−0.438926	−	1.20594i	−0.940191	−	0.340647i	$-0.889354\pi$
$337$	−8.05762	−	22.1381i	−0.438926	−	1.20594i	0.501265	−	0.865294i	$-0.332868\pi$
$338$	8.31360	−	11.9352i	0.452200	−	0.649191i
$339$	4.19454	−	13.5332i	0.227816	−	0.735024i
$340$	26.4531	+	21.9766i	1.43462	+	1.19185i
$341$			1.37878i			0.0746653i
$342$	−7.95628	−	16.6942i	−0.430226	−	0.902721i
$343$	14.1176			0.762279
$344$	4.30873	−	3.06449i	0.232311	−	0.165226i
$345$	−14.3136	−	4.43641i	−0.770618	−	0.238848i
$346$	0.0330317	+	0.0230086i	0.00177580	+	0.00123695i
$347$	14.9427	−	5.43872i	0.802169	−	0.291966i	0.0917839	−	0.995779i	$-0.470743\pi$
$347$	14.9427	−	5.43872i	0.802169	−	0.291966i	0.710385	+	0.703813i	$0.248521\pi$
$348$	13.1641	−	8.56865i	0.705670	−	0.459328i
$349$	−29.5980	+	17.0884i	−1.58435	+	0.914723i	−0.590133	+	0.807306i	$0.700925\pi$
$349$	−29.5980	+	17.0884i	−1.58435	+	0.914723i	−0.994214	+	0.107417i	$0.965742\pi$
$350$	−0.571193	−	0.568398i	−0.0305315	−	0.0303822i
$351$	1.73057	−	8.38499i	0.0923708	−	0.447558i
$352$	−1.08588	−	2.25604i	−0.0578777	−	0.120247i
$353$	−3.61673	−	2.08812i	−0.192499	−	0.111139i	0.400653	−	0.916230i	$-0.368783\pi$
$353$	−3.61673	−	2.08812i	−0.192499	−	0.111139i	−0.593152	+	0.805091i	$0.702117\pi$
$354$	−1.81019	+	1.41021i	−0.0962104	+	0.0749518i
$355$	24.7348	−	20.7550i	1.31279	−	1.10156i
$356$	28.0578	+	4.80558i	1.48706	+	0.254695i
$357$	−13.9927	+	0.679342i	−0.740572	+	0.0359546i
$358$	6.21417	+	8.82860i	0.328429	+	0.466606i
$359$	−28.1760	−	4.96818i	−1.48707	−	0.262211i	−0.629671	−	0.776862i	$-0.716810\pi$
$359$	−28.1760	−	4.96818i	−1.48707	−	0.262211i	−0.857399	+	0.514652i	$0.827921\pi$
$360$	−0.341033	−	19.9254i	−0.0179740	−	1.05016i
$361$	18.6857	+	3.44135i	0.983460	+	0.181124i
$362$	6.40329	−	24.1340i	0.336549	−	1.26845i
$363$	18.2497	−	4.13937i	0.957860	−	0.217260i
$364$	−1.26186	−	3.41472i	−0.0661393	−	0.178980i
$365$	29.1181	+	10.5981i	1.52411	+	0.554731i
$366$	6.42614	+	12.1266i	0.335900	+	0.633869i
$367$	−24.8114	+	20.8192i	−1.29514	+	1.08675i	−0.304180	+	0.952615i	$0.598382\pi$
$367$	−24.8114	+	20.8192i	−1.29514	+	1.08675i	−0.990963	+	0.134139i	$0.957173\pi$
$368$	−12.8329	−	7.24218i	−0.668961	−	0.377524i
$369$	−1.85557	−	6.66431i	−0.0965973	−	0.346930i
$370$	2.33297	+	0.198344i	0.121285	+	0.0103114i
$371$	−12.9066	+	2.27578i	−0.670077	+	0.118153i
$372$	−6.48517	+	8.62505i	−0.336240	+	0.447188i
$373$	14.3194	+	24.8019i	0.741428	+	1.28419i	0.951845	+	0.306580i	$0.0991846\pi$
$373$	14.3194	+	24.8019i	0.741428	+	1.28419i	−0.210417	+	0.977612i	$0.567482\pi$
$374$	4.14879	−	1.94701i	0.214529	−	0.100678i
$375$	−12.3889	−	13.3884i	−0.639762	−	0.691376i
$376$	4.01979	+	8.45746i	0.207305	+	0.436160i
$377$	−4.80235	+	5.72322i	−0.247334	+	0.294761i
$378$	5.58578	+	5.89049i	0.287301	+	0.302974i
$379$	−7.62025			−0.391426			−0.195713	−	0.980661i	$-0.562702\pi$
$379$	−7.62025			−0.391426			−0.195713	+	0.980661i	$0.562702\pi$
$380$	16.7846	+	11.7251i	0.861033	+	0.601483i
$381$	15.9209	−	6.68583i	0.815652	−	0.342525i
$382$	12.2396	−	26.4169i	0.626234	−	1.35161i
$383$	12.8703	+	10.7994i	0.657639	+	0.551825i	0.909378	−	0.415970i	$-0.136558\pi$
$383$	12.8703	+	10.7994i	0.657639	+	0.551825i	−0.251739	+	0.967795i	$0.581002\pi$
$384$	3.81859	−	19.2203i	0.194867	−	0.980830i
$385$	−1.07907	+	0.392750i	−0.0549946	+	0.0200164i
$386$	4.88588	−	2.29293i	0.248685	−	0.116707i
$387$	1.39856	−	5.43092i	0.0710929	−	0.276069i
$388$	−5.26981	−	9.02506i	−0.267534	−	0.458178i
$389$	−3.10634	−	17.6169i	−0.157498	−	0.893213i	−0.956467	−	0.291841i	$-0.905732\pi$
$389$	−3.10634	−	17.6169i	−0.157498	−	0.893213i	0.798969	−	0.601372i	$-0.205379\pi$
$390$	2.91656	+	9.01906i	0.147686	+	0.456698i
$391$	13.4860	−	23.3584i	0.682015	−	1.18128i
$392$	−15.8210	−	4.11472i	−0.799081	−	0.207825i
$393$	−28.6932	−	14.7593i	−1.44738	−	0.744507i
$394$	−1.46159	−	16.2471i	−0.0736339	−	0.818515i
$395$	−5.00312	+	13.7460i	−0.251734	+	0.691635i
$396$	−2.42303	−	1.08692i	−0.121762	−	0.0546197i
$397$	−9.47726	−	1.67110i	−0.475650	−	0.0838699i	−0.0693163	−	0.997595i	$-0.522082\pi$
$397$	−9.47726	−	1.67110i	−0.475650	−	0.0838699i	−0.406334	+	0.913725i	$0.633193\pi$
$398$	3.52216	−	13.2750i	0.176550	−	0.665416i
$399$	−8.26772	+	1.09755i	−0.413904	+	0.0549464i
$400$	1.04907	+	1.77657i	0.0524535	+	0.0888284i
$401$	0.936746	−	5.31255i	0.0467789	−	0.265296i	−0.952444	−	0.304714i	$-0.901439\pi$
$401$	0.936746	−	5.31255i	0.0467789	−	0.265296i	0.999223	+	0.0394177i	$0.0125503\pi$
$402$	11.4479	+	7.17570i	0.570971	+	0.357891i
$403$	1.75553	−	4.82327i	0.0874491	−	0.240264i
$404$	−5.60809	−	0.960521i	−0.279013	−	0.0477877i
$405$	−13.9001	−	15.9238i	−0.690700	−	0.791260i
$406$	−1.85019	−	6.83788i	−0.0918233	−	0.339358i
$407$	0.156006	−	0.270211i	0.00773295	−	0.0133939i
$408$	35.1108	+	7.33437i	1.73825	+	0.363106i
$409$	−11.0819	+	1.95403i	−0.547963	+	0.0966206i	−0.440774	−	0.897618i	$-0.645296\pi$
$409$	−11.0819	+	1.95403i	−0.547963	+	0.0966206i	−0.107189	+	0.994239i	$0.534185\pi$
$410$	5.42893	+	5.40237i	0.268116	+	0.266804i
$411$	−23.7063	−	18.0074i	−1.16934	−	0.888240i
$412$	−6.78873	−	37.4265i	−0.334457	−	1.84387i
$413$	0.353945	+	0.972457i	0.0174165	+	0.0478515i
$414$	−15.3575	+	2.90171i	−0.754782	+	0.142611i
$415$	−10.4778	−	8.79193i	−0.514336	−	0.431579i
$416$	0.926150	+	9.27468i	0.0454083	+	0.454729i
$417$	3.99321	−	1.67691i	0.195548	−	0.0821187i
$418$	2.36471	−	1.36103i	0.115662	−	0.0665700i
$419$	−1.84128			−0.0899524			−0.0449762	−	0.998988i	$-0.514321\pi$
$419$	−1.84128			−0.0899524			−0.0449762	+	0.998988i	$0.514321\pi$
$420$	−8.59751	−	2.61860i	−0.419516	−	0.127774i
$421$	−15.2363	−	12.7848i	−0.742573	−	0.623093i	0.190954	−	0.981599i	$-0.438842\pi$
$421$	−15.2363	−	12.7848i	−0.742573	−	0.623093i	−0.933527	+	0.358506i	$0.883286\pi$
$422$	9.54451	−	13.7024i	0.464620	−	0.667021i
$423$	9.04214	+	4.10949i	0.439644	+	0.199810i
$424$	33.4484	+	2.67855i	1.62440	+	0.130082i
$425$	−3.27054	+	1.88825i	−0.158644	+	0.0915934i
$426$	12.6590	−	31.2066i	0.613331	−	1.51197i
$427$	6.09538	−	1.07478i	0.294976	−	0.0520123i
$428$	−22.7975	−	8.17121i	−1.10196	−	0.394970i
$429$	1.25314	+	0.158764i	0.0605023	+	0.00766520i
$430$	1.62168	+	5.99337i	0.0782044	+	0.289026i
$431$	−18.2483	+	15.3122i	−0.878992	+	0.737562i	−0.965972	−	0.258648i	$-0.916723\pi$
$431$	−18.2483	+	15.3122i	−0.878992	+	0.737562i	0.0869797	+	0.996210i	$0.472278\pi$
$432$	−10.0450	−	18.1961i	−0.483291	−	0.875460i
$433$	−6.09493	+	16.7457i	−0.292904	+	0.804747i	0.702735	+	0.711452i	$0.251962\pi$
$433$	−6.09493	+	16.7457i	−0.292904	+	0.804747i	−0.995639	+	0.0932947i	$0.970260\pi$
$434$	2.80119	+	3.97970i	0.134461	+	0.191032i
$435$	4.07997	+	17.9878i	0.195620	+	0.862450i
$436$	17.0608	+	9.73880i	0.817063	+	0.466404i
$437$	6.84144	−	14.5272i	0.327270	−	0.694930i
$438$	32.0100	−	4.45316i	1.52950	−	0.212780i
$439$	13.7897	+	2.43150i	0.658146	+	0.116049i	0.492740	−	0.870177i	$-0.335995\pi$
$439$	13.7897	+	2.43150i	0.658146	+	0.116049i	0.165406	+	0.986226i	$0.447106\pi$
$440$	2.92699	−	0.277791i	0.139539	−	0.0132432i
$441$	−15.6422	+	7.48073i	−0.744866	+	0.356225i
$442$	−16.9924	+	1.52864i	−0.808244	+	0.0727098i
$443$	−15.0640	+	12.6402i	−0.715714	+	0.600555i	−0.926196	−	0.377043i	$-0.876941\pi$
$443$	−15.0640	+	12.6402i	−0.715714	+	0.600555i	0.210482	+	0.977598i	$0.432497\pi$
$444$	2.24686	−	0.956536i	0.106631	−	0.0453952i
$445$	−16.7138	+	28.9492i	−0.792312	+	1.37232i
$446$	0.856513	−	10.0745i	0.0405571	−	0.477040i
$447$	−33.1725	+	21.3614i	−1.56900	+	1.01036i
$448$	−7.71773	−	4.30569i	−0.364628	−	0.203425i
$449$	−9.18992	−	15.9174i	−0.433699	−	0.751189i	0.563489	−	0.826123i	$-0.309459\pi$
$449$	−9.18992	−	15.9174i	−0.433699	−	0.751189i	−0.997188	+	0.0749344i	$0.976125\pi$
$450$	2.06535	+	0.723295i	0.0973616	+	0.0340964i
$451$	0.959076	−	0.349075i	0.0451611	−	0.0164373i
$452$	10.5775	+	12.4809i	0.497523	+	0.587053i
$453$	−0.985537	−	0.305461i	−0.0463046	−	0.0143518i
$454$	6.21664	−	13.4174i	0.291761	−	0.629711i
$455$	4.27489			0.200410
$456$	21.1942	+	2.60855i	0.992511	+	0.122157i
$457$	−0.964998			−0.0451407			−0.0225704	−	0.999745i	$-0.507185\pi$
$457$	−0.964998			−0.0451407			−0.0225704	+	0.999745i	$0.507185\pi$
$458$	−9.21106	+	19.8803i	−0.430405	+	0.928946i
$459$	33.4852	−	18.0590i	1.56295	−	0.842921i
$460$	13.2006	−	11.1874i	0.615482	−	0.521616i
$461$	9.70273	−	3.53150i	0.451901	−	0.164479i	−0.106035	−	0.994362i	$-0.533816\pi$
$461$	9.70273	−	3.53150i	0.451901	−	0.164479i	0.557936	+	0.829884i	$0.311593\pi$
$462$	−0.802638	+	0.888921i	−0.0373421	+	0.0413563i
$463$	−12.5906	−	21.8076i	−0.585135	−	1.01348i	−0.994859	−	0.101274i	$-0.967708\pi$
$463$	−12.5906	−	21.8076i	−0.585135	−	1.01348i	0.409724	−	0.912210i	$-0.365625\pi$
$464$	0.177907	+	18.1362i	0.00825914	+	0.841953i
$465$	−6.86067	−	10.6540i	−0.318156	−	0.494069i
$466$	−1.07003	+	12.5859i	−0.0495681	+	0.583030i
$467$	−14.1976	+	24.5909i	−0.656986	+	1.13793i	0.324406	+	0.945918i	$0.394836\pi$
$467$	−14.1976	+	24.5909i	−0.656986	+	1.13793i	−0.981392	+	0.192015i	$0.938498\pi$
$468$	7.09235	+	6.88737i	0.327844	+	0.318369i
$469$	4.66773	−	3.91669i	0.215536	−	0.180856i
$470$	−10.9520	+	0.985242i	−0.505177	+	0.0454458i
$471$	−34.0153	+	1.65144i	−1.56734	+	0.0760942i
$472$	−0.250344	−	2.63779i	−0.0115230	−	0.121414i
$473$	0.814827	+	0.143676i	0.0374658	+	0.00660623i
$474$	2.10223	+	15.1112i	0.0965587	+	0.694080i
$475$	−1.84659	+	1.28257i	−0.0847273	+	0.0588484i
$476$	8.01939	−	14.0487i	0.367568	−	0.643920i
$477$	28.9538	−	20.6976i	1.32570	−	0.947678i
$478$	−19.4359	−	27.6130i	−0.888977	−	1.26299i
$479$	12.5812	−	34.5664i	0.574848	−	1.57938i	−0.221900	−	0.975069i	$-0.571226\pi$
$479$	12.5812	−	34.5664i	0.574848	−	1.57938i	0.796748	−	0.604312i	$-0.206552\pi$
$480$	19.6165	+	12.0295i	0.895368	+	0.549068i
$481$	−0.889787	+	0.746620i	−0.0405708	+	0.0340429i
$482$	1.71273	+	6.32985i	0.0780125	+	0.288317i
$483$	−0.885928	+	6.99273i	−0.0403111	+	0.318180i
$484$	−7.29076	+	20.3411i	−0.331398	+	0.924594i
$485$	12.0860	−	2.13108i	0.548796	−	0.0967675i
$486$	−20.5864	−	7.88669i	−0.933818	−	0.357747i
$487$	12.1127	−	6.99329i	0.548880	−	0.316896i	−0.199790	−	0.979839i	$-0.564026\pi$
$487$	12.1127	−	6.99329i	0.548880	−	0.316896i	0.748670	+	0.662943i	$0.230693\pi$
$488$	−15.7966	−	1.26500i	−0.715080	−	0.0572637i
$489$	−26.2793	+	24.3175i	−1.18839	+	1.09967i
$490$	10.9720	−	15.7518i	0.495666	−	0.711592i
$491$	1.11470	+	0.935343i	0.0503056	+	0.0422114i	0.667594	−	0.744526i	$-0.267324\pi$
$491$	1.11470	+	0.935343i	0.0503056	+	0.0422114i	−0.617288	+	0.786737i	$0.711769\pi$
$492$	7.64144	+	2.32740i	0.344503	+	0.104927i
$493$	−33.1984			−1.49518
$494$	−10.0052	+	1.75030i	−0.450154	+	0.0787498i
$495$	2.18349	−	2.22652i	0.0981404	−	0.100074i
$496$	−4.37641	−	11.6667i	−0.196507	−	0.523851i
$497$	−11.6345	−	9.76248i	−0.521878	−	0.437907i
$498$	−13.9497	−	2.98545i	−0.625099	−	0.133781i
$499$	10.9215	+	30.0067i	0.488915	+	1.34328i	0.901663	+	0.432439i	$0.142347\pi$
$499$	10.9215	+	30.0067i	0.488915	+	1.34328i	−0.412748	+	0.910845i	$0.635431\pi$
$500$	20.7248	−	3.75924i	0.926840	−	0.168118i
$501$	5.51803	−	7.26434i	0.246527	−	0.324547i
$502$	−13.3309	−	13.2657i	−0.594986	−	0.592075i
$503$	−28.6024	+	5.04338i	−1.27532	+	0.224873i	−0.769991	−	0.638055i	$-0.779739\pi$
$503$	−28.6024	+	5.04338i	−1.27532	+	0.224873i	−0.505327	+	0.862928i	$0.668628\pi$
$504$	−9.20202	+	1.78545i	−0.409891	+	0.0795303i
$505$	3.34070	−	5.78626i	0.148659	−	0.257485i
$506$	−0.602265	−	2.22584i	−0.0267740	−	0.0989505i
$507$	15.8414	+	8.14853i	0.703541	+	0.361889i
$508$	−3.36603	+	19.6529i	−0.149344	+	0.871956i
$509$	−10.9711	+	30.1429i	−0.486286	+	1.33606i	0.417733	+	0.908570i	$0.362825\pi$
$509$	−10.9711	+	30.1429i	−0.486286	+	1.33606i	−0.904019	+	0.427491i	$0.859397\pi$
$510$	−22.3701	+	35.6887i	−0.990565	+	1.58032i
$511$	2.53096	−	14.3538i	0.111963	−	0.634974i
$512$	16.3492	+	15.6430i	0.722540	+	0.691330i
$513$	18.9694	−	12.3759i	0.837519	−	0.546408i
$514$	−5.01969	+	18.9192i	−0.221409	+	0.834489i
$515$	43.9880	+	7.75627i	1.93834	+	0.341782i
$516$	4.42141	+	4.73135i	0.194642	+	0.208286i
$517$	−0.501180	+	1.37698i	−0.0220419	+	0.0605596i
$518$	−0.0986758	−	1.09688i	−0.00433557	−	0.0481942i
$519$	−0.0225517	+	0.0438424i	−0.000989911	+	0.00192447i
$520$	−10.5929	−	2.75500i	−0.464530	−	0.120815i
$521$	−5.34384	+	9.25580i	−0.234118	+	0.405504i	−0.959016	−	0.283352i	$-0.908554\pi$
$521$	−5.34384	+	9.25580i	−0.234118	+	0.405504i	0.724898	+	0.688856i	$0.241887\pi$
$522$	12.5445	+	14.5845i	0.549057	+	0.638348i
$523$	−5.16100	−	29.2695i	−0.225675	−	1.27987i	−0.861391	−	0.507943i	$-0.830406\pi$
$523$	−5.16100	−	29.2695i	−0.225675	−	1.27987i	0.635716	−	0.771923i	$-0.280705\pi$
$524$	32.1749	−	18.7872i	1.40557	−	0.820722i
$525$	0.596971	−	0.785896i	0.0260539	−	0.0342993i
$526$	22.4951	−	10.5569i	0.980833	−	0.460302i
$527$	21.4325	−	7.80080i	0.933615	−	0.339808i
$528$	2.56176	−	1.68542i	0.111486	−	0.0733486i
$529$	7.22321	+	6.06099i	0.314053	+	0.263521i
$530$	−16.5651	+	35.7526i	−0.719542	+	1.55300i
$531$	−2.00653	−	1.96775i	−0.0870760	−	0.0853931i
$532$	4.06036	−	8.73269i	0.176039	−	0.378610i
$533$	−3.79950			−0.164575
$534$	−1.26537	+	34.8411i	−0.0547580	+	1.50772i
$535$	18.2799	−	21.7851i	0.790309	−	0.941853i
$536$	−14.0905	+	6.69715i	−0.608617	+	0.289273i
$537$	−9.70511	+	8.98059i	−0.418807	+	0.387541i
$538$	3.05884	−	1.43551i	0.131876	−	0.0618890i
$539$	−1.27906	−	2.21540i	−0.0550930	−	0.0954238i
$540$	24.1314	−	3.65796i	1.03845	−	0.157414i
$541$	18.0933	−	3.19034i	0.777893	−	0.137164i	0.229415	−	0.973329i	$-0.426319\pi$
$541$	18.0933	−	3.19034i	0.777893	−	0.137164i	0.548478	+	0.836165i	$0.315208\pi$
$542$	10.2986	+	0.875572i	0.442365	+	0.0376090i
$543$	30.3382	+	3.84362i	1.30193	+	0.164946i
$544$	−28.9254	+	29.6436i	−1.24017	+	1.27096i
$545$	−17.6715	+	14.8282i	−0.756964	+	0.635169i
$546$	3.93961	−	2.08768i	0.168600	−	0.0893443i
$547$	10.1650	+	3.69976i	0.434624	+	0.158190i	0.550061	−	0.835125i	$-0.314605\pi$
$547$	10.1650	+	3.69976i	0.434624	+	0.158190i	−0.115437	+	0.993315i	$0.536827\pi$
$548$	32.2443	−	11.9154i	1.37741	−	0.509000i
$549$	−13.6740	+	9.77484i	−0.583592	+	0.417180i
$550$	−0.0827970	+	0.312062i	−0.00353047	+	0.0133063i
$551$	−19.6956	+	1.64779i	−0.839062	+	0.0701982i
$552$	6.70182	−	16.7566i	0.285248	−	0.713209i
$553$	6.77608	+	1.19481i	0.288148	+	0.0508083i
$554$	1.24436	+	1.76789i	0.0528678	+	0.0751103i
$555$	0.139057	+	2.86422i	0.00590266	+	0.121580i
$556$	−0.844255	+	4.92926i	−0.0358044	+	0.209047i
$557$	−29.6360	+	24.8676i	−1.25572	+	1.05367i	−0.259593	+	0.965718i	$0.583588\pi$
$557$	−29.6360	+	24.8676i	−1.25572	+	1.05367i	−0.996125	+	0.0879539i	$0.971967\pi$
$558$	−11.5256	−	6.46797i	−0.487916	−	0.273811i
$559$	−2.66750	−	1.54008i	−0.112823	−	0.0651385i
$560$	7.88405	−	6.74839i	0.333162	−	0.285172i
$561$	3.03888	+	4.71913i	0.128302	+	0.199242i
$562$	−21.5068	−	21.4016i	−0.907211	−	0.902772i
$563$	−18.1468	+	10.4771i	−0.764798	+	0.441556i	−0.831016	−	0.556249i	$-0.812240\pi$
$563$	−18.1468	+	10.4771i	−0.764798	+	0.441556i	0.0662176	+	0.997805i	$0.478907\pi$
$564$	−9.61185	+	6.25646i	−0.404732	+	0.263444i
$565$	−18.0530	+	6.57075i	−0.759495	+	0.276433i
$566$	−31.8284	−	22.1703i	−1.33785	−	0.931889i
$567$	−6.24092	+	7.73945i	−0.262094	+	0.325026i
$568$	22.5380	+	31.6888i	0.945672	+	1.32963i
$569$	35.3414			1.48159			0.740795	−	0.671731i	$-0.234449\pi$
$569$	35.3414			1.48159			0.740795	+	0.671731i	$0.234449\pi$
$570$	−11.5001	+	22.2834i	−0.481687	+	0.933347i
$571$		−	5.94332i		−	0.248720i	−0.992237	−	0.124360i	$-0.960312\pi$
$571$		−	5.94332i		−	0.248720i	0.992237	−	0.124360i	$-0.0396878\pi$
$572$	−0.932060	+	1.12192i	−0.0389714	+	0.0469096i
$573$	34.0596	+	10.5565i	1.42286	+	0.441006i
$574$	2.05907	−	2.95606i	0.0859439	−	0.123384i
$575$	0.649879	+	1.78553i	0.0271018	+	0.0744617i
$576$	23.9527	+	1.50611i	0.998029	+	0.0627545i
$577$	−11.9848	−	20.7583i	−0.498934	−	0.864179i	0.501065	−	0.865409i	$-0.332942\pi$
$577$	−11.9848	−	20.7583i	−0.498934	−	0.864179i	−0.999999	+	0.00123069i	$0.999608\pi$
$578$	−36.6965	−	36.5169i	−1.52637	−	1.51890i
$579$	3.57878	+	5.55755i	0.148729	+	0.230964i
$580$	−20.0492	−	7.18615i	−0.832497	−	0.298388i
$581$	−3.21680	+	5.57167i	−0.133455	+	0.231152i
$582$	10.0973	−	7.86623i	0.418548	−	0.326066i
$583$	3.37524	+	4.02245i	0.139788	+	0.166593i
$584$	−15.5220	+	33.9367i	−0.642305	+	1.40431i
$585$	−10.4732	+	5.00870i	−0.433013	+	0.207084i
$586$	5.75392	+	8.17471i	0.237692	+	0.337694i
$587$	6.28807	−	35.6614i	0.259536	−	1.47190i	−0.524618	−	0.851338i	$-0.675792\pi$
$587$	6.28807	−	35.6614i	0.259536	−	1.47190i	0.784154	−	0.620566i	$-0.213097\pi$
$588$	2.41899	−	19.8746i	0.0997574	−	0.819616i
$589$	12.3281	−	5.69177i	0.507969	−	0.234525i
$590$	3.00739	+	0.797929i	0.123812	+	0.0328502i
$591$	19.4840	−	4.41932i	0.801463	−	0.181787i
$592$	−0.462385	+	2.78160i	−0.0190039	+	0.114323i
$593$	−3.41040	+	9.37000i	−0.140048	+	0.384780i	−0.989811	−	0.142385i	$-0.954523\pi$
$593$	−3.41040	+	9.37000i	−0.140048	+	0.384780i	0.849763	+	0.527165i	$0.176745\pi$
$594$	0.924897	−	3.11821i	0.0379490	−	0.127942i
$595$	12.2102	+	14.5516i	0.500570	+	0.596556i
$596$	−0.223448	−	45.5586i	−0.00915279	−	1.86615i
$597$	16.6876	+	2.11420i	0.682979	+	0.0865284i
$598$	−0.727183	+	8.55327i	−0.0297367	+	0.349769i
$599$	−0.565079	−	3.20472i	−0.0230885	−	0.130941i	0.971085	−	0.238735i	$-0.0767326\pi$
$599$	−0.565079	−	3.20472i	−0.0230885	−	0.130941i	−0.994173	+	0.107793i	$0.965622\pi$
$600$	−1.98574	+	1.56268i	−0.0810673	+	0.0637961i
$601$	−26.6086	+	15.3625i	−1.08539	+	0.626649i	−0.932345	−	0.361571i	$-0.882240\pi$
$601$	−26.6086	+	15.3625i	−1.08539	+	0.626649i	−0.153043	+	0.988220i	$0.548907\pi$
$602$	2.64380	−	1.24073i	0.107753	−	0.0505683i
$603$	−6.84660	+	15.0646i	−0.278815	+	0.613478i
$604$	0.908904	−	0.770289i	0.0369828	−	0.0313426i
$605$	−19.4378	−	16.3102i	−0.790258	−	0.663105i
$606$	0.252918	−	6.96390i	0.0102741	−	0.282889i
$607$			42.1244i			1.70978i	0.518813	+	0.854888i	$0.326374\pi$
$607$			42.1244i			1.70978i	−0.518813	+	0.854888i	$0.673626\pi$
$608$	−15.6892	+	19.0223i	−0.636281	+	0.771457i
$609$	7.99911	−	3.35915i	0.324140	−	0.136120i
$610$	7.82319	−	16.8849i	0.316752	−	0.683648i
$611$	3.50647	−	4.17884i	0.141856	−	0.169058i
$612$	−3.18673	+	43.8143i	−0.128816	+	1.77109i
$613$	12.2026	+	33.5265i	0.492860	+	1.35412i	0.898051	+	0.439891i	$0.144983\pi$
$613$	12.2026	+	33.5265i	0.492860	+	1.35412i	−0.405191	+	0.914232i	$0.632795\pi$
$614$	−6.69049	−	14.2564i	−0.270006	−	0.575343i
$615$	−5.67394	+	7.46959i	−0.228795	+	0.301203i
$616$	−0.367751	−	1.33316i	−0.0148171	−	0.0537144i
$617$	−19.7384	+	3.48041i	−0.794637	+	0.140116i	−0.556207	−	0.831044i	$-0.687744\pi$
$617$	−19.7384	+	3.48041i	−0.794637	+	0.140116i	−0.238430	+	0.971160i	$0.576633\pi$
$618$	44.3258	−	14.3340i	1.78305	−	0.576597i
$619$	−21.8679	−	12.6254i	−0.878943	−	0.507458i	−0.00863338	−	0.999963i	$-0.502748\pi$
$619$	−21.8679	−	12.6254i	−0.878943	−	0.507458i	−0.870310	+	0.492505i	$0.836081\pi$
$620$	14.6321	−	0.0717650i	0.587639	−	0.00288215i
$621$	−6.02262	−	18.1697i	−0.241680	−	0.729126i
$622$	13.1093	−	1.17931i	0.525634	−	0.0472861i
$623$	14.7751	+	5.37769i	0.591951	+	0.215452i
$624$	−11.1075	+	2.63421i	−0.444657	+	0.105453i
$625$	−4.74284	+	26.8980i	−0.189714	+	1.07592i
$626$	5.32367	−	20.0649i	0.212777	−	0.801954i
$627$	2.03711	+	2.64888i	0.0813543	+	0.105786i
$628$	19.4946	−	34.1514i	0.777921	−	1.36279i
$629$	−5.08294	−	0.896259i	−0.202670	−	0.0357362i
$630$	1.77891	−	10.8626i	0.0708737	−	0.432778i
$631$	−37.5908	−	13.6819i	−1.49647	−	0.544669i	−0.541323	−	0.840815i	$-0.682076\pi$
$631$	−37.5908	−	13.6819i	−1.49647	−	0.544669i	−0.955143	+	0.296146i	$0.904298\pi$
$632$	−16.0207	−	7.32758i	−0.637269	−	0.291475i
$633$	18.1869	+	9.35501i	0.722864	+	0.371828i
$634$	10.0068	+	36.9827i	0.397419	+	1.46877i
$635$	−20.2773	−	11.7071i	−0.804679	−	0.464582i
$636$	2.19420	+	41.0383i	0.0870056	+	1.62727i
$637$	1.65368	+	9.37847i	0.0655211	+	0.371588i
$638$	−2.00198	+	2.01182i	−0.0792590	+	0.0796487i
$639$	39.9420	+	10.2858i	1.58008	+	0.406900i
$640$	−23.8853	+	11.6411i	−0.944148	+	0.460156i
$641$	24.7088	−	8.99327i	0.975939	−	0.355213i	0.195679	−	0.980668i	$-0.437309\pi$
$641$	24.7088	−	8.99327i	0.975939	−	0.355213i	0.780260	+	0.625455i	$0.215087\pi$
$642$	6.20724	−	29.0037i	0.244980	−	1.14468i
$643$	11.2479	−	13.4047i	0.443573	−	0.528630i	−0.497214	−	0.867628i	$-0.665644\pi$
$643$	11.2479	−	13.4047i	0.443573	−	0.528630i	0.940787	+	0.338998i	$0.110088\pi$
$644$	−6.26046	−	5.20104i	−0.246697	−	0.204950i
$645$	−7.01118	+	2.94428i	−0.276065	+	0.115931i
$646$	−34.5354	−	29.0579i	−1.35878	−	1.14327i
$647$		−	23.2418i		−	0.913730i	−0.889536	−	0.456865i	$-0.848972\pi$
$647$		−	23.2418i		−	0.913730i	0.889536	−	0.456865i	$-0.151028\pi$
$648$	20.4524	−	15.1558i	0.803446	−	0.595378i
$649$	0.266520	−	0.317626i	0.0104618	−	0.0124679i
$650$	0.686971	−	0.986235i	0.0269452	−	0.0386833i
$651$	−4.37481	+	4.04822i	−0.171462	+	0.158662i
$652$	−7.37877	−	40.6794i	−0.288975	−	1.59313i
$653$	−10.2711	−	17.7900i	−0.401937	−	0.696176i	0.592022	−	0.805922i	$-0.298330\pi$
$653$	−10.2711	−	17.7900i	−0.401937	−	0.696176i	−0.993960	+	0.109746i	$0.964996\pi$
$654$	−9.04407	+	22.2952i	−0.353651	+	0.871812i
$655$	7.59744	+	43.0872i	0.296857	+	1.68356i
$656$	−7.00731	+	5.99794i	−0.273590	+	0.234180i
$657$	10.6170	+	38.1312i	0.414210	+	1.48764i
$658$	1.35093	+	4.99272i	0.0526646	+	0.194636i
$659$	−25.5550	−	30.4552i	−0.995480	−	1.18637i	−0.982464	−	0.186452i	$-0.940301\pi$
$659$	−25.5550	−	30.4552i	−0.995480	−	1.18637i	−0.0130161	−	0.999915i	$-0.504143\pi$
$660$	0.813737	+	3.50777i	0.0316747	+	0.136540i
$661$	12.1227	+	4.41232i	0.471520	+	0.171619i	0.566841	−	0.823827i	$-0.308165\pi$
$661$	12.1227	+	4.41232i	0.471520	+	0.171619i	−0.0953209	+	0.995447i	$0.530388\pi$
$662$	20.1431	−	14.1781i	0.782884	−	0.551047i
$663$	−4.62205	−	20.3777i	−0.179505	−	0.791405i
$664$	11.5618	−	11.7331i	0.448683	−	0.455334i
$665$	7.96621	+	8.02696i	0.308916	+	0.311272i
$666$	1.52692	+	2.57167i	0.0591669	+	0.0996503i
$667$	−2.90055	+	16.4498i	−0.112310	+	0.636940i
$668$	3.65124	+	9.88066i	0.141271	+	0.382294i
$669$	12.3686	−	0.600493i	0.478198	−	0.0232164i
$670$	−1.64146	−	18.2465i	−0.0634151	−	0.704923i
$671$	−1.59402	−	1.89968i	−0.0615365	−	0.0733364i
$672$	3.97007	−	10.0694i	0.153149	−	0.388434i
$673$	29.6187	+	17.1003i	1.14172	+	0.659170i	0.946855	−	0.321661i	$-0.104241\pi$
$673$	29.6187	+	17.1003i	1.14172	+	0.659170i	0.194861	+	0.980831i	$0.437575\pi$
$674$	−2.82239	+	33.1976i	−0.108715	+	1.27872i
$675$	−0.541736	+	2.62484i	−0.0208514	+	0.101030i
$676$	−17.7636	+	10.3723i	−0.683216	+	0.398936i
$677$	25.9372	−	14.9748i	0.996847	−	0.575530i	0.0895331	−	0.995984i	$-0.471463\pi$
$677$	25.9372	−	14.9748i	0.996847	−	0.575530i	0.907314	+	0.420454i	$0.138129\pi$
$678$	−13.4282	+	14.8717i	−0.515707	+	0.571145i
$679$	−1.97433	−	5.42443i	−0.0757678	−	0.208170i
$680$	−20.8783	−	43.9269i	−0.800644	−	1.68452i
$681$	17.2992	+	5.36178i	0.662907	+	0.205464i
$682$	0.819725	−	1.76922i	0.0313889	−	0.0677469i
$683$			32.7756i			1.25412i	0.778969	+	0.627062i	$0.215743\pi$
$683$			32.7756i			1.25412i	−0.778969	+	0.627062i	$0.784257\pi$
$684$	0.284110	+	26.1519i	0.0108632	+	0.999941i
$685$			40.3666i			1.54233i
$686$	−18.1153	−	8.39330i	−0.691647	−	0.320458i
$687$	−25.6319	−	7.94443i	−0.977916	−	0.303099i
$688$	−7.35078	+	1.37062i	−0.280246	+	0.0522544i
$689$	−6.68573	−	18.3689i	−0.254706	−	0.699799i
$690$	15.7293	+	14.2025i	0.598803	+	0.540680i
$691$	−35.7991	+	20.6686i	−1.36186	+	0.786271i	−0.989872	−	0.141966i	$-0.954658\pi$
$691$	−35.7991	+	20.6686i	−1.36186	+	0.786271i	−0.371989	+	0.928237i	$0.621324\pi$
$692$	−0.0287063	−	0.0491623i	−0.00109125	−	0.00186887i
$693$	−1.20971	−	0.829580i	−0.0459532	−	0.0315131i
$694$	−22.4076	−	1.90505i	−0.850582	−	0.0723149i
$695$	−5.08586	−	2.93632i	−0.192918	−	0.111381i
$696$	−21.9861	+	3.16866i	−0.833383	+	0.120108i
$697$	−10.8524	−	12.9334i	−0.411064	−	0.489887i
$698$	48.1390	−	4.33060i	1.82209	−	0.163916i
$699$	−15.4519	+	0.750187i	−0.584445	+	0.0283747i
$700$	0.395012	+	1.06894i	0.0149300	+	0.0404023i
$701$	−0.972931	+	5.51777i	−0.0367471	+	0.208403i	−0.997653	−	0.0684718i	$-0.978188\pi$
$701$	−0.972931	+	5.51777i	−0.0367471	+	0.208403i	0.960906	+	0.276875i	$0.0892988\pi$
$702$	−7.20573	+	9.73054i	−0.271963	+	0.367255i
$703$	−3.06004	−	0.279434i	−0.115412	−	0.0105391i
$704$	0.0520976	+	3.54048i	0.00196350	+	0.133437i
$705$	−2.97902	−	13.1339i	−0.112196	−	0.494652i
$706$	3.39945	+	4.82967i	0.127940	+	0.181767i
$707$	−2.95319	−	1.07487i	−0.111066	−	0.0404247i
$708$	3.16120	−	0.733338i	0.118805	−	0.0275605i
$709$	−27.1851	−	32.3979i	−1.02096	−	1.21673i	−0.976007	−	0.217740i	$-0.930132\pi$
$709$	−27.1851	−	32.3979i	−1.02096	−	1.21673i	−0.0449498	−	0.998989i	$-0.514313\pi$
$710$	−44.0785	+	11.9267i	−1.65424	+	0.447603i
$711$	−18.0008	+	5.01205i	−0.675084	+	0.187967i
$712$	−33.1460	−	22.8475i	−1.24220	−	0.856247i
$713$	−1.99274	−	11.3014i	−0.0746285	−	0.423239i
$714$	18.3589	+	7.44732i	0.687066	+	0.278709i
$715$	−0.856390	−	1.48331i	−0.0320272	−	0.0554727i
$716$	−2.72502	−	15.0231i	−0.101839	−	0.561441i
$717$	30.3544	−	28.0883i	1.13361	−	1.04898i
$718$	33.2009	+	23.1264i	1.23905	+	0.863070i
$719$	9.16165	−	10.9184i	0.341672	−	0.407189i	−0.567658	−	0.823264i	$-0.692150\pi$
$719$	9.16165	−	10.9184i	0.341672	−	0.407189i	0.909330	+	0.416076i	$0.136595\pi$
$720$	−11.4086	+	25.7705i	−0.425173	+	0.960410i
$721$		−	21.0097i		−	0.782443i
$722$	−21.9311	−	15.5250i	−0.816191	−	0.577782i
$723$	−7.40480	+	3.10958i	−0.275388	+	0.115646i
$724$	−22.5649	+	27.1612i	−0.838616	+	1.00944i
$725$	1.50333	−	1.79160i	0.0558322	−	0.0665382i
$726$	−25.8785	−	5.53841i	−0.960442	−	0.205550i
$727$	−3.02661	+	1.10160i	−0.112251	+	0.0408560i	−0.397535	−	0.917587i	$-0.630134\pi$
$727$	−3.02661	+	1.10160i	−0.112251	+	0.0408560i	0.285284	+	0.958443i	$0.407912\pi$
$728$	−0.410962	+	5.13189i	−0.0152313	+	0.190201i
$729$	6.22185	−	26.2733i	0.230439	−	0.973087i
$730$	−31.0627	−	30.9107i	−1.14968	−	1.14406i
$731$	−2.37670	−	13.4790i	−0.0879056	−	0.498537i
$732$	−1.03625	−	19.3811i	−0.0383010	−	0.716346i
$733$	−27.8212	−	16.0626i	−1.02760	−	0.593285i	−0.111304	−	0.993786i	$-0.535503\pi$
$733$	−27.8212	−	16.0626i	−1.02760	−	0.593285i	−0.916296	+	0.400502i	$0.868836\pi$
$734$	44.2149	−	11.9636i	1.63200	−	0.441586i
$735$	20.9070	+	10.7542i	0.771166	+	0.396674i
$736$	12.1612	+	16.9225i	0.448267	+	0.623771i
$737$	−2.29411	−	0.834989i	−0.0845048	−	0.0307572i
$738$	−1.58109	+	9.65467i	−0.0582008	+	0.355393i
$739$	3.69228	+	0.651048i	0.135823	+	0.0239492i	0.241146	−	0.970489i	$-0.422477\pi$
$739$	3.69228	+	0.651048i	0.135823	+	0.0239492i	−0.105324	+	0.994438i	$0.533588\pi$
$740$	−2.87568	−	1.64152i	−0.105712	−	0.0603436i
$741$	−3.75356	−	11.8601i	−0.137890	−	0.435691i
$742$	17.9144	+	4.75310i	0.657659	+	0.174492i
$743$	2.79490	−	15.8507i	0.102535	−	0.581504i	−0.889641	−	0.456660i	$-0.849046\pi$
$743$	2.79490	−	15.8507i	0.102535	−	0.581504i	0.992176	−	0.124845i	$-0.0398432\pi$
$744$	13.4494	−	7.21184i	0.493080	−	0.264399i
$745$	50.2730	+	18.2979i	1.84186	+	0.670383i
$746$	−3.62885	−	40.3384i	−0.132862	−	1.47689i
$747$	1.35286	−	17.4192i	0.0494987	−	0.637335i
$748$	−6.48117	+	0.0317878i	−0.236975	+	0.00116228i
$749$	−11.5844	−	6.68827i	−0.423286	−	0.244384i
$750$	7.93738	+	24.5453i	0.289832	+	0.896267i
$751$	51.1419	−	9.01770i	1.86620	−	0.329061i	0.877569	−	0.479450i	$-0.159164\pi$
$751$	51.1419	−	9.01770i	1.86620	−	0.329061i	0.988627	+	0.150390i	$0.0480528\pi$
$752$	−0.129900	−	13.2423i	−0.00473697	−	0.482896i
$753$	13.9325	−	18.3418i	0.507728	−	0.668411i
$754$	9.56486	−	4.48876i	0.348332	−	0.163471i
$755$	0.478505	+	1.31468i	0.0174146	+	0.0478461i
$756$	−3.66547	−	10.8794i	−0.133312	−	0.395681i
$757$	21.1302	−	25.1820i	0.767991	−	0.915256i	−0.230334	−	0.973112i	$-0.573982\pi$
$757$	21.1302	−	25.1820i	0.767991	−	0.915256i	0.998325	+	0.0578558i	$0.0184264\pi$
$758$	9.77811	+	4.53045i	0.355157	+	0.164553i
$759$	2.60384	−	1.09346i	0.0945132	−	0.0396899i
$760$	−14.5667	−	25.0242i	−0.528391	−	0.907724i
$761$		−	23.8579i		−	0.864847i	−0.901671	−	0.432423i	$-0.857659\pi$
$761$		−	23.8579i		−	0.864847i	0.901671	−	0.432423i	$-0.142341\pi$
$762$	−24.4042	−	0.886321i	−0.884070	−	0.0321080i
$763$	8.31211	+	6.97469i	0.300919	+	0.252501i
$764$	−31.4112	+	26.6207i	−1.13642	+	0.963104i
$765$	−46.9637	−	21.3442i	−1.69797	−	0.771700i
$766$	−10.0942	−	21.5093i	−0.364719	−	0.777162i
$767$	−1.33676	+	0.771777i	−0.0482675	+	0.0278672i
$768$	−16.3269	+	22.3927i	−0.589146	+	0.808027i
$769$	−3.50229	−	19.8625i	−0.126296	−	0.716258i	−0.980530	−	0.196370i	$-0.937085\pi$
$769$	−3.50229	−	19.8625i	−0.126296	−	0.716258i	0.854234	−	0.519888i	$-0.174026\pi$
$770$	1.61814	+	0.137571i	0.0583137	+	0.00495772i
$771$	−23.7828	−	3.01310i	−0.856516	−	0.108514i
$772$	−7.63265	+	0.0374353i	−0.274705	+	0.00134733i
$773$	4.88457	+	5.82121i	0.175686	+	0.209374i	0.846700	−	0.532070i	$-0.178586\pi$
$773$	4.88457	+	5.82121i	0.175686	+	0.209374i	−0.671015	+	0.741444i	$0.734141\pi$
$774$	−5.02343	+	6.13733i	−0.180563	+	0.220602i
$775$	−0.549550	+	1.50988i	−0.0197404	+	0.0542364i
$776$	1.39644	+	14.7138i	0.0501292	+	0.528194i
$777$	1.31541	−	0.298360i	0.0471902	−	0.0107036i
$778$	−6.48777	+	24.4524i	−0.232598	+	0.876661i
$779$	−7.08034	−	7.13433i	−0.253679	−	0.255614i
$780$	1.61963	−	13.3070i	0.0579919	−	0.476467i
$781$	−1.05667	+	5.99269i	−0.0378107	+	0.214435i
$782$	−31.1921	+	21.9551i	−1.11543	+	0.785113i
$783$	−15.6615	+	17.6019i	−0.559696	+	0.629041i
$784$	17.8548	+	14.6859i	0.637671	+	0.524497i
$785$	29.6823	+	35.3740i	1.05941	+	1.26255i
$786$	28.0436	+	35.9976i	1.00028	+	1.28399i
$787$	2.23087	−	3.86397i	0.0795218	−	0.137736i	−0.823522	−	0.567284i	$-0.807994\pi$
$787$	2.23087	−	3.86397i	0.0795218	−	0.137736i	0.903044	+	0.429549i	$0.141327\pi$
$788$	−7.78385	+	21.7168i	−0.277288	+	0.773628i
$789$	16.4771	+	25.5875i	0.586600	+	0.910940i
$790$	14.5922	−	14.6640i	0.519168	−	0.521721i
$791$	4.51825	+	7.82585i	0.160651	+	0.278255i
$792$	2.46297	+	2.83526i	0.0875177	+	0.100747i
$793$	3.15746	+	8.67505i	0.112125	+	0.308060i
$794$	11.1675	+	7.77880i	0.396318	+	0.276059i
$795$	−46.0962	−	14.2872i	−1.63486	−	0.506715i
$796$	−12.4119	+	14.9401i	−0.439928	+	0.529539i
$797$			42.1638i			1.49352i	0.665095	+	0.746759i	$0.268391\pi$
$797$			42.1638i			1.49352i	−0.665095	+	0.746759i	$0.731609\pi$
$798$	11.2615	+	3.50703i	0.398651	+	0.124148i
$799$	24.2400			0.857551
$800$	−0.289922	−	2.90335i	−0.0102503	−	0.102649i
$801$	−42.4987	+	4.13636i	−1.50162	+	0.146151i
$802$	−4.36047	+	6.26001i	−0.153973	+	0.221049i
$803$	−5.48754	+	1.99730i	−0.193651	+	0.0704832i
$804$	−10.4235	−	16.0138i	−0.367610	−	0.564763i
$805$	8.27711	−	4.77879i	0.291730	−	0.168430i
$806$	−5.12022	+	5.14539i	−0.180352	+	0.181239i
$807$	2.24053	+	3.47935i	0.0788702	+	0.122479i
$808$	6.62510	+	4.56668i	0.233070	+	0.160655i
$809$	14.0770	+	8.12734i	0.494920	+	0.285742i	0.726613	−	0.687047i	$-0.241093\pi$
$809$	14.0770	+	8.12734i	0.494920	+	0.285742i	−0.231693	+	0.972789i	$0.574427\pi$
$810$	8.36907	+	28.6970i	0.294059	+	1.00831i
$811$	−21.7018	+	18.2099i	−0.762052	+	0.639437i	−0.938660	−	0.344844i	$-0.887932\pi$
$811$	−21.7018	+	18.2099i	−0.762052	+	0.639437i	0.176608	+	0.984281i	$0.443487\pi$
$812$	−1.69119	+	9.87418i	−0.0593492	+	0.346516i
$813$	0.613855	+	12.6438i	0.0215288	+	0.443438i
$814$	−0.360831	+	0.253978i	−0.0126471	+	0.00890192i
$815$	47.8112	+	8.43040i	1.67475	+	0.295304i
$816$	−40.6928	−	30.2856i	−1.42453	−	1.06021i
$817$	−2.07905	−	7.87869i	−0.0727367	−	0.275641i
$818$	15.3817	+	4.08111i	0.537808	+	0.142693i
$819$	3.17558	+	4.44230i	0.110964	+	0.155227i
$820$	−3.75441	−	10.1598i	−0.131110	−	0.354797i
$821$	19.0323	+	6.92719i	0.664232	+	0.241761i	0.652062	−	0.758165i	$-0.273904\pi$
$821$	19.0323	+	6.92719i	0.664232	+	0.241761i	0.0121693	+	0.999926i	$0.496126\pi$
$822$	19.7134	+	37.2007i	0.687583	+	1.29752i
$823$	−34.8056	+	29.2054i	−1.21325	+	1.01803i	−0.214097	+	0.976813i	$0.568681\pi$
$823$	−34.8056	+	29.2054i	−1.21325	+	1.01803i	−0.999150	+	0.0412222i	$0.986875\pi$
$824$	−13.5399	+	52.0608i	−0.471686	+	1.81362i
$825$	−0.392284	−	0.0496995i	−0.0136576	−	0.00173031i
$826$	0.123979	−	1.45826i	0.00431377	−	0.0507395i
$827$	12.9547	−	2.28427i	0.450480	−	0.0794318i	0.0561948	−	0.998420i	$-0.482103\pi$
$827$	12.9547	−	2.28427i	0.450480	−	0.0794318i	0.394286	+	0.918988i	$0.370992\pi$
$828$	21.4315	+	5.40708i	0.744798	+	0.187909i
$829$	15.0314	+	26.0352i	0.522062	+	0.904238i	0.999671	+	0.0256655i	$0.00817048\pi$
$829$	15.0314	+	26.0352i	0.522062	+	0.904238i	−0.477608	+	0.878573i	$0.658496\pi$
$830$	8.21782	+	17.5109i	0.285245	+	0.607813i
$831$	−1.94340	+	1.79832i	−0.0674159	+	0.0623831i
$832$	4.32564	−	12.4517i	0.149965	−	0.431684i
$833$	−27.2006	+	32.4165i	−0.942447	+	1.12316i
$834$	−6.12095	−	0.222303i	−0.211951	−	0.00769774i
$835$	−12.3696			−0.428067
$836$	−3.84351	+	0.340549i	−0.132930	+	0.0117781i
$837$	5.97487	−	15.0436i	0.206522	−	0.519984i
$838$	2.36268	+	1.09469i	0.0816175	+	0.0378155i
$839$	−31.9987	−	26.8501i	−1.10472	−	0.926967i	−0.106983	−	0.994261i	$-0.534119\pi$
$839$	−31.9987	−	26.8501i	−1.10472	−	0.926967i	−0.997733	+	0.0672939i	$0.978564\pi$
$840$	9.47528	+	8.47157i	0.326928	+	0.292297i
$841$	−7.93137	+	2.88678i	−0.273495	+	0.0995442i
$842$	11.9500	+	25.4635i	0.411823	+	0.877532i
$843$	22.4774	−	29.5909i	0.774164	−	1.01917i
$844$	−20.3937	+	11.9081i	−0.701981	+	0.409892i
$845$	−4.19452	−	23.7883i	−0.144296	−	0.818342i
$846$	−9.15943	−	10.6490i	−0.314908	−	0.366120i
$847$	−5.96761	+	10.3362i	−0.205049	+	0.355156i
$848$	−41.3276	−	23.3230i	−1.41920	−	0.800916i
$849$	21.7302	−	42.2452i	0.745777	−	1.44985i
$850$	5.31929	−	0.478524i	0.182450	−	0.0164132i
$851$	−0.888193	+	2.44029i	−0.0304469	+	0.0836521i
$852$	−34.7969	+	32.5175i	−1.19212	+	1.11403i
$853$	6.96183	+	1.22756i	0.238368	+	0.0420308i	0.291556	−	0.956554i	$-0.405827\pi$
$853$	6.96183	+	1.22756i	0.238368	+	0.0420308i	−0.0531876	+	0.998585i	$0.516938\pi$
$854$	−8.46042	−	2.24474i	−0.289510	−	0.0768135i
$855$	−28.9215	−	10.3318i	−0.989095	−	0.353341i
$856$	24.3952	+	24.0388i	0.833809	+	0.821630i
$857$	2.05897	−	11.6770i	0.0703331	−	0.398879i	−0.929235	−	0.369489i	$-0.879533\pi$
$857$	2.05897	−	11.6770i	0.0703331	−	0.398879i	0.999568	−	0.0293894i	$-0.00935630\pi$
$858$	−1.51361	−	0.948750i	−0.0516738	−	0.0323898i
$859$	−8.29613	+	22.7934i	−0.283060	+	0.777701i	0.713933	+	0.700214i	$0.246912\pi$
$859$	−8.29613	+	22.7934i	−0.283060	+	0.777701i	−0.996993	+	0.0774875i	$0.975310\pi$
$860$	1.48232	−	8.65467i	0.0505468	−	0.295122i
$861$	3.92352	+	2.01819i	0.133713	+	0.0687797i
$862$	32.5193	−	8.79906i	1.10761	−	0.299697i
$863$	−10.3213	+	17.8771i	−0.351342	+	0.608543i	−0.986485	−	0.163852i	$-0.947608\pi$
$863$	−10.3213	+	17.8771i	−0.351342	+	0.608543i	0.635143	+	0.772395i	$0.280941\pi$
$864$	2.07143	+	29.3208i	0.0704716	+	0.997514i
$865$	0.0658360	−	0.0116087i	0.00223849	−	0.000394706i
$866$	17.7766	−	17.8640i	0.604075	−	0.607045i
$867$	38.3526	−	50.4902i	1.30252	−	1.71474i
$868$	−1.22837	−	6.77204i	−0.0416936	−	0.229858i
$869$	−0.942879	−	2.59054i	−0.0319850	−	0.0878780i
$870$	5.45894	−	25.5072i	0.185075	−	0.864774i
$871$	6.96214	+	5.84193i	0.235903	+	0.197946i
$872$	−16.1020	−	22.6397i	−0.545282	−	0.766676i
$873$	11.1925	+	10.9762i	0.378810	+	0.371489i
$874$	−17.4156	+	14.5735i	−0.589091	+	0.492956i
$875$	11.6341			0.393303
$876$	−43.7220	−	13.3167i	−1.47723	−	0.449928i
$877$	35.4415	+	29.7389i	1.19677	+	1.00421i	0.999716	+	0.0238207i	$0.00758309\pi$
$877$	35.4415	+	29.7389i	1.19677	+	1.00421i	0.197058	+	0.980392i	$0.436861\pi$
$878$	−16.2490	−	11.3184i	−0.548377	−	0.381977i
$879$	−8.98630	+	8.31544i	−0.303100	+	0.280473i
$880$	−3.92099	−	1.38372i	−0.132177	−	0.0466452i
$881$	19.7962	−	11.4293i	0.666951	−	0.385064i	−0.127970	−	0.991778i	$-0.540846\pi$
$881$	19.7962	−	11.4293i	0.666951	−	0.385064i	0.794920	+	0.606714i	$0.207513\pi$
$882$	24.5192	−	0.299375i	0.825603	−	0.0100805i
$883$	3.00711	−	0.530235i	0.101197	−	0.0178438i	−0.122820	−	0.992429i	$-0.539194\pi$
$883$	3.00711	−	0.530235i	0.101197	−	0.0178438i	0.224018	+	0.974585i	$0.428083\pi$
$884$	22.7130	+	8.14091i	0.763920	+	0.273809i
$885$	−0.478962	+	3.78051i	−0.0161001	+	0.127080i
$886$	26.8447	−	7.26363i	0.901867	−	0.244026i
$887$	−17.5840	+	14.7547i	−0.590413	+	0.495415i	−0.888348	−	0.459171i	$-0.848147\pi$
$887$	−17.5840	+	14.7547i	−0.590413	+	0.495415i	0.297935	+	0.954586i	$0.403702\pi$
$888$	−3.45179	−	0.108415i	−0.115835	−	0.00363816i
$889$	−3.76676	+	10.3491i	−0.126333	+	0.347098i
$890$	38.6579	−	27.2101i	1.29581	−	0.912083i
$891$	3.93570	+	0.615043i	0.131851	+	0.0206047i
$892$	−7.08861	+	12.4181i	−0.237344	+	0.415788i
$893$	14.3809	−	1.20314i	0.481238	−	0.0402617i
$894$	55.2660	−	7.68848i	1.84837	−	0.257141i
$895$	17.6569	+	3.11340i	0.590207	+	0.104069i
$896$	7.34334	+	10.1133i	0.245324	+	0.337863i
$897$	−10.5010	+	0.509821i	−0.350618	+	0.0170224i
$898$	2.32893	+	25.8885i	0.0777175	+	0.863910i
$899$	−10.8203	+	9.07930i	−0.360877	+	0.302811i
$900$	−2.22019	−	2.15602i	−0.0740063	−	0.0718674i
$901$	43.4308	−	75.2244i	1.44689	−	2.50609i
$902$	−1.43820	−	0.122273i	−0.0478867	−	0.00407124i
$903$	1.93652	+	3.00725i	0.0644433	+	0.100075i
$904$	−6.15251	−	22.3038i	−0.204629	−	0.741814i
$905$	−20.7329	−	35.9105i	−0.689185	−	1.19370i
$906$	1.08301	+	0.977889i	0.0359806	+	0.0324882i
$907$	−28.1858	+	10.2588i	−0.935894	+	0.340637i	−0.764543	−	0.644573i	$-0.777035\pi$
$907$	−28.1858	+	10.2588i	−0.935894	+	0.340637i	−0.171351	+	0.985210i	$0.554813\pi$
$908$	−15.9541	+	13.5209i	−0.529454	+	0.448708i
$909$	8.49449	−	0.826760i	0.281744	−	0.0274219i
$910$	−5.48543	−	2.54154i	−0.181840	−	0.0842512i
$911$	36.5933			1.21239			0.606195	−	0.795316i	$-0.292695\pi$
$911$	36.5933			1.21239			0.606195	+	0.795316i	$0.292695\pi$
$912$	−25.6450	−	15.9478i	−0.849192	−	0.528084i
$913$	2.57770			0.0853093
$914$	1.23826	+	0.573718i	0.0409580	+	0.0189769i
$915$	21.7698	+	6.74741i	0.719687	+	0.223062i
$916$	23.6388	−	20.0337i	0.781048	−	0.661932i
$917$	19.3384	−	7.03860i	0.638610	−	0.232435i
$918$	−53.7039	+	3.26496i	−1.77249	+	0.107760i
$919$	−11.0329	−	19.1095i	−0.363941	−	0.630364i	0.624665	−	0.780893i	$-0.285236\pi$
$919$	−11.0329	−	19.1095i	−0.363941	−	0.630364i	−0.988606	+	0.150529i	$0.951902\pi$
$920$	−23.5899	+	6.50728i	−0.777737	+	0.214539i
$921$	16.2163	−	10.4425i	0.534344	−	0.344091i
$922$	−14.5499	−	1.23700i	−0.479174	−	0.0407385i
$923$	11.3266	−	19.6183i	0.372820	−	0.645743i
$924$	1.55841	−	0.663451i	0.0512680	−	0.0218259i
$925$	0.278539	−	0.233722i	0.00915830	−	0.00768473i
$926$	3.19074	+	35.4684i	0.104854	+	1.16556i
$927$	24.6162	+	51.4724i	0.808502	+	1.69057i
$928$	10.5542	−	23.3777i	0.346458	−	0.767411i
$929$	−25.8434	−	4.55689i	−0.847895	−	0.149507i	−0.267213	−	0.963637i	$-0.586103\pi$
$929$	−25.8434	−	4.55689i	−0.847895	−	0.149507i	−0.580682	+	0.814131i	$0.697214\pi$
$930$	2.46932	+	17.7498i	0.0809721	+	0.582040i
$931$	−14.5283	+	20.5818i	−0.476147	+	0.674541i
$932$	8.85570	−	15.5137i	0.290078	−	0.508169i
$933$	3.56582	+	15.7210i	0.116740	+	0.514683i
$934$	32.8380	−	23.1136i	1.07449	−	0.756300i
$935$	2.60306	−	7.15186i	0.0851293	−	0.233891i
$936$	−5.00599	−	13.0543i	−0.163626	−	0.426693i
$937$	37.1264	−	31.1528i	1.21287	−	1.01772i	0.213701	−	0.976899i	$-0.431448\pi$
$937$	37.1264	−	31.1528i	1.21287	−	1.01772i	0.999167	−	0.0408179i	$-0.0129964\pi$
$938$	−8.31810	+	2.25070i	−0.271595	+	0.0734881i
$939$	25.2230	+	3.19557i	0.823122	+	0.104283i
$940$	14.6390	+	5.24701i	0.477473	+	0.171139i
$941$	8.17962	−	1.44229i	0.266648	−	0.0470173i	−0.0387254	−	0.999250i	$-0.512330\pi$
$941$	8.17962	−	1.44229i	0.266648	−	0.0470173i	0.305374	+	0.952233i	$0.401219\pi$
$942$	44.6295	+	18.1040i	1.45411	+	0.589859i
$943$	−7.35666	+	4.24737i	−0.239566	+	0.138313i
$944$	−1.24701	+	3.53359i	−0.0405866	+	0.115008i
$945$	13.4755	+	0.390870i	0.438358	+	0.0127150i
$946$	−0.960146	−	0.668798i	−0.0312170	−	0.0217445i
$947$	−33.7003	−	28.2779i	−1.09511	−	0.918909i	−0.0980263	−	0.995184i	$-0.531253\pi$
$947$	−33.7003	−	28.2779i	−1.09511	−	0.918909i	−0.997087	+	0.0762748i	$0.975697\pi$
$948$	6.28648	−	20.6401i	0.204176	−	0.670360i
$949$	21.7396			0.705698
$950$	3.13202	−	0.547914i	0.101616	−	0.0177767i
$951$	−43.2632	+	18.1680i	−1.40291	+	0.589137i
$952$	−18.6426	+	13.2591i	−0.604210	+	0.429731i
$953$	14.9650	+	12.5571i	0.484765	+	0.406766i	0.852146	−	0.523305i	$-0.175301\pi$
$953$	14.9650	+	12.5571i	0.484765	+	0.406766i	−0.367381	+	0.930071i	$0.619746\pi$
$954$	−49.4581	+	9.34479i	−1.60127	+	0.302549i
$955$	−16.5368	−	45.4346i	−0.535119	−	1.47023i
$956$	8.52298	+	46.9874i	0.275653	+	1.51968i
$957$	−2.76803	−	2.10261i	−0.0894778	−	0.0679678i
$958$	−36.6945	+	36.8749i	−1.18555	+	1.19138i
$959$	18.6987	−	3.29709i	0.603813	−	0.106468i
$960$	−18.0196	−	27.0985i	−0.581579	−	0.874600i
$961$	−10.6480	+	18.4428i	−0.343483	+	0.594929i
$962$	1.58564	−	0.429041i	0.0511230	−	0.0138328i
$963$	36.2174	+	2.81283i	1.16709	+	0.0906422i
$964$	1.56554	−	9.14056i	0.0504227	−	0.294398i
$965$	3.06553	−	8.42249i	0.0986831	−	0.271129i
$966$	5.29417	−	8.44619i	0.170337	−	0.271752i
$967$	4.52755	−	25.6770i	0.145596	−	0.825718i	−0.821290	−	0.570511i	$-0.806745\pi$
$967$	4.52755	−	25.6770i	0.145596	−	0.825718i	0.966886	−	0.255207i	$-0.0821436\pi$
$968$	21.4486	−	21.7666i	0.689386	−	0.699604i
$969$	29.6501	−	46.6525i	0.952499	−	1.49870i
$970$	−16.7754	−	4.45089i	−0.538626	−	0.142910i
$971$	9.98870	+	1.76128i	0.320553	+	0.0565221i	0.331609	−	0.943417i	$-0.392408\pi$
$971$	9.98870	+	1.76128i	0.320553	+	0.0565221i	−0.0110567	+	0.999939i	$0.503520\pi$
$972$	21.7271	+	22.3592i	0.696897	+	0.717171i
$973$	−0.944764	+	2.59572i	−0.0302877	+	0.0832149i
$974$	−19.7005	+	1.77226i	−0.631243	+	0.0567868i
$975$	1.30901	+	0.673332i	0.0419219	+	0.0215639i
$976$	19.5178	+	11.0147i	0.624748	+	0.352573i
$977$	−14.2606	+	24.7002i	−0.456238	+	0.790228i	−0.998758	−	0.0498149i	$-0.984137\pi$
$977$	−14.2606	+	24.7002i	−0.456238	+	0.790228i	0.542520	+	0.840043i	$0.317470\pi$
$978$	48.1784	−	15.5798i	1.54058	−	0.498187i
$979$	−1.09393	−	6.20401i	−0.0349623	−	0.198281i
$980$	−23.4439	+	13.6891i	−0.748888	+	0.437282i
$981$	−28.5361	−	7.34857i	−0.911086	−	0.234622i
$982$	−0.874265	−	1.86293i	−0.0278989	−	0.0594484i
$983$	41.2809	−	15.0250i	1.31665	−	0.479223i	0.414270	−	0.910154i	$-0.364037\pi$
$983$	41.2809	−	15.0250i	1.31665	−	0.479223i	0.902385	+	0.430931i	$0.141815\pi$
$984$	−8.42160	−	7.52950i	−0.268471	−	0.240032i
$985$	−20.7524	−	17.4133i	−0.661226	−	0.554835i
$986$	42.5994	+	19.7374i	1.35664	+	0.628566i
$987$	−5.84060	+	2.45270i	−0.185908	+	0.0780705i
$988$	13.8790	+	3.70241i	0.441549	+	0.117789i
$989$	−6.88648			−0.218977
$990$	−4.12552	+	1.55887i	−0.131118	+	0.0495440i
$991$	−4.66262	+	5.55669i	−0.148113	+	0.176514i	−0.835000	−	0.550250i	$-0.814532\pi$
$991$	−4.66262	+	5.55669i	−0.148113	+	0.176514i	0.686887	+	0.726764i	$0.258977\pi$
$992$	−1.32049	+	17.5723i	−0.0419256	+	0.557922i
$993$	20.4899	+	22.1429i	0.650226	+	0.702684i
$994$	9.12500	+	19.4440i	0.289427	+	0.616726i
$995$	−11.4042	−	19.7527i	−0.361538	−	0.626203i
$996$	16.1249	+	12.1243i	0.510937	+	0.384173i
$997$	25.1230	−	4.42985i	0.795652	−	0.140295i	0.238977	−	0.971025i	$-0.423188\pi$
$997$	25.1230	−	4.42985i	0.795652	−	0.140295i	0.556675	+	0.830730i	$0.312077\pi$
$998$	3.82556	−	44.9970i	0.121096	−	1.42435i
$999$	−2.87310	+	2.27218i	−0.0909008	+	0.0718884i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.bj.a.173.11	yes	456
3.2	odd	2	inner	456.2.bj.a.173.66	yes	456
8.5	even	2	inner	456.2.bj.a.173.76	yes	456
19.10	odd	18	inner	456.2.bj.a.29.1	✓	456
24.5	odd	2	inner	456.2.bj.a.173.1	yes	456
57.29	even	18	inner	456.2.bj.a.29.76	yes	456
152.29	odd	18	inner	456.2.bj.a.29.66	yes	456
456.29	even	18	inner	456.2.bj.a.29.11	yes	456

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bj.a.29.1	✓	456	19.10	odd	18	inner
456.2.bj.a.29.11	yes	456	456.29	even	18	inner
456.2.bj.a.29.66	yes	456	152.29	odd	18	inner
456.2.bj.a.29.76	yes	456	57.29	even	18	inner
456.2.bj.a.173.1	yes	456	24.5	odd	2	inner
456.2.bj.a.173.11	yes	456	1.1	even	1	trivial
456.2.bj.a.173.66	yes	456	3.2	odd	2	inner
456.2.bj.a.173.76	yes	456	8.5	even	2	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:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bj (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28317 - 0.594528i) q^{2} +(0.512773 - 1.65441i) q^{3} +(1.29307 + 1.52577i) q^{4} +(-2.20694 + 0.803259i) q^{5} +(-1.64157 + 1.81804i) q^{6} +(0.552347 + 0.956693i) q^{7} +(-0.752130 - 2.72659i) q^{8} +(-2.47413 - 1.69667i) q^{9} +O(q^{10})\)	\(q+(-1.28317 - 0.594528i) q^{2} +(0.512773 - 1.65441i) q^{3} +(1.29307 + 1.52577i) q^{4} +(-2.20694 + 0.803259i) q^{5} +(-1.64157 + 1.81804i) q^{6} +(0.552347 + 0.956693i) q^{7} +(-0.752130 - 2.72659i) q^{8} +(-2.47413 - 1.69667i) q^{9} +(3.30945 + 0.281363i) q^{10} +(0.221304 - 0.383309i) q^{11} +(3.18729 - 1.35690i) q^{12} +(-1.26221 + 1.05912i) q^{13} +(-0.139977 - 1.55599i) q^{14} +(0.197261 + 4.06306i) q^{15} +(-0.655919 + 3.94585i) q^{16} +(-7.21044 - 1.27139i) q^{17} +(2.16602 + 3.64806i) q^{18} +(-4.34084 - 0.396393i) q^{19} +(-4.07932 - 2.32859i) q^{20} +(1.86599 - 0.423240i) q^{21} +(-0.511860 + 0.360282i) q^{22} +(-1.25995 + 3.46169i) q^{23} +(-4.89656 - 0.153792i) q^{24} +(0.395123 - 0.331548i) q^{25} +(2.24932 - 0.608619i) q^{26} +(-4.07565 + 3.22321i) q^{27} +(-0.745463 + 2.07983i) q^{28} +(4.46539 - 0.787368i) q^{29} +(2.16248 - 5.33090i) q^{30} +(-2.69779 + 1.55757i) q^{31} +(3.18758 - 4.67326i) q^{32} +(-0.520671 - 0.562677i) q^{33} +(8.49637 + 5.91822i) q^{34} +(-1.98747 - 1.66768i) q^{35} +(-0.610510 - 5.96886i) q^{36} +0.704942 q^{37} +(5.33439 + 3.08939i) q^{38} +(1.10499 + 2.63130i) q^{39} +(3.85006 + 5.41326i) q^{40} +(1.76645 + 1.48223i) q^{41} +(-2.64602 - 0.566290i) q^{42} +(0.639362 + 1.75663i) q^{43} +(0.871003 - 0.157990i) q^{44} +(6.82311 + 1.75708i) q^{45} +(3.67481 - 3.69288i) q^{46} +(-3.26043 + 0.574902i) q^{47} +(6.19171 + 3.10849i) q^{48} +(2.88983 - 5.00533i) q^{49} +(-0.704126 + 0.190522i) q^{50} +(-5.80072 + 11.2771i) q^{51} +(-3.24811 - 0.556317i) q^{52} +(-4.05761 + 11.1482i) q^{53} +(7.14606 - 1.71285i) q^{54} +(-0.180507 + 1.02370i) q^{55} +(2.19307 - 2.22558i) q^{56} +(-2.88166 + 6.97825i) q^{57} +(-6.19798 - 1.64446i) q^{58} +(0.922560 + 0.162672i) q^{59} +(-5.94421 + 5.55481i) q^{60} +(1.91628 - 5.26494i) q^{61} +(4.38775 - 0.394723i) q^{62} +(0.256616 - 3.30413i) q^{63} +(-6.86860 + 4.10150i) q^{64} +(1.93487 - 3.35130i) q^{65} +(0.333585 + 1.03157i) q^{66} +(-0.957812 - 5.43202i) q^{67} +(-7.38378 - 12.6454i) q^{68} +(5.08098 + 3.85953i) q^{69} +(1.55878 + 3.32153i) q^{70} +(-12.9192 + 4.70222i) q^{71} +(-2.76526 + 8.02205i) q^{72} +(-10.1071 - 8.48087i) q^{73} +(-0.904564 - 0.419107i) q^{74} +(-0.345907 - 0.823703i) q^{75} +(-5.00822 - 7.13566i) q^{76} +0.488946 q^{77} +(0.146486 - 4.03337i) q^{78} +(4.00362 - 4.77133i) q^{79} +(-1.72197 - 9.23513i) q^{80} +(3.24262 + 8.39556i) q^{81} +(-1.38544 - 2.95216i) q^{82} +(2.91194 + 5.04363i) q^{83} +(3.05863 + 2.29978i) q^{84} +(16.9342 - 2.98596i) q^{85} +(0.223953 - 2.63418i) q^{86} +(0.987101 - 7.79131i) q^{87} +(-1.21158 - 0.315106i) q^{88} +(10.9032 - 9.14891i) q^{89} +(-7.71061 - 6.31117i) q^{90} +(-1.71043 - 0.622547i) q^{91} +(-6.91094 + 2.55383i) q^{92} +(1.19350 + 5.26192i) q^{93} +(4.52549 + 1.20072i) q^{94} +(9.89836 - 2.61200i) q^{95} +(-6.09697 - 7.66987i) q^{96} +(-5.14609 - 0.907395i) q^{97} +(-6.68396 + 4.70463i) q^{98} +(-1.19788 + 0.572877i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 456 q - 6 q^{4} - 6 q^{6} - 12 q^{7} - 12 q^{9}+O(q^{10}) \) 456 * q - 6 * q^4 - 6 * q^6 - 12 * q^7 - 12 * q^9	\( 456 q - 6 q^{4} - 6 q^{6} - 12 q^{7} - 12 q^{9} - 6 q^{10} - 9 q^{12} - 12 q^{15} - 6 q^{16} + 6 q^{24} - 24 q^{25} + 12 q^{28} - 6 q^{30} - 36 q^{31} + 6 q^{33} + 30 q^{34} - 66 q^{36} - 24 q^{39} - 42 q^{40} + 39 q^{42} - 18 q^{46} - 15 q^{48} - 168 q^{49} - 36 q^{52} - 45 q^{54} + 36 q^{55} - 12 q^{57} - 96 q^{58} - 18 q^{60} + 30 q^{63} - 48 q^{64} - 18 q^{66} - 78 q^{70} + 60 q^{72} - 12 q^{76} + 45 q^{78} - 24 q^{79} - 156 q^{82} - 9 q^{84} - 6 q^{87} - 90 q^{88} + 84 q^{90} - 162 q^{96} - 24 q^{97}+O(q^{100}) \) 456 * q - 6 * q^4 - 6 * q^6 - 12 * q^7 - 12 * q^9 - 6 * q^10 - 9 * q^12 - 12 * q^15 - 6 * q^16 + 6 * q^24 - 24 * q^25 + 12 * q^28 - 6 * q^30 - 36 * q^31 + 6 * q^33 + 30 * q^34 - 66 * q^36 - 24 * q^39 - 42 * q^40 + 39 * q^42 - 18 * q^46 - 15 * q^48 - 168 * q^49 - 36 * q^52 - 45 * q^54 + 36 * q^55 - 12 * q^57 - 96 * q^58 - 18 * q^60 + 30 * q^63 - 48 * q^64 - 18 * q^66 - 78 * q^70 + 60 * q^72 - 12 * q^76 + 45 * q^78 - 24 * q^79 - 156 * q^82 - 9 * q^84 - 6 * q^87 - 90 * q^88 + 84 * q^90 - 162 * q^96 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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