LMFDB - Embedded newform 666.2.bs.a.89.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(17,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 7]))

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

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

chi := DirichletCharacter("666.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.bs (of order $36$, degree $12$, 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:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			89.5
Character	$\chi$	$=$	666.89
Dual form			666.2.bs.a.449.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.906308 - 0.422618i) q^{2} +(0.642788 - 0.766044i) q^{4} +(-0.733836 + 0.513837i) q^{5} +(-0.650195 + 3.68744i) q^{7} +(0.258819 - 0.965926i) q^{8} +O(q^{10})$	\(q+(0.906308 - 0.422618i) q^{2} +(0.642788 - 0.766044i) q^{4} +(-0.733836 + 0.513837i) q^{5} +(-0.650195 + 3.68744i) q^{7} +(0.258819 - 0.965926i) q^{8} +(-0.447924 + 0.775827i) q^{10} +(-0.331435 - 0.574062i) q^{11} +(5.44248 - 0.476155i) q^{13} +(0.969102 + 3.61674i) q^{14} +(-0.173648 - 0.984808i) q^{16} +(6.75861 + 0.591301i) q^{17} +(-1.75011 + 3.75313i) q^{19} +(-0.0780783 + 0.892439i) q^{20} +(-0.542991 - 0.380207i) q^{22} +(-2.17412 + 0.582554i) q^{23} +(-1.43561 + 3.94432i) q^{25} +(4.73133 - 2.73164i) q^{26} +(2.40681 + 2.86832i) q^{28} +(5.24193 + 1.40457i) q^{29} +(6.59614 + 6.59614i) q^{31} +(-0.573576 - 0.819152i) q^{32} +(6.37527 - 2.32041i) q^{34} +(-1.41761 - 3.04007i) q^{35} +(-2.08195 - 5.71537i) q^{37} +4.14112i q^{38} +(0.306398 + 0.841822i) q^{40} +(-8.43708 - 7.07955i) q^{41} +(0.641826 - 0.641826i) q^{43} +(-0.652800 - 0.115106i) q^{44} +(-1.72423 + 1.44680i) q^{46} +(-11.2441 - 6.49176i) q^{47} +(-6.59661 - 2.40097i) q^{49} +(0.365832 + 4.18148i) q^{50} +(3.13360 - 4.47525i) q^{52} +(4.46640 - 0.787548i) q^{53} +(0.538194 + 0.250964i) q^{55} +(3.39351 + 1.58242i) q^{56} +(5.34440 - 0.942362i) q^{58} +(5.83653 - 8.33542i) q^{59} +(0.502323 + 5.74158i) q^{61} +(8.76578 + 3.19048i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(-3.74922 + 3.14597i) q^{65} +(-4.60581 - 0.812129i) q^{67} +(4.79731 - 4.79731i) q^{68} +(-2.56958 - 2.15613i) q^{70} +(-1.77700 - 4.88227i) q^{71} +10.2121i q^{73} +(-4.30231 - 4.30001i) q^{74} +(1.75011 + 3.75313i) q^{76} +(2.33232 - 0.848894i) q^{77} +(-3.74578 - 5.34952i) q^{79} +(0.633460 + 0.633460i) q^{80} +(-10.6385 - 2.85059i) q^{82} +(2.76443 + 3.29452i) q^{83} +(-5.26354 + 3.03891i) q^{85} +(0.310445 - 0.852939i) q^{86} +(-0.640283 + 0.171563i) q^{88} +(-0.823256 - 0.576450i) q^{89} +(-1.78288 + 20.3784i) q^{91} +(-0.951236 + 2.03993i) q^{92} +(-12.9341 - 1.13159i) q^{94} +(-0.644202 - 3.65345i) q^{95} +(-2.89811 - 10.8159i) q^{97} +(-6.99325 + 0.611830i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q+O(q^{10}) $ 72 * q	$ 72 q + 12 q^{13} - 24 q^{19} - 12 q^{22} + 72 q^{34} + 72 q^{37} + 24 q^{40} + 24 q^{43} + 36 q^{46} - 48 q^{49} - 12 q^{52} + 60 q^{55} + 120 q^{61} + 60 q^{67} - 60 q^{70} + 24 q^{76} - 12 q^{79} - 48 q^{82} + 108 q^{85} - 24 q^{88} - 168 q^{91} - 84 q^{94} - 264 q^{97}+O(q^{100}) $ 72 * q + 12 * q^13 - 24 * q^19 - 12 * q^22 + 72 * q^34 + 72 * q^37 + 24 * q^40 + 24 * q^43 + 36 * q^46 - 48 * q^49 - 12 * q^52 + 60 * q^55 + 120 * q^61 + 60 * q^67 - 60 * q^70 + 24 * q^76 - 12 * q^79 - 48 * q^82 + 108 * q^85 - 24 * q^88 - 168 * q^91 - 84 * q^94 - 264 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{13}{36}\right)$

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 $

$2$	0.906308	−	0.422618i	0.640856	−	0.298836i
$2$	0.906308	−	0.422618i	0.640856	−	0.298836i
$3$		0			0
$3$		0			0
$4$	0.642788	−	0.766044i	0.321394	−	0.383022i
$5$	−0.733836	+	0.513837i	−0.328181	+	0.229795i	−0.726041	−	0.687651i	$-0.758642\pi$
$5$	−0.733836	+	0.513837i	−0.328181	+	0.229795i	0.397860	+	0.917446i	$0.369753\pi$
$6$		0			0
$7$	−0.650195	+	3.68744i	−0.245751	+	1.39372i	0.572992	+	0.819561i	$0.305782\pi$
$7$	−0.650195	+	3.68744i	−0.245751	+	1.39372i	−0.818743	+	0.574160i	$0.805329\pi$
$8$	0.258819	−	0.965926i	0.0915064	−	0.341506i
$9$		0			0
$10$	−0.447924	+	0.775827i	−0.141646	+	0.245338i
$11$	−0.331435	−	0.574062i	−0.0999314	−	0.173086i	0.811725	−	0.584040i	$-0.198529\pi$
$11$	−0.331435	−	0.574062i	−0.0999314	−	0.173086i	−0.911656	+	0.410954i	$0.865196\pi$
$12$		0			0
$13$	5.44248	−	0.476155i	1.50947	−	0.132062i	0.697850	−	0.716244i	$-0.254140\pi$
$13$	5.44248	−	0.476155i	1.50947	−	0.132062i	0.811623	+	0.584182i	$0.198585\pi$
$14$	0.969102	+	3.61674i	0.259004	+	0.966614i
$15$		0			0
$16$	−0.173648	−	0.984808i	−0.0434120	−	0.246202i
$17$	6.75861	+	0.591301i	1.63920	+	0.143412i	0.869143	−	0.494560i	$-0.164671\pi$
$17$	6.75861	+	0.591301i	1.63920	+	0.143412i	0.770059	+	0.637972i	$0.220226\pi$
$18$		0			0
$19$	−1.75011	+	3.75313i	−0.401503	+	0.861026i	0.596777	+	0.802407i	$0.296448\pi$
$19$	−1.75011	+	3.75313i	−0.401503	+	0.861026i	−0.998280	+	0.0586193i	$0.981330\pi$
$20$	−0.0780783	+	0.892439i	−0.0174588	+	0.199555i
$21$		0			0
$22$	−0.542991	−	0.380207i	−0.115766	−	0.0810603i
$23$	−2.17412	+	0.582554i	−0.453336	+	0.121471i	−0.478260	−	0.878218i	$-0.658732\pi$
$23$	−2.17412	+	0.582554i	−0.453336	+	0.121471i	0.0249241	+	0.999689i	$0.492066\pi$
$24$		0			0
$25$	−1.43561	+	3.94432i	−0.287123	+	0.788864i
$26$	4.73133	−	2.73164i	0.927890	−	0.535718i
$27$		0			0
$28$	2.40681	+	2.86832i	0.454843	+	0.542061i
$29$	5.24193	+	1.40457i	0.973402	+	0.260822i	0.710263	−	0.703936i	$-0.248576\pi$
$29$	5.24193	+	1.40457i	0.973402	+	0.260822i	0.263138	+	0.964758i	$0.415242\pi$
$30$		0			0
$31$	6.59614	+	6.59614i	1.18470	+	1.18470i	0.978512	+	0.206189i	$0.0661063\pi$
$31$	6.59614	+	6.59614i	1.18470	+	1.18470i	0.206189	+	0.978512i	$0.433894\pi$
$32$	−0.573576	−	0.819152i	−0.101395	−	0.144807i
$33$		0			0
$34$	6.37527	−	2.32041i	1.09335	−	0.397947i
$35$	−1.41761	−	3.04007i	−0.239619	−	0.513866i
$36$		0			0
$37$	−2.08195	−	5.71537i	−0.342271	−	0.939601i
$37$	−2.08195	−	5.71537i	−0.342271	−	0.939601i
$38$			4.14112i			0.671778i
$39$		0			0
$40$	0.306398	+	0.841822i	0.0484458	+	0.133104i
$41$	−8.43708	−	7.07955i	−1.31765	−	1.10564i	−0.986798	−	0.161957i	$-0.948219\pi$
$41$	−8.43708	−	7.07955i	−1.31765	−	1.10564i	−0.330852	−	0.943683i	$-0.607336\pi$
$42$		0			0
$43$	0.641826	−	0.641826i	0.0978776	−	0.0978776i	−0.656472	−	0.754350i	$-0.727952\pi$
$43$	0.641826	−	0.641826i	0.0978776	−	0.0978776i	0.754350	+	0.656472i	$0.227952\pi$
$44$	−0.652800	−	0.115106i	−0.0984133	−	0.0173529i
$45$		0			0
$46$	−1.72423	+	1.44680i	−0.254223	+	0.213319i
$47$	−11.2441	−	6.49176i	−1.64011	−	0.946921i	−0.980791	−	0.195062i	$-0.937509\pi$
$47$	−11.2441	−	6.49176i	−1.64011	−	0.946921i	−0.659324	−	0.751859i	$-0.729157\pi$
$48$		0			0
$49$	−6.59661	−	2.40097i	−0.942372	−	0.342996i
$50$	0.365832	+	4.18148i	0.0517365	+	0.591351i
$51$		0			0
$52$	3.13360	−	4.47525i	0.434553	−	0.620605i
$53$	4.46640	−	0.787548i	0.613508	−	0.108178i	0.141745	−	0.989903i	$-0.454729\pi$
$53$	4.46640	−	0.787548i	0.613508	−	0.108178i	0.471763	+	0.881725i	$0.343618\pi$
$54$		0			0
$55$	0.538194	+	0.250964i	0.0725700	+	0.0338400i
$56$	3.39351	+	1.58242i	0.453477	+	0.211460i
$57$		0			0
$58$	5.34440	−	0.942362i	0.701754	−	0.123738i
$59$	5.83653	−	8.33542i	0.759851	−	1.08518i	−0.233757	−	0.972295i	$-0.575102\pi$
$59$	5.83653	−	8.33542i	0.759851	−	1.08518i	0.993608	−	0.112885i	$-0.0360091\pi$
$60$		0			0
$61$	0.502323	+	5.74158i	0.0643159	+	0.735134i	0.958062	+	0.286561i	$0.0925120\pi$
$61$	0.502323	+	5.74158i	0.0643159	+	0.735134i	−0.893746	+	0.448573i	$0.851932\pi$
$62$	8.76578	+	3.19048i	1.11326	+	0.405192i
$63$		0			0
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	−3.74922	+	3.14597i	−0.465034	+	0.390210i
$66$		0			0
$67$	−4.60581	−	0.812129i	−0.562690	−	0.0992174i	−0.114934	−	0.993373i	$-0.536666\pi$
$67$	−4.60581	−	0.812129i	−0.562690	−	0.0992174i	−0.447756	+	0.894156i	$0.647777\pi$
$68$	4.79731	−	4.79731i	0.581759	−	0.581759i
$69$		0			0
$70$	−2.56958	−	2.15613i	−0.307123	−	0.257707i
$71$	−1.77700	−	4.88227i	−0.210891	−	0.579419i	0.788473	−	0.615069i	$-0.210872\pi$
$71$	−1.77700	−	4.88227i	−0.210891	−	0.579419i	−0.999364	+	0.0356504i	$0.988650\pi$
$72$		0			0
$73$			10.2121i			1.19523i	0.801781	+	0.597617i	$0.203886\pi$
$73$			10.2121i			1.19523i	−0.801781	+	0.597617i	$0.796114\pi$
$74$	−4.30231	−	4.30001i	−0.500133	−	0.499867i
$75$		0			0
$76$	1.75011	+	3.75313i	0.200752	+	0.430513i
$77$	2.33232	−	0.848894i	0.265792	−	0.0967405i
$78$		0			0
$79$	−3.74578	−	5.34952i	−0.421433	−	0.601868i	0.551155	−	0.834403i	$-0.314187\pi$
$79$	−3.74578	−	5.34952i	−0.421433	−	0.601868i	−0.972588	+	0.232534i	$0.925298\pi$
$80$	0.633460	+	0.633460i	0.0708230	+	0.0708230i
$81$		0			0
$82$	−10.6385	−	2.85059i	−1.17483	−	0.314795i
$83$	2.76443	+	3.29452i	0.303436	+	0.361620i	0.896118	−	0.443816i	$-0.146376\pi$
$83$	2.76443	+	3.29452i	0.303436	+	0.361620i	−0.592682	+	0.805436i	$0.701931\pi$
$84$		0			0
$85$	−5.26354	+	3.03891i	−0.570911	+	0.329616i
$86$	0.310445	−	0.852939i	0.0334761	−	0.0919748i
$87$		0			0
$88$	−0.640283	+	0.171563i	−0.0682544	+	0.0182887i
$89$	−0.823256	−	0.576450i	−0.0872650	−	0.0611036i	0.529130	−	0.848541i	$-0.322519\pi$
$89$	−0.823256	−	0.576450i	−0.0872650	−	0.0611036i	−0.616395	+	0.787437i	$0.711407\pi$
$90$		0			0
$91$	−1.78288	+	20.3784i	−0.186897	+	2.13624i
$92$	−0.951236	+	2.03993i	−0.0991732	+	0.212678i
$93$		0			0
$94$	−12.9341	−	1.13159i	−1.33405	−	0.116714i
$95$	−0.644202	−	3.65345i	−0.0660937	−	0.374836i
$96$		0			0
$97$	−2.89811	−	10.8159i	−0.294259	−	1.09819i	−0.941804	−	0.336162i	$-0.890871\pi$
$97$	−2.89811	−	10.8159i	−0.294259	−	1.09819i	0.647546	−	0.762027i	$-0.275795\pi$
$98$	−6.99325	+	0.611830i	−0.706425	+	0.0618042i
$99$		0			0
$100$	2.09873	+	3.63510i	0.209873	+	0.363510i
$101$	−3.36909	+	5.83544i	−0.335237	+	0.580648i	−0.983530	−	0.180743i	$-0.942150\pi$
$101$	−3.36909	+	5.83544i	−0.335237	+	0.580648i	0.648293	+	0.761391i	$0.275483\pi$
$102$		0			0
$103$	4.59047	−	17.1319i	0.452312	−	1.68805i	−0.243560	−	0.969886i	$-0.578315\pi$
$103$	4.59047	−	17.1319i	0.452312	−	1.68805i	0.695872	−	0.718166i	$-0.255018\pi$
$104$	0.948687	−	5.38027i	0.0930264	−	0.527579i
$105$		0			0
$106$	3.71511	−	2.60134i	0.360843	−	0.252665i
$107$	−8.45323	+	10.0742i	−0.817205	+	0.973907i	−0.999957	−	0.00925238i	$-0.997055\pi$
$107$	−8.45323	+	10.0742i	−0.817205	+	0.973907i	0.182753	+	0.983159i	$0.441499\pi$
$108$		0			0
$109$	−2.04583	+	0.953988i	−0.195955	+	0.0913755i	−0.518119	−	0.855308i	$-0.673368\pi$
$109$	−2.04583	+	0.953988i	−0.195955	+	0.0913755i	0.322164	+	0.946684i	$0.395590\pi$
$110$	0.593831			0.0566196
$111$		0			0
$112$	3.74432			0.353805
$113$	−3.29767	+	1.53773i	−0.310219	+	0.144657i	−0.571492	−	0.820607i	$-0.693635\pi$
$113$	−3.29767	+	1.53773i	−0.310219	+	0.144657i	0.261274	+	0.965265i	$0.415858\pi$
$114$		0			0
$115$	1.29611	−	1.54464i	0.120863	−	0.144039i
$116$	4.44541	−	3.11271i	0.412746	−	0.289008i
$117$		0			0
$118$	1.76699	−	10.0211i	0.162664	−	0.922515i
$119$	−6.57480	+	24.5375i	−0.602711	+	2.24935i
$120$		0			0
$121$	5.28030	−	9.14575i	0.480027	−	0.831432i
$122$	2.88175	+	4.99135i	0.260902	+	0.451895i
$123$		0			0
$124$	9.29285	−	0.813019i	0.834523	−	0.0730113i
$125$	−2.13255	−	7.95877i	−0.190741	−	0.711854i
$126$		0			0
$127$	−0.837519	−	4.74981i	−0.0743178	−	0.421477i	−0.999155	−	0.0411128i	$-0.986910\pi$
$127$	−0.837519	−	4.74981i	−0.0743178	−	0.421477i	0.924837	−	0.380364i	$-0.124201\pi$
$128$	−0.996195	−	0.0871557i	−0.0880520	−	0.00770355i
$129$		0			0
$130$	−2.06840	+	4.43571i	−0.181411	+	0.389037i
$131$	−0.676517	+	7.73263i	−0.0591076	+	0.675603i	0.907620	+	0.419793i	$0.137897\pi$
$131$	−0.676517	+	7.73263i	−0.0591076	+	0.675603i	−0.966727	+	0.255809i	$0.917658\pi$
$132$		0			0
$133$	−12.7015	−	8.89369i	−1.10136	−	0.771181i
$134$	−4.51751	+	1.21046i	−0.390253	+	0.104568i
$135$		0			0
$136$	2.32041	−	6.37527i	0.198973	−	0.546675i
$137$	0.221317	−	0.127777i	0.0189084	−	0.0109167i	−0.490516	−	0.871432i	$-0.663192\pi$
$137$	0.221317	−	0.127777i	0.0189084	−	0.0109167i	0.509424	+	0.860515i	$0.329858\pi$
$138$		0			0
$139$	−0.790124	−	0.941634i	−0.0670175	−	0.0798683i	0.731494	−	0.681848i	$-0.238823\pi$
$139$	−0.790124	−	0.941634i	−0.0670175	−	0.0798683i	−0.798512	+	0.601979i	$0.794379\pi$
$140$	−3.24005	−	0.868169i	−0.273834	−	0.0733736i
$141$		0			0
$142$	−3.67385	−	3.67385i	−0.308302	−	0.308302i
$143$	−2.07717	−	2.96651i	−0.173702	−	0.248072i
$144$		0			0
$145$	−4.56844	+	1.66277i	−0.379388	+	0.138086i
$146$	4.31582	+	9.25530i	0.357179	+	0.765974i
$147$		0			0
$148$	−5.71648	−	2.07890i	−0.469892	−	0.170885i
$149$		−	18.6996i		−	1.53193i	−0.642881	−	0.765966i	$-0.722261\pi$
$149$		−	18.6996i		−	1.53193i	0.642881	−	0.765966i	$-0.277739\pi$
$150$		0			0
$151$	5.58529	+	15.3455i	0.454525	+	1.24880i	0.929508	+	0.368801i	$0.120232\pi$
$151$	5.58529	+	15.3455i	0.454525	+	1.24880i	−0.474984	+	0.879995i	$0.657546\pi$
$152$	3.17228	+	2.66186i	0.257306	+	0.215905i
$153$		0			0
$154$	1.75504	−	1.75504i	0.141425	−	0.141425i
$155$	−8.22983	−	1.45114i	−0.661036	−	0.116558i
$156$		0			0
$157$	15.5798	−	13.0730i	1.24340	−	1.04334i	0.246153	−	0.969231i	$-0.420834\pi$
$157$	15.5798	−	13.0730i	1.24340	−	1.04334i	0.997250	−	0.0741079i	$-0.0236109\pi$
$158$	−5.65563	−	3.26528i	−0.449938	−	0.259772i
$159$		0			0
$160$	0.841822	+	0.306398i	0.0665519	+	0.0242229i
$161$	−0.734530	−	8.39572i	−0.0578891	−	0.661675i
$162$		0			0
$163$	1.72079	−	2.45754i	0.134782	−	0.192489i	−0.746087	−	0.665848i	$-0.768070\pi$
$163$	1.72079	−	2.45754i	0.134782	−	0.192489i	0.880870	+	0.473359i	$0.156959\pi$
$164$	−10.8465	+	1.91253i	−0.846969	+	0.149344i
$165$		0			0
$166$	3.89775	+	1.81755i	0.302524	+	0.141069i
$167$	−4.18587	−	1.95190i	−0.323912	−	0.151043i	0.253860	−	0.967241i	$-0.418300\pi$
$167$	−4.18587	−	1.95190i	−0.323912	−	0.151043i	−0.577772	+	0.816198i	$0.696078\pi$
$168$		0			0
$169$	16.5914	−	2.92551i	1.27626	−	0.225039i
$170$	−3.48609	+	4.97865i	−0.267371	+	0.381845i
$171$		0			0
$172$	−0.0791094	−	0.904225i	−0.00603204	−	0.0689465i
$173$	20.6159	+	7.50358i	1.56740	+	0.570487i	0.972416	−	0.233252i	$-0.0749367\pi$
$173$	20.6159	+	7.50358i	1.56740	+	0.570487i	0.594983	+	0.803739i	$0.297159\pi$
$174$		0			0
$175$	−13.6110	−	7.85832i	−1.02890	−	0.594033i
$176$	−0.507788	+	0.426085i	−0.0382760	+	0.0321173i
$177$		0			0
$178$	−0.989742	−	0.174518i	−0.0741843	−	0.0130807i
$179$	−7.67128	+	7.67128i	−0.573379	+	0.573379i	−0.933071	−	0.359692i	$-0.882882\pi$
$179$	−7.67128	+	7.67128i	−0.573379	+	0.573379i	0.359692	+	0.933071i	$0.382882\pi$
$180$		0			0
$181$	−18.5266	−	15.5456i	−1.37707	−	1.15550i	−0.970283	−	0.241974i	$-0.922205\pi$
$181$	−18.5266	−	15.5456i	−1.37707	−	1.15550i	−0.406786	−	0.913523i	$-0.633351\pi$
$182$	6.99645	+	19.2226i	0.518611	+	1.42487i
$183$		0			0
$184$			2.25082i			0.165932i
$185$	4.46458	+	3.12436i	0.328243	+	0.229707i
$186$		0			0
$187$	−1.90060	−	4.07584i	−0.138985	−	0.298055i
$188$	−12.2005	+	4.44063i	−0.889814	+	0.323866i
$189$		0			0
$190$	−2.12786	−	3.03890i	−0.154371	−	0.220465i
$191$	3.70335	+	3.70335i	0.267965	+	0.267965i	0.828280	−	0.560315i	$-0.189320\pi$
$191$	3.70335	+	3.70335i	0.267965	+	0.267965i	−0.560315	+	0.828280i	$0.689320\pi$
$192$		0			0
$193$	−4.87217	−	1.30550i	−0.350707	−	0.0939716i	0.0791650	−	0.996862i	$-0.474775\pi$
$193$	−4.87217	−	1.30550i	−0.350707	−	0.0939716i	−0.429872	+	0.902890i	$0.641441\pi$
$194$	−7.19758	−	8.57774i	−0.516756	−	0.615846i
$195$		0			0
$196$	−6.07947	+	3.50998i	−0.434248	+	0.250713i
$197$	−3.29521	+	9.05352i	−0.234774	+	0.645037i	0.765225	+	0.643763i	$0.222628\pi$
$197$	−3.29521	+	9.05352i	−0.234774	+	0.645037i	−0.999999	+	0.00127375i	$0.999595\pi$
$198$		0			0
$199$	12.2060	−	3.27060i	0.865264	−	0.231847i	0.201225	−	0.979545i	$-0.435508\pi$
$199$	12.2060	−	3.27060i	0.865264	−	0.231847i	0.664039	+	0.747698i	$0.268841\pi$
$200$	3.43835	+	2.40756i	0.243128	+	0.170240i
$201$		0			0
$202$	−0.587271	+	6.71254i	−0.0413203	+	0.472293i
$203$	−8.58754	+	18.4160i	−0.602727	+	1.29255i
$204$		0			0
$205$	9.82917	+	0.859941i	0.686499	+	0.0600609i
$206$	−3.07986	−	17.4667i	−0.214584	−	1.21697i
$207$		0			0
$208$	−1.41400	−	5.27711i	−0.0980431	−	0.365902i
$209$	2.73458	−	0.239244i	0.189155	−	0.0165489i
$210$		0			0
$211$	5.21636	+	9.03500i	0.359109	+	0.621995i	0.987812	−	0.155650i	$-0.0497472\pi$
$211$	5.21636	+	9.03500i	0.359109	+	0.621995i	−0.628703	+	0.777645i	$0.716414\pi$
$212$	2.26765	−	3.92769i	0.155743	−	0.269755i
$213$		0			0
$214$	−3.40370	+	12.7028i	−0.232672	+	0.868345i
$215$	−0.141201	+	0.800789i	−0.00962981	+	0.0546134i
$216$		0			0
$217$	−28.6116	+	20.0341i	−1.94228	+	1.36000i
$218$	−1.45098	+	1.72921i	−0.0982729	+	0.117117i
$219$		0			0
$220$	0.538194	−	0.250964i	0.0362850	−	0.0169200i
$221$	37.0651			2.49327
$222$		0			0
$223$	−16.5075			−1.10542			−0.552710	−	0.833373i	$-0.686406\pi$
$223$	−16.5075			−1.10542			−0.552710	+	0.833373i	$0.686406\pi$
$224$	3.39351	−	1.58242i	0.226738	−	0.105730i
$225$		0			0
$226$	−2.33883	+	2.78731i	−0.155577	+	0.185409i
$227$	−8.20761	+	5.74703i	−0.544759	+	0.381444i	−0.813318	−	0.581819i	$-0.802341\pi$
$227$	−8.20761	+	5.74703i	−0.544759	+	0.381444i	0.268560	+	0.963263i	$0.413452\pi$
$228$		0			0
$229$	4.46665	−	25.3316i	0.295165	−	1.67396i	−0.371368	−	0.928486i	$-0.621111\pi$
$229$	4.46665	−	25.3316i	0.295165	−	1.67396i	0.666532	−	0.745476i	$-0.267778\pi$
$230$	0.521880	−	1.94768i	0.0344118	−	0.128426i
$231$		0			0
$232$	2.71342	−	4.69978i	0.178145	−	0.308556i
$233$	−6.90323	−	11.9567i	−0.452246	−	0.783313i	0.546279	−	0.837603i	$-0.316044\pi$
$233$	−6.90323	−	11.9567i	−0.452246	−	0.783313i	−0.998525	+	0.0542904i	$0.982710\pi$
$234$		0			0
$235$	11.5870	−	1.01373i	0.755853	−	0.0661286i
$236$	−2.63366	−	9.82895i	−0.171437	−	0.639810i
$237$		0			0
$238$	4.41120	+	25.0171i	0.285936	+	1.62162i
$239$	12.9157	+	1.12998i	0.835448	+	0.0730923i	0.496847	−	0.867838i	$-0.334491\pi$
$239$	12.9157	+	1.12998i	0.835448	+	0.0730923i	0.338601	+	0.940930i	$0.390046\pi$
$240$		0			0
$241$	3.63504	−	7.79538i	0.234154	−	0.502144i	−0.753760	−	0.657150i	$-0.771762\pi$
$241$	3.63504	−	7.79538i	0.234154	−	0.502144i	0.987914	+	0.155006i	$0.0495396\pi$
$242$	0.920417	−	10.5204i	0.0591667	−	0.676278i
$243$		0			0
$244$	4.72119	+	3.30581i	0.302243	+	0.211633i
$245$	6.07454	−	1.62767i	0.388088	−	0.103988i
$246$		0			0
$247$	−7.73788	+	21.2596i	−0.492349	+	1.35272i
$248$	8.07859	−	4.66417i	0.512991	−	0.296175i
$249$		0			0
$250$	−5.29626	−	6.31184i	−0.334965	−	0.399196i
$251$	−4.54243	−	1.21714i	−0.286716	−	0.0768253i	0.112595	−	0.993641i	$-0.464084\pi$
$251$	−4.54243	−	1.21714i	−0.286716	−	0.0768253i	−0.399311	+	0.916816i	$0.630750\pi$
$252$		0			0
$253$	1.05500	+	1.05500i	0.0663274	+	0.0663274i
$254$	−2.76640	−	3.95084i	−0.173580	−	0.247897i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	6.88789	+	14.7711i	0.429655	+	0.921398i	0.995308	+	0.0967548i	$0.0308463\pi$
$257$	6.88789	+	14.7711i	0.429655	+	0.921398i	−0.565653	+	0.824643i	$0.691376\pi$
$258$		0			0
$259$	22.4288	−	3.96097i	1.39366	−	0.246123i
$260$			4.89426i			0.303529i
$261$		0			0
$262$	2.65482	+	7.29405i	0.164015	+	0.450628i
$263$	−1.44872	−	1.21562i	−0.0893318	−	0.0749583i	0.597028	−	0.802220i	$-0.296348\pi$
$263$	−1.44872	−	1.21562i	−0.0893318	−	0.0749583i	−0.686360	+	0.727262i	$0.740793\pi$
$264$		0			0
$265$	−2.87294	+	2.87294i	−0.176483	+	0.176483i
$266$	−15.2701	−	2.69253i	−0.936271	−	0.165090i
$267$		0			0
$268$	−3.58269	+	3.00623i	−0.218847	+	0.183635i
$269$	1.20930	+	0.698189i	0.0737323	+	0.0425694i	0.536413	−	0.843956i	$-0.319779\pi$
$269$	1.20930	+	0.698189i	0.0737323	+	0.0425694i	−0.462681	+	0.886525i	$0.653112\pi$
$270$		0			0
$271$	17.8179	+	6.48518i	1.08236	+	0.393947i	0.820785	−	0.571237i	$-0.193536\pi$
$271$	17.8179	+	6.48518i	1.08236	+	0.393947i	0.261574	+	0.965183i	$0.415758\pi$
$272$	−0.591301	−	6.75861i	−0.0358529	−	0.409801i
$273$		0			0
$274$	0.146580	−	0.209338i	0.00885522	−	0.0126466i
$275$	2.74010	−	0.483153i	0.165234	−	0.0291352i
$276$		0			0
$277$	6.65534	+	3.10344i	0.399881	+	0.186468i	0.612146	−	0.790745i	$-0.290306\pi$
$277$	6.65534	+	3.10344i	0.399881	+	0.186468i	−0.212265	+	0.977212i	$0.568084\pi$
$278$	−1.11405	−	0.519489i	−0.0668161	−	0.0311569i
$279$		0			0
$280$	−3.30339	+	0.582476i	−0.197415	+	0.0348096i
$281$	−5.52343	+	7.88828i	−0.329500	+	0.470575i	−0.949384	−	0.314119i	$-0.898291\pi$
$281$	−5.52343	+	7.88828i	−0.329500	+	0.470575i	0.619883	+	0.784694i	$0.287180\pi$
$282$		0			0
$283$	−0.483639	−	5.52802i	−0.0287494	−	0.328607i	−0.996927	−	0.0783412i	$-0.975038\pi$
$283$	−0.483639	−	5.52802i	−0.0287494	−	0.328607i	0.968177	−	0.250266i	$-0.0805179\pi$
$284$	−4.88227	−	1.77700i	−0.289709	−	0.105446i
$285$		0			0
$286$	−3.13626	−	1.81072i	−0.185451	−	0.107070i
$287$	31.5911	−	26.5081i	1.86477	−	1.56472i
$288$		0			0
$289$	28.5874	+	5.04073i	1.68161	+	0.296513i
$290$	−3.43769	+	3.43769i	−0.201868	+	0.201868i
$291$		0			0
$292$	7.82291	+	6.56420i	0.457801	+	0.384141i
$293$	−6.83718	−	18.7850i	−0.399432	−	1.09743i	−0.962562	−	0.271062i	$-0.912625\pi$
$293$	−6.83718	−	18.7850i	−0.399432	−	1.09743i	0.563130	−	0.826368i	$-0.309597\pi$
$294$		0			0
$295$			9.11586i			0.530746i
$296$	−6.05947	+	0.531765i	−0.352200	+	0.0309082i
$297$		0			0
$298$	−7.90280	−	16.9476i	−0.457797	−	0.981749i
$299$	−11.5552	+	4.20576i	−0.668256	+	0.243225i
$300$		0			0
$301$	1.94938	+	2.78401i	0.112361	+	0.160467i
$302$	11.5473	+	11.5473i	0.664470	+	0.664470i
$303$		0			0
$304$	4.00001	+	1.07180i	0.229416	+	0.0614719i
$305$	−3.31886	−	3.95526i	−0.190037	−	0.226478i
$306$		0			0
$307$	−14.5432	+	8.39655i	−0.830027	+	0.479216i	−0.853862	−	0.520500i	$-0.825746\pi$
$307$	−14.5432	+	8.39655i	−0.830027	+	0.479216i	0.0238351	+	0.999716i	$0.492412\pi$
$308$	0.848894	−	2.33232i	0.0483702	−	0.132896i
$309$		0			0
$310$	−8.07204	+	2.16290i	−0.458461	+	0.122844i
$311$	−18.0360	−	12.6290i	−1.02273	−	0.716123i	−0.0632776	−	0.997996i	$-0.520155\pi$
$311$	−18.0360	−	12.6290i	−1.02273	−	0.716123i	−0.959452	+	0.281873i	$0.909044\pi$
$312$		0			0
$313$	1.73394	−	19.8191i	0.0980083	−	1.12024i	−0.774810	−	0.632195i	$-0.782154\pi$
$313$	1.73394	−	19.8191i	0.0980083	−	1.12024i	0.872818	−	0.488046i	$-0.162290\pi$
$314$	8.59520	−	18.4325i	0.485055	−	1.04020i
$315$		0			0
$316$	−6.50571	−	0.569176i	−0.365975	−	0.0320187i
$317$	4.61126	+	26.1518i	0.258994	+	1.46883i	0.785607	+	0.618725i	$0.212351\pi$
$317$	4.61126	+	26.1518i	0.258994	+	1.46883i	−0.526613	+	0.850105i	$0.676538\pi$
$318$		0			0
$319$	−0.931048	−	3.47472i	−0.0521287	−	0.194547i
$320$	0.892439	−	0.0780783i	0.0498889	−	0.00436471i
$321$		0			0
$322$	−4.21389	−	7.29868i	−0.234831	−	0.406739i
$323$	−14.0475	+	24.3311i	−0.781626	+	1.35382i
$324$		0			0
$325$	−5.93520	+	22.1505i	−0.329225	+	1.22869i
$326$	0.520962	−	2.95452i	0.0288534	−	0.163636i
$327$		0			0
$328$	−9.02199	+	6.31727i	−0.498156	+	0.348813i
$329$	31.2488	−	37.2409i	1.72280	−	2.05316i
$330$		0			0
$331$	4.37988	−	2.04237i	0.240740	−	0.112259i	−0.298504	−	0.954408i	$-0.596488\pi$
$331$	4.37988	−	2.04237i	0.240740	−	0.112259i	0.539244	+	0.842149i	$0.318710\pi$
$332$	4.30069			0.236031
$333$		0			0
$334$	−4.61860			−0.252718
$335$	3.79721	−	1.77067i	0.207464	−	0.0967420i
$336$		0			0
$337$	−5.34843	+	6.37401i	−0.291347	+	0.347214i	−0.891787	−	0.452456i	$-0.850548\pi$
$337$	−5.34843	+	6.37401i	−0.291347	+	0.347214i	0.600439	+	0.799670i	$0.294992\pi$
$338$	13.8005	−	9.66323i	0.750649	−	0.525610i
$339$		0			0
$340$	−1.05540	+	5.98548i	−0.0572372	+	0.324608i
$341$	1.60040	−	5.97279i	0.0866667	−	0.323445i
$342$		0			0
$343$	0.0373740	−	0.0647336i	0.00201800	−	0.00349529i
$344$	−0.453840	−	0.786073i	−0.0244694	−	0.0423822i
$345$		0			0
$346$	21.8555	−	1.91211i	1.17496	−	0.102796i
$347$	2.05424	+	7.66651i	0.110277	+	0.411560i	0.998890	−	0.0470976i	$-0.0149972\pi$
$347$	2.05424	+	7.66651i	0.110277	+	0.411560i	−0.888613	+	0.458657i	$0.848331\pi$
$348$		0			0
$349$	0.00304447	+	0.0172660i	0.000162967	+	0.000924230i	0.984889	−	0.173186i	$-0.0554062\pi$
$349$	0.00304447	+	0.0172660i	0.000162967	+	0.000924230i	−0.984726	+	0.174110i	$0.944295\pi$
$350$	−15.6568	−	1.36980i	−0.836893	−	0.0732186i
$351$		0			0
$352$	−0.280141	+	0.600764i	−0.0149316	+	0.0320208i
$353$	0.286291	−	3.27232i	0.0152377	−	0.174168i	−0.984762	−	0.173906i	$-0.944361\pi$
$353$	0.286291	−	3.27232i	0.0152377	−	0.174168i	1.00000		0.000261927i	$-8.33739e-5\pi$
$354$		0			0
$355$	3.81272	+	2.66970i	0.202358	+	0.141693i
$356$	−0.970765	+	0.260116i	−0.0514505	+	0.0137861i
$357$		0			0
$358$	−3.71052	+	10.1946i	−0.196107	+	0.538800i
$359$	30.1034	−	17.3802i	1.58880	−	0.917292i	0.595291	−	0.803510i	$-0.297037\pi$
$359$	30.1034	−	17.3802i	1.58880	−	0.917292i	0.993506	−	0.113782i	$-0.0362966\pi$
$360$		0			0
$361$	1.18990	+	1.41807i	0.0626262	+	0.0746350i
$362$	−23.3606	−	6.25946i	−1.22781	−	0.328990i
$363$		0			0
$364$	14.4648	+	14.4648i	0.758159	+	0.758159i
$365$	−5.24735	−	7.49400i	−0.274659	−	0.392254i
$366$		0			0
$367$	−21.4875	+	7.82081i	−1.12164	+	0.408243i	−0.835250	−	0.549871i	$-0.814677\pi$
$367$	−21.4875	+	7.82081i	−1.12164	+	0.408243i	−0.286389	+	0.958114i	$0.592455\pi$
$368$	0.951236	+	2.03993i	0.0495866	+	0.106339i
$369$		0			0
$370$	5.36670	+	0.944817i	0.279001	+	0.0491187i
$371$			16.9817i			0.881644i
$372$		0			0
$373$	1.55287	+	4.26647i	0.0804044	+	0.220909i	0.973381	−	0.229195i	$-0.0736092\pi$
$373$	1.55287	+	4.26647i	0.0804044	+	0.220909i	−0.892976	+	0.450104i	$0.851387\pi$
$374$	−3.44505	−	2.89074i	−0.178139	−	0.149477i
$375$		0			0
$376$	−9.18074	+	9.18074i	−0.473460	+	0.473460i
$377$	29.1979	+	5.14838i	1.50377	+	0.265155i
$378$		0			0
$379$	23.8082	−	19.9775i	1.22295	−	1.02617i	0.224280	−	0.974525i	$-0.427997\pi$
$379$	23.8082	−	19.9775i	1.22295	−	1.02617i	0.998665	−	0.0516480i	$-0.0164474\pi$
$380$	−3.21279	−	1.85491i	−0.164813	−	0.0951547i
$381$		0			0
$382$	4.92148	+	1.79127i	0.251805	+	0.0916495i
$383$	−3.14474	−	35.9445i	−0.160688	−	1.83668i	−0.466424	−	0.884561i	$-0.654458\pi$
$383$	−3.14474	−	35.9445i	−0.160688	−	1.83668i	0.305735	−	0.952116i	$-0.401098\pi$
$384$		0			0
$385$	−1.27534	+	1.82138i	−0.0649976	+	0.0928262i
$386$	−4.96742	+	0.875889i	−0.252835	+	0.0445816i
$387$		0			0
$388$	−10.1483	−	4.73224i	−0.515203	−	0.240243i
$389$	16.1395	+	7.52597i	0.818304	+	0.381582i	0.786253	−	0.617905i	$-0.212018\pi$
$389$	16.1395	+	7.52597i	0.818304	+	0.381582i	0.0320513	+	0.999486i	$0.489796\pi$
$390$		0			0
$391$	−15.0385	+	2.65169i	−0.760529	+	0.134102i
$392$	−4.02649	+	5.75042i	−0.203368	+	0.290440i
$393$		0			0
$394$	0.839707	+	9.59789i	0.0423038	+	0.483535i
$395$	5.49757	+	2.00095i	0.276613	+	0.100679i
$396$		0			0
$397$	−2.99244	−	1.72769i	−0.150186	−	0.0867100i	0.423024	−	0.906119i	$-0.360969\pi$
$397$	−2.99244	−	1.72769i	−0.150186	−	0.0867100i	−0.573210	+	0.819409i	$0.694302\pi$
$398$	9.68022	−	8.12267i	0.485226	−	0.407153i
$399$		0			0
$400$	4.13369	+	0.728881i	0.206684	+	0.0364440i
$401$	−9.67007	+	9.67007i	−0.482900	+	0.482900i	−0.906057	−	0.423157i	$-0.860922\pi$
$401$	−9.67007	+	9.67007i	−0.482900	+	0.482900i	0.423157	+	0.906057i	$0.360922\pi$
$402$		0			0
$403$	39.0401	+	32.7586i	1.94473	+	1.63182i
$404$	2.30459	+	6.33182i	0.114658	+	0.315020i
$405$		0			0
$406$			20.3199i			1.00846i
$407$	−2.59095	+	3.08945i	−0.128429	+	0.153138i
$408$		0			0
$409$	−7.81066	−	16.7500i	−0.386212	−	0.828235i	−0.999270	−	0.0381971i	$-0.987839\pi$
$409$	−7.81066	−	16.7500i	−0.386212	−	0.828235i	0.613058	−	0.790038i	$-0.289939\pi$
$410$	9.27168	−	3.37461i	0.457895	−	0.166660i
$411$		0			0
$412$	−10.1731	−	14.5286i	−0.501191	−	0.715775i
$413$	26.9415	+	26.9415i	1.32570	+	1.32570i
$414$		0			0
$415$	−3.72149	−	0.997169i	−0.182681	−	0.0489491i
$416$	−3.51172	−	4.18511i	−0.172176	−	0.205192i
$417$		0			0
$418$	2.37726	−	1.37251i	0.116276	−	0.0671317i
$419$	9.07076	−	24.9217i	0.443136	−	1.21751i	−0.494283	−	0.869301i	$-0.664569\pi$
$419$	9.07076	−	24.9217i	0.443136	−	1.21751i	0.937419	−	0.348204i	$-0.113208\pi$
$420$		0			0
$421$	8.57712	−	2.29823i	0.418023	−	0.112009i	−0.0436754	−	0.999046i	$-0.513907\pi$
$421$	8.57712	−	2.29823i	0.418023	−	0.112009i	0.461699	+	0.887037i	$0.347240\pi$
$422$	8.54599	+	5.98396i	0.416012	+	0.291295i
$423$		0			0
$424$	0.395278	−	4.51805i	0.0191964	−	0.219416i
$425$	−12.0350	+	25.8092i	−0.583785	+	1.25193i
$426$		0			0
$427$	−21.4983	−	1.88086i	−1.04038	−	0.0910212i
$428$	2.28363	+	12.9511i	0.110383	+	0.626015i
$429$		0			0
$430$	0.210457	+	0.785436i	0.0101491	+	0.0378771i
$431$	−26.0962	+	2.28312i	−1.25701	+	0.109974i	−0.696126	−	0.717920i	$-0.745094\pi$
$431$	−26.0962	+	2.28312i	−1.25701	+	0.109974i	−0.560884	+	0.827894i	$0.689539\pi$
$432$		0			0
$433$	11.5509	+	20.0068i	0.555102	+	0.961465i	0.997896	+	0.0648416i	$0.0206542\pi$
$433$	11.5509	+	20.0068i	0.555102	+	0.961465i	−0.442793	+	0.896624i	$0.646012\pi$
$434$	−17.4642	+	30.2488i	−0.838308	+	1.45199i
$435$		0			0
$436$	−0.584239	+	2.18041i	−0.0279800	+	0.104423i
$437$	1.61856	−	9.17929i	0.0774260	−	0.439105i
$438$		0			0
$439$	−18.6676	+	13.0712i	−0.890957	+	0.623855i	−0.926822	−	0.375502i	$-0.877470\pi$
$439$	−18.6676	+	13.0712i	−0.890957	+	0.623855i	0.0358646	+	0.999357i	$0.488582\pi$
$440$	0.381707	−	0.454901i	0.0181972	−	0.0216866i
$441$		0			0
$442$	33.5924	−	15.6644i	1.59783	−	0.745080i
$443$	5.13631			0.244033			0.122017	−	0.992528i	$-0.461064\pi$
$443$	5.13631			0.244033			0.122017	+	0.992528i	$0.461064\pi$
$444$		0			0
$445$	0.900337			0.0426801
$446$	−14.9608	+	6.97635i	−0.708416	+	0.330340i
$447$		0			0
$448$	2.40681	−	2.86832i	0.113711	−	0.135515i
$449$	7.71506	−	5.40215i	0.364096	−	0.254943i	−0.377184	−	0.926138i	$-0.623108\pi$
$449$	7.71506	−	5.40215i	0.364096	−	0.254943i	0.741281	+	0.671195i	$0.234219\pi$
$450$		0			0
$451$	−1.26776	+	7.18982i	−0.0596964	+	0.338555i
$452$	−0.941733	+	3.51460i	−0.0442954	+	0.165313i
$453$		0			0
$454$	−5.00982	+	8.67727i	−0.235123	+	0.407244i
$455$	−9.16285	−	15.8705i	−0.429561	−	0.744022i
$456$		0			0
$457$	20.7563	−	1.81594i	0.970937	−	0.0849460i	0.409362	−	0.912372i	$-0.365751\pi$
$457$	20.7563	−	1.81594i	0.970937	−	0.0849460i	0.561575	+	0.827426i	$0.310196\pi$
$458$	−6.65745	−	24.8460i	−0.311082	−	1.16098i
$459$		0			0
$460$	−0.350142	−	1.98576i	−0.0163255	−	0.0925864i
$461$	−28.8642	−	2.52529i	−1.34434	−	0.117614i	−0.607844	−	0.794057i	$-0.707965\pi$
$461$	−28.8642	−	2.52529i	−1.34434	−	0.117614i	−0.736496	+	0.676442i	$0.763521\pi$
$462$		0			0
$463$	6.40311	−	13.7315i	0.297578	−	0.638158i	−0.699493	−	0.714639i	$-0.746591\pi$
$463$	6.40311	−	13.7315i	0.297578	−	0.638158i	0.997071	+	0.0764815i	$0.0243686\pi$
$464$	0.472981	−	5.40619i	0.0219576	−	0.250976i
$465$		0			0
$466$	−11.3096	−	7.91906i	−0.523907	−	0.366843i
$467$	−21.7713	+	5.83361i	−1.00746	+	0.269947i	−0.724567	−	0.689205i	$-0.757960\pi$
$467$	−21.7713	+	5.83361i	−1.00746	+	0.269947i	−0.282891	+	0.959152i	$0.591293\pi$
$468$		0			0
$469$	5.98936	−	16.4556i	0.276563	−	0.759850i
$470$	10.0730	−	5.81563i	0.464632	−	0.268255i
$471$		0			0
$472$	−6.54080	−	7.79502i	−0.301065	−	0.358795i
$473$	−0.581172	−	0.155725i	−0.0267223	−	0.00716022i
$474$		0			0
$475$	−12.2910	−	12.2910i	−0.563952	−	0.563952i
$476$	14.5706	+	20.8090i	0.667843	+	0.953778i
$477$		0			0
$478$	12.1832	−	4.43431i	0.557245	−	0.202821i
$479$	−10.4824	−	22.4796i	−0.478954	−	1.02712i	−0.986237	−	0.165341i	$-0.947128\pi$
$479$	−10.4824	−	22.4796i	−0.478954	−	1.02712i	0.507282	−	0.861780i	$-0.330650\pi$
$480$		0			0
$481$	−14.0524	−	30.1145i	−0.640734	−	1.37310i
$482$		−	8.60125i		−	0.391776i
$483$		0			0
$484$	−3.61194	−	9.92372i	−0.164179	−	0.451078i
$485$	7.68435	+	6.44794i	0.348928	+	0.292786i
$486$		0			0
$487$	6.23998	−	6.23998i	0.282760	−	0.282760i	−0.551449	−	0.834209i	$-0.685925\pi$
$487$	6.23998	−	6.23998i	0.282760	−	0.282760i	0.834209	+	0.551449i	$0.185925\pi$
$488$	5.67595	+	1.00082i	0.256938	+	0.0453051i
$489$		0			0
$490$	4.81752	−	4.04238i	0.217633	−	0.182616i
$491$	10.1527	+	5.86167i	0.458185	+	0.264533i	0.711281	−	0.702908i	$-0.248115\pi$
$491$	10.1527	+	5.86167i	0.458185	+	0.264533i	−0.253096	+	0.967441i	$0.581449\pi$
$492$		0			0
$493$	34.5976	+	12.5925i	1.55820	+	0.567138i
$494$	1.97181	+	22.5379i	0.0887161	+	1.01403i
$495$		0			0
$496$	5.35052	−	7.64134i	0.240246	−	0.343106i
$497$	19.1585	−	3.37816i	0.859375	−	0.151531i
$498$		0			0
$499$	26.2122	+	12.2230i	1.17342	+	0.547175i	0.908822	−	0.417184i	$-0.136983\pi$
$499$	26.2122	+	12.2230i	1.17342	+	0.547175i	0.264598	+	0.964359i	$0.414761\pi$
$500$	−7.46755	−	3.48217i	−0.333959	−	0.155728i
$501$		0			0
$502$	−4.63123	+	0.816611i	−0.206702	+	0.0364471i
$503$	4.55039	−	6.49863i	0.202892	−	0.289760i	−0.704792	−	0.709414i	$-0.748960\pi$
$503$	4.55039	−	6.49863i	0.202892	−	0.289760i	0.907684	+	0.419654i	$0.137849\pi$
$504$		0			0
$505$	−0.526106	−	6.01342i	−0.0234114	−	0.267594i
$506$	1.40202	+	0.510294i	0.0623274	+	0.0226853i
$507$		0			0
$508$	−4.17691	−	2.41154i	−0.185320	−	0.106995i
$509$	−17.4394	+	14.6334i	−0.772987	+	0.648613i	−0.941472	−	0.337091i	$-0.890557\pi$
$509$	−17.4394	+	14.6334i	−0.772987	+	0.648613i	0.168485	+	0.985704i	$0.446113\pi$
$510$		0			0
$511$	−37.6565	−	6.63985i	−1.66582	−	0.293730i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	12.4851	+	10.4762i	0.550694	+	0.462087i
$515$	5.43434	+	14.9307i	0.239466	+	0.657926i
$516$		0			0
$517$			8.60639i			0.378509i
$518$	18.6534	−	13.0687i	0.819583	−	0.574204i
$519$		0			0
$520$	2.06840	+	4.43571i	0.0907055	+	0.194519i
$521$	−3.52422	+	1.28271i	−0.154399	+	0.0561965i	−0.418063	−	0.908418i	$-0.637291\pi$
$521$	−3.52422	+	1.28271i	−0.154399	+	0.0561965i	0.263665	+	0.964614i	$0.415069\pi$
$522$		0			0
$523$	3.74122	+	5.34302i	0.163592	+	0.233634i	0.892576	−	0.450897i	$-0.148896\pi$
$523$	3.74122	+	5.34302i	0.163592	+	0.233634i	−0.728984	+	0.684531i	$0.760007\pi$
$524$	5.48868	+	5.48868i	0.239774	+	0.239774i
$525$		0			0
$526$	−1.82673	−	0.489470i	−0.0796491	−	0.0213419i
$527$	40.6804	+	48.4810i	1.77207	+	2.11187i
$528$		0			0
$529$	−15.5311	+	8.96691i	−0.675267	+	0.389866i
$530$	−1.38961	+	3.81792i	−0.0603608	+	0.165840i
$531$		0			0
$532$	−14.9773	+	4.01317i	−0.649350	+	0.173993i
$533$	−49.2896	−	34.5129i	−2.13497	−	1.49492i
$534$		0			0
$535$	1.02680	−	11.7364i	0.0443924	−	0.507408i
$536$	−1.97653	+	4.23868i	−0.0853731	+	0.183083i
$537$		0			0
$538$	1.39106	+	0.121702i	0.0599731	+	0.00524696i
$539$	0.808041	+	4.58263i	0.0348048	+	0.197388i
$540$		0			0
$541$	−1.00317	−	3.74388i	−0.0431297	−	0.160962i	0.941002	−	0.338400i	$-0.109886\pi$
$541$	−1.00317	−	3.74388i	−0.0431297	−	0.160962i	−0.984132	+	0.177438i	$0.943219\pi$
$542$	18.8892	−	1.65259i	0.811362	−	0.0709850i
$543$		0			0
$544$	−3.39221	−	5.87548i	−0.145440	−	0.251909i
$545$	1.01111	−	1.75130i	0.0433113	−	0.0750173i
$546$		0			0
$547$	−10.9834	+	40.9906i	−0.469616	+	1.75263i	0.171496	+	0.985185i	$0.445140\pi$
$547$	−10.9834	+	40.9906i	−0.469616	+	1.75263i	−0.641112	+	0.767447i	$0.721527\pi$
$548$	0.0443766	−	0.251672i	0.00189567	−	0.0107509i
$549$		0			0
$550$	2.27918	−	1.59590i	0.0971847	−	0.0680494i
$551$	−14.4455	+	17.2155i	−0.615399	+	0.733403i
$552$		0			0
$553$	22.1615	−	10.3341i	0.942404	−	0.439450i
$554$	7.34336			0.311989
$555$		0			0
$556$	−1.22922			−0.0521303
$557$	−5.49455	+	2.56215i	−0.232812	+	0.108562i	−0.535524	−	0.844520i	$-0.679886\pi$
$557$	−5.49455	+	2.56215i	−0.232812	+	0.108562i	0.302712	+	0.953082i	$0.402108\pi$
$558$		0			0
$559$	3.18752	−	3.79873i	0.134818	−	0.160669i
$560$	−2.74772	+	1.92397i	−0.116112	+	0.0813027i
$561$		0			0
$562$	−1.67220	+	9.48351i	−0.0705375	+	0.400038i
$563$	−10.6185	+	39.6288i	−0.447516	+	1.67015i	0.261689	+	0.965152i	$0.415720\pi$
$563$	−10.6185	+	39.6288i	−0.447516	+	1.67015i	−0.709206	+	0.705002i	$0.750946\pi$
$564$		0			0
$565$	1.62981	−	2.82291i	0.0685665	−	0.118761i
$566$	−2.77457	−	4.80569i	−0.116624	−	0.201998i
$567$		0			0
$568$	−5.17583	+	0.452827i	−0.217173	+	0.0190002i
$569$	7.86279	+	29.3443i	0.329625	+	1.23018i	0.909580	+	0.415530i	$0.136404\pi$
$569$	7.86279	+	29.3443i	0.329625	+	1.23018i	−0.579954	+	0.814649i	$0.696930\pi$
$570$		0			0
$571$	4.38666	+	24.8780i	0.183576	+	1.04111i	0.927771	+	0.373149i	$0.121722\pi$
$571$	4.38666	+	24.8780i	0.183576	+	1.04111i	−0.744195	+	0.667962i	$0.767167\pi$
$572$	−3.60766	−	0.315629i	−0.150844	−	0.0131971i
$573$		0			0
$574$	17.4285	−	37.3755i	0.727451	−	1.56002i
$575$	0.823421	−	9.41175i	0.0343390	−	0.392497i
$576$		0			0
$577$	−23.9361	−	16.7602i	−0.996471	−	0.697736i	−0.0429543	−	0.999077i	$-0.513677\pi$
$577$	−23.9361	−	16.7602i	−0.996471	−	0.697736i	−0.953517	+	0.301341i	$0.902566\pi$
$578$	28.0393	−	7.51310i	1.16628	−	0.312504i
$579$		0			0
$580$	−1.66277	+	4.56844i	−0.0690430	+	0.189694i
$581$	−13.9458	+	8.05159i	−0.578568	+	0.334036i
$582$		0			0
$583$	−1.93242	−	2.30297i	−0.0800329	−	0.0953794i
$584$	9.86412	+	2.64308i	0.408180	+	0.109372i
$585$		0			0
$586$	−14.1355	−	14.1355i	−0.583931	−	0.583931i
$587$	6.45245	+	9.21506i	0.266321	+	0.380346i	0.929932	−	0.367732i	$-0.119866\pi$
$587$	6.45245	+	9.21506i	0.266321	+	0.380346i	−0.663611	+	0.748078i	$0.730977\pi$
$588$		0			0
$589$	−36.3001	+	13.2122i	−1.49572	+	0.544398i
$590$	3.85253	+	8.26178i	0.158606	+	0.340132i
$591$		0			0
$592$	−5.26701	+	3.04279i	−0.216473	+	0.125058i
$593$			17.5776i			0.721825i	0.932600	+	0.360913i	$0.117535\pi$
$593$			17.5776i			0.721825i	−0.932600	+	0.360913i	$0.882465\pi$
$594$		0			0
$595$	−7.78346	−	21.3849i	−0.319091	−	0.876694i
$596$	−14.3247	−	12.0199i	−0.586764	−	0.492354i
$597$		0			0
$598$	−8.69516	+	8.69516i	−0.355572	+	0.355572i
$599$	−39.4039	−	6.94797i	−1.61000	−	0.283886i	−0.704971	−	0.709236i	$-0.749040\pi$
$599$	−39.4039	−	6.94797i	−1.61000	−	0.283886i	−0.905029	+	0.425350i	$0.860151\pi$
$600$		0			0
$601$	−0.0431022	+	0.0361671i	−0.00175818	+	0.00147529i	−0.643666	−	0.765306i	$-0.722588\pi$
$601$	−0.0431022	+	0.0361671i	−0.00175818	+	0.00147529i	0.641908	+	0.766782i	$0.278143\pi$
$602$	2.94331	+	1.69932i	0.119960	+	0.0692592i
$603$		0			0
$604$	15.3455	+	5.58529i	0.624398	+	0.227262i
$605$	0.824554	+	9.42470i	0.0335229	+	0.383168i
$606$		0			0
$607$	25.2014	−	35.9914i	1.02289	−	1.46084i	0.140645	−	0.990060i	$-0.455082\pi$
$607$	25.2014	−	35.9914i	1.02289	−	1.46084i	0.882249	−	0.470784i	$-0.156029\pi$
$608$	4.07820	−	0.719097i	0.165393	−	0.0291632i
$609$		0			0
$610$	−4.67948	−	2.18208i	−0.189466	−	0.0883496i
$611$	−64.2867	−	29.9774i	−2.60076	−	1.21275i
$612$		0			0
$613$	−28.8891	+	5.09392i	−1.16682	+	0.205742i	−0.723307	−	0.690527i	$-0.757379\pi$
$613$	−28.8891	+	5.09392i	−1.16682	+	0.205742i	−0.443512	+	0.896268i	$0.646268\pi$
$614$	−9.63212	+	13.7561i	−0.388721	+	0.555151i
$615$		0			0
$616$	−0.216321	−	2.47256i	−0.00871581	−	0.0996221i
$617$	−0.176760	−	0.0643353i	−0.00711608	−	0.00259004i	0.338460	−	0.940981i	$-0.390094\pi$
$617$	−0.176760	−	0.0643353i	−0.00711608	−	0.00259004i	−0.345576	+	0.938391i	$0.612316\pi$
$618$		0			0
$619$	−2.28460	−	1.31901i	−0.0918259	−	0.0530157i	0.453384	−	0.891315i	$-0.350217\pi$
$619$	−2.28460	−	1.31901i	−0.0918259	−	0.0530157i	−0.545210	+	0.838300i	$0.683550\pi$
$620$	−6.40167	+	5.37164i	−0.257097	+	0.215730i
$621$		0			0
$622$	−21.6834	−	3.82337i	−0.869426	−	0.153303i
$623$	2.66090	−	2.66090i	0.106607	−	0.106607i
$624$		0			0
$625$	−10.4227	−	8.74571i	−0.416909	−	0.349829i
$626$	−6.80442	−	18.6950i	−0.271959	−	0.747202i
$627$		0			0
$628$		−	20.3380i		−	0.811574i
$629$	−10.6916	−	39.8590i	−0.426302	−	1.58928i
$630$		0			0
$631$	−13.8266	−	29.6512i	−0.550428	−	1.18040i	−0.963007	−	0.269475i	$-0.913150\pi$
$631$	−13.8266	−	29.6512i	−0.550428	−	1.18040i	0.412580	−	0.910922i	$-0.364628\pi$
$632$	−6.13672	+	2.23358i	−0.244106	+	0.0888472i
$633$		0			0
$634$	15.2314	+	21.7528i	0.604918	+	0.863912i
$635$	3.05523	+	3.05523i	0.121243	+	0.121243i
$636$		0			0
$637$	−37.0451	−	9.92622i	−1.46778	−	0.393291i
$638$	−2.31230	−	2.75569i	−0.0915446	−	0.109099i
$639$		0			0
$640$	0.775827	−	0.447924i	0.0306673	−	0.0177058i
$641$	10.5478	−	28.9798i	0.416612	−	1.14463i	−0.536997	−	0.843584i	$-0.680441\pi$
$641$	10.5478	−	28.9798i	0.416612	−	1.14463i	0.953609	−	0.301048i	$-0.0973365\pi$
$642$		0			0
$643$	11.9687	−	3.20701i	0.472001	−	0.126472i	−0.0149746	−	0.999888i	$-0.504767\pi$
$643$	11.9687	−	3.20701i	0.472001	−	0.126472i	0.486976	+	0.873416i	$0.338100\pi$
$644$	−6.90364	−	4.83398i	−0.272041	−	0.190485i
$645$		0			0
$646$	−2.44865	+	27.9882i	−0.0963408	+	1.10118i
$647$	5.28905	−	11.3424i	0.207934	−	0.445916i	−0.774488	−	0.632588i	$-0.781993\pi$
$647$	5.28905	−	11.3424i	0.207934	−	0.445916i	0.982422	+	0.186672i	$0.0597703\pi$
$648$		0			0
$649$	−6.71948	−	0.587879i	−0.263763	−	0.0230763i
$650$	3.98207	+	22.5834i	0.156190	+	0.885796i
$651$		0			0
$652$	−0.776483	−	2.89787i	−0.0304094	−	0.113490i
$653$	−35.9425	+	3.14456i	−1.40654	+	0.123056i	−0.764998	−	0.644032i	$-0.777260\pi$
$653$	−35.9425	+	3.14456i	−1.40654	+	0.123056i	−0.641541	+	0.767089i	$0.721705\pi$
$654$		0			0
$655$	−3.47686	−	6.02210i	−0.135852	−	0.235303i
$656$	−5.50691	+	9.53825i	−0.215009	+	0.372406i
$657$		0			0
$658$	12.5824	−	46.9580i	0.490512	−	1.83061i
$659$	−1.12968	+	6.40673i	−0.0440061	+	0.249571i	−0.998873	−	0.0474631i	$-0.984886\pi$
$659$	−1.12968	+	6.40673i	−0.0440061	+	0.249571i	0.954867	+	0.297034i	$0.0959975\pi$
$660$		0			0
$661$	−4.40189	+	3.08224i	−0.171214	+	0.119885i	−0.656043	−	0.754724i	$-0.727771\pi$
$661$	−4.40189	+	3.08224i	−0.171214	+	0.119885i	0.484829	+	0.874609i	$0.338882\pi$
$662$	3.10638	−	3.70203i	0.120733	−	0.143884i
$663$		0			0
$664$	3.89775	−	1.81755i	0.151262	−	0.0705346i
$665$	13.8907			0.538660
$666$		0			0
$667$	−12.2148			−0.472960
$668$	−4.18587	+	1.95190i	−0.161956	+	0.0755214i
$669$		0			0
$670$	2.69313	−	3.20954i	0.104045	−	0.123996i
$671$	3.12954	−	2.19132i	0.120814	−	0.0845952i
$672$		0			0
$673$	−5.19493	+	29.4619i	−0.200250	+	1.13567i	0.704492	+	0.709712i	$0.251175\pi$
$673$	−5.19493	+	29.4619i	−0.200250	+	1.13567i	−0.904741	+	0.425961i	$0.859936\pi$
$674$	−2.15355	+	8.03715i	−0.0829516	+	0.309580i
$675$		0			0
$676$	8.42366	−	14.5902i	0.323987	−	0.561162i
$677$	−10.0337	−	17.3788i	−0.385625	−	0.667922i	0.606231	−	0.795289i	$-0.292681\pi$
$677$	−10.0337	−	17.3788i	−0.385625	−	0.667922i	−0.991856	+	0.127367i	$0.959348\pi$
$678$		0			0
$679$	41.7673	−	3.65417i	1.60288	−	0.140234i
$680$	1.57305	+	5.87072i	0.0603239	+	0.225132i
$681$		0			0
$682$	−1.07375	−	6.08954i	−0.0411160	−	0.233181i
$683$	33.5778	+	2.93768i	1.28482	+	0.112407i	0.709023	−	0.705185i	$-0.249136\pi$
$683$	33.5778	+	2.93768i	1.28482	+	0.112407i	0.575797	+	0.817593i	$0.304692\pi$
$684$		0			0
$685$	−0.0967534	+	0.207488i	−0.00369676	+	0.00792772i
$686$	0.00651471	−	0.0744635i	0.000248733	−	0.00284303i
$687$		0			0
$688$	−0.743527	−	0.520623i	−0.0283467	−	0.0198486i
$689$	23.9333	−	6.41292i	0.911787	−	0.244313i
$690$		0			0
$691$	14.4634	−	39.7379i	0.550215	−	1.51170i	−0.283204	−	0.959060i	$-0.591397\pi$
$691$	14.4634	−	39.7379i	0.550215	−	1.51170i	0.833419	−	0.552642i	$-0.186380\pi$
$692$	18.9997	−	10.9695i	0.722261	−	0.416998i
$693$		0			0
$694$	5.10178	+	6.08006i	0.193661	+	0.230796i
$695$	1.06367	+	0.285009i	0.0403472	+	0.0108110i
$696$		0			0
$697$	−52.8367	−	52.8367i	−2.00133	−	2.00133i
$698$	0.0100562	+	0.0143617i	0.000380631	+	0.000543598i
$699$		0			0
$700$	−14.7688	+	5.37541i	−0.558208	+	0.203171i
$701$	−14.1742	−	30.3966i	−0.535351	−	1.14806i	−0.969018	−	0.246990i	$-0.920558\pi$
$701$	−14.1742	−	30.3966i	−0.535351	−	1.14806i	0.433667	−	0.901073i	$-0.357219\pi$
$702$		0			0
$703$	25.0942	+	2.18871i	0.946444	+	0.0825486i
$704$			0.662870i			0.0249829i
$705$		0			0
$706$	−1.12347	−	3.08672i	−0.0422825	−	0.116170i
$707$	−19.3273	−	16.2175i	−0.726876	−	0.609922i
$708$		0			0
$709$	−23.8794	+	23.8794i	−0.896809	+	0.896809i	−0.995153	−	0.0983437i	$-0.968646\pi$
$709$	−23.8794	+	23.8794i	−0.896809	+	0.896809i	0.0983437	+	0.995153i	$0.468646\pi$
$710$	4.58376	+	0.808241i	0.172025	+	0.0303327i
$711$		0			0
$712$	−0.769883	+	0.646008i	−0.0288526	+	0.0242102i
$713$	−18.1834	−	10.4982i	−0.680974	−	0.393161i
$714$		0			0
$715$	3.04861	+	1.10960i	0.114011	+	0.0414968i
$716$	0.945538	+	10.8075i	0.0353364	+	0.403897i
$717$		0			0
$718$	19.9378	−	28.4741i	0.744070	−	1.06264i
$719$	−1.69450	+	0.298785i	−0.0631940	+	0.0111428i	−0.205156	−	0.978729i	$-0.565770\pi$
$719$	−1.69450	+	0.298785i	−0.0631940	+	0.0111428i	0.141962	+	0.989872i	$0.454659\pi$
$720$		0			0
$721$	60.1880	+	28.0661i	2.24152	+	1.04524i
$722$	1.67771	+	0.782331i	0.0624381	+	0.0291153i
$723$		0			0
$724$	−23.8173	+	4.19963i	−0.885163	+	0.156078i
$725$	−13.0655	+	18.6594i	−0.485239	+	0.692993i
$726$		0			0
$727$	1.09638	+	12.5317i	0.0406625	+	0.464774i	0.989042	+	0.147636i	$0.0471664\pi$
$727$	1.09638	+	12.5317i	0.0406625	+	0.464774i	−0.948379	+	0.317138i	$0.897278\pi$
$728$	19.2226	+	6.99645i	0.712437	+	0.259306i
$729$		0			0
$730$	−7.92282	−	4.57424i	−0.293237	−	0.169300i
$731$	4.71736	−	3.95834i	0.174478	−	0.146404i
$732$		0			0
$733$	−19.6428	−	3.46355i	−0.725522	−	0.127929i	−0.201323	−	0.979525i	$-0.564524\pi$
$733$	−19.6428	−	3.46355i	−0.725522	−	0.127929i	−0.524199	+	0.851596i	$0.675635\pi$
$734$	−16.1691	+	16.1691i	−0.596811	+	0.596811i
$735$		0			0
$736$	1.72423	+	1.44680i	0.0635558	+	0.0533296i
$737$	1.06032	+	2.91319i	0.0390572	+	0.107309i
$738$		0			0
$739$			7.10110i			0.261218i	0.991434	+	0.130609i	$0.0416933\pi$
$739$			7.10110i			0.261218i	−0.991434	+	0.130609i	$0.958307\pi$
$740$	5.26318	−	1.41177i	0.193478	−	0.0518977i
$741$		0			0
$742$	7.17676	+	15.3906i	0.263467	+	0.565007i
$743$	−30.8896	+	11.2429i	−1.13323	+	0.412462i	−0.839464	−	0.543415i	$-0.817131\pi$
$743$	−30.8896	+	11.2429i	−1.13323	+	0.412462i	−0.293766	+	0.955877i	$0.594909\pi$
$744$		0			0
$745$	9.60857	+	13.7225i	0.352031	+	0.502752i
$746$	3.21046	+	3.21046i	0.117543	+	0.117543i
$747$		0			0
$748$	−4.34395	−	1.16396i	−0.158831	−	0.0425585i
$749$	−31.6516	−	37.7209i	−1.15653	−	1.37829i
$750$		0			0
$751$	−12.3493	+	7.12988i	−0.450633	+	0.260173i	−0.708098	−	0.706115i	$-0.750446\pi$
$751$	−12.3493	+	7.12988i	−0.450633	+	0.260173i	0.257464	+	0.966288i	$0.417113\pi$
$752$	−4.44063	+	12.2005i	−0.161933	+	0.444907i
$753$		0			0
$754$	28.6381	−	7.67355i	1.04294	−	0.279454i
$755$	−11.9838	−	8.39112i	−0.436134	−	0.305384i
$756$		0			0
$757$	−2.01570	+	23.0396i	−0.0732619	+	0.837387i	0.867305	+	0.497778i	$0.165851\pi$
$757$	−2.01570	+	23.0396i	−0.0732619	+	0.837387i	−0.940566	+	0.339610i	$0.889705\pi$
$758$	13.1347	−	28.1675i	0.477075	−	1.02309i
$759$		0			0
$760$	−3.69570	−	0.323331i	−0.134057	−	0.0117285i
$761$	−1.06677	−	6.04995i	−0.0386704	−	0.219311i	0.959349	−	0.282224i	$-0.0910720\pi$
$761$	−1.06677	−	6.04995i	−0.0386704	−	0.219311i	−0.998019	+	0.0629131i	$0.979961\pi$
$762$		0			0
$763$	−2.18758	−	8.16417i	−0.0791958	−	0.295563i
$764$	5.21740	−	0.456463i	0.188759	−	0.0165143i
$765$		0			0
$766$	−18.0409	−	31.2478i	−0.651844	−	1.12903i
$767$	27.7962	−	48.1445i	1.00366	−	1.73840i
$768$		0			0
$769$	7.24158	−	27.0259i	0.261138	−	0.974580i	−0.703434	−	0.710761i	$-0.748351\pi$
$769$	7.24158	−	27.0259i	0.261138	−	0.974580i	0.964572	−	0.263820i	$-0.0849824\pi$
$770$	−0.386106	+	2.18972i	−0.0139143	+	0.0789119i
$771$		0			0
$772$	−4.13184	+	2.89315i	−0.148708	+	0.104127i
$773$	−7.88738	+	9.39982i	−0.283690	+	0.338088i	−0.889005	−	0.457898i	$-0.848603\pi$
$773$	−7.88738	+	9.39982i	−0.283690	+	0.338088i	0.605315	+	0.795986i	$0.293047\pi$
$774$		0			0
$775$	−35.4868	+	16.5478i	−1.27472	+	0.594413i
$776$	−11.1974			−0.401965
$777$		0			0
$778$	17.8080			0.638446
$779$	41.3363	−	19.2754i	1.48103	−	0.690613i
$780$		0			0
$781$	−2.21377	+	2.63826i	−0.0792148	+	0.0944045i
$782$	−12.5089	+	8.75879i	−0.447316	+	0.313214i
$783$		0			0
$784$	−1.21900	+	6.91331i	−0.0435358	+	0.246904i
$785$	−4.71562	+	17.5989i	−0.168308	+	0.628132i
$786$		0			0
$787$	−21.8398	+	37.8277i	−0.778506	+	1.34841i	0.154297	+	0.988025i	$0.450689\pi$
$787$	−21.8398	+	37.8277i	−0.778506	+	1.34841i	−0.932803	+	0.360388i	$0.882644\pi$
$788$	4.81728	+	8.34377i	0.171608	+	0.297234i
$789$		0			0
$790$	5.82813	−	0.509895i	0.207356	−	0.0181413i
$791$	−3.52615	−	13.1598i	−0.125376	−	0.467908i
$792$		0			0
$793$	5.46777	+	31.0092i	0.194166	+	1.10117i
$794$	−3.44222	−	0.301155i	−0.122160	−	0.0106876i
$795$		0			0
$796$	5.34047	−	11.4527i	0.189288	−	0.405929i
$797$	−3.90660	+	44.6526i	−0.138379	+	1.58168i	0.536597	+	0.843838i	$0.319709\pi$
$797$	−3.90660	+	44.6526i	−0.138379	+	1.58168i	−0.674976	+	0.737839i	$0.735846\pi$
$798$		0			0
$799$	−72.1556	−	50.5239i	−2.55268	−	1.78741i
$800$	4.05443	−	1.08638i	0.143346	−	0.0384094i
$801$		0			0
$802$	−4.67731	+	12.8508i	−0.165162	+	0.453778i
$803$	5.86238	−	3.38464i	0.206879	−	0.119442i
$804$		0			0
$805$	4.85306	+	5.78365i	0.171048	+	0.203847i
$806$	49.2268	+	13.1903i	1.73394	+	0.464607i
$807$		0			0
$808$	4.76461	+	4.76461i	0.167619	+	0.167619i
$809$	−15.9030	−	22.7119i	−0.559121	−	0.798508i	0.435706	−	0.900089i	$-0.356499\pi$
$809$	−15.9030	−	22.7119i	−0.559121	−	0.798508i	−0.994827	+	0.101581i	$0.967610\pi$
$810$		0			0
$811$	−27.5210	+	10.0168i	−0.966393	+	0.351738i	−0.776536	−	0.630073i	$-0.783025\pi$
$811$	−27.5210	+	10.0168i	−0.966393	+	0.351738i	−0.189858	+	0.981812i	$0.560803\pi$
$812$	8.58754	+	18.4160i	0.301364	+	0.646277i
$813$		0			0
$814$	−1.04254	+	3.89497i	−0.0365410	+	0.136519i
$815$			2.68763i			0.0941437i
$816$		0			0
$817$	1.28559	+	3.53212i	0.0449770	+	0.123573i
$818$	−14.1577	−	11.8797i	−0.495013	−	0.415365i
$819$		0			0
$820$	6.97682	−	6.97682i	0.243641	−	0.243641i
$821$	22.6676	+	3.99690i	0.791103	+	0.139493i	0.554577	−	0.832132i	$-0.312880\pi$
$821$	22.6676	+	3.99690i	0.791103	+	0.139493i	0.236526	+	0.971625i	$0.423991\pi$
$822$		0			0
$823$	−20.7968	+	17.4506i	−0.724932	+	0.608290i	−0.928745	−	0.370720i	$-0.879111\pi$
$823$	−20.7968	+	17.4506i	−0.724932	+	0.608290i	0.203813	+	0.979010i	$0.434667\pi$
$824$	−15.3600	−	8.86810i	−0.535091	−	0.308935i
$825$		0			0
$826$	35.8033	+	13.0313i	1.24575	+	0.453418i
$827$	4.63941	+	53.0287i	0.161328	+	1.84399i	0.457933	+	0.888987i	$0.348590\pi$
$827$	4.63941	+	53.0287i	0.161328	+	1.84399i	−0.296605	+	0.955000i	$0.595855\pi$
$828$		0			0
$829$	20.8768	−	29.8151i	0.725081	−	1.03552i	−0.272230	−	0.962232i	$-0.587761\pi$
$829$	20.8768	−	29.8151i	0.725081	−	1.03552i	0.997311	−	0.0732904i	$-0.0233500\pi$
$830$	−3.79423	+	0.669026i	−0.131700	+	0.0232222i
$831$		0			0
$832$	−4.95140	−	2.30888i	−0.171659	−	0.0800459i
$833$	−43.1642	−	20.1278i	−1.49555	−	0.697386i
$834$		0			0
$835$	4.07470	−	0.718480i	0.141011	−	0.0248640i
$836$	1.57448	−	2.24859i	0.0544545	−	0.0777691i
$837$		0			0
$838$	−2.31147	−	26.4202i	−0.0798484	−	0.912671i
$839$	23.3283	+	8.49081i	0.805383	+	0.293135i	0.711715	−	0.702468i	$-0.247919\pi$
$839$	23.3283	+	8.49081i	0.805383	+	0.293135i	0.0936676	+	0.995604i	$0.470141\pi$
$840$		0			0
$841$	0.390261	+	0.225318i	0.0134573	+	0.00776957i
$842$	6.80224	−	5.70776i	0.234421	−	0.196702i
$843$		0			0
$844$	10.2742	+	1.81162i	0.353653	+	0.0623586i
$845$	−10.6721	+	10.6721i	−0.367132	+	0.367132i
$846$		0			0
$847$	30.2912	+	25.4173i	1.04082	+	0.873349i
$848$	−1.55117	−	4.26179i	−0.0532673	−	0.146351i
$849$		0			0
$850$			28.4773i			0.976764i
$851$	7.85593	+	11.2131i	0.269298	+	0.384379i
$852$		0			0
$853$	18.6752	+	40.0490i	0.639425	+	1.37125i	0.912427	+	0.409238i	$0.134206\pi$
$853$	18.6752	+	40.0490i	0.639425	+	1.37125i	−0.273002	+	0.962013i	$0.588017\pi$
$854$	−20.2790	+	7.38095i	−0.693933	+	0.252571i
$855$		0			0
$856$	7.54304	+	10.7726i	0.257816	+	0.368199i
$857$	18.7606	+	18.7606i	0.640849	+	0.640849i	0.950764	−	0.309915i	$-0.100301\pi$
$857$	18.7606	+	18.7606i	0.640849	+	0.640849i	−0.309915	+	0.950764i	$0.600301\pi$
$858$		0			0
$859$	25.3340	+	6.78824i	0.864387	+	0.231612i	0.663659	−	0.748035i	$-0.269003\pi$
$859$	25.3340	+	6.78824i	0.864387	+	0.231612i	0.200728	+	0.979647i	$0.435669\pi$
$860$	0.522678	+	0.622903i	0.0178232	+	0.0212408i
$861$		0			0
$862$	−22.6863	+	13.0979i	−0.772699	+	0.446118i
$863$	11.1915	−	30.7483i	0.380962	−	1.04668i	−0.589990	−	0.807410i	$-0.700868\pi$
$863$	11.1915	−	30.7483i	0.380962	−	1.04668i	0.970952	−	0.239274i	$-0.0769093\pi$
$864$		0			0
$865$	−18.9843	+	5.08683i	−0.645486	+	0.172958i
$866$	18.9239	+	13.2507i	0.643062	+	0.450277i
$867$		0			0
$868$	−3.04421	+	34.7955i	−0.103327	+	1.18103i
$869$	−1.82948	+	3.92333i	−0.0620608	+	0.133090i
$870$		0			0
$871$	−25.4538	−	2.22692i	−0.862468	−	0.0754561i
$872$	0.391981	+	2.22303i	0.0132741	+	0.0752814i
$873$		0			0
$874$	−2.41242	−	9.00329i	−0.0816015	−	0.304541i
$875$	30.7341	−	2.68888i	1.03900	−	0.0909008i
$876$		0			0
$877$	16.8362	+	29.1612i	0.568520	+	0.984705i	0.996713	+	0.0810176i	$0.0258170\pi$
$877$	16.8362	+	29.1612i	0.568520	+	0.984705i	−0.428193	+	0.903687i	$0.640850\pi$
$878$	−11.3945	+	19.7358i	−0.384545	+	0.666052i
$879$		0			0
$880$	0.153695	−	0.573597i	0.00518105	−	0.0193359i
$881$	−9.68673	+	54.9362i	−0.326354	+	1.85085i	0.173629	+	0.984811i	$0.444451\pi$
$881$	−9.68673	+	54.9362i	−0.326354	+	1.85085i	−0.499983	+	0.866035i	$0.666661\pi$
$882$		0			0
$883$	32.5954	−	22.8236i	1.09692	−	0.768074i	0.122427	−	0.992477i	$-0.460932\pi$
$883$	32.5954	−	22.8236i	1.09692	−	0.768074i	0.974496	+	0.224403i	$0.0720433\pi$
$884$	23.8250	−	28.3935i	0.801322	−	0.954978i
$885$		0			0
$886$	4.65508	−	2.17070i	0.156390	−	0.0729260i
$887$	25.9616			0.871704			0.435852	−	0.900018i	$-0.356447\pi$
$887$	25.9616			0.871704			0.435852	+	0.900018i	$0.356447\pi$
$888$		0			0
$889$	18.0592			0.605685
$890$	0.815982	−	0.380499i	0.0273518	−	0.0127543i
$891$		0			0
$892$	−10.6108	+	12.6454i	−0.355275	+	0.423401i
$893$	44.0428	−	30.8391i	1.47383	−	1.03199i
$894$		0			0
$895$	1.68767	−	9.57126i	0.0564126	−	0.319932i
$896$	0.969102	−	3.61674i	0.0323754	−	0.120827i
$897$		0			0
$898$	4.70918	−	8.15653i	0.157147	−	0.272187i
$899$	25.3117	+	43.8412i	0.844194	+	1.46219i
$900$		0			0
$901$	30.6523	−	2.68173i	1.02118	−	0.0893415i
$902$	1.88957	+	7.05197i	0.0629158	+	0.234805i
$903$		0			0
$904$	0.631832	+	3.58330i	0.0210144	+	0.119179i
$905$	21.5834	+	1.88830i	0.717456	+	0.0627693i
$906$		0			0
$907$	4.07223	−	8.73293i	0.135216	−	0.289972i	−0.827027	−	0.562161i	$-0.809970\pi$
$907$	4.07223	−	8.73293i	0.135216	−	0.289972i	0.962244	+	0.272189i	$0.0877477\pi$
$908$	−0.873270	+	9.98152i	−0.0289805	+	0.331248i
$909$		0			0
$910$	−15.0115	−	10.5112i	−0.497628	−	0.348443i
$911$	48.1425	−	12.8998i	1.59503	−	0.427388i	0.651496	−	0.758652i	$-0.274142\pi$
$911$	48.1425	−	12.8998i	1.59503	−	0.427388i	0.943538	+	0.331264i	$0.107475\pi$
$912$		0			0
$913$	0.975031	−	2.67887i	0.0322688	−	0.0886578i
$914$	18.0441	−	10.4178i	0.596846	−	0.344589i
$915$		0			0
$916$	−16.5341	−	19.7045i	−0.546301	−	0.651056i
$917$	−28.0737	−	7.52233i	−0.927076	−	0.248409i
$918$		0			0
$919$	19.4304	+	19.4304i	0.640949	+	0.640949i	0.950789	−	0.309840i	$-0.100276\pi$
$919$	19.4304	+	19.4304i	0.640949	+	0.640949i	−0.309840	+	0.950789i	$0.600276\pi$
$920$	−1.15655	−	1.65173i	−0.0381304	−	0.0544559i
$921$		0			0
$922$	−27.2271	+	9.90984i	−0.896676	+	0.326363i
$923$	−11.9960	−	25.7255i	−0.394854	−	0.846766i
$924$		0			0
$925$	25.5321	−	0.00681500i	0.839491	−	0.000224076i
$926$		−	15.1511i		−	0.497895i
$927$		0			0
$928$	−1.85609	−	5.09957i	−0.0609291	−	0.167401i
$929$	−45.6600	−	38.3133i	−1.49806	−	1.25702i	−0.883757	−	0.467946i	$-0.844994\pi$
$929$	−45.6600	−	38.3133i	−1.49806	−	1.25702i	−0.614299	−	0.789073i	$-0.710561\pi$
$930$		0			0
$931$	20.5559	−	20.5559i	0.673694	−	0.673694i
$932$	−13.5967	−	2.39747i	−0.445375	−	0.0785316i
$933$		0			0
$934$	−17.2661	+	14.4880i	−0.564965	+	0.474062i
$935$	3.48904	+	2.01440i	0.114104	+	0.0658779i
$936$		0			0
$937$	21.1795	+	7.70870i	0.691903	+	0.251832i	0.663950	−	0.747777i	$-0.268879\pi$
$937$	21.1795	+	7.70870i	0.691903	+	0.251832i	0.0279533	+	0.999609i	$0.491101\pi$
$938$	−1.52625	−	17.4451i	−0.0498337	−	0.569602i
$939$		0			0
$940$	6.67142	−	9.52778i	0.217598	−	0.310762i
$941$	34.8984	−	6.15352i	1.13765	−	0.200599i	0.427075	−	0.904216i	$-0.359544\pi$
$941$	34.8984	−	6.15352i	1.13765	−	0.200599i	0.710579	+	0.703617i	$0.248433\pi$
$942$		0			0
$943$	22.4674	+	10.4767i	0.731641	+	0.341170i
$944$	−9.22229	−	4.30043i	−0.300160	−	0.139967i
$945$		0			0
$946$	−0.592533	+	0.104479i	−0.0192649	+	0.00339692i
$947$	−30.9758	+	44.2380i	−1.00658	+	1.43754i	−0.110379	+	0.993890i	$0.535206\pi$
$947$	−30.9758	+	44.2380i	−1.00658	+	1.43754i	−0.896199	+	0.443653i	$0.853682\pi$
$948$		0			0
$949$	4.86254	+	55.5791i	0.157845	+	1.80417i
$950$	−16.3339	−	5.94505i	−0.529941	−	0.192883i
$951$		0			0
$952$	21.9997	+	12.7015i	0.713015	+	0.411659i
$953$	−37.7784	+	31.6998i	−1.22376	+	1.02686i	−0.225142	+	0.974326i	$0.572285\pi$
$953$	−37.7784	+	31.6998i	−1.22376	+	1.02686i	−0.998619	+	0.0525316i	$0.983271\pi$
$954$		0			0
$955$	−4.62057	−	0.814732i	−0.149518	−	0.0263641i
$956$	9.16768	−	9.16768i	0.296504	−	0.296504i
$957$		0			0
$958$	−19.0006	−	15.9434i	−0.613882	−	0.515108i
$959$	0.327272	+	0.899172i	0.0105682	+	0.0290358i
$960$		0			0
$961$			56.0181i			1.80704i
$962$	−25.4627	−	21.3542i	−0.820951	−	0.688486i
$963$		0			0
$964$	−3.63504	−	7.79538i	−0.117077	−	0.251072i
$965$	4.24619	−	1.54549i	0.136690	−	0.0497510i
$966$		0			0
$967$	−4.73618	−	6.76397i	−0.152305	−	0.217515i	0.735748	−	0.677256i	$-0.236831\pi$
$967$	−4.73618	−	6.76397i	−0.152305	−	0.217515i	−0.888053	+	0.459741i	$0.847942\pi$
$968$	−7.46747	−	7.46747i	−0.240014	−	0.240014i
$969$		0			0
$970$	9.68940	+	2.59627i	0.311108	+	0.0833611i
$971$	−34.8963	−	41.5878i	−1.11988	−	1.33462i	−0.936135	−	0.351640i	$-0.885624\pi$
$971$	−34.8963	−	41.5878i	−1.11988	−	1.33462i	−0.183740	−	0.982975i	$-0.558820\pi$
$972$		0			0
$973$	3.98595	−	2.30129i	0.127784	−	0.0737760i
$974$	3.01821	−	8.29247i	0.0967097	−	0.265708i
$975$		0			0
$976$	5.56712	−	1.49171i	0.178199	−	0.0477483i
$977$	−32.7532	−	22.9340i	−1.04787	−	0.733724i	−0.0830226	−	0.996548i	$-0.526457\pi$
$977$	−32.7532	−	22.9340i	−1.04787	−	0.733724i	−0.964844	+	0.262824i	$0.915346\pi$
$978$		0			0
$979$	−0.0580624	+	0.663656i	−0.00185568	+	0.0212105i
$980$	2.65777	−	5.69961i	0.0848994	−	0.182067i
$981$		0			0
$982$	11.6787	+	1.02176i	0.372683	+	0.0326055i
$983$	0.689163	+	3.90844i	0.0219809	+	0.124660i	0.993824	−	0.110970i	$-0.0353958\pi$
$983$	0.689163	+	3.90844i	0.0219809	+	0.124660i	−0.971843	+	0.235630i	$0.924285\pi$
$984$		0			0
$985$	−2.23389	−	8.33700i	−0.0711777	−	0.265639i
$986$	36.6779	−	3.20890i	1.16806	−	0.102192i
$987$		0			0
$988$	11.3120	+	19.5930i	0.359883	+	0.623336i
$989$	−1.02151	+	1.76931i	−0.0324821	+	0.0562607i
$990$		0			0
$991$	−9.14709	+	34.1374i	−0.290567	+	1.08441i	0.654108	+	0.756402i	$0.273044\pi$
$991$	−9.14709	+	34.1374i	−0.290567	+	1.08441i	−0.944675	+	0.328009i	$0.893622\pi$
$992$	1.61985	−	9.18663i	0.0514303	−	0.291676i
$993$		0			0
$994$	15.9358	−	11.1584i	0.505453	−	0.353922i
$995$	−7.27668	+	8.67201i	−0.230686	+	0.274921i
$996$		0			0
$997$	32.1255	−	14.9804i	1.01742	−	0.474433i	0.158949	−	0.987287i	$-0.449190\pi$
$997$	32.1255	−	14.9804i	1.01742	−	0.474433i	0.858476	+	0.512854i	$0.171412\pi$
$998$	28.9220			0.915510
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.bs.a.89.5	yes	72
3.2	odd	2	inner	666.2.bs.a.89.2	✓	72
37.5	odd	36	inner	666.2.bs.a.449.2	yes	72
111.5	even	36	inner	666.2.bs.a.449.5	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.bs.a.89.2	✓	72	3.2	odd	2	inner
666.2.bs.a.89.5	yes	72	1.1	even	1	trivial
666.2.bs.a.449.2	yes	72	37.5	odd	36	inner
666.2.bs.a.449.5	yes	72	111.5	even	36	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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.bs (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.906308 - 0.422618i) q^{2} +(0.642788 - 0.766044i) q^{4} +(-0.733836 + 0.513837i) q^{5} +(-0.650195 + 3.68744i) q^{7} +(0.258819 - 0.965926i) q^{8} +O(q^{10})\)	\(q+(0.906308 - 0.422618i) q^{2} +(0.642788 - 0.766044i) q^{4} +(-0.733836 + 0.513837i) q^{5} +(-0.650195 + 3.68744i) q^{7} +(0.258819 - 0.965926i) q^{8} +(-0.447924 + 0.775827i) q^{10} +(-0.331435 - 0.574062i) q^{11} +(5.44248 - 0.476155i) q^{13} +(0.969102 + 3.61674i) q^{14} +(-0.173648 - 0.984808i) q^{16} +(6.75861 + 0.591301i) q^{17} +(-1.75011 + 3.75313i) q^{19} +(-0.0780783 + 0.892439i) q^{20} +(-0.542991 - 0.380207i) q^{22} +(-2.17412 + 0.582554i) q^{23} +(-1.43561 + 3.94432i) q^{25} +(4.73133 - 2.73164i) q^{26} +(2.40681 + 2.86832i) q^{28} +(5.24193 + 1.40457i) q^{29} +(6.59614 + 6.59614i) q^{31} +(-0.573576 - 0.819152i) q^{32} +(6.37527 - 2.32041i) q^{34} +(-1.41761 - 3.04007i) q^{35} +(-2.08195 - 5.71537i) q^{37} +4.14112i q^{38} +(0.306398 + 0.841822i) q^{40} +(-8.43708 - 7.07955i) q^{41} +(0.641826 - 0.641826i) q^{43} +(-0.652800 - 0.115106i) q^{44} +(-1.72423 + 1.44680i) q^{46} +(-11.2441 - 6.49176i) q^{47} +(-6.59661 - 2.40097i) q^{49} +(0.365832 + 4.18148i) q^{50} +(3.13360 - 4.47525i) q^{52} +(4.46640 - 0.787548i) q^{53} +(0.538194 + 0.250964i) q^{55} +(3.39351 + 1.58242i) q^{56} +(5.34440 - 0.942362i) q^{58} +(5.83653 - 8.33542i) q^{59} +(0.502323 + 5.74158i) q^{61} +(8.76578 + 3.19048i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(-3.74922 + 3.14597i) q^{65} +(-4.60581 - 0.812129i) q^{67} +(4.79731 - 4.79731i) q^{68} +(-2.56958 - 2.15613i) q^{70} +(-1.77700 - 4.88227i) q^{71} +10.2121i q^{73} +(-4.30231 - 4.30001i) q^{74} +(1.75011 + 3.75313i) q^{76} +(2.33232 - 0.848894i) q^{77} +(-3.74578 - 5.34952i) q^{79} +(0.633460 + 0.633460i) q^{80} +(-10.6385 - 2.85059i) q^{82} +(2.76443 + 3.29452i) q^{83} +(-5.26354 + 3.03891i) q^{85} +(0.310445 - 0.852939i) q^{86} +(-0.640283 + 0.171563i) q^{88} +(-0.823256 - 0.576450i) q^{89} +(-1.78288 + 20.3784i) q^{91} +(-0.951236 + 2.03993i) q^{92} +(-12.9341 - 1.13159i) q^{94} +(-0.644202 - 3.65345i) q^{95} +(-2.89811 - 10.8159i) q^{97} +(-6.99325 + 0.611830i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 72 * q	\( 72 q + 12 q^{13} - 24 q^{19} - 12 q^{22} + 72 q^{34} + 72 q^{37} + 24 q^{40} + 24 q^{43} + 36 q^{46} - 48 q^{49} - 12 q^{52} + 60 q^{55} + 120 q^{61} + 60 q^{67} - 60 q^{70} + 24 q^{76} - 12 q^{79} - 48 q^{82} + 108 q^{85} - 24 q^{88} - 168 q^{91} - 84 q^{94} - 264 q^{97}+O(q^{100}) \) 72 * q + 12 * q^13 - 24 * q^19 - 12 * q^22 + 72 * q^34 + 72 * q^37 + 24 * q^40 + 24 * q^43 + 36 * q^46 - 48 * q^49 - 12 * q^52 + 60 * q^55 + 120 * q^61 + 60 * q^67 - 60 * q^70 + 24 * q^76 - 12 * q^79 - 48 * q^82 + 108 * q^85 - 24 * q^88 - 168 * q^91 - 84 * q^94 - 264 * q^97

Introduction

L-functions

Modular forms

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Database

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