LMFDB - Embedded newform 666.2.bs.b.35.7

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:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			35.7
Character	$\chi$	$=$	666.35
Dual form			666.2.bs.b.647.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(0.252650 - 0.541810i) q^{5} +(1.12060 - 0.407863i) q^{7} +(0.965926 + 0.258819i) q^{8} +O(q^{10})$	\(q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(0.252650 - 0.541810i) q^{5} +(1.12060 - 0.407863i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.298910 - 0.517728i) q^{10} +(2.26675 + 3.92612i) q^{11} +(0.863842 - 0.604868i) q^{13} +(1.15188 - 0.308645i) q^{14} +(0.939693 + 0.342020i) q^{16} +(-0.0396193 - 0.0277417i) q^{17} +(-0.471895 - 5.39378i) q^{19} +(0.342896 - 0.489706i) q^{20} +(1.91594 + 4.10875i) q^{22} +(-0.0598314 - 0.223294i) q^{23} +(2.98421 + 3.55645i) q^{25} +(0.913272 - 0.527278i) q^{26} +(1.17440 - 0.207078i) q^{28} +(-0.452441 + 1.68853i) q^{29} +(3.79807 - 3.79807i) q^{31} +(0.906308 + 0.422618i) q^{32} +(-0.0370507 - 0.0310892i) q^{34} +(0.0621341 - 0.710196i) q^{35} +(3.12536 - 5.21844i) q^{37} -5.41439i q^{38} +(0.384272 - 0.457957i) q^{40} +(-0.0888565 + 0.503930i) q^{41} +(-1.08810 - 1.08810i) q^{43} +(1.55055 + 4.26010i) q^{44} +(-0.0401424 - 0.227659i) q^{46} +(-0.595692 - 0.343923i) q^{47} +(-4.27293 + 3.58541i) q^{49} +(2.66289 + 3.80300i) q^{50} +(0.955752 - 0.445675i) q^{52} +(-3.98395 + 10.9458i) q^{53} +(2.69991 - 0.236211i) q^{55} +(1.18797 - 0.103934i) q^{56} +(-0.597884 + 1.64267i) q^{58} +(-10.1304 + 4.72388i) q^{59} +(-2.76057 - 3.94250i) q^{61} +(4.11464 - 3.45259i) q^{62} +(0.866025 + 0.500000i) q^{64} +(-0.109474 - 0.620858i) q^{65} +(0.174776 + 0.480194i) q^{67} +(-0.0342001 - 0.0342001i) q^{68} +(0.123795 - 0.702078i) q^{70} +(-2.51578 + 2.99819i) q^{71} -1.94900i q^{73} +(3.56828 - 4.92619i) q^{74} +(0.471895 - 5.39378i) q^{76} +(4.14143 + 3.47507i) q^{77} +(-9.92022 - 4.62587i) q^{79} +(0.422723 - 0.422723i) q^{80} +(-0.132439 + 0.494269i) q^{82} +(-4.31441 + 0.760747i) q^{83} +(-0.0250406 + 0.0144572i) q^{85} +(-0.989128 - 1.17880i) q^{86} +(1.17336 + 4.37902i) q^{88} +(-2.39445 - 5.13492i) q^{89} +(0.721313 - 1.03014i) q^{91} +(-0.0201479 - 0.230291i) q^{92} +(-0.563451 - 0.394532i) q^{94} +(-3.04163 - 1.10706i) q^{95} +(1.01305 - 0.271447i) q^{97} +(-4.56916 + 3.19936i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q - 12 q^{13} + 24 q^{19} + 12 q^{22} + 48 q^{31} + 72 q^{34} + 24 q^{37} + 72 q^{43} + 60 q^{46} + 12 q^{52} - 60 q^{55} + 12 q^{58} - 120 q^{61} + 36 q^{67} + 12 q^{70} - 24 q^{76} + 60 q^{79} + 96 q^{82} - 108 q^{85} - 24 q^{88} + 216 q^{91} - 60 q^{94} + 24 q^{97}+O(q^{100}) $ 96 * q - 12 * q^13 + 24 * q^19 + 12 * q^22 + 48 * q^31 + 72 * q^34 + 24 * q^37 + 72 * q^43 + 60 * q^46 + 12 * q^52 - 60 * q^55 + 12 * q^58 - 120 * q^61 + 36 * q^67 + 12 * q^70 - 24 * q^76 + 60 * q^79 + 96 * q^82 - 108 * q^85 - 24 * q^88 + 216 * q^91 - 60 * q^94 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{19}{36}\right)$

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 $

$2$	0.996195	+	0.0871557i	0.704416	+	0.0616284i
$2$	0.996195	+	0.0871557i	0.704416	+	0.0616284i
$3$		0			0
$3$		0			0
$4$	0.984808	+	0.173648i	0.492404	+	0.0868241i
$5$	0.252650	−	0.541810i	0.112988	−	0.242305i	−0.841679	−	0.539978i	$-0.818433\pi$
$5$	0.252650	−	0.541810i	0.112988	−	0.242305i	0.954668	+	0.297673i	$0.0962105\pi$
$6$		0			0
$7$	1.12060	−	0.407863i	0.423545	−	0.154158i	−0.121449	−	0.992598i	$-0.538754\pi$
$7$	1.12060	−	0.407863i	0.423545	−	0.154158i	0.544994	+	0.838440i	$0.316532\pi$
$8$	0.965926	+	0.258819i	0.341506	+	0.0915064i
$9$		0			0
$10$	0.298910	−	0.517728i	0.0945238	−	0.163720i
$11$	2.26675	+	3.92612i	0.683451	+	1.18377i	0.973921	+	0.226887i	$0.0728549\pi$
$11$	2.26675	+	3.92612i	0.683451	+	1.18377i	−0.290470	+	0.956884i	$0.593812\pi$
$12$		0			0
$13$	0.863842	−	0.604868i	0.239587	−	0.167760i	−0.447617	−	0.894226i	$-0.647727\pi$
$13$	0.863842	−	0.604868i	0.239587	−	0.167760i	0.687203	+	0.726465i	$0.258838\pi$
$14$	1.15188	−	0.308645i	0.307853	−	0.0824889i
$15$		0			0
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	−0.0396193	−	0.0277417i	−0.00960910	−	0.00672836i	0.568762	−	0.822502i	$-0.307423\pi$
$17$	−0.0396193	−	0.0277417i	−0.00960910	−	0.00672836i	−0.578371	+	0.815774i	$0.696311\pi$
$18$		0			0
$19$	−0.471895	−	5.39378i	−0.108260	−	1.23742i	−0.834901	−	0.550401i	$-0.814475\pi$
$19$	−0.471895	−	5.39378i	−0.108260	−	1.23742i	0.726641	−	0.687018i	$-0.241081\pi$
$20$	0.342896	−	0.489706i	0.0766739	−	0.109502i
$21$		0			0
$22$	1.91594	+	4.10875i	0.408480	+	0.875987i
$23$	−0.0598314	−	0.223294i	−0.0124757	−	0.0465600i	0.959407	−	0.282024i	$-0.0910057\pi$
$23$	−0.0598314	−	0.223294i	−0.0124757	−	0.0465600i	−0.971883	+	0.235464i	$0.924339\pi$
$24$		0			0
$25$	2.98421	+	3.55645i	0.596842	+	0.711289i
$26$	0.913272	−	0.527278i	0.179107	−	0.103408i
$27$		0			0
$28$	1.17440	−	0.207078i	0.221940	−	0.0391340i
$29$	−0.452441	+	1.68853i	−0.0840161	+	0.313552i	−0.995126	−	0.0986109i	$-0.968560\pi$
$29$	−0.452441	+	1.68853i	−0.0840161	+	0.313552i	0.911110	+	0.412163i	$0.135227\pi$
$30$		0			0
$31$	3.79807	−	3.79807i	0.682153	−	0.682153i	−0.278332	−	0.960485i	$-0.589781\pi$
$31$	3.79807	−	3.79807i	0.682153	−	0.682153i	0.960485	+	0.278332i	$0.0897815\pi$
$32$	0.906308	+	0.422618i	0.160214	+	0.0747091i
$33$		0			0
$34$	−0.0370507	−	0.0310892i	−0.00635414	−	0.00533176i
$35$	0.0621341	−	0.710196i	0.0105026	−	0.120045i
$36$		0			0
$37$	3.12536	−	5.21844i	0.513806	−	0.857907i
$37$	3.12536	−	5.21844i	0.513806	−	0.857907i
$38$		−	5.41439i		−	0.878329i
$39$		0			0
$40$	0.384272	−	0.457957i	0.0607587	−	0.0724094i
$41$	−0.0888565	+	0.503930i	−0.0138771	+	0.0787007i	−0.990960	−	0.134159i	$-0.957167\pi$
$41$	−0.0888565	+	0.503930i	−0.0138771	+	0.0787007i	0.977083	+	0.212860i	$0.0682778\pi$
$42$		0			0
$43$	−1.08810	−	1.08810i	−0.165934	−	0.165934i	0.619255	−	0.785190i	$-0.287435\pi$
$43$	−1.08810	−	1.08810i	−0.165934	−	0.165934i	−0.785190	+	0.619255i	$0.787435\pi$
$44$	1.55055	+	4.26010i	0.233754	+	0.642234i
$45$		0			0
$46$	−0.0401424	−	0.227659i	−0.00591867	−	0.0335664i
$47$	−0.595692	−	0.343923i	−0.0868907	−	0.0501663i	0.455925	−	0.890018i	$-0.349308\pi$
$47$	−0.595692	−	0.343923i	−0.0868907	−	0.0501663i	−0.542816	+	0.839852i	$0.682642\pi$
$48$		0			0
$49$	−4.27293	+	3.58541i	−0.610418	+	0.512202i
$50$	2.66289	+	3.80300i	0.376590	+	0.537826i
$51$		0			0
$52$	0.955752	−	0.445675i	0.132539	−	0.0618039i
$53$	−3.98395	+	10.9458i	−0.547238	+	1.50352i	0.290186	+	0.956970i	$0.406283\pi$
$53$	−3.98395	+	10.9458i	−0.547238	+	1.50352i	−0.837424	+	0.546554i	$0.815939\pi$
$54$		0			0
$55$	2.69991	−	0.236211i	0.364055	−	0.0318507i
$56$	1.18797	−	0.103934i	0.158750	−	0.0138888i
$57$		0			0
$58$	−0.597884	+	1.64267i	−0.0785061	+	0.215694i
$59$	−10.1304	+	4.72388i	−1.31887	+	0.614997i	−0.949348	−	0.314227i	$-0.898255\pi$
$59$	−10.1304	+	4.72388i	−1.31887	+	0.614997i	−0.369518	+	0.929224i	$0.620477\pi$
$60$		0			0
$61$	−2.76057	−	3.94250i	−0.353455	−	0.504786i	0.602572	−	0.798064i	$-0.294143\pi$
$61$	−2.76057	−	3.94250i	−0.353455	−	0.504786i	−0.956027	+	0.293278i	$0.905254\pi$
$62$	4.11464	−	3.45259i	0.522560	−	0.438480i
$63$		0			0
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	−0.109474	−	0.620858i	−0.0135786	−	0.0770079i
$66$		0			0
$67$	0.174776	+	0.480194i	0.0213523	+	0.0586651i	0.949911	−	0.312521i	$-0.101173\pi$
$67$	0.174776	+	0.480194i	0.0213523	+	0.0586651i	−0.928559	+	0.371186i	$0.878951\pi$
$68$	−0.0342001	−	0.0342001i	−0.00414737	−	0.00414737i
$69$		0			0
$70$	0.123795	−	0.702078i	0.0147964	−	0.0839144i
$71$	−2.51578	+	2.99819i	−0.298568	+	0.355820i	−0.894383	−	0.447302i	$-0.852385\pi$
$71$	−2.51578	+	2.99819i	−0.298568	+	0.355820i	0.595815	+	0.803122i	$0.296829\pi$
$72$		0			0
$73$		−	1.94900i		−	0.228113i	−0.993474	−	0.114056i	$-0.963616\pi$
$73$		−	1.94900i		−	0.228113i	0.993474	−	0.114056i	$-0.0363844\pi$
$74$	3.56828	−	4.92619i	0.414804	−	0.572658i
$75$		0			0
$76$	0.471895	−	5.39378i	0.0541300	−	0.618709i
$77$	4.14143	+	3.47507i	0.471960	+	0.396021i
$78$		0			0
$79$	−9.92022	−	4.62587i	−1.11611	−	0.520451i	−0.225056	−	0.974346i	$-0.572257\pi$
$79$	−9.92022	−	4.62587i	−1.11611	−	0.520451i	−0.891055	+	0.453894i	$0.850034\pi$
$80$	0.422723	−	0.422723i	0.0472619	−	0.0472619i
$81$		0			0
$82$	−0.132439	+	0.494269i	−0.0146254	+	0.0545828i
$83$	−4.31441	+	0.760747i	−0.473568	+	0.0835029i	−0.405338	−	0.914167i	$-0.632846\pi$
$83$	−4.31441	+	0.760747i	−0.473568	+	0.0835029i	−0.0682300	+	0.997670i	$0.521735\pi$
$84$		0			0
$85$	−0.0250406	+	0.0144572i	−0.00271603	+	0.00156810i
$86$	−0.989128	−	1.17880i	−0.106660	−	0.127113i
$87$		0			0
$88$	1.17336	+	4.37902i	0.125080	+	0.466805i
$89$	−2.39445	−	5.13492i	−0.253812	−	0.544301i	0.737576	−	0.675265i	$-0.235971\pi$
$89$	−2.39445	−	5.13492i	−0.253812	−	0.544301i	−0.991387	+	0.130964i	$0.958193\pi$
$90$		0			0
$91$	0.721313	−	1.03014i	0.0756142	−	0.107988i
$92$	−0.0201479	−	0.230291i	−0.00210056	−	0.0240095i
$93$		0			0
$94$	−0.563451	−	0.394532i	−0.0581155	−	0.0406929i
$95$	−3.04163	−	1.10706i	−0.312064	−	0.113582i
$96$		0			0
$97$	1.01305	−	0.271447i	0.102860	−	0.0275613i	−0.207022	−	0.978336i	$-0.566377\pi$
$97$	1.01305	−	0.271447i	0.102860	−	0.0275613i	0.309882	+	0.950775i	$0.399710\pi$
$98$	−4.56916	+	3.19936i	−0.461555	+	0.323184i
$99$		0			0
$100$	2.32131	+	4.02062i	0.232131	+	0.402062i
$101$	5.79273	−	10.0333i	0.576398	−	0.998351i	−0.419490	−	0.907760i	$-0.637791\pi$
$101$	5.79273	−	10.0333i	0.576398	−	0.998351i	0.995888	−	0.0905907i	$-0.0288755\pi$
$102$		0			0
$103$	−6.13970	−	1.64513i	−0.604963	−	0.162099i	−0.0566803	−	0.998392i	$-0.518052\pi$
$103$	−6.13970	−	1.64513i	−0.604963	−	0.162099i	−0.548283	+	0.836293i	$0.684718\pi$
$104$	0.990958	−	0.360679i	0.0971715	−	0.0353675i
$105$		0			0
$106$	−4.92278	+	10.5569i	−0.478143	+	1.02538i
$107$	−16.2650	−	2.86796i	−1.57240	−	0.277256i	−0.681622	−	0.731704i	$-0.738725\pi$
$107$	−16.2650	−	2.86796i	−1.57240	−	0.277256i	−0.890773	+	0.454448i	$0.849836\pi$
$108$		0			0
$109$	3.17130	+	0.277453i	0.303756	+	0.0265752i	0.238015	−	0.971262i	$-0.423503\pi$
$109$	3.17130	+	0.277453i	0.303756	+	0.0265752i	0.0657410	+	0.997837i	$0.479059\pi$
$110$	2.71022			0.258409
$111$		0			0
$112$	1.19251			0.112682
$113$	−1.34319	−	0.117514i	−0.126356	−	0.0110547i	0.0238022	−	0.999717i	$-0.492423\pi$
$113$	−1.34319	−	0.117514i	−0.126356	−	0.0110547i	−0.150158	+	0.988662i	$0.547978\pi$
$114$		0			0
$115$	−0.136099	−	0.0239979i	−0.0126913	−	0.00223782i
$116$	−0.738778	+	1.58431i	−0.0685938	+	0.147100i
$117$		0			0
$118$	−10.5036	+	3.82298i	−0.966931	+	0.351934i
$119$	−0.0557121	−	0.0149280i	−0.00510712	−	0.00136845i
$120$		0			0
$121$	−4.77630	+	8.27280i	−0.434210	+	0.752073i
$122$	−2.40645	−	4.16810i	−0.217870	−	0.377362i
$123$		0			0
$124$	4.39989	−	3.08084i	0.395122	−	0.276668i
$125$	5.56813	−	1.49198i	0.498029	−	0.133446i
$126$		0			0
$127$	−1.67935	−	0.611235i	−0.149018	−	0.0542383i	0.266434	−	0.963853i	$-0.414155\pi$
$127$	−1.67935	−	0.611235i	−0.149018	−	0.0542383i	−0.415453	+	0.909615i	$0.636377\pi$
$128$	0.819152	+	0.573576i	0.0724035	+	0.0506975i
$129$		0			0
$130$	−0.0549461	−	0.628036i	−0.00481909	−	0.0550824i
$131$	−0.665292	+	0.950135i	−0.0581268	+	0.0830137i	−0.847163	−	0.531333i	$-0.821691\pi$
$131$	−0.665292	+	0.950135i	−0.0581268	+	0.0830137i	0.789036	+	0.614346i	$0.210580\pi$
$132$		0			0
$133$	−2.72873	−	5.85178i	−0.236611	−	0.507414i
$134$	0.132260	+	0.493600i	0.0114255	+	0.0426405i
$135$		0			0
$136$	−0.0310892	−	0.0370507i	−0.00266588	−	0.00317707i
$137$	8.83533	−	5.10108i	0.754853	−	0.435815i	−0.0725915	−	0.997362i	$-0.523127\pi$
$137$	8.83533	−	5.10108i	0.754853	−	0.435815i	0.827445	+	0.561547i	$0.189794\pi$
$138$		0			0
$139$	−15.6284	+	2.75571i	−1.32558	+	0.233736i	−0.791227	−	0.611523i	$-0.790557\pi$
$139$	−15.6284	+	2.75571i	−1.32558	+	0.233736i	−0.534357	+	0.845259i	$0.679446\pi$
$140$	0.184514	−	0.688617i	0.0155943	−	0.0581988i
$141$		0			0
$142$	−2.76752	+	2.76752i	−0.232245	+	0.232245i
$143$	4.33290	+	2.02047i	0.362335	+	0.168960i
$144$		0			0
$145$	0.800554	+	0.671744i	0.0664824	+	0.0557853i
$146$	0.169866	−	1.94158i	0.0140582	−	0.160686i
$147$		0			0
$148$	3.98405	−	4.59645i	0.327487	−	0.377826i
$149$		−	8.83152i		−	0.723506i	−0.932274	−	0.361753i	$-0.882178\pi$
$149$		−	8.83152i		−	0.723506i	0.932274	−	0.361753i	$-0.117822\pi$
$150$		0			0
$151$	−13.4260	+	16.0005i	−1.09259	+	1.30210i	−0.142619	+	0.989778i	$0.545552\pi$
$151$	−13.4260	+	16.0005i	−1.09259	+	1.30210i	−0.949975	+	0.312326i	$0.898892\pi$
$152$	0.940198	−	5.33213i	0.0762601	−	0.432493i
$153$		0			0
$154$	3.82280	+	3.82280i	0.308050	+	0.308050i
$155$	−1.09825	−	3.01741i	−0.0882134	−	0.242364i
$156$		0			0
$157$	1.64768	+	9.34447i	0.131499	+	0.745770i	0.977234	+	0.212166i	$0.0680517\pi$
$157$	1.64768	+	9.34447i	0.131499	+	0.745770i	−0.845734	+	0.533604i	$0.820837\pi$
$158$	−9.47930	−	5.47287i	−0.754132	−	0.435398i
$159$		0			0
$160$	0.457957	−	0.384272i	0.0362047	−	0.0303793i
$161$	−0.158120	−	0.225819i	−0.0124616	−	0.0177970i
$162$		0			0
$163$	14.0306	−	6.54257i	1.09896	−	0.512454i	0.213394	−	0.976966i	$-0.431548\pi$
$163$	14.0306	−	6.54257i	1.09896	−	0.512454i	0.885567	+	0.464512i	$0.153770\pi$
$164$	−0.175013	+	0.480845i	−0.0136662	+	0.0375477i
$165$		0			0
$166$	−4.36430	+	0.381827i	−0.338735	+	0.0296355i
$167$	−13.6807	+	1.19691i	−1.05864	+	0.0926194i	−0.603157	−	0.797623i	$-0.706091\pi$
$167$	−13.6807	+	1.19691i	−1.05864	+	0.0926194i	−0.455488	+	0.890242i	$0.650535\pi$
$168$		0			0
$169$	−4.06591	+	11.1710i	−0.312762	+	0.859306i
$170$	−0.0262053	+	0.0122197i	−0.00200985	+	0.000937211i
$171$		0			0
$172$	−0.882625	−	1.26052i	−0.0672996	−	0.0961137i
$173$	13.4042	−	11.2475i	1.01911	−	0.855131i	0.0295904	−	0.999562i	$-0.490580\pi$
$173$	13.4042	−	11.2475i	1.01911	−	0.855131i	0.989515	+	0.144431i	$0.0461353\pi$
$174$		0			0
$175$	4.79464	+	2.76819i	0.362441	+	0.209255i
$176$	0.787234	+	4.46462i	0.0593400	+	0.336534i
$177$		0			0
$178$	−1.93780	−	5.32407i	−0.145245	−	0.399056i
$179$	−9.46556	−	9.46556i	−0.707489	−	0.707489i	0.258517	−	0.966007i	$-0.416766\pi$
$179$	−9.46556	−	9.46556i	−0.707489	−	0.707489i	−0.966007	+	0.258517i	$0.916766\pi$
$180$		0			0
$181$	−3.36457	+	19.0814i	−0.250087	+	1.41831i	0.558289	+	0.829646i	$0.311458\pi$
$181$	−3.36457	+	19.0814i	−0.250087	+	1.41831i	−0.808376	+	0.588666i	$0.799653\pi$
$182$	0.808351	−	0.963356i	0.0599190	−	0.0714087i
$183$		0			0
$184$		−	0.231171i		−	0.0170421i
$185$	−2.03778	−	3.01179i	−0.149821	−	0.221431i
$186$		0			0
$187$	0.0191105	−	0.218434i	0.00139750	−	0.0159735i
$188$	−0.526921	−	0.442139i	−0.0384297	−	0.0322463i
$189$		0			0
$190$	−2.93357	−	1.36794i	−0.212823	−	0.0992411i
$191$	6.46072	−	6.46072i	0.467481	−	0.467481i	−0.433616	−	0.901098i	$-0.642763\pi$
$191$	6.46072	−	6.46072i	0.467481	−	0.467481i	0.901098	+	0.433616i	$0.142763\pi$
$192$		0			0
$193$	−3.49144	+	13.0302i	−0.251319	+	0.937936i	0.718782	+	0.695236i	$0.244700\pi$
$193$	−3.49144	+	13.0302i	−0.251319	+	0.937936i	−0.970101	+	0.242701i	$0.921967\pi$
$194$	1.03286	−	0.182121i	0.0741548	−	0.0130755i
$195$		0			0
$196$	−4.83061	+	2.78896i	−0.345044	+	0.199211i
$197$	3.42564	+	4.08252i	0.244067	+	0.290867i	0.874146	−	0.485664i	$-0.161422\pi$
$197$	3.42564	+	4.08252i	0.244067	+	0.290867i	−0.630079	+	0.776531i	$0.716978\pi$
$198$		0			0
$199$	−2.32154	−	8.66410i	−0.164570	−	0.614182i	−0.998095	−	0.0617005i	$-0.980348\pi$
$199$	−2.32154	−	8.66410i	−0.164570	−	0.614182i	0.833525	−	0.552482i	$-0.186319\pi$
$200$	1.96205	+	4.20763i	0.138738	+	0.297525i
$201$		0			0
$202$	6.64514	−	9.49025i	0.467551	−	0.667732i
$203$	0.181687	+	2.07670i	0.0127519	+	0.145755i
$204$		0			0
$205$	0.250585	+	0.175461i	0.0175016	+	0.0122548i
$206$	−5.97296	−	2.17398i	−0.416156	−	0.151468i
$207$		0			0
$208$	1.01862	−	0.272939i	0.0706288	−	0.0189249i
$209$	20.1070	−	14.0791i	1.39083	−	0.973870i
$210$		0			0
$211$	−4.71615	−	8.16862i	−0.324673	−	0.562351i	0.656773	−	0.754088i	$-0.271921\pi$
$211$	−4.71615	−	8.16862i	−0.324673	−	0.562351i	−0.981446	+	0.191738i	$0.938588\pi$
$212$	−5.82415	+	10.0877i	−0.400004	+	0.692828i
$213$		0			0
$214$	−15.9531	−	4.27463i	−1.09053	−	0.292208i
$215$	−0.864454	+	0.314636i	−0.0589553	+	0.0214580i
$216$		0			0
$217$	2.70700	−	5.80519i	0.183763	−	0.394082i
$218$	3.13505	+	0.552794i	0.212333	+	0.0374400i
$219$		0			0
$220$	2.69991	+	0.236211i	0.182028	+	0.0159254i
$221$	−0.0510049			−0.00343096
$222$		0			0
$223$	17.5516			1.17534			0.587671	−	0.809100i	$-0.300045\pi$
$223$	17.5516			1.17534			0.587671	+	0.809100i	$0.300045\pi$
$224$	1.18797	+	0.103934i	0.0793749	+	0.00694441i
$225$		0			0
$226$	−1.32783	−	0.234133i	−0.0883261	−	0.0155743i
$227$	2.15852	−	4.62895i	0.143266	−	0.307234i	−0.821561	−	0.570120i	$-0.806897\pi$
$227$	2.15852	−	4.62895i	0.143266	−	0.307234i	0.964827	+	0.262886i	$0.0846743\pi$
$228$		0			0
$229$	0.0549770	−	0.0200100i	0.00363298	−	0.00132230i	−0.340203	−	0.940352i	$-0.610496\pi$
$229$	0.0549770	−	0.0200100i	0.00363298	−	0.00132230i	0.343836	+	0.939030i	$0.388274\pi$
$230$	−0.133490	−	0.0357684i	−0.00880205	−	0.00235850i
$231$		0			0
$232$	−0.874048	+	1.51390i	−0.0573841	+	0.0993922i
$233$	7.90895	+	13.6987i	0.518133	+	0.897432i	0.999778	+	0.0210661i	$0.00670605\pi$
$233$	7.90895	+	13.6987i	0.518133	+	0.897432i	−0.481645	+	0.876366i	$0.659961\pi$
$234$		0			0
$235$	−0.336843	+	0.235860i	−0.0219732	+	0.0153858i
$236$	−10.7968	+	2.89299i	−0.702811	+	0.188318i
$237$		0			0
$238$	−0.0541990	−	0.0197268i	−0.00351320	−	0.00127870i
$239$	8.76072	+	6.13432i	0.566684	+	0.396796i	0.821513	−	0.570190i	$-0.193130\pi$
$239$	8.76072	+	6.13432i	0.566684	+	0.396796i	−0.254829	+	0.966986i	$0.582019\pi$
$240$		0			0
$241$	1.43440	+	16.3953i	0.0923979	+	1.05611i	0.890924	+	0.454152i	$0.150058\pi$
$241$	1.43440	+	16.3953i	0.0923979	+	1.05611i	−0.798526	+	0.601960i	$0.794387\pi$
$242$	−5.47915	+	7.82504i	−0.352213	+	0.503013i
$243$		0			0
$244$	−2.03402	−	4.36198i	−0.130215	−	0.279247i
$245$	0.863056	+	3.22097i	0.0551386	+	0.205780i
$246$		0			0
$247$	−3.67017	−	4.37394i	−0.233527	−	0.278307i
$248$	4.65166	−	2.68564i	0.295381	−	0.170538i
$249$		0			0
$250$	5.67698	−	1.00100i	0.359043	−	0.0633091i
$251$	−1.36754	+	5.10372i	−0.0863182	+	0.322144i	−0.995561	−	0.0941233i	$-0.969995\pi$
$251$	−1.36754	+	5.10372i	−0.0863182	+	0.322144i	0.909242	+	0.416267i	$0.136662\pi$
$252$		0			0
$253$	0.741056	−	0.741056i	0.0465898	−	0.0465898i
$254$	−1.61969	−	0.755274i	−0.101628	−	0.0473901i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−2.48613	+	28.4166i	−0.155081	+	1.77258i	0.377314	+	0.926085i	$0.376848\pi$
$257$	−2.48613	+	28.4166i	−0.155081	+	1.77258i	−0.532395	+	0.846496i	$0.678708\pi$
$258$		0			0
$259$	1.37385	−	7.12248i	0.0853669	−	0.442569i
$260$		−	0.630435i		−	0.0390979i
$261$		0			0
$262$	−0.745570	+	0.888535i	−0.0460614	+	0.0548939i
$263$	2.15331	−	12.2120i	0.132779	−	0.753026i	−0.843602	−	0.536969i	$-0.819569\pi$
$263$	2.15331	−	12.2120i	0.132779	−	0.753026i	0.976381	−	0.216057i	$-0.0693198\pi$
$264$		0			0
$265$	4.92401	+	4.92401i	0.302479	+	0.302479i
$266$	−2.20833	−	6.06734i	−0.135401	−	0.372012i
$267$		0			0
$268$	0.0887363	+	0.503249i	0.00542043	+	0.0307408i
$269$	−8.52263	−	4.92054i	−0.519634	−	0.300011i	0.217151	−	0.976138i	$-0.430324\pi$
$269$	−8.52263	−	4.92054i	−0.519634	−	0.300011i	−0.736785	+	0.676127i	$0.763657\pi$
$270$		0			0
$271$	20.7195	−	17.3857i	1.25862	−	1.05611i	0.262793	−	0.964852i	$-0.415356\pi$
$271$	20.7195	−	17.3857i	1.25862	−	1.05611i	0.995827	−	0.0912560i	$-0.0290881\pi$
$272$	−0.0277417	−	0.0396193i	−0.00168209	−	0.00240227i
$273$		0			0
$274$	9.24630	−	4.31162i	0.558589	−	0.260474i
$275$	−7.19859	+	19.7780i	−0.434091	+	1.19266i
$276$		0			0
$277$	12.5252	−	1.09581i	0.752565	−	0.0658409i	0.295583	−	0.955317i	$-0.404486\pi$
$277$	12.5252	−	1.09581i	0.752565	−	0.0658409i	0.456982	+	0.889476i	$0.348930\pi$
$278$	−15.8091	+	1.38312i	−0.948167	+	0.0829538i
$279$		0			0
$280$	0.243829	−	0.669915i	0.0145716	−	0.0400351i
$281$	23.4865	−	10.9520i	1.40109	−	0.653339i	0.432415	−	0.901675i	$-0.357661\pi$
$281$	23.4865	−	10.9520i	1.40109	−	0.653339i	0.968674	+	0.248336i	$0.0798837\pi$
$282$		0			0
$283$	−2.80108	−	4.00035i	−0.166507	−	0.237796i	0.727224	−	0.686400i	$-0.240810\pi$
$283$	−2.80108	−	4.00035i	−0.166507	−	0.237796i	−0.893731	+	0.448604i	$0.851921\pi$
$284$	−2.99819	+	2.51578i	−0.177910	+	0.149284i
$285$		0			0
$286$	4.14032	+	2.39041i	0.244822	+	0.141348i
$287$	0.105963	+	0.600944i	0.00625477	+	0.0354726i
$288$		0			0
$289$	−5.81354	−	15.9726i	−0.341973	−	0.939563i
$290$	0.738961	+	0.738961i	0.0433933	+	0.0433933i
$291$		0			0
$292$	0.338440	−	1.91939i	0.0198057	−	0.112324i
$293$	7.77415	−	9.26487i	0.454171	−	0.541260i	−0.489562	−	0.871968i	$-0.662843\pi$
$293$	7.77415	−	9.26487i	0.454171	−	0.541260i	0.943733	+	0.330709i	$0.107288\pi$
$294$		0			0
$295$			6.68224i			0.389055i
$296$	4.36950	−	4.23173i	0.253972	−	0.245964i
$297$		0			0
$298$	0.769717	−	8.79791i	0.0445885	−	0.509649i
$299$	−0.186748	−	0.156700i	−0.0107999	−	0.00906221i
$300$		0			0
$301$	−1.66312	−	0.775526i	−0.0958607	−	0.0447006i
$302$	−14.7695	+	14.7695i	−0.849888	+	0.849888i
$303$		0			0
$304$	1.40135	−	5.22989i	0.0803727	−	0.299955i
$305$	−2.83355	+	0.499630i	−0.162248	+	0.0286088i
$306$		0			0
$307$	20.3230	−	11.7335i	1.15989	−	0.669665i	0.208616	−	0.977998i	$-0.433104\pi$
$307$	20.3230	−	11.7335i	1.15989	−	0.669665i	0.951279	+	0.308332i	$0.0997709\pi$
$308$	3.47507	+	4.14143i	0.198011	+	0.235980i
$309$		0			0
$310$	−0.831084	−	3.10165i	−0.0472024	−	0.176162i
$311$	8.54433	+	18.3234i	0.484504	+	1.03902i	0.984884	+	0.173217i	$0.0554160\pi$
$311$	8.54433	+	18.3234i	0.484504	+	1.03902i	−0.500380	+	0.865806i	$0.666806\pi$
$312$		0			0
$313$	11.0875	−	15.8346i	0.626704	−	0.895026i	−0.372754	−	0.927930i	$-0.621587\pi$
$313$	11.0875	−	15.8346i	0.626704	−	0.895026i	0.999459	+	0.0329038i	$0.0104755\pi$
$314$	0.826988	+	9.45252i	0.0466696	+	0.533436i
$315$		0			0
$316$	−8.96623	−	6.27822i	−0.504390	−	0.353178i
$317$	−24.7963	−	9.02513i	−1.39270	−	0.506902i	−0.466697	−	0.884417i	$-0.654556\pi$
$317$	−24.7963	−	9.02513i	−1.39270	−	0.506902i	−0.926003	+	0.377515i	$0.876778\pi$
$318$		0			0
$319$	−7.65496	+	2.05114i	−0.428595	+	0.114842i
$320$	0.489706	−	0.342896i	0.0273754	−	0.0191685i
$321$		0			0
$322$	−0.137837	−	0.238741i	−0.00768136	−	0.0133045i
$323$	−0.130937	+	0.226789i	−0.00728552	+	0.0126189i
$324$		0			0
$325$	4.72907	+	1.26715i	0.262322	+	0.0702888i
$326$	14.5474	−	5.29483i	0.805707	−	0.293253i
$327$		0			0
$328$	−0.216256	+	0.463762i	−0.0119407	+	0.0256070i
$329$	−0.807804	−	0.142438i	−0.0445357	−	0.00785284i
$330$		0			0
$331$	−2.80213	−	0.245154i	−0.154019	−	0.0134749i	0.00988548	−	0.999951i	$-0.496853\pi$
$331$	−2.80213	−	0.245154i	−0.154019	−	0.0134749i	−0.163904	+	0.986476i	$0.552409\pi$
$332$	−4.38097			−0.240437
$333$		0			0
$334$	−13.7330			−0.751434
$335$	0.304331	+	0.0266255i	0.0166274	+	0.00145471i
$336$		0			0
$337$	7.66687	+	1.35188i	0.417641	+	0.0736414i	0.378520	−	0.925593i	$-0.376433\pi$
$337$	7.66687	+	1.35188i	0.417641	+	0.0736414i	0.0391210	+	0.999234i	$0.487544\pi$
$338$	−5.02405	+	10.7741i	−0.273272	+	0.586034i
$339$		0			0
$340$	−0.0271706	+	0.00988929i	−0.00147353	+	0.000536322i
$341$	23.5210	+	6.30242i	1.27373	+	0.341295i
$342$		0			0
$343$	−7.49966	+	12.9898i	−0.404944	+	0.701383i
$344$	−0.769405	−	1.33265i	−0.0414835	−	0.0718516i
$345$		0			0
$346$	14.3335	−	10.0364i	0.770574	−	0.539562i
$347$	−27.4649	+	7.35920i	−1.47439	+	0.395063i	−0.904435	−	0.426610i	$-0.859708\pi$
$347$	−27.4649	+	7.35920i	−1.47439	+	0.395063i	−0.569959	+	0.821673i	$0.693041\pi$
$348$		0			0
$349$	19.9377	+	7.25672i	1.06724	+	0.388443i	0.815143	−	0.579259i	$-0.196658\pi$
$349$	19.9377	+	7.25672i	1.06724	+	0.388443i	0.252095	+	0.967702i	$0.418880\pi$
$350$	4.53513	+	3.17553i	0.242413	+	0.169739i
$351$		0			0
$352$	0.395120	+	4.51625i	0.0210600	+	0.240717i
$353$	2.54484	−	3.63441i	0.135448	−	0.193440i	−0.745698	−	0.666284i	$-0.767884\pi$
$353$	2.54484	−	3.63441i	0.135448	−	0.193440i	0.881146	+	0.472844i	$0.156773\pi$
$354$		0			0
$355$	0.988837	+	2.12057i	0.0524820	+	0.112548i
$356$	−1.46641	−	5.47270i	−0.0777194	−	0.290053i
$357$		0			0
$358$	−8.60456	−	10.2545i	−0.454765	−	0.541968i
$359$	4.74631	−	2.74028i	0.250500	−	0.144626i	−0.369493	−	0.929234i	$-0.620469\pi$
$359$	4.74631	−	2.74028i	0.250500	−	0.144626i	0.619993	+	0.784607i	$0.287135\pi$
$360$		0			0
$361$	−10.1589	+	1.79128i	−0.534676	+	0.0942779i
$362$	−5.01483	+	18.7156i	−0.263573	+	0.983670i
$363$		0			0
$364$	0.889237	−	0.889237i	0.0466087	−	0.0466087i
$365$	−1.05598	−	0.492414i	−0.0552728	−	0.0257741i
$366$		0			0
$367$	−3.48223	−	2.92194i	−0.181771	−	0.152524i	0.547362	−	0.836896i	$-0.315632\pi$
$367$	−3.48223	−	2.92194i	−0.181771	−	0.152524i	−0.729133	+	0.684372i	$0.760077\pi$
$368$	0.0201479	−	0.230291i	0.00105028	−	0.0120048i
$369$		0			0
$370$	−1.76753	−	3.17793i	−0.0918896	−	0.165213i
$371$			13.8907i			0.721172i
$372$		0			0
$373$	−20.3218	+	24.2186i	−1.05222	+	1.25399i	−0.0859993	+	0.996295i	$0.527408\pi$
$373$	−20.3218	+	24.2186i	−1.05222	+	1.25399i	−0.966226	+	0.257698i	$0.917036\pi$
$374$	0.0380755	−	0.215937i	0.00196884	−	0.0111658i
$375$		0			0
$376$	−0.486381	−	0.486381i	−0.0250832	−	0.0250832i
$377$	0.630502	+	1.73229i	0.0324725	+	0.0892175i
$378$		0			0
$379$	−0.982850	−	5.57402i	−0.0504856	−	0.286318i	0.949104	−	0.314963i	$-0.101992\pi$
$379$	−0.982850	−	5.57402i	−0.0504856	−	0.286318i	−0.999590	+	0.0286445i	$0.990881\pi$
$380$	−2.80318	−	1.61842i	−0.143800	−	0.0830230i
$381$		0			0
$382$	6.99922	−	5.87304i	0.358111	−	0.300491i
$383$	2.80548	+	4.00664i	0.143353	+	0.204730i	0.884408	−	0.466716i	$-0.154563\pi$
$383$	2.80548	+	4.00664i	0.143353	+	0.204730i	−0.741054	+	0.671445i	$0.765674\pi$
$384$		0			0
$385$	2.92916	−	1.36589i	0.149284	−	0.0696122i
$386$	−4.61381	+	12.6763i	−0.234837	+	0.645209i
$387$		0			0
$388$	1.04480	−	0.0914081i	0.0530417	−	0.00464054i
$389$	19.7146	−	1.72480i	0.999570	−	0.0874511i	0.424391	−	0.905479i	$-0.360488\pi$
$389$	19.7146	−	1.72480i	0.999570	−	0.0874511i	0.575179	+	0.818028i	$0.304933\pi$
$390$		0			0
$391$	−0.00382408	+	0.0105066i	−0.000193392	+	0.000531340i
$392$	−5.05531	+	2.35733i	−0.255332	+	0.119063i
$393$		0			0
$394$	3.05679	+	4.36555i	0.153999	+	0.219933i
$395$	−5.01268	+	4.20614i	−0.252216	+	0.211634i
$396$		0			0
$397$	23.7844	+	13.7319i	1.19371	+	0.689187i	0.959145	−	0.282915i	$-0.0913013\pi$
$397$	23.7844	+	13.7319i	1.19371	+	0.689187i	0.234561	+	0.972101i	$0.424635\pi$
$398$	−1.55758	−	8.83347i	−0.0780744	−	0.442782i
$399$		0			0
$400$	1.58787	+	4.36263i	0.0793933	+	0.218131i
$401$	15.4462	+	15.4462i	0.771344	+	0.771344i	0.978342	−	0.206997i	$-0.0663691\pi$
$401$	15.4462	+	15.4462i	0.771344	+	0.771344i	−0.206997	+	0.978342i	$0.566369\pi$
$402$		0			0
$403$	0.983598	−	5.57826i	0.0489965	−	0.277873i
$404$	7.44699	−	8.87497i	0.370501	−	0.441546i
$405$		0			0
$406$			2.08463i			0.103458i
$407$	27.5727	+	0.441643i	1.36673	+	0.0218914i
$408$		0			0
$409$	1.69189	−	19.3384i	0.0836587	−	0.956223i	−0.832135	−	0.554573i	$-0.812881\pi$
$409$	1.69189	−	19.3384i	0.0836587	−	0.956223i	0.915793	−	0.401650i	$-0.131563\pi$
$410$	0.234339	+	0.196634i	0.0115732	+	0.00971104i
$411$		0			0
$412$	−5.76076	−	2.68628i	−0.283812	−	0.132344i
$413$	−9.42538	+	9.42538i	−0.463793	+	0.463793i
$414$		0			0
$415$	−0.677856	+	2.52979i	−0.0332746	+	0.124183i
$416$	1.03853	−	0.183122i	0.0509184	−	0.00897828i
$417$		0			0
$418$	21.2576	−	12.2731i	1.03974	−	0.600295i
$419$	−23.6403	−	28.1735i	−1.15491	−	1.37636i	−0.913949	−	0.405828i	$-0.866983\pi$
$419$	−23.6403	−	28.1735i	−1.15491	−	1.37636i	−0.240957	−	0.970536i	$-0.577461\pi$
$420$		0			0
$421$	−6.05566	−	22.6000i	−0.295135	−	1.10146i	−0.941110	−	0.338100i	$-0.890216\pi$
$421$	−6.05566	−	22.6000i	−0.295135	−	1.10146i	0.645976	−	0.763358i	$-0.276451\pi$
$422$	−3.98626	−	8.54857i	−0.194048	−	0.416138i
$423$		0			0
$424$	−6.68119	+	9.54173i	−0.324467	+	0.463387i
$425$	−0.0195704	−	0.223691i	−0.000949306	−	0.0108506i
$426$		0			0
$427$	−4.70149	−	3.29202i	−0.227521	−	0.159312i
$428$	−15.5199	−	5.64877i	−0.750181	−	0.273044i
$429$		0			0
$430$	−0.888587	+	0.238096i	−0.0428515	+	0.0114820i
$431$	22.0915	−	15.4687i	1.06411	−	0.745099i	0.0959407	−	0.995387i	$-0.469414\pi$
$431$	22.0915	−	15.4687i	1.06411	−	0.745099i	0.968172	+	0.250288i	$0.0805252\pi$
$432$		0			0
$433$	6.21835	+	10.7705i	0.298835	+	0.517597i	0.975870	−	0.218354i	$-0.0700687\pi$
$433$	6.21835	+	10.7705i	0.298835	+	0.517597i	−0.677035	+	0.735951i	$0.736735\pi$
$434$	3.20266	−	5.54717i	0.153733	−	0.266273i
$435$		0			0
$436$	3.07494	+	0.823929i	0.147263	+	0.0394590i
$437$	−1.17616	+	0.428089i	−0.0562635	+	0.0204783i
$438$		0			0
$439$	−0.306298	+	0.656858i	−0.0146188	+	0.0313501i	−0.913482	−	0.406880i	$-0.866617\pi$
$439$	−0.306298	+	0.656858i	−0.0146188	+	0.0313501i	0.898863	+	0.438230i	$0.144394\pi$
$440$	2.66905	+	0.470625i	0.127242	+	0.0224362i
$441$		0			0
$442$	−0.0508108	−	0.00444537i	−0.00241682	−	0.000211445i
$443$	12.7230			0.604488			0.302244	−	0.953231i	$-0.402264\pi$
$443$	12.7230			0.604488			0.302244	+	0.953231i	$0.402264\pi$
$444$		0			0
$445$	−3.38711			−0.160564
$446$	17.4848	+	1.52972i	0.827929	+	0.0724344i
$447$		0			0
$448$	1.17440	+	0.207078i	0.0554850	+	0.00978350i
$449$	9.03777	−	19.3816i	0.426519	−	0.914672i	−0.569197	−	0.822201i	$-0.692746\pi$
$449$	9.03777	−	19.3816i	0.426519	−	0.914672i	0.995715	−	0.0924707i	$-0.0294765\pi$
$450$		0			0
$451$	−2.17991	+	0.793422i	−0.102648	+	0.0373608i
$452$	−1.30237	−	0.348970i	−0.0612585	−	0.0164142i
$453$		0			0
$454$	2.55374	−	4.42321i	0.119853	−	0.207592i
$455$	−0.375901	−	0.651080i	−0.0176225	−	0.0305231i
$456$		0			0
$457$	20.3582	−	14.2549i	0.952315	−	0.666818i	0.00943664	−	0.999955i	$-0.496996\pi$
$457$	20.3582	−	14.2549i	0.952315	−	0.666818i	0.942878	+	0.333137i	$0.108107\pi$
$458$	0.0565117	−	0.0151423i	0.00264062	−	0.000707552i
$459$		0			0
$460$	−0.129864	−	0.0472667i	−0.00605495	−	0.00220382i
$461$	1.95520	+	1.36905i	0.0910628	+	0.0637628i	0.618221	−	0.786004i	$-0.287854\pi$
$461$	1.95520	+	1.36905i	0.0910628	+	0.0637628i	−0.527158	+	0.849767i	$0.676743\pi$
$462$		0			0
$463$	2.34327	+	26.7838i	0.108901	+	1.24475i	0.832304	+	0.554320i	$0.187022\pi$
$463$	2.34327	+	26.7838i	0.108901	+	1.24475i	−0.723402	+	0.690427i	$0.757423\pi$
$464$	−1.00267	+	1.43196i	−0.0465477	+	0.0664769i
$465$		0			0
$466$	6.68494	+	14.3359i	0.309674	+	0.664097i
$467$	6.91775	+	25.8174i	0.320115	+	1.19469i	0.919132	+	0.393950i	$0.128892\pi$
$467$	6.91775	+	25.8174i	0.320115	+	1.19469i	−0.599016	+	0.800737i	$0.704442\pi$
$468$		0			0
$469$	0.391707	+	0.466819i	0.0180874	+	0.0215557i
$470$	−0.356117	+	0.205604i	−0.0164265	+	0.00948382i
$471$		0			0
$472$	−11.0078	+	1.94098i	−0.506677	+	0.0893409i
$473$	1.80557	−	6.73849i	0.0830203	−	0.309836i
$474$		0			0
$475$	17.7745	−	17.7745i	0.815548	−	0.815548i
$476$	−0.0522735	−	0.0243755i	−0.00239595	−	0.00111725i
$477$		0			0
$478$	8.19274	+	6.87453i	0.374727	+	0.314433i
$479$	−0.154256	+	1.76316i	−0.00704814	+	0.0805606i	−0.998904	−	0.0468041i	$-0.985096\pi$
$479$	−0.154256	+	1.76316i	−0.00704814	+	0.0805606i	0.991856	+	0.127365i	$0.0406519\pi$
$480$		0			0
$481$	−0.456657	−	6.39834i	−0.0208218	−	0.291739i
$482$			16.4579i			0.749637i
$483$		0			0
$484$	−6.14030	+	7.31772i	−0.279105	+	0.332624i
$485$	0.108875	−	0.617463i	0.00494378	−	0.0280376i
$486$		0			0
$487$	30.5932	+	30.5932i	1.38631	+	1.38631i	0.832927	+	0.553382i	$0.186663\pi$
$487$	30.5932	+	30.5932i	1.38631	+	1.38631i	0.553382	+	0.832927i	$0.313337\pi$
$488$	−1.64611	−	4.52266i	−0.0745160	−	0.204731i
$489$		0			0
$490$	0.579046	+	3.28393i	0.0261586	+	0.148353i
$491$	−28.5178	−	16.4648i	−1.28699	−	0.743045i	−0.308876	−	0.951102i	$-0.599953\pi$
$491$	−28.5178	−	16.4648i	−1.28699	−	0.743045i	−0.978117	+	0.208057i	$0.933286\pi$
$492$		0			0
$493$	0.0647682	−	0.0543470i	0.00291701	−	0.00244767i
$494$	−3.27499	−	4.67717i	−0.147349	−	0.210436i
$495$		0			0
$496$	4.86803	−	2.27000i	0.218581	−	0.101926i
$497$	−1.59632	+	4.38586i	−0.0716048	+	0.196733i
$498$		0			0
$499$	−12.6991	+	1.11102i	−0.568488	+	0.0497363i	−0.367777	−	0.929914i	$-0.619881\pi$
$499$	−12.6991	+	1.11102i	−0.568488	+	0.0497363i	−0.200712	+	0.979650i	$0.564325\pi$
$500$	5.74262	−	0.502414i	0.256818	−	0.0224686i
$501$		0			0
$502$	−1.80715	+	4.96511i	−0.0806571	+	0.221604i
$503$	−2.15717	+	1.00591i	−0.0961835	+	0.0448511i	−0.470115	−	0.882605i	$-0.655787\pi$
$503$	−2.15717	+	1.00591i	−0.0961835	+	0.0448511i	0.373931	+	0.927456i	$0.378010\pi$
$504$		0			0
$505$	−3.97260	−	5.67347i	−0.176779	−	0.252466i
$506$	0.802824	−	0.673649i	0.0356899	−	0.0299474i
$507$		0			0
$508$	−1.54770	−	0.893565i	−0.0686681	−	0.0396455i
$509$	−1.35404	−	7.67912i	−0.0600166	−	0.340371i	0.939983	−	0.341221i	$-0.110840\pi$
$509$	−1.35404	−	7.67912i	−0.0600166	−	0.340371i	−1.00000		0.000850181i	$0.999729\pi$
$510$		0			0
$511$	−0.794924	−	2.18404i	−0.0351654	−	0.0966161i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	−4.95335	+	28.0918i	−0.218483	+	1.23908i
$515$	−2.44254	+	2.91091i	−0.107631	+	0.128270i
$516$		0			0
$517$		−	3.11835i		−	0.137145i
$518$	1.98939	−	6.97564i	0.0874086	−	0.306492i
$519$		0			0
$520$	0.0549461	−	0.628036i	0.00240954	−	0.0275412i
$521$	5.30274	+	4.44952i	0.232317	+	0.194937i	0.751513	−	0.659718i	$-0.229324\pi$
$521$	5.30274	+	4.44952i	0.232317	+	0.194937i	−0.519196	+	0.854655i	$0.673769\pi$
$522$		0			0
$523$	−37.0655	−	17.2839i	−1.62076	−	0.755774i	−0.621151	−	0.783691i	$-0.713335\pi$
$523$	−37.0655	−	17.2839i	−1.62076	−	0.755774i	−0.999610	+	0.0279171i	$0.991113\pi$
$524$	−0.820173	+	0.820173i	−0.0358294	+	0.0358294i
$525$		0			0
$526$	3.20947	−	11.9779i	0.139939	−	0.522261i
$527$	−0.255842	+	0.0451118i	−0.0111446	+	0.00196510i
$528$		0			0
$529$	19.8723	−	11.4733i	0.864013	−	0.498838i
$530$	4.47611	+	5.33442i	0.194430	+	0.231713i
$531$		0			0
$532$	−1.67112	−	6.23672i	−0.0724524	−	0.270396i
$533$	0.228054	+	0.489063i	0.00987810	+	0.0211837i
$534$		0			0
$535$	−5.66323	+	8.08794i	−0.244843	+	0.349672i
$536$	0.0445376	+	0.509067i	0.00192373	+	0.0219884i
$537$		0			0
$538$	−8.06134	−	5.64461i	−0.347549	−	0.243357i
$539$	−23.7624	−	8.64882i	−1.02352	−	0.372531i
$540$		0			0
$541$	−38.1108	+	10.2118i	−1.63851	+	0.439038i	−0.956364	−	0.292178i	$-0.905620\pi$
$541$	−38.1108	+	10.2118i	−1.63851	+	0.439038i	−0.682146	+	0.731216i	$0.738953\pi$
$542$	22.1559	−	15.5138i	0.951679	−	0.666373i
$543$		0			0
$544$	−0.0241831	−	0.0418864i	−0.00103684	−	0.00179586i
$545$	0.951556	−	1.64814i	0.0407602	−	0.0705987i
$546$		0			0
$547$	−10.7585	−	2.88273i	−0.459999	−	0.123256i	0.0213751	−	0.999772i	$-0.493196\pi$
$547$	−10.7585	−	2.88273i	−0.459999	−	0.123256i	−0.481374	+	0.876515i	$0.659862\pi$
$548$	9.58690	−	3.48934i	0.409532	−	0.149057i
$549$		0			0
$550$	−8.89496	+	19.0753i	−0.379282	+	0.813374i
$551$	9.32108	+	1.64356i	0.397091	+	0.0700179i
$552$		0			0
$553$	−13.0033	−	1.13764i	−0.552955	−	0.0483773i
$554$	12.5730			0.534177
$555$		0			0
$556$	−15.8695			−0.673016
$557$	−20.3741	−	1.78250i	−0.863277	−	0.0755270i	−0.353089	−	0.935590i	$-0.614869\pi$
$557$	−20.3741	−	1.78250i	−0.863277	−	0.0755270i	−0.510188	+	0.860063i	$0.670424\pi$
$558$		0			0
$559$	−1.59811	−	0.281790i	−0.0675928	−	0.0119184i
$560$	0.301288	−	0.646115i	0.0127318	−	0.0273033i
$561$		0			0
$562$	24.3517	−	8.86329i	1.02721	−	0.373875i
$563$	30.7892	+	8.24994i	1.29761	+	0.347694i	0.840546	−	0.541740i	$-0.182234\pi$
$563$	30.7892	+	8.24994i	1.29761	+	0.347694i	0.457064	+	0.889434i	$0.348901\pi$
$564$		0			0
$565$	−0.403026	+	0.698061i	−0.0169554	+	0.0293677i
$566$	−2.44176	−	4.22926i	−0.102635	−	0.177769i
$567$		0			0
$568$	−3.20605	+	2.24490i	−0.134523	+	0.0941939i
$569$	−28.6798	+	7.68472i	−1.20232	+	0.322160i	−0.803744	−	0.594976i	$-0.797162\pi$
$569$	−28.6798	+	7.68472i	−1.20232	+	0.322160i	−0.398574	+	0.917136i	$0.630495\pi$
$570$		0			0
$571$	29.1082	+	10.5945i	1.21814	+	0.443366i	0.869520	−	0.493898i	$-0.164428\pi$
$571$	29.1082	+	10.5945i	1.21814	+	0.443366i	0.348619	+	0.937264i	$0.386651\pi$
$572$	3.91622	+	2.74217i	0.163746	+	0.114656i
$573$		0			0
$574$	0.0531837	+	0.607892i	0.00221984	+	0.0253729i
$575$	0.615583	−	0.879143i	0.0256716	−	0.0366628i
$576$		0			0
$577$	6.66571	+	14.2947i	0.277497	+	0.595094i	0.994821	−	0.101646i	$-0.0324109\pi$
$577$	6.66571	+	14.2947i	0.277497	+	0.595094i	−0.717324	+	0.696740i	$0.754633\pi$
$578$	−4.39932	−	16.4185i	−0.182988	−	0.682919i
$579$		0			0
$580$	0.671744	+	0.800554i	0.0278927	+	0.0332412i
$581$	−4.52443	+	2.61218i	−0.187705	+	0.108372i
$582$		0			0
$583$	−52.0053	+	9.16993i	−2.15384	+	0.379780i
$584$	0.504437	−	1.88259i	0.0208738	−	0.0779019i
$585$		0			0
$586$	8.55205	−	8.55205i	0.353282	−	0.353282i
$587$	−36.4955	−	17.0181i	−1.50633	−	0.702413i	−0.518089	−	0.855327i	$-0.673356\pi$
$587$	−36.4955	−	17.0181i	−1.50633	−	0.702413i	−0.988239	+	0.152914i	$0.951134\pi$
$588$		0			0
$589$	−22.2782	−	18.6937i	−0.917959	−	0.770259i
$590$	−0.582395	+	6.65681i	−0.0239768	+	0.274056i
$591$		0			0
$592$	4.72169	−	3.83480i	0.194060	−	0.157609i
$593$		−	25.9182i		−	1.06433i	−0.846639	−	0.532167i	$-0.821378\pi$
$593$		−	25.9182i		−	1.06433i	0.846639	−	0.532167i	$-0.178622\pi$
$594$		0			0
$595$	−0.0221638	+	0.0264138i	−0.000908627	+	0.00108286i
$596$	1.53358	−	8.69735i	0.0628177	−	0.356257i
$597$		0			0
$598$	−0.172380	−	0.172380i	−0.00704915	−	0.00704915i
$599$	−4.56891	−	12.5530i	−0.186681	−	0.512901i	0.810681	−	0.585488i	$-0.199097\pi$
$599$	−4.56891	−	12.5530i	−0.186681	−	0.512901i	−0.997362	+	0.0725864i	$0.976875\pi$
$600$		0			0
$601$	4.86781	+	27.6067i	0.198562	+	1.12610i	0.907254	+	0.420583i	$0.138174\pi$
$601$	4.86781	+	27.6067i	0.198562	+	1.12610i	−0.708692	+	0.705518i	$0.750714\pi$
$602$	−1.58920	−	0.917526i	−0.0647710	−	0.0373955i
$603$		0			0
$604$	−16.0005	+	13.4260i	−0.651052	+	0.546297i
$605$	3.27555	+	4.67797i	0.133170	+	0.190187i
$606$		0			0
$607$	20.7538	−	9.67764i	0.842370	−	0.392803i	0.0469756	−	0.998896i	$-0.485042\pi$
$607$	20.7538	−	9.67764i	0.842370	−	0.392803i	0.795394	+	0.606093i	$0.207264\pi$
$608$	1.85183	−	5.08786i	0.0751016	−	0.206340i
$609$		0			0
$610$	−2.86631	+	0.250769i	−0.116053	+	0.0101534i
$611$	−0.722612	+	0.0632204i	−0.0292338	+	0.00255762i
$612$		0			0
$613$	−9.87288	+	27.1255i	−0.398762	+	1.09559i	0.564126	+	0.825688i	$0.309213\pi$
$613$	−9.87288	+	27.1255i	−0.398762	+	1.09559i	−0.962888	+	0.269901i	$0.913009\pi$
$614$	21.2683	−	9.91757i	0.858319	−	0.400241i
$615$		0			0
$616$	3.10090	+	4.42854i	0.124939	+	0.178431i
$617$	−18.0464	+	15.1427i	−0.726520	+	0.609623i	−0.929181	−	0.369626i	$-0.879486\pi$
$617$	−18.0464	+	15.1427i	−0.726520	+	0.609623i	0.202660	+	0.979249i	$0.435041\pi$
$618$		0			0
$619$	−13.1526	−	7.59366i	−0.528648	−	0.305215i	0.211818	−	0.977309i	$-0.432062\pi$
$619$	−13.1526	−	7.59366i	−0.528648	−	0.305215i	−0.740466	+	0.672094i	$0.765395\pi$
$620$	−0.557595	−	3.16228i	−0.0223936	−	0.127000i
$621$		0			0
$622$	6.91482	+	18.9983i	0.277259	+	0.761763i
$623$	−4.77756	−	4.77756i	−0.191409	−	0.191409i
$624$		0			0
$625$	−3.43248	+	19.4666i	−0.137299	+	0.778663i
$626$	12.4254	−	14.8080i	0.496619	−	0.591848i
$627$		0			0
$628$			9.48862i			0.378637i
$629$	−0.268593	+	0.120048i	−0.0107095	+	0.00478664i
$630$		0			0
$631$	0.161210	−	1.84264i	0.00641767	−	0.0733544i	−0.992310	−	0.123774i	$-0.960500\pi$
$631$	0.161210	−	1.84264i	0.00641767	−	0.0733544i	0.998728	+	0.0504195i	$0.0160558\pi$
$632$	−8.38493	−	7.03579i	−0.333535	−	0.279869i
$633$		0			0
$634$	−23.9154	−	11.1519i	−0.949801	−	0.442900i
$635$	−0.755461	+	0.755461i	−0.0299796	+	0.0299796i
$636$		0			0
$637$	−1.52243	+	5.68179i	−0.0603209	+	0.225121i
$638$	−7.80460	+	1.37616i	−0.308987	+	0.0544827i
$639$		0			0
$640$	0.517728	−	0.298910i	0.0204650	−	0.0118155i
$641$	−28.3827	−	33.8252i	−1.12105	−	1.33602i	−0.935478	−	0.353386i	$-0.885030\pi$
$641$	−28.3827	−	33.8252i	−1.12105	−	1.33602i	−0.185573	−	0.982630i	$-0.559414\pi$
$642$		0			0
$643$	−0.484627	−	1.80865i	−0.0191118	−	0.0713263i	0.955711	−	0.294306i	$-0.0950884\pi$
$643$	−0.484627	−	1.80865i	−0.0191118	−	0.0713263i	−0.974823	+	0.222979i	$0.928422\pi$
$644$	−0.116505	−	0.249846i	−0.00459094	−	0.00984529i
$645$		0			0
$646$	−0.150204	+	0.214514i	−0.00590972	+	0.00843995i
$647$	−1.03932	−	11.8795i	−0.0408601	−	0.467033i	−0.988869	−	0.148789i	$-0.952463\pi$
$647$	−1.03932	−	11.8795i	−0.0408601	−	0.467033i	0.948009	−	0.318244i	$-0.103093\pi$
$648$		0			0
$649$	−41.5096	−	29.0654i	−1.62940	−	1.14092i
$650$	4.60063	+	1.67449i	0.180452	+	0.0656790i
$651$		0			0
$652$	14.9535	−	4.00679i	0.585626	−	0.156918i
$653$	−1.41649	+	0.991840i	−0.0554317	+	0.0388137i	−0.600964	−	0.799276i	$-0.705216\pi$
$653$	−1.41649	+	0.991840i	−0.0554317	+	0.0388137i	0.545532	+	0.838090i	$0.316328\pi$
$654$		0			0
$655$	0.346706	+	0.600513i	0.0135469	+	0.0234640i
$656$	−0.255852	+	0.443149i	−0.00998935	+	0.0173021i
$657$		0			0
$658$	−0.792316	−	0.212300i	−0.0308877	−	0.00827633i
$659$	−26.0155	+	9.46888i	−1.01342	+	0.368855i	−0.794746	−	0.606942i	$-0.792396\pi$
$659$	−26.0155	+	9.46888i	−1.01342	+	0.368855i	−0.218675	+	0.975798i	$0.570174\pi$
$660$		0			0
$661$	−20.0720	+	43.0445i	−0.780710	+	1.67424i	−0.0430444	+	0.999073i	$0.513706\pi$
$661$	−20.0720	+	43.0445i	−0.780710	+	1.67424i	−0.737666	+	0.675166i	$0.764072\pi$
$662$	−2.77010	−	0.488443i	−0.107663	−	0.0189839i
$663$		0			0
$664$	−4.36430	−	0.381827i	−0.169368	−	0.0148177i
$665$	−3.85996			−0.149683
$666$		0			0
$667$	0.404109			0.0156472
$668$	−13.6807	−	1.19691i	−0.529322	−	0.0463097i
$669$		0			0
$670$	0.300852	+	0.0530484i	0.0116229	+	0.00204944i
$671$	9.22124	−	19.7750i	0.355982	−	0.763406i
$672$		0			0
$673$	28.2890	−	10.2964i	1.09046	−	0.396895i	0.266670	−	0.963788i	$-0.414077\pi$
$673$	28.2890	−	10.2964i	1.09046	−	0.396895i	0.823792	+	0.566893i	$0.191855\pi$
$674$	7.51987	+	2.01494i	0.289655	+	0.0776127i
$675$		0			0
$676$	−5.94396	+	10.2952i	−0.228614	+	0.395971i
$677$	20.8551	+	36.1221i	0.801528	+	1.38829i	0.918610	+	0.395165i	$0.129312\pi$
$677$	20.8551	+	36.1221i	0.801528	+	1.38829i	−0.117083	+	0.993122i	$0.537354\pi$
$678$		0			0
$679$	1.02451	−	0.717370i	0.0393171	−	0.0275301i
$680$	−0.0279291	+	0.00748358i	−0.00107103	+	0.000286982i
$681$		0			0
$682$	22.8822	+	8.32843i	0.876203	+	0.318912i
$683$	−17.6269	−	12.3425i	−0.674476	−	0.472273i	0.185475	−	0.982649i	$-0.440617\pi$
$683$	−17.6269	−	12.3425i	−0.674476	−	0.472273i	−0.859952	+	0.510376i	$0.829506\pi$
$684$		0			0
$685$	−0.531568	−	6.07586i	−0.0203102	−	0.232146i
$686$	−8.60326	+	12.2867i	−0.328474	+	0.469109i
$687$		0			0
$688$	−0.650329	−	1.39464i	−0.0247936	−	0.0531700i
$689$	3.17928	+	11.8652i	0.121121	+	0.452029i
$690$		0			0
$691$	−28.0778	−	33.4618i	−1.06813	−	1.27295i	−0.960358	−	0.278771i	$-0.910073\pi$
$691$	−28.0778	−	33.4618i	−1.06813	−	1.27295i	−0.107772	−	0.994176i	$-0.534372\pi$
$692$	15.1537	−	8.74899i	0.576057	−	0.332587i
$693$		0			0
$694$	−28.0018	+	4.93747i	−1.06293	+	0.187424i
$695$	−2.45544	+	9.16384i	−0.0931403	+	0.347604i
$696$		0			0
$697$	0.0175003	−	0.0175003i	0.000662873	−	0.000662873i
$698$	19.2293	+	8.96678i	0.727841	+	0.339398i
$699$		0			0
$700$	4.24111	+	3.55871i	0.160299	+	0.134507i
$701$	−1.77937	+	20.3383i	−0.0672061	+	0.768169i	0.885572	+	0.464502i	$0.153767\pi$
$701$	−1.77937	+	20.3383i	−0.0672061	+	0.768169i	−0.952778	+	0.303667i	$0.901789\pi$
$702$		0			0
$703$	−29.6220	−	14.3949i	−1.11721	−	0.542915i
$704$			4.53350i			0.170863i
$705$		0			0
$706$	2.85192	−	3.39878i	0.107333	−	0.127915i
$707$	2.39909	−	13.6059i	0.0902270	−	0.511703i
$708$		0			0
$709$	10.4520	+	10.4520i	0.392533	+	0.392533i	0.875589	−	0.483056i	$-0.160473\pi$
$709$	10.4520	+	10.4520i	0.392533	+	0.392533i	−0.483056	+	0.875589i	$0.660473\pi$
$710$	0.800255	+	2.19868i	0.0300330	+	0.0825150i
$711$		0			0
$712$	−0.983849	−	5.57968i	−0.0368713	−	0.209108i
$713$	−1.07533	−	0.620841i	−0.0402714	−	0.0232507i
$714$		0			0
$715$	2.18941	−	1.83714i	0.0818795	−	0.0687050i
$716$	−7.67808	−	10.9654i	−0.286943	−	0.409797i
$717$		0			0
$718$	4.96708	−	2.31619i	0.185370	−	0.0864393i
$719$	−12.3740	+	33.9973i	−0.461472	+	1.26788i	0.462906	+	0.886407i	$0.346807\pi$
$719$	−12.3740	+	33.9973i	−0.461472	+	1.26788i	−0.924378	+	0.381477i	$0.875416\pi$
$720$		0			0
$721$	−7.55111	+	0.660637i	−0.281218	+	0.0246034i
$722$	−10.2763	+	0.899061i	−0.382445	+	0.0334596i
$723$		0			0
$724$	−6.62692	+	18.2073i	−0.246287	+	0.676669i
$725$	−7.35535	+	3.42986i	−0.273171	+	0.127382i
$726$		0			0
$727$	8.89453	+	12.7027i	0.329880	+	0.471117i	0.949492	−	0.313791i	$-0.101599\pi$
$727$	8.89453	+	12.7027i	0.329880	+	0.471117i	−0.619612	+	0.784908i	$0.712710\pi$
$728$	0.963356	−	0.808351i	0.0357043	−	0.0299595i
$729$		0			0
$730$	−1.00905	−	0.582575i	−0.0373466	−	0.0215621i
$731$	0.0129240	+	0.0732958i	0.000478012	+	0.00271094i
$732$		0			0
$733$	−13.5714	−	37.2871i	−0.501271	−	1.37723i	−0.890035	−	0.455893i	$-0.849320\pi$
$733$	−13.5714	−	37.2871i	−0.501271	−	1.37723i	0.388764	−	0.921338i	$-0.372902\pi$
$734$	−3.21432	−	3.21432i	−0.118643	−	0.118643i
$735$		0			0
$736$	0.0401424	−	0.227659i	0.00147967	−	0.00839161i
$737$	−1.48913	+	1.77467i	−0.0548527	+	0.0653710i
$738$		0			0
$739$		−	14.5362i		−	0.534723i	−0.963596	−	0.267362i	$-0.913848\pi$
$739$		−	14.5362i		−	0.534723i	0.963596	−	0.267362i	$-0.0861518\pi$
$740$	−1.48383	−	3.31989i	−0.0545467	−	0.122042i
$741$		0			0
$742$	−1.21066	+	13.8379i	−0.0444447	+	0.508005i
$743$	20.7375	+	17.4008i	0.760785	+	0.638375i	0.938331	−	0.345738i	$-0.112371\pi$
$743$	20.7375	+	17.4008i	0.760785	+	0.638375i	−0.177546	+	0.984113i	$0.556816\pi$
$744$		0			0
$745$	−4.78500	−	2.23128i	−0.175309	−	0.0817479i
$746$	−22.3553	+	22.3553i	−0.818486	+	0.818486i
$747$		0			0
$748$	0.0567508	−	0.211797i	0.00207502	−	0.00774406i
$749$	−19.3962	+	3.42007i	−0.708722	+	0.124967i
$750$		0			0
$751$	4.18112	−	2.41397i	0.152571	−	0.0880869i	−0.421771	−	0.906702i	$-0.638591\pi$
$751$	4.18112	−	2.41397i	0.152571	−	0.0880869i	0.574342	+	0.818616i	$0.305258\pi$
$752$	−0.442139	−	0.526921i	−0.0161232	−	0.0192148i
$753$		0			0
$754$	0.477124	+	1.78065i	0.0173758	+	0.0648475i
$755$	5.27715	+	11.3169i	0.192055	+	0.411863i
$756$		0			0
$757$	15.4003	−	21.9940i	0.559735	−	0.799384i	−0.435154	−	0.900356i	$-0.643306\pi$
$757$	15.4003	−	21.9940i	0.559735	−	0.799384i	0.994889	+	0.100971i	$0.0321951\pi$
$758$	−0.493302	−	5.63847i	−0.0179176	−	0.204799i
$759$		0			0
$760$	−2.65146	−	1.85657i	−0.0961785	−	0.0673449i
$761$	−29.0679	−	10.5799i	−1.05371	−	0.383520i	−0.243649	−	0.969863i	$-0.578345\pi$
$761$	−29.0679	−	10.5799i	−1.05371	−	0.383520i	−0.810062	+	0.586344i	$0.800567\pi$
$762$		0			0
$763$	3.66691	−	0.982546i	0.132751	−	0.0355705i
$764$	7.48446	−	5.24067i	0.270778	−	0.189601i
$765$		0			0
$766$	2.44560	+	4.23590i	0.0883631	+	0.153049i
$767$	−5.89373	+	10.2082i	−0.212810	+	0.368598i
$768$		0			0
$769$	−40.1369	−	10.7546i	−1.44737	−	0.387822i	−0.552264	−	0.833669i	$-0.686236\pi$
$769$	−40.1369	−	10.7546i	−1.44737	−	0.387822i	−0.895109	+	0.445847i	$0.852903\pi$
$770$	3.03706	−	1.10540i	0.109448	−	0.0398358i
$771$		0			0
$772$	−5.70107	+	12.2260i	−0.205186	+	0.440023i
$773$	−29.8687	−	5.26665i	−1.07430	−	0.189428i	−0.391607	−	0.920133i	$-0.628081\pi$
$773$	−29.8687	−	5.26665i	−1.07430	−	0.189428i	−0.682694	+	0.730704i	$0.739192\pi$
$774$		0			0
$775$	24.8419	+	2.17338i	0.892346	+	0.0780702i
$776$	1.04879			0.0376494
$777$		0			0
$778$	19.7899			0.709503
$779$	2.76002	+	0.241471i	0.0988881	+	0.00865158i
$780$		0			0
$781$	−17.4739	−	3.08112i	−0.625266	−	0.110251i
$782$	−0.00472524	+	0.0101333i	−0.000168974	+	0.000362366i
$783$		0			0
$784$	−5.24152	+	1.90776i	−0.187197	+	0.0681342i
$785$	5.47921	+	1.46815i	0.195561	+	0.0524005i
$786$		0			0
$787$	1.89043	−	3.27431i	0.0673864	−	0.116717i	−0.830364	−	0.557222i	$-0.811867\pi$
$787$	1.89043	−	3.27431i	0.0673864	−	0.116717i	0.897750	+	0.440505i	$0.145201\pi$
$788$	2.66467	+	4.61535i	0.0949251	+	0.164415i
$789$		0			0
$790$	−5.36020	+	3.75325i	−0.190707	+	0.133535i
$791$	−1.55310	+	0.416151i	−0.0552218	+	0.0147966i
$792$		0			0
$793$	−4.76939	−	1.73592i	−0.169366	−	0.0616442i
$794$	22.4971	+	15.7526i	0.798392	+	0.559040i
$795$		0			0
$796$	−0.781764	−	8.93561i	−0.0277089	−	0.316714i
$797$	13.5400	−	19.3371i	0.479611	−	0.684955i	−0.504318	−	0.863518i	$-0.668256\pi$
$797$	13.5400	−	19.3371i	0.479611	−	0.684955i	0.983928	+	0.178563i	$0.0571448\pi$
$798$		0			0
$799$	0.0140599	+	0.0301515i	0.000497403	+	0.00106668i
$800$	1.20160	+	4.48442i	0.0424828	+	0.158548i
$801$		0			0
$802$	14.0412	+	16.7336i	0.495811	+	0.590884i
$803$	7.65200	−	4.41789i	0.270033	−	0.155904i
$804$		0			0
$805$	−0.162300	+	0.0286179i	−0.00572032	+	0.00100865i
$806$	1.46603	−	5.47131i	0.0516388	−	0.192719i
$807$		0			0
$808$	8.19215	−	8.19215i	0.288199	−	0.288199i
$809$	−34.9902	−	16.3162i	−1.23019	−	0.573647i	−0.304711	−	0.952445i	$-0.598560\pi$
$809$	−34.9902	−	16.3162i	−1.23019	−	0.573647i	−0.925480	+	0.378797i	$0.876338\pi$
$810$		0			0
$811$	11.1576	+	9.36231i	0.391795	+	0.328755i	0.817312	−	0.576195i	$-0.195463\pi$
$811$	11.1576	+	9.36231i	0.391795	+	0.328755i	−0.425517	+	0.904951i	$0.639908\pi$
$812$	−0.181687	+	2.07670i	−0.00637597	+	0.0728777i
$813$		0			0
$814$	27.4292	+	2.84308i	0.961395	+	0.0996498i
$815$		−	9.25489i		−	0.324185i
$816$		0			0
$817$	−5.35552	+	6.38246i	−0.187366	+	0.223294i
$818$	3.37091	−	19.1174i	0.117861	−	0.668423i
$819$		0			0
$820$	0.216309	+	0.216309i	0.00755385	+	0.00755385i
$821$	5.01893	+	13.7894i	0.175162	+	0.481253i	0.995943	−	0.0899902i	$-0.0286836\pi$
$821$	5.01893	+	13.7894i	0.175162	+	0.481253i	−0.820781	+	0.571243i	$0.806461\pi$
$822$		0			0
$823$	2.55547	+	14.4928i	0.0890781	+	0.505187i	0.996402	+	0.0847545i	$0.0270106\pi$
$823$	2.55547	+	14.4928i	0.0890781	+	0.505187i	−0.907324	+	0.420433i	$0.861878\pi$
$824$	−5.50471	−	3.17814i	−0.191766	−	0.110716i
$825$		0			0
$826$	−10.2110	+	8.56804i	−0.355286	+	0.298120i
$827$	22.3676	+	31.9442i	0.777796	+	1.11081i	0.991008	+	0.133802i	$0.0427186\pi$
$827$	22.3676	+	31.9442i	0.777796	+	1.11081i	−0.213212	+	0.977006i	$0.568392\pi$
$828$		0			0
$829$	49.3382	−	23.0068i	1.71359	−	0.799058i	0.719015	−	0.694995i	$-0.244593\pi$
$829$	49.3382	−	23.0068i	1.71359	−	0.799058i	0.994571	−	0.104063i	$-0.0331845\pi$
$830$	−0.895762	+	2.46109i	−0.0310924	+	0.0854256i
$831$		0			0
$832$	1.05054	−	0.0919106i	0.0364210	−	0.00318643i
$833$	0.268756	−	0.0235131i	0.00931185	−	0.000814681i
$834$		0			0
$835$	−2.80793	+	7.71474i	−0.0971726	+	0.266979i
$836$	22.2463	−	10.3736i	0.769405	−	0.358780i
$837$		0			0
$838$	−21.0949	−	30.1266i	−0.728711	−	1.04071i
$839$	40.0489	−	33.6050i	1.38264	−	1.16017i	0.414418	−	0.910087i	$-0.363985\pi$
$839$	40.0489	−	33.6050i	1.38264	−	1.16017i	0.968223	−	0.250087i	$-0.0804591\pi$
$840$		0			0
$841$	22.4683	+	12.9721i	0.774769	+	0.447313i
$842$	−4.06289	−	23.0418i	−0.140016	−	0.794073i
$843$		0			0
$844$	−3.22604	−	8.86347i	−0.111045	−	0.305093i
$845$	5.02529	+	5.02529i	0.172875	+	0.172875i
$846$		0			0
$847$	−1.97813	+	11.2185i	−0.0679694	+	0.385474i
$848$	−7.48738	+	8.92312i	−0.257118	+	0.306421i
$849$		0			0
$850$		−	0.224546i		−	0.00770185i
$851$	−1.35224	−	0.385646i	−0.0463542	−	0.0132198i
$852$		0			0
$853$	3.14029	−	35.8937i	0.107522	−	1.22898i	−0.730336	−	0.683088i	$-0.760636\pi$
$853$	3.14029	−	35.8937i	0.107522	−	1.22898i	0.837857	−	0.545889i	$-0.183808\pi$
$854$	−4.39668	−	3.68925i	−0.150451	−	0.126244i
$855$		0			0
$856$	−14.9685	−	6.97992i	−0.511612	−	0.238569i
$857$	−38.0024	+	38.0024i	−1.29814	+	1.29814i	−0.368516	+	0.929621i	$0.620134\pi$
$857$	−38.0024	+	38.0024i	−1.29814	+	1.29814i	−0.929621	+	0.368516i	$0.879866\pi$
$858$		0			0
$859$	12.8455	−	47.9400i	0.438282	−	1.63569i	−0.294805	−	0.955557i	$-0.595255\pi$
$859$	12.8455	−	47.9400i	0.438282	−	1.63569i	0.733087	−	0.680135i	$-0.238079\pi$
$860$	−0.905957	+	0.159745i	−0.0308929	+	0.00544725i
$861$		0			0
$862$	23.3557	−	13.4844i	0.795497	−	0.459280i
$863$	3.84227	+	4.57904i	0.130792	+	0.155872i	0.827466	−	0.561516i	$-0.189782\pi$
$863$	3.84227	+	4.57904i	0.130792	+	0.155872i	−0.696673	+	0.717388i	$0.745337\pi$
$864$		0			0
$865$	−2.70742	−	10.1042i	−0.0920550	−	0.343554i
$866$	5.25598	+	11.2715i	0.178605	+	0.383020i
$867$		0			0
$868$	3.67394	−	5.24693i	0.124702	−	0.178092i
$869$	−4.32489	−	49.4337i	−0.146712	−	1.67692i
$870$		0			0
$871$	0.441433	+	0.309095i	0.0149574	+	0.0104733i
$872$	2.99143	+	1.08879i	0.101303	+	0.0368712i
$873$		0			0
$874$	−1.20900	+	0.323950i	−0.0408950	+	0.0109578i
$875$	5.63110	−	3.94294i	0.190366	−	0.133296i
$876$		0			0
$877$	11.3852	+	19.7197i	0.384450	+	0.665887i	0.991693	−	0.128629i	$-0.0410577\pi$
$877$	11.3852	+	19.7197i	0.384450	+	0.665887i	−0.607242	+	0.794517i	$0.707724\pi$
$878$	−0.362381	+	0.627663i	−0.0122298	+	0.0211826i
$879$		0			0
$880$	2.61787	+	0.701456i	0.0882484	+	0.0236461i
$881$	30.5232	−	11.1095i	1.02835	−	0.374290i	0.227900	−	0.973685i	$-0.426814\pi$
$881$	30.5232	−	11.1095i	1.02835	−	0.374290i	0.800454	+	0.599395i	$0.204592\pi$
$882$		0			0
$883$	−7.38026	+	15.8270i	−0.248366	+	0.532622i	−0.990481	−	0.137651i	$-0.956045\pi$
$883$	−7.38026	+	15.8270i	−0.248366	+	0.532622i	0.742115	+	0.670272i	$0.233823\pi$
$884$	−0.0502300	−	0.00885691i	−0.00168942	−	0.000297890i
$885$		0			0
$886$	12.6746	+	1.10888i	0.425811	+	0.0372536i
$887$	42.7684			1.43602			0.718011	−	0.696031i	$-0.245053\pi$
$887$	42.7684			1.43602			0.718011	+	0.696031i	$0.245053\pi$
$888$		0			0
$889$	−2.13118			−0.0714773
$890$	−3.37422	−	0.295206i	−0.113104	−	0.00989533i
$891$		0			0
$892$	17.2849	+	3.04780i	0.578743	+	0.102048i
$893$	−1.57394	+	3.37533i	−0.0526700	+	0.112951i
$894$		0			0
$895$	−7.52000	+	2.73706i	−0.251366	+	0.0914897i
$896$	1.15188	+	0.308645i	0.0384816	+	0.0103111i
$897$		0			0
$898$	10.6926	−	18.5201i	0.356816	−	0.618024i
$899$	4.69476	+	8.13156i	0.156579	+	0.271203i
$900$		0			0
$901$	0.461498	−	0.323144i	0.0153747	−	0.0107655i
$902$	−2.24077	+	0.600411i	−0.0746093	+	0.0199915i
$903$		0			0
$904$	−1.26700	−	0.461151i	−0.0421399	−	0.0153377i
$905$	9.48845	+	6.64388i	0.315407	+	0.220850i
$906$		0			0
$907$	4.68863	+	53.5913i	0.155683	+	1.77947i	0.525923	+	0.850532i	$0.323720\pi$
$907$	4.68863	+	53.5913i	0.155683	+	1.77947i	−0.370240	+	0.928936i	$0.620724\pi$
$908$	2.92953	−	4.18381i	0.0972200	−	0.138844i
$909$		0			0
$910$	−0.317725	−	0.681364i	−0.0105325	−	0.0225870i
$911$	2.73906	+	10.2223i	0.0907490	+	0.338680i	0.996341	−	0.0854706i	$-0.0272394\pi$
$911$	2.73906	+	10.2223i	0.0907490	+	0.338680i	−0.905592	+	0.424151i	$0.860573\pi$
$912$		0			0
$913$	−12.7665	−	15.2145i	−0.422509	−	0.503526i
$914$	21.5231	−	12.4264i	0.711921	−	0.411028i
$915$		0			0
$916$	0.0576164	−	0.0101593i	0.00190370	−	0.000335674i
$917$	−0.357997	+	1.33606i	−0.0118221	+	0.0441207i
$918$		0			0
$919$	−6.91035	+	6.91035i	−0.227952	+	0.227952i	−0.811836	−	0.583885i	$-0.801532\pi$
$919$	−6.91035	+	6.91035i	−0.227952	+	0.227952i	0.583885	+	0.811836i	$0.301532\pi$
$920$	−0.125251	−	0.0584053i	−0.00412939	−	0.00192556i
$921$		0			0
$922$	1.82844	+	1.53424i	0.0602165	+	0.0505276i
$923$	−0.359725	+	4.11168i	−0.0118405	+	0.135338i
$924$		0			0
$925$	27.8858	−	4.45778i	0.916881	−	0.146571i
$926$			26.8861i			0.883531i
$927$		0			0
$928$	−1.12365	+	1.33912i	−0.0368858	+	0.0439588i
$929$	−6.08342	+	34.5008i	−0.199591	+	1.13194i	0.706137	+	0.708075i	$0.250436\pi$
$929$	−6.08342	+	34.5008i	−0.199591	+	1.13194i	−0.905728	+	0.423860i	$0.860675\pi$
$930$		0			0
$931$	21.3553	+	21.3553i	0.699892	+	0.699892i
$932$	5.41004	+	14.8640i	0.177212	+	0.486886i
$933$		0			0
$934$	4.64129	+	26.3221i	0.151868	+	0.861285i
$935$	−0.113521	−	0.0655416i	−0.00371255	−	0.00214344i
$936$		0			0
$937$	33.5369	−	28.1408i	1.09560	−	0.919319i	0.0984806	−	0.995139i	$-0.468602\pi$
$937$	33.5369	−	28.1408i	1.09560	−	0.919319i	0.997122	+	0.0758196i	$0.0241573\pi$
$938$	0.349531	+	0.499182i	0.0114126	+	0.0162989i
$939$		0			0
$940$	−0.372682	+	0.173784i	−0.0121555	+	0.00566822i
$941$	−14.4396	+	39.6724i	−0.470717	+	1.29328i	0.446461	+	0.894803i	$0.352684\pi$
$941$	−14.4396	+	39.6724i	−0.470717	+	1.29328i	−0.917177	+	0.398480i	$0.869538\pi$
$942$		0			0
$943$	0.117841	−	0.0103097i	0.00383743	−	0.000335732i
$944$	−11.1351	+	0.974197i	−0.362417	+	0.0317074i
$945$		0			0
$946$	2.38600	−	6.55548i	0.0775755	−	0.213137i
$947$	−43.1334	+	20.1134i	−1.40165	+	0.653598i	−0.968794	−	0.247867i	$-0.920270\pi$
$947$	−43.1334	+	20.1134i	−1.40165	+	0.653598i	−0.432852	+	0.901465i	$0.642493\pi$
$948$		0			0
$949$	−1.17889	−	1.68362i	−0.0382683	−	0.0546527i
$950$	19.2560	−	16.1577i	0.624746	−	0.524224i
$951$		0			0
$952$	−0.0499501	−	0.0288387i	−0.00161889	−	0.000934667i
$953$	−1.10513	−	6.26749i	−0.0357986	−	0.203024i	0.961663	−	0.274235i	$-0.0884247\pi$
$953$	−1.10513	−	6.26749i	−0.0357986	−	0.203024i	−0.997461	+	0.0712112i	$0.977314\pi$
$954$		0			0
$955$	−1.86818	−	5.13278i	−0.0604528	−	0.166093i
$956$	7.56241	+	7.56241i	0.244586	+	0.244586i
$957$		0			0
$958$	−0.307338	+	1.74300i	−0.00992965	+	0.0563138i
$959$	7.82029	−	9.31986i	0.252530	−	0.300954i
$960$		0			0
$961$			2.14936i			0.0693343i
$962$	0.102732	−	6.41379i	0.00331222	−	0.206789i
$963$		0			0
$964$	−1.43440	+	16.3953i	−0.0461989	+	0.528056i
$965$	6.17779	+	5.18378i	0.198870	+	0.166872i
$966$		0			0
$967$	11.7707	+	5.48875i	0.378519	+	0.176506i	0.602560	−	0.798073i	$-0.294147\pi$
$967$	11.7707	+	5.48875i	0.378519	+	0.176506i	−0.224041	+	0.974580i	$0.571925\pi$
$968$	−6.75472	+	6.75472i	−0.217105	+	0.217105i
$969$		0			0
$970$	0.162277	−	0.605625i	0.00521039	−	0.0194454i
$971$	−2.77960	+	0.490118i	−0.0892016	+	0.0157286i	−0.218071	−	0.975933i	$-0.569976\pi$
$971$	−2.77960	+	0.490118i	−0.0892016	+	0.0157286i	0.128869	+	0.991662i	$0.458865\pi$
$972$		0			0
$973$	−16.3892	+	9.46228i	−0.525412	+	0.303347i
$974$	27.8104	+	33.1431i	0.891103	+	1.06197i
$975$		0			0
$976$	−1.24567	−	4.64891i	−0.0398730	−	0.148808i
$977$	−0.843234	−	1.80832i	−0.0269775	−	0.0578534i	0.892357	−	0.451330i	$-0.149050\pi$
$977$	−0.843234	−	1.80832i	−0.0269775	−	0.0578534i	−0.919335	+	0.393476i	$0.871272\pi$
$978$		0			0
$979$	14.7327	−	21.0405i	0.470860	−	0.672458i
$980$	0.290629	+	3.32190i	0.00928380	+	0.106114i
$981$		0			0
$982$	−26.9743	−	18.8876i	−0.860785	−	0.602728i
$983$	−7.84797	−	2.85643i	−0.250312	−	0.0911059i	0.213817	−	0.976874i	$-0.431410\pi$
$983$	−7.84797	−	2.85643i	−0.250312	−	0.0911059i	−0.464129	+	0.885768i	$0.653633\pi$
$984$		0			0
$985$	3.07743	−	0.824596i	0.0980552	−	0.0262738i
$986$	0.0692584	−	0.0484953i	0.00220564	−	0.00154440i
$987$		0			0
$988$	−2.85489	−	4.94481i	−0.0908260	−	0.157315i
$989$	−0.177864	+	0.308069i	−0.00565574	+	0.00979604i
$990$		0			0
$991$	38.1958	+	10.2345i	1.21333	+	0.325111i	0.808068	−	0.589090i	$-0.200514\pi$
$991$	38.1958	+	10.2345i	1.21333	+	0.325111i	0.405262	+	0.914200i	$0.367180\pi$
$992$	5.04735	−	1.83709i	0.160254	−	0.0583275i
$993$		0			0
$994$	−1.97250	+	4.23004i	−0.0625639	+	0.134169i
$995$	−5.28083	−	0.931153i	−0.167414	−	0.0295195i
$996$		0			0
$997$	49.9703	+	4.37183i	1.58258	+	0.138457i	0.844236	−	0.535972i	$-0.180055\pi$
$997$	49.9703	+	4.37183i	1.58258	+	0.138457i	0.738339	+	0.674429i	$0.235610\pi$
$998$	−12.7476			−0.403518
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.bs.b.35.7	yes	96
3.2	odd	2	inner	666.2.bs.b.35.2	✓	96
37.18	odd	36	inner	666.2.bs.b.647.2	yes	96
111.92	even	36	inner	666.2.bs.b.647.7	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.bs.b.35.2	✓	96	3.2	odd	2	inner
666.2.bs.b.35.7	yes	96	1.1	even	1	trivial
666.2.bs.b.647.2	yes	96	37.18	odd	36	inner
666.2.bs.b.647.7	yes	96	111.92	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)

\(f(q)\)	\(=\)	\(q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(0.252650 - 0.541810i) q^{5} +(1.12060 - 0.407863i) q^{7} +(0.965926 + 0.258819i) q^{8} +O(q^{10})\)	\(q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(0.252650 - 0.541810i) q^{5} +(1.12060 - 0.407863i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.298910 - 0.517728i) q^{10} +(2.26675 + 3.92612i) q^{11} +(0.863842 - 0.604868i) q^{13} +(1.15188 - 0.308645i) q^{14} +(0.939693 + 0.342020i) q^{16} +(-0.0396193 - 0.0277417i) q^{17} +(-0.471895 - 5.39378i) q^{19} +(0.342896 - 0.489706i) q^{20} +(1.91594 + 4.10875i) q^{22} +(-0.0598314 - 0.223294i) q^{23} +(2.98421 + 3.55645i) q^{25} +(0.913272 - 0.527278i) q^{26} +(1.17440 - 0.207078i) q^{28} +(-0.452441 + 1.68853i) q^{29} +(3.79807 - 3.79807i) q^{31} +(0.906308 + 0.422618i) q^{32} +(-0.0370507 - 0.0310892i) q^{34} +(0.0621341 - 0.710196i) q^{35} +(3.12536 - 5.21844i) q^{37} -5.41439i q^{38} +(0.384272 - 0.457957i) q^{40} +(-0.0888565 + 0.503930i) q^{41} +(-1.08810 - 1.08810i) q^{43} +(1.55055 + 4.26010i) q^{44} +(-0.0401424 - 0.227659i) q^{46} +(-0.595692 - 0.343923i) q^{47} +(-4.27293 + 3.58541i) q^{49} +(2.66289 + 3.80300i) q^{50} +(0.955752 - 0.445675i) q^{52} +(-3.98395 + 10.9458i) q^{53} +(2.69991 - 0.236211i) q^{55} +(1.18797 - 0.103934i) q^{56} +(-0.597884 + 1.64267i) q^{58} +(-10.1304 + 4.72388i) q^{59} +(-2.76057 - 3.94250i) q^{61} +(4.11464 - 3.45259i) q^{62} +(0.866025 + 0.500000i) q^{64} +(-0.109474 - 0.620858i) q^{65} +(0.174776 + 0.480194i) q^{67} +(-0.0342001 - 0.0342001i) q^{68} +(0.123795 - 0.702078i) q^{70} +(-2.51578 + 2.99819i) q^{71} -1.94900i q^{73} +(3.56828 - 4.92619i) q^{74} +(0.471895 - 5.39378i) q^{76} +(4.14143 + 3.47507i) q^{77} +(-9.92022 - 4.62587i) q^{79} +(0.422723 - 0.422723i) q^{80} +(-0.132439 + 0.494269i) q^{82} +(-4.31441 + 0.760747i) q^{83} +(-0.0250406 + 0.0144572i) q^{85} +(-0.989128 - 1.17880i) q^{86} +(1.17336 + 4.37902i) q^{88} +(-2.39445 - 5.13492i) q^{89} +(0.721313 - 1.03014i) q^{91} +(-0.0201479 - 0.230291i) q^{92} +(-0.563451 - 0.394532i) q^{94} +(-3.04163 - 1.10706i) q^{95} +(1.01305 - 0.271447i) q^{97} +(-4.56916 + 3.19936i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q - 12 q^{13} + 24 q^{19} + 12 q^{22} + 48 q^{31} + 72 q^{34} + 24 q^{37} + 72 q^{43} + 60 q^{46} + 12 q^{52} - 60 q^{55} + 12 q^{58} - 120 q^{61} + 36 q^{67} + 12 q^{70} - 24 q^{76} + 60 q^{79} + 96 q^{82} - 108 q^{85} - 24 q^{88} + 216 q^{91} - 60 q^{94} + 24 q^{97}+O(q^{100}) \) 96 * q - 12 * q^13 + 24 * q^19 + 12 * q^22 + 48 * q^31 + 72 * q^34 + 24 * q^37 + 72 * q^43 + 60 * q^46 + 12 * q^52 - 60 * q^55 + 12 * q^58 - 120 * q^61 + 36 * q^67 + 12 * q^70 - 24 * q^76 + 60 * q^79 + 96 * q^82 - 108 * q^85 - 24 * q^88 + 216 * q^91 - 60 * q^94 + 24 * q^97

Introduction

L-functions

Modular forms

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Database

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