LMFDB - Embedded newform 675.3.g.k.568.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,3,Mod(82,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("675.82");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	675.g (of order $4$, degree $2$, 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:	$18.3924178443$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 217x^{12} + 9264x^{8} + 59497x^{4} + 28561 $ x^16 + 217x^12 + 9264x^8 + 59497*x^4 + 28561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{8} $
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			568.8
Root			$2.52312 - 2.52312i$ of defining polynomial
Character	$\chi$	$=$	675.568
Dual form			675.3.g.k.82.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.52312 - 2.52312i) q^{2} -8.73230i q^{4} +(4.39136 - 4.39136i) q^{7} +(-11.9402 - 11.9402i) q^{8} +O(q^{10})$	\(q+(2.52312 - 2.52312i) q^{2} -8.73230i q^{4} +(4.39136 - 4.39136i) q^{7} +(-11.9402 - 11.9402i) q^{8} -20.6606 q^{11} +(-4.07650 - 4.07650i) q^{13} -22.1599i q^{14} -25.3238 q^{16} +(3.85449 - 3.85449i) q^{17} -18.4907i q^{19} +(-52.1293 + 52.1293i) q^{22} +(14.1766 + 14.1766i) q^{23} -20.5710 q^{26} +(-38.3466 - 38.3466i) q^{28} -10.6404i q^{29} -33.1465 q^{31} +(-16.1344 + 16.1344i) q^{32} -19.4507i q^{34} +(35.8023 - 35.8023i) q^{37} +(-46.6542 - 46.6542i) q^{38} +12.0583 q^{41} +(-35.5972 - 35.5972i) q^{43} +180.415i q^{44} +71.5385 q^{46} +(-0.615624 + 0.615624i) q^{47} +10.4320i q^{49} +(-35.5972 + 35.5972i) q^{52} +(11.6767 + 11.6767i) q^{53} -104.867 q^{56} +(-26.8470 - 26.8470i) q^{58} +84.1251i q^{59} +69.7745 q^{61} +(-83.6326 + 83.6326i) q^{62} -19.8770i q^{64} +(38.4564 - 38.4564i) q^{67} +(-33.6586 - 33.6586i) q^{68} +107.003 q^{71} +(-8.17407 - 8.17407i) q^{73} -180.667i q^{74} -161.466 q^{76} +(-90.7282 + 90.7282i) q^{77} +73.0992i q^{79} +(30.4246 - 30.4246i) q^{82} +(-4.18896 - 4.18896i) q^{83} -179.632 q^{86} +(246.691 + 246.691i) q^{88} +6.20731i q^{89} -35.8027 q^{91} +(123.794 - 123.794i) q^{92} +3.10659i q^{94} +(54.9464 - 54.9464i) q^{97} +(26.3212 + 26.3212i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^7	$ 16 q + 8 q^{7} - 28 q^{13} - 20 q^{16} - 176 q^{22} - 80 q^{28} - 208 q^{31} + 176 q^{37} + 188 q^{43} + 188 q^{46} + 188 q^{52} - 504 q^{58} + 296 q^{61} - 304 q^{67} + 56 q^{73} - 732 q^{76} + 76 q^{82} + 1128 q^{88} + 200 q^{91} + 284 q^{97}+O(q^{100}) $ 16 * q + 8 * q^7 - 28 * q^13 - 20 * q^16 - 176 * q^22 - 80 * q^28 - 208 * q^31 + 176 * q^37 + 188 * q^43 + 188 * q^46 + 188 * q^52 - 504 * q^58 + 296 * q^61 - 304 * q^67 + 56 * q^73 - 732 * q^76 + 76 * q^82 + 1128 * q^88 + 200 * q^91 + 284 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	2.52312	−	2.52312i	1.26156	−	1.26156i	0.311225	−	0.950336i	$-0.399261\pi$
$2$	2.52312	−	2.52312i	1.26156	−	1.26156i	0.950336	−	0.311225i	$-0.100739\pi$
$3$		0			0
$3$		0			0
$4$		−	8.73230i		−	2.18307i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	4.39136	−	4.39136i	0.627337	−	0.627337i	−0.320061	−	0.947397i	$-0.603703\pi$
$7$	4.39136	−	4.39136i	0.627337	−	0.627337i	0.947397	+	0.320061i	$0.103703\pi$
$8$	−11.9402	−	11.9402i	−1.49252	−	1.49252i
$9$		0			0
$10$		0			0
$11$	−20.6606			−1.87824			−0.939120	−	0.343589i	$-0.888357\pi$
$11$	−20.6606			−1.87824			−0.939120	+	0.343589i	$0.888357\pi$
$12$		0			0
$13$	−4.07650	−	4.07650i	−0.313577	−	0.313577i	0.532717	−	0.846294i	$-0.321171\pi$
$13$	−4.07650	−	4.07650i	−0.313577	−	0.313577i	−0.846294	+	0.532717i	$0.821171\pi$
$14$		−	22.1599i		−	1.58285i
$15$		0			0
$16$	−25.3238			−1.58274
$17$	3.85449	−	3.85449i	0.226735	−	0.226735i	−0.584592	−	0.811327i	$-0.698746\pi$
$17$	3.85449	−	3.85449i	0.226735	−	0.226735i	0.811327	+	0.584592i	$0.198746\pi$
$18$		0			0
$19$		−	18.4907i		−	0.973193i	−0.873627	−	0.486597i	$-0.838238\pi$
$19$		−	18.4907i		−	0.973193i	0.873627	−	0.486597i	$-0.161762\pi$
$20$		0			0
$21$		0			0
$22$	−52.1293	+	52.1293i	−2.36952	+	2.36952i
$23$	14.1766	+	14.1766i	0.616373	+	0.616373i	0.944599	−	0.328226i	$-0.106451\pi$
$23$	14.1766	+	14.1766i	0.616373	+	0.616373i	−0.328226	+	0.944599i	$0.606451\pi$
$24$		0			0
$25$		0			0
$26$	−20.5710			−0.791193
$27$		0			0
$28$	−38.3466	−	38.3466i	−1.36952	−	1.36952i
$29$		−	10.6404i		−	0.366910i	−0.983028	−	0.183455i	$-0.941272\pi$
$29$		−	10.6404i		−	0.366910i	0.983028	−	0.183455i	$-0.0587281\pi$
$30$		0			0
$31$	−33.1465			−1.06924			−0.534620	−	0.845092i	$-0.679545\pi$
$31$	−33.1465			−1.06924			−0.534620	+	0.845092i	$0.679545\pi$
$32$	−16.1344	+	16.1344i	−0.504200	+	0.504200i
$33$		0			0
$34$		−	19.4507i		−	0.572080i
$35$		0			0
$36$		0			0
$37$	35.8023	−	35.8023i	0.967629	−	0.967629i	−0.0318634	−	0.999492i	$-0.510144\pi$
$37$	35.8023	−	35.8023i	0.967629	−	0.967629i	0.999492	+	0.0318634i	$0.0101442\pi$
$38$	−46.6542	−	46.6542i	−1.22774	−	1.22774i
$39$		0			0
$40$		0			0
$41$	12.0583			0.294106			0.147053	−	0.989129i	$-0.453021\pi$
$41$	12.0583			0.294106			0.147053	+	0.989129i	$0.453021\pi$
$42$		0			0
$43$	−35.5972	−	35.5972i	−0.827842	−	0.827842i	0.159376	−	0.987218i	$-0.449052\pi$
$43$	−35.5972	−	35.5972i	−0.827842	−	0.827842i	−0.987218	+	0.159376i	$0.949052\pi$
$44$			180.415i			4.10034i
$45$		0			0
$46$	71.5385			1.55518
$47$	−0.615624	+	0.615624i	−0.0130984	+	0.0130984i	−0.713626	−	0.700527i	$-0.752948\pi$
$47$	−0.615624	+	0.615624i	−0.0130984	+	0.0130984i	0.700527	+	0.713626i	$0.252948\pi$
$48$		0			0
$49$			10.4320i			0.212898i
$50$		0			0
$51$		0			0
$52$	−35.5972	+	35.5972i	−0.684561	+	0.684561i
$53$	11.6767	+	11.6767i	0.220315	+	0.220315i	0.808631	−	0.588316i	$-0.200209\pi$
$53$	11.6767	+	11.6767i	0.220315	+	0.220315i	−0.588316	+	0.808631i	$0.700209\pi$
$54$		0			0
$55$		0			0
$56$	−104.867			−1.87263
$57$		0			0
$58$	−26.8470	−	26.8470i	−0.462879	−	0.462879i
$59$			84.1251i			1.42585i	0.701241	+	0.712924i	$0.252630\pi$
$59$			84.1251i			1.42585i	−0.701241	+	0.712924i	$0.747370\pi$
$60$		0			0
$61$	69.7745			1.14384			0.571922	−	0.820308i	$-0.306198\pi$
$61$	69.7745			1.14384			0.571922	+	0.820308i	$0.306198\pi$
$62$	−83.6326	+	83.6326i	−1.34891	+	1.34891i
$63$		0			0
$64$		−	19.8770i		−	0.310578i
$65$		0			0
$66$		0			0
$67$	38.4564	−	38.4564i	0.573976	−	0.573976i	−0.359261	−	0.933237i	$-0.616971\pi$
$67$	38.4564	−	38.4564i	0.573976	−	0.573976i	0.933237	+	0.359261i	$0.116971\pi$
$68$	−33.6586	−	33.6586i	−0.494979	−	0.494979i
$69$		0			0
$70$		0			0
$71$	107.003			1.50709			0.753543	−	0.657399i	$-0.228343\pi$
$71$	107.003			1.50709			0.753543	+	0.657399i	$0.228343\pi$
$72$		0			0
$73$	−8.17407	−	8.17407i	−0.111974	−	0.111974i	0.648900	−	0.760874i	$-0.275229\pi$
$73$	−8.17407	−	8.17407i	−0.111974	−	0.111974i	−0.760874	+	0.648900i	$0.775229\pi$
$74$		−	180.667i		−	2.44145i
$75$		0			0
$76$	−161.466			−2.12455
$77$	−90.7282	+	90.7282i	−1.17829	+	1.17829i
$78$		0			0
$79$			73.0992i			0.925306i	0.886539	+	0.462653i	$0.153102\pi$
$79$			73.0992i			0.925306i	−0.886539	+	0.462653i	$0.846898\pi$
$80$		0			0
$81$		0			0
$82$	30.4246	−	30.4246i	0.371032	−	0.371032i
$83$	−4.18896	−	4.18896i	−0.0504694	−	0.0504694i	0.681422	−	0.731891i	$-0.261362\pi$
$83$	−4.18896	−	4.18896i	−0.0504694	−	0.0504694i	−0.731891	+	0.681422i	$0.761362\pi$
$84$		0			0
$85$		0			0
$86$	−179.632			−2.08875
$87$		0			0
$88$	246.691	+	246.691i	2.80331	+	2.80331i
$89$			6.20731i			0.0697451i	0.999392	+	0.0348725i	$0.0111025\pi$
$89$			6.20731i			0.0697451i	−0.999392	+	0.0348725i	$0.988897\pi$
$90$		0			0
$91$	−35.8027			−0.393436
$92$	123.794	−	123.794i	1.34559	−	1.34559i
$93$		0			0
$94$			3.10659i			0.0330488i
$95$		0			0
$96$		0			0
$97$	54.9464	−	54.9464i	0.566458	−	0.566458i	−0.364677	−	0.931134i	$-0.618820\pi$
$97$	54.9464	−	54.9464i	0.566458	−	0.566458i	0.931134	+	0.364677i	$0.118820\pi$
$98$	26.3212	+	26.3212i	0.268583	+	0.268583i
$99$		0			0
$100$		0			0
$101$	−28.8331			−0.285476			−0.142738	−	0.989760i	$-0.545591\pi$
$101$	−28.8331			−0.285476			−0.142738	+	0.989760i	$0.545591\pi$
$102$		0			0
$103$	53.8436	+	53.8436i	0.522754	+	0.522754i	0.918402	−	0.395648i	$-0.129480\pi$
$103$	53.8436	+	53.8436i	0.522754	+	0.522754i	−0.395648	+	0.918402i	$0.629480\pi$
$104$			97.3481i			0.936039i
$105$		0			0
$106$	58.9235			0.555882
$107$	14.0751	−	14.0751i	0.131543	−	0.131543i	−0.638270	−	0.769813i	$-0.720350\pi$
$107$	14.0751	−	14.0751i	0.131543	−	0.131543i	0.769813	+	0.638270i	$0.220350\pi$
$108$		0			0
$109$		−	18.6923i		−	0.171489i	−0.996317	−	0.0857447i	$-0.972673\pi$
$109$		−	18.6923i		−	0.171489i	0.996317	−	0.0857447i	$-0.0273269\pi$
$110$		0			0
$111$		0			0
$112$	−111.206	+	111.206i	−0.992909	+	0.992909i
$113$	−104.114	−	104.114i	−0.921362	−	0.921362i	0.0757641	−	0.997126i	$-0.475860\pi$
$113$	−104.114	−	104.114i	−0.921362	−	0.921362i	−0.997126	+	0.0757641i	$0.975860\pi$
$114$		0			0
$115$		0			0
$116$	−92.9150			−0.800991
$117$		0			0
$118$	212.258	+	212.258i	1.79880	+	1.79880i
$119$		−	33.8529i		−	0.284478i
$120$		0			0
$121$	305.862			2.52779
$122$	176.050	−	176.050i	1.44303	−	1.44303i
$123$		0			0
$124$			289.445i			2.33423i
$125$		0			0
$126$		0			0
$127$	37.9268	−	37.9268i	0.298637	−	0.298637i	−0.541843	−	0.840480i	$-0.682273\pi$
$127$	37.9268	−	37.9268i	0.298637	−	0.298637i	0.840480	+	0.541843i	$0.182273\pi$
$128$	−114.690	−	114.690i	−0.896014	−	0.896014i
$129$		0			0
$130$		0			0
$131$	65.4186			0.499378			0.249689	−	0.968326i	$-0.419672\pi$
$131$	65.4186			0.499378			0.249689	+	0.968326i	$0.419672\pi$
$132$		0			0
$133$	−81.1991	−	81.1991i	−0.610520	−	0.610520i
$134$		−	194.060i		−	1.44821i
$135$		0			0
$136$	−92.0465			−0.676813
$137$	90.3791	−	90.3791i	0.659701	−	0.659701i	−0.295608	−	0.955309i	$-0.595522\pi$
$137$	90.3791	−	90.3791i	0.659701	−	0.659701i	0.955309	+	0.295608i	$0.0955222\pi$
$138$		0			0
$139$		−	247.432i		−	1.78008i	−0.455879	−	0.890042i	$-0.650675\pi$
$139$		−	247.432i		−	1.78008i	0.455879	−	0.890042i	$-0.349325\pi$
$140$		0			0
$141$		0			0
$142$	269.982	−	269.982i	1.90128	−	1.90128i
$143$	84.2231	+	84.2231i	0.588972	+	0.588972i
$144$		0			0
$145$		0			0
$146$	−41.2484			−0.282523
$147$		0			0
$148$	−312.636	−	312.636i	−2.11241	−	2.11241i
$149$		−	22.9399i		−	0.153959i	−0.997033	−	0.0769795i	$-0.975472\pi$
$149$		−	22.9399i		−	0.153959i	0.997033	−	0.0769795i	$-0.0245276\pi$
$150$		0			0
$151$	−4.48158			−0.0296793			−0.0148397	−	0.999890i	$-0.504724\pi$
$151$	−4.48158			−0.0296793			−0.0148397	+	0.999890i	$0.504724\pi$
$152$	−220.782	+	220.782i	−1.45251	+	1.45251i
$153$		0			0
$154$			457.837i			2.97297i
$155$		0			0
$156$		0			0
$157$	130.611	−	130.611i	0.831918	−	0.831918i	−0.155861	−	0.987779i	$-0.549815\pi$
$157$	130.611	−	130.611i	0.831918	−	0.831918i	0.987779	+	0.155861i	$0.0498152\pi$
$158$	184.438	+	184.438i	1.16733	+	1.16733i
$159$		0			0
$160$		0			0
$161$	124.509			0.773347
$162$		0			0
$163$	−33.3255	−	33.3255i	−0.204451	−	0.204451i	0.597453	−	0.801904i	$-0.296180\pi$
$163$	−33.3255	−	33.3255i	−0.204451	−	0.204451i	−0.801904	+	0.597453i	$0.796180\pi$
$164$		−	105.297i		−	0.642054i
$165$		0			0
$166$	−21.1385			−0.127341
$167$	−32.9436	+	32.9436i	−0.197267	+	0.197267i	−0.798827	−	0.601560i	$-0.794546\pi$
$167$	−32.9436	+	32.9436i	−0.197267	+	0.197267i	0.601560	+	0.798827i	$0.294546\pi$
$168$		0			0
$169$		−	135.764i		−	0.803339i
$170$		0			0
$171$		0			0
$172$	−310.845	+	310.845i	−1.80724	+	1.80724i
$173$	143.990	+	143.990i	0.832311	+	0.832311i	0.987832	−	0.155522i	$-0.0497059\pi$
$173$	143.990	+	143.990i	0.832311	+	0.832311i	−0.155522	+	0.987832i	$0.549706\pi$
$174$		0			0
$175$		0			0
$176$	523.206			2.97276
$177$		0			0
$178$	15.6618	+	15.6618i	0.0879877	+	0.0879877i
$179$			151.248i			0.844962i	0.906372	+	0.422481i	$0.138841\pi$
$179$			151.248i			0.844962i	−0.906372	+	0.422481i	$0.861159\pi$
$180$		0			0
$181$	76.1404			0.420665			0.210333	−	0.977630i	$-0.432545\pi$
$181$	76.1404			0.420665			0.210333	+	0.977630i	$0.432545\pi$
$182$	−90.3346	+	90.3346i	−0.496344	+	0.496344i
$183$		0			0
$184$		−	338.541i		−	1.83990i
$185$		0			0
$186$		0			0
$187$	−79.6363	+	79.6363i	−0.425863	+	0.425863i
$188$	5.37581	+	5.37581i	0.0285947	+	0.0285947i
$189$		0			0
$190$		0			0
$191$	−204.368			−1.06999			−0.534994	−	0.844856i	$-0.679686\pi$
$191$	−204.368			−1.06999			−0.534994	+	0.844856i	$0.679686\pi$
$192$		0			0
$193$	−206.929	−	206.929i	−1.07217	−	1.07217i	−0.997185	−	0.0749840i	$-0.976109\pi$
$193$	−206.929	−	206.929i	−1.07217	−	1.07217i	−0.0749840	−	0.997185i	$-0.523891\pi$
$194$		−	277.273i		−	1.42924i
$195$		0			0
$196$	91.0952			0.464771
$197$	−52.7467	+	52.7467i	−0.267750	+	0.267750i	−0.828193	−	0.560443i	$-0.810631\pi$
$197$	−52.7467	+	52.7467i	−0.267750	+	0.267750i	0.560443	+	0.828193i	$0.310631\pi$
$198$		0			0
$199$		−	102.233i		−	0.513734i	−0.966447	−	0.256867i	$-0.917310\pi$
$199$		−	102.233i		−	0.513734i	0.966447	−	0.256867i	$-0.0826902\pi$
$200$		0			0
$201$		0			0
$202$	−72.7494	+	72.7494i	−0.360146	+	0.360146i
$203$	−46.7257	−	46.7257i	−0.230176	−	0.230176i
$204$		0			0
$205$		0			0
$206$	271.708			1.31897
$207$		0			0
$208$	103.232	+	103.232i	0.496310	+	0.496310i
$209$			382.029i			1.82789i
$210$		0			0
$211$	−140.544			−0.666085			−0.333042	−	0.942912i	$-0.608075\pi$
$211$	−140.544			−0.666085			−0.333042	+	0.942912i	$0.608075\pi$
$212$	101.964	−	101.964i	0.480964	−	0.480964i
$213$		0			0
$214$		−	71.0265i		−	0.331900i
$215$		0			0
$216$		0			0
$217$	−145.558	+	145.558i	−0.670774	+	0.670774i
$218$	−47.1631	−	47.1631i	−0.216344	−	0.216344i
$219$		0			0
$220$		0			0
$221$	−31.4257			−0.142198
$222$		0			0
$223$	249.385	+	249.385i	1.11832	+	1.11832i	0.991988	+	0.126331i	$0.0403200\pi$
$223$	249.385	+	249.385i	1.11832	+	1.11832i	0.126331	+	0.991988i	$0.459680\pi$
$224$			141.704i			0.632607i
$225$		0			0
$226$	−525.384			−2.32471
$227$	−180.115	+	180.115i	−0.793456	+	0.793456i	−0.982054	−	0.188598i	$-0.939606\pi$
$227$	−180.115	+	180.115i	−0.793456	+	0.793456i	0.188598	+	0.982054i	$0.439606\pi$
$228$		0			0
$229$			308.106i			1.34544i	0.739897	+	0.672720i	$0.234874\pi$
$229$			308.106i			1.34544i	−0.739897	+	0.672720i	$0.765126\pi$
$230$		0			0
$231$		0			0
$232$	−127.048	+	127.048i	−0.547620	+	0.547620i
$233$	278.738	+	278.738i	1.19630	+	1.19630i	0.975266	+	0.221033i	$0.0709429\pi$
$233$	278.738	+	278.738i	1.19630	+	1.19630i	0.221033	+	0.975266i	$0.429057\pi$
$234$		0			0
$235$		0			0
$236$	734.605			3.11273
$237$		0			0
$238$	−85.4150	−	85.4150i	−0.358887	−	0.358887i
$239$			392.788i			1.64346i	0.569875	+	0.821732i	$0.306992\pi$
$239$			392.788i			1.64346i	−0.569875	+	0.821732i	$0.693008\pi$
$240$		0			0
$241$	−124.433			−0.516321			−0.258160	−	0.966102i	$-0.583116\pi$
$241$	−124.433			−0.516321			−0.258160	+	0.966102i	$0.583116\pi$
$242$	771.728	−	771.728i	3.18896	−	3.18896i
$243$		0			0
$244$		−	609.292i		−	2.49710i
$245$		0			0
$246$		0			0
$247$	−75.3772	+	75.3772i	−0.305171	+	0.305171i
$248$	395.774	+	395.774i	1.59586	+	1.59586i
$249$		0			0
$250$		0			0
$251$	−11.9714			−0.0476946			−0.0238473	−	0.999716i	$-0.507592\pi$
$251$	−11.9714			−0.0476946			−0.0238473	+	0.999716i	$0.507592\pi$
$252$		0			0
$253$	−292.897	−	292.897i	−1.15770	−	1.15770i
$254$		−	191.388i		−	0.753497i
$255$		0			0
$256$	−499.245			−1.95017
$257$	−212.404	+	212.404i	−0.826473	+	0.826473i	−0.987027	−	0.160554i	$-0.948672\pi$
$257$	−212.404	+	212.404i	−0.826473	+	0.826473i	0.160554	+	0.987027i	$0.448672\pi$
$258$		0			0
$259$		−	314.441i		−	1.21406i
$260$		0			0
$261$		0			0
$262$	165.059	−	165.059i	0.629997	−	0.629997i
$263$	−2.21097	−	2.21097i	−0.00840674	−	0.00840674i	0.702891	−	0.711298i	$-0.251892\pi$
$263$	−2.21097	−	2.21097i	−0.00840674	−	0.00840674i	−0.711298	+	0.702891i	$0.751892\pi$
$264$		0			0
$265$		0			0
$266$	−409.751			−1.54042
$267$		0			0
$268$	−335.813	−	335.813i	−1.25303	−	1.25303i
$269$		−	441.324i		−	1.64061i	−0.571927	−	0.820304i	$-0.693804\pi$
$269$		−	441.324i		−	1.64061i	0.571927	−	0.820304i	$-0.306196\pi$
$270$		0			0
$271$	395.437			1.45918			0.729589	−	0.683886i	$-0.239711\pi$
$271$	395.437			1.45918			0.729589	+	0.683886i	$0.239711\pi$
$272$	−97.6104	+	97.6104i	−0.358862	+	0.358862i
$273$		0			0
$274$		−	456.075i		−	1.66451i
$275$		0			0
$276$		0			0
$277$	−95.1449	+	95.1449i	−0.343483	+	0.343483i	−0.857675	−	0.514192i	$-0.828092\pi$
$277$	−95.1449	+	95.1449i	−0.343483	+	0.343483i	0.514192	+	0.857675i	$0.328092\pi$
$278$	−624.300	−	624.300i	−2.24568	−	2.24568i
$279$		0			0
$280$		0			0
$281$	387.164			1.37781			0.688904	−	0.724853i	$-0.258092\pi$
$281$	387.164			1.37781			0.688904	+	0.724853i	$0.258092\pi$
$282$		0			0
$283$	39.1743	+	39.1743i	0.138425	+	0.138425i	0.772924	−	0.634499i	$-0.218793\pi$
$283$	39.1743	+	39.1743i	0.138425	+	0.138425i	−0.634499	+	0.772924i	$0.718793\pi$
$284$		−	934.382i		−	3.29008i
$285$		0			0
$286$	425.010			1.48605
$287$	52.9524	−	52.9524i	0.184503	−	0.184503i
$288$		0			0
$289$			259.286i			0.897183i
$290$		0			0
$291$		0			0
$292$	−71.3784	+	71.3784i	−0.244447	+	0.244447i
$293$	−310.954	−	310.954i	−1.06128	−	1.06128i	−0.997996	−	0.0632822i	$-0.979843\pi$
$293$	−310.954	−	310.954i	−1.06128	−	1.06128i	−0.0632822	−	0.997996i	$-0.520157\pi$
$294$		0			0
$295$		0			0
$296$	−854.970			−2.88841
$297$		0			0
$298$	−57.8802	−	57.8802i	−0.194229	−	0.194229i
$299$		−	115.582i		−	0.386561i
$300$		0			0
$301$	−312.640			−1.03867
$302$	−11.3076	+	11.3076i	−0.0374423	+	0.0374423i
$303$		0			0
$304$			468.254i			1.54031i
$305$		0			0
$306$		0			0
$307$	352.515	−	352.515i	1.14826	−	1.14826i	0.161361	−	0.986895i	$-0.448412\pi$
$307$	352.515	−	352.515i	1.14826	−	1.14826i	0.986895	−	0.161361i	$-0.0515883\pi$
$308$	792.266	+	792.266i	2.57229	+	2.57229i
$309$		0			0
$310$		0			0
$311$	−191.198			−0.614786			−0.307393	−	0.951583i	$-0.599457\pi$
$311$	−191.198			−0.614786			−0.307393	+	0.951583i	$0.599457\pi$
$312$		0			0
$313$	152.885	+	152.885i	0.488450	+	0.488450i	0.907817	−	0.419367i	$-0.137748\pi$
$313$	152.885	+	152.885i	0.488450	+	0.488450i	−0.419367	+	0.907817i	$0.637748\pi$
$314$		−	659.096i		−	2.09903i
$315$		0			0
$316$	638.324			2.02001
$317$	96.0449	−	96.0449i	0.302981	−	0.302981i	−0.539198	−	0.842179i	$-0.681273\pi$
$317$	96.0449	−	96.0449i	0.302981	−	0.302981i	0.842179	+	0.539198i	$0.181273\pi$
$318$		0			0
$319$			219.837i			0.689145i
$320$		0			0
$321$		0			0
$322$	314.151	−	314.151i	0.975624	−	0.975624i
$323$	−71.2722	−	71.2722i	−0.220657	−	0.220657i
$324$		0			0
$325$		0			0
$326$	−168.169			−0.515855
$327$		0			0
$328$	−143.978	−	143.978i	−0.438958	−	0.438958i
$329$			5.40685i			0.0164342i
$330$		0			0
$331$	−371.750			−1.12311			−0.561556	−	0.827439i	$-0.689797\pi$
$331$	−371.750			−1.12311			−0.561556	+	0.827439i	$0.689797\pi$
$332$	−36.5792	+	36.5792i	−0.110178	+	0.110178i
$333$		0			0
$334$			166.242i			0.497729i
$335$		0			0
$336$		0			0
$337$	−362.115	+	362.115i	−1.07452	+	1.07452i	−0.0775344	+	0.996990i	$0.524705\pi$
$337$	−362.115	+	362.115i	−1.07452	+	1.07452i	−0.996990	+	0.0775344i	$0.975295\pi$
$338$	−342.550	−	342.550i	−1.01346	−	1.01346i
$339$		0			0
$340$		0			0
$341$	684.827			2.00829
$342$		0			0
$343$	260.987	+	260.987i	0.760895	+	0.760895i
$344$			850.072i			2.47114i
$345$		0			0
$346$	726.608			2.10002
$347$	20.8181	−	20.8181i	0.0599945	−	0.0599945i	−0.676473	−	0.736467i	$-0.736492\pi$
$347$	20.8181	−	20.8181i	0.0599945	−	0.0599945i	0.736467	+	0.676473i	$0.236492\pi$
$348$		0			0
$349$			443.992i			1.27218i	0.771613	+	0.636092i	$0.219450\pi$
$349$			443.992i			1.27218i	−0.771613	+	0.636092i	$0.780550\pi$
$350$		0			0
$351$		0			0
$352$	333.347	−	333.347i	0.947009	−	0.947009i
$353$	−134.580	−	134.580i	−0.381248	−	0.381248i	0.490304	−	0.871552i	$-0.336886\pi$
$353$	−134.580	−	134.580i	−0.381248	−	0.381248i	−0.871552	+	0.490304i	$0.836886\pi$
$354$		0			0
$355$		0			0
$356$	54.2041			0.152259
$357$		0			0
$358$	381.618	+	381.618i	1.06597	+	1.06597i
$359$			216.292i			0.602484i	0.953548	+	0.301242i	$0.0974011\pi$
$359$			216.292i			0.602484i	−0.953548	+	0.301242i	$0.902599\pi$
$360$		0			0
$361$	19.0951			0.0528949
$362$	192.112	−	192.112i	0.530695	−	0.530695i
$363$		0			0
$364$			312.640i			0.858901i
$365$		0			0
$366$		0			0
$367$	−242.834	+	242.834i	−0.661673	+	0.661673i	−0.955774	−	0.294102i	$-0.904980\pi$
$367$	−242.834	+	242.834i	−0.661673	+	0.661673i	0.294102	+	0.955774i	$0.404980\pi$
$368$	−359.005	−	359.005i	−0.975557	−	0.975557i
$369$		0			0
$370$		0			0
$371$	102.553			0.276423
$372$		0			0
$373$	415.397	+	415.397i	1.11366	+	1.11366i	0.992651	+	0.121013i	$0.0386142\pi$
$373$	415.397	+	415.397i	1.11366	+	1.11366i	0.121013	+	0.992651i	$0.461386\pi$
$374$			401.864i			1.07450i
$375$		0			0
$376$	14.7013			0.0390992
$377$	−43.3755	+	43.3755i	−0.115054	+	0.115054i
$378$		0			0
$379$		−	87.8194i		−	0.231713i	−0.993266	−	0.115857i	$-0.963039\pi$
$379$		−	87.8194i		−	0.231713i	0.993266	−	0.115857i	$-0.0369613\pi$
$380$		0			0
$381$		0			0
$382$	−515.645	+	515.645i	−1.34986	+	1.34986i
$383$	157.427	+	157.427i	0.411038	+	0.411038i	0.882100	−	0.471062i	$-0.156129\pi$
$383$	157.427	+	157.427i	0.411038	+	0.411038i	−0.471062	+	0.882100i	$0.656129\pi$
$384$		0			0
$385$		0			0
$386$	−1044.21			−2.70521
$387$		0			0
$388$	−479.808	−	479.808i	−1.23662	−	1.23662i
$389$			506.212i			1.30132i	0.759370	+	0.650659i	$0.225507\pi$
$389$			506.212i			1.30132i	−0.759370	+	0.650659i	$0.774493\pi$
$390$		0			0
$391$	109.287			0.279507
$392$	124.560	−	124.560i	0.317754	−	0.317754i
$393$		0			0
$394$			266.173i			0.675566i
$395$		0			0
$396$		0			0
$397$	434.470	−	434.470i	1.09438	−	1.09438i	0.0993269	−	0.995055i	$-0.468331\pi$
$397$	434.470	−	434.470i	1.09438	−	1.09438i	0.995055	−	0.0993269i	$-0.0316690\pi$
$398$	−257.946	−	257.946i	−0.648107	−	0.648107i
$399$		0			0
$400$		0			0
$401$	−378.912			−0.944918			−0.472459	−	0.881353i	$-0.656633\pi$
$401$	−378.912			−0.944918			−0.472459	+	0.881353i	$0.656633\pi$
$402$		0			0
$403$	135.122	+	135.122i	0.335289	+	0.335289i
$404$			251.779i			0.623216i
$405$		0			0
$406$	−235.790			−0.580762
$407$	−739.698	+	739.698i	−1.81744	+	1.81744i
$408$		0			0
$409$		−	136.322i		−	0.333305i	−0.986016	−	0.166652i	$-0.946704\pi$
$409$		−	136.322i		−	0.333305i	0.986016	−	0.166652i	$-0.0532958\pi$
$410$		0			0
$411$		0			0
$412$	470.179	−	470.179i	1.14121	−	1.14121i
$413$	369.423	+	369.423i	0.894487	+	0.894487i
$414$		0			0
$415$		0			0
$416$	131.544			0.316211
$417$		0			0
$418$	963.906	+	963.906i	2.30600	+	2.30600i
$419$			396.260i			0.945728i	0.881136	+	0.472864i	$0.156780\pi$
$419$			396.260i			0.945728i	−0.881136	+	0.472864i	$0.843220\pi$
$420$		0			0
$421$	−606.586			−1.44082			−0.720410	−	0.693548i	$-0.756046\pi$
$421$	−606.586			−1.44082			−0.720410	+	0.693548i	$0.756046\pi$
$422$	−354.609	+	354.609i	−0.840307	+	0.840307i
$423$		0			0
$424$		−	278.843i		−	0.657650i
$425$		0			0
$426$		0			0
$427$	306.405	−	306.405i	0.717576	−	0.717576i
$428$	−122.908	−	122.908i	−0.287168	−	0.287168i
$429$		0			0
$430$		0			0
$431$	137.454			0.318920			0.159460	−	0.987204i	$-0.449025\pi$
$431$	137.454			0.318920			0.159460	+	0.987204i	$0.449025\pi$
$432$		0			0
$433$	−101.718	−	101.718i	−0.234915	−	0.234915i	0.579826	−	0.814740i	$-0.303121\pi$
$433$	−101.718	−	101.718i	−0.234915	−	0.234915i	−0.814740	+	0.579826i	$0.803121\pi$
$434$			734.521i			1.69244i
$435$		0			0
$436$	−163.227			−0.374374
$437$	262.134	−	262.134i	0.599850	−	0.599850i
$438$		0			0
$439$			818.214i			1.86381i	0.362700	+	0.931906i	$0.381855\pi$
$439$			818.214i			1.86381i	−0.362700	+	0.931906i	$0.618145\pi$
$440$		0			0
$441$		0			0
$442$	−79.2908	+	79.2908i	−0.179391	+	0.179391i
$443$	−131.035	−	131.035i	−0.295789	−	0.295789i	0.543573	−	0.839362i	$-0.317071\pi$
$443$	−131.035	−	131.035i	−0.295789	−	0.295789i	−0.839362	+	0.543573i	$0.817071\pi$
$444$		0			0
$445$		0			0
$446$	1258.46			2.82166
$447$		0			0
$448$	−87.2871	−	87.2871i	−0.194837	−	0.194837i
$449$		−	548.270i		−	1.22109i	−0.791981	−	0.610546i	$-0.790950\pi$
$449$		−	548.270i		−	1.22109i	0.791981	−	0.610546i	$-0.209050\pi$
$450$		0			0
$451$	−249.133			−0.552401
$452$	−909.153	+	909.153i	−2.01140	+	2.01140i
$453$		0			0
$454$			908.902i			2.00199i
$455$		0			0
$456$		0			0
$457$	−248.434	+	248.434i	−0.543620	+	0.543620i	−0.924588	−	0.380968i	$-0.875591\pi$
$457$	−248.434	+	248.434i	−0.543620	+	0.543620i	0.380968	+	0.924588i	$0.375591\pi$
$458$	777.389	+	777.389i	1.69736	+	1.69736i
$459$		0			0
$460$		0			0
$461$	−149.391			−0.324060			−0.162030	−	0.986786i	$-0.551804\pi$
$461$	−149.391			−0.324060			−0.162030	+	0.986786i	$0.551804\pi$
$462$		0			0
$463$	−352.014	−	352.014i	−0.760289	−	0.760289i	0.216085	−	0.976374i	$-0.430671\pi$
$463$	−352.014	−	352.014i	−0.760289	−	0.760289i	−0.976374	+	0.216085i	$0.930671\pi$
$464$			269.455i			0.580722i
$465$		0			0
$466$	1406.58			3.01841
$467$	439.025	−	439.025i	0.940095	−	0.940095i	−0.0582090	−	0.998304i	$-0.518539\pi$
$467$	439.025	−	439.025i	0.940095	−	0.940095i	0.998304	+	0.0582090i	$0.0185390\pi$
$468$		0			0
$469$		−	337.751i		−	0.720152i
$470$		0			0
$471$		0			0
$472$	1004.47	−	1004.47i	2.12811	−	2.12811i
$473$	735.461	+	735.461i	1.55489	+	1.55489i
$474$		0			0
$475$		0			0
$476$	−295.614			−0.621037
$477$		0			0
$478$	991.051	+	991.051i	2.07333	+	2.07333i
$479$		−	292.967i		−	0.611622i	−0.952092	−	0.305811i	$-0.901073\pi$
$479$		−	292.967i		−	0.611622i	0.952092	−	0.305811i	$-0.0989275\pi$
$480$		0			0
$481$	−291.896			−0.606852
$482$	−313.961	+	313.961i	−0.651370	+	0.651370i
$483$		0			0
$484$		−	2670.88i		−	5.51834i
$485$		0			0
$486$		0			0
$487$	−542.274	+	542.274i	−1.11350	+	1.11350i	−0.120824	+	0.992674i	$0.538554\pi$
$487$	−542.274	+	542.274i	−1.11350	+	1.11350i	−0.992674	+	0.120824i	$0.961446\pi$
$488$	−833.119	−	833.119i	−1.70721	−	1.70721i
$489$		0			0
$490$		0			0
$491$	−682.723			−1.39048			−0.695238	−	0.718780i	$-0.744701\pi$
$491$	−682.723			−1.39048			−0.695238	+	0.718780i	$0.744701\pi$
$492$		0			0
$493$	−41.0133	−	41.0133i	−0.0831913	−	0.0831913i
$494$			380.372i			0.769983i
$495$		0			0
$496$	839.395			1.69233
$497$	469.889	−	469.889i	0.945450	−	0.945450i
$498$		0			0
$499$		−	410.186i		−	0.822016i	−0.911632	−	0.411008i	$-0.865177\pi$
$499$		−	410.186i		−	0.822016i	0.911632	−	0.411008i	$-0.134823\pi$
$500$		0			0
$501$		0			0
$502$	−30.2052	+	30.2052i	−0.0601697	+	0.0601697i
$503$	−543.846	−	543.846i	−1.08120	−	1.08120i	−0.996397	−	0.0848064i	$-0.972973\pi$
$503$	−543.846	−	543.846i	−1.08120	−	1.08120i	−0.0848064	−	0.996397i	$-0.527027\pi$
$504$		0			0
$505$		0			0
$506$	−1478.03			−2.92101
$507$		0			0
$508$	−331.188	−	331.188i	−0.651946	−	0.651946i
$509$		−	117.094i		−	0.230047i	−0.993363	−	0.115024i	$-0.963306\pi$
$509$		−	117.094i		−	0.230047i	0.993363	−	0.115024i	$-0.0366944\pi$
$510$		0			0
$511$	−71.7905			−0.140490
$512$	−800.897	+	800.897i	−1.56425	+	1.56425i
$513$		0			0
$514$			1071.84i			2.08529i
$515$		0			0
$516$		0			0
$517$	12.7192	−	12.7192i	0.0246019	−	0.0246019i
$518$	−793.373	−	793.373i	−1.53161	−	1.53161i
$519$		0			0
$520$		0			0
$521$	400.865			0.769414			0.384707	−	0.923039i	$-0.374302\pi$
$521$	400.865			0.769414			0.384707	+	0.923039i	$0.374302\pi$
$522$		0			0
$523$	212.510	+	212.510i	0.406330	+	0.406330i	0.880457	−	0.474127i	$-0.157236\pi$
$523$	212.510	+	212.510i	0.406330	+	0.406330i	−0.474127	+	0.880457i	$0.657236\pi$
$524$		−	571.254i		−	1.09018i
$525$		0			0
$526$	−11.1571			−0.0212112
$527$	−127.763	+	127.763i	−0.242434	+	0.242434i
$528$		0			0
$529$		−	127.049i		−	0.240169i
$530$		0			0
$531$		0			0
$532$	−709.055	+	709.055i	−1.33281	+	1.33281i
$533$	−49.1557	−	49.1557i	−0.0922247	−	0.0922247i
$534$		0			0
$535$		0			0
$536$	−918.351			−1.71334
$537$		0			0
$538$	−1113.51	−	1113.51i	−2.06973	−	2.06973i
$539$		−	215.531i		−	0.399873i
$540$		0			0
$541$	−253.010			−0.467671			−0.233836	−	0.972276i	$-0.575128\pi$
$541$	−253.010			−0.467671			−0.233836	+	0.972276i	$0.575128\pi$
$542$	997.737	−	997.737i	1.84084	−	1.84084i
$543$		0			0
$544$			124.380i			0.228640i
$545$		0			0
$546$		0			0
$547$	−549.424	+	549.424i	−1.00443	+	1.00443i	−0.00444067	+	0.999990i	$0.501414\pi$
$547$	−549.424	+	549.424i	−1.00443	+	1.00443i	−0.999990	+	0.00444067i	$0.998586\pi$
$548$	−789.217	−	789.217i	−1.44018	−	1.44018i
$549$		0			0
$550$		0			0
$551$	−196.748			−0.357074
$552$		0			0
$553$	321.004	+	321.004i	0.580478	+	0.580478i
$554$			480.124i			0.866651i
$555$		0			0
$556$	−2160.65			−3.88605
$557$	488.571	−	488.571i	0.877147	−	0.877147i	−0.116091	−	0.993239i	$-0.537037\pi$
$557$	488.571	−	488.571i	0.877147	−	0.877147i	0.993239	+	0.116091i	$0.0370365\pi$
$558$		0			0
$559$			290.224i			0.519184i
$560$		0			0
$561$		0			0
$562$	976.862	−	976.862i	1.73819	−	1.73819i
$563$	−722.486	−	722.486i	−1.28328	−	1.28328i	−0.938790	−	0.344490i	$-0.888052\pi$
$563$	−722.486	−	722.486i	−1.28328	−	1.28328i	−0.344490	−	0.938790i	$-0.611948\pi$
$564$		0			0
$565$		0			0
$566$	197.683			0.349263
$567$		0			0
$568$	−1277.63	−	1277.63i	−2.24936	−	2.24936i
$569$			44.8358i			0.0787975i	0.999224	+	0.0393987i	$0.0125443\pi$
$569$			44.8358i			0.0787975i	−0.999224	+	0.0393987i	$0.987456\pi$
$570$		0			0
$571$	−117.428			−0.205653			−0.102826	−	0.994699i	$-0.532789\pi$
$571$	−117.428			−0.205653			−0.102826	+	0.994699i	$0.532789\pi$
$572$	735.461	−	735.461i	1.28577	−	1.28577i
$573$		0			0
$574$		−	267.211i		−	0.465524i
$575$		0			0
$576$		0			0
$577$	−443.056	+	443.056i	−0.767862	+	0.767862i	−0.977730	−	0.209868i	$-0.932697\pi$
$577$	−443.056	+	443.056i	−0.767862	+	0.767862i	0.209868	+	0.977730i	$0.432697\pi$
$578$	654.210	+	654.210i	1.13185	+	1.13185i
$579$		0			0
$580$		0			0
$581$	−36.7904			−0.0633226
$582$		0			0
$583$	−241.248	−	241.248i	−0.413805	−	0.413805i
$584$			195.199i			0.334246i
$585$		0			0
$586$	−1569.15			−2.67773
$587$	182.831	−	182.831i	0.311468	−	0.311468i	−0.534010	−	0.845478i	$-0.679316\pi$
$587$	182.831	−	182.831i	0.311468	−	0.311468i	0.845478	+	0.534010i	$0.179316\pi$
$588$		0			0
$589$			612.900i			1.04058i
$590$		0			0
$591$		0			0
$592$	−906.649	+	906.649i	−1.53150	+	1.53150i
$593$	545.602	+	545.602i	0.920071	+	0.920071i	0.997034	−	0.0769628i	$-0.0245223\pi$
$593$	545.602	+	545.602i	0.920071	+	0.920071i	−0.0769628	+	0.997034i	$0.524522\pi$
$594$		0			0
$595$		0			0
$596$	−200.318			−0.336104
$597$		0			0
$598$	−291.627	−	291.627i	−0.487670	−	0.487670i
$599$			117.320i			0.195859i	0.995193	+	0.0979296i	$0.0312220\pi$
$599$			117.320i			0.195859i	−0.995193	+	0.0979296i	$0.968778\pi$
$600$		0			0
$601$	1000.71			1.66508			0.832540	−	0.553964i	$-0.186886\pi$
$601$	1000.71			1.66508			0.832540	+	0.553964i	$0.186886\pi$
$602$	−788.829	+	788.829i	−1.31035	+	1.31035i
$603$		0			0
$604$			39.1345i			0.0647922i
$605$		0			0
$606$		0			0
$607$	−320.716	+	320.716i	−0.528362	+	0.528362i	−0.920084	−	0.391721i	$-0.871880\pi$
$607$	−320.716	+	320.716i	−0.528362	+	0.528362i	0.391721	+	0.920084i	$0.371880\pi$
$608$	298.336	+	298.336i	0.490684	+	0.490684i
$609$		0			0
$610$		0			0
$611$	5.01918			0.00821470
$612$		0			0
$613$	508.458	+	508.458i	0.829459	+	0.829459i	0.987442	−	0.157983i	$-0.0504992\pi$
$613$	508.458	+	508.458i	0.829459	+	0.829459i	−0.157983	+	0.987442i	$0.550499\pi$
$614$		−	1778.88i		−	2.89719i
$615$		0			0
$616$	2166.62			3.51724
$617$	−253.929	+	253.929i	−0.411555	+	0.411555i	−0.882280	−	0.470725i	$-0.843992\pi$
$617$	−253.929	+	253.929i	−0.411555	+	0.411555i	0.470725	+	0.882280i	$0.343992\pi$
$618$		0			0
$619$			430.073i			0.694787i	0.937719	+	0.347393i	$0.112933\pi$
$619$			430.073i			0.694787i	−0.937719	+	0.347393i	$0.887067\pi$
$620$		0			0
$621$		0			0
$622$	−482.417	+	482.417i	−0.775590	+	0.775590i
$623$	27.2585	+	27.2585i	0.0437536	+	0.0437536i
$624$		0			0
$625$		0			0
$626$	771.494			1.23242
$627$		0			0
$628$	−1140.53	−	1140.53i	−1.81614	−	1.81614i
$629$		−	275.999i		−	0.438790i
$630$		0			0
$631$	−42.6090			−0.0675261			−0.0337631	−	0.999430i	$-0.510749\pi$
$631$	−42.6090			−0.0675261			−0.0337631	+	0.999430i	$0.510749\pi$
$632$	872.816	−	872.816i	1.38104	−	1.38104i
$633$		0			0
$634$		−	484.666i		−	0.764457i
$635$		0			0
$636$		0			0
$637$	42.5260	−	42.5260i	0.0667597	−	0.0667597i
$638$	554.676	+	554.676i	0.869399	+	0.869399i
$639$		0			0
$640$		0			0
$641$	858.647			1.33954			0.669772	−	0.742567i	$-0.266392\pi$
$641$	858.647			1.33954			0.669772	+	0.742567i	$0.266392\pi$
$642$		0			0
$643$	−712.636	−	712.636i	−1.10830	−	1.10830i	−0.993374	−	0.114925i	$-0.963337\pi$
$643$	−712.636	−	712.636i	−1.10830	−	1.10830i	−0.114925	−	0.993374i	$-0.536663\pi$
$644$		−	1087.25i		−	1.68827i
$645$		0			0
$646$	−359.657			−0.556744
$647$	−509.877	+	509.877i	−0.788063	+	0.788063i	−0.981176	−	0.193113i	$-0.938141\pi$
$647$	−509.877	+	509.877i	−0.788063	+	0.788063i	0.193113	+	0.981176i	$0.438141\pi$
$648$		0			0
$649$		−	1738.08i		−	2.67809i
$650$		0			0
$651$		0			0
$652$	−291.009	+	291.009i	−0.446332	+	0.446332i
$653$	−37.4444	−	37.4444i	−0.0573422	−	0.0573422i	0.677854	−	0.735196i	$-0.262910\pi$
$653$	−37.4444	−	37.4444i	−0.0573422	−	0.0573422i	−0.735196	+	0.677854i	$0.762910\pi$
$654$		0			0
$655$		0			0
$656$	−305.363			−0.465492
$657$		0			0
$658$	13.6421	+	13.6421i	0.0207327	+	0.0207327i
$659$		−	830.172i		−	1.25975i	−0.776698	−	0.629873i	$-0.783107\pi$
$659$		−	830.172i		−	1.25975i	0.776698	−	0.629873i	$-0.216893\pi$
$660$		0			0
$661$	701.677			1.06154			0.530770	−	0.847516i	$-0.321903\pi$
$661$	701.677			1.06154			0.530770	+	0.847516i	$0.321903\pi$
$662$	−937.971	+	937.971i	−1.41687	+	1.41687i
$663$		0			0
$664$			100.034i			0.150653i
$665$		0			0
$666$		0			0
$667$	150.844	−	150.844i	0.226153	−	0.226153i
$668$	287.673	+	287.673i	0.430649	+	0.430649i
$669$		0			0
$670$		0			0
$671$	−1441.59			−2.14841
$672$		0			0
$673$	364.264	+	364.264i	0.541254	+	0.541254i	0.923897	−	0.382642i	$-0.124986\pi$
$673$	364.264	+	364.264i	0.541254	+	0.541254i	−0.382642	+	0.923897i	$0.624986\pi$
$674$			1827.32i			2.71116i
$675$		0			0
$676$	−1185.53			−1.75375
$677$	−378.986	+	378.986i	−0.559802	+	0.559802i	−0.929251	−	0.369449i	$-0.879547\pi$
$677$	−378.986	+	378.986i	−0.559802	+	0.559802i	0.369449	+	0.929251i	$0.379547\pi$
$678$		0			0
$679$		−	482.578i		−	0.710719i
$680$		0			0
$681$		0			0
$682$	1727.90	−	1727.90i	2.53358	−	2.53358i
$683$	−111.371	−	111.371i	−0.163061	−	0.163061i	0.620860	−	0.783921i	$-0.286784\pi$
$683$	−111.371	−	111.371i	−0.163061	−	0.163061i	−0.783921	+	0.620860i	$0.786784\pi$
$684$		0			0
$685$		0			0
$686$	1317.00			1.91983
$687$		0			0
$688$	901.456	+	901.456i	1.31026	+	1.31026i
$689$		−	95.2001i		−	0.138171i
$690$		0			0
$691$	681.088			0.985656			0.492828	−	0.870127i	$-0.335963\pi$
$691$	681.088			0.985656			0.492828	+	0.870127i	$0.335963\pi$
$692$	1257.36	−	1257.36i	1.81700	−	1.81700i
$693$		0			0
$694$		−	105.053i		−	0.151373i
$695$		0			0
$696$		0			0
$697$	46.4787	−	46.4787i	0.0666840	−	0.0666840i
$698$	1120.25	+	1120.25i	1.60494	+	1.60494i
$699$		0			0
$700$		0			0
$701$	722.405			1.03053			0.515267	−	0.857030i	$-0.327693\pi$
$701$	722.405			1.03053			0.515267	+	0.857030i	$0.327693\pi$
$702$		0			0
$703$	−662.008	−	662.008i	−0.941690	−	0.941690i
$704$			410.672i			0.583341i
$705$		0			0
$706$	−679.126			−0.961935
$707$	−126.616	+	126.616i	−0.179090	+	0.179090i
$708$		0			0
$709$		−	583.352i		−	0.822782i	−0.911459	−	0.411391i	$-0.865043\pi$
$709$		−	583.352i		−	0.822782i	0.911459	−	0.411391i	$-0.134957\pi$
$710$		0			0
$711$		0			0
$712$	74.1163	−	74.1163i	0.104096	−	0.104096i
$713$	−469.904	−	469.904i	−0.659051	−	0.659051i
$714$		0			0
$715$		0			0
$716$	1320.74			1.84462
$717$		0			0
$718$	545.730	+	545.730i	0.760070	+	0.760070i
$719$			1116.43i			1.55276i	0.630266	+	0.776379i	$0.282946\pi$
$719$			1116.43i			1.55276i	−0.630266	+	0.776379i	$0.717054\pi$
$720$		0			0
$721$	472.893			0.655885
$722$	48.1792	−	48.1792i	0.0667301	−	0.0667301i
$723$		0			0
$724$		−	664.880i		−	0.918343i
$725$		0			0
$726$		0			0
$727$	297.676	−	297.676i	0.409458	−	0.409458i	−0.472092	−	0.881549i	$-0.656501\pi$
$727$	297.676	−	297.676i	0.409458	−	0.409458i	0.881549	+	0.472092i	$0.156501\pi$
$728$	427.490	+	427.490i	0.587212	+	0.587212i
$729$		0			0
$730$		0			0
$731$	−274.418			−0.375401
$732$		0			0
$733$	270.064	+	270.064i	0.368437	+	0.368437i	0.866907	−	0.498470i	$-0.166105\pi$
$733$	270.064	+	270.064i	0.368437	+	0.368437i	−0.498470	+	0.866907i	$0.666105\pi$
$734$			1225.40i			1.66948i
$735$		0			0
$736$	−457.461			−0.621551
$737$	−794.534	+	794.534i	−1.07806	+	1.07806i
$738$		0			0
$739$			1406.06i			1.90266i	0.308177	+	0.951329i	$0.400281\pi$
$739$			1406.06i			1.90266i	−0.308177	+	0.951329i	$0.599719\pi$
$740$		0			0
$741$		0			0
$742$	258.754	−	258.754i	0.348725	−	0.348725i
$743$	−135.249	−	135.249i	−0.182031	−	0.182031i	0.610209	−	0.792240i	$-0.291085\pi$
$743$	−135.249	−	135.249i	−0.182031	−	0.182031i	−0.792240	+	0.610209i	$0.791085\pi$
$744$		0			0
$745$		0			0
$746$	2096.19			2.80991
$747$		0			0
$748$	695.408	+	695.408i	0.929689	+	0.929689i
$749$		−	123.618i		−	0.165044i
$750$		0			0
$751$	−115.124			−0.153294			−0.0766472	−	0.997058i	$-0.524422\pi$
$751$	−115.124			−0.153294			−0.0766472	+	0.997058i	$0.524422\pi$
$752$	15.5899	−	15.5899i	0.0207313	−	0.0207313i
$753$		0			0
$754$			218.884i			0.290296i
$755$		0			0
$756$		0			0
$757$	737.945	−	737.945i	0.974828	−	0.974828i	−0.0248625	−	0.999691i	$-0.507915\pi$
$757$	737.945	−	737.945i	0.974828	−	0.974828i	0.999691	+	0.0248625i	$0.00791481\pi$
$758$	−221.579	−	221.579i	−0.292321	−	0.292321i
$759$		0			0
$760$		0			0
$761$	1011.38			1.32902			0.664509	−	0.747280i	$-0.268641\pi$
$761$	1011.38			1.32902			0.664509	+	0.747280i	$0.268641\pi$
$762$		0			0
$763$	−82.0847	−	82.0847i	−0.107582	−	0.107582i
$764$			1784.60i			2.33586i
$765$		0			0
$766$	794.418			1.03710
$767$	342.936	−	342.936i	0.447113	−	0.447113i
$768$		0			0
$769$		−	653.574i		−	0.849901i	−0.905217	−	0.424950i	$-0.860292\pi$
$769$		−	653.574i		−	0.849901i	0.905217	−	0.424950i	$-0.139708\pi$
$770$		0			0
$771$		0			0
$772$	−1806.96	+	1806.96i	−2.34062	+	2.34062i
$773$	2.30444	+	2.30444i	0.00298116	+	0.00298116i	0.708596	−	0.705615i	$-0.249329\pi$
$773$	2.30444	+	2.30444i	0.00298116	+	0.00298116i	−0.705615	+	0.708596i	$0.749329\pi$
$774$		0			0
$775$		0			0
$776$	−1312.14			−1.69090
$777$		0			0
$778$	1277.24	+	1277.24i	1.64169	+	1.64169i
$779$		−	222.967i		−	0.286222i
$780$		0			0
$781$	−2210.75			−2.83067
$782$	275.745	−	275.745i	0.352615	−	0.352615i
$783$		0			0
$784$		−	264.177i		−	0.336961i
$785$		0			0
$786$		0			0
$787$	36.7027	−	36.7027i	0.0466362	−	0.0466362i	−0.683404	−	0.730040i	$-0.739501\pi$
$787$	36.7027	−	36.7027i	0.0466362	−	0.0466362i	0.730040	+	0.683404i	$0.239501\pi$
$788$	460.600	+	460.600i	0.584518	+	0.584518i
$789$		0			0
$790$		0			0
$791$	−914.402			−1.15601
$792$		0			0
$793$	−284.436	−	284.436i	−0.358683	−	0.358683i
$794$		−	2192.44i		−	2.76126i
$795$		0			0
$796$	−892.729			−1.12152
$797$	645.951	−	645.951i	0.810479	−	0.810479i	−0.174227	−	0.984706i	$-0.555743\pi$
$797$	645.951	−	645.951i	0.810479	−	0.810479i	0.984706	+	0.174227i	$0.0557426\pi$
$798$		0			0
$799$			4.74584i			0.00593972i
$800$		0			0
$801$		0			0
$802$	−956.041	+	956.041i	−1.19207	+	1.19207i
$803$	168.881	+	168.881i	0.210313	+	0.210313i
$804$		0			0
$805$		0			0
$806$	681.856			0.845976
$807$		0			0
$808$	344.272	+	344.272i	0.426079	+	0.426079i
$809$		−	467.239i		−	0.577552i	−0.957397	−	0.288776i	$-0.906752\pi$
$809$		−	467.239i		−	0.577552i	0.957397	−	0.288776i	$-0.0932483\pi$
$810$		0			0
$811$	984.857			1.21437			0.607187	−	0.794559i	$-0.292298\pi$
$811$	984.857			1.21437			0.607187	+	0.794559i	$0.292298\pi$
$812$	−408.023	+	408.023i	−0.502491	+	0.502491i
$813$		0			0
$814$			3732.70i			4.58562i
$815$		0			0
$816$		0			0
$817$	−658.216	+	658.216i	−0.805650	+	0.805650i
$818$	−343.956	−	343.956i	−0.420485	−	0.420485i
$819$		0			0
$820$		0			0
$821$	−966.156			−1.17680			−0.588402	−	0.808569i	$-0.700243\pi$
$821$	−966.156			−1.17680			−0.588402	+	0.808569i	$0.700243\pi$
$822$		0			0
$823$	21.7648	+	21.7648i	0.0264457	+	0.0264457i	0.720206	−	0.693760i	$-0.244047\pi$
$823$	21.7648	+	21.7648i	0.0264457	+	0.0264457i	−0.693760	+	0.720206i	$0.744047\pi$
$824$		−	1285.80i		−	1.56044i
$825$		0			0
$826$	1864.20			2.25690
$827$	434.978	−	434.978i	0.525971	−	0.525971i	−0.393398	−	0.919368i	$-0.628700\pi$
$827$	434.978	−	434.978i	0.525971	−	0.525971i	0.919368	+	0.393398i	$0.128700\pi$
$828$		0			0
$829$			308.711i			0.372390i	0.982513	+	0.186195i	$0.0596156\pi$
$829$			308.711i			0.372390i	−0.982513	+	0.186195i	$0.940384\pi$
$830$		0			0
$831$		0			0
$832$	−81.0286	+	81.0286i	−0.0973902	+	0.0973902i
$833$	40.2100	+	40.2100i	0.0482713	+	0.0482713i
$834$		0			0
$835$		0			0
$836$	3335.99			3.99042
$837$		0			0
$838$	999.812	+	999.812i	1.19309	+	1.19309i
$839$			349.372i			0.416414i	0.978085	+	0.208207i	$0.0667628\pi$
$839$			349.372i			0.416414i	−0.978085	+	0.208207i	$0.933237\pi$
$840$		0			0
$841$	727.782			0.865377
$842$	−1530.49	+	1530.49i	−1.81768	+	1.81768i
$843$		0			0
$844$			1227.27i			1.45411i
$845$		0			0
$846$		0			0
$847$	1343.15	−	1343.15i	1.58577	−	1.58577i
$848$	−295.698	−	295.698i	−0.348701	−	0.348701i
$849$		0			0
$850$		0			0
$851$	1015.11			1.19284
$852$		0			0
$853$	475.927	+	475.927i	0.557945	+	0.557945i	0.928722	−	0.370777i	$-0.120909\pi$
$853$	475.927	+	475.927i	0.557945	+	0.557945i	−0.370777	+	0.928722i	$0.620909\pi$
$854$		−	1546.19i		−	1.81053i
$855$		0			0
$856$	−336.118			−0.392662
$857$	1100.97	−	1100.97i	1.28468	−	1.28468i	0.346705	−	0.937974i	$-0.387301\pi$
$857$	1100.97	−	1100.97i	1.28468	−	1.28468i	0.937974	−	0.346705i	$-0.112699\pi$
$858$		0			0
$859$			374.005i			0.435396i	0.976016	+	0.217698i	$0.0698547\pi$
$859$			374.005i			0.435396i	−0.976016	+	0.217698i	$0.930145\pi$
$860$		0			0
$861$		0			0
$862$	346.814	−	346.814i	0.402337	−	0.402337i
$863$	−169.154	−	169.154i	−0.196007	−	0.196007i	0.602279	−	0.798286i	$-0.294260\pi$
$863$	−169.154	−	169.154i	−0.196007	−	0.196007i	−0.798286	+	0.602279i	$0.794260\pi$
$864$		0			0
$865$		0			0
$866$	−513.294			−0.592718
$867$		0			0
$868$	1271.06	+	1271.06i	1.46435	+	1.46435i
$869$		−	1510.28i		−	1.73795i
$870$		0			0
$871$	−313.535			−0.359971
$872$	−223.190	+	223.190i	−0.255951	+	0.255951i
$873$		0			0
$874$		−	1322.79i		−	1.51350i
$875$		0			0
$876$		0			0
$877$	865.805	−	865.805i	0.987235	−	0.987235i	−0.0126849	−	0.999920i	$-0.504038\pi$
$877$	865.805	−	865.805i	0.987235	−	0.987235i	0.999920	+	0.0126849i	$0.00403784\pi$
$878$	2064.45	+	2064.45i	2.35131	+	2.35131i
$879$		0			0
$880$		0			0
$881$	−1252.48			−1.42165			−0.710827	−	0.703366i	$-0.751679\pi$
$881$	−1252.48			−1.42165			−0.710827	+	0.703366i	$0.751679\pi$
$882$		0			0
$883$	−997.163	−	997.163i	−1.12929	−	1.12929i	−0.990293	−	0.138998i	$-0.955612\pi$
$883$	−997.163	−	997.163i	−1.12929	−	1.12929i	−0.138998	−	0.990293i	$-0.544388\pi$
$884$			274.418i			0.310428i
$885$		0			0
$886$	−661.233			−0.746313
$887$	481.697	−	481.697i	0.543063	−	0.543063i	−0.381362	−	0.924426i	$-0.624545\pi$
$887$	481.697	−	481.697i	0.543063	−	0.543063i	0.924426	+	0.381362i	$0.124545\pi$
$888$		0			0
$889$		−	333.101i		−	0.374691i
$890$		0			0
$891$		0			0
$892$	2177.70	−	2177.70i	2.44137	−	2.44137i
$893$	11.3833	+	11.3833i	0.0127473	+	0.0127473i
$894$		0			0
$895$		0			0
$896$	−1007.29			−1.12420
$897$		0			0
$898$	−1383.35	−	1383.35i	−1.54048	−	1.54048i
$899$			352.691i			0.392315i
$900$		0			0
$901$	90.0155			0.0999062
$902$	−628.592	+	628.592i	−0.696887	+	0.696887i
$903$		0			0
$904$			2486.27i			2.75030i
$905$		0			0
$906$		0			0
$907$	62.4184	−	62.4184i	0.0688185	−	0.0688185i	−0.671860	−	0.740678i	$-0.734504\pi$
$907$	62.4184	−	62.4184i	0.0688185	−	0.0688185i	0.740678	+	0.671860i	$0.234504\pi$
$908$	1572.81	+	1572.81i	1.73217	+	1.73217i
$909$		0			0
$910$		0			0
$911$	−1319.23			−1.44812			−0.724058	−	0.689739i	$-0.757725\pi$
$911$	−1319.23			−1.44812			−0.724058	+	0.689739i	$0.757725\pi$
$912$		0			0
$913$	86.5466	+	86.5466i	0.0947937	+	0.0947937i
$914$			1253.66i			1.37162i
$915$		0			0
$916$	2690.47			2.93720
$917$	287.276	−	287.276i	0.313278	−	0.313278i
$918$		0			0
$919$		−	669.478i		−	0.728486i	−0.931304	−	0.364243i	$-0.881328\pi$
$919$		−	669.478i		−	0.728486i	0.931304	−	0.364243i	$-0.118672\pi$
$920$		0			0
$921$		0			0
$922$	−376.933	+	376.933i	−0.408821	+	0.408821i
$923$	−436.198	−	436.198i	−0.472587	−	0.472587i
$924$		0			0
$925$		0			0
$926$	−1776.35			−1.91830
$927$		0			0
$928$	171.676	+	171.676i	0.184996	+	0.184996i
$929$		−	1410.96i		−	1.51880i	−0.650626	−	0.759398i	$-0.725494\pi$
$929$		−	1410.96i		−	1.51880i	0.650626	−	0.759398i	$-0.274506\pi$
$930$		0			0
$931$	192.894			0.207191
$932$	2434.02	−	2434.02i	2.61161	−	2.61161i
$933$		0			0
$934$		−	2215.43i		−	2.37198i
$935$		0			0
$936$		0			0
$937$	482.685	−	482.685i	0.515139	−	0.515139i	−0.400958	−	0.916097i	$-0.631323\pi$
$937$	482.685	−	482.685i	0.515139	−	0.515139i	0.916097	+	0.400958i	$0.131323\pi$
$938$	−852.188	−	852.188i	−0.908516	−	0.908516i
$939$		0			0
$940$		0			0
$941$	734.717			0.780784			0.390392	−	0.920649i	$-0.372340\pi$
$941$	734.717			0.780784			0.390392	+	0.920649i	$0.372340\pi$
$942$		0			0
$943$	170.946	+	170.946i	0.181279	+	0.181279i
$944$		−	2130.37i		−	2.25674i
$945$		0			0
$946$	3711.31			3.92317
$947$	−486.842	+	486.842i	−0.514088	+	0.514088i	−0.915777	−	0.401688i	$-0.868424\pi$
$947$	−486.842	+	486.842i	−0.514088	+	0.514088i	0.401688	+	0.915777i	$0.368424\pi$
$948$		0			0
$949$			66.6431i			0.0702246i
$950$		0			0
$951$		0			0
$952$	−404.209	+	404.209i	−0.424589	+	0.424589i
$953$	−47.5647	−	47.5647i	−0.0499105	−	0.0499105i	0.681711	−	0.731622i	$-0.261236\pi$
$953$	−47.5647	−	47.5647i	−0.0499105	−	0.0499105i	−0.731622	+	0.681711i	$0.761236\pi$
$954$		0			0
$955$		0			0
$956$	3429.94			3.58780
$957$		0			0
$958$	−739.191	−	739.191i	−0.771598	−	0.771598i
$959$		−	793.774i		−	0.827710i
$960$		0			0
$961$	137.688			0.143276
$962$	−736.489	+	736.489i	−0.765581	+	0.765581i
$963$		0			0
$964$			1086.59i			1.12717i
$965$		0			0
$966$		0			0
$967$	773.213	−	773.213i	0.799600	−	0.799600i	−0.183432	−	0.983032i	$-0.558721\pi$
$967$	773.213	−	773.213i	0.799600	−	0.799600i	0.983032	+	0.183432i	$0.0587208\pi$
$968$	−3652.04	−	3652.04i	−3.77277	−	3.77277i
$969$		0			0
$970$		0			0
$971$	−1595.62			−1.64327			−0.821637	−	0.570011i	$-0.806939\pi$
$971$	−1595.62			−1.64327			−0.821637	+	0.570011i	$0.806939\pi$
$972$		0			0
$973$	−1086.56	−	1086.56i	−1.11671	−	1.11671i
$974$			2736.45i			2.80949i
$975$		0			0
$976$	−1766.96			−1.81041
$977$	1017.40	−	1017.40i	1.04135	−	1.04135i	0.0422453	−	0.999107i	$-0.486549\pi$
$977$	1017.40	−	1017.40i	1.04135	−	1.04135i	0.999107	−	0.0422453i	$-0.0134511\pi$
$978$		0			0
$979$		−	128.247i		−	0.130998i
$980$		0			0
$981$		0			0
$982$	−1722.60	+	1722.60i	−1.75417	+	1.75417i
$983$	268.852	+	268.852i	0.273501	+	0.273501i	0.830508	−	0.557007i	$-0.188050\pi$
$983$	268.852	+	268.852i	0.273501	+	0.273501i	−0.557007	+	0.830508i	$0.688050\pi$
$984$		0			0
$985$		0			0
$986$	−206.963			−0.209902
$987$		0			0
$988$	658.216	+	658.216i	0.666210	+	0.666210i
$989$		−	1009.29i		−	1.02052i
$990$		0			0
$991$	563.583			0.568701			0.284350	−	0.958720i	$-0.408222\pi$
$991$	563.583			0.568701			0.284350	+	0.958720i	$0.408222\pi$
$992$	534.799	−	534.799i	0.539112	−	0.539112i
$993$		0			0
$994$		−	2371.17i		−	2.38549i
$995$		0			0
$996$		0			0
$997$	864.713	−	864.713i	0.867315	−	0.867315i	−0.124860	−	0.992174i	$-0.539848\pi$
$997$	864.713	−	864.713i	0.867315	−	0.867315i	0.992174	+	0.124860i	$0.0398481\pi$
$998$	−1034.95	−	1034.95i	−1.03702	−	1.03702i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.3.g.k.568.8		16
3.2	odd	2	inner	675.3.g.k.568.1		16
5.2	odd	4	inner	675.3.g.k.82.8		16
5.3	odd	4		135.3.g.a.82.1	yes	16
5.4	even	2		135.3.g.a.28.1	✓	16
15.2	even	4	inner	675.3.g.k.82.1		16
15.8	even	4		135.3.g.a.82.8	yes	16
15.14	odd	2		135.3.g.a.28.8	yes	16
45.4	even	6		405.3.l.o.298.1		32
45.13	odd	12		405.3.l.o.217.8		32
45.14	odd	6		405.3.l.o.298.8		32
45.23	even	12		405.3.l.o.217.1		32
45.29	odd	6		405.3.l.o.28.1		32
45.34	even	6		405.3.l.o.28.8		32
45.38	even	12		405.3.l.o.352.8		32
45.43	odd	12		405.3.l.o.352.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.g.a.28.1	✓	16	5.4	even	2
135.3.g.a.28.8	yes	16	15.14	odd	2
135.3.g.a.82.1	yes	16	5.3	odd	4
135.3.g.a.82.8	yes	16	15.8	even	4
405.3.l.o.28.1		32	45.29	odd	6
405.3.l.o.28.8		32	45.34	even	6
405.3.l.o.217.1		32	45.23	even	12
405.3.l.o.217.8		32	45.13	odd	12
405.3.l.o.298.1		32	45.4	even	6
405.3.l.o.298.8		32	45.14	odd	6
405.3.l.o.352.1		32	45.43	odd	12
405.3.l.o.352.8		32	45.38	even	12
675.3.g.k.82.1		16	15.2	even	4	inner
675.3.g.k.82.8		16	5.2	odd	4	inner
675.3.g.k.568.1		16	3.2	odd	2	inner
675.3.g.k.568.8		16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	675.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.52312 - 2.52312i) q^{2} -8.73230i q^{4} +(4.39136 - 4.39136i) q^{7} +(-11.9402 - 11.9402i) q^{8} +O(q^{10})\)	\(q+(2.52312 - 2.52312i) q^{2} -8.73230i q^{4} +(4.39136 - 4.39136i) q^{7} +(-11.9402 - 11.9402i) q^{8} -20.6606 q^{11} +(-4.07650 - 4.07650i) q^{13} -22.1599i q^{14} -25.3238 q^{16} +(3.85449 - 3.85449i) q^{17} -18.4907i q^{19} +(-52.1293 + 52.1293i) q^{22} +(14.1766 + 14.1766i) q^{23} -20.5710 q^{26} +(-38.3466 - 38.3466i) q^{28} -10.6404i q^{29} -33.1465 q^{31} +(-16.1344 + 16.1344i) q^{32} -19.4507i q^{34} +(35.8023 - 35.8023i) q^{37} +(-46.6542 - 46.6542i) q^{38} +12.0583 q^{41} +(-35.5972 - 35.5972i) q^{43} +180.415i q^{44} +71.5385 q^{46} +(-0.615624 + 0.615624i) q^{47} +10.4320i q^{49} +(-35.5972 + 35.5972i) q^{52} +(11.6767 + 11.6767i) q^{53} -104.867 q^{56} +(-26.8470 - 26.8470i) q^{58} +84.1251i q^{59} +69.7745 q^{61} +(-83.6326 + 83.6326i) q^{62} -19.8770i q^{64} +(38.4564 - 38.4564i) q^{67} +(-33.6586 - 33.6586i) q^{68} +107.003 q^{71} +(-8.17407 - 8.17407i) q^{73} -180.667i q^{74} -161.466 q^{76} +(-90.7282 + 90.7282i) q^{77} +73.0992i q^{79} +(30.4246 - 30.4246i) q^{82} +(-4.18896 - 4.18896i) q^{83} -179.632 q^{86} +(246.691 + 246.691i) q^{88} +6.20731i q^{89} -35.8027 q^{91} +(123.794 - 123.794i) q^{92} +3.10659i q^{94} +(54.9464 - 54.9464i) q^{97} +(26.3212 + 26.3212i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^7	\( 16 q + 8 q^{7} - 28 q^{13} - 20 q^{16} - 176 q^{22} - 80 q^{28} - 208 q^{31} + 176 q^{37} + 188 q^{43} + 188 q^{46} + 188 q^{52} - 504 q^{58} + 296 q^{61} - 304 q^{67} + 56 q^{73} - 732 q^{76} + 76 q^{82} + 1128 q^{88} + 200 q^{91} + 284 q^{97}+O(q^{100}) \) 16 * q + 8 * q^7 - 28 * q^13 - 20 * q^16 - 176 * q^22 - 80 * q^28 - 208 * q^31 + 176 * q^37 + 188 * q^43 + 188 * q^46 + 188 * q^52 - 504 * q^58 + 296 * q^61 - 304 * q^67 + 56 * q^73 - 732 * q^76 + 76 * q^82 + 1128 * q^88 + 200 * q^91 + 284 * q^97

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