LMFDB - Embedded newform 261.2.g.b.215.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,2,Mod(17,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("261.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.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:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.40960000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 7x^{4} + 1 $ x^8 + 7*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			215.3
Root			$-0.437016 + 0.437016i$ of defining polynomial
Character	$\chi$	$=$	261.215
Dual form			261.2.g.b.17.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.270091 - 0.270091i) q^{2} +1.85410i q^{4} -3.70246 q^{5} -1.00000 q^{7} +(1.04096 + 1.04096i) q^{8} +O(q^{10})$	\(q+(0.270091 - 0.270091i) q^{2} +1.85410i q^{4} -3.70246 q^{5} -1.00000 q^{7} +(1.04096 + 1.04096i) q^{8} +(-1.00000 + 1.00000i) q^{10} +(-1.58114 + 1.58114i) q^{11} +5.00000i q^{13} +(-0.270091 + 0.270091i) q^{14} -3.14590 q^{16} +(-1.04096 + 1.04096i) q^{17} +(-1.85410 - 1.85410i) q^{19} -6.86474i q^{20} +0.854102i q^{22} +0.540182i q^{23} +8.70820 q^{25} +(1.35045 + 1.35045i) q^{26} -1.85410i q^{28} +(1.04096 - 5.28360i) q^{29} +(4.85410 + 4.85410i) q^{31} +(-2.93159 + 2.93159i) q^{32} +0.562306i q^{34} +3.70246 q^{35} +(4.85410 - 4.85410i) q^{37} -1.00155 q^{38} +(-3.85410 - 3.85410i) q^{40} +(4.24264 + 4.24264i) q^{41} +(-5.70820 - 5.70820i) q^{43} +(-2.93159 - 2.93159i) q^{44} +(0.145898 + 0.145898i) q^{46} +(8.44588 + 8.44588i) q^{47} -6.00000 q^{49} +(2.35201 - 2.35201i) q^{50} -9.27051 q^{52} +2.62210i q^{53} +(5.85410 - 5.85410i) q^{55} +(-1.04096 - 1.04096i) q^{56} +(-1.14590 - 1.70820i) q^{58} +10.5672i q^{59} +(2.85410 + 2.85410i) q^{61} +2.62210 q^{62} -4.70820i q^{64} -18.5123i q^{65} -14.7082i q^{67} +(-1.93004 - 1.93004i) q^{68} +(1.00000 - 1.00000i) q^{70} -1.62054 q^{71} +(-8.85410 + 8.85410i) q^{73} -2.62210i q^{74} +(3.43769 - 3.43769i) q^{76} +(1.58114 - 1.58114i) q^{77} +(9.85410 + 9.85410i) q^{79} +11.6476 q^{80} +2.29180 q^{82} -9.48683i q^{83} +(3.85410 - 3.85410i) q^{85} -3.08347 q^{86} -3.29180 q^{88} +(-12.6885 + 12.6885i) q^{89} -5.00000i q^{91} -1.00155 q^{92} +4.56231 q^{94} +(6.86474 + 6.86474i) q^{95} +(4.14590 - 4.14590i) q^{97} +(-1.62054 + 1.62054i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{7}+O(q^{10}) $ 8 * q - 8 * q^7	$ 8 q - 8 q^{7} - 8 q^{10} - 52 q^{16} + 12 q^{19} + 16 q^{25} + 12 q^{31} + 12 q^{37} - 4 q^{40} + 8 q^{43} + 28 q^{46} - 48 q^{49} + 60 q^{52} + 20 q^{55} - 36 q^{58} - 4 q^{61} + 8 q^{70} - 44 q^{73} + 108 q^{76} + 52 q^{79} + 72 q^{82} + 4 q^{85} - 80 q^{88} - 44 q^{94} + 60 q^{97}+O(q^{100}) $ 8 * q - 8 * q^7 - 8 * q^10 - 52 * q^16 + 12 * q^19 + 16 * q^25 + 12 * q^31 + 12 * q^37 - 4 * q^40 + 8 * q^43 + 28 * q^46 - 48 * q^49 + 60 * q^52 + 20 * q^55 - 36 * q^58 - 4 * q^61 + 8 * q^70 - 44 * q^73 + 108 * q^76 + 52 * q^79 + 72 * q^82 + 4 * q^85 - 80 * q^88 - 44 * q^94 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.270091	−	0.270091i	0.190983	−	0.190983i	−0.605138	−	0.796121i	$-0.706882\pi$
$2$	0.270091	−	0.270091i	0.190983	−	0.190983i	0.796121	+	0.605138i	$0.206882\pi$
$3$		0			0
$3$		0			0
$4$			1.85410i			0.927051i
$5$	−3.70246			−1.65579			−0.827895	−	0.560883i	$-0.810462\pi$
$5$	−3.70246			−1.65579			−0.827895	+	0.560883i	$0.810462\pi$
$6$		0			0
$7$	−1.00000			−0.377964			−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000			−0.377964			−0.188982	+	0.981981i	$0.560519\pi$
$8$	1.04096	+	1.04096i	0.368034	+	0.368034i
$9$		0			0
$10$	−1.00000	+	1.00000i	−0.316228	+	0.316228i
$11$	−1.58114	+	1.58114i	−0.476731	+	0.476731i	−0.904085	−	0.427353i	$-0.859446\pi$
$11$	−1.58114	+	1.58114i	−0.476731	+	0.476731i	0.427353	+	0.904085i	$0.359446\pi$
$12$		0			0
$13$			5.00000i			1.38675i	0.720577	+	0.693375i	$0.243877\pi$
$13$			5.00000i			1.38675i	−0.720577	+	0.693375i	$0.756123\pi$
$14$	−0.270091	+	0.270091i	−0.0721848	+	0.0721848i
$15$		0			0
$16$	−3.14590			−0.786475
$17$	−1.04096	+	1.04096i	−0.252469	+	0.252469i	−0.821982	−	0.569513i	$-0.807132\pi$
$17$	−1.04096	+	1.04096i	−0.252469	+	0.252469i	0.569513	+	0.821982i	$0.307132\pi$
$18$		0			0
$19$	−1.85410	−	1.85410i	−0.425360	−	0.425360i	0.461684	−	0.887044i	$-0.347245\pi$
$19$	−1.85410	−	1.85410i	−0.425360	−	0.425360i	−0.887044	+	0.461684i	$0.847245\pi$
$20$		−	6.86474i		−	1.53500i
$21$		0			0
$22$			0.854102i			0.182095i
$23$			0.540182i			0.112636i	0.998413	+	0.0563178i	$0.0179360\pi$
$23$			0.540182i			0.112636i	−0.998413	+	0.0563178i	$0.982064\pi$
$24$		0			0
$25$	8.70820			1.74164
$26$	1.35045	+	1.35045i	0.264846	+	0.264846i
$27$		0			0
$28$		−	1.85410i		−	0.350392i
$29$	1.04096	−	5.28360i	0.193301	−	0.981140i
$29$	1.04096	−	5.28360i	0.193301	−	0.981140i
$30$		0			0
$31$	4.85410	+	4.85410i	0.871822	+	0.871822i	0.992671	−	0.120849i	$-0.0385615\pi$
$31$	4.85410	+	4.85410i	0.871822	+	0.871822i	−0.120849	+	0.992671i	$0.538562\pi$
$32$	−2.93159	+	2.93159i	−0.518237	+	0.518237i
$33$		0			0
$34$			0.562306i			0.0964347i
$35$	3.70246			0.625830
$36$		0			0
$37$	4.85410	−	4.85410i	0.798009	−	0.798009i	−0.184772	−	0.982781i	$-0.559155\pi$
$37$	4.85410	−	4.85410i	0.798009	−	0.798009i	0.982781	+	0.184772i	$0.0591547\pi$
$38$	−1.00155			−0.162473
$39$		0			0
$40$	−3.85410	−	3.85410i	−0.609387	−	0.609387i
$41$	4.24264	+	4.24264i	0.662589	+	0.662589i	0.955990	−	0.293400i	$-0.0947869\pi$
$41$	4.24264	+	4.24264i	0.662589	+	0.662589i	−0.293400	+	0.955990i	$0.594787\pi$
$42$		0			0
$43$	−5.70820	−	5.70820i	−0.870493	−	0.870493i	0.122033	−	0.992526i	$-0.461059\pi$
$43$	−5.70820	−	5.70820i	−0.870493	−	0.870493i	−0.992526	+	0.122033i	$0.961059\pi$
$44$	−2.93159	−	2.93159i	−0.441954	−	0.441954i
$45$		0			0
$46$	0.145898	+	0.145898i	0.0215115	+	0.0215115i
$47$	8.44588	+	8.44588i	1.23196	+	1.23196i	0.963211	+	0.268747i	$0.0866095\pi$
$47$	8.44588	+	8.44588i	1.23196	+	1.23196i	0.268747	+	0.963211i	$0.413391\pi$
$48$		0			0
$49$	−6.00000			−0.857143
$50$	2.35201	−	2.35201i	0.332624	−	0.332624i
$51$		0			0
$52$	−9.27051			−1.28559
$53$			2.62210i			0.360173i	0.983651	+	0.180086i	$0.0576377\pi$
$53$			2.62210i			0.360173i	−0.983651	+	0.180086i	$0.942362\pi$
$54$		0			0
$55$	5.85410	−	5.85410i	0.789367	−	0.789367i
$56$	−1.04096	−	1.04096i	−0.139104	−	0.139104i
$57$		0			0
$58$	−1.14590	−	1.70820i	−0.150464	−	0.224298i
$59$			10.5672i			1.37573i	0.725838	+	0.687866i	$0.241452\pi$
$59$			10.5672i			1.37573i	−0.725838	+	0.687866i	$0.758548\pi$
$60$		0			0
$61$	2.85410	+	2.85410i	0.365430	+	0.365430i	0.865808	−	0.500377i	$-0.166805\pi$
$61$	2.85410	+	2.85410i	0.365430	+	0.365430i	−0.500377	+	0.865808i	$0.666805\pi$
$62$	2.62210			0.333007
$63$		0			0
$64$		−	4.70820i		−	0.588525i
$65$		−	18.5123i		−	2.29617i
$66$		0			0
$67$		−	14.7082i		−	1.79689i	−0.439083	−	0.898447i	$-0.644697\pi$
$67$		−	14.7082i		−	1.79689i	0.439083	−	0.898447i	$-0.355303\pi$
$68$	−1.93004	−	1.93004i	−0.234052	−	0.234052i
$69$		0			0
$70$	1.00000	−	1.00000i	0.119523	−	0.119523i
$71$	−1.62054			−0.192323			−0.0961616	−	0.995366i	$-0.530657\pi$
$71$	−1.62054			−0.192323			−0.0961616	+	0.995366i	$0.530657\pi$
$72$		0			0
$73$	−8.85410	+	8.85410i	−1.03629	+	1.03629i	−0.0369782	+	0.999316i	$0.511773\pi$
$73$	−8.85410	+	8.85410i	−1.03629	+	1.03629i	−0.999316	+	0.0369782i	$0.988227\pi$
$74$		−	2.62210i		−	0.304812i
$75$		0			0
$76$	3.43769	−	3.43769i	0.394331	−	0.394331i
$77$	1.58114	−	1.58114i	0.180187	−	0.180187i
$78$		0			0
$79$	9.85410	+	9.85410i	1.10867	+	1.10867i	0.993325	+	0.115348i	$0.0367983\pi$
$79$	9.85410	+	9.85410i	1.10867	+	1.10867i	0.115348	+	0.993325i	$0.463202\pi$
$80$	11.6476			1.30224
$81$		0			0
$82$	2.29180			0.253087
$83$		−	9.48683i		−	1.04132i	−0.853766	−	0.520658i	$-0.825687\pi$
$83$		−	9.48683i		−	1.04132i	0.853766	−	0.520658i	$-0.174313\pi$
$84$		0			0
$85$	3.85410	−	3.85410i	0.418036	−	0.418036i
$86$	−3.08347			−0.332499
$87$		0			0
$88$	−3.29180			−0.350907
$89$	−12.6885	+	12.6885i	−1.34498	+	1.34498i	−0.453956	+	0.891024i	$0.649988\pi$
$89$	−12.6885	+	12.6885i	−1.34498	+	1.34498i	−0.891024	+	0.453956i	$0.850012\pi$
$90$		0			0
$91$		−	5.00000i		−	0.524142i
$92$	−1.00155			−0.104419
$93$		0			0
$94$	4.56231			0.470566
$95$	6.86474	+	6.86474i	0.704307	+	0.704307i
$96$		0			0
$97$	4.14590	−	4.14590i	0.420952	−	0.420952i	−0.464579	−	0.885532i	$-0.653794\pi$
$97$	4.14590	−	4.14590i	0.420952	−	0.420952i	0.885532	+	0.464579i	$0.153794\pi$
$98$	−1.62054	+	1.62054i	−0.163700	+	0.163700i
$99$		0			0
$100$			16.1459i			1.61459i
$101$	−5.28360	+	5.28360i	−0.525738	+	0.525738i	−0.919299	−	0.393561i	$-0.871243\pi$
$101$	−5.28360	+	5.28360i	−0.525738	+	0.525738i	0.393561	+	0.919299i	$0.371243\pi$
$102$		0			0
$103$	−12.0000			−1.18240			−0.591198	−	0.806527i	$-0.701345\pi$
$103$	−12.0000			−1.18240			−0.591198	+	0.806527i	$0.701345\pi$
$104$	−5.20479	+	5.20479i	−0.510371	+	0.510371i
$105$		0			0
$106$	0.708204	+	0.708204i	0.0687868	+	0.0687868i
$107$		−	1.54173i		−	0.149045i	−0.997219	−	0.0745225i	$-0.976257\pi$
$107$		−	1.54173i		−	0.149045i	0.997219	−	0.0745225i	$-0.0237433\pi$
$108$		0			0
$109$			12.4164i			1.18928i	0.803993	+	0.594638i	$0.202705\pi$
$109$			12.4164i			1.18928i	−0.803993	+	0.594638i	$0.797295\pi$
$110$		−	3.16228i		−	0.301511i
$111$		0			0
$112$	3.14590			0.297259
$113$	4.20323	+	4.20323i	0.395407	+	0.395407i	0.876610	−	0.481202i	$-0.159800\pi$
$113$	4.20323	+	4.20323i	0.395407	+	0.395407i	−0.481202	+	0.876610i	$0.659800\pi$
$114$		0			0
$115$		−	2.00000i		−	0.186501i
$116$	9.79633	+	1.93004i	0.909566	+	0.179200i
$117$		0			0
$118$	2.85410	+	2.85410i	0.262741	+	0.262741i
$119$	1.04096	−	1.04096i	0.0954244	−	0.0954244i
$120$		0			0
$121$			6.00000i			0.545455i
$122$	1.54173			0.139582
$123$		0			0
$124$	−9.00000	+	9.00000i	−0.808224	+	0.808224i
$125$	−13.7295			−1.22800
$126$		0			0
$127$	−6.70820	−	6.70820i	−0.595257	−	0.595257i	0.343790	−	0.939047i	$-0.388289\pi$
$127$	−6.70820	−	6.70820i	−0.595257	−	0.595257i	−0.939047	+	0.343790i	$0.888289\pi$
$128$	−7.13483	−	7.13483i	−0.630636	−	0.630636i
$129$		0			0
$130$	−5.00000	−	5.00000i	−0.438529	−	0.438529i
$131$	−5.82378	−	5.82378i	−0.508826	−	0.508826i	0.405340	−	0.914166i	$-0.367153\pi$
$131$	−5.82378	−	5.82378i	−0.508826	−	0.508826i	−0.914166	+	0.405340i	$0.867153\pi$
$132$		0			0
$133$	1.85410	+	1.85410i	0.160771	+	0.160771i
$134$	−3.97255	−	3.97255i	−0.343176	−	0.343176i
$135$		0			0
$136$	−2.16718			−0.185835
$137$	2.62210	−	2.62210i	0.224021	−	0.224021i	−0.586168	−	0.810189i	$-0.699364\pi$
$137$	2.62210	−	2.62210i	0.224021	−	0.224021i	0.810189	+	0.586168i	$0.199364\pi$
$138$		0			0
$139$	10.7082			0.908258			0.454129	−	0.890936i	$-0.349951\pi$
$139$	10.7082			0.908258			0.454129	+	0.890936i	$0.349951\pi$
$140$			6.86474i			0.580176i
$141$		0			0
$142$	−0.437694	+	0.437694i	−0.0367305	+	0.0367305i
$143$	−7.90569	−	7.90569i	−0.661107	−	0.661107i
$144$		0			0
$145$	−3.85410	+	19.5623i	−0.320066	+	1.62456i
$146$			4.78282i			0.395829i
$147$		0			0
$148$	9.00000	+	9.00000i	0.739795	+	0.739795i
$149$	5.24419			0.429621			0.214810	−	0.976656i	$-0.431087\pi$
$149$	5.24419			0.429621			0.214810	+	0.976656i	$0.431087\pi$
$150$		0			0
$151$			12.0000i			0.976546i	0.872691	+	0.488273i	$0.162373\pi$
$151$			12.0000i			0.976546i	−0.872691	+	0.488273i	$0.837627\pi$
$152$		−	3.86008i		−	0.313094i
$153$		0			0
$154$		−	0.854102i		−	0.0688255i
$155$	−17.9721	−	17.9721i	−1.44355	−	1.44355i
$156$		0			0
$157$	−3.00000	+	3.00000i	−0.239426	+	0.239426i	−0.816612	−	0.577186i	$-0.804151\pi$
$157$	−3.00000	+	3.00000i	−0.239426	+	0.239426i	0.577186	+	0.816612i	$0.304151\pi$
$158$	5.32300			0.423475
$159$		0			0
$160$	10.8541	−	10.8541i	0.858092	−	0.858092i
$161$		−	0.540182i		−	0.0425723i
$162$		0			0
$163$	1.29180	−	1.29180i	0.101181	−	0.101181i	−0.654704	−	0.755885i	$-0.727207\pi$
$163$	1.29180	−	1.29180i	0.101181	−	0.101181i	0.755885	+	0.654704i	$0.227207\pi$
$164$	−7.86629	+	7.86629i	−0.614254	+	0.614254i
$165$		0			0
$166$	−2.56231	−	2.56231i	−0.198874	−	0.198874i
$167$	23.2951			1.80263			0.901315	−	0.433164i	$-0.142603\pi$
$167$	23.2951			1.80263			0.901315	+	0.433164i	$0.142603\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$		−	2.08191i		−	0.159676i
$171$		0			0
$172$	10.5836	−	10.5836i	0.806991	−	0.806991i
$173$	1.08036			0.0821385			0.0410692	−	0.999156i	$-0.486924\pi$
$173$	1.08036			0.0821385			0.0410692	+	0.999156i	$0.486924\pi$
$174$		0			0
$175$	−8.70820			−0.658278
$176$	4.97410	−	4.97410i	0.374937	−	0.374937i
$177$		0			0
$178$			6.85410i			0.513737i
$179$	−0.540182			−0.0403751			−0.0201875	−	0.999796i	$-0.506426\pi$
$179$	−0.540182			−0.0403751			−0.0201875	+	0.999796i	$0.506426\pi$
$180$		0			0
$181$	2.70820			0.201299			0.100650	−	0.994922i	$-0.467908\pi$
$181$	2.70820			0.201299			0.100650	+	0.994922i	$0.467908\pi$
$182$	−1.35045	−	1.35045i	−0.100102	−	0.100102i
$183$		0			0
$184$	−0.562306	+	0.562306i	−0.0414537	+	0.0414537i
$185$	−17.9721	+	17.9721i	−1.32134	+	1.32134i
$186$		0			0
$187$		−	3.29180i		−	0.240720i
$188$	−15.6595	+	15.6595i	−1.14209	+	1.14209i
$189$		0			0
$190$	3.70820			0.269021
$191$	17.9721	−	17.9721i	1.30042	−	1.30042i	0.372307	−	0.928110i	$-0.378567\pi$
$191$	17.9721	−	17.9721i	1.30042	−	1.30042i	0.928110	−	0.372307i	$-0.121433\pi$
$192$		0			0
$193$	0.708204	+	0.708204i	0.0509776	+	0.0509776i	0.732136	−	0.681158i	$-0.238524\pi$
$193$	0.708204	+	0.708204i	0.0509776	+	0.0509776i	−0.681158	+	0.732136i	$0.738524\pi$
$194$		−	2.23954i		−	0.160789i
$195$		0			0
$196$		−	11.1246i		−	0.794615i
$197$			21.5958i			1.53863i	0.638867	+	0.769317i	$0.279403\pi$
$197$			21.5958i			1.53863i	−0.638867	+	0.769317i	$0.720597\pi$
$198$		0			0
$199$	9.29180			0.658678			0.329339	−	0.944212i	$-0.393174\pi$
$199$	9.29180			0.658678			0.329339	+	0.944212i	$0.393174\pi$
$200$	9.06487	+	9.06487i	0.640983	+	0.640983i
$201$		0			0
$202$			2.85410i			0.200814i
$203$	−1.04096	+	5.28360i	−0.0730609	+	0.370836i
$204$		0			0
$205$	−15.7082	−	15.7082i	−1.09711	−	1.09711i
$206$	−3.24109	+	3.24109i	−0.225817	+	0.225817i
$207$		0			0
$208$		−	15.7295i		−	1.09064i
$209$	5.86319			0.405565
$210$		0			0
$211$	−0.708204	+	0.708204i	−0.0487548	+	0.0487548i	−0.731064	−	0.682309i	$-0.760976\pi$
$211$	−0.708204	+	0.708204i	−0.0487548	+	0.0487548i	0.682309	+	0.731064i	$0.260976\pi$
$212$	−4.86163			−0.333898
$213$		0			0
$214$	−0.416408	−	0.416408i	−0.0284651	−	0.0284651i
$215$	21.1344	+	21.1344i	1.44135	+	1.44135i
$216$		0			0
$217$	−4.85410	−	4.85410i	−0.329518	−	0.329518i
$218$	3.35356	+	3.35356i	0.227132	+	0.227132i
$219$		0			0
$220$	10.8541	+	10.8541i	0.731783	+	0.731783i
$221$	−5.20479	−	5.20479i	−0.350112	−	0.350112i
$222$		0			0
$223$	13.2918			0.890084			0.445042	−	0.895510i	$-0.353189\pi$
$223$	13.2918			0.890084			0.445042	+	0.895510i	$0.353189\pi$
$224$	2.93159	−	2.93159i	0.195875	−	0.195875i
$225$		0			0
$226$	2.27051			0.151032
$227$		−	9.48683i		−	0.629663i	−0.949148	−	0.314832i	$-0.898052\pi$
$227$		−	9.48683i		−	0.629663i	0.949148	−	0.314832i	$-0.101948\pi$
$228$		0			0
$229$	−13.8541	+	13.8541i	−0.915505	+	0.915505i	−0.996698	−	0.0811935i	$-0.974127\pi$
$229$	−13.8541	+	13.8541i	−0.915505	+	0.915505i	0.0811935	+	0.996698i	$0.474127\pi$
$230$	−0.540182	−	0.540182i	−0.0356185	−	0.0356185i
$231$		0			0
$232$	6.58359	−	4.41641i	0.432234	−	0.289951i
$233$		−	19.0525i		−	1.24817i	−0.781357	−	0.624085i	$-0.785472\pi$
$233$		−	19.0525i		−	1.24817i	0.781357	−	0.624085i	$-0.214528\pi$
$234$		0			0
$235$	−31.2705	−	31.2705i	−2.03986	−	2.03986i
$236$	−19.5927			−1.27537
$237$		0			0
$238$		−	0.562306i		−	0.0364489i
$239$		−	16.3516i		−	1.05770i	−0.848717	−	0.528848i	$-0.822624\pi$
$239$		−	16.3516i		−	1.05770i	0.848717	−	0.528848i	$-0.177376\pi$
$240$		0			0
$241$		−	4.70820i		−	0.303282i	−0.988436	−	0.151641i	$-0.951544\pi$
$241$		−	4.70820i		−	0.303282i	0.988436	−	0.151641i	$-0.0484558\pi$
$242$	1.62054	+	1.62054i	0.104173	+	0.104173i
$243$		0			0
$244$	−5.29180	+	5.29180i	−0.338773	+	0.338773i
$245$	22.2148			1.41925
$246$		0			0
$247$	9.27051	−	9.27051i	0.589868	−	0.589868i
$248$			10.1058i			0.641721i
$249$		0			0
$250$	−3.70820	+	3.70820i	−0.234527	+	0.234527i
$251$	15.3894	−	15.3894i	0.971372	−	0.971372i	−0.0282296	−	0.999601i	$-0.508987\pi$
$251$	15.3894	−	15.3894i	0.971372	−	0.971372i	0.999601	+	0.0282296i	$0.00898697\pi$
$252$		0			0
$253$	−0.854102	−	0.854102i	−0.0536969	−	0.0536969i
$254$	−3.62365			−0.227368
$255$		0			0
$256$	5.56231			0.347644
$257$		−	22.2148i		−	1.38572i	−0.721073	−	0.692859i	$-0.756351\pi$
$257$		−	22.2148i		−	1.38572i	0.721073	−	0.692859i	$-0.243649\pi$
$258$		0			0
$259$	−4.85410	+	4.85410i	−0.301619	+	0.301619i
$260$	34.3237			2.12866
$261$		0			0
$262$	−3.14590			−0.194354
$263$	8.48528	−	8.48528i	0.523225	−	0.523225i	−0.395319	−	0.918544i	$-0.629366\pi$
$263$	8.48528	−	8.48528i	0.523225	−	0.523225i	0.918544	+	0.395319i	$0.129366\pi$
$264$		0			0
$265$		−	9.70820i		−	0.596370i
$266$	1.00155			0.0614091
$267$		0			0
$268$	27.2705			1.66581
$269$	−16.3910	−	16.3910i	−0.999375	−	0.999375i	0.000624389	−	1.00000i	$-0.499801\pi$
$269$	−16.3910	−	16.3910i	−0.999375	−	0.999375i	−1.00000		0.000624389i	$0.999801\pi$
$270$		0			0
$271$	18.4164	−	18.4164i	1.11872	−	1.11872i	0.126787	−	0.991930i	$-0.459533\pi$
$271$	18.4164	−	18.4164i	1.11872	−	1.11872i	0.991930	−	0.126787i	$-0.0404665\pi$
$272$	3.27475	−	3.27475i	0.198561	−	0.198561i
$273$		0			0
$274$		−	1.41641i		−	0.0855683i
$275$	−13.7689	+	13.7689i	−0.830295	+	0.830295i
$276$		0			0
$277$	−2.70820			−0.162720			−0.0813601	−	0.996685i	$-0.525926\pi$
$277$	−2.70820			−0.162720			−0.0813601	+	0.996685i	$0.525926\pi$
$278$	2.89219	−	2.89219i	0.173462	−	0.173462i
$279$		0			0
$280$	3.85410	+	3.85410i	0.230327	+	0.230327i
$281$			26.4574i			1.57832i	0.614190	+	0.789158i	$0.289483\pi$
$281$			26.4574i			1.57832i	−0.614190	+	0.789158i	$0.710517\pi$
$282$		0			0
$283$			15.7082i			0.933756i	0.884322	+	0.466878i	$0.154621\pi$
$283$			15.7082i			0.933756i	−0.884322	+	0.466878i	$0.845379\pi$
$284$		−	3.00465i		−	0.178293i
$285$		0			0
$286$	−4.27051			−0.252521
$287$	−4.24264	−	4.24264i	−0.250435	−	0.250435i
$288$		0			0
$289$			14.8328i			0.872519i
$290$	4.24264	+	6.32456i	0.249136	+	0.371391i
$291$		0			0
$292$	−16.4164	−	16.4164i	−0.960698	−	0.960698i
$293$	−13.1499	+	13.1499i	−0.768225	+	0.768225i	−0.977794	−	0.209569i	$-0.932794\pi$
$293$	−13.1499	+	13.1499i	−0.768225	+	0.768225i	0.209569	+	0.977794i	$0.432794\pi$
$294$		0			0
$295$		−	39.1246i		−	2.27792i
$296$	10.1058			0.587389
$297$		0			0
$298$	1.41641	−	1.41641i	0.0820503	−	0.0820503i
$299$	−2.70091			−0.156198
$300$		0			0
$301$	5.70820	+	5.70820i	0.329015	+	0.329015i
$302$	3.24109	+	3.24109i	0.186504	+	0.186504i
$303$		0			0
$304$	5.83282	+	5.83282i	0.334535	+	0.334535i
$305$	−10.5672	−	10.5672i	−0.605076	−	0.605076i
$306$		0			0
$307$	−14.5623	−	14.5623i	−0.831115	−	0.831115i	0.156555	−	0.987669i	$-0.449961\pi$
$307$	−14.5623	−	14.5623i	−0.831115	−	0.831115i	−0.987669	+	0.156555i	$0.949961\pi$
$308$	2.93159	+	2.93159i	0.167043	+	0.167043i
$309$		0			0
$310$	−9.70820			−0.551389
$311$	4.20323	−	4.20323i	0.238344	−	0.238344i	−0.577820	−	0.816164i	$-0.696097\pi$
$311$	4.20323	−	4.20323i	0.238344	−	0.238344i	0.816164	+	0.577820i	$0.196097\pi$
$312$		0			0
$313$	13.0000			0.734803			0.367402	−	0.930062i	$-0.380247\pi$
$313$	13.0000			0.734803			0.367402	+	0.930062i	$0.380247\pi$
$314$			1.62054i			0.0914526i
$315$		0			0
$316$	−18.2705	+	18.2705i	−1.02780	+	1.02780i
$317$	1.04096	+	1.04096i	0.0584660	+	0.0584660i	0.735735	−	0.677269i	$-0.236837\pi$
$317$	1.04096	+	1.04096i	0.0584660	+	0.0584660i	−0.677269	+	0.735735i	$0.736837\pi$
$318$		0			0
$319$	6.70820	+	10.0000i	0.375587	+	0.559893i
$320$			17.4319i			0.974475i
$321$		0			0
$322$	−0.145898	−	0.145898i	−0.00813058	−	0.00813058i
$323$	3.86008			0.214781
$324$		0			0
$325$			43.5410i			2.41522i
$326$		−	0.697804i		−	0.0386478i
$327$		0			0
$328$			8.83282i			0.487711i
$329$	−8.44588	−	8.44588i	−0.465636	−	0.465636i
$330$		0			0
$331$	−19.8541	+	19.8541i	−1.09128	+	1.09128i	−0.0958880	+	0.995392i	$0.530569\pi$
$331$	−19.8541	+	19.8541i	−1.09128	+	1.09128i	−0.995392	+	0.0958880i	$0.969431\pi$
$332$	17.5896			0.965352
$333$		0			0
$334$	6.29180	−	6.29180i	0.344272	−	0.344272i
$335$			54.4565i			2.97528i
$336$		0			0
$337$	9.56231	−	9.56231i	0.520892	−	0.520892i	−0.396949	−	0.917841i	$-0.629931\pi$
$337$	9.56231	−	9.56231i	0.520892	−	0.520892i	0.917841	+	0.396949i	$0.129931\pi$
$338$	−3.24109	+	3.24109i	−0.176292	+	0.176292i
$339$		0			0
$340$	7.14590	+	7.14590i	0.387541	+	0.387541i
$341$	−15.3500			−0.831250
$342$		0			0
$343$	13.0000			0.701934
$344$		−	11.8840i		−	0.640742i
$345$		0			0
$346$	0.291796	−	0.291796i	0.0156871	−	0.0156871i
$347$	−6.86474			−0.368518			−0.184259	−	0.982878i	$-0.558989\pi$
$347$	−6.86474			−0.368518			−0.184259	+	0.982878i	$0.558989\pi$
$348$		0			0
$349$	−3.70820			−0.198496			−0.0992478	−	0.995063i	$-0.531644\pi$
$349$	−3.70820			−0.198496			−0.0992478	+	0.995063i	$0.531644\pi$
$350$	−2.35201	+	2.35201i	−0.125720	+	0.125720i
$351$		0			0
$352$		−	9.27051i		−	0.494120i
$353$	−16.3516			−0.870306			−0.435153	−	0.900356i	$-0.643306\pi$
$353$	−16.3516			−0.870306			−0.435153	+	0.900356i	$0.643306\pi$
$354$		0			0
$355$	6.00000			0.318447
$356$	−23.5258	−	23.5258i	−1.24687	−	1.24687i
$357$		0			0
$358$	−0.145898	+	0.145898i	−0.00771095	+	0.00771095i
$359$	−20.6730	+	20.6730i	−1.09108	+	1.09108i	−0.0956670	+	0.995413i	$0.530498\pi$
$359$	−20.6730	+	20.6730i	−1.09108	+	1.09108i	−0.995413	+	0.0956670i	$0.969502\pi$
$360$		0			0
$361$		−	12.1246i		−	0.638137i
$362$	0.731461	−	0.731461i	0.0384447	−	0.0384447i
$363$		0			0
$364$	9.27051			0.485907
$365$	32.7820	−	32.7820i	1.71589	−	1.71589i
$366$		0			0
$367$	−2.00000	−	2.00000i	−0.104399	−	0.104399i	0.652978	−	0.757377i	$-0.273519\pi$
$367$	−2.00000	−	2.00000i	−0.104399	−	0.104399i	−0.757377	+	0.652978i	$0.773519\pi$
$368$		−	1.69936i		−	0.0885851i
$369$		0			0
$370$			9.70820i			0.504705i
$371$		−	2.62210i		−	0.136132i
$372$		0			0
$373$	−9.70820			−0.502672			−0.251336	−	0.967900i	$-0.580870\pi$
$373$	−9.70820			−0.502672			−0.251336	+	0.967900i	$0.580870\pi$
$374$	−0.889084	−	0.889084i	−0.0459734	−	0.0459734i
$375$		0			0
$376$			17.5836i			0.906805i
$377$	26.4180	+	5.20479i	1.36060	+	0.268060i
$378$		0			0
$379$	1.56231	+	1.56231i	0.0802503	+	0.0802503i	0.746093	−	0.665842i	$-0.231928\pi$
$379$	1.56231	+	1.56231i	0.0802503	+	0.0802503i	−0.665842	+	0.746093i	$0.731928\pi$
$380$	−12.7279	+	12.7279i	−0.652929	+	0.652929i
$381$		0			0
$382$		−	9.70820i		−	0.496715i
$383$	−6.94355			−0.354799			−0.177399	−	0.984139i	$-0.556768\pi$
$383$	−6.94355			−0.354799			−0.177399	+	0.984139i	$0.556768\pi$
$384$		0			0
$385$	−5.85410	+	5.85410i	−0.298353	+	0.298353i
$386$	0.382559			0.0194717
$387$		0			0
$388$	7.68692	+	7.68692i	0.390244	+	0.390244i
$389$	−3.20168	−	3.20168i	−0.162332	−	0.162332i	0.621267	−	0.783599i	$-0.286618\pi$
$389$	−3.20168	−	3.20168i	−0.162332	−	0.162332i	−0.783599	+	0.621267i	$0.786618\pi$
$390$		0			0
$391$	−0.562306	−	0.562306i	−0.0284370	−	0.0284370i
$392$	−6.24574	−	6.24574i	−0.315458	−	0.315458i
$393$		0			0
$394$	5.83282	+	5.83282i	0.293853	+	0.293853i
$395$	−36.4844	−	36.4844i	−1.83573	−	1.83573i
$396$		0			0
$397$	12.0000			0.602263			0.301131	−	0.953583i	$-0.402636\pi$
$397$	12.0000			0.602263			0.301131	+	0.953583i	$0.402636\pi$
$398$	2.50963	−	2.50963i	0.125796	−	0.125796i
$399$		0			0
$400$	−27.3951			−1.36976
$401$		−	20.6730i		−	1.03236i	−0.856480	−	0.516181i	$-0.827353\pi$
$401$		−	20.6730i		−	1.03236i	0.856480	−	0.516181i	$-0.172647\pi$
$402$		0			0
$403$	−24.2705	+	24.2705i	−1.20900	+	1.20900i
$404$	−9.79633	−	9.79633i	−0.487386	−	0.487386i
$405$		0			0
$406$	1.14590	+	1.70820i	0.0568700	+	0.0847767i
$407$			15.3500i			0.760872i
$408$		0			0
$409$	6.70820	+	6.70820i	0.331699	+	0.331699i	0.853232	−	0.521532i	$-0.174639\pi$
$409$	6.70820	+	6.70820i	0.331699	+	0.331699i	−0.521532	+	0.853232i	$0.674639\pi$
$410$	−8.48528			−0.419058
$411$		0			0
$412$		−	22.2492i		−	1.09614i
$413$		−	10.5672i		−	0.519978i
$414$		0			0
$415$			35.1246i			1.72420i
$416$	−14.6580	−	14.6580i	−0.718666	−	0.718666i
$417$		0			0
$418$	1.58359	−	1.58359i	0.0774560	−	0.0774560i
$419$	20.5154			1.00224			0.501121	−	0.865377i	$-0.332921\pi$
$419$	20.5154			1.00224			0.501121	+	0.865377i	$0.332921\pi$
$420$		0			0
$421$	2.70820	−	2.70820i	0.131990	−	0.131990i	−0.638025	−	0.770015i	$-0.720249\pi$
$421$	2.70820	−	2.70820i	0.131990	−	0.131990i	0.770015	+	0.638025i	$0.220249\pi$
$422$			0.382559i			0.0186227i
$423$		0			0
$424$	−2.72949	+	2.72949i	−0.132556	+	0.132556i
$425$	−9.06487	+	9.06487i	−0.439711	+	0.439711i
$426$		0			0
$427$	−2.85410	−	2.85410i	−0.138120	−	0.138120i
$428$	2.85853			0.138172
$429$		0			0
$430$	11.4164			0.550548
$431$			20.0540i			0.965969i	0.875629	+	0.482984i	$0.160447\pi$
$431$			20.0540i			0.965969i	−0.875629	+	0.482984i	$0.839553\pi$
$432$		0			0
$433$	−8.14590	+	8.14590i	−0.391467	+	0.391467i	−0.875210	−	0.483743i	$-0.839277\pi$
$433$	−8.14590	+	8.14590i	−0.391467	+	0.391467i	0.483743	+	0.875210i	$0.339277\pi$
$434$	−2.62210			−0.125865
$435$		0			0
$436$	−23.0213			−1.10252
$437$	1.00155	−	1.00155i	0.0479107	−	0.0479107i
$438$		0			0
$439$			16.7082i			0.797439i	0.917073	+	0.398720i	$0.130545\pi$
$439$			16.7082i			0.797439i	−0.917073	+	0.398720i	$0.869455\pi$
$440$	12.1877			0.581028
$441$		0			0
$442$	−2.81153			−0.133731
$443$	23.8747	+	23.8747i	1.13432	+	1.13432i	0.989451	+	0.144871i	$0.0462767\pi$
$443$	23.8747	+	23.8747i	1.13432	+	1.13432i	0.144871	+	0.989451i	$0.453723\pi$
$444$		0			0
$445$	46.9787	−	46.9787i	2.22700	−	2.22700i
$446$	3.58999	−	3.58999i	0.169991	−	0.169991i
$447$		0			0
$448$			4.70820i			0.222442i
$449$	−22.7943	+	22.7943i	−1.07573	+	1.07573i	−0.0788446	+	0.996887i	$0.525123\pi$
$449$	−22.7943	+	22.7943i	−1.07573	+	1.07573i	−0.996887	+	0.0788446i	$0.974877\pi$
$450$		0			0
$451$	−13.4164			−0.631754
$452$	−7.79323	+	7.79323i	−0.366563	+	0.366563i
$453$		0			0
$454$	−2.56231	−	2.56231i	−0.120255	−	0.120255i
$455$			18.5123i			0.867870i
$456$		0			0
$457$			18.1246i			0.847834i	0.905701	+	0.423917i	$0.139345\pi$
$457$			18.1246i			0.847834i	−0.905701	+	0.423917i	$0.860655\pi$
$458$			7.48373i			0.349692i
$459$		0			0
$460$	3.70820			0.172896
$461$	9.48683	+	9.48683i	0.441846	+	0.441846i	0.892632	−	0.450786i	$-0.148856\pi$
$461$	9.48683	+	9.48683i	0.441846	+	0.441846i	−0.450786	+	0.892632i	$0.648856\pi$
$462$		0			0
$463$		−	9.29180i		−	0.431826i	−0.976413	−	0.215913i	$-0.930727\pi$
$463$		−	9.29180i		−	0.431826i	0.976413	−	0.215913i	$-0.0692728\pi$
$464$	−3.27475	+	16.6217i	−0.152026	+	0.771641i
$465$		0			0
$466$	−5.14590	−	5.14590i	−0.238379	−	0.238379i
$467$	16.9706	−	16.9706i	0.785304	−	0.785304i	−0.195416	−	0.980720i	$-0.562606\pi$
$467$	16.9706	−	16.9706i	0.785304	−	0.785304i	0.980720	+	0.195416i	$0.0626058\pi$
$468$		0			0
$469$			14.7082i			0.679162i
$470$	−16.8918			−0.779158
$471$		0			0
$472$	−11.0000	+	11.0000i	−0.506316	+	0.506316i
$473$	18.0509			0.829982
$474$		0			0
$475$	−16.1459	−	16.1459i	−0.740825	−	0.740825i
$476$	1.93004	+	1.93004i	0.0884633	+	0.0884633i
$477$		0			0
$478$	−4.41641	−	4.41641i	−0.202002	−	0.202002i
$479$	1.54173	+	1.54173i	0.0704436	+	0.0704436i	0.741451	−	0.671007i	$-0.234138\pi$
$479$	1.54173	+	1.54173i	0.0704436	+	0.0704436i	−0.671007	+	0.741451i	$0.734138\pi$
$480$		0			0
$481$	24.2705	+	24.2705i	1.10664	+	1.10664i
$482$	−1.27164	−	1.27164i	−0.0579217	−	0.0579217i
$483$		0			0
$484$	−11.1246			−0.505664
$485$	−15.3500	+	15.3500i	−0.697008	+	0.697008i
$486$		0			0
$487$	14.8328			0.672139			0.336070	−	0.941837i	$-0.390902\pi$
$487$	14.8328			0.672139			0.336070	+	0.941837i	$0.390902\pi$
$488$			5.94200i			0.268982i
$489$		0			0
$490$	6.00000	−	6.00000i	0.271052	−	0.271052i
$491$	9.48683	+	9.48683i	0.428135	+	0.428135i	0.887993	−	0.459858i	$-0.152100\pi$
$491$	9.48683	+	9.48683i	0.428135	+	0.428135i	−0.459858	+	0.887993i	$0.652100\pi$
$492$		0			0
$493$	4.41641	+	6.58359i	0.198905	+	0.296510i
$494$		−	5.00776i		−	0.225310i
$495$		0			0
$496$	−15.2705	−	15.2705i	−0.685666	−	0.685666i
$497$	1.62054			0.0726914
$498$		0			0
$499$		−	1.29180i		−	0.0578287i	−0.999582	−	0.0289144i	$-0.990795\pi$
$499$		−	1.29180i		−	0.0578287i	0.999582	−	0.0289144i	$-0.00920501\pi$
$500$		−	25.4558i		−	1.13842i
$501$		0			0
$502$		−	8.31308i		−	0.371031i
$503$	−27.4984	−	27.4984i	−1.22609	−	1.22609i	−0.965431	−	0.260660i	$-0.916060\pi$
$503$	−27.4984	−	27.4984i	−1.22609	−	1.22609i	−0.260660	−	0.965431i	$-0.583940\pi$
$504$		0			0
$505$	19.5623	−	19.5623i	0.870511	−	0.870511i
$506$	−0.461370			−0.0205104
$507$		0			0
$508$	12.4377	−	12.4377i	0.551833	−	0.551833i
$509$		−	2.08191i		−	0.0922792i	−0.998935	−	0.0461396i	$-0.985308\pi$
$509$		−	2.08191i		−	0.0922792i	0.998935	−	0.0461396i	$-0.0146919\pi$
$510$		0			0
$511$	8.85410	−	8.85410i	0.391682	−	0.391682i
$512$	15.7720	−	15.7720i	0.697030	−	0.697030i
$513$		0			0
$514$	−6.00000	−	6.00000i	−0.264649	−	0.264649i
$515$	44.4295			1.95780
$516$		0			0
$517$	−26.7082			−1.17463
$518$			2.62210i			0.115208i
$519$		0			0
$520$	19.2705	−	19.2705i	0.845068	−	0.845068i
$521$	25.2982			1.10834			0.554168	−	0.832405i	$-0.313037\pi$
$521$	25.2982			1.10834			0.554168	+	0.832405i	$0.313037\pi$
$522$		0			0
$523$	7.29180			0.318848			0.159424	−	0.987210i	$-0.449036\pi$
$523$	7.29180			0.318848			0.159424	+	0.987210i	$0.449036\pi$
$524$	10.7979	−	10.7979i	0.471708	−	0.471708i
$525$		0			0
$526$		−	4.58359i		−	0.199854i
$527$	−10.1058			−0.440217
$528$		0			0
$529$	22.7082			0.987313
$530$	−2.62210	−	2.62210i	−0.113897	−	0.113897i
$531$		0			0
$532$	−3.43769	+	3.43769i	−0.149043	+	0.149043i
$533$	−21.2132	+	21.2132i	−0.918846	+	0.918846i
$534$		0			0
$535$			5.70820i			0.246787i
$536$	15.3106	−	15.3106i	0.661318	−	0.661318i
$537$		0			0
$538$	−8.85410			−0.381727
$539$	9.48683	−	9.48683i	0.408627	−	0.408627i
$540$		0			0
$541$	−5.27051	−	5.27051i	−0.226597	−	0.226597i	0.584673	−	0.811269i	$-0.301223\pi$
$541$	−5.27051	−	5.27051i	−0.226597	−	0.226597i	−0.811269	+	0.584673i	$0.801223\pi$
$542$		−	9.94820i		−	0.427312i
$543$		0			0
$544$		−	6.10333i		−	0.261678i
$545$		−	45.9712i		−	1.96919i
$546$		0			0
$547$	20.4164			0.872943			0.436471	−	0.899718i	$-0.356228\pi$
$547$	20.4164			0.872943			0.436471	+	0.899718i	$0.356228\pi$
$548$	4.86163	+	4.86163i	0.207679	+	0.207679i
$549$		0			0
$550$			7.43769i			0.317144i
$551$	−11.7264	+	7.86629i	−0.499560	+	0.335115i
$552$		0			0
$553$	−9.85410	−	9.85410i	−0.419039	−	0.419039i
$554$	−0.731461	+	0.731461i	−0.0310768	+	0.0310768i
$555$		0			0
$556$			19.8541i			0.842001i
$557$	34.9427			1.48057			0.740284	−	0.672294i	$-0.234691\pi$
$557$	34.9427			1.48057			0.740284	+	0.672294i	$0.234691\pi$
$558$		0			0
$559$	28.5410	−	28.5410i	1.20716	−	1.20716i
$560$	−11.6476			−0.492199
$561$		0			0
$562$	7.14590	+	7.14590i	0.301432	+	0.301432i
$563$	−12.6885	−	12.6885i	−0.534757	−	0.534757i	0.387227	−	0.921984i	$-0.373433\pi$
$563$	−12.6885	−	12.6885i	−0.534757	−	0.534757i	−0.921984	+	0.387227i	$0.873433\pi$
$564$		0			0
$565$	−15.5623	−	15.5623i	−0.654711	−	0.654711i
$566$	4.24264	+	4.24264i	0.178331	+	0.178331i
$567$		0			0
$568$	−1.68692	−	1.68692i	−0.0707815	−	0.0707815i
$569$	25.8778	+	25.8778i	1.08485	+	1.08485i	0.996049	+	0.0888051i	$0.0283048\pi$
$569$	25.8778	+	25.8778i	1.08485	+	1.08485i	0.0888051	+	0.996049i	$0.471695\pi$
$570$		0			0
$571$	−11.1246			−0.465551			−0.232775	−	0.972531i	$-0.574781\pi$
$571$	−11.1246			−0.465551			−0.232775	+	0.972531i	$0.574781\pi$
$572$	14.6580	−	14.6580i	0.612880	−	0.612880i
$573$		0			0
$574$	−2.29180			−0.0956577
$575$			4.70401i			0.196171i
$576$		0			0
$577$	19.1246	−	19.1246i	0.796168	−	0.796168i	−0.186321	−	0.982489i	$-0.559656\pi$
$577$	19.1246	−	19.1246i	0.796168	−	0.796168i	0.982489	+	0.186321i	$0.0596564\pi$
$578$	4.00621	+	4.00621i	0.166636	+	0.166636i
$579$		0			0
$580$	−36.2705	−	7.14590i	−1.50605	−	0.296717i
$581$			9.48683i			0.393580i
$582$		0			0
$583$	−4.14590	−	4.14590i	−0.171706	−	0.171706i
$584$	−18.4335			−0.762783
$585$		0			0
$586$			7.10333i			0.293436i
$587$			6.40337i			0.264295i	0.991230	+	0.132148i	$0.0421873\pi$
$587$			6.40337i			0.264295i	−0.991230	+	0.132148i	$0.957813\pi$
$588$		0			0
$589$		−	18.0000i		−	0.741677i
$590$	−10.5672	−	10.5672i	−0.435045	−	0.435045i
$591$		0			0
$592$	−15.2705	+	15.2705i	−0.627614	+	0.627614i
$593$	−3.70246			−0.152042			−0.0760209	−	0.997106i	$-0.524222\pi$
$593$	−3.70246			−0.152042			−0.0760209	+	0.997106i	$0.524222\pi$
$594$		0			0
$595$	−3.85410	+	3.85410i	−0.158003	+	0.158003i
$596$			9.72327i			0.398281i
$597$		0			0
$598$	−0.729490	+	0.729490i	−0.0298311	+	0.0298311i
$599$	0.579587	−	0.579587i	0.0236813	−	0.0236813i	−0.695167	−	0.718848i	$-0.744670\pi$
$599$	0.579587	−	0.579587i	0.0236813	−	0.0236813i	0.718848	+	0.695167i	$0.244670\pi$
$600$		0			0
$601$	−21.2705	−	21.2705i	−0.867642	−	0.867642i	0.124569	−	0.992211i	$-0.460245\pi$
$601$	−21.2705	−	21.2705i	−0.867642	−	0.867642i	−0.992211	+	0.124569i	$0.960245\pi$
$602$	3.08347			0.125673
$603$		0			0
$604$	−22.2492			−0.905308
$605$		−	22.2148i		−	0.903158i
$606$		0			0
$607$	−1.58359	+	1.58359i	−0.0642760	+	0.0642760i	−0.738514	−	0.674238i	$-0.764472\pi$
$607$	−1.58359	+	1.58359i	−0.0642760	+	0.0642760i	0.674238	+	0.738514i	$0.264472\pi$
$608$	10.8709			0.440875
$609$		0			0
$610$	−5.70820			−0.231118
$611$	−42.2294	+	42.2294i	−1.70842	+	1.70842i
$612$		0			0
$613$		−	14.4164i		−	0.582273i	−0.956681	−	0.291137i	$-0.905967\pi$
$613$		−	14.4164i		−	0.582273i	0.956681	−	0.291137i	$-0.0940334\pi$
$614$	−7.86629			−0.317458
$615$		0			0
$616$	3.29180			0.132630
$617$	16.3516	+	16.3516i	0.658289	+	0.658289i	0.954975	−	0.296686i	$-0.0958814\pi$
$617$	16.3516	+	16.3516i	0.658289	+	0.658289i	−0.296686	+	0.954975i	$0.595881\pi$
$618$		0			0
$619$	−17.2705	+	17.2705i	−0.694160	+	0.694160i	−0.963145	−	0.268984i	$-0.913312\pi$
$619$	−17.2705	+	17.2705i	−0.694160	+	0.694160i	0.268984	+	0.963145i	$0.413312\pi$
$620$	33.3221	−	33.3221i	1.33825	−	1.33825i
$621$		0			0
$622$		−	2.27051i		−	0.0910392i
$623$	12.6885	−	12.6885i	0.508355	−	0.508355i
$624$		0			0
$625$	7.29180			0.291672
$626$	3.51118	−	3.51118i	0.140335	−	0.140335i
$627$		0			0
$628$	−5.56231	−	5.56231i	−0.221960	−	0.221960i
$629$			10.1058i			0.402946i
$630$		0			0
$631$		−	16.7082i		−	0.665143i	−0.943078	−	0.332572i	$-0.892084\pi$
$631$		−	16.7082i		−	0.665143i	0.943078	−	0.332572i	$-0.107916\pi$
$632$			20.5154i			0.816059i
$633$		0			0
$634$	0.562306			0.0223320
$635$	24.8369	+	24.8369i	0.985620	+	0.985620i
$636$		0			0
$637$		−	30.0000i		−	1.18864i
$638$	4.51273	+	0.889084i	0.178661	+	0.0351992i
$639$		0			0
$640$	26.4164	+	26.4164i	1.04420	+	1.04420i
$641$	−20.6336	+	20.6336i	−0.814979	+	0.814979i	−0.985376	−	0.170397i	$-0.945495\pi$
$641$	−20.6336	+	20.6336i	−0.814979	+	0.814979i	0.170397	+	0.985376i	$0.445495\pi$
$642$		0			0
$643$			32.7082i			1.28989i	0.764231	+	0.644943i	$0.223119\pi$
$643$			32.7082i			1.28989i	−0.764231	+	0.644943i	$0.776881\pi$
$644$	1.00155			0.0394667
$645$		0			0
$646$	1.04257	−	1.04257i	0.0410195	−	0.0410195i
$647$	−36.4844			−1.43435			−0.717175	−	0.696893i	$-0.754565\pi$
$647$	−36.4844			−1.43435			−0.717175	+	0.696893i	$0.754565\pi$
$648$		0			0
$649$	−16.7082	−	16.7082i	−0.655854	−	0.655854i
$650$	11.7600	+	11.7600i	0.461266	+	0.461266i
$651$		0			0
$652$	2.39512	+	2.39512i	0.0938002	+	0.0938002i
$653$	6.90414	+	6.90414i	0.270180	+	0.270180i	0.829173	−	0.558993i	$-0.188812\pi$
$653$	6.90414	+	6.90414i	0.270180	+	0.270180i	−0.558993	+	0.829173i	$0.688812\pi$
$654$		0			0
$655$	21.5623	+	21.5623i	0.842509	+	0.842509i
$656$	−13.3469	−	13.3469i	−0.521109	−	0.521109i
$657$		0			0
$658$	−4.56231			−0.177857
$659$	4.20323	−	4.20323i	0.163735	−	0.163735i	−0.620484	−	0.784219i	$-0.713064\pi$
$659$	4.20323	−	4.20323i	0.163735	−	0.163735i	0.784219	+	0.620484i	$0.213064\pi$
$660$		0			0
$661$	13.2918			0.516991			0.258495	−	0.966012i	$-0.416773\pi$
$661$	13.2918			0.516991			0.258495	+	0.966012i	$0.416773\pi$
$662$			10.7248i			0.416832i
$663$		0			0
$664$	9.87539	−	9.87539i	0.383239	−	0.383239i
$665$	−6.86474	−	6.86474i	−0.266203	−	0.266203i
$666$		0			0
$667$	2.85410	+	0.562306i	0.110511	+	0.0217726i
$668$			43.1915i			1.67113i
$669$		0			0
$670$	14.7082	+	14.7082i	0.568227	+	0.568227i
$671$	−9.02546			−0.348424
$672$		0			0
$673$		−	36.1246i		−	1.39250i	−0.717799	−	0.696251i	$-0.754850\pi$
$673$		−	36.1246i		−	1.39250i	0.717799	−	0.696251i	$-0.245150\pi$
$674$		−	5.16538i		−	0.198963i
$675$		0			0
$676$		−	22.2492i		−	0.855739i
$677$	0.0394057	+	0.0394057i	0.00151448	+	0.00151448i	0.707864	−	0.706349i	$-0.249659\pi$
$677$	0.0394057	+	0.0394057i	0.00151448	+	0.00151448i	−0.706349	+	0.707864i	$0.749659\pi$
$678$		0			0
$679$	−4.14590	+	4.14590i	−0.159105	+	0.159105i
$680$	8.02391			0.307703
$681$		0			0
$682$	−4.14590	+	4.14590i	−0.158755	+	0.158755i
$683$		−	44.4295i		−	1.70005i	−0.526744	−	0.850024i	$-0.676587\pi$
$683$		−	44.4295i		−	1.70005i	0.526744	−	0.850024i	$-0.323413\pi$
$684$		0			0
$685$	−9.70820	+	9.70820i	−0.370931	+	0.370931i
$686$	3.51118	−	3.51118i	0.134057	−	0.134057i
$687$		0			0
$688$	17.9574	+	17.9574i	0.684621	+	0.684621i
$689$	−13.1105			−0.499470
$690$		0			0
$691$	39.2492			1.49311			0.746555	−	0.665323i	$-0.231706\pi$
$691$	39.2492			1.49311			0.746555	+	0.665323i	$0.231706\pi$
$692$			2.00310i			0.0761466i
$693$		0			0
$694$	−1.85410	+	1.85410i	−0.0703807	+	0.0703807i
$695$	−39.6467			−1.50388
$696$		0			0
$697$	−8.83282			−0.334567
$698$	−1.00155	+	1.00155i	−0.0379093	+	0.0379093i
$699$		0			0
$700$		−	16.1459i		−	0.610258i
$701$	−18.5911			−0.702176			−0.351088	−	0.936342i	$-0.614188\pi$
$701$	−18.5911			−0.702176			−0.351088	+	0.936342i	$0.614188\pi$
$702$		0			0
$703$	−18.0000			−0.678883
$704$	7.44432	+	7.44432i	0.280569	+	0.280569i
$705$		0			0
$706$	−4.41641	+	4.41641i	−0.166214	+	0.166214i
$707$	5.28360	−	5.28360i	0.198710	−	0.198710i
$708$		0			0
$709$			44.8328i			1.68373i	0.539687	+	0.841866i	$0.318543\pi$
$709$			44.8328i			1.68373i	−0.539687	+	0.841866i	$0.681457\pi$
$710$	1.62054	−	1.62054i	0.0608180	−	0.0608180i
$711$		0			0
$712$	−26.4164			−0.989997
$713$	−2.62210	+	2.62210i	−0.0981983	+	0.0981983i
$714$		0			0
$715$	29.2705	+	29.2705i	1.09466	+	1.09466i
$716$		−	1.00155i		−	0.0374297i
$717$		0			0
$718$			11.1672i			0.416756i
$719$		−	0.157623i		−	0.00587834i	−0.999996	−	0.00293917i	$-0.999064\pi$
$719$		−	0.157623i		−	0.00587834i	0.999996	−	0.00293917i	$-0.000935568\pi$
$720$		0			0
$721$	12.0000			0.446903
$722$	−3.27475	−	3.27475i	−0.121873	−	0.121873i
$723$		0			0
$724$			5.02129i			0.186615i
$725$	9.06487	−	46.0106i	0.336661	−	1.70879i
$726$		0			0
$727$	36.8541	+	36.8541i	1.36684	+	1.36684i	0.864902	+	0.501941i	$0.167381\pi$
$727$	36.8541	+	36.8541i	1.36684	+	1.36684i	0.501941	+	0.864902i	$0.332619\pi$
$728$	5.20479	−	5.20479i	0.192902	−	0.192902i
$729$		0			0
$730$		−	17.7082i		−	0.655410i
$731$	11.8840			0.439545
$732$		0			0
$733$	−11.4164	+	11.4164i	−0.421675	+	0.421675i	−0.885780	−	0.464105i	$-0.846376\pi$
$733$	−11.4164	+	11.4164i	−0.421675	+	0.421675i	0.464105	+	0.885780i	$0.346376\pi$
$734$	−1.08036			−0.0398769
$735$		0			0
$736$	−1.58359	−	1.58359i	−0.0583720	−	0.0583720i
$737$	23.2557	+	23.2557i	0.856635	+	0.856635i
$738$		0			0
$739$	−24.2705	−	24.2705i	−0.892805	−	0.892805i	0.101981	−	0.994786i	$-0.467482\pi$
$739$	−24.2705	−	24.2705i	−0.892805	−	0.892805i	−0.994786	+	0.101981i	$0.967482\pi$
$740$	−33.3221	−	33.3221i	−1.22495	−	1.22495i
$741$		0			0
$742$	−0.708204	−	0.708204i	−0.0259990	−	0.0259990i
$743$	13.6901	+	13.6901i	0.502240	+	0.502240i	0.912133	−	0.409894i	$-0.134434\pi$
$743$	13.6901	+	13.6901i	0.502240	+	0.502240i	−0.409894	+	0.912133i	$0.634434\pi$
$744$		0			0
$745$	−19.4164			−0.711362
$746$	−2.62210	+	2.62210i	−0.0960018	+	0.0960018i
$747$		0			0
$748$	6.10333			0.223160
$749$			1.54173i			0.0563337i
$750$		0			0
$751$	1.41641	−	1.41641i	0.0516855	−	0.0516855i	−0.680792	−	0.732477i	$-0.738364\pi$
$751$	1.41641	−	1.41641i	0.0516855	−	0.0516855i	0.732477	+	0.680792i	$0.238364\pi$
$752$	−26.5699	−	26.5699i	−0.968903	−	0.968903i
$753$		0			0
$754$	8.54102	−	5.72949i	0.311046	−	0.208656i
$755$		−	44.4295i		−	1.61696i
$756$		0			0
$757$	5.70820	+	5.70820i	0.207468	+	0.207468i	0.803190	−	0.595722i	$-0.203134\pi$
$757$	5.70820	+	5.70820i	0.207468	+	0.207468i	−0.595722	+	0.803190i	$0.703134\pi$
$758$	0.843929			0.0306529
$759$		0			0
$760$			14.2918i			0.518418i
$761$			13.2681i			0.480968i	0.970653	+	0.240484i	$0.0773062\pi$
$761$			13.2681i			0.480968i	−0.970653	+	0.240484i	$0.922694\pi$
$762$		0			0
$763$		−	12.4164i		−	0.449504i
$764$	33.3221	+	33.3221i	1.20555	+	1.20555i
$765$		0			0
$766$	−1.87539	+	1.87539i	−0.0677605	+	0.0677605i
$767$	−52.8360			−1.90780
$768$		0			0
$769$	−32.5623	+	32.5623i	−1.17423	+	1.17423i	−0.193035	+	0.981192i	$0.561833\pi$
$769$	−32.5623	+	32.5623i	−1.17423	+	1.17423i	−0.981192	+	0.193035i	$0.938167\pi$
$770$			3.16228i			0.113961i
$771$		0			0
$772$	−1.31308	+	1.31308i	−0.0472589	+	0.0472589i
$773$	−16.3516	+	16.3516i	−0.588125	+	0.588125i	−0.937123	−	0.348998i	$-0.886522\pi$
$773$	−16.3516	+	16.3516i	−0.588125	+	0.588125i	0.348998	+	0.937123i	$0.386522\pi$
$774$		0			0
$775$	42.2705	+	42.2705i	1.51840	+	1.51840i
$776$	8.63141			0.309849
$777$		0			0
$778$	−1.72949			−0.0620052
$779$		−	15.7326i		−	0.563678i
$780$		0			0
$781$	2.56231	−	2.56231i	0.0916865	−	0.0916865i
$782$	−0.303747			−0.0108620
$783$		0			0
$784$	18.8754			0.674121
$785$	11.1074	−	11.1074i	0.396439	−	0.396439i
$786$		0			0
$787$			17.1246i			0.610426i	0.952284	+	0.305213i	$0.0987277\pi$
$787$			17.1246i			0.610426i	−0.952284	+	0.305213i	$0.901272\pi$
$788$	−40.0407			−1.42639
$789$		0			0
$790$	−19.7082			−0.701186
$791$	−4.20323	−	4.20323i	−0.149450	−	0.149450i
$792$		0			0
$793$	−14.2705	+	14.2705i	−0.506761	+	0.506761i
$794$	3.24109	−	3.24109i	0.115022	−	0.115022i
$795$		0			0
$796$			17.2279i			0.610628i
$797$	−12.7279	+	12.7279i	−0.450846	+	0.450846i	−0.895635	−	0.444789i	$-0.853279\pi$
$797$	−12.7279	+	12.7279i	−0.450846	+	0.450846i	0.444789	+	0.895635i	$0.353279\pi$
$798$		0			0
$799$	−17.5836			−0.622063
$800$	−25.5289	+	25.5289i	−0.902583	+	0.902583i
$801$		0			0
$802$	−5.58359	−	5.58359i	−0.197163	−	0.197163i
$803$		−	27.9991i		−	0.988068i
$804$		0			0
$805$			2.00000i			0.0704907i
$806$			13.1105i			0.461797i
$807$		0			0
$808$	−11.0000			−0.386979
$809$	3.66305	+	3.66305i	0.128786	+	0.128786i	0.768562	−	0.639776i	$-0.220973\pi$
$809$	3.66305	+	3.66305i	0.128786	+	0.128786i	−0.639776	+	0.768562i	$0.720973\pi$
$810$		0			0
$811$			39.8328i			1.39872i	0.714770	+	0.699360i	$0.246531\pi$
$811$			39.8328i			1.39872i	−0.714770	+	0.699360i	$0.753469\pi$
$812$	−9.79633	−	1.93004i	−0.343784	−	0.0677312i
$813$		0			0
$814$	4.14590	+	4.14590i	0.145314	+	0.145314i
$815$	−4.78282	+	4.78282i	−0.167535	+	0.167535i
$816$		0			0
$817$			21.1672i			0.740546i
$818$	3.62365			0.126698
$819$		0			0
$820$	29.1246	−	29.1246i	1.01708	−	1.01708i
$821$	53.9163			1.88169			0.940847	−	0.338833i	$-0.110032\pi$
$821$	53.9163			1.88169			0.940847	+	0.338833i	$0.110032\pi$
$822$		0			0
$823$	−39.1246	−	39.1246i	−1.36380	−	1.36380i	−0.869018	−	0.494780i	$-0.835249\pi$
$823$	−39.1246	−	39.1246i	−1.36380	−	1.36380i	−0.494780	−	0.869018i	$-0.664751\pi$
$824$	−12.4915	−	12.4915i	−0.435162	−	0.435162i
$825$		0			0
$826$	−2.85410	−	2.85410i	−0.0993069	−	0.0993069i
$827$	−1.00155	−	1.00155i	−0.0348274	−	0.0348274i	0.689479	−	0.724306i	$-0.257840\pi$
$827$	−1.00155	−	1.00155i	−0.0348274	−	0.0348274i	−0.724306	+	0.689479i	$0.757840\pi$
$828$		0			0
$829$	−3.41641	−	3.41641i	−0.118657	−	0.118657i	0.645285	−	0.763942i	$-0.276739\pi$
$829$	−3.41641	−	3.41641i	−0.118657	−	0.118657i	−0.763942	+	0.645285i	$0.776739\pi$
$830$	9.48683	+	9.48683i	0.329293	+	0.329293i
$831$		0			0
$832$	23.5410			0.816138
$833$	6.24574	−	6.24574i	0.216402	−	0.216402i
$834$		0			0
$835$	−86.2492			−2.98478
$836$			10.8709i			0.375979i
$837$		0			0
$838$	5.54102	−	5.54102i	0.191411	−	0.191411i
$839$	5.90259	+	5.90259i	0.203780	+	0.203780i	0.801617	−	0.597837i	$-0.203973\pi$
$839$	5.90259	+	5.90259i	0.203780	+	0.203780i	−0.597837	+	0.801617i	$0.703973\pi$
$840$		0			0
$841$	−26.8328	−	11.0000i	−0.925270	−	0.379310i
$842$		−	1.46292i		−	0.0504156i
$843$		0			0
$844$	−1.31308	−	1.31308i	−0.0451982	−	0.0451982i
$845$	44.4295			1.52842
$846$		0			0
$847$		−	6.00000i		−	0.206162i
$848$		−	8.24885i		−	0.283267i
$849$		0			0
$850$			4.89667i			0.167955i
$851$	2.62210	+	2.62210i	0.0898843	+	0.0898843i
$852$		0			0
$853$	10.0000	−	10.0000i	0.342393	−	0.342393i	−0.514873	−	0.857266i	$-0.672161\pi$
$853$	10.0000	−	10.0000i	0.342393	−	0.342393i	0.857266	+	0.514873i	$0.172161\pi$
$854$	−1.54173			−0.0527570
$855$		0			0
$856$	1.60488	−	1.60488i	0.0548536	−	0.0548536i
$857$			19.5927i			0.669272i	0.942347	+	0.334636i	$0.108613\pi$
$857$			19.5927i			0.669272i	−0.942347	+	0.334636i	$0.891387\pi$
$858$		0			0
$859$	3.58359	−	3.58359i	0.122271	−	0.122271i	−0.643324	−	0.765594i	$-0.722445\pi$
$859$	3.58359	−	3.58359i	0.122271	−	0.122271i	0.765594	+	0.643324i	$0.222445\pi$
$860$	−39.1853	+	39.1853i	−1.33621	+	1.33621i
$861$		0			0
$862$	5.41641	+	5.41641i	0.184484	+	0.184484i
$863$	−3.62365			−0.123350			−0.0616752	−	0.998096i	$-0.519644\pi$
$863$	−3.62365			−0.123350			−0.0616752	+	0.998096i	$0.519644\pi$
$864$		0			0
$865$	−4.00000			−0.136004
$866$			4.40026i			0.149527i
$867$		0			0
$868$	9.00000	−	9.00000i	0.305480	−	0.305480i
$869$	−31.1614			−1.05708
$870$		0			0
$871$	73.5410			2.49184
$872$	−12.9250	+	12.9250i	−0.437694	+	0.437694i
$873$		0			0
$874$		−	0.541020i		−	0.0183003i
$875$	13.7295			0.464141
$876$		0			0
$877$	14.2918			0.482600			0.241300	−	0.970451i	$-0.422426\pi$
$877$	14.2918			0.482600			0.241300	+	0.970451i	$0.422426\pi$
$878$	4.51273	+	4.51273i	0.152297	+	0.152297i
$879$		0			0
$880$	−18.4164	+	18.4164i	−0.620817	+	0.620817i
$881$	−4.66461	+	4.66461i	−0.157155	+	0.157155i	−0.781305	−	0.624150i	$-0.785445\pi$
$881$	−4.66461	+	4.66461i	−0.157155	+	0.157155i	0.624150	+	0.781305i	$0.285445\pi$
$882$		0			0
$883$		−	14.2918i		−	0.480957i	−0.970654	−	0.240479i	$-0.922696\pi$
$883$		−	14.2918i		−	0.480957i	0.970654	−	0.240479i	$-0.0773044\pi$
$884$	9.65021	−	9.65021i	0.324572	−	0.324572i
$885$		0			0
$886$	12.8967			0.433272
$887$	−30.0416	+	30.0416i	−1.00870	+	1.00870i	−0.00873765	+	0.999962i	$0.502781\pi$
$887$	−30.0416	+	30.0416i	−1.00870	+	1.00870i	−0.999962	+	0.00873765i	$0.997219\pi$
$888$		0			0
$889$	6.70820	+	6.70820i	0.224986	+	0.224986i
$890$		−	25.3770i		−	0.850640i
$891$		0			0
$892$			24.6443i			0.825154i
$893$		−	31.3190i		−	1.04805i
$894$		0			0
$895$	2.00000			0.0668526
$896$	7.13483	+	7.13483i	0.238358	+	0.238358i
$897$		0			0
$898$			12.3131i			0.410893i
$899$	30.7000	−	20.5942i	1.02390	−	0.686855i
$900$		0			0
$901$	−2.72949	−	2.72949i	−0.0909325	−	0.0909325i
$902$	−3.62365	+	3.62365i	−0.120654	+	0.120654i
$903$		0			0
$904$			8.75078i			0.291046i
$905$	−10.0270			−0.333309
$906$		0			0
$907$	−2.41641	+	2.41641i	−0.0802355	+	0.0802355i	−0.746086	−	0.665850i	$-0.768069\pi$
$907$	−2.41641	+	2.41641i	−0.0802355	+	0.0802355i	0.665850	+	0.746086i	$0.268069\pi$
$908$	17.5896			0.583730
$909$		0			0
$910$	5.00000	+	5.00000i	0.165748	+	0.165748i
$911$	−5.28360	−	5.28360i	−0.175053	−	0.175053i	0.614142	−	0.789195i	$-0.289502\pi$
$911$	−5.28360	−	5.28360i	−0.175053	−	0.175053i	−0.789195	+	0.614142i	$0.789502\pi$
$912$		0			0
$913$	15.0000	+	15.0000i	0.496428	+	0.496428i
$914$	4.89529	+	4.89529i	0.161922	+	0.161922i
$915$		0			0
$916$	−25.6869	−	25.6869i	−0.848720	−	0.848720i
$917$	5.82378	+	5.82378i	0.192318	+	0.192318i
$918$		0			0
$919$	34.1246			1.12567			0.562834	−	0.826570i	$-0.309711\pi$
$919$	34.1246			1.12567			0.562834	+	0.826570i	$0.309711\pi$
$920$	2.08191	−	2.08191i	0.0686387	−	0.0686387i
$921$		0			0
$922$	5.12461			0.168770
$923$		−	8.10272i		−	0.266704i
$924$		0			0
$925$	42.2705	−	42.2705i	1.38985	−	1.38985i
$926$	−2.50963	−	2.50963i	−0.0824715	−	0.0824715i
$927$		0			0
$928$	12.4377	+	18.5410i	0.408287	+	0.608639i
$929$		−	3.16228i		−	0.103751i	−0.998654	−	0.0518755i	$-0.983480\pi$
$929$		−	3.16228i		−	0.103751i	0.998654	−	0.0518755i	$-0.0165199\pi$
$930$		0			0
$931$	11.1246	+	11.1246i	0.364594	+	0.364594i
$932$	35.3252			1.15712
$933$		0			0
$934$		−	9.16718i		−	0.299959i
$935$			12.1877i			0.398582i
$936$		0			0
$937$		−	31.5410i		−	1.03040i	−0.857070	−	0.515200i	$-0.827718\pi$
$937$		−	31.5410i		−	1.03040i	0.857070	−	0.515200i	$-0.172282\pi$
$938$	3.97255	+	3.97255i	0.129708	+	0.129708i
$939$		0			0
$940$	57.9787	−	57.9787i	1.89106	−	1.89106i
$941$	−15.8902			−0.518006			−0.259003	−	0.965877i	$-0.583394\pi$
$941$	−15.8902			−0.518006			−0.259003	+	0.965877i	$0.583394\pi$
$942$		0			0
$943$	−2.29180	+	2.29180i	−0.0746311	+	0.0746311i
$944$		−	33.2433i		−	1.08198i
$945$		0			0
$946$	4.87539	−	4.87539i	0.158513	−	0.158513i
$947$	30.1204	−	30.1204i	0.978783	−	0.978783i	−0.0209965	−	0.999780i	$-0.506684\pi$
$947$	30.1204	−	30.1204i	0.978783	−	0.978783i	0.999780	+	0.0209965i	$0.00668387\pi$
$948$		0			0
$949$	−44.2705	−	44.2705i	−1.43708	−	1.43708i
$950$	−8.72172			−0.282970
$951$		0			0
$952$	2.16718			0.0702388
$953$		−	11.5687i		−	0.374748i	−0.982289	−	0.187374i	$-0.940002\pi$
$953$		−	11.5687i		−	0.374748i	0.982289	−	0.187374i	$-0.0599977\pi$
$954$		0			0
$955$	−66.5410	+	66.5410i	−2.15322	+	2.15322i
$956$	30.3175			0.980537
$957$		0			0
$958$	0.832816			0.0269071
$959$	−2.62210	+	2.62210i	−0.0846719	+	0.0846719i
$960$		0			0
$961$			16.1246i			0.520149i
$962$	13.1105			0.422699
$963$		0			0
$964$	8.72949			0.281158
$965$	−2.62210	−	2.62210i	−0.0844083	−	0.0844083i
$966$		0			0
$967$	−22.6869	+	22.6869i	−0.729562	+	0.729562i	−0.970532	−	0.240970i	$-0.922534\pi$
$967$	−22.6869	+	22.6869i	−0.729562	+	0.729562i	0.240970	+	0.970532i	$0.422534\pi$
$968$	−6.24574	+	6.24574i	−0.200746	+	0.200746i
$969$		0			0
$970$			8.29180i			0.266234i
$971$	−17.5107	+	17.5107i	−0.561947	+	0.561947i	−0.929860	−	0.367913i	$-0.880072\pi$
$971$	−17.5107	+	17.5107i	−0.561947	+	0.561947i	0.367913	+	0.929860i	$0.380072\pi$
$972$		0			0
$973$	−10.7082			−0.343289
$974$	4.00621	−	4.00621i	0.128367	−	0.128367i
$975$		0			0
$976$	−8.97871	−	8.97871i	−0.287402	−	0.287402i
$977$		−	36.3268i		−	1.16220i	−0.813833	−	0.581098i	$-0.802623\pi$
$977$		−	36.3268i		−	1.16220i	0.813833	−	0.581098i	$-0.197377\pi$
$978$		0			0
$979$		−	40.1246i		−	1.28239i
$980$			41.1884i			1.31572i
$981$		0			0
$982$	5.12461			0.163533
$983$	−25.4558	−	25.4558i	−0.811915	−	0.811915i	0.173006	−	0.984921i	$-0.444652\pi$
$983$	−25.4558	−	25.4558i	−0.811915	−	0.811915i	−0.984921	+	0.173006i	$0.944652\pi$
$984$		0			0
$985$		−	79.9574i		−	2.54766i
$986$	2.97100	+	0.585336i	0.0946159	+	0.0186409i
$987$		0			0
$988$	17.1885	+	17.1885i	0.546838	+	0.546838i
$989$	3.08347	−	3.08347i	0.0980485	−	0.0980485i
$990$		0			0
$991$		−	28.1246i		−	0.893408i	−0.894682	−	0.446704i	$-0.852598\pi$
$991$		−	28.1246i		−	0.893408i	0.894682	−	0.446704i	$-0.147402\pi$
$992$	−28.4605			−0.903622
$993$		0			0
$994$	0.437694	−	0.437694i	0.0138828	−	0.0138828i
$995$	−34.4025			−1.09063
$996$		0			0
$997$	−21.7082	−	21.7082i	−0.687506	−	0.687506i	0.274174	−	0.961680i	$-0.411595\pi$
$997$	−21.7082	−	21.7082i	−0.687506	−	0.687506i	−0.961680	+	0.274174i	$0.911595\pi$
$998$	−0.348902	−	0.348902i	−0.0110443	−	0.0110443i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.g.b.215.3	yes	8
3.2	odd	2	inner	261.2.g.b.215.2	yes	8
29.17	odd	4	inner	261.2.g.b.17.2	✓	8
87.17	even	4	inner	261.2.g.b.17.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.g.b.17.2	✓	8	29.17	odd	4	inner
261.2.g.b.17.3	yes	8	87.17	even	4	inner
261.2.g.b.215.2	yes	8	3.2	odd	2	inner
261.2.g.b.215.3	yes	8	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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.270091 - 0.270091i) q^{2} +1.85410i q^{4} -3.70246 q^{5} -1.00000 q^{7} +(1.04096 + 1.04096i) q^{8} +O(q^{10})\)	\(q+(0.270091 - 0.270091i) q^{2} +1.85410i q^{4} -3.70246 q^{5} -1.00000 q^{7} +(1.04096 + 1.04096i) q^{8} +(-1.00000 + 1.00000i) q^{10} +(-1.58114 + 1.58114i) q^{11} +5.00000i q^{13} +(-0.270091 + 0.270091i) q^{14} -3.14590 q^{16} +(-1.04096 + 1.04096i) q^{17} +(-1.85410 - 1.85410i) q^{19} -6.86474i q^{20} +0.854102i q^{22} +0.540182i q^{23} +8.70820 q^{25} +(1.35045 + 1.35045i) q^{26} -1.85410i q^{28} +(1.04096 - 5.28360i) q^{29} +(4.85410 + 4.85410i) q^{31} +(-2.93159 + 2.93159i) q^{32} +0.562306i q^{34} +3.70246 q^{35} +(4.85410 - 4.85410i) q^{37} -1.00155 q^{38} +(-3.85410 - 3.85410i) q^{40} +(4.24264 + 4.24264i) q^{41} +(-5.70820 - 5.70820i) q^{43} +(-2.93159 - 2.93159i) q^{44} +(0.145898 + 0.145898i) q^{46} +(8.44588 + 8.44588i) q^{47} -6.00000 q^{49} +(2.35201 - 2.35201i) q^{50} -9.27051 q^{52} +2.62210i q^{53} +(5.85410 - 5.85410i) q^{55} +(-1.04096 - 1.04096i) q^{56} +(-1.14590 - 1.70820i) q^{58} +10.5672i q^{59} +(2.85410 + 2.85410i) q^{61} +2.62210 q^{62} -4.70820i q^{64} -18.5123i q^{65} -14.7082i q^{67} +(-1.93004 - 1.93004i) q^{68} +(1.00000 - 1.00000i) q^{70} -1.62054 q^{71} +(-8.85410 + 8.85410i) q^{73} -2.62210i q^{74} +(3.43769 - 3.43769i) q^{76} +(1.58114 - 1.58114i) q^{77} +(9.85410 + 9.85410i) q^{79} +11.6476 q^{80} +2.29180 q^{82} -9.48683i q^{83} +(3.85410 - 3.85410i) q^{85} -3.08347 q^{86} -3.29180 q^{88} +(-12.6885 + 12.6885i) q^{89} -5.00000i q^{91} -1.00155 q^{92} +4.56231 q^{94} +(6.86474 + 6.86474i) q^{95} +(4.14590 - 4.14590i) q^{97} +(-1.62054 + 1.62054i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{7}+O(q^{10}) \) 8 * q - 8 * q^7	\( 8 q - 8 q^{7} - 8 q^{10} - 52 q^{16} + 12 q^{19} + 16 q^{25} + 12 q^{31} + 12 q^{37} - 4 q^{40} + 8 q^{43} + 28 q^{46} - 48 q^{49} + 60 q^{52} + 20 q^{55} - 36 q^{58} - 4 q^{61} + 8 q^{70} - 44 q^{73} + 108 q^{76} + 52 q^{79} + 72 q^{82} + 4 q^{85} - 80 q^{88} - 44 q^{94} + 60 q^{97}+O(q^{100}) \) 8 * q - 8 * q^7 - 8 * q^10 - 52 * q^16 + 12 * q^19 + 16 * q^25 + 12 * q^31 + 12 * q^37 - 4 * q^40 + 8 * q^43 + 28 * q^46 - 48 * q^49 + 60 * q^52 + 20 * q^55 - 36 * q^58 - 4 * q^61 + 8 * q^70 - 44 * q^73 + 108 * q^76 + 52 * q^79 + 72 * q^82 + 4 * q^85 - 80 * q^88 - 44 * q^94 + 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more