LMFDB - Embedded newform 588.2.n.c.263.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(263,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("588.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.n (of order $6$, degree $2$, not 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:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.11007531417600000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{12} + 48x^{8} - 7x^{4} + 1 $ x^16 - 7x^12 + 48x^8 - 7*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			263.1
Root			$0.159959 + 0.596975i$ of defining polynomial
Character	$\chi$	$=$	588.263
Dual form			588.2.n.c.275.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40126 - 0.190983i) q^{2} +(-1.40294 + 1.01575i) q^{3} +(1.92705 + 0.535233i) q^{4} +(-2.12132 + 1.22474i) q^{5} +(2.15988 - 1.15539i) q^{6} +(-2.59808 - 1.11803i) q^{8} +(0.936492 - 2.85008i) q^{9} +(3.20642 - 1.31105i) q^{10} +(1.73205 - 3.00000i) q^{11} +(-3.24721 + 1.20651i) q^{12} +5.47723 q^{13} +(1.73205 - 3.87298i) q^{15} +(3.42705 + 2.06284i) q^{16} +(4.24264 + 2.44949i) q^{17} +(-1.85658 + 3.81485i) q^{18} +(-3.67423 + 2.12132i) q^{19} +(-4.74342 + 1.22474i) q^{20} +(-3.00000 + 3.87298i) q^{22} +(4.78060 - 1.07047i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-7.67501 - 1.04606i) q^{26} +(1.58114 + 4.94975i) q^{27} +4.47214i q^{29} +(-3.16672 + 5.09626i) q^{30} +(-7.34847 - 4.24264i) q^{31} +(-4.40822 - 3.54508i) q^{32} +(0.617292 + 5.96816i) q^{33} +(-5.47723 - 4.24264i) q^{34} +(3.33013 - 4.99102i) q^{36} +(1.00000 + 1.73205i) q^{37} +(5.55369 - 2.27080i) q^{38} +(-7.68423 + 5.56351i) q^{39} +(6.88066 - 0.810272i) q^{40} +7.74597i q^{43} +(4.94345 - 4.85410i) q^{44} +(1.50403 + 7.19291i) q^{45} +(-6.90329 + 0.586988i) q^{48} +(-0.866025 + 1.11803i) q^{50} +(-8.44025 + 0.872983i) q^{51} +(10.5549 + 2.93159i) q^{52} +(3.87298 + 2.23607i) q^{53} +(-1.27027 - 7.23785i) q^{54} +8.48528i q^{55} +(3.00000 - 6.70820i) q^{57} +(0.854102 - 6.26662i) q^{58} +(-4.74342 + 8.21584i) q^{59} +(5.41070 - 6.53639i) q^{60} +(2.73861 + 4.74342i) q^{61} +(9.48683 + 7.34847i) q^{62} +(5.50000 + 5.80948i) q^{64} +(-11.6190 + 6.70820i) q^{65} +(0.274831 - 8.48083i) q^{66} +(6.70820 + 3.87298i) q^{67} +(6.86474 + 6.99109i) q^{68} -3.46410 q^{71} +(-5.61957 + 6.35771i) q^{72} +(-5.47723 + 9.48683i) q^{73} +(-1.07047 - 2.61803i) q^{74} +(0.178197 + 1.72286i) q^{75} +(-8.21584 + 2.12132i) q^{76} +(11.8301 - 6.32836i) q^{78} +(13.4164 - 7.74597i) q^{79} +(-9.79633 - 0.178688i) q^{80} +(-7.24597 - 5.33816i) q^{81} +9.48683 q^{83} -12.0000 q^{85} +(1.47935 - 10.8541i) q^{86} +(-4.54259 - 6.27415i) q^{87} +(-7.85410 + 5.85774i) q^{88} +(8.48528 - 4.89898i) q^{89} +(-0.733809 - 10.3664i) q^{90} +(14.6190 - 1.51205i) q^{93} +(5.19615 - 9.00000i) q^{95} +(9.78540 + 0.495889i) q^{96} +(-6.92820 - 7.74597i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 16 q^{9} + 28 q^{16} - 20 q^{18} - 48 q^{22} + 8 q^{25} - 12 q^{30} - 16 q^{36} + 16 q^{37} + 48 q^{57} - 40 q^{58} + 60 q^{60} + 88 q^{64} - 20 q^{72} + 120 q^{78} + 8 q^{81} - 192 q^{85}+ \cdots + 48 q^{93}+O(q^{100}) $ 16 * q + 4 * q^4 - 16 * q^9 + 28 * q^16 - 20 * q^18 - 48 * q^22 + 8 * q^25 - 12 * q^30 - 16 * q^36 + 16 * q^37 + 48 * q^57 - 40 * q^58 + 60 * q^60 + 88 * q^64 - 20 * q^72 + 120 * q^78 + 8 * q^81 - 192 * q^85 - 72 * q^88 + 48 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.40126	−	0.190983i	−0.990839	−	0.135045i
$2$	−1.40126	−	0.190983i	−0.990839	−	0.135045i
$3$	−1.40294	+	1.01575i	−0.809989	+	0.586445i
$3$	−1.40294	+	1.01575i	−0.809989	+	0.586445i
$4$	1.92705	+	0.535233i	0.963525	+	0.267617i
$5$	−2.12132	+	1.22474i	−0.948683	+	0.547723i	−0.892672	−	0.450708i	$-0.851172\pi$
$5$	−2.12132	+	1.22474i	−0.948683	+	0.547723i	−0.0560116	+	0.998430i	$0.517838\pi$
$6$	2.15988	−	1.15539i	0.881766	−	0.471688i
$7$		0			0
$7$		0			0
$8$	−2.59808	−	1.11803i	−0.918559	−	0.395285i
$9$	0.936492	−	2.85008i	0.312164	−	0.950028i
$10$	3.20642	−	1.31105i	1.01396	−	0.414590i
$11$	1.73205	−	3.00000i	0.522233	−	0.904534i	−0.477432	−	0.878668i	$-0.658432\pi$
$11$	1.73205	−	3.00000i	0.522233	−	0.904534i	0.999665	−	0.0258656i	$-0.00823419\pi$
$12$	−3.24721	+	1.20651i	−0.937387	+	0.348289i
$13$	5.47723			1.51911			0.759555	−	0.650444i	$-0.225417\pi$
$13$	5.47723			1.51911			0.759555	+	0.650444i	$0.225417\pi$
$14$		0			0
$15$	1.73205	−	3.87298i	0.447214	−	1.00000i
$16$	3.42705	+	2.06284i	0.856763	+	0.515711i
$17$	4.24264	+	2.44949i	1.02899	+	0.594089i	0.916696	−	0.399586i	$-0.130846\pi$
$17$	4.24264	+	2.44949i	1.02899	+	0.594089i	0.112296	+	0.993675i	$0.464180\pi$
$18$	−1.85658	+	3.81485i	−0.437601	+	0.899169i
$19$	−3.67423	+	2.12132i	−0.842927	+	0.486664i	−0.858258	−	0.513218i	$-0.828453\pi$
$19$	−3.67423	+	2.12132i	−0.842927	+	0.486664i	0.0153309	+	0.999882i	$0.495120\pi$
$20$	−4.74342	+	1.22474i	−1.06066	+	0.273861i
$21$		0			0
$22$	−3.00000	+	3.87298i	−0.639602	+	0.825723i
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$	4.78060	−	1.07047i	0.975835	−	0.218508i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−7.67501	−	1.04606i	−1.50519	−	0.205149i
$27$	1.58114	+	4.94975i	0.304290	+	0.952579i
$28$		0			0
$29$			4.47214i			0.830455i	0.909718	+	0.415227i	$0.136298\pi$
$29$			4.47214i			0.830455i	−0.909718	+	0.415227i	$0.863702\pi$
$30$	−3.16672	+	5.09626i	−0.578162	+	0.930445i
$31$	−7.34847	−	4.24264i	−1.31982	−	0.762001i	−0.336124	−	0.941818i	$-0.609116\pi$
$31$	−7.34847	−	4.24264i	−1.31982	−	0.762001i	−0.983700	+	0.179817i	$0.942449\pi$
$32$	−4.40822	−	3.54508i	−0.779270	−	0.626688i
$33$	0.617292	+	5.96816i	0.107457	+	1.03892i
$34$	−5.47723	−	4.24264i	−0.939336	−	0.727607i
$35$		0			0
$36$	3.33013	−	4.99102i	0.555021	−	0.831836i
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	0.936442	−	0.350823i	$-0.114098\pi$
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	−0.772043	+	0.635571i	$0.780765\pi$
$38$	5.55369	−	2.27080i	0.900927	−	0.368373i
$39$	−7.68423	+	5.56351i	−1.23046	+	0.890874i
$40$	6.88066	−	0.810272i	1.08793	−	0.128115i
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$		0			0
$43$			7.74597i			1.18125i	0.806947	+	0.590624i	$0.201119\pi$
$43$			7.74597i			1.18125i	−0.806947	+	0.590624i	$0.798881\pi$
$44$	4.94345	−	4.85410i	0.745253	−	0.731783i
$45$	1.50403	+	7.19291i	0.224207	+	1.07226i
$46$		0			0
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$	−6.90329	+	0.586988i	−0.996404	+	0.0847245i
$49$		0			0
$50$	−0.866025	+	1.11803i	−0.122474	+	0.158114i
$51$	−8.44025	+	0.872983i	−1.18187	+	0.122242i
$52$	10.5549	+	2.93159i	1.46370	+	0.406539i
$53$	3.87298	+	2.23607i	0.531995	+	0.307148i	0.741829	−	0.670590i	$-0.233959\pi$
$53$	3.87298	+	2.23607i	0.531995	+	0.307148i	−0.209833	+	0.977737i	$0.567292\pi$
$54$	−1.27027	−	7.23785i	−0.172861	−	0.984946i
$55$			8.48528i			1.14416i
$56$		0			0
$57$	3.00000	−	6.70820i	0.397360	−	0.888523i
$58$	0.854102	−	6.26662i	0.112149	−	0.822847i
$59$	−4.74342	+	8.21584i	−0.617540	+	1.06961i	0.372393	+	0.928075i	$0.378537\pi$
$59$	−4.74342	+	8.21584i	−0.617540	+	1.06961i	−0.989933	+	0.141536i	$0.954796\pi$
$60$	5.41070	−	6.53639i	0.698518	−	0.843844i
$61$	2.73861	+	4.74342i	0.350643	+	0.607332i	0.986362	−	0.164588i	$-0.0526296\pi$
$61$	2.73861	+	4.74342i	0.350643	+	0.607332i	−0.635719	+	0.771921i	$0.719296\pi$
$62$	9.48683	+	7.34847i	1.20483	+	0.933257i
$63$		0			0
$64$	5.50000	+	5.80948i	0.687500	+	0.726184i
$65$	−11.6190	+	6.70820i	−1.44115	+	0.832050i
$66$	0.274831	−	8.48083i	0.0338294	−	1.04392i
$67$	6.70820	+	3.87298i	0.819538	+	0.473160i	0.850257	−	0.526368i	$-0.176447\pi$
$67$	6.70820	+	3.87298i	0.819538	+	0.473160i	−0.0307194	+	0.999528i	$0.509780\pi$
$68$	6.86474	+	6.99109i	0.832472	+	0.847795i
$69$		0			0
$70$		0			0
$71$	−3.46410			−0.411113			−0.205557	−	0.978645i	$-0.565900\pi$
$71$	−3.46410			−0.411113			−0.205557	+	0.978645i	$0.565900\pi$
$72$	−5.61957	+	6.35771i	−0.662272	+	0.749263i
$73$	−5.47723	+	9.48683i	−0.641061	+	1.11035i	0.344136	+	0.938920i	$0.388172\pi$
$73$	−5.47723	+	9.48683i	−0.641061	+	1.11035i	−0.985196	+	0.171430i	$0.945161\pi$
$74$	−1.07047	−	2.61803i	−0.124439	−	0.304340i
$75$	0.178197	+	1.72286i	0.0205764	+	0.198939i
$76$	−8.21584	+	2.12132i	−0.942421	+	0.243332i
$77$		0			0
$78$	11.8301	−	6.32836i	1.33950	−	0.716545i
$79$	13.4164	−	7.74597i	1.50946	−	0.871489i	0.509525	−	0.860456i	$-0.329821\pi$
$79$	13.4164	−	7.74597i	1.50946	−	0.871489i	0.999939	−	0.0110333i	$-0.00351208\pi$
$80$	−9.79633	−	0.178688i	−1.09526	−	0.0199779i
$81$	−7.24597	−	5.33816i	−0.805107	−	0.593129i
$82$		0			0
$83$	9.48683			1.04132			0.520658	−	0.853766i	$-0.325687\pi$
$83$	9.48683			1.04132			0.520658	+	0.853766i	$0.325687\pi$
$84$		0			0
$85$	−12.0000			−1.30158
$86$	1.47935	−	10.8541i	0.159522	−	1.17043i
$87$	−4.54259	−	6.27415i	−0.487016	−	0.672659i
$88$	−7.85410	+	5.85774i	−0.837250	+	0.624437i
$89$	8.48528	−	4.89898i	0.899438	−	0.519291i	0.0224202	−	0.999749i	$-0.492863\pi$
$89$	8.48528	−	4.89898i	0.899438	−	0.519291i	0.877018	+	0.480458i	$0.159529\pi$
$90$	−0.733809	−	10.3664i	−0.0773503	−	1.09271i
$91$		0			0
$92$		0			0
$93$	14.6190	−	1.51205i	1.51591	−	0.156792i
$94$		0			0
$95$	5.19615	−	9.00000i	0.533114	−	0.923381i
$96$	9.78540	+	0.495889i	0.998718	+	0.0506115i
$97$		0			0			−	1.00000i	$-0.5\pi$
$97$		0			0				1.00000i	$0.5\pi$
$98$		0			0
$99$	−6.92820	−	7.74597i	−0.696311	−	0.778499i
$100$	1.42705	−	1.40126i	0.142705	−	0.140126i
$101$	−6.36396	−	3.67423i	−0.633238	−	0.365600i	0.148767	−	0.988872i	$-0.452470\pi$
$101$	−6.36396	−	3.67423i	−0.633238	−	0.365600i	−0.782005	+	0.623272i	$0.785803\pi$
$102$	11.9937	+	0.388670i	1.18755	+	0.0384840i
$103$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$103$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$104$	−14.2302	−	6.12372i	−1.39539	−	0.600481i
$105$		0			0
$106$	−5.00000	−	3.87298i	−0.485643	−	0.376177i
$107$	8.66025	+	15.0000i	0.837218	+	1.45010i	0.892211	+	0.451618i	$0.149153\pi$
$107$	8.66025	+	15.0000i	0.837218	+	1.45010i	−0.0549930	+	0.998487i	$0.517514\pi$
$108$	0.397666	+	10.3847i	0.0382655	+	0.999268i
$109$	−5.00000	+	8.66025i	−0.478913	+	0.829502i	−0.999708	−	0.0241802i	$-0.992302\pi$
$109$	−5.00000	+	8.66025i	−0.478913	+	0.829502i	0.520794	+	0.853682i	$0.325636\pi$
$110$	1.62054	−	11.8901i	0.154513	−	1.13367i
$111$	−3.16228	−	1.41421i	−0.300150	−	0.134231i
$112$		0			0
$113$		−	4.47214i		−	0.420703i	−0.977626	−	0.210352i	$-0.932539\pi$
$113$		−	4.47214i		−	0.420703i	0.977626	−	0.210352i	$-0.0674609\pi$
$114$	−5.48493	+	8.82698i	−0.513711	+	0.826722i
$115$		0			0
$116$	−2.39364	+	8.61803i	−0.222243	+	0.800164i
$117$	5.12938	−	15.6106i	0.474211	−	1.44320i
$118$	8.21584	−	10.6066i	0.756329	−	0.976417i
$119$		0			0
$120$	−8.83013	+	8.12581i	−0.806077	+	0.741782i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−2.93159	−	7.16978i	−0.265414	−	0.649122i
$123$		0			0
$124$	−11.8901	−	12.1089i	−1.06776	−	1.08741i
$125$		−	9.79796i		−	0.876356i
$126$		0			0
$127$			7.74597i			0.687343i	0.939090	+	0.343672i	$0.111671\pi$
$127$			7.74597i			0.687343i	−0.939090	+	0.343672i	$0.888329\pi$
$128$	−6.59741	−	9.19098i	−0.583134	−	0.812376i
$129$	−7.86799	−	10.8671i	−0.692738	−	0.956798i
$130$	17.5623	−	7.18091i	1.54032	−	0.629807i
$131$	4.74342	+	8.21584i	0.414434	+	0.717821i	0.995369	−	0.0961291i	$-0.0306462\pi$
$131$	4.74342	+	8.21584i	0.414434	+	0.717821i	−0.580935	+	0.813950i	$0.697313\pi$
$132$	−2.00480	+	11.8313i	−0.174496	+	1.02979i
$133$		0			0
$134$	−8.66025	−	6.70820i	−0.748132	−	0.579501i
$135$	−9.41628	−	8.56351i	−0.810424	−	0.737029i
$136$	−8.28409	−	11.1074i	−0.710355	−	0.952450i
$137$	7.74597	+	4.47214i	0.661783	+	0.382080i	0.792956	−	0.609279i	$-0.208541\pi$
$137$	7.74597	+	4.47214i	0.661783	+	0.382080i	−0.131173	+	0.991359i	$0.541874\pi$
$138$		0			0
$139$		−	4.24264i		−	0.359856i	−0.983680	−	0.179928i	$-0.942414\pi$
$139$		−	4.24264i		−	0.359856i	0.983680	−	0.179928i	$-0.0575865\pi$
$140$		0			0
$141$		0			0
$142$	4.85410	+	0.661585i	0.407347	+	0.0555189i
$143$	9.48683	−	16.4317i	0.793329	−	1.37409i
$144$	9.08868	−	7.83555i	0.757390	−	0.652963i
$145$	−5.47723	−	9.48683i	−0.454859	−	0.787839i
$146$	9.48683	−	12.2474i	0.785136	−	1.01361i
$147$		0			0
$148$	1.00000	+	3.87298i	0.0821995	+	0.318357i
$149$	−3.87298	+	2.23607i	−0.317287	+	0.183186i	−0.650183	−	0.759778i	$-0.725308\pi$
$149$	−3.87298	+	2.23607i	−0.317287	+	0.183186i	0.332896	+	0.942964i	$0.391974\pi$
$150$	0.0793369	−	2.44820i	0.00647783	−	0.199895i
$151$	−6.70820	−	3.87298i	−0.545906	−	0.315179i	0.201563	−	0.979476i	$-0.435398\pi$
$151$	−6.70820	−	3.87298i	−0.545906	−	0.315179i	−0.747469	+	0.664297i	$0.768731\pi$
$152$	11.9176	−	1.40343i	0.966649	−	0.113833i
$153$	10.9545	−	9.79796i	0.885615	−	0.792118i
$154$		0			0
$155$	20.7846			1.66946
$156$	−17.7857	+	6.60831i	−1.42399	+	0.529088i
$157$	2.73861	−	4.74342i	0.218565	−	0.378566i	−0.735804	−	0.677194i	$-0.763196\pi$
$157$	2.73861	−	4.74342i	0.218565	−	0.378566i	0.954370	+	0.298628i	$0.0965291\pi$
$158$	−20.2792	+	8.29180i	−1.61333	+	0.659660i
$159$	−7.70486	+	0.796921i	−0.611035	+	0.0632000i
$160$	13.6931	+	2.12132i	1.08253	+	0.167705i
$161$		0			0
$162$	9.13397	+	8.86400i	0.717633	+	0.696422i
$163$	−6.70820	+	3.87298i	−0.525427	+	0.303355i	−0.739152	−	0.673538i	$-0.764774\pi$
$163$	−6.70820	+	3.87298i	−0.525427	+	0.303355i	0.213725	+	0.976894i	$0.431440\pi$
$164$		0			0
$165$	−8.61895	−	11.9044i	−0.670984	−	0.926753i
$166$	−13.2935	−	1.81182i	−1.03178	−	0.140625i
$167$	−18.9737			−1.46823			−0.734113	−	0.679027i	$-0.762402\pi$
$167$	−18.9737			−1.46823			−0.734113	+	0.679027i	$0.762402\pi$
$168$		0			0
$169$	17.0000			1.30769
$170$	16.8151	+	2.29180i	1.28966	+	0.175773i
$171$	2.60505	+	12.4585i	0.199213	+	0.952724i
$172$	−4.14590	+	14.9269i	−0.316122	+	1.13816i
$173$	−2.12132	+	1.22474i	−0.161281	+	0.0931156i	−0.578468	−	0.815705i	$-0.696349\pi$
$173$	−2.12132	+	1.22474i	−0.161281	+	0.0931156i	0.417187	+	0.908821i	$0.363016\pi$
$174$	5.16708	+	9.65926i	0.391715	+	0.732266i
$175$		0			0
$176$	12.1244	−	6.70820i	0.913908	−	0.505650i
$177$	−1.69052	−	16.3445i	−0.127068	−	1.22853i
$178$	−12.8257	+	5.24419i	−0.961326	+	0.393069i
$179$	−5.19615	+	9.00000i	−0.388379	+	0.672692i	−0.992232	−	0.124404i	$-0.960298\pi$
$179$	−5.19615	+	9.00000i	−0.388379	+	0.672692i	0.603853	+	0.797096i	$0.293631\pi$
$180$	−0.951543	+	14.6661i	−0.0709239	+	1.09315i
$181$	−16.4317			−1.22136			−0.610678	−	0.791879i	$-0.709103\pi$
$181$	−16.4317			−1.22136			−0.610678	+	0.791879i	$0.709103\pi$
$182$		0			0
$183$	−8.66025	−	3.87298i	−0.640184	−	0.286299i
$184$		0			0
$185$	−4.24264	−	2.44949i	−0.311925	−	0.180090i
$186$	−20.7737	−	0.673196i	−1.52320	−	0.0493611i
$187$	14.6969	−	8.48528i	1.07475	−	0.620505i
$188$		0			0
$189$		0			0
$190$	−9.00000	+	11.6190i	−0.652929	+	0.842927i
$191$	1.73205	+	3.00000i	0.125327	+	0.217072i	0.921861	−	0.387522i	$-0.126669\pi$
$191$	1.73205	+	3.00000i	0.125327	+	0.217072i	−0.796534	+	0.604594i	$0.793335\pi$
$192$	−13.6172	−	2.56371i	−0.982735	−	0.185020i
$193$	8.00000	−	13.8564i	0.575853	−	0.997406i	−0.420096	−	0.907480i	$-0.638004\pi$
$193$	8.00000	−	13.8564i	0.575853	−	0.997406i	0.995948	−	0.0899262i	$-0.0286631\pi$
$194$		0			0
$195$	9.48683	−	21.2132i	0.679366	−	1.51911i
$196$		0			0
$197$			22.3607i			1.59313i	0.604551	+	0.796566i	$0.293352\pi$
$197$			22.3607i			1.59313i	−0.604551	+	0.796566i	$0.706648\pi$
$198$	8.22886	+	12.1773i	0.584799	+	0.865401i
$199$	14.6969	+	8.48528i	1.04184	+	0.601506i	0.920353	−	0.391088i	$-0.127901\pi$
$199$	14.6969	+	8.48528i	1.04184	+	0.601506i	0.121485	+	0.992593i	$0.461234\pi$
$200$	−2.26728	+	1.69098i	−0.160321	+	0.119571i
$201$	−13.3452	+	1.38031i	−0.941299	+	0.0973594i
$202$	8.21584	+	6.36396i	0.578064	+	0.447767i
$203$		0			0
$204$	−16.7321	−	2.83522i	−1.17148	−	0.198505i
$205$		0			0
$206$		0			0
$207$		0			0
$208$	18.7707	+	11.2987i	1.30152	+	0.783421i
$209$			14.6969i			1.01661i
$210$		0			0
$211$		−	7.74597i		−	0.533254i	−0.963800	−	0.266627i	$-0.914091\pi$
$211$		−	7.74597i		−	0.533254i	0.963800	−	0.266627i	$-0.0859092\pi$
$212$	6.26662	+	6.38197i	0.430393	+	0.438315i
$213$	4.85993	−	3.51867i	0.332997	−	0.241095i
$214$	−9.27051	−	22.6728i	−0.633719	−	1.54988i
$215$	−9.48683	−	16.4317i	−0.646997	−	1.12063i
$216$	1.42607	−	14.6276i	0.0970316	−	0.995281i
$217$		0			0
$218$	8.66025	−	11.1803i	0.586546	−	0.757228i
$219$	−1.95205	−	18.8730i	−0.131907	−	1.27532i
$220$	−4.54160	+	16.3516i	−0.306195	+	1.10242i
$221$	23.2379	+	13.4164i	1.56315	+	0.902485i
$222$	4.16108	+	2.58562i	0.279273	+	0.173535i
$223$		−	8.48528i		−	0.568216i	−0.958792	−	0.284108i	$-0.908302\pi$
$223$		−	8.48528i		−	0.568216i	0.958792	−	0.284108i	$-0.0916975\pi$
$224$		0			0
$225$	−2.00000	−	2.23607i	−0.133333	−	0.149071i
$226$	−0.854102	+	6.26662i	−0.0568140	+	0.416849i
$227$	−4.74342	+	8.21584i	−0.314832	+	0.545304i	−0.979402	−	0.201922i	$-0.935281\pi$
$227$	−4.74342	+	8.21584i	−0.314832	+	0.545304i	0.664570	+	0.747226i	$0.268615\pi$
$228$	9.37161	−	11.3214i	0.620650	−	0.749775i
$229$	2.73861	+	4.74342i	0.180973	+	0.313454i	0.942212	−	0.335017i	$-0.108742\pi$
$229$	2.73861	+	4.74342i	0.180973	+	0.313454i	−0.761239	+	0.648471i	$0.775409\pi$
$230$		0			0
$231$		0			0
$232$	5.00000	−	11.6190i	0.328266	−	0.762821i
$233$	−7.74597	+	4.47214i	−0.507455	+	0.292979i	−0.731787	−	0.681533i	$-0.761313\pi$
$233$	−7.74597	+	4.47214i	−0.507455	+	0.292979i	0.224332	+	0.974513i	$0.427980\pi$
$234$	−10.1689	+	20.8948i	−0.664764	+	1.36594i
$235$		0			0
$236$	−13.5382	+	13.2935i	−0.881261	+	0.865334i
$237$	−10.9545	+	24.4949i	−0.711568	+	1.59111i
$238$		0			0
$239$	6.92820			0.448148			0.224074	−	0.974572i	$-0.428064\pi$
$239$	6.92820			0.448148			0.224074	+	0.974572i	$0.428064\pi$
$240$	13.9252	−	9.69996i	0.898867	−	0.626130i
$241$	10.9545	−	18.9737i	0.705638	−	1.22220i	−0.260822	−	0.965387i	$-0.583994\pi$
$241$	10.9545	−	18.9737i	0.705638	−	1.22220i	0.966461	−	0.256814i	$-0.0826729\pi$
$242$	0.535233	+	1.30902i	0.0344061	+	0.0841468i
$243$	15.5879	+	0.129018i	0.999966	+	0.00827648i
$244$	2.73861	+	10.6066i	0.175322	+	0.679018i
$245$		0			0
$246$		0			0
$247$	−20.1246	+	11.6190i	−1.28050	+	0.739296i
$248$	14.3485	+	19.2385i	0.911129	+	1.22165i
$249$	−13.3095	+	9.63628i	−0.843454	+	0.610674i
$250$	−1.87124	+	13.7295i	−0.118348	+	0.868328i
$251$	9.48683			0.598804			0.299402	−	0.954127i	$-0.403213\pi$
$251$	9.48683			0.598804			0.299402	+	0.954127i	$0.403213\pi$
$252$		0			0
$253$		0			0
$254$	1.47935	−	10.8541i	0.0928225	−	0.681047i
$255$	16.8353	−	12.1890i	1.05427	−	0.763307i
$256$	7.48936	+	14.1389i	0.468085	+	0.883684i
$257$	−4.24264	+	2.44949i	−0.264649	+	0.152795i	−0.626453	−	0.779459i	$-0.715494\pi$
$257$	−4.24264	+	2.44949i	−0.264649	+	0.152795i	0.361805	+	0.932254i	$0.382161\pi$
$258$	8.94965	+	16.7303i	0.557181	+	1.04158i
$259$		0			0
$260$	−25.9808	+	6.70820i	−1.61126	+	0.416025i
$261$	12.7460	+	4.18812i	0.788956	+	0.259238i
$262$	−5.07767	−	12.4184i	−0.313699	−	0.767213i
$263$	1.73205	−	3.00000i	0.106803	−	0.184988i	−0.807671	−	0.589634i	$-0.799272\pi$
$263$	1.73205	−	3.00000i	0.106803	−	0.184988i	0.914473	+	0.404646i	$0.132605\pi$
$264$	5.06883	−	16.1959i	0.311965	−	0.996788i
$265$	−10.9545			−0.672927
$266$		0			0
$267$	−6.92820	+	15.4919i	−0.423999	+	0.948091i
$268$	10.8541	+	11.0539i	0.663020	+	0.675224i
$269$	2.12132	+	1.22474i	0.129339	+	0.0746740i	0.563274	−	0.826270i	$-0.309542\pi$
$269$	2.12132	+	1.22474i	0.129339	+	0.0746740i	−0.433934	+	0.900944i	$0.642875\pi$
$270$	11.5592	+	13.7980i	0.703468	+	0.839722i
$271$	−7.34847	+	4.24264i	−0.446388	+	0.257722i	−0.706303	−	0.707909i	$-0.749639\pi$
$271$	−7.34847	+	4.24264i	−0.446388	+	0.257722i	0.259916	+	0.965631i	$0.416305\pi$
$272$	9.48683	+	17.1464i	0.575224	+	1.03965i
$273$		0			0
$274$	−10.0000	−	7.74597i	−0.604122	−	0.467951i
$275$	−1.73205	−	3.00000i	−0.104447	−	0.180907i
$276$		0			0
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	−0.894503	−	0.447062i	$-0.852470\pi$
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	0.834419	+	0.551131i	$0.185804\pi$
$278$	−0.810272	+	5.94504i	−0.0485969	+	0.356560i
$279$	−18.9737	+	16.9706i	−1.13592	+	1.01600i
$280$		0			0
$281$		−	8.94427i		−	0.533571i	−0.963756	−	0.266785i	$-0.914039\pi$
$281$		−	8.94427i		−	0.533571i	0.963756	−	0.266785i	$-0.0859614\pi$
$282$		0			0
$283$	25.7196	+	14.8492i	1.52887	+	0.882696i	0.999409	+	0.0343638i	$0.0109405\pi$
$283$	25.7196	+	14.8492i	1.52887	+	0.882696i	0.529465	+	0.848332i	$0.322393\pi$
$284$	−6.67550	−	1.85410i	−0.396118	−	0.110021i
$285$	1.85188	+	17.9045i	0.109696	+	1.06057i
$286$	−16.4317	+	21.2132i	−0.971625	+	1.25436i
$287$		0			0
$288$	−14.2321	+	9.24385i	−0.838632	+	0.544699i
$289$	3.50000	+	6.06218i	0.205882	+	0.356599i
$290$	5.86319	+	14.3396i	0.344298	+	0.842048i
$291$		0			0
$292$	−15.6326	+	15.3500i	−0.914826	+	0.898292i
$293$			2.44949i			0.143101i	0.997437	+	0.0715504i	$0.0227947\pi$
$293$			2.44949i			0.143101i	−0.997437	+	0.0715504i	$0.977205\pi$
$294$		0			0
$295$		−	23.2379i		−	1.35296i
$296$	−0.661585	−	5.61803i	−0.0384538	−	0.326542i
$297$	17.5879	+	3.82980i	1.02055	+	0.222227i
$298$	5.85410	−	2.39364i	0.339119	−	0.138660i
$299$		0			0
$300$	−0.578737	+	3.41542i	−0.0334134	+	0.197189i
$301$		0			0
$302$	8.66025	+	6.70820i	0.498342	+	0.386014i
$303$	12.6604	−	1.30948i	0.727320	−	0.0752274i
$304$	−16.9677	−	0.309496i	−0.973167	−	0.0177508i
$305$	−11.6190	−	6.70820i	−0.665299	−	0.384111i
$306$	−17.2213	+	11.6374i	−0.984474	+	0.665264i
$307$		−	21.2132i		−	1.21070i	−0.795959	−	0.605351i	$-0.793033\pi$
$307$		−	21.2132i		−	1.21070i	0.795959	−	0.605351i	$-0.206967\pi$
$308$		0			0
$309$		0			0
$310$	−29.1246	−	3.96951i	−1.65417	−	0.225453i
$311$	9.48683	−	16.4317i	0.537949	−	0.931755i	−0.461065	−	0.887366i	$-0.652533\pi$
$311$	9.48683	−	16.4317i	0.537949	−	0.931755i	0.999014	−	0.0443887i	$-0.0141340\pi$
$312$	26.1844	−	5.86319i	1.48240	−	0.331938i
$313$	5.47723	+	9.48683i	0.309591	+	0.536228i	0.978273	−	0.207321i	$-0.0664745\pi$
$313$	5.47723	+	9.48683i	0.309591	+	0.536228i	−0.668682	+	0.743549i	$0.733141\pi$
$314$	−4.74342	+	6.12372i	−0.267686	+	0.345582i
$315$		0			0
$316$	30.0000	−	7.74597i	1.68763	−	0.435745i
$317$	−3.87298	+	2.23607i	−0.217528	+	0.125590i	−0.604805	−	0.796373i	$-0.706749\pi$
$317$	−3.87298	+	2.23607i	−0.217528	+	0.125590i	0.387277	+	0.921963i	$0.373416\pi$
$318$	10.9487	+	0.354805i	0.613973	+	0.0198965i
$319$	13.4164	+	7.74597i	0.751175	+	0.433691i
$320$	−18.7824	−	5.58766i	−1.04997	−	0.312360i
$321$	−27.3861	−	12.2474i	−1.52854	−	0.683586i
$322$		0			0
$323$	−20.7846			−1.15649
$324$	−11.1062	−	14.1652i	−0.617010	−	0.786955i
$325$	2.73861	−	4.74342i	0.151911	−	0.263117i
$326$	10.1396	−	4.14590i	0.561581	−	0.229620i
$327$	−1.78197	−	17.2286i	−0.0985432	−	0.952744i
$328$		0			0
$329$		0			0
$330$	9.80385	+	18.3272i	0.539684	+	1.00888i
$331$	20.1246	−	11.6190i	1.10615	−	0.638635i	0.168320	−	0.985732i	$-0.446166\pi$
$331$	20.1246	−	11.6190i	1.10615	−	0.638635i	0.937829	+	0.347097i	$0.112833\pi$
$332$	18.2816	+	5.07767i	1.00333	+	0.278673i
$333$	5.87298	−	1.22803i	0.321838	−	0.0672958i
$334$	26.5870	+	3.62365i	1.45478	+	0.198277i
$335$	−18.9737			−1.03664
$336$		0			0
$337$	−8.00000			−0.435788			−0.217894	−	0.975972i	$-0.569919\pi$
$337$	−8.00000			−0.435788			−0.217894	+	0.975972i	$0.569919\pi$
$338$	−23.8214	−	3.24671i	−1.29571	−	0.176598i
$339$	4.54259	+	6.27415i	0.246719	+	0.340765i
$340$	−23.1246	−	6.42280i	−1.25411	−	0.348325i
$341$	−25.4558	+	14.6969i	−1.37851	+	0.795884i
$342$	−1.27099	−	17.9551i	−0.0687275	−	0.970899i
$343$		0			0
$344$	8.66025	−	20.1246i	0.466930	−	1.08505i
$345$		0			0
$346$	3.20642	−	1.31105i	0.172378	−	0.0704824i
$347$	12.1244	−	21.0000i	0.650870	−	1.12734i	−0.332043	−	0.943264i	$-0.607738\pi$
$347$	12.1244	−	21.0000i	0.650870	−	1.12734i	0.982912	−	0.184075i	$-0.0589288\pi$
$348$	−5.39566	−	14.5219i	−0.289238	−	0.778458i
$349$	16.4317			0.879567			0.439784	−	0.898104i	$-0.355055\pi$
$349$	16.4317			0.879567			0.439784	+	0.898104i	$0.355055\pi$
$350$		0			0
$351$	8.66025	+	27.1109i	0.462250	+	1.44707i
$352$	−18.2705	+	7.08438i	−0.973821	+	0.377599i
$353$	12.7279	+	7.34847i	0.677439	+	0.391120i	0.798889	−	0.601478i	$-0.205421\pi$
$353$	12.7279	+	7.34847i	0.677439	+	0.391120i	−0.121450	+	0.992597i	$0.538755\pi$
$354$	−0.752656	+	23.2257i	−0.0400032	+	1.23443i
$355$	7.34847	−	4.24264i	0.390016	−	0.225176i
$356$	18.9737	−	4.89898i	1.00560	−	0.259645i
$357$		0			0
$358$	9.00000	−	11.6190i	0.475665	−	0.614081i
$359$	13.8564	+	24.0000i	0.731313	+	1.26667i	0.956322	+	0.292315i	$0.0944255\pi$
$359$	13.8564	+	24.0000i	0.731313	+	1.26667i	−0.225009	+	0.974357i	$0.572241\pi$
$360$	4.13433	−	20.3693i	0.217899	−	1.07355i
$361$	−0.500000	+	0.866025i	−0.0263158	+	0.0455803i
$362$	23.0250	+	3.13817i	1.21017	+	0.164939i
$363$	1.58114	+	0.707107i	0.0829883	+	0.0371135i
$364$		0			0
$365$		−	26.8328i		−	1.40449i
$366$	11.3956	+	7.08101i	0.595657	+	0.370130i
$367$	−22.0454	−	12.7279i	−1.15076	−	0.664392i	−0.201688	−	0.979450i	$-0.564643\pi$
$367$	−22.0454	−	12.7279i	−1.15076	−	0.664392i	−0.949073	+	0.315058i	$0.897976\pi$
$368$		0			0
$369$		0			0
$370$	5.47723	+	4.24264i	0.284747	+	0.220564i
$371$		0			0
$372$	28.9808	+	4.91075i	1.50258	+	0.254610i
$373$	−13.0000	−	22.5167i	−0.673114	−	1.16587i	−0.977016	−	0.213165i	$-0.931623\pi$
$373$	−13.0000	−	22.5167i	−0.673114	−	1.16587i	0.303902	−	0.952703i	$-0.401711\pi$
$374$	−22.2148	+	9.08321i	−1.14870	+	0.469681i
$375$	9.95231	+	13.7460i	0.513935	+	0.709839i
$376$		0			0
$377$			24.4949i			1.26155i
$378$		0			0
$379$		−	7.74597i		−	0.397884i	−0.980011	−	0.198942i	$-0.936250\pi$
$379$		−	7.74597i		−	0.397884i	0.980011	−	0.198942i	$-0.0637505\pi$
$380$	14.8303	−	14.5623i	0.760781	−	0.747031i
$381$	−7.86799	−	10.8671i	−0.403089	−	0.556740i
$382$	−1.85410	−	4.53457i	−0.0948641	−	0.232009i
$383$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$383$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$384$	18.5916	+	6.19307i	0.948746	+	0.316039i
$385$		0			0
$386$	−13.8564	+	17.8885i	−0.705273	+	0.910503i
$387$	22.0767	+	7.25403i	1.12222	+	0.368743i
$388$		0			0
$389$	−27.1109	−	15.6525i	−1.37458	−	0.793612i	−0.383076	−	0.923717i	$-0.625135\pi$
$389$	−27.1109	−	15.6525i	−1.37458	−	0.793612i	−0.991500	+	0.130105i	$0.958469\pi$
$390$	−17.3449	+	27.9134i	−0.878291	+	1.41345i
$391$		0			0
$392$		0			0
$393$	−15.0000	−	6.70820i	−0.756650	−	0.338384i
$394$	4.27051	−	31.3331i	0.215145	−	1.57854i
$395$	−18.9737	+	32.8634i	−0.954669	+	1.65353i
$396$	−9.20510	−	18.6351i	−0.462574	−	0.936448i
$397$	−19.1703	−	33.2039i	−0.962129	−	1.66646i	−0.717138	−	0.696932i	$-0.754548\pi$
$397$	−19.1703	−	33.2039i	−0.962129	−	1.66646i	−0.244992	−	0.969525i	$-0.578785\pi$
$398$	−18.9737	−	14.6969i	−0.951064	−	0.736691i
$399$		0			0
$400$	3.50000	−	1.93649i	0.175000	−	0.0968246i
$401$	3.87298	−	2.23607i	0.193408	−	0.111664i	−0.400169	−	0.916441i	$-0.631049\pi$
$401$	3.87298	−	2.23607i	0.193408	−	0.111664i	0.593577	+	0.804777i	$0.297715\pi$
$402$	18.9637	+	0.614541i	0.945824	+	0.0306505i
$403$	−40.2492	−	23.2379i	−2.00496	−	1.15756i
$404$	−10.2971	−	10.4866i	−0.512300	−	0.521730i
$405$	21.9089	+	2.44949i	1.08866	+	0.121716i
$406$		0			0
$407$	6.92820			0.343418
$408$	22.9045	+	7.16841i	1.13394	+	0.354889i
$409$	5.47723	−	9.48683i	0.270831	−	0.469094i	−0.698244	−	0.715860i	$-0.746035\pi$
$409$	5.47723	−	9.48683i	0.270831	−	0.469094i	0.969075	+	0.246767i	$0.0793681\pi$
$410$		0			0
$411$	−15.4097	+	1.59384i	−0.760106	+	0.0786184i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−20.1246	+	11.6190i	−0.987878	+	0.570352i
$416$	−24.1448	−	19.4172i	−1.18380	−	0.952008i
$417$	4.30948	+	5.95218i	0.211036	+	0.291479i
$418$	2.80687	−	20.5942i	0.137288	−	1.00730i
$419$	28.4605			1.39039			0.695193	−	0.718823i	$-0.255319\pi$
$419$	28.4605			1.39039			0.695193	+	0.718823i	$0.255319\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	−1.47935	+	10.8541i	−0.0720135	+	0.528369i
$423$		0			0
$424$	−7.56231	−	10.1396i	−0.367258	−	0.492423i
$425$	4.24264	−	2.44949i	0.205798	−	0.118818i
$426$	−7.48203	+	4.00240i	−0.362506	+	0.193917i
$427$		0			0
$428$	8.66025	+	33.5410i	0.418609	+	1.62127i
$429$	3.38105	+	32.6890i	0.163239	+	1.57824i
$430$	10.1553	+	24.8369i	0.489734	+	1.19774i
$431$	−10.3923	+	18.0000i	−0.500580	+	0.867029i	0.499420	+	0.866360i	$0.333546\pi$
$431$	−10.3923	+	18.0000i	−0.500580	+	0.867029i	−1.00000		0.000669521i	$0.999787\pi$
$432$	−4.79191	+	20.2247i	−0.230551	+	0.973060i
$433$	21.9089			1.05287			0.526437	−	0.850214i	$-0.323527\pi$
$433$	21.9089			1.05287			0.526437	+	0.850214i	$0.323527\pi$
$434$		0			0
$435$	17.3205	+	7.74597i	0.830455	+	0.371391i
$436$	−14.2705	+	14.0126i	−0.683433	+	0.671081i
$437$		0			0
$438$	−0.869092	+	26.8187i	−0.0415268	+	1.28145i
$439$	−14.6969	+	8.48528i	−0.701447	+	0.404980i	−0.807886	−	0.589339i	$-0.799388\pi$
$439$	−14.6969	+	8.48528i	−0.701447	+	0.404980i	0.106439	+	0.994319i	$0.466055\pi$
$440$	9.48683	−	22.0454i	0.452267	−	1.05097i
$441$		0			0
$442$	−30.0000	−	23.2379i	−1.42695	−	1.10531i
$443$	−15.5885	−	27.0000i	−0.740630	−	1.28281i	−0.952209	−	0.305448i	$-0.901194\pi$
$443$	−15.5885	−	27.0000i	−0.740630	−	1.28281i	0.211579	−	0.977361i	$-0.432139\pi$
$444$	−5.33694	−	4.41782i	−0.253280	−	0.209660i
$445$	−12.0000	+	20.7846i	−0.568855	+	0.985285i
$446$	−1.62054	+	11.8901i	−0.0767350	+	0.563011i
$447$	3.16228	−	7.07107i	0.149571	−	0.334450i
$448$		0			0
$449$			35.7771i			1.68843i	0.536009	+	0.844213i	$0.319931\pi$
$449$			35.7771i			1.68843i	−0.536009	+	0.844213i	$0.680069\pi$
$450$	2.37547	+	3.51528i	0.111981	+	0.165712i
$451$		0			0
$452$	2.39364	−	8.61803i	0.112587	−	0.405358i
$453$	13.3452	−	1.38031i	0.627013	−	0.0648525i
$454$	8.21584	−	10.6066i	0.385588	−	0.497792i
$455$		0			0
$456$	−15.2942	+	14.0743i	−0.716218	+	0.659091i
$457$	14.0000	+	24.2487i	0.654892	+	1.13431i	0.981921	+	0.189292i	$0.0606194\pi$
$457$	14.0000	+	24.2487i	0.654892	+	1.13431i	−0.327028	+	0.945015i	$0.606047\pi$
$458$	−2.93159	−	7.16978i	−0.136984	−	0.335022i
$459$	−5.41615	+	24.8730i	−0.252804	+	1.16097i
$460$		0			0
$461$		−	36.7423i		−	1.71126i	−0.517587	−	0.855631i	$-0.673169\pi$
$461$		−	36.7423i		−	1.71126i	0.517587	−	0.855631i	$-0.326831\pi$
$462$		0			0
$463$			15.4919i			0.719971i	0.932958	+	0.359986i	$0.117218\pi$
$463$			15.4919i			0.719971i	−0.932958	+	0.359986i	$0.882782\pi$
$464$	−9.22531	+	15.3262i	−0.428274	+	0.711503i
$465$	−29.1596	+	21.1120i	−1.35224	+	0.979047i
$466$	11.7082	−	4.78727i	0.542372	−	0.221766i
$467$	14.2302	+	24.6475i	0.658497	+	1.14055i	0.981005	+	0.193984i	$0.0621410\pi$
$467$	14.2302	+	24.6475i	0.658497	+	1.14055i	−0.322507	+	0.946567i	$0.604526\pi$
$468$	18.2399	−	27.3369i	0.843138	−	1.26365i
$469$		0			0
$470$		0			0
$471$	0.976025	+	9.43649i	0.0449729	+	0.434811i
$472$	21.5093	−	16.0421i	0.990048	−	0.738396i
$473$	23.2379	+	13.4164i	1.06848	+	0.616887i
$474$	20.0281	−	32.2316i	0.919922	−	1.48045i
$475$			4.24264i			0.194666i
$476$		0			0
$477$	10.0000	−	8.94427i	0.457869	−	0.409530i
$478$	−9.70820	−	1.32317i	−0.444043	−	0.0605203i
$479$	18.9737	−	32.8634i	0.866929	−	1.50156i	0.00180988	−	0.999998i	$-0.499424\pi$
$479$	18.9737	−	32.8634i	0.866929	−	1.50156i	0.865119	−	0.501567i	$-0.167243\pi$
$480$	−21.3653	+	10.9327i	−0.975189	+	0.499006i
$481$	5.47723	+	9.48683i	0.249740	+	0.432562i
$482$	−18.9737	+	24.4949i	−0.864227	+	1.11571i
$483$		0			0
$484$	−0.500000	−	1.93649i	−0.0227273	−	0.0880223i
$485$		0			0
$486$	−21.8181	−	3.15782i	−0.989688	−	0.143241i
$487$	6.70820	+	3.87298i	0.303978	+	0.175502i	0.644228	−	0.764833i	$-0.277179\pi$
$487$	6.70820	+	3.87298i	0.303978	+	0.175502i	−0.340251	+	0.940335i	$0.610512\pi$
$488$	−1.81182	−	15.3856i	−0.0820174	−	0.696474i
$489$	5.47723	−	12.2474i	0.247689	−	0.553849i
$490$		0			0
$491$	−31.1769			−1.40699			−0.703497	−	0.710698i	$-0.748379\pi$
$491$	−31.1769			−1.40699			−0.703497	+	0.710698i	$0.748379\pi$
$492$		0			0
$493$	−10.9545	+	18.9737i	−0.493364	+	0.854531i
$494$	30.4188	−	12.4377i	1.36861	−	0.559598i
$495$	24.1838	+	7.94640i	1.08698	+	0.357164i
$496$	−16.4317	−	29.6985i	−0.737804	−	1.33350i
$497$		0			0
$498$	20.4904	−	10.9610i	0.918196	−	0.491176i
$499$	−20.1246	+	11.6190i	−0.900901	+	0.520136i	−0.877493	−	0.479590i	$-0.840785\pi$
$499$	−20.1246	+	11.6190i	−0.900901	+	0.520136i	−0.0234088	+	0.999726i	$0.507452\pi$
$500$	5.24419	−	18.8812i	0.234527	−	0.844391i
$501$	26.6190	−	19.2726i	1.18925	−	0.861034i
$502$	−13.2935	−	1.81182i	−0.593318	−	0.0808657i
$503$	−18.9737			−0.845994			−0.422997	−	0.906131i	$-0.639022\pi$
$503$	−18.9737			−0.845994			−0.422997	+	0.906131i	$0.639022\pi$
$504$		0			0
$505$	18.0000			0.800989
$506$		0			0
$507$	−23.8500	+	17.2678i	−1.05922	+	0.766890i
$508$	−4.14590	+	14.9269i	−0.183944	+	0.662273i
$509$	31.8198	−	18.3712i	1.41039	−	0.814288i	0.414963	−	0.909838i	$-0.363794\pi$
$509$	31.8198	−	18.3712i	1.41039	−	0.814288i	0.995425	+	0.0955502i	$0.0304610\pi$
$510$	−25.9185	+	13.8647i	−1.14769	+	0.613941i
$511$		0			0
$512$	−7.79423	−	21.2426i	−0.344459	−	0.938801i
$513$	−16.3095	−	14.8324i	−0.720081	−	0.654868i
$514$	6.41285	−	2.62210i	0.282859	−	0.115656i
$515$		0			0
$516$	−9.34556	−	25.1527i	−0.411415	−	1.10729i
$517$		0			0
$518$		0			0
$519$	1.73205	−	3.87298i	0.0760286	−	0.170005i
$520$	37.6869	−	4.43804i	1.65268	−	0.194621i
$521$	−25.4558	−	14.6969i	−1.11524	−	0.643885i	−0.175059	−	0.984558i	$-0.556012\pi$
$521$	−25.4558	−	14.6969i	−1.11524	−	0.643885i	−0.940182	+	0.340673i	$0.889345\pi$
$522$	−17.0605	−	8.30290i	−0.746719	−	0.363408i
$523$	−18.3712	+	10.6066i	−0.803315	+	0.463794i	−0.844629	−	0.535352i	$-0.820179\pi$
$523$	−18.3712	+	10.6066i	−0.803315	+	0.463794i	0.0413138	+	0.999146i	$0.486846\pi$
$524$	4.74342	+	18.3712i	0.207217	+	0.802548i
$525$		0			0
$526$	−3.00000	+	3.87298i	−0.130806	+	0.168870i
$527$	−20.7846	−	36.0000i	−0.905392	−	1.56818i
$528$	−10.1959	+	21.7266i	−0.443719	+	0.945528i
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$	15.3500	+	2.09211i	0.666762	+	0.0908756i
$531$	18.9737	+	21.2132i	0.823387	+	0.920575i
$532$		0			0
$533$		0			0
$534$	12.6669	−	20.3850i	0.548150	−	0.882147i
$535$	−36.7423	−	21.2132i	−1.58851	−	0.917127i
$536$	−13.0983	−	17.5623i	−0.565760	−	0.758576i
$537$	−1.85188	−	17.9045i	−0.0799144	−	0.772636i
$538$	−2.73861	−	2.12132i	−0.118070	−	0.0914566i
$539$		0			0
$540$	−13.5622	−	21.5422i	−0.583623	−	0.927030i
$541$	−19.0000	−	32.9090i	−0.816874	−	1.41487i	−0.907975	−	0.419025i	$-0.862372\pi$
$541$	−19.0000	−	32.9090i	−0.816874	−	1.41487i	0.0911008	−	0.995842i	$-0.470961\pi$
$542$	11.1074	−	4.54160i	0.477103	−	0.195079i
$543$	23.0527	−	16.6905i	0.989285	−	0.716259i
$544$	−10.0188	−	25.8384i	−0.429554	−	1.10781i
$545$		−	24.4949i		−	1.04925i
$546$		0			0
$547$		−	38.7298i		−	1.65597i	−0.560752	−	0.827984i	$-0.689488\pi$
$547$		−	38.7298i		−	1.65597i	0.560752	−	0.827984i	$-0.310512\pi$
$548$	12.5332	+	12.7639i	0.535393	+	0.545248i
$549$	16.0838	−	3.36311i	0.686441	−	0.143534i
$550$	1.85410	+	4.53457i	0.0790592	+	0.193355i
$551$	−9.48683	−	16.4317i	−0.404153	−	0.700013i
$552$		0			0
$553$		0			0
$554$	1.73205	−	2.23607i	0.0735878	−	0.0950014i
$555$	8.44025	−	0.872983i	0.358269	−	0.0370561i
$556$	2.27080	−	8.17578i	0.0963035	−	0.346731i
$557$	−19.3649	−	11.1803i	−0.820518	−	0.473726i	0.0300772	−	0.999548i	$-0.490425\pi$
$557$	−19.3649	−	11.1803i	−0.820518	−	0.473726i	−0.850595	+	0.525821i	$0.823758\pi$
$558$	29.8281	−	20.1565i	1.26272	−	0.853293i
$559$			42.4264i			1.79445i
$560$		0			0
$561$	−12.0000	+	26.8328i	−0.506640	+	1.13288i
$562$	−1.70820	+	12.5332i	−0.0720562	+	0.528683i
$563$	−4.74342	+	8.21584i	−0.199911	+	0.346256i	−0.948499	−	0.316779i	$-0.897399\pi$
$563$	−4.74342	+	8.21584i	−0.199911	+	0.346256i	0.748588	+	0.663035i	$0.230732\pi$
$564$		0			0
$565$	5.47723	+	9.48683i	0.230429	+	0.399114i
$566$	−33.2039	−	25.7196i	−1.39566	−	1.08108i
$567$		0			0
$568$	9.00000	+	3.87298i	0.377632	+	0.162507i
$569$	27.1109	−	15.6525i	1.13655	−	0.656186i	0.190974	−	0.981595i	$-0.438835\pi$
$569$	27.1109	−	15.6525i	1.13655	−	0.656186i	0.945573	+	0.325409i	$0.105502\pi$
$570$	0.824493	−	25.4425i	0.0345342	−	1.06567i
$571$	20.1246	+	11.6190i	0.842189	+	0.486238i	0.858008	−	0.513637i	$-0.171702\pi$
$571$	20.1246	+	11.6190i	0.842189	+	0.486238i	−0.0158188	+	0.999875i	$0.505036\pi$
$572$	27.0764	−	26.5870i	1.13212	−	1.11166i
$573$	−5.47723	−	2.44949i	−0.228814	−	0.102329i
$574$		0			0
$575$		0			0
$576$	21.7082	−	10.2349i	0.904508	−	0.426456i
$577$	−21.9089	+	37.9473i	−0.912080	+	1.57977i	−0.100958	+	0.994891i	$0.532191\pi$
$577$	−21.9089	+	37.9473i	−0.912080	+	1.57977i	−0.811122	+	0.584877i	$0.801143\pi$
$578$	−3.74663	−	9.16312i	−0.155839	−	0.381136i
$579$	2.85115	+	27.5658i	0.118490	+	1.14559i
$580$	−5.47723	−	21.2132i	−0.227429	−	0.880830i
$581$		0			0
$582$		0			0
$583$	13.4164	−	7.74597i	0.555651	−	0.320805i
$584$	24.8369	−	18.5238i	1.02776	−	0.766520i
$585$	8.23790	+	39.3972i	0.340595	+	1.62887i
$586$	0.467811	−	3.43237i	0.0193251	−	0.141790i
$587$	9.48683			0.391564			0.195782	−	0.980647i	$-0.437276\pi$
$587$	9.48683			0.391564			0.195782	+	0.980647i	$0.437276\pi$
$588$		0			0
$589$	36.0000			1.48335
$590$	−4.43804	+	32.5623i	−0.182711	+	1.34057i
$591$	−22.7129	−	31.3707i	−0.934285	−	1.29042i
$592$	−0.145898	+	7.99867i	−0.00599637	+	0.328743i
$593$	29.6985	−	17.1464i	1.21957	−	0.704119i	0.254745	−	0.967008i	$-0.418009\pi$
$593$	29.6985	−	17.1464i	1.21957	−	0.704119i	0.964826	+	0.262889i	$0.0846753\pi$
$594$	−23.9137	−	8.72552i	−0.981191	−	0.358012i
$595$		0			0
$596$	−8.66025	+	2.23607i	−0.354738	+	0.0915929i
$597$	−29.2379	+	3.02410i	−1.19663	+	0.123768i
$598$		0			0
$599$	12.1244	−	21.0000i	0.495388	−	0.858037i	−0.504598	−	0.863354i	$-0.668359\pi$
$599$	12.1244	−	21.0000i	0.495388	−	0.858037i	0.999986	+	0.00531761i	$0.00169266\pi$
$600$	1.46325	−	4.67535i	0.0597368	−	0.190870i
$601$	−10.9545			−0.446841			−0.223421	−	0.974722i	$-0.571722\pi$
$601$	−10.9545			−0.446841			−0.223421	+	0.974722i	$0.571722\pi$
$602$		0			0
$603$	17.3205	−	15.4919i	0.705346	−	0.630880i
$604$	−10.8541	−	11.0539i	−0.441647	−	0.449776i
$605$	2.12132	+	1.22474i	0.0862439	+	0.0497930i
$606$	−17.9906	−	0.583005i	−0.730816	−	0.0236830i
$607$	22.0454	−	12.7279i	0.894795	−	0.516610i	0.0192875	−	0.999814i	$-0.493860\pi$
$607$	22.0454	−	12.7279i	0.894795	−	0.516610i	0.875508	+	0.483204i	$0.160527\pi$
$608$	23.7171	+	3.67423i	0.961855	+	0.149010i
$609$		0			0
$610$	15.0000	+	11.6190i	0.607332	+	0.470438i
$611$		0			0
$612$	26.3540	−	13.0180i	1.06530	−	0.526221i
$613$	7.00000	−	12.1244i	0.282727	−	0.489698i	−0.689328	−	0.724449i	$-0.742094\pi$
$613$	7.00000	−	12.1244i	0.282727	−	0.489698i	0.972056	+	0.234751i	$0.0754275\pi$
$614$	−4.05136	+	29.7252i	−0.163500	+	1.19961i
$615$		0			0
$616$		0			0
$617$		−	22.3607i		−	0.900207i	−0.892976	−	0.450104i	$-0.851387\pi$
$617$		−	22.3607i		−	0.900207i	0.892976	−	0.450104i	$-0.148613\pi$
$618$		0			0
$619$	3.67423	+	2.12132i	0.147680	+	0.0852631i	0.572019	−	0.820240i	$-0.306160\pi$
$619$	3.67423	+	2.12132i	0.147680	+	0.0852631i	−0.424339	+	0.905503i	$0.639494\pi$
$620$	40.0530	+	11.1246i	1.60857	+	0.446775i
$621$		0			0
$622$	−16.4317	+	21.2132i	−0.658850	+	0.850572i
$623$		0			0
$624$	−37.8109	+	3.21507i	−1.51365	+	0.128706i
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	−5.86319	−	14.3396i	−0.234340	−	0.573124i
$627$	−14.9285	−	20.6190i	−0.596185	−	0.823442i
$628$	7.81628	−	7.67501i	0.311904	−	0.306266i
$629$			9.79796i			0.390670i
$630$		0			0
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$	−43.5171	+	5.12461i	−1.73102	+	0.203846i
$633$	7.86799	+	10.8671i	0.312724	+	0.431930i
$634$	5.85410	−	2.39364i	0.232496	−	0.0950634i
$635$	−9.48683	−	16.4317i	−0.376473	−	0.652071i
$636$	−15.2742	−	2.58819i	−0.605662	−	0.102628i
$637$		0			0
$638$	−17.3205	−	13.4164i	−0.685725	−	0.531161i
$639$	−3.24410	+	9.87298i	−0.128335	+	0.390569i
$640$	25.2518	+	11.4169i	0.998166	+	0.451292i
$641$	−27.1109	−	15.6525i	−1.07082	−	0.618236i	−0.142411	−	0.989808i	$-0.545486\pi$
$641$	−27.1109	−	15.6525i	−1.07082	−	0.618236i	−0.928404	+	0.371572i	$0.878819\pi$
$642$	36.0360	+	22.3921i	1.42223	+	0.883747i
$643$			21.2132i			0.836567i	0.908317	+	0.418284i	$0.137368\pi$
$643$			21.2132i			0.836567i	−0.908317	+	0.418284i	$0.862632\pi$
$644$		0			0
$645$	30.0000	+	13.4164i	1.18125	+	0.528271i
$646$	29.1246	+	3.96951i	1.14589	+	0.156178i
$647$	−9.48683	+	16.4317i	−0.372966	+	0.645996i	−0.990020	−	0.140925i	$-0.954992\pi$
$647$	−9.48683	+	16.4317i	−0.372966	+	0.645996i	0.617054	+	0.786920i	$0.288326\pi$
$648$	12.8573	+	21.9702i	0.505084	+	0.863070i
$649$	16.4317	+	28.4605i	0.645000	+	1.11717i
$650$	−4.74342	+	6.12372i	−0.186052	+	0.240192i
$651$		0			0
$652$	−15.0000	+	3.87298i	−0.587445	+	0.151678i
$653$	27.1109	−	15.6525i	1.06093	−	0.612529i	0.135241	−	0.990813i	$-0.456819\pi$
$653$	27.1109	−	15.6525i	1.06093	−	0.612529i	0.925690	+	0.378284i	$0.123486\pi$
$654$	−0.793369	+	24.4820i	−0.0310232	+	0.957324i
$655$	−20.1246	−	11.6190i	−0.786334	−	0.453990i
$656$		0			0
$657$	21.9089	+	24.4949i	0.854748	+	0.955637i
$658$		0			0
$659$	24.2487			0.944596			0.472298	−	0.881439i	$-0.343425\pi$
$659$	24.2487			0.944596			0.472298	+	0.881439i	$0.343425\pi$
$660$	−10.2376	−	27.5534i	−0.398496	−	1.07252i
$661$	−19.1703	+	33.2039i	−0.745638	+	1.29148i	0.204258	+	0.978917i	$0.434522\pi$
$661$	−19.1703	+	33.2039i	−0.745638	+	1.29148i	−0.949896	+	0.312566i	$0.898812\pi$
$662$	−30.4188	+	12.4377i	−1.18226	+	0.483405i
$663$	−46.2292	+	4.78153i	−1.79539	+	0.185699i
$664$	−24.6475	−	10.6066i	−0.956509	−	0.411616i
$665$		0			0
$666$	−8.46410	+	0.599153i	−0.327977	+	0.0232167i
$667$		0			0
$668$	−36.5632	−	10.1553i	−1.41467	−	0.392922i
$669$	8.61895	+	11.9044i	0.333228	+	0.460249i
$670$	26.5870	+	3.62365i	1.02715	+	0.139994i
$671$	18.9737			0.732470
$672$		0			0
$673$	−26.0000			−1.00223			−0.501113	−	0.865382i	$-0.667076\pi$
$673$	−26.0000			−1.00223			−0.501113	+	0.865382i	$0.667076\pi$
$674$	11.2101	+	1.52786i	0.431796	+	0.0588511i
$675$	5.07718	+	1.10557i	0.195421	+	0.0425533i
$676$	32.7599	+	9.09896i	1.25999	+	0.349960i
$677$	6.36396	−	3.67423i	0.244587	−	0.141212i	−0.372696	−	0.927953i	$-0.621567\pi$
$677$	6.36396	−	3.67423i	0.244587	−	0.141212i	0.617283	+	0.786741i	$0.288233\pi$
$678$	−5.16708	−	9.65926i	−0.198441	−	0.370962i
$679$		0			0
$680$	31.1769	+	13.4164i	1.19558	+	0.514496i
$681$	−1.69052	−	16.3445i	−0.0647811	−	0.626322i
$682$	38.4771	−	15.7326i	1.47336	−	0.602432i
$683$	−19.0526	+	33.0000i	−0.729026	+	1.26271i	0.228269	+	0.973598i	$0.426693\pi$
$683$	−19.0526	+	33.0000i	−0.729026	+	1.26271i	−0.957295	+	0.289112i	$0.906640\pi$
$684$	−1.64812	+	25.4024i	−0.0630175	+	0.971286i
$685$	−21.9089			−0.837096
$686$		0			0
$687$	−8.66025	−	3.87298i	−0.330409	−	0.147764i
$688$	−15.9787	+	26.5458i	−0.609183	+	1.01205i
$689$	21.2132	+	12.2474i	0.808159	+	0.466591i
$690$		0			0
$691$	11.0227	−	6.36396i	0.419323	−	0.242096i	−0.275464	−	0.961311i	$-0.588832\pi$
$691$	11.0227	−	6.36396i	0.419323	−	0.242096i	0.694788	+	0.719215i	$0.255498\pi$
$692$	−4.74342	+	1.22474i	−0.180318	+	0.0465578i
$693$		0			0
$694$	−21.0000	+	27.1109i	−0.797149	+	1.02912i
$695$	5.19615	+	9.00000i	0.197101	+	0.341389i
$696$	4.78727	+	21.3795i	0.181461	+	0.810387i
$697$		0			0
$698$	−23.0250	−	3.13817i	−0.871510	−	0.118782i
$699$	6.32456	−	14.1421i	0.239217	−	0.534905i
$700$		0			0
$701$		−	22.3607i		−	0.844551i	−0.906467	−	0.422276i	$-0.861231\pi$
$701$		−	22.3607i		−	0.844551i	0.906467	−	0.422276i	$-0.138769\pi$
$702$	−6.95754	−	39.6433i	−0.262595	−	1.49624i
$703$	−7.34847	−	4.24264i	−0.277153	−	0.160014i
$704$	26.9547	−	6.43769i	1.01589	−	0.242630i
$705$		0			0
$706$	−16.4317	−	12.7279i	−0.618414	−	0.479022i
$707$		0			0
$708$	5.49038	−	32.4015i	0.206341	−	1.21772i
$709$	−5.00000	−	8.66025i	−0.187779	−	0.325243i	0.756730	−	0.653727i	$-0.226796\pi$
$709$	−5.00000	−	8.66025i	−0.187779	−	0.325243i	−0.944509	+	0.328484i	$0.893462\pi$
$710$	−11.1074	+	4.54160i	−0.416852	+	0.170443i
$711$	−9.51231	−	45.4919i	−0.356739	−	1.70608i
$712$	−27.5226	+	3.24109i	−1.03145	+	0.121465i
$713$		0			0
$714$		0			0
$715$			46.4758i			1.73810i
$716$	−14.8303	+	14.5623i	−0.554236	+	0.544219i
$717$	−9.71987	+	7.03734i	−0.362995	+	0.262814i
$718$	−14.8328	−	36.2765i	−0.553556	−	1.35383i
$719$	18.9737	+	32.8634i	0.707598	+	1.22560i	0.965746	+	0.259491i	$0.0835547\pi$
$719$	18.9737	+	32.8634i	0.707598	+	1.22560i	−0.258147	+	0.966106i	$0.583112\pi$
$720$	−9.68346	+	27.7530i	−0.360881	+	1.03429i
$721$		0			0
$722$	0.866025	−	1.11803i	0.0322301	−	0.0416089i
$723$	3.90410	+	37.7460i	0.145195	+	1.40379i
$724$	−31.6647	−	8.79478i	−1.17681	−	0.326855i
$725$	3.87298	+	2.23607i	0.143839	+	0.0830455i
$726$	−2.08054	−	1.29281i	−0.0772160	−	0.0479807i
$727$			16.9706i			0.629403i	0.949191	+	0.314702i	$0.101904\pi$
$727$			16.9706i			0.629403i	−0.949191	+	0.314702i	$0.898096\pi$
$728$		0			0
$729$	−22.0000	+	15.6525i	−0.814815	+	0.579721i
$730$	−5.12461	+	37.5997i	−0.189670	+	1.39163i
$731$	−18.9737	+	32.8634i	−0.701766	+	1.21550i
$732$	−14.6158	−	12.0987i	−0.540216	−	0.447180i
$733$	8.21584	+	14.2302i	0.303459	+	0.525606i	0.976917	−	0.213619i	$-0.0685252\pi$
$733$	8.21584	+	14.2302i	0.303459	+	0.525606i	−0.673458	+	0.739225i	$0.735192\pi$
$734$	28.4605	+	22.0454i	1.05050	+	0.813711i
$735$		0			0
$736$		0			0
$737$	23.2379	−	13.4164i	0.855979	−	0.494200i
$738$		0			0
$739$	33.5410	+	19.3649i	1.23383	+	0.712350i	0.967825	−	0.251623i	$-0.0809642\pi$
$739$	33.5410	+	19.3649i	1.23383	+	0.712350i	0.266001	+	0.963973i	$0.414298\pi$
$740$	−6.86474	−	6.99109i	−0.252353	−	0.256998i
$741$	16.4317	−	36.7423i	0.603633	−	1.34976i
$742$		0			0
$743$	−13.8564			−0.508342			−0.254171	−	0.967159i	$-0.581803\pi$
$743$	−13.8564			−0.508342			−0.254171	+	0.967159i	$0.581803\pi$
$744$	−39.6717	−	12.4161i	−1.45443	−	0.455195i
$745$	5.47723	−	9.48683i	0.200670	−	0.347571i
$746$	13.9161	+	34.0344i	0.509503	+	1.24609i
$747$	8.88434	−	27.0383i	0.325061	−	0.989279i
$748$	32.8634	−	8.48528i	1.20160	−	0.310253i
$749$		0			0
$750$	−11.3205	−	21.1624i	−0.413367	−	0.772741i
$751$	6.70820	−	3.87298i	0.244786	−	0.141327i	−0.372589	−	0.927997i	$-0.621530\pi$
$751$	6.70820	−	3.87298i	0.244786	−	0.141327i	0.617374	+	0.786669i	$0.288196\pi$
$752$		0			0
$753$	−13.3095	+	9.63628i	−0.485024	+	0.351166i
$754$	4.67811	−	34.3237i	0.170367	−	1.24999i
$755$	18.9737			0.690522
$756$		0			0
$757$	−38.0000			−1.38113			−0.690567	−	0.723269i	$-0.742639\pi$
$757$	−38.0000			−1.38113			−0.690567	+	0.723269i	$0.742639\pi$
$758$	−1.47935	+	10.8541i	−0.0537323	+	0.394239i
$759$		0			0
$760$	−23.5623	+	17.5732i	−0.854695	+	0.637447i
$761$	−42.4264	+	24.4949i	−1.53796	+	0.887939i	−0.538998	+	0.842307i	$0.681197\pi$
$761$	−42.4264	+	24.4949i	−1.53796	+	0.887939i	−0.998958	+	0.0456321i	$0.985470\pi$
$762$	8.94965	+	16.7303i	0.324212	+	0.606076i
$763$		0			0
$764$	1.73205	+	6.70820i	0.0626634	+	0.242694i
$765$	−11.2379	+	34.2010i	−0.406307	+	1.23654i
$766$		0			0
$767$	−25.9808	+	45.0000i	−0.938111	+	1.62486i
$768$	−24.8688	−	12.2288i	−0.897376	−	0.441268i
$769$	21.9089			0.790055			0.395028	−	0.918669i	$-0.370735\pi$
$769$	21.9089			0.790055			0.395028	+	0.918669i	$0.370735\pi$
$770$		0			0
$771$	3.46410	−	7.74597i	0.124757	−	0.278964i
$772$	22.8328	−	22.4201i	0.821771	−	0.806918i
$773$	2.12132	+	1.22474i	0.0762986	+	0.0440510i	0.537664	−	0.843159i	$-0.319307\pi$
$773$	2.12132	+	1.22474i	0.0762986	+	0.0440510i	−0.461365	+	0.887210i	$0.652640\pi$
$774$	−29.5497	−	14.3810i	−1.06214	−	0.516916i
$775$	−7.34847	+	4.24264i	−0.263965	+	0.152400i
$776$		0			0
$777$		0			0
$778$	35.0000	+	27.1109i	1.25481	+	0.971972i
$779$		0			0
$780$	29.6356	−	35.8013i	1.06113	−	1.28189i
$781$	−6.00000	+	10.3923i	−0.214697	+	0.371866i
$782$		0			0
$783$	−22.1359	+	7.07107i	−0.791074	+	0.252699i
$784$		0			0
$785$			13.4164i			0.478852i
$786$	19.7377	+	12.2647i	0.704021	+	0.437466i
$787$	−18.3712	−	10.6066i	−0.654862	−	0.378085i	0.135455	−	0.990784i	$-0.456750\pi$
$787$	−18.3712	−	10.6066i	−0.654862	−	0.378085i	−0.790316	+	0.612699i	$0.790084\pi$
$788$	−11.9682	+	43.0902i	−0.426349	+	1.53502i
$789$	0.617292	+	5.96816i	0.0219762	+	0.212472i
$790$	32.8634	−	42.4264i	1.16923	−	1.50946i
$791$		0			0
$792$	9.33975	+	27.8706i	0.331873	+	0.990338i
$793$	15.0000	+	25.9808i	0.532666	+	0.922604i
$794$	20.5211	+	50.1885i	0.728268	+	1.78112i
$795$	15.3685	−	11.1270i	0.545063	−	0.394635i
$796$	23.7801	+	24.2179i	0.842865	+	0.858379i
$797$			41.6413i			1.47501i	0.675341	+	0.737506i	$0.263997\pi$
$797$			41.6413i			1.47501i	−0.675341	+	0.737506i	$0.736003\pi$
$798$		0			0
$799$		0			0
$800$	−5.27424	+	2.04508i	−0.186473	+	0.0723047i
$801$	−6.01611	−	28.7716i	−0.212569	−	1.01660i
$802$	−5.85410	+	2.39364i	−0.206716	+	0.0845222i
$803$	18.9737	+	32.8634i	0.669566	+	1.15972i
$804$	−26.4557	−	4.48288i	−0.933020	−	0.158099i
$805$		0			0
$806$	51.9615	+	40.2492i	1.83027	+	1.41772i
$807$	−4.22013	+	0.436492i	−0.148556	+	0.0153652i
$808$	12.4261	+	16.6611i	0.437150	+	0.586134i
$809$	−19.3649	−	11.1803i	−0.680834	−	0.393080i	0.119335	−	0.992854i	$-0.461924\pi$
$809$	−19.3649	−	11.1803i	−0.680834	−	0.393080i	−0.800169	+	0.599774i	$0.795257\pi$
$810$	−30.2322	−	7.61660i	−1.06225	−	0.267620i
$811$		−	12.7279i		−	0.446938i	−0.974711	−	0.223469i	$-0.928262\pi$
$811$		−	12.7279i		−	0.446938i	0.974711	−	0.223469i	$-0.0717381\pi$
$812$		0			0
$813$	6.00000	−	13.4164i	0.210429	−	0.470534i
$814$	−9.70820	−	1.32317i	−0.340272	−	0.0463771i
$815$	9.48683	−	16.4317i	0.332309	−	0.575577i
$816$	−30.7260	−	14.4192i	−1.07563	−	0.504772i
$817$	−16.4317	−	28.4605i	−0.574872	−	0.995707i
$818$	−9.48683	+	12.2474i	−0.331699	+	0.428222i
$819$		0			0
$820$		0			0
$821$	−27.1109	+	15.6525i	−0.946176	+	0.546275i	−0.891891	−	0.452250i	$-0.850621\pi$
$821$	−27.1109	+	15.6525i	−0.946176	+	0.546275i	−0.0542853	+	0.998525i	$0.517288\pi$
$822$	21.8974	+	0.709611i	0.763760	+	0.0247505i
$823$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$823$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$824$		0			0
$825$	5.47723	+	2.44949i	0.190693	+	0.0852803i
$826$		0			0
$827$	17.3205			0.602293			0.301147	−	0.953578i	$-0.402631\pi$
$827$	17.3205			0.602293			0.301147	+	0.953578i	$0.402631\pi$
$828$		0			0
$829$	24.6475	−	42.6907i	0.856044	−	1.48271i	−0.0196299	−	0.999807i	$-0.506249\pi$
$829$	24.6475	−	42.6907i	0.856044	−	1.48271i	0.875673	−	0.482904i	$-0.160418\pi$
$830$	30.4188	−	12.4377i	1.05585	−	0.431719i
$831$	−0.356394	−	3.44572i	−0.0123632	−	0.119531i
$832$	30.1247	+	31.8198i	1.04439	+	1.10315i
$833$		0			0
$834$	−4.90192	−	9.16358i	−0.169740	−	0.317309i
$835$	40.2492	−	23.2379i	1.39288	−	0.804181i
$836$	−7.86629	+	28.3217i	−0.272061	+	0.979528i
$837$	9.38105	−	43.0813i	0.324257	−	1.48911i
$838$	−39.8805	−	5.43547i	−1.37765	−	0.187765i
$839$	−18.9737			−0.655044			−0.327522	−	0.944844i	$-0.606214\pi$
$839$	−18.9737			−0.655044			−0.327522	+	0.944844i	$0.606214\pi$
$840$		0			0
$841$	9.00000			0.310345
$842$	14.0126	+	1.90983i	0.482906	+	0.0658171i
$843$	9.08517	+	12.5483i	0.312910	+	0.432186i
$844$	4.14590	−	14.9269i	0.142708	−	0.513804i
$845$	−36.0624	+	20.8207i	−1.24059	+	0.716253i
$846$		0			0
$847$		0			0
$848$	8.66025	+	15.6525i	0.297394	+	0.537508i
$849$	−51.1663	+	5.29218i	−1.75602	+	0.181627i
$850$	−6.41285	+	2.62210i	−0.219959	+	0.0899372i
$851$		0			0
$852$	11.2486	−	4.17946i	0.385372	−	0.143186i
$853$	16.4317			0.562610			0.281305	−	0.959618i	$-0.409233\pi$
$853$	16.4317			0.562610			0.281305	+	0.959618i	$0.409233\pi$
$854$		0			0
$855$	−20.7846	−	23.2379i	−0.710819	−	0.794719i
$856$	−5.72949	−	48.6536i	−0.195830	−	1.66295i
$857$	16.9706	+	9.79796i	0.579703	+	0.334692i	0.761015	−	0.648734i	$-0.224701\pi$
$857$	16.9706	+	9.79796i	0.579703	+	0.334692i	−0.181312	+	0.983426i	$0.558034\pi$
$858$	1.50531	−	46.4514i	0.0513905	−	1.58583i
$859$	−40.4166	+	23.3345i	−1.37900	+	0.796164i	−0.992039	−	0.125934i	$-0.959807\pi$
$859$	−40.4166	+	23.3345i	−1.37900	+	0.796164i	−0.386957	+	0.922098i	$0.626474\pi$
$860$	−9.48683	−	36.7423i	−0.323498	−	1.25290i
$861$		0			0
$862$	18.0000	−	23.2379i	0.613082	−	0.791486i
$863$	−8.66025	−	15.0000i	−0.294798	−	0.510606i	0.680140	−	0.733083i	$-0.261919\pi$
$863$	−8.66025	−	15.0000i	−0.294798	−	0.510606i	−0.974938	+	0.222477i	$0.928586\pi$
$864$	10.5773	−	27.4248i	0.359846	−	0.933012i
$865$	3.00000	−	5.19615i	0.102003	−	0.176674i
$866$	−30.7000	−	4.18423i	−1.04323	−	0.142186i
$867$	−11.0680	−	4.94975i	−0.375888	−	0.168102i
$868$		0			0
$869$		−	53.6656i		−	1.82048i
$870$	−22.7912	−	14.1620i	−0.772693	−	0.480138i
$871$	36.7423	+	21.2132i	1.24497	+	0.718782i
$872$	22.6728	−	16.9098i	0.767799	−	0.572639i
$873$		0			0
$874$		0			0
$875$		0			0
$876$	6.33975	−	37.4140i	0.214200	−	1.26410i
$877$	−11.0000	−	19.0526i	−0.371444	−	0.643359i	0.618344	−	0.785907i	$-0.287804\pi$
$877$	−11.0000	−	19.0526i	−0.371444	−	0.643359i	−0.989788	+	0.142548i	$0.954470\pi$
$878$	22.2148	−	9.08321i	0.749712	−	0.306543i
$879$	−2.48808	−	3.43649i	−0.0839207	−	0.115910i
$880$	−17.5038	+	29.0795i	−0.590053	+	0.980269i
$881$		−	44.0908i		−	1.48546i	−0.669593	−	0.742729i	$-0.733531\pi$
$881$		−	44.0908i		−	1.48546i	0.669593	−	0.742729i	$-0.266469\pi$
$882$		0			0
$883$			54.2218i			1.82471i	0.409403	+	0.912354i	$0.365737\pi$
$883$			54.2218i			1.82471i	−0.409403	+	0.912354i	$0.634263\pi$
$884$	37.5997	+	38.2918i	1.26462	+	1.28789i
$885$	23.6040	+	32.6014i	0.793439	+	1.09588i
$886$	16.6869	+	40.8111i	0.560608	+	1.37108i
$887$	−28.4605	−	49.2950i	−0.955610	−	1.65517i	−0.732966	−	0.680265i	$-0.761865\pi$
$887$	−28.4605	−	49.2950i	−0.955610	−	1.65517i	−0.222644	−	0.974900i	$-0.571469\pi$
$888$	6.63470	+	7.20977i	0.222646	+	0.241944i
$889$		0			0
$890$	20.7846	−	26.8328i	0.696702	−	0.899438i
$891$	−28.5649	+	12.4919i	−0.956959	+	0.418496i
$892$	4.54160	−	16.3516i	0.152064	−	0.547491i
$893$		0			0
$894$	−5.78162	+	9.30445i	−0.193366	+	0.311187i
$895$		−	25.4558i		−	0.850895i
$896$		0			0
$897$		0			0
$898$	6.83282	−	50.1329i	0.228014	−	1.67296i
$899$	18.9737	−	32.8634i	0.632807	−	1.09605i
$900$	−2.65728	−	5.37948i	−0.0885761	−	0.179316i
$901$	10.9545	+	18.9737i	0.364946	+	0.632104i
$902$		0			0
$903$		0			0
$904$	−5.00000	+	11.6190i	−0.166298	+	0.386441i
$905$	34.8569	−	20.1246i	1.15868	−	0.668965i
$906$	−18.9637	−	0.614541i	−0.630027	−	0.0204168i
$907$	−6.70820	−	3.87298i	−0.222742	−	0.128600i	0.384477	−	0.923135i	$-0.374382\pi$
$907$	−6.70820	−	3.87298i	−0.222742	−	0.128600i	−0.607219	+	0.794534i	$0.707715\pi$
$908$	−13.5382	+	13.2935i	−0.449281	+	0.441160i
$909$	−16.4317	+	14.6969i	−0.545004	+	0.487467i
$910$		0			0
$911$	−20.7846			−0.688625			−0.344312	−	0.938855i	$-0.611888\pi$
$911$	−20.7846			−0.688625			−0.344312	+	0.938855i	$0.611888\pi$
$912$	24.1191	−	16.8008i	0.798664	−	0.556331i
$913$	16.4317	−	28.4605i	0.543809	−	0.941905i
$914$	−14.9865	−	36.6525i	−0.495710	−	1.21236i
$915$	23.1146	−	2.39076i	0.764145	−	0.0790362i
$916$	2.73861	+	10.6066i	0.0904863	+	0.350452i
$917$		0			0
$918$	12.3397	−	33.8191i	0.407272	−	1.11620i
$919$	26.8328	−	15.4919i	0.885133	−	0.511032i	0.0127855	−	0.999918i	$-0.495930\pi$
$919$	26.8328	−	15.4919i	0.885133	−	0.511032i	0.872347	+	0.488887i	$0.162597\pi$
$920$		0			0
$921$	21.5474	+	29.7609i	0.710010	+	0.980655i
$922$	−7.01716	+	51.4855i	−0.231098	+	1.69559i
$923$	−18.9737			−0.624526
$924$		0			0
$925$	2.00000			0.0657596
$926$	2.95870	−	21.7082i	0.0972288	−	0.713376i
$927$		0			0
$928$	15.8541	−	19.7141i	0.520436	−	0.647148i
$929$	−21.2132	+	12.2474i	−0.695983	+	0.401826i	−0.805849	−	0.592121i	$-0.798291\pi$
$929$	−21.2132	+	12.2474i	−0.695983	+	0.401826i	0.109867	+	0.993946i	$0.464958\pi$
$930$	44.8922	−	24.0144i	1.47207	−	0.787464i
$931$		0			0
$932$	−17.3205	+	4.47214i	−0.567352	+	0.146490i
$933$	3.38105	+	32.6890i	0.110691	+	1.07019i
$934$	−15.2330	−	37.2553i	−0.498439	−	1.21903i
$935$	−20.7846	+	36.0000i	−0.679729	+	1.17733i
$936$	−30.7796	+	34.8226i	−1.00606	+	1.13821i
$937$	10.9545			0.357866			0.178933	−	0.983861i	$-0.442735\pi$
$937$	10.9545			0.357866			0.178933	+	0.983861i	$0.442735\pi$
$938$		0			0
$939$	−17.3205	−	7.74597i	−0.565233	−	0.252780i
$940$		0			0
$941$	10.6066	+	6.12372i	0.345765	+	0.199628i	0.662819	−	0.748780i	$-0.269360\pi$
$941$	10.6066	+	6.12372i	0.345765	+	0.199628i	−0.317053	+	0.948408i	$0.602693\pi$
$942$	0.434546	−	13.4094i	0.0141583	−	0.436901i
$943$		0			0
$944$	−33.2039	+	18.3712i	−1.08070	+	0.597931i
$945$		0			0
$946$	−30.0000	−	23.2379i	−0.975384	−	0.755529i
$947$	−5.19615	−	9.00000i	−0.168852	−	0.292461i	0.769164	−	0.639051i	$-0.220673\pi$
$947$	−5.19615	−	9.00000i	−0.168852	−	0.292461i	−0.938017	+	0.346590i	$0.887339\pi$
$948$	−34.2203	+	41.3397i	−1.11142	+	1.34265i
$949$	−30.0000	+	51.9615i	−0.973841	+	1.68674i
$950$	0.810272	−	5.94504i	0.0262887	−	0.192882i
$951$	3.16228	−	7.07107i	0.102544	−	0.229295i
$952$		0			0
$953$			8.94427i			0.289733i	0.989451	+	0.144867i	$0.0462753\pi$
$953$			8.94427i			0.289733i	−0.989451	+	0.144867i	$0.953725\pi$
$954$	−15.7208	+	10.6234i	−0.508979	+	0.343946i
$955$	−7.34847	−	4.24264i	−0.237791	−	0.137289i
$956$	13.3510	+	3.70820i	0.431802	+	0.119932i
$957$	−26.6904	+	2.76062i	−0.862779	+	0.0892380i
$958$	−32.8634	+	42.4264i	−1.06177	+	1.37073i
$959$		0			0
$960$	32.0263	−	11.2391i	1.03364	−	0.362740i
$961$	20.5000	+	35.5070i	0.661290	+	1.14539i
$962$	−5.86319	−	14.3396i	−0.189037	−	0.462326i
$963$	50.8615	−	10.6351i	1.63899	−	0.342711i
$964$	31.2651	−	30.7000i	1.00698	−	0.988782i
$965$			39.1918i			1.26163i
$966$		0			0
$967$			23.2379i			0.747280i	0.927574	+	0.373640i	$0.121891\pi$
$967$			23.2379i			0.747280i	−0.927574	+	0.373640i	$0.878109\pi$
$968$	0.330792	+	2.80902i	0.0106321	+	0.0902852i
$969$	29.1596	−	21.1120i	0.936741	−	0.678216i
$970$		0			0
$971$	−23.7171	−	41.0792i	−0.761117	−	1.31829i	−0.942275	−	0.334840i	$-0.891318\pi$
$971$	−23.7171	−	41.0792i	−0.761117	−	1.31829i	0.181158	−	0.983454i	$-0.442016\pi$
$972$	29.9697	+	8.59180i	0.961278	+	0.275582i
$973$		0			0
$974$	−8.66025	−	6.70820i	−0.277492	−	0.214945i
$975$	0.976025	+	9.43649i	0.0312578	+	0.302210i
$976$	−0.399558	+	21.9053i	−0.0127895	+	0.701170i
$977$	30.9839	+	17.8885i	0.991262	+	0.572305i	0.905651	−	0.424023i	$-0.139383\pi$
$977$	30.9839	+	17.8885i	0.991262	+	0.572305i	0.0856105	+	0.996329i	$0.472716\pi$
$978$	−10.0141	+	16.1158i	−0.320214	+	0.515326i
$979$		−	33.9411i		−	1.08476i
$980$		0			0
$981$	20.0000	+	22.3607i	0.638551	+	0.713922i
$982$	43.6869	+	5.95426i	1.39411	+	0.190008i
$983$	−9.48683	+	16.4317i	−0.302583	+	0.524089i	−0.976720	−	0.214517i	$-0.931182\pi$
$983$	−9.48683	+	16.4317i	−0.302583	+	0.524089i	0.674137	+	0.738606i	$0.264516\pi$
$984$		0			0
$985$	−27.3861	−	47.4342i	−0.872595	−	1.51138i
$986$	18.9737	−	24.4949i	0.604245	−	0.780076i
$987$		0			0
$988$	−45.0000	+	11.6190i	−1.43164	+	0.369648i
$989$		0			0
$990$	−32.3701	−	15.7536i	−1.02879	−	0.500684i
$991$	13.4164	+	7.74597i	0.426186	+	0.246059i	0.697721	−	0.716370i	$-0.254198\pi$
$991$	13.4164	+	7.74597i	0.426186	+	0.246059i	−0.271534	+	0.962429i	$0.587531\pi$
$992$	17.3531	+	44.7534i	0.550962	+	1.42092i
$993$	−16.4317	+	36.7423i	−0.521443	+	1.16598i
$994$		0			0
$995$	−41.5692			−1.31783
$996$	−30.8057	+	11.4459i	−0.976116	+	0.362678i
$997$	2.73861	−	4.74342i	0.0867327	−	0.150226i	−0.819396	−	0.573229i	$-0.805691\pi$
$997$	2.73861	−	4.74342i	0.0867327	−	0.150226i	0.906128	+	0.423003i	$0.139024\pi$
$998$	30.4188	−	12.4377i	0.962890	−	0.393708i
$999$	−6.99208	+	7.68836i	−0.221219	+	0.243249i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.n.c.263.1		16
3.2	odd	2	inner	588.2.n.c.263.8		16
4.3	odd	2	inner	588.2.n.c.263.4		16
7.2	even	3	inner	588.2.n.c.275.5		16
7.3	odd	6		588.2.e.b.491.5	yes	8
7.4	even	3		588.2.e.b.491.6	yes	8
7.5	odd	6	inner	588.2.n.c.275.6		16
7.6	odd	2	inner	588.2.n.c.263.2		16
12.11	even	2	inner	588.2.n.c.263.5		16
21.2	odd	6	inner	588.2.n.c.275.4		16
21.5	even	6	inner	588.2.n.c.275.3		16
21.11	odd	6		588.2.e.b.491.3	yes	8
21.17	even	6		588.2.e.b.491.4	yes	8
21.20	even	2	inner	588.2.n.c.263.7		16
28.3	even	6		588.2.e.b.491.2	yes	8
28.11	odd	6		588.2.e.b.491.1	✓	8
28.19	even	6	inner	588.2.n.c.275.7		16
28.23	odd	6	inner	588.2.n.c.275.8		16
28.27	even	2	inner	588.2.n.c.263.3		16
84.11	even	6		588.2.e.b.491.8	yes	8
84.23	even	6	inner	588.2.n.c.275.1		16
84.47	odd	6	inner	588.2.n.c.275.2		16
84.59	odd	6		588.2.e.b.491.7	yes	8
84.83	odd	2	inner	588.2.n.c.263.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.e.b.491.1	✓	8	28.11	odd	6
588.2.e.b.491.2	yes	8	28.3	even	6
588.2.e.b.491.3	yes	8	21.11	odd	6
588.2.e.b.491.4	yes	8	21.17	even	6
588.2.e.b.491.5	yes	8	7.3	odd	6
588.2.e.b.491.6	yes	8	7.4	even	3
588.2.e.b.491.7	yes	8	84.59	odd	6
588.2.e.b.491.8	yes	8	84.11	even	6
588.2.n.c.263.1		16	1.1	even	1	trivial
588.2.n.c.263.2		16	7.6	odd	2	inner
588.2.n.c.263.3		16	28.27	even	2	inner
588.2.n.c.263.4		16	4.3	odd	2	inner
588.2.n.c.263.5		16	12.11	even	2	inner
588.2.n.c.263.6		16	84.83	odd	2	inner
588.2.n.c.263.7		16	21.20	even	2	inner
588.2.n.c.263.8		16	3.2	odd	2	inner
588.2.n.c.275.1		16	84.23	even	6	inner
588.2.n.c.275.2		16	84.47	odd	6	inner
588.2.n.c.275.3		16	21.5	even	6	inner
588.2.n.c.275.4		16	21.2	odd	6	inner
588.2.n.c.275.5		16	7.2	even	3	inner
588.2.n.c.275.6		16	7.5	odd	6	inner
588.2.n.c.275.7		16	28.19	even	6	inner
588.2.n.c.275.8		16	28.23	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.40126 - 0.190983i) q^{2} +(-1.40294 + 1.01575i) q^{3} +(1.92705 + 0.535233i) q^{4} +(-2.12132 + 1.22474i) q^{5} +(2.15988 - 1.15539i) q^{6} +(-2.59808 - 1.11803i) q^{8} +(0.936492 - 2.85008i) q^{9} +(3.20642 - 1.31105i) q^{10} +(1.73205 - 3.00000i) q^{11} +(-3.24721 + 1.20651i) q^{12} +5.47723 q^{13} +(1.73205 - 3.87298i) q^{15} +(3.42705 + 2.06284i) q^{16} +(4.24264 + 2.44949i) q^{17} +(-1.85658 + 3.81485i) q^{18} +(-3.67423 + 2.12132i) q^{19} +(-4.74342 + 1.22474i) q^{20} +(-3.00000 + 3.87298i) q^{22} +(4.78060 - 1.07047i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-7.67501 - 1.04606i) q^{26} +(1.58114 + 4.94975i) q^{27} +4.47214i q^{29} +(-3.16672 + 5.09626i) q^{30} +(-7.34847 - 4.24264i) q^{31} +(-4.40822 - 3.54508i) q^{32} +(0.617292 + 5.96816i) q^{33} +(-5.47723 - 4.24264i) q^{34} +(3.33013 - 4.99102i) q^{36} +(1.00000 + 1.73205i) q^{37} +(5.55369 - 2.27080i) q^{38} +(-7.68423 + 5.56351i) q^{39} +(6.88066 - 0.810272i) q^{40} +7.74597i q^{43} +(4.94345 - 4.85410i) q^{44} +(1.50403 + 7.19291i) q^{45} +(-6.90329 + 0.586988i) q^{48} +(-0.866025 + 1.11803i) q^{50} +(-8.44025 + 0.872983i) q^{51} +(10.5549 + 2.93159i) q^{52} +(3.87298 + 2.23607i) q^{53} +(-1.27027 - 7.23785i) q^{54} +8.48528i q^{55} +(3.00000 - 6.70820i) q^{57} +(0.854102 - 6.26662i) q^{58} +(-4.74342 + 8.21584i) q^{59} +(5.41070 - 6.53639i) q^{60} +(2.73861 + 4.74342i) q^{61} +(9.48683 + 7.34847i) q^{62} +(5.50000 + 5.80948i) q^{64} +(-11.6190 + 6.70820i) q^{65} +(0.274831 - 8.48083i) q^{66} +(6.70820 + 3.87298i) q^{67} +(6.86474 + 6.99109i) q^{68} -3.46410 q^{71} +(-5.61957 + 6.35771i) q^{72} +(-5.47723 + 9.48683i) q^{73} +(-1.07047 - 2.61803i) q^{74} +(0.178197 + 1.72286i) q^{75} +(-8.21584 + 2.12132i) q^{76} +(11.8301 - 6.32836i) q^{78} +(13.4164 - 7.74597i) q^{79} +(-9.79633 - 0.178688i) q^{80} +(-7.24597 - 5.33816i) q^{81} +9.48683 q^{83} -12.0000 q^{85} +(1.47935 - 10.8541i) q^{86} +(-4.54259 - 6.27415i) q^{87} +(-7.85410 + 5.85774i) q^{88} +(8.48528 - 4.89898i) q^{89} +(-0.733809 - 10.3664i) q^{90} +(14.6190 - 1.51205i) q^{93} +(5.19615 - 9.00000i) q^{95} +(9.78540 + 0.495889i) q^{96} +(-6.92820 - 7.74597i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 16 q^{9} + 28 q^{16} - 20 q^{18} - 48 q^{22} + 8 q^{25} - 12 q^{30} - 16 q^{36} + 16 q^{37} + 48 q^{57} - 40 q^{58} + 60 q^{60} + 88 q^{64} - 20 q^{72} + 120 q^{78} + 8 q^{81} - 192 q^{85}+ \cdots + 48 q^{93}+O(q^{100}) \) 16 * q + 4 * q^4 - 16 * q^9 + 28 * q^16 - 20 * q^18 - 48 * q^22 + 8 * q^25 - 12 * q^30 - 16 * q^36 + 16 * q^37 + 48 * q^57 - 40 * q^58 + 60 * q^60 + 88 * q^64 - 20 * q^72 + 120 * q^78 + 8 * q^81 - 192 * q^85 - 72 * q^88 + 48 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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