LMFDB - Embedded newform 588.2.n.c.275.6

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			275.6
Root			$-0.418778 + 1.56290i$ of defining polynomial
Character	$\chi$	$=$	588.275
Dual form			588.2.n.c.263.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.535233 + 1.30902i) q^{2} +(0.178197 + 1.72286i) q^{3} +(-1.42705 + 1.40126i) q^{4} +(-2.12132 - 1.22474i) q^{5} +(-2.15988 + 1.15539i) q^{6} +(-2.59808 - 1.11803i) q^{8} +(-2.93649 + 0.614017i) q^{9} +(0.467811 - 3.43237i) q^{10} +(1.73205 + 3.00000i) q^{11} +(-2.66847 - 2.20891i) q^{12} -5.47723 q^{13} +(1.73205 - 3.87298i) q^{15} +(0.0729490 - 3.99933i) q^{16} +(4.24264 - 2.44949i) q^{17} +(-2.37547 - 3.51528i) q^{18} +(-3.67423 - 2.12132i) q^{19} +(4.74342 - 1.22474i) q^{20} +(-3.00000 + 3.87298i) q^{22} +(1.46325 - 4.67535i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-2.93159 - 7.16978i) q^{26} +(-1.58114 - 4.94975i) q^{27} +4.47214i q^{29} +(5.99685 + 0.194335i) q^{30} +(-7.34847 + 4.24264i) q^{31} +(5.27424 - 2.04508i) q^{32} +(-4.85993 + 3.51867i) q^{33} +(5.47723 + 4.24264i) q^{34} +(3.33013 - 4.99102i) q^{36} +(1.00000 - 1.73205i) q^{37} +(0.810272 - 5.94504i) q^{38} +(-0.976025 - 9.43649i) q^{39} +(4.14205 + 5.55369i) q^{40} +7.74597i q^{43} +(-6.67550 - 1.85410i) q^{44} +(6.98125 + 2.29393i) q^{45} +(6.90329 - 0.586988i) q^{48} +(-0.866025 + 1.11803i) q^{50} +(4.97615 + 6.87298i) q^{51} +(7.81628 - 7.67501i) q^{52} +(-3.87298 + 2.23607i) q^{53} +(5.63303 - 4.71901i) q^{54} -8.48528i q^{55} +(3.00000 - 6.70820i) q^{57} +(-5.85410 + 2.39364i) q^{58} +(4.74342 + 8.21584i) q^{59} +(2.95533 + 7.95400i) 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} +(-7.20720 - 4.47843i) q^{66} +(-6.70820 + 3.87298i) q^{67} +(-2.62210 + 9.44058i) q^{68} -3.46410 q^{71} +(8.31572 + 1.68784i) q^{72} +(5.47723 + 9.48683i) q^{73} +(2.80252 + 0.381966i) q^{74} +(-1.40294 + 1.01575i) q^{75} +(8.21584 - 2.12132i) q^{76} +(11.8301 - 6.32836i) q^{78} +(-13.4164 - 7.74597i) q^{79} +(-5.05291 + 8.39453i) q^{80} +(8.24597 - 3.60611i) q^{81} -9.48683 q^{83} -12.0000 q^{85} +(-10.1396 + 4.14590i) q^{86} +(-7.70486 + 0.796921i) q^{87} +(-1.14590 - 9.73072i) q^{88} +(8.48528 + 4.89898i) q^{89} +(0.733809 + 10.3664i) q^{90} +(-8.61895 - 11.9044i) q^{93} +(5.19615 + 9.00000i) q^{95} +(4.46325 + 8.72235i) 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 $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.535233	+	1.30902i	0.378467	+	0.925615i
$2$	0.535233	+	1.30902i	0.378467	+	0.925615i
$3$	0.178197	+	1.72286i	0.102882	+	0.994694i
$3$	0.178197	+	1.72286i	0.102882	+	0.994694i
$4$	−1.42705	+	1.40126i	−0.713525	+	0.700629i
$5$	−2.12132	−	1.22474i	−0.948683	−	0.547723i	−0.0560116	−	0.998430i	$-0.517838\pi$
$5$	−2.12132	−	1.22474i	−0.948683	−	0.547723i	−0.892672	+	0.450708i	$0.851172\pi$
$6$	−2.15988	+	1.15539i	−0.881766	+	0.471688i
$7$		0			0
$7$		0			0
$8$	−2.59808	−	1.11803i	−0.918559	−	0.395285i
$9$	−2.93649	+	0.614017i	−0.978831	+	0.204672i
$10$	0.467811	−	3.43237i	0.147935	−	1.08541i
$11$	1.73205	+	3.00000i	0.522233	+	0.904534i	0.999665	+	0.0258656i	$0.00823419\pi$
$11$	1.73205	+	3.00000i	0.522233	+	0.904534i	−0.477432	+	0.878668i	$0.658432\pi$
$12$	−2.66847	−	2.20891i	−0.770320	−	0.637657i
$13$	−5.47723			−1.51911			−0.759555	−	0.650444i	$-0.774583\pi$
$13$	−5.47723			−1.51911			−0.759555	+	0.650444i	$0.774583\pi$
$14$		0			0
$15$	1.73205	−	3.87298i	0.447214	−	1.00000i
$16$	0.0729490	−	3.99933i	0.0182373	−	0.999834i
$17$	4.24264	−	2.44949i	1.02899	−	0.594089i	0.112296	−	0.993675i	$-0.464180\pi$
$17$	4.24264	−	2.44949i	1.02899	−	0.594089i	0.916696	+	0.399586i	$0.130846\pi$
$18$	−2.37547	−	3.51528i	−0.559903	−	0.828558i
$19$	−3.67423	−	2.12132i	−0.842927	−	0.486664i	0.0153309	−	0.999882i	$-0.495120\pi$
$19$	−3.67423	−	2.12132i	−0.842927	−	0.486664i	−0.858258	+	0.513218i	$0.828453\pi$
$20$	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	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	1.46325	−	4.67535i	0.298684	−	0.954352i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−2.93159	−	7.16978i	−0.574933	−	1.40611i
$27$	−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	$0.863702\pi$
$30$	5.99685	+	0.194335i	1.09487	+	0.0354805i
$31$	−7.34847	+	4.24264i	−1.31982	+	0.762001i	−0.983700	−	0.179817i	$-0.942449\pi$
$31$	−7.34847	+	4.24264i	−1.31982	+	0.762001i	−0.336124	+	0.941818i	$0.609116\pi$
$32$	5.27424	−	2.04508i	0.932363	−	0.361523i
$33$	−4.85993	+	3.51867i	−0.846006	+	0.612522i
$34$	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	−0.772043	−	0.635571i	$-0.780765\pi$
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	0.936442	+	0.350823i	$0.114098\pi$
$38$	0.810272	−	5.94504i	0.131444	−	0.964412i
$39$	−0.976025	−	9.43649i	−0.156289	−	1.51105i
$40$	4.14205	+	5.55369i	0.654915	+	0.878115i
$41$		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	$0.798881\pi$
$44$	−6.67550	−	1.85410i	−1.00637	−	0.279516i
$45$	6.98125	+	2.29393i	1.04070	+	0.341958i
$46$		0			0
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$	6.90329	−	0.586988i	0.996404	−	0.0847245i
$49$		0			0
$50$	−0.866025	+	1.11803i	−0.122474	+	0.158114i
$51$	4.97615	+	6.87298i	0.696801	+	0.962410i
$52$	7.81628	−	7.67501i	1.08392	−	1.06433i
$53$	−3.87298	+	2.23607i	−0.531995	+	0.307148i	−0.741829	−	0.670590i	$-0.766041\pi$
$53$	−3.87298	+	2.23607i	−0.531995	+	0.307148i	0.209833	+	0.977737i	$0.432708\pi$
$54$	5.63303	−	4.71901i	0.766558	−	0.642175i
$55$		−	8.48528i		−	1.14416i
$56$		0			0
$57$	3.00000	−	6.70820i	0.397360	−	0.888523i
$58$	−5.85410	+	2.39364i	−0.768681	+	0.314300i
$59$	4.74342	+	8.21584i	0.617540	+	1.06961i	0.989933	+	0.141536i	$0.0452041\pi$
$59$	4.74342	+	8.21584i	0.617540	+	1.06961i	−0.372393	+	0.928075i	$0.621463\pi$
$60$	2.95533	+	7.95400i	0.381531	+	1.02686i
$61$	−2.73861	+	4.74342i	−0.350643	+	0.607332i	−0.986362	−	0.164588i	$-0.947370\pi$
$61$	−2.73861	+	4.74342i	−0.350643	+	0.607332i	0.635719	+	0.771921i	$0.280704\pi$
$62$	−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
$66$	−7.20720	−	4.47843i	−0.887145	−	0.551256i
$67$	−6.70820	+	3.87298i	−0.819538	+	0.473160i	−0.850257	−	0.526368i	$-0.823553\pi$
$67$	−6.70820	+	3.87298i	−0.819538	+	0.473160i	0.0307194	+	0.999528i	$0.490220\pi$
$68$	−2.62210	+	9.44058i	−0.317976	+	1.14484i
$69$		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	$0.565900\pi$
$72$	8.31572	+	1.68784i	0.980017	+	0.198913i
$73$	5.47723	+	9.48683i	0.641061	+	1.11035i	0.985196	+	0.171430i	$0.0548387\pi$
$73$	5.47723	+	9.48683i	0.641061	+	1.11035i	−0.344136	+	0.938920i	$0.611828\pi$
$74$	2.80252	+	0.381966i	0.325786	+	0.0444026i
$75$	−1.40294	+	1.01575i	−0.161998	+	0.117289i
$76$	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	−0.999939	−	0.0110333i	$-0.996488\pi$
$79$	−13.4164	−	7.74597i	−1.50946	−	0.871489i	−0.509525	−	0.860456i	$-0.670179\pi$
$80$	−5.05291	+	8.39453i	−0.564933	+	0.938537i
$81$	8.24597	−	3.60611i	0.916219	−	0.400679i
$82$		0			0
$83$	−9.48683			−1.04132			−0.520658	−	0.853766i	$-0.674313\pi$
$83$	−9.48683			−1.04132			−0.520658	+	0.853766i	$0.674313\pi$
$84$		0			0
$85$	−12.0000			−1.30158
$86$	−10.1396	+	4.14590i	−1.09338	+	0.447064i
$87$	−7.70486	+	0.796921i	−0.826048	+	0.0854389i
$88$	−1.14590	−	9.73072i	−0.122153	−	1.03730i
$89$	8.48528	+	4.89898i	0.899438	+	0.519291i	0.877018	−	0.480458i	$-0.159529\pi$
$89$	8.48528	+	4.89898i	0.899438	+	0.519291i	0.0224202	+	0.999749i	$0.492863\pi$
$90$	0.733809	+	10.3664i	0.0773503	+	1.09271i
$91$		0			0
$92$		0			0
$93$	−8.61895	−	11.9044i	−0.893743	−	1.23442i
$94$		0			0
$95$	5.19615	+	9.00000i	0.533114	+	0.923381i
$96$	4.46325	+	8.72235i	0.455528	+	0.890221i
$97$		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
$100$	−1.92705	−	0.535233i	−0.192705	−	0.0535233i
$101$	−6.36396	+	3.67423i	−0.633238	+	0.365600i	−0.782005	−	0.623272i	$-0.785803\pi$
$101$	−6.36396	+	3.67423i	−0.633238	+	0.365600i	0.148767	+	0.988872i	$0.452470\pi$
$102$	−6.33345	+	10.1925i	−0.627105	+	1.00921i
$103$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$103$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$104$	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	−0.0549930	−	0.998487i	$-0.517514\pi$
$107$	8.66025	−	15.0000i	0.837218	−	1.45010i	0.892211	−	0.451618i	$-0.149153\pi$
$108$	9.19224	+	4.84796i	0.884524	+	0.466495i
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	0.520794	−	0.853682i	$-0.325636\pi$
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	−0.999708	+	0.0241802i	$0.992302\pi$
$110$	11.1074	−	4.54160i	1.05905	−	0.433025i
$111$	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	$-0.0674609\pi$
$114$	10.3869	+	0.336598i	0.972818	+	0.0315253i
$115$		0			0
$116$	−6.26662	−	6.38197i	−0.581841	−	0.592551i
$117$	16.0838	−	3.36311i	1.48695	−	0.310920i
$118$	−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
$122$	−7.67501	−	1.04606i	−0.694863	−	0.0947056i
$123$		0			0
$124$	4.54160	−	16.3516i	0.407848	−	1.46841i
$125$			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	$0.888329\pi$
$128$	−4.66092	+	10.3090i	−0.411971	+	0.911197i
$129$	−13.3452	+	1.38031i	−1.17498	+	0.121529i
$130$	−2.56231	+	18.7999i	−0.224729	+	1.64886i
$131$	−4.74342	+	8.21584i	−0.414434	+	0.717821i	−0.995369	−	0.0961291i	$-0.969354\pi$
$131$	−4.74342	+	8.21584i	−0.414434	+	0.717821i	0.580935	+	0.813950i	$0.302687\pi$
$132$	2.00480	−	11.8313i	0.174496	−	1.02979i
$133$		0			0
$134$	−8.66025	−	6.70820i	−0.748132	−	0.579501i
$135$	−2.70808	+	12.4365i	−0.233074	+	1.07036i
$136$	−13.7613	+	1.62054i	−1.18002	+	0.138961i
$137$	−7.74597	+	4.47214i	−0.661783	+	0.382080i	−0.792956	−	0.609279i	$-0.791459\pi$
$137$	−7.74597	+	4.47214i	−0.661783	+	0.382080i	0.131173	+	0.991359i	$0.458126\pi$
$138$		0			0
$139$			4.24264i			0.359856i	0.983680	+	0.179928i	$0.0575865\pi$
$139$			4.24264i			0.359856i	−0.983680	+	0.179928i	$0.942414\pi$
$140$		0			0
$141$		0			0
$142$	−1.85410	−	4.53457i	−0.155593	−	0.380532i
$143$	−9.48683	−	16.4317i	−0.793329	−	1.37409i
$144$	2.24144	+	11.7888i	0.186787	+	0.982400i
$145$	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	$-0.274692\pi$
$149$	3.87298	+	2.23607i	0.317287	+	0.183186i	−0.332896	+	0.942964i	$0.608026\pi$
$150$	−2.08054	−	1.29281i	−0.169875	−	0.105557i
$151$	6.70820	−	3.87298i	0.545906	−	0.315179i	−0.201563	−	0.979476i	$-0.564602\pi$
$151$	6.70820	−	3.87298i	0.545906	−	0.315179i	0.747469	+	0.664297i	$0.231269\pi$
$152$	7.17423	+	9.61927i	0.581907	+	0.780226i
$153$	−10.9545	+	9.79796i	−0.885615	+	0.792118i
$154$		0			0
$155$	20.7846			1.66946
$156$	14.6158	+	12.0987i	1.17020	+	0.968671i
$157$	−2.73861	−	4.74342i	−0.218565	−	0.378566i	0.735804	−	0.677194i	$-0.236804\pi$
$157$	−2.73861	−	4.74342i	−0.218565	−	0.378566i	−0.954370	+	0.298628i	$0.903471\pi$
$158$	2.95870	−	21.7082i	0.235381	−	1.72701i
$159$	−4.54259	−	6.27415i	−0.360250	−	0.497572i
$160$	−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	$-0.235226\pi$
$163$	6.70820	+	3.87298i	0.525427	+	0.303355i	−0.213725	+	0.976894i	$0.568560\pi$
$164$		0			0
$165$	14.6190	−	1.51205i	1.13808	−	0.117713i
$166$	−5.07767	−	12.4184i	−0.394103	−	0.963857i
$167$	18.9737			1.46823			0.734113	−	0.679027i	$-0.237598\pi$
$167$	18.9737			1.46823			0.734113	+	0.679027i	$0.237598\pi$
$168$		0			0
$169$	17.0000			1.30769
$170$	−6.42280	−	15.7082i	−0.492606	−	1.20476i
$171$	12.0919	+	3.97320i	0.924690	+	0.303838i
$172$	−10.8541	−	11.0539i	−0.827618	−	0.842851i
$173$	−2.12132	−	1.22474i	−0.161281	−	0.0931156i	0.417187	−	0.908821i	$-0.363016\pi$
$173$	−2.12132	−	1.22474i	−0.161281	−	0.0931156i	−0.578468	+	0.815705i	$0.696349\pi$
$174$	−5.16708	−	9.65926i	−0.391715	−	0.732266i
$175$		0			0
$176$	12.1244	−	6.70820i	0.913908	−	0.505650i
$177$	−13.3095	+	9.63628i	−1.00040	+	0.724307i
$178$	−1.87124	+	13.7295i	−0.140256	+	1.02907i
$179$	−5.19615	−	9.00000i	−0.388379	−	0.672692i	0.603853	−	0.797096i	$-0.293631\pi$
$179$	−5.19615	−	9.00000i	−0.388379	−	0.672692i	−0.992232	+	0.124404i	$0.960298\pi$
$180$	−13.1770	+	6.50899i	−0.982155	+	0.485152i
$181$	16.4317			1.22136			0.610678	−	0.791879i	$-0.290897\pi$
$181$	16.4317			1.22136			0.610678	+	0.791879i	$0.290897\pi$
$182$		0			0
$183$	−8.66025	−	3.87298i	−0.640184	−	0.286299i
$184$		0			0
$185$	−4.24264	+	2.44949i	−0.311925	+	0.180090i
$186$	10.9699	−	17.6540i	0.804349	−	1.29445i
$187$	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	−0.796534	−	0.604594i	$-0.793335\pi$
$191$	1.73205	−	3.00000i	0.125327	−	0.217072i	0.921861	+	0.387522i	$0.126669\pi$
$192$	−9.02883	+	10.5110i	−0.651599	+	0.758563i
$193$	8.00000	+	13.8564i	0.575853	+	0.997406i	0.995948	+	0.0899262i	$0.0286631\pi$
$193$	8.00000	+	13.8564i	0.575853	+	0.997406i	−0.420096	+	0.907480i	$0.638004\pi$
$194$		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	$0.706648\pi$
$198$	6.43140	−	13.2150i	0.457060	−	0.939152i
$199$	14.6969	−	8.48528i	1.04184	−	0.601506i	0.121485	−	0.992593i	$-0.461234\pi$
$199$	14.6969	−	8.48528i	1.04184	−	0.601506i	0.920353	+	0.391088i	$0.127901\pi$
$200$	−0.330792	−	2.80902i	−0.0233905	−	0.198627i
$201$	−7.86799	−	10.8671i	−0.554965	−	0.766509i
$202$	−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
$208$	−0.399558	+	21.9053i	−0.0277044	+	1.51886i
$209$		−	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	$-0.0859092\pi$
$212$	2.39364	−	8.61803i	0.164396	−	0.591889i
$213$	−0.617292	−	5.96816i	−0.0422962	−	0.408932i
$214$	24.2705	+	3.30792i	1.65910	+	0.226125i
$215$	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
$219$	−15.3685	+	11.1270i	−1.03850	+	0.751894i
$220$	11.8901	+	12.1089i	0.801629	+	0.816384i
$221$	−23.2379	+	13.4164i	−1.56315	+	0.902485i
$222$	−0.158674	+	4.89641i	−0.0106495	+	0.328625i
$223$			8.48528i			0.568216i	0.958792	+	0.284108i	$0.0916975\pi$
$223$			8.48528i			0.568216i	−0.958792	+	0.284108i	$0.908302\pi$
$224$		0			0
$225$	−2.00000	−	2.23607i	−0.133333	−	0.149071i
$226$	5.85410	−	2.39364i	0.389409	−	0.159222i
$227$	4.74342	+	8.21584i	0.314832	+	0.545304i	0.979402	−	0.201922i	$-0.0647186\pi$
$227$	4.74342	+	8.21584i	0.314832	+	0.545304i	−0.664570	+	0.747226i	$0.731385\pi$
$228$	5.11878	+	13.7767i	0.338999	+	0.912386i
$229$	−2.73861	+	4.74342i	−0.180973	+	0.313454i	−0.942212	−	0.335017i	$-0.891258\pi$
$229$	−2.73861	+	4.74342i	−0.180973	+	0.313454i	0.761239	+	0.648471i	$0.224591\pi$
$230$		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	$-0.238687\pi$
$233$	7.74597	+	4.47214i	0.507455	+	0.292979i	−0.224332	+	0.974513i	$0.572020\pi$
$234$	13.0110	+	19.2540i	0.850553	+	1.25867i
$235$		0			0
$236$	−18.2816	−	5.07767i	−1.19003	−	0.330528i
$237$	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	$0.428064\pi$
$240$	−15.3630	−	7.20958i	−0.991678	−	0.465376i
$241$	−10.9545	−	18.9737i	−0.705638	−	1.22220i	−0.966461	−	0.256814i	$-0.917327\pi$
$241$	−10.9545	−	18.9737i	−0.705638	−	1.22220i	0.260822	−	0.965387i	$-0.416006\pi$
$242$	−1.40126	−	0.190983i	−0.0900763	−	0.0122769i
$243$	7.68223	+	13.5640i	0.492815	+	0.870134i
$244$	−2.73861	−	10.6066i	−0.175322	−	0.679018i
$245$		0			0
$246$		0			0
$247$	20.1246	+	11.6190i	1.28050	+	0.739296i
$248$	23.8353	−	2.80687i	1.51354	−	0.178236i
$249$	−1.69052	−	16.3445i	−0.107133	−	1.03579i
$250$	−12.8257	+	5.24419i	−0.811168	+	0.331672i
$251$	−9.48683			−0.598804			−0.299402	−	0.954127i	$-0.596787\pi$
$251$	−9.48683			−0.598804			−0.299402	+	0.954127i	$0.596787\pi$
$252$		0			0
$253$		0			0
$254$	−10.1396	+	4.14590i	−0.636215	+	0.260137i
$255$	−2.13836	−	20.6743i	−0.133910	−	1.29468i
$256$	−15.9894	−	0.583495i	−0.999335	−	0.0364684i
$257$	−4.24264	−	2.44949i	−0.264649	−	0.152795i	0.361805	−	0.932254i	$-0.382161\pi$
$257$	−4.24264	−	2.44949i	−0.264649	−	0.152795i	−0.626453	+	0.779459i	$0.715494\pi$
$258$	−8.94965	−	16.7303i	−0.557181	−	1.04158i
$259$		0			0
$260$	−25.9808	+	6.70820i	−1.61126	+	0.416025i
$261$	−2.74597	−	13.1324i	−0.169971	−	0.812875i
$262$	−13.2935	−	1.81182i	−0.821276	−	0.111935i
$263$	1.73205	+	3.00000i	0.106803	+	0.184988i	0.914473	−	0.404646i	$-0.132605\pi$
$263$	1.73205	+	3.00000i	0.106803	+	0.184988i	−0.807671	+	0.589634i	$0.799272\pi$
$264$	16.5605	−	3.70821i	1.01923	−	0.228224i
$265$	10.9545			0.672927
$266$		0			0
$267$	−6.92820	+	15.4919i	−0.423999	+	0.948091i
$268$	4.14590	−	14.9269i	0.253251	−	0.911804i
$269$	2.12132	−	1.22474i	0.129339	−	0.0746740i	−0.433934	−	0.900944i	$-0.642875\pi$
$269$	2.12132	−	1.22474i	0.129339	−	0.0746740i	0.563274	+	0.826270i	$0.309542\pi$
$270$	−17.7290	+	3.11151i	−1.07895	+	0.189360i
$271$	−7.34847	−	4.24264i	−0.446388	−	0.257722i	0.259916	−	0.965631i	$-0.416305\pi$
$271$	−7.34847	−	4.24264i	−0.446388	−	0.257722i	−0.706303	+	0.707909i	$0.749639\pi$
$272$	−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	0.834419	−	0.551131i	$-0.185804\pi$
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	−0.894503	+	0.447062i	$0.852470\pi$
$278$	−5.55369	+	2.27080i	−0.333088	+	0.136194i
$279$	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	0.529465	−	0.848332i	$-0.322393\pi$
$283$	25.7196	−	14.8492i	1.52887	−	0.882696i	0.999409	−	0.0343638i	$-0.0109405\pi$
$284$	4.94345	−	4.85410i	0.293340	−	0.288038i
$285$	−14.5798	+	10.5560i	−0.863633	+	0.625284i
$286$	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
$290$	15.3500	+	2.09211i	0.901384	+	0.122853i
$291$		0			0
$292$	−21.1098	−	5.86319i	−1.23536	−	0.343117i
$293$		−	2.44949i		−	0.143101i	−0.997437	−	0.0715504i	$-0.977205\pi$
$293$		−	2.44949i		−	0.143101i	0.997437	−	0.0715504i	$-0.0227947\pi$
$294$		0			0
$295$		−	23.2379i		−	1.35296i
$296$	−4.53457	+	3.38197i	−0.263566	+	0.196573i
$297$	12.1106	−	13.3166i	0.702730	−	0.772709i
$298$	−0.854102	+	6.26662i	−0.0494768	+	0.363015i
$299$		0			0
$300$	0.578737	−	3.41542i	0.0334134	−	0.197189i
$301$		0			0
$302$	8.66025	+	6.70820i	0.498342	+	0.386014i
$303$	−7.46423	−	10.3095i	−0.428809	−	0.592264i
$304$	−8.75190	+	14.5397i	−0.501956	+	0.833912i
$305$	11.6190	−	6.70820i	0.665299	−	0.384111i
$306$	−18.6889	−	9.09537i	−1.06837	−	0.519948i
$307$			21.2132i			1.21070i	0.795959	+	0.605351i	$0.206967\pi$
$307$			21.2132i			1.21070i	−0.795959	+	0.605351i	$0.793033\pi$
$308$		0			0
$309$		0			0
$310$	11.1246	+	27.2074i	0.631835	+	1.54528i
$311$	−9.48683	−	16.4317i	−0.537949	−	0.931755i	−0.999014	−	0.0443887i	$-0.985866\pi$
$311$	−9.48683	−	16.4317i	−0.537949	−	0.931755i	0.461065	−	0.887366i	$-0.347467\pi$
$312$	−8.01453	+	25.6080i	−0.453733	+	1.44976i
$313$	−5.47723	+	9.48683i	−0.309591	+	0.536228i	−0.978273	−	0.207321i	$-0.933525\pi$
$313$	−5.47723	+	9.48683i	−0.309591	+	0.536228i	0.668682	+	0.743549i	$0.266859\pi$
$314$	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	$-0.293251\pi$
$317$	3.87298	+	2.23607i	0.217528	+	0.125590i	−0.387277	+	0.921963i	$0.626584\pi$
$318$	5.78162	−	9.30445i	0.324217	−	0.521768i
$319$	−13.4164	+	7.74597i	−0.751175	+	0.433691i
$320$	−4.55214	−	19.0599i	−0.254472	−	1.06548i
$321$	27.3861	+	12.2474i	1.52854	+	0.683586i
$322$		0			0
$323$	−20.7846			−1.15649
$324$	−6.71432	+	16.7008i	−0.373018	+	0.927824i
$325$	−2.73861	−	4.74342i	−0.151911	−	0.263117i
$326$	−1.47935	+	10.8541i	−0.0819335	+	0.601153i
$327$	14.0294	−	10.1575i	0.775829	−	0.561713i
$328$		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	$-0.553834\pi$
$331$	−20.1246	−	11.6190i	−1.10615	−	0.638635i	−0.937829	+	0.347097i	$0.887167\pi$
$332$	13.5382	−	13.2935i	0.743005	−	0.729576i
$333$	−1.87298	+	5.70017i	−0.102639	+	0.312367i
$334$	10.1553	+	24.8369i	0.555675	+	1.35901i
$335$	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	$0.569919\pi$
$338$	9.09896	+	22.2533i	0.494918	+	1.21042i
$339$	7.70486	−	0.796921i	0.418471	−	0.0432828i
$340$	17.1246	−	16.8151i	0.928712	−	0.911927i
$341$	−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
$346$	0.467811	−	3.43237i	0.0251497	−	0.184525i
$347$	12.1244	+	21.0000i	0.650870	+	1.12734i	0.982912	+	0.184075i	$0.0589288\pi$
$347$	12.1244	+	21.0000i	0.650870	+	1.12734i	−0.332043	+	0.943264i	$0.607738\pi$
$348$	9.87854	−	11.9338i	0.529545	−	0.639716i
$349$	−16.4317			−0.879567			−0.439784	−	0.898104i	$-0.644945\pi$
$349$	−16.4317			−0.879567			−0.439784	+	0.898104i	$0.644945\pi$
$350$		0			0
$351$	8.66025	+	27.1109i	0.462250	+	1.44707i
$352$	15.2705	+	12.2805i	0.813921	+	0.654555i
$353$	12.7279	−	7.34847i	0.677439	−	0.391120i	−0.121450	−	0.992597i	$-0.538755\pi$
$353$	12.7279	−	7.34847i	0.677439	−	0.391120i	0.798889	+	0.601478i	$0.205421\pi$
$354$	−19.7377	−	12.2647i	−1.04905	−	0.651860i
$355$	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	−0.225009	−	0.974357i	$-0.572241\pi$
$359$	13.8564	−	24.0000i	0.731313	−	1.26667i	0.956322	−	0.292315i	$-0.0944255\pi$
$360$	−15.5731	−	13.7651i	−0.820777	−	0.725483i
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$	8.79478	+	21.5093i	0.462243	+	1.13051i
$363$	−1.58114	−	0.707107i	−0.0829883	−	0.0371135i
$364$		0			0
$365$		−	26.8328i		−	1.40449i
$366$	0.434546	−	13.4094i	0.0227141	−	0.700919i
$367$	−22.0454	+	12.7279i	−1.15076	+	0.664392i	−0.949073	−	0.315058i	$-0.897976\pi$
$367$	−22.0454	+	12.7279i	−1.15076	+	0.664392i	−0.201688	+	0.979450i	$0.564643\pi$
$368$		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	0.303902	+	0.952703i	$0.401711\pi$
$373$	−13.0000	+	22.5167i	−0.673114	+	1.16587i	−0.977016	+	0.213165i	$0.931623\pi$
$374$	−3.24109	+	23.7801i	−0.167593	+	1.22964i
$375$	−16.8805	+	1.74597i	−0.871706	+	0.0901613i
$376$		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	$-0.0637505\pi$
$380$	−20.0265	−	5.56231i	−1.02734	−	0.285340i
$381$	−13.3452	+	1.38031i	−0.683696	+	0.0707153i
$382$	4.85410	+	0.661585i	0.248357	+	0.0338496i
$383$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$383$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$384$	−18.5916	−	6.19307i	−0.948746	−	0.316039i
$385$		0			0
$386$	−13.8564	+	17.8885i	−0.705273	+	0.910503i
$387$	−4.75615	−	22.7460i	−0.241769	−	1.15624i
$388$		0			0
$389$	27.1109	−	15.6525i	1.37458	−	0.793612i	0.383076	−	0.923717i	$-0.374865\pi$
$389$	27.1109	−	15.6525i	1.37458	−	0.793612i	0.991500	+	0.130105i	$0.0415314\pi$
$390$	−32.8461	−	1.06442i	−1.66323	−	0.0538988i
$391$		0			0
$392$		0			0
$393$	−15.0000	−	6.70820i	−0.756650	−	0.338384i
$394$	−29.2705	+	11.9682i	−1.47463	+	0.602948i
$395$	18.9737	+	32.8634i	0.954669	+	1.65353i
$396$	20.7410	+	1.34569i	1.04227	+	0.0676232i
$397$	19.1703	−	33.2039i	0.962129	−	1.66646i	0.244992	−	0.969525i	$-0.421215\pi$
$397$	19.1703	−	33.2039i	0.962129	−	1.66646i	0.717138	−	0.696932i	$-0.245452\pi$
$398$	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	$-0.368951\pi$
$401$	−3.87298	−	2.23607i	−0.193408	−	0.111664i	−0.593577	+	0.804777i	$0.702285\pi$
$402$	10.0141	−	16.1158i	0.499456	−	0.803782i
$403$	40.2492	−	23.2379i	2.00496	−	1.15756i
$404$	3.93314	−	14.1609i	0.195681	−	0.704530i
$405$	−21.9089	−	2.44949i	−1.08866	−	0.121716i
$406$		0			0
$407$	6.92820			0.343418
$408$	−5.24420	−	23.4200i	−0.259626	−	1.15946i
$409$	−5.47723	−	9.48683i	−0.270831	−	0.469094i	0.698244	−	0.715860i	$-0.253965\pi$
$409$	−5.47723	−	9.48683i	−0.270831	−	0.469094i	−0.969075	+	0.246767i	$0.920632\pi$
$410$		0			0
$411$	−9.08517	−	12.5483i	−0.448138	−	0.618962i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	20.1246	+	11.6190i	0.987878	+	0.570352i
$416$	−28.8882	+	11.2014i	−1.41636	+	0.549193i
$417$	−7.30948	+	0.756026i	−0.357947	+	0.0370227i
$418$	19.2385	−	7.86629i	0.940988	−	0.384753i
$419$	−28.4605			−1.39039			−0.695193	−	0.718823i	$-0.744681\pi$
$419$	−28.4605			−1.39039			−0.695193	+	0.718823i	$0.744681\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	10.1396	−	4.14590i	0.493588	−	0.201819i
$423$		0			0
$424$	12.5623	−	1.47935i	0.610080	−	0.0718435i
$425$	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
$429$	26.6190	−	19.2726i	1.28518	−	0.930488i
$430$	26.5870	+	3.62365i	1.28214	+	0.174748i
$431$	−10.3923	−	18.0000i	−0.500580	−	0.867029i	−1.00000		0.000669521i	$-0.999787\pi$
$431$	−10.3923	−	18.0000i	−0.500580	−	0.867029i	0.499420	−	0.866360i	$-0.333546\pi$
$432$	−19.9110	+	5.96242i	−0.957970	+	0.286867i
$433$	−21.9089			−1.05287			−0.526437	−	0.850214i	$-0.676473\pi$
$433$	−21.9089			−1.05287			−0.526437	+	0.850214i	$0.676473\pi$
$434$		0			0
$435$	17.3205	+	7.74597i	0.830455	+	0.371391i
$436$	19.2705	+	5.35233i	0.922890	+	0.256330i
$437$		0			0
$438$	−22.7912	−	14.1620i	−1.08900	−	0.676688i
$439$	−14.6969	−	8.48528i	−0.701447	−	0.404980i	0.106439	−	0.994319i	$-0.466055\pi$
$439$	−14.6969	−	8.48528i	−0.701447	−	0.404980i	−0.807886	+	0.589339i	$0.799388\pi$
$440$	−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	0.211579	+	0.977361i	$0.432139\pi$
$443$	−15.5885	+	27.0000i	−0.740630	+	1.28281i	−0.952209	+	0.305448i	$0.901194\pi$
$444$	−6.49441	+	2.41301i	−0.308211	+	0.114517i
$445$	−12.0000	−	20.7846i	−0.568855	−	0.985285i
$446$	−11.1074	+	4.54160i	−0.525950	+	0.215051i
$447$	−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	$0.680069\pi$
$450$	1.85658	−	3.81485i	0.0875202	−	0.179834i
$451$		0			0
$452$	6.26662	+	6.38197i	0.294757	+	0.300182i
$453$	7.86799	+	10.8671i	0.369670	+	0.510583i
$454$	−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	−0.327028	−	0.945015i	$-0.606047\pi$
$457$	14.0000	−	24.2487i	0.654892	−	1.13431i	0.981921	−	0.189292i	$-0.0606194\pi$
$458$	−7.67501	−	1.04606i	−0.358630	−	0.0488790i
$459$	−18.8326	−	17.1270i	−0.879029	−	0.799421i
$460$		0			0
$461$			36.7423i			1.71126i	0.517587	+	0.855631i	$0.326831\pi$
$461$			36.7423i			1.71126i	−0.517587	+	0.855631i	$0.673169\pi$
$462$		0			0
$463$			15.4919i			0.719971i	0.932958	+	0.359986i	$0.117218\pi$
$463$			15.4919i			0.719971i	−0.932958	+	0.359986i	$0.882782\pi$
$464$	17.8856	+	0.326238i	0.830317	+	0.0151452i
$465$	3.70375	+	35.8090i	0.171758	+	1.66060i
$466$	−1.70820	+	12.5332i	−0.0791310	+	0.580591i
$467$	−14.2302	+	24.6475i	−0.658497	+	1.14055i	0.322507	+	0.946567i	$0.395474\pi$
$467$	−14.2302	+	24.6475i	−0.658497	+	1.14055i	−0.981005	+	0.193984i	$0.937859\pi$
$468$	−18.2399	+	27.3369i	−0.843138	+	1.26365i
$469$		0			0
$470$		0			0
$471$	7.68423	−	5.56351i	0.354071	−	0.256353i
$472$	−3.13817	−	26.6487i	−0.144446	−	1.22660i
$473$	−23.2379	+	13.4164i	−1.06848	+	0.616887i
$474$	37.9274	+	1.22908i	1.74206	+	0.0564536i
$475$		−	4.24264i		−	0.194666i
$476$		0			0
$477$	10.0000	−	8.94427i	0.457869	−	0.409530i
$478$	3.70820	+	9.06914i	0.169609	+	0.414813i
$479$	−18.9737	−	32.8634i	−0.866929	−	1.50156i	−0.865119	−	0.501567i	$-0.832757\pi$
$479$	−18.9737	−	32.8634i	−0.866929	−	1.50156i	−0.00180988	−	0.999998i	$-0.500576\pi$
$480$	1.21467	−	23.9692i	0.0554421	−	1.09404i
$481$	−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
$486$	−13.6438	+	17.3161i	−0.618895	+	0.785474i
$487$	−6.70820	+	3.87298i	−0.303978	+	0.175502i	−0.644228	−	0.764833i	$-0.722821\pi$
$487$	−6.70820	+	3.87298i	−0.303978	+	0.175502i	0.340251	+	0.940335i	$0.389488\pi$
$488$	12.4184	−	9.26190i	0.562156	−	0.419266i
$489$	−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
$494$	−4.43804	+	32.5623i	−0.199677	+	1.46505i
$495$	5.21011	+	24.9170i	0.234177	+	1.11993i
$496$	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	$-0.159215\pi$
$499$	20.1246	+	11.6190i	0.900901	+	0.520136i	0.0234088	+	0.999726i	$0.492548\pi$
$500$	−13.7295	−	13.9822i	−0.614001	−	0.625302i
$501$	3.38105	+	32.6890i	0.151054	+	1.46044i
$502$	−5.07767	−	12.4184i	−0.226627	−	0.554261i
$503$	18.9737			0.845994			0.422997	−	0.906131i	$-0.360978\pi$
$503$	18.9737			0.845994			0.422997	+	0.906131i	$0.360978\pi$
$504$		0			0
$505$	18.0000			0.800989
$506$		0			0
$507$	3.02935	+	29.2886i	0.134538	+	1.30075i
$508$	−10.8541	−	11.0539i	−0.481573	−	0.490437i
$509$	31.8198	+	18.3712i	1.41039	+	0.814288i	0.995425	−	0.0955502i	$-0.0304610\pi$
$509$	31.8198	+	18.3712i	1.41039	+	0.814288i	0.414963	+	0.909838i	$0.363794\pi$
$510$	25.9185	−	13.8647i	1.14769	−	0.613941i
$511$		0			0
$512$	−7.79423	−	21.2426i	−0.344459	−	0.938801i
$513$	−4.69052	+	21.5406i	−0.207092	+	0.951042i
$514$	0.935622	−	6.86474i	0.0412685	−	0.302791i
$515$		0			0
$516$	17.1101	−	20.6699i	0.753232	−	0.909940i
$517$		0			0
$518$		0			0
$519$	1.73205	−	3.87298i	0.0760286	−	0.170005i
$520$	−22.6869	−	30.4188i	−0.994887	−	1.33395i
$521$	−25.4558	+	14.6969i	−1.11524	+	0.643885i	−0.940182	−	0.340673i	$-0.889345\pi$
$521$	−25.4558	+	14.6969i	−1.11524	+	0.643885i	−0.175059	+	0.984558i	$0.556012\pi$
$522$	15.7208	−	10.6234i	0.688080	−	0.464974i
$523$	−18.3712	−	10.6066i	−0.803315	−	0.463794i	0.0413138	−	0.999146i	$-0.486846\pi$
$523$	−18.3712	−	10.6066i	−0.803315	−	0.463794i	−0.844629	+	0.535352i	$0.820179\pi$
$524$	−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
$528$	13.7178	+	19.6932i	0.596991	+	0.857036i
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	5.86319	+	14.3396i	0.254680	+	0.622871i
$531$	−18.9737	−	21.2132i	−0.823387	−	0.920575i
$532$		0			0
$533$		0			0
$534$	−23.9874	−	0.777340i	−1.03804	−	0.0336388i
$535$	−36.7423	+	21.2132i	−1.58851	+	0.917127i
$536$	21.7586	−	2.56231i	0.939826	−	0.110675i
$537$	14.5798	−	10.5560i	0.629165	−	0.455526i
$538$	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	0.0911008	+	0.995842i	$0.470961\pi$
$541$	−19.0000	+	32.9090i	−0.816874	+	1.41487i	−0.907975	+	0.419025i	$0.862372\pi$
$542$	1.62054	−	11.8901i	0.0696083	−	0.510722i
$543$	2.92808	+	28.3095i	0.125656	+	1.21488i
$544$	17.3673	−	21.5958i	0.744617	−	0.925911i
$545$			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	$-0.310512\pi$
$548$	4.78727	−	17.2361i	0.204502	−	0.736288i
$549$	5.12938	−	15.6106i	0.218916	−	0.666242i
$550$	−4.85410	−	0.661585i	−0.206980	−	0.0282101i
$551$	9.48683	−	16.4317i	0.404153	−	0.700013i
$552$		0			0
$553$		0			0
$554$	1.73205	−	2.23607i	0.0735878	−	0.0950014i
$555$	−4.97615	−	6.87298i	−0.211226	−	0.291742i
$556$	−5.94504	−	6.05446i	−0.252126	−	0.256766i
$557$	19.3649	−	11.1803i	0.820518	−	0.473726i	−0.0300772	−	0.999548i	$-0.509575\pi$
$557$	19.3649	−	11.1803i	0.820518	−	0.473726i	0.850595	+	0.525821i	$0.176242\pi$
$558$	32.3701	+	15.7536i	1.37034	+	0.666905i
$559$		−	42.4264i		−	1.79445i
$560$		0			0
$561$	−12.0000	+	26.8328i	−0.506640	+	1.13288i
$562$	11.7082	−	4.78727i	0.493881	−	0.201939i
$563$	4.74342	+	8.21584i	0.199911	+	0.346256i	0.948499	−	0.316779i	$-0.102601\pi$
$563$	4.74342	+	8.21584i	0.199911	+	0.346256i	−0.748588	+	0.663035i	$0.769268\pi$
$564$		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	$-0.561165\pi$
$569$	−27.1109	−	15.6525i	−1.13655	−	0.656186i	−0.945573	+	0.325409i	$0.894498\pi$
$570$	−21.6216	−	13.4353i	−0.905629	−	0.562742i
$571$	−20.1246	+	11.6190i	−0.842189	+	0.486238i	−0.858008	−	0.513637i	$-0.828298\pi$
$571$	−20.1246	+	11.6190i	−0.842189	+	0.486238i	0.0158188	+	0.999875i	$0.494964\pi$
$572$	36.5632	+	10.1553i	1.52879	+	0.424616i
$573$	5.47723	+	2.44949i	0.228814	+	0.102329i
$574$		0			0
$575$		0			0
$576$	−19.7178	−	13.6824i	−0.821576	−	0.570099i
$577$	21.9089	+	37.9473i	0.912080	+	1.57977i	0.811122	+	0.584877i	$0.198857\pi$
$577$	21.9089	+	37.9473i	0.912080	+	1.57977i	0.100958	+	0.994891i	$0.467809\pi$
$578$	9.80881	+	1.33688i	0.407993	+	0.0556069i
$579$	−22.4471	+	16.2520i	−0.932868	+	0.675412i
$580$	5.47723	+	21.2132i	0.227429	+	0.880830i
$581$		0			0
$582$		0			0
$583$	−13.4164	−	7.74597i	−0.555651	−	0.320805i
$584$	−3.62365	−	30.7712i	−0.149948	−	1.27332i
$585$	−38.2379	−	12.5644i	−1.58094	−	0.519472i
$586$	3.20642	−	1.31105i	0.132456	−	0.0541589i
$587$	−9.48683			−0.391564			−0.195782	−	0.980647i	$-0.562724\pi$
$587$	−9.48683			−0.391564			−0.195782	+	0.980647i	$0.562724\pi$
$588$		0			0
$589$	36.0000			1.48335
$590$	30.4188	−	12.4377i	1.25232	−	0.512052i
$591$	−38.5243	+	3.98461i	−1.58468	+	0.163905i
$592$	−6.85410	−	4.12569i	−0.281702	−	0.169565i
$593$	29.6985	+	17.1464i	1.21957	+	0.704119i	0.964826	−	0.262889i	$-0.0846753\pi$
$593$	29.6985	+	17.1464i	1.21957	+	0.704119i	0.254745	+	0.967008i	$0.418009\pi$
$594$	23.9137	+	8.72552i	0.981191	+	0.358012i
$595$		0			0
$596$	−8.66025	+	2.23607i	−0.354738	+	0.0915929i
$597$	17.2379	+	23.8087i	0.705500	+	0.974426i
$598$		0			0
$599$	12.1244	+	21.0000i	0.495388	+	0.858037i	0.999986	−	0.00531761i	$-0.00169266\pi$
$599$	12.1244	+	21.0000i	0.495388	+	0.858037i	−0.504598	+	0.863354i	$0.668359\pi$
$600$	4.78060	−	1.07047i	0.195167	−	0.0437016i
$601$	10.9545			0.446841			0.223421	−	0.974722i	$-0.428278\pi$
$601$	10.9545			0.446841			0.223421	+	0.974722i	$0.428278\pi$
$602$		0			0
$603$	17.3205	−	15.4919i	0.705346	−	0.630880i
$604$	−4.14590	+	14.9269i	−0.168694	+	0.607366i
$605$	2.12132	−	1.22474i	0.0862439	−	0.0497930i
$606$	9.50017	−	15.2888i	0.385918	−	0.621064i
$607$	22.0454	+	12.7279i	0.894795	+	0.516610i	0.875508	−	0.483204i	$-0.160527\pi$
$607$	22.0454	+	12.7279i	0.894795	+	0.516610i	0.0192875	+	0.999814i	$0.493860\pi$
$608$	−23.7171	−	3.67423i	−0.961855	−	0.149010i
$609$		0			0
$610$	15.0000	+	11.6190i	0.607332	+	0.470438i
$611$		0			0
$612$	1.90309	−	29.3322i	0.0769277	−	1.18568i
$613$	7.00000	+	12.1244i	0.282727	+	0.489698i	0.972056	−	0.234751i	$-0.0754275\pi$
$613$	7.00000	+	12.1244i	0.282727	+	0.489698i	−0.689328	+	0.724449i	$0.742094\pi$
$614$	−27.7684	+	11.3540i	−1.12064	+	0.458211i
$615$		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	−0.424339	−	0.905503i	$-0.639494\pi$
$619$	3.67423	−	2.12132i	0.147680	−	0.0852631i	0.572019	+	0.820240i	$0.306160\pi$
$620$	−29.6607	+	29.1246i	−1.19120	+	1.16967i
$621$		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
$626$	−15.3500	−	2.09211i	−0.613510	−	0.0836177i
$627$	25.3208	−	2.61895i	1.01121	−	0.104591i
$628$	10.5549	+	2.93159i	0.421186	+	0.116983i
$629$		−	9.79796i		−	0.390670i
$630$		0			0
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$	26.1966	+	35.1246i	1.04204	+	1.39718i
$633$	13.3452	−	1.38031i	0.530425	−	0.0548623i
$634$	−0.854102	+	6.26662i	−0.0339207	+	0.248879i
$635$	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
$639$	10.1723	−	2.12702i	0.402410	−	0.0841435i
$640$	22.5132	−	16.1603i	0.889913	−	0.638792i
$641$	27.1109	−	15.6525i	1.07082	−	0.618236i	0.142411	−	0.989808i	$-0.454514\pi$
$641$	27.1109	−	15.6525i	1.07082	−	0.618236i	0.928404	+	0.371572i	$0.121181\pi$
$642$	−1.37416	+	42.4041i	−0.0542336	+	1.67356i
$643$		−	21.2132i		−	0.836567i	−0.908317	−	0.418284i	$-0.862632\pi$
$643$		−	21.2132i		−	0.836567i	0.908317	−	0.418284i	$-0.137368\pi$
$644$		0			0
$645$	30.0000	+	13.4164i	1.18125	+	0.528271i
$646$	−11.1246	−	27.2074i	−0.437692	−	1.07046i
$647$	9.48683	+	16.4317i	0.372966	+	0.645996i	0.990020	−	0.140925i	$-0.0450075\pi$
$647$	9.48683	+	16.4317i	0.372966	+	0.645996i	−0.617054	+	0.786920i	$0.711674\pi$
$648$	−25.4554	+	0.149679i	−0.999983	+	0.00587995i
$649$	−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	$-0.543181\pi$
$653$	−27.1109	−	15.6525i	−1.06093	−	0.612529i	−0.925690	+	0.378284i	$0.876514\pi$
$654$	20.8054	+	12.9281i	0.813555	+	0.505529i
$655$	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	$0.343425\pi$
$660$	−18.7432	+	22.6427i	−0.729579	+	0.881366i
$661$	19.1703	+	33.2039i	0.745638	+	1.29148i	0.949896	+	0.312566i	$0.101188\pi$
$661$	19.1703	+	33.2039i	0.745638	+	1.29148i	−0.204258	+	0.978917i	$0.565478\pi$
$662$	4.43804	−	32.5623i	0.172489	−	1.26557i
$663$	−27.2555	−	37.6449i	−1.05852	−	1.46201i
$664$	24.6475	+	10.6066i	0.956509	+	0.411616i
$665$		0			0
$666$	−8.46410	+	0.599153i	−0.327977	+	0.0232167i
$667$		0			0
$668$	−27.0764	+	26.5870i	−1.04762	+	1.02868i
$669$	−14.6190	+	1.51205i	−0.565201	+	0.0584593i
$670$	10.1553	+	24.8369i	0.392335	+	0.959531i
$671$	−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	$0.667076\pi$
$674$	−4.28187	−	10.4721i	−0.164931	−	0.403372i
$675$	3.49604	−	3.84418i	0.134563	−	0.147963i
$676$	−24.2599	+	23.8214i	−0.933072	+	0.916208i
$677$	6.36396	+	3.67423i	0.244587	+	0.141212i	0.617283	−	0.786741i	$-0.288233\pi$
$677$	6.36396	+	3.67423i	0.244587	+	0.141212i	−0.372696	+	0.927953i	$0.621567\pi$
$678$	5.16708	+	9.65926i	0.198441	+	0.370962i
$679$		0			0
$680$	31.1769	+	13.4164i	1.19558	+	0.514496i
$681$	−13.3095	+	9.63628i	−0.510020	+	0.369263i
$682$	5.61373	−	41.1884i	0.214961	−	1.57719i
$683$	−19.0526	−	33.0000i	−0.729026	−	1.26271i	−0.957295	−	0.289112i	$-0.906640\pi$
$683$	−19.0526	−	33.0000i	−0.729026	−	1.26271i	0.228269	−	0.973598i	$-0.426693\pi$
$684$	−22.8232	+	11.2739i	−0.872667	+	0.431068i
$685$	21.9089			0.837096
$686$		0			0
$687$	−8.66025	−	3.87298i	−0.330409	−	0.147764i
$688$	30.9787	+	0.565061i	1.18105	+	0.0215427i
$689$	21.2132	−	12.2474i	0.808159	−	0.466591i
$690$		0			0
$691$	11.0227	+	6.36396i	0.419323	+	0.242096i	0.694788	−	0.719215i	$-0.255498\pi$
$691$	11.0227	+	6.36396i	0.419323	+	0.242096i	−0.275464	+	0.961311i	$0.588832\pi$
$692$	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
$696$	20.9088	+	6.54384i	0.792546	+	0.248044i
$697$		0			0
$698$	−8.79478	−	21.5093i	−0.332887	−	0.814141i
$699$	−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	$-0.138769\pi$
$702$	−30.8534	+	25.8471i	−1.16448	+	0.975535i
$703$	−7.34847	+	4.24264i	−0.277153	+	0.160014i
$704$	−7.90215	+	26.5623i	−0.297823	+	1.00110i
$705$		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	−0.944509	−	0.328484i	$-0.893462\pi$
$709$	−5.00000	+	8.66025i	−0.187779	+	0.325243i	0.756730	+	0.653727i	$0.226796\pi$
$710$	−1.62054	+	11.8901i	−0.0608180	+	0.446226i
$711$	44.1533	+	14.5081i	1.65588	+	0.544095i
$712$	−16.5682	−	22.2148i	−0.620919	−	0.832533i
$713$		0			0
$714$		0			0
$715$			46.4758i			1.73810i
$716$	20.0265	+	5.56231i	0.748425	+	0.207873i
$717$	1.23458	+	11.9363i	0.0461064	+	0.445770i
$718$	38.8328	+	5.29268i	1.44923	+	0.197521i
$719$	−18.9737	+	32.8634i	−0.707598	+	1.22560i	0.258147	+	0.966106i	$0.416888\pi$
$719$	−18.9737	+	32.8634i	−0.707598	+	1.22560i	−0.965746	+	0.259491i	$0.916445\pi$
$720$	9.68346	−	27.7530i	0.360881	−	1.03429i
$721$		0			0
$722$	0.866025	−	1.11803i	0.0322301	−	0.0416089i
$723$	30.7369	−	22.2540i	1.14312	−	0.827636i
$724$	−23.4488	+	23.0250i	−0.871469	+	0.855718i
$725$	−3.87298	+	2.23607i	−0.143839	+	0.0830455i
$726$	0.0793369	−	2.44820i	0.00294447	−	0.0908614i
$727$		−	16.9706i		−	0.629403i	−0.949191	−	0.314702i	$-0.898096\pi$
$727$		−	16.9706i		−	0.629403i	0.949191	−	0.314702i	$-0.101904\pi$
$728$		0			0
$729$	−22.0000	+	15.6525i	−0.814815	+	0.579721i
$730$	35.1246	−	14.3618i	1.30002	−	0.531555i
$731$	18.9737	+	32.8634i	0.701766	+	1.21550i
$732$	17.7857	−	6.60831i	0.657377	−	0.244250i
$733$	−8.21584	+	14.2302i	−0.303459	+	0.525606i	−0.976917	−	0.213619i	$-0.931475\pi$
$733$	−8.21584	+	14.2302i	−0.303459	+	0.525606i	0.673458	+	0.739225i	$0.264808\pi$
$734$	−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	$-0.919036\pi$
$739$	−33.5410	+	19.3649i	−1.23383	+	0.712350i	−0.266001	+	0.963973i	$0.585702\pi$
$740$	2.62210	−	9.44058i	0.0963902	−	0.347043i
$741$	−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	$0.581803\pi$
$744$	9.08321	+	40.5647i	0.333007	+	1.48717i
$745$	−5.47723	−	9.48683i	−0.200670	−	0.347571i
$746$	−36.4327	−	4.96556i	−1.33390	−	0.181802i
$747$	27.8580	−	5.82508i	1.01927	−	0.213128i
$748$	−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	$-0.378470\pi$
$751$	−6.70820	−	3.87298i	−0.244786	−	0.141327i	−0.617374	+	0.786669i	$0.711804\pi$
$752$		0			0
$753$	−1.69052	−	16.3445i	−0.0616062	−	0.595626i
$754$	32.0642	−	13.1105i	1.16771	−	0.477456i
$755$	−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	$0.742639\pi$
$758$	10.1396	−	4.14590i	0.368287	−	0.150586i
$759$		0			0
$760$	−3.43769	−	29.1922i	−0.124698	−	1.05891i
$761$	−42.4264	−	24.4949i	−1.53796	−	0.887939i	−0.998958	−	0.0456321i	$-0.985470\pi$
$761$	−42.4264	−	24.4949i	−1.53796	−	0.887939i	−0.538998	−	0.842307i	$-0.681197\pi$
$762$	−8.94965	−	16.7303i	−0.324212	−	0.606076i
$763$		0			0
$764$	1.73205	+	6.70820i	0.0626634	+	0.242694i
$765$	35.2379	−	7.36820i	1.27403	−	0.266398i
$766$		0			0
$767$	−25.9808	−	45.0000i	−0.938111	−	1.62486i
$768$	−1.84397	−	27.6514i	−0.0665387	−	0.997784i
$769$	−21.9089			−0.790055			−0.395028	−	0.918669i	$-0.629265\pi$
$769$	−21.9089			−0.790055			−0.395028	+	0.918669i	$0.629265\pi$
$770$		0			0
$771$	3.46410	−	7.74597i	0.124757	−	0.278964i
$772$	−30.8328	−	8.56373i	−1.10970	−	0.308215i
$773$	2.12132	−	1.22474i	0.0762986	−	0.0440510i	−0.461365	−	0.887210i	$-0.652640\pi$
$773$	2.12132	−	1.22474i	0.0762986	−	0.0440510i	0.537664	+	0.843159i	$0.319307\pi$
$774$	27.2292	−	18.4003i	0.978734	−	0.661384i
$775$	−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
$780$	−16.1870	−	43.5658i	−0.579587	−	1.55991i
$781$	−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
$786$	0.752656	−	23.2257i	0.0268463	−	0.828434i
$787$	−18.3712	+	10.6066i	−0.654862	+	0.378085i	−0.790316	−	0.612699i	$-0.790084\pi$
$787$	−18.3712	+	10.6066i	−0.654862	+	0.378085i	0.135455	+	0.990784i	$0.456750\pi$
$788$	−31.3331	−	31.9098i	−1.11620	−	1.13674i
$789$	−4.85993	+	3.51867i	−0.173018	+	0.125268i
$790$	−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
$794$	53.7251	+	7.32240i	1.90663	+	0.259862i
$795$	1.95205	+	18.8730i	0.0692321	+	0.669356i
$796$	−9.08321	+	32.7031i	−0.321946	+	1.15913i
$797$		−	41.6413i		−	1.47501i	−0.675341	−	0.737506i	$-0.736003\pi$
$797$		−	41.6413i		−	1.47501i	0.675341	−	0.737506i	$-0.263997\pi$
$798$		0			0
$799$		0			0
$800$	4.40822	+	3.54508i	0.155854	+	0.125338i
$801$	−27.9250	−	9.17571i	−0.986682	−	0.324208i
$802$	0.854102	−	6.26662i	0.0301594	−	0.221282i
$803$	−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
$807$	2.48808	+	3.43649i	0.0875844	+	0.120970i
$808$	20.6420	−	2.43082i	0.726182	−	0.0855158i
$809$	19.3649	−	11.1803i	0.680834	−	0.393080i	−0.119335	−	0.992854i	$-0.538076\pi$
$809$	19.3649	−	11.1803i	0.680834	−	0.393080i	0.800169	+	0.599774i	$0.204743\pi$
$810$	−8.51995	−	29.9902i	−0.299360	−	1.05375i
$811$			12.7279i			0.446938i	0.974711	+	0.223469i	$0.0717381\pi$
$811$			12.7279i			0.446938i	−0.974711	+	0.223469i	$0.928262\pi$
$812$		0			0
$813$	6.00000	−	13.4164i	0.210429	−	0.470534i
$814$	3.70820	+	9.06914i	0.129972	+	0.317873i
$815$	−9.48683	−	16.4317i	−0.332309	−	0.575577i
$816$	27.8504	−	19.3999i	0.974958	−	0.679133i
$817$	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	$-0.149379\pi$
$821$	27.1109	+	15.6525i	0.946176	+	0.546275i	0.0542853	+	0.998525i	$0.482712\pi$
$822$	11.5632	−	18.6089i	0.403314	−	0.649060i
$823$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$823$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$824$		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	−0.875673	−	0.482904i	$-0.839582\pi$
$829$	−24.6475	−	42.6907i	−0.856044	−	1.48271i	0.0196299	−	0.999807i	$-0.493751\pi$
$830$	−4.43804	+	32.5623i	−0.154047	+	1.13025i
$831$	2.80588	−	2.03151i	0.0973350	−	0.0704722i
$832$	−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
$836$	20.5942	+	20.9733i	0.712266	+	0.725376i
$837$	32.6190	+	29.6649i	1.12748	+	1.02537i
$838$	−15.2330	−	37.2553i	−0.526215	−	1.28696i
$839$	18.9737			0.655044			0.327522	−	0.944844i	$-0.393786\pi$
$839$	18.9737			0.655044			0.327522	+	0.944844i	$0.393786\pi$
$840$		0			0
$841$	9.00000			0.310345
$842$	−5.35233	−	13.0902i	−0.184454	−	0.451117i
$843$	15.4097	−	1.59384i	0.530739	−	0.0548948i
$844$	10.8541	+	11.0539i	0.373614	+	0.380491i
$845$	−36.0624	−	20.8207i	−1.24059	−	0.716253i
$846$		0			0
$847$		0			0
$848$	8.66025	+	15.6525i	0.297394	+	0.537508i
$849$	30.1663	+	41.6652i	1.03531	+	1.42995i
$850$	−0.935622	+	6.86474i	−0.0320916	+	0.235459i
$851$		0			0
$852$	9.24384	+	7.65188i	0.316689	+	0.262149i
$853$	−16.4317			−0.562610			−0.281305	−	0.959618i	$-0.590767\pi$
$853$	−16.4317			−0.562610			−0.281305	+	0.959618i	$0.590767\pi$
$854$		0			0
$855$	−20.7846	−	23.2379i	−0.710819	−	0.794719i
$856$	−39.2705	+	29.2887i	−1.34224	+	1.00107i
$857$	16.9706	−	9.79796i	0.579703	−	0.334692i	−0.181312	−	0.983426i	$-0.558034\pi$
$857$	16.9706	−	9.79796i	0.579703	−	0.334692i	0.761015	+	0.648734i	$0.224701\pi$
$858$	39.4755	+	24.5293i	1.34767	+	0.837418i
$859$	−40.4166	−	23.3345i	−1.37900	−	0.796164i	−0.386957	−	0.922098i	$-0.626474\pi$
$859$	−40.4166	−	23.3345i	−1.37900	−	0.796164i	−0.992039	+	0.125934i	$0.959807\pi$
$860$	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	−0.974938	−	0.222477i	$-0.928586\pi$
$863$	−8.66025	+	15.0000i	−0.294798	+	0.510606i	0.680140	+	0.733083i	$0.261919\pi$
$864$	−18.4620	−	22.8726i	−0.628089	−	0.778142i
$865$	3.00000	+	5.19615i	0.102003	+	0.176674i
$866$	−11.7264	−	28.6791i	−0.398478	−	0.974556i
$867$	11.0680	+	4.94975i	0.375888	+	0.168102i
$868$		0			0
$869$		−	53.6656i		−	1.82048i
$870$	−0.869092	+	26.8187i	−0.0294650	+	0.909240i
$871$	36.7423	−	21.2132i	1.24497	−	0.718782i
$872$	3.30792	+	28.0902i	0.112020	+	0.951253i
$873$		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	−0.989788	−	0.142548i	$-0.954470\pi$
$877$	−11.0000	+	19.0526i	−0.371444	+	0.643359i	0.618344	+	0.785907i	$0.287804\pi$
$878$	3.24109	−	23.7801i	0.109381	−	0.802541i
$879$	4.22013	−	0.436492i	0.142341	−	0.0147225i
$880$	−33.9355	−	0.618993i	−1.14396	−	0.0208662i
$881$			44.0908i			1.48546i	0.669593	+	0.742729i	$0.266469\pi$
$881$			44.0908i			1.48546i	−0.669593	+	0.742729i	$0.733531\pi$
$882$		0			0
$883$			54.2218i			1.82471i	0.409403	+	0.912354i	$0.365737\pi$
$883$			54.2218i			1.82471i	−0.409403	+	0.912354i	$0.634263\pi$
$884$	14.3618	−	51.7082i	0.483040	−	1.73914i
$885$	40.0356	−	4.14092i	1.34578	−	0.139196i
$886$	−43.6869	−	5.95426i	−1.46769	−	0.200037i
$887$	28.4605	−	49.2950i	0.955610	−	1.65517i	0.222644	−	0.974900i	$-0.428531\pi$
$887$	28.4605	−	49.2950i	0.955610	−	1.65517i	0.732966	−	0.680265i	$-0.238135\pi$
$888$	−6.63470	−	7.20977i	−0.222646	−	0.241944i
$889$		0			0
$890$	20.7846	−	26.8328i	0.696702	−	0.899438i
$891$	25.1008	+	18.4919i	0.840907	+	0.619503i
$892$	−11.8901	−	12.1089i	−0.398109	−	0.405437i
$893$		0			0
$894$	−10.9487	−	0.354805i	−0.366179	−	0.0118665i
$895$			25.4558i			0.850895i
$896$		0			0
$897$		0			0
$898$	−46.8328	+	19.1491i	−1.56283	+	0.639013i
$899$	−18.9737	−	32.8634i	−0.632807	−	1.09605i
$900$	5.98741	+	0.388466i	0.199580	+	0.0129489i
$901$	−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
$906$	−10.0141	+	16.1158i	−0.332695	+	0.535411i
$907$	6.70820	−	3.87298i	0.222742	−	0.128600i	−0.384477	−	0.923135i	$-0.625618\pi$
$907$	6.70820	−	3.87298i	0.222742	−	0.128600i	0.607219	+	0.794534i	$0.292285\pi$
$908$	−18.2816	−	5.07767i	−0.606697	−	0.168508i
$909$	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	$0.611888\pi$
$912$	−26.6095	−	12.4874i	−0.881129	−	0.413498i
$913$	−16.4317	−	28.4605i	−0.543809	−	0.941905i
$914$	39.2352	+	5.34752i	1.29779	+	0.176880i
$915$	13.6278	+	18.8224i	0.450520	+	0.622251i
$916$	−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	$-0.504070\pi$
$919$	−26.8328	−	15.4919i	−0.885133	−	0.511032i	−0.872347	+	0.488887i	$0.837403\pi$
$920$		0			0
$921$	−36.5474	+	3.78013i	−1.20428	+	0.124559i
$922$	−48.0964	+	19.6657i	−1.58397	+	0.647656i
$923$	18.9737			0.624526
$924$		0			0
$925$	2.00000			0.0657596
$926$	−20.2792	+	8.29180i	−0.666416	+	0.272485i
$927$		0			0
$928$	9.14590	+	23.5871i	0.300229	+	0.774285i
$929$	−21.2132	−	12.2474i	−0.695983	−	0.401826i	0.109867	−	0.993946i	$-0.464958\pi$
$929$	−21.2132	−	12.2474i	−0.695983	−	0.401826i	−0.805849	+	0.592121i	$0.798291\pi$
$930$	−44.8922	+	24.0144i	−1.47207	+	0.787464i
$931$		0			0
$932$	−17.3205	+	4.47214i	−0.567352	+	0.146490i
$933$	26.6190	−	19.2726i	0.871465	−	0.630955i
$934$	−39.8805	−	5.43547i	−1.30493	−	0.177854i
$935$	−20.7846	−	36.0000i	−0.679729	−	1.17733i
$936$	−45.5471	−	9.24465i	−1.48875	−	0.302171i
$937$	−10.9545			−0.357866			−0.178933	−	0.983861i	$-0.557265\pi$
$937$	−10.9545			−0.357866			−0.178933	+	0.983861i	$0.557265\pi$
$938$		0			0
$939$	−17.3205	−	7.74597i	−0.565233	−	0.252780i
$940$		0			0
$941$	10.6066	−	6.12372i	0.345765	−	0.199628i	−0.317053	−	0.948408i	$-0.602693\pi$
$941$	10.6066	−	6.12372i	0.345765	−	0.199628i	0.662819	+	0.748780i	$0.269360\pi$
$942$	11.3956	+	7.08101i	0.371288	+	0.230712i
$943$		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	−0.938017	−	0.346590i	$-0.887339\pi$
$947$	−5.19615	+	9.00000i	−0.168852	+	0.292461i	0.769164	+	0.639051i	$0.220673\pi$
$948$	18.6911	+	50.3055i	0.607059	+	1.63385i
$949$	−30.0000	−	51.9615i	−0.973841	−	1.68674i
$950$	5.55369	−	2.27080i	0.180185	−	0.0736745i
$951$	−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	$0.953725\pi$
$954$	17.0605	+	8.30290i	0.552355	+	0.268816i
$955$	−7.34847	+	4.24264i	−0.237791	+	0.137289i
$956$	−9.88690	+	9.70820i	−0.319765	+	0.313986i
$957$	−15.7360	−	21.7343i	−0.508672	−	0.702570i
$958$	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
$962$	−15.3500	−	2.09211i	−0.494904	−	0.0674525i
$963$	−16.2205	+	49.3649i	−0.522699	+	1.59076i
$964$	42.2196	+	11.7264i	1.35980	+	0.377681i
$965$		−	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	$0.878109\pi$
$968$	2.26728	−	1.69098i	0.0728733	−	0.0543503i
$969$	−3.70375	−	35.8090i	−0.118982	−	1.15035i
$970$		0			0
$971$	23.7171	−	41.0792i	0.761117	−	1.31829i	−0.181158	−	0.983454i	$-0.557984\pi$
$971$	23.7171	−	41.0792i	0.761117	−	1.31829i	0.942275	−	0.334840i	$-0.108682\pi$
$972$	−29.9697	−	8.59180i	−0.961278	−	0.275582i
$973$		0			0
$974$	−8.66025	−	6.70820i	−0.277492	−	0.214945i
$975$	7.68423	−	5.56351i	0.246092	−	0.178175i
$976$	18.7707	+	11.2987i	0.600836	+	0.361661i
$977$	−30.9839	+	17.8885i	−0.991262	+	0.572305i	−0.905651	−	0.424023i	$-0.860617\pi$
$977$	−30.9839	+	17.8885i	−0.991262	+	0.572305i	−0.0856105	+	0.996329i	$0.527284\pi$
$978$	−18.9637	−	0.614541i	−0.606393	−	0.0196509i
$979$			33.9411i			1.08476i
$980$		0			0
$981$	20.0000	+	22.3607i	0.638551	+	0.713922i
$982$	−16.6869	−	40.8111i	−0.532501	−	1.30233i
$983$	9.48683	+	16.4317i	0.302583	+	0.524089i	0.976720	−	0.214517i	$-0.0688177\pi$
$983$	9.48683	+	16.4317i	0.302583	+	0.524089i	−0.674137	+	0.738606i	$0.735484\pi$
$984$		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
$990$	−29.8281	+	20.1565i	−0.947999	+	0.640616i
$991$	−13.4164	+	7.74597i	−0.426186	+	0.246059i	−0.697721	−	0.716370i	$-0.745802\pi$
$991$	−13.4164	+	7.74597i	−0.426186	+	0.246059i	0.271534	+	0.962429i	$0.412469\pi$
$992$	−30.0810	+	37.4050i	−0.955074	+	1.18761i
$993$	16.4317	−	36.7423i	0.521443	−	1.16598i
$994$		0			0
$995$	−41.5692			−1.31783
$996$	25.3153	+	20.9555i	0.802146	+	0.664002i
$997$	−2.73861	−	4.74342i	−0.0867327	−	0.150226i	0.819396	−	0.573229i	$-0.194309\pi$
$997$	−2.73861	−	4.74342i	−0.0867327	−	0.150226i	−0.906128	+	0.423003i	$0.860976\pi$
$998$	−4.43804	+	32.5623i	−0.140484	+	1.03074i
$999$	−10.1544	−	2.21113i	−0.321270	−	0.0699572i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.e.b.491.1	✓	8	28.19	even	6
588.2.e.b.491.2	yes	8	28.23	odd	6
588.2.e.b.491.3	yes	8	21.5	even	6
588.2.e.b.491.4	yes	8	21.2	odd	6
588.2.e.b.491.5	yes	8	7.2	even	3
588.2.e.b.491.6	yes	8	7.5	odd	6
588.2.e.b.491.7	yes	8	84.23	even	6
588.2.e.b.491.8	yes	8	84.47	odd	6
588.2.n.c.263.1		16	7.3	odd	6	inner
588.2.n.c.263.2		16	7.4	even	3	inner
588.2.n.c.263.3		16	28.11	odd	6	inner
588.2.n.c.263.4		16	28.3	even	6	inner
588.2.n.c.263.5		16	84.59	odd	6	inner
588.2.n.c.263.6		16	84.11	even	6	inner
588.2.n.c.263.7		16	21.11	odd	6	inner
588.2.n.c.263.8		16	21.17	even	6	inner
588.2.n.c.275.1		16	84.83	odd	2	inner
588.2.n.c.275.2		16	12.11	even	2	inner
588.2.n.c.275.3		16	3.2	odd	2	inner
588.2.n.c.275.4		16	21.20	even	2	inner
588.2.n.c.275.5		16	7.6	odd	2	inner
588.2.n.c.275.6		16	1.1	even	1	trivial
588.2.n.c.275.7		16	4.3	odd	2	inner
588.2.n.c.275.8		16	28.27	even	2	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+(0.535233 + 1.30902i) q^{2} +(0.178197 + 1.72286i) q^{3} +(-1.42705 + 1.40126i) q^{4} +(-2.12132 - 1.22474i) q^{5} +(-2.15988 + 1.15539i) q^{6} +(-2.59808 - 1.11803i) q^{8} +(-2.93649 + 0.614017i) q^{9} +(0.467811 - 3.43237i) q^{10} +(1.73205 + 3.00000i) q^{11} +(-2.66847 - 2.20891i) q^{12} -5.47723 q^{13} +(1.73205 - 3.87298i) q^{15} +(0.0729490 - 3.99933i) q^{16} +(4.24264 - 2.44949i) q^{17} +(-2.37547 - 3.51528i) q^{18} +(-3.67423 - 2.12132i) q^{19} +(4.74342 - 1.22474i) q^{20} +(-3.00000 + 3.87298i) q^{22} +(1.46325 - 4.67535i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-2.93159 - 7.16978i) q^{26} +(-1.58114 - 4.94975i) q^{27} +4.47214i q^{29} +(5.99685 + 0.194335i) q^{30} +(-7.34847 + 4.24264i) q^{31} +(5.27424 - 2.04508i) q^{32} +(-4.85993 + 3.51867i) q^{33} +(5.47723 + 4.24264i) q^{34} +(3.33013 - 4.99102i) q^{36} +(1.00000 - 1.73205i) q^{37} +(0.810272 - 5.94504i) q^{38} +(-0.976025 - 9.43649i) q^{39} +(4.14205 + 5.55369i) q^{40} +7.74597i q^{43} +(-6.67550 - 1.85410i) q^{44} +(6.98125 + 2.29393i) q^{45} +(6.90329 - 0.586988i) q^{48} +(-0.866025 + 1.11803i) q^{50} +(4.97615 + 6.87298i) q^{51} +(7.81628 - 7.67501i) q^{52} +(-3.87298 + 2.23607i) q^{53} +(5.63303 - 4.71901i) q^{54} -8.48528i q^{55} +(3.00000 - 6.70820i) q^{57} +(-5.85410 + 2.39364i) q^{58} +(4.74342 + 8.21584i) q^{59} +(2.95533 + 7.95400i) 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} +(-7.20720 - 4.47843i) q^{66} +(-6.70820 + 3.87298i) q^{67} +(-2.62210 + 9.44058i) q^{68} -3.46410 q^{71} +(8.31572 + 1.68784i) q^{72} +(5.47723 + 9.48683i) q^{73} +(2.80252 + 0.381966i) q^{74} +(-1.40294 + 1.01575i) q^{75} +(8.21584 - 2.12132i) q^{76} +(11.8301 - 6.32836i) q^{78} +(-13.4164 - 7.74597i) q^{79} +(-5.05291 + 8.39453i) q^{80} +(8.24597 - 3.60611i) q^{81} -9.48683 q^{83} -12.0000 q^{85} +(-10.1396 + 4.14590i) q^{86} +(-7.70486 + 0.796921i) q^{87} +(-1.14590 - 9.73072i) q^{88} +(8.48528 + 4.89898i) q^{89} +(0.733809 + 10.3664i) q^{90} +(-8.61895 - 11.9044i) q^{93} +(5.19615 + 9.00000i) q^{95} +(4.46325 + 8.72235i) 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

Groups

Database

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