LMFDB - Embedded newform 396.2.j.c.361.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [396,2,Mod(37,396)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("396.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(396, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 396 = 2^{2} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	396.j (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,7,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.16207592004$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 132)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			361.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	396.361
Dual form			396.2.j.c.181.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19098 + 3.66547i) q^{5} +(0.190983 + 0.138757i) q^{7} +(-3.30902 - 0.224514i) q^{11} +(-1.92705 + 5.93085i) q^{13} +(-0.736068 - 2.26538i) q^{17} +(4.11803 - 2.99193i) q^{19} +0.236068 q^{23} +(-7.97214 + 5.79210i) q^{25} +(3.61803 + 2.62866i) q^{29} +(-1.97214 + 6.06961i) q^{31} +(-0.281153 + 0.865300i) q^{35} +(3.04508 + 2.21238i) q^{37} +(7.66312 - 5.56758i) q^{41} +9.47214 q^{43} +(2.92705 - 2.12663i) q^{47} +(-2.14590 - 6.60440i) q^{49} +(-2.02786 + 6.24112i) q^{53} +(-3.11803 - 12.3965i) q^{55} +(1.73607 + 1.26133i) q^{59} +(-0.809017 - 2.48990i) q^{61} -24.0344 q^{65} -0.145898 q^{67} +(0.427051 + 1.31433i) q^{71} +(-2.61803 - 1.90211i) q^{73} +(-0.600813 - 0.502029i) q^{77} +(4.39919 - 13.5393i) q^{79} +(-4.78115 - 14.7149i) q^{83} +(7.42705 - 5.39607i) q^{85} -1.00000 q^{89} +(-1.19098 + 0.865300i) q^{91} +(15.8713 + 11.5312i) q^{95} +(-1.57295 + 4.84104i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 7 q^{5} + 3 q^{7} - 11 q^{11} - q^{13} + 6 q^{17} + 12 q^{19} - 8 q^{23} - 14 q^{25} + 10 q^{29} + 10 q^{31} + 19 q^{35} + q^{37} + 15 q^{41} + 20 q^{43} + 5 q^{47} - 22 q^{49} - 26 q^{53} - 8 q^{55}+ \cdots - 13 q^{97}+O(q^{100}) $ 4 * q + 7 * q^5 + 3 * q^7 - 11 * q^11 - q^13 + 6 * q^17 + 12 * q^19 - 8 * q^23 - 14 * q^25 + 10 * q^29 + 10 * q^31 + 19 * q^35 + q^37 + 15 * q^41 + 20 * q^43 + 5 * q^47 - 22 * q^49 - 26 * q^53 - 8 * q^55 - 2 * q^59 - q^61 - 38 * q^65 - 14 * q^67 - 5 * q^71 - 6 * q^73 - 27 * q^77 - 7 * q^79 + q^83 + 23 * q^85 - 4 * q^89 - 7 * q^91 + 21 * q^95 - 13 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/396\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.19098	+	3.66547i	0.532624	+	1.63925i	0.748728	+	0.662877i	$0.230665\pi$
$5$	1.19098	+	3.66547i	0.532624	+	1.63925i	−0.216104	+	0.976370i	$0.569335\pi$
$6$		0			0
$7$	0.190983	+	0.138757i	0.0721848	+	0.0524453i	0.623292	−	0.781989i	$-0.285795\pi$
$7$	0.190983	+	0.138757i	0.0721848	+	0.0524453i	−0.551108	+	0.834434i	$0.685795\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.30902	−	0.224514i	−0.997706	−	0.0676935i
$11$	−3.30902	−	0.224514i	−0.997706	−	0.0676935i
$12$		0			0
$13$	−1.92705	+	5.93085i	−0.534468	+	1.64492i	0.210329	+	0.977631i	$0.432547\pi$
$13$	−1.92705	+	5.93085i	−0.534468	+	1.64492i	−0.744796	+	0.667292i	$0.767453\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.736068	−	2.26538i	−0.178523	−	0.549436i	0.821254	−	0.570563i	$-0.193275\pi$
$17$	−0.736068	−	2.26538i	−0.178523	−	0.549436i	−0.999777	+	0.0211262i	$0.993275\pi$
$18$		0			0
$19$	4.11803	−	2.99193i	0.944742	−	0.686395i	−0.00481560	−	0.999988i	$-0.501533\pi$
$19$	4.11803	−	2.99193i	0.944742	−	0.686395i	0.949557	+	0.313593i	$0.101533\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.236068			0.0492236			0.0246118	−	0.999697i	$-0.492165\pi$
$23$	0.236068			0.0492236			0.0246118	+	0.999697i	$0.492165\pi$
$24$		0			0
$25$	−7.97214	+	5.79210i	−1.59443	+	1.15842i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.61803	+	2.62866i	0.671852	+	0.488129i	0.870645	−	0.491912i	$-0.163702\pi$
$29$	3.61803	+	2.62866i	0.671852	+	0.488129i	−0.198793	+	0.980042i	$0.563702\pi$
$30$		0			0
$31$	−1.97214	+	6.06961i	−0.354206	+	1.09013i	0.602262	+	0.798298i	$0.294266\pi$
$31$	−1.97214	+	6.06961i	−0.354206	+	1.09013i	−0.956468	+	0.291836i	$0.905734\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.281153	+	0.865300i	−0.0475235	+	0.146262i
$36$		0			0
$37$	3.04508	+	2.21238i	0.500609	+	0.363714i	0.809250	−	0.587465i	$-0.199874\pi$
$37$	3.04508	+	2.21238i	0.500609	+	0.363714i	−0.308641	+	0.951179i	$0.599874\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	7.66312	−	5.56758i	1.19678	−	0.869510i	0.202814	−	0.979217i	$-0.434991\pi$
$41$	7.66312	−	5.56758i	1.19678	−	0.869510i	0.993964	+	0.109707i	$0.0349913\pi$
$42$		0			0
$43$	9.47214			1.44449			0.722244	−	0.691639i	$-0.243111\pi$
$43$	9.47214			1.44449			0.722244	+	0.691639i	$0.243111\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.92705	−	2.12663i	0.426954	−	0.310200i	−0.353476	−	0.935444i	$-0.615000\pi$
$47$	2.92705	−	2.12663i	0.426954	−	0.310200i	0.780430	+	0.625243i	$0.215000\pi$
$48$		0			0
$49$	−2.14590	−	6.60440i	−0.306557	−	0.943485i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−2.02786	+	6.24112i	−0.278549	+	0.857284i	0.709710	+	0.704494i	$0.248826\pi$
$53$	−2.02786	+	6.24112i	−0.278549	+	0.857284i	−0.988259	+	0.152790i	$0.951174\pi$
$54$		0			0
$55$	−3.11803	−	12.3965i	−0.420436	−	1.67154i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.73607	+	1.26133i	0.226017	+	0.164211i	0.695031	−	0.718980i	$-0.255391\pi$
$59$	1.73607	+	1.26133i	0.226017	+	0.164211i	−0.469014	+	0.883191i	$0.655391\pi$
$60$		0			0
$61$	−0.809017	−	2.48990i	−0.103584	−	0.318799i	0.885811	−	0.464045i	$-0.153602\pi$
$61$	−0.809017	−	2.48990i	−0.103584	−	0.318799i	−0.989396	+	0.145246i	$0.953602\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−24.0344			−2.98111
$66$		0			0
$67$	−0.145898			−0.0178243			−0.00891214	−	0.999960i	$-0.502837\pi$
$67$	−0.145898			−0.0178243			−0.00891214	+	0.999960i	$0.502837\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.427051	+	1.31433i	0.0506816	+	0.155982i	0.973194	−	0.229985i	$-0.0738678\pi$
$71$	0.427051	+	1.31433i	0.0506816	+	0.155982i	−0.922512	+	0.385967i	$0.873868\pi$
$72$		0			0
$73$	−2.61803	−	1.90211i	−0.306418	−	0.222625i	0.423940	−	0.905690i	$-0.360647\pi$
$73$	−2.61803	−	1.90211i	−0.306418	−	0.222625i	−0.730358	+	0.683065i	$0.760647\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.600813	−	0.502029i	−0.0684690	−	0.0572115i
$78$		0			0
$79$	4.39919	−	13.5393i	0.494947	−	1.52329i	−0.322092	−	0.946708i	$-0.604386\pi$
$79$	4.39919	−	13.5393i	0.494947	−	1.52329i	0.817039	−	0.576582i	$-0.195614\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.78115	−	14.7149i	−0.524800	−	1.61517i	−0.764712	−	0.644373i	$-0.777119\pi$
$83$	−4.78115	−	14.7149i	−0.524800	−	1.61517i	0.239912	−	0.970795i	$-0.422881\pi$
$84$		0			0
$85$	7.42705	−	5.39607i	0.805577	−	0.585286i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.00000			−0.106000			−0.0529999	−	0.998595i	$-0.516878\pi$
$89$	−1.00000			−0.106000			−0.0529999	+	0.998595i	$0.516878\pi$
$90$		0			0
$91$	−1.19098	+	0.865300i	−0.124849	+	0.0907081i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	15.8713	+	11.5312i	1.62836	+	1.18308i
$96$		0			0
$97$	−1.57295	+	4.84104i	−0.159709	+	0.491533i	−0.998608	−	0.0527545i	$-0.983200\pi$
$97$	−1.57295	+	4.84104i	−0.159709	+	0.491533i	0.838899	+	0.544288i	$0.183200\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.83688	−	5.65334i	0.182776	−	0.562528i	−0.817126	−	0.576458i	$-0.804434\pi$
$101$	1.83688	−	5.65334i	0.182776	−	0.562528i	0.999903	+	0.0139302i	$0.00443427\pi$
$102$		0			0
$103$	−10.0902	−	7.33094i	−0.994214	−	0.722339i	−0.0333741	−	0.999443i	$-0.510625\pi$
$103$	−10.0902	−	7.33094i	−0.994214	−	0.722339i	−0.960840	+	0.277104i	$0.910625\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.28115	−	3.83698i	0.510548	−	0.370935i	−0.302483	−	0.953155i	$-0.597816\pi$
$107$	5.28115	−	3.83698i	0.510548	−	0.370935i	0.813032	+	0.582220i	$0.197816\pi$
$108$		0			0
$109$	−8.00000			−0.766261			−0.383131	−	0.923694i	$-0.625154\pi$
$109$	−8.00000			−0.766261			−0.383131	+	0.923694i	$0.625154\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	9.89919	−	7.19218i	0.931237	−	0.676583i	−0.0150583	−	0.999887i	$-0.504793\pi$
$113$	9.89919	−	7.19218i	0.931237	−	0.676583i	0.946295	+	0.323303i	$0.104793\pi$
$114$		0			0
$115$	0.281153	+	0.865300i	0.0262176	+	0.0806896i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.173762	−	0.534785i	0.0159287	−	0.0490236i
$120$		0			0
$121$	10.8992	+	1.48584i	0.990835	+	0.135076i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−15.1353	−	10.9964i	−1.35374	−	0.983548i
$126$		0			0
$127$	4.85410	+	14.9394i	0.430732	+	1.32566i	0.897398	+	0.441223i	$0.145455\pi$
$127$	4.85410	+	14.9394i	0.430732	+	1.32566i	−0.466666	+	0.884434i	$0.654545\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	8.56231			0.748092			0.374046	−	0.927410i	$-0.377970\pi$
$131$	8.56231			0.748092			0.374046	+	0.927410i	$0.377970\pi$
$132$		0			0
$133$	1.20163			0.104194
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.48936	+	19.9722i	0.554423	+	1.70634i	0.697462	+	0.716622i	$0.254313\pi$
$137$	6.48936	+	19.9722i	0.554423	+	1.70634i	−0.143039	+	0.989717i	$0.545687\pi$
$138$		0			0
$139$	−3.07295	−	2.23263i	−0.260644	−	0.189369i	0.449787	−	0.893136i	$-0.351500\pi$
$139$	−3.07295	−	2.23263i	−0.260644	−	0.189369i	−0.710431	+	0.703767i	$0.751500\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	7.70820	−	19.1926i	0.644592	−	1.60497i
$144$		0			0
$145$	−5.32624	+	16.3925i	−0.442320	+	1.36132i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	5.21885	+	16.0620i	0.427545	+	1.31585i	0.900537	+	0.434780i	$0.143174\pi$
$149$	5.21885	+	16.0620i	0.427545	+	1.31585i	−0.472992	+	0.881067i	$0.656826\pi$
$150$		0			0
$151$	−3.61803	+	2.62866i	−0.294431	+	0.213917i	−0.725188	−	0.688551i	$-0.758247\pi$
$151$	−3.61803	+	2.62866i	−0.294431	+	0.213917i	0.430756	+	0.902468i	$0.358247\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−24.5967			−1.97566
$156$		0			0
$157$	13.9443	−	10.1311i	1.11287	−	0.808550i	0.129760	−	0.991545i	$-0.458579\pi$
$157$	13.9443	−	10.1311i	1.11287	−	0.808550i	0.983114	+	0.182995i	$0.0585792\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.0450850	+	0.0327561i	0.00355319	+	0.00258155i
$162$		0			0
$163$	−1.50000	+	4.61653i	−0.117489	+	0.361594i	−0.992458	−	0.122585i	$-0.960882\pi$
$163$	−1.50000	+	4.61653i	−0.117489	+	0.361594i	0.874969	+	0.484179i	$0.160882\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.190983	−	0.587785i	0.0147787	−	0.0454842i	−0.943395	−	0.331671i	$-0.892388\pi$
$167$	0.190983	−	0.587785i	0.0147787	−	0.0454842i	0.958174	+	0.286187i	$0.0923877\pi$
$168$		0			0
$169$	−20.9443	−	15.2169i	−1.61110	−	1.17053i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	4.50000	−	3.26944i	0.342129	−	0.248571i	−0.403431	−	0.915010i	$-0.632182\pi$
$173$	4.50000	−	3.26944i	0.342129	−	0.248571i	0.745559	+	0.666439i	$0.232182\pi$
$174$		0			0
$175$	−2.32624			−0.175847
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−14.5172	+	10.5474i	−1.08507	+	0.788348i	−0.978560	−	0.205964i	$-0.933967\pi$
$179$	−14.5172	+	10.5474i	−1.08507	+	0.788348i	−0.106508	+	0.994312i	$0.533967\pi$
$180$		0			0
$181$	1.83688	+	5.65334i	0.136534	+	0.420209i	0.995826	−	0.0912773i	$-0.0290950\pi$
$181$	1.83688	+	5.65334i	0.136534	+	0.420209i	−0.859291	+	0.511487i	$0.829095\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−4.48278	+	13.7966i	−0.329580	+	1.01434i
$186$		0			0
$187$	1.92705	+	7.66145i	0.140920	+	0.560261i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−17.5172	−	12.7270i	−1.26750	−	0.920894i	−0.268401	−	0.963307i	$-0.586495\pi$
$191$	−17.5172	−	12.7270i	−1.26750	−	0.920894i	−0.999100	+	0.0424133i	$0.986495\pi$
$192$		0			0
$193$	4.73607	+	14.5761i	0.340910	+	1.04921i	0.963737	+	0.266853i	$0.0859838\pi$
$193$	4.73607	+	14.5761i	0.340910	+	1.04921i	−0.622828	+	0.782359i	$0.714016\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	5.90983			0.421058			0.210529	−	0.977588i	$-0.432481\pi$
$197$	5.90983			0.421058			0.210529	+	0.977588i	$0.432481\pi$
$198$		0			0
$199$	−10.4164			−0.738400			−0.369200	−	0.929350i	$-0.620368\pi$
$199$	−10.4164			−0.738400			−0.369200	+	0.929350i	$0.620368\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.326238	+	1.00406i	0.0228974	+	0.0704710i
$204$		0			0
$205$	29.5344	+	21.4580i	2.06277	+	1.49869i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−14.2984	+	8.97578i	−0.989039	+	0.620868i
$210$		0			0
$211$	5.79180	−	17.8253i	0.398724	−	1.22715i	−0.527300	−	0.849679i	$-0.676796\pi$
$211$	5.79180	−	17.8253i	0.398724	−	1.22715i	0.926023	−	0.377466i	$-0.123204\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	11.2812	+	34.7198i	0.769368	+	2.36787i
$216$		0			0
$217$	−1.21885	+	0.885544i	−0.0827407	+	0.0601147i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	14.8541			0.999195
$222$		0			0
$223$	6.04508	−	4.39201i	0.404809	−	0.294111i	−0.366688	−	0.930344i	$-0.619508\pi$
$223$	6.04508	−	4.39201i	0.404809	−	0.294111i	0.771497	+	0.636233i	$0.219508\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	10.2812	+	7.46969i	0.682384	+	0.495781i	0.874148	−	0.485660i	$-0.161421\pi$
$227$	10.2812	+	7.46969i	0.682384	+	0.495781i	−0.191764	+	0.981441i	$0.561421\pi$
$228$		0			0
$229$	3.38197	−	10.4086i	0.223487	−	0.687821i	−0.774955	−	0.632016i	$-0.782228\pi$
$229$	3.38197	−	10.4086i	0.223487	−	0.687821i	0.998442	−	0.0558047i	$-0.0177724\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.371323	+	1.14281i	−0.0243262	+	0.0748683i	−0.962483	−	0.271343i	$-0.912532\pi$
$233$	−0.371323	+	1.14281i	−0.0243262	+	0.0748683i	0.938156	+	0.346212i	$0.112532\pi$
$234$		0			0
$235$	11.2812	+	8.19624i	0.735901	+	0.534664i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	14.1631	−	10.2901i	0.916136	−	0.665612i	−0.0264232	−	0.999651i	$-0.508412\pi$
$239$	14.1631	−	10.2901i	0.916136	−	0.665612i	0.942559	+	0.334039i	$0.108412\pi$
$240$		0			0
$241$	−23.7082			−1.52718			−0.763590	−	0.645702i	$-0.776565\pi$
$241$	−23.7082			−1.52718			−0.763590	+	0.645702i	$0.776565\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	21.6525	−	15.7314i	1.38333	−	1.00505i
$246$		0			0
$247$	9.80902	+	30.1891i	0.624133	+	1.92088i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−7.44427	+	22.9111i	−0.469878	+	1.44614i	0.382864	+	0.923805i	$0.374938\pi$
$251$	−7.44427	+	22.9111i	−0.469878	+	1.44614i	−0.852742	+	0.522332i	$0.825062\pi$
$252$		0			0
$253$	−0.781153	−	0.0530006i	−0.0491107	−	0.00333212i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−2.26393	−	1.64484i	−0.141220	−	0.102602i	0.514932	−	0.857231i	$-0.327817\pi$
$257$	−2.26393	−	1.64484i	−0.141220	−	0.102602i	−0.656152	+	0.754628i	$0.727817\pi$
$258$		0			0
$259$	0.274575	+	0.845055i	0.0170613	+	0.0525092i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−23.8541			−1.47091			−0.735453	−	0.677575i	$-0.763031\pi$
$263$	−23.8541			−1.47091			−0.735453	+	0.677575i	$0.763031\pi$
$264$		0			0
$265$	−25.2918			−1.55366
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−8.79837	−	27.0786i	−0.536446	−	1.65101i	−0.740503	−	0.672053i	$-0.765413\pi$
$269$	−8.79837	−	27.0786i	−0.536446	−	1.65101i	0.204057	−	0.978959i	$-0.434587\pi$
$270$		0			0
$271$	1.97214	+	1.43284i	0.119799	+	0.0870389i	0.646071	−	0.763277i	$-0.276411\pi$
$271$	1.97214	+	1.43284i	0.119799	+	0.0870389i	−0.526273	+	0.850316i	$0.676411\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	27.6803	−	17.3763i	1.66919	−	1.04783i
$276$		0			0
$277$	0.791796	−	2.43690i	0.0475744	−	0.146419i	−0.924447	−	0.381310i	$-0.875473\pi$
$277$	0.791796	−	2.43690i	0.0475744	−	0.146419i	0.972022	+	0.234891i	$0.0754732\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−5.29180	−	16.2865i	−0.315682	−	0.971570i	−0.975473	−	0.220120i	$-0.929355\pi$
$281$	−5.29180	−	16.2865i	−0.315682	−	0.971570i	0.659791	−	0.751449i	$-0.270645\pi$
$282$		0			0
$283$	−18.7984	+	13.6578i	−1.11745	+	0.811873i	−0.983820	−	0.179159i	$-0.942662\pi$
$283$	−18.7984	+	13.6578i	−1.11745	+	0.811873i	−0.133627	+	0.991032i	$0.542662\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.23607			0.131991
$288$		0			0
$289$	9.16312	−	6.65740i	0.539007	−	0.391612i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−4.04508	−	2.93893i	−0.236316	−	0.171694i	0.463324	−	0.886189i	$-0.346657\pi$
$293$	−4.04508	−	2.93893i	−0.236316	−	0.171694i	−0.699641	+	0.714495i	$0.746657\pi$
$294$		0			0
$295$	−2.55573	+	7.86572i	−0.148800	+	0.457960i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.454915	+	1.40008i	−0.0263084	+	0.0809690i
$300$		0			0
$301$	1.80902	+	1.31433i	0.104270	+	0.0757566i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	8.16312	−	5.93085i	0.467419	−	0.339600i
$306$		0			0
$307$	−0.673762			−0.0384536			−0.0192268	−	0.999815i	$-0.506120\pi$
$307$	−0.673762			−0.0384536			−0.0192268	+	0.999815i	$0.506120\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−23.6074	+	17.1518i	−1.33865	+	0.972588i	−0.339160	+	0.940729i	$0.610143\pi$
$311$	−23.6074	+	17.1518i	−1.33865	+	0.972588i	−0.999492	+	0.0318591i	$0.989857\pi$
$312$		0			0
$313$	−0.309017	−	0.951057i	−0.0174667	−	0.0537569i	0.941943	−	0.335772i	$-0.108997\pi$
$313$	−0.309017	−	0.951057i	−0.0174667	−	0.0537569i	−0.959410	+	0.282015i	$0.908997\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.63525	+	8.11048i	−0.148011	+	0.455530i	−0.997386	−	0.0722595i	$-0.976979\pi$
$317$	−2.63525	+	8.11048i	−0.148011	+	0.455530i	0.849375	+	0.527790i	$0.176979\pi$
$318$		0			0
$319$	−11.3820	−	9.51057i	−0.637268	−	0.532489i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−9.80902	−	7.12667i	−0.545788	−	0.396538i
$324$		0			0
$325$	−18.9894	−	58.4432i	−1.05334	−	3.24185i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.854102			0.0470882
$330$		0			0
$331$	11.9443			0.656517			0.328258	−	0.944588i	$-0.393538\pi$
$331$	11.9443			0.656517			0.328258	+	0.944588i	$0.393538\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.173762	−	0.534785i	−0.00949364	−	0.0292184i
$336$		0			0
$337$	14.2361	+	10.3431i	0.775488	+	0.563425i	0.903621	−	0.428332i	$-0.140899\pi$
$337$	14.2361	+	10.3431i	0.775488	+	0.563425i	−0.128133	+	0.991757i	$0.540899\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	7.88854	−	19.6417i	0.427189	−	1.06366i
$342$		0			0
$343$	1.01722	−	3.13068i	0.0549248	−	0.169041i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	2.47214	+	7.60845i	0.132711	+	0.408443i	0.995227	−	0.0975871i	$-0.0311124\pi$
$347$	2.47214	+	7.60845i	0.132711	+	0.408443i	−0.862516	+	0.506030i	$0.831112\pi$
$348$		0			0
$349$	22.8435	−	16.5967i	1.22278	−	0.888403i	0.226454	−	0.974022i	$-0.427287\pi$
$349$	22.8435	−	16.5967i	1.22278	−	0.888403i	0.996328	+	0.0856184i	$0.0272866\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	10.4721			0.557376			0.278688	−	0.960382i	$-0.410101\pi$
$353$	10.4721			0.557376			0.278688	+	0.960382i	$0.410101\pi$
$354$		0			0
$355$	−4.30902	+	3.13068i	−0.228699	+	0.166159i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−18.7984	−	13.6578i	−0.992140	−	0.720832i	−0.0317515	−	0.999496i	$-0.510109\pi$
$359$	−18.7984	−	13.6578i	−0.992140	−	0.720832i	−0.960389	+	0.278664i	$0.910109\pi$
$360$		0			0
$361$	2.13525	−	6.57164i	0.112382	−	0.345876i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	3.85410	−	11.8617i	0.201733	−	0.620870i
$366$		0			0
$367$	4.35410	+	3.16344i	0.227282	+	0.165130i	0.695599	−	0.718431i	$-0.255139\pi$
$367$	4.35410	+	3.16344i	0.227282	+	0.165130i	−0.468316	+	0.883561i	$0.655139\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−1.25329	+	0.910568i	−0.0650675	+	0.0472743i
$372$		0			0
$373$	−13.9443			−0.722007			−0.361004	−	0.932564i	$-0.617566\pi$
$373$	−13.9443			−0.722007			−0.361004	+	0.932564i	$0.617566\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−22.5623	+	16.3925i	−1.16202	+	0.844255i
$378$		0			0
$379$	−3.92705	−	12.0862i	−0.201719	−	0.620827i	−0.999832	−	0.0183198i	$-0.994168\pi$
$379$	−3.92705	−	12.0862i	−0.201719	−	0.620827i	0.798113	−	0.602508i	$-0.205832\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−3.16312	+	9.73508i	−0.161628	+	0.497439i	−0.998772	−	0.0495430i	$-0.984224\pi$
$383$	−3.16312	+	9.73508i	−0.161628	+	0.497439i	0.837144	+	0.546982i	$0.184224\pi$
$384$		0			0
$385$	1.12461	−	2.80017i	0.0573155	−	0.142710i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	13.0172	+	9.45756i	0.659999	+	0.479518i	0.866663	−	0.498895i	$-0.166261\pi$
$389$	13.0172	+	9.45756i	0.659999	+	0.479518i	−0.206663	+	0.978412i	$0.566261\pi$
$390$		0			0
$391$	−0.173762	−	0.534785i	−0.00878753	−	0.0270452i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	54.8673			2.76067
$396$		0			0
$397$	27.1803			1.36414			0.682071	−	0.731286i	$-0.261079\pi$
$397$	27.1803			1.36414			0.682071	+	0.731286i	$0.261079\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	0.881966	+	2.71441i	0.0440433	+	0.135551i	0.970660	−	0.240456i	$-0.0772969\pi$
$401$	0.881966	+	2.71441i	0.0440433	+	0.135551i	−0.926617	+	0.376007i	$0.877297\pi$
$402$		0			0
$403$	−32.1976	−	23.3929i	−1.60387	−	1.16528i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−9.57953	−	8.00448i	−0.474840	−	0.396767i
$408$		0			0
$409$	3.05573	−	9.40456i	0.151096	−	0.465026i	−0.846648	−	0.532153i	$-0.821383\pi$
$409$	3.05573	−	9.40456i	0.151096	−	0.465026i	0.997744	+	0.0671269i	$0.0213832\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	0.156541	+	0.481784i	0.00770289	+	0.0237070i
$414$		0			0
$415$	48.2426	−	35.0503i	2.36814	−	1.72055i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−17.8541			−0.872230			−0.436115	−	0.899891i	$-0.643646\pi$
$419$	−17.8541			−0.872230			−0.436115	+	0.899891i	$0.643646\pi$
$420$		0			0
$421$	7.50000	−	5.44907i	0.365528	−	0.265571i	−0.389826	−	0.920888i	$-0.627465\pi$
$421$	7.50000	−	5.44907i	0.365528	−	0.265571i	0.755354	+	0.655317i	$0.227465\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	18.9894	+	13.7966i	0.921119	+	0.669232i
$426$		0			0
$427$	0.190983	−	0.587785i	0.00924232	−	0.0284449i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−4.11803	+	12.6740i	−0.198359	+	0.610485i	0.801562	+	0.597911i	$0.204003\pi$
$431$	−4.11803	+	12.6740i	−0.198359	+	0.610485i	−0.999921	+	0.0125740i	$0.995997\pi$
$432$		0			0
$433$	12.0902	+	8.78402i	0.581016	+	0.422133i	0.839090	−	0.543992i	$-0.183088\pi$
$433$	12.0902	+	8.78402i	0.581016	+	0.422133i	−0.258074	+	0.966125i	$0.583088\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.972136	−	0.706298i	0.0465036	−	0.0337868i
$438$		0			0
$439$	−19.3607			−0.924035			−0.462017	−	0.886871i	$-0.652874\pi$
$439$	−19.3607			−0.924035			−0.462017	+	0.886871i	$0.652874\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	0.145898	−	0.106001i	0.00693182	−	0.00503627i	−0.584314	−	0.811528i	$-0.698636\pi$
$443$	0.145898	−	0.106001i	0.00693182	−	0.00503627i	0.591246	+	0.806491i	$0.298636\pi$
$444$		0			0
$445$	−1.19098	−	3.66547i	−0.0564580	−	0.173760i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	2.32624	−	7.15942i	0.109782	−	0.337874i	−0.881041	−	0.473040i	$-0.843157\pi$
$449$	2.32624	−	7.15942i	0.109782	−	0.337874i	0.990823	+	0.135166i	$0.0431567\pi$
$450$		0			0
$451$	−26.6074	+	16.7027i	−1.25289	+	0.786502i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−4.59017	−	3.33495i	−0.215190	−	0.156345i
$456$		0			0
$457$	0.354102	+	1.08981i	0.0165642	+	0.0509793i	0.958997	−	0.283416i	$-0.0914678\pi$
$457$	0.354102	+	1.08981i	0.0165642	+	0.0509793i	−0.942433	+	0.334396i	$0.891468\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−19.5623			−0.911107			−0.455554	−	0.890208i	$-0.650559\pi$
$461$	−19.5623			−0.911107			−0.455554	+	0.890208i	$0.650559\pi$
$462$		0			0
$463$	21.2148			0.985935			0.492967	−	0.870048i	$-0.335912\pi$
$463$	21.2148			0.985935			0.492967	+	0.870048i	$0.335912\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−6.12868	−	18.8621i	−0.283601	−	0.872835i	−0.986814	−	0.161856i	$-0.948252\pi$
$467$	−6.12868	−	18.8621i	−0.283601	−	0.872835i	0.703213	−	0.710979i	$-0.251748\pi$
$468$		0			0
$469$	−0.0278640	−	0.0202444i	−0.00128664	−	0.000934800i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−31.3435	−	2.12663i	−1.44117	−	0.0977824i
$474$		0			0
$475$	−15.5000	+	47.7041i	−0.711189	+	2.18881i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−4.11803	−	12.6740i	−0.188158	−	0.579090i	0.811831	−	0.583893i	$-0.198471\pi$
$479$	−4.11803	−	12.6740i	−0.188158	−	0.579090i	−0.999988	+	0.00480282i	$0.998471\pi$
$480$		0			0
$481$	−18.9894	+	13.7966i	−0.865840	+	0.629070i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−19.6180			−0.890809
$486$		0			0
$487$	−28.9894	+	21.0620i	−1.31363	+	0.954410i	−0.313645	+	0.949540i	$0.601550\pi$
$487$	−28.9894	+	21.0620i	−1.31363	+	0.954410i	−0.999988	+	0.00487004i	$0.998450\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−4.16312	−	3.02468i	−0.187879	−	0.136502i	0.489870	−	0.871796i	$-0.337044\pi$
$491$	−4.16312	−	3.02468i	−0.187879	−	0.136502i	−0.677749	+	0.735294i	$0.737044\pi$
$492$		0			0
$493$	3.29180	−	10.1311i	0.148255	−	0.456282i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.100813	+	0.310271i	−0.00452208	+	0.0139175i
$498$		0			0
$499$	−12.3541	−	8.97578i	−0.553046	−	0.401811i	0.275862	−	0.961197i	$-0.411037\pi$
$499$	−12.3541	−	8.97578i	−0.553046	−	0.401811i	−0.828907	+	0.559386i	$0.811037\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	13.9443	−	10.1311i	0.621744	−	0.451724i	−0.231786	−	0.972767i	$-0.574457\pi$
$503$	13.9443	−	10.1311i	0.621744	−	0.451724i	0.853530	+	0.521043i	$0.174457\pi$
$504$		0			0
$505$	22.9098			1.01947
$506$		0			0
$507$		0			0
$508$		0			0
$509$	10.3090	−	7.48994i	0.456939	−	0.331986i	−0.335390	−	0.942079i	$-0.608868\pi$
$509$	10.3090	−	7.48994i	0.456939	−	0.331986i	0.792329	+	0.610094i	$0.208868\pi$
$510$		0			0
$511$	−0.236068	−	0.726543i	−0.0104430	−	0.0321403i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	14.8541	−	45.7162i	0.654550	−	2.01450i
$516$		0			0
$517$	−10.1631	+	6.37988i	−0.446973	+	0.280587i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	12.0000	+	8.71851i	0.525730	+	0.381965i	0.818758	−	0.574139i	$-0.194663\pi$
$521$	12.0000	+	8.71851i	0.525730	+	0.381965i	−0.293028	+	0.956104i	$0.594663\pi$
$522$		0			0
$523$	−6.73607	−	20.7315i	−0.294548	−	0.906525i	−0.983373	−	0.181597i	$-0.941873\pi$
$523$	−6.73607	−	20.7315i	−0.294548	−	0.906525i	0.688825	−	0.724927i	$-0.258127\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	15.2016			0.662193
$528$		0			0
$529$	−22.9443			−0.997577
$530$		0			0
$531$		0			0
$532$		0			0
$533$	18.2533	+	56.1778i	0.790638	+	2.43333i
$534$		0			0
$535$	20.3541	+	14.7881i	0.879985	+	0.639346i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	5.61803	+	22.3358i	0.241986	+	0.962073i
$540$		0			0
$541$	−1.95492	+	6.01661i	−0.0840484	+	0.258674i	−0.984245	−	0.176809i	$-0.943423\pi$
$541$	−1.95492	+	6.01661i	−0.0840484	+	0.258674i	0.900197	+	0.435483i	$0.143423\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−9.52786	−	29.3238i	−0.408129	−	1.25609i
$546$		0			0
$547$	−10.7812	+	7.83297i	−0.460969	+	0.334913i	−0.793911	−	0.608034i	$-0.791959\pi$
$547$	−10.7812	+	7.83297i	−0.460969	+	0.334913i	0.332942	+	0.942947i	$0.391959\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	22.7639			0.969776
$552$		0			0
$553$	2.71885	−	1.97536i	0.115617	−	0.0840008i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	4.11803	+	2.99193i	0.174487	+	0.126772i	0.671601	−	0.740913i	$-0.265607\pi$
$557$	4.11803	+	2.99193i	0.174487	+	0.126772i	−0.497114	+	0.867685i	$0.665607\pi$
$558$		0			0
$559$	−18.2533	+	56.1778i	−0.772032	+	2.37607i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−12.5795	+	38.7158i	−0.530164	+	1.63168i	0.223709	+	0.974656i	$0.428184\pi$
$563$	−12.5795	+	38.7158i	−0.530164	+	1.63168i	−0.753873	+	0.657021i	$0.771816\pi$
$564$		0			0
$565$	38.1525	+	27.7194i	1.60509	+	1.16616i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	3.94427	−	2.86568i	0.165352	−	0.120136i	−0.502032	−	0.864849i	$-0.667414\pi$
$569$	3.94427	−	2.86568i	0.165352	−	0.120136i	0.667384	+	0.744714i	$0.267414\pi$
$570$		0			0
$571$	24.3262			1.01802			0.509011	−	0.860760i	$-0.330011\pi$
$571$	24.3262			1.01802			0.509011	+	0.860760i	$0.330011\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−1.88197	+	1.36733i	−0.0784834	+	0.0570215i
$576$		0			0
$577$	9.03444	+	27.8052i	0.376109	+	1.15754i	0.942728	+	0.333564i	$0.108251\pi$
$577$	9.03444	+	27.8052i	0.376109	+	1.15754i	−0.566619	+	0.823980i	$0.691749\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1.12868	−	3.47371i	0.0468254	−	0.144114i
$582$		0			0
$583$	8.11146	−	20.1967i	0.335942	−	0.836462i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	20.8435	+	15.1437i	0.860302	+	0.625046i	0.927967	−	0.372662i	$-0.121555\pi$
$587$	20.8435	+	15.1437i	0.860302	+	0.625046i	−0.0676654	+	0.997708i	$0.521555\pi$
$588$		0			0
$589$	10.0385	+	30.8953i	0.413629	+	1.27302i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−19.4508			−0.798751			−0.399375	−	0.916788i	$-0.630773\pi$
$593$	−19.4508			−0.798751			−0.399375	+	0.916788i	$0.630773\pi$
$594$		0			0
$595$	2.16718			0.0888459
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−12.5623	−	38.6628i	−0.513282	−	1.57972i	−0.786386	−	0.617735i	$-0.788050\pi$
$599$	−12.5623	−	38.6628i	−0.513282	−	1.57972i	0.273105	−	0.961984i	$-0.411950\pi$
$600$		0			0
$601$	−16.1353	−	11.7229i	−0.658171	−	0.478189i	0.207874	−	0.978156i	$-0.433346\pi$
$601$	−16.1353	−	11.7229i	−0.658171	−	0.478189i	−0.866045	+	0.499967i	$0.833346\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	7.53444	+	41.7202i	0.306319	+	1.69617i
$606$		0			0
$607$	2.68034	−	8.24924i	0.108792	−	0.334826i	−0.881810	−	0.471605i	$-0.843675\pi$
$607$	2.68034	−	8.24924i	0.108792	−	0.334826i	0.990602	+	0.136779i	$0.0436749\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	6.97214	+	21.4580i	0.282062	+	0.868099i
$612$		0			0
$613$	−13.8541	+	10.0656i	−0.559562	+	0.406546i	−0.831299	−	0.555826i	$-0.812402\pi$
$613$	−13.8541	+	10.0656i	−0.559562	+	0.406546i	0.271737	+	0.962372i	$0.412402\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	7.00000			0.281809			0.140905	−	0.990023i	$-0.454999\pi$
$617$	7.00000			0.281809			0.140905	+	0.990023i	$0.454999\pi$
$618$		0			0
$619$	6.04508	−	4.39201i	0.242972	−	0.176530i	−0.459634	−	0.888108i	$-0.652019\pi$
$619$	6.04508	−	4.39201i	0.242972	−	0.176530i	0.702607	+	0.711579i	$0.252019\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−0.190983	−	0.138757i	−0.00765157	−	0.00555919i
$624$		0			0
$625$	7.05573	−	21.7153i	0.282229	−	0.868612i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	2.77051	−	8.52675i	0.110467	−	0.339984i
$630$		0			0
$631$	−6.25329	−	4.54328i	−0.248940	−	0.180865i	0.456317	−	0.889817i	$-0.349168\pi$
$631$	−6.25329	−	4.54328i	−0.248940	−	0.180865i	−0.705257	+	0.708952i	$0.749168\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−48.9787	+	35.5851i	−1.94366	+	1.41215i
$636$		0			0
$637$	43.3050			1.71580
$638$		0			0
$639$		0			0
$640$		0			0
$641$	20.2082	−	14.6821i	0.798176	−	0.579909i	−0.112202	−	0.993685i	$-0.535791\pi$
$641$	20.2082	−	14.6821i	0.798176	−	0.579909i	0.910378	+	0.413777i	$0.135791\pi$
$642$		0			0
$643$	−12.4098	−	38.1935i	−0.489396	−	1.50621i	−0.825512	−	0.564385i	$-0.809113\pi$
$643$	−12.4098	−	38.1935i	−0.489396	−	1.50621i	0.336116	−	0.941821i	$-0.390887\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−11.0279	+	33.9403i	−0.433550	+	1.33433i	0.461015	+	0.887392i	$0.347485\pi$
$647$	−11.0279	+	33.9403i	−0.433550	+	1.33433i	−0.894565	+	0.446938i	$0.852515\pi$
$648$		0			0
$649$	−5.46149	−	4.56352i	−0.214382	−	0.179134i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−17.1074	−	12.4292i	−0.669464	−	0.486394i	0.200382	−	0.979718i	$-0.435782\pi$
$653$	−17.1074	−	12.4292i	−0.669464	−	0.486394i	−0.869846	+	0.493324i	$0.835782\pi$
$654$		0			0
$655$	10.1976	+	31.3849i	0.398452	+	1.22631i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−9.70820			−0.378178			−0.189089	−	0.981960i	$-0.560553\pi$
$659$	−9.70820			−0.378178			−0.189089	+	0.981960i	$0.560553\pi$
$660$		0			0
$661$	−13.3262			−0.518331			−0.259165	−	0.965833i	$-0.583447\pi$
$661$	−13.3262			−0.518331			−0.259165	+	0.965833i	$0.583447\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	1.43112	+	4.40452i	0.0554963	+	0.170800i
$666$		0			0
$667$	0.854102	+	0.620541i	0.0330710	+	0.0240275i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	2.11803	+	8.42075i	0.0817658	+	0.325080i
$672$		0			0
$673$	10.9615	−	33.7360i	0.422534	−	1.30043i	−0.482801	−	0.875730i	$-0.660381\pi$
$673$	10.9615	−	33.7360i	0.422534	−	1.30043i	0.905335	−	0.424697i	$-0.139619\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−0.763932	−	2.35114i	−0.0293603	−	0.0903617i	0.935303	−	0.353849i	$-0.115127\pi$
$677$	−0.763932	−	2.35114i	−0.0293603	−	0.0903617i	−0.964663	+	0.263487i	$0.915127\pi$
$678$		0			0
$679$	−0.972136	+	0.706298i	−0.0373072	+	0.0271052i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	37.6525			1.44073			0.720366	−	0.693594i	$-0.243974\pi$
$683$	37.6525			1.44073			0.720366	+	0.693594i	$0.243974\pi$
$684$		0			0
$685$	−65.4787	+	47.5731i	−2.50181	+	1.81767i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−33.1074	−	24.0539i	−1.26129	−	0.916382i
$690$		0			0
$691$	10.0557	−	30.9483i	0.382538	−	1.17733i	−0.555713	−	0.831374i	$-0.687555\pi$
$691$	10.0557	−	30.9483i	0.382538	−	1.17733i	0.938251	−	0.345956i	$-0.112445\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	4.52380	−	13.9228i	0.171597	−	0.528123i
$696$		0			0
$697$	−18.2533	−	13.2618i	−0.691393	−	0.502326i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−23.0623	+	16.7557i	−0.871051	+	0.632856i	−0.930869	−	0.365354i	$-0.880948\pi$
$701$	−23.0623	+	16.7557i	−0.871051	+	0.632856i	0.0598176	+	0.998209i	$0.480948\pi$
$702$		0			0
$703$	19.1591			0.722597
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.13525	−	0.824811i	0.0426957	−	0.0310202i
$708$		0			0
$709$	5.17376	+	15.9232i	0.194305	+	0.598008i	0.999984	+	0.00565642i	$0.00180051\pi$
$709$	5.17376	+	15.9232i	0.194305	+	0.598008i	−0.805679	+	0.592352i	$0.798199\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−0.465558	+	1.43284i	−0.0174353	+	0.0536603i
$714$		0			0
$715$	79.5304	+	5.39607i	2.97427	+	0.201802i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	15.4271	+	11.2084i	0.575332	+	0.418003i	0.837038	−	0.547144i	$-0.184285\pi$
$719$	15.4271	+	11.2084i	0.575332	+	0.418003i	−0.261706	+	0.965148i	$0.584285\pi$
$720$		0			0
$721$	−0.909830	−	2.80017i	−0.0338838	−	0.104284i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−44.0689			−1.63668
$726$		0			0
$727$	−8.85410			−0.328380			−0.164190	−	0.986429i	$-0.552501\pi$
$727$	−8.85410			−0.328380			−0.164190	+	0.986429i	$0.552501\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−6.97214	−	21.4580i	−0.257874	−	0.793654i
$732$		0			0
$733$	−36.0344	−	26.1806i	−1.33096	−	0.967001i	−0.999725	−	0.0234534i	$-0.992534\pi$
$733$	−36.0344	−	26.1806i	−1.33096	−	0.967001i	−0.331238	−	0.943547i	$-0.607466\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.482779	+	0.0327561i	0.0177834	+	0.00120659i
$738$		0			0
$739$	−3.96149	+	12.1922i	−0.145726	+	0.448498i	−0.997104	−	0.0760550i	$-0.975768\pi$
$739$	−3.96149	+	12.1922i	−0.145726	+	0.448498i	0.851378	+	0.524553i	$0.175768\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−3.54508	−	10.9106i	−0.130057	−	0.400273i	0.864732	−	0.502234i	$-0.167488\pi$
$743$	−3.54508	−	10.9106i	−0.130057	−	0.400273i	−0.994788	+	0.101961i	$0.967488\pi$
$744$		0			0
$745$	−52.6591	+	38.2590i	−1.92928	+	1.40170i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.54102			0.0563076
$750$		0			0
$751$	33.6803	−	24.4702i	1.22901	−	0.892930i	0.232197	−	0.972669i	$-0.425409\pi$
$751$	33.6803	−	24.4702i	1.22901	−	0.892930i	0.996816	+	0.0797385i	$0.0254085\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−13.9443	−	10.1311i	−0.507484	−	0.368709i
$756$		0			0
$757$	−3.21885	+	9.90659i	−0.116991	+	0.360061i	−0.992357	−	0.123399i	$-0.960620\pi$
$757$	−3.21885	+	9.90659i	−0.116991	+	0.360061i	0.875366	+	0.483461i	$0.160620\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	9.03851	−	27.8177i	0.327646	−	1.00839i	−0.642587	−	0.766213i	$-0.722139\pi$
$761$	9.03851	−	27.8177i	0.327646	−	1.00839i	0.970232	−	0.242176i	$-0.0778613\pi$
$762$		0			0
$763$	−1.52786	−	1.11006i	−0.0553124	−	0.0401868i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−10.8262	+	7.86572i	−0.390913	+	0.284015i
$768$		0			0
$769$	−33.5623			−1.21029			−0.605144	−	0.796116i	$-0.706884\pi$
$769$	−33.5623			−1.21029			−0.605144	+	0.796116i	$0.706884\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	23.7533	−	17.2578i	0.854346	−	0.620719i	−0.0719946	−	0.997405i	$-0.522936\pi$
$773$	23.7533	−	17.2578i	0.854346	−	0.620719i	0.926341	+	0.376686i	$0.122936\pi$
$774$		0			0
$775$	−19.4336	−	59.8106i	−0.698077	−	2.14846i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	14.8992	−	45.8550i	0.533819	−	1.64293i
$780$		0			0
$781$	−1.11803	−	4.44501i	−0.0400064	−	0.159055i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	53.7426	+	39.0463i	1.91816	+	1.39362i
$786$		0			0
$787$	13.8328	+	42.5730i	0.493087	+	1.51756i	0.819917	+	0.572482i	$0.194019\pi$
$787$	13.8328	+	42.5730i	0.493087	+	1.51756i	−0.326831	+	0.945083i	$0.605981\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	2.88854			0.102705
$792$		0			0
$793$	16.3262			0.579762
$794$		0			0
$795$		0			0
$796$		0			0
$797$	15.1459	+	46.6143i	0.536495	+	1.65116i	0.740396	+	0.672171i	$0.234638\pi$
$797$	15.1459	+	46.6143i	0.536495	+	1.65116i	−0.203901	+	0.978992i	$0.565362\pi$
$798$		0			0
$799$	−6.97214	−	5.06555i	−0.246656	−	0.179206i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	8.23607	+	6.88191i	0.290645	+	0.242857i
$804$		0			0
$805$	−0.0663712	+	0.204270i	−0.00233928	+	0.00719956i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−10.8992	−	33.5442i	−0.383195	−	1.17935i	−0.937781	−	0.347227i	$-0.887123\pi$
$809$	−10.8992	−	33.5442i	−0.383195	−	1.17935i	0.554586	−	0.832126i	$-0.312877\pi$
$810$		0			0
$811$	1.78115	−	1.29408i	0.0625447	−	0.0454414i	−0.556074	−	0.831133i	$-0.687693\pi$
$811$	1.78115	−	1.29408i	0.0625447	−	0.0454414i	0.618618	+	0.785692i	$0.287693\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−18.7082			−0.655320
$816$		0			0
$817$	39.0066	−	28.3399i	1.36467	−	0.991489i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	22.1353	+	16.0822i	0.772526	+	0.561273i	0.902727	−	0.430215i	$-0.141562\pi$
$821$	22.1353	+	16.0822i	0.772526	+	0.561273i	−0.130201	+	0.991488i	$0.541562\pi$
$822$		0			0
$823$	7.16312	−	22.0458i	0.249691	−	0.768469i	−0.745139	−	0.666909i	$-0.767617\pi$
$823$	7.16312	−	22.0458i	0.249691	−	0.768469i	0.994829	−	0.101559i	$-0.0323832\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	12.7082	−	39.1118i	0.441908	−	1.36005i	−0.443932	−	0.896060i	$-0.646417\pi$
$827$	12.7082	−	39.1118i	0.441908	−	1.36005i	0.885840	−	0.463991i	$-0.153583\pi$
$828$		0			0
$829$	−3.83688	−	2.78766i	−0.133260	−	0.0968193i	0.519158	−	0.854678i	$-0.326246\pi$
$829$	−3.83688	−	2.78766i	−0.133260	−	0.0968193i	−0.652419	+	0.757859i	$0.726246\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−13.3820	+	9.72257i	−0.463658	+	0.336867i
$834$		0			0
$835$	2.38197			0.0824313
$836$		0			0
$837$		0			0
$838$		0			0
$839$	30.6074	−	22.2376i	1.05668	−	0.767726i	0.0832124	−	0.996532i	$-0.473482\pi$
$839$	30.6074	−	22.2376i	1.05668	−	0.767726i	0.973472	+	0.228806i	$0.0734820\pi$
$840$		0			0
$841$	−2.78115	−	8.55951i	−0.0959018	−	0.295155i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	30.8328	−	94.8936i	1.06068	−	3.26444i
$846$		0			0
$847$	1.87539	+	1.79611i	0.0644391	+	0.0617151i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	0.718847	+	0.522273i	0.0246418	+	0.0179033i
$852$		0			0
$853$	3.28773	+	10.1186i	0.112570	+	0.346454i	0.991432	−	0.130621i	$-0.0416970\pi$
$853$	3.28773	+	10.1186i	0.112570	+	0.346454i	−0.878863	+	0.477075i	$0.841697\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	50.1935			1.71458			0.857289	−	0.514836i	$-0.172147\pi$
$857$	50.1935			1.71458			0.857289	+	0.514836i	$0.172147\pi$
$858$		0			0
$859$	8.81966			0.300923			0.150461	−	0.988616i	$-0.451924\pi$
$859$	8.81966			0.300923			0.150461	+	0.988616i	$0.451924\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	4.43769	+	13.6578i	0.151061	+	0.464918i	0.997741	−	0.0671854i	$-0.0214019\pi$
$863$	4.43769	+	13.6578i	0.151061	+	0.464918i	−0.846680	+	0.532103i	$0.821402\pi$
$864$		0			0
$865$	17.3435	+	12.6008i	0.589695	+	0.428439i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−17.5967	+	43.8141i	−0.596929	+	1.48629i
$870$		0			0
$871$	0.281153	−	0.865300i	0.00952650	−	0.0293196i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.36475	−	4.20025i	−0.0461368	−	0.141994i
$876$		0			0
$877$	−0.718847	+	0.522273i	−0.0242737	+	0.0176359i	−0.599856	−	0.800108i	$-0.704775\pi$
$877$	−0.718847	+	0.522273i	−0.0242737	+	0.0176359i	0.575582	+	0.817744i	$0.304775\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−40.5623			−1.36658			−0.683289	−	0.730148i	$-0.739451\pi$
$881$	−40.5623			−1.36658			−0.683289	+	0.730148i	$0.739451\pi$
$882$		0			0
$883$	−12.0902	+	8.78402i	−0.406867	+	0.295606i	−0.772332	−	0.635219i	$-0.780910\pi$
$883$	−12.0902	+	8.78402i	−0.406867	+	0.295606i	0.365465	+	0.930825i	$0.380910\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−26.9336	−	19.5684i	−0.904343	−	0.657043i	0.0352350	−	0.999379i	$-0.488782\pi$
$887$	−26.9336	−	19.5684i	−0.904343	−	0.657043i	−0.939578	+	0.342336i	$0.888782\pi$
$888$		0			0
$889$	−1.14590	+	3.52671i	−0.0384322	+	0.118282i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	5.69098	−	17.5150i	0.190441	−	0.586119i
$894$		0			0
$895$	−55.9508	−	40.6507i	−1.87023	−	1.35880i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−23.0902	+	16.7760i	−0.770100	+	0.559511i
$900$		0			0
$901$	15.6312			0.520750
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−18.5344	+	13.4661i	−0.616106	+	0.447627i
$906$		0			0
$907$	−13.2467	−	40.7692i	−0.439850	−	1.35372i	−0.888034	−	0.459777i	$-0.847929\pi$
$907$	−13.2467	−	40.7692i	−0.439850	−	1.35372i	0.448184	−	0.893941i	$-0.352071\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−7.89261	+	24.2910i	−0.261494	+	0.804795i	0.730987	+	0.682392i	$0.239060\pi$
$911$	−7.89261	+	24.2910i	−0.261494	+	0.804795i	−0.992480	+	0.122403i	$0.960940\pi$
$912$		0			0
$913$	12.5172	+	49.7652i	0.414260	+	1.64699i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.63525	+	1.18808i	0.0540009	+	0.0392339i
$918$		0			0
$919$	−4.89261	−	15.0579i	−0.161392	−	0.496714i	0.837360	−	0.546652i	$-0.184098\pi$
$919$	−4.89261	−	15.0579i	−0.161392	−	0.496714i	−0.998752	+	0.0499374i	$0.984098\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−8.61803			−0.283666
$924$		0			0
$925$	−37.0902			−1.21952
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−6.05166	−	18.6251i	−0.198549	−	0.611070i	−0.999917	−	0.0128984i	$-0.995894\pi$
$929$	−6.05166	−	18.6251i	−0.198549	−	0.611070i	0.801368	−	0.598171i	$-0.204106\pi$
$930$		0			0
$931$	−28.5967	−	20.7768i	−0.937221	−	0.680931i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−25.7877	+	16.1882i	−0.843349	+	0.529411i
$936$		0			0
$937$	6.10739	−	18.7966i	0.199520	−	0.614059i	−0.800374	−	0.599501i	$-0.795366\pi$
$937$	6.10739	−	18.7966i	0.199520	−	0.614059i	0.999894	−	0.0145580i	$-0.00463413\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	0.791796	+	2.43690i	0.0258118	+	0.0794406i	0.963133	−	0.269027i	$-0.0867021\pi$
$941$	0.791796	+	2.43690i	0.0258118	+	0.0794406i	−0.937321	+	0.348468i	$0.886702\pi$
$942$		0			0
$943$	1.80902	−	1.31433i	0.0589097	−	0.0428004i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	2.79837			0.0909349			0.0454675	−	0.998966i	$-0.485522\pi$
$947$	2.79837			0.0909349			0.0454675	+	0.998966i	$0.485522\pi$
$948$		0			0
$949$	16.3262	−	11.8617i	0.529972	−	0.385047i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	28.1246	+	20.4337i	0.911046	+	0.661913i	0.941279	−	0.337630i	$-0.109625\pi$
$953$	28.1246	+	20.4337i	0.911046	+	0.661913i	−0.0302335	+	0.999543i	$0.509625\pi$
$954$		0			0
$955$	25.7877	−	79.3665i	0.834471	−	2.56824i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.53193	+	4.71479i	−0.0494686	+	0.152249i
$960$		0			0
$961$	−7.87132	−	5.71885i	−0.253914	−	0.184479i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−47.7877	+	34.7198i	−1.53834	+	1.11767i
$966$		0			0
$967$	14.7295			0.473668			0.236834	−	0.971550i	$-0.423890\pi$
$967$	14.7295			0.473668			0.236834	+	0.971550i	$0.423890\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1.90983	−	1.38757i	0.0612894	−	0.0445293i	−0.556719	−	0.830701i	$-0.687940\pi$
$971$	1.90983	−	1.38757i	0.0612894	−	0.0445293i	0.618008	+	0.786172i	$0.287940\pi$
$972$		0			0
$973$	−0.277088	−	0.852788i	−0.00888302	−	0.0273391i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	10.1631	−	31.2789i	0.325147	−	1.00070i	−0.646227	−	0.763145i	$-0.723654\pi$
$977$	10.1631	−	31.2789i	0.325147	−	1.00070i	0.971374	−	0.237554i	$-0.0763458\pi$
$978$		0			0
$979$	3.30902	+	0.224514i	0.105757	+	0.00717550i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−29.7984	−	21.6498i	−0.950421	−	0.690521i	0.000485770	−	1.00000i	$-0.499845\pi$
$983$	−29.7984	−	21.6498i	−0.950421	−	0.690521i	−0.950906	+	0.309479i	$0.899845\pi$
$984$		0			0
$985$	7.03851	+	21.6623i	0.224265	+	0.690218i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2.23607			0.0711028
$990$		0			0
$991$	43.2705			1.37453			0.687267	−	0.726405i	$-0.258810\pi$
$991$	43.2705			1.37453			0.687267	+	0.726405i	$0.258810\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−12.4058	−	38.1810i	−0.393289	−	1.21042i
$996$		0			0
$997$	−23.6803	−	17.2048i	−0.749964	−	0.544881i	0.145852	−	0.989306i	$-0.453408\pi$
$997$	−23.6803	−	17.2048i	−0.749964	−	0.544881i	−0.895816	+	0.444426i	$0.853408\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	396.2.j.c.361.1		4
3.2	odd	2		132.2.i.b.97.1	yes	4
11.4	even	5		4356.2.a.v.1.2		2
11.5	even	5	inner	396.2.j.c.181.1		4
11.7	odd	10		4356.2.a.s.1.2		2
12.11	even	2		528.2.y.a.97.1		4
33.2	even	10		1452.2.i.p.1213.1		4
33.5	odd	10		132.2.i.b.49.1	✓	4
33.8	even	10		1452.2.i.p.565.1		4
33.14	odd	10		1452.2.i.o.565.1		4
33.17	even	10		1452.2.i.j.1237.1		4
33.20	odd	10		1452.2.i.o.1213.1		4
33.26	odd	10		1452.2.a.j.1.1		2
33.29	even	10		1452.2.a.i.1.1		2
33.32	even	2		1452.2.i.j.493.1		4
132.59	even	10		5808.2.a.cc.1.1		2
132.71	even	10		528.2.y.a.49.1		4
132.95	odd	10		5808.2.a.cf.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.i.b.49.1	✓	4	33.5	odd	10
132.2.i.b.97.1	yes	4	3.2	odd	2
396.2.j.c.181.1		4	11.5	even	5	inner
396.2.j.c.361.1		4	1.1	even	1	trivial
528.2.y.a.49.1		4	132.71	even	10
528.2.y.a.97.1		4	12.11	even	2
1452.2.a.i.1.1		2	33.29	even	10
1452.2.a.j.1.1		2	33.26	odd	10
1452.2.i.j.493.1		4	33.32	even	2
1452.2.i.j.1237.1		4	33.17	even	10
1452.2.i.o.565.1		4	33.14	odd	10
1452.2.i.o.1213.1		4	33.20	odd	10
1452.2.i.p.565.1		4	33.8	even	10
1452.2.i.p.1213.1		4	33.2	even	10
4356.2.a.s.1.2		2	11.7	odd	10
4356.2.a.v.1.2		2	11.4	even	5
5808.2.a.cc.1.1		2	132.59	even	10
5808.2.a.cf.1.1		2	132.95	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 396 = 2^{2} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	396.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.19098 + 3.66547i) q^{5} +(0.190983 + 0.138757i) q^{7} +(-3.30902 - 0.224514i) q^{11} +(-1.92705 + 5.93085i) q^{13} +(-0.736068 - 2.26538i) q^{17} +(4.11803 - 2.99193i) q^{19} +0.236068 q^{23} +(-7.97214 + 5.79210i) q^{25} +(3.61803 + 2.62866i) q^{29} +(-1.97214 + 6.06961i) q^{31} +(-0.281153 + 0.865300i) q^{35} +(3.04508 + 2.21238i) q^{37} +(7.66312 - 5.56758i) q^{41} +9.47214 q^{43} +(2.92705 - 2.12663i) q^{47} +(-2.14590 - 6.60440i) q^{49} +(-2.02786 + 6.24112i) q^{53} +(-3.11803 - 12.3965i) q^{55} +(1.73607 + 1.26133i) q^{59} +(-0.809017 - 2.48990i) q^{61} -24.0344 q^{65} -0.145898 q^{67} +(0.427051 + 1.31433i) q^{71} +(-2.61803 - 1.90211i) q^{73} +(-0.600813 - 0.502029i) q^{77} +(4.39919 - 13.5393i) q^{79} +(-4.78115 - 14.7149i) q^{83} +(7.42705 - 5.39607i) q^{85} -1.00000 q^{89} +(-1.19098 + 0.865300i) q^{91} +(15.8713 + 11.5312i) q^{95} +(-1.57295 + 4.84104i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 7 q^{5} + 3 q^{7} - 11 q^{11} - q^{13} + 6 q^{17} + 12 q^{19} - 8 q^{23} - 14 q^{25} + 10 q^{29} + 10 q^{31} + 19 q^{35} + q^{37} + 15 q^{41} + 20 q^{43} + 5 q^{47} - 22 q^{49} - 26 q^{53} - 8 q^{55}+ \cdots - 13 q^{97}+O(q^{100}) \) 4 * q + 7 * q^5 + 3 * q^7 - 11 * q^11 - q^13 + 6 * q^17 + 12 * q^19 - 8 * q^23 - 14 * q^25 + 10 * q^29 + 10 * q^31 + 19 * q^35 + q^37 + 15 * q^41 + 20 * q^43 + 5 * q^47 - 22 * q^49 - 26 * q^53 - 8 * q^55 - 2 * q^59 - q^61 - 38 * q^65 - 14 * q^67 - 5 * q^71 - 6 * q^73 - 27 * q^77 - 7 * q^79 + q^83 + 23 * q^85 - 4 * q^89 - 7 * q^91 + 21 * q^95 - 13 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more