LMFDB - Embedded newform 927.2.w.a.80.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [927,2,Mod(80,927)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(927, base_ring=CyclotomicField(34))

chi = DirichletCharacter(H, H._module([17, 25]))

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

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

chi := DirichletCharacter("927.80");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 927 = 3^{2} \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	927.w (of order $34$, degree $16$, 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:	$7.40213226737$
Analytic rank:	$0$
Dimension:	$576$
Relative dimension:	$36$ over $\Q(\zeta_{34})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{34}]$

Embedding invariants

Embedding label			80.15
Character	$\chi$	$=$	927.80
Dual form			927.2.w.a.197.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.607968 + 0.302732i) q^{2} +(-0.927291 + 1.22793i) q^{4} +(-0.905941 - 0.825874i) q^{5} +(-2.56947 + 0.480316i) q^{7} +(0.441623 - 2.36248i) q^{8} +O(q^{10})$	\(q+(-0.607968 + 0.302732i) q^{2} +(-0.927291 + 1.22793i) q^{4} +(-0.905941 - 0.825874i) q^{5} +(-2.56947 + 0.480316i) q^{7} +(0.441623 - 2.36248i) q^{8} +(0.800802 + 0.227848i) q^{10} +(1.85000 + 3.71530i) q^{11} +(-1.91729 + 0.358404i) q^{13} +(1.41675 - 1.06988i) q^{14} +(-0.395481 - 1.38997i) q^{16} +(2.13537 - 0.197872i) q^{17} +(-2.31861 + 1.43562i) q^{19} +(1.85419 - 0.346608i) q^{20} +(-2.24948 - 1.69873i) q^{22} +(-1.96007 - 0.975997i) q^{23} +(-0.322681 - 3.48229i) q^{25} +(1.05715 - 0.798324i) q^{26} +(1.79285 - 3.60052i) q^{28} +(3.18971 - 3.49895i) q^{29} +(-0.283420 + 0.0806400i) q^{31} +(3.89955 + 4.27760i) q^{32} +(-1.23834 + 0.766746i) q^{34} +(2.72446 + 1.68692i) q^{35} +(-3.88028 - 10.0162i) q^{37} +(0.975032 - 1.57473i) q^{38} +(-2.35119 + 1.77554i) q^{40} +(-5.34845 - 5.86697i) q^{41} +(3.25610 - 8.40496i) q^{43} +(-6.27762 - 1.17349i) q^{44} +1.48712 q^{46} +11.6669 q^{47} +(-0.155858 + 0.0603798i) q^{49} +(1.25038 + 2.01943i) q^{50} +(1.33779 - 2.68665i) q^{52} +(8.50169 - 5.26402i) q^{53} +(1.39238 - 4.89371i) q^{55} +6.28242i q^{56} +(-0.879999 + 3.09287i) q^{58} +(1.05844 - 5.66217i) q^{59} +(0.131933 + 1.42378i) q^{61} +(0.147898 - 0.134827i) q^{62} +(-0.970661 - 0.376036i) q^{64} +(2.03295 + 1.25875i) q^{65} +(-2.40117 + 12.8451i) q^{67} +(-1.73714 + 2.80558i) q^{68} +(-2.16707 - 0.200809i) q^{70} +(0.412129 - 0.375705i) q^{71} +(9.01207 + 9.88577i) q^{73} +(5.39130 + 4.91482i) q^{74} +(0.387180 - 4.17833i) q^{76} +(-6.53803 - 8.65775i) q^{77} +(-3.99599 - 3.64282i) q^{79} +(-0.789660 + 1.58585i) q^{80} +(5.02781 + 1.94778i) q^{82} +(-0.946334 - 5.06244i) q^{83} +(-2.09794 - 1.58429i) q^{85} +(0.564848 + 6.09568i) q^{86} +(9.59431 - 2.72982i) q^{88} +(-7.05643 - 9.34423i) q^{89} +(4.75426 - 1.84181i) q^{91} +(3.01601 - 1.50179i) q^{92} +(-7.09308 + 3.53193i) q^{94} +(3.28617 + 0.614291i) q^{95} +(-0.252334 + 2.72312i) q^{97} +(0.0764779 - 0.0838922i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 576 q + 40 q^{4} - 16 q^{7}+O(q^{10}) $ 576 * q + 40 * q^4 - 16 * q^7	$ 576 q + 40 q^{4} - 16 q^{7} - 136 q^{10} + 8 q^{13} - 64 q^{16} - 8 q^{19} - 132 q^{25} + 228 q^{28} + 180 q^{34} - 108 q^{49} - 16 q^{52} + 8 q^{55} - 96 q^{58} + 32 q^{61} - 84 q^{64} + 204 q^{73} + 80 q^{76} + 40 q^{79} + 128 q^{82} - 68 q^{85} - 68 q^{88} - 284 q^{91} - 136 q^{94} - 424 q^{97}+O(q^{100}) $ 576 * q + 40 * q^4 - 16 * q^7 - 136 * q^10 + 8 * q^13 - 64 * q^16 - 8 * q^19 - 132 * q^25 + 228 * q^28 + 180 * q^34 - 108 * q^49 - 16 * q^52 + 8 * q^55 - 96 * q^58 + 32 * q^61 - 84 * q^64 + 204 * q^73 + 80 * q^76 + 40 * q^79 + 128 * q^82 - 68 * q^85 - 68 * q^88 - 284 * q^91 - 136 * q^94 - 424 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/927\mathbb{Z}\right)^\times$.

$n$	$722$	$829$
$\chi(n)$	$-1$	$e\left(\frac{25}{34}\right)$

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 $

$2$	−0.607968	+	0.302732i	−0.429898	+	0.214064i	−0.647646	−	0.761941i	$-0.724247\pi$
$2$	−0.607968	+	0.302732i	−0.429898	+	0.214064i	0.217748	+	0.976005i	$0.430129\pi$
$3$		0			0
$3$		0			0
$4$	−0.927291	+	1.22793i	−0.463645	+	0.613966i
$5$	−0.905941	−	0.825874i	−0.405149	−	0.369342i	0.445316	−	0.895373i	$-0.353091\pi$
$5$	−0.905941	−	0.825874i	−0.405149	−	0.369342i	−0.850465	+	0.526031i	$0.823679\pi$
$6$		0			0
$7$	−2.56947	+	0.480316i	−0.971167	+	0.181542i	−0.645347	−	0.763890i	$-0.723287\pi$
$7$	−2.56947	+	0.480316i	−0.971167	+	0.181542i	−0.325819	+	0.945432i	$0.605640\pi$
$8$	0.441623	−	2.36248i	0.156137	−	0.835261i
$9$		0			0
$10$	0.800802	+	0.227848i	0.253236	+	0.0720518i
$11$	1.85000	+	3.71530i	0.557796	+	1.12020i	0.977183	+	0.212397i	$0.0681271\pi$
$11$	1.85000	+	3.71530i	0.557796	+	1.12020i	−0.419388	+	0.907807i	$0.637755\pi$
$12$		0			0
$13$	−1.91729	+	0.358404i	−0.531761	+	0.0994033i	−0.442780	−	0.896630i	$-0.646008\pi$
$13$	−1.91729	+	0.358404i	−0.531761	+	0.0994033i	−0.0889803	+	0.996033i	$0.528361\pi$
$14$	1.41675	−	1.06988i	0.378641	−	0.285937i
$15$		0			0
$16$	−0.395481	−	1.38997i	−0.0988703	−	0.347493i
$17$	2.13537	−	0.197872i	0.517905	−	0.0479909i	0.169859	−	0.985468i	$-0.445669\pi$
$17$	2.13537	−	0.197872i	0.517905	−	0.0479909i	0.348046	+	0.937478i	$0.386845\pi$
$18$		0			0
$19$	−2.31861	+	1.43562i	−0.531926	+	0.329354i	−0.765975	−	0.642870i	$-0.777743\pi$
$19$	−2.31861	+	1.43562i	−0.531926	+	0.329354i	0.234049	+	0.972225i	$0.424802\pi$
$20$	1.85419	−	0.346608i	0.414609	−	0.0775038i
$21$		0			0
$22$	−2.24948	−	1.69873i	−0.479591	−	0.362170i
$23$	−1.96007	−	0.975997i	−0.408702	−	0.203509i	0.229618	−	0.973281i	$-0.426252\pi$
$23$	−1.96007	−	0.975997i	−0.408702	−	0.203509i	−0.638319	+	0.769772i	$0.720370\pi$
$24$		0			0
$25$	−0.322681	−	3.48229i	−0.0645362	−	0.696457i
$26$	1.05715	−	0.798324i	0.207324	−	0.156564i
$27$		0			0
$28$	1.79285	−	3.60052i	0.338816	−	0.680434i
$29$	3.18971	−	3.49895i	0.592314	−	0.649738i	−0.367616	−	0.929978i	$-0.619826\pi$
$29$	3.18971	−	3.49895i	0.592314	−	0.649738i	0.959930	+	0.280240i	$0.0904140\pi$
$30$		0			0
$31$	−0.283420	+	0.0806400i	−0.0509037	+	0.0144834i	−0.299019	−	0.954247i	$-0.596659\pi$
$31$	−0.283420	+	0.0806400i	−0.0509037	+	0.0144834i	0.248115	+	0.968731i	$0.420189\pi$
$32$	3.89955	+	4.27760i	0.689349	+	0.756180i
$33$		0			0
$34$	−1.23834	+	0.766746i	−0.212373	+	0.131496i
$35$	2.72446	+	1.68692i	0.460518	+	0.285141i
$36$		0			0
$37$	−3.88028	−	10.0162i	−0.637915	−	1.64665i	−0.756727	−	0.653731i	$-0.773203\pi$
$37$	−3.88028	−	10.0162i	−0.637915	−	1.64665i	0.118813	−	0.992917i	$-0.462091\pi$
$38$	0.975032	−	1.57473i	0.158171	−	0.255455i
$39$		0			0
$40$	−2.35119	+	1.77554i	−0.371756	+	0.280737i
$41$	−5.34845	−	5.86697i	−0.835288	−	0.916267i	0.162225	−	0.986754i	$-0.448133\pi$
$41$	−5.34845	−	5.86697i	−0.835288	−	0.916267i	−0.997513	+	0.0704869i	$0.977545\pi$
$42$		0			0
$43$	3.25610	−	8.40496i	0.496551	−	1.28174i	−0.429063	−	0.903275i	$-0.641156\pi$
$43$	3.25610	−	8.40496i	0.496551	−	1.28174i	0.925613	−	0.378470i	$-0.123550\pi$
$44$	−6.27762	−	1.17349i	−0.946387	−	0.176910i
$45$		0			0
$46$	1.48712			0.219264
$47$	11.6669			1.70179			0.850893	−	0.525338i	$-0.176061\pi$
$47$	11.6669			1.70179			0.850893	+	0.525338i	$0.176061\pi$
$48$		0			0
$49$	−0.155858	+	0.0603798i	−0.0222654	+	0.00862568i
$50$	1.25038	+	2.01943i	0.176830	+	0.285591i
$51$		0			0
$52$	1.33779	−	2.68665i	0.185518	−	0.372571i
$53$	8.50169	−	5.26402i	1.16780	−	0.723069i	0.201245	−	0.979541i	$-0.435501\pi$
$53$	8.50169	−	5.26402i	1.16780	−	0.723069i	0.966552	+	0.256472i	$0.0825600\pi$
$54$		0			0
$55$	1.39238	−	4.89371i	0.187748	−	0.659867i
$56$			6.28242i			0.839523i
$57$		0			0
$58$	−0.879999	+	3.09287i	−0.115550	+	0.406114i
$59$	1.05844	−	5.66217i	0.137797	−	0.737151i	−0.842358	−	0.538919i	$-0.818833\pi$
$59$	1.05844	−	5.66217i	0.137797	−	0.737151i	0.980155	−	0.198232i	$-0.0635201\pi$
$60$		0			0
$61$	0.131933	+	1.42378i	0.0168923	+	0.182297i	1.00000		0.000732714i	$-0.000233230\pi$
$61$	0.131933	+	1.42378i	0.0168923	+	0.182297i	−0.983107	+	0.183029i	$0.941410\pi$
$62$	0.147898	−	0.134827i	0.0187831	−	0.0171230i
$63$		0			0
$64$	−0.970661	−	0.376036i	−0.121333	−	0.0470045i
$65$	2.03295	+	1.25875i	0.252156	+	0.156128i
$66$		0			0
$67$	−2.40117	+	12.8451i	−0.293350	+	1.56928i	0.445419	+	0.895322i	$0.353055\pi$
$67$	−2.40117	+	12.8451i	−0.293350	+	1.56928i	−0.738769	+	0.673959i	$0.764592\pi$
$68$	−1.73714	+	2.80558i	−0.210659	+	0.340226i
$69$		0			0
$70$	−2.16707	−	0.200809i	−0.259015	−	0.0240012i
$71$	0.412129	−	0.375705i	0.0489107	−	0.0445880i	−0.648871	−	0.760898i	$-0.724759\pi$
$71$	0.412129	−	0.375705i	0.0489107	−	0.0445880i	0.697782	+	0.716310i	$0.254170\pi$
$72$		0			0
$73$	9.01207	+	9.88577i	1.05478	+	1.15704i	0.987226	+	0.159327i	$0.0509324\pi$
$73$	9.01207	+	9.88577i	1.05478	+	1.15704i	0.0675574	+	0.997715i	$0.478479\pi$
$74$	5.39130	+	4.91482i	0.626726	+	0.571336i
$75$		0			0
$76$	0.387180	−	4.17833i	0.0444125	−	0.479288i
$77$	−6.53803	−	8.65775i	−0.745077	−	0.986642i
$78$		0			0
$79$	−3.99599	−	3.64282i	−0.449584	−	0.409850i	0.416980	−	0.908915i	$-0.363088\pi$
$79$	−3.99599	−	3.64282i	−0.449584	−	0.409850i	−0.866564	+	0.499066i	$0.833677\pi$
$80$	−0.789660	+	1.58585i	−0.0882866	+	0.177303i
$81$		0			0
$82$	5.02781	+	1.94778i	0.555229	+	0.215097i
$83$	−0.946334	−	5.06244i	−0.103874	−	0.555675i	−0.994827	−	0.101581i	$-0.967610\pi$
$83$	−0.946334	−	5.06244i	−0.103874	−	0.555675i	0.890954	−	0.454094i	$-0.150037\pi$
$84$		0			0
$85$	−2.09794	−	1.58429i	−0.227554	−	0.171840i
$86$	0.564848	+	6.09568i	0.0609091	+	0.657314i
$87$		0			0
$88$	9.59431	−	2.72982i	1.02276	−	0.290999i
$89$	−7.05643	−	9.34423i	−0.747981	−	0.990486i	−0.999742	−	0.0226971i	$-0.992775\pi$
$89$	−7.05643	−	9.34423i	−0.747981	−	0.990486i	0.251762	−	0.967789i	$-0.418990\pi$
$90$		0			0
$91$	4.75426	−	1.84181i	0.498382	−	0.193074i
$92$	3.01601	−	1.50179i	0.314441	−	0.156573i
$93$		0			0
$94$	−7.09308	+	3.53193i	−0.731595	+	0.364291i
$95$	3.28617	+	0.614291i	0.337154	+	0.0630249i
$96$		0			0
$97$	−0.252334	+	2.72312i	−0.0256206	+	0.276491i	0.973280	+	0.229620i	$0.0737484\pi$
$97$	−0.252334	+	2.72312i	−0.0256206	+	0.276491i	−0.998901	+	0.0468705i	$0.985075\pi$
$98$	0.0764779	−	0.0838922i	0.00772543	−	0.00847440i
$99$		0			0
$100$	4.57523	+	2.83286i	0.457523	+	0.283286i
$101$	−4.15381	−	8.34198i	−0.413320	−	0.830058i	−0.999798	−	0.0200928i	$-0.993604\pi$
$101$	−4.15381	−	8.34198i	−0.413320	−	0.830058i	0.586479	−	0.809965i	$-0.300514\pi$
$102$		0			0
$103$	−4.41976	−	9.13596i	−0.435492	−	0.900192i
$103$	−4.41976	−	9.13596i	−0.435492	−	0.900192i
$104$			4.68783i			0.459680i
$105$		0			0
$106$	−3.57517	+	5.77409i	−0.347251	+	0.560830i
$107$	4.90431	+	3.70356i	0.474118	+	0.358037i	0.812490	−	0.582975i	$-0.198112\pi$
$107$	4.90431	+	3.70356i	0.474118	+	0.358037i	−0.338372	+	0.941012i	$0.609876\pi$
$108$		0			0
$109$	−7.32147	−	0.678434i	−0.701270	−	0.0649822i	−0.264277	−	0.964447i	$-0.585133\pi$
$109$	−7.32147	−	0.678434i	−0.701270	−	0.0649822i	−0.436993	+	0.899465i	$0.643957\pi$
$110$	0.634960	+	3.39674i	0.0605410	+	0.323866i
$111$		0			0
$112$	1.68380	+	3.38153i	0.159104	+	0.319525i
$113$	0.195939	−	0.688653i	0.0184324	−	0.0647830i	−0.952064	−	0.305899i	$-0.901043\pi$
$113$	0.195939	−	0.688653i	0.0184324	−	0.0647830i	0.970496	+	0.241116i	$0.0775135\pi$
$114$		0			0
$115$	0.969653	+	2.50296i	0.0904206	+	0.233402i
$116$	1.33868	+	7.16129i	0.124293	+	0.664909i
$117$		0			0
$118$	1.07062	+	3.76284i	0.0985586	+	0.346398i
$119$	−5.39173	+	1.53408i	−0.494259	+	0.140629i
$120$		0			0
$121$	−3.75197	+	4.96841i	−0.341088	+	0.451673i
$122$	−0.511235	−	0.825673i	−0.0462851	−	0.0747530i
$123$		0			0
$124$	0.163792	−	0.422797i	0.0147090	−	0.0379683i
$125$	−6.27741	+	8.31263i	−0.561468	+	0.743504i
$126$		0			0
$127$	10.9584	−	12.0208i	0.972401	−	1.06667i	−0.0253524	−	0.999679i	$-0.508071\pi$
$127$	10.9584	−	12.0208i	0.972401	−	1.06667i	0.997753	−	0.0669944i	$-0.0213410\pi$
$128$	−10.8232	+	1.00292i	−0.956648	+	0.0886464i
$129$		0			0
$130$	−1.61703	−	0.149840i	−0.141823	−	0.0131418i
$131$	2.65122	+	1.32015i	0.231638	+	0.115342i	0.557811	−	0.829968i	$-0.311642\pi$
$131$	2.65122	+	1.32015i	0.231638	+	0.115342i	−0.326173	+	0.945310i	$0.605759\pi$
$132$		0			0
$133$	5.26803	−	4.80245i	0.456796	−	0.416425i
$134$	−2.42880	−	8.53634i	−0.209816	−	0.737427i
$135$		0			0
$136$	0.475564	−	5.13216i	0.0407793	−	0.440079i
$137$	−10.0880	−	16.2927i	−0.861876	−	1.39198i	−0.919271	−	0.393626i	$-0.871220\pi$
$137$	−10.0880	−	16.2927i	−0.861876	−	1.39198i	0.0573945	−	0.998352i	$-0.481721\pi$
$138$		0			0
$139$	−19.6962	−	3.68186i	−1.67061	−	0.312291i	−0.738442	−	0.674318i	$-0.764438\pi$
$139$	−19.6962	−	3.68186i	−1.67061	−	0.312291i	−0.932168	+	0.362027i	$0.882085\pi$
$140$	−4.59779	+	1.78119i	−0.388584	+	0.150538i
$141$		0			0
$142$	−0.136823	+	0.353181i	−0.0114819	+	0.0296383i
$143$	−4.87856	−	6.46026i	−0.407966	−	0.540234i
$144$		0			0
$145$	−5.77938	+	0.535538i	−0.479951	+	0.0444740i
$146$	−8.47179	−	3.28199i	−0.701131	−	0.271619i
$147$		0			0
$148$	15.8973	+	4.52318i	1.30675	+	0.371803i
$149$			2.60225i			0.213185i	0.994303	+	0.106592i	$0.0339939\pi$
$149$			2.60225i			0.213185i	−0.994303	+	0.106592i	$0.966006\pi$
$150$		0			0
$151$	2.64863	+	0.753602i	0.215543	+	0.0613272i	0.379711	−	0.925105i	$-0.376023\pi$
$151$	2.64863	+	0.753602i	0.215543	+	0.0613272i	−0.164168	+	0.986432i	$0.552494\pi$
$152$	2.36767	+	6.11166i	0.192043	+	0.495721i
$153$		0			0
$154$	6.59589	+	3.28436i	0.531512	+	0.264661i
$155$	0.323360	+	0.161014i	0.0259729	+	0.0129330i
$156$		0			0
$157$	5.88788	+	15.1984i	0.469904	+	1.21296i	0.943250	+	0.332085i	$0.107752\pi$
$157$	5.88788	+	15.1984i	0.469904	+	1.21296i	−0.473346	+	0.880877i	$0.656954\pi$
$158$	3.53223	+	1.00501i	0.281009	+	0.0799541i
$159$		0			0
$160$		−	7.09579i		−	0.560971i
$161$	5.50511	+	1.56634i	0.433863	+	0.123445i
$162$		0			0
$163$	−7.18067	−	2.78181i	−0.562433	−	0.217888i	0.0632057	−	0.998001i	$-0.479868\pi$
$163$	−7.18067	−	2.78181i	−0.562433	−	0.217888i	−0.625639	+	0.780113i	$0.715162\pi$
$164$	12.1638	−	1.12714i	0.949834	−	0.0880151i
$165$		0			0
$166$	2.10790	+	2.79132i	0.163605	+	0.216648i
$167$	−4.56761	+	11.7904i	−0.353452	+	0.912365i	0.636540	+	0.771244i	$0.280365\pi$
$167$	−4.56761	+	11.7904i	−0.353452	+	0.912365i	−0.989992	+	0.141122i	$0.954929\pi$
$168$		0			0
$169$	−8.57459	+	3.32181i	−0.659584	+	0.255524i
$170$	1.75510	+	0.328084i	0.134610	+	0.0251629i
$171$		0			0
$172$	7.30137	+	11.7921i	0.556724	+	0.899140i
$173$	−0.123368	+	1.33135i	−0.00937947	+	0.101221i	−0.999137	−	0.0415388i	$-0.986774\pi$
$173$	−0.123368	+	1.33135i	−0.00937947	+	0.101221i	0.989757	+	0.142759i	$0.0455975\pi$
$174$		0			0
$175$	2.50172	+	8.79262i	0.189112	+	0.664660i
$176$	4.43252	−	4.04078i	0.334114	−	0.304585i
$177$		0			0
$178$	7.11889	+	3.54478i	0.533583	+	0.265693i
$179$	−4.82717	−	0.447303i	−0.360800	−	0.0334330i	−0.0896585	−	0.995973i	$-0.528578\pi$
$179$	−4.82717	−	0.447303i	−0.360800	−	0.0334330i	−0.271141	+	0.962540i	$0.587401\pi$
$180$		0			0
$181$	18.8643	−	1.74803i	1.40217	−	0.129930i	0.635565	−	0.772047i	$-0.280767\pi$
$181$	18.8643	−	1.74803i	1.40217	−	0.129930i	0.766607	+	0.642117i	$0.221943\pi$
$182$	−2.33287	+	2.55903i	−0.172923	+	0.189688i
$183$		0			0
$184$	−3.17138	+	4.19958i	−0.233797	+	0.309598i
$185$	−4.75678	+	12.2787i	−0.349726	+	0.902746i
$186$		0			0
$187$	4.68559	+	7.56749i	0.342645	+	0.553390i
$188$	−10.8186	+	14.3261i	−0.789026	+	1.04484i
$189$		0			0
$190$	−2.18385	+	0.621359i	−0.158433	+	0.0450781i
$191$	0.599458	+	2.10687i	0.0433752	+	0.152448i	0.980488	−	0.196578i	$-0.0629830\pi$
$191$	0.599458	+	2.10687i	0.0433752	+	0.152448i	−0.937113	+	0.349026i	$0.886512\pi$
$192$		0			0
$193$	−1.23131	−	6.58695i	−0.0886319	−	0.474139i	−0.998273	−	0.0587440i	$-0.981290\pi$
$193$	−1.23131	−	6.58695i	−0.0886319	−	0.474139i	0.909641	−	0.415395i	$-0.136357\pi$
$194$	−0.670964	−	1.73196i	−0.0481724	−	0.124347i
$195$		0			0
$196$	0.0703836	−	0.247373i	0.00502740	−	0.0176695i
$197$	−3.48871	−	7.00627i	−0.248560	−	0.499176i	0.735384	−	0.677650i	$-0.237002\pi$
$197$	−3.48871	−	7.00627i	−0.248560	−	0.499176i	−0.983945	+	0.178474i	$0.942884\pi$
$198$		0			0
$199$	−1.93730	−	10.3636i	−0.137332	−	0.734659i	−0.980425	−	0.196892i	$-0.936915\pi$
$199$	−1.93730	−	10.3636i	−0.137332	−	0.734659i	0.843094	−	0.537767i	$-0.180732\pi$
$200$	−8.36932	−	0.775531i	−0.591800	−	0.0548384i
$201$		0			0
$202$	5.05077	+	3.81416i	0.355371	+	0.268364i
$203$	−6.51525	+	10.5225i	−0.457281	+	0.738534i
$204$		0			0
$205$			9.73227i			0.679732i
$206$	5.45282	+	4.21636i	0.379916	+	0.293768i
$207$		0			0
$208$	1.25642	+	2.52324i	0.0871173	+	0.174955i
$209$	−9.62319	−	5.95843i	−0.665650	−	0.412153i
$210$		0			0
$211$	−10.3056	+	11.3047i	−0.709465	+	0.778246i	−0.982998	−	0.183616i	$-0.941220\pi$
$211$	−10.3056	+	11.3047i	−0.709465	+	0.778246i	0.273533	+	0.961863i	$0.411808\pi$
$212$	−1.41968	+	15.3208i	−0.0975039	+	1.05224i
$213$		0			0
$214$	−4.10285	−	0.766956i	−0.280465	−	0.0524280i
$215$	−9.89127	+	4.92527i	−0.674579	+	0.335901i
$216$		0			0
$217$	0.689505	−	0.343333i	0.0468067	−	0.0233069i
$218$	4.65661	−	1.80398i	0.315385	−	0.122181i
$219$		0			0
$220$	4.71800	+	6.24764i	0.318087	+	0.421215i
$221$	−4.02322	+	1.14470i	−0.270631	+	0.0770011i
$222$		0			0
$223$	−0.523151	−	5.64570i	−0.0350328	−	0.378064i	−0.995143	−	0.0984415i	$-0.968614\pi$
$223$	−0.523151	−	5.64570i	−0.0350328	−	0.378064i	0.960110	−	0.279622i	$-0.0902093\pi$
$224$	−12.0744	−	9.11813i	−0.806752	−	0.609230i
$225$		0			0
$226$	0.0893529	+	0.477996i	0.00594367	+	0.0317958i
$227$	14.3720	+	5.56776i	0.953906	+	0.369545i	0.787363	−	0.616489i	$-0.211446\pi$
$227$	14.3720	+	5.56776i	0.953906	+	0.369545i	0.166543	+	0.986034i	$0.446740\pi$
$228$		0			0
$229$	−0.478592	+	0.961142i	−0.0316262	+	0.0635140i	−0.910413	−	0.413701i	$-0.864236\pi$
$229$	−0.478592	+	0.961142i	−0.0316262	+	0.0635140i	0.878787	+	0.477215i	$0.158354\pi$
$230$	−1.34725	−	1.22818i	−0.0888347	−	0.0809836i
$231$		0			0
$232$	−6.85752	−	9.08083i	−0.450218	−	0.596186i
$233$	−0.459055	+	4.95400i	−0.0300737	+	0.324547i	0.967386	+	0.253308i	$0.0815187\pi$
$233$	−0.459055	+	4.95400i	−0.0300737	+	0.324547i	−0.997459	+	0.0712387i	$0.977305\pi$
$234$		0			0
$235$	−10.5695	−	9.63536i	−0.689477	−	0.628541i
$236$	5.97127	+	6.55017i	0.388696	+	0.426380i
$237$		0			0
$238$	2.81359	−	2.56492i	0.182378	−	0.166259i
$239$	−7.15881	−	0.663361i	−0.463065	−	0.0429093i	−0.141793	−	0.989896i	$-0.545287\pi$
$239$	−7.15881	−	0.663361i	−0.463065	−	0.0429093i	−0.321272	+	0.946987i	$0.604110\pi$
$240$		0			0
$241$	−9.32611	+	15.0622i	−0.600747	+	0.970240i	0.397858	+	0.917447i	$0.369754\pi$
$241$	−9.32611	+	15.0622i	−0.600747	+	0.970240i	−0.998605	+	0.0527934i	$0.983188\pi$
$242$	0.776980	−	4.15647i	0.0499461	−	0.267188i
$243$		0			0
$244$	−1.87065	−	1.15825i	−0.119756	−	0.0741497i
$245$	0.191064	+	0.0740187i	0.0122067	+	0.00472888i
$246$		0			0
$247$	3.93092	−	3.58350i	0.250118	−	0.228013i
$248$	0.0653451	+	0.705185i	0.00414941	+	0.0447793i
$249$		0			0
$250$	1.29996	−	6.95419i	0.0822169	−	0.439821i
$251$	−4.15941	+	14.6188i	−0.262540	+	0.922732i	0.712679	+	0.701490i	$0.247482\pi$
$251$	−4.15941	+	14.6188i	−0.262540	+	0.922732i	−0.975219	+	0.221242i	$0.928989\pi$
$252$		0			0
$253$		−	9.08782i		−	0.571347i
$254$	−3.02328	+	10.6257i	−0.189697	+	0.666717i
$255$		0			0
$256$	8.04664	−	4.98227i	0.502915	−	0.311392i
$257$	3.90523	−	7.84275i	0.243601	−	0.489217i	−0.739294	−	0.673383i	$-0.764841\pi$
$257$	3.90523	−	7.84275i	0.243601	−	0.489217i	0.982895	+	0.184165i	$0.0589582\pi$
$258$		0			0
$259$	14.7812	+	23.8724i	0.918458	+	1.48336i
$260$	−3.43079	+	1.32910i	−0.212769	+	0.0824270i
$261$		0			0
$262$	−2.01151			−0.124271
$263$	−11.1713			−0.688852			−0.344426	−	0.938813i	$-0.611926\pi$
$263$	−11.1713			−0.688852			−0.344426	+	0.938813i	$0.611926\pi$
$264$		0			0
$265$	−12.0494	−	2.25243i	−0.740192	−	0.138366i
$266$	−1.74894	+	4.51454i	−0.107234	+	0.276804i
$267$		0			0
$268$	−13.5463	−	14.8596i	−0.827475	−	0.907697i
$269$	7.14463	−	5.39537i	0.435616	−	0.328962i	−0.361946	−	0.932199i	$-0.617888\pi$
$269$	7.14463	−	5.39537i	0.435616	−	0.328962i	0.797562	+	0.603237i	$0.206123\pi$
$270$		0			0
$271$	4.68613	−	7.56836i	0.284662	−	0.459745i	−0.676221	−	0.736699i	$-0.736384\pi$
$271$	4.68613	−	7.56836i	0.284662	−	0.459745i	0.960883	+	0.276953i	$0.0893248\pi$
$272$	−1.11954	−	2.88986i	−0.0678819	−	0.175223i
$273$		0			0
$274$	11.0655	+	6.85147i	0.668491	+	0.413912i
$275$	12.3408	−	7.64108i	0.744176	−	0.460775i
$276$		0			0
$277$	−18.4404	−	20.2282i	−1.10798	−	1.21539i	−0.974511	−	0.224339i	$-0.927978\pi$
$277$	−18.4404	−	20.2282i	−1.10798	−	1.21539i	−0.133465	−	0.991053i	$-0.542610\pi$
$278$	13.0893	−	3.72422i	0.785042	−	0.223364i
$279$		0			0
$280$	5.18849	−	5.69150i	0.310071	−	0.340132i
$281$	−3.21514	+	6.45687i	−0.191799	+	0.385185i	−0.970100	−	0.242707i	$-0.921964\pi$
$281$	−3.21514	+	6.45687i	−0.191799	+	0.385185i	0.778300	+	0.627892i	$0.216082\pi$
$282$		0			0
$283$	4.40165	−	3.32397i	0.261651	−	0.197590i	−0.463656	−	0.886015i	$-0.653463\pi$
$283$	4.40165	−	3.32397i	0.261651	−	0.197590i	0.725307	+	0.688426i	$0.241698\pi$
$284$	0.0791768	+	0.854453i	0.00469828	+	0.0507025i
$285$		0			0
$286$	4.92174	+	2.45073i	0.291029	+	0.144915i
$287$	16.5607	+	12.5060i	0.977545	+	0.738208i
$288$		0			0
$289$	−12.1899	+	2.27868i	−0.717051	+	0.134040i
$290$	3.35155	−	2.07519i	0.196810	−	0.121860i
$291$		0			0
$292$	−20.4959	+	1.89922i	−1.19943	+	0.111144i
$293$	−0.238781	−	0.839229i	−0.0139498	−	0.0490283i	0.954538	−	0.298088i	$-0.0963490\pi$
$293$	−0.238781	−	0.839229i	−0.0139498	−	0.0490283i	−0.968488	+	0.249060i	$0.919878\pi$
$294$		0			0
$295$	−5.63512	+	4.25545i	−0.328090	+	0.247762i
$296$	−25.3766	+	4.74370i	−1.47498	+	0.275722i
$297$		0			0
$298$	−0.787784	−	1.58208i	−0.0456351	−	0.0916477i
$299$	4.10782	+	1.16877i	0.237561	+	0.0675920i
$300$		0			0
$301$	−4.32940	+	23.1602i	−0.249542	+	1.33493i
$302$	−1.83843	+	0.343661i	−0.105789	+	0.0197755i
$303$		0			0
$304$	2.91244	+	2.65504i	0.167040	+	0.152277i
$305$	1.05634	−	1.39882i	0.0604859	−	0.0800963i
$306$		0			0
$307$	9.11655	−	4.53950i	0.520309	−	0.259083i	−0.166345	−	0.986068i	$-0.553196\pi$
$307$	9.11655	−	4.53950i	0.520309	−	0.259083i	0.686654	+	0.726984i	$0.259079\pi$
$308$	16.6938			0.951216
$309$		0			0
$310$	−0.245337			−0.0139342
$311$	27.6436	−	13.7649i	1.56753	−	0.780535i	0.568417	−	0.822741i	$-0.307556\pi$
$311$	27.6436	−	13.7649i	1.56753	−	0.780535i	0.999109	+	0.0422060i	$0.0134386\pi$
$312$		0			0
$313$	−13.1881	+	17.4639i	−0.745435	+	0.987116i	0.254364	+	0.967108i	$0.418134\pi$
$313$	−13.1881	+	17.4639i	−0.745435	+	0.987116i	−0.999800	+	0.0200075i	$0.993631\pi$
$314$	−8.18068	−	7.45767i	−0.461662	−	0.420861i
$315$		0			0
$316$	8.17858	−	1.52884i	0.460081	−	0.0860041i
$317$	2.12308	−	11.3575i	0.119244	−	0.637899i	−0.870167	−	0.492757i	$-0.835989\pi$
$317$	2.12308	−	11.3575i	0.119244	−	0.637899i	0.989411	−	0.145142i	$-0.0463638\pi$
$318$		0			0
$319$	18.9006	+	5.37768i	1.05823	+	0.301092i
$320$	0.568803	+	1.14231i	0.0317971	+	0.0638571i
$321$		0			0
$322$	−3.82111	+	0.714289i	−0.212942	+	0.0398058i
$323$	−4.66703	+	3.52438i	−0.259681	+	0.196102i
$324$		0			0
$325$	1.86674	+	6.56090i	0.103548	+	0.363933i
$326$	5.20776	−	0.482570i	0.288431	−	0.0267271i
$327$		0			0
$328$	−16.2226	+	10.0446i	−0.895742	+	0.554620i
$329$	−29.9776	+	5.60378i	−1.65272	+	0.308947i
$330$		0			0
$331$	24.2962	+	18.3476i	1.33544	+	1.00848i	0.997738	+	0.0672213i	$0.0214133\pi$
$331$	24.2962	+	18.3476i	1.33544	+	1.00848i	0.337699	+	0.941254i	$0.390351\pi$
$332$	7.09386	+	3.53232i	0.389326	+	0.193861i
$333$		0			0
$334$	−0.792360	−	8.55092i	−0.0433560	−	0.467886i
$335$	12.7838	−	9.65385i	0.698452	−	0.527446i
$336$		0			0
$337$	−4.61794	+	9.27408i	−0.251555	+	0.505191i	−0.984563	−	0.175029i	$-0.943998\pi$
$337$	−4.61794	+	9.27408i	−0.251555	+	0.505191i	0.733008	+	0.680220i	$0.238116\pi$
$338$	4.20746	−	4.61536i	0.228855	−	0.251043i
$339$		0			0
$340$	3.89080	−	1.10703i	0.211008	−	0.0600370i
$341$	−0.823928	−	0.903806i	−0.0446182	−	0.0489439i
$342$		0			0
$343$	15.9286	−	9.86256i	0.860063	−	0.532528i
$344$	−18.4186	−	11.4043i	−0.993062	−	0.614878i
$345$		0			0
$346$	−0.328038	−	0.846765i	−0.0176355	−	0.0455224i
$347$	−2.02741	+	3.27438i	−0.108837	+	0.175778i	−0.900081	−	0.435723i	$-0.856493\pi$
$347$	−2.02741	+	3.27438i	−0.108837	+	0.175778i	0.791244	+	0.611501i	$0.209434\pi$
$348$		0			0
$349$	18.0591	−	13.6376i	0.966681	−	0.730004i	0.00381778	−	0.999993i	$-0.498785\pi$
$349$	18.0591	−	13.6376i	0.966681	−	0.730004i	0.962863	+	0.269989i	$0.0870201\pi$
$350$	−4.18277	−	4.58828i	−0.223579	−	0.245254i
$351$		0			0
$352$	−8.67840	+	22.4015i	−0.462560	+	1.19401i
$353$	21.0184	+	3.92901i	1.11869	+	0.209120i	0.710447	−	0.703751i	$-0.248493\pi$
$353$	21.0184	+	3.92901i	1.11869	+	0.209120i	0.408247	+	0.912871i	$0.366140\pi$
$354$		0			0
$355$	−0.683649			−0.0362843
$356$	18.0174			0.954922
$357$		0			0
$358$	3.07018	−	1.18939i	0.162264	−	0.0628614i
$359$	−19.0354	−	30.7433i	−1.00465	−	1.62257i	−0.756662	−	0.653807i	$-0.773171\pi$
$359$	−19.0354	−	30.7433i	−1.00465	−	1.62257i	−0.247991	−	0.968762i	$-0.579770\pi$
$360$		0			0
$361$	−5.15409	+	10.3508i	−0.271268	+	0.544779i
$362$	−10.9397	+	6.77358i	−0.574978	+	0.356011i
$363$		0			0
$364$	−2.14697	+	7.54581i	−0.112532	+	0.395508i
$365$		−	16.3988i		−	0.858350i
$366$		0			0
$367$	3.21185	−	11.2885i	0.167657	−	0.589253i	−0.831761	−	0.555134i	$-0.812667\pi$
$367$	3.21185	−	11.2885i	0.167657	−	0.589253i	0.999418	−	0.0341191i	$-0.0108626\pi$
$368$	−0.581439	+	3.11043i	−0.0303096	+	0.162142i
$369$		0			0
$370$	−0.825177	−	8.90507i	−0.0428989	−	0.462953i
$371$	−19.3164	+	17.6092i	−1.00286	+	0.914226i
$372$		0			0
$373$	−14.8244	−	5.74299i	−0.767577	−	0.297361i	−0.0545627	−	0.998510i	$-0.517376\pi$
$373$	−14.8244	−	5.74299i	−0.767577	−	0.297361i	−0.713014	+	0.701149i	$0.752671\pi$
$374$	−5.13962	−	3.18231i	−0.265763	−	0.164554i
$375$		0			0
$376$	5.15236	−	27.5627i	0.265713	−	1.42144i
$377$	−4.86157	+	7.85170i	−0.250383	+	0.404383i
$378$		0			0
$379$	2.92800	+	0.271319i	0.150401	+	0.0139367i	0.167205	−	0.985922i	$-0.446526\pi$
$379$	2.92800	+	0.271319i	0.150401	+	0.0139367i	−0.0168043	+	0.999859i	$0.505349\pi$
$380$	−3.80154	+	3.46556i	−0.195015	+	0.177779i
$381$		0			0
$382$	−1.00227	−	1.09944i	−0.0512806	−	0.0562521i
$383$	−1.73634	−	1.58289i	−0.0887230	−	0.0808817i	0.628119	−	0.778117i	$-0.283825\pi$
$383$	−1.73634	−	1.58289i	−0.0887230	−	0.0808817i	−0.716842	+	0.697235i	$0.754413\pi$
$384$		0			0
$385$	−1.22714	+	13.2430i	−0.0625410	+	0.674925i
$386$	2.74268	+	3.63190i	0.139599	+	0.184859i
$387$		0			0
$388$	−3.10981	−	2.83497i	−0.157877	−	0.143924i
$389$	8.45150	−	16.9729i	0.428508	−	0.860560i	−0.570715	−	0.821148i	$-0.693334\pi$
$389$	8.45150	−	16.9729i	0.428508	−	0.860560i	0.999223	−	0.0394117i	$-0.0125484\pi$
$390$		0			0
$391$	−4.37860	−	1.69628i	−0.221435	−	0.0857845i
$392$	0.0738152	+	0.394876i	0.00372823	+	0.0199443i
$393$		0			0
$394$	4.24205	+	3.20344i	0.213711	+	0.161387i
$395$	0.611614	+	6.60036i	0.0307736	+	0.332100i
$396$		0			0
$397$	7.75164	−	2.20553i	0.389043	−	0.110692i	−0.0734861	−	0.997296i	$-0.523412\pi$
$397$	7.75164	−	2.20553i	0.389043	−	0.110692i	0.462530	+	0.886604i	$0.346942\pi$
$398$	4.31522	+	5.71428i	0.216303	+	0.286431i
$399$		0			0
$400$	−4.71267	+	1.82570i	−0.235633	+	0.0912848i
$401$	−29.0262	+	14.4534i	−1.44950	+	0.721766i	−0.986373	−	0.164525i	$-0.947391\pi$
$401$	−29.0262	+	14.4534i	−1.44950	+	0.721766i	−0.463128	+	0.886291i	$0.653273\pi$
$402$		0			0
$403$	0.514497	−	0.256189i	0.0256289	−	0.0127617i
$404$	14.0952	+	2.63484i	0.701261	+	0.131088i
$405$		0			0
$406$	0.775568	−	8.36971i	0.0384908	−	0.415382i
$407$	30.0345	−	32.9463i	1.48876	−	1.63309i
$408$		0			0
$409$	−21.7789	−	13.4849i	−1.07690	−	0.666787i	−0.131043	−	0.991377i	$-0.541833\pi$
$409$	−21.7789	−	13.4849i	−1.07690	−	0.666787i	−0.945855	+	0.324590i	$0.894774\pi$
$410$	−2.94627	−	5.91691i	−0.145506	−	0.292215i
$411$		0			0
$412$	15.3167	+	3.04452i	0.754601	+	0.149993i
$413$			15.0571i			0.740913i
$414$		0			0
$415$	−3.32361	+	5.36782i	−0.163150	+	0.263496i
$416$	−9.00967	−	6.80379i	−0.441736	−	0.333583i
$417$		0			0
$418$	7.65440	+	0.709285i	0.374389	+	0.0346922i
$419$	−4.48466	−	23.9908i	−0.219090	−	1.17203i	−0.898737	−	0.438489i	$-0.855514\pi$
$419$	−4.48466	−	23.9908i	−0.219090	−	1.17203i	0.679646	−	0.733540i	$-0.262133\pi$
$420$		0			0
$421$	−16.3991	−	32.9338i	−0.799241	−	1.60509i	−0.796151	−	0.605098i	$-0.793134\pi$
$421$	−16.3991	−	32.9338i	−0.799241	−	1.60509i	−0.00309050	−	0.999995i	$-0.500984\pi$
$422$	2.84317	−	9.99272i	0.138403	−	0.486438i
$423$		0			0
$424$	−8.68158	−	22.4098i	−0.421615	−	1.08831i
$425$	−1.37809	−	7.37214i	−0.0668472	−	0.357601i
$426$		0			0
$427$	−1.02286	−	3.59499i	−0.0494998	−	0.173974i
$428$	−9.09544	+	2.58788i	−0.439645	+	0.125090i
$429$		0			0
$430$	4.52254	−	5.98881i	0.218096	−	0.288806i
$431$	20.2794	+	32.7523i	0.976823	+	1.57762i	0.805658	+	0.592382i	$0.201812\pi$
$431$	20.2794	+	32.7523i	0.976823	+	1.57762i	0.171166	+	0.985242i	$0.445247\pi$
$432$		0			0
$433$	0.280835	−	0.724918i	0.0134961	−	0.0348373i	−0.925561	−	0.378597i	$-0.876407\pi$
$433$	0.280835	−	0.724918i	0.0134961	−	0.0348373i	0.939058	+	0.343760i	$0.111701\pi$
$434$	−0.315259	+	0.417471i	−0.0151329	+	0.0200392i
$435$		0			0
$436$	7.62221	−	8.36116i	0.365037	−	0.400427i
$437$	5.94579	−	0.550959i	0.284426	−	0.0263559i
$438$		0			0
$439$	5.43292	+	0.503434i	0.259299	+	0.0240276i	0.221133	−	0.975244i	$-0.429025\pi$
$439$	5.43292	+	0.503434i	0.259299	+	0.0240276i	0.0381667	+	0.999271i	$0.487848\pi$
$440$	−10.9464	−	5.45064i	−0.521847	−	0.259849i
$441$		0			0
$442$	2.09945	−	1.91390i	0.0998606	−	0.0910350i
$443$	−4.29132	−	15.0824i	−0.203887	−	0.716587i	−0.994543	−	0.104327i	$-0.966731\pi$
$443$	−4.29132	−	15.0824i	−0.203887	−	0.716587i	0.790656	−	0.612260i	$-0.209740\pi$
$444$		0			0
$445$	−1.32445	+	14.2930i	−0.0627847	+	0.677555i
$446$	2.02719	+	3.27403i	0.0959904	+	0.155030i
$447$		0			0
$448$	2.67470	+	0.499987i	0.126368	+	0.0236222i
$449$	19.9450	−	7.72672i	0.941261	−	0.364647i	0.158775	−	0.987315i	$-0.449245\pi$
$449$	19.9450	−	7.72672i	0.941261	−	0.364647i	0.782486	+	0.622668i	$0.213951\pi$
$450$		0			0
$451$	11.9029	−	30.7250i	0.560487	−	1.44678i
$452$	0.663927	+	0.879181i	0.0312285	+	0.0413532i
$453$		0			0
$454$	−10.4233	+	0.965859i	−0.489189	+	0.0453300i
$455$	−5.82819	−	2.25785i	−0.273230	−	0.105850i
$456$		0			0
$457$	30.0328	+	8.54505i	1.40487	+	0.399721i	0.889378	−	0.457172i	$-0.151138\pi$
$457$	30.0328	+	8.54505i	1.40487	+	0.399721i	0.515495	+	0.856893i	$0.327608\pi$
$458$		−	0.729229i		−	0.0340746i
$459$		0			0
$460$	−3.97262	−	1.13031i	−0.185224	−	0.0527008i
$461$	7.51549	+	19.3997i	0.350031	+	0.903535i	0.990743	+	0.135753i	$0.0433454\pi$
$461$	7.51549	+	19.3997i	0.350031	+	0.903535i	−0.640711	+	0.767782i	$0.721360\pi$
$462$		0			0
$463$	−20.5008	−	10.2082i	−0.952753	−	0.474414i	−0.0989966	−	0.995088i	$-0.531563\pi$
$463$	−20.5008	−	10.2082i	−0.952753	−	0.474414i	−0.853756	+	0.520673i	$0.825681\pi$
$464$	−6.12491	−	3.04984i	−0.284342	−	0.141585i
$465$		0			0
$466$	−1.22064	−	3.15084i	−0.0565452	−	0.145960i
$467$	26.4686	+	7.53096i	1.22482	+	0.348491i	0.823431	−	0.567416i	$-0.192057\pi$
$467$	26.4686	+	7.53096i	1.22482	+	0.348491i	0.401389	+	0.915908i	$0.368527\pi$
$468$		0			0
$469$		−	34.1584i		−	1.57729i
$470$	9.34284	+	2.65827i	0.430953	+	0.122617i
$471$		0			0
$472$	−12.9093	−	5.00109i	−0.594199	−	0.230194i
$473$	37.2507	−	3.45179i	1.71279	−	0.158713i
$474$		0			0
$475$	5.74742	+	7.61081i	0.263710	+	0.349208i
$476$	3.11596	−	8.04321i	0.142820	−	0.368660i
$477$		0			0
$478$	4.55315	−	1.76390i	0.208256	−	0.0806789i
$479$	23.8099	+	4.45085i	1.08790	+	0.203364i	0.697003	−	0.717068i	$-0.254517\pi$
$479$	23.8099	+	4.45085i	1.08790	+	0.203364i	0.390901	+	0.920433i	$0.372164\pi$
$480$		0			0
$481$	11.0295	+	17.8132i	0.502900	+	0.812212i
$482$	1.11017	−	11.9806i	0.0505668	−	0.545703i
$483$		0			0
$484$	−2.62170	−	9.21432i	−0.119168	−	0.418833i
$485$	2.47755	−	2.25859i	0.112500	−	0.102557i
$486$		0			0
$487$	−20.1509	−	10.0340i	−0.913125	−	0.454682i	−0.0731586	−	0.997320i	$-0.523308\pi$
$487$	−20.1509	−	10.0340i	−0.913125	−	0.454682i	−0.839967	+	0.542638i	$0.817426\pi$
$488$	3.42191	+	0.317087i	0.154903	+	0.0143539i
$489$		0			0
$490$	−0.138569	+	0.0128403i	−0.00625990	+	0.000580065i
$491$	29.5024	−	32.3626i	1.33142	−	1.46050i	0.552281	−	0.833658i	$-0.313757\pi$
$491$	29.5024	−	32.3626i	1.33142	−	1.46050i	0.779143	−	0.626846i	$-0.215654\pi$
$492$		0			0
$493$	6.11889	−	8.10271i	0.275581	−	0.364928i
$494$	−1.30503	+	3.36867i	−0.0587161	+	0.151564i
$495$		0			0
$496$	0.224175	+	0.362055i	0.0100657	+	0.0162567i
$497$	−0.878493	+	1.16331i	−0.0394058	+	0.0521817i
$498$		0			0
$499$	−11.0031	+	3.13066i	−0.492567	+	0.140147i	−0.510823	−	0.859686i	$-0.670659\pi$
$499$	−11.0031	+	3.13066i	−0.492567	+	0.140147i	0.0182558	+	0.999833i	$0.494189\pi$
$500$	−4.38636	−	15.4164i	−0.196164	−	0.689445i
$501$		0			0
$502$	−1.89680	−	10.1470i	−0.0846582	−	0.452881i
$503$	6.39776	+	16.5145i	0.285262	+	0.736346i	0.999342	+	0.0362816i	$0.0115513\pi$
$503$	6.39776	+	16.5145i	0.285262	+	0.736346i	−0.714080	+	0.700065i	$0.753155\pi$
$504$		0			0
$505$	−3.12632	+	10.9879i	−0.139119	+	0.488953i
$506$	2.75118	+	5.52511i	0.122305	+	0.245621i
$507$		0			0
$508$	4.59909	+	24.6029i	0.204051	+	1.09158i
$509$	−20.2887	−	1.88002i	−0.899280	−	0.0833305i	−0.367315	−	0.930097i	$-0.619723\pi$
$509$	−20.2887	−	1.88002i	−0.899280	−	0.0833305i	−0.531965	+	0.846766i	$0.678546\pi$
$510$		0			0
$511$	−27.9045	−	21.0725i	−1.23442	−	0.932193i
$512$	8.06041	−	13.0180i	0.356223	−	0.575320i
$513$		0			0
$514$			5.95038i			0.262460i
$515$	−3.54110	+	11.9268i	−0.156040	+	0.525558i
$516$		0			0
$517$	21.5837	+	43.3459i	0.949249	+	1.90635i
$518$	−16.2134	−	10.0389i	−0.712377	−	0.441085i
$519$		0			0
$520$	3.87156	−	4.24690i	0.169779	−	0.186239i
$521$	3.93402	−	42.4548i	0.172352	−	1.85998i	−0.269641	−	0.962961i	$-0.586905\pi$
$521$	3.93402	−	42.4548i	0.172352	−	1.85998i	0.441993	−	0.897018i	$-0.354271\pi$
$522$		0			0
$523$	−10.5222	−	1.96694i	−0.460105	−	0.0860085i	−0.0514061	−	0.998678i	$-0.516370\pi$
$523$	−10.5222	−	1.96694i	−0.460105	−	0.0860085i	−0.408699	+	0.912669i	$0.634017\pi$
$524$	−4.07950	+	2.03135i	−0.178214	+	0.0887399i
$525$		0			0
$526$	6.79179	−	3.38191i	0.296136	−	0.147458i
$527$	−0.589252	+	0.228277i	−0.0256682	+	0.00994392i
$528$		0			0
$529$	−10.9713	−	14.5284i	−0.477013	−	0.631668i
$530$	8.00756	−	2.27835i	0.347826	−	0.0989651i
$531$		0			0
$532$	1.01208	+	10.9221i	0.0438791	+	0.473531i
$533$	12.3573	+	9.33178i	0.535253	+	0.404204i
$534$		0			0
$535$	−1.38434	−	7.40555i	−0.0598501	−	0.320170i
$536$	29.2859	+	11.3454i	1.26496	+	0.490047i
$537$		0			0
$538$	−2.71035	+	5.44312i	−0.116852	+	0.234670i
$539$	−0.512666	−	0.467357i	−0.0220821	−	0.0201305i
$540$		0			0
$541$	−6.18277	−	8.18731i	−0.265818	−	0.352000i	0.645458	−	0.763796i	$-0.276666\pi$
$541$	−6.18277	−	8.18731i	−0.265818	−	0.352000i	−0.911276	+	0.411796i	$0.864902\pi$
$542$	−0.557832	+	6.01997i	−0.0239609	+	0.258580i
$543$		0			0
$544$	9.17341	+	8.36267i	0.393307	+	0.358546i
$545$	6.07252	+	6.66124i	0.260118	+	0.285336i
$546$		0			0
$547$	9.50222	−	8.66242i	0.406286	−	0.370378i	−0.444600	−	0.895729i	$-0.646654\pi$
$547$	9.50222	−	8.66242i	0.406286	−	0.370378i	0.850886	+	0.525351i	$0.176066\pi$
$548$	29.3608	+	2.72068i	1.25423	+	0.116222i
$549$		0			0
$550$	−5.18959	+	8.38148i	−0.221285	+	0.357388i
$551$	−2.37253	+	12.6919i	−0.101073	+	0.540693i
$552$		0			0
$553$	12.0173	+	7.44077i	0.511026	+	0.316414i
$554$	17.3349	+	6.71557i	0.736489	+	0.285317i
$555$		0			0
$556$	22.7852	−	20.7714i	0.966306	−	0.880905i
$557$	−2.95360	−	31.8744i	−0.125148	−	1.35056i	−0.794340	−	0.607474i	$-0.792183\pi$
$557$	−2.95360	−	31.8744i	−0.125148	−	1.35056i	0.669192	−	0.743090i	$-0.266641\pi$
$558$		0			0
$559$	−3.23052	+	17.2818i	−0.136636	+	0.730940i
$560$	1.26729	−	4.45407i	0.0535529	−	0.188219i
$561$		0			0
$562$		−	4.89890i		−	0.206648i
$563$	−3.75348	+	13.1921i	−0.158190	+	0.555981i	0.841682	+	0.539974i	$0.181566\pi$
$563$	−3.75348	+	13.1921i	−0.158190	+	0.555981i	−0.999872	+	0.0160069i	$0.994905\pi$
$564$		0			0
$565$	−0.746250	+	0.462058i	−0.0313950	+	0.0194389i
$566$	−1.66979	+	3.35339i	−0.0701865	+	0.140953i
$567$		0			0
$568$	−0.705588	−	1.13956i	−0.0296058	−	0.0478150i
$569$	−14.6673	+	5.68214i	−0.614885	+	0.238208i	−0.648485	−	0.761228i	$-0.724597\pi$
$569$	−14.6673	+	5.68214i	−0.614885	+	0.238208i	0.0336000	+	0.999435i	$0.489303\pi$
$570$		0			0
$571$	−10.3924			−0.434909			−0.217454	−	0.976071i	$-0.569775\pi$
$571$	−10.3924			−0.434909			−0.217454	+	0.976071i	$0.569775\pi$
$572$	12.4566			0.520837
$573$		0			0
$574$	−13.8543	−	2.58982i	−0.578269	−	0.108097i
$575$	−2.76622	+	7.14044i	−0.115359	+	0.297777i
$576$		0			0
$577$	−19.9664	−	21.9021i	−0.831213	−	0.911797i	0.166021	−	0.986122i	$-0.446908\pi$
$577$	−19.9664	−	21.9021i	−0.831213	−	0.911797i	−0.997234	+	0.0743249i	$0.976320\pi$
$578$	6.72122	−	5.07563i	0.279566	−	0.211118i
$579$		0			0
$580$	4.70156	−	7.59328i	0.195222	−	0.315294i
$581$	4.86314	+	12.5532i	0.201757	+	0.520795i
$582$		0			0
$583$	35.2855	+	21.8479i	1.46138	+	0.904847i
$584$	27.3348	−	16.9250i	1.13112	−	0.700362i
$585$		0			0
$586$	0.399233	+	0.437938i	0.0164922	+	0.0180910i
$587$	−9.87679	+	2.81019i	−0.407659	+	0.115989i	−0.471277	−	0.881985i	$-0.656207\pi$
$587$	−9.87679	+	2.81019i	−0.407659	+	0.115989i	0.0636179	+	0.997974i	$0.479736\pi$
$588$		0			0
$589$	0.541372	−	0.593857i	0.0223068	−	0.0244694i
$590$	2.13771	−	4.29311i	0.0880083	−	0.176744i
$591$		0			0
$592$	−12.3876	+	9.35469i	−0.509128	+	0.384476i
$593$	3.37825	+	36.4571i	0.138728	+	1.49711i	0.725984	+	0.687712i	$0.241385\pi$
$593$	3.37825	+	36.4571i	0.138728	+	1.49711i	−0.587256	+	0.809401i	$0.699792\pi$
$594$		0			0
$595$	6.15154	+	3.06311i	0.252189	+	0.125575i
$596$	−3.19538	−	2.41304i	−0.130888	−	0.0988420i
$597$		0			0
$598$	−2.85125	+	0.532990i	−0.116596	+	0.0217956i
$599$	2.71003	−	1.67798i	0.110729	−	0.0685605i	−0.469950	−	0.882693i	$-0.655728\pi$
$599$	2.71003	−	1.67798i	0.110729	−	0.0685605i	0.580679	+	0.814132i	$0.302787\pi$
$600$		0			0
$601$	19.5293	−	1.80965i	0.796616	−	0.0738173i	0.313743	−	0.949508i	$-0.398417\pi$
$601$	19.5293	−	1.80965i	0.796616	−	0.0738173i	0.482873	+	0.875691i	$0.339593\pi$
$602$	−4.37921	−	15.3913i	−0.178483	−	0.627303i
$603$		0			0
$604$	−3.38143	+	2.55353i	−0.137588	+	0.103902i
$605$	7.50234	−	1.40243i	0.305013	−	0.0570169i
$606$		0			0
$607$	1.34473	+	2.70059i	0.0545810	+	0.109613i	0.920774	−	0.390095i	$-0.127558\pi$
$607$	1.34473	+	2.70059i	0.0545810	+	0.109613i	−0.866193	+	0.499709i	$0.833440\pi$
$608$	−15.1825	−	4.31981i	−0.615734	−	0.175191i
$609$		0			0
$610$	−0.218753	+	1.17023i	−0.00885706	+	0.0473811i
$611$	−22.3688	+	4.18145i	−0.904943	+	0.169163i
$612$		0			0
$613$	−16.6747	−	15.2010i	−0.673484	−	0.613962i	0.262948	−	0.964810i	$-0.415305\pi$
$613$	−16.6747	−	15.2010i	−0.673484	−	0.613962i	−0.936432	+	0.350848i	$0.885893\pi$
$614$	−4.16832	+	5.51975i	−0.168220	+	0.222759i
$615$		0			0
$616$	−23.3411	+	11.6225i	−0.940438	+	0.468283i
$617$	−6.08410			−0.244937			−0.122468	−	0.992472i	$-0.539081\pi$
$617$	−6.08410			−0.244937			−0.122468	+	0.992472i	$0.539081\pi$
$618$		0			0
$619$	−5.50076			−0.221094			−0.110547	−	0.993871i	$-0.535260\pi$
$619$	−5.50076			−0.221094			−0.110547	+	0.993871i	$0.535260\pi$
$620$	−0.497563	+	0.247757i	−0.0199826	+	0.00995017i
$621$		0			0
$622$	−12.6394	+	16.7372i	−0.506792	+	0.671101i
$623$	22.6194	+	20.6204i	0.906229	+	0.826137i
$624$		0			0
$625$	−4.63614	+	0.866646i	−0.185446	+	0.0346658i
$626$	2.73107	−	14.6099i	0.109156	−	0.583930i
$627$		0			0
$628$	−24.1223	−	6.86339i	−0.962586	−	0.273879i
$629$	−10.2678	−	20.6205i	−0.409403	−	0.822192i
$630$		0			0
$631$	−3.00854	+	0.562393i	−0.119768	+	0.0223885i	−0.243292	−	0.969953i	$-0.578227\pi$
$631$	−3.00854	+	0.562393i	−0.119768	+	0.0223885i	0.123524	+	0.992342i	$0.460580\pi$
$632$	−10.3708	+	7.83167i	−0.412528	+	0.311527i
$633$		0			0
$634$	2.14751	+	7.54770i	0.0852883	+	0.299757i
$635$	−19.8553	+	1.83987i	−0.787934	+	0.0730129i
$636$		0			0
$637$	0.277185	−	0.171626i	0.0109825	−	0.00680006i
$638$	−13.1190	+	2.45236i	−0.519384	+	0.0970897i
$639$		0			0
$640$	10.6335	+	8.03004i	0.420326	+	0.317415i
$641$	−39.3324	−	19.5852i	−1.55354	−	0.773570i	−0.555228	−	0.831698i	$-0.687369\pi$
$641$	−39.3324	−	19.5852i	−1.55354	−	0.773570i	−0.998309	+	0.0581285i	$0.981487\pi$
$642$		0			0
$643$	−4.14153	−	44.6942i	−0.163326	−	1.76257i	−0.545154	−	0.838336i	$-0.683529\pi$
$643$	−4.14153	−	44.6942i	−0.163326	−	1.76257i	0.381828	−	0.924233i	$-0.375295\pi$
$644$	−7.02819	+	5.30744i	−0.276950	+	0.209143i
$645$		0			0
$646$	1.77046	−	3.55557i	0.0696580	−	0.139892i
$647$	−10.8471	+	11.8987i	−0.426444	+	0.467786i	−0.914241	−	0.405170i	$-0.867212\pi$
$647$	−10.8471	+	11.8987i	−0.426444	+	0.467786i	0.487798	+	0.872957i	$0.337800\pi$
$648$		0			0
$649$	22.9948	−	6.54257i	0.902623	−	0.256818i
$650$	−3.12111	−	3.42370i	−0.122420	−	0.134288i
$651$		0			0
$652$	10.0744	−	6.23783i	0.394545	−	0.244292i
$653$	21.6691	+	13.4169i	0.847977	+	0.525045i	0.880292	−	0.474433i	$-0.157347\pi$
$653$	21.6691	+	13.4169i	0.847977	+	0.525045i	−0.0323150	+	0.999478i	$0.510288\pi$
$654$		0			0
$655$	−1.31157	−	3.38555i	−0.0512472	−	0.132284i
$656$	−6.03972	+	9.75448i	−0.235811	+	0.380848i
$657$		0			0
$658$	16.5290	−	12.4821i	0.644367	−	0.486603i
$659$	−26.0003	−	28.5210i	−1.01283	−	1.11102i	−0.993798	−	0.111201i	$-0.964530\pi$
$659$	−26.0003	−	28.5210i	−1.01283	−	1.11102i	−0.0190300	−	0.999819i	$-0.506058\pi$
$660$		0			0
$661$	−9.43154	+	24.3456i	−0.366844	+	0.946935i	0.619904	+	0.784678i	$0.287172\pi$
$661$	−9.43154	+	24.3456i	−0.366844	+	0.946935i	−0.986749	+	0.162257i	$0.948123\pi$
$662$	−20.3257	−	3.79953i	−0.789981	−	0.147673i
$663$		0			0
$664$	−12.3778			−0.480352
$665$	−8.73874			−0.338874
$666$		0			0
$667$	−9.66700	+	3.74502i	−0.374308	+	0.145008i
$668$	−10.2422	−	16.5418i	−0.396284	−	0.640021i
$669$		0			0
$670$	−4.84959	+	9.73929i	−0.187356	+	0.376262i
$671$	−5.04570	+	3.12416i	−0.194787	+	0.120607i
$672$		0			0
$673$	2.33801	−	8.21725i	0.0901236	−	0.316752i	−0.903635	−	0.428303i	$-0.859111\pi$
$673$	2.33801	−	8.21725i	0.0901236	−	0.316752i	0.993759	+	0.111552i	$0.0355821\pi$
$674$		−	7.03634i		−	0.271030i
$675$		0			0
$676$	3.87218	−	13.6093i	0.148930	−	0.523434i
$677$	−0.0590824	+	0.316063i	−0.00227072	+	0.0121473i	−0.984090	−	0.177672i	$-0.943143\pi$
$677$	−0.0590824	+	0.316063i	−0.00227072	+	0.0121473i	0.981819	+	0.189820i	$0.0607903\pi$
$678$		0			0
$679$	−0.659594	−	7.11815i	−0.0253129	−	0.273170i
$680$	−4.66935	+	4.25667i	−0.179061	+	0.163236i
$681$		0			0
$682$	0.774533	+	0.300056i	0.0296584	+	0.0114897i
$683$	28.0563	+	17.3718i	1.07355	+	0.664712i	0.945026	−	0.326995i	$-0.106036\pi$
$683$	28.0563	+	17.3718i	1.07355	+	0.664712i	0.128520	+	0.991707i	$0.458977\pi$
$684$		0			0
$685$	−4.31657	+	23.0916i	−0.164928	+	0.882285i
$686$	−6.69836	+	10.8182i	−0.255744	+	0.413041i
$687$		0			0
$688$	−12.9704	−	1.20188i	−0.494492	−	0.0458214i
$689$	−14.4136	+	13.1397i	−0.549113	+	0.500583i
$690$		0			0
$691$	31.7005	+	34.7738i	1.20594	+	1.32286i	0.932587	+	0.360946i	$0.117546\pi$
$691$	31.7005	+	34.7738i	1.20594	+	1.32286i	0.273358	+	0.961912i	$0.411866\pi$
$692$	−1.52041	−	1.38603i	−0.0577972	−	0.0526891i
$693$		0			0
$694$	0.241341	−	2.60448i	0.00916117	−	0.0988647i
$695$	14.8028	+	19.6021i	0.561503	+	0.743551i
$696$		0			0
$697$	−12.5819	−	11.4699i	−0.476572	−	0.434453i
$698$	−6.85082	+	13.7583i	−0.259307	+	0.520759i
$699$		0			0
$700$	−13.1166	−	5.08138i	−0.495759	−	0.192058i
$701$	3.76848	+	20.1596i	0.142334	+	0.761418i	0.977421	+	0.211301i	$0.0677699\pi$
$701$	3.76848	+	20.1596i	0.142334	+	0.761418i	−0.835087	+	0.550117i	$0.814583\pi$
$702$		0			0
$703$	23.3763	+	17.6530i	0.881653	+	0.665794i
$704$	−0.398636	−	4.30196i	−0.0150241	−	0.162136i
$705$		0			0
$706$	−13.9679	+	3.97422i	−0.525690	+	0.149572i
$707$	14.6799	+	19.4393i	0.552093	+	0.731089i
$708$		0			0
$709$	−9.48924	+	3.67615i	−0.356376	+	0.138061i	−0.532773	−	0.846258i	$-0.678850\pi$
$709$	−9.48924	+	3.67615i	−0.356376	+	0.138061i	0.176397	+	0.984319i	$0.443556\pi$
$710$	0.415637	−	0.206963i	0.0155986	−	0.00776716i
$711$		0			0
$712$	−25.1918	+	12.5440i	−0.944103	+	0.470107i
$713$	0.634226	+	0.118557i	0.0237520	+	0.00444001i
$714$		0			0
$715$	−0.915674	+	9.88169i	−0.0342442	+	0.369554i
$716$	5.02545	−	5.51266i	0.187810	−	0.206018i
$717$		0			0
$718$	20.8799	+	12.9283i	0.779232	+	0.482480i
$719$	−3.74092	−	7.51278i	−0.139513	−	0.280179i	0.814377	−	0.580336i	$-0.197079\pi$
$719$	−3.74092	−	7.51278i	−0.139513	−	0.280179i	−0.953890	+	0.300156i	$0.902961\pi$
$720$		0			0
$721$	15.7446	+	21.3516i	0.586359	+	0.795176i
$722$		−	7.85327i		−	0.292268i
$723$		0			0
$724$	−15.3462	+	24.7850i	−0.570338	+	0.921127i
$725$	−13.2136	−	9.97844i	−0.490740	−	0.370590i
$726$		0			0
$727$	−6.55771	−	0.607661i	−0.243212	−	0.0225369i	−0.0300283	−	0.999549i	$-0.509560\pi$
$727$	−6.55771	−	0.607661i	−0.243212	−	0.0225369i	−0.213184	+	0.977012i	$0.568383\pi$
$728$	−2.25164	−	12.0452i	−0.0834514	−	0.446426i
$729$		0			0
$730$	4.96443	+	9.96992i	0.183742	+	0.369003i
$731$	5.28989	−	18.5920i	0.195654	−	0.687651i
$732$		0			0
$733$	−11.3841	−	29.3858i	−0.420482	−	1.08539i	−0.968520	−	0.248935i	$-0.919919\pi$
$733$	−11.3841	−	29.3858i	−0.420482	−	1.08539i	0.548039	−	0.836453i	$-0.315375\pi$
$734$	1.46468	+	7.83536i	0.0540624	+	0.289208i
$735$		0			0
$736$	−3.46845	−	12.1903i	−0.127849	−	0.449341i
$737$	−52.1656	+	14.8424i	−1.92155	+	0.546727i
$738$		0			0
$739$	−15.8853	+	21.0355i	−0.584349	+	0.773804i	−0.990128	−	0.140168i	$-0.955236\pi$
$739$	−15.8853	+	21.0355i	−0.584349	+	0.773804i	0.405778	+	0.913972i	$0.367000\pi$
$740$	−10.6664	−	17.2269i	−0.392106	−	0.633274i
$741$		0			0
$742$	6.41288	−	16.5535i	0.235424	−	0.607700i
$743$	−26.6306	+	35.2646i	−0.976983	+	1.29373i	−0.0211645	+	0.999776i	$0.506737\pi$
$743$	−26.6306	+	35.2646i	−0.976983	+	1.29373i	−0.955818	+	0.293958i	$0.905027\pi$
$744$		0			0
$745$	2.14913	−	2.35748i	0.0787380	−	0.0863715i
$746$	10.7513	−	0.996258i	0.393634	−	0.0364756i
$747$		0			0
$748$	−13.6373	−	1.26368i	−0.498628	−	0.0462047i
$749$	−14.3803	−	7.16056i	−0.525446	−	0.261641i
$750$		0			0
$751$	7.89424	−	7.19655i	0.288065	−	0.262606i	−0.516744	−	0.856140i	$-0.672856\pi$
$751$	7.89424	−	7.19655i	0.288065	−	0.262606i	0.804809	+	0.593534i	$0.202268\pi$
$752$	−4.61403	−	16.2166i	−0.168256	−	0.591359i
$753$		0			0
$754$	0.578716	−	6.24534i	0.0210756	−	0.227442i
$755$	−1.77713	−	2.87016i	−0.0646762	−	0.104456i
$756$		0			0
$757$	−25.8897	−	4.83963i	−0.940978	−	0.175899i	−0.309155	−	0.951012i	$-0.600046\pi$
$757$	−25.8897	−	4.83963i	−0.940978	−	0.175899i	−0.631823	+	0.775112i	$0.717693\pi$
$758$	−1.86227	+	0.721446i	−0.0676405	+	0.0262041i
$759$		0			0
$760$	2.90249	−	7.49220i	0.105285	−	0.271771i
$761$	13.0020	+	17.2175i	0.471324	+	0.624133i	0.970132	−	0.242579i	$-0.0779934\pi$
$761$	13.0020	+	17.2175i	0.471324	+	0.624133i	−0.498808	+	0.866712i	$0.666229\pi$
$762$		0			0
$763$	19.1381	−	1.77341i	0.692847	−	0.0642017i
$764$	−3.14297	−	1.21759i	−0.113709	−	0.0440510i
$765$		0			0
$766$	1.53483	+	0.436697i	0.0554557	+	0.0157785i
$767$			11.2354i			0.405686i
$768$		0			0
$769$	29.8413	+	8.49059i	1.07611	+	0.306178i	0.764890	−	0.644161i	$-0.222793\pi$
$769$	29.8413	+	8.49059i	1.07611	+	0.306178i	0.311215	+	0.950339i	$0.399264\pi$
$770$	−3.26301	−	8.42281i	−0.117591	−	0.303537i
$771$		0			0
$772$	9.23011	+	4.59605i	0.332199	+	0.165415i
$773$	−6.40058	−	3.18711i	−0.230213	−	0.114632i	0.326931	−	0.945048i	$-0.393985\pi$
$773$	−6.40058	−	3.18711i	−0.230213	−	0.114632i	−0.557144	+	0.830416i	$0.688103\pi$
$774$		0			0
$775$	0.372266	+	0.960928i	0.0133722	+	0.0345176i
$776$	6.32186	+	1.79872i	0.226942	+	0.0645704i
$777$		0			0
$778$			12.8775i			0.461681i
$779$	20.8237	+	5.92486i	0.746087	+	0.212280i
$780$		0			0
$781$	2.15829	+	0.836127i	0.0772298	+	0.0299190i
$782$	3.17557	−	0.294259i	0.113558	−	0.0105227i
$783$		0			0
$784$	0.145565	+	0.192759i	0.00519876	+	0.00688427i
$785$	7.21787	−	18.6315i	0.257617	−	0.664985i
$786$		0			0
$787$	0.632071	−	0.244866i	0.0225309	−	0.00872852i	−0.349950	−	0.936768i	$-0.613801\pi$
$787$	0.632071	−	0.244866i	0.0225309	−	0.00872852i	0.372481	+	0.928040i	$0.378507\pi$
$788$	11.8383	+	2.21296i	0.421721	+	0.0788333i
$789$		0			0
$790$	−2.36998	−	3.82766i	−0.0843203	−	0.136182i
$791$	−0.172686	+	1.86358i	−0.00614002	+	0.0662614i
$792$		0			0
$793$	−0.763242	−	2.68252i	−0.0271035	−	0.0952590i
$794$	−4.04506	+	3.68756i	−0.143554	+	0.130867i
$795$		0			0
$796$	14.5223	+	7.23123i	0.514728	+	0.256304i
$797$	0.817780	+	0.0757785i	0.0289672	+	0.00268421i	0.106742	−	0.994287i	$-0.465958\pi$
$797$	0.817780	+	0.0757785i	0.0289672	+	0.00268421i	−0.0777750	+	0.996971i	$0.524782\pi$
$798$		0			0
$799$	24.9131	−	2.30854i	0.881363	−	0.0816703i
$800$	13.6375	−	14.9596i	0.482159	−	0.528903i
$801$		0			0
$802$	13.2715	−	17.5744i	0.468634	−	0.620572i
$803$	−20.0563	+	51.7712i	−0.707771	+	1.82697i
$804$		0			0
$805$	−3.69370	−	5.96554i	−0.130186	−	0.210257i
$806$	−0.235241	+	0.311510i	−0.00828601	+	0.0109725i
$807$		0			0
$808$	−21.5421	+	6.12927i	−0.757850	+	0.215627i
$809$	7.59310	+	26.6870i	0.266959	+	0.938264i	0.973137	+	0.230229i	$0.0739475\pi$
$809$	7.59310	+	26.6870i	0.266959	+	0.938264i	−0.706178	+	0.708035i	$0.749582\pi$
$810$		0			0
$811$	−0.158643	−	0.848665i	−0.00557071	−	0.0298007i	0.980075	−	0.198629i	$-0.0636488\pi$
$811$	−0.158643	−	0.848665i	−0.00557071	−	0.0298007i	−0.985646	+	0.168828i	$0.946002\pi$
$812$	−6.87936	−	17.7577i	−0.241418	−	0.623173i
$813$		0			0
$814$	−8.28613	+	29.1227i	−0.290429	+	1.02075i
$815$	4.20784	+	8.45048i	0.147394	+	0.296007i
$816$		0			0
$817$	4.51673	+	24.1624i	0.158020	+	0.845334i
$818$	17.3232	+	1.60523i	0.605692	+	0.0561256i
$819$		0			0
$820$	−11.9506	−	9.02465i	−0.417332	−	0.315154i
$821$	−12.8085	+	20.6865i	−0.447021	+	0.721963i	−0.993290	−	0.115646i	$-0.963106\pi$
$821$	−12.8085	+	20.6865i	−0.447021	+	0.721963i	0.546270	+	0.837609i	$0.316047\pi$
$822$		0			0
$823$		−	6.05956i		−	0.211223i	−0.994407	−	0.105611i	$-0.966320\pi$
$823$		−	6.05956i		−	0.211223i	0.994407	−	0.105611i	$-0.0336800\pi$
$824$	−23.5353	+	6.40694i	−0.819893	+	0.223196i
$825$		0			0
$826$	−4.55828	−	9.15425i	−0.158603	−	0.318517i
$827$	−14.1728	−	8.77541i	−0.492836	−	0.305151i	0.257419	−	0.966300i	$-0.417128\pi$
$827$	−14.1728	−	8.77541i	−0.492836	−	0.305151i	−0.750255	+	0.661149i	$0.770069\pi$
$828$		0			0
$829$	9.50751	−	10.4292i	0.330210	−	0.362223i	−0.551368	−	0.834262i	$-0.685894\pi$
$829$	9.50751	−	10.4292i	0.330210	−	0.362223i	0.881577	+	0.472040i	$0.156482\pi$
$830$	0.395639	−	4.26963i	0.0137328	−	0.148201i
$831$		0			0
$832$	1.99581	+	0.373082i	0.0691924	+	0.0129343i
$833$	−0.320868	+	0.159773i	−0.0111174	+	0.00553582i
$834$		0			0
$835$	13.8753	−	6.90909i	0.480176	−	0.239099i
$836$	16.2400	−	6.29142i	0.561673	−	0.217593i
$837$		0			0
$838$	9.98933	+	13.2280i	0.345076	+	0.456954i
$839$	−17.0003	+	4.83699i	−0.586914	+	0.166992i	−0.554072	−	0.832469i	$-0.686927\pi$
$839$	−17.0003	+	4.83699i	−0.586914	+	0.166992i	−0.0328427	+	0.999461i	$0.510456\pi$
$840$		0			0
$841$	0.607415	+	6.55505i	0.0209453	+	0.226036i
$842$	19.9402	+	15.0582i	0.687185	+	0.518938i
$843$		0			0
$844$	−4.32511	−	23.1373i	−0.148876	−	0.796418i
$845$	10.5115	+	4.07216i	0.361605	+	0.140087i
$846$		0			0
$847$	7.25414	−	14.5683i	0.249255	−	0.500572i
$848$	−10.6791	−	9.73530i	−0.366722	−	0.334311i
$849$		0			0
$850$	3.06962	+	4.06483i	0.105287	+	0.139423i
$851$	−2.17013	+	23.4195i	−0.0743913	+	0.802810i
$852$		0			0
$853$	14.5998	+	13.3095i	0.499887	+	0.455707i	0.883938	−	0.467605i	$-0.154883\pi$
$853$	14.5998	+	13.3095i	0.499887	+	0.455707i	−0.384051	+	0.923312i	$0.625471\pi$
$854$	1.71019	+	1.87598i	0.0585213	+	0.0641949i
$855$		0			0
$856$	10.9154	−	9.95073i	0.373082	−	0.340109i
$857$	3.20362	+	0.296859i	0.109433	+	0.0101405i	0.146846	−	0.989159i	$-0.453088\pi$
$857$	3.20362	+	0.296859i	0.109433	+	0.0101405i	−0.0374122	+	0.999300i	$0.511911\pi$
$858$		0			0
$859$	−14.8831	+	24.0370i	−0.507803	+	0.820131i	−0.998694	−	0.0510906i	$-0.983730\pi$
$859$	−14.8831	+	24.0370i	−0.507803	+	0.820131i	0.490891	+	0.871221i	$0.336671\pi$
$860$	3.12419	−	16.7130i	0.106534	−	0.569907i
$861$		0			0
$862$	−22.2444	−	13.7731i	−0.757647	−	0.469115i
$863$	24.3092	+	9.41743i	0.827495	+	0.320573i	0.737481	−	0.675367i	$-0.236015\pi$
$863$	24.3092	+	9.41743i	0.827495	+	0.320573i	0.0900132	+	0.995941i	$0.471309\pi$
$864$		0			0
$865$	1.21129	−	1.10424i	0.0411851	−	0.0375452i
$866$	0.0487174	+	0.525745i	0.00165548	+	0.0178655i
$867$		0			0
$868$	−0.217783	+	1.16503i	−0.00739203	+	0.0395438i
$869$	6.14161	−	21.5855i	0.208340	−	0.732238i
$870$		0			0
$871$		−	25.4884i		−	0.863642i
$872$	−4.83612	+	16.9972i	−0.163772	+	0.575598i
$873$		0			0
$874$	−3.44806	+	2.13495i	−0.116632	+	0.0722157i
$875$	12.1369	−	24.3741i	0.410302	−	0.823997i
$876$		0			0
$877$	19.7091	+	31.8314i	0.665531	+	1.07487i	0.991577	+	0.129515i	$0.0413421\pi$
$877$	19.7091	+	31.8314i	0.665531	+	1.07487i	−0.326047	+	0.945354i	$0.605717\pi$
$878$	−3.45545	+	1.33865i	−0.116616	+	0.0451772i
$879$		0			0
$880$	−7.35278			−0.247862
$881$	−58.1348			−1.95861			−0.979306	−	0.202384i	$-0.935131\pi$
$881$	−58.1348			−1.95861			−0.979306	+	0.202384i	$0.935131\pi$
$882$		0			0
$883$	26.7675	+	5.00372i	0.900799	+	0.168389i	0.613725	−	0.789520i	$-0.289670\pi$
$883$	26.7675	+	5.00372i	0.900799	+	0.168389i	0.287074	+	0.957908i	$0.407317\pi$
$884$	2.32507	−	6.00171i	0.0782007	−	0.201859i
$885$		0			0
$886$	7.17492	+	7.87051i	0.241046	+	0.264415i
$887$	46.2994	−	34.9637i	1.55458	−	1.17397i	0.640837	−	0.767677i	$-0.278587\pi$
$887$	46.2994	−	34.9637i	1.55458	−	1.17397i	0.913745	−	0.406289i	$-0.133177\pi$
$888$		0			0
$889$	−22.3834	+	36.1505i	−0.750717	+	1.21245i
$890$	−3.52174	−	9.09067i	−0.118049	−	0.304720i
$891$		0			0
$892$	7.41764	+	4.59281i	0.248361	+	0.153779i
$893$	−27.0509	+	16.7492i	−0.905224	+	0.560491i
$894$		0			0
$895$	4.00372	+	4.39187i	0.133829	+	0.146804i
$896$	27.3282	−	7.77554i	0.912971	−	0.259763i
$897$		0			0
$898$	−9.78678	+	10.7356i	−0.326589	+	0.358251i
$899$	−0.621873	+	1.24889i	−0.0207406	+	0.0416528i
$900$		0			0
$901$	17.1127	−	12.9229i	0.570107	−	0.430525i
$902$	2.06484	+	22.2832i	0.0687518	+	0.741950i
$903$		0			0
$904$	−1.54040	−	0.767026i	−0.0512328	−	0.0255109i
$905$	−18.5336	−	13.9959i	−0.616078	−	0.465240i
$906$		0			0
$907$	22.6100	−	4.22655i	0.750754	−	0.140340i	0.205554	−	0.978646i	$-0.434101\pi$
$907$	22.6100	−	4.22655i	0.750754	−	0.140340i	0.545201	+	0.838306i	$0.316453\pi$
$908$	−20.1639	+	12.4850i	−0.669162	+	0.414328i
$909$		0			0
$910$	4.22688	−	0.391678i	0.140120	−	0.0129840i
$911$	1.74066	+	6.11779i	0.0576707	+	0.202692i	0.985307	−	0.170794i	$-0.0546332\pi$
$911$	1.74066	+	6.11779i	0.0576707	+	0.202692i	−0.927636	+	0.373485i	$0.878163\pi$
$912$		0			0
$913$	17.0578	−	12.8814i	0.564529	−	0.426313i
$914$	−20.8458	+	3.89676i	−0.689518	+	0.128893i
$915$		0			0
$916$	−0.736423	−	1.47894i	−0.0243321	−	0.0488654i
$917$	−7.44630	−	2.11865i	−0.245898	−	0.0699641i
$918$		0			0
$919$	−2.69880	+	14.4373i	−0.0890250	+	0.476242i	0.909183	+	0.416397i	$0.136708\pi$
$919$	−2.69880	+	14.4373i	−0.0890250	+	0.476242i	−0.998208	+	0.0598444i	$0.980940\pi$
$920$	6.34141	−	1.18541i	0.209070	−	0.0390820i
$921$		0			0
$922$	−10.4421	−	9.51923i	−0.343892	−	0.313499i
$923$	−0.655516	+	0.868044i	−0.0215766	+	0.0285720i
$924$		0			0
$925$	−33.6270	+	16.7443i	−1.10565	+	0.550548i
$926$	15.5542			0.511142
$927$		0			0
$928$	27.4055			0.899630
$929$	−39.5643	+	19.7007i	−1.29806	+	0.646358i	−0.956013	−	0.293324i	$-0.905239\pi$
$929$	−39.5643	+	19.7007i	−1.29806	+	0.646358i	−0.342049	+	0.939682i	$0.611121\pi$
$930$		0			0
$931$	0.274692	−	0.363751i	0.00900266	−	0.0119214i
$932$	−5.65749	−	5.15748i	−0.185317	−	0.168939i
$933$		0			0
$934$	−18.3719	+	3.43431i	−0.601148	+	0.112374i
$935$	2.00493	−	10.7254i	0.0655681	−	0.350758i
$936$		0			0
$937$	56.3240	+	16.0256i	1.84003	+	0.523532i	0.999824	−	0.0187425i	$-0.00596628\pi$
$937$	56.3240	+	16.0256i	1.84003	+	0.523532i	0.840201	+	0.542275i	$0.182437\pi$
$938$	10.3408	+	20.7672i	0.337641	+	0.678074i
$939$		0			0
$940$	21.6325	−	4.04382i	0.705576	−	0.131895i
$941$	13.3971	−	10.1170i	0.436732	−	0.329805i	−0.361268	−	0.932462i	$-0.617656\pi$
$941$	13.3971	−	10.1170i	0.436732	−	0.329805i	0.798000	+	0.602657i	$0.205891\pi$
$942$		0			0
$943$	4.75717	+	16.7197i	0.154915	+	0.544469i
$944$	−8.28885	+	0.768075i	−0.269779	+	0.0249987i
$945$		0			0
$946$	−21.6023	+	13.3756i	−0.702351	+	0.434877i
$947$	−40.8055	+	7.62787i	−1.32600	+	0.247872i	−0.798660	−	0.601782i	$-0.794458\pi$
$947$	−40.8055	+	7.62787i	−1.32600	+	0.247872i	−0.527340	+	0.849654i	$0.676811\pi$
$948$		0			0
$949$	−20.8219	−	15.7239i	−0.675906	−	0.510421i
$950$	−5.79828	−	2.88720i	−0.188121	−	0.0936732i
$951$		0			0
$952$	1.24311	+	13.4153i	0.0402895	+	0.434793i
$953$	32.1207	−	24.2564i	1.04049	−	0.785742i	0.0632757	−	0.997996i	$-0.479845\pi$
$953$	32.1207	−	24.2564i	1.04049	−	0.785742i	0.977214	+	0.212254i	$0.0680805\pi$
$954$		0			0
$955$	1.19694	−	2.40378i	0.0387321	−	0.0777845i
$956$	7.45286	−	8.17540i	0.241043	−	0.264411i
$957$		0			0
$958$	−15.8231	+	4.50206i	−0.511221	+	0.145455i
$959$	33.7464	+	37.0180i	1.08973	+	1.19538i
$960$		0			0
$961$	−26.2829	+	16.2737i	−0.847836	+	0.524958i
$962$	−12.0982	−	7.49088i	−0.390061	−	0.241516i
$963$		0			0
$964$	−9.84731	−	25.4188i	−0.317161	−	0.818686i
$965$	−4.32449	+	6.98430i	−0.139210	+	0.224832i
$966$		0			0
$967$	22.4220	−	16.9323i	0.721043	−	0.544507i	−0.177109	−	0.984191i	$-0.556674\pi$
$967$	22.4220	−	16.9323i	0.721043	−	0.544507i	0.898152	+	0.439685i	$0.144910\pi$
$968$	10.0808	+	11.0581i	0.324009	+	0.355421i
$969$		0			0
$970$	−0.822525	+	2.12318i	−0.0264097	+	0.0681713i
$971$	−44.4899	−	8.31660i	−1.42775	−	0.266892i	−0.587557	−	0.809183i	$-0.699910\pi$
$971$	−44.4899	−	8.31660i	−1.42775	−	0.266892i	−0.840191	+	0.542291i	$0.817557\pi$
$972$		0			0
$973$	52.3771			1.67913
$974$	15.2887			0.489882
$975$		0			0
$976$	1.92684	−	0.746462i	0.0616767	−	0.0238937i
$977$	−1.84592	−	2.98126i	−0.0590562	−	0.0953791i	0.819350	−	0.573293i	$-0.194334\pi$
$977$	−1.84592	−	2.98126i	−0.0590562	−	0.0953791i	−0.878407	+	0.477914i	$0.841393\pi$
$978$		0			0
$979$	21.6622	−	43.5036i	0.692327	−	1.39038i
$980$	−0.268062	+	0.165977i	−0.00856293	+	0.00530194i
$981$		0			0
$982$	−8.13932	+	28.6068i	−0.259736	+	0.912878i
$983$			57.1040i			1.82133i	0.413141	+	0.910667i	$0.364432\pi$
$983$			57.1040i			1.82133i	−0.413141	+	0.910667i	$0.635568\pi$
$984$		0			0
$985$	−2.62573	+	9.22850i	−0.0836628	+	0.294044i
$986$	−1.26714	+	6.77857i	−0.0403538	+	0.215874i
$987$		0			0
$988$	0.755194	+	8.14985i	0.0240259	+	0.259281i
$989$	−14.5854	+	13.2963i	−0.463788	+	0.422799i
$990$		0			0
$991$	−1.96679	−	0.761940i	−0.0624773	−	0.0242038i	0.329800	−	0.944051i	$-0.393019\pi$
$991$	−1.96679	−	0.761940i	−0.0624773	−	0.0242038i	−0.392278	+	0.919847i	$0.628313\pi$
$992$	−1.45016	−	0.897898i	−0.0460425	−	0.0285083i
$993$		0			0
$994$	0.181924	−	0.973205i	0.00577026	−	0.0308682i
$995$	−6.80398	+	10.9888i	−0.215701	+	0.348369i
$996$		0			0
$997$	−47.1724	−	4.37117i	−1.49397	−	0.138436i	−0.685972	−	0.727628i	$-0.740623\pi$
$997$	−47.1724	−	4.37117i	−1.49397	−	0.138436i	−0.807993	+	0.589192i	$0.799446\pi$
$998$	5.74179	−	5.23434i	0.181753	−	0.165690i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	927.2.w.a.80.15	✓	576
3.2	odd	2	inner	927.2.w.a.80.22	yes	576
103.94	odd	34	inner	927.2.w.a.197.22	yes	576
309.197	even	34	inner	927.2.w.a.197.15	yes	576

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
927.2.w.a.80.15	✓	576	1.1	even	1	trivial
927.2.w.a.80.22	yes	576	3.2	odd	2	inner
927.2.w.a.197.15	yes	576	309.197	even	34	inner
927.2.w.a.197.22	yes	576	103.94	odd	34	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:	\( N \)	\(=\)	\( 927 = 3^{2} \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	927.w (of order \(34\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.607968 + 0.302732i) q^{2} +(-0.927291 + 1.22793i) q^{4} +(-0.905941 - 0.825874i) q^{5} +(-2.56947 + 0.480316i) q^{7} +(0.441623 - 2.36248i) q^{8} +O(q^{10})\)	\(q+(-0.607968 + 0.302732i) q^{2} +(-0.927291 + 1.22793i) q^{4} +(-0.905941 - 0.825874i) q^{5} +(-2.56947 + 0.480316i) q^{7} +(0.441623 - 2.36248i) q^{8} +(0.800802 + 0.227848i) q^{10} +(1.85000 + 3.71530i) q^{11} +(-1.91729 + 0.358404i) q^{13} +(1.41675 - 1.06988i) q^{14} +(-0.395481 - 1.38997i) q^{16} +(2.13537 - 0.197872i) q^{17} +(-2.31861 + 1.43562i) q^{19} +(1.85419 - 0.346608i) q^{20} +(-2.24948 - 1.69873i) q^{22} +(-1.96007 - 0.975997i) q^{23} +(-0.322681 - 3.48229i) q^{25} +(1.05715 - 0.798324i) q^{26} +(1.79285 - 3.60052i) q^{28} +(3.18971 - 3.49895i) q^{29} +(-0.283420 + 0.0806400i) q^{31} +(3.89955 + 4.27760i) q^{32} +(-1.23834 + 0.766746i) q^{34} +(2.72446 + 1.68692i) q^{35} +(-3.88028 - 10.0162i) q^{37} +(0.975032 - 1.57473i) q^{38} +(-2.35119 + 1.77554i) q^{40} +(-5.34845 - 5.86697i) q^{41} +(3.25610 - 8.40496i) q^{43} +(-6.27762 - 1.17349i) q^{44} +1.48712 q^{46} +11.6669 q^{47} +(-0.155858 + 0.0603798i) q^{49} +(1.25038 + 2.01943i) q^{50} +(1.33779 - 2.68665i) q^{52} +(8.50169 - 5.26402i) q^{53} +(1.39238 - 4.89371i) q^{55} +6.28242i q^{56} +(-0.879999 + 3.09287i) q^{58} +(1.05844 - 5.66217i) q^{59} +(0.131933 + 1.42378i) q^{61} +(0.147898 - 0.134827i) q^{62} +(-0.970661 - 0.376036i) q^{64} +(2.03295 + 1.25875i) q^{65} +(-2.40117 + 12.8451i) q^{67} +(-1.73714 + 2.80558i) q^{68} +(-2.16707 - 0.200809i) q^{70} +(0.412129 - 0.375705i) q^{71} +(9.01207 + 9.88577i) q^{73} +(5.39130 + 4.91482i) q^{74} +(0.387180 - 4.17833i) q^{76} +(-6.53803 - 8.65775i) q^{77} +(-3.99599 - 3.64282i) q^{79} +(-0.789660 + 1.58585i) q^{80} +(5.02781 + 1.94778i) q^{82} +(-0.946334 - 5.06244i) q^{83} +(-2.09794 - 1.58429i) q^{85} +(0.564848 + 6.09568i) q^{86} +(9.59431 - 2.72982i) q^{88} +(-7.05643 - 9.34423i) q^{89} +(4.75426 - 1.84181i) q^{91} +(3.01601 - 1.50179i) q^{92} +(-7.09308 + 3.53193i) q^{94} +(3.28617 + 0.614291i) q^{95} +(-0.252334 + 2.72312i) q^{97} +(0.0764779 - 0.0838922i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 576 q + 40 q^{4} - 16 q^{7}+O(q^{10}) \) 576 * q + 40 * q^4 - 16 * q^7	\( 576 q + 40 q^{4} - 16 q^{7} - 136 q^{10} + 8 q^{13} - 64 q^{16} - 8 q^{19} - 132 q^{25} + 228 q^{28} + 180 q^{34} - 108 q^{49} - 16 q^{52} + 8 q^{55} - 96 q^{58} + 32 q^{61} - 84 q^{64} + 204 q^{73} + 80 q^{76} + 40 q^{79} + 128 q^{82} - 68 q^{85} - 68 q^{88} - 284 q^{91} - 136 q^{94} - 424 q^{97}+O(q^{100}) \) 576 * q + 40 * q^4 - 16 * q^7 - 136 * q^10 + 8 * q^13 - 64 * q^16 - 8 * q^19 - 132 * q^25 + 228 * q^28 + 180 * q^34 - 108 * q^49 - 16 * q^52 + 8 * q^55 - 96 * q^58 + 32 * q^61 - 84 * q^64 + 204 * q^73 + 80 * q^76 + 40 * q^79 + 128 * q^82 - 68 * q^85 - 68 * q^88 - 284 * q^91 - 136 * q^94 - 424 * q^97

Introduction

L-functions

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