LMFDB - Embedded newform 621.2.s.a.251.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [621,2,Mod(17,621)] 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("621.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(621, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([55, 21])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 621 = 3^{3} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	621.s (of order $66$, degree $20$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.95870996552$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	no (minimal twist has level 207)
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			251.16
Character	$\chi$	$=$	621.251
Dual form			621.2.s.a.287.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.672471 + 1.30441i) q^{2} +(-0.0891590 + 0.125206i) q^{4} +(0.637451 + 2.62761i) q^{5} +(0.985992 - 0.341255i) q^{7} +(2.68195 + 0.385606i) q^{8} +(-2.99882 + 2.59849i) q^{10} +(0.0523085 + 1.09809i) q^{11} +(0.273590 - 0.790486i) q^{13} +(1.10819 + 1.05666i) q^{14} +(1.40109 + 4.04818i) q^{16} +(1.94122 - 4.25068i) q^{17} +(-2.86472 + 1.30827i) q^{19} +(-0.385828 - 0.154462i) q^{20} +(-1.39719 + 0.806666i) q^{22} +(-0.391306 + 4.77984i) q^{23} +(-2.05380 + 1.05881i) q^{25} +(1.21510 - 0.174705i) q^{26} +(-0.0451828 + 0.153878i) q^{28} +(-2.31627 + 1.64941i) q^{29} +(-0.469073 + 0.187789i) q^{31} +(-0.598728 + 0.627927i) q^{32} +(6.85005 - 0.326308i) q^{34} +(1.52521 + 2.37327i) q^{35} +(-0.606716 - 2.06629i) q^{37} +(-3.63297 - 2.85700i) q^{38} +(0.696389 + 7.29292i) q^{40} +(-8.46710 + 2.05410i) q^{41} +(4.37823 - 10.9363i) q^{43} +(-0.142152 - 0.0913553i) q^{44} +(-6.49802 + 2.70388i) q^{46} +(10.9285 + 6.30957i) q^{47} +(-4.64665 + 3.65416i) q^{49} +(-2.76225 - 1.96699i) q^{50} +(0.0745809 + 0.104734i) q^{52} +(-5.36725 + 6.19414i) q^{53} +(-2.85201 + 0.837425i) q^{55} +(2.77597 - 0.535025i) q^{56} +(-3.70913 - 1.91219i) q^{58} +(-4.38212 - 1.51667i) q^{59} +(1.61936 - 2.05918i) q^{61} +(-0.560392 - 0.485582i) q^{62} +(6.99883 + 2.05504i) q^{64} +(2.25149 + 0.214991i) q^{65} +(-1.38147 - 0.0658073i) q^{67} +(0.359135 + 0.622040i) q^{68} +(-2.07006 + 3.58545i) q^{70} +(4.43366 - 6.89892i) q^{71} +(-1.42222 - 3.11423i) q^{73} +(2.28729 - 2.18092i) q^{74} +(0.0916114 - 0.475325i) q^{76} +(0.426305 + 1.06486i) q^{77} +(-2.89846 - 15.0386i) q^{79} +(-9.74392 + 6.26203i) q^{80} +(-8.37327 - 9.66327i) q^{82} +(3.17600 - 13.0917i) q^{83} +(12.4066 + 2.39117i) q^{85} +(17.2096 - 1.64332i) q^{86} +(-0.283142 + 2.96519i) q^{88} +(-2.12858 - 14.8046i) q^{89} -0.872777i q^{91} +(-0.563578 - 0.475160i) q^{92} +(-0.881181 + 18.4983i) q^{94} +(-5.26374 - 6.69340i) q^{95} +(5.31660 + 5.57589i) q^{97} +(-7.89127 - 3.60382i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q + 27 q^{2} - 29 q^{4} + 33 q^{5} - 11 q^{7} - 44 q^{10} + 33 q^{11} - 9 q^{13} + 33 q^{14} + 3 q^{16} - 44 q^{19} + 33 q^{20} + 27 q^{23} + 11 q^{25} - 44 q^{28} - 27 q^{29} - 3 q^{31} + 33 q^{32}+ \cdots + 22 q^{97}+O(q^{100}) $ 440 * q + 27 * q^2 - 29 * q^4 + 33 * q^5 - 11 * q^7 - 44 * q^10 + 33 * q^11 - 9 * q^13 + 33 * q^14 + 3 * q^16 - 44 * q^19 + 33 * q^20 + 27 * q^23 + 11 * q^25 - 44 * q^28 - 27 * q^29 - 3 * q^31 + 33 * q^32 - 11 * q^34 - 44 * q^37 + 33 * q^38 - 77 * q^40 - 9 * q^41 - 11 * q^43 - 36 * q^46 + 120 * q^47 + 35 * q^49 + 3 * q^50 - 38 * q^52 - 44 * q^55 - 165 * q^56 - 10 * q^58 + 9 * q^59 - 11 * q^61 - 22 * q^64 - 198 * q^65 - 11 * q^67 - 70 * q^70 - 36 * q^73 - 231 * q^74 - 11 * q^76 - 39 * q^77 - 11 * q^79 - 10 * q^82 - 66 * q^83 + q^85 + 33 * q^86 - 99 * q^88 - 63 * q^92 - 42 * q^94 + 93 * q^95 + 22 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/621\mathbb{Z}\right)^\times$.

$n$	$28$	$461$
$\chi(n)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.672471	+	1.30441i	0.475509	+	0.922358i	0.997585	+	0.0694594i	$0.0221274\pi$
$2$	0.672471	+	1.30441i	0.475509	+	0.922358i	−0.522076	+	0.852899i	$0.674842\pi$
$3$		0			0
$3$		0			0
$4$	−0.0891590	+	0.125206i	−0.0445795	+	0.0626032i
$5$	0.637451	+	2.62761i	0.285077	+	1.17510i	0.916619	+	0.399761i	$0.130907\pi$
$5$	0.637451	+	2.62761i	0.285077	+	1.17510i	−0.631543	+	0.775341i	$0.717578\pi$
$6$		0			0
$7$	0.985992	−	0.341255i	0.372670	−	0.128982i	−0.134312	−	0.990939i	$-0.542882\pi$
$7$	0.985992	−	0.341255i	0.372670	−	0.128982i	0.506982	+	0.861957i	$0.330761\pi$
$8$	2.68195	+	0.385606i	0.948213	+	0.136332i
$9$		0			0
$10$	−2.99882	+	2.59849i	−0.948309	+	0.821714i
$11$	0.0523085	+	1.09809i	0.0157716	+	0.331087i	0.992940	+	0.118619i	$0.0378468\pi$
$11$	0.0523085	+	1.09809i	0.0157716	+	0.331087i	−0.977168	+	0.212467i	$0.931850\pi$
$12$		0			0
$13$	0.273590	−	0.790486i	0.0758802	−	0.219241i	−0.900681	−	0.434481i	$-0.856932\pi$
$13$	0.273590	−	0.790486i	0.0758802	−	0.219241i	0.976561	+	0.215239i	$0.0690531\pi$
$14$	1.10819	+	1.05666i	0.296176	+	0.282403i
$15$		0			0
$16$	1.40109	+	4.04818i	0.350273	+	1.01205i
$17$	1.94122	−	4.25068i	0.470815	−	1.03094i	−0.514072	−	0.857747i	$-0.671864\pi$
$17$	1.94122	−	4.25068i	0.470815	−	1.03094i	0.984888	−	0.173195i	$-0.0554090\pi$
$18$		0			0
$19$	−2.86472	+	1.30827i	−0.657211	+	0.300138i	−0.715967	−	0.698134i	$-0.754014\pi$
$19$	−2.86472	+	1.30827i	−0.657211	+	0.300138i	0.0587558	+	0.998272i	$0.481287\pi$
$20$	−0.385828	−	0.154462i	−0.0862737	−	0.0345388i
$21$		0			0
$22$	−1.39719	+	0.806666i	−0.297881	+	0.171982i
$23$	−0.391306	+	4.77984i	−0.0815929	+	0.996666i
$23$	−0.391306	+	4.77984i	−0.0815929	+	0.996666i
$24$		0			0
$25$	−2.05380	+	1.05881i	−0.410761	+	0.211762i
$26$	1.21510	−	0.174705i	0.238301	−	0.0342625i
$27$		0			0
$28$	−0.0451828	+	0.153878i	−0.00853874	+	0.0290803i
$29$	−2.31627	+	1.64941i	−0.430120	+	0.306287i	−0.774536	−	0.632530i	$-0.782016\pi$
$29$	−2.31627	+	1.64941i	−0.430120	+	0.306287i	0.344416	+	0.938817i	$0.388077\pi$
$30$		0			0
$31$	−0.469073	+	0.187789i	−0.0842480	+	0.0337278i	−0.413404	−	0.910548i	$-0.635660\pi$
$31$	−0.469073	+	0.187789i	−0.0842480	+	0.0337278i	0.329156	+	0.944276i	$0.393236\pi$
$32$	−0.598728	+	0.627927i	−0.105841	+	0.111003i
$33$		0			0
$34$	6.85005	−	0.326308i	1.17477	−	0.0559614i
$35$	1.52521	+	2.37327i	0.257807	+	0.401155i
$36$		0			0
$37$	−0.606716	−	2.06629i	−0.0997435	−	0.339695i	0.894469	−	0.447131i	$-0.147554\pi$
$37$	−0.606716	−	2.06629i	−0.0997435	−	0.339695i	−0.994212	+	0.107436i	$0.965736\pi$
$38$	−3.63297	−	2.85700i	−0.589345	−	0.463466i
$39$		0			0
$40$	0.696389	+	7.29292i	0.110109	+	1.15311i
$41$	−8.46710	+	2.05410i	−1.32234	+	0.320796i	−0.833955	−	0.551833i	$-0.813929\pi$
$41$	−8.46710	+	2.05410i	−1.32234	+	0.320796i	−0.488384	+	0.872629i	$0.662414\pi$
$42$		0			0
$43$	4.37823	−	10.9363i	0.667673	−	1.66777i	−0.0742144	−	0.997242i	$-0.523645\pi$
$43$	4.37823	−	10.9363i	0.667673	−	1.66777i	0.741887	−	0.670524i	$-0.233931\pi$
$44$	−0.142152	−	0.0913553i	−0.0214302	−	0.0137723i
$45$		0			0
$46$	−6.49802	+	2.70388i	−0.958081	+	0.398665i
$47$	10.9285	+	6.30957i	1.59408	+	0.920345i	0.992596	+	0.121464i	$0.0387589\pi$
$47$	10.9285	+	6.30957i	1.59408	+	0.920345i	0.601489	+	0.798881i	$0.294574\pi$
$48$		0			0
$49$	−4.64665	+	3.65416i	−0.663807	+	0.522023i
$50$	−2.76225	−	1.96699i	−0.390641	−	0.278174i
$51$		0			0
$52$	0.0745809	+	0.104734i	0.0103425	+	0.0145240i
$53$	−5.36725	+	6.19414i	−0.737249	+	0.850830i	−0.993268	−	0.115841i	$-0.963044\pi$
$53$	−5.36725	+	6.19414i	−0.737249	+	0.850830i	0.256019	+	0.966672i	$0.417589\pi$
$54$		0			0
$55$	−2.85201	+	0.837425i	−0.384564	+	0.112918i
$56$	2.77597	−	0.535025i	0.370955	−	0.0714957i
$57$		0			0
$58$	−3.70913	−	1.91219i	−0.487032	−	0.251083i
$59$	−4.38212	−	1.51667i	−0.570504	−	0.197453i	0.0265597	−	0.999647i	$-0.491545\pi$
$59$	−4.38212	−	1.51667i	−0.570504	−	0.197453i	−0.597064	+	0.802194i	$0.703666\pi$
$60$		0			0
$61$	1.61936	−	2.05918i	0.207337	−	0.263651i	−0.671252	−	0.741229i	$-0.734243\pi$
$61$	1.61936	−	2.05918i	0.207337	−	0.263651i	0.878589	+	0.477579i	$0.158485\pi$
$62$	−0.560392	−	0.485582i	−0.0711698	−	0.0616690i
$63$		0			0
$64$	6.99883	+	2.05504i	0.874853	+	0.256880i
$65$	2.25149	+	0.214991i	0.279263	+	0.0266664i
$66$		0			0
$67$	−1.38147	−	0.0658073i	−0.168773	−	0.00803964i	−0.0369746	−	0.999316i	$-0.511772\pi$
$67$	−1.38147	−	0.0658073i	−0.168773	−	0.00803964i	−0.131798	+	0.991277i	$0.542075\pi$
$68$	0.359135	+	0.622040i	0.0435515	+	0.0754334i
$69$		0			0
$70$	−2.07006	+	3.58545i	−0.247420	+	0.428543i
$71$	4.43366	−	6.89892i	0.526179	−	0.818751i	−0.471839	−	0.881685i	$-0.656409\pi$
$71$	4.43366	−	6.89892i	0.526179	−	0.818751i	0.998018	+	0.0629343i	$0.0200459\pi$
$72$		0			0
$73$	−1.42222	−	3.11423i	−0.166458	−	0.364493i	0.807959	−	0.589238i	$-0.200572\pi$
$73$	−1.42222	−	3.11423i	−0.166458	−	0.364493i	−0.974417	+	0.224746i	$0.927845\pi$
$74$	2.28729	−	2.18092i	0.265892	−	0.253527i
$75$		0			0
$76$	0.0916114	−	0.475325i	0.0105085	−	0.0545235i
$77$	0.426305	+	1.06486i	0.0485819	+	0.121352i
$78$		0			0
$79$	−2.89846	−	15.0386i	−0.326102	−	1.69198i	−0.661534	−	0.749915i	$-0.730094\pi$
$79$	−2.89846	−	15.0386i	−0.326102	−	1.69198i	0.335432	−	0.942064i	$-0.391118\pi$
$80$	−9.74392	+	6.26203i	−1.08940	+	0.700117i
$81$		0			0
$82$	−8.37327	−	9.66327i	−0.924673	−	1.06713i
$83$	3.17600	−	13.0917i	0.348612	−	1.43700i	−0.480047	−	0.877243i	$-0.659381\pi$
$83$	3.17600	−	13.0917i	0.348612	−	1.43700i	0.828659	−	0.559754i	$-0.189104\pi$
$84$		0			0
$85$	12.4066	+	2.39117i	1.34568	+	0.259359i
$86$	17.2096	−	1.64332i	1.85576	−	0.177204i
$87$		0			0
$88$	−0.283142	+	2.96519i	−0.0301830	+	0.316091i
$89$	−2.12858	−	14.8046i	−0.225629	−	1.56929i	−0.716206	−	0.697889i	$-0.754123\pi$
$89$	−2.12858	−	14.8046i	−0.225629	−	1.56929i	0.490577	−	0.871398i	$-0.336786\pi$
$90$		0			0
$91$		−	0.872777i		−	0.0914919i
$92$	−0.563578	−	0.475160i	−0.0587571	−	0.0495389i
$93$		0			0
$94$	−0.881181	+	18.4983i	−0.0908868	+	1.90795i
$95$	−5.26374	−	6.69340i	−0.540049	−	0.686728i
$96$		0			0
$97$	5.31660	+	5.57589i	0.539819	+	0.566146i	0.935988	−	0.352032i	$-0.114509\pi$
$97$	5.31660	+	5.57589i	0.539819	+	0.566146i	−0.396169	+	0.918177i	$0.629661\pi$
$98$	−7.89127	−	3.60382i	−0.797139	−	0.364041i
$99$		0			0
$100$	0.0505455	−	0.351552i	0.00505455	−	0.0351552i
$101$	−6.80833	−	1.65168i	−0.677454	−	0.164349i	−0.117753	−	0.993043i	$-0.537569\pi$
$101$	−6.80833	−	1.65168i	−0.677454	−	0.164349i	−0.559702	+	0.828694i	$0.689084\pi$
$102$		0			0
$103$	3.71857	−	7.21302i	0.366402	−	0.710720i	−0.631506	−	0.775371i	$-0.717563\pi$
$103$	3.71857	−	7.21302i	0.366402	−	0.710720i	0.997908	+	0.0646506i	$0.0205933\pi$
$104$	1.03857	−	2.01455i	0.101840	−	0.197543i
$105$		0			0
$106$	−11.6890	−	2.83573i	−1.13534	−	0.275430i
$107$	0.331396	−	2.30491i	0.0320372	−	0.222824i	−0.967513	−	0.252822i	$-0.918641\pi$
$107$	0.331396	−	2.30491i	0.0320372	−	0.222824i	0.999550	+	0.0299985i	$0.00955025\pi$
$108$		0			0
$109$	3.38104	+	1.54407i	0.323845	+	0.147895i	0.570703	−	0.821157i	$-0.306671\pi$
$109$	3.38104	+	1.54407i	0.323845	+	0.147895i	−0.246858	+	0.969052i	$0.579398\pi$
$110$	−3.01024	−	3.15705i	−0.287015	−	0.301013i
$111$		0			0
$112$	2.76293	+	3.51335i	0.261072	+	0.331980i
$113$	0.0994895	−	2.08854i	0.00935918	−	0.196473i	−0.989345	−	0.145588i	$-0.953493\pi$
$113$	0.0994895	−	2.08854i	0.00935918	−	0.196473i	0.998704	−	0.0508855i	$-0.0162043\pi$
$114$		0			0
$115$	−12.8090	+	2.01871i	−1.19444	+	0.188246i
$116$		−	0.437071i		−	0.0405810i
$117$		0			0
$118$	−0.968492	−	6.73601i	−0.0891569	−	0.620100i
$119$	0.463461	−	4.85359i	0.0424854	−	0.444928i
$120$		0			0
$121$	9.74713	−	0.930738i	0.886102	−	0.0846125i
$122$	3.77499	+	0.727569i	0.341771	+	0.0658710i
$123$		0			0
$124$	0.0183098	−	0.0754740i	0.00164427	−	0.00677776i
$125$	4.76181	+	5.49542i	0.425909	+	0.491525i
$126$		0			0
$127$	−5.27382	+	3.38928i	−0.467976	+	0.300750i	−0.753295	−	0.657683i	$-0.771537\pi$
$127$	−5.27382	+	3.38928i	−0.467976	+	0.300750i	0.285319	+	0.958433i	$0.407900\pi$
$128$	2.35429	+	12.2152i	0.208091	+	1.07968i
$129$		0			0
$130$	1.23362	+	3.08144i	0.108196	+	0.270260i
$131$	−2.45141	+	12.7191i	−0.214181	+	1.11127i	0.702509	+	0.711675i	$0.252063\pi$
$131$	−2.45141	+	12.7191i	−0.214181	+	1.11127i	−0.916690	+	0.399600i	$0.869149\pi$
$132$		0			0
$133$	−2.37813	+	2.26755i	−0.206210	+	0.196621i
$134$	−0.843156	−	1.84625i	−0.0728376	−	0.159492i
$135$		0			0
$136$	6.84535	−	10.6516i	0.586984	−	0.913365i
$137$	−4.68128	+	8.10821i	−0.399949	+	0.692731i	−0.993719	−	0.111903i	$-0.964305\pi$
$137$	−4.68128	+	8.10821i	−0.399949	+	0.692731i	0.593771	+	0.804634i	$0.297639\pi$
$138$		0			0
$139$	−6.12117	−	10.6022i	−0.519191	−	0.899265i	−0.999751	−	0.0223035i	$-0.992900\pi$
$139$	−6.12117	−	10.6022i	−0.519191	−	0.899265i	0.480560	−	0.876962i	$-0.340433\pi$
$140$	−0.433134	−	0.0206327i	−0.0366065	−	0.00174378i
$141$		0			0
$142$	11.9805	+	1.14400i	1.00538	+	0.0960026i
$143$	0.882336	+	0.259077i	0.0737847	+	0.0216651i
$144$		0			0
$145$	−5.81050	−	5.03483i	−0.482536	−	0.418120i
$146$	3.10583	−	3.94939i	0.257040	−	0.326854i
$147$		0			0
$148$	0.312806	+	0.108263i	0.0257125	+	0.00889919i
$149$	−2.64274	−	1.36242i	−0.216501	−	0.111614i	0.346565	−	0.938026i	$-0.387348\pi$
$149$	−2.64274	−	1.36242i	−0.216501	−	0.111614i	−0.563066	+	0.826412i	$0.690378\pi$
$150$		0			0
$151$	19.2531	−	3.71072i	1.56679	−	0.301974i	0.669296	−	0.742996i	$-0.266596\pi$
$151$	19.2531	−	3.71072i	1.56679	−	0.301974i	0.897496	+	0.441022i	$0.145384\pi$
$152$	−8.18751	+	2.40407i	−0.664095	+	0.194996i
$153$		0			0
$154$	−1.10233	+	1.27216i	−0.0888287	+	0.102514i
$155$	−0.792446	−	1.11283i	−0.0636508	−	0.0893850i
$156$		0			0
$157$	−12.5164	−	8.91288i	−0.998916	−	0.711325i	−0.0412330	−	0.999150i	$-0.513129\pi$
$157$	−12.5164	−	8.91288i	−0.998916	−	0.711325i	−0.957683	+	0.287825i	$0.907068\pi$
$158$	17.6675	−	13.8938i	1.40555	−	1.10533i
$159$		0			0
$160$	−2.03161	−	1.17295i	−0.160613	−	0.0927297i
$161$	1.24532	+	4.84642i	0.0981450	+	0.381951i
$162$		0			0
$163$	−0.973816	−	0.625834i	−0.0762752	−	0.0490191i	0.501947	−	0.864898i	$-0.332617\pi$
$163$	−0.973816	−	0.625834i	−0.0762752	−	0.0490191i	−0.578223	+	0.815879i	$0.696253\pi$
$164$	0.497733	−	1.24328i	0.0388664	−	0.0970836i
$165$		0			0
$166$	19.2127	−	4.66095i	1.49119	−	0.361760i
$167$	−2.33707	−	24.4749i	−0.180848	−	1.89392i	−0.397393	−	0.917649i	$-0.630085\pi$
$167$	−2.33707	−	24.4749i	−0.180848	−	1.89392i	0.216545	−	0.976273i	$-0.430521\pi$
$168$		0			0
$169$	9.66867	+	7.60353i	0.743744	+	0.584887i
$170$	5.22398	+	17.7913i	0.400661	+	1.36453i
$171$		0			0
$172$	0.978933	+	1.52325i	0.0746429	+	0.116147i
$173$	−15.5344	+	0.739995i	−1.18106	+	0.0562608i	−0.628906	−	0.777482i	$-0.716497\pi$
$173$	−15.5344	+	0.739995i	−1.18106	+	0.0562608i	−0.552154	+	0.833742i	$0.686194\pi$
$174$		0			0
$175$	−1.66371	+	1.74485i	−0.125765	+	0.131898i
$176$	−4.37198	+	1.75028i	−0.329551	+	0.131932i
$177$		0			0
$178$	17.8799	−	12.7322i	1.34016	−	0.954321i
$179$	4.07254	−	13.8698i	0.304396	−	1.03668i	−0.655238	−	0.755423i	$-0.727432\pi$
$179$	4.07254	−	13.8698i	0.304396	−	1.03668i	0.959633	−	0.281254i	$-0.0907503\pi$
$180$		0			0
$181$	12.9898	−	1.86766i	0.965527	−	0.138822i	0.358523	−	0.933521i	$-0.383280\pi$
$181$	12.9898	−	1.86766i	0.965527	−	0.138822i	0.607004	+	0.794699i	$0.292371\pi$
$182$	1.13846	−	0.586917i	0.0843883	−	0.0435052i
$183$		0			0
$184$	−2.89260	+	12.6684i	−0.213245	+	0.933927i
$185$	5.04264	−	2.91137i	0.370742	−	0.214048i
$186$		0			0
$187$	4.76917	+	1.90929i	0.348757	+	0.139621i
$188$	−1.76437	+	0.805762i	−0.128680	+	0.0587662i
$189$		0			0
$190$	5.19123	−	11.3672i	0.376611	−	0.824664i
$191$	8.25170	+	23.8417i	0.597072	+	1.72513i	0.684556	+	0.728960i	$0.259996\pi$
$191$	8.25170	+	23.8417i	0.597072	+	1.72513i	−0.0874844	+	0.996166i	$0.527883\pi$
$192$		0			0
$193$	13.4446	+	12.8194i	0.967767	+	0.922764i	0.997046	−	0.0768077i	$-0.0244727\pi$
$193$	13.4446	+	12.8194i	0.967767	+	0.922764i	−0.0292793	+	0.999571i	$0.509321\pi$
$194$	−3.69800	+	10.6847i	−0.265501	+	0.767114i
$195$		0			0
$196$	−0.0432339	−	0.907591i	−0.00308814	−	0.0648280i
$197$	−14.4226	+	12.4972i	−1.02757	+	0.890391i	−0.994037	−	0.109047i	$-0.965220\pi$
$197$	−14.4226	+	12.4972i	−1.02757	+	0.890391i	−0.0335294	+	0.999438i	$0.510675\pi$
$198$		0			0
$199$	1.81677	+	0.261211i	0.128787	+	0.0185168i	0.206407	−	0.978466i	$-0.433823\pi$
$199$	1.81677	+	0.261211i	0.128787	+	0.0185168i	−0.0776198	+	0.996983i	$0.524732\pi$
$200$	−5.91648	+	2.04772i	−0.418359	+	0.144795i
$201$		0			0
$202$	−2.42393	−	9.99158i	−0.170547	−	0.703005i
$203$	−1.72095	+	2.41674i	−0.120787	+	0.169622i
$204$		0			0
$205$	−10.7947	−	20.9388i	−0.753936	−	1.46243i
$206$	11.9094			0.829766
$207$		0			0
$208$	3.58336			0.248461
$209$	−1.58645	−	3.07728i	−0.109737	−	0.212860i
$210$		0			0
$211$	7.85558	−	11.0316i	0.540800	−	0.759448i	−0.450255	−	0.892900i	$-0.648667\pi$
$211$	7.85558	−	11.0316i	0.540800	−	0.759448i	0.991055	+	0.133452i	$0.0426063\pi$
$212$	−0.297007	−	1.22428i	−0.0203985	−	0.0840837i
$213$		0			0
$214$	3.22940	−	1.11771i	0.220757	−	0.0764049i
$215$	31.5272	+	4.53292i	2.15013	+	0.309143i
$216$		0			0
$217$	−0.398419	+	0.345232i	−0.0270464	+	0.0234358i
$218$	0.259549	+	5.44861i	0.0175789	+	0.369026i
$219$		0			0
$220$	0.149431	−	0.431753i	0.0100747	−	0.0291088i
$221$	−2.82901	−	2.69745i	−0.190300	−	0.181450i
$222$		0			0
$223$	6.11936	+	17.6807i	0.409783	+	1.18399i	0.941484	+	0.337057i	$0.109432\pi$
$223$	6.11936	+	17.6807i	0.409783	+	1.18399i	−0.531702	+	0.846932i	$0.678447\pi$
$224$	−0.376057	+	0.823450i	−0.0251264	+	0.0550191i
$225$		0			0
$226$	2.79122	−	1.27471i	0.185669	−	0.0847923i
$227$	−20.9592	−	8.39079i	−1.39111	−	0.556916i	−0.449396	−	0.893333i	$-0.648361\pi$
$227$	−20.9592	−	8.39079i	−1.39111	−	0.556916i	−0.941713	+	0.336416i	$0.890785\pi$
$228$		0			0
$229$	−17.6045	+	10.1640i	−1.16334	+	0.671655i	−0.952102	−	0.305780i	$-0.901083\pi$
$229$	−17.6045	+	10.1640i	−1.16334	+	0.671655i	−0.211238	+	0.977435i	$0.567750\pi$
$230$	−11.2469	−	15.3507i	−0.741599	−	1.01219i
$231$		0			0
$232$	−6.84813	+	3.53046i	−0.449602	+	0.231786i
$233$	−16.7476	+	2.40795i	−1.09717	+	0.157750i	−0.667045	−	0.745018i	$-0.732441\pi$
$233$	−16.7476	+	2.40795i	−1.09717	+	0.157750i	−0.430129	+	0.902767i	$0.641532\pi$
$234$		0			0
$235$	−9.61270	+	32.7378i	−0.627063	+	2.13558i
$236$	0.580602	−	0.413445i	0.0377940	−	0.0269130i
$237$		0			0
$238$	6.64274	−	2.65935i	0.430585	−	0.172380i
$239$	5.29939	−	5.55784i	0.342789	−	0.359507i	−0.529662	−	0.848209i	$-0.677681\pi$
$239$	5.29939	−	5.55784i	0.342789	−	0.359507i	0.872451	+	0.488702i	$0.162530\pi$
$240$		0			0
$241$	−27.1238	+	1.29207i	−1.74720	+	0.0832294i	−0.896671	−	0.442698i	$-0.854021\pi$
$241$	−27.1238	+	1.29207i	−1.74720	+	0.0832294i	−0.850530	+	0.525927i	$0.823718\pi$
$242$	7.76872	+	12.0884i	0.499393	+	0.777070i
$243$		0			0
$244$	0.113442	+	0.386348i	0.00726238	+	0.0247334i
$245$	−12.5637	−	9.88022i	−0.802667	−	0.631224i
$246$		0			0
$247$	0.250414	+	2.62245i	0.0159334	+	0.166862i
$248$	−1.33044	+	0.322762i	−0.0844833	+	0.0204954i
$249$		0			0
$250$	−3.96611	+	9.90687i	−0.250839	+	0.626565i
$251$	3.59135	+	2.30802i	0.226684	+	0.145681i	0.649053	−	0.760743i	$-0.275165\pi$
$251$	3.59135	+	2.30802i	0.226684	+	0.145681i	−0.422369	+	0.906424i	$0.638802\pi$
$252$		0			0
$253$	−5.26916	−	0.179663i	−0.331270	−	0.0112953i
$254$	−7.96751	−	4.60004i	−0.499926	−	0.288632i
$255$		0			0
$256$	−2.88304	+	2.26725i	−0.180190	+	0.141703i
$257$	9.57252	+	6.81656i	0.597118	+	0.425205i	0.838249	−	0.545287i	$-0.183579\pi$
$257$	9.57252	+	6.81656i	0.597118	+	0.425205i	−0.241132	+	0.970492i	$0.577519\pi$
$258$		0			0
$259$	−1.30335	−	1.83030i	−0.0809861	−	0.113729i
$260$	−0.227659	+	0.262732i	−0.0141188	+	0.0162940i
$261$		0			0
$262$	−18.2395	+	5.35559i	−1.12684	+	0.330869i
$263$	−7.67274	+	1.47880i	−0.473121	+	0.0911867i	−0.420238	−	0.907414i	$-0.638053\pi$
$263$	−7.67274	+	1.47880i	−0.473121	+	0.0911867i	−0.0528836	+	0.998601i	$0.516841\pi$
$264$		0			0
$265$	−19.6971	−	10.1546i	−1.20999	−	0.623791i
$266$	−4.55704	−	1.57721i	−0.279410	−	0.0967047i
$267$		0			0
$268$	0.131410	−	0.167101i	0.00802712	−	0.0102073i
$269$	−5.31672	−	4.60697i	−0.324166	−	0.280892i	0.477540	−	0.878610i	$-0.341529\pi$
$269$	−5.31672	−	4.60697i	−0.324166	−	0.280892i	−0.801706	+	0.597718i	$0.796074\pi$
$270$		0			0
$271$	10.5066	+	3.08500i	0.638228	+	0.187401i	0.584808	−	0.811172i	$-0.301170\pi$
$271$	10.5066	+	3.08500i	0.638228	+	0.187401i	0.0534194	+	0.998572i	$0.482988\pi$
$272$	19.9274	+	1.90283i	1.20827	+	0.115376i
$273$		0			0
$274$	−13.7245	−	0.653777i	−0.829126	−	0.0394961i
$275$	−1.27010	−	2.19988i	−0.0765899	−	0.132658i
$276$		0			0
$277$	−16.1784	+	28.0218i	−0.972066	+	1.68367i	−0.282771	+	0.959188i	$0.591253\pi$
$277$	−16.1784	+	28.0218i	−0.972066	+	1.68367i	−0.689296	+	0.724480i	$0.742080\pi$
$278$	9.71330	−	15.1142i	0.582565	−	0.906489i
$279$		0			0
$280$	3.17538	+	6.95311i	0.189765	+	0.415528i
$281$	11.5526	−	11.0154i	0.689172	−	0.657124i	−0.262255	−	0.964999i	$-0.584466\pi$
$281$	11.5526	−	11.0154i	0.689172	−	0.657124i	0.951427	+	0.307875i	$0.0996178\pi$
$282$		0			0
$283$	1.27746	−	6.62811i	0.0759373	−	0.394000i	−0.923995	−	0.382403i	$-0.875096\pi$
$283$	1.27746	−	6.62811i	0.0759373	−	0.394000i	0.999933	−	0.0115967i	$-0.00369142\pi$
$284$	0.468487	+	1.17022i	0.0277996	+	0.0694400i
$285$		0			0
$286$	0.255402	+	1.32515i	0.0151022	+	0.0783579i
$287$	−7.64752	+	4.91476i	−0.451419	+	0.290109i
$288$		0			0
$289$	−3.16732	−	3.65528i	−0.186313	−	0.215017i
$290$	2.66009	−	10.9651i	0.156206	−	0.643890i
$291$		0			0
$292$	0.516725	+	0.0995905i	0.0302390	+	0.00582809i
$293$	0.517528	−	0.0494179i	0.0302343	−	0.00288703i	−0.0799279	−	0.996801i	$-0.525469\pi$
$293$	0.517528	−	0.0494179i	0.0302343	−	0.00288703i	0.110162	+	0.993914i	$0.464863\pi$
$294$		0			0
$295$	1.19182	−	12.4813i	0.0693904	−	0.726690i
$296$	−0.830410	−	5.77563i	−0.0482666	−	0.335702i
$297$		0			0
$298$		−	4.36341i		−	0.252765i
$299$	3.67134	+	1.61704i	0.212319	+	0.0935157i
$300$		0			0
$301$	0.584834	−	12.2772i	0.0337093	−	0.707644i
$302$	17.7874	+	22.6186i	1.02355	+	1.30155i
$303$		0			0
$304$	−9.30986	−	9.76390i	−0.533957	−	0.559998i
$305$	6.44297	+	2.94241i	0.368924	+	0.168482i
$306$		0			0
$307$	−2.59688	+	18.0617i	−0.148212	+	1.03084i	0.770933	+	0.636916i	$0.219790\pi$
$307$	−2.59688	+	18.0617i	−0.148212	+	1.03084i	−0.919145	+	0.393920i	$0.871119\pi$
$308$	−0.171336	−	0.0415656i	−0.00976276	−	0.00236842i
$309$		0			0
$310$	0.918698	−	1.78203i	0.0521785	−	0.101212i
$311$	−2.64984	+	5.13997i	−0.150258	+	0.291461i	−0.951937	−	0.306295i	$-0.900911\pi$
$311$	−2.64984	+	5.13997i	−0.150258	+	0.291461i	0.801678	+	0.597756i	$0.203941\pi$
$312$		0			0
$313$	−31.8174	−	7.71881i	−1.79842	−	0.436293i	−0.809800	−	0.586706i	$-0.800424\pi$
$313$	−31.8174	−	7.71881i	−1.79842	−	0.436293i	−0.988623	+	0.150413i	$0.951940\pi$
$314$	3.20916	−	22.3202i	0.181103	−	1.25960i
$315$		0			0
$316$	2.14136	+	0.977925i	0.120461	+	0.0550126i
$317$	6.14216	+	6.44171i	0.344978	+	0.361803i	0.873250	−	0.487273i	$-0.162008\pi$
$317$	6.14216	+	6.44171i	0.344978	+	0.361803i	−0.528272	+	0.849075i	$0.677160\pi$
$318$		0			0
$319$	−1.93236	−	2.45719i	−0.108191	−	0.137576i
$320$	−0.938435	+	19.7002i	−0.0524601	+	1.10127i
$321$		0			0
$322$	−5.48428	+	4.88349i	−0.305627	+	0.272146i
$323$			14.7166i			0.818856i
$324$		0			0
$325$	0.275074	+	1.91318i	0.0152584	+	0.106124i
$326$	0.161482	−	1.69111i	0.00894364	−	0.0936620i
$327$		0			0
$328$	−23.5004	+	2.24402i	−1.29759	+	0.123905i
$329$	12.9286	+	2.49178i	0.712776	+	0.137376i
$330$		0			0
$331$	−2.11407	+	8.71430i	−0.116200	+	0.478982i	0.883740	+	0.467979i	$0.155018\pi$
$331$	−2.11407	+	8.71430i	−0.116200	+	0.478982i	−0.999939	+	0.0110029i	$0.996498\pi$
$332$	1.35599	+	1.56490i	0.0744196	+	0.0858848i
$333$		0			0
$334$	30.3537	−	19.5071i	1.66088	−	1.06738i
$335$	−0.707700	−	3.67190i	−0.0386658	−	0.200617i
$336$		0			0
$337$	2.90689	+	7.26106i	0.158348	+	0.395535i	0.986233	−	0.165364i	$-0.0528798\pi$
$337$	2.90689	+	7.26106i	0.158348	+	0.395535i	−0.827884	+	0.560899i	$0.810456\pi$
$338$	−3.41623	+	17.7251i	−0.185818	+	0.964117i
$339$		0			0
$340$	−1.40555	+	1.34019i	−0.0762264	+	0.0726818i
$341$	−0.230745	−	0.505262i	−0.0124956	−	0.0273615i
$342$		0			0
$343$	−7.28320	+	11.3329i	−0.393256	+	0.611918i
$344$	15.9593	−	27.6423i	0.860467	−	1.49037i
$345$		0			0
$346$	−11.4117	−	19.7656i	−0.613497	−	1.06261i
$347$	−25.7711	−	1.22763i	−1.38347	−	0.0659026i	−0.657408	−	0.753535i	$-0.728347\pi$
$347$	−25.7711	−	1.22763i	−1.38347	−	0.0659026i	−0.726059	+	0.687633i	$0.758650\pi$
$348$		0			0
$349$	6.80326	+	0.649633i	0.364170	+	0.0347740i	0.275537	−	0.961290i	$-0.411144\pi$
$349$	6.80326	+	0.649633i	0.364170	+	0.0347740i	0.0886328	+	0.996064i	$0.471750\pi$
$350$	−3.39480	−	0.996803i	−0.181460	−	0.0532813i
$351$		0			0
$352$	−0.720839	−	0.624611i	−0.0384209	−	0.0332919i
$353$	−1.53771	+	1.95536i	−0.0818441	+	0.104073i	−0.825251	−	0.564766i	$-0.808966\pi$
$353$	−1.53771	+	1.95536i	−0.0818441	+	0.104073i	0.743407	+	0.668840i	$0.233209\pi$
$354$		0			0
$355$	20.9539	+	7.25221i	1.11212	+	0.384907i
$356$	2.04341	+	1.05345i	0.108301	+	0.0558329i
$357$		0			0
$358$	20.8306	−	4.01477i	1.10093	−	0.212187i
$359$	−17.3286	+	5.08813i	−0.914568	+	0.268541i	−0.704963	−	0.709245i	$-0.749036\pi$
$359$	−17.3286	+	5.08813i	−0.914568	+	0.268541i	−0.209606	+	0.977786i	$0.567218\pi$
$360$		0			0
$361$	−5.94733	+	6.86358i	−0.313017	+	0.361241i
$362$	11.1715	+	15.6881i	0.587160	+	0.824551i
$363$		0			0
$364$	0.109277	+	0.0778159i	0.00572768	+	0.00407866i
$365$	7.27637	−	5.72220i	0.380863	−	0.299514i
$366$		0			0
$367$	12.3720	+	7.14298i	0.645814	+	0.372861i	0.786850	−	0.617144i	$-0.211710\pi$
$367$	12.3720	+	7.14298i	0.645814	+	0.372861i	−0.141037	+	0.990004i	$0.545044\pi$
$368$	−19.8979	+	5.11291i	−1.03725	+	0.266529i
$369$		0			0
$370$	7.18865	+	4.61986i	0.373720	+	0.240175i
$371$	−3.17828	+	7.93897i	−0.165008	+	0.412171i
$372$		0			0
$373$	−10.2511	+	2.48690i	−0.530783	+	0.128767i	−0.492189	−	0.870488i	$-0.663803\pi$
$373$	−10.2511	+	2.48690i	−0.530783	+	0.128767i	−0.0385943	+	0.999255i	$0.512288\pi$
$374$	0.716632	+	7.50491i	0.0370561	+	0.388070i
$375$		0			0
$376$	26.8767	+	21.1360i	1.38606	+	1.09001i
$377$	0.670126	+	2.28224i	0.0345132	+	0.117541i
$378$		0			0
$379$	−1.69081	−	2.63095i	−0.0868511	−	0.135143i	0.795110	−	0.606465i	$-0.207413\pi$
$379$	−1.69081	−	2.63095i	−0.0868511	−	0.135143i	−0.881961	+	0.471322i	$0.843777\pi$
$380$	1.30737	−	0.0622775i	0.0670665	−	0.00319477i
$381$		0			0
$382$	−25.5504	+	26.7965i	−1.30727	+	1.37103i
$383$	8.69031	−	3.47908i	0.444054	−	0.177773i	−0.138850	−	0.990313i	$-0.544341\pi$
$383$	8.69031	−	3.47908i	0.444054	−	0.177773i	0.582904	+	0.812541i	$0.301916\pi$
$384$		0			0
$385$	−2.52628	+	1.79896i	−0.128751	+	0.0916833i
$386$	−7.68070	+	26.1581i	−0.390937	+	1.33141i
$387$		0			0
$388$	−1.17216	+	0.168531i	−0.0595074	+	0.00855587i
$389$	−6.08878	+	3.13898i	−0.308713	+	0.159153i	−0.605621	−	0.795753i	$-0.707075\pi$
$389$	−6.08878	+	3.13898i	−0.308713	+	0.159153i	0.296907	+	0.954906i	$0.404045\pi$
$390$		0			0
$391$	19.5580	+	10.9420i	0.989089	+	0.553363i
$392$	−13.8711	+	8.00851i	−0.700599	+	0.404491i
$393$		0			0
$394$	−26.0003	−	10.4090i	−1.30988	−	0.524395i
$395$	37.6680	−	17.2024i	1.89528	−	0.865547i
$396$		0			0
$397$	−6.03124	+	13.2066i	−0.302699	+	0.662819i	−0.998461	−	0.0554537i	$-0.982339\pi$
$397$	−6.03124	+	13.2066i	−0.302699	+	0.662819i	0.695762	+	0.718272i	$0.255067\pi$
$398$	0.880995	+	2.54547i	0.0441603	+	0.127593i
$399$		0			0
$400$	−7.16382	−	6.83069i	−0.358191	−	0.341534i
$401$	−6.38414	+	18.4458i	−0.318809	+	0.921137i	0.665764	+	0.746162i	$0.268106\pi$
$401$	−6.38414	+	18.4458i	−0.318809	+	0.921137i	−0.984573	+	0.174975i	$0.944016\pi$
$402$		0			0
$403$	0.0201106	+	0.422173i	0.00100178	+	0.0210299i
$404$	0.813826	−	0.705184i	0.0404893	−	0.0350842i
$405$		0			0
$406$	−4.30971	−	0.619643i	−0.213887	−	0.0307524i
$407$	2.23723	−	0.774313i	0.110895	−	0.0383813i
$408$		0			0
$409$	−5.09887	−	21.0178i	−0.252123	−	1.03927i	−0.947280	−	0.320407i	$-0.896180\pi$
$409$	−5.09887	−	21.0178i	−0.252123	−	1.03927i	0.695157	−	0.718858i	$-0.255335\pi$
$410$	20.0537	−	28.1615i	0.990383	−	1.39080i
$411$		0			0
$412$	0.571572	+	1.10869i	0.0281593	+	0.0546215i
$413$	−4.83831			−0.238078
$414$		0			0
$415$	36.4243			1.78800
$416$	0.332562	+	0.645080i	0.0163052	+	0.0316277i
$417$		0			0
$418$	2.94720	−	4.13877i	0.144152	−	0.202434i
$419$	6.57281	+	27.0935i	0.321103	+	1.32360i	0.872194	+	0.489159i	$0.162696\pi$
$419$	6.57281	+	27.0935i	0.321103	+	1.32360i	−0.551092	+	0.834445i	$0.685788\pi$
$420$		0			0
$421$	0.467046	−	0.161646i	0.0227625	−	0.00787816i	−0.315663	−	0.948871i	$-0.602227\pi$
$421$	0.467046	−	0.161646i	0.0227625	−	0.00787816i	0.338425	+	0.940993i	$0.390106\pi$
$422$	19.6724	+	2.82847i	0.957638	+	0.137688i
$423$		0			0
$424$	−16.7832	+	14.5427i	−0.815064	+	0.706257i
$425$	0.513774	+	10.7855i	0.0249217	+	0.523171i
$426$		0			0
$427$	0.893966	−	2.58295i	0.0432621	−	0.124998i
$428$	0.259042	+	0.246996i	0.0125213	+	0.0119390i
$429$		0			0
$430$	15.2883	+	44.1727i	0.737267	+	2.13019i
$431$	5.40362	−	11.8323i	0.260283	−	0.569941i	−0.733700	−	0.679474i	$-0.762208\pi$
$431$	5.40362	−	11.8323i	0.260283	−	0.569941i	0.993983	+	0.109533i	$0.0349355\pi$
$432$		0			0
$433$	22.1861	−	10.1320i	1.06619	−	0.486915i	0.196499	−	0.980504i	$-0.437043\pi$
$433$	22.1861	−	10.1320i	1.06619	−	0.486915i	0.869695	+	0.493589i	$0.164315\pi$
$434$	−0.718249	−	0.287544i	−0.0344771	−	0.0138025i
$435$		0			0
$436$	−0.494777	+	0.285660i	−0.0236955	+	0.0136806i
$437$	−5.13235	−	14.2048i	−0.245514	−	0.679509i
$438$		0			0
$439$	−5.42450	+	2.79652i	−0.258897	+	0.133471i	−0.582790	−	0.812623i	$-0.698039\pi$
$439$	−5.42450	+	2.79652i	−0.258897	+	0.133471i	0.323892	+	0.946094i	$0.395008\pi$
$440$	−7.97186	+	1.14618i	−0.380043	+	0.0546420i
$441$		0			0
$442$	1.61616	−	5.50415i	0.0768731	−	0.261806i
$443$	4.59811	−	3.27430i	0.218463	−	0.155567i	−0.465587	−	0.885002i	$-0.654157\pi$
$443$	4.59811	−	3.27430i	0.218463	−	0.155567i	0.684049	+	0.729436i	$0.260217\pi$
$444$		0			0
$445$	37.5439	−	15.0303i	1.77975	−	0.712505i
$446$	−18.9479	+	19.8719i	−0.897207	+	0.940964i
$447$		0			0
$448$	7.60208	−	0.362132i	0.359164	−	0.0171091i
$449$	−11.7076	−	18.2173i	−0.552514	−	0.859728i	0.446878	−	0.894595i	$-0.352536\pi$
$449$	−11.7076	−	18.2173i	−0.552514	−	0.859728i	−0.999392	+	0.0348669i	$0.988899\pi$
$450$		0			0
$451$	−2.69848	−	9.19019i	−0.127067	−	0.432749i
$452$	0.252628	+	0.198669i	0.0118826	+	0.00934461i
$453$		0			0
$454$	−3.14940	−	32.9820i	−0.147808	−	1.54792i
$455$	2.29332	−	0.556352i	0.107512	−	0.0260822i
$456$		0			0
$457$	7.35741	−	18.3779i	0.344165	−	0.859683i	−0.650780	−	0.759266i	$-0.725558\pi$
$457$	7.35741	−	18.3779i	0.344165	−	0.859683i	0.994945	−	0.100417i	$-0.0320176\pi$
$458$	−25.0966	−	16.1286i	−1.17269	−	0.753639i
$459$		0			0
$460$	0.889281	−	1.78375i	0.0414629	−	0.0831679i
$461$	27.2976	+	15.7603i	1.27138	+	0.734030i	0.975247	−	0.221118i	$-0.0709705\pi$
$461$	27.2976	+	15.7603i	1.27138	+	0.734030i	0.296130	+	0.955148i	$0.404304\pi$
$462$		0			0
$463$	11.7716	−	9.25731i	0.547074	−	0.430224i	−0.305987	−	0.952036i	$-0.598986\pi$
$463$	11.7716	−	9.25731i	0.547074	−	0.430224i	0.853060	+	0.521812i	$0.174744\pi$
$464$	−9.92240	−	7.06571i	−0.460636	−	0.328017i
$465$		0			0
$466$	−14.4032	−	20.2265i	−0.667218	−	0.936976i
$467$	15.3268	−	17.6881i	0.709239	−	0.818506i	−0.280730	−	0.959787i	$-0.590577\pi$
$467$	15.3268	−	17.6881i	0.709239	−	0.818506i	0.989970	+	0.141281i	$0.0451220\pi$
$468$		0			0
$469$	−1.38457	+	0.406547i	−0.0639335	+	0.0187726i
$470$	−49.1679	+	9.47633i	−2.26795	+	0.437111i
$471$		0			0
$472$	−11.1678	−	5.75740i	−0.514040	−	0.265006i
$473$	12.2380	+	4.23563i	0.562706	+	0.194754i
$474$		0			0
$475$	4.49836	−	5.72013i	0.206399	−	0.262457i
$476$	0.566378	+	0.490770i	0.0259599	+	0.0224944i
$477$		0			0
$478$	10.8134	+	3.17510i	0.494593	+	0.145226i
$479$	−6.17711	−	0.589842i	−0.282239	−	0.0269506i	−0.0470235	−	0.998894i	$-0.514974\pi$
$479$	−6.17711	−	0.589842i	−0.282239	−	0.0269506i	−0.235216	+	0.971943i	$0.575580\pi$
$480$		0			0
$481$	−1.79936	−	0.0857142i	−0.0820438	−	0.00390823i
$482$	−19.9254	−	34.5118i	−0.907577	−	1.57197i
$483$		0			0
$484$	−0.752510	+	1.30339i	−0.0342050	+	0.0592448i
$485$	−11.2622	+	17.5243i	−0.511389	+	0.795737i
$486$		0			0
$487$	14.0170	+	30.6929i	0.635170	+	1.39083i	0.903955	+	0.427628i	$0.140651\pi$
$487$	14.0170	+	30.6929i	0.635170	+	1.39083i	−0.268785	+	0.963200i	$0.586622\pi$
$488$	5.13706	−	4.89818i	0.232544	−	0.221730i
$489$		0			0
$490$	4.43914	−	23.0324i	0.200540	−	1.04050i
$491$	12.7886	+	31.9444i	0.577142	+	1.44163i	0.873628	+	0.486594i	$0.161761\pi$
$491$	12.7886	+	31.9444i	0.577142	+	1.44163i	−0.296487	+	0.955037i	$0.595815\pi$
$492$		0			0
$493$	2.51471	+	13.0476i	0.113257	+	0.587633i
$494$	−3.25236	+	2.09016i	−0.146331	+	0.0940409i
$495$		0			0
$496$	−1.41742	−	1.63579i	−0.0636439	−	0.0734490i
$497$	2.01727	−	8.31528i	0.0904867	−	0.372991i
$498$		0			0
$499$	20.1935	+	3.89197i	0.903983	+	0.174229i	0.620001	−	0.784601i	$-0.287132\pi$
$499$	20.1935	+	3.89197i	0.903983	+	0.174229i	0.283982	+	0.958830i	$0.408344\pi$
$500$	−1.11262	+	0.106242i	−0.0497579	+	0.00475130i
$501$		0			0
$502$	−0.595530	+	6.23668i	−0.0265798	+	0.278356i
$503$	−0.408017	−	2.83782i	−0.0181926	−	0.126532i	0.978701	−	0.205290i	$-0.0658137\pi$
$503$	−0.408017	−	2.83782i	−0.0181926	−	0.126532i	−0.996894	+	0.0787577i	$0.974905\pi$
$504$		0			0
$505$		−	18.9425i		−	0.842930i
$506$	−3.30901	−	6.99398i	−0.147103	−	0.310920i
$507$		0			0
$508$	0.0458496	−	0.962501i	0.00203425	−	0.0427041i
$509$	−16.5546	−	21.0509i	−0.733770	−	0.933065i	0.265750	−	0.964042i	$-0.414380\pi$
$509$	−16.5546	−	21.0509i	−0.733770	−	0.933065i	−0.999520	+	0.0309774i	$0.990138\pi$
$510$		0			0
$511$	−2.46504	−	2.58526i	−0.109047	−	0.114365i
$512$	17.7355	+	8.09951i	0.783804	+	0.357951i
$513$		0			0
$514$	−2.45436	+	17.0705i	−0.108257	+	0.752945i
$515$	21.3234	+	5.17300i	0.939621	+	0.227950i
$516$		0			0
$517$	−6.35682	+	12.3305i	−0.279573	+	0.542295i
$518$	1.51100	−	2.93092i	0.0663893	−	0.128777i
$519$		0			0
$520$	5.95548	+	1.44478i	0.261165	+	0.0633579i
$521$	−1.89252	+	13.1628i	−0.0829129	+	0.576672i	0.905438	+	0.424479i	$0.139543\pi$
$521$	−1.89252	+	13.1628i	−0.0829129	+	0.576672i	−0.988351	+	0.152193i	$0.951366\pi$
$522$		0			0
$523$	−36.4077	−	16.6268i	−1.59200	−	0.727041i	−0.594945	−	0.803767i	$-0.702826\pi$
$523$	−36.4077	−	16.6268i	−1.59200	−	0.727041i	−0.997052	+	0.0767259i	$0.975553\pi$
$524$	−1.37395	−	1.44096i	−0.0600212	−	0.0629484i
$525$		0			0
$526$	−7.08866	−	9.01396i	−0.309080	−	0.393027i
$527$	−0.112345	+	2.35842i	−0.00489384	+	0.102734i
$528$		0			0
$529$	−22.6938	−	3.74076i	−0.986685	−	0.162642i
$530$		−	32.5218i		−	1.41266i
$531$		0			0
$532$	−0.0718790	−	0.499929i	−0.00311635	−	0.0216747i
$533$	−0.692779	+	7.25511i	−0.0300076	+	0.314254i
$534$		0			0
$535$	6.26764	−	0.598488i	0.270974	−	0.0258749i
$536$	−3.67965	−	0.709194i	−0.158936	−	0.0306325i
$537$		0			0
$538$	2.43404	−	10.0333i	0.104939	−	0.432564i
$539$	−4.25566	−	4.91129i	−0.183304	−	0.211544i
$540$		0			0
$541$	35.7999	−	23.0072i	1.53916	−	0.989158i	0.551213	−	0.834365i	$-0.314165\pi$
$541$	35.7999	−	23.0072i	1.53916	−	0.989158i	0.987947	−	0.154793i	$-0.0494711\pi$
$542$	3.04124	+	15.7794i	0.130632	+	0.677785i
$543$		0			0
$544$	1.50686	+	3.76395i	0.0646059	+	0.161378i
$545$	−1.90196	+	9.86832i	−0.0814711	+	0.422712i
$546$		0			0
$547$	−12.2196	+	11.6514i	−0.522474	+	0.498178i	−0.904793	−	0.425853i	$-0.859974\pi$
$547$	−12.2196	+	11.6514i	−0.522474	+	0.498178i	0.382318	+	0.924031i	$0.375126\pi$
$548$	−0.597821	−	1.30905i	−0.0255377	−	0.0559197i
$549$		0			0
$550$	2.01544	−	3.13609i	0.0859387	−	0.133723i
$551$	4.47758	−	7.75539i	0.190751	−	0.330391i
$552$		0			0
$553$	−7.98987	−	13.8389i	−0.339764	−	0.588488i
$554$	−47.4315	−	2.25944i	−2.01517	−	0.0959944i
$555$		0			0
$556$	1.87322	+	0.178871i	0.0794421	+	0.00758580i
$557$	−0.132902	−	0.0390237i	−0.00563126	−	0.00165349i	0.278916	−	0.960316i	$-0.410025\pi$
$557$	−0.132902	−	0.0390237i	−0.00563126	−	0.00165349i	−0.284547	+	0.958662i	$0.591843\pi$
$558$		0			0
$559$	−7.44714	−	6.45298i	−0.314980	−	0.272932i
$560$	−7.47047	+	9.49947i	−0.315685	+	0.401426i
$561$		0			0
$562$	22.1374	+	7.66184i	0.933811	+	0.323195i
$563$	−0.782589	−	0.403453i	−0.0329822	−	0.0170035i	0.441657	−	0.897184i	$-0.354391\pi$
$563$	−0.782589	−	0.403453i	−0.0329822	−	0.0170035i	−0.474639	+	0.880181i	$0.657421\pi$
$564$		0			0
$565$	5.55129	−	1.06992i	0.233544	−	0.0450120i
$566$	9.50484	−	2.79087i	0.399518	−	0.117309i
$567$		0			0
$568$	14.5511	−	16.7929i	0.610552	−	0.704614i
$569$	17.2331	+	24.2005i	0.722450	+	1.01454i	0.998572	+	0.0534168i	$0.0170112\pi$
$569$	17.2331	+	24.2005i	0.722450	+	1.01454i	−0.276122	+	0.961123i	$0.589049\pi$
$570$		0			0
$571$	15.6834	+	11.1681i	0.656330	+	0.467370i	0.859067	−	0.511863i	$-0.171044\pi$
$571$	15.6834	+	11.1681i	0.656330	+	0.467370i	−0.202737	+	0.979233i	$0.564984\pi$
$572$	−0.111106	+	0.0873750i	−0.00464559	+	0.00365333i
$573$		0			0
$574$	−11.5536	−	6.67048i	−0.482238	−	0.278421i
$575$	−4.25728	−	10.2312i	−0.177541	−	0.426670i
$576$		0			0
$577$	−4.05986	−	2.60911i	−0.169014	−	0.108619i	0.453399	−	0.891308i	$-0.350211\pi$
$577$	−4.05986	−	2.60911i	−0.169014	−	0.108619i	−0.622413	+	0.782689i	$0.713848\pi$
$578$	2.63806	−	6.58956i	0.109729	−	0.274090i
$579$		0			0
$580$	1.14845	−	0.278611i	0.0476868	−	0.0115687i
$581$	−1.33608	−	13.9921i	−0.0554301	−	0.580490i
$582$		0			0
$583$	−7.08248	−	5.56972i	−0.293326	−	0.230674i
$584$	−2.61346	−	8.90062i	−0.108146	−	0.368310i
$585$		0			0
$586$	0.412484	+	0.641838i	0.0170396	+	0.0265141i
$587$	23.1617	−	1.10333i	0.955984	−	0.0455391i	0.436212	−	0.899844i	$-0.356320\pi$
$587$	23.1617	−	1.10333i	0.955984	−	0.0455391i	0.519772	+	0.854305i	$0.326017\pi$
$588$		0			0
$589$	1.09808	−	1.15164i	0.0452457	−	0.0474524i
$590$	17.0822	−	6.83869i	0.703264	−	0.281544i
$591$		0			0
$592$	7.51464	−	5.35115i	0.308850	−	0.219931i
$593$	−5.58492	+	19.0205i	−0.229345	+	0.781077i	0.761744	+	0.647878i	$0.224343\pi$
$593$	−5.58492	+	19.0205i	−0.229345	+	0.781077i	−0.991089	+	0.133199i	$0.957475\pi$
$594$		0			0
$595$	13.0488	−	1.87613i	0.534947	−	0.0769138i
$596$	0.406208	−	0.209415i	0.0166389	−	0.00857796i
$597$		0			0
$598$	0.359586	+	5.87635i	0.0147046	+	0.240302i
$599$	31.0663	−	17.9361i	1.26933	−	0.732851i	0.294472	−	0.955660i	$-0.404856\pi$
$599$	31.0663	−	17.9361i	1.26933	−	0.732851i	0.974862	+	0.222810i	$0.0715228\pi$
$600$		0			0
$601$	−14.4045	−	5.76670i	−0.587572	−	0.235228i	0.0587758	−	0.998271i	$-0.481280\pi$
$601$	−14.4045	−	5.76670i	−0.587572	−	0.235228i	−0.646348	+	0.763043i	$0.723705\pi$
$602$	16.4078	−	7.49318i	0.668731	−	0.305399i
$603$		0			0
$604$	−1.25198	+	2.74145i	−0.0509423	+	0.111548i
$605$	8.65893	+	25.0183i	0.352035	+	1.01714i
$606$		0			0
$607$	15.0366	+	14.3374i	0.610317	+	0.581937i	0.930896	−	0.365286i	$-0.119029\pi$
$607$	15.0366	+	14.3374i	0.610317	+	0.581937i	−0.320578	+	0.947222i	$0.603877\pi$
$608$	0.893685	−	2.58213i	0.0362437	−	0.104719i
$609$		0			0
$610$	0.494602	+	10.3830i	0.0200259	+	0.420394i
$611$	7.97755	−	6.91259i	0.322737	−	0.279653i
$612$		0			0
$613$	21.8606	+	3.14308i	0.882941	+	0.126948i	0.568846	−	0.822444i	$-0.307390\pi$
$613$	21.8606	+	3.14308i	0.882941	+	0.126948i	0.314095	+	0.949392i	$0.398299\pi$
$614$	−25.3062	+	8.75857i	−1.02128	+	0.353467i
$615$		0			0
$616$	0.732712	+	3.02028i	0.0295218	+	0.121691i
$617$	17.6189	−	24.7423i	0.709310	−	0.996086i	−0.289928	−	0.957048i	$-0.593631\pi$
$617$	17.6189	−	24.7423i	0.709310	−	0.996086i	0.999238	−	0.0390376i	$-0.0124292\pi$
$618$		0			0
$619$	−3.03509	−	5.88725i	−0.121990	−	0.236628i	0.819931	−	0.572463i	$-0.194012\pi$
$619$	−3.03509	−	5.88725i	−0.121990	−	0.236628i	−0.941921	+	0.335835i	$0.890982\pi$
$620$	0.209988			0.00843331
$621$		0			0
$622$	−8.48657			−0.340281
$623$	−7.15092	−	13.8708i	−0.286495	−	0.555724i
$624$		0			0
$625$	−18.1060	+	25.4263i	−0.724239	+	1.01705i
$626$	−11.3277	−	46.6936i	−0.452748	−	1.86625i
$627$		0			0
$628$	2.23190	−	0.772467i	0.0890624	−	0.0308248i
$629$	−9.96089	−	1.43216i	−0.397167	−	0.0571040i
$630$		0			0
$631$	26.1918	−	22.6953i	1.04268	−	0.903486i	0.0472393	−	0.998884i	$-0.484958\pi$
$631$	26.1918	−	22.6953i	1.04268	−	0.903486i	0.995439	+	0.0953975i	$0.0304122\pi$
$632$	−1.97453	−	41.4506i	−0.0785427	−	1.64881i
$633$		0			0
$634$	−4.27222	+	12.3438i	−0.169672	+	0.490234i
$635$	−12.2675	−	11.6970i	−0.486821	−	0.464183i
$636$		0			0
$637$	1.61729	+	4.67285i	0.0640794	+	0.185145i
$638$	1.90574	−	4.17298i	0.0754488	−	0.165210i
$639$		0			0
$640$	−30.5960	+	13.9727i	−1.20941	+	0.552321i
$641$	18.2337	+	7.29969i	0.720189	+	0.288320i	0.702660	−	0.711526i	$-0.251996\pi$
$641$	18.2337	+	7.29969i	0.720189	+	0.288320i	0.0175296	+	0.999846i	$0.494420\pi$
$642$		0			0
$643$	−41.5551	+	23.9919i	−1.63878	+	0.946147i	−0.657519	+	0.753438i	$0.728394\pi$
$643$	−41.5551	+	23.9919i	−1.63878	+	0.946147i	−0.981256	+	0.192710i	$0.938272\pi$
$644$	−0.717834	−	0.276180i	−0.0282866	−	0.0108830i
$645$		0			0
$646$	−19.1966	+	9.89652i	−0.755279	+	0.389373i
$647$	−29.8180	+	4.28718i	−1.17227	+	0.168547i	−0.700814	−	0.713344i	$-0.747180\pi$
$647$	−29.8180	+	4.28718i	−1.17227	+	0.168547i	−0.471454	+	0.881891i	$0.656271\pi$
$648$		0			0
$649$	1.43622	−	4.89130i	0.0563764	−	0.192000i
$650$	−2.31060	+	1.64537i	−0.0906292	+	0.0645367i
$651$		0			0
$652$	0.165183	−	0.0661292i	0.00646906	−	0.00258982i
$653$	18.0183	−	18.8971i	0.705111	−	0.739499i	−0.269599	−	0.962973i	$-0.586891\pi$
$653$	18.0183	−	18.8971i	0.705111	−	0.739499i	0.974710	+	0.223473i	$0.0717396\pi$
$654$		0			0
$655$	−34.9835	+	1.66647i	−1.36692	+	0.0651144i
$656$	−20.1785	−	31.3984i	−0.787839	−	1.22590i
$657$		0			0
$658$	5.44379	+	18.5398i	0.212221	+	0.722758i
$659$	−19.9477	−	15.6870i	−0.777052	−	0.611081i	0.148843	−	0.988861i	$-0.452445\pi$
$659$	−19.9477	−	15.6870i	−0.777052	−	0.611081i	−0.925895	+	0.377780i	$0.876688\pi$
$660$		0			0
$661$	−2.60598	−	27.2911i	−0.101361	−	1.06150i	−0.892862	−	0.450331i	$-0.851306\pi$
$661$	−2.60598	−	27.2911i	−0.101361	−	1.06150i	0.791501	−	0.611168i	$-0.209300\pi$
$662$	−12.7887	+	3.10250i	−0.497047	+	0.120582i
$663$		0			0
$664$	13.5661	−	33.8865i	0.526467	−	1.31505i
$665$	−7.47416	−	4.80335i	−0.289836	−	0.186266i
$666$		0			0
$667$	−6.97753	−	11.7168i	−0.270171	−	0.453677i
$668$	3.27278	+	1.88954i	0.126628	+	0.0731085i
$669$		0			0
$670$	4.31376	−	3.39238i	0.166655	−	0.131059i
$671$	2.34587	+	1.67049i	0.0905613	+	0.0644884i
$672$		0			0
$673$	10.4199	+	14.6327i	0.401658	+	0.564050i	0.965025	−	0.262157i	$-0.0844338\pi$
$673$	10.4199	+	14.6327i	0.401658	+	0.564050i	−0.563367	+	0.826207i	$0.690494\pi$
$674$	−7.51662	+	8.67464i	−0.289529	+	0.334135i
$675$		0			0
$676$	−1.81406	+	0.532656i	−0.0697715	+	0.0204868i
$677$	22.4154	−	4.32022i	0.861495	−	0.166040i	0.260678	−	0.965426i	$-0.416054\pi$
$677$	22.4154	−	4.32022i	0.861495	−	0.166040i	0.600817	+	0.799386i	$0.294842\pi$
$678$		0			0
$679$	7.14492	+	3.68346i	0.274197	+	0.141358i
$680$	32.3517	+	11.1970i	1.24063	+	0.429387i
$681$		0			0
$682$	0.503900	−	0.640761i	0.0192953	−	0.0245360i
$683$	7.05211	+	6.11069i	0.269842	+	0.233819i	0.779261	−	0.626699i	$-0.215594\pi$
$683$	7.05211	+	6.11069i	0.269842	+	0.233819i	−0.509420	+	0.860518i	$0.670140\pi$
$684$		0			0
$685$	−24.2893	−	7.13198i	−0.928046	−	0.272499i
$686$	−19.6805	−	1.87926i	−0.751404	−	0.0717504i
$687$		0			0
$688$	50.4064	+	2.40115i	1.92172	+	0.0915430i
$689$	3.42796	+	5.93739i	0.130595	+	0.226197i
$690$		0			0
$691$	−6.97069	+	12.0736i	−0.265178	+	0.459301i	−0.967610	−	0.252449i	$-0.918764\pi$
$691$	−6.97069	+	12.0736i	−0.265178	+	0.459301i	0.702433	+	0.711750i	$0.252097\pi$
$692$	1.29238	−	2.01098i	0.0491290	−	0.0764461i
$693$		0			0
$694$	−15.7290	−	34.4417i	−0.597065	−	1.30739i
$695$	23.9564	−	22.8424i	0.908719	−	0.866462i
$696$		0			0
$697$	−7.70521	+	39.9784i	−0.291856	+	1.51429i
$698$	3.72761	+	9.31111i	0.141092	+	0.352431i
$699$		0			0
$700$	−0.0701314	−	0.363876i	−0.00265072	−	0.0137532i
$701$	1.40337	−	0.901892i	0.0530046	−	0.0340640i	−0.513870	−	0.857868i	$-0.671789\pi$
$701$	1.40337	−	0.901892i	0.0530046	−	0.0340640i	0.566875	+	0.823804i	$0.308152\pi$
$702$		0			0
$703$	4.44133	+	5.12557i	0.167508	+	0.193315i
$704$	−1.89052	+	7.79284i	−0.0712517	+	0.293704i
$705$		0			0
$706$	−3.58466	−	0.690886i	−0.134910	−	0.0260018i
$707$	−7.27660	+	0.694831i	−0.273665	+	0.0261318i
$708$		0			0
$709$	2.89302	−	30.2970i	0.108650	−	1.13783i	−0.762560	−	0.646918i	$-0.776058\pi$
$709$	2.89302	−	30.2970i	0.108650	−	1.13783i	0.871209	−	0.490912i	$-0.163336\pi$
$710$	4.63101	+	32.2094i	0.173799	+	1.20880i
$711$		0			0
$712$		−	40.5261i		−	1.51878i
$713$	−0.714048	−	2.31558i	−0.0267413	−	0.0867191i
$714$		0			0
$715$	−0.118308	+	2.48358i	−0.00442445	+	0.0928807i
$716$	1.37348	+	1.74652i	0.0513294	+	0.0652707i
$717$		0			0
$718$	−18.2900	−	19.1820i	−0.682577	−	0.715866i
$719$	−7.80894	−	3.56623i	−0.291224	−	0.132998i	0.264446	−	0.964401i	$-0.414811\pi$
$719$	−7.80894	−	3.56623i	−0.291224	−	0.132998i	−0.555670	+	0.831403i	$0.687538\pi$
$720$		0			0
$721$	1.20500	−	8.38096i	0.0448766	−	0.312123i
$722$	−12.9523	−	3.14220i	−0.482036	−	0.116941i
$723$		0			0
$724$	−0.924319	+	1.79293i	−0.0343520	+	0.0666337i
$725$	3.01075	−	5.84004i	0.111817	−	0.216894i
$726$		0			0
$727$	15.9932	+	3.87991i	0.593155	+	0.143898i	0.521089	−	0.853502i	$-0.325526\pi$
$727$	15.9932	+	3.87991i	0.593155	+	0.143898i	0.0720655	+	0.997400i	$0.477041\pi$
$728$	0.336548	−	2.34074i	0.0124733	−	0.0867537i
$729$		0			0
$730$	12.3573	+	5.64337i	0.457363	+	0.208870i
$731$	−37.9875	−	39.8402i	−1.40502	−	1.47354i
$732$		0			0
$733$	−26.4101	−	33.5831i	−0.975478	−	1.24042i	−0.970666	−	0.240433i	$-0.922711\pi$
$733$	−26.4101	−	33.5831i	−0.975478	−	1.24042i	−0.00481226	−	0.999988i	$-0.501532\pi$
$734$	−0.997573	+	20.9416i	−0.0368211	+	0.772970i
$735$		0			0
$736$	−2.76711	−	3.10753i	−0.101997	−	0.114545i
$737$		−	1.52042i		−	0.0560052i
$738$		0			0
$739$	2.37514	+	16.5195i	0.0873711	+	0.607679i	0.985719	+	0.168396i	$0.0538586\pi$
$739$	2.37514	+	16.5195i	0.0873711	+	0.607679i	−0.898348	+	0.439284i	$0.855232\pi$
$740$	−0.0850749	+	0.890945i	−0.00312742	+	0.0327518i
$741$		0			0
$742$	−12.4930	+	1.19294i	−0.458632	+	0.0437941i
$743$	−14.9452	−	2.88046i	−0.548287	−	0.105674i	−0.0924178	−	0.995720i	$-0.529460\pi$
$743$	−14.9452	−	2.88046i	−0.548287	−	0.105674i	−0.455870	+	0.890047i	$0.650672\pi$
$744$		0			0
$745$	1.89530	−	7.81255i	0.0694386	−	0.286230i
$746$	−10.1375	−	11.6993i	−0.371161	−	0.428343i
$747$		0			0
$748$	−0.664270	+	0.426900i	−0.0242881	+	0.0156090i
$749$	−0.459808	−	2.38571i	−0.0168010	−	0.0871720i
$750$		0			0
$751$	−3.46811	−	8.66293i	−0.126553	−	0.316115i	0.851538	−	0.524294i	$-0.175671\pi$
$751$	−3.46811	−	8.66293i	−0.126553	−	0.316115i	−0.978091	+	0.208179i	$0.933246\pi$
$752$	−10.2305	+	53.0808i	−0.373068	+	1.93566i
$753$		0			0
$754$	−2.52634	+	2.40886i	−0.0920038	+	0.0877255i
$755$	22.0232	+	48.2241i	0.801507	+	1.75505i
$756$		0			0
$757$	−25.6627	+	39.9320i	−0.932727	+	1.45135i	−0.0408031	+	0.999167i	$0.512992\pi$
$757$	−25.6627	+	39.9320i	−0.932727	+	1.45135i	−0.891924	+	0.452185i	$0.850645\pi$
$758$	2.29483	−	3.97475i	0.0833518	−	0.144370i
$759$		0			0
$760$	−11.5361	−	19.9811i	−0.418458	−	0.724790i
$761$	−25.6982	−	1.22416i	−0.931560	−	0.0443757i	−0.423688	−	0.905808i	$-0.639265\pi$
$761$	−25.6982	−	1.22416i	−0.931560	−	0.0443757i	−0.507872	+	0.861433i	$0.669568\pi$
$762$		0			0
$763$	3.86060	+	0.368642i	0.139763	+	0.0133458i
$764$	−3.72085	−	1.09254i	−0.134616	−	0.0395267i
$765$		0			0
$766$	10.3821	+	8.99617i	0.375122	+	0.325045i
$767$	−2.39781	+	3.04906i	−0.0865799	+	0.110095i
$768$		0			0
$769$	0.916418	+	0.317175i	0.0330469	+	0.0114376i	0.343541	−	0.939138i	$-0.388373\pi$
$769$	0.916418	+	0.317175i	0.0330469	+	0.0114376i	−0.310495	+	0.950575i	$0.600495\pi$
$770$	−4.04543	−	2.08556i	−0.145787	−	0.0751585i
$771$		0			0
$772$	−2.80379	+	0.540386i	−0.100910	+	0.0194489i
$773$	−12.8080	+	3.76076i	−0.460671	+	0.135265i	−0.503830	−	0.863803i	$-0.668076\pi$
$773$	−12.8080	+	3.76076i	−0.460671	+	0.135265i	0.0431586	+	0.999068i	$0.486258\pi$
$774$		0			0
$775$	0.764552	−	0.882340i	0.0274635	−	0.0316946i
$776$	12.1088	+	17.0044i	0.434679	+	0.610421i
$777$		0			0
$778$	−8.18906	−	5.83140i	−0.293592	−	0.209066i
$779$	21.5685	−	16.9617i	0.772773	−	0.607715i
$780$		0			0
$781$	7.80755	+	4.50769i	0.279376	+	0.161298i
$782$	−1.12077	+	32.8699i	−0.0400785	+	1.17542i
$783$		0			0
$784$	−21.3031	−	13.6907i	−0.760825	−	0.488952i
$785$	15.4410	−	38.5697i	0.551112	−	1.37661i
$786$		0			0
$787$	22.6388	−	5.49212i	0.806988	−	0.195773i	0.189017	−	0.981974i	$-0.439470\pi$
$787$	22.6388	−	5.49212i	0.806988	−	0.195773i	0.617971	+	0.786201i	$0.287955\pi$
$788$	−0.278830	−	2.92004i	−0.00993291	−	0.104022i
$789$		0			0
$790$	47.7697	+	37.5665i	1.69957	+	1.33656i
$791$	−0.614629	−	2.09324i	−0.0218537	−	0.0744269i
$792$		0			0
$793$	−1.18471	−	1.84345i	−0.0420704	−	0.0654628i
$794$	−21.2826	+	1.01382i	−0.755292	+	0.0359790i
$795$		0			0
$796$	−0.194686	+	0.204181i	−0.00690048	+	0.00723701i
$797$	−44.5026	+	17.8162i	−1.57636	+	0.631081i	−0.984567	−	0.175006i	$-0.944006\pi$
$797$	−44.5026	+	17.8162i	−1.57636	+	0.631081i	−0.591797	+	0.806087i	$0.701581\pi$
$798$		0			0
$799$	48.0346	−	34.2053i	1.69934	−	1.21010i
$800$	0.564814	−	1.92358i	0.0199692	−	0.0680088i
$801$		0			0
$802$	−28.3540	+	4.07669i	−1.00121	+	0.143953i
$803$	3.34531	−	1.72463i	0.118053	−	0.0608607i
$804$		0			0
$805$	−11.9407	+	6.36157i	−0.420853	+	0.224216i
$806$	−0.537164	+	0.310132i	−0.0189208	+	0.0109239i
$807$		0			0
$808$	−17.6227	−	7.05507i	−0.619965	−	0.248196i
$809$	−24.2648	+	11.0814i	−0.853106	+	0.389600i	−0.793462	−	0.608619i	$-0.791724\pi$
$809$	−24.2648	+	11.0814i	−0.853106	+	0.389600i	−0.0596437	+	0.998220i	$0.518996\pi$
$810$		0			0
$811$	−19.8777	+	43.5261i	−0.698000	+	1.52841i	0.144379	+	0.989522i	$0.453881\pi$
$811$	−19.8777	+	43.5261i	−0.698000	+	1.52841i	−0.842379	+	0.538885i	$0.818846\pi$
$812$	−0.149153	−	0.430948i	−0.00523423	−	0.0151233i
$813$		0			0
$814$	2.51450	+	2.39757i	0.0881331	+	0.0840347i
$815$	1.02369	−	2.95775i	0.0358581	−	0.103605i
$816$		0			0
$817$	1.76525	+	37.0573i	0.0617584	+	1.29647i
$818$	23.9871	−	20.7849i	0.838688	−	0.726727i
$819$		0			0
$820$	3.58412	+	0.515319i	0.125163	+	0.0179957i
$821$	5.90075	−	2.04227i	0.205937	−	0.0712756i	−0.222152	−	0.975012i	$-0.571308\pi$
$821$	5.90075	−	2.04227i	0.205937	−	0.0712756i	0.428089	+	0.903736i	$0.359187\pi$
$822$		0			0
$823$	8.11056	+	33.4322i	0.282716	+	1.16537i	0.919108	+	0.394006i	$0.128911\pi$
$823$	8.11056	+	33.4322i	0.282716	+	1.16537i	−0.636392	+	0.771366i	$0.719574\pi$
$824$	12.7544	−	17.9111i	0.444321	−	0.623961i
$825$		0			0
$826$	−3.25362	−	6.31115i	−0.113208	−	0.219593i
$827$	−6.97282			−0.242469			−0.121234	−	0.992624i	$-0.538685\pi$
$827$	−6.97282			−0.242469			−0.121234	+	0.992624i	$0.538685\pi$
$828$		0			0
$829$	34.2211			1.18855			0.594274	−	0.804263i	$-0.297440\pi$
$829$	34.2211			1.18855			0.594274	+	0.804263i	$0.297440\pi$
$830$	24.4943	+	47.5123i	0.850209	+	1.64918i
$831$		0			0
$832$	3.53929	−	4.97024i	0.122703	−	0.172312i
$833$	6.51252	+	26.8450i	0.225645	+	0.930123i
$834$		0			0
$835$	62.8206	−	21.7424i	2.17400	−	0.752427i
$836$	0.526742	+	0.0757340i	0.0182177	+	0.00261932i
$837$		0			0
$838$	−30.9211	+	26.7932i	−1.06815	+	0.925557i
$839$	0.577297	+	12.1190i	0.0199305	+	0.418393i	0.986681	+	0.162670i	$0.0520105\pi$
$839$	0.577297	+	12.1190i	0.0199305	+	0.418393i	−0.966750	+	0.255723i	$0.917686\pi$
$840$		0			0
$841$	−6.84042	+	19.7641i	−0.235877	+	0.681520i
$842$	0.524929	+	0.500518i	0.0180902	+	0.0172490i
$843$		0			0
$844$	0.680833	+	1.96714i	0.0234352	+	0.0677116i
$845$	−13.8158	+	30.2524i	−0.475278	+	1.04071i
$846$		0			0
$847$	9.29297	−	4.24396i	0.319310	−	0.145824i
$848$	−32.5950	−	13.0491i	−1.11932	−	0.448107i
$849$		0			0
$850$	−13.7232	+	7.92308i	−0.470701	+	0.271759i
$851$	10.1139	−	2.09146i	0.346701	−	0.0716942i
$852$		0			0
$853$	−24.8112	+	12.7911i	−0.849519	+	0.437958i	−0.827276	−	0.561795i	$-0.810111\pi$
$853$	−24.8112	+	12.7911i	−0.849519	+	0.437958i	−0.0222428	+	0.999753i	$0.507081\pi$
$854$	3.97039	−	0.570856i	0.135864	−	0.0195343i
$855$		0			0
$856$	1.77757	−	6.05386i	0.0607562	−	0.206917i
$857$	−2.90551	+	2.06900i	−0.0992503	+	0.0706758i	−0.628605	−	0.777725i	$-0.716374\pi$
$857$	−2.90551	+	2.06900i	−0.0992503	+	0.0706758i	0.529354	+	0.848401i	$0.322434\pi$
$858$		0			0
$859$	−33.6031	+	13.4527i	−1.14652	+	0.458999i	−0.865602	−	0.500732i	$-0.833064\pi$
$859$	−33.6031	+	13.4527i	−1.14652	+	0.458999i	−0.280921	+	0.959731i	$0.590640\pi$
$860$	−3.37848	+	3.54325i	−0.115205	+	0.120824i
$861$		0			0
$862$	19.0679	−	0.908318i	0.649457	−	0.0309374i
$863$	−7.97847	−	12.4147i	−0.271590	−	0.422603i	0.678489	−	0.734610i	$-0.262635\pi$
$863$	−7.97847	−	12.4147i	−0.271590	−	0.422603i	−0.950080	+	0.312008i	$0.898999\pi$
$864$		0			0
$865$	−11.8468	−	40.3466i	−0.402805	−	1.37183i
$866$	28.1358	+	22.1263i	0.956095	+	0.751881i
$867$		0			0
$868$	−0.00770258	−	0.0806650i	−0.000261443	−	0.00273795i
$869$	16.3622	−	3.96942i	0.555049	−	0.134653i
$870$		0			0
$871$	−0.429975	+	1.07403i	−0.0145691	+	0.0363920i
$872$	8.47238	+	5.44487i	0.286911	+	0.184386i
$873$		0			0
$874$	15.0776	−	16.2470i	0.510007	−	0.549564i
$875$	6.57044	+	3.79345i	0.222121	+	0.128242i
$876$		0			0
$877$	12.7608	−	10.0352i	0.430901	−	0.338864i	−0.379035	−	0.925382i	$-0.623744\pi$
$877$	12.7608	−	10.0352i	0.430901	−	0.338864i	0.809936	+	0.586518i	$0.199502\pi$
$878$	−7.29564	−	5.19520i	−0.246216	−	0.175330i
$879$		0			0
$880$	−7.38597	−	10.3721i	−0.248981	−	0.349645i
$881$	32.0624	−	37.0020i	1.08021	−	1.24663i	0.112746	−	0.993624i	$-0.464035\pi$
$881$	32.0624	−	37.0020i	1.08021	−	1.24663i	0.967465	−	0.253006i	$-0.0814191\pi$
$882$		0			0
$883$	−1.17065	+	0.343734i	−0.0393955	+	0.0115676i	−0.301371	−	0.953507i	$-0.597444\pi$
$883$	−1.17065	+	0.343734i	−0.0393955	+	0.0115676i	0.261975	+	0.965075i	$0.415626\pi$
$884$	0.589970	−	0.113707i	0.0198428	−	0.00382439i
$885$		0			0
$886$	7.36313	+	3.79596i	0.247369	+	0.127528i
$887$	42.4402	+	14.6887i	1.42500	+	0.493198i	0.927355	−	0.374182i	$-0.122076\pi$
$887$	42.4402	+	14.6887i	1.42500	+	0.493198i	0.497647	+	0.867380i	$0.334198\pi$
$888$		0			0
$889$	−4.04334	+	5.14152i	−0.135609	+	0.172441i
$890$	44.8529	+	38.8652i	1.50347	+	1.30277i
$891$		0			0
$892$	−2.75934	−	0.810214i	−0.0923894	−	0.0271280i
$893$	−39.5617	−	3.77768i	−1.32388	−	0.126415i
$894$		0			0
$895$	39.0404	+	1.85972i	1.30498	+	0.0621637i
$896$	6.48980	+	11.2407i	0.216809	+	0.375524i
$897$		0			0
$898$	15.8899	−	27.5221i	0.530252	−	0.918424i
$899$	0.776759	−	1.20866i	0.0259064	−	0.0403111i
$900$		0			0
$901$	15.9103	+	34.8387i	0.530049	+	1.16064i
$902$	10.1731	−	9.70007i	0.338729	−	0.322977i
$903$		0			0
$904$	1.07218	−	5.56300i	0.0356602	−	0.185023i
$905$	13.1879	+	32.9417i	0.438379	+	1.09502i
$906$		0			0
$907$	8.01202	+	41.5703i	0.266035	+	1.38032i	0.831489	+	0.555541i	$0.187489\pi$
$907$	8.01202	+	41.5703i	0.266035	+	1.38032i	−0.565454	+	0.824780i	$0.691299\pi$
$908$	2.91928	−	1.87611i	0.0968797	−	0.0622608i
$909$		0			0
$910$	2.26790	+	2.61730i	0.0751802	+	0.0867626i
$911$	−0.0468582	+	0.193152i	−0.00155248	+	0.00639942i	−0.972583	−	0.232558i	$-0.925290\pi$
$911$	−0.0468582	+	0.193152i	−0.00155248	+	0.00639942i	0.971030	+	0.238957i	$0.0768056\pi$
$912$		0			0
$913$	14.5420	+	2.80273i	0.481268	+	0.0927569i
$914$	28.9200	−	2.76153i	0.956589	−	0.0913432i
$915$		0			0
$916$	0.297008	−	3.11041i	0.00981343	−	0.102771i
$917$	1.92339	+	13.3775i	0.0635161	+	0.441764i
$918$		0			0
$919$			13.8209i			0.455910i	0.973672	+	0.227955i	$0.0732039\pi$
$919$			13.8209i			0.455910i	−0.973672	+	0.227955i	$0.926796\pi$
$920$	−35.1315	+	0.474867i	−1.15825	+	0.0156559i
$921$		0			0
$922$	−2.20105	+	46.2057i	−0.0724877	+	1.52170i
$923$	−4.24049	−	5.39222i	−0.139577	−	0.177487i
$924$		0			0
$925$	3.43388	+	3.60135i	0.112905	+	0.118412i
$926$	19.9914	+	9.12978i	0.656959	+	0.300023i
$927$		0			0
$928$	0.351105	−	2.44199i	0.0115256	−	0.0801623i
$929$	−20.4997	−	4.97316i	−0.672572	−	0.163164i	−0.115092	−	0.993355i	$-0.536716\pi$
$929$	−20.4997	−	4.97316i	−0.672572	−	0.163164i	−0.557480	+	0.830191i	$0.688232\pi$
$930$		0			0
$931$	8.53069	−	16.5472i	0.279582	−	0.542313i
$932$	1.19171	−	2.31160i	0.0390358	−	0.0757190i
$933$		0			0
$934$	33.3793	+	8.09774i	1.09221	+	0.264966i
$935$	−1.97675	+	13.7486i	−0.0646466	+	0.449627i
$936$		0			0
$937$	−7.22931	−	3.30152i	−0.236171	−	0.107856i	0.293814	−	0.955863i	$-0.405075\pi$
$937$	−7.22931	−	3.30152i	−0.236171	−	0.107856i	−0.529985	+	0.848007i	$0.677803\pi$
$938$	−1.46139	−	1.53266i	−0.0477160	−	0.0500431i
$939$		0			0
$940$	−3.24193	−	4.12244i	−0.105740	−	0.134459i
$941$	0.00105958	−	0.0222434i	3.45414e−5	−	0.000725113i	−0.998850	−	0.0479445i	$-0.984733\pi$
$941$	0.00105958	−	0.0222434i	3.45414e−5	−	0.000725113i	0.998885	+	0.0472194i	$0.0150360\pi$
$942$		0			0
$943$	−6.50503	−	41.2752i	−0.211833	−	1.34410i
$944$		−	19.8646i		−	0.646539i
$945$		0			0
$946$	2.70472	+	18.8118i	0.0879382	+	0.611624i
$947$	−0.290588	+	3.04318i	−0.00944285	+	0.0988900i	−0.998965	−	0.0454937i	$-0.985514\pi$
$947$	−0.290588	+	3.04318i	−0.00944285	+	0.0988900i	0.989522	+	0.144384i	$0.0461200\pi$
$948$		0			0
$949$	−2.85086	+	0.272224i	−0.0925428	+	0.00883676i
$950$	10.4864	+	2.02109i	0.340224	+	0.0655728i
$951$		0			0
$952$	3.11455	−	12.8384i	0.100943	−	0.416094i
$953$	29.2523	+	33.7589i	0.947575	+	1.09356i	0.995505	+	0.0947087i	$0.0301920\pi$
$953$	29.2523	+	33.7589i	0.947575	+	1.09356i	−0.0479305	+	0.998851i	$0.515263\pi$
$954$		0			0
$955$	−57.3866	+	36.8801i	−1.85699	+	1.19341i
$956$	0.223388	+	1.15905i	0.00722490	+	0.0374863i
$957$		0			0
$958$	−3.38453	−	8.45414i	−0.109349	−	0.273141i
$959$	−1.84873	+	9.59214i	−0.0596987	+	0.309746i
$960$		0			0
$961$	−22.2510	+	21.2163i	−0.717774	+	0.684396i
$962$	−1.09821	−	2.40475i	−0.0354078	−	0.0775322i
$963$		0			0
$964$	2.25656	−	3.51128i	0.0726789	−	0.113091i
$965$	−25.1142	+	43.4990i	−0.808454	+	1.40028i
$966$		0			0
$967$	−13.6653	−	23.6690i	−0.439447	−	0.761144i	0.558200	−	0.829706i	$-0.311492\pi$
$967$	−13.6653	−	23.6690i	−0.439447	−	0.761144i	−0.997647	+	0.0685623i	$0.978159\pi$
$968$	26.5002	+	1.26236i	0.851749	+	0.0405738i
$969$		0			0
$970$	−30.4324	−	2.90594i	−0.977125	−	0.0933041i
$971$	−29.7050	−	8.72218i	−0.953280	−	0.279908i	−0.232128	−	0.972685i	$-0.574569\pi$
$971$	−29.7050	−	8.72218i	−0.953280	−	0.279908i	−0.721152	+	0.692777i	$0.756387\pi$
$972$		0			0
$973$	−9.65347	−	8.36478i	−0.309476	−	0.268163i
$974$	−30.6102	+	38.9240i	−0.980813	+	1.24721i
$975$		0			0
$976$	10.6048	+	3.67036i	0.339451	+	0.117485i
$977$	41.6589	+	21.4767i	1.33279	+	0.687099i	0.969618	−	0.244624i	$-0.0786646\pi$
$977$	41.6589	+	21.4767i	1.33279	+	0.687099i	0.363168	+	0.931723i	$0.381695\pi$
$978$		0			0
$979$	16.1455	−	3.11178i	0.516011	−	0.0994530i
$980$	2.35724	−	0.692147i	0.0752991	−	0.0221098i
$981$		0			0
$982$	−33.0687	+	38.1633i	−1.05526	+	1.21784i
$983$	−28.7788	−	40.4142i	−0.917902	−	1.28901i	−0.957093	−	0.289781i	$-0.906418\pi$
$983$	−28.7788	−	40.4142i	−0.917902	−	1.28901i	0.0391912	−	0.999232i	$-0.487522\pi$
$984$		0			0
$985$	−42.0315	−	29.9305i	−1.33924	−	0.953665i
$986$	−15.3283	+	12.0543i	−0.488154	+	0.383888i
$987$		0			0
$988$	−0.350674	−	0.202462i	−0.0111564	−	0.00644117i
$989$	50.5604	+	25.2067i	1.60773	+	0.801525i
$990$		0			0
$991$	−17.8109	−	11.4464i	−0.565782	−	0.363606i	0.226266	−	0.974066i	$-0.427348\pi$
$991$	−17.8109	−	11.4464i	−0.565782	−	0.363606i	−0.792047	+	0.610460i	$0.790985\pi$
$992$	0.162929	−	0.406978i	0.00517302	−	0.0129216i
$993$		0			0
$994$	12.2031	−	2.96044i	0.387059	−	0.0938995i
$995$	0.471737	+	4.94026i	0.0149551	+	0.156617i
$996$		0			0
$997$	10.5293	+	8.28031i	0.333465	+	0.262240i	0.770825	−	0.637046i	$-0.219844\pi$
$997$	10.5293	+	8.28031i	0.333465	+	0.262240i	−0.437360	+	0.899286i	$0.644086\pi$
$998$	8.50278	+	28.9578i	0.269151	+	0.916644i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	621.2.s.a.251.16		440
3.2	odd	2		207.2.o.a.182.7	yes	440
9.4	even	3		207.2.o.a.113.7	yes	440
9.5	odd	6	inner	621.2.s.a.44.16		440
23.11	odd	22	inner	621.2.s.a.494.16		440
69.11	even	22		207.2.o.a.11.7	✓	440
207.103	odd	66		207.2.o.a.149.7	yes	440
207.149	even	66	inner	621.2.s.a.287.16		440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.7	✓	440	69.11	even	22
207.2.o.a.113.7	yes	440	9.4	even	3
207.2.o.a.149.7	yes	440	207.103	odd	66
207.2.o.a.182.7	yes	440	3.2	odd	2
621.2.s.a.44.16		440	9.5	odd	6	inner
621.2.s.a.251.16		440	1.1	even	1	trivial
621.2.s.a.287.16		440	207.149	even	66	inner
621.2.s.a.494.16		440	23.11	odd	22	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 621 = 3^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	621.s (of order \(66\), degree \(20\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.672471 + 1.30441i) q^{2} +(-0.0891590 + 0.125206i) q^{4} +(0.637451 + 2.62761i) q^{5} +(0.985992 - 0.341255i) q^{7} +(2.68195 + 0.385606i) q^{8} +(-2.99882 + 2.59849i) q^{10} +(0.0523085 + 1.09809i) q^{11} +(0.273590 - 0.790486i) q^{13} +(1.10819 + 1.05666i) q^{14} +(1.40109 + 4.04818i) q^{16} +(1.94122 - 4.25068i) q^{17} +(-2.86472 + 1.30827i) q^{19} +(-0.385828 - 0.154462i) q^{20} +(-1.39719 + 0.806666i) q^{22} +(-0.391306 + 4.77984i) q^{23} +(-2.05380 + 1.05881i) q^{25} +(1.21510 - 0.174705i) q^{26} +(-0.0451828 + 0.153878i) q^{28} +(-2.31627 + 1.64941i) q^{29} +(-0.469073 + 0.187789i) q^{31} +(-0.598728 + 0.627927i) q^{32} +(6.85005 - 0.326308i) q^{34} +(1.52521 + 2.37327i) q^{35} +(-0.606716 - 2.06629i) q^{37} +(-3.63297 - 2.85700i) q^{38} +(0.696389 + 7.29292i) q^{40} +(-8.46710 + 2.05410i) q^{41} +(4.37823 - 10.9363i) q^{43} +(-0.142152 - 0.0913553i) q^{44} +(-6.49802 + 2.70388i) q^{46} +(10.9285 + 6.30957i) q^{47} +(-4.64665 + 3.65416i) q^{49} +(-2.76225 - 1.96699i) q^{50} +(0.0745809 + 0.104734i) q^{52} +(-5.36725 + 6.19414i) q^{53} +(-2.85201 + 0.837425i) q^{55} +(2.77597 - 0.535025i) q^{56} +(-3.70913 - 1.91219i) q^{58} +(-4.38212 - 1.51667i) q^{59} +(1.61936 - 2.05918i) q^{61} +(-0.560392 - 0.485582i) q^{62} +(6.99883 + 2.05504i) q^{64} +(2.25149 + 0.214991i) q^{65} +(-1.38147 - 0.0658073i) q^{67} +(0.359135 + 0.622040i) q^{68} +(-2.07006 + 3.58545i) q^{70} +(4.43366 - 6.89892i) q^{71} +(-1.42222 - 3.11423i) q^{73} +(2.28729 - 2.18092i) q^{74} +(0.0916114 - 0.475325i) q^{76} +(0.426305 + 1.06486i) q^{77} +(-2.89846 - 15.0386i) q^{79} +(-9.74392 + 6.26203i) q^{80} +(-8.37327 - 9.66327i) q^{82} +(3.17600 - 13.0917i) q^{83} +(12.4066 + 2.39117i) q^{85} +(17.2096 - 1.64332i) q^{86} +(-0.283142 + 2.96519i) q^{88} +(-2.12858 - 14.8046i) q^{89} -0.872777i q^{91} +(-0.563578 - 0.475160i) q^{92} +(-0.881181 + 18.4983i) q^{94} +(-5.26374 - 6.69340i) q^{95} +(5.31660 + 5.57589i) q^{97} +(-7.89127 - 3.60382i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q + 27 q^{2} - 29 q^{4} + 33 q^{5} - 11 q^{7} - 44 q^{10} + 33 q^{11} - 9 q^{13} + 33 q^{14} + 3 q^{16} - 44 q^{19} + 33 q^{20} + 27 q^{23} + 11 q^{25} - 44 q^{28} - 27 q^{29} - 3 q^{31} + 33 q^{32}+ \cdots + 22 q^{97}+O(q^{100}) \) 440 * q + 27 * q^2 - 29 * q^4 + 33 * q^5 - 11 * q^7 - 44 * q^10 + 33 * q^11 - 9 * q^13 + 33 * q^14 + 3 * q^16 - 44 * q^19 + 33 * q^20 + 27 * q^23 + 11 * q^25 - 44 * q^28 - 27 * q^29 - 3 * q^31 + 33 * q^32 - 11 * q^34 - 44 * q^37 + 33 * q^38 - 77 * q^40 - 9 * q^41 - 11 * q^43 - 36 * q^46 + 120 * q^47 + 35 * q^49 + 3 * q^50 - 38 * q^52 - 44 * q^55 - 165 * q^56 - 10 * q^58 + 9 * q^59 - 11 * q^61 - 22 * q^64 - 198 * q^65 - 11 * q^67 - 70 * q^70 - 36 * q^73 - 231 * q^74 - 11 * q^76 - 39 * q^77 - 11 * q^79 - 10 * q^82 - 66 * q^83 + q^85 + 33 * q^86 - 99 * q^88 - 63 * q^92 - 42 * q^94 + 93 * q^95 + 22 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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