LMFDB - Embedded newform 230.2.l.a.17.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(7,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

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

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

chi := DirichletCharacter("230.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			17.7
Character	$\chi$	$=$	230.17
Dual form			230.2.l.a.203.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.936950 - 0.349464i) q^{2} +(-1.94498 + 1.06204i) q^{3} +(0.755750 - 0.654861i) q^{4} +(-1.77597 - 1.35866i) q^{5} +(-1.45120 + 1.67478i) q^{6} +(-3.01546 - 4.02819i) q^{7} +(0.479249 - 0.877679i) q^{8} +(1.03309 - 1.60752i) q^{9} +(-2.13879 - 0.652357i) q^{10} +(1.58353 - 0.723173i) q^{11} +(-0.774429 + 2.07632i) q^{12} +(-0.286592 - 0.214540i) q^{13} +(-4.23304 - 2.72041i) q^{14} +(4.89716 + 0.756414i) q^{15} +(0.142315 - 0.989821i) q^{16} +(-0.152966 - 2.13874i) q^{17} +(0.406183 - 1.86719i) q^{18} +(-0.840634 - 0.970143i) q^{19} +(-2.23192 + 0.136206i) q^{20} +(10.1431 + 4.63220i) q^{21} +(1.23096 - 1.23096i) q^{22} +(-4.06631 + 2.54267i) q^{23} +2.21605i q^{24} +(1.30811 + 4.82585i) q^{25} +(-0.343496 - 0.100860i) q^{26} +(0.172183 - 2.40743i) q^{27} +(-4.91683 - 1.06959i) q^{28} +(1.98168 + 1.71713i) q^{29} +(4.85273 - 1.00266i) q^{30} +(-8.43162 + 2.47575i) q^{31} +(-0.212565 - 0.977147i) q^{32} +(-2.31189 + 3.08832i) q^{33} +(-0.890734 - 1.95044i) q^{34} +(-0.117565 + 11.2509i) q^{35} +(-0.271944 - 1.89141i) q^{36} +(8.59708 - 1.87018i) q^{37} +(-1.12666 - 0.615204i) q^{38} +(0.785264 + 0.112904i) q^{39} +(-2.04359 + 0.907593i) q^{40} +(7.16256 - 4.60310i) q^{41} +(11.1224 + 0.795486i) q^{42} +(-2.22999 - 4.08392i) q^{43} +(0.723173 - 1.58353i) q^{44} +(-4.01880 + 1.45129i) q^{45} +(-2.92135 + 3.80338i) q^{46} +(-1.60762 - 1.60762i) q^{47} +(0.774429 + 2.07632i) q^{48} +(-5.16114 + 17.5772i) q^{49} +(2.91209 + 4.06445i) q^{50} +(2.56894 + 3.99735i) q^{51} +(-0.357085 + 0.0255393i) q^{52} +(6.18386 - 4.62918i) q^{53} +(-0.679983 - 2.31581i) q^{54} +(-3.79484 - 0.867141i) q^{55} +(-4.98061 + 0.716104i) q^{56} +(2.66534 + 0.994122i) q^{57} +(2.45681 + 0.916342i) q^{58} +(12.7331 - 1.83074i) q^{59} +(4.19637 - 2.63530i) q^{60} +(-2.29221 - 7.80653i) q^{61} +(-7.03482 + 5.26620i) q^{62} +(-9.59064 + 0.685936i) q^{63} +(-0.540641 - 0.841254i) q^{64} +(0.217491 + 0.770395i) q^{65} +(-1.08687 + 3.70153i) q^{66} +(1.91069 + 5.12275i) q^{67} +(-1.51618 - 1.51618i) q^{68} +(5.20847 - 9.26400i) q^{69} +(3.82163 + 10.5826i) q^{70} +(5.18399 - 11.3514i) q^{71} +(-0.915780 - 1.67713i) q^{72} +(-9.66299 - 0.691111i) q^{73} +(7.40147 - 4.75664i) q^{74} +(-7.66948 - 7.99692i) q^{75} +(-1.27062 - 0.182687i) q^{76} +(-7.68815 - 4.19805i) q^{77} +(0.775209 - 0.168636i) q^{78} +(-1.85277 - 12.8863i) q^{79} +(-1.59757 + 1.56453i) q^{80} +(4.60329 + 10.0798i) q^{81} +(5.10234 - 6.81593i) q^{82} +(-0.422472 - 1.94207i) q^{83} +(10.6991 - 3.14153i) q^{84} +(-2.63415 + 4.00616i) q^{85} +(-3.51657 - 3.04713i) q^{86} +(-5.67798 - 1.23517i) q^{87} +(0.124191 - 1.73641i) q^{88} +(-0.850880 - 0.249841i) q^{89} +(-3.25824 + 2.76421i) q^{90} +1.80138i q^{91} +(-1.40802 + 4.58448i) q^{92} +(13.7700 - 13.7700i) q^{93} +(-2.06807 - 0.944454i) q^{94} +(0.174845 + 2.86507i) q^{95} +(1.45120 + 1.67478i) q^{96} +(-1.33036 + 6.11554i) q^{97} +(1.30688 + 18.2726i) q^{98} +(0.473413 - 3.29266i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{22}\right)$

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 $

$2$	0.936950	−	0.349464i	0.662524	−	0.247108i
$2$	0.936950	−	0.349464i	0.662524	−	0.247108i
$3$	−1.94498	+	1.06204i	−1.12293	+	0.613168i	−0.929822	−	0.368009i	$-0.880040\pi$
$3$	−1.94498	+	1.06204i	−1.12293	+	0.613168i	−0.193111	+	0.981177i	$0.561858\pi$
$4$	0.755750	−	0.654861i	0.377875	−	0.327430i
$5$	−1.77597	−	1.35866i	−0.794236	−	0.607610i
$5$	−1.77597	−	1.35866i	−0.794236	−	0.607610i
$6$	−1.45120	+	1.67478i	−0.592451	+	0.683725i
$7$	−3.01546	−	4.02819i	−1.13974	−	1.52251i	−0.817571	−	0.575828i	$-0.804680\pi$
$7$	−3.01546	−	4.02819i	−1.13974	−	1.52251i	−0.322166	−	0.946683i	$-0.604411\pi$
$8$	0.479249	−	0.877679i	0.169440	−	0.310306i
$9$	1.03309	−	1.60752i	0.344364	−	0.535840i
$10$	−2.13879	−	0.652357i	−0.676345	−	0.206293i
$11$	1.58353	−	0.723173i	0.477452	−	0.218045i	−0.162128	−	0.986770i	$-0.551836\pi$
$11$	1.58353	−	0.723173i	0.477452	−	0.218045i	0.639580	+	0.768725i	$0.279108\pi$
$12$	−0.774429	+	2.07632i	−0.223558	+	0.599383i
$13$	−0.286592	−	0.214540i	−0.0794863	−	0.0595027i	0.558796	−	0.829305i	$-0.311264\pi$
$13$	−0.286592	−	0.214540i	−0.0794863	−	0.0595027i	−0.638282	+	0.769803i	$0.720355\pi$
$14$	−4.23304	−	2.72041i	−1.13133	−	0.727060i
$15$	4.89716	+	0.756414i	1.26444	+	0.195305i
$16$	0.142315	−	0.989821i	0.0355787	−	0.247455i
$17$	−0.152966	−	2.13874i	−0.0370996	−	0.518721i	−0.981692	−	0.190475i	$-0.938997\pi$
$17$	−0.152966	−	2.13874i	−0.0370996	−	0.518721i	0.944592	−	0.328246i	$-0.106457\pi$
$18$	0.406183	−	1.86719i	0.0957383	−	0.440102i
$19$	−0.840634	−	0.970143i	−0.192855	−	0.222566i	0.651084	−	0.759005i	$-0.274314\pi$
$19$	−0.840634	−	0.970143i	−0.192855	−	0.222566i	−0.843939	+	0.536439i	$0.819769\pi$
$20$	−2.23192	+	0.136206i	−0.499072	+	0.0304565i
$21$	10.1431	+	4.63220i	2.21340	+	1.01083i
$22$	1.23096	−	1.23096i	0.262442	−	0.262442i
$23$	−4.06631	+	2.54267i	−0.847884	+	0.530182i
$23$	−4.06631	+	2.54267i	−0.847884	+	0.530182i
$24$			2.21605i			0.452349i
$25$	1.30811	+	4.82585i	0.261621	+	0.965171i
$26$	−0.343496	−	0.100860i	−0.0673651	−	0.0197802i
$27$	0.172183	−	2.40743i	0.0331366	−	0.463310i
$28$	−4.91683	−	1.06959i	−0.929194	−	0.202134i
$29$	1.98168	+	1.71713i	0.367988	+	0.318863i	0.819151	−	0.573578i	$-0.194445\pi$
$29$	1.98168	+	1.71713i	0.367988	+	0.318863i	−0.451163	+	0.892442i	$0.648991\pi$
$30$	4.85273	−	1.00266i	0.885983	−	0.183060i
$31$	−8.43162	+	2.47575i	−1.51436	+	0.444658i	−0.930223	−	0.366994i	$-0.880387\pi$
$31$	−8.43162	+	2.47575i	−1.51436	+	0.444658i	−0.584141	+	0.811652i	$0.698569\pi$
$32$	−0.212565	−	0.977147i	−0.0375766	−	0.172737i
$33$	−2.31189	+	3.08832i	−0.402449	+	0.537608i
$34$	−0.890734	−	1.95044i	−0.152760	−	0.334497i
$35$	−0.117565	+	11.2509i	−0.0198721	+	1.90175i
$36$	−0.271944	−	1.89141i	−0.0453241	−	0.315236i
$37$	8.59708	−	1.87018i	1.41335	−	0.307456i	0.559871	−	0.828580i	$-0.310851\pi$
$37$	8.59708	−	1.87018i	1.41335	−	0.307456i	0.853481	+	0.521124i	$0.174487\pi$
$38$	−1.12666	−	0.615204i	−0.182769	−	0.0997992i
$39$	0.785264	+	0.112904i	0.125743	+	0.0180791i
$40$	−2.04359	+	0.907593i	−0.323121	+	0.143503i
$41$	7.16256	−	4.60310i	1.11860	−	0.718884i	0.155453	−	0.987843i	$-0.450316\pi$
$41$	7.16256	−	4.60310i	1.11860	−	0.718884i	0.963151	+	0.268960i	$0.0866799\pi$
$42$	11.1224	+	0.795486i	1.71622	+	0.122746i
$43$	−2.22999	−	4.08392i	−0.340070	−	0.622792i	0.650546	−	0.759467i	$-0.274540\pi$
$43$	−2.22999	−	4.08392i	−0.340070	−	0.622792i	−0.990616	+	0.136675i	$0.956358\pi$
$44$	0.723173	−	1.58353i	0.109022	−	0.238726i
$45$	−4.01880	+	1.45129i	−0.599088	+	0.216345i
$46$	−2.92135	+	3.80338i	−0.430730	+	0.560778i
$47$	−1.60762	−	1.60762i	−0.234496	−	0.234496i	0.580071	−	0.814566i	$-0.303025\pi$
$47$	−1.60762	−	1.60762i	−0.234496	−	0.234496i	−0.814566	+	0.580071i	$0.803025\pi$
$48$	0.774429	+	2.07632i	0.111779	+	0.299692i
$49$	−5.16114	+	17.5772i	−0.737306	+	2.51103i
$50$	2.91209	+	4.06445i	0.411832	+	0.574799i
$51$	2.56894	+	3.99735i	0.359723	+	0.559740i
$52$	−0.357085	+	0.0255393i	−0.0495188	+	0.00354166i
$53$	6.18386	−	4.62918i	0.849419	−	0.635867i	−0.0832788	−	0.996526i	$-0.526539\pi$
$53$	6.18386	−	4.62918i	0.849419	−	0.635867i	0.932698	+	0.360659i	$0.117448\pi$
$54$	−0.679983	−	2.31581i	−0.0925340	−	0.315142i
$55$	−3.79484	−	0.867141i	−0.511696	−	0.116925i
$56$	−4.98061	+	0.716104i	−0.665562	+	0.0956934i
$57$	2.66534	+	0.994122i	0.353033	+	0.131675i
$58$	2.45681	+	0.916342i	0.322595	+	0.120322i
$59$	12.7331	−	1.83074i	1.65771	−	0.238342i	0.751060	−	0.660234i	$-0.229543\pi$
$59$	12.7331	−	1.83074i	1.65771	−	0.238342i	0.906646	+	0.421891i	$0.138634\pi$
$60$	4.19637	−	2.63530i	0.541749	−	0.340215i
$61$	−2.29221	−	7.80653i	−0.293487	−	0.999524i	−0.965807	−	0.259263i	$-0.916520\pi$
$61$	−2.29221	−	7.80653i	−0.293487	−	0.999524i	0.672320	−	0.740261i	$-0.265298\pi$
$62$	−7.03482	+	5.26620i	−0.893423	+	0.668808i
$63$	−9.59064	+	0.685936i	−1.20831	+	0.0864198i
$64$	−0.540641	−	0.841254i	−0.0675801	−	0.105157i
$65$	0.217491	+	0.770395i	0.0269764	+	0.0955558i
$66$	−1.08687	+	3.70153i	−0.133784	+	0.455627i
$67$	1.91069	+	5.12275i	0.233427	+	0.625843i	0.999864	−	0.0164765i	$-0.00524488\pi$
$67$	1.91069	+	5.12275i	0.233427	+	0.625843i	−0.766437	+	0.642320i	$0.777972\pi$
$68$	−1.51618	−	1.51618i	−0.183864	−	0.183864i
$69$	5.20847	−	9.26400i	0.627026	−	1.11525i
$70$	3.82163	+	10.5826i	0.456772	+	1.26486i
$71$	5.18399	−	11.3514i	0.615227	−	1.34716i	−0.303714	−	0.952763i	$-0.598227\pi$
$71$	5.18399	−	11.3514i	0.615227	−	1.34716i	0.918941	−	0.394396i	$-0.129046\pi$
$72$	−0.915780	−	1.67713i	−0.107926	−	0.197651i
$73$	−9.66299	−	0.691111i	−1.13097	−	0.0808884i	−0.506717	−	0.862113i	$-0.669141\pi$
$73$	−9.66299	−	0.691111i	−1.13097	−	0.0808884i	−0.624251	+	0.781224i	$0.714596\pi$
$74$	7.40147	−	4.75664i	0.860404	−	0.552948i
$75$	−7.66948	−	7.99692i	−0.885595	−	0.923405i
$76$	−1.27062	−	0.182687i	−0.145750	−	0.0209557i
$77$	−7.68815	−	4.19805i	−0.876146	−	0.478412i
$78$	0.775209	−	0.168636i	0.0877751	−	0.0190943i
$79$	−1.85277	−	12.8863i	−0.208453	−	1.44982i	−0.778208	−	0.628007i	$-0.783871\pi$
$79$	−1.85277	−	12.8863i	−0.208453	−	1.44982i	0.569755	−	0.821814i	$-0.307038\pi$
$80$	−1.59757	+	1.56453i	−0.178614	+	0.174920i
$81$	4.60329	+	10.0798i	0.511477	+	1.11998i
$82$	5.10234	−	6.81593i	0.563460	−	0.752694i
$83$	−0.422472	−	1.94207i	−0.0463723	−	0.213170i	0.948130	−	0.317882i	$-0.102972\pi$
$83$	−0.422472	−	1.94207i	−0.0463723	−	0.213170i	−0.994503	+	0.104712i	$0.966608\pi$
$84$	10.6991	−	3.14153i	1.16737	−	0.342769i
$85$	−2.63415	+	4.00616i	−0.285714	+	0.434529i
$86$	−3.51657	−	3.04713i	−0.379202	−	0.328580i
$87$	−5.67798	−	1.23517i	−0.608743	−	0.132424i
$88$	0.124191	−	1.73641i	0.0132388	−	0.185102i
$89$	−0.850880	−	0.249841i	−0.0901931	−	0.0264831i	0.236325	−	0.971674i	$-0.424057\pi$
$89$	−0.850880	−	0.249841i	−0.0901931	−	0.0264831i	−0.326518	+	0.945191i	$0.605875\pi$
$90$	−3.25824	+	2.76421i	−0.343449	+	0.291373i
$91$			1.80138i			0.188836i
$92$	−1.40802	+	4.58448i	−0.146796	+	0.477965i
$93$	13.7700	−	13.7700i	1.42788	−	1.42788i
$94$	−2.06807	−	0.944454i	−0.213305	−	0.0974130i
$95$	0.174845	+	2.86507i	0.0179387	+	0.293950i
$96$	1.45120	+	1.67478i	0.148113	+	0.170931i
$97$	−1.33036	+	6.11554i	−0.135077	+	0.620939i	0.858973	+	0.512020i	$0.171103\pi$
$97$	−1.33036	+	6.11554i	−0.135077	+	0.620939i	−0.994051	+	0.108919i	$0.965261\pi$
$98$	1.30688	+	18.2726i	0.132015	+	1.84581i
$99$	0.473413	−	3.29266i	0.0475798	−	0.330925i
$100$	4.14886	+	2.79051i	0.414886	+	0.279051i
$101$	−6.06881	−	3.90018i	−0.603869	−	0.388083i	0.202685	−	0.979244i	$-0.435033\pi$
$101$	−6.06881	−	3.90018i	−0.603869	−	0.388083i	−0.806553	+	0.591161i	$0.798670\pi$
$102$	3.80390	+	2.84756i	0.376642	+	0.281951i
$103$	−3.08047	+	8.25906i	−0.303528	+	0.813789i	0.692222	+	0.721685i	$0.256632\pi$
$103$	−3.08047	+	8.25906i	−0.303528	+	0.813789i	−0.995749	+	0.0921041i	$0.970641\pi$
$104$	−0.325646	+	0.148718i	−0.0319322	+	0.0145830i
$105$	−11.7202	−	22.0076i	−1.14378	−	2.14772i
$106$	4.17623	−	6.49835i	0.405632	−	0.631175i
$107$	−8.88994	+	16.2807i	−0.859423	+	1.57392i	−0.0411016	+	0.999155i	$0.513087\pi$
$107$	−8.88994	+	16.2807i	−0.859423	+	1.57392i	−0.818321	+	0.574761i	$0.805095\pi$
$108$	−1.44640	−	1.93217i	−0.139180	−	0.185923i
$109$	0.870493	−	1.00460i	0.0833781	−	0.0962235i	−0.712528	−	0.701644i	$-0.752450\pi$
$109$	0.870493	−	1.00460i	0.0833781	−	0.0962235i	0.795906	+	0.605421i	$0.206995\pi$
$110$	−3.85861	+	0.513692i	−0.367904	+	0.0489786i
$111$	−14.7349	+	12.7679i	−1.39858	+	1.21187i
$112$	−4.41633	+	2.41150i	−0.417304	+	0.227865i
$113$	7.80568	−	2.91137i	0.734297	−	0.273879i	0.0456320	−	0.998958i	$-0.485470\pi$
$113$	7.80568	−	2.91137i	0.734297	−	0.273879i	0.688665	+	0.725080i	$0.258197\pi$
$114$	2.84470			0.266431
$115$	10.6762	+	1.00903i	0.995563	+	0.0940923i
$116$	2.62213			0.243459
$117$	−0.640953	+	0.239063i	−0.0592561	+	0.0221014i
$118$	11.2905	−	6.16507i	1.03937	−	0.567541i
$119$	−8.15398	+	7.06546i	−0.747474	+	0.647690i
$120$	3.01085	−	3.93562i	0.274851	−	0.359272i
$121$	−5.21888	+	6.02291i	−0.474444	+	0.547538i
$122$	−4.87578	−	6.51329i	−0.441433	−	0.589685i
$123$	−9.04236	+	16.5598i	−0.815322	+	1.49315i
$124$	−4.75093	+	7.39259i	−0.426646	+	0.663874i
$125$	4.23353	−	10.3478i	0.378658	−	0.925537i
$126$	−8.74624	+	3.99427i	−0.779177	+	0.355838i
$127$	2.36920	−	6.35208i	0.210233	−	0.563656i	−0.788443	−	0.615108i	$-0.789112\pi$
$127$	2.36920	−	6.35208i	0.210233	−	0.563656i	0.998675	+	0.0514526i	$0.0163851\pi$
$128$	−0.800541	−	0.599278i	−0.0707585	−	0.0529692i
$129$	8.67456	+	5.57480i	0.763752	+	0.490834i
$130$	0.473004	+	0.645816i	0.0414852	+	0.0566418i
$131$	1.37277	−	9.54782i	0.119939	−	0.834197i	−0.837680	−	0.546161i	$-0.816089\pi$
$131$	1.37277	−	9.54782i	0.119939	−	0.834197i	0.957620	−	0.288036i	$-0.0930022\pi$
$132$	0.275212	+	3.84797i	0.0239541	+	0.334922i
$133$	−1.37302	+	6.31166i	−0.119056	+	0.547290i
$134$	3.58043	+	4.13204i	0.309302	+	0.356954i
$135$	−3.57666	+	4.04157i	−0.307830	+	0.347843i
$136$	−1.95044	−	0.890734i	−0.167248	−	0.0763798i
$137$	2.69378	−	2.69378i	0.230145	−	0.230145i	−0.582608	−	0.812753i	$-0.697968\pi$
$137$	2.69378	−	2.69378i	0.230145	−	0.230145i	0.812753	+	0.582608i	$0.197968\pi$
$138$	1.64264	−	10.5001i	0.139830	−	0.893826i
$139$			4.84147i			0.410648i	0.978694	+	0.205324i	$0.0658248\pi$
$139$			4.84147i			0.410648i	−0.978694	+	0.205324i	$0.934175\pi$
$140$	7.27892	+	8.57985i	0.615181	+	0.725129i
$141$	4.83414	+	1.41943i	0.407108	+	0.119538i
$142$	0.890247	−	12.4473i	0.0747079	−	1.04455i
$143$	−0.608976	−	0.132475i	−0.0509251	−	0.0110781i
$144$	−1.44413	−	1.25135i	−0.120345	−	0.104279i
$145$	−1.18640	−	5.74198i	−0.0985248	−	0.476846i
$146$	−9.29525	+	2.72933i	−0.769281	+	0.225881i
$147$	−8.62938	−	39.6686i	−0.711740	−	3.27181i
$148$	5.27253	−	7.04328i	0.433400	−	0.578954i
$149$	−2.81382	−	6.16141i	−0.230517	−	0.504762i	0.758660	−	0.651487i	$-0.225854\pi$
$149$	−2.81382	−	6.16141i	−0.230517	−	0.504762i	−0.989177	+	0.146724i	$0.953127\pi$
$150$	−9.98055	−	4.81251i	−0.814909	−	0.392939i
$151$	−0.967841	−	6.73148i	−0.0787618	−	0.547800i	−0.990551	−	0.137142i	$-0.956208\pi$
$151$	−0.967841	−	6.73148i	−0.0787618	−	0.547800i	0.911790	−	0.410658i	$-0.134701\pi$
$152$	−1.25435	+	0.272866i	−0.101741	+	0.0221324i
$153$	−3.59610	−	1.96362i	−0.290727	−	0.158749i
$154$	−8.67047	−	1.24663i	−0.698687	−	0.100456i
$155$	18.3380	+	7.05884i	1.47294	+	0.566980i
$156$	0.667399	−	0.428912i	0.0534347	−	0.0343404i
$157$	−5.64895	−	0.404021i	−0.450835	−	0.0322444i	−0.155924	−	0.987769i	$-0.549835\pi$
$157$	−5.64895	−	0.404021i	−0.450835	−	0.0322444i	−0.294911	+	0.955525i	$0.595290\pi$
$158$	−6.23925	−	11.4263i	−0.496368	−	0.909030i
$159$	−7.11111	+	15.5712i	−0.563947	+	1.23487i
$160$	−0.950098	+	2.02418i	−0.0751119	+	0.160026i
$161$	22.5041	+	8.71252i	1.77357	+	0.686643i
$162$	7.83559	+	7.83559i	0.615622	+	0.615622i
$163$	−3.04893	−	8.17450i	−0.238811	−	0.640276i	0.761155	−	0.648570i	$-0.224633\pi$
$163$	−3.04893	−	8.17450i	−0.238811	−	0.640276i	−0.999966	+	0.00829377i	$0.997360\pi$
$164$	2.39872	−	8.16927i	0.187308	−	0.637913i
$165$	8.30181	−	2.34369i	0.646295	−	0.182456i
$166$	−1.07452	−	1.67198i	−0.0833989	−	0.129771i
$167$	18.4914	−	1.32253i	1.43091	−	0.102340i	0.665745	−	0.746179i	$-0.268114\pi$
$167$	18.4914	−	1.32253i	1.43091	−	0.102340i	0.765161	+	0.643839i	$0.222659\pi$
$168$	8.92665	−	6.68240i	0.688706	−	0.515559i
$169$	−3.62642	−	12.3504i	−0.278955	−	0.950034i
$170$	−1.06806	+	4.67411i	−0.0819164	+	0.358488i
$171$	−2.42798	+	0.349090i	−0.185672	+	0.0266956i
$172$	−4.35971	−	1.62609i	−0.332425	−	0.123988i
$173$	−5.28979	−	1.97299i	−0.402175	−	0.150004i	0.140233	−	0.990119i	$-0.455215\pi$
$173$	−5.28979	−	1.97299i	−0.402175	−	0.150004i	−0.542409	+	0.840115i	$0.682487\pi$
$174$	−5.75163	+	0.826959i	−0.436030	+	0.0626916i
$175$	15.4949	−	19.8215i	1.17130	−	1.49836i
$176$	−0.490453	−	1.67033i	−0.0369693	−	0.125906i
$177$	−22.8213	+	17.0838i	−1.71535	+	1.28410i
$178$	−0.884542	+	0.0632637i	−0.0662992	+	0.00474181i
$179$	10.0153	+	15.5842i	0.748582	+	1.16482i	0.981340	+	0.192282i	$0.0615887\pi$
$179$	10.0153	+	15.5842i	0.748582	+	1.16482i	−0.232758	+	0.972535i	$0.574775\pi$
$180$	−2.08682	+	3.72856i	−0.155542	+	0.277911i
$181$	0.0263216	−	0.0896432i	0.00195647	−	0.00666313i	−0.958509	−	0.285062i	$-0.907986\pi$
$181$	0.0263216	−	0.0896432i	0.00195647	−	0.00666313i	0.960465	+	0.278399i	$0.0898038\pi$
$182$	0.629518	+	1.68780i	0.0466630	+	0.125108i
$183$	12.7491	+	12.7491i	0.942442	+	0.942442i
$184$	0.282871	+	4.78748i	0.0208535	+	0.352938i
$185$	−17.8091	−	8.35911i	−1.30935	−	0.614574i
$186$	8.08967	−	17.7139i	0.593163	−	1.29885i
$187$	−1.78891	−	3.27614i	−0.130818	−	0.239575i
$188$	−2.26773	−	0.162191i	−0.165391	−	0.0118290i
$189$	−10.2168	+	6.56592i	−0.743161	+	0.477600i
$190$	1.16506	+	2.62333i	0.0845224	+	0.190316i
$191$	7.95083	+	1.14316i	0.575302	+	0.0827159i	0.423824	−	0.905745i	$-0.360688\pi$
$191$	7.95083	+	1.14316i	0.575302	+	0.0827159i	0.151478	+	0.988461i	$0.451597\pi$
$192$	1.94498	+	1.06204i	0.140367	+	0.0766460i
$193$	−2.62732	+	0.571539i	−0.189119	+	0.0411403i	−0.306127	−	0.951991i	$-0.599033\pi$
$193$	−2.62732	+	0.571539i	−0.189119	+	0.0411403i	0.117008	+	0.993131i	$0.462670\pi$
$194$	0.890688	+	6.19487i	0.0639476	+	0.444766i
$195$	−1.24120	−	1.26742i	−0.0888845	−	0.0907617i
$196$	7.61011	+	16.6638i	0.543579	+	1.19027i
$197$	0.0326122	−	0.0435648i	0.00232353	−	0.00310387i	−0.799378	−	0.600828i	$-0.794837\pi$
$197$	0.0326122	−	0.0435648i	0.00232353	−	0.00310387i	0.801701	+	0.597725i	$0.203928\pi$
$198$	−0.707103	−	3.25050i	−0.0502516	−	0.231003i
$199$	−20.2602	+	5.94892i	−1.43620	+	0.421708i	−0.904955	−	0.425507i	$-0.860096\pi$
$199$	−20.2602	+	5.94892i	−1.43620	+	0.421708i	−0.531250	+	0.847215i	$0.678277\pi$
$200$	4.86246	+	1.16469i	0.343828	+	0.0823560i
$201$	−9.15680	−	7.93441i	−0.645871	−	0.559650i
$202$	−7.04914	−	1.53345i	−0.495976	−	0.107893i
$203$	0.941258	−	13.1605i	0.0660634	−	0.923686i
$204$	4.55918	+	1.33870i	0.319206	+	0.0937275i
$205$	−18.9745	−	1.55652i	−1.32524	−	0.108712i
$206$			8.81483i			0.614159i
$207$	−0.113476	+	9.16348i	−0.00788713	+	0.636906i
$208$	−0.253142	+	0.253142i	−0.0175523	+	0.0175523i
$209$	−2.03275	−	0.928326i	−0.140608	−	0.0642136i
$210$	−18.6721	−	16.5242i	−1.28850	−	1.14028i
$211$	0.944061	+	1.08950i	0.0649918	+	0.0750045i	0.787314	−	0.616552i	$-0.211471\pi$
$211$	0.944061	+	1.08950i	0.0649918	+	0.0750045i	−0.722323	+	0.691556i	$0.756925\pi$
$212$	1.64198	−	7.54807i	0.112772	−	0.518404i
$213$	1.97283	+	27.5837i	0.135176	+	1.89001i
$214$	−2.63990	+	18.3609i	−0.180460	+	1.25513i
$215$	−1.58826	+	10.2827i	−0.108319	+	0.701274i
$216$	−2.03043	−	1.30488i	−0.138153	−	0.0887857i
$217$	35.3980	+	26.4986i	2.40297	+	1.79884i
$218$	0.464536	−	1.24547i	0.0314623	−	0.0843538i
$219$	19.5283	−	8.91827i	1.31960	−	0.602641i
$220$	−3.43580	+	1.82975i	−0.231642	+	0.123362i
$221$	−0.415006	+	0.645763i	−0.0279164	+	0.0434387i
$222$	−9.34397	+	17.1122i	−0.627126	+	1.14850i
$223$	16.3541	+	21.8465i	1.09515	+	1.46295i	0.872860	+	0.487970i	$0.162262\pi$
$223$	16.3541	+	21.8465i	1.09515	+	1.46295i	0.222290	+	0.974980i	$0.428647\pi$
$224$	−3.29515	+	3.80280i	−0.220166	+	0.254085i
$225$	9.10905	+	2.88274i	0.607270	+	0.192183i
$226$	6.29611	−	5.45561i	0.418811	−	0.362902i
$227$	21.0589	−	11.4990i	1.39773	−	0.763218i	0.408944	−	0.912559i	$-0.365897\pi$
$227$	21.0589	−	11.4990i	1.39773	−	0.763218i	0.988786	+	0.149341i	$0.0477153\pi$
$228$	2.66534	−	0.994122i	0.176517	−	0.0658373i
$229$	15.0265			0.992982			0.496491	−	0.868042i	$-0.334622\pi$
$229$	15.0265			0.992982			0.496491	+	0.868042i	$0.334622\pi$
$230$	10.3557	−	2.78555i	0.682835	−	0.183674i
$231$	19.4118			1.27720
$232$	2.45681	−	0.916342i	0.161297	−	0.0601608i
$233$	3.74790	−	2.04651i	0.245533	−	0.134071i	−0.351771	−	0.936086i	$-0.614420\pi$
$233$	3.74790	−	2.04651i	0.245533	−	0.134071i	0.597304	+	0.802015i	$0.296239\pi$
$234$	−0.516997	+	0.447980i	−0.0337971	+	0.0292854i
$235$	0.670874	+	5.03928i	0.0437630	+	0.328727i
$236$	8.42414	−	9.72198i	0.548365	−	0.632847i
$237$	17.2893	+	23.0958i	1.12306	+	1.50024i
$238$	−5.17074	+	9.46951i	−0.335169	+	0.613817i
$239$	−9.88846	+	15.3867i	−0.639631	+	0.995286i	0.358461	+	0.933545i	$0.383302\pi$
$239$	−9.88846	+	15.3867i	−0.639631	+	0.995286i	−0.998092	+	0.0617411i	$0.980335\pi$
$240$	1.44565	−	4.73966i	0.0933165	−	0.305944i
$241$	−21.1235	+	9.64676i	−1.36068	+	0.621402i	−0.956084	−	0.293092i	$-0.905316\pi$
$241$	−21.1235	+	9.64676i	−1.36068	+	0.621402i	−0.404597	+	0.914495i	$0.632588\pi$
$242$	−2.78504	+	7.46698i	−0.179029	+	0.479996i
$243$	−13.8619	−	10.3769i	−0.889244	−	0.665680i
$244$	−6.84453	−	4.39871i	−0.438176	−	0.281599i
$245$	33.0474	−	24.2043i	2.11132	−	1.54636i
$246$	−2.68516	+	18.6757i	−0.171200	+	1.19072i
$247$	0.0327843	+	0.458384i	0.00208602	+	0.0291663i
$248$	−1.86794	+	8.58676i	−0.118614	+	0.545260i
$249$	2.88425	+	3.32860i	0.182782	+	0.210942i
$250$	0.350413	−	11.1748i	0.0221621	−	0.706759i
$251$	17.2470	+	7.87643i	1.08862	+	0.497156i	0.877144	−	0.480228i	$-0.159446\pi$
$251$	17.2470	+	7.87643i	1.08862	+	0.497156i	0.211475	+	0.977383i	$0.432173\pi$
$252$	−6.79893	+	6.79893i	−0.428292	+	0.428292i
$253$	−4.60033	+	6.96703i	−0.289220	+	0.438013i
$254$		−	6.77953i		−	0.425385i
$255$	0.868675	−	10.5895i	0.0543985	−	0.663137i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	−1.95658	+	27.3566i	−0.122048	+	1.70646i	0.455609	+	0.890180i	$0.349421\pi$
$257$	−1.95658	+	27.3566i	−0.122048	+	1.70646i	−0.577658	+	0.816279i	$0.696033\pi$
$258$	10.0758	+	2.19186i	0.627293	+	0.136459i
$259$	−33.4576	−	28.9912i	−2.07895	−	1.80142i
$260$	0.668870	+	0.439800i	0.0414816	+	0.0272752i
$261$	4.80758	−	1.41163i	0.297582	−	0.0873779i
$262$	−2.05040	−	9.42556i	−0.126674	−	0.582313i
$263$	−3.63465	+	4.85533i	−0.224122	+	0.299392i	−0.898482	−	0.439011i	$-0.855329\pi$
$263$	−3.63465	+	4.85533i	−0.224122	+	0.299392i	0.674359	+	0.738403i	$0.264420\pi$
$264$	1.60259	+	3.50917i	0.0986324	+	0.215975i
$265$	−17.2718	−	0.180480i	−1.06100	−	0.0110868i
$266$	0.919250	+	6.39353i	0.0563628	+	0.392012i
$267$	1.92028	−	0.417732i	0.117519	−	0.0255648i
$268$	4.79869	+	2.62028i	0.293126	+	0.160059i
$269$	−1.72287	−	0.247711i	−0.105045	−	0.0151032i	0.0895919	−	0.995979i	$-0.471444\pi$
$269$	−1.72287	−	0.247711i	−0.105045	−	0.0151032i	−0.194637	+	0.980875i	$0.562353\pi$
$270$	−1.93876	+	5.03666i	−0.117989	+	0.306521i
$271$	−3.11247	+	2.00026i	−0.189069	+	0.121507i	−0.631751	−	0.775171i	$-0.717663\pi$
$271$	−3.11247	+	2.00026i	−0.189069	+	0.121507i	0.442682	+	0.896679i	$0.354027\pi$
$272$	−2.13874	−	0.152966i	−0.129680	−	0.00927491i
$273$	−1.91314	−	3.50365i	−0.115788	−	0.212050i
$274$	1.58256	−	3.46532i	0.0956059	−	0.209348i
$275$	5.56135	+	6.69589i	0.335362	+	0.403777i
$276$	−2.13033	−	10.4121i	−0.128231	−	0.626734i
$277$	−7.90299	−	7.90299i	−0.474845	−	0.474845i	0.428634	−	0.903478i	$-0.358995\pi$
$277$	−7.90299	−	7.90299i	−0.474845	−	0.474845i	−0.903478	+	0.428634i	$0.858995\pi$
$278$	1.69192	+	4.53621i	0.101475	+	0.272064i
$279$	−4.73082	+	16.1117i	−0.283227	+	0.964582i
$280$	9.81833	+	5.49516i	0.586757	+	0.328399i
$281$	−14.9057	−	23.1938i	−0.889201	−	1.38362i	−0.923248	−	0.384203i	$-0.874476\pi$
$281$	−14.9057	−	23.1938i	−0.889201	−	1.38362i	0.0340475	−	0.999420i	$-0.489160\pi$
$282$	5.02539	−	0.359423i	0.299258	−	0.0214033i
$283$	15.0950	−	11.3000i	0.897306	−	0.671715i	−0.0476672	−	0.998863i	$-0.515179\pi$
$283$	15.0950	−	11.3000i	0.897306	−	0.671715i	0.944973	+	0.327149i	$0.106088\pi$
$284$	−3.51576	−	11.9736i	−0.208622	−	0.710501i
$285$	−3.38289	−	5.38681i	−0.200385	−	0.319087i
$286$	−0.616875	+	0.0886932i	−0.0364766	+	0.00524454i
$287$	−40.1406	−	14.9717i	−2.36942	−	0.883749i
$288$	−1.79038	−	0.667779i	−0.105499	−	0.0393492i
$289$	12.2762	−	1.76504i	0.722127	−	0.103826i
$290$	−3.11821	−	4.96535i	−0.183108	−	0.291575i
$291$	−3.90743	−	13.3075i	−0.229058	−	0.780099i
$292$	−7.75538	+	5.80561i	−0.453849	+	0.339747i
$293$	17.6604	−	1.26310i	1.03173	−	0.0737909i	0.454809	−	0.890589i	$-0.349708\pi$
$293$	17.6604	−	1.26310i	1.03173	−	0.0737909i	0.576923	+	0.816798i	$0.304253\pi$
$294$	−21.9481	−	34.1519i	−1.28004	−	1.99178i
$295$	−25.1009	−	14.0486i	−1.46143	−	0.817939i
$296$	2.47872	−	8.44176i	0.144073	−	0.490667i
$297$	−1.46833	−	3.93675i	−0.0852012	−	0.228433i
$298$	−4.78960	−	4.78960i	−0.277454	−	0.277454i
$299$	1.71087	+	0.143678i	0.0989424	+	0.00830911i
$300$	−11.0331	−	1.02123i	−0.636995	−	0.0589608i
$301$	−9.72634	+	21.2977i	−0.560617	+	1.22758i
$302$	−3.25923	−	5.96883i	−0.187548	−	0.343468i
$303$	15.9458	+	1.14047i	0.916065	+	0.0655182i
$304$	−1.07990	+	0.694012i	−0.0619367	+	0.0398043i
$305$	−6.53552	+	16.9785i	−0.374223	+	0.972183i
$306$	−4.05558	−	0.583104i	−0.231842	−	0.0333338i
$307$	6.20754	+	3.38957i	0.354283	+	0.193453i	0.646528	−	0.762890i	$-0.276220\pi$
$307$	6.20754	+	3.38957i	0.354283	+	0.193453i	−0.292245	+	0.956343i	$0.594402\pi$
$308$	−8.55945	+	1.86199i	−0.487720	+	0.106097i
$309$	−2.77999	−	19.3353i	−0.158148	−	1.09994i
$310$	19.6486	+	0.205315i	1.11596	+	0.0116611i
$311$	−2.36784	−	5.18484i	−0.134268	−	0.294005i	0.830541	−	0.556957i	$-0.188031\pi$
$311$	−2.36784	−	5.18484i	−0.134268	−	0.294005i	−0.964809	+	0.262952i	$0.915304\pi$
$312$	0.475431	−	0.635101i	0.0269160	−	0.0359555i
$313$	1.88372	+	8.65932i	0.106474	+	0.489453i	0.999242	+	0.0389360i	$0.0123968\pi$
$313$	1.88372	+	8.65932i	0.106474	+	0.489453i	−0.892768	+	0.450517i	$0.851240\pi$
$314$	−5.43397	+	1.59556i	−0.306657	+	0.0900425i
$315$	17.9646	+	11.8122i	1.01219	+	0.665541i
$316$	−9.83895	−	8.52550i	−0.553484	−	0.479597i
$317$	6.37138	+	1.38601i	0.357852	+	0.0778460i	0.387897	−	0.921703i	$-0.373201\pi$
$317$	6.37138	+	1.38601i	0.357852	+	0.0778460i	−0.0300451	+	0.999549i	$0.509565\pi$
$318$	−1.22119	+	17.0745i	−0.0684809	+	0.957488i
$319$	4.37983	+	1.28603i	0.245223	+	0.0720040i
$320$	−0.182815	+	2.22858i	−0.0102197	+	0.124582i
$321$		−	41.1071i		−	2.29437i
$322$	24.1299	+	0.298814i	1.34471	+	0.0166522i
$323$	−1.94630	+	1.94630i	−0.108295	+	0.108295i
$324$	10.0798	+	4.60329i	0.559989	+	0.255738i
$325$	0.660446	−	1.66369i	0.0366350	−	0.0922850i
$326$	−5.71339	−	6.59361i	−0.316435	−	0.365186i
$327$	−0.626163	+	2.87843i	−0.0346269	+	0.159177i
$328$	−0.607393	−	8.49246i	−0.0335377	−	0.468918i
$329$	−1.62808	+	11.3235i	−0.0897587	+	0.624286i
$330$	6.95934	−	5.09711i	0.383099	−	0.280586i
$331$	−8.34577	−	5.36350i	−0.458725	−	0.294805i	0.290796	−	0.956785i	$-0.406080\pi$
$331$	−8.34577	−	5.36350i	−0.458725	−	0.294805i	−0.749521	+	0.661980i	$0.769716\pi$
$332$	−1.59107	−	1.19106i	−0.0873213	−	0.0653679i
$333$	5.87521	−	15.7521i	0.321960	−	0.863208i
$334$	16.8633	−	7.70122i	0.922720	−	0.421392i
$335$	3.56674	−	11.6938i	0.194872	−	0.638900i
$336$	6.02856	−	9.38062i	0.328885	−	0.511755i
$337$	−1.53790	+	2.81645i	−0.0837747	+	0.153422i	−0.916208	−	0.400704i	$-0.868766\pi$
$337$	−1.53790	+	2.81645i	−0.0837747	+	0.153422i	0.832433	+	0.554126i	$0.186947\pi$
$338$	−7.71380	−	10.3044i	−0.419576	−	0.560487i
$339$	−12.0899	+	13.9525i	−0.656633	+	0.757795i
$340$	0.632715	+	4.75265i	0.0343138	+	0.257749i
$341$	−11.5613	+	10.0179i	−0.626081	+	0.542502i
$342$	−2.15290	+	1.17557i	−0.116415	+	0.0635676i
$343$	53.3655	−	19.9043i	2.88147	−	1.07473i
$344$	−4.65309			−0.250878
$345$	−21.8367	+	9.37603i	−1.17565	+	0.504788i
$346$	−5.64576			−0.303518
$347$	−19.8996	+	7.42215i	−1.06826	+	0.398442i	−0.821249	−	0.570570i	$-0.806723\pi$
$347$	−19.8996	+	7.42215i	−1.06826	+	0.398442i	−0.247015	+	0.969012i	$0.579450\pi$
$348$	−5.09999	+	2.78481i	−0.273388	+	0.149281i
$349$	13.3736	−	11.5883i	0.715873	−	0.620307i	−0.218819	−	0.975765i	$-0.570221\pi$
$349$	13.3736	−	11.5883i	0.715873	−	0.620307i	0.934692	+	0.355458i	$0.115675\pi$
$350$	7.59104	−	23.9866i	0.405758	−	1.28214i
$351$	−0.565835	+	0.653009i	−0.0302021	+	0.0348550i
$352$	−1.04325	−	1.39362i	−0.0556054	−	0.0742801i
$353$	−10.4659	+	19.1668i	−0.557043	+	1.02015i	0.435723	+	0.900081i	$0.356493\pi$
$353$	−10.4659	+	19.1668i	−0.557043	+	1.02015i	−0.992766	+	0.120067i	$0.961689\pi$
$354$	−15.4122	+	23.9818i	−0.819149	+	1.27462i
$355$	−24.6292	+	13.1164i	−1.30718	+	0.696144i
$356$	−0.806663	+	0.368391i	−0.0427531	+	0.0195247i
$357$	8.35552	−	22.4020i	0.442221	−	1.18564i
$358$	14.8300	+	11.1016i	0.783789	+	0.586737i
$359$	−17.0610	−	10.9644i	−0.900443	−	0.578680i	0.00647836	−	0.999979i	$-0.497938\pi$
$359$	−17.0610	−	10.9644i	−0.900443	−	0.578680i	−0.906922	+	0.421299i	$0.861574\pi$
$360$	−0.652244	+	4.22275i	−0.0343763	+	0.222558i
$361$	2.46947	−	17.1755i	0.129972	−	0.903976i
$362$	−0.00666506	−	0.0931897i	−0.000350308	−	0.00489794i
$363$	3.75405	−	17.2571i	0.197037	−	0.905762i
$364$	1.17965	+	1.36139i	0.0618307	+	0.0713564i
$365$	16.2221	+	14.3561i	0.849106	+	0.751431i
$366$	16.4007	+	7.48993i	0.857276	+	0.391505i
$367$	25.6411	−	25.6411i	1.33845	−	1.33845i	0.440896	−	0.897558i	$-0.354661\pi$
$367$	25.6411	−	25.6411i	1.33845	−	1.33845i	0.897558	−	0.440896i	$-0.145339\pi$
$368$	1.93809	+	4.38678i	0.101030	+	0.228677i
$369$		−	16.2694i		−	0.846951i
$370$	−19.6074	−	1.60844i	−1.01934	−	0.0836186i
$371$	−37.2944	−	10.9506i	−1.93623	−	0.568528i
$372$	1.38924	−	19.4241i	0.0720286	−	1.00709i
$373$	−7.79052	−	1.69472i	−0.403378	−	0.0877495i	0.00629906	−	0.999980i	$-0.497995\pi$
$373$	−7.79052	−	1.69472i	−0.403378	−	0.0877495i	−0.409677	+	0.912231i	$0.634359\pi$
$374$	−2.82101	−	2.44442i	−0.145871	−	0.126398i
$375$	2.75566	+	24.6224i	0.142301	+	1.27150i
$376$	−2.18143	+	0.640525i	−0.112498	+	0.0330325i
$377$	−0.199539	−	0.917265i	−0.0102768	−	0.0472415i
$378$	−7.27805	+	9.72233i	−0.374342	+	0.500063i
$379$	11.4836	+	25.1455i	0.589871	+	1.29164i	0.935520	+	0.353273i	$0.114931\pi$
$379$	11.4836	+	25.1455i	0.589871	+	1.29164i	−0.345649	+	0.938364i	$0.612341\pi$
$380$	2.00836	+	2.05078i	0.103027	+	0.105203i
$381$	2.13810	+	14.8708i	0.109538	+	0.761856i
$382$	7.84902	−	1.70745i	0.401591	−	0.0873607i
$383$	8.91501	+	4.86796i	0.455536	+	0.248741i	0.690598	−	0.723239i	$-0.257348\pi$
$383$	8.91501	+	4.86796i	0.455536	+	0.248741i	−0.235062	+	0.971980i	$0.575529\pi$
$384$	2.19349	+	0.315376i	0.111936	+	0.0160940i
$385$	7.95018	+	17.9011i	0.405179	+	0.912326i
$386$	−2.26194	+	1.45366i	−0.115130	+	0.0739893i
$387$	−8.86877	−	0.634307i	−0.450825	−	0.0322436i
$388$	2.99941	+	5.49302i	0.152272	+	0.278866i
$389$	−1.75863	+	3.85087i	−0.0891662	+	0.195247i	−0.948961	−	0.315392i	$-0.897864\pi$
$389$	−1.75863	+	3.85087i	−0.0891662	+	0.195247i	0.859795	+	0.510639i	$0.170591\pi$
$390$	−1.60586	−	0.753750i	−0.0813160	−	0.0381676i
$391$	6.06011	+	8.30783i	0.306473	+	0.420145i
$392$	12.9537	+	12.9537i	0.654260	+	0.654260i
$393$	7.47014	+	20.0282i	0.376819	+	1.01029i
$394$	0.0153317	−	0.0522149i	0.000772398	−	0.00263055i
$395$	−14.2176	+	25.4029i	−0.715365	+	1.27816i
$396$	−1.79845	−	2.79845i	−0.0903756	−	0.140627i
$397$	−27.0934	+	1.93776i	−1.35978	+	0.0972535i	−0.732089	−	0.681209i	$-0.761455\pi$
$397$	−27.0934	+	1.93776i	−1.35978	+	0.0972535i	−0.627692	+	0.778462i	$0.716000\pi$
$398$	−16.9038	+	12.6540i	−0.847312	+	0.634290i
$399$	−4.03273	−	13.7342i	−0.201889	−	0.687571i
$400$	4.96290	−	0.608000i	0.248145	−	0.0304000i
$401$	−10.1113	+	1.45379i	−0.504937	+	0.0725989i	−0.390076	−	0.920783i	$-0.627551\pi$
$401$	−10.1113	+	1.45379i	−0.504937	+	0.0725989i	−0.114861	+	0.993382i	$0.536642\pi$
$402$	−11.3522	−	4.23417i	−0.566199	−	0.211181i
$403$	2.94758	+	1.09939i	0.146829	+	0.0547646i
$404$	−7.14058	+	1.02666i	−0.355257	+	0.0510782i
$405$	5.51971	−	24.1557i	0.274276	−	1.20031i
$406$	−3.71721	−	12.6597i	−0.184482	−	0.628289i
$407$	12.2613	−	9.17867i	0.607768	−	0.454970i
$408$	4.73955	−	0.338979i	0.234643	−	0.0167820i
$409$	−6.93756	−	10.7951i	−0.343040	−	0.533781i	0.626275	−	0.779602i	$-0.284579\pi$
$409$	−6.93756	−	10.7951i	−0.343040	−	0.533781i	−0.969315	+	0.245821i	$0.920942\pi$
$410$	−18.3221	+	5.17253i	−0.904864	+	0.255453i
$411$	−2.37845	+	8.10025i	−0.117320	+	0.399556i
$412$	3.08047	+	8.25906i	0.151764	+	0.406894i
$413$	−45.7707	−	45.7707i	−2.25223	−	2.25223i
$414$	3.09599	+	8.62538i	0.152159	+	0.423914i
$415$	−1.88831	+	4.02305i	−0.0926936	+	0.197484i
$416$	−0.148718	+	0.325646i	−0.00729148	+	0.0159661i
$417$	−5.14182	−	9.41655i	−0.251796	−	0.461130i
$418$	−2.22900	−	0.159421i	−0.109024	−	0.00779755i
$419$	15.1802	−	9.75572i	0.741601	−	0.476598i	−0.114489	−	0.993425i	$-0.536523\pi$
$419$	15.1802	−	9.75572i	0.741601	−	0.476598i	0.856090	+	0.516826i	$0.172887\pi$
$420$	−23.2695	−	8.95712i	−1.13543	−	0.437063i
$421$	13.2032	+	1.89833i	0.643483	+	0.0925189i	0.456328	−	0.889811i	$-0.349164\pi$
$421$	13.2032	+	1.89833i	0.643483	+	0.0925189i	0.187155	+	0.982330i	$0.440073\pi$
$422$	1.26528	+	0.690895i	0.0615929	+	0.0336322i
$423$	−4.24510	+	0.923466i	−0.206404	+	0.0449005i
$424$	−1.09933	−	7.64598i	−0.0533880	−	0.371321i
$425$	10.1212	−	3.53589i	0.490948	−	0.171516i
$426$	11.4880	+	25.1552i	0.556594	+	1.21877i
$427$	−24.5341	+	32.7737i	−1.18729	+	1.58603i
$428$	3.94303	+	18.1258i	0.190594	+	0.876144i
$429$	1.32514	−	0.389096i	0.0639783	−	0.0187857i
$430$	2.10531	+	10.1894i	0.101527	+	0.491377i
$431$	−14.7117	−	12.7477i	−0.708637	−	0.614037i	0.224112	−	0.974563i	$-0.428052\pi$
$431$	−14.7117	−	12.7477i	−0.708637	−	0.614037i	−0.932749	+	0.360526i	$0.882597\pi$
$432$	−2.35842	−	0.513043i	−0.113469	−	0.0246838i
$433$	2.16360	−	30.2511i	0.103976	−	1.45377i	−0.631054	−	0.775739i	$-0.717378\pi$
$433$	2.16360	−	30.2511i	0.103976	−	1.45377i	0.735030	−	0.678034i	$-0.237168\pi$
$434$	42.4265	+	12.4575i	2.03654	+	0.597981i
$435$	8.40572	+	9.90804i	0.403023	+	0.475054i
$436$		−	1.32928i		−	0.0636609i
$437$	5.88502	+	1.80745i	0.281519	+	0.0864620i
$438$	15.1804	−	15.1804i	0.725348	−	0.725348i
$439$	−4.92216	−	2.24788i	−0.234922	−	0.107285i	0.294476	−	0.955659i	$-0.404855\pi$
$439$	−4.92216	−	2.24788i	−0.234922	−	0.107285i	−0.529398	+	0.848374i	$0.677582\pi$
$440$	−2.57974	+	2.91507i	−0.122984	+	0.138971i
$441$	22.9238	+	26.4555i	1.09161	+	1.25979i
$442$	−0.163169	+	0.750077i	−0.00776117	+	0.0356775i
$443$	−0.281797	−	3.94003i	−0.0133886	−	0.187197i	−0.999745	−	0.0225739i	$-0.992814\pi$
$443$	−0.281797	−	3.94003i	−0.0133886	−	0.187197i	0.986357	−	0.164623i	$-0.0526407\pi$
$444$	−2.77473	+	19.2987i	−0.131683	+	0.915874i
$445$	1.17169	+	1.59976i	0.0555432	+	0.0758360i
$446$	22.9575	+	14.7539i	1.08707	+	0.698618i
$447$	12.0165	+	8.99542i	0.568360	+	0.425469i
$448$	−1.75844	+	4.71457i	−0.0830786	+	0.222742i
$449$	−8.73154	+	3.98756i	−0.412067	+	0.188185i	−0.610652	−	0.791899i	$-0.709093\pi$
$449$	−8.73154	+	3.98756i	−0.412067	+	0.188185i	0.198585	+	0.980084i	$0.436365\pi$
$450$	9.54214	−	0.482306i	0.449821	−	0.0227361i
$451$	8.01329	−	12.4689i	0.377331	−	0.587138i
$452$	3.99260	−	7.31190i	0.187796	−	0.343923i
$453$	9.03152	+	12.0647i	0.424338	+	0.566849i
$454$	15.7126	−	18.1334i	0.737431	−	0.851041i
$455$	2.44746	−	3.19919i	0.114739	−	0.149980i
$456$	2.14988	−	1.86288i	0.100677	−	0.0872375i
$457$	5.03488	−	2.74925i	0.235522	−	0.128605i	−0.357155	−	0.934045i	$-0.616253\pi$
$457$	5.03488	−	2.74925i	0.235522	−	0.128605i	0.592677	+	0.805441i	$0.298071\pi$
$458$	14.0791	−	5.25124i	0.657874	−	0.245374i
$459$	−5.17520			−0.241558
$460$	8.72933	−	6.22887i	0.407007	−	0.290423i
$461$	6.90801			0.321738			0.160869	−	0.986976i	$-0.448570\pi$
$461$	6.90801			0.321738			0.160869	+	0.986976i	$0.448570\pi$
$462$	18.1878	−	6.78371i	0.846175	−	0.315607i
$463$	34.2021	−	18.6758i	1.58951	−	0.867936i	0.591403	−	0.806376i	$-0.298574\pi$
$463$	34.2021	−	18.6758i	1.58951	−	0.867936i	0.998103	−	0.0615598i	$-0.0196075\pi$
$464$	1.98168	−	1.71713i	0.0919970	−	0.0797159i
$465$	−43.1637	+	5.74633i	−2.00167	+	0.266480i
$466$	2.79641	−	3.22723i	0.129541	−	0.149499i
$467$	8.04004	+	10.7402i	0.372049	+	0.496999i	0.947020	−	0.321175i	$-0.104078\pi$
$467$	8.04004	+	10.7402i	0.372049	+	0.496999i	−0.574971	+	0.818174i	$0.694987\pi$
$468$	−0.327847	+	0.600407i	−0.0151547	+	0.0277538i
$469$	14.8738	−	23.1440i	0.686807	−	1.06869i
$470$	2.38963	+	4.48711i	0.110225	+	0.206975i
$471$	11.4162	−	5.21359i	0.526029	−	0.240229i
$472$	4.49552	−	12.0529i	0.206923	−	0.554782i
$473$	−6.48463	−	4.85434i	−0.298164	−	0.223203i
$474$	24.2704	+	15.5976i	1.11478	+	0.716423i
$475$	3.58213	−	5.32582i	0.164359	−	0.244366i
$476$	−1.53547	+	10.6794i	−0.0703782	+	0.489491i
$477$	−1.05301	−	14.7231i	−0.0482142	−	0.674122i
$478$	−3.88787	+	17.8723i	−0.177827	+	0.817459i
$479$	−6.98068	−	8.05614i	−0.318955	−	0.368094i	0.573519	−	0.819192i	$-0.305578\pi$
$479$	−6.98068	−	8.05614i	−0.318955	−	0.368094i	−0.892474	+	0.451098i	$0.851032\pi$
$480$	−0.301839	−	4.94603i	−0.0137770	−	0.225754i
$481$	−2.86508	−	1.30844i	−0.130636	−	0.0596597i
$482$	−16.4204	+	16.4204i	−0.747930	+	0.747930i
$483$	−53.0231	+	6.95457i	−2.41263	+	0.316444i
$484$			7.96946i			0.362248i
$485$	10.6716	−	9.05350i	0.484572	−	0.411098i
$486$	−16.6143	−	4.87840i	−0.753640	−	0.221289i
$487$	0.100589	−	1.40642i	0.00455811	−	0.0637308i	−0.994664	−	0.103168i	$-0.967102\pi$
$487$	0.100589	−	1.40642i	0.00455811	−	0.0637308i	0.999222	+	0.0394374i	$0.0125566\pi$
$488$	−7.95017	−	1.72945i	−0.359887	−	0.0782887i
$489$	14.6117	+	12.6611i	0.660766	+	0.572557i
$490$	22.5052	−	34.2271i	1.01668	−	1.54622i
$491$	17.4594	−	5.12655i	0.787933	−	0.231358i	0.137078	−	0.990560i	$-0.456229\pi$
$491$	17.4594	−	5.12655i	0.787933	−	0.231358i	0.650855	+	0.759202i	$0.274411\pi$
$492$	4.01063	+	18.4366i	0.180813	+	0.831185i
$493$	3.36937	−	4.50095i	0.151749	−	0.202713i
$494$	0.190906	+	0.418026i	0.00858928	+	0.0188079i
$495$	−5.31436	+	5.20444i	−0.238863	+	0.233922i
$496$	1.25060	+	8.69814i	0.0561538	+	0.390558i
$497$	−61.3575	+	13.3475i	−2.75226	+	0.598718i
$498$	3.86563	+	2.11079i	0.173223	+	0.0945869i
$499$	14.7567	+	2.12170i	0.660602	+	0.0949802i	0.464458	−	0.885595i	$-0.346249\pi$
$499$	14.7567	+	2.12170i	0.660602	+	0.0949802i	0.196144	+	0.980575i	$0.437158\pi$
$500$	−3.57689	−	10.5927i	−0.159963	−	0.473721i
$501$	−34.5608	+	22.2109i	−1.54406	+	0.992308i
$502$	18.9121	+	1.35262i	0.844087	+	0.0603703i
$503$	−12.5513	−	22.9860i	−0.559636	−	1.02490i	−0.992361	−	0.123370i	$-0.960630\pi$
$503$	−12.5513	−	22.9860i	−0.559636	−	1.02490i	0.432725	−	0.901526i	$-0.357552\pi$
$504$	−3.99427	+	8.74624i	−0.177919	+	0.389588i
$505$	5.47898	+	15.1720i	0.243811	+	0.675146i
$506$	−1.87555	+	8.13541i	−0.0833782	+	0.361663i
$507$	20.1699	+	20.1699i	0.895778	+	0.895778i
$508$	−2.36920	−	6.35208i	−0.105116	−	0.281828i
$509$	−3.02829	+	10.3134i	−0.134227	+	0.457135i	−0.998985	−	0.0450548i	$-0.985654\pi$
$509$	−3.02829	+	10.3134i	−0.134227	+	0.457135i	0.864758	+	0.502189i	$0.167472\pi$
$510$	−2.88673	−	10.2254i	−0.127827	−	0.452786i
$511$	26.3544	+	41.0083i	1.16585	+	1.81410i
$512$	−0.997452	+	0.0713392i	−0.0440816	+	0.00315278i
$513$	−2.48029	+	1.85672i	−0.109508	+	0.0819763i
$514$	7.72694	+	26.3155i	0.340821	+	1.16073i
$515$	16.6920	−	10.4825i	0.735538	−	0.461914i
$516$	10.2065	−	1.46747i	0.449317	−	0.0646020i
$517$	−3.70830	−	1.38313i	−0.163091	−	0.0608298i
$518$	−41.4795	−	15.4710i	−1.82250	−	0.679759i
$519$	12.3839	−	1.78054i	0.543594	−	0.0781570i
$520$	0.780392	+	0.178324i	0.0342225	+	0.00782002i
$521$	−4.10241	−	13.9715i	−0.179730	−	0.612104i	−0.999238	−	0.0390361i	$-0.987571\pi$
$521$	−4.10241	−	13.9715i	−0.179730	−	0.612104i	0.819508	−	0.573068i	$-0.194247\pi$
$522$	4.01114	−	3.00271i	0.175563	−	0.131425i
$523$	−30.5251	+	2.18320i	−1.33477	+	0.0954645i	−0.720402	−	0.693556i	$-0.756043\pi$
$523$	−30.5251	+	2.18320i	−1.33477	+	0.0954645i	−0.614366	+	0.789021i	$0.710588\pi$
$524$	−5.21502	−	8.11473i	−0.227819	−	0.354494i
$525$	−9.08606	+	55.0085i	−0.396548	+	2.40077i
$526$	−1.70872	+	5.81938i	−0.0745039	+	0.253737i
$527$	6.58473	+	17.6543i	0.286835	+	0.769035i
$528$	2.72787	+	2.72787i	0.118715	+	0.118715i
$529$	10.0697	−	20.6785i	0.437813	−	0.899066i
$530$	−16.2459	+	5.86677i	−0.705676	+	0.254836i
$531$	10.2115	−	22.3600i	0.443141	−	0.970343i
$532$	3.09560	+	5.66917i	0.134211	+	0.245790i
$533$	−3.04028	−	0.217445i	−0.131689	−	0.00941860i
$534$	1.65323	−	1.06246i	0.0715421	−	0.0459773i
$535$	37.9081	−	16.8356i	1.63891	−	0.727867i
$536$	5.41182	+	0.778103i	0.233755	+	0.0336089i
$537$	−36.0306	−	19.6742i	−1.55484	−	0.849005i
$538$	−1.70080	+	0.369987i	−0.0733269	+	0.0159513i
$539$	4.53857	+	31.5664i	0.195490	+	1.35966i
$540$	−0.0563914	+	5.39663i	−0.00242670	+	0.232234i
$541$	18.1850	+	39.8197i	0.781835	+	1.71198i	0.698669	+	0.715445i	$0.253776\pi$
$541$	18.1850	+	39.8197i	0.781835	+	1.71198i	0.0831662	+	0.996536i	$0.473497\pi$
$542$	−2.21721	+	2.96184i	−0.0952371	+	0.127222i
$543$	0.0440096	+	0.202309i	0.00188863	+	0.00868190i
$544$	−2.05735	+	0.604092i	−0.0882081	+	0.0259002i
$545$	−2.91088	+	0.601438i	−0.124688	+	0.0257628i
$546$	−3.01691	−	2.61417i	−0.129112	−	0.111876i
$547$	25.7076	+	5.59236i	1.09918	+	0.239112i	0.725346	−	0.688384i	$-0.241680\pi$
$547$	25.7076	+	5.59236i	1.09918	+	0.239112i	0.373833	+	0.927496i	$0.378043\pi$
$548$	0.271773	−	3.79988i	0.0116096	−	0.162323i
$549$	−14.9172	−	4.38009i	−0.636652	−	0.186938i
$550$	7.55068	+	4.33022i	0.321962	+	0.184641i
$551$		−	3.36599i		−	0.143396i
$552$	−5.63467	−	9.01113i	−0.239827	−	0.383539i
$553$	−46.3214	+	46.3214i	−1.96979	+	1.96979i
$554$	−10.1665	−	4.64289i	−0.431934	−	0.197258i
$555$	43.5159	−	2.65562i	1.84715	−	0.112725i
$556$	3.17049	+	3.65894i	0.134459	+	0.155173i
$557$	−3.76690	+	17.3162i	−0.159609	+	0.733709i	0.825863	+	0.563871i	$0.190688\pi$
$557$	−3.76690	+	17.3162i	−0.159609	+	0.733709i	−0.985472	+	0.169839i	$0.945675\pi$
$558$	1.19792	+	16.7491i	0.0507119	+	0.709046i
$559$	−0.237067	+	1.64884i	−0.0100269	+	0.0697385i
$560$	11.1196	+	1.71754i	0.469891	+	0.0725792i
$561$	6.95876	+	4.47213i	0.293799	+	0.188813i
$562$	−22.0713	−	16.5224i	−0.931022	−	0.696954i
$563$	2.89206	−	7.75391i	0.121886	−	0.326788i	−0.861650	−	0.507503i	$-0.830568\pi$
$563$	2.89206	−	7.75391i	0.121886	−	0.326788i	0.983536	+	0.180715i	$0.0578412\pi$
$564$	4.58293	−	2.09296i	0.192976	−	0.0881293i
$565$	−17.8182	−	5.43475i	−0.749616	−	0.228642i
$566$	10.1943	−	15.8627i	0.428500	−	0.666759i
$567$	26.7223	−	48.9382i	1.12223	−	2.05521i
$568$	−7.47843	−	9.99001i	−0.313788	−	0.419172i
$569$	21.5223	−	24.8380i	0.902260	−	1.04126i	−0.0966834	−	0.995315i	$-0.530823\pi$
$569$	21.5223	−	24.8380i	0.902260	−	1.04126i	0.998944	−	0.0459488i	$-0.0146311\pi$
$570$	−5.05209	−	3.86497i	−0.211609	−	0.161886i
$571$	−8.19056	+	7.09716i	−0.342764	+	0.297007i	−0.809183	−	0.587557i	$-0.800090\pi$
$571$	−8.19056	+	7.09716i	−0.342764	+	0.297007i	0.466418	+	0.884564i	$0.345544\pi$
$572$	−0.546986	+	0.298677i	−0.0228706	+	0.0124883i
$573$	−16.6783	+	6.22067i	−0.696745	+	0.259872i
$574$	−42.8418			−1.78818
$575$	−17.5897	−	16.2973i	−0.733541	−	0.679645i
$576$	−1.91086			−0.0796193
$577$	29.0389	−	10.8309i	1.20890	−	0.450898i	0.337435	−	0.941349i	$-0.390441\pi$
$577$	29.0389	−	10.8309i	1.20890	−	0.450898i	0.871469	+	0.490451i	$0.163168\pi$
$578$	10.8853	−	5.94383i	0.452770	−	0.247231i
$579$	4.50309	−	3.90195i	0.187142	−	0.162159i
$580$	−4.65682	−	3.56258i	−0.193364	−	0.147928i
$581$	−6.54908	+	7.55804i	−0.271701	+	0.313560i
$582$	−8.31156	−	11.1029i	−0.344525	−	0.460232i
$583$	6.44462	−	11.8024i	0.266909	−	0.488807i
$584$	−5.23755	+	8.14979i	−0.216731	+	0.337241i
$585$	1.46311	+	0.446267i	0.0604923	+	0.0184509i
$586$	16.1055	−	7.35514i	0.665312	−	0.303838i
$587$	5.42194	−	14.5368i	0.223787	−	0.599997i	−0.775730	−	0.631065i	$-0.782618\pi$
$587$	5.42194	−	14.5368i	0.223787	−	0.599997i	0.999517	+	0.0310678i	$0.00989077\pi$
$588$	−32.4991	−	24.3285i	−1.34024	−	1.00329i
$589$	9.48974	+	6.09868i	0.391018	+	0.251292i
$590$	−28.4277	−	4.39094i	−1.17035	−	0.180772i
$591$	−0.0171625	+	0.119368i	−0.000705973	+	0.00491015i
$592$	−0.627653	−	8.77573i	−0.0257964	−	0.360680i
$593$	−5.71880	+	26.2889i	−0.234843	+	1.07956i	0.697106	+	0.716968i	$0.254471\pi$
$593$	−5.71880	+	26.2889i	−0.234843	+	1.07956i	−0.931949	+	0.362588i	$0.881893\pi$
$594$	−2.75150	−	3.17541i	−0.112896	−	0.130288i
$595$	24.0807	−	1.46956i	0.987213	−	0.0602461i
$596$	−6.16141	−	2.81382i	−0.252381	−	0.115259i
$597$	33.0876	−	33.0876i	1.35418	−	1.35418i
$598$	1.65321	−	0.463270i	0.0676049	−	0.0189445i
$599$			3.77428i			0.154213i	0.997023	+	0.0771065i	$0.0245681\pi$
$599$			3.77428i			0.154213i	−0.997023	+	0.0771065i	$0.975432\pi$
$600$	−10.6943	+	2.89882i	−0.436594	+	0.118344i
$601$	9.96065	+	2.92471i	0.406304	+	0.119301i	0.478497	−	0.878089i	$-0.341182\pi$
$601$	9.96065	+	2.92471i	0.406304	+	0.119301i	−0.0721935	+	0.997391i	$0.523000\pi$
$602$	−1.67030	+	23.3539i	−0.0680765	+	0.951834i
$603$	10.2088	+	2.22080i	0.415736	+	0.0904378i
$604$	−5.13963	−	4.45351i	−0.209128	−	0.181211i
$605$	17.4516	−	3.60581i	0.709510	−	0.146597i
$606$	15.3390	−	4.50394i	0.623104	−	0.182960i
$607$	−2.10250	−	9.66502i	−0.0853377	−	0.392291i	0.914589	−	0.404384i	$-0.132514\pi$
$607$	−2.10250	−	9.66502i	−0.0853377	−	0.392291i	−0.999927	+	0.0120932i	$0.996151\pi$
$608$	−0.769283	+	1.02764i	−0.0311985	+	0.0416764i
$609$	12.1462	+	26.5965i	0.492190	+	1.07775i
$610$	−0.190094	+	18.1919i	−0.00769668	+	0.736568i
$611$	0.115832	+	0.805630i	0.00468607	+	0.0325923i
$612$	−4.00365	+	0.870940i	−0.161838	+	0.0352057i
$613$	−5.62642	−	3.07226i	−0.227249	−	0.124087i	0.361591	−	0.932337i	$-0.382234\pi$
$613$	−5.62642	−	3.07226i	−0.227249	−	0.124087i	−0.588840	+	0.808249i	$0.700415\pi$
$614$	7.00068	+	1.00655i	0.282525	+	0.0406209i
$615$	38.5581	−	17.1242i	1.55481	−	0.690516i
$616$	−7.36907	+	4.73582i	−0.296908	+	0.190811i
$617$	7.36561	+	0.526799i	0.296528	+	0.0212081i	0.218811	−	0.975767i	$-0.429782\pi$
$617$	7.36561	+	0.526799i	0.296528	+	0.0212081i	0.0777174	+	0.996975i	$0.475237\pi$
$618$	−9.36169	−	17.1447i	−0.376582	−	0.689659i
$619$	−13.1875	+	28.8765i	−0.530049	+	1.16065i	0.435444	+	0.900216i	$0.356592\pi$
$619$	−13.1875	+	28.8765i	−0.530049	+	1.16065i	−0.965493	+	0.260430i	$0.916136\pi$
$620$	18.4815	−	6.67410i	0.742233	−	0.268038i
$621$	5.42114	+	10.2271i	0.217543	+	0.410401i
$622$	−4.03046	−	4.03046i	−0.161607	−	0.161607i
$623$	1.55939	+	4.18089i	0.0624757	+	0.167504i
$624$	0.223510	−	0.761203i	0.00894754	−	0.0304725i
$625$	−21.5777	+	12.6254i	−0.863109	+	0.505018i
$626$	4.79107	+	7.45505i	0.191490	+	0.297964i
$627$	4.93957	−	0.353285i	0.197267	−	0.0141088i
$628$	−4.53377	+	3.39394i	−0.180917	+	0.135433i
$629$	−5.31489	−	18.1009i	−0.211919	−	0.721728i
$630$	20.9599	+	4.78944i	0.835061	+	0.190816i
$631$	−34.2805	+	4.92880i	−1.36469	+	0.196212i	−0.785439	−	0.618939i	$-0.787563\pi$
$631$	−34.2805	+	4.92880i	−1.36469	+	0.196212i	−0.579248	+	0.815152i	$0.696654\pi$
$632$	−12.1980	−	4.54961i	−0.485209	−	0.180974i
$633$	−2.99327	−	1.11643i	−0.118972	−	0.0443742i
$634$	6.45402	−	0.927948i	0.256322	−	0.0368535i
$635$	−12.8379	+	8.06213i	−0.509457	+	0.319936i
$636$	4.82272	+	16.4247i	0.191233	+	0.651281i
$637$	5.25016	−	3.93022i	0.208019	−	0.155721i
$638$	4.55310	−	0.325644i	0.180259	−	0.0128924i
$639$	−12.8920	−	20.0604i	−0.510000	−	0.793576i
$640$	0.607521	+	2.15196i	0.0240144	+	0.0850636i
$641$	4.29599	−	14.6308i	0.169681	−	0.577882i	−0.830113	−	0.557596i	$-0.811724\pi$
$641$	4.29599	−	14.6308i	0.169681	−	0.577882i	0.999794	−	0.0202864i	$-0.00645780\pi$
$642$	−14.3655	−	38.5153i	−0.566959	−	1.52008i
$643$	28.7566	+	28.7566i	1.13405	+	1.13405i	0.989497	+	0.144550i	$0.0461736\pi$
$643$	28.7566	+	28.7566i	1.13405	+	1.13405i	0.144550	+	0.989497i	$0.453826\pi$
$644$	22.7130	−	8.15258i	0.895016	−	0.321257i
$645$	−7.83148	−	21.6864i	−0.308364	−	0.853901i
$646$	−1.14342	+	2.50374i	−0.0449873	+	0.0985084i
$647$	−1.57548	−	2.88527i	−0.0619384	−	0.113432i	0.844875	−	0.534963i	$-0.179675\pi$
$647$	−1.57548	−	2.88527i	−0.0619384	−	0.113432i	−0.906814	+	0.421531i	$0.861493\pi$
$648$	11.0530	+	0.790523i	0.434201	+	0.0310547i
$649$	18.8393	−	12.1073i	0.739506	−	0.475252i
$650$	0.0374045	−	1.78960i	0.00146712	−	0.0701938i
$651$	−96.9909	−	13.9452i	−3.80137	−	0.546555i
$652$	−7.65739	−	4.18125i	−0.299887	−	0.163750i
$653$	29.7007	−	6.46098i	1.16228	−	0.252838i	0.410252	−	0.911972i	$-0.365441\pi$
$653$	29.7007	−	6.46098i	1.16228	−	0.252838i	0.752025	+	0.659135i	$0.229077\pi$
$654$	0.419223	+	2.91576i	0.0163929	+	0.114015i
$655$	−15.4102	+	15.0915i	−0.602126	+	0.589672i
$656$	−3.53691	−	7.74475i	−0.138093	−	0.302382i
$657$	−11.0937	+	14.8195i	−0.432807	+	0.578163i
$658$	2.43174	+	11.1785i	0.0947990	+	0.435784i
$659$	−21.4385	+	6.29492i	−0.835127	+	0.245215i	−0.671218	−	0.741260i	$-0.734229\pi$
$659$	−21.4385	+	6.29492i	−0.835127	+	0.245215i	−0.163909	+	0.986475i	$0.552410\pi$
$660$	4.73930	−	7.20777i	0.184477	−	0.280562i
$661$	15.6005	+	13.5179i	0.606790	+	0.525786i	0.903170	−	0.429284i	$-0.141234\pi$
$661$	15.6005	+	13.5179i	0.606790	+	0.525786i	−0.296380	+	0.955070i	$0.595779\pi$
$662$	−9.69392	−	2.10878i	−0.376765	−	0.0819602i
$663$	0.121354	−	1.69675i	0.00471299	−	0.0658962i
$664$	−1.90698	−	0.559941i	−0.0740053	−	0.0217299i
$665$	11.0138	−	9.34383i	0.427097	−	0.362338i
$666$		−	16.8121i		−	0.651454i
$667$	−12.4242	−	1.94365i	−0.481067	−	0.0752583i
$668$	13.1088	−	13.1088i	0.507194	−	0.507194i
$669$	−55.0102	−	25.1223i	−2.12682	−	0.971284i
$670$	−0.744702	−	12.2029i	−0.0287703	−	0.471441i
$671$	−9.27525	−	10.7042i	−0.358067	−	0.413231i
$672$	2.37027	−	10.8959i	0.0914350	−	0.420320i
$673$	−1.51131	−	21.1309i	−0.0582568	−	0.814537i	−0.939647	−	0.342147i	$-0.888846\pi$
$673$	−1.51131	−	21.1309i	−0.0582568	−	0.814537i	0.881390	−	0.472390i	$-0.156609\pi$
$674$	−0.456685	+	3.17632i	−0.0175909	+	0.122347i
$675$	11.8431	−	2.31824i	0.455842	−	0.0892291i
$676$	−10.8285	−	6.95904i	−0.416480	−	0.267655i
$677$	−1.40178	−	1.04936i	−0.0538750	−	0.0403303i	0.572001	−	0.820253i	$-0.306167\pi$
$677$	−1.40178	−	1.04936i	−0.0538750	−	0.0403303i	−0.625876	+	0.779923i	$0.715258\pi$
$678$	−6.45173	+	17.2978i	−0.247777	+	0.664316i
$679$	28.6462	−	13.0823i	1.09934	−	0.502051i
$680$	2.25370	+	4.23189i	0.0864256	+	0.162285i
$681$	−28.7467	+	44.7308i	−1.10158	+	1.71409i
$682$	−7.33147	+	13.4266i	−0.280736	+	0.514130i
$683$	−2.51124	−	3.35463i	−0.0960900	−	0.128361i	0.749919	−	0.661529i	$-0.230092\pi$
$683$	−2.51124	−	3.35463i	−0.0960900	−	0.128361i	−0.846009	+	0.533168i	$0.821001\pi$
$684$	−1.60634	+	1.85381i	−0.0614198	+	0.0708823i
$685$	−8.44399	+	1.12414i	−0.322628	+	0.0429511i
$686$	43.0450	−	37.2987i	1.64347	−	1.42407i
$687$	−29.2263	+	15.9588i	−1.11505	+	0.608865i
$688$	−4.35971	+	1.62609i	−0.166212	+	0.0619940i
$689$	−2.76539			−0.105353
$690$	−17.1833	+	16.4160i	−0.654156	+	0.624946i
$691$	34.9272			1.32869			0.664347	−	0.747424i	$-0.268710\pi$
$691$	34.9272			1.32869			0.664347	+	0.747424i	$0.268710\pi$
$692$	−5.28979	+	1.97299i	−0.201088	+	0.0750018i
$693$	−14.6910	+	8.02189i	−0.558065	+	0.304727i
$694$	−16.0511	+	13.9084i	−0.609292	+	0.527954i
$695$	6.57789	−	8.59828i	0.249514	−	0.326151i
$696$	−3.80525	+	4.39149i	−0.144237	+	0.166459i
$697$	−10.9405	−	14.6147i	−0.414400	−	0.553573i
$698$	8.48071	−	15.5313i	0.320999	−	0.587867i
$699$	−5.11611	+	7.96083i	−0.193509	+	0.301106i
$700$	−1.27004	−	25.1271i	−0.0480031	−	0.949714i
$701$	2.23413	−	1.02029i	0.0843819	−	0.0385359i	−0.372777	−	0.927921i	$-0.621594\pi$
$701$	2.23413	−	1.02029i	0.0843819	−	0.0385359i	0.457159	+	0.889385i	$0.348867\pi$
$702$	−0.301956	+	0.809575i	−0.0113966	+	0.0305555i
$703$	−9.04134	−	6.76826i	−0.341001	−	0.255270i
$704$	−1.46449	−	0.941172i	−0.0551951	−	0.0354718i
$705$	−6.65675	−	9.08880i	−0.250708	−	0.342304i
$706$	−3.10789	+	21.6158i	−0.116967	+	0.813522i
$707$	2.58959	+	36.2071i	0.0973914	+	1.36171i
$708$	−6.05966	+	27.8558i	−0.227736	+	1.04689i
$709$	−5.44202	−	6.28042i	−0.204379	−	0.235866i	0.644302	−	0.764771i	$-0.277148\pi$
$709$	−5.44202	−	6.28042i	−0.204379	−	0.235866i	−0.848681	+	0.528905i	$0.822603\pi$
$710$	−18.4926	+	20.8964i	−0.694016	+	0.784228i
$711$	−22.6291	−	10.3343i	−0.848656	−	0.387568i
$712$	−0.627063	+	0.627063i	−0.0235002	+	0.0235002i
$713$	27.9906	−	31.5060i	1.04826	−	1.17991i
$714$		−	23.9095i		−	0.894791i
$715$	0.901533	+	1.06266i	0.0337154	+	0.0397412i
$716$	17.7746	+	5.21908i	0.664266	+	0.195046i
$717$	2.89153	−	40.4288i	0.107986	−	1.50984i
$718$	−19.8169	−	4.31091i	−0.739562	−	0.160882i
$719$	30.6431	+	26.5524i	1.14280	+	0.990239i	1.00000		0.000486585i	$0.000154885\pi$
$719$	30.6431	+	26.5524i	1.14280	+	0.990239i	0.142796	+	0.989752i	$0.454391\pi$
$720$	0.864578	+	4.18444i	0.0322209	+	0.155945i
$721$	42.5580	−	12.4962i	1.58494	−	0.465382i
$722$	−3.68847	−	16.9556i	−0.137271	−	0.631022i
$723$	30.8394	−	41.1967i	1.14693	−	1.53212i
$724$	−0.0388113	−	0.0849848i	−0.00144241	−	0.00315844i
$725$	−5.69439	+	11.8095i	−0.211484	+	0.438593i
$726$	−2.51338	−	17.4809i	−0.0932802	−	0.648778i
$727$	20.4278	−	4.44381i	0.757627	−	0.164812i	0.182871	−	0.983137i	$-0.441461\pi$
$727$	20.4278	−	4.44381i	0.757627	−	0.164812i	0.574755	+	0.818325i	$0.305097\pi$
$728$	1.58103	+	0.863310i	0.0585970	+	0.0319964i
$729$	5.07665	+	0.729912i	0.188024	+	0.0270338i
$730$	20.2163	+	7.78186i	0.748238	+	0.288019i
$731$	−8.39333	+	5.39407i	−0.310439	+	0.199507i
$732$	17.9840	+	1.28624i	0.664710	+	0.0475410i
$733$	−9.23637	−	16.9152i	−0.341153	−	0.624776i	0.649627	−	0.760253i	$-0.274925\pi$
$733$	−9.23637	−	16.9152i	−0.341153	−	0.624776i	−0.990780	+	0.135477i	$0.956743\pi$
$734$	15.0638	−	32.9851i	0.556014	−	1.21750i
$735$	−38.5706	+	82.1745i	−1.42270	+	3.03105i
$736$	3.34891	+	3.43290i	0.123443	+	0.126538i
$737$	6.73026	+	6.73026i	0.247912	+	0.247912i
$738$	−5.68557	−	15.2436i	−0.209289	−	0.561125i
$739$	1.77735	−	6.05309i	0.0653808	−	0.222666i	−0.920322	−	0.391163i	$-0.872073\pi$
$739$	1.77735	−	6.05309i	0.0653808	−	0.222666i	0.985702	+	0.168496i	$0.0538911\pi$
$740$	−18.9332	+	5.34506i	−0.696000	+	0.196488i
$741$	−0.550587	−	0.856729i	−0.0202263	−	0.0314727i
$742$	−38.7698	+	2.77287i	−1.42329	+	0.101795i
$743$	−36.0691	+	27.0010i	−1.32325	+	0.990571i	−0.324242	+	0.945974i	$0.605109\pi$
$743$	−36.0691	+	27.0010i	−1.32325	+	0.990571i	−0.999005	+	0.0445965i	$0.985800\pi$
$744$	−5.48637	−	18.6849i	−0.201140	−	0.685021i
$745$	−3.37399	+	14.7655i	−0.123613	+	0.540965i
$746$	−7.89157	+	1.13464i	−0.288931	+	0.0415420i
$747$	−3.55837	−	1.32720i	−0.130194	−	0.0485599i
$748$	−3.49738	−	1.30445i	−0.127877	−	0.0476956i
$749$	92.3890	−	13.2835i	3.37582	−	0.485370i
$750$	11.1866	+	22.1070i	0.408476	+	0.807233i
$751$	12.6267	+	43.0026i	0.460755	+	1.56919i	0.782682	+	0.622421i	$0.213851\pi$
$751$	12.6267	+	43.0026i	0.460755	+	1.56919i	−0.321928	+	0.946764i	$0.604331\pi$
$752$	−1.82005	+	1.36247i	−0.0663703	+	0.0496842i
$753$	−41.9100	+	2.99747i	−1.52729	+	0.109234i
$754$	−0.507509	−	0.789699i	−0.0184824	−	0.0287591i
$755$	−7.42692	+	13.2698i	−0.270293	+	0.482939i
$756$	−3.42156	+	11.6528i	−0.124441	+	0.423807i
$757$	−1.21406	−	3.25501i	−0.0441256	−	0.118305i	0.913018	−	0.407920i	$-0.133746\pi$
$757$	−1.21406	−	3.25501i	−0.0441256	−	0.118305i	−0.957143	+	0.289614i	$0.906473\pi$
$758$	19.5470	+	19.5470i	0.709978	+	0.709978i
$759$	1.54828	−	18.4364i	0.0561990	−	0.669200i
$760$	2.59841	+	1.21963i	0.0942542	+	0.0442405i
$761$	−8.23365	+	18.0292i	−0.298470	+	0.653557i	−0.998144	−	0.0609051i	$-0.980601\pi$
$761$	−8.23365	+	18.0292i	−0.298470	+	0.653557i	0.699674	+	0.714462i	$0.253329\pi$
$762$	7.20012	+	13.1860i	0.260833	+	0.477679i
$763$	−6.67166	−	0.477167i	−0.241530	−	0.0172746i
$764$	6.75745	−	4.34275i	0.244476	−	0.157115i
$765$	3.71866	+	8.37318i	0.134449	+	0.302733i
$766$	10.0541	+	1.44556i	0.363269	+	0.0522302i
$767$	−4.04196	−	2.20708i	−0.145947	−	0.0796930i
$768$	2.16540	−	0.471055i	0.0781373	−	0.0169977i
$769$	2.55038	+	17.7383i	0.0919690	+	0.639659i	0.982711	+	0.185148i	$0.0592766\pi$
$769$	2.55038	+	17.7383i	0.0919690	+	0.639659i	−0.890742	+	0.454510i	$0.849814\pi$
$770$	13.7047	+	13.9942i	0.493884	+	0.504315i
$771$	−25.2483	−	55.2860i	−0.909294	−	1.99108i
$772$	−1.61132	+	2.15247i	−0.0579927	+	0.0774692i
$773$	−1.94191	−	8.92680i	−0.0698455	−	0.321075i	0.928946	−	0.370214i	$-0.120716\pi$
$773$	−1.94191	−	8.92680i	−0.0698455	−	0.321075i	−0.998792	+	0.0491396i	$0.984352\pi$
$774$	−8.53126	+	2.50500i	−0.306650	+	0.0900405i
$775$	−22.9770	−	37.4512i	−0.825360	−	1.34529i
$776$	4.72991	+	4.09849i	0.169794	+	0.147127i
$777$	95.8641	+	20.8539i	3.43910	+	0.748131i
$778$	−0.302010	+	4.22265i	−0.0108276	+	0.151389i
$779$	−10.4868	−	3.07919i	−0.375727	−	0.110323i
$780$	−1.76802	−	0.145035i	−0.0633053	−	0.00519307i
$781$		−	21.7241i		−	0.777351i
$782$	8.58131	+	5.66623i	0.306867	+	0.202624i
$783$	4.47508	−	4.47508i	0.159926	−	0.159926i
$784$	16.6638	+	7.61011i	0.595136	+	0.271789i
$785$	9.48341	+	8.39251i	0.338477	+	0.299541i
$786$	13.9983	+	16.1549i	0.499303	+	0.576226i
$787$	−0.484437	+	2.22692i	−0.0172683	+	0.0793812i	−0.984975	−	0.172699i	$-0.944751\pi$
$787$	−0.484437	+	2.22692i	−0.0172683	+	0.0793812i	0.967706	+	0.252080i	$0.0811148\pi$
$788$	−0.00388222	−	0.0542806i	−0.000138298	−	0.00193367i
$789$	1.91278	−	13.3036i	0.0680966	−	0.473622i
$790$	−4.44377	+	28.7698i	−0.158102	+	1.02358i
$791$	−35.2653	−	22.6636i	−1.25389	−	0.805825i
$792$	−2.66302	−	1.99351i	−0.0946261	−	0.0708362i
$793$	−1.01789	+	2.72906i	−0.0361462	+	0.0969117i
$794$	−24.7080	+	11.2838i	−0.876855	+	0.400446i
$795$	33.7849	−	17.9923i	1.19823	−	0.638120i
$796$	−11.4159	+	17.7635i	−0.404626	+	0.629610i
$797$	−2.85313	+	5.22513i	−0.101063	+	0.185083i	−0.923318	−	0.384036i	$-0.874534\pi$
$797$	−2.85313	+	5.22513i	−0.101063	+	0.185083i	0.822255	+	0.569119i	$0.192716\pi$
$798$	−8.57809	−	11.4590i	−0.303661	−	0.405644i
$799$	−3.19237	+	3.68420i	−0.112938	+	0.130337i
$800$	4.43751	−	2.30402i	0.156890	−	0.0814594i
$801$	−1.28066	+	1.10970i	−0.0452499	+	0.0392093i
$802$	−8.96578	+	4.89569i	−0.316593	+	0.172873i
$803$	−15.8014	+	5.89362i	−0.557620	+	0.207981i
$804$	−12.1162			−0.427305
$805$	−28.1292	−	46.0485i	−0.991424	−	1.62300i
$806$	3.14593			0.110811
$807$	3.61401	−	1.34796i	0.127219	−	0.0474504i
$808$	−6.33158	+	3.45730i	−0.222744	+	0.121628i
$809$	23.2295	−	20.1285i	0.816705	−	0.707679i	−0.142683	−	0.989768i	$-0.545573\pi$
$809$	23.2295	−	20.1285i	0.816705	−	0.707679i	0.959388	+	0.282090i	$0.0910275\pi$
$810$	−3.26986	−	24.5616i	−0.114891	−	0.863006i
$811$	4.96207	−	5.72654i	0.174242	−	0.201086i	−0.661911	−	0.749583i	$-0.730254\pi$
$811$	4.96207	−	5.72654i	0.174242	−	0.201086i	0.836153	+	0.548497i	$0.184800\pi$
$812$	−7.90694	−	10.5624i	−0.277479	−	0.370669i
$813$	3.92933	−	7.19602i	0.137807	−	0.252376i
$814$	8.28057	−	12.8848i	0.290234	−	0.451613i
$815$	−5.69154	+	18.6601i	−0.199366	+	0.653634i
$816$	4.32226	−	1.97391i	0.151309	−	0.0691006i
$817$	−2.08738	+	5.59649i	−0.0730283	+	0.195796i
$818$	−10.2726	−	7.68999i	−0.359174	−	0.268874i
$819$	2.89576	+	1.86099i	0.101186	+	0.0650283i
$820$	−15.3593	+	11.2493i	−0.536369	+	0.392843i
$821$	2.94066	−	20.4527i	0.102630	−	0.713805i	−0.871922	−	0.489644i	$-0.837127\pi$
$821$	2.94066	−	20.4527i	0.102630	−	0.713805i	0.974552	−	0.224161i	$-0.0719641\pi$
$822$	0.602261	+	8.42071i	0.0210063	+	0.293706i
$823$	−9.98508	+	45.9007i	−0.348058	+	1.60000i	0.387058	+	0.922055i	$0.373491\pi$
$823$	−9.98508	+	45.9007i	−0.348058	+	1.60000i	−0.735116	+	0.677941i	$0.762872\pi$
$824$	5.77249	+	6.66181i	0.201094	+	0.232075i
$825$	−17.9280	−	7.11699i	−0.624173	−	0.247782i
$826$	−58.8801	−	26.8896i	−2.04870	−	0.935610i
$827$	−14.1744	+	14.1744i	−0.492892	+	0.492892i	−0.909216	−	0.416324i	$-0.863318\pi$
$827$	−14.1744	+	14.1744i	−0.492892	+	0.492892i	0.416324	+	0.909216i	$0.363318\pi$
$828$	5.91504	+	6.99961i	0.205562	+	0.243253i
$829$		−	22.0932i		−	0.767328i	−0.923473	−	0.383664i	$-0.874662\pi$
$829$		−	22.0932i		−	0.767328i	0.923473	−	0.383664i	$-0.125338\pi$
$830$	−0.363344	+	4.42929i	−0.0126118	+	0.153743i
$831$	23.7644	+	6.97787i	0.824379	+	0.242059i
$832$	−0.0255393	+	0.357085i	−0.000885414	+	0.0123797i
$833$	38.3826	+	8.34962i	1.32988	+	0.289297i
$834$	−8.10838	−	7.02595i	−0.280770	−	0.243289i
$835$	−34.6369	−	22.7747i	−1.19866	−	0.788150i
$836$	−2.14417	+	0.629586i	−0.0741578	+	0.0217747i
$837$	4.50840	+	20.7248i	0.155833	+	0.716354i
$838$	10.8138	−	14.4456i	0.373557	−	0.499013i
$839$	16.7131	+	36.5965i	0.576999	+	1.26345i	0.942986	+	0.332831i	$0.108004\pi$
$839$	16.7131	+	36.5965i	0.576999	+	1.26345i	−0.365988	+	0.930620i	$0.619269\pi$
$840$	−24.9325	−	0.260529i	−0.860253	−	0.00898912i
$841$	−3.14863	−	21.8992i	−0.108574	−	0.755146i
$842$	13.0341	−	2.83540i	0.449185	−	0.0977142i
$843$	53.6240	+	29.2809i	1.84691	+	1.00849i
$844$	1.42695	+	0.205164i	0.0491175	+	0.00706203i
$845$	−10.3396	+	26.8610i	−0.355694	+	0.924047i
$846$	−3.65473	+	2.34875i	−0.125652	+	0.0807518i
$847$	39.9988	+	2.86077i	1.37437	+	0.0982971i
$848$	−3.70201	−	6.77972i	−0.127127	−	0.232817i
$849$	−17.3585	+	38.0097i	−0.595741	+	1.30449i
$850$	8.24734	−	6.84993i	0.282882	−	0.234951i
$851$	−30.2031	+	29.4642i	−1.03535	+	1.01002i
$852$	19.5545	+	19.5545i	0.669925	+	0.669925i
$853$	3.11498	+	8.35160i	0.106655	+	0.285953i	0.979304	−	0.202395i	$-0.0648724\pi$
$853$	3.11498	+	8.35160i	0.106655	+	0.285953i	−0.872649	+	0.488348i	$0.837600\pi$
$854$	−11.5340	+	39.2811i	−0.394685	+	1.34417i
$855$	4.78630	+	2.67881i	0.163688	+	0.0916135i
$856$	10.0287	+	15.6050i	0.342775	+	0.533369i
$857$	32.5304	−	2.32662i	1.11122	−	0.0794758i	0.496362	−	0.868116i	$-0.334669\pi$
$857$	32.5304	−	2.32662i	1.11122	−	0.0794758i	0.614855	+	0.788640i	$0.289214\pi$
$858$	1.10561	−	0.827651i	0.0377450	−	0.0282555i
$859$	−11.8193	−	40.2528i	−0.403269	−	1.37341i	−0.871758	−	0.489937i	$-0.837020\pi$
$859$	−11.8193	−	40.2528i	−0.403269	−	1.37341i	0.468489	−	0.883469i	$-0.344799\pi$
$860$	5.53340	+	8.81123i	0.188687	+	0.300460i
$861$	93.9730	−	13.5113i	3.20259	−	0.460463i
$862$	−18.2390	−	6.80279i	−0.621223	−	0.231704i
$863$	24.7137	+	9.21773i	0.841264	+	0.313775i	0.732900	−	0.680336i	$-0.238166\pi$
$863$	24.7137	+	9.21773i	0.841264	+	0.313775i	0.108363	+	0.994111i	$0.465439\pi$
$864$	−2.38901	+	0.343488i	−0.0812758	+	0.0116857i
$865$	6.71387	+	10.6910i	0.228278	+	0.363504i
$866$	−8.54448	−	29.0998i	−0.290353	−	0.988852i
$867$	−22.0023	+	16.4707i	−0.747237	+	0.559375i
$868$	44.1049	−	3.15445i	1.49702	−	0.107069i
$869$	−12.2529	−	19.0659i	−0.415652	−	0.646768i
$870$	11.3382	+	6.34583i	0.384402	+	0.215144i
$871$	0.551447	−	1.87806i	0.0186851	−	0.0636355i
$872$	−0.464536	−	1.24547i	−0.0157312	−	0.0421769i
$873$	8.45649	+	8.45649i	0.286209	+	0.286209i
$874$	6.14561	−	0.363117i	0.207878	−	0.0122826i
$875$	−54.4489	+	14.1500i	−1.84071	+	0.478357i
$876$	8.91827	−	19.5283i	0.301320	−	0.659800i
$877$	11.6649	+	21.3626i	0.393895	+	0.721364i	0.997090	−	0.0762290i	$-0.0242880\pi$
$877$	11.6649	+	21.3626i	0.393895	+	0.721364i	−0.603196	+	0.797593i	$0.706106\pi$
$878$	−5.39737	−	0.386027i	−0.182152	−	0.0130278i
$879$	−33.0076	+	21.2127i	−1.11332	+	0.715487i
$880$	−1.39838	+	3.63280i	−0.0471393	+	0.122462i
$881$	2.96830	+	0.426778i	0.100005	+	0.0143785i	0.192135	−	0.981368i	$-0.438459\pi$
$881$	2.96830	+	0.426778i	0.100005	+	0.0143785i	−0.0921308	+	0.995747i	$0.529368\pi$
$882$	30.7237	+	16.7764i	1.03452	+	0.564892i
$883$	−13.0779	+	2.84493i	−0.440108	+	0.0957396i	−0.427159	−	0.904177i	$-0.640486\pi$
$883$	−13.0779	+	2.84493i	−0.440108	+	0.0957396i	−0.0129490	+	0.999916i	$0.504122\pi$
$884$	0.109244	+	0.759806i	0.00367426	+	0.0255550i
$885$	63.7407	+	0.666051i	2.14262	+	0.0223891i
$886$	−1.64093	−	3.59314i	−0.0551281	−	0.120714i
$887$	−20.3466	+	27.1799i	−0.683173	+	0.912612i	−0.999349	−	0.0360887i	$-0.988510\pi$
$887$	−20.3466	+	27.1799i	−0.683173	+	0.912612i	0.316176	+	0.948701i	$0.397601\pi$
$888$	4.14441	+	19.0515i	0.139077	+	0.639328i
$889$	−32.7316	+	9.61086i	−1.09778	+	0.322338i
$890$	1.65687	+	1.08943i	0.0555384	+	0.0365179i
$891$	14.5789	+	12.6327i	0.488411	+	0.423211i
$892$	26.6660	+	5.80084i	0.892844	+	0.194226i
$893$	−0.208202	+	2.91104i	−0.00696721	+	0.0974143i
$894$	14.4024	+	4.22893i	0.481689	+	0.141437i
$895$	3.38664	−	41.2844i	0.113203	−	1.37998i
$896$			5.03183i			0.168102i
$897$	−3.48020	+	1.53756i	−0.116201	+	0.0513377i
$898$	−6.78750	+	6.78750i	−0.226502	+	0.226502i
$899$	−20.9599	−	9.57208i	−0.699053	−	0.319247i
$900$	8.77196	−	3.78653i	0.292399	−	0.126218i
$901$	−10.8465	−	12.5176i	−0.361350	−	0.417021i
$902$	3.15061	−	14.4831i	0.104904	−	0.482235i
$903$	−3.70147	−	51.7533i	−0.123177	−	1.72224i
$904$	1.18562	−	8.24615i	0.0394331	−	0.274263i
$905$	−0.168541	+	0.123441i	−0.00560248	+	0.00410333i
$906$	12.6783	+	8.14782i	0.421207	+	0.270693i
$907$	−34.5697	−	25.8785i	−1.14787	−	0.859283i	−0.156151	−	0.987733i	$-0.549909\pi$
$907$	−34.5697	−	25.8785i	−1.14787	−	0.859283i	−0.991716	+	0.128450i	$0.959000\pi$
$908$	8.38500	−	22.4811i	0.278266	−	0.746060i
$909$	−12.5393	+	5.72649i	−0.415901	+	0.189936i
$910$	1.17514	−	3.85278i	0.0389556	−	0.127718i
$911$	0.440235	−	0.685019i	0.0145856	−	0.0226957i	−0.833884	−	0.551939i	$-0.813888\pi$
$911$	0.440235	−	0.685019i	0.0145856	−	0.0226957i	0.848470	+	0.529244i	$0.177524\pi$
$912$	1.36332	−	2.49674i	0.0451441	−	0.0826752i
$913$	−2.07345	−	2.76981i	−0.0686212	−	0.0916672i
$914$	3.75667	−	4.33542i	0.124259	−	0.143403i
$915$	−5.32032	−	39.9637i	−0.175884	−	1.32116i
$916$	11.3563	−	9.84029i	0.375223	−	0.325132i
$917$	−42.5999	+	23.2613i	−1.40677	+	0.768156i
$918$	−4.84890	+	1.80855i	−0.160038	+	0.0596909i
$919$	−27.5439			−0.908589			−0.454294	−	0.890852i	$-0.650109\pi$
$919$	−27.5439			−0.908589			−0.454294	+	0.890852i	$0.650109\pi$
$920$	6.00217	−	8.88673i	0.197886	−	0.292987i
$921$	−15.6734			−0.516455
$922$	6.47246	−	2.41410i	0.213159	−	0.0795043i
$923$	−3.92101	+	2.14103i	−0.129062	+	0.0704730i
$924$	14.6704	−	12.7120i	0.482622	−	0.418194i
$925$	20.2711	+	39.0419i	0.666510	+	1.28369i
$926$	25.5191	−	29.4507i	0.838611	−	0.967809i
$927$	10.0942	+	13.4843i	0.331537	+	0.442882i
$928$	1.25665	−	2.30139i	0.0412517	−	0.0755469i
$929$	−3.56807	+	5.55202i	−0.117065	+	0.182156i	−0.894841	−	0.446385i	$-0.852711\pi$
$929$	−3.56807	+	5.55202i	−0.117065	+	0.182156i	0.777776	+	0.628541i	$0.216348\pi$
$930$	−38.4341	+	20.4682i	−1.26030	+	0.671178i
$931$	21.3910	−	9.76896i	0.701063	−	0.320165i
$932$	1.49230	−	4.00100i	0.0488818	−	0.131057i
$933$	10.1119	+	7.56966i	0.331048	+	0.247820i
$934$	11.2864	+	7.25336i	0.369304	+	0.237337i
$935$	−1.27411	+	8.24881i	−0.0416678	+	0.269765i
$936$	−0.0973554	+	0.677122i	−0.00318216	+	0.0221324i
$937$	−1.04561	−	14.6196i	−0.0341586	−	0.477600i	−0.985524	−	0.169536i	$-0.945773\pi$
$937$	−1.04561	−	14.6196i	−0.0341586	−	0.477600i	0.951365	−	0.308065i	$-0.0996813\pi$
$938$	5.84796	−	26.8827i	0.190943	−	0.877750i
$939$	−12.8603	−	14.8416i	−0.419681	−	0.484337i
$940$	3.80704	+	3.36911i	0.124172	+	0.109888i
$941$	−27.3669	−	12.4980i	−0.892135	−	0.407424i	−0.0840300	−	0.996463i	$-0.526779\pi$
$941$	−27.3669	−	12.4980i	−0.892135	−	0.407424i	−0.808105	+	0.589039i	$0.799506\pi$
$942$	8.87441	−	8.87441i	0.289144	−	0.289144i
$943$	−17.4210	+	36.9296i	−0.567307	+	1.20259i
$944$		−	12.8640i		−	0.418688i
$945$	27.0655	+	2.22024i	0.880439	+	0.0722243i
$946$	−7.77219	−	2.28212i	−0.252696	−	0.0741982i
$947$	2.03698	−	28.4807i	0.0661929	−	0.925498i	−0.850518	−	0.525947i	$-0.823711\pi$
$947$	2.03698	−	28.4807i	0.0661929	−	0.925498i	0.916711	−	0.399552i	$-0.130834\pi$
$948$	28.1910	+	6.13257i	0.915600	+	0.199177i
$949$	2.62106	+	2.27116i	0.0850833	+	0.0737251i
$950$	1.49509	−	6.24186i	0.0485072	−	0.202513i
$951$	−13.8642	+	4.07089i	−0.449577	+	0.132008i
$952$	2.29342	+	10.5427i	0.0743302	+	0.341691i
$953$	−16.6151	+	22.1952i	−0.538216	+	0.718973i	−0.984395	−	0.175971i	$-0.943694\pi$
$953$	−16.6151	+	22.1952i	−0.538216	+	0.718973i	0.446179	+	0.894944i	$0.352784\pi$
$954$	−6.13180	−	13.4268i	−0.198524	−	0.434708i
$955$	−12.5672	−	12.8327i	−0.406666	−	0.415255i
$956$	2.60298	+	18.1041i	0.0841862	+	0.585528i
$957$	−9.88448	+	2.15024i	−0.319520	+	0.0695073i
$958$	−9.35588	−	5.10870i	−0.302275	−	0.165054i
$959$	−18.9741	−	2.72806i	−0.612704	−	0.0880936i
$960$	−2.01127	−	4.52870i	−0.0649134	−	0.146163i
$961$	38.8841	−	24.9893i	1.25433	−	0.806106i
$962$	−3.14169	−	0.224698i	−0.101292	−	0.00724456i
$963$	16.9875	+	31.1102i	0.547414	+	1.00251i
$964$	−9.64676	+	21.1235i	−0.310701	+	0.680341i
$965$	5.44256	+	2.55460i	0.175202	+	0.0822354i
$966$	−47.2496	+	25.0457i	−1.52023	+	0.805833i
$967$	−25.3215	−	25.3215i	−0.814284	−	0.814284i	0.170989	−	0.985273i	$-0.445304\pi$
$967$	−25.3215	−	25.3215i	−0.814284	−	0.814284i	−0.985273	+	0.170989i	$0.945304\pi$
$968$	2.78504	+	7.46698i	0.0895146	+	0.239998i
$969$	1.71846	−	5.85254i	0.0552049	−	0.188011i
$970$	6.83487	−	12.2120i	0.219454	−	0.392104i
$971$	23.5281	+	36.6104i	0.755052	+	1.17488i	0.979705	+	0.200445i	$0.0642386\pi$
$971$	23.5281	+	36.6104i	0.755052	+	1.17488i	−0.224653	+	0.974439i	$0.572125\pi$
$972$	−17.2716	+	1.23529i	−0.553987	+	0.0396219i
$973$	19.5023	−	14.5993i	0.625216	−	0.468031i
$974$	−0.397245	−	1.35289i	−0.0127286	−	0.0433495i
$975$	0.482350	+	3.93726i	0.0154476	+	0.126093i
$976$	−8.05329	+	1.15789i	−0.257780	+	0.0370631i
$977$	−40.5904	−	15.1394i	−1.29860	−	0.484353i	−0.397357	−	0.917664i	$-0.630072\pi$
$977$	−40.5904	−	15.1394i	−1.29860	−	0.484353i	−0.901244	+	0.433311i	$0.857345\pi$
$978$	18.1151	+	6.75658i	0.579256	+	0.216051i
$979$	−1.52807	+	0.219703i	−0.0488374	+	0.00702175i
$980$	9.12511	−	39.9339i	0.291491	−	1.27564i
$981$	−0.715621	−	2.43718i	−0.0228480	−	0.0778132i
$982$	14.5671	−	10.9048i	0.464853	−	0.347985i
$983$	42.6028	−	3.04701i	1.35882	−	0.0971846i	0.627178	−	0.778876i	$-0.284210\pi$
$983$	42.6028	−	3.04701i	1.35882	−	0.0971846i	0.731640	+	0.681691i	$0.238755\pi$
$984$	10.2007	+	15.8726i	0.325186	+	0.505999i
$985$	−0.117108	+	0.0330608i	−0.00373137	+	0.00105341i
$986$	1.58401	−	5.39464i	0.0504451	−	0.171800i
$987$	−8.85944	−	23.7531i	−0.281999	−	0.756068i
$988$	0.324955	+	0.324955i	0.0103382	+	0.0103382i
$989$	19.4519	+	10.9364i	0.618533	+	0.347756i
$990$	−3.16052	+	6.73348i	−0.100448	+	0.214004i
$991$	−2.43766	+	5.33773i	−0.0774349	+	0.169559i	−0.944390	−	0.328827i	$-0.893347\pi$
$991$	−2.43766	+	5.33773i	−0.0774349	+	0.169559i	0.866955	+	0.498386i	$0.166074\pi$
$992$	4.21144	+	7.71268i	0.133713	+	0.244878i
$993$	21.9286	+	1.56836i	0.695882	+	0.0497705i
$994$	−52.8244	+	33.9482i	−1.67549	+	1.07677i
$995$	44.0639	+	16.9615i	1.39692	+	0.537717i
$996$	4.35954	+	0.626808i	0.138137	+	0.0198612i
$997$	20.4598	+	11.1719i	0.647967	+	0.353817i	0.769386	−	0.638785i	$-0.220563\pi$
$997$	20.4598	+	11.1719i	0.647967	+	0.353817i	−0.121419	+	0.992601i	$0.538744\pi$
$998$	14.5678	−	3.16902i	0.461135	−	0.100314i
$999$	−3.02206	−	21.0189i	−0.0956136	−	0.665007i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.17.7	✓	240
5.3	odd	4	inner	230.2.l.a.63.1	yes	240
23.19	odd	22	inner	230.2.l.a.157.1	yes	240
115.88	even	44	inner	230.2.l.a.203.7	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.17.7	✓	240	1.1	even	1	trivial
230.2.l.a.63.1	yes	240	5.3	odd	4	inner
230.2.l.a.157.1	yes	240	23.19	odd	22	inner
230.2.l.a.203.7	yes	240	115.88	even	44	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.936950 - 0.349464i) q^{2} +(-1.94498 + 1.06204i) q^{3} +(0.755750 - 0.654861i) q^{4} +(-1.77597 - 1.35866i) q^{5} +(-1.45120 + 1.67478i) q^{6} +(-3.01546 - 4.02819i) q^{7} +(0.479249 - 0.877679i) q^{8} +(1.03309 - 1.60752i) q^{9} +(-2.13879 - 0.652357i) q^{10} +(1.58353 - 0.723173i) q^{11} +(-0.774429 + 2.07632i) q^{12} +(-0.286592 - 0.214540i) q^{13} +(-4.23304 - 2.72041i) q^{14} +(4.89716 + 0.756414i) q^{15} +(0.142315 - 0.989821i) q^{16} +(-0.152966 - 2.13874i) q^{17} +(0.406183 - 1.86719i) q^{18} +(-0.840634 - 0.970143i) q^{19} +(-2.23192 + 0.136206i) q^{20} +(10.1431 + 4.63220i) q^{21} +(1.23096 - 1.23096i) q^{22} +(-4.06631 + 2.54267i) q^{23} +2.21605i q^{24} +(1.30811 + 4.82585i) q^{25} +(-0.343496 - 0.100860i) q^{26} +(0.172183 - 2.40743i) q^{27} +(-4.91683 - 1.06959i) q^{28} +(1.98168 + 1.71713i) q^{29} +(4.85273 - 1.00266i) q^{30} +(-8.43162 + 2.47575i) q^{31} +(-0.212565 - 0.977147i) q^{32} +(-2.31189 + 3.08832i) q^{33} +(-0.890734 - 1.95044i) q^{34} +(-0.117565 + 11.2509i) q^{35} +(-0.271944 - 1.89141i) q^{36} +(8.59708 - 1.87018i) q^{37} +(-1.12666 - 0.615204i) q^{38} +(0.785264 + 0.112904i) q^{39} +(-2.04359 + 0.907593i) q^{40} +(7.16256 - 4.60310i) q^{41} +(11.1224 + 0.795486i) q^{42} +(-2.22999 - 4.08392i) q^{43} +(0.723173 - 1.58353i) q^{44} +(-4.01880 + 1.45129i) q^{45} +(-2.92135 + 3.80338i) q^{46} +(-1.60762 - 1.60762i) q^{47} +(0.774429 + 2.07632i) q^{48} +(-5.16114 + 17.5772i) q^{49} +(2.91209 + 4.06445i) q^{50} +(2.56894 + 3.99735i) q^{51} +(-0.357085 + 0.0255393i) q^{52} +(6.18386 - 4.62918i) q^{53} +(-0.679983 - 2.31581i) q^{54} +(-3.79484 - 0.867141i) q^{55} +(-4.98061 + 0.716104i) q^{56} +(2.66534 + 0.994122i) q^{57} +(2.45681 + 0.916342i) q^{58} +(12.7331 - 1.83074i) q^{59} +(4.19637 - 2.63530i) q^{60} +(-2.29221 - 7.80653i) q^{61} +(-7.03482 + 5.26620i) q^{62} +(-9.59064 + 0.685936i) q^{63} +(-0.540641 - 0.841254i) q^{64} +(0.217491 + 0.770395i) q^{65} +(-1.08687 + 3.70153i) q^{66} +(1.91069 + 5.12275i) q^{67} +(-1.51618 - 1.51618i) q^{68} +(5.20847 - 9.26400i) q^{69} +(3.82163 + 10.5826i) q^{70} +(5.18399 - 11.3514i) q^{71} +(-0.915780 - 1.67713i) q^{72} +(-9.66299 - 0.691111i) q^{73} +(7.40147 - 4.75664i) q^{74} +(-7.66948 - 7.99692i) q^{75} +(-1.27062 - 0.182687i) q^{76} +(-7.68815 - 4.19805i) q^{77} +(0.775209 - 0.168636i) q^{78} +(-1.85277 - 12.8863i) q^{79} +(-1.59757 + 1.56453i) q^{80} +(4.60329 + 10.0798i) q^{81} +(5.10234 - 6.81593i) q^{82} +(-0.422472 - 1.94207i) q^{83} +(10.6991 - 3.14153i) q^{84} +(-2.63415 + 4.00616i) q^{85} +(-3.51657 - 3.04713i) q^{86} +(-5.67798 - 1.23517i) q^{87} +(0.124191 - 1.73641i) q^{88} +(-0.850880 - 0.249841i) q^{89} +(-3.25824 + 2.76421i) q^{90} +1.80138i q^{91} +(-1.40802 + 4.58448i) q^{92} +(13.7700 - 13.7700i) q^{93} +(-2.06807 - 0.944454i) q^{94} +(0.174845 + 2.86507i) q^{95} +(1.45120 + 1.67478i) q^{96} +(-1.33036 + 6.11554i) q^{97} +(1.30688 + 18.2726i) q^{98} +(0.473413 - 3.29266i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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