LMFDB - Embedded newform 378.2.z.a.41.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(41,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([17, 9]))

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

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

chi := DirichletCharacter("378.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.z (of order $18$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.18
Character	$\chi$	$=$	378.41
Dual form			378.2.z.a.83.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984808 - 0.173648i) q^{2} +(-0.0750633 - 1.73042i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-2.14704 - 1.80158i) q^{5} +(-0.374408 - 1.69110i) q^{6} +(2.53928 + 0.743006i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.98873 + 0.259783i) q^{9} +O(q^{10})$	\(q+(0.984808 - 0.173648i) q^{2} +(-0.0750633 - 1.73042i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-2.14704 - 1.80158i) q^{5} +(-0.374408 - 1.69110i) q^{6} +(2.53928 + 0.743006i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.98873 + 0.259783i) q^{9} +(-2.42726 - 1.40138i) q^{10} +(-3.45351 - 4.11574i) q^{11} +(-0.662376 - 1.60039i) q^{12} +(2.86511 + 0.505196i) q^{13} +(2.62972 + 0.290777i) q^{14} +(-2.95633 + 3.85051i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-0.473965 + 0.820932i) q^{17} +(-2.89821 + 0.774824i) q^{18} +(-0.211551 + 0.122139i) q^{19} +(-2.63373 - 0.958599i) q^{20} +(1.09511 - 4.44980i) q^{21} +(-4.11574 - 3.45351i) q^{22} +(0.103339 + 0.283921i) q^{23} +(-0.930218 - 1.46106i) q^{24} +(0.495843 + 2.81206i) q^{25} +2.90931 q^{26} +(0.673878 + 5.15227i) q^{27} +(2.64027 - 0.170287i) q^{28} +(6.17949 - 1.08961i) q^{29} +(-2.24278 + 4.30538i) q^{30} +(-1.27129 - 3.49284i) q^{31} +(0.642788 - 0.766044i) q^{32} +(-6.86274 + 6.28498i) q^{33} +(-0.324211 + 0.890763i) q^{34} +(-4.11334 - 6.16997i) q^{35} +(-2.71964 + 1.26632i) q^{36} +(-2.84955 + 4.93556i) q^{37} +(-0.187127 + 0.157019i) q^{38} +(0.659138 - 4.99577i) q^{39} +(-2.76018 - 0.486694i) q^{40} +(-0.505122 + 2.86469i) q^{41} +(0.305771 - 4.57236i) q^{42} +(7.36730 - 6.18190i) q^{43} +(-4.65291 - 2.68636i) q^{44} +(6.88493 + 4.82667i) q^{45} +(0.151071 + 0.261663i) q^{46} +(12.6003 + 4.58613i) q^{47} +(-1.16980 - 1.27733i) q^{48} +(5.89588 + 3.77340i) q^{49} +(0.976619 + 2.68324i) q^{50} +(1.45614 + 0.758539i) q^{51} +(2.86511 - 0.505196i) q^{52} +1.40916i q^{53} +(1.55832 + 4.95698i) q^{54} +15.0584i q^{55} +(2.57058 - 0.626178i) q^{56} +(0.227231 + 0.356904i) q^{57} +(5.89640 - 2.14612i) q^{58} +(8.84872 + 7.42496i) q^{59} +(-1.46109 + 4.62942i) q^{60} +(4.43433 - 12.1832i) q^{61} +(-1.85850 - 3.21902i) q^{62} +(-7.78224 - 1.56098i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-5.24134 - 6.24639i) q^{65} +(-5.66710 + 7.38120i) q^{66} +(-0.239571 + 1.35868i) q^{67} +(-0.164606 + 0.933529i) q^{68} +(0.483547 - 0.200132i) q^{69} +(-5.12226 - 5.36196i) q^{70} +(-3.49176 - 2.01597i) q^{71} +(-2.45843 + 1.71934i) q^{72} +(-11.8393 + 6.83540i) q^{73} +(-1.94920 + 5.35539i) q^{74} +(4.82884 - 1.06910i) q^{75} +(-0.157019 + 0.187127i) q^{76} +(-5.71142 - 13.0170i) q^{77} +(-0.218382 - 5.03433i) q^{78} +(1.23285 + 6.99182i) q^{79} -2.80276 q^{80} +(8.86503 - 1.55284i) q^{81} +2.90888i q^{82} +(2.12140 + 12.0310i) q^{83} +(-0.492857 - 4.55600i) q^{84} +(2.49659 - 0.908686i) q^{85} +(6.18190 - 7.36730i) q^{86} +(-2.34934 - 10.6114i) q^{87} +(-5.04870 - 1.83758i) q^{88} +(-7.16195 - 12.4049i) q^{89} +(7.61848 + 3.55778i) q^{90} +(6.89995 + 3.41163i) q^{91} +(0.194214 + 0.231455i) q^{92} +(-5.94867 + 2.46206i) q^{93} +(13.2052 + 2.32844i) q^{94} +(0.674249 + 0.118888i) q^{95} +(-1.37383 - 1.05479i) q^{96} +(2.31776 + 2.76220i) q^{97} +(6.46156 + 2.69226i) q^{98} +(11.3908 + 11.4037i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9}+O(q^{10}) $ 144 * q - 12 * q^9	$ 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) $ 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.984808	−	0.173648i	0.696364	−	0.122788i
$2$	0.984808	−	0.173648i	0.696364	−	0.122788i
$3$	−0.0750633	−	1.73042i	−0.0433378	−	0.999060i
$3$	−0.0750633	−	1.73042i	−0.0433378	−	0.999060i
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$	−2.14704	−	1.80158i	−0.960184	−	0.805690i	0.0207992	−	0.999784i	$-0.493379\pi$
$5$	−2.14704	−	1.80158i	−0.960184	−	0.805690i	−0.980983	+	0.194094i	$0.937823\pi$
$6$	−0.374408	−	1.69110i	−0.152851	−	0.690389i
$7$	2.53928	+	0.743006i	0.959758	+	0.280830i
$7$	2.53928	+	0.743006i	0.959758	+	0.280830i
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	−2.98873	+	0.259783i	−0.996244	+	0.0865942i
$10$	−2.42726	−	1.40138i	−0.767566	−	0.443155i
$11$	−3.45351	−	4.11574i	−1.04127	−	1.24094i	−0.969903	−	0.243492i	$-0.921707\pi$
$11$	−3.45351	−	4.11574i	−1.04127	−	1.24094i	−0.0713711	−	0.997450i	$-0.522737\pi$
$12$	−0.662376	−	1.60039i	−0.191212	−	0.461994i
$13$	2.86511	+	0.505196i	0.794638	+	0.140116i	0.556207	−	0.831044i	$-0.312256\pi$
$13$	2.86511	+	0.505196i	0.794638	+	0.140116i	0.238430	+	0.971160i	$0.423367\pi$
$14$	2.62972	+	0.290777i	0.702823	+	0.0777134i
$15$	−2.95633	+	3.85051i	−0.763321	+	0.994198i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−0.473965	+	0.820932i	−0.114953	+	0.199105i	−0.917761	−	0.397133i	$-0.870005\pi$
$17$	−0.473965	+	0.820932i	−0.114953	+	0.199105i	0.802808	+	0.596238i	$0.203339\pi$
$18$	−2.89821	+	0.774824i	−0.683116	+	0.182628i
$19$	−0.211551	+	0.122139i	−0.0485330	+	0.0280206i	−0.524070	−	0.851675i	$-0.675587\pi$
$19$	−0.211551	+	0.122139i	−0.0485330	+	0.0280206i	0.475537	+	0.879696i	$0.342254\pi$
$20$	−2.63373	−	0.958599i	−0.588920	−	0.214349i
$21$	1.09511	−	4.44980i	0.238972	−	0.971026i
$22$	−4.11574	−	3.45351i	−0.877478	−	0.736292i
$23$	0.103339	+	0.283921i	0.0215476	+	0.0592017i	0.950000	−	0.312250i	$-0.101083\pi$
$23$	0.103339	+	0.283921i	0.0215476	+	0.0592017i	−0.928452	+	0.371451i	$0.878860\pi$
$24$	−0.930218	−	1.46106i	−0.189880	−	0.298237i
$25$	0.495843	+	2.81206i	0.0991685	+	0.562413i
$26$	2.90931			0.570562
$27$	0.673878	+	5.15227i	0.129688	+	0.991555i
$28$	2.64027	−	0.170287i	0.498963	−	0.0321813i
$29$	6.17949	−	1.08961i	1.14750	−	0.202336i	0.432618	−	0.901577i	$-0.357590\pi$
$29$	6.17949	−	1.08961i	1.14750	−	0.202336i	0.714885	+	0.699242i	$0.246479\pi$
$30$	−2.24278	+	4.30538i	−0.409474	+	0.786051i
$31$	−1.27129	−	3.49284i	−0.228331	−	0.627333i	0.771631	−	0.636070i	$-0.219441\pi$
$31$	−1.27129	−	3.49284i	−0.228331	−	0.627333i	−0.999962	+	0.00873703i	$0.997219\pi$
$32$	0.642788	−	0.766044i	0.113630	−	0.135419i
$33$	−6.86274	+	6.28498i	−1.19465	+	1.09408i
$34$	−0.324211	+	0.890763i	−0.0556018	+	0.152765i
$35$	−4.11334	−	6.16997i	−0.695282	−	1.04292i
$36$	−2.71964	+	1.26632i	−0.453273	+	0.211054i
$37$	−2.84955	+	4.93556i	−0.468462	+	0.811401i	−0.999350	−	0.0360414i	$-0.988525\pi$
$37$	−2.84955	+	4.93556i	−0.468462	+	0.811401i	0.530888	+	0.847442i	$0.321859\pi$
$38$	−0.187127	+	0.157019i	−0.0303561	+	0.0254718i
$39$	0.659138	−	4.99577i	0.105547	−	0.799964i
$40$	−2.76018	−	0.486694i	−0.436422	−	0.0769530i
$41$	−0.505122	+	2.86469i	−0.0788868	+	0.447389i	0.919622	+	0.392804i	$0.128495\pi$
$41$	−0.505122	+	2.86469i	−0.0788868	+	0.447389i	−0.998509	+	0.0545856i	$0.982616\pi$
$42$	0.305771	−	4.57236i	0.0471815	−	0.705531i
$43$	7.36730	−	6.18190i	1.12350	−	0.942731i	0.124727	−	0.992191i	$-0.460194\pi$
$43$	7.36730	−	6.18190i	1.12350	−	0.942731i	0.998776	+	0.0494600i	$0.0157500\pi$
$44$	−4.65291	−	2.68636i	−0.701452	−	0.404984i
$45$	6.88493	+	4.82667i	1.02635	+	0.719517i
$46$	0.151071	+	0.261663i	0.0222743	+	0.0385801i
$47$	12.6003	+	4.58613i	1.83794	+	0.668956i	0.990401	+	0.138222i	$0.0441388\pi$
$47$	12.6003	+	4.58613i	1.83794	+	0.668956i	0.847539	+	0.530733i	$0.178083\pi$
$48$	−1.16980	−	1.27733i	−0.168846	−	0.184367i
$49$	5.89588	+	3.77340i	0.842269	+	0.539057i
$50$	0.976619	+	2.68324i	0.138115	+	0.379467i
$51$	1.45614	+	0.758539i	0.203900	+	0.106217i
$52$	2.86511	−	0.505196i	0.397319	−	0.0700580i
$53$			1.40916i			0.193563i	0.995306	+	0.0967815i	$0.0308548\pi$
$53$			1.40916i			0.193563i	−0.995306	+	0.0967815i	$0.969145\pi$
$54$	1.55832	+	4.95698i	0.212061	+	0.674559i
$55$			15.0584i			2.03048i
$56$	2.57058	−	0.626178i	0.343509	−	0.0836765i
$57$	0.227231	+	0.356904i	0.0300975	+	0.0472731i
$58$	5.89640	−	2.14612i	0.774236	−	0.281799i
$59$	8.84872	+	7.42496i	1.15200	+	0.966647i	0.999765	−	0.0216967i	$-0.00690681\pi$
$59$	8.84872	+	7.42496i	1.15200	+	0.966647i	0.152240	+	0.988344i	$0.451351\pi$
$60$	−1.46109	+	4.62942i	−0.188625	+	0.597656i
$61$	4.43433	−	12.1832i	0.567758	−	1.55990i	−0.240238	−	0.970714i	$-0.577225\pi$
$61$	4.43433	−	12.1832i	0.567758	−	1.55990i	0.807996	−	0.589188i	$-0.200552\pi$
$62$	−1.85850	−	3.21902i	−0.236030	−	0.408816i
$63$	−7.78224	−	1.56098i	−0.980471	−	0.196666i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	−5.24134	−	6.24639i	−0.650108	−	0.774769i
$66$	−5.66710	+	7.38120i	−0.697572	+	0.908563i
$67$	−0.239571	+	1.35868i	−0.0292683	+	0.165989i	−0.995939	−	0.0900361i	$-0.971302\pi$
$67$	−0.239571	+	1.35868i	−0.0292683	+	0.165989i	0.966670	+	0.256025i	$0.0824129\pi$
$68$	−0.164606	+	0.933529i	−0.0199615	+	0.113207i
$69$	0.483547	−	0.200132i	0.0582122	−	0.0240931i
$70$	−5.12226	−	5.36196i	−0.612227	−	0.640877i
$71$	−3.49176	−	2.01597i	−0.414395	−	0.239251i	0.278281	−	0.960500i	$-0.410235\pi$
$71$	−3.49176	−	2.01597i	−0.414395	−	0.239251i	−0.692676	+	0.721248i	$0.743569\pi$
$72$	−2.45843	+	1.71934i	−0.289728	+	0.202627i
$73$	−11.8393	+	6.83540i	−1.38568	+	0.800023i	−0.992825	−	0.119577i	$-0.961846\pi$
$73$	−11.8393	+	6.83540i	−1.38568	+	0.800023i	−0.392855	+	0.919600i	$0.628513\pi$
$74$	−1.94920	+	5.35539i	−0.226590	+	0.622552i
$75$	4.82884	−	1.06910i	0.557587	−	0.123449i
$76$	−0.157019	+	0.187127i	−0.0180113	+	0.0214650i
$77$	−5.71142	−	13.0170i	−0.650877	−	1.48342i
$78$	−0.218382	−	5.03433i	−0.0247269	−	0.570026i
$79$	1.23285	+	6.99182i	0.138706	+	0.786641i	0.972207	+	0.234123i	$0.0752218\pi$
$79$	1.23285	+	6.99182i	0.138706	+	0.786641i	−0.833501	+	0.552518i	$0.813667\pi$
$80$	−2.80276			−0.313358
$81$	8.86503	−	1.55284i	0.985003	−	0.172538i
$82$			2.90888i			0.321232i
$83$	2.12140	+	12.0310i	0.232854	+	1.32058i	0.847087	+	0.531454i	$0.178354\pi$
$83$	2.12140	+	12.0310i	0.232854	+	1.32058i	−0.614234	+	0.789124i	$0.710535\pi$
$84$	−0.492857	−	4.55600i	−0.0537751	−	0.497100i
$85$	2.49659	−	0.908686i	0.270794	−	0.0985608i
$86$	6.18190	−	7.36730i	0.666612	−	0.794437i
$87$	−2.34934	−	10.6114i	−0.251876	−	1.13766i
$88$	−5.04870	−	1.83758i	−0.538193	−	0.195886i
$89$	−7.16195	−	12.4049i	−0.759165	−	1.31491i	−0.943277	−	0.332007i	$-0.892274\pi$
$89$	−7.16195	−	12.4049i	−0.759165	−	1.31491i	0.184112	−	0.982905i	$-0.441059\pi$
$90$	7.61848	+	3.55778i	0.803058	+	0.375023i
$91$	6.89995	+	3.41163i	0.723311	+	0.357636i
$92$	0.194214	+	0.231455i	0.0202482	+	0.0241308i
$93$	−5.94867	+	2.46206i	−0.616848	+	0.255303i
$94$	13.2052	+	2.32844i	1.36202	+	0.240160i
$95$	0.674249	+	0.118888i	0.0691765	+	0.0121977i
$96$	−1.37383	−	1.05479i	−0.140216	−	0.107654i
$97$	2.31776	+	2.76220i	0.235333	+	0.280459i	0.870767	−	0.491697i	$-0.163623\pi$
$97$	2.31776	+	2.76220i	0.235333	+	0.280459i	−0.635434	+	0.772156i	$0.719179\pi$
$98$	6.46156	+	2.69226i	0.652716	+	0.271960i
$99$	11.3908	+	11.4037i	1.14482	+	1.14611i
$100$	1.42772	+	2.47289i	0.142772	+	0.247289i
$101$	−8.24231	−	2.99996i	−0.820141	−	0.298507i	−0.102335	−	0.994750i	$-0.532631\pi$
$101$	−8.24231	−	2.99996i	−0.820141	−	0.298507i	−0.717806	+	0.696243i	$0.754853\pi$
$102$	1.56573	+	0.494159i	0.155031	+	0.0489291i
$103$	−1.56891	+	1.86975i	−0.154589	+	0.184232i	−0.837780	−	0.546007i	$-0.816147\pi$
$103$	−1.56891	+	1.86975i	−0.154589	+	0.184232i	0.683191	+	0.730239i	$0.260591\pi$
$104$	2.73385	−	0.995041i	0.268076	−	0.0975718i
$105$	−10.3679	+	7.58096i	−1.01180	+	0.739826i
$106$	0.244698	+	1.38775i	0.0237672	+	0.134790i
$107$		−	12.8021i		−	1.23762i	−0.785539	−	0.618812i	$-0.787614\pi$
$107$		−	12.8021i		−	1.23762i	0.785539	−	0.618812i	$-0.212386\pi$
$108$	2.39542	+	4.61107i	0.230499	+	0.443700i
$109$	1.51794			0.145392			0.0726962	−	0.997354i	$-0.476840\pi$
$109$	1.51794			0.145392			0.0726962	+	0.997354i	$0.476840\pi$
$110$	2.61487	+	14.8296i	0.249318	+	1.41395i
$111$	8.75450	+	4.56044i	0.830941	+	0.432858i
$112$	2.42280	−	1.06304i	0.228933	−	0.100448i
$113$	−8.80621	+	10.4948i	−0.828419	+	0.987271i	0.171579	+	0.985170i	$0.445113\pi$
$113$	−8.80621	+	10.4948i	−0.828419	+	0.987271i	−0.999998	+	0.00210074i	$0.999331\pi$
$114$	0.285755	+	0.312023i	0.0267634	+	0.0292237i
$115$	0.289634	−	0.795762i	0.0270085	−	0.0742052i
$116$	5.43416	−	3.13741i	0.504549	−	0.291301i
$117$	−8.69428	−	0.765589i	−0.803786	−	0.0707787i
$118$	10.0036	+	5.77559i	0.920907	+	0.531686i
$119$	−1.81349	+	1.73242i	−0.166242	+	0.158810i
$120$	−0.634998	+	4.81281i	−0.0579671	+	0.439347i
$121$	−3.10241	+	17.5946i	−0.282037	+	1.59951i
$122$	2.25137	−	12.7682i	0.203829	−	1.15597i
$123$	4.99504	+	0.659042i	0.450388	+	0.0594238i
$124$	−2.38925	−	2.84739i	−0.214561	−	0.255703i
$125$	−3.00533	+	5.20539i	−0.268805	+	0.465584i
$126$	−7.93508	−	0.185897i	−0.706913	−	0.0165610i
$127$	2.22327	+	3.85081i	0.197283	+	0.341704i	0.947647	−	0.319321i	$-0.103455\pi$
$127$	2.22327	+	3.85081i	0.197283	+	0.341704i	−0.750363	+	0.661025i	$0.770122\pi$
$128$	0.342020	−	0.939693i	0.0302306	−	0.0830579i
$129$	−11.2503	−	12.2845i	−0.990536	−	1.08159i
$130$	−6.24639	−	5.24134i	−0.547844	−	0.459696i
$131$	9.14073	−	3.32695i	0.798629	−	0.290677i	0.0897109	−	0.995968i	$-0.471406\pi$
$131$	9.14073	−	3.32695i	0.798629	−	0.290677i	0.708918	+	0.705291i	$0.249183\pi$
$132$	−4.29927	+	8.25315i	−0.374204	+	0.718344i
$133$	−0.627936	+	0.152961i	−0.0544489	+	0.0132634i
$134$			1.37964i			0.119182i
$135$	7.83537	−	12.2762i	0.674361	−	1.05656i
$136$			0.947931i			0.0812844i
$137$	−11.4023	+	2.01053i	−0.974164	+	0.171771i	−0.638004	−	0.770033i	$-0.720239\pi$
$137$	−11.4023	+	2.01053i	−0.974164	+	0.171771i	−0.336160	+	0.941805i	$0.609128\pi$
$138$	0.441448	−	0.281059i	0.0375786	−	0.0239253i
$139$	1.04944	+	2.88331i	0.0890122	+	0.244559i	0.976209	−	0.216833i	$-0.0695726\pi$
$139$	1.04944	+	2.88331i	0.0890122	+	0.244559i	−0.887197	+	0.461392i	$0.847350\pi$
$140$	−5.97553	−	4.39103i	−0.505025	−	0.371110i
$141$	6.99012	−	22.1481i	0.588675	−	1.86520i
$142$	−3.78878	−	1.37900i	−0.317947	−	0.115723i
$143$	−7.81544	−	13.5367i	−0.653560	−	1.13200i
$144$	−2.12252	+	2.12012i	−0.176876	+	0.176677i
$145$	−15.2306	−	8.79340i	−1.26483	−	0.730252i
$146$	−10.4724	+	8.78742i	−0.866705	+	0.727252i
$147$	6.08702	−	10.4856i	0.502049	−	0.864839i
$148$	−0.989637	+	5.61251i	−0.0813476	+	0.461345i
$149$	−14.8804	−	2.62382i	−1.21905	−	0.214952i	−0.473135	−	0.880990i	$-0.656878\pi$
$149$	−14.8804	−	2.62382i	−1.21905	−	0.214952i	−0.745918	+	0.666038i	$0.767989\pi$
$150$	4.56983	−	1.89138i	0.373125	−	0.154430i
$151$	−14.2791	+	11.9816i	−1.16202	+	0.975049i	−0.999931	−	0.0117270i	$-0.996267\pi$
$151$	−14.2791	+	11.9816i	−1.16202	+	0.975049i	−0.162087	+	0.986776i	$0.551823\pi$
$152$	−0.122139	+	0.211551i	−0.00990676	+	0.0171590i
$153$	1.20329	−	2.57667i	0.0972803	−	0.208312i
$154$	−7.88503	−	11.8275i	−0.635394	−	0.953084i
$155$	−3.56312	+	9.78959i	−0.286197	+	0.786319i
$156$	−1.08927	−	4.91993i	−0.0872112	−	0.393909i
$157$	14.0831	−	16.7835i	1.12395	−	1.33947i	0.190117	−	0.981761i	$-0.439113\pi$
$157$	14.0831	−	16.7835i	1.12395	−	1.33947i	0.933833	−	0.357710i	$-0.116442\pi$
$158$	2.42823	+	6.67151i	0.193180	+	0.530757i
$159$	2.43844	−	0.105776i	0.193381	−	0.00838860i
$160$	−2.76018	+	0.486694i	−0.218211	+	0.0384765i
$161$	0.0514511	+	0.797737i	0.00405492	+	0.0628705i
$162$	8.46070	−	3.06865i	0.664735	−	0.241096i
$163$	4.24081			0.332166			0.166083	−	0.986112i	$-0.446888\pi$
$163$	4.24081			0.332166			0.166083	+	0.986112i	$0.446888\pi$
$164$	0.505122	+	2.86469i	0.0394434	+	0.223695i
$165$	26.0574	−	1.13033i	2.02857	−	0.0879964i
$166$	4.17834	+	11.4799i	0.324302	+	0.891012i
$167$	0.608984	+	0.510998i	0.0471246	+	0.0395422i	0.666046	−	0.745911i	$-0.267986\pi$
$167$	0.608984	+	0.510998i	0.0471246	+	0.0395422i	−0.618921	+	0.785453i	$0.712430\pi$
$168$	−1.27651	−	4.40120i	−0.0984848	−	0.339560i
$169$	−4.26239	−	1.55138i	−0.327876	−	0.119337i
$170$	2.30087	−	1.32841i	0.176469	−	0.101884i
$171$	0.600538	−	0.419997i	0.0459243	−	0.0321180i
$172$	4.80867	−	8.32885i	0.366657	−	0.635069i
$173$	−6.23129	+	5.22867i	−0.473756	+	0.397529i	−0.848163	−	0.529736i	$-0.822291\pi$
$173$	−6.23129	+	5.22867i	−0.473756	+	0.397529i	0.374406	+	0.927265i	$0.377847\pi$
$174$	−4.15629	−	10.0422i	−0.315088	−	0.761296i
$175$	−0.830297	+	7.50903i	−0.0627646	+	0.567629i
$176$	−5.29109	−	0.932962i	−0.398831	−	0.0703247i
$177$	12.1841	−	15.8694i	0.915813	−	1.19281i
$178$	−9.20722	−	10.9727i	−0.690110	−	0.822442i
$179$	12.4107	+	7.16534i	0.927622	+	0.535563i	0.886059	−	0.463573i	$-0.153433\pi$
$179$	12.4107	+	7.16534i	0.927622	+	0.535563i	0.0415635	+	0.999136i	$0.486766\pi$
$180$	8.12054	+	2.18080i	0.605269	+	0.162547i
$181$	−21.2822	+	12.2873i	−1.58189	+	0.913306i	−0.587310	+	0.809362i	$0.699813\pi$
$181$	−21.2822	+	12.2873i	−1.58189	+	0.913306i	−0.994583	+	0.103944i	$0.966854\pi$
$182$	7.38754	+	2.16163i	0.547601	+	0.160231i
$183$	−21.4150	−	6.75876i	−1.58304	−	0.499622i
$184$	0.231455	+	0.194214i	0.0170631	+	0.0143176i
$185$	15.0099	−	5.46314i	1.10355	−	0.401658i
$186$	−5.43076	+	3.45763i	−0.398203	+	0.253526i
$187$	5.01559	−	0.884384i	0.366776	−	0.0646725i
$188$	13.4089			0.977948
$189$	−2.11700	+	13.5838i	−0.153989	+	0.988073i
$190$	0.684650			0.0496698
$191$	11.5001	−	2.02778i	0.832117	−	0.146725i	0.258669	−	0.965966i	$-0.416716\pi$
$191$	11.5001	−	2.02778i	0.832117	−	0.146725i	0.573449	+	0.819241i	$0.305605\pi$
$192$	−1.53612	−	0.800205i	−0.110860	−	0.0577498i
$193$	12.3582	−	4.49803i	0.889565	−	0.323775i	0.143502	−	0.989650i	$-0.454164\pi$
$193$	12.3582	−	4.49803i	0.889565	−	0.323775i	0.746063	+	0.665875i	$0.231942\pi$
$194$	2.76220	+	2.31776i	0.198314	+	0.166406i
$195$	−10.4155	+	9.53861i	−0.745867	+	0.683074i
$196$	6.83090	+	1.52933i	0.487921	+	0.109238i
$197$	−4.95847	+	2.86277i	−0.353276	+	0.203964i	−0.666127	−	0.745838i	$-0.732049\pi$
$197$	−4.95847	+	2.86277i	−0.353276	+	0.203964i	0.312851	+	0.949802i	$0.398716\pi$
$198$	13.1980	+	9.25243i	0.937941	+	0.657542i
$199$	−15.9473	−	9.20720i	−1.13048	−	0.652681i	−0.186422	−	0.982470i	$-0.559689\pi$
$199$	−15.9473	−	9.20720i	−1.13048	−	0.652681i	−0.944055	+	0.329789i	$0.893022\pi$
$200$	1.83544	+	2.18740i	0.129785	+	0.154672i
$201$	2.36907	+	0.312573i	0.167101	+	0.0220472i
$202$	−8.63803	−	1.52312i	−0.607770	−	0.107166i
$203$	16.5011	+	1.82457i	1.15815	+	0.128060i
$204$	1.62776	+	0.214765i	0.113966	+	0.0150366i
$205$	6.24548	−	5.24058i	0.436203	−	0.366018i
$206$	−1.22039	+	2.11378i	−0.0850288	+	0.147274i
$207$	−0.382610	−	0.821719i	−0.0265932	−	0.0571134i
$208$	2.51953	−	1.45465i	0.174698	−	0.100862i
$209$	1.23328	+	0.448879i	0.0853080	+	0.0310496i
$210$	−8.89397	+	9.26616i	−0.613742	+	0.639426i
$211$	−20.8913	−	17.5298i	−1.43821	−	1.20680i	−0.940651	−	0.339376i	$-0.889784\pi$
$211$	−20.8913	−	17.5298i	−1.43821	−	1.20680i	−0.497563	−	0.867428i	$-0.665772\pi$
$212$	0.481961	+	1.32418i	0.0331012	+	0.0909449i
$213$	−3.22637	+	6.19354i	−0.221067	+	0.424374i
$214$	−2.22306	−	12.6076i	−0.151965	−	0.861838i
$215$	−26.9550			−1.83832
$216$	3.15973	+	4.12506i	0.214992	+	0.280675i
$217$	−0.632960	−	9.81388i	−0.0429681	−	0.666210i
$218$	1.49488	−	0.263588i	0.101246	−	0.0178524i
$219$	12.7168	+	19.9738i	0.859324	+	1.34971i
$220$	5.15028	+	14.1503i	0.347232	+	0.954012i
$221$	−1.77269	+	2.11261i	−0.119244	+	0.142110i
$222$	9.41341	+	2.97095i	0.631787	+	0.199397i
$223$	8.35687	−	22.9603i	0.559618	−	1.53754i	−0.260577	−	0.965453i	$-0.583913\pi$
$223$	8.35687	−	22.9603i	0.559618	−	1.53754i	0.820195	−	0.572084i	$-0.193865\pi$
$224$	2.20139	−	1.46761i	0.147087	−	0.0980586i
$225$	−2.21247	−	8.27569i	−0.147498	−	0.551713i
$226$	−6.85002	+	11.8646i	−0.455656	+	0.789220i
$227$	12.6126	−	10.5833i	0.837130	−	0.702436i	−0.119786	−	0.992800i	$-0.538221\pi$
$227$	12.6126	−	10.5833i	0.837130	−	0.702436i	0.956916	+	0.290364i	$0.0937763\pi$
$228$	0.335596	+	0.257662i	0.0222254	+	0.0170641i
$229$	11.0698	+	1.95190i	0.731510	+	0.128985i	0.526983	−	0.849876i	$-0.323323\pi$
$229$	11.0698	+	1.95190i	0.731510	+	0.128985i	0.204527	+	0.978861i	$0.434434\pi$
$230$	0.147051	−	0.833967i	0.00969625	−	0.0549902i
$231$	−22.0962	+	10.8603i	−1.45382	+	0.714554i
$232$	4.80679	−	4.03338i	0.315581	−	0.264804i
$233$	1.79517	+	1.03644i	0.117605	+	0.0678996i	0.557649	−	0.830077i	$-0.311704\pi$
$233$	1.79517	+	1.03644i	0.117605	+	0.0678996i	−0.440043	+	0.897977i	$0.645037\pi$
$234$	−8.69513	+	0.755787i	−0.568419	+	0.0494074i
$235$	−18.7910	−	32.5470i	−1.22579	−	2.12313i
$236$	10.8546	+	3.95074i	0.706572	+	0.257171i
$237$	12.0063	−	2.65817i	0.779891	−	0.172667i
$238$	−1.48511	+	2.02101i	−0.0962651	+	0.131002i
$239$	4.84561	+	13.3132i	0.313437	+	0.861160i	0.991957	+	0.126578i	$0.0403994\pi$
$239$	4.84561	+	13.3132i	0.313437	+	0.861160i	−0.678520	+	0.734582i	$0.737378\pi$
$240$	0.210384	+	4.84996i	0.0135802	+	0.313063i
$241$	1.02110	−	0.180047i	0.0657746	−	0.0115978i	−0.140664	−	0.990057i	$-0.544924\pi$
$241$	1.02110	−	0.180047i	0.0657746	−	0.0115978i	0.206439	+	0.978460i	$0.433813\pi$
$242$			17.8661i			1.14847i
$243$	−3.35251	−	15.2237i	−0.215064	−	0.976600i
$244$		−	12.9651i		−	0.830007i
$245$	−5.86060	−	18.7235i	−0.374420	−	1.19620i
$246$	5.03360	−	0.218350i	0.320931	−	0.0139215i
$247$	−0.667819	+	0.243066i	−0.0424923	+	0.0154659i
$248$	−2.84739	−	2.38925i	−0.180810	−	0.151717i
$249$	20.6596	−	4.57401i	1.30925	−	0.289866i
$250$	−2.05577	+	5.64818i	−0.130018	+	0.357222i
$251$	4.27148	+	7.39842i	0.269614	+	0.466984i	0.968762	−	0.247992i	$-0.0797707\pi$
$251$	4.27148	+	7.39842i	0.269614	+	0.466984i	−0.699148	+	0.714976i	$0.746437\pi$
$252$	−7.84681	+	1.19484i	−0.494302	+	0.0752678i
$253$	0.811663	−	1.40584i	0.0510288	−	0.0883845i
$254$	2.85818	+	3.40624i	0.179338	+	0.213727i
$255$	−1.75981	−	4.25195i	−0.110204	−	0.266268i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	3.98557	−	22.6033i	0.248613	−	1.40995i	−0.563337	−	0.826227i	$-0.690483\pi$
$257$	3.98557	−	22.6033i	0.248613	−	1.40995i	0.811950	−	0.583727i	$-0.198406\pi$
$258$	−13.2126	−	10.1443i	−0.822580	−	0.631556i
$259$	−10.9029	+	10.4155i	−0.677476	+	0.647190i
$260$	−7.06164	−	4.07704i	−0.437944	−	0.252847i
$261$	−18.1858	+	4.86188i	−1.12567	+	0.300943i
$262$	8.42414	−	4.86368i	0.520445	−	0.300479i
$263$	−7.88878	+	21.6742i	−0.486443	+	1.33649i	0.417437	+	0.908706i	$0.362928\pi$
$263$	−7.88878	+	21.6742i	−0.486443	+	1.33649i	−0.903880	+	0.427786i	$0.859294\pi$
$264$	−2.80081	+	8.87433i	−0.172378	+	0.546177i
$265$	2.53871	−	3.02552i	0.155952	−	0.185856i
$266$	−0.591835	+	0.259677i	−0.0362877	+	0.0159218i
$267$	−20.9281	+	13.3244i	−1.28078	+	0.815437i
$268$	0.239571	+	1.35868i	0.0146341	+	0.0829944i
$269$	−21.7007			−1.32312			−0.661559	−	0.749893i	$-0.730105\pi$
$269$	−21.7007			−1.32312			−0.661559	+	0.749893i	$0.730105\pi$
$270$	5.58460	−	13.4502i	0.339868	−	0.818556i
$271$			9.94757i			0.604272i	0.953265	+	0.302136i	$0.0976996\pi$
$271$			9.94757i			0.604272i	−0.953265	+	0.302136i	$0.902300\pi$
$272$	0.164606	+	0.933529i	0.00998073	+	0.0566035i
$273$	5.38562	−	12.1959i	0.325953	−	0.738130i
$274$	−10.8799	+	3.95998i	−0.657281	+	0.239231i
$275$	9.86132	−	11.7523i	0.594660	−	0.708688i
$276$	0.385936	−	0.353445i	0.0232306	−	0.0212749i
$277$	−9.20585	−	3.35066i	−0.553126	−	0.201321i	0.0503089	−	0.998734i	$-0.483979\pi$
$277$	−9.20585	−	3.35066i	−0.553126	−	0.201321i	−0.603435	+	0.797412i	$0.706202\pi$
$278$	1.53418	+	2.65727i	0.0920138	+	0.159373i
$279$	4.70693	+	10.1089i	0.281796	+	0.605205i
$280$	−6.64724	−	3.28668i	−0.397249	−	0.196417i
$281$	13.3280	+	15.8837i	0.795083	+	0.947543i	0.999509	−	0.0313394i	$-0.00997726\pi$
$281$	13.3280	+	15.8837i	0.795083	+	0.947543i	−0.204426	+	0.978882i	$0.565533\pi$
$282$	3.03796	−	23.0254i	0.180908	−	1.37114i
$283$	−0.0941297	−	0.0165976i	−0.00559543	−	0.000986625i	0.170850	−	0.985297i	$-0.445349\pi$
$283$	−0.0941297	−	0.0165976i	−0.00559543	−	0.000986625i	−0.176445	+	0.984310i	$0.556460\pi$
$284$	−3.97068	−	0.700138i	−0.235616	−	0.0415455i
$285$	0.155116	−	1.17566i	0.00918826	−	0.0696401i
$286$	−10.0473	−	11.9739i	−0.594111	−	0.708034i
$287$	−3.41113	+	6.89894i	−0.201353	+	0.407232i
$288$	−1.72211	+	2.45649i	−0.101477	+	0.144750i
$289$	8.05071	+	13.9442i	0.473571	+	0.820250i
$290$	−16.5262	−	6.01504i	−0.970451	−	0.353215i
$291$	4.60580	−	4.21805i	0.269997	−	0.247266i
$292$	−8.78742	+	10.4724i	−0.514245	+	0.612853i
$293$	−1.92130	+	0.699296i	−0.112244	+	0.0408533i	−0.397531	−	0.917589i	$-0.630133\pi$
$293$	−1.92130	+	0.699296i	−0.112244	+	0.0408533i	0.285288	+	0.958442i	$0.407911\pi$
$294$	4.17373	−	11.3833i	0.243417	−	0.663889i
$295$	−5.62188	−	31.8833i	−0.327319	−	1.85632i
$296$			5.69909i			0.331253i
$297$	18.8782	−	20.5669i	1.09542	−	1.19342i
$298$	−15.1100			−0.875298
$299$	0.152641	+	0.865671i	0.00882747	+	0.0500631i
$300$	4.17197	−	2.65619i	0.240869	−	0.153355i
$301$	23.3008	−	10.2236i	1.34304	−	0.589280i
$302$	−11.9816	+	14.2791i	−0.689464	+	0.821671i
$303$	−4.57250	+	14.4879i	−0.262683	+	0.832307i
$304$	−0.0835478	+	0.229546i	−0.00479180	+	0.0131654i
$305$	−31.4697	+	18.1690i	−1.80195	+	1.04036i
$306$	0.737576	−	2.74648i	0.0421644	−	0.157006i
$307$	22.4148	+	12.9412i	1.27928	+	0.738591i	0.976716	−	0.214539i	$-0.0688248\pi$
$307$	22.4148	+	12.9412i	1.27928	+	0.738591i	0.302562	+	0.953130i	$0.402158\pi$
$308$	−9.81906	−	10.2786i	−0.559493	−	0.585675i
$309$	3.35323	+	2.57452i	0.190758	+	0.146460i
$310$	−1.80904	+	10.2596i	−0.102747	+	0.582706i
$311$	−4.30869	+	24.4358i	−0.244324	+	1.38563i	0.577735	+	0.816225i	$0.303937\pi$
$311$	−4.30869	+	24.4358i	−0.244324	+	1.38563i	−0.822058	+	0.569404i	$0.807174\pi$
$312$	−1.92706	−	4.65603i	−0.109098	−	0.263596i
$313$	11.6016	+	13.8262i	0.655759	+	0.781503i	0.986770	−	0.162124i	$-0.0518344\pi$
$313$	11.6016	+	13.8262i	0.655759	+	0.781503i	−0.331012	+	0.943627i	$0.607390\pi$
$314$	10.9547	−	18.9740i	0.618208	−	1.07077i
$315$	13.8965	+	17.3718i	0.782980	+	0.978790i
$316$	3.54984	+	6.14850i	0.199694	+	0.345880i
$317$	3.54406	−	9.73724i	0.199054	−	0.546898i	−0.799499	−	0.600668i	$-0.794902\pi$
$317$	3.54406	−	9.73724i	0.199054	−	0.546898i	0.998553	+	0.0537699i	$0.0171238\pi$
$318$	2.38303	−	0.527600i	0.133634	−	0.0295864i
$319$	−25.8255	−	21.6702i	−1.44595	−	1.21330i
$320$	−2.63373	+	0.958599i	−0.147230	+	0.0535873i
$321$	−22.1530	+	0.960967i	−1.23646	+	0.0536360i
$322$	0.189195	+	0.776683i	0.0105434	+	0.0432829i
$323$		−	0.231558i		−	0.0128842i
$324$	7.79930	−	4.49121i	0.433294	−	0.249512i
$325$			8.30736i			0.460810i
$326$	4.17638	−	0.736408i	0.231308	−	0.0407859i
$327$	−0.113942	−	2.62668i	−0.00630099	−	0.145256i
$328$	0.994896	+	2.73346i	0.0549340	+	0.150930i
$329$	28.5881	+	21.0075i	1.57611	+	1.15818i
$330$	25.4653	−	5.63799i	1.40182	−	0.310361i
$331$	16.0033	+	5.82473i	0.879622	+	0.320156i	0.742057	−	0.670337i	$-0.233850\pi$
$331$	16.0033	+	5.82473i	0.879622	+	0.320156i	0.137565	+	0.990493i	$0.456073\pi$
$332$	6.10832	+	10.5799i	0.335238	+	0.580649i
$333$	7.23435	−	15.4913i	0.396440	−	0.848919i
$334$	0.688466	+	0.397486i	0.0376712	+	0.0217495i
$335$	2.96213	−	2.48552i	0.161838	−	0.135799i
$336$	−2.02138	−	4.11267i	−0.110275	−	0.224364i
$337$	1.78231	−	10.1080i	0.0970888	−	0.550618i	−0.896998	−	0.442034i	$-0.854257\pi$
$337$	1.78231	−	10.1080i	0.0970888	−	0.550618i	0.994087	−	0.108584i	$-0.0346317\pi$
$338$	−4.46703	−	0.787657i	−0.242974	−	0.0428429i
$339$	18.8215	+	14.4507i	1.02225	+	0.784854i
$340$	2.03524	−	1.70777i	0.110376	−	0.0926168i
$341$	−9.98521	+	17.2949i	−0.540729	+	0.936571i
$342$	0.518483	−	0.517899i	0.0280363	−	0.0280048i
$343$	12.1676	+	13.9624i	0.656991	+	0.753899i
$344$	3.28932	−	9.03734i	0.177348	−	0.487260i
$345$	−1.39875	−	0.441456i	−0.0753060	−	0.0237672i
$346$	−5.22867	+	6.23129i	−0.281095	+	0.334996i
$347$	7.62446	+	20.9480i	0.409302	+	1.12455i	0.957559	+	0.288239i	$0.0930696\pi$
$347$	7.62446	+	20.9480i	0.409302	+	1.12455i	−0.548256	+	0.836310i	$0.684708\pi$
$348$	−5.83696	−	9.16789i	−0.312894	−	0.491450i
$349$	−11.8031	+	2.08121i	−0.631807	+	0.111405i	−0.480375	−	0.877063i	$-0.659500\pi$
$349$	−11.8031	+	2.08121i	−0.631807	+	0.111405i	−0.151432	+	0.988468i	$0.548388\pi$
$350$	0.486246	+	7.53913i	0.0259910	+	0.402983i
$351$	−0.672172	+	15.1022i	−0.0358779	+	0.806098i
$352$	−5.37272			−0.286367
$353$	4.14606	+	23.5135i	0.220672	+	1.25150i	0.870788	+	0.491659i	$0.163610\pi$
$353$	4.14606	+	23.5135i	0.220672	+	1.25150i	−0.650115	+	0.759836i	$0.725279\pi$
$354$	9.24331	−	17.7440i	0.491276	−	0.943084i
$355$	3.86501	+	10.6190i	0.205133	+	0.563599i
$356$	−10.9727	−	9.20722i	−0.581554	−	0.487982i
$357$	3.13394	+	3.00806i	0.165866	+	0.159203i
$358$	13.4664	+	4.90138i	0.711724	+	0.259046i
$359$	13.6340	−	7.87157i	0.719573	−	0.415446i	−0.0950226	−	0.995475i	$-0.530292\pi$
$359$	13.6340	−	7.87157i	0.719573	−	0.415446i	0.814595	+	0.580030i	$0.196959\pi$
$360$	8.37586	+	0.737550i	0.441447	+	0.0388723i
$361$	−9.47016	+	16.4028i	−0.498430	+	0.863306i
$362$	−18.8252	+	15.7962i	−0.989431	+	0.830231i
$363$	30.6791	+	4.04777i	1.61023	+	0.212453i
$364$	7.65067	+	0.845959i	0.401004	+	0.0443403i
$365$	37.7338	+	6.65349i	1.97508	+	0.348260i
$366$	−22.2633	−	2.93740i	−1.16372	−	0.153541i
$367$	−4.52071	−	5.38757i	−0.235979	−	0.281229i	0.635039	−	0.772480i	$-0.280984\pi$
$367$	−4.52071	−	5.38757i	−0.235979	−	0.281229i	−0.871018	+	0.491251i	$0.836540\pi$
$368$	0.261663	+	0.151071i	0.0136401	+	0.00787514i
$369$	0.765478	−	8.69301i	0.0398492	−	0.452540i
$370$	13.8332	−	7.98658i	0.719152	−	0.415203i
$371$	−1.04701	+	3.57825i	−0.0543583	+	0.185774i
$372$	−4.74785	+	4.34814i	−0.246164	+	0.225441i
$373$	−19.5831	−	16.4322i	−1.01397	−	0.850825i	−0.0251156	−	0.999685i	$-0.507995\pi$
$373$	−19.5831	−	16.4322i	−1.01397	−	0.850825i	−0.988858	+	0.148859i	$0.952440\pi$
$374$	4.78582	−	1.74190i	0.247469	−	0.0900713i
$375$	9.23312	+	4.80977i	0.476796	+	0.248375i
$376$	13.2052	−	2.32844i	0.681008	−	0.120080i
$377$	18.2554			0.940200
$378$	0.273952	+	13.7450i	0.0140906	+	0.706966i
$379$	−21.1805			−1.08797			−0.543985	−	0.839095i	$-0.683085\pi$
$379$	−21.1805			−1.08797			−0.543985	+	0.839095i	$0.683085\pi$
$380$	0.674249	−	0.118888i	0.0345882	−	0.00609884i
$381$	6.49665	−	4.13625i	0.332833	−	0.211906i
$382$	10.9733	−	3.99394i	0.561441	−	0.204348i
$383$	−8.57383	−	7.19430i	−0.438102	−	0.367611i	0.396896	−	0.917863i	$-0.370087\pi$
$383$	−8.57383	−	7.19430i	−0.438102	−	0.367611i	−0.834999	+	0.550252i	$0.814532\pi$
$384$	−1.65174	−	0.521303i	−0.0842900	−	0.0266026i
$385$	−11.1885	+	38.2375i	−0.570218	+	1.94876i
$386$	11.3894	−	6.57568i	0.579706	−	0.334693i
$387$	−20.4129	+	20.3899i	−1.03765	+	1.03648i
$388$	3.12271	+	1.80290i	0.158532	+	0.0915283i
$389$	−6.56008	−	7.81799i	−0.332609	−	0.396388i	0.573657	−	0.819096i	$-0.305524\pi$
$389$	−6.56008	−	7.81799i	−0.332609	−	0.396388i	−0.906266	+	0.422708i	$0.861080\pi$
$390$	−8.60086	+	11.2023i	−0.435522	+	0.567252i
$391$	−0.282059	−	0.0497346i	−0.0142643	−	0.00251519i
$392$	6.99269	+	0.319919i	0.353184	+	0.0161583i
$393$	−6.44317	−	15.5676i	−0.325015	−	0.785282i
$394$	−4.38602	+	3.68031i	−0.220965	+	0.185411i
$395$	9.94933	−	17.2328i	0.500605	−	0.867074i
$396$	14.6042	+	6.82006i	0.733887	+	0.342721i
$397$	−1.02285	+	0.590540i	−0.0513351	+	0.0296384i	−0.525448	−	0.850826i	$-0.676102\pi$
$397$	−1.02285	+	0.590540i	−0.0513351	+	0.0296384i	0.474113	+	0.880464i	$0.342769\pi$
$398$	−17.3039	−	6.29809i	−0.867365	−	0.315695i
$399$	0.311822	+	1.07511i	0.0156106	+	0.0538230i
$400$	2.18740	+	1.83544i	0.109370	+	0.0917722i
$401$	3.66036	+	10.0568i	0.182790	+	0.502210i	0.996916	−	0.0784775i	$-0.0250059\pi$
$401$	3.66036	+	10.0568i	0.182790	+	0.502210i	−0.814126	+	0.580688i	$0.802784\pi$
$402$	2.38735	−	0.103560i	0.119070	−	0.00516511i
$403$	−1.87782	−	10.6496i	−0.0935406	−	0.530495i
$404$	−8.77128			−0.436388
$405$	−21.8311	−	12.6370i	−1.08480	−	0.627939i
$406$	16.5672	−	1.06852i	0.822216	−	0.0530299i
$407$	30.1544	−	5.31704i	1.49470	−	0.263556i
$408$	1.64032	−	0.0711548i	0.0812080	−	0.00352269i
$409$	5.29875	+	14.5582i	0.262006	+	0.719857i	0.999032	+	0.0439918i	$0.0140075\pi$
$409$	5.29875	+	14.5582i	0.262006	+	0.719857i	−0.737025	+	0.675865i	$0.763770\pi$
$410$	5.24058	−	6.24548i	0.258814	−	0.308442i
$411$	4.33497	+	19.5799i	0.213828	+	0.965804i
$412$	−0.834798	+	2.29359i	−0.0411275	+	0.112997i
$413$	16.9526	+	25.4287i	0.834182	+	1.25126i
$414$	−0.519487	−	0.742795i	−0.0255314	−	0.0365064i
$415$	17.1201	−	29.6529i	0.840394	−	1.45561i
$416$	2.22866	−	1.87007i	0.109269	−	0.0916875i
$417$	4.91057	−	2.03240i	0.240472	−	0.0995272i
$418$	1.29249	+	0.227902i	0.0632180	+	0.0111470i
$419$	−1.39741	+	7.92510i	−0.0682679	+	0.387166i	0.931460	+	0.363843i	$0.118536\pi$
$419$	−1.39741	+	7.92510i	−0.0682679	+	0.387166i	−0.999728	+	0.0233229i	$0.992575\pi$
$420$	−7.14980	+	10.6698i	−0.348874	+	0.520633i
$421$	−1.78713	+	1.49958i	−0.0870996	+	0.0730853i	−0.685298	−	0.728263i	$-0.740328\pi$
$421$	−1.78713	+	1.49958i	−0.0870996	+	0.0730853i	0.598198	+	0.801348i	$0.295884\pi$
$422$	−23.6179	−	13.6358i	−1.14970	−	0.663780i
$423$	−38.8503	−	10.4334i	−1.88896	−	0.507288i
$424$	0.704580	+	1.22037i	0.0342174	+	0.0592663i
$425$	−2.54353	−	0.925768i	−0.123379	−	0.0449063i
$426$	−2.10186	+	6.65970i	−0.101835	+	0.322664i
$427$	20.3122	−	27.6419i	0.982977	−	1.33768i
$428$	−4.37857	−	12.0300i	−0.211646	−	0.581494i
$429$	−22.8376	+	14.5401i	−1.10261	+	0.702004i
$430$	−26.5455	+	4.68069i	−1.28014	+	0.225723i
$431$			0.304337i			0.0146594i	0.999973	+	0.00732969i	$0.00233313\pi$
$431$			0.304337i			0.0146594i	−0.999973	+	0.00732969i	$0.997667\pi$
$432$	3.82804	+	3.51371i	0.184176	+	0.169053i
$433$			4.57215i			0.219723i	0.993947	+	0.109862i	$0.0350408\pi$
$433$			4.57215i			0.219723i	−0.993947	+	0.109862i	$0.964959\pi$
$434$	−2.32751	−	9.55487i	−0.111724	−	0.458649i
$435$	−14.0730	+	27.0155i	−0.674751	+	1.29529i
$436$	1.42640	−	0.519166i	0.0683121	−	0.0248636i
$437$	−0.0565392	−	0.0474420i	−0.00270464	−	0.00226946i
$438$	15.9921	+	17.4621i	0.764130	+	0.834373i
$439$	0.779667	−	2.14212i	0.0372115	−	0.102238i	−0.919695	−	0.392633i	$-0.871564\pi$
$439$	0.779667	−	2.14212i	0.0372115	−	0.102238i	0.956907	+	0.290395i	$0.0937866\pi$
$440$	7.52921	+	13.0410i	0.358941	+	0.621704i
$441$	−18.6015	−	9.74603i	−0.885785	−	0.464097i
$442$	−1.37891	+	2.38834i	−0.0655881	+	0.113602i
$443$	−18.6857	−	22.2687i	−0.887784	−	1.05802i	−0.997943	−	0.0641054i	$-0.979581\pi$
$443$	−18.6857	−	22.2687i	−0.887784	−	1.05802i	0.110159	−	0.993914i	$-0.464864\pi$
$444$	9.78630	+	1.29120i	0.464437	+	0.0612775i
$445$	−6.97135	+	39.5365i	−0.330474	+	1.87421i
$446$	4.24290	−	24.0627i	0.200907	−	1.13940i
$447$	−3.42335	+	25.9464i	−0.161919	+	1.22722i
$448$	1.91310	−	1.82758i	0.0903856	−	0.0863449i
$449$	3.91704	+	2.26150i	0.184856	+	0.106727i	0.589572	−	0.807716i	$-0.299296\pi$
$449$	3.91704	+	2.26150i	0.184856	+	0.106727i	−0.404716	+	0.914442i	$0.632630\pi$
$450$	−3.61591	−	7.76577i	−0.170456	−	0.366082i
$451$	13.5348	−	7.81430i	0.637327	−	0.367961i
$452$	−4.68569	+	12.8738i	−0.220396	+	0.605534i
$453$	21.8051	+	23.8096i	1.02449	+	1.11867i
$454$	10.5833	−	12.6126i	0.496697	−	0.591941i
$455$	−8.66813	−	19.7557i	−0.406368	−	0.926160i
$456$	0.375240	+	0.195472i	0.0175722	+	0.00915382i
$457$	5.36803	+	30.4436i	0.251106	+	1.42409i	0.805874	+	0.592087i	$0.201696\pi$
$457$	5.36803	+	30.4436i	0.251106	+	1.42409i	−0.554768	+	0.832005i	$0.687193\pi$
$458$	11.2405			0.525235
$459$	−4.54906	−	1.88879i	−0.212332	−	0.0881611i
$460$		−	0.846832i		−	0.0394838i
$461$	−3.90927	−	22.1706i	−0.182073	−	1.03259i	−0.929659	−	0.368421i	$-0.879898\pi$
$461$	−3.90927	−	22.1706i	−0.182073	−	1.03259i	0.747586	−	0.664165i	$-0.231213\pi$
$462$	−19.8746	+	14.5322i	−0.924652	+	0.676101i
$463$	34.0483	−	12.3926i	1.58236	−	0.575931i	0.606643	−	0.794974i	$-0.292516\pi$
$463$	34.0483	−	12.3926i	1.58236	−	0.575931i	0.975715	+	0.219043i	$0.0702936\pi$
$464$	4.03338	−	4.80679i	0.187245	−	0.223150i
$465$	17.2076	+	5.43087i	0.797983	+	0.251850i
$466$	1.94787	+	0.708968i	0.0902335	+	0.0328423i
$467$	9.71447	+	16.8260i	0.449532	+	0.778612i	0.998356	−	0.0573259i	$-0.0182574\pi$
$467$	9.71447	+	16.8260i	0.449532	+	0.778612i	−0.548823	+	0.835938i	$0.684924\pi$
$468$	−8.43179	+	2.25420i	−0.389760	+	0.104200i
$469$	−1.61784	+	3.27206i	−0.0747051	+	0.151090i
$470$	−24.1572	−	28.7895i	−1.11429	−	1.32796i
$471$	−30.0997	−	23.1098i	−1.38692	−	1.06484i
$472$	11.3757	+	2.00584i	0.523609	+	0.0923263i
$473$	−50.8862	−	8.97261i	−2.33975	−	0.412561i
$474$	11.3623	−	4.70266i	0.521887	−	0.216000i
$475$	−0.448358	−	0.534332i	−0.0205721	−	0.0245168i
$476$	−1.11160	+	2.24819i	−0.0509501	+	0.103046i
$477$	−0.366075	−	4.21160i	−0.0167614	−	0.192836i
$478$	7.08381	+	12.2695i	0.324006	+	0.561195i
$479$	−8.12673	−	2.95789i	−0.371320	−	0.135149i	0.149618	−	0.988744i	$-0.452196\pi$
$479$	−8.12673	−	2.95789i	−0.371320	−	0.135149i	−0.520938	+	0.853595i	$0.674418\pi$
$480$	1.04937	+	4.73974i	0.0478971	+	0.216339i
$481$	−10.6577	+	12.7013i	−0.485948	+	0.579131i
$482$	0.974319	−	0.354623i	0.0443790	−	0.0161526i
$483$	1.37656	−	0.148913i	0.0626357	−	0.00677578i
$484$	3.10241	+	17.5946i	0.141019	+	0.799757i
$485$		−	10.1062i		−	0.458898i
$486$	−5.94514	−	14.4102i	−0.269677	−	0.653662i
$487$	11.7431			0.532129			0.266065	−	0.963955i	$-0.414277\pi$
$487$	11.7431			0.532129			0.266065	+	0.963955i	$0.414277\pi$
$488$	−2.25137	−	12.7682i	−0.101915	−	0.577987i
$489$	−0.318329	−	7.33839i	−0.0143953	−	0.331854i
$490$	−9.02287	−	17.4214i	−0.407612	−	0.787018i
$491$	0.558540	−	0.665642i	0.0252065	−	0.0300400i	−0.753294	−	0.657684i	$-0.771536\pi$
$491$	0.558540	−	0.665642i	0.0252065	−	0.0300400i	0.778500	+	0.627644i	$0.215981\pi$
$492$	4.91921	−	1.08911i	0.221775	−	0.0491008i
$493$	−2.03437	+	5.58938i	−0.0916234	+	0.251733i
$494$	−0.615465	+	0.355339i	−0.0276911	+	0.0159875i
$495$	−3.91191	−	45.0055i	−0.175827	−	2.02285i
$496$	−3.21902	−	1.85850i	−0.144538	−	0.0834492i
$497$	−7.36867	−	7.71350i	−0.330530	−	0.345998i
$498$	19.5514	−	8.09201i	0.876120	−	0.362612i
$499$	−1.99339	+	11.3051i	−0.0892364	+	0.506085i	0.907125	+	0.420861i	$0.138272\pi$
$499$	−1.99339	+	11.3051i	−0.0892364	+	0.506085i	−0.996362	+	0.0852244i	$0.972839\pi$
$500$	−1.04374	+	5.91935i	−0.0466775	+	0.264721i
$501$	0.838531	−	1.09216i	0.0374628	−	0.0487940i
$502$	5.49131	+	6.54429i	0.245089	+	0.292086i
$503$	21.1918	−	36.7052i	0.944894	−	1.63660i	0.188930	−	0.981991i	$-0.439498\pi$
$503$	21.1918	−	36.7052i	0.944894	−	1.63660i	0.755964	−	0.654613i	$-0.227168\pi$
$504$	−7.52011	+	2.53927i	−0.334972	+	0.113108i
$505$	12.2919	+	21.2902i	0.546982	+	0.947400i
$506$	0.555210	−	1.52543i	0.0246821	−	0.0678135i
$507$	−2.36460	+	7.49219i	−0.105016	+	0.332740i
$508$	3.40624	+	2.85818i	0.151128	+	0.126811i
$509$	27.7138	−	10.0870i	1.22839	−	0.447099i	0.355346	−	0.934735i	$-0.384363\pi$
$509$	27.7138	−	10.0870i	1.22839	−	0.447099i	0.873047	+	0.487636i	$0.162141\pi$
$510$	−2.47142	−	3.88177i	−0.109436	−	0.171888i
$511$	−35.1419	+	8.56035i	−1.55459	+	0.378688i
$512$		−	1.00000i		−	0.0441942i
$513$	−0.771851	−	1.00766i	−0.0340781	−	0.0444892i
$514$		−	22.9520i		−	1.01237i
$515$	6.73700	−	1.18791i	0.296868	−	0.0523458i
$516$	−14.7734	−	7.69584i	−0.650363	−	0.338790i
$517$	−24.6400	−	67.6977i	−1.08366	−	2.97734i
$518$	−8.92866	+	12.1506i	−0.392303	+	0.533866i
$519$	9.51556	+	10.3903i	0.417687	+	0.456083i
$520$	−7.66233	−	2.78886i	−0.336015	−	0.122300i
$521$	−0.00768736	−	0.0133149i	−0.000336789	−	0.000583337i	0.865857	−	0.500292i	$-0.166774\pi$
$521$	−0.00768736	−	0.0133149i	−0.000336789	−	0.000583337i	−0.866194	+	0.499708i	$0.833441\pi$
$522$	−17.0652	+	7.94595i	−0.746925	+	0.347785i
$523$	−34.6851	−	20.0255i	−1.51668	−	0.875653i	−0.999808	−	0.0195870i	$-0.993765\pi$
$523$	−34.6851	−	20.0255i	−1.51668	−	0.875653i	−0.516867	−	0.856066i	$-0.672902\pi$
$524$	7.45159	−	6.25263i	0.325524	−	0.273147i
$525$	13.0561	+	0.873113i	0.569816	+	0.0381058i
$526$	−4.00524	+	22.7148i	−0.174637	+	0.990414i
$527$	3.46993	+	0.611843i	0.151153	+	0.0266523i
$528$	−1.21725	+	9.22586i	−0.0529741	+	0.401504i
$529$	17.5491	−	14.7254i	0.763004	−	0.640236i
$530$	1.97477	−	3.42039i	0.0857783	−	0.148572i
$531$	−28.3753	−	19.8925i	−1.23138	−	0.863259i
$532$	−0.537751	+	0.358503i	−0.0233145	+	0.0155431i
$533$	−2.89446	+	7.95246i	−0.125373	+	0.344459i
$534$	−18.2964	+	16.7560i	−0.791761	+	0.725105i
$535$	−23.0640	+	27.4866i	−0.997142	+	1.18835i
$536$	0.471863	+	1.29643i	0.0203814	+	0.0559974i
$537$	11.4675	−	22.0137i	0.494859	−	0.949961i
$538$	−21.3711	+	3.76829i	−0.921371	+	0.162463i
$539$	−4.83119	−	37.2974i	−0.208094	−	1.60651i
$540$	3.16415	−	14.2157i	0.136163	−	0.611745i
$541$	−4.22483			−0.181640			−0.0908199	−	0.995867i	$-0.528949\pi$
$541$	−4.22483			−0.181640			−0.0908199	+	0.995867i	$0.528949\pi$
$542$	1.72738	+	9.79644i	0.0741972	+	0.420793i
$543$	22.8597	+	35.9049i	0.981004	+	1.54083i
$544$	0.324211	+	0.890763i	0.0139004	+	0.0381912i
$545$	−3.25907	−	2.73469i	−0.139603	−	0.117141i
$546$	3.18601	−	12.9458i	0.136348	−	0.554031i
$547$	10.3237	+	3.75751i	0.441408	+	0.160660i	0.553157	−	0.833077i	$-0.313423\pi$
$547$	10.3237	+	3.75751i	0.441408	+	0.160660i	−0.111749	+	0.993737i	$0.535645\pi$
$548$	−10.0270	+	5.78910i	−0.428333	+	0.247298i
$549$	−10.0880	+	37.5644i	−0.430547	+	1.60321i
$550$	7.67074	−	13.2861i	0.327082	−	0.566522i
$551$	−1.17419	+	0.985264i	−0.0500222	+	0.0419736i
$552$	0.318698	−	0.415093i	0.0135647	−	0.0176675i
$553$	−2.06442	+	18.6702i	−0.0877881	+	0.793937i
$554$	−9.64783	−	1.70117i	−0.409897	−	0.0722759i
$555$	−10.5802	−	25.5633i	−0.449106	−	1.08510i
$556$	1.97230	+	2.35049i	0.0836441	+	0.0996832i
$557$	7.91094	+	4.56738i	0.335197	+	0.193526i	0.658146	−	0.752890i	$-0.271341\pi$
$557$	7.91094	+	4.56738i	0.335197	+	0.193526i	−0.322949	+	0.946416i	$0.604674\pi$
$558$	6.39081	+	9.13798i	0.270545	+	0.386842i
$559$	24.2312	−	13.9899i	1.02487	−	0.591709i
$560$	−7.11698	−	2.08247i	−0.300747	−	0.0880002i
$561$	−1.90684	−	8.61271i	−0.0805070	−	0.363629i
$562$	15.8837	+	13.3280i	0.670014	+	0.562208i
$563$	−39.6355	+	14.4262i	−1.67044	+	0.607990i	−0.991951	−	0.126622i	$-0.959587\pi$
$563$	−39.6355	+	14.4262i	−1.67044	+	0.607990i	−0.678488	+	0.734612i	$0.737364\pi$
$564$	−1.00652	−	23.2031i	−0.0423821	−	0.977029i
$565$	37.8145	−	6.66772i	1.59087	−	0.280513i
$566$	−0.0955818			−0.00401760
$567$	23.6646	+	2.64367i	0.993818	+	0.111024i
$568$	−4.03193			−0.169176
$569$	14.0605	−	2.47925i	0.589448	−	0.103936i	0.129035	−	0.991640i	$-0.458812\pi$
$569$	14.0605	−	2.47925i	0.589448	−	0.103936i	0.460414	+	0.887704i	$0.347701\pi$
$570$	−0.0513921	−	1.18474i	−0.00215258	−	0.0496231i
$571$	4.50855	−	1.64098i	0.188677	−	0.0686727i	−0.245954	−	0.969282i	$-0.579101\pi$
$571$	4.50855	−	1.64098i	0.188677	−	0.0686727i	0.434631	+	0.900609i	$0.356879\pi$
$572$	−11.9739	−	10.0473i	−0.500656	−	0.420100i
$573$	−4.37215	−	19.7478i	−0.182649	−	0.824977i
$574$	−2.16132	+	7.38647i	−0.0902117	+	0.308305i
$575$	−0.747165	+	0.431376i	−0.0311589	+	0.0179896i
$576$	−1.26939	+	2.71821i	−0.0528911	+	0.113259i
$577$	19.3505	+	11.1720i	0.805572	+	0.465097i	0.845416	−	0.534109i	$-0.179353\pi$
$577$	19.3505	+	11.1720i	0.805572	+	0.465097i	−0.0398438	+	0.999206i	$0.512686\pi$
$578$	10.3498	+	12.3344i	0.430495	+	0.513044i
$579$	−8.71115	−	21.0473i	−0.362023	−	0.874698i
$580$	−17.3196	−	3.05392i	−0.719158	−	0.126807i
$581$	−3.55232	+	32.1264i	−0.147375	+	1.33283i
$582$	3.80337	−	4.95376i	0.157655	−	0.205340i
$583$	5.79973	−	4.86655i	0.240200	−	0.201552i
$584$	−6.83540	+	11.8393i	−0.282851	+	0.489912i
$585$	17.2877	+	17.3072i	0.714757	+	0.715563i
$586$	−1.77068	+	1.02230i	−0.0731461	+	0.0422309i
$587$	−21.9122	−	7.97538i	−0.904413	−	0.329179i	−0.152393	−	0.988320i	$-0.548698\pi$
$587$	−21.9122	−	7.97538i	−0.904413	−	0.329179i	−0.752020	+	0.659141i	$0.770920\pi$
$588$	2.13363	−	11.9351i	0.0879895	−	0.492197i
$589$	0.695554	+	0.583639i	0.0286598	+	0.0240484i
$590$	−11.0730	−	30.4227i	−0.455866	−	1.25248i
$591$	5.32601	+	8.36536i	0.219083	+	0.344105i
$592$	0.989637	+	5.61251i	0.0406738	+	0.230673i
$593$	−16.7880			−0.689401			−0.344701	−	0.938713i	$-0.612020\pi$
$593$	−16.7880			−0.689401			−0.344701	+	0.938713i	$0.612020\pi$
$594$	15.0199	−	23.5326i	0.616275	−	0.965556i
$595$	7.01471	−	0.452423i	0.287575	−	0.0185475i
$596$	−14.8804	+	2.62382i	−0.609526	+	0.107476i
$597$	−14.7353	+	28.2868i	−0.603075	+	1.15770i
$598$	0.300644	+	0.826014i	0.0122943	+	0.0337782i
$599$	22.5053	−	26.8208i	0.919542	−	1.09587i	−0.0755727	−	0.997140i	$-0.524079\pi$
$599$	22.5053	−	26.8208i	0.919542	−	1.09587i	0.995115	−	0.0987270i	$-0.0314770\pi$
$600$	3.64735	−	3.34029i	0.148902	−	0.136367i
$601$	−4.00672	+	11.0084i	−0.163437	+	0.449041i	−0.994195	−	0.107594i	$-0.965685\pi$
$601$	−4.00672	+	11.0084i	−0.163437	+	0.449041i	0.830757	+	0.556635i	$0.187908\pi$
$602$	21.1715	−	14.1145i	0.862887	−	0.575262i
$603$	0.363054	−	4.12295i	0.0147847	−	0.167900i
$604$	−9.32004	+	16.1428i	−0.379227	+	0.656840i
$605$	38.3591	−	32.1871i	1.55952	−	1.30859i
$606$	−1.98724	+	15.0618i	−0.0807261	+	0.611843i
$607$	−34.5452	−	6.09125i	−1.40215	−	0.247236i	−0.579121	−	0.815242i	$-0.696604\pi$
$607$	−34.5452	−	6.09125i	−1.40215	−	0.247236i	−0.823025	+	0.568005i	$0.807715\pi$
$608$	−0.0424183	+	0.240566i	−0.00172029	+	0.00975625i
$609$	1.91866	−	28.6908i	0.0777481	−	1.16261i
$610$	−27.8366	+	23.3577i	−1.12707	+	0.945724i
$611$	33.7843	+	19.5054i	1.36677	+	0.789102i
$612$	0.249450	−	2.83283i	0.0100834	−	0.114510i
$613$	−14.2980	−	24.7648i	−0.577490	−	1.00024i	−0.995766	−	0.0919224i	$-0.970699\pi$
$613$	−14.2980	−	24.7648i	−0.577490	−	1.00024i	0.418276	−	0.908320i	$-0.362634\pi$
$614$	24.3214	+	8.85228i	0.981533	+	0.357249i
$615$	−9.53722	−	10.4139i	−0.384578	−	0.419931i
$616$	−11.4547	−	8.41734i	−0.461524	−	0.339144i
$617$	−12.1982	−	33.5143i	−0.491082	−	1.34924i	−0.899691	−	0.436527i	$-0.856208\pi$
$617$	−12.1982	−	33.5143i	−0.491082	−	1.34924i	0.408609	−	0.912710i	$-0.366014\pi$
$618$	3.74935	+	1.95313i	0.150821	+	0.0785664i
$619$	34.9977	−	6.17103i	1.40668	−	0.248035i	0.581792	−	0.813338i	$-0.302352\pi$
$619$	34.9977	−	6.17103i	1.40668	−	0.248035i	0.824883	+	0.565303i	$0.191241\pi$
$620$			10.4179i			0.418391i
$621$	−1.39320	+	0.723758i	−0.0559072	+	0.0290434i
$622$			24.8128i			0.994902i
$623$	−8.96930	−	36.8208i	−0.359348	−	1.47519i
$624$	−2.70629	−	4.25067i	−0.108338	−	0.170163i
$625$	29.2467	−	10.6449i	1.16987	−	0.425797i
$626$	13.8262	+	11.6016i	0.552606	+	0.463692i
$627$	0.684176	−	2.16780i	0.0273234	−	0.0865735i
$628$	7.49344	−	20.5880i	0.299021	−	0.821552i
$629$	−2.70117	−	4.67857i	−0.107703	−	0.186547i
$630$	16.7020	+	14.6948i	0.665423	+	0.585454i
$631$	16.8880	−	29.2508i	0.672300	−	1.16446i	−0.304951	−	0.952368i	$-0.598640\pi$
$631$	16.8880	−	29.2508i	0.672300	−	1.16446i	0.977250	−	0.212089i	$-0.0680267\pi$
$632$	4.56358	+	5.43867i	0.181530	+	0.216339i
$633$	−28.7659	+	37.4666i	−1.14334	+	1.48916i
$634$	1.79937	−	10.2047i	0.0714621	−	0.405281i
$635$	2.16410	−	12.2732i	0.0858797	−	0.487048i
$636$	2.25521	−	0.933394i	0.0894249	−	0.0370115i
$637$	14.9860	+	13.7898i	0.593768	+	0.546371i
$638$	−29.1962	−	16.8564i	−1.15589	−	0.667352i
$639$	10.9596	+	5.11808i	0.433556	+	0.202468i
$640$	−2.42726	+	1.40138i	−0.0959458	+	0.0553943i
$641$	2.74024	−	7.52876i	0.108233	−	0.297368i	−0.873739	−	0.486396i	$-0.838311\pi$
$641$	2.74024	−	7.52876i	0.108233	−	0.297368i	0.981972	+	0.189028i	$0.0605336\pi$
$642$	−21.6496	+	4.79320i	−0.854442	+	0.189173i
$643$	−10.5957	+	12.6274i	−0.417853	+	0.497978i	−0.933377	−	0.358897i	$-0.883153\pi$
$643$	−10.5957	+	12.6274i	−0.417853	+	0.497978i	0.515524	+	0.856875i	$0.327597\pi$
$644$	0.321190	+	0.732030i	0.0126567	+	0.0288460i
$645$	2.02333	+	46.6436i	0.0796687	+	1.83659i
$646$	−0.0402096	−	0.228040i	−0.00158203	−	0.00897212i
$647$	4.03618			0.158679			0.0793394	−	0.996848i	$-0.474719\pi$
$647$	4.03618			0.158679			0.0793394	+	0.996848i	$0.474719\pi$
$648$	6.90092	−	5.77731i	0.271094	−	0.226954i
$649$		−	62.0612i		−	2.43612i
$650$	1.44256	+	8.18115i	0.0565818	+	0.320891i
$651$	−16.9347	+	1.83195i	−0.663722	+	0.0717998i
$652$	3.98505	−	1.45044i	0.156067	−	0.0568037i
$653$	−17.1181	+	20.4005i	−0.669883	+	0.798335i	−0.988768	−	0.149458i	$-0.952247\pi$
$653$	−17.1181	+	20.4005i	−0.669883	+	0.798335i	0.318885	+	0.947793i	$0.396691\pi$
$654$	−0.568329	−	2.56699i	−0.0222234	−	0.100377i
$655$	−25.6192	−	9.32464i	−1.00103	−	0.364344i
$656$	1.45444	+	2.51917i	0.0567864	+	0.0983569i
$657$	33.6086	−	23.5048i	1.31120	−	0.917010i
$658$	31.8017	+	15.7241i	1.23976	+	0.612990i
$659$	9.49979	+	11.3214i	0.370059	+	0.441019i	0.918650	−	0.395071i	$-0.129280\pi$
$659$	9.49979	+	11.3214i	0.370059	+	0.441019i	−0.548591	+	0.836091i	$0.684836\pi$
$660$	24.0994	−	9.97433i	0.938067	−	0.388250i
$661$	−4.89542	−	0.863195i	−0.190410	−	0.0335744i	0.0776299	−	0.996982i	$-0.475265\pi$
$661$	−4.89542	−	0.863195i	−0.190410	−	0.0335744i	−0.268040	+	0.963408i	$0.586376\pi$
$662$	16.7716	+	2.95729i	0.651848	+	0.114938i
$663$	3.78878	+	2.90893i	0.147144	+	0.112973i
$664$	7.85270	+	9.35849i	0.304744	+	0.363180i
$665$	1.62377	+	0.802862i	0.0629672	+	0.0311336i
$666$	4.43441	−	16.5122i	0.171830	−	0.639835i
$667$	0.947946	+	1.64189i	0.0367046	+	0.0635742i
$668$	0.747029	+	0.271896i	0.0289034	+	0.0105200i
$669$	−40.3584	−	12.7375i	−1.56034	−	0.492458i
$670$	2.48552	−	2.96213i	0.0960240	−	0.114437i
$671$	−65.4570	+	23.8244i	−2.52694	+	0.919731i
$672$	−2.70482	−	3.69918i	−0.104341	−	0.142699i
$673$	−1.87117	−	10.6119i	−0.0721282	−	0.409059i	−0.999399	−	0.0346677i	$-0.988963\pi$
$673$	−1.87117	−	10.6119i	−0.0721282	−	0.409059i	0.927271	−	0.374391i	$-0.122148\pi$
$674$		−	10.2639i		−	0.395352i
$675$	−14.1544	+	4.44970i	−0.544802	+	0.171269i
$676$	−4.53594			−0.174459
$677$	−4.21944	−	23.9296i	−0.162166	−	0.919690i	−0.951938	−	0.306289i	$-0.900912\pi$
$677$	−4.21944	−	23.9296i	−0.162166	−	0.919690i	0.789772	−	0.613400i	$-0.210199\pi$
$678$	21.0449	+	10.9628i	0.808226	+	0.421025i
$679$	3.83311	+	8.73611i	0.147101	+	0.335261i
$680$	1.70777	−	2.03524i	0.0654900	−	0.0780479i
$681$	−19.2603	−	21.0308i	−0.738055	−	0.805902i
$682$	−6.83028	+	18.7661i	−0.261545	+	0.718589i
$683$	0.466410	−	0.269282i	0.0178467	−	0.0103038i	−0.491050	−	0.871131i	$-0.663387\pi$
$683$	0.466410	−	0.269282i	0.0178467	−	0.0103038i	0.508897	+	0.860828i	$0.330053\pi$
$684$	0.420674	−	0.600064i	0.0160849	−	0.0229440i
$685$	28.1033	+	16.2254i	1.07377	+	0.619942i
$686$	14.4073	+	11.6374i	0.550074	+	0.444318i
$687$	2.54668	−	19.3019i	0.0971618	−	0.736413i
$688$	1.67003	−	9.47122i	0.0636694	−	0.361087i
$689$	−0.711901	+	4.03739i	−0.0271213	+	0.153812i
$690$	−1.45415	−	0.191860i	−0.0553587	−	0.00730399i
$691$	−8.01618	−	9.55331i	−0.304950	−	0.363425i	0.591706	−	0.806154i	$-0.298455\pi$
$691$	−8.01618	−	9.55331i	−0.304950	−	0.363425i	−0.896655	+	0.442729i	$0.854010\pi$
$692$	−4.06719	+	7.04457i	−0.154611	+	0.267795i
$693$	20.4515	+	37.4206i	0.776888	+	1.42149i
$694$	11.1462	+	19.3058i	0.423104	+	0.732838i
$695$	2.94132	−	8.08121i	0.111571	−	0.306538i
$696$	−7.34027	−	8.01503i	−0.278232	−	0.303809i
$697$	−2.11231	−	1.77243i	−0.0800093	−	0.0671358i
$698$	−11.2624	+	4.09918i	−0.426289	+	0.155156i
$699$	1.65873	−	3.18420i	0.0627390	−	0.120438i
$700$	1.78802	+	7.34016i	0.0675806	+	0.277432i
$701$		−	11.3417i		−	0.428369i	−0.976793	−	0.214185i	$-0.931291\pi$
$701$		−	11.3417i		−	0.428369i	0.976793	−	0.214185i	$-0.0687094\pi$
$702$	1.96052	+	14.9895i	0.0739950	+	0.565743i
$703$		−	1.39216i		−	0.0525063i
$704$	−5.29109	+	0.932962i	−0.199416	+	0.0351623i
$705$	−54.9095	+	34.9595i	−2.06801	+	1.31665i
$706$	8.16614	+	22.4363i	0.307337	+	0.844401i
$707$	−18.7005	−	13.7418i	−0.703307	−	0.516814i
$708$	6.02167	−	19.0795i	0.226308	−	0.717053i
$709$	−11.0328	−	4.01562i	−0.414347	−	0.150810i	0.126431	−	0.991975i	$-0.459648\pi$
$709$	−11.0328	−	4.01562i	−0.414347	−	0.150810i	−0.540778	+	0.841166i	$0.681870\pi$
$710$	5.65026	+	9.78654i	0.212051	+	0.367282i
$711$	−5.50100	−	20.5764i	−0.206304	−	0.771675i
$712$	−12.4049	−	7.16195i	−0.464892	−	0.268405i
$713$	0.860318	−	0.721893i	0.0322192	−	0.0270351i
$714$	3.60867	+	2.41816i	0.135051	+	0.0904973i
$715$	−7.60745	+	43.1440i	−0.284502	+	1.61349i
$716$	14.1130	+	2.48850i	0.527427	+	0.0929995i
$717$	22.6738	−	9.38429i	0.846767	−	0.350463i
$718$	12.0599	−	10.1195i	0.450073	−	0.377656i
$719$	−9.49117	+	16.4392i	−0.353961	+	0.613078i	−0.986940	−	0.161091i	$-0.948499\pi$
$719$	−9.49117	+	16.4392i	−0.353961	+	0.613078i	0.632979	+	0.774169i	$0.281832\pi$
$720$	8.37669	−	0.728107i	0.312181	−	0.0271350i
$721$	−5.37313	+	3.58211i	−0.200106	+	0.133405i
$722$	−6.47797	+	17.7981i	−0.241085	+	0.662376i
$723$	−0.388204	−	1.75341i	−0.0144375	−	0.0652102i
$724$	−15.7962	+	18.8252i	−0.587062	+	0.699633i
$725$	6.12811	+	16.8369i	0.227592	+	0.625305i
$726$	30.9159	−	1.34109i	1.14740	−	0.0497724i
$727$	16.5106	−	2.91126i	0.612344	−	0.107973i	0.141129	−	0.989991i	$-0.454927\pi$
$727$	16.5106	−	2.91126i	0.612344	−	0.107973i	0.471215	+	0.882018i	$0.343816\pi$
$728$	7.68134	−	0.495418i	0.284689	−	0.0183614i
$729$	−26.0918	+	6.94400i	−0.966362	+	0.257185i
$730$	38.3159			1.41814
$731$	1.58307	+	8.97806i	0.0585521	+	0.332066i
$732$	−22.4351	+	0.973205i	−0.829227	+	0.0359707i
$733$	6.00752	+	16.5055i	0.221893	+	0.609645i	0.999825	−	0.0187029i	$-0.00595366\pi$
$733$	6.00752	+	16.5055i	0.221893	+	0.609645i	−0.777932	+	0.628348i	$0.783731\pi$
$734$	−5.38757	−	4.52071i	−0.198859	−	0.166862i
$735$	−31.9597	+	11.5468i	−1.17885	+	0.425909i
$736$	0.283921	+	0.103339i	0.0104655	+	0.00380912i
$737$	6.41932	−	3.70620i	0.236459	−	0.136519i
$738$	−0.755677	−	8.69387i	−0.0278169	−	0.320026i
$739$	−14.8317	+	25.6893i	−0.545593	+	0.944995i	0.452976	+	0.891523i	$0.350362\pi$
$739$	−14.8317	+	25.6893i	−0.545593	+	0.944995i	−0.998569	+	0.0534726i	$0.982971\pi$
$740$	12.2362	−	10.2674i	0.449810	−	0.377435i
$741$	0.470736	+	1.13736i	0.0172929	+	0.0417821i
$742$	−0.409751	+	3.70570i	−0.0150424	+	0.136041i
$743$	−33.5884	−	5.92255i	−1.23224	−	0.217277i	−0.480653	−	0.876911i	$-0.659600\pi$
$743$	−33.5884	−	5.92255i	−1.23224	−	0.217277i	−0.751587	+	0.659634i	$0.770711\pi$
$744$	−3.92067	+	5.10654i	−0.143739	+	0.187215i
$745$	27.2218	+	32.4417i	0.997330	+	1.18857i
$746$	−22.1390	−	12.7820i	−0.810566	−	0.467981i
$747$	−9.46574	−	35.4064i	−0.346333	−	1.29545i
$748$	4.41063	−	2.54648i	0.161269	−	0.0931086i
$749$	9.51203	−	32.5081i	0.347562	−	1.18782i
$750$	9.92806	+	3.13338i	0.362521	+	0.114415i
$751$	9.27586	+	7.78337i	0.338481	+	0.284019i	0.796145	−	0.605106i	$-0.206869\pi$
$751$	9.27586	+	7.78337i	0.338481	+	0.284019i	−0.457664	+	0.889125i	$0.651314\pi$
$752$	12.6003	−	4.58613i	0.459485	−	0.167239i
$753$	12.4818	−	7.94682i	0.454861	−	0.289598i
$754$	17.9780	−	3.17001i	0.654722	−	0.115445i
$755$	52.2436			1.90134
$756$	2.65658	+	13.4886i	0.0966190	+	0.490576i
$757$	−5.74566			−0.208830			−0.104415	−	0.994534i	$-0.533297\pi$
$757$	−5.74566			−0.208830			−0.104415	+	0.994534i	$0.533297\pi$
$758$	−20.8587	+	3.67796i	−0.757623	+	0.133589i
$759$	−2.49363	−	1.29899i	−0.0905130	−	0.0471505i
$760$	0.643361	−	0.234164i	0.0233372	−	0.00849403i
$761$	−3.27963	−	2.75194i	−0.118887	−	0.0997577i	0.581406	−	0.813613i	$-0.302503\pi$
$761$	−3.27963	−	2.75194i	−0.118887	−	0.0997577i	−0.700293	+	0.713856i	$0.746947\pi$
$762$	5.67970	−	5.20154i	0.205754	−	0.188432i
$763$	3.85448	+	1.12784i	0.139541	+	0.0408305i
$764$	10.1130	−	5.83875i	0.365876	−	0.211239i
$765$	−7.22558	+	3.36439i	−0.261242	+	0.121640i
$766$	−9.69285	−	5.59617i	−0.350217	−	0.202198i
$767$	21.6015	+	25.7436i	0.779984	+	0.929549i
$768$	−1.71717	−	0.226562i	−0.0619630	−	0.00817535i
$769$	−38.9273	−	6.86393i	−1.40375	−	0.247520i	−0.580069	−	0.814567i	$-0.696974\pi$
$769$	−38.9273	−	6.86393i	−1.40375	−	0.247520i	−0.823685	+	0.567048i	$0.808085\pi$
$770$	−4.37864	+	39.5995i	−0.157795	+	1.42707i
$771$	−39.4124	−	5.20004i	−1.41940	−	0.187275i
$772$	10.0745	−	8.45353i	0.362590	−	0.304249i
$773$	−20.9764	+	36.3322i	−0.754469	+	1.30678i	0.191169	+	0.981557i	$0.438772\pi$
$773$	−20.9764	+	36.3322i	−0.754469	+	1.30678i	−0.945638	+	0.325222i	$0.894561\pi$
$774$	−16.5621	+	23.6248i	−0.595314	+	0.849177i
$775$	9.19174	−	5.30685i	0.330177	−	0.190628i
$776$	3.38834	+	1.23326i	0.121634	+	0.0442713i
$777$	18.8417	+	18.0849i	0.675942	+	0.648792i
$778$	−7.81799	−	6.56008i	−0.280289	−	0.235190i
$779$	−0.243031	−	0.667722i	−0.00870748	−	0.0239236i
$780$	−6.52493	+	12.5257i	−0.233630	+	0.448491i
$781$	3.76164	+	21.3333i	0.134602	+	0.763366i
$782$	−0.286410			−0.0102420
$783$	9.77820	+	31.1042i	0.349444	+	1.11157i
$784$	6.94200	−	0.899208i	0.247929	−	0.0321146i
$785$	−60.4736	+	10.6631i	−2.15840	+	0.380584i
$786$	−9.04857	−	14.2122i	−0.322752	−	0.506934i
$787$	0.121615	+	0.334133i	0.00433509	+	0.0119106i	0.941841	−	0.336058i	$-0.109094\pi$
$787$	0.121615	+	0.334133i	0.00433509	+	0.0119106i	−0.937506	+	0.347969i	$0.886872\pi$
$788$	−3.68031	+	4.38602i	−0.131106	+	0.156246i
$789$	38.0978	+	12.0240i	1.35632	+	0.428065i
$790$	6.80575	−	18.6986i	0.242138	−	0.665267i
$791$	−30.1592	+	20.1063i	−1.07234	+	0.714896i
$792$	15.5666	+	4.18046i	0.553134	+	0.148546i
$793$	18.8598	−	32.6661i	0.669729	−	1.16001i
$794$	−0.904760	+	0.759184i	−0.0321087	+	0.0269424i
$795$	−5.42599	−	4.16594i	−0.192440	−	0.147751i
$796$	−18.1346	−	3.19763i	−0.642765	−	0.113337i
$797$	−0.0298632	+	0.169363i	−0.00105781	+	0.00599913i	−0.985332	−	0.170648i	$-0.945414\pi$
$797$	−0.0298632	+	0.169363i	−0.00105781	+	0.00599913i	0.984274	+	0.176647i	$0.0565251\pi$
$798$	0.493777	+	1.00463i	0.0174795	+	0.0355636i
$799$	−9.73700	+	8.17031i	−0.344470	+	0.289045i
$800$	2.47289	+	1.42772i	0.0874298	+	0.0504776i
$801$	24.6277	+	35.2142i	0.870177	+	1.24423i
$802$	5.35109	+	9.26836i	0.188953	+	0.327277i
$803$	69.0198	+	25.1211i	2.43565	+	0.886506i
$804$	2.33310	−	0.516547i	0.0822822	−	0.0182172i
$805$	1.32672	−	1.80546i	0.0467606	−	0.0636342i
$806$	−3.69857	−	10.1617i	−0.130277	−	0.357932i
$807$	1.62893	+	37.5515i	0.0573410	+	1.32187i
$808$	−8.63803	+	1.52312i	−0.303885	+	0.0535831i
$809$		−	21.2262i		−	0.746273i	−0.927776	−	0.373137i	$-0.878282\pi$
$809$		−	21.2262i		−	0.746273i	0.927776	−	0.373137i	$-0.121718\pi$
$810$	−23.6938	−	8.65411i	−0.832516	−	0.304074i
$811$			5.19130i			0.182291i	0.995838	+	0.0911456i	$0.0290529\pi$
$811$			5.19130i			0.182291i	−0.995838	+	0.0911456i	$0.970947\pi$
$812$	16.1300	−	3.92915i	0.566051	−	0.137886i
$813$	17.2135	−	0.746697i	0.603704	−	0.0261878i
$814$	28.7730	−	10.4725i	1.00849	−	0.367062i
$815$	−9.10516	−	7.64014i	−0.318940	−	0.267622i
$816$	1.60305	−	0.354913i	0.0561178	−	0.0124244i
$817$	−0.803507	+	2.20762i	−0.0281112	+	0.0772348i
$818$	7.74626	+	13.4169i	0.270842	+	0.469111i
$819$	−21.5084	−	8.40395i	−0.751563	−	0.293658i
$820$	4.07645	−	7.06061i	0.142356	−	0.246567i
$821$	21.0867	+	25.1302i	0.735933	+	0.877050i	0.996074	−	0.0885201i	$-0.0282138\pi$
$821$	21.0867	+	25.1302i	0.735933	+	0.877050i	−0.260142	+	0.965570i	$0.583769\pi$
$822$	7.66912	+	18.5297i	0.267491	+	0.646296i
$823$	7.27112	−	41.2365i	0.253455	−	1.43742i	−0.546552	−	0.837425i	$-0.684060\pi$
$823$	7.27112	−	41.2365i	0.253455	−	1.43742i	0.800007	−	0.599990i	$-0.204829\pi$
$824$	−0.423838	+	2.40370i	−0.0147651	+	0.0837370i
$825$	−21.0766	−	16.1821i	−0.733794	−	0.563388i
$826$	21.1107	+	22.0986i	0.734534	+	0.768908i
$827$	46.2108	+	26.6798i	1.60691	+	0.927749i	0.990057	+	0.140669i	$0.0449253\pi$
$827$	46.2108	+	26.6798i	1.60691	+	0.927749i	0.616851	+	0.787080i	$0.288408\pi$
$828$	−0.640580	−	0.641303i	−0.0222617	−	0.0222868i
$829$	−21.7292	+	12.5454i	−0.754688	+	0.435719i	−0.827385	−	0.561635i	$-0.810173\pi$
$829$	−21.7292	+	12.5454i	−0.754688	+	0.435719i	0.0726976	+	0.997354i	$0.476839\pi$
$830$	11.7109	−	32.1753i	0.406490	−	1.11682i
$831$	−5.10703	+	16.1815i	−0.177161	+	0.561331i
$832$	1.87007	−	2.22866i	0.0648329	−	0.0772648i
$833$	−5.89215	+	3.05166i	−0.204151	+	0.105734i
$834$	4.48305	−	2.85424i	0.155235	−	0.0988342i
$835$	−0.386908	−	2.19426i	−0.0133895	−	0.0759356i
$836$	1.31243			0.0453915
$837$	17.1394	−	8.90378i	0.592423	−	0.307760i
$838$			8.04736i			0.277991i
$839$	0.495527	+	2.81027i	0.0171075	+	0.0970214i	0.992166	−	0.124927i	$-0.0398696\pi$
$839$	0.495527	+	2.81027i	0.0171075	+	0.0970214i	−0.975058	+	0.221948i	$0.928758\pi$
$840$	−5.18838	+	11.7493i	−0.179016	+	0.405388i
$841$	9.74781	−	3.54791i	0.336131	−	0.122342i
$842$	−1.49958	+	1.78713i	−0.0516791	+	0.0615887i
$843$	26.4851	−	24.2554i	0.912195	−	0.835400i
$844$	−25.6269	−	9.32744i	−0.882115	−	0.321064i
$845$	6.35656	+	11.0099i	0.218672	+	0.378752i
$846$	−40.0718	−	3.52859i	−1.37770	−	0.121315i
$847$	−20.9508	+	42.3726i	−0.719879	+	1.45594i
$848$	0.905790	+	1.07948i	0.0311050	+	0.0370695i
$849$	−0.0216552	+	0.164130i	−0.000743204	+	0.00563293i
$850$	−2.66564	−	0.470024i	−0.0914307	−	0.0161217i
$851$	−1.69578	−	0.299012i	−0.0581305	−	0.0102500i
$852$	−0.913482	+	6.92351i	−0.0312954	+	0.237196i
$853$	−1.89941	−	2.26363i	−0.0650345	−	0.0775051i	0.732546	−	0.680717i	$-0.238332\pi$
$853$	−1.89941	−	2.26363i	−0.0650345	−	0.0775051i	−0.797581	+	0.603212i	$0.793887\pi$
$854$	15.2037	−	30.7491i	0.520259	−	1.05221i
$855$	−2.04603	−	0.180167i	−0.0699729	−	0.00616158i
$856$	−6.40105	−	11.0869i	−0.218783	−	0.378944i
$857$	13.7976	+	5.02193i	0.471319	+	0.171546i	0.566750	−	0.823890i	$-0.308201\pi$
$857$	13.7976	+	5.02193i	0.471319	+	0.171546i	−0.0954310	+	0.995436i	$0.530423\pi$
$858$	−19.9658	+	18.2849i	−0.681622	+	0.624238i
$859$	−23.1900	+	27.6367i	−0.791231	+	0.942953i	−0.999382	−	0.0351440i	$-0.988811\pi$
$859$	−23.1900	+	27.6367i	−0.791231	+	0.942953i	0.208151	+	0.978097i	$0.433255\pi$
$860$	−25.3295	+	9.21917i	−0.863727	+	0.314371i
$861$	12.1941	+	5.38484i	0.415575	+	0.183515i
$862$	0.0528475	+	0.299713i	0.00179999	+	0.0102083i
$863$			23.9065i			0.813787i	0.913476	+	0.406893i	$0.133388\pi$
$863$			23.9065i			0.813787i	−0.913476	+	0.406893i	$0.866612\pi$
$864$	4.38003	+	2.79559i	0.149012	+	0.0951081i
$865$	22.7987			0.775178
$866$	0.793945	+	4.50269i	0.0269794	+	0.153008i
$867$	23.5251	−	14.9778i	0.798956	−	0.508674i
$868$	−3.95133	−	9.00555i	−0.134117	−	0.305668i
$869$	24.5188	−	29.2204i	0.831745	−	0.991235i
$870$	−9.16806	+	29.0488i	−0.310826	+	0.984847i
$871$	−1.37279	+	3.77172i	−0.0465154	+	0.127800i
$872$	1.31458	−	0.758970i	0.0445171	−	0.0257020i
$873$	−7.64474	−	7.65336i	−0.258735	−	0.259027i
$874$	−0.0639184	−	0.0369033i	−0.00216207	−	0.00124827i
$875$	−11.4990	+	10.9850i	−0.388738	+	0.371360i
$876$	18.7814	+	14.4199i	0.634564	+	0.487202i
$877$	1.87546	−	10.6362i	0.0633297	−	0.359160i	−0.936631	−	0.350317i	$-0.886074\pi$
$877$	1.87546	−	10.6362i	0.0633297	−	0.359160i	0.999961	−	0.00884345i	$-0.00281499\pi$
$878$	0.395847	−	2.24496i	0.0133592	−	0.0757638i
$879$	1.35430	+	3.27217i	0.0456793	+	0.110368i
$880$	9.67936	+	11.5354i	0.326291	+	0.388859i
$881$	5.10105	−	8.83528i	0.171859	−	0.297668i	−0.767211	−	0.641395i	$-0.778356\pi$
$881$	5.10105	−	8.83528i	0.171859	−	0.297668i	0.939070	+	0.343727i	$0.111689\pi$
$882$	−20.0113	−	6.36786i	−0.673814	−	0.214417i
$883$	−16.4850	−	28.5529i	−0.554765	−	0.960882i	−0.997922	−	0.0644374i	$-0.979475\pi$
$883$	−16.4850	−	28.5529i	−0.554765	−	0.960882i	0.443156	−	0.896444i	$-0.353859\pi$
$884$	−0.943230	+	2.59150i	−0.0317243	+	0.0871617i
$885$	−54.7496	+	12.1215i	−1.84039	+	0.407460i
$886$	−22.2687	−	18.6857i	−0.748133	−	0.627758i
$887$	29.3193	−	10.6714i	0.984447	−	0.358310i	0.200880	−	0.979616i	$-0.435620\pi$
$887$	29.3193	−	10.6714i	0.984447	−	0.358310i	0.783568	+	0.621306i	$0.213398\pi$
$888$	9.86184	−	0.427793i	0.330942	−	0.0143558i
$889$	2.78432	+	11.4302i	0.0933831	+	0.383356i
$890$			40.1464i			1.34571i
$891$	−37.0066	−	31.1234i	−1.23977	−	1.04267i
$892$		−	24.4339i		−	0.818106i
$893$	−3.22574	+	0.568785i	−0.107945	+	0.0190337i
$894$	1.13421	+	26.1467i	0.0379335	+	0.874476i
$895$	−13.7374	−	37.7432i	−0.459190	−	1.26161i
$896$	1.56668	−	2.13202i	0.0523392	−	0.0712258i
$897$	1.48652	−	0.329114i	0.0496335	−	0.0109888i
$898$	4.25023	+	1.54696i	0.141832	+	0.0516227i
$899$	−11.6618	−	20.1988i	−0.388942	−	0.673667i
$900$	−4.90949	−	7.01990i	−0.163650	−	0.233997i
$901$	−1.15682	−	0.667893i	−0.0385394	−	0.0222507i
$902$	11.9722	−	10.0459i	0.398631	−	0.334491i
$903$	−19.4402	−	39.5529i	−0.646931	−	1.31624i
$904$	−2.37899	+	13.4919i	−0.0791239	+	0.448734i
$905$	67.8301	+	11.9603i	2.25475	+	0.397573i
$906$	25.6083	+	19.6614i	0.850779	+	0.653207i
$907$	28.8586	−	24.2152i	0.958234	−	0.804054i	−0.0224311	−	0.999748i	$-0.507141\pi$
$907$	28.8586	−	24.2152i	0.958234	−	0.804054i	0.980665	+	0.195695i	$0.0626962\pi$
$908$	8.23232	−	14.2588i	0.273199	−	0.473195i
$909$	25.4134	+	6.82485i	0.842909	+	0.226366i
$910$	−11.9670	−	17.9503i	−0.396701	−	0.595048i
$911$	15.4249	−	42.3795i	0.511049	−	1.40409i	−0.369097	−	0.929391i	$-0.620333\pi$
$911$	15.4249	−	42.3795i	0.511049	−	1.40409i	0.880146	−	0.474704i	$-0.157445\pi$
$912$	0.403483	+	0.127343i	0.0133606	+	0.00421674i
$913$	42.1903	−	50.2805i	1.39630	−	1.66404i
$914$	10.5730	+	29.0490i	0.349722	+	0.960854i
$915$	33.8024	+	53.0921i	1.11747	+	1.75517i
$916$	11.0698	−	1.95190i	0.365755	−	0.0644925i
$917$	25.6828	−	1.65645i	0.848121	−	0.0547007i
$918$	−4.80793	−	1.07016i	−0.158685	−	0.0353205i
$919$	−41.7355			−1.37673			−0.688364	−	0.725366i	$-0.741671\pi$
$919$	−41.7355			−1.37673			−0.688364	+	0.725366i	$0.741671\pi$
$920$	−0.147051	−	0.833967i	−0.00484812	−	0.0274951i
$921$	20.7112	−	39.7584i	0.682456	−	1.31008i
$922$	−7.69976	−	21.1549i	−0.253578	−	0.696700i
$923$	−8.98580	−	7.53998i	−0.295771	−	0.248181i
$924$	−17.0492	+	17.7627i	−0.560877	+	0.584349i
$925$	−15.2920	−	5.56584i	−0.502799	−	0.183004i
$926$	31.3791	−	18.1167i	1.03118	−	0.595352i
$927$	4.20331	−	5.99575i	0.138055	−	0.196926i
$928$	3.13741	−	5.43416i	0.102991	−	0.178385i
$929$	−28.6790	+	24.0645i	−0.940928	+	0.789532i	−0.977747	−	0.209790i	$-0.932722\pi$
$929$	−28.6790	+	24.0645i	−0.940928	+	0.789532i	0.0368186	+	0.999322i	$0.488278\pi$
$930$	17.8892	+	2.36029i	0.586611	+	0.0773970i
$931$	−1.70816	−	0.0781490i	−0.0559825	−	0.00256123i
$932$	2.04139	+	0.359952i	0.0668680	+	0.0117906i
$933$	42.6077	+	5.62163i	1.39491	+	0.184044i
$934$	12.4887	+	14.8834i	0.408642	+	0.487001i
$935$	−12.3619	−	7.13717i	−0.404278	−	0.233410i
$936$	−7.91226	+	3.68412i	−0.258620	+	0.120419i
$937$	4.68060	−	2.70235i	0.152909	−	0.0882818i	−0.421594	−	0.906785i	$-0.638529\pi$
$937$	4.68060	−	2.70235i	0.152909	−	0.0882818i	0.574502	+	0.818503i	$0.305196\pi$
$938$	−1.02508	+	3.50328i	−0.0334700	+	0.114386i
$939$	23.0543	−	21.1135i	0.752350	−	0.689011i
$940$	−28.7895	−	24.1572i	−0.939009	−	0.787922i
$941$	8.48097	−	3.08682i	0.276472	−	0.100627i	−0.200063	−	0.979783i	$-0.564115\pi$
$941$	8.48097	−	3.08682i	0.276472	−	0.100627i	0.476535	+	0.879156i	$0.341893\pi$
$942$	−33.6554	−	17.5320i	−1.09655	−	0.571222i
$943$	−0.865545	+	0.152619i	−0.0281860	+	0.00496996i
$944$	11.5512			0.375959
$945$	29.0175	−	25.3509i	0.943938	−	0.824663i
$946$	−51.6712			−1.67998
$947$	−22.7694	+	4.01486i	−0.739907	+	0.130465i	−0.530883	−	0.847445i	$-0.678140\pi$
$947$	−22.7694	+	4.01486i	−0.739907	+	0.130465i	−0.209024	+	0.977911i	$0.567029\pi$
$948$	10.3730	−	6.60425i	0.336901	−	0.214496i
$949$	−37.3740	+	13.6030i	−1.21321	+	0.441572i
$950$	−0.534332	−	0.448358i	−0.0173360	−	0.0145466i
$951$	−17.1156	−	5.40182i	−0.555010	−	0.175166i
$952$	−0.704318	+	2.40706i	−0.0228271	+	0.0780133i
$953$	−37.1436	+	21.4449i	−1.20320	+	0.694667i	−0.961265	−	0.275625i	$-0.911115\pi$
$953$	−37.1436	+	21.4449i	−1.20320	+	0.694667i	−0.241934	+	0.970293i	$0.577782\pi$
$954$	−1.09185	−	4.08405i	−0.0353500	−	0.132226i
$955$	−28.3443	−	16.3646i	−0.917200	−	0.529546i
$956$	9.10677	+	10.8530i	0.294534	+	0.351012i
$957$	−35.5601	+	46.3157i	−1.14949	+	1.49718i
$958$	−8.51690	−	1.50176i	−0.275168	−	0.0485196i
$959$	−30.4475	−	3.36667i	−0.983200	−	0.108715i
$960$	1.85648	+	4.48551i	0.0599176	+	0.144769i
$961$	13.1636	−	11.0456i	0.424632	−	0.356309i
$962$	−8.29020	+	14.3590i	−0.267287	+	0.462954i
$963$	3.32576	+	38.2620i	0.107171	+	1.23298i
$964$	0.897937	−	0.518424i	0.0289206	−	0.0166973i
$965$	−34.6371	−	12.6069i	−1.11501	−	0.405830i
$966$	1.32979	−	0.385688i	0.0427853	−	0.0124093i
$967$	−11.9906	−	10.0613i	−0.385593	−	0.323551i	0.429301	−	0.903162i	$-0.358760\pi$
$967$	−11.9906	−	10.0613i	−0.385593	−	0.323551i	−0.814893	+	0.579611i	$0.803205\pi$
$968$	6.11056	+	16.7886i	0.196401	+	0.539607i
$969$	−0.400694	+	0.0173815i	−0.0128721	+	0.000558375i
$970$	−1.75492	−	9.95263i	−0.0563470	−	0.319560i
$971$	29.3324			0.941322			0.470661	−	0.882314i	$-0.344015\pi$
$971$	29.3324			0.941322			0.470661	+	0.882314i	$0.344015\pi$
$972$	−8.35714	−	13.1590i	−0.268055	−	0.422074i
$973$	0.522502	+	8.10127i	0.0167507	+	0.259715i
$974$	11.5647	−	2.03916i	0.370556	−	0.0653390i
$975$	14.3753	−	0.623578i	0.460377	−	0.0199705i
$976$	−4.43433	−	12.1832i	−0.141940	−	0.389976i
$977$	−25.2745	+	30.1209i	−0.808602	+	0.963654i	−0.999840	−	0.0178895i	$-0.994305\pi$
$977$	−25.2745	+	30.1209i	−0.808602	+	0.963654i	0.191238	+	0.981544i	$0.438750\pi$
$978$	−1.58779	−	7.17163i	−0.0507720	−	0.229323i
$979$	−26.3213	+	72.3171i	−0.841231	+	2.31126i
$980$	−11.9110	−	15.5899i	−0.380482	−	0.498001i
$981$	−4.53672	+	0.394335i	−0.144846	+	0.0125901i
$982$	0.434467	−	0.752519i	0.0138644	−	0.0240138i
$983$	18.3345	−	15.3844i	0.584779	−	0.490688i	−0.301734	−	0.953392i	$-0.597565\pi$
$983$	18.3345	−	15.3844i	0.584779	−	0.490688i	0.886512	+	0.462705i	$0.153121\pi$
$984$	4.65536	−	1.92677i	0.148407	−	0.0614233i
$985$	15.8035	+	2.78659i	0.503542	+	0.0887880i
$986$	−1.03288	+	5.85773i	−0.0328935	+	0.186548i
$987$	34.2060	−	51.0465i	1.08879	−	1.62483i
$988$	−0.544411	+	0.456815i	−0.0173200	+	0.0145332i
$989$	2.51650	+	1.45290i	0.0800201	+	0.0461996i
$990$	−11.6676	−	43.6425i	−0.370821	−	1.38705i
$991$	25.4105	+	44.0123i	0.807192	+	1.39810i	0.914801	+	0.403904i	$0.132347\pi$
$991$	25.4105	+	44.0123i	0.807192	+	1.39810i	−0.107610	+	0.994193i	$0.534320\pi$
$992$	−3.49284	−	1.27129i	−0.110898	−	0.0403635i
$993$	8.87799	−	28.1297i	0.281734	−	0.892670i
$994$	−8.59616	−	6.31676i	−0.272654	−	0.200355i
$995$	17.6520	+	48.4985i	0.559607	+	1.53751i
$996$	17.8492	−	11.3641i	0.565575	−	0.360087i
$997$	4.87802	−	0.860127i	0.154489	−	0.0272405i	−0.0958689	−	0.995394i	$-0.530563\pi$
$997$	4.87802	−	0.860127i	0.154489	−	0.0272405i	0.250357	+	0.968153i	$0.419452\pi$
$998$			11.4795i			0.363377i
$999$	−27.3496	−	11.3557i	−0.865302	−	0.359277i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.z.a.41.18	✓	144
7.6	odd	2	inner	378.2.z.a.41.19	yes	144
27.2	odd	18	inner	378.2.z.a.83.19	yes	144
189.83	even	18	inner	378.2.z.a.83.18	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.z.a.41.18	✓	144	1.1	even	1	trivial
378.2.z.a.41.19	yes	144	7.6	odd	2	inner
378.2.z.a.83.18	yes	144	189.83	even	18	inner
378.2.z.a.83.19	yes	144	27.2	odd	18	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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.z (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.984808 - 0.173648i) q^{2} +(-0.0750633 - 1.73042i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-2.14704 - 1.80158i) q^{5} +(-0.374408 - 1.69110i) q^{6} +(2.53928 + 0.743006i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.98873 + 0.259783i) q^{9} +O(q^{10})\)	\(q+(0.984808 - 0.173648i) q^{2} +(-0.0750633 - 1.73042i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-2.14704 - 1.80158i) q^{5} +(-0.374408 - 1.69110i) q^{6} +(2.53928 + 0.743006i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.98873 + 0.259783i) q^{9} +(-2.42726 - 1.40138i) q^{10} +(-3.45351 - 4.11574i) q^{11} +(-0.662376 - 1.60039i) q^{12} +(2.86511 + 0.505196i) q^{13} +(2.62972 + 0.290777i) q^{14} +(-2.95633 + 3.85051i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-0.473965 + 0.820932i) q^{17} +(-2.89821 + 0.774824i) q^{18} +(-0.211551 + 0.122139i) q^{19} +(-2.63373 - 0.958599i) q^{20} +(1.09511 - 4.44980i) q^{21} +(-4.11574 - 3.45351i) q^{22} +(0.103339 + 0.283921i) q^{23} +(-0.930218 - 1.46106i) q^{24} +(0.495843 + 2.81206i) q^{25} +2.90931 q^{26} +(0.673878 + 5.15227i) q^{27} +(2.64027 - 0.170287i) q^{28} +(6.17949 - 1.08961i) q^{29} +(-2.24278 + 4.30538i) q^{30} +(-1.27129 - 3.49284i) q^{31} +(0.642788 - 0.766044i) q^{32} +(-6.86274 + 6.28498i) q^{33} +(-0.324211 + 0.890763i) q^{34} +(-4.11334 - 6.16997i) q^{35} +(-2.71964 + 1.26632i) q^{36} +(-2.84955 + 4.93556i) q^{37} +(-0.187127 + 0.157019i) q^{38} +(0.659138 - 4.99577i) q^{39} +(-2.76018 - 0.486694i) q^{40} +(-0.505122 + 2.86469i) q^{41} +(0.305771 - 4.57236i) q^{42} +(7.36730 - 6.18190i) q^{43} +(-4.65291 - 2.68636i) q^{44} +(6.88493 + 4.82667i) q^{45} +(0.151071 + 0.261663i) q^{46} +(12.6003 + 4.58613i) q^{47} +(-1.16980 - 1.27733i) q^{48} +(5.89588 + 3.77340i) q^{49} +(0.976619 + 2.68324i) q^{50} +(1.45614 + 0.758539i) q^{51} +(2.86511 - 0.505196i) q^{52} +1.40916i q^{53} +(1.55832 + 4.95698i) q^{54} +15.0584i q^{55} +(2.57058 - 0.626178i) q^{56} +(0.227231 + 0.356904i) q^{57} +(5.89640 - 2.14612i) q^{58} +(8.84872 + 7.42496i) q^{59} +(-1.46109 + 4.62942i) q^{60} +(4.43433 - 12.1832i) q^{61} +(-1.85850 - 3.21902i) q^{62} +(-7.78224 - 1.56098i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-5.24134 - 6.24639i) q^{65} +(-5.66710 + 7.38120i) q^{66} +(-0.239571 + 1.35868i) q^{67} +(-0.164606 + 0.933529i) q^{68} +(0.483547 - 0.200132i) q^{69} +(-5.12226 - 5.36196i) q^{70} +(-3.49176 - 2.01597i) q^{71} +(-2.45843 + 1.71934i) q^{72} +(-11.8393 + 6.83540i) q^{73} +(-1.94920 + 5.35539i) q^{74} +(4.82884 - 1.06910i) q^{75} +(-0.157019 + 0.187127i) q^{76} +(-5.71142 - 13.0170i) q^{77} +(-0.218382 - 5.03433i) q^{78} +(1.23285 + 6.99182i) q^{79} -2.80276 q^{80} +(8.86503 - 1.55284i) q^{81} +2.90888i q^{82} +(2.12140 + 12.0310i) q^{83} +(-0.492857 - 4.55600i) q^{84} +(2.49659 - 0.908686i) q^{85} +(6.18190 - 7.36730i) q^{86} +(-2.34934 - 10.6114i) q^{87} +(-5.04870 - 1.83758i) q^{88} +(-7.16195 - 12.4049i) q^{89} +(7.61848 + 3.55778i) q^{90} +(6.89995 + 3.41163i) q^{91} +(0.194214 + 0.231455i) q^{92} +(-5.94867 + 2.46206i) q^{93} +(13.2052 + 2.32844i) q^{94} +(0.674249 + 0.118888i) q^{95} +(-1.37383 - 1.05479i) q^{96} +(2.31776 + 2.76220i) q^{97} +(6.46156 + 2.69226i) q^{98} +(11.3908 + 11.4037i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9}+O(q^{10}) \) 144 * q - 12 * q^9	\( 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) \) 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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