LMFDB - Embedded newform 378.2.z.a.83.19

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			83.19
Character	$\chi$	$=$	378.83
Dual form			378.2.z.a.41.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984808 + 0.173648i) q^{2} +(0.0750633 - 1.73042i) q^{3} +(0.939693 + 0.342020i) q^{4} +(2.14704 - 1.80158i) q^{5} +(0.374408 - 1.69110i) q^{6} +(2.42280 - 1.06304i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.98873 - 0.259783i) q^{9} +O(q^{10})$	\(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} +(2.42280 - 1.06304i) 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} +(2.57058 - 0.626178i) 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} +(-1.65765 - 4.27226i) 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} +(3.28668 - 6.64724i) 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} +(-0.890596 - 4.49520i) 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} +(4.73988 - 5.15107i) 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} +(2.62972 + 0.290777i) 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} +(-7.51725 + 2.54775i) 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} +(4.39103 - 5.97553i) 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} +(-3.99196 + 13.6428i) 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} +(-0.0964824 - 4.58156i) 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} +(-6.40453 + 4.26972i) 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} +(5.56235 - 4.24974i) 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 $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

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

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	$-0.506621\pi$
$5$	2.14704	−	1.80158i	0.960184	−	0.805690i	0.980983	+	0.194094i	$0.0621766\pi$
$6$	0.374408	−	1.69110i	0.152851	−	0.690389i
$7$	2.42280	−	1.06304i	0.915731	−	0.401792i
$7$	2.42280	−	1.06304i	0.915731	−	0.401792i
$8$	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	−0.0713711	+	0.997450i	$0.522737\pi$
$11$	−3.45351	+	4.11574i	−1.04127	+	1.24094i	−0.969903	+	0.243492i	$0.921707\pi$
$12$	0.662376	−	1.60039i	0.191212	−	0.461994i
$13$	−2.86511	+	0.505196i	−0.794638	+	0.140116i	−0.556207	−	0.831044i	$-0.687744\pi$
$13$	−2.86511	+	0.505196i	−0.794638	+	0.140116i	−0.238430	+	0.971160i	$0.576633\pi$
$14$	2.57058	−	0.626178i	0.687017	−	0.167353i
$15$	−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	$-0.129995\pi$
$17$	0.473965	+	0.820932i	0.114953	+	0.199105i	−0.802808	+	0.596238i	$0.796661\pi$
$18$	−2.89821	−	0.774824i	−0.683116	−	0.182628i
$19$	0.211551	+	0.122139i	0.0485330	+	0.0280206i	0.524070	−	0.851675i	$-0.324413\pi$
$19$	0.211551	+	0.122139i	0.0485330	+	0.0280206i	−0.475537	+	0.879696i	$0.657746\pi$
$20$	2.63373	−	0.958599i	0.588920	−	0.214349i
$21$	−1.65765	−	4.27226i	−0.361729	−	0.932283i
$22$	−4.11574	+	3.45351i	−0.877478	+	0.736292i
$23$	0.103339	−	0.283921i	0.0215476	−	0.0592017i	−0.928452	−	0.371451i	$-0.878860\pi$
$23$	0.103339	−	0.283921i	0.0215476	−	0.0592017i	0.950000	+	0.312250i	$0.101083\pi$
$24$	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	0.714885	−	0.699242i	$-0.246479\pi$
$29$	6.17949	+	1.08961i	1.14750	+	0.202336i	0.432618	+	0.901577i	$0.357590\pi$
$30$	−2.24278	−	4.30538i	−0.409474	−	0.786051i
$31$	1.27129	−	3.49284i	0.228331	−	0.627333i	−0.771631	−	0.636070i	$-0.780559\pi$
$31$	1.27129	−	3.49284i	0.228331	−	0.627333i	0.999962	+	0.00873703i	$0.00278112\pi$
$32$	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
$35$	3.28668	−	6.64724i	0.555550	−	1.12359i
$36$	−2.71964	−	1.26632i	−0.453273	−	0.211054i
$37$	−2.84955	−	4.93556i	−0.468462	−	0.811401i	0.530888	−	0.847442i	$-0.321859\pi$
$37$	−2.84955	−	4.93556i	−0.468462	−	0.811401i	−0.999350	+	0.0360414i	$0.988525\pi$
$38$	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	0.998509	+	0.0545856i	$0.0173838\pi$
$41$	0.505122	+	2.86469i	0.0788868	+	0.447389i	−0.919622	+	0.392804i	$0.871505\pi$
$42$	−0.890596	−	4.49520i	−0.137422	−	0.693625i
$43$	7.36730	+	6.18190i	1.12350	+	0.942731i	0.998776	−	0.0494600i	$-0.0157500\pi$
$43$	7.36730	+	6.18190i	1.12350	+	0.942731i	0.124727	+	0.992191i	$0.460194\pi$
$44$	−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	−0.847539	+	0.530733i	$0.821917\pi$
$47$	−12.6003	+	4.58613i	−1.83794	+	0.668956i	−0.990401	+	0.138222i	$0.955861\pi$
$48$	1.16980	−	1.27733i	0.168846	−	0.184367i
$49$	4.73988	−	5.15107i	0.677126	−	0.735867i
$50$	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	$-0.969145\pi$
$53$		−	1.40916i		−	0.193563i	0.995306	−	0.0967815i	$-0.0308548\pi$
$54$	−1.55832	+	4.95698i	−0.212061	+	0.674559i
$55$			15.0584i			2.03048i
$56$	2.62972	+	0.290777i	0.351412	+	0.0388567i
$57$	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	$-0.993093\pi$
$59$	−8.84872	+	7.42496i	−1.15200	+	0.966647i	−0.152240	+	0.988344i	$0.548649\pi$
$60$	−1.46109	−	4.62942i	−0.188625	−	0.597656i
$61$	−4.43433	−	12.1832i	−0.567758	−	1.55990i	−0.807996	−	0.589188i	$-0.799448\pi$
$61$	−4.43433	−	12.1832i	−0.567758	−	1.55990i	0.240238	−	0.970714i	$-0.422775\pi$
$62$	1.85850	−	3.21902i	0.236030	−	0.408816i
$63$	−7.51725	+	2.54775i	−0.947084	+	0.320986i
$64$	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	0.966670	−	0.256025i	$-0.0824129\pi$
$67$	−0.239571	−	1.35868i	−0.0292683	−	0.165989i	−0.995939	+	0.0900361i	$0.971302\pi$
$68$	0.164606	+	0.933529i	0.0199615	+	0.113207i
$69$	−0.483547	−	0.200132i	−0.0582122	−	0.0240931i
$70$	4.39103	−	5.97553i	0.524828	−	0.714213i
$71$	−3.49176	+	2.01597i	−0.414395	+	0.239251i	−0.692676	−	0.721248i	$-0.743569\pi$
$71$	−3.49176	+	2.01597i	−0.414395	+	0.239251i	0.278281	+	0.960500i	$0.410235\pi$
$72$	−2.45843	−	1.71934i	−0.289728	−	0.202627i
$73$	11.8393	+	6.83540i	1.38568	+	0.800023i	0.992825	−	0.119577i	$-0.0381540\pi$
$73$	11.8393	+	6.83540i	1.38568	+	0.800023i	0.392855	+	0.919600i	$0.371487\pi$
$74$	−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
$77$	−3.99196	+	13.6428i	−0.454926	+	1.55474i
$78$	−0.218382	+	5.03433i	−0.0247269	+	0.570026i
$79$	1.23285	−	6.99182i	0.138706	−	0.786641i	−0.833501	−	0.552518i	$-0.813667\pi$
$79$	1.23285	−	6.99182i	0.138706	−	0.786641i	0.972207	−	0.234123i	$-0.0752218\pi$
$80$	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	0.614234	+	0.789124i	$0.289465\pi$
$83$	−2.12140	+	12.0310i	−0.232854	+	1.32058i	−0.847087	+	0.531454i	$0.821646\pi$
$84$	−0.0964824	−	4.58156i	−0.0105271	−	0.499889i
$85$	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	−0.184112	−	0.982905i	$-0.558941\pi$
$89$	7.16195	−	12.4049i	0.759165	−	1.31491i	0.943277	−	0.332007i	$-0.107726\pi$
$90$	−7.61848	+	3.55778i	−0.803058	+	0.375023i
$91$	−6.40453	+	4.26972i	−0.671377	+	0.447588i
$92$	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	$-0.836377\pi$
$97$	−2.31776	+	2.76220i	−0.235333	+	0.280459i	0.635434	+	0.772156i	$0.280821\pi$
$98$	5.56235	−	4.24974i	0.561882	−	0.429289i
$99$	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	$-0.467369\pi$
$101$	8.24231	−	2.99996i	0.820141	−	0.298507i	0.717806	+	0.696243i	$0.245147\pi$
$102$	1.56573	−	0.494159i	0.155031	−	0.0489291i
$103$	1.56891	+	1.86975i	0.154589	+	0.184232i	0.837780	−	0.546007i	$-0.183853\pi$
$103$	1.56891	+	1.86975i	0.154589	+	0.184232i	−0.683191	+	0.730239i	$0.739409\pi$
$104$	−2.73385	−	0.995041i	−0.268076	−	0.0975718i
$105$	−11.2558	−	6.18631i	−1.09846	−	0.603722i
$106$	0.244698	−	1.38775i	0.0237672	−	0.134790i
$107$			12.8021i			1.23762i	0.785539	+	0.618812i	$0.212386\pi$
$107$			12.8021i			1.23762i	−0.785539	+	0.618812i	$0.787614\pi$
$108$	−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
$112$	2.53928	+	0.743006i	0.239939	+	0.0702075i
$113$	−8.80621	−	10.4948i	−0.828419	−	0.987271i	−0.999998	−	0.00210074i	$-0.999331\pi$
$113$	−8.80621	−	10.4948i	−0.828419	−	0.987271i	0.171579	−	0.985170i	$-0.445113\pi$
$114$	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
$119$	2.02101	+	1.48511i	0.185265	+	0.136139i
$120$	−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
$126$	−7.84545	+	1.20368i	−0.698929	+	0.107233i
$127$	2.22327	−	3.85081i	0.197283	−	0.341704i	−0.750363	−	0.661025i	$-0.770122\pi$
$127$	2.22327	−	3.85081i	0.197283	−	0.341704i	0.947647	+	0.319321i	$0.103455\pi$
$128$	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	$-0.528594\pi$
$131$	−9.14073	−	3.32695i	−0.798629	−	0.290677i	−0.708918	+	0.705291i	$0.750817\pi$
$132$	4.29927	+	8.25315i	0.374204	+	0.718344i
$133$	0.642382	+	0.0710302i	0.0557016	+	0.00615910i
$134$		−	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	−0.336160	−	0.941805i	$-0.609128\pi$
$137$	−11.4023	−	2.01053i	−0.974164	−	0.171771i	−0.638004	+	0.770033i	$0.720239\pi$
$138$	−0.441448	−	0.281059i	−0.0375786	−	0.0239253i
$139$	−1.04944	+	2.88331i	−0.0890122	+	0.244559i	−0.976209	−	0.216833i	$-0.930427\pi$
$139$	−1.04944	+	2.88331i	−0.0890122	+	0.244559i	0.887197	+	0.461392i	$0.152650\pi$
$140$	5.36196	−	5.12226i	0.453168	−	0.432910i
$141$	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
$147$	−8.55774	−	8.58866i	−0.705830	−	0.708381i
$148$	−0.989637	−	5.61251i	−0.0813476	−	0.461345i
$149$	−14.8804	+	2.62382i	−1.21905	+	0.214952i	−0.745918	−	0.666038i	$-0.767989\pi$
$149$	−14.8804	+	2.62382i	−1.21905	+	0.214952i	−0.473135	+	0.880990i	$0.656878\pi$
$150$	−4.56983	−	1.89138i	−0.373125	−	0.154430i
$151$	−14.2791	−	11.9816i	−1.16202	−	0.975049i	−0.162087	−	0.986776i	$-0.551823\pi$
$151$	−14.2791	−	11.9816i	−1.16202	−	0.975049i	−0.999931	+	0.0117270i	$0.996267\pi$
$152$	0.122139	+	0.211551i	0.00990676	+	0.0171590i
$153$	−1.20329	−	2.57667i	−0.0972803	−	0.208312i
$154$	−6.30037	+	12.7424i	−0.507698	+	1.02681i
$155$	−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	−0.933833	−	0.357710i	$-0.883558\pi$
$157$	−14.0831	−	16.7835i	−1.12395	−	1.33947i	−0.190117	−	0.981761i	$-0.560887\pi$
$158$	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	$-0.732014\pi$
$167$	−0.608984	+	0.510998i	−0.0471246	+	0.0395422i	0.618921	+	0.785453i	$0.287570\pi$
$168$	0.700563	−	4.52871i	0.0540496	−	0.349398i
$169$	−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	$-0.177709\pi$
$173$	6.23129	+	5.22867i	0.473756	+	0.397529i	−0.374406	+	0.927265i	$0.622153\pi$
$174$	4.15629	−	10.0422i	0.315088	−	0.761296i
$175$	−1.78802	−	7.34016i	−0.135161	−	0.554864i
$176$	−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	0.0415635	−	0.999136i	$-0.486766\pi$
$179$	12.4107	−	7.16534i	0.927622	−	0.535563i	0.886059	+	0.463573i	$0.153433\pi$
$180$	−8.12054	+	2.18080i	−0.605269	+	0.162547i
$181$	21.2822	+	12.2873i	1.58189	+	0.913306i	0.994583	+	0.103944i	$0.0331462\pi$
$181$	21.2822	+	12.2873i	1.58189	+	0.913306i	0.587310	+	0.809362i	$0.300187\pi$
$182$	−7.04866	+	3.09271i	−0.522481	+	0.229247i
$183$	−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
$189$	3.84441	+	13.1993i	0.279640	+	0.960105i
$190$	0.684650			0.0496698
$191$	11.5001	+	2.02778i	0.832117	+	0.146725i	0.573449	−	0.819241i	$-0.305605\pi$
$191$	11.5001	+	2.02778i	0.832117	+	0.146725i	0.258669	+	0.965966i	$0.416716\pi$
$192$	1.53612	−	0.800205i	0.110860	−	0.0577498i
$193$	12.3582	+	4.49803i	0.889565	+	0.323775i	0.746063	−	0.665875i	$-0.231942\pi$
$193$	12.3582	+	4.49803i	0.889565	+	0.323775i	0.143502	+	0.989650i	$0.454164\pi$
$194$	−2.76220	+	2.31776i	−0.198314	+	0.166406i
$195$	10.4155	+	9.53861i	0.745867	+	0.683074i
$196$	6.21580	−	3.21928i	0.443986	−	0.229949i
$197$	−4.95847	−	2.86277i	−0.353276	−	0.203964i	0.312851	−	0.949802i	$-0.398716\pi$
$197$	−4.95847	−	2.86277i	−0.353276	−	0.203964i	−0.666127	+	0.745838i	$0.732049\pi$
$198$	13.1980	−	9.25243i	0.937941	−	0.657542i
$199$	15.9473	−	9.20720i	1.13048	−	0.652681i	0.186422	−	0.982470i	$-0.440311\pi$
$199$	15.9473	−	9.20720i	1.13048	−	0.652681i	0.944055	+	0.329789i	$0.106978\pi$
$200$	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
$203$	16.1300	−	3.92915i	1.13210	−	0.275773i
$204$	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
$210$	−10.0106	−	8.04688i	−0.690797	−	0.555288i
$211$	−20.8913	+	17.5298i	−1.43821	+	1.20680i	−0.497563	+	0.867428i	$0.665772\pi$
$211$	−20.8913	+	17.5298i	−1.43821	+	1.20680i	−0.940651	+	0.339376i	$0.889784\pi$
$212$	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	−0.820195	−	0.572084i	$-0.806135\pi$
$223$	−8.35687	−	22.9603i	−0.559618	−	1.53754i	0.260577	−	0.965453i	$-0.416087\pi$
$224$	2.37168	+	1.17266i	0.158465	+	0.0783516i
$225$	−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	$-0.461779\pi$
$227$	−12.6126	−	10.5833i	−0.837130	−	0.702436i	−0.956916	+	0.290364i	$0.906224\pi$
$228$	0.335596	−	0.257662i	0.0222254	−	0.0170641i
$229$	−11.0698	+	1.95190i	−0.731510	+	0.128985i	−0.526983	−	0.849876i	$-0.676677\pi$
$229$	−11.0698	+	1.95190i	−0.731510	+	0.128985i	−0.204527	+	0.978861i	$0.565566\pi$
$230$	−0.147051	−	0.833967i	−0.00969625	−	0.0549902i
$231$	23.3082	+	7.93186i	1.53357	+	0.521878i
$232$	4.80679	+	4.03338i	0.315581	+	0.264804i
$233$	1.79517	−	1.03644i	0.117605	−	0.0678996i	−0.440043	−	0.897977i	$-0.645037\pi$
$233$	1.79517	−	1.03644i	0.117605	−	0.0678996i	0.557649	+	0.830077i	$0.311704\pi$
$234$	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
$238$	1.73242	+	1.81349i	0.112296	+	0.117551i
$239$	4.84561	−	13.3132i	0.313437	−	0.861160i	−0.678520	−	0.734582i	$-0.737378\pi$
$239$	4.84561	−	13.3132i	0.313437	−	0.861160i	0.991957	−	0.126578i	$-0.0403994\pi$
$240$	0.210384	−	4.84996i	0.0135802	−	0.313063i
$241$	−1.02110	−	0.180047i	−0.0657746	−	0.0115978i	0.140664	−	0.990057i	$-0.455076\pi$
$241$	−1.02110	−	0.180047i	−0.0657746	−	0.0115978i	−0.206439	+	0.978460i	$0.566187\pi$
$242$		−	17.8661i		−	1.14847i
$243$	3.35251	−	15.2237i	0.215064	−	0.976600i
$244$		−	12.9651i		−	0.830007i
$245$	0.896655	−	19.5988i	0.0572852	−	1.25212i
$246$	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	$-0.920229\pi$
$251$	−4.27148	+	7.39842i	−0.269614	+	0.466984i	0.699148	+	0.714976i	$0.253563\pi$
$252$	−7.93528	−	0.176952i	−0.499876	−	0.0111469i
$253$	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	−0.811950	−	0.583727i	$-0.801594\pi$
$257$	−3.98557	−	22.6033i	−0.248613	−	1.40995i	0.563337	−	0.826227i	$-0.309517\pi$
$258$	13.2126	−	10.1443i	0.822580	−	0.631556i
$259$	−12.1506	−	8.92866i	−0.755000	−	0.554800i
$260$	−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	−0.903880	−	0.427786i	$-0.859294\pi$
$263$	−7.88878	−	21.6742i	−0.486443	−	1.33649i	0.417437	−	0.908706i	$-0.362928\pi$
$264$	2.80081	+	8.87433i	0.172378	+	0.546177i
$265$	−2.53871	−	3.02552i	−0.155952	−	0.185856i
$266$	0.620289	+	0.181500i	0.0380324	+	0.0111285i
$267$	−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	$-0.269895\pi$
$269$	21.7007			1.32312			0.661559	+	0.749893i	$0.269895\pi$
$270$	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
$273$	6.90767	+	11.4030i	0.418071	+	0.690144i
$274$	−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	−0.603435	−	0.797412i	$-0.706202\pi$
$277$	−9.20585	+	3.35066i	−0.553126	+	0.201321i	0.0503089	+	0.998734i	$0.483979\pi$
$278$	−1.53418	+	2.65727i	−0.0920138	+	0.159373i
$279$	−4.70693	+	10.1089i	−0.281796	+	0.605205i
$280$	6.16997	−	4.11334i	0.368726	−	0.245819i
$281$	13.3280	−	15.8837i	0.795083	−	0.947543i	−0.204426	−	0.978882i	$-0.565533\pi$
$281$	13.3280	−	15.8837i	0.795083	−	0.947543i	0.999509	+	0.0313394i	$0.00997726\pi$
$282$	3.03796	+	23.0254i	0.180908	+	1.37114i
$283$	0.0941297	−	0.0165976i	0.00559543	−	0.000986625i	−0.170850	−	0.985297i	$-0.554651\pi$
$283$	0.0941297	−	0.0165976i	0.00559543	−	0.000986625i	0.176445	+	0.984310i	$0.443540\pi$
$284$	−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
$287$	4.26909	+	6.40360i	0.251997	+	0.377992i
$288$	−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	$-0.369867\pi$
$293$	1.92130	+	0.699296i	0.112244	+	0.0408533i	−0.285288	+	0.958442i	$0.592089\pi$
$294$	−6.93632	−	9.94422i	−0.404534	−	0.579959i
$295$	−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
$301$	24.4211	+	7.14574i	1.40761	+	0.411873i
$302$	−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	$-0.931175\pi$
$307$	−22.4148	+	12.9412i	−1.27928	+	0.738591i	−0.302562	+	0.953130i	$0.597842\pi$
$308$	−8.41734	+	11.4547i	−0.479622	+	0.652694i
$309$	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	0.822058	+	0.569404i	$0.192826\pi$
$311$	4.30869	+	24.4358i	0.244324	+	1.38563i	−0.577735	+	0.816225i	$0.696063\pi$
$312$	−1.92706	+	4.65603i	−0.109098	+	0.263596i
$313$	−11.6016	+	13.8262i	−0.655759	+	0.781503i	−0.986770	−	0.162124i	$-0.948166\pi$
$313$	−11.6016	+	13.8262i	−0.655759	+	0.781503i	0.331012	+	0.943627i	$0.392610\pi$
$314$	−10.9547	−	18.9740i	−0.618208	−	1.07077i
$315$	−11.5498	+	19.0130i	−0.650760	+	1.07126i
$316$	3.54984	−	6.14850i	0.199694	−	0.345880i
$317$	3.54406	+	9.73724i	0.199054	+	0.546898i	0.998553	−	0.0537699i	$-0.0171238\pi$
$317$	3.54406	+	9.73724i	0.199054	+	0.546898i	−0.799499	+	0.600668i	$0.794902\pi$
$318$	−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
$322$	0.0878561	−	0.794552i	0.00489603	−	0.0442786i
$323$			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
$329$	−25.6527	+	24.5059i	−1.41428	+	1.35105i
$330$	25.4653	+	5.63799i	1.40182	+	0.310361i
$331$	16.0033	−	5.82473i	0.879622	−	0.320156i	0.137565	−	0.990493i	$-0.456073\pi$
$331$	16.0033	−	5.82473i	0.879622	−	0.320156i	0.742057	+	0.670337i	$0.233850\pi$
$332$	−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
$336$	1.47632	−	4.33826i	0.0805400	−	0.236671i
$337$	1.78231	+	10.1080i	0.0970888	+	0.550618i	0.994087	+	0.108584i	$0.0346317\pi$
$337$	1.78231	+	10.1080i	0.0970888	+	0.550618i	−0.896998	+	0.442034i	$0.854257\pi$
$338$	−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
$343$	6.00797	−	17.5187i	0.324400	−	0.945920i
$344$	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	−0.548256	−	0.836310i	$-0.684708\pi$
$347$	7.62446	−	20.9480i	0.409302	−	1.12455i	0.957559	−	0.288239i	$-0.0930696\pi$
$348$	5.83696	−	9.16789i	0.312894	−	0.491450i
$349$	11.8031	+	2.08121i	0.631807	+	0.111405i	0.480375	−	0.877063i	$-0.340500\pi$
$349$	11.8031	+	2.08121i	0.631807	+	0.111405i	0.151432	+	0.988468i	$0.451612\pi$
$350$	−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	0.650115	+	0.759836i	$0.274721\pi$
$353$	−4.14606	+	23.5135i	−0.220672	+	1.25150i	−0.870788	+	0.491659i	$0.836390\pi$
$354$	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
$357$	2.72157	−	3.38572i	0.144041	−	0.179191i
$358$	13.4664	−	4.90138i	0.711724	−	0.259046i
$359$	13.6340	+	7.87157i	0.719573	+	0.415446i	0.814595	−	0.580030i	$-0.196959\pi$
$359$	13.6340	+	7.87157i	0.719573	+	0.415446i	−0.0950226	+	0.995475i	$0.530292\pi$
$360$	−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
$364$	−7.47862	+	1.82174i	−0.391986	+	0.0954853i
$365$	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	$-0.719016\pi$
$367$	4.52071	−	5.38757i	0.235979	−	0.281229i	0.871018	+	0.491251i	$0.163460\pi$
$368$	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
$371$	−1.49800	−	3.41411i	−0.0777721	−	0.177252i
$372$	−4.74785	−	4.34814i	−0.246164	−	0.225441i
$373$	−19.5831	+	16.4322i	−1.01397	+	0.850825i	−0.988858	−	0.148859i	$-0.952440\pi$
$373$	−19.5831	+	16.4322i	−1.01397	+	0.850825i	−0.0251156	+	0.999685i	$0.507995\pi$
$374$	−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
$378$	1.49398	+	13.6663i	0.0768419	+	0.702919i
$379$	−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	$-0.629913\pi$
$383$	8.57383	−	7.19430i	0.438102	−	0.367611i	0.834999	+	0.550252i	$0.185468\pi$
$384$	1.65174	−	0.521303i	0.0842900	−	0.0266026i
$385$	16.0077	+	36.4835i	0.815829	+	1.85937i
$386$	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	−0.906266	−	0.422708i	$-0.861080\pi$
$389$	−6.56008	+	7.81799i	−0.332609	+	0.396388i	0.573657	+	0.819096i	$0.305524\pi$
$390$	8.60086	+	11.2023i	0.435522	+	0.567252i
$391$	0.282059	−	0.0497346i	0.0142643	−	0.00251519i
$392$	6.68039	−	2.09101i	0.337411	−	0.105612i
$393$	−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	$-0.323898\pi$
$397$	1.02285	+	0.590540i	0.0513351	+	0.0296384i	−0.474113	+	0.880464i	$0.657231\pi$
$398$	17.3039	−	6.29809i	0.867365	−	0.315695i
$399$	0.171132	−	1.10626i	0.00856730	−	0.0553824i
$400$	2.18740	−	1.83544i	0.109370	−	0.0917722i
$401$	3.66036	−	10.0568i	0.182790	−	0.502210i	−0.814126	−	0.580688i	$-0.802784\pi$
$401$	3.66036	−	10.0568i	0.182790	−	0.502210i	0.996916	+	0.0784775i	$0.0250059\pi$
$402$	−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	0.737025	+	0.675865i	$0.236230\pi$
$409$	−5.29875	+	14.5582i	−0.262006	+	0.719857i	−0.999032	+	0.0439918i	$0.985992\pi$
$410$	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
$413$	−13.5456	+	27.3957i	−0.666535	+	1.34805i
$414$	−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	0.999728	+	0.0233229i	$0.00742458\pi$
$419$	1.39741	+	7.92510i	0.0682679	+	0.387166i	−0.931460	+	0.363843i	$0.881464\pi$
$420$	−8.46118	−	9.66295i	−0.412864	−	0.471504i
$421$	−1.78713	−	1.49958i	−0.0870996	−	0.0730853i	0.598198	−	0.801348i	$-0.295884\pi$
$421$	−1.78713	−	1.49958i	−0.0870996	−	0.0730853i	−0.685298	+	0.728263i	$0.740328\pi$
$422$	−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
$427$	−23.6948	−	24.8036i	−1.14667	−	1.20033i
$428$	−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	$-0.997667\pi$
$431$		−	0.304337i		−	0.0146594i	0.999973	−	0.00732969i	$-0.00233313\pi$
$432$	−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	$0.964959\pi$
$434$	1.08082	−	9.77470i	0.0518810	−	0.469201i
$435$	−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	$-0.128436\pi$
$439$	−0.779667	−	2.14212i	−0.0372115	−	0.102238i	−0.956907	+	0.290395i	$0.906213\pi$
$440$	−7.52921	+	13.0410i	−0.358941	+	0.621704i
$441$	−15.5044	+	14.1638i	−0.738305	+	0.674467i
$442$	−1.37891	−	2.38834i	−0.0655881	−	0.113602i
$443$	−18.6857	+	22.2687i	−0.887784	+	1.05802i	0.110159	+	0.993914i	$0.464864\pi$
$443$	−18.6857	+	22.2687i	−0.887784	+	1.05802i	−0.997943	+	0.0641054i	$0.979581\pi$
$444$	−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
$448$	2.13202	+	1.56668i	0.100728	+	0.0740188i
$449$	3.91704	−	2.26150i	0.184856	−	0.106727i	−0.404716	−	0.914442i	$-0.632630\pi$
$449$	3.91704	−	2.26150i	0.184856	−	0.106727i	0.589572	+	0.807716i	$0.299296\pi$
$450$	−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
$455$	−6.05853	+	20.7055i	−0.284028	+	0.970688i
$456$	0.375240	−	0.195472i	0.0175722	−	0.00915382i
$457$	5.36803	−	30.4436i	0.251106	−	1.42409i	−0.554768	−	0.832005i	$-0.687193\pi$
$457$	5.36803	−	30.4436i	0.251106	−	1.42409i	0.805874	−	0.592087i	$-0.201696\pi$
$458$	−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	−0.747586	−	0.664165i	$-0.768787\pi$
$461$	3.90927	−	22.1706i	0.182073	−	1.03259i	0.929659	−	0.368421i	$-0.120102\pi$
$462$	21.5768	+	11.8588i	1.00384	+	0.551721i
$463$	34.0483	+	12.3926i	1.58236	+	0.575931i	0.975715	−	0.219043i	$-0.0702936\pi$
$463$	34.0483	+	12.3926i	1.58236	+	0.575931i	0.606643	+	0.794974i	$0.292516\pi$
$464$	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	$-0.981743\pi$
$467$	−9.71447	+	16.8260i	−0.449532	+	0.778612i	0.548823	+	0.835938i	$0.315076\pi$
$468$	8.43179	+	2.25420i	0.389760	+	0.104200i
$469$	−2.02476	−	3.03712i	−0.0934948	−	0.140241i
$470$	−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
$476$	1.39119	+	2.08677i	0.0637650	+	0.0956469i
$477$	−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	$-0.547804\pi$
$479$	8.12673	−	2.95789i	0.371320	−	0.135149i	0.520938	+	0.853595i	$0.325582\pi$
$480$	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
$483$	−1.38428	+	0.0291515i	−0.0629871	+	0.00132644i
$484$	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
$490$	4.28633	−	19.1453i	0.193637	−	0.864898i
$491$	0.558540	+	0.665642i	0.0252065	+	0.0300400i	0.778500	−	0.627644i	$-0.215981\pi$
$491$	0.558540	+	0.665642i	0.0252065	+	0.0300400i	−0.753294	+	0.657684i	$0.771536\pi$
$492$	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
$497$	−6.31676	+	8.59616i	−0.283345	+	0.385590i
$498$	19.5514	+	8.09201i	0.876120	+	0.362612i
$499$	−1.99339	−	11.3051i	−0.0892364	−	0.506085i	−0.996362	−	0.0852244i	$-0.972839\pi$
$499$	−1.99339	−	11.3051i	−0.0892364	−	0.506085i	0.907125	−	0.420861i	$-0.138272\pi$
$500$	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	−0.755964	−	0.654613i	$-0.772832\pi$
$503$	−21.1918	−	36.7052i	−0.944894	−	1.63660i	−0.188930	−	0.981991i	$-0.560502\pi$
$504$	−7.78400	−	1.55221i	−0.346727	−	0.0691409i
$505$	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	$-0.615637\pi$
$509$	−27.7138	−	10.0870i	−1.22839	−	0.447099i	−0.873047	+	0.487636i	$0.837859\pi$
$510$	2.47142	−	3.88177i	0.109436	−	0.171888i
$511$	35.9504	+	3.97515i	1.59035	+	0.175850i
$512$			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
$518$	−10.4155	−	10.9029i	−0.457632	−	0.479048i
$519$	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	$-0.833226\pi$
$521$	0.00768736	−	0.0133149i	0.000336789	−	0.000583337i	0.866194	+	0.499708i	$0.166559\pi$
$522$	−17.0652	−	7.94595i	−0.746925	−	0.347785i
$523$	34.6851	−	20.0255i	1.51668	−	0.875653i	0.516867	−	0.856066i	$-0.327098\pi$
$523$	34.6851	−	20.0255i	1.51668	−	0.875653i	0.999808	−	0.0195870i	$-0.00623514\pi$
$524$	−7.45159	−	6.25263i	−0.325524	−	0.273147i
$525$	−12.8358	+	2.54305i	−0.560200	+	0.110988i
$526$	−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
$532$	0.579348	+	0.286454i	0.0251179	+	0.0124194i
$533$	−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
$546$	4.82261	+	12.4293i	0.206389	+	0.531925i
$547$	10.3237	−	3.75751i	0.441408	−	0.160660i	−0.111749	−	0.993737i	$-0.535645\pi$
$547$	10.3237	−	3.75751i	0.441408	−	0.160660i	0.553157	+	0.833077i	$0.313423\pi$
$548$	−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
$553$	−4.44566	−	18.2503i	−0.189049	−	0.776082i
$554$	−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	−0.322949	−	0.946416i	$-0.604674\pi$
$557$	7.91094	−	4.56738i	0.335197	−	0.193526i	0.658146	+	0.752890i	$0.271341\pi$
$558$	−6.39081	+	9.13798i	−0.270545	+	0.386842i
$559$	−24.2312	−	13.9899i	−1.02487	−	0.591709i
$560$	6.79051	−	2.97945i	0.286951	−	0.125905i
$561$	−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	$-0.0404134\pi$
$563$	39.6355	+	14.4262i	1.67044	+	0.607990i	0.678488	+	0.734612i	$0.262636\pi$
$564$	−1.00652	+	23.2031i	−0.0423821	+	0.977029i
$565$	−37.8145	−	6.66772i	−1.59087	−	0.280513i
$566$	0.0955818			0.00401760
$567$	23.1289	−	5.66168i	0.971322	−	0.237768i
$568$	−4.03193			−0.169176
$569$	14.0605	+	2.47925i	0.589448	+	0.103936i	0.460414	−	0.887704i	$-0.347701\pi$
$569$	14.0605	+	2.47925i	0.589448	+	0.103936i	0.129035	+	0.991640i	$0.458812\pi$
$570$	0.0513921	−	1.18474i	0.00215258	−	0.0496231i
$571$	4.50855	+	1.64098i	0.188677	+	0.0686727i	0.434631	−	0.900609i	$-0.356879\pi$
$571$	4.50855	+	1.64098i	0.188677	+	0.0686727i	−0.245954	+	0.969282i	$0.579101\pi$
$572$	11.9739	−	10.0473i	0.500656	−	0.420100i
$573$	4.37215	−	19.7478i	0.182649	−	0.824977i
$574$	3.09226	+	7.04763i	0.129069	+	0.294162i
$575$	−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	$-0.820647\pi$
$577$	−19.3505	+	11.1720i	−0.805572	+	0.465097i	0.0398438	+	0.999206i	$0.487314\pi$
$578$	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
$581$	7.64979	+	31.4039i	0.317367	+	1.30285i
$582$	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	$-0.451302\pi$
$587$	21.9122	−	7.97538i	0.904413	−	0.329179i	0.752020	+	0.659141i	$0.229080\pi$
$588$	−5.10415	−	10.9976i	−0.210491	−	0.453534i
$589$	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	$-0.387980\pi$
$593$	16.7880			0.689401			0.344701	+	0.938713i	$0.387980\pi$
$594$	−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	0.995115	+	0.0987270i	$0.0314770\pi$
$599$	22.5053	+	26.8208i	0.919542	+	1.09587i	−0.0755727	+	0.997140i	$0.524079\pi$
$600$	−3.64735	−	3.34029i	−0.148902	−	0.136367i
$601$	4.00672	+	11.0084i	0.163437	+	0.449041i	0.994195	−	0.107594i	$-0.0343146\pi$
$601$	4.00672	+	11.0084i	0.163437	+	0.449041i	−0.830757	+	0.556635i	$0.812092\pi$
$602$	22.8092	+	11.2779i	0.929635	+	0.459651i
$603$	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	$-0.303396\pi$
$607$	34.5452	−	6.09125i	1.40215	−	0.247236i	0.823025	+	0.568005i	$0.192285\pi$
$608$	0.0424183	+	0.240566i	0.00172029	+	0.00975625i
$609$	−5.58833	−	28.2066i	−0.226451	−	1.14299i
$610$	−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	0.418276	+	0.908320i	$0.362634\pi$
$613$	−14.2980	+	24.7648i	−0.577490	+	1.00024i	−0.995766	+	0.0919224i	$0.970699\pi$
$614$	−24.3214	+	8.85228i	−0.981533	+	0.357249i
$615$	9.53722	−	10.4139i	0.384578	−	0.419931i
$616$	−10.2786	+	9.81906i	−0.414135	+	0.395621i
$617$	−12.1982	+	33.5143i	−0.491082	+	1.34924i	0.408609	+	0.912710i	$0.366014\pi$
$617$	−12.1982	+	33.5143i	−0.491082	+	1.34924i	−0.899691	+	0.436527i	$0.856208\pi$
$618$	3.74935	−	1.95313i	0.150821	−	0.0785664i
$619$	−34.9977	−	6.17103i	−1.40668	−	0.248035i	−0.581792	−	0.813338i	$-0.697648\pi$
$619$	−34.9977	−	6.17103i	−1.40668	−	0.248035i	−0.824883	+	0.565303i	$0.808759\pi$
$620$		−	10.4179i		−	0.418391i
$621$	1.39320	+	0.723758i	0.0559072	+	0.0290434i
$622$			24.8128i			0.994902i
$623$	4.16506	−	37.6679i	0.166869	−	1.50913i
$624$	−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
$630$	−14.6759	+	16.7185i	−0.584704	+	0.666083i
$631$	16.8880	+	29.2508i	0.672300	+	1.16446i	0.977250	+	0.212089i	$0.0680267\pi$
$631$	16.8880	+	29.2508i	0.672300	+	1.16446i	−0.304951	+	0.952368i	$0.598640\pi$
$632$	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
$637$	−10.9780	+	17.1529i	−0.434963	+	0.679624i
$638$	−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	0.981972	−	0.189028i	$-0.0605336\pi$
$641$	2.74024	+	7.52876i	0.108233	+	0.297368i	−0.873739	+	0.486396i	$0.838311\pi$
$642$	21.6496	+	4.79320i	0.854442	+	0.189173i
$643$	10.5957	+	12.6274i	0.417853	+	0.497978i	0.933377	−	0.358897i	$-0.116847\pi$
$643$	10.5957	+	12.6274i	0.417853	+	0.497978i	−0.515524	+	0.856875i	$0.672403\pi$
$644$	0.224494	−	0.767225i	0.00884630	−	0.0302329i
$645$	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	$-0.525281\pi$
$647$	−4.03618			−0.158679			−0.0793394	+	0.996848i	$0.525281\pi$
$648$	6.90092	+	5.77731i	0.271094	+	0.226954i
$649$		−	62.0612i		−	2.43612i
$650$	−1.44256	+	8.18115i	−0.0565818	+	0.320891i
$651$	−17.0297	+	0.358626i	−0.667446	+	0.0140556i
$652$	3.98505	+	1.45044i	0.156067	+	0.0568037i
$653$	−17.1181	−	20.4005i	−0.669883	−	0.798335i	0.318885	−	0.947793i	$-0.396691\pi$
$653$	−17.1181	−	20.4005i	−0.669883	−	0.798335i	−0.988768	+	0.149458i	$0.952247\pi$
$654$	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
$658$	−29.5184	+	19.6790i	−1.15075	+	0.767169i
$659$	9.49979	−	11.3214i	0.370059	−	0.441019i	−0.548591	−	0.836091i	$-0.684836\pi$
$659$	9.49979	−	11.3214i	0.370059	−	0.441019i	0.918650	+	0.395071i	$0.129280\pi$
$660$	24.0994	+	9.97433i	0.938067	+	0.388250i
$661$	4.89542	−	0.863195i	0.190410	−	0.0335744i	−0.0776299	−	0.996982i	$-0.524735\pi$
$661$	4.89542	−	0.863195i	0.190410	−	0.0335744i	0.268040	+	0.963408i	$0.413624\pi$
$662$	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
$665$	1.50718	−	1.00480i	0.0584461	−	0.0389644i
$666$	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
$672$	2.20722	−	4.01599i	0.0851455	−	0.154920i
$673$	−1.87117	+	10.6119i	−0.0721282	+	0.409059i	0.927271	+	0.374391i	$0.122148\pi$
$673$	−1.87117	+	10.6119i	−0.0721282	+	0.409059i	−0.999399	+	0.0346677i	$0.988963\pi$
$674$			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	−0.789772	−	0.613400i	$-0.789801\pi$
$677$	4.21944	−	23.9296i	0.162166	−	0.919690i	0.951938	−	0.306289i	$-0.0990876\pi$
$678$	−21.0449	+	10.9628i	−0.808226	+	0.421025i
$679$	−2.67913	+	9.15613i	−0.102816	+	0.351380i
$680$	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	0.508897	−	0.860828i	$-0.330053\pi$
$683$	0.466410	+	0.269282i	0.0178467	+	0.0103038i	−0.491050	+	0.871131i	$0.663387\pi$
$684$	−0.420674	−	0.600064i	−0.0160849	−	0.0229440i
$685$	−28.1033	+	16.2254i	−1.07377	+	0.619942i
$686$	8.95878	−	16.2093i	0.342048	−	0.618872i
$687$	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	$-0.701545\pi$
$691$	8.01618	−	9.55331i	0.304950	−	0.363425i	0.896655	+	0.442729i	$0.145990\pi$
$692$	4.06719	+	7.04457i	0.154611	+	0.267795i
$693$	15.4751	−	39.7377i	0.587849	−	1.50951i
$694$	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
$700$	0.830297	−	7.50903i	0.0313823	−	0.283815i
$701$			11.3417i			0.428369i	0.976793	+	0.214185i	$0.0687094\pi$
$701$			11.3417i			0.428369i	−0.976793	+	0.214185i	$0.931291\pi$
$702$	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
$707$	16.7804	−	16.0302i	0.631090	−	0.602878i
$708$	6.02167	+	19.0795i	0.226308	+	0.717053i
$709$	−11.0328	+	4.01562i	−0.414347	+	0.150810i	−0.540778	−	0.841166i	$-0.681870\pi$
$709$	−11.0328	+	4.01562i	−0.414347	+	0.150810i	0.126431	+	0.991975i	$0.459648\pi$
$710$	−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
$714$	3.26814	−	2.86169i	0.122307	−	0.107096i
$715$	−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	$-0.0515013\pi$
$719$	9.49117	+	16.4392i	0.353961	+	0.613078i	−0.632979	+	0.774169i	$0.718168\pi$
$720$	−8.37669	−	0.728107i	−0.312181	−	0.0271350i
$721$	5.78876	+	2.86221i	0.215585	+	0.106594i
$722$	−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	$-0.545073\pi$
$727$	−16.5106	−	2.91126i	−0.612344	−	0.107973i	−0.471215	+	0.882018i	$0.656184\pi$
$728$	−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	$-0.994046\pi$
$733$	−6.00752	+	16.5055i	−0.221893	+	0.609645i	0.777932	+	0.628348i	$0.216269\pi$
$734$	5.38757	−	4.52071i	0.198859	−	0.166862i
$735$	−33.8469	−	3.02274i	−1.24846	−	0.111496i
$736$	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	−0.998569	−	0.0534726i	$-0.982971\pi$
$739$	−14.8317	−	25.6893i	−0.545593	−	0.944995i	0.452976	−	0.891523i	$-0.350362\pi$
$740$	−12.2362	−	10.2674i	−0.449810	−	0.377435i
$741$	−0.470736	+	1.13736i	−0.0172929	+	0.0417821i
$742$	−0.882384	−	3.62236i	−0.0323934	−	0.132981i
$743$	−33.5884	+	5.92255i	−1.23224	+	0.217277i	−0.751587	−	0.659634i	$-0.770711\pi$
$743$	−33.5884	+	5.92255i	−1.23224	+	0.217277i	−0.480653	+	0.876911i	$0.659600\pi$
$744$	−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
$749$	13.6092	+	31.0169i	0.497268	+	1.13333i
$750$	9.92806	−	3.13338i	0.362521	−	0.114415i
$751$	9.27586	−	7.78337i	0.338481	−	0.284019i	−0.457664	−	0.889125i	$-0.651314\pi$
$751$	9.27586	−	7.78337i	0.338481	−	0.284019i	0.796145	+	0.605106i	$0.206869\pi$
$752$	−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
$756$	−0.901850	+	13.7181i	−0.0328000	+	0.498923i
$757$	−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	$-0.697497\pi$
$761$	3.27963	−	2.75194i	0.118887	−	0.0997577i	0.700293	+	0.713856i	$0.253053\pi$
$762$	−5.67970	−	5.20154i	−0.205754	−	0.188432i
$763$	3.67766	−	1.61363i	0.133140	−	0.0584175i
$764$	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	$-0.303026\pi$
$769$	38.9273	−	6.86393i	1.40375	−	0.247520i	0.823685	+	0.567048i	$0.191915\pi$
$770$	9.42924	+	38.7089i	0.339806	+	1.39497i
$771$	−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	0.945638	+	0.325222i	$0.105439\pi$
$773$	20.9764	+	36.3322i	0.754469	+	1.30678i	−0.191169	+	0.981557i	$0.561228\pi$
$774$	−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
$777$	−16.3624	+	20.3554i	−0.586999	+	0.730247i
$778$	−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	$-0.890906\pi$
$787$	−0.121615	+	0.334133i	−0.00433509	+	0.0119106i	0.937506	+	0.347969i	$0.113128\pi$
$788$	−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
$791$	−32.4921	−	16.0655i	−1.15529	−	0.571223i
$792$	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	$-0.0545860\pi$
$797$	0.0298632	+	0.169363i	0.00105781	+	0.00599913i	−0.984274	+	0.176647i	$0.943475\pi$
$798$	0.360632	−	1.05974i	0.0127662	−	0.0375143i
$799$	−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
$805$	−1.54765	−	1.62008i	−0.0545476	−	0.0571002i
$806$	−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	$0.121718\pi$
$809$			21.2262i			0.746273i	−0.927776	+	0.373137i	$0.878282\pi$
$810$	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	$0.970947\pi$
$812$	16.5011	+	1.82457i	0.579073	+	0.0640300i
$813$	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
$819$	20.2506	−	11.0972i	0.707613	−	0.387769i
$820$	4.07645	+	7.06061i	0.142356	+	0.246567i
$821$	21.0867	−	25.1302i	0.735933	−	0.877050i	−0.260142	−	0.965570i	$-0.583769\pi$
$821$	21.0867	−	25.1302i	0.735933	−	0.877050i	0.996074	+	0.0885201i	$0.0282138\pi$
$822$	−7.66912	+	18.5297i	−0.267491	+	0.646296i
$823$	7.27112	+	41.2365i	0.253455	+	1.43742i	0.800007	+	0.599990i	$0.204829\pi$
$823$	7.27112	+	41.2365i	0.253455	+	1.43742i	−0.546552	+	0.837425i	$0.684060\pi$
$824$	0.423838	+	2.40370i	0.0147651	+	0.0837370i
$825$	21.0766	−	16.1821i	0.733794	−	0.563388i
$826$	−18.0970	+	24.6273i	−0.629676	+	0.856895i
$827$	46.2108	−	26.6798i	1.60691	−	0.927749i	0.616851	−	0.787080i	$-0.288408\pi$
$827$	46.2108	−	26.6798i	1.60691	−	0.927749i	0.990057	−	0.140669i	$-0.0449253\pi$
$828$	−0.640580	+	0.641303i	−0.0222617	+	0.0222868i
$829$	21.7292	+	12.5454i	0.754688	+	0.435719i	0.827385	−	0.561635i	$-0.189827\pi$
$829$	21.7292	+	12.5454i	0.754688	+	0.435719i	−0.0726976	+	0.997354i	$0.523161\pi$
$830$	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
$833$	6.47522	+	1.44969i	0.224353	+	0.0502290i
$834$	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	$-0.960130\pi$
$839$	−0.495527	+	2.81027i	−0.0171075	+	0.0970214i	0.975058	+	0.221948i	$0.0712415\pi$
$840$	−6.65469	−	10.9854i	−0.229608	−	0.379033i
$841$	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
$847$	−26.2204	−	39.3302i	−0.900942	−	1.35140i
$848$	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	$-0.761668\pi$
$853$	1.89941	−	2.26363i	0.0650345	−	0.0775051i	0.797581	+	0.603212i	$0.206113\pi$
$854$	−19.0277	−	28.5413i	−0.651114	−	0.976664i
$855$	−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	$-0.691799\pi$
$857$	−13.7976	+	5.02193i	−0.471319	+	0.171546i	0.0954310	+	0.995436i	$0.469577\pi$
$858$	−19.9658	−	18.2849i	−0.681622	−	0.624238i
$859$	23.1900	+	27.6367i	0.791231	+	0.942953i	0.999382	−	0.0351440i	$-0.0111890\pi$
$859$	23.1900	+	27.6367i	0.791231	+	0.942953i	−0.208151	+	0.978097i	$0.566745\pi$
$860$	25.3295	+	9.21917i	0.863727	+	0.314371i
$861$	11.4014	−	6.90667i	0.388558	−	0.235379i
$862$	0.0528475	−	0.299713i	0.00179999	−	0.0102083i
$863$		−	23.9065i		−	0.813787i	−0.913476	−	0.406893i	$-0.866612\pi$
$863$		−	23.9065i		−	0.813787i	0.913476	−	0.406893i	$-0.133388\pi$
$864$	−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
$868$	2.76176	−	9.43852i	0.0937402	−	0.320364i
$869$	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
$875$	12.8149	+	9.41681i	0.433221	+	0.318346i
$876$	18.7814	−	14.4199i	0.634564	−	0.487202i
$877$	1.87546	+	10.6362i	0.0633297	+	0.359160i	0.999961	+	0.00884345i	$0.00281499\pi$
$877$	1.87546	+	10.6362i	0.0633297	+	0.359160i	−0.936631	+	0.350317i	$0.886074\pi$
$878$	−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	$-0.221644\pi$
$881$	−5.10105	−	8.83528i	−0.171859	−	0.297668i	−0.939070	+	0.343727i	$0.888311\pi$
$882$	−17.7284	+	11.2563i	−0.596945	+	0.379020i
$883$	−16.4850	+	28.5529i	−0.554765	+	0.960882i	0.443156	+	0.896444i	$0.353859\pi$
$883$	−16.4850	+	28.5529i	−0.554765	+	0.960882i	−0.997922	+	0.0644374i	$0.979475\pi$
$884$	−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	$-0.564380\pi$
$887$	−29.3193	−	10.6714i	−0.984447	−	0.358310i	−0.783568	+	0.621306i	$0.786602\pi$
$888$	−9.86184	−	0.427793i	−0.330942	−	0.0143558i
$889$	1.29295	−	11.6932i	0.0433641	−	0.392176i
$890$		−	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
$896$	1.82758	+	1.91310i	0.0610551	+	0.0639123i
$897$	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
$903$	14.1983	−	41.7225i	0.472489	−	1.38844i
$904$	−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	0.980665	−	0.195695i	$-0.0626962\pi$
$907$	28.8586	+	24.2152i	0.958234	+	0.804054i	−0.0224311	+	0.999748i	$0.507141\pi$
$908$	−8.23232	−	14.2588i	−0.273199	−	0.473195i
$909$	−25.4134	+	6.82485i	−0.842909	+	0.226366i
$910$	−9.56196	+	19.3389i	−0.316976	+	0.641077i
$911$	15.4249	+	42.3795i	0.511049	+	1.40409i	0.880146	+	0.474704i	$0.157445\pi$
$911$	15.4249	+	42.3795i	0.511049	+	1.40409i	−0.369097	+	0.929391i	$0.620333\pi$
$912$	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
$924$	19.1897	+	15.4254i	0.631295	+	0.507458i
$925$	−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	$-0.0672779\pi$
$929$	28.6790	+	24.0645i	0.940928	+	0.789532i	−0.0368186	+	0.999322i	$0.511722\pi$
$930$	−17.8892	+	2.36029i	−0.586611	+	0.0773970i
$931$	1.63187	−	0.510788i	0.0534824	−	0.0167404i
$932$	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	$-0.361471\pi$
$937$	−4.68060	−	2.70235i	−0.152909	−	0.0882818i	−0.574502	+	0.818503i	$0.694804\pi$
$938$	−1.46661	−	3.34258i	−0.0478865	−	0.109139i
$939$	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	$-0.435885\pi$
$941$	−8.48097	−	3.08682i	−0.276472	−	0.100627i	−0.476535	+	0.879156i	$0.658107\pi$
$942$	−33.6554	+	17.5320i	−1.09655	+	0.571222i
$943$	0.865545	+	0.152619i	0.0281860	+	0.00496996i
$944$	−11.5512			−0.375959
$945$	32.0336	+	21.4133i	1.04205	+	0.696574i
$946$	−51.6712			−1.67998
$947$	−22.7694	−	4.01486i	−0.739907	−	0.130465i	−0.209024	−	0.977911i	$-0.567029\pi$
$947$	−22.7694	−	4.01486i	−0.739907	−	0.130465i	−0.530883	+	0.847445i	$0.678140\pi$
$948$	−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
$952$	1.00769	+	2.29664i	0.0326594	+	0.0744346i
$953$	−37.1436	−	21.4449i	−1.20320	−	0.694667i	−0.241934	−	0.970293i	$-0.577782\pi$
$953$	−37.1436	−	21.4449i	−1.20320	−	0.694667i	−0.961265	+	0.275625i	$0.911115\pi$
$954$	−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
$959$	−29.7627	+	7.25001i	−0.961088	+	0.234115i
$960$	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
$966$	−1.36832	−	0.211670i	−0.0440249	−	0.00681037i
$967$	−11.9906	+	10.0613i	−0.385593	+	0.323551i	−0.814893	−	0.579611i	$-0.803205\pi$
$967$	−11.9906	+	10.0613i	−0.385593	+	0.323551i	0.429301	+	0.903162i	$0.358760\pi$
$968$	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	$-0.655985\pi$
$971$	−29.3324			−0.941322			−0.470661	+	0.882314i	$0.655985\pi$
$972$	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	0.191238	−	0.981544i	$-0.438750\pi$
$977$	−25.2745	−	30.1209i	−0.808602	−	0.963654i	−0.999840	+	0.0178895i	$0.994305\pi$
$978$	1.58779	−	7.17163i	0.0507720	−	0.229323i
$979$	26.3213	+	72.3171i	0.841231	+	2.31126i
$980$	7.54576	−	18.1102i	0.241041	−	0.578508i
$981$	−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	$-0.402435\pi$
$983$	−18.3345	−	15.3844i	−0.584779	−	0.490688i	−0.886512	+	0.462705i	$0.846879\pi$
$984$	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
$987$	40.4800	+	46.2295i	1.28849	+	1.47150i
$988$	−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	−0.107610	−	0.994193i	$-0.534320\pi$
$991$	25.4105	−	44.0123i	0.807192	−	1.39810i	0.914801	−	0.403904i	$-0.132347\pi$
$992$	3.49284	−	1.27129i	0.110898	−	0.0403635i
$993$	−8.87799	−	28.1297i	−0.281734	−	0.892670i
$994$	−7.71350	+	7.36867i	−0.244657	+	0.233720i
$995$	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	$-0.469437\pi$
$997$	−4.87802	−	0.860127i	−0.154489	−	0.0272405i	−0.250357	+	0.968153i	$0.580548\pi$
$998$		−	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.83.19	yes	144
7.6	odd	2	inner	378.2.z.a.83.18	yes	144
27.14	odd	18	inner	378.2.z.a.41.18	✓	144
189.41	even	18	inner	378.2.z.a.41.19	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.z.a.41.18	✓	144	27.14	odd	18	inner
378.2.z.a.41.19	yes	144	189.41	even	18	inner
378.2.z.a.83.18	yes	144	7.6	odd	2	inner
378.2.z.a.83.19	yes	144	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.984808 + 0.173648i) q^{2} +(0.0750633 - 1.73042i) q^{3} +(0.939693 + 0.342020i) q^{4} +(2.14704 - 1.80158i) q^{5} +(0.374408 - 1.69110i) q^{6} +(2.42280 - 1.06304i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.98873 - 0.259783i) q^{9} +O(q^{10})\)	\(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} +(2.42280 - 1.06304i) 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} +(2.57058 - 0.626178i) 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} +(-1.65765 - 4.27226i) 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} +(3.28668 - 6.64724i) 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} +(-0.890596 - 4.49520i) 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} +(4.73988 - 5.15107i) 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} +(2.62972 + 0.290777i) 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} +(-7.51725 + 2.54775i) 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} +(4.39103 - 5.97553i) 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} +(-3.99196 + 13.6428i) 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} +(-0.0964824 - 4.58156i) 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} +(-6.40453 + 4.26972i) 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} +(5.56235 - 4.24974i) 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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