LMFDB - Embedded newform 384.2.v.a.13.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(13,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.v (of order $32$, degree $16$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			13.11
Character	$\chi$	$=$	384.13
Dual form			384.2.v.a.325.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.612256 - 1.27481i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(-1.25028 + 1.56102i) q^{4} +(0.189500 + 1.92402i) q^{5} +(-1.04219 + 0.955951i) q^{6} +(0.476963 - 0.713825i) q^{7} +(2.75550 + 0.638130i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})$	\(q+(-0.612256 - 1.27481i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(-1.25028 + 1.56102i) q^{4} +(0.189500 + 1.92402i) q^{5} +(-1.04219 + 0.955951i) q^{6} +(0.476963 - 0.713825i) q^{7} +(2.75550 + 0.638130i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(2.33674 - 1.41957i) q^{10} +(1.06219 - 0.567753i) q^{11} +(1.85674 + 0.743307i) q^{12} +(2.36283 + 0.232719i) q^{13} +(-1.20202 - 0.170993i) q^{14} +(1.78617 - 0.739855i) q^{15} +(-0.873578 - 3.90344i) q^{16} +(2.31292 + 0.958043i) q^{17} +(1.21732 + 0.719815i) q^{18} +(5.82696 - 4.78206i) q^{19} +(-3.24037 - 2.10976i) q^{20} +(-0.821543 - 0.249212i) q^{21} +(-1.37411 - 1.00648i) q^{22} +(-0.204164 + 1.02640i) q^{23} +(-0.189227 - 2.82209i) q^{24} +(1.23797 - 0.246247i) q^{25} +(-1.14999 - 3.15465i) q^{26} +(0.773010 + 0.634393i) q^{27} +(0.517958 + 1.63703i) q^{28} +(-0.377671 + 0.706573i) q^{29} +(-2.03677 - 1.82404i) q^{30} +(2.13037 - 2.13037i) q^{31} +(-4.44130 + 3.50355i) q^{32} +(-0.851643 - 0.851643i) q^{33} +(-0.194777 - 3.53511i) q^{34} +(1.46380 + 0.782418i) q^{35} +(0.172316 - 1.99256i) q^{36} +(-0.783750 + 0.955002i) q^{37} +(-9.66381 - 4.50042i) q^{38} +(-0.463196 - 2.32864i) q^{39} +(-0.705611 + 5.42258i) q^{40} +(-9.21349 - 1.83268i) q^{41} +(0.185296 + 1.19989i) q^{42} +(2.08700 - 6.87991i) q^{43} +(-0.441766 + 2.36796i) q^{44} +(-1.22649 - 1.49449i) q^{45} +(1.43347 - 0.368150i) q^{46} +(-2.53591 + 6.12224i) q^{47} +(-3.48177 + 1.96907i) q^{48} +(2.39673 + 5.78622i) q^{49} +(-1.07187 - 1.42741i) q^{50} +(0.245385 - 2.49143i) q^{51} +(-3.31749 + 3.39747i) q^{52} +(1.02350 + 1.91484i) q^{53} +(0.335451 - 1.37385i) q^{54} +(1.29366 + 1.93609i) q^{55} +(1.76978 - 1.66258i) q^{56} +(-6.26762 - 4.18789i) q^{57} +(1.13198 + 0.0488553i) q^{58} +(4.98169 - 0.490653i) q^{59} +(-1.07829 + 3.71328i) q^{60} +(4.04828 - 1.22803i) q^{61} +(-4.02015 - 1.41149i) q^{62} +0.858510i q^{63} +(7.18558 + 3.51674i) q^{64} +4.59025i q^{65} +(-0.564260 + 1.60711i) q^{66} +(3.74011 - 1.13455i) q^{67} +(-4.38734 + 2.41269i) q^{68} +(1.04147 - 0.102576i) q^{69} +(0.101213 - 2.34511i) q^{70} +(13.0171 + 8.69775i) q^{71} +(-2.64564 + 1.00029i) q^{72} +(-2.96864 - 4.44289i) q^{73} +(1.69730 + 0.414427i) q^{74} +(-0.595006 - 1.11318i) q^{75} +(0.179547 + 15.0749i) q^{76} +(0.101349 - 1.02902i) q^{77} +(-2.68499 + 2.01621i) q^{78} +(2.08586 + 5.03571i) q^{79} +(7.34478 - 2.42049i) q^{80} +(0.382683 - 0.923880i) q^{81} +(3.30470 + 12.8675i) q^{82} +(-5.32161 - 6.48441i) q^{83} +(1.41619 - 0.970860i) q^{84} +(-1.40500 + 4.63167i) q^{85} +(-10.0484 + 1.55174i) q^{86} +(0.785780 + 0.156301i) q^{87} +(3.28917 - 0.886628i) q^{88} +(-0.166186 - 0.835474i) q^{89} +(-1.15426 + 2.47856i) q^{90} +(1.29310 - 1.57565i) q^{91} +(-1.34697 - 1.60200i) q^{92} +(-2.65705 - 1.42022i) q^{93} +(9.35733 - 0.515569i) q^{94} +(10.3050 + 10.3050i) q^{95} +(4.64193 + 3.23303i) q^{96} +(-11.0074 + 11.0074i) q^{97} +(5.90892 - 6.59803i) q^{98} +(-0.567753 + 1.06219i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{15}{32}\right)$	$1$

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 $

$2$	−0.612256	−	1.27481i	−0.432931	−	0.901427i
$2$	−0.612256	−	1.27481i	−0.432931	−	0.901427i
$3$	−0.290285	−	0.956940i	−0.167596	−	0.552490i
$3$	−0.290285	−	0.956940i	−0.167596	−	0.552490i
$4$	−1.25028	+	1.56102i	−0.625142	+	0.780511i
$5$	0.189500	+	1.92402i	0.0847469	+	0.860450i	0.939758	+	0.341840i	$0.111050\pi$
$5$	0.189500	+	1.92402i	0.0847469	+	0.860450i	−0.855011	+	0.518610i	$0.826450\pi$
$6$	−1.04219	+	0.955951i	−0.425472	+	0.390265i
$7$	0.476963	−	0.713825i	0.180275	−	0.269801i	−0.730316	−	0.683110i	$-0.760627\pi$
$7$	0.476963	−	0.713825i	0.180275	−	0.269801i	0.910591	+	0.413309i	$0.135627\pi$
$8$	2.75550	+	0.638130i	0.974217	+	0.225613i
$9$	−0.831470	+	0.555570i	−0.277157	+	0.185190i
$10$	2.33674	−	1.41957i	0.738944	−	0.448908i
$11$	1.06219	−	0.567753i	0.320263	−	0.171184i	−0.303430	−	0.952854i	$-0.598132\pi$
$11$	1.06219	−	0.567753i	0.320263	−	0.171184i	0.623692	+	0.781670i	$0.285632\pi$
$12$	1.85674	+	0.743307i	0.535996	+	0.214574i
$13$	2.36283	+	0.232719i	0.655332	+	0.0645445i	0.420218	−	0.907423i	$-0.361954\pi$
$13$	2.36283	+	0.232719i	0.655332	+	0.0645445i	0.235114	+	0.971968i	$0.424454\pi$
$14$	−1.20202	−	0.170993i	−0.321252	−	0.0456998i
$15$	1.78617	−	0.739855i	0.461187	−	0.191030i
$16$	−0.873578	−	3.90344i	−0.218395	−	0.975861i
$17$	2.31292	+	0.958043i	0.560966	+	0.232360i	0.645104	−	0.764094i	$-0.276814\pi$
$17$	2.31292	+	0.958043i	0.560966	+	0.232360i	−0.0841386	+	0.996454i	$0.526814\pi$
$18$	1.21732	+	0.719815i	0.286925	+	0.169662i
$19$	5.82696	−	4.78206i	1.33680	−	1.09708i	0.349714	−	0.936856i	$-0.386279\pi$
$19$	5.82696	−	4.78206i	1.33680	−	1.09708i	0.987081	−	0.160223i	$-0.0512214\pi$
$20$	−3.24037	−	2.10976i	−0.724569	−	0.471758i
$21$	−0.821543	−	0.249212i	−0.179275	−	0.0543826i
$22$	−1.37411	−	1.00648i	−0.292961	−	0.214583i
$23$	−0.204164	+	1.02640i	−0.0425711	+	0.214019i	−0.996216	−	0.0869159i	$-0.972299\pi$
$23$	−0.204164	+	1.02640i	−0.0425711	+	0.214019i	0.953645	+	0.300935i	$0.0972989\pi$
$24$	−0.189227	−	2.82209i	−0.0386259	−	0.576057i
$25$	1.23797	−	0.246247i	0.247593	−	0.0492493i
$26$	−1.14999	−	3.15465i	−0.225531	−	0.618677i
$27$	0.773010	+	0.634393i	0.148766	+	0.122089i
$28$	0.517958	+	1.63703i	0.0978848	+	0.309370i
$29$	−0.377671	+	0.706573i	−0.0701317	+	0.131207i	−0.914544	−	0.404487i	$-0.867450\pi$
$29$	−0.377671	+	0.706573i	−0.0701317	+	0.131207i	0.844412	+	0.535694i	$0.179950\pi$
$30$	−2.03677	−	1.82404i	−0.371861	−	0.333024i
$31$	2.13037	−	2.13037i	0.382626	−	0.382626i	−0.489421	−	0.872047i	$-0.662792\pi$
$31$	2.13037	−	2.13037i	0.382626	−	0.382626i	0.872047	+	0.489421i	$0.162792\pi$
$32$	−4.44130	+	3.50355i	−0.785118	+	0.619347i
$33$	−0.851643	−	0.851643i	−0.148252	−	0.148252i
$34$	−0.194777	−	3.53511i	−0.0334040	−	0.606266i
$35$	1.46380	+	0.782418i	0.247428	+	0.132253i
$36$	0.172316	−	1.99256i	0.0287194	−	0.332094i
$37$	−0.783750	+	0.955002i	−0.128848	+	0.157001i	−0.833438	−	0.552613i	$-0.813631\pi$
$37$	−0.783750	+	0.955002i	−0.128848	+	0.157001i	0.704590	+	0.709614i	$0.251131\pi$
$38$	−9.66381	−	4.50042i	−1.56768	−	0.730064i
$39$	−0.463196	−	2.32864i	−0.0741707	−	0.372881i
$40$	−0.705611	+	5.42258i	−0.111567	+	0.857385i
$41$	−9.21349	−	1.83268i	−1.43891	−	0.286216i	−0.586862	−	0.809687i	$-0.699637\pi$
$41$	−9.21349	−	1.83268i	−1.43891	−	0.286216i	−0.852043	+	0.523471i	$0.824637\pi$
$42$	0.185296	+	1.19989i	0.0285918	+	0.185148i
$43$	2.08700	−	6.87991i	0.318264	−	1.04918i	−0.641207	−	0.767368i	$-0.721566\pi$
$43$	2.08700	−	6.87991i	0.318264	−	1.04918i	0.959471	−	0.281808i	$-0.0909341\pi$
$44$	−0.441766	+	2.36796i	−0.0665987	+	0.356983i
$45$	−1.22649	−	1.49449i	−0.182835	−	0.222785i
$46$	1.43347	−	0.368150i	0.211353	−	0.0542808i
$47$	−2.53591	+	6.12224i	−0.369901	+	0.893020i	0.623865	+	0.781532i	$0.285562\pi$
$47$	−2.53591	+	6.12224i	−0.369901	+	0.893020i	−0.993766	+	0.111488i	$0.964438\pi$
$48$	−3.48177	+	1.96907i	−0.502551	+	0.284211i
$49$	2.39673	+	5.78622i	0.342390	+	0.826603i
$50$	−1.07187	−	1.42741i	−0.151585	−	0.201866i
$51$	0.245385	−	2.49143i	0.0343607	−	0.348870i
$52$	−3.31749	+	3.39747i	−0.460053	+	0.471144i
$53$	1.02350	+	1.91484i	0.140589	+	0.263023i	0.942355	−	0.334615i	$-0.108606\pi$
$53$	1.02350	+	1.91484i	0.140589	+	0.263023i	−0.801766	+	0.597638i	$0.796106\pi$
$54$	0.335451	−	1.37385i	0.0456491	−	0.186958i
$55$	1.29366	+	1.93609i	0.174436	+	0.261063i
$56$	1.76978	−	1.66258i	0.236497	−	0.222172i
$57$	−6.26762	−	4.18789i	−0.830167	−	0.554700i
$58$	1.13198	+	0.0488553i	0.148636	+	0.00641502i
$59$	4.98169	−	0.490653i	0.648560	−	0.0638776i	0.231613	−	0.972808i	$-0.425600\pi$
$59$	4.98169	−	0.490653i	0.648560	−	0.0638776i	0.416948	+	0.908930i	$0.363100\pi$
$60$	−1.07829	+	3.71328i	−0.139206	+	0.479382i
$61$	4.04828	−	1.22803i	0.518330	−	0.157234i	−0.0202714	−	0.999795i	$-0.506453\pi$
$61$	4.04828	−	1.22803i	0.518330	−	0.157234i	0.538601	+	0.842561i	$0.318953\pi$
$62$	−4.02015	−	1.41149i	−0.510560	−	0.179259i
$63$			0.858510i			0.108162i
$64$	7.18558	+	3.51674i	0.898197	+	0.439592i
$65$			4.59025i			0.569350i
$66$	−0.564260	+	1.60711i	−0.0694556	+	0.197821i
$67$	3.74011	−	1.13455i	0.456927	−	0.138607i	−0.0534268	−	0.998572i	$-0.517014\pi$
$67$	3.74011	−	1.13455i	0.456927	−	0.138607i	0.510354	+	0.859964i	$0.329514\pi$
$68$	−4.38734	+	2.41269i	−0.532043	+	0.292582i
$69$	1.04147	−	0.102576i	0.125378	−	0.0123487i
$70$	0.101213	−	2.34511i	0.0120973	−	0.280294i
$71$	13.0171	+	8.69775i	1.54485	+	1.03223i	0.978049	+	0.208375i	$0.0668175\pi$
$71$	13.0171	+	8.69775i	1.54485	+	1.03223i	0.566797	+	0.823858i	$0.308182\pi$
$72$	−2.64564	+	1.00029i	−0.311792	+	0.117885i
$73$	−2.96864	−	4.44289i	−0.347453	−	0.520001i	0.616046	−	0.787710i	$-0.288733\pi$
$73$	−2.96864	−	4.44289i	−0.347453	−	0.520001i	−0.963500	+	0.267709i	$0.913733\pi$
$74$	1.69730	+	0.414427i	0.197307	+	0.0481761i
$75$	−0.595006	−	1.11318i	−0.0687054	−	0.128539i
$76$	0.179547	+	15.0749i	0.0205955	+	1.72921i
$77$	0.101349	−	1.02902i	0.0115498	−	0.117267i
$78$	−2.68499	+	2.01621i	−0.304015	+	0.228291i
$79$	2.08586	+	5.03571i	0.234678	+	0.566562i	0.996717	−	0.0809692i	$-0.0258015\pi$
$79$	2.08586	+	5.03571i	0.234678	+	0.566562i	−0.762039	+	0.647531i	$0.775802\pi$
$80$	7.34478	−	2.42049i	0.821171	−	0.270619i
$81$	0.382683	−	0.923880i	0.0425204	−	0.102653i
$82$	3.30470	+	12.8675i	0.364943	+	1.42098i
$83$	−5.32161	−	6.48441i	−0.584123	−	0.711756i	0.394157	−	0.919043i	$-0.371037\pi$
$83$	−5.32161	−	6.48441i	−0.584123	−	0.711756i	−0.978280	+	0.207287i	$0.933537\pi$
$84$	1.41619	−	0.970860i	0.154519	−	0.105930i
$85$	−1.40500	+	4.63167i	−0.152394	+	0.502375i
$86$	−10.0484	+	1.55174i	−1.08354	+	0.167329i
$87$	0.785780	+	0.156301i	0.0842444	+	0.0167573i
$88$	3.28917	−	0.886628i	0.350627	−	0.0945148i
$89$	−0.166186	−	0.835474i	−0.0176157	−	0.0885601i	0.970977	−	0.239171i	$-0.0768758\pi$
$89$	−0.166186	−	0.835474i	−0.0176157	−	0.0885601i	−0.988593	+	0.150611i	$0.951876\pi$
$90$	−1.15426	+	2.47856i	−0.121670	+	0.261263i
$91$	1.29310	−	1.57565i	0.135554	−	0.165173i
$92$	−1.34697	−	1.60200i	−0.140432	−	0.167020i
$93$	−2.65705	−	1.42022i	−0.275524	−	0.147270i
$94$	9.35733	−	0.515569i	0.965134	−	0.0531769i
$95$	10.3050	+	10.3050i	1.05727	+	1.05727i
$96$	4.64193	+	3.23303i	0.473765	+	0.329969i
$97$	−11.0074	+	11.0074i	−1.11763	+	1.11763i	−0.125547	+	0.992088i	$0.540069\pi$
$97$	−11.0074	+	11.0074i	−1.11763	+	1.11763i	−0.992088	+	0.125547i	$0.959931\pi$
$98$	5.90892	−	6.59803i	0.596891	−	0.666502i
$99$	−0.567753	+	1.06219i	−0.0570613	+	0.106754i
$100$	−1.16341	+	2.24037i	−0.116341	+	0.224037i
$101$	−3.79676	−	3.11592i	−0.377791	−	0.310045i	0.426265	−	0.904598i	$-0.359829\pi$
$101$	−3.79676	−	3.11592i	−0.377791	−	0.310045i	−0.804057	+	0.594553i	$0.797329\pi$
$102$	−3.32634	+	1.21258i	−0.329357	+	0.120063i
$103$	−8.67332	+	1.72523i	−0.854608	+	0.169992i	−0.602905	−	0.797813i	$-0.705990\pi$
$103$	−8.67332	+	1.72523i	−0.854608	+	0.169992i	−0.251702	+	0.967805i	$0.580990\pi$
$104$	6.36228	+	2.14905i	0.623873	+	0.210732i
$105$	0.323808	−	1.62789i	0.0316005	−	0.158866i
$106$	1.81441	−	2.47714i	0.176231	−	0.240601i
$107$	−10.3395	−	3.13647i	−0.999562	−	0.303214i	−0.252232	−	0.967667i	$-0.581165\pi$
$107$	−10.3395	−	3.13647i	−0.999562	−	0.303214i	−0.747330	+	0.664453i	$0.768665\pi$
$108$	−1.95678	+	0.413514i	−0.188292	+	0.0397904i
$109$	3.81639	−	3.13203i	0.365544	−	0.299994i	−0.433634	−	0.901089i	$-0.642769\pi$
$109$	3.81639	−	3.13203i	0.365544	−	0.299994i	0.799177	+	0.601095i	$0.205269\pi$
$110$	1.67610	−	2.83455i	0.159810	−	0.270264i
$111$	1.14139	+	0.472779i	0.108336	+	0.0448742i
$112$	−3.20304	−	1.23821i	−0.302659	−	0.117000i
$113$	11.9507	−	4.95014i	1.12423	−	0.465670i	0.258412	−	0.966035i	$-0.416801\pi$
$113$	11.9507	−	4.95014i	1.12423	−	0.465670i	0.865815	+	0.500365i	$0.166801\pi$
$114$	−1.50138	+	10.5541i	−0.140617	+	0.988481i
$115$	−2.01351	−	0.198313i	−0.187761	−	0.0184928i
$116$	−0.630779	−	1.47297i	−0.0585664	−	0.136762i
$117$	−2.09391	+	1.11922i	−0.193582	+	0.103472i
$118$	−3.67556	−	6.05030i	−0.338363	−	0.556975i
$119$	1.78705	−	1.19407i	0.163819	−	0.109460i
$120$	5.39391	−	0.898864i	0.492395	−	0.0820547i
$121$	−5.30537	+	7.94004i	−0.482306	+	0.721822i
$122$	−4.04410	−	4.40892i	−0.366135	−	0.399165i
$123$	0.920772	+	9.34876i	0.0830232	+	0.842949i
$124$	0.661986	+	5.98913i	0.0594481	+	0.537839i
$125$	3.51447	+	11.5856i	0.314343	+	1.03625i
$126$	1.09444	−	0.525628i	0.0975003	−	0.0468267i
$127$	−17.7242			−1.57277			−0.786386	−	0.617736i	$-0.788050\pi$
$127$	−17.7242			−1.57277			−0.786386	+	0.617736i	$0.788050\pi$
$128$	0.0837580	−	11.3134i	0.00740323	−	0.999973i
$129$	−7.18948			−0.632999
$130$	5.85170	−	2.81041i	0.513228	−	0.246489i
$131$	−1.34537	−	4.43510i	−0.117546	−	0.387497i	0.878348	−	0.478021i	$-0.158646\pi$
$131$	−1.34537	−	4.43510i	−0.117546	−	0.387497i	−0.995894	+	0.0905244i	$0.971146\pi$
$132$	2.39423	−	0.264637i	0.208391	−	0.0230337i
$133$	−0.634313	−	6.44029i	−0.0550019	−	0.558444i
$134$	−3.73624	−	4.07330i	−0.322762	−	0.351879i
$135$	−1.07410	+	1.60751i	−0.0924441	+	0.138352i
$136$	5.76190	+	4.11584i	0.494079	+	0.352930i
$137$	−17.8468	+	11.9249i	−1.52476	+	1.01881i	−0.540646	+	0.841250i	$0.681820\pi$
$137$	−17.8468	+	11.9249i	−1.52476	+	1.01881i	−0.984110	+	0.177559i	$0.943180\pi$
$138$	−0.768412	−	1.26487i	−0.0654116	−	0.107673i
$139$	−6.58190	+	3.51810i	−0.558269	+	0.298401i	−0.726297	−	0.687381i	$-0.758760\pi$
$139$	−6.58190	+	3.51810i	−0.558269	+	0.298401i	0.168028	+	0.985782i	$0.446260\pi$
$140$	−3.05154	+	1.30678i	−0.257902	+	0.110443i
$141$	6.59475	+	0.649527i	0.555379	+	0.0547000i
$142$	3.11818	−	21.9196i	0.261672	−	1.83945i
$143$	2.64191	−	1.09431i	0.220927	−	0.0915110i
$144$	2.89499	+	2.76026i	0.241249	+	0.230022i
$145$	−1.43103	−	0.592753i	−0.118841	−	0.0492254i
$146$	−3.84627	+	6.50464i	−0.318320	+	0.538328i
$147$	4.84133	−	3.97318i	0.399306	−	0.327702i
$148$	−0.510869	−	2.41747i	−0.0419932	−	0.198715i
$149$	−9.28237	−	2.81577i	−0.760441	−	0.230677i	−0.113833	−	0.993500i	$-0.536313\pi$
$149$	−9.28237	−	2.81577i	−0.760441	−	0.230677i	−0.646608	+	0.762823i	$0.723813\pi$
$150$	−1.05479	+	1.44007i	−0.0861236	+	0.117581i
$151$	3.71798	−	18.6915i	0.302565	−	1.52109i	−0.467998	−	0.883730i	$-0.655024\pi$
$151$	3.71798	−	18.6915i	0.302565	−	1.52109i	0.770562	−	0.637365i	$-0.219976\pi$
$152$	19.1078	−	9.45861i	1.54984	−	0.767195i
$153$	−2.45538	+	0.488406i	−0.198506	+	0.0394853i
$154$	−1.37385	+	0.500820i	−0.110708	+	0.0403572i
$155$	4.50259	+	3.69518i	0.361657	+	0.296804i
$156$	4.21419	+	2.18841i	0.337405	+	0.175213i
$157$	5.44340	−	10.1839i	0.434430	−	0.812762i	−0.565498	−	0.824750i	$-0.691316\pi$
$157$	5.44340	−	10.1839i	0.434430	−	0.812762i	0.999928	+	0.0119877i	$0.00381589\pi$
$158$	5.14250	−	5.74223i	0.409115	−	0.456827i
$159$	1.53528	−	1.53528i	0.121755	−	0.121755i
$160$	−7.58255	−	7.88124i	−0.599453	−	0.623067i
$161$	0.635292	+	0.635292i	0.0500681	+	0.0500681i
$162$	−1.41207	+	0.0778022i	−0.110943	+	0.00611272i
$163$	−11.4695	−	6.13055i	−0.898357	−	0.480182i	−0.0435049	−	0.999053i	$-0.513852\pi$
$163$	−11.4695	−	6.13055i	−0.898357	−	0.480182i	−0.854852	+	0.518871i	$0.826352\pi$
$164$	14.3803	−	12.0911i	1.12292	−	0.944155i
$165$	1.47720	−	1.79997i	0.115000	−	0.140127i
$166$	−5.00820	+	10.7542i	−0.388711	+	0.834685i
$167$	1.88679	+	9.48552i	0.146004	+	0.734012i	0.982533	+	0.186089i	$0.0595812\pi$
$167$	1.88679	+	9.48552i	0.146004	+	0.734012i	−0.836529	+	0.547923i	$0.815419\pi$
$168$	−2.10473	−	1.21096i	−0.162384	−	0.0934273i
$169$	−7.22139	−	1.43642i	−0.555492	−	0.110494i
$170$	6.76472	−	1.04466i	0.518830	−	0.0801216i
$171$	−2.18817	+	7.21342i	−0.167333	+	0.551624i
$172$	8.13034	+	11.8597i	0.619933	+	0.904293i
$173$	−3.32777	−	4.05490i	−0.253006	−	0.308288i	0.630983	−	0.775797i	$-0.282652\pi$
$173$	−3.32777	−	4.05490i	−0.253006	−	0.308288i	−0.883989	+	0.467508i	$0.845152\pi$
$174$	−0.281844	−	1.09742i	−0.0213665	−	0.0831950i
$175$	0.414686	−	1.00114i	0.0313473	−	0.0756792i
$176$	−3.14410	−	3.65022i	−0.236995	−	0.275146i
$177$	−1.91563	−	4.62475i	−0.143988	−	0.347617i
$178$	−0.963323	+	0.723380i	−0.0722041	+	0.0542196i
$179$	1.24971	−	12.6886i	0.0934080	−	0.948387i	−0.828244	−	0.560368i	$-0.810660\pi$
$179$	1.24971	−	12.6886i	0.0934080	−	0.948387i	0.921652	−	0.388019i	$-0.126840\pi$
$180$	3.86639	−	0.0460499i	0.288184	−	0.00343236i
$181$	10.8003	+	20.2060i	0.802781	+	1.50190i	0.863842	+	0.503763i	$0.168052\pi$
$181$	10.8003	+	20.2060i	0.802781	+	1.50190i	−0.0610610	+	0.998134i	$0.519448\pi$
$182$	−2.80037	−	0.683759i	−0.207577	−	0.0506836i
$183$	−2.35031	−	3.51749i	−0.173740	−	0.260020i
$184$	−1.21755	+	2.69797i	−0.0897591	+	0.198897i
$185$	−1.98597	−	1.32698i	−0.146011	−	0.0975616i
$186$	−0.183720	+	4.25678i	−0.0134710	+	0.312122i
$187$	3.00070	−	0.295543i	0.219433	−	0.0216122i
$188$	−6.38633	−	11.6132i	−0.465771	−	0.846977i
$189$	0.821543	−	0.249212i	0.0597585	−	0.0181275i
$190$	6.82763	−	19.4462i	0.495328	−	1.41078i
$191$			14.4522i			1.04573i	0.852417	+	0.522863i	$0.175136\pi$
$191$			14.4522i			1.04573i	−0.852417	+	0.522863i	$0.824864\pi$
$192$	1.27944	−	7.89703i	0.0923360	−	0.569919i
$193$			8.31344i			0.598414i	0.954188	+	0.299207i	$0.0967222\pi$
$193$			8.31344i			0.598414i	−0.954188	+	0.299207i	$0.903278\pi$
$194$	20.7717	+	7.29302i	1.49132	+	0.523608i
$195$	4.39259	−	1.33248i	0.314560	−	0.0954208i
$196$	−12.0290	−	3.49307i	−0.859215	−	0.249505i
$197$	−1.80037	+	0.177321i	−0.128271	+	0.0126336i	−0.161949	−	0.986799i	$-0.551778\pi$
$197$	−1.80037	+	0.177321i	−0.128271	+	0.0126336i	0.0336777	+	0.999433i	$0.489278\pi$
$198$	1.70170	+	0.0734443i	0.120935	+	0.00521946i
$199$	1.95970	+	1.30943i	0.138919	+	0.0928228i	0.623088	−	0.782152i	$-0.285878\pi$
$199$	1.95970	+	1.30943i	0.138919	+	0.0928228i	−0.484169	+	0.874975i	$0.660878\pi$
$200$	3.56835	+	0.111450i	0.252321	+	0.00788072i
$201$	−2.17139	−	3.24972i	−0.153158	−	0.229218i
$202$	−1.64762	+	6.74789i	−0.115926	+	0.474780i
$203$	0.324234	+	0.606600i	0.0227568	+	0.0425749i
$204$	3.58238	+	3.49805i	0.250817	+	0.244913i
$205$	1.78016	−	18.0743i	0.124332	−	1.26236i
$206$	7.50964	+	10.0006i	0.523221	+	0.696772i
$207$	−0.400482	−	0.966849i	−0.0278354	−	0.0672006i
$208$	−1.15572	−	9.42648i	−0.0801344	−	0.653609i
$209$	3.47431	−	8.38773i	0.240323	−	0.580191i
$210$	−2.27351	+	0.583894i	−0.156887	+	0.0402925i
$211$	−17.3488	−	21.1395i	−1.19434	−	1.45531i	−0.858064	−	0.513543i	$-0.828333\pi$
$211$	−17.3488	−	21.1395i	−1.19434	−	1.45531i	−0.336275	−	0.941764i	$-0.609167\pi$
$212$	−4.26877	−	0.796382i	−0.293180	−	0.0546957i
$213$	4.54456	−	14.9814i	0.311388	−	1.02651i
$214$	2.33205	+	15.1013i	0.159416	+	1.03230i
$215$	13.6326	+	2.71169i	0.929735	+	0.184936i
$216$	1.72521	+	2.24135i	0.117385	+	0.152505i
$217$	−0.504605	−	2.53682i	−0.0342548	−	0.172211i
$218$	−6.32935	−	2.94757i	−0.428678	−	0.199634i
$219$	−3.38983	+	4.13052i	−0.229063	+	0.279114i
$220$	−4.63972	−	0.401241i	−0.312810	−	0.0270517i
$221$	5.24209	+	2.80196i	0.352621	+	0.188480i
$222$	−0.0961193	−	1.74452i	−0.00645111	−	0.117084i
$223$	−11.5721	−	11.5721i	−0.774928	−	0.774928i	0.204036	−	0.978963i	$-0.434594\pi$
$223$	−11.5721	−	11.5721i	−0.774928	−	0.774928i	−0.978963	+	0.204036i	$0.934594\pi$
$224$	0.382593	+	4.84137i	0.0255630	+	0.323478i
$225$	−0.892524	+	0.892524i	−0.0595016	+	0.0595016i
$226$	−13.6274	−	12.2041i	−0.906480	−	0.811806i
$227$	1.52619	−	2.85531i	0.101297	−	0.189513i	−0.826167	−	0.563425i	$-0.809484\pi$
$227$	1.52619	−	2.85531i	0.101297	−	0.189513i	0.927465	+	0.373911i	$0.121984\pi$
$228$	14.3737	−	4.54784i	0.951921	−	0.301188i
$229$	8.98251	+	7.37175i	0.593581	+	0.487139i	0.882562	−	0.470196i	$-0.155817\pi$
$229$	8.98251	+	7.37175i	0.593581	+	0.487139i	−0.288982	+	0.957335i	$0.593317\pi$
$230$	0.979973	+	2.68826i	0.0646175	+	0.177259i
$231$	−1.01413	+	0.201722i	−0.0667246	+	0.0132724i
$232$	−1.49156	+	1.70596i	−0.0979256	+	0.112002i
$233$	4.81874	−	24.2254i	0.315686	−	1.58706i	−0.418568	−	0.908186i	$-0.637468\pi$
$233$	4.81874	−	24.2254i	0.315686	−	1.58706i	0.734254	−	0.678875i	$-0.237532\pi$
$234$	2.70881	+	1.98409i	0.177080	+	0.129704i
$235$	−12.2599	−	3.71900i	−0.799747	−	0.242601i
$236$	−5.46260	+	8.38998i	−0.355585	+	0.546141i
$237$	4.21338	−	3.45784i	0.273689	−	0.224611i
$238$	−2.61635	−	1.54708i	−0.169593	−	0.100282i
$239$	−22.0976	−	9.15310i	−1.42937	−	0.592065i	−0.472175	−	0.881505i	$-0.656531\pi$
$239$	−22.0976	−	9.15310i	−1.42937	−	0.592065i	−0.957196	+	0.289439i	$0.906531\pi$
$240$	−4.44834	−	6.32588i	−0.287139	−	0.408334i
$241$	10.8791	−	4.50628i	0.700786	−	0.290275i	−0.00369982	−	0.999993i	$-0.501178\pi$
$241$	10.8791	−	4.50628i	0.700786	−	0.290275i	0.704486	+	0.709718i	$0.251178\pi$
$242$	13.3703	+	1.90200i	0.859475	+	0.122265i
$243$	−0.995185	−	0.0980171i	−0.0638411	−	0.00628780i
$244$	−3.14452	+	7.85485i	−0.201307	+	0.502855i
$245$	−10.6787	+	5.70786i	−0.682234	+	0.364662i
$246$	11.3541	−	6.89765i	0.723914	−	0.439778i
$247$	14.8810	−	9.94316i	0.946855	−	0.632668i
$248$	7.22970	−	4.51079i	0.459086	−	0.286435i
$249$	−4.66041	+	6.97479i	−0.295341	+	0.442009i
$250$	12.6177	−	11.5737i	0.798016	−	0.731983i
$251$	0.669459	+	6.79713i	0.0422559	+	0.429031i	0.992918	+	0.118803i	$0.0379056\pi$
$251$	0.669459	+	6.79713i	0.0422559	+	0.429031i	−0.950662	+	0.310229i	$0.899594\pi$
$252$	−1.34015	−	1.07338i	−0.0844217	−	0.0676167i
$253$	0.365881	+	1.20615i	0.0230028	+	0.0758299i
$254$	10.8518	+	22.5950i	0.680901	+	1.41774i
$255$	4.84008			0.303098
$256$	−14.4737	+	6.81992i	−0.904608	+	0.426245i
$257$	−9.48295			−0.591530			−0.295765	−	0.955261i	$-0.595575\pi$
$257$	−9.48295			−0.591530			−0.295765	+	0.955261i	$0.595575\pi$
$258$	4.40181	+	9.16523i	0.274045	+	0.570602i
$259$	0.307885	+	1.01496i	0.0191310	+	0.0630666i
$260$	−7.16548	−	5.73911i	−0.444384	−	0.355925i
$261$	−0.0785288	−	0.797316i	−0.00486081	−	0.0493526i
$262$	−4.83020	+	4.43052i	−0.298411	+	0.273718i
$263$	−2.10764	+	3.15430i	−0.129963	+	0.194503i	−0.890744	−	0.454506i	$-0.849816\pi$
$263$	−2.10764	+	3.15430i	−0.129963	+	0.194503i	0.760781	+	0.649008i	$0.224816\pi$
$264$	−1.80325	−	2.89016i	−0.110982	−	0.177877i
$265$	−3.49024	+	2.33210i	−0.214404	+	0.143260i
$266$	−7.82179	+	4.75174i	−0.479585	+	0.291348i
$267$	−0.751257	+	0.401555i	−0.0459762	+	0.0245748i
$268$	−2.90514	+	7.25690i	−0.177460	+	0.443286i
$269$	21.9416	+	2.16106i	1.33780	+	0.131762i	0.741476	−	0.670980i	$-0.234126\pi$
$269$	21.9416	+	2.16106i	1.33780	+	0.131762i	0.596327	+	0.802742i	$0.296626\pi$
$270$	2.70690	+	0.385070i	0.164736	+	0.0234346i
$271$	−25.5722	+	10.5924i	−1.55340	+	0.643440i	−0.983928	−	0.178568i	$-0.942854\pi$
$271$	−25.5722	+	10.5924i	−1.55340	+	0.643440i	−0.569475	+	0.822009i	$0.692854\pi$
$272$	1.71915	−	9.86528i	0.104239	−	0.598171i
$273$	−1.88317	−	0.780035i	−0.113975	−	0.0472099i
$274$	26.1288	+	15.4502i	1.57850	+	0.933383i
$275$	1.17515	−	0.964419i	0.0708641	−	0.0581567i
$276$	−1.14201	+	1.75401i	−0.0687410	+	0.105579i
$277$	26.7157	+	8.10412i	1.60519	+	0.486930i	0.960678	−	0.277664i	$-0.0895601\pi$
$277$	26.7157	+	8.10412i	1.60519	+	0.486930i	0.644513	+	0.764593i	$0.277060\pi$
$278$	8.51471	+	6.23669i	0.510679	+	0.374052i
$279$	−0.587768	+	2.95491i	−0.0351888	+	0.176906i
$280$	3.53422	+	3.09005i	0.211210	+	0.184666i
$281$	9.01383	−	1.79296i	0.537720	−	0.106959i	0.0812429	−	0.996694i	$-0.474111\pi$
$281$	9.01383	−	1.79296i	0.537720	−	0.106959i	0.456477	+	0.889735i	$0.349111\pi$
$282$	−3.20966	−	8.80474i	−0.191132	−	0.524315i
$283$	6.03263	+	4.95085i	0.358603	+	0.294298i	0.796393	−	0.604779i	$-0.206739\pi$
$283$	6.03263	+	4.95085i	0.358603	+	0.294298i	−0.437790	+	0.899077i	$0.644239\pi$
$284$	−29.8525	+	9.44532i	−1.77142	+	0.560477i
$285$	6.86989	−	12.8527i	0.406937	−	0.761326i
$286$	−3.01257	−	2.69793i	−0.178137	−	0.159532i
$287$	−5.70270	+	5.70270i	−0.336620	+	0.336620i
$288$	1.74633	−	5.38055i	0.102904	−	0.317052i
$289$	−7.58906	−	7.58906i	−0.446415	−	0.446415i
$290$	0.120511	+	2.18721i	0.00707663	+	0.128437i
$291$	13.7287	+	7.33816i	0.804793	+	0.430171i
$292$	10.6471	+	0.920757i	0.623074	+	0.0538832i
$293$	−2.57738	+	3.14055i	−0.150572	+	0.183473i	−0.842834	−	0.538174i	$-0.819114\pi$
$293$	−2.57738	+	3.14055i	−0.150572	+	0.183473i	0.692262	+	0.721647i	$0.256614\pi$
$294$	−8.02919	−	3.73918i	−0.468272	−	0.218073i
$295$	1.88806	+	9.49191i	0.109927	+	0.552640i
$296$	−2.76904	+	2.13138i	−0.160947	+	0.123884i
$297$	1.18126	+	0.234968i	0.0685438	+	0.0136342i
$298$	2.09361	+	13.5572i	0.121279	+	0.785350i
$299$	−0.721268	+	2.37770i	−0.0417120	+	0.137506i
$300$	2.48162	+	0.462971i	0.143276	+	0.0267297i
$301$	−3.91563	−	4.77121i	−0.225693	−	0.275008i
$302$	−26.1045	+	6.70429i	−1.50215	+	0.385789i
$303$	−1.87961	+	4.53777i	−0.107981	+	0.260688i
$304$	−23.7568	−	18.5677i	−1.36255	−	1.06493i
$305$	3.12992	+	7.55629i	0.179218	+	0.432672i
$306$	2.12595	+	2.83112i	0.121532	+	0.161844i
$307$	−1.16290	+	11.8071i	−0.0663704	+	0.673870i	0.903227	+	0.429163i	$0.141192\pi$
$307$	−1.16290	+	11.8071i	−0.0663704	+	0.673870i	−0.969597	+	0.244706i	$0.921308\pi$
$308$	1.47960	+	1.44477i	0.0843080	+	0.0823234i
$309$	4.16868	+	7.79904i	0.237148	+	0.443672i
$310$	1.95392	−	8.00235i	0.110975	−	0.454503i
$311$	3.08544	+	4.61769i	0.174959	+	0.261845i	0.908577	−	0.417717i	$-0.137170\pi$
$311$	3.08544	+	4.61769i	0.174959	+	0.261845i	−0.733618	+	0.679562i	$0.762170\pi$
$312$	0.209640	−	6.71216i	0.0118686	−	0.380001i
$313$	9.28404	+	6.20339i	0.524765	+	0.350637i	0.789565	−	0.613667i	$-0.210306\pi$
$313$	9.28404	+	6.20339i	0.524765	+	0.350637i	−0.264801	+	0.964303i	$0.585306\pi$
$314$	−16.3153	−	0.704156i	−0.920724	−	0.0397378i
$315$	−1.65179	+	0.162688i	−0.0930681	+	0.00916641i
$316$	−10.4688	−	3.04000i	−0.588915	−	0.171013i
$317$	−29.8999	+	9.07003i	−1.67934	+	0.509424i	−0.978910	−	0.204293i	$-0.934511\pi$
$317$	−29.8999	+	9.07003i	−1.67934	+	0.509424i	−0.700435	+	0.713716i	$0.747011\pi$
$318$	−2.89717	−	1.01720i	−0.162465	−	0.0570420i
$319$			0.964938i			0.0540262i
$320$	−5.40462	+	14.4917i	−0.302128	+	0.810108i
$321$			10.8048i			0.603065i
$322$	0.420916	−	1.19884i	0.0234567	−	0.0668087i
$323$	18.0587	−	5.47805i	1.00481	−	0.304807i
$324$	0.963733	+	1.75249i	0.0535407	+	0.0973605i
$325$	2.98241	−	0.293742i	0.165434	−	0.0162939i
$326$	−0.793046	+	18.3749i	−0.0439227	+	1.01769i
$327$	−4.10500	−	2.74287i	−0.227007	−	0.151681i
$328$	−24.2183	−	10.9293i	−1.33723	−	0.603472i
$329$	3.16067	+	4.73028i	0.174253	+	0.260789i
$330$	−3.19904	−	0.781103i	−0.176101	−	0.0429983i
$331$	10.0571	+	18.8155i	0.552788	+	1.03419i	0.990814	+	0.135232i	$0.0431779\pi$
$331$	10.0571	+	18.8155i	0.552788	+	1.03419i	−0.438026	+	0.898962i	$0.644322\pi$
$332$	16.7758	−	0.199805i	0.920693	−	0.0109657i
$333$	0.121094	−	1.22948i	0.00663588	−	0.0673753i
$334$	10.9370	−	8.21287i	0.598449	−	0.449388i
$335$	2.89165	+	6.98107i	0.157988	+	0.381416i
$336$	−0.255104	+	3.42455i	−0.0139171	+	0.186825i
$337$	−11.1873	+	27.0084i	−0.609409	+	1.47124i	0.254236	+	0.967142i	$0.418176\pi$
$337$	−11.1873	+	27.0084i	−0.609409	+	1.47124i	−0.863645	+	0.504101i	$0.831824\pi$
$338$	2.59017	+	10.0854i	0.140887	+	0.548572i
$339$	−8.20609	−	9.99915i	−0.445694	−	0.543079i
$340$	−5.47348	−	7.98414i	−0.296841	−	0.433001i
$341$	1.05334	−	3.47239i	0.0570414	−	0.188040i
$342$	10.5355	−	1.62696i	0.569693	−	0.0879761i
$343$	11.1676	+	2.22137i	0.602994	+	0.119943i
$344$	10.1410	−	17.6258i	0.546766	−	0.950320i
$345$	0.394717	+	1.98438i	0.0212509	+	0.106835i
$346$	−3.13178	+	6.72491i	−0.168366	+	0.361534i
$347$	−0.885524	+	1.07901i	−0.0475374	+	0.0579245i	−0.796236	−	0.604986i	$-0.793179\pi$
$347$	−0.885524	+	1.07901i	−0.0475374	+	0.0579245i	0.748699	+	0.662910i	$0.230679\pi$
$348$	−1.22644	+	1.03120i	−0.0657440	+	0.0552780i
$349$	15.4992	+	8.28449i	0.829653	+	0.443459i	0.830820	−	0.556541i	$-0.187872\pi$
$349$	15.4992	+	8.28449i	0.829653	+	0.443459i	−0.00116777	+	0.999999i	$0.500372\pi$
$350$	−1.53016	+	0.0843086i	−0.0817905	+	0.00450649i
$351$	1.67886	+	1.67886i	0.0896109	+	0.0896109i
$352$	−2.72835	+	6.24300i	−0.145422	+	0.332753i
$353$	22.1434	−	22.1434i	1.17858	−	1.17858i	0.198468	−	0.980107i	$-0.436404\pi$
$353$	22.1434	−	22.1434i	1.17858	−	1.17858i	0.980107	−	0.198468i	$-0.0635965\pi$
$354$	−4.72282	+	5.27360i	−0.251015	+	0.280289i
$355$	−14.2679	+	26.6934i	−0.757264	+	1.41674i
$356$	1.51197	+	0.785160i	0.0801344	+	0.0416134i
$357$	−1.66141	−	1.36348i	−0.0879310	−	0.0721631i
$358$	−16.9406	+	6.17550i	−0.895341	+	0.326385i
$359$	−8.13745	+	1.61864i	−0.429478	+	0.0854285i	−0.405096	−	0.914274i	$-0.632762\pi$
$359$	−8.13745	+	1.61864i	−0.429478	+	0.0854285i	−0.0243822	+	0.999703i	$0.507762\pi$
$360$	−2.42593	−	4.90073i	−0.127858	−	0.258291i
$361$	7.37861	−	37.0948i	0.388348	−	1.95236i
$362$	19.1462	−	26.1396i	1.00630	−	1.37387i
$363$	9.13821	+	2.77205i	0.479632	+	0.145495i
$364$	0.842879	+	3.98857i	0.0441788	+	0.209058i
$365$	7.98567	−	6.55367i	0.417989	−	0.343035i
$366$	−3.04514	+	5.14980i	−0.159172	+	0.269185i
$367$	−21.2161	−	8.78798i	−1.10747	−	0.458729i	−0.247404	−	0.968912i	$-0.579578\pi$
$367$	−21.2161	−	8.78798i	−1.10747	−	0.458729i	−0.860066	+	0.510183i	$0.829578\pi$
$368$	4.18485	−	0.0996998i	0.218150	−	0.00519721i
$369$	8.67892	−	3.59492i	0.451806	−	0.187144i
$370$	−0.475728	+	3.34419i	−0.0247319	+	0.173856i
$371$	1.85503	+	0.182705i	0.0963084	+	0.00948555i
$372$	5.53907	−	2.37203i	0.287188	−	0.122984i
$373$	−5.64765	+	3.01873i	−0.292424	+	0.156304i	−0.611085	−	0.791565i	$-0.709267\pi$
$373$	−5.64765	+	3.01873i	−0.292424	+	0.156304i	0.318661	+	0.947869i	$0.396767\pi$
$374$	−2.21396	−	3.64437i	−0.114481	−	0.188446i
$375$	10.0666	−	6.72627i	0.519835	−	0.347343i
$376$	−10.8945	+	15.2516i	−0.561841	+	0.786541i
$377$	−1.05681	+	1.58162i	−0.0544283	+	0.0814576i
$378$	−0.820693	−	0.894730i	−0.0422119	−	0.0460199i
$379$	−0.646335	−	6.56234i	−0.0332000	−	0.337085i	−0.997409	−	0.0719413i	$-0.977081\pi$
$379$	−0.646335	−	6.56234i	−0.0332000	−	0.337085i	0.964209	−	0.265144i	$-0.0854194\pi$
$380$	−28.9705	+	3.20215i	−1.48616	+	0.164267i
$381$	5.14507	+	16.9610i	0.263590	+	0.868940i
$382$	18.4238	−	8.84846i	0.942645	−	0.452726i
$383$	−20.4199			−1.04341			−0.521704	−	0.853127i	$-0.674703\pi$
$383$	−20.4199			−1.04341			−0.521704	+	0.853127i	$0.674703\pi$
$384$	−10.8506	+	3.20395i	−0.553715	+	0.163501i
$385$	1.99906			0.101881
$386$	10.5981	−	5.08995i	0.539427	−	0.259072i
$387$	2.08700	+	6.87991i	0.106088	+	0.349725i
$388$	−3.42042	−	30.9452i	−0.173645	−	1.57101i
$389$	−0.101027	−	1.02575i	−0.00512228	−	0.0520074i	0.992284	−	0.123987i	$-0.0395682\pi$
$389$	−0.101027	−	1.02575i	−0.00512228	−	0.0520074i	−0.997406	+	0.0719800i	$0.977068\pi$
$390$	−4.38805	−	4.78391i	−0.222198	−	0.242242i
$391$	−1.45555	+	2.17839i	−0.0736104	+	0.110166i
$392$	2.91183	+	17.4734i	0.147070	+	0.882538i
$393$	−3.85359	+	2.57488i	−0.194388	+	0.129886i
$394$	1.32834	+	2.18657i	0.0669209	+	0.110158i
$395$	−9.29357	+	4.96752i	−0.467610	+	0.249943i
$396$	−0.948251	−	2.21431i	−0.0476514	−	0.111274i
$397$	−3.28254	−	0.323302i	−0.164746	−	0.0162260i	0.0153079	−	0.999883i	$-0.495127\pi$
$397$	−3.28254	−	0.323302i	−0.164746	−	0.0162260i	−0.180054	+	0.983657i	$0.557627\pi$
$398$	0.469435	−	3.29995i	0.0235307	−	0.165411i
$399$	−5.97884	+	2.47652i	−0.299316	+	0.123981i
$400$	−2.04267	−	4.61721i	−0.102133	−	0.230861i
$401$	32.1087	+	13.2999i	1.60343	+	0.664163i	0.991896	−	0.127054i	$-0.0405523\pi$
$401$	32.1087	+	13.2999i	1.60343	+	0.664163i	0.611535	+	0.791217i	$0.290552\pi$
$402$	−2.81333	+	4.75778i	−0.140316	+	0.237296i
$403$	5.52949	−	4.53793i	0.275443	−	0.226051i
$404$	9.61104	−	2.03104i	0.478167	−	0.101048i
$405$	1.85009	+	0.561217i	0.0919315	+	0.0278871i
$406$	0.574785	−	0.784732i	0.0285261	−	0.0389456i
$407$	−0.290287	+	1.45937i	−0.0143890	+	0.0723383i
$408$	2.26602	−	6.70856i	0.112185	−	0.332123i
$409$	18.1535	−	3.61096i	0.897633	−	0.178550i	0.275351	−	0.961344i	$-0.411206\pi$
$409$	18.1535	−	3.61096i	0.897633	−	0.178550i	0.622282	+	0.782793i	$0.286206\pi$
$410$	−24.1312	+	8.79672i	−1.19175	+	0.434439i
$411$	16.5920	+	13.6167i	0.818425	+	0.671664i
$412$	8.15099	−	15.6963i	0.401571	−	0.773300i
$413$	2.02584	−	3.79008i	0.0996849	−	0.186497i
$414$	−0.987352	+	1.10250i	−0.0485257	+	0.0541848i
$415$	11.4677	−	11.4677i	0.562928	−	0.562928i
$416$	−11.3094	+	7.24474i	−0.554488	+	0.355203i
$417$	5.27723	+	5.27723i	0.258427	+	0.258427i
$418$	−12.8199	+	0.706352i	−0.627043	+	0.0345488i
$419$	−32.9031	−	17.5871i	−1.60742	−	0.859185i	−0.997786	−	0.0665039i	$-0.978816\pi$
$419$	−32.9031	−	17.5871i	−1.60742	−	0.859185i	−0.609636	−	0.792681i	$-0.708684\pi$
$420$	2.13633	+	2.54080i	0.104242	+	0.123978i
$421$	−16.9760	+	20.6853i	−0.827358	+	1.00814i	0.172375	+	0.985031i	$0.444856\pi$
$421$	−16.9760	+	20.6853i	−0.827358	+	1.00814i	−0.999733	+	0.0231068i	$0.992644\pi$
$422$	−16.3270	+	35.0592i	−0.794787	+	1.70666i
$423$	−1.29280	−	6.49933i	−0.0628580	−	0.316008i
$424$	1.59835	+	5.92946i	0.0776225	+	0.287960i
$425$	3.09923	+	0.616476i	0.150335	+	0.0299035i
$426$	−21.8809	+	3.37901i	−1.06013	+	0.163714i
$427$	1.05428	−	3.47549i	0.0510201	−	0.168191i
$428$	17.8235	−	12.2188i	0.861530	−	0.590617i
$429$	−1.81410	−	2.21048i	−0.0875854	−	0.106723i
$430$	−4.88975	−	19.0392i	−0.235805	−	0.918153i
$431$	7.97273	−	19.2479i	0.384033	−	0.927138i	−0.607144	−	0.794592i	$-0.707685\pi$
$431$	7.97273	−	19.2479i	0.384033	−	0.927138i	0.991177	−	0.132546i	$-0.0423151\pi$
$432$	1.80103	−	3.57159i	0.0866522	−	0.171838i
$433$	−6.06950	−	14.6531i	−0.291682	−	0.704182i	0.708317	−	0.705895i	$-0.249455\pi$
$433$	−6.06950	−	14.6531i	−0.291682	−	0.704182i	−0.999999	+	0.00171277i	$0.999455\pi$
$434$	−2.92502	+	2.19646i	−0.140405	+	0.105433i
$435$	−0.151822	+	1.54148i	−0.00727933	+	0.0739083i
$436$	0.117595	+	9.87339i	0.00563178	+	0.472850i
$437$	3.71866	+	6.95712i	0.177888	+	0.332804i
$438$	7.34107	+	1.79245i	0.350770	+	0.0856467i
$439$	16.8952	+	25.2855i	0.806364	+	1.20681i	0.975235	+	0.221171i	$0.0709879\pi$
$439$	16.8952	+	25.2855i	0.806364	+	1.20681i	−0.168871	+	0.985638i	$0.554012\pi$
$440$	2.32919	+	6.16043i	0.111040	+	0.293687i
$441$	−5.20746	−	3.47951i	−0.247974	−	0.165691i
$442$	0.362460	−	8.39819i	0.0172405	−	0.399461i
$443$	13.6317	−	1.34260i	0.647661	−	0.0637891i	0.231148	−	0.972919i	$-0.425752\pi$
$443$	13.6317	−	1.34260i	0.647661	−	0.0637891i	0.416513	+	0.909130i	$0.363252\pi$
$444$	−2.16508	+	1.19063i	−0.102750	+	0.0565046i
$445$	1.57598	−	0.478068i	0.0747086	−	0.0226626i
$446$	−7.66717	+	21.8374i	−0.363051	+	1.03403i
$447$			9.70005i			0.458796i
$448$	5.93759	−	3.45189i	0.280525	−	0.163087i
$449$		−	8.05576i		−	0.380175i	−0.981767	−	0.190087i	$-0.939123\pi$
$449$		−	8.05576i		−	0.380175i	0.981767	−	0.190087i	$-0.0608771\pi$
$450$	1.68425	+	0.591345i	0.0793964	+	0.0278763i
$451$	−10.8270	+	3.28433i	−0.509823	+	0.154653i
$452$	−7.21449	+	24.8444i	−0.339341	+	1.16858i
$453$	−18.9659	+	1.86798i	−0.891098	+	0.0877655i
$454$	−4.57440	−	0.197428i	−0.214687	−	0.00926574i
$455$	3.27663	+	2.18938i	0.153611	+	0.102640i
$456$	−14.5980	−	15.5393i	−0.683615	−	0.727694i
$457$	3.65779	+	5.47427i	0.171104	+	0.256076i	0.907104	−	0.420906i	$-0.138288\pi$
$457$	3.65779	+	5.47427i	0.171104	+	0.256076i	−0.736000	+	0.676981i	$0.763288\pi$
$458$	3.89799	−	15.9644i	0.182141	−	0.745967i
$459$	1.18014	+	2.20788i	0.0550840	+	0.103055i
$460$	2.82703	−	2.89519i	0.131811	−	0.134989i
$461$	3.69830	−	37.5494i	0.172247	−	1.74885i	−0.389032	−	0.921224i	$-0.627190\pi$
$461$	3.69830	−	37.5494i	0.172247	−	1.74885i	0.561279	−	0.827627i	$-0.310310\pi$
$462$	0.878063	+	1.16931i	0.0408512	+	0.0544014i
$463$	−8.15250	−	19.6819i	−0.378879	−	0.914695i	−0.992177	−	0.124843i	$-0.960157\pi$
$463$	−8.15250	−	19.6819i	−0.378879	−	0.914695i	0.613297	−	0.789852i	$-0.289843\pi$
$464$	3.08799	+	0.856970i	0.143356	+	0.0397838i
$465$	2.22904	−	5.38137i	0.103369	−	0.249555i
$466$	−33.8331	+	8.68920i	−1.56729	+	0.402519i
$467$	−12.7731	−	15.5641i	−0.591070	−	0.720221i	0.388472	−	0.921460i	$-0.373003\pi$
$467$	−12.7731	−	15.5641i	−0.591070	−	0.720221i	−0.979542	+	0.201240i	$0.935503\pi$
$468$	0.870861	−	4.66799i	0.0402556	−	0.215778i
$469$	0.974023	−	3.21092i	0.0449762	−	0.148267i
$470$	2.76518	+	17.9060i	0.127548	+	0.825943i
$471$	−11.3255	−	2.25278i	−0.521852	−	0.103803i
$472$	14.0401	+	1.82697i	0.646250	+	0.0840930i
$473$	−1.68930	−	8.49267i	−0.0776740	−	0.390493i
$474$	−6.98776	−	3.25419i	−0.320958	−	0.149470i
$475$	6.03600	−	7.35489i	0.276951	−	0.337466i
$476$	−0.370354	+	4.28256i	−0.0169751	+	0.196291i
$477$	−1.91484	−	1.02350i	−0.0876744	−	0.0468629i
$478$	1.86089	+	33.7742i	0.0851151	+	1.54480i
$479$	30.3688	+	30.3688i	1.38758	+	1.38758i	0.830366	+	0.557219i	$0.188131\pi$
$479$	30.3688	+	30.3688i	1.38758	+	1.38758i	0.557219	+	0.830366i	$0.311869\pi$
$480$	−5.34078	+	9.54385i	−0.243772	+	0.435615i
$481$	−2.07412	+	2.07412i	−0.0945716	+	0.0945716i
$482$	−12.4055	−	11.1098i	−0.565054	−	0.506039i
$483$	0.423521	−	0.792353i	0.0192709	−	0.0360533i
$484$	−5.76136	−	18.2091i	−0.261880	−	0.827687i
$485$	−23.2645	−	19.0926i	−1.05638	−	0.866953i
$486$	0.484355	+	1.32868i	0.0219708	+	0.0602703i
$487$	−3.66012	+	0.728043i	−0.165856	+	0.0329908i	−0.277320	−	0.960778i	$-0.589446\pi$
$487$	−3.66012	+	0.728043i	−0.165856	+	0.0329908i	0.111464	+	0.993768i	$0.464446\pi$
$488$	11.9387	−	0.800516i	0.540440	−	0.0362377i
$489$	−2.53717	+	12.7552i	−0.114735	+	0.576810i
$490$	13.8145	+	10.1186i	0.624076	+	0.457111i
$491$	−20.4660	−	6.20828i	−0.923616	−	0.280176i	−0.207563	−	0.978222i	$-0.566553\pi$
$491$	−20.4660	−	6.20828i	−0.923616	−	0.280176i	−0.716053	+	0.698046i	$0.754053\pi$
$492$	−15.7448	−	10.2513i	−0.709832	−	0.462162i
$493$	−1.55045	+	1.27242i	−0.0698288	+	0.0573070i
$494$	−21.7866	−	12.8827i	−0.980227	−	0.579619i
$495$	−2.15127	−	0.891085i	−0.0966924	−	0.0400513i
$496$	−10.1768	−	6.45474i	−0.456953	−	0.289826i
$497$	12.4173	−	5.14343i	0.556994	−	0.230714i
$498$	11.7449	+	1.67078i	0.526302	+	0.0748692i
$499$	−1.02227	−	0.100685i	−0.0457632	−	0.00450729i	0.0751096	−	0.997175i	$-0.476069\pi$
$499$	−1.02227	−	0.100685i	−0.0457632	−	0.00450729i	−0.120873	+	0.992668i	$0.538569\pi$
$500$	−22.4795	−	8.99919i	−1.00531	−	0.402456i
$501$	8.52937	−	4.55904i	0.381064	−	0.203683i
$502$	8.25518	−	5.01502i	0.368447	−	0.223831i
$503$	12.9873	−	8.67786i	0.579077	−	0.386927i	−0.231259	−	0.972892i	$-0.574285\pi$
$503$	12.9873	−	8.67786i	0.579077	−	0.386927i	0.810336	+	0.585966i	$0.199285\pi$
$504$	−0.547841	+	2.36563i	−0.0244028	+	0.105373i
$505$	5.27562	−	7.89552i	0.234762	−	0.351346i
$506$	1.31360	−	1.20490i	0.0583966	−	0.0535644i
$507$	0.721687	+	7.32741i	0.0320512	+	0.325422i
$508$	22.1603	−	27.6679i	0.983206	−	1.22757i
$509$	3.89781	+	12.8493i	0.172767	+	0.569537i	0.999971	+	0.00763496i	$0.00243031\pi$
$509$	3.89781	+	12.8493i	0.172767	+	0.569537i	−0.827204	+	0.561902i	$0.810070\pi$
$510$	−2.96337	−	6.17018i	−0.131220	−	0.273220i
$511$	−4.58738			−0.202934
$512$	17.5557	+	14.2757i	0.775861	+	0.630903i
$513$	7.53800			0.332811
$514$	5.80600	+	12.0890i	0.256092	+	0.533221i
$515$	−4.96298	−	16.3608i	−0.218695	−	0.720941i
$516$	8.98890	−	11.2229i	0.395714	−	0.494062i
$517$	0.782293	+	7.94276i	0.0344052	+	0.349322i
$518$	1.10538	−	1.01391i	0.0485675	−	0.0445487i
$519$	−2.91430	+	4.36155i	−0.127923	+	0.191451i
$520$	−2.92918	+	12.6484i	−0.128453	+	0.554671i
$521$	16.3814	−	10.9457i	0.717682	−	0.479540i	−0.142326	−	0.989820i	$-0.545458\pi$
$521$	16.3814	−	10.9457i	0.717682	−	0.479540i	0.860008	+	0.510280i	$0.170458\pi$
$522$	−0.968348	+	0.588271i	−0.0423834	+	0.0257479i
$523$	−15.4884	+	8.27873i	−0.677261	+	0.362003i	−0.773893	−	0.633317i	$-0.781693\pi$
$523$	−15.4884	+	8.27873i	−0.677261	+	0.362003i	0.0966319	+	0.995320i	$0.469193\pi$
$524$	8.60539	+	3.44498i	0.375928	+	0.150495i
$525$	−1.07841	−	0.106214i	−0.0470657	−	0.00463556i
$526$	5.31156	+	0.755597i	0.231595	+	0.0329456i
$527$	6.96837	−	2.88639i	0.303547	−	0.125733i
$528$	−2.58036	+	4.06832i	−0.112296	+	0.177051i
$529$	20.2374	+	8.38261i	0.879887	+	0.364461i
$530$	5.10991	+	3.02155i	0.221960	+	0.131248i
$531$	−3.86953	+	3.17564i	−0.167923	+	0.137811i
$532$	10.8465	+	7.06202i	0.470256	+	0.306177i
$533$	−21.3434	−	6.47446i	−0.924487	−	0.280440i
$534$	0.971869	+	0.711856i	0.0420569	+	0.0308050i
$535$	4.07530	−	20.4879i	0.176190	−	0.885769i
$536$	11.0299	−	0.739577i	0.476418	−	0.0319449i
$537$	−12.5050	+	2.48739i	−0.539629	+	0.107339i
$538$	−10.6789	−	29.2945i	−0.460402	−	1.26298i
$539$	5.83093	+	4.78532i	0.251156	+	0.206118i
$540$	−1.16642	−	3.68654i	−0.0501948	−	0.158643i
$541$	2.88580	−	5.39896i	0.124070	−	0.232119i	−0.812216	−	0.583357i	$-0.801739\pi$
$541$	2.88580	−	5.39896i	0.124070	−	0.232119i	0.936286	+	0.351237i	$0.114239\pi$
$542$	29.1600	+	26.1145i	1.25253	+	1.12171i
$543$	16.2007	−	16.2007i	0.695240	−	0.695240i
$544$	−13.6289	+	3.84849i	−0.584335	+	0.165003i
$545$	6.74930	+	6.74930i	0.289108	+	0.289108i
$546$	0.158587	+	2.87827i	0.00678688	+	0.123179i
$547$	35.0379	+	18.7282i	1.49811	+	0.800759i	0.997877	−	0.0651292i	$-0.0207460\pi$
$547$	35.0379	+	18.7282i	1.49811	+	0.800759i	0.500238	+	0.865888i	$0.333246\pi$
$548$	3.69862	−	42.7687i	0.157997	−	1.82699i
$549$	−2.68377	+	3.27018i	−0.114540	+	0.139568i
$550$	−1.94894	−	0.907620i	−0.0831033	−	0.0387010i
$551$	1.17820	+	5.92321i	0.0501930	+	0.252337i
$552$	2.93523	+	0.381946i	0.124932	+	0.0162567i
$553$	4.58950	+	0.912908i	0.195165	+	0.0388208i
$554$	−6.02564	−	39.0193i	−0.256005	−	1.65777i
$555$	−0.693346	+	2.28566i	−0.0294309	+	0.0970207i
$556$	2.73742	−	14.6731i	0.116092	−	0.622278i
$557$	−11.6209	−	14.1601i	−0.492394	−	0.599984i	0.466228	−	0.884665i	$-0.345613\pi$
$557$	−11.6209	−	14.1601i	−0.492394	−	0.599984i	−0.958623	+	0.284680i	$0.908113\pi$
$558$	4.12682	−	1.05987i	0.174702	−	0.0448679i
$559$	6.53231	−	15.7704i	0.276287	−	0.667016i
$560$	1.77538	−	6.39737i	0.0750235	−	0.270338i
$561$	−1.15387	−	2.78570i	−0.0487165	−	0.117612i
$562$	−7.80446	−	10.3932i	−0.329211	−	0.438410i
$563$	−0.656972	+	6.67034i	−0.0276880	+	0.281121i	0.971364	+	0.237595i	$0.0763592\pi$
$563$	−0.656972	+	6.67034i	−0.0276880	+	0.281121i	−0.999052	+	0.0435262i	$0.986141\pi$
$564$	−9.25924	+	9.48246i	−0.389884	+	0.399284i
$565$	11.7888	+	22.0554i	0.495961	+	0.927877i
$566$	2.61788	−	10.7217i	0.110038	−	0.450665i
$567$	−0.476963	−	0.713825i	−0.0200305	−	0.0299778i
$568$	30.3183	+	32.2733i	1.27213	+	1.35416i
$569$	2.10121	+	1.40398i	0.0880873	+	0.0588581i	0.598834	−	0.800873i	$-0.295631\pi$
$569$	2.10121	+	1.40398i	0.0880873	+	0.0588581i	−0.510747	+	0.859731i	$0.670631\pi$
$570$	−20.5908	−	0.888686i	−0.862456	−	0.0372230i
$571$	27.0247	−	2.66170i	1.13095	−	0.111389i	0.484819	−	0.874615i	$-0.338886\pi$
$571$	27.0247	−	2.66170i	1.13095	−	0.111389i	0.646132	+	0.763226i	$0.276386\pi$
$572$	−1.59489	+	5.49227i	−0.0666855	+	0.229644i
$573$	13.8299	−	4.19526i	0.577753	−	0.175259i
$574$	10.7614	+	3.77835i	0.449171	+	0.157705i
$575$			1.32092i			0.0550864i
$576$	−7.92839	+	1.06803i	−0.330349	+	0.0445014i
$577$			21.1957i			0.882391i	0.897411	+	0.441195i	$0.145445\pi$
$577$			21.1957i			0.882391i	−0.897411	+	0.441195i	$0.854555\pi$
$578$	−5.02816	+	14.3211i	−0.209144	+	0.595678i
$579$	7.95546	−	2.41326i	0.330618	−	0.100292i
$580$	2.71450	−	1.49276i	0.112713	−	0.0619836i
$581$	−7.16694	+	0.705882i	−0.297335	+	0.0292849i
$582$	0.949261	−	21.9944i	0.0393482	−	0.911696i
$583$	2.17431	+	1.45283i	0.0900506	+	0.0601699i
$584$	−5.34496	−	14.1368i	−0.221176	−	0.584984i
$585$	−2.55021	−	3.81665i	−0.105438	−	0.157799i
$586$	5.58162	+	1.36285i	0.230575	+	0.0562989i
$587$	7.18553	+	13.4432i	0.296579	+	0.554859i	0.985438	−	0.170036i	$-0.0543883\pi$
$587$	7.18553	+	13.4432i	0.296579	+	0.554859i	−0.688859	+	0.724895i	$0.741888\pi$
$588$	0.149177	+	12.5250i	0.00615195	+	0.516524i
$589$	2.22602	−	22.6011i	0.0917215	−	0.931264i
$590$	10.9444	−	8.21840i	0.450574	−	0.338346i
$591$	0.692307	+	1.67138i	0.0284777	+	0.0687513i
$592$	4.41246	+	2.22505i	0.181351	+	0.0914491i
$593$	5.63142	−	13.5955i	0.231255	−	0.558298i	−0.765071	−	0.643946i	$-0.777296\pi$
$593$	5.63142	−	13.5955i	0.231255	−	0.558298i	0.996325	+	0.0856480i	$0.0272960\pi$
$594$	−0.423696	−	1.64975i	−0.0173845	−	0.0676900i
$595$	2.63607	+	3.21206i	0.108068	+	0.131681i
$596$	16.0011	−	10.9695i	0.655430	−	0.449326i
$597$	0.684174	−	2.25542i	0.0280014	−	0.0923081i
$598$	3.47272	−	0.536283i	0.142010	−	0.0219302i
$599$	−40.0418	−	7.96482i	−1.63607	−	0.325434i	−0.710406	−	0.703792i	$-0.751489\pi$
$599$	−40.0418	−	7.96482i	−1.63607	−	0.325434i	−0.925659	+	0.378358i	$0.876489\pi$
$600$	−0.929187	−	3.44705i	−0.0379339	−	0.140725i
$601$	7.20469	+	36.2204i	0.293886	+	1.47746i	0.792091	+	0.610403i	$0.208993\pi$
$601$	7.20469	+	36.2204i	0.293886	+	1.47746i	−0.498205	+	0.867059i	$0.666007\pi$
$602$	−3.68502	+	7.91289i	−0.150190	+	0.322505i
$603$	−2.47947	+	3.02124i	−0.100972	+	0.123034i
$604$	24.5294	+	29.1736i	0.998085	+	1.18706i
$605$	−16.2822	−	8.70302i	−0.661966	−	0.353828i
$606$	6.93560	−	0.382137i	0.281740	−	0.0155233i
$607$	0.716922	+	0.716922i	0.0290990	+	0.0290990i	0.721507	−	0.692408i	$-0.243450\pi$
$607$	0.716922	+	0.716922i	0.0290990	+	0.0290990i	−0.692408	+	0.721507i	$0.743450\pi$
$608$	−9.12503	+	41.6536i	−0.370069	+	1.68928i
$609$	0.486359	−	0.486359i	0.0197083	−	0.0197083i
$610$	7.71652	−	8.61644i	0.312433	−	0.348869i
$611$	−7.41670	+	13.8757i	−0.300048	+	0.561350i
$612$	2.30752	−	4.44356i	0.0932758	−	0.179620i
$613$	−33.4334	−	27.4381i	−1.35036	−	1.10821i	−0.984083	−	0.177709i	$-0.943131\pi$
$613$	−33.4334	−	27.4381i	−1.35036	−	1.10821i	−0.366280	−	0.930505i	$-0.619369\pi$
$614$	15.7639	−	5.74652i	0.636178	−	0.231911i
$615$	−17.8128	+	3.54318i	−0.718280	+	0.142875i
$616$	0.935913	−	2.77078i	0.0377090	−	0.111638i
$617$	2.66985	−	13.4222i	0.107484	−	0.540358i	−0.889096	−	0.457721i	$-0.848666\pi$
$617$	2.66985	−	13.4222i	0.107484	−	0.540358i	0.996580	−	0.0826370i	$-0.0263342\pi$
$618$	7.39001	−	10.0893i	0.297270	−	0.405851i
$619$	5.91832	+	1.79530i	0.237877	+	0.0721593i	0.406973	−	0.913440i	$-0.366584\pi$
$619$	5.91832	+	1.79530i	0.237877	+	0.0721593i	−0.169095	+	0.985600i	$0.554084\pi$
$620$	−11.3978	+	2.40862i	−0.457746	+	0.0967324i
$621$	−0.808963	+	0.663899i	−0.0324626	+	0.0266413i
$622$	3.99760	−	6.76056i	0.160289	−	0.271074i
$623$	−0.675647	−	0.279862i	−0.0270692	−	0.0112124i
$624$	−8.68509	+	3.84231i	−0.347682	+	0.153816i
$625$	−15.7944	+	6.54224i	−0.631775	+	0.261690i
$626$	2.22394	−	15.6335i	0.0888866	−	0.624839i
$627$	−9.03509	−	0.889879i	−0.360827	−	0.0355383i
$628$	9.09147	+	21.2300i	0.362789	+	0.847170i
$629$	−2.72769	+	1.45798i	−0.108760	+	0.0581334i
$630$	1.21872	+	2.00612i	0.0485549	+	0.0799257i
$631$	26.4560	−	17.6773i	1.05320	−	0.703724i	0.0966548	−	0.995318i	$-0.469186\pi$
$631$	26.4560	−	17.6773i	1.05320	−	0.703724i	0.956542	+	0.291594i	$0.0941857\pi$
$632$	2.53415	+	15.2070i	0.100803	+	0.604901i
$633$	−15.1932	+	22.7382i	−0.603876	+	0.903764i
$634$	29.8690	+	32.5635i	1.18625	+	1.29326i
$635$	−3.35874	−	34.1019i	−0.133288	−	1.35329i
$636$	0.477068	+	4.31614i	0.0189170	+	0.171146i
$637$	4.31651	+	14.2296i	0.171026	+	0.563799i
$638$	1.23011	−	0.590790i	0.0487007	−	0.0233896i
$639$	−15.6555			−0.619323
$640$	21.7831	−	1.98274i	0.861054	−	0.0783745i
$641$	−28.5176			−1.12638			−0.563188	−	0.826329i	$-0.690425\pi$
$641$	−28.5176			−1.12638			−0.563188	+	0.826329i	$0.690425\pi$
$642$	13.7741	−	6.61531i	0.543619	−	0.261085i
$643$	7.29472	+	24.0475i	0.287676	+	0.948339i	0.975041	+	0.222027i	$0.0712673\pi$
$643$	7.29472	+	24.0475i	0.287676	+	0.948339i	−0.687365	+	0.726312i	$0.741233\pi$
$644$	−1.78600	+	0.197409i	−0.0703783	+	0.00777901i
$645$	−1.36241	−	13.8327i	−0.0536447	−	0.544664i
$646$	−18.0400	−	19.6675i	−0.709776	−	0.773806i
$647$	14.0235	−	20.9876i	0.551319	−	0.825107i	−0.446241	−	0.894913i	$-0.647238\pi$
$647$	14.0235	−	20.9876i	0.551319	−	0.825107i	0.997561	+	0.0698051i	$0.0222377\pi$
$648$	1.64404	−	2.30155i	0.0645840	−	0.0904134i
$649$	5.01293	−	3.34953i	0.196775	−	0.131481i
$650$	−2.20047	−	3.62216i	−0.0863094	−	0.142073i
$651$	−2.28111	+	1.21928i	−0.0894036	+	0.0477872i
$652$	23.9100	−	10.2391i	0.936388	−	0.400996i
$653$	−15.4043	−	1.51719i	−0.602816	−	0.0593722i	−0.207995	−	0.978130i	$-0.566694\pi$
$653$	−15.4043	−	1.51719i	−0.602816	−	0.0593722i	−0.394822	+	0.918758i	$0.629194\pi$
$654$	−0.983332	+	6.91244i	−0.0384513	+	0.270298i
$655$	8.27830	−	3.42898i	0.323460	−	0.133981i
$656$	0.894955	+	37.5653i	0.0349421	+	1.46668i
$657$	4.93667	+	2.04484i	0.192598	+	0.0797767i
$658$	4.09507	−	6.92540i	0.159642	−	0.269980i
$659$	14.1513	−	11.6137i	0.551258	−	0.452406i	−0.317066	−	0.948404i	$-0.602698\pi$
$659$	14.1513	−	11.6137i	0.551258	−	0.452406i	0.868324	+	0.495998i	$0.165198\pi$
$660$	0.962875	+	4.55641i	0.0374799	+	0.177358i
$661$	37.6609	+	11.4243i	1.46484	+	0.444354i	0.919241	−	0.393695i	$-0.128803\pi$
$661$	37.6609	+	11.4243i	1.46484	+	0.444354i	0.545596	+	0.838048i	$0.316303\pi$
$662$	17.8287	−	24.3408i	0.692932	−	0.946033i
$663$	1.15961	−	5.82973i	0.0450354	−	0.226408i
$664$	−10.5258	−	21.2637i	−0.408481	−	0.825191i
$665$	12.2711	−	2.44087i	0.475852	−	0.0946528i
$666$	−1.64150	+	0.598388i	−0.0636068	+	0.0231870i
$667$	−0.648120	−	0.531899i	−0.0250953	−	0.0205952i
$668$	−17.1661	−	8.91428i	−0.664177	−	0.344904i
$669$	−7.71463	+	14.4331i	−0.298265	+	0.558014i
$670$	7.12911	−	7.96051i	0.275421	−	0.307541i
$671$	3.60283	−	3.60283i	0.139086	−	0.139086i
$672$	4.52184	−	1.77149i	0.174434	−	0.0683369i
$673$	−0.778490	−	0.778490i	−0.0300086	−	0.0300086i	0.691943	−	0.721952i	$-0.256755\pi$
$673$	−0.778490	−	0.778490i	−0.0300086	−	0.0300086i	−0.721952	+	0.691943i	$0.756755\pi$
$674$	41.2801	−	2.27445i	1.59005	−	0.0876085i
$675$	1.11318	+	0.595006i	0.0428462	+	0.0229018i
$676$	11.2711	−	9.47681i	0.433503	−	0.364493i
$677$	−14.1765	+	17.2741i	−0.544845	+	0.663896i	−0.970531	−	0.240975i	$-0.922533\pi$
$677$	−14.1765	+	17.2741i	−0.544845	+	0.663896i	0.425686	+	0.904871i	$0.360033\pi$
$678$	−7.72279	+	16.5833i	−0.296592	+	0.636876i
$679$	2.60724	+	13.1075i	0.100057	+	0.503020i
$680$	−6.82709	+	11.8660i	−0.261807	+	0.455040i
$681$	−3.17539	−	0.631624i	−0.121681	−	0.0242039i
$682$	−5.07155	+	0.783185i	−0.194200	+	0.0299897i
$683$	3.85256	−	12.7002i	0.147414	−	0.485960i	−0.851871	−	0.523751i	$-0.824532\pi$
$683$	3.85256	−	12.7002i	0.147414	−	0.485960i	0.999286	+	0.0377913i	$0.0120322\pi$
$684$	−8.52447	−	12.4346i	−0.325941	−	0.475449i
$685$	−26.3257	−	32.0779i	−1.00585	−	1.22564i
$686$	−4.00560	−	15.5966i	−0.152935	−	0.595482i
$687$	4.44684	−	10.7356i	0.169658	−	0.409590i
$688$	−28.6785	−	2.13633i	−1.09336	−	0.0814470i
$689$	1.97274	+	4.76263i	0.0751556	+	0.181442i
$690$	2.28804	−	1.71814i	0.0871041	−	0.0654084i
$691$	−4.74536	+	48.1804i	−0.180522	+	1.83287i	0.297734	+	0.954649i	$0.403769\pi$
$691$	−4.74536	+	48.1804i	−0.180522	+	1.83287i	−0.478256	+	0.878220i	$0.658731\pi$
$692$	10.4904	−	0.124944i	0.398787	−	0.00474967i
$693$	0.487421	+	0.911901i	0.0185156	+	0.0346403i
$694$	1.91771	+	0.468242i	0.0727951	+	0.0177742i
$695$	−8.01617	−	11.9971i	−0.304071	−	0.455074i
$696$	2.06548	+	0.932118i	0.0782917	+	0.0353319i
$697$	−19.5543	−	13.0658i	−0.740672	−	0.494901i
$698$	1.07168	−	24.8308i	0.0405636	−	0.939858i
$699$	−24.5811	+	2.42103i	−0.929743	+	0.0915717i
$700$	1.04433	+	1.89905i	0.0394719	+	0.0717772i
$701$	−27.9556	+	8.48025i	−1.05587	+	0.320294i	−0.770046	−	0.637988i	$-0.779767\pi$
$701$	−27.9556	+	8.48025i	−1.05587	+	0.320294i	−0.285823	+	0.958282i	$0.592267\pi$
$702$	1.11234	−	3.16812i	0.0419824	−	0.119573i
$703$			9.31269i			0.351235i
$704$	9.62909	−	0.344186i	0.362910	−	0.0129720i
$705$			12.8116i			0.482511i
$706$	−41.7861	−	14.6712i	−1.57264	−	0.552158i
$707$	−4.03513	+	1.22404i	−0.151757	+	0.0460349i
$708$	9.61442	+	2.79190i	0.361332	+	0.104926i
$709$	−15.0597	+	1.48325i	−0.565579	+	0.0557047i	−0.376766	−	0.926308i	$-0.622964\pi$
$709$	−15.0597	+	1.48325i	−0.565579	+	0.0557047i	−0.188813	+	0.982013i	$0.560464\pi$
$710$	42.7647	+	1.84570i	1.60493	+	0.0692677i
$711$	−4.53202	−	3.02820i	−0.169964	−	0.113566i
$712$	0.0752151	−	2.40820i	0.00281880	−	0.0902511i
$713$	1.75167	+	2.62156i	0.0656006	+	0.0981782i
$714$	−0.720974	+	2.95278i	−0.0269818	+	0.110505i
$715$	2.60613	+	4.87572i	0.0974636	+	0.182342i
$716$	18.2446	+	17.8151i	0.681833	+	0.665783i
$717$	−2.34440	+	23.8030i	−0.0875530	+	0.888941i
$718$	7.04566	+	9.38268i	0.262942	+	0.350159i
$719$	−11.3883	−	27.4938i	−0.424712	−	1.02534i	−0.980939	−	0.194315i	$-0.937752\pi$
$719$	−11.3883	−	27.4938i	−0.424712	−	1.02534i	0.556227	−	0.831030i	$-0.312248\pi$
$720$	−4.76221	+	6.09310i	−0.177477	+	0.227076i
$721$	−2.90534	+	7.01411i	−0.108200	+	0.261219i
$722$	−51.8064	+	13.3052i	−1.92803	+	0.495167i
$723$	−7.47028	−	9.10257i	−0.277823	−	0.338528i
$724$	−45.0454	−	8.40367i	−1.67410	−	0.312320i
$725$	−0.293552	+	0.967713i	−0.0109023	+	0.0359399i
$726$	−2.06109	−	13.3467i	−0.0764944	−	0.495342i
$727$	16.0993	+	3.20235i	0.597089	+	0.118768i	0.484377	−	0.874859i	$-0.339046\pi$
$727$	16.0993	+	3.20235i	0.597089	+	0.118768i	0.112712	+	0.993628i	$0.464046\pi$
$728$	4.56862	−	3.51654i	0.169324	−	0.130332i
$729$	0.195090	+	0.980785i	0.00722557	+	0.0363254i
$730$	−13.2440	−	6.16769i	−0.490181	−	0.228276i
$731$	11.4183	−	13.9132i	0.422321	−	0.514600i
$732$	8.42943	+	0.728974i	0.311561	+	0.0269437i
$733$	−41.1515	−	21.9959i	−1.51996	−	0.812438i	−0.520815	−	0.853669i	$-0.674372\pi$
$733$	−41.1515	−	21.9959i	−1.51996	−	0.812438i	−0.999150	+	0.0412312i	$0.986872\pi$
$734$	1.78666	+	32.4270i	0.0659468	+	1.19690i
$735$	8.56193	+	8.56193i	0.315811	+	0.315811i
$736$	−2.68930	−	5.27385i	−0.0991289	−	0.194397i
$737$	3.32857	−	3.32857i	0.122609	−	0.122609i
$738$	−9.89657	−	8.86296i	−0.364298	−	0.326250i
$739$	−8.61034	+	16.1088i	−0.316737	+	0.592573i	−0.989030	−	0.147712i	$-0.952809\pi$
$739$	−8.61034	+	16.1088i	−0.316737	+	0.592573i	0.672294	+	0.740284i	$0.265309\pi$
$740$	4.55447	−	1.44104i	0.167426	−	0.0529735i
$741$	−13.8347	−	11.3539i	−0.508232	−	0.417095i
$742$	−0.902840	−	2.47667i	−0.0331443	−	0.0909216i
$743$	−37.2994	+	7.41930i	−1.36838	+	0.272188i	−0.823971	−	0.566632i	$-0.808246\pi$
$743$	−37.2994	+	7.41930i	−1.36838	+	0.272188i	−0.544410	+	0.838820i	$0.683246\pi$
$744$	−6.41523	−	5.60898i	−0.235194	−	0.205635i
$745$	3.65861	−	18.3931i	0.134041	−	0.673871i
$746$	7.30612	+	5.35144i	0.267496	+	0.195930i
$747$	8.02730	+	2.43506i	0.293704	+	0.0890940i
$748$	−3.29037	+	5.05366i	−0.120308	+	0.184780i
$749$	−7.17047	+	5.88465i	−0.262003	+	0.215020i
$750$	−14.7380	−	8.71477i	−0.538157	−	0.318218i
$751$	−25.8691	−	10.7153i	−0.943978	−	0.391008i	−0.143014	−	0.989721i	$-0.545679\pi$
$751$	−25.8691	−	10.7153i	−0.943978	−	0.391008i	−0.800964	+	0.598712i	$0.795679\pi$
$752$	26.1131	+	4.55054i	0.952248	+	0.165941i
$753$	6.31012	−	2.61374i	0.229953	−	0.0952499i
$754$	2.66330	+	0.378869i	0.0969918	+	0.0137976i
$755$	36.6675	+	3.61143i	1.33447	+	0.131434i
$756$	−0.638136	+	1.59403i	−0.0232088	+	0.0579744i
$757$	−29.1373	+	15.5742i	−1.05901	+	0.566055i	−0.906483	−	0.422243i	$-0.861243\pi$
$757$	−29.1373	+	15.5742i	−1.05901	+	0.566055i	−0.152532	+	0.988299i	$0.548743\pi$
$758$	−7.97002	+	4.84179i	−0.289484	+	0.175862i
$759$	1.04800	−	0.700253i	0.0380401	−	0.0254176i
$760$	21.8195	+	34.9714i	0.791477	+	1.26855i
$761$	8.93620	−	13.3740i	0.323937	−	0.484806i	−0.633382	−	0.773839i	$-0.718334\pi$
$761$	8.93620	−	13.3740i	0.323937	−	0.484806i	0.957319	+	0.289033i	$0.0933338\pi$
$762$	18.4720	−	16.9435i	0.669170	−	0.613798i
$763$	−0.415446	−	4.21809i	−0.0150402	−	0.152705i
$764$	−22.5602	−	18.0694i	−0.816200	−	0.653727i
$765$	−1.40500	−	4.63167i	−0.0507979	−	0.167458i
$766$	12.5022	+	26.0315i	0.451723	+	0.940556i
$767$	11.8851			0.429145
$768$	10.7278	+	11.8708i	0.387105	+	0.428349i
$769$	−28.0274			−1.01070			−0.505348	−	0.862916i	$-0.668636\pi$
$769$	−28.0274			−1.01070			−0.505348	+	0.862916i	$0.668636\pi$
$770$	−1.22393	−	2.54842i	−0.0441076	−	0.0918386i
$771$	2.75276	+	9.07462i	0.0991381	+	0.326814i
$772$	−12.9775	−	10.3942i	−0.467069	−	0.374094i
$773$	5.40040	+	54.8312i	0.194239	+	1.97214i	0.231499	+	0.972835i	$0.425637\pi$
$773$	5.40040	+	54.8312i	0.194239	+	1.97214i	−0.0372599	+	0.999306i	$0.511863\pi$
$774$	7.49280	−	6.87279i	0.269323	−	0.247037i
$775$	2.11273	−	3.16192i	0.0758915	−	0.113580i
$776$	−37.3551	+	23.3068i	−1.34097	+	0.836666i
$777$	0.881882	−	0.589255i	0.0316374	−	0.0211394i
$778$	−1.24578	+	0.756810i	−0.0446633	+	0.0271330i
$779$	−62.4506	+	33.3805i	−2.23752	+	1.19598i
$780$	−3.41196	+	8.52291i	−0.122168	+	0.305169i
$781$	18.7648	+	1.84817i	0.671458	+	0.0661328i
$782$	3.66820	+	0.521822i	0.131175	+	0.0186603i
$783$	−0.740188	+	0.306596i	−0.0264522	+	0.0109568i
$784$	20.4924	−	14.4102i	0.731873	−	0.514651i
$785$	20.6256	+	8.54339i	0.736158	+	0.304927i
$786$	5.64187	+	3.33610i	0.201239	+	0.118995i
$787$	24.0061	−	19.7013i	0.855724	−	0.702275i	−0.100491	−	0.994938i	$-0.532041\pi$
$787$	24.0061	−	19.7013i	0.855724	−	0.702275i	0.956216	+	0.292663i	$0.0945415\pi$
$788$	1.97418	−	3.03213i	0.0703272	−	0.108015i
$789$	3.63030	+	1.10124i	0.129242	+	0.0392051i
$790$	12.0227	+	8.80615i	0.427748	+	0.313309i
$791$	2.16650	−	10.8917i	0.0770319	−	0.387266i
$792$	−2.24226	+	2.56457i	−0.0796752	+	0.0911280i
$793$	9.85120	−	1.95953i	0.349826	−	0.0695848i
$794$	1.59761	+	4.38256i	0.0566969	+	0.155531i
$795$	3.24485	+	2.66298i	0.115083	+	0.0944461i
$796$	−4.49422	+	1.42197i	−0.159293	+	0.0504005i
$797$	−21.4792	+	40.1848i	−0.760834	+	1.42342i	0.140403	+	0.990094i	$0.455160\pi$
$797$	−21.4792	+	40.1848i	−0.760834	+	1.42342i	−0.901237	+	0.433326i	$0.857340\pi$
$798$	6.81767	+	6.10563i	0.241343	+	0.216137i
$799$	−11.7307	+	11.7307i	−0.415004	+	0.415004i
$800$	−4.63543	+	5.43093i	−0.163887	+	0.192013i
$801$	0.602343	+	0.602343i	0.0212828	+	0.0212828i
$802$	−2.70395	−	49.0754i	−0.0954799	−	1.73291i
$803$	−5.67573	−	3.03374i	−0.200292	−	0.107058i
$804$	7.78774	+	0.673481i	0.274653	+	0.0237519i
$805$	−1.10193	+	1.34271i	−0.0388379	+	0.0473242i
$806$	−9.17047	−	4.27067i	−0.323016	−	0.150428i
$807$	−4.30131	−	21.6241i	−0.151413	−	0.761205i
$808$	−8.47361	−	11.0087i	−0.298101	−	0.387286i
$809$	−38.3608	−	7.63043i	−1.34869	−	0.268272i	−0.532685	−	0.846313i	$-0.678817\pi$
$809$	−38.3608	−	7.63043i	−1.34869	−	0.268272i	−0.816007	+	0.578042i	$0.803817\pi$
$810$	−0.417281	−	2.70212i	−0.0146618	−	0.0949427i
$811$	11.2045	−	36.9362i	0.393442	−	1.29700i	−0.506969	−	0.861964i	$-0.669234\pi$
$811$	11.2045	−	36.9362i	0.393442	−	1.29700i	0.900411	−	0.435040i	$-0.143266\pi$
$812$	−1.35230	−	0.252285i	−0.0474564	−	0.00885348i
$813$	17.5595	+	21.3963i	0.615838	+	0.750401i
$814$	2.03815	−	0.523448i	0.0714372	−	0.0183468i
$815$	9.62188	−	23.2293i	0.337040	−	0.813686i
$816$	−9.93953	+	1.21862i	−0.347953	+	0.0426601i
$817$	−20.7393	−	50.0690i	−0.725576	−	1.75169i
$818$	−15.7179	−	20.9315i	−0.549563	−	0.731851i
$819$	−0.199791	+	2.02852i	−0.00698127	+	0.0708821i
$820$	25.9886	+	25.3768i	0.907562	+	0.886198i
$821$	−9.08737	−	17.0013i	−0.317152	−	0.593349i	0.671948	−	0.740598i	$-0.265458\pi$
$821$	−9.08737	−	17.0013i	−0.317152	−	0.593349i	−0.989099	+	0.147250i	$0.952958\pi$
$822$	7.20017	−	29.4886i	0.251135	−	1.02853i
$823$	2.42167	+	3.62429i	0.0844141	+	0.126335i	0.871274	−	0.490797i	$-0.163294\pi$
$823$	2.42167	+	3.62429i	0.0844141	+	0.126335i	−0.786860	+	0.617132i	$0.788294\pi$
$824$	−25.0003	−	0.780832i	−0.870926	−	0.0272016i
$825$	−1.26402	−	0.844591i	−0.0440075	−	0.0294049i
$826$	−6.07196	−	0.262061i	−0.211271	−	0.00911828i
$827$	−17.6998	+	1.74328i	−0.615484	+	0.0606199i	−0.400955	−	0.916098i	$-0.631322\pi$
$827$	−17.6998	+	1.74328i	−0.615484	+	0.0606199i	−0.214529	+	0.976718i	$0.568822\pi$
$828$	2.00999	+	0.583675i	0.0698519	+	0.0202841i
$829$	0.591082	−	0.179303i	0.0205291	−	0.00622744i	−0.280003	−	0.959999i	$-0.590336\pi$
$829$	0.591082	−	0.179303i	0.0205291	−	0.00622744i	0.300533	+	0.953772i	$0.402836\pi$
$830$	−21.6403	−	7.59798i	−0.751147	−	0.263730i
$831$		−	27.9178i		−	0.968459i
$832$	16.1599	+	9.98168i	0.560244	+	0.346052i
$833$			15.6792i			0.543254i
$834$	3.49645	−	9.95849i	0.121072	−	0.344834i
$835$	−17.8928	+	5.42773i	−0.619207	+	0.187834i
$836$	8.74955	+	15.9105i	0.302610	+	0.550277i
$837$	2.99829	−	0.295306i	0.103636	−	0.0102073i
$838$	−2.27506	+	52.7130i	−0.0785906	+	1.82094i
$839$	1.51148	+	1.00994i	0.0521820	+	0.0348669i	0.581388	−	0.813627i	$-0.302510\pi$
$839$	1.51148	+	1.00994i	0.0521820	+	0.0348669i	−0.529206	+	0.848494i	$0.677510\pi$
$840$	1.93106	−	4.27903i	0.0666280	−	0.147641i
$841$	15.7549	+	23.5789i	0.543273	+	0.813066i
$842$	36.7634	+	8.97645i	1.26695	+	0.309349i
$843$	−4.33233	−	8.10523i	−0.149214	−	0.279159i
$844$	54.6902	−	0.651377i	1.88251	−	0.0224213i
$845$	1.39526	−	14.1663i	0.0479985	−	0.487337i
$846$	−7.49390	+	5.62733i	−0.257645	+	0.193472i
$847$	3.13734	+	7.57421i	0.107800	+	0.260253i
$848$	6.58035	−	5.66794i	0.225970	−	0.194638i
$849$	2.98649	−	7.21003i	0.102496	−	0.247447i
$850$	−1.11164	−	4.32838i	−0.0381288	−	0.148462i
$851$	−0.820202	−	0.999419i	−0.0281162	−	0.0342596i
$852$	17.7043	+	25.8252i	0.606540	+	0.884756i
$853$	6.71196	−	22.1264i	0.229813	−	0.757593i	−0.763870	−	0.645370i	$-0.776703\pi$
$853$	6.71196	−	22.1264i	0.229813	−	0.757593i	0.993683	−	0.112222i	$-0.0357969\pi$
$854$	−5.07608	+	0.783886i	−0.173700	+	0.0268240i
$855$	−14.2935	−	2.84314i	−0.488826	−	0.0972335i
$856$	−26.4892	−	15.2405i	−0.905381	−	0.520910i
$857$	8.68022	+	43.6384i	0.296511	+	1.49066i	0.785768	+	0.618521i	$0.212268\pi$
$857$	8.68022	+	43.6384i	0.296511	+	1.49066i	−0.489258	+	0.872139i	$0.662732\pi$
$858$	−1.70726	+	3.66601i	−0.0582847	+	0.125156i
$859$	5.14885	−	6.27389i	0.175676	−	0.214062i	−0.677727	−	0.735314i	$-0.737035\pi$
$859$	5.14885	−	6.27389i	0.175676	−	0.214062i	0.853403	+	0.521252i	$0.174535\pi$
$860$	−21.2776	+	17.8904i	−0.725561	+	0.610057i
$861$	7.11255	+	3.80174i	0.242395	+	0.129563i
$862$	−29.4188	+	1.62091i	−1.00201	+	0.0552085i
$863$	34.8833	+	34.8833i	1.18744	+	1.18744i	0.977773	+	0.209668i	$0.0672384\pi$
$863$	34.8833	+	34.8833i	1.18744	+	1.18744i	0.209668	+	0.977773i	$0.432762\pi$
$864$	−5.65580	−	0.109244i	−0.192414	−	0.00371656i
$865$	7.17111	−	7.17111i	0.243825	−	0.243825i
$866$	−14.9638	+	16.7089i	−0.508491	+	0.567792i
$867$	−5.05929	+	9.46526i	−0.171822	+	0.321457i
$868$	4.59093	+	2.38405i	0.155826	+	0.0809198i
$869$	5.07462	+	4.16464i	0.172145	+	0.141276i
$870$	2.05805	−	0.750235i	0.0697744	−	0.0254354i
$871$	9.10128	−	1.81036i	0.308385	−	0.0613416i
$872$	12.5147	−	6.19496i	0.423801	−	0.209788i
$873$	3.03694	−	15.2677i	0.102785	−	0.516735i
$874$	6.59224	−	9.00012i	0.222986	−	0.304434i
$875$	9.94639	+	3.01720i	0.336249	+	0.102000i
$876$	−2.20958	−	10.4559i	−0.0746547	−	0.353273i
$877$	−43.8972	+	36.0255i	−1.48230	+	1.21649i	−0.560899	+	0.827884i	$0.689544\pi$
$877$	−43.8972	+	36.0255i	−1.48230	+	1.21649i	−0.921403	+	0.388609i	$0.872956\pi$
$878$	21.8900	−	37.0194i	0.738751	−	1.24934i
$879$	3.75349	+	1.55475i	0.126602	+	0.0524403i
$880$	6.42731	−	6.74104i	0.216665	−	0.227240i
$881$	−26.0395	+	10.7859i	−0.877293	+	0.363387i	−0.775447	−	0.631413i	$-0.782475\pi$
$881$	−26.0395	+	10.7859i	−0.877293	+	0.363387i	−0.101847	+	0.994800i	$0.532475\pi$
$882$	−1.24742	+	8.76888i	−0.0420028	+	0.295264i
$883$	−14.1645	−	1.39508i	−0.476674	−	0.0469483i	−0.143172	−	0.989698i	$-0.545730\pi$
$883$	−14.1645	−	1.39508i	−0.476674	−	0.0469483i	−0.333502	+	0.942750i	$0.608230\pi$
$884$	−10.9280	+	4.67978i	−0.367549	+	0.157398i
$885$	8.53512	−	4.56211i	0.286905	−	0.153354i
$886$	−10.0577	−	16.5558i	−0.337894	−	0.556203i
$887$	−6.20753	+	4.14774i	−0.208429	+	0.139267i	−0.655403	−	0.755279i	$-0.727501\pi$
$887$	−6.20753	+	4.14774i	−0.208429	+	0.139267i	0.446975	+	0.894547i	$0.352501\pi$
$888$	2.84341	+	2.03110i	0.0954185	+	0.0681593i
$889$	−8.45380	+	12.6520i	−0.283531	+	0.424334i
$890$	−1.57435	−	1.71638i	−0.0527724	−	0.0575331i
$891$	−0.118052	−	1.19861i	−0.00395490	−	0.0401548i
$892$	32.5328	−	3.59590i	1.08928	−	0.120400i
$893$	14.5002	+	47.8009i	0.485232	+	1.59960i
$894$	12.3657	−	5.93892i	0.413572	−	0.198627i
$895$	24.6499			0.823956
$896$	−8.03584	−	5.45586i	−0.268459	−	0.182267i
$897$	2.48469			0.0829614
$898$	−10.2696	+	4.93219i	−0.342700	+	0.164589i
$899$	0.700683	+	2.30984i	0.0233691	+	0.0770375i
$900$	−0.277341	−	2.50916i	−0.00924468	−	0.0836386i
$901$	0.532782	+	5.40943i	0.0177495	+	0.180214i
$902$	10.8158	+	11.7915i	0.360127	+	0.392614i
$903$	−3.42912	+	5.13203i	−0.114114	+	0.170783i
$904$	36.0890	−	6.01402i	1.20030	−	0.200023i
$905$	−36.8301	+	24.6091i	−1.22427	+	0.818034i
$906$	13.9933	+	23.0343i	0.464898	+	0.765263i
$907$	20.1251	−	10.7571i	0.668244	−	0.357184i	−0.102135	−	0.994771i	$-0.532567\pi$
$907$	20.1251	−	10.7571i	0.668244	−	0.357184i	0.770379	+	0.637587i	$0.220067\pi$
$908$	2.54902	+	5.95237i	0.0845922	+	0.197536i
$909$	4.88800	+	0.481426i	0.162125	+	0.0159679i
$910$	0.784901	−	5.51755i	0.0260192	−	0.182905i
$911$	13.0708	−	5.41408i	0.433053	−	0.179377i	−0.155498	−	0.987836i	$-0.549698\pi$
$911$	13.0708	−	5.41408i	0.433053	−	0.179377i	0.588552	+	0.808460i	$0.299698\pi$
$912$	−10.8719	+	28.1237i	−0.360006	+	0.931270i
$913$	−9.33411	−	3.86631i	−0.308914	−	0.127956i
$914$	4.73915	−	8.01465i	0.156757	−	0.265101i
$915$	6.32235	−	5.18862i	0.209010	−	0.171530i
$916$	−22.7382	+	4.80510i	−0.751290	+	0.158765i
$917$	−3.80758	−	1.15502i	−0.125737	−	0.0381420i
$918$	2.09208	−	2.85624i	0.0690490	−	0.0942699i
$919$	0.819640	−	4.12061i	0.0270374	−	0.135926i	−0.964909	−	0.262585i	$-0.915425\pi$
$919$	0.819640	−	4.12061i	0.0270374	−	0.135926i	0.991946	+	0.126658i	$0.0404251\pi$
$920$	−5.42168	−	1.83134i	−0.178748	−	0.0603773i
$921$	11.6363	−	2.31461i	0.383429	−	0.0762689i
$922$	−50.1327	+	18.2752i	−1.65103	+	0.601863i
$923$	28.7331	+	23.5806i	0.945761	+	0.776166i
$924$	0.953053	−	1.83528i	0.0313532	−	0.0603764i
$925$	−0.735089	+	1.37526i	−0.0241696	+	0.0452181i
$926$	−20.0993	+	22.4433i	−0.660503	+	0.737531i
$927$	6.25312	−	6.25312i	0.205379	−	0.205379i
$928$	−0.798167	−	4.46129i	−0.0262011	−	0.146449i
$929$	−7.17696	−	7.17696i	−0.235468	−	0.235468i	0.579502	−	0.814971i	$-0.303247\pi$
$929$	−7.17696	−	7.17696i	−0.235468	−	0.235468i	−0.814971	+	0.579502i	$0.803247\pi$
$930$	−8.22497	+	0.453178i	−0.269707	+	0.0148603i
$931$	41.6357	+	22.2547i	1.36455	+	0.729370i
$932$	31.7916	+	37.8108i	1.04137	+	1.23854i
$933$	3.52319	−	4.29302i	0.115344	−	0.140547i
$934$	−12.0209	+	25.8125i	−0.393334	+	0.844612i
$935$	1.13726	+	5.71741i	0.0371925	+	0.186979i
$936$	−6.48399	+	1.74782i	−0.211936	+	0.0571294i
$937$	−14.0247	−	2.78969i	−0.458168	−	0.0911352i	−0.0393898	−	0.999224i	$-0.512541\pi$
$937$	−14.0247	−	2.78969i	−0.458168	−	0.0911352i	−0.418778	+	0.908089i	$0.637541\pi$
$938$	−4.68967	+	0.724213i	−0.153123	+	0.0236464i
$939$	3.24126	−	10.6850i	0.105775	−	0.348692i
$940$	21.1338	−	14.4882i	0.689308	−	0.472552i
$941$	34.5436	+	42.0915i	1.12609	+	1.37214i	0.919205	+	0.393779i	$0.128833\pi$
$941$	34.5436	+	42.0915i	1.12609	+	1.37214i	0.206885	+	0.978365i	$0.433667\pi$
$942$	4.06224	+	15.8171i	0.132355	+	0.515351i
$943$	3.76212	−	9.08257i	0.122512	−	0.295769i
$944$	−6.26713	−	19.0171i	−0.203978	−	0.618954i
$945$	0.635173	+	1.53344i	0.0206622	+	0.0498829i
$946$	−9.79226	+	7.35323i	−0.318374	+	0.239074i
$947$	2.65930	−	27.0004i	0.0864158	−	0.877394i	−0.850066	−	0.526677i	$-0.823438\pi$
$947$	2.65930	−	27.0004i	0.0864158	−	0.877394i	0.936481	−	0.350717i	$-0.114062\pi$
$948$	0.129828	+	10.9005i	0.00421661	+	0.354031i
$949$	−5.98046	−	11.1887i	−0.194134	−	0.363199i
$950$	−13.0717	−	3.19168i	−0.424101	−	0.103552i
$951$	17.3590	+	25.9795i	0.562903	+	0.842443i
$952$	5.68620	−	2.14989i	0.184291	−	0.0696784i
$953$	34.7073	+	23.1907i	1.12428	+	0.751219i	0.971500	−	0.237041i	$-0.0761775\pi$
$953$	34.7073	+	23.1907i	1.12428	+	0.751219i	0.152780	+	0.988260i	$0.451178\pi$
$954$	−0.132400	+	3.06770i	−0.00428660	+	0.0993204i
$955$	−27.8064	+	2.73869i	−0.899794	+	0.0886220i
$956$	41.9164	−	23.0508i	1.35567	−	0.745515i
$957$	0.923389	−	0.280107i	0.0298489	−	0.00905457i
$958$	20.1210	−	57.3079i	0.650079	−	1.85153i
$959$			18.4272i			0.595046i
$960$	15.4365	+	0.965197i	0.498212	+	0.0311516i
$961$			21.9230i			0.707195i
$962$	3.91400	+	1.37421i	0.126192	+	0.0443065i
$963$	10.3395	−	3.13647i	0.333187	−	0.101071i
$964$	−6.56760	+	22.6167i	−0.211528	+	0.728434i
$965$	−15.9953	+	1.57540i	−0.514906	+	0.0507138i
$966$	−1.26940	−	0.0547865i	−0.0408424	−	0.00176273i
$967$	−32.3460	−	21.6129i	−1.04018	−	0.695025i	−0.0866222	−	0.996241i	$-0.527607\pi$
$967$	−32.3460	−	21.6129i	−1.04018	−	0.695025i	−0.953556	+	0.301217i	$0.902607\pi$
$968$	−19.6857	+	18.4933i	−0.632723	+	0.594397i
$969$	−10.4843	−	15.6909i	−0.336805	−	0.504065i
$970$	−10.0957	+	41.3474i	−0.324153	+	1.32758i
$971$	23.0982	+	43.2137i	0.741257	+	1.38679i	0.915592	+	0.402108i	$0.131722\pi$
$971$	23.0982	+	43.2137i	0.741257	+	1.38679i	−0.174336	+	0.984686i	$0.555778\pi$
$972$	1.39727	−	1.43096i	0.0448175	−	0.0458979i
$973$	−0.628013	+	6.37632i	−0.0201332	+	0.204416i
$974$	3.16905	+	4.22021i	0.101543	+	0.135224i
$975$	−1.14684	−	2.76872i	−0.0367283	−	0.0886700i
$976$	−8.33005	−	14.7295i	−0.266638	−	0.471479i
$977$	2.56954	−	6.20343i	0.0822070	−	0.198465i	−0.877431	−	0.479702i	$-0.840745\pi$
$977$	2.56954	−	6.20343i	0.0822070	−	0.198465i	0.959638	+	0.281237i	$0.0907447\pi$
$978$	17.8139	−	4.57504i	0.569624	−	0.146294i
$979$	−0.650864	−	0.793080i	−0.0208017	−	0.0253470i
$980$	4.44126	−	23.8061i	0.141871	−	0.760456i
$981$	−1.43315	+	4.72446i	−0.0457569	+	0.150840i
$982$	4.61603	+	29.8913i	0.147303	+	0.953869i
$983$	−36.0036	−	7.16155i	−1.14833	−	0.228418i	−0.416001	−	0.909364i	$-0.636569\pi$
$983$	−36.0036	−	7.16155i	−1.14833	−	0.228418i	−0.732334	+	0.680946i	$0.761569\pi$
$984$	−3.42853	+	26.3481i	−0.109298	+	0.839946i
$985$	−0.682342	−	3.43036i	−0.0217412	−	0.109300i
$986$	2.57137	+	1.19748i	0.0818891	+	0.0381356i
$987$	3.60910	−	4.39770i	0.114879	−	0.139980i
$988$	−3.08398	+	35.6613i	−0.0981145	+	1.13454i
$989$	6.63546	+	3.54673i	0.210995	+	0.112779i
$990$	0.181164	+	3.28803i	0.00575776	+	0.104501i
$991$	−15.1208	−	15.1208i	−0.480329	−	0.480329i	0.424908	−	0.905237i	$-0.360306\pi$
$991$	−15.1208	−	15.1208i	−0.480329	−	0.480329i	−0.905237	+	0.424908i	$0.860306\pi$
$992$	−1.99774	+	16.9255i	−0.0634282	+	0.537385i
$993$	15.0859	−	15.0859i	0.478737	−	0.478737i
$994$	−14.1595	−	12.6807i	−0.449112	−	0.402206i
$995$	−2.14801	+	4.01864i	−0.0680964	+	0.127399i
$996$	−5.06097	−	15.9955i	−0.160363	−	0.506836i
$997$	−23.2167	−	19.0534i	−0.735279	−	0.603428i	0.190414	−	0.981704i	$-0.439017\pi$
$997$	−23.2167	−	19.0534i	−0.735279	−	0.603428i	−0.925693	+	0.378276i	$0.876517\pi$
$998$	0.497539	+	1.36485i	0.0157493	+	0.0432036i
$999$	−1.21169	+	0.241021i	−0.0383363	+	0.00762556i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.13.11	✓	512
128.69	even	32	inner	384.2.v.a.325.11	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.13.11	✓	512	1.1	even	1	trivial
384.2.v.a.325.11	yes	512	128.69	even	32	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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.612256 - 1.27481i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(-1.25028 + 1.56102i) q^{4} +(0.189500 + 1.92402i) q^{5} +(-1.04219 + 0.955951i) q^{6} +(0.476963 - 0.713825i) q^{7} +(2.75550 + 0.638130i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})\)	\(q+(-0.612256 - 1.27481i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(-1.25028 + 1.56102i) q^{4} +(0.189500 + 1.92402i) q^{5} +(-1.04219 + 0.955951i) q^{6} +(0.476963 - 0.713825i) q^{7} +(2.75550 + 0.638130i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(2.33674 - 1.41957i) q^{10} +(1.06219 - 0.567753i) q^{11} +(1.85674 + 0.743307i) q^{12} +(2.36283 + 0.232719i) q^{13} +(-1.20202 - 0.170993i) q^{14} +(1.78617 - 0.739855i) q^{15} +(-0.873578 - 3.90344i) q^{16} +(2.31292 + 0.958043i) q^{17} +(1.21732 + 0.719815i) q^{18} +(5.82696 - 4.78206i) q^{19} +(-3.24037 - 2.10976i) q^{20} +(-0.821543 - 0.249212i) q^{21} +(-1.37411 - 1.00648i) q^{22} +(-0.204164 + 1.02640i) q^{23} +(-0.189227 - 2.82209i) q^{24} +(1.23797 - 0.246247i) q^{25} +(-1.14999 - 3.15465i) q^{26} +(0.773010 + 0.634393i) q^{27} +(0.517958 + 1.63703i) q^{28} +(-0.377671 + 0.706573i) q^{29} +(-2.03677 - 1.82404i) q^{30} +(2.13037 - 2.13037i) q^{31} +(-4.44130 + 3.50355i) q^{32} +(-0.851643 - 0.851643i) q^{33} +(-0.194777 - 3.53511i) q^{34} +(1.46380 + 0.782418i) q^{35} +(0.172316 - 1.99256i) q^{36} +(-0.783750 + 0.955002i) q^{37} +(-9.66381 - 4.50042i) q^{38} +(-0.463196 - 2.32864i) q^{39} +(-0.705611 + 5.42258i) q^{40} +(-9.21349 - 1.83268i) q^{41} +(0.185296 + 1.19989i) q^{42} +(2.08700 - 6.87991i) q^{43} +(-0.441766 + 2.36796i) q^{44} +(-1.22649 - 1.49449i) q^{45} +(1.43347 - 0.368150i) q^{46} +(-2.53591 + 6.12224i) q^{47} +(-3.48177 + 1.96907i) q^{48} +(2.39673 + 5.78622i) q^{49} +(-1.07187 - 1.42741i) q^{50} +(0.245385 - 2.49143i) q^{51} +(-3.31749 + 3.39747i) q^{52} +(1.02350 + 1.91484i) q^{53} +(0.335451 - 1.37385i) q^{54} +(1.29366 + 1.93609i) q^{55} +(1.76978 - 1.66258i) q^{56} +(-6.26762 - 4.18789i) q^{57} +(1.13198 + 0.0488553i) q^{58} +(4.98169 - 0.490653i) q^{59} +(-1.07829 + 3.71328i) q^{60} +(4.04828 - 1.22803i) q^{61} +(-4.02015 - 1.41149i) q^{62} +0.858510i q^{63} +(7.18558 + 3.51674i) q^{64} +4.59025i q^{65} +(-0.564260 + 1.60711i) q^{66} +(3.74011 - 1.13455i) q^{67} +(-4.38734 + 2.41269i) q^{68} +(1.04147 - 0.102576i) q^{69} +(0.101213 - 2.34511i) q^{70} +(13.0171 + 8.69775i) q^{71} +(-2.64564 + 1.00029i) q^{72} +(-2.96864 - 4.44289i) q^{73} +(1.69730 + 0.414427i) q^{74} +(-0.595006 - 1.11318i) q^{75} +(0.179547 + 15.0749i) q^{76} +(0.101349 - 1.02902i) q^{77} +(-2.68499 + 2.01621i) q^{78} +(2.08586 + 5.03571i) q^{79} +(7.34478 - 2.42049i) q^{80} +(0.382683 - 0.923880i) q^{81} +(3.30470 + 12.8675i) q^{82} +(-5.32161 - 6.48441i) q^{83} +(1.41619 - 0.970860i) q^{84} +(-1.40500 + 4.63167i) q^{85} +(-10.0484 + 1.55174i) q^{86} +(0.785780 + 0.156301i) q^{87} +(3.28917 - 0.886628i) q^{88} +(-0.166186 - 0.835474i) q^{89} +(-1.15426 + 2.47856i) q^{90} +(1.29310 - 1.57565i) q^{91} +(-1.34697 - 1.60200i) q^{92} +(-2.65705 - 1.42022i) q^{93} +(9.35733 - 0.515569i) q^{94} +(10.3050 + 10.3050i) q^{95} +(4.64193 + 3.23303i) q^{96} +(-11.0074 + 11.0074i) q^{97} +(5.90892 - 6.59803i) q^{98} +(-0.567753 + 1.06219i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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