LMFDB - Embedded newform 390.2.be.b.257.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(17,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 2]))

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

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

chi := DirichletCharacter("390.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.be (of order $12$, degree $4$, 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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			257.14
Character	$\chi$	$=$	390.257
Dual form			390.2.be.b.173.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-1.62291 + 0.605124i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.23558 + 0.0464880i) q^{5} +(0.164466 + 1.72422i) q^{6} +(-0.193934 - 0.723770i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.26765 - 1.96412i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-1.62291 + 0.605124i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.23558 + 0.0464880i) q^{5} +(0.164466 + 1.72422i) q^{6} +(-0.193934 - 0.723770i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.26765 - 1.96412i) q^{9} +(-0.533708 + 2.17144i) q^{10} +(1.36771 + 2.36895i) q^{11} +(1.70804 + 0.287401i) q^{12} +(2.93920 + 2.08833i) q^{13} -0.749302 q^{14} +(3.60001 - 1.42825i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.01358 + 7.51480i) q^{17} +(-1.31028 - 2.69873i) q^{18} +(1.53847 - 2.66471i) q^{19} +(1.95932 + 1.07753i) q^{20} +(0.752706 + 1.05726i) q^{21} +(2.64222 - 0.707980i) q^{22} +(-1.98330 + 7.40179i) q^{23} +(0.719681 - 1.57546i) q^{24} +(4.99568 - 0.207856i) q^{25} +(2.77789 - 2.29855i) q^{26} +(-2.49165 + 4.55979i) q^{27} +(-0.193934 + 0.723770i) q^{28} +(-3.14010 - 5.43882i) q^{29} +(-0.447832 - 3.84700i) q^{30} +4.13375i q^{31} +(0.965926 - 0.258819i) q^{32} +(-3.65317 - 3.01694i) q^{33} +7.77989 q^{34} +(0.467201 + 1.60903i) q^{35} +(-2.94590 + 0.567151i) q^{36} +(0.0784427 + 0.0210187i) q^{37} +(-2.17572 - 2.17572i) q^{38} +(-6.03374 - 1.61059i) q^{39} +(1.54793 - 1.61367i) q^{40} +(2.28275 + 3.95384i) q^{41} +(1.21605 - 0.453420i) q^{42} +(-1.63882 - 6.11617i) q^{43} -2.73542i q^{44} +(-4.97822 + 4.49637i) q^{45} +(6.63626 + 3.83145i) q^{46} +(-3.72808 - 3.72808i) q^{47} +(-1.33551 - 1.10292i) q^{48} +(5.57595 - 3.21927i) q^{49} +(1.09220 - 4.87925i) q^{50} +(-7.81524 - 10.9773i) q^{51} +(-1.50125 - 3.27815i) q^{52} +(4.30283 + 4.30283i) q^{53} +(3.75953 + 3.58691i) q^{54} +(-3.16776 - 5.23240i) q^{55} +(0.648914 + 0.374651i) q^{56} +(-0.884314 + 5.25553i) q^{57} +(-6.06621 + 1.62544i) q^{58} +(0.215169 + 0.124228i) q^{59} +(-3.83183 - 0.563105i) q^{60} +(-5.13415 + 8.89261i) q^{61} +(3.99290 + 1.06989i) q^{62} +(-1.86134 - 1.26035i) q^{63} -1.00000i q^{64} +(-6.66790 - 4.53200i) q^{65} +(-3.85965 + 2.74785i) q^{66} +(-7.31758 - 1.96074i) q^{67} +(2.01358 - 7.51480i) q^{68} +(-1.26028 - 13.2126i) q^{69} +(1.67513 - 0.0348335i) q^{70} +(2.56731 - 4.44671i) q^{71} +(-0.214630 + 2.99231i) q^{72} +(8.65726 + 8.65726i) q^{73} +(0.0406050 - 0.0703298i) q^{74} +(-7.98174 + 3.36033i) q^{75} +(-2.66471 + 1.53847i) q^{76} +(1.44933 - 1.44933i) q^{77} +(-3.11736 + 5.41129i) q^{78} +16.1671i q^{79} +(-1.15805 - 1.91283i) q^{80} +(1.28448 - 8.90787i) q^{81} +(4.40993 - 1.18164i) q^{82} +(-6.03976 + 6.03976i) q^{83} +(-0.123234 - 1.29196i) q^{84} +(-4.85089 - 16.7064i) q^{85} -6.33192 q^{86} +(8.38725 + 6.92654i) q^{87} +(-2.64222 - 0.707980i) q^{88} +(9.45097 - 5.45652i) q^{89} +(3.05470 + 5.97234i) q^{90} +(0.941462 - 2.53230i) q^{91} +(5.41848 - 5.41848i) q^{92} +(-2.50143 - 6.70869i) q^{93} +(-4.56594 + 2.63615i) q^{94} +(-3.31550 + 6.02869i) q^{95} +(-1.41099 + 1.00454i) q^{96} +(1.28358 + 4.79038i) q^{97} +(-1.66642 - 6.21916i) q^{98} +(7.75438 + 2.68559i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 4 q^{3} + 24 q^{7}+O(q^{10}) $ 96 * q + 4 * q^3 + 24 * q^7	$ 96 q + 4 q^{3} + 24 q^{7} + 16 q^{10} - 8 q^{12} + 40 q^{13} + 48 q^{16} - 8 q^{22} + 64 q^{25} - 32 q^{27} + 24 q^{28} - 8 q^{30} - 96 q^{33} - 24 q^{36} + 72 q^{37} - 8 q^{42} + 16 q^{43} - 60 q^{45} + 24 q^{46} - 4 q^{48} - 128 q^{51} - 8 q^{52} + 32 q^{61} - 120 q^{63} - 16 q^{66} - 96 q^{67} - 24 q^{72} - 4 q^{75} - 24 q^{76} - 16 q^{78} - 48 q^{81} + 32 q^{82} + 32 q^{87} + 8 q^{88} - 56 q^{90} - 56 q^{91} - 12 q^{93} + 24 q^{97}+O(q^{100}) $ 96 * q + 4 * q^3 + 24 * q^7 + 16 * q^10 - 8 * q^12 + 40 * q^13 + 48 * q^16 - 8 * q^22 + 64 * q^25 - 32 * q^27 + 24 * q^28 - 8 * q^30 - 96 * q^33 - 24 * q^36 + 72 * q^37 - 8 * q^42 + 16 * q^43 - 60 * q^45 + 24 * q^46 - 4 * q^48 - 128 * q^51 - 8 * q^52 + 32 * q^61 - 120 * q^63 - 16 * q^66 - 96 * q^67 - 24 * q^72 - 4 * q^75 - 24 * q^76 - 16 * q^78 - 48 * q^81 + 32 * q^82 + 32 * q^87 + 8 * q^88 - 56 * q^90 - 56 * q^91 - 12 * q^93 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	−1.62291	+	0.605124i	−0.936985	+	0.349368i
$3$	−1.62291	+	0.605124i	−0.936985	+	0.349368i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−2.23558	+	0.0464880i	−0.999784	+	0.0207900i
$5$	−2.23558	+	0.0464880i	−0.999784	+	0.0207900i
$6$	0.164466	+	1.72422i	0.0671428	+	0.703912i
$7$	−0.193934	−	0.723770i	−0.0733000	−	0.273559i	0.919542	−	0.392991i	$-0.128560\pi$
$7$	−0.193934	−	0.723770i	−0.0733000	−	0.273559i	−0.992842	+	0.119431i	$0.961893\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	2.26765	−	1.96412i	0.755884	−	0.654706i
$10$	−0.533708	+	2.17144i	−0.168773	+	0.686670i
$11$	1.36771	+	2.36895i	0.412381	+	0.714264i	0.995150	−	0.0983738i	$-0.0313641\pi$
$11$	1.36771	+	2.36895i	0.412381	+	0.714264i	−0.582769	+	0.812638i	$0.698031\pi$
$12$	1.70804	+	0.287401i	0.493069	+	0.0829654i
$13$	2.93920	+	2.08833i	0.815186	+	0.579199i
$13$	2.93920	+	2.08833i	0.815186	+	0.579199i
$14$	−0.749302			−0.200259
$15$	3.60001	−	1.42825i	0.929520	−	0.368773i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	2.01358	+	7.51480i	0.488366	+	1.82261i	0.564400	+	0.825501i	$0.309108\pi$
$17$	2.01358	+	7.51480i	0.488366	+	1.82261i	−0.0760342	+	0.997105i	$0.524226\pi$
$18$	−1.31028	−	2.69873i	−0.308836	−	0.636098i
$19$	1.53847	−	2.66471i	0.352949	−	0.611325i	−0.633816	−	0.773484i	$-0.718512\pi$
$19$	1.53847	−	2.66471i	0.352949	−	0.611325i	0.986765	+	0.162159i	$0.0518456\pi$
$20$	1.95932	+	1.07753i	0.438117	+	0.240944i
$21$	0.752706	+	1.05726i	0.164254	+	0.230712i
$22$	2.64222	−	0.707980i	0.563322	−	0.150942i
$23$	−1.98330	+	7.40179i	−0.413547	+	1.54338i	0.374181	+	0.927356i	$0.377924\pi$
$23$	−1.98330	+	7.40179i	−0.413547	+	1.54338i	−0.787728	+	0.616023i	$0.788743\pi$
$24$	0.719681	−	1.57546i	0.146904	−	0.321588i
$25$	4.99568	−	0.207856i	0.999136	−	0.0415711i
$26$	2.77789	−	2.29855i	0.544790	−	0.450782i
$27$	−2.49165	+	4.55979i	−0.479518	+	0.877532i
$28$	−0.193934	+	0.723770i	−0.0366500	+	0.136780i
$29$	−3.14010	−	5.43882i	−0.583102	−	1.00996i	−0.995109	−	0.0987820i	$-0.968505\pi$
$29$	−3.14010	−	5.43882i	−0.583102	−	1.00996i	0.412007	−	0.911181i	$-0.364828\pi$
$30$	−0.447832	−	3.84700i	−0.0817626	−	0.702364i
$31$			4.13375i			0.742444i	0.928544	+	0.371222i	$0.121061\pi$
$31$			4.13375i			0.742444i	−0.928544	+	0.371222i	$0.878939\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	−3.65317	−	3.01694i	−0.635936	−	0.525182i
$34$	7.77989			1.33424
$35$	0.467201	+	1.60903i	0.0789715	+	0.271976i
$36$	−2.94590	+	0.567151i	−0.490984	+	0.0945252i
$37$	0.0784427	+	0.0210187i	0.0128959	+	0.00345545i	0.265261	−	0.964177i	$-0.414542\pi$
$37$	0.0784427	+	0.0210187i	0.0128959	+	0.00345545i	−0.252365	+	0.967632i	$0.581208\pi$
$38$	−2.17572	−	2.17572i	−0.352949	−	0.352949i
$39$	−6.03374	−	1.61059i	−0.966171	−	0.257901i
$40$	1.54793	−	1.61367i	0.244748	−	0.255143i
$41$	2.28275	+	3.95384i	0.356506	+	0.617486i	0.987374	−	0.158404i	$-0.0506348\pi$
$41$	2.28275	+	3.95384i	0.356506	+	0.617486i	−0.630869	+	0.775889i	$0.717301\pi$
$42$	1.21605	−	0.453420i	0.187640	−	0.0699643i
$43$	−1.63882	−	6.11617i	−0.249918	−	0.932707i	−0.970847	−	0.239698i	$-0.922951\pi$
$43$	−1.63882	−	6.11617i	−0.249918	−	0.932707i	0.720929	−	0.693009i	$-0.243715\pi$
$44$		−	2.73542i		−	0.412381i
$45$	−4.97822	+	4.49637i	−0.742109	+	0.670279i
$46$	6.63626	+	3.83145i	0.978463	+	0.564916i
$47$	−3.72808	−	3.72808i	−0.543796	−	0.543796i	0.380844	−	0.924639i	$-0.375634\pi$
$47$	−3.72808	−	3.72808i	−0.543796	−	0.543796i	−0.924639	+	0.380844i	$0.875634\pi$
$48$	−1.33551	−	1.10292i	−0.192764	−	0.159192i
$49$	5.57595	−	3.21927i	0.796564	−	0.459896i
$50$	1.09220	−	4.87925i	0.154461	−	0.690030i
$51$	−7.81524	−	10.9773i	−1.09435	−	1.53714i
$52$	−1.50125	−	3.27815i	−0.208186	−	0.454597i
$53$	4.30283	+	4.30283i	0.591040	+	0.591040i	0.937912	−	0.346873i	$-0.112756\pi$
$53$	4.30283	+	4.30283i	0.591040	+	0.591040i	−0.346873	+	0.937912i	$0.612756\pi$
$54$	3.75953	+	3.58691i	0.511607	+	0.488117i
$55$	−3.16776	−	5.23240i	−0.427141	−	0.705536i
$56$	0.648914	+	0.374651i	0.0867148	+	0.0500648i
$57$	−0.884314	+	5.25553i	−0.117130	+	0.696112i
$58$	−6.06621	+	1.62544i	−0.796533	+	0.213430i
$59$	0.215169	+	0.124228i	0.0280126	+	0.0161731i	0.513941	−	0.857826i	$-0.328185\pi$
$59$	0.215169	+	0.124228i	0.0280126	+	0.0161731i	−0.485928	+	0.873999i	$0.661518\pi$
$60$	−3.83183	−	0.563105i	−0.494687	−	0.0726966i
$61$	−5.13415	+	8.89261i	−0.657361	+	1.13858i	0.323936	+	0.946079i	$0.394994\pi$
$61$	−5.13415	+	8.89261i	−0.657361	+	1.13858i	−0.981296	+	0.192503i	$0.938339\pi$
$62$	3.99290	+	1.06989i	0.507099	+	0.135877i
$63$	−1.86134	−	1.26035i	−0.234507	−	0.158789i
$64$		−	1.00000i		−	0.125000i
$65$	−6.66790	−	4.53200i	−0.827052	−	0.562126i
$66$	−3.85965	+	2.74785i	−0.475091	+	0.338237i
$67$	−7.31758	−	1.96074i	−0.893984	−	0.239542i	−0.217553	−	0.976048i	$-0.569808\pi$
$67$	−7.31758	−	1.96074i	−0.893984	−	0.239542i	−0.676431	+	0.736506i	$0.736474\pi$
$68$	2.01358	−	7.51480i	0.244183	−	0.911303i
$69$	−1.26028	−	13.2126i	−0.151720	−	1.59060i
$70$	1.67513	−	0.0348335i	0.200216	−	0.00416340i
$71$	2.56731	−	4.44671i	0.304683	−	0.527727i	−0.672507	−	0.740090i	$-0.734783\pi$
$71$	2.56731	−	4.44671i	0.304683	−	0.527727i	0.977191	+	0.212363i	$0.0681160\pi$
$72$	−0.214630	+	2.99231i	−0.0252944	+	0.352647i
$73$	8.65726	+	8.65726i	1.01326	+	1.01326i	0.999911	+	0.0133448i	$0.00424790\pi$
$73$	8.65726	+	8.65726i	1.01326	+	1.01326i	0.0133448	+	0.999911i	$0.495752\pi$
$74$	0.0406050	−	0.0703298i	0.00472023	−	0.00817568i
$75$	−7.98174	+	3.36033i	−0.921652	+	0.388018i
$76$	−2.66471	+	1.53847i	−0.305663	+	0.176474i
$77$	1.44933	−	1.44933i	0.165166	−	0.165166i
$78$	−3.11736	+	5.41129i	−0.352971	+	0.612708i
$79$			16.1671i			1.81894i	0.415767	+	0.909471i	$0.363513\pi$
$79$			16.1671i			1.81894i	−0.415767	+	0.909471i	$0.636487\pi$
$80$	−1.15805	−	1.91283i	−0.129474	−	0.213861i
$81$	1.28448	−	8.90787i	0.142720	−	0.989763i
$82$	4.40993	−	1.18164i	0.486996	−	0.130490i
$83$	−6.03976	+	6.03976i	−0.662950	+	0.662950i	−0.956074	−	0.293124i	$-0.905305\pi$
$83$	−6.03976	+	6.03976i	−0.662950	+	0.662950i	0.293124	+	0.956074i	$0.405305\pi$
$84$	−0.123234	−	1.29196i	−0.0134460	−	0.140965i
$85$	−4.85089	−	16.7064i	−0.526152	−	1.81206i
$86$	−6.33192			−0.682789
$87$	8.38725	+	6.92654i	0.899207	+	0.742603i
$88$	−2.64222	−	0.707980i	−0.281661	−	0.0754709i
$89$	9.45097	−	5.45652i	1.00180	−	0.578390i	0.0930199	−	0.995664i	$-0.470348\pi$
$89$	9.45097	−	5.45652i	1.00180	−	0.578390i	0.908780	+	0.417275i	$0.137015\pi$
$90$	3.05470	+	5.97234i	0.321994	+	0.629539i
$91$	0.941462	−	2.53230i	0.0986921	−	0.265457i
$92$	5.41848	−	5.41848i	0.564916	−	0.564916i
$93$	−2.50143	−	6.70869i	−0.259386	−	0.695659i
$94$	−4.56594	+	2.63615i	−0.470941	+	0.271898i
$95$	−3.31550	+	6.02869i	−0.340163	+	0.618531i
$96$	−1.41099	+	1.00454i	−0.144009	+	0.102526i
$97$	1.28358	+	4.79038i	0.130328	+	0.486390i	0.999973	−	0.00728654i	$-0.00231940\pi$
$97$	1.28358	+	4.79038i	0.130328	+	0.486390i	−0.869646	+	0.493676i	$0.835653\pi$
$98$	−1.66642	−	6.21916i	−0.168334	−	0.628230i
$99$	7.75438	+	2.68559i	0.779345	+	0.269912i
$100$	−4.43031	−	2.31783i	−0.443031	−	0.231783i
$101$	3.87196	−	2.23548i	0.385274	−	0.222438i	−0.294836	−	0.955548i	$-0.595265\pi$
$101$	3.87196	−	2.23548i	0.385274	−	0.222438i	0.680111	+	0.733110i	$0.261932\pi$
$102$	−12.6260	+	4.70780i	−1.25016	+	0.466141i
$103$	−10.9536	+	10.9536i	−1.07929	+	1.07929i	−0.0827136	+	0.996573i	$0.526359\pi$
$103$	−10.9536	+	10.9536i	−1.07929	+	1.07929i	−0.996573	+	0.0827136i	$0.973641\pi$
$104$	−3.55500	+	0.601652i	−0.348596	+	0.0589969i
$105$	−1.73189	−	2.32860i	−0.169015	−	0.227248i
$106$	5.26987	−	3.04256i	0.511855	−	0.295520i
$107$	−5.47574	−	1.46722i	−0.529360	−	0.141842i	−0.0157673	−	0.999876i	$-0.505019\pi$
$107$	−5.47574	−	1.46722i	−0.529360	−	0.141842i	−0.513593	+	0.858034i	$0.671686\pi$
$108$	4.43773	−	2.70307i	0.427020	−	0.260103i
$109$	3.85609			0.369346			0.184673	−	0.982800i	$-0.440877\pi$
$109$	3.85609			0.369346			0.184673	+	0.982800i	$0.440877\pi$
$110$	−5.87398	+	1.70558i	−0.560062	+	0.162621i
$111$	−0.140024	+	0.0133562i	−0.0132905	+	0.00126772i
$112$	0.529836	−	0.529836i	0.0500648	−	0.0500648i
$113$	1.19531	−	0.320283i	0.112445	−	0.0301297i	−0.202158	−	0.979353i	$-0.564795\pi$
$113$	1.19531	−	0.320283i	0.112445	−	0.0301297i	0.314603	+	0.949223i	$0.398129\pi$
$114$	4.84758	+	2.21441i	0.454017	+	0.207399i
$115$	4.08975	−	16.6395i	0.381371	−	1.55164i
$116$			6.28020i			0.583102i
$117$	10.7668	−	1.03732i	0.995391	−	0.0959006i
$118$	0.175685	−	0.175685i	0.0161731	−	0.0161731i
$119$	5.04848	−	2.91474i	0.462794	−	0.267194i
$120$	−1.53567	+	3.55552i	−0.140187	+	0.324573i
$121$	1.75873	−	3.04621i	0.159885	−	0.276928i
$122$	7.26079	+	7.26079i	0.657361	+	0.657361i
$123$	−6.09725	−	5.03536i	−0.549770	−	0.454023i
$124$	2.06688	−	3.57993i	0.185611	−	0.321488i
$125$	−11.1586	+	0.696918i	−0.998055	+	0.0623342i
$126$	−1.69915	+	1.47172i	−0.151373	+	0.131111i
$127$	−3.08831	+	11.5257i	−0.274043	+	1.02274i	0.682437	+	0.730944i	$0.260920\pi$
$127$	−3.08831	+	11.5257i	−0.274043	+	1.02274i	−0.956480	+	0.291798i	$0.905747\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	6.36070	+	8.93428i	0.560028	+	0.786620i
$130$	−6.10336	+	5.26773i	−0.535300	+	0.462011i
$131$			7.76241i			0.678205i	0.940749	+	0.339102i	$0.110123\pi$
$131$			7.76241i			0.678205i	−0.940749	+	0.339102i	$0.889877\pi$
$132$	1.65527	+	4.43934i	0.144073	+	0.386395i
$133$	−2.22699	−	0.596721i	−0.193105	−	0.0517423i
$134$	−3.78786	+	6.56076i	−0.327221	+	0.566763i
$135$	5.35832	−	10.3096i	0.461171	−	0.887311i
$136$	−6.73758	−	3.88995i	−0.577743	−	0.333560i
$137$	−2.80890	+	0.752641i	−0.239980	+	0.0643025i	−0.376804	−	0.926293i	$-0.622977\pi$
$137$	−2.80890	+	0.752641i	−0.239980	+	0.0643025i	0.136824	+	0.990595i	$0.456310\pi$
$138$	−13.0885	−	2.20232i	−1.11417	−	0.187474i
$139$	−2.41220	−	1.39268i	−0.204600	−	0.118126i	0.394199	−	0.919025i	$-0.371022\pi$
$139$	−2.41220	−	1.39268i	−0.204600	−	0.118126i	−0.598799	+	0.800899i	$0.704355\pi$
$140$	0.399908	−	1.62706i	0.0337984	−	0.137512i
$141$	8.30627	+	3.79437i	0.699514	+	0.319544i
$142$	−3.63072	−	3.63072i	−0.304683	−	0.304683i
$143$	−0.927171	+	9.81903i	−0.0775339	+	0.821109i
$144$	2.83480	+	0.981784i	0.236233	+	0.0818153i
$145$	7.27280	+	12.0130i	0.603973	+	0.997622i
$146$	10.6029	−	6.12161i	0.877505	−	0.506628i
$147$	−7.10118	+	8.59872i	−0.585695	+	0.709210i
$148$	−0.0574241	−	0.0574241i	−0.00472023	−	0.00472023i
$149$	−19.9346	−	11.5092i	−1.63311	−	0.942874i	−0.983128	−	0.182920i	$-0.941445\pi$
$149$	−19.9346	−	11.5092i	−1.63311	−	0.942874i	−0.649977	−	0.759954i	$-0.725222\pi$
$150$	1.18001	+	8.57949i	0.0963471	+	0.700512i
$151$		−	4.79147i		−	0.389925i	−0.980811	−	0.194962i	$-0.937542\pi$
$151$		−	4.79147i		−	0.389925i	0.980811	−	0.194962i	$-0.0624584\pi$
$152$	0.796370	+	2.97209i	0.0645941	+	0.241069i
$153$	19.3261	+	13.0860i	1.56242	+	1.05794i
$154$	−1.02483	−	1.77506i	−0.0825830	−	0.143038i
$155$	−0.192170	−	9.24135i	−0.0154354	−	0.742283i
$156$	4.42008	+	4.41168i	0.353889	+	0.353217i
$157$	−3.59970	−	3.59970i	−0.287288	−	0.287288i	0.548719	−	0.836007i	$-0.315116\pi$
$157$	−3.59970	−	3.59970i	−0.287288	−	0.287288i	−0.836007	+	0.548719i	$0.815116\pi$
$158$	15.6162	+	4.18436i	1.24236	+	0.332890i
$159$	−9.58684	−	4.37935i	−0.760286	−	0.347305i
$160$	−2.14738	+	0.623516i	−0.169765	+	0.0492933i
$161$	5.74182			0.452519
$162$	−8.27189	−	3.54624i	−0.649901	−	0.278619i
$163$	18.2707	−	4.89561i	1.43107	−	0.383454i	0.541673	−	0.840589i	$-0.317791\pi$
$163$	18.2707	−	4.89561i	1.43107	−	0.383454i	0.889397	+	0.457135i	$0.151124\pi$
$164$		−	4.56550i		−	0.356506i
$165$	8.30723	+	6.57480i	0.646717	+	0.511848i
$166$	4.27076	+	7.39717i	0.331475	+	0.574132i
$167$	6.01915	−	22.4638i	0.465776	−	1.73830i	−0.188528	−	0.982068i	$-0.560372\pi$
$167$	6.01915	−	22.4638i	0.465776	−	1.73830i	0.654304	−	0.756231i	$-0.272962\pi$
$168$	−1.27984	−	0.215350i	−0.0987416	−	0.0166146i
$169$	4.27775	+	12.2760i	0.329057	+	0.944310i
$170$	−17.3926	+	0.361671i	−1.33395	+	0.0277389i
$171$	−1.74509	−	9.06435i	−0.133450	−	0.693169i
$172$	−1.63882	+	6.11617i	−0.124959	+	0.466354i
$173$	17.0148	−	4.55910i	1.29361	−	0.346622i	0.454580	−	0.890706i	$-0.349789\pi$
$173$	17.0148	−	4.55910i	1.29361	−	0.346622i	0.839031	+	0.544084i	$0.183123\pi$
$174$	8.86130	−	6.30874i	0.671774	−	0.478264i
$175$	−1.11927	−	3.57541i	−0.0846088	−	0.270276i
$176$	−1.36771	+	2.36895i	−0.103095	+	0.178566i
$177$	−0.424372	−	0.0714063i	−0.0318977	−	0.00536723i
$178$	−2.82450	−	10.5412i	−0.211705	−	0.790095i
$179$	−1.28691	−	2.22899i	−0.0961878	−	0.166602i	0.813916	−	0.580983i	$-0.197332\pi$
$179$	−1.28691	−	2.22899i	−0.0961878	−	0.166602i	−0.910104	+	0.414380i	$0.863998\pi$
$180$	6.55945	−	1.40486i	0.488912	−	0.104712i
$181$	15.4455			1.14805			0.574026	−	0.818837i	$-0.305381\pi$
$181$	15.4455			1.14805			0.574026	+	0.818837i	$0.305381\pi$
$182$	−2.20234	−	1.56479i	−0.163249	−	0.115990i
$183$	2.95112	−	17.5387i	0.218153	−	1.29650i
$184$	−3.83145	−	6.63626i	−0.282458	−	0.489232i
$185$	−0.176343	−	0.0433424i	−0.0129650	−	0.00318659i
$186$	−7.12752	+	0.679860i	−0.522615	+	0.0498497i
$187$	−15.0482	+	15.0482i	−1.10043	+	1.10043i
$188$	1.36457	+	5.09265i	0.0995216	+	0.371420i
$189$	3.78345	+	0.919085i	0.275206	+	0.0668536i
$190$	4.96516	+	4.76287i	0.360210	+	0.345535i
$191$	−5.81737	−	3.35866i	−0.420930	−	0.243024i	0.274545	−	0.961574i	$-0.411473\pi$
$191$	−5.81737	−	3.35866i	−0.420930	−	0.243024i	−0.695475	+	0.718550i	$0.744806\pi$
$192$	0.605124	+	1.62291i	0.0436710	+	0.117123i
$193$	6.23907	−	23.2845i	0.449098	−	1.67606i	−0.255784	−	0.966734i	$-0.582334\pi$
$193$	6.23907	−	23.2845i	0.449098	−	1.67606i	0.704883	−	0.709324i	$-0.251000\pi$
$194$	4.95937			0.356062
$195$	13.5638	+	3.32011i	0.971324	+	0.237758i
$196$	−6.43855			−0.459896
$197$	0.874848	−	3.26498i	0.0623303	−	0.232620i	−0.927732	−	0.373246i	$-0.878245\pi$
$197$	0.874848	−	3.26498i	0.0623303	−	0.232620i	0.990063	+	0.140626i	$0.0449115\pi$
$198$	4.60107	−	6.79508i	0.326984	−	0.482905i
$199$	0.216313	+	0.124888i	0.0153340	+	0.00885309i	0.507647	−	0.861565i	$-0.330515\pi$
$199$	0.216313	+	0.124888i	0.0153340	+	0.00885309i	−0.492313	+	0.870418i	$0.663849\pi$
$200$	−3.38550	+	3.67945i	−0.239391	+	0.260177i
$201$	13.0622	−	1.24594i	0.921339	−	0.0878821i
$202$	−1.15717	−	4.31861i	−0.0814180	−	0.303856i
$203$	−3.32748	+	3.32748i	−0.233543	+	0.233543i
$204$	1.27952	+	13.4143i	0.0895846	+	0.939188i
$205$	−5.28708	−	8.73302i	−0.369266	−	0.609940i
$206$	7.74534	+	13.4153i	0.539643	+	0.934690i
$207$	10.0405	+	20.6801i	0.697866	+	1.43737i
$208$	−0.338950	+	3.58958i	−0.0235019	+	0.248893i
$209$	8.41672			0.582197
$210$	−2.69750	+	1.07019i	−0.186145	+	0.0738502i
$211$	−5.14120	−	8.90481i	−0.353935	−	0.613033i	0.633000	−	0.774151i	$-0.281823\pi$
$211$	−5.14120	−	8.90481i	−0.353935	−	0.613033i	−0.986935	+	0.161119i	$0.948490\pi$
$212$	−1.57495	−	5.87778i	−0.108168	−	0.403688i
$213$	−1.47569	+	8.77013i	−0.101113	+	0.600919i
$214$	−2.83445	+	4.90942i	−0.193759	+	0.335601i
$215$	3.94806	+	13.5970i	0.269255	+	0.927310i
$216$	−1.46240	−	4.98612i	−0.0995034	−	0.339263i
$217$	2.99189	−	0.801673i	0.203102	−	0.0544211i
$218$	0.998030	−	3.72470i	0.0675951	−	0.252268i
$219$	−19.2886	−	8.81121i	−1.30341	−	0.595406i
$220$	0.127164	+	6.11527i	0.00857341	+	0.412291i
$221$	−9.77507	+	26.2925i	−0.657542	+	1.76862i
$222$	−0.0233398	+	0.138710i	−0.00156646	+	0.00930959i
$223$	1.75897	−	6.56458i	0.117790	−	0.439597i	−0.881691	−	0.471827i	$-0.843595\pi$
$223$	1.75897	−	6.56458i	0.117790	−	0.439597i	0.999480	+	0.0322309i	$0.0102612\pi$
$224$	−0.374651	−	0.648914i	−0.0250324	−	0.0433574i
$225$	10.9202	−	10.2834i	0.728013	−	0.685563i
$226$		−	1.23748i		−	0.0823158i
$227$	15.9597	−	4.27638i	1.05928	−	0.283833i	0.313198	−	0.949688i	$-0.398600\pi$
$227$	15.9597	−	4.27638i	1.05928	−	0.283833i	0.746081	+	0.665855i	$0.231933\pi$
$228$	3.39360	−	4.10927i	0.224747	−	0.272143i
$229$	−3.66722			−0.242337			−0.121168	−	0.992632i	$-0.538664\pi$
$229$	−3.66722			−0.242337			−0.121168	+	0.992632i	$0.538664\pi$
$230$	−15.0140	−	8.25702i	−0.989996	−	0.544452i
$231$	−1.47510	+	3.22914i	−0.0970544	+	0.212462i
$232$	6.06621	+	1.62544i	0.398266	+	0.106715i
$233$	−3.62133	−	3.62133i	−0.237241	−	0.237241i	0.578466	−	0.815707i	$-0.303652\pi$
$233$	−3.62133	−	3.62133i	−0.237241	−	0.237241i	−0.815707	+	0.578466i	$0.803652\pi$
$234$	1.78467	−	10.6684i	0.116668	−	0.697416i
$235$	8.50774	+	8.16112i	0.554984	+	0.532373i
$236$	−0.124228	−	0.215169i	−0.00808654	−	0.0140063i
$237$	−9.78310	−	26.2377i	−0.635481	−	1.70432i
$238$	−1.50878	−	5.63085i	−0.0977998	−	0.364994i
$239$			9.07051i			0.586723i	0.956002	+	0.293361i	$0.0947739\pi$
$239$			9.07051i			0.586723i	−0.956002	+	0.293361i	$0.905226\pi$
$240$	3.03691	+	2.40358i	0.196032	+	0.155150i
$241$	0.313009	+	0.180716i	0.0201627	+	0.0116409i	0.510047	−	0.860146i	$-0.329628\pi$
$241$	0.313009	+	0.180716i	0.0201627	+	0.0116409i	−0.489885	+	0.871787i	$0.662961\pi$
$242$	−2.48722	−	2.48722i	−0.159885	−	0.159885i
$243$	3.30577	+	15.2339i	0.212065	+	0.977255i
$244$	8.89261	−	5.13415i	0.569291	−	0.328680i
$245$	−12.3158	+	7.45617i	−0.786830	+	0.476357i
$246$	−6.44187	+	4.58624i	−0.410719	+	0.292408i
$247$	10.0866	−	4.61926i	0.641798	−	0.293917i
$248$	−2.92300	−	2.92300i	−0.185611	−	0.185611i
$249$	6.14717	−	13.4568i	0.389561	−	0.852789i
$250$	−2.21489	+	10.9588i	−0.140082	+	0.693092i
$251$	0.203371	+	0.117416i	0.0128367	+	0.00741125i	0.506405	−	0.862296i	$-0.330974\pi$
$251$	0.203371	+	0.117416i	0.0128367	+	0.00741125i	−0.493568	+	0.869707i	$0.664308\pi$
$252$	0.981796	+	2.02217i	0.0618473	+	0.127384i
$253$	−20.2470	+	5.42517i	−1.27292	+	0.341078i
$254$	10.3337	+	5.96615i	0.648392	+	0.374350i
$255$	17.9820	+	24.1775i	1.12607	+	1.51405i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.74774	+	0.468305i	0.109021	+	0.0292121i	0.312917	−	0.949780i	$-0.398694\pi$
$257$	1.74774	+	0.468305i	0.109021	+	0.0292121i	−0.203896	+	0.978993i	$0.565360\pi$
$258$	10.2761	−	3.83160i	0.639763	−	0.238545i
$259$		−	0.0608507i		−	0.00378108i
$260$	3.50857	+	7.25878i	0.217592	+	0.450171i
$261$	−17.8031	−	6.16580i	−1.10199	−	0.381654i
$262$	7.49791	+	2.00906i	0.463222	+	0.124120i
$263$	3.31539	−	12.3732i	0.204436	−	0.762965i	−0.785185	−	0.619261i	$-0.787432\pi$
$263$	3.31539	−	12.3732i	0.204436	−	0.762965i	0.989621	−	0.143704i	$-0.0459012\pi$
$264$	4.71648	−	0.449883i	0.290280	−	0.0276884i
$265$	−9.81938	−	9.41932i	−0.603200	−	0.578624i
$266$	−1.15278	+	1.99667i	−0.0706813	+	0.122424i
$267$	−12.0362	+	14.5744i	−0.736601	+	0.891940i
$268$	5.35684	+	5.35684i	0.327221	+	0.327221i
$269$	−8.14185	+	14.1021i	−0.496417	+	0.859820i	−0.999991	−	0.00413206i	$-0.998685\pi$
$269$	−8.14185	+	14.1021i	−0.496417	+	0.859820i	0.503574	+	0.863952i	$0.332018\pi$
$270$	−8.57150	−	7.84407i	−0.521645	−	0.477375i
$271$	11.9257	−	6.88531i	0.724435	−	0.418253i	−0.0919479	−	0.995764i	$-0.529309\pi$
$271$	11.9257	−	6.88531i	0.724435	−	0.418253i	0.816383	+	0.577511i	$0.195976\pi$
$272$	−5.50121	+	5.50121i	−0.333560	+	0.333560i
$273$	0.00444890	+	4.67939i	0.000269260	+	0.283209i
$274$			2.90798i			0.175678i
$275$	7.32505	+	11.5502i	0.441717	+	0.696504i
$276$	−5.51484	+	12.0725i	−0.331954	+	0.726682i
$277$	−11.2193	+	3.00619i	−0.674100	+	0.180625i	−0.579601	−	0.814900i	$-0.696792\pi$
$277$	−11.2193	+	3.00619i	−0.674100	+	0.180625i	−0.0944990	+	0.995525i	$0.530125\pi$
$278$	−1.96955	+	1.96955i	−0.118126	+	0.118126i
$279$	8.11918	+	9.37391i	0.486082	+	0.561201i
$280$	−1.46812	−	0.807397i	−0.0877369	−	0.0482512i
$281$	20.1679			1.20312			0.601559	−	0.798828i	$-0.294547\pi$
$281$	20.1679			1.20312			0.601559	+	0.798828i	$0.294547\pi$
$282$	5.81490	−	7.04118i	0.346272	−	0.419296i
$283$	−13.8504	−	3.71120i	−0.823320	−	0.220608i	−0.177523	−	0.984117i	$-0.556808\pi$
$283$	−13.8504	−	3.71120i	−0.823320	−	0.220608i	−0.645798	+	0.763509i	$0.723475\pi$
$284$	−4.44671	+	2.56731i	−0.263864	+	0.152342i
$285$	1.73264	−	11.7903i	0.102633	−	0.698397i
$286$	9.24449	+	3.43693i	0.546638	+	0.203230i
$287$	2.41897	−	2.41897i	0.142787	−	0.142787i
$288$	1.68203	−	2.48410i	0.0991146	−	0.146377i
$289$	−37.6953	+	21.7634i	−2.21737	+	1.28020i
$290$	13.4860	−	3.91581i	0.791923	−	0.229944i
$291$	−4.98190	−	6.99762i	−0.292044	−	0.410208i
$292$	−3.16878	−	11.8260i	−0.185439	−	0.692067i
$293$	5.05729	+	18.8741i	0.295450	+	1.10264i	0.940859	+	0.338798i	$0.110020\pi$
$293$	5.05729	+	18.8741i	0.295450	+	1.10264i	−0.645409	+	0.763837i	$0.723313\pi$
$294$	6.46780	+	9.08472i	0.377210	+	0.529832i
$295$	−0.486803	−	0.267719i	−0.0283428	−	0.0155872i
$296$	−0.0703298	+	0.0406050i	−0.00408784	+	0.00236011i
$297$	−14.2098	+	0.333892i	−0.824534	+	0.0193744i
$298$	−16.2765	+	16.2765i	−0.942874	+	0.942874i
$299$	−21.2867	+	17.6135i	−1.23104	+	1.01862i
$300$	8.59256	+	1.08074i	0.496091	+	0.0623963i
$301$	−4.10888	+	2.37226i	−0.236832	+	0.136735i
$302$	−4.62821	−	1.24012i	−0.266323	−	0.0713611i
$303$	−4.93109	+	5.97098i	−0.283284	+	0.343024i
$304$	3.07694			0.176474
$305$	11.0644	−	20.1189i	0.633548	−	1.15200i
$306$	17.6421	−	15.2806i	1.00853	−	0.873535i
$307$	4.20739	−	4.20739i	0.240128	−	0.240128i	−0.576775	−	0.816903i	$-0.695689\pi$
$307$	4.20739	−	4.20739i	0.240128	−	0.240128i	0.816903	+	0.576775i	$0.195689\pi$
$308$	−1.97982	+	0.530490i	−0.112811	+	0.0302275i
$309$	11.1484	−	24.4049i	0.634208	−	1.38834i
$310$	−8.97620	−	2.20622i	−0.509814	−	0.125305i
$311$			11.9551i			0.677912i	0.940802	+	0.338956i	$0.110074\pi$
$311$			11.9551i			0.677912i	−0.940802	+	0.338956i	$0.889926\pi$
$312$	5.40536	−	3.12764i	0.306018	−	0.177068i
$313$	−8.77948	+	8.77948i	−0.496245	+	0.496245i	−0.910267	−	0.414022i	$-0.864124\pi$
$313$	−8.77948	+	8.77948i	−0.496245	+	0.496245i	0.414022	+	0.910267i	$0.364124\pi$
$314$	−4.40872	+	2.54537i	−0.248798	+	0.143644i
$315$	4.21978	+	2.73109i	0.237758	+	0.153879i
$316$	8.08356	−	14.0011i	0.454736	−	0.787625i
$317$	−4.55342	−	4.55342i	−0.255745	−	0.255745i	0.567576	−	0.823321i	$-0.307881\pi$
$317$	−4.55342	−	4.55342i	−0.255745	−	0.255745i	−0.823321	+	0.567576i	$0.807881\pi$
$318$	−6.71139	+	8.12672i	−0.376356	+	0.455724i
$319$	8.58951	−	14.8775i	0.480920	−	0.832978i
$320$	0.0464880	+	2.23558i	0.00259876	+	0.124973i
$321$	9.77447	−	0.932340i	0.545558	−	0.0520381i
$322$	1.48609	−	5.54617i	0.0828167	−	0.309076i
$323$	23.1226	+	6.19567i	1.28657	+	0.344736i
$324$	−5.56633	+	7.07220i	−0.309240	+	0.392900i
$325$	15.1173	+	9.82170i	0.838560	+	0.544810i
$326$		−	18.9152i		−	1.04762i
$327$	−6.25807	+	2.33341i	−0.346072	+	0.129038i
$328$	−4.40993	−	1.18164i	−0.243498	−	0.0652450i
$329$	−1.97527	+	3.42127i	−0.108900	+	0.188621i
$330$	8.50084	−	6.32248i	0.467956	−	0.348041i
$331$	6.54374	+	3.77803i	0.359676	+	0.207659i	0.668939	−	0.743317i	$-0.266749\pi$
$331$	6.54374	+	3.77803i	0.359676	+	0.207659i	−0.309262	+	0.950977i	$0.600082\pi$
$332$	8.25047	−	2.21071i	0.452803	−	0.121328i
$333$	0.219164	−	0.106408i	0.0120101	−	0.00583111i
$334$	−20.1405	−	11.6281i	−1.10204	−	0.636262i
$335$	16.4502	+	4.04322i	0.898771	+	0.220905i
$336$	−0.539258	+	1.18049i	−0.0294189	+	0.0644011i
$337$	−18.7234	−	18.7234i	−1.01993	−	1.01993i	−0.999797	−	0.0201306i	$-0.993592\pi$
$337$	−18.7234	−	18.7234i	−1.01993	−	1.01993i	−0.0201306	−	0.999797i	$-0.506408\pi$
$338$	12.9649	−	0.954717i	0.705197	−	0.0519297i
$339$	−1.74607	+	1.24310i	−0.0948334	+	0.0675160i
$340$	−4.15219	+	16.8936i	−0.225184	+	0.916183i
$341$	−9.79264	+	5.65378i	−0.530301	+	0.306169i
$342$	−9.20716	−	0.660402i	−0.497866	−	0.0357105i
$343$	−7.12023	−	7.12023i	−0.384456	−	0.384456i
$344$	5.48361	+	3.16596i	0.295656	+	0.170697i
$345$	3.43169	+	29.4792i	0.184756	+	1.58711i
$346$		−	17.6150i		−	0.946989i
$347$	−5.65682	−	21.1115i	−0.303674	−	1.13333i	−0.934081	−	0.357062i	$-0.883778\pi$
$347$	−5.65682	−	21.1115i	−0.303674	−	1.13333i	0.630407	−	0.776265i	$-0.282888\pi$
$348$	−3.80030	−	10.1922i	−0.203717	−	0.546358i
$349$	8.42181	+	14.5870i	0.450809	+	0.780824i	0.998436	−	0.0558982i	$-0.0178022\pi$
$349$	8.42181	+	14.5870i	0.450809	+	0.780824i	−0.547627	+	0.836722i	$0.684469\pi$
$350$	−3.74327	+	0.155747i	−0.200086	+	0.00832500i
$351$	−16.8458	+	8.19872i	−0.899162	+	0.437616i
$352$	1.93424	+	1.93424i	0.103095	+	0.103095i
$353$	−30.7002	−	8.22610i	−1.63401	−	0.437831i	−0.678934	−	0.734199i	$-0.737558\pi$
$353$	−30.7002	−	8.22610i	−1.63401	−	0.437831i	−0.955074	+	0.296368i	$0.904225\pi$
$354$	−0.178809	+	0.391431i	−0.00950358	+	0.0208043i
$355$	−5.53272	+	10.0603i	−0.293646	+	0.533947i
$356$	−10.9130			−0.578390
$357$	−6.42944	+	7.78531i	−0.340282	+	0.412042i
$358$	−2.48611	+	0.666151i	−0.131395	+	0.0352072i
$359$		−	2.71790i		−	0.143445i	−0.997425	−	0.0717225i	$-0.977150\pi$
$359$		−	2.71790i		−	0.143445i	0.997425	−	0.0717225i	$-0.0228496\pi$
$360$	0.340717	−	6.69955i	0.0179573	−	0.353097i
$361$	4.76623	+	8.25535i	0.250854	+	0.434492i
$362$	3.99758	−	14.9192i	0.210108	−	0.784135i
$363$	−1.01092	+	6.00796i	−0.0530596	+	0.315336i
$364$	−2.08148	+	1.72230i	−0.109099	+	0.0902733i
$365$	−19.7565	−	18.9516i	−1.03410	−	0.991971i
$366$	−16.1773	−	7.38990i	−0.845599	−	0.386276i
$367$	5.38414	−	20.0939i	0.281050	−	1.04889i	−0.670628	−	0.741794i	$-0.733975\pi$
$367$	5.38414	−	20.0939i	0.281050	−	1.04889i	0.951678	−	0.307099i	$-0.0993581\pi$
$368$	−7.40179	+	1.98330i	−0.385845	+	0.103387i
$369$	12.9423	+	4.48233i	0.673748	+	0.233341i
$370$	−0.0875063	+	0.159116i	−0.00454924	+	0.00827204i
$371$	2.27980	−	3.94873i	0.118361	−	0.205008i
$372$	−1.18804	+	7.06061i	−0.0615972	+	0.366076i
$373$	4.09975	+	15.3005i	0.212277	+	0.792229i	0.987107	+	0.160060i	$0.0511687\pi$
$373$	4.09975	+	15.3005i	0.212277	+	0.792229i	−0.774830	+	0.632170i	$0.782165\pi$
$374$	10.6406	+	18.4301i	0.550215	+	0.953000i
$375$	17.6876	−	7.88336i	0.913386	−	0.407095i
$376$	5.27230			0.271898
$377$	2.12867	−	22.5433i	0.109632	−	1.16104i
$378$	1.86700	−	3.41666i	0.0960280	−	0.175734i
$379$	−4.19360	−	7.26352i	−0.215411	−	0.373102i	0.737989	−	0.674813i	$-0.235776\pi$
$379$	−4.19360	−	7.26352i	−0.215411	−	0.373102i	−0.953399	+	0.301711i	$0.902442\pi$
$380$	5.88565	−	3.56325i	0.301928	−	0.182791i
$381$	−1.96245	−	20.5740i	−0.100539	−	1.05404i
$382$	−4.74986	+	4.74986i	−0.243024	+	0.243024i
$383$	−7.67769	−	28.6535i	−0.392312	−	1.46413i	−0.826311	−	0.563214i	$-0.809565\pi$
$383$	−7.67769	−	28.6535i	−0.392312	−	1.46413i	0.434000	−	0.900913i	$-0.357102\pi$
$384$	1.72422	−	0.164466i	0.0879890	−	0.00839285i
$385$	−3.17272	+	3.30747i	−0.161697	+	0.168564i
$386$	−20.8763	−	12.0530i	−1.06258	−	0.613480i
$387$	−15.7292	−	10.6505i	−0.799558	−	0.541395i
$388$	1.28358	−	4.79038i	0.0651639	−	0.243195i
$389$	−23.6160			−1.19738			−0.598690	−	0.800981i	$-0.704312\pi$
$389$	−23.6160			−1.19738			−0.598690	+	0.800981i	$0.704312\pi$
$390$	6.71755	−	12.2423i	0.340156	−	0.619914i
$391$	−59.6165			−3.01494
$392$	−1.66642	+	6.21916i	−0.0841668	+	0.314115i
$393$	−4.69722	−	12.5977i	−0.236943	−	0.635468i
$394$	−2.92730	−	1.69008i	−0.147475	−	0.0851448i
$395$	−0.751576	−	36.1429i	−0.0378159	−	1.81855i
$396$	−5.37269	−	6.20298i	−0.269988	−	0.311712i
$397$	−4.73976	−	17.6890i	−0.237882	−	0.887786i	−0.976829	−	0.214023i	$-0.931343\pi$
$397$	−4.73976	−	17.6890i	−0.237882	−	0.887786i	0.738947	−	0.673763i	$-0.235323\pi$
$398$	0.176619	−	0.176619i	0.00885309	−	0.00885309i
$399$	3.97529	−	0.379184i	0.199014	−	0.0189829i
$400$	2.67785	+	4.22246i	0.133892	+	0.211123i
$401$	0.233727	+	0.404827i	0.0116718	+	0.0202161i	0.871802	−	0.489858i	$-0.162951\pi$
$401$	0.233727	+	0.404827i	0.0116718	+	0.0202161i	−0.860131	+	0.510074i	$0.829618\pi$
$402$	2.17727	−	12.9396i	0.108592	−	0.645370i
$403$	−8.63264	+	12.1499i	−0.430023	+	0.605230i
$404$	−4.47095			−0.222438
$405$	−2.45745	+	19.9740i	−0.122112	+	0.992516i
$406$	2.35288	+	4.07531i	0.116772	+	0.202254i
$407$	0.0574950	+	0.214574i	0.00284992	+	0.0106360i
$408$	13.2884	+	2.23595i	0.657872	+	0.110696i
$409$	11.4553	−	19.8411i	0.566427	−	0.981080i	−0.430488	−	0.902596i	$-0.641659\pi$
$409$	11.4553	−	19.8411i	0.566427	−	0.981080i	0.996915	−	0.0784843i	$-0.0250081\pi$
$410$	−9.80385	+	2.84666i	−0.484177	+	0.140587i
$411$	4.10313	−	2.92120i	0.202393	−	0.144092i
$412$	14.9628	−	4.00928i	0.737167	−	0.197523i
$413$	0.0481839	−	0.179825i	0.00237097	−	0.00884859i
$414$	22.5741	−	4.34602i	1.10946	−	0.213595i
$415$	13.2216	−	13.7832i	0.649024	−	0.676590i
$416$	3.37955	+	1.25645i	0.165696	+	0.0616027i
$417$	4.75752	+	0.800517i	0.232977	+	0.0392015i
$418$	2.17841	−	8.12993i	0.106549	−	0.397648i
$419$	12.2840	+	21.2765i	0.600112	+	1.03942i	0.992804	+	0.119754i	$0.0382105\pi$
$419$	12.2840	+	21.2765i	0.600112	+	1.03942i	−0.392692	+	0.919670i	$0.628456\pi$
$420$	0.335561	+	2.88257i	0.0163737	+	0.140655i
$421$			1.36907i			0.0667243i	0.999443	+	0.0333621i	$0.0106215\pi$
$421$			1.36907i			0.0667243i	−0.999443	+	0.0333621i	$0.989379\pi$
$422$	−9.93203	+	2.66128i	−0.483484	+	0.129549i
$423$	−15.7764	−	1.13159i	−0.767073	−	0.0550199i
$424$	−6.08513			−0.295520
$425$	11.6212	+	37.1230i	0.563712	+	1.80073i
$426$	8.08936	+	3.69529i	0.391931	+	0.179037i
$427$	7.43189	+	1.99137i	0.359654	+	0.0963691i
$428$	4.00852	+	4.00852i	0.193759	+	0.193759i
$429$	−4.43702	−	16.4964i	−0.214221	−	0.796455i
$430$	14.1556	−	0.294358i	0.682641	−	0.0141952i
$431$	−12.8012	−	22.1723i	−0.616611	−	1.06800i	−0.990100	−	0.140367i	$-0.955172\pi$
$431$	−12.8012	−	22.1723i	−0.616611	−	1.06800i	0.373489	−	0.927635i	$-0.378162\pi$
$432$	−5.19472	+	0.122062i	−0.249931	+	0.00587272i
$433$	1.62968	+	6.08204i	0.0783174	+	0.292284i	0.993965	−	0.109697i	$-0.0349882\pi$
$433$	1.62968	+	6.08204i	0.0783174	+	0.292284i	−0.915648	+	0.401982i	$0.868322\pi$
$434$		−	3.09743i		−	0.148681i
$435$	−19.0724	−	15.0950i	−0.914452	−	0.723748i
$436$	−3.33947	−	1.92804i	−0.159932	−	0.0923366i
$437$	16.6723	+	16.6723i	0.797546	+	0.797546i
$438$	−13.5032	+	16.3509i	−0.645210	+	0.781275i
$439$	−14.2147	+	8.20688i	−0.678433	+	0.391693i	−0.799264	−	0.600980i	$-0.794777\pi$
$439$	−14.2147	+	8.20688i	−0.678433	+	0.391693i	0.120832	+	0.992673i	$0.461444\pi$
$440$	5.93981	+	1.45992i	0.283169	+	0.0695988i
$441$	6.32126	−	18.2520i	0.301012	−	0.869143i
$442$	22.8666	+	16.2470i	1.08765	+	0.772791i
$443$	8.73069	+	8.73069i	0.414808	+	0.414808i	0.883410	−	0.468602i	$-0.155242\pi$
$443$	8.73069	+	8.73069i	0.414808	+	0.414808i	−0.468602	+	0.883410i	$0.655242\pi$
$444$	0.127943	+	0.0584452i	0.00607189	+	0.00277369i
$445$	−20.8748	+	12.6379i	−0.989559	+	0.599092i
$446$	−5.88564	−	3.39807i	−0.278693	−	0.160903i
$447$	39.3165	+	6.61553i	1.85961	+	0.312904i
$448$	−0.723770	+	0.193934i	−0.0341949	+	0.00916250i
$449$	−0.242695	−	0.140120i	−0.0114535	−	0.00661267i	0.494262	−	0.869313i	$-0.335438\pi$
$449$	−0.242695	−	0.140120i	−0.0114535	−	0.00661267i	−0.505716	+	0.862700i	$0.668772\pi$
$450$	−7.10669	−	13.2097i	−0.335013	−	0.622709i
$451$	−6.24429	+	10.8154i	−0.294032	+	0.509278i
$452$	−1.19531	−	0.320283i	−0.0562227	−	0.0150648i
$453$	2.89943	+	7.77611i	0.136227	+	0.365354i
$454$		−	16.5226i		−	0.775446i
$455$	−1.98700	+	5.70494i	−0.0931519	+	0.267452i
$456$	−3.09092	−	4.34153i	−0.144745	−	0.203311i
$457$	13.2899	+	3.56102i	0.621676	+	0.166578i	0.555890	−	0.831256i	$-0.312378\pi$
$457$	13.2899	+	3.56102i	0.621676	+	0.166578i	0.0657866	+	0.997834i	$0.479044\pi$
$458$	−0.949147	+	3.54226i	−0.0443507	+	0.165519i
$459$	−39.2830	−	9.54273i	−1.83358	−	0.445417i
$460$	−11.8616	+	12.3654i	−0.553049	+	0.576539i
$461$	−9.12779	+	15.8098i	−0.425124	+	0.736336i	−0.996432	−	0.0843998i	$-0.973103\pi$
$461$	−9.12779	+	15.8098i	−0.425124	+	0.736336i	0.571308	+	0.820736i	$0.306436\pi$
$462$	2.73733	+	2.26060i	0.127352	+	0.105173i
$463$	25.9449	+	25.9449i	1.20576	+	1.20576i	0.972387	+	0.233375i	$0.0749768\pi$
$463$	25.9449	+	25.9449i	1.20576	+	1.20576i	0.233375	+	0.972387i	$0.425023\pi$
$464$	3.14010	−	5.43882i	0.145776	−	0.252491i
$465$	5.90403	+	14.8816i	0.273793	+	0.690116i
$466$	−4.43521	+	2.56067i	−0.205457	+	0.118621i
$467$	−2.64890	+	2.64890i	−0.122577	+	0.122577i	−0.765734	−	0.643157i	$-0.777624\pi$
$467$	−2.64890	+	2.64890i	−0.122577	+	0.122577i	0.643157	+	0.765734i	$0.277624\pi$
$468$	−9.84298	−	4.48505i	−0.454992	−	0.207322i
$469$			5.67649i			0.262116i
$470$	10.0850	−	6.10560i	0.465187	−	0.281630i
$471$	8.02025	+	3.66372i	0.369554	+	0.168815i
$472$	−0.239990	+	0.0643050i	−0.0110464	+	0.00295988i
$473$	12.2474	−	12.2474i	0.563138	−	0.563138i
$474$	−27.8757	+	2.65893i	−1.28037	+	0.122129i
$475$	7.13182	−	13.6318i	0.327230	−	0.625469i
$476$	−5.82949			−0.267194
$477$	18.2086	+	1.30605i	0.833714	+	0.0597999i
$478$	8.76144	+	2.34762i	0.400739	+	0.107378i
$479$	10.0713	−	5.81464i	0.460167	−	0.265678i	−0.251947	−	0.967741i	$-0.581071\pi$
$479$	10.0713	−	5.81464i	0.460167	−	0.265678i	0.712115	+	0.702063i	$0.247738\pi$
$480$	3.10769	−	2.31134i	0.141846	−	0.105498i
$481$	0.186665	+	0.225592i	0.00851118	+	0.0102861i
$482$	0.255571	−	0.255571i	0.0116409	−	0.0116409i
$483$	−9.31843	+	3.47451i	−0.424003	+	0.158096i
$484$	−3.04621	+	1.75873i	−0.138464	+	0.0799423i
$485$	−3.09225	−	10.6496i	−0.140412	−	0.483575i
$486$	15.5704	+	0.749693i	0.706289	+	0.0340068i
$487$	10.9616	+	40.9091i	0.496716	+	1.85377i	0.520202	+	0.854044i	$0.325857\pi$
$487$	10.9616	+	40.9091i	0.496716	+	1.85377i	−0.0234860	+	0.999724i	$0.507477\pi$
$488$	−2.65763	−	9.91842i	−0.120305	−	0.448986i
$489$	−26.6892	+	19.0011i	−1.20693	+	0.859262i
$490$	4.01454	+	13.8260i	0.181358	+	0.624594i
$491$	30.0469	−	17.3476i	1.35600	−	0.782887i	0.366917	−	0.930253i	$-0.380413\pi$
$491$	30.0469	−	17.3476i	1.35600	−	0.782887i	0.989082	+	0.147367i	$0.0470798\pi$
$492$	2.76269	+	7.40938i	0.124552	+	0.334040i
$493$	34.5488	−	34.5488i	1.55600	−	1.55600i
$494$	−1.85125	−	10.9385i	−0.0832915	−	0.492147i
$495$	−17.4604	−	5.64339i	−0.784788	−	0.253651i
$496$	−3.57993	+	2.06688i	−0.160744	+	0.0928055i
$497$	−3.71628	−	0.995774i	−0.166698	−	0.0446666i
$498$	−11.4072	−	9.42058i	−0.511171	−	0.422146i
$499$	20.9491			0.937809			0.468904	−	0.883249i	$-0.344649\pi$
$499$	20.9491			0.937809			0.468904	+	0.883249i	$0.344649\pi$
$500$	10.0121	+	4.97575i	0.447754	+	0.222522i
$501$	3.82484	+	40.0989i	0.170881	+	1.79149i
$502$	0.166052	−	0.166052i	0.00741125	−	0.00741125i
$503$	40.5259	−	10.8589i	1.80696	−	0.484173i	0.811930	−	0.583754i	$-0.198417\pi$
$503$	40.5259	−	10.8589i	1.80696	−	0.484173i	0.995029	+	0.0995811i	$0.0317503\pi$
$504$	2.20737	−	0.424967i	0.0983241	−	0.0189295i
$505$	−8.55217	+	5.17760i	−0.380567	+	0.230400i
$506$			20.9613i			0.931841i
$507$	−14.3709	−	17.3343i	−0.638234	−	0.769842i
$508$	8.43741	−	8.43741i	0.374350	−	0.374350i
$509$	−6.34056	+	3.66072i	−0.281040	+	0.162259i	−0.633894	−	0.773420i	$-0.718545\pi$
$509$	−6.34056	+	3.66072i	−0.281040	+	0.162259i	0.352854	+	0.935678i	$0.385211\pi$
$510$	28.0077	−	11.1116i	1.24020	−	0.492032i
$511$	4.58693	−	7.94480i	0.202914	−	0.351457i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	8.31717	+	13.6546i	0.367212	+	0.602866i
$514$	0.904695	−	1.56698i	0.0399044	−	0.0691165i
$515$	23.9784	−	24.9968i	1.05662	−	1.10149i
$516$	−1.04138	−	10.9177i	−0.0458443	−	0.480623i
$517$	3.73268	−	13.9305i	0.164163	−	0.612665i
$518$	−0.0587773	−	0.0157493i	−0.00258253	−	0.000691986i
$519$	−24.8546	+	17.6951i	−1.09100	+	0.776726i
$520$	7.91953	−	1.51031i	0.347294	−	0.0662315i
$521$			13.3481i			0.584790i	0.956298	+	0.292395i	$0.0944522\pi$
$521$			13.3481i			0.584790i	−0.956298	+	0.292395i	$0.905548\pi$
$522$	−10.5635	+	15.6007i	−0.462352	+	0.682823i
$523$	4.41930	+	1.18415i	0.193243	+	0.0517792i	0.354142	−	0.935192i	$-0.384773\pi$
$523$	4.41930	+	1.18415i	0.193243	+	0.0517792i	−0.160900	+	0.986971i	$0.551440\pi$
$524$	3.88120	−	6.72244i	0.169551	−	0.293671i
$525$	3.98003	+	5.12526i	0.173703	+	0.223685i
$526$	−11.0935	−	6.40485i	−0.483700	−	0.279265i
$527$	−31.0643	+	8.32366i	−1.35318	+	0.362584i
$528$	0.786163	−	4.67221i	0.0342133	−	0.203332i
$529$	−30.9344	−	17.8600i	−1.34497	−	0.776520i
$530$	−11.6398	+	7.04689i	−0.505601	+	0.306097i
$531$	0.731926	−	0.140912i	0.0317629	−	0.00611505i
$532$	1.63027	+	1.63027i	0.0706813	+	0.0706813i
$533$	−1.54747	+	16.3882i	−0.0670285	+	0.709853i
$534$	10.9626	+	15.3982i	0.474399	+	0.666344i
$535$	12.3097	+	3.02554i	0.532195	+	0.130806i
$536$	6.56076	−	3.78786i	0.283382	−	0.163610i
$537$	3.43734	+	2.83870i	0.148332	+	0.122499i
$538$	11.5143	+	11.5143i	0.496417	+	0.496417i
$539$	15.2526	+	8.80608i	0.656975	+	0.379305i
$540$	−9.79525	+	6.24924i	−0.421521	+	0.268924i
$541$		−	30.0718i		−	1.29289i	−0.762962	−	0.646444i	$-0.776255\pi$
$541$		−	30.0718i		−	1.29289i	0.762962	−	0.646444i	$-0.223745\pi$
$542$	−3.56410	−	13.3014i	−0.153091	−	0.571344i
$543$	−25.0666	+	9.34642i	−1.07571	+	0.401093i
$544$	3.88995	+	6.73758i	0.166780	+	0.288872i
$545$	−8.62062	+	0.179262i	−0.369267	+	0.00767873i
$546$	4.52109	+	1.20682i	0.193485	+	0.0516470i
$547$	19.1391	+	19.1391i	0.818328	+	0.818328i	0.985866	−	0.167538i	$-0.0535817\pi$
$547$	19.1391	+	19.1391i	0.818328	+	0.818328i	−0.167538	+	0.985866i	$0.553582\pi$
$548$	2.80890	+	0.752641i	0.119990	+	0.0321513i
$549$	5.82368	+	30.2494i	0.248549	+	1.29101i
$550$	13.0525	−	4.08604i	0.556561	−	0.174229i
$551$	−19.3238			−0.823221
$552$	10.2338	+	8.45153i	0.435581	+	0.359721i
$553$	11.7013	−	3.13535i	0.497589	−	0.133328i
$554$			11.6150i			0.493475i
$555$	0.312415	−	0.0363684i	0.0132613	−	0.00154375i
$556$	1.39268	+	2.41220i	0.0590630	+	0.102300i
$557$	2.08046	−	7.76438i	0.0881519	−	0.328987i	−0.907740	−	0.419532i	$-0.862194\pi$
$557$	2.08046	−	7.76438i	0.0881519	−	0.328987i	0.995892	+	0.0905447i	$0.0288608\pi$
$558$	11.1559	−	5.41638i	0.472267	−	0.229294i
$559$	7.95577	−	21.3990i	0.336493	−	0.905082i
$560$	−1.15986	+	1.20912i	−0.0490132	+	0.0510949i
$561$	15.3157	−	33.5277i	0.646631	−	1.41554i
$562$	5.21984	−	19.4807i	0.220186	−	0.821745i
$563$	8.19701	−	2.19638i	0.345463	−	0.0925665i	−0.0819156	−	0.996639i	$-0.526104\pi$
$563$	8.19701	−	2.19638i	0.345463	−	0.0925665i	0.427379	+	0.904073i	$0.359437\pi$
$564$	−5.29625	−	7.43916i	−0.223012	−	0.313245i
$565$	−2.65733	+	0.771587i	−0.111795	+	0.0324609i
$566$	−7.16949	+	12.4179i	−0.301356	+	0.521964i
$567$	−6.69635	+	0.797868i	−0.281220	+	0.0335073i
$568$	1.32894	+	4.95966i	0.0557609	+	0.208103i
$569$	−2.09053	−	3.62090i	−0.0876394	−	0.151796i	0.818873	−	0.573974i	$-0.194599\pi$
$569$	−2.09053	−	3.62090i	−0.0876394	−	0.151796i	−0.906513	+	0.422178i	$0.861266\pi$
$570$	−10.9401	−	4.72515i	−0.458231	−	0.197915i
$571$	−27.1939			−1.13803			−0.569015	−	0.822327i	$-0.692675\pi$
$571$	−27.1939			−1.13803			−0.569015	+	0.822327i	$0.692675\pi$
$572$	5.71247	−	8.03995i	0.238850	−	0.336167i
$573$	11.4734	+	1.93056i	0.479310	+	0.0806504i
$574$	−1.71047	−	2.96262i	−0.0713935	−	0.123657i
$575$	−8.36944	+	37.3892i	−0.349030	+	1.55924i
$576$	−1.96412	−	2.26765i	−0.0818383	−	0.0944854i
$577$	−10.3326	+	10.3326i	−0.430153	+	0.430153i	−0.888680	−	0.458527i	$-0.848377\pi$
$577$	−10.3326	+	10.3326i	−0.430153	+	0.430153i	0.458527	+	0.888680i	$0.348377\pi$
$578$	11.2655	+	42.0436i	0.468585	+	1.74878i
$579$	3.96459	+	41.5640i	0.164763	+	1.72734i
$580$	−0.291954	−	14.0399i	−0.0121227	−	0.582976i
$581$	5.54271	+	3.20009i	0.229950	+	0.132762i
$582$	−8.04860	+	3.00103i	−0.333625	+	0.124397i
$583$	−4.30815	+	16.0782i	−0.178425	+	0.665892i
$584$	−12.2432			−0.506628
$585$	−24.0219	+	2.81955i	−0.993182	+	0.116574i
$586$	19.5399			0.807185
$587$	−5.28813	+	19.7356i	−0.218265	+	0.814575i	0.766727	+	0.641973i	$0.221884\pi$
$587$	−5.28813	+	19.7356i	−0.218265	+	0.814575i	−0.984992	+	0.172601i	$0.944783\pi$
$588$	10.4492	−	3.89612i	0.430916	−	0.160673i
$589$	11.0152	+	6.35965i	0.453875	+	0.262045i
$590$	−0.384591	+	0.400925i	−0.0158333	+	0.0165058i
$591$	0.555918	+	5.82814i	0.0228674	+	0.239738i
$592$	0.0210187	+	0.0784427i	0.000863862	+	0.00322398i
$593$	−20.2317	+	20.2317i	−0.830816	+	0.830816i	−0.987628	−	0.156812i	$-0.949878\pi$
$593$	−20.2317	+	20.2317i	−0.830816	+	0.830816i	0.156812	+	0.987628i	$0.449878\pi$
$594$	−3.35524	+	13.8120i	−0.137667	+	0.566713i
$595$	−11.1508	+	6.75085i	−0.457139	+	0.276758i
$596$	11.5092	+	19.9346i	0.471437	+	0.816553i
$597$	−0.426628	−	0.0717860i	−0.0174607	−	0.00293800i
$598$	11.5039	+	25.1201i	0.470431	+	1.02724i
$599$	5.90125			0.241119			0.120559	−	0.992706i	$-0.461531\pi$
$599$	5.90125			0.241119			0.120559	+	0.992706i	$0.461531\pi$
$600$	3.26783	−	8.02006i	0.133409	−	0.327417i
$601$	21.9815	+	38.0731i	0.896646	+	1.55304i	0.831755	+	0.555143i	$0.187337\pi$
$601$	21.9815	+	38.0731i	0.896646	+	1.55304i	0.0648907	+	0.997892i	$0.479330\pi$
$602$	1.22797	+	4.58286i	0.0500484	+	0.186783i
$603$	−20.4448	+	9.92631i	−0.832578	+	0.404231i
$604$	−2.39574	+	4.14954i	−0.0974811	+	0.168842i
$605$	−3.79018	+	6.89182i	−0.154093	+	0.280192i
$606$	4.49127	+	6.30847i	0.182445	+	0.256264i
$607$	−38.6316	+	10.3513i	−1.56801	+	0.420146i	−0.935188	−	0.354153i	$-0.884769\pi$
$607$	−38.6316	+	10.3513i	−1.56801	+	0.420146i	−0.632820	+	0.774299i	$0.718103\pi$
$608$	0.796370	−	2.97209i	0.0322971	−	0.120534i
$609$	3.38665	−	7.41373i	0.137234	−	0.300419i
$610$	−16.5696	−	15.8946i	−0.670885	−	0.643552i
$611$	−3.17209	−	18.7430i	−0.128329	−	0.758261i
$612$	−10.1938	−	20.9959i	−0.412062	−	0.848707i
$613$	9.58562	−	35.7740i	0.387159	−	1.44490i	−0.447575	−	0.894246i	$-0.647712\pi$
$613$	9.58562	−	35.7740i	0.387159	−	1.44490i	0.834735	−	0.550652i	$-0.185621\pi$
$614$	−2.97507	−	5.15298i	−0.120064	−	0.207957i
$615$	13.8650	+	10.9735i	0.559091	+	0.442495i
$616$			2.04966i			0.0825830i
$617$	30.2479	−	8.10489i	1.21773	−	0.326291i	0.407941	−	0.913008i	$-0.366247\pi$
$617$	30.2479	−	8.10489i	1.21773	−	0.326291i	0.809792	+	0.586718i	$0.199580\pi$
$618$	−20.6879	−	17.0849i	−0.832189	−	0.687257i
$619$	41.8510			1.68213			0.841067	−	0.540930i	$-0.181928\pi$
$619$	41.8510			1.68213			0.841067	+	0.540930i	$0.181928\pi$
$620$	−4.45425	+	8.09933i	−0.178887	+	0.325277i
$621$	−28.8089	−	27.4861i	−1.15606	−	1.10298i
$622$	11.5477	+	3.09421i	0.463022	+	0.124066i
$623$	−5.78212	−	5.78212i	−0.231656	−	0.231656i
$624$	−1.62206	−	6.03067i	−0.0649343	−	0.241420i
$625$	24.9136	−	2.07676i	0.996544	−	0.0830703i
$626$	6.20803	+	10.7526i	0.248123	+	0.429761i
$627$	−13.6596	+	5.09316i	−0.545510	+	0.203401i
$628$	1.31758	+	4.91729i	0.0525773	+	0.196221i
$629$			0.631804i			0.0251917i
$630$	3.73019	−	3.36914i	0.148614	−	0.134230i
$631$	19.8719	+	11.4731i	0.791089	+	0.456735i	0.840346	−	0.542051i	$-0.182352\pi$
$631$	19.8719	+	11.4731i	0.791089	+	0.456735i	−0.0492571	+	0.998786i	$0.515685\pi$
$632$	−11.4319	−	11.4319i	−0.454736	−	0.454736i
$633$	13.7322	+	11.3406i	0.545806	+	0.450749i
$634$	−5.57678	+	3.21975i	−0.221482	+	0.127873i
$635$	6.36836	−	25.9103i	0.252721	−	1.02822i
$636$	6.11278	+	8.58605i	0.242387	+	0.340459i
$637$	23.1117	+	2.18234i	0.915719	+	0.0864676i
$638$	−12.1474	−	12.1474i	−0.480920	−	0.480920i
$639$	−2.91210	−	15.1261i	−0.115201	−	0.598378i
$640$	2.17144	+	0.533708i	0.0858337	+	0.0210967i
$641$	−18.7174	−	10.8065i	−0.739295	−	0.426832i	0.0825181	−	0.996590i	$-0.473704\pi$
$641$	−18.7174	−	10.8065i	−0.739295	−	0.426832i	−0.821813	+	0.569758i	$0.807037\pi$
$642$	1.62925	−	9.68272i	0.0643013	−	0.382146i
$643$	12.2114	−	3.27203i	0.481570	−	0.129036i	−0.00986377	−	0.999951i	$-0.503140\pi$
$643$	12.2114	−	3.27203i	0.481570	−	0.129036i	0.491433	+	0.870915i	$0.336473\pi$
$644$	−4.97256	−	2.87091i	−0.195946	−	0.113130i
$645$	−14.6352	−	19.6776i	−0.576261	−	0.774807i
$646$	11.9691	−	20.7311i	0.470919	−	0.815655i
$647$	0.713201	+	0.191102i	0.0280388	+	0.00751298i	0.272811	−	0.962068i	$-0.412047\pi$
$647$	0.713201	+	0.191102i	0.0280388	+	0.00751298i	−0.244772	+	0.969581i	$0.578713\pi$
$648$	5.39055	+	7.20708i	0.211761	+	0.283121i
$649$			0.679631i			0.0266778i
$650$	13.3997	−	12.0602i	0.525579	−	0.473040i
$651$	−4.37044	+	3.11150i	−0.171291	+	0.121949i
$652$	−18.2707	−	4.89561i	−0.715535	−	0.191727i
$653$	4.22226	−	15.7577i	0.165230	−	0.616646i	−0.832781	−	0.553603i	$-0.813253\pi$
$653$	4.22226	−	15.7577i	0.165230	−	0.616646i	0.998011	−	0.0630436i	$-0.0200807\pi$
$654$	0.634194	+	6.64877i	0.0247989	+	0.259987i
$655$	−0.360858	−	17.3535i	−0.0140999	−	0.678058i
$656$	−2.28275	+	3.95384i	−0.0891264	+	0.154371i
$657$	36.6355	+	2.62776i	1.42929	+	0.102519i
$658$	2.79345	+	2.79345i	0.108900	+	0.108900i
$659$	18.3967	−	31.8641i	0.716635	−	1.24125i	−0.245691	−	0.969348i	$-0.579015\pi$
$659$	18.3967	−	31.8641i	0.716635	−	1.24125i	0.962326	−	0.271899i	$-0.0876518\pi$
$660$	−3.90687	−	9.84756i	−0.152075	−	0.383316i
$661$	−9.03343	+	5.21545i	−0.351360	+	0.202858i	−0.665284	−	0.746590i	$-0.731690\pi$
$661$	−9.03343	+	5.21545i	−0.351360	+	0.202858i	0.313924	+	0.949448i	$0.398356\pi$
$662$	5.34294	−	5.34294i	0.207659	−	0.207659i
$663$	−0.0461923	−	48.5854i	−0.00179396	−	1.88690i
$664$		−	8.54152i		−	0.331475i
$665$	5.00637	+	1.23049i	0.194139	+	0.0477165i
$666$	−0.0460583	−	0.239236i	−0.00178472	−	0.00927022i
$667$	46.4847	−	12.4555i	1.79990	−	0.482281i
$668$	−16.4446	+	16.4446i	−0.636262	+	0.636262i
$669$	1.11773	+	11.7181i	0.0432140	+	0.453047i
$670$	8.16308	−	14.8432i	0.315367	−	0.573444i
$671$	−28.0882			−1.08433
$672$	1.00070	+	0.826417i	0.0386027	+	0.0318797i
$673$	32.5192	+	8.71349i	1.25352	+	0.335880i	0.823696	−	0.567031i	$-0.191908\pi$
$673$	32.5192	+	8.71349i	1.25352	+	0.335880i	0.429826	+	0.902912i	$0.358575\pi$
$674$	−22.9314	+	13.2394i	−0.883284	+	0.509964i
$675$	−11.4997	+	23.2971i	−0.442624	+	0.896707i
$676$	2.43338	−	12.7702i	0.0935914	−	0.491163i
$677$	−15.8574	+	15.8574i	−0.609449	+	0.609449i	−0.942802	−	0.333353i	$-0.891820\pi$
$677$	−15.8574	+	15.8574i	−0.609449	+	0.609449i	0.333353	+	0.942802i	$0.391820\pi$
$678$	0.748827	+	2.00831i	0.0287585	+	0.0771287i
$679$	3.21821	−	1.85803i	0.123503	−	0.0713047i
$680$	15.2433	+	8.38309i	0.584553	+	0.321477i
$681$	−23.3133	+	16.5977i	−0.893367	+	0.636026i
$682$	2.92661	+	10.9223i	0.112066	+	0.418235i
$683$	−9.93797	−	37.0890i	−0.380266	−	1.41917i	−0.845496	−	0.533981i	$-0.820695\pi$
$683$	−9.93797	−	37.0890i	−0.380266	−	1.41917i	0.465231	−	0.885190i	$-0.345971\pi$
$684$	−3.02089	+	8.72251i	−0.115506	+	0.333513i
$685$	6.24454	−	1.81317i	0.238591	−	0.0692778i
$686$	−8.72047	+	5.03476i	−0.332949	+	0.192228i
$687$	5.95156	−	2.21912i	0.227066	−	0.0846648i
$688$	4.47735	−	4.47735i	0.170697	−	0.170697i
$689$	3.66113	+	21.6326i	0.139478	+	0.824137i
$690$	29.3629	+	4.31502i	1.11783	+	0.164270i
$691$	−15.0642	+	8.69731i	−0.573068	+	0.330861i	−0.758374	−	0.651820i	$-0.774006\pi$
$691$	−15.0642	+	8.69731i	−0.573068	+	0.330861i	0.185305	+	0.982681i	$0.440673\pi$
$692$	−17.0148	−	4.55910i	−0.646805	−	0.173311i
$693$	0.439917	−	6.13322i	0.0167111	−	0.232982i
$694$	−21.8563			−0.829653
$695$	5.45742	+	3.00133i	0.207012	+	0.113847i
$696$	−10.8285	+	1.03288i	−0.410453	+	0.0391511i
$697$	−25.1158	+	25.1158i	−0.951328	+	0.951328i
$698$	16.2697	−	4.35945i	0.615817	−	0.165008i
$699$	8.06843	+	3.68573i	0.305176	+	0.139407i
$700$	−0.818390	+	3.65603i	−0.0309322	+	0.138185i
$701$			0.264759i			0.00999980i	0.999988	+	0.00499990i	$0.00159152\pi$
$701$			0.264759i			0.00999980i	−0.999988	+	0.00499990i	$0.998408\pi$
$702$	3.55935	+	18.3938i	0.134339	+	0.694228i
$703$	0.176690	−	0.176690i	0.00666400	−	0.00666400i
$704$	2.36895	−	1.36771i	0.0892830	−	0.0515476i
$705$	−18.7458	−	8.09650i	−0.706006	−	0.304932i
$706$	−15.8916	+	27.5251i	−0.598089	+	1.03592i
$707$	−2.36887	−	2.36887i	−0.0890907	−	0.0890907i
$708$	0.331814	+	0.274026i	0.0124703	+	0.0102985i
$709$	1.91951	−	3.32468i	0.0720886	−	0.124861i	−0.827728	−	0.561130i	$-0.810367\pi$
$709$	1.91951	−	3.32468i	0.0720886	−	0.124861i	0.899817	+	0.436269i	$0.143700\pi$
$710$	8.28557	+	7.94800i	0.310952	+	0.298283i
$711$	31.7541	+	36.6614i	1.19087	+	1.37491i
$712$	−2.82450	+	10.5412i	−0.105853	+	0.395048i
$713$	−30.5971	−	8.19848i	−1.14587	−	0.307036i
$714$	5.85597	+	8.22535i	0.219154	+	0.307826i
$715$	1.61630	−	21.9944i	0.0604463	−	0.822543i
$716$			2.57381i			0.0961878i
$717$	−5.48878	−	14.7206i	−0.204982	−	0.549751i
$718$	−2.62529	−	0.703443i	−0.0979748	−	0.0262523i
$719$	16.1311	−	27.9399i	0.601588	−	1.04198i	−0.390993	−	0.920394i	$-0.627868\pi$
$719$	16.1311	−	27.9399i	0.601588	−	1.04198i	0.992581	−	0.121587i	$-0.0387984\pi$
$720$	−6.38308	−	2.06308i	−0.237883	−	0.0768863i
$721$	10.0521	+	5.80360i	0.374361	+	0.216137i
$722$	9.20765	−	2.46718i	0.342673	−	0.0918190i
$723$	−0.617340	−	0.103876i	−0.0229591	−	0.00386318i
$724$	−13.3762	−	7.72274i	−0.497121	−	0.287013i
$725$	−16.8174	−	26.5179i	−0.624584	−	0.984850i
$726$	5.54160	+	2.53145i	0.205668	+	0.0939509i
$727$	−4.61828	−	4.61828i	−0.171283	−	0.171283i	0.616260	−	0.787543i	$-0.288647\pi$
$727$	−4.61828	−	4.61828i	−0.171283	−	0.171283i	−0.787543	+	0.616260i	$0.788647\pi$
$728$	1.12489	+	2.45632i	0.0416912	+	0.0910373i
$729$	−14.5834	−	22.7228i	−0.540124	−	0.841585i
$730$	−23.4192	+	14.1783i	−0.866783	+	0.524762i
$731$	42.6619	−	24.6308i	1.57791	−	0.911005i
$732$	−11.3251	+	13.7134i	−0.418587	+	0.506861i
$733$	−30.9392	−	30.9392i	−1.14277	−	1.14277i	−0.987942	−	0.154824i	$-0.950519\pi$
$733$	−30.9392	−	30.9392i	−1.14277	−	1.14277i	−0.154824	−	0.987942i	$-0.549481\pi$
$734$	−18.0157	−	10.4014i	−0.664971	−	0.383921i
$735$	15.4755	−	19.5533i	0.570824	−	0.721234i
$736$			7.66289i			0.282458i
$737$	−5.36345	−	20.0167i	−0.197565	−	0.737323i
$738$	7.67931	−	11.3412i	0.282679	−	0.417474i
$739$	25.2446	+	43.7249i	0.928637	+	1.60845i	0.785605	+	0.618729i	$0.212352\pi$
$739$	25.2446	+	43.7249i	0.928637	+	1.60845i	0.143032	+	0.989718i	$0.454315\pi$
$740$	0.131046	+	0.125707i	0.00481734	+	0.00462108i
$741$	−13.5745	+	13.6003i	−0.498670	+	0.499619i
$742$	−3.22412	−	3.22412i	−0.118361	−	0.118361i
$743$	−14.1736	−	3.79781i	−0.519979	−	0.139328i	−0.0107222	−	0.999943i	$-0.503413\pi$
$743$	−14.1736	−	3.79781i	−0.519979	−	0.139328i	−0.509257	+	0.860615i	$0.670080\pi$
$744$	6.51254	+	2.97498i	0.238761	+	0.109068i
$745$	45.1005	+	24.8032i	1.65235	+	0.908718i
$746$	15.8402			0.579952
$747$	−1.83326	+	25.5589i	−0.0670756	+	0.935151i
$748$	20.5562	−	5.50801i	0.751608	−	0.201393i
$749$			4.24772i			0.155208i
$750$	−3.03685	−	19.1253i	−0.110890	−	0.698358i
$751$	−3.62524	−	6.27910i	−0.132287	−	0.229127i	0.792271	−	0.610169i	$-0.208899\pi$
$751$	−3.62524	−	6.27910i	−0.132287	−	0.229127i	−0.924558	+	0.381042i	$0.875565\pi$
$752$	1.36457	−	5.09265i	0.0497608	−	0.185710i
$753$	−0.401103	−	0.0674910i	−0.0146170	−	0.00245951i
$754$	−21.2242	−	7.89078i	−0.772941	−	0.287365i
$755$	0.222746	+	10.7117i	0.00810655	+	0.389840i
$756$	−2.81702	−	2.68768i	−0.102454	−	0.0977499i
$757$	12.0609	−	45.0117i	0.438359	−	1.63598i	−0.294539	−	0.955640i	$-0.595166\pi$
$757$	12.0609	−	45.0117i	0.438359	−	1.63598i	0.732898	−	0.680339i	$-0.238167\pi$
$758$	−8.10140	+	2.17076i	−0.294256	+	0.0788457i
$759$	29.5761	−	21.0565i	1.07354	−	0.764302i
$760$	−1.91852	−	6.60734i	−0.0695920	−	0.239674i
$761$	19.3030	−	33.4337i	0.699733	−	1.21197i	−0.268826	−	0.963189i	$-0.586636\pi$
$761$	19.3030	−	33.4337i	0.699733	−	1.21197i	0.968559	−	0.248784i	$-0.0800309\pi$
$762$	−20.3808	−	3.42935i	−0.738320	−	0.124232i
$763$	−0.747825	−	2.79092i	−0.0270731	−	0.101038i
$764$	3.35866	+	5.81737i	0.121512	+	0.210465i
$765$	−43.8134	−	28.3565i	−1.58408	−	1.02523i
$766$	−29.6643			−1.07181
$767$	0.372995	+	0.814473i	0.0134681	+	0.0294089i
$768$	0.287401	−	1.70804i	0.0103707	−	0.0616336i
$769$	15.5112	+	26.8663i	0.559350	+	0.968822i	0.997551	+	0.0699452i	$0.0222825\pi$
$769$	15.5112	+	26.8663i	0.559350	+	0.968822i	−0.438201	+	0.898877i	$0.644384\pi$
$770$	2.37361	+	3.92064i	0.0855390	+	0.141290i
$771$	−3.11980	+	0.297582i	−0.112357	+	0.0107172i
$772$	−17.0455	+	17.0455i	−0.613480	+	0.613480i
$773$	−3.05263	−	11.3926i	−0.109796	−	0.409763i	0.889049	−	0.457811i	$-0.151366\pi$
$773$	−3.05263	−	11.3926i	−0.109796	−	0.409763i	−0.998845	+	0.0480486i	$0.984700\pi$
$774$	−14.3586	+	12.4366i	−0.516109	+	0.447026i
$775$	0.859223	+	20.6509i	0.0308642	+	0.741802i
$776$	−4.29494	−	2.47969i	−0.154179	−	0.0890155i
$777$	0.0368222	+	0.0987550i	0.00132099	+	0.00354282i
$778$	−6.11228	+	22.8113i	−0.219136	+	0.817826i
$779$	14.0477			0.503313
$780$	−10.0865	−	9.65720i	−0.361156	−	0.345783i
$781$	14.0453			0.502582
$782$	−15.4299	+	57.5851i	−0.551771	+	2.05924i
$783$	32.6239	−	0.766576i	1.16588	−	0.0273952i
$784$	5.57595	+	3.21927i	0.199141	+	0.114974i
$785$	8.21479	+	7.88010i	0.293198	+	0.281253i
$786$	−13.3841	+	1.27665i	−0.477396	+	0.0455365i
$787$	−5.90775	−	22.0480i	−0.210589	−	0.785928i	−0.987673	−	0.156531i	$-0.949969\pi$
$787$	−5.90775	−	22.0480i	−0.210589	−	0.785928i	0.777084	−	0.629397i	$-0.216698\pi$
$788$	−2.39013	+	2.39013i	−0.0851448	+	0.0851448i
$789$	2.10675	+	22.0868i	0.0750024	+	0.786311i
$790$	−35.1059	−	8.62852i	−1.24901	−	0.306989i
$791$	−0.463622	−	0.803017i	−0.0164845	−	0.0285520i
$792$	−7.38218	+	3.58417i	−0.262314	+	0.127358i
$793$	−33.6610	+	15.4153i	−1.19534	+	0.547414i
$794$	−18.3130			−0.649904
$795$	21.6358	+	9.34474i	0.767342	+	0.331424i
$796$	−0.124888	−	0.216313i	−0.00442655	−	0.00766700i
$797$	10.1693	+	37.9523i	0.360214	+	1.34434i	0.873794	+	0.486296i	$0.161652\pi$
$797$	10.1693	+	37.9523i	0.360214	+	1.34434i	−0.513580	+	0.858042i	$0.671681\pi$
$798$	0.662618	−	3.93798i	0.0234564	−	0.139403i
$799$	20.5090	−	35.5226i	0.725555	−	1.25670i
$800$	4.77166	−	1.49375i	0.168704	−	0.0528120i
$801$	10.7142	−	30.9363i	0.378569	−	1.09308i
$802$	0.451526	−	0.120986i	0.0159439	−	0.00427216i
$803$	−8.66795	+	32.3492i	−0.305885	+	1.14158i
$804$	−11.9352	−	5.45210i	−0.420922	−	0.192281i
$805$	−12.8363	+	0.266925i	−0.452421	+	0.00940789i
$806$	9.50162	+	11.4831i	0.334680	+	0.404476i
$807$	4.67995	−	27.8132i	0.164742	−	0.979071i
$808$	−1.15717	+	4.31861i	−0.0407090	+	0.151928i
$809$	12.2383	+	21.1973i	0.430275	+	0.745258i	0.996897	−	0.0787197i	$-0.0250832\pi$
$809$	12.2383	+	21.1973i	0.430275	+	0.745258i	−0.566622	+	0.823978i	$0.691750\pi$
$810$	18.6574	+	7.54337i	0.655553	+	0.265047i
$811$		−	7.67847i		−	0.269627i	−0.990871	−	0.134814i	$-0.956956\pi$
$811$		−	7.67847i		−	0.269627i	0.990871	−	0.134814i	$-0.0430436\pi$
$812$	4.54542	−	1.21794i	0.159513	−	0.0427414i
$813$	−15.1878	+	18.3907i	−0.532661	+	0.644991i
$814$	0.222143			0.00778612
$815$	−40.6181	+	11.7939i	−1.42279	+	0.413123i
$816$	5.59904	−	12.2569i	0.196006	−	0.429076i
$817$	−18.8191	−	5.04255i	−0.658396	−	0.176417i
$818$	−16.2002	−	16.2002i	−0.566427	−	0.566427i
$819$	−2.83883	−	7.59151i	−0.0991967	−	0.265269i
$820$	0.212241	+	10.2066i	0.00741177	+	0.356428i
$821$	−2.43721	−	4.22137i	−0.0850592	−	0.147327i	0.820357	−	0.571851i	$-0.193775\pi$
$821$	−2.43721	−	4.22137i	−0.0850592	−	0.147327i	−0.905416	+	0.424525i	$0.860441\pi$
$822$	−1.75969	−	4.71938i	−0.0613762	−	0.164607i
$823$	−6.23632	−	23.2743i	−0.217384	−	0.811289i	−0.985314	−	0.170755i	$-0.945379\pi$
$823$	−6.23632	−	23.2743i	−0.217384	−	0.811289i	0.767929	−	0.640535i	$-0.221287\pi$
$824$		−	15.4907i		−	0.539643i
$825$	−18.8772	−	14.3123i	−0.657219	−	0.498292i
$826$	−0.161226	−	0.0930841i	−0.00560978	−	0.00323881i
$827$	33.2276	+	33.2276i	1.15544	+	1.15544i	0.985445	+	0.169993i	$0.0543746\pi$
$827$	33.2276	+	33.2276i	1.15544	+	1.15544i	0.169993	+	0.985445i	$0.445625\pi$
$828$	1.64468	−	22.9298i	0.0571568	−	0.796865i
$829$	−3.07368	+	1.77459i	−0.106753	+	0.0616341i	−0.552426	−	0.833562i	$-0.686298\pi$
$829$	−3.07368	+	1.77459i	−0.106753	+	0.0616341i	0.445673	+	0.895196i	$0.352965\pi$
$830$	−9.89152	−	16.3385i	−0.343340	−	0.567116i
$831$	16.3887	−	11.6678i	0.568517	−	0.404752i
$832$	2.08833	−	2.93920i	0.0723999	−	0.101898i
$833$	35.4198	+	35.4198i	1.22722	+	1.22722i
$834$	2.00458	−	4.38822i	0.0694128	−	0.151952i
$835$	−12.4120	+	50.4995i	−0.429536	+	1.74761i
$836$	−7.28910	−	4.20836i	−0.252099	−	0.145549i
$837$	−18.8490	−	10.2999i	−0.651518	−	0.356015i
$838$	23.7308	−	6.35866i	0.819768	−	0.219656i
$839$	−21.3517	−	12.3274i	−0.737144	−	0.425590i	0.0838861	−	0.996475i	$-0.473267\pi$
$839$	−21.3517	−	12.3274i	−0.737144	−	0.425590i	−0.821030	+	0.570885i	$0.806600\pi$
$840$	2.87120	+	0.421936i	0.0990657	+	0.0145582i
$841$	−5.22048	+	9.04214i	−0.180017	+	0.311798i
$842$	1.32242	+	0.354341i	0.0455735	+	0.0122114i
$843$	−32.7307	+	12.2041i	−1.12730	+	0.420331i
$844$			10.2824i			0.353935i
$845$	−10.1340	−	27.2452i	−0.348619	−	0.937265i
$846$	−5.17626	+	14.9459i	−0.177963	+	0.513851i
$847$	−2.54583	−	0.682153i	−0.0874758	−	0.0234391i
$848$	−1.57495	+	5.87778i	−0.0540839	+	0.201844i
$849$	24.7236	−	2.35827i	0.848513	−	0.0809355i
$850$	38.8658	−	1.61709i	1.33309	−	0.0554659i
$851$	−0.311151	+	0.538930i	−0.0106661	+	0.0184743i
$852$	5.66305	−	6.85731i	0.194013	−	0.234928i
$853$	−34.7608	−	34.7608i	−1.19019	−	1.19019i	−0.977015	−	0.213171i	$-0.931621\pi$
$853$	−34.7608	−	34.7608i	−1.19019	−	1.19019i	−0.213171	−	0.977015i	$-0.568379\pi$
$854$	3.84703	−	6.66325i	0.131643	−	0.228012i
$855$	4.32267	+	20.1830i	0.147832	+	0.690244i
$856$	4.90942	−	2.83445i	0.167800	−	0.0968796i
$857$	33.7517	−	33.7517i	1.15294	−	1.15294i	0.166976	−	0.985961i	$-0.446600\pi$
$857$	33.7517	−	33.7517i	1.15294	−	1.15294i	0.985961	−	0.166976i	$-0.0534003\pi$
$858$	−17.0827	+	0.0162413i	−0.583194	+	0.000554469i
$859$		−	39.3614i		−	1.34299i	−0.741008	−	0.671496i	$-0.765652\pi$
$859$		−	39.3614i		−	1.34299i	0.741008	−	0.671496i	$-0.234348\pi$
$860$	3.37940	−	13.7494i	0.115237	−	0.468851i
$861$	−2.46198	+	5.38953i	−0.0839041	+	0.183675i
$862$	−24.7300	+	6.62638i	−0.842306	+	0.225695i
$863$	21.3848	−	21.3848i	0.727948	−	0.727948i	−0.242263	−	0.970211i	$-0.577890\pi$
$863$	21.3848	−	21.3848i	0.727948	−	0.727948i	0.970211	+	0.242263i	$0.0778895\pi$
$864$	−1.22659	+	5.04930i	−0.0417294	+	0.171781i
$865$	−37.8261	+	10.9832i	−1.28613	+	0.373441i
$866$	6.29660			0.213967
$867$	48.0063	−	58.1302i	1.63038	−	1.97420i
$868$	−2.99189	−	0.801673i	−0.101551	−	0.0272106i
$869$	−38.2990	+	22.1119i	−1.29921	+	0.750096i
$870$	−19.5169	+	14.5157i	−0.661685	+	0.492127i
$871$	−17.4131	−	21.0445i	−0.590021	−	0.713066i
$872$	−2.72667	+	2.72667i	−0.0923366	+	0.0923366i
$873$	12.3196	+	8.34182i	0.416955	+	0.282328i
$874$	20.4194	−	11.7891i	0.690695	−	0.398773i
$875$	2.66843	+	7.94110i	0.0902095	+	0.268458i
$876$	12.2988	+	17.2751i	0.415539	+	0.583670i
$877$	−12.0925	−	45.1299i	−0.408335	−	1.52393i	−0.797820	−	0.602895i	$-0.794014\pi$
$877$	−12.0925	−	45.1299i	−0.408335	−	1.52393i	0.389485	−	0.921033i	$-0.372653\pi$
$878$	4.24820	+	15.8545i	0.143370	+	0.535063i
$879$	−19.6287	−	27.5706i	−0.662059	−	0.929932i
$880$	2.94751	−	5.35956i	0.0993605	−	0.180671i
$881$	9.94815	−	5.74357i	0.335162	−	0.193506i	−0.322969	−	0.946410i	$-0.604681\pi$
$881$	9.94815	−	5.74357i	0.335162	−	0.193506i	0.658130	+	0.752904i	$0.271348\pi$
$882$	−15.9940	−	10.8298i	−0.538547	−	0.364660i
$883$	−8.01622	+	8.01622i	−0.269767	+	0.269767i	−0.829006	−	0.559239i	$-0.811093\pi$
$883$	−8.01622	+	8.01622i	−0.269767	+	0.269767i	0.559239	+	0.829006i	$0.311093\pi$
$884$	21.6117	−	17.8824i	0.726880	−	0.601451i
$885$	0.952039	+	0.139907i	0.0320024	+	0.00470291i
$886$	10.6929	−	6.17353i	0.359234	−	0.207404i
$887$	−25.5966	−	6.85858i	−0.859448	−	0.230288i	−0.197929	−	0.980216i	$-0.563421\pi$
$887$	−25.5966	−	6.85858i	−0.859448	−	0.230288i	−0.661520	+	0.749928i	$0.730088\pi$
$888$	0.0895677	−	0.108456i	0.00300570	−	0.00363955i
$889$	8.94089			0.299868
$890$	6.80445	+	23.4344i	0.228086	+	0.785523i
$891$	22.8591	−	9.14053i	0.765807	−	0.306219i
$892$	−4.80560	+	4.80560i	−0.160903	+	0.160903i
$893$	−15.6698	+	4.19870i	−0.524368	+	0.140504i
$894$	16.5660	−	36.2646i	0.554049	−	1.21287i
$895$	2.98061	+	4.92326i	0.0996307	+	0.164566i
$896$			0.749302i			0.0250324i
$897$	23.8880	−	41.4662i	0.797596	−	1.38451i
$898$	−0.198160	+	0.198160i	−0.00661267	+	0.00661267i
$899$	22.4827	−	12.9804i	0.749841	−	0.432921i
$900$	−14.5989	+	3.44563i	−0.486630	+	0.114854i
$901$	−23.6708	+	40.9991i	−0.788589	+	1.36588i
$902$	8.83075	+	8.83075i	0.294032	+	0.294032i
$903$	5.23281	−	6.33634i	0.174137	−	0.210860i
$904$	−0.618739	+	1.07169i	−0.0205790	+	0.0356438i
$905$	−34.5297	+	0.718028i	−1.14780	+	0.0238681i
$906$	8.26158	−	0.788032i	0.274473	−	0.0261806i
$907$	−9.58341	+	35.7658i	−0.318212	+	1.18758i	0.602750	+	0.797930i	$0.294072\pi$
$907$	−9.58341	+	35.7658i	−0.318212	+	1.18758i	−0.920962	+	0.389653i	$0.872595\pi$
$908$	−15.9597	−	4.27638i	−0.529640	−	0.141917i
$909$	4.38951	−	12.6743i	0.145591	−	0.420379i
$910$	4.99627	+	3.39584i	0.165625	+	0.112571i
$911$			28.6195i			0.948206i	0.880469	+	0.474103i	$0.157228\pi$
$911$			28.6195i			0.948206i	−0.880469	+	0.474103i	$0.842772\pi$
$912$	−4.99358	+	1.86193i	−0.165354	+	0.0616546i
$913$	−22.5685	−	6.04722i	−0.746909	−	0.200134i
$914$	6.87937	−	11.9154i	0.227549	−	0.394127i
$915$	−5.78214	+	39.3464i	−0.191152	+	1.30075i
$916$	3.17591	+	1.83361i	0.104935	+	0.0605842i
$917$	5.61820	−	1.50539i	0.185529	−	0.0497124i
$918$	−19.3848	+	35.4747i	−0.639793	+	1.17084i
$919$	−18.5185	−	10.6917i	−0.610870	−	0.352686i	0.162436	−	0.986719i	$-0.448065\pi$
$919$	−18.5185	−	10.6917i	−0.610870	−	0.352686i	−0.773306	+	0.634033i	$0.781398\pi$
$920$	8.87403	+	14.6578i	0.292568	+	0.483254i
$921$	−4.28221	+	9.37419i	−0.141104	+	0.308890i
$922$	12.9086	+	12.9086i	0.425124	+	0.425124i
$923$	16.8320	−	7.70836i	0.554033	−	0.253724i
$924$	2.89205	−	2.05897i	0.0951413	−	0.0677352i
$925$	0.396244	+	0.0886977i	0.0130284	+	0.00291636i
$926$	31.7759	−	18.3458i	1.04422	−	0.602881i
$927$	−3.32476	+	46.3530i	−0.109199	+	1.52243i
$928$	−4.44077	−	4.44077i	−0.145776	−	0.145776i
$929$	−29.1951	−	16.8558i	−0.957860	−	0.553021i	−0.0623461	−	0.998055i	$-0.519858\pi$
$929$	−29.1951	−	16.8558i	−0.957860	−	0.553021i	−0.895514	+	0.445034i	$0.853192\pi$
$930$	15.9026	−	1.85123i	0.521466	−	0.0607041i
$931$		−	19.8110i		−	0.649279i
$932$	1.32550	+	4.94683i	0.0434182	+	0.162039i
$933$	−7.23432	−	19.4020i	−0.236841	−	0.635193i
$934$	1.87306	+	3.24423i	0.0612883	+	0.106154i
$935$	32.9419	−	34.3410i	1.07731	−	1.12307i
$936$	−6.87978	+	8.34678i	−0.224873	+	0.272823i
$937$	−2.14102	−	2.14102i	−0.0699440	−	0.0699440i	0.671269	−	0.741213i	$-0.265749\pi$
$937$	−2.14102	−	2.14102i	−0.0699440	−	0.0699440i	−0.741213	+	0.671269i	$0.765749\pi$
$938$	5.48307	+	1.46918i	0.179029	+	0.0479706i
$939$	8.93560	−	19.5609i	0.291602	−	0.638347i
$940$	−3.28736	−	11.3216i	−0.107222	−	0.369270i
$941$	−21.0431			−0.685987			−0.342993	−	0.939338i	$-0.611441\pi$
$941$	−21.0431			−0.685987			−0.342993	+	0.939338i	$0.611441\pi$
$942$	5.61467	−	6.79873i	0.182936	−	0.221514i
$943$	−33.7928	+	9.05476i	−1.10045	+	0.294864i
$944$			0.248456i			0.00808654i
$945$	−8.50096	−	1.87881i	−0.276536	−	0.0611176i
$946$	−8.66025	−	15.0000i	−0.281569	−	0.487692i
$947$	−1.87280	+	6.98938i	−0.0608578	+	0.227124i	−0.989656	−	0.143462i	$-0.954177\pi$
$947$	−1.87280	+	6.98938i	−0.0608578	+	0.227124i	0.928798	+	0.370586i	$0.120843\pi$
$948$	−4.64644	+	27.6141i	−0.150909	+	0.896863i
$949$	7.36616	+	43.5246i	0.239116	+	1.41287i
$950$	−11.3214	−	10.4170i	−0.367316	−	0.337971i
$951$	10.1452	+	4.63439i	0.328979	+	0.150280i
$952$	−1.50878	+	5.63085i	−0.0488999	+	0.182497i
$953$	−12.9574	+	3.47191i	−0.419730	+	0.112466i	−0.462501	−	0.886619i	$-0.653048\pi$
$953$	−12.9574	+	3.47191i	−0.419730	+	0.112466i	0.0427714	+	0.999085i	$0.486381\pi$
$954$	5.97428	−	17.2501i	0.193424	−	0.558493i
$955$	13.1614	+	7.23813i	0.425891	+	0.234220i
$956$	4.53526	−	7.85530i	0.146681	−	0.254058i
$957$	−4.93726	+	29.3424i	−0.159599	+	0.948507i
$958$	−3.00988	−	11.2330i	−0.0972448	−	0.362923i
$959$	1.08948	+	1.88703i	0.0351811	+	0.0609354i
$960$	−1.42825	−	3.60001i	−0.0460966	−	0.116190i
$961$	13.9121			0.448777
$962$	0.266218	−	0.121917i	0.00858321	−	0.00393075i
$963$	−15.2989	+	7.42786i	−0.492999	+	0.239360i
$964$	−0.180716	−	0.313009i	−0.00582047	−	0.0100813i
$965$	−12.8655	+	52.3446i	−0.414156	+	1.68503i
$966$	0.944331	+	9.90019i	0.0303834	+	0.318533i
$967$	−21.5350	+	21.5350i	−0.692518	+	0.692518i	−0.962785	−	0.270267i	$-0.912888\pi$
$967$	−21.5350	+	21.5350i	−0.692518	+	0.692518i	0.270267	+	0.962785i	$0.412888\pi$
$968$	0.910386	+	3.39761i	0.0292609	+	0.109203i
$969$	−41.2749	+	3.93701i	−1.32594	+	0.126475i
$970$	−11.0871	+	0.230551i	−0.355985	+	0.00740255i
$971$	16.6031	+	9.58579i	0.532818	+	0.307623i	0.742163	−	0.670219i	$-0.233800\pi$
$971$	16.6031	+	9.58579i	0.532818	+	0.307623i	−0.209345	+	0.977842i	$0.567133\pi$
$972$	4.75407	−	14.8458i	0.152487	−	0.476180i
$973$	−0.540177	+	2.01597i	−0.0173173	+	0.0646289i
$974$	42.3522			1.35705
$975$	−30.4774	−	6.79184i	−0.976057	−	0.217513i
$976$	−10.2683			−0.328680
$977$	−9.11224	+	34.0073i	−0.291526	+	1.08799i	0.652411	+	0.757866i	$0.273758\pi$
$977$	−9.11224	+	34.0073i	−0.291526	+	1.08799i	−0.943937	+	0.330125i	$0.892909\pi$
$978$	11.4460	+	30.6976i	0.366004	+	0.981601i
$979$	25.8524	+	14.9259i	0.826246	+	0.477033i
$980$	14.3939	−	0.299315i	0.459797	−	0.00956126i
$981$	8.74426	−	7.57382i	0.279183	−	0.241813i
$982$	−8.97978	−	33.5130i	−0.286556	−	1.06944i
$983$	−11.4129	+	11.4129i	−0.364015	+	0.364015i	−0.865289	−	0.501274i	$-0.832865\pi$
$983$	−11.4129	+	11.4129i	−0.364015	+	0.364015i	0.501274	+	0.865289i	$0.332865\pi$
$984$	7.87195	−	0.750867i	0.250948	−	0.0239368i
$985$	−1.80401	+	7.33980i	−0.0574807	+	0.233865i
$986$	−24.4297	−	42.3134i	−0.777999	−	1.34753i
$987$	1.13539	−	6.74768i	0.0361398	−	0.214781i
$988$	−11.0449	−	1.04293i	−0.351386	−	0.0331799i
$989$	48.5209			1.54287
$990$	−9.97019	+	15.4049i	−0.316873	+	0.489599i
$991$	8.36798	+	14.4938i	0.265817	+	0.460409i	0.967777	−	0.251807i	$-0.0810248\pi$
$991$	8.36798	+	14.4938i	0.265817	+	0.460409i	−0.701960	+	0.712216i	$0.747691\pi$
$992$	1.06989	+	3.99290i	0.0339692	+	0.126775i
$993$	−12.9061	−	2.17162i	−0.409561	−	0.0689142i
$994$	−1.92369	+	3.33193i	−0.0610157	+	0.105682i
$995$	−0.489391	−	0.269142i	−0.0155148	−	0.00853239i
$996$	−12.0520	+	8.58033i	−0.381882	+	0.271878i
$997$	−39.8400	+	10.6751i	−1.26174	+	0.338083i	−0.826862	−	0.562404i	$-0.809876\pi$
$997$	−39.8400	+	10.6751i	−1.26174	+	0.338083i	−0.434882	+	0.900488i	$0.643210\pi$
$998$	5.42202	−	20.2352i	0.171631	−	0.640535i
$999$	−0.291293	+	0.305311i	−0.00921609	+	0.00965962i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.be.b.257.14	yes	96
3.2	odd	2	inner	390.2.be.b.257.4	yes	96
5.3	odd	4	inner	390.2.be.b.23.5	yes	96
13.4	even	6	inner	390.2.be.b.17.23	yes	96
15.8	even	4	inner	390.2.be.b.23.23	yes	96
39.17	odd	6	inner	390.2.be.b.17.5	✓	96
65.43	odd	12	inner	390.2.be.b.173.4	yes	96
195.173	even	12	inner	390.2.be.b.173.14	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.be.b.17.5	✓	96	39.17	odd	6	inner
390.2.be.b.17.23	yes	96	13.4	even	6	inner
390.2.be.b.23.5	yes	96	5.3	odd	4	inner
390.2.be.b.23.23	yes	96	15.8	even	4	inner
390.2.be.b.173.4	yes	96	65.43	odd	12	inner
390.2.be.b.173.14	yes	96	195.173	even	12	inner
390.2.be.b.257.4	yes	96	3.2	odd	2	inner
390.2.be.b.257.14	yes	96	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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-1.62291 + 0.605124i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.23558 + 0.0464880i) q^{5} +(0.164466 + 1.72422i) q^{6} +(-0.193934 - 0.723770i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.26765 - 1.96412i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-1.62291 + 0.605124i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.23558 + 0.0464880i) q^{5} +(0.164466 + 1.72422i) q^{6} +(-0.193934 - 0.723770i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.26765 - 1.96412i) q^{9} +(-0.533708 + 2.17144i) q^{10} +(1.36771 + 2.36895i) q^{11} +(1.70804 + 0.287401i) q^{12} +(2.93920 + 2.08833i) q^{13} -0.749302 q^{14} +(3.60001 - 1.42825i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.01358 + 7.51480i) q^{17} +(-1.31028 - 2.69873i) q^{18} +(1.53847 - 2.66471i) q^{19} +(1.95932 + 1.07753i) q^{20} +(0.752706 + 1.05726i) q^{21} +(2.64222 - 0.707980i) q^{22} +(-1.98330 + 7.40179i) q^{23} +(0.719681 - 1.57546i) q^{24} +(4.99568 - 0.207856i) q^{25} +(2.77789 - 2.29855i) q^{26} +(-2.49165 + 4.55979i) q^{27} +(-0.193934 + 0.723770i) q^{28} +(-3.14010 - 5.43882i) q^{29} +(-0.447832 - 3.84700i) q^{30} +4.13375i q^{31} +(0.965926 - 0.258819i) q^{32} +(-3.65317 - 3.01694i) q^{33} +7.77989 q^{34} +(0.467201 + 1.60903i) q^{35} +(-2.94590 + 0.567151i) q^{36} +(0.0784427 + 0.0210187i) q^{37} +(-2.17572 - 2.17572i) q^{38} +(-6.03374 - 1.61059i) q^{39} +(1.54793 - 1.61367i) q^{40} +(2.28275 + 3.95384i) q^{41} +(1.21605 - 0.453420i) q^{42} +(-1.63882 - 6.11617i) q^{43} -2.73542i q^{44} +(-4.97822 + 4.49637i) q^{45} +(6.63626 + 3.83145i) q^{46} +(-3.72808 - 3.72808i) q^{47} +(-1.33551 - 1.10292i) q^{48} +(5.57595 - 3.21927i) q^{49} +(1.09220 - 4.87925i) q^{50} +(-7.81524 - 10.9773i) q^{51} +(-1.50125 - 3.27815i) q^{52} +(4.30283 + 4.30283i) q^{53} +(3.75953 + 3.58691i) q^{54} +(-3.16776 - 5.23240i) q^{55} +(0.648914 + 0.374651i) q^{56} +(-0.884314 + 5.25553i) q^{57} +(-6.06621 + 1.62544i) q^{58} +(0.215169 + 0.124228i) q^{59} +(-3.83183 - 0.563105i) q^{60} +(-5.13415 + 8.89261i) q^{61} +(3.99290 + 1.06989i) q^{62} +(-1.86134 - 1.26035i) q^{63} -1.00000i q^{64} +(-6.66790 - 4.53200i) q^{65} +(-3.85965 + 2.74785i) q^{66} +(-7.31758 - 1.96074i) q^{67} +(2.01358 - 7.51480i) q^{68} +(-1.26028 - 13.2126i) q^{69} +(1.67513 - 0.0348335i) q^{70} +(2.56731 - 4.44671i) q^{71} +(-0.214630 + 2.99231i) q^{72} +(8.65726 + 8.65726i) q^{73} +(0.0406050 - 0.0703298i) q^{74} +(-7.98174 + 3.36033i) q^{75} +(-2.66471 + 1.53847i) q^{76} +(1.44933 - 1.44933i) q^{77} +(-3.11736 + 5.41129i) q^{78} +16.1671i q^{79} +(-1.15805 - 1.91283i) q^{80} +(1.28448 - 8.90787i) q^{81} +(4.40993 - 1.18164i) q^{82} +(-6.03976 + 6.03976i) q^{83} +(-0.123234 - 1.29196i) q^{84} +(-4.85089 - 16.7064i) q^{85} -6.33192 q^{86} +(8.38725 + 6.92654i) q^{87} +(-2.64222 - 0.707980i) q^{88} +(9.45097 - 5.45652i) q^{89} +(3.05470 + 5.97234i) q^{90} +(0.941462 - 2.53230i) q^{91} +(5.41848 - 5.41848i) q^{92} +(-2.50143 - 6.70869i) q^{93} +(-4.56594 + 2.63615i) q^{94} +(-3.31550 + 6.02869i) q^{95} +(-1.41099 + 1.00454i) q^{96} +(1.28358 + 4.79038i) q^{97} +(-1.66642 - 6.21916i) q^{98} +(7.75438 + 2.68559i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 4 q^{3} + 24 q^{7}+O(q^{10}) \) 96 * q + 4 * q^3 + 24 * q^7	\( 96 q + 4 q^{3} + 24 q^{7} + 16 q^{10} - 8 q^{12} + 40 q^{13} + 48 q^{16} - 8 q^{22} + 64 q^{25} - 32 q^{27} + 24 q^{28} - 8 q^{30} - 96 q^{33} - 24 q^{36} + 72 q^{37} - 8 q^{42} + 16 q^{43} - 60 q^{45} + 24 q^{46} - 4 q^{48} - 128 q^{51} - 8 q^{52} + 32 q^{61} - 120 q^{63} - 16 q^{66} - 96 q^{67} - 24 q^{72} - 4 q^{75} - 24 q^{76} - 16 q^{78} - 48 q^{81} + 32 q^{82} + 32 q^{87} + 8 q^{88} - 56 q^{90} - 56 q^{91} - 12 q^{93} + 24 q^{97}+O(q^{100}) \) 96 * q + 4 * q^3 + 24 * q^7 + 16 * q^10 - 8 * q^12 + 40 * q^13 + 48 * q^16 - 8 * q^22 + 64 * q^25 - 32 * q^27 + 24 * q^28 - 8 * q^30 - 96 * q^33 - 24 * q^36 + 72 * q^37 - 8 * q^42 + 16 * q^43 - 60 * q^45 + 24 * q^46 - 4 * q^48 - 128 * q^51 - 8 * q^52 + 32 * q^61 - 120 * q^63 - 16 * q^66 - 96 * q^67 - 24 * q^72 - 4 * q^75 - 24 * q^76 - 16 * q^78 - 48 * q^81 + 32 * q^82 + 32 * q^87 + 8 * q^88 - 56 * q^90 - 56 * q^91 - 12 * q^93 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more