LMFDB - Embedded newform 961.2.c.k.521.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(439,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("961.439");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.c (of order $3$, degree $2$, not 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:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			521.3
Character	$\chi$	$=$	961.521
Dual form			961.2.c.k.439.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.80264 q^{2} +(-0.0954837 - 0.165383i) q^{3} +1.24951 q^{4} +(1.23318 - 2.13593i) q^{5} +(0.172123 + 0.298125i) q^{6} +(0.526075 + 0.911189i) q^{7} +1.35286 q^{8} +(1.48177 - 2.56649i) q^{9} +(-2.22298 + 3.85032i) q^{10} +(2.68479 - 4.65018i) q^{11} +(-0.119308 - 0.206647i) q^{12} +(0.616723 - 1.06819i) q^{13} +(-0.948325 - 1.64255i) q^{14} -0.470995 q^{15} -4.93774 q^{16} +(-2.83695 - 4.91374i) q^{17} +(-2.67109 + 4.62646i) q^{18} +(2.33141 + 4.03812i) q^{19} +(1.54087 - 2.66887i) q^{20} +(0.100463 - 0.174007i) q^{21} +(-4.83970 + 8.38261i) q^{22} +5.98388 q^{23} +(-0.129176 - 0.223740i) q^{24} +(-0.541477 - 0.937865i) q^{25} +(-1.11173 + 1.92557i) q^{26} -1.13884 q^{27} +(0.657337 + 1.13854i) q^{28} -3.60796 q^{29} +0.849035 q^{30} +6.19525 q^{32} -1.02541 q^{33} +(5.11400 + 8.85771i) q^{34} +2.59499 q^{35} +(1.85148 - 3.20686i) q^{36} +(2.67703 + 4.63676i) q^{37} +(-4.20269 - 7.27928i) q^{38} -0.235548 q^{39} +(1.66832 - 2.88962i) q^{40} +(-5.28142 + 9.14769i) q^{41} +(-0.181099 + 0.313673i) q^{42} +(-1.51189 - 2.61867i) q^{43} +(3.35467 - 5.81046i) q^{44} +(-3.65457 - 6.32991i) q^{45} -10.7868 q^{46} +5.63413 q^{47} +(0.471474 + 0.816617i) q^{48} +(2.94649 - 5.10347i) q^{49} +(0.976088 + 1.69063i) q^{50} +(-0.541765 + 0.938365i) q^{51} +(0.770601 - 1.33472i) q^{52} +(0.454343 - 0.786945i) q^{53} +2.05292 q^{54} +(-6.62166 - 11.4691i) q^{55} +(0.711707 + 1.23271i) q^{56} +(0.445223 - 0.771149i) q^{57} +6.50384 q^{58} +(-1.53258 - 2.65451i) q^{59} -0.588514 q^{60} -9.12376 q^{61} +3.11808 q^{63} -1.29232 q^{64} +(-1.52106 - 2.63456i) q^{65} +1.84845 q^{66} +(-3.98244 + 6.89779i) q^{67} +(-3.54480 - 6.13978i) q^{68} +(-0.571363 - 0.989630i) q^{69} -4.67783 q^{70} +(-3.03430 + 5.25556i) q^{71} +(2.00462 - 3.47211i) q^{72} +(-1.89448 + 3.28134i) q^{73} +(-4.82573 - 8.35841i) q^{74} +(-0.103404 + 0.179102i) q^{75} +(2.91312 + 5.04568i) q^{76} +5.64960 q^{77} +0.424608 q^{78} +(-4.25507 - 7.37000i) q^{79} +(-6.08914 + 10.5467i) q^{80} +(-4.33656 - 7.51114i) q^{81} +(9.52050 - 16.4900i) q^{82} +(6.61668 - 11.4604i) q^{83} +(0.125530 - 0.217424i) q^{84} -13.9939 q^{85} +(2.72539 + 4.72052i) q^{86} +(0.344501 + 0.596693i) q^{87} +(3.63214 - 6.29106i) q^{88} -0.881934 q^{89} +(6.58788 + 11.4105i) q^{90} +1.29777 q^{91} +7.47693 q^{92} -10.1563 q^{94} +11.5002 q^{95} +(-0.591545 - 1.02459i) q^{96} +8.64199 q^{97} +(-5.31146 + 9.19972i) q^{98} +(-7.95645 - 13.7810i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 32 q^{4} - 8 q^{5} - 8 q^{7} + 24 q^{8} - 20 q^{9} - 20 q^{10} - 28 q^{14} - 32 q^{16} + 8 q^{18} - 16 q^{19} + 20 q^{20} - 12 q^{25} + 20 q^{28} + 48 q^{32} - 80 q^{33} + 112 q^{35} - 40 q^{36}+ \cdots - 4 q^{98}+O(q^{100}) $ 24 * q + 32 * q^4 - 8 * q^5 - 8 * q^7 + 24 * q^8 - 20 * q^9 - 20 * q^10 - 28 * q^14 - 32 * q^16 + 8 * q^18 - 16 * q^19 + 20 * q^20 - 12 * q^25 + 20 * q^28 + 48 * q^32 - 80 * q^33 + 112 * q^35 - 40 * q^36 - 36 * q^38 - 32 * q^39 + 16 * q^40 - 32 * q^41 - 16 * q^45 + 96 * q^47 + 20 * q^49 - 20 * q^50 - 16 * q^51 + 8 * q^56 - 40 * q^59 - 16 * q^63 - 56 * q^64 + 48 * q^66 - 16 * q^67 - 24 * q^69 + 24 * q^70 - 72 * q^71 - 36 * q^72 - 36 * q^76 - 208 * q^78 + 20 * q^80 + 36 * q^81 + 4 * q^82 - 64 * q^87 + 44 * q^90 + 32 * q^94 + 80 * q^95 - 16 * q^97 - 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.80264			−1.27466			−0.637329	−	0.770591i	$-0.719961\pi$
$2$	−1.80264			−1.27466			−0.637329	+	0.770591i	$0.719961\pi$
$3$	−0.0954837	−	0.165383i	−0.0551275	−	0.0954837i	0.837145	−	0.546982i	$-0.184223\pi$
$3$	−0.0954837	−	0.165383i	−0.0551275	−	0.0954837i	−0.892272	+	0.451498i	$0.850890\pi$
$4$	1.24951			0.624755
$5$	1.23318	−	2.13593i	0.551496	−	0.955219i	−0.446671	−	0.894698i	$-0.647391\pi$
$5$	1.23318	−	2.13593i	0.551496	−	0.955219i	0.998167	−	0.0605206i	$-0.0192761\pi$
$6$	0.172123	+	0.298125i	0.0702688	+	0.121709i
$7$	0.526075	+	0.911189i	0.198838	+	0.344397i	0.948152	−	0.317818i	$-0.102950\pi$
$7$	0.526075	+	0.911189i	0.198838	+	0.344397i	−0.749314	+	0.662215i	$0.769617\pi$
$8$	1.35286			0.478309
$9$	1.48177	−	2.56649i	0.493922	−	0.855498i
$10$	−2.22298	+	3.85032i	−0.702969	+	1.21758i
$11$	2.68479	−	4.65018i	0.809493	−	1.40208i	−0.103722	−	0.994606i	$-0.533075\pi$
$11$	2.68479	−	4.65018i	0.809493	−	1.40208i	0.913215	−	0.407477i	$-0.133591\pi$
$12$	−0.119308	−	0.206647i	−0.0344412	−	0.0596540i
$13$	0.616723	−	1.06819i	0.171048	−	0.296264i	−0.767738	−	0.640763i	$-0.778618\pi$
$13$	0.616723	−	1.06819i	0.171048	−	0.296264i	0.938787	+	0.344499i	$0.111951\pi$
$14$	−0.948325	−	1.64255i	−0.253450	−	0.438989i
$15$	−0.470995			−0.121610
$16$	−4.93774			−1.23444
$17$	−2.83695	−	4.91374i	−0.688062	−	1.19176i	−0.972464	−	0.233053i	$-0.925129\pi$
$17$	−2.83695	−	4.91374i	−0.688062	−	1.19176i	0.284402	−	0.958705i	$-0.408205\pi$
$18$	−2.67109	+	4.62646i	−0.629582	+	1.09047i
$19$	2.33141	+	4.03812i	0.534862	+	0.926409i	0.999170	+	0.0407346i	$0.0129698\pi$
$19$	2.33141	+	4.03812i	0.534862	+	0.926409i	−0.464308	+	0.885674i	$0.653697\pi$
$20$	1.54087	−	2.66887i	0.344550	−	0.596778i
$21$	0.100463	−	0.174007i	0.0219229	−	0.0379715i
$22$	−4.83970	+	8.38261i	−1.03183	+	1.78718i
$23$	5.98388			1.24773			0.623863	−	0.781534i	$-0.285562\pi$
$23$	5.98388			1.24773			0.623863	+	0.781534i	$0.285562\pi$
$24$	−0.129176	−	0.223740i	−0.0263680	−	0.0456707i
$25$	−0.541477	−	0.937865i	−0.108295	−	0.187573i
$26$	−1.11173	+	1.92557i	−0.218028	+	0.377635i
$27$	−1.13884			−0.219170
$28$	0.657337	+	1.13854i	0.124225	+	0.215164i
$29$	−3.60796			−0.669980			−0.334990	−	0.942222i	$-0.608733\pi$
$29$	−3.60796			−0.669980			−0.334990	+	0.942222i	$0.608733\pi$
$30$	0.849035			0.155012
$31$		0			0
$31$		0			0
$32$	6.19525			1.09518
$33$	−1.02541			−0.178501
$34$	5.11400	+	8.85771i	0.877044	+	1.51908i
$35$	2.59499			0.438633
$36$	1.85148	−	3.20686i	0.308580	−	0.534477i
$37$	2.67703	+	4.63676i	0.440102	+	0.762278i	0.997697	−	0.0678348i	$-0.0216091\pi$
$37$	2.67703	+	4.63676i	0.440102	+	0.762278i	−0.557595	+	0.830113i	$0.688276\pi$
$38$	−4.20269	−	7.27928i	−0.681767	−	1.18085i
$39$	−0.235548			−0.0377178
$40$	1.66832	−	2.88962i	0.263785	−	0.456890i
$41$	−5.28142	+	9.14769i	−0.824820	+	1.42863i	0.0772375	+	0.997013i	$0.475390\pi$
$41$	−5.28142	+	9.14769i	−0.824820	+	1.42863i	−0.902057	+	0.431617i	$0.857943\pi$
$42$	−0.181099	+	0.313673i	−0.0279442	+	0.0484008i
$43$	−1.51189	−	2.61867i	−0.230561	−	0.399343i	0.727412	−	0.686201i	$-0.240723\pi$
$43$	−1.51189	−	2.61867i	−0.230561	−	0.399343i	−0.957973	+	0.286857i	$0.907389\pi$
$44$	3.35467	−	5.81046i	0.505735	−	0.875959i
$45$	−3.65457	−	6.32991i	−0.544792	−	0.943607i
$46$	−10.7868			−1.59043
$47$	5.63413			0.821822			0.410911	−	0.911676i	$-0.365211\pi$
$47$	5.63413			0.821822			0.410911	+	0.911676i	$0.365211\pi$
$48$	0.471474	+	0.816617i	0.0680514	+	0.117869i
$49$	2.94649	−	5.10347i	0.420927	−	0.729067i
$50$	0.976088	+	1.69063i	0.138040	+	0.239092i
$51$	−0.541765	+	0.938365i	−0.0758623	+	0.131397i
$52$	0.770601	−	1.33472i	0.106863	−	0.185092i
$53$	0.454343	−	0.786945i	0.0624088	−	0.108095i	−0.833133	−	0.553073i	$-0.813455\pi$
$53$	0.454343	−	0.786945i	0.0624088	−	0.108095i	0.895542	+	0.444978i	$0.146788\pi$
$54$	2.05292			0.279367
$55$	−6.62166	−	11.4691i	−0.892864	−	1.54649i
$56$	0.711707	+	1.23271i	0.0951059	+	0.164728i
$57$	0.445223	−	0.771149i	0.0589713	−	0.102141i
$58$	6.50384			0.853997
$59$	−1.53258	−	2.65451i	−0.199525	−	0.345588i	0.748849	−	0.662740i	$-0.230607\pi$
$59$	−1.53258	−	2.65451i	−0.199525	−	0.345588i	−0.948375	+	0.317153i	$0.897273\pi$
$60$	−0.588514			−0.0759768
$61$	−9.12376			−1.16818			−0.584089	−	0.811690i	$-0.698548\pi$
$61$	−9.12376			−1.16818			−0.584089	+	0.811690i	$0.698548\pi$
$62$		0			0
$63$	3.11808			0.392841
$64$	−1.29232			−0.161540
$65$	−1.52106	−	2.63456i	−0.188665	−	0.326777i
$66$	1.84845			0.227528
$67$	−3.98244	+	6.89779i	−0.486532	+	0.842699i	−0.999880	−	0.0154820i	$-0.995072\pi$
$67$	−3.98244	+	6.89779i	−0.486532	+	0.842699i	0.513348	+	0.858181i	$0.328405\pi$
$68$	−3.54480	−	6.13978i	−0.429870	−	0.744557i
$69$	−0.571363	−	0.989630i	−0.0687841	−	0.119137i
$70$	−4.67783			−0.559107
$71$	−3.03430	+	5.25556i	−0.360105	+	0.623720i	−0.987978	−	0.154596i	$-0.950592\pi$
$71$	−3.03430	+	5.25556i	−0.360105	+	0.623720i	0.627873	+	0.778316i	$0.283926\pi$
$72$	2.00462	−	3.47211i	0.236247	−	0.409192i
$73$	−1.89448	+	3.28134i	−0.221732	+	0.384052i	−0.955334	−	0.295528i	$-0.904504\pi$
$73$	−1.89448	+	3.28134i	−0.221732	+	0.384052i	0.733602	+	0.679580i	$0.237838\pi$
$74$	−4.82573	−	8.35841i	−0.560979	−	0.971645i
$75$	−0.103404	+	0.179102i	−0.0119401	+	0.0206809i
$76$	2.91312	+	5.04568i	0.334158	+	0.578779i
$77$	5.64960			0.643832
$78$	0.424608			0.0480774
$79$	−4.25507	−	7.37000i	−0.478733	−	0.829189i	0.520970	−	0.853575i	$-0.325570\pi$
$79$	−4.25507	−	7.37000i	−0.478733	−	0.829189i	−0.999703	+	0.0243856i	$0.992237\pi$
$80$	−6.08914	+	10.5467i	−0.680786	+	1.17916i
$81$	−4.33656	−	7.51114i	−0.481840	−	0.834571i
$82$	9.52050	−	16.4900i	1.05136	−	1.82102i
$83$	6.61668	−	11.4604i	0.726275	−	1.25795i	−0.232172	−	0.972675i	$-0.574583\pi$
$83$	6.61668	−	11.4604i	0.726275	−	1.25795i	0.958447	−	0.285270i	$-0.0920834\pi$
$84$	0.125530	−	0.217424i	0.0136964	−	0.0237229i
$85$	−13.9939			−1.51785
$86$	2.72539	+	4.72052i	0.293887	+	0.509026i
$87$	0.344501	+	0.596693i	0.0369344	+	0.0639722i
$88$	3.63214	−	6.29106i	0.387188	−	0.670629i
$89$	−0.881934			−0.0934848			−0.0467424	−	0.998907i	$-0.514884\pi$
$89$	−0.881934			−0.0934848			−0.0467424	+	0.998907i	$0.514884\pi$
$90$	6.58788	+	11.4105i	0.694424	+	1.20278i
$91$	1.29777			0.136043
$92$	7.47693			0.779524
$93$		0			0
$94$	−10.1563			−1.04754
$95$	11.5002			1.17990
$96$	−0.591545	−	1.02459i	−0.0603744	−	0.104571i
$97$	8.64199			0.877461			0.438730	−	0.898619i	$-0.355428\pi$
$97$	8.64199			0.877461			0.438730	+	0.898619i	$0.355428\pi$
$98$	−5.31146	+	9.19972i	−0.536538	+	0.929312i
$99$	−7.95645	−	13.7810i	−0.799653	−	1.38504i
$100$	−0.676581	−	1.17187i	−0.0676581	−	0.117187i
$101$	9.94132			0.989198			0.494599	−	0.869121i	$-0.335315\pi$
$101$	9.94132			0.989198			0.494599	+	0.869121i	$0.335315\pi$
$102$	0.976607	−	1.69153i	0.0966985	−	0.167487i
$103$	4.50403	−	7.80121i	0.443795	−	0.768676i	−0.554172	−	0.832402i	$-0.686965\pi$
$103$	4.50403	−	7.80121i	0.443795	−	0.768676i	0.997967	+	0.0637261i	$0.0202984\pi$
$104$	0.834340	−	1.44512i	0.0818138	−	0.141706i
$105$	−0.247779	−	0.429166i	−0.0241808	−	0.0418823i
$106$	−0.819017	+	1.41858i	−0.0795499	+	0.137785i
$107$	−0.147427	−	0.255350i	−0.0142523	−	0.0246857i	0.858811	−	0.512292i	$-0.171203\pi$
$107$	−0.147427	−	0.255350i	−0.0142523	−	0.0246857i	−0.873064	+	0.487606i	$0.837870\pi$
$108$	−1.42299			−0.136928
$109$	2.18591			0.209372			0.104686	−	0.994505i	$-0.466616\pi$
$109$	2.18591			0.209372			0.104686	+	0.994505i	$0.466616\pi$
$110$	11.9365	+	20.6746i	1.13810	+	1.97124i
$111$	0.511226	−	0.885469i	0.0485234	−	0.0840450i
$112$	−2.59763	−	4.49922i	−0.245453	−	0.425136i
$113$	−5.30388	+	9.18658i	−0.498947	+	0.864201i	−0.999999	−	0.00121588i	$-0.999613\pi$
$113$	−5.30388	+	9.18658i	−0.498947	+	0.864201i	0.501053	+	0.865417i	$0.332946\pi$
$114$	−0.802577	+	1.39010i	−0.0751683	+	0.130195i
$115$	7.37922	−	12.7812i	0.688116	−	1.19185i
$116$	−4.50818			−0.418574
$117$	−1.82768	−	3.16563i	−0.168969	−	0.292662i
$118$	2.76269	+	4.78512i	0.254326	+	0.440506i
$119$	2.98490	−	5.17000i	0.273625	−	0.473933i
$120$	−0.637191			−0.0581673
$121$	−8.91615	−	15.4432i	−0.810559	−	1.40393i
$122$	16.4469			1.48903
$123$	2.01716			0.181881
$124$		0			0
$125$	9.66086			0.864094
$126$	−5.62078			−0.500739
$127$	−10.1665	−	17.6089i	−0.902134	−	1.56254i	−0.824719	−	0.565543i	$-0.808667\pi$
$127$	−10.1665	−	17.6089i	−0.902134	−	1.56254i	−0.0774147	−	0.996999i	$-0.524667\pi$
$128$	−10.0609			−0.889268
$129$	−0.288721	+	0.500080i	−0.0254205	+	0.0440296i
$130$	2.74193	+	4.74916i	0.240483	+	0.416529i
$131$	−2.71969	−	4.71064i	−0.237620	−	0.411570i	0.722411	−	0.691464i	$-0.243034\pi$
$131$	−2.71969	−	4.71064i	−0.237620	−	0.411570i	−0.960031	+	0.279894i	$0.909701\pi$
$132$	−1.28126			−0.111520
$133$	−2.45300	+	4.24871i	−0.212702	+	0.368410i
$134$	7.17890	−	12.4342i	0.620163	−	1.07415i
$135$	−1.40440	+	2.43249i	−0.120871	+	0.209355i
$136$	−3.83800	−	6.64761i	−0.329106	−	0.570028i
$137$	−2.19493	+	3.80173i	−0.187525	+	0.324803i	−0.944425	−	0.328728i	$-0.893380\pi$
$137$	−2.19493	+	3.80173i	−0.187525	+	0.324803i	0.756899	+	0.653532i	$0.226713\pi$
$138$	1.02996	+	1.78395i	0.0876762	+	0.151860i
$139$	−6.72518			−0.570422			−0.285211	−	0.958465i	$-0.592064\pi$
$139$	−6.72518			−0.570422			−0.285211	+	0.958465i	$0.592064\pi$
$140$	3.24247			0.274038
$141$	−0.537967	−	0.931786i	−0.0453050	−	0.0784706i
$142$	5.46975	−	9.47388i	0.459011	−	0.795030i
$143$	−3.31154	−	5.73575i	−0.276924	−	0.479647i
$144$	−7.31658	+	12.6727i	−0.609715	+	1.05606i
$145$	−4.44927	+	7.70635i	−0.369491	+	0.639978i
$146$	3.41507	−	5.91507i	0.282633	−	0.489535i
$147$	−1.12537			−0.0928187
$148$	3.34498	+	5.79368i	0.274956	+	0.476238i
$149$	−1.10847	−	1.91993i	−0.0908097	−	0.157287i	0.817042	−	0.576578i	$-0.195612\pi$
$149$	−1.10847	−	1.91993i	−0.0908097	−	0.157287i	−0.907852	+	0.419291i	$0.862279\pi$
$150$	0.186401	−	0.322856i	0.0152196	−	0.0263611i
$151$	−4.74507			−0.386148			−0.193074	−	0.981184i	$-0.561846\pi$
$151$	−4.74507			−0.386148			−0.193074	+	0.981184i	$0.561846\pi$
$152$	3.15408	+	5.46302i	0.255829	+	0.443109i
$153$	−16.8148			−1.35939
$154$	−10.1842			−0.820666
$155$		0			0
$156$	−0.294319			−0.0235644
$157$	4.04839			0.323096			0.161548	−	0.986865i	$-0.448351\pi$
$157$	4.04839			0.323096			0.161548	+	0.986865i	$0.448351\pi$
$158$	7.67036	+	13.2855i	0.610221	+	1.05693i
$159$	−0.173529			−0.0137618
$160$	7.63987	−	13.2327i	0.603985	−	1.04613i
$161$	3.14797	+	5.45245i	0.248095	+	0.429713i
$162$	7.81725	+	13.5399i	0.614181	+	1.06379i
$163$	−1.08429			−0.0849284			−0.0424642	−	0.999098i	$-0.513521\pi$
$163$	−1.08429			−0.0849284			−0.0424642	+	0.999098i	$0.513521\pi$
$164$	−6.59919	+	11.4301i	−0.515311	+	0.892544i
$165$	−1.26452	+	2.19021i	−0.0984428	+	0.170508i
$166$	−11.9275	+	20.6590i	−0.925753	+	1.60345i
$167$	5.57501	+	9.65620i	0.431407	+	0.747219i	0.996995	−	0.0774691i	$-0.0246839\pi$
$167$	5.57501	+	9.65620i	0.431407	+	0.747219i	−0.565588	+	0.824688i	$0.691351\pi$
$168$	0.135913	−	0.235408i	0.0104859	−	0.0181621i
$169$	5.73931	+	9.94077i	0.441485	+	0.764675i
$170$	25.2260			1.93474
$171$	13.8184			1.05672
$172$	−1.88912	−	3.27206i	−0.144044	−	0.249492i
$173$	3.81909	−	6.61485i	0.290360	−	0.502918i	−0.683535	−	0.729918i	$-0.739558\pi$
$173$	3.81909	−	6.61485i	0.290360	−	0.502918i	0.973895	+	0.227000i	$0.0728917\pi$
$174$	−0.621011	−	1.07562i	−0.0470787	−	0.0815427i
$175$	0.569715	−	0.986776i	0.0430664	−	0.0745932i
$176$	−13.2568	+	22.9614i	−0.999268	+	1.73078i
$177$	−0.292673	+	0.506925i	−0.0219987	+	0.0381028i
$178$	1.58981			0.119161
$179$	6.66579	+	11.5455i	0.498225	+	0.862950i	0.999998	−	0.00204894i	$-0.000652198\pi$
$179$	6.66579	+	11.5455i	0.498225	+	0.862950i	−0.501773	+	0.864999i	$0.667319\pi$
$180$	−4.56643	−	7.90929i	−0.340362	−	0.589524i
$181$	−10.4890	+	18.1674i	−0.779638	+	1.35037i	0.152513	+	0.988301i	$0.451263\pi$
$181$	−10.4890	+	18.1674i	−0.779638	+	1.35037i	−0.932151	+	0.362070i	$0.882070\pi$
$182$	−2.33941			−0.173409
$183$	0.871170	+	1.50891i	0.0643988	+	0.111542i
$184$	8.09537			0.596798
$185$	13.2051			0.970857
$186$		0			0
$187$	−30.4664			−2.22793
$188$	7.03990			0.513438
$189$	−0.599116	−	1.03770i	−0.0435793	−	0.0754815i
$190$	−20.7307			−1.50397
$191$	−3.78330	+	6.55288i	−0.273750	+	0.474149i	−0.969819	−	0.243826i	$-0.921598\pi$
$191$	−3.78330	+	6.55288i	−0.273750	+	0.474149i	0.696069	+	0.717975i	$0.254931\pi$
$192$	0.123395	+	0.213727i	0.00890530	+	0.0154244i
$193$	6.41373	+	11.1089i	0.461671	+	0.799637i	0.999044	−	0.0437073i	$-0.0139169\pi$
$193$	6.41373	+	11.1089i	0.461671	+	0.799637i	−0.537374	+	0.843344i	$0.680584\pi$
$194$	−15.5784			−1.11846
$195$	−0.290473	+	0.503114i	−0.0208012	+	0.0360288i
$196$	3.68167	−	6.37684i	0.262976	−	0.455489i
$197$	8.86072	−	15.3472i	0.631300	−	1.09344i	−0.355986	−	0.934491i	$-0.615855\pi$
$197$	8.86072	−	15.3472i	0.631300	−	1.09344i	0.987286	−	0.158952i	$-0.0508117\pi$
$198$	14.3426	+	24.8421i	1.01928	+	1.76545i
$199$	−0.117245	+	0.203075i	−0.00831130	+	0.0143956i	−0.870151	−	0.492785i	$-0.835979\pi$
$199$	−0.117245	+	0.203075i	−0.00831130	+	0.0143956i	0.861840	+	0.507181i	$0.169312\pi$
$200$	−0.732543	−	1.26880i	−0.0517986	−	0.0897178i
$201$	1.52103			0.107285
$202$	−17.9206			−1.26089
$203$	−1.89806	−	3.28753i	−0.133217	−	0.230739i
$204$	−0.676941	+	1.17250i	−0.0473954	+	0.0820912i
$205$	13.0259	+	22.5615i	0.909769	+	1.57577i
$206$	−8.11914	+	14.0628i	−0.565688	+	0.979800i
$207$	8.86672	−	15.3576i	0.616279	−	1.06743i
$208$	−3.04522	+	5.27447i	−0.211148	+	0.365719i
$209$	25.0373			1.73187
$210$	0.446656	+	0.773631i	0.0308222	+	0.0533856i
$211$	−8.18778	−	14.1817i	−0.563670	−	0.976305i	−0.997172	−	0.0751525i	$-0.976056\pi$
$211$	−8.18778	−	14.1817i	−0.563670	−	0.976305i	0.433502	−	0.901153i	$-0.357278\pi$
$212$	0.567706	−	0.983296i	0.0389902	−	0.0675331i
$213$	1.15890			0.0794068
$214$	0.265757	+	0.460305i	0.0181668	+	0.0314658i
$215$	−7.45774			−0.508614
$216$	−1.54069			−0.104831
$217$		0			0
$218$	−3.94041			−0.266878
$219$	0.723568			0.0488942
$220$	−8.27384	−	14.3307i	−0.557822	−	0.966176i
$221$	−6.99845			−0.470766
$222$	−0.921556	+	1.59618i	−0.0618508	+	0.107129i
$223$	4.89874	+	8.48486i	0.328044	+	0.568188i	0.982124	−	0.188237i	$-0.0602773\pi$
$223$	4.89874	+	8.48486i	0.328044	+	0.568188i	−0.654080	+	0.756426i	$0.726944\pi$
$224$	3.25917	+	5.64505i	0.217762	+	0.377176i
$225$	−3.20937			−0.213958
$226$	9.56098	−	16.5601i	0.635987	−	1.10156i
$227$	0.721335	−	1.24939i	0.0478767	−	0.0829248i	−0.841094	−	0.540889i	$-0.818088\pi$
$227$	0.721335	−	1.24939i	0.0478767	−	0.0829248i	0.888971	+	0.457964i	$0.151421\pi$
$228$	0.556311	−	0.963560i	0.0368426	−	0.0638133i
$229$	13.9290	+	24.1257i	0.920452	+	1.59427i	0.798717	+	0.601707i	$0.205512\pi$
$229$	13.9290	+	24.1257i	0.920452	+	1.59427i	0.121735	+	0.992563i	$0.461154\pi$
$230$	−13.3021	+	23.0399i	−0.877113	+	1.51920i
$231$	−0.539444	−	0.934345i	−0.0354928	−	0.0614754i
$232$	−4.88106			−0.320458
$233$	−15.2785			−1.00093			−0.500463	−	0.865758i	$-0.666837\pi$
$233$	−15.2785			−1.00093			−0.500463	+	0.865758i	$0.666837\pi$
$234$	3.29464	+	5.70649i	0.215378	+	0.373045i
$235$	6.94790	−	12.0341i	0.453231	−	0.785020i
$236$	−1.91498	−	3.31684i	−0.124654	−	0.215908i
$237$	−0.812579	+	1.40743i	−0.0527827	+	0.0914223i
$238$	−5.38070	+	9.31965i	−0.348779	+	0.604103i
$239$	−2.27901	+	3.94737i	−0.147417	+	0.255334i	−0.930272	−	0.366870i	$-0.880429\pi$
$239$	−2.27901	+	3.94737i	−0.147417	+	0.255334i	0.782855	+	0.622204i	$0.213763\pi$
$240$	2.32565			0.150120
$241$	4.01025	+	6.94595i	0.258323	+	0.447428i	0.965793	−	0.259315i	$-0.0834969\pi$
$241$	4.01025	+	6.94595i	0.258323	+	0.447428i	−0.707470	+	0.706743i	$0.750164\pi$
$242$	16.0726	+	27.8386i	1.03319	+	1.78953i
$243$	−2.53640	+	4.39317i	−0.162710	+	0.281822i
$244$	−11.4002			−0.729826
$245$	−7.26712	−	12.5870i	−0.464279	−	0.804155i
$246$	−3.63621			−0.231836
$247$	5.75133			0.365949
$248$		0			0
$249$	−2.52714			−0.160151
$250$	−17.4151			−1.10143
$251$	5.90190	+	10.2224i	0.372525	+	0.645232i	0.989953	−	0.141395i	$-0.0451588\pi$
$251$	5.90190	+	10.2224i	0.372525	+	0.645232i	−0.617428	+	0.786627i	$0.711825\pi$
$252$	3.89608			0.245430
$253$	16.0654	−	27.8262i	1.01003	−	1.74942i
$254$	18.3266	+	31.7426i	1.14991	+	1.99171i
$255$	1.33619	+	2.31435i	0.0836755	+	0.144930i
$256$	20.7208			1.29505
$257$	−0.0531055	+	0.0919815i	−0.00331263	+	0.00573765i	−0.867677	−	0.497128i	$-0.834388\pi$
$257$	−0.0531055	+	0.0919815i	−0.00331263	+	0.00573765i	0.864364	+	0.502866i	$0.167721\pi$
$258$	0.520461	−	0.901465i	0.0324025	−	0.0561227i
$259$	−2.81664	+	4.87857i	−0.175018	+	0.303140i
$260$	−1.90058	−	3.29191i	−0.117869	−	0.204155i
$261$	−5.34614	+	9.25979i	−0.330918	+	0.573167i
$262$	4.90262	+	8.49158i	0.302885	+	0.524612i
$263$	23.7611			1.46517			0.732585	−	0.680675i	$-0.238314\pi$
$263$	23.7611			1.46517			0.732585	+	0.680675i	$0.238314\pi$
$264$	−1.38724			−0.0853788
$265$	−1.12058	−	1.94089i	−0.0688364	−	0.119228i
$266$	4.42187	−	7.65890i	0.271122	−	0.469597i
$267$	0.0842103	+	0.145857i	0.00515359	+	0.00892627i
$268$	−4.97610	+	8.61886i	−0.303964	+	0.526481i
$269$	−1.28859	+	2.23191i	−0.0785669	+	0.136082i	−0.902632	−	0.430414i	$-0.858368\pi$
$269$	−1.28859	+	2.23191i	−0.0785669	+	0.136082i	0.824065	+	0.566495i	$0.191701\pi$
$270$	2.53162	−	4.38490i	0.154070	−	0.266856i
$271$	−29.0802			−1.76650			−0.883248	−	0.468907i	$-0.844648\pi$
$271$	−29.0802			−1.76650			−0.883248	+	0.468907i	$0.844648\pi$
$272$	14.0081	+	24.2628i	0.849368	+	1.47115i
$273$	−0.123916	−	0.214629i	−0.00749973	−	0.0129899i
$274$	3.95666	−	6.85314i	0.239031	−	0.414014i
$275$	−5.81500			−0.350657
$276$	−0.713925	−	1.23655i	−0.0429732	−	0.0744318i
$277$	12.0316			0.722909			0.361454	−	0.932390i	$-0.382280\pi$
$277$	12.0316			0.722909			0.361454	+	0.932390i	$0.382280\pi$
$278$	12.1231			0.727094
$279$		0			0
$280$	3.51066			0.209802
$281$	−31.1377			−1.85752			−0.928759	−	0.370684i	$-0.879123\pi$
$281$	−31.1377			−1.85752			−0.928759	+	0.370684i	$0.879123\pi$
$282$	0.969761	+	1.67968i	0.0577484	+	0.100023i
$283$	5.73801			0.341090			0.170545	−	0.985350i	$-0.445447\pi$
$283$	5.73801			0.341090			0.170545	+	0.985350i	$0.445447\pi$
$284$	−3.79139	+	6.56688i	−0.224978	+	0.389673i
$285$	−1.09808	−	1.90194i	−0.0650448	−	0.112661i
$286$	5.96951	+	10.3395i	0.352984	+	0.611387i
$287$	−11.1137			−0.656021
$288$	9.17991	−	15.9001i	0.540932	−	0.936921i
$289$	−7.59658	+	13.1577i	−0.446858	+	0.773980i
$290$	8.02042	−	13.8918i	0.470976	−	0.815754i
$291$	−0.825169	−	1.42923i	−0.0483723	−	0.0837832i
$292$	−2.36718	+	4.10007i	−0.138528	+	0.239938i
$293$	−0.639514	−	1.10767i	−0.0373608	−	0.0647108i	0.846740	−	0.532006i	$-0.178562\pi$
$293$	−0.639514	−	1.10767i	−0.0373608	−	0.0647108i	−0.884101	+	0.467296i	$0.845228\pi$
$294$	2.02863			0.118312
$295$	−7.55981			−0.440149
$296$	3.62166	+	6.27289i	0.210504	+	0.364604i
$297$	−3.05754	+	5.29582i	−0.177417	+	0.307294i
$298$	1.99818	+	3.46095i	0.115751	+	0.200487i
$299$	3.69040	−	6.39195i	0.213421	−	0.369656i
$300$	−0.129205	+	0.223789i	−0.00745965	+	0.0129205i
$301$	1.59074	−	2.75523i	0.0916885	−	0.158809i
$302$	8.55365			0.492207
$303$	−0.949234	−	1.64412i	−0.0545320	−	0.0944523i
$304$	−11.5119	−	19.9392i	−0.660253	−	1.14359i
$305$	−11.2513	+	19.4878i	−0.644245	+	1.11587i
$306$	30.3110			1.73276
$307$	7.84659	+	13.5907i	0.447828	+	0.775662i	0.998244	−	0.0592290i	$-0.0188642\pi$
$307$	7.84659	+	13.5907i	0.447828	+	0.775662i	−0.550416	+	0.834891i	$0.685531\pi$
$308$	7.05923			0.402237
$309$	−1.72025			−0.0978613
$310$		0			0
$311$	27.4565			1.55692			0.778459	−	0.627695i	$-0.216002\pi$
$311$	27.4565			1.55692			0.778459	+	0.627695i	$0.216002\pi$
$312$	−0.318664			−0.0180408
$313$	−6.40409	−	11.0922i	−0.361981	−	0.626969i	0.626306	−	0.779577i	$-0.284566\pi$
$313$	−6.40409	−	11.0922i	−0.361981	−	0.626969i	−0.988287	+	0.152608i	$0.951233\pi$
$314$	−7.29778			−0.411838
$315$	3.84516	−	6.66002i	0.216650	−	0.375250i
$316$	−5.31676	−	9.20889i	−0.299091	−	0.518041i
$317$	4.76143	+	8.24704i	0.267428	+	0.463200i	0.968197	−	0.250189i	$-0.0804928\pi$
$317$	4.76143	+	8.24704i	0.267428	+	0.463200i	−0.700769	+	0.713389i	$0.747159\pi$
$318$	0.312811			0.0175416
$319$	−9.68659	+	16.7777i	−0.542345	+	0.939368i
$320$	−1.59367	+	2.76031i	−0.0890887	+	0.154306i
$321$	−0.0281537	+	0.0487636i	−0.00157138	+	0.00272172i
$322$	−5.67467	−	9.82881i	−0.316237	−	0.547738i
$323$	13.2282	−	22.9119i	0.736036	−	1.27485i
$324$	−5.41857	−	9.38525i	−0.301032	−	0.521403i
$325$	−1.33576			−0.0740948
$326$	1.95459			0.108255
$327$	−0.208719	−	0.361512i	−0.0115422	−	0.0199916i
$328$	−7.14503	+	12.3756i	−0.394519	+	0.683326i
$329$	2.96398	+	5.13376i	0.163409	+	0.283033i
$330$	2.27948	−	3.94817i	0.125481	−	0.217339i
$331$	−10.7916	+	18.6916i	−0.593159	+	1.02738i	0.400645	+	0.916233i	$0.368786\pi$
$331$	−10.7916	+	18.6916i	−0.593159	+	1.02738i	−0.993804	+	0.111148i	$0.964547\pi$
$332$	8.26761	−	14.3199i	0.453744	−	0.785908i
$333$	15.8669			0.869503
$334$	−10.0497	−	17.4066i	−0.549897	−	0.952449i
$335$	9.82214	+	17.0125i	0.536641	+	0.929490i
$336$	−0.496062	+	0.859204i	−0.0270624	+	0.0468734i
$337$	−4.54798			−0.247744			−0.123872	−	0.992298i	$-0.539531\pi$
$337$	−4.54798			−0.247744			−0.123872	+	0.992298i	$0.539531\pi$
$338$	−10.3459	−	17.9196i	−0.562743	−	0.974699i
$339$	2.02573			0.110023
$340$	−17.4855			−0.948287
$341$		0			0
$342$	−24.9096			−1.34696
$343$	13.5654			0.732461
$344$	−2.04538	−	3.54270i	−0.110279	−	0.191009i
$345$	−2.81838			−0.151737
$346$	−6.88444	+	11.9242i	−0.370110	+	0.641049i
$347$	−14.6947	−	25.4520i	−0.788855	−	1.36634i	−0.926669	−	0.375879i	$-0.877341\pi$
$347$	−14.6947	−	25.4520i	−0.788855	−	1.36634i	0.137813	−	0.990458i	$-0.455993\pi$
$348$	0.430458	+	0.745574i	0.0230749	+	0.0399670i
$349$	−6.75125			−0.361386			−0.180693	−	0.983540i	$-0.557834\pi$
$349$	−6.75125			−0.361386			−0.180693	+	0.983540i	$0.557834\pi$
$350$	−1.02699	+	1.77880i	−0.0548950	+	0.0950809i
$351$	−0.702348	+	1.21650i	−0.0374886	+	0.0649321i
$352$	16.6329	−	28.8091i	0.886538	−	1.53553i
$353$	−3.89034	−	6.73827i	−0.207062	−	0.358642i	0.743726	−	0.668485i	$-0.233057\pi$
$353$	−3.89034	−	6.73827i	−0.207062	−	0.358642i	−0.950788	+	0.309843i	$0.899724\pi$
$354$	0.527584	−	0.913803i	0.0280408	−	0.0485681i
$355$	7.48369	+	12.9621i	0.397193	+	0.687958i
$356$	−1.10199			−0.0584051
$357$	−1.14004			−0.0603372
$358$	−12.0160	−	20.8124i	−0.635066	−	1.09997i
$359$	−1.29368	+	2.24072i	−0.0682780	+	0.118261i	−0.898143	−	0.439703i	$-0.855084\pi$
$359$	−1.29368	+	2.24072i	−0.0682780	+	0.118261i	0.829865	+	0.557964i	$0.188417\pi$
$360$	−4.94413	−	8.56349i	−0.260579	−	0.451336i
$361$	−1.37095	+	2.37455i	−0.0721552	+	0.124976i
$362$	18.9078	−	32.7493i	0.993772	−	1.72126i
$363$	−1.70269	+	2.94915i	−0.0893682	+	0.154790i
$364$	1.62158			0.0849938
$365$	4.67248	+	8.09298i	0.244569	+	0.423606i
$366$	−1.57041	−	2.72002i	−0.0820865	−	0.142178i
$367$	17.6139	−	30.5081i	0.919437	−	1.59251i	0.119166	−	0.992874i	$-0.461978\pi$
$367$	17.6139	−	30.5081i	0.919437	−	1.59251i	0.800271	−	0.599638i	$-0.204689\pi$
$368$	−29.5469			−1.54024
$369$	15.6517	+	27.1095i	0.814793	+	1.41126i
$370$	−23.8040			−1.23751
$371$	0.956075			0.0496369
$372$		0			0
$373$	6.68493			0.346133			0.173066	−	0.984910i	$-0.444632\pi$
$373$	6.68493			0.346133			0.173066	+	0.984910i	$0.444632\pi$
$374$	54.9200			2.83984
$375$	−0.922455	−	1.59774i	−0.0476354	−	0.0825069i
$376$	7.62219			0.393085
$377$	−2.22511	+	3.85400i	−0.114599	+	0.198491i
$378$	1.07999	+	1.87060i	0.0555487	+	0.0962131i
$379$	−8.78943	−	15.2237i	−0.451483	−	0.781991i	0.546996	−	0.837135i	$-0.315771\pi$
$379$	−8.78943	−	15.2237i	−0.451483	−	0.781991i	−0.998478	+	0.0551445i	$0.982438\pi$
$380$	14.3696			0.737147
$381$	−1.94148	+	3.36273i	−0.0994648	+	0.172278i
$382$	6.81994	−	11.8125i	0.348938	−	0.604379i
$383$	−16.2889	+	28.2131i	−0.832322	+	1.44162i	0.0638703	+	0.997958i	$0.479656\pi$
$383$	−16.2889	+	28.2131i	−0.832322	+	1.44162i	−0.896192	+	0.443666i	$0.853678\pi$
$384$	0.960653	+	1.66390i	0.0490231	+	0.0849106i
$385$	6.96698	−	12.0672i	0.355070	−	0.615000i
$386$	−11.5617	−	20.0254i	−0.588473	−	1.01926i
$387$	−8.96106			−0.455516
$388$	10.7983			0.548198
$389$	−4.19400	−	7.26422i	−0.212644	−	0.368311i	0.739897	−	0.672720i	$-0.234874\pi$
$389$	−4.19400	−	7.26422i	−0.212644	−	0.368311i	−0.952541	+	0.304409i	$0.901541\pi$
$390$	0.523619	−	0.906934i	0.0265145	−	0.0459244i
$391$	−16.9760	−	29.4033i	−0.858513	−	1.48699i
$392$	3.98619	−	6.90429i	0.201333	−	0.348719i
$393$	−0.519371	+	0.899578i	−0.0261988	+	0.0453777i
$394$	−15.9727	+	27.6655i	−0.804692	+	1.39377i
$395$	−20.9891			−1.05608
$396$	−9.94167	−	17.2195i	−0.499588	−	0.865311i
$397$	−13.1250	−	22.7332i	−0.658727	−	1.14095i	−0.980946	−	0.194283i	$-0.937762\pi$
$397$	−13.1250	−	22.7332i	−0.658727	−	1.14095i	0.322219	−	0.946665i	$-0.395571\pi$
$398$	0.211351	−	0.366071i	0.0105941	−	0.0183495i
$399$	0.936884			0.0469029
$400$	2.67367	+	4.63094i	0.133684	+	0.231547i
$401$	2.68824			0.134245			0.0671223	−	0.997745i	$-0.478618\pi$
$401$	2.68824			0.134245			0.0671223	+	0.997745i	$0.478618\pi$
$402$	−2.74187			−0.136752
$403$		0			0
$404$	12.4218			0.618007
$405$	−21.3911			−1.06293
$406$	3.42151	+	5.92623i	0.169807	+	0.294114i
$407$	28.7490			1.42504
$408$	−0.732933	+	1.26948i	−0.0362856	+	0.0628485i
$409$	−1.54776	−	2.68079i	−0.0765316	−	0.132557i	0.825220	−	0.564812i	$-0.191051\pi$
$409$	−1.54776	−	2.68079i	−0.0765316	−	0.132557i	−0.901751	+	0.432255i	$0.857718\pi$
$410$	−23.4810	−	40.6703i	−1.15965	−	2.00856i
$411$	0.838319			0.0413512
$412$	5.62783	−	9.74770i	0.277264	−	0.480234i
$413$	1.61251	−	2.79294i	0.0793463	−	0.137432i
$414$	−15.9835	+	27.6842i	−0.785546	+	1.36061i
$415$	−16.3191	−	28.2656i	−0.801075	−	1.38750i
$416$	3.82075	−	6.61774i	0.187328	−	0.324461i
$417$	0.642145	+	1.11223i	0.0314460	+	0.0544660i
$418$	−45.1333			−2.20754
$419$	32.6796			1.59650			0.798250	−	0.602326i	$-0.205759\pi$
$419$	32.6796			1.59650			0.798250	+	0.602326i	$0.205759\pi$
$420$	−0.309603	−	0.536247i	−0.0151071	−	0.0261662i
$421$	−6.81717	+	11.8077i	−0.332248	+	0.575471i	−0.982952	−	0.183860i	$-0.941141\pi$
$421$	−6.81717	+	11.8077i	−0.332248	+	0.575471i	0.650704	+	0.759332i	$0.274474\pi$
$422$	14.7596	+	25.5644i	0.718487	+	1.24446i
$423$	8.34846	−	14.4599i	0.405916	−	0.703067i
$424$	0.614663	−	1.06463i	0.0298507	−	0.0517029i
$425$	−3.07229	+	5.32136i	−0.149028	+	0.258124i
$426$	−2.08909			−0.101217
$427$	−4.79979	−	8.31347i	−0.232278	−	0.402317i
$428$	−0.184211	−	0.319063i	−0.00890418	−	0.0154225i
$429$	−0.632395	+	1.09534i	−0.0305323	+	0.0528835i
$430$	13.4436			0.648309
$431$	−13.9133	−	24.0986i	−0.670181	−	1.16079i	−0.977853	−	0.209294i	$-0.932883\pi$
$431$	−13.9133	−	24.0986i	−0.670181	−	1.16079i	0.307672	−	0.951492i	$-0.400450\pi$
$432$	5.62330			0.270551
$433$	2.12857			0.102292			0.0511462	−	0.998691i	$-0.483713\pi$
$433$	2.12857			0.102292			0.0511462	+	0.998691i	$0.483713\pi$
$434$		0			0
$435$	1.69933			0.0814766
$436$	2.73132			0.130806
$437$	13.9509	+	24.1637i	0.667362	+	1.15590i
$438$	−1.30433			−0.0623235
$439$	−4.69991	+	8.14048i	−0.224314	+	0.388524i	−0.956114	−	0.292997i	$-0.905348\pi$
$439$	−4.69991	+	8.14048i	−0.224314	+	0.388524i	0.731799	+	0.681520i	$0.238681\pi$
$440$	−8.95819	−	15.5160i	−0.427065	−	0.739698i
$441$	−8.73201	−	15.1243i	−0.415810	−	0.720204i
$442$	12.6157			0.600067
$443$	−15.7041	+	27.2003i	−0.746123	+	1.29232i	0.203545	+	0.979066i	$0.434754\pi$
$443$	−15.7041	+	27.2003i	−0.746123	+	1.29232i	−0.949668	+	0.313258i	$0.898580\pi$
$444$	0.638782	−	1.10640i	0.0303153	−	0.0525076i
$445$	−1.08759	+	1.88375i	−0.0515565	+	0.0892984i
$446$	−8.83066	−	15.2952i	−0.418144	−	0.724247i
$447$	−0.211682	+	0.366644i	−0.0100122	+	0.0173417i
$448$	−0.679858	−	1.17755i	−0.0321203	−	0.0556339i
$449$	−24.1150			−1.13806			−0.569028	−	0.822318i	$-0.692680\pi$
$449$	−24.1150			−1.13806			−0.569028	+	0.822318i	$0.692680\pi$
$450$	5.78533			0.272723
$451$	28.3590	+	49.1192i	1.33537	+	2.31293i
$452$	−6.62725	+	11.4787i	−0.311720	+	0.539914i
$453$	0.453077	+	0.784752i	0.0212874	+	0.0368708i
$454$	−1.30031	+	2.25220i	−0.0610264	+	0.105701i
$455$	1.60039	−	2.77195i	0.0750273	−	0.129951i
$456$	0.602326	−	1.04326i	0.0282065	−	0.0488551i
$457$	3.70612			0.173365			0.0866826	−	0.996236i	$-0.472373\pi$
$457$	3.70612			0.173365			0.0866826	+	0.996236i	$0.472373\pi$
$458$	−25.1089	−	43.4899i	−1.17326	−	2.03215i
$459$	3.23083	+	5.59597i	0.150802	+	0.261197i
$460$	9.22042	−	15.9702i	0.429904	−	0.744616i
$461$	17.0725			0.795144			0.397572	−	0.917571i	$-0.369853\pi$
$461$	17.0725			0.795144			0.397572	+	0.917571i	$0.369853\pi$
$462$	0.972424	+	1.68429i	0.0452413	+	0.0783602i
$463$	4.91245			0.228301			0.114150	−	0.993463i	$-0.463585\pi$
$463$	4.91245			0.228301			0.114150	+	0.993463i	$0.463585\pi$
$464$	17.8152			0.827048
$465$		0			0
$466$	27.5416			1.27584
$467$	−2.57047			−0.118947			−0.0594735	−	0.998230i	$-0.518942\pi$
$467$	−2.57047			−0.118947			−0.0594735	+	0.998230i	$0.518942\pi$
$468$	−2.28370	−	3.95549i	−0.105564	−	0.182842i
$469$	−8.38025			−0.386964
$470$	−12.5246	+	21.6932i	−0.577715	+	1.00063i
$471$	−0.386555	−	0.669533i	−0.0178115	−	0.0308504i
$472$	−2.07337	−	3.59118i	−0.0954346	−	0.165298i
$473$	−16.2364			−0.746550
$474$	1.46479	−	2.53709i	0.0672800	−	0.116532i
$475$	2.52481	−	4.37310i	0.115846	−	0.200651i
$476$	3.72967	−	6.45997i	0.170949	−	0.296092i
$477$	−1.34646	−	2.33214i	−0.0616501	−	0.106781i
$478$	4.10824	−	7.11568i	0.187907	−	0.325464i
$479$	−1.02661	−	1.77815i	−0.0469071	−	0.0812455i	0.841619	−	0.540072i	$-0.181603\pi$
$479$	−1.02661	−	1.77815i	−0.0469071	−	0.0812455i	−0.888526	+	0.458827i	$0.848270\pi$
$480$	−2.91793			−0.133185
$481$	6.60395			0.301114
$482$	−7.22903	−	12.5210i	−0.329273	−	0.570318i
$483$	0.601160	−	1.04124i	0.0273537	−	0.0473781i
$484$	−11.1408	−	19.2965i	−0.506401	−	0.877112i
$485$	10.6571	−	18.4587i	0.483916	−	0.838167i
$486$	4.57222	−	7.91931i	0.207400	−	0.359227i
$487$	8.85568	−	15.3385i	0.401289	−	0.695053i	−0.592593	−	0.805502i	$-0.701896\pi$
$487$	8.85568	−	15.3385i	0.401289	−	0.695053i	0.993882	+	0.110449i	$0.0352290\pi$
$488$	−12.3432			−0.558750
$489$	0.103532	+	0.179323i	0.00468189	+	0.00810928i
$490$	13.1000	+	22.6899i	0.591797	+	1.02502i
$491$	−11.2360	+	19.4613i	−0.507072	+	0.878275i	0.492894	+	0.870089i	$0.335939\pi$
$491$	−11.2360	+	19.4613i	−0.507072	+	0.878275i	−0.999966	+	0.00818549i	$0.997394\pi$
$492$	2.52046			0.113631
$493$	10.2356	+	17.7286i	0.460988	+	0.798454i
$494$	−10.3676			−0.466460
$495$	−39.2470			−1.76402
$496$		0			0
$497$	−6.38508			−0.286410
$498$	4.55552			0.204138
$499$	10.0002	+	17.3208i	0.447668	+	0.775384i	0.998234	−	0.0594077i	$-0.0189212\pi$
$499$	10.0002	+	17.3208i	0.447668	+	0.775384i	−0.550566	+	0.834792i	$0.685588\pi$
$500$	12.0714			0.539847
$501$	1.06464	−	1.84402i	0.0475648	−	0.0823847i
$502$	−10.6390	−	18.4273i	−0.474842	−	0.822451i
$503$	−6.26537	−	10.8519i	−0.279359	−	0.483864i	0.691867	−	0.722025i	$-0.256789\pi$
$503$	−6.26537	−	10.8519i	−0.279359	−	0.483864i	−0.971226	+	0.238161i	$0.923455\pi$
$504$	4.21833			0.187900
$505$	12.2595	−	21.2340i	0.545539	−	0.944901i
$506$	−28.9602	+	50.1606i	−1.28744	+	2.22991i
$507$	1.09602	−	1.89836i	0.0486760	−	0.0843093i
$508$	−12.7032	−	22.0026i	−0.563613	−	0.976206i
$509$	13.2033	−	22.8688i	0.585226	−	1.01364i	−0.409621	−	0.912256i	$-0.634339\pi$
$509$	13.2033	−	22.8688i	0.585226	−	1.01364i	0.994847	−	0.101386i	$-0.0323277\pi$
$510$	−2.40867	−	4.17194i	−0.106658	−	0.184737i
$511$	−3.98656			−0.176355
$512$	−17.2304			−0.761483
$513$	−2.65510	−	4.59877i	−0.117226	−	0.203041i
$514$	0.0957301	−	0.165809i	0.00422248	−	0.00731354i
$515$	−11.1086	−	19.2406i	−0.489502	−	0.847843i
$516$	−0.360761	+	0.624856i	−0.0158816	+	0.0275077i
$517$	15.1264	−	26.1997i	0.665259	−	1.15226i
$518$	5.07739	−	8.79430i	0.223088	−	0.386400i
$519$	−1.45864			−0.0640273
$520$	−2.05779	−	3.56419i	−0.0902399	−	0.156300i
$521$	12.1247	+	21.0006i	0.531193	+	0.920053i	0.999337	+	0.0364011i	$0.0115894\pi$
$521$	12.1247	+	21.0006i	0.531193	+	0.920053i	−0.468144	+	0.883652i	$0.655077\pi$
$522$	9.63717	−	16.6921i	0.421808	−	0.730592i
$523$	35.8536			1.56777			0.783885	−	0.620906i	$-0.213235\pi$
$523$	35.8536			1.56777			0.783885	+	0.620906i	$0.213235\pi$
$524$	−3.39828	−	5.88599i	−0.148454	−	0.257131i
$525$	−0.217594			−0.00949658
$526$	−42.8327			−1.86759
$527$		0			0
$528$	5.06323			0.220349
$529$	12.8069			0.556821
$530$	2.01999	+	3.49873i	0.0877429	+	0.151975i
$531$	−9.08371			−0.394199
$532$	−3.06504	+	5.30881i	−0.132887	+	0.230166i
$533$	6.51434	+	11.2832i	0.282168	+	0.488729i
$534$	−0.151801	−	0.262927i	−0.00656906	−	0.0113780i
$535$	−0.727215			−0.0314403
$536$	−5.38769	+	9.33175i	−0.232713	+	0.403070i
$537$	1.27295	−	2.20481i	0.0549318	−	0.0951446i
$538$	2.32287	−	4.02333i	0.100146	−	0.173458i
$539$	−15.8214	−	27.4034i	−0.681475	−	1.18035i
$540$	−1.75481	+	3.03942i	−0.0755150	+	0.130796i
$541$	−7.51861	−	13.0226i	−0.323250	−	0.559886i	0.657906	−	0.753100i	$-0.271442\pi$
$541$	−7.51861	−	13.0226i	−0.323250	−	0.559886i	−0.981157	+	0.193214i	$0.938109\pi$
$542$	52.4211			2.25168
$543$	4.00609			0.171918
$544$	−17.5756	−	30.4419i	−0.753549	−	1.30518i
$545$	2.69563	−	4.66896i	0.115468	−	0.199996i
$546$	0.223376	+	0.386898i	0.00955960	+	0.0165577i
$547$	20.2494	−	35.0730i	0.865803	−	1.49961i	−0.000445445	−	1.00000i	$-0.500142\pi$
$547$	20.2494	−	35.0730i	0.865803	−	1.49961i	0.866248	−	0.499614i	$-0.166525\pi$
$548$	−2.74259	+	4.75030i	−0.117157	+	0.202923i
$549$	−13.5193	+	23.4161i	−0.576989	+	0.999374i
$550$	10.4823			0.446969
$551$	−8.41162	−	14.5694i	−0.358347	−	0.620676i
$552$	−0.772976	−	1.33883i	−0.0329000	−	0.0569845i
$553$	4.47698	−	7.75435i	0.190380	−	0.329748i
$554$	−21.6886			−0.921462
$555$	−1.26087	−	2.18389i	−0.0535209	−	0.0927010i
$556$	−8.40318			−0.356374
$557$	32.3465			1.37057			0.685284	−	0.728276i	$-0.259678\pi$
$557$	32.3465			1.37057			0.685284	+	0.728276i	$0.259678\pi$
$558$		0			0
$559$	−3.72966			−0.157748
$560$	−12.8134			−0.541464
$561$	2.90905	+	5.03861i	0.122820	+	0.212730i
$562$	56.1300			2.36770
$563$	−14.3093	+	24.7844i	−0.603064	+	1.04454i	0.389290	+	0.921115i	$0.372720\pi$
$563$	−14.3093	+	24.7844i	−0.603064	+	1.04454i	−0.992354	+	0.123422i	$0.960613\pi$
$564$	−0.672196	−	1.16428i	−0.0283045	−	0.0490249i
$565$	13.0813	+	22.6575i	0.550334	+	0.953206i
$566$	−10.3436			−0.434773
$567$	4.56271	−	7.90285i	0.191616	−	0.331888i
$568$	−4.10499	+	7.11004i	−0.172241	+	0.298331i
$569$	18.6749	−	32.3459i	0.782894	−	1.35601i	−0.147356	−	0.989084i	$-0.547076\pi$
$569$	18.6749	−	32.3459i	0.782894	−	1.35601i	0.930249	−	0.366928i	$-0.119590\pi$
$570$	1.97945	+	3.42850i	0.0829100	+	0.143604i
$571$	−4.99035	+	8.64353i	−0.208840	+	0.361721i	−0.951349	−	0.308115i	$-0.900302\pi$
$571$	−4.99035	+	8.64353i	−0.208840	+	0.361721i	0.742510	+	0.669835i	$0.233635\pi$
$572$	−4.13780	−	7.16688i	−0.173010	−	0.299662i
$573$	1.44498			0.0603647
$574$	20.0340			0.836203
$575$	−3.24013	−	5.61208i	−0.135123	−	0.234040i
$576$	−1.91492	+	3.31673i	−0.0797882	+	0.138197i
$577$	19.2162	+	33.2834i	0.799980	+	1.38561i	0.919629	+	0.392789i	$0.128490\pi$
$577$	19.2162	+	33.2834i	0.799980	+	1.38561i	−0.119649	+	0.992816i	$0.538177\pi$
$578$	13.6939	−	23.7185i	0.569591	−	0.986561i
$579$	1.22481	−	2.12144i	0.0509015	−	0.0881640i
$580$	−5.55941	+	9.62917i	−0.230842	+	0.399830i
$581$	13.9235			0.577644
$582$	1.48748	+	2.57639i	0.0616581	+	0.106795i
$583$	−2.43963	−	4.22556i	−0.101039	−	0.175005i
$584$	−2.56297	+	4.43920i	−0.106057	+	0.183695i
$585$	−9.01543			−0.372742
$586$	1.15281	+	1.99673i	0.0476223	+	0.0824842i
$587$	30.3071			1.25091			0.625453	−	0.780261i	$-0.284914\pi$
$587$	30.3071			1.25091			0.625453	+	0.780261i	$0.284914\pi$
$588$	−1.40616			−0.0579890
$589$		0			0
$590$	13.6276			0.561040
$591$	−3.38422			−0.139208
$592$	−13.2185	−	22.8951i	−0.543277	−	0.940984i
$593$	2.16459			0.0888889			0.0444445	−	0.999012i	$-0.485848\pi$
$593$	2.16459			0.0888889			0.0444445	+	0.999012i	$0.485848\pi$
$594$	5.51165	−	9.54645i	0.226146	−	0.391696i
$595$	−7.36185	−	12.7511i	−0.301806	−	0.522744i
$596$	−1.38505	−	2.39898i	−0.0567338	−	0.0982659i
$597$	0.0447801			0.00183273
$598$	−6.65246	+	11.5224i	−0.272039	+	0.471186i
$599$	13.2374	−	22.9279i	0.540866	−	0.936807i	−0.457989	−	0.888958i	$-0.651430\pi$
$599$	13.2374	−	22.9279i	0.540866	−	0.936807i	0.998855	−	0.0478493i	$-0.0152367\pi$
$600$	−0.139892	+	0.242300i	−0.00571106	+	0.00989185i
$601$	20.5359	+	35.5692i	0.837677	+	1.45090i	0.891832	+	0.452367i	$0.149420\pi$
$601$	20.5359	+	35.5692i	0.837677	+	1.45090i	−0.0541551	+	0.998533i	$0.517247\pi$
$602$	−2.86752	+	4.96670i	−0.116872	+	0.202427i
$603$	11.8021	+	20.4418i	0.480618	+	0.832455i
$604$	−5.92901			−0.241248
$605$	−43.9809			−1.78808
$606$	1.71113	+	2.96376i	0.0695098	+	0.120394i
$607$	−19.6102	+	33.9658i	−0.795953	+	1.37863i	0.126280	+	0.991995i	$0.459696\pi$
$607$	−19.6102	+	33.9658i	−0.795953	+	1.37863i	−0.922232	+	0.386636i	$0.873637\pi$
$608$	14.4437	+	25.0172i	0.585768	+	1.01458i
$609$	−0.362467	+	0.627811i	−0.0146879	+	0.0254402i
$610$	20.2820	−	35.1294i	0.821193	−	1.42235i
$611$	3.47469	−	6.01834i	0.140571	−	0.243476i
$612$	−21.0103			−0.849289
$613$	10.8671	+	18.8223i	0.438917	+	0.760227i	0.997606	−	0.0691502i	$-0.0220288\pi$
$613$	10.8671	+	18.8223i	0.438917	+	0.760227i	−0.558689	+	0.829377i	$0.688695\pi$
$614$	−14.1446	−	24.4991i	−0.570829	−	0.988704i
$615$	2.48752	−	4.30852i	0.100307	−	0.173736i
$616$	7.64313			0.307950
$617$	6.77309	+	11.7313i	0.272674	+	0.472286i	0.969546	−	0.244910i	$-0.0787586\pi$
$617$	6.77309	+	11.7313i	0.272674	+	0.472286i	−0.696872	+	0.717196i	$0.745425\pi$
$618$	3.10098			0.124740
$619$	42.3785			1.70334			0.851668	−	0.524082i	$-0.175592\pi$
$619$	42.3785			1.70334			0.851668	+	0.524082i	$0.175592\pi$
$620$		0			0
$621$	−6.81469			−0.273464
$622$	−49.4943			−1.98454
$623$	−0.463964	−	0.803609i	−0.0185883	−	0.0321959i
$624$	1.16307			0.0465602
$625$	14.6210	−	25.3243i	0.584840	−	1.01297i
$626$	11.5443	+	19.9953i	0.461402	+	0.799171i
$627$	−2.39066	−	4.14074i	−0.0954737	−	0.165365i
$628$	5.05850			0.201856
$629$	15.1892	−	26.3085i	0.605634	−	1.04899i
$630$	−6.93145	+	12.0056i	−0.276155	+	0.478315i
$631$	−11.4421	+	19.8184i	−0.455505	+	0.788957i	−0.998717	−	0.0506381i	$-0.983874\pi$
$631$	−11.4421	+	19.8184i	−0.455505	+	0.788957i	0.543212	+	0.839595i	$0.317208\pi$
$632$	−5.75652	−	9.97059i	−0.228982	−	0.396609i
$633$	−1.56360	+	2.70823i	−0.0621475	+	0.107643i
$634$	−8.58314	−	14.8664i	−0.340880	−	0.590422i
$635$	−50.1487			−1.99009
$636$	−0.216827			−0.00859774
$637$	−3.63433	−	6.29485i	−0.143997	−	0.249411i
$638$	17.4614	−	30.2441i	0.691304	−	1.19737i
$639$	8.99224	+	15.5750i	0.355727	+	0.616138i
$640$	−12.4069	+	21.4895i	−0.490427	+	0.849445i
$641$	−11.7265	+	20.3109i	−0.463170	+	0.802234i	−0.999117	−	0.0420179i	$-0.986621\pi$
$641$	−11.7265	+	20.3109i	−0.463170	+	0.802234i	0.535947	+	0.844252i	$0.319955\pi$
$642$	0.0507509	−	0.0879032i	0.00200298	−	0.00346926i
$643$	14.5344			0.573180			0.286590	−	0.958053i	$-0.407478\pi$
$643$	14.5344			0.573180			0.286590	+	0.958053i	$0.407478\pi$
$644$	3.93343	+	6.81290i	0.154999	+	0.268466i
$645$	0.712092	+	1.23338i	0.0280386	+	0.0485643i
$646$	−23.8457	+	41.3019i	−0.938195	+	1.62500i
$647$	−4.94376			−0.194359			−0.0971796	−	0.995267i	$-0.530982\pi$
$647$	−4.94376			−0.194359			−0.0971796	+	0.995267i	$0.530982\pi$
$648$	−5.86676	−	10.1615i	−0.230468	−	0.399183i
$649$	−16.4586			−0.646057
$650$	2.40790			0.0944456
$651$		0			0
$652$	−1.35484			−0.0530595
$653$	15.8388			0.619820			0.309910	−	0.950766i	$-0.399701\pi$
$653$	15.8388			0.619820			0.309910	+	0.950766i	$0.399701\pi$
$654$	0.376245	+	0.651675i	0.0147123	+	0.0254825i
$655$	−13.4155			−0.524186
$656$	26.0783	−	45.1690i	1.01819	−	1.76355i
$657$	5.61436	+	9.72435i	0.219037	+	0.379383i
$658$	−5.34298	−	9.25431i	−0.208291	−	0.360771i
$659$	23.8208			0.927926			0.463963	−	0.885855i	$-0.346427\pi$
$659$	23.8208			0.927926			0.463963	+	0.885855i	$0.346427\pi$
$660$	−1.58003	+	2.73670i	−0.0615027	+	0.106526i
$661$	−20.6050	+	35.6889i	−0.801441	+	1.38814i	0.117227	+	0.993105i	$0.462599\pi$
$661$	−20.6050	+	35.6889i	−0.801441	+	1.38814i	−0.918668	+	0.395031i	$0.870734\pi$
$662$	19.4533	−	33.6942i	0.756075	−	1.30956i
$663$	0.668237	+	1.15742i	0.0259522	+	0.0449505i
$664$	8.95145	−	15.5044i	0.347384	−	0.601686i
$665$	6.04998	+	10.4789i	0.234608	+	0.406353i
$666$	−28.6024			−1.10832
$667$	−21.5896			−0.835952
$668$	6.96603	+	12.0655i	0.269524	+	0.466829i
$669$	0.935499	−	1.62033i	0.0361685	−	0.0626457i
$670$	−17.7058	−	30.6673i	−0.684034	−	1.18478i
$671$	−24.4953	+	42.4272i	−0.945632	+	1.63788i
$672$	0.622395	−	1.07802i	0.0240094	−	0.0415855i
$673$	−20.1038	+	34.8208i	−0.774945	+	1.34224i	0.159880	+	0.987136i	$0.448889\pi$
$673$	−20.1038	+	34.8208i	−0.774945	+	1.34224i	−0.934825	+	0.355108i	$0.884444\pi$
$674$	8.19837			0.315789
$675$	0.616655	+	1.06808i	0.0237351	+	0.0411104i
$676$	7.17133	+	12.4211i	0.275820	+	0.477735i
$677$	15.8290	−	27.4165i	0.608356	−	1.05370i	−0.383155	−	0.923684i	$-0.625163\pi$
$677$	15.8290	−	27.4165i	0.608356	−	1.05370i	0.991511	−	0.130020i	$-0.0415040\pi$
$678$	−3.65167			−0.140242
$679$	4.54634	+	7.87449i	0.174472	+	0.302195i
$680$	−18.9318			−0.726002
$681$	−0.275503			−0.0105573
$682$		0			0
$683$	10.8397			0.414771			0.207386	−	0.978259i	$-0.433505\pi$
$683$	10.8397			0.414771			0.207386	+	0.978259i	$0.433505\pi$
$684$	17.2663			0.660192
$685$	5.41349	+	9.37644i	0.206839	+	0.358255i
$686$	−24.4535			−0.933637
$687$	2.65998	−	4.60722i	0.101484	−	0.175776i
$688$	7.46532	+	12.9303i	0.284613	+	0.492964i
$689$	−0.560407	−	0.970653i	−0.0213498	−	0.0369789i
$690$	5.08053			0.193412
$691$	13.2380	−	22.9289i	0.503597	−	0.872255i	−0.496395	−	0.868097i	$-0.665343\pi$
$691$	13.2380	−	22.9289i	0.503597	−	0.872255i	0.999991	−	0.00415798i	$-0.00132353\pi$
$692$	4.77199	−	8.26533i	0.181404	−	0.314201i
$693$	8.37138	−	14.4997i	0.318002	−	0.550796i
$694$	26.4893	+	45.8809i	1.00552	+	1.74161i
$695$	−8.29337	+	14.3645i	−0.314585	+	0.544878i
$696$	0.466062	+	0.807243i	0.0176660	+	0.0305985i
$697$	59.9325			2.27011
$698$	12.1701			0.460644
$699$	1.45885	+	2.52680i	0.0551786	+	0.0955722i
$700$	0.711865	−	1.23299i	0.0269060	−	0.0466025i
$701$	−5.36333	−	9.28956i	−0.202570	−	0.350862i	0.746786	−	0.665065i	$-0.231596\pi$
$701$	−5.36333	−	9.28956i	−0.202570	−	0.350862i	−0.949356	+	0.314203i	$0.898263\pi$
$702$	1.26608	−	2.19292i	0.0477851	−	0.0827663i
$703$	−12.4825	+	21.6204i	−0.470787	+	0.815428i
$704$	−3.46960	+	6.00953i	−0.130766	+	0.226493i
$705$	−2.65365			−0.0999421
$706$	7.01289	+	12.1467i	0.263933	+	0.457146i
$707$	5.22988	+	9.05842i	0.196690	+	0.340677i
$708$	−0.365698	+	0.633408i	−0.0137438	+	0.0238049i
$709$	−33.5629			−1.26048			−0.630240	−	0.776400i	$-0.717044\pi$
$709$	−33.5629			−1.26048			−0.630240	+	0.776400i	$0.717044\pi$
$710$	−13.4904	−	23.3660i	−0.506285	−	0.876912i
$711$	−25.2201			−0.945826
$712$	−1.19313			−0.0447146
$713$		0			0
$714$	2.05508			0.0769093
$715$	−16.3349			−0.610891
$716$	8.32898	+	14.4262i	0.311268	+	0.539133i
$717$	0.870434			0.0325070
$718$	2.33204	−	4.03922i	0.0870311	−	0.150742i
$719$	4.62689	+	8.01401i	0.172554	+	0.298872i	0.939312	−	0.343064i	$-0.111465\pi$
$719$	4.62689	+	8.01401i	0.172554	+	0.298872i	−0.766758	+	0.641936i	$0.778131\pi$
$720$	18.0454	+	31.2555i	0.672511	+	1.16482i
$721$	9.47784			0.352973
$722$	2.47133	−	4.28046i	0.0919732	−	0.159302i
$723$	0.765826	−	1.32645i	0.0284814	−	0.0493312i
$724$	−13.1061	+	22.7004i	−0.487083	+	0.843652i
$725$	1.95362	+	3.38378i	0.0725558	+	0.125670i
$726$	3.06934	−	5.31626i	0.113914	−	0.197305i
$727$	−22.8024	−	39.4949i	−0.845693	−	1.46478i	−0.885018	−	0.465557i	$-0.845854\pi$
$727$	−22.8024	−	39.4949i	−0.845693	−	1.46478i	0.0393244	−	0.999226i	$-0.487479\pi$
$728$	1.75570			0.0650707
$729$	−25.0506			−0.927800
$730$	−8.42280	−	14.5887i	−0.311742	−	0.539953i
$731$	−8.57831	+	14.8581i	−0.317280	+	0.549546i
$732$	1.08854	+	1.88540i	0.0402335	+	0.0696864i
$733$	−18.9850	+	32.8830i	−0.701227	+	1.21456i	0.266810	+	0.963749i	$0.414031\pi$
$733$	−18.9850	+	32.8830i	−0.701227	+	1.21456i	−0.968036	+	0.250811i	$0.919303\pi$
$734$	−31.7515	+	54.9952i	−1.17197	+	2.02991i
$735$	−1.38778	+	2.40371i	−0.0511891	+	0.0886621i
$736$	37.0717			1.36648
$737$	21.3840	+	37.0381i	0.787689	+	1.36432i
$738$	−28.2143	−	48.8686i	−1.03858	−	1.79888i
$739$	−13.1610	+	22.7955i	−0.484134	+	0.838545i	−0.999834	−	0.0182243i	$-0.994199\pi$
$739$	−13.1610	+	22.7955i	−0.484134	+	0.838545i	0.515700	+	0.856769i	$0.327532\pi$
$740$	16.4999			0.606548
$741$	−0.549158	−	0.951170i	−0.0201738	−	0.0349421i
$742$	−1.72346			−0.0632701
$743$	−53.3973			−1.95896			−0.979479	−	0.201545i	$-0.935404\pi$
$743$	−53.3973			−1.95896			−0.979479	+	0.201545i	$0.935404\pi$
$744$		0			0
$745$	−5.46780			−0.200325
$746$	−12.0505			−0.441201
$747$	−19.6087	−	33.9633i	−0.717446	−	1.24265i
$748$	−38.0681			−1.39191
$749$	0.155115	−	0.268667i	0.00566778	−	0.00981688i
$750$	1.66285	+	2.88015i	0.0607188	+	0.105168i
$751$	−4.44379	−	7.69688i	−0.162156	−	0.280863i	0.773485	−	0.633814i	$-0.218512\pi$
$751$	−4.44379	−	7.69688i	−0.162156	−	0.280863i	−0.935642	+	0.352951i	$0.885178\pi$
$752$	−27.8199			−1.01449
$753$	1.12707	−	1.95214i	0.0410727	−	0.0711401i
$754$	4.01107	−	6.94737i	0.146074	−	0.253008i
$755$	−5.85153	+	10.1352i	−0.212959	+	0.368856i
$756$	−0.748602	−	1.29662i	−0.0272264	−	0.0471575i
$757$	−19.5691	+	33.8948i	−0.711253	+	1.23193i	0.253135	+	0.967431i	$0.418538\pi$
$757$	−19.5691	+	33.8948i	−0.711253	+	1.23193i	−0.964387	+	0.264495i	$0.914795\pi$
$758$	15.8442	+	27.4429i	0.575486	+	0.996772i
$759$	−6.13595			−0.222721
$760$	15.5582			0.564355
$761$	−8.37682	−	14.5091i	−0.303659	−	0.525954i	0.673303	−	0.739367i	$-0.264875\pi$
$761$	−8.37682	−	14.5091i	−0.303659	−	0.525954i	−0.976962	+	0.213414i	$0.931542\pi$
$762$	3.49978	−	6.06180i	0.126784	−	0.219596i
$763$	1.14995	+	1.99178i	0.0416311	+	0.0721072i
$764$	−4.72728	+	8.18789i	−0.171027	+	0.296227i
$765$	−20.7357	+	35.9153i	−0.749701	+	1.29852i
$766$	29.3630	−	50.8581i	1.06093	−	1.83758i
$767$	−3.78071			−0.136514
$768$	−1.97850	−	3.42687i	−0.0713931	−	0.123656i
$769$	−8.61075	−	14.9142i	−0.310511	−	0.537822i	0.667962	−	0.744196i	$-0.267167\pi$
$769$	−8.61075	−	14.9142i	−0.310511	−	0.537822i	−0.978473	+	0.206374i	$0.933834\pi$
$770$	−12.5590	+	21.7528i	−0.452594	+	0.783915i
$771$	0.0202828			0.000730469
$772$	8.01403	+	13.8807i	0.288431	+	0.499577i
$773$	29.4949			1.06086			0.530430	−	0.847729i	$-0.322031\pi$
$773$	29.4949			1.06086			0.530430	+	0.847729i	$0.322031\pi$
$774$	16.1536			0.580628
$775$		0			0
$776$	11.6914			0.419697
$777$	1.07577			0.0385932
$778$	7.56028	+	13.0948i	0.271049	+	0.469471i
$779$	−49.2527			−1.76466
$780$	−0.362950	+	0.628647i	−0.0129957	+	0.0225092i
$781$	16.2929	+	28.2201i	0.583005	+	1.00979i
$782$	30.6016	+	53.0035i	1.09431	+	1.89540i
$783$	4.10888			0.146840
$784$	−14.5490	+	25.1996i	−0.519608	+	0.899987i
$785$	4.99240	−	8.64709i	0.178186	−	0.308628i
$786$	0.936240	−	1.62161i	0.0333946	−	0.0578411i
$787$	7.55251	+	13.0813i	0.269218	+	0.466299i	0.968660	−	0.248390i	$-0.0799015\pi$
$787$	7.55251	+	13.0813i	0.269218	+	0.466299i	−0.699442	+	0.714689i	$0.746568\pi$
$788$	11.0716	−	19.1765i	0.394408	−	0.683135i
$789$	−2.26879	−	3.92967i	−0.0807712	−	0.139900i
$790$	37.8358			1.34614
$791$	−11.1610			−0.396838
$792$	−10.7640	−	18.6437i	−0.382481	−	0.662477i
$793$	−5.62683	+	9.74595i	−0.199815	+	0.346089i
$794$	23.6597	+	40.9798i	0.839652	+	1.45432i
$795$	−0.213993	+	0.370647i	−0.00758956	+	0.0131455i
$796$	−0.146499	+	0.253744i	−0.00519253	+	0.00899372i
$797$	−20.6294	+	35.7312i	−0.730731	+	1.26566i	0.225839	+	0.974165i	$0.427488\pi$
$797$	−20.6294	+	35.7312i	−0.730731	+	1.26566i	−0.956571	+	0.291500i	$0.905846\pi$
$798$	−1.68886			−0.0597852
$799$	−15.9837	−	27.6846i	−0.565464	−	0.979412i
$800$	−3.35458	−	5.81031i	−0.118602	−	0.205426i
$801$	−1.30682	+	2.26348i	−0.0461742	+	0.0799760i
$802$	−4.84594			−0.171116
$803$	10.1726	+	17.6194i	0.358982	+	0.621774i
$804$	1.90055			0.0670271
$805$	15.5281			0.547294
$806$		0			0
$807$	0.492158			0.0173248
$808$	13.4492			0.473142
$809$	9.72461	+	16.8435i	0.341899	+	0.592187i	0.984785	−	0.173775i	$-0.0555966\pi$
$809$	9.72461	+	16.8435i	0.341899	+	0.592187i	−0.642886	+	0.765962i	$0.722263\pi$
$810$	38.5604			1.35487
$811$	−8.01689	+	13.8857i	−0.281511	+	0.487591i	−0.971757	−	0.235983i	$-0.924169\pi$
$811$	−8.01689	+	13.8857i	−0.281511	+	0.487591i	0.690246	+	0.723575i	$0.257502\pi$
$812$	−2.37164	−	4.10781i	−0.0832283	−	0.144156i
$813$	2.77668	+	4.80936i	0.0973825	+	0.168671i
$814$	−51.8242			−1.81644
$815$	−1.33713	+	2.31598i	−0.0468377	+	0.0811252i
$816$	2.67510	−	4.63340i	0.0936471	−	0.162202i
$817$	7.04967	−	12.2104i	0.246637	−	0.427187i
$818$	2.79005	+	4.83250i	0.0975517	+	0.168965i
$819$	1.92299	−	3.33072i	0.0671948	−	0.116385i
$820$	16.2760	+	28.1909i	0.568383	+	0.984469i
$821$	20.5256			0.716347			0.358174	−	0.933655i	$-0.383400\pi$
$821$	20.5256			0.716347			0.358174	+	0.933655i	$0.383400\pi$
$822$	−1.51119			−0.0527087
$823$	13.3261	+	23.0815i	0.464520	+	0.804572i	0.999180	−	0.0404953i	$-0.0128936\pi$
$823$	13.3261	+	23.0815i	0.464520	+	0.804572i	−0.534660	+	0.845067i	$0.679560\pi$
$824$	6.09333	−	10.5540i	0.212271	−	0.367664i
$825$	0.555237	+	0.961699i	0.0193309	+	0.0334821i
$826$	−2.90677	+	5.03467i	−0.101139	+	0.175179i
$827$	12.8049	−	22.1787i	0.445269	−	0.771228i	−0.552802	−	0.833312i	$-0.686442\pi$
$827$	12.8049	−	22.1787i	0.445269	−	0.771228i	0.998071	+	0.0620846i	$0.0197749\pi$
$828$	11.0791	−	19.1895i	0.385024	−	0.666881i
$829$	35.2641			1.22477			0.612387	−	0.790558i	$-0.290209\pi$
$829$	35.2641			1.22477			0.612387	+	0.790558i	$0.290209\pi$
$830$	29.4175	+	50.9527i	1.02110	+	1.76859i
$831$	−1.14882	−	1.98982i	−0.0398522	−	0.0690260i
$832$	−0.797003	+	1.38045i	−0.0276311	+	0.0478585i
$833$	−33.4362			−1.15850
$834$	−1.15756	−	2.00495i	−0.0400829	−	0.0694256i
$835$	27.5000			0.951677
$836$	31.2844			1.08199
$837$		0			0
$838$	−58.9095			−2.03499
$839$	21.3665			0.737652			0.368826	−	0.929498i	$-0.379760\pi$
$839$	21.3665			0.737652			0.368826	+	0.929498i	$0.379760\pi$
$840$	−0.335211	−	0.580602i	−0.0115659	−	0.0200327i
$841$	−15.9827			−0.551126
$842$	12.2889	−	21.2850i	0.423504	−	0.733530i
$843$	2.97314	+	5.14963i	0.102400	+	0.177363i
$844$	−10.2307	−	17.7201i	−0.352156	−	0.609952i
$845$	28.3104			0.973909
$846$	−15.0493	+	26.0661i	−0.517404	+	0.896170i
$847$	9.38113	−	16.2486i	0.322339	−	0.558308i
$848$	−2.24343	+	3.88573i	−0.0770397	+	0.133437i
$849$	−0.547887	−	0.948968i	−0.0188034	−	0.0325685i
$850$	5.53823	−	9.59249i	0.189960	−	0.329020i
$851$	16.0191	+	27.7458i	0.549126	+	0.951115i
$852$	1.44806			0.0496098
$853$	17.8835			0.612318			0.306159	−	0.951980i	$-0.400956\pi$
$853$	17.8835			0.612318			0.306159	+	0.951980i	$0.400956\pi$
$854$	8.65229	+	14.9862i	0.296075	+	0.512817i
$855$	17.0406	−	29.5152i	0.582777	−	1.00940i
$856$	−0.199448	−	0.345454i	−0.00681699	−	0.0118074i
$857$	10.2556	−	17.7633i	0.350326	−	0.606782i	−0.635981	−	0.771705i	$-0.719404\pi$
$857$	10.2556	−	17.7633i	0.350326	−	0.606782i	0.986306	+	0.164923i	$0.0527376\pi$
$858$	1.13998	−	1.97450i	0.0389183	−	0.0674085i
$859$	13.9501	−	24.1623i	0.475971	−	0.824406i	−0.523650	−	0.851934i	$-0.675430\pi$
$859$	13.9501	−	24.1623i	0.475971	−	0.824406i	0.999621	+	0.0275272i	$0.00876330\pi$
$860$	−9.31853			−0.317759
$861$	1.06118	+	1.83801i	0.0361648	+	0.0626393i
$862$	25.0807	+	43.4410i	0.854252	+	1.47961i
$863$	18.0809	−	31.3170i	0.615480	−	1.06604i	−0.374820	−	0.927097i	$-0.622296\pi$
$863$	18.0809	−	31.3170i	0.615480	−	1.06604i	0.990300	−	0.138945i	$-0.0443710\pi$
$864$	−7.05540			−0.240030
$865$	−9.41926	−	16.3146i	−0.320264	−	0.554714i
$866$	−3.83704			−0.130388
$867$	2.90140			0.0985366
$868$		0			0
$869$	−45.6958			−1.55012
$870$	−3.06328			−0.103855
$871$	4.91212	+	8.50804i	0.166441	+	0.288284i
$872$	2.95723			0.100145
$873$	12.8054	−	22.1796i	0.433397	−	0.750666i
$874$	−25.1484	−	43.5584i	−0.850658	−	1.47338i
$875$	5.08234	+	8.80288i	0.171815	+	0.297592i
$876$	0.904107			0.0305469
$877$	9.19873	−	15.9327i	0.310619	−	0.538008i	−0.667877	−	0.744271i	$-0.732797\pi$
$877$	9.19873	−	15.9327i	0.310619	−	0.538008i	0.978497	+	0.206263i	$0.0661303\pi$
$878$	8.47224	−	14.6744i	0.285924	−	0.495235i
$879$	−0.122126	+	0.211529i	−0.00411921	+	0.00713469i
$880$	32.6961	+	56.6312i	1.10218	+	1.90904i
$881$	−16.6459	+	28.8315i	−0.560814	+	0.971358i	0.436612	+	0.899650i	$0.356178\pi$
$881$	−16.6459	+	28.8315i	−0.560814	+	0.971358i	−0.997426	+	0.0717082i	$0.977155\pi$
$882$	15.7407	+	27.2637i	0.530016	+	0.918015i
$883$	5.25732			0.176923			0.0884615	−	0.996080i	$-0.471805\pi$
$883$	5.25732			0.176923			0.0884615	+	0.996080i	$0.471805\pi$
$884$	−8.74463			−0.294114
$885$	0.721838	+	1.25026i	0.0242643	+	0.0420271i
$886$	28.3088	−	49.0323i	0.951053	−	1.64727i
$887$	−18.1140	−	31.3743i	−0.608208	−	1.05345i	−0.991536	−	0.129835i	$-0.958555\pi$
$887$	−18.1140	−	31.3743i	−0.608208	−	1.05345i	0.383328	−	0.923612i	$-0.374778\pi$
$888$	0.691618	−	1.19792i	0.0232092	−	0.0401995i
$889$	10.6967	−	18.5273i	0.358757	−	0.621385i
$890$	1.96052	−	3.39573i	0.0657169	−	0.113825i
$891$	−46.5709			−1.56018
$892$	6.12103	+	10.6019i	0.204947	+	0.354979i
$893$	13.1355	+	22.7513i	0.439561	+	0.761343i
$894$	0.381587	−	0.660928i	0.0127622	−	0.0221047i
$895$	32.8805			1.09908
$896$	−5.29280	−	9.16740i	−0.176820	−	0.306261i
$897$	−1.40949			−0.0470615
$898$	43.4706			1.45063
$899$		0			0
$900$	−4.01014			−0.133671
$901$	−5.15579			−0.171764
$902$	−51.1210	−	88.5442i	−1.70214	−	2.94820i
$903$	−0.607557			−0.0202182
$904$	−7.17541	+	12.4282i	−0.238651	+	0.413355i
$905$	25.8696	+	44.8074i	0.859934	+	1.48945i
$906$	−0.816734	−	1.41462i	−0.0271342	−	0.0469978i
$907$	−17.4318			−0.578814			−0.289407	−	0.957206i	$-0.593458\pi$
$907$	−17.4318			−0.578814			−0.289407	+	0.957206i	$0.593458\pi$
$908$	0.901315	−	1.56112i	0.0299112	−	0.0518077i
$909$	14.7307	−	25.5143i	0.488587	−	0.846257i
$910$	−2.88492	+	4.99683i	−0.0956342	+	0.165643i
$911$	−9.19230	−	15.9215i	−0.304555	−	0.527504i	0.672607	−	0.739999i	$-0.265174\pi$
$911$	−9.19230	−	15.9215i	−0.304555	−	0.527504i	−0.977162	+	0.212495i	$0.931841\pi$
$912$	−2.19840	+	3.80774i	−0.0727963	+	0.126087i
$913$	−35.5287	−	61.5376i	−1.17583	−	2.03660i
$914$	−6.68081			−0.220982
$915$	4.29725			0.142063
$916$	17.4044	+	30.1453i	0.575057	+	0.996028i
$917$	2.86152	−	4.95630i	0.0944957	−	0.163671i
$918$	−5.82403	−	10.0875i	−0.192222	−	0.332938i
$919$	−19.4188	+	33.6344i	−0.640568	+	1.10950i	0.344738	+	0.938699i	$0.387968\pi$
$919$	−19.4188	+	33.6344i	−0.640568	+	1.10950i	−0.985306	+	0.170797i	$0.945366\pi$
$920$	9.98306	−	17.2912i	0.329132	−	0.570073i
$921$	1.49844	−	2.59538i	0.0493754	−	0.0855206i
$922$	−30.7755			−1.01354
$923$	3.74264	+	6.48244i	0.123190	+	0.213372i
$924$	−0.674042	−	1.16747i	−0.0221743	−	0.0384071i
$925$	2.89910	−	5.02139i	0.0953219	−	0.165102i
$926$	−8.85538			−0.291006
$927$	−13.3478	−	23.1191i	−0.438400	−	0.759332i
$928$	−22.3522			−0.733747
$929$	−45.3781			−1.48881			−0.744404	−	0.667729i	$-0.767266\pi$
$929$	−45.3781			−1.48881			−0.744404	+	0.667729i	$0.767266\pi$
$930$		0			0
$931$	27.4779			0.900552
$932$	−19.0906			−0.625334
$933$	−2.62165	−	4.54084i	−0.0858290	−	0.148660i
$934$	4.63363			0.151617
$935$	−37.5706	+	65.0743i	−1.22869	+	2.12816i
$936$	−2.47259	−	4.28266i	−0.0808192	−	0.139983i
$937$	13.0246	+	22.5593i	0.425496	+	0.736981i	0.996467	−	0.0839893i	$-0.0267662\pi$
$937$	13.0246	+	22.5593i	0.425496	+	0.736981i	−0.570970	+	0.820971i	$0.693433\pi$
$938$	15.1066			0.493247
$939$	−1.22297	+	2.11825i	−0.0399102	+	0.0691265i
$940$	8.68148	−	15.0368i	0.283159	−	0.490445i
$941$	−20.4539	+	35.4271i	−0.666777	+	1.15489i	0.312023	+	0.950074i	$0.398993\pi$
$941$	−20.4539	+	35.4271i	−0.666777	+	1.15489i	−0.978800	+	0.204817i	$0.934340\pi$
$942$	0.696819	+	1.20693i	0.0227036	+	0.0393238i
$943$	−31.6034	+	54.7387i	−1.02915	+	1.78254i
$944$	7.56750	+	13.1073i	0.246301	+	0.426606i
$945$	−2.95528			−0.0961351
$946$	29.2684			0.951597
$947$	19.5270	+	33.8218i	0.634544	+	1.09906i	0.986612	+	0.163087i	$0.0521452\pi$
$947$	19.5270	+	33.8218i	0.634544	+	1.09906i	−0.352068	+	0.935974i	$0.614521\pi$
$948$	−1.01533	+	1.75860i	−0.0329763	+	0.0571166i
$949$	2.33674	+	4.04735i	0.0758538	+	0.131383i
$950$	−4.55132	+	7.88312i	−0.147664	+	0.255762i
$951$	0.909277	−	1.57491i	0.0294853	−	0.0510701i
$952$	4.03816	−	6.99429i	0.130877	−	0.226686i
$953$	−7.91279			−0.256320			−0.128160	−	0.991753i	$-0.540907\pi$
$953$	−7.91279			−0.256320			−0.128160	+	0.991753i	$0.540907\pi$
$954$	2.42718	+	4.20400i	0.0785829	+	0.136110i
$955$	9.33101	+	16.1618i	0.301944	+	0.522983i
$956$	−2.84765	+	4.93228i	−0.0920996	+	0.159521i
$957$	3.69964			0.119592
$958$	1.85061	+	3.20536i	0.0597906	+	0.103560i
$959$	−4.61879			−0.149149
$960$	0.608676			0.0196449
$961$		0			0
$962$	−11.9045			−0.383818
$963$	−0.873807			−0.0281580
$964$	5.01085	+	8.67904i	0.161389	+	0.279533i
$965$	31.6372			1.01844
$966$	−1.08368	+	1.87698i	−0.0348667	+	0.0603909i
$967$	−5.71906	−	9.90569i	−0.183912	−	0.318546i	0.759297	−	0.650744i	$-0.225543\pi$
$967$	−5.71906	−	9.90569i	−0.183912	−	0.318546i	−0.943210	+	0.332198i	$0.892210\pi$
$968$	−12.0623	−	20.8925i	−0.387697	−	0.671512i
$969$	−5.05231			−0.162303
$970$	−19.2110	+	33.2744i	−0.616828	+	1.06838i
$971$	15.9682	−	27.6577i	0.512443	−	0.887577i	−0.487453	−	0.873149i	$-0.662074\pi$
$971$	15.9682	−	27.6577i	0.512443	−	0.887577i	0.999896	−	0.0144275i	$-0.00459259\pi$
$972$	−3.16926	+	5.48932i	−0.101654	+	0.176070i
$973$	−3.53795	−	6.12791i	−0.113422	−	0.196452i
$974$	−15.9636	+	27.6498i	−0.511507	+	0.885955i
$975$	0.127544	+	0.220912i	0.00408467	+	0.00707485i
$976$	45.0508			1.44204
$977$	−11.7696			−0.376541			−0.188271	−	0.982117i	$-0.560288\pi$
$977$	−11.7696			−0.376541			−0.188271	+	0.982117i	$0.560288\pi$
$978$	−0.186631	−	0.323255i	−0.00596782	−	0.0103366i
$979$	−2.36780	+	4.10116i	−0.0756753	+	0.131073i
$980$	−9.08034	−	15.7276i	−0.290061	−	0.502400i
$981$	3.23901	−	5.61012i	0.103414	−	0.179118i
$982$	20.2544	−	35.0817i	0.646344	−	1.11950i
$983$	26.6822	−	46.2149i	0.851030	−	1.47403i	−0.0292507	−	0.999572i	$-0.509312\pi$
$983$	26.6822	−	46.2149i	0.851030	−	1.47403i	0.880280	−	0.474454i	$-0.157355\pi$
$984$	2.72894			0.0869953
$985$	−21.8538	−	37.8518i	−0.696319	−	1.20606i
$986$	−18.4511	−	31.9582i	−0.587602	−	1.01776i
$987$	0.566023	−	0.980380i	0.0180167	−	0.0312058i
$988$	7.18635			0.228628
$989$	−9.04697	−	15.6698i	−0.287677	−	0.498271i
$990$	70.7482			2.24853
$991$	−11.6584			−0.370343			−0.185171	−	0.982706i	$-0.559284\pi$
$991$	−11.6584			−0.370343			−0.185171	+	0.982706i	$0.559284\pi$
$992$		0			0
$993$	4.12168			0.130798
$994$	11.5100			0.365075
$995$	0.289170	+	0.500857i	0.00916729	+	0.0158782i
$996$	−3.15769			−0.100055
$997$	−13.0744	+	22.6455i	−0.414071	+	0.717191i	−0.995330	−	0.0965266i	$-0.969227\pi$
$997$	−13.0744	+	22.6455i	−0.414071	+	0.717191i	0.581260	+	0.813718i	$0.302560\pi$
$998$	−18.0267	−	31.2231i	−0.570624	−	0.988350i
$999$	−3.04871	−	5.28052i	−0.0964570	−	0.167068i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.c.k.521.3		24
31.2	even	5		961.2.g.v.844.3		96
31.3	odd	30		961.2.d.r.628.3		48
31.4	even	5		961.2.g.v.338.9		96
31.5	even	3	inner	961.2.c.k.439.3		24
31.6	odd	6		961.2.a.k.1.3	✓	12
31.7	even	15		961.2.d.r.388.9		48
31.8	even	5		961.2.g.v.732.10		96
31.9	even	15		961.2.g.v.816.9		96
31.10	even	15		961.2.g.v.547.4		96
31.11	odd	30		961.2.g.v.235.9		96
31.12	odd	30		961.2.d.r.531.3		48
31.13	odd	30		961.2.g.v.846.4		96
31.14	even	15		961.2.d.r.374.9		48
31.15	odd	10		961.2.g.v.448.3		96
31.16	even	5		961.2.g.v.448.4		96
31.17	odd	30		961.2.d.r.374.10		48
31.18	even	15		961.2.g.v.846.3		96
31.19	even	15		961.2.d.r.531.4		48
31.20	even	15		961.2.g.v.235.10		96
31.21	odd	30		961.2.g.v.547.3		96
31.22	odd	30		961.2.g.v.816.10		96
31.23	odd	10		961.2.g.v.732.9		96
31.24	odd	30		961.2.d.r.388.10		48
31.25	even	3		961.2.a.k.1.4	yes	12
31.26	odd	6	inner	961.2.c.k.439.4		24
31.27	odd	10		961.2.g.v.338.10		96
31.28	even	15		961.2.d.r.628.4		48
31.29	odd	10		961.2.g.v.844.4		96
31.30	odd	2	inner	961.2.c.k.521.4		24
93.56	odd	6		8649.2.a.bp.1.10		12
93.68	even	6		8649.2.a.bp.1.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.k.1.3	✓	12	31.6	odd	6
961.2.a.k.1.4	yes	12	31.25	even	3
961.2.c.k.439.3		24	31.5	even	3	inner
961.2.c.k.439.4		24	31.26	odd	6	inner
961.2.c.k.521.3		24	1.1	even	1	trivial
961.2.c.k.521.4		24	31.30	odd	2	inner
961.2.d.r.374.9		48	31.14	even	15
961.2.d.r.374.10		48	31.17	odd	30
961.2.d.r.388.9		48	31.7	even	15
961.2.d.r.388.10		48	31.24	odd	30
961.2.d.r.531.3		48	31.12	odd	30
961.2.d.r.531.4		48	31.19	even	15
961.2.d.r.628.3		48	31.3	odd	30
961.2.d.r.628.4		48	31.28	even	15
961.2.g.v.235.9		96	31.11	odd	30
961.2.g.v.235.10		96	31.20	even	15
961.2.g.v.338.9		96	31.4	even	5
961.2.g.v.338.10		96	31.27	odd	10
961.2.g.v.448.3		96	31.15	odd	10
961.2.g.v.448.4		96	31.16	even	5
961.2.g.v.547.3		96	31.21	odd	30
961.2.g.v.547.4		96	31.10	even	15
961.2.g.v.732.9		96	31.23	odd	10
961.2.g.v.732.10		96	31.8	even	5
961.2.g.v.816.9		96	31.9	even	15
961.2.g.v.816.10		96	31.22	odd	30
961.2.g.v.844.3		96	31.2	even	5
961.2.g.v.844.4		96	31.29	odd	10
961.2.g.v.846.3		96	31.18	even	15
961.2.g.v.846.4		96	31.13	odd	30
8649.2.a.bp.1.9		12	93.68	even	6
8649.2.a.bp.1.10		12	93.56	odd	6

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.80264 q^{2} +(-0.0954837 - 0.165383i) q^{3} +1.24951 q^{4} +(1.23318 - 2.13593i) q^{5} +(0.172123 + 0.298125i) q^{6} +(0.526075 + 0.911189i) q^{7} +1.35286 q^{8} +(1.48177 - 2.56649i) q^{9} +(-2.22298 + 3.85032i) q^{10} +(2.68479 - 4.65018i) q^{11} +(-0.119308 - 0.206647i) q^{12} +(0.616723 - 1.06819i) q^{13} +(-0.948325 - 1.64255i) q^{14} -0.470995 q^{15} -4.93774 q^{16} +(-2.83695 - 4.91374i) q^{17} +(-2.67109 + 4.62646i) q^{18} +(2.33141 + 4.03812i) q^{19} +(1.54087 - 2.66887i) q^{20} +(0.100463 - 0.174007i) q^{21} +(-4.83970 + 8.38261i) q^{22} +5.98388 q^{23} +(-0.129176 - 0.223740i) q^{24} +(-0.541477 - 0.937865i) q^{25} +(-1.11173 + 1.92557i) q^{26} -1.13884 q^{27} +(0.657337 + 1.13854i) q^{28} -3.60796 q^{29} +0.849035 q^{30} +6.19525 q^{32} -1.02541 q^{33} +(5.11400 + 8.85771i) q^{34} +2.59499 q^{35} +(1.85148 - 3.20686i) q^{36} +(2.67703 + 4.63676i) q^{37} +(-4.20269 - 7.27928i) q^{38} -0.235548 q^{39} +(1.66832 - 2.88962i) q^{40} +(-5.28142 + 9.14769i) q^{41} +(-0.181099 + 0.313673i) q^{42} +(-1.51189 - 2.61867i) q^{43} +(3.35467 - 5.81046i) q^{44} +(-3.65457 - 6.32991i) q^{45} -10.7868 q^{46} +5.63413 q^{47} +(0.471474 + 0.816617i) q^{48} +(2.94649 - 5.10347i) q^{49} +(0.976088 + 1.69063i) q^{50} +(-0.541765 + 0.938365i) q^{51} +(0.770601 - 1.33472i) q^{52} +(0.454343 - 0.786945i) q^{53} +2.05292 q^{54} +(-6.62166 - 11.4691i) q^{55} +(0.711707 + 1.23271i) q^{56} +(0.445223 - 0.771149i) q^{57} +6.50384 q^{58} +(-1.53258 - 2.65451i) q^{59} -0.588514 q^{60} -9.12376 q^{61} +3.11808 q^{63} -1.29232 q^{64} +(-1.52106 - 2.63456i) q^{65} +1.84845 q^{66} +(-3.98244 + 6.89779i) q^{67} +(-3.54480 - 6.13978i) q^{68} +(-0.571363 - 0.989630i) q^{69} -4.67783 q^{70} +(-3.03430 + 5.25556i) q^{71} +(2.00462 - 3.47211i) q^{72} +(-1.89448 + 3.28134i) q^{73} +(-4.82573 - 8.35841i) q^{74} +(-0.103404 + 0.179102i) q^{75} +(2.91312 + 5.04568i) q^{76} +5.64960 q^{77} +0.424608 q^{78} +(-4.25507 - 7.37000i) q^{79} +(-6.08914 + 10.5467i) q^{80} +(-4.33656 - 7.51114i) q^{81} +(9.52050 - 16.4900i) q^{82} +(6.61668 - 11.4604i) q^{83} +(0.125530 - 0.217424i) q^{84} -13.9939 q^{85} +(2.72539 + 4.72052i) q^{86} +(0.344501 + 0.596693i) q^{87} +(3.63214 - 6.29106i) q^{88} -0.881934 q^{89} +(6.58788 + 11.4105i) q^{90} +1.29777 q^{91} +7.47693 q^{92} -10.1563 q^{94} +11.5002 q^{95} +(-0.591545 - 1.02459i) q^{96} +8.64199 q^{97} +(-5.31146 + 9.19972i) q^{98} +(-7.95645 - 13.7810i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 32 q^{4} - 8 q^{5} - 8 q^{7} + 24 q^{8} - 20 q^{9} - 20 q^{10} - 28 q^{14} - 32 q^{16} + 8 q^{18} - 16 q^{19} + 20 q^{20} - 12 q^{25} + 20 q^{28} + 48 q^{32} - 80 q^{33} + 112 q^{35} - 40 q^{36}+ \cdots - 4 q^{98}+O(q^{100}) \) 24 * q + 32 * q^4 - 8 * q^5 - 8 * q^7 + 24 * q^8 - 20 * q^9 - 20 * q^10 - 28 * q^14 - 32 * q^16 + 8 * q^18 - 16 * q^19 + 20 * q^20 - 12 * q^25 + 20 * q^28 + 48 * q^32 - 80 * q^33 + 112 * q^35 - 40 * q^36 - 36 * q^38 - 32 * q^39 + 16 * q^40 - 32 * q^41 - 16 * q^45 + 96 * q^47 + 20 * q^49 - 20 * q^50 - 16 * q^51 + 8 * q^56 - 40 * q^59 - 16 * q^63 - 56 * q^64 + 48 * q^66 - 16 * q^67 - 24 * q^69 + 24 * q^70 - 72 * q^71 - 36 * q^72 - 36 * q^76 - 208 * q^78 + 20 * q^80 + 36 * q^81 + 4 * q^82 - 64 * q^87 + 44 * q^90 + 32 * q^94 + 80 * q^95 - 16 * q^97 - 4 * q^98

Introduction

L-functions

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