LMFDB - Embedded newform 630.2.bw.a.493.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(103,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9, 10]))

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

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

chi := DirichletCharacter("630.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bw (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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			493.17
Character	$\chi$	$=$	630.493
Dual form			630.2.bw.a.607.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.908144 + 1.47488i) q^{3} -1.00000i q^{4} +(-0.622124 - 2.14778i) q^{5} +(-1.68505 - 0.400744i) q^{6} +(2.39737 + 1.11920i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.35055 + 2.67881i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.908144 + 1.47488i) q^{3} -1.00000i q^{4} +(-0.622124 - 2.14778i) q^{5} +(-1.68505 - 0.400744i) q^{6} +(2.39737 + 1.11920i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.35055 + 2.67881i) q^{9} +(1.95862 + 1.07880i) q^{10} +(-1.41494 - 2.45075i) q^{11} +(1.47488 - 0.908144i) q^{12} +(3.83238 + 1.02688i) q^{13} +(-2.48659 + 0.903808i) q^{14} +(2.60274 - 2.86805i) q^{15} -1.00000 q^{16} +(-1.00900 + 0.270360i) q^{17} +(-0.939221 - 2.84919i) q^{18} +(1.63918 + 2.83913i) q^{19} +(-2.14778 + 0.622124i) q^{20} +(0.526479 + 4.55223i) q^{21} +(2.73345 + 0.732426i) q^{22} +(8.78787 - 2.35470i) q^{23} +(-0.400744 + 1.68505i) q^{24} +(-4.22592 + 2.67237i) q^{25} +(-3.43602 + 1.98379i) q^{26} +(-5.17742 + 0.440843i) q^{27} +(1.11920 - 2.39737i) q^{28} +(6.84521 + 3.95209i) q^{29} +(0.187601 + 3.86844i) q^{30} +1.07501i q^{31} +(0.707107 - 0.707107i) q^{32} +(2.32959 - 4.31250i) q^{33} +(0.522296 - 0.904644i) q^{34} +(0.912324 - 5.84531i) q^{35} +(2.67881 + 1.35055i) q^{36} +(4.85581 + 1.30111i) q^{37} +(-3.16664 - 0.848500i) q^{38} +(1.96582 + 6.58487i) q^{39} +(1.07880 - 1.95862i) q^{40} +(5.73201 - 3.30938i) q^{41} +(-3.59119 - 2.84664i) q^{42} +(-5.98661 + 1.60411i) q^{43} +(-2.45075 + 1.41494i) q^{44} +(6.59370 + 1.23413i) q^{45} +(-4.54894 + 7.87899i) q^{46} +(1.30987 + 1.30987i) q^{47} +(-0.908144 - 1.47488i) q^{48} +(4.49480 + 5.36626i) q^{49} +(1.09853 - 4.87783i) q^{50} +(-1.31507 - 1.24263i) q^{51} +(1.02688 - 3.83238i) q^{52} +(-11.9066 + 3.19037i) q^{53} +(3.34926 - 3.97271i) q^{54} +(-4.38340 + 4.56365i) q^{55} +(0.903808 + 2.48659i) q^{56} +(-2.69878 + 4.99593i) q^{57} +(-7.63484 + 2.04575i) q^{58} -11.3003 q^{59} +(-2.86805 - 2.60274i) q^{60} -4.39972i q^{61} +(-0.760149 - 0.760149i) q^{62} +(-6.23588 + 4.91058i) q^{63} +1.00000i q^{64} +(-0.178694 - 8.86997i) q^{65} +(1.40213 + 4.69667i) q^{66} +(5.19227 - 5.19227i) q^{67} +(0.270360 + 1.00900i) q^{68} +(11.4536 + 10.8227i) q^{69} +(3.48815 + 4.77837i) q^{70} -10.6201 q^{71} +(-2.84919 + 0.939221i) q^{72} +(0.670554 + 2.50254i) q^{73} +(-4.35360 + 2.51355i) q^{74} +(-7.77918 - 3.80584i) q^{75} +(2.83913 - 1.63918i) q^{76} +(-0.649273 - 7.45895i) q^{77} +(-6.04625 - 3.26616i) q^{78} +1.96770i q^{79} +(0.622124 + 2.14778i) q^{80} +(-5.35203 - 7.23573i) q^{81} +(-1.71306 + 6.39323i) q^{82} +(-1.44279 - 5.38455i) q^{83} +(4.55223 - 0.526479i) q^{84} +(1.20840 + 1.99891i) q^{85} +(3.09890 - 5.36745i) q^{86} +(0.387581 + 13.6849i) q^{87} +(0.732426 - 2.73345i) q^{88} +(6.47588 + 11.2166i) q^{89} +(-5.53512 + 3.78979i) q^{90} +(8.03837 + 6.75101i) q^{91} +(-2.35470 - 8.78787i) q^{92} +(-1.58552 + 0.976266i) q^{93} -1.85243 q^{94} +(5.07807 - 5.28688i) q^{95} +(1.68505 + 0.400744i) q^{96} +(5.08796 - 1.36332i) q^{97} +(-6.97282 - 0.616214i) q^{98} +(8.47603 - 0.480497i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q+O(q^{10}) $ 192 * q	$ 192 q + 8 q^{11} - 12 q^{15} - 192 q^{16} + 36 q^{17} - 8 q^{18} + 8 q^{23} + 36 q^{27} + 12 q^{30} + 48 q^{35} - 16 q^{36} - 12 q^{41} + 4 q^{42} + 48 q^{45} + 12 q^{46} - 16 q^{50} - 24 q^{51} - 40 q^{53} - 4 q^{56} - 32 q^{57} - 12 q^{58} - 16 q^{60} - 12 q^{63} + 16 q^{65} - 36 q^{68} + 16 q^{71} - 8 q^{72} + 96 q^{75} - 64 q^{77} - 16 q^{78} + 16 q^{81} + 168 q^{83} + 8 q^{86} - 36 q^{87} - 36 q^{90} + 8 q^{92} - 48 q^{93} - 128 q^{95} - 48 q^{98}+O(q^{100}) $ 192 * q + 8 * q^11 - 12 * q^15 - 192 * q^16 + 36 * q^17 - 8 * q^18 + 8 * q^23 + 36 * q^27 + 12 * q^30 + 48 * q^35 - 16 * q^36 - 12 * q^41 + 4 * q^42 + 48 * q^45 + 12 * q^46 - 16 * q^50 - 24 * q^51 - 40 * q^53 - 4 * q^56 - 32 * q^57 - 12 * q^58 - 16 * q^60 - 12 * q^63 + 16 * q^65 - 36 * q^68 + 16 * q^71 - 8 * q^72 + 96 * q^75 - 64 * q^77 - 16 * q^78 + 16 * q^81 + 168 * q^83 + 8 * q^86 - 36 * q^87 - 36 * q^90 + 8 * q^92 - 48 * q^93 - 128 * q^95 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.908144	+	1.47488i	0.524317	+	0.851523i
$3$	0.908144	+	1.47488i	0.524317	+	0.851523i
$4$		−	1.00000i		−	0.500000i
$5$	−0.622124	−	2.14778i	−0.278222	−	0.960517i
$5$	−0.622124	−	2.14778i	−0.278222	−	0.960517i
$6$	−1.68505	−	0.400744i	−0.687920	−	0.163603i
$7$	2.39737	+	1.11920i	0.906122	+	0.423016i
$7$	2.39737	+	1.11920i	0.906122	+	0.423016i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−1.35055	+	2.67881i	−0.450183	+	0.892936i
$10$	1.95862	+	1.07880i	0.619369	+	0.341147i
$11$	−1.41494	−	2.45075i	−0.426620	−	0.738928i	0.569950	−	0.821679i	$-0.306963\pi$
$11$	−1.41494	−	2.45075i	−0.426620	−	0.738928i	−0.996570	+	0.0827515i	$0.973629\pi$
$12$	1.47488	−	0.908144i	0.425762	−	0.262159i
$13$	3.83238	+	1.02688i	1.06291	+	0.284806i	0.747578	−	0.664174i	$-0.231217\pi$
$13$	3.83238	+	1.02688i	1.06291	+	0.284806i	0.315334	+	0.948981i	$0.397883\pi$
$14$	−2.48659	+	0.903808i	−0.664569	+	0.241553i
$15$	2.60274	−	2.86805i	0.672026	−	0.740528i
$16$	−1.00000			−0.250000
$17$	−1.00900	+	0.270360i	−0.244718	+	0.0655720i	−0.379093	−	0.925359i	$-0.623764\pi$
$17$	−1.00900	+	0.270360i	−0.244718	+	0.0655720i	0.134375	+	0.990931i	$0.457097\pi$
$18$	−0.939221	−	2.84919i	−0.221377	−	0.671560i
$19$	1.63918	+	2.83913i	0.376053	+	0.651342i	0.990484	−	0.137628i	$-0.0439479\pi$
$19$	1.63918	+	2.83913i	0.376053	+	0.651342i	−0.614431	+	0.788970i	$0.710615\pi$
$20$	−2.14778	+	0.622124i	−0.480258	+	0.139111i
$21$	0.526479	+	4.55223i	0.114887	+	0.993379i
$22$	2.73345	+	0.732426i	0.582774	+	0.156154i
$23$	8.78787	−	2.35470i	1.83240	−	0.490990i	0.834226	−	0.551423i	$-0.185915\pi$
$23$	8.78787	−	2.35470i	1.83240	−	0.490990i	0.998172	+	0.0604338i	$0.0192484\pi$
$24$	−0.400744	+	1.68505i	−0.0818015	+	0.343960i
$25$	−4.22592	+	2.67237i	−0.845185	+	0.534474i
$26$	−3.43602	+	1.98379i	−0.673859	+	0.389053i
$27$	−5.17742	+	0.440843i	−0.996395	+	0.0848403i
$28$	1.11920	−	2.39737i	0.211508	−	0.453061i
$29$	6.84521	+	3.95209i	1.27112	+	0.733884i	0.975200	−	0.221328i	$-0.0710390\pi$
$29$	6.84521	+	3.95209i	1.27112	+	0.733884i	0.295924	+	0.955211i	$0.404372\pi$
$30$	0.187601	+	3.86844i	0.0342511	+	0.706277i
$31$			1.07501i			0.193078i	0.995329	+	0.0965390i	$0.0307773\pi$
$31$			1.07501i			0.193078i	−0.995329	+	0.0965390i	$0.969223\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	2.32959	−	4.31250i	0.405530	−	0.750709i
$34$	0.522296	−	0.904644i	0.0895731	−	0.155145i
$35$	0.912324	−	5.84531i	0.154211	−	0.988038i
$36$	2.67881	+	1.35055i	0.446468	+	0.225092i
$37$	4.85581	+	1.30111i	0.798290	+	0.213901i	0.634833	−	0.772649i	$-0.281069\pi$
$37$	4.85581	+	1.30111i	0.798290	+	0.213901i	0.163457	+	0.986550i	$0.447736\pi$
$38$	−3.16664	−	0.848500i	−0.513697	−	0.137645i
$39$	1.96582	+	6.58487i	0.314784	+	1.05442i
$40$	1.07880	−	1.95862i	0.170574	−	0.309685i
$41$	5.73201	−	3.30938i	0.895189	−	0.516838i	0.0195531	−	0.999809i	$-0.493776\pi$
$41$	5.73201	−	3.30938i	0.895189	−	0.516838i	0.875636	+	0.482971i	$0.160442\pi$
$42$	−3.59119	−	2.84664i	−0.554133	−	0.439246i
$43$	−5.98661	+	1.60411i	−0.912949	+	0.244624i	−0.684569	−	0.728948i	$-0.740010\pi$
$43$	−5.98661	+	1.60411i	−0.912949	+	0.244624i	−0.228380	+	0.973572i	$0.573343\pi$
$44$	−2.45075	+	1.41494i	−0.369464	+	0.213310i
$45$	6.59370	+	1.23413i	0.982931	+	0.183974i
$46$	−4.54894	+	7.87899i	−0.670704	+	1.16169i
$47$	1.30987	+	1.30987i	0.191064	+	0.191064i	0.796156	−	0.605092i	$-0.206864\pi$
$47$	1.30987	+	1.30987i	0.191064	+	0.191064i	−0.605092	+	0.796156i	$0.706864\pi$
$48$	−0.908144	−	1.47488i	−0.131079	−	0.212881i
$49$	4.49480	+	5.36626i	0.642115	+	0.766609i
$50$	1.09853	−	4.87783i	0.155355	−	0.689829i
$51$	−1.31507	−	1.24263i	−0.184146	−	0.174003i
$52$	1.02688	−	3.83238i	0.142403	−	0.531456i
$53$	−11.9066	+	3.19037i	−1.63550	+	0.438231i	−0.955502	−	0.294985i	$-0.904685\pi$
$53$	−11.9066	+	3.19037i	−1.63550	+	0.438231i	−0.679997	+	0.733215i	$0.738019\pi$
$54$	3.34926	−	3.97271i	0.455777	−	0.540617i
$55$	−4.38340	+	4.56365i	−0.591057	+	0.615362i
$56$	0.903808	+	2.48659i	0.120776	+	0.332285i
$57$	−2.69878	+	4.99593i	−0.357462	+	0.661727i
$58$	−7.63484	+	2.04575i	−1.00250	+	0.268620i
$59$	−11.3003			−1.47118			−0.735590	−	0.677427i	$-0.763095\pi$
$59$	−11.3003			−1.47118			−0.735590	+	0.677427i	$0.763095\pi$
$60$	−2.86805	−	2.60274i	−0.370264	−	0.336013i
$61$		−	4.39972i		−	0.563326i	−0.959513	−	0.281663i	$-0.909114\pi$
$61$		−	4.39972i		−	0.563326i	0.959513	−	0.281663i	$-0.0908860\pi$
$62$	−0.760149	−	0.760149i	−0.0965390	−	0.0965390i
$63$	−6.23588	+	4.91058i	−0.785647	+	0.618674i
$64$			1.00000i			0.125000i
$65$	−0.178694	−	8.86997i	−0.0221643	−	1.10018i
$66$	1.40213	+	4.69667i	0.172590	+	0.578120i
$67$	5.19227	−	5.19227i	0.634336	−	0.634336i	−0.314816	−	0.949153i	$-0.601943\pi$
$67$	5.19227	−	5.19227i	0.634336	−	0.634336i	0.949153	+	0.314816i	$0.101943\pi$
$68$	0.270360	+	1.00900i	0.0327860	+	0.122359i
$69$	11.4536	+	10.8227i	1.37885	+	1.30289i
$70$	3.48815	+	4.77837i	0.416914	+	0.571124i
$71$	−10.6201			−1.26038			−0.630188	−	0.776443i	$-0.717022\pi$
$71$	−10.6201			−1.26038			−0.630188	+	0.776443i	$0.717022\pi$
$72$	−2.84919	+	0.939221i	−0.335780	+	0.110688i
$73$	0.670554	+	2.50254i	0.0784824	+	0.292900i	0.994000	−	0.109377i	$-0.0348855\pi$
$73$	0.670554	+	2.50254i	0.0784824	+	0.292900i	−0.915518	+	0.402277i	$0.868219\pi$
$74$	−4.35360	+	2.51355i	−0.506096	+	0.292194i
$75$	−7.77918	−	3.80584i	−0.898262	−	0.439461i
$76$	2.83913	−	1.63918i	0.325671	−	0.188026i
$77$	−0.649273	−	7.45895i	−0.0739915	−	0.850026i
$78$	−6.04625	−	3.26616i	−0.684604	−	0.369820i
$79$			1.96770i			0.221383i	0.993855	+	0.110692i	$0.0353066\pi$
$79$			1.96770i			0.221383i	−0.993855	+	0.110692i	$0.964693\pi$
$80$	0.622124	+	2.14778i	0.0695555	+	0.240129i
$81$	−5.35203	−	7.23573i	−0.594670	−	0.803970i
$82$	−1.71306	+	6.39323i	−0.189176	+	0.706014i
$83$	−1.44279	−	5.38455i	−0.158366	−	0.591032i	−0.998794	−	0.0491070i	$-0.984362\pi$
$83$	−1.44279	−	5.38455i	−0.158366	−	0.591032i	0.840427	−	0.541925i	$-0.182304\pi$
$84$	4.55223	−	0.526479i	0.496689	−	0.0574436i
$85$	1.20840	+	1.99891i	0.131069	+	0.216812i
$86$	3.09890	−	5.36745i	0.334163	−	0.578786i
$87$	0.387581	+	13.6849i	0.0415530	+	1.46718i
$88$	0.732426	−	2.73345i	0.0780769	−	0.291387i
$89$	6.47588	+	11.2166i	0.686442	+	1.18895i	0.972981	+	0.230884i	$0.0741617\pi$
$89$	6.47588	+	11.2166i	0.686442	+	1.18895i	−0.286540	+	0.958068i	$0.592505\pi$
$90$	−5.53512	+	3.78979i	−0.583453	+	0.399479i
$91$	8.03837	+	6.75101i	0.842651	+	0.707699i
$92$	−2.35470	−	8.78787i	−0.245495	−	0.916199i
$93$	−1.58552	+	0.976266i	−0.164410	+	0.101234i
$94$	−1.85243			−0.191064
$95$	5.07807	−	5.28688i	0.520999	−	0.542423i
$96$	1.68505	+	0.400744i	0.171980	+	0.0409008i
$97$	5.08796	−	1.36332i	0.516604	−	0.138424i	0.00890895	−	0.999960i	$-0.497164\pi$
$97$	5.08796	−	1.36332i	0.516604	−	0.138424i	0.507696	+	0.861537i	$0.330497\pi$
$98$	−6.97282	−	0.616214i	−0.704362	−	0.0622470i
$99$	8.47603	−	0.480497i	0.851873	−	0.0482917i
$100$	2.67237	+	4.22592i	0.267237	+	0.422592i
$101$	5.20624	−	3.00582i	0.518040	−	0.299091i	−0.218092	−	0.975928i	$-0.569983\pi$
$101$	5.20624	−	3.00582i	0.518040	−	0.299091i	0.736133	+	0.676837i	$0.236650\pi$
$102$	1.80856	−	0.0512216i	0.179074	−	0.00507169i
$103$	−3.67051	−	13.6985i	−0.361666	−	1.34975i	−0.871885	−	0.489710i	$-0.837102\pi$
$103$	−3.67051	−	13.6985i	−0.361666	−	1.34975i	0.510219	−	0.860044i	$-0.329564\pi$
$104$	1.98379	+	3.43602i	0.194526	+	0.336930i
$105$	9.44966	−	3.96281i	0.922193	−	0.386731i
$106$	6.16331	−	10.6752i	0.598634	−	1.03686i
$107$	−7.73812	−	2.07342i	−0.748073	−	0.200445i	−0.135410	−	0.990790i	$-0.543235\pi$
$107$	−7.73812	−	2.07342i	−0.748073	−	0.200445i	−0.612663	+	0.790344i	$0.709902\pi$
$108$	0.440843	+	5.17742i	0.0424202	+	0.498197i
$109$	−2.29550	−	1.32531i	−0.219869	−	0.126942i	0.386020	−	0.922490i	$-0.373849\pi$
$109$	−2.29550	−	1.32531i	−0.219869	−	0.126942i	−0.605890	+	0.795549i	$0.707183\pi$
$110$	−0.127454	−	6.32652i	−0.0121522	−	0.603210i
$111$	2.49079	+	8.34334i	0.236415	+	0.791915i
$112$	−2.39737	−	1.11920i	−0.226531	−	0.105754i
$113$	3.08075	−	11.4975i	0.289813	−	1.08160i	−0.655438	−	0.755249i	$-0.727516\pi$
$113$	3.08075	−	11.4975i	0.289813	−	1.08160i	0.945250	−	0.326346i	$-0.105817\pi$
$114$	−1.62433	−	5.44098i	−0.152133	−	0.509595i
$115$	−10.5245	−	17.4095i	−0.981417	−	1.62344i
$116$	3.95209	−	6.84521i	0.366942	−	0.635562i
$117$	−7.92665	+	8.87937i	−0.732819	+	0.820898i
$118$	7.99055	−	7.99055i	0.735590	−	0.735590i
$119$	−2.72153	−	0.481112i	−0.249483	−	0.0441035i
$120$	3.86844	−	0.187601i	0.353138	−	0.0171256i
$121$	1.49590	−	2.59097i	0.135990	−	0.235542i
$122$	3.11107	+	3.11107i	0.281663	+	0.281663i
$123$	10.0864	+	5.44864i	0.909463	+	0.491288i
$124$	1.07501			0.0965390
$125$	8.36871	+	7.41382i	0.748520	+	0.663112i
$126$	0.937133	−	7.88174i	0.0834865	−	0.702161i
$127$	6.45881	−	6.45881i	0.573126	−	0.573126i	−0.359874	−	0.933001i	$-0.617180\pi$
$127$	6.45881	−	6.45881i	0.573126	−	0.573126i	0.933001	+	0.359874i	$0.117180\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−7.80257	−	7.37278i	−0.686978	−	0.649137i
$130$	6.39837	+	6.14566i	0.561174	+	0.539010i
$131$	8.79114	+	5.07556i	0.768085	+	0.443454i	0.832191	−	0.554489i	$-0.187086\pi$
$131$	8.79114	+	5.07556i	0.768085	+	0.443454i	−0.0641060	+	0.997943i	$0.520420\pi$
$132$	−4.31250	−	2.32959i	−0.375355	−	0.202765i
$133$	0.752168	+	8.64103i	0.0652213	+	0.749272i
$134$			7.34297i			0.634336i
$135$	4.16783	+	10.8457i	0.358710	+	0.933449i
$136$	−0.904644	−	0.522296i	−0.0775726	−	0.0447865i
$137$	−0.823469	−	0.220648i	−0.0703537	−	0.0188512i	0.223470	−	0.974711i	$-0.428261\pi$
$137$	−0.823469	−	0.220648i	−0.0703537	−	0.0188512i	−0.293824	+	0.955859i	$0.594928\pi$
$138$	−15.7517	+	0.446114i	−1.34087	+	0.0379758i
$139$	7.95504	+	13.7785i	0.674738	+	1.16868i	0.976545	+	0.215311i	$0.0690766\pi$
$139$	7.95504	+	13.7785i	0.674738	+	1.16868i	−0.301808	+	0.953369i	$0.597590\pi$
$140$	−5.84531	−	0.912324i	−0.494019	−	0.0771055i
$141$	−0.742351	+	3.12145i	−0.0625172	+	0.262873i
$142$	7.50955	−	7.50955i	0.630188	−	0.630188i
$143$	−2.90596	−	10.8452i	−0.243008	−	0.906920i
$144$	1.35055	−	2.67881i	0.112546	−	0.223234i
$145$	4.22964	−	17.1607i	0.351253	−	1.42512i
$146$	−2.24372	−	1.29541i	−0.185691	−	0.107209i
$147$	−3.83267	+	11.5026i	−0.316113	+	0.948721i
$148$	1.30111	−	4.85581i	0.106951	−	0.399145i
$149$	−13.1620	−	7.59907i	−1.07827	−	0.622540i	−0.147841	−	0.989011i	$-0.547232\pi$
$149$	−13.1620	−	7.59907i	−1.07827	−	0.622540i	−0.930429	+	0.366471i	$0.880566\pi$
$150$	8.19184	−	2.80957i	0.668861	−	0.229401i
$151$	−1.88796	−	3.27004i	−0.153640	−	0.266112i	0.778923	−	0.627119i	$-0.215766\pi$
$151$	−1.88796	−	3.27004i	−0.153640	−	0.266112i	−0.932563	+	0.361007i	$0.882433\pi$
$152$	−0.848500	+	3.16664i	−0.0688224	+	0.256849i
$153$	0.638459	−	3.06805i	0.0516164	−	0.248037i
$154$	5.73338	+	4.81517i	0.462009	+	0.388017i
$155$	2.30889	−	0.668791i	0.185455	−	0.0537186i
$156$	6.58487	−	1.96582i	0.527212	−	0.157392i
$157$	−14.3440	−	14.3440i	−1.14477	−	1.14477i	−0.987566	−	0.157207i	$-0.949751\pi$
$157$	−14.3440	−	14.3440i	−1.14477	−	1.14477i	−0.157207	−	0.987566i	$-0.550249\pi$
$158$	−1.39137	−	1.39137i	−0.110692	−	0.110692i
$159$	−15.5183	−	14.6635i	−1.23068	−	1.16289i
$160$	−1.95862	−	1.07880i	−0.154842	−	0.0852868i
$161$	23.7032	+	4.19024i	1.86807	+	0.330237i
$162$	8.90089	+	1.33197i	0.699320	+	0.104650i
$163$	−1.18074	+	4.40657i	−0.0924824	+	0.345149i	−0.996626	−	0.0820803i	$-0.973844\pi$
$163$	−1.18074	+	4.40657i	−0.0924824	+	0.345149i	0.904143	+	0.427229i	$0.140510\pi$
$164$	−3.30938	−	5.73201i	−0.258419	−	0.447595i
$165$	−10.7116	−	2.32055i	−0.833896	−	0.180654i
$166$	4.82766	+	2.78725i	0.374699	+	0.216333i
$167$	0.920393	−	3.43495i	0.0712221	−	0.265805i	−0.921128	−	0.389260i	$-0.872731\pi$
$167$	0.920393	−	3.43495i	0.0712221	−	0.265805i	0.992350	+	0.123455i	$0.0393975\pi$
$168$	−2.84664	+	3.59119i	−0.219623	+	0.277066i
$169$	2.37435	+	1.37083i	0.182642	+	0.105449i
$170$	−2.26791	−	0.558978i	−0.173941	−	0.0428716i
$171$	−9.81929	+	0.556645i	−0.750900	+	0.0425677i
$172$	1.60411	+	5.98661i	0.122312	+	0.456475i
$173$	−11.3990	+	11.3990i	−0.866652	+	0.866652i	−0.992100	−	0.125448i	$-0.959963\pi$
$173$	−11.3990	+	11.3990i	−0.866652	+	0.866652i	0.125448	+	0.992100i	$0.459963\pi$
$174$	−9.95077	−	9.40265i	−0.754366	−	0.712813i
$175$	−13.1220	+	1.67703i	−0.991932	+	0.126772i
$176$	1.41494	+	2.45075i	0.106655	+	0.184732i
$177$	−10.2623	−	16.6667i	−0.771364	−	1.25274i
$178$	−12.5104	−	3.35216i	−0.937697	−	0.251255i
$179$	−14.7148	−	8.49562i	−1.09984	−	0.634993i	−0.163661	−	0.986517i	$-0.552330\pi$
$179$	−14.7148	−	8.49562i	−1.09984	−	0.634993i	−0.936179	+	0.351524i	$0.885664\pi$
$180$	1.23413	−	6.59370i	0.0919869	−	0.491466i
$181$		−	10.8648i		−	0.807571i	−0.914854	−	0.403785i	$-0.867694\pi$
$181$		−	10.8648i		−	0.807571i	0.914854	−	0.403785i	$-0.132306\pi$
$182$	−10.4577	+	0.910301i	−0.775175	+	0.0674760i
$183$	6.48906	−	3.99558i	0.479685	−	0.295361i
$184$	7.87899	+	4.54894i	0.580847	+	0.335352i
$185$	−0.226414	−	11.2387i	−0.0166463	−	0.826283i
$186$	0.430805	−	1.81145i	0.0315881	−	0.132822i
$187$	2.09026	+	2.09026i	0.152855	+	0.152855i
$188$	1.30987	−	1.30987i	0.0955318	−	0.0955318i
$189$	−12.9056	−	4.73768i	−0.938744	−	0.344615i
$190$	0.147652	+	7.32913i	0.0107118	+	0.531711i
$191$	−24.8433			−1.79760			−0.898800	−	0.438358i	$-0.855560\pi$
$191$	−24.8433			−1.79760			−0.898800	+	0.438358i	$0.855560\pi$
$192$	−1.47488	+	0.908144i	−0.106440	+	0.0655396i
$193$	−10.4058	−	10.4058i	−0.749024	−	0.749024i	0.225272	−	0.974296i	$-0.427673\pi$
$193$	−10.4058	−	10.4058i	−0.749024	−	0.749024i	−0.974296	+	0.225272i	$0.927673\pi$
$194$	−2.63372	+	4.56174i	−0.189090	+	0.327514i
$195$	12.9199	−	8.31876i	0.925211	−	0.595719i
$196$	5.36626	−	4.49480i	0.383304	−	0.321057i
$197$	15.6701	−	15.6701i	1.11645	−	1.11645i	0.124192	−	0.992258i	$-0.460366\pi$
$197$	15.6701	−	15.6701i	1.11645	−	1.11645i	0.992258	−	0.124192i	$-0.0396340\pi$
$198$	−5.65369	+	6.33322i	−0.401790	+	0.450082i
$199$	−2.70089	+	4.67808i	−0.191461	+	0.331620i	−0.945735	−	0.324940i	$-0.894656\pi$
$199$	−2.70089	+	4.67808i	−0.191461	+	0.331620i	0.754274	+	0.656560i	$0.227989\pi$
$200$	−4.87783	−	1.09853i	−0.344915	−	0.0776777i
$201$	12.3733	+	2.94265i	0.872745	+	0.207559i
$202$	−1.55593	+	5.80681i	−0.109475	+	0.408566i
$203$	11.9874	+	17.1358i	0.841349	+	1.20269i
$204$	−1.24263	+	1.31507i	−0.0870013	+	0.0920730i
$205$	−10.6738	−	10.2523i	−0.745493	−	0.716049i
$206$	12.2818	+	7.09087i	0.855710	+	0.494045i
$207$	−5.56066	+	26.7212i	−0.386492	+	1.85725i
$208$	−3.83238	−	1.02688i	−0.265728	−	0.0712016i
$209$	4.63867	−	8.03441i	0.320863	−	0.555751i
$210$	−3.87979	+	9.48405i	−0.267731	+	0.654462i
$211$	−5.46352	−	9.46309i	−0.376124	−	0.651466i	0.614371	−	0.789018i	$-0.289410\pi$
$211$	−5.46352	−	9.46309i	−0.376124	−	0.651466i	−0.990495	+	0.137552i	$0.956077\pi$
$212$	3.19037	+	11.9066i	0.219115	+	0.817749i
$213$	−9.64459	−	15.6634i	−0.660836	−	1.07324i
$214$	6.93781	−	4.00555i	0.474259	−	0.273814i
$215$	7.16968	+	11.8600i	0.488968	+	0.808843i
$216$	−3.97271	−	3.34926i	−0.270309	−	0.227889i
$217$	−1.20315	+	2.57721i	−0.0816751	+	0.174952i
$218$	2.56030	−	0.686031i	0.173406	−	0.0464639i
$219$	−3.08199	+	3.26165i	−0.208262	+	0.220402i
$220$	4.56365	+	4.38340i	0.307681	+	0.295529i
$221$	−4.14450			−0.278789
$222$	−7.66088	−	4.13838i	−0.514165	−	0.277750i
$223$	4.44321	+	16.5823i	0.297539	+	1.11043i	0.939180	+	0.343426i	$0.111588\pi$
$223$	4.44321	+	16.5823i	0.297539	+	1.11043i	−0.641640	+	0.767006i	$0.721746\pi$
$224$	2.48659	−	0.903808i	0.166142	−	0.0603882i
$225$	−1.45145	−	14.9296i	−0.0967632	−	0.995307i
$226$	5.95155	+	10.3084i	0.395891	+	0.685704i
$227$	−4.92402	+	18.3767i	−0.326819	+	1.21970i	0.585653	+	0.810562i	$0.300838\pi$
$227$	−4.92402	+	18.3767i	−0.326819	+	1.21970i	−0.912471	+	0.409141i	$0.865828\pi$
$228$	4.99593	+	2.69878i	0.330864	+	0.178731i
$229$	2.78880	−	4.83035i	0.184289	−	0.319199i	−0.759047	−	0.651035i	$-0.774335\pi$
$229$	2.78880	−	4.83035i	0.184289	−	0.319199i	0.943337	+	0.331837i	$0.107668\pi$
$230$	19.7523	+	4.86841i	1.30243	+	0.321014i
$231$	10.4114	−	7.73140i	0.685022	−	0.508689i
$232$	2.04575	+	7.63484i	0.134310	+	0.501252i
$233$	−1.16900	+	4.36277i	−0.0765838	+	0.285815i	−0.993588	−	0.113063i	$-0.963934\pi$
$233$	−1.16900	+	4.36277i	−0.0765838	+	0.285815i	0.917004	+	0.398878i	$0.130600\pi$
$234$	−0.673671	−	11.8837i	−0.0440393	−	0.776859i
$235$	1.99841	−	3.62821i	0.130362	−	0.236678i
$236$			11.3003i			0.735590i
$237$	−2.90212	+	1.78695i	−0.188513	+	0.116075i
$238$	2.26461	−	1.58422i	0.146793	−	0.102690i
$239$	5.11986	−	2.95595i	0.331176	−	0.191205i	−0.325187	−	0.945650i	$-0.605427\pi$
$239$	5.11986	−	2.95595i	0.331176	−	0.191205i	0.656363	+	0.754445i	$0.272094\pi$
$240$	−2.60274	+	2.86805i	−0.168006	+	0.185132i
$241$	22.9464	−	13.2481i	1.47811	−	0.853387i	0.478416	−	0.878133i	$-0.341211\pi$
$241$	22.9464	−	13.2481i	1.47811	−	0.853387i	0.999694	+	0.0247460i	$0.00787771\pi$
$242$	0.774332	+	2.88985i	0.0497760	+	0.185766i
$243$	5.81142	−	14.4647i	0.372803	−	0.927910i
$244$	−4.39972			−0.281663
$245$	8.72923	−	12.9923i	0.557690	−	0.830049i
$246$	−10.9850	+	3.27941i	−0.700375	+	0.209087i
$247$	3.36649	+	12.5639i	0.214204	+	0.799422i
$248$	−0.760149	+	0.760149i	−0.0482695	+	0.0482695i
$249$	6.63132	−	7.01789i	0.420243	−	0.444741i
$250$	−11.1599	+	0.675214i	−0.705816	+	0.0427043i
$251$			22.2931i			1.40713i	0.710631	+	0.703565i	$0.248410\pi$
$251$			22.2931i			1.40713i	−0.710631	+	0.703565i	$0.751590\pi$
$252$	4.91058	+	6.23588i	0.309337	+	0.392824i
$253$	−18.2051	−	18.2051i	−1.14454	−	1.14454i
$254$			9.13413i			0.573126i
$255$	−1.85076	+	3.59754i	−0.115899	+	0.225287i
$256$	1.00000			0.0625000
$257$	0.116728	−	0.0312772i	0.00728131	−	0.00195102i	−0.255177	−	0.966894i	$-0.582134\pi$
$257$	0.116728	−	0.0312772i	0.00728131	−	0.00195102i	0.262458	+	0.964943i	$0.415467\pi$
$258$	10.7306	−	0.303909i	0.668057	−	0.0189205i
$259$	10.1850	+	8.55385i	0.632865	+	0.531510i
$260$	−8.86997	+	0.178694i	−0.550092	+	0.0110821i
$261$	−19.8317	+	12.9995i	−1.22755	+	0.804651i
$262$	−9.80524	+	2.62731i	−0.605770	+	0.162315i
$263$	4.92930	−	18.3964i	0.303954	−	1.13437i	−0.629889	−	0.776685i	$-0.716899\pi$
$263$	4.92930	−	18.3964i	0.303954	−	1.13437i	0.933842	−	0.357685i	$-0.116434\pi$
$264$	4.69667	−	1.40213i	0.289060	−	0.0862949i
$265$	14.2596	+	23.5880i	0.875960	+	1.44900i
$266$	−6.64199	−	5.57826i	−0.407247	−	0.342025i
$267$	−10.6621	+	19.7374i	−0.652507	+	1.20791i
$268$	−5.19227	−	5.19227i	−0.317168	−	0.317168i
$269$	−14.9887	+	25.9612i	−0.913878	+	1.58288i	−0.105343	+	0.994436i	$0.533594\pi$
$269$	−14.9887	+	25.9612i	−0.913878	+	1.58288i	−0.808535	+	0.588448i	$0.799739\pi$
$270$	−10.6162	−	4.72197i	−0.646079	−	0.287370i
$271$	3.35162	−	1.93506i	0.203596	−	0.117546i	−0.394735	−	0.918795i	$-0.629164\pi$
$271$	3.35162	−	1.93506i	0.203596	−	0.117546i	0.598332	+	0.801248i	$0.295830\pi$
$272$	1.00900	−	0.270360i	0.0611796	−	0.0163930i
$273$	−2.65694	+	17.9865i	−0.160806	+	1.08859i
$274$	0.738302	−	0.426259i	0.0446025	−	0.0257512i
$275$	12.5287	+	6.57543i	0.755511	+	0.396513i
$276$	10.8227	−	11.4536i	0.651447	−	0.689423i
$277$	11.1297	+	2.98219i	0.668717	+	0.179182i	0.577177	−	0.816619i	$-0.304154\pi$
$277$	11.1297	+	2.98219i	0.668717	+	0.179182i	0.0915403	+	0.995801i	$0.470821\pi$
$278$	−15.3680	−	4.11783i	−0.921709	−	0.246971i
$279$	−2.87975	−	1.45186i	−0.172406	−	0.0869205i
$280$	4.77837	−	3.48815i	0.285562	−	0.208457i
$281$	−2.66639	+	4.61832i	−0.159063	+	0.275506i	−0.934531	−	0.355881i	$-0.884181\pi$
$281$	−2.66639	+	4.61832i	−0.159063	+	0.275506i	0.775468	+	0.631387i	$0.217514\pi$
$282$	−1.68227	−	2.73212i	−0.100178	−	0.162695i
$283$	−3.04958	+	3.04958i	−0.181279	+	0.181279i	−0.791913	−	0.610634i	$-0.790915\pi$
$283$	−3.04958	+	3.04958i	−0.181279	+	0.181279i	0.610634	+	0.791913i	$0.290915\pi$
$284$			10.6201i			0.630188i
$285$	12.4091	+	2.68830i	0.735054	+	0.159241i
$286$	9.72352	+	5.61388i	0.574964	+	0.331956i
$287$	17.4456	−	1.51857i	1.02978	−	0.0896386i
$288$	0.939221	+	2.84919i	0.0553441	+	0.167890i
$289$	−13.7774	+	7.95441i	−0.810438	+	0.467907i
$290$	9.14364	+	15.1253i	0.536933	+	0.888186i
$291$	6.63133	+	6.26606i	0.388736	+	0.367323i
$292$	2.50254	−	0.670554i	0.146450	−	0.0392412i
$293$	0.481217	+	0.128942i	0.0281130	+	0.00753286i	0.272848	−	0.962057i	$-0.412034\pi$
$293$	0.481217	+	0.128942i	0.0281130	+	0.00753286i	−0.244735	+	0.969590i	$0.578701\pi$
$294$	−5.42348	−	10.8437i	−0.316304	−	0.632417i
$295$	7.03021	+	24.2707i	0.409315	+	1.41309i
$296$	2.51355	+	4.35360i	0.146097	+	0.253048i
$297$	8.40613	+	12.0648i	0.487773	+	0.700069i
$298$	14.6803	−	3.93357i	0.850405	−	0.227865i
$299$	36.0965			2.08752
$300$	−3.80584	+	7.77918i	−0.219730	+	0.449131i
$301$	−16.1474	−	2.85454i	−0.930723	−	0.164533i
$302$	3.64726	+	0.977279i	0.209876	+	0.0562361i
$303$	9.16125	+	4.94887i	0.526300	+	0.284305i
$304$	−1.63918	−	2.83913i	−0.0940131	−	0.162836i
$305$	−9.44963	+	2.73717i	−0.541084	+	0.156730i
$306$	1.71798	+	2.62090i	0.0982104	+	0.149827i
$307$	−17.9801	−	17.9801i	−1.02618	−	1.02618i	−0.999648	−	0.0265323i	$-0.991554\pi$
$307$	−17.9801	−	17.9801i	−1.02618	−	1.02618i	−0.0265323	−	0.999648i	$-0.508446\pi$
$308$	−7.45895	+	0.649273i	−0.425013	+	0.0369958i
$309$	16.8703	−	17.8538i	0.959720	−	1.01567i
$310$	−1.15973	+	2.10554i	−0.0658681	+	0.119587i
$311$			10.0621i			0.570569i	0.958443	+	0.285285i	$0.0920881\pi$
$311$			10.0621i			0.570569i	−0.958443	+	0.285285i	$0.907912\pi$
$312$	−3.26616	+	6.04625i	−0.184910	+	0.342302i
$313$	1.49781	−	1.49781i	0.0846615	−	0.0846615i	−0.663508	−	0.748169i	$-0.730933\pi$
$313$	1.49781	−	1.49781i	0.0846615	−	0.0846615i	0.748169	+	0.663508i	$0.230933\pi$
$314$	20.2854			1.14477
$315$	14.4263	+	10.3383i	0.812832	+	0.582499i
$316$	1.96770			0.110692
$317$	11.9754	−	11.9754i	0.672606	−	0.672606i	−0.285710	−	0.958316i	$-0.592229\pi$
$317$	11.9754	−	11.9754i	0.672606	−	0.672606i	0.958316	+	0.285710i	$0.0922294\pi$
$318$	21.3418	−	0.604436i	1.19679	−	0.0338951i
$319$		−	22.3678i		−	1.25236i
$320$	2.14778	−	0.622124i	0.120065	−	0.0347778i
$321$	−3.96928	−	13.2958i	−0.221543	−	0.742098i
$322$	−19.7236	+	13.7977i	−1.09916	+	0.768918i
$323$	−2.42152	−	2.42152i	−0.134737	−	0.134737i
$324$	−7.23573	+	5.35203i	−0.401985	+	0.297335i
$325$	−18.9396	+	5.90201i	−1.05058	+	0.327385i
$326$	−2.28101	−	3.95082i	−0.126333	−	0.218816i
$327$	−0.129973	−	4.58917i	−0.00718753	−	0.253782i
$328$	6.39323	+	1.71306i	0.353007	+	0.0945879i
$329$	1.67424	+	4.60624i	0.0923040	+	0.253950i
$330$	9.21511	−	5.93337i	0.507275	−	0.326621i
$331$	−34.0512			−1.87163			−0.935813	−	0.352497i	$-0.885333\pi$
$331$	−34.0512			−1.87163			−0.935813	+	0.352497i	$0.885333\pi$
$332$	−5.38455	+	1.44279i	−0.295516	+	0.0791832i
$333$	−10.0434	+	11.2506i	−0.550377	+	0.616527i
$334$	1.77806	+	3.07969i	0.0972912	+	0.168513i
$335$	−14.3821	−	7.92162i	−0.785777	−	0.432804i
$336$	−0.526479	−	4.55223i	−0.0287218	−	0.248345i
$337$	−32.1674	−	8.61924i	−1.75227	−	0.469520i	−0.767163	−	0.641452i	$-0.778332\pi$
$337$	−32.1674	−	8.61924i	−1.75227	−	0.469520i	−0.985109	+	0.171933i	$0.944999\pi$
$338$	−2.64825	+	0.709595i	−0.144046	+	0.0385969i
$339$	19.7552	−	5.89766i	1.07296	−	0.320317i
$340$	1.99891	−	1.20840i	0.108406	−	0.0655345i
$341$	2.63458	−	1.52108i	0.142671	−	0.0823710i
$342$	6.54968	−	7.33689i	0.354166	−	0.396734i
$343$	4.76983	+	17.8955i	0.257546	+	0.966266i
$344$	−5.36745	−	3.09890i	−0.289393	−	0.167081i
$345$	16.1192	−	31.3328i	0.867827	−	1.68690i
$346$		−	16.1207i		−	0.866652i
$347$	10.2925	−	10.2925i	0.552530	−	0.552530i	−0.374640	−	0.927170i	$-0.622234\pi$
$347$	10.2925	−	10.2925i	0.552530	−	0.552530i	0.927170	+	0.374640i	$0.122234\pi$
$348$	13.6849	−	0.387581i	0.733590	−	0.0207765i
$349$	−16.7984	+	29.0957i	−0.899199	+	1.55746i	−0.0706777	+	0.997499i	$0.522516\pi$
$349$	−16.7984	+	29.0957i	−0.899199	+	1.55746i	−0.828521	+	0.559958i	$0.810817\pi$
$350$	8.09283	−	10.4645i	0.432580	−	0.559352i
$351$	−20.2946	−	3.62713i	−1.08324	−	0.193602i
$352$	−2.73345	−	0.732426i	−0.145693	−	0.0390385i
$353$	24.3107	+	6.51402i	1.29393	+	0.346706i	0.839150	−	0.543900i	$-0.183053\pi$
$353$	24.3107	+	6.51402i	1.29393	+	0.346706i	0.454775	+	0.890606i	$0.349720\pi$
$354$	19.0417	+	4.52854i	1.01205	+	0.240689i
$355$	6.60702	+	22.8097i	0.350664	+	1.21061i
$356$	11.2166	−	6.47588i	0.594476	−	0.343221i
$357$	−1.76196	−	4.45086i	−0.0932529	−	0.235564i
$358$	16.4123	−	4.39766i	0.867416	−	0.232423i
$359$	−13.7601	+	7.94442i	−0.726232	+	0.419290i	−0.817042	−	0.576578i	$-0.804388\pi$
$359$	−13.7601	+	7.94442i	−0.726232	+	0.419290i	0.0908101	+	0.995868i	$0.471054\pi$
$360$	3.78979	+	5.53512i	0.199739	+	0.291726i
$361$	4.12621	−	7.14680i	0.217169	−	0.376148i
$362$	7.68254	+	7.68254i	0.403785	+	0.403785i
$363$	5.17986	−	0.146702i	0.271872	−	0.00769988i
$364$	6.75101	−	8.03837i	0.353849	−	0.421325i
$365$	4.95774	−	2.99709i	0.259500	−	0.156875i
$366$	−1.76316	+	7.41376i	−0.0921618	+	0.387523i
$367$	−3.61645	+	13.4968i	−0.188777	+	0.704526i	0.805013	+	0.593257i	$0.202158\pi$
$367$	−3.61645	+	13.4968i	−0.188777	+	0.704526i	−0.993790	+	0.111269i	$0.964509\pi$
$368$	−8.78787	+	2.35470i	−0.458099	+	0.122747i
$369$	1.12383	+	19.8244i	0.0585040	+	1.03202i
$370$	8.10703	+	7.78684i	0.421465	+	0.404818i
$371$	−32.1152	−	5.67732i	−1.66734	−	0.294752i
$372$	0.976266	+	1.58552i	0.0506171	+	0.0822052i
$373$	−12.4343	+	3.33176i	−0.643823	+	0.172512i	−0.565934	−	0.824450i	$-0.691484\pi$
$373$	−12.4343	+	3.33176i	−0.643823	+	0.172512i	−0.0778884	+	0.996962i	$0.524818\pi$
$374$	−2.95607			−0.152855
$375$	−3.33450	+	19.0757i	−0.172193	+	0.985063i
$376$			1.85243i			0.0955318i
$377$	22.1752	+	22.1752i	1.14208	+	1.14208i
$378$	12.4757	−	5.77559i	0.641680	−	0.297064i
$379$		−	9.39265i		−	0.482468i	−0.970467	−	0.241234i	$-0.922448\pi$
$379$		−	9.39265i		−	0.482468i	0.970467	−	0.241234i	$-0.0775521\pi$
$380$	−5.28688	−	5.07807i	−0.271211	−	0.260499i
$381$	15.3915	+	3.66045i	0.788530	+	0.187530i
$382$	17.5669	−	17.5669i	0.898800	−	0.898800i
$383$	−1.51522	−	5.65489i	−0.0774242	−	0.288951i	0.916348	−	0.400383i	$-0.131123\pi$
$383$	−1.51522	−	5.65489i	−0.0774242	−	0.288951i	−0.993772	+	0.111432i	$0.964456\pi$
$384$	0.400744	−	1.68505i	0.0204504	−	0.0859900i
$385$	−15.6163	+	6.03488i	−0.795878	+	0.307566i
$386$	14.7160			0.749024
$387$	3.78812	−	18.2034i	0.192561	−	0.925331i
$388$	−1.36332	−	5.08796i	−0.0692119	−	0.258302i
$389$	−12.0407	+	6.95172i	−0.610490	+	0.352466i	−0.773157	−	0.634215i	$-0.781324\pi$
$389$	−12.0407	+	6.95172i	−0.610490	+	0.352466i	0.162667	+	0.986681i	$0.447990\pi$
$390$	−3.25348	+	15.0180i	−0.164746	+	0.760465i
$391$	−8.23033	+	4.75179i	−0.416226	+	0.240308i
$392$	−0.616214	+	6.97282i	−0.0311235	+	0.352181i
$393$	0.497761	+	17.5752i	0.0251087	+	0.886553i
$394$			22.1609i			1.11645i
$395$	4.22618	−	1.22415i	0.212642	−	0.0615937i
$396$	−0.480497	−	8.47603i	−0.0241459	−	0.425936i
$397$	4.61113	−	17.2090i	0.231426	−	0.863694i	−0.748301	−	0.663359i	$-0.769130\pi$
$397$	4.61113	−	17.2090i	0.231426	−	0.863694i	0.979727	−	0.200335i	$-0.0642030\pi$
$398$	−1.39808	−	5.21771i	−0.0700795	−	0.261540i
$399$	−12.0614	+	8.95665i	−0.603826	+	0.448393i
$400$	4.22592	−	2.67237i	0.211296	−	0.133619i
$401$	−16.8403	+	29.1683i	−0.840964	+	1.45659i	0.0481161	+	0.998842i	$0.484678\pi$
$401$	−16.8403	+	29.1683i	−0.840964	+	1.45659i	−0.889080	+	0.457751i	$0.848655\pi$
$402$	−10.8300	+	6.66848i	−0.540152	+	0.332593i
$403$	−1.10391	+	4.11986i	−0.0549899	+	0.205225i
$404$	−3.00582	−	5.20624i	−0.149545	−	0.259020i
$405$	−12.2111	+	15.9965i	−0.606776	+	0.794873i
$406$	−20.5932	−	3.64046i	−1.02202	−	0.180673i
$407$	−3.68198	−	13.7413i	−0.182509	−	0.681133i
$408$	−0.0512216	−	1.80856i	−0.00253585	−	0.0895372i
$409$	2.27522			0.112503			0.0562513	−	0.998417i	$-0.482085\pi$
$409$	2.27522			0.112503			0.0562513	+	0.998417i	$0.482085\pi$
$410$	14.7970	−	0.298100i	0.730771	−	0.0147221i
$411$	−0.422399	−	1.41490i	−0.0208354	−	0.0697918i
$412$	−13.6985	+	3.67051i	−0.674877	+	0.180833i
$413$	−27.0911	−	12.6473i	−1.33307	−	0.622333i
$414$	−14.9627	−	22.8267i	−0.735379	−	1.12187i
$415$	−10.6673	+	6.44865i	−0.523635	+	0.316552i
$416$	3.43602	−	1.98379i	0.168465	−	0.0972632i
$417$	−13.0974	+	24.2456i	−0.641382	+	1.18731i
$418$	2.40115	+	8.96121i	0.117444	+	0.438307i
$419$	−4.29767	−	7.44378i	−0.209955	−	0.363653i	0.741745	−	0.670682i	$-0.233998\pi$
$419$	−4.29767	−	7.44378i	−0.209955	−	0.363653i	−0.951700	+	0.307029i	$0.900665\pi$
$420$	−3.96281	−	9.44966i	−0.193365	−	0.461096i
$421$	0.196579	−	0.340485i	0.00958067	−	0.0165942i	−0.861195	−	0.508274i	$-0.830284\pi$
$421$	0.196579	−	0.340485i	0.00958067	−	0.0165942i	0.870776	+	0.491680i	$0.163617\pi$
$422$	10.5547	+	2.82812i	0.513795	+	0.137671i
$423$	−5.27792	+	1.73984i	−0.256621	+	0.0845940i
$424$	−10.6752	−	6.16331i	−0.518432	−	0.299317i
$425$	3.54145	−	3.83894i	0.171786	−	0.186216i
$426$	17.8955	+	4.25594i	0.867037	+	0.206201i
$427$	4.92414	−	10.5478i	0.238296	−	0.510442i
$428$	−2.07342	+	7.73812i	−0.100223	+	0.374036i
$429$	13.3563	−	14.1349i	0.644850	−	0.682441i
$430$	−13.4560	−	3.31654i	−0.648906	−	0.159938i
$431$	−17.2369	+	29.8552i	−0.830273	+	1.43807i	0.0675488	+	0.997716i	$0.478482\pi$
$431$	−17.2369	+	29.8552i	−0.830273	+	1.43807i	−0.897822	+	0.440359i	$0.854851\pi$
$432$	5.17742	−	0.440843i	0.249099	−	0.0212101i
$433$	19.0712	−	19.0712i	0.916503	−	0.916503i	−0.0802703	−	0.996773i	$-0.525578\pi$
$433$	19.0712	−	19.0712i	0.916503	−	0.916503i	0.996773	+	0.0802703i	$0.0255783\pi$
$434$	−0.971606	−	2.67312i	−0.0466386	−	0.128314i
$435$	29.1511	−	9.34616i	1.39769	−	0.448114i
$436$	−1.32531	+	2.29550i	−0.0634708	+	0.109935i
$437$	21.0902	+	21.0902i	1.00888	+	1.00888i
$438$	−0.127041	−	4.48564i	−0.00607025	−	0.214332i
$439$	5.65221			0.269765			0.134883	−	0.990862i	$-0.456934\pi$
$439$	5.65221			0.269765			0.134883	+	0.990862i	$0.456934\pi$
$440$	−6.32652	+	0.127454i	−0.301605	+	0.00607612i
$441$	−20.4456	+	4.79331i	−0.973602	+	0.228253i
$442$	2.93061	−	2.93061i	0.139395	−	0.139395i
$443$	−17.7821	−	17.7821i	−0.844853	−	0.844853i	0.144632	−	0.989485i	$-0.453800\pi$
$443$	−17.7821	−	17.7821i	−0.844853	−	0.844853i	−0.989485	+	0.144632i	$0.953800\pi$
$444$	8.34334	−	2.49079i	0.395957	−	0.118208i
$445$	20.0619	−	20.8869i	0.951025	−	0.990132i
$446$	−14.8673	−	8.58362i	−0.703986	−	0.406446i
$447$	−0.745240	−	26.3134i	−0.0352487	−	1.24458i
$448$	−1.11920	+	2.39737i	−0.0528770	+	0.113265i
$449$		−	7.36485i		−	0.347569i	−0.984784	−	0.173784i	$-0.944400\pi$
$449$		−	7.36485i		−	0.347569i	0.984784	−	0.173784i	$-0.0555996\pi$
$450$	11.5832	+	9.53050i	0.546035	+	0.449272i
$451$	−16.2209	−	9.36513i	−0.763812	−	0.440987i
$452$	−11.4975	−	3.08075i	−0.540798	−	0.144906i
$453$	3.10838	−	5.75418i	0.146045	−	0.270355i
$454$	−9.51247	−	16.4761i	−0.446442	−	0.773261i
$455$	9.49884	−	21.4646i	0.445312	−	1.00628i
$456$	−5.44098	+	1.62433i	−0.254797	+	0.0760663i
$457$	5.42174	−	5.42174i	0.253618	−	0.253618i	−0.568834	−	0.822452i	$-0.692605\pi$
$457$	5.42174	−	5.42174i	0.253618	−	0.253618i	0.822452	+	0.568834i	$0.192605\pi$
$458$	1.44359	+	5.38756i	0.0674546	+	0.251744i
$459$	5.10482	−	1.84458i	0.238273	−	0.0860976i
$460$	−17.4095	+	10.5245i	−0.811722	+	0.490709i
$461$	14.1520	+	8.17068i	0.659126	+	0.380546i	0.791944	−	0.610594i	$-0.209069\pi$
$461$	14.1520	+	8.17068i	0.659126	+	0.380546i	−0.132818	+	0.991140i	$0.542403\pi$
$462$	−1.89507	+	12.8289i	−0.0881666	+	0.596855i
$463$	−10.2007	+	38.0696i	−0.474068	+	1.76925i	0.150851	+	0.988557i	$0.451799\pi$
$463$	−10.2007	+	38.0696i	−0.474068	+	1.76925i	−0.624919	+	0.780690i	$0.714868\pi$
$464$	−6.84521	−	3.95209i	−0.317781	−	0.183471i
$465$	3.08319	+	2.79798i	0.142980	+	0.129753i
$466$	−2.25834	−	3.91156i	−0.104615	−	0.181199i
$467$	3.19675	−	11.9304i	0.147928	−	0.552075i	−0.851679	−	0.524063i	$-0.824416\pi$
$467$	3.19675	−	11.9304i	0.147928	−	0.552075i	0.999608	−	0.0280122i	$-0.00891772\pi$
$468$	8.87937	+	7.92665i	0.410449	+	0.366410i
$469$	18.2590	−	6.63664i	0.843121	−	0.306452i
$470$	1.15244	+	3.97862i	0.0531581	+	0.183520i
$471$	8.12926	−	34.1820i	0.374577	−	1.57502i
$472$	−7.99055	−	7.99055i	−0.367795	−	0.367795i
$473$	12.4019	+	12.4019i	0.570242	+	0.570242i
$474$	0.788543	−	3.31568i	0.0362190	−	0.152294i
$475$	−14.5142	−	7.61749i	−0.665959	−	0.349514i
$476$	−0.481112	+	2.72153i	−0.0220517	+	0.124741i
$477$	7.53409	−	36.2043i	0.344962	−	1.65768i
$478$	−1.53011	+	5.71046i	−0.0699857	+	0.261190i
$479$	−3.69462	−	6.39927i	−0.168812	−	0.292390i	0.769191	−	0.639019i	$-0.220660\pi$
$479$	−3.69462	−	6.39927i	−0.168812	−	0.292390i	−0.938002	+	0.346629i	$0.887326\pi$
$480$	−0.187601	−	3.86844i	−0.00856279	−	0.176569i
$481$	17.2732	+	9.97271i	0.787592	+	0.454716i
$482$	−6.85774	+	25.5934i	−0.312361	+	1.16575i
$483$	15.3458	+	38.7647i	0.698258	+	1.76386i
$484$	−2.59097	−	1.49590i	−0.117771	−	0.0679952i
$485$	−6.09345	−	10.0797i	−0.276689	−	0.457695i
$486$	6.11878	+	14.3374i	0.277554	+	0.650357i
$487$	7.94050	+	29.6344i	0.359818	+	1.34286i	0.874311	+	0.485366i	$0.161314\pi$
$487$	7.94050	+	29.6344i	0.359818	+	1.34286i	−0.514493	+	0.857495i	$0.672020\pi$
$488$	3.11107	−	3.11107i	0.140832	−	0.140832i
$489$	−7.57144	+	2.26035i	−0.342392	+	0.102217i
$490$	3.01447	+	15.3595i	0.136180	+	0.693870i
$491$	−6.14269	−	10.6395i	−0.277216	−	0.480152i	0.693476	−	0.720480i	$-0.256078\pi$
$491$	−6.14269	−	10.6395i	−0.277216	−	0.480152i	−0.970692	+	0.240328i	$0.922745\pi$
$492$	5.44864	−	10.0864i	0.245644	−	0.454731i
$493$	−7.97530	−	2.13698i	−0.359189	−	0.0962445i
$494$	−11.2645	−	6.50355i	−0.506813	−	0.292609i
$495$	−6.30514	−	17.9057i	−0.283395	−	0.804802i
$496$		−	1.07501i		−	0.0482695i
$497$	−25.4604	−	11.8860i	−1.14205	−	0.533159i
$498$	0.273346	+	9.65145i	0.0122489	+	0.432492i
$499$	35.7736	+	20.6539i	1.60145	+	0.924595i	0.991199	+	0.132384i	$0.0422632\pi$
$499$	35.7736	+	20.6539i	1.60145	+	0.924595i	0.610247	+	0.792211i	$0.291070\pi$
$500$	7.41382	−	8.36871i	0.331556	−	0.374260i
$501$	5.90200	−	1.76196i	0.263682	−	0.0787186i
$502$	−15.7636	−	15.7636i	−0.703565	−	0.703565i
$503$	12.9448	−	12.9448i	0.577178	−	0.577178i	−0.356947	−	0.934125i	$-0.616182\pi$
$503$	12.9448	−	12.9448i	0.577178	−	0.577178i	0.934125	+	0.356947i	$0.116182\pi$
$504$	−7.88174	−	0.937133i	−0.351080	−	0.0417432i
$505$	−9.69478	−	9.31187i	−0.431412	−	0.414373i
$506$	25.7459			1.14454
$507$	0.134438	+	4.74680i	0.00597058	+	0.210813i
$508$	−6.45881	−	6.45881i	−0.286563	−	0.286563i
$509$	−13.1433	+	22.7648i	−0.582565	+	1.00903i	0.412610	+	0.910908i	$0.364617\pi$
$509$	−13.1433	+	22.7648i	−0.582565	+	1.00903i	−0.995174	+	0.0981234i	$0.968716\pi$
$510$	−1.23516	−	3.85253i	−0.0546939	−	0.170593i
$511$	−1.19326	+	6.75001i	−0.0527869	+	0.298603i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−9.73831	−	13.9768i	−0.429957	−	0.617089i
$514$	−0.0604230	+	0.104656i	−0.00266514	+	0.00461616i
$515$	−27.1379	+	16.4056i	−1.19584	+	0.722918i
$516$	−7.37278	+	7.80257i	−0.324568	+	0.343489i
$517$	1.35677	−	5.06353i	0.0596707	−	0.222694i
$518$	−13.2504	+	1.15339i	−0.582187	+	0.0506772i
$519$	−27.1642	−	6.46026i	−1.19238	−	0.283574i
$520$	6.14566	−	6.39837i	0.269505	−	0.280587i
$521$	9.00760	+	5.20054i	0.394630	+	0.227840i	0.684164	−	0.729328i	$-0.260167\pi$
$521$	9.00760	+	5.20054i	0.394630	+	0.227840i	−0.289534	+	0.957168i	$0.593500\pi$
$522$	4.83106	−	23.2152i	0.211450	−	1.01610i
$523$	2.71990	+	0.728796i	0.118933	+	0.0318680i	0.317795	−	0.948160i	$-0.397058\pi$
$523$	2.71990	+	0.728796i	0.118933	+	0.0318680i	−0.198862	+	0.980028i	$0.563724\pi$
$524$	5.07556	−	8.79114i	0.221727	−	0.384043i
$525$	−14.3901	−	17.8304i	−0.628036	−	0.778184i
$526$	9.52268	+	16.4938i	0.415208	+	0.719162i
$527$	−0.290641	−	1.08469i	−0.0126605	−	0.0472497i
$528$	−2.32959	+	4.31250i	−0.101382	+	0.187677i
$529$	51.7635	−	29.8857i	2.25059	−	1.29938i
$530$	−26.7623	−	6.59617i	−1.16248	−	0.286519i
$531$	15.2617	−	30.2715i	0.662300	−	1.31367i
$532$	8.64103	−	0.752168i	0.374636	−	0.0326106i
$533$	25.3656	−	6.79670i	1.09871	−	0.294398i
$534$	−6.41724	−	21.4957i	−0.277701	−	0.930208i
$535$	0.360809	+	17.9097i	0.0155991	+	0.774305i
$536$	7.34297			0.317168
$537$	−0.833165	−	29.4179i	−0.0359537	−	1.26948i
$538$	−7.75873	−	28.9560i	−0.334503	−	1.24838i
$539$	6.79147	−	18.6086i	0.292529	−	0.801527i
$540$	10.8457	−	4.16783i	0.466725	−	0.179355i
$541$	−16.3838	−	28.3776i	−0.704396	−	1.22005i	−0.966909	−	0.255122i	$-0.917884\pi$
$541$	−16.3838	−	28.3776i	−0.704396	−	1.22005i	0.262513	−	0.964929i	$-0.415449\pi$
$542$	−1.00166	+	3.73825i	−0.0430250	+	0.160571i
$543$	16.0242	−	9.86676i	0.687665	−	0.423423i
$544$	−0.522296	+	0.904644i	−0.0223933	+	0.0387863i
$545$	−1.41839	+	5.75475i	−0.0607571	+	0.246506i
$546$	−10.8397	−	14.5971i	−0.463895	−	0.624700i
$547$	−6.60466	−	24.6489i	−0.282395	−	1.05391i	−0.950722	−	0.310045i	$-0.899656\pi$
$547$	−6.60466	−	24.6489i	−0.282395	−	1.05391i	0.668327	−	0.743868i	$-0.267011\pi$
$548$	−0.220648	+	0.823469i	−0.00942561	+	0.0351769i
$549$	11.7860	+	5.94204i	0.503014	+	0.253600i
$550$	−13.5087	+	4.20962i	−0.576012	+	0.179499i
$551$			25.9126i			1.10392i
$552$	0.446114	+	15.7517i	0.0189879	+	0.670435i
$553$	−2.20224	+	4.71731i	−0.0936487	+	0.200600i
$554$	−9.97859	+	5.76114i	−0.423950	+	0.244767i
$555$	16.3701	−	10.5403i	0.694871	−	0.447409i
$556$	13.7785	−	7.95504i	0.584340	−	0.337369i
$557$	−0.780515	−	2.91292i	−0.0330715	−	0.123424i	0.947417	−	0.320003i	$-0.103684\pi$
$557$	−0.780515	−	2.91292i	−0.0330715	−	0.123424i	−0.980488	+	0.196578i	$0.937017\pi$
$558$	3.06291	−	1.00967i	0.129663	−	0.0427429i
$559$	−24.5902			−1.04006
$560$	−0.912324	+	5.84531i	−0.0385527	+	0.247009i
$561$	−1.18463	+	4.98113i	−0.0500150	+	0.210304i
$562$	−1.38022	−	5.15107i	−0.0582212	−	0.217285i
$563$	3.20320	−	3.20320i	0.134999	−	0.134999i	−0.636378	−	0.771377i	$-0.719568\pi$
$563$	3.20320	−	3.20320i	0.134999	−	0.134999i	0.771377	+	0.636378i	$0.219568\pi$
$564$	3.12145	+	0.742351i	0.131437	+	0.0312586i
$565$	−26.6107	+	0.536100i	−1.11952	+	0.0225539i
$566$		−	4.31276i		−	0.181279i
$567$	−4.73263	−	23.3367i	−0.198752	−	0.980050i
$568$	−7.50955	−	7.50955i	−0.315094	−	0.315094i
$569$			16.1152i			0.675585i	0.941221	+	0.337793i	$0.109680\pi$
$569$			16.1152i			0.675585i	−0.941221	+	0.337793i	$0.890320\pi$
$570$	−10.6755	+	6.87367i	−0.447148	+	0.287906i
$571$	−19.3505			−0.809793			−0.404896	−	0.914363i	$-0.632692\pi$
$571$	−19.3505			−0.809793			−0.404896	+	0.914363i	$0.632692\pi$
$572$	−10.8452	+	2.90596i	−0.453460	+	0.121504i
$573$	−22.5613	−	36.6410i	−0.942513	−	1.53070i
$574$	−11.2621	+	13.4097i	−0.470072	+	0.559710i
$575$	−30.8442	+	33.4352i	−1.28629	+	1.39435i
$576$	−2.67881	−	1.35055i	−0.111617	−	0.0562729i
$577$	29.1260	−	7.80428i	1.21253	−	0.324897i	0.404776	−	0.914416i	$-0.367349\pi$
$577$	29.1260	−	7.80428i	1.21253	−	0.324897i	0.807754	+	0.589519i	$0.200683\pi$
$578$	4.11751	−	15.3667i	0.171266	−	0.639172i
$579$	5.89734	−	24.7972i	0.245085	−	1.03054i
$580$	−17.1607	−	4.22964i	−0.712559	−	0.175626i
$581$	2.56747	−	14.5236i	0.106517	−	0.602538i
$582$	−9.11983	+	0.258289i	−0.378029	+	0.0107064i
$583$	24.6659	+	24.6659i	1.02156	+	1.02156i
$584$	−1.29541	+	2.24372i	−0.0536045	+	0.0928457i
$585$	24.0023	+	11.5006i	0.992373	+	0.475493i
$586$	−0.431447	+	0.249096i	−0.0178229	+	0.0102901i
$587$	14.3840	−	3.85419i	0.593693	−	0.159079i	0.0505523	−	0.998721i	$-0.483902\pi$
$587$	14.3840	−	3.85419i	0.593693	−	0.159079i	0.543140	+	0.839642i	$0.317235\pi$
$588$	11.5026	+	3.83267i	0.474361	+	0.158057i
$589$	−3.05211	+	1.76213i	−0.125760	+	0.0726075i
$590$	−22.1331	−	12.1908i	−0.911204	−	0.501889i
$591$	37.3423	+	8.88085i	1.53606	+	0.365309i
$592$	−4.85581	−	1.30111i	−0.199573	−	0.0534753i
$593$	35.0109	+	9.38115i	1.43773	+	0.385238i	0.891737	−	0.452554i	$-0.149487\pi$
$593$	35.0109	+	9.38115i	1.43773	+	0.385238i	0.545990	+	0.837792i	$0.316154\pi$
$594$	−14.4751	−	2.58705i	−0.593921	−	0.106148i
$595$	0.659807	+	6.14457i	0.0270494	+	0.251903i
$596$	−7.59907	+	13.1620i	−0.311270	+	0.539135i
$597$	−9.35240	+	0.264876i	−0.382768	+	0.0108407i
$598$	−25.5241	+	25.5241i	−1.04376	+	1.04376i
$599$			20.1388i			0.822850i	0.911444	+	0.411425i	$0.134969\pi$
$599$			20.1388i			0.822850i	−0.911444	+	0.411425i	$0.865031\pi$
$600$	−2.80957	−	8.19184i	−0.114700	−	0.334431i
$601$	21.1181	+	12.1925i	0.861425	+	0.497344i	0.864489	−	0.502651i	$-0.167642\pi$
$601$	21.1181	+	12.1925i	0.861425	+	0.497344i	−0.00306400	+	0.999995i	$0.500975\pi$
$602$	13.4364	−	9.39950i	0.547628	−	0.383095i
$603$	6.89668	+	20.9215i	0.280854	+	0.851989i
$604$	−3.27004	+	1.88796i	−0.133056	+	0.0768199i
$605$	−6.49546	−	1.60095i	−0.264078	−	0.0650880i
$606$	−9.97736	+	2.97861i	−0.405303	+	0.120998i
$607$	−27.9312	+	7.48413i	−1.13369	+	0.303772i	−0.776412	−	0.630226i	$-0.782962\pi$
$607$	−27.9312	+	7.48413i	−1.13369	+	0.303772i	−0.357279	+	0.933998i	$0.616296\pi$
$608$	3.16664	+	0.848500i	0.128424	+	0.0344112i
$609$	−14.3869	+	33.2417i	−0.582988	+	1.34702i
$610$	4.74643	−	8.61737i	0.192177	−	0.348907i
$611$	3.67483	+	6.36500i	0.148668	+	0.257500i
$612$	−3.06805	−	0.638459i	−0.124019	−	0.0258082i
$613$	−1.89216	+	0.507002i	−0.0764235	+	0.0204776i	−0.296828	−	0.954931i	$-0.595929\pi$
$613$	−1.89216	+	0.507002i	−0.0764235	+	0.0204776i	0.220405	+	0.975409i	$0.429262\pi$
$614$	25.4277			1.02618
$615$	5.42749	−	25.0532i	0.218857	−	1.01024i
$616$	4.81517	−	5.73338i	0.194009	−	0.231004i
$617$	28.5098	+	7.63919i	1.14776	+	0.307542i	0.782068	−	0.623193i	$-0.214165\pi$
$617$	28.5098	+	7.63919i	1.14776	+	0.307542i	0.365694	+	0.930735i	$0.380832\pi$
$618$	0.695402	+	24.5537i	0.0279732	+	0.987693i
$619$	−15.0568	−	26.0791i	−0.605184	−	1.04821i	−0.992022	−	0.126062i	$-0.959766\pi$
$619$	−15.0568	−	26.0791i	−0.605184	−	1.04821i	0.386839	−	0.922147i	$-0.373567\pi$
$620$	−0.668791	−	2.30889i	−0.0268593	−	0.0927273i
$621$	−44.4604	+	16.0654i	−1.78414	+	0.644681i
$622$	−7.11498	−	7.11498i	−0.285285	−	0.285285i
$623$	2.97159	+	34.1380i	0.119054	+	1.36771i
$624$	−1.96582	−	6.58487i	−0.0786959	−	0.263606i
$625$	10.7169	−	22.5865i	0.428675	−	0.903459i
$626$			2.11823i			0.0846615i
$627$	16.0624	−	0.454914i	0.641469	−	0.0181675i
$628$	−14.3440	+	14.3440i	−0.572386	+	0.572386i
$629$	−5.25128			−0.209382
$630$	−17.5113	+	2.89066i	−0.697665	+	0.115167i
$631$	−17.6592			−0.703001			−0.351501	−	0.936188i	$-0.614329\pi$
$631$	−17.6592			−0.703001			−0.351501	+	0.936188i	$0.614329\pi$
$632$	−1.39137	+	1.39137i	−0.0553458	+	0.0553458i
$633$	8.99527	−	16.6519i	0.357530	−	0.661853i
$634$			16.9358i			0.672606i
$635$	−17.8903	−	9.85392i	−0.709954	−	0.391041i
$636$	−14.6635	+	15.5183i	−0.581447	+	0.615342i
$637$	11.7153	+	25.1812i	0.464176	+	0.997716i
$638$	15.8164	+	15.8164i	0.626179	+	0.626179i
$639$	14.3430	−	28.4492i	0.567400	−	1.12543i
$640$	−1.07880	+	1.95862i	−0.0426434	+	0.0774212i
$641$	1.95285	+	3.38243i	0.0771329	+	0.133598i	0.902012	−	0.431711i	$-0.142090\pi$
$641$	1.95285	+	3.38243i	0.0771329	+	0.133598i	−0.824879	+	0.565309i	$0.808757\pi$
$642$	12.2082	+	6.59484i	0.481821	+	0.260277i
$643$	−19.6222	−	5.25776i	−0.773825	−	0.207346i	−0.149764	−	0.988722i	$-0.547851\pi$
$643$	−19.6222	−	5.25776i	−0.773825	−	0.207346i	−0.624061	+	0.781376i	$0.714518\pi$
$644$	4.19024	−	23.7032i	0.165119	−	0.934036i
$645$	−10.9809	+	21.3450i	−0.432374	+	0.840458i
$646$	3.42454			0.134737
$647$	−16.1002	+	4.31403i	−0.632963	+	0.169602i	−0.561014	−	0.827806i	$-0.689589\pi$
$647$	−16.1002	+	4.31403i	−0.632963	+	0.169602i	−0.0719493	+	0.997408i	$0.522922\pi$
$648$	1.33197	−	8.90089i	0.0523249	−	0.349660i
$649$	15.9893	+	27.6943i	0.627635	+	1.08710i
$650$	9.21895	−	17.5657i	0.361597	−	0.688982i
$651$	−4.89371	+	0.565972i	−0.191800	+	0.0221822i
$652$	4.40657	+	1.18074i	0.172574	+	0.0462412i
$653$	43.1690	−	11.5671i	1.68933	−	0.452655i	0.719115	−	0.694891i	$-0.244547\pi$
$653$	43.1690	−	11.5671i	1.68933	−	0.452655i	0.970217	+	0.242236i	$0.0778807\pi$
$654$	3.33694	+	3.15313i	0.130485	+	0.123297i
$655$	5.43203	−	22.0391i	0.212247	−	0.861137i
$656$	−5.73201	+	3.30938i	−0.223797	+	0.129209i
$657$	−7.60944	−	1.58352i	−0.296873	−	0.0617790i
$658$	−4.44097	−	2.07323i	−0.173127	−	0.0808230i
$659$	−35.4457	−	20.4646i	−1.38077	−	0.797187i	−0.388518	−	0.921441i	$-0.627013\pi$
$659$	−35.4457	−	20.4646i	−1.38077	−	0.797187i	−0.992250	+	0.124254i	$0.960346\pi$
$660$	−2.32055	+	10.7116i	−0.0903271	+	0.416948i
$661$		−	38.7946i		−	1.50894i	−0.656337	−	0.754468i	$-0.727895\pi$
$661$		−	38.7946i		−	1.50894i	0.656337	−	0.754468i	$-0.272105\pi$
$662$	24.0779	−	24.0779i	0.935813	−	0.935813i
$663$	−3.76380	−	6.11265i	−0.146174	−	0.237396i
$664$	2.78725	−	4.82766i	0.108166	−	0.187350i
$665$	18.0911	−	6.99128i	0.701542	−	0.271110i
$666$	−0.853573	−	15.0571i	−0.0330753	−	0.583452i
$667$	69.4608	+	18.6120i	2.68953	+	0.720658i
$668$	−3.43495	−	0.920393i	−0.132902	−	0.0356111i
$669$	−20.4218	+	21.6123i	−0.789553	+	0.835580i
$670$	15.7711	−	4.56824i	0.609291	−	0.176486i
$671$	−10.7826	+	6.22533i	−0.416257	+	0.240326i
$672$	3.59119	+	2.84664i	0.138533	+	0.109811i
$673$	14.2080	−	3.80701i	0.547677	−	0.146750i	0.0256382	−	0.999671i	$-0.491838\pi$
$673$	14.2080	−	3.80701i	0.547677	−	0.146750i	0.522039	+	0.852922i	$0.325172\pi$
$674$	28.8405	−	16.6511i	1.11090	−	0.641376i
$675$	20.7013	−	15.6989i	0.796793	−	0.604253i
$676$	1.37083	−	2.37435i	0.0527243	−	0.0913212i
$677$	−9.54315	−	9.54315i	−0.366773	−	0.366773i	0.499526	−	0.866299i	$-0.333508\pi$
$677$	−9.54315	−	9.54315i	−0.366773	−	0.366773i	−0.866299	+	0.499526i	$0.833508\pi$
$678$	−9.79879	+	18.1393i	−0.376320	+	0.696637i
$679$	13.7236	+	2.42605i	0.526662	+	0.0931032i
$680$	−0.558978	+	2.26791i	−0.0214358	+	0.0869704i
$681$	−31.5751	+	9.42633i	−1.20996	+	0.361218i
$682$	−0.787368	+	2.93850i	−0.0301499	+	0.112521i
$683$	33.0664	−	8.86011i	1.26525	−	0.339023i	0.437041	−	0.899442i	$-0.356027\pi$
$683$	33.0664	−	8.86011i	1.26525	−	0.339023i	0.828209	+	0.560419i	$0.189360\pi$
$684$	0.556645	+	9.81929i	0.0212838	+	0.375450i
$685$	0.0383962	+	1.90590i	0.00146705	+	0.0728208i
$686$	−16.0268	−	9.28125i	−0.611906	−	0.354360i
$687$	9.65683	−	0.273498i	0.368431	−	0.0104346i
$688$	5.98661	−	1.60411i	0.228237	−	0.0611560i
$689$	−48.9068			−1.86320
$690$	10.7576	+	33.5536i	0.409536	+	1.27736i
$691$			11.6758i			0.444170i	0.975027	+	0.222085i	$0.0712863\pi$
$691$			11.6758i			0.444170i	−0.975027	+	0.222085i	$0.928714\pi$
$692$	11.3990	+	11.3990i	0.433326	+	0.433326i
$693$	20.8580	+	8.33440i	0.792329	+	0.316598i
$694$			14.5558i			0.552530i
$695$	24.6443	−	25.6576i	0.934810	−	0.973250i
$696$	−9.40265	+	9.95077i	−0.356407	+	0.377183i
$697$	−4.88887	+	4.88887i	−0.185179	+	0.185179i
$698$	−8.69550	−	32.4520i	−0.329130	−	1.22833i
$699$	−7.49619	+	2.23789i	−0.283532	+	0.0846447i
$700$	1.67703	+	13.1220i	0.0633859	+	0.495966i
$701$	13.0379			0.492434			0.246217	−	0.969215i	$-0.420812\pi$
$701$	13.0379			0.492434			0.246217	+	0.969215i	$0.420812\pi$
$702$	16.9152	−	11.7856i	0.638422	−	0.444821i
$703$	4.26550	+	15.9190i	0.160876	+	0.600398i
$704$	2.45075	−	1.41494i	0.0923660	−	0.0533275i
$705$	7.16601	−	0.347518i	0.269888	−	0.0130883i
$706$	−21.7963	+	12.5841i	−0.820316	+	0.473610i
$707$	15.8454	−	1.37928i	0.595928	−	0.0518733i
$708$	−16.6667	+	10.2623i	−0.626372	+	0.385682i
$709$			27.4813i			1.03208i	0.856564	+	0.516041i	$0.172595\pi$
$709$			27.4813i			1.03208i	−0.856564	+	0.516041i	$0.827405\pi$
$710$	−20.8007	−	11.4570i	−0.780638	−	0.429974i
$711$	−5.27109	−	2.65747i	−0.197681	−	0.0996631i
$712$	−3.35216	+	12.5104i	−0.125628	+	0.468848i
$713$	2.53134	+	9.44708i	0.0947993	+	0.353796i
$714$	4.39313	+	1.90134i	0.164409	+	0.0711558i
$715$	−21.4852	+	12.9884i	−0.803501	+	0.485739i
$716$	−8.49562	+	14.7148i	−0.317496	+	0.549920i
$717$	9.00924	+	4.86675i	0.336456	+	0.181752i
$718$	4.11233	−	15.3474i	0.153471	−	0.572761i
$719$	−8.55504	−	14.8178i	−0.319049	−	0.552610i	0.661241	−	0.750174i	$-0.270030\pi$
$719$	−8.55504	−	14.8178i	−0.319049	−	0.552610i	−0.980290	+	0.197564i	$0.936697\pi$
$720$	−6.59370	−	1.23413i	−0.245733	−	0.0459935i
$721$	6.53174	−	36.9485i	0.243255	−	1.37603i
$722$	2.13588	+	7.97122i	0.0794893	+	0.296658i
$723$	40.3781	+	21.8121i	1.50168	+	0.811199i
$724$	−10.8648			−0.403785
$725$	−39.4888	+	1.59173i	−1.46658	+	0.0591152i
$726$	−3.55898	+	3.76645i	−0.132086	+	0.139786i
$727$	14.2425	−	3.81626i	0.528224	−	0.141537i	0.0151557	−	0.999885i	$-0.495176\pi$
$727$	14.2425	−	3.81626i	0.528224	−	0.141537i	0.513068	+	0.858348i	$0.328509\pi$
$728$	0.910301	+	10.4577i	0.0337380	+	0.387587i
$729$	26.6113	−	4.56486i	0.985604	−	0.169069i
$730$	−1.38639	+	5.62492i	−0.0513126	+	0.208188i
$731$	5.60679	−	3.23708i	0.207375	−	0.119728i
$732$	−3.99558	−	6.48906i	−0.147681	−	0.239843i
$733$	1.53457	+	5.72709i	0.0566806	+	0.211535i	0.988458	−	0.151495i	$-0.0484088\pi$
$733$	1.53457	+	5.72709i	0.0566806	+	0.211535i	−0.931777	+	0.363030i	$0.881742\pi$
$734$	−6.98644	−	12.1009i	−0.257874	−	0.446651i
$735$	27.0895	+	1.07568i	0.999213	+	0.0396769i
$736$	4.54894	−	7.87899i	0.167676	−	0.290423i
$737$	−20.0717	−	5.37819i	−0.739349	−	0.198108i
$738$	−14.8127	−	13.2233i	−0.545261	−	0.486757i
$739$	−19.7361	−	11.3947i	−0.726005	−	0.419159i	0.0909539	−	0.995855i	$-0.471008\pi$
$739$	−19.7361	−	11.3947i	−0.726005	−	0.419159i	−0.816959	+	0.576696i	$0.804342\pi$
$740$	−11.2387	+	0.226414i	−0.413142	+	0.00832314i
$741$	−15.4730	+	16.3750i	−0.568415	+	0.601551i
$742$	26.7234	−	18.6944i	0.981046	−	0.686294i
$743$	−9.69757	+	36.1918i	−0.355769	+	1.32775i	0.523744	+	0.851876i	$0.324535\pi$
$743$	−9.69757	+	36.1918i	−0.355769	+	1.32775i	−0.879513	+	0.475874i	$0.842132\pi$
$744$	−1.81145	−	0.430805i	−0.0664111	−	0.0157941i
$745$	−8.13276	+	32.9966i	−0.297961	+	1.20890i
$746$	6.43646	−	11.1483i	0.235655	−	0.408167i
$747$	16.3727	+	3.40716i	0.599047	+	0.124661i
$748$	2.09026	−	2.09026i	0.0764274	−	0.0764274i
$749$	−16.2306	−	13.6312i	−0.593054	−	0.498075i
$750$	−11.1307	−	15.8464i	−0.406435	−	0.578628i
$751$	3.12743	−	5.41688i	0.114122	−	0.197665i	−0.803307	−	0.595566i	$-0.796928\pi$
$751$	3.12743	−	5.41688i	0.114122	−	0.197665i	0.917428	+	0.397901i	$0.130261\pi$
$752$	−1.30987	−	1.30987i	−0.0477659	−	0.0477659i
$753$	−32.8797	+	20.2454i	−1.19820	+	0.737782i
$754$	−31.3604			−1.14208
$755$	−5.84878	+	6.08929i	−0.212859	+	0.221612i
$756$	−4.73768	+	12.9056i	−0.172308	+	0.469372i
$757$	5.05461	−	5.05461i	0.183713	−	0.183713i	−0.609259	−	0.792972i	$-0.708533\pi$
$757$	5.05461	−	5.05461i	0.183713	−	0.183713i	0.792972	+	0.609259i	$0.208533\pi$
$758$	6.64161	+	6.64161i	0.241234	+	0.241234i
$759$	10.3175	−	43.3832i	0.374502	−	1.57471i
$760$	7.32913	−	0.147652i	0.265855	−	0.00535592i
$761$	−6.24885	−	3.60778i	−0.226521	−	0.130782i	0.382445	−	0.923978i	$-0.375082\pi$
$761$	−6.24885	−	3.60778i	−0.226521	−	0.130782i	−0.608966	+	0.793196i	$0.708415\pi$
$762$	−13.4718	+	8.29510i	−0.488030	+	0.300500i
$763$	−4.01990	−	5.74638i	−0.145530	−	0.208033i
$764$			24.8433i			0.898800i
$765$	−6.98670	+	0.537436i	−0.252605	+	0.0194310i
$766$	5.07003	+	2.92718i	0.183188	+	0.105763i
$767$	−43.3073	−	11.6041i	−1.56373	−	0.419001i
$768$	0.908144	+	1.47488i	0.0327698	+	0.0532202i
$769$	5.97633	+	10.3513i	0.215512	+	0.373277i	0.953431	−	0.301612i	$-0.0975247\pi$
$769$	5.97633	+	10.3513i	0.215512	+	0.373277i	−0.737919	+	0.674889i	$0.764191\pi$
$770$	6.77505	−	15.3097i	0.244156	−	0.551722i
$771$	0.152136	+	0.143756i	0.00547905	+	0.00517725i
$772$	−10.4058	+	10.4058i	−0.374512	+	0.374512i
$773$	0.457178	+	1.70621i	0.0164436	+	0.0613682i	0.973660	−	0.228004i	$-0.0732200\pi$
$773$	0.457178	+	1.70621i	0.0164436	+	0.0613682i	−0.957217	+	0.289373i	$0.906553\pi$
$774$	10.1931	+	15.5503i	0.366385	+	0.558946i
$775$	−2.87283	−	4.54292i	−0.103195	−	0.163187i
$776$	4.56174	+	2.63372i	0.163757	+	0.0945452i
$777$	−3.36647	+	22.7898i	−0.120772	+	0.817579i
$778$	3.59848	−	13.4297i	0.129012	−	0.481478i
$779$	18.7915	+	10.8493i	0.673277	+	0.388716i
$780$	−8.31876	−	12.9199i	−0.297859	−	0.462606i
$781$	15.0268	+	26.0272i	0.537701	+	0.931326i
$782$	2.45971	−	9.17975i	0.0879589	−	0.328267i
$783$	−37.1828	−	17.4439i	−1.32880	−	0.623395i
$784$	−4.49480	−	5.36626i	−0.160529	−	0.191652i
$785$	−21.8840	+	39.7314i	−0.781072	+	1.41807i
$786$	−12.7795	−	12.0756i	−0.455831	−	0.430722i
$787$	−23.5303	−	23.5303i	−0.838765	−	0.838765i	0.149931	−	0.988696i	$-0.452095\pi$
$787$	−23.5303	−	23.5303i	−0.838765	−	0.838765i	−0.988696	+	0.149931i	$0.952095\pi$
$788$	−15.6701	−	15.6701i	−0.558225	−	0.558225i
$789$	31.6090	−	9.43644i	1.12531	−	0.335946i
$790$	−2.12276	+	3.85397i	−0.0755243	+	0.137118i
$791$	20.2537	−	24.1159i	0.720138	−	0.857462i
$792$	6.33322	+	5.65369i	0.225041	+	0.200895i
$793$	4.51800	−	16.8614i	0.160439	−	0.598766i
$794$	8.90802	+	15.4291i	0.316134	+	0.547560i
$795$	−21.8397	+	42.4525i	−0.774575	+	1.50563i
$796$	4.67808	+	2.70089i	0.165810	+	0.0957304i
$797$	7.18855	−	26.8280i	0.254631	−	0.950298i	−0.713664	−	0.700489i	$-0.752965\pi$
$797$	7.18855	−	26.8280i	0.254631	−	0.950298i	0.968295	−	0.249809i	$-0.0803678\pi$
$798$	2.19539	−	14.8620i	0.0777161	−	0.526110i
$799$	−1.67579	−	0.967518i	−0.0592852	−	0.0342283i
$800$	−1.09853	+	4.87783i	−0.0388389	+	0.172457i
$801$	−38.7930	+	2.19913i	−1.37068	+	0.0777025i
$802$	−8.71718	−	32.5330i	−0.307814	−	1.14878i
$803$	5.18430	−	5.18430i	0.182950	−	0.182950i
$804$	2.94265	−	12.3733i	0.103779	−	0.436373i
$805$	−5.74658	−	53.5161i	−0.202540	−	1.88619i
$806$	−2.13260	−	3.69377i	−0.0751176	−	0.130107i
$807$	−51.9016	+	1.46994i	−1.82702	+	0.0517445i
$808$	5.80681	+	1.55593i	0.204283	+	0.0547374i
$809$	−12.3716	−	7.14276i	−0.434963	−	0.251126i	0.266496	−	0.963836i	$-0.414134\pi$
$809$	−12.3716	−	7.14276i	−0.434963	−	0.251126i	−0.701459	+	0.712710i	$0.747468\pi$
$810$	−2.67666	−	19.9458i	−0.0940484	−	0.700824i
$811$			34.3236i			1.20526i	0.798019	+	0.602632i	$0.205881\pi$
$811$			34.3236i			1.20526i	−0.798019	+	0.602632i	$0.794119\pi$
$812$	17.1358	−	11.9874i	0.601347	−	0.420674i
$813$	5.89773	+	3.18593i	0.206843	+	0.111735i
$814$	12.3202	+	7.11304i	0.431821	+	0.249312i
$815$	10.1989	−	0.205467i	0.357252	−	0.00719719i
$816$	1.31507	+	1.24263i	0.0460365	+	0.0435007i
$817$	−14.3674	−	14.3674i	−0.502651	−	0.502651i
$818$	−1.60883	+	1.60883i	−0.0562513	+	0.0562513i
$819$	−28.9409	+	12.4157i	−1.01128	+	0.433839i
$820$	−10.2523	+	10.6738i	−0.358024	+	0.372746i
$821$	14.8319			0.517638			0.258819	−	0.965926i	$-0.416667\pi$
$821$	14.8319			0.517638			0.258819	+	0.965926i	$0.416667\pi$
$822$	1.29917	+	0.701804i	0.0453136	+	0.0244782i
$823$	0.0226406	+	0.0226406i	0.000789202	+	0.000789202i	0.707501	−	0.706712i	$-0.249822\pi$
$823$	0.0226406	+	0.0226406i	0.000789202	+	0.000789202i	−0.706712	+	0.707501i	$0.749822\pi$
$824$	7.09087	−	12.2818i	0.247022	−	0.427855i
$825$	1.67991	+	24.4498i	0.0584869	+	0.851233i
$826$	28.0993	−	10.2133i	0.977700	−	0.355368i
$827$	−15.6441	+	15.6441i	−0.544000	+	0.544000i	−0.924699	−	0.380699i	$-0.875683\pi$
$827$	−15.6441	+	15.6441i	−0.544000	+	0.544000i	0.380699	+	0.924699i	$0.375683\pi$
$828$	26.7212	+	5.56066i	0.928625	+	0.193246i
$829$	22.6293	−	39.1951i	0.785948	−	1.36130i	−0.142482	−	0.989797i	$-0.545508\pi$
$829$	22.6293	−	39.1951i	0.785948	−	1.36130i	0.928431	−	0.371505i	$-0.121158\pi$
$830$	2.98300	−	12.1028i	0.103542	−	0.420093i
$831$	5.70897	+	19.1232i	0.198042	+	0.663376i
$832$	−1.02688	+	3.83238i	−0.0356008	+	0.132864i
$833$	−5.98608	−	4.19933i	−0.207405	−	0.145498i
$834$	−7.88300	−	26.4055i	−0.272966	−	0.914348i
$835$	−7.95012	+	0.160163i	−0.275125	+	0.00554267i
$836$	−8.03441	−	4.63867i	−0.277876	−	0.160432i
$837$	−0.473912	−	5.56579i	−0.0163808	−	0.192382i
$838$	8.30246	+	2.22464i	0.286804	+	0.0768488i
$839$	8.81891	−	15.2748i	0.304462	−	0.527344i	−0.672679	−	0.739934i	$-0.734857\pi$
$839$	8.81891	−	15.2748i	0.304462	−	0.527344i	0.977141	+	0.212590i	$0.0681899\pi$
$840$	9.48405	+	3.87979i	0.327231	+	0.133865i
$841$	16.7380	+	28.9910i	0.577171	+	0.999689i
$842$	0.101757	+	0.379761i	0.00350677	+	0.0130874i
$843$	−9.23294	+	0.261493i	−0.317999	+	0.00900628i
$844$	−9.46309	+	5.46352i	−0.325733	+	0.188062i
$845$	1.46711	−	5.95241i	0.0504700	−	0.204769i
$846$	2.50180	−	4.96231i	0.0860137	−	0.170608i
$847$	6.48602	−	4.53732i	0.222862	−	0.155904i
$848$	11.9066	−	3.19037i	0.408875	−	0.109558i
$849$	−7.26722	−	1.72831i	−0.249410	−	0.0593155i
$850$	0.210358	+	5.21873i	0.00721522	+	0.179001i
$851$	45.7360			1.56781
$852$	−15.6634	+	9.64459i	−0.536619	+	0.330418i
$853$	9.57032	+	35.7169i	0.327682	+	1.22292i	0.911589	+	0.411104i	$0.134857\pi$
$853$	9.57032	+	35.7169i	0.327682	+	1.22292i	−0.583907	+	0.811821i	$0.698477\pi$
$854$	3.97650	+	10.9403i	0.136073	+	0.374369i
$855$	7.30436	+	20.7434i	0.249804	+	0.709408i
$856$	−4.00555	−	6.93781i	−0.136907	−	0.237130i
$857$	−13.1441	+	49.0545i	−0.448994	+	1.67567i	0.256176	+	0.966630i	$0.417537\pi$
$857$	−13.1441	+	49.0545i	−0.448994	+	1.67567i	−0.705170	+	0.709039i	$0.749129\pi$
$858$	0.550553	+	19.4393i	0.0187956	+	0.663645i
$859$	2.42379	−	4.19813i	0.0826987	−	0.143238i	−0.821710	−	0.569906i	$-0.806979\pi$
$859$	2.42379	−	4.19813i	0.0826987	−	0.143238i	0.904408	+	0.426668i	$0.140313\pi$
$860$	11.8600	−	7.16968i	0.404422	−	0.244484i
$861$	18.0828	+	24.3511i	0.616262	+	0.829884i
$862$	−8.92248	−	33.2992i	−0.303901	−	1.13417i
$863$	10.9835	−	40.9910i	0.373883	−	1.39535i	−0.481086	−	0.876673i	$-0.659758\pi$
$863$	10.9835	−	40.9910i	0.373883	−	1.39535i	0.854970	−	0.518678i	$-0.173576\pi$
$864$	−3.34926	+	3.97271i	−0.113944	+	0.135154i
$865$	31.5742	+	17.3910i	1.07356	+	0.591312i
$866$			26.9707i			0.916503i
$867$	−24.2437	−	13.0963i	−0.823360	−	0.444775i
$868$	2.57721	+	1.20315i	0.0874761	+	0.0408376i
$869$	4.82233	−	2.78417i	0.163586	−	0.0944466i
$870$	−14.0042	+	27.2217i	−0.474788	+	0.922902i
$871$	25.2306	−	14.5669i	0.854907	−	0.493581i
$872$	−0.686031	−	2.56030i	−0.0232319	−	0.0867028i
$873$	−3.21949	+	15.4709i	−0.108963	+	0.523611i
$874$	−29.8260			−1.00888
$875$	11.7654	+	27.1399i	0.397744	+	0.917497i
$876$	3.26165	+	3.08199i	0.110201	+	0.104131i
$877$	−8.33053	−	31.0899i	−0.281302	−	1.04983i	−0.951500	−	0.307650i	$-0.900457\pi$
$877$	−8.33053	−	31.0899i	−0.281302	−	1.04983i	0.670198	−	0.742183i	$-0.266209\pi$
$878$	−3.99672	+	3.99672i	−0.134883	+	0.134883i
$879$	0.246841	+	0.826836i	0.00832573	+	0.0278885i
$880$	4.38340	−	4.56365i	0.147764	−	0.153840i
$881$		−	10.7334i		−	0.361616i	−0.983518	−	0.180808i	$-0.942129\pi$
$881$		−	10.7334i		−	0.361616i	0.983518	−	0.180808i	$-0.0578713\pi$
$882$	11.0679	−	17.8466i	0.372674	−	0.600927i
$883$	−5.36522	−	5.36522i	−0.180554	−	0.180554i	0.611043	−	0.791597i	$-0.290750\pi$
$883$	−5.36522	−	5.36522i	−0.180554	−	0.180554i	−0.791597	+	0.611043i	$0.790750\pi$
$884$			4.14450i			0.139395i
$885$	−29.4119	+	32.4100i	−0.988670	+	1.08945i
$886$	25.1477			0.844853
$887$	−43.5535	+	11.6701i	−1.46238	+	0.391844i	−0.900312	−	0.435246i	$-0.856662\pi$
$887$	−43.5535	+	11.6701i	−1.46238	+	0.391844i	−0.562070	+	0.827090i	$0.689995\pi$
$888$	−4.13838	+	7.66088i	−0.138875	+	0.257082i
$889$	22.7128	−	8.25550i	0.761764	−	0.276881i
$890$	0.583330	+	28.9551i	0.0195533	+	0.970578i
$891$	−10.1601	+	23.3546i	−0.340377	+	0.782408i
$892$	16.5823	−	4.44321i	0.555216	−	0.148770i
$893$	−1.57179	+	5.86599i	−0.0525979	+	0.196298i
$894$	19.1333	+	18.0794i	0.639915	+	0.604666i
$895$	−9.09228	+	36.8896i	−0.303921	+	1.23308i
$896$	−0.903808	−	2.48659i	−0.0301941	−	0.0830711i
$897$	32.7808	+	53.2381i	1.09452	+	1.77757i
$898$	5.20774	+	5.20774i	0.173784	+	0.173784i
$899$	−4.24854	+	7.35869i	−0.141697	+	0.245426i
$900$	−14.9296	+	1.45145i	−0.497654	+	0.0483816i
$901$	11.1512	−	6.43815i	0.371501	−	0.214486i
$902$	18.0920	−	4.84775i	0.602399	−	0.161412i
$903$	−10.4541	−	26.4079i	−0.347890	−	0.878800i
$904$	10.3084	−	5.95155i	0.342852	−	0.197946i
$905$	−23.3351	+	6.75922i	−0.775685	+	0.224684i
$906$	1.87086	+	6.26678i	0.0621552	+	0.208200i
$907$	3.69728	+	0.990682i	0.122766	+	0.0328951i	0.319679	−	0.947526i	$-0.396425\pi$
$907$	3.69728	+	0.990682i	0.122766	+	0.0328951i	−0.196913	+	0.980421i	$0.563092\pi$
$908$	18.3767	+	4.92402i	0.609852	+	0.163409i
$909$	1.02074	+	18.0060i	0.0338559	+	0.597223i
$910$	8.46109	+	21.8945i	0.280483	+	0.725795i
$911$	7.24086	−	12.5415i	0.239900	−	0.415520i	−0.720785	−	0.693159i	$-0.756219\pi$
$911$	7.24086	−	12.5415i	0.239900	−	0.415520i	0.960686	+	0.277639i	$0.0895519\pi$
$912$	2.69878	−	4.99593i	0.0893655	−	0.165432i
$913$	−11.1547	+	11.1547i	−0.369167	+	0.369167i
$914$			7.66750i			0.253618i
$915$	−12.6186	−	11.4513i	−0.417159	−	0.378570i
$916$	−4.83035	−	2.78880i	−0.159599	−	0.0921447i
$917$	15.3951	+	22.0070i	0.508391	+	0.726736i
$918$	−2.30534	+	4.91397i	−0.0760876	+	0.162185i
$919$	16.5778	−	9.57120i	0.546851	−	0.315725i	−0.201000	−	0.979591i	$-0.564419\pi$
$919$	16.5778	−	9.57120i	0.546851	−	0.315725i	0.747851	+	0.663867i	$0.231086\pi$
$920$	4.86841	−	19.7523i	0.160507	−	0.651215i
$921$	10.1900	−	42.8471i	0.335772	−	1.41186i
$922$	−15.7845	+	4.22945i	−0.519836	+	0.139290i
$923$	−40.7003	−	10.9056i	−1.33967	−	0.358963i
$924$	−7.73140	−	10.4114i	−0.254344	−	0.342511i
$925$	−23.9973	+	7.47813i	−0.789027	+	0.245879i
$926$	−19.7063	−	34.1323i	−0.647589	−	1.12166i
$927$	41.6529	+	8.66794i	1.36806	+	0.284692i
$928$	7.63484	−	2.04575i	0.250626	−	0.0671550i
$929$	20.5600			0.674552			0.337276	−	0.941406i	$-0.390494\pi$
$929$	20.5600			0.674552			0.337276	+	0.941406i	$0.390494\pi$
$930$	−4.15862	+	0.201674i	−0.136367	+	0.00661314i
$931$	−7.86777	+	21.5576i	−0.257856	+	0.706522i
$932$	4.36277	+	1.16900i	0.142907	+	0.0382919i
$933$	−14.8404	+	9.13783i	−0.485853	+	0.299159i
$934$	6.17565	+	10.6965i	0.202074	+	0.350002i
$935$	3.18902	−	5.78981i	0.104292	−	0.189347i
$936$	−11.8837	+	0.673671i	−0.388429	+	0.0220196i
$937$	1.94812	+	1.94812i	0.0636423	+	0.0636423i	0.738212	−	0.674569i	$-0.235671\pi$
$937$	1.94812	+	1.94812i	0.0636423	+	0.0636423i	−0.674569	+	0.738212i	$0.735671\pi$
$938$	−8.21822	+	17.6039i	−0.268335	+	0.574786i
$939$	3.56933	+	0.848867i	0.116481	+	0.0277017i
$940$	−3.62821	−	1.99841i	−0.118339	−	0.0651809i
$941$		−	0.496104i		−	0.0161725i	−0.999967	−	0.00808626i	$-0.997426\pi$
$941$		−	0.496104i		−	0.0161725i	0.999967	−	0.00808626i	$-0.00257397\pi$
$942$	18.4221	+	29.9186i	0.600224	+	0.974801i
$943$	42.5796	−	42.5796i	1.38658	−	1.38658i
$944$	11.3003			0.367795
$945$	−2.14662	+	30.6658i	−0.0698295	+	0.997559i
$946$	−17.5390			−0.570242
$947$	18.6508	−	18.6508i	0.606070	−	0.606070i	−0.335846	−	0.941917i	$-0.609022\pi$
$947$	18.6508	−	18.6508i	0.606070	−	0.606070i	0.941917	+	0.335846i	$0.109022\pi$
$948$	1.78695	+	2.90212i	0.0580375	+	0.0942565i
$949$			10.2793i			0.333680i
$950$	15.6495	−	4.87675i	0.507737	−	0.158223i
$951$	28.5377	+	6.78692i	0.925399	+	0.220081i
$952$	−1.58422	−	2.26461i	−0.0513448	−	0.0733965i
$953$	2.24563	+	2.24563i	0.0727433	+	0.0727433i	0.742542	−	0.669799i	$-0.233620\pi$
$953$	2.24563	+	2.24563i	0.0727433	+	0.0727433i	−0.669799	+	0.742542i	$0.733620\pi$
$954$	20.2729	+	30.9277i	0.656359	+	1.00132i
$955$	15.4556	+	53.3580i	0.500132	+	1.72663i
$956$	−2.95595	−	5.11986i	−0.0956023	−	0.165588i
$957$	32.9899	−	20.3132i	1.06641	−	0.656633i
$958$	7.13746	+	1.91248i	0.230601	+	0.0617893i
$959$	−1.72722	−	1.45060i	−0.0557747	−	0.0468423i
$960$	2.86805	+	2.60274i	0.0925660	+	0.0840032i
$961$	29.8443			0.962721
$962$	−19.2658	+	5.16225i	−0.621154	+	0.166438i
$963$	16.0050	−	17.9287i	0.515755	−	0.577744i
$964$	−13.2481	−	22.9464i	−0.426694	−	0.739055i
$965$	−15.8757	+	28.8230i	−0.511055	+	0.927846i
$966$	−38.2619	−	16.5597i	−1.23106	−	0.532799i
$967$	26.8436	+	7.19271i	0.863231	+	0.231302i	0.663159	−	0.748479i	$-0.269216\pi$
$967$	26.8436	+	7.19271i	0.863231	+	0.231302i	0.200073	+	0.979781i	$0.435882\pi$
$968$	2.88985	−	0.774332i	0.0928832	−	0.0248880i
$969$	1.37236	−	5.77053i	0.0440867	−	0.185376i
$970$	11.4361	+	2.81869i	0.367192	+	0.0905028i
$971$	35.0246	−	20.2215i	1.12399	−	0.648938i	0.181577	−	0.983377i	$-0.441880\pi$
$971$	35.0246	−	20.2215i	1.12399	−	0.648938i	0.942418	+	0.334438i	$0.108547\pi$
$972$	−14.4647	−	5.81142i	−0.463955	−	0.186402i
$973$	3.65033	+	41.9356i	0.117024	+	1.34439i
$974$	−26.5694	−	15.3399i	−0.851340	−	0.491521i
$975$	−25.9046	−	22.5738i	−0.829612	−	0.722939i
$976$			4.39972i			0.140832i
$977$	18.5018	−	18.5018i	0.591924	−	0.591924i	−0.346227	−	0.938151i	$-0.612537\pi$
$977$	18.5018	−	18.5018i	0.591924	−	0.591924i	0.938151	+	0.346227i	$0.112537\pi$
$978$	3.75551	−	6.95213i	0.120088	−	0.222304i
$979$	18.3259	−	31.7415i	0.585700	−	1.01446i
$980$	−12.9923	−	8.72923i	−0.415025	−	0.278845i
$981$	6.65044	−	4.35932i	0.212332	−	0.139182i
$982$	11.8668	+	3.17969i	0.378684	+	0.101468i
$983$	22.1239	+	5.92807i	0.705641	+	0.189076i	0.593756	−	0.804645i	$-0.297644\pi$
$983$	22.1239	+	5.92807i	0.705641	+	0.189076i	0.111885	+	0.993721i	$0.464311\pi$
$984$	3.27941	+	10.9850i	0.104544	+	0.350188i
$985$	−43.4048	−	23.9072i	−1.38299	−	0.761748i
$986$	7.15046	−	4.12832i	0.227717	−	0.131472i
$987$	−5.27320	+	6.65244i	−0.167848	+	0.211749i
$988$	12.5639	−	3.36649i	0.399711	−	0.107102i
$989$	−48.8323	+	28.1934i	−1.55278	+	0.896497i
$990$	17.1197	+	8.20285i	0.544098	+	0.260704i
$991$	9.26515	−	16.0477i	0.294317	−	0.509772i	−0.680509	−	0.732740i	$-0.738241\pi$
$991$	9.26515	−	16.0477i	0.294317	−	0.509772i	0.974826	+	0.222968i	$0.0715745\pi$
$992$	0.760149	+	0.760149i	0.0241348	+	0.0241348i
$993$	−30.9234	−	50.2215i	−0.981325	−	1.59373i
$994$	26.4079	−	9.59854i	0.837606	−	0.304447i
$995$	11.7278	+	2.89057i	0.371795	+	0.0916374i
$996$	−7.01789	−	6.63132i	−0.222370	−	0.210121i
$997$	3.69013	−	13.7718i	0.116868	−	0.436156i	−0.882552	−	0.470215i	$-0.844177\pi$
$997$	3.69013	−	13.7718i	0.116868	−	0.436156i	0.999420	+	0.0340583i	$0.0108432\pi$
$998$	−39.9002	+	10.6912i	−1.26302	+	0.338425i
$999$	−25.7141	−	4.59574i	−0.813559	−	0.145403i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bw.a.493.17	yes	192
5.2	odd	4	inner	630.2.bw.a.367.20	yes	192
7.5	odd	6		630.2.cg.a.313.47	yes	192
9.4	even	3		630.2.cg.a.283.11	yes	192
35.12	even	12		630.2.cg.a.187.11	yes	192
45.22	odd	12		630.2.cg.a.157.47	yes	192
63.40	odd	6	inner	630.2.bw.a.103.20	✓	192
315.292	even	12	inner	630.2.bw.a.607.17	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bw.a.103.20	✓	192	63.40	odd	6	inner
630.2.bw.a.367.20	yes	192	5.2	odd	4	inner
630.2.bw.a.493.17	yes	192	1.1	even	1	trivial
630.2.bw.a.607.17	yes	192	315.292	even	12	inner
630.2.cg.a.157.47	yes	192	45.22	odd	12
630.2.cg.a.187.11	yes	192	35.12	even	12
630.2.cg.a.283.11	yes	192	9.4	even	3
630.2.cg.a.313.47	yes	192	7.5	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bw (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.908144 + 1.47488i) q^{3} -1.00000i q^{4} +(-0.622124 - 2.14778i) q^{5} +(-1.68505 - 0.400744i) q^{6} +(2.39737 + 1.11920i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.35055 + 2.67881i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.908144 + 1.47488i) q^{3} -1.00000i q^{4} +(-0.622124 - 2.14778i) q^{5} +(-1.68505 - 0.400744i) q^{6} +(2.39737 + 1.11920i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.35055 + 2.67881i) q^{9} +(1.95862 + 1.07880i) q^{10} +(-1.41494 - 2.45075i) q^{11} +(1.47488 - 0.908144i) q^{12} +(3.83238 + 1.02688i) q^{13} +(-2.48659 + 0.903808i) q^{14} +(2.60274 - 2.86805i) q^{15} -1.00000 q^{16} +(-1.00900 + 0.270360i) q^{17} +(-0.939221 - 2.84919i) q^{18} +(1.63918 + 2.83913i) q^{19} +(-2.14778 + 0.622124i) q^{20} +(0.526479 + 4.55223i) q^{21} +(2.73345 + 0.732426i) q^{22} +(8.78787 - 2.35470i) q^{23} +(-0.400744 + 1.68505i) q^{24} +(-4.22592 + 2.67237i) q^{25} +(-3.43602 + 1.98379i) q^{26} +(-5.17742 + 0.440843i) q^{27} +(1.11920 - 2.39737i) q^{28} +(6.84521 + 3.95209i) q^{29} +(0.187601 + 3.86844i) q^{30} +1.07501i q^{31} +(0.707107 - 0.707107i) q^{32} +(2.32959 - 4.31250i) q^{33} +(0.522296 - 0.904644i) q^{34} +(0.912324 - 5.84531i) q^{35} +(2.67881 + 1.35055i) q^{36} +(4.85581 + 1.30111i) q^{37} +(-3.16664 - 0.848500i) q^{38} +(1.96582 + 6.58487i) q^{39} +(1.07880 - 1.95862i) q^{40} +(5.73201 - 3.30938i) q^{41} +(-3.59119 - 2.84664i) q^{42} +(-5.98661 + 1.60411i) q^{43} +(-2.45075 + 1.41494i) q^{44} +(6.59370 + 1.23413i) q^{45} +(-4.54894 + 7.87899i) q^{46} +(1.30987 + 1.30987i) q^{47} +(-0.908144 - 1.47488i) q^{48} +(4.49480 + 5.36626i) q^{49} +(1.09853 - 4.87783i) q^{50} +(-1.31507 - 1.24263i) q^{51} +(1.02688 - 3.83238i) q^{52} +(-11.9066 + 3.19037i) q^{53} +(3.34926 - 3.97271i) q^{54} +(-4.38340 + 4.56365i) q^{55} +(0.903808 + 2.48659i) q^{56} +(-2.69878 + 4.99593i) q^{57} +(-7.63484 + 2.04575i) q^{58} -11.3003 q^{59} +(-2.86805 - 2.60274i) q^{60} -4.39972i q^{61} +(-0.760149 - 0.760149i) q^{62} +(-6.23588 + 4.91058i) q^{63} +1.00000i q^{64} +(-0.178694 - 8.86997i) q^{65} +(1.40213 + 4.69667i) q^{66} +(5.19227 - 5.19227i) q^{67} +(0.270360 + 1.00900i) q^{68} +(11.4536 + 10.8227i) q^{69} +(3.48815 + 4.77837i) q^{70} -10.6201 q^{71} +(-2.84919 + 0.939221i) q^{72} +(0.670554 + 2.50254i) q^{73} +(-4.35360 + 2.51355i) q^{74} +(-7.77918 - 3.80584i) q^{75} +(2.83913 - 1.63918i) q^{76} +(-0.649273 - 7.45895i) q^{77} +(-6.04625 - 3.26616i) q^{78} +1.96770i q^{79} +(0.622124 + 2.14778i) q^{80} +(-5.35203 - 7.23573i) q^{81} +(-1.71306 + 6.39323i) q^{82} +(-1.44279 - 5.38455i) q^{83} +(4.55223 - 0.526479i) q^{84} +(1.20840 + 1.99891i) q^{85} +(3.09890 - 5.36745i) q^{86} +(0.387581 + 13.6849i) q^{87} +(0.732426 - 2.73345i) q^{88} +(6.47588 + 11.2166i) q^{89} +(-5.53512 + 3.78979i) q^{90} +(8.03837 + 6.75101i) q^{91} +(-2.35470 - 8.78787i) q^{92} +(-1.58552 + 0.976266i) q^{93} -1.85243 q^{94} +(5.07807 - 5.28688i) q^{95} +(1.68505 + 0.400744i) q^{96} +(5.08796 - 1.36332i) q^{97} +(-6.97282 - 0.616214i) q^{98} +(8.47603 - 0.480497i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \) 192 * q	\( 192 q + 8 q^{11} - 12 q^{15} - 192 q^{16} + 36 q^{17} - 8 q^{18} + 8 q^{23} + 36 q^{27} + 12 q^{30} + 48 q^{35} - 16 q^{36} - 12 q^{41} + 4 q^{42} + 48 q^{45} + 12 q^{46} - 16 q^{50} - 24 q^{51} - 40 q^{53} - 4 q^{56} - 32 q^{57} - 12 q^{58} - 16 q^{60} - 12 q^{63} + 16 q^{65} - 36 q^{68} + 16 q^{71} - 8 q^{72} + 96 q^{75} - 64 q^{77} - 16 q^{78} + 16 q^{81} + 168 q^{83} + 8 q^{86} - 36 q^{87} - 36 q^{90} + 8 q^{92} - 48 q^{93} - 128 q^{95} - 48 q^{98}+O(q^{100}) \) 192 * q + 8 * q^11 - 12 * q^15 - 192 * q^16 + 36 * q^17 - 8 * q^18 + 8 * q^23 + 36 * q^27 + 12 * q^30 + 48 * q^35 - 16 * q^36 - 12 * q^41 + 4 * q^42 + 48 * q^45 + 12 * q^46 - 16 * q^50 - 24 * q^51 - 40 * q^53 - 4 * q^56 - 32 * q^57 - 12 * q^58 - 16 * q^60 - 12 * q^63 + 16 * q^65 - 36 * q^68 + 16 * q^71 - 8 * q^72 + 96 * q^75 - 64 * q^77 - 16 * q^78 + 16 * q^81 + 168 * q^83 + 8 * q^86 - 36 * q^87 - 36 * q^90 + 8 * q^92 - 48 * q^93 - 128 * q^95 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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