LMFDB - Embedded newform 845.2.t.i.427.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(188,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 5]))

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

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

chi := DirichletCharacter("845.188");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$845 = 5 \cdot 13^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	845.t (of order $12$ , degree $4$ , 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			427.4
Character	$\chi$	$=$	845.427
Dual form			845.2.t.i.188.4

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.14313 + 1.23734i) q^{2} +(2.72271 + 0.729547i) q^{3} +(2.06202 - 3.57152i) q^{4} +(0.759153 - 2.10326i) q^{5} +(-6.73782 + 1.80539i) q^{6} +(-0.220974 + 0.382738i) q^{7} +5.25630i q^{8} +(4.28282 + 2.47268i) q^{9} +(0.975475 + 5.44689i) q^{10} +(3.98968 + 1.06903i) q^{11} +(8.21985 - 8.21985i) q^{12} -1.09368i q^{14} +(3.60137 - 5.17271i) q^{15} +(-2.37979 - 4.12192i) q^{16} +(-0.346700 - 1.29390i) q^{17} -12.2382 q^{18} +(-0.371174 - 1.38524i) q^{19} +(-5.94643 - 7.04828i) q^{20} +(-0.880871 + 0.880871i) q^{21} +(-9.87318 + 2.64551i) q^{22} +(0.235566 - 0.879145i) q^{23} +(-3.83472 + 14.3114i) q^{24} +(-3.84737 - 3.19339i) q^{25} +(3.87743 + 3.87743i) q^{27} +(0.911303 + 1.57842i) q^{28} +(1.24945 - 0.721369i) q^{29} +(-1.31783 + 15.5419i) q^{30} +(7.50088 + 7.50088i) q^{31} +(1.09625 + 0.632918i) q^{32} +(10.0828 + 5.82132i) q^{33} +(2.34402 + 2.34402i) q^{34} +(0.637242 + 0.755321i) q^{35} +(17.6625 - 10.1974i) q^{36} +(-3.81978 - 6.61605i) q^{37} +(2.50949 + 2.50949i) q^{38} +(11.0553 + 3.99033i) q^{40} +(0.848868 - 3.16802i) q^{41} +(0.797889 - 2.97776i) q^{42} +(-8.12475 + 2.17702i) q^{43} +(12.0449 - 12.0449i) q^{44} +(8.45200 - 7.13071i) q^{45} +(0.582950 + 2.17560i) q^{46} +4.78823 q^{47} +(-3.47234 - 12.9589i) q^{48} +(3.40234 + 5.89303i) q^{49} +(12.1967 + 2.08335i) q^{50} -3.77585i q^{51} +(5.43744 - 5.43744i) q^{53} +(-13.1076 - 3.51216i) q^{54} +(5.27723 - 7.57977i) q^{55} +(-2.01178 - 1.16150i) q^{56} -4.04239i q^{57} +(-1.78516 + 3.09198i) q^{58} +(-2.13003 + 0.570740i) q^{59} +(-11.0483 - 23.5286i) q^{60} +(3.08621 - 5.34547i) q^{61} +(-25.3565 - 6.79426i) q^{62} +(-1.89278 + 1.09280i) q^{63} +6.38663 q^{64} -28.8118 q^{66} +(-8.11555 + 4.68551i) q^{67} +(-5.33610 - 1.42980i) q^{68} +(1.28275 - 2.22180i) q^{69} +(-2.30028 - 0.830268i) q^{70} +(8.38527 - 2.24683i) q^{71} +(-12.9972 + 22.5118i) q^{72} +7.94958i q^{73} +(16.3726 + 9.45272i) q^{74} +(-8.14554 - 11.5015i) q^{75} +(-5.71278 - 1.53074i) q^{76} +(-1.29077 + 1.29077i) q^{77} +13.0958i q^{79} +(-10.4761 + 1.87614i) q^{80} +(0.310283 + 0.537427i) q^{81} +(2.10068 + 7.83983i) q^{82} +5.50169 q^{83} +(1.32968 + 4.96242i) q^{84} +(-2.98461 - 0.253071i) q^{85} +(14.7187 - 14.7187i) q^{86} +(3.92815 - 1.05255i) q^{87} +(-5.61915 + 20.9710i) q^{88} +(3.91732 - 14.6196i) q^{89} +(-9.29066 + 25.7401i) q^{90} +(-2.65414 - 2.65414i) q^{92} +(14.9505 + 25.8950i) q^{93} +(-10.2618 + 5.92466i) q^{94} +(-3.19530 - 0.270935i) q^{95} +(2.52301 + 2.52301i) q^{96} +(-5.09238 - 2.94008i) q^{97} +(-14.5833 - 8.41970i) q^{98} +(14.4437 + 14.4437i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$144 q + 4 q^{3} + 80 q^{4} + 12 q^{10} + 128 q^{12} - 80 q^{16} - 8 q^{17} - 24 q^{22} - 36 q^{23} - 96 q^{25} - 128 q^{27} + 4 q^{30} - 80 q^{35} + 56 q^{38} - 48 q^{40} + 56 q^{42} - 76 q^{43} + 76 q^{48}+ \cdots + 92 q^{95}+O(q^{100})$ 144 * q + 4 * q^3 + 80 * q^4 + 12 * q^10 + 128 * q^12 - 80 * q^16 - 8 * q^17 - 24 * q^22 - 36 * q^23 - 96 * q^25 - 128 * q^27 + 4 * q^30 - 80 * q^35 + 56 * q^38 - 48 * q^40 + 56 * q^42 - 76 * q^43 + 76 * q^48 - 8 * q^49 - 32 * q^53 - 12 * q^55 - 8 * q^61 - 148 * q^62 - 240 * q^64 + 80 * q^66 + 48 * q^68 + 40 * q^69 + 164 * q^75 + 344 * q^77 - 16 * q^81 - 44 * q^82 - 20 * q^87 - 124 * q^88 - 600 * q^90 - 8 * q^92 + 92 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$ .

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{4}\right)$

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

)

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

$2$	−2.14313	+	1.23734i	−1.51542	+	0.874931i	−0.515589	+	0.856836i	$0.672427\pi$
$2$	−2.14313	+	1.23734i	−1.51542	+	0.874931i	−0.999836	+	0.0180946i	$0.994240\pi$
$3$	2.72271	+	0.729547i	1.57196	+	0.421204i	0.936424	−	0.350871i	$-0.114114\pi$
$3$	2.72271	+	0.729547i	1.57196	+	0.421204i	0.635531	+	0.772075i	$0.280781\pi$
$4$	2.06202	−	3.57152i	1.03101	−	1.78576i
$5$	0.759153	−	2.10326i	0.339503	−	0.940605i
$5$	0.759153	−	2.10326i	0.339503	−	0.940605i
$6$	−6.73782	+	1.80539i	−2.75070	+	0.737049i
$7$	−0.220974	+	0.382738i	−0.0835202	+	0.144661i	−0.904760	−	0.425922i	$-0.859950\pi$
$7$	−0.220974	+	0.382738i	−0.0835202	+	0.144661i	0.821239	+	0.570584i	$0.193283\pi$
$8$			5.25630i			1.85838i
$9$	4.28282	+	2.47268i	1.42761	+	0.824228i
$10$	0.975475	+	5.44689i	0.308472	+	1.72246i
$11$	3.98968	+	1.06903i	1.20293	+	0.322325i	0.803986	−	0.594648i	$-0.202708\pi$
$11$	3.98968	+	1.06903i	1.20293	+	0.322325i	0.398949	+	0.916973i	$0.369375\pi$
$12$	8.21985	−	8.21985i	2.37287	−	2.37287i
$13$		0			0
$13$		0			0
$14$		−	1.09368i		−	0.292298i
$15$	3.60137	−	5.17271i	0.929871	−	1.33559i
$16$	−2.37979	−	4.12192i	−0.594948	−	1.03048i
$17$	−0.346700	−	1.29390i	−0.0840872	−	0.313818i	0.911053	−	0.412290i	$-0.135271\pi$
$17$	−0.346700	−	1.29390i	−0.0840872	−	0.313818i	−0.995140	+	0.0984726i	$0.968604\pi$
$18$	−12.2382			−2.88457
$19$	−0.371174	−	1.38524i	−0.0851532	−	0.317796i	0.910190	−	0.414191i	$-0.135935\pi$
$19$	−0.371174	−	1.38524i	−0.0851532	−	0.317796i	−0.995343	+	0.0963949i	$0.969269\pi$
$20$	−5.94643	−	7.04828i	−1.32966	−	1.57604i
$21$	−0.880871	+	0.880871i	−0.192222	+	0.192222i
$22$	−9.87318	+	2.64551i	−2.10497	+	0.564025i
$23$	0.235566	−	0.879145i	0.0491189	−	0.183314i	−0.937008	−	0.349308i	$-0.886417\pi$
$23$	0.235566	−	0.879145i	0.0491189	−	0.183314i	0.986127	+	0.165994i	$0.0530832\pi$
$24$	−3.83472	+	14.3114i	−0.782758	+	2.92129i
$25$	−3.84737	−	3.19339i	−0.769475	−	0.638677i
$26$		0			0
$27$	3.87743	+	3.87743i	0.746212	+	0.746212i
$28$	0.911303	+	1.57842i	0.172220	+	0.298294i
$29$	1.24945	−	0.721369i	0.232017	−	0.133955i	−0.379485	−	0.925198i	$-0.623899\pi$
$29$	1.24945	−	0.721369i	0.232017	−	0.133955i	0.611502	+	0.791243i	$0.290566\pi$
$30$	−1.31783	+	15.5419i	−0.240602	+	2.83756i
$31$	7.50088	+	7.50088i	1.34720	+	1.34720i	0.888690	+	0.458509i	$0.151616\pi$
$31$	7.50088	+	7.50088i	1.34720	+	1.34720i	0.458509	+	0.888690i	$0.348384\pi$
$32$	1.09625	+	0.632918i	0.193791	+	0.111885i
$33$	10.0828	+	5.82132i	1.75520	+	1.01336i
$34$	2.34402	+	2.34402i	0.401996	+	0.401996i
$35$	0.637242	+	0.755321i	0.107714	+	0.127672i
$36$	17.6625	−	10.1974i	2.94374	−	1.69957i
$37$	−3.81978	−	6.61605i	−0.627968	−	1.08767i	−0.987959	−	0.154716i	$-0.950554\pi$
$37$	−3.81978	−	6.61605i	−0.627968	−	1.08767i	0.359991	−	0.932956i	$-0.382780\pi$
$38$	2.50949	+	2.50949i	0.407093	+	0.407093i
$39$		0			0
$40$	11.0553	+	3.99033i	1.74800	+	0.630927i
$41$	0.848868	−	3.16802i	0.132571	−	0.494762i	−0.867425	−	0.497568i	$-0.834227\pi$
$41$	0.848868	−	3.16802i	0.132571	−	0.494762i	0.999996	+	0.00280623i	$0.000893252\pi$
$42$	0.797889	−	2.97776i	0.123117	−	0.459479i
$43$	−8.12475	+	2.17702i	−1.23901	+	0.331993i	−0.818083	−	0.575100i	$-0.804963\pi$
$43$	−8.12475	+	2.17702i	−1.23901	+	0.331993i	−0.420930	+	0.907093i	$0.638296\pi$
$44$	12.0449	−	12.0449i	1.81583	−	1.81583i
$45$	8.45200	−	7.13071i	1.25995	−	1.06298i
$46$	0.582950	+	2.17560i	0.0859513	+	0.320775i
$47$	4.78823			0.698435			0.349217	−	0.937042i	$-0.386447\pi$
$47$	4.78823			0.698435			0.349217	+	0.937042i	$0.386447\pi$
$48$	−3.47234	−	12.9589i	−0.501189	−	1.87046i
$49$	3.40234	+	5.89303i	0.486049	+	0.841861i
$50$	12.1967	+	2.08335i	1.72488	+	0.294630i
$51$		−	3.77585i		−	0.528725i
$52$		0			0
$53$	5.43744	−	5.43744i	0.746890	−	0.746890i	−0.227004	−	0.973894i	$-0.572893\pi$
$53$	5.43744	−	5.43744i	0.746890	−	0.746890i	0.973894	+	0.227004i	$0.0728931\pi$
$54$	−13.1076	−	3.51216i	−1.78371	−	0.477944i
$55$	5.27723	−	7.57977i	0.711581	−	1.02206i
$56$	−2.01178	−	1.16150i	−0.268836	−	0.155212i
$57$		−	4.04239i		−	0.535428i
$58$	−1.78516	+	3.09198i	−0.234403	+	0.405997i
$59$	−2.13003	+	0.570740i	−0.277306	+	0.0743040i	−0.394792	−	0.918771i	$-0.629183\pi$
$59$	−2.13003	+	0.570740i	−0.277306	+	0.0743040i	0.117486	+	0.993075i	$0.462517\pi$
$60$	−11.0483	−	23.5286i	−1.42633	−	3.03753i
$61$	3.08621	−	5.34547i	0.395149	−	0.684418i	−0.597971	−	0.801518i	$-0.704026\pi$
$61$	3.08621	−	5.34547i	0.395149	−	0.684418i	0.993120	+	0.117100i	$0.0373597\pi$
$62$	−25.3565	−	6.79426i	−3.22028	−	0.862872i
$63$	−1.89278	+	1.09280i	−0.238468	+	0.137679i
$64$	6.38663			0.798328
$65$		0			0
$66$	−28.8118			−3.54649
$67$	−8.11555	+	4.68551i	−0.991472	+	0.572427i	−0.905714	−	0.423889i	$-0.860665\pi$
$67$	−8.11555	+	4.68551i	−0.991472	+	0.572427i	−0.0857582	+	0.996316i	$0.527331\pi$
$68$	−5.33610	−	1.42980i	−0.647097	−	0.173389i
$69$	1.28275	−	2.22180i	0.154426	−	0.267473i
$70$	−2.30028	−	0.830268i	−0.274937	−	0.0992360i
$71$	8.38527	−	2.24683i	0.995148	−	0.266649i	0.275737	−	0.961233i	$-0.411078\pi$
$71$	8.38527	−	2.24683i	0.995148	−	0.266649i	0.719411	+	0.694584i	$0.244412\pi$
$72$	−12.9972	+	22.5118i	−1.53173	+	2.65304i
$73$			7.94958i			0.930428i	0.885198	+	0.465214i	$0.154023\pi$
$73$			7.94958i			0.930428i	−0.885198	+	0.465214i	$0.845977\pi$
$74$	16.3726	+	9.45272i	1.90328	+	1.09886i
$75$	−8.14554	−	11.5015i	−0.940566	−	1.32808i
$76$	−5.71278	−	1.53074i	−0.655301	−	0.175587i
$77$	−1.29077	+	1.29077i	−0.147097	+	0.147097i
$78$		0			0
$79$			13.0958i			1.47340i	0.676222	+	0.736698i	$0.263616\pi$
$79$			13.0958i			1.47340i	−0.676222	+	0.736698i	$0.736384\pi$
$80$	−10.4761	+	1.87614i	−1.17126	+	0.209759i
$81$	0.310283	+	0.537427i	0.0344759	+	0.0597141i
$82$	2.10068	+	7.83983i	0.231981	+	0.865764i
$83$	5.50169			0.603889			0.301944	−	0.953326i	$-0.402364\pi$
$83$	5.50169			0.603889			0.301944	+	0.953326i	$0.402364\pi$
$84$	1.32968	+	4.96242i	0.145080	+	0.541444i
$85$	−2.98461	−	0.253071i	−0.323726	−	0.0274494i
$86$	14.7187	−	14.7187i	1.58716	−	1.58716i
$87$	3.92815	−	1.05255i	0.421142	−	0.112845i
$88$	−5.61915	+	20.9710i	−0.599004	+	2.23551i
$89$	3.91732	−	14.6196i	0.415235	−	1.54968i	−0.369129	−	0.929378i	$-0.620344\pi$
$89$	3.91732	−	14.6196i	0.415235	−	1.54968i	0.784364	−	0.620300i	$-0.212989\pi$
$90$	−9.29066	+	25.7401i	−0.979322	+	2.71324i
$91$		0			0
$92$	−2.65414	−	2.65414i	−0.276713	−	0.276713i
$93$	14.9505	+	25.8950i	1.55029	+	2.68518i
$94$	−10.2618	+	5.92466i	−1.05843	+	0.611082i
$95$	−3.19530	−	0.270935i	−0.327830	−	0.0277974i
$96$	2.52301	+	2.52301i	0.257504	+	0.257504i
$97$	−5.09238	−	2.94008i	−0.517052	−	0.298520i	0.218675	−	0.975798i	$-0.429826\pi$
$97$	−5.09238	−	2.94008i	−0.517052	−	0.298520i	−0.735728	+	0.677277i	$0.763160\pi$
$98$	−14.5833	−	8.41970i	−1.47314	−	0.850518i
$99$	14.4437	+	14.4437i	1.45165	+	1.45165i
$100$	−19.3386	+	7.15615i	−1.93386	+	0.715615i
$101$	0.269135	−	0.155385i	0.0267800	−	0.0154614i	−0.486550	−	0.873653i	$-0.661745\pi$
$101$	0.269135	−	0.155385i	0.0267800	−	0.0154614i	0.513330	+	0.858191i	$0.328412\pi$
$102$	4.67201	+	8.09216i	0.462598	+	0.801243i
$103$	7.56701	+	7.56701i	0.745600	+	0.745600i	0.973649	−	0.228050i	$-0.0732349\pi$
$103$	7.56701	+	7.56701i	0.745600	+	0.745600i	−0.228050	+	0.973649i	$0.573235\pi$
$104$		0			0
$105$	1.18398	+	2.52141i	0.115545	+	0.246065i
$106$	−4.92521	+	18.3811i	−0.478378	+	1.78533i
$107$	−1.37367	+	5.12661i	−0.132798	+	0.495608i	−0.999997	−	0.00235266i	$-0.999251\pi$
$107$	−1.37367	+	5.12661i	−0.132798	+	0.495608i	0.867199	+	0.497961i	$0.165918\pi$
$108$	21.8436	−	5.85298i	2.10190	−	0.563204i
$109$	−13.4300	+	13.4300i	−1.28636	+	1.28636i	−0.349382	+	0.936980i	$0.613609\pi$
$109$	−13.4300	+	13.4300i	−1.28636	+	1.28636i	−0.936980	+	0.349382i	$0.886391\pi$
$110$	−1.93107	+	22.7742i	−0.184120	+	2.17143i
$111$	−5.57342	−	20.8003i	−0.529005	−	1.97427i
$112$	2.10348			0.198761
$113$	1.02733	+	3.83405i	0.0966430	+	0.360677i	0.997263	−	0.0739299i	$-0.0235541\pi$
$113$	1.02733	+	3.83405i	0.0966430	+	0.360677i	−0.900620	+	0.434607i	$0.856887\pi$
$114$	5.00181	+	8.66340i	0.468463	+	0.811401i
$115$	−1.67024	−	1.16286i	−0.155750	−	0.108437i
$116$		−	5.94990i		−	0.552435i
$117$		0			0
$118$	3.85874	−	3.85874i	0.355226	−	0.355226i
$119$	0.571837	+	0.153223i	0.0524202	+	0.0140460i
$120$	27.1893	+	18.9299i	2.48203	+	1.72806i
$121$	5.24847	+	3.03020i	0.477133	+	0.275473i
$122$			15.2748i			1.38291i
$123$	4.62244	−	8.00630i	0.416791	−	0.721904i
$124$	42.2565	−	11.3226i	3.79474	−	1.01680i
$125$	−9.63725	+	5.66775i	−0.861982	+	0.506939i
$126$	2.70432	−	4.68402i	0.240920	−	0.417286i
$127$	10.6703	+	2.85911i	0.946839	+	0.253705i	0.699020	−	0.715102i	$-0.253620\pi$
$127$	10.6703	+	2.85911i	0.946839	+	0.253705i	0.247818	+	0.968807i	$0.420286\pi$
$128$	−15.8799	+	9.16826i	−1.40360	+	0.810367i
$129$	−23.7096			−2.08751
$130$		0			0
$131$	−17.7882			−1.55416			−0.777079	−	0.629403i	$-0.783300\pi$
$131$	−17.7882			−1.55416			−0.777079	+	0.629403i	$0.783300\pi$
$132$	41.5819	−	24.0073i	3.61924	−	2.08957i
$133$	0.612204	+	0.164040i	0.0530848	+	0.0142240i
$134$	11.5951	−	20.0834i	1.00167	−	1.73494i
$135$	11.0988	−	5.21167i	0.955232	−	0.448549i
$136$	6.80114	−	1.82236i	0.583193	−	0.156266i
$137$	−6.00306	+	10.3976i	−0.512876	+	0.888327i	0.487012	+	0.873395i	$0.338087\pi$
$137$	−6.00306	+	10.3976i	−0.512876	+	0.888327i	−0.999889	+	0.0149323i	$0.995247\pi$
$138$			6.34881i			0.540447i
$139$	−13.0307	−	7.52327i	−1.10525	−	0.638116i	−0.167654	−	0.985846i	$-0.553619\pi$
$139$	−13.0307	−	7.52327i	−1.10525	−	0.638116i	−0.937595	+	0.347730i	$0.886953\pi$
$140$	4.01164	−	0.718439i	0.339046	−	0.0607192i
$141$	13.0369	+	3.49324i	1.09791	+	0.294184i
$142$	−15.1907	+	15.1907i	−1.27477	+	1.27477i
$143$		0			0
$144$		−	23.5379i		−	1.96149i
$145$	−0.568702	−	3.17554i	−0.0472282	−	0.263714i
$146$	−9.83633	−	17.0370i	−0.814061	−	1.40999i
$147$	4.96434	+	18.5272i	0.409452	+	1.52809i
$148$	−31.5058			−2.58976
$149$	−1.78004	−	6.64322i	−0.145827	−	0.544234i	−0.999717	−	0.0237805i	$-0.992430\pi$
$149$	−1.78004	−	6.64322i	−0.145827	−	0.544234i	0.853890	−	0.520453i	$-0.174237\pi$
$150$	31.6882	+	14.5704i	2.58733	+	1.18967i
$151$	−7.05119	+	7.05119i	−0.573818	+	0.573818i	−0.933193	−	0.359375i	$-0.882990\pi$
$151$	−7.05119	+	7.05119i	−0.573818	+	0.573818i	0.359375	+	0.933193i	$0.382990\pi$
$152$	7.28124	−	1.95100i	0.590587	−	0.158247i
$153$	1.71456	−	6.39883i	0.138614	−	0.517315i
$154$	1.16918	−	4.36343i	0.0942150	−	0.351615i
$155$	21.4706	−	10.0820i	1.72456	−	0.809803i
$156$		0			0
$157$	−7.83033	−	7.83033i	−0.624928	−	0.624928i	0.321859	−	0.946788i	$-0.395692\pi$
$157$	−7.83033	−	7.83033i	−0.624928	−	0.624928i	−0.946788	+	0.321859i	$0.895692\pi$
$158$	−16.2040	−	28.0661i	−1.28912	−	2.23282i
$159$	18.7714	−	10.8377i	1.48867	−	0.859484i
$160$	2.16341	−	1.82520i	0.171032	−	0.144295i
$161$	0.284428	+	0.284428i	0.0224161	+	0.0224161i
$162$	−1.32996	−	0.767852i	−0.104491	−	0.0603281i
$163$	−6.40690	−	3.69903i	−0.501827	−	0.289730i	0.227641	−	0.973745i	$-0.426899\pi$
$163$	−6.40690	−	3.69903i	−0.501827	−	0.289730i	−0.729468	+	0.684015i	$0.760232\pi$
$164$	−9.56426	−	9.56426i	−0.746843	−	0.746843i
$165$	19.8981	−	16.7875i	1.54907	−	1.30690i
$166$	−11.7909	+	6.80746i	−0.915148	+	0.528361i
$167$	−3.33244	−	5.77195i	−0.257872	−	0.446647i	0.707800	−	0.706413i	$-0.249688\pi$
$167$	−3.33244	−	5.77195i	−0.257872	−	0.446647i	−0.965672	+	0.259766i	$0.916355\pi$
$168$	−4.63012	−	4.63012i	−0.357222	−	0.357222i
$169$		0			0
$170$	6.70955	−	3.15061i	0.514599	−	0.241641i
$171$	1.83559	−	6.85053i	0.140371	−	0.523873i
$172$	−8.97811	+	33.5068i	−0.684574	+	2.55487i
$173$	8.07371	−	2.16335i	0.613833	−	0.164476i	0.0615104	−	0.998106i	$-0.480408\pi$
$173$	8.07371	−	2.16335i	0.613833	−	0.164476i	0.552323	+	0.833630i	$0.313742\pi$
$174$	−7.11621	+	7.11621i	−0.539478	+	0.539478i
$175$	2.07240	−	0.766880i	0.156659	−	0.0579707i
$176$	−5.08815	−	18.9892i	−0.383534	−	1.43137i
$177$	−6.21583			−0.467210
$178$	9.69411	+	36.1789i	0.726604	+	2.71172i
$179$	1.06260	+	1.84047i	0.0794221	+	0.137563i	0.903001	−	0.429639i	$-0.141359\pi$
$179$	1.06260	+	1.84047i	0.0794221	+	0.137563i	−0.823579	+	0.567202i	$0.808026\pi$
$180$	−8.03930	−	44.8901i	−0.599214	−	3.34591i
$181$		−	5.02011i		−	0.373142i	−0.982441	−	0.186571i	$-0.940263\pi$
$181$		−	5.02011i		−	0.373142i	0.982441	−	0.186571i	$-0.0597374\pi$
$182$		0			0
$183$	12.3026	−	12.3026i	0.909436	−	0.909436i
$184$	4.62105	+	1.23821i	0.340668	+	0.0912817i
$185$	−16.8150	+	3.01138i	−1.23627	+	0.221401i
$186$	−64.0817	−	36.9976i	−4.69870	−	2.71279i
$187$		−	5.53290i		−	0.404606i
$188$	9.87340	−	17.1012i	0.720092	−	1.24724i
$189$	−2.34085	+	0.627228i	−0.170272	+	0.0456242i
$190$	7.18319	−	3.37301i	0.521123	−	0.244704i
$191$	−6.33509	+	10.9727i	−0.458391	+	0.793956i	−0.998876	−	0.0473973i	$-0.984907\pi$
$191$	−6.33509	+	10.9727i	−0.458391	+	0.793956i	0.540485	+	0.841353i	$0.318241\pi$
$192$	17.3889	+	4.65934i	1.25494	+	0.336259i
$193$	−11.0663	+	6.38916i	−0.796573	+	0.459902i	−0.842271	−	0.539054i	$-0.818782\pi$
$193$	−11.0663	+	6.38916i	−0.796573	+	0.459902i	0.0456985	+	0.998955i	$0.485449\pi$
$194$	14.5515			1.04474
$195$		0			0
$196$	28.0627			2.00448
$197$	−3.04805	+	1.75979i	−0.217165	+	0.125380i	−0.604637	−	0.796501i	$-0.706682\pi$
$197$	−3.04805	+	1.75979i	−0.217165	+	0.125380i	0.387472	+	0.921881i	$0.373348\pi$
$198$	−48.8265	−	13.0830i	−3.46995	−	0.929771i
$199$	1.34969	−	2.33774i	0.0956772	−	0.165718i	−0.814214	−	0.580565i	$-0.802832\pi$
$199$	1.34969	−	2.33774i	0.0956772	−	0.165718i	0.909891	+	0.414847i	$0.136165\pi$
$200$	16.7854	−	20.2229i	1.18691	−	1.42998i
$201$	−25.5146	+	6.83661i	−1.79966	+	0.482217i
$202$	−0.384529	+	0.666023i	−0.0270553	+	0.0468612i
$203$			0.637614i			0.0447518i
$204$	−13.4855	−	7.78587i	−0.944175	−	0.545120i
$205$	−6.01874	−	4.19040i	−0.420367	−	0.292670i
$206$	−25.5801	−	6.85416i	−1.78225	−	0.477552i
$207$	3.18273	−	3.18273i	0.221215	−	0.221215i
$208$		0			0
$209$		−	5.92347i		−	0.409735i
$210$	−5.65728	−	3.93874i	−0.390389	−	0.271799i
$211$	1.74525	+	3.02286i	0.120148	+	0.208103i	0.919826	−	0.392327i	$-0.128330\pi$
$211$	1.74525	+	3.02286i	0.120148	+	0.208103i	−0.799678	+	0.600429i	$0.794996\pi$
$212$	−8.20782	−	30.6320i	−0.563715	−	2.10381i
$213$	24.4698			1.67664
$214$	−3.39940	−	12.6867i	−0.232378	−	0.867246i
$215$	−1.58910	+	18.7411i	−0.108375	+	1.27813i
$216$	−20.3809	+	20.3809i	−1.38675	+	1.38675i
$217$	−4.52837	+	1.21337i	−0.307406	+	0.0823691i
$218$	12.1648	−	45.3998i	0.823907	−	3.07486i
$219$	−5.79959	+	21.6444i	−0.391900	+	1.46259i
$220$	−16.1895	−	34.4773i	−1.09150	−	2.32446i
$221$		0			0
$222$	37.6816	+	37.6816i	2.52902	+	2.52902i
$223$	−1.14738	−	1.98731i	−0.0768340	−	0.133080i	0.825048	−	0.565062i	$-0.191148\pi$
$223$	−1.14738	−	1.98731i	−0.0768340	−	0.133080i	−0.901882	+	0.431982i	$0.857814\pi$
$224$	−0.484483	+	0.279716i	−0.0323709	+	0.0186893i
$225$	−8.58136	−	23.1900i	−0.572090	−	1.54600i
$226$	−6.94572	−	6.94572i	−0.462022	−	0.462022i
$227$	−8.68500	−	5.01429i	−0.576444	−	0.332810i	0.183275	−	0.983062i	$-0.441330\pi$
$227$	−8.68500	−	5.01429i	−0.576444	−	0.332810i	−0.759719	+	0.650252i	$0.774663\pi$
$228$	−14.4375	−	8.33548i	−0.956146	−	0.552031i
$229$	−12.2678	−	12.2678i	−0.810682	−	0.810682i	0.174054	−	0.984736i	$-0.444313\pi$
$229$	−12.2678	−	12.2678i	−0.810682	−	0.810682i	−0.984736	+	0.174054i	$0.944313\pi$
$230$	5.01839	+	0.425519i	0.330903	+	0.0280579i
$231$	−4.45608	+	2.57272i	−0.293188	+	0.169272i
$232$	3.79173	+	6.56747i	0.248939	+	0.431176i
$233$	−13.6965	−	13.6965i	−0.897288	−	0.897288i	0.0979076	−	0.995196i	$-0.468785\pi$
$233$	−13.6965	−	13.6965i	−0.897288	−	0.897288i	−0.995196	+	0.0979076i	$0.968785\pi$
$234$		0			0
$235$	3.63500	−	10.0709i	0.237121	−	0.656951i
$236$	−2.35375	+	8.78431i	−0.153216	+	0.571810i
$237$	−9.55402	+	35.6561i	−0.620601	+	2.31611i
$238$	−1.41511	+	0.379178i	−0.0917281	+	0.0245785i
$239$	−2.57961	+	2.57961i	−0.166861	+	0.166861i	−0.785598	−	0.618737i	$-0.787645\pi$
$239$	−2.57961	+	2.57961i	−0.166861	+	0.166861i	0.618737	+	0.785598i	$0.287645\pi$
$240$	−29.8920	−	2.53460i	−1.92952	−	0.163608i
$241$	−1.18720	−	4.43069i	−0.0764743	−	0.285406i	0.917089	−	0.398682i	$-0.130532\pi$
$241$	−1.18720	−	4.43069i	−0.0764743	−	0.285406i	−0.993564	+	0.113276i	$0.963866\pi$
$242$	−14.9976			−0.964080
$243$	−3.80498	−	14.2004i	−0.244090	−	0.910955i
$244$	−12.7276	−	22.0449i	−0.814803	−	1.41128i
$245$	14.9774	−	2.68229i	0.956874	−	0.171365i
$246$			22.8781i			1.45865i
$247$		0			0
$248$	−39.4269	+	39.4269i	−2.50361	+	2.50361i
$249$	14.9795	+	4.01374i	0.949286	+	0.254361i
$250$	13.6410	−	24.0713i	0.862733	−	1.52240i
$251$	20.2536	+	11.6934i	1.27839	+	0.738081i	0.976553	−	0.215277i	$-0.0690654\pi$
$251$	20.2536	+	11.6934i	1.27839	+	0.738081i	0.301841	+	0.953358i	$0.402399\pi$
$252$			9.01346i			0.567794i
$253$	1.87967	−	3.25568i	0.118174	−	0.204683i
$254$	−26.4056	+	7.07537i	−1.65684	+	0.443948i
$255$	−7.94158	−	2.86645i	−0.497321	−	0.179504i
$256$	16.3019	−	28.2357i	1.01887	−	1.76473i
$257$	−18.9298	−	5.07224i	−1.18081	−	0.316397i	−0.385563	−	0.922682i	$-0.625993\pi$
$257$	−18.9298	−	5.07224i	−1.18081	−	0.316397i	−0.795248	+	0.606284i	$0.792659\pi$
$258$	50.8128	−	29.3368i	3.16346	−	1.82643i
$259$	3.37628			0.209792
$260$		0			0
$261$	7.13488			0.441638
$262$	38.1224	−	22.0100i	2.35521	−	1.35978i
$263$	27.9379	+	7.48593i	1.72272	+	0.461602i	0.978486	−	0.206313i	$-0.0661465\pi$
$263$	27.9379	+	7.48593i	1.72272	+	0.461602i	0.744237	+	0.667915i	$0.232813\pi$
$264$	−30.5986	+	52.9984i	−1.88321	+	3.26182i
$265$	−7.30848	−	15.5642i	−0.448956	−	0.956100i
$266$	−1.51501	+	0.405945i	−0.0928911	+	0.0248901i
$267$	21.3314	−	36.9471i	1.30546	−	2.26113i
$268$			38.6464i			2.36071i
$269$	−7.75057	−	4.47480i	−0.472561	−	0.272833i	0.244750	−	0.969586i	$-0.421294\pi$
$269$	−7.75057	−	4.47480i	−0.472561	−	0.272833i	−0.717311	+	0.696753i	$0.754627\pi$
$270$	−17.3376	+	24.9023i	−1.05513	+	1.51550i
$271$	−3.67974	−	0.985983i	−0.223528	−	0.0598942i	0.145317	−	0.989385i	$-0.453580\pi$
$271$	−3.67974	−	0.985983i	−0.223528	−	0.0598942i	−0.368845	+	0.929491i	$0.620247\pi$
$272$	−4.50829	+	4.50829i	−0.273355	+	0.273355i
$273$		0			0
$274$		−	29.7113i		−	1.79492i
$275$	−11.9360	−	16.8536i	−0.719766	−	1.01631i
$276$	−5.29012	−	9.16276i	−0.318428	−	0.551533i
$277$	1.44055	+	5.37619i	0.0865541	+	0.323024i	0.995604	−	0.0936632i	$-0.0298577\pi$
$277$	1.44055	+	5.37619i	0.0865541	+	0.323024i	−0.909050	+	0.416687i	$0.863191\pi$
$278$	37.2354			2.23323
$279$	13.5776	+	50.6722i	0.812868	+	3.03367i
$280$	−3.97019	+	3.34954i	−0.237264	+	0.200173i
$281$	15.5773	−	15.5773i	0.929266	−	0.929266i	−0.0683927	−	0.997658i	$-0.521787\pi$
$281$	15.5773	−	15.5773i	0.929266	−	0.929266i	0.997658	+	0.0683927i	$0.0217871\pi$
$282$	−32.2622	+	8.64464i	−1.92119	+	0.514781i
$283$	−5.29807	+	19.7727i	−0.314938	+	1.17536i	0.609110	+	0.793086i	$0.291527\pi$
$283$	−5.29807	+	19.7727i	−0.314938	+	1.17536i	−0.924048	+	0.382277i	$0.875140\pi$
$284$	9.26598	−	34.5811i	0.549835	−	2.05201i
$285$	−8.50219	−	3.06880i	−0.503626	−	0.181780i
$286$		0			0
$287$	1.02494	+	1.02494i	0.0605005	+	0.0605005i
$288$	3.13001	+	5.42134i	0.184438	+	0.319456i
$289$	13.1684	−	7.60281i	0.774615	−	0.447224i
$290$	5.14803	+	6.10193i	0.302302	+	0.358318i
$291$	−11.7201	−	11.7201i	−0.687045	−	0.687045i
$292$	28.3921	+	16.3922i	1.66152	+	0.959279i
$293$	4.46887	+	2.58010i	0.261074	+	0.150731i	0.624825	−	0.780765i	$-0.285171\pi$
$293$	4.46887	+	2.58010i	0.261074	+	0.150731i	−0.363750	+	0.931497i	$0.618504\pi$
$294$	−33.5636	−	33.5636i	−1.95747	−	1.95747i
$295$	−0.416606	+	4.91328i	−0.0242558	+	0.286062i
$296$	34.7759	−	20.0779i	2.02131	−	1.16700i
$297$	11.3246	+	19.6148i	0.657121	+	1.13817i
$298$	12.0348	+	12.0348i	0.697157	+	0.697157i
$299$		0			0
$300$	−57.8740	+	5.37569i	−3.34136	+	0.310365i
$301$	0.962129	−	3.59071i	0.0554562	−	0.206965i
$302$	6.38693	−	23.8364i	0.367527	−	1.37163i
$303$	0.846137	−	0.226722i	0.0486093	−	0.0130248i
$304$	−4.82653	+	4.82653i	−0.276821	+	0.276821i
$305$	−8.90000	−	10.5491i	−0.509612	−	0.604041i
$306$	4.24299	+	15.8350i	0.242555	+	0.905229i
$307$	13.3745			0.763324			0.381662	−	0.924302i	$-0.375352\pi$
$307$	13.3745			0.763324			0.381662	+	0.924302i	$0.375352\pi$
$308$	1.94842	+	7.27162i	0.111022	+	0.414339i
$309$	15.0823	+	26.1232i	0.857999	+	1.48610i
$310$	−33.5396	+	48.1734i	−1.90492	+	2.73607i
$311$		−	7.63846i		−	0.433138i	−0.976267	−	0.216569i	$-0.930513\pi$
$311$		−	7.63846i		−	0.433138i	0.976267	−	0.216569i	$-0.0694866\pi$
$312$		0			0
$313$	−9.74863	+	9.74863i	−0.551025	+	0.551025i	−0.926737	−	0.375712i	$-0.877398\pi$
$313$	−9.74863	+	9.74863i	−0.551025	+	0.551025i	0.375712	+	0.926737i	$0.377398\pi$
$314$	26.4702	+	7.09267i	1.49380	+	0.400263i
$315$	0.861522	+	4.81060i	0.0485413	+	0.271046i
$316$	46.7720	+	27.0038i	2.63113	+	1.51908i
$317$			21.4710i			1.20593i	0.797768	+	0.602965i	$0.206014\pi$
$317$			21.4710i			1.20593i	−0.797768	+	0.602965i	$0.793986\pi$
$318$	−26.8198	+	46.4532i	−1.50398	+	2.60497i
$319$	5.75607	−	1.54233i	0.322278	−	0.0863542i
$320$	4.84842	−	13.4327i	0.271035	−	0.750911i
$321$	−7.48021	+	12.9561i	−0.417505	+	0.723139i
$322$	−0.961501	−	0.257633i	−0.0535823	−	0.0143573i
$323$	−1.66368	+	0.960527i	−0.0925697	+	0.0534452i
$324$	2.55924			0.142180
$325$		0			0
$326$	18.3078			1.01398
$327$	−46.3638	+	26.7682i	−2.56393	+	1.48028i
$328$	16.6521	+	4.46190i	0.919456	+	0.246367i
$329$	−1.05807	+	1.83263i	−0.0583334	+	0.101036i
$330$	−21.8726	+	60.5986i	−1.20405	+	3.33584i
$331$	−5.46340	+	1.46391i	−0.300296	+	0.0804640i	−0.405821	−	0.913953i	$-0.633014\pi$
$331$	−5.46340	+	1.46391i	−0.300296	+	0.0804640i	0.105525	+	0.994417i	$0.466348\pi$
$332$	11.3446	−	19.6494i	0.622614	−	1.07840i
$333$		−	37.7804i		−	2.07035i
$334$	14.2837	+	8.24671i	0.781570	+	0.451240i
$335$	3.69390	+	20.6261i	0.201819	+	1.12692i
$336$	5.72717	+	1.53459i	0.312443	+	0.0837188i
$337$	−9.24570	+	9.24570i	−0.503645	+	0.503645i	−0.912569	−	0.408924i	$-0.865904\pi$
$337$	−9.24570	+	9.24570i	−0.503645	+	0.503645i	0.408924	+	0.912569i	$0.365904\pi$
$338$		0			0
$339$			11.1885i			0.607674i
$340$	−7.05816	+	10.1377i	−0.382782	+	0.549796i
$341$	21.9075	+	37.9448i	1.18636	+	2.05483i
$342$	4.54250	+	16.9529i	0.245631	+	0.916706i
$343$	−6.10094			−0.329420
$344$	−11.4431	−	42.7061i	−0.616969	−	2.30256i
$345$	−3.69920	−	4.38464i	−0.199158	−	0.236061i
$346$	−14.6263	+	14.6263i	−0.786313	+	0.786313i
$347$	−30.1886	+	8.08902i	−1.62061	+	0.434241i	−0.951181	−	0.308634i	$-0.900128\pi$
$347$	−30.1886	+	8.08902i	−1.62061	+	0.434241i	−0.669429	+	0.742876i	$0.733461\pi$
$348$	4.34073	−	16.1998i	0.232688	−	0.868402i
$349$	4.21666	−	15.7368i	0.225713	−	0.842371i	−0.756405	−	0.654104i	$-0.773046\pi$
$349$	4.21666	−	15.7368i	0.225713	−	0.842371i	0.982118	−	0.188268i	$-0.0602873\pi$
$350$	−3.49253	+	4.20779i	−0.186684	+	0.224916i
$351$		0			0
$352$	3.69707	+	3.69707i	0.197054	+	0.197054i
$353$	−4.47142	−	7.74473i	−0.237990	−	0.412211i	0.722147	−	0.691739i	$-0.243155\pi$
$353$	−4.47142	−	7.74473i	−0.237990	−	0.412211i	−0.960137	+	0.279528i	$0.909822\pi$
$354$	13.3214	−	7.69109i	0.708022	−	0.408777i
$355$	1.64005	−	19.3420i	0.0870448	−	1.02657i
$356$	−44.1367	−	44.1367i	−2.33924	−	2.33924i
$357$	1.44516	+	0.834364i	0.0764860	+	0.0441592i
$358$	−4.55457	−	2.62958i	−0.240717	−	0.138978i
$359$	6.31120	+	6.31120i	0.333093	+	0.333093i	0.853760	−	0.520667i	$-0.174317\pi$
$359$	6.31120	+	6.31120i	0.333093	+	0.333093i	−0.520667	+	0.853760i	$0.674317\pi$
$360$	37.4811	+	44.4262i	1.97543	+	2.34147i
$361$	14.6734	−	8.47167i	0.772282	−	0.445877i
$362$	6.21158	+	10.7588i	0.326473	+	0.565469i
$363$	12.0794	+	12.0794i	0.634002	+	0.634002i
$364$		0			0
$365$	16.7200	+	6.03495i	0.875165	+	0.315884i
$366$	−11.1437	+	41.5887i	−0.582488	+	2.17388i
$367$	7.25880	−	27.0902i	0.378906	−	1.41410i	−0.468646	−	0.883386i	$-0.655258\pi$
$367$	7.25880	−	27.0902i	0.378906	−	1.41410i	0.847553	−	0.530712i	$-0.178075\pi$
$368$	−4.18436	+	1.12120i	−0.218125	+	0.0584464i
$369$	11.4691	−	11.4691i	0.597055	−	0.597055i
$370$	32.3108	−	27.2597i	1.67976	−	1.41716i
$371$	0.879582	+	3.28264i	0.0456656	+	0.170426i
$372$	123.312			6.39345
$373$	−6.29904	−	23.5084i	−0.326152	−	1.21722i	−0.913149	−	0.407627i	$-0.866356\pi$
$373$	−6.29904	−	23.5084i	−0.326152	−	1.21722i	0.586997	−	0.809589i	$-0.300310\pi$
$374$	6.84607	+	11.8577i	0.354002	+	0.613149i
$375$	−30.3743	+	8.40078i	−1.56852	+	0.433814i
$376$			25.1683i			1.29796i
$377$		0			0
$378$	4.24066	−	4.24066i	0.218116	−	0.218116i
$379$	1.97063	+	0.528030i	0.101225	+	0.0271231i	0.309076	−	0.951037i	$-0.399980\pi$
$379$	1.97063	+	0.528030i	0.101225	+	0.0271231i	−0.207851	+	0.978160i	$0.566647\pi$
$380$	−7.55640	+	10.8534i	−0.387635	+	0.556767i
$381$	26.9663	+	15.5690i	1.38153	+	0.797625i
$382$		−	31.3546i		−	1.60424i
$383$	6.40442	−	11.0928i	0.327251	−	0.566815i	−0.654715	−	0.755876i	$-0.727211\pi$
$383$	6.40442	−	11.0928i	0.327251	−	0.566815i	0.981965	+	0.189061i	$0.0605445\pi$
$384$	−49.9249	+	13.3773i	−2.54772	+	0.682660i
$385$	1.73493	+	3.69472i	0.0884204	+	0.188301i
$386$	15.8111	−	27.3856i	0.804764	−	1.39389i
$387$	−40.1799	−	10.7662i	−2.04246	−	0.547275i
$388$	−21.0011	+	12.1250i	−1.06617	+	0.615554i
$389$	−13.4366			−0.681261			−0.340630	−	0.940197i	$-0.610640\pi$
$389$	−13.4366			−0.681261			−0.340630	+	0.940197i	$0.610640\pi$
$390$		0			0
$391$	−1.21920			−0.0616575
$392$	−30.9755	+	17.8837i	−1.56450	+	0.903264i
$393$	−48.4319	−	12.9773i	−2.44307	−	0.654618i
$394$	4.35493	−	7.54295i	0.219398	−	0.380008i
$395$	27.5439	+	9.94174i	1.38588	+	0.500223i
$396$	81.3691	−	21.8028i	4.08895	−	1.09563i
$397$	−15.6443	+	27.0968i	−0.785167	+	1.35995i	0.143733	+	0.989617i	$0.454089\pi$
$397$	−15.6443	+	27.0968i	−0.785167	+	1.35995i	−0.928899	+	0.370332i	$0.879244\pi$
$398$			6.68011i			0.334844i
$399$	1.54718	+	0.893263i	0.0774557	+	0.0447191i
$400$	−4.00693	+	23.4581i	−0.200347	+	1.17291i
$401$	2.60528	+	0.698082i	0.130101	+	0.0348606i	0.323282	−	0.946303i	$-0.395214\pi$
$401$	2.60528	+	0.698082i	0.130101	+	0.0348606i	−0.193181	+	0.981163i	$0.561880\pi$
$402$	46.2219	−	46.2219i	2.30534	−	2.30534i
$403$		0			0
$404$		−	1.28163i		−	0.0637634i
$405$	1.36590	−	0.244617i	0.0678720	−	0.0121551i
$406$	−0.788945	−	1.36649i	−0.0391547	−	0.0678179i
$407$	−8.16694	−	30.4794i	−0.404820	−	1.51081i
$408$	19.8470			0.982573
$409$	8.67218	+	32.3650i	0.428812	+	1.60035i	0.755456	+	0.655199i	$0.227415\pi$
$409$	8.67218	+	32.3650i	0.428812	+	1.60035i	−0.326645	+	0.945147i	$0.605918\pi$
$410$	18.0839	+	1.53337i	0.893100	+	0.0757277i
$411$	−23.9301	+	23.9301i	−1.18039	+	1.18039i
$412$	42.6290	−	11.4224i	2.10018	−	0.562742i
$413$	0.252237	−	0.941361i	0.0124118	−	0.0463213i
$414$	−2.88290	+	10.7591i	−0.141687	+	0.528783i
$415$	4.17662	−	11.5715i	0.205022	−	0.568021i
$416$		0			0
$417$	−29.9902	−	29.9902i	−1.46862	−	1.46862i
$418$	7.32935	+	12.6948i	0.358490	+	0.620923i
$419$	−28.8543	+	16.6590i	−1.40962	+	0.813847i	−0.995352	−	0.0963065i	$-0.969297\pi$
$419$	−28.8543	+	16.6590i	−1.40962	+	0.813847i	−0.414272	+	0.910153i	$0.635964\pi$
$420$	11.4467	+	0.970585i	0.558540	+	0.0473597i
$421$	12.9149	+	12.9149i	0.629432	+	0.629432i	0.947925	−	0.318494i	$-0.103177\pi$
$421$	12.9149	+	12.9149i	0.629432	+	0.629432i	−0.318494	+	0.947925i	$0.603177\pi$
$422$	−7.48062	−	4.31894i	−0.364151	−	0.210243i
$423$	20.5071	+	11.8398i	0.997089	+	0.575670i
$424$	28.5808	+	28.5808i	1.38801	+	1.38801i
$425$	−2.79805	+	6.08528i	−0.135725	+	0.295179i
$426$	−52.4420	+	30.2774i	−2.54082	+	1.46695i
$427$	1.36394	+	2.36242i	0.0660058	+	0.114325i
$428$	15.4773	+	15.4773i	0.748121	+	0.748121i
$429$		0			0
$430$	−19.7835	−	42.1310i	−0.954045	−	2.03174i
$431$	0.201538	−	0.752150i	0.00970774	−	0.0362298i	−0.960902	−	0.276888i	$-0.910697\pi$
$431$	0.201538	−	0.752150i	0.00970774	−	0.0362298i	0.970610	+	0.240659i	$0.0773634\pi$
$432$	6.75498	−	25.2099i	0.324999	−	1.21291i
$433$	−2.42635	+	0.650137i	−0.116603	+	0.0312436i	−0.316649	−	0.948543i	$-0.602558\pi$
$433$	−2.42635	+	0.650137i	−0.116603	+	0.0312436i	0.200046	+	0.979787i	$0.435891\pi$
$434$	8.20355	−	8.20355i	0.393783	−	0.393783i
$435$	0.768296	−	9.06096i	0.0368370	−	0.434440i
$436$	20.2726	+	75.6585i	0.970883	+	3.62338i
$437$	−1.30526			−0.0624392
$438$	−14.3521	−	53.5629i	−0.685771	−	2.55933i
$439$	−14.0076	−	24.2619i	−0.668548	−	1.15796i	−0.978310	−	0.207145i	$-0.933583\pi$
$439$	−14.0076	−	24.2619i	−0.668548	−	1.15796i	0.309762	−	0.950814i	$-0.399750\pi$
$440$	39.8415	+	27.7387i	1.89937	+	1.32239i
$441$			33.6517i			1.60246i
$442$		0			0
$443$	−13.2326	+	13.2326i	−0.628700	+	0.628700i	−0.947741	−	0.319041i	$-0.896639\pi$
$443$	−13.2326	+	13.2326i	−0.628700	+	0.628700i	0.319041	+	0.947741i	$0.396639\pi$
$444$	−85.7810	−	22.9850i	−4.07099	−	1.09082i
$445$	−27.7750	−	19.3377i	−1.31666	−	0.916693i
$446$	4.91796	+	2.83939i	0.232872	+	0.134449i
$447$		−	19.3862i		−	0.916934i
$448$	−1.41128	+	2.44440i	−0.0666765	+	0.115487i
$449$	−28.6828	+	7.68553i	−1.35362	+	0.362702i	−0.861471	−	0.507806i	$-0.830457\pi$
$449$	−28.6828	+	7.68553i	−1.35362	+	0.362702i	−0.492153	+	0.870509i	$0.663790\pi$
$450$	47.0849	+	39.0813i	2.21960	+	1.84231i
$451$	6.77343	−	11.7319i	0.318948	−	0.552435i
$452$	15.8117	+	4.23674i	0.743721	+	0.199280i
$453$	−24.3425	+	14.0541i	−1.14371	+	0.660321i
$454$	24.8175			1.16474
$455$		0			0
$456$	21.2480			0.995030
$457$	24.1534	−	13.9450i	1.12985	−	0.652317i	0.185950	−	0.982559i	$-0.440464\pi$
$457$	24.1534	−	13.9450i	1.12985	−	0.652317i	0.943896	+	0.330242i	$0.107130\pi$
$458$	41.4711	+	11.1121i	1.93782	+	0.519237i
$459$	3.67271	−	6.36132i	0.171428	−	0.296921i
$460$	−7.59723	+	3.56744i	−0.354223	+	0.166333i
$461$	9.88373	−	2.64834i	0.460331	−	0.123345i	−0.0211982	−	0.999775i	$-0.506748\pi$
$461$	9.88373	−	2.64834i	0.460331	−	0.123345i	0.481529	+	0.876430i	$0.340081\pi$
$462$	6.36665	−	11.0274i	0.296203	−	0.513039i
$463$		−	21.6485i		−	1.00609i	−0.864260	−	0.503046i	$-0.832213\pi$
$463$		−	21.6485i		−	1.00609i	0.864260	−	0.503046i	$-0.167787\pi$
$464$	−5.94685	−	3.43342i	−0.276076	−	0.159392i
$465$	65.8134	−	11.7864i	3.05202	−	0.546582i
$466$	46.3007	+	12.4062i	2.14484	+	0.574707i
$467$	−3.57228	+	3.57228i	−0.165305	+	0.165305i	−0.784912	−	0.619607i	$-0.787292\pi$
$467$	−3.57228	+	3.57228i	−0.165305	+	0.165305i	0.619607	+	0.784912i	$0.287292\pi$
$468$		0			0
$469$		−	4.14150i		−	0.191237i
$470$	4.67079	+	26.0809i	0.215448	+	1.20302i
$471$	−15.6071	−	27.0323i	−0.719137	−	1.24558i
$472$	−2.99998	−	11.1961i	−0.138085	−	0.515341i
$473$	−34.7425			−1.59746
$474$	−23.6431	−	88.2374i	−1.08597	−	4.05288i
$475$	−2.99556	+	6.51484i	−0.137446	+	0.298922i
$476$	1.72638	−	1.72638i	0.0791283	−	0.0791283i
$477$	36.7326	−	9.84248i	1.68187	−	0.450656i
$478$	2.33660	−	8.72029i	0.106873	−	0.398857i
$479$	−3.29604	+	12.3010i	−0.150600	+	0.562046i	0.848842	+	0.528646i	$0.177300\pi$
$479$	−3.29604	+	12.3010i	−0.150600	+	0.562046i	−0.999442	+	0.0333998i	$0.989367\pi$
$480$	7.22189	−	3.39119i	0.329633	−	0.154786i
$481$		0			0
$482$	8.02660	+	8.02660i	0.365602	+	0.365602i
$483$	0.566910	+	0.981917i	0.0257953	+	0.0446788i
$484$	21.6449	−	12.4967i	0.983857	−	0.568030i
$485$	−10.0496	+	8.47860i	−0.456331	+	0.384993i
$486$	25.7253	+	25.7253i	1.16692	+	1.16692i
$487$	9.50122	+	5.48553i	0.430541	+	0.248573i	0.699577	−	0.714557i	$-0.253372\pi$
$487$	9.50122	+	5.48553i	0.430541	+	0.248573i	−0.269036	+	0.963130i	$0.586705\pi$
$488$	28.0974	+	16.2220i	1.27191	+	0.734338i
$489$	−14.7455	−	14.7455i	−0.666814	−	0.666814i
$490$	−28.7798	+	24.2807i	−1.30014	+	1.09689i
$491$	−6.46377	+	3.73186i	−0.291706	+	0.168416i	−0.638711	−	0.769447i	$-0.720532\pi$
$491$	−6.46377	+	3.73186i	−0.291706	+	0.168416i	0.347005	+	0.937863i	$0.387199\pi$
$492$	−19.0631	−	33.0182i	−0.859430	−	1.48858i
$493$	−1.36657	−	1.36657i	−0.0615470	−	0.0615470i
$494$		0			0
$495$	41.3438	−	19.4138i	1.85826	−	0.872587i
$496$	13.0675	−	48.7686i	0.586748	−	2.18977i
$497$	−0.992978	+	3.70585i	−0.0445412	+	0.166230i
$498$	−37.0694	+	9.93272i	−1.66112	+	0.445096i
$499$	−16.9986	+	16.9986i	−0.760962	+	0.760962i	−0.976496	−	0.215534i	$-0.930851\pi$
$499$	−16.9986	+	16.9986i	−0.760962	+	0.760962i	0.215534	+	0.976496i	$0.430851\pi$
$500$	0.370274	+	46.1066i	0.0165592	+	2.06195i
$501$	−4.86234	−	18.1465i	−0.217233	−	0.810726i
$502$	−57.8748			−2.58308
$503$	−4.87942	−	18.2102i	−0.217563	−	0.811955i	−0.985249	−	0.171129i	$-0.945259\pi$
$503$	−4.87942	−	18.2102i	−0.217563	−	0.811955i	0.767686	−	0.640826i	$-0.221408\pi$
$504$	−5.74406	−	9.94901i	−0.255861	−	0.443164i
$505$	−0.122500	−	0.684022i	−0.00545119	−	0.0304386i
$506$			9.30315i			0.413575i
$507$		0			0
$508$	32.2137	−	32.2137i	1.42925	−	1.42925i
$509$	−15.4715	−	4.14558i	−0.685763	−	0.183750i	−0.100918	−	0.994895i	$-0.532178\pi$
$509$	−15.4715	−	4.14558i	−0.685763	−	0.183750i	−0.584845	+	0.811145i	$0.698845\pi$
$510$	20.5667	−	3.68325i	0.910707	−	0.163097i
$511$	−3.04260	−	1.75665i	−0.134597	−	0.0777096i
$512$			44.0107i			1.94502i
$513$	3.93197	−	6.81038i	0.173601	−	0.300686i
$514$	46.8453	−	12.5522i	2.06626	−	0.553652i
$515$	21.6599	−	10.1708i	0.954448	−	0.448181i
$516$	−48.8895	+	84.6791i	−2.15224	+	3.72779i
$517$	19.1035	+	5.11877i	0.840171	+	0.225123i
$518$	−7.23583	+	4.17761i	−0.317924	+	0.183553i
$519$	23.5606			1.03420
$520$		0			0
$521$	23.3580			1.02333			0.511666	−	0.859185i	$-0.329029\pi$
$521$	23.3580			1.02333			0.511666	+	0.859185i	$0.329029\pi$
$522$	−15.2910	+	8.82826i	−0.669269	+	0.386402i
$523$	−20.4399	−	5.47685i	−0.893774	−	0.239486i	−0.217434	−	0.976075i	$-0.569769\pi$
$523$	−20.4399	−	5.47685i	−0.893774	−	0.239486i	−0.676341	+	0.736589i	$0.736435\pi$
$524$	−36.6795	+	63.5307i	−1.60235	+	2.77535i
$525$	6.20200	−	0.576079i	0.270678	−	0.0251422i
$526$	−69.1373	+	18.5253i	−3.01453	+	0.807740i
$527$	7.10486	−	12.3060i	0.309492	−	0.536057i
$528$		−	55.4141i		−	2.41159i
$529$	19.2012	+	11.0858i	0.834834	+	0.481992i
$530$	34.9212	+	24.3131i	1.51688	+	1.05609i
$531$	−10.5338	−	2.82252i	−0.457127	−	0.122487i
$532$	1.84824	−	1.84824i	0.0801315	−	0.0801315i
$533$		0			0
$534$			105.577i			4.56876i
$535$	9.73976	+	6.78107i	0.421086	+	0.293171i
$536$	−24.6285	−	42.6577i	−1.06379	−	1.84253i
$537$	1.55043	+	5.78627i	0.0669059	+	0.249696i
$538$	22.1474			0.954840
$539$	7.27443	+	27.1485i	0.313332	+	1.16937i
$540$	4.27233	−	50.3861i	0.183852	−	2.16827i
$541$	−25.8055	+	25.8055i	−1.10947	+	1.10947i	−0.116246	+	0.993220i	$0.537086\pi$
$541$	−25.8055	+	25.8055i	−1.10947	+	1.10947i	−0.993220	+	0.116246i	$0.962914\pi$
$542$	9.10617	−	2.43999i	0.391144	−	0.104807i
$543$	3.66241	−	13.6683i	0.157169	−	0.586562i
$544$	0.438866	−	1.63787i	0.0188162	−	0.0702231i
$545$	18.0513	+	38.4422i	0.773234	+	1.64668i
$546$		0			0
$547$	−7.39762	−	7.39762i	−0.316299	−	0.316299i	0.531045	−	0.847344i	$-0.321800\pi$
$547$	−7.39762	−	7.39762i	−0.316299	−	0.316299i	−0.847344	+	0.531045i	$0.821800\pi$
$548$	24.7568	+	42.8801i	1.05756	+	1.83175i
$549$	26.4353	−	15.2625i	1.12823	−	0.651386i
$550$	46.4340	+	21.3506i	1.97995	+	0.910393i
$551$	−1.46303	−	1.46303i	−0.0623273	−	0.0623273i
$552$	11.6784	+	6.74254i	0.497067	+	0.286982i
$553$	−5.01227	−	2.89383i	−0.213143	−	0.123058i
$554$	−9.73946	−	9.73946i	−0.413790	−	0.413790i
$555$	−47.9794	−	4.06826i	−2.03661	−	0.172688i
$556$	−53.7390	+	31.0262i	−2.27904	+	1.31581i
$557$	18.4480	+	31.9529i	0.781666	+	1.35389i	0.930970	+	0.365095i	$0.118963\pi$
$557$	18.4480	+	31.9529i	0.781666	+	1.35389i	−0.149304	+	0.988791i	$0.547703\pi$
$558$	−91.7973	−	91.7973i	−3.88609	−	3.88609i
$559$		0			0
$560$	1.59687	−	4.42417i	0.0674799	−	0.186955i
$561$	4.03651	−	15.0645i	0.170422	−	0.636022i
$562$	−14.1099	+	52.6588i	−0.595189	+	2.22128i
$563$	−38.8103	+	10.3992i	−1.63566	+	0.438274i	−0.955548	−	0.294835i	$-0.904735\pi$
$563$	−38.8103	+	10.3992i	−1.63566	+	0.438274i	−0.680111	+	0.733109i	$0.738069\pi$
$564$	39.3585	−	39.3585i	1.65729	−	1.65729i
$565$	8.84388	+	0.749890i	0.372065	+	0.0315481i
$566$	−13.1110	−	48.9310i	−0.551097	−	2.05672i
$567$	−0.274258			−0.0115177
$568$	11.8100	+	44.0755i	0.495536	+	1.84937i
$569$	−0.604646	−	1.04728i	−0.0253481	−	0.0439042i	0.853073	−	0.521791i	$-0.174736\pi$
$569$	−0.604646	−	1.04728i	−0.0253481	−	0.0439042i	−0.878421	+	0.477887i	$0.841403\pi$
$570$	22.0185	−	3.94325i	0.922253	−	0.165165i
$571$		−	9.82830i		−	0.411302i	−0.978625	−	0.205651i	$-0.934069\pi$
$571$		−	9.82830i		−	0.411302i	0.978625	−	0.205651i	$-0.0659311\pi$
$572$		0			0
$573$	−25.2537	+	25.2537i	−1.05499	+	1.05499i
$574$	−3.46479	−	0.928388i	−0.144618	−	0.0387502i
$575$	−3.71376	+	2.63014i	−0.154874	+	0.109685i
$576$	27.3527	+	15.7921i	1.13970	+	0.658005i
$577$		−	27.8253i		−	1.15838i	−0.815191	−	0.579192i	$-0.803368\pi$
$577$		−	27.8253i		−	1.15838i	0.815191	−	0.579192i	$-0.196632\pi$
$578$	−18.8145	+	32.5877i	−0.782580	+	1.35547i
$579$	−34.7916	+	9.32238i	−1.44589	+	0.387425i
$580$	−12.5142	−	4.51688i	−0.519623	−	0.187553i
$581$	−1.21573	+	2.10570i	−0.0504369	+	0.0873593i
$582$	39.6195	+	10.6160i	1.64228	+	0.440048i
$583$	27.5065	−	15.8809i	1.13920	−	0.657718i
$584$	−41.7854			−1.72909
$585$		0			0
$586$	−12.7699			−0.527518
$587$	20.8782	−	12.0541i	0.861737	−	0.497524i	−0.00285679	−	0.999996i	$-0.500909\pi$
$587$	20.8782	−	12.0541i	0.861737	−	0.497524i	0.864593	+	0.502472i	$0.167576\pi$
$588$	76.4066	+	20.4731i	3.15095	+	0.844296i
$589$	7.60640	−	13.1747i	0.313416	−	0.542853i
$590$	−5.18655	−	11.0453i	−0.213527	−	0.454728i
$591$	−9.58281	+	2.56771i	−0.394184	+	0.105621i
$592$	−18.1805	+	31.4896i	−0.747216	+	1.29422i
$593$			0.437434i			0.0179633i	0.999960	+	0.00898164i	$0.00285898\pi$
$593$			0.437434i			0.0179633i	−0.999960	+	0.00898164i	$0.997141\pi$
$594$	−48.5404	−	28.0248i	−1.99164	−	1.14987i
$595$	0.756379	−	1.08640i	0.0310085	−	0.0445380i
$596$	−27.3969	−	7.34096i	−1.12222	−	0.300698i
$597$	5.38030	−	5.38030i	0.220201	−	0.220201i
$598$		0			0
$599$			5.31972i			0.217358i	0.994077	+	0.108679i	$0.0346621\pi$
$599$			5.31972i			0.217358i	−0.994077	+	0.108679i	$0.965338\pi$
$600$	60.4553	−	42.8154i	2.46808	−	1.74793i
$601$	−10.3583	−	17.9412i	−0.422526	−	0.731836i	0.573660	−	0.819094i	$-0.305523\pi$
$601$	−10.3583	−	17.9412i	−0.422526	−	0.731836i	−0.996186	+	0.0872573i	$0.972190\pi$
$602$	2.38096	+	8.88586i	0.0970406	+	0.362161i
$603$	−46.3432			−1.88724
$604$	10.6438	+	39.7231i	0.433089	+	1.61631i
$605$	10.3577	−	8.73848i	0.421100	−	0.355270i
$606$	−1.53285	+	1.53285i	−0.0622679	+	0.0622679i
$607$	30.1127	−	8.06867i	1.22224	−	0.327497i	0.410684	−	0.911778i	$-0.365290\pi$
$607$	30.1127	−	8.06867i	1.22224	−	0.327497i	0.811552	+	0.584280i	$0.198623\pi$
$608$	0.469846	−	1.75349i	0.0190548	−	0.0711133i
$609$	−0.465170	+	1.73604i	−0.0188496	+	0.0703478i
$610$	32.1267	+	11.5959i	1.30077	+	0.469503i
$611$		0			0
$612$	−19.3181	−	19.3181i	−0.780887	−	0.780887i
$613$	−4.11284	−	7.12364i	−0.166116	−	0.287721i	0.770935	−	0.636914i	$-0.219789\pi$
$613$	−4.11284	−	7.12364i	−0.166116	−	0.287721i	−0.937051	+	0.349193i	$0.886456\pi$
$614$	−28.6634	+	16.5488i	−1.15676	+	0.667856i
$615$	−13.3302	−	15.8002i	−0.537524	−	0.637125i
$616$	−6.78469	−	6.78469i	−0.273363	−	0.273363i
$617$	−27.4335	−	15.8388i	−1.10443	−	0.637645i	−0.167051	−	0.985948i	$-0.553424\pi$
$617$	−27.4335	−	15.8388i	−1.10443	−	0.637645i	−0.937382	+	0.348304i	$0.886758\pi$
$618$	−64.6466	−	37.3237i	−2.60047	−	1.50138i
$619$	12.3890	+	12.3890i	0.497958	+	0.497958i	0.910802	−	0.412844i	$-0.135465\pi$
$619$	12.3890	+	12.3890i	0.497958	+	0.497958i	−0.412844	+	0.910802i	$0.635465\pi$
$620$	8.26482	−	97.4718i	0.331923	−	3.91456i
$621$	4.32221	−	2.49543i	0.173444	−	0.100138i
$622$	9.45137	+	16.3703i	0.378965	+	0.656387i
$623$	4.72986	+	4.72986i	0.189498	+	0.189498i
$624$		0			0
$625$	4.60457	+	24.5723i	0.184183	+	0.982892i
$626$	8.83026	−	32.9550i	0.352928	−	1.31715i
$627$	4.32145	−	16.1279i	0.172582	−	0.644085i
$628$	−44.1124	+	11.8199i	−1.76028	+	0.471665i
$629$	−7.23621	+	7.23621i	−0.288527	+	0.288527i
$630$	−7.79870	−	9.24376i	−0.310708	−	0.368280i
$631$	−5.23975	−	19.5550i	−0.208591	−	0.778473i	−0.988325	−	0.152362i	$-0.951312\pi$
$631$	−5.23975	−	19.5550i	−0.208591	−	0.778473i	0.779734	−	0.626111i	$-0.215355\pi$
$632$	−68.8356			−2.73813
$633$	2.54649	+	9.50361i	0.101214	+	0.377735i
$634$	−26.5669	−	46.0152i	−1.05511	−	1.82750i
$635$	14.1138	−	20.2719i	0.560091	−	0.804467i
$636$		−	89.3899i		−	3.54454i
$637$		0			0
$638$	−10.4276	+	10.4276i	−0.412834	+	0.412834i
$639$	41.4682	+	11.1114i	1.64046	+	0.439559i
$640$	7.22793	+	40.3596i	0.285709	+	1.59535i
$641$	−5.43607	−	3.13852i	−0.214712	−	0.123964i	0.388787	−	0.921328i	$-0.372894\pi$
$641$	−5.43607	−	3.13852i	−0.214712	−	0.123964i	−0.603499	+	0.797363i	$0.706227\pi$
$642$		−	37.0222i		−	1.46115i
$643$	14.8651	−	25.7471i	0.586223	−	1.01537i	−0.408499	−	0.912759i	$-0.633948\pi$
$643$	14.8651	−	25.7471i	0.586223	−	1.01537i	0.994722	−	0.102609i	$-0.0327191\pi$
$644$	1.60233	−	0.429344i	0.0631408	−	0.0169185i
$645$	−17.9992	+	49.8673i	−0.708717	+	1.96352i
$646$	2.37700	−	4.11708i	0.0935216	−	0.161984i
$647$	−16.2487	−	4.35384i	−0.638804	−	0.171167i	−0.0751423	−	0.997173i	$-0.523941\pi$
$647$	−16.2487	−	4.35384i	−0.638804	−	0.171167i	−0.563662	+	0.826006i	$0.690608\pi$
$648$	−2.82487	+	1.63094i	−0.110972	+	0.0640695i
$649$	−9.10829			−0.357531
$650$		0			0
$651$	−13.2146			−0.517922
$652$	−26.4223	+	15.2549i	−1.03478	+	0.597428i
$653$	−9.28949	−	2.48911i	−0.363526	−	0.0974064i	0.0724325	−	0.997373i	$-0.476924\pi$
$653$	−9.28949	−	2.48911i	−0.363526	−	0.0974064i	−0.435958	+	0.899967i	$0.643590\pi$
$654$	66.2426	−	114.736i	2.59029	−	4.48652i
$655$	−13.5039	+	37.4131i	−0.527642	+	1.46185i
$656$	−15.0784	+	4.04026i	−0.588714	+	0.157746i
$657$	−19.6568	+	34.0466i	−0.766885	+	1.32828i
$658$		−	5.23678i		−	0.204151i
$659$	17.2958	+	9.98573i	0.673748	+	0.388989i	0.797495	−	0.603325i	$-0.206158\pi$
$659$	17.2958	+	9.98573i	0.673748	+	0.388989i	−0.123747	+	0.992314i	$0.539491\pi$
$660$	−18.9265	−	105.683i	−0.736714	−	4.11369i
$661$	−26.1148	−	6.99745i	−1.01575	−	0.272169i	−0.287720	−	0.957715i	$-0.592897\pi$
$661$	−26.1148	−	6.99745i	−1.01575	−	0.272169i	−0.728030	+	0.685545i	$0.759564\pi$
$662$	9.89744	−	9.89744i	0.384675	−	0.384675i
$663$		0			0
$664$			28.9185i			1.12226i
$665$	0.809773	−	1.16309i	0.0314017	−	0.0451027i
$666$	46.7472	+	80.9685i	1.81142	+	3.13747i
$667$	−0.339860	−	1.26838i	−0.0131594	−	0.0491117i
$668$	−27.4862			−1.06347
$669$	−1.67413	−	6.24794i	−0.0647256	−	0.241559i
$670$	−33.4380	−	39.6339i	−1.29182	−	1.53119i
$671$	18.0275	−	18.0275i	0.695944	−	0.695944i
$672$	−1.52317	+	0.408133i	−0.0587576	+	0.0157441i
$673$	−11.4957	+	42.9024i	−0.443125	+	1.65376i	0.277715	+	0.960663i	$0.410423\pi$
$673$	−11.4957	+	42.9024i	−0.443125	+	1.65376i	−0.720840	+	0.693101i	$0.756244\pi$
$674$	8.37471	−	31.2548i	0.322582	−	1.20389i
$675$	−2.53579	−	27.3001i	−0.0976027	−	1.05078i
$676$		0			0
$677$	3.25358	+	3.25358i	0.125045	+	0.125045i	0.766860	−	0.641815i	$-0.221818\pi$
$677$	3.25358	+	3.25358i	0.125045	+	0.125045i	−0.641815	+	0.766860i	$0.721818\pi$
$678$	−13.8439	−	23.9784i	−0.531673	−	0.920884i
$679$	2.25056	−	1.29936i	0.0863686	−	0.0498650i
$680$	1.33021	−	15.6880i	0.0510114	−	0.601607i
$681$	−19.9885	−	19.9885i	−0.765963	−	0.765963i
$682$	−93.9013	−	54.2139i	−3.59567	−	2.07596i
$683$	35.1467	+	20.2920i	1.34485	+	0.776450i	0.987515	−	0.157526i	$-0.0503517\pi$
$683$	35.1467	+	20.2920i	1.34485	+	0.776450i	0.357336	+	0.933976i	$0.383685\pi$
$684$	−20.6818	−	20.6818i	−0.790787	−	0.790787i
$685$	17.3116	+	20.5193i	0.661442	+	0.784004i
$686$	13.0751	−	7.54893i	0.499211	−	0.288220i
$687$	−24.4518	−	42.3517i	−0.932893	−	1.61582i
$688$	28.3087	+	28.3087i	1.07926	+	1.07926i
$689$		0			0
$690$	13.3532	+	4.81972i	0.508347	+	0.183484i
$691$	−8.37467	+	31.2547i	−0.318587	+	1.18898i	0.602016	+	0.798484i	$0.294364\pi$
$691$	−8.37467	+	31.2547i	−0.318587	+	1.18898i	−0.920603	+	0.390500i	$0.872302\pi$
$692$	8.92171	−	33.2963i	0.339152	−	1.26573i
$693$	−8.71982	+	2.33647i	−0.331239	+	0.0887551i
$694$	54.6894	−	54.6894i	2.07598	−	2.07598i
$695$	−25.7157	+	21.6956i	−0.975451	+	0.822960i
$696$	5.53249	+	20.6475i	0.209709	+	0.782643i
$697$	−4.39341			−0.166412
$698$	10.4349	+	38.9435i	0.394966	+	1.47403i
$699$	−27.2993	−	47.2838i	−1.03256	−	1.78844i
$700$	1.53439	−	8.98292i	0.0579945	−	0.339523i
$701$		−	43.2837i		−	1.63480i	−0.576070	−	0.817400i	$-0.695414\pi$
$701$		−	43.2837i		−	1.63480i	0.576070	−	0.817400i	$-0.304586\pi$
$702$		0			0
$703$	−7.74702	+	7.74702i	−0.292185	+	0.292185i
$704$	25.4806	+	6.82751i	0.960337	+	0.257321i
$705$	17.2442	−	24.7681i	0.649454	−	0.932821i
$706$	19.1657	+	11.0653i	0.721312	+	0.416449i
$707$			0.137344i			0.00516536i
$708$	−12.8171	+	22.1999i	−0.481698	+	0.834325i
$709$	6.48477	−	1.73759i	0.243540	−	0.0652565i	−0.134984	−	0.990848i	$-0.543098\pi$
$709$	6.48477	−	1.73759i	0.243540	−	0.0652565i	0.378524	+	0.925591i	$0.376432\pi$
$710$	20.4178	+	43.4819i	0.766267	+	1.63185i
$711$	−32.3819	+	56.0870i	−1.21441	+	2.10343i
$712$	76.8452	+	20.5906i	2.87989	+	0.771665i
$713$	8.36132	−	4.82741i	0.313134	−	0.180788i
$714$	−4.12956			−0.154545
$715$		0			0
$716$	8.76436			0.327540
$717$	−8.90546	+	5.14157i	−0.332580	+	0.192015i
$718$	−21.3349	−	5.71666i	−0.796210	−	0.213344i
$719$	−7.55903	+	13.0926i	−0.281904	+	0.488272i	−0.971854	−	0.235585i	$-0.924299\pi$
$719$	−7.55903	+	13.0926i	−0.281904	+	0.488272i	0.689950	+	0.723857i	$0.257633\pi$
$720$	−49.5062	−	17.8689i	−1.84499	−	0.665933i
$721$	−4.56829	+	1.22407i	−0.170132	+	0.0455867i
$722$	−20.9647	+	36.3118i	−0.780224	+	1.35139i
$723$		−	12.9296i		−	0.480857i
$724$	−17.9294	−	10.3516i	−0.666341	−	0.384712i
$725$	−7.11071	−	1.21459i	−0.264085	−	0.0451089i
$726$	−40.8340	−	10.9414i	−1.51549	−	0.406074i
$727$	0.0541137	−	0.0541137i	0.00200697	−	0.00200697i	−0.706103	−	0.708110i	$-0.749548\pi$
$727$	0.0541137	−	0.0541137i	0.00200697	−	0.00200697i	0.708110	+	0.706103i	$0.249548\pi$
$728$		0			0
$729$		−	43.3011i		−	1.60374i
$730$	−43.3005	+	7.75462i	−1.60262	+	0.287011i
$731$	5.63371	+	9.75787i	0.208370	+	0.360908i
$732$	−18.5708	−	69.3072i	−0.686397	−	2.56167i
$733$	40.5596			1.49810			0.749052	−	0.662511i	$-0.230509\pi$
$733$	40.5596			1.49810			0.749052	+	0.662511i	$0.230509\pi$
$734$	17.9632	+	67.0396i	0.663034	+	2.47448i
$735$	42.7360	+	3.62367i	1.57634	+	0.133661i
$736$	0.814665	−	0.814665i	0.0300289	−	0.0300289i
$737$	−37.3874	+	10.0179i	−1.37718	+	0.369015i
$738$	−10.3886	+	38.7708i	−0.382410	+	1.42717i
$739$	9.05839	−	33.8064i	0.333218	−	1.24359i	−0.572570	−	0.819856i	$-0.694053\pi$
$739$	9.05839	−	33.8064i	0.333218	−	1.24359i	0.905788	−	0.423731i	$-0.139280\pi$
$740$	−23.9177	+	66.2647i	−0.879232	+	2.43594i
$741$		0			0
$742$	−5.94681	−	5.94681i	−0.218314	−	0.218314i
$743$	−5.28840	−	9.15977i	−0.194012	−	0.336039i	0.752564	−	0.658519i	$-0.228817\pi$
$743$	−5.28840	−	9.15977i	−0.194012	−	0.336039i	−0.946576	+	0.322480i	$0.895484\pi$
$744$	−136.112	+	78.5841i	−4.99009	+	2.88103i
$745$	−15.3237	−	1.29933i	−0.561418	−	0.0476037i
$746$	42.5875	+	42.5875i	1.55924	+	1.55924i
$747$	23.5627	+	13.6039i	0.862115	+	0.497742i
$748$	−19.7608	−	11.4089i	−0.722528	−	0.417152i
$749$	−1.65860	−	1.65860i	−0.0606040	−	0.0606040i
$750$	54.7016	−	55.5873i	1.99742	−	2.02976i
$751$	37.2113	−	21.4840i	1.35786	−	0.783961i	0.368524	−	0.929618i	$-0.379863\pi$
$751$	37.2113	−	21.4840i	1.35786	−	0.783961i	0.989335	+	0.145658i	$0.0465298\pi$
$752$	−11.3950	−	19.7367i	−0.415532	−	0.719723i
$753$	46.6136	+	46.6136i	1.69870	+	1.69870i
$754$		0			0
$755$	9.47753	+	20.1834i	0.344923	+	0.734549i
$756$	−2.58671	+	9.65374i	−0.0940778	+	0.351103i
$757$	−5.60171	+	20.9059i	−0.203597	+	0.759836i	0.786275	+	0.617877i	$0.212007\pi$
$757$	−5.60171	+	20.9059i	−0.203597	+	0.759836i	−0.989872	+	0.141959i	$0.954660\pi$
$758$	−4.87668	+	1.30670i	−0.177129	+	0.0474616i
$759$	7.49296	−	7.49296i	0.271977	−	0.271977i
$760$	1.42412	−	16.7954i	0.0516581	−	0.609234i
$761$	11.5014	+	42.9239i	0.416927	+	1.55599i	0.780945	+	0.624599i	$0.214738\pi$
$761$	11.5014	+	42.9239i	0.416927	+	1.55599i	−0.364019	+	0.931392i	$0.618596\pi$
$762$	−77.0566			−2.79147
$763$	−2.17249	−	8.10785i	−0.0786495	−	0.293524i
$764$	26.1261	+	45.2517i	0.945209	+	1.63715i
$765$	−12.1568	−	8.46385i	−0.439529	−	0.306011i
$766$			31.6978i			1.14529i
$767$		0			0
$768$	64.9844	−	64.9844i	2.34492	−	2.34492i
$769$	−36.7437	−	9.84545i	−1.32501	−	0.355036i	−0.474159	−	0.880439i	$-0.657248\pi$
$769$	−36.7437	−	9.84545i	−1.32501	−	0.355036i	−0.850853	+	0.525403i	$0.823915\pi$
$770$	−8.28982	−	5.77159i	−0.298744	−	0.207994i
$771$	−47.8400	−	27.6204i	−1.72291	−	0.994725i
$772$			52.6982i			1.89665i
$773$	10.4294	−	18.0643i	0.375121	−	0.649729i	−0.615224	−	0.788352i	$-0.710934\pi$
$773$	10.4294	−	18.0643i	0.375121	−	0.649729i	0.990345	+	0.138623i	$0.0442678\pi$
$774$	99.4323	−	26.6428i	3.57402	−	0.957656i
$775$	−4.90549	−	52.8119i	−0.176210	−	1.89706i
$776$	15.4540	−	26.7670i	0.554765	−	0.960881i
$777$	9.19262	+	2.46316i	0.329784	+	0.0883652i
$778$	28.7964	−	16.6256i	1.03240	−	0.596056i
$779$	−4.70355			−0.168522
$780$		0			0
$781$	35.8565			1.28305
$782$	2.61291	−	1.50856i	0.0934374	−	0.0539461i
$783$	7.64171	+	2.04759i	0.273092	+	0.0731749i
$784$	16.1937	−	28.0483i	0.578347	−	1.00173i
$785$	−22.4136	+	10.5248i	−0.799976	+	0.375645i
$786$	119.853	−	32.1146i	4.27503	−	1.14549i
$787$	7.43241	−	12.8733i	0.264937	−	0.458884i	−0.702610	−	0.711575i	$-0.747982\pi$
$787$	7.43241	−	12.8733i	0.264937	−	0.458884i	0.967547	+	0.252691i	$0.0813156\pi$
$788$			14.5149i			0.517072i
$789$	70.6053	+	40.7640i	2.51362	+	1.45124i
$790$	−71.3316	+	12.7747i	−2.53786	+	0.454502i
$791$	−1.69445	−	0.454026i	−0.0602476	−	0.0161433i
$792$	−75.9204	+	75.9204i	−2.69771	+	2.69771i
$793$		0			0
$794$		−	77.4294i		−	2.74787i
$795$	−8.54405	−	47.7086i	−0.303026	−	1.69205i
$796$	−5.56618	−	9.64090i	−0.197288	−	0.341713i
$797$	11.1818	+	41.7312i	0.396081	+	1.47820i	0.819931	+	0.572463i	$0.194012\pi$
$797$	11.1818	+	41.7312i	0.396081	+	1.47820i	−0.423850	+	0.905733i	$0.639321\pi$
$798$	−4.42108			−0.156504
$799$	−1.66008	−	6.19550i	−0.0587294	−	0.219181i
$800$	−2.19652	−	5.93581i	−0.0776586	−	0.209863i
$801$	52.9269	−	52.9269i	1.87008	−	1.87008i
$802$	−6.44723	+	1.72753i	−0.227660	+	0.0610012i
$803$	−8.49836	+	31.7163i	−0.299901	+	1.11924i
$804$	−28.1944	+	105.223i	−0.994339	+	3.71093i
$805$	0.814149	−	0.382300i	0.0286950	−	0.0134743i
$806$		0			0
$807$	−17.8380	−	17.8380i	−0.627926	−	0.627926i
$808$	0.816752	+	1.41466i	0.0287332	+	0.0497674i
$809$	48.4759	−	27.9876i	1.70432	−	0.983990i	0.763049	−	0.646341i	$-0.223701\pi$
$809$	48.4759	−	27.9876i	1.70432	−	0.983990i	0.941272	−	0.337650i	$-0.109632\pi$
$810$	−2.62463	+	2.21433i	−0.0922201	+	0.0778035i
$811$	−18.9005	−	18.9005i	−0.663687	−	0.663687i	0.292560	−	0.956247i	$-0.405493\pi$
$811$	−18.9005	−	18.9005i	−0.663687	−	0.663687i	−0.956247	+	0.292560i	$0.905493\pi$
$812$	2.27725	+	1.31477i	0.0799158	+	0.0461394i
$813$	−9.29953	−	5.36909i	−0.326149	−	0.188302i
$814$	55.2162	+	55.2162i	1.93533	+	1.93533i
$815$	−12.6438	+	10.6672i	−0.442894	+	0.373657i
$816$	−15.5638	+	8.98574i	−0.544840	+	0.314564i
$817$	6.03140	+	10.4467i	0.211012	+	0.365483i
$818$	−58.6321	−	58.6321i	−2.05002	−	2.05002i
$819$		0			0
$820$	−27.3768	+	12.8553i	−0.956040	+	0.448928i
$821$	8.66813	−	32.3499i	0.302520	−	1.12902i	−0.632540	−	0.774528i	$-0.717988\pi$
$821$	8.66813	−	32.3499i	0.302520	−	1.12902i	0.935059	−	0.354491i	$-0.115346\pi$
$822$	21.6758	−	80.8951i	0.756030	−	2.82154i
$823$	38.5249	−	10.3227i	1.34289	−	0.359827i	0.485386	−	0.874300i	$-0.338679\pi$
$823$	38.5249	−	10.3227i	1.34289	−	0.359827i	0.857507	+	0.514473i	$0.172012\pi$
$824$	−39.7745	+	39.7745i	−1.38561	+	1.38561i
$825$	−20.2027	−	54.5952i	−0.703367	−	1.90076i
$826$	0.624205	+	2.32957i	0.0217189	+	0.0810560i
$827$	27.1098			0.942699			0.471349	−	0.881947i	$-0.343767\pi$
$827$	27.1098			0.942699			0.471349	+	0.881947i	$0.343767\pi$
$828$	−4.80434	−	17.9300i	−0.166962	−	0.623112i
$829$	10.0563	+	17.4180i	0.349269	+	0.604951i	0.986120	−	0.166036i	$-0.0530967\pi$
$829$	10.0563	+	17.4180i	0.349269	+	0.604951i	−0.636851	+	0.770987i	$0.719763\pi$
$830$	5.36676	+	29.9671i	0.186283	+	1.04017i
$831$			15.6887i			0.544236i
$832$		0			0
$833$	6.44541	−	6.44541i	0.223320	−	0.223320i
$834$	101.381	+	27.1649i	3.51054	+	0.940645i
$835$	−14.6697	+	2.62718i	−0.507667	+	0.0909172i
$836$	−21.1558	−	12.2143i	−0.731688	−	0.422440i
$837$			58.1683i			2.01059i
$838$	41.2257	−	71.4051i	1.42412	−	2.46665i
$839$	28.4290	−	7.61753i	0.981478	−	0.262986i	0.267811	−	0.963471i	$-0.413700\pi$
$839$	28.4290	−	7.61753i	0.981478	−	0.262986i	0.713667	+	0.700485i	$0.247033\pi$
$840$	−13.2533	+	6.22336i	−0.457282	+	0.214726i
$841$	−13.4593	+	23.3121i	−0.464112	+	0.803866i
$842$	−43.6583	−	11.6982i	−1.50457	−	0.403147i
$843$	53.7769	−	31.0481i	1.85217	−	1.06935i
$844$	14.3949			0.495495
$845$		0			0
$846$	−58.5993			−2.01468
$847$	−2.31955	+	1.33919i	−0.0797006	+	0.0460151i
$848$	−35.3526	−	9.47271i	−1.21401	−	0.325294i
$849$	−28.8502	+	49.9700i	−0.990136	+	1.71497i
$850$	−1.53296	−	16.5037i	−0.0525802	−	0.566072i
$851$	−6.71628	+	1.79962i	−0.230231	+	0.0616902i
$852$	50.4571	−	87.3943i	1.72863	−	2.99408i
$853$			47.4233i			1.62374i	0.583836	+	0.811872i	$0.301551\pi$
$853$			47.4233i			1.62374i	−0.583836	+	0.811872i	$0.698449\pi$
$854$	−5.84623	−	3.37532i	−0.200054	−	0.115501i
$855$	−13.0149	−	9.06132i	−0.445101	−	0.309891i
$856$	−26.9470	−	7.22043i	−0.921030	−	0.246789i
$857$	−23.5126	+	23.5126i	−0.803177	+	0.803177i	−0.983591	−	0.180414i	$-0.942256\pi$
$857$	−23.5126	+	23.5126i	−0.803177	+	0.803177i	0.180414	+	0.983591i	$0.442256\pi$
$858$		0			0
$859$			33.6217i			1.14716i	0.819151	+	0.573578i	$0.194445\pi$
$859$			33.6217i			1.14716i	−0.819151	+	0.573578i	$0.805555\pi$
$860$	63.6575	+	44.3200i	2.17070	+	1.51130i
$861$	2.04287	+	3.53836i	0.0696210	+	0.120587i
$862$	0.498742	+	1.86133i	0.0169872	+	0.0633971i
$863$	52.2651			1.77912			0.889562	−	0.456814i	$-0.151009\pi$
$863$	52.2651			1.77912			0.889562	+	0.456814i	$0.151009\pi$
$864$	1.79652	+	6.70471i	0.0611189	+	0.228099i
$865$	1.57911	−	18.6234i	0.0536915	−	0.633215i
$866$	4.39554	−	4.39554i	0.149367	−	0.149367i
$867$	41.4004	−	11.0932i	1.40603	−	0.376745i
$868$	−5.00399	+	18.6751i	−0.169846	+	0.633876i
$869$	−13.9999	+	52.2482i	−0.474913	+	1.77240i
$870$	9.56492	+	20.3695i	0.324281	+	0.690590i
$871$		0			0
$872$	−70.5922	−	70.5922i	−2.39055	−	2.39055i
$873$	−14.5398	−	25.1837i	−0.492098	−	0.852338i
$874$	2.79736	−	1.61505i	0.0946220	−	0.0546300i
$875$	−0.0396800	−	4.94096i	−0.00134143	−	0.167035i
$876$	65.3444	+	65.3444i	2.20778	+	2.20778i
$877$	30.9244	+	17.8542i	1.04424	+	0.602894i	0.921032	−	0.389487i	$-0.127348\pi$
$877$	30.9244	+	17.8542i	1.04424	+	0.602894i	0.123211	+	0.992381i	$0.460681\pi$
$878$	60.0405	+	34.6644i	2.02627	+	1.16987i
$879$	10.2851	+	10.2851i	0.346908	+	0.346908i
$880$	−43.8019	−	3.71405i	−1.47656	−	0.125200i
$881$	−41.1366	+	23.7502i	−1.38593	+	0.800166i	−0.992853	−	0.119341i	$-0.961922\pi$
$881$	−41.1366	+	23.7502i	−1.38593	+	0.800166i	−0.393075	+	0.919507i	$0.628589\pi$
$882$	−41.6385	−	72.1200i	−1.40204	−	2.42841i
$883$	−19.6601	−	19.6601i	−0.661616	−	0.661616i	0.294145	−	0.955761i	$-0.404965\pi$
$883$	−19.6601	−	19.6601i	−0.661616	−	0.661616i	−0.955761	+	0.294145i	$0.904965\pi$
$884$		0			0
$885$	−4.71876	+	13.0735i	−0.158619	+	0.439460i
$886$	11.9860	−	44.7324i	0.402678	−	1.50282i
$887$	−4.27974	+	15.9722i	−0.143699	+	0.536294i	0.856110	+	0.516793i	$0.172874\pi$
$887$	−4.27974	+	15.9722i	−0.143699	+	0.536294i	−0.999810	+	0.0195007i	$0.993792\pi$
$888$	109.332	−	29.2955i	3.66896	−	0.983094i
$889$	−3.45215	+	3.45215i	−0.115781	+	0.115781i
$890$	83.4528	+	7.07612i	2.79734	+	0.237192i
$891$	0.663406	+	2.47587i	0.0222249	+	0.0829446i
$892$	−9.46363			−0.316866
$893$	−1.77727	−	6.63285i	−0.0594740	−	0.221960i
$894$	23.9873	+	41.5471i	0.802254	+	1.38954i
$895$	4.67765	−	0.837713i	0.156357	−	0.0280017i
$896$		−	8.10377i		−	0.270728i
$897$		0			0
$898$	51.9614	−	51.9614i	1.73398	−	1.73398i
$899$	14.7829	+	3.96106i	0.493036	+	0.132109i
$900$	−100.518	−	17.1698i	−3.35062	−	0.572325i
$901$	−8.92068	−	5.15036i	−0.297191	−	0.171583i
$902$			33.5241i			1.11623i
$903$	5.23919	−	9.07454i	0.174349	−	0.301982i
$904$	−20.1529	+	5.39995i	−0.670275	+	0.179600i
$905$	−10.5586	−	3.81103i	−0.350979	−	0.126683i
$906$	34.7795	−	60.2398i	1.15547	−	2.00133i
$907$	23.4193	+	6.27519i	0.777626	+	0.208364i	0.625738	−	0.780033i	$-0.284798\pi$
$907$	23.4193	+	6.27519i	0.777626	+	0.208364i	0.151888	+	0.988398i	$0.451465\pi$
$908$	−35.8172	+	20.6791i	−1.18864	+	0.686259i
$909$	1.53688			0.0509749
$910$		0			0
$911$	−6.15035			−0.203770			−0.101885	−	0.994796i	$-0.532487\pi$
$911$	−6.15035			−0.203770			−0.101885	+	0.994796i	$0.532487\pi$
$912$	−16.6624	+	9.62005i	−0.551748	+	0.318552i
$913$	21.9500	+	5.88149i	0.726439	+	0.194649i
$914$	−34.5093	+	59.7718i	−1.14147	+	1.97708i
$915$	−16.5360	−	35.2151i	−0.546663	−	1.16418i
$916$	−69.1113	+	18.5183i	−2.28350	+	0.611862i
$917$	3.93071	−	6.80820i	0.129804	−	0.224827i
$918$			18.1776i			0.599949i
$919$	−31.0509	−	17.9272i	−1.02427	−	0.591365i	−0.108935	−	0.994049i	$-0.534744\pi$
$919$	−31.0509	−	17.9272i	−1.02427	−	0.591365i	−0.915339	+	0.402684i	$0.868077\pi$
$920$	6.11234	−	8.77926i	0.201518	−	0.289444i
$921$	36.4149	+	9.75734i	1.19991	+	0.321515i
$922$	−17.9053	+	17.9053i	−0.589679	+	0.589679i
$923$		0			0
$924$			21.2200i			0.698085i
$925$	−6.43149	+	37.6524i	−0.211466	+	1.23800i
$926$	26.7866	+	46.3957i	0.880261	+	1.52466i
$927$	13.6973	+	51.1189i	0.449878	+	1.67897i
$928$	1.82627			0.0599503
$929$	−6.85824	−	25.5953i	−0.225012	−	0.839755i	−0.982400	−	0.186790i	$-0.940192\pi$
$929$	−6.85824	−	25.5953i	−0.225012	−	0.839755i	0.757388	−	0.652965i	$-0.226475\pi$
$930$	−126.463	+	106.693i	−4.14689	+	3.49861i
$931$	6.90041	−	6.90041i	0.226152	−	0.226152i
$932$	−77.1597	+	20.6749i	−2.52745	+	0.677228i
$933$	5.57262	−	20.7973i	0.182439	−	0.680873i
$934$	3.23575	−	12.0760i	0.105877	−	0.395139i
$935$	−11.6371	−	4.20032i	−0.380574	−	0.137365i
$936$		0			0
$937$	27.0963	+	27.0963i	0.885197	+	0.885197i	0.994057	−	0.108860i	$-0.0347199\pi$
$937$	27.0963	+	27.0963i	0.885197	+	0.885197i	−0.108860	+	0.994057i	$0.534720\pi$
$938$	5.12444	+	8.87579i	0.167319	+	0.289805i
$939$	−33.6547	+	19.4306i	−1.09828	+	0.634093i
$940$	−28.4729	−	33.7487i	−0.928682	−	1.10076i
$941$	−4.45875	−	4.45875i	−0.145351	−	0.145351i	0.630687	−	0.776038i	$-0.282773\pi$
$941$	−4.45875	−	4.45875i	−0.145351	−	0.145351i	−0.776038	+	0.630687i	$0.782773\pi$
$942$	66.8962	+	38.6225i	2.17960	+	1.25839i
$943$	−2.58518	−	1.49256i	−0.0841851	−	0.0486043i
$944$	7.42157	+	7.42157i	0.241551	+	0.241551i
$945$	−0.457840	+	5.39957i	−0.0148935	+	0.175648i
$946$	74.4579	−	42.9883i	2.42083	−	1.39767i
$947$	−11.9677	−	20.7286i	−0.388896	−	0.673588i	0.603405	−	0.797435i	$-0.293810\pi$
$947$	−11.9677	−	20.7286i	−0.388896	−	0.673588i	−0.992301	+	0.123847i	$0.960477\pi$
$948$	107.646	+	107.646i	3.49617	+	3.49617i
$949$		0			0
$950$	−1.64118	−	17.6687i	−0.0532468	−	0.573249i
$951$	−15.6641	+	58.4592i	−0.507943	+	1.89567i
$952$	−0.805387	+	3.00575i	−0.0261027	+	0.0974168i
$953$	38.5618	−	10.3326i	1.24914	−	0.334706i	0.427136	−	0.904187i	$-0.359523\pi$
$953$	38.5618	−	10.3326i	1.24914	−	0.334706i	0.822004	+	0.569481i	$0.192856\pi$
$954$	−66.5445	+	66.5445i	−2.15446	+	2.15446i
$955$	18.2691	+	21.6543i	0.591174	+	0.700715i
$956$	3.89392	+	14.5323i	0.125938	+	0.470008i
$957$	16.7973			0.542980
$958$	−8.15663	−	30.4410i	−0.263529	−	0.983503i
$959$	−2.65304	−	4.59519i	−0.0856710	−	0.148387i
$960$	23.0006	−	33.0362i	0.742342	−	1.06624i
$961$			81.5265i			2.62989i
$962$		0			0
$963$	−18.5597	+	18.5597i	−0.598077	+	0.598077i
$964$	−18.2723	−	4.89606i	−0.588512	−	0.157691i
$965$	5.03699	+	28.1257i	0.162146	+	0.905399i
$966$	−2.42993	−	1.40292i	−0.0781817	−	0.0451382i
$967$		−	34.0256i		−	1.09419i	−0.837071	−	0.547095i	$-0.815734\pi$
$967$		−	34.0256i		−	1.09419i	0.837071	−	0.547095i	$-0.184266\pi$
$968$	−15.9277	+	27.5875i	−0.511934	+	0.886696i
$969$	−5.23047	+	1.40150i	−0.168027	+	0.0450226i
$970$	11.0468	−	30.6056i	0.354692	−	0.982686i
$971$	14.3991	−	24.9399i	0.462088	−	0.800360i	−0.536977	−	0.843597i	$-0.680434\pi$
$971$	14.3991	−	24.9399i	0.462088	−	0.800360i	0.999065	+	0.0432369i	$0.0137670\pi$
$972$	−58.5628	−	15.6919i	−1.87840	−	0.503317i
$973$	5.75888	−	3.32489i	0.184621	−	0.106591i
$974$	−27.1498			−0.869937
$975$		0			0
$976$	−29.3781			−0.940372
$977$	21.6277	−	12.4868i	0.691932	−	0.399487i	−0.112403	−	0.993663i	$-0.535855\pi$
$977$	21.6277	−	12.4868i	0.691932	−	0.399487i	0.804336	+	0.594175i	$0.202521\pi$
$978$	49.8468	+	13.3564i	1.59392	+	0.427091i
$979$	31.2577	−	54.1400i	0.999002	−	1.73032i
$980$	21.3039	−	59.0231i	0.680528	−	1.88542i
$981$	−90.7265	+	24.3101i	−2.89667	+	0.776161i
$982$	9.23515	−	15.9958i	0.294706	−	0.510445i
$983$		−	13.7007i		−	0.436986i	−0.975839	−	0.218493i	$-0.929886\pi$
$983$		−	13.7007i		−	0.436986i	0.975839	−	0.218493i	$-0.0701140\pi$
$984$	42.0835	+	24.2969i	1.34157	+	0.774557i
$985$	1.38736	+	7.74679i	0.0442050	+	0.246833i
$986$	4.61964	+	1.23783i	0.147119	+	0.0394205i
$987$	−4.21781	+	4.21781i	−0.134254	+	0.134254i
$988$		0			0
$989$			7.65567i			0.243436i
$990$	−64.5838	+	92.7627i	−2.05261	+	2.94819i
$991$	7.91869	+	13.7156i	0.251545	+	0.435689i	0.963951	−	0.266078i	$-0.0857279\pi$
$991$	7.91869	+	13.7156i	0.251545	+	0.435689i	−0.712406	+	0.701767i	$0.752395\pi$
$992$	3.47537	+	12.9703i	0.110343	+	0.411806i
$993$	−15.9432			−0.505943
$994$	−2.45730	−	9.17078i	−0.0779409	−	0.290879i
$995$	−3.89223	−	4.61345i	−0.123392	−	0.146256i
$996$	45.2231	−	45.2231i	1.43295	−	1.43295i
$997$	−10.1567	+	2.72147i	−0.321665	+	0.0861898i	−0.416038	−	0.909347i	$-0.636582\pi$
$997$	−10.1567	+	2.72147i	−0.321665	+	0.0861898i	0.0943737	+	0.995537i	$0.469915\pi$
$998$	15.3973	−	57.4633i	0.487392	−	1.81897i
$999$	10.8423	−	40.4642i	0.343037	−	1.28023i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.t.i.427.4		144
5.3	odd	4		845.2.o.i.258.33		144
13.2	odd	12		845.2.k.f.577.4	yes	72
13.3	even	3		845.2.f.f.437.4	yes	72
13.4	even	6	inner	845.2.t.i.657.4		144
13.5	odd	4		845.2.o.i.587.33		144
13.6	odd	12		845.2.o.i.357.33		144
13.7	odd	12		845.2.o.i.357.4		144
13.8	odd	4		845.2.o.i.587.4		144
13.9	even	3	inner	845.2.t.i.657.33		144
13.10	even	6		845.2.f.f.437.33	yes	72
13.11	odd	12		845.2.k.f.577.33	yes	72
13.12	even	2	inner	845.2.t.i.427.33		144
65.3	odd	12		845.2.k.f.268.4	yes	72
65.8	even	4	inner	845.2.t.i.418.4		144
65.18	even	4	inner	845.2.t.i.418.33		144
65.23	odd	12		845.2.k.f.268.33	yes	72
65.28	even	12		845.2.f.f.408.33	yes	72
65.33	even	12	inner	845.2.t.i.188.33		144
65.38	odd	4		845.2.o.i.258.4		144
65.43	odd	12		845.2.o.i.488.4		144
65.48	odd	12		845.2.o.i.488.33		144
65.58	even	12	inner	845.2.t.i.188.4		144
65.63	even	12		845.2.f.f.408.4	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.f.f.408.4	✓	72	65.63	even	12
845.2.f.f.408.33	yes	72	65.28	even	12
845.2.f.f.437.4	yes	72	13.3	even	3
845.2.f.f.437.33	yes	72	13.10	even	6
845.2.k.f.268.4	yes	72	65.3	odd	12
845.2.k.f.268.33	yes	72	65.23	odd	12
845.2.k.f.577.4	yes	72	13.2	odd	12
845.2.k.f.577.33	yes	72	13.11	odd	12
845.2.o.i.258.4		144	65.38	odd	4
845.2.o.i.258.33		144	5.3	odd	4
845.2.o.i.357.4		144	13.7	odd	12
845.2.o.i.357.33		144	13.6	odd	12
845.2.o.i.488.4		144	65.43	odd	12
845.2.o.i.488.33		144	65.48	odd	12
845.2.o.i.587.4		144	13.8	odd	4
845.2.o.i.587.33		144	13.5	odd	4
845.2.t.i.188.4		144	65.58	even	12	inner
845.2.t.i.188.33		144	65.33	even	12	inner
845.2.t.i.418.4		144	65.8	even	4	inner
845.2.t.i.418.33		144	65.18	even	4	inner
845.2.t.i.427.4		144	1.1	even	1	trivial
845.2.t.i.427.33		144	13.12	even	2	inner
845.2.t.i.657.4		144	13.4	even	6	inner
845.2.t.i.657.33		144	13.9	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	845.2.t.i.427.4

Level	$845$
Weight	$2$
Character	845.427
Analytic conductor	$6.747$
Analytic rank	$0$
Dimension	$144$
Inner twists	$8$