LMFDB - Embedded newform 39.4.k.a.11.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [39,4,Mod(2,39)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(39, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("39.2");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 39 = 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	39.k (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:	$2.30107449022$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.7
Character	$\chi$	$=$	39.11
Dual form			39.4.k.a.32.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.385245 + 0.103226i) q^{2} +(-3.91264 + 3.41924i) q^{3} +(-6.79045 - 3.92047i) q^{4} +(-9.27643 + 9.27643i) q^{5} +(-1.86028 + 0.913360i) q^{6} +(2.08748 + 7.79057i) q^{7} +(-4.46744 - 4.46744i) q^{8} +(3.61755 - 26.7566i) q^{9} +O(q^{10})$	\(q+(0.385245 + 0.103226i) q^{2} +(-3.91264 + 3.41924i) q^{3} +(-6.79045 - 3.92047i) q^{4} +(-9.27643 + 9.27643i) q^{5} +(-1.86028 + 0.913360i) q^{6} +(2.08748 + 7.79057i) q^{7} +(-4.46744 - 4.46744i) q^{8} +(3.61755 - 26.7566i) q^{9} +(-4.53127 + 2.61613i) q^{10} +(-4.51122 + 16.8361i) q^{11} +(39.9736 - 7.87881i) q^{12} +(-7.38167 + 46.2873i) q^{13} +3.21676i q^{14} +(4.57698 - 68.0137i) q^{15} +(30.1038 + 52.1413i) q^{16} +(43.3605 - 75.1027i) q^{17} +(4.15562 - 9.93441i) q^{18} +(-81.1539 + 21.7451i) q^{19} +(99.3590 - 26.6232i) q^{20} +(-34.8054 - 23.3441i) q^{21} +(-3.47585 + 6.02035i) q^{22} +(-4.88572 - 8.46231i) q^{23} +(32.7548 + 2.20423i) q^{24} -47.1042i q^{25} +(-7.62181 + 17.0700i) q^{26} +(77.3330 + 117.058i) q^{27} +(16.3678 - 61.0854i) q^{28} +(-218.975 + 126.425i) q^{29} +(8.78405 - 25.7295i) q^{30} +(95.7551 + 95.7551i) q^{31} +(19.2966 + 72.0158i) q^{32} +(-39.9159 - 81.2986i) q^{33} +(24.4570 - 24.4570i) q^{34} +(-91.6330 - 52.9044i) q^{35} +(-129.463 + 167.506i) q^{36} +(-310.420 - 83.1767i) q^{37} -33.5088 q^{38} +(-129.386 - 206.345i) q^{39} +82.8838 q^{40} +(-121.857 - 32.6516i) q^{41} +(-10.9989 - 12.5860i) q^{42} +(126.080 + 72.7922i) q^{43} +(96.6385 - 96.6385i) q^{44} +(214.647 + 281.763i) q^{45} +(-1.00867 - 3.76440i) q^{46} +(373.880 + 373.880i) q^{47} +(-296.069 - 101.078i) q^{48} +(240.711 - 138.975i) q^{49} +(4.86238 - 18.1467i) q^{50} +(87.1400 + 442.110i) q^{51} +(231.592 - 285.372i) q^{52} -493.417i q^{53} +(17.7087 + 53.0789i) q^{54} +(-114.331 - 198.027i) q^{55} +(25.4783 - 44.1296i) q^{56} +(243.174 - 362.566i) q^{57} +(-97.4094 + 26.1008i) q^{58} +(539.817 - 144.644i) q^{59} +(-297.725 + 443.899i) q^{60} +(-44.4884 + 77.0562i) q^{61} +(27.0048 + 46.7736i) q^{62} +(216.001 - 27.6710i) q^{63} -451.925i q^{64} +(-360.905 - 497.856i) q^{65} +(-6.98528 - 35.4402i) q^{66} +(-77.5543 + 289.437i) q^{67} +(-588.875 + 339.987i) q^{68} +(48.0508 + 16.4045i) q^{69} +(-29.8401 - 29.8401i) q^{70} +(287.376 + 1072.50i) q^{71} +(-135.695 + 103.372i) q^{72} +(266.833 - 266.833i) q^{73} +(-111.002 - 64.0868i) q^{74} +(161.061 + 184.302i) q^{75} +(636.322 + 170.502i) q^{76} -140.580 q^{77} +(-28.5449 - 92.8495i) q^{78} -1062.25 q^{79} +(-762.941 - 204.429i) q^{80} +(-702.827 - 193.586i) q^{81} +(-43.5745 - 25.1577i) q^{82} +(453.618 - 453.618i) q^{83} +(144.824 + 294.971i) q^{84} +(294.453 + 1098.92i) q^{85} +(41.0576 + 41.0576i) q^{86} +(424.492 - 1243.39i) q^{87} +(95.3679 - 55.0607i) q^{88} +(-213.716 + 797.598i) q^{89} +(53.6065 + 130.705i) q^{90} +(-376.013 + 39.1162i) q^{91} +76.6172i q^{92} +(-702.066 - 47.2455i) q^{93} +(105.441 + 182.629i) q^{94} +(551.101 - 954.535i) q^{95} +(-321.740 - 215.792i) q^{96} +(-600.433 + 160.886i) q^{97} +(107.079 - 28.6916i) q^{98} +(434.156 + 181.610i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{3} - 12 q^{4} - 50 q^{6} + 20 q^{7} - 2 q^{9}+O(q^{10}) $ 48 * q - 2 * q^3 - 12 * q^4 - 50 * q^6 + 20 * q^7 - 2 * q^9	$ 48 q - 2 q^{3} - 12 q^{4} - 50 q^{6} + 20 q^{7} - 2 q^{9} - 156 q^{10} - 80 q^{13} + 70 q^{15} + 260 q^{16} + 256 q^{18} + 260 q^{19} + 82 q^{21} + 212 q^{22} - 1194 q^{24} - 248 q^{27} - 756 q^{28} - 1062 q^{30} - 180 q^{31} + 10 q^{33} - 396 q^{34} + 3060 q^{36} + 1932 q^{37} + 538 q^{39} + 360 q^{40} + 968 q^{42} + 1416 q^{43} - 386 q^{45} - 144 q^{46} - 410 q^{48} - 3000 q^{49} - 4336 q^{52} + 1930 q^{54} - 1012 q^{55} - 1274 q^{57} + 908 q^{58} - 2860 q^{60} + 836 q^{61} - 5150 q^{63} + 1376 q^{66} - 136 q^{67} - 1674 q^{69} + 1808 q^{70} - 3900 q^{72} + 3572 q^{73} + 5796 q^{75} + 8400 q^{76} + 12292 q^{78} - 3760 q^{79} + 2494 q^{81} + 2544 q^{82} + 1084 q^{84} + 4980 q^{85} + 2318 q^{87} - 8436 q^{88} - 8908 q^{91} - 1214 q^{93} - 8464 q^{94} - 6968 q^{96} - 204 q^{97} - 13094 q^{99}+O(q^{100}) $ 48 * q - 2 * q^3 - 12 * q^4 - 50 * q^6 + 20 * q^7 - 2 * q^9 - 156 * q^10 - 80 * q^13 + 70 * q^15 + 260 * q^16 + 256 * q^18 + 260 * q^19 + 82 * q^21 + 212 * q^22 - 1194 * q^24 - 248 * q^27 - 756 * q^28 - 1062 * q^30 - 180 * q^31 + 10 * q^33 - 396 * q^34 + 3060 * q^36 + 1932 * q^37 + 538 * q^39 + 360 * q^40 + 968 * q^42 + 1416 * q^43 - 386 * q^45 - 144 * q^46 - 410 * q^48 - 3000 * q^49 - 4336 * q^52 + 1930 * q^54 - 1012 * q^55 - 1274 * q^57 + 908 * q^58 - 2860 * q^60 + 836 * q^61 - 5150 * q^63 + 1376 * q^66 - 136 * q^67 - 1674 * q^69 + 1808 * q^70 - 3900 * q^72 + 3572 * q^73 + 5796 * q^75 + 8400 * q^76 + 12292 * q^78 - 3760 * q^79 + 2494 * q^81 + 2544 * q^82 + 1084 * q^84 + 4980 * q^85 + 2318 * q^87 - 8436 * q^88 - 8908 * q^91 - 1214 * q^93 - 8464 * q^94 - 6968 * q^96 - 204 * q^97 - 13094 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/39\mathbb{Z}\right)^\times$.

$n$	$14$	$28$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	0.385245	+	0.103226i	0.136205	+	0.0364959i	0.326277	−	0.945274i	$-0.394206\pi$
$2$	0.385245	+	0.103226i	0.136205	+	0.0364959i	−0.190073	+	0.981770i	$0.560872\pi$
$3$	−3.91264	+	3.41924i	−0.752988	+	0.658034i
$3$	−3.91264	+	3.41924i	−0.752988	+	0.658034i
$4$	−6.79045	−	3.92047i	−0.848806	−	0.490058i
$5$	−9.27643	+	9.27643i	−0.829709	+	0.829709i	−0.987476	−	0.157767i	$-0.949570\pi$
$5$	−9.27643	+	9.27643i	−0.829709	+	0.829709i	0.157767	+	0.987476i	$0.449570\pi$
$6$	−1.86028	+	0.913360i	−0.126576	+	0.0621463i
$7$	2.08748	+	7.79057i	0.112713	+	0.420651i	0.999106	−	0.0422831i	$-0.0134631\pi$
$7$	2.08748	+	7.79057i	0.112713	+	0.420651i	−0.886392	+	0.462935i	$0.846796\pi$
$8$	−4.46744	−	4.46744i	−0.197435	−	0.197435i
$9$	3.61755	−	26.7566i	0.133983	−	0.990984i
$10$	−4.53127	+	2.61613i	−0.143291	+	0.0827293i
$11$	−4.51122	+	16.8361i	−0.123653	+	0.461479i	−0.999788	−	0.0205864i	$-0.993447\pi$
$11$	−4.51122	+	16.8361i	−0.123653	+	0.461479i	0.876135	+	0.482066i	$0.160113\pi$
$12$	39.9736	−	7.87881i	0.961616	−	0.189535i
$13$	−7.38167	+	46.2873i	−0.157485	+	0.987521i
$13$	−7.38167	+	46.2873i	−0.157485	+	0.987521i
$14$			3.21676i			0.0614083i
$15$	4.57698	−	68.0137i	0.0787848	−	1.17074i
$16$	30.1038	+	52.1413i	0.470372	+	0.814708i
$17$	43.3605	−	75.1027i	0.618616	−	1.07147i	−0.371122	−	0.928584i	$-0.621027\pi$
$17$	43.3605	−	75.1027i	0.618616	−	1.07147i	0.989738	−	0.142891i	$-0.0456398\pi$
$18$	4.15562	−	9.93441i	0.0544160	−	0.130087i
$19$	−81.1539	+	21.7451i	−0.979893	+	0.262562i	−0.713000	−	0.701164i	$-0.752664\pi$
$19$	−81.1539	+	21.7451i	−0.979893	+	0.262562i	−0.266894	+	0.963726i	$0.585997\pi$
$20$	99.3590	−	26.6232i	1.11087	−	0.297656i
$21$	−34.8054	−	23.3441i	−0.361675	−	0.242577i
$22$	−3.47585	+	6.02035i	−0.0336842	+	0.0583428i
$23$	−4.88572	−	8.46231i	−0.0442932	−	0.0767180i	0.843029	−	0.537868i	$-0.180770\pi$
$23$	−4.88572	−	8.46231i	−0.0442932	−	0.0767180i	−0.887322	+	0.461150i	$0.847437\pi$
$24$	32.7548	+	2.20423i	0.278585	+	0.0187474i
$25$		−	47.1042i		−	0.376833i
$26$	−7.62181	+	17.0700i	−0.0574908	+	0.128758i
$27$	77.3330	+	117.058i	0.551213	+	0.834365i
$28$	16.3678	−	61.0854i	0.110472	−	0.412287i
$29$	−218.975	+	126.425i	−1.40216	+	0.809537i	−0.994614	−	0.103648i	$-0.966949\pi$
$29$	−218.975	+	126.425i	−1.40216	+	0.809537i	−0.407545	+	0.913185i	$0.633615\pi$
$30$	8.78405	−	25.7295i	0.0534580	−	0.156585i
$31$	95.7551	+	95.7551i	0.554778	+	0.554778i	0.927816	−	0.373038i	$-0.121684\pi$
$31$	95.7551	+	95.7551i	0.554778	+	0.554778i	−0.373038	+	0.927816i	$0.621684\pi$
$32$	19.2966	+	72.0158i	0.106600	+	0.397835i
$33$	−39.9159	−	81.2986i	−0.210560	−	0.428856i
$34$	24.4570	−	24.4570i	0.123363	−	0.123363i
$35$	−91.6330	−	52.9044i	−0.442537	−	0.255499i
$36$	−129.463	+	167.506i	−0.599365	+	0.775493i
$37$	−310.420	−	83.1767i	−1.37926	−	0.369572i	−0.508408	−	0.861116i	$-0.669766\pi$
$37$	−310.420	−	83.1767i	−1.37926	−	0.369572i	−0.870853	+	0.491544i	$0.836433\pi$
$38$	−33.5088			−0.143049
$39$	−129.386	−	206.345i	−0.531238	−	0.847223i
$40$	82.8838			0.327627
$41$	−121.857	−	32.6516i	−0.464169	−	0.124374i	0.0191526	−	0.999817i	$-0.493903\pi$
$41$	−121.857	−	32.6516i	−0.464169	−	0.124374i	−0.483322	+	0.875443i	$0.660570\pi$
$42$	−10.9989	−	12.5860i	−0.0404087	−	0.0462397i
$43$	126.080	+	72.7922i	0.447139	+	0.258156i	0.706621	−	0.707592i	$-0.250219\pi$
$43$	126.080	+	72.7922i	0.447139	+	0.258156i	−0.259482	+	0.965748i	$0.583552\pi$
$44$	96.6385	−	96.6385i	0.331109	−	0.331109i
$45$	214.647	+	281.763i	0.711061	+	0.933395i
$46$	−1.00867	−	3.76440i	−0.00323304	−	0.0120659i
$47$	373.880	+	373.880i	1.16034	+	1.16034i	0.984401	+	0.175938i	$0.0562958\pi$
$47$	373.880	+	373.880i	1.16034	+	1.16034i	0.175938	+	0.984401i	$0.443704\pi$
$48$	−296.069	−	101.078i	−0.890290	−	0.303945i
$49$	240.711	−	138.975i	0.701782	−	0.405174i
$50$	4.86238	−	18.1467i	0.0137529	−	0.0513265i
$51$	87.1400	+	442.110i	0.239256	+	1.21388i
$52$	231.592	−	285.372i	0.617617	−	0.761037i
$53$		−	493.417i		−	1.27879i	−0.768877	−	0.639396i	$-0.779184\pi$
$53$		−	493.417i		−	1.27879i	0.768877	−	0.639396i	$-0.220816\pi$
$54$	17.7087	+	53.0789i	0.0446269	+	0.133761i
$55$	−114.331	−	198.027i	−0.280297	−	0.485489i
$56$	25.4783	−	44.1296i	0.0607978	−	0.105305i
$57$	243.174	−	362.566i	0.565074	−	0.842509i
$58$	−97.4094	+	26.1008i	−0.220526	+	0.0590897i
$59$	539.817	−	144.644i	1.19116	−	0.319169i	0.391814	−	0.920045i	$-0.371848\pi$
$59$	539.817	−	144.644i	1.19116	−	0.319169i	0.799343	+	0.600875i	$0.205181\pi$
$60$	−297.725	+	443.899i	−0.640602	+	0.955120i
$61$	−44.4884	+	77.0562i	−0.0933796	+	0.161738i	−0.908931	−	0.416946i	$-0.863100\pi$
$61$	−44.4884	+	77.0562i	−0.0933796	+	0.161738i	0.815552	+	0.578684i	$0.196434\pi$
$62$	27.0048	+	46.7736i	0.0553163	+	0.0958106i
$63$	216.001	−	27.6710i	0.431960	−	0.0553367i
$64$		−	451.925i		−	0.882667i
$65$	−360.905	−	497.856i	−0.688688	−	0.950022i
$66$	−6.98528	−	35.4402i	−0.0130277	−	0.0660968i
$67$	−77.5543	+	289.437i	−0.141414	+	0.527766i	0.858474	+	0.512856i	$0.171413\pi$
$67$	−77.5543	+	289.437i	−0.141414	+	0.527766i	−0.999889	+	0.0149095i	$0.995254\pi$
$68$	−588.875	+	339.987i	−1.05017	+	0.606316i
$69$	48.0508	+	16.4045i	0.0838353	+	0.0286214i
$70$	−29.8401	−	29.8401i	−0.0509510	−	0.0509510i
$71$	287.376	+	1072.50i	0.480356	+	1.79271i	0.600118	+	0.799912i	$0.295120\pi$
$71$	287.376	+	1072.50i	0.480356	+	1.79271i	−0.119762	+	0.992803i	$0.538213\pi$
$72$	−135.695	+	103.372i	−0.222108	+	0.169202i
$73$	266.833	−	266.833i	0.427814	−	0.427814i	−0.460069	−	0.887883i	$-0.652175\pi$
$73$	266.833	−	266.833i	0.427814	−	0.427814i	0.887883	+	0.460069i	$0.152175\pi$
$74$	−111.002	−	64.0868i	−0.174374	−	0.100675i
$75$	161.061	+	184.302i	0.247969	+	0.283751i
$76$	636.322	+	170.502i	0.960409	+	0.257341i
$77$	−140.580			−0.208059
$78$	−28.5449	−	92.8495i	−0.0414369	−	0.134784i
$79$	−1062.25			−1.51281			−0.756407	−	0.654101i	$-0.773047\pi$
$79$	−1062.25			−1.51281			−0.756407	+	0.654101i	$0.773047\pi$
$80$	−762.941	−	204.429i	−1.06624	−	0.285699i
$81$	−702.827	−	193.586i	−0.964097	−	0.265550i
$82$	−43.5745	−	25.1577i	−0.0586829	−	0.0338806i
$83$	453.618	−	453.618i	0.599892	−	0.599892i	−0.340392	−	0.940284i	$-0.610560\pi$
$83$	453.618	−	453.618i	0.599892	−	0.599892i	0.940284	+	0.340392i	$0.110560\pi$
$84$	144.824	+	294.971i	0.188115	+	0.383142i
$85$	294.453	+	1098.92i	0.375741	+	1.40228i
$86$	41.0576	+	41.0576i	0.0514808	+	0.0514808i
$87$	424.492	−	1243.39i	0.523107	−	1.53224i
$88$	95.3679	−	55.0607i	0.115526	−	0.0666987i
$89$	−213.716	+	797.598i	−0.254537	+	0.949946i	0.713810	+	0.700339i	$0.246968\pi$
$89$	−213.716	+	797.598i	−0.254537	+	0.949946i	−0.968347	+	0.249607i	$0.919699\pi$
$90$	53.6065	+	130.705i	0.0627847	+	0.153084i
$91$	−376.013	+	39.1162i	−0.433153	+	0.0450603i
$92$			76.6172i			0.0868249i
$93$	−702.066	−	47.2455i	−0.782805	−	0.0526788i
$94$	105.441	+	182.629i	0.115696	+	0.200391i
$95$	551.101	−	954.535i	0.595176	−	1.03088i
$96$	−321.740	−	215.792i	−0.342057	−	0.229419i
$97$	−600.433	+	160.886i	−0.628503	+	0.168407i	−0.558990	−	0.829174i	$-0.688811\pi$
$97$	−600.433	+	160.886i	−0.628503	+	0.168407i	−0.0695125	+	0.997581i	$0.522144\pi$
$98$	107.079	−	28.6916i	0.110373	−	0.0295744i
$99$	434.156	+	181.610i	0.440751	+	0.184369i
$100$	−184.670	+	319.858i	−0.184670	+	0.319858i
$101$	200.129	+	346.634i	0.197164	+	0.341499i	0.947608	−	0.319436i	$-0.103493\pi$
$101$	200.129	+	346.634i	0.197164	+	0.341499i	−0.750443	+	0.660935i	$0.770160\pi$
$102$	−12.0671	+	179.316i	−0.0117139	+	0.174068i
$103$		−	87.2345i		−	0.0834512i	−0.999129	−	0.0417256i	$-0.986714\pi$
$103$		−	87.2345i		−	0.0834512i	0.999129	−	0.0417256i	$-0.0132855\pi$
$104$	239.763	−	173.809i	0.226064	−	0.163878i
$105$	539.420	−	106.320i	0.501353	−	0.0988167i
$106$	50.9335	−	190.086i	0.0466707	−	0.174178i
$107$	−414.024	+	239.037i	−0.374067	+	0.215968i	−0.675234	−	0.737604i	$-0.735957\pi$
$107$	−414.024	+	239.037i	−0.374067	+	0.215968i	0.301167	+	0.953571i	$0.402624\pi$
$108$	−66.2033	−	1098.06i	−0.0589853	−	0.978340i
$109$	449.652	+	449.652i	0.395127	+	0.395127i	0.876510	−	0.481383i	$-0.159865\pi$
$109$	449.652	+	449.652i	0.395127	+	0.395127i	−0.481383	+	0.876510i	$0.659865\pi$
$110$	−23.6038	−	88.0908i	−0.0204594	−	0.0763557i
$111$	1498.96	−	735.959i	1.28176	−	0.629317i
$112$	−343.370	+	343.370i	−0.289691	+	0.289691i
$113$	−1157.06	−	668.028i	−0.963247	−	0.556131i	−0.0660761	−	0.997815i	$-0.521048\pi$
$113$	−1157.06	−	668.028i	−0.963247	−	0.556131i	−0.897171	+	0.441684i	$0.854381\pi$
$114$	131.108	−	114.575i	0.107714	−	0.0941308i
$115$	123.822	+	33.1780i	0.100404	+	0.0269032i
$116$	1982.58			1.58688
$117$	1211.78	+	364.954i	0.957517	+	0.288377i
$118$	222.893			0.173890
$119$	675.607	+	181.028i	0.520444	+	0.139452i
$120$	−324.295	+	283.400i	−0.246699	+	0.215590i
$121$	889.577	+	513.598i	0.668352	+	0.385873i
$122$	−25.0932	+	25.0932i	−0.0186215	+	0.0186215i
$123$	588.428	−	288.906i	0.431356	−	0.211787i
$124$	−274.815	−	1025.62i	−0.199025	−	0.742773i
$125$	−722.595	−	722.595i	−0.517047	−	0.517047i
$126$	86.0695	+	11.6368i	0.0608546	+	0.00822768i
$127$	−862.810	+	498.144i	−0.602850	+	0.348056i	−0.770162	−	0.637848i	$-0.779825\pi$
$127$	−862.810	+	498.144i	−0.602850	+	0.348056i	0.167312	+	0.985904i	$0.446491\pi$
$128$	201.023	−	750.229i	0.138813	−	0.518058i
$129$	−742.199	+	146.288i	−0.506566	+	0.0998442i
$130$	−87.6451	−	229.051i	−0.0591307	−	0.154532i
$131$			1333.22i			0.889193i	0.895731	+	0.444597i	$0.146653\pi$
$131$			1333.22i			0.889193i	−0.895731	+	0.444597i	$0.853347\pi$
$132$	−47.6813	+	708.542i	−0.0314404	+	0.467202i
$133$	−338.814	−	586.843i	−0.220894	−	0.382599i
$134$	−59.7549	+	103.498i	−0.0385226	+	0.0667232i
$135$	−1803.26	−	368.507i	−1.14963	−	0.234934i
$136$	−529.228	+	141.806i	−0.333683	+	0.0894101i
$137$	−978.465	+	262.179i	−0.610189	+	0.163500i	−0.550664	−	0.834727i	$-0.685625\pi$
$137$	−978.465	+	262.179i	−0.610189	+	0.163500i	−0.0595253	+	0.998227i	$0.518959\pi$
$138$	16.8180	+	11.2799i	0.0103742	+	0.00695801i
$139$	−1084.15	+	1877.81i	−0.661558	+	1.14585i	0.318648	+	0.947873i	$0.396771\pi$
$139$	−1084.15	+	1877.81i	−0.661558	+	1.14585i	−0.980206	+	0.197979i	$0.936562\pi$
$140$	414.819	+	718.488i	0.250419	+	0.433738i
$141$	−2741.24	−	184.472i	−1.63726	−	0.110180i
$142$			442.841i			0.261707i
$143$	−745.996	−	333.090i	−0.436247	−	0.194786i
$144$	1504.02	−	616.851i	0.870385	−	0.356974i
$145$	858.531	−	3204.08i	0.491704	−	1.83506i
$146$	130.340	−	75.2519i	0.0738837	−	0.0426568i
$147$	−466.629	+	1366.81i	−0.261816	+	0.766888i
$148$	1781.80	+	1781.80i	0.989613	+	0.989613i
$149$	146.320	+	546.073i	0.0804496	+	0.300242i	0.994414	−	0.105553i	$-0.0336613\pi$
$149$	146.320	+	546.073i	0.0804496	+	0.300242i	−0.913964	+	0.405795i	$0.866995\pi$
$150$	43.0231	+	87.6271i	0.0234188	+	0.0476981i
$151$	1650.20	−	1650.20i	0.889349	−	0.889349i	−0.105112	−	0.994460i	$-0.533520\pi$
$151$	1650.20	−	1650.20i	0.889349	−	0.889349i	0.994460	+	0.105112i	$0.0335200\pi$
$152$	459.695	+	265.405i	0.245304	+	0.141626i
$153$	−1852.63	−	1431.87i	−0.978930	−	0.756598i
$154$	−54.1577	−	14.5115i	−0.0283387	−	0.00759332i
$155$	−1776.53			−0.920609
$156$	69.6163	+	1908.43i	0.0357293	+	0.979465i
$157$	1168.29			0.593885			0.296943	−	0.954895i	$-0.404033\pi$
$157$	1168.29			0.593885			0.296943	+	0.954895i	$0.404033\pi$
$158$	−409.226	−	109.652i	−0.206053	−	0.0552116i
$159$	1687.11	+	1930.56i	0.841489	+	0.962916i
$160$	−847.053	−	489.046i	−0.418534	−	0.241641i
$161$	55.7274	−	55.7274i	0.0272791	−	0.0272791i
$162$	−250.777	−	147.128i	−0.121623	−	0.0713548i
$163$	−350.882	−	1309.51i	−0.168609	−	0.629256i	−0.997552	−	0.0699237i	$-0.977724\pi$
$163$	−350.882	−	1309.51i	−0.168609	−	0.629256i	0.828944	−	0.559332i	$-0.188942\pi$
$164$	699.457	+	699.457i	0.333039	+	0.333039i
$165$	1124.44	+	383.883i	0.530529	+	0.181123i
$166$	221.579	−	127.929i	0.103602	−	0.0598145i
$167$	152.132	−	567.765i	0.0704930	−	0.263084i	−0.921681	−	0.387950i	$-0.873183\pi$
$167$	152.132	−	567.765i	0.0704930	−	0.263084i	0.992174	+	0.124866i	$0.0398501\pi$
$168$	51.2027	+	259.780i	0.0235141	+	0.119300i
$169$	−2088.02	−	683.355i	−0.950397	−	0.311040i
$170$			453.747i			0.204711i
$171$	288.246	+	2250.06i	0.128905	+	1.00624i
$172$	−570.758	−	988.582i	−0.253023	−	0.438248i
$173$	−717.496	+	1242.74i	−0.315319	+	0.546149i	−0.979505	−	0.201419i	$-0.935445\pi$
$173$	−717.496	+	1242.74i	−0.315319	+	0.546149i	0.664186	+	0.747567i	$0.268778\pi$
$174$	291.883	−	435.190i	0.127170	−	0.189607i
$175$	366.969	−	98.3289i	0.158516	−	0.0424741i
$176$	−1013.66	+	271.610i	−0.434134	+	0.116326i
$177$	−1617.54	+	2411.71i	−0.686903	+	1.02415i
$178$	−164.666	+	285.210i	−0.0693383	+	0.120098i
$179$	−983.392	−	1703.29i	−0.410627	−	0.711226i	0.584332	−	0.811515i	$-0.301357\pi$
$179$	−983.392	−	1703.29i	−0.410627	−	0.711226i	−0.994958	+	0.100289i	$0.968023\pi$
$180$	−352.908	−	2754.81i	−0.146135	−	1.14073i
$181$		−	2351.61i		−	0.965712i	−0.875700	−	0.482856i	$-0.839599\pi$
$181$		−	2351.61i		−	0.965712i	0.875700	−	0.482856i	$-0.160401\pi$
$182$	−148.895	−	23.7451i	−0.0606420	−	0.00967090i
$183$	−89.4066	−	453.610i	−0.0361155	−	0.183234i
$184$	−15.9782	+	59.6316i	−0.00640180	+	0.0238918i
$185$	3651.17	−	2108.00i	1.45102	−	0.837748i
$186$	−265.590	−	90.6726i	−0.104699	−	0.0357443i
$187$	1068.83	+	1068.83i	0.417970	+	0.417970i
$188$	−1073.03	−	4004.59i	−0.416269	−	1.55354i
$189$	−750.519	+	846.825i	−0.288848	+	0.325912i
$190$	310.842	−	310.842i	0.118689	−	0.118689i
$191$	3023.01	+	1745.34i	1.14522	+	0.661194i	0.947718	−	0.319108i	$-0.103383\pi$
$191$	3023.01	+	1745.34i	1.14522	+	0.661194i	0.197503	+	0.980302i	$0.436717\pi$
$192$	1545.24	+	1768.22i	0.580825	+	0.664638i
$193$	4153.73	+	1112.99i	1.54918	+	0.415102i	0.929219	−	0.369530i	$-0.120481\pi$
$193$	4153.73	+	1112.99i	1.54918	+	0.415102i	0.619962	+	0.784632i	$0.287148\pi$
$194$	−247.922			−0.0917512
$195$	3114.38	+	713.911i	1.14372	+	0.262175i
$196$	−2179.38			−0.794235
$197$	4643.22	+	1244.15i	1.67927	+	0.449959i	0.967586	−	0.252542i	$-0.0812667\pi$
$197$	4643.22	+	1244.15i	1.67927	+	0.449959i	0.711683	+	0.702501i	$0.247933\pi$
$198$	148.510	+	114.781i	0.0533037	+	0.0411975i
$199$	−123.546	−	71.3295i	−0.0440099	−	0.0254091i	0.477834	−	0.878450i	$-0.341422\pi$
$199$	−123.546	−	71.3295i	−0.0440099	−	0.0254091i	−0.521843	+	0.853041i	$0.674756\pi$
$200$	−210.435	+	210.435i	−0.0744001	+	0.0744001i
$201$	−686.212	−	1397.64i	−0.240804	−	0.490457i
$202$	41.3171	+	154.198i	0.0143914	+	0.0537095i
$203$	−1442.03	−	1442.03i	−0.498575	−	0.498575i
$204$	1141.56	−	3343.75i	0.391790	−	1.14760i
$205$	1433.29	−	827.511i	0.488319	−	0.281931i
$206$	9.00488	−	33.6067i	0.00304563	−	0.0113664i
$207$	−244.097	+	100.112i	−0.0819608	+	0.0336149i
$208$	−2635.70	+	1008.53i	−0.878619	+	0.336198i
$209$		−	1464.41i		−	0.484667i
$210$	218.784	+	14.7231i	0.0718930	+	0.00483804i
$211$	1033.04	+	1789.27i	0.337048	+	0.583785i	0.983876	−	0.178851i	$-0.0572381\pi$
$211$	1033.04	+	1789.27i	0.337048	+	0.583785i	−0.646828	+	0.762636i	$0.723905\pi$
$212$	−1934.42	+	3350.52i	−0.626683	+	1.08545i
$213$	−4791.55	−	3213.71i	−1.54137	−	1.03380i
$214$	−184.175	+	49.3496i	−0.0588316	+	0.0157639i
$215$	−1844.82	+	494.318i	−0.585189	+	0.156801i
$216$	177.470	−	868.431i	0.0559041	−	0.273561i
$217$	−546.101	+	945.874i	−0.170837	+	0.295899i
$218$	126.810	+	219.642i	0.0393976	+	0.0682387i
$219$	−131.655	+	1956.39i	−0.0406229	+	0.603655i
$220$			1792.92i			0.549448i
$221$	3156.22	+	2561.42i	0.960681	+	0.779638i
$222$	653.438	−	128.793i	0.197549	−	0.0389369i
$223$	−106.418	+	397.157i	−0.0319564	+	0.119263i	−0.980062	−	0.198694i	$-0.936330\pi$
$223$	−106.418	+	397.157i	−0.0319564	+	0.119263i	0.948105	+	0.317957i	$0.102997\pi$
$224$	−520.764	+	300.663i	−0.155335	+	0.0896825i
$225$	−1260.35	−	170.402i	−0.373436	−	0.0504894i
$226$	−376.793	−	376.793i	−0.110902	−	0.110902i
$227$	−639.247	−	2385.70i	−0.186909	−	0.697554i	−0.994214	−	0.107419i	$-0.965741\pi$
$227$	−639.247	−	2385.70i	−0.186909	−	0.697554i	0.807305	−	0.590135i	$-0.200925\pi$
$228$	−3072.69	+	1508.63i	−0.892516	+	0.438207i
$229$	−715.743	+	715.743i	−0.206540	+	0.206540i	−0.802795	−	0.596255i	$-0.796655\pi$
$229$	−715.743	+	715.743i	−0.206540	+	0.206540i	0.596255	+	0.802795i	$0.296655\pi$
$230$	44.2770	+	25.5633i	0.0126936	+	0.00732868i
$231$	550.039	−	480.677i	0.156666	−	0.136910i
$232$	1543.06	+	413.461i	0.436666	+	0.117004i
$233$	−2579.01			−0.725137			−0.362568	−	0.931957i	$-0.618100\pi$
$233$	−2579.01			−0.725137			−0.362568	+	0.931957i	$0.618100\pi$
$234$	429.161	+	265.685i	0.119894	+	0.0742237i
$235$	−6936.53			−1.92549
$236$	−4232.67	−	1134.14i	−1.16747	−	0.312823i
$237$	4156.20	−	3632.09i	1.13913	−	0.995483i
$238$	241.588	+	139.481i	0.0657974	+	0.0379882i
$239$	−3170.20	+	3170.20i	−0.858005	+	0.858005i	−0.991103	−	0.133098i	$-0.957507\pi$
$239$	−3170.20	+	3170.20i	−0.858005	+	0.858005i	0.133098	+	0.991103i	$0.457507\pi$
$240$	3684.11	−	1808.82i	0.990868	−	0.486496i
$241$	976.518	+	3644.41i	0.261008	+	0.974097i	0.964648	+	0.263540i	$0.0848901\pi$
$241$	976.518	+	3644.41i	0.261008	+	0.974097i	−0.703640	+	0.710557i	$0.748443\pi$
$242$	289.689	+	289.689i	0.0769499	+	0.0769499i
$243$	3411.83	−	1645.70i	0.900695	−	0.434452i
$244$	604.192	−	348.831i	0.158522	−	0.0915229i
$245$	−943.751	+	3522.13i	−0.246098	+	0.918451i
$246$	256.512	−	50.5585i	0.0664821	−	0.0131036i
$247$	−407.471	−	3916.91i	−0.104967	−	1.00902i
$248$		−	855.561i		−	0.219065i
$249$	−223.815	+	3325.87i	−0.0569625	+	0.846460i
$250$	−203.785	−	352.967i	−0.0515541	−	0.0892943i
$251$	1349.09	−	2336.69i	0.339258	−	0.587611i	−0.645036	−	0.764152i	$-0.723157\pi$
$251$	1349.09	−	2336.69i	0.339258	−	0.587611i	0.984293	+	0.176541i	$0.0564908\pi$
$252$	−1575.22	−	658.924i	−0.393769	−	0.164716i
$253$	164.513	−	44.0811i	0.0408808	−	0.0109540i
$254$	−383.815	+	102.843i	−0.0948137	+	0.0254053i
$255$	−4909.55	−	3292.85i	−1.20568	−	0.808653i
$256$	−1652.82	+	2862.76i	−0.403519	+	0.698916i
$257$	−1058.94	−	1834.14i	−0.257023	−	0.445177i	0.708420	−	0.705791i	$-0.249408\pi$
$257$	−1058.94	−	1834.14i	−0.257023	−	0.445177i	−0.965443	+	0.260614i	$0.916075\pi$
$258$	−301.029	−	20.2578i	−0.0726406	−	0.00488835i
$259$		−	2591.98i		−	0.621844i
$260$	498.878	+	4795.58i	0.118996	+	1.14388i
$261$	2590.55	+	6316.36i	0.614372	+	1.49798i
$262$	−137.624	+	513.618i	−0.0324520	+	0.121112i
$263$	2902.33	−	1675.66i	0.680476	−	0.392873i	−0.119558	−	0.992827i	$-0.538148\pi$
$263$	2902.33	−	1675.66i	0.680476	−	0.392873i	0.800034	+	0.599954i	$0.204814\pi$
$264$	−184.875	+	541.519i	−0.0430994	+	0.126243i
$265$	4577.14	+	4577.14i	1.06103	+	1.06103i
$266$	−69.9489	−	261.053i	−0.0161235	−	0.0601736i
$267$	−1890.99	−	3851.46i	−0.433433	−	0.882792i
$268$	1661.36	−	1661.36i	0.378669	−	0.378669i
$269$	2819.10	+	1627.61i	0.638973	+	0.368911i	0.784219	−	0.620484i	$-0.213064\pi$
$269$	2819.10	+	1627.61i	0.638973	+	0.368911i	−0.145246	+	0.989396i	$0.546397\pi$
$270$	−656.656	−	328.109i	−0.148010	−	0.0739557i
$271$	−1871.71	−	501.522i	−0.419550	−	0.112418i	0.0428667	−	0.999081i	$-0.486351\pi$
$271$	−1871.71	−	501.522i	−0.419550	−	0.112418i	−0.462417	+	0.886663i	$0.653018\pi$
$272$	5221.27			1.16392
$273$	1337.46	−	1438.73i	0.296508	−	0.318959i
$274$	−404.013			−0.0890777
$275$	793.050	+	212.497i	0.173901	+	0.0465966i
$276$	−261.973	−	299.776i	−0.0571337	−	0.0653781i
$277$	1705.03	+	984.400i	0.369839	+	0.213527i	0.673388	−	0.739289i	$-0.264838\pi$
$277$	1705.03	+	984.400i	0.369839	+	0.213527i	−0.303549	+	0.952816i	$0.598172\pi$
$278$	−611.503	+	611.503i	−0.131926	+	0.131926i
$279$	2908.48	−	2215.68i	0.624107	−	0.475445i
$280$	173.018	+	645.713i	0.0369279	+	0.137817i
$281$	−4013.15	−	4013.15i	−0.851972	−	0.851972i	0.138404	−	0.990376i	$-0.455803\pi$
$281$	−4013.15	−	4013.15i	−0.851972	−	0.851972i	−0.990376	+	0.138404i	$0.955803\pi$
$282$	−1037.01	−	354.035i	−0.218982	−	0.0747605i
$283$	623.493	−	359.974i	0.130964	−	0.0756121i	−0.433087	−	0.901352i	$-0.642576\pi$
$283$	623.493	−	359.974i	0.130964	−	0.0756121i	0.564051	+	0.825740i	$0.309242\pi$
$284$	2253.30	−	8409.42i	0.470805	−	1.75707i
$285$	1107.53	+	5619.10i	0.230190	+	1.16788i
$286$	−253.008	−	205.328i	−0.0523100	−	0.0424520i
$287$		−	1017.50i		−	0.209272i
$288$	1996.70	−	255.790i	0.408531	−	0.0523352i
$289$	−1303.77	−	2258.20i	−0.265372	−	0.459638i
$290$	661.489	−	1145.73i	0.133945	−	0.231999i
$291$	1799.17	−	2682.51i	0.362438	−	0.540384i
$292$	−2858.02	+	765.805i	−0.572784	+	0.153477i
$293$	6009.42	−	1610.22i	1.19820	−	0.321058i	0.396081	−	0.918216i	$-0.370370\pi$
$293$	6009.42	−	1610.22i	1.19820	−	0.321058i	0.802124	+	0.597158i	$0.203703\pi$
$294$	−320.857	+	478.388i	−0.0636488	+	0.0948985i
$295$	−3665.80	+	6349.35i	−0.723495	+	1.25313i
$296$	1015.19	+	1758.37i	0.199348	+	0.345281i
$297$	−2319.67	+	773.911i	−0.453201	+	0.151202i
$298$			225.476i			0.0438304i
$299$	427.762	−	163.681i	0.0827362	−	0.0316585i
$300$	−371.125	−	1882.92i	−0.0714230	−	0.362369i
$301$	−303.904	+	1134.19i	−0.0581952	+	0.217187i
$302$	806.077	−	465.389i	0.153591	−	0.0886759i
$303$	−1968.26	−	671.965i	−0.373180	−	0.127404i
$304$	−3576.86	−	3576.86i	−0.674826	−	0.674826i
$305$	−302.113	−	1127.50i	−0.0567178	−	0.211674i
$306$	−565.911	−	742.859i	−0.105722	−	0.138779i
$307$	4713.68	−	4713.68i	0.876300	−	0.876300i	−0.116849	−	0.993150i	$-0.537279\pi$
$307$	4713.68	−	4713.68i	0.876300	−	0.876300i	0.993150	+	0.116849i	$0.0372795\pi$
$308$	954.600	+	551.139i	0.176602	+	0.101961i
$309$	298.276	+	341.317i	0.0549137	+	0.0628378i
$310$	−684.400	−	183.384i	−0.125391	−	0.0335985i
$311$	−7918.09			−1.44371			−0.721855	−	0.692044i	$-0.756710\pi$
$311$	−7918.09			−1.44371			−0.721855	+	0.692044i	$0.756710\pi$
$312$	−343.813	+	1499.86i	−0.0623865	+	0.272156i
$313$	4753.29			0.858376			0.429188	−	0.903215i	$-0.358800\pi$
$313$	4753.29			0.858376			0.429188	+	0.903215i	$0.358800\pi$
$314$	450.079	+	120.598i	0.0808900	+	0.0216744i
$315$	−1747.03	+	2260.40i	−0.312488	+	0.404315i
$316$	7213.15	+	4164.51i	1.28409	+	0.741367i
$317$	−3448.47	+	3448.47i	−0.610995	+	0.610995i	−0.943205	−	0.332210i	$-0.892206\pi$
$317$	−3448.47	+	3448.47i	−0.610995	+	0.610995i	0.332210	+	0.943205i	$0.392206\pi$
$318$	450.667	+	917.894i	0.0794722	+	0.161865i
$319$	−1140.66	−	4257.01i	−0.200203	−	0.747169i
$320$	4192.25	+	4192.25i	0.732356	+	0.732356i
$321$	802.602	−	2350.91i	0.139554	−	0.408770i
$322$	27.2213	−	15.7162i	0.00471112	−	0.00271997i
$323$	−1885.76	+	7037.75i	−0.324850	+	1.21236i
$324$	4013.56	+	4069.94i	0.688196	+	0.697864i
$325$	2180.32	+	347.708i	0.372131	+	0.0593457i
$326$		−	540.702i		−	0.0918611i
$327$	−3296.80	−	221.858i	−0.557533	−	0.0375192i
$328$	398.522	+	690.260i	0.0670875	+	0.116199i
$329$	−2132.27	+	3693.20i	−0.357313	+	0.618884i
$330$	393.557	+	263.960i	0.0656503	+	0.0440319i
$331$	−2176.61	+	583.220i	−0.361442	+	0.0968480i	−0.434970	−	0.900445i	$-0.643241\pi$
$331$	−2176.61	+	583.220i	−0.361442	+	0.0968480i	0.0735279	+	0.997293i	$0.476574\pi$
$332$	−4858.66	+	1301.87i	−0.803173	+	0.215210i
$333$	−3348.48	+	8004.86i	−0.551037	+	1.31731i
$334$	117.216	−	203.025i	0.0192030	−	0.0332605i
$335$	−1965.51	−	3404.37i	−0.320559	−	0.555225i
$336$	169.418	−	2517.55i	0.0275075	−	0.408761i
$337$		−	10958.3i		−	1.77132i	−0.464336	−	0.885659i	$-0.653707\pi$
$337$		−	10958.3i		−	1.77132i	0.464336	−	0.885659i	$-0.346293\pi$
$338$	−733.860	−	478.798i	−0.118097	−	0.0770507i
$339$	6811.31	−	1342.51i	1.09127	−	0.215089i
$340$	2308.79	−	8616.52i	0.368270	−	1.37440i
$341$	−2044.11	+	1180.17i	−0.324619	+	0.187419i
$342$	−121.220	+	896.580i	−0.0191661	+	0.141759i
$343$	3541.33	+	3541.33i	0.557475	+	0.557475i
$344$	−238.059	−	888.449i	−0.0373119	−	0.139250i
$345$	−597.915	+	293.564i	−0.0933063	+	0.0458115i
$346$	−404.695	+	404.695i	−0.0628801	+	0.0628801i
$347$	−7402.99	−	4274.12i	−1.14528	−	0.661229i	−0.197550	−	0.980293i	$-0.563298\pi$
$347$	−7402.99	−	4274.12i	−1.14528	−	0.661229i	−0.947733	+	0.319064i	$0.896632\pi$
$348$	−7757.14	+	6778.93i	−1.19490	+	1.04422i
$349$	−4141.49	−	1109.71i	−0.635212	−	0.170204i	−0.0731780	−	0.997319i	$-0.523314\pi$
$349$	−4141.49	−	1109.71i	−0.635212	−	0.170204i	−0.562033	+	0.827114i	$0.689981\pi$
$350$	151.523			0.0231407
$351$	−5989.15	+	2715.45i	−0.910761	+	0.412934i
$352$	−1299.52			−0.196774
$353$	4912.09	+	1316.19i	0.740635	+	0.198452i	0.609360	−	0.792894i	$-0.291426\pi$
$353$	4912.09	+	1316.19i	0.740635	+	0.198452i	0.131274	+	0.991346i	$0.458093\pi$
$354$	−872.101	+	762.125i	−0.130937	+	0.114425i
$355$	−12614.8	−	7283.17i	−1.88599	−	1.08887i
$356$	4578.18	−	4578.18i	0.681581	−	0.681581i
$357$	−3262.39	+	1601.77i	−0.483653	+	0.237463i
$358$	−203.024	−	757.694i	−0.0299724	−	0.111859i
$359$	3520.53	+	3520.53i	0.517566	+	0.517566i	0.916834	−	0.399268i	$-0.130736\pi$
$359$	3520.53	+	3520.53i	0.517566	+	0.517566i	−0.399268	+	0.916834i	$0.630736\pi$
$360$	299.836	−	2217.69i	0.0438965	−	0.324673i
$361$	173.030	−	99.8990i	0.0252267	−	0.0145647i
$362$	242.748	−	905.947i	0.0352446	−	0.131535i
$363$	−5236.71	+	1032.16i	−0.757179	+	0.149240i
$364$	2706.65	+	1208.53i	0.389745	+	0.174023i
$365$			4950.51i			0.709922i
$366$	12.3809	−	183.980i	0.00176820	−	0.0262754i
$367$	4636.12	+	8030.00i	0.659410	+	1.14213i	0.980769	+	0.195174i	$0.0625272\pi$
$367$	4636.12	+	8030.00i	0.659410	+	1.14213i	−0.321359	+	0.946958i	$0.604139\pi$
$368$	294.158	−	509.496i	0.0416685	−	0.0721720i
$369$	−1314.47	+	3142.37i	−0.185443	+	0.443320i
$370$	1624.19	−	435.202i	0.228210	−	0.0611488i
$371$	3844.00	−	1030.00i	0.537926	−	0.144137i
$372$	4582.11	+	3073.24i	0.638633	+	0.428334i
$373$	2570.35	−	4451.98i	0.356804	−	0.618003i	−0.630621	−	0.776091i	$-0.717200\pi$
$373$	2570.35	−	4451.98i	0.356804	−	0.618003i	0.987425	+	0.158088i	$0.0505331\pi$
$374$	301.429	+	522.091i	0.0416752	+	0.0721836i
$375$	5297.98	+	356.528i	0.729564	+	0.0490960i
$376$		−	3340.57i		−	0.458183i
$377$	−4235.48	−	11069.0i	−0.578616	−	1.51215i
$378$	−376.548	+	248.762i	−0.0512369	+	0.0338490i
$379$	−392.052	+	1463.16i	−0.0531356	+	0.198305i	−0.987391	−	0.158300i	$-0.949399\pi$
$379$	−392.052	+	1463.16i	−0.0531356	+	0.198305i	0.934256	+	0.356604i	$0.116065\pi$
$380$	−7484.44	+	4321.14i	−1.01038	+	0.583342i
$381$	1672.59	−	4899.22i	0.224907	−	0.658778i
$382$	984.436	+	984.436i	0.131854	+	0.131854i
$383$	3340.19	+	12465.8i	0.445629	+	1.66311i	0.714271	+	0.699870i	$0.246759\pi$
$383$	3340.19	+	12465.8i	0.445629	+	1.66311i	−0.268642	+	0.963240i	$0.586575\pi$
$384$	1778.68	+	3622.72i	0.236375	+	0.481436i
$385$	1304.08	−	1304.08i	0.172629	−	0.172629i
$386$	1485.31	+	857.547i	0.195856	+	0.113078i
$387$	2403.77	−	3110.13i	0.315737	−	0.408519i
$388$	4707.95	+	1261.49i	0.616006	+	0.165058i
$389$	4921.52			0.641468			0.320734	−	0.947169i	$-0.396070\pi$
$389$	4921.52			0.641468			0.320734	+	0.947169i	$0.396070\pi$
$390$	1126.11	+	596.516i	0.146212	+	0.0774507i
$391$	−847.390			−0.109602
$392$	−1696.23	−	454.502i	−0.218552	−	0.0585608i
$393$	−4558.62	−	5216.43i	−0.585119	−	0.669552i
$394$	1660.35	+	958.604i	0.212303	+	0.122573i
$395$	9853.88	−	9853.88i	1.25520	−	1.25520i
$396$	−2236.12	−	2935.31i	−0.283761	−	0.372487i
$397$	2728.21	+	10181.8i	0.344899	+	1.28718i	0.892730	+	0.450592i	$0.148787\pi$
$397$	2728.21	+	10181.8i	0.344899	+	1.28718i	−0.547831	+	0.836589i	$0.684546\pi$
$398$	−40.2325	−	40.2325i	−0.00506702	−	0.00506702i
$399$	3332.22	+	1137.62i	0.418094	+	0.142737i
$400$	2456.08	−	1418.02i	0.307009	−	0.177252i
$401$	1573.47	−	5872.27i	0.195949	−	0.731290i	−0.796071	−	0.605204i	$-0.793092\pi$
$401$	1573.47	−	5872.27i	0.195949	−	0.731290i	0.992019	−	0.126086i	$-0.0402416\pi$
$402$	−120.087	−	609.269i	−0.0148990	−	0.0755910i
$403$	−5139.08	+	3725.41i	−0.635225	+	0.460486i
$404$		−	3138.40i		−	0.386488i
$405$	8315.51	−	4723.93i	1.02025	−	0.579590i
$406$	−406.680	−	704.391i	−0.0497123	−	0.0861042i
$407$	2800.74	−	4851.02i	0.341099	−	0.590802i
$408$	1585.81	−	2364.40i	0.192425	−	0.286900i
$409$	−12176.5	+	3262.69i	−1.47210	+	0.394449i	−0.903652	−	0.428267i	$-0.859124\pi$
$409$	−12176.5	+	3262.69i	−1.47210	+	0.394449i	−0.568452	+	0.822716i	$0.692457\pi$
$410$	637.589	−	170.842i	0.0768007	−	0.0205787i
$411$	2931.93	−	4371.42i	0.351877	−	0.524638i
$412$	−342.000	+	592.361i	−0.0408959	+	0.0708338i
$413$	2253.71	+	3903.55i	0.268518	+	0.465087i
$414$	−104.371	+	13.3706i	−0.0123903	+	0.00158727i
$415$			8415.90i			0.995471i
$416$	−3475.86	+	361.589i	−0.409658	+	0.0426162i
$417$	−2178.78	−	11054.2i	−0.255864	−	1.29814i
$418$	151.165	−	564.157i	0.0176884	−	0.0660139i
$419$	−1321.13	+	762.753i	−0.154036	+	0.0889330i	−0.575037	−	0.818127i	$-0.695012\pi$
$419$	−1321.13	+	762.753i	−0.154036	+	0.0889330i	0.421001	+	0.907060i	$0.361679\pi$
$420$	−4079.73	−	1392.82i	−0.473977	−	0.161816i
$421$	1192.56	+	1192.56i	0.138057	+	0.138057i	0.772758	−	0.634701i	$-0.218877\pi$
$421$	1192.56	+	1192.56i	0.138057	+	0.138057i	−0.634701	+	0.772758i	$0.718877\pi$
$422$	213.273	+	795.945i	0.0246018	+	0.0918151i
$423$	11356.3	−	8651.20i	1.30534	−	0.994411i
$424$	−2204.31	+	2204.31i	−0.252478	+	0.252478i
$425$	−3537.65	−	2042.46i	−0.403768	−	0.233115i
$426$	−1514.18	−	1732.68i	−0.172212	−	0.197063i
$427$	−693.181	−	185.737i	−0.0785606	−	0.0210502i
$428$	3748.54			0.423347
$429$	4057.73	−	1247.48i	0.456665	−	0.140394i
$430$	−761.735			−0.0854282
$431$	−12585.3	−	3372.23i	−1.40653	−	0.376879i	−0.525846	−	0.850580i	$-0.676251\pi$
$431$	−12585.3	−	3372.23i	−1.40653	−	0.376879i	−0.880686	+	0.473701i	$0.842918\pi$
$432$	−3775.55	+	7556.14i	−0.420489	+	0.841540i
$433$	8046.81	+	4645.83i	0.893083	+	0.515622i	0.874950	−	0.484214i	$-0.160894\pi$
$433$	8046.81	+	4645.83i	0.893083	+	0.515622i	0.0181336	+	0.999836i	$0.494228\pi$
$434$	−308.022	+	308.022i	−0.0340680	+	0.0340680i
$435$	7596.41	+	15471.9i	0.837287	+	1.70534i
$436$	−1290.49	−	4816.18i	−0.141751	−	0.529021i
$437$	580.509	+	580.509i	0.0635458	+	0.0635458i
$438$	−252.670	+	740.098i	−0.0275640	+	0.0807381i
$439$	−2574.82	+	1486.57i	−0.279930	+	0.161618i	−0.633392	−	0.773831i	$-0.718338\pi$
$439$	−2574.82	+	1486.57i	−0.279930	+	0.161618i	0.353461	+	0.935449i	$0.385005\pi$
$440$	−373.907	+	1395.44i	−0.0405121	+	0.151193i
$441$	−2847.70	−	6943.35i	−0.307494	−	0.749741i
$442$	951.514	+	1312.58i	0.102396	+	0.141251i
$443$			7839.82i			0.840815i	0.907335	+	0.420408i	$0.138113\pi$
$443$			7839.82i			0.840815i	−0.907335	+	0.420408i	$0.861887\pi$
$444$	−13063.9	−	879.136i	−1.39637	−	0.0939684i
$445$	−5416.34	−	9381.37i	−0.576987	−	0.999370i
$446$	−81.9940	+	142.018i	−0.00870522	+	0.0150779i
$447$	−2439.65	−	1636.29i	−0.258147	−	0.173140i
$448$	3520.76	−	943.384i	0.371295	−	0.0994882i
$449$	−491.353	+	131.658i	−0.0516445	+	0.0138381i	−0.284549	−	0.958662i	$-0.591844\pi$
$449$	−491.353	+	131.658i	−0.0516445	+	0.0138381i	0.232904	+	0.972500i	$0.425177\pi$
$450$	−467.952	−	195.747i	−0.0490211	−	0.0205058i
$451$	1099.45	−	1904.30i	0.114792	−	0.198825i
$452$	5237.96	+	9072.42i	0.545073	+	0.944094i
$453$	−814.209	+	12099.1i	−0.0844478	+	1.25489i
$454$		−	985.068i		−	0.101832i
$455$	3125.20	−	3850.92i	0.322004	−	0.396778i
$456$	−2706.11	+	533.374i	−0.277906	+	0.0547753i
$457$	−2359.36	+	8805.25i	−0.241501	+	0.901296i	0.733608	+	0.679573i	$0.237835\pi$
$457$	−2359.36	+	8805.25i	−0.241501	+	0.901296i	−0.975110	+	0.221723i	$0.928832\pi$
$458$	−349.620	+	201.853i	−0.0356696	+	0.0205938i
$459$	12144.6	−	732.212i	1.23499	−	0.0744591i
$460$	−710.733	−	710.733i	−0.0720394	−	0.0720394i
$461$	1712.08	+	6389.57i	0.172971	+	0.645536i	0.996888	+	0.0788261i	$0.0251172\pi$
$461$	1712.08	+	6389.57i	0.172971	+	0.645536i	−0.823918	+	0.566710i	$0.808216\pi$
$462$	261.518	−	128.400i	0.0263353	−	0.0129301i
$463$	−6978.45	+	6978.45i	−0.700467	+	0.700467i	−0.964511	−	0.264044i	$-0.914944\pi$
$463$	−6978.45	+	6978.45i	−0.700467	+	0.700467i	0.264044	+	0.964511i	$0.414944\pi$
$464$	−13184.0	−	7611.77i	−1.31907	−	0.761568i
$465$	6950.93	−	6074.39i	0.693208	−	0.605792i
$466$	−993.553	−	266.222i	−0.0987671	−	0.0264646i
$467$	7546.08			0.747732			0.373866	−	0.927483i	$-0.378032\pi$
$467$	7546.08			0.747732			0.373866	+	0.927483i	$0.378032\pi$
$468$	−6797.76	−	7228.96i	−0.671425	−	0.714015i
$469$	−2416.77			−0.237945
$470$	−2672.27	−	716.031i	−0.262260	−	0.0702725i
$471$	−4571.12	+	3994.68i	−0.447189	+	0.390797i
$472$	−3057.79	−	1765.42i	−0.298191	−	0.172161i
$473$	−1794.31	+	1794.31i	−0.174424	+	0.174424i
$474$	1976.08	−	970.216i	0.191486	−	0.0940158i
$475$	1024.29	+	3822.69i	0.0989420	+	0.369257i
$476$	−3877.96	−	3877.96i	−0.373416	−	0.373416i
$477$	−13202.1	−	1784.96i	−1.26726	−	0.171337i
$478$	−1548.55	+	894.056i	−0.148178	+	0.0855506i
$479$	−2233.30	+	8334.80i	−0.213032	+	0.795045i	0.773818	+	0.633407i	$0.218344\pi$
$479$	−2233.30	+	8334.80i	−0.213032	+	0.795045i	−0.986850	+	0.161638i	$0.948322\pi$
$480$	4986.38	−	982.817i	0.474159	−	0.0934568i
$481$	6141.43	−	13754.5i	0.582173	−	1.30385i
$482$			1504.79i			0.142202i
$483$	−27.4959	+	408.587i	−0.00259028	+	0.0384914i
$484$	−4027.08	−	6975.11i	−0.378201	−	0.655063i
$485$	4077.43	−	7062.32i	0.381746	−	0.661203i
$486$	1484.27	−	281.809i	0.138535	−	0.0263027i
$487$	13107.2	−	3512.07i	1.21960	−	0.326791i	0.409079	−	0.912499i	$-0.365850\pi$
$487$	13107.2	−	3512.07i	1.21960	−	0.326791i	0.810522	+	0.585708i	$0.199184\pi$
$488$	542.994	−	145.495i	0.0503692	−	0.0134964i
$489$	5850.41	+	3923.89i	0.541032	+	0.362872i
$490$	−727.151	+	1259.46i	−0.0670395	+	0.116116i
$491$	−885.643	−	1533.98i	−0.0814023	−	0.140993i	0.822450	−	0.568837i	$-0.192607\pi$
$491$	−885.643	−	1533.98i	−0.0814023	−	0.140993i	−0.903852	+	0.427844i	$0.859273\pi$
$492$	−5128.34	−	345.111i	−0.469925	−	0.0316236i
$493$			21927.5i			2.00317i
$494$	247.351	−	1551.03i	0.0225280	−	0.141263i
$495$	−5712.11	+	2342.73i	−0.518667	+	0.212723i
$496$	−2110.21	+	7875.40i	−0.191030	+	0.712935i
$497$	−7755.52	+	4477.65i	−0.699965	+	0.404125i
$498$	−429.540	+	1258.17i	−0.0386509	+	0.113213i
$499$	−6158.97	−	6158.97i	−0.552532	−	0.552532i	0.374639	−	0.927171i	$-0.377767\pi$
$499$	−6158.97	−	6158.97i	−0.552532	−	0.552532i	−0.927171	+	0.374639i	$0.877767\pi$
$500$	2073.83	+	7739.65i	0.185489	+	0.692255i
$501$	1346.09	+	2741.64i	0.120037	+	0.244486i
$502$	760.937	−	760.937i	0.0676539	−	0.0676539i
$503$	1904.60	+	1099.62i	0.168831	+	0.0974748i	0.582035	−	0.813164i	$-0.302257\pi$
$503$	1904.60	+	1099.62i	0.168831	+	0.0974748i	−0.413203	+	0.910639i	$0.635590\pi$
$504$	−1088.59	−	841.352i	−0.0962095	−	0.0743587i
$505$	−5072.01	−	1359.04i	−0.446934	−	0.119756i
$506$	67.9281			0.00596793
$507$	10506.2	−	4465.73i	0.920313	−	0.391184i
$508$	7811.82			0.682270
$509$	−2770.61	−	742.382i	−0.241267	−	0.0646474i	0.136159	−	0.990687i	$-0.456524\pi$
$509$	−2770.61	−	742.382i	−0.241267	−	0.0646474i	−0.377426	+	0.926040i	$0.623191\pi$
$510$	−1551.47	−	1775.35i	−0.134707	−	0.154145i
$511$	2635.79	+	1521.77i	0.228181	+	0.131740i
$512$	−5325.90	+	5325.90i	−0.459714	+	0.459714i
$513$	−8821.31	−	7818.10i	−0.759202	−	0.672861i
$514$	−218.621	−	815.904i	−0.0187606	−	0.0700155i
$515$	809.224	+	809.224i	0.0692402	+	0.0692402i
$516$	5613.38	+	1916.41i	0.478905	+	0.163498i
$517$	−7981.32	+	4608.02i	−0.678952	+	0.391993i
$518$	267.560	−	998.546i	0.0226948	−	0.0846981i
$519$	−1441.92	−	7315.69i	−0.121953	−	0.618734i
$520$	−611.821	+	3836.47i	−0.0515964	+	0.323539i
$521$		−	8470.91i		−	0.712318i	−0.934425	−	0.356159i	$-0.884086\pi$
$521$		−	8470.91i		−	0.712318i	0.934425	−	0.356159i	$-0.115914\pi$
$522$	345.984	+	2700.76i	0.0290101	+	0.226454i
$523$	−1288.59	−	2231.91i	−0.107737	−	0.186605i	0.807116	−	0.590392i	$-0.201027\pi$
$523$	−1288.59	−	2231.91i	−0.107737	−	0.186605i	−0.914853	+	0.403787i	$0.867694\pi$
$524$	5226.86	−	9053.19i	0.435757	−	0.754752i
$525$	−1099.61	+	1639.48i	−0.0914110	+	0.136291i
$526$	1291.08	−	345.944i	0.107022	−	0.0286766i
$527$	11343.5	−	3039.47i	0.937626	−	0.251236i
$528$	3037.39	−	4528.67i	0.250352	−	0.373267i
$529$	6035.76	−	10454.2i	0.496076	−	0.859229i
$530$	1290.84	+	2235.80i	0.105794	+	0.183240i
$531$	−1917.35	−	14966.9i	−0.156697	−	1.22318i
$532$			5313.23i			0.433003i
$533$	2410.86	−	5399.42i	0.195921	−	0.438790i
$534$	−330.922	−	1678.96i	−0.0268173	−	0.136059i
$535$	1623.25	−	6058.06i	0.131176	−	0.489557i
$536$	1639.51	−	946.573i	0.132120	−	0.0762793i
$537$	9671.61	+	3301.89i	0.777208	+	0.265339i
$538$	918.034	+	918.034i	0.0735674	+	0.0735674i
$539$	1253.89	+	4679.58i	0.100202	+	0.373959i
$540$	10800.2	+	9571.93i	0.860678	+	0.762796i
$541$	2462.90	−	2462.90i	0.195727	−	0.195727i	−0.602439	−	0.798165i	$-0.705804\pi$
$541$	2462.90	−	2462.90i	0.195727	−	0.195727i	0.798165	+	0.602439i	$0.205804\pi$
$542$	−669.295	−	386.418i	−0.0530419	−	0.0306237i
$543$	8040.73	+	9201.01i	0.635471	+	0.727170i
$544$	6245.29	+	1673.42i	0.492214	+	0.131888i
$545$	−8342.33			−0.655681
$546$	663.764	−	416.203i	0.0520265	−	0.0326224i
$547$	−438.582			−0.0342823			−0.0171411	−	0.999853i	$-0.505456\pi$
$547$	−438.582			−0.0342823			−0.0171411	+	0.999853i	$0.505456\pi$
$548$	7672.08	+	2055.73i	0.598056	+	0.160249i
$549$	1900.82	+	1469.11i	0.147769	+	0.114208i
$550$	283.583	+	163.727i	0.0219855	+	0.0126934i
$551$	15021.5	−	15021.5i	1.16141	−	1.16141i
$552$	−141.378	−	287.951i	−0.0109012	−	0.0222029i
$553$	−2217.42	−	8275.53i	−0.170514	−	0.636368i
$554$	555.239	+	555.239i	0.0425809	+	0.0425809i
$555$	−7077.94	+	20732.1i	−0.541336	+	1.58564i
$556$	14723.8	−	8500.76i	1.12307	−	0.648404i
$557$	−1707.29	+	6371.71i	−0.129875	+	0.484700i	−0.999966	−	0.00819010i	$-0.997393\pi$
$557$	−1707.29	+	6371.71i	−0.129875	+	0.484700i	0.870091	+	0.492890i	$0.164060\pi$
$558$	1349.19	−	553.349i	0.102358	−	0.0419805i
$559$	−4300.03	+	5298.56i	−0.325352	+	0.400904i
$560$		−	6370.49i		−	0.480719i
$561$	−7836.51	−	527.358i	−0.589765	−	0.0396882i
$562$	−1131.78	−	1960.31i	−0.0849491	−	0.147136i
$563$	−5255.63	+	9103.02i	−0.393425	+	0.681432i	−0.992899	−	0.118962i	$-0.962043\pi$
$563$	−5255.63	+	9103.02i	−0.393425	+	0.681432i	0.599474	+	0.800395i	$0.295377\pi$
$564$	17891.0	+	11999.6i	1.33572	+	0.895876i
$565$	16930.3	−	4536.46i	1.26064	−	0.337788i
$566$	277.356	−	74.3174i	0.0205974	−	0.00551907i
$567$	41.0123	−	5879.53i	0.00303766	−	0.435480i
$568$	3507.51	−	6075.19i	0.259105	−	0.448784i
$569$	−4855.53	−	8410.03i	−0.357741	−	0.619625i	0.629842	−	0.776723i	$-0.283120\pi$
$569$	−4855.53	−	8410.03i	−0.357741	−	0.619625i	−0.987583	+	0.157098i	$0.949786\pi$
$570$	−153.369	+	2279.06i	−0.0112700	+	0.167472i
$571$		−	12838.3i		−	0.940923i	−0.882421	−	0.470462i	$-0.844087\pi$
$571$		−	12838.3i		−	0.940923i	0.882421	−	0.470462i	$-0.155913\pi$
$572$	3759.78	+	5186.48i	0.274832	+	0.379122i
$573$	−17795.7	+	3507.53i	−1.29743	+	0.255723i
$574$	105.032	−	391.986i	0.00763758	−	0.0285038i
$575$	−398.610	+	230.138i	−0.0289099	+	0.0166911i
$576$	−12092.0	−	1634.86i	−0.874708	−	0.118263i
$577$	−11174.3	−	11174.3i	−0.806225	−	0.806225i	0.177835	−	0.984060i	$-0.443091\pi$
$577$	−11174.3	−	11174.3i	−0.806225	−	0.806225i	−0.984060	+	0.177835i	$0.943091\pi$
$578$	−269.167	−	1004.55i	−0.0193700	−	0.0722899i
$579$	−20057.6	+	9847.89i	−1.43967	+	0.706847i
$580$	−18391.3	+	18391.3i	−1.31665	+	1.31665i
$581$	4480.86	+	2587.03i	0.319961	+	0.184730i
$582$	970.028	−	847.704i	0.0690876	−	0.0603754i
$583$	8307.21	+	2225.91i	0.590136	+	0.158127i
$584$	−2384.12			−0.168931
$585$	−14626.5	+	7855.55i	−1.03373	+	0.555192i
$586$	2481.32			0.174918
$587$	3095.75	+	829.503i	0.217675	+	0.0583258i	0.366008	−	0.930612i	$-0.380724\pi$
$587$	3095.75	+	829.503i	0.217675	+	0.0583258i	−0.148333	+	0.988937i	$0.547391\pi$
$588$	8527.14	−	7451.84i	0.598050	−	0.522634i
$589$	−9853.10	−	5688.69i	−0.689287	−	0.397960i
$590$	−2067.65	+	2067.65i	−0.144278	+	0.144278i
$591$	−22421.3	+	11008.4i	−1.56056	+	0.766202i
$592$	−5007.87	−	18689.6i	−0.347673	−	1.29753i
$593$	3772.38	+	3772.38i	0.261236	+	0.261236i	0.825556	−	0.564320i	$-0.190862\pi$
$593$	3772.38	+	3772.38i	0.261236	+	0.261236i	−0.564320	+	0.825556i	$0.690862\pi$
$594$	−973.528	+	58.6952i	−0.0672464	+	0.00405437i
$595$	−7946.52	+	4587.92i	−0.547522	+	0.316112i
$596$	1147.28	−	4281.72i	0.0788499	−	0.294272i
$597$	727.285	−	143.348i	0.0498590	−	0.00982721i
$598$	181.689	−	18.9009i	0.0124245	−	0.00129250i
$599$			3711.84i			0.253192i	0.991954	+	0.126596i	$0.0404051\pi$
$599$			3711.84i			0.253192i	−0.991954	+	0.126596i	$0.959595\pi$
$600$	103.829	−	1542.89i	0.00706464	−	0.104980i
$601$	11370.7	+	19694.6i	0.771747	+	1.33671i	0.936605	+	0.350388i	$0.113950\pi$
$601$	11370.7	+	19694.6i	0.771747	+	1.33671i	−0.164858	+	0.986317i	$0.552716\pi$
$602$	−234.155	+	405.569i	−0.0158529	+	0.0274580i
$603$	7463.77	+	3122.14i	0.504060	+	0.210851i
$604$	−17675.2	+	4736.05i	−1.19072	+	0.319052i
$605$	−13016.4	+	3487.75i	−0.874700	+	0.234375i
$606$	−688.899	−	462.047i	−0.0461792	−	0.0309726i
$607$	8310.20	−	14393.7i	0.555685	−	0.962474i	−0.442165	−	0.896934i	$-0.645789\pi$
$607$	8310.20	−	14393.7i	0.555685	−	0.962474i	0.997850	−	0.0655408i	$-0.0208772\pi$
$608$	−3131.98	−	5424.76i	−0.208912	−	0.361847i
$609$	10572.8	+	711.497i	0.703500	+	0.0473420i
$610$		−	465.550i		−	0.0309009i
$611$	−20065.7	+	14546.0i	−1.32860	+	0.963123i
$612$	6966.60	+	16986.2i	0.460144	+	1.12194i
$613$	5842.51	−	21804.5i	0.384954	−	1.43667i	−0.453286	−	0.891365i	$-0.649748\pi$
$613$	5842.51	−	21804.5i	0.384954	−	1.43667i	0.838240	−	0.545302i	$-0.183585\pi$
$614$	2302.50	−	1329.35i	0.151338	−	0.0873748i
$615$	−2778.49	+	8138.53i	−0.182178	+	0.533621i
$616$	628.033	+	628.033i	0.0410782	+	0.0410782i
$617$	−6037.74	−	22533.2i	−0.393955	−	1.47026i	−0.823552	−	0.567240i	$-0.808011\pi$
$617$	−6037.74	−	22533.2i	−0.393955	−	1.47026i	0.429597	−	0.903021i	$-0.358656\pi$
$618$	79.6765	+	162.281i	0.00518618	+	0.0105629i
$619$	6944.59	−	6944.59i	0.450931	−	0.450931i	−0.444732	−	0.895664i	$-0.646701\pi$
$619$	6944.59	−	6944.59i	0.450931	−	0.450931i	0.895664	+	0.444732i	$0.146701\pi$
$620$	12063.4	+	6964.83i	0.781418	+	0.451152i
$621$	612.755	−	1226.33i	0.0395958	−	0.0792446i
$622$	−3050.41	−	817.354i	−0.196640	−	0.0526896i
$623$	−6659.87			−0.428286
$624$	6864.12	−	12958.1i	0.440360	−	0.831314i
$625$	19294.2			1.23483
$626$	1831.18	+	490.663i	0.116915	+	0.0313272i
$627$	5007.18	+	5729.72i	0.318927	+	0.364949i
$628$	−7933.23	−	4580.25i	−0.504093	−	0.291038i
$629$	−19706.7	+	19706.7i	−1.24922	+	1.24922i
$630$	−906.365	+	690.470i	−0.0573182	+	0.0436650i
$631$	4646.15	+	17339.7i	0.293123	+	1.09395i	0.942697	+	0.333650i	$0.108281\pi$
$631$	4646.15	+	17339.7i	0.293123	+	1.09395i	−0.649574	+	0.760298i	$0.725053\pi$
$632$	4745.54	+	4745.54i	0.298683	+	0.298683i
$633$	−10159.9	−	3468.58i	−0.637943	−	0.217794i
$634$	−1684.48	+	972.535i	−0.105519	+	0.0609216i
$635$	3382.80	−	12624.8i	0.211405	−	0.788975i
$636$	−3887.53	−	19723.6i	−0.242375	−	1.22971i
$637$	4655.91	+	12167.7i	0.289598	+	0.756834i
$638$		−	1757.74i		−	0.109075i
$639$	29736.1	−	3809.37i	1.84091	−	0.235832i
$640$	5094.66	+	8824.22i	0.314663	+	0.545012i
$641$	−13618.0	+	23587.1i	−0.839127	+	1.45341i	0.0514990	+	0.998673i	$0.483600\pi$
$641$	−13618.0	+	23587.1i	−0.839127	+	1.45341i	−0.890626	+	0.454737i	$0.849733\pi$
$642$	551.874	−	822.828i	0.0339264	−	0.0505832i
$643$	10552.3	−	2827.48i	0.647188	−	0.173414i	0.0797310	−	0.996816i	$-0.474594\pi$
$643$	10552.3	−	2827.48i	0.647188	−	0.173414i	0.567457	+	0.823403i	$0.307927\pi$
$644$	−596.892	+	159.937i	−0.0365230	+	0.00978631i
$645$	5527.93	−	8241.98i	0.337461	−	0.503144i
$646$	−1452.96	+	2516.60i	−0.0884921	+	0.153273i
$647$	−3237.16	−	5606.92i	−0.196701	−	0.340697i	0.750756	−	0.660580i	$-0.229690\pi$
$647$	−3237.16	−	5606.92i	−0.196701	−	0.340697i	−0.947457	+	0.319883i	$0.896356\pi$
$648$	2275.00	+	4004.67i	0.137918	+	0.242775i
$649$			9740.93i			0.589160i
$650$	804.067	+	359.019i	0.0485201	+	0.0216644i
$651$	−1097.48	−	5568.12i	−0.0660730	−	0.335225i
$652$	−2751.24	+	10267.8i	−0.165256	+	0.616744i
$653$	4894.25	−	2825.70i	0.293303	−	0.169338i	−0.346128	−	0.938187i	$-0.612504\pi$
$653$	4894.25	−	2825.70i	0.293303	−	0.169338i	0.639430	+	0.768849i	$0.279170\pi$
$654$	−1247.17	−	425.785i	−0.0745693	−	0.0254580i
$655$	−12367.6	−	12367.6i	−0.737772	−	0.737772i
$656$	−1965.88	−	7336.75i	−0.117004	−	0.436664i
$657$	−6174.25	−	8104.81i	−0.366637	−	0.481276i
$658$	−1202.68	+	1202.68i	−0.0712545	+	0.0712545i
$659$	19830.2	+	11449.0i	1.17219	+	0.676767i	0.954196	−	0.299182i	$-0.0967139\pi$
$659$	19830.2	+	11449.0i	1.17219	+	0.676767i	0.217999	+	0.975949i	$0.430047\pi$
$660$	−6130.43	−	7015.05i	−0.361555	−	0.413728i
$661$	−15487.7	−	4149.92i	−0.911349	−	0.244195i	−0.227465	−	0.973786i	$-0.573044\pi$
$661$	−15487.7	−	4149.92i	−0.911349	−	0.244195i	−0.683884	+	0.729591i	$0.739711\pi$
$662$	−898.731			−0.0527646
$663$	−21107.3	+	769.960i	−1.23641	+	0.0451022i
$664$	−4053.02			−0.236879
$665$	8586.78	+	2300.82i	0.500724	+	0.134169i
$666$	−2116.30	+	2738.18i	−0.123130	+	0.159313i
$667$	2139.70	+	1235.36i	0.124212	+	0.0717139i
$668$	−3258.95	+	3258.95i	−0.188761	+	0.188761i
$669$	−941.601	−	1917.80i	−0.0544162	−	0.110832i
$670$	−405.784	−	1514.41i	−0.0233982	−	0.0873234i
$671$	−1096.63	−	1096.63i	−0.0630922	−	0.0630922i
$672$	1009.52	−	2957.00i	0.0579511	−	0.169745i
$673$	−28070.5	+	16206.5i	−1.60778	+	0.928254i	−0.617919	+	0.786242i	$0.712024\pi$
$673$	−28070.5	+	16206.5i	−1.60778	+	0.928254i	−0.989865	+	0.142013i	$0.954643\pi$
$674$	1131.18	−	4221.61i	0.0646459	−	0.241262i
$675$	5513.93	−	3642.71i	0.314417	−	0.207715i
$676$	11499.5	+	12826.3i	0.654275	+	0.729762i
$677$		−	24143.1i		−	1.37060i	−0.728263	−	0.685298i	$-0.759672\pi$
$677$		−	24143.1i		−	1.37060i	0.728263	−	0.685298i	$-0.240328\pi$
$678$	2762.60	+	185.909i	0.156486	+	0.0105307i
$679$	−2506.78	−	4341.87i	−0.141681	−	0.245399i
$680$	3593.89	−	6224.80i	0.202675	−	0.351044i
$681$	10658.4	+	7148.66i	0.599754	+	0.402258i
$682$	−909.309	+	243.649i	−0.0510546	+	0.0136800i
$683$	2066.48	−	553.711i	0.115771	−	0.0310207i	−0.200468	−	0.979700i	$-0.564246\pi$
$683$	2066.48	−	553.711i	0.115771	−	0.0310207i	0.316239	+	0.948679i	$0.397580\pi$
$684$	6863.97	−	16409.0i	0.383699	−	0.917271i
$685$	6644.57	−	11508.7i	0.370622	−	0.641936i
$686$	998.724	+	1729.84i	0.0555852	+	0.0962764i
$687$	353.147	−	5247.74i	0.0196119	−	0.291432i
$688$			8765.29i			0.485717i
$689$	22838.9	+	3642.24i	1.26283	+	0.201391i
$690$	−260.647	+	51.3736i	−0.0143807	+	0.00283444i
$691$	−6283.63	+	23450.8i	−0.345934	+	1.29104i	0.545583	+	0.838057i	$0.316308\pi$
$691$	−6283.63	+	23450.8i	−0.345934	+	1.29104i	−0.891517	+	0.452987i	$0.850358\pi$
$692$	9744.23	−	5625.83i	0.535289	−	0.309049i
$693$	−508.554	+	3761.43i	−0.0278765	+	0.206183i
$694$	−2410.76	−	2410.76i	−0.131861	−	0.131861i
$695$	−7362.28	−	27476.4i	−0.401823	−	1.49962i
$696$	−7451.15	+	3658.36i	−0.405798	+	0.199238i
$697$	−7736.03	+	7736.03i	−0.420406	+	0.420406i
$698$	−1480.94	−	855.020i	−0.0803070	−	0.0463653i
$699$	10090.8	−	8818.28i	0.546020	−	0.477164i
$700$	−2877.38	−	770.990i	−0.155364	−	0.0416296i
$701$	16536.2			0.890959			0.445479	−	0.895292i	$-0.353033\pi$
$701$	16536.2			0.890959			0.445479	+	0.895292i	$0.353033\pi$
$702$	−2587.60	+	427.877i	−0.139120	+	0.0230045i
$703$	27000.4			1.44856
$704$	7608.66	+	2038.73i	0.407332	+	0.109144i
$705$	27140.2	−	23717.7i	1.44987	−	1.26704i
$706$	1756.49	+	1014.11i	0.0936352	+	0.0540603i
$707$	−2282.71	+	2282.71i	−0.121429	+	0.121429i
$708$	20438.8	−	10035.0i	1.08494	−	0.532684i
$709$	−1732.72	−	6466.61i	−0.0917825	−	0.342537i	0.904729	−	0.425987i	$-0.140073\pi$
$709$	−1732.72	−	6466.61i	−0.0917825	−	0.342537i	−0.996512	+	0.0834495i	$0.973406\pi$
$710$	−4107.99	−	4107.99i	−0.217141	−	0.217141i
$711$	−3842.74	+	28422.1i	−0.202692	+	1.49917i
$712$	4517.99	−	2608.46i	0.237807	−	0.137298i
$713$	342.477	−	1278.14i	0.0179886	−	0.0671344i
$714$	−1422.16	+	280.309i	−0.0745422	+	0.0146923i
$715$	10010.1	−	3830.29i	0.523574	−	0.200342i
$716$			15421.4i			0.804924i
$717$	1564.17	−	23243.5i	0.0814716	−	1.21066i
$718$	992.856	+	1719.68i	0.0516059	+	0.0893841i
$719$	3685.95	−	6384.25i	0.191186	−	0.331144i	−0.754458	−	0.656349i	$-0.772100\pi$
$719$	3685.95	−	6384.25i	0.191186	−	0.331144i	0.945644	+	0.325205i	$0.105433\pi$
$720$	−8229.80	+	19674.1i	−0.425982	+	1.01835i
$721$	679.607	−	182.100i	0.0351039	−	0.00940605i
$722$	76.9712	−	20.6244i	0.00396755	−	0.00106310i
$723$	−16281.9	−	10920.3i	−0.837525	−	0.561731i
$724$	−9219.41	+	15968.5i	−0.473255	+	0.819702i
$725$	5955.16	+	10314.6i	0.305061	+	0.528381i
$726$	−2123.96	−	142.932i	−0.108578	−	0.00730676i
$727$		−	2273.83i		−	0.115999i	−0.998317	−	0.0579997i	$-0.981528\pi$
$727$		−	2273.83i		−	0.115999i	0.998317	−	0.0579997i	$-0.0184723\pi$
$728$	1854.57	+	1505.07i	0.0944160	+	0.0766231i
$729$	−7722.21	+	18104.9i	−0.392329	+	0.919825i
$730$	−511.022	+	1907.16i	−0.0259093	+	0.0966947i
$731$	10933.8	−	6312.62i	0.553215	−	0.319399i
$732$	−1171.25	+	3430.73i	−0.0591403	+	0.173229i
$733$	7931.80	+	7931.80i	0.399683	+	0.399683i	0.878121	−	0.478438i	$-0.158797\pi$
$733$	7931.80	+	7931.80i	0.399683	+	0.399683i	−0.478438	+	0.878121i	$0.658797\pi$
$734$	957.137	+	3572.09i	0.0481316	+	0.179630i
$735$	−8350.45	−	17007.7i	−0.419063	−	0.853524i
$736$	515.143	−	515.143i	0.0257995	−	0.0257995i
$737$	−4523.12	−	2611.42i	−0.226067	−	0.130520i
$738$	−830.767	+	1074.89i	−0.0414376	+	0.0536143i
$739$	−24495.3	−	6563.48i	−1.21931	−	0.326714i	−0.408904	−	0.912578i	$-0.634089\pi$
$739$	−24495.3	−	6563.48i	−1.21931	−	0.326714i	−0.810410	+	0.585864i	$0.800755\pi$
$740$	−33057.4			−1.64218
$741$	14987.1	+	13932.2i	0.743005	+	0.690705i
$742$	1587.20			0.0785285
$743$	−11425.9	−	3061.57i	−0.564167	−	0.151168i	−0.0345472	−	0.999403i	$-0.510999\pi$
$743$	−11425.9	−	3061.57i	−0.564167	−	0.151168i	−0.529620	+	0.848235i	$0.677666\pi$
$744$	2925.37	+	3347.51i	0.144152	+	0.164954i
$745$	−6422.93	−	3708.28i	−0.315863	−	0.182364i
$746$	1449.78	−	1449.78i	0.0711530	−	0.0711530i
$747$	−10496.3	−	13778.2i	−0.514107	−	0.674858i
$748$	−3067.51	−	11448.1i	−0.149946	−	0.559604i
$749$	−2726.50	−	2726.50i	−0.133009	−	0.133009i
$750$	2004.22	+	684.241i	0.0975783	+	0.0333133i
$751$	18566.4	−	10719.3i	0.902128	−	0.520844i	0.0242382	−	0.999706i	$-0.492284\pi$
$751$	18566.4	−	10719.3i	0.902128	−	0.520844i	0.877890	+	0.478862i	$0.158951\pi$
$752$	−8239.38	+	30749.8i	−0.399547	+	1.49113i
$753$	2711.21	+	13755.5i	0.131211	+	0.665708i
$754$	−489.089	−	4701.48i	−0.0236228	−	0.227079i
$755$			30616.0i			1.47580i
$756$	8416.31	−	2807.93i	0.404892	−	0.135084i
$757$	−3389.21	−	5870.28i	−0.162725	−	0.281848i	0.773120	−	0.634260i	$-0.218695\pi$
$757$	−3389.21	−	5870.28i	−0.162725	−	0.281848i	−0.935845	+	0.352412i	$0.885362\pi$
$758$	−302.072	+	523.205i	−0.0144746	+	0.0250708i
$759$	−492.956	+	734.983i	−0.0235747	+	0.0351491i
$760$	−6726.34	+	1802.32i	−0.321040	+	0.0860223i
$761$	−12313.0	+	3299.25i	−0.586525	+	0.157159i	−0.539864	−	0.841752i	$-0.681524\pi$
$761$	−12313.0	+	3299.25i	−0.586525	+	0.157159i	−0.0466602	+	0.998911i	$0.514858\pi$
$762$	1150.09	−	1714.74i	0.0546761	−	0.0815205i
$763$	−2564.41	+	4441.69i	−0.121675	+	0.210747i
$764$	−13685.1	−	23703.2i	−0.648047	−	1.12245i
$765$	30468.4	−	3903.18i	1.43998	−	0.184470i
$766$			5147.17i			0.242787i
$767$	2710.40	+	26054.4i	0.127597	+	1.22656i
$768$	−3321.60	−	16852.3i	−0.156065	−	0.791805i
$769$	−8286.89	+	30927.1i	−0.388599	+	1.45027i	0.443815	+	0.896118i	$0.353625\pi$
$769$	−8286.89	+	30927.1i	−0.388599	+	1.45027i	−0.832414	+	0.554154i	$0.813042\pi$
$770$	637.005	−	367.775i	0.0298131	−	0.0172126i
$771$	10414.6	+	3555.56i	0.486477	+	0.166083i
$772$	−23842.2	−	23842.2i	−1.11153	−	1.11153i
$773$	−5418.18	−	20220.9i	−0.252107	−	0.940874i	−0.969677	−	0.244389i	$-0.921413\pi$
$773$	−5418.18	−	20220.9i	−0.252107	−	0.940874i	0.717571	−	0.696486i	$-0.245254\pi$
$774$	1247.09	−	950.031i	0.0579142	−	0.0441191i
$775$	4510.47	−	4510.47i	0.209059	−	0.209059i
$776$	3401.15	+	1963.65i	0.157338	+	0.0908390i
$777$	8862.60	+	10141.5i	0.409194	+	0.468241i
$778$	1895.99	+	508.030i	0.0873710	+	0.0234110i
$779$	10599.2			0.487492
$780$	−18349.2	−	17057.6i	−0.842316	−	0.783026i
$781$	−19353.2			−0.886698
$782$	−326.453	−	87.4727i	−0.0149283	−	0.00400002i
$783$	−31733.1	−	15856.0i	−1.44834	−	0.723685i
$784$	14492.7	+	8367.34i	0.660197	+	0.381165i
$785$	−10837.6	+	10837.6i	−0.492752	+	0.492752i
$786$	−1217.71	−	2480.17i	−0.0552601	−	0.112551i
$787$	7656.13	+	28573.1i	0.346775	+	1.29418i	0.890525	+	0.454934i	$0.150337\pi$
$787$	7656.13	+	28573.1i	0.346775	+	1.29418i	−0.543751	+	0.839247i	$0.682996\pi$
$788$	−26651.9	−	26651.9i	−1.20487	−	1.20487i
$789$	−5626.28	+	16480.0i	−0.253867	+	0.743605i
$790$	4813.34	−	2778.98i	0.216773	−	0.125154i
$791$	2788.99	−	10408.6i	0.125367	−	0.467875i
$792$	−1128.24	−	2750.90i	−0.0506189	−	0.123420i
$793$	−3238.32	−	2628.05i	−0.145014	−	0.117686i
$794$			4204.12i			0.187908i
$795$	−33559.1	−	2258.36i	−1.49713	−	0.100749i
$796$	559.289	+	968.718i	0.0249039	+	0.0431348i
$797$	−1914.87	+	3316.66i	−0.0851045	+	0.147405i	−0.905436	−	0.424483i	$-0.860456\pi$
$797$	−1914.87	+	3316.66i	−0.0851045	+	0.147405i	0.820331	+	0.571889i	$0.193789\pi$
$798$	1166.29	+	782.234i	0.0517370	+	0.0347002i
$799$	44291.0	−	11867.7i	1.96108	−	0.525470i
$800$	3392.25	−	908.950i	0.149918	−	0.0401703i
$801$	20567.8	+	8603.64i	0.907277	+	0.379519i
$802$	1212.34	−	2099.84i	0.0533782	−	0.0924538i
$803$	3288.68	+	5696.16i	0.144527	+	0.250328i
$804$	−819.711	+	12180.9i	−0.0359565	+	0.534311i
$805$			1033.90i			0.0452674i
$806$	−2364.36	+	904.709i	−0.103326	+	0.0395372i
$807$	−16595.3	+	3270.95i	−0.723896	+	0.142680i
$808$	654.502	−	2442.63i	0.0284967	−	0.106351i
$809$	6884.54	−	3974.79i	0.299193	−	0.172739i	−0.342887	−	0.939377i	$-0.611405\pi$
$809$	6884.54	−	3974.79i	0.299193	−	0.172739i	0.642080	+	0.766637i	$0.278072\pi$
$810$	3691.14	−	961.494i	0.160115	−	0.0417080i
$811$	−6332.02	−	6332.02i	−0.274164	−	0.274164i	0.556610	−	0.830774i	$-0.312102\pi$
$811$	−6332.02	−	6332.02i	−0.274164	−	0.274164i	−0.830774	+	0.556610i	$0.812102\pi$
$812$	4138.60	+	15445.5i	0.178863	+	0.667524i
$813$	9038.14	−	4437.54i	0.389891	−	0.191429i
$814$	1579.72	−	1579.72i	0.0680212	−	0.0680212i
$815$	15402.5	+	8892.63i	0.661995	+	0.382203i
$816$	−20429.0	+	17852.8i	−0.876418	+	0.765898i
$817$	−11814.7	−	3165.75i	−0.505930	−	0.135564i
$818$	−5027.74			−0.214903
$819$	−313.632	+	10202.3i	−0.0133812	+	0.435285i
$820$	−12976.9			−0.552651
$821$	19377.7	+	5192.25i	0.823737	+	0.220720i	0.645979	−	0.763355i	$-0.276449\pi$
$821$	19377.7	+	5192.25i	0.823737	+	0.220720i	0.177757	+	0.984074i	$0.443116\pi$
$822$	1580.76	−	1381.42i	0.0670745	−	0.0586161i
$823$	−6469.58	−	3735.21i	−0.274016	−	0.158203i	0.356695	−	0.934221i	$-0.383903\pi$
$823$	−6469.58	−	3735.21i	−0.274016	−	0.158203i	−0.630711	+	0.776018i	$0.717237\pi$
$824$	−389.715	+	389.715i	−0.0164762	+	0.0164762i
$825$	−3829.50	+	1880.21i	−0.161607	+	0.0793459i
$826$	465.284	+	1736.46i	0.0195996	+	0.0731469i
$827$	−9708.99	−	9708.99i	−0.408240	−	0.408240i	0.472884	−	0.881125i	$-0.343213\pi$
$827$	−9708.99	−	9708.99i	−0.408240	−	0.408240i	−0.881125	+	0.472884i	$0.843213\pi$
$828$	2050.01	+	277.166i	0.0860420	+	0.0116331i
$829$	10149.5	−	5859.81i	0.425218	−	0.245500i	−0.272089	−	0.962272i	$-0.587715\pi$
$829$	10149.5	−	5859.81i	0.425218	−	0.245500i	0.697307	+	0.716772i	$0.254381\pi$
$830$	−868.741	+	3242.19i	−0.0363306	+	0.135588i
$831$	−10037.1	+	1978.31i	−0.418992	+	0.0825834i
$832$	20918.4	+	3335.97i	0.871652	+	0.139007i
$833$		−	24104.1i		−	1.00259i
$834$	301.715	−	4483.47i	0.0125270	−	0.186151i
$835$	3855.59	+	6678.07i	0.159794	+	0.276771i
$836$	−5741.17	+	9944.00i	−0.237515	+	0.411388i
$837$	−3803.88	+	18613.9i	−0.157087	+	0.768688i
$838$	−587.694	+	157.472i	−0.0242262	+	0.00649139i
$839$	−36097.2	+	9672.20i	−1.48535	+	0.398000i	−0.908166	−	0.418611i	$-0.862517\pi$
$839$	−36097.2	+	9672.20i	−1.48535	+	0.398000i	−0.577189	+	0.816611i	$0.695850\pi$
$840$	−2884.81	−	1934.85i	−0.118494	−	0.0794747i
$841$	19772.2	−	34246.4i	0.810701	−	1.40418i
$842$	336.325	+	582.532i	0.0137655	+	0.0238425i
$843$	29423.9	+	1980.08i	1.20215	+	0.0808988i
$844$		−	16199.9i		−	0.660693i
$845$	25708.5	−	13030.3i	1.04663	−	0.530480i
$846$	5267.97	−	2160.57i	0.214086	−	0.0878038i
$847$	−2144.25	+	8002.44i	−0.0869861	+	0.324636i
$848$	25727.4	−	14853.7i	1.04184	−	0.601508i
$849$	−1208.67	+	3540.32i	−0.0488590	+	0.143114i
$850$	−1152.03	−	1152.03i	−0.0464873	−	0.0464873i
$851$	812.755	+	3033.24i	0.0327390	+	0.122184i
$852$	19937.5	+	40607.6i	0.801700	+	1.63286i
$853$	2532.28	−	2532.28i	0.101646	−	0.101646i	−0.654455	−	0.756101i	$-0.727102\pi$
$853$	2532.28	−	2532.28i	0.101646	−	0.101646i	0.756101	+	0.654455i	$0.227102\pi$
$854$	−247.872	−	143.109i	−0.00993207	−	0.00573428i
$855$	−23546.4	−	18198.6i	−0.941837	−	0.727930i
$856$	2917.51	+	781.744i	0.116493	+	0.0312143i
$857$	30352.1			1.20981			0.604905	−	0.796298i	$-0.293211\pi$
$857$	30352.1			1.20981			0.604905	+	0.796298i	$0.293211\pi$
$858$	1691.99	−	61.7212i	0.0673237	−	0.00245586i
$859$	3256.38			0.129344			0.0646718	−	0.997907i	$-0.479400\pi$
$859$	3256.38			0.129344			0.0646718	+	0.997907i	$0.479400\pi$
$860$	14465.1	+	3875.91i	0.573554	+	0.153683i
$861$	3479.08	+	3981.11i	0.137708	+	0.157579i
$862$	−4500.34	−	2598.27i	−0.177822	−	0.102665i
$863$	18360.4	−	18360.4i	0.724212	−	0.724212i	−0.245248	−	0.969460i	$-0.578869\pi$
$863$	18360.4	−	18360.4i	0.724212	−	0.724212i	0.969460	+	0.245248i	$0.0788694\pi$
$864$	−6937.77	+	7828.02i	−0.273180	+	0.308235i
$865$	−4872.38	−	18184.0i	−0.191521	−	0.714767i
$866$	2620.42	+	2620.42i	0.102824	+	0.102824i
$867$	12822.5	+	4377.62i	0.502280	+	0.171478i
$868$	7416.53	−	4281.94i	0.290016	−	0.167441i
$869$	4792.04	−	17884.1i	0.187064	−	0.698133i
$870$	1329.37	+	6744.64i	0.0518044	+	0.262833i
$871$	−12824.8	−	5726.30i	−0.498910	−	0.222765i
$872$		−	4017.59i		−	0.156024i
$873$	2132.65	+	16647.5i	0.0826795	+	0.645399i
$874$	163.715	+	283.562i	0.00633607	+	0.0109744i
$875$	4121.03	−	7137.83i	0.159218	−	0.275775i
$876$	8563.95	−	12768.6i	0.330307	−	0.492478i
$877$	−16754.5	+	4489.35i	−0.645107	+	0.172856i	−0.566516	−	0.824051i	$-0.691709\pi$
$877$	−16754.5	+	4489.35i	−0.645107	+	0.172856i	−0.0785916	+	0.996907i	$0.525042\pi$
$878$	−1145.39	+	306.906i	−0.0440262	+	0.0117968i
$879$	−18007.0	+	26847.9i	−0.690967	+	1.03021i
$880$	6883.59	−	11922.7i	0.263688	−	0.456721i
$881$	18097.3	+	31345.5i	0.692070	+	1.19870i	0.971158	+	0.238436i	$0.0766346\pi$
$881$	18097.3	+	31345.5i	0.692070	+	1.19870i	−0.279088	+	0.960266i	$0.590032\pi$
$882$	−380.327	−	2968.85i	−0.0145196	−	0.113341i
$883$		−	2834.73i		−	0.108037i	−0.998540	−	0.0540183i	$-0.982797\pi$
$883$		−	2834.73i		−	0.108037i	0.998540	−	0.0540183i	$-0.0172029\pi$
$884$	−11390.2	−	29767.1i	−0.433364	−	1.13255i
$885$	−7367.01	−	37377.0i	−0.279819	−	1.41968i
$886$	−809.275	+	3020.25i	−0.0306864	+	0.114523i
$887$	1098.68	−	634.324i	0.0415898	−	0.0240119i	−0.479061	−	0.877782i	$-0.659023\pi$
$887$	1098.68	−	634.324i	0.0415898	−	0.0240119i	0.520651	+	0.853770i	$0.325689\pi$
$888$	−9984.38	−	3408.67i	−0.377313	−	0.128815i
$889$	−5681.92	−	5681.92i	−0.214359	−	0.214359i
$890$	−1118.22	−	4173.24i	−0.0421154	−	0.157177i
$891$	6429.84	−	10959.5i	0.241759	−	0.412075i
$892$	2279.67	−	2279.67i	0.0855704	−	0.0855704i
$893$	−38471.8	−	22211.7i	−1.44167	−	0.832348i
$894$	−770.957	−	882.207i	−0.0288419	−	0.0330038i
$895$	24922.8	+	6678.04i	0.930811	+	0.249410i
$896$	6264.34			0.233568
$897$	−1114.02	+	2103.05i	−0.0414670	+	0.0782817i
$898$	−202.882			−0.00753925
$899$	−33073.8	−	8862.11i	−1.22700	−	0.328774i
$900$	7890.25	+	6098.24i	0.292232	+	0.225861i
$901$	−37056.9	−	21394.8i	−1.37019	−	0.791082i
$902$	620.132	−	620.132i	0.0228915	−	0.0228915i
$903$	−2688.99	−	5476.79i	−0.0990963	−	0.201834i
$904$	2184.72	+	8153.47i	0.0803790	+	0.299978i
$905$	21814.5	+	21814.5i	0.801260	+	0.801260i
$906$	−1562.61	+	4577.07i	−0.0573006	+	0.167840i
$907$	15748.0	−	9092.12i	0.576521	−	0.332854i	−0.183229	−	0.983070i	$-0.558655\pi$
$907$	15748.0	−	9092.12i	0.576521	−	0.332854i	0.759749	+	0.650216i	$0.225322\pi$
$908$	−5012.29	+	18706.1i	−0.183193	+	0.683684i
$909$	9998.71	−	4100.81i	0.364836	−	0.149632i
$910$	1601.48	−	1160.95i	0.0583392	−	0.0422912i
$911$			15408.4i			0.560377i	0.959945	+	0.280188i	$0.0903969\pi$
$911$			15408.4i			0.560377i	−0.959945	+	0.280188i	$0.909603\pi$
$912$	26225.1	+	1764.82i	0.952194	+	0.0640779i
$913$	5590.78	+	9683.52i	0.202659	+	0.351016i
$914$	−1817.86	+	3148.63i	−0.0657873	+	0.113947i
$915$	5037.25	+	3378.51i	0.181996	+	0.122066i
$916$	7666.26	−	2054.17i	0.276529	−	0.0740956i
$917$	−10386.6	+	2783.08i	−0.374041	+	0.100224i
$918$	4754.22	+	971.557i	0.170929	+	0.0349304i
$919$	8316.17	−	14404.0i	0.298504	−	0.517024i	−0.677290	−	0.735716i	$-0.736846\pi$
$919$	8316.17	−	14404.0i	0.298504	−	0.517024i	0.975794	+	0.218692i	$0.0701791\pi$
$920$	−404.947	−	701.389i	−0.0145116	−	0.0251349i
$921$	−2325.73	+	34560.2i	−0.0832088	+	1.23648i
$922$			2638.28i			0.0942378i
$923$	−51764.6	+	5385.00i	−1.84599	+	0.192036i
$924$	−5619.49	+	1107.60i	−0.200073	+	0.0394344i
$925$	−3917.97	+	14622.1i	−0.139267	+	0.519752i
$926$	−3408.77	+	1968.06i	−0.120971	+	0.0698427i
$927$	−2334.09	−	315.575i	−0.0826987	−	0.0111811i
$928$	−13330.1	−	13330.1i	−0.471532	−	0.471532i
$929$	9818.93	+	36644.7i	0.346769	+	1.29416i	0.890532	+	0.454921i	$0.150333\pi$
$929$	9818.93	+	36644.7i	0.346769	+	1.29416i	−0.543763	+	0.839239i	$0.683001\pi$
$930$	3304.85	−	1622.61i	0.116527	−	0.0572124i
$931$	−16512.6	+	16512.6i	−0.581288	+	0.581288i
$932$	17512.7	+	10110.9i	0.615500	+	0.355359i
$933$	30980.7	−	27073.9i	1.08710	−	0.950010i
$934$	2907.09	+	778.953i	0.101845	+	0.0272892i
$935$	−19829.8			−0.693586
$936$	−3783.16	−	7043.99i	−0.132112	−	0.245983i
$937$	10988.6			0.383118			0.191559	−	0.981481i	$-0.438646\pi$
$937$	10988.6			0.383118			0.191559	+	0.981481i	$0.438646\pi$
$938$	−931.049	−	249.474i	−0.0324092	−	0.00868402i
$939$	−18597.9	+	16252.6i	−0.646347	+	0.564840i
$940$	47102.1	+	27194.4i	1.63436	+	0.943601i
$941$	−2947.34	+	2947.34i	−0.102105	+	0.102105i	−0.756314	−	0.654209i	$-0.773002\pi$
$941$	−2947.34	+	2947.34i	−0.102105	+	0.102105i	0.654209	+	0.756314i	$0.273002\pi$
$942$	−2173.36	+	1067.07i	−0.0751717	+	0.0369078i
$943$	319.053	+	1190.72i	0.0110178	+	0.0411190i
$944$	23792.5	+	23792.5i	0.820317	+	0.820317i
$945$	−893.374	−	14817.6i	−0.0307529	−	0.510072i
$946$	−876.468	+	506.029i	−0.0301231	+	0.0173916i
$947$	10943.3	−	40840.9i	0.375511	−	1.40143i	−0.477085	−	0.878857i	$-0.658307\pi$
$947$	10943.3	−	40840.9i	0.375511	−	1.40143i	0.852596	−	0.522570i	$-0.175027\pi$
$948$	−42461.9	+	8369.26i	−1.45475	+	0.286731i
$949$	10381.3	+	14320.6i	0.355101	+	0.489850i
$950$			1578.40i			0.0539055i
$951$	1701.47	−	25283.8i	0.0580169	−	0.862128i
$952$	−2209.50	−	3826.97i	−0.0752210	−	0.130287i
$953$	−5146.62	+	8914.21i	−0.174938	+	0.303001i	−0.940140	−	0.340789i	$-0.889306\pi$
$953$	−5146.62	+	8914.21i	−0.174938	+	0.303001i	0.765202	+	0.643790i	$0.222639\pi$
$954$	−4901.80	−	2050.45i	−0.166354	−	0.0695868i
$955$	−44233.2	+	11852.3i	−1.49880	+	0.401602i
$956$	33955.7	−	9098.40i	1.14875	−	0.307807i
$957$	19018.8	+	12756.0i	0.642413	+	0.430869i
$958$	−1720.74	+	2980.40i	−0.0580318	+	0.100514i
$959$	−4085.05	−	7075.51i	−0.137553	−	0.238248i
$960$	−30737.1	−	2068.45i	−1.03337	−	0.0695407i
$961$		−	11452.9i		−	0.384442i
$962$	3785.78	−	4664.89i	0.126880	−	0.156343i
$963$	4898.05	+	11942.6i	0.163902	+	0.399630i
$964$	7656.81	−	28575.6i	0.255819	−	0.954728i
$965$	−48856.3	+	28207.2i	−1.62978	+	0.940956i
$966$	−52.7695	+	154.568i	−0.00175759	+	0.00514818i
$967$	40487.2	+	40487.2i	1.34641	+	1.34641i	0.889524	+	0.456889i	$0.151036\pi$
$967$	40487.2	+	40487.2i	1.34641	+	1.34641i	0.456889	+	0.889524i	$0.348964\pi$
$968$	−1679.67	−	6268.60i	−0.0557712	−	0.208141i
$969$	−16685.5	−	33984.1i	−0.553163	−	1.12665i
$970$	2299.83	−	2299.83i	0.0761268	−	0.0761268i
$971$	−19150.1	−	11056.3i	−0.632909	−	0.365410i	0.148969	−	0.988842i	$-0.452405\pi$
$971$	−19150.1	−	11056.3i	−0.632909	−	0.365410i	−0.781878	+	0.623432i	$0.785738\pi$
$972$	−29619.7	−	2200.90i	−0.977422	−	0.0726276i
$973$	−16892.3	−	4526.29i	−0.556571	−	0.149133i
$974$	5412.04			0.178042
$975$	−9719.72	+	6094.60i	−0.319262	+	0.200188i
$976$	−5357.08			−0.175693
$977$	1880.46	+	503.867i	0.0615774	+	0.0164996i	0.289476	−	0.957185i	$-0.406519\pi$
$977$	1880.46	+	503.867i	0.0615774	+	0.0164996i	−0.227899	+	0.973685i	$0.573186\pi$
$978$	1848.79	+	2115.57i	0.0604477	+	0.0691704i
$979$	−12464.3	−	7196.27i	−0.406906	−	0.234927i
$980$	20216.9	−	20216.9i	0.658984	−	0.658984i
$981$	13657.8	−	10404.5i	0.444505	−	0.338624i
$982$	−182.843	−	682.379i	−0.00594170	−	0.0221747i
$983$	−15017.3	−	15017.3i	−0.487261	−	0.487261i	0.420180	−	0.907441i	$-0.361967\pi$
$983$	−15017.3	−	15017.3i	−0.487261	−	0.487261i	−0.907441	+	0.420180i	$0.861967\pi$
$984$	−3919.44	−	1338.10i	−0.126979	−	0.0433506i
$985$	−54613.8	+	31531.3i	−1.76664	+	1.01997i
$986$	−2263.49	+	8447.45i	−0.0731076	+	0.272841i
$987$	−4285.14	−	21740.9i	−0.138194	−	0.701136i
$988$	−12589.2	+	28195.0i	−0.405380	+	0.907897i
$989$		−	1422.57i		−	0.0457382i
$990$	−2442.39	+	312.885i	−0.0784084	+	0.0100446i
$991$	−15968.2	−	27657.7i	−0.511853	−	0.886556i	−0.999906	−	0.0137416i	$-0.995626\pi$
$991$	−15968.2	−	27657.7i	−0.511853	−	0.886556i	0.488052	−	0.872814i	$-0.337708\pi$
$992$	−5048.14	+	8743.63i	−0.161571	+	0.279849i
$993$	6522.12	−	9724.29i	0.208432	−	0.310766i
$994$	−3449.99	+	924.422i	−0.110088	+	0.0294979i
$995$	1807.75	−	484.385i	0.0575975	−	0.0154332i
$996$	14558.8	−	21706.7i	0.463165	−	0.690565i
$997$	−30025.6	+	52005.9i	−0.953781	+	1.65200i	−0.216649	+	0.976250i	$0.569513\pi$
$997$	−30025.6	+	52005.9i	−0.953781	+	1.65200i	−0.737132	+	0.675748i	$0.763821\pi$
$998$	−1736.95	−	3008.48i	−0.0550923	−	0.0954226i
$999$	−14269.2	−	42769.4i	−0.451909	−	1.35452i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.4.k.a.11.7	yes	48
3.2	odd	2	inner	39.4.k.a.11.6	✓	48
13.6	odd	12	inner	39.4.k.a.32.6	yes	48
39.32	even	12	inner	39.4.k.a.32.7	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.k.a.11.6	✓	48	3.2	odd	2	inner
39.4.k.a.11.7	yes	48	1.1	even	1	trivial
39.4.k.a.32.6	yes	48	13.6	odd	12	inner
39.4.k.a.32.7	yes	48	39.32	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 39 = 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	39.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.385245 + 0.103226i) q^{2} +(-3.91264 + 3.41924i) q^{3} +(-6.79045 - 3.92047i) q^{4} +(-9.27643 + 9.27643i) q^{5} +(-1.86028 + 0.913360i) q^{6} +(2.08748 + 7.79057i) q^{7} +(-4.46744 - 4.46744i) q^{8} +(3.61755 - 26.7566i) q^{9} +O(q^{10})\)	\(q+(0.385245 + 0.103226i) q^{2} +(-3.91264 + 3.41924i) q^{3} +(-6.79045 - 3.92047i) q^{4} +(-9.27643 + 9.27643i) q^{5} +(-1.86028 + 0.913360i) q^{6} +(2.08748 + 7.79057i) q^{7} +(-4.46744 - 4.46744i) q^{8} +(3.61755 - 26.7566i) q^{9} +(-4.53127 + 2.61613i) q^{10} +(-4.51122 + 16.8361i) q^{11} +(39.9736 - 7.87881i) q^{12} +(-7.38167 + 46.2873i) q^{13} +3.21676i q^{14} +(4.57698 - 68.0137i) q^{15} +(30.1038 + 52.1413i) q^{16} +(43.3605 - 75.1027i) q^{17} +(4.15562 - 9.93441i) q^{18} +(-81.1539 + 21.7451i) q^{19} +(99.3590 - 26.6232i) q^{20} +(-34.8054 - 23.3441i) q^{21} +(-3.47585 + 6.02035i) q^{22} +(-4.88572 - 8.46231i) q^{23} +(32.7548 + 2.20423i) q^{24} -47.1042i q^{25} +(-7.62181 + 17.0700i) q^{26} +(77.3330 + 117.058i) q^{27} +(16.3678 - 61.0854i) q^{28} +(-218.975 + 126.425i) q^{29} +(8.78405 - 25.7295i) q^{30} +(95.7551 + 95.7551i) q^{31} +(19.2966 + 72.0158i) q^{32} +(-39.9159 - 81.2986i) q^{33} +(24.4570 - 24.4570i) q^{34} +(-91.6330 - 52.9044i) q^{35} +(-129.463 + 167.506i) q^{36} +(-310.420 - 83.1767i) q^{37} -33.5088 q^{38} +(-129.386 - 206.345i) q^{39} +82.8838 q^{40} +(-121.857 - 32.6516i) q^{41} +(-10.9989 - 12.5860i) q^{42} +(126.080 + 72.7922i) q^{43} +(96.6385 - 96.6385i) q^{44} +(214.647 + 281.763i) q^{45} +(-1.00867 - 3.76440i) q^{46} +(373.880 + 373.880i) q^{47} +(-296.069 - 101.078i) q^{48} +(240.711 - 138.975i) q^{49} +(4.86238 - 18.1467i) q^{50} +(87.1400 + 442.110i) q^{51} +(231.592 - 285.372i) q^{52} -493.417i q^{53} +(17.7087 + 53.0789i) q^{54} +(-114.331 - 198.027i) q^{55} +(25.4783 - 44.1296i) q^{56} +(243.174 - 362.566i) q^{57} +(-97.4094 + 26.1008i) q^{58} +(539.817 - 144.644i) q^{59} +(-297.725 + 443.899i) q^{60} +(-44.4884 + 77.0562i) q^{61} +(27.0048 + 46.7736i) q^{62} +(216.001 - 27.6710i) q^{63} -451.925i q^{64} +(-360.905 - 497.856i) q^{65} +(-6.98528 - 35.4402i) q^{66} +(-77.5543 + 289.437i) q^{67} +(-588.875 + 339.987i) q^{68} +(48.0508 + 16.4045i) q^{69} +(-29.8401 - 29.8401i) q^{70} +(287.376 + 1072.50i) q^{71} +(-135.695 + 103.372i) q^{72} +(266.833 - 266.833i) q^{73} +(-111.002 - 64.0868i) q^{74} +(161.061 + 184.302i) q^{75} +(636.322 + 170.502i) q^{76} -140.580 q^{77} +(-28.5449 - 92.8495i) q^{78} -1062.25 q^{79} +(-762.941 - 204.429i) q^{80} +(-702.827 - 193.586i) q^{81} +(-43.5745 - 25.1577i) q^{82} +(453.618 - 453.618i) q^{83} +(144.824 + 294.971i) q^{84} +(294.453 + 1098.92i) q^{85} +(41.0576 + 41.0576i) q^{86} +(424.492 - 1243.39i) q^{87} +(95.3679 - 55.0607i) q^{88} +(-213.716 + 797.598i) q^{89} +(53.6065 + 130.705i) q^{90} +(-376.013 + 39.1162i) q^{91} +76.6172i q^{92} +(-702.066 - 47.2455i) q^{93} +(105.441 + 182.629i) q^{94} +(551.101 - 954.535i) q^{95} +(-321.740 - 215.792i) q^{96} +(-600.433 + 160.886i) q^{97} +(107.079 - 28.6916i) q^{98} +(434.156 + 181.610i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{3} - 12 q^{4} - 50 q^{6} + 20 q^{7} - 2 q^{9}+O(q^{10}) \) 48 * q - 2 * q^3 - 12 * q^4 - 50 * q^6 + 20 * q^7 - 2 * q^9	\( 48 q - 2 q^{3} - 12 q^{4} - 50 q^{6} + 20 q^{7} - 2 q^{9} - 156 q^{10} - 80 q^{13} + 70 q^{15} + 260 q^{16} + 256 q^{18} + 260 q^{19} + 82 q^{21} + 212 q^{22} - 1194 q^{24} - 248 q^{27} - 756 q^{28} - 1062 q^{30} - 180 q^{31} + 10 q^{33} - 396 q^{34} + 3060 q^{36} + 1932 q^{37} + 538 q^{39} + 360 q^{40} + 968 q^{42} + 1416 q^{43} - 386 q^{45} - 144 q^{46} - 410 q^{48} - 3000 q^{49} - 4336 q^{52} + 1930 q^{54} - 1012 q^{55} - 1274 q^{57} + 908 q^{58} - 2860 q^{60} + 836 q^{61} - 5150 q^{63} + 1376 q^{66} - 136 q^{67} - 1674 q^{69} + 1808 q^{70} - 3900 q^{72} + 3572 q^{73} + 5796 q^{75} + 8400 q^{76} + 12292 q^{78} - 3760 q^{79} + 2494 q^{81} + 2544 q^{82} + 1084 q^{84} + 4980 q^{85} + 2318 q^{87} - 8436 q^{88} - 8908 q^{91} - 1214 q^{93} - 8464 q^{94} - 6968 q^{96} - 204 q^{97} - 13094 q^{99}+O(q^{100}) \) 48 * q - 2 * q^3 - 12 * q^4 - 50 * q^6 + 20 * q^7 - 2 * q^9 - 156 * q^10 - 80 * q^13 + 70 * q^15 + 260 * q^16 + 256 * q^18 + 260 * q^19 + 82 * q^21 + 212 * q^22 - 1194 * q^24 - 248 * q^27 - 756 * q^28 - 1062 * q^30 - 180 * q^31 + 10 * q^33 - 396 * q^34 + 3060 * q^36 + 1932 * q^37 + 538 * q^39 + 360 * q^40 + 968 * q^42 + 1416 * q^43 - 386 * q^45 - 144 * q^46 - 410 * q^48 - 3000 * q^49 - 4336 * q^52 + 1930 * q^54 - 1012 * q^55 - 1274 * q^57 + 908 * q^58 - 2860 * q^60 + 836 * q^61 - 5150 * q^63 + 1376 * q^66 - 136 * q^67 - 1674 * q^69 + 1808 * q^70 - 3900 * q^72 + 3572 * q^73 + 5796 * q^75 + 8400 * q^76 + 12292 * q^78 - 3760 * q^79 + 2494 * q^81 + 2544 * q^82 + 1084 * q^84 + 4980 * q^85 + 2318 * q^87 - 8436 * q^88 - 8908 * q^91 - 1214 * q^93 - 8464 * q^94 - 6968 * q^96 - 204 * q^97 - 13094 * q^99

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