LMFDB - Embedded newform 48.4.j.a.37.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,4,Mod(13,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("48.13");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	48.j (of order $4$, degree $2$, 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:	$2.83209168028$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.7
Character	$\chi$	$=$	48.37
Dual form			48.4.j.a.13.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.220074 + 2.81985i) q^{2} +(2.12132 - 2.12132i) q^{3} +(-7.90313 - 1.24115i) q^{4} +(10.2951 + 10.2951i) q^{5} +(5.51496 + 6.44866i) q^{6} +32.8369i q^{7} +(5.23914 - 22.0125i) q^{8} -9.00000i q^{9} +O(q^{10})$	\(q+(-0.220074 + 2.81985i) q^{2} +(2.12132 - 2.12132i) q^{3} +(-7.90313 - 1.24115i) q^{4} +(10.2951 + 10.2951i) q^{5} +(5.51496 + 6.44866i) q^{6} +32.8369i q^{7} +(5.23914 - 22.0125i) q^{8} -9.00000i q^{9} +(-31.2964 + 26.7650i) q^{10} +(-18.2226 - 18.2226i) q^{11} +(-19.3980 + 14.1322i) q^{12} +(22.5535 - 22.5535i) q^{13} +(-92.5952 - 7.22655i) q^{14} +43.6785 q^{15} +(60.9191 + 19.6180i) q^{16} +50.1440 q^{17} +(25.3787 + 1.98067i) q^{18} +(-6.68982 + 6.68982i) q^{19} +(-68.5859 - 94.1415i) q^{20} +(69.6576 + 69.6576i) q^{21} +(55.3953 - 47.3746i) q^{22} -186.886i q^{23} +(-35.5817 - 57.8095i) q^{24} +86.9788i q^{25} +(58.6342 + 68.5611i) q^{26} +(-19.0919 - 19.0919i) q^{27} +(40.7556 - 259.515i) q^{28} +(118.332 - 118.332i) q^{29} +(-9.61250 + 123.167i) q^{30} -250.110 q^{31} +(-68.7265 + 167.465i) q^{32} -77.3118 q^{33} +(-11.0354 + 141.399i) q^{34} +(-338.060 + 338.060i) q^{35} +(-11.1704 + 71.1282i) q^{36} +(198.913 + 198.913i) q^{37} +(-17.3921 - 20.3366i) q^{38} -95.6866i q^{39} +(280.559 - 172.684i) q^{40} -186.565i q^{41} +(-211.754 + 181.094i) q^{42} +(10.9329 + 10.9329i) q^{43} +(121.398 + 166.632i) q^{44} +(92.6560 - 92.6560i) q^{45} +(526.990 + 41.1287i) q^{46} +23.1346 q^{47} +(170.845 - 87.6129i) q^{48} -735.263 q^{49} +(-245.267 - 19.1418i) q^{50} +(106.371 - 106.371i) q^{51} +(-206.236 + 150.251i) q^{52} +(134.664 + 134.664i) q^{53} +(58.0379 - 49.6347i) q^{54} -375.207i q^{55} +(722.823 + 172.037i) q^{56} +28.3825i q^{57} +(307.637 + 359.721i) q^{58} +(220.943 + 220.943i) q^{59} +(-345.197 - 54.2116i) q^{60} +(-453.845 + 453.845i) q^{61} +(55.0427 - 705.274i) q^{62} +295.532 q^{63} +(-457.103 - 230.653i) q^{64} +464.383 q^{65} +(17.0143 - 218.008i) q^{66} +(-184.273 + 184.273i) q^{67} +(-396.294 - 62.2363i) q^{68} +(-396.444 - 396.444i) q^{69} +(-878.880 - 1027.68i) q^{70} -18.8163i q^{71} +(-198.113 - 47.1523i) q^{72} -828.683i q^{73} +(-604.680 + 517.129i) q^{74} +(184.510 + 184.510i) q^{75} +(61.1736 - 44.5675i) q^{76} +(598.373 - 598.373i) q^{77} +(269.822 + 21.0581i) q^{78} +1048.37 q^{79} +(425.200 + 829.138i) q^{80} -81.0000 q^{81} +(526.085 + 41.0581i) q^{82} +(-173.404 + 173.404i) q^{83} +(-464.058 - 636.969i) q^{84} +(516.238 + 516.238i) q^{85} +(-33.2353 + 28.4232i) q^{86} -502.041i q^{87} +(-496.595 + 305.654i) q^{88} +335.168i q^{89} +(240.885 + 281.668i) q^{90} +(740.589 + 740.589i) q^{91} +(-231.953 + 1476.98i) q^{92} +(-530.564 + 530.564i) q^{93} +(-5.09131 + 65.2360i) q^{94} -137.745 q^{95} +(209.457 + 501.039i) q^{96} -687.122 q^{97} +(161.812 - 2073.33i) q^{98} +(-164.003 + 164.003i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{4} + 84 q^{8}+O(q^{10}) $ 24 * q - 20 * q^4 + 84 * q^8	$ 24 q - 20 q^{4} + 84 q^{8} + 72 q^{10} - 40 q^{11} - 24 q^{12} - 348 q^{14} + 120 q^{15} - 192 q^{16} - 36 q^{18} + 24 q^{19} + 80 q^{20} + 704 q^{22} + 228 q^{24} - 20 q^{26} - 344 q^{28} + 400 q^{29} - 408 q^{30} - 744 q^{31} - 960 q^{32} - 704 q^{34} - 456 q^{35} + 108 q^{36} + 16 q^{37} + 1256 q^{38} + 1744 q^{40} + 660 q^{42} + 1240 q^{43} - 200 q^{44} - 1432 q^{46} - 528 q^{48} - 1176 q^{49} + 708 q^{50} + 744 q^{51} + 1008 q^{52} + 752 q^{53} + 108 q^{54} + 1344 q^{56} + 1936 q^{58} - 1376 q^{59} - 1224 q^{60} - 912 q^{61} - 996 q^{62} - 504 q^{63} - 56 q^{64} + 976 q^{65} - 1368 q^{66} - 2256 q^{67} - 1568 q^{68} - 528 q^{69} - 1760 q^{70} - 612 q^{72} - 2740 q^{74} + 1104 q^{75} - 1880 q^{76} + 1904 q^{77} + 1692 q^{78} + 5992 q^{79} + 712 q^{80} - 1944 q^{81} - 40 q^{82} + 2680 q^{83} + 1800 q^{84} - 240 q^{85} - 1712 q^{86} - 3936 q^{88} + 648 q^{90} - 3496 q^{91} + 5296 q^{92} + 5272 q^{94} - 7728 q^{95} + 2880 q^{96} + 6760 q^{98} - 360 q^{99}+O(q^{100}) $ 24 * q - 20 * q^4 + 84 * q^8 + 72 * q^10 - 40 * q^11 - 24 * q^12 - 348 * q^14 + 120 * q^15 - 192 * q^16 - 36 * q^18 + 24 * q^19 + 80 * q^20 + 704 * q^22 + 228 * q^24 - 20 * q^26 - 344 * q^28 + 400 * q^29 - 408 * q^30 - 744 * q^31 - 960 * q^32 - 704 * q^34 - 456 * q^35 + 108 * q^36 + 16 * q^37 + 1256 * q^38 + 1744 * q^40 + 660 * q^42 + 1240 * q^43 - 200 * q^44 - 1432 * q^46 - 528 * q^48 - 1176 * q^49 + 708 * q^50 + 744 * q^51 + 1008 * q^52 + 752 * q^53 + 108 * q^54 + 1344 * q^56 + 1936 * q^58 - 1376 * q^59 - 1224 * q^60 - 912 * q^61 - 996 * q^62 - 504 * q^63 - 56 * q^64 + 976 * q^65 - 1368 * q^66 - 2256 * q^67 - 1568 * q^68 - 528 * q^69 - 1760 * q^70 - 612 * q^72 - 2740 * q^74 + 1104 * q^75 - 1880 * q^76 + 1904 * q^77 + 1692 * q^78 + 5992 * q^79 + 712 * q^80 - 1944 * q^81 - 40 * q^82 + 2680 * q^83 + 1800 * q^84 - 240 * q^85 - 1712 * q^86 - 3936 * q^88 + 648 * q^90 - 3496 * q^91 + 5296 * q^92 + 5272 * q^94 - 7728 * q^95 + 2880 * q^96 + 6760 * q^98 - 360 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.220074	+	2.81985i	−0.0778079	+	0.996968i
$2$	−0.220074	+	2.81985i	−0.0778079	+	0.996968i
$3$	2.12132	−	2.12132i	0.408248	−	0.408248i
$3$	2.12132	−	2.12132i	0.408248	−	0.408248i
$4$	−7.90313	−	1.24115i	−0.987892	−	0.155144i
$5$	10.2951	+	10.2951i	0.920823	+	0.920823i	0.997088	−	0.0762646i	$-0.0242994\pi$
$5$	10.2951	+	10.2951i	0.920823	+	0.920823i	−0.0762646	+	0.997088i	$0.524299\pi$
$6$	5.51496	+	6.44866i	0.375246	+	0.438776i
$7$			32.8369i			1.77303i	0.462703	+	0.886513i	$0.346880\pi$
$7$			32.8369i			1.77303i	−0.462703	+	0.886513i	$0.653120\pi$
$8$	5.23914	−	22.0125i	0.231539	−	0.972826i
$9$		−	9.00000i		−	0.333333i
$10$	−31.2964	+	26.7650i	−0.989679	+	0.846384i
$11$	−18.2226	−	18.2226i	−0.499483	−	0.499483i	0.411794	−	0.911277i	$-0.364902\pi$
$11$	−18.2226	−	18.2226i	−0.499483	−	0.499483i	−0.911277	+	0.411794i	$0.864902\pi$
$12$	−19.3980	+	14.1322i	−0.466642	+	0.339968i
$13$	22.5535	−	22.5535i	0.481171	−	0.481171i	−0.424334	−	0.905506i	$-0.639492\pi$
$13$	22.5535	−	22.5535i	0.481171	−	0.481171i	0.905506	+	0.424334i	$0.139492\pi$
$14$	−92.5952	−	7.22655i	−1.76765	−	0.137955i
$15$	43.6785			0.751849
$16$	60.9191	+	19.6180i	0.951861	+	0.306531i
$17$	50.1440			0.715394			0.357697	−	0.933838i	$-0.383562\pi$
$17$	50.1440			0.715394			0.357697	+	0.933838i	$0.383562\pi$
$18$	25.3787	+	1.98067i	0.332323	+	0.0259360i
$19$	−6.68982	+	6.68982i	−0.0807763	+	0.0807763i	−0.746341	−	0.665564i	$-0.768191\pi$
$19$	−6.68982	+	6.68982i	−0.0807763	+	0.0807763i	0.665564	+	0.746341i	$0.268191\pi$
$20$	−68.5859	−	94.1415i	−0.766813	−	1.05253i
$21$	69.6576	+	69.6576i	0.723835	+	0.723835i
$22$	55.3953	−	47.3746i	0.536832	−	0.459105i
$23$		−	186.886i		−	1.69428i	−0.531373	−	0.847138i	$-0.678324\pi$
$23$		−	186.886i		−	1.69428i	0.531373	−	0.847138i	$-0.321676\pi$
$24$	−35.5817	−	57.8095i	−0.302629	−	0.491680i
$25$			86.9788i			0.695830i
$26$	58.6342	+	68.5611i	0.442274	+	0.517152i
$27$	−19.0919	−	19.0919i	−0.136083	−	0.136083i
$28$	40.7556	−	259.515i	0.275074	−	1.75156i
$29$	118.332	−	118.332i	0.757715	−	0.757715i	−0.218191	−	0.975906i	$-0.570016\pi$
$29$	118.332	−	118.332i	0.757715	−	0.757715i	0.975906	+	0.218191i	$0.0700156\pi$
$30$	−9.61250	+	123.167i	−0.0584998	+	0.749570i
$31$	−250.110			−1.44907			−0.724534	−	0.689239i	$-0.757945\pi$
$31$	−250.110			−1.44907			−0.724534	+	0.689239i	$0.757945\pi$
$32$	−68.7265	+	167.465i	−0.379664	+	0.925124i
$33$	−77.3118			−0.407826
$34$	−11.0354	+	141.399i	−0.0556633	+	0.713225i
$35$	−338.060	+	338.060i	−1.63264	+	1.63264i
$36$	−11.1704	+	71.1282i	−0.0517147	+	0.329297i
$37$	198.913	+	198.913i	0.883813	+	0.883813i	0.993920	−	0.110107i	$-0.0351194\pi$
$37$	198.913	+	198.913i	0.883813	+	0.883813i	−0.110107	+	0.993920i	$0.535119\pi$
$38$	−17.3921	−	20.3366i	−0.0742464	−	0.0868165i
$39$		−	95.6866i		−	0.392875i
$40$	280.559	−	172.684i	1.10901	−	0.682593i
$41$		−	186.565i		−	0.710647i	−0.934743	−	0.355324i	$-0.884371\pi$
$41$		−	186.565i		−	0.710647i	0.934743	−	0.355324i	$-0.115629\pi$
$42$	−211.754	+	181.094i	−0.777961	+	0.665321i
$43$	10.9329	+	10.9329i	0.0387734	+	0.0387734i	0.726228	−	0.687454i	$-0.241272\pi$
$43$	10.9329	+	10.9329i	0.0387734	+	0.0387734i	−0.687454	+	0.726228i	$0.741272\pi$
$44$	121.398	+	166.632i	0.415943	+	0.570927i
$45$	92.6560	−	92.6560i	0.306941	−	0.306941i
$46$	526.990	+	41.1287i	1.68914	+	0.131828i
$47$	23.1346			0.0717983			0.0358992	−	0.999355i	$-0.488570\pi$
$47$	23.1346			0.0717983			0.0358992	+	0.999355i	$0.488570\pi$
$48$	170.845	−	87.6129i	0.513736	−	0.263455i
$49$	−735.263			−2.14362
$50$	−245.267	−	19.1418i	−0.693721	−	0.0541411i
$51$	106.371	−	106.371i	0.292058	−	0.292058i
$52$	−206.236	+	150.251i	−0.549996	+	0.400694i
$53$	134.664	+	134.664i	0.349011	+	0.349011i	0.859741	−	0.510730i	$-0.170625\pi$
$53$	134.664	+	134.664i	0.349011	+	0.349011i	−0.510730	+	0.859741i	$0.670625\pi$
$54$	58.0379	−	49.6347i	0.146259	−	0.125082i
$55$		−	375.207i		−	0.919870i
$56$	722.823	+	172.037i	1.72485	+	0.410526i
$57$			28.3825i			0.0659536i
$58$	307.637	+	359.721i	0.696462	+	0.814374i
$59$	220.943	+	220.943i	0.487531	+	0.487531i	0.907526	−	0.419995i	$-0.137968\pi$
$59$	220.943	+	220.943i	0.487531	+	0.487531i	−0.419995	+	0.907526i	$0.637968\pi$
$60$	−345.197	−	54.2116i	−0.742745	−	0.116645i
$61$	−453.845	+	453.845i	−0.952604	+	0.952604i	−0.998927	−	0.0463225i	$-0.985250\pi$
$61$	−453.845	+	453.845i	−0.952604	+	0.952604i	0.0463225	+	0.998927i	$0.485250\pi$
$62$	55.0427	−	705.274i	0.112749	−	1.44467i
$63$	295.532			0.591009
$64$	−457.103	−	230.653i	−0.892779	−	0.450495i
$65$	464.383			0.886147
$66$	17.0143	−	218.008i	0.0317321	−	0.406590i
$67$	−184.273	+	184.273i	−0.336007	+	0.336007i	−0.854862	−	0.518855i	$-0.826358\pi$
$67$	−184.273	+	184.273i	−0.336007	+	0.336007i	0.518855	+	0.854862i	$0.326358\pi$
$68$	−396.294	−	62.2363i	−0.706732	−	0.110989i
$69$	−396.444	−	396.444i	−0.691685	−	0.691685i
$70$	−878.880	−	1027.68i	−1.50066	−	1.75473i
$71$		−	18.8163i		−	0.0314519i	−0.999876	−	0.0157259i	$-0.994994\pi$
$71$		−	18.8163i		−	0.0314519i	0.999876	−	0.0157259i	$-0.00500593\pi$
$72$	−198.113	−	47.1523i	−0.324275	−	0.0771798i
$73$		−	828.683i		−	1.32863i	−0.747453	−	0.664315i	$-0.768723\pi$
$73$		−	828.683i		−	1.32863i	0.747453	−	0.664315i	$-0.231277\pi$
$74$	−604.680	+	517.129i	−0.949901	+	0.812366i
$75$	184.510	+	184.510i	0.284071	+	0.284071i
$76$	61.1736	−	44.5675i	0.0923302	−	0.0672663i
$77$	598.373	−	598.373i	0.885596	−	0.885596i
$78$	269.822	+	21.0581i	0.391684	+	0.0305688i
$79$	1048.37			1.49304			0.746522	−	0.665361i	$-0.231722\pi$
$79$	1048.37			1.49304			0.746522	+	0.665361i	$0.231722\pi$
$80$	425.200	+	829.138i	0.594234	+	1.15876i
$81$	−81.0000			−0.111111
$82$	526.085	+	41.0581i	0.708493	+	0.0552940i
$83$	−173.404	+	173.404i	−0.229320	+	0.229320i	−0.812409	−	0.583088i	$-0.801844\pi$
$83$	−173.404	+	173.404i	−0.229320	+	0.229320i	0.583088	+	0.812409i	$0.301844\pi$
$84$	−464.058	−	636.969i	−0.602772	−	0.827369i
$85$	516.238	+	516.238i	0.658751	+	0.658751i
$86$	−33.2353	+	28.4232i	−0.0416727	+	0.0356390i
$87$		−	502.041i		−	0.618672i
$88$	−496.595	+	305.654i	−0.601560	+	0.370260i
$89$			335.168i			0.399188i	0.979879	+	0.199594i	$0.0639623\pi$
$89$			335.168i			0.399188i	−0.979879	+	0.199594i	$0.936038\pi$
$90$	240.885	+	281.668i	0.282128	+	0.329893i
$91$	740.589	+	740.589i	0.853130	+	0.853130i
$92$	−231.953	+	1476.98i	−0.262857	+	1.67376i
$93$	−530.564	+	530.564i	−0.591579	+	0.591579i
$94$	−5.09131	+	65.2360i	−0.00558648	+	0.0715807i
$95$	−137.745			−0.148761
$96$	209.457	+	501.039i	0.222683	+	0.532678i
$97$	−687.122			−0.719244			−0.359622	−	0.933098i	$-0.617094\pi$
$97$	−687.122			−0.719244			−0.359622	+	0.933098i	$0.617094\pi$
$98$	161.812	−	2073.33i	0.166791	−	2.13712i
$99$	−164.003	+	164.003i	−0.166494	+	0.166494i
$100$	107.954	−	687.405i	0.107954	−	0.687405i
$101$	51.6403	+	51.6403i	0.0508752	+	0.0508752i	0.732087	−	0.681211i	$-0.238547\pi$
$101$	51.6403	+	51.6403i	0.0508752	+	0.0508752i	−0.681211	+	0.732087i	$0.738547\pi$
$102$	276.542	+	323.361i	0.268448	+	0.313897i
$103$			116.260i			0.111218i	0.998453	+	0.0556089i	$0.0177100\pi$
$103$			116.260i			0.111218i	−0.998453	+	0.0556089i	$0.982290\pi$
$104$	−378.299	−	614.622i	−0.356686	−	0.579506i
$105$			1434.27i			1.33305i
$106$	−409.370	+	350.097i	−0.375108	+	0.320797i
$107$	−330.891	−	330.891i	−0.298958	−	0.298958i	0.541648	−	0.840605i	$-0.317801\pi$
$107$	−330.891	−	330.891i	−0.298958	−	0.298958i	−0.840605	+	0.541648i	$0.817801\pi$
$108$	127.190	+	174.582i	0.113323	+	0.155547i
$109$	508.212	−	508.212i	0.446586	−	0.446586i	−0.447632	−	0.894218i	$-0.647732\pi$
$109$	508.212	−	508.212i	0.446586	−	0.446586i	0.894218	+	0.447632i	$0.147732\pi$
$110$	1058.03	+	82.5733i	0.917082	+	0.0715732i
$111$	843.916			0.721630
$112$	−644.194	+	2000.39i	−0.543488	+	1.68767i
$113$	−1947.12			−1.62097			−0.810486	−	0.585758i	$-0.800797\pi$
$113$	−1947.12			−1.62097			−0.810486	+	0.585758i	$0.800797\pi$
$114$	−80.0345	−	6.24625i	−0.0657536	−	0.00513171i
$115$	1924.01	−	1924.01i	1.56013	−	1.56013i
$116$	−1082.06	+	788.327i	−0.866095	+	0.630985i
$117$	−202.982	−	202.982i	−0.160390	−	0.160390i
$118$	−671.651	+	574.403i	−0.523987	+	0.448120i
$119$			1646.57i			1.26841i
$120$	228.838	−	961.474i	0.174083	−	0.731418i
$121$		−	666.876i		−	0.501034i
$122$	−1179.90	−	1379.65i	−0.875596	−	1.02384i
$123$	−395.764	−	395.764i	−0.290121	−	0.290121i
$124$	1976.65	+	310.425i	1.43152	+	0.224814i
$125$	391.433	−	391.433i	0.280087	−	0.280087i
$126$	−65.0389	+	833.357i	−0.0459852	+	0.589217i
$127$	−2298.87			−1.60623			−0.803117	−	0.595821i	$-0.796827\pi$
$127$	−2298.87			−1.60623			−0.803117	+	0.595821i	$0.796827\pi$
$128$	751.005	−	1238.20i	0.518595	−	0.855020i
$129$	46.3845			0.0316583
$130$	−102.199	+	1309.49i	−0.0689493	+	0.883461i
$131$	−916.347	+	916.347i	−0.611157	+	0.611157i	−0.943248	−	0.332090i	$-0.892246\pi$
$131$	−916.347	+	916.347i	−0.611157	+	0.611157i	0.332090	+	0.943248i	$0.392246\pi$
$132$	611.006	+	95.9557i	0.402888	+	0.0632718i
$133$	−219.673	−	219.673i	−0.143219	−	0.143219i
$134$	−479.068	−	560.175i	−0.308844	−	0.361132i
$135$		−	393.106i		−	0.250616i
$136$	262.711	−	1103.80i	0.165642	−	0.695953i
$137$		−	867.840i		−	0.541201i	−0.962692	−	0.270601i	$-0.912778\pi$
$137$		−	867.840i		−	0.541201i	0.962692	−	0.270601i	$-0.0872223\pi$
$138$	1205.16	−	1030.67i	0.743407	−	0.635770i
$139$	−241.394	−	241.394i	−0.147300	−	0.147300i	0.629611	−	0.776911i	$-0.283214\pi$
$139$	−241.394	−	241.394i	−0.147300	−	0.147300i	−0.776911	+	0.629611i	$0.783214\pi$
$140$	3091.32	−	2252.15i	1.86617	−	1.35958i
$141$	49.0758	−	49.0758i	0.0293115	−	0.0293115i
$142$	53.0592	+	4.14098i	0.0313565	+	0.00244721i
$143$	−821.967			−0.480674
$144$	176.562	−	548.272i	0.102177	−	0.317287i
$145$	2436.49			1.39544
$146$	2336.76	+	182.371i	1.32460	+	0.103378i
$147$	−1559.73	+	1559.73i	−0.875130	+	0.875130i
$148$	−1325.15	−	1818.92i	−0.735993	−	1.01023i
$149$	−1733.18	−	1733.18i	−0.952939	−	0.952939i	0.0460022	−	0.998941i	$-0.485352\pi$
$149$	−1733.18	−	1733.18i	−0.952939	−	0.952939i	−0.998941	+	0.0460022i	$0.985352\pi$
$150$	−560.896	+	479.685i	−0.305313	+	0.261107i
$151$			1719.99i			0.926959i	0.886108	+	0.463479i	$0.153399\pi$
$151$			1719.99i			0.926959i	−0.886108	+	0.463479i	$0.846601\pi$
$152$	112.211	+	182.309i	0.0598784	+	0.0972842i
$153$		−	451.296i		−	0.238465i
$154$	1555.64	+	1819.01i	0.814005	+	0.951818i
$155$	−2574.91	−	2574.91i	−1.33433	−	1.33433i
$156$	−118.762	+	756.224i	−0.0609522	+	0.388118i
$157$	−1613.85	+	1613.85i	−0.820377	+	0.820377i	−0.986162	−	0.165785i	$-0.946984\pi$
$157$	−1613.85	+	1613.85i	−0.820377	+	0.820377i	0.165785	+	0.986162i	$0.446984\pi$
$158$	−230.718	+	2956.24i	−0.116171	+	1.48852i
$159$	571.332			0.284966
$160$	−2431.62	+	1016.53i	−1.20148	+	0.502273i
$161$	6136.74			3.00400
$162$	17.8260	−	228.408i	0.00864532	−	0.110774i
$163$	2582.38	−	2582.38i	1.24090	−	1.24090i	0.281278	−	0.959626i	$-0.409242\pi$
$163$	2582.38	−	2582.38i	1.24090	−	1.24090i	0.959626	−	0.281278i	$-0.0907583\pi$
$164$	−231.555	+	1474.45i	−0.110253	+	0.702043i
$165$	−795.934	−	795.934i	−0.375536	−	0.375536i
$166$	−450.813	−	527.136i	−0.210782	−	0.246468i
$167$		−	1938.49i		−	0.898233i	−0.893473	−	0.449117i	$-0.851739\pi$
$167$		−	1938.49i		−	0.898233i	0.893473	−	0.449117i	$-0.148261\pi$
$168$	1898.29	−	1168.39i	0.871762	−	0.536569i
$169$			1179.68i			0.536948i
$170$	−1569.32	+	1342.10i	−0.708010	+	0.605498i
$171$	60.2084	+	60.2084i	0.0269254	+	0.0269254i
$172$	−72.8350	−	99.9738i	−0.0322884	−	0.0443194i
$173$	−2044.47	+	2044.47i	−0.898487	+	0.898487i	−0.995302	−	0.0968155i	$-0.969134\pi$
$173$	−2044.47	+	2044.47i	−0.898487	+	0.898487i	0.0968155	+	0.995302i	$0.469134\pi$
$174$	1415.68	+	110.486i	0.616796	+	0.0481375i
$175$	−2856.11			−1.23373
$176$	−752.612	−	1467.59i	−0.322331	−	0.628545i
$177$	937.383			0.398068
$178$	−945.124	−	73.7617i	−0.397978	−	0.0310600i
$179$	−676.126	+	676.126i	−0.282324	+	0.282324i	−0.834035	−	0.551711i	$-0.813975\pi$
$179$	−676.126	+	676.126i	−0.282324	+	0.282324i	0.551711	+	0.834035i	$0.313975\pi$
$180$	−847.273	+	617.273i	−0.350845	+	0.255604i
$181$	1298.63	+	1298.63i	0.533295	+	0.533295i	0.921551	−	0.388257i	$-0.126923\pi$
$181$	1298.63	+	1298.63i	0.533295	+	0.533295i	−0.388257	+	0.921551i	$0.626923\pi$
$182$	−2251.34	+	1925.37i	−0.916923	+	0.784163i
$183$			1925.50i			0.777798i
$184$	−4113.82	−	979.120i	−1.64823	−	0.392292i
$185$			4095.66i			1.62767i
$186$	−1379.35	−	1612.87i	−0.543756	−	0.635815i
$187$	−913.752	−	913.752i	−0.357327	−	0.357327i
$188$	−182.835	−	28.7135i	−0.0709290	−	0.0111391i
$189$	626.918	−	626.918i	0.241278	−	0.241278i
$190$	30.3141	−	388.420i	0.0115748	−	0.148310i
$191$	2290.42			0.867692			0.433846	−	0.900987i	$-0.357156\pi$
$191$	2290.42			0.867692			0.433846	+	0.900987i	$0.357156\pi$
$192$	−1458.95	+	480.372i	−0.548389	+	0.180562i
$193$	128.763			0.0480235			0.0240117	−	0.999712i	$-0.492356\pi$
$193$	128.763			0.0480235			0.0240117	+	0.999712i	$0.492356\pi$
$194$	151.218	−	1937.58i	0.0559629	−	0.717063i
$195$	985.104	−	985.104i	0.361768	−	0.361768i
$196$	5810.88	+	912.573i	2.11767	+	0.332570i
$197$	725.669	+	725.669i	0.262446	+	0.262446i	0.826047	−	0.563601i	$-0.190585\pi$
$197$	725.669	+	725.669i	0.262446	+	0.262446i	−0.563601	+	0.826047i	$0.690585\pi$
$198$	−426.372	−	498.557i	−0.153035	−	0.178944i
$199$			2779.71i			0.990192i	0.868838	+	0.495096i	$0.164867\pi$
$199$			2779.71i			0.990192i	−0.868838	+	0.495096i	$0.835133\pi$
$200$	1914.62	+	455.694i	0.676921	+	0.161112i
$201$			781.802i			0.274349i
$202$	−156.983	+	134.253i	−0.0546795	+	0.0467625i
$203$	3885.66	+	3885.66i	1.34345	+	1.34345i
$204$	−972.691	+	708.644i	−0.333833	+	0.243211i
$205$	1920.71	−	1920.71i	0.654381	−	0.654381i
$206$	−327.836	−	25.5858i	−0.110881	−	0.00865363i
$207$	−1681.97			−0.564758
$208$	1816.40	−	931.486i	0.605502	−	0.310514i
$209$	243.811			0.0806928
$210$	−4044.42	−	315.645i	−1.32901	−	0.103722i
$211$	691.983	−	691.983i	0.225773	−	0.225773i	−0.585151	−	0.810924i	$-0.698965\pi$
$211$	691.983	−	691.983i	0.225773	−	0.225773i	0.810924	+	0.585151i	$0.198965\pi$
$212$	−897.131	−	1231.41i	−0.290638	−	0.398932i
$213$	−39.9154	−	39.9154i	−0.0128402	−	0.0128402i
$214$	1005.88	−	860.244i	0.321312	−	0.274790i
$215$			225.111i			0.0714068i
$216$	−520.286	+	320.236i	−0.163893	+	0.100876i
$217$		−	8212.84i		−	2.56924i
$218$	1321.24	+	1544.93i	0.410484	+	0.479980i
$219$	−1757.90	−	1757.90i	−0.542411	−	0.542411i
$220$	−465.689	+	2965.31i	−0.142712	+	0.908733i
$221$	1130.92	−	1130.92i	0.344227	−	0.344227i
$222$	−185.724	+	2379.72i	−0.0561485	+	0.719442i
$223$	−2188.31			−0.657130			−0.328565	−	0.944481i	$-0.606565\pi$
$223$	−2188.31			−0.657130			−0.328565	+	0.944481i	$0.606565\pi$
$224$	−5499.05	−	2256.77i	−1.64027	−	0.673154i
$225$	782.809			0.231943
$226$	428.511	−	5490.60i	0.126124	−	1.61606i
$227$	3063.77	−	3063.77i	0.895814	−	0.895814i	−0.0992483	−	0.995063i	$-0.531644\pi$
$227$	3063.77	−	3063.77i	0.895814	−	0.895814i	0.995063	+	0.0992483i	$0.0316438\pi$
$228$	35.2270	−	224.311i	0.0102323	−	0.0651550i
$229$	3654.19	+	3654.19i	1.05448	+	1.05448i	0.998428	+	0.0560514i	$0.0178511\pi$
$229$	3654.19	+	3654.19i	1.05448	+	1.05448i	0.0560514	+	0.998428i	$0.482149\pi$
$230$	5002.00	+	5848.84i	1.43401	+	1.67679i
$231$		−	2538.68i		−	0.723086i
$232$	−1984.83	−	3224.75i	−0.561684	−	0.912565i
$233$			4142.40i			1.16471i	0.812935	+	0.582355i	$0.197869\pi$
$233$			4142.40i			1.16471i	−0.812935	+	0.582355i	$0.802131\pi$
$234$	617.050	−	527.708i	0.172384	−	0.147425i
$235$	238.173	+	238.173i	0.0661135	+	0.0661135i
$236$	−1471.92	−	2020.37i	−0.405991	−	0.557266i
$237$	2223.92	−	2223.92i	0.609533	−	0.609533i
$238$	−4643.09	−	362.368i	−1.26457	−	0.0986925i
$239$	3081.29			0.833942			0.416971	−	0.908920i	$-0.363092\pi$
$239$	3081.29			0.833942			0.416971	+	0.908920i	$0.363092\pi$
$240$	2660.85	+	856.884i	0.715655	+	0.230465i
$241$	−5328.92			−1.42434			−0.712170	−	0.702007i	$-0.752287\pi$
$241$	−5328.92			−1.42434			−0.712170	+	0.702007i	$0.752287\pi$
$242$	1880.49	+	146.762i	0.499515	+	0.0389844i
$243$	−171.827	+	171.827i	−0.0453609	+	0.0453609i
$244$	4150.09	−	3023.50i	1.08886	−	0.793279i
$245$	−7569.61	−	7569.61i	−1.97390	−	1.97390i
$246$	1203.09	−	1028.90i	0.311815	−	0.266667i
$247$			301.758i			0.0777345i
$248$	−1310.36	+	5505.56i	−0.335516	+	1.40969i
$249$			735.692i			0.187239i
$250$	1017.64	+	1189.93i	0.257444	+	0.301030i
$251$	360.857	+	360.857i	0.0907455	+	0.0907455i	0.751022	−	0.660277i	$-0.229561\pi$
$251$	360.857	+	360.857i	0.0907455	+	0.0907455i	−0.660277	+	0.751022i	$0.729561\pi$
$252$	−2335.63	−	366.800i	−0.583853	−	0.0916915i
$253$	−3405.53	+	3405.53i	−0.846261	+	0.846261i
$254$	505.922	−	6482.47i	0.124978	−	1.60136i
$255$	2190.21			0.537868
$256$	3326.27	+	2390.22i	0.812077	+	0.583550i
$257$	−4829.14			−1.17211			−0.586057	−	0.810270i	$-0.699321\pi$
$257$	−4829.14			−1.17211			−0.586057	+	0.810270i	$0.699321\pi$
$258$	−10.2080	+	130.797i	−0.00246327	+	0.0315624i
$259$	−6531.68	+	6531.68i	−1.56702	+	1.56702i
$260$	−3670.08	−	576.370i	−0.875418	−	0.137480i
$261$	−1064.99	−	1064.99i	−0.252572	−	0.252572i
$262$	−2382.30	−	2785.63i	−0.561752	−	0.656857i
$263$		−	2949.69i		−	0.691581i	−0.938312	−	0.345791i	$-0.887611\pi$
$263$		−	2949.69i		−	0.691581i	0.938312	−	0.345791i	$-0.112389\pi$
$264$	−405.047	+	1701.83i	−0.0944278	+	0.396743i
$265$			2772.77i			0.642754i
$266$	667.790	−	571.101i	0.153928	−	0.131641i
$267$	710.999	+	710.999i	0.162968	+	0.162968i
$268$	1685.04	−	1227.62i	0.384068	−	0.279809i
$269$	−2262.88	+	2262.88i	−0.512900	+	0.512900i	−0.915414	−	0.402514i	$-0.868137\pi$
$269$	−2262.88	+	2262.88i	−0.512900	+	0.512900i	0.402514	+	0.915414i	$0.368137\pi$
$270$	1108.50	+	86.5125i	0.249857	+	0.0194999i
$271$	1330.31			0.298194			0.149097	−	0.988823i	$-0.452363\pi$
$271$	1330.31			0.298194			0.149097	+	0.988823i	$0.452363\pi$
$272$	3054.72	+	983.723i	0.680955	+	0.219290i
$273$	3142.05			0.696577
$274$	2447.18	+	190.989i	0.539561	+	0.0421098i
$275$	1584.98	−	1584.98i	0.347555	−	0.347555i
$276$	2641.10	+	3625.20i	0.575999	+	0.790621i
$277$	−3226.46	−	3226.46i	−0.699853	−	0.699853i	0.264525	−	0.964379i	$-0.414785\pi$
$277$	−3226.46	−	3226.46i	−0.699853	−	0.699853i	−0.964379	+	0.264525i	$0.914785\pi$
$278$	733.818	−	627.570i	0.158315	−	0.135393i
$279$			2250.99i			0.483023i
$280$	5670.41	+	9212.69i	1.21026	+	1.96630i
$281$		−	6371.42i		−	1.35262i	−0.736615	−	0.676312i	$-0.763577\pi$
$281$		−	6371.42i		−	1.35262i	0.736615	−	0.676312i	$-0.236423\pi$
$282$	127.586	+	149.187i	0.0269420	+	0.0315033i
$283$	2438.64	+	2438.64i	0.512234	+	0.512234i	0.915210	−	0.402976i	$-0.132024\pi$
$283$	2438.64	+	2438.64i	0.512234	+	0.512234i	−0.402976	+	0.915210i	$0.632024\pi$
$284$	−23.3539	+	148.708i	−0.00487957	+	0.0310711i
$285$	−292.201	+	292.201i	−0.0607316	+	0.0607316i
$286$	180.894	−	2317.83i	0.0374002	−	0.479216i
$287$	6126.22			1.26000
$288$	1507.19	+	618.539i	0.308375	+	0.126555i
$289$	−2398.58			−0.488212
$290$	−536.207	+	6870.53i	−0.108576	+	1.39121i
$291$	−1457.61	+	1457.61i	−0.293630	+	0.293630i
$292$	−1028.52	+	6549.19i	−0.206129	+	1.31254i
$293$	6920.93	+	6920.93i	1.37995	+	1.37995i	0.844684	+	0.535265i	$0.179788\pi$
$293$	6920.93	+	6920.93i	1.37995	+	1.37995i	0.535265	+	0.844684i	$0.320212\pi$
$294$	−4054.95	−	4741.46i	−0.804385	−	0.940569i
$295$			4549.27i			0.897860i
$296$	5420.71	−	3336.44i	1.06443	−	0.655158i
$297$			695.806i			0.135942i
$298$	5268.75	−	4505.89i	1.02420	−	0.875904i
$299$	−4214.93	−	4214.93i	−0.815237	−	0.815237i
$300$	−1229.20	−	1687.21i	−0.236560	−	0.324704i
$301$	−359.003	+	359.003i	−0.0687462	+	0.0687462i
$302$	−4850.12	−	378.525i	−0.924149	−	0.0721247i
$303$	219.091			0.0415394
$304$	−538.779	+	276.297i	−0.101648	+	0.0521274i
$305$	−9344.76			−1.75436
$306$	1272.59	+	99.3184i	0.237742	+	0.0185544i
$307$	2964.65	−	2964.65i	0.551146	−	0.551146i	−0.375626	−	0.926771i	$-0.622572\pi$
$307$	2964.65	−	2964.65i	0.551146	−	0.551146i	0.926771	+	0.375626i	$0.122572\pi$
$308$	−5471.69	+	3986.35i	−1.01227	+	0.737478i
$309$	246.625	+	246.625i	0.0454045	+	0.0454045i
$310$	7827.54	−	6694.20i	1.43411	−	1.22647i
$311$		−	3503.10i		−	0.638722i	−0.947633	−	0.319361i	$-0.896532\pi$
$311$		−	3503.10i		−	0.638722i	0.947633	−	0.319361i	$-0.103468\pi$
$312$	−2106.30	−	501.315i	−0.382199	−	0.0909660i
$313$			119.690i			0.0216144i	0.999942	+	0.0108072i	$0.00344010\pi$
$313$			119.690i			0.0216144i	−0.999942	+	0.0108072i	$0.996560\pi$
$314$	−4195.65	−	4905.98i	−0.754058	−	0.881721i
$315$	3042.54	+	3042.54i	0.544215	+	0.544215i
$316$	−8285.38	−	1301.18i	−1.47497	−	0.231637i
$317$	−1793.71	+	1793.71i	−0.317806	+	0.317806i	−0.847924	−	0.530118i	$-0.822148\pi$
$317$	−1793.71	+	1793.71i	−0.317806	+	0.317806i	0.530118	+	0.847924i	$0.322148\pi$
$318$	−125.735	+	1611.07i	−0.0221726	+	0.284102i
$319$	−4312.63			−0.756931
$320$	−2331.32	−	7080.53i	−0.407265	−	1.23692i
$321$	−1403.85			−0.244098
$322$	−1350.54	+	17304.7i	−0.233735	+	2.99489i
$323$	−335.454	+	335.454i	−0.0577869	+	0.0577869i
$324$	640.154	+	100.533i	0.109766	+	0.0172382i
$325$	1961.68	+	1961.68i	0.334814	+	0.334814i
$326$	6713.61	+	7850.24i	1.14059	+	1.33369i
$327$		−	2156.16i		−	0.364636i
$328$	−4106.77	−	977.440i	−0.691336	−	0.164543i
$329$			759.667i			0.127300i
$330$	2419.58	−	2069.25i	0.403617	−	0.345177i
$331$	−1546.84	−	1546.84i	−0.256864	−	0.256864i	0.566913	−	0.823778i	$-0.308138\pi$
$331$	−1546.84	−	1546.84i	−0.256864	−	0.256864i	−0.823778	+	0.566913i	$0.808138\pi$
$332$	1585.66	−	1155.22i	0.262122	−	0.190966i
$333$	1790.22	−	1790.22i	0.294604	−	0.294604i
$334$	5466.26	+	426.612i	0.895510	+	0.0698897i
$335$	−3794.21			−0.618806
$336$	2876.94	+	5610.02i	0.467112	+	0.910868i
$337$	2433.56			0.393367			0.196683	−	0.980467i	$-0.436983\pi$
$337$	2433.56			0.393367			0.196683	+	0.980467i	$0.436983\pi$
$338$	−3326.51	−	259.616i	−0.535320	−	0.0417788i
$339$	−4130.47	+	4130.47i	−0.661759	+	0.661759i
$340$	−3439.17	−	4720.63i	−0.548574	−	0.752976i
$341$	4557.65	+	4557.65i	0.723784	+	0.723784i
$342$	−183.029	+	156.528i	−0.0289388	+	0.0247488i
$343$		−	12880.7i		−	2.02767i
$344$	297.940	−	183.382i	0.0466973	−	0.0287422i
$345$		−	8162.88i		−	1.27384i
$346$	−5315.17	−	6215.04i	−0.825854	−	0.965672i
$347$	1171.50	+	1171.50i	0.181237	+	0.181237i	0.791895	−	0.610658i	$-0.209095\pi$
$347$	1171.50	+	1171.50i	0.181237	+	0.181237i	−0.610658	+	0.791895i	$0.709095\pi$
$348$	−623.109	+	3967.70i	−0.0959832	+	0.611181i
$349$	7672.16	−	7672.16i	1.17674	−	1.17674i	0.196166	−	0.980571i	$-0.437151\pi$
$349$	7672.16	−	7672.16i	1.17674	−	1.17674i	0.980571	−	0.196166i	$-0.0628492\pi$
$350$	628.556	−	8053.82i	0.0959936	−	1.22999i
$351$	−861.179			−0.130958
$352$	4304.02	−	1799.28i	0.651719	−	0.272448i
$353$	−2040.98			−0.307734			−0.153867	−	0.988092i	$-0.549173\pi$
$353$	−2040.98			−0.307734			−0.153867	+	0.988092i	$0.549173\pi$
$354$	−206.294	+	2643.28i	−0.0309728	+	0.396861i
$355$	193.716	−	193.716i	0.0289616	−	0.0289616i
$356$	415.994	−	2648.88i	0.0619316	−	0.394355i
$357$	3492.91	+	3492.91i	0.517827	+	0.517827i
$358$	−1757.78	−	2055.37i	−0.259501	−	0.303435i
$359$			4623.13i			0.679664i	0.940486	+	0.339832i	$0.110370\pi$
$359$			4623.13i			0.679664i	−0.940486	+	0.339832i	$0.889630\pi$
$360$	−1554.16	−	2525.03i	−0.227531	−	0.369669i
$361$			6769.49i			0.986950i
$362$	−3947.74	+	3376.15i	−0.573172	+	0.490183i
$363$	−1414.66	−	1414.66i	−0.204546	−	0.204546i
$364$	−4933.79	−	6772.16i	−0.710442	−	0.975158i
$365$	8531.38	−	8531.38i	1.22343	−	1.22343i
$366$	−5429.62	−	423.752i	−0.775440	−	0.0605188i
$367$	10876.3			1.54697			0.773487	−	0.633813i	$-0.218511\pi$
$367$	10876.3			1.54697			0.773487	+	0.633813i	$0.218511\pi$
$368$	3666.32	−	11384.9i	0.519348	−	1.61271i
$369$	−1679.08			−0.236882
$370$	−11549.2	−	901.348i	−1.62274	−	0.126646i
$371$	−4421.96	+	4421.96i	−0.618805	+	0.618805i
$372$	4851.63	−	3534.61i	0.676196	−	0.492636i
$373$	−621.022	−	621.022i	−0.0862073	−	0.0862073i	0.662688	−	0.748895i	$-0.269415\pi$
$373$	−621.022	−	621.022i	−0.0862073	−	0.0862073i	−0.748895	+	0.662688i	$0.769415\pi$
$374$	2777.74	−	2375.55i	0.384046	−	0.328441i
$375$		−	1660.71i		−	0.228690i
$376$	121.205	−	509.250i	0.0166241	−	0.0698472i
$377$		−	5337.62i		−	0.729181i
$378$	1629.85	+	1905.79i	0.221774	+	0.259320i
$379$	8642.89	+	8642.89i	1.17139	+	1.17139i	0.981879	+	0.189507i	$0.0606889\pi$
$379$	8642.89	+	8642.89i	1.17139	+	1.17139i	0.189507	+	0.981879i	$0.439311\pi$
$380$	1088.62	+	170.962i	0.146960	+	0.0230794i
$381$	−4876.64	+	4876.64i	−0.655742	+	0.655742i
$382$	−504.062	+	6458.65i	−0.0675133	+	0.865061i
$383$	−3607.79			−0.481330			−0.240665	−	0.970608i	$-0.577365\pi$
$383$	−3607.79			−0.481330			−0.240665	+	0.970608i	$0.577365\pi$
$384$	−1033.50	−	4219.74i	−0.137345	−	0.560776i
$385$	12320.6			1.63095
$386$	−28.3373	+	363.091i	−0.00373661	+	0.0478779i
$387$	98.3963	−	98.3963i	0.0129245	−	0.0129245i
$388$	5430.42	+	852.823i	0.710535	+	0.111586i
$389$	3437.52	+	3437.52i	0.448045	+	0.448045i	0.894704	−	0.446659i	$-0.147386\pi$
$389$	3437.52	+	3437.52i	0.448045	+	0.448045i	−0.446659	+	0.894704i	$0.647386\pi$
$390$	2561.05	+	2994.64i	0.332523	+	0.388820i
$391$		−	9371.18i		−	1.21207i
$392$	−3852.14	+	16185.0i	−0.496333	+	2.08537i
$393$			3887.73i			0.499008i
$394$	−2205.98	+	1886.58i	−0.282070	+	0.241230i
$395$	10793.1	+	10793.1i	1.37483	+	1.37483i
$396$	1499.69	−	1092.59i	0.190309	−	0.138648i
$397$	1579.30	−	1579.30i	0.199655	−	0.199655i	−0.600197	−	0.799852i	$-0.704911\pi$
$397$	1579.30	−	1579.30i	0.199655	−	0.199655i	0.799852	+	0.600197i	$0.204911\pi$
$398$	−7838.36	−	611.741i	−0.987190	−	0.0770447i
$399$	−931.994			−0.116937
$400$	−1706.35	+	5298.67i	−0.213294	+	0.662333i
$401$	2316.77			0.288513			0.144257	−	0.989540i	$-0.453921\pi$
$401$	2316.77			0.288513			0.144257	+	0.989540i	$0.453921\pi$
$402$	−2204.57	−	172.054i	−0.273517	−	0.0213465i
$403$	−5640.87	+	5640.87i	−0.697250	+	0.697250i
$404$	−344.026	−	472.213i	−0.0423662	−	0.0581522i
$405$	−833.904	−	833.904i	−0.102314	−	0.102314i
$406$	−11812.1	+	10101.9i	−1.44391	+	1.23484i
$407$		−	7249.40i		−	0.882898i
$408$	−1784.21	−	2898.80i	−0.216499	−	0.351745i
$409$		−	669.173i		−	0.0809009i	−0.999182	−	0.0404504i	$-0.987121\pi$
$409$		−	669.173i		−	0.0809009i	0.999182	−	0.0404504i	$-0.0128793\pi$
$410$	4993.41	+	5838.81i	0.601481	+	0.703313i
$411$	−1840.97	−	1840.97i	−0.220945	−	0.220945i
$412$	144.296	−	918.818i	0.0172548	−	0.109871i
$413$	−7255.09	+	7255.09i	−0.864406	+	0.864406i
$414$	370.158	−	4742.91i	0.0439427	−	0.563046i
$415$	−3570.44			−0.422327
$416$	2226.91	+	5326.97i	0.262460	+	0.627827i
$417$	−1024.15			−0.120270
$418$	−53.6565	+	687.512i	−0.00627853	+	0.0804481i
$419$	−3656.45	+	3656.45i	−0.426323	+	0.426323i	−0.887374	−	0.461051i	$-0.847473\pi$
$419$	−3656.45	+	3656.45i	−0.426323	+	0.426323i	0.461051	+	0.887374i	$0.347473\pi$
$420$	1780.14	−	11335.2i	0.206814	−	1.31691i
$421$	−837.867	−	837.867i	−0.0969956	−	0.0969956i	0.656944	−	0.753939i	$-0.271849\pi$
$421$	−837.867	−	837.867i	−0.0969956	−	0.0969956i	−0.753939	+	0.656944i	$0.771849\pi$
$422$	1799.00	+	2103.58i	0.207521	+	0.242655i
$423$		−	208.211i		−	0.0239328i
$424$	3669.83	−	2258.78i	0.420336	−	0.258717i
$425$			4361.46i			0.497793i
$426$	121.340	−	103.771i	0.0138003	−	0.0118022i
$427$	−14902.9	−	14902.9i	−1.68899	−	1.68899i
$428$	2204.39	+	3025.76i	0.248956	+	0.341719i
$429$	−1743.66	+	1743.66i	−0.196234	+	0.196234i
$430$	−634.781	−	49.5412i	−0.0711904	−	0.00555602i
$431$	−6690.20			−0.747693			−0.373846	−	0.927491i	$-0.621961\pi$
$431$	−6690.20			−0.747693			−0.373846	+	0.927491i	$0.621961\pi$
$432$	−788.516	−	1537.60i	−0.0878182	−	0.171245i
$433$	−7836.97			−0.869794			−0.434897	−	0.900480i	$-0.643215\pi$
$433$	−7836.97			−0.869794			−0.434897	+	0.900480i	$0.643215\pi$
$434$	23159.0	+	1807.43i	2.56145	+	0.199907i
$435$	5168.57	−	5168.57i	0.569687	−	0.569687i
$436$	−4647.24	+	3385.70i	−0.510464	+	0.371894i
$437$	1250.23	+	1250.23i	0.136857	+	0.136857i
$438$	5343.89	−	4570.15i	0.582970	−	0.498563i
$439$			6041.06i			0.656775i	0.944543	+	0.328387i	$0.106505\pi$
$439$			6041.06i			0.656775i	−0.944543	+	0.328387i	$0.893495\pi$
$440$	−8259.25	−	1965.76i	−0.894873	−	0.212986i
$441$			6617.36i			0.714541i
$442$	2940.15	+	3437.93i	0.316400	+	0.369967i
$443$	−8281.65	−	8281.65i	−0.888201	−	0.888201i	0.106149	−	0.994350i	$-0.466148\pi$
$443$	−8281.65	−	8281.65i	−0.888201	−	0.888201i	−0.994350	+	0.106149i	$0.966148\pi$
$444$	−6669.58	−	1047.43i	−0.712892	−	0.111957i
$445$	−3450.59	+	3450.59i	−0.367581	+	0.367581i
$446$	481.590	−	6170.70i	0.0511299	−	0.655138i
$447$	−7353.28			−0.778072
$448$	7573.95	−	15009.8i	0.798740	−	1.58292i
$449$	15502.7			1.62944			0.814718	−	0.579858i	$-0.196892\pi$
$449$	15502.7			1.62944			0.814718	+	0.579858i	$0.196892\pi$
$450$	−172.276	+	2207.41i	−0.0180470	+	0.231240i
$451$	−3399.69	+	3399.69i	−0.354956	+	0.354956i
$452$	15388.4	+	2416.68i	1.60135	+	0.251484i
$453$	3648.65	+	3648.65i	0.378429	+	0.378429i
$454$	7965.14	+	9313.65i	0.823397	+	0.962800i
$455$			15248.9i			1.57116i
$456$	624.771	+	148.700i	0.0641613	+	0.0152709i
$457$		−	4866.06i		−	0.498085i	−0.968493	−	0.249043i	$-0.919884\pi$
$457$		−	4866.06i		−	0.498085i	0.968493	−	0.249043i	$-0.0801159\pi$
$458$	−11108.5	+	9500.09i	−1.13333	+	0.969236i
$459$	−957.343	−	957.343i	−0.0973528	−	0.0973528i
$460$	−17593.7	+	12817.7i	−1.78328	+	1.29919i
$461$	7449.82	−	7449.82i	0.752653	−	0.752653i	−0.222321	−	0.974974i	$-0.571363\pi$
$461$	7449.82	−	7449.82i	0.752653	−	0.752653i	0.974974	+	0.222321i	$0.0713633\pi$
$462$	7158.70	+	558.698i	0.720894	+	0.0562618i
$463$	6924.56			0.695058			0.347529	−	0.937669i	$-0.387021\pi$
$463$	6924.56			0.695058			0.347529	+	0.937669i	$0.387021\pi$
$464$	9530.13	−	4887.25i	0.953502	−	0.488976i
$465$	−10924.4			−1.08948
$466$	−11680.9	−	911.633i	−1.16118	−	0.0906236i
$467$	4040.04	−	4040.04i	0.400323	−	0.400323i	−0.478024	−	0.878347i	$-0.658647\pi$
$467$	4040.04	−	4040.04i	0.400323	−	0.400323i	0.878347	+	0.478024i	$0.158647\pi$
$468$	1352.26	+	1856.12i	0.133565	+	0.183332i
$469$	−6050.94	−	6050.94i	−0.595750	−	0.595750i
$470$	−724.028	+	619.197i	−0.0710573	+	0.0607690i
$471$			6846.98i			0.669835i
$472$	6021.07	−	3705.97i	0.587166	−	0.361400i
$473$		−	398.452i		−	0.0387333i
$474$	5781.70	+	6760.56i	0.560258	+	0.655111i
$475$	−581.872	−	581.872i	−0.0562066	−	0.0562066i
$476$	2043.65	−	13013.1i	0.196787	−	1.25305i
$477$	1211.98	−	1211.98i	0.116337	−	0.116337i
$478$	−678.112	+	8688.79i	−0.0648873	+	0.831414i
$479$	−9957.56			−0.949839			−0.474919	−	0.880029i	$-0.657523\pi$
$479$	−9957.56			−0.949839			−0.474919	+	0.880029i	$0.657523\pi$
$480$	−3001.87	+	7314.63i	−0.285450	+	0.695554i
$481$	8972.38			0.850531
$482$	1172.76	−	15026.8i	0.110825	−	1.42002i
$483$	13018.0	−	13018.0i	1.22638	−	1.22638i
$484$	−827.695	+	5270.41i	−0.0777324	+	0.494967i
$485$	−7074.00	−	7074.00i	−0.662296	−	0.662296i
$486$	−446.712	−	522.341i	−0.0416940	−	0.0487528i
$487$			7671.90i			0.713854i	0.934132	+	0.356927i	$0.116176\pi$
$487$			7671.90i			0.713854i	−0.934132	+	0.356927i	$0.883824\pi$
$488$	7612.51	+	12368.0i	0.706152	+	1.14728i
$489$		−	10956.1i		−	1.01319i
$490$	23011.1	−	19679.3i	2.12150	−	1.81433i
$491$	−13794.0	−	13794.0i	−1.26785	−	1.26785i	−0.947196	−	0.320656i	$-0.896097\pi$
$491$	−13794.0	−	13794.0i	−1.26785	−	1.26785i	−0.320656	−	0.947196i	$-0.603903\pi$
$492$	2636.57	+	3618.98i	0.241597	+	0.331618i
$493$	5933.64	−	5933.64i	0.542065	−	0.542065i
$494$	−850.914	−	66.4092i	−0.0774988	−	0.00604836i
$495$	−3376.86			−0.306623
$496$	−15236.5	−	4906.66i	−1.37931	−	0.444184i
$497$	617.869			0.0557650
$498$	−2074.54	−	161.907i	−0.186672	−	0.0145687i
$499$	2138.01	−	2138.01i	0.191805	−	0.191805i	−0.604671	−	0.796476i	$-0.706695\pi$
$499$	2138.01	−	2138.01i	0.191805	−	0.191805i	0.796476	+	0.604671i	$0.206695\pi$
$500$	−3579.37	+	2607.72i	−0.320149	+	0.233241i
$501$	−4112.16	−	4112.16i	−0.366702	−	0.366702i
$502$	−1096.98	+	938.149i	−0.0975311	+	0.0834096i
$503$			1414.75i			0.125409i	0.998032	+	0.0627045i	$0.0199726\pi$
$503$			1414.75i			0.125409i	−0.998032	+	0.0627045i	$0.980027\pi$
$504$	1548.33	−	6505.41i	0.136842	−	0.574948i
$505$			1063.28i			0.0936942i
$506$	−8853.64	−	10352.6i	−0.777850	−	0.909542i
$507$	2502.47	+	2502.47i	0.219208	+	0.219208i
$508$	18168.3	+	2853.25i	1.58679	+	0.249198i
$509$	−10526.7	+	10526.7i	−0.916677	+	0.916677i	−0.996786	−	0.0801087i	$-0.974473\pi$
$509$	−10526.7	+	10526.7i	−0.916677	+	0.916677i	0.0801087	+	0.996786i	$0.474473\pi$
$510$	−482.009	+	6176.07i	−0.0418504	+	0.536237i
$511$	27211.4			2.35570
$512$	−7472.09	+	8853.56i	−0.644967	+	0.764211i
$513$	255.443			0.0219845
$514$	1062.77	−	13617.5i	0.0911997	−	1.16856i
$515$	−1196.91	+	1196.91i	−0.102412	+	0.102412i
$516$	−366.583	−	57.5702i	−0.0312750	−	0.00491160i
$517$	−421.571	−	421.571i	−0.0358620	−	0.0358620i
$518$	−16980.9	−	19855.8i	−1.44035	−	1.68420i
$519$			8673.95i			0.733611i
$520$	2432.97	−	10222.2i	0.205178	−	0.862067i
$521$			2004.13i			0.168527i	0.996444	+	0.0842636i	$0.0268538\pi$
$521$			2004.13i			0.168527i	−0.996444	+	0.0842636i	$0.973146\pi$
$522$	3237.49	−	2768.74i	0.271458	−	0.232154i
$523$	1006.02	+	1006.02i	0.0841110	+	0.0841110i	0.747911	−	0.663800i	$-0.231057\pi$
$523$	1006.02	+	1006.02i	0.0841110	+	0.0841110i	−0.663800	+	0.747911i	$0.731057\pi$
$524$	8379.34	−	6104.69i	0.698575	−	0.508940i
$525$	−6058.73	+	6058.73i	−0.503666	+	0.503666i
$526$	8317.70	+	649.151i	0.689485	+	0.0538105i
$527$	−12541.5			−1.03665
$528$	−4709.76	−	1516.70i	−0.388193	−	0.125011i
$529$	−22759.2			−1.87057
$530$	−7818.80	−	610.214i	−0.640805	−	0.0500113i
$531$	1988.49	−	1988.49i	0.162510	−	0.162510i
$532$	1463.46	+	2008.75i	0.119265	+	0.163704i
$533$	−4207.70	−	4207.70i	−0.341943	−	0.341943i
$534$	−2161.38	+	1848.44i	−0.175154	+	0.149794i
$535$		−	6813.12i		−	0.550574i
$536$	3090.88	+	5021.73i	0.249077	+	0.404675i
$537$			2868.56i			0.230517i
$538$	−5882.99	−	6878.99i	−0.471438	−	0.551253i
$539$	13398.4	+	13398.4i	1.07070	+	1.07070i
$540$	−487.905	+	3106.77i	−0.0388816	+	0.247582i
$541$	−13442.8	+	13442.8i	−1.06830	+	1.06830i	−0.0708153	+	0.997489i	$0.522560\pi$
$541$	−13442.8	+	13442.8i	−1.06830	+	1.06830i	−0.997489	+	0.0708153i	$0.977440\pi$
$542$	−292.766	+	3751.27i	−0.0232018	+	0.297290i
$543$	5509.61			0.435433
$544$	−3446.22	+	8397.38i	−0.271609	+	0.661828i
$545$	10464.2			0.822454
$546$	−691.484	+	8860.12i	−0.0541992	+	0.694466i
$547$	10996.4	−	10996.4i	0.859546	−	0.859546i	−0.131739	−	0.991284i	$-0.542056\pi$
$547$	10996.4	−	10996.4i	0.859546	−	0.859546i	0.991284	+	0.131739i	$0.0420559\pi$
$548$	−1077.12	+	6858.66i	−0.0839642	+	0.534649i
$549$	4084.60	+	4084.60i	0.317535	+	0.317535i
$550$	4120.59	+	4818.21i	0.319459	+	0.373544i
$551$			1583.24i			0.122411i
$552$	−10803.8	+	6649.71i	−0.833041	+	0.512736i
$553$			34425.1i			2.64721i
$554$	9808.21	−	8388.09i	0.752186	−	0.643277i
$555$	8688.21	+	8688.21i	0.664494	+	0.664494i
$556$	1608.16	+	2207.37i	0.122664	+	0.168369i
$557$	7583.67	−	7583.67i	0.576895	−	0.576895i	−0.357151	−	0.934046i	$-0.616252\pi$
$557$	7583.67	−	7583.67i	0.576895	−	0.576895i	0.934046	+	0.357151i	$0.116252\pi$
$558$	−6347.46	−	495.384i	−0.481558	−	0.0375830i
$559$	493.152			0.0373133
$560$	−27226.3	+	13962.2i	−2.05451	+	1.05359i
$561$	−3876.72			−0.291756
$562$	17966.5	+	1402.18i	1.34852	+	0.105245i
$563$	7263.00	−	7263.00i	0.543693	−	0.543693i	−0.380917	−	0.924609i	$-0.624392\pi$
$563$	7263.00	−	7263.00i	0.543693	−	0.543693i	0.924609	+	0.380917i	$0.124392\pi$
$564$	−448.763	+	326.942i	−0.0335041	+	0.0244091i
$565$	−20045.8	−	20045.8i	−1.49263	−	1.49263i
$566$	−7413.30	+	6339.93i	−0.550537	+	0.470825i
$567$		−	2659.79i		−	0.197003i
$568$	−414.194	−	98.5812i	−0.0305972	−	0.00728235i
$569$		−	26176.3i		−	1.92859i	−0.264835	−	0.964294i	$-0.585318\pi$
$569$		−	26176.3i		−	1.92859i	0.264835	−	0.964294i	$-0.414682\pi$
$570$	−759.658	−	888.270i	−0.0558221	−	0.0652729i
$571$	−3443.57	−	3443.57i	−0.252380	−	0.252380i	0.569566	−	0.821946i	$-0.307111\pi$
$571$	−3443.57	−	3443.57i	−0.252380	−	0.252380i	−0.821946	+	0.569566i	$0.807111\pi$
$572$	6496.12	+	1020.19i	0.474854	+	0.0745736i
$573$	4858.72	−	4858.72i	0.354234	−	0.354234i
$574$	−1348.22	+	17275.0i	−0.0980377	+	1.25618i
$575$	16255.1			1.17893
$576$	−2075.88	+	4113.93i	−0.150165	+	0.297593i
$577$	20621.2			1.48782			0.743909	−	0.668281i	$-0.232970\pi$
$577$	20621.2			1.48782			0.743909	+	0.668281i	$0.232970\pi$
$578$	527.866	−	6763.65i	0.0379867	−	0.486732i
$579$	273.147	−	273.147i	0.0196055	−	0.0196055i
$580$	−19255.9	−	3024.05i	−1.37855	−	0.216495i
$581$	−5694.06	−	5694.06i	−0.406591	−	0.406591i
$582$	−3789.45	−	4431.01i	−0.269893	−	0.315587i
$583$		−	4907.86i		−	0.348650i
$584$	−18241.4	−	4341.58i	−1.29252	−	0.307630i
$585$		−	4179.44i		−	0.295382i
$586$	−21039.1	+	17992.9i	−1.48314	+	1.26839i
$587$	16989.3	+	16989.3i	1.19459	+	1.19459i	0.975765	+	0.218823i	$0.0702218\pi$
$587$	16989.3	+	16989.3i	1.19459	+	1.19459i	0.218823	+	0.975765i	$0.429778\pi$
$588$	14262.6	−	10390.9i	1.00031	−	0.728763i
$589$	1673.19	−	1673.19i	0.117050	−	0.117050i
$590$	−12828.3	−	1001.18i	−0.895139	−	0.0698606i
$591$	3078.75			0.214286
$592$	8215.32	+	16019.9i	0.570351	+	1.11218i
$593$	2210.09			0.153048			0.0765239	−	0.997068i	$-0.475618\pi$
$593$	2210.09			0.153048			0.0765239	+	0.997068i	$0.475618\pi$
$594$	−1962.07	−	153.129i	−0.135530	−	0.0105774i
$595$	−16951.7	+	16951.7i	−1.16798	+	1.16798i
$596$	11546.4	+	15848.7i	0.793558	+	1.08924i
$597$	5896.65	+	5896.65i	0.404244	+	0.404244i
$598$	12813.1	−	10957.9i	0.876197	−	0.749333i
$599$			16545.3i			1.12859i	0.825574	+	0.564294i	$0.190852\pi$
$599$			16545.3i			1.12859i	−0.825574	+	0.564294i	$0.809148\pi$
$600$	5028.20	−	3094.86i	0.342126	−	0.210578i
$601$			19182.8i			1.30197i	0.759092	+	0.650983i	$0.225643\pi$
$601$			19182.8i			1.30197i	−0.759092	+	0.650983i	$0.774357\pi$
$602$	−933.329	−	1091.34i	−0.0631888	−	0.0738868i
$603$	1658.45	+	1658.45i	0.112002	+	0.112002i
$604$	2134.77	−	13593.3i	0.143812	−	0.915735i
$605$	6865.57	−	6865.57i	0.461364	−	0.461364i
$606$	−48.2162	+	617.804i	−0.00323210	+	0.0414135i
$607$	−8375.82			−0.560073			−0.280036	−	0.959989i	$-0.590347\pi$
$607$	−8375.82			−0.560073			−0.280036	+	0.959989i	$0.590347\pi$
$608$	−660.545	−	1580.08i	−0.0440603	−	0.105396i
$609$	16485.5			1.09692
$610$	2056.54	−	26350.9i	0.136503	−	1.74904i
$611$	521.766	−	521.766i	0.0345473	−	0.0345473i
$612$	−560.127	+	3566.65i	−0.0369964	+	0.235577i
$613$	−9161.47	−	9161.47i	−0.603635	−	0.603635i	0.337640	−	0.941275i	$-0.390371\pi$
$613$	−9161.47	−	9161.47i	−0.603635	−	0.603635i	−0.941275	+	0.337640i	$0.890371\pi$
$614$	7707.45	+	9012.33i	0.506592	+	0.592359i
$615$		−	8148.87i		−	0.534299i
$616$	−10036.7	−	16306.7i	−0.656480	−	1.06658i
$617$		−	7849.67i		−	0.512181i	−0.966653	−	0.256091i	$-0.917565\pi$
$617$		−	7849.67i		−	0.512181i	0.966653	−	0.256091i	$-0.0824346\pi$
$618$	−749.721	+	641.170i	−0.0487997	+	0.0417340i
$619$	19459.4	+	19459.4i	1.26355	+	1.26355i	0.949360	+	0.314190i	$0.101733\pi$
$619$	19459.4	+	19459.4i	1.26355	+	1.26355i	0.314190	+	0.949360i	$0.398267\pi$
$620$	17154.0	+	23545.7i	1.11116	+	1.52519i
$621$	−3568.00	+	3568.00i	−0.230562	+	0.230562i
$622$	9878.22	+	770.941i	0.636785	+	0.0496976i
$623$	−11005.9			−0.707771
$624$	1877.18	−	5829.14i	0.120428	−	0.373962i
$625$	18932.0			1.21165
$626$	−337.509	−	26.3407i	−0.0215488	−	0.00168177i
$627$	517.202	−	517.202i	0.0329427	−	0.0329427i
$628$	14757.5	−	10751.4i	0.937720	−	0.683167i
$629$	9974.28	+	9974.28i	0.632274	+	0.632274i
$630$	−9249.09	+	7909.92i	−0.584909	+	0.500221i
$631$			27115.0i			1.71067i	0.518078	+	0.855334i	$0.326648\pi$
$631$			27115.0i			1.71067i	−0.518078	+	0.855334i	$0.673352\pi$
$632$	5492.54	−	23077.2i	0.345699	−	1.45247i
$633$		−	2935.83i		−	0.184343i
$634$	−4663.24	−	5452.74i	−0.292115	−	0.341571i
$635$	−23667.1	−	23667.1i	−1.47906	−	1.47906i
$636$	−4515.32	−	709.110i	−0.281516	−	0.0442108i
$637$	−16582.8	+	16582.8i	−1.03145	+	1.03145i
$638$	949.098	−	12161.0i	0.0588952	−	0.754636i
$639$	−169.347			−0.0104840
$640$	20479.1	−	5015.74i	1.26486	−	0.309789i
$641$	−22843.0			−1.40755			−0.703777	−	0.710421i	$-0.748505\pi$
$641$	−22843.0			−1.40755			−0.703777	+	0.710421i	$0.748505\pi$
$642$	308.951	−	3958.66i	0.0189927	−	0.243358i
$643$	10235.4	−	10235.4i	0.627754	−	0.627754i	−0.319749	−	0.947502i	$-0.603598\pi$
$643$	10235.4	−	10235.4i	0.627754	−	0.627754i	0.947502	+	0.319749i	$0.103598\pi$
$644$	−48499.5	−	7616.63i	−2.96762	−	0.466052i
$645$	477.533	+	477.533i	0.0291517	+	0.0291517i
$646$	−872.106	−	1019.76i	−0.0531154	−	0.0621080i
$647$		−	3376.19i		−	0.205149i	−0.994725	−	0.102575i	$-0.967292\pi$
$647$		−	3376.19i		−	0.205149i	0.994725	−	0.102575i	$-0.0327080\pi$
$648$	−424.370	+	1783.01i	−0.0257266	+	0.108092i
$649$		−	8052.30i		−	0.487027i
$650$	−5963.36	+	5099.93i	−0.359850	+	0.307747i
$651$	−17422.1	−	17422.1i	−1.04889	−	1.04889i
$652$	−23614.0	+	17203.8i	−1.41840	+	1.03336i
$653$	2226.27	−	2226.27i	0.133416	−	0.133416i	−0.637245	−	0.770661i	$-0.719926\pi$
$653$	2226.27	−	2226.27i	0.133416	−	0.133416i	0.770661	+	0.637245i	$0.219926\pi$
$654$	6080.06	+	474.515i	0.363531	+	0.0283716i
$655$	−18867.8			−1.12554
$656$	3660.03	−	11365.4i	0.217835	−	0.676437i
$657$	−7458.14			−0.442877
$658$	−2142.15	−	167.183i	−0.126914	−	0.00990497i
$659$	18279.8	−	18279.8i	1.08055	−	1.08055i	0.0840908	−	0.996458i	$-0.473201\pi$
$659$	18279.8	−	18279.8i	1.08055	−	1.08055i	0.996458	−	0.0840908i	$-0.0267986\pi$
$660$	5302.50	+	7278.25i	0.312726	+	0.429251i
$661$	2202.71	+	2202.71i	0.129615	+	0.129615i	0.768938	−	0.639323i	$-0.220785\pi$
$661$	2202.71	+	2202.71i	0.129615	+	0.129615i	−0.639323	+	0.768938i	$0.720785\pi$
$662$	4702.29	−	4021.45i	0.276072	−	0.236100i
$663$		−	4798.10i		−	0.281060i
$664$	2908.58	+	4725.56i	0.169992	+	0.276186i
$665$		−	4523.12i		−	0.263758i
$666$	4654.16	+	5442.12i	0.270789	+	0.316634i
$667$	−22114.6	−	22114.6i	−1.28378	−	1.28378i
$668$	−2405.96	+	15320.2i	−0.139356	+	0.887358i
$669$	−4642.10	+	4642.10i	−0.268272	+	0.268272i
$670$	835.008	−	10699.1i	0.0481480	−	0.616930i
$671$	16540.4			0.951619
$672$	−16452.6	+	6877.91i	−0.944452	+	0.394823i
$673$	−9151.57			−0.524171			−0.262086	−	0.965045i	$-0.584410\pi$
$673$	−9151.57			−0.524171			−0.262086	+	0.965045i	$0.584410\pi$
$674$	−535.564	+	6862.29i	−0.0306070	+	0.392174i
$675$	1660.59	−	1660.59i	0.0946905	−	0.0946905i
$676$	1464.16	−	9323.13i	0.0833043	−	0.530447i
$677$	17555.1	+	17555.1i	0.996597	+	0.996597i	0.999994	−	0.00339762i	$-0.00108150\pi$
$677$	17555.1	+	17555.1i	0.996597	+	0.996597i	−0.00339762	+	0.999994i	$0.501081\pi$
$678$	−10738.3	−	12556.3i	−0.608263	−	0.711243i
$679$		−	22563.0i		−	1.27524i
$680$	14068.3	−	8659.06i	0.793377	−	0.488323i
$681$		−	12998.5i		−	0.731429i
$682$	−13854.9	+	11848.9i	−0.777906	+	0.665274i
$683$	−933.246	−	933.246i	−0.0522836	−	0.0522836i	0.680482	−	0.732765i	$-0.261771\pi$
$683$	−933.246	−	933.246i	−0.0522836	−	0.0522836i	−0.732765	+	0.680482i	$0.761771\pi$
$684$	−401.107	−	550.563i	−0.0224221	−	0.0307767i
$685$	8934.52	−	8934.52i	0.498351	−	0.498351i
$686$	36321.7	+	2834.71i	2.02153	+	0.157769i
$687$	15503.4			0.860979
$688$	451.542	+	880.506i	0.0250216	+	0.0487921i
$689$	6074.31			0.335868
$690$	23018.1	+	1796.44i	1.26998	+	0.0991147i
$691$	−14135.0	+	14135.0i	−0.778175	+	0.778175i	−0.979520	−	0.201345i	$-0.935469\pi$
$691$	−14135.0	+	14135.0i	−0.778175	+	0.778175i	0.201345	+	0.979520i	$0.435469\pi$
$692$	18695.2	−	13620.2i	1.02700	−	0.748213i
$693$	−5385.35	−	5385.35i	−0.295199	−	0.295199i
$694$	−3561.27	+	3045.64i	−0.194790	+	0.166586i
$695$		−	4970.35i		−	0.271275i
$696$	−11051.2	−	2630.26i	−0.601860	−	0.143247i
$697$		−	9355.10i		−	0.508393i
$698$	19945.9	+	23322.8i	1.08161	+	1.26473i
$699$	8787.35	+	8787.35i	0.475491	+	0.475491i
$700$	22572.3	+	3544.87i	1.21879	+	0.191405i
$701$	−22882.9	+	22882.9i	−1.23292	+	1.23292i	−0.270077	+	0.962839i	$0.587049\pi$
$701$	−22882.9	+	22882.9i	−1.23292	+	1.23292i	−0.962839	+	0.270077i	$0.912951\pi$
$702$	189.523	−	2428.40i	0.0101896	−	0.130561i
$703$	−2661.38			−0.142782
$704$	4126.49	+	12532.7i	0.220913	+	0.670942i
$705$	1010.48			0.0539815
$706$	449.166	−	5755.25i	0.0239442	−	0.306802i
$707$	−1695.71	+	1695.71i	−0.0902031	+	0.0902031i
$708$	−7408.26	−	1163.43i	−0.393248	−	0.0617578i
$709$	−5612.43	−	5612.43i	−0.297291	−	0.297291i	0.542661	−	0.839952i	$-0.317417\pi$
$709$	−5612.43	−	5612.43i	−0.297291	−	0.297291i	−0.839952	+	0.542661i	$0.817417\pi$
$710$	503.619	+	588.882i	0.0266204	+	0.0311273i
$711$		−	9435.30i		−	0.497681i
$712$	7377.89	+	1755.99i	0.388340	+	0.0924278i
$713$			46742.0i			2.45512i
$714$	−10618.2	+	9080.79i	−0.556548	+	0.475966i
$715$	−8462.24	−	8462.24i	−0.442615	−	0.442615i
$716$	6182.69	−	4504.34i	0.322707	−	0.235105i
$717$	6536.41	−	6536.41i	0.340455	−	0.340455i
$718$	−13036.5	−	1017.43i	−0.677604	−	0.0528833i
$719$	−29244.9			−1.51690			−0.758450	−	0.651732i	$-0.774043\pi$
$719$	−29244.9			−1.51690			−0.758450	+	0.651732i	$0.774043\pi$
$720$	7462.25	−	3826.80i	0.386252	−	0.198078i
$721$	−3817.62			−0.197192
$722$	−19089.0	−	1489.79i	−0.983958	−	0.0767925i
$723$	−11304.3	+	11304.3i	−0.581484	+	0.581484i
$724$	−8651.44	−	11875.0i	−0.444100	−	0.609575i
$725$	10292.4	+	10292.4i	0.527241	+	0.527241i
$726$	4300.46	−	3677.80i	0.219841	−	0.188011i
$727$			3308.71i			0.168794i	0.996432	+	0.0843971i	$0.0268964\pi$
$727$			3308.71i			0.168794i	−0.996432	+	0.0843971i	$0.973104\pi$
$728$	20182.3	−	12422.2i	1.02748	−	0.632413i
$729$			729.000i			0.0370370i
$730$	22179.7	+	25934.8i	1.12453	+	1.31492i
$731$	548.220	+	548.220i	0.0277382	+	0.0277382i
$732$	2389.84	−	15217.5i	0.120671	−	0.768380i
$733$	25116.9	−	25116.9i	1.26564	−	1.26564i	0.317323	−	0.948318i	$-0.397216\pi$
$733$	25116.9	−	25116.9i	1.26564	−	1.26564i	0.948318	−	0.317323i	$-0.102784\pi$
$734$	−2393.59	+	30669.6i	−0.120367	+	1.54228i
$735$	−32115.2			−1.61168
$736$	31296.9	+	12844.0i	1.56742	+	0.643255i
$737$	6715.84			0.335660
$738$	369.523	−	4734.77i	0.0184313	−	0.236164i
$739$	−17503.6	+	17503.6i	−0.871286	+	0.871286i	−0.992613	−	0.121327i	$-0.961285\pi$
$739$	−17503.6	+	17503.6i	−0.871286	+	0.871286i	0.121327	+	0.992613i	$0.461285\pi$
$740$	5083.34	−	32368.6i	0.252523	−	1.60796i
$741$	640.126	+	640.126i	0.0317350	+	0.0317350i
$742$	−11496.1	−	13442.4i	−0.568781	−	0.665077i
$743$			14568.9i			0.719356i	0.933077	+	0.359678i	$0.117113\pi$
$743$			14568.9i			0.719356i	−0.933077	+	0.359678i	$0.882887\pi$
$744$	8899.35	+	14458.7i	0.438530	+	0.712477i
$745$		−	35686.6i		−	1.75498i
$746$	1887.86	−	1614.52i	0.0926535	−	0.0792383i
$747$	1560.64	+	1560.64i	0.0764402	+	0.0764402i
$748$	6087.40	+	8355.61i	0.297563	+	0.408437i
$749$	10865.4	−	10865.4i	0.530060	−	0.530060i
$750$	4682.95	+	365.479i	0.227996	+	0.0177939i
$751$	10015.9			0.486665			0.243333	−	0.969943i	$-0.421759\pi$
$751$	10015.9			0.486665			0.243333	+	0.969943i	$0.421759\pi$
$752$	1409.34	+	453.853i	0.0683420	+	0.0220084i
$753$	1530.99			0.0740934
$754$	15051.3	+	1174.67i	0.726971	+	0.0567361i
$755$	−17707.5	+	17707.5i	−0.853565	+	0.853565i
$756$	−5732.72	+	4176.52i	−0.275790	+	0.200924i
$757$	1632.84	+	1632.84i	0.0783971	+	0.0783971i	0.745218	−	0.666821i	$-0.232345\pi$
$757$	1632.84	+	1632.84i	0.0783971	+	0.0783971i	−0.666821	+	0.745218i	$0.732345\pi$
$758$	−26273.7	+	22469.6i	−1.25898	+	1.07669i
$759$			14448.5i			0.690970i
$760$	−721.665	+	3032.11i	−0.0344441	+	0.144719i
$761$		−	5379.15i		−	0.256234i	−0.991759	−	0.128117i	$-0.959107\pi$
$761$		−	5379.15i		−	0.256234i	0.991759	−	0.128117i	$-0.0408933\pi$
$762$	−12678.2	−	14824.6i	−0.602732	−	0.704776i
$763$	16688.1	+	16688.1i	0.791809	+	0.791809i
$764$	−18101.5	−	2842.76i	−0.857186	−	0.134617i
$765$	4646.14	−	4646.14i	0.219584	−	0.219584i
$766$	793.980	−	10173.4i	0.0374513	−	0.479871i
$767$	9966.11			0.469172
$768$	12126.5	−	1985.66i	0.569762	−	0.0932961i
$769$	1737.59			0.0814812			0.0407406	−	0.999170i	$-0.487028\pi$
$769$	1737.59			0.0814812			0.0407406	+	0.999170i	$0.487028\pi$
$770$	−2711.45	+	34742.4i	−0.126901	+	1.62601i
$771$	−10244.1	+	10244.1i	−0.478514	+	0.478514i
$772$	−1017.63	−	159.814i	−0.0474420	−	0.00745056i
$773$	−2551.94	−	2551.94i	−0.118741	−	0.118741i	0.645239	−	0.763980i	$-0.276758\pi$
$773$	−2551.94	−	2551.94i	−0.118741	−	0.118741i	−0.763980	+	0.645239i	$0.776758\pi$
$774$	255.809	+	299.118i	0.0118797	+	0.0138909i
$775$		−	21754.3i		−	1.00831i
$776$	−3599.93	+	15125.3i	−0.166533	+	0.699699i
$777$			27711.6i			1.27947i
$778$	−10449.8	+	8936.80i	−0.481548	+	0.411825i
$779$	1248.09	+	1248.09i	0.0574035	+	0.0574035i
$780$	−9008.08	+	6562.75i	−0.413514	+	0.301262i
$781$	−342.881	+	342.881i	−0.0157097	+	0.0157097i
$782$	26425.3	+	2062.35i	1.20840	+	0.0943090i
$783$	−4518.37			−0.206224
$784$	−44791.5	−	14424.4i	−2.04043	−	0.657087i
$785$	−33229.5			−1.51084
$786$	−10962.8	−	855.588i	−0.497495	−	0.0388267i
$787$	−12908.2	+	12908.2i	−0.584658	+	0.584658i	−0.936180	−	0.351522i	$-0.885664\pi$
$787$	−12908.2	+	12908.2i	−0.584658	+	0.584658i	0.351522	+	0.936180i	$0.385664\pi$
$788$	−4834.40	−	6635.73i	−0.218551	−	0.299985i
$789$	−6257.24	−	6257.24i	−0.282337	−	0.282337i
$790$	−32810.1	+	28059.6i	−1.47763	+	1.26369i
$791$		−	63937.5i		−	2.87403i
$792$	2750.89	+	4469.36i	0.123420	+	0.200520i
$793$			20471.6i			0.916732i
$794$	4105.84	+	4800.96i	0.183515	+	0.214584i
$795$	5881.93	+	5881.93i	0.262403	+	0.262403i
$796$	3450.04	−	21968.4i	0.153622	−	0.978202i
$797$	7292.39	−	7292.39i	0.324102	−	0.324102i	−0.526236	−	0.850339i	$-0.676397\pi$
$797$	7292.39	−	7292.39i	0.324102	−	0.324102i	0.850339	+	0.526236i	$0.176397\pi$
$798$	205.108	−	2628.08i	0.00909866	−	0.116583i
$799$	1160.06			0.0513641
$800$	−14565.9	−	5977.75i	−0.643730	−	0.264182i
$801$	3016.51			0.133063
$802$	−509.860	+	6532.94i	−0.0224486	+	0.287639i
$803$	−15100.7	+	15100.7i	−0.663628	+	0.663628i
$804$	970.336	−	6178.69i	0.0425636	−	0.271027i
$805$	63178.5	+	63178.5i	2.76615	+	2.76615i
$806$	−14665.0	−	17147.8i	−0.640884	−	0.749388i
$807$			9600.59i			0.418781i
$808$	1407.28	−	866.182i	0.0612723	−	0.0377131i
$809$		−	13623.8i		−	0.592073i	−0.955177	−	0.296036i	$-0.904335\pi$
$809$		−	13623.8i		−	0.592073i	0.955177	−	0.296036i	$-0.0956650\pi$
$810$	2535.01	−	2167.97i	0.109964	−	0.0940427i
$811$	6432.57	+	6432.57i	0.278518	+	0.278518i	0.832517	−	0.553999i	$-0.186899\pi$
$811$	6432.57	+	6432.57i	0.278518	+	0.278518i	−0.553999	+	0.832517i	$0.686899\pi$
$812$	−25886.2	−	35531.6i	−1.11875	−	1.53561i
$813$	2822.01	−	2822.01i	0.121737	−	0.121737i
$814$	20442.3	+	1595.41i	0.880222	+	0.0686965i
$815$	53171.7			2.28531
$816$	8566.84	−	4393.25i	0.367524	−	0.188474i
$817$	−146.279			−0.00626394
$818$	1886.97	+	147.268i	0.0806556	+	0.00629473i
$819$	6665.30	−	6665.30i	0.284377	−	0.284377i
$820$	−17563.5	+	12795.7i	−0.747980	+	0.544934i
$821$	−10383.1	−	10383.1i	−0.441380	−	0.441380i	0.451096	−	0.892475i	$-0.351033\pi$
$821$	−10383.1	−	10383.1i	−0.441380	−	0.441380i	−0.892475	+	0.451096i	$0.851033\pi$
$822$	5596.41	−	4786.11i	0.237466	−	0.203084i
$823$		−	13572.9i		−	0.574876i	−0.957799	−	0.287438i	$-0.907196\pi$
$823$		−	13572.9i		−	0.574876i	0.957799	−	0.287438i	$-0.0928035\pi$
$824$	2559.18	+	609.102i	0.108196	+	0.0257513i
$825$		−	6724.49i		−	0.283778i
$826$	−18861.6	−	22054.9i	−0.794528	−	0.929043i
$827$	14405.3	+	14405.3i	0.605708	+	0.605708i	0.941821	−	0.336114i	$-0.109113\pi$
$827$	14405.3	+	14405.3i	0.605708	+	0.605708i	−0.336114	+	0.941821i	$0.609113\pi$
$828$	13292.8	+	2087.58i	0.557920	+	0.0876189i
$829$	30030.7	−	30030.7i	1.25815	−	1.25815i	0.306177	−	0.951975i	$-0.400950\pi$
$829$	30030.7	−	30030.7i	1.25815	−	1.25815i	0.951975	−	0.306177i	$-0.0990500\pi$
$830$	785.760	−	10068.1i	0.0328604	−	0.421047i
$831$	−13688.7			−0.571428
$832$	−15511.3	+	5107.24i	−0.646345	+	0.212814i
$833$	−36869.0			−1.53353
$834$	225.388	−	2887.94i	0.00935797	−	0.119906i
$835$	19957.0	−	19957.0i	0.827114	−	0.827114i
$836$	−1926.87	−	302.607i	−0.0797157	−	0.0125190i
$837$	4775.07	+	4775.07i	0.197193	+	0.197193i
$838$	−9505.96	−	11115.3i	−0.391859	−	0.458202i
$839$			5825.32i			0.239705i	0.992792	+	0.119852i	$0.0382421\pi$
$839$			5825.32i			0.239705i	−0.992792	+	0.119852i	$0.961758\pi$
$840$	31571.8	+	7514.32i	1.29682	+	0.308653i
$841$		−	3616.01i		−	0.148264i
$842$	2547.05	−	2178.27i	0.104249	−	0.0891545i
$843$	−13515.8	−	13515.8i	−0.552206	−	0.552206i
$844$	−6327.69	+	4609.98i	−0.258066	+	0.188012i
$845$	−12144.9	+	12144.9i	−0.494434	+	0.494434i
$846$	587.124	+	45.8218i	0.0238602	+	0.00186216i
$847$	21898.2			0.888346
$848$	5561.78	+	10845.5i	0.225227	+	0.439192i
$849$	10346.3			0.418237
$850$	−12298.7	−	959.844i	−0.496284	−	0.0387322i
$851$	37173.9	−	37173.9i	1.49742	−	1.49742i
$852$	265.916	+	364.998i	0.0106926	+	0.0146768i
$853$	16206.3	+	16206.3i	0.650521	+	0.650521i	0.953118	−	0.302598i	$-0.0978539\pi$
$853$	16206.3	+	16206.3i	0.650521	+	0.650521i	−0.302598	+	0.953118i	$0.597854\pi$
$854$	45303.6	−	38744.1i	1.81529	−	1.55245i
$855$			1239.70i			0.0495871i
$856$	−9017.34	+	5550.17i	−0.360054	+	0.221613i
$857$			2342.64i			0.0933759i	0.998910	+	0.0466879i	$0.0148666\pi$
$857$			2342.64i			0.0933759i	−0.998910	+	0.0466879i	$0.985133\pi$
$858$	−4533.12	−	5300.58i	−0.180371	−	0.210908i
$859$	−12182.8	−	12182.8i	−0.483904	−	0.483904i	0.422472	−	0.906376i	$-0.361162\pi$
$859$	−12182.8	−	12182.8i	−0.483904	−	0.483904i	−0.906376	+	0.422472i	$0.861162\pi$
$860$	279.398	−	1779.09i	0.0110783	−	0.0705422i
$861$	12995.7	−	12995.7i	0.514391	−	0.514391i
$862$	1472.34	−	18865.4i	0.0581764	−	0.745426i
$863$	−29827.9			−1.17654			−0.588269	−	0.808665i	$-0.700190\pi$
$863$	−29827.9			−1.17654			−0.588269	+	0.808665i	$0.700190\pi$
$864$	4509.35	−	1885.11i	0.177559	−	0.0742278i
$865$	−42096.1			−1.65469
$866$	1724.71	−	22099.1i	0.0676768	−	0.867157i
$867$	−5088.16	+	5088.16i	−0.199312	+	0.199312i
$868$	−10193.4	+	64907.2i	−0.398602	+	2.53813i
$869$	−19103.9	−	19103.9i	−0.745750	−	0.745750i
$870$	13437.1	+	15712.1i	0.523634	+	0.612286i
$871$			8312.00i			0.323354i
$872$	−8524.44	−	13849.6i	−0.331048	−	0.537853i
$873$			6184.10i			0.239748i
$874$	−3800.61	+	3250.32i	−0.147091	+	0.125794i
$875$	12853.4	+	12853.4i	0.496601	+	0.496601i
$876$	11711.1	+	16074.8i	0.451691	+	0.619995i
$877$	−26406.8	+	26406.8i	−1.01675	+	1.01675i	−0.0168967	+	0.999857i	$0.505379\pi$
$877$	−26406.8	+	26406.8i	−1.01675	+	1.01675i	−0.999857	+	0.0168967i	$0.994621\pi$
$878$	−17034.9	−	1329.48i	−0.654783	−	0.0511023i
$879$	29363.0			1.12672
$880$	7360.80	−	22857.3i	0.281969	−	0.875589i
$881$	30799.2			1.17781			0.588906	−	0.808202i	$-0.299559\pi$
$881$	30799.2			1.17781			0.588906	+	0.808202i	$0.299559\pi$
$882$	−18660.0	−	1456.31i	−0.712375	−	0.0555969i
$883$	31934.4	−	31934.4i	1.21708	−	1.21708i	0.248424	−	0.968651i	$-0.420087\pi$
$883$	31934.4	−	31934.4i	1.21708	−	1.21708i	0.968651	−	0.248424i	$-0.0799125\pi$
$884$	−10341.5	+	7534.20i	−0.393464	+	0.286654i
$885$	9650.46	+	9650.46i	0.366550	+	0.366550i
$886$	25175.6	−	21530.5i	0.954618	−	0.816399i
$887$			8071.18i			0.305528i	0.988263	+	0.152764i	$0.0488175\pi$
$887$			8071.18i			0.305528i	−0.988263	+	0.152764i	$0.951183\pi$
$888$	4421.39	−	18576.7i	0.167086	−	0.702020i
$889$		−	75487.8i		−	2.84790i
$890$	−8970.77	−	10489.5i	−0.337866	−	0.395068i
$891$	1476.03	+	1476.03i	0.0554981	+	0.0554981i
$892$	17294.5	+	2716.02i	0.649173	+	0.101950i
$893$	−154.766	+	154.766i	−0.00579960	+	0.00579960i
$894$	1618.26	−	20735.2i	0.0605401	−	0.775713i
$895$	−13921.6			−0.519941
$896$	40658.7	+	24660.7i	1.51597	+	0.919482i
$897$	−17882.4			−0.665638
$898$	−3411.74	+	43715.3i	−0.126783	+	1.62450i
$899$	−29596.1	+	29596.1i	−1.09798	+	1.09798i
$900$	−6186.65	−	971.585i	−0.229135	−	0.0359846i
$901$	6752.60	+	6752.60i	0.249680	+	0.249680i
$902$	−8838.44	−	10334.8i	−0.326262	−	0.381498i
$903$			1523.12i			0.0561311i
$904$	−10201.2	+	42861.1i	−0.375319	+	1.57692i
$905$			26739.1i			0.982140i
$906$	−11091.6	+	9485.68i	−0.406727	+	0.347837i
$907$	5166.14	+	5166.14i	0.189128	+	0.189128i	0.795319	−	0.606191i	$-0.207303\pi$
$907$	5166.14	+	5166.14i	0.189128	+	0.189128i	−0.606191	+	0.795319i	$0.707303\pi$
$908$	−28016.0	+	20410.8i	−1.02395	+	0.745987i
$909$	464.762	−	464.762i	0.0169584	−	0.0169584i
$910$	−42999.6	−	3355.88i	−1.56640	−	0.122249i
$911$	31180.6			1.13398			0.566992	−	0.823723i	$-0.308107\pi$
$911$	31180.6			1.13398			0.566992	+	0.823723i	$0.308107\pi$
$912$	−556.808	+	1729.04i	−0.0202168	+	0.0627786i
$913$	6319.74			0.229083
$914$	13721.6	+	1070.89i	0.496575	+	0.0387550i
$915$	−19823.2	+	19823.2i	−0.716214	+	0.716214i
$916$	−24344.2	−	33415.0i	−0.878115	−	1.20531i
$917$	−30090.0	−	30090.0i	−1.08360	−	1.08360i
$918$	2910.25	−	2488.88i	0.104632	−	0.0894828i
$919$			27889.6i			1.00108i	0.865713	+	0.500541i	$0.166866\pi$
$919$			27889.6i			1.00108i	−0.865713	+	0.500541i	$0.833134\pi$
$920$	−32272.1	−	52432.4i	−1.15650	−	1.87896i
$921$		−	12578.0i		−	0.450009i
$922$	19367.9	+	22646.9i	0.691808	+	0.808933i
$923$	−424.374	−	424.374i	−0.0151337	−	0.0151337i
$924$	−3150.89	+	20063.5i	−0.112183	+	0.714331i
$925$	−17301.2	+	17301.2i	−0.614984	+	0.614984i
$926$	−1523.92	+	19526.2i	−0.0540810	+	0.692951i
$927$	1046.34			0.0370726
$928$	11684.0	+	27949.1i	0.413303	+	0.988658i
$929$	17906.3			0.632385			0.316192	−	0.948695i	$-0.397595\pi$
$929$	17906.3			0.632385			0.316192	+	0.948695i	$0.397595\pi$
$930$	2404.18	−	30805.3i	0.0847701	−	1.08618i
$931$	4918.78	−	4918.78i	0.173154	−	0.173154i
$932$	5141.34	−	32737.9i	0.180698	−	1.15061i
$933$	−7431.19	−	7431.19i	−0.260757	−	0.260757i
$934$	10503.2	+	12281.4i	0.367961	+	0.430258i
$935$		−	18814.4i		−	0.658070i
$936$	−5531.60	+	3404.69i	−0.193169	+	0.118895i
$937$			10815.1i			0.377070i	0.982067	+	0.188535i	$0.0603738\pi$
$937$			10815.1i			0.377070i	−0.982067	+	0.188535i	$0.939626\pi$
$938$	18394.4	−	15731.1i	0.640297	−	0.547589i
$939$	253.901	+	253.901i	0.00882402	+	0.00882402i
$940$	−1586.70	−	2177.92i	−0.0550559	−	0.0755702i
$941$	−29716.3	+	29716.3i	−1.02946	+	1.02946i	−0.0299093	+	0.999553i	$0.509522\pi$
$941$	−29716.3	+	29716.3i	−1.02946	+	1.02946i	−0.999553	+	0.0299093i	$0.990478\pi$
$942$	−19307.5	−	1506.84i	−0.667804	−	0.0521184i
$943$	−34866.3			−1.20403
$944$	9125.20	+	17794.1i	0.314619	+	0.613506i
$945$	12908.4			0.444349
$946$	1123.58	+	87.6889i	0.0386158	+	0.00301375i
$947$	−15362.1	+	15362.1i	−0.527138	+	0.527138i	−0.919718	−	0.392580i	$-0.871583\pi$
$947$	−15362.1	+	15362.1i	−0.527138	+	0.527138i	0.392580	+	0.919718i	$0.371583\pi$
$948$	−20336.2	+	14815.7i	−0.696718	+	0.507587i
$949$	−18689.7	−	18689.7i	−0.639299	−	0.639299i
$950$	1768.85	−	1512.74i	0.0604095	−	0.0516629i
$951$			7610.05i			0.259488i
$952$	36245.2	+	8626.62i	1.23394	+	0.293688i
$953$			24261.6i			0.824671i	0.911032	+	0.412336i	$0.135287\pi$
$953$			24261.6i			0.824671i	−0.911032	+	0.412336i	$0.864713\pi$
$954$	3150.88	+	3684.33i	0.106932	+	0.125036i
$955$	23580.2	+	23580.2i	0.798991	+	0.798991i
$956$	−24351.9	−	3824.35i	−0.823845	−	0.129381i
$957$	−9148.47	+	9148.47i	−0.309016	+	0.309016i
$958$	2191.40	−	28078.9i	0.0739049	−	0.946959i
$959$	28497.2			0.959565
$960$	−19965.6	−	10074.6i	−0.671235	−	0.338704i
$961$	32764.1			1.09980
$962$	−1974.59	+	25300.8i	−0.0661780	+	0.847952i
$963$	−2978.02	+	2978.02i	−0.0996525	+	0.0996525i
$964$	42115.2	+	6614.00i	1.40709	+	0.220978i
$965$	1325.63	+	1325.63i	0.0442211	+	0.0442211i
$966$	33843.9	+	39573.8i	1.12724	+	1.31808i
$967$		−	6229.01i		−	0.207147i	−0.994622	−	0.103574i	$-0.966972\pi$
$967$		−	6229.01i		−	0.207147i	0.994622	−	0.103574i	$-0.0330277\pi$
$968$	−14679.6	−	3493.86i	−0.487419	−	0.116009i
$969$			1423.21i			0.0471828i
$970$	21504.4	−	18390.8i	0.711820	−	0.608757i
$971$	−1224.70	−	1224.70i	−0.0404762	−	0.0404762i	0.686579	−	0.727055i	$-0.259112\pi$
$971$	−1224.70	−	1224.70i	−0.0404762	−	0.0404762i	−0.727055	+	0.686579i	$0.759112\pi$
$972$	1571.23	−	1144.71i	0.0518492	−	0.0377742i
$973$	7926.62	−	7926.62i	0.261167	−	0.261167i
$974$	−21633.6	−	1688.39i	−0.711690	−	0.0555435i
$975$	8322.70			0.273374
$976$	−36551.3	+	18744.3i	−1.19875	+	0.614744i
$977$	−35749.1			−1.17064			−0.585320	−	0.810802i	$-0.699031\pi$
$977$	−35749.1			−1.17064			−0.585320	+	0.810802i	$0.699031\pi$
$978$	30894.6	+	2411.15i	1.01012	+	0.0788345i
$979$	6107.62	−	6107.62i	0.199387	−	0.199387i
$980$	50428.6	+	69218.7i	1.64376	+	2.25624i
$981$	−4573.91	−	4573.91i	−0.148862	−	0.148862i
$982$	41932.8	−	35861.4i	1.36266	−	1.16536i
$983$		−	53895.9i		−	1.74874i	−0.485259	−	0.874371i	$-0.661275\pi$
$983$		−	53895.9i		−	1.74874i	0.485259	−	0.874371i	$-0.338725\pi$
$984$	−10785.2	+	6638.30i	−0.349411	+	0.215062i
$985$			14941.7i			0.483332i
$986$	15426.2	+	18037.8i	0.498244	+	0.582598i
$987$	1611.50	+	1611.50i	0.0519701	+	0.0519701i
$988$	374.528	−	2384.84i	0.0120600	−	0.0767933i
$989$	2043.21	−	2043.21i	0.0656928	−	0.0656928i
$990$	743.159	−	9522.25i	0.0238577	−	0.305694i
$991$	−9898.33			−0.317286			−0.158643	−	0.987336i	$-0.550712\pi$
$991$	−9898.33			−0.317286			−0.158643	+	0.987336i	$0.550712\pi$
$992$	17189.2	−	41884.8i	0.550159	−	1.34057i
$993$	−6562.70			−0.209729
$994$	−135.977	+	1742.30i	−0.00433896	+	0.0555960i
$995$	−28617.4	+	28617.4i	−0.911791	+	0.911791i
$996$	913.106	−	5814.28i	0.0290491	−	0.184972i
$997$	−37538.1	−	37538.1i	−1.19242	−	1.19242i	−0.976386	−	0.216034i	$-0.930688\pi$
$997$	−37538.1	−	37538.1i	−1.19242	−	1.19242i	−0.216034	−	0.976386i	$-0.569312\pi$
$998$	5558.37	+	6499.41i	0.176300	+	0.206147i
$999$		−	7595.24i		−	0.240543i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.4.j.a.37.7	yes	24
3.2	odd	2		144.4.k.b.37.6		24
4.3	odd	2		192.4.j.a.49.5		24
8.3	odd	2		384.4.j.a.97.11		24
8.5	even	2		384.4.j.b.97.2		24
12.11	even	2		576.4.k.b.433.3		24
16.3	odd	4		192.4.j.a.145.5		24
16.5	even	4		384.4.j.b.289.2		24
16.11	odd	4		384.4.j.a.289.11		24
16.13	even	4	inner	48.4.j.a.13.7	✓	24
48.29	odd	4		144.4.k.b.109.6		24
48.35	even	4		576.4.k.b.145.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.j.a.13.7	✓	24	16.13	even	4	inner
48.4.j.a.37.7	yes	24	1.1	even	1	trivial
144.4.k.b.37.6		24	3.2	odd	2
144.4.k.b.109.6		24	48.29	odd	4
192.4.j.a.49.5		24	4.3	odd	2
192.4.j.a.145.5		24	16.3	odd	4
384.4.j.a.97.11		24	8.3	odd	2
384.4.j.a.289.11		24	16.11	odd	4
384.4.j.b.97.2		24	8.5	even	2
384.4.j.b.289.2		24	16.5	even	4
576.4.k.b.145.3		24	48.35	even	4
576.4.k.b.433.3		24	12.11	even	2

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	48.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.220074 + 2.81985i) q^{2} +(2.12132 - 2.12132i) q^{3} +(-7.90313 - 1.24115i) q^{4} +(10.2951 + 10.2951i) q^{5} +(5.51496 + 6.44866i) q^{6} +32.8369i q^{7} +(5.23914 - 22.0125i) q^{8} -9.00000i q^{9} +O(q^{10})\)	\(q+(-0.220074 + 2.81985i) q^{2} +(2.12132 - 2.12132i) q^{3} +(-7.90313 - 1.24115i) q^{4} +(10.2951 + 10.2951i) q^{5} +(5.51496 + 6.44866i) q^{6} +32.8369i q^{7} +(5.23914 - 22.0125i) q^{8} -9.00000i q^{9} +(-31.2964 + 26.7650i) q^{10} +(-18.2226 - 18.2226i) q^{11} +(-19.3980 + 14.1322i) q^{12} +(22.5535 - 22.5535i) q^{13} +(-92.5952 - 7.22655i) q^{14} +43.6785 q^{15} +(60.9191 + 19.6180i) q^{16} +50.1440 q^{17} +(25.3787 + 1.98067i) q^{18} +(-6.68982 + 6.68982i) q^{19} +(-68.5859 - 94.1415i) q^{20} +(69.6576 + 69.6576i) q^{21} +(55.3953 - 47.3746i) q^{22} -186.886i q^{23} +(-35.5817 - 57.8095i) q^{24} +86.9788i q^{25} +(58.6342 + 68.5611i) q^{26} +(-19.0919 - 19.0919i) q^{27} +(40.7556 - 259.515i) q^{28} +(118.332 - 118.332i) q^{29} +(-9.61250 + 123.167i) q^{30} -250.110 q^{31} +(-68.7265 + 167.465i) q^{32} -77.3118 q^{33} +(-11.0354 + 141.399i) q^{34} +(-338.060 + 338.060i) q^{35} +(-11.1704 + 71.1282i) q^{36} +(198.913 + 198.913i) q^{37} +(-17.3921 - 20.3366i) q^{38} -95.6866i q^{39} +(280.559 - 172.684i) q^{40} -186.565i q^{41} +(-211.754 + 181.094i) q^{42} +(10.9329 + 10.9329i) q^{43} +(121.398 + 166.632i) q^{44} +(92.6560 - 92.6560i) q^{45} +(526.990 + 41.1287i) q^{46} +23.1346 q^{47} +(170.845 - 87.6129i) q^{48} -735.263 q^{49} +(-245.267 - 19.1418i) q^{50} +(106.371 - 106.371i) q^{51} +(-206.236 + 150.251i) q^{52} +(134.664 + 134.664i) q^{53} +(58.0379 - 49.6347i) q^{54} -375.207i q^{55} +(722.823 + 172.037i) q^{56} +28.3825i q^{57} +(307.637 + 359.721i) q^{58} +(220.943 + 220.943i) q^{59} +(-345.197 - 54.2116i) q^{60} +(-453.845 + 453.845i) q^{61} +(55.0427 - 705.274i) q^{62} +295.532 q^{63} +(-457.103 - 230.653i) q^{64} +464.383 q^{65} +(17.0143 - 218.008i) q^{66} +(-184.273 + 184.273i) q^{67} +(-396.294 - 62.2363i) q^{68} +(-396.444 - 396.444i) q^{69} +(-878.880 - 1027.68i) q^{70} -18.8163i q^{71} +(-198.113 - 47.1523i) q^{72} -828.683i q^{73} +(-604.680 + 517.129i) q^{74} +(184.510 + 184.510i) q^{75} +(61.1736 - 44.5675i) q^{76} +(598.373 - 598.373i) q^{77} +(269.822 + 21.0581i) q^{78} +1048.37 q^{79} +(425.200 + 829.138i) q^{80} -81.0000 q^{81} +(526.085 + 41.0581i) q^{82} +(-173.404 + 173.404i) q^{83} +(-464.058 - 636.969i) q^{84} +(516.238 + 516.238i) q^{85} +(-33.2353 + 28.4232i) q^{86} -502.041i q^{87} +(-496.595 + 305.654i) q^{88} +335.168i q^{89} +(240.885 + 281.668i) q^{90} +(740.589 + 740.589i) q^{91} +(-231.953 + 1476.98i) q^{92} +(-530.564 + 530.564i) q^{93} +(-5.09131 + 65.2360i) q^{94} -137.745 q^{95} +(209.457 + 501.039i) q^{96} -687.122 q^{97} +(161.812 - 2073.33i) q^{98} +(-164.003 + 164.003i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{4} + 84 q^{8}+O(q^{10}) \) 24 * q - 20 * q^4 + 84 * q^8	\( 24 q - 20 q^{4} + 84 q^{8} + 72 q^{10} - 40 q^{11} - 24 q^{12} - 348 q^{14} + 120 q^{15} - 192 q^{16} - 36 q^{18} + 24 q^{19} + 80 q^{20} + 704 q^{22} + 228 q^{24} - 20 q^{26} - 344 q^{28} + 400 q^{29} - 408 q^{30} - 744 q^{31} - 960 q^{32} - 704 q^{34} - 456 q^{35} + 108 q^{36} + 16 q^{37} + 1256 q^{38} + 1744 q^{40} + 660 q^{42} + 1240 q^{43} - 200 q^{44} - 1432 q^{46} - 528 q^{48} - 1176 q^{49} + 708 q^{50} + 744 q^{51} + 1008 q^{52} + 752 q^{53} + 108 q^{54} + 1344 q^{56} + 1936 q^{58} - 1376 q^{59} - 1224 q^{60} - 912 q^{61} - 996 q^{62} - 504 q^{63} - 56 q^{64} + 976 q^{65} - 1368 q^{66} - 2256 q^{67} - 1568 q^{68} - 528 q^{69} - 1760 q^{70} - 612 q^{72} - 2740 q^{74} + 1104 q^{75} - 1880 q^{76} + 1904 q^{77} + 1692 q^{78} + 5992 q^{79} + 712 q^{80} - 1944 q^{81} - 40 q^{82} + 2680 q^{83} + 1800 q^{84} - 240 q^{85} - 1712 q^{86} - 3936 q^{88} + 648 q^{90} - 3496 q^{91} + 5296 q^{92} + 5272 q^{94} - 7728 q^{95} + 2880 q^{96} + 6760 q^{98} - 360 q^{99}+O(q^{100}) \) 24 * q - 20 * q^4 + 84 * q^8 + 72 * q^10 - 40 * q^11 - 24 * q^12 - 348 * q^14 + 120 * q^15 - 192 * q^16 - 36 * q^18 + 24 * q^19 + 80 * q^20 + 704 * q^22 + 228 * q^24 - 20 * q^26 - 344 * q^28 + 400 * q^29 - 408 * q^30 - 744 * q^31 - 960 * q^32 - 704 * q^34 - 456 * q^35 + 108 * q^36 + 16 * q^37 + 1256 * q^38 + 1744 * q^40 + 660 * q^42 + 1240 * q^43 - 200 * q^44 - 1432 * q^46 - 528 * q^48 - 1176 * q^49 + 708 * q^50 + 744 * q^51 + 1008 * q^52 + 752 * q^53 + 108 * q^54 + 1344 * q^56 + 1936 * q^58 - 1376 * q^59 - 1224 * q^60 - 912 * q^61 - 996 * q^62 - 504 * q^63 - 56 * q^64 + 976 * q^65 - 1368 * q^66 - 2256 * q^67 - 1568 * q^68 - 528 * q^69 - 1760 * q^70 - 612 * q^72 - 2740 * q^74 + 1104 * q^75 - 1880 * q^76 + 1904 * q^77 + 1692 * q^78 + 5992 * q^79 + 712 * q^80 - 1944 * q^81 - 40 * q^82 + 2680 * q^83 + 1800 * q^84 - 240 * q^85 - 1712 * q^86 - 3936 * q^88 + 648 * q^90 - 3496 * q^91 + 5296 * q^92 + 5272 * q^94 - 7728 * q^95 + 2880 * q^96 + 6760 * q^98 - 360 * q^99

Introduction

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