LMFDB - Embedded newform 240.4.bc.a.43.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,4,Mod(43,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0, 3]))

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

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

chi := DirichletCharacter("240.43");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	240.bc (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:	$14.1604584014$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.20
Character	$\chi$	$=$	240.43
Dual form			240.4.bc.a.67.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.265755 + 2.81591i) q^{2} +3.00000i q^{3} +(-7.85875 + 1.49669i) q^{4} +(10.7738 + 2.98740i) q^{5} +(-8.44774 + 0.797266i) q^{6} +(6.90177 - 6.90177i) q^{7} +(-6.30305 - 21.7318i) q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+(0.265755 + 2.81591i) q^{2} +3.00000i q^{3} +(-7.85875 + 1.49669i) q^{4} +(10.7738 + 2.98740i) q^{5} +(-8.44774 + 0.797266i) q^{6} +(6.90177 - 6.90177i) q^{7} +(-6.30305 - 21.7318i) q^{8} -9.00000 q^{9} +(-5.54906 + 31.1321i) q^{10} +(-36.9924 + 36.9924i) q^{11} +(-4.49007 - 23.5762i) q^{12} -55.4185 q^{13} +(21.2690 + 17.6006i) q^{14} +(-8.96220 + 32.3215i) q^{15} +(59.5198 - 23.5242i) q^{16} +(-90.6558 + 90.6558i) q^{17} +(-2.39180 - 25.3432i) q^{18} +(-4.99032 + 4.99032i) q^{19} +(-89.1400 - 7.35217i) q^{20} +(20.7053 + 20.7053i) q^{21} +(-113.998 - 94.3365i) q^{22} +(14.0067 + 14.0067i) q^{23} +(65.1954 - 18.9092i) q^{24} +(107.151 + 64.3715i) q^{25} +(-14.7278 - 156.054i) q^{26} -27.0000i q^{27} +(-43.9094 + 64.5690i) q^{28} +(-87.8631 - 87.8631i) q^{29} +(-93.3963 - 16.6472i) q^{30} -259.764i q^{31} +(82.0598 + 161.351i) q^{32} +(-110.977 - 110.977i) q^{33} +(-279.371 - 231.187i) q^{34} +(94.9768 - 53.7401i) q^{35} +(70.7287 - 13.4702i) q^{36} -28.1377 q^{37} +(-15.3785 - 12.7261i) q^{38} -166.255i q^{39} +(-2.98637 - 252.965i) q^{40} +347.706i q^{41} +(-52.8018 + 63.8069i) q^{42} -170.628 q^{43} +(235.348 - 346.080i) q^{44} +(-96.9645 - 26.8866i) q^{45} +(-35.7193 + 43.1641i) q^{46} +(362.891 + 362.891i) q^{47} +(70.5726 + 178.560i) q^{48} +247.731i q^{49} +(-152.789 + 318.835i) q^{50} +(-271.967 - 271.967i) q^{51} +(435.520 - 82.9442i) q^{52} -563.247i q^{53} +(76.0297 - 7.17539i) q^{54} +(-509.061 + 288.039i) q^{55} +(-193.490 - 106.486i) q^{56} +(-14.9710 - 14.9710i) q^{57} +(224.065 - 270.765i) q^{58} +(-53.2609 - 53.2609i) q^{59} +(22.0565 - 267.420i) q^{60} +(-206.514 + 206.514i) q^{61} +(731.473 - 69.0337i) q^{62} +(-62.1159 + 62.1159i) q^{63} +(-432.543 + 273.953i) q^{64} +(-597.070 - 165.557i) q^{65} +(283.010 - 341.995i) q^{66} +987.531 q^{67} +(576.757 - 848.124i) q^{68} +(-42.0201 + 42.0201i) q^{69} +(176.568 + 253.165i) q^{70} +811.980 q^{71} +(56.7275 + 195.586i) q^{72} +(-380.571 + 380.571i) q^{73} +(-7.47775 - 79.2334i) q^{74} +(-193.115 + 321.453i) q^{75} +(31.7487 - 46.6867i) q^{76} +510.626i q^{77} +(468.161 - 44.1833i) q^{78} -930.985 q^{79} +(711.533 - 75.6361i) q^{80} +81.0000 q^{81} +(-979.110 + 92.4047i) q^{82} +465.665i q^{83} +(-193.707 - 131.728i) q^{84} +(-1247.54 + 705.885i) q^{85} +(-45.3452 - 480.473i) q^{86} +(263.589 - 263.589i) q^{87} +(1037.08 + 570.747i) q^{88} -235.233 q^{89} +(49.9416 - 280.189i) q^{90} +(-382.486 + 382.486i) q^{91} +(-131.039 - 89.1115i) q^{92} +779.292 q^{93} +(-925.429 + 1118.31i) q^{94} +(-68.6730 + 38.8568i) q^{95} +(-484.053 + 246.180i) q^{96} +(-601.313 + 601.313i) q^{97} +(-697.590 + 65.8359i) q^{98} +(332.932 - 332.932i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{2} - 10 q^{4} - 80 q^{8} - 648 q^{9}+O(q^{10}) $ 72 * q - 2 * q^2 - 10 * q^4 - 80 * q^8 - 648 * q^9	$ 72 q - 2 q^{2} - 10 q^{4} - 80 q^{8} - 648 q^{9} + 12 q^{12} - 110 q^{14} - 22 q^{16} - 124 q^{17} + 18 q^{18} + 12 q^{19} + 100 q^{20} - 238 q^{22} - 88 q^{23} + 126 q^{24} - 184 q^{25} + 12 q^{26} + 102 q^{28} - 282 q^{30} + 468 q^{32} - 186 q^{34} + 228 q^{35} + 90 q^{36} + 238 q^{38} - 882 q^{40} + 18 q^{42} - 432 q^{43} + 1770 q^{44} + 1106 q^{46} + 896 q^{47} - 432 q^{48} + 274 q^{50} - 372 q^{51} - 1272 q^{52} + 688 q^{55} + 622 q^{56} + 36 q^{57} - 246 q^{58} - 688 q^{59} - 570 q^{60} + 2552 q^{61} + 836 q^{62} - 634 q^{64} + 340 q^{65} + 750 q^{66} - 1848 q^{67} + 478 q^{68} + 264 q^{69} + 2458 q^{70} + 224 q^{71} + 720 q^{72} + 296 q^{73} + 1040 q^{74} - 552 q^{75} - 3766 q^{76} - 516 q^{78} + 928 q^{79} + 872 q^{80} + 5832 q^{81} - 472 q^{82} + 270 q^{84} - 3424 q^{85} - 1844 q^{86} + 2334 q^{88} - 1968 q^{89} - 848 q^{91} + 818 q^{92} - 792 q^{93} - 310 q^{94} - 1240 q^{95} - 510 q^{96} - 1176 q^{97} + 2812 q^{98}+O(q^{100}) $ 72 * q - 2 * q^2 - 10 * q^4 - 80 * q^8 - 648 * q^9 + 12 * q^12 - 110 * q^14 - 22 * q^16 - 124 * q^17 + 18 * q^18 + 12 * q^19 + 100 * q^20 - 238 * q^22 - 88 * q^23 + 126 * q^24 - 184 * q^25 + 12 * q^26 + 102 * q^28 - 282 * q^30 + 468 * q^32 - 186 * q^34 + 228 * q^35 + 90 * q^36 + 238 * q^38 - 882 * q^40 + 18 * q^42 - 432 * q^43 + 1770 * q^44 + 1106 * q^46 + 896 * q^47 - 432 * q^48 + 274 * q^50 - 372 * q^51 - 1272 * q^52 + 688 * q^55 + 622 * q^56 + 36 * q^57 - 246 * q^58 - 688 * q^59 - 570 * q^60 + 2552 * q^61 + 836 * q^62 - 634 * q^64 + 340 * q^65 + 750 * q^66 - 1848 * q^67 + 478 * q^68 + 264 * q^69 + 2458 * q^70 + 224 * q^71 + 720 * q^72 + 296 * q^73 + 1040 * q^74 - 552 * q^75 - 3766 * q^76 - 516 * q^78 + 928 * q^79 + 872 * q^80 + 5832 * q^81 - 472 * q^82 + 270 * q^84 - 3424 * q^85 - 1844 * q^86 + 2334 * q^88 - 1968 * q^89 - 848 * q^91 + 818 * q^92 - 792 * q^93 - 310 * q^94 - 1240 * q^95 - 510 * q^96 - 1176 * q^97 + 2812 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.265755	+	2.81591i	0.0939587	+	0.995576i
$2$	0.265755	+	2.81591i	0.0939587	+	0.995576i
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	−7.85875	+	1.49669i	−0.982344	+	0.187086i
$5$	10.7738	+	2.98740i	0.963641	+	0.267201i
$5$	10.7738	+	2.98740i	0.963641	+	0.267201i
$6$	−8.44774	+	0.797266i	−0.574796	+	0.0542471i
$7$	6.90177	−	6.90177i	0.372660	−	0.372660i	−0.495785	−	0.868445i	$-0.665120\pi$
$7$	6.90177	−	6.90177i	0.372660	−	0.372660i	0.868445	+	0.495785i	$0.165120\pi$
$8$	−6.30305	−	21.7318i	−0.278558	−	0.960419i
$9$	−9.00000			−0.333333
$10$	−5.54906	+	31.1321i	−0.175477	+	0.984484i
$11$	−36.9924	+	36.9924i	−1.01397	+	1.01397i	−0.0140654	+	0.999901i	$0.504477\pi$
$11$	−36.9924	+	36.9924i	−1.01397	+	1.01397i	−0.999901	+	0.0140654i	$0.995523\pi$
$12$	−4.49007	−	23.5762i	−0.108014	−	0.567156i
$13$	−55.4185			−1.18233			−0.591166	−	0.806550i	$-0.701332\pi$
$13$	−55.4185			−1.18233			−0.591166	+	0.806550i	$0.701332\pi$
$14$	21.2690	+	17.6006i	0.406026	+	0.335997i
$15$	−8.96220	+	32.3215i	−0.154269	+	0.556358i
$16$	59.5198	−	23.5242i	0.929998	−	0.367566i
$17$	−90.6558	+	90.6558i	−1.29337	+	1.29337i	−0.360677	+	0.932691i	$0.617454\pi$
$17$	−90.6558	+	90.6558i	−1.29337	+	1.29337i	−0.932691	+	0.360677i	$0.882546\pi$
$18$	−2.39180	−	25.3432i	−0.0313196	−	0.331859i
$19$	−4.99032	+	4.99032i	−0.0602557	+	0.0602557i	−0.736593	−	0.676337i	$-0.763566\pi$
$19$	−4.99032	+	4.99032i	−0.0602557	+	0.0602557i	0.676337	+	0.736593i	$0.263566\pi$
$20$	−89.1400	−	7.35217i	−0.996616	−	0.0821997i
$21$	20.7053	+	20.7053i	0.215156	+	0.215156i
$22$	−113.998	−	94.3365i	−1.10475	−	0.914210i
$23$	14.0067	+	14.0067i	0.126983	+	0.126983i	0.767742	−	0.640759i	$-0.221380\pi$
$23$	14.0067	+	14.0067i	0.126983	+	0.126983i	−0.640759	+	0.767742i	$0.721380\pi$
$24$	65.1954	−	18.9092i	0.554498	−	0.160826i
$25$	107.151	+	64.3715i	0.857207	+	0.514972i
$26$	−14.7278	−	156.054i	−0.111090	−	1.17710i
$27$		−	27.0000i		−	0.192450i
$28$	−43.9094	+	64.5690i	−0.296361	+	0.435800i
$29$	−87.8631	−	87.8631i	−0.562613	−	0.562613i	0.367436	−	0.930049i	$-0.380236\pi$
$29$	−87.8631	−	87.8631i	−0.562613	−	0.562613i	−0.930049	+	0.367436i	$0.880236\pi$
$30$	−93.3963	−	16.6472i	−0.568392	−	0.101312i
$31$		−	259.764i		−	1.50500i	−0.658593	−	0.752500i	$-0.728848\pi$
$31$		−	259.764i		−	1.50500i	0.658593	−	0.752500i	$-0.271152\pi$
$32$	82.0598	+	161.351i	0.453321	+	0.891347i
$33$	−110.977	−	110.977i	−0.585414	−	0.585414i
$34$	−279.371	−	231.187i	−1.40917	−	1.16612i
$35$	94.9768	−	53.7401i	0.458686	−	0.259535i
$36$	70.7287	−	13.4702i	0.327448	−	0.0623620i
$37$	−28.1377			−0.125022			−0.0625110	−	0.998044i	$-0.519911\pi$
$37$	−28.1377			−0.125022			−0.0625110	+	0.998044i	$0.519911\pi$
$38$	−15.3785	−	12.7261i	−0.0656507	−	0.0543276i
$39$		−	166.255i		−	0.682620i
$40$	−2.98637	−	252.965i	−0.0118047	−	0.999930i
$41$			347.706i			1.32445i	0.749304	+	0.662226i	$0.230388\pi$
$41$			347.706i			1.32445i	−0.749304	+	0.662226i	$0.769612\pi$
$42$	−52.8018	+	63.8069i	−0.193988	+	0.234419i
$43$	−170.628			−0.605128			−0.302564	−	0.953129i	$-0.597843\pi$
$43$	−170.628			−0.605128			−0.302564	+	0.953129i	$0.597843\pi$
$44$	235.348	−	346.080i	0.806364	−	1.18576i
$45$	−96.9645	−	26.8866i	−0.321214	−	0.0890671i
$46$	−35.7193	+	43.1641i	−0.114490	+	0.138352i
$47$	362.891	+	362.891i	1.12623	+	1.12623i	0.990784	+	0.135451i	$0.0432482\pi$
$47$	362.891	+	362.891i	1.12623	+	1.12623i	0.135451	+	0.990784i	$0.456752\pi$
$48$	70.5726	+	178.560i	0.212214	+	0.536934i
$49$			247.731i			0.722249i
$50$	−152.789	+	318.835i	−0.432152	+	0.901801i
$51$	−271.967	−	271.967i	−0.746726	−	0.746726i
$52$	435.520	−	82.9442i	1.16146	−	0.221198i
$53$		−	563.247i		−	1.45977i	−0.683569	−	0.729886i	$-0.739573\pi$
$53$		−	563.247i		−	1.45977i	0.683569	−	0.729886i	$-0.260427\pi$
$54$	76.0297	−	7.17539i	0.191599	−	0.0180824i
$55$	−509.061	+	288.039i	−1.24803	+	0.706166i
$56$	−193.490	−	106.486i	−0.461718	−	0.254103i
$57$	−14.9710	−	14.9710i	−0.0347887	−	0.0347887i
$58$	224.065	−	270.765i	0.507261	−	0.612986i
$59$	−53.2609	−	53.2609i	−0.117525	−	0.117525i	0.645898	−	0.763423i	$-0.276483\pi$
$59$	−53.2609	−	53.2609i	−0.117525	−	0.117525i	−0.763423	+	0.645898i	$0.776483\pi$
$60$	22.0565	−	267.420i	0.0474580	−	0.575396i
$61$	−206.514	+	206.514i	−0.433466	+	0.433466i	−0.889806	−	0.456340i	$-0.849160\pi$
$61$	−206.514	+	206.514i	−0.433466	+	0.433466i	0.456340	+	0.889806i	$0.349160\pi$
$62$	731.473	−	69.0337i	1.49834	−	0.141408i
$63$	−62.1159	+	62.1159i	−0.124220	+	0.124220i
$64$	−432.543	+	273.953i	−0.844811	+	0.535065i
$65$	−597.070	−	165.557i	−1.13934	−	0.315921i
$66$	283.010	−	341.995i	0.527819	−	0.637829i
$67$	987.531			1.80069			0.900344	−	0.435178i	$-0.143315\pi$
$67$	987.531			1.80069			0.900344	+	0.435178i	$0.143315\pi$
$68$	576.757	−	848.124i	1.02856	−	1.51250i
$69$	−42.0201	+	42.0201i	−0.0733135	+	0.0733135i
$70$	176.568	+	253.165i	0.301485	+	0.432271i
$71$	811.980			1.35724			0.678621	−	0.734488i	$-0.262578\pi$
$71$	811.980			1.35724			0.678621	+	0.734488i	$0.262578\pi$
$72$	56.7275	+	195.586i	0.0928527	+	0.320140i
$73$	−380.571	+	380.571i	−0.610170	+	0.610170i	−0.942990	−	0.332820i	$-0.892000\pi$
$73$	−380.571	+	380.571i	−0.610170	+	0.610170i	0.332820	+	0.942990i	$0.392000\pi$
$74$	−7.47775	−	79.2334i	−0.0117469	−	0.124469i
$75$	−193.115	+	321.453i	−0.297319	+	0.494909i
$76$	31.7487	−	46.6867i	0.0479188	−	0.0704648i
$77$			510.626i			0.755730i
$78$	468.161	−	44.1833i	0.679600	−	0.0641381i
$79$	−930.985			−1.32587			−0.662936	−	0.748676i	$-0.730690\pi$
$79$	−930.985			−1.32587			−0.662936	+	0.748676i	$0.730690\pi$
$80$	711.533	−	75.6361i	0.994398	−	0.105705i
$81$	81.0000			0.111111
$82$	−979.110	+	92.4047i	−1.31859	+	0.124444i
$83$			465.665i			0.615824i	0.951415	+	0.307912i	$0.0996302\pi$
$83$			465.665i			0.615824i	−0.951415	+	0.307912i	$0.900370\pi$
$84$	−193.707	−	131.728i	−0.251609	−	0.171104i
$85$	−1247.54	+	705.885i	−1.59193	+	0.900752i
$86$	−45.3452	−	480.473i	−0.0568570	−	0.602451i
$87$	263.589	−	263.589i	0.324825	−	0.324825i
$88$	1037.08	+	570.747i	1.25628	+	0.691384i
$89$	−235.233			−0.280165			−0.140082	−	0.990140i	$-0.544737\pi$
$89$	−235.233			−0.280165			−0.140082	+	0.990140i	$0.544737\pi$
$90$	49.9416	−	280.189i	0.0584923	−	0.328161i
$91$	−382.486	+	382.486i	−0.440609	+	0.440609i
$92$	−131.039	−	89.1115i	−0.148497	−	0.100984i
$93$	779.292			0.868912
$94$	−925.429	+	1118.31i	−1.01543	+	1.22707i
$95$	−68.6730	+	38.8568i	−0.0741653	+	0.0419645i
$96$	−484.053	+	246.180i	−0.514620	+	0.261725i
$97$	−601.313	+	601.313i	−0.629424	+	0.629424i	−0.947923	−	0.318499i	$-0.896821\pi$
$97$	−601.313	+	601.313i	−0.629424	+	0.629424i	0.318499	+	0.947923i	$0.396821\pi$
$98$	−697.590	+	65.8359i	−0.719053	+	0.0678615i
$99$	332.932	−	332.932i	0.337989	−	0.337989i
$100$	−938.416	−	345.508i	−0.938416	−	0.345508i
$101$	375.367	+	375.367i	0.369806	+	0.369806i	0.867406	−	0.497600i	$-0.165785\pi$
$101$	375.367	+	375.367i	0.369806	+	0.369806i	−0.497600	+	0.867406i	$0.665785\pi$
$102$	693.560	−	838.113i	0.673261	−	0.813584i
$103$	170.381	+	170.381i	0.162992	+	0.162992i	0.783891	−	0.620899i	$-0.213232\pi$
$103$	170.381	+	170.381i	0.162992	+	0.162992i	−0.620899	+	0.783891i	$0.713232\pi$
$104$	349.306	+	1204.34i	0.329348	+	1.13554i
$105$	161.220	+	284.930i	0.149843	+	0.264822i
$106$	1586.06	−	149.686i	1.45331	−	0.137158i
$107$		−	920.536i		−	0.831697i	−0.909434	−	0.415849i	$-0.863485\pi$
$107$		−	920.536i		−	0.831697i	0.909434	−	0.415849i	$-0.136515\pi$
$108$	40.4106	+	212.186i	0.0360047	+	0.189052i
$109$	241.373	+	241.373i	0.212104	+	0.212104i	0.805161	−	0.593057i	$-0.202079\pi$
$109$	241.373	+	241.373i	0.212104	+	0.212104i	−0.593057	+	0.805161i	$0.702079\pi$
$110$	−946.378	−	1356.92i	−0.820306	−	1.17616i
$111$		−	84.4132i		−	0.0721815i
$112$	248.434	−	573.151i	0.209596	−	0.483550i
$113$	890.386	+	890.386i	0.741243	+	0.741243i	0.972817	−	0.231574i	$-0.0743875\pi$
$113$	890.386	+	890.386i	0.741243	+	0.741243i	−0.231574	+	0.972817i	$0.574387\pi$
$114$	38.1784	−	46.1356i	0.0313661	−	0.0379035i
$115$	109.062	+	192.750i	0.0884357	+	0.156296i
$116$	821.997	+	558.990i	0.657936	+	0.447422i
$117$	498.766			0.394111
$118$	135.824	−	164.132i	0.105963	−	0.128048i
$119$			1251.37i			0.963974i
$120$	758.894	−	8.95912i	0.577310	−	0.00681543i
$121$		−	1405.88i		−	1.05626i
$122$	−636.408	−	526.644i	−0.472276	−	0.390820i
$123$	−1043.12			−0.764673
$124$	388.786	+	2041.42i	0.281564	+	1.47843i
$125$	962.122	+	1013.63i	0.688438	+	0.725295i
$126$	−191.421	−	158.405i	−0.135342	−	0.111999i
$127$	890.247	+	890.247i	0.622021	+	0.622021i	0.946048	−	0.324027i	$-0.105037\pi$
$127$	890.247	+	890.247i	0.622021	+	0.622021i	−0.324027	+	0.946048i	$0.605037\pi$
$128$	−886.380	−	1145.20i	−0.612076	−	0.790799i
$129$		−	511.883i		−	0.349371i
$130$	307.521	−	1725.29i	0.207472	−	1.16399i
$131$	−435.352	−	435.352i	−0.290358	−	0.290358i	0.546864	−	0.837222i	$-0.315822\pi$
$131$	−435.352	−	435.352i	−0.290358	−	0.290358i	−0.837222	+	0.546864i	$0.815822\pi$
$132$	1038.24	+	706.044i	0.684600	+	0.465555i
$133$			68.8841i			0.0449098i
$134$	262.442	+	2780.80i	0.169190	+	1.79272i
$135$	80.6598	−	290.893i	0.0514229	−	0.185453i
$136$	2541.52	+	1398.71i	1.60245	+	0.881897i
$137$	1745.15	+	1745.15i	1.08831	+	1.08831i	0.995703	+	0.0926074i	$0.0295202\pi$
$137$	1745.15	+	1745.15i	1.08831	+	1.08831i	0.0926074	+	0.995703i	$0.470480\pi$
$138$	−129.492	−	107.158i	−0.0798776	−	0.0661007i
$139$	−2047.72	−	2047.72i	−1.24954	−	1.24954i	−0.955924	−	0.293613i	$-0.905142\pi$
$139$	−2047.72	−	2047.72i	−1.24954	−	1.24954i	−0.293613	−	0.955924i	$-0.594858\pi$
$140$	−665.967	+	564.481i	−0.402032	+	0.340767i
$141$	−1088.67	+	1088.67i	−0.650232	+	0.650232i
$142$	215.788	+	2286.47i	0.127525	+	1.35124i
$143$	2050.06	−	2050.06i	1.19885	−	1.19885i
$144$	−535.679	+	211.718i	−0.309999	+	0.122522i
$145$	−684.140	−	1209.10i	−0.391826	−	0.692487i
$146$	−1172.79	−	970.516i	−0.664802	−	0.550140i
$147$	−743.194			−0.416990
$148$	221.127	−	42.1134i	0.122815	−	0.0233899i
$149$	−2116.26	+	2116.26i	−1.16356	+	1.16356i	−0.179872	+	0.983690i	$0.557568\pi$
$149$	−2116.26	+	2116.26i	−1.16356	+	1.16356i	−0.983690	+	0.179872i	$0.942432\pi$
$150$	−956.504	−	458.366i	−0.520655	−	0.249503i
$151$	1755.27			0.945970			0.472985	−	0.881070i	$-0.343176\pi$
$151$	1755.27			0.945970			0.472985	+	0.881070i	$0.343176\pi$
$152$	139.903	+	76.9945i	0.0746555	+	0.0410860i
$153$	815.902	−	815.902i	0.431123	−	0.431123i
$154$	−1437.88	+	135.702i	−0.752387	+	0.0710074i
$155$	776.019	−	2798.65i	0.402138	−	1.45028i
$156$	248.833	+	1306.56i	0.127709	+	0.670567i
$157$			2595.49i			1.31938i	0.751537	+	0.659690i	$0.229313\pi$
$157$			2595.49i			1.31938i	−0.751537	+	0.659690i	$0.770687\pi$
$158$	−247.414	−	2621.57i	−0.124577	−	1.32001i
$159$	1689.74			0.842800
$160$	402.078	+	1983.52i	0.198669	+	0.980067i
$161$	193.342			0.0946428
$162$	21.5262	+	228.089i	0.0104399	+	0.110620i
$163$			2067.72i			0.993599i	0.867865	+	0.496799i	$0.165492\pi$
$163$			2067.72i			0.993599i	−0.867865	+	0.496799i	$0.834508\pi$
$164$	−520.407	−	2732.53i	−0.247786	−	1.30107i
$165$	−864.116	−	1527.18i	−0.407705	−	0.720552i
$166$	−1311.27	+	123.753i	−0.613099	+	0.0578620i
$167$	2308.94	−	2308.94i	1.06988	−	1.06988i	0.0725179	−	0.997367i	$-0.476897\pi$
$167$	2308.94	−	2308.94i	1.06988	−	1.06988i	0.997367	−	0.0725179i	$-0.0231034\pi$
$168$	319.457	−	580.470i	0.146706	−	0.266573i
$169$	874.210			0.397911
$170$	−2319.25	−	3325.36i	−1.04634	−	1.50026i
$171$	44.9129	−	44.9129i	0.0200852	−	0.0200852i
$172$	1340.92	−	255.377i	0.594443	−	0.113211i
$173$	922.419			0.405377			0.202688	−	0.979243i	$-0.435032\pi$
$173$	922.419			0.405377			0.202688	+	0.979243i	$0.435032\pi$
$174$	812.295	+	672.194i	0.353908	+	0.292867i
$175$	1183.81	−	295.253i	0.511357	−	0.127537i
$176$	−1331.57	+	3072.00i	−0.570287	+	1.31569i
$177$	159.783	−	159.783i	0.0678531	−	0.0678531i
$178$	−62.5144	−	662.396i	−0.0263239	−	0.278925i
$179$	−750.775	+	750.775i	−0.313495	+	0.313495i	−0.846262	−	0.532767i	$-0.821152\pi$
$179$	−750.775	+	750.775i	−0.313495	+	0.313495i	0.532767	+	0.846262i	$0.321152\pi$
$180$	802.260	+	66.1695i	0.332205	+	0.0273999i
$181$	−1292.61	−	1292.61i	−0.530821	−	0.530821i	0.389996	−	0.920817i	$-0.372477\pi$
$181$	−1292.61	−	1292.61i	−0.530821	−	0.530821i	−0.920817	+	0.389996i	$0.872477\pi$
$182$	−1178.69	−	975.399i	−0.480058	−	0.397260i
$183$	−619.542	−	619.542i	−0.250262	−	0.250262i
$184$	216.106	−	392.676i	0.0865846	−	0.157329i
$185$	−303.151	−	84.0587i	−0.120476	−	0.0334060i
$186$	207.101	+	2194.42i	0.0816418	+	0.865068i
$187$		−	6707.15i		−	2.62286i
$188$	−3395.00	−	2308.73i	−1.31705	−	0.895647i
$189$	−186.348	−	186.348i	−0.0717185	−	0.0717185i
$190$	−127.668	−	183.051i	−0.0487473	−	0.0698943i
$191$			1261.89i			0.478048i	0.971014	+	0.239024i	$0.0768275\pi$
$191$			1261.89i			0.478048i	−0.971014	+	0.239024i	$0.923172\pi$
$192$	−821.860	−	1297.63i	−0.308920	−	0.487752i
$193$	−2005.47	−	2005.47i	−0.747963	−	0.747963i	0.226134	−	0.974096i	$-0.427391\pi$
$193$	−2005.47	−	2005.47i	−0.747963	−	0.747963i	−0.974096	+	0.226134i	$0.927391\pi$
$194$	−1853.05	−	1533.44i	−0.685779	−	0.567499i
$195$	496.672	−	1791.21i	0.182397	−	0.657801i
$196$	−370.777	−	1946.86i	−0.135123	−	0.709496i
$197$	−2471.99			−0.894019			−0.447009	−	0.894529i	$-0.647511\pi$
$197$	−2471.99			−0.894019			−0.447009	+	0.894529i	$0.647511\pi$
$198$	1025.99	+	849.029i	0.368251	+	0.304737i
$199$		−	1008.32i		−	0.359184i	−0.983741	−	0.179592i	$-0.942522\pi$
$199$		−	1008.32i		−	0.359184i	0.983741	−	0.179592i	$-0.0574778\pi$
$200$	723.532	−	2734.32i	0.255807	−	0.966728i
$201$			2962.59i			1.03963i
$202$	−957.246	+	1156.76i	−0.333424	+	0.402917i
$203$	−1212.82			−0.419327
$204$	2544.37	+	1730.27i	0.873244	+	0.593840i
$205$	−1038.74	+	3746.12i	−0.353895	+	1.27630i
$206$	−434.500	+	525.059i	−0.146956	+	0.177586i
$207$	−126.060	−	126.060i	−0.0423276	−	0.0423276i
$208$	−3298.50	+	1303.68i	−1.09957	+	0.434585i
$209$		−	369.208i		−	0.122195i
$210$	−759.494	+	529.704i	−0.249572	+	0.174062i
$211$	504.088	+	504.088i	0.164469	+	0.164469i	0.784543	−	0.620074i	$-0.212898\pi$
$211$	504.088	+	504.088i	0.164469	+	0.164469i	−0.620074	+	0.784543i	$0.712898\pi$
$212$	843.006	+	4426.42i	0.273103	+	1.43400i
$213$			2435.94i			0.783605i
$214$	2592.15	−	244.637i	0.828018	−	0.0781452i
$215$	−1838.32	−	509.734i	−0.583126	−	0.161691i
$216$	−586.759	+	170.182i	−0.184833	+	0.0536085i
$217$	−1792.83	−	1792.83i	−0.560854	−	0.560854i
$218$	−615.539	+	743.831i	−0.191236	+	0.231094i
$219$	−1141.71	−	1141.71i	−0.352282	−	0.352282i
$220$	3569.48	−	3025.53i	1.09388	−	0.927187i
$221$	5024.01	−	5024.01i	1.52919	−	1.52919i
$222$	237.700	−	22.4332i	0.0718621	−	0.00678208i
$223$	1993.49	−	1993.49i	0.598629	−	0.598629i	−0.341319	−	0.939948i	$-0.610874\pi$
$223$	1993.49	−	1993.49i	0.598629	−	0.598629i	0.939948	+	0.341319i	$0.110874\pi$
$224$	1679.97	+	547.250i	0.501105	+	0.163235i
$225$	−964.358	−	579.344i	−0.285736	−	0.171657i
$226$	−2270.63	+	2743.88i	−0.668318	+	0.807611i
$227$	420.947			0.123080			0.0615402	−	0.998105i	$-0.480399\pi$
$227$	420.947			0.123080			0.0615402	+	0.998105i	$0.480399\pi$
$228$	140.060	+	95.2462i	0.0406829	+	0.0276659i
$229$	−808.259	+	808.259i	−0.233237	+	0.233237i	−0.814042	−	0.580805i	$-0.802738\pi$
$229$	−808.259	+	808.259i	−0.233237	+	0.233237i	0.580805	+	0.814042i	$0.302738\pi$
$230$	−513.783	+	358.334i	−0.147295	+	0.102730i
$231$	−1531.88			−0.436321
$232$	−1355.62	+	2463.23i	−0.383624	+	0.697064i
$233$	2508.53	−	2508.53i	0.705318	−	0.705318i	−0.260229	−	0.965547i	$-0.583798\pi$
$233$	2508.53	−	2508.53i	0.705318	−	0.705318i	0.965547	+	0.260229i	$0.0837981\pi$
$234$	132.550	+	1404.48i	0.0370302	+	0.392367i
$235$	2825.62	+	4993.82i	0.784354	+	1.38622i
$236$	498.279	+	338.849i	0.137437	+	0.0934627i
$237$		−	2792.95i		−	0.765493i
$238$	−3523.75	+	332.558i	−0.959709	+	0.0905737i
$239$	−707.840			−0.191575			−0.0957874	−	0.995402i	$-0.530537\pi$
$239$	−707.840			−0.191575			−0.0957874	+	0.995402i	$0.530537\pi$
$240$	226.908	+	2134.60i	0.0610286	+	0.574116i
$241$	530.479			0.141789			0.0708945	−	0.997484i	$-0.477415\pi$
$241$	530.479			0.141789			0.0708945	+	0.997484i	$0.477415\pi$
$242$	3958.83	−	373.619i	1.05158	−	0.0992444i
$243$			243.000i			0.0641500i
$244$	1313.85	−	1932.03i	0.344717	−	0.506908i
$245$	−740.073	+	2669.01i	−0.192986	+	0.695988i
$246$	−277.214	−	2937.33i	−0.0718476	−	0.761290i
$247$	276.556	−	276.556i	0.0712423	−	0.0712423i
$248$	−5645.14	+	1637.31i	−1.44543	+	0.419230i
$249$	−1396.99			−0.355546
$250$	−2598.61	+	2978.63i	−0.657402	+	0.753540i
$251$	720.562	−	720.562i	0.181201	−	0.181201i	−0.610678	−	0.791879i	$-0.709103\pi$
$251$	720.562	−	720.562i	0.181201	−	0.181201i	0.791879	+	0.610678i	$0.209103\pi$
$252$	395.185	−	581.121i	0.0987870	−	0.145267i
$253$	−1036.28			−0.257512
$254$	−2270.27	+	2743.45i	−0.560825	+	0.677714i
$255$	−2117.65	−	3742.61i	−0.520050	−	0.919102i
$256$	2989.22	−	2800.31i	0.729791	−	0.683670i
$257$	3065.48	−	3065.48i	0.744044	−	0.744044i	−0.229309	−	0.973354i	$-0.573647\pi$
$257$	3065.48	−	3065.48i	0.744044	−	0.744044i	0.973354	+	0.229309i	$0.0736467\pi$
$258$	1441.42	−	136.036i	0.347825	−	0.0328264i
$259$	−194.200	+	194.200i	−0.0465907	+	0.0465907i
$260$	4940.01	+	407.446i	1.17833	+	0.0971874i
$261$	790.768	+	790.768i	0.187538	+	0.187538i
$262$	1110.22	−	1341.61i	0.261791	−	0.316355i
$263$	5531.76	+	5531.76i	1.29697	+	1.29697i	0.930385	+	0.366583i	$0.119472\pi$
$263$	5531.76	+	5531.76i	1.29697	+	1.29697i	0.366583	+	0.930385i	$0.380528\pi$
$264$	−1712.24	+	3111.23i	−0.399171	+	0.725315i
$265$	1682.65	−	6068.33i	0.390053	−	1.40670i
$266$	−193.972	+	18.3063i	−0.0447112	+	0.00421967i
$267$		−	705.699i		−	0.161753i
$268$	−7760.76	+	1478.03i	−1.76890	+	0.336884i
$269$	692.839	+	692.839i	0.157038	+	0.157038i	0.781253	−	0.624215i	$-0.214581\pi$
$269$	692.839	+	692.839i	0.157038	+	0.157038i	−0.624215	+	0.781253i	$0.714581\pi$
$270$	840.567	+	149.825i	0.189464	+	0.0337705i
$271$			1312.01i			0.294092i	0.989130	+	0.147046i	$0.0469766\pi$
$271$			1312.01i			0.294092i	−0.989130	+	0.147046i	$0.953023\pi$
$272$	−3263.21	+	7528.42i	−0.727432	+	1.67823i
$273$	−1147.46	−	1147.46i	−0.254385	−	0.254385i
$274$	−4450.42	+	5377.99i	−0.981239	+	1.18575i
$275$	−6345.03	+	1582.51i	−1.39134	+	0.347015i
$276$	267.335	−	393.117i	0.0583031	−	0.0857350i
$277$	−3244.20			−0.703701			−0.351851	−	0.936056i	$-0.614448\pi$
$277$	−3244.20			−0.703701			−0.351851	+	0.936056i	$0.614448\pi$
$278$	5222.02	−	6310.41i	1.12660	−	1.36141i
$279$			2337.88i			0.501667i
$280$	−1766.51	−	1725.29i	−0.377033	−	0.368235i
$281$			1163.60i			0.247028i	0.992343	+	0.123514i	$0.0394164\pi$
$281$			1163.60i			0.247028i	−0.992343	+	0.123514i	$0.960584\pi$
$282$	−3354.93	−	2776.29i	−0.708450	−	0.586260i
$283$	−2311.20			−0.485465			−0.242732	−	0.970093i	$-0.578044\pi$
$283$	−2311.20			−0.485465			−0.242732	+	0.970093i	$0.578044\pi$
$284$	−6381.14	+	1215.28i	−1.33328	+	0.253921i
$285$	−116.570	−	206.019i	−0.0242282	−	0.0428193i
$286$	6317.62	+	5227.99i	1.30618	+	1.08090i
$287$	2399.78	+	2399.78i	0.493571	+	0.493571i
$288$	−738.539	−	1452.16i	−0.151107	−	0.297116i
$289$		−	11523.9i		−	2.34560i
$290$	3222.92	−	2247.80i	0.652608	−	0.455157i
$291$	−1803.94	−	1803.94i	−0.363398	−	0.363398i
$292$	2421.21	−	3560.41i	0.485243	−	0.713551i
$293$			8718.86i			1.73844i	0.494430	+	0.869218i	$0.335377\pi$
$293$			8718.86i			1.73844i	−0.494430	+	0.869218i	$0.664623\pi$
$294$	−197.508	−	2092.77i	−0.0391799	−	0.415146i
$295$	−414.712	−	732.936i	−0.0818491	−	0.144655i
$296$	177.353	+	611.484i	0.0348259	+	0.120074i
$297$	998.795	+	998.795i	0.195138	+	0.195138i
$298$	−6521.61	−	5396.80i	−1.26774	−	1.04909i
$299$	−776.231	−	776.231i	−0.150136	−	0.150136i
$300$	1036.52	−	2815.25i	0.199479	−	0.541795i
$301$	−1177.63	+	1177.63i	−0.225507	+	0.225507i
$302$	466.471	+	4942.68i	0.0888821	+	0.941785i
$303$	−1126.10	+	1126.10i	−0.213508	+	0.213508i
$304$	−179.630	+	414.417i	−0.0338898	+	0.0781856i
$305$	−2841.89	+	1608.01i	−0.533528	+	0.301883i
$306$	2514.34	+	2080.68i	0.469723	+	0.388708i
$307$	7022.40			1.30550			0.652752	−	0.757572i	$-0.273614\pi$
$307$	7022.40			1.30550			0.652752	+	0.757572i	$0.273614\pi$
$308$	−764.248	−	4012.88i	−0.141387	−	0.742387i
$309$	−511.144	+	511.144i	−0.0941035	+	0.0941035i
$310$	8087.00	+	1441.45i	1.48165	+	0.264092i
$311$	−9327.57			−1.70070			−0.850350	−	0.526217i	$-0.823610\pi$
$311$	−9327.57			−1.70070			−0.850350	+	0.526217i	$0.823610\pi$
$312$	−3613.03	+	1047.92i	−0.655602	+	0.190149i
$313$	4296.36	−	4296.36i	0.775861	−	0.775861i	−0.203263	−	0.979124i	$-0.565155\pi$
$313$	4296.36	−	4296.36i	0.775861	−	0.775861i	0.979124	+	0.203263i	$0.0651546\pi$
$314$	−7308.68	+	689.766i	−1.31354	+	0.123967i
$315$	−854.791	+	483.661i	−0.152895	+	0.0865118i
$316$	7316.37	−	1393.39i	1.30246	−	0.248052i
$317$		−	5925.83i		−	1.04993i	−0.851124	−	0.524965i	$-0.824078\pi$
$317$		−	5925.83i		−	1.04993i	0.851124	−	0.524965i	$-0.175922\pi$
$318$	449.058	+	4758.17i	0.0791884	+	0.839072i
$319$	6500.53			1.14094
$320$	−5478.55	+	1659.35i	−0.957064	+	0.289876i
$321$	2761.61			0.480181
$322$	51.3817	+	544.435i	0.00889252	+	0.0942241i
$323$		−	904.803i		−	0.155866i
$324$	−636.559	+	121.232i	−0.109149	+	0.0207873i
$325$	−5938.14	−	3567.37i	−1.01350	−	0.608868i
$326$	−5822.53	+	549.509i	−0.989203	+	0.0933573i
$327$	−724.118	+	724.118i	−0.122458	+	0.122458i
$328$	7556.28	−	2191.61i	1.27203	−	0.368937i
$329$	5009.17			0.839406
$330$	4070.77	−	2839.13i	0.679057	−	0.473604i
$331$	−1173.95	+	1173.95i	−0.194943	+	0.194943i	−0.797828	−	0.602885i	$-0.794018\pi$
$331$	−1173.95	+	1173.95i	−0.194943	+	0.194943i	0.602885	+	0.797828i	$0.294018\pi$
$332$	−696.955	−	3659.54i	−0.115212	−	0.604950i
$333$	253.239			0.0416740
$334$	7115.38	+	5888.15i	1.16568	+	0.964627i
$335$	10639.5	+	2950.15i	1.73522	+	0.481146i
$336$	1719.45	+	745.301i	0.279178	+	0.121010i
$337$	407.868	−	407.868i	0.0659288	−	0.0659288i	−0.673374	−	0.739302i	$-0.735155\pi$
$337$	407.868	−	407.868i	0.0659288	−	0.0659288i	0.739302	+	0.673374i	$0.235155\pi$
$338$	232.326	+	2461.70i	0.0373872	+	0.396151i
$339$	−2671.16	+	2671.16i	−0.427957	+	0.427957i
$340$	8747.58	−	7414.54i	1.39531	−	1.18268i
$341$	9609.29	+	9609.29i	1.52602	+	1.52602i
$342$	138.407	+	114.535i	0.0218836	+	0.0181092i
$343$	4077.09	+	4077.09i	0.641814	+	0.641814i
$344$	1075.48	+	3708.05i	0.168563	+	0.581176i
$345$	−578.249	+	327.187i	−0.0902373	+	0.0510584i
$346$	245.138	+	2597.45i	0.0380887	+	0.403584i
$347$			890.445i			0.137757i	0.997625	+	0.0688784i	$0.0219420\pi$
$347$			890.445i			0.137757i	−0.997625	+	0.0688784i	$0.978058\pi$
$348$	−1676.97	+	2465.99i	−0.258319	+	0.379859i
$349$	−1046.51	−	1046.51i	−0.160511	−	0.160511i	0.622282	−	0.782793i	$-0.286206\pi$
$349$	−1046.51	−	1046.51i	−0.160511	−	0.160511i	−0.782793	+	0.622282i	$0.786206\pi$
$350$	1146.01	+	3255.04i	0.175020	+	0.497111i
$351$			1496.30i			0.227540i
$352$	−9004.36	−	2933.17i	−1.36345	−	0.444144i
$353$	9360.30	+	9360.30i	1.41133	+	1.41133i	0.750820	+	0.660507i	$0.229658\pi$
$353$	9360.30	+	9360.30i	1.41133	+	1.41133i	0.660507	+	0.750820i	$0.270342\pi$
$354$	492.397	+	407.471i	0.0739283	+	0.0611776i
$355$	8748.13	+	2425.71i	1.30789	+	0.362657i
$356$	1848.64	−	352.071i	0.275218	−	0.0524149i
$357$	−3754.11			−0.556551
$358$	−2313.64	−	1914.60i	−0.341563	−	0.282652i
$359$			6375.28i			0.937254i	0.883396	+	0.468627i	$0.155251\pi$
$359$			6375.28i			0.937254i	−0.883396	+	0.468627i	$0.844749\pi$
$360$	26.8774	+	2276.68i	0.00393489	+	0.333310i
$361$			6809.19i			0.992738i
$362$	3296.35	−	3983.38i	0.478598	−	0.578348i
$363$	4217.63			0.609830
$364$	2433.40	−	3578.32i	0.350397	−	0.515261i
$365$	−5237.12	+	2963.29i	−0.751023	+	0.424947i
$366$	1579.93	−	1909.22i	0.225640	−	0.272669i
$367$	−1443.33	−	1443.33i	−0.205289	−	0.205289i	0.596972	−	0.802262i	$-0.296370\pi$
$367$	−1443.33	−	1443.33i	−0.205289	−	0.205289i	−0.802262	+	0.596972i	$0.796370\pi$
$368$	1163.17	+	504.181i	0.164768	+	0.0714191i
$369$		−	3129.35i		−	0.441484i
$370$	156.138	−	875.986i	0.0219385	−	0.123082i
$371$	−3887.40	−	3887.40i	−0.543999	−	0.543999i
$372$	−6124.26	+	1166.36i	−0.853570	+	0.162561i
$373$			2927.87i			0.406433i	0.979134	+	0.203217i	$0.0651395\pi$
$373$			2927.87i			0.406433i	−0.979134	+	0.203217i	$0.934860\pi$
$374$	18886.8	−	1782.46i	2.61126	−	0.246441i
$375$	−3040.89	+	2886.37i	−0.418749	+	0.397470i
$376$	5598.95	−	10173.6i	0.767936	−	1.39538i
$377$	4869.24	+	4869.24i	0.665195	+	0.665195i
$378$	475.216	−	574.262i	0.0646627	−	0.0781398i
$379$	−3037.09	−	3037.09i	−0.411622	−	0.411622i	0.470681	−	0.882303i	$-0.344008\pi$
$379$	−3037.09	−	3037.09i	−0.411622	−	0.411622i	−0.882303	+	0.470681i	$0.844008\pi$
$380$	481.527	−	408.148i	0.0650048	−	0.0550988i
$381$	−2670.74	+	2670.74i	−0.359124	+	0.359124i
$382$	−3553.38	+	335.354i	−0.475933	+	0.0449168i
$383$	1506.00	−	1506.00i	0.200922	−	0.200922i	−0.599473	−	0.800395i	$-0.704623\pi$
$383$	1506.00	−	1506.00i	0.200922	−	0.200922i	0.800395	+	0.599473i	$0.204623\pi$
$384$	3435.60	−	2659.14i	0.456568	−	0.353382i
$385$	−1525.44	+	5501.40i	−0.201932	+	0.728252i
$386$	5114.27	−	6180.19i	0.674376	−	0.814932i
$387$	1535.65			0.201709
$388$	3825.59	−	5625.55i	0.500554	−	0.736067i
$389$	10003.4	−	10003.4i	1.30384	−	1.30384i	0.378053	−	0.925784i	$-0.376594\pi$
$389$	10003.4	−	10003.4i	1.30384	−	1.30384i	0.925784	−	0.378053i	$-0.123406\pi$
$390$	5175.88	+	922.562i	0.672028	+	0.119784i
$391$	−2539.58			−0.328471
$392$	5383.65	−	1561.46i	0.693662	−	0.201188i
$393$	1306.05	−	1306.05i	0.167638	−	0.167638i
$394$	−656.943	−	6960.90i	−0.0840008	−	0.890064i
$395$	−10030.3	−	2781.23i	−1.27767	−	0.354275i
$396$	−2118.13	+	3114.72i	−0.268788	+	0.395254i
$397$		−	6283.52i		−	0.794360i	−0.917741	−	0.397180i	$-0.869989\pi$
$397$		−	6283.52i		−	0.794360i	0.917741	−	0.397180i	$-0.130011\pi$
$398$	2839.33	−	267.966i	0.357595	−	0.0337485i
$399$	−206.652			−0.0259287
$400$	7891.89	+	1310.74i	0.986486	+	0.163843i
$401$	−13210.4			−1.64513			−0.822563	−	0.568674i	$-0.807457\pi$
$401$	−13210.4			−1.64513			−0.822563	+	0.568674i	$0.807457\pi$
$402$	−8342.41	+	787.325i	−1.03503	+	0.0976821i
$403$			14395.7i			1.77941i
$404$	−3511.72	−	2388.11i	−0.432462	−	0.294091i
$405$	872.680	+	241.980i	0.107071	+	0.0296890i
$406$	−322.314	−	3415.20i	−0.0393994	−	0.417472i
$407$	1040.88	−	1040.88i	0.126768	−	0.126768i
$408$	−4196.12	+	7624.57i	−0.509164	+	0.925177i
$409$	−1857.43			−0.224558			−0.112279	−	0.993677i	$-0.535815\pi$
$409$	−1857.43			−0.224558			−0.112279	+	0.993677i	$0.535815\pi$
$410$	−10824.8	−	1929.44i	−1.30390	−	0.232411i
$411$	−5235.46	+	5235.46i	−0.628336	+	0.628336i
$412$	−1593.99	−	1083.98i	−0.190608	−	0.129621i
$413$	−735.188			−0.0875938
$414$	321.474	−	388.477i	0.0381633	−	0.0461173i
$415$	−1391.13	+	5017.00i	−0.164549	+	0.593433i
$416$	−4547.63	−	8941.84i	−0.535976	−	1.05387i
$417$	6143.17	−	6143.17i	0.721421	−	0.721421i
$418$	1039.66	−	98.1191i	0.121654	−	0.0114812i
$419$	−7226.47	+	7226.47i	−0.842569	+	0.842569i	−0.989192	−	0.146624i	$-0.953159\pi$
$419$	−7226.47	+	7226.47i	−0.842569	+	0.842569i	0.146624	+	0.989192i	$0.453159\pi$
$420$	−1693.44	−	1997.90i	−0.196742	−	0.232113i
$421$	−1692.74	−	1692.74i	−0.195960	−	0.195960i	0.602305	−	0.798266i	$-0.294249\pi$
$421$	−1692.74	−	1692.74i	−0.195960	−	0.195960i	−0.798266	+	0.602305i	$0.794249\pi$
$422$	−1285.51	+	1553.43i	−0.148288	+	0.179194i
$423$	−3266.02	−	3266.02i	−0.375412	−	0.375412i
$424$	−12240.4	+	3550.18i	−1.40199	+	0.406632i
$425$	−15549.5	+	3878.20i	−1.77473	+	0.442636i
$426$	−6859.40	+	647.364i	−0.780138	+	0.0736265i
$427$			2850.62i			0.323071i
$428$	1377.76	+	7234.26i	0.155599	+	0.817012i
$429$	6150.19	+	6150.19i	0.692154	+	0.692154i
$430$	946.824	−	5312.00i	0.106186	−	0.595738i
$431$		−	9661.56i		−	1.07977i	−0.841739	−	0.539885i	$-0.818468\pi$
$431$		−	9661.56i		−	1.07977i	0.841739	−	0.539885i	$-0.181532\pi$
$432$	−635.153	−	1607.04i	−0.0707380	−	0.178978i
$433$	−10067.4	−	10067.4i	−1.11734	−	1.11734i	−0.992131	−	0.125204i	$-0.960041\pi$
$433$	−10067.4	−	10067.4i	−1.11734	−	1.11734i	−0.125204	−	0.992131i	$-0.539959\pi$
$434$	4572.00	−	5524.91i	0.505675	−	0.611070i
$435$	3627.31	−	2052.42i	0.399808	−	0.226221i
$436$	−2258.15	−	1535.63i	−0.248040	−	0.168677i
$437$	−139.796			−0.0153029
$438$	2911.55	−	3518.38i	0.317624	−	0.383824i
$439$			2261.97i			0.245918i	0.992412	+	0.122959i	$0.0392383\pi$
$439$			2261.97i			0.245918i	−0.992412	+	0.122959i	$0.960762\pi$
$440$	9468.24	+	9247.30i	1.02587	+	1.00193i
$441$		−	2229.58i		−	0.240750i
$442$	15482.3	+	12812.0i	1.66611	+	1.37875i
$443$	7936.53			0.851187			0.425593	−	0.904914i	$-0.360065\pi$
$443$	7936.53			0.851187			0.425593	+	0.904914i	$0.360065\pi$
$444$	126.340	+	663.382i	0.0135041	+	0.0709070i
$445$	−2534.36	−	702.735i	−0.269978	−	0.0748603i
$446$	6143.29	+	5083.73i	0.652227	+	0.539734i
$447$	−6348.78	−	6348.78i	−0.671783	−	0.671783i
$448$	−1094.55	+	4876.07i	−0.115430	+	0.514225i
$449$		−	11300.0i		−	1.18771i	−0.804574	−	0.593853i	$-0.797606\pi$
$449$		−	11300.0i		−	1.18771i	0.804574	−	0.593853i	$-0.202394\pi$
$450$	1375.10	−	2869.51i	0.144051	−	0.300600i
$451$	−12862.5	−	12862.5i	−1.34295	−	1.34295i
$452$	−8329.95	−	5664.69i	−0.866832	−	0.589479i
$453$			5265.80i			0.546156i
$454$	111.869	+	1185.35i	0.0115645	+	0.122536i
$455$	−5263.47	+	2978.20i	−0.542319	+	0.306857i
$456$	−230.984	+	419.709i	−0.0237210	+	0.0431024i
$457$	6381.45	+	6381.45i	0.653199	+	0.653199i	0.953762	−	0.300563i	$-0.0971746\pi$
$457$	6381.45	+	6381.45i	0.653199	+	0.653199i	−0.300563	+	0.953762i	$0.597175\pi$
$458$	−2490.79	−	2061.19i	−0.254120	−	0.210290i
$459$	2447.71	+	2447.71i	0.248909	+	0.248909i
$460$	−1145.58	−	1351.54i	−0.116115	−	0.136991i
$461$	−533.654	+	533.654i	−0.0539148	+	0.0539148i	−0.733550	−	0.679635i	$-0.762138\pi$
$461$	−533.654	+	533.654i	−0.0539148	+	0.0539148i	0.679635	+	0.733550i	$0.262138\pi$
$462$	−407.105	−	4313.64i	−0.0409962	−	0.434391i
$463$	−9150.88	+	9150.88i	−0.918526	+	0.918526i	−0.996922	−	0.0783961i	$-0.975020\pi$
$463$	−9150.88	+	9150.88i	−0.918526	+	0.918526i	0.0783961	+	0.996922i	$0.475020\pi$
$464$	−7296.51	−	3162.69i	−0.730025	−	0.316431i
$465$	8395.96	+	2328.06i	0.837319	+	0.232174i
$466$	7730.45	+	6397.14i	0.768468	+	0.635927i
$467$	−11187.8			−1.10858			−0.554291	−	0.832323i	$-0.687010\pi$
$467$	−11187.8			−1.10858			−0.554291	+	0.832323i	$0.687010\pi$
$468$	−3919.68	+	746.498i	−0.387152	+	0.0737327i
$469$	6815.71	−	6815.71i	0.671045	−	0.671045i
$470$	−13311.3	+	9283.84i	−1.30639	+	0.911132i
$471$	−7786.47			−0.761745
$472$	−821.749	+	1493.16i	−0.0801358	+	0.145611i
$473$	6311.93	−	6311.93i	0.613579	−	0.613579i
$474$	7864.72	−	742.242i	0.762107	−	0.0719247i
$475$	−855.952	+	213.483i	−0.0826817	+	0.0206216i
$476$	−1872.91	−	9834.20i	−0.180346	−	0.946953i
$477$			5069.22i			0.486591i
$478$	−188.112	−	1993.22i	−0.0180001	−	0.190727i
$479$	−7142.75			−0.681337			−0.340669	−	0.940183i	$-0.610653\pi$
$479$	−7142.75			−0.681337			−0.340669	+	0.940183i	$0.610653\pi$
$480$	−5950.55	+	1206.24i	−0.565842	+	0.114702i
$481$	1559.35			0.147818
$482$	140.978	+	1493.78i	0.0133223	+	0.141162i
$483$			580.026i			0.0546421i
$484$	2104.16	+	11048.4i	0.197611	+	1.03761i
$485$	−8274.81	+	4682.08i	−0.774721	+	0.438355i
$486$	−684.267	+	64.5785i	−0.0638662	+	0.00602745i
$487$	−7010.92	+	7010.92i	−0.652351	+	0.652351i	−0.953559	−	0.301207i	$-0.902610\pi$
$487$	−7010.92	+	7010.92i	−0.652351	+	0.652351i	0.301207	+	0.953559i	$0.402610\pi$
$488$	5789.59	+	3186.26i	0.537054	+	0.295564i
$489$	−6203.17			−0.573655
$490$	−7712.40	−	1374.68i	−0.711042	−	0.126738i
$491$	−11024.9	+	11024.9i	−1.01333	+	1.01333i	−0.0134229	+	0.999910i	$0.504273\pi$
$491$	−11024.9	+	11024.9i	−1.01333	+	1.01333i	−0.999910	+	0.0134229i	$0.995727\pi$
$492$	8197.60	−	1561.22i	0.751171	−	0.143060i
$493$	15930.6			1.45533
$494$	852.255	+	705.263i	0.0776210	+	0.0642333i
$495$	4581.55	−	2592.35i	0.416011	−	0.235389i
$496$	−6110.74	−	15461.1i	−0.553186	−	1.39965i
$497$	5604.09	−	5604.09i	0.505791	−	0.505791i
$498$	−371.259	−	3933.82i	−0.0334066	−	0.353973i
$499$	11270.2	−	11270.2i	1.01107	−	1.01107i	0.0111295	−	0.999938i	$-0.496457\pi$
$499$	11270.2	−	11270.2i	1.01107	−	1.01107i	0.999938	−	0.0111295i	$-0.00354271\pi$
$500$	−9078.16	−	6525.87i	−0.811975	−	0.583692i
$501$	6926.81	+	6926.81i	0.617698	+	0.617698i
$502$	2220.53	+	1837.55i	0.197425	+	0.163374i
$503$	−820.733	−	820.733i	−0.0727529	−	0.0727529i	0.669794	−	0.742547i	$-0.266382\pi$
$503$	−820.733	−	820.733i	−0.0727529	−	0.0727529i	−0.742547	+	0.669794i	$0.766382\pi$
$504$	1741.41	+	958.371i	0.153906	+	0.0847009i
$505$	2922.77	+	5165.52i	0.257548	+	0.455173i
$506$	−275.398	−	2918.09i	−0.0241955	−	0.256373i
$507$			2622.63i			0.229734i
$508$	−8328.65	−	5663.81i	−0.727410	−	0.494667i
$509$	−6553.62	−	6553.62i	−0.570696	−	0.570696i	0.361627	−	0.932323i	$-0.382221\pi$
$509$	−6553.62	−	6553.62i	−0.570696	−	0.570696i	−0.932323	+	0.361627i	$0.882221\pi$
$510$	9976.08	−	6957.75i	0.866173	−	0.604107i
$511$			5253.22i			0.454773i
$512$	8679.85	+	7673.20i	0.749216	+	0.662326i
$513$	134.739	+	134.739i	0.0115962	+	0.0115962i
$514$	9446.80	+	7817.46i	0.810662	+	0.670843i
$515$	1326.66	+	2344.66i	0.113514	+	0.200617i
$516$	766.130	+	4022.76i	0.0653624	+	0.343202i
$517$	−26848.4			−2.28393
$518$	−598.460	−	495.241i	−0.0507622	−	0.0420070i
$519$			2767.26i			0.234045i
$520$	165.500	+	14018.9i	0.0139571	+	1.18225i
$521$		−	7445.07i		−	0.626055i	−0.949744	−	0.313027i	$-0.898657\pi$
$521$		−	7445.07i		−	0.626055i	0.949744	−	0.313027i	$-0.101343\pi$
$522$	−2016.58	+	2436.88i	−0.169087	+	0.204329i
$523$	−3539.23			−0.295908			−0.147954	−	0.988994i	$-0.547269\pi$
$523$	−3539.23			−0.295908			−0.147954	+	0.988994i	$0.547269\pi$
$524$	4072.90	+	2769.73i	0.339553	+	0.230909i
$525$	885.759	+	3551.42i	0.0736337	+	0.295232i
$526$	−14106.9	+	17047.0i	−1.16937	+	1.41309i
$527$	23549.1	+	23549.1i	1.94652	+	1.94652i
$528$	−9216.00	−	3994.70i	−0.759611	−	0.329255i
$529$		−	11774.6i		−	0.967751i
$530$	17535.1	+	3125.49i	1.43712	+	0.256156i
$531$	479.348	+	479.348i	0.0391750	+	0.0391750i
$532$	−103.098	−	541.343i	−0.00840201	−	0.0441169i
$533$		−	19269.3i		−	1.56594i
$534$	1987.19	−	187.543i	0.161038	−	0.0151981i
$535$	2750.01	−	9917.70i	0.222231	−	0.801457i
$536$	−6224.46	−	21460.8i	−0.501597	−	1.72942i
$537$	−2252.33	−	2252.33i	−0.180996	−	0.180996i
$538$	−1766.85	+	2135.10i	−0.141588	+	0.171098i
$539$	−9164.18	−	9164.18i	−0.732336	−	0.732336i
$540$	−198.508	+	2406.78i	−0.0158193	+	0.191799i
$541$	1056.39	−	1056.39i	0.0839513	−	0.0839513i	−0.663884	−	0.747835i	$-0.731093\pi$
$541$	1056.39	−	1056.39i	0.0839513	−	0.0839513i	0.747835	+	0.663884i	$0.231093\pi$
$542$	−3694.51	+	348.674i	−0.292791	+	0.0276325i
$543$	3877.82	−	3877.82i	0.306470	−	0.306470i
$544$	−22066.6	−	7188.21i	−1.73915	−	0.566529i
$545$	1879.43	+	3321.59i	0.147717	+	0.261066i
$546$	2926.20	−	3536.08i	0.229358	−	0.277162i
$547$	−2443.35			−0.190988			−0.0954938	−	0.995430i	$-0.530443\pi$
$547$	−2443.35			−0.190988			−0.0954938	+	0.995430i	$0.530443\pi$
$548$	−16326.7	−	11102.8i	−1.27270	−	0.865487i
$549$	1858.63	−	1858.63i	0.144489	−	0.144489i
$550$	−6142.44	−	17446.5i	−0.476208	−	1.35258i
$551$	876.931			0.0678013
$552$	1178.03	+	648.319i	0.0908338	+	0.0499896i
$553$	−6425.44	+	6425.44i	−0.494100	+	0.494100i
$554$	−862.164	−	9135.40i	−0.0661189	−	0.700588i
$555$	252.176	−	909.453i	0.0192870	−	0.0695570i
$556$	19157.4	+	13027.7i	1.46125	+	0.993704i
$557$			416.513i			0.0316844i	0.999875	+	0.0158422i	$0.00504295\pi$
$557$			416.513i			0.0316844i	−0.999875	+	0.0158422i	$0.994957\pi$
$558$	−6583.26	+	621.303i	−0.499447	+	0.0471359i
$559$	9455.94			0.715462
$560$	4388.81	−	5432.86i	0.331181	−	0.409964i
$561$	20121.5			1.51431
$562$	−3276.61	+	309.234i	−0.245935	+	0.0232104i
$563$		−	7675.90i		−	0.574601i	−0.957840	−	0.287301i	$-0.907242\pi$
$563$		−	7675.90i		−	0.574601i	0.957840	−	0.287301i	$-0.0927579\pi$
$564$	6926.19	−	10185.0i	0.517102	−	0.760400i
$565$	6932.93	+	12252.8i	0.516231	+	0.912354i
$566$	−614.213	−	6508.14i	−0.0456136	−	0.483317i
$567$	559.043	−	559.043i	0.0414067	−	0.0414067i
$568$	−5117.95	−	17645.8i	−0.378071	−	1.30352i
$569$	−13866.6			−1.02165			−0.510826	−	0.859684i	$-0.670660\pi$
$569$	−13866.6			−1.02165			−0.510826	+	0.859684i	$0.670660\pi$
$570$	549.153	−	383.003i	0.0403535	−	0.0281443i
$571$	−6505.84	+	6505.84i	−0.476814	+	0.476814i	−0.904111	−	0.427297i	$-0.859466\pi$
$571$	−6505.84	+	6505.84i	−0.476814	+	0.476814i	0.427297	+	0.904111i	$0.359466\pi$
$572$	−13042.6	+	19179.2i	−0.953391	+	1.40197i
$573$	−3785.67			−0.276001
$574$	−6119.83	+	7395.34i	−0.445012	+	0.537762i
$575$	599.198	+	2402.46i	0.0434579	+	0.174243i
$576$	3892.89	−	2465.58i	0.281604	−	0.178355i
$577$	−7498.36	+	7498.36i	−0.541007	+	0.541007i	−0.923824	−	0.382817i	$-0.874954\pi$
$577$	−7498.36	+	7498.36i	−0.541007	+	0.541007i	0.382817	+	0.923824i	$0.374954\pi$
$578$	32450.4	−	3062.55i	2.33522	−	0.220390i
$579$	6016.41	−	6016.41i	0.431837	−	0.431837i
$580$	7186.13	+	8478.10i	0.514462	+	0.606955i
$581$	3213.91	+	3213.91i	0.229493	+	0.229493i
$582$	4600.33	−	5559.15i	0.327646	−	0.395935i
$583$	20835.9	+	20835.9i	1.48016	+	1.48016i
$584$	10669.2	+	5871.73i	0.755987	+	0.416052i
$585$	5373.63	+	1490.02i	0.379781	+	0.105307i
$586$	−24551.6	+	2317.08i	−1.73074	+	0.163341i
$587$		−	17040.6i		−	1.19819i	−0.800677	−	0.599097i	$-0.795526\pi$
$587$		−	17040.6i		−	1.19819i	0.800677	−	0.599097i	$-0.204474\pi$
$588$	5840.57	−	1112.33i	0.409628	−	0.0780131i
$589$	1296.31	+	1296.31i	0.0906848	+	0.0906848i
$590$	1953.67	−	1362.58i	0.136324	−	0.0950786i
$591$		−	7415.96i		−	0.516162i
$592$	−1674.75	+	661.917i	−0.116270	+	0.0459538i
$593$	−16490.1	−	16490.1i	−1.14194	−	1.14194i	−0.988096	−	0.153840i	$-0.950836\pi$
$593$	−16490.1	−	16490.1i	−1.14194	−	1.14194i	−0.153840	−	0.988096i	$-0.549164\pi$
$594$	−2547.09	+	3077.96i	−0.175940	+	0.212610i
$595$	−3738.34	+	13482.0i	−0.257575	+	0.928924i
$596$	13463.8	−	19798.5i	0.925331	−	1.36070i
$597$	3024.95			0.207375
$598$	1979.51	−	2392.09i	0.135365	−	0.163578i
$599$		−	18444.4i		−	1.25813i	−0.777353	−	0.629064i	$-0.783438\pi$
$599$		−	18444.4i		−	1.25813i	0.777353	−	0.629064i	$-0.216562\pi$
$600$	8202.96	+	2170.60i	0.558141	+	0.147690i
$601$		−	17371.7i		−	1.17904i	−0.807752	−	0.589522i	$-0.799316\pi$
$601$		−	17371.7i		−	1.17904i	0.807752	−	0.589522i	$-0.200684\pi$
$602$	−3629.08	−	3003.15i	−0.245698	−	0.203321i
$603$	−8887.78			−0.600230
$604$	−13794.2	+	2627.09i	−0.929268	+	0.176978i
$605$	4199.92	−	15146.7i	0.282233	−	1.01785i
$606$	−3470.27	−	2871.74i	−0.232624	−	0.192502i
$607$	−2903.15	−	2903.15i	−0.194127	−	0.194127i	0.603350	−	0.797477i	$-0.293832\pi$
$607$	−2903.15	−	2903.15i	−0.194127	−	0.194127i	−0.797477	+	0.603350i	$0.793832\pi$
$608$	−1214.70	−	395.689i	−0.0810240	−	0.0263936i
$609$		−	3638.46i		−	0.242098i
$610$	−5283.26	−	7575.18i	−0.350677	−	0.502803i
$611$	−20110.9	−	20110.9i	−1.33158	−	1.33158i
$612$	−5190.82	+	7633.12i	−0.342853	+	0.504168i
$613$		−	11367.2i		−	0.748966i	−0.927234	−	0.374483i	$-0.877820\pi$
$613$		−	11367.2i		−	0.748966i	0.927234	−	0.374483i	$-0.122180\pi$
$614$	1866.24	+	19774.5i	0.122663	+	1.29973i
$615$	−11238.4	−	3116.21i	−0.736870	−	0.204322i
$616$	11096.8	−	3218.50i	0.725818	−	0.210515i
$617$	14790.2	+	14790.2i	0.965043	+	0.965043i	0.999409	−	0.0343667i	$-0.0109414\pi$
$617$	14790.2	+	14790.2i	0.965043	+	0.965043i	−0.0343667	+	0.999409i	$0.510941\pi$
$618$	−1575.18	−	1303.50i	−0.102529	−	0.0848454i
$619$	16533.8	+	16533.8i	1.07358	+	1.07358i	0.997068	+	0.0765163i	$0.0243797\pi$
$619$	16533.8	+	16533.8i	1.07358	+	1.07358i	0.0765163	+	0.997068i	$0.475620\pi$
$620$	−1909.83	+	23155.4i	−0.123711	+	1.49991i
$621$	378.181	−	378.181i	0.0244378	−	0.0244378i
$622$	−2478.85	−	26265.6i	−0.159796	−	1.69318i
$623$	−1623.52	+	1623.52i	−0.104406	+	0.104406i
$624$	−3911.03	−	9895.50i	−0.250908	−	0.634835i
$625$	7337.62	+	13794.9i	0.469607	+	0.882875i
$626$	13240.0	+	10956.4i	0.845328	+	0.699530i
$627$	1107.62			0.0705491
$628$	−3884.64	−	20397.3i	−0.246838	−	1.29609i
$629$	2550.85	−	2550.85i	0.161699	−	0.161699i
$630$	−1589.11	−	2278.48i	−0.100495	−	0.144090i
$631$	25739.3			1.62388			0.811938	−	0.583744i	$-0.198413\pi$
$631$	25739.3			1.62388			0.811938	+	0.583744i	$0.198413\pi$
$632$	5868.04	+	20232.0i	0.369333	+	1.27339i
$633$	−1512.27	+	1512.27i	−0.0949560	+	0.0949560i
$634$	16686.6	−	1574.82i	1.04529	−	0.0986501i
$635$	6931.85	+	12250.9i	0.433200	+	0.765610i
$636$	−13279.3	+	2529.02i	−0.827919	+	0.157676i
$637$		−	13728.9i		−	0.853938i
$638$	1727.55	+	18304.9i	0.107201	+	1.13589i
$639$	−7307.82			−0.452414
$640$	−6128.54	−	14986.2i	−0.378518	−	0.925594i
$641$	8179.70			0.504023			0.252012	−	0.967724i	$-0.418908\pi$
$641$	8179.70			0.504023			0.252012	+	0.967724i	$0.418908\pi$
$642$	733.912	+	7776.45i	0.0451171	+	0.478056i
$643$			27689.3i			1.69823i	0.528210	+	0.849114i	$0.322863\pi$
$643$			27689.3i			1.69823i	−0.528210	+	0.849114i	$0.677137\pi$
$644$	−1519.43	+	289.373i	−0.0929718	+	0.0177064i
$645$	1529.20	−	5514.95i	0.0933523	−	0.336668i
$646$	2547.85	−	240.456i	0.155176	−	0.0146449i
$647$	−914.554	+	914.554i	−0.0555716	+	0.0555716i	−0.734346	−	0.678775i	$-0.762511\pi$
$647$	−914.554	+	914.554i	−0.0555716	+	0.0555716i	0.678775	+	0.734346i	$0.262511\pi$
$648$	−510.547	−	1760.28i	−0.0309509	−	0.106713i
$649$	3940.50			0.238333
$650$	8467.32	−	17669.3i	0.510947	−	1.06623i
$651$	5378.49	−	5378.49i	0.323809	−	0.323809i
$652$	−3094.74	−	16249.7i	−0.185888	−	0.976055i
$653$	−24329.1			−1.45799			−0.728997	−	0.684517i	$-0.760013\pi$
$653$	−24329.1			−1.45799			−0.728997	+	0.684517i	$0.760013\pi$
$654$	−2231.49	−	1846.62i	−0.133422	−	0.110410i
$655$	−3389.83	−	5990.97i	−0.202216	−	0.357384i
$656$	8179.50	+	20695.4i	0.486823	+	1.23174i
$657$	3425.14	−	3425.14i	0.203390	−	0.203390i
$658$	1331.21	+	14105.4i	0.0788695	+	0.835693i
$659$	−1416.57	+	1416.57i	−0.0837355	+	0.0837355i	−0.747734	−	0.663998i	$-0.768858\pi$
$659$	−1416.57	+	1416.57i	−0.0837355	+	0.0837355i	0.663998	+	0.747734i	$0.268858\pi$
$660$	9076.59	+	10708.4i	0.535312	+	0.631554i
$661$	−6236.90	−	6236.90i	−0.367001	−	0.367001i	0.499382	−	0.866382i	$-0.333561\pi$
$661$	−6236.90	−	6236.90i	−0.367001	−	0.367001i	−0.866382	+	0.499382i	$0.833561\pi$
$662$	−3617.72	−	2993.76i	−0.212397	−	0.175764i
$663$	15072.0	+	15072.0i	0.882879	+	0.882879i
$664$	10119.7	−	2935.11i	0.591449	−	0.171543i
$665$	−205.784	+	742.146i	−0.0120000	+	0.0432770i
$666$	67.2997	+	713.101i	0.00391563	+	0.0414896i
$667$		−	2461.35i		−	0.142884i
$668$	−14689.6	+	21601.1i	−0.850834	+	1.25116i
$669$	5980.48	+	5980.48i	0.345619	+	0.345619i
$670$	−5479.87	+	30743.9i	−0.315979	+	1.77275i
$671$		−	15278.9i		−	0.879040i
$672$	−1641.75	+	5039.90i	−0.0942438	+	0.289313i
$673$	24115.4	+	24115.4i	1.38125	+	1.38125i	0.842409	+	0.538838i	$0.181137\pi$
$673$	24115.4	+	24115.4i	1.38125	+	1.38125i	0.538838	+	0.842409i	$0.318863\pi$
$674$	1256.92	+	1040.13i	0.0718317	+	0.0594425i
$675$	1738.03	−	2893.07i	0.0991064	−	0.164970i
$676$	−6870.20	+	1308.42i	−0.390885	+	0.0744436i
$677$	34127.5			1.93741			0.968705	−	0.248214i	$-0.0798437\pi$
$677$	34127.5			1.93741			0.968705	+	0.248214i	$0.0798437\pi$
$678$	−8231.63	−	6811.88i	−0.466274	−	0.385854i
$679$			8300.24i			0.469122i
$680$	23203.4	+	22662.0i	1.30855	+	1.27801i
$681$			1262.84i			0.0710605i
$682$	−24505.2	+	29612.7i	−1.37589	+	1.66265i
$683$	16542.0			0.926737			0.463369	−	0.886166i	$-0.346641\pi$
$683$	16542.0			0.926737			0.463369	+	0.886166i	$0.346641\pi$
$684$	−285.739	+	420.180i	−0.0159729	+	0.0234883i
$685$	13588.5	+	24015.5i	0.757942	+	1.33954i
$686$	−10397.2	+	12564.2i	−0.578670	+	0.699278i
$687$	−2424.78	−	2424.78i	−0.134659	−	0.134659i
$688$	−10155.7	+	4013.88i	−0.562767	+	0.222424i
$689$			31214.3i			1.72594i
$690$	−1075.00	−	1541.35i	−0.0593111	−	0.0850407i
$691$	2763.72	+	2763.72i	0.152152	+	0.152152i	0.779078	−	0.626926i	$-0.215687\pi$
$691$	2763.72	+	2763.72i	0.152152	+	0.152152i	−0.626926	+	0.779078i	$0.715687\pi$
$692$	−7249.06	+	1380.57i	−0.398219	+	0.0758404i
$693$		−	4595.63i		−	0.251910i
$694$	−2507.42	+	236.641i	−0.137147	+	0.0129434i
$695$	−15944.5	−	28179.2i	−0.870227	−	1.53798i
$696$	−7389.69	−	4066.85i	−0.402450	−	0.221485i
$697$	−31521.5	−	31521.5i	−1.71300	−	1.71300i
$698$	2668.77	−	3225.00i	0.144720	−	0.174883i
$699$	7525.58	+	7525.58i	0.407215	+	0.407215i
$700$	−8861.34	+	4092.11i	−0.478467	+	0.220953i
$701$	22331.6	−	22331.6i	1.20321	−	1.20321i	0.230031	−	0.973183i	$-0.426117\pi$
$701$	22331.6	−	22331.6i	1.20321	−	1.20321i	0.973183	−	0.230031i	$-0.0738828\pi$
$702$	−4213.45	+	397.650i	−0.226533	+	0.0213794i
$703$	140.416	−	140.416i	0.00753329	−	0.00753329i
$704$	5866.61	−	26135.0i	0.314071	−	1.39915i
$705$	−14981.5	+	8476.87i	−0.800333	+	0.452847i
$706$	−23870.2	+	28845.3i	−1.27248	+	1.53769i
$707$	5181.39			0.275624
$708$	−1016.55	+	1494.84i	−0.0539607	+	0.0793494i
$709$	11664.1	−	11664.1i	0.617847	−	0.617847i	−0.327132	−	0.944979i	$-0.606082\pi$
$709$	11664.1	−	11664.1i	0.617847	−	0.617847i	0.944979	+	0.327132i	$0.106082\pi$
$710$	−4505.73	+	25278.6i	−0.238165	+	1.33618i
$711$	8378.86			0.441958
$712$	1482.69	+	5112.04i	0.0780421	+	0.269076i
$713$	3638.44	−	3638.44i	0.191109	−	0.191109i
$714$	−997.675	−	10571.3i	−0.0522928	−	0.554088i
$715$	28211.4	−	15962.7i	1.47559	−	0.834923i
$716$	4776.48	−	7023.83i	0.249309	−	0.366610i
$717$		−	2123.52i		−	0.110606i
$718$	−17952.2	+	1694.26i	−0.933108	+	0.0880632i
$719$	−12561.1			−0.651530			−0.325765	−	0.945451i	$-0.605622\pi$
$719$	−12561.1			−0.651530			−0.325765	+	0.945451i	$0.605622\pi$
$720$	−6403.80	+	680.725i	−0.331466	+	0.0352349i
$721$	2351.87			0.121481
$722$	−19174.1	+	1809.58i	−0.988347	+	0.0932764i
$723$			1591.44i			0.0818620i
$724$	12092.9	+	8223.64i	0.620758	+	0.422140i
$725$	−3758.73	−	15070.5i	−0.192546	−	0.772005i
$726$	1120.86	+	11876.5i	0.0572988	+	0.607132i
$727$	8239.94	−	8239.94i	0.420361	−	0.420361i	−0.464967	−	0.885328i	$-0.653934\pi$
$727$	8239.94	−	8239.94i	0.420361	−	0.420361i	0.885328	+	0.464967i	$0.153934\pi$
$728$	10722.9	+	5901.28i	0.545904	+	0.300434i
$729$	−729.000			−0.0370370
$730$	−9736.16	−	13959.8i	−0.493632	−	0.707773i
$731$	15468.4	−	15468.4i	0.782653	−	0.782653i
$732$	5796.09	+	3941.56i	0.292663	+	0.199022i
$733$	−12006.6			−0.605014			−0.302507	−	0.953147i	$-0.597824\pi$
$733$	−12006.6			−0.605014			−0.302507	+	0.953147i	$0.597824\pi$
$734$	3680.72	−	4447.87i	0.185093	−	0.223670i
$735$	−8007.04	−	2220.22i	−0.401829	−	0.111420i
$736$	−1110.61	+	3409.39i	−0.0556218	+	0.170750i
$737$	−36531.2	+	36531.2i	−1.82584	+	1.82584i
$738$	8811.99	−	831.642i	0.439531	−	0.0414813i
$739$	6865.36	−	6865.36i	0.341741	−	0.341741i	−0.515281	−	0.857021i	$-0.672312\pi$
$739$	6865.36	−	6865.36i	0.341741	−	0.341741i	0.857021	+	0.515281i	$0.172312\pi$
$740$	2508.20	+	206.873i	0.124599	+	0.0102768i
$741$	829.669	+	829.669i	0.0411318	+	0.0411318i
$742$	9913.49	−	11979.7i	0.490479	−	0.592706i
$743$	−5501.99	−	5501.99i	−0.271667	−	0.271667i	0.558104	−	0.829771i	$-0.311529\pi$
$743$	−5501.99	−	5501.99i	−0.271667	−	0.271667i	−0.829771	+	0.558104i	$0.811529\pi$
$744$	−4911.92	−	16935.4i	−0.242042	−	0.834520i
$745$	−29122.3	+	16478.1i	−1.43216	+	0.810350i
$746$	−8244.64	+	778.098i	−0.404635	+	0.0381879i
$747$		−	4190.98i		−	0.205275i
$748$	10038.5	+	52709.8i	0.490701	+	2.57655i
$749$	−6353.33	−	6353.33i	−0.309941	−	0.309941i
$750$	−8935.89	−	7795.82i	−0.435057	−	0.379551i
$751$		−	34558.5i		−	1.67917i	−0.543226	−	0.839587i	$-0.682797\pi$
$751$		−	34558.5i		−	1.67917i	0.543226	−	0.839587i	$-0.317203\pi$
$752$	30135.9	+	13062.5i	1.46136	+	0.633430i
$753$	2161.69	+	2161.69i	0.104617	+	0.104617i
$754$	−12417.3	+	15005.4i	−0.599752	+	0.724753i
$755$	18910.9	+	5243.68i	0.911575	+	0.252764i
$756$	1743.36	+	1185.56i	0.0838698	+	0.0570347i
$757$	−26018.0			−1.24920			−0.624598	−	0.780946i	$-0.714737\pi$
$757$	−26018.0			−1.24920			−0.624598	+	0.780946i	$0.714737\pi$
$758$	7745.06	−	9359.30i	0.371126	−	0.448477i
$759$		−	3108.85i		−	0.148675i
$760$	1277.28	+	1247.47i	0.0609628	+	0.0595402i
$761$			35602.9i			1.69593i	0.530050	+	0.847966i	$0.322173\pi$
$761$			35602.9i			1.69593i	−0.530050	+	0.847966i	$0.677827\pi$
$762$	−8230.35	−	6810.82i	−0.391278	−	0.323793i
$763$	3331.80			0.158085
$764$	−1888.66	−	9916.88i	−0.0894362	−	0.469608i
$765$	11227.8	−	6352.96i	0.530644	−	0.300251i
$766$	4641.01	+	3840.55i	0.218912	+	0.181155i
$767$	2951.64	+	2951.64i	0.138954	+	0.138954i
$768$	8400.94	+	8967.67i	0.394717	+	0.421345i
$769$		−	1559.19i		−	0.0731156i	−0.999332	−	0.0365578i	$-0.988361\pi$
$769$		−	1559.19i		−	0.0731156i	0.999332	−	0.0365578i	$-0.0116393\pi$
$770$	−15896.9	−	2833.50i	−0.744004	−	0.132613i
$771$	9196.44	+	9196.44i	0.429574	+	0.429574i
$772$	18762.0	+	12758.9i	0.874690	+	0.594823i
$773$			22875.9i			1.06441i	0.846615	+	0.532205i	$0.178636\pi$
$773$			22875.9i			1.06441i	−0.846615	+	0.532205i	$0.821364\pi$
$774$	408.107	+	4324.26i	0.0189523	+	0.200817i
$775$	16721.4	−	27833.9i	0.775033	−	1.29010i
$776$	16857.7	+	9277.51i	0.779842	+	0.429180i
$777$	−582.600	−	582.600i	−0.0268992	−	0.0268992i
$778$	30827.2	+	25510.3i	1.42058	+	1.17556i
$779$	−1735.16	−	1735.16i	−0.0798058	−	0.0798058i
$780$	−1222.34	+	14820.0i	−0.0561112	+	0.680310i
$781$	−30037.1	+	30037.1i	−1.37620	+	1.37620i
$782$	−674.907	−	7151.24i	−0.0308627	−	0.327018i
$783$	−2372.30	+	2372.30i	−0.108275	+	0.108275i
$784$	5827.68	+	14744.9i	0.265474	+	0.671689i
$785$	−7753.78	+	27963.4i	−0.352540	+	1.27141i
$786$	4024.83	+	3330.65i	0.182647	+	0.151145i
$787$	11916.9			0.539759			0.269880	−	0.962894i	$-0.413016\pi$
$787$	11916.9			0.539759			0.269880	+	0.962894i	$0.413016\pi$
$788$	19426.7	−	3699.79i	0.878234	−	0.167258i
$789$	−16595.3	+	16595.3i	−0.748805	+	0.748805i
$790$	5166.09	−	28983.5i	0.232660	−	1.30530i
$791$	12290.5			0.552464
$792$	−9333.69	−	5136.72i	−0.418761	−	0.230461i
$793$	11444.7	−	11444.7i	0.512501	−	0.512501i
$794$	17693.9	−	1669.88i	0.790846	−	0.0746370i
$795$	18205.0	+	5047.94i	0.812157	+	0.225197i
$796$	1509.14	+	7924.11i	0.0671984	+	0.352842i
$797$		−	18667.6i		−	0.829662i	−0.909899	−	0.414831i	$-0.863841\pi$
$797$		−	18667.6i		−	0.829662i	0.909899	−	0.414831i	$-0.136159\pi$
$798$	−54.9190	−	581.915i	−0.00243623	−	0.0258140i
$799$	−65796.3			−2.91327
$800$	−1593.63	+	22571.2i	−0.0704293	+	0.997517i
$801$	2117.10			0.0933882
$802$	−3510.73	−	37199.3i	−0.154574	−	1.63785i
$803$		−	28156.5i		−	1.23738i
$804$	−4434.08	−	23282.3i	−0.194500	−	1.02127i
$805$	2083.04	+	577.590i	0.0912017	+	0.0252887i
$806$	−40537.1	+	3825.74i	−1.77154	+	0.167191i
$807$	−2078.52	+	2078.52i	−0.0906657	+	0.0906657i
$808$	5791.45	−	10523.4i	0.252157	−	0.458182i
$809$	16746.1			0.727765			0.363883	−	0.931445i	$-0.381451\pi$
$809$	16746.1			0.727765			0.363883	+	0.931445i	$0.381451\pi$
$810$	−449.474	+	2521.70i	−0.0194974	+	0.109387i
$811$	−8756.96	+	8756.96i	−0.379160	+	0.379160i	−0.870799	−	0.491639i	$-0.836398\pi$
$811$	−8756.96	+	8756.96i	−0.379160	+	0.379160i	0.491639	+	0.870799i	$0.336398\pi$
$812$	9531.25	−	1815.22i	0.411923	−	0.0784502i
$813$	−3936.04			−0.169794
$814$	3207.65	+	2654.41i	0.138118	+	0.114296i
$815$	−6177.12	+	22277.3i	−0.265491	+	0.957472i
$816$	−22585.3	−	9789.64i	−0.968925	−	0.419983i
$817$	851.488	−	851.488i	0.0364624	−	0.0364624i
$818$	−493.623	−	5230.37i	−0.0210992	−	0.223564i
$819$	3442.37	−	3442.37i	0.146870	−	0.146870i
$820$	2556.39	−	30994.5i	0.108870	−	1.31997i
$821$	−7938.47	−	7938.47i	−0.337460	−	0.337460i	0.517951	−	0.855411i	$-0.326695\pi$
$821$	−7938.47	−	7938.47i	−0.337460	−	0.337460i	−0.855411	+	0.517951i	$0.826695\pi$
$822$	−16134.0	−	13351.3i	−0.684594	−	0.566519i
$823$	−8113.92	−	8113.92i	−0.343662	−	0.343662i	0.514080	−	0.857742i	$-0.328133\pi$
$823$	−8113.92	−	8113.92i	−0.343662	−	0.343662i	−0.857742	+	0.514080i	$0.828133\pi$
$824$	2628.77	−	4776.62i	0.111138	−	0.201943i
$825$	−4747.53	−	19035.1i	−0.200349	−	0.803293i
$826$	−195.380	−	2070.23i	−0.00823020	−	0.0872063i
$827$		−	11326.1i		−	0.476234i	−0.971236	−	0.238117i	$-0.923470\pi$
$827$		−	11326.1i		−	0.476234i	0.971236	−	0.238117i	$-0.0765302\pi$
$828$	1179.35	+	802.004i	0.0494991	+	0.0336613i
$829$	16343.8	+	16343.8i	0.684733	+	0.684733i	0.961063	−	0.276330i	$-0.0891182\pi$
$829$	16343.8	+	16343.8i	0.684733	+	0.684733i	−0.276330	+	0.961063i	$0.589118\pi$
$830$	−14497.1	−	2584.00i	−0.606268	−	0.108063i
$831$		−	9732.61i		−	0.406282i
$832$	23970.9	−	15182.1i	0.998847	−	0.632625i
$833$	−22458.3	−	22458.3i	−0.934133	−	0.934133i
$834$	18931.2	+	15666.1i	0.786013	+	0.650446i
$835$	31773.8	−	17978.4i	1.31686	−	0.745110i
$836$	552.590	+	2901.51i	0.0228609	+	0.120037i
$837$	−7013.63			−0.289637
$838$	−22269.6	−	18428.7i	−0.918008	−	0.759675i
$839$			20967.6i			0.862792i	0.902163	+	0.431396i	$0.141979\pi$
$839$			20967.6i			0.862792i	−0.902163	+	0.431396i	$0.858021\pi$
$840$	5175.87	−	5299.54i	0.212601	−	0.217680i
$841$		−	8949.16i		−	0.366934i
$842$	4316.77	−	5216.48i	0.176681	−	0.213506i
$843$	−3490.81			−0.142622
$844$	−4715.97	−	3207.04i	−0.192334	−	0.130795i
$845$	9418.59	+	2611.62i	0.383443	+	0.106322i
$846$	8328.86	−	10064.8i	0.338478	−	0.409024i
$847$	−9703.03	−	9703.03i	−0.393625	−	0.393625i
$848$	−13249.9	−	33524.4i	−0.536562	−	1.35759i
$849$		−	6933.60i		−	0.280283i
$850$	−15053.0	−	42755.4i	−0.607429	−	1.72529i
$851$	−394.117	−	394.117i	−0.0158756	−	0.0158756i
$852$	−3645.84	−	19143.4i	−0.146602	−	0.769769i
$853$		−	13976.2i		−	0.561003i	−0.959854	−	0.280502i	$-0.909499\pi$
$853$		−	13976.2i		−	0.561003i	0.959854	−	0.280502i	$-0.0905008\pi$
$854$	−8027.11	+	757.568i	−0.321642	+	0.0303553i
$855$	618.057	−	349.711i	0.0247218	−	0.0139882i
$856$	−20004.9	+	5802.19i	−0.798778	+	0.231676i
$857$	1618.40	+	1618.40i	0.0645081	+	0.0645081i	0.738625	−	0.674117i	$-0.235476\pi$
$857$	1618.40	+	1618.40i	0.0645081	+	0.0645081i	−0.674117	+	0.738625i	$0.735476\pi$
$858$	−15684.0	+	18952.9i	−0.624058	+	0.754126i
$859$	7773.93	+	7773.93i	0.308781	+	0.308781i	0.844437	−	0.535655i	$-0.179935\pi$
$859$	7773.93	+	7773.93i	0.308781	+	0.308781i	−0.535655	+	0.844437i	$0.679935\pi$
$860$	15209.8	+	1254.48i	0.603080	+	0.0497413i
$861$	−7199.35	+	7199.35i	−0.284963	+	0.284963i
$862$	27206.1	−	2567.61i	1.07499	−	0.101454i
$863$	−5364.02	+	5364.02i	−0.211580	+	0.211580i	−0.804938	−	0.593359i	$-0.797802\pi$
$863$	−5364.02	+	5364.02i	−0.211580	+	0.211580i	0.593359	+	0.804938i	$0.297802\pi$
$864$	4356.48	−	2215.62i	0.171540	−	0.0872416i
$865$	9937.99	+	2755.64i	0.390638	+	0.108317i
$866$	25673.3	−	31024.3i	1.00741	−	1.21738i
$867$	34571.8			1.35423
$868$	16772.7	+	11406.1i	0.655879	+	0.446023i
$869$	34439.4	−	34439.4i	1.34439	−	1.34439i
$870$	6743.41	+	9668.76i	0.262785	+	0.376784i
$871$	−54727.5			−2.12901
$872$	3724.08	−	6766.85i	0.144625	−	0.262792i
$873$	5411.82	−	5411.82i	0.209808	−	0.209808i
$874$	−37.1516	−	393.654i	−0.00143784	−	0.0152352i
$875$	13636.2	+	355.501i	0.526842	+	0.0137350i
$876$	10681.2	+	7263.64i	0.411969	+	0.280155i
$877$			2719.47i			0.104709i	0.998629	+	0.0523546i	$0.0166726\pi$
$877$			2719.47i			0.104709i	−0.998629	+	0.0523546i	$0.983327\pi$
$878$	−6369.51	+	601.130i	−0.244830	+	0.0231061i
$879$	−26156.6			−1.00369
$880$	−23523.4	+	29119.3i	−0.901105	+	1.11547i
$881$	23238.2			0.888667			0.444334	−	0.895861i	$-0.353440\pi$
$881$	23238.2			0.888667			0.444334	+	0.895861i	$0.353440\pi$
$882$	6278.31	−	592.523i	0.239684	−	0.0226205i
$883$		−	13582.3i		−	0.517644i	−0.965925	−	0.258822i	$-0.916666\pi$
$883$		−	13582.3i		−	0.517644i	0.965925	−	0.258822i	$-0.0833343\pi$
$884$	−31963.0	+	47001.8i	−1.21610	+	1.78828i
$885$	2198.81	−	1244.14i	0.0835165	−	0.0472556i
$886$	2109.17	+	22348.6i	0.0799764	+	0.847421i
$887$	−7139.38	+	7139.38i	−0.270256	+	0.270256i	−0.829203	−	0.558947i	$-0.811205\pi$
$887$	−7139.38	+	7139.38i	−0.270256	+	0.270256i	0.558947	+	0.829203i	$0.311205\pi$
$888$	−1834.45	+	532.060i	−0.0693245	+	0.0201067i
$889$	12288.6			0.463605
$890$	1305.32	−	7323.30i	0.0491624	−	0.275817i
$891$	−2996.39	+	2996.39i	−0.112663	+	0.112663i
$892$	−12682.7	+	18650.0i	−0.476064	+	0.700054i
$893$	−3621.88			−0.135724
$894$	16190.4	−	19564.8i	0.605691	−	0.731931i
$895$	−10331.6	+	5845.86i	−0.385863	+	0.218330i
$896$	−14021.5	−	1786.31i	−0.522796	−	0.0666033i
$897$	2328.69	−	2328.69i	0.0866809	−	0.0866809i
$898$	31819.8	−	3003.04i	1.18245	−	0.111595i
$899$	−22823.7	+	22823.7i	−0.846732	+	0.846732i
$900$	8445.74	+	3109.57i	0.312805	+	0.115169i
$901$	51061.6	+	51061.6i	1.88802	+	1.88802i
$902$	32801.4	−	39637.9i	1.21083	−	1.46319i
$903$	−3532.90	−	3532.90i	−0.130197	−	0.130197i
$904$	13737.6	−	24961.9i	0.505425	−	0.918384i
$905$	−10064.8	−	17787.9i	−0.369685	−	0.653357i
$906$	−14828.0	+	1399.41i	−0.543740	+	0.0513161i
$907$			8723.32i			0.319353i	0.987169	+	0.159676i	$0.0510451\pi$
$907$			8723.32i			0.319353i	−0.987169	+	0.159676i	$0.948955\pi$
$908$	−3308.12	+	630.027i	−0.120907	+	0.0230266i
$909$	−3378.30	−	3378.30i	−0.123269	−	0.123269i
$910$	−9785.14	−	14030.0i	−0.356455	−	0.511088i
$911$			34464.2i			1.25340i	0.779260	+	0.626701i	$0.215595\pi$
$911$			34464.2i			1.25340i	−0.779260	+	0.626701i	$0.784405\pi$
$912$	−1243.25	−	538.890i	−0.0451405	−	0.0195663i
$913$	−17226.1	−	17226.1i	−0.624425	−	0.624425i
$914$	−16273.7	+	19665.5i	−0.588935	+	0.711683i
$915$	−4824.02	−	8525.66i	−0.174292	−	0.308032i
$916$	5142.19	−	7561.62i	0.185483	−	0.272754i
$917$	−6009.39			−0.216410
$918$	−6242.04	+	7543.02i	−0.224420	+	0.271195i
$919$		−	31894.1i		−	1.14482i	−0.819968	−	0.572410i	$-0.806009\pi$
$919$		−	31894.1i		−	1.14482i	0.819968	−	0.572410i	$-0.193991\pi$
$920$	3501.37	−	3585.03i	0.125475	−	0.128473i
$921$			21067.2i			0.753733i
$922$	−1644.54	−	1360.90i	−0.0587420	−	0.0486105i
$923$	−44998.7			−1.60471
$924$	12038.6	−	2292.74i	0.428617	−	0.0816296i
$925$	−3014.98	−	1811.27i	−0.107170	−	0.0643828i
$926$	−28200.0	−	23336.2i	−1.00077	−	0.828159i
$927$	−1533.43	−	1533.43i	−0.0543307	−	0.0543307i
$928$	6966.77	−	21386.8i	0.246439	−	0.756527i
$929$			47373.4i			1.67306i	0.547924	+	0.836528i	$0.315418\pi$
$929$			47373.4i			1.67306i	−0.547924	+	0.836528i	$0.684582\pi$
$930$	−4324.34	+	24261.0i	−0.152474	+	0.855429i
$931$	−1236.26	−	1236.26i	−0.0435196	−	0.0435196i
$932$	−15959.4	+	23468.4i	−0.560909	+	0.824819i
$933$		−	27982.7i		−	0.981900i
$934$	−2973.21	−	31503.8i	−0.104161	−	1.10368i
$935$	20037.0	−	72261.7i	0.700833	−	2.52750i
$936$	−3143.75	−	10839.1i	−0.109783	−	0.378512i
$937$	36520.6	+	36520.6i	1.27329	+	1.27329i	0.944350	+	0.328943i	$0.106693\pi$
$937$	36520.6	+	36520.6i	1.27329	+	1.27329i	0.328943	+	0.944350i	$0.393307\pi$
$938$	21003.8	+	17381.1i	0.731127	+	0.605026i
$939$	12889.1	+	12889.1i	0.447944	+	0.447944i
$940$	−29680.0	−	35016.1i	−1.02985	−	1.21500i
$941$	−14693.8	+	14693.8i	−0.509038	+	0.509038i	−0.914231	−	0.405193i	$-0.867204\pi$
$941$	−14693.8	+	14693.8i	−0.509038	+	0.509038i	0.405193	+	0.914231i	$0.367204\pi$
$942$	−2069.30	−	21926.0i	−0.0715726	−	0.758375i
$943$	−4870.22	+	4870.22i	−0.168182	+	0.168182i
$944$	−4423.00	−	1917.16i	−0.152496	−	0.0660998i
$945$	−1450.98	−	2564.37i	−0.0499476	−	0.0882742i
$946$	19451.3	+	16096.4i	0.668516	+	0.553214i
$947$	−26142.0			−0.897043			−0.448522	−	0.893772i	$-0.648049\pi$
$947$	−26142.0			−0.897043			−0.448522	+	0.893772i	$0.648049\pi$
$948$	4180.18	+	21949.1i	0.143213	+	0.751977i
$949$	21090.7	−	21090.7i	0.721424	−	0.721424i
$950$	−828.623	−	2353.55i	−0.0282990	−	0.0803783i
$951$	17777.5			0.606178
$952$	27194.5	−	7887.45i	0.925819	−	0.268523i
$953$	641.156	−	641.156i	0.0217934	−	0.0217934i	−0.696126	−	0.717920i	$-0.745095\pi$
$953$	641.156	−	641.156i	0.0217934	−	0.0217934i	0.717920	+	0.696126i	$0.245095\pi$
$954$	−14274.5	+	1347.17i	−0.484438	+	0.0457194i
$955$	−3769.77	+	13595.4i	−0.127735	+	0.460667i
$956$	5562.74	−	1059.42i	0.188192	−	0.0358410i
$957$			19501.6i			0.658722i
$958$	−1898.22	−	20113.4i	−0.0640176	−	0.678323i
$959$	24089.3			0.811140
$960$	−4978.04	−	16435.7i	−0.167360	−	0.552561i
$961$	−37686.3			−1.26502
$962$	414.406	+	4391.00i	0.0138887	+	0.147164i
$963$			8284.83i			0.277232i
$964$	−4168.90	+	793.962i	−0.139286	+	0.0265268i
$965$	−15615.4	−	27597.7i	−0.520911	−	0.920624i
$966$	−1633.30	+	154.145i	−0.0544003	+	0.00513410i
$967$	−12866.4	+	12866.4i	−0.427876	+	0.427876i	−0.887904	−	0.460028i	$-0.847839\pi$
$967$	−12866.4	+	12866.4i	−0.427876	+	0.427876i	0.460028	+	0.887904i	$0.347839\pi$
$968$	−30552.2	+	8861.31i	−1.01445	+	0.294229i
$969$	2714.41			0.0899891
$970$	−15383.4	−	22056.9i	−0.509208	−	0.730107i
$971$	−21087.0	+	21087.0i	−0.696926	+	0.696926i	−0.963746	−	0.266820i	$-0.914027\pi$
$971$	−21087.0	+	21087.0i	−0.696926	+	0.696926i	0.266820	+	0.963746i	$0.414027\pi$
$972$	−363.695	−	1909.68i	−0.0120016	−	0.0630174i
$973$	−28265.8			−0.931306
$974$	−21605.3	−	17879.0i	−0.710759	−	0.588171i
$975$	10702.1	−	17814.4i	0.351530	−	0.585147i
$976$	−7433.61	+	17149.8i	−0.243795	+	0.562449i
$977$	−36173.3	+	36173.3i	−1.18453	+	1.18453i	−0.205972	+	0.978558i	$0.566036\pi$
$977$	−36173.3	+	36173.3i	−1.18453	+	1.18453i	−0.978558	+	0.205972i	$0.933964\pi$
$978$	−1648.53	−	17467.6i	−0.0538998	−	0.571117i
$979$	8701.84	−	8701.84i	0.284077	−	0.284077i
$980$	1821.36	−	22082.8i	0.0593686	−	0.719804i
$981$	−2172.35	−	2172.35i	−0.0707012	−	0.0707012i
$982$	−33975.1	−	28115.2i	−1.10406	−	0.913638i
$983$	−3420.13	−	3420.13i	−0.110972	−	0.110972i	0.649441	−	0.760412i	$-0.275003\pi$
$983$	−3420.13	−	3420.13i	−0.110972	−	0.110972i	−0.760412	+	0.649441i	$0.775003\pi$
$984$	6574.82	+	22668.8i	0.213006	+	0.734406i
$985$	−26632.8	−	7384.81i	−0.861513	−	0.238883i
$986$	4233.64	+	44859.2i	0.136741	+	1.44889i
$987$			15027.5i			0.484631i
$988$	−1759.47	+	2587.30i	−0.0566560	+	0.0833129i
$989$	−2389.93	−	2389.93i	−0.0768407	−	0.0768407i
$990$	8517.40	+	12212.3i	0.273435	+	0.392054i
$991$			14248.8i			0.456738i	0.973575	+	0.228369i	$0.0733392\pi$
$991$			14248.8i			0.456738i	−0.973575	+	0.228369i	$0.926661\pi$
$992$	41913.2	−	21316.2i	1.34148	−	0.682248i
$993$	−3521.85	−	3521.85i	−0.112550	−	0.112550i
$994$	17270.0	+	14291.3i	0.551076	+	0.456030i
$995$	3012.25	−	10863.4i	0.0959745	−	0.346125i
$996$	10978.6	−	2090.87i	0.349268	−	0.0665177i
$997$	−16112.5			−0.511825			−0.255912	−	0.966700i	$-0.582376\pi$
$997$	−16112.5			−0.511825			−0.255912	+	0.966700i	$0.582376\pi$
$998$	34731.0	+	28740.8i	1.10159	+	0.911596i
$999$			759.718i			0.0240605i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.4.bc.a.43.20	yes	72
5.2	odd	4		240.4.y.b.187.2	yes	72
16.3	odd	4		240.4.y.b.163.2	✓	72
80.67	even	4	inner	240.4.bc.a.67.20	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.4.y.b.163.2	✓	72	16.3	odd	4
240.4.y.b.187.2	yes	72	5.2	odd	4
240.4.bc.a.43.20	yes	72	1.1	even	1	trivial
240.4.bc.a.67.20	yes	72	80.67	even	4	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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	240.bc (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.265755 + 2.81591i) q^{2} +3.00000i q^{3} +(-7.85875 + 1.49669i) q^{4} +(10.7738 + 2.98740i) q^{5} +(-8.44774 + 0.797266i) q^{6} +(6.90177 - 6.90177i) q^{7} +(-6.30305 - 21.7318i) q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+(0.265755 + 2.81591i) q^{2} +3.00000i q^{3} +(-7.85875 + 1.49669i) q^{4} +(10.7738 + 2.98740i) q^{5} +(-8.44774 + 0.797266i) q^{6} +(6.90177 - 6.90177i) q^{7} +(-6.30305 - 21.7318i) q^{8} -9.00000 q^{9} +(-5.54906 + 31.1321i) q^{10} +(-36.9924 + 36.9924i) q^{11} +(-4.49007 - 23.5762i) q^{12} -55.4185 q^{13} +(21.2690 + 17.6006i) q^{14} +(-8.96220 + 32.3215i) q^{15} +(59.5198 - 23.5242i) q^{16} +(-90.6558 + 90.6558i) q^{17} +(-2.39180 - 25.3432i) q^{18} +(-4.99032 + 4.99032i) q^{19} +(-89.1400 - 7.35217i) q^{20} +(20.7053 + 20.7053i) q^{21} +(-113.998 - 94.3365i) q^{22} +(14.0067 + 14.0067i) q^{23} +(65.1954 - 18.9092i) q^{24} +(107.151 + 64.3715i) q^{25} +(-14.7278 - 156.054i) q^{26} -27.0000i q^{27} +(-43.9094 + 64.5690i) q^{28} +(-87.8631 - 87.8631i) q^{29} +(-93.3963 - 16.6472i) q^{30} -259.764i q^{31} +(82.0598 + 161.351i) q^{32} +(-110.977 - 110.977i) q^{33} +(-279.371 - 231.187i) q^{34} +(94.9768 - 53.7401i) q^{35} +(70.7287 - 13.4702i) q^{36} -28.1377 q^{37} +(-15.3785 - 12.7261i) q^{38} -166.255i q^{39} +(-2.98637 - 252.965i) q^{40} +347.706i q^{41} +(-52.8018 + 63.8069i) q^{42} -170.628 q^{43} +(235.348 - 346.080i) q^{44} +(-96.9645 - 26.8866i) q^{45} +(-35.7193 + 43.1641i) q^{46} +(362.891 + 362.891i) q^{47} +(70.5726 + 178.560i) q^{48} +247.731i q^{49} +(-152.789 + 318.835i) q^{50} +(-271.967 - 271.967i) q^{51} +(435.520 - 82.9442i) q^{52} -563.247i q^{53} +(76.0297 - 7.17539i) q^{54} +(-509.061 + 288.039i) q^{55} +(-193.490 - 106.486i) q^{56} +(-14.9710 - 14.9710i) q^{57} +(224.065 - 270.765i) q^{58} +(-53.2609 - 53.2609i) q^{59} +(22.0565 - 267.420i) q^{60} +(-206.514 + 206.514i) q^{61} +(731.473 - 69.0337i) q^{62} +(-62.1159 + 62.1159i) q^{63} +(-432.543 + 273.953i) q^{64} +(-597.070 - 165.557i) q^{65} +(283.010 - 341.995i) q^{66} +987.531 q^{67} +(576.757 - 848.124i) q^{68} +(-42.0201 + 42.0201i) q^{69} +(176.568 + 253.165i) q^{70} +811.980 q^{71} +(56.7275 + 195.586i) q^{72} +(-380.571 + 380.571i) q^{73} +(-7.47775 - 79.2334i) q^{74} +(-193.115 + 321.453i) q^{75} +(31.7487 - 46.6867i) q^{76} +510.626i q^{77} +(468.161 - 44.1833i) q^{78} -930.985 q^{79} +(711.533 - 75.6361i) q^{80} +81.0000 q^{81} +(-979.110 + 92.4047i) q^{82} +465.665i q^{83} +(-193.707 - 131.728i) q^{84} +(-1247.54 + 705.885i) q^{85} +(-45.3452 - 480.473i) q^{86} +(263.589 - 263.589i) q^{87} +(1037.08 + 570.747i) q^{88} -235.233 q^{89} +(49.9416 - 280.189i) q^{90} +(-382.486 + 382.486i) q^{91} +(-131.039 - 89.1115i) q^{92} +779.292 q^{93} +(-925.429 + 1118.31i) q^{94} +(-68.6730 + 38.8568i) q^{95} +(-484.053 + 246.180i) q^{96} +(-601.313 + 601.313i) q^{97} +(-697.590 + 65.8359i) q^{98} +(332.932 - 332.932i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{2} - 10 q^{4} - 80 q^{8} - 648 q^{9}+O(q^{10}) \) 72 * q - 2 * q^2 - 10 * q^4 - 80 * q^8 - 648 * q^9	\( 72 q - 2 q^{2} - 10 q^{4} - 80 q^{8} - 648 q^{9} + 12 q^{12} - 110 q^{14} - 22 q^{16} - 124 q^{17} + 18 q^{18} + 12 q^{19} + 100 q^{20} - 238 q^{22} - 88 q^{23} + 126 q^{24} - 184 q^{25} + 12 q^{26} + 102 q^{28} - 282 q^{30} + 468 q^{32} - 186 q^{34} + 228 q^{35} + 90 q^{36} + 238 q^{38} - 882 q^{40} + 18 q^{42} - 432 q^{43} + 1770 q^{44} + 1106 q^{46} + 896 q^{47} - 432 q^{48} + 274 q^{50} - 372 q^{51} - 1272 q^{52} + 688 q^{55} + 622 q^{56} + 36 q^{57} - 246 q^{58} - 688 q^{59} - 570 q^{60} + 2552 q^{61} + 836 q^{62} - 634 q^{64} + 340 q^{65} + 750 q^{66} - 1848 q^{67} + 478 q^{68} + 264 q^{69} + 2458 q^{70} + 224 q^{71} + 720 q^{72} + 296 q^{73} + 1040 q^{74} - 552 q^{75} - 3766 q^{76} - 516 q^{78} + 928 q^{79} + 872 q^{80} + 5832 q^{81} - 472 q^{82} + 270 q^{84} - 3424 q^{85} - 1844 q^{86} + 2334 q^{88} - 1968 q^{89} - 848 q^{91} + 818 q^{92} - 792 q^{93} - 310 q^{94} - 1240 q^{95} - 510 q^{96} - 1176 q^{97} + 2812 q^{98}+O(q^{100}) \) 72 * q - 2 * q^2 - 10 * q^4 - 80 * q^8 - 648 * q^9 + 12 * q^12 - 110 * q^14 - 22 * q^16 - 124 * q^17 + 18 * q^18 + 12 * q^19 + 100 * q^20 - 238 * q^22 - 88 * q^23 + 126 * q^24 - 184 * q^25 + 12 * q^26 + 102 * q^28 - 282 * q^30 + 468 * q^32 - 186 * q^34 + 228 * q^35 + 90 * q^36 + 238 * q^38 - 882 * q^40 + 18 * q^42 - 432 * q^43 + 1770 * q^44 + 1106 * q^46 + 896 * q^47 - 432 * q^48 + 274 * q^50 - 372 * q^51 - 1272 * q^52 + 688 * q^55 + 622 * q^56 + 36 * q^57 - 246 * q^58 - 688 * q^59 - 570 * q^60 + 2552 * q^61 + 836 * q^62 - 634 * q^64 + 340 * q^65 + 750 * q^66 - 1848 * q^67 + 478 * q^68 + 264 * q^69 + 2458 * q^70 + 224 * q^71 + 720 * q^72 + 296 * q^73 + 1040 * q^74 - 552 * q^75 - 3766 * q^76 - 516 * q^78 + 928 * q^79 + 872 * q^80 + 5832 * q^81 - 472 * q^82 + 270 * q^84 - 3424 * q^85 - 1844 * q^86 + 2334 * q^88 - 1968 * q^89 - 848 * q^91 + 818 * q^92 - 792 * q^93 - 310 * q^94 - 1240 * q^95 - 510 * q^96 - 1176 * q^97 + 2812 * q^98

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