LMFDB - Embedded newform 230.4.l.a.7.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,4,Mod(7,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.7"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.5704393013$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			7.9
Character	$\chi$	$=$	230.7
Dual form			230.4.l.a.33.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.99490 + 0.142678i) q^{2} +(-0.143842 + 0.661230i) q^{3} +(3.95929 - 0.569259i) q^{4} +(10.6128 - 3.51689i) q^{5} +(0.192607 - 1.33961i) q^{6} +(-7.16158 + 13.1154i) q^{7} +(-7.81717 + 1.70052i) q^{8} +(24.1435 + 11.0260i) q^{9} +(-20.6697 + 8.53008i) q^{10} +(24.5384 - 21.2626i) q^{11} +(-0.193099 + 2.69988i) q^{12} +(-36.6808 + 20.0292i) q^{13} +(12.4154 - 27.1859i) q^{14} +(0.798912 + 7.52337i) q^{15} +(15.3519 - 4.50772i) q^{16} +(9.48612 + 12.6720i) q^{17} +(-49.7372 - 18.5510i) q^{18} +(8.10752 + 56.3890i) q^{19} +(40.0171 - 19.9658i) q^{20} +(-7.64219 - 6.62200i) q^{21} +(-45.9180 + 45.9180i) q^{22} +(-10.4325 - 109.810i) q^{23} -5.41355i q^{24} +(100.263 - 74.6482i) q^{25} +(70.3169 - 45.1899i) q^{26} +(-21.7128 + 29.0049i) q^{27} +(-20.8886 + 56.0046i) q^{28} +(34.0703 + 4.89857i) q^{29} +(-2.66718 - 14.8944i) q^{30} +(79.8548 + 51.3195i) q^{31} +(-29.9824 + 11.1829i) q^{32} +(10.5298 + 19.2840i) q^{33} +(-20.7319 - 23.9259i) q^{34} +(-29.8787 + 164.378i) q^{35} +(101.868 + 29.9111i) q^{36} +(149.001 + 399.487i) q^{37} +(-24.2192 - 111.334i) q^{38} +(-7.96769 - 27.1355i) q^{39} +(-76.9815 + 45.5395i) q^{40} +(101.452 + 222.149i) q^{41} +(16.1903 + 12.1199i) q^{42} +(9.81886 + 2.13596i) q^{43} +(85.0506 - 98.1536i) q^{44} +(295.008 + 32.1063i) q^{45} +(36.4793 + 217.571i) q^{46} +(180.757 + 180.757i) q^{47} +(0.772397 + 10.7995i) q^{48} +(64.7130 + 100.695i) q^{49} +(-189.364 + 163.221i) q^{50} +(-9.74359 + 4.44975i) q^{51} +(-133.828 + 100.182i) q^{52} +(612.918 + 334.679i) q^{53} +(39.1766 - 60.9600i) q^{54} +(185.643 - 311.955i) q^{55} +(33.6802 - 114.704i) q^{56} +(-38.4523 - 2.75016i) q^{57} +(-68.6659 - 4.91108i) q^{58} +(21.1230 - 71.9384i) q^{59} +(7.44587 + 29.3324i) q^{60} +(69.9852 - 108.899i) q^{61} +(-166.625 - 90.9840i) q^{62} +(-317.516 + 237.690i) q^{63} +(58.2164 - 26.5866i) q^{64} +(-318.845 + 341.569i) q^{65} +(-23.7574 - 36.9673i) q^{66} +(-65.5355 - 916.306i) q^{67} +(44.7719 + 44.7719i) q^{68} +(74.1100 + 8.89694i) q^{69} +(36.1520 - 332.182i) q^{70} +(372.219 - 429.563i) q^{71} +(-207.484 - 45.1354i) q^{72} +(-437.058 - 327.177i) q^{73} +(-354.240 - 775.678i) q^{74} +(34.9376 + 77.0343i) q^{75} +(64.1999 + 218.645i) q^{76} +(103.135 + 474.106i) q^{77} +(19.7664 + 52.9958i) q^{78} +(-307.002 - 90.1439i) q^{79} +(147.073 - 101.830i) q^{80} +(453.241 + 523.068i) q^{81} +(-234.083 - 428.691i) q^{82} +(-1274.02 + 475.186i) q^{83} +(-34.0272 - 21.8680i) q^{84} +(145.240 + 101.123i) q^{85} +(-19.8924 - 2.86010i) q^{86} +(-8.13981 + 21.8237i) q^{87} +(-155.663 + 207.942i) q^{88} +(211.363 - 135.834i) q^{89} +(-593.093 - 21.9577i) q^{90} -624.526i q^{91} +(-103.815 - 428.829i) q^{92} +(-45.4204 + 45.4204i) q^{93} +(-386.383 - 334.803i) q^{94} +(284.358 + 569.932i) q^{95} +(-3.08172 - 21.4338i) q^{96} +(-605.095 - 225.689i) q^{97} +(-143.463 - 191.645i) q^{98} +(826.885 - 242.795i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q + 16 q^{3} + 16 q^{6} + 64 q^{12} - 192 q^{13} + 1152 q^{16} + 144 q^{18} + 1660 q^{23} - 880 q^{25} - 304 q^{26} - 728 q^{27} - 352 q^{28} - 608 q^{31} - 3872 q^{33} - 688 q^{35} - 2816 q^{36} - 2376 q^{37}+ \cdots + 14352 q^{98}+O(q^{100}) $ 720 * q + 16 * q^3 + 16 * q^6 + 64 * q^12 - 192 * q^13 + 1152 * q^16 + 144 * q^18 + 1660 * q^23 - 880 * q^25 - 304 * q^26 - 728 * q^27 - 352 * q^28 - 608 * q^31 - 3872 * q^33 - 688 * q^35 - 2816 * q^36 - 2376 * q^37 + 2208 * q^41 + 256 * q^46 + 3640 * q^47 - 256 * q^48 - 272 * q^50 - 768 * q^52 + 2360 * q^55 - 3872 * q^56 - 7656 * q^57 + 2112 * q^61 + 1376 * q^62 + 10912 * q^66 + 1104 * q^70 + 22752 * q^71 - 128 * q^72 + 1296 * q^73 - 5396 * q^75 + 752 * q^77 - 6000 * q^78 - 3928 * q^81 - 80 * q^82 + 3060 * q^85 - 10472 * q^86 - 6760 * q^87 - 1104 * q^92 + 5288 * q^93 + 9392 * q^95 - 256 * q^96 + 25344 * q^97 + 14352 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{19}{22}\right)$

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 $

$2$	−1.99490	+	0.142678i	−0.705305	+	0.0504444i
$2$	−1.99490	+	0.142678i	−0.705305	+	0.0504444i
$3$	−0.143842	+	0.661230i	−0.0276824	+	0.127254i	−0.988914	−	0.148487i	$-0.952560\pi$
$3$	−0.143842	+	0.661230i	−0.0276824	+	0.127254i	0.961232	+	0.275741i	$0.0889232\pi$
$4$	3.95929	−	0.569259i	0.494911	−	0.0711574i
$5$	10.6128	−	3.51689i	0.949237	−	0.314561i
$5$	10.6128	−	3.51689i	0.949237	−	0.314561i
$6$	0.192607	−	1.33961i	0.0131053	−	0.0911491i
$7$	−7.16158	+	13.1154i	−0.386689	+	0.708168i	−0.996429	−	0.0844336i	$-0.973092\pi$
$7$	−7.16158	+	13.1154i	−0.386689	+	0.708168i	0.609740	+	0.792601i	$0.291274\pi$
$8$	−7.81717	+	1.70052i	−0.345474	+	0.0751532i
$9$	24.1435	+	11.0260i	0.894205	+	0.408370i
$10$	−20.6697	+	8.53008i	−0.653634	+	0.269745i
$11$	24.5384	−	21.2626i	0.672601	−	0.582812i	−0.250151	−	0.968207i	$-0.580480\pi$
$11$	24.5384	−	21.2626i	0.672601	−	0.582812i	0.922752	+	0.385395i	$0.125935\pi$
$12$	−0.193099	+	2.69988i	−0.00464525	+	0.0649490i
$13$	−36.6808	+	20.0292i	−0.782571	+	0.427316i	−0.820272	−	0.571973i	$-0.806178\pi$
$13$	−36.6808	+	20.0292i	−0.782571	+	0.427316i	0.0377015	+	0.999289i	$0.487996\pi$
$14$	12.4154	−	27.1859i	0.237010	−	0.518981i
$15$	0.798912	+	7.52337i	0.0137519	+	0.129502i
$16$	15.3519	−	4.50772i	0.239873	−	0.0704331i
$17$	9.48612	+	12.6720i	0.135337	+	0.180789i	0.863090	−	0.505051i	$-0.168526\pi$
$17$	9.48612	+	12.6720i	0.135337	+	0.180789i	−0.727753	+	0.685839i	$0.759435\pi$
$18$	−49.7372	−	18.5510i	−0.651287	−	0.242918i
$19$	8.10752	+	56.3890i	0.0978943	+	0.680870i	0.978383	+	0.206802i	$0.0663057\pi$
$19$	8.10752	+	56.3890i	0.0978943	+	0.680870i	−0.880488	+	0.474068i	$0.842785\pi$
$20$	40.0171	−	19.9658i	0.447404	−	0.223225i
$21$	−7.64219	−	6.62200i	−0.0794125	−	0.0688113i
$22$	−45.9180	+	45.9180i	−0.444989	+	0.444989i
$23$	−10.4325	−	109.810i	−0.0945793	−	0.995517i
$23$	−10.4325	−	109.810i	−0.0945793	−	0.995517i
$24$		−	5.41355i		−	0.0460432i
$25$	100.263	−	74.6482i	0.802103	−	0.597185i
$26$	70.3169	−	45.1899i	0.530396	−	0.340865i
$27$	−21.7128	+	29.0049i	−0.154764	+	0.206741i
$28$	−20.8886	+	56.0046i	−0.140985	+	0.377996i
$29$	34.0703	+	4.89857i	0.218162	+	0.0313670i	0.250529	−	0.968109i	$-0.419395\pi$
$29$	34.0703	+	4.89857i	0.218162	+	0.0313670i	−0.0323670	+	0.999476i	$0.510305\pi$
$30$	−2.66718	−	14.8944i	−0.0162319	−	0.0906446i
$31$	79.8548	+	51.3195i	0.462656	+	0.297331i	0.751127	−	0.660158i	$-0.229511\pi$
$31$	79.8548	+	51.3195i	0.462656	+	0.297331i	−0.288471	+	0.957489i	$0.593147\pi$
$32$	−29.9824	+	11.1829i	−0.165631	+	0.0617771i
$33$	10.5298	+	19.2840i	0.0555458	+	0.101725i
$34$	−20.7319	−	23.9259i	−0.104573	−	0.120684i
$35$	−29.8787	+	164.378i	−0.144298	+	0.793856i
$36$	101.868	+	29.9111i	0.471610	+	0.138477i
$37$	149.001	+	399.487i	0.662043	+	1.77501i	0.631378	+	0.775476i	$0.282490\pi$
$37$	149.001	+	399.487i	0.662043	+	1.77501i	0.0306652	+	0.999530i	$0.490237\pi$
$38$	−24.2192	−	111.334i	−0.103391	−	0.475283i
$39$	−7.96769	−	27.1355i	−0.0327142	−	0.111414i
$40$	−76.9815	+	45.5395i	−0.304296	+	0.180011i
$41$	101.452	+	222.149i	0.386443	+	0.846192i	0.998467	+	0.0553530i	$0.0176284\pi$
$41$	101.452	+	222.149i	0.386443	+	0.846192i	−0.612024	+	0.790839i	$0.709644\pi$
$42$	16.1903	+	12.1199i	0.0594812	+	0.0445271i
$43$	9.81886	+	2.13596i	0.0348224	+	0.00757514i	0.229943	−	0.973204i	$-0.426146\pi$
$43$	9.81886	+	2.13596i	0.0348224	+	0.00757514i	−0.195120	+	0.980779i	$0.562510\pi$
$44$	85.0506	−	98.1536i	0.291406	−	0.336300i
$45$	295.008	+	32.1063i	0.977270	+	0.106358i
$46$	36.4793	+	217.571i	0.116926	+	0.697373i
$47$	180.757	+	180.757i	0.560982	+	0.560982i	0.929586	−	0.368604i	$-0.120164\pi$
$47$	180.757	+	180.757i	0.560982	+	0.560982i	−0.368604	+	0.929586i	$0.620164\pi$
$48$	0.772397	+	10.7995i	0.00232262	+	0.0324745i
$49$	64.7130	+	100.695i	0.188668	+	0.293573i
$50$	−189.364	+	163.221i	−0.535603	+	0.461660i
$51$	−9.74359	+	4.44975i	−0.0267524	+	0.0122174i
$52$	−133.828	+	100.182i	−0.356896	+	0.267169i
$53$	612.918	+	334.679i	1.58851	+	0.867390i	0.998185	+	0.0602212i	$0.0191806\pi$
$53$	612.918	+	334.679i	1.58851	+	0.867390i	0.590321	+	0.807169i	$0.299001\pi$
$54$	39.1766	−	60.9600i	0.0987270	−	0.153622i
$55$	185.643	−	311.955i	0.455128	−	0.764800i
$56$	33.6802	−	114.704i	0.0803697	−	0.273714i
$57$	−38.4523	−	2.75016i	−0.0893532	−	0.00639066i
$58$	−68.6659	−	4.91108i	−0.155453	−	0.0111182i
$59$	21.1230	−	71.9384i	0.0466099	−	0.158739i	−0.932900	−	0.360136i	$-0.882730\pi$
$59$	21.1230	−	71.9384i	0.0466099	−	0.158739i	0.979510	+	0.201398i	$0.0645483\pi$
$60$	7.44587	+	29.3324i	0.0160210	+	0.0631133i
$61$	69.9852	−	108.899i	0.146896	−	0.228575i	−0.760006	−	0.649916i	$-0.774804\pi$
$61$	69.9852	−	108.899i	0.146896	−	0.228575i	0.906902	+	0.421341i	$0.138440\pi$
$62$	−166.625	−	90.9840i	−0.341312	−	0.186371i
$63$	−317.516	+	237.690i	−0.634973	+	0.475335i
$64$	58.2164	−	26.5866i	0.113704	−	0.0519269i
$65$	−318.845	+	341.569i	−0.608429	+	0.651790i
$66$	−23.7574	−	36.9673i	−0.0443082	−	0.0689448i
$67$	−65.5355	−	916.306i	−0.119499	−	1.67081i	−0.604731	−	0.796430i	$-0.706720\pi$
$67$	−65.5355	−	916.306i	−0.119499	−	1.67081i	0.485232	−	0.874385i	$-0.338735\pi$
$68$	44.7719	+	44.7719i	0.0798440	+	0.0798440i
$69$	74.1100	+	8.89694i	0.129301	+	0.0155227i
$70$	36.1520	−	332.182i	0.0617284	−	0.567190i
$71$	372.219	−	429.563i	0.622173	−	0.718025i	−0.353945	−	0.935266i	$-0.615160\pi$
$71$	372.219	−	429.563i	0.622173	−	0.718025i	0.976118	+	0.217241i	$0.0697056\pi$
$72$	−207.484	−	45.1354i	−0.339614	−	0.0738786i
$73$	−437.058	−	327.177i	−0.700736	−	0.524565i	0.188466	−	0.982080i	$-0.439649\pi$
$73$	−437.058	−	327.177i	−0.700736	−	0.524565i	−0.889202	+	0.457515i	$0.848740\pi$
$74$	−354.240	−	775.678i	−0.556481	−	1.21852i
$75$	34.9376	+	77.0343i	0.0537899	+	0.118602i
$76$	64.1999	+	218.645i	0.0968979	+	0.330004i
$77$	103.135	+	474.106i	0.152641	+	0.701681i
$78$	19.7664	+	52.9958i	0.0286937	+	0.0769307i
$79$	−307.002	−	90.1439i	−0.437221	−	0.128380i	0.0557123	−	0.998447i	$-0.482257\pi$
$79$	−307.002	−	90.1439i	−0.437221	−	0.128380i	−0.492933	+	0.870067i	$0.664075\pi$
$80$	147.073	−	101.830i	0.205541	−	0.142312i
$81$	453.241	+	523.068i	0.621730	+	0.717515i
$82$	−234.083	−	428.691i	−0.315246	−	0.577330i
$83$	−1274.02	+	475.186i	−1.68484	+	0.628414i	−0.995390	−	0.0959149i	$-0.969422\pi$
$83$	−1274.02	+	475.186i	−1.68484	+	0.628414i	−0.689454	+	0.724329i	$0.742150\pi$
$84$	−34.0272	−	21.8680i	−0.0441985	−	0.0284047i
$85$	145.240	+	101.123i	0.185336	+	0.129040i
$86$	−19.8924	−	2.86010i	−0.0249425	−	0.00358619i
$87$	−8.13981	+	21.8237i	−0.0100308	+	0.0268936i
$88$	−155.663	+	207.942i	−0.188566	+	0.251894i
$89$	211.363	−	135.834i	0.251735	−	0.161780i	−0.408688	−	0.912674i	$-0.634014\pi$
$89$	211.363	−	135.834i	0.251735	−	0.161780i	0.660423	+	0.750894i	$0.270377\pi$
$90$	−593.093	−	21.9577i	−0.694638	−	0.0257172i
$91$		−	624.526i		−	0.719430i
$92$	−103.815	−	428.829i	−0.117647	−	0.485962i
$93$	−45.4204	+	45.4204i	−0.0506439	+	0.0506439i
$94$	−386.383	−	334.803i	−0.423962	−	0.367365i
$95$	284.358	+	569.932i	0.307100	+	0.615513i
$96$	−3.08172	−	21.4338i	−0.00327632	−	0.0227873i
$97$	−605.095	−	225.689i	−0.633382	−	0.236239i	0.0122057	−	0.999926i	$-0.496115\pi$
$97$	−605.095	−	225.689i	−0.633382	−	0.236239i	−0.645588	+	0.763686i	$0.723387\pi$
$98$	−143.463	−	191.645i	−0.147877	−	0.197541i
$99$	826.885	−	242.795i	0.839445	−	0.246483i
$100$	354.475	−	352.629i	0.354475	−	0.352629i
$101$	−100.502	+	220.070i	−0.0990136	+	0.216810i	−0.952656	−	0.304050i	$-0.901661\pi$
$101$	−100.502	+	220.070i	−0.0990136	+	0.216810i	0.853643	+	0.520859i	$0.174388\pi$
$102$	18.8026	−	10.2670i	0.0182523	−	0.00996653i
$103$	−89.8632	+	1256.45i	−0.0859659	+	1.20196i	0.753091	+	0.657916i	$0.228562\pi$
$103$	−89.8632	+	1256.45i	−0.0859659	+	1.20196i	−0.839057	+	0.544044i	$0.816893\pi$
$104$	252.680	−	218.948i	0.238243	−	0.206439i
$105$	−104.394	−	43.4011i	−0.0970266	−	0.0403382i
$106$	−1270.46	−	580.202i	−1.16414	−	0.531643i
$107$	470.856	−	102.428i	0.425415	−	0.0925433i	0.00523946	−	0.999986i	$-0.498332\pi$
$107$	470.856	−	102.428i	0.425415	−	0.0925433i	0.420175	+	0.907443i	$0.361969\pi$
$108$	−69.4559	+	127.199i	−0.0618833	+	0.113331i
$109$	308.099	−	2142.88i	0.270739	−	1.88303i	−0.170073	−	0.985431i	$-0.554400\pi$
$109$	308.099	−	2142.88i	0.270739	−	1.88303i	0.440812	−	0.897599i	$-0.354691\pi$
$110$	−325.830	+	648.808i	−0.282424	+	0.562376i
$111$	−285.585	+	41.0609i	−0.244203	+	0.0351111i
$112$	−50.8229	+	233.629i	−0.0428778	+	0.197106i
$113$	−1010.39	+	72.2648i	−0.841150	+	0.0601602i	−0.485262	−	0.874369i	$-0.661276\pi$
$113$	−1010.39	+	72.2648i	−0.841150	+	0.0601602i	−0.355887	+	0.934529i	$0.615821\pi$
$114$	77.1010			0.0633436
$115$	−496.907	−	1128.70i	−0.402929	−	0.915231i
$116$	137.683			0.110203
$117$	−1106.45	+	79.1346i	−0.874282	+	0.0625299i
$118$	−31.8744	+	146.524i	−0.0248667	+	0.114310i
$119$	−234.134	+	33.6634i	−0.180362	+	0.0259321i
$120$	−19.0389	−	57.4530i	−0.0144834	−	0.0437059i
$121$	−39.3880	+	273.950i	−0.0295928	+	0.205823i
$122$	−124.076	+	227.229i	−0.0920765	+	0.168626i
$123$	−161.485	+	35.1289i	−0.118379	+	0.0257517i
$124$	345.382	+	157.731i	0.250131	+	0.114231i
$125$	801.540	−	1144.84i	0.573535	−	0.819181i
$126$	599.502	−	519.471i	0.423872	−	0.367287i
$127$	46.0715	−	644.164i	0.0321905	−	0.450081i	−0.955639	−	0.294541i	$-0.904833\pi$
$127$	46.0715	−	644.164i	0.0321905	−	0.450081i	0.987829	−	0.155541i	$-0.0497120\pi$
$128$	−112.343	+	61.3439i	−0.0775766	+	0.0423600i
$129$	−2.82472	+	6.18528i	−0.00192793	+	0.00422158i
$130$	587.331	−	726.889i	0.396249	−	0.490403i
$131$	−1475.80	+	433.333i	−0.984282	+	0.289011i	−0.733991	−	0.679159i	$-0.762345\pi$
$131$	−1475.80	+	433.333i	−0.984282	+	0.289011i	−0.250291	+	0.968171i	$0.580526\pi$
$132$	52.6683	+	70.3565i	0.0347287	+	0.0463921i
$133$	−797.630	−	297.500i	−0.520025	−	0.193959i
$134$	261.474	+	1818.59i	0.168567	+	1.17241i
$135$	−128.426	+	384.185i	−0.0818754	+	0.244929i
$136$	−95.7036	−	82.9277i	−0.0603421	−	0.0522867i
$137$	1045.74	−	1045.74i	0.652144	−	0.652144i	−0.301365	−	0.953509i	$-0.597442\pi$
$137$	1045.74	−	1045.74i	0.652144	−	0.652144i	0.953509	+	0.301365i	$0.0974423\pi$
$138$	−149.112	−	7.17464i	−0.0919800	−	0.00442570i
$139$		−	2871.98i		−	1.75250i	−0.481853	−	0.876252i	$-0.660036\pi$
$139$		−	2871.98i		−	1.75250i	0.481853	−	0.876252i	$-0.339964\pi$
$140$	−24.7246	+	667.829i	−0.0149258	+	0.403156i
$141$	−145.522	+	93.5216i	−0.0869163	+	0.0558577i
$142$	−681.252	+	910.046i	−0.402601	+	0.537812i
$143$	−474.214	+	1271.42i	−0.277313	+	0.743504i
$144$	420.351	+	60.4373i	0.243259	+	0.0349753i
$145$	378.809	−	67.8341i	0.216954	−	0.0388505i
$146$	918.569	+	590.329i	0.520694	+	0.334630i
$147$	−75.8912	+	28.3060i	−0.0425810	+	0.0158819i
$148$	817.348	+	1496.86i	0.453957	+	0.831360i
$149$	−559.309	−	645.477i	−0.307519	−	0.354896i	0.580863	−	0.814002i	$-0.302715\pi$
$149$	−559.309	−	645.477i	−0.307519	−	0.354896i	−0.888382	+	0.459106i	$0.848170\pi$
$150$	−80.6883	−	148.691i	−0.0439211	−	0.0809373i
$151$	1013.24	+	297.515i	0.546070	+	0.160341i	0.543120	−	0.839655i	$-0.317243\pi$
$151$	1013.24	+	297.515i	0.546070	+	0.160341i	0.00294993	+	0.999996i	$0.499061\pi$
$152$	−159.269	−	427.016i	−0.0849894	−	0.227865i
$153$	89.3075	+	410.540i	0.0471901	+	0.216929i
$154$	−273.390	−	931.081i	−0.143055	−	0.487199i
$155$	1027.97	+	263.803i	0.532699	+	0.136704i
$156$	−46.9935	−	102.901i	−0.0241185	−	0.0528122i
$157$	−504.345	−	377.548i	−0.256377	−	0.191921i	0.463356	−	0.886172i	$-0.346645\pi$
$157$	−504.345	−	377.548i	−0.256377	−	0.191921i	−0.719733	+	0.694251i	$0.755736\pi$
$158$	625.301	+	136.026i	0.314850	+	0.0684914i
$159$	−309.463	+	357.139i	−0.154352	+	0.178132i
$160$	−278.868	+	224.126i	−0.137790	+	0.110742i
$161$	1514.92	+	649.584i	0.741566	+	0.317977i
$162$	−978.803	−	978.803i	−0.474704	−	0.474704i
$163$	28.2989	+	395.670i	0.0135984	+	0.190131i	0.999711	+	0.0240508i	$0.00765636\pi$
$163$	28.2989	+	395.670i	0.0135984	+	0.190131i	−0.986112	+	0.166080i	$0.946889\pi$
$164$	528.139	+	821.800i	0.251468	+	0.391291i
$165$	179.571	+	167.625i	0.0847247	+	0.0790882i
$166$	2473.75	−	1129.72i	1.15663	−	0.528215i
$167$	−1474.24	+	1103.60i	−0.683115	+	0.511373i	−0.883552	−	0.468333i	$-0.844855\pi$
$167$	−1474.24	+	1103.60i	−0.683115	+	0.511373i	0.200437	+	0.979707i	$0.435764\pi$
$168$	71.0012	+	38.7696i	0.0326063	+	0.0178044i
$169$	−243.477	+	378.858i	−0.110823	+	0.172443i
$170$	−304.169	−	181.009i	−0.137227	−	0.0816632i
$171$	−426.000	+	1450.82i	−0.190509	+	0.648814i
$172$	40.0916	+	2.86741i	0.0177730	+	0.00127115i
$173$	2307.69	+	165.049i	1.01416	+	0.0725343i	0.568514	−	0.822674i	$-0.307519\pi$
$173$	2307.69	+	165.049i	1.01416	+	0.0725343i	0.445649	+	0.895208i	$0.352973\pi$
$174$	13.1244	−	44.6975i	0.00571814	−	0.0194742i
$175$	261.004	+	1849.59i	0.112743	+	0.798948i
$176$	280.865	−	437.034i	0.120290	−	0.187174i
$177$	44.5295	+	24.3149i	0.0189098	+	0.0103255i
$178$	−402.267	+	301.134i	−0.169389	+	0.126803i
$179$	−678.099	+	309.677i	−0.283148	+	0.129309i	−0.551927	−	0.833893i	$-0.686107\pi$
$179$	−678.099	+	309.677i	−0.283148	+	0.129309i	0.268779	+	0.963202i	$0.413380\pi$
$180$	1186.30	−	40.8180i	0.491229	−	0.0169022i
$181$	2272.18	+	3535.59i	0.933095	+	1.45192i	0.891620	+	0.452784i	$0.149569\pi$
$181$	2272.18	+	3535.59i	0.933095	+	1.45192i	0.0414743	+	0.999140i	$0.486795\pi$
$182$	89.1063	+	1245.87i	0.0362912	+	0.507417i
$183$	61.9405	+	61.9405i	0.0250206	+	0.0250206i
$184$	268.286	+	840.661i	0.107491	+	0.336817i
$185$	2986.27	+	3715.65i	1.18678	+	1.47665i
$186$	84.1289	−	97.0900i	0.0331647	−	0.0382741i
$187$	502.214	+	109.250i	0.196393	+	0.0427227i
$188$	818.567	+	612.772i	0.317554	+	0.237718i
$189$	−224.914	−	492.494i	−0.0865615	−	0.189543i
$190$	−648.583	−	1096.39i	−0.247648	−	0.418633i
$191$	43.2655	+	147.349i	0.0163905	+	0.0558208i	0.967282	−	0.253703i	$-0.0816486\pi$
$191$	43.2655	+	147.349i	0.0163905	+	0.0558208i	−0.950892	+	0.309524i	$0.899830\pi$
$192$	9.20587	+	42.3187i	0.00346029	+	0.0159067i
$193$	−1490.29	−	3995.63i	−0.555822	−	1.49022i	−0.845968	−	0.533234i	$-0.820977\pi$
$193$	−1490.29	−	3995.63i	−0.555822	−	1.49022i	0.290146	−	0.956982i	$-0.406296\pi$
$194$	1239.31	+	363.893i	0.458644	+	0.134670i
$195$	−179.992	−	259.962i	−0.0661000	−	0.0954679i
$196$	313.539	+	361.843i	0.114264	+	0.131867i
$197$	−389.703	−	713.688i	−0.140940	−	0.258113i	0.797669	−	0.603096i	$-0.206066\pi$
$197$	−389.703	−	713.688i	−0.140940	−	0.258113i	−0.938609	+	0.344983i	$0.887885\pi$
$198$	−1614.91	+	602.332i	−0.579631	+	0.216191i
$199$	−3618.29	−	2325.33i	−1.28891	−	0.828334i	−0.296954	−	0.954892i	$-0.595971\pi$
$199$	−3618.29	−	2325.33i	−1.28891	−	0.828334i	−0.991959	+	0.126558i	$0.959607\pi$
$200$	−656.832	+	754.037i	−0.232225	+	0.266592i
$201$	615.315	+	88.4690i	0.215925	+	0.0310454i
$202$	169.094	−	453.358i	0.0588980	−	0.157912i
$203$	−308.244	+	411.766i	−0.106574	+	0.142366i
$204$	−36.0446	+	23.1644i	−0.0123707	+	0.00795017i
$205$	1857.97	+	2000.83i	0.633005	+	0.681678i
$206$		−	2519.32i		−	0.852085i
$207$	958.882	−	2766.22i	0.321966	−	0.928820i
$208$	−472.833	+	472.833i	−0.157621	+	0.157621i
$209$	1397.92	+	1211.31i	0.462663	+	0.400899i
$210$	214.448	+	71.6863i	0.0704682	+	0.0235563i
$211$	−457.118	−	3179.33i	−0.149144	−	1.03732i	−0.917626	−	0.397445i	$-0.869897\pi$
$211$	−457.118	−	3179.33i	−0.149144	−	1.03732i	0.768482	−	0.639871i	$-0.221012\pi$
$212$	2617.24	+	976.179i	0.847890	+	0.316247i
$213$	230.500	+	307.911i	0.0741482	+	0.0990504i
$214$	−924.699	+	271.516i	−0.295379	+	0.0867311i
$215$	111.717	−	11.8634i	0.0354375	−	0.00376313i
$216$	120.409	−	263.660i	0.0379297	−	0.0830544i
$217$	−1244.96	+	679.802i	−0.389464	+	0.212663i
$218$	−308.886	+	4318.79i	−0.0959652	+	1.34177i
$219$	279.207	−	241.934i	0.0861508	−	0.0746501i
$220$	557.429	−	1340.80i	0.170827	−	0.410894i
$221$	−601.768	−	274.818i	−0.183164	−	0.0836484i
$222$	563.856	−	122.659i	0.170466	−	0.0370827i
$223$	659.008	−	1206.88i	0.197894	−	0.362416i	−0.759822	−	0.650131i	$-0.774714\pi$
$223$	659.008	−	1206.88i	0.197894	−	0.362416i	0.957716	+	0.287715i	$0.0928956\pi$
$224$	68.0530	−	473.319i	0.0202990	−	0.141183i
$225$	3243.77	−	696.773i	0.961117	−	0.206451i
$226$	2005.33	−	288.323i	0.590232	−	0.0848626i
$227$	3.42671	−	15.7523i	0.00100193	−	0.00460581i	−0.976643	−	0.214868i	$-0.931068\pi$
$227$	3.42671	−	15.7523i	0.00100193	−	0.00460581i	0.977645	+	0.210262i	$0.0674316\pi$
$228$	−153.809	+	11.0006i	−0.0446766	+	0.00319533i
$229$	−3602.64			−1.03960			−0.519802	−	0.854287i	$-0.673994\pi$
$229$	−3602.64			−1.03960			−0.519802	+	0.854287i	$0.673994\pi$
$230$	1152.32	+	2180.75i	0.330356	+	0.625192i
$231$	−328.328			−0.0935169
$232$	−274.664	+	19.6443i	−0.0777265	+	0.00555911i
$233$	−1114.43	+	5122.94i	−0.313342	+	1.44041i	0.503724	+	0.863864i	$0.331963\pi$
$233$	−1114.43	+	5122.94i	−0.313342	+	1.44041i	−0.817066	+	0.576544i	$0.804401\pi$
$234$	2195.96	−	315.732i	0.613481	−	0.0882053i
$235$	2554.04	+	1282.64i	0.708968	+	0.356042i
$236$	42.6805	−	296.849i	0.0117723	−	0.0818781i
$237$	103.766	−	190.032i	0.0284401	−	0.0520841i
$238$	462.272	−	100.561i	0.125902	−	0.0273883i
$239$	−236.564	−	108.035i	−0.0640253	−	0.0292394i	0.383145	−	0.923688i	$-0.374841\pi$
$239$	−236.564	−	108.035i	−0.0640253	−	0.0292394i	−0.447170	+	0.894449i	$0.647568\pi$
$240$	46.1781	+	111.897i	0.0124199	+	0.0300954i
$241$	−1240.47	+	1074.88i	−0.331560	+	0.287298i	−0.804691	−	0.593694i	$-0.797669\pi$
$241$	−1240.47	+	1074.88i	−0.331560	+	0.287298i	0.473131	+	0.880992i	$0.343124\pi$
$242$	39.4887	−	552.124i	0.0104894	−	0.146661i
$243$	−1269.66	+	693.285i	−0.335179	+	0.183022i
$244$	215.100	−	471.002i	0.0564358	−	0.123577i
$245$	1040.92	+	841.071i	0.271437	+	0.219323i
$246$	317.134	−	93.1191i	0.0821941	−	0.0241344i
$247$	−1426.82	−	1906.01i	−0.367556	−	0.490997i
$248$	−711.509	−	265.379i	−0.182181	−	0.0679499i
$249$	−130.949	−	910.772i	−0.0333276	−	0.231799i
$250$	−1435.65	+	2398.21i	−0.363194	+	0.606704i
$251$	−3925.57	−	3401.52i	−0.987170	−	0.855387i	0.00231906	−	0.999997i	$-0.499262\pi$
$251$	−3925.57	−	3401.52i	−0.987170	−	0.855387i	−0.989489	+	0.144610i	$0.953807\pi$
$252$	−1121.83	+	1121.83i	−0.280431	+	0.280431i
$253$	−2590.84	−	2472.73i	−0.643813	−	0.614464i
$254$			1291.62i			0.319069i
$255$	−87.7574	+	81.4914i	−0.0215513	+	0.0200125i
$256$	215.361	−	138.404i	0.0525783	−	0.0337901i
$257$	−1639.64	+	2190.31i	−0.397969	+	0.531625i	−0.954107	−	0.299465i	$-0.903192\pi$
$257$	−1639.64	+	2190.31i	−0.397969	+	0.531625i	0.556138	+	0.831090i	$0.312283\pi$
$258$	4.75254	−	12.7421i	0.00114682	−	0.00307475i
$259$	−6306.53	−	906.742i	−1.51301	−	0.217537i
$260$	−1067.96	+	1533.87i	−0.254738	+	0.365872i
$261$	768.566	+	493.927i	0.182272	+	0.117139i
$262$	2882.25	−	1075.02i	0.679640	−	0.253493i
$263$	−1504.72	−	2755.68i	−0.352794	−	0.646094i	0.639667	−	0.768652i	$-0.279072\pi$
$263$	−1504.72	−	2755.68i	−0.352794	−	0.646094i	−0.992461	+	0.122558i	$0.960890\pi$
$264$	−115.106	−	132.840i	−0.0268345	−	0.0309687i
$265$	7681.81	+	1396.31i	1.78072	+	0.323678i
$266$	1633.64	+	479.680i	0.376560	+	0.110568i
$267$	59.4150	+	159.298i	0.0136185	+	0.0365126i
$268$	−781.090	−	3590.61i	−0.178032	−	0.818401i
$269$	69.2585	+	235.873i	0.0156980	+	0.0534625i	0.966970	−	0.254892i	$-0.0820399\pi$
$269$	69.2585	+	235.873i	0.0156980	+	0.0534625i	−0.951272	+	0.308354i	$0.900222\pi$
$270$	201.383	−	784.736i	0.0453919	−	0.176880i
$271$	−2075.58	−	4544.88i	−0.465248	−	1.01875i	−0.986260	−	0.165202i	$-0.947172\pi$
$271$	−2075.58	−	4544.88i	−0.465248	−	1.01875i	0.521011	−	0.853550i	$-0.325555\pi$
$272$	202.752	+	151.778i	0.0451971	+	0.0338342i
$273$	412.955	+	89.8329i	0.0915501	+	0.0199155i
$274$	−1936.95	+	2235.36i	−0.427063	+	0.492857i
$275$	873.074	−	3963.60i	0.191448	−	0.869142i
$276$	298.487	−	6.96231i	0.0650972	−	0.00151841i
$277$	−1953.96	−	1953.96i	−0.423834	−	0.423834i	0.462688	−	0.886521i	$-0.346885\pi$
$277$	−1953.96	−	1953.96i	−0.423834	−	0.423834i	−0.886521	+	0.462688i	$0.846885\pi$
$278$	409.769	+	5729.32i	0.0884041	+	1.23605i
$279$	1362.13	+	2119.51i	0.292288	+	0.454809i
$280$	−45.9615	−	1335.78i	−0.00980973	−	0.285101i
$281$	−2719.48	+	1241.94i	−0.577333	+	0.263659i	−0.682609	−	0.730784i	$-0.739155\pi$
$281$	−2719.48	+	1241.94i	−0.577333	+	0.263659i	0.105276	+	0.994443i	$0.466427\pi$
$282$	276.960	−	207.330i	0.0584848	−	0.0437812i
$283$	−1534.89	−	838.114i	−0.322402	−	0.176045i	0.309895	−	0.950771i	$-0.399706\pi$
$283$	−1534.89	−	838.114i	−0.322402	−	0.176045i	−0.632297	+	0.774726i	$0.717888\pi$
$284$	1229.19	−	1912.65i	0.256827	−	0.399631i
$285$	−417.758	+	106.046i	−0.0868276	+	0.0220407i
$286$	764.607	−	2604.01i	0.158085	−	0.538386i
$287$	−3640.14	−	260.348i	−0.748679	−	0.0535466i
$288$	−847.183	−	60.5917i	−0.173336	−	0.0123972i
$289$	1313.56	−	4473.57i	0.267364	−	0.910558i
$290$	−746.009	+	189.370i	−0.151059	+	0.0383456i
$291$	236.270	−	367.643i	0.0475958	−	0.0740605i
$292$	−1916.69	−	1046.59i	−0.384129	−	0.209750i
$293$	5571.83	−	4171.02i	1.11096	−	0.831651i	0.123942	−	0.992289i	$-0.460446\pi$
$293$	5571.83	−	4171.02i	1.11096	−	0.831651i	0.987013	+	0.160639i	$0.0513554\pi$
$294$	147.357	−	67.2957i	0.0292314	−	0.0133495i
$295$	−28.8254	−	837.755i	−0.00568909	−	0.165342i
$296$	−1844.10	−	2869.48i	−0.362116	−	0.563463i
$297$	83.9236	+	1173.41i	0.0163964	+	0.229252i
$298$	1207.86	+	1207.86i	0.234797	+	0.234797i
$299$	2582.07	+	3818.95i	0.499416	+	0.738648i
$300$	182.180	+	285.112i	0.0350606	+	0.0548699i
$301$	−98.3326	+	113.482i	−0.0188299	+	0.0217308i
$302$	−2063.77	−	448.946i	−0.393234	−	0.0855429i
$303$	−131.060	−	98.1105i	−0.0248489	−	0.0186016i
$304$	378.652	+	829.131i	0.0714380	+	0.156427i
$305$	359.752	−	1401.85i	0.0675388	−	0.263180i
$306$	−236.735	−	806.246i	−0.0442263	−	0.150621i
$307$	137.178	+	630.598i	0.0255022	+	0.117232i	0.988138	−	0.153567i	$-0.0490760\pi$
$307$	137.178	+	630.598i	0.0255022	+	0.117232i	−0.962636	+	0.270798i	$0.912712\pi$
$308$	678.232	+	1818.41i	0.125474	+	0.336408i
$309$	−817.877	−	240.150i	−0.150574	−	0.0442126i
$310$	−2088.34	−	379.593i	−0.382611	−	0.0695466i
$311$	1851.15	+	2136.34i	0.337520	+	0.389519i	0.898984	−	0.437982i	$-0.144307\pi$
$311$	1851.15	+	2136.34i	0.337520	+	0.389519i	−0.561463	+	0.827502i	$0.689761\pi$
$312$	108.429	+	198.573i	0.0196750	+	0.0360321i
$313$	5568.43	−	2076.92i	1.00558	−	0.375062i	0.207904	−	0.978149i	$-0.433336\pi$
$313$	5568.43	−	2076.92i	1.00558	−	0.375062i	0.797675	+	0.603087i	$0.206063\pi$
$314$	1059.99	+	681.214i	0.190505	+	0.122430i
$315$	−2533.81	+	3639.23i	−0.453219	+	0.650943i
$316$	−1266.82	−	182.142i	−0.225520	−	0.0324249i
$317$	2277.20	−	6105.42i	0.403471	−	1.08175i	−0.563333	−	0.826230i	$-0.690481\pi$
$317$	2277.20	−	6105.42i	0.403471	−	1.08175i	0.966804	−	0.255519i	$-0.0822462\pi$
$318$	566.393	−	756.612i	0.0998796	−	0.133424i
$319$	940.187	−	604.222i	0.165017	−	0.106050i
$320$	524.337	−	486.899i	0.0915979	−	0.0850577i
$321$			326.078i			0.0566974i
$322$	−3114.79	−	1079.71i	−0.539070	−	0.186863i
$323$	−637.651	+	637.651i	−0.109845	+	0.109845i
$324$	2092.27	+	1812.97i	0.358757	+	0.310865i
$325$	−2182.58	+	4746.34i	−0.372516	+	0.810091i
$326$	−112.907	−	785.286i	−0.0191820	−	0.133414i
$327$	1372.62	+	511.959i	0.232128	+	0.0865793i
$328$	−1170.84	−	1564.06i	−0.197100	−	0.263295i
$329$	−3665.22	+	1076.21i	−0.614195	+	0.180344i
$330$	−382.143	−	308.774i	−0.0637463	−	0.0515074i
$331$	−4643.72	+	10168.3i	−0.771124	+	1.68853i	−0.0469625	+	0.998897i	$0.514954\pi$
$331$	−4643.72	+	10168.3i	−0.771124	+	1.68853i	−0.724162	+	0.689630i	$0.757773\pi$
$332$	−4773.71	+	2606.64i	−0.789131	+	0.430898i
$333$	−807.326	+	11287.9i	−0.132856	+	1.85758i
$334$	2783.51	−	2411.92i	0.456008	−	0.395133i
$335$	−3918.07	−	9494.09i	−0.639005	−	1.54841i
$336$	−147.172	−	67.2113i	−0.0238955	−	0.0109127i
$337$	−4232.51	+	920.725i	−0.684152	+	0.148828i	−0.541191	−	0.840900i	$-0.682026\pi$
$337$	−4232.51	+	920.725i	−0.684152	+	0.148828i	−0.142962	+	0.989728i	$0.545663\pi$
$338$	431.659	−	790.524i	0.0694650	−	0.127216i
$339$	97.5532	−	678.497i	0.0156294	−	0.108705i
$340$	632.613	+	317.697i	0.100907	+	0.0506751i
$341$	3050.70	−	438.624i	0.484471	−	0.0696564i
$342$	642.828	−	2955.03i	0.101638	−	0.467222i
$343$	−6896.62	+	493.256i	−1.08566	+	0.0776481i
$344$	−80.3880			−0.0125995
$345$	817.804	−	166.216i	0.127621	−	0.0259384i
$346$	−4627.16			−0.718953
$347$	8506.19	−	608.375i	1.31595	−	0.0941189i	0.604361	−	0.796710i	$-0.293428\pi$
$347$	8506.19	−	608.375i	1.31595	−	0.0941189i	0.711593	+	0.702592i	$0.247974\pi$
$348$	−19.8045	+	91.0399i	−0.00305067	+	0.0140237i
$349$	−488.218	+	70.1952i	−0.0748818	+	0.0107664i	−0.179654	−	0.983730i	$-0.557498\pi$
$349$	−488.218	+	70.1952i	−0.0748818	+	0.0107664i	0.104772	+	0.994496i	$0.466589\pi$
$350$	−784.574	−	3652.52i	−0.119821	−	0.557815i
$351$	215.497	−	1498.81i	0.0327703	−	0.227922i
$352$	−497.943	+	911.914i	−0.0753990	+	0.138083i
$353$	4562.88	−	992.594i	0.687982	−	0.149661i	0.145033	−	0.989427i	$-0.453671\pi$
$353$	4562.88	−	992.594i	0.687982	−	0.149661i	0.542949	+	0.839766i	$0.317308\pi$
$354$	−92.3012	−	42.1526i	−0.0138581	−	0.00632876i
$355$	2439.55	−	5867.92i	0.364727	−	0.877288i
$356$	759.520	−	658.127i	0.113074	−	0.0979794i
$357$	11.4190	−	159.659i	0.00169288	−	0.0236696i
$358$	1308.56	−	714.527i	0.193183	−	0.105486i
$359$	491.867	−	1077.04i	0.0723112	−	0.158340i	−0.870025	−	0.493008i	$-0.835897\pi$
$359$	491.867	−	1077.04i	0.0723112	−	0.158340i	0.942336	+	0.334669i	$0.108624\pi$
$360$	−2360.72	+	250.687i	−0.345614	+	0.0367010i
$361$	3467.17	−	1018.05i	0.505493	−	0.148426i
$362$	−5037.24	−	6728.97i	−0.731358	−	0.976980i
$363$	−175.478	−	65.4500i	−0.0253725	−	0.00946345i
$364$	−355.517	−	2472.68i	−0.0511928	−	0.356053i
$365$	−5789.05	−	1935.18i	−0.830172	−	0.277512i
$366$	−132.403	−	114.728i	−0.0189093	−	0.0163850i
$367$	3064.09	−	3064.09i	0.435816	−	0.435816i	−0.454785	−	0.890601i	$-0.650284\pi$
$367$	3064.09	−	3064.09i	0.435816	−	0.435816i	0.890601	+	0.454785i	$0.150284\pi$
$368$	−655.150	−	1638.76i	−0.0928045	−	0.232136i
$369$			6482.08i			0.914481i
$370$	−6487.46	−	6986.29i	−0.911532	−	0.981622i
$371$	−8778.92	+	5641.87i	−1.22851	+	0.789519i
$372$	−153.977	+	205.689i	−0.0214605	+	0.0286679i
$373$	650.043	−	1742.83i	0.0902358	−	0.241932i	−0.883990	−	0.467505i	$-0.845153\pi$
$373$	650.043	−	1742.83i	0.0902358	−	0.241932i	0.974226	+	0.225574i	$0.0724256\pi$
$374$	−1017.46	−	146.288i	−0.140672	−	0.0202256i
$375$	641.707	+	694.678i	0.0883670	+	0.0956614i
$376$	−1720.39	−	1105.63i	−0.235964	−	0.151645i
$377$	−1347.84	+	502.719i	−0.184131	+	0.0686772i
$378$	518.951	+	950.388i	0.0706137	+	0.129319i
$379$	6925.27	+	7992.19i	0.938595	+	1.08320i	0.996392	+	0.0848677i	$0.0270468\pi$
$379$	6925.27	+	7992.19i	0.938595	+	1.08320i	−0.0577976	+	0.998328i	$0.518408\pi$
$380$	1450.29	+	2094.65i	0.195785	+	0.282772i
$381$	419.314	+	123.122i	0.0563834	+	0.0165557i
$382$	−107.334	−	287.774i	−0.0143761	−	0.0385439i
$383$	−1342.50	−	6171.39i	−0.179109	−	0.823351i	−0.975748	−	0.218896i	$-0.929755\pi$
$383$	−1342.50	−	6171.39i	−0.179109	−	0.823351i	0.796639	−	0.604455i	$-0.206609\pi$
$384$	−24.4028	−	83.1083i	−0.00324297	−	0.0110445i
$385$	2761.94	+	4668.88i	0.365614	+	0.618047i
$386$	3543.08	+	7758.27i	0.467197	+	1.02302i
$387$	213.511	+	159.832i	0.0280449	+	0.0209941i
$388$	−2524.22	−	549.110i	−0.330278	−	0.0718475i
$389$	2532.56	−	2922.73i	0.330092	−	0.380946i	−0.566307	−	0.824194i	$-0.691628\pi$
$389$	2532.56	−	2922.73i	0.330092	−	0.380946i	0.896399	+	0.443248i	$0.146174\pi$
$390$	396.158	+	492.918i	0.0514365	+	0.0639996i
$391$	1292.54	−	1173.87i	0.167178	−	0.151829i
$392$	−677.108	−	677.108i	−0.0872426	−	0.0872426i
$393$	−74.2515	−	1038.17i	−0.00953052	−	0.133254i
$394$	879.249	+	1368.14i	0.112426	+	0.174939i
$395$	−3575.18	+	123.014i	−0.455409	+	0.0156697i
$396$	3135.66	−	1432.01i	0.397911	−	0.181720i
$397$	6278.70	−	4700.17i	0.793750	−	0.594194i	−0.123574	−	0.992335i	$-0.539436\pi$
$397$	6278.70	−	4700.17i	0.793750	−	0.594194i	0.917324	+	0.398142i	$0.130345\pi$
$398$	7549.91	+	4122.56i	0.950862	+	0.519210i
$399$	311.449	−	484.623i	0.0390775	−	0.0608058i
$400$	1202.73	−	1597.95i	0.150341	−	0.199743i
$401$	328.991	−	1120.44i	0.0409701	−	0.139531i	−0.936468	−	0.350753i	$-0.885926\pi$
$401$	328.991	−	1120.44i	0.0409701	−	0.139531i	0.977438	+	0.211221i	$0.0677440\pi$
$402$	−1240.12	−	88.6950i	−0.153859	−	0.0110042i
$403$	−3957.03	−	283.012i	−0.489115	−	0.0349822i
$404$	−272.641	+	928.531i	−0.0335753	+	0.114347i
$405$	6649.73	+	3957.22i	0.815871	+	0.485520i
$406$	556.167	−	865.413i	0.0679855	−	0.105788i
$407$	12150.4	+	6634.61i	1.47978	+	0.808023i
$408$	68.6004	−	51.3536i	0.00832409	−	0.00623133i
$409$	−1944.06	+	887.825i	−0.235031	+	0.107335i	−0.529449	−	0.848342i	$-0.677601\pi$
$409$	−1944.06	+	887.825i	−0.235031	+	0.107335i	0.294418	+	0.955677i	$0.404874\pi$
$410$	−3991.94	−	3726.37i	−0.480849	−	0.448859i
$411$	541.054	+	841.896i	0.0649348	+	0.101041i
$412$	359.453	+	5025.81i	0.0429829	+	0.600980i
$413$	792.231	+	792.231i	0.0943901	+	0.0943901i
$414$	−1518.20	+	5655.16i	−0.180230	+	0.671343i
$415$	−11849.8	+	9523.65i	−1.40164	+	1.12650i
$416$	875.794	−	1010.72i	0.103220	−	0.119122i
$417$	1899.04	+	413.110i	0.223013	+	0.0485134i
$418$	−2961.55	−	2216.99i	−0.346541	−	0.259418i
$419$	−6191.15	−	13556.7i	−0.721855	−	1.58064i	−0.811286	−	0.584649i	$-0.801232\pi$
$419$	−6191.15	−	13556.7i	−0.721855	−	1.58064i	0.0894308	−	0.995993i	$-0.471495\pi$
$420$	−438.032	−	112.410i	−0.0508899	−	0.0130597i
$421$	3222.72	+	10975.6i	0.373078	+	1.27059i	0.905587	+	0.424161i	$0.139431\pi$
$421$	3222.72	+	10975.6i	0.373078	+	1.27059i	−0.532509	+	0.846424i	$0.678751\pi$
$422$	1365.53	+	6277.23i	0.157519	+	0.724101i
$423$	2371.09	+	6357.14i	0.272545	+	0.730721i
$424$	−5360.42	−	1573.96i	−0.613974	−	0.180279i
$425$	1897.05	+	562.407i	0.216518	+	0.0641900i
$426$	−503.757	−	581.366i	−0.0572937	−	0.0661204i
$427$	927.056	+	1697.78i	0.105066	+	0.192415i
$428$	1805.95	−	673.583i	0.203957	−	0.0760721i
$429$	−772.486	−	496.447i	−0.0869370	−	0.0558710i
$430$	−221.173	+	39.6059i	−0.0248044	+	0.00444178i
$431$	−6549.77	−	941.715i	−0.731998	−	0.105245i	−0.233771	−	0.972292i	$-0.575107\pi$
$431$	−6549.77	−	941.715i	−0.731998	−	0.105245i	−0.498228	+	0.867046i	$0.666016\pi$
$432$	−202.586	+	543.155i	−0.0225624	+	0.0604921i
$433$	9907.80	−	13235.3i	1.09963	−	1.46893i	0.231337	−	0.972874i	$-0.425690\pi$
$433$	9907.80	−	13235.3i	1.09963	−	1.46893i	0.868290	−	0.496057i	$-0.165219\pi$
$434$	2386.59	−	1533.77i	0.263963	−	0.169639i
$435$	−9.63459	+	260.237i	−0.00106194	+	0.0286837i
$436$		−	8659.65i		−	0.951197i
$437$	6107.48	−	1478.56i	0.668559	−	0.161852i
$438$	−522.472	+	522.472i	−0.0569969	+	0.0569969i
$439$	−4026.76	−	3489.21i	−0.437783	−	0.379341i	0.407900	−	0.913027i	$-0.366261\pi$
$439$	−4026.76	−	3489.21i	−0.437783	−	0.379341i	−0.845683	+	0.533685i	$0.820807\pi$
$440$	−920.714	+	2754.30i	−0.0997575	+	0.298423i
$441$	452.135	+	3144.67i	0.0488214	+	0.339560i
$442$	1239.68	+	462.377i	0.133406	+	0.0497580i
$443$	−10214.0	−	13644.4i	−1.09545	−	1.46335i	−0.872563	−	0.488502i	$-0.837543\pi$
$443$	−10214.0	−	13644.4i	−1.09545	−	1.46335i	−0.222885	−	0.974845i	$-0.571547\pi$
$444$	−1107.34	+	325.144i	−0.118360	+	0.0347537i
$445$	1765.43	−	2184.92i	0.188066	−	0.232753i
$446$	−1142.46	+	2501.64i	−0.121294	+	0.265597i
$447$	507.260	−	276.985i	0.0536747	−	0.0293086i
$448$	−68.2269	+	953.936i	−0.00719513	+	0.100601i
$449$	−2225.45	+	1928.37i	−0.233910	+	0.202684i	−0.763927	−	0.645303i	$-0.776731\pi$
$449$	−2225.45	+	1928.37i	−0.233910	+	0.202684i	0.530017	+	0.847987i	$0.322186\pi$
$450$	−6371.60	+	1852.81i	−0.667466	+	0.194094i
$451$	7212.95	+	3294.05i	0.753093	+	0.343926i
$452$	−3959.30	+	861.294i	−0.412013	+	0.0896280i
$453$	−342.472	+	627.192i	−0.0355204	+	0.0650508i
$454$	−4.58845	+	31.9133i	−0.000474331	+	0.00329905i
$455$	−2196.39	−	6627.97i	−0.226304	−	0.682910i
$456$	305.265	−	43.8905i	0.0313494	−	0.00450737i
$457$	−52.1893	+	239.911i	−0.00534205	+	0.0245570i	−0.979741	−	0.200270i	$-0.935818\pi$
$457$	−52.1893	+	239.911i	−0.00534205	+	0.0245570i	0.974399	+	0.224827i	$0.0721817\pi$
$458$	7186.93	−	514.019i	0.733238	−	0.0524422i
$459$	−573.520			−0.0583216
$460$	−2609.92	−	4185.97i	−0.264539	−	0.424286i
$461$	−14889.0			−1.50423			−0.752117	−	0.659030i	$-0.770967\pi$
$461$	−14889.0			−1.50423			−0.752117	+	0.659030i	$0.770967\pi$
$462$	654.983	−	46.8453i	0.0659580	−	0.00471741i
$463$	2058.26	−	9461.65i	0.206599	−	0.949720i	−0.750705	−	0.660637i	$-0.770286\pi$
$463$	2058.26	−	9461.65i	0.206599	−	0.949720i	0.957304	−	0.289083i	$-0.0933502\pi$
$464$	545.125	−	78.3771i	0.0545405	−	0.00784174i
$465$	−322.299	+	641.777i	−0.0321425	+	0.0640036i
$466$	1492.24	−	10378.8i	0.148341	−	1.03173i
$467$	491.424	−	899.976i	0.0486947	−	0.0891776i	−0.852198	−	0.523219i	$-0.824731\pi$
$467$	491.424	−	899.976i	0.0486947	−	0.0891776i	0.900893	+	0.434041i	$0.142913\pi$
$468$	−4335.69	+	943.171i	−0.428242	+	0.0931583i
$469$	12487.1	+	5702.67i	1.22943	+	0.561460i
$470$	−5278.08	−	2194.33i	−0.517999	−	0.215355i
$471$	322.192	−	279.181i	0.0315198	−	0.0273121i
$472$	−42.7895	+	598.275i	−0.00417277	+	0.0583429i
$473$	286.355	−	156.362i	0.0278364	−	0.0151998i
$474$	−179.889	+	393.902i	−0.0174316	+	0.0381698i
$475$	5022.22	+	5048.51i	0.485127	+	0.487667i
$476$	−907.841	+	266.566i	−0.0874177	+	0.0256682i
$477$	11107.9	+	14838.4i	1.06623	+	1.42432i
$478$	487.337	+	181.767i	0.0466324	+	0.0173930i
$479$	2289.45	+	15923.5i	0.218388	+	1.51892i	0.743991	+	0.668189i	$0.232930\pi$
$479$	2289.45	+	15923.5i	0.218388	+	1.51892i	−0.525604	+	0.850730i	$0.676161\pi$
$480$	−108.086	−	216.635i	−0.0102780	−	0.0205999i
$481$	−13466.9	−	11669.1i	−1.27658	−	1.10617i
$482$	2321.26	−	2321.26i	0.219358	−	0.219358i
$483$	−647.432	+	908.270i	−0.0609921	+	0.0855647i
$484$			1107.07i			0.103970i
$485$	−7215.47	−	267.134i	−0.675541	−	0.0250101i
$486$	2433.93	−	1564.19i	0.227171	−	0.145994i
$487$	−7278.52	+	9722.96i	−0.677251	+	0.904701i	−0.999114	−	0.0420849i	$-0.986600\pi$
$487$	−7278.52	+	9722.96i	−0.677251	+	0.904701i	0.321863	+	0.946786i	$0.395691\pi$
$488$	−361.901	+	970.295i	−0.0335707	+	0.0900065i
$489$	−265.699	−	38.2018i	−0.0245713	−	0.00353281i
$490$	−2196.54	−	1529.34i	−0.202509	−	0.140997i
$491$	17388.8	+	11175.1i	1.59826	+	1.02714i	0.968062	+	0.250711i	$0.0806644\pi$
$491$	17388.8	+	11175.1i	1.59826	+	1.02714i	0.630202	+	0.776431i	$0.282972\pi$
$492$	−619.367	+	231.012i	−0.0567545	+	0.0211683i
$493$	261.121	+	478.207i	0.0238545	+	0.0436863i
$494$	3118.31	+	3598.72i	0.284007	+	0.327762i
$495$	7921.68	−	5484.80i	0.719299	−	0.498028i
$496$	1457.26	+	427.889i	0.131921	+	0.0387354i
$497$	2968.24	+	7958.17i	0.267895	+	0.718255i
$498$	391.179	+	1798.22i	0.0351991	+	0.161808i
$499$	−1385.10	−	4717.21i	−0.124260	−	0.423189i	0.873741	−	0.486391i	$-0.161687\pi$
$499$	−1385.10	−	4717.21i	−0.124260	−	0.423189i	−0.998001	+	0.0632020i	$0.979869\pi$
$500$	2521.82	−	4989.03i	0.225558	−	0.446233i
$501$	−517.677	−	1133.56i	−0.0461639	−	0.101085i
$502$	8316.45	+	6225.62i	0.739405	+	0.553512i
$503$	8426.61	+	1833.10i	0.746966	+	0.162492i	0.569909	−	0.821708i	$-0.306979\pi$
$503$	8426.61	+	1833.10i	0.746966	+	0.162492i	0.177057	+	0.984201i	$0.443342\pi$
$504$	2077.88	−	2398.01i	0.183644	−	0.211936i
$505$	−292.650	+	2689.01i	−0.0257877	+	0.236949i
$506$	5521.28	+	4563.20i	0.485081	+	0.400908i
$507$	−215.490	−	215.490i	−0.0188762	−	0.0188762i
$508$	−184.286	−	2576.66i	−0.0160952	−	0.225041i
$509$	7591.12	+	11812.0i	0.661042	+	1.02860i	0.996255	+	0.0864594i	$0.0275553\pi$
$509$	7591.12	+	11812.0i	0.661042	+	1.02860i	−0.335213	+	0.942142i	$0.608808\pi$
$510$	163.441	−	175.089i	0.0141907	−	0.0152021i
$511$	7421.10	−	3389.10i	0.642446	−	0.293395i
$512$	−409.877	+	306.830i	−0.0353793	+	0.0264846i
$513$	−1811.59	−	989.206i	−0.155914	−	0.0851355i
$514$	2958.42	−	4603.40i	0.253872	−	0.395033i
$515$	3465.11	+	13650.5i	0.296487	+	1.16799i
$516$	−7.66285	+	26.0973i	−0.000653756	+	0.00222649i
$517$	8278.87	+	592.116i	0.704263	+	0.0503699i
$518$	12710.3	+	909.058i	1.07810	+	0.0771075i
$519$	−441.077	+	1502.17i	−0.0373047	+	0.127048i
$520$	1911.62	−	3212.30i	0.161212	−	0.270902i
$521$	−1767.26	+	2749.91i	−0.148609	+	0.231239i	−0.907575	−	0.419891i	$-0.862068\pi$
$521$	−1767.26	+	2749.91i	−0.148609	+	0.231239i	0.758966	+	0.651130i	$0.225705\pi$
$522$	−1603.69	−	875.680i	−0.134467	−	0.0734243i
$523$	10652.1	−	7974.03i	0.890596	−	0.666692i	−0.0527120	−	0.998610i	$-0.516787\pi$
$523$	10652.1	−	7974.03i	0.890596	−	0.666692i	0.943308	+	0.331918i	$0.107696\pi$
$524$	−5596.42	+	2555.80i	−0.466567	+	0.213074i
$525$	−1260.55	−	93.4650i	−0.104790	−	0.00776981i
$526$	3394.94	+	5282.64i	0.281419	+	0.437897i
$527$	107.192	+	1498.74i	0.00886026	+	0.123883i
$528$	248.580	+	248.580i	0.0204887	+	0.0204887i
$529$	−11949.3	+	2291.18i	−0.982110	+	0.188311i
$530$	−15523.7	−	1689.47i	−1.27228	−	0.138464i
$531$	1303.18	−	1503.95i	0.106503	−	0.122911i
$532$	−3327.40	−	723.831i	−0.271167	−	0.0589888i
$533$	−8170.82	−	6116.60i	−0.664011	−	0.497072i
$534$	−141.256	−	309.307i	−0.0114471	−	0.0250656i
$535$	4636.87	−	2743.00i	0.374709	−	0.221664i
$536$	2070.50	+	7051.48i	0.166851	+	0.568242i
$537$	−107.229	−	492.924i	−0.00861689	−	0.0396112i
$538$	−171.818	−	460.662i	−0.0137688	−	0.0369155i
$539$	3729.00	+	1094.93i	0.297995	+	0.0874994i
$540$	−289.776	+	1594.21i	−0.0230925	+	0.127044i
$541$	4106.59	+	4739.26i	0.326352	+	0.376630i	0.895088	−	0.445890i	$-0.147113\pi$
$541$	4106.59	+	4739.26i	0.326352	+	0.376630i	−0.568736	+	0.822520i	$0.692567\pi$
$542$	4789.03	+	8770.46i	0.379532	+	0.695062i
$543$	−2664.67	+	993.871i	−0.210593	+	0.0785471i
$544$	−426.125	−	273.854i	−0.0335845	−	0.0215835i
$545$	−4266.48	−	23825.5i	−0.335332	−	1.87261i
$546$	−836.623	−	120.288i	−0.0655754	−	0.00942832i
$547$	−6315.52	+	16932.6i	−0.493660	+	1.32355i	0.416439	+	0.909164i	$0.363278\pi$
$547$	−6315.52	+	16932.6i	−0.493660	+	1.32355i	−0.910099	+	0.414391i	$0.863995\pi$
$548$	3545.09	−	4735.68i	0.276348	−	0.369158i
$549$	2890.41	−	1857.55i	0.224699	−	0.144405i
$550$	−1176.18	+	8031.57i	−0.0911862	+	0.622668i
$551$			1960.91i			0.151611i
$552$	−594.461	+	56.4768i	−0.0458368	+	0.00435474i
$553$	3380.90	−	3380.90i	0.259983	−	0.259983i
$554$	4176.75	+	3619.17i	0.320312	+	0.277552i
$555$	−2886.45	+	1440.14i	−0.220762	+	0.110145i
$556$	−1634.90	−	11371.0i	−0.124704	−	0.867333i
$557$	18175.6	+	6779.16i	1.38263	+	0.515695i	0.927197	−	0.374573i	$-0.122211\pi$
$557$	18175.6	+	6779.16i	1.38263	+	0.515695i	0.455435	+	0.890269i	$0.349484\pi$
$558$	−3019.72	−	4033.88i	−0.229095	−	0.306035i
$559$	−402.945	+	118.315i	−0.0304879	+	0.00895207i
$560$	282.276	+	2658.20i	0.0213006	+	0.200588i
$561$	−144.479	+	316.364i	−0.0108732	+	0.0238091i
$562$	5247.90	−	2865.57i	0.393896	−	0.215083i
$563$	−1250.42	+	17483.2i	−0.0936039	+	1.30875i	0.705994	+	0.708218i	$0.250500\pi$
$563$	−1250.42	+	17483.2i	−0.0936039	+	1.30875i	−0.799598	+	0.600536i	$0.794954\pi$
$564$	−522.927	+	453.119i	−0.0390411	+	0.0338293i
$565$	−10469.0	+	4320.38i	−0.779527	+	0.321699i
$566$	3181.54	+	1452.96i	0.236272	+	0.107902i
$567$	−10106.2	+	2198.47i	−0.748537	+	0.162834i
$568$	−2179.22	+	3990.94i	−0.160982	+	0.294817i
$569$	765.661	−	5325.29i	0.0564116	−	0.392351i	−0.941981	−	0.335667i	$-0.891038\pi$
$569$	765.661	−	5325.29i	0.0564116	−	0.392351i	0.998392	−	0.0566837i	$-0.0180527\pi$
$570$	818.257	−	271.156i	0.0601281	−	0.0199254i
$571$	6182.46	−	888.903i	0.453114	−	0.0651479i	0.0880200	−	0.996119i	$-0.471946\pi$
$571$	6182.46	−	888.903i	0.453114	−	0.0651479i	0.365094	+	0.930971i	$0.381037\pi$
$572$	−1153.78	+	5303.85i	−0.0843392	+	0.387701i
$573$	−103.655	+	7.41353i	−0.00755714	+	0.000540497i
$574$	7298.89			0.530748
$575$	−9243.08	−	10231.1i	−0.670371	−	0.742026i
$576$	1698.69			0.122880
$577$	−23012.8	+	1645.91i	−1.66037	+	0.118752i	−0.869730	−	0.493528i	$-0.835707\pi$
$577$	−23012.8	+	1645.91i	−1.66037	+	0.118752i	−0.790641	+	0.612280i	$0.790253\pi$
$578$	−1982.14	+	9111.77i	−0.142641	+	0.655709i
$579$	2856.40	−	410.688i	0.205022	−	0.0294777i
$580$	1461.20	−	484.215i	0.104609	−	0.0346654i
$581$	2891.73	−	20112.4i	0.206488	−	1.43615i
$582$	−418.881	+	767.123i	−0.0298336	+	0.0546362i
$583$	22156.2	−	4819.78i	1.57395	−	0.342393i
$584$	3972.93	+	1814.38i	0.281509	+	0.128561i
$585$	−11464.2	+	4731.09i	−0.810231	+	0.334370i
$586$	−10520.2	+	9115.77i	−0.741610	+	0.642609i
$587$	699.878	−	9785.57i	0.0492113	−	0.688064i	−0.911638	−	0.410994i	$-0.865182\pi$
$587$	699.878	−	9785.57i	0.0492113	−	0.688064i	0.960850	−	0.277071i	$-0.0893636\pi$
$588$	−284.362	+	155.273i	−0.0199437	+	0.0108901i
$589$	−2246.43	+	4919.00i	−0.157152	+	0.344116i
$590$	177.034	+	1667.13i	0.0123531	+	0.116330i
$591$	527.967	−	155.025i	0.0367473	−	0.0107900i
$592$	4088.22	+	5461.22i	0.283826	+	0.379147i
$593$	−2429.95	−	906.323i	−0.168273	−	0.0627626i	0.263916	−	0.964546i	$-0.414986\pi$
$593$	−2429.95	−	906.323i	−0.168273	−	0.0627626i	−0.432189	+	0.901783i	$0.642259\pi$
$594$	−334.839	−	2328.86i	−0.0231290	−	0.160866i
$595$	−2366.43	+	1180.69i	−0.163049	+	0.0813504i
$596$	−2581.91	−	2237.23i	−0.177448	−	0.153760i
$597$	2058.04	−	2058.04i	0.141089	−	0.141089i
$598$	−5695.87	−	7250.04i	−0.389501	−	0.495779i
$599$			1041.02i			0.0710100i	0.999369	+	0.0355050i	$0.0113040\pi$
$599$			1041.02i			0.0710100i	−0.999369	+	0.0355050i	$0.988696\pi$
$600$	−404.112	−	542.779i	−0.0274963	−	0.0369314i
$601$	−21925.9	+	14090.9i	−1.48814	+	0.956372i	−0.491821	+	0.870696i	$0.663669\pi$
$601$	−21925.9	+	14090.9i	−1.48814	+	0.956372i	−0.996323	+	0.0856760i	$0.972695\pi$
$602$	179.973	−	240.415i	0.0121846	−	0.0162767i
$603$	8520.91	−	22845.5i	0.575453	−	1.54285i
$604$	4181.08	+	601.149i	0.281665	+	0.0404974i
$605$	545.435	+	3045.90i	0.0366531	+	0.204683i
$606$	275.451	+	177.021i	0.0184644	+	0.0118663i
$607$	11726.3	−	4373.67i	0.784109	−	0.292458i	0.0746552	−	0.997209i	$-0.476214\pi$
$607$	11726.3	−	4373.67i	0.784109	−	0.292458i	0.709454	+	0.704752i	$0.248942\pi$
$608$	−873.673	−	1600.01i	−0.0582765	−	0.106725i
$609$	−227.933	−	263.049i	−0.0151664	−	0.0175029i
$610$	−517.657	+	2847.89i	−0.0343595	+	0.189029i
$611$	−10250.7	−	3009.89i	−0.678725	−	0.199292i
$612$	587.298	+	1574.61i	0.0387910	+	0.104003i
$613$	1817.08	+	8352.97i	0.119724	+	0.550364i	0.997461	+	0.0712201i	$0.0226893\pi$
$613$	1817.08	+	8352.97i	0.119724	+	0.550364i	−0.877736	+	0.479144i	$0.840947\pi$
$614$	−363.630	−	1238.41i	−0.0239005	−	0.0813977i
$615$	−1590.26	+	940.740i	−0.104269	+	0.0616818i
$616$	−1612.46	−	3530.79i	−0.105467	−	0.230941i
$617$	−20623.8	−	15438.8i	−1.34568	−	1.00736i	−0.997553	−	0.0699148i	$-0.977727\pi$
$617$	−20623.8	−	15438.8i	−1.34568	−	1.00736i	−0.348126	−	0.937448i	$-0.613182\pi$
$618$	1665.85	+	362.384i	0.108431	+	0.0235877i
$619$	11241.2	−	12973.0i	0.729921	−	0.842373i	−0.262542	−	0.964921i	$-0.584561\pi$
$619$	11241.2	−	12973.0i	0.729921	−	0.842373i	0.992463	+	0.122547i	$0.0391063\pi$
$620$	4220.19	+	459.292i	0.273366	+	0.0297510i
$621$	3411.54	+	2081.68i	0.220451	+	0.134517i
$622$	−3997.67	−	3997.67i	−0.257704	−	0.257704i
$623$	267.841	+	3744.90i	0.0172244	+	0.240829i
$624$	−244.638	−	380.665i	−0.0156945	−	0.0244211i
$625$	4480.30	−	14968.9i	0.286739	−	0.958009i
$626$	−10812.2	+	4937.75i	−0.690321	+	0.315259i
$627$	−1002.03	+	750.113i	−0.0638235	+	0.0477777i
$628$	−2211.77	−	1207.72i	−0.140540	−	0.0767408i
$629$	−3648.84	+	5677.71i	−0.231302	+	0.359913i
$630$	4535.46	−	7621.43i	0.286821	−	0.481976i
$631$	−6939.05	+	23632.2i	−0.437780	+	1.49094i	0.385179	+	0.922842i	$0.374140\pi$
$631$	−6939.05	+	23632.2i	−0.437780	+	1.49094i	−0.822959	+	0.568100i	$0.807679\pi$
$632$	2553.18	+	182.607i	0.160696	+	0.0114932i
$633$	2168.02	+	155.060i	0.136131	+	0.00973628i
$634$	−3671.69	+	12504.6i	−0.230002	+	0.783316i
$635$	−1776.51	−	6998.41i	−0.111021	−	0.437360i
$636$	−1021.95	+	1590.18i	−0.0637151	+	0.0991427i
$637$	−4390.58	−	2397.44i	−0.273094	−	0.149121i
$638$	−1789.37	+	1339.51i	−0.111038	+	0.0831217i
$639$	13723.0	−	6267.10i	0.849570	−	0.387985i
$640$	−976.533	+	1046.13i	−0.0603138	+	0.0646123i
$641$	−2188.59	−	3405.51i	−0.134858	−	0.209844i	0.767256	−	0.641341i	$-0.221622\pi$
$641$	−2188.59	−	3405.51i	−0.134858	−	0.209844i	−0.902114	+	0.431498i	$0.857985\pi$
$642$	−46.5242	−	650.493i	−0.00286007	−	0.0399890i
$643$	−16590.8	−	16590.8i	−1.01754	−	1.01754i	−0.999843	−	0.0176956i	$-0.994367\pi$
$643$	−16590.8	−	16590.8i	−1.01754	−	1.01754i	−0.0176956	−	0.999843i	$-0.505633\pi$
$644$	6367.77	+	1709.51i	0.389635	+	0.104602i
$645$	−8.22523	+	75.5774i	−0.000502121	+	0.00461373i
$646$	1181.07	−	1363.03i	0.0719330	−	0.0830151i
$647$	−6139.44	−	1335.55i	−0.373054	−	0.0811530i	0.0221294	−	0.999755i	$-0.492955\pi$
$647$	−6139.44	−	1335.55i	−0.373054	−	0.0811530i	−0.395184	+	0.918602i	$0.629319\pi$
$648$	−4432.56	−	3318.17i	−0.268715	−	0.201157i
$649$	−1011.28	−	2214.39i	−0.0611649	−	0.133933i
$650$	3676.83	−	9779.91i	0.221873	−	0.590153i
$651$	−270.427	−	920.991i	−0.0162809	−	0.0554478i
$652$	337.282	+	1550.46i	0.0202592	+	0.0931300i
$653$	−2978.20	−	7984.86i	−0.178478	−	0.478517i	0.816648	−	0.577137i	$-0.195830\pi$
$653$	−2978.20	−	7984.86i	−0.178478	−	0.478517i	−0.995125	+	0.0986196i	$0.968557\pi$
$654$	−2811.28	−	825.467i	−0.168089	−	0.0493552i
$655$	−14138.3	+	9789.10i	−0.843406	+	0.583957i
$656$	2558.87	+	2953.09i	0.152297	+	0.175760i
$657$	−6944.67	−	12718.2i	−0.412385	−	0.755228i
$658$	7158.21	−	2669.87i	0.424097	−	0.158180i
$659$	−4505.31	−	2895.39i	−0.266316	−	0.171151i	0.400667	−	0.916224i	$-0.368778\pi$
$659$	−4505.31	−	2895.39i	−0.266316	−	0.171151i	−0.666983	+	0.745073i	$0.732415\pi$
$660$	806.394	+	561.451i	0.0475589	+	0.0331128i
$661$	−3601.01	−	517.746i	−0.211895	−	0.0304660i	0.0355495	−	0.999368i	$-0.488682\pi$
$661$	−3601.01	−	517.746i	−0.211895	−	0.0304660i	−0.247445	+	0.968902i	$0.579591\pi$
$662$	7812.98	−	20947.4i	0.458701	−	1.22983i
$663$	268.277	−	358.377i	0.0157150	−	0.0209928i
$664$	9151.19	−	5881.11i	0.534842	−	0.343722i
$665$	−9511.36	−	352.133i	−0.554639	−	0.0205340i
$666$		−	22633.5i		−	1.31686i
$667$	182.472	−	3792.35i	0.0105927	−	0.220151i
$668$	−5208.70	+	5208.70i	−0.301693	+	0.301693i
$669$	703.234	+	609.356i	0.0406407	+	0.0352153i
$670$	9170.77	+	18380.8i	0.528802	+	1.05987i
$671$	−598.158	−	4160.28i	−0.0344138	−	0.239353i
$672$	303.184	+	113.082i	0.0174041	+	0.00649140i
$673$	−15541.6	−	20761.1i	−0.890169	−	1.18913i	−0.981145	−	0.193273i	$-0.938090\pi$
$673$	−15541.6	−	20761.1i	−0.890169	−	1.18913i	0.0909765	−	0.995853i	$-0.471001\pi$
$674$	8312.08	−	2440.65i	0.475029	−	0.139481i
$675$	−11.8255	+	4528.94i	−0.000674317	+	0.258250i
$676$	−748.328	+	1638.61i	−0.0425767	+	0.0932299i
$677$	23351.1	−	12750.7i	1.32564	−	0.723853i	0.348671	−	0.937245i	$-0.386633\pi$
$677$	23351.1	−	12750.7i	1.32564	−	0.723853i	0.976967	+	0.213392i	$0.0684511\pi$
$678$	−97.8024	+	1367.46i	−0.00553994	+	0.0774585i
$679$	7293.44	−	6319.80i	0.412219	−	0.357189i
$680$	−1307.33	−	543.515i	−0.0737263	−	0.0306513i
$681$	9.92302	+	4.53169i	0.000558371	+	0.000255000i
$682$	−6023.27	+	1310.28i	−0.338186	+	0.0735678i
$683$	−5696.04	+	10431.5i	−0.319111	+	0.584409i	−0.987165	−	0.159705i	$-0.948946\pi$
$683$	−5696.04	+	10431.5i	−0.319111	+	0.584409i	0.668054	+	0.744113i	$0.267128\pi$
$684$	−860.761	+	5986.73i	−0.0481170	+	0.334661i
$685$	7420.47	−	14776.0i	0.413900	−	0.824178i
$686$	13687.7	−	1968.00i	0.761806	−	0.109531i
$687$	518.210	−	2382.17i	0.0287787	−	0.132293i
$688$	160.366	−	11.4696i	0.00888649	−	0.000635575i
$689$	−29185.7			−1.61377
$690$	−1607.73	+	448.268i	−0.0887030	+	0.0247323i
$691$	−16912.4			−0.931083			−0.465541	−	0.885026i	$-0.654140\pi$
$691$	−16912.4			−0.931083			−0.465541	+	0.885026i	$0.654140\pi$
$692$	9230.74	−	660.196i	0.507081	−	0.0362672i
$693$	−2737.43	+	12583.8i	−0.150053	+	0.689780i
$694$	−16882.2	+	2427.30i	−0.923402	+	0.132765i
$695$	−10100.4	−	30479.7i	−0.551269	−	1.66354i
$696$	26.5187	−	184.441i	0.00144424	−	0.0100449i
$697$	−1852.68	+	3392.93i	−0.100682	+	0.184385i
$698$	963.934	−	209.691i	0.0522714	−	0.0113709i
$699$	−3227.14	−	1473.79i	−0.174623	−	0.0797478i
$700$	2086.29	+	7174.48i	0.112649	+	0.387386i
$701$	−2077.36	+	1800.04i	−0.111927	+	0.0969853i	−0.709026	−	0.705182i	$-0.750865\pi$
$701$	−2077.36	+	1800.04i	−0.111927	+	0.0969853i	0.597099	+	0.802167i	$0.296320\pi$
$702$	−216.047	+	3020.74i	−0.0116156	+	0.162408i
$703$	−21318.6	+	11640.9i	−1.14374	+	0.624528i
$704$	863.238	−	1890.23i	0.0462138	−	0.101194i
$705$	−1215.49	+	1504.31i	−0.0649336	+	0.0803627i
$706$	−8960.88	+	2631.15i	−0.477687	+	0.140262i
$707$	−2166.56	−	2894.18i	−0.115250	−	0.153956i
$708$	190.146	+	70.9209i	0.0100934	+	0.00376465i
$709$	−2224.70	−	15473.1i	−0.117842	−	0.819611i	−0.959924	−	0.280261i	$-0.909579\pi$
$709$	−2224.70	−	15473.1i	−0.117842	−	0.819611i	0.842082	−	0.539350i	$-0.181330\pi$
$710$	−4029.45	+	12054.0i	−0.212990	+	0.637154i
$711$	−6418.19	−	5561.39i	−0.338538	−	0.293345i
$712$	−1421.27	+	1421.27i	−0.0748094	+	0.0748094i
$713$	4802.30	−	9304.21i	0.252240	−	0.488703i
$714$			320.133i			0.0167797i
$715$	−561.297	+	15161.0i	−0.0293585	+	0.792994i
$716$	−2508.50	+	1612.12i	−0.130932	+	0.0841447i
$717$	105.464	−	140.883i	0.00549319	−	0.00733804i
$718$	−827.557	+	2218.77i	−0.0430141	+	0.115325i
$719$	−16111.5	−	2316.49i	−0.835687	−	0.120154i	−0.288831	−	0.957380i	$-0.593267\pi$
$719$	−16111.5	−	2316.49i	−0.835687	−	0.120154i	−0.546856	+	0.837226i	$0.684176\pi$
$720$	4673.65	−	836.920i	0.241912	−	0.0433197i
$721$	−15835.4	−	10176.8i	−0.817947	−	0.525663i
$722$	−6771.43	+	2525.61i	−0.349039	+	0.130185i
$723$	−532.308	−	974.849i	−0.0273814	−	0.0501453i
$724$	11008.9	+	12704.9i	0.565114	+	0.652176i
$725$	3781.66	−	2052.14i	0.193720	−	0.105124i
$726$	359.400	+	105.529i	0.0183727	+	0.00539472i
$727$	11518.9	+	30883.4i	0.587637	+	1.57552i	0.801078	+	0.598560i	$0.204260\pi$
$727$	11518.9	+	30883.4i	0.587637	+	1.57552i	−0.213441	+	0.976956i	$0.568467\pi$
$728$	1062.02	+	4882.03i	0.0540674	+	0.248544i
$729$	4989.00	+	16991.0i	0.253468	+	0.863231i
$730$	11824.7	+	3034.53i	0.599524	+	0.153853i
$731$	66.0760	+	144.686i	0.00334324	+	0.00732068i
$732$	280.500	+	209.980i	0.0141634	+	0.0106026i
$733$	25324.3	+	5508.97i	1.27609	+	0.277597i	0.799039	−	0.601279i	$-0.205342\pi$
$733$	25324.3	+	5508.97i	1.27609	+	0.277597i	0.477051	+	0.878875i	$0.341706\pi$
$734$	−5675.39	+	6549.75i	−0.285399	+	0.329367i
$735$	−705.869	+	567.307i	−0.0354236	+	0.0284700i
$736$	1540.78	+	3175.69i	0.0771655	+	0.159046i
$737$	−21091.2	−	21091.2i	−1.05415	−	1.05415i
$738$	−924.852	−	12931.1i	−0.0461305	−	0.644988i
$739$	−3240.02	−	5041.57i	−0.161280	−	0.250957i	0.751203	−	0.660072i	$-0.229474\pi$
$739$	−3240.02	−	5041.57i	−0.161280	−	0.250957i	−0.912483	+	0.409114i	$0.865838\pi$
$740$	13938.7	+	13011.4i	0.692426	+	0.646361i
$741$	1465.54	−	669.292i	0.0726560	−	0.0331809i
$742$	16708.1	−	12507.6i	0.826651	−	0.618823i
$743$	27306.7	+	14910.6i	1.34830	+	0.736228i	0.981024	−	0.193884i	$-0.0621087\pi$
$743$	27306.7	+	14910.6i	1.34830	+	0.736228i	0.367276	+	0.930112i	$0.380291\pi$
$744$	277.821	−	432.298i	0.0136901	−	0.0213022i
$745$	−8205.90	−	4883.28i	−0.403545	−	0.240147i
$746$	−1048.11	+	3569.53i	−0.0514397	+	0.175187i
$747$	−35998.8	−	2574.68i	−1.76322	−	0.126108i
$748$	2050.60	+	146.662i	0.100237	+	0.00716910i
$749$	−2028.68	+	6909.04i	−0.0989669	+	0.337050i
$750$	−1379.26	−	1294.26i	−0.0671513	−	0.0630128i
$751$	19854.4	−	30894.1i	0.964712	−	1.50112i	0.102401	−	0.994743i	$-0.467348\pi$
$751$	19854.4	−	30894.1i	0.964712	−	1.50112i	0.862311	−	0.506378i	$-0.169016\pi$
$752$	3589.77	+	1960.16i	0.174076	+	0.0950528i
$753$	2813.85	−	2106.42i	0.136178	−	0.101942i
$754$	2617.09	−	1195.18i	0.126404	−	0.0577268i
$755$	11799.7	−	406.002i	0.568787	−	0.0195708i
$756$	−1170.86	−	1821.89i	−0.0563276	−	0.0876475i
$757$	1036.32	+	14489.7i	0.0497566	+	0.695688i	0.959713	+	0.280983i	$0.0906605\pi$
$757$	1036.32	+	14489.7i	0.0497566	+	0.695688i	−0.909956	+	0.414705i	$0.863885\pi$
$758$	−14955.6	−	14955.6i	−0.716637	−	0.716637i
$759$	2007.71	−	1357.46i	0.0960150	−	0.0649178i
$760$	−3192.05	−	3971.70i	−0.152353	−	0.189564i
$761$	−9830.74	+	11345.3i	−0.468284	+	0.540428i	−0.939933	−	0.341358i	$-0.889113\pi$
$761$	−9830.74	+	11345.3i	−0.468284	+	0.540428i	0.471650	+	0.881786i	$0.343659\pi$
$762$	−854.057	−	185.789i	−0.0406027	−	0.00883257i
$763$	25898.3	+	19387.2i	1.22881	+	0.919875i
$764$	255.180	+	558.767i	0.0120839	+	0.0264600i
$765$	2391.63	+	4042.89i	0.113032	+	0.191073i
$766$	3558.69	+	12119.8i	0.167860	+	0.571679i
$767$	666.062	+	3061.84i	0.0313561	+	0.144141i
$768$	60.5390	+	162.311i	0.00284442	+	0.00762618i
$769$	18988.0	+	5575.38i	0.890409	+	0.261448i	0.694773	−	0.719229i	$-0.255505\pi$
$769$	18988.0	+	5575.38i	0.890409	+	0.261448i	0.195636	+	0.980677i	$0.437323\pi$
$770$	−6175.95	−	8919.89i	−0.289046	−	0.417468i
$771$	−1212.45	−	1399.24i	−0.0566345	−	0.0653597i
$772$	−8175.04	−	14971.5i	−0.381122	−	0.697973i
$773$	−7531.40	+	2809.07i	−0.350434	+	0.130705i	−0.518516	−	0.855068i	$-0.673515\pi$
$773$	−7531.40	+	2809.07i	−0.350434	+	0.130705i	0.168082	+	0.985773i	$0.446243\pi$
$774$	−448.738	−	288.386i	−0.0208392	−	0.0133926i
$775$	11837.4	−	815.565i	0.548660	−	0.0378012i
$776$	5113.92	+	735.270i	0.236571	+	0.0340138i
$777$	1506.71	−	4039.64i	0.0695660	−	0.186514i
$778$	−4635.20	+	6191.90i	−0.213599	+	0.285335i
$779$	−11704.3	+	7521.87i	−0.538316	+	0.345955i
$780$	−860.626	−	926.800i	−0.0395068	−	0.0425446i
$781$		−	18455.2i		−	0.845554i
$782$	−2411.01	+	2526.17i	−0.110253	+	0.115519i
$783$	−881.844	+	881.844i	−0.0402485	+	0.0402485i
$784$	1447.37	+	1254.16i	0.0659336	+	0.0571318i
$785$	−6680.31	−	2233.11i	−0.303733	−	0.101533i
$786$	296.249	+	2060.46i	0.0134439	+	0.0935040i
$787$	32842.9	+	12249.8i	1.48758	+	0.554838i	0.956307	−	0.292365i	$-0.0944422\pi$
$787$	32842.9	+	12249.8i	1.48758	+	0.554838i	0.531270	+	0.847202i	$0.321715\pi$
$788$	−1949.22	−	2603.85i	−0.0881194	−	0.117714i
$789$	2038.58	−	598.581i	0.0919840	−	0.0270090i
$790$	7114.59	−	755.503i	0.320412	−	0.0340248i
$791$	6288.23	−	13769.3i	0.282660	−	0.618938i
$792$	−6051.03	+	3304.11i	−0.271482	+	0.148240i
$793$	−385.948	+	5396.25i	−0.0172830	+	0.241648i
$794$	−11854.8	+	10272.2i	−0.529862	+	0.459128i
$795$	−2028.25	+	4878.59i	−0.0904836	+	0.217643i
$796$	−15649.6	−	7146.91i	−0.696839	−	0.318236i
$797$	7426.42	−	1615.52i	0.330059	−	0.0718000i	−0.0444821	−	0.999010i	$-0.514164\pi$
$797$	7426.42	−	1615.52i	0.330059	−	0.0718000i	0.374541	+	0.927210i	$0.377800\pi$
$798$	−552.165	+	1011.21i	−0.0244943	+	0.0448579i
$799$	−575.866	+	4005.24i	−0.0254977	+	0.177340i
$800$	−2171.34	+	3359.36i	−0.0959607	+	0.148464i
$801$	6600.74	−	949.044i	0.291168	−	0.0418637i
$802$	−496.443	+	2282.11i	−0.0218579	+	0.100479i
$803$	−17681.4	+	1264.60i	−0.777038	+	0.0555748i
$804$	2486.57			0.109073
$805$	18362.0	+	1566.10i	0.803945	+	0.0685686i
$806$	7934.27			0.346740
$807$	−165.928	+	11.8674i	−0.00723786	+	0.000517662i
$808$	411.412	−	1891.23i	0.0179127	−	0.0823431i
$809$	−15558.0	+	2236.90i	−0.676130	+	0.0972128i	−0.471822	−	0.881694i	$-0.656403\pi$
$809$	−15558.0	+	2236.90i	−0.676130	+	0.0972128i	−0.204308	+	0.978907i	$0.565494\pi$
$810$	−13830.2	−	6945.49i	−0.599930	−	0.301284i
$811$	−2517.36	+	17508.6i	−0.108997	+	0.758089i	0.859871	+	0.510511i	$0.170544\pi$
$811$	−2517.36	+	17508.6i	−0.108997	+	0.758089i	−0.968868	+	0.247578i	$0.920365\pi$
$812$	−986.025	+	1805.77i	−0.0426141	+	0.0780420i
$813$	3303.76	−	718.690i	0.142519	−	0.0310031i
$814$	−25185.5	−	11501.8i	−1.08446	−	0.495256i
$815$	1691.86	+	4099.64i	0.0727157	+	0.176201i
$816$	−129.524	+	112.233i	−0.00555668	+	0.00481489i
$817$	−40.8382	+	570.993i	−0.00174877	+	0.0244511i
$818$	3751.55	−	2048.50i	0.160354	−	0.0875601i
$819$	6886.01	−	15078.3i	0.293793	−	0.643317i
$820$	8495.21	+	6864.19i	0.361787	+	0.292327i
$821$	32772.3	−	9622.80i	1.39313	−	0.409060i	0.502811	−	0.864397i	$-0.332299\pi$
$821$	32772.3	−	9622.80i	1.39313	−	0.409060i	0.890319	+	0.455337i	$0.150481\pi$
$822$	−1199.47	−	1602.31i	−0.0508958	−	0.0679888i
$823$	−19293.8	−	7196.20i	−0.817179	−	0.304792i	−0.0941045	−	0.995562i	$-0.529999\pi$
$823$	−19293.8	−	7196.20i	−0.817179	−	0.304792i	−0.723074	+	0.690770i	$0.757271\pi$
$824$	−1434.15	−	9974.72i	−0.0606322	−	0.421706i
$825$	2495.27	+	1147.43i	0.105302	+	0.0484224i
$826$	−1693.46	−	1467.39i	−0.0713353	−	0.0618124i
$827$	5953.70	−	5953.70i	0.250339	−	0.250339i	−0.570770	−	0.821110i	$-0.693355\pi$
$827$	5953.70	−	5953.70i	0.250339	−	0.250339i	0.821110	+	0.570770i	$0.193355\pi$
$828$	2221.79	−	11498.1i	0.0932519	−	0.482593i
$829$			41515.5i			1.73932i	0.493655	+	0.869658i	$0.335661\pi$
$829$			41515.5i			1.73932i	−0.493655	+	0.869658i	$0.664339\pi$
$830$	22280.3	−	20689.5i	0.931760	−	0.865231i
$831$	1573.08	−	1010.95i	0.0656671	−	0.0422017i
$832$	−1602.92	+	2141.25i	−0.0667923	+	0.0892240i
$833$	−662.134	+	1775.25i	−0.0275409	+	0.0738401i
$834$	−3847.34	−	553.164i	−0.159739	−	0.0229670i
$835$	−11764.6	+	16897.1i	−0.487580	+	0.700295i
$836$	6224.33	+	4000.14i	0.257504	+	0.165488i
$837$	−3222.39	+	1201.89i	−0.133073	+	0.0496336i
$838$	14285.0	+	26161.0i	0.588863	+	1.07842i
$839$	−8329.87	−	9613.18i	−0.342764	−	0.395571i	0.558028	−	0.829822i	$-0.311558\pi$
$839$	−8329.87	−	9613.18i	−0.342764	−	0.395571i	−0.900792	+	0.434252i	$0.857013\pi$
$840$	889.870	+	161.750i	0.0365517	+	0.00664394i
$841$	−22264.3	−	6537.38i	−0.912882	−	0.268046i
$842$	−7994.99	−	21435.4i	−0.327228	−	0.877331i
$843$	−430.036	−	1976.84i	−0.0175697	−	0.0807664i
$844$	−3619.72	−	12327.6i	−0.147626	−	0.502766i
$845$	−1251.57	+	4877.03i	−0.0509531	+	0.198550i
$846$	−5637.13	−	12343.6i	−0.229088	−	0.501633i
$847$	−3310.90	−	2478.51i	−0.134314	−	0.100546i
$848$	10918.1	+	2375.09i	0.442133	+	0.0961802i
$849$	774.967	−	894.360i	0.0313272	−	0.0361535i
$850$	−3864.67	−	851.282i	−0.155949	−	0.0343514i
$851$	42313.0	−	20529.4i	1.70443	−	0.826954i
$852$	1087.89	+	1087.89i	0.0437449	+	0.0437449i
$853$	1255.68	+	17556.8i	0.0504030	+	0.704727i	0.958342	+	0.285624i	$0.0922008\pi$
$853$	1255.68	+	17556.8i	0.0504030	+	0.704727i	−0.907939	+	0.419103i	$0.862345\pi$
$854$	−2091.62	−	3254.63i	−0.0838102	−	0.130411i
$855$	581.339	+	16895.5i	0.0232531	+	0.675805i
$856$	−3506.58	+	1601.40i	−0.140015	+	0.0639425i
$857$	17498.3	−	13099.0i	0.697467	−	0.522117i	−0.190694	−	0.981649i	$-0.561074\pi$
$857$	17498.3	−	13099.0i	0.697467	−	0.522117i	0.888161	+	0.459532i	$0.151983\pi$
$858$	1611.87	+	880.147i	0.0641355	+	0.0350206i
$859$	9482.79	−	14755.5i	0.376657	−	0.586090i	−0.600235	−	0.799824i	$-0.704926\pi$
$859$	9482.79	−	14755.5i	0.376657	−	0.586090i	0.976892	+	0.213734i	$0.0685625\pi$
$860$	435.568	−	110.567i	0.0172706	−	0.00438406i
$861$	695.755	−	2369.52i	0.0275392	−	0.0937899i
$862$	13200.5	+	944.120i	0.521591	+	0.0373050i
$863$	24033.5	+	1718.91i	0.947982	+	0.0678010i	0.536761	−	0.843734i	$-0.319648\pi$
$863$	24033.5	+	1718.91i	0.947982	+	0.0678010i	0.411221	+	0.911535i	$0.365102\pi$
$864$	326.644	−	1112.45i	0.0128619	−	0.0438035i
$865$	25071.5	−	6364.26i	0.985497	−	0.250163i
$866$	−17876.7	+	27816.7i	−0.701474	+	1.09151i
$867$	2769.11	+	1512.05i	0.108471	+	0.0592295i
$868$	−4542.19	+	3400.24i	−0.177617	+	0.132963i
$869$	−9450.04	+	4315.69i	−0.368896	+	0.168469i
$870$	−17.9101	−	520.523i	−0.000697942	−	0.0202843i
$871$	20756.8	+	32298.2i	0.807482	+	1.25647i
$872$	1235.54	+	17275.2i	0.0479826	+	0.670884i
$873$	−12120.7	−	12120.7i	−0.469900	−	0.469900i
$874$	−11972.9	+	3820.99i	−0.463374	+	0.147880i
$875$	9274.80	+	18711.4i	0.358338	+	0.722927i
$876$	967.735	−	1116.83i	0.0373251	−	0.0430754i
$877$	−15924.4	−	3464.14i	−0.613146	−	0.133382i	−0.104741	−	0.994500i	$-0.533401\pi$
$877$	−15924.4	−	3464.14i	−0.613146	−	0.133382i	−0.508405	+	0.861118i	$0.669765\pi$
$878$	8530.84	+	6386.11i	0.327907	+	0.245468i
$879$	1956.54	+	4284.23i	0.0750768	+	0.164395i
$880$	1443.76	−	5625.92i	0.0553057	−	0.215511i
$881$	12035.0	+	40987.6i	0.460239	+	1.56743i	0.783669	+	0.621179i	$0.213346\pi$
$881$	12035.0	+	40987.6i	0.460239	+	1.56743i	−0.323430	+	0.946252i	$0.604836\pi$
$882$	−1350.64	−	6208.80i	−0.0515629	−	0.237031i
$883$	8060.46	+	21610.9i	0.307198	+	0.823631i	0.995195	+	0.0979165i	$0.0312178\pi$
$883$	8060.46	+	21610.9i	0.307198	+	0.823631i	−0.687996	+	0.725714i	$0.741509\pi$
$884$	−2539.02	−	745.522i	−0.0966022	−	0.0283650i
$885$	558.095	+	101.444i	0.0211979	+	0.00385311i
$886$	22322.8	+	25761.9i	0.846443	+	0.976847i
$887$	2723.02	+	4986.84i	0.103078	+	0.188773i	0.924128	−	0.382083i	$-0.124793\pi$
$887$	2723.02	+	4986.84i	0.103078	+	0.188773i	−0.821050	+	0.570856i	$0.806611\pi$
$888$	2162.64	−	806.624i	0.0817269	−	0.0304826i
$889$	8118.56	+	5217.48i	0.306285	+	0.196838i
$890$	−3210.13	+	4610.60i	−0.120903	+	0.173649i
$891$	22243.6	+	3198.15i	0.836352	+	0.120249i
$892$	1922.17	−	5153.54i	0.0721514	−	0.193445i
$893$	−8727.23	+	11658.2i	−0.327039	+	0.436873i
$894$	−972.416	+	624.934i	−0.0363786	+	0.0233791i
$895$	−6107.42	+	5671.35i	−0.228099	+	0.211813i
$896$		−	1912.75i		−	0.0713174i
$897$	−2896.61	+	1158.02i	−0.107821	+	0.0431050i
$898$	4164.43	−	4164.43i	0.154754	−	0.154754i
$899$	2469.28	+	2139.65i	0.0916076	+	0.0793784i
$900$	12446.4	−	4605.27i	0.460977	−	0.170566i
$901$	1573.18	+	10941.7i	0.0581689	+	0.404573i
$902$	−14859.1	−	5542.17i	−0.548509	−	0.204583i
$903$	−60.8932	−	81.3438i	−0.00224408	−	0.00299773i
$904$	7775.54	−	2283.11i	0.286074	−	0.0839988i
$905$	36548.5	+	29531.4i	1.34245	+	1.08471i
$906$	593.713	−	1300.05i	0.0217713	−	0.0476725i
$907$	−1090.20	+	595.295i	−0.0399113	+	0.0217932i	−0.499081	−	0.866555i	$-0.666329\pi$
$907$	−1090.20	+	595.295i	−0.0399113	+	0.0217932i	0.459169	+	0.888349i	$0.348147\pi$
$908$	4.60017	−	64.3187i	0.000168130	−	0.00235076i
$909$	−4852.97	+	4205.12i	−0.177077	+	0.153438i
$910$	5327.26	+	12908.8i	0.194063	+	0.470244i
$911$	18704.1	+	8541.86i	0.680234	+	0.310652i	0.725401	−	0.688327i	$-0.241655\pi$
$911$	18704.1	+	8541.86i	0.680234	+	0.310652i	−0.0451665	+	0.998979i	$0.514382\pi$
$912$	−602.712	+	131.112i	−0.0218835	+	0.00476047i
$913$	−21158.8	+	38749.4i	−0.766980	+	1.40462i
$914$	69.8827	−	486.045i	0.00252901	−	0.0175896i
$915$	875.200	+	439.524i	0.0316210	+	0.0158800i
$916$	−14263.9	+	2050.84i	−0.514511	+	0.0739755i
$917$	4885.68	−	22459.1i	0.175942	−	0.808794i
$918$	1144.12	−	81.8289i	0.0411345	−	0.00294200i
$919$	27142.2			0.974254			0.487127	−	0.873331i	$-0.338045\pi$
$919$	27142.2			0.974254			0.487127	+	0.873331i	$0.338045\pi$
$920$	5803.78	+	7978.23i	0.207984	+	0.285907i
$921$	−436.702			−0.0156241
$922$	29702.2	−	2124.34i	1.06094	−	0.0758802i
$923$	−5049.46	+	23212.0i	−0.180070	+	0.827770i
$924$	−1299.95	+	186.904i	−0.0462825	+	0.00665442i
$925$	44760.2	+	28931.1i	1.59103	+	1.02838i
$926$	−2756.05	+	19168.8i	−0.0978072	+	0.680264i
$927$	−16023.2	+	29344.4i	−0.567715	+	1.03969i
$928$	−1076.29	+	234.132i	−0.0380721	+	0.00828208i
$929$	−32544.8	−	14862.7i	−1.14937	−	0.524897i	−0.252673	−	0.967552i	$-0.581310\pi$
$929$	−32544.8	−	14862.7i	−1.14937	−	0.524897i	−0.896692	+	0.442654i	$0.854037\pi$
$930$	551.388	−	1326.27i	0.0194416	−	0.0467635i
$931$	−5153.45	+	4465.49i	−0.181415	+	0.157197i
$932$	−1496.06	+	20917.6i	−0.0525804	+	0.735170i
$933$	−1678.88	+	916.738i	−0.0589111	+	0.0321679i
$934$	−851.937	+	1865.48i	−0.0298461	+	0.0653538i
$935$	5714.11	−	606.786i	0.199863	−	0.0212235i
$936$	8514.71	−	2500.14i	0.297342	−	0.0873074i
$937$	−13286.6	−	17748.8i	−0.463238	−	0.618814i	0.506713	−	0.862115i	$-0.330861\pi$
$937$	−13286.6	−	17748.8i	−0.463238	−	0.618814i	−0.969951	+	0.243301i	$0.921770\pi$
$938$	−25724.2	−	9594.64i	−0.895443	−	0.333983i
$939$	572.347	+	3980.76i	0.0198912	+	0.138346i
$940$	10842.3	+	3624.41i	0.376211	+	0.125761i
$941$	−38048.8	−	32969.5i	−1.31813	−	1.14216i	−0.979545	−	0.201225i	$-0.935508\pi$
$941$	−38048.8	−	32969.5i	−1.31813	−	1.14216i	−0.338580	−	0.940937i	$-0.609947\pi$
$942$	−602.909	+	602.909i	−0.0208533	+	0.0208533i
$943$	23335.7	−	13458.0i	0.805850	−	0.464743i
$944$		−	1199.61i		−	0.0413601i
$945$	−4119.02	−	4435.74i	−0.141790	−	0.152693i
$946$	−548.942	+	352.783i	−0.0188664	+	0.0121247i
$947$	18254.3	−	24384.9i	0.626383	−	0.836750i	−0.369325	−	0.929300i	$-0.620411\pi$
$947$	18254.3	−	24384.9i	0.626383	−	0.836750i	0.995708	+	0.0925505i	$0.0295020\pi$
$948$	302.660	−	811.462i	0.0103691	−	0.0278007i
$949$	22584.7	+	3247.19i	0.772531	+	0.111073i
$950$	−10739.2	−	9354.74i	−0.366762	−	0.319482i
$951$	3709.53	+	2383.97i	0.126488	+	0.0812886i
$952$	1773.02	−	661.303i	0.0603613	−	0.0225136i
$953$	−15733.6	−	28813.9i	−0.534796	−	0.979406i	−0.995760	−	0.0919869i	$-0.970678\pi$
$953$	−15733.6	−	28813.9i	−0.534796	−	0.979406i	0.460964	−	0.887419i	$-0.347504\pi$
$954$	−24276.2	−	28016.2i	−0.823869	−	0.950796i
$955$	977.378	+	1411.62i	0.0331175	+	0.0478314i
$956$	−998.124	−	293.076i	−0.0337674	−	0.00991501i
$957$	264.291	+	708.592i	0.00892719	+	0.0239347i
$958$	−6839.17	−	31439.2i	−0.230651	−	1.06028i
$959$	6226.21	+	21204.5i	0.209650	+	0.714004i
$960$	246.530	+	416.744i	0.00828827	+	0.0140108i
$961$	−8632.54	−	18902.6i	−0.289770	−	0.634508i
$962$	28530.1	+	21357.3i	0.956181	+	0.715788i
$963$	12497.5	+	2718.67i	0.418200	+	0.0909738i
$964$	−4299.50	+	4961.89i	−0.143649	+	0.165780i
$965$	−29868.4	−	37163.6i	−0.996370	−	1.23973i
$966$	1161.97	−	1904.29i	0.0387018	−	0.0634259i
$967$	−16350.2	−	16350.2i	−0.543729	−	0.543729i	0.380891	−	0.924620i	$-0.375617\pi$
$967$	−16350.2	−	16350.2i	−0.543729	−	0.543729i	−0.924620	+	0.380891i	$0.875617\pi$
$968$	−157.955	−	2208.49i	−0.00524468	−	0.0733303i
$969$	−329.913	−	513.355i	−0.0109374	−	0.0170189i
$970$	14432.3	−	496.585i	0.477724	−	0.0164375i
$971$	49595.1	−	22649.3i	1.63912	−	0.748559i	0.639323	−	0.768938i	$-0.279215\pi$
$971$	49595.1	−	22649.3i	1.63912	−	0.748559i	0.999792	+	0.0203791i	$0.00648732\pi$
$972$	−4632.27	+	3467.68i	−0.152860	+	0.114430i
$973$	37667.3	+	20567.9i	1.24107	+	0.677674i
$974$	13132.7	−	20434.9i	0.432031	−	0.672254i
$975$	−2824.48	−	2125.91i	−0.0927750	−	0.0698293i
$976$	583.518	−	1987.28i	0.0191373	−	0.0651755i
$977$	−3295.74	−	235.716i	−0.107922	−	0.00771874i	0.0172736	−	0.999851i	$-0.494501\pi$
$977$	−3295.74	−	235.716i	−0.107922	−	0.00771874i	−0.125196	+	0.992132i	$0.539956\pi$
$978$	535.495	+	38.2994i	0.0175084	+	0.00125223i
$979$	2298.30	−	7827.29i	0.0750296	−	0.255527i
$980$	4600.09	+	2737.49i	0.149943	+	0.0892304i
$981$	31065.9	−	48339.5i	1.01107	−	1.57325i
$982$	−36283.5	−	19812.3i	−1.17908	−	0.643825i
$983$	−38784.6	+	29033.8i	−1.25843	+	0.942049i	−0.999714	−	0.0239038i	$-0.992390\pi$
$983$	−38784.6	+	29033.8i	−1.25843	+	0.942049i	−0.258717	+	0.965953i	$0.583300\pi$
$984$	1202.62	−	549.217i	0.0389614	−	0.0177931i
$985$	−6645.81	−	6203.68i	−0.214978	−	0.200676i
$986$	−589.140	−	916.720i	−0.0190284	−	0.0296088i
$987$	−184.408	−	2578.35i	−0.00594707	−	0.0831509i
$988$	−6734.19	−	6734.19i	−0.216845	−	0.216845i
$989$	132.114	−	1100.49i	0.00424771	−	0.0353827i
$990$	−15020.4	+	12071.9i	−0.482202	+	0.387546i
$991$	−26283.4	+	30332.6i	−0.842502	+	0.972299i	−0.999884	−	0.0152387i	$-0.995149\pi$
$991$	−26283.4	+	30332.6i	−0.842502	+	0.972299i	0.157382	+	0.987538i	$0.449695\pi$
$992$	−2968.14	−	645.678i	−0.0949984	−	0.0206656i
$993$	−6055.65	−	4533.20i	−0.193525	−	0.144871i
$994$	−7056.82	−	15452.3i	−0.225180	−	0.493075i
$995$	−46578.1	−	11953.1i	−1.48405	−	0.380844i
$996$	−1036.93	−	3531.46i	−0.0329884	−	0.112348i
$997$	−4847.32	−	22282.7i	−0.153978	−	0.707825i	−0.987792	−	0.155780i	$-0.950211\pi$
$997$	−4847.32	−	22282.7i	−0.153978	−	0.707825i	0.833814	−	0.552046i	$-0.186153\pi$
$998$	3436.18	+	9212.76i	0.108988	+	0.292209i
$999$	−14822.3	−	4352.22i	−0.469426	−	0.137836i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.l.a.7.9	✓	720
5.3	odd	4	inner	230.4.l.a.53.27	yes	720
23.10	odd	22	inner	230.4.l.a.217.27	yes	720
115.33	even	44	inner	230.4.l.a.33.9	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.l.a.7.9	✓	720	1.1	even	1	trivial
230.4.l.a.33.9	yes	720	115.33	even	44	inner
230.4.l.a.53.27	yes	720	5.3	odd	4	inner
230.4.l.a.217.27	yes	720	23.10	odd	22	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99490 + 0.142678i) q^{2} +(-0.143842 + 0.661230i) q^{3} +(3.95929 - 0.569259i) q^{4} +(10.6128 - 3.51689i) q^{5} +(0.192607 - 1.33961i) q^{6} +(-7.16158 + 13.1154i) q^{7} +(-7.81717 + 1.70052i) q^{8} +(24.1435 + 11.0260i) q^{9} +(-20.6697 + 8.53008i) q^{10} +(24.5384 - 21.2626i) q^{11} +(-0.193099 + 2.69988i) q^{12} +(-36.6808 + 20.0292i) q^{13} +(12.4154 - 27.1859i) q^{14} +(0.798912 + 7.52337i) q^{15} +(15.3519 - 4.50772i) q^{16} +(9.48612 + 12.6720i) q^{17} +(-49.7372 - 18.5510i) q^{18} +(8.10752 + 56.3890i) q^{19} +(40.0171 - 19.9658i) q^{20} +(-7.64219 - 6.62200i) q^{21} +(-45.9180 + 45.9180i) q^{22} +(-10.4325 - 109.810i) q^{23} -5.41355i q^{24} +(100.263 - 74.6482i) q^{25} +(70.3169 - 45.1899i) q^{26} +(-21.7128 + 29.0049i) q^{27} +(-20.8886 + 56.0046i) q^{28} +(34.0703 + 4.89857i) q^{29} +(-2.66718 - 14.8944i) q^{30} +(79.8548 + 51.3195i) q^{31} +(-29.9824 + 11.1829i) q^{32} +(10.5298 + 19.2840i) q^{33} +(-20.7319 - 23.9259i) q^{34} +(-29.8787 + 164.378i) q^{35} +(101.868 + 29.9111i) q^{36} +(149.001 + 399.487i) q^{37} +(-24.2192 - 111.334i) q^{38} +(-7.96769 - 27.1355i) q^{39} +(-76.9815 + 45.5395i) q^{40} +(101.452 + 222.149i) q^{41} +(16.1903 + 12.1199i) q^{42} +(9.81886 + 2.13596i) q^{43} +(85.0506 - 98.1536i) q^{44} +(295.008 + 32.1063i) q^{45} +(36.4793 + 217.571i) q^{46} +(180.757 + 180.757i) q^{47} +(0.772397 + 10.7995i) q^{48} +(64.7130 + 100.695i) q^{49} +(-189.364 + 163.221i) q^{50} +(-9.74359 + 4.44975i) q^{51} +(-133.828 + 100.182i) q^{52} +(612.918 + 334.679i) q^{53} +(39.1766 - 60.9600i) q^{54} +(185.643 - 311.955i) q^{55} +(33.6802 - 114.704i) q^{56} +(-38.4523 - 2.75016i) q^{57} +(-68.6659 - 4.91108i) q^{58} +(21.1230 - 71.9384i) q^{59} +(7.44587 + 29.3324i) q^{60} +(69.9852 - 108.899i) q^{61} +(-166.625 - 90.9840i) q^{62} +(-317.516 + 237.690i) q^{63} +(58.2164 - 26.5866i) q^{64} +(-318.845 + 341.569i) q^{65} +(-23.7574 - 36.9673i) q^{66} +(-65.5355 - 916.306i) q^{67} +(44.7719 + 44.7719i) q^{68} +(74.1100 + 8.89694i) q^{69} +(36.1520 - 332.182i) q^{70} +(372.219 - 429.563i) q^{71} +(-207.484 - 45.1354i) q^{72} +(-437.058 - 327.177i) q^{73} +(-354.240 - 775.678i) q^{74} +(34.9376 + 77.0343i) q^{75} +(64.1999 + 218.645i) q^{76} +(103.135 + 474.106i) q^{77} +(19.7664 + 52.9958i) q^{78} +(-307.002 - 90.1439i) q^{79} +(147.073 - 101.830i) q^{80} +(453.241 + 523.068i) q^{81} +(-234.083 - 428.691i) q^{82} +(-1274.02 + 475.186i) q^{83} +(-34.0272 - 21.8680i) q^{84} +(145.240 + 101.123i) q^{85} +(-19.8924 - 2.86010i) q^{86} +(-8.13981 + 21.8237i) q^{87} +(-155.663 + 207.942i) q^{88} +(211.363 - 135.834i) q^{89} +(-593.093 - 21.9577i) q^{90} -624.526i q^{91} +(-103.815 - 428.829i) q^{92} +(-45.4204 + 45.4204i) q^{93} +(-386.383 - 334.803i) q^{94} +(284.358 + 569.932i) q^{95} +(-3.08172 - 21.4338i) q^{96} +(-605.095 - 225.689i) q^{97} +(-143.463 - 191.645i) q^{98} +(826.885 - 242.795i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q + 16 q^{3} + 16 q^{6} + 64 q^{12} - 192 q^{13} + 1152 q^{16} + 144 q^{18} + 1660 q^{23} - 880 q^{25} - 304 q^{26} - 728 q^{27} - 352 q^{28} - 608 q^{31} - 3872 q^{33} - 688 q^{35} - 2816 q^{36} - 2376 q^{37}+ \cdots + 14352 q^{98}+O(q^{100}) \) 720 * q + 16 * q^3 + 16 * q^6 + 64 * q^12 - 192 * q^13 + 1152 * q^16 + 144 * q^18 + 1660 * q^23 - 880 * q^25 - 304 * q^26 - 728 * q^27 - 352 * q^28 - 608 * q^31 - 3872 * q^33 - 688 * q^35 - 2816 * q^36 - 2376 * q^37 + 2208 * q^41 + 256 * q^46 + 3640 * q^47 - 256 * q^48 - 272 * q^50 - 768 * q^52 + 2360 * q^55 - 3872 * q^56 - 7656 * q^57 + 2112 * q^61 + 1376 * q^62 + 10912 * q^66 + 1104 * q^70 + 22752 * q^71 - 128 * q^72 + 1296 * q^73 - 5396 * q^75 + 752 * q^77 - 6000 * q^78 - 3928 * q^81 - 80 * q^82 + 3060 * q^85 - 10472 * q^86 - 6760 * q^87 - 1104 * q^92 + 5288 * q^93 + 9392 * q^95 - 256 * q^96 + 25344 * q^97 + 14352 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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