LMFDB - Embedded newform 33.7.h.a.5.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [33,7,Mod(5,33)] 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("33.5"); S:= CuspForms(chi, 7); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(33, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 4])) N = Newforms(chi, 7, names="a")

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	33.h (of order $10$, degree $4$, 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:	$7.59178475946$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			5.6
Character	$\chi$	$=$	33.5
Dual form			33.7.h.a.20.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-9.48700 + 3.08251i) q^{2} +(-4.13517 - 26.6815i) q^{3} +(28.7242 - 20.8694i) q^{4} +(-210.493 - 68.3933i) q^{5} +(121.476 + 240.380i) q^{6} +(290.276 - 210.898i) q^{7} +(167.074 - 229.958i) q^{8} +(-694.801 + 220.665i) q^{9} +2207.77 q^{10} +(-979.624 + 901.054i) q^{11} +(-675.604 - 680.105i) q^{12} +(622.975 + 1917.32i) q^{13} +(-2103.75 + 2895.57i) q^{14} +(-954.409 + 5899.07i) q^{15} +(-1578.37 + 4857.73i) q^{16} +(3892.09 + 1264.62i) q^{17} +(5911.37 - 4235.18i) q^{18} +(-2591.87 - 1883.10i) q^{19} +(-7473.56 + 2428.31i) q^{20} +(-6827.41 - 6872.89i) q^{21} +(6516.18 - 11568.0i) q^{22} -8032.42i q^{23} +(-6826.49 - 3506.87i) q^{24} +(26988.7 + 19608.4i) q^{25} +(-11820.3 - 16269.3i) q^{26} +(8760.77 + 17625.8i) q^{27} +(3936.65 - 12115.8i) q^{28} +(18470.0 + 25421.8i) q^{29} +(-9129.49 - 58906.5i) q^{30} +(-13111.2 - 40352.2i) q^{31} -32759.0i q^{32} +(28092.3 + 22411.8i) q^{33} -40822.4 q^{34} +(-75525.0 + 24539.6i) q^{35} +(-15352.5 + 20838.5i) q^{36} +(-9972.40 + 7245.37i) q^{37} +(30393.8 + 9875.53i) q^{38} +(48580.8 - 24550.3i) q^{39} +(-50895.4 + 36977.7i) q^{40} +(5178.43 - 7127.50i) q^{41} +(85957.4 + 44157.6i) q^{42} -48965.3 q^{43} +(-9334.50 + 46326.2i) q^{44} +(161343. + 1071.37i) q^{45} +(24760.0 + 76203.6i) q^{46} +(-56788.8 + 78163.1i) q^{47} +(136138. + 22025.7i) q^{48} +(3426.75 - 10546.4i) q^{49} +(-316485. - 102832. i) q^{50} +(17647.4 - 109076. i) q^{51} +(57907.7 + 42072.4i) q^{52} +(-20323.0 + 6603.34i) q^{53} +(-137445. - 140211. i) q^{54} +(267830. - 122666. i) q^{55} -101987. i q^{56} +(-39526.1 + 76941.8i) q^{57} +(-253588. - 184242. i) q^{58} +(201717. + 277639. i) q^{59} +(95695.2 + 189364. i) q^{60} +(-109974. + 338464. i) q^{61} +(248772. + 342406. i) q^{62} +(-155146. + 210586. i) q^{63} +(-35.6075 - 109.589i) q^{64} -446189. i q^{65} +(-335597. - 126026. i) q^{66} -14649.5 q^{67} +(138189. - 44900.3i) q^{68} +(-214317. + 33215.4i) q^{69} +(640862. - 465614. i) q^{70} +(-332066. - 107895. i) q^{71} +(-65339.6 + 196642. i) q^{72} +(-216710. + 157449. i) q^{73} +(72274.2 - 99476.9i) q^{74} +(411579. - 801182. i) q^{75} -113749. q^{76} +(-94331.0 + 468155. i) q^{77} +(-385209. + 382660. i) q^{78} +(68408.7 + 210540. i) q^{79} +(664471. - 914566. i) q^{80} +(434055. - 306636. i) q^{81} +(-27157.2 + 83581.2i) q^{82} +(-142726. - 46374.5i) q^{83} +(-339545. - 54934.8i) q^{84} +(-732765. - 532385. i) q^{85} +(464534. - 150936. i) q^{86} +(601914. - 597930. i) q^{87} +(43534.6 + 375815. i) q^{88} +151502. i q^{89} +(-1.53396e6 + 487176. i) q^{90} +(585193. + 425168. i) q^{91} +(-167631. - 230725. i) q^{92} +(-1.02244e6 + 516690. i) q^{93} +(297817. - 916585. i) q^{94} +(416778. + 573646. i) q^{95} +(-874058. + 135464. i) q^{96} +(83506.1 + 257005. i) q^{97} +110617. i q^{98} +(481813. - 842221. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 33 q^{3} + 634 q^{4} + 109 q^{6} + 402 q^{7} - 2471 q^{9} - 1016 q^{10} + 7594 q^{12} - 1830 q^{13} - 6973 q^{15} - 15506 q^{16} - 291 q^{18} - 32466 q^{19} + 5434 q^{21} + 40940 q^{22} + 10011 q^{24}+ \cdots - 1274785 q^{99}+O(q^{100}) $ 88 * q + 33 * q^3 + 634 * q^4 + 109 * q^6 + 402 * q^7 - 2471 * q^9 - 1016 * q^10 + 7594 * q^12 - 1830 * q^13 - 6973 * q^15 - 15506 * q^16 - 291 * q^18 - 32466 * q^19 + 5434 * q^21 + 40940 * q^22 + 10011 * q^24 + 68152 * q^25 + 65385 * q^27 - 37986 * q^28 + 20928 * q^30 + 96222 * q^31 - 67159 * q^33 - 186548 * q^34 - 107169 * q^36 - 112854 * q^37 - 257545 * q^39 + 246958 * q^40 - 130324 * q^42 + 40328 * q^43 + 505478 * q^45 - 30630 * q^46 + 647882 * q^48 - 327700 * q^49 + 88197 * q^51 - 132630 * q^52 - 1639642 * q^54 - 216226 * q^55 + 174477 * q^57 + 1571894 * q^58 + 772854 * q^60 + 559626 * q^61 + 1129495 * q^63 + 1406654 * q^64 + 34620 * q^66 - 3229336 * q^67 - 2492844 * q^69 - 2066360 * q^70 - 2672882 * q^72 + 1068798 * q^73 - 1207057 * q^75 + 913268 * q^76 + 6763180 * q^78 - 255558 * q^79 + 3363409 * q^81 - 3580072 * q^82 - 2958906 * q^84 - 2098978 * q^85 + 365046 * q^87 + 2251838 * q^88 - 813500 * q^90 + 7887166 * q^91 + 4000307 * q^93 + 11260802 * q^94 + 4588186 * q^96 + 3850038 * q^97 - 1274785 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$

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 $

$2$	−9.48700	+	3.08251i	−1.18588	+	0.385314i	−0.834546	−	0.550938i	$-0.814270\pi$
$2$	−9.48700	+	3.08251i	−1.18588	+	0.385314i	−0.351329	+	0.936252i	$0.614270\pi$
$3$	−4.13517	−	26.6815i	−0.153154	−	0.988202i
$3$	−4.13517	−	26.6815i	−0.153154	−	0.988202i
$4$	28.7242	−	20.8694i	0.448816	−	0.326084i
$5$	−210.493	−	68.3933i	−1.68394	−	0.547146i	−0.698272	−	0.715832i	$-0.746048\pi$
$5$	−210.493	−	68.3933i	−1.68394	−	0.547146i	−0.985670	+	0.168686i	$0.946048\pi$
$6$	121.476	+	240.380i	0.562390	+	1.11287i
$7$	290.276	−	210.898i	0.846286	−	0.614863i	−0.0778334	−	0.996966i	$-0.524800\pi$
$7$	290.276	−	210.898i	0.846286	−	0.614863i	0.924120	+	0.382104i	$0.124800\pi$
$8$	167.074	−	229.958i	0.326316	−	0.449136i
$9$	−694.801	+	220.665i	−0.953087	+	0.302695i
$10$	2207.77			2.20777
$11$	−979.624	+	901.054i	−0.736006	+	0.676975i
$11$	−979.624	+	901.054i	−0.736006	+	0.676975i
$12$	−675.604	−	680.105i	−0.390975	−	0.393580i
$13$	622.975	+	1917.32i	0.283557	+	0.872699i	0.986827	+	0.161776i	$0.0517223\pi$
$13$	622.975	+	1917.32i	0.283557	+	0.872699i	−0.703270	+	0.710922i	$0.748278\pi$
$14$	−2103.75	+	2895.57i	−0.766674	+	1.05524i
$15$	−954.409	+	5899.07i	−0.282788	+	1.74787i
$16$	−1578.37	+	4857.73i	−0.385344	+	1.18597i
$17$	3892.09	+	1264.62i	0.792202	+	0.257402i	0.677042	−	0.735945i	$-0.263262\pi$
$17$	3892.09	+	1264.62i	0.792202	+	0.257402i	0.115161	+	0.993347i	$0.463262\pi$
$18$	5911.37	−	4235.18i	1.01361	−	0.726197i
$19$	−2591.87	−	1883.10i	−0.377879	−	0.274545i	0.382592	−	0.923917i	$-0.375032\pi$
$19$	−2591.87	−	1883.10i	−0.377879	−	0.274545i	−0.760470	+	0.649373i	$0.775032\pi$
$20$	−7473.56	+	2428.31i	−0.934195	+	0.303538i
$21$	−6827.41	−	6872.89i	−0.737221	−	0.742133i
$22$	6516.18	−	11568.0i	0.611963	−	1.08640i
$23$		−	8032.42i		−	0.660181i	−0.943949	−	0.330090i	$-0.892921\pi$
$23$		−	8032.42i		−	0.660181i	0.943949	−	0.330090i	$-0.107079\pi$
$24$	−6826.49	−	3506.87i	−0.493814	−	0.253680i
$25$	26988.7	+	19608.4i	1.72728	+	1.25494i
$26$	−11820.3	−	16269.3i	−0.672526	−	0.925653i
$27$	8760.77	+	17625.8i	0.445093	+	0.895484i
$28$	3936.65	−	12115.8i	0.179330	−	0.551920i
$29$	18470.0	+	25421.8i	0.757309	+	1.04235i	0.997433	+	0.0716044i	$0.0228119\pi$
$29$	18470.0	+	25421.8i	0.757309	+	1.04235i	−0.240124	+	0.970742i	$0.577188\pi$
$30$	−9129.49	−	58906.5i	−0.338129	−	2.18172i
$31$	−13111.2	−	40352.2i	−0.440107	−	1.35451i	−0.887762	−	0.460303i	$-0.847741\pi$
$31$	−13111.2	−	40352.2i	−0.440107	−	1.35451i	0.447655	−	0.894206i	$-0.352259\pi$
$32$		−	32759.0i		−	0.999726i
$33$	28092.3	+	22411.8i	0.781711	+	0.623641i
$34$	−40822.4			−1.03863
$35$	−75525.0	+	24539.6i	−1.76152	+	0.572351i
$36$	−15352.5	+	20838.5i	−0.329057	+	0.446641i
$37$	−9972.40	+	7245.37i	−0.196877	+	0.143039i	−0.681856	−	0.731486i	$-0.738827\pi$
$37$	−9972.40	+	7245.37i	−0.196877	+	0.143039i	0.484980	+	0.874526i	$0.338827\pi$
$38$	30393.8	+	9875.53i	0.553903	+	0.179974i
$39$	48580.8	−	24550.3i	0.818975	−	0.413869i
$40$	−50895.4	+	36977.7i	−0.795241	+	0.577776i
$41$	5178.43	−	7127.50i	0.0751358	−	0.103416i	−0.769795	−	0.638291i	$-0.779642\pi$
$41$	5178.43	−	7127.50i	0.0751358	−	0.103416i	0.844931	+	0.534876i	$0.179642\pi$
$42$	85957.4	+	44157.6i	1.16021	+	0.596015i
$43$	−48965.3			−0.615861			−0.307931	−	0.951409i	$-0.599636\pi$
$43$	−48965.3			−0.615861			−0.307931	+	0.951409i	$0.599636\pi$
$44$	−9334.50	+	46326.2i	−0.109580	+	0.543837i
$45$	161343.	+	1071.37i	1.77056	+	0.0117571i
$46$	24760.0	+	76203.6i	0.254377	+	0.782892i
$47$	−56788.8	+	78163.1i	−0.546977	+	0.752849i	−0.989598	−	0.143859i	$-0.954049\pi$
$47$	−56788.8	+	78163.1i	−0.546977	+	0.752849i	0.442621	+	0.896709i	$0.354049\pi$
$48$	136138.	+	22025.7i	1.23099	+	0.199162i
$49$	3426.75	−	10546.4i	0.0291269	−	0.0896433i
$50$	−316485.	−	102832.i	−2.53188	−	0.822657i
$51$	17647.4	−	109076.i	0.133036	−	0.822278i
$52$	57907.7	+	42072.4i	0.411838	+	0.299218i
$53$	−20323.0	+	6603.34i	−0.136509	+	0.0443543i	−0.376474	−	0.926427i	$-0.622864\pi$
$53$	−20323.0	+	6603.34i	−0.136509	+	0.0443543i	0.239966	+	0.970781i	$0.422864\pi$
$54$	−137445.	−	140211.i	−0.872868	−	0.890432i
$55$	267830.	−	122666.i	1.60980	−	0.737284i
$56$		−	101987.i		−	0.580737i
$57$	−39526.1	+	76941.8i	−0.213432	+	0.415468i
$58$	−253588.	−	184242.i	−1.29970	−	0.944291i
$59$	201717.	+	277639.i	0.982168	+	1.35184i	0.935653	+	0.352921i	$0.114812\pi$
$59$	201717.	+	277639.i	0.982168	+	1.35184i	0.0465155	+	0.998918i	$0.485188\pi$
$60$	95695.2	+	189364.i	0.443033	+	0.876685i
$61$	−109974.	+	338464.i	−0.484506	+	1.49116i	0.348188	+	0.937425i	$0.386797\pi$
$61$	−109974.	+	338464.i	−0.484506	+	1.49116i	−0.832694	+	0.553733i	$0.813203\pi$
$62$	248772.	+	342406.i	1.04382	+	1.43670i
$63$	−155146.	+	210586.i	−0.620469	+	0.842185i
$64$	−35.6075	−	109.589i	−0.000135832	−	0.000418047i
$65$		−	446189.i		−	1.62472i
$66$	−335597.	−	126026.i	−1.16731	−	0.438356i
$67$	−14649.5			−0.0487079			−0.0243539	−	0.999703i	$-0.507753\pi$
$67$	−14649.5			−0.0487079			−0.0243539	+	0.999703i	$0.507753\pi$
$68$	138189.	−	44900.3i	0.439487	−	0.142798i
$69$	−214317.	+	33215.4i	−0.652392	+	0.101110i
$70$	640862.	−	465614.i	1.86840	−	1.35747i
$71$	−332066.	−	107895.i	−0.927791	−	0.301457i	−0.194132	−	0.980975i	$-0.562189\pi$
$71$	−332066.	−	107895.i	−0.927791	−	0.301457i	−0.733659	+	0.679518i	$0.762189\pi$
$72$	−65339.6	+	196642.i	−0.175057	+	0.526840i
$73$	−216710.	+	157449.i	−0.557071	+	0.404736i	−0.830386	−	0.557189i	$-0.811880\pi$
$73$	−216710.	+	157449.i	−0.557071	+	0.404736i	0.273315	+	0.961925i	$0.411880\pi$
$74$	72274.2	−	99476.9i	0.178356	−	0.245486i
$75$	411579.	−	801182.i	0.975594	−	1.89910i
$76$	−113749.			−0.259122
$77$	−94331.0	+	468155.i	−0.206625	+	1.02546i
$78$	−385209.	+	382660.i	−0.811732	+	0.806360i
$79$	68408.7	+	210540.i	0.138749	+	0.427026i	0.996154	−	0.0876161i	$-0.0279249\pi$
$79$	68408.7	+	210540.i	0.138749	+	0.427026i	−0.857405	+	0.514642i	$0.827925\pi$
$80$	664471.	−	914566.i	1.29780	−	1.78626i
$81$	434055.	−	306636.i	0.816751	−	0.576990i
$82$	−27157.2	+	83581.2i	−0.0492542	+	0.151589i
$83$	−142726.	−	46374.5i	−0.249614	−	0.0811044i	0.181538	−	0.983384i	$-0.441893\pi$
$83$	−142726.	−	46374.5i	−0.249614	−	0.0811044i	−0.431151	+	0.902280i	$0.641893\pi$
$84$	−339545.	−	54934.8i	−0.572874	−	0.0926851i
$85$	−732765.	−	532385.i	−1.19319	−	0.866900i
$86$	464534.	−	150936.i	0.730334	−	0.237300i
$87$	601914.	−	597930.i	0.914064	−	0.908015i
$88$	43534.6	+	375815.i	0.0638831	+	0.551475i
$89$			151502.i			0.214906i	0.994210	+	0.107453i	$0.0342694\pi$
$89$			151502.i			0.214906i	−0.994210	+	0.107453i	$0.965731\pi$
$90$	−1.53396e6	+	487176.i	−2.10420	+	0.668280i
$91$	585193.	+	425168.i	0.776560	+	0.564204i
$92$	−167631.	−	230725.i	−0.215274	−	0.296299i
$93$	−1.02244e6	+	516690.i	−1.27112	+	0.642364i
$94$	297817.	−	916585.i	0.358563	−	1.10354i
$95$	416778.	+	573646.i	0.486110	+	0.669072i
$96$	−874058.	+	135464.i	−0.987931	+	0.153112i
$97$	83506.1	+	257005.i	0.0914962	+	0.281596i	0.986325	−	0.164814i	$-0.0527023\pi$
$97$	83506.1	+	257005.i	0.0914962	+	0.281596i	−0.894829	+	0.446410i	$0.852702\pi$
$98$			110617.i			0.117529i
$99$	481813.	−	842221.i	0.496561	−	0.868002i
$100$	1.18444e6			1.18444
$101$	1.04826e6	−	340599.i	1.01743	−	0.330582i	0.247620	−	0.968857i	$-0.420352\pi$
$101$	1.04826e6	−	340599.i	1.01743	−	0.330582i	0.769808	+	0.638275i	$0.220352\pi$
$102$	168808.	+	1.08920e6i	0.159071	+	1.02638i
$103$	−416371.	+	302511.i	−0.381038	+	0.276840i	−0.761773	−	0.647844i	$-0.775671\pi$
$103$	−416371.	+	302511.i	−0.381038	+	0.276840i	0.380735	+	0.924684i	$0.375671\pi$
$104$	544985.	+	177076.i	0.484490	+	0.157420i
$105$	967060.	+	1.91364e6i	0.835383	+	1.65308i
$106$	172449.	−	125292.i	0.144792	−	0.105197i
$107$	89809.9	−	123613.i	0.0733116	−	0.100905i	−0.770786	−	0.637094i	$-0.780136\pi$
$107$	89809.9	−	123613.i	0.0733116	−	0.100905i	0.844098	+	0.536189i	$0.180136\pi$
$108$	619486.	+	323456.i	0.491768	+	0.256770i
$109$	−1.07819e6			−0.832561			−0.416281	−	0.909236i	$-0.636667\pi$
$109$	−1.07819e6			−0.832561			−0.416281	+	0.909236i	$0.636667\pi$
$110$	−2.16278e6	+	1.98932e6i	−1.62493	+	1.49460i
$111$	234555.	+	236117.i	0.171504	+	0.172647i
$112$	566321.	+	1.74296e6i	0.403096	+	1.24060i
$113$	−1.02661e6	+	1.41301e6i	−0.711493	+	0.979286i	0.288271	+	0.957549i	$0.406920\pi$
$113$	−1.02661e6	+	1.41301e6i	−0.711493	+	0.979286i	−0.999764	+	0.0217368i	$0.993080\pi$
$114$	137810.	−	851787.i	0.0930180	−	0.574932i
$115$	−549363.	+	1.69077e6i	−0.361215	+	1.11171i
$116$	1.06107e6	+	344763.i	0.679784	+	0.220875i
$117$	−855928.	−	1.19469e6i	−0.534416	−	0.745927i
$118$	−2.76951e6	−	2.01217e6i	−1.68561	−	1.22467i
$119$	1.39649e6	−	453746.i	0.828697	−	0.269260i
$120$	1.19708e6	+	1.20506e6i	0.692755	+	0.697370i
$121$	147765.	−	1.76539e6i	0.0834093	−	0.996515i
$122$		−	3.55001e6i		−	1.95501i
$123$	−211586.	−	108695.i	−0.113703	−	0.0584108i
$124$	−1.21873e6	−	885462.i	−0.639210	−	0.464413i
$125$	−2.30716e6	−	3.17553e6i	−1.18126	−	1.62587i
$126$	822740.	−	2.47607e6i	0.411293	−	1.23780i
$127$	695123.	−	2.13937e6i	0.339352	−	1.04442i	−0.625186	−	0.780475i	$-0.714977\pi$
$127$	695123.	−	2.13937e6i	0.339352	−	1.04442i	0.964538	−	0.263942i	$-0.0850229\pi$
$128$	1.23301e6	+	1.69710e6i	0.587946	+	0.809239i
$129$	202480.	+	1.30646e6i	0.0943218	+	0.608595i
$130$	1.37538e6	+	4.23300e6i	0.626028	+	1.92672i
$131$		−	21148.4i		−	0.00940727i	−0.999989	−	0.00470363i	$-0.998503\pi$
$131$		−	21148.4i		−	0.00940727i	0.999989	−	0.00470363i	$-0.00149722\pi$
$132$	1.27465e6	+	57491.6i	0.554203	+	0.0249967i
$133$	−1.14950e6			−0.488601
$134$	138980.	−	45157.4i	0.0577615	−	0.0187678i
$135$	−638593.	−	4.30928e6i	−0.259551	−	1.75147i
$136$	941075.	−	683731.i	0.374117	−	0.271812i
$137$	1.37007e6	+	445162.i	0.532819	+	0.173123i	0.563055	−	0.826419i	$-0.309626\pi$
$137$	1.37007e6	+	445162.i	0.532819	+	0.173123i	−0.0302359	+	0.999543i	$0.509626\pi$
$138$	1.93084e6	−	975748.i	0.734697	−	0.371279i
$139$	−2.42382e6	+	1.76101e6i	−0.902518	+	0.655718i	−0.939111	−	0.343613i	$-0.888349\pi$
$139$	−2.42382e6	+	1.76101e6i	−0.902518	+	0.655718i	0.0365937	+	0.999330i	$0.488349\pi$
$140$	−1.65727e6	+	2.28104e6i	−0.603962	+	0.831282i
$141$	2.32034e6	+	1.19199e6i	0.827739	+	0.425222i
$142$	3.48290e6			1.21640
$143$	−2.33789e6	−	1.31692e6i	−0.799495	−	0.450350i
$144$	24724.9	−	3.72344e6i	0.00828032	−	1.24697i
$145$	−2.14913e6	−	6.61433e6i	−0.704949	−	2.16961i
$146$	1.57059e6	−	2.16173e6i	0.504666	−	0.694613i
$147$	−295565.	−	47819.3i	−0.0930466	−	0.0150540i
$148$	−135243.	+	416235.i	−0.0417186	+	0.128397i
$149$	−2.81436e6	−	914440.i	−0.850786	−	0.276437i	−0.149011	−	0.988836i	$-0.547609\pi$
$149$	−2.81436e6	−	914440.i	−0.850786	−	0.276437i	−0.701775	+	0.712398i	$0.747609\pi$
$150$	−1.43499e6	+	8.86951e6i	−0.425184	+	2.62800i
$151$	2.64356e6	+	1.92066e6i	0.767818	+	0.557852i	0.901298	−	0.433199i	$-0.142615\pi$
$151$	2.64356e6	+	1.92066e6i	0.767818	+	0.557852i	−0.133481	+	0.991051i	$0.542615\pi$
$152$	−866068.	+	281403.i	−0.246616	+	0.0801304i
$153$	−2.98328e6	−	19810.0i	−0.832952	−	0.00553108i
$154$	−548176.	−	4.73216e6i	−0.150092	−	1.29568i
$155$			9.39056e6i			2.52172i
$156$	883095.	−	1.71904e6i	0.232613	−	0.452805i
$157$	5.92609e6	+	4.30555e6i	1.53133	+	1.11258i	0.955493	+	0.295013i	$0.0953240\pi$
$157$	5.92609e6	+	4.30555e6i	1.53133	+	1.11258i	0.575838	+	0.817564i	$0.304676\pi$
$158$	−1.29799e6	−	1.78653e6i	−0.329078	−	0.452937i
$159$	260226.	+	514941.i	0.0647380	+	0.128105i
$160$	−2.24050e6	+	6.89554e6i	−0.546996	+	1.68348i
$161$	−1.69402e6	−	2.33162e6i	−0.405921	−	0.558702i
$162$	−3.17267e6	+	4.24704e6i	−0.746243	+	0.998944i
$163$	−572366.	−	1.76156e6i	−0.132163	−	0.406757i	0.862975	−	0.505247i	$-0.168599\pi$
$163$	−572366.	−	1.76156e6i	−0.132163	−	0.406757i	−0.995138	+	0.0984903i	$0.968599\pi$
$164$		−	312802.i		−	0.0709151i
$165$	−4.38042e6	−	6.63885e6i	−0.975133	−	1.47789i
$166$	1.49699e6			0.327261
$167$	−579532.	+	188301.i	−0.124431	+	0.0404300i	−0.370571	−	0.928804i	$-0.620838\pi$
$167$	−579532.	+	188301.i	−0.124431	+	0.0404300i	0.246140	+	0.969234i	$0.420838\pi$
$168$	−2.72116e6	+	421733.i	−0.573886	+	0.0889425i
$169$	616955.	−	448244.i	0.127818	−	0.0928656i
$170$	8.59283e6	+	2.79198e6i	1.74900	+	0.568284i
$171$	2.21637e6	+	736448.i	0.443255	+	0.147283i
$172$	−1.40649e6	+	1.02187e6i	−0.276408	+	0.200822i
$173$	−2.09773e6	+	2.88728e6i	−0.405147	+	0.557636i	−0.962026	−	0.272957i	$-0.911998\pi$
$173$	−2.09773e6	+	2.88728e6i	−0.405147	+	0.557636i	0.556880	+	0.830593i	$0.311998\pi$
$174$	−3.86723e6	+	7.52797e6i	−0.734095	+	1.42899i
$175$	1.19695e7			2.23339
$176$	−2.83086e6	−	6.18094e6i	−0.519255	−	1.13375i
$177$	6.57369e6	−	6.53018e6i	1.18547	−	1.17762i
$178$	−467006.	−	1.43730e6i	−0.0828061	−	0.254851i
$179$	−5.82390e6	+	8.01592e6i	−1.01544	+	1.39764i	−0.100091	+	0.994978i	$0.531913\pi$
$179$	−5.82390e6	+	8.01592e6i	−1.01544	+	1.39764i	−0.915351	+	0.402658i	$0.868087\pi$
$180$	4.65679e6	−	3.33634e6i	0.798490	−	0.572075i
$181$	−445639.	+	1.37154e6i	−0.0751532	+	0.231298i	−0.981575	−	0.191075i	$-0.938803\pi$
$181$	−445639.	+	1.37154e6i	−0.0751532	+	0.231298i	0.906422	+	0.422373i	$0.138803\pi$
$182$	−6.86232e6	−	2.22970e6i	−1.13830	−	0.369856i
$183$	9.48549e6	+	1.53465e6i	1.54777	+	0.250413i
$184$	−1.84712e6	−	1.34201e6i	−0.296511	−	0.215428i
$185$	2.59465e6	−	843054.i	0.409792	−	0.133150i
$186$	8.10717e6	−	8.05351e6i	1.25988	−	1.25155i
$187$	−4.95227e6	+	2.26813e6i	−0.757320	+	0.346852i
$188$			3.43032e6i			0.516251i
$189$	6.26029e6	+	3.26872e6i	0.927276	+	0.484164i
$190$	−5.72225e6	−	4.15745e6i	−0.834268	−	0.606131i
$191$	−5.59238e6	−	7.69724e6i	−0.802595	−	1.10468i	−0.992424	−	0.122860i	$-0.960794\pi$
$191$	−5.59238e6	−	7.69724e6i	−0.802595	−	1.10468i	0.189829	−	0.981817i	$-0.439206\pi$
$192$	−2776.74	+	1403.23i	−0.000392312	+	0.000198255i
$193$	−558015.	+	1.71740e6i	−0.0776201	+	0.238890i	−0.982336	−	0.187125i	$-0.940083\pi$
$193$	−558015.	+	1.71740e6i	−0.0776201	+	0.238890i	0.904716	+	0.426015i	$0.140083\pi$
$194$	−1.58445e6	−	2.18080e6i	−0.217006	−	0.298683i
$195$	−1.19050e7	+	1.84507e6i	−1.60555	+	0.248833i
$196$	−121667.	−	374452.i	−0.0161586	−	0.0497311i
$197$			819617.i			0.107204i	0.998562	+	0.0536022i	$0.0170703\pi$
$197$			819617.i			0.107204i	−0.998562	+	0.0536022i	$0.982930\pi$
$198$	−1.97480e6	+	9.47535e6i	−0.254406	+	1.22067i
$199$	2.11410e6			0.268266			0.134133	−	0.990963i	$-0.457175\pi$
$199$	2.11410e6			0.268266			0.134133	+	0.990963i	$0.457175\pi$
$200$	9.01822e6	−	2.93020e6i	1.12728	−	0.366274i
$201$	60578.3	+	390871.i	0.00745983	+	0.0481333i
$202$	−8.89491e6	+	6.46253e6i	−1.07916	+	0.784059i
$203$	1.07228e7	+	3.48405e6i	1.28180	+	0.416482i
$204$	−1.76944e6	−	3.50141e6i	−0.208423	−	0.412432i
$205$	−1.57750e6	+	1.14612e6i	−0.183108	+	0.133036i
$206$	3.01761e6	−	4.15339e6i	0.345193	−	0.475117i
$207$	1.77247e6	+	5.58093e6i	0.199833	+	0.629210i
$208$	−1.02971e7			−1.14426
$209$	4.23583e6	−	490681.i	0.463981	−	0.0537478i
$210$	−1.50733e7	−	1.51738e7i	−1.62761	−	1.63846i
$211$	−1.96341e6	−	6.04276e6i	−0.209008	−	0.643262i	−0.999525	−	0.0308209i	$-0.990188\pi$
$211$	−1.96341e6	−	6.04276e6i	−0.209008	−	0.643262i	0.790517	−	0.612441i	$-0.209812\pi$
$212$	−445954.	+	613804.i	−0.0468040	+	0.0644202i
$213$	−1.50564e6	+	9.30618e6i	−0.155806	+	0.963014i
$214$	−470989.	+	1.44955e6i	−0.0480584	+	0.147908i
$215$	1.03068e7	+	3.34889e6i	1.03707	+	0.336966i
$216$	5.51689e6	+	930209.i	0.547436	+	0.0923037i
$217$	−1.23161e7	−	8.94815e6i	−1.20529	−	0.875697i
$218$	1.02288e7	−	3.32354e6i	0.987314	−	0.320798i
$219$	5.09711e6	+	5.13106e6i	0.485279	+	0.488512i
$220$	5.13324e6	−	9.11291e6i	0.482085	−	0.855833i
$221$			8.25020e6i			0.764342i
$222$	−2.95305e6	−	1.51703e6i	−0.269906	−	0.138655i
$223$	4.99382e6	+	3.62822e6i	0.450317	+	0.327174i	0.789721	−	0.613466i	$-0.210225\pi$
$223$	4.99382e6	+	3.62822e6i	0.450317	+	0.327174i	−0.339404	+	0.940641i	$0.610225\pi$
$224$	−6.90881e6	−	9.50916e6i	−0.614694	−	0.846054i
$225$	−2.30786e7	−	7.66850e6i	−2.02611	−	0.673229i
$226$	5.38384e6	−	1.65698e7i	0.466409	−	1.43546i
$227$	2.37256e6	+	3.26554e6i	0.202833	+	0.279176i	0.898300	−	0.439382i	$-0.144803\pi$
$227$	2.37256e6	+	3.26554e6i	0.202833	+	0.279176i	−0.695467	+	0.718558i	$0.744803\pi$
$228$	470369.	+	3.03498e6i	0.0396857	+	0.256065i
$229$	5.51270e6	+	1.69664e7i	0.459048	+	1.41280i	0.866316	+	0.499496i	$0.166481\pi$
$229$	5.51270e6	+	1.69664e7i	0.459048	+	1.41280i	−0.407268	+	0.913309i	$0.633519\pi$
$230$		−	1.77337e7i		−	1.45753i
$231$	1.28811e7	+	580989.i	1.04500	+	0.0471337i
$232$	8.93180e6			0.715278
$233$	−2.04435e7	+	6.64248e6i	−1.61617	+	0.525125i	−0.971033	−	0.238944i	$-0.923199\pi$
$233$	−2.04435e7	+	6.64248e6i	−1.61617	+	0.525125i	−0.645134	+	0.764069i	$0.723199\pi$
$234$	1.18028e7	+	8.69558e6i	0.921167	+	0.678658i
$235$	1.72995e7	−	1.25688e7i	1.33300	−	0.968479i
$236$	1.15883e7	+	3.76527e6i	0.881625	+	0.286457i
$237$	5.33464e6	−	2.69586e6i	0.400738	−	0.202513i
$238$	−1.18498e7	+	8.60937e6i	−0.878981	+	0.638617i
$239$	1.51821e7	−	2.08963e7i	1.11208	−	1.53065i	0.293775	−	0.955875i	$-0.405088\pi$
$239$	1.51821e7	−	2.08963e7i	1.11208	−	1.53065i	0.818309	−	0.574778i	$-0.194912\pi$
$240$	−2.71497e7	−	1.39472e7i	−1.96395	−	1.00891i
$241$	−2.11925e7			−1.51402			−0.757009	−	0.653404i	$-0.773340\pi$
$241$	−2.11925e7			−1.51402			−0.757009	+	0.653404i	$0.773340\pi$
$242$	4.03999e6	+	1.72037e7i	0.285058	+	1.21388i
$243$	−9.97639e6	−	1.03132e7i	−0.695271	−	0.718747i
$244$	3.90463e6	+	1.20172e7i	0.268788	+	0.827245i
$245$	−1.44261e6	+	1.98558e6i	−0.0980960	+	0.135017i
$246$	2.34237e6	+	378971.i	0.157344	+	0.0254566i
$247$	1.99584e6	−	6.14257e6i	0.132445	−	0.407623i
$248$	−1.14698e7	−	3.72678e6i	−0.751973	−	0.244331i
$249$	−647143.	+	3.99990e6i	−0.0419181	+	0.259090i
$250$	3.16766e7	+	2.30144e7i	2.02730	+	1.47292i
$251$	1.68801e7	−	5.48468e6i	1.06747	−	0.346841i	0.277966	−	0.960591i	$-0.410340\pi$
$251$	1.68801e7	−	5.48468e6i	1.06747	−	0.346841i	0.789500	+	0.613750i	$0.210340\pi$
$252$	−61666.9	+	9.28671e6i	−0.00385346	+	0.580310i
$253$	7.23764e6	+	7.86875e6i	0.446926	+	0.485897i
$254$			2.24389e7i			1.36931i
$255$	−1.11747e7	+	2.17528e7i	−0.673931	+	1.31188i
$256$	−1.69229e7	−	1.22952e7i	−1.00869	−	0.732854i
$257$	−1.38182e6	−	1.90191e6i	−0.0814050	−	0.112044i	0.766372	−	0.642396i	$-0.222060\pi$
$257$	−1.38182e6	−	1.90191e6i	−0.0814050	−	0.112044i	−0.847777	+	0.530352i	$0.822060\pi$
$258$	−5.94812e6	−	1.17703e7i	−0.346354	−	0.685374i
$259$	−1.36672e6	+	4.20632e6i	−0.0786645	+	0.242104i
$260$	−9.31168e6	−	1.28164e7i	−0.529795	−	0.729200i
$261$	−1.84427e7	−	1.35874e7i	−1.03729	−	0.764214i
$262$	65190.2	+	200635.i	0.00362475	+	0.0111558i
$263$			2.24387e7i			1.23347i	0.787169	+	0.616737i	$0.211546\pi$
$263$			2.24387e7i			1.23347i	−0.787169	+	0.616737i	$0.788454\pi$
$264$	9.84726e6	−	2.71562e6i	0.535185	−	0.147590i
$265$	4.72947e6			0.254141
$266$	1.09053e7	−	3.54335e6i	0.579419	−	0.188265i
$267$	4.04229e6	−	626485.i	0.212370	−	0.0329137i
$268$	−420796.	+	305726.i	−0.0218609	+	0.0158828i
$269$	−1.98465e7	−	6.44853e6i	−1.01960	−	0.331287i	−0.248927	−	0.968522i	$-0.580078\pi$
$269$	−1.98465e7	−	6.44853e6i	−1.01960	−	0.331287i	−0.770669	+	0.637236i	$0.780078\pi$
$270$	1.93418e7	+	3.89137e7i	0.982663	+	1.97702i
$271$	2.12585e7	−	1.54452e7i	1.06813	−	0.776042i	0.0925555	−	0.995708i	$-0.470496\pi$
$271$	2.12585e7	−	1.54452e7i	1.06813	−	0.776042i	0.975575	+	0.219665i	$0.0704964\pi$
$272$	−1.22863e7	+	1.69107e7i	−0.610541	+	0.840338i
$273$	8.92423e6	−	1.73720e7i	0.438614	−	0.853809i
$274$	−1.43700e7			−0.698564
$275$	−4.41070e7	+	5.10938e6i	−2.12085	+	0.245680i
$276$	−5.46289e6	+	5.42674e6i	−0.259834	+	0.258114i
$277$	2.69340e6	+	8.28944e6i	0.126725	+	0.390019i	0.994211	−	0.107442i	$-0.0342659\pi$
$277$	2.69340e6	+	8.28944e6i	0.126725	+	0.390019i	−0.867487	+	0.497461i	$0.834266\pi$
$278$	1.75664e7	−	2.41781e7i	0.817616	−	1.12535i
$279$	1.80140e7	+	2.51435e7i	0.829463	+	1.15775i
$280$	−6.97521e6	+	2.14675e7i	−0.317748	+	0.977928i
$281$	5.58509e6	+	1.81470e6i	0.251716	+	0.0817875i	0.432157	−	0.901798i	$-0.357753\pi$
$281$	5.58509e6	+	1.81470e6i	0.251716	+	0.0817875i	−0.180441	+	0.983586i	$0.557753\pi$
$282$	−2.56874e7	−	4.15595e6i	−1.14544	−	0.185320i
$283$	1.47329e7	+	1.07041e7i	0.650022	+	0.472268i	0.863279	−	0.504728i	$-0.168407\pi$
$283$	1.47329e7	+	1.07041e7i	0.650022	+	0.472268i	−0.213257	+	0.976996i	$0.568407\pi$
$284$	−1.17900e7	+	3.83082e6i	−0.514707	+	0.167239i
$285$	1.35823e7	−	1.34924e7i	0.586729	−	0.582846i
$286$	2.62390e7	+	5.28703e6i	1.12163	+	0.226003i
$287$		−	3.16107e6i		−	0.133717i
$288$	7.22876e6	+	2.27610e7i	0.302612	+	0.952826i
$289$	−5.97860e6	−	4.34371e6i	−0.247689	−	0.179956i
$290$	4.07775e7	+	5.61254e7i	1.67196	+	2.30126i
$291$	6.51197e6	−	3.29083e6i	0.264261	−	0.133544i
$292$	−2.93896e6	+	9.04520e6i	−0.118044	+	0.363304i
$293$	−1.58541e7	−	2.18212e7i	−0.630286	−	0.867514i	0.367765	−	0.929919i	$-0.380123\pi$
$293$	−1.58541e7	−	2.18212e7i	−0.630286	−	0.867514i	−0.998051	+	0.0624047i	$0.980123\pi$
$294$	2.95143e6	−	457420.i	0.116142	−	0.0180000i
$295$	−2.34713e7	−	7.22371e7i	−0.914262	−	2.81381i
$296$			3.50374e6i			0.135101i
$297$	−2.44641e7	−	9.37274e6i	−0.933812	−	0.357764i
$298$	2.95186e7			1.11544
$299$	1.54007e7	−	5.00399e6i	0.576139	−	0.187199i
$300$	−4.89787e6	−	3.16027e7i	−0.181403	−	1.17047i
$301$	−1.42134e7	+	1.03267e7i	−0.521195	+	0.378670i
$302$	−3.09999e7	−	1.00725e7i	−1.12548	−	0.365692i
$303$	−1.34224e7	−	2.65606e7i	−0.482506	−	0.954794i
$304$	1.32385e7	−	9.61835e6i	0.471215	−	0.342358i
$305$	4.62974e7	−	6.37229e7i	1.63176	−	2.24593i
$306$	2.83635e7	−	9.00807e6i	0.989909	−	0.314389i
$307$	−3.56180e7			−1.23099			−0.615494	−	0.788141i	$-0.711044\pi$
$307$	−3.56180e7			−1.23099			−0.615494	+	0.788141i	$0.711044\pi$
$308$	7.06051e6	+	1.54160e7i	0.241648	+	0.527618i
$309$	9.79320e6	+	9.85844e6i	0.331932	+	0.334143i
$310$	−2.89465e7	−	8.90883e7i	−0.971654	−	2.99044i
$311$	3.92183e6	−	5.39793e6i	0.130379	−	0.179451i	−0.738837	−	0.673885i	$-0.764624\pi$
$311$	3.92183e6	−	5.39793e6i	0.130379	−	0.179451i	0.869215	+	0.494433i	$0.164624\pi$
$312$	2.47105e6	−	1.52732e7i	0.0813613	−	0.502884i
$313$	−1.60139e7	+	4.92856e7i	−0.522231	+	1.60726i	0.247496	+	0.968889i	$0.420392\pi$
$313$	−1.60139e7	+	4.92856e7i	−0.522231	+	1.60726i	−0.769727	+	0.638373i	$0.779608\pi$
$314$	−6.94927e7	−	2.25796e7i	−2.24466	−	0.729334i
$315$	4.70598e7	−	3.37158e7i	1.50563	−	1.07870i
$316$	6.35883e6	+	4.61996e6i	0.201519	+	0.146412i
$317$	−1.62935e7	+	5.29409e6i	−0.511491	+	0.166193i	−0.553380	−	0.832929i	$-0.686662\pi$
$317$	−1.62935e7	+	5.29409e6i	−0.511491	+	0.166193i	0.0418895	+	0.999122i	$0.486662\pi$
$318$	−4.05608e6	−	4.08310e6i	−0.126132	−	0.126972i
$319$	−4.10001e7	−	8.26132e6i	−1.26303	−	0.254494i
$320$			25502.9i			0.000778288i
$321$	−3.66955e6	−	1.88510e6i	−0.110942	−	0.0569927i
$322$	2.32584e7	+	1.68982e7i	0.696647	+	0.506144i
$323$	−7.70638e6	−	1.06069e7i	−0.228688	−	0.314762i
$324$	6.06860e6	−	1.78663e7i	0.178424	−	0.525291i
$325$	−2.07823e7	+	6.39615e7i	−0.605403	+	1.86324i
$326$	1.08601e7	+	1.49476e7i	0.313458	+	0.431438i
$327$	4.45850e6	+	2.87677e7i	0.127510	+	0.822739i
$328$	−773842.	−	2.38164e6i	−0.0219296	−	0.0674924i
$329$			3.46655e7i			0.973442i
$330$	6.20214e7	+	4.94800e7i	1.72584	+	1.37685i
$331$	−3.65485e7			−1.00782			−0.503912	−	0.863755i	$-0.668107\pi$
$331$	−3.65485e7			−1.00782			−0.503912	+	0.863755i	$0.668107\pi$
$332$	−5.06749e6	+	1.64653e6i	−0.138477	+	0.0449940i
$333$	5.33003e6	−	7.23464e6i	0.144343	−	0.195923i
$334$	4.91758e6	−	3.57283e6i	0.131981	−	0.0958900i
$335$	3.08362e6	+	1.00193e6i	0.0820213	+	0.0266503i
$336$	4.41628e7	−	2.23177e7i	1.16423	−	0.588344i
$337$	1.38512e6	−	1.00635e6i	0.0361907	−	0.0262941i	−0.569543	−	0.821962i	$-0.692880\pi$
$337$	1.38512e6	−	1.00635e6i	0.0361907	−	0.0262941i	0.605734	+	0.795668i	$0.292880\pi$
$338$	−4.47134e6	+	6.15427e6i	−0.115794	+	0.159377i
$339$	4.19463e7	+	2.15484e7i	1.07670	+	0.553117i
$340$	−3.21586e7			−0.818203
$341$	4.92036e7	+	2.77160e7i	1.24089	+	0.698985i
$342$	−2.32968e7	−	154698.i	−0.582395	−	0.00386730i
$343$	1.18149e7	+	3.63625e7i	0.292784	+	0.901096i
$344$	−8.18082e6	+	1.12599e7i	−0.200966	+	0.276605i
$345$	4.73838e7	+	7.66621e6i	1.15391	+	0.186691i
$346$	1.10011e7	−	3.38580e7i	0.265588	−	0.817396i
$347$	−9.60147e6	−	3.11971e6i	−0.229800	−	0.0746664i	0.191854	−	0.981424i	$-0.438550\pi$
$347$	−9.60147e6	−	3.11971e6i	−0.229800	−	0.0746664i	−0.421653	+	0.906757i	$0.638550\pi$
$348$	4.81108e6	−	2.97366e7i	0.114158	−	0.705593i
$349$	−1.07772e7	−	7.83008e6i	−0.253530	−	0.184200i	0.453760	−	0.891124i	$-0.350082\pi$
$349$	−1.07772e7	−	7.83008e6i	−0.253530	−	0.184200i	−0.707290	+	0.706924i	$0.750082\pi$
$350$	−1.13555e8	+	3.68963e7i	−2.64852	+	0.860555i
$351$	−2.83366e7	+	2.77776e7i	−0.655279	+	0.642353i
$352$	2.95176e7	+	3.20915e7i	0.676790	+	0.735804i
$353$		−	2.18364e7i		−	0.496428i	−0.968705	−	0.248214i	$-0.920156\pi$
$353$		−	2.18364e7i		−	0.496428i	0.968705	−	0.248214i	$-0.0798436\pi$
$354$	−4.22352e7	+	8.22153e7i	−0.952062	+	1.85329i
$355$	6.25183e7	+	4.54222e7i	1.39740	+	1.01527i
$356$	3.16174e6	+	4.35177e6i	0.0700772	+	0.0964530i
$357$	−1.78813e7	−	3.53840e7i	−0.393002	−	0.777682i
$358$	3.05422e7	−	9.39993e7i	0.665658	−	2.04869i
$359$	3.27183e6	+	4.50329e6i	0.0707144	+	0.0973300i	0.842909	−	0.538056i	$-0.180841\pi$
$359$	3.27183e6	+	4.50329e6i	0.0707144	+	0.0973300i	−0.772195	+	0.635386i	$0.780841\pi$
$360$	2.72025e7	−	3.69230e7i	0.583044	−	0.791387i
$361$	−1.13663e7	−	3.49818e7i	−0.241600	−	0.743567i
$362$		−	1.43854e7i		−	0.303248i
$363$	−4.77142e7	+	3.35760e6i	−0.997533	+	0.0701954i
$364$	2.56822e7			0.532510
$365$	5.63844e7	−	1.83204e7i	1.15953	−	0.376753i
$366$	−9.47194e7	+	1.46799e7i	−1.93195	+	0.299419i
$367$	−6.76713e7	+	4.91661e7i	−1.36901	+	0.994643i	−0.371195	+	0.928555i	$0.621052\pi$
$367$	−6.76713e7	+	4.91661e7i	−1.36901	+	0.994643i	−0.997814	+	0.0660880i	$0.978948\pi$
$368$	3.90193e7	+	1.26781e7i	0.782953	+	0.254397i
$369$	−2.02519e6	+	6.09489e6i	−0.0403076	+	0.121307i
$370$	−2.20167e7	+	1.59961e7i	−0.434658	+	0.315798i
$371$	−4.50665e6	+	6.20287e6i	−0.0882535	+	0.121471i
$372$	−1.85857e7	+	3.61791e7i	−0.361037	+	0.702796i
$373$	1.00002e8			1.92700			0.963500	−	0.267709i	$-0.0862665\pi$
$373$	1.00002e8			1.92700			0.963500	+	0.267709i	$0.0862665\pi$
$374$	3.99906e7	−	3.67832e7i	0.764440	−	0.703129i
$375$	−7.51873e7	+	7.46896e7i	−1.42577	+	1.41634i
$376$	8.48627e6	+	2.61180e7i	0.159644	+	0.491334i
$377$	−3.72353e7	+	5.12500e7i	−0.694914	+	0.956467i
$378$	−6.94673e7	−	1.17130e7i	−1.28619	−	0.216866i
$379$	−612065.	+	1.88374e6i	−0.0112429	+	0.0346022i	−0.956521	−	0.291665i	$-0.905791\pi$
$379$	−612065.	+	1.88374e6i	−0.0112429	+	0.0346022i	0.945278	+	0.326267i	$0.105791\pi$
$380$	2.39432e7	+	7.77963e6i	0.436347	+	0.141778i
$381$	−5.99559e7	−	9.70025e6i	−1.08407	−	0.175391i
$382$	7.67817e7	+	5.57852e7i	1.37742	+	1.00076i
$383$	2.36416e6	−	768163.i	0.0420805	−	0.0136728i	−0.287901	−	0.957660i	$-0.592957\pi$
$383$	2.36416e6	−	768163.i	0.0420805	−	0.0136728i	0.329982	+	0.943987i	$0.392957\pi$
$384$	4.01823e7	−	3.99164e7i	0.709645	−	0.704948i
$385$	5.18746e7	−	9.20917e7i	0.909019	−	1.61376i
$386$		−	1.80130e7i		−	0.313202i
$387$	3.40211e7	−	1.08049e7i	0.586969	−	0.186418i
$388$	7.76218e6	+	5.63956e6i	0.132889	+	0.0965495i
$389$	−1.51202e7	−	2.08112e7i	−0.256868	−	0.353548i	0.661034	−	0.750356i	$-0.270118\pi$
$389$	−1.51202e7	−	2.08112e7i	−0.256868	−	0.353548i	−0.917902	+	0.396808i	$0.870118\pi$
$390$	1.07255e8	−	5.42014e7i	1.80811	−	0.913728i
$391$	1.01579e7	−	3.12629e7i	0.169932	−	0.522997i
$392$	−1.85272e6	−	2.55004e6i	−0.0307575	−	0.0423340i
$393$	−564270.	+	87452.2i	−0.00929628	+	0.00144076i
$394$	−2.52648e6	−	7.77571e6i	−0.0413073	−	0.127131i
$395$		−	4.89959e7i		−	0.795003i
$396$	−3.73693e6	−	3.42473e7i	−0.0601769	−	0.551493i
$397$	7.15475e7			1.14347			0.571733	−	0.820440i	$-0.306271\pi$
$397$	7.15475e7			1.14347			0.571733	+	0.820440i	$0.306271\pi$
$398$	−2.00564e7	+	6.51673e6i	−0.318130	+	0.103367i
$399$	4.75338e6	+	3.06703e7i	0.0748313	+	0.482836i
$400$	−1.37850e8	+	1.00154e8i	−2.15391	+	1.56491i
$401$	−6.79705e7	−	2.20850e7i	−1.05411	−	0.342502i	−0.269832	−	0.962907i	$-0.586968\pi$
$401$	−6.79705e7	−	2.20850e7i	−1.05411	−	0.342502i	−0.784282	+	0.620405i	$0.786968\pi$
$402$	−1.77957e6	−	3.52146e6i	−0.0273928	−	0.0542057i
$403$	6.92001e7	−	5.02768e7i	1.05728	−	0.768161i
$404$	2.30023e7	−	3.16599e7i	0.348840	−	0.480137i
$405$	−1.12337e8	+	3.48582e7i	−1.69106	+	0.524735i
$406$	−1.12467e8			−1.68053
$407$	3.24073e6	−	1.60834e7i	0.0480684	−	0.238558i
$408$	−2.21345e7	−	2.22819e7i	−0.325903	−	0.328074i
$409$	−4.04057e7	−	1.24356e8i	−0.590572	−	1.81759i	−0.575636	−	0.817706i	$-0.695245\pi$
$409$	−4.04057e7	−	1.24356e8i	−0.590572	−	1.81759i	−0.0149365	−	0.999888i	$-0.504755\pi$
$410$	1.14328e7	−	1.57359e7i	0.165882	−	0.228318i
$411$	6.21211e6	−	3.83962e7i	0.0894774	−	0.553048i
$412$	−5.64671e6	+	1.73788e7i	−0.0807427	+	0.248501i
$413$	1.17107e8	+	3.80504e7i	1.66239	+	0.540144i
$414$	−3.40187e7	−	4.74826e7i	−0.479421	−	0.669166i
$415$	2.68711e7	+	1.95230e7i	0.375959	+	0.273150i
$416$	6.28095e7	−	2.04080e7i	0.872460	−	0.283479i
$417$	5.70091e7	+	5.73890e7i	0.786206	+	0.791444i
$418$	−3.86728e7	+	1.77121e7i	−0.529514	+	0.242517i
$419$		−	5.50702e7i		−	0.748642i	−0.927299	−	0.374321i	$-0.877876\pi$
$419$		−	5.50702e7i		−	0.748642i	0.927299	−	0.374321i	$-0.122124\pi$
$420$	6.77145e7	+	3.47859e7i	0.913974	+	0.469522i
$421$	−9.95474e6	−	7.23254e6i	−0.133409	−	0.0969270i	0.519080	−	0.854726i	$-0.326275\pi$
$421$	−9.95474e6	−	7.23254e6i	−0.133409	−	0.0969270i	−0.652488	+	0.757799i	$0.726275\pi$
$422$	3.72537e7	+	5.12754e7i	0.495716	+	0.682294i
$423$	2.22091e7	−	6.68391e7i	0.293433	−	0.883099i
$424$	−1.87696e6	+	5.77668e6i	−0.0246239	+	0.0757845i
$425$	8.02452e7	+	1.10448e8i	1.04533	+	1.43877i
$426$	−1.44024e7	−	9.29289e7i	−0.186297	−	1.20205i
$427$	3.94587e7	+	1.21441e8i	0.506826	+	1.55985i
$428$		−	5.42495e6i		−	0.0691934i
$429$	−2.54697e7	+	6.78240e7i	−0.322591	+	0.859036i
$430$	−1.08104e8			−1.35968
$431$	7.58300e7	−	2.46386e7i	0.947129	−	0.307741i	0.205580	−	0.978640i	$-0.434092\pi$
$431$	7.58300e7	−	2.46386e7i	0.947129	−	0.307741i	0.741548	+	0.670899i	$0.234092\pi$
$432$	−9.94491e7	+	1.47374e7i	−1.23353	+	0.182797i
$433$	1.26363e7	−	9.18078e6i	0.155652	−	0.113088i	−0.507233	−	0.861809i	$-0.669332\pi$
$433$	1.26363e7	−	9.18078e6i	0.155652	−	0.113088i	0.662885	+	0.748721i	$0.269332\pi$
$434$	1.44425e8	+	4.69266e7i	1.76675	+	0.574051i
$435$	−1.67593e8	+	8.46932e7i	−2.03605	+	1.02892i
$436$	−3.09702e7	+	2.25011e7i	−0.373666	+	0.271485i
$437$	−1.51259e7	+	2.08190e7i	−0.181249	+	0.249468i
$438$	−6.41728e7	−	3.29665e7i	−0.763710	−	0.392329i
$439$	−1.20838e8			−1.42827			−0.714135	−	0.700008i	$-0.753180\pi$
$439$	−1.20838e8			−1.42827			−0.714135	+	0.700008i	$0.753180\pi$
$440$	1.65395e7	−	8.20838e7i	0.194162	−	0.963605i
$441$	−53679.4	+	8.08384e6i	−0.000625881	+	0.0942545i
$442$	−2.54314e7	−	7.82697e7i	−0.294512	−	0.906414i
$443$	5.59431e7	−	7.69991e7i	0.643481	−	0.885675i	−0.355315	−	0.934747i	$-0.615626\pi$
$443$	5.59431e7	−	7.69991e7i	0.643481	−	0.885675i	0.998795	+	0.0490718i	$0.0156263\pi$
$444$	1.16650e7	+	1.88728e6i	0.133271	+	0.0215619i
$445$	1.03617e7	−	3.18900e7i	0.117585	−	0.361888i
$446$	−5.85604e7	−	1.90274e7i	−0.660085	−	0.214474i
$447$	−1.27608e7	+	7.88725e7i	−0.142874	+	0.883087i
$448$	−33448.0	−	24301.4i	−0.000371994	−	0.000270270i
$449$	−1.23122e8	+	4.00047e7i	−1.36018	+	0.441949i	−0.896103	−	0.443846i	$-0.853614\pi$
$449$	−1.23122e8	+	4.00047e7i	−1.36018	+	0.441949i	−0.464077	+	0.885795i	$0.653614\pi$
$450$	2.42585e8	+	1.61085e6i	2.66212	+	0.0176773i
$451$	1.34935e6	+	1.16483e7i	0.0147094	+	0.126980i
$452$			6.20122e7i			0.671525i
$453$	4.03144e7	−	7.84762e7i	0.433676	−	0.844197i
$454$	−3.25745e7	−	2.36668e7i	−0.348105	−	0.252913i
$455$	−9.41004e7	−	1.29518e8i	−0.998981	−	1.37498i
$456$	1.10896e7	+	2.19443e7i	0.116955	+	0.231434i
$457$	1.83580e7	−	5.65002e7i	0.192343	−	0.591972i	−0.807654	−	0.589657i	$-0.799263\pi$
$457$	1.83580e7	−	5.65002e7i	0.192343	−	0.591972i	0.999997	−	0.00231534i	$-0.000736997\pi$
$458$	−1.04598e8	−	1.43967e8i	−1.08875	−	1.49853i
$459$	1.18078e7	+	7.96803e7i	0.122104	+	0.823972i
$460$	1.95052e7	+	6.00308e7i	0.200390	+	0.616738i
$461$			1.77711e8i			1.81389i	0.421247	+	0.906946i	$0.361592\pi$
$461$			1.77711e8i			1.81389i	−0.421247	+	0.906946i	$0.638408\pi$
$462$	−1.23994e8	+	3.41944e7i	−1.25741	+	0.346760i
$463$	1.42784e8			1.43858			0.719292	−	0.694708i	$-0.244466\pi$
$463$	1.42784e8			1.43858			0.719292	+	0.694708i	$0.244466\pi$
$464$	−1.52645e8	+	4.95972e7i	−1.52801	+	0.496482i
$465$	2.50554e8	−	3.88316e7i	2.49197	−	0.386212i
$466$	1.73471e8	−	1.26034e8i	1.71424	−	1.24546i
$467$	−1.32992e8	−	4.32118e7i	−1.30580	−	0.424279i	−0.428202	−	0.903683i	$-0.640853\pi$
$467$	−1.32992e8	−	4.32118e7i	−1.30580	−	0.424279i	−0.877594	+	0.479404i	$0.840853\pi$
$468$	−4.95182e7	−	1.64537e7i	−0.483089	−	0.160519i
$469$	−4.25241e6	+	3.08956e6i	−0.0412208	+	0.0299487i
$470$	−1.25377e8	+	1.72566e8i	−1.20760	+	1.66212i
$471$	9.03731e7	−	1.75921e8i	0.864921	−	1.68366i
$472$	9.75469e7			0.927657
$473$	4.79675e7	−	4.41203e7i	0.453277	−	0.416923i
$474$	−4.22997e7	+	4.20198e7i	−0.397194	+	0.394565i
$475$	−3.30264e7	−	1.01645e8i	−0.308163	−	0.948429i
$476$	3.06436e7	−	4.21772e7i	0.284131	−	0.391072i
$477$	1.26633e7	−	9.07257e6i	0.116679	−	0.0835941i
$478$	−7.96192e7	+	2.45043e8i	−0.729011	+	2.24366i
$479$	9.52590e7	+	3.09515e7i	0.866761	+	0.281628i	0.708449	−	0.705762i	$-0.249395\pi$
$479$	9.52590e7	+	3.09515e7i	0.866761	+	0.281628i	0.158311	+	0.987389i	$0.449395\pi$
$480$	1.93248e8	+	3.12655e7i	1.74739	+	0.282710i
$481$	−2.01042e7	−	1.46066e7i	−0.180656	−	0.131254i
$482$	2.01053e8	−	6.53262e7i	1.79544	−	0.583373i
$483$	−5.52060e7	+	5.48406e7i	−0.489942	+	0.486699i
$484$	−3.25981e7	−	5.37931e7i	−0.287512	−	0.474450i
$485$		−	5.98090e7i		−	0.524254i
$486$	1.26437e8	+	6.70893e7i	1.10145	+	0.584446i
$487$	4.52944e7	+	3.29083e7i	0.392155	+	0.284917i	0.766338	−	0.642438i	$-0.222077\pi$
$487$	4.52944e7	+	3.29083e7i	0.392155	+	0.284917i	−0.374183	+	0.927355i	$0.622077\pi$
$488$	5.94587e7	+	8.18379e7i	0.511630	+	0.704199i
$489$	−4.46342e7	+	2.25559e7i	−0.381717	+	0.192901i
$490$	7.56546e6	−	2.32841e7i	0.0643054	−	0.197912i
$491$	−1.20867e7	−	1.66359e7i	−0.102109	−	0.140540i	0.754905	−	0.655834i	$-0.227683\pi$
$491$	−1.20867e7	−	1.66359e7i	−0.102109	−	0.140540i	−0.857014	+	0.515294i	$0.827683\pi$
$492$	−8.34603e6	+	1.29349e6i	−0.0700784	+	0.0108610i
$493$	3.97381e7	+	1.22301e8i	0.331640	+	1.02068i
$494$			6.44267e7i			0.534423i
$495$	−1.59020e8	+	1.44329e8i	−1.31110	+	1.18997i
$496$	2.16714e8			1.77600
$497$	−1.19146e8	+	3.87128e7i	−0.970531	+	0.315345i
$498$	−6.19031e6	−	3.99419e7i	−0.0501215	−	0.323400i
$499$	−1.27645e8	+	9.27392e7i	−1.02731	+	0.746383i	−0.967768	−	0.251843i	$-0.918963\pi$
$499$	−1.27645e8	+	9.27392e7i	−1.02731	+	0.746383i	−0.0595397	+	0.998226i	$0.518963\pi$
$500$	−1.32542e8	−	4.30657e7i	−1.06034	−	0.344525i
$501$	7.42062e6	+	1.46841e7i	0.0590102	+	0.116771i
$502$	−1.43235e8	+	1.04066e8i	−1.13224	+	0.822620i
$503$	−1.06285e8	+	1.46288e8i	−0.835153	+	1.14949i	0.151789	+	0.988413i	$0.451497\pi$
$503$	−1.06285e8	+	1.46288e8i	−0.835153	+	1.14949i	−0.986942	+	0.161076i	$0.948503\pi$
$504$	2.25049e7	+	7.08605e7i	0.175786	+	0.553494i
$505$	−2.43945e8			−1.89417
$506$	−9.29190e7	−	5.23407e7i	−0.717221	−	0.404006i
$507$	−1.45110e7	−	1.46077e7i	−0.111346	−	0.112088i
$508$	−2.46804e7	−	7.59584e7i	−0.188261	−	0.579408i
$509$	−4.70944e7	+	6.48199e7i	−0.357121	+	0.491536i	−0.949344	−	0.314239i	$-0.898251\pi$
$509$	−4.70944e7	+	6.48199e7i	−0.357121	+	0.491536i	0.592222	+	0.805775i	$0.298251\pi$
$510$	3.89613e7	−	2.40815e8i	0.293713	−	1.81540i
$511$	−2.97001e7	+	9.14074e7i	−0.222584	+	0.685045i
$512$	7.07647e7	+	2.29928e7i	0.527238	+	0.171310i
$513$	1.04844e7	−	6.21812e7i	0.0776593	−	0.460582i
$514$	1.89720e7	+	1.37839e7i	0.139708	+	0.101504i
$515$	1.08333e8	−	3.51994e7i	0.793118	−	0.257700i
$516$	3.30811e7	+	3.33015e7i	0.240786	+	0.242390i
$517$	−1.47975e7	−	1.27740e8i	−0.107082	−	0.924392i
$518$		−	4.41182e7i		−	0.317416i
$519$	8.57114e7	+	4.40312e7i	0.613108	+	0.314962i
$520$	−1.02605e8	−	7.45466e7i	−0.729721	−	0.530173i
$521$	1.00653e8	+	1.38537e8i	0.711727	+	0.979608i	0.999758	+	0.0219873i	$0.00699935\pi$
$521$	1.00653e8	+	1.38537e8i	0.711727	+	0.979608i	−0.288031	+	0.957621i	$0.593001\pi$
$522$	2.16849e8	+	7.20539e7i	1.52456	+	0.506578i
$523$	−2.13560e7	+	6.57270e7i	−0.149285	+	0.459451i	−0.997537	−	0.0701413i	$-0.977655\pi$
$523$	−2.13560e7	+	6.57270e7i	−0.149285	+	0.459451i	0.848252	+	0.529592i	$0.177655\pi$
$524$	−441353.	−	607471.i	−0.00306756	−	0.00422213i
$525$	−4.94961e7	−	3.19365e8i	−0.342053	−	2.20704i
$526$	−6.91675e7	−	2.12876e8i	−0.475275	−	1.46275i
$527$		−	1.73635e8i		−	1.18633i
$528$	−1.53210e8	+	1.01091e8i	−1.04085	+	0.686768i
$529$	8.35161e7			0.564161
$530$	−4.48685e7	+	1.45786e7i	−0.301379	+	0.0979241i
$531$	−2.01418e8	−	1.48392e8i	−1.34529	−	0.991123i
$532$	−3.30185e7	+	2.39893e7i	−0.219292	+	0.159325i
$533$	1.68917e7	+	5.48846e6i	0.111556	+	0.0362467i
$534$	−3.64180e7	+	1.84039e7i	−0.239162	+	0.120861i
$535$	−2.73586e7	+	1.98772e7i	−0.178662	+	0.129806i
$536$	−2.44756e6	+	3.36877e6i	−0.0158942	+	0.0218765i
$537$	2.37959e8	+	1.22243e8i	1.53667	+	0.789408i
$538$	2.08162e8			1.33676
$539$	6.14599e6	+	1.34192e7i	0.0392487	+	0.0856962i
$540$	−1.08275e8	−	1.10454e8i	−0.687618	−	0.701454i
$541$	7.35254e7	+	2.26288e8i	0.464350	+	1.42912i	0.859798	+	0.510634i	$0.170589\pi$
$541$	7.35254e7	+	2.26288e8i	0.464350	+	1.42912i	−0.395448	+	0.918488i	$0.629411\pi$
$542$	−1.54069e8	+	2.12058e8i	−0.967650	+	1.33186i
$543$	3.84374e7	+	6.21877e6i	0.240079	+	0.0388423i
$544$	4.14276e7	−	1.27501e8i	0.257332	−	0.791985i
$545$	2.26951e8	+	7.37410e7i	1.40198	+	0.455533i
$546$	−3.11149e7	+	1.92317e8i	−0.191157	+	1.18152i
$547$	5.66815e7	+	4.11815e7i	0.346321	+	0.251617i	0.747324	−	0.664460i	$-0.231338\pi$
$547$	5.66815e7	+	4.11815e7i	0.346321	+	0.251617i	−0.401003	+	0.916077i	$0.631338\pi$
$548$	4.86443e7	−	1.58055e7i	0.295590	−	0.0960431i
$549$	1.72272e6	−	2.59433e8i	0.0104111	−	1.56786i
$550$	4.02693e8	−	1.84433e8i	2.42040	−	1.10854i
$551$		−	1.00671e8i		−	0.601796i
$552$	−2.81686e7	+	5.48332e7i	−0.167474	+	0.326007i
$553$	6.42599e7	+	4.66876e7i	0.379984	+	0.276074i
$554$	−5.11046e7	−	7.03395e7i	−0.300560	−	0.413685i
$555$	−3.32232e7	−	6.57429e7i	−0.194340	−	0.384565i
$556$	−3.28712e7	+	1.01167e8i	−0.191245	+	0.588593i
$557$	−1.32458e8	−	1.82313e8i	−0.766501	−	1.05500i	−0.996645	−	0.0818411i	$-0.973920\pi$
$557$	−1.32458e8	−	1.82313e8i	−0.766501	−	1.05500i	0.230145	−	0.973156i	$-0.426080\pi$
$558$	−2.48404e8	−	1.83008e8i	−1.42974	−	1.05334i
$559$	−3.05041e7	−	9.38820e7i	−0.174632	−	0.537461i
$560$		−	4.05612e8i		−	2.30965i
$561$	8.09956e7	+	1.22755e8i	0.458747	+	0.695264i
$562$	−5.85796e7			−0.330018
$563$	−1.16364e8	+	3.78090e7i	−0.652069	+	0.211870i	−0.616326	−	0.787491i	$-0.711380\pi$
$563$	−1.16364e8	+	3.78090e7i	−0.652069	+	0.211870i	−0.0357428	+	0.999361i	$0.511380\pi$
$564$	9.15259e7	−	1.41849e7i	0.510160	−	0.0790661i
$565$	3.12734e8	−	2.27215e8i	1.73392	−	1.25977i
$566$	−1.72766e8	−	5.61351e7i	−0.952816	−	0.309589i
$567$	6.13270e7	−	1.80550e8i	0.336436	−	0.990488i
$568$	−8.02909e7	+	5.83348e7i	−0.438149	+	0.318334i
$569$	−2.38392e7	+	3.28118e7i	−0.129406	+	0.178112i	−0.868803	−	0.495157i	$-0.835110\pi$
$569$	−2.38392e7	+	3.28118e7i	−0.129406	+	0.178112i	0.739397	+	0.673269i	$0.235110\pi$
$570$	−8.72645e7	+	1.69870e8i	−0.471209	+	0.917257i
$571$	−1.88098e8			−1.01036			−0.505180	−	0.863014i	$-0.668574\pi$
$571$	−1.88098e8			−1.01036			−0.505180	+	0.863014i	$0.668574\pi$
$572$	−9.46372e7	+	1.09628e7i	−0.505678	+	0.0585780i
$573$	−1.82248e8	+	1.81042e8i	−0.968723	+	0.962312i
$574$	9.74403e6	+	2.99890e7i	0.0515232	+	0.158572i
$575$	1.57503e8	−	2.16784e8i	0.828487	−	1.14031i
$576$	48922.5	+	68284.9i	0.000256001	+	0.000357320i
$577$	8.14976e7	−	2.50824e8i	0.424246	−	1.30569i	−0.479469	−	0.877559i	$-0.659171\pi$
$577$	8.14976e7	−	2.50824e8i	0.424246	−	1.30569i	0.903715	−	0.428135i	$-0.140829\pi$
$578$	7.01085e7	+	2.27796e7i	0.363067	+	0.117968i
$579$	4.81301e7	+	7.78695e6i	0.247960	+	0.0401173i
$580$	−1.99769e8	−	1.45140e8i	−1.02387	−	0.743883i
$581$	−5.12102e7	+	1.66392e7i	−0.261113	+	0.0848407i
$582$	−5.16350e7	+	5.12933e7i	−0.261924	+	0.260191i
$583$	1.39589e7	−	2.47809e7i	0.0704444	−	0.125058i
$584$			7.61398e7i			0.382273i
$585$	9.84582e7	+	3.10013e8i	0.491795	+	1.54850i
$586$	2.17672e8	+	1.58148e8i	1.08171	+	0.785905i
$587$	−1.70850e8	−	2.35154e8i	−0.844695	−	1.16262i	−0.985007	−	0.172516i	$-0.944810\pi$
$587$	−1.70850e8	−	2.35154e8i	−0.844695	−	1.16262i	0.140312	−	0.990107i	$-0.455190\pi$
$588$	−9.48782e6	+	4.79467e6i	−0.0466696	+	0.0235845i
$589$	−4.20048e7	+	1.29277e8i	−0.205567	+	0.632669i
$590$	4.45344e8	+	6.12963e8i	2.16840	+	2.98455i
$591$	2.18686e7	−	3.38925e6i	0.105940	−	0.0164188i
$592$	−1.94559e7	−	5.98790e7i	−0.0937747	−	0.288609i
$593$			2.09831e8i			1.00625i	0.864214	+	0.503125i	$0.167816\pi$
$593$			2.09831e8i			1.00625i	−0.864214	+	0.503125i	$0.832184\pi$
$594$	2.60982e8	+	1.35084e7i	1.24524	+	0.0644530i
$595$	−3.24983e8			−1.54280
$596$	−9.99240e7	+	3.24673e7i	−0.471988	+	0.153358i
$597$	−8.74215e6	−	5.64072e7i	−0.0410861	−	0.265101i
$598$	−1.30682e8	+	9.49458e7i	−0.611098	+	0.443989i
$599$	1.12408e8	+	3.65237e7i	0.523020	+	0.169939i	0.558615	−	0.829427i	$-0.311333\pi$
$599$	1.12408e8	+	3.65237e7i	0.523020	+	0.169939i	−0.0355955	+	0.999366i	$0.511333\pi$
$600$	−1.15474e8	−	2.28502e8i	−0.534601	−	1.05788i
$601$	−2.07934e8	+	1.51073e8i	−0.957861	+	0.695927i	−0.952653	−	0.304060i	$-0.901658\pi$
$601$	−2.07934e8	+	1.51073e8i	−0.957861	+	0.695927i	−0.00520787	+	0.999986i	$0.501658\pi$
$602$	1.03011e8	−	1.41782e8i	0.472165	−	0.649879i
$603$	1.01785e7	−	3.23263e6i	0.0464229	−	0.0147436i
$604$	1.16017e8			0.526515
$605$	−1.51844e8	+	3.61495e8i	−0.685696	+	1.63244i
$606$	2.09212e8	+	2.10606e8i	0.940087	+	0.946351i
$607$	−4.25583e7	−	1.30981e8i	−0.190291	−	0.585656i	0.809708	−	0.586833i	$-0.199625\pi$
$607$	−4.25583e7	−	1.30981e8i	−0.190291	−	0.585656i	−0.999999	+	0.00117699i	$0.999625\pi$
$608$	−6.16886e7	+	8.49071e7i	−0.274470	+	0.377775i
$609$	4.86190e7	−	3.00507e8i	0.215255	−	1.33046i
$610$	−2.42797e8	+	7.47251e8i	−1.06968	+	3.29213i
$611$	−1.85242e8	−	6.01886e7i	−0.812110	−	0.263871i
$612$	−8.61058e7	+	6.16902e7i	−0.375646	+	0.269130i
$613$	−1.81084e8	−	1.31565e8i	−0.786138	−	0.571163i	0.120677	−	0.992692i	$-0.461494\pi$
$613$	−1.81084e8	−	1.31565e8i	−0.786138	−	0.571163i	−0.906815	+	0.421529i	$0.861494\pi$
$614$	3.37908e8	−	1.09793e8i	1.45980	−	0.474317i
$615$	3.71033e7	+	3.73505e7i	0.159510	+	0.160573i
$616$	9.18956e7	+	9.99087e7i	0.393145	+	0.427426i
$617$		−	1.10958e8i		−	0.472392i	−0.971705	−	0.236196i	$-0.924099\pi$
$617$		−	1.10958e8i		−	0.472392i	0.971705	−	0.236196i	$-0.0759007\pi$
$618$	−1.23297e8	−	6.33394e7i	−0.522380	−	0.268354i
$619$	−9.60887e7	−	6.98125e7i	−0.405135	−	0.294348i	0.366494	−	0.930420i	$-0.380558\pi$
$619$	−9.60887e7	−	6.98125e7i	−0.405135	−	0.294348i	−0.771629	+	0.636072i	$0.780558\pi$
$620$	1.95975e8	+	2.69736e8i	0.822291	+	1.13179i
$621$	1.41578e8	−	7.03702e7i	0.591181	−	0.293842i
$622$	−2.05672e7	+	6.32993e7i	−0.0854680	+	0.263044i
$623$	3.19514e7	+	4.39773e7i	0.132137	+	0.181872i
$624$	4.25802e7	+	2.74742e8i	0.175248	+	1.13076i
$625$	1.07381e8	+	3.30484e8i	0.439831	+	1.35366i
$626$		−	5.16935e8i		−	2.10724i
$627$	−3.06080e7	−	1.10989e8i	−0.124174	−	0.450275i
$628$	2.60076e8			1.05008
$629$	−4.79761e7	+	1.55884e7i	−0.192785	+	0.0626396i
$630$	−3.42527e8	+	4.64925e8i	−1.36985	+	1.85935i
$631$	3.07959e8	−	2.23745e8i	1.22576	−	0.890565i	0.229192	−	0.973381i	$-0.426392\pi$
$631$	3.07959e8	−	2.23745e8i	1.22576	−	0.890565i	0.996565	+	0.0828165i	$0.0263915\pi$
$632$	5.98447e7	+	1.94447e7i	0.237069	+	0.0770283i
$633$	−1.53111e8	+	7.73745e7i	−0.603662	+	0.305061i
$634$	1.38258e8	−	1.00450e8i	0.542527	−	0.394169i
$635$	−2.92637e8	+	4.02780e8i	−1.14290	+	1.57306i
$636$	1.82213e7	+	9.36053e6i	0.0708284	+	0.0363856i
$637$	2.23557e7			0.0864907
$638$	4.14433e8	−	4.80082e7i	1.59585	−	0.184864i
$639$	2.54529e8	+	1.69016e6i	0.975515	+	0.00647775i
$640$	−1.43470e8	−	4.41556e8i	−0.547296	−	1.68440i
$641$	−2.29082e7	+	3.15305e7i	−0.0869795	+	0.119717i	−0.850289	−	0.526316i	$-0.823573\pi$
$641$	−2.29082e7	+	3.15305e7i	−0.0869795	+	0.119717i	0.763310	+	0.646033i	$0.223573\pi$
$642$	4.06238e7	+	6.57252e6i	0.153524	+	0.0248386i
$643$	−6.50247e7	+	2.00125e8i	−0.244594	+	0.752782i	0.751109	+	0.660178i	$0.229519\pi$
$643$	−6.50247e7	+	2.00125e8i	−0.244594	+	0.752782i	−0.995703	+	0.0926041i	$0.970481\pi$
$644$	−9.73188e7	−	3.16208e7i	−0.364367	−	0.118390i
$645$	4.67329e7	−	2.88850e8i	0.174158	−	1.07645i
$646$	1.05806e8	+	7.68729e7i	0.392477	+	0.285151i
$647$	7.76723e6	−	2.52373e6i	0.0286783	−	0.00931814i	−0.294643	−	0.955607i	$-0.595201\pi$
$647$	7.76723e6	−	2.52373e6i	0.0286783	−	0.00931814i	0.323321	+	0.946289i	$0.395201\pi$
$648$	2.00607e6	−	1.51045e8i	0.00737261	−	0.555114i
$649$	−4.47775e8	−	9.02244e7i	−1.63804	−	0.330058i
$650$		−	6.70864e8i		−	2.44284i
$651$	−1.87821e8	+	3.65613e8i	−0.680770	+	1.32519i
$652$	−5.32034e7	−	3.86545e7i	−0.191954	−	0.139463i
$653$	1.40189e8	+	1.92954e8i	0.503471	+	0.692969i	0.982801	−	0.184666i	$-0.0591203\pi$
$653$	1.40189e8	+	1.92954e8i	0.503471	+	0.692969i	−0.479330	+	0.877635i	$0.659120\pi$
$654$	−1.30975e8	−	2.59176e8i	−0.468224	−	0.926534i
$655$	−1.44641e6	+	4.45158e6i	−0.00514715	+	0.0158413i
$656$	2.64500e7	+	3.64053e7i	0.0936944	+	0.128959i
$657$	1.15827e8	−	1.57216e8i	0.408426	−	0.554371i
$658$	−1.06857e8	−	3.28872e8i	−0.375081	−	1.15438i
$659$			5.69225e6i			0.0198897i	0.999951	+	0.00994483i	$0.00316559\pi$
$659$			5.69225e6i			0.0198897i	−0.999951	+	0.00994483i	$0.996834\pi$
$660$	−2.64373e8	−	9.92790e7i	−0.919569	−	0.345323i
$661$	3.28619e8			1.13786			0.568929	−	0.822387i	$-0.307358\pi$
$661$	3.28619e8			1.13786			0.568929	+	0.822387i	$0.307358\pi$
$662$	3.46735e8	−	1.12661e8i	1.19515	−	0.388329i
$663$	2.20127e8	−	3.41160e7i	0.755324	−	0.117062i
$664$	−3.45100e7	+	2.50729e7i	−0.117880	+	0.0856448i
$665$	2.41961e8	+	7.86181e7i	0.822775	+	0.267336i
$666$	−2.82651e7	+	8.50650e7i	−0.0956816	+	0.287957i
$667$	2.04198e8	−	1.48359e8i	0.688137	−	0.499961i
$668$	−1.27169e7	+	1.75033e7i	−0.0426630	+	0.0587205i
$669$	7.61560e7	−	1.48246e8i	0.254346	−	0.495112i
$670$	−3.23428e7			−0.107536
$671$	−1.97242e8	−	4.30660e8i	−0.652877	−	1.42550i
$672$	−2.25149e8	+	2.23659e8i	−0.741930	+	0.737019i
$673$	3.62307e7	+	1.11507e8i	0.118859	+	0.365810i	0.992732	−	0.120344i	$-0.0383996\pi$
$673$	3.62307e7	+	1.11507e8i	0.118859	+	0.365810i	−0.873873	+	0.486153i	$0.838400\pi$
$674$	−1.00385e7	+	1.38169e7i	−0.0327862	+	0.0451263i
$675$	−1.09173e8	+	6.47482e8i	−0.354979	+	2.10531i
$676$	8.36698e6	−	2.57509e7i	0.0270850	−	0.0833590i
$677$	−1.03770e8	−	3.37168e7i	−0.334430	−	0.108663i	0.136988	−	0.990573i	$-0.456258\pi$
$677$	−1.03770e8	−	3.37168e7i	−0.334430	−	0.108663i	−0.471418	+	0.881910i	$0.656258\pi$
$678$	−4.64368e8	−	7.51300e7i	−1.48996	−	0.241059i
$679$	7.84418e7	+	5.69913e7i	0.250575	+	0.182053i
$680$	−2.44852e8	+	7.95573e7i	−0.778713	+	0.253019i
$681$	7.73186e7	−	7.68068e7i	0.244817	−	0.243197i
$682$	−5.52229e8	−	1.11272e8i	−1.74087	−	0.350777i
$683$			3.51234e8i			1.10239i	0.834377	+	0.551194i	$0.185828\pi$
$683$			3.51234e8i			1.10239i	−0.834377	+	0.551194i	$0.814172\pi$
$684$	7.90326e7	−	2.51003e7i	0.246966	−	0.0784350i
$685$	−2.57943e8	−	1.87407e8i	−0.802513	−	0.583060i
$686$	−2.24176e8	−	3.08551e8i	−0.694410	−	0.955774i
$687$	4.29891e8	−	2.17246e8i	1.32583	−	0.670009i
$688$	7.72853e7	−	2.37860e8i	0.237319	−	0.730392i
$689$	−2.53214e7	−	3.48520e7i	−0.0774160	−	0.106554i
$690$	−4.73162e8	+	7.33319e7i	−1.44033	+	0.223226i
$691$	8.26635e7	+	2.54412e8i	0.250542	+	0.771088i	0.994675	+	0.103057i	$0.0328625\pi$
$691$	8.26635e7	+	2.54412e8i	0.250542	+	0.771088i	−0.744134	+	0.668031i	$0.767138\pi$
$692$			1.26713e8i			0.382388i
$693$	−3.77640e7	−	3.46090e8i	−0.113469	−	1.03989i
$694$	1.00706e8			0.301284
$695$	6.30637e8	−	2.04906e8i	1.87856	−	0.610381i
$696$	−3.69345e7	−	2.38313e8i	−0.109548	−	0.706839i
$697$	2.91685e7	−	2.11921e7i	0.0861421	−	0.0625859i
$698$	1.26379e8	+	4.10632e7i	0.371630	+	0.120750i
$699$	2.61768e8	+	5.17993e8i	0.766453	+	1.51668i
$700$	3.43816e8	−	2.49797e8i	1.00238	−	0.728270i
$701$	1.90393e8	−	2.62053e8i	0.552709	−	0.760738i	−0.437668	−	0.899137i	$-0.644195\pi$
$701$	1.90393e8	−	2.62053e8i	0.552709	−	0.760738i	0.990377	+	0.138398i	$0.0441954\pi$
$702$	1.83204e8	−	3.50874e8i	0.529571	−	1.01424i
$703$	3.94909e7			0.113666
$704$	133627.	+	75271.4i	0.000382981	+	0.000215731i
$705$	−4.06890e8	−	4.09601e8i	−1.16121	−	1.16894i
$706$	6.73108e7	+	2.07161e8i	0.191281	+	0.588701i
$707$	2.32452e8	−	3.19943e8i	0.657772	−	0.905346i
$708$	5.25433e7	−	3.24763e8i	0.148053	−	0.915096i
$709$	5.97151e7	−	1.83784e8i	0.167550	−	0.515667i	−0.831665	−	0.555278i	$-0.812612\pi$
$709$	5.97151e7	−	1.83784e8i	0.167550	−	0.515667i	0.999215	+	0.0396110i	$0.0126119\pi$
$710$	−7.33126e8	−	2.38207e8i	−2.04835	−	0.665548i
$711$	−9.39892e7	−	1.31188e8i	−0.261499	−	0.364994i
$712$	3.48390e7	+	2.53120e7i	0.0965218	+	0.0701272i
$713$	−3.24126e8	+	1.05315e8i	−0.894221	+	0.290550i
$714$	2.78711e8	+	2.80568e8i	0.765703	+	0.770804i
$715$	4.02040e8	+	4.37097e8i	1.09990	+	1.19580i
$716$			3.51792e8i			0.958400i
$717$	−6.20326e8	−	3.18670e8i	−1.68292	−	0.864538i
$718$	−4.49213e7	−	3.26373e7i	−0.121361	−	0.0881739i
$719$	2.41129e8	+	3.31885e8i	0.648727	+	0.892897i	0.999043	−	0.0437349i	$-0.0139257\pi$
$719$	2.41129e8	+	3.31885e8i	0.648727	+	0.892897i	−0.350316	+	0.936632i	$0.613926\pi$
$720$	−2.59863e8	+	7.82067e8i	−0.696220	+	2.09530i
$721$	−5.70635e7	+	1.75623e8i	−0.152248	+	0.468572i
$722$	2.15664e8	+	2.96835e8i	0.573014	+	0.788686i
$723$	8.76346e7	+	5.65447e8i	0.231879	+	1.49616i
$724$	1.58224e7	+	4.86964e7i	0.0416925	+	0.128316i
$725$			1.04827e9i			2.75080i
$726$	4.42314e8	−	1.78933e8i	1.15590	−	0.467607i
$727$	−241246.			−0.000627853			−0.000313926	−	1.00000i	$-0.500100\pi$
$727$	−241246.			−0.000627853			−0.000313926		1.00000i	$0.500100\pi$
$728$	1.95541e8	−	6.35352e7i	0.506809	−	0.164672i
$729$	−2.33918e8	+	3.08832e8i	−0.603784	+	0.797148i
$730$	−4.78446e8	+	3.47611e8i	−1.22988	+	0.893563i
$731$	−1.90577e8	−	6.19223e7i	−0.487886	−	0.158524i
$732$	3.04490e8	−	1.53874e8i	0.776319	−	0.392313i
$733$	−2.61204e8	+	1.89776e8i	−0.663235	+	0.481869i	−0.867754	−	0.496994i	$-0.834437\pi$
$733$	−2.61204e8	+	1.89776e8i	−0.663235	+	0.481869i	0.204519	+	0.978863i	$0.434437\pi$
$734$	4.90442e8	−	6.75036e8i	1.24022	−	1.70702i
$735$	5.89437e7	+	3.02803e7i	0.148448	+	0.0762601i
$736$	−2.63134e8			−0.660000
$737$	1.43510e7	−	1.32000e7i	0.0358493	−	0.0329740i
$738$	425413.	−	6.40649e7i	0.00105838	−	0.159386i
$739$	−1.45677e8	−	4.48346e8i	−0.360958	−	1.11091i	−0.952474	−	0.304620i	$-0.901470\pi$
$739$	−1.45677e8	−	4.48346e8i	−0.360958	−	1.11091i	0.591516	−	0.806293i	$-0.298530\pi$
$740$	5.69353e7	−	7.83648e7i	0.140503	−	0.193386i
$741$	−1.72146e8	−	2.78514e7i	−0.423099	−	0.0684530i
$742$	2.36342e7	−	7.27385e7i	0.0578533	−	0.178054i
$743$	3.53359e8	+	1.14813e8i	0.861488	+	0.279914i	0.706250	−	0.707963i	$-0.250386\pi$
$743$	3.53359e8	+	1.14813e8i	0.861488	+	0.279914i	0.155238	+	0.987877i	$0.450386\pi$
$744$	−5.20061e7	+	3.21443e8i	−0.126280	+	0.780522i
$745$	5.29860e8	+	3.84966e8i	1.28142	+	0.931009i
$746$	−9.48718e8	+	3.08257e8i	−2.28518	+	0.742500i
$747$	1.09399e8	+	726448.i	0.262454	+	0.00174278i
$748$	−9.49155e7	+	1.68501e8i	−0.226795	+	0.402622i
$749$		−	5.48225e7i		−	0.130471i
$750$	4.83070e8	−	9.40346e8i	1.14505	−	2.22897i
$751$	4.23964e8	+	3.08028e8i	1.00094	+	0.727227i	0.962290	−	0.272026i	$-0.0876936\pi$
$751$	4.23964e8	+	3.08028e8i	1.00094	+	0.727227i	0.0386522	+	0.999253i	$0.487694\pi$
$752$	−2.90061e8	−	3.99235e8i	−0.682081	−	0.938804i
$753$	−2.16141e8	−	4.27706e8i	−0.506236	−	1.00175i
$754$	1.95273e8	−	6.00988e8i	0.455541	−	1.40201i
$755$	−4.25090e8	−	5.85086e8i	−0.987734	−	1.35950i
$756$	2.48038e8	−	3.67568e7i	0.574054	−	0.0850691i
$757$	3.68353e7	+	1.13367e8i	0.0849135	+	0.261337i	0.984494	−	0.175418i	$-0.0561277\pi$
$757$	3.68353e7	+	1.13367e8i	0.0849135	+	0.261337i	−0.899581	+	0.436755i	$0.856128\pi$
$758$		−	1.97578e7i		−	0.0453660i
$759$	1.80021e8	−	2.25649e8i	0.411716	−	0.516070i
$760$	2.01547e8			0.459130
$761$	−3.41670e8	+	1.11015e8i	−0.775269	+	0.251900i	−0.669819	−	0.742524i	$-0.733628\pi$
$761$	−3.41670e8	+	1.11015e8i	−0.775269	+	0.251900i	−0.105450	+	0.994425i	$0.533628\pi$
$762$	5.98703e8	−	9.27887e7i	1.35315	−	0.209715i
$763$	−3.12973e8	+	2.27388e8i	−0.704585	+	0.511911i
$764$	−3.21273e8	−	1.04388e8i	−0.720434	−	0.234083i
$765$	6.26605e8	+	2.08206e8i	1.39962	+	0.465061i
$766$	−2.00609e7	+	1.45751e7i	−0.0446339	+	0.0324284i
$767$	−4.06659e8	+	5.59718e8i	−0.901247	+	1.24046i
$768$	−2.58076e8	+	5.02372e8i	−0.569723	+	1.10903i
$769$	−3.60022e7			−0.0791682			−0.0395841	−	0.999216i	$-0.512603\pi$
$769$	−3.60022e7			−0.0791682			−0.0395841	+	0.999216i	$0.512603\pi$
$770$	−2.08261e8	+	1.03358e9i	−0.456179	+	2.26397i
$771$	−4.50316e7	+	4.47336e7i	−0.0982550	+	0.0976047i
$772$	1.98124e7	+	6.09762e7i	0.0430611	+	0.132528i
$773$	1.82076e8	−	2.50607e8i	0.394199	−	0.542568i	−0.565078	−	0.825038i	$-0.691154\pi$
$773$	1.82076e8	−	2.50607e8i	0.394199	−	0.542568i	0.959276	+	0.282470i	$0.0911537\pi$
$774$	−2.89452e8	+	2.07377e8i	−0.624243	+	0.447236i
$775$	4.37388e8	−	1.34614e9i	0.939641	−	2.89192i
$776$	7.30521e7	+	2.37361e7i	0.156332	+	0.0507953i
$777$	1.17882e8	+	1.90721e7i	0.251296	+	0.0406571i
$778$	2.07596e8	+	1.50828e8i	0.440840	+	0.320289i
$779$	−2.68436e7	+	8.72203e6i	−0.0567844	+	0.0184504i
$780$	−3.03456e8	+	3.01447e8i	−0.639457	+	0.635225i
$781$	4.22519e8	−	1.93513e8i	0.886939	−	0.406217i
$782$			3.27903e8i			0.685686i
$783$	−2.86268e8	+	5.48264e8i	−0.596332	+	1.14210i
$784$	4.58231e7	+	3.32924e7i	0.0950902	+	0.0690871i
$785$	−9.52928e8	−	1.31159e9i	−1.96993	−	2.71138i
$786$	5.08366e6	−	2.56903e6i	0.0104691	−	0.00529056i
$787$	−3.97401e7	+	1.22307e8i	−0.0815276	+	0.250916i	−0.983509	−	0.180858i	$-0.942112\pi$
$787$	−3.97401e7	+	1.22307e8i	−0.0815276	+	0.250916i	0.901982	+	0.431775i	$0.142112\pi$
$788$	1.71049e7	+	2.35428e7i	0.0349576	+	0.0481150i
$789$	5.98697e8	−	9.27877e7i	1.21892	−	0.188912i
$790$	1.51031e8	+	4.64824e8i	0.306326	+	0.942774i
$791$			6.26673e8i			1.26623i
$792$	−1.13177e8	−	2.51510e8i	−0.227815	−	0.506267i
$793$	−7.17455e8			−1.43872
$794$	−6.78771e8	+	2.20546e8i	−1.35601	+	0.440593i
$795$	−1.95571e7	−	1.26189e8i	−0.0389228	−	0.251143i
$796$	6.07257e7	−	4.41198e7i	0.120402	−	0.0874772i
$797$	5.18466e8	+	1.68460e8i	1.02411	+	0.332752i	0.772458	−	0.635066i	$-0.219027\pi$
$797$	5.18466e8	+	1.68460e8i	1.02411	+	0.332752i	0.251649	+	0.967819i	$0.419027\pi$
$798$	−1.39637e8	−	2.76317e8i	−0.274784	−	0.543750i
$799$	−3.19873e8	+	2.32402e8i	−0.627101	+	0.455616i
$800$	6.42353e8	−	8.84123e8i	1.25460	−	1.72680i
$801$	−3.34311e7	−	1.05264e8i	−0.0650508	−	0.204824i
$802$	7.12914e8			1.38202
$803$	7.04243e7	−	3.49508e8i	0.136012	−	0.675011i
$804$	9.89729e6	+	9.96323e6i	0.0190436	+	0.0191704i
$805$	1.97112e8	+	6.06649e8i	0.377855	+	1.16292i
$806$	−5.01522e8	+	6.90286e8i	−0.957822	+	1.31833i
$807$	−8.99875e7	+	5.56201e8i	−0.171223	+	1.05830i
$808$	9.68131e7	−	2.97960e8i	0.183527	−	0.564838i
$809$	5.29990e8	+	1.72204e8i	1.00097	+	0.325236i	0.763254	−	0.646098i	$-0.223600\pi$
$809$	5.29990e8	+	1.72204e8i	1.00097	+	0.325236i	0.237719	+	0.971334i	$0.423600\pi$
$810$	9.58293e8	−	6.76981e8i	1.80320	−	1.27386i
$811$	−4.96630e8	−	3.60823e8i	−0.931044	−	0.676443i	0.0152041	−	0.999884i	$-0.495160\pi$
$811$	−4.96630e8	−	3.60823e8i	−0.931044	−	0.676443i	−0.946248	+	0.323441i	$0.895160\pi$
$812$	3.80714e8	−	1.23701e8i	0.711100	−	0.231050i
$813$	−5.00008e8	−	5.03339e8i	−0.930476	−	0.936675i
$814$	1.88325e7	+	1.62573e8i	0.0349169	+	0.301422i
$815$			4.09942e8i			0.757267i
$816$	5.02007e8	+	2.57888e8i	0.923931	+	0.474637i
$817$	1.26912e8	+	9.22066e7i	0.232721	+	0.169081i
$818$	7.66658e8	+	1.05521e9i	1.40069	+	1.92788i
$819$	−5.00412e8	−	1.66275e8i	−0.910912	−	0.302675i
$820$	−2.13936e7	+	6.58427e7i	−0.0388009	+	0.119417i
$821$	−4.40900e8	−	6.06847e8i	−0.796729	−	1.09660i	−0.993237	−	0.116101i	$-0.962960\pi$
$821$	−4.40900e8	−	6.06847e8i	−0.796729	−	1.09660i	0.196508	−	0.980502i	$-0.437040\pi$
$822$	5.94225e7	+	3.83414e8i	0.106988	+	0.690323i
$823$	−2.29493e8	−	7.06307e8i	−0.411690	−	1.26705i	−0.915178	−	0.403049i	$-0.867950\pi$
$823$	−2.29493e8	−	7.06307e8i	−0.411690	−	1.26705i	0.503489	−	0.864002i	$-0.332050\pi$
$824$			1.46289e8i			0.261476i
$825$	3.18716e8	+	1.15571e9i	0.567599	+	2.05820i
$826$	−1.22829e9			−2.17951
$827$	8.01263e8	−	2.60346e8i	1.41664	−	0.460293i	0.502105	−	0.864807i	$-0.332559\pi$
$827$	8.01263e8	−	2.60346e8i	1.41664	−	0.460293i	0.914532	+	0.404514i	$0.132559\pi$
$828$	1.67383e8	+	1.23317e8i	0.294863	+	0.217237i
$829$	−7.51251e8	+	5.45815e8i	−1.31862	+	0.958037i	−0.318676	+	0.947864i	$0.603238\pi$
$829$	−7.51251e8	+	5.45815e8i	−1.31862	+	0.958037i	−0.999948	+	0.0101733i	$0.996762\pi$
$830$	−3.15106e8	−	1.02384e8i	−0.551089	−	0.179060i
$831$	2.10037e8	−	1.06142e8i	0.366009	−	0.184963i
$832$	187934.	−	136542.i	0.000326313	−	0.000237081i
$833$	2.66744e7	−	3.67142e7i	0.0461487	−	0.0635183i
$834$	−7.17748e8	−	3.68718e8i	−1.23730	−	0.635617i
$835$	1.34866e8			0.231656
$836$	1.11431e8	−	1.02494e8i	0.190716	−	0.175419i
$837$	5.96376e8	−	5.84612e8i	1.01705	−	0.996992i
$838$	1.69755e8	+	5.22451e8i	0.288462	+	0.887796i
$839$	−3.59699e7	+	4.95083e7i	−0.0609050	+	0.0838286i	−0.838383	−	0.545082i	$-0.816499\pi$
$839$	−3.59699e7	+	4.95083e7i	−0.0609050	+	0.0838286i	0.777478	+	0.628910i	$0.216499\pi$
$840$	6.01627e8	+	9.73371e7i	1.01506	+	0.164225i
$841$	−1.21316e8	+	3.73371e8i	−0.203952	+	0.627701i
$842$	1.16735e8	+	3.79295e7i	0.195553	+	0.0635391i
$843$	2.53237e7	−	1.56522e8i	0.0422712	−	0.261272i
$844$	−1.82506e8	−	1.32598e8i	−0.303563	−	0.220552i
$845$	−1.60522e8	+	5.21566e7i	−0.266050	+	0.0864449i
$846$	−4.66525e6	+	7.02562e8i	−0.00770484	+	1.16031i
$847$	−3.29424e8	−	5.43613e8i	−0.542132	−	0.894622i
$848$		−	1.09146e8i		−	0.178987i
$849$	2.24677e8	−	4.37357e8i	0.367143	−	0.714683i
$850$	−1.10174e9	−	8.00464e8i	−1.79401	−	1.30342i
$851$	5.81979e7	+	8.01025e7i	0.0944318	+	0.129974i
$852$	1.50966e8	+	2.98734e8i	0.244095	+	0.483022i
$853$	2.12931e8	−	6.55333e8i	0.343077	−	1.05588i	−0.619529	−	0.784974i	$-0.712676\pi$
$853$	2.12931e8	−	6.55333e8i	0.343077	−	1.05588i	0.962605	−	0.270907i	$-0.0873237\pi$
$854$	−7.48689e8	−	1.03048e9i	−1.20207	−	1.65450i
$855$	−4.16161e8	−	3.06601e8i	−0.665830	−	0.490542i
$856$	−1.34208e7	−	4.13049e7i	−0.0213972	−	0.0658538i
$857$		−	8.27098e8i		−	1.31406i	−0.753865	−	0.657029i	$-0.771813\pi$
$857$		−	8.27098e8i		−	1.31406i	0.753865	−	0.657029i	$-0.228187\pi$
$858$	3.25630e7	−	7.21957e8i	0.0515541	−	1.14301i
$859$	−1.63485e8			−0.257927			−0.128964	−	0.991649i	$-0.541165\pi$
$859$	−1.63485e8			−0.257927			−0.128964	+	0.991649i	$0.541165\pi$
$860$	3.65945e8	−	1.18903e8i	0.575334	−	0.186937i
$861$	−8.43418e7	+	1.30715e7i	−0.132140	+	0.0204794i
$862$	−6.43450e8	+	4.67494e8i	−1.00460	+	0.729884i
$863$	−6.91705e7	−	2.24749e7i	−0.107619	−	0.0349675i	0.254713	−	0.967017i	$-0.418019\pi$
$863$	−6.91705e7	−	2.24749e7i	−0.107619	−	0.0349675i	−0.362331	+	0.932049i	$0.618019\pi$
$864$	5.77404e8	−	2.86994e8i	0.895239	−	0.444971i
$865$	6.39029e8	−	4.64281e8i	0.987352	−	0.717353i
$866$	−9.15803e7	+	1.26049e8i	−0.141009	+	0.194083i
$867$	−9.11740e7	+	1.77480e8i	−0.139899	+	0.272328i
$868$	−5.40511e8			−0.826505
$869$	−2.56723e8	−	1.44610e8i	−0.391206	−	0.220364i
$870$	1.32889e9	−	1.32009e9i	2.01804	−	2.00469i
$871$	−9.12629e6	−	2.80878e7i	−0.0138115	−	0.0425073i
$872$	−1.80138e8	+	2.47938e8i	−0.271678	+	0.373933i
$873$	−1.14732e8	−	1.60141e8i	−0.172442	−	0.240691i
$874$	7.93244e7	−	2.44135e8i	0.118815	−	0.365676i
$875$	−1.33942e9	−	4.35206e8i	−1.99937	−	0.649636i
$876$	2.53492e8	+	4.10124e7i	0.377096	+	0.0610103i
$877$	−1.71659e8	−	1.24717e8i	−0.254488	−	0.184896i	0.453226	−	0.891396i	$-0.350273\pi$
$877$	−1.71659e8	−	1.24717e8i	−0.254488	−	0.184896i	−0.707713	+	0.706500i	$0.750273\pi$
$878$	1.14639e9	−	3.72485e8i	1.69375	−	0.550333i
$879$	−5.16663e8	+	5.13244e8i	−0.760748	+	0.755713i
$880$	1.73142e8	+	1.49466e9i	0.254070	+	2.19327i
$881$			1.33809e9i			1.95685i	0.206612	+	0.978423i	$0.433756\pi$
$881$			1.33809e9i			1.95685i	−0.206612	+	0.978423i	$0.566244\pi$
$882$	−2.44093e7	−	7.68569e7i	−0.0355754	−	0.112015i
$883$	8.08417e8	+	5.87349e8i	1.17423	+	0.853128i	0.991509	−	0.130036i	$-0.0415094\pi$
$883$	8.08417e8	+	5.87349e8i	1.17423	+	0.853128i	0.182721	+	0.983165i	$0.441509\pi$
$884$	1.72176e8	+	2.36980e8i	0.249239	+	0.343049i
$885$	−1.83033e9	+	9.24960e8i	−2.64059	+	1.33442i
$886$	−2.93382e8	+	9.02936e8i	−0.421824	+	1.29824i
$887$	−1.41796e8	−	1.95165e8i	−0.203186	−	0.279661i	0.695248	−	0.718769i	$-0.255294\pi$
$887$	−1.41796e8	−	1.95165e8i	−0.203186	−	0.279661i	−0.898434	+	0.439109i	$0.855294\pi$
$888$	9.34850e7	−	1.44886e7i	0.133507	−	0.0206912i
$889$	−2.49411e8	−	7.67607e8i	−0.354985	−	1.09253i
$890$			3.34481e8i			0.474462i
$891$	−1.48915e8	+	6.91495e8i	−0.210526	+	0.977588i
$892$	2.19162e8			0.308796
$893$	2.94378e8	−	9.56493e7i	0.413382	−	0.134316i
$894$	−1.22064e8	−	7.87599e8i	−0.170835	−	1.10228i
$895$	1.77412e9	−	1.28898e9i	2.47466	−	1.79794i
$896$	7.15828e8	+	2.32587e8i	0.995142	+	0.323341i
$897$	−1.97198e8	−	3.90221e8i	−0.273229	−	0.540671i
$898$	1.04474e9	−	7.59050e8i	1.44271	−	1.04819i
$899$	7.83660e8	−	1.07862e9i	1.07857	−	1.48453i
$900$	−8.22952e8	+	2.61365e8i	−1.12888	+	0.358525i
$901$	−8.74496e7			−0.119559
$902$	−4.87074e7	−	1.06348e8i	−0.0663705	−	0.144914i
$903$	3.34306e8	+	3.36533e8i	0.454026	+	0.457051i
$904$	1.53412e8	+	4.72154e8i	0.207661	+	0.639114i
$905$	1.87607e8	−	2.58220e8i	0.253107	−	0.348372i
$906$	−1.40559e8	+	8.68774e8i	−0.189005	+	1.16821i
$907$	−7.84265e7	+	2.41372e8i	−0.105109	+	0.323493i	−0.989756	−	0.142769i	$-0.954399\pi$
$907$	−7.84265e7	+	2.41372e8i	−0.105109	+	0.323493i	0.884647	+	0.466262i	$0.154399\pi$
$908$	1.36300e8	+	4.42864e7i	0.182069	+	0.0591579i
$909$	−6.53172e8	+	4.67962e8i	−0.869632	+	0.623044i
$910$	1.29197e9	+	9.38672e8i	1.71447	+	1.24563i
$911$	1.05689e9	−	3.43403e8i	1.39789	−	0.454202i	0.489381	−	0.872070i	$-0.337223\pi$
$911$	1.05689e9	−	3.43403e8i	1.39789	−	0.454202i	0.908508	+	0.417868i	$0.137223\pi$
$912$	−3.11375e8	−	3.13450e8i	−0.410487	−	0.413222i
$913$	1.81604e8	−	8.31742e7i	0.238623	−	0.109289i
$914$			5.92606e8i			0.776118i
$915$	−1.89167e9	−	9.71777e8i	−2.46934	−	1.26854i
$916$	5.12425e8	+	3.72298e8i	0.666720	+	0.484401i
$917$	−4.46015e6	−	6.13887e6i	−0.00578418	−	0.00796124i
$918$	−3.57636e8	−	7.19529e8i	−0.462289	−	0.930080i
$919$	−2.69106e8	+	8.28223e8i	−0.346718	+	1.06709i	0.613939	+	0.789353i	$0.289584\pi$
$919$	−2.69106e8	+	8.28223e8i	−0.346718	+	1.06709i	−0.960657	+	0.277736i	$0.910416\pi$
$920$	2.97020e8	+	4.08813e8i	0.381437	+	0.525003i
$921$	1.47286e8	+	9.50339e8i	0.188531	+	1.21647i
$922$	−5.47796e8	−	1.68594e9i	−0.698918	−	2.15105i
$923$		−	7.03893e8i		−	0.895162i
$924$	3.82125e8	−	2.52133e8i	0.484384	−	0.319605i
$925$	−4.11212e8			−0.519566
$926$	−1.35459e9	+	4.40132e8i	−1.70598	+	0.554307i
$927$	2.22541e8	−	3.02063e8i	0.279364	−	0.379191i
$928$	8.32793e8	−	6.05060e8i	1.04206	−	0.757102i
$929$	9.30547e8	+	3.02353e8i	1.16062	+	0.377109i	0.825135	−	0.564935i	$-0.191099\pi$
$929$	9.30547e8	+	3.02353e8i	1.16062	+	0.377109i	0.335488	+	0.942045i	$0.391099\pi$
$930$	−2.25731e9	+	1.14073e9i	−2.80635	+	1.41819i
$931$	−2.87417e7	+	2.08821e7i	−0.0356175	+	0.0258776i
$932$	−4.48598e8	+	6.17442e8i	−0.554127	+	0.762690i
$933$	−1.60242e8	−	8.23188e7i	−0.197302	−	0.101357i
$934$	1.39490e9			1.71199
$935$	1.19754e9	−	1.38724e8i	1.46506	−	0.169713i
$936$	−4.17731e8	−	2.77387e6i	−0.509411	−	0.00338266i
$937$	1.06900e8	+	3.29004e8i	0.129945	+	0.399929i	0.994770	−	0.102145i	$-0.0325705\pi$
$937$	1.06900e8	+	3.29004e8i	0.129945	+	0.399929i	−0.864825	+	0.502074i	$0.832571\pi$
$938$	3.08190e7	−	4.24187e7i	0.0373431	−	0.0513984i
$939$	1.38123e9	+	2.23469e8i	1.66828	+	0.269911i
$940$	2.34611e8	−	7.22057e8i	0.282465	−	0.869337i
$941$	−5.74651e8	−	1.86715e8i	−0.689660	−	0.224084i	−0.0568405	−	0.998383i	$-0.518103\pi$
$941$	−5.74651e8	−	1.86715e8i	−0.689660	−	0.224084i	−0.632820	+	0.774299i	$0.718103\pi$
$942$	−3.15091e8	+	1.94754e9i	−0.376950	+	2.32988i
$943$	−5.72511e7	−	4.15954e7i	−0.0682730	−	0.0496032i
$944$	−1.66708e9	+	5.41667e8i	−1.98171	+	0.643897i
$945$	−1.09419e9	−	1.11620e9i	−1.29657	−	1.32266i
$946$	−3.19067e8	+	5.66430e8i	−0.376884	+	0.669072i
$947$			4.87332e8i			0.573819i	0.957958	+	0.286909i	$0.0926278\pi$
$947$			4.87332e8i			0.573819i	−0.957958	+	0.286909i	$0.907372\pi$
$948$	9.69724e7	−	1.88767e8i	0.113821	−	0.221565i
$949$	−4.36885e8	−	3.17416e8i	−0.511174	−	0.371390i
$950$	6.26644e8	+	8.62501e8i	0.730886	+	1.00598i
$951$	2.08631e8	+	4.12843e8i	0.242570	+	0.480003i
$952$	1.28974e8	−	3.96942e8i	0.149483	−	0.460061i
$953$	7.14274e8	+	9.83114e8i	0.825251	+	1.13586i	0.988788	+	0.149324i	$0.0477096\pi$
$953$	7.14274e8	+	9.83114e8i	0.825251	+	1.13586i	−0.163537	+	0.986537i	$0.552290\pi$
$954$	−9.21705e7	+	1.25106e8i	−0.106157	+	0.144090i
$955$	6.50715e8	+	2.00270e9i	0.747104	+	2.29935i
$956$		−	9.17071e8i		−	1.04961i
$957$	−5.08818e7	+	1.12810e9i	−0.0580533	+	1.28710i
$958$	−9.99130e8			−1.13639
$959$	4.91581e8	−	1.59724e8i	0.557365	−	0.181099i
$960$	680455.	−	105459.i	0.000769106	−	0.000119198i
$961$	−7.38389e8	+	5.36471e8i	−0.831984	+	0.604472i
$962$	2.35754e8	+	7.66011e7i	0.264810	+	0.0860419i
$963$	−3.51230e7	+	1.05704e8i	−0.0393290	+	0.118362i
$964$	−6.08738e8	+	4.42274e8i	−0.679515	+	0.493697i
$965$	2.34916e8	−	3.23335e8i	0.261416	−	0.359808i
$966$	3.54692e8	−	6.90446e8i	0.393478	−	0.765946i
$967$	−4.28573e8			−0.473964			−0.236982	−	0.971514i	$-0.576158\pi$
$967$	−4.28573e8			−0.473964			−0.236982	+	0.971514i	$0.576158\pi$
$968$	−3.81277e8	−	3.28930e8i	−0.420353	−	0.362641i
$969$	−2.51141e8	+	2.49479e8i	−0.276024	+	0.274197i
$970$	1.84362e8	+	5.67408e8i	0.202002	+	0.621700i
$971$	−1.27910e8	+	1.76053e8i	−0.139716	+	0.192303i	−0.873141	−	0.487468i	$-0.837921\pi$
$971$	−1.27910e8	+	1.76053e8i	−0.139716	+	0.192303i	0.733425	+	0.679771i	$0.237921\pi$
$972$	−5.01794e8	−	8.80388e7i	−0.546420	−	0.0958683i
$973$	−3.32184e8	+	1.02236e9i	−0.360612	+	1.10985i
$974$	−5.31149e8	−	1.72581e8i	−0.574830	−	0.186773i
$975$	1.79252e9	+	2.90012e8i	1.93398	+	0.312897i
$976$	−1.47059e9	−	1.06844e9i	−1.58176	−	1.14922i
$977$	−9.60496e7	+	3.12084e7i	−0.102994	+	0.0334648i	−0.360061	−	0.932929i	$-0.617244\pi$
$977$	−9.60496e7	+	3.12084e7i	−0.102994	+	0.0334648i	0.257067	+	0.966394i	$0.417244\pi$
$978$	3.53916e8	−	3.51573e8i	0.378341	−	0.375837i
$979$	−1.36511e8	−	1.48415e8i	−0.145486	−	0.158172i
$980$			8.71407e7i			0.0925855i
$981$	7.49128e8	−	2.37919e8i	0.793504	−	0.252012i
$982$	1.65946e8	+	1.20567e8i	0.175240	+	0.127319i
$983$	5.57610e8	+	7.67485e8i	0.587043	+	0.807996i	0.994445	−	0.105253i	$-0.0335652\pi$
$983$	5.57610e8	+	7.67485e8i	0.587043	+	0.807996i	−0.407402	+	0.913249i	$0.633565\pi$
$984$	−6.03457e7	+	3.04957e7i	−0.0633375	+	0.0320076i
$985$	5.60563e7	−	1.72523e8i	0.0586564	−	0.180526i
$986$	−7.53991e8	−	1.03778e9i	−0.786567	−	1.08262i
$987$	9.24927e8	−	1.43348e8i	0.961958	−	0.149087i
$988$	−7.08624e7	−	2.18092e8i	−0.0734760	−	0.226136i
$989$			3.93310e8i			0.406580i
$990$	1.06373e9	−	1.85943e9i	1.09629	−	1.91635i
$991$	1.18110e9			1.21358			0.606788	−	0.794863i	$-0.292458\pi$
$991$	1.18110e9			1.21358			0.606788	+	0.794863i	$0.292458\pi$
$992$	−1.32190e9	+	4.29511e8i	−1.35414	+	0.439986i
$993$	1.51134e8	+	9.75166e8i	0.154353	+	0.995935i
$994$	1.01100e9	−	7.34537e8i	1.02942	−	0.747919i
$995$	−4.45002e8	−	1.44590e8i	−0.451744	−	0.146781i
$996$	6.48867e7	+	1.28399e8i	0.0656716	+	0.129953i
$997$	1.60802e8	−	1.16829e8i	0.162258	−	0.117887i	−0.503694	−	0.863882i	$-0.668026\pi$
$997$	1.60802e8	−	1.16829e8i	0.162258	−	0.117887i	0.665951	+	0.745995i	$0.268026\pi$
$998$	9.25094e8	−	1.27328e9i	0.930667	−	1.28095i
$999$	−2.15071e8	−	1.12297e8i	−0.215718	−	0.112634i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.7.h.a.5.6	✓	88
3.2	odd	2	inner	33.7.h.a.5.17	yes	88
11.9	even	5	inner	33.7.h.a.20.17	yes	88
33.20	odd	10	inner	33.7.h.a.20.6	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.7.h.a.5.6	✓	88	1.1	even	1	trivial
33.7.h.a.5.17	yes	88	3.2	odd	2	inner
33.7.h.a.20.6	yes	88	33.20	odd	10	inner
33.7.h.a.20.17	yes	88	11.9	even	5	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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	33.h (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-9.48700 + 3.08251i) q^{2} +(-4.13517 - 26.6815i) q^{3} +(28.7242 - 20.8694i) q^{4} +(-210.493 - 68.3933i) q^{5} +(121.476 + 240.380i) q^{6} +(290.276 - 210.898i) q^{7} +(167.074 - 229.958i) q^{8} +(-694.801 + 220.665i) q^{9} +2207.77 q^{10} +(-979.624 + 901.054i) q^{11} +(-675.604 - 680.105i) q^{12} +(622.975 + 1917.32i) q^{13} +(-2103.75 + 2895.57i) q^{14} +(-954.409 + 5899.07i) q^{15} +(-1578.37 + 4857.73i) q^{16} +(3892.09 + 1264.62i) q^{17} +(5911.37 - 4235.18i) q^{18} +(-2591.87 - 1883.10i) q^{19} +(-7473.56 + 2428.31i) q^{20} +(-6827.41 - 6872.89i) q^{21} +(6516.18 - 11568.0i) q^{22} -8032.42i q^{23} +(-6826.49 - 3506.87i) q^{24} +(26988.7 + 19608.4i) q^{25} +(-11820.3 - 16269.3i) q^{26} +(8760.77 + 17625.8i) q^{27} +(3936.65 - 12115.8i) q^{28} +(18470.0 + 25421.8i) q^{29} +(-9129.49 - 58906.5i) q^{30} +(-13111.2 - 40352.2i) q^{31} -32759.0i q^{32} +(28092.3 + 22411.8i) q^{33} -40822.4 q^{34} +(-75525.0 + 24539.6i) q^{35} +(-15352.5 + 20838.5i) q^{36} +(-9972.40 + 7245.37i) q^{37} +(30393.8 + 9875.53i) q^{38} +(48580.8 - 24550.3i) q^{39} +(-50895.4 + 36977.7i) q^{40} +(5178.43 - 7127.50i) q^{41} +(85957.4 + 44157.6i) q^{42} -48965.3 q^{43} +(-9334.50 + 46326.2i) q^{44} +(161343. + 1071.37i) q^{45} +(24760.0 + 76203.6i) q^{46} +(-56788.8 + 78163.1i) q^{47} +(136138. + 22025.7i) q^{48} +(3426.75 - 10546.4i) q^{49} +(-316485. - 102832. i) q^{50} +(17647.4 - 109076. i) q^{51} +(57907.7 + 42072.4i) q^{52} +(-20323.0 + 6603.34i) q^{53} +(-137445. - 140211. i) q^{54} +(267830. - 122666. i) q^{55} -101987. i q^{56} +(-39526.1 + 76941.8i) q^{57} +(-253588. - 184242. i) q^{58} +(201717. + 277639. i) q^{59} +(95695.2 + 189364. i) q^{60} +(-109974. + 338464. i) q^{61} +(248772. + 342406. i) q^{62} +(-155146. + 210586. i) q^{63} +(-35.6075 - 109.589i) q^{64} -446189. i q^{65} +(-335597. - 126026. i) q^{66} -14649.5 q^{67} +(138189. - 44900.3i) q^{68} +(-214317. + 33215.4i) q^{69} +(640862. - 465614. i) q^{70} +(-332066. - 107895. i) q^{71} +(-65339.6 + 196642. i) q^{72} +(-216710. + 157449. i) q^{73} +(72274.2 - 99476.9i) q^{74} +(411579. - 801182. i) q^{75} -113749. q^{76} +(-94331.0 + 468155. i) q^{77} +(-385209. + 382660. i) q^{78} +(68408.7 + 210540. i) q^{79} +(664471. - 914566. i) q^{80} +(434055. - 306636. i) q^{81} +(-27157.2 + 83581.2i) q^{82} +(-142726. - 46374.5i) q^{83} +(-339545. - 54934.8i) q^{84} +(-732765. - 532385. i) q^{85} +(464534. - 150936. i) q^{86} +(601914. - 597930. i) q^{87} +(43534.6 + 375815. i) q^{88} +151502. i q^{89} +(-1.53396e6 + 487176. i) q^{90} +(585193. + 425168. i) q^{91} +(-167631. - 230725. i) q^{92} +(-1.02244e6 + 516690. i) q^{93} +(297817. - 916585. i) q^{94} +(416778. + 573646. i) q^{95} +(-874058. + 135464. i) q^{96} +(83506.1 + 257005. i) q^{97} +110617. i q^{98} +(481813. - 842221. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 33 q^{3} + 634 q^{4} + 109 q^{6} + 402 q^{7} - 2471 q^{9} - 1016 q^{10} + 7594 q^{12} - 1830 q^{13} - 6973 q^{15} - 15506 q^{16} - 291 q^{18} - 32466 q^{19} + 5434 q^{21} + 40940 q^{22} + 10011 q^{24}+ \cdots - 1274785 q^{99}+O(q^{100}) \) 88 * q + 33 * q^3 + 634 * q^4 + 109 * q^6 + 402 * q^7 - 2471 * q^9 - 1016 * q^10 + 7594 * q^12 - 1830 * q^13 - 6973 * q^15 - 15506 * q^16 - 291 * q^18 - 32466 * q^19 + 5434 * q^21 + 40940 * q^22 + 10011 * q^24 + 68152 * q^25 + 65385 * q^27 - 37986 * q^28 + 20928 * q^30 + 96222 * q^31 - 67159 * q^33 - 186548 * q^34 - 107169 * q^36 - 112854 * q^37 - 257545 * q^39 + 246958 * q^40 - 130324 * q^42 + 40328 * q^43 + 505478 * q^45 - 30630 * q^46 + 647882 * q^48 - 327700 * q^49 + 88197 * q^51 - 132630 * q^52 - 1639642 * q^54 - 216226 * q^55 + 174477 * q^57 + 1571894 * q^58 + 772854 * q^60 + 559626 * q^61 + 1129495 * q^63 + 1406654 * q^64 + 34620 * q^66 - 3229336 * q^67 - 2492844 * q^69 - 2066360 * q^70 - 2672882 * q^72 + 1068798 * q^73 - 1207057 * q^75 + 913268 * q^76 + 6763180 * q^78 - 255558 * q^79 + 3363409 * q^81 - 3580072 * q^82 - 2958906 * q^84 - 2098978 * q^85 + 365046 * q^87 + 2251838 * q^88 - 813500 * q^90 + 7887166 * q^91 + 4000307 * q^93 + 11260802 * q^94 + 4588186 * q^96 + 3850038 * q^97 - 1274785 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more