LMFDB - Embedded newform 96.6.o.a.11.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [96,6,Mod(11,96)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(96, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([4, 5, 4])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("96.11"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 96 = 2^{5} \cdot 3 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	96.o (of order $8$, 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:	$15.3968467020$
Analytic rank:	$0$
Dimension:	$312$
Relative dimension:	$78$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			11.3
Character	$\chi$	$=$	96.11
Dual form			96.6.o.a.35.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.58086 - 0.924104i) q^{2} +(6.74983 + 14.0513i) q^{3} +(30.2921 + 10.3146i) q^{4} +(-19.2402 - 7.96957i) q^{5} +(-24.6850 - 84.6561i) q^{6} +(71.2494 - 71.2494i) q^{7} +(-159.524 - 85.5573i) q^{8} +(-151.879 + 189.688i) q^{9} +(100.012 + 62.2571i) q^{10} +(-490.018 - 202.972i) q^{11} +(59.5328 + 495.265i) q^{12} +(-107.258 - 258.943i) q^{13} +(-463.475 + 331.791i) q^{14} +(-17.8855 - 324.144i) q^{15} +(811.218 + 624.901i) q^{16} +984.954 q^{17} +(1022.91 - 918.272i) q^{18} +(-1017.24 + 421.354i) q^{19} +(-500.624 - 439.870i) q^{20} +(1482.07 + 520.227i) q^{21} +(2547.16 + 1585.59i) q^{22} +(590.784 - 590.784i) q^{23} +(125.432 - 2819.02i) q^{24} +(-1903.04 - 1903.04i) q^{25} +(359.300 + 1544.24i) q^{26} +(-3690.53 - 853.743i) q^{27} +(2893.20 - 1423.38i) q^{28} +(-2251.12 - 5434.69i) q^{29} +(-199.727 + 1825.53i) q^{30} -1527.38i q^{31} +(-3949.83 - 4237.13i) q^{32} +(-455.514 - 8255.43i) q^{33} +(-5496.89 - 910.200i) q^{34} +(-1938.68 + 803.029i) q^{35} +(-6557.30 + 4179.47i) q^{36} +(4935.89 - 11916.3i) q^{37} +(6066.45 - 1411.49i) q^{38} +(2914.52 - 3254.93i) q^{39} +(2387.43 + 2917.48i) q^{40} +(-3960.89 - 3960.89i) q^{41} +(-7790.49 - 4272.90i) q^{42} +(6340.08 - 15306.3i) q^{43} +(-12750.1 - 11202.8i) q^{44} +(4433.93 - 2439.23i) q^{45} +(-3843.03 + 2751.14i) q^{46} +16559.8i q^{47} +(-3305.09 + 15616.7i) q^{48} +6654.04i q^{49} +(8861.98 + 12379.2i) q^{50} +(6648.28 + 13839.9i) q^{51} +(-578.165 - 8950.23i) q^{52} +(-5467.12 + 13198.8i) q^{53} +(19807.4 + 8175.06i) q^{54} +(7810.47 + 7810.47i) q^{55} +(-17461.9 + 5270.09i) q^{56} +(-12786.8 - 11449.5i) q^{57} +(7540.99 + 32410.6i) q^{58} +(13143.6 - 31731.4i) q^{59} +(2801.63 - 10003.5i) q^{60} +(5070.49 - 2100.26i) q^{61} +(-1411.45 + 8524.08i) q^{62} +(2693.85 + 24336.5i) q^{63} +(18127.9 + 27296.9i) q^{64} +5836.92i q^{65} +(-5086.71 + 46493.4i) q^{66} +(-18293.4 - 44164.1i) q^{67} +(29836.3 + 10159.4i) q^{68} +(12289.0 + 4313.60i) q^{69} +(11561.6 - 2690.05i) q^{70} +(17083.0 + 17083.0i) q^{71} +(40457.7 - 17265.4i) q^{72} +(15571.0 - 15571.0i) q^{73} +(-38558.4 + 61941.9i) q^{74} +(13895.0 - 39585.3i) q^{75} +(-35160.4 + 2271.28i) q^{76} +(-49375.1 + 20451.9i) q^{77} +(-19273.4 + 15472.0i) q^{78} -28451.8 q^{79} +(-10627.9 - 18488.3i) q^{80} +(-12914.3 - 57619.5i) q^{81} +(18444.9 + 25765.5i) q^{82} +(30948.2 + 74715.6i) q^{83} +(39529.1 + 31045.7i) q^{84} +(-18950.8 - 7849.66i) q^{85} +(-49527.7 + 79563.5i) q^{86} +(61169.9 - 68314.6i) q^{87} +(60803.9 + 74303.6i) q^{88} +(-66406.6 + 66406.6i) q^{89} +(-26999.3 + 9515.62i) q^{90} +(-26091.6 - 10807.5i) q^{91} +(23989.7 - 11802.4i) q^{92} +(21461.7 - 10309.5i) q^{93} +(15303.0 - 92418.2i) q^{94} +22930.0 q^{95} +(32876.7 - 84100.2i) q^{96} -133261. q^{97} +(6149.02 - 37135.3i) q^{98} +(112925. - 62123.4i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 312 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 4 q^{9} + 192 q^{10} - 4 q^{12} - 8 q^{13} - 8 q^{15} - 6696 q^{16} - 4 q^{18} - 8 q^{19} - 4 q^{21} + 5576 q^{22} - 11024 q^{24} - 8 q^{25} + 7460 q^{27}+ \cdots + 339516 q^{99}+O(q^{100}) $ 312 * q - 4 * q^3 - 8 * q^4 - 4 * q^6 - 8 * q^7 - 4 * q^9 + 192 * q^10 - 4 * q^12 - 8 * q^13 - 8 * q^15 - 6696 * q^16 - 4 * q^18 - 8 * q^19 - 4 * q^21 + 5576 * q^22 - 11024 * q^24 - 8 * q^25 + 7460 * q^27 - 8 * q^28 + 32564 * q^30 - 8 * q^33 - 264 * q^34 + 3264 * q^36 - 8 * q^37 + 44900 * q^39 - 60136 * q^40 - 7264 * q^42 - 8 * q^43 - 4 * q^45 + 63320 * q^46 + 112368 * q^48 - 976 * q^51 - 55024 * q^52 - 115328 * q^54 - 110056 * q^55 - 4 * q^57 - 123568 * q^58 + 44648 * q^60 - 96168 * q^61 + 187432 * q^64 + 17564 * q^66 + 97848 * q^67 - 4 * q^69 - 143480 * q^70 + 179936 * q^72 - 8 * q^73 + 12496 * q^75 - 234928 * q^76 - 708428 * q^78 + 355344 * q^79 + 251552 * q^82 + 387560 * q^84 - 25008 * q^85 - 282188 * q^87 + 111632 * q^88 + 453536 * q^90 + 200104 * q^91 + 968 * q^93 - 671008 * q^94 - 911336 * q^96 - 16 * q^97 + 339516 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/96\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$65$
$\chi(n)$	$-1$	$e\left(\frac{5}{8}\right)$	$-1$

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 $

$2$	−5.58086	−	0.924104i	−0.986567	−	0.163360i
$2$	−5.58086	−	0.924104i	−0.986567	−	0.163360i
$3$	6.74983	+	14.0513i	0.433002	+	0.901393i
$3$	6.74983	+	14.0513i	0.433002	+	0.901393i
$4$	30.2921	+	10.3146i	0.946627	+	0.322331i
$5$	−19.2402	−	7.96957i	−0.344180	−	0.142564i	0.203896	−	0.978993i	$-0.434640\pi$
$5$	−19.2402	−	7.96957i	−0.344180	−	0.142564i	−0.548076	+	0.836429i	$0.684640\pi$
$6$	−24.6850	−	84.6561i	−0.279934	−	0.960019i
$7$	71.2494	−	71.2494i	0.549587	−	0.549587i	−0.376734	−	0.926321i	$-0.622953\pi$
$7$	71.2494	−	71.2494i	0.549587	−	0.549587i	0.926321	+	0.376734i	$0.122953\pi$
$8$	−159.524	−	85.5573i	−0.881255	−	0.472642i
$9$	−151.879	+	189.688i	−0.625018	+	0.780610i
$10$	100.012	+	62.2571i	0.316267	+	0.196874i
$11$	−490.018	−	202.972i	−1.22104	−	0.505772i	−0.323300	−	0.946296i	$-0.604792\pi$
$11$	−490.018	−	202.972i	−1.22104	−	0.505772i	−0.897741	+	0.440525i	$0.854792\pi$
$12$	59.5328	+	495.265i	0.119345	+	0.992853i
$13$	−107.258	−	258.943i	−0.176023	−	0.424957i	0.811103	−	0.584904i	$-0.198868\pi$
$13$	−107.258	−	258.943i	−0.176023	−	0.424957i	−0.987126	+	0.159947i	$0.948868\pi$
$14$	−463.475	+	331.791i	−0.631984	+	0.452423i
$15$	−17.8855	−	324.144i	−0.0205245	−	0.371972i
$16$	811.218	+	624.901i	0.792205	+	0.610254i
$17$	984.954			0.826597			0.413298	−	0.910596i	$-0.364377\pi$
$17$	984.954			0.826597			0.413298	+	0.910596i	$0.364377\pi$
$18$	1022.91	−	918.272i	0.744143	−	0.668021i
$19$	−1017.24	+	421.354i	−0.646456	+	0.267771i	−0.681727	−	0.731607i	$-0.738771\pi$
$19$	−1017.24	+	421.354i	−0.646456	+	0.267771i	0.0352705	+	0.999378i	$0.488771\pi$
$20$	−500.624	−	439.870i	−0.279857	−	0.245895i
$21$	1482.07	+	520.227i	0.733366	+	0.257421i
$22$	2547.16	+	1585.59i	1.12202	+	0.698447i
$23$	590.784	−	590.784i	0.232867	−	0.232867i	−0.581021	−	0.813889i	$-0.697347\pi$
$23$	590.784	−	590.784i	0.232867	−	0.232867i	0.813889	+	0.581021i	$0.197347\pi$
$24$	125.432	−	2819.02i	0.0444510	−	0.999012i
$25$	−1903.04	−	1903.04i	−0.608971	−	0.608971i
$26$	359.300	+	1544.24i	0.104237	+	0.448004i
$27$	−3690.53	−	853.743i	−0.974271	−	0.225381i
$28$	2893.20	−	1423.38i	0.697403	−	0.343105i
$29$	−2251.12	−	5434.69i	−0.497055	−	1.20000i	−0.951062	−	0.308999i	$-0.900006\pi$
$29$	−2251.12	−	5434.69i	−0.497055	−	1.20000i	0.454008	−	0.890998i	$-0.349994\pi$
$30$	−199.727	+	1825.53i	−0.0405166	+	0.370328i
$31$		−	1527.38i		−	0.285458i	−0.989762	−	0.142729i	$-0.954412\pi$
$31$		−	1527.38i		−	0.285458i	0.989762	−	0.142729i	$-0.0455877\pi$
$32$	−3949.83	−	4237.13i	−0.681872	−	0.731471i
$33$	−455.514	−	8255.43i	−0.0728143	−	1.31964i
$34$	−5496.89	−	910.200i	−0.815493	−	0.135033i
$35$	−1938.68	+	803.029i	−0.267508	+	0.110805i
$36$	−6557.30	+	4179.47i	−0.843274	+	0.537484i
$37$	4935.89	−	11916.3i	0.592735	−	1.43099i	−0.288116	−	0.957596i	$-0.593029\pi$
$37$	4935.89	−	11916.3i	0.592735	−	1.43099i	0.880851	−	0.473394i	$-0.156971\pi$
$38$	6066.45	−	1411.49i	0.681515	−	0.158569i
$39$	2914.52	−	3254.93i	0.306835	−	0.342673i
$40$	2387.43	+	2917.48i	0.235928	+	0.288309i
$41$	−3960.89	−	3960.89i	−0.367987	−	0.367987i	0.498755	−	0.866743i	$-0.333791\pi$
$41$	−3960.89	−	3960.89i	−0.367987	−	0.367987i	−0.866743	+	0.498755i	$0.833791\pi$
$42$	−7790.49	−	4272.90i	−0.681462	−	0.373766i
$43$	6340.08	−	15306.3i	0.522906	−	1.26241i	−0.413184	−	0.910647i	$-0.635583\pi$
$43$	6340.08	−	15306.3i	0.522906	−	1.26241i	0.936090	−	0.351760i	$-0.114417\pi$
$44$	−12750.1	−	11202.8i	−0.992845	−	0.872357i
$45$	4433.93	−	2439.23i	0.326406	−	0.179565i
$46$	−3843.03	+	2751.14i	−0.267780	+	0.191698i
$47$			16559.8i			1.09348i	0.837302	+	0.546741i	$0.184132\pi$
$47$			16559.8i			1.09348i	−0.837302	+	0.546741i	$0.815868\pi$
$48$	−3305.09	+	15616.7i	−0.207052	+	0.978330i
$49$			6654.04i			0.395909i
$50$	8861.98	+	12379.2i	0.501309	+	0.700272i
$51$	6648.28	+	13839.9i	0.357918	+	0.745089i
$52$	−578.165	−	8950.23i	−0.0296513	−	0.459014i
$53$	−5467.12	+	13198.8i	−0.267343	+	0.645423i	−0.999357	−	0.0358670i	$-0.988581\pi$
$53$	−5467.12	+	13198.8i	−0.267343	+	0.645423i	0.732014	+	0.681290i	$0.238581\pi$
$54$	19807.4	+	8175.06i	0.924365	+	0.381511i
$55$	7810.47	+	7810.47i	0.348153	+	0.348153i
$56$	−17461.9	+	5270.09i	−0.744084	+	0.224568i
$57$	−12786.8	−	11449.5i	−0.521284	−	0.466766i
$58$	7540.99	+	32410.6i	0.294346	+	1.26508i
$59$	13143.6	−	31731.4i	0.491567	−	1.18675i	−0.462355	−	0.886695i	$-0.652995\pi$
$59$	13143.6	−	31731.4i	0.491567	−	1.18675i	0.953922	−	0.300053i	$-0.0970045\pi$
$60$	2801.63	−	10003.5i	0.100469	−	0.358734i
$61$	5070.49	−	2100.26i	0.174472	−	0.0722685i	−0.293738	−	0.955886i	$-0.594899\pi$
$61$	5070.49	−	2100.26i	0.174472	−	0.0722685i	0.468209	+	0.883617i	$0.344899\pi$
$62$	−1411.45	+	8524.08i	−0.0466324	+	0.281623i
$63$	2693.85	+	24336.5i	0.0855111	+	0.772515i
$64$	18127.9	+	27296.9i	0.553219	+	0.833036i
$65$			5836.92i			0.171356i
$66$	−5086.71	+	46493.4i	−0.143740	+	1.31381i
$67$	−18293.4	−	44164.1i	−0.497859	−	1.20194i	−0.950634	−	0.310314i	$-0.899566\pi$
$67$	−18293.4	−	44164.1i	−0.497859	−	1.20194i	0.452775	−	0.891625i	$-0.350434\pi$
$68$	29836.3	+	10159.4i	0.782479	+	0.266438i
$69$	12289.0	+	4313.60i	0.310737	+	0.109073i
$70$	11561.6	−	2690.05i	0.282016	−	0.0656169i
$71$	17083.0	+	17083.0i	0.402177	+	0.402177i	0.879000	−	0.476823i	$-0.158212\pi$
$71$	17083.0	+	17083.0i	0.402177	+	0.402177i	−0.476823	+	0.879000i	$0.658212\pi$
$72$	40457.7	−	17265.4i	0.919749	−	0.392506i
$73$	15571.0	−	15571.0i	0.341986	−	0.341986i	−0.515128	−	0.857113i	$-0.672256\pi$
$73$	15571.0	−	15571.0i	0.341986	−	0.341986i	0.857113	+	0.515128i	$0.172256\pi$
$74$	−38558.4	+	61941.9i	−0.818539	+	1.31494i
$75$	13895.0	−	39585.3i	0.285237	−	0.812608i
$76$	−35160.4	+	2271.28i	−0.698264	+	0.0451063i
$77$	−49375.1	+	20451.9i	−0.949034	+	0.393103i
$78$	−19273.4	+	15472.0i	−0.358692	+	0.287945i
$79$	−28451.8			−0.512911			−0.256456	−	0.966556i	$-0.582555\pi$
$79$	−28451.8			−0.512911			−0.256456	+	0.966556i	$0.582555\pi$
$80$	−10627.9	−	18488.3i	−0.185661	−	0.322977i
$81$	−12914.3	−	57619.5i	−0.218704	−	0.975791i
$82$	18444.9	+	25765.5i	0.302930	+	0.423159i
$83$	30948.2	+	74715.6i	0.493106	+	1.19046i	0.953131	+	0.302557i	$0.0978403\pi$
$83$	30948.2	+	74715.6i	0.493106	+	1.19046i	−0.460025	+	0.887906i	$0.652160\pi$
$84$	39529.1	+	31045.7i	0.611249	+	0.480069i
$85$	−18950.8	−	7849.66i	−0.284498	−	0.117843i
$86$	−49527.7	+	79563.5i	−0.722108	+	1.16003i
$87$	61169.9	−	68314.6i	0.866443	−	0.967643i
$88$	60803.9	+	74303.6i	0.836999	+	1.02283i
$89$	−66406.6	+	66406.6i	−0.888662	+	0.888662i	−0.994395	−	0.105733i	$-0.966281\pi$
$89$	−66406.6	+	66406.6i	−0.888662	+	0.888662i	0.105733	+	0.994395i	$0.466281\pi$
$90$	−26999.3	+	9515.62i	−0.351355	+	0.123831i
$91$	−26091.6	−	10807.5i	−0.330291	−	0.136811i
$92$	23989.7	−	11802.4i	0.295499	−	0.145378i
$93$	21461.7	−	10309.5i	0.257310	−	0.123604i
$94$	15303.0	−	92418.2i	0.178631	−	1.07879i
$95$	22930.0			0.260672
$96$	32876.7	−	84100.2i	0.364091	−	0.931363i
$97$	−133261.			−1.43805			−0.719027	−	0.694982i	$-0.755412\pi$
$97$	−133261.			−1.43805			−0.719027	+	0.694982i	$0.755412\pi$
$98$	6149.02	−	37135.3i	0.0646756	−	0.390590i
$99$	112925.	−	62123.4i	1.15798	−	0.637040i
$100$	−38017.8	−	77275.9i	−0.380178	−	0.772759i
$101$	−155459.	−	64393.1i	−1.51639	−	0.628111i	−0.539528	−	0.841967i	$-0.681397\pi$
$101$	−155459.	−	64393.1i	−1.51639	−	0.628111i	−0.976865	+	0.213857i	$0.931397\pi$
$102$	−24313.6	−	83382.4i	−0.231392	−	0.793549i
$103$	−71484.0	+	71484.0i	−0.663920	+	0.663920i	−0.956302	−	0.292382i	$-0.905552\pi$
$103$	−71484.0	+	71484.0i	−0.663920	+	0.663920i	0.292382	+	0.956302i	$0.405552\pi$
$104$	−5044.28	+	50484.3i	−0.0457315	+	0.457691i
$105$	−24369.4	−	21820.8i	−0.215711	−	0.193151i
$106$	42708.3	−	68608.5i	0.369188	−	0.593080i
$107$	−328.422	−	136.037i	−0.00277314	−	0.00114867i	0.381296	−	0.924453i	$-0.375478\pi$
$107$	−328.422	−	136.037i	−0.00277314	−	0.00114867i	−0.384070	+	0.923304i	$0.625478\pi$
$108$	−102988.	−	63928.0i	−0.849624	−	0.527390i
$109$	17500.0	+	42248.8i	0.141082	+	0.340603i	0.978589	−	0.205824i	$-0.0659875\pi$
$109$	17500.0	+	42248.8i	0.141082	+	0.340603i	−0.837507	+	0.546427i	$0.815988\pi$
$110$	−36371.5	−	50806.8i	−0.286602	−	0.400350i
$111$	200756.	−	11077.2i	1.54654	−	0.0853341i
$112$	102323.	−	13275.0i	0.770774	−	0.0999979i
$113$	−50900.2			−0.374993			−0.187497	−	0.982265i	$-0.560037\pi$
$113$	−50900.2			−0.374993			−0.187497	+	0.982265i	$0.560037\pi$
$114$	60780.8	+	75714.3i	0.438030	+	0.545652i
$115$	−16075.1	+	6658.53i	−0.113347	+	0.0469498i
$116$	−12134.5	−	187848.i	−0.0837295	−	1.29617i
$117$	65408.6	+	18982.6i	0.441744	+	0.128201i
$118$	−102675.	+	164942.i	−0.678831	+	1.09050i
$119$	70177.4	−	70177.4i	0.454287	−	0.454287i
$120$	−24879.8	+	53239.1i	−0.157722	+	0.337503i
$121$	85039.6	+	85039.6i	0.528029	+	0.528029i
$122$	−30238.5	+	7035.63i	−0.183934	+	0.0427960i
$123$	28920.4	−	82391.1i	0.172362	−	0.491041i
$124$	15754.3	−	46267.4i	0.0920119	−	0.270222i
$125$	46353.4	+	111907.i	0.265342	+	0.640593i
$126$	7455.42	−	138308.i	0.0418356	−	0.776106i
$127$			210944.i			1.16054i	0.814426	+	0.580268i	$0.197052\pi$
$127$			210944.i			1.16054i	−0.814426	+	0.580268i	$0.802948\pi$
$128$	−75944.1	−	169092.i	−0.409703	−	0.912219i
$129$	257868.	−	14228.5i	1.36434	−	0.0752810i
$130$	5393.92	−	32575.0i	0.0279928	−	0.169054i
$131$	115407.	−	47803.3i	0.587564	−	0.243377i	−0.0690385	−	0.997614i	$-0.521993\pi$
$131$	115407.	−	47803.3i	0.587564	−	0.243377i	0.656602	+	0.754237i	$0.271993\pi$
$132$	71352.9	−	254772.i	0.356432	−	1.27268i
$133$	−42456.5	+	102499.i	−0.208120	+	0.502447i
$134$	61280.6	+	263379.i	0.294823	+	1.26712i
$135$	64202.8	+	45838.2i	0.303193	+	0.216468i
$136$	−157124.	−	84270.1i	−0.728442	−	0.390684i
$137$	−221372.	−	221372.i	−1.00768	−	1.00768i	−0.999970	−	0.00770545i	$-0.997547\pi$
$137$	−221372.	−	221372.i	−1.00768	−	1.00768i	−0.00770545	−	0.999970i	$-0.502453\pi$
$138$	−64596.9	−	35429.9i	−0.288745	−	0.158370i
$139$	−36404.0	+	87887.0i	−0.159813	+	0.385823i	−0.983421	−	0.181337i	$-0.941958\pi$
$139$	−36404.0	+	87887.0i	−0.159813	+	0.385823i	0.823608	+	0.567159i	$0.191958\pi$
$140$	−67009.7	+	4328.68i	−0.288946	+	0.0186653i
$141$	−232688.	+	111776.i	−0.985657	+	0.473480i
$142$	−79551.2	−	111124.i	−0.331075	−	0.462474i
$143$			148657.i			0.607918i
$144$	−241744.	+	58969.0i	−0.971514	+	0.236983i
$145$			122505.i			0.483877i
$146$	−101289.	+	72510.2i	−0.393258	+	0.281525i
$147$	−93498.0	+	44913.6i	−0.356869	+	0.171429i
$148$	272430.	−	310057.i	1.02235	−	1.16356i
$149$	196274.	−	473846.i	0.724263	−	1.74852i	0.0634364	−	0.997986i	$-0.479794\pi$
$149$	196274.	−	473846.i	0.724263	−	1.74852i	0.660826	−	0.750539i	$-0.270206\pi$
$150$	−114127.	+	208080.i	−0.414153	+	0.755096i
$151$	276796.	+	276796.i	0.987912	+	0.987912i	0.999928	−	0.0120161i	$-0.00382493\pi$
$151$	276796.	+	276796.i	0.987912	+	0.987912i	−0.0120161	+	0.999928i	$0.503825\pi$
$152$	198324.	+	19816.1i	0.696252	+	0.0695680i
$153$	−149594.	+	186834.i	−0.516638	+	0.645250i
$154$	294456.	−	68511.2i	1.00050	−	0.232788i
$155$	−12172.5	+	29387.1i	−0.0406960	+	0.0982488i
$156$	121860.	−	68536.5i	0.400913	−	0.225481i
$157$	−479153.	+	198472.i	−1.55141	+	0.642613i	−0.983570	−	0.180529i	$-0.942219\pi$
$157$	−479153.	+	198472.i	−1.55141	+	0.642613i	−0.567836	+	0.823142i	$0.692219\pi$
$158$	158786.	+	26292.4i	0.506021	+	0.0837892i
$159$	−222363.	+	12269.4i	−0.697540	+	0.0384885i
$160$	42227.5	+	113002.i	0.130405	+	0.348968i
$161$		−	84186.0i		−	0.255962i
$162$	18826.3	+	333501.i	0.0563609	+	0.998410i
$163$	−29642.3	−	71562.9i	−0.0873863	−	0.210969i	0.874145	−	0.485665i	$-0.161423\pi$
$163$	−29642.3	−	71562.9i	−0.0873863	−	0.210969i	−0.961531	+	0.274696i	$0.911423\pi$
$164$	−79128.6	−	160838.i	−0.229733	−	0.466961i
$165$	−57028.0	+	162467.i	−0.163072	+	0.464574i
$166$	−103673.	−	445577.i	−0.292008	−	1.25502i
$167$	82057.2	+	82057.2i	0.227680	+	0.227680i	0.811723	−	0.584043i	$-0.198530\pi$
$167$	82057.2	+	82057.2i	0.227680	+	0.227680i	−0.584043	+	0.811723i	$0.698530\pi$
$168$	−191917.	−	209791.i	−0.524614	−	0.573473i
$169$	206997.	−	206997.i	0.557502	−	0.557502i
$170$	98507.7	+	61320.4i	0.261425	+	0.162736i
$171$	74571.8	−	256953.i	0.195022	−	0.671992i
$172$	349932.	−	398264.i	0.901910	−	1.02648i
$173$	−215040.	+	89072.3i	−0.546265	+	0.226270i	−0.638710	−	0.769447i	$-0.720532\pi$
$173$	−215040.	+	89072.3i	−0.546265	+	0.226270i	0.0924453	+	0.995718i	$0.470532\pi$
$174$	−404511.	+	324727.i	−1.01288	+	0.813102i
$175$	−271180.			−0.669365
$176$	−270674.	−	470867.i	−0.658666	−	1.14582i
$177$	534584.	−	29497.0i	1.28258	−	0.0707693i
$178$	431973.	−	309240.i	1.02190	−	0.731552i
$179$	267319.	+	645366.i	0.623588	+	1.50548i	0.847461	+	0.530857i	$0.178130\pi$
$179$	267319.	+	645366.i	0.623588	+	1.50548i	−0.223873	+	0.974618i	$0.571870\pi$
$180$	159473.	−	28155.2i	0.366864	−	0.0647706i
$181$	−568705.	−	235565.i	−1.29030	−	0.534460i	−0.371225	−	0.928543i	$-0.621062\pi$
$181$	−568705.	−	235565.i	−1.29030	−	0.534460i	−0.919075	+	0.394083i	$0.871062\pi$
$182$	135626.	+	84426.4i	0.303504	+	0.188929i
$183$	63736.4	+	57070.6i	0.140689	+	0.125975i
$184$	−144790.	+	43698.4i	−0.315278	+	0.0951526i
$185$	−189935.	+	189935.i	−0.408015	+	0.408015i
$186$	−129302.	+	37703.3i	−0.274045	+	0.0799093i
$187$	−482645.	−	199918.i	−1.00931	−	0.418069i
$188$	−170808.	+	501632.i	−0.352463	+	1.03512i
$189$	−323777.	+	202120.i	−0.659313	+	0.411580i
$190$	−127969.	−	21189.7i	−0.257170	−	0.0425833i
$191$	648066.			1.28539			0.642696	−	0.766121i	$-0.277816\pi$
$191$	648066.			1.28539			0.642696	+	0.766121i	$0.277816\pi$
$192$	−261198.	+	438970.i	−0.511347	+	0.859374i
$193$	709870.			1.37178			0.685891	−	0.727704i	$-0.259413\pi$
$193$	709870.			1.37178			0.685891	+	0.727704i	$0.259413\pi$
$194$	743714.	+	123147.i	1.41874	+	0.234920i
$195$	−82016.4	+	39398.2i	−0.154459	+	0.0741977i
$196$	−68633.7	+	201564.i	−0.127614	+	0.374778i
$197$	98689.9	+	40878.7i	0.181179	+	0.0750467i	0.471429	−	0.881904i	$-0.343738\pi$
$197$	98689.9	+	40878.7i	0.181179	+	0.0750467i	−0.290250	+	0.956951i	$0.593738\pi$
$198$	−687628.	+	242347.i	−1.24649	+	0.439314i
$199$	155594.	−	155594.i	0.278523	−	0.278523i	−0.553996	−	0.832519i	$-0.686898\pi$
$199$	155594.	−	155594.i	0.278523	−	0.278523i	0.832519	+	0.553996i	$0.186898\pi$
$200$	140761.	+	466399.i	0.248833	+	0.824484i
$201$	497087.	−	555147.i	0.867845	−	0.969209i
$202$	808088.	+	503029.i	1.39341	+	0.867391i
$203$	−547610.	−	226828.i	−0.932677	−	0.386328i
$204$	58637.0	+	487814.i	0.0986499	+	0.820689i
$205$	44641.9	+	107775.i	0.0741921	+	0.179116i
$206$	465001.	−	332884.i	0.763459	−	0.546543i
$207$	22336.8	+	201793.i	0.0362322	+	0.327325i
$208$	74804.1	−	277084.i	0.119886	−	0.444072i
$209$	583989.			0.924781
$210$	115838.	+	144299.i	0.181260	+	0.225795i
$211$	−408739.	+	169305.i	−0.632033	+	0.261797i	−0.675617	−	0.737253i	$-0.736123\pi$
$211$	−408739.	+	169305.i	−0.632033	+	0.261797i	0.0435833	+	0.999050i	$0.486123\pi$
$212$	−301750.	+	343427.i	−0.461114	+	0.524802i
$213$	−124731.	+	355345.i	−0.188376	+	0.536663i
$214$	1707.16	+	1062.70i	0.00254824	+	0.00158626i
$215$	−243969.	+	243969.i	−0.359948	+	0.359948i
$216$	515685.	+	451945.i	0.752056	+	0.659099i
$217$	−108825.	−	108825.i	−0.156884	−	0.156884i
$218$	−58623.0	−	251957.i	−0.0835462	−	0.359075i
$219$	323894.	+	113691.i	0.456344	+	0.160183i
$220$	156033.	+	317157.i	0.217351	+	0.441792i
$221$	−105644.	−	255047.i	−0.145500	−	0.351268i
$222$	−1.13063e6	−	123699.i	−1.53970	−	0.168455i
$223$			149298.i			0.201044i	0.994935	+	0.100522i	$0.0320513\pi$
$223$			149298.i			0.201044i	−0.994935	+	0.100522i	$0.967949\pi$
$224$	−583316.	−	20470.6i	−0.776755	−	0.0272590i
$225$	650016.	−	71951.5i	0.855988	−	0.0947509i
$226$	284067.	+	47037.0i	0.369956	+	0.0612589i
$227$	−195001.	+	80772.2i	−0.251173	+	0.104039i	−0.504718	−	0.863284i	$-0.668403\pi$
$227$	−195001.	+	80772.2i	−0.251173	+	0.104039i	0.253545	+	0.967324i	$0.418403\pi$
$228$	−269241.	−	478719.i	−0.343008	−	0.609879i
$229$	−411713.	+	993962.i	−0.518806	+	1.25251i	0.419830	+	0.907603i	$0.362090\pi$
$229$	−411713.	+	993962.i	−0.518806	+	1.25251i	−0.938637	+	0.344907i	$0.887910\pi$
$230$	95866.2	−	22305.3i	0.119494	−	0.0278028i
$231$	−620650.	−	555740.i	−0.765273	−	0.685238i
$232$	−105869.	+	1.05956e6i	−0.129137	+	1.29243i
$233$	205696.	+	205696.i	0.248219	+	0.248219i	0.820240	−	0.572020i	$-0.193840\pi$
$233$	205696.	+	205696.i	0.248219	+	0.248219i	−0.572020	+	0.820240i	$0.693840\pi$
$234$	−347495.	−	166383.i	−0.414867	−	0.198642i
$235$	131975.	−	318615.i	0.155891	−	0.376355i
$236$	725441.	−	825638.i	0.847857	−	0.964961i
$237$	−192045.	−	399786.i	−0.222092	−	0.462335i
$238$	−456502.	+	326799.i	−0.522396	+	0.373972i
$239$			4114.74i			0.00465959i	0.999997	+	0.00232979i	$0.000741597\pi$
$239$			4114.74i			0.00465959i	−0.999997	+	0.00232979i	$0.999258\pi$
$240$	188049.	−	274128.i	0.210738	−	0.307203i
$241$		−	1.17701e6i		−	1.30538i	−0.757625	−	0.652690i	$-0.773641\pi$
$241$		−	1.17701e6i		−	1.30538i	0.757625	−	0.652690i	$-0.226359\pi$
$242$	−396009.	−	553180.i	−0.434677	−	0.607195i
$243$	722461.	−	570385.i	0.784872	−	0.619658i
$244$	175259.	−	11321.3i	0.188454	−	0.0121737i
$245$	53029.8	−	128025.i	0.0564423	−	0.136264i
$246$	−237539.	+	433088.i	−0.250263	+	0.456287i
$247$	218213.	+	218213.i	0.227582	+	0.227582i
$248$	−130678.	+	243653.i	−0.134919	+	0.251561i
$249$	−840958.	+	939181.i	−0.859559	+	0.959955i
$250$	−155278.	−	667373.i	−0.157131	−	0.675334i
$251$	723299.	−	1.74620e6i	0.724659	−	1.74948i	0.0650387	−	0.997883i	$-0.479283\pi$
$251$	723299.	−	1.74620e6i	0.724659	−	1.74948i	0.659620	−	0.751599i	$-0.270717\pi$
$252$	−169419.	+	764989.i	−0.168058	+	0.758846i
$253$	−409407.	+	169582.i	−0.402119	+	0.166563i
$254$	194934.	−	1.17725e6i	0.189585	−	1.14495i
$255$	−17616.4	−	319267.i	−0.0169655	−	0.307471i
$256$	267575.	+	1.01386e6i	0.255179	+	0.966894i
$257$		−	893595.i		−	0.843933i	−0.906611	−	0.421967i	$-0.861340\pi$
$257$		−	893595.i		−	0.843933i	0.906611	−	0.421967i	$-0.138660\pi$
$258$	−1.45228e6	−	158890.i	−1.35831	−	0.148609i
$259$	−497349.	−	1.20071e6i	−0.460693	−	1.11221i
$260$	−60205.4	+	176812.i	−0.0552335	+	0.162211i
$261$	1.37280e6	+	398407.i	1.24740	+	0.362014i
$262$	−688247.	+	160135.i	−0.619429	+	0.144123i
$263$	−537968.	−	537968.i	−0.479587	−	0.479587i	0.425413	−	0.904999i	$-0.360129\pi$
$263$	−537968.	−	537968.i	−0.479587	−	0.479587i	−0.904999	+	0.425413i	$0.860129\pi$
$264$	−633647.	+	1.35591e6i	−0.559548	+	1.19735i
$265$	210377.	−	210377.i	0.184028	−	0.184028i
$266$	331663.	−	532799.i	0.287404	−	0.461699i
$267$	−1.38134e6	−	484867.i	−1.18583	−	0.416241i
$268$	−98609.3	−	1.52651e6i	−0.0838650	−	1.29826i
$269$	262232.	−	108620.i	0.220955	−	0.0915227i	−0.269460	−	0.963012i	$-0.586845\pi$
$269$	262232.	−	108620.i	0.220955	−	0.0915227i	0.490415	+	0.871489i	$0.336845\pi$
$270$	−315948.	−	315147.i	−0.263758	−	0.263089i
$271$	1.72568e6			1.42737			0.713684	−	0.700468i	$-0.247025\pi$
$271$	1.72568e6			1.42737			0.713684	+	0.700468i	$0.247025\pi$
$272$	799013.	+	615498.i	0.654835	+	0.504434i
$273$	−24254.3	−	439570.i	−0.0196962	−	0.356961i
$274$	1.03088e6	+	1.44002e6i	0.829525	+	1.15875i
$275$	546258.	+	1.31878e6i	0.435579	+	1.05158i
$276$	327766.	+	257424.i	0.258995	+	0.203412i
$277$	−99682.8	−	41290.0i	−0.0780586	−	0.0323330i	0.343312	−	0.939221i	$-0.388451\pi$
$277$	−99682.8	−	41290.0i	−0.0780586	−	0.0323330i	−0.421371	+	0.906888i	$0.638451\pi$
$278$	284382.	−	456844.i	0.220694	−	0.354533i
$279$	289725.	+	231977.i	0.222831	+	0.178416i
$280$	377972.	+	37766.1i	0.288114	+	0.0287877i
$281$	857618.	−	857618.i	0.647930	−	0.647930i	−0.304563	−	0.952492i	$-0.598510\pi$
$281$	857618.	−	857618.i	0.647930	−	0.647930i	0.952492	+	0.304563i	$0.0985103\pi$
$282$	1.40189e6	−	408780.i	1.04976	−	0.306103i
$283$	−1.83346e6	−	759446.i	−1.36084	−	0.563677i	−0.421549	−	0.906806i	$-0.638513\pi$
$283$	−1.83346e6	−	759446.i	−1.36084	−	0.563677i	−0.939289	+	0.343128i	$0.888513\pi$
$284$	341274.	+	693682.i	0.251078	+	0.510346i
$285$	154773.	+	322196.i	0.112871	+	0.234968i
$286$	137374.	−	829633.i	0.0993094	−	0.599751i
$287$	−564422.			−0.404482
$288$	1.40363e6	−	105702.i	0.997177	−	0.0750933i
$289$	−449722.			−0.316738
$290$	113208.	−	683685.i	0.0790461	−	0.477377i
$291$	−899493.	−	1.87250e6i	−0.622680	−	1.29625i
$292$	632284.	−	311068.i	0.433966	−	0.213500i
$293$	1.23933e6	+	513346.i	0.843368	+	0.349334i	0.762181	−	0.647365i	$-0.224129\pi$
$293$	1.23933e6	+	513346.i	0.843368	+	0.349334i	0.0811872	+	0.996699i	$0.474129\pi$
$294$	563305.	−	164255.i	0.380080	−	0.110828i
$295$	−505771.	+	505771.i	−0.338375	+	0.338375i
$296$	−1.80692e6	+	1.47863e6i	−1.19870	+	0.980914i
$297$	1.63514e6	+	1.16742e6i	1.07563	+	0.767958i
$298$	−1.53326e6	+	2.46309e6i	−1.00017	+	1.60672i
$299$	−216345.	−	89613.1i	−0.139949	−	0.0579687i
$300$	829215.	−	1.05580e6i	0.531942	−	0.677296i
$301$	−638839.	−	1.54229e6i	−0.406420	−	0.981185i
$302$	−1.28897e6	−	1.80055e6i	−0.813255	−	1.13603i
$303$	−144512.	−	2.61905e6i	−0.0904270	−	1.63884i
$304$	−1.08851e6	−	293863.i	−0.675535	−	0.182373i
$305$	−114296.			−0.0703526
$306$	1.00752e6	−	904456.i	0.615106	−	0.552184i
$307$	−457493.	+	189500.i	−0.277037	+	0.114753i	−0.516876	−	0.856060i	$-0.672905\pi$
$307$	−457493.	+	189500.i	−0.277037	+	0.114753i	0.239839	+	0.970813i	$0.422905\pi$
$308$	−1.70663e6	+	110244.i	−1.02509	+	0.0662186i
$309$	−1.48695e6	−	521939.i	−0.885931	−	0.310974i
$310$	95089.9	−	152757.i	0.0561992	−	0.0902809i
$311$	−2.24542e6	+	2.24542e6i	−1.31642	+	1.31642i	−0.399839	+	0.916585i	$0.630934\pi$
$311$	−2.24542e6	+	2.24542e6i	−1.31642	+	1.31642i	−0.916585	+	0.399839i	$0.869066\pi$
$312$	−743419.	+	269882.i	−0.432362	+	0.156959i
$313$	448450.	+	448450.i	0.258734	+	0.258734i	0.824539	−	0.565805i	$-0.191435\pi$
$313$	448450.	+	448450.i	0.258734	+	0.258734i	−0.565805	+	0.824539i	$0.691435\pi$
$314$	2.85750e6	−	664856.i	1.63554	−	0.380543i
$315$	142121.	−	489709.i	0.0807016	−	0.278075i
$316$	−861864.	−	293469.i	−0.485536	−	0.165327i
$317$	−1.25991e6	−	3.04168e6i	−0.704191	−	1.70007i	−0.714030	−	0.700115i	$-0.753132\pi$
$317$	−1.25991e6	−	3.04168e6i	−0.704191	−	1.70007i	0.00983992	−	0.999952i	$-0.496868\pi$
$318$	1.25231e6	+	137012.i	0.694457	+	0.0759787i
$319$			3.12001e6i			1.71664i
$320$	−131240.	−	669671.i	−0.0716461	−	0.365583i
$321$	−305.296	−	5532.98i	−0.000165371	−	0.00299707i
$322$	−77796.6	+	469830.i	−0.0418139	+	0.252523i
$323$	−1.00193e6	+	415015.i	−0.534359	+	0.221339i
$324$	203122.	−	1.87862e6i	0.107497	−	0.994205i
$325$	−288662.	+	696892.i	−0.151594	+	0.365980i
$326$	99298.2	+	426775.i	0.0517485	+	0.222411i
$327$	−475530.	+	531071.i	−0.245928	+	0.274652i
$328$	292974.	+	970740.i	0.150364	+	0.498217i
$329$	1.17988e6	+	1.17988e6i	0.600963	+	0.600963i
$330$	468402.	−	854005.i	0.236774	−	0.431693i
$331$	1.15092e6	−	2.77857e6i	0.577399	−	1.39396i	−0.317741	−	0.948178i	$-0.602924\pi$
$331$	1.15092e6	−	2.77857e6i	0.577399	−	1.39396i	0.895139	−	0.445786i	$-0.147076\pi$
$332$	166824.	+	2.58251e6i	0.0830643	+	1.28587i
$333$	1.51072e6	+	2.74612e6i	0.746574	+	1.35709i
$334$	−382121.	−	533779.i	−0.187428	−	0.261816i
$335$			995519.i			0.484660i
$336$	877193.	+	1.34816e6i	0.423884	+	0.651470i
$337$			1.79629e6i			0.861591i	0.902450	+	0.430796i	$0.141767\pi$
$337$			1.79629e6i			0.861591i	−0.902450	+	0.430796i	$0.858233\pi$
$338$	−1.34651e6	+	963934.i	−0.641087	+	0.458939i
$339$	−343568.	−	715215.i	−0.162373	−	0.338016i
$340$	−493092.	−	433252.i	−0.231329	−	0.203256i
$341$	−310015.	+	748442.i	−0.144376	+	0.348556i
$342$	−653627.	+	1.36511e6i	−0.302179	+	0.631106i
$343$	1.67159e6	+	1.67159e6i	0.767173	+	0.767173i
$344$	−2.32096e6	+	1.89929e6i	−1.05748	+	0.865355i
$345$	−202066.	−	180933.i	−0.0913996	−	0.0818407i
$346$	1.28242e6	−	298382.i	0.575890	−	0.133993i
$347$	−1.55891e6	+	3.76354e6i	−0.695019	+	1.67793i	0.0393948	+	0.999224i	$0.487457\pi$
$347$	−1.55891e6	+	3.76354e6i	−0.695019	+	1.67793i	−0.734414	+	0.678702i	$0.762543\pi$
$348$	2.55760e6	−	1.43845e6i	1.13210	−	0.636716i
$349$	1.79860e6	−	745006.i	0.790446	−	0.327413i	0.0493229	−	0.998783i	$-0.484294\pi$
$349$	1.79860e6	−	745006.i	0.790446	−	0.327413i	0.741123	+	0.671370i	$0.234294\pi$
$350$	1.51342e6	+	250599.i	0.660373	+	0.109348i
$351$	174767.	+	1.04721e6i	0.0757167	+	0.453696i
$352$	1.07547e6	+	2.87798e6i	0.462636	+	1.23803i
$353$		−	3.02994e6i		−	1.29419i	−0.762410	−	0.647094i	$-0.775984\pi$
$353$		−	3.02994e6i		−	1.29419i	0.762410	−	0.647094i	$-0.224016\pi$
$354$	−3.01070e6	−	329393.i	−1.27691	−	0.139703i
$355$	−192537.	−	464824.i	−0.0810853	−	0.195757i
$356$	−2.69655e6	+	1.32664e6i	−1.12767	+	0.554788i
$357$	1.45977e6	+	512400.i	0.606198	+	0.212784i
$358$	−895488.	−	3.84873e6i	−0.369277	−	1.58712i
$359$	192524.	+	192524.i	0.0788406	+	0.0788406i	0.745427	−	0.666587i	$-0.232245\pi$
$359$	192524.	+	192524.i	0.0788406	+	0.0788406i	−0.666587	+	0.745427i	$0.732245\pi$
$360$	−916013.	+	9761.31i	−0.372517	+	0.00396965i
$361$	−893630.	+	893630.i	−0.360902	+	0.360902i
$362$	2.95618e6	+	1.84020e6i	1.18566	+	0.738063i
$363$	−620916.	+	1.76892e6i	−0.247324	+	0.704600i
$364$	−678892.	−	596505.i	−0.268564	−	0.235972i
$365$	−423683.	+	175495.i	−0.166460	+	0.0689498i
$366$	−302965.	−	377402.i	−0.118220	−	0.147266i
$367$	−300085.			−0.116300			−0.0581499	−	0.998308i	$-0.518520\pi$
$367$	−300085.			−0.116300			−0.0581499	+	0.998308i	$0.518520\pi$
$368$	848436.	−	110074.i	0.326587	−	0.0423705i
$369$	1.35291e6	−	149756.i	0.517254	−	0.0572558i
$370$	1.23552e6	−	884483.i	0.469188	−	0.335881i
$371$	550877.	+	1.32994e6i	0.207788	+	0.501644i
$372$	756457.	−	90928.9i	0.283417	−	0.0340678i
$373$	3.44341e6	+	1.42631e6i	1.28149	+	0.530812i	0.916439	−	0.400174i	$-0.131050\pi$
$373$	3.44341e6	+	1.42631e6i	1.28149	+	0.530812i	0.365055	+	0.930986i	$0.381050\pi$
$374$	2.50883e6	+	1.56173e6i	0.927454	+	0.577334i
$375$	−1.25956e6	+	1.40668e6i	−0.462532	+	0.516556i
$376$	1.41682e6	−	2.64169e6i	0.516825	−	0.963636i
$377$	−1.16582e6	+	1.16582e6i	−0.422454	+	0.422454i
$378$	1.99373e6	−	828798.i	0.717692	−	0.298345i
$379$	1.11454e6	+	461658.i	0.398564	+	0.165091i	0.572957	−	0.819586i	$-0.305796\pi$
$379$	1.11454e6	+	461658.i	0.398564	+	0.165091i	−0.174393	+	0.984676i	$0.555796\pi$
$380$	694596.	+	236513.i	0.246759	+	0.0840226i
$381$	−2.96405e6	+	1.42384e6i	−1.04610	+	0.502514i
$382$	−3.61676e6	−	598880.i	−1.26812	−	0.209982i
$383$	4.73671e6			1.64998			0.824992	−	0.565145i	$-0.191180\pi$
$383$	4.73671e6			1.64998			0.824992	+	0.565145i	$0.191180\pi$
$384$	1.86336e6	−	2.20846e6i	0.644866	−	0.764296i
$385$	1.11298e6			0.382681
$386$	−3.96169e6	−	655993.i	−1.35335	−	0.224094i
$387$	1.94050e6	+	3.52735e6i	0.658622	+	1.19721i
$388$	−4.03676e6	−	1.37454e6i	−1.36130	−	0.463529i
$389$	3.30911e6	+	1.37068e6i	1.10876	+	0.459263i	0.860510	−	0.509433i	$-0.170145\pi$
$389$	3.30911e6	+	1.37068e6i	1.10876	+	0.459263i	0.248249	+	0.968696i	$0.420145\pi$
$390$	494130.	−	144084.i	0.164505	−	0.0479684i
$391$	581895.	−	581895.i	0.192488	−	0.192488i
$392$	569302.	−	1.06148e6i	0.187123	−	0.348896i
$393$	1.45068e6	+	1.29896e6i	0.473794	+	0.424243i
$394$	−512999.	−	319338.i	−0.166485	−	0.103636i
$395$	547420.	+	226749.i	0.176534	+	0.0731227i
$396$	4.06151e6	−	717069.i	1.30152	−	0.229786i
$397$	687020.	+	1.65861e6i	0.218773	+	0.528164i	0.994719	−	0.102635i	$-0.0327273\pi$
$397$	687020.	+	1.65861e6i	0.218773	+	0.528164i	−0.775946	+	0.630799i	$0.782727\pi$
$398$	−1.01214e6	+	724565.i	−0.320281	+	0.229282i
$399$	−1.72682e6	+	95281.6i	−0.543019	+	0.0299624i
$400$	−354570.	−	2.73299e6i	−0.110803	−	0.854058i
$401$	−2.24145e6			−0.696095			−0.348048	−	0.937477i	$-0.613155\pi$
$401$	−2.24145e6			−0.696095			−0.348048	+	0.937477i	$0.613155\pi$
$402$	−3.28719e6	+	2.63884e6i	−1.01452	+	0.814418i
$403$	−395503.	+	163823.i	−0.121307	+	0.0502471i
$404$	−4.04498e6	−	3.55410e6i	−1.23300	−	1.08337i
$405$	−210729.	+	1.21153e6i	−0.0638391	+	0.367027i
$406$	2.84652e6	+	1.77194e6i	0.857038	+	0.533500i
$407$	−4.83734e6	+	4.83734e6i	−1.44751	+	1.44751i
$408$	123545.	−	2.77661e6i	0.0367431	−	0.825780i
$409$	−16914.8	−	16914.8i	−0.00499987	−	0.00499987i	0.704602	−	0.709602i	$-0.251125\pi$
$409$	−16914.8	−	16914.8i	−0.00499987	−	0.00499987i	−0.709602	+	0.704602i	$0.751125\pi$
$410$	−149545.	−	642732.i	−0.0439352	−	0.188830i
$411$	1.61634e6	−	4.60479e6i	0.471986	−	1.34464i
$412$	−2.90272e6	+	1.42807e6i	−0.842486	+	0.414482i
$413$	−1.32437e6	−	3.19731e6i	−0.382062	−	0.922380i
$414$	61818.6	−	1.14682e6i	0.0177263	−	0.328847i
$415$		−	1.68419e6i		−	0.480033i
$416$	−673526.	+	1.47724e6i	−0.190819	+	0.418522i
$417$	−1.48065e6	+	81698.5i	−0.416977	+	0.0230077i
$418$	−3.25916e6	−	539666.i	−0.912358	−	0.151072i
$419$	−1.10880e6	+	459279.i	−0.308544	+	0.127803i	−0.531582	−	0.847007i	$-0.678402\pi$
$419$	−1.10880e6	+	459279.i	−0.308544	+	0.127803i	0.223039	+	0.974810i	$0.428402\pi$
$420$	−513128.	−	912357.i	−0.141939	−	0.252372i
$421$	1.65340e6	−	3.99166e6i	0.454645	−	1.09761i	−0.515891	−	0.856654i	$-0.672539\pi$
$421$	1.65340e6	−	3.99166e6i	0.454645	−	1.09761i	0.970536	−	0.240956i	$-0.0774610\pi$
$422$	2.43757e6	−	567152.i	0.666310	−	0.155031i
$423$	−3.14121e6	−	2.51510e6i	−0.853583	−	0.683446i
$424$	2.00139e6	−	1.63777e6i	0.540651	−	0.442424i
$425$	−1.87440e6	−	1.87440e6i	−0.503374	−	0.503374i
$426$	1.02448e6	−	1.86787e6i	0.273515	−	0.498681i
$427$	211627.	−	510912.i	0.0561695	−	0.135605i
$428$	−8545.41	−	7508.37i	−0.00225488	−	0.00198124i
$429$	−2.08883e6	+	1.00341e6i	−0.547973	+	0.263230i
$430$	1.58701e6	−	1.13611e6i	0.413913	−	0.296311i
$431$		−	5.81040e6i		−	1.50665i	−0.657647	−	0.753326i	$-0.728448\pi$
$431$		−	5.81040e6i		−	1.50665i	0.657647	−	0.753326i	$-0.271552\pi$
$432$	−2.46032e6	−	2.99879e6i	−0.634283	−	0.773101i
$433$		−	427368.i		−	0.109542i	−0.998499	−	0.0547712i	$-0.982557\pi$
$433$		−	427368.i		−	0.109542i	0.998499	−	0.0547712i	$-0.0174429\pi$
$434$	506770.	+	707901.i	0.129148	+	0.180405i
$435$	−1.72136e6	+	826891.i	−0.436163	+	0.209520i
$436$	94332.8	+	1.46031e6i	0.0237655	+	0.367899i
$437$	−352039.	+	849898.i	−0.0881835	+	0.212894i
$438$	−1.70254e6	−	933806.i	−0.424046	−	0.232580i
$439$	−1.44839e6	−	1.44839e6i	−0.358694	−	0.358694i	0.504638	−	0.863331i	$-0.331626\pi$
$439$	−1.44839e6	−	1.44839e6i	−0.358694	−	0.358694i	−0.863331	+	0.504638i	$0.831626\pi$
$440$	−577715.	−	1.91420e6i	−0.142260	−	0.471363i
$441$	−1.26219e6	−	1.01061e6i	−0.309050	−	0.247450i
$442$	353894.	+	1.52101e6i	0.0861623	+	0.370318i
$443$	1.97181e6	−	4.76038e6i	0.477371	−	1.15248i	−0.483466	−	0.875363i	$-0.660622\pi$
$443$	1.97181e6	−	4.76038e6i	0.477371	−	1.15248i	0.960837	−	0.277113i	$-0.0893777\pi$
$444$	6.19557e6	+	1.73516e6i	1.49150	+	0.417718i
$445$	1.80691e6	−	748448.i	0.432551	−	0.179168i
$446$	137967.	−	833212.i	0.0328426	−	0.198344i
$447$	7.98298e6	−	440481.i	1.88972	−	0.104270i
$448$	3.23649e6	+	653288.i	0.761867	+	0.153783i
$449$		−	6.31222e6i		−	1.47763i	−0.673908	−	0.738816i	$-0.735385\pi$
$449$		−	6.31222e6i		−	1.47763i	0.673908	−	0.738816i	$-0.264615\pi$
$450$	−3.69414e6	−	199130.i	−0.859967	−	0.0463560i
$451$	1.13696e6	+	2.74486e6i	0.263210	+	0.635445i
$452$	−1.54187e6	−	525015.i	−0.354979	−	0.120872i
$453$	−2.02103e6	+	5.75769e6i	−0.462729	+	1.31826i
$454$	1.16292e6	−	270577.i	0.264795	−	0.0616101i
$455$	415877.	+	415877.i	0.0941752	+	0.0941752i
$456$	1.06021e6	+	2.92047e6i	0.238771	+	0.657720i
$457$	−960190.	+	960190.i	−0.215063	+	0.215063i	−0.806414	−	0.591351i	$-0.798595\pi$
$457$	−960190.	+	960190.i	−0.215063	+	0.215063i	0.591351	+	0.806414i	$0.298595\pi$
$458$	3.21624e6	−	5.16670e6i	0.716447	−	1.15093i
$459$	−3.63501e6	−	840898.i	−0.805329	−	0.186299i
$460$	−555628.	+	35892.4i	−0.122431	+	0.00790875i
$461$	−8.22834e6	+	3.40829e6i	−1.80327	+	0.746938i	−0.818161	+	0.574989i	$0.805006\pi$
$461$	−8.22834e6	+	3.40829e6i	−1.80327	+	0.746938i	−0.985106	+	0.171949i	$0.944994\pi$
$462$	2.95020e6	+	3.67505e6i	0.643053	+	0.801048i
$463$	4.09919e6			0.888680			0.444340	−	0.895858i	$-0.353438\pi$
$463$	4.09919e6			0.888680			0.444340	+	0.895858i	$0.353438\pi$
$464$	1.56999e6	−	5.81545e6i	0.338534	−	1.25397i
$465$	−495090.	+	27317.8i	−0.106182	+	0.00585887i
$466$	−957876.	−	1.33804e6i	−0.204336	−	0.285434i
$467$	1.15862e6	+	2.79715e6i	0.245837	+	0.593503i	0.997842	−	0.0656537i	$-0.0209133\pi$
$467$	1.15862e6	+	2.79715e6i	0.245837	+	0.593503i	−0.752005	+	0.659157i	$0.770913\pi$
$468$	1.78556e6	+	1.24968e6i	0.376843	+	0.263746i
$469$	−4.45006e6	−	1.84328e6i	−0.934187	−	0.386953i
$470$	−1.03097e6	+	1.65619e6i	−0.215278	+	0.345832i
$471$	−6.02300e6	−	5.39309e6i	−1.25101	−	1.12017i
$472$	−4.81156e6	+	3.93739e6i	−0.994103	+	0.813492i
$473$	−6.21351e6	+	6.21351e6i	−1.27698	+	1.27698i
$474$	702334.	+	2.40862e6i	0.143581	+	0.492405i
$475$	2.73770e6	+	1.13399e6i	0.556738	+	0.230609i
$476$	2.84967e6	−	1.40197e6i	0.576471	−	0.283609i
$477$	−1.67331e6	−	3.04167e6i	−0.336729	−	0.612092i
$478$	3802.44	−	22963.8i	0.000761190	−	0.00459699i
$479$	9.56631e6			1.90505			0.952524	−	0.304464i	$-0.0984773\pi$
$479$	9.56631e6			1.90505			0.952524	+	0.304464i	$0.0984773\pi$
$480$	−1.30280e6	+	1.35610e6i	−0.258092	+	0.268650i
$481$	−3.61504e6			−0.712444
$482$	−1.08768e6	+	6.56872e6i	−0.213247	+	1.28784i
$483$	1.18292e6	−	568242.i	0.230722	−	0.110832i
$484$	1.69888e6	+	3.45318e6i	0.329647	+	0.670047i
$485$	2.56398e6	+	1.06204e6i	0.494949	+	0.205015i
$486$	−4.55905e6	+	2.51561e6i	−0.875556	+	0.483117i
$487$	2.10986e6	−	2.10986e6i	0.403116	−	0.403116i	−0.476213	−	0.879330i	$-0.657991\pi$
$487$	2.10986e6	−	2.10986e6i	0.403116	−	0.403116i	0.879330	+	0.476213i	$0.157991\pi$
$488$	−988558.	−	98774.5i	−0.187911	−	0.0187757i
$489$	805473.	−	899552.i	0.152328	−	0.170119i
$490$	−414261.	+	665487.i	−0.0779442	+	0.125213i
$491$	5.38410e6	+	2.23017e6i	1.00788	+	0.417478i	0.824682	−	0.565597i	$-0.191354\pi$
$491$	5.38410e6	+	2.23017e6i	1.00788	+	0.417478i	0.183200	+	0.983076i	$0.441354\pi$
$492$	1.72589e6	−	2.19749e6i	0.321440	−	0.409275i
$493$	−2.21725e6	−	5.35292e6i	−0.410864	−	0.991913i
$494$	−1.01617e6	−	1.41947e6i	−0.187347	−	0.261703i
$495$	−2.66780e6	+	295304.i	−0.489374	+	0.0541697i
$496$	954458.	−	1.23904e6i	0.174202	−	0.226141i
$497$	2.43430e6			0.442062
$498$	5.56117e6	−	4.46431e6i	1.00483	−	0.806642i
$499$	3.01658e6	−	1.24951e6i	0.542329	−	0.224640i	−0.0946643	−	0.995509i	$-0.530178\pi$
$499$	3.01658e6	−	1.24951e6i	0.542329	−	0.224640i	0.636994	+	0.770869i	$0.280178\pi$
$500$	249865.	+	3.86801e6i	0.0446972	+	0.691931i
$501$	−599140.	+	1.70688e6i	−0.106643	+	0.303815i
$502$	−5.65030e6	+	9.07689e6i	−1.00072	+	1.60760i
$503$	798097.	−	798097.i	0.140649	−	0.140649i	−0.633277	−	0.773925i	$-0.718291\pi$
$503$	798097.	−	798097.i	0.140649	−	0.140649i	0.773925	+	0.633277i	$0.218291\pi$
$504$	1.65243e6	−	4.11274e6i	0.289766	−	0.721198i
$505$	2.47788e6	+	2.47788e6i	0.432366	+	0.432366i
$506$	2.44156e6	−	568079.i	0.423926	−	0.0986354i
$507$	4.30577e6	+	1.51138e6i	0.743928	+	0.261129i
$508$	−2.17580e6	+	6.38994e6i	−0.374076	+	1.09859i
$509$	−4.17733e6	−	1.00850e7i	−0.714669	−	1.72536i	−0.687992	−	0.725718i	$-0.741508\pi$
$509$	−4.17733e6	−	1.00850e7i	−0.714669	−	1.72536i	−0.0266765	−	0.999644i	$-0.508492\pi$
$510$	−196722.	+	1.79807e6i	−0.0334909	+	0.306112i
$511$		−	2.21884e6i		−	0.375902i
$512$	−556384.	−	5.90549e6i	−0.0937993	−	0.995591i
$513$	4.11388e6	−	686561.i	0.690174	−	0.115182i
$514$	−825775.	+	4.98703e6i	−0.137865	+	0.832596i
$515$	1.94507e6	−	805673.i	0.323159	−	0.133857i
$516$	7.95813e6	+	2.22880e6i	1.31579	+	0.368507i
$517$	3.36119e6	−	8.11462e6i	0.553052	−	1.33519i
$518$	1.66606e6	+	7.16059e6i	0.272814	+	1.17253i
$519$	−2.70307e6	−	2.42037e6i	−0.440492	−	0.394424i
$520$	499391.	−	931129.i	0.0809902	−	0.151009i
$521$	352651.	+	352651.i	0.0569182	+	0.0569182i	0.734993	−	0.678075i	$-0.237185\pi$
$521$	352651.	+	352651.i	0.0569182	+	0.0569182i	−0.678075	+	0.734993i	$0.737185\pi$
$522$	−7.29322e6	−	3.49206e6i	−1.17150	−	0.560926i
$523$	−3.80292e6	+	9.18106e6i	−0.607943	+	1.46770i	0.257290	+	0.966334i	$0.417171\pi$
$523$	−3.80292e6	+	9.18106e6i	−0.607943	+	1.46770i	−0.865233	+	0.501370i	$0.832829\pi$
$524$	3.98900e6	−	257680.i	0.634651	−	0.0409971i
$525$	−1.83042e6	−	3.81044e6i	−0.289837	−	0.603361i
$526$	2.50519e6	+	3.49946e6i	0.394799	+	0.551489i
$527$		−	1.50440e6i		−	0.235958i
$528$	4.78930e6	−	6.98161e6i	0.747631	−	1.08986i
$529$			5.73829e6i			0.891545i
$530$	−1.36850e6	+	979677.i	−0.211619	+	0.151493i
$531$	4.02283e6	+	7.31252e6i	0.619149	+	1.12546i
$532$	−2.34333e6	+	2.66698e6i	−0.358967	+	0.408546i
$533$	−600808.	+	1.45048e6i	−0.0916047	+	0.221153i
$534$	7.26097e6	+	3.98248e6i	1.10190	+	0.604366i
$535$	5234.76	+	5234.76i	0.000790701	+	0.000790701i
$536$	−860329.	+	8.61037e6i	−0.129346	+	1.29452i
$537$	−7.26389e6	+	8.11231e6i	−1.08701	+	1.21397i
$538$	−1.56385e6	+	363864.i	−0.232938	+	0.0541979i
$539$	1.35058e6	−	3.26060e6i	0.200239	−	0.483421i
$540$	1.47203e6	+	2.05076e6i	0.217237	+	0.302643i
$541$	1.03801e7	−	4.29957e6i	1.52478	−	0.631585i	0.546239	−	0.837630i	$-0.316059\pi$
$541$	1.03801e7	−	4.29957e6i	1.52478	−	0.631585i	0.978543	+	0.206044i	$0.0660592\pi$
$542$	−9.63076e6	−	1.59470e6i	−1.40819	−	0.233175i
$543$	−528660.	−	9.58108e6i	−0.0769443	−	1.39449i
$544$	−3.89040e6	−	4.17338e6i	−0.563633	−	0.604632i
$545$		−	952345.i		−	0.137342i
$546$	−270848.	+	2.47559e6i	−0.0388816	+	0.355384i
$547$	−2.74614e6	−	6.62978e6i	−0.392423	−	0.947394i	−0.989411	−	0.145143i	$-0.953636\pi$
$547$	−2.74614e6	−	6.62978e6i	−0.392423	−	0.947394i	0.596987	−	0.802251i	$-0.296364\pi$
$548$	−4.42245e6	−	8.98917e6i	−0.629088	−	1.27870i
$549$	−371707.	+	1.28080e6i	−0.0526345	+	0.181364i
$550$	−1.82990e6	−	7.86476e6i	−0.257941	−	1.10861i
$551$	4.57986e6	+	4.57986e6i	0.642649	+	0.642649i
$552$	−1.59133e6	−	1.73954e6i	−0.222286	−	0.242988i
$553$	−2.02718e6	+	2.02718e6i	−0.281889	+	0.281889i
$554$	518160.	+	322551.i	0.0717281	+	0.0446503i
$555$	−3.95087e6	−	1.38681e6i	−0.544453	−	0.191111i
$556$	−2.00927e6	+	2.28679e6i	−0.275646	+	0.313717i
$557$	−1.49448e6	+	619035.i	−0.204105	+	0.0845429i	−0.482394	−	0.875954i	$-0.660233\pi$
$557$	−1.49448e6	+	619035.i	−0.204105	+	0.0845429i	0.278289	+	0.960497i	$0.410233\pi$
$558$	−1.40255e6	−	1.56237e6i	−0.190692	−	0.212421i
$559$	−4.64348e6			−0.628513
$560$	−2.07451e6	−	560053.i	−0.279541	−	0.0754673i
$561$	−448660.	−	8.13122e6i	−0.0601880	−	1.09081i
$562$	−5.57877e6	+	3.99372e6i	−0.745072	+	0.533380i
$563$	3.33565e6	+	8.05297e6i	0.443516	+	1.07074i	0.974706	+	0.223490i	$0.0717449\pi$
$563$	3.33565e6	+	8.05297e6i	0.443516	+	1.07074i	−0.531190	+	0.847253i	$0.678255\pi$
$564$	−8.20152e6	+	985853.i	−1.08567	+	0.130501i
$565$	979332.	+	405653.i	0.129065	+	0.0534605i
$566$	9.53051e6	+	5.93267e6i	1.25047	+	0.778412i
$567$	−5.02549e6	−	3.18522e6i	−0.656479	−	0.416085i
$568$	−1.26357e6	−	4.18672e6i	−0.164335	−	0.544506i
$569$	23652.9	−	23652.9i	0.00306269	−	0.00306269i	−0.705574	−	0.708636i	$-0.749311\pi$
$569$	23652.9	−	23652.9i	0.00306269	−	0.00306269i	0.708636	+	0.705574i	$0.249311\pi$
$570$	−566026.	−	1.94116e6i	−0.0729709	−	0.250250i
$571$	−4.72898e6	−	1.95881e6i	−0.606983	−	0.251421i	0.0579547	−	0.998319i	$-0.481542\pi$
$571$	−4.72898e6	−	1.95881e6i	−0.606983	−	0.251421i	−0.664938	+	0.746898i	$0.731542\pi$
$572$	−1.53333e6	+	4.50312e6i	−0.195951	+	0.575471i
$573$	4.37434e6	+	9.10618e6i	0.556577	+	1.15864i
$574$	3.14996e6	+	521585.i	0.399049	+	0.0660762i
$575$	−2.24856e6			−0.283619
$576$	−7.93116e6	−	707194.i	−0.996048	−	0.0888142i
$577$	−6.20988e6			−0.776504			−0.388252	−	0.921553i	$-0.626921\pi$
$577$	−6.20988e6			−0.776504			−0.388252	+	0.921553i	$0.626921\pi$
$578$	2.50984e6	+	415590.i	0.312483	+	0.0517423i
$579$	4.79150e6	+	9.97461e6i	0.593985	+	1.23652i
$580$	−1.26359e6	+	3.71094e6i	−0.155969	+	0.458051i
$581$	7.52848e6	+	3.11840e6i	0.925267	+	0.383258i
$582$	3.28956e6	+	1.12814e7i	0.402560	+	1.38056i
$583$	5.35797e6	−	5.35797e6i	0.652873	−	0.652873i
$584$	−3.81615e6	+	1.15173e6i	−0.463013	+	0.139740i
$585$	−1.10719e6	−	886508.i	−0.133762	−	0.107101i
$586$	−6.44213e6	−	4.01018e6i	−0.774971	−	0.482414i
$587$	−9.77689e6	−	4.04972e6i	−1.17113	−	0.485098i	−0.289565	−	0.957158i	$-0.593511\pi$
$587$	−9.77689e6	−	4.04972e6i	−1.17113	−	0.485098i	−0.881566	+	0.472060i	$0.843511\pi$
$588$	−3.29551e6	+	396133.i	−0.393079	+	0.0472496i
$589$	643567.	+	1.55371e6i	0.0764373	+	0.184536i
$590$	3.29002e6	−	2.35525e6i	0.389107	−	0.278553i
$591$	91740.7	+	1.66265e6i	0.0108042	+	0.195809i
$592$	1.14506e7	−	6.58227e6i	1.34284	−	0.771918i
$593$	2.84053e6			0.331713			0.165856	−	0.986150i	$-0.446961\pi$
$593$	2.84053e6			0.331713			0.165856	+	0.986150i	$0.446961\pi$
$594$	−8.04668e6	−	8.02628e6i	−0.935730	−	0.933357i
$595$	−1.90952e6	+	790947.i	−0.221121	+	0.0915915i
$596$	1.08331e7	−	1.23293e7i	1.24921	−	1.42175i
$597$	3.23654e6	+	1.13607e6i	0.371659	+	0.130458i
$598$	1.12458e6	+	700044.i	0.128599	+	0.0800520i
$599$	−1.34624e6	+	1.34624e6i	−0.153304	+	0.153304i	−0.779592	−	0.626288i	$-0.784574\pi$
$599$	−1.34624e6	+	1.34624e6i	−0.153304	+	0.153304i	0.626288	+	0.779592i	$0.284574\pi$
$600$	−5.60340e6	+	5.12600e6i	−0.635439	+	0.581300i
$601$	−5.48527e6	−	5.48527e6i	−0.619458	−	0.619458i	0.325934	−	0.945392i	$-0.394321\pi$
$601$	−5.48527e6	−	5.48527e6i	−0.619458	−	0.619458i	−0.945392	+	0.325934i	$0.894321\pi$
$602$	2.14003e6	+	9.19768e6i	0.240674	+	1.03440i
$603$	1.11558e7	+	3.23758e6i	1.24942	+	0.362600i
$604$	5.52969e6	+	1.12398e7i	0.616749	+	1.25362i
$605$	−958454.	−	2.31391e6i	−0.106459	−	0.257015i
$606$	−1.61377e6	+	1.47501e7i	−0.178509	+	1.63160i
$607$		−	7.95276e6i		−	0.876085i	−0.898954	−	0.438043i	$-0.855672\pi$
$607$		−	7.95276e6i		−	0.876085i	0.898954	−	0.438043i	$-0.144328\pi$
$608$	5.80325e6	+	2.64590e6i	0.636667	+	0.290279i
$609$	−509050.	−	9.22570e6i	−0.0556183	−	1.00799i
$610$	637868.	+	105621.i	0.0694075	+	0.0114928i
$611$	4.28805e6	−	1.77617e6i	0.464683	−	0.192478i
$612$	−6.45864e6	+	4.11659e6i	−0.697048	+	0.444282i
$613$	1.14026e6	−	2.75283e6i	0.122561	−	0.295888i	−0.850677	−	0.525689i	$-0.823807\pi$
$613$	1.14026e6	−	2.75283e6i	0.122561	−	0.295888i	0.973238	+	0.229801i	$0.0738075\pi$
$614$	2.72832e6	−	634801.i	0.292062	−	0.0679542i
$615$	−1.21306e6	+	1.35474e6i	−0.129328	+	0.144434i
$616$	9.62633e6	+	961842.i	1.02214	+	0.102130i
$617$	3.69874e6	+	3.69874e6i	0.391148	+	0.391148i	0.875097	−	0.483948i	$-0.160798\pi$
$617$	3.69874e6	+	3.69874e6i	0.391148	+	0.391148i	−0.483948	+	0.875097i	$0.660798\pi$
$618$	7.81613e6	+	4.28697e6i	0.823229	+	0.451522i
$619$	866906.	−	2.09290e6i	0.0909380	−	0.219544i	−0.871866	−	0.489745i	$-0.837090\pi$
$619$	866906.	−	2.09290e6i	0.0909380	−	0.219544i	0.962804	+	0.270201i	$0.0870900\pi$
$620$	−671847.	+	764641.i	−0.0701926	+	0.0798874i
$621$	−2.68468e6	+	1.67593e6i	−0.279360	+	0.174392i
$622$	1.46064e7	−	1.04564e7i	1.51379	−	1.08369i
$623$			9.46287e6i			0.976794i
$624$	4.39832e6	−	819177.i	0.452194	−	0.0842202i
$625$			5.88777e6i			0.602908i
$626$	−2.08832e6	−	2.91715e6i	−0.212991	−	0.297525i
$627$	3.94183e6	+	8.20582e6i	0.400432	+	0.833591i
$628$	−1.65617e7	+	1.06985e6i	−1.67574	+	0.108249i
$629$	4.86162e6	−	1.17370e7i	0.489953	−	1.18285i
$630$	−1.24570e6	+	2.60167e6i	−0.125044	+	0.261156i
$631$	−1.42129e6	−	1.42129e6i	−0.142105	−	0.142105i	0.632475	−	0.774580i	$-0.282039\pi$
$631$	−1.42129e6	−	1.42129e6i	−0.142105	−	0.142105i	−0.774580	+	0.632475i	$0.782039\pi$
$632$	4.53875e6	+	2.43426e6i	0.452005	+	0.242423i
$633$	−5.13789e6	−	4.60054e6i	−0.509654	−	0.456352i
$634$	4.22054e6	+	1.81395e7i	0.417008	+	1.79227i
$635$	1.68113e6	−	4.05862e6i	0.165451	−	0.399433i
$636$	−6.86238e6	−	1.92191e6i	−0.672716	−	0.188404i
$637$	1.72301e6	−	713696.i	0.168244	−	0.0696890i
$638$	2.88321e6	−	1.74124e7i	0.280431	−	1.69358i
$639$	−5.83499e6	+	645886.i	−0.565312	+	0.0625754i
$640$	113589.	+	3.85862e6i	0.0109619	+	0.372376i
$641$		−	9.34386e6i		−	0.898217i	−0.893477	−	0.449108i	$-0.851742\pi$
$641$		−	9.34386e6i		−	0.898217i	0.893477	−	0.449108i	$-0.148258\pi$
$642$	−3409.24	+	31161.0i	−0.000326452	+	0.00298382i
$643$	4.44504e6	+	1.07313e7i	0.423983	+	1.02359i	0.981161	+	0.193192i	$0.0618841\pi$
$643$	4.44504e6	+	1.07313e7i	0.423983	+	1.02359i	−0.557178	+	0.830393i	$0.688116\pi$
$644$	868344.	−	2.55017e6i	0.0825044	−	0.242300i
$645$	−5.07485e6	−	1.78134e6i	−0.480312	−	0.168596i
$646$	5.97517e6	−	1.39025e6i	0.563338	−	0.131072i
$647$	−952781.	−	952781.i	−0.0894813	−	0.0894813i	0.660949	−	0.750431i	$-0.270154\pi$
$647$	−952781.	−	952781.i	−0.0894813	−	0.0894813i	−0.750431	+	0.660949i	$0.770154\pi$
$648$	−2.86963e6	+	1.02966e7i	−0.268466	+	0.963289i
$649$	−1.28812e7	+	1.28812e7i	−1.20045	+	1.20045i
$650$	2.25498e6	−	3.62251e6i	0.209344	−	0.336299i
$651$	794582.	−	2.26368e6i	0.0734829	−	0.209345i
$652$	−159785.	−	2.47354e6i	−0.0147203	−	0.227876i
$653$	−873241.	+	361708.i	−0.0801403	+	0.0331952i	−0.422393	−	0.906413i	$-0.638810\pi$
$653$	−873241.	+	361708.i	−0.0801403	+	0.0331952i	0.342253	+	0.939608i	$0.388810\pi$
$654$	3.14463e6	−	2.52440e6i	0.287492	−	0.230788i
$655$	−2.60144e6			−0.236924
$656$	−737984.	−	5.68831e6i	−0.0669557	−	0.516088i
$657$	588719.	+	5.31853e6i	0.0532101	+	0.480705i
$658$	−5.49441e6	−	7.67508e6i	−0.494717	−	0.691063i
$659$	1.59213e6	+	3.84373e6i	0.142812	+	0.344778i	0.979060	−	0.203573i	$-0.0652556\pi$
$659$	1.59213e6	+	3.84373e6i	0.142812	+	0.344778i	−0.836248	+	0.548352i	$0.815256\pi$
$660$	−3.40327e6	+	4.33323e6i	−0.304115	+	0.387215i
$661$	1.80396e7	+	7.47226e6i	1.60592	+	0.665194i	0.992237	−	0.124359i	$-0.0396876\pi$
$661$	1.80396e7	+	7.47226e6i	1.60592	+	0.665194i	0.613682	+	0.789553i	$0.289688\pi$
$662$	−8.99083e6	+	1.44433e7i	−0.797360	+	1.28091i
$663$	2.87067e6	−	3.20596e6i	0.253629	−	0.283253i
$664$	1.45548e6	−	1.45668e7i	0.128111	−	1.28216i
$665$	1.63375e6	−	1.63375e6i	0.143262	−	0.143262i
$666$	−5.89342e6	−	1.67218e7i	−0.514851	−	1.46082i
$667$	−4.54065e6	−	1.88080e6i	−0.395188	−	0.163692i
$668$	1.63930e6	+	3.33207e6i	0.142140	+	0.288917i
$669$	−2.09784e6	+	1.00774e6i	−0.181220	+	0.0870526i
$670$	919962.	−	5.55585e6i	0.0791741	−	0.478150i
$671$	−2.91092e6			−0.249588
$672$	−3.64965e6	−	8.33454e6i	−0.311765	−	0.711965i
$673$	−7.55789e6			−0.643225			−0.321613	−	0.946871i	$-0.604225\pi$
$673$	−7.55789e6			−0.643225			−0.321613	+	0.946871i	$0.604225\pi$
$674$	1.65996e6	−	1.00248e7i	0.140750	−	0.850017i
$675$	5.39851e6	+	8.64792e6i	0.456052	+	0.730554i
$676$	8.40544e6	−	4.13527e6i	0.707447	−	0.348046i
$677$	3.85507e6	+	1.59682e6i	0.323266	+	0.133901i	0.538415	−	0.842680i	$-0.319023\pi$
$677$	3.85507e6	+	1.59682e6i	0.323266	+	0.133901i	−0.215148	+	0.976581i	$0.569023\pi$
$678$	1.25647e6	+	4.30901e6i	0.104973	+	0.360001i
$679$	−9.49480e6	+	9.49480e6i	−0.790335	+	0.790335i
$680$	2.35151e6	+	2.87359e6i	0.195018	+	0.238315i
$681$	−2.45118e6	−	2.19483e6i	−0.202539	−	0.181356i
$682$	2.42179e6	−	3.89046e6i	0.199377	−	0.320288i
$683$	−1.41131e7	−	5.84583e6i	−1.15763	−	0.479506i	−0.280545	−	0.959841i	$-0.590515\pi$
$683$	−1.41131e7	−	5.84583e6i	−1.15763	−	0.479506i	−0.877085	+	0.480335i	$0.840515\pi$
$684$	4.90930e6	−	7.01447e6i	0.401217	−	0.573264i
$685$	2.49501e6	+	6.02349e6i	0.203164	+	0.490480i
$686$	−7.78417e6	−	1.08736e7i	−0.631542	−	0.882193i
$687$	−1.67455e7	+	923973.i	−1.35365	+	0.0746908i
$688$	1.47081e7	−	8.45484e6i	1.18464	−	0.680980i
$689$	4.00412e6			0.321336
$690$	960500.	+	1.19649e6i	0.0768023	+	0.0956723i
$691$	−6.41692e6	+	2.65798e6i	−0.511248	+	0.211766i	−0.623368	−	0.781929i	$-0.714236\pi$
$691$	−6.41692e6	+	2.65798e6i	−0.511248	+	0.211766i	0.112120	+	0.993695i	$0.464236\pi$
$692$	−7.43274e6	+	480139.i	−0.590043	+	0.0381155i
$693$	3.61959e6	−	1.24721e7i	0.286304	−	0.986521i
$694$	1.21780e7	−	1.95632e7i	0.959789	−	1.54185i
$695$	1.40084e6	−	1.40084e6i	0.110009	−	0.110009i
$696$	−1.56029e7	+	5.66428e6i	−1.22091	+	0.443223i
$697$	−3.90129e6	−	3.90129e6i	−0.304177	−	0.304177i
$698$	−1.07262e7	+	2.49568e6i	−0.833313	+	0.193888i
$699$	−1.50189e6	+	4.27871e6i	−0.116264	+	0.331223i
$700$	−8.21462e6	−	2.79712e6i	−0.633639	−	0.215757i
$701$	1.98754e6	+	4.79836e6i	0.152764	+	0.368806i	0.981672	−	0.190580i	$-0.0610370\pi$
$701$	1.98754e6	+	4.79836e6i	0.152764	+	0.368806i	−0.828907	+	0.559386i	$0.811037\pi$
$702$	−7622.81	−	6.00582e6i	−0.000583811	−	0.459970i
$703$			1.42015e7i			1.08379i
$704$	−3.34248e6	−	1.70554e7i	−0.254177	−	1.29697i
$705$	5.36778e6	−	296180.i	0.406744	−	0.0224431i
$706$	−2.79998e6	+	1.69097e7i	−0.211419	+	1.27680i
$707$	−1.56643e7	+	6.48838e6i	−1.17859	+	0.488188i
$708$	1.64979e7	+	4.62049e6i	1.23693	+	0.346422i
$709$	3.61839e6	−	8.73556e6i	0.270333	−	0.652643i	−0.729164	−	0.684339i	$-0.760091\pi$
$709$	3.61839e6	−	8.73556e6i	0.270333	−	0.652643i	0.999498	+	0.0316963i	$0.0100909\pi$
$710$	644974.	+	2.77204e6i	0.0480172	+	0.206374i
$711$	4.32125e6	−	5.39698e6i	0.320579	−	0.400384i
$712$	1.62750e7	−	4.91189e6i	1.20316	−	0.363118i
$713$	−902349.	−	902349.i	−0.0664738	−	0.0664738i
$714$	−7.67328e6	−	4.20861e6i	−0.563294	−	0.308954i
$715$	1.18473e6	−	2.86019e6i	0.0866672	−	0.209233i
$716$	1.44097e6	+	2.23068e7i	0.105044	+	1.62613i
$717$	−57817.5	+	27773.8i	−0.00420012	+	0.00201761i
$718$	−896540.	−	1.25236e6i	−0.0649021	−	0.0906608i
$719$		−	2.28088e7i		−	1.64543i	−0.568452	−	0.822716i	$-0.692458\pi$
$719$		−	2.28088e7i		−	1.64543i	0.568452	−	0.822716i	$-0.307542\pi$
$720$	5.12117e6	+	792015.i	0.368161	+	0.0569380i
$721$			1.01864e7i			0.729763i
$722$	5.81303e6	−	4.16142e6i	0.415011	−	0.297097i
$723$	1.65385e7	−	7.94461e6i	1.17666	−	0.565232i
$724$	−1.47975e7	−	1.30017e7i	−1.04916	−	0.921837i
$725$	−6.05845e6	+	1.46264e7i	−0.428071	+	1.03346i
$726$	5.09992e6	−	9.29833e6i	0.359105	−	0.654732i
$727$	1.92729e7	+	1.92729e7i	1.35242	+	1.35242i	0.882947	+	0.469473i	$0.155556\pi$
$727$	1.92729e7	+	1.92729e7i	1.35242	+	1.35242i	0.469473	+	0.882947i	$0.344444\pi$
$728$	3.23757e6	+	3.95638e6i	0.226408	+	0.276675i
$729$	1.28912e7	+	6.30153e6i	0.898407	+	0.439165i
$730$	2.52669e6	−	587888.i	0.175487	−	0.0408307i
$731$	6.24469e6	−	1.50760e7i	0.432233	−	1.04350i
$732$	1.34205e6	+	2.38620e6i	0.0925743	+	0.164600i
$733$	1.59415e6	−	660320.i	0.109590	−	0.0453936i	−0.327215	−	0.944950i	$-0.606110\pi$
$733$	1.59415e6	−	660320.i	0.109590	−	0.0453936i	0.436805	+	0.899556i	$0.356110\pi$
$734$	1.67473e6	+	277310.i	0.114737	+	0.0189987i
$735$	2.15687e6	−	119010.i	0.147267	−	0.00812581i
$736$	−4.83672e6	−	169737.i	−0.329122	−	0.0115500i
$737$			2.53542e7i			1.71942i
$738$	−7.68881e6	−	414461.i	−0.519658	−	0.0280119i
$739$	−9.66477e6	−	2.33328e7i	−0.650999	−	1.57165i	−0.811330	−	0.584588i	$-0.801256\pi$
$739$	−9.66477e6	−	2.33328e7i	−0.650999	−	1.57165i	0.160331	−	0.987063i	$-0.448744\pi$
$740$	−7.71264e6	+	3.79443e6i	−0.517754	+	0.254722i
$741$	−1.59328e6	+	4.53909e6i	−0.106598	+	0.303685i
$742$	−1.84537e6	−	7.93125e6i	−0.123048	−	0.528850i
$743$	−1.38605e7	−	1.38605e7i	−0.921098	−	0.921098i	0.0760092	−	0.997107i	$-0.475782\pi$
$743$	−1.38605e7	−	1.38605e7i	−0.921098	−	0.921098i	−0.997107	+	0.0760092i	$0.975782\pi$
$744$	−4.30571e6	−	191582.i	−0.285176	−	0.0126889i
$745$	−7.55270e6	+	7.55270e6i	−0.498553	+	0.498553i
$746$	−1.78991e7	−	1.11421e7i	−1.17757	−	0.733026i
$747$	−1.88731e7	−	5.47725e6i	−1.23749	−	0.359138i
$748$	−1.25582e7	−	1.10342e7i	−0.820682	−	0.721087i
$749$	−33092.4	+	13707.3i	−0.00215538	+	0.000892787i
$750$	8.32937e6	−	6.68652e6i	0.540703	−	0.434058i
$751$	1.94726e7			1.25987			0.629933	−	0.776649i	$-0.283082\pi$
$751$	1.94726e7			1.25987			0.629933	+	0.776649i	$0.283082\pi$
$752$	−1.03483e7	+	1.34336e7i	−0.667302	+	0.866262i
$753$	2.94186e7	−	1.62324e6i	1.89075	−	0.104327i
$754$	7.58365e6	−	5.42896e6i	0.485791	−	0.347767i
$755$	−3.11968e6	−	7.53158e6i	−0.199179	−	0.480860i
$756$	−1.18927e7	+	2.78299e6i	−0.756788	+	0.177095i
$757$	−1.86780e6	−	773667.i	−0.118465	−	0.0490698i	0.322664	−	0.946514i	$-0.395422\pi$
$757$	−1.86780e6	−	773667.i	−0.118465	−	0.0490698i	−0.441129	+	0.897444i	$0.645422\pi$
$758$	−5.79348e6	−	3.60640e6i	−0.366241	−	0.227982i
$759$	−5.14628e6	−	4.60806e6i	−0.324257	−	0.290345i
$760$	−3.65788e6	−	1.96183e6i	−0.229718	−	0.123204i
$761$	−8.86441e6	+	8.86441e6i	−0.554866	+	0.554866i	−0.927841	−	0.372975i	$-0.878338\pi$
$761$	−8.86441e6	+	8.86441e6i	−0.554866	+	0.554866i	0.372975	+	0.927841i	$0.378338\pi$
$762$	1.78577e7	−	5.20716e6i	1.11414	−	0.324873i
$763$	4.25707e6	+	1.76334e6i	0.264728	+	0.109654i
$764$	1.96312e7	+	6.68453e6i	1.21679	+	0.414322i
$765$	4.36722e6	−	2.40253e6i	0.269806	−	0.148428i
$766$	−2.64349e7	−	4.37721e6i	−1.62782	−	0.269541i
$767$	−9.62635e6			−0.590844
$768$	−1.24400e7	+	1.06032e7i	−0.761058	+	0.648684i
$769$	−8.61222e6			−0.525169			−0.262584	−	0.964909i	$-0.584575\pi$
$769$	−8.61222e6			−0.525169			−0.262584	+	0.964909i	$0.584575\pi$
$770$	−6.21140e6	−	1.02851e6i	−0.377540	−	0.0625147i
$771$	1.25562e7	−	6.03162e6i	0.760715	−	0.365425i
$772$	2.15034e7	+	7.32202e6i	1.29857	+	0.442168i
$773$	1.28767e7	+	5.33368e6i	0.775094	+	0.321054i	0.734934	−	0.678139i	$-0.237213\pi$
$773$	1.28767e7	+	5.33368e6i	0.775094	+	0.321054i	0.0401600	+	0.999193i	$0.487213\pi$
$774$	−7.57002e6	−	2.14789e7i	−0.454197	−	1.28872i
$775$	−2.90665e6	+	2.90665e6i	−0.173836	+	0.173836i
$776$	2.12584e7	+	1.14015e7i	1.26729	+	0.679685i
$777$	1.35145e7	−	1.50930e7i	0.803059	−	0.896856i
$778$	−1.72010e7	−	1.07075e7i	−1.01884	−	0.634221i
$779$	5.69811e6	+	2.36023e6i	0.336424	+	0.139351i
$780$	−2.89082e6	+	347488.i	−0.170132	+	0.0204505i
$781$	−4.90359e6	−	1.18383e7i	−0.287665	−	0.694485i
$782$	−3.78521e6	+	2.70974e6i	−0.221347	+	0.158457i
$783$	3.66801e6	+	2.19788e7i	0.213809	+	1.28115i
$784$	−4.15811e6	+	5.39788e6i	−0.241605	+	0.313641i
$785$	1.08008e7			0.625576
$786$	−6.89567e6	−	8.58990e6i	−0.398125	−	0.495943i
$787$	−1.80620e7	+	7.48152e6i	−1.03951	+	0.430579i	−0.836136	−	0.548522i	$-0.815191\pi$
$787$	−1.80620e7	+	7.48152e6i	−1.03951	+	0.430579i	−0.203374	+	0.979101i	$0.565191\pi$
$788$	2.56787e6	+	2.25625e6i	0.147319	+	0.129441i
$789$	3.92797e6	−	1.11904e7i	0.224634	−	0.639958i
$790$	−2.84554e6	−	1.77133e6i	−0.162217	−	0.100979i
$791$	−3.62661e6	+	3.62661e6i	−0.206091	+	0.206091i
$792$	−2.33294e7	+	248605.i	−1.32157	+	0.0140830i
$793$	−1.08770e6	−	1.08770e6i	−0.0614221	−	0.0614221i
$794$	−2.30143e6	−	9.89137e6i	−0.129553	−	0.556808i
$795$	4.37609e6	+	1.53607e6i	0.245566	+	0.0861971i
$796$	6.31816e6	−	3.10838e6i	0.353434	−	0.173881i
$797$	1.03262e7	+	2.49296e7i	0.575830	+	1.39018i	0.896524	+	0.442994i	$0.146084\pi$
$797$	1.03262e7	+	2.49296e7i	0.575830	+	1.39018i	−0.320694	+	0.947183i	$0.603916\pi$
$798$	9.72520e6	+	1.06401e6i	0.540619	+	0.0591477i
$799$			1.63107e7i			0.903869i
$800$	−546758.	+	1.55801e7i	−0.0302044	+	0.860686i
$801$	−2.51075e6	−	2.26824e7i	−0.138268	−	1.24913i
$802$	1.25092e7	+	2.07133e6i	0.686744	+	0.113714i
$803$	−1.07905e7	+	4.46958e6i	−0.590545	+	0.244612i
$804$	2.07839e7	−	1.16893e7i	1.13393	−	0.637746i
$805$	−670926.	+	1.61976e6i	−0.0364909	+	0.0880969i
$806$	2.35864e6	−	548786.i	0.127886	−	0.0297554i
$807$	3.29627e6	+	2.95154e6i	0.178172	+	0.159538i
$808$	1.92901e7	+	2.35729e7i	1.03946	+	1.27024i
$809$	775163.	+	775163.i	0.0416410	+	0.0416410i	0.727621	−	0.685980i	$-0.240626\pi$
$809$	775163.	+	775163.i	0.0416410	+	0.0416410i	−0.685980	+	0.727621i	$0.740626\pi$
$810$	2.29563e6	−	6.56667e6i	0.122939	−	0.351668i
$811$	−2.17649e6	+	5.25452e6i	−0.116200	+	0.280531i	−0.971270	−	0.237982i	$-0.923514\pi$
$811$	−2.17649e6	+	5.25452e6i	−0.116200	+	0.280531i	0.855070	+	0.518513i	$0.173514\pi$
$812$	−1.42486e7	−	1.25194e7i	−0.758372	−	0.666339i
$813$	1.16480e7	+	2.42480e7i	0.618053	+	1.28662i
$814$	3.14668e7	−	2.25264e7i	1.66453	−	1.19160i
$815$			1.61312e6i			0.0850695i
$816$	−3.25536e6	+	1.53817e7i	−0.171149	+	0.808684i
$817$			1.82416e7i			0.956110i
$818$	78768.1	+	110030.i	0.00411592	+	0.00574948i
$819$	6.01282e6	−	3.30783e6i	0.313234	−	0.172319i
$820$	240639.	+	3.72519e6i	0.0124978	+	0.193470i
$821$	−3.65008e6	+	8.81207e6i	−0.188993	+	0.456268i	−0.989766	−	0.142699i	$-0.954422\pi$
$821$	−3.65008e6	+	8.81207e6i	−0.188993	+	0.456268i	0.800774	+	0.598967i	$0.204422\pi$
$822$	−1.32759e7	+	2.42050e7i	−0.685306	+	1.24947i
$823$	−1.50502e7	−	1.50502e7i	−0.774538	−	0.774538i	0.204358	−	0.978896i	$-0.434489\pi$
$823$	−1.50502e7	−	1.50502e7i	−0.774538	−	0.774538i	−0.978896	+	0.204358i	$0.934489\pi$
$824$	1.75194e7	−	5.28744e6i	0.898879	−	0.271286i
$825$	−1.48435e7	+	1.65772e7i	−0.759280	+	0.847964i
$826$	4.43648e6	+	1.90676e7i	0.226250	+	0.972403i
$827$	−4.60094e6	+	1.11076e7i	−0.233928	+	0.564753i	−0.996633	−	0.0819945i	$-0.973871\pi$
$827$	−4.60094e6	+	1.11076e7i	−0.233928	+	0.564753i	0.762705	+	0.646747i	$0.223871\pi$
$828$	−1.40478e6	+	6.34311e6i	−0.0712086	+	0.321534i
$829$	7.40615e6	−	3.06773e6i	0.374288	−	0.155035i	−0.187606	−	0.982244i	$-0.560073\pi$
$829$	7.40615e6	−	3.06773e6i	0.374288	−	0.155035i	0.561894	+	0.827209i	$0.310073\pi$
$830$	−1.55637e6	+	9.39923e6i	−0.0784181	+	0.473584i
$831$	−92663.7	−	1.67938e6i	−0.00465487	−	0.0843617i
$832$	5.12398e6	−	7.62188e6i	0.256625	−	0.381728i
$833$			6.55392e6i			0.327257i
$834$	8.33880e6	+	912326.i	0.415134	+	0.0454187i
$835$	−924840.	−	2.23276e6i	−0.0459040	−	0.110822i
$836$	1.76902e7	+	6.02361e6i	0.875422	+	0.298085i
$837$	−1.30399e6	+	5.63683e6i	−0.0643368	+	0.278113i
$838$	6.61246e6	−	1.53853e6i	0.325277	−	0.0756825i
$839$	−3.25945e6	−	3.25945e6i	−0.159860	−	0.159860i	0.622645	−	0.782505i	$-0.286058\pi$
$839$	−3.25945e6	−	3.25945e6i	−0.159860	−	0.159860i	−0.782505	+	0.622645i	$0.786058\pi$
$840$	2.02058e6	+	5.56592e6i	0.0988050	+	0.272169i
$841$	−9.96476e6	+	9.96476e6i	−0.485822	+	0.485822i
$842$	−1.29161e7	+	2.07490e7i	−0.627843	+	1.00860i
$843$	1.78394e7	+	6.26189e6i	0.864594	+	0.303484i
$844$	−1.41279e7	+	912630.i	−0.682685	+	0.0441000i
$845$	−5.63234e6	+	2.33299e6i	−0.271361	+	0.112401i
$846$	1.52064e7	+	1.69392e7i	0.730468	+	0.813706i
$847$	1.21181e7			0.580396
$848$	−1.26830e7	+	7.29070e6i	−0.605663	+	0.348160i
$849$	−1.70436e6	−	3.08887e7i	−0.0811507	−	1.47072i
$850$	8.72864e6	+	1.21929e7i	0.414381	+	0.578843i
$851$	−4.12390e6	−	9.95598e6i	−0.195202	−	0.471260i
$852$	−7.44361e6	+	9.47760e6i	−0.351305	+	0.447300i
$853$	−1.73376e7	−	7.18149e6i	−0.815863	−	0.337942i	−0.0645725	−	0.997913i	$-0.520568\pi$
$853$	−1.73376e7	−	7.18149e6i	−0.815863	−	0.337942i	−0.751291	+	0.659971i	$0.770568\pi$
$854$	−1.65319e6	+	2.65576e6i	−0.0775674	+	0.124608i
$855$	−3.48259e6	+	4.34954e6i	−0.162925	+	0.203483i
$856$	40752.2	+	49800.0i	0.00190093	+	0.00232298i
$857$	2.03516e7	−	2.03516e7i	0.946555	−	0.946555i	−0.0520877	−	0.998643i	$-0.516588\pi$
$857$	2.03516e7	−	2.03516e7i	0.946555	−	0.946555i	0.998643	+	0.0520877i	$0.0165876\pi$
$858$	1.25847e7	−	3.66960e6i	0.583613	−	0.170177i
$859$	−2.32339e7	−	9.62379e6i	−1.07433	−	0.445003i	−0.225816	−	0.974170i	$-0.572505\pi$
$859$	−2.32339e7	−	9.62379e6i	−1.07433	−	0.445003i	−0.848518	+	0.529167i	$0.822505\pi$
$860$	−9.90678e6	+	4.87389e6i	−0.456758	+	0.224714i
$861$	−3.80976e6	−	7.93088e6i	−0.175142	−	0.364597i
$862$	−5.36941e6	+	3.24271e7i	−0.246127	+	1.48641i
$863$	1.23042e7			0.562376			0.281188	−	0.959653i	$-0.409272\pi$
$863$	1.23042e7			0.562376			0.281188	+	0.959653i	$0.409272\pi$
$864$	1.09595e7	+	1.90094e7i	0.499468	+	0.866332i
$865$	4.84728e6			0.220271
$866$	−394932.	+	2.38508e6i	−0.0178948	+	0.108071i
$867$	−3.03555e6	−	6.31919e6i	−0.137148	−	0.285505i
$868$	−2.17404e6	−	4.41901e6i	−0.0979419	−	0.199079i
$869$	1.39419e7	+	5.77492e6i	0.626286	+	0.259416i
$870$	1.03708e7	−	3.02405e6i	0.464531	−	0.135454i
$871$	−9.47387e6	+	9.47387e6i	−0.423138	+	0.423138i
$872$	823019.	−	8.23696e6i	0.0366538	−	0.366839i
$873$	2.02397e7	−	2.52781e7i	0.898810	−	1.12256i
$874$	2.75008e6	−	4.41784e6i	0.121777	−	0.195628i
$875$	1.12760e7	+	4.67066e6i	0.497890	+	0.206233i
$876$	8.63874e6	+	6.78477e6i	0.380356	+	0.298727i
$877$	−9.05125e6	−	2.18517e7i	−0.397383	−	0.959368i	−0.988284	−	0.152624i	$-0.951228\pi$
$877$	−9.05125e6	−	2.18517e7i	−0.397383	−	0.959368i	0.590901	−	0.806744i	$-0.298772\pi$
$878$	6.74479e6	+	9.42172e6i	0.295279	+	0.412471i
$879$	1.15206e6	+	2.08792e7i	0.0502925	+	0.911468i
$880$	1.45523e6	+	1.12168e7i	0.0633468	+	0.488271i
$881$	−2.88435e7			−1.25201			−0.626006	−	0.779818i	$-0.715311\pi$
$881$	−2.88435e7			−1.25201			−0.626006	+	0.779818i	$0.715311\pi$
$882$	6.11021e6	+	6.80648e6i	0.264475	+	0.294612i
$883$	−1.25120e7	+	5.18263e6i	−0.540038	+	0.223691i	−0.635993	−	0.771695i	$-0.719409\pi$
$883$	−1.25120e7	+	5.18263e6i	−0.540038	+	0.223691i	0.0959554	+	0.995386i	$0.469409\pi$
$884$	−569466.	−	8.81556e6i	−0.0245097	−	0.379419i
$885$	−1.05206e7	−	3.69288e6i	−0.451526	−	0.158492i
$886$	−1.54035e7	+	2.47448e7i	−0.659227	+	1.05901i
$887$	−2.00464e7	+	2.00464e7i	−0.855516	+	0.855516i	−0.990806	−	0.135290i	$-0.956803\pi$
$887$	−2.00464e7	+	2.00464e7i	−0.855516	+	0.855516i	0.135290	+	0.990806i	$0.456803\pi$
$888$	−3.29732e7	−	1.54091e7i	−1.40323	−	0.655758i
$889$	1.50297e7	+	1.50297e7i	0.637815	+	0.637815i
$890$	−1.07758e7	+	2.50721e6i	−0.456009	+	0.106100i
$891$	−5.36693e6	+	3.08558e7i	−0.226481	+	1.30210i
$892$	−1.53995e6	+	4.52255e6i	−0.0648028	+	0.190314i
$893$	−6.97756e6	−	1.68453e7i	−0.292803	−	0.706888i
$894$	−4.49590e7	−	4.91884e6i	−1.88136	−	0.205835i
$895$		−	1.45474e7i		−	0.607056i
$896$	−1.74587e7	−	6.63676e6i	−0.726511	−	0.276176i
$897$	−201111.	−	3.64481e6i	−0.00834556	−	0.151249i
$898$	−5.83314e6	+	3.52276e7i	−0.241386	+	1.45778i
$899$	−8.30082e6	+	3.43831e6i	−0.342548	+	0.141888i
$900$	2.04325e7	+	4.52509e6i	0.840842	+	0.186218i
$901$	−5.38486e6	+	1.30002e7i	−0.220985	+	0.533505i
$902$	−3.80867e6	−	1.63693e7i	−0.155868	−	0.669907i
$903$	1.73592e7	−	1.93868e7i	0.708452	−	0.791199i
$904$	8.11981e6	+	4.35488e6i	0.330464	+	0.177237i
$905$	9.06467e6	+	9.06467e6i	0.367901	+	0.367901i
$906$	1.65998e7	−	3.02652e7i	0.671864	−	1.22496i
$907$	9.36205e6	−	2.26020e7i	0.377879	−	0.912281i	−0.614484	−	0.788929i	$-0.710636\pi$
$907$	9.36205e6	−	2.26020e7i	0.377879	−	0.912281i	0.992363	−	0.123351i	$-0.0393642\pi$
$908$	−6.74013e6	+	435398.i	−0.271302	+	0.0175255i
$909$	3.58256e7	−	1.97087e7i	1.43808	−	0.791131i
$910$	−1.93664e6	−	2.70527e6i	−0.0775256	−	0.108295i
$911$		−	3.32177e7i		−	1.32609i	−0.748578	−	0.663047i	$-0.769263\pi$
$911$		−	3.32177e7i		−	1.32609i	0.748578	−	0.663047i	$-0.230737\pi$
$912$	−3.21808e6	−	1.72785e7i	−0.128118	−	0.687890i
$913$		−	4.28936e7i		−	1.70300i
$914$	6.24600e6	−	4.47137e6i	0.247307	−	0.177042i
$915$	−771476.	−	1.60600e6i	−0.0304628	−	0.0634153i
$916$	−2.27239e7	+	2.58625e7i	−0.894839	+	1.01843i
$917$	4.81675e6	−	1.16287e7i	0.189161	−	0.456674i
$918$	1.95094e7	+	8.05206e6i	0.764077	+	0.315355i
$919$	4.32225e6	+	4.32225e6i	0.168819	+	0.168819i	0.786460	−	0.617641i	$-0.211912\pi$
$919$	4.32225e6	+	4.32225e6i	0.168819	+	0.168819i	−0.617641	+	0.786460i	$0.711912\pi$
$920$	3.13405e6	+	313148.i	0.122078	+	0.0121977i
$921$	−5.75072e6	−	5.14929e6i	−0.223395	−	0.200031i
$922$	4.90709e7	−	1.14174e7i	1.90106	−	0.442322i
$923$	2.59123e6	−	6.25578e6i	0.100116	−	0.241700i
$924$	−1.30685e7	−	2.32362e7i	−0.503555	−	0.895336i
$925$	−3.20703e7	+	1.32839e7i	−1.23239	+	0.510473i
$926$	−2.28770e7	−	3.78808e6i	−0.876742	−	0.145175i
$927$	−2.70272e6	−	2.44166e7i	−0.103300	−	0.933224i
$928$	−1.41360e7	+	3.10044e7i	−0.538835	+	1.18183i
$929$			4.08017e7i			1.55110i	0.631289	+	0.775548i	$0.282526\pi$
$929$			4.08017e7i			1.55110i	−0.631289	+	0.775548i	$0.717474\pi$
$930$	2.78827e6	+	305058.i	0.105713	+	0.0115658i
$931$	−2.80371e6	−	6.76875e6i	−0.106013	−	0.255938i
$932$	4.10928e6	+	8.35262e6i	0.154962	+	0.314980i
$933$	−4.67073e7	−	1.63949e7i	−1.75663	−	0.616601i
$934$	−3.88122e6	−	1.66812e7i	−0.145580	−	0.625690i
$935$	7.69295e6	+	7.69295e6i	0.287782	+	0.287782i
$936$	−8.81015e6	−	8.62436e6i	−0.328695	−	0.321764i
$937$	1.70976e7	−	1.70976e7i	0.636190	−	0.636190i	−0.313424	−	0.949613i	$-0.601476\pi$
$937$	1.70976e7	−	1.70976e7i	0.636190	−	0.636190i	0.949613	+	0.313424i	$0.101476\pi$
$938$	2.31318e7	+	1.43994e7i	0.858425	+	0.534364i
$939$	−3.27435e6	+	9.32828e6i	−0.121189	+	0.345253i
$940$	7.28418e6	−	8.29025e6i	0.268881	−	0.306019i
$941$	1.00920e7	−	4.18024e6i	0.371538	−	0.153896i	−0.189099	−	0.981958i	$-0.560557\pi$
$941$	1.00920e7	−	4.18024e6i	0.371538	−	0.153896i	0.560636	+	0.828062i	$0.310557\pi$
$942$	2.86297e7	+	3.56639e7i	1.05121	+	1.30949i
$943$	−4.68006e6			−0.171385
$944$	3.04912e7	−	1.75276e7i	1.11364	−	0.640167i
$945$	7.84036e6	−	1.30847e6i	0.285599	−	0.0476632i
$946$	4.04187e7	−	2.89348e7i	1.46843	−	1.05122i
$947$	−1.34297e7	−	3.24222e7i	−0.486622	−	1.17481i	−0.956409	−	0.292030i	$-0.905669\pi$
$947$	−1.34297e7	−	3.24222e7i	−0.486622	−	1.17481i	0.469787	−	0.882780i	$-0.344331\pi$
$948$	−1.69382e6	−	1.40912e7i	−0.0612132	−	0.509246i
$949$	−5.70209e6	−	2.36188e6i	−0.205527	−	0.0851319i
$950$	−1.42308e7	−	8.85856e6i	−0.511587	−	0.318459i
$951$	3.42355e7	−	3.82342e7i	1.22751	−	1.37088i
$952$	−1.71992e7	+	5.19080e6i	−0.615057	+	0.185627i
$953$	3.85355e7	−	3.85355e7i	1.37445	−	1.37445i	0.520727	−	0.853723i	$-0.325661\pi$
$953$	3.85355e7	−	3.85355e7i	1.37445	−	1.37445i	0.853723	−	0.520727i	$-0.174339\pi$
$954$	6.52771e6	+	1.85215e7i	0.232215	+	0.658877i
$955$	−1.24689e7	−	5.16480e6i	−0.442406	−	0.183251i
$956$	−42441.8	+	124644.i	−0.00150193	+	0.00441089i
$957$	−4.38403e7	+	2.10596e7i	−1.54737	+	0.743309i
$958$	−5.33883e7	−	8.84027e6i	−1.87946	−	0.311209i
$959$	−3.15452e7			−1.10761
$960$	8.52391e6	−	6.36427e6i	0.298511	−	0.222880i
$961$	2.62963e7			0.918514
$962$	2.01751e7	+	3.34068e6i	0.702874	+	0.116385i
$963$	75685.1	−	41636.5i	0.00262993	−	0.00144680i
$964$	1.21404e7	−	3.56540e7i	0.420764	−	1.23571i
$965$	−1.36581e7	−	5.65736e6i	−0.472140	−	0.195567i
$966$	−7.12686e6	+	2.07813e6i	−0.245728	+	0.0716524i
$967$	2.03420e7	−	2.03420e7i	0.699563	−	0.699563i	−0.264753	−	0.964316i	$-0.585291\pi$
$967$	2.03420e7	−	2.03420e7i	0.699563	−	0.699563i	0.964316	+	0.264753i	$0.0852906\pi$
$968$	−6.29011e6	−	2.08416e7i	−0.215759	−	0.714897i
$969$	−1.25944e7	−	1.12772e7i	−0.430892	−	0.385827i
$970$	−1.33278e7	−	8.29647e6i	−0.454809	−	0.283116i
$971$	3.29304e7	+	1.36402e7i	1.12085	+	0.464273i	0.864663	−	0.502353i	$-0.167532\pi$
$971$	3.29304e7	+	1.36402e7i	1.12085	+	0.464273i	0.256192	+	0.966626i	$0.417532\pi$
$972$	2.77681e7	−	9.82623e6i	0.942716	−	0.333596i
$973$	3.66814e6	+	8.85566e6i	0.124212	+	0.299874i
$974$	−1.37245e7	+	9.82509e6i	−0.463554	+	0.331848i
$975$	−1.17407e7	+	647821.i	−0.395532	+	0.0218245i
$976$	5.42573e6	+	1.46478e6i	0.182320	+	0.0492206i
$977$	−2.84024e7			−0.951958			−0.475979	−	0.879457i	$-0.657906\pi$
$977$	−2.84024e7			−0.951958			−0.475979	+	0.879457i	$0.657906\pi$
$978$	−5.32651e6	+	4.27593e6i	−0.178072	+	0.142950i
$979$	4.60191e7	−	1.90617e7i	1.53455	−	0.635632i
$980$	2.92691e6	−	3.33117e6i	0.0973519	−	0.110798i
$981$	−1.06720e7	−	3.09718e6i	−0.354057	−	0.102753i
$982$	−2.79870e7	−	1.74217e7i	−0.926143	−	0.576518i
$983$	8.09109e6	−	8.09109e6i	0.267069	−	0.267069i	−0.560849	−	0.827918i	$-0.689525\pi$
$983$	8.09109e6	−	8.09109e6i	0.267069	−	0.267069i	0.827918	+	0.560849i	$0.189525\pi$
$984$	−1.16627e7	+	1.06690e7i	−0.383981	+	0.351266i
$985$	−1.57303e6	−	1.57303e6i	−0.0516591	−	0.0516591i
$986$	7.42753e6	+	3.19229e7i	0.243306	+	1.04571i
$987$	−8.61488e6	+	2.45429e7i	−0.281486	+	0.801922i
$988$	4.35935e6	+	8.86091e6i	0.142079	+	0.288793i
$989$	−5.29710e6	−	1.27883e7i	−0.172206	−	0.415741i
$990$	1.51615e7	+	817274.i	0.491649	+	0.0265021i
$991$			4.29681e7i			1.38983i	0.719091	+	0.694916i	$0.244558\pi$
$991$			4.29681e7i			1.38983i	−0.719091	+	0.694916i	$0.755442\pi$
$992$	−6.47170e6	+	6.03287e6i	−0.208804	+	0.194646i
$993$	4.68111e7	−	2.58292e6i	1.50652	−	0.0831262i
$994$	−1.35855e7	−	2.24955e6i	−0.436124	−	0.0722153i
$995$	−4.23369e6	+	1.75365e6i	−0.135569	+	0.0561546i
$996$	−3.51616e7	+	1.97756e7i	−1.12311	+	0.631657i
$997$	8.31580e6	−	2.00761e7i	0.264951	−	0.639649i	−0.734280	−	0.678847i	$-0.762480\pi$
$997$	8.31580e6	−	2.00761e7i	0.264951	−	0.639649i	0.999231	+	0.0391974i	$0.0124801\pi$
$998$	−1.79898e7	+	4.18570e6i	−0.571741	+	0.133028i
$999$	−2.83895e7	+	3.97634e7i	−0.900003	+	1.26058i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	96.6.o.a.11.3	✓	312
3.2	odd	2	inner	96.6.o.a.11.76	yes	312
32.3	odd	8	inner	96.6.o.a.35.76	yes	312
96.35	even	8	inner	96.6.o.a.35.3	yes	312

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.6.o.a.11.3	✓	312	1.1	even	1	trivial
96.6.o.a.11.76	yes	312	3.2	odd	2	inner
96.6.o.a.35.3	yes	312	96.35	even	8	inner
96.6.o.a.35.76	yes	312	32.3	odd	8	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:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	96.o (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.58086 - 0.924104i) q^{2} +(6.74983 + 14.0513i) q^{3} +(30.2921 + 10.3146i) q^{4} +(-19.2402 - 7.96957i) q^{5} +(-24.6850 - 84.6561i) q^{6} +(71.2494 - 71.2494i) q^{7} +(-159.524 - 85.5573i) q^{8} +(-151.879 + 189.688i) q^{9} +(100.012 + 62.2571i) q^{10} +(-490.018 - 202.972i) q^{11} +(59.5328 + 495.265i) q^{12} +(-107.258 - 258.943i) q^{13} +(-463.475 + 331.791i) q^{14} +(-17.8855 - 324.144i) q^{15} +(811.218 + 624.901i) q^{16} +984.954 q^{17} +(1022.91 - 918.272i) q^{18} +(-1017.24 + 421.354i) q^{19} +(-500.624 - 439.870i) q^{20} +(1482.07 + 520.227i) q^{21} +(2547.16 + 1585.59i) q^{22} +(590.784 - 590.784i) q^{23} +(125.432 - 2819.02i) q^{24} +(-1903.04 - 1903.04i) q^{25} +(359.300 + 1544.24i) q^{26} +(-3690.53 - 853.743i) q^{27} +(2893.20 - 1423.38i) q^{28} +(-2251.12 - 5434.69i) q^{29} +(-199.727 + 1825.53i) q^{30} -1527.38i q^{31} +(-3949.83 - 4237.13i) q^{32} +(-455.514 - 8255.43i) q^{33} +(-5496.89 - 910.200i) q^{34} +(-1938.68 + 803.029i) q^{35} +(-6557.30 + 4179.47i) q^{36} +(4935.89 - 11916.3i) q^{37} +(6066.45 - 1411.49i) q^{38} +(2914.52 - 3254.93i) q^{39} +(2387.43 + 2917.48i) q^{40} +(-3960.89 - 3960.89i) q^{41} +(-7790.49 - 4272.90i) q^{42} +(6340.08 - 15306.3i) q^{43} +(-12750.1 - 11202.8i) q^{44} +(4433.93 - 2439.23i) q^{45} +(-3843.03 + 2751.14i) q^{46} +16559.8i q^{47} +(-3305.09 + 15616.7i) q^{48} +6654.04i q^{49} +(8861.98 + 12379.2i) q^{50} +(6648.28 + 13839.9i) q^{51} +(-578.165 - 8950.23i) q^{52} +(-5467.12 + 13198.8i) q^{53} +(19807.4 + 8175.06i) q^{54} +(7810.47 + 7810.47i) q^{55} +(-17461.9 + 5270.09i) q^{56} +(-12786.8 - 11449.5i) q^{57} +(7540.99 + 32410.6i) q^{58} +(13143.6 - 31731.4i) q^{59} +(2801.63 - 10003.5i) q^{60} +(5070.49 - 2100.26i) q^{61} +(-1411.45 + 8524.08i) q^{62} +(2693.85 + 24336.5i) q^{63} +(18127.9 + 27296.9i) q^{64} +5836.92i q^{65} +(-5086.71 + 46493.4i) q^{66} +(-18293.4 - 44164.1i) q^{67} +(29836.3 + 10159.4i) q^{68} +(12289.0 + 4313.60i) q^{69} +(11561.6 - 2690.05i) q^{70} +(17083.0 + 17083.0i) q^{71} +(40457.7 - 17265.4i) q^{72} +(15571.0 - 15571.0i) q^{73} +(-38558.4 + 61941.9i) q^{74} +(13895.0 - 39585.3i) q^{75} +(-35160.4 + 2271.28i) q^{76} +(-49375.1 + 20451.9i) q^{77} +(-19273.4 + 15472.0i) q^{78} -28451.8 q^{79} +(-10627.9 - 18488.3i) q^{80} +(-12914.3 - 57619.5i) q^{81} +(18444.9 + 25765.5i) q^{82} +(30948.2 + 74715.6i) q^{83} +(39529.1 + 31045.7i) q^{84} +(-18950.8 - 7849.66i) q^{85} +(-49527.7 + 79563.5i) q^{86} +(61169.9 - 68314.6i) q^{87} +(60803.9 + 74303.6i) q^{88} +(-66406.6 + 66406.6i) q^{89} +(-26999.3 + 9515.62i) q^{90} +(-26091.6 - 10807.5i) q^{91} +(23989.7 - 11802.4i) q^{92} +(21461.7 - 10309.5i) q^{93} +(15303.0 - 92418.2i) q^{94} +22930.0 q^{95} +(32876.7 - 84100.2i) q^{96} -133261. q^{97} +(6149.02 - 37135.3i) q^{98} +(112925. - 62123.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 312 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 4 q^{9} + 192 q^{10} - 4 q^{12} - 8 q^{13} - 8 q^{15} - 6696 q^{16} - 4 q^{18} - 8 q^{19} - 4 q^{21} + 5576 q^{22} - 11024 q^{24} - 8 q^{25} + 7460 q^{27}+ \cdots + 339516 q^{99}+O(q^{100}) \) 312 * q - 4 * q^3 - 8 * q^4 - 4 * q^6 - 8 * q^7 - 4 * q^9 + 192 * q^10 - 4 * q^12 - 8 * q^13 - 8 * q^15 - 6696 * q^16 - 4 * q^18 - 8 * q^19 - 4 * q^21 + 5576 * q^22 - 11024 * q^24 - 8 * q^25 + 7460 * q^27 - 8 * q^28 + 32564 * q^30 - 8 * q^33 - 264 * q^34 + 3264 * q^36 - 8 * q^37 + 44900 * q^39 - 60136 * q^40 - 7264 * q^42 - 8 * q^43 - 4 * q^45 + 63320 * q^46 + 112368 * q^48 - 976 * q^51 - 55024 * q^52 - 115328 * q^54 - 110056 * q^55 - 4 * q^57 - 123568 * q^58 + 44648 * q^60 - 96168 * q^61 + 187432 * q^64 + 17564 * q^66 + 97848 * q^67 - 4 * q^69 - 143480 * q^70 + 179936 * q^72 - 8 * q^73 + 12496 * q^75 - 234928 * q^76 - 708428 * q^78 + 355344 * q^79 + 251552 * q^82 + 387560 * q^84 - 25008 * q^85 - 282188 * q^87 + 111632 * q^88 + 453536 * q^90 + 200104 * q^91 + 968 * q^93 - 671008 * q^94 - 911336 * q^96 - 16 * q^97 + 339516 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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