LMFDB - Embedded newform 96.6.o.a.11.76

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			11.76
Character	$\chi$	$=$	96.11
Dual form			96.6.o.a.35.76

$q$-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} +(5.16293 + 14.7086i) q^{3} +(30.2921 + 10.3146i) q^{4} +(19.2402 + 7.96957i) q^{5} +(15.2213 + 86.8580i) q^{6} +(71.2494 - 71.2494i) q^{7} +(159.524 + 85.5573i) q^{8} +(-189.688 + 151.879i) q^{9} +(100.012 + 62.2571i) q^{10} +(490.018 + 202.972i) q^{11} +(4.68228 + 498.809i) 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} +(-1198.98 + 672.327i) q^{18} +(-1017.24 + 421.354i) q^{19} +(500.624 + 439.870i) q^{20} +(1415.84 + 680.126i) q^{21} +(2547.16 + 1585.59i) q^{22} +(-590.784 + 590.784i) q^{23} +(-434.820 + 2788.11i) q^{24} +(-1903.04 - 1903.04i) q^{25} +(-359.300 - 1544.24i) q^{26} +(-3213.29 - 2005.91i) q^{27} +(2893.20 - 1423.38i) q^{28} +(2251.12 + 5434.69i) q^{29} +(-399.359 + 1792.48i) 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} +(-7312.62 + 2644.19i) q^{36} +(4935.89 - 11916.3i) q^{37} +(-6066.45 + 1411.49i) q^{38} +(3254.93 - 2914.52i) q^{39} +(2387.43 + 2917.48i) q^{40} +(3960.89 + 3960.89i) q^{41} +(7273.09 + 5104.07i) q^{42} +(6340.08 - 15306.3i) q^{43} +(12750.1 + 11202.8i) q^{44} +(-4860.06 + 1410.46i) q^{45} +(-3843.03 + 2751.14i) q^{46} -16559.8i q^{47} +(-5003.17 + 15158.2i) q^{48} +6654.04i q^{49} +(-8861.98 - 12379.2i) q^{50} +(-5085.25 - 14487.3i) q^{51} +(-578.165 - 8950.23i) q^{52} +(5467.12 - 13198.8i) q^{53} +(-16079.3 - 14164.1i) q^{54} +(7810.47 + 7810.47i) q^{55} +(17461.9 - 5270.09i) q^{56} +(-11449.5 - 12786.8i) q^{57} +(7540.99 + 32410.6i) q^{58} +(-13143.6 + 31731.4i) q^{59} +(-3885.20 + 9634.52i) 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} +(-10171.0 + 45651.5i) q^{66} +(-18293.4 - 44164.1i) q^{67} +(-29836.3 - 10159.4i) q^{68} +(-11739.8 - 5639.45i) q^{69} +(11561.6 - 2690.05i) q^{70} +(-17083.0 - 17083.0i) q^{71} +(-43254.3 + 7999.22i) q^{72} +(15571.0 - 15571.0i) q^{73} +(38558.4 - 61941.9i) q^{74} +(18165.8 - 37816.3i) q^{75} +(-35160.4 + 2271.28i) q^{76} +(49375.1 - 20451.9i) q^{77} +(20858.6 - 13257.6i) 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} +(35873.4 + 35206.2i) q^{84} +(-18950.8 - 7849.66i) q^{85} +(49527.7 - 79563.5i) q^{86} +(-68314.6 + 61169.9i) q^{87} +(60803.9 + 74303.6i) q^{88} +(66406.6 - 66406.6i) q^{89} +(-28426.8 + 3380.41i) q^{90} +(-26091.6 - 10807.5i) q^{91} +(-23989.7 + 11802.4i) q^{92} +(22465.6 - 7885.74i) q^{93} +(15303.0 - 92418.2i) q^{94} -22930.0 q^{95} +(-41929.8 + 79972.6i) q^{96} -133261. q^{97} +(-6149.02 + 37135.3i) q^{98} +(-123778. + 35922.2i) 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
$3$	5.16293	+	14.7086i	0.331202	+	0.943560i
$3$	5.16293	+	14.7086i	0.331202	+	0.943560i
$4$	30.2921	+	10.3146i	0.946627	+	0.322331i
$5$	19.2402	+	7.96957i	0.344180	+	0.142564i	0.548076	−	0.836429i	$-0.315360\pi$
$5$	19.2402	+	7.96957i	0.344180	+	0.142564i	−0.203896	+	0.978993i	$0.565360\pi$
$6$	15.2213	+	86.8580i	0.172613	+	0.984990i
$7$	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
$9$	−189.688	+	151.879i	−0.780610	+	0.625018i
$10$	100.012	+	62.2571i	0.316267	+	0.196874i
$11$	490.018	+	202.972i	1.22104	+	0.505772i	0.897741	−	0.440525i	$-0.145208\pi$
$11$	490.018	+	202.972i	1.22104	+	0.505772i	0.323300	+	0.946296i	$0.395208\pi$
$12$	4.68228	+	498.809i	0.00938652	+	0.999956i
$13$	−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	$-0.635623\pi$
$17$	−984.954			−0.826597			−0.413298	+	0.910596i	$0.635623\pi$
$18$	−1198.98	+	672.327i	−0.872227	+	0.489102i
$19$	−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
$21$	1415.84	+	680.126i	0.700592	+	0.336544i
$22$	2547.16	+	1585.59i	1.12202	+	0.698447i
$23$	−590.784	+	590.784i	−0.232867	+	0.232867i	−0.813889	−	0.581021i	$-0.802653\pi$
$23$	−590.784	+	590.784i	−0.232867	+	0.232867i	0.581021	+	0.813889i	$0.302653\pi$
$24$	−434.820	+	2788.11i	−0.154092	+	0.988056i
$25$	−1903.04	−	1903.04i	−0.608971	−	0.608971i
$26$	−359.300	−	1544.24i	−0.104237	−	0.448004i
$27$	−3213.29	−	2005.91i	−0.848282	−	0.529545i
$28$	2893.20	−	1423.38i	0.697403	−	0.343105i
$29$	2251.12	+	5434.69i	0.497055	+	1.20000i	0.951062	+	0.308999i	$0.0999939\pi$
$29$	2251.12	+	5434.69i	0.497055	+	1.20000i	−0.454008	+	0.890998i	$0.650006\pi$
$30$	−399.359	+	1792.48i	−0.0810141	+	0.363622i
$31$		−	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
$36$	−7312.62	+	2644.19i	−0.940409	+	0.340044i
$37$	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
$39$	3254.93	−	2914.52i	0.342673	−	0.306835i
$40$	2387.43	+	2917.48i	0.235928	+	0.288309i
$41$	3960.89	+	3960.89i	0.367987	+	0.367987i	0.866743	−	0.498755i	$-0.166209\pi$
$41$	3960.89	+	3960.89i	0.367987	+	0.367987i	−0.498755	+	0.866743i	$0.666209\pi$
$42$	7273.09	+	5104.07i	0.636203	+	0.446471i
$43$	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
$45$	−4860.06	+	1410.46i	−0.357775	+	0.103832i
$46$	−3843.03	+	2751.14i	−0.267780	+	0.191698i
$47$		−	16559.8i		−	1.09348i	−0.837302	−	0.546741i	$-0.815868\pi$
$47$		−	16559.8i		−	1.09348i	0.837302	−	0.546741i	$-0.184132\pi$
$48$	−5003.17	+	15158.2i	−0.313431	+	0.949611i
$49$			6654.04i			0.395909i
$50$	−8861.98	−	12379.2i	−0.501309	−	0.700272i
$51$	−5085.25	−	14487.3i	−0.273771	−	0.779944i
$52$	−578.165	−	8950.23i	−0.0296513	−	0.459014i
$53$	5467.12	−	13198.8i	0.267343	−	0.645423i	−0.732014	−	0.681290i	$-0.761419\pi$
$53$	5467.12	−	13198.8i	0.267343	−	0.645423i	0.999357	+	0.0358670i	$0.0114193\pi$
$54$	−16079.3	−	14164.1i	−0.750380	−	0.661006i
$55$	7810.47	+	7810.47i	0.348153	+	0.348153i
$56$	17461.9	−	5270.09i	0.744084	−	0.224568i
$57$	−11449.5	−	12786.8i	−0.466766	−	0.521284i
$58$	7540.99	+	32410.6i	0.294346	+	1.26508i
$59$	−13143.6	+	31731.4i	−0.491567	+	1.18675i	0.462355	+	0.886695i	$0.347005\pi$
$59$	−13143.6	+	31731.4i	−0.491567	+	1.18675i	−0.953922	+	0.300053i	$0.902995\pi$
$60$	−3885.20	+	9634.52i	−0.139327	+	0.345503i
$61$	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
$66$	−10171.0	+	45651.5i	−0.287412	+	1.29002i
$67$	−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
$69$	−11739.8	−	5639.45i	−0.296851	−	0.142598i
$70$	11561.6	−	2690.05i	0.282016	−	0.0656169i
$71$	−17083.0	−	17083.0i	−0.402177	−	0.402177i	0.476823	−	0.879000i	$-0.341788\pi$
$71$	−17083.0	−	17083.0i	−0.402177	−	0.402177i	−0.879000	+	0.476823i	$0.841788\pi$
$72$	−43254.3	+	7999.22i	−0.983326	+	0.181851i
$73$	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
$75$	18165.8	−	37816.3i	0.372908	−	0.776294i
$76$	−35160.4	+	2271.28i	−0.698264	+	0.0451063i
$77$	49375.1	−	20451.9i	0.949034	−	0.393103i
$78$	20858.6	−	13257.6i	0.388195	−	0.246734i
$79$	−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	$-0.902160\pi$
$83$	−30948.2	−	74715.6i	−0.493106	−	1.19046i	0.460025	−	0.887906i	$-0.347840\pi$
$84$	35873.4	+	35206.2i	0.554721	+	0.544404i
$85$	−18950.8	−	7849.66i	−0.284498	−	0.117843i
$86$	49527.7	−	79563.5i	0.722108	−	1.16003i
$87$	−68314.6	+	61169.9i	−0.967643	+	0.866443i
$88$	60803.9	+	74303.6i	0.836999	+	1.02283i
$89$	66406.6	−	66406.6i	0.888662	−	0.888662i	−0.105733	−	0.994395i	$-0.533719\pi$
$89$	66406.6	−	66406.6i	0.888662	−	0.888662i	0.994395	+	0.105733i	$0.0337188\pi$
$90$	−28426.8	+	3380.41i	−0.369931	+	0.0439909i
$91$	−26091.6	−	10807.5i	−0.330291	−	0.136811i
$92$	−23989.7	+	11802.4i	−0.295499	+	0.145378i
$93$	22465.6	−	7885.74i	0.269346	−	0.0945442i
$94$	15303.0	−	92418.2i	0.178631	−	1.07879i
$95$	−22930.0			−0.260672
$96$	−41929.8	+	79972.6i	−0.464349	+	0.885652i
$97$	−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
$99$	−123778.	+	35922.2i	−1.26927	+	0.368363i
$100$	−38017.8	−	77275.9i	−0.380178	−	0.772759i
$101$	155459.	+	64393.1i	1.51639	+	0.628111i	0.976865	−	0.213857i	$-0.0686026\pi$
$101$	155459.	+	64393.1i	1.51639	+	0.628111i	0.539528	+	0.841967i	$0.318603\pi$
$102$	−14992.3	−	85551.2i	−0.142682	−	0.814189i
$103$	−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
$105$	21820.8	+	24369.4i	0.193151	+	0.215711i
$106$	42708.3	−	68608.5i	0.369188	−	0.593080i
$107$	328.422	+	136.037i	0.00277314	+	0.00114867i	0.384070	−	0.923304i	$-0.374522\pi$
$107$	328.422	+	136.037i	0.00277314	+	0.00114867i	−0.381296	+	0.924453i	$0.624522\pi$
$108$	−76647.0	−	93907.0i	−0.632318	−	0.774709i
$109$	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	$-0.439963\pi$
$113$	50900.2			0.374993			0.187497	+	0.982265i	$0.439963\pi$
$114$	−52081.7	−	81941.8i	−0.375339	−	0.590532i
$115$	−16075.1	+	6658.53i	−0.113347	+	0.0469498i
$116$	12134.5	+	187848.i	0.0837295	+	1.29617i
$117$	59673.6	+	32828.2i	0.403011	+	0.221708i
$118$	−102675.	+	164942.i	−0.678831	+	1.09050i
$119$	−70177.4	+	70177.4i	−0.454287	+	0.454287i
$120$	−30586.1	+	50178.6i	−0.193897	+	0.318101i
$121$	85039.6	+	85039.6i	0.528029	+	0.528029i
$122$	30238.5	−	7035.63i	0.183934	−	0.0427960i
$123$	−37809.5	+	78709.1i	−0.225340	+	0.469096i
$124$	15754.3	−	46267.4i	0.0920119	−	0.270222i
$125$	−46353.4	−	111907.i	−0.265342	−	0.640593i
$126$	−37523.5	+	133329.i	−0.210560	+	0.748168i
$127$			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	−0.656602	−	0.754237i	$-0.728007\pi$
$131$	−115407.	+	47803.3i	−0.587564	+	0.243377i	0.0690385	+	0.997614i	$0.478007\pi$
$132$	−98949.8	+	245376.i	−0.494288	+	1.22573i
$133$	−42456.5	+	102499.i	−0.208120	+	0.502447i
$134$	−61280.6	−	263379.i	−0.294823	−	1.26712i
$135$	−45838.2	−	64202.8i	−0.216468	−	0.303193i
$136$	−157124.	−	84270.1i	−0.728442	−	0.390684i
$137$	221372.	+	221372.i	1.00768	+	1.00768i	0.999970	+	0.00770545i	$0.00245274\pi$
$137$	221372.	+	221372.i	1.00768	+	1.00768i	0.00770545	+	0.999970i	$0.497547\pi$
$138$	−60306.8	−	42321.8i	−0.269568	−	0.189176i
$139$	−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
$141$	243573.	−	85497.4i	1.03177	−	0.362164i
$142$	−79551.2	−	111124.i	−0.331075	−	0.462474i
$143$		−	148657.i		−	0.607918i
$144$	−248788.	+	4671.13i	−0.999824	+	0.0187722i
$145$			122505.i			0.483877i
$146$	101289.	−	72510.2i	0.393258	−	0.281525i
$147$	−97871.8	+	34354.3i	−0.373563	+	0.131126i
$148$	272430.	−	310057.i	1.02235	−	1.16356i
$149$	−196274.	+	473846.i	−0.724263	+	1.74852i	−0.0634364	+	0.997986i	$0.520206\pi$
$149$	−196274.	+	473846.i	−0.724263	+	1.74852i	−0.660826	+	0.750539i	$0.729794\pi$
$150$	136327.	−	194261.i	0.494714	−	0.704947i
$151$	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
$153$	186834.	−	149594.i	0.645250	−	0.516638i
$154$	294456.	−	68511.2i	1.00050	−	0.232788i
$155$	12172.5	−	29387.1i	0.0406960	−	0.0982488i
$156$	128661.	−	54713.4i	0.423286	−	0.180004i
$157$	−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
$162$	125319.	−	309632.i	0.375171	−	0.926955i
$163$	−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
$165$	−74556.4	+	155206.i	−0.213194	+	0.443812i
$166$	−103673.	−	445577.i	−0.292008	−	1.25502i
$167$	−82057.2	−	82057.2i	−0.227680	−	0.227680i	0.584043	−	0.811723i	$-0.301470\pi$
$167$	−82057.2	−	82057.2i	−0.227680	−	0.227680i	−0.811723	+	0.584043i	$0.801470\pi$
$168$	167671.	+	229632.i	0.458336	+	0.627710i
$169$	206997.	−	206997.i	0.557502	−	0.557502i
$170$	−98507.7	−	61320.4i	−0.261425	−	0.162736i
$171$	128963.	−	234424.i	0.337269	−	0.613072i
$172$	349932.	−	398264.i	0.901910	−	1.02648i
$173$	215040.	−	89072.3i	0.546265	−	0.226270i	−0.0924453	−	0.995718i	$-0.529468\pi$
$173$	215040.	−	89072.3i	0.546265	−	0.226270i	0.638710	+	0.769447i	$0.279468\pi$
$174$	−437782.	+	278251.i	−1.09619	+	0.696729i
$175$	−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	$-0.821870\pi$
$179$	−267319.	−	645366.i	−0.623588	−	1.50548i	0.223873	−	0.974618i	$-0.428130\pi$
$180$	−161770.	−	7403.68i	−0.372148	−	0.0170320i
$181$	−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
$183$	57070.6	+	63736.4i	0.125975	+	0.140689i
$184$	−144790.	+	43698.4i	−0.315278	+	0.0951526i
$185$	189935.	−	189935.i	0.408015	−	0.408015i
$186$	132665.	−	23248.7i	0.281173	−	0.0492738i
$187$	−482645.	−	199918.i	−1.00931	−	0.418069i
$188$	170808.	−	501632.i	0.352463	−	1.03512i
$189$	−371865.	+	86024.8i	−0.757235	+	0.175174i
$190$	−127969.	−	21189.7i	−0.257170	−	0.0425833i
$191$	−648066.			−1.28539			−0.642696	−	0.766121i	$-0.722184\pi$
$191$	−648066.			−1.28539			−0.642696	+	0.766121i	$0.722184\pi$
$192$	−307907.	+	407569.i	−0.602792	+	0.797899i
$193$	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
$195$	85853.1	−	30135.6i	0.161685	−	0.0567536i
$196$	−68633.7	+	201564.i	−0.127614	+	0.374778i
$197$	−98689.9	−	40878.7i	−0.181179	−	0.0750467i	0.290250	−	0.956951i	$-0.406262\pi$
$197$	−98689.9	−	40878.7i	−0.181179	−	0.0750467i	−0.471429	+	0.881904i	$0.656262\pi$
$198$	−723984.	+	86093.5i	−1.31240	+	0.156066i
$199$	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
$201$	555147.	−	497087.i	0.969209	−	0.867845i
$202$	808088.	+	503029.i	1.39341	+	0.867391i
$203$	547610.	+	226828.i	0.932677	+	0.386328i
$204$	−4611.83	−	491304.i	−0.00775886	−	0.826560i
$205$	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
$210$	99258.8	+	156167.i	0.155318	+	0.244366i
$211$	−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
$213$	163069.	−	339465.i	0.246276	−	0.512680i
$214$	1707.16	+	1062.70i	0.00254824	+	0.00158626i
$215$	243969.	−	243969.i	0.359948	−	0.359948i
$216$	−340976.	−	594912.i	−0.497267	−	0.867597i
$217$	−108825.	−	108825.i	−0.156884	−	0.156884i
$218$	58623.0	+	251957.i	0.0835462	+	0.359075i
$219$	309419.	+	148636.i	0.435950	+	0.209418i
$220$	156033.	+	317157.i	0.217351	+	0.441792i
$221$	105644.	+	255047.i	0.145500	+	0.351268i
$222$	1.11016e6	+	247340.i	1.51182	+	0.336830i
$223$			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	−0.253545	−	0.967324i	$-0.581597\pi$
$227$	195001.	−	80772.2i	0.251173	−	0.104039i	0.504718	+	0.863284i	$0.331597\pi$
$228$	−214938.	−	505435.i	−0.273827	−	0.643914i
$229$	−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
$231$	555740.	+	620650.i	0.685238	+	0.765273i
$232$	−105869.	+	1.05956e6i	−0.129137	+	1.29243i
$233$	−205696.	−	205696.i	−0.248219	−	0.248219i	0.572020	−	0.820240i	$-0.306160\pi$
$233$	−205696.	−	205696.i	−0.248219	−	0.248219i	−0.820240	+	0.572020i	$0.806160\pi$
$234$	302693.	+	238354.i	0.361379	+	0.284566i
$235$	131975.	−	318615.i	0.155891	−	0.376355i
$236$	−725441.	+	825638.i	−0.847857	+	0.964961i
$237$	−146895.	−	418488.i	−0.169877	−	0.483963i
$238$	−456502.	+	326799.i	−0.522396	+	0.373972i
$239$		−	4114.74i		−	0.00465959i	−0.999997	−	0.00232979i	$-0.999258\pi$
$239$		−	4114.74i		−	0.00465959i	0.999997	−	0.00232979i	$-0.000741597\pi$
$240$	−217067.	+	251775.i	−0.243257	+	0.282153i
$241$		−	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
$243$	914180.	−	107534.i	0.993153	−	0.116824i
$244$	175259.	−	11321.3i	0.188454	−	0.0121737i
$245$	−53029.8	+	128025.i	−0.0564423	+	0.136264i
$246$	−283745.	+	404325.i	−0.298944	+	0.425983i
$247$	218213.	+	218213.i	0.227582	+	0.227582i
$248$	130678.	−	243653.i	0.134919	−	0.251561i
$249$	939181.	−	840958.i	0.959955	−	0.859559i
$250$	−155278.	−	667373.i	−0.157131	−	0.675334i
$251$	−723299.	+	1.74620e6i	−0.724659	+	1.74948i	−0.0650387	+	0.997883i	$0.520717\pi$
$251$	−723299.	+	1.74620e6i	−0.724659	+	1.74948i	−0.659620	+	0.751599i	$0.729283\pi$
$252$	−332624.	+	709417.i	−0.329953	+	0.703721i
$253$	−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	$0.138660\pi$
$257$			893595.i			0.843933i	−0.906611	+	0.421967i	$0.861340\pi$
$258$	1.42598e6	+	317705.i	1.33372	+	0.297149i
$259$	−497349.	−	1.20071e6i	−0.460693	−	1.11221i
$260$	60205.4	−	176812.i	0.0552335	−	0.162211i
$261$	−1.25243e6	−	688998.i	−1.13803	−	0.626061i
$262$	−688247.	+	160135.i	−0.619429	+	0.144123i
$263$	537968.	+	537968.i	0.479587	+	0.479587i	0.904999	−	0.425413i	$-0.139871\pi$
$263$	537968.	+	537968.i	0.479587	+	0.479587i	−0.425413	+	0.904999i	$0.639871\pi$
$264$	−778978.	+	1.27797e6i	−0.687884	+	1.12852i
$265$	210377.	−	210377.i	0.184028	−	0.184028i
$266$	−331663.	+	532799.i	−0.287404	+	0.461699i
$267$	1.31960e6	+	633898.i	1.13283	+	0.544179i
$268$	−98609.3	−	1.52651e6i	−0.0838650	−	1.29826i
$269$	−262232.	+	108620.i	−0.220955	+	0.0915227i	−0.490415	−	0.871489i	$-0.663155\pi$
$269$	−262232.	+	108620.i	−0.220955	+	0.0915227i	0.269460	+	0.963012i	$0.413155\pi$
$270$	−196487.	−	400666.i	−0.164030	−	0.334482i
$271$	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
$276$	−297454.	−	291922.i	−0.235043	−	0.230671i
$277$	−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
$279$	231977.	+	289725.i	0.178416	+	0.222831i
$280$	377972.	+	37766.1i	0.288114	+	0.0287877i
$281$	−857618.	+	857618.i	−0.647930	+	0.647930i	−0.952492	−	0.304563i	$-0.901490\pi$
$281$	−857618.	+	857618.i	−0.647930	+	0.647930i	0.304563	+	0.952492i	$0.401490\pi$
$282$	1.43835e6	−	252063.i	1.07707	−	0.188749i
$283$	−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
$285$	−118386.	−	337268.i	−0.0863351	−	0.245959i
$286$	137374.	−	829633.i	0.0993094	−	0.599751i
$287$	564422.			0.404482
$288$	−1.39277e6	−	203837.i	−0.989459	−	0.144811i
$289$	−449722.			−0.316738
$290$	−113208.	+	683685.i	−0.0790461	+	0.477377i
$291$	−688020.	−	1.96009e6i	−0.476287	−	1.35689i
$292$	632284.	−	311068.i	0.433966	−	0.213500i
$293$	−1.23933e6	−	513346.i	−0.843368	−	0.349334i	−0.0811872	−	0.996699i	$-0.525871\pi$
$293$	−1.23933e6	−	513346.i	−0.843368	−	0.349334i	−0.762181	+	0.647365i	$0.775871\pi$
$294$	−577956.	+	101283.i	−0.389966	+	0.0683391i
$295$	−505771.	+	505771.i	−0.338375	+	0.338375i
$296$	1.80692e6	−	1.47863e6i	1.19870	−	0.980914i
$297$	−1.16742e6	−	1.63514e6i	−0.767958	−	1.07563i
$298$	−1.53326e6	+	2.46309e6i	−1.00017	+	1.60672i
$299$	216345.	+	89613.1i	0.139949	+	0.0579687i
$300$	940340.	−	958161.i	0.603228	−	0.614661i
$301$	−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
$306$	1.18094e6	−	662211.i	0.720980	−	0.404290i
$307$	−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
$309$	−1.42050e6	−	682365.i	−0.846340	−	0.406556i
$310$	95089.9	−	152757.i	0.0561992	−	0.0902809i
$311$	2.24542e6	−	2.24542e6i	1.31642	−	1.31642i	0.399839	−	0.916585i	$-0.369066\pi$
$311$	2.24542e6	−	2.24542e6i	1.31642	−	1.31642i	0.916585	−	0.399839i	$-0.130934\pi$
$312$	768598.	−	186452.i	0.447006	−	0.108438i
$313$	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
$315$	−245782.	+	446772.i	−0.139564	+	0.253693i
$316$	−861864.	−	293469.i	−0.485536	−	0.165327i
$317$	1.25991e6	+	3.04168e6i	0.704191	+	1.70007i	0.714030	+	0.700115i	$0.246868\pi$
$317$	1.25991e6	+	3.04168e6i	0.704191	+	1.70007i	−0.00983992	+	0.999952i	$0.503132\pi$
$318$	1.22964e6	+	273960.i	0.681882	+	0.151922i
$319$			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
$324$	985521.	−	1.61221e6i	0.521559	−	0.853215i
$325$	−288662.	+	696892.i	−0.151594	+	0.365980i
$326$	−99298.2	−	426775.i	−0.0517485	−	0.222411i
$327$	−531071.	+	475530.i	−0.274652	+	0.245928i
$328$	292974.	+	970740.i	0.150364	+	0.498217i
$329$	−1.17988e6	−	1.17988e6i	−0.600963	−	0.600963i
$330$	−559516.	+	797287.i	−0.282831	+	0.403023i
$331$	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
$333$	873559.	+	3.01004e6i	0.431700	+	1.48752i
$334$	−382121.	−	533779.i	−0.187428	−	0.261816i
$335$		−	995519.i		−	0.484660i
$336$	723543.	+	1.43649e6i	0.349636	+	0.694151i
$337$			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
$339$	262794.	+	748672.i	0.124199	+	0.353828i
$340$	−493092.	−	433252.i	−0.231329	−	0.203256i
$341$	310015.	−	748442.i	0.144376	−	0.348556i
$342$	936358.	−	1.18911e6i	0.432889	−	0.549740i
$343$	1.67159e6	+	1.67159e6i	0.767173	+	0.767173i
$344$	2.32096e6	−	1.89929e6i	1.05748	−	0.865355i
$345$	−180933.	−	202066.i	−0.0818407	−	0.0913996i
$346$	1.28242e6	−	298382.i	0.575890	−	0.133993i
$347$	1.55891e6	−	3.76354e6i	0.695019	−	1.67793i	−0.0393948	−	0.999224i	$-0.512543\pi$
$347$	1.55891e6	−	3.76354e6i	0.695019	−	1.67793i	0.734414	−	0.678702i	$-0.237457\pi$
$348$	−2.70033e6	+	1.14833e6i	−1.19528	+	0.508297i
$349$	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	$0.224016\pi$
$353$			3.02994e6i			1.29419i	−0.762410	+	0.647094i	$0.775984\pi$
$354$	−2.95618e6	−	658630.i	−1.25379	−	0.279340i
$355$	−192537.	−	464824.i	−0.0810853	−	0.195757i
$356$	2.69655e6	−	1.32664e6i	1.12767	−	0.554788i
$357$	−1.39454e6	−	669893.i	−0.579108	−	0.278186i
$358$	−895488.	−	3.84873e6i	−0.369277	−	1.58712i
$359$	−192524.	−	192524.i	−0.0788406	−	0.0788406i	0.666587	−	0.745427i	$-0.267755\pi$
$359$	−192524.	−	192524.i	−0.0788406	−	0.0788406i	−0.745427	+	0.666587i	$0.767755\pi$
$360$	−895973.	−	190811.i	−0.364367	−	0.0775974i
$361$	−893630.	+	893630.i	−0.360902	+	0.360902i
$362$	−2.95618e6	−	1.84020e6i	−1.18566	−	0.738063i
$363$	−811764.	+	1.68987e6i	−0.323343	+	0.673112i
$364$	−678892.	−	596505.i	−0.268564	−	0.235972i
$365$	423683.	−	175495.i	0.166460	−	0.0689498i
$366$	259604.	+	408443.i	0.101300	+	0.159378i
$367$	−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
$372$	761868.	−	7151.60i	0.285445	−	0.00267945i
$373$	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
$375$	1.40668e6	−	1.25956e6i	0.516556	−	0.462532i
$376$	1.41682e6	−	2.64169e6i	0.516825	−	0.963636i
$377$	1.16582e6	−	1.16582e6i	0.422454	−	0.422454i
$378$	−2.15482e6	+	136451.i	−0.775680	+	0.0491187i
$379$	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
$381$	−3.10270e6	+	1.08909e6i	−1.09503	+	0.384372i
$382$	−3.61676e6	−	598880.i	−1.26812	−	0.209982i
$383$	−4.73671e6			−1.64998			−0.824992	−	0.565145i	$-0.808820\pi$
$383$	−4.73671e6			−1.64998			−0.824992	+	0.565145i	$0.808820\pi$
$384$	−2.09503e6	+	1.99005e6i	−0.725039	+	0.688708i
$385$	1.11298e6			0.382681
$386$	3.96169e6	+	655993.i	1.35335	+	0.224094i
$387$	1.12208e6	+	3.86636e6i	0.380842	+	1.31227i
$388$	−4.03676e6	−	1.37454e6i	−1.36130	−	0.463529i
$389$	−3.30911e6	−	1.37068e6i	−1.10876	−	0.459263i	−0.248249	−	0.968696i	$-0.579855\pi$
$389$	−3.30911e6	−	1.37068e6i	−1.10876	−	0.459263i	−0.860510	+	0.509433i	$0.829855\pi$
$390$	506983.	−	88845.6i	0.168784	−	0.0295784i
$391$	581895.	−	581895.i	0.192488	−	0.192488i
$392$	−569302.	+	1.06148e6i	−0.187123	+	0.348896i
$393$	−1.29896e6	−	1.45068e6i	−0.424243	−	0.473794i
$394$	−512999.	−	319338.i	−0.166485	−	0.103636i
$395$	−547420.	−	226749.i	−0.176534	−	0.0731227i
$396$	−4.12001e6	−	188560.i	−1.32026	−	0.0604242i
$397$	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	$-0.386845\pi$
$401$	2.24145e6			0.696095			0.348048	+	0.937477i	$0.386845\pi$
$402$	3.55756e6	−	2.26116e6i	1.09796	−	0.697857i
$403$	−395503.	+	163823.i	−0.121307	+	0.0502471i
$404$	4.04498e6	+	3.55410e6i	1.23300	+	1.08337i
$405$	707676.	−	1.00569e6i	0.214386	−	0.304668i
$406$	2.84652e6	+	1.77194e6i	0.857038	+	0.533500i
$407$	4.83734e6	−	4.83734e6i	1.44751	−	1.44751i
$408$	428278.	−	2.74616e6i	0.127372	−	0.816724i
$409$	−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
$411$	−2.11315e6	+	4.39901e6i	−0.617058	+	1.28455i
$412$	−2.90272e6	+	1.42807e6i	−0.842486	+	0.414482i
$413$	1.32437e6	+	3.19731e6i	0.382062	+	0.922380i
$414$	311136.	−	1.10554e6i	0.0892173	−	0.317009i
$415$		−	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	−0.223039	−	0.974810i	$-0.571598\pi$
$419$	1.10880e6	−	459279.i	0.308544	−	0.127803i	0.531582	+	0.847007i	$0.321598\pi$
$420$	409635.	+	963272.i	0.113312	+	0.266456i
$421$	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
$423$	2.51510e6	+	3.14121e6i	0.683446	+	0.853583i
$424$	2.00139e6	−	1.63777e6i	0.540651	−	0.442424i
$425$	1.87440e6	+	1.87440e6i	0.503374	+	0.503374i
$426$	1.22377e6	−	1.74382e6i	0.326719	−	0.465561i
$427$	211627.	−	510912.i	0.0561695	−	0.135605i
$428$	8545.41	+	7508.37i	0.00225488	+	0.00198124i
$429$	2.18654e6	−	767505.i	0.573607	−	0.201344i
$430$	1.58701e6	−	1.13611e6i	0.413913	−	0.296311i
$431$			5.81040e6i			1.50665i	0.657647	+	0.753326i	$0.271552\pi$
$431$			5.81040e6i			1.50665i	−0.657647	+	0.753326i	$0.728448\pi$
$432$	−1.35318e6	−	3.63522e6i	−0.348857	−	0.937176i
$433$		−	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
$435$	−1.80189e6	+	632487.i	−0.456567	+	0.160261i
$436$	94332.8	+	1.46031e6i	0.0237655	+	0.367899i
$437$	352039.	−	849898.i	0.0881835	−	0.212894i
$438$	1.58947e6	+	1.11545e6i	0.395884	+	0.277821i
$439$	−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
$441$	−1.01061e6	−	1.26219e6i	−0.247450	−	0.309050i
$442$	353894.	+	1.52101e6i	0.0861623	+	0.370318i
$443$	−1.97181e6	+	4.76038e6i	−0.477371	+	1.15248i	0.483466	+	0.875363i	$0.339378\pi$
$443$	−1.97181e6	+	4.76038e6i	−0.477371	+	1.15248i	−0.960837	+	0.277113i	$0.910622\pi$
$444$	5.96706e6	+	2.40627e6i	1.43649	+	0.579277i
$445$	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	$0.264615\pi$
$449$			6.31222e6i			1.47763i	−0.673908	+	0.738816i	$0.735385\pi$
$450$	3.56116e6	+	1.00223e6i	0.829010	+	0.233312i
$451$	1.13696e6	+	2.74486e6i	0.263210	+	0.635445i
$452$	1.54187e6	+	525015.i	0.354979	+	0.120872i
$453$	−2.64222e6	+	5.50038e6i	−0.604955	+	1.25935i
$454$	1.16292e6	−	270577.i	0.264795	−	0.0616101i
$455$	−415877.	−	415877.i	−0.0941752	−	0.0941752i
$456$	−732466.	−	3.01939e6i	−0.164959	−	0.679997i
$457$	−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
$459$	3.16494e6	+	1.97573e6i	0.701187	+	0.437720i
$460$	−555628.	+	35892.4i	−0.122431	+	0.00790875i
$461$	8.22834e6	−	3.40829e6i	1.80327	−	0.746938i	0.818161	−	0.574989i	$-0.194994\pi$
$461$	8.22834e6	−	3.40829e6i	1.80327	−	0.746938i	0.985106	−	0.171949i	$-0.0550064\pi$
$462$	2.52796e6	+	3.97732e6i	0.551018	+	0.866934i
$463$	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	0.752005	−	0.659157i	$-0.229087\pi$
$467$	−1.15862e6	−	2.79715e6i	−0.245837	−	0.593503i	−0.997842	+	0.0656537i	$0.979087\pi$
$468$	1.46903e6	+	1.60994e6i	0.310038	+	0.339778i
$469$	−4.45006e6	−	1.84328e6i	−0.934187	−	0.386953i
$470$	1.03097e6	−	1.65619e6i	0.215278	−	0.345832i
$471$	−5.39309e6	−	6.02300e6i	−1.12017	−	1.25101i
$472$	−4.81156e6	+	3.93739e6i	−0.994103	+	0.813492i
$473$	6.21351e6	−	6.21351e6i	1.27698	−	1.27698i
$474$	−433074.	−	2.47127e6i	−0.0885353	−	0.505212i
$475$	2.73770e6	+	1.13399e6i	0.556738	+	0.230609i
$476$	−2.84967e6	+	1.40197e6i	−0.576471	+	0.283609i
$477$	967577.	+	3.33400e6i	0.194711	+	0.670918i
$478$	3802.44	−	22963.8i	0.000761190	−	0.00459699i
$479$	−9.56631e6			−1.90505			−0.952524	−	0.304464i	$-0.901523\pi$
$479$	−9.56631e6			−1.90505			−0.952524	+	0.304464i	$0.901523\pi$
$480$	−1.44409e6	+	1.20453e6i	−0.286082	+	0.238624i
$481$	−3.61504e6			−0.712444
$482$	1.08768e6	−	6.56872e6i	0.213247	−	1.28784i
$483$	−1.23826e6	+	434647.i	−0.241515	+	0.0847751i
$484$	1.69888e6	+	3.45318e6i	0.329647	+	0.670047i
$485$	−2.56398e6	−	1.06204e6i	−0.494949	−	0.205015i
$486$	5.20129e6	+	244662.i	0.998896	+	0.0469868i
$487$	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
$489$	899552.	−	805473.i	0.170119	−	0.152328i
$490$	−414261.	+	665487.i	−0.0779442	+	0.125213i
$491$	−5.38410e6	−	2.23017e6i	−1.00788	−	0.417478i	−0.183200	−	0.983076i	$-0.558646\pi$
$491$	−5.38410e6	−	2.23017e6i	−1.00788	−	0.417478i	−0.824682	+	0.565597i	$0.808646\pi$
$492$	−1.95718e6	+	1.99427e6i	−0.364517	+	0.371425i
$493$	−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
$498$	6.01857e6	−	3.82537e6i	1.08748	−	0.691194i
$499$	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
$501$	783294.	−	1.63061e6i	0.139422	−	0.290238i
$502$	−5.65030e6	+	9.07689e6i	−1.00072	+	1.60760i
$503$	−798097.	+	798097.i	−0.140649	+	0.140649i	−0.773925	−	0.633277i	$-0.781709\pi$
$503$	−798097.	+	798097.i	−0.140649	+	0.140649i	0.633277	+	0.773925i	$0.281709\pi$
$504$	−2.51190e6	+	3.65178e6i	−0.440480	+	0.640366i
$505$	2.47788e6	+	2.47788e6i	0.432366	+	0.432366i
$506$	−2.44156e6	+	568079.i	−0.423926	+	0.0986354i
$507$	4.11335e6	+	1.97593e6i	0.710683	+	0.341391i
$508$	−2.17580e6	+	6.38994e6i	−0.374076	+	1.09859i
$509$	4.17733e6	+	1.00850e7i	0.714669	+	1.72536i	0.687992	+	0.725718i	$0.258492\pi$
$509$	4.17733e6	+	1.00850e7i	0.714669	+	1.72536i	0.0266765	+	0.999644i	$0.491508\pi$
$510$	393350.	−	1.76551e6i	0.0669660	−	0.300569i
$511$		−	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
$516$	7.66461e6	+	3.09082e6i	1.26726	+	0.511033i
$517$	3.36119e6	−	8.11462e6i	0.553052	−	1.33519i
$518$	−1.66606e6	−	7.16059e6i	−0.272814	−	1.17253i
$519$	2.42037e6	+	2.70307e6i	0.394424	+	0.440492i
$520$	499391.	−	931129.i	0.0809902	−	0.151009i
$521$	−352651.	−	352651.i	−0.0569182	−	0.0569182i	0.678075	−	0.734993i	$-0.262815\pi$
$521$	−352651.	−	352651.i	−0.0569182	−	0.0569182i	−0.734993	+	0.678075i	$0.762815\pi$
$522$	−6.35293e6	−	5.00258e6i	−1.02047	−	0.803559i
$523$	−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
$525$	−1.40009e6	−	3.98870e6i	−0.221695	−	0.631586i
$526$	2.50519e6	+	3.49946e6i	0.394799	+	0.551489i
$527$			1.50440e6i			0.235958i
$528$	−5.52834e6	+	6.41231e6i	−0.862999	+	1.00099i
$529$			5.73829e6i			0.891545i
$530$	1.36850e6	−	979677.i	0.211619	−	0.151493i
$531$	−2.32616e6	−	8.01530e6i	−0.358017	−	1.23363i
$532$	−2.34333e6	+	2.66698e6i	−0.358967	+	0.408546i
$533$	600808.	−	1.45048e6i	0.0916047	−	0.221153i
$534$	6.77874e6	+	4.75715e6i	1.02872	+	0.721928i
$535$	5234.76	+	5234.76i	0.000790701	+	0.000790701i
$536$	860329.	−	8.61037e6i	0.129346	−	1.29452i
$537$	8.11231e6	−	7.26389e6i	1.21397	−	1.08701i
$538$	−1.56385e6	+	363864.i	−0.232938	+	0.0541979i
$539$	−1.35058e6	+	3.26060e6i	−0.200239	+	0.483421i
$540$	−726308.	−	2.41764e6i	−0.107186	−	0.356785i
$541$	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
$546$	541568.	−	2.43076e6i	0.0777448	−	0.348948i
$547$	−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
$549$	−642825.	+	1.16850e6i	−0.0910252	+	0.165462i
$550$	−1.82990e6	−	7.86476e6i	−0.257941	−	1.10861i
$551$	−4.57986e6	−	4.57986e6i	−0.642649	−	0.642649i
$552$	−1.39029e6	−	1.90405e6i	−0.194203	−	0.265969i
$553$	−2.02718e6	+	2.02718e6i	−0.281889	+	0.281889i
$554$	−518160.	−	322551.i	−0.0717281	−	0.0446503i
$555$	3.77431e6	+	1.81307e6i	0.520122	+	0.249851i
$556$	−2.00927e6	+	2.28679e6i	−0.275646	+	0.313717i
$557$	1.49448e6	−	619035.i	0.204105	−	0.0845429i	−0.278289	−	0.960497i	$-0.589767\pi$
$557$	1.49448e6	−	619035.i	0.204105	−	0.0845429i	0.482394	+	0.875954i	$0.339767\pi$
$558$	1.02690e6	+	1.83129e6i	0.139618	+	0.248984i
$559$	−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	$-0.928255\pi$
$563$	−3.33565e6	−	8.05297e6i	−0.443516	−	1.07074i	0.531190	−	0.847253i	$-0.321745\pi$
$564$	8.26019e6	−	77537.8i	1.09343	−	0.0102640i
$565$	979332.	+	405653.i	0.129065	+	0.0534605i
$566$	−9.53051e6	−	5.93267e6i	−1.25047	−	0.778412i
$567$	−3.18522e6	−	5.02549e6i	−0.416085	−	0.656479i
$568$	−1.26357e6	−	4.18672e6i	−0.164335	−	0.544506i
$569$	−23652.9	+	23652.9i	−0.00306269	+	0.00306269i	−0.708636	−	0.705574i	$-0.750689\pi$
$569$	−23652.9	+	23652.9i	−0.00306269	+	0.00306269i	0.705574	+	0.708636i	$0.250689\pi$
$570$	−349024.	−	1.99165e6i	−0.0449954	−	0.256759i
$571$	−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
$573$	−3.34592e6	−	9.53216e6i	−0.425725	−	1.21284i
$574$	3.14996e6	+	521585.i	0.399049	+	0.0660762i
$575$	2.24856e6			0.283619
$576$	−7.58449e6	−	2.42465e6i	−0.952511	−	0.304504i
$577$	−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
$579$	3.66501e6	+	1.04412e7i	0.454338	+	1.29436i
$580$	−1.26359e6	+	3.71094e6i	−0.155969	+	0.458051i
$581$	−7.52848e6	−	3.11840e6i	−0.925267	−	0.383258i
$582$	−2.02841e6	−	1.15748e7i	−0.248227	−	1.41647i
$583$	5.35797e6	−	5.35797e6i	0.652873	−	0.652873i
$584$	3.81615e6	−	1.15173e6i	0.463013	−	0.139740i
$585$	886508.	+	1.10719e6i	0.107101	+	0.133762i
$586$	−6.44213e6	−	4.01018e6i	−0.774971	−	0.482414i
$587$	9.77689e6	+	4.04972e6i	1.17113	+	0.485098i	0.881566	−	0.472060i	$-0.156489\pi$
$587$	9.77689e6	+	4.04972e6i	1.17113	+	0.485098i	0.289565	+	0.957158i	$0.406489\pi$
$588$	−3.31909e6	+	31156.1i	−0.395891	+	0.00371620i
$589$	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	$-0.553039\pi$
$593$	−2.84053e6			−0.331713			−0.165856	+	0.986150i	$0.553039\pi$
$594$	−5.00420e6	−	1.02043e7i	−0.581927	−	1.18664i
$595$	−1.90952e6	+	790947.i	−0.221121	+	0.0915915i
$596$	−1.08331e7	+	1.23293e7i	−1.24921	+	1.42175i
$597$	3.09190e6	+	1.48526e6i	0.355050	+	0.170556i
$598$	1.12458e6	+	700044.i	0.128599	+	0.0800520i
$599$	1.34624e6	−	1.34624e6i	0.153304	−	0.153304i	−0.626288	−	0.779592i	$-0.715426\pi$
$599$	1.34624e6	−	1.34624e6i	0.153304	−	0.153304i	0.779592	+	0.626288i	$0.215426\pi$
$600$	6.13335e6	−	4.47839e6i	0.695536	−	0.507860i
$601$	−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
$603$	1.01777e7	+	5.59902e6i	1.13987	+	0.627074i
$604$	5.52969e6	+	1.12398e7i	0.616749	+	1.25362i
$605$	958454.	+	2.31391e6i	0.106459	+	0.257015i
$606$	−3.22677e6	+	1.44830e7i	−0.356933	+	1.60205i
$607$		−	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
$612$	7.20260e6	−	2.60440e6i	0.777339	−	0.281080i
$613$	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
$615$	−1.35474e6	+	1.21306e6i	−0.144434	+	0.129328i
$616$	9.62633e6	+	961842.i	1.02214	+	0.102130i
$617$	−3.69874e6	−	3.69874e6i	−0.391148	−	0.391148i	0.483948	−	0.875097i	$-0.339202\pi$
$617$	−3.69874e6	−	3.69874e6i	−0.391148	−	0.391148i	−0.875097	+	0.483948i	$0.839202\pi$
$618$	−7.29703e6	−	5.12087e6i	−0.768555	−	0.539353i
$619$	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
$621$	3.08342e6	−	713298.i	0.320851	−	0.0742236i
$622$	1.46064e7	−	1.04564e7i	1.51379	−	1.08369i
$623$		−	9.46287e6i		−	0.976794i
$624$	4.46174e6	−	330301.i	0.458715	−	0.0339585i
$625$			5.88777e6i			0.602908i
$626$	2.08832e6	+	2.91715e6i	0.212991	+	0.297525i
$627$	−3.01509e6	−	8.58968e6i	−0.306289	−	0.872586i
$628$	−1.65617e7	+	1.06985e6i	−1.67574	+	0.108249i
$629$	−4.86162e6	+	1.17370e7i	−0.489953	+	1.18285i
$630$	−1.78454e6	+	2.26624e6i	−0.179133	+	0.227486i
$631$	−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
$633$	−4.60054e6	−	5.13789e6i	−0.456352	−	0.509654i
$634$	4.22054e6	+	1.81395e7i	0.417008	+	1.79227i
$635$	−1.68113e6	+	4.05862e6i	−0.165451	+	0.399433i
$636$	6.60927e6	+	2.66525e6i	0.647904	+	0.261273i
$637$	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	$0.148258\pi$
$641$			9.34386e6i			0.898217i	−0.893477	+	0.449108i	$0.851742\pi$
$642$	−6816.87	+	30596.7i	−0.000652750	+	0.00292979i
$643$	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
$645$	4.84806e6	+	2.32886e6i	0.458848	+	0.220417i
$646$	5.97517e6	−	1.39025e6i	0.563338	−	0.131072i
$647$	952781.	+	952781.i	0.0894813	+	0.0894813i	0.750431	−	0.660949i	$-0.229846\pi$
$647$	952781.	+	952781.i	0.0894813	+	0.0894813i	−0.660949	+	0.750431i	$0.729846\pi$
$648$	6.98991e6	−	8.08679e6i	0.653934	−	0.756552i
$649$	−1.28812e7	+	1.28812e7i	−1.20045	+	1.20045i
$650$	−2.25498e6	+	3.62251e6i	−0.209344	+	0.336299i
$651$	1.03881e6	−	2.16252e6i	0.0960690	−	0.199989i
$652$	−159785.	−	2.47354e6i	−0.0147203	−	0.227876i
$653$	873241.	−	361708.i	0.0801403	−	0.0331952i	−0.342253	−	0.939608i	$-0.611190\pi$
$653$	873241.	−	361708.i	0.0801403	−	0.0331952i	0.422393	+	0.906413i	$0.361190\pi$
$654$	−3.40327e6	+	2.16310e6i	−0.311138	+	0.197757i
$655$	−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	0.836248	−	0.548352i	$-0.184744\pi$
$659$	−1.59213e6	−	3.84373e6i	−0.142812	−	0.344778i	−0.979060	+	0.203573i	$0.934744\pi$
$660$	−3.85936e6	+	3.93250e6i	−0.344870	+	0.351406i
$661$	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
$663$	−3.20596e6	+	2.87067e6i	−0.283253	+	0.253629i
$664$	1.45548e6	−	1.45668e7i	0.128111	−	1.28216i
$665$	−1.63375e6	+	1.63375e6i	−0.143262	+	0.143262i
$666$	2.09363e6	+	1.76059e7i	0.182900	+	1.53806i
$667$	−4.54065e6	−	1.88080e6i	−0.395188	−	0.163692i
$668$	−1.63930e6	−	3.33207e6i	−0.142140	−	0.288917i
$669$	−2.19597e6	+	770816.i	−0.189697	+	0.0665864i
$670$	919962.	−	5.55585e6i	0.0791741	−	0.478150i
$671$	2.91092e6			0.249588
$672$	2.71053e6	+	8.68548e6i	0.231543	+	0.741943i
$673$	−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
$675$	2.29768e6	+	9.93233e6i	0.194102	+	0.839057i
$676$	8.40544e6	−	4.13527e6i	0.707447	−	0.348046i
$677$	−3.85507e6	−	1.59682e6i	−0.323266	−	0.133901i	0.215148	−	0.976581i	$-0.430977\pi$
$677$	−3.85507e6	−	1.59682e6i	−0.323266	−	0.133901i	−0.538415	+	0.842680i	$0.680977\pi$
$678$	774768.	+	4.42109e6i	0.0647287	+	0.369364i
$679$	−9.49480e6	+	9.49480e6i	−0.790335	+	0.790335i
$680$	−2.35151e6	−	2.87359e6i	−0.195018	−	0.238315i
$681$	2.19483e6	+	2.45118e6i	0.181356	+	0.202539i
$682$	2.42179e6	−	3.89046e6i	0.199377	−	0.320288i
$683$	1.41131e7	+	5.84583e6i	1.15763	+	0.479506i	0.877085	−	0.480335i	$-0.159485\pi$
$683$	1.41131e7	+	5.84583e6i	1.15763	+	0.479506i	0.280545	+	0.959841i	$0.409485\pi$
$684$	6.32455e6	−	5.77098e6i	0.516880	−	0.471638i
$685$	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
$690$	−823031.	−	1.29490e6i	−0.0658102	−	0.103541i
$691$	−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
$693$	−6.25967e6	+	1.13785e7i	−0.495129	+	0.900023i
$694$	1.21780e7	−	1.95632e7i	0.959789	−	1.54185i
$695$	−1.40084e6	+	1.40084e6i	−0.110009	+	0.110009i
$696$	−1.61314e7	+	3.91327e6i	−1.26226	+	0.306208i
$697$	−3.90129e6	−	3.90129e6i	−0.304177	−	0.304177i
$698$	1.07262e7	−	2.49568e6i	0.833313	−	0.193888i
$699$	1.96351e6	−	4.08750e6i	0.151999	−	0.316421i
$700$	−8.21462e6	−	2.79712e6i	−0.633639	−	0.215757i
$701$	−1.98754e6	−	4.79836e6i	−0.152764	−	0.368806i	0.828907	−	0.559386i	$-0.188963\pi$
$701$	−1.98754e6	−	4.79836e6i	−0.152764	−	0.368806i	−0.981672	+	0.190580i	$0.938963\pi$
$702$	−1.94308e6	+	5.68281e6i	−0.148815	+	0.435232i
$703$			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
$708$	−1.58894e7	−	6.40755e6i	−1.19131	−	0.480406i
$709$	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
$711$	5.39698e6	−	4.32125e6i	0.400384	−	0.320579i
$712$	1.62750e7	−	4.91189e6i	1.20316	−	0.363118i
$713$	902349.	+	902349.i	0.0664738	+	0.0664738i
$714$	−7.16366e6	−	5.02728e6i	−0.525884	−	0.369052i
$715$	1.18473e6	−	2.86019e6i	0.0866672	−	0.209233i
$716$	−1.44097e6	−	2.23068e7i	−0.105044	−	1.62613i
$717$	60522.2	−	21244.1i	0.00439660	−	0.00154327i
$718$	−896540.	−	1.25236e6i	−0.0649021	−	0.0906608i
$719$			2.28088e7i			1.64543i	0.568452	+	0.822716i	$0.307542\pi$
$719$			2.28088e7i			1.64543i	−0.568452	+	0.822716i	$0.692458\pi$
$720$	−4.82397e6	−	1.89286e6i	−0.346796	−	0.136078i
$721$			1.01864e7i			0.729763i
$722$	−5.81303e6	+	4.16142e6i	−0.415011	+	0.297097i
$723$	1.73122e7	−	6.07681e6i	1.23170	−	0.432345i
$724$	−1.47975e7	−	1.30017e7i	−1.04916	−	0.921837i
$725$	6.05845e6	−	1.46264e7i	0.428071	−	1.03346i
$726$	−6.09196e6	+	8.68079e6i	−0.428959	+	0.611248i
$727$	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
$729$	6.30153e6	+	1.28912e7i	0.439165	+	0.898407i
$730$	2.52669e6	−	587888.i	0.175487	−	0.0408307i
$731$	−6.24469e6	+	1.50760e7i	−0.432233	+	1.04350i
$732$	1.07137e6	+	2.51937e6i	0.0739030	+	0.173786i
$733$	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
$738$	−7.41202e6	−	2.08600e6i	−0.500952	−	0.140985i
$739$	−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
$741$	−2.08300e6	+	4.33624e6i	−0.139362	+	0.290113i
$742$	−1.84537e6	−	7.93125e6i	−0.123048	−	0.528850i
$743$	1.38605e7	+	1.38605e7i	0.921098	+	0.921098i	0.997107	−	0.0760092i	$-0.0242179\pi$
$743$	1.38605e7	+	1.38605e7i	0.921098	+	0.921098i	−0.0760092	+	0.997107i	$0.524218\pi$
$744$	4.25849e6	+	664133.i	0.282048	+	0.0439868i
$745$	−7.55270e6	+	7.55270e6i	−0.498553	+	0.498553i
$746$	1.78991e7	+	1.11421e7i	1.17757	+	0.733026i
$747$	1.72183e7	+	9.47227e6i	1.12898	+	0.621087i
$748$	−1.25582e7	−	1.10342e7i	−0.820682	−	0.721087i
$749$	33092.4	−	13707.3i	0.00215538	−	0.000892787i
$750$	9.01446e6	−	5.72954e6i	0.585176	−	0.371934i
$751$	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
$756$	−1.21519e7	−	1.22977e6i	−0.773283	−	0.0782562i
$757$	−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
$759$	−4.60806e6	−	5.14628e6i	−0.290345	−	0.324257i
$760$	−3.65788e6	−	1.96183e6i	−0.229718	−	0.123204i
$761$	8.86441e6	−	8.86441e6i	0.554866	−	0.554866i	−0.372975	−	0.927841i	$-0.621662\pi$
$761$	8.86441e6	−	8.86441e6i	0.554866	−	0.554866i	0.927841	+	0.372975i	$0.121662\pi$
$762$	−1.83222e7	+	3.21085e6i	−1.14312	+	0.200324i
$763$	4.25707e6	+	1.76334e6i	0.264728	+	0.109654i
$764$	−1.96312e7	−	6.68453e6i	−1.21679	−	0.414322i
$765$	4.78694e6	−	1.38924e6i	0.295736	−	0.0858271i
$766$	−2.64349e7	−	4.37721e6i	−1.62782	−	0.269541i
$767$	9.62635e6			0.590844
$768$	−1.35311e7	+	9.17016e6i	−0.827806	+	0.561014i
$769$	−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
$771$	−1.31436e7	+	4.61357e6i	−0.796301	+	0.279513i
$772$	2.15034e7	+	7.32202e6i	1.29857	+	0.442168i
$773$	−1.28767e7	−	5.33368e6i	−0.775094	−	0.321054i	−0.0401600	−	0.999193i	$-0.512787\pi$
$773$	−1.28767e7	−	5.33368e6i	−0.775094	−	0.321054i	−0.734934	+	0.678139i	$0.762787\pi$
$774$	2.68924e6	+	2.26145e7i	0.161353	+	1.35686i
$775$	−2.90665e6	+	2.90665e6i	−0.173836	+	0.173836i
$776$	−2.12584e7	−	1.14015e7i	−1.26729	−	0.679685i
$777$	1.50930e7	−	1.35145e7i	0.896856	−	0.803059i
$778$	−1.72010e7	−	1.07075e7i	−1.01884	−	0.634221i
$779$	−5.69811e6	−	2.36023e6i	−0.336424	−	0.139351i
$780$	2.91150e6	−	27330.1i	0.171349	−	0.00160844i
$781$	−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
$786$	−5.90874e6	−	9.29641e6i	−0.341145	−	0.536734i
$787$	−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
$789$	−5.13529e6	+	1.06903e7i	−0.293679	+	0.611359i
$790$	−2.84554e6	−	1.77133e6i	−0.162217	−	0.100979i
$791$	3.62661e6	−	3.62661e6i	0.206091	−	0.206091i
$792$	−2.28190e7	−	4.85964e6i	−1.29266	−	0.275291i
$793$	−1.08770e6	−	1.08770e6i	−0.0614221	−	0.0614221i
$794$	2.30143e6	+	9.89137e6i	0.129553	+	0.556808i
$795$	4.18053e6	+	2.00820e6i	0.234592	+	0.112691i
$796$	6.31816e6	−	3.10838e6i	0.353434	−	0.173881i
$797$	−1.03262e7	−	2.49296e7i	−0.575830	−	1.39018i	−0.896524	−	0.442994i	$-0.853916\pi$
$797$	−1.03262e7	−	2.49296e7i	−0.575830	−	1.39018i	0.320694	−	0.947183i	$-0.396084\pi$
$798$	−9.54910e6	−	2.12751e6i	−0.530830	−	0.118267i
$799$			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
$804$	2.19438e7	−	9.33168e6i	1.19721	−	0.509120i
$805$	−670926.	+	1.61976e6i	−0.0364909	+	0.0880969i
$806$	−2.35864e6	+	548786.i	−0.127886	+	0.0297554i
$807$	−2.95154e6	−	3.29627e6i	−0.159538	−	0.178172i
$808$	1.92901e7	+	2.35729e7i	1.03946	+	1.27024i
$809$	−775163.	−	775163.i	−0.0416410	−	0.0416410i	0.685980	−	0.727621i	$-0.259374\pi$
$809$	−775163.	−	775163.i	−0.0416410	−	0.0416410i	−0.727621	+	0.685980i	$0.759374\pi$
$810$	4.87881e6	−	4.95866e6i	0.261277	−	0.265554i
$811$	−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
$813$	8.90955e6	+	2.53823e7i	0.472748	+	1.34681i
$814$	3.14668e7	−	2.25264e7i	1.66453	−	1.19160i
$815$		−	1.61312e6i		−	0.0850695i
$816$	4.92790e6	−	1.49302e7i	0.259081	−	0.784945i
$817$			1.82416e7i			0.956110i
$818$	−78768.1	−	110030.i	−0.00411592	−	0.00574948i
$819$	6.59070e6	−	1.91272e6i	0.343338	−	0.0996418i
$820$	240639.	+	3.72519e6i	0.0124978	+	0.193470i
$821$	3.65008e6	−	8.81207e6i	0.188993	−	0.456268i	−0.800774	−	0.598967i	$-0.795578\pi$
$821$	3.65008e6	−	8.81207e6i	0.188993	−	0.456268i	0.989766	+	0.142699i	$0.0455780\pi$
$822$	−1.58583e7	+	2.25975e7i	−0.818612	+	1.16649i
$823$	−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
$825$	1.65772e7	−	1.48435e7i	0.847964	−	0.759280i
$826$	4.43648e6	+	1.90676e7i	0.226250	+	0.972403i
$827$	4.60094e6	−	1.11076e7i	0.233928	−	0.564753i	−0.762705	−	0.646747i	$-0.776129\pi$
$827$	4.60094e6	−	1.11076e7i	0.233928	−	0.564753i	0.996633	+	0.0819945i	$0.0261290\pi$
$828$	2.75804e6	−	5.88232e6i	0.139805	−	0.298176i
$829$	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
$834$	−8.18781e6	−	1.82422e6i	−0.407617	−	0.0908160i
$835$	−924840.	−	2.23276e6i	−0.0459040	−	0.110822i
$836$	−1.76902e7	−	6.02361e6i	−0.875422	−	0.298085i
$837$	−3.06378e6	+	4.90790e6i	−0.151163	+	0.242149i
$838$	6.61246e6	−	1.53853e6i	0.325277	−	0.0756825i
$839$	3.25945e6	+	3.25945e6i	0.159860	+	0.159860i	0.782505	−	0.622645i	$-0.213942\pi$
$839$	3.25945e6	+	3.25945e6i	0.159860	+	0.159860i	−0.622645	+	0.782505i	$0.713942\pi$
$840$	1.39596e6	+	5.75444e6i	0.0682611	+	0.281387i
$841$	−9.96476e6	+	9.96476e6i	−0.485822	+	0.485822i
$842$	1.29161e7	−	2.07490e7i	0.627843	−	1.00860i
$843$	−1.70422e7	−	8.18657e6i	−0.825956	−	0.396765i
$844$	−1.41279e7	+	912630.i	−0.682685	+	0.0441000i
$845$	5.63234e6	−	2.33299e6i	0.271361	−	0.112401i
$846$	1.11336e7	+	1.98549e7i	0.534824	+	0.953764i
$847$	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
$852$	8.44114e6	−	8.60112e6i	0.398384	−	0.405934i
$853$	−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
$855$	4.34954e6	−	3.48259e6i	0.203483	−	0.162925i
$856$	40752.2	+	49800.0i	0.00190093	+	0.00232298i
$857$	−2.03516e7	+	2.03516e7i	−0.946555	+	0.946555i	−0.998643	−	0.0520877i	$-0.983412\pi$
$857$	−2.03516e7	+	2.03516e7i	−0.946555	+	0.946555i	0.0520877	+	0.998643i	$0.483412\pi$
$858$	1.29120e7	−	2.26275e6i	0.598793	−	0.104935i
$859$	−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
$861$	2.91407e6	+	8.30188e6i	0.133965	+	0.381653i
$862$	−5.36941e6	+	3.24271e7i	−0.246127	+	1.48641i
$863$	−1.23042e7			−0.562376			−0.281188	−	0.959653i	$-0.590728\pi$
$863$	−1.23042e7			−0.562376			−0.281188	+	0.959653i	$0.590728\pi$
$864$	−4.19261e6	−	2.15381e7i	−0.191073	−	0.981576i
$865$	4.84728e6			0.220271
$866$	394932.	−	2.38508e6i	0.0178948	−	0.108071i
$867$	−2.32189e6	−	6.61480e6i	−0.104904	−	0.298861i
$868$	−2.17404e6	−	4.41901e6i	−0.0979419	−	0.199079i
$869$	−1.39419e7	−	5.77492e6i	−0.626286	−	0.259416i
$870$	−1.06406e7	+	1.86469e6i	−0.476614	+	0.0835236i
$871$	−9.47387e6	+	9.47387e6i	−0.423138	+	0.423138i
$872$	−823019.	+	8.23696e6i	−0.0366538	+	0.366839i
$873$	2.52781e7	−	2.02397e7i	1.12256	−	0.898810i
$874$	2.75008e6	−	4.41784e6i	0.121777	−	0.195628i
$875$	−1.12760e7	−	4.67066e6i	−0.497890	−	0.206233i
$876$	7.83983e6	+	7.69402e6i	0.345181	+	0.338761i
$877$	−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	$-0.284689\pi$
$881$	2.88435e7			1.25201			0.626006	+	0.779818i	$0.284689\pi$
$882$	−4.47369e6	−	7.97803e6i	−0.193640	−	0.345322i
$883$	−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
$885$	−1.00505e7	−	4.82794e6i	−0.431348	−	0.207207i
$886$	−1.54035e7	+	2.47448e7i	−0.659227	+	1.05901i
$887$	2.00464e7	−	2.00464e7i	0.855516	−	0.855516i	−0.135290	−	0.990806i	$-0.543197\pi$
$887$	2.00464e7	−	2.00464e7i	0.855516	−	0.855516i	0.990806	+	0.135290i	$0.0431968\pi$
$888$	3.10777e7	+	1.89432e7i	1.32256	+	0.806160i
$889$	1.50297e7	+	1.50297e7i	0.637815	+	0.637815i
$890$	1.07758e7	−	2.50721e6i	0.456009	−	0.106100i
$891$	1.80234e7	−	2.56134e7i	0.760574	−	1.08087i
$892$	−1.53995e6	+	4.52255e6i	−0.0648028	+	0.190314i
$893$	6.97756e6	+	1.68453e7i	0.292803	+	0.706888i
$894$	−4.41449e7	−	9.83536e6i	−1.84730	−	0.411573i
$895$		−	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
$900$	1.89482e7	+	8.88420e6i	0.779760	+	0.365605i
$901$	−5.38486e6	+	1.30002e7i	−0.220985	+	0.533505i
$902$	3.80867e6	+	1.63693e7i	0.155868	+	0.669907i
$903$	1.93868e7	−	1.73592e7i	0.791199	−	0.708452i
$904$	8.11981e6	+	4.35488e6i	0.330464	+	0.177237i
$905$	−9.06467e6	−	9.06467e6i	−0.367901	−	0.367901i
$906$	−1.98288e7	+	2.82552e7i	−0.802556	+	1.14361i
$907$	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
$909$	−3.92687e7	+	1.13964e7i	−1.57629	+	0.457464i
$910$	−1.93664e6	−	2.70527e6i	−0.0775256	−	0.108295i
$911$			3.32177e7i			1.32609i	0.748578	+	0.663047i	$0.230737\pi$
$911$			3.32177e7i			1.32609i	−0.748578	+	0.663047i	$0.769263\pi$
$912$	−1.29757e6	−	1.75277e7i	−0.0516586	−	0.697810i
$913$		−	4.28936e7i		−	1.70300i
$914$	−6.24600e6	+	4.47137e6i	−0.247307	+	0.177042i
$915$	590101.	+	1.68113e6i	0.0233009	+	0.0663818i
$916$	−2.27239e7	+	2.58625e7i	−0.894839	+	1.01843i
$917$	−4.81675e6	+	1.16287e7i	−0.189161	+	0.456674i
$918$	1.58373e7	+	1.39510e7i	0.620262	+	0.546386i
$919$	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
$921$	−5.14929e6	−	5.75072e6i	−0.200031	−	0.223395i
$922$	4.90709e7	−	1.14174e7i	1.90106	−	0.442322i
$923$	−2.59123e6	+	6.25578e6i	−0.100116	+	0.241700i
$924$	1.04328e7	+	2.45330e7i	0.401993	+	0.945302i
$925$	−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	$-0.717474\pi$
$929$		−	4.08017e7i		−	1.55110i	0.631289	−	0.775548i	$-0.282526\pi$
$930$	2.73779e6	+	609972.i	0.103799	+	0.0231261i
$931$	−2.80371e6	−	6.76875e6i	−0.106013	−	0.255938i
$932$	−4.10928e6	−	8.35262e6i	−0.154962	−	0.314980i
$933$	4.46200e7	+	2.14341e7i	1.67813	+	0.806122i
$934$	−3.88122e6	−	1.66812e7i	−0.145580	−	0.625690i
$935$	−7.69295e6	−	7.69295e6i	−0.287782	−	0.287782i
$936$	6.71068e6	+	1.03424e7i	0.250367	+	0.385862i
$937$	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
$939$	−4.28077e6	+	8.91141e6i	−0.158438	+	0.329824i
$940$	7.28418e6	−	8.29025e6i	0.268881	−	0.306019i
$941$	−1.00920e7	+	4.18024e6i	−0.371538	+	0.153896i	−0.560636	−	0.828062i	$-0.689443\pi$
$941$	−1.00920e7	+	4.18024e6i	−0.371538	+	0.153896i	0.189099	+	0.981958i	$0.439443\pi$
$942$	−2.45322e7	−	3.85973e7i	−0.900760	−	1.41719i
$943$	−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	$0.0943307\pi$
$947$	1.34297e7	+	3.24222e7i	0.486622	+	1.17481i	−0.469787	+	0.882780i	$0.655669\pi$
$948$	−133219.	−	1.41920e7i	−0.00481445	−	0.512889i
$949$	−5.70209e6	−	2.36188e6i	−0.205527	−	0.0851319i
$950$	1.42308e7	+	8.85856e6i	0.511587	+	0.318459i
$951$	−3.82342e7	+	3.42355e7i	−1.37088	+	1.22751i
$952$	−1.71992e7	+	5.19080e6i	−0.615057	+	0.185627i
$953$	−3.85355e7	+	3.85355e7i	−1.37445	+	1.37445i	−0.520727	+	0.853723i	$0.674339\pi$
$953$	−3.85355e7	+	3.85355e7i	−1.37445	+	1.37445i	−0.853723	+	0.520727i	$0.825661\pi$
$954$	2.31896e6	+	1.95007e7i	0.0824938	+	0.693713i
$955$	−1.24689e7	−	5.16480e6i	−0.442406	−	0.183251i
$956$	42441.8	−	124644.i	0.00150193	−	0.00441089i
$957$	−4.58911e7	+	1.61084e7i	−1.61975	+	0.568556i
$958$	−5.33883e7	−	8.84027e6i	−1.87946	−	0.311209i
$959$	3.15452e7			1.10761
$960$	−9.17236e6	+	5.38783e6i	−0.321220	+	0.188684i
$961$	2.62963e7			0.918514
$962$	−2.01751e7	−	3.34068e6i	−0.702874	−	0.116385i
$963$	−82958.9	+	24075.9i	−0.00288269	+	0.000836599i
$964$	1.21404e7	−	3.56540e7i	0.420764	−	1.23571i
$965$	1.36581e7	+	5.65736e6i	0.472140	+	0.195567i
$966$	−7.31223e6	+	1.28142e6i	−0.252120	+	0.0441824i
$967$	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
$969$	1.12772e7	+	1.25944e7i	0.385827	+	0.430892i
$970$	−1.33278e7	−	8.29647e6i	−0.454809	−	0.283116i
$971$	−3.29304e7	−	1.36402e7i	−1.12085	−	0.464273i	−0.256192	−	0.966626i	$-0.582468\pi$
$971$	−3.29304e7	−	1.36402e7i	−1.12085	−	0.464273i	−0.864663	+	0.502353i	$0.832468\pi$
$972$	2.88016e7	+	6.17195e6i	0.977801	+	0.209535i
$973$	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	$-0.342094\pi$
$977$	2.84024e7			0.951958			0.475979	+	0.879457i	$0.342094\pi$
$978$	5.76461e6	−	3.66395e6i	0.192718	−	0.122491i
$979$	4.60191e7	−	1.90617e7i	1.53455	−	0.635632i
$980$	−2.92691e6	+	3.33117e6i	−0.0973519	+	0.110798i
$981$	−9.73628e6	−	5.35621e6i	−0.323013	−	0.177699i
$982$	−2.79870e7	−	1.74217e7i	−0.926143	−	0.576518i
$983$	−8.09109e6	+	8.09109e6i	−0.267069	+	0.267069i	−0.827918	−	0.560849i	$-0.810475\pi$
$983$	−8.09109e6	+	8.09109e6i	−0.267069	+	0.267069i	0.560849	+	0.827918i	$0.310475\pi$
$984$	−1.27657e7	+	9.32112e6i	−0.420296	+	0.306888i
$985$	−1.57303e6	−	1.57303e6i	−0.0516591	−	0.0516591i
$986$	−7.42753e6	−	3.19229e7i	−0.243306	−	1.04571i
$987$	1.12628e7	−	2.34461e7i	0.368004	−	0.766085i
$988$	4.35935e6	+	8.86091e6i	0.142079	+	0.288793i
$989$	5.29710e6	+	1.27883e7i	0.172206	+	0.415741i
$990$	−1.46157e7	−	4.11338e6i	−0.473951	−	0.133386i
$991$			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
$996$	3.71239e7	−	1.57871e7i	1.18578	−	0.504259i
$997$	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
$999$	−3.97634e7	+	2.83895e7i	−1.26058	+	0.900003i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.6.o.a.11.3	✓	312	3.2	odd	2	inner
96.6.o.a.11.76	yes	312	1.1	even	1	trivial
96.6.o.a.35.3	yes	312	32.3	odd	8	inner
96.6.o.a.35.76	yes	312	96.35	even	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} +(5.16293 + 14.7086i) q^{3} +(30.2921 + 10.3146i) q^{4} +(19.2402 + 7.96957i) q^{5} +(15.2213 + 86.8580i) q^{6} +(71.2494 - 71.2494i) q^{7} +(159.524 + 85.5573i) q^{8} +(-189.688 + 151.879i) q^{9} +(100.012 + 62.2571i) q^{10} +(490.018 + 202.972i) q^{11} +(4.68228 + 498.809i) 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} +(-1198.98 + 672.327i) q^{18} +(-1017.24 + 421.354i) q^{19} +(500.624 + 439.870i) q^{20} +(1415.84 + 680.126i) q^{21} +(2547.16 + 1585.59i) q^{22} +(-590.784 + 590.784i) q^{23} +(-434.820 + 2788.11i) q^{24} +(-1903.04 - 1903.04i) q^{25} +(-359.300 - 1544.24i) q^{26} +(-3213.29 - 2005.91i) q^{27} +(2893.20 - 1423.38i) q^{28} +(2251.12 + 5434.69i) q^{29} +(-399.359 + 1792.48i) 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} +(-7312.62 + 2644.19i) q^{36} +(4935.89 - 11916.3i) q^{37} +(-6066.45 + 1411.49i) q^{38} +(3254.93 - 2914.52i) q^{39} +(2387.43 + 2917.48i) q^{40} +(3960.89 + 3960.89i) q^{41} +(7273.09 + 5104.07i) q^{42} +(6340.08 - 15306.3i) q^{43} +(12750.1 + 11202.8i) q^{44} +(-4860.06 + 1410.46i) q^{45} +(-3843.03 + 2751.14i) q^{46} -16559.8i q^{47} +(-5003.17 + 15158.2i) q^{48} +6654.04i q^{49} +(-8861.98 - 12379.2i) q^{50} +(-5085.25 - 14487.3i) q^{51} +(-578.165 - 8950.23i) q^{52} +(5467.12 - 13198.8i) q^{53} +(-16079.3 - 14164.1i) q^{54} +(7810.47 + 7810.47i) q^{55} +(17461.9 - 5270.09i) q^{56} +(-11449.5 - 12786.8i) q^{57} +(7540.99 + 32410.6i) q^{58} +(-13143.6 + 31731.4i) q^{59} +(-3885.20 + 9634.52i) 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} +(-10171.0 + 45651.5i) q^{66} +(-18293.4 - 44164.1i) q^{67} +(-29836.3 - 10159.4i) q^{68} +(-11739.8 - 5639.45i) q^{69} +(11561.6 - 2690.05i) q^{70} +(-17083.0 - 17083.0i) q^{71} +(-43254.3 + 7999.22i) q^{72} +(15571.0 - 15571.0i) q^{73} +(38558.4 - 61941.9i) q^{74} +(18165.8 - 37816.3i) q^{75} +(-35160.4 + 2271.28i) q^{76} +(49375.1 - 20451.9i) q^{77} +(20858.6 - 13257.6i) 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} +(35873.4 + 35206.2i) q^{84} +(-18950.8 - 7849.66i) q^{85} +(49527.7 - 79563.5i) q^{86} +(-68314.6 + 61169.9i) q^{87} +(60803.9 + 74303.6i) q^{88} +(66406.6 - 66406.6i) q^{89} +(-28426.8 + 3380.41i) q^{90} +(-26091.6 - 10807.5i) q^{91} +(-23989.7 + 11802.4i) q^{92} +(22465.6 - 7885.74i) q^{93} +(15303.0 - 92418.2i) q^{94} -22930.0 q^{95} +(-41929.8 + 79972.6i) q^{96} -133261. q^{97} +(-6149.02 + 37135.3i) q^{98} +(-123778. + 35922.2i) 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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