LMFDB - Embedded newform 96.6.o.a.11.2

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			11.2
Character	$\chi$	$=$	96.11
Dual form			96.6.o.a.35.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.64922 + 0.293734i) q^{2} +(15.5875 + 0.174756i) q^{3} +(31.8274 - 3.31874i) q^{4} +(-102.440 - 42.4320i) q^{5} +(-88.1085 + 3.59134i) q^{6} +(-65.5079 + 65.5079i) q^{7} +(-178.825 + 28.0971i) q^{8} +(242.939 + 5.44800i) q^{9} +(591.170 + 209.618i) q^{10} +(266.694 + 110.468i) q^{11} +(496.689 - 46.1687i) q^{12} +(200.527 + 484.114i) q^{13} +(350.827 - 389.311i) q^{14} +(-1589.37 - 679.310i) q^{15} +(1001.97 - 211.254i) q^{16} -99.7498 q^{17} +(-1374.02 + 40.5824i) q^{18} +(812.754 - 336.654i) q^{19} +(-3401.22 - 1010.53i) q^{20} +(-1032.55 + 1009.65i) q^{21} +(-1539.06 - 545.723i) q^{22} +(2890.06 - 2890.06i) q^{23} +(-2792.35 + 406.712i) q^{24} +(6483.76 + 6483.76i) q^{25} +(-1275.02 - 2675.97i) q^{26} +(3785.85 + 127.375i) q^{27} +(-1867.54 + 2302.35i) q^{28} +(887.731 + 2143.17i) q^{29} +(9178.22 + 3370.72i) q^{30} +1455.85i q^{31} +(-5598.31 + 1487.73i) q^{32} +(4137.78 + 1768.53i) q^{33} +(563.509 - 29.2999i) q^{34} +(9490.26 - 3930.99i) q^{35} +(7750.20 - 632.854i) q^{36} +(1069.59 - 2582.23i) q^{37} +(-4492.54 + 2140.56i) q^{38} +(3041.10 + 7581.16i) q^{39} +(19511.1 + 4709.66i) q^{40} +(9039.11 + 9039.11i) q^{41} +(5536.54 - 6007.06i) q^{42} +(5994.35 - 14471.6i) q^{43} +(8854.80 + 2630.83i) q^{44} +(-24655.5 - 10866.5i) q^{45} +(-15477.7 + 17175.5i) q^{46} +19593.3i q^{47} +(15655.1 - 3117.81i) q^{48} +8224.43i q^{49} +(-38532.7 - 34723.7i) q^{50} +(-1554.85 - 17.4318i) q^{51} +(7988.89 + 14742.6i) q^{52} +(1219.55 - 2944.26i) q^{53} +(-21424.5 + 392.461i) q^{54} +(-22632.7 - 22632.7i) q^{55} +(9873.90 - 13555.1i) q^{56} +(12727.6 - 5105.55i) q^{57} +(-5644.51 - 11846.5i) q^{58} +(-17376.4 + 41950.4i) q^{59} +(-52839.9 - 16346.0i) q^{60} +(-19685.7 + 8154.08i) q^{61} +(-427.632 - 8224.42i) q^{62} +(-16271.3 + 15557.5i) q^{63} +(31189.1 - 10048.9i) q^{64} -58101.4i q^{65} +(-23894.7 - 8775.40i) q^{66} +(6254.85 + 15100.5i) q^{67} +(-3174.78 + 331.043i) q^{68} +(45553.8 - 44543.7i) q^{69} +(-52457.9 + 24994.7i) q^{70} +(11316.8 + 11316.8i) q^{71} +(-43596.7 + 5851.63i) q^{72} +(54937.2 - 54937.2i) q^{73} +(-5283.89 + 14901.8i) q^{74} +(99932.4 + 102199. i) q^{75} +(24750.6 - 13412.1i) q^{76} +(-24707.1 + 10234.0i) q^{77} +(-19406.7 - 41934.4i) q^{78} -1446.73 q^{79} +(-111606. - 20874.9i) q^{80} +(58989.6 + 2647.06i) q^{81} +(-53719.1 - 48408.9i) q^{82} +(-37184.8 - 89772.0i) q^{83} +(-29512.7 + 35561.5i) q^{84} +(10218.4 + 4232.58i) q^{85} +(-29612.6 + 83514.2i) q^{86} +(13463.0 + 33561.8i) q^{87} +(-50795.5 - 12261.2i) q^{88} +(-80372.3 + 80372.3i) q^{89} +(142476. + 54145.0i) q^{90} +(-44849.3 - 18577.2i) q^{91} +(82391.9 - 101575. i) q^{92} +(-254.418 + 22693.0i) q^{93} +(-5755.21 - 110687. i) q^{94} -97543.3 q^{95} +(-87523.5 + 22211.7i) q^{96} +2107.93 q^{97} +(-2415.79 - 46461.7i) q^{98} +(64188.5 + 28290.0i) 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 $

$2$	−5.64922	+	0.293734i	−0.998651	+	0.0519253i
$2$	−5.64922	+	0.293734i	−0.998651	+	0.0519253i
$3$	15.5875	+	0.174756i	0.999937	+	0.0112106i
$3$	15.5875	+	0.174756i	0.999937	+	0.0112106i
$4$	31.8274	−	3.31874i	0.994608	−	0.103710i
$5$	−102.440	−	42.4320i	−1.83250	−	0.759047i	−0.965327	−	0.261042i	$-0.915934\pi$
$5$	−102.440	−	42.4320i	−1.83250	−	0.759047i	−0.867174	−	0.498005i	$-0.834066\pi$
$6$	−88.1085	+	3.59134i	−0.999170	+	0.0407266i
$7$	−65.5079	+	65.5079i	−0.505299	+	0.505299i	−0.913080	−	0.407781i	$-0.866303\pi$
$7$	−65.5079	+	65.5079i	−0.505299	+	0.505299i	0.407781	+	0.913080i	$0.366303\pi$
$8$	−178.825	+	28.0971i	−0.987881	+	0.155216i
$9$	242.939	+	5.44800i	0.999749	+	0.0224197i
$10$	591.170	+	209.618i	1.86944	+	0.662870i
$11$	266.694	+	110.468i	0.664556	+	0.275268i	0.689354	−	0.724424i	$-0.257894\pi$
$11$	266.694	+	110.468i	0.664556	+	0.275268i	−0.0247985	+	0.999692i	$0.507894\pi$
$12$	496.689	−	46.1687i	0.995708	−	0.0925539i
$13$	200.527	+	484.114i	0.329089	+	0.794491i	0.998660	+	0.0517436i	$0.0164779\pi$
$13$	200.527	+	484.114i	0.329089	+	0.794491i	−0.669571	+	0.742748i	$0.733522\pi$
$14$	350.827	−	389.311i	0.478380	−	0.530855i
$15$	−1589.37	−	679.310i	−1.82388	−	0.779543i
$16$	1001.97	−	211.254i	0.978488	−	0.206302i
$17$	−99.7498			−0.0837124			−0.0418562	−	0.999124i	$-0.513327\pi$
$17$	−99.7498			−0.0837124			−0.0418562	+	0.999124i	$0.513327\pi$
$18$	−1374.02	+	40.5824i	−0.999564	+	0.0295228i
$19$	812.754	−	336.654i	0.516505	−	0.213944i	−0.109176	−	0.994022i	$-0.534821\pi$
$19$	812.754	−	336.654i	0.516505	−	0.213944i	0.625681	+	0.780079i	$0.284821\pi$
$20$	−3401.22	−	1010.53i	−1.90134	−	0.564904i
$21$	−1032.55	+	1009.65i	−0.510932	+	0.499603i
$22$	−1539.06	−	545.723i	−0.677953	−	0.240389i
$23$	2890.06	−	2890.06i	1.13917	−	1.13917i	0.150567	−	0.988600i	$-0.451890\pi$
$23$	2890.06	−	2890.06i	1.13917	−	1.13917i	0.988600	−	0.150567i	$-0.0481101\pi$
$24$	−2792.35	+	406.712i	−0.989559	+	0.144131i
$25$	6483.76	+	6483.76i	2.07480	+	2.07480i
$26$	−1275.02	−	2675.97i	−0.369899	−	0.776332i
$27$	3785.85	+	127.375i	0.999434	+	0.0336261i
$28$	−1867.54	+	2302.35i	−0.450169	+	0.554979i
$29$	887.731	+	2143.17i	0.196014	+	0.473219i	0.991074	−	0.133311i	$-0.0425610\pi$
$29$	887.731	+	2143.17i	0.196014	+	0.473219i	−0.795061	+	0.606530i	$0.792561\pi$
$30$	9178.22	+	3370.72i	1.86189	+	0.683786i
$31$			1455.85i			0.272090i	0.990703	+	0.136045i	$0.0434391\pi$
$31$			1455.85i			0.272090i	−0.990703	+	0.136045i	$0.956561\pi$
$32$	−5598.31	+	1487.73i	−0.966456	+	0.256832i
$33$	4137.78	+	1768.53i	0.661428	+	0.282701i
$34$	563.509	−	29.2999i	0.0835994	−	0.00434679i
$35$	9490.26	−	3930.99i	1.30951	−	0.542416i
$36$	7750.20	−	632.854i	0.996683	−	0.0813856i
$37$	1069.59	−	2582.23i	0.128444	−	0.310092i	−0.846555	−	0.532302i	$-0.821327\pi$
$37$	1069.59	−	2582.23i	0.128444	−	0.310092i	0.974999	+	0.222210i	$0.0713271\pi$
$38$	−4492.54	+	2140.56i	−0.504700	+	0.240475i
$39$	3041.10	+	7581.16i	0.320162	+	0.798131i
$40$	19511.1	+	4709.66i	1.92811	+	0.465414i
$41$	9039.11	+	9039.11i	0.839781	+	0.839781i	0.988830	−	0.149049i	$-0.0476211\pi$
$41$	9039.11	+	9039.11i	0.839781	+	0.839781i	−0.149049	+	0.988830i	$0.547621\pi$
$42$	5536.54	−	6007.06i	0.484301	−	0.525459i
$43$	5994.35	−	14471.6i	0.494391	−	1.19357i	−0.458073	−	0.888915i	$-0.651460\pi$
$43$	5994.35	−	14471.6i	0.494391	−	1.19357i	0.952464	−	0.304651i	$-0.0985398\pi$
$44$	8854.80	+	2630.83i	0.689520	+	0.204862i
$45$	−24655.5	−	10866.5i	−1.81502	−	0.799940i
$46$	−15477.7	+	17175.5i	−1.07848	+	1.19678i
$47$			19593.3i			1.29379i	0.762581	+	0.646893i	$0.223932\pi$
$47$			19593.3i			1.29379i	−0.762581	+	0.646893i	$0.776068\pi$
$48$	15655.1	−	3117.81i	0.980740	−	0.195320i
$49$			8224.43i			0.489346i
$50$	−38532.7	−	34723.7i	−2.17974	−	1.96427i
$51$	−1554.85	−	17.4318i	−0.0837071	−	0.000938464i
$52$	7988.89	+	14742.6i	0.409712	+	0.756077i
$53$	1219.55	−	2944.26i	0.0596364	−	0.143975i	−0.891253	−	0.453507i	$-0.850173\pi$
$53$	1219.55	−	2944.26i	0.0596364	−	0.143975i	0.950889	+	0.309533i	$0.100173\pi$
$54$	−21424.5	+	392.461i	−0.999832	+	0.0183152i
$55$	−22632.7	−	22632.7i	−1.00886	−	1.00886i
$56$	9873.90	−	13555.1i	0.420745	−	0.577606i
$57$	12727.6	−	5105.55i	0.518871	−	0.208140i
$58$	−5644.51	−	11846.5i	−0.220321	−	0.462402i
$59$	−17376.4	+	41950.4i	−0.649877	+	1.56894i	0.163078	+	0.986613i	$0.447858\pi$
$59$	−17376.4	+	41950.4i	−0.649877	+	1.56894i	−0.812954	+	0.582328i	$0.802142\pi$
$60$	−52839.9	−	16346.0i	−1.89489	−	0.586184i
$61$	−19685.7	+	8154.08i	−0.677371	+	0.280576i	−0.694727	−	0.719273i	$-0.744475\pi$
$61$	−19685.7	+	8154.08i	−0.677371	+	0.280576i	0.0173567	+	0.999849i	$0.494475\pi$
$62$	−427.632	−	8224.42i	−0.0141283	−	0.271723i
$63$	−16271.3	+	15557.5i	−0.516501	+	0.493843i
$64$	31189.1	−	10048.9i	0.951816	−	0.306670i
$65$		−	58101.4i		−	1.70570i
$66$	−23894.7	−	8775.40i	−0.675215	−	0.247975i
$67$	6254.85	+	15100.5i	0.170228	+	0.410966i	0.985852	−	0.167615i	$-0.0536066\pi$
$67$	6254.85	+	15100.5i	0.170228	+	0.410966i	−0.815625	+	0.578581i	$0.803607\pi$
$68$	−3174.78	+	331.043i	−0.0832609	+	0.00868185i
$69$	45553.8	−	44543.7i	1.15187	−	1.12632i
$70$	−52457.9	+	24994.7i	−1.27958	+	0.609680i
$71$	11316.8	+	11316.8i	0.266426	+	0.266426i	0.827658	−	0.561232i	$-0.189672\pi$
$71$	11316.8	+	11316.8i	0.266426	+	0.266426i	−0.561232	+	0.827658i	$0.689672\pi$
$72$	−43596.7	+	5851.63i	−0.991112	+	0.133029i
$73$	54937.2	−	54937.2i	1.20659	−	1.20659i	0.234463	−	0.972125i	$-0.424667\pi$
$73$	54937.2	−	54937.2i	1.20659	−	1.20659i	0.972125	−	0.234463i	$-0.0753332\pi$
$74$	−5283.89	+	14901.8i	−0.112169	+	0.316343i
$75$	99932.4	+	102199.i	2.05141	+	2.09793i
$76$	24750.6	−	13412.1i	0.491532	−	0.266357i
$77$	−24707.1	+	10234.0i	−0.474892	+	0.196707i
$78$	−19406.7	−	41934.4i	−0.361173	−	0.780430i
$79$	−1446.73			−0.0260807			−0.0130403	−	0.999915i	$-0.504151\pi$
$79$	−1446.73			−0.0260807			−0.0130403	+	0.999915i	$0.504151\pi$
$80$	−111606.	−	20874.9i	−1.94967	−	0.364669i
$81$	58989.6	+	2647.06i	0.998995	+	0.0448282i
$82$	−53719.1	−	48408.9i	−0.882254	−	0.795043i
$83$	−37184.8	−	89772.0i	−0.592475	−	1.43036i	−0.881105	−	0.472920i	$-0.843200\pi$
$83$	−37184.8	−	89772.0i	−0.592475	−	1.43036i	0.288630	−	0.957441i	$-0.406800\pi$
$84$	−29512.7	+	35561.5i	−0.456363	+	0.549897i
$85$	10218.4	+	4232.58i	0.153403	+	0.0635416i
$86$	−29612.6	+	83514.2i	−0.431748	+	1.21763i
$87$	13463.0	+	33561.8i	0.190696	+	0.475386i
$88$	−50795.5	−	12261.2i	−0.699228	−	0.168782i
$89$	−80372.3	+	80372.3i	−1.07555	+	1.07555i	−0.0786494	+	0.996902i	$0.525061\pi$
$89$	−80372.3	+	80372.3i	−1.07555	+	1.07555i	−0.996902	+	0.0786494i	$0.974939\pi$
$90$	142476.	+	54145.0i	1.85411	+	0.704616i
$91$	−44849.3	−	18577.2i	−0.567744	−	0.235167i
$92$	82391.9	−	101575.i	1.01488	−	1.25117i
$93$	−254.418	+	22693.0i	−0.00305028	+	0.272073i
$94$	−5755.21	−	110687.i	−0.0671802	−	1.29204i
$95$	−97543.3			−1.10889
$96$	−87523.5	+	22211.7i	−0.969274	+	0.245982i
$97$	2107.93			0.0227471			0.0113736	−	0.999935i	$-0.496380\pi$
$97$	2107.93			0.0227471			0.0113736	+	0.999935i	$0.496380\pi$
$98$	−2415.79	−	46461.7i	−0.0254094	−	0.488686i
$99$	64188.5	+	28290.0i	0.658217	+	0.290098i
$100$	227879.	+	184844.i	2.27879	+	1.84844i
$101$	131595.	+	54508.3i	1.28362	+	0.531691i	0.917077	−	0.398711i	$-0.130542\pi$
$101$	131595.	+	54508.3i	1.28362	+	0.531691i	0.366540	+	0.930402i	$0.380542\pi$
$102$	8788.80	−	358.235i	0.0836429	−	0.00340932i
$103$	13096.2	−	13096.2i	0.121633	−	0.121633i	−0.643670	−	0.765303i	$-0.722589\pi$
$103$	13096.2	−	13096.2i	0.121633	−	0.121633i	0.765303	+	0.643670i	$0.222589\pi$
$104$	−49461.4	−	80937.7i	−0.448418	−	0.733783i
$105$	148616.	−	59615.8i	1.31551	−	0.527701i
$106$	−6024.70	+	16991.0i	−0.0520800	+	0.146877i
$107$	123273.	+	51061.2i	1.04089	+	0.431153i	0.836633	−	0.547764i	$-0.184521\pi$
$107$	123273.	+	51061.2i	1.04089	+	0.431153i	0.204262	+	0.978916i	$0.434521\pi$
$108$	120917.	−	8510.21i	0.997532	−	0.0702071i
$109$	−40685.3	−	98223.0i	−0.327998	−	0.791857i	−0.998741	−	0.0501673i	$-0.984025\pi$
$109$	−40685.3	−	98223.0i	−0.327998	−	0.791857i	0.670743	−	0.741690i	$-0.265975\pi$
$110$	134505.	+	121209.i	1.05988	+	0.955112i
$111$	17123.5	−	40063.5i	0.131912	−	0.308632i
$112$	−51798.3	+	79475.8i	−0.390185	+	0.598674i
$113$	−183322.			−1.35057			−0.675287	−	0.737555i	$-0.735980\pi$
$113$	−183322.			−1.35057			−0.675287	+	0.737555i	$0.735980\pi$
$114$	−70401.4	+	32580.9i	−0.507364	+	0.234802i
$115$	−418689.	+	173427.i	−2.95221	+	1.22284i
$116$	35366.8	+	65265.5i	0.244034	+	0.450338i
$117$	46078.3	+	118703.i	0.311194	+	0.801670i
$118$	85841.1	−	242091.i	0.567532	−	1.60057i
$119$	6534.40	−	6534.40i	0.0422998	−	0.0422998i
$120$	303306.	+	76821.4i	1.92277	+	0.487000i
$121$	−54957.8	−	54957.8i	−0.341245	−	0.341245i
$122$	108814.	−	51846.6i	0.661888	−	0.315370i
$123$	139317.	+	142477.i	0.830314	+	0.849143i
$124$	4831.58	+	46336.0i	0.0282186	+	0.270623i
$125$	−256477.	−	619190.i	−1.46816	−	3.54445i
$126$	87350.4	−	92667.4i	0.490161	−	0.519997i
$127$			138464.i			0.761778i	0.924621	+	0.380889i	$0.124382\pi$
$127$			138464.i			0.761778i	−0.924621	+	0.380889i	$0.875618\pi$
$128$	−173243.	+	65930.0i	−0.934608	+	0.355679i
$129$	95965.7	−	224529.i	0.507741	−	1.18795i
$130$	17066.3	+	328228.i	0.0885690	+	1.70340i
$131$	−51436.5	+	21305.7i	−0.261874	+	0.108472i	−0.509758	−	0.860318i	$-0.670265\pi$
$131$	−51436.5	+	21305.7i	−0.261874	+	0.108472i	0.247883	+	0.968790i	$0.420265\pi$
$132$	137564.	+	42555.5i	0.687180	+	0.212579i
$133$	−31188.3	+	75295.2i	−0.152884	+	0.369095i
$134$	−39770.6	−	83469.1i	−0.191338	−	0.401572i
$135$	−382418.	−	173690.i	−1.80594	−	0.820238i
$136$	17837.8	−	2802.68i	0.0826978	−	0.0129935i
$137$	96110.7	+	96110.7i	0.437492	+	0.437492i	0.891167	−	0.453675i	$-0.149887\pi$
$137$	96110.7	+	96110.7i	0.437492	+	0.437492i	−0.453675	+	0.891167i	$0.649887\pi$
$138$	−244260.	+	265018.i	−1.09183	+	1.18462i
$139$	60317.1	−	145618.i	0.264791	−	0.639262i	−0.734432	−	0.678683i	$-0.762551\pi$
$139$	60317.1	−	145618.i	0.264791	−	0.639262i	0.999223	+	0.0394205i	$0.0125512\pi$
$140$	289005.	−	156609.i	1.24619	−	0.675300i
$141$	−3424.03	+	305410.i	−0.0145041	+	1.29370i
$142$	−67255.2	−	60606.9i	−0.279901	−	0.252233i
$143$			151262.i			0.618571i
$144$	244569.	−	45863.0i	0.982868	−	0.184313i
$145$		−	257215.i		−	1.01596i
$146$	−294215.	+	326489.i	−1.14231	+	1.26761i
$147$	−1437.27	+	128198.i	−0.00548585	+	0.489315i
$148$	25472.7	−	85735.4i	0.0955918	−	0.321741i
$149$	82903.6	−	200147.i	0.305920	−	0.738556i	−0.693909	−	0.720063i	$-0.744113\pi$
$149$	82903.6	−	200147.i	0.305920	−	0.738556i	0.999829	−	0.0184933i	$-0.00588694\pi$
$150$	−594559.	−	547989.i	−2.15758	−	1.98858i
$151$	232501.	+	232501.i	0.829817	+	0.829817i	0.987491	−	0.157674i	$-0.0503996\pi$
$151$	232501.	+	232501.i	0.829817	+	0.829817i	−0.157674	+	0.987491i	$0.550400\pi$
$152$	−135882.	+	83038.2i	−0.477038	+	0.291521i
$153$	−24233.1	−	543.436i	−0.0836913	−	0.00187681i
$154$	136570.	−	65071.5i	0.464037	−	0.221100i
$155$	61774.6	−	149137.i	0.206529	−	0.498605i
$156$	121950.	+	231196.i	0.401210	+	0.760623i
$157$	133733.	−	55394.1i	0.433003	−	0.179356i	−0.155526	−	0.987832i	$-0.549707\pi$
$157$	133733.	−	55394.1i	0.433003	−	0.179356i	0.588529	+	0.808476i	$0.299707\pi$
$158$	8172.89	−	424.953i	0.0260455	−	0.00135425i
$159$	19524.3	−	45680.5i	0.0612466	−	0.143297i
$160$	636618.	+	85144.4i	1.96598	+	0.262940i
$161$			378644.i			1.15124i
$162$	−334023.	+	2373.42i	−0.999975	+	0.00710536i
$163$	3894.58	+	9402.36i	0.0114813	+	0.0277184i	0.929516	−	0.368781i	$-0.120225\pi$
$163$	3894.58	+	9402.36i	0.0114813	+	0.0277184i	−0.918035	+	0.396500i	$0.870225\pi$
$164$	317690.	+	257693.i	0.922347	+	0.748159i
$165$	−348832.	−	356742.i	−0.997485	−	1.02010i
$166$	236434.	+	496220.i	0.665947	+	1.39767i
$167$	215498.	+	215498.i	0.597931	+	0.597931i	0.939762	−	0.341830i	$-0.111047\pi$
$167$	215498.	+	215498.i	0.597931	+	0.597931i	−0.341830	+	0.939762i	$0.611047\pi$
$168$	156278.	−	209564.i	0.427194	−	0.572852i
$169$	68388.4	−	68388.4i	0.184190	−	0.184190i
$170$	−58969.1	−	20909.3i	−0.156495	−	0.0554904i
$171$	199284.	−	77358.4i	0.521172	−	0.202310i
$172$	142757.	−	480489.i	0.367940	−	1.23840i
$173$	555969.	−	230290.i	1.41233	−	0.585005i	0.459406	−	0.888226i	$-0.348062\pi$
$173$	555969.	−	230290.i	1.41233	−	0.585005i	0.952920	+	0.303222i	$0.0980623\pi$
$174$	−85913.4	−	185643.i	−0.215124	−	0.464843i
$175$	−849475.			−2.09679
$176$	290557.	+	54346.0i	0.707048	+	0.132247i
$177$	−278186.	+	650865.i	−0.667424	+	1.56156i
$178$	430433.	−	477649.i	1.01825	−	1.12995i
$179$	−77422.9	−	186915.i	−0.180608	−	0.436026i	0.807484	−	0.589889i	$-0.200829\pi$
$179$	−77422.9	−	186915.i	−0.180608	−	0.436026i	−0.988092	+	0.153863i	$0.950829\pi$
$180$	−820784.	−	264027.i	−1.88820	−	0.607390i
$181$	−87879.2	−	36400.7i	−0.199384	−	0.0825874i	0.280757	−	0.959779i	$-0.409414\pi$
$181$	−87879.2	−	36400.7i	−0.199384	−	0.0825874i	−0.480141	+	0.877191i	$0.659414\pi$
$182$	258821.	+	91773.0i	0.579189	+	0.205370i
$183$	−308275.	+	123661.i	−0.680473	+	0.272965i
$184$	−435614.	+	598019.i	−0.948544	+	1.30218i
$185$	−219138.	+	219138.i	−0.470748	+	0.470748i
$186$	−5228.45	−	128273.i	−0.0110813	−	0.271864i
$187$	−26602.7	−	11019.2i	−0.0556315	−	0.0230433i
$188$	65024.9	+	623604.i	0.134179	+	1.28681i
$189$	−256347.	+	239659.i	−0.522004	+	0.488022i
$190$	551044.	−	28651.8i	1.10739	−	0.0575795i
$191$	410380.			0.813958			0.406979	−	0.913437i	$-0.366582\pi$
$191$	410380.			0.813958			0.406979	+	0.913437i	$0.366582\pi$
$192$	487916.	−	151187.i	0.955194	−	0.295980i
$193$	−87639.4			−0.169358			−0.0846791	−	0.996408i	$-0.526986\pi$
$193$	−87639.4			−0.169358			−0.0846791	+	0.996408i	$0.526986\pi$
$194$	−11908.2	+	619.170i	−0.0227164	+	0.00118115i
$195$	10153.5	−	905654.i	0.0191219	−	1.70559i
$196$	27294.7	+	261763.i	0.0507503	+	0.486707i
$197$	−471653.	−	195365.i	−0.865878	−	0.358659i	−0.0948747	−	0.995489i	$-0.530245\pi$
$197$	−471653.	−	195365.i	−0.865878	−	0.358659i	−0.771004	+	0.636831i	$0.780245\pi$
$198$	−370925.	−	140962.i	−0.672393	−	0.255528i
$199$	−393538.	+	393538.i	−0.704455	+	0.704455i	−0.965364	−	0.260908i	$-0.915978\pi$
$199$	−393538.	+	393538.i	−0.704455	+	0.704455i	0.260908	+	0.965364i	$0.415978\pi$
$200$	−1.34164e6	−	977287.i	−2.37170	−	1.72762i
$201$	94858.5	+	236473.i	0.165610	+	0.412848i
$202$	−759419.	−	269276.i	−1.30949	−	0.464322i
$203$	−198548.	−	82241.3i	−0.338162	−	0.140071i
$204$	−49544.7	+	4605.32i	−0.0833530	+	0.00774790i
$205$	−542419.	−	1.30951e6i	−0.901467	−	2.17633i
$206$	−70136.7	+	77830.3i	−0.115153	+	0.127785i
$207$	717853.	−	686363.i	1.16442	−	1.11334i
$208$	303193.	+	442707.i	0.485915	+	0.709509i
$209$	253946.			0.402138
$210$	−822054.	+	380436.i	−1.28633	+	0.595297i
$211$	253893.	−	105166.i	0.392595	−	0.162618i	−0.177648	−	0.984094i	$-0.556849\pi$
$211$	253893.	−	105166.i	0.392595	−	0.162618i	0.570243	+	0.821476i	$0.306849\pi$
$212$	29044.0	−	97755.7i	0.0443831	−	0.149383i
$213$	174423.	+	178378.i	0.263423	+	0.269396i
$214$	−711392.	−	252247.i	−1.06188	−	0.376522i
$215$	−1.22812e6	+	1.22812e6i	−1.81194	+	1.81194i
$216$	−680586.	+	83593.4i	−0.992541	+	0.121910i
$217$	−95369.6	−	95369.6i	−0.137487	−	0.137487i
$218$	258692.	+	542933.i	0.368673	+	0.773758i
$219$	865932.	−	846731.i	1.22004	−	1.19299i
$220$	−795454.	−	645230.i	−1.10805	−	0.898789i
$221$	−20002.5	−	48290.2i	−0.0275488	−	0.0665087i
$222$	−84966.6	+	231357.i	−0.115709	+	0.315066i
$223$			492827.i			0.663640i	0.943343	+	0.331820i	$0.107663\pi$
$223$			492827.i			0.663640i	−0.943343	+	0.331820i	$0.892337\pi$
$224$	269275.	−	464192.i	0.358572	−	0.618126i
$225$	1.53983e6	+	1.61048e6i	2.02776	+	2.12080i
$226$	1.03563e6	−	53847.9i	1.34875	−	0.0701290i
$227$	748840.	−	310180.i	0.964549	−	0.399529i	0.155869	−	0.987778i	$-0.450182\pi$
$227$	748840.	−	310180.i	0.964549	−	0.399529i	0.808680	+	0.588249i	$0.200182\pi$
$228$	388143.	−	204736.i	0.494487	−	0.260830i
$229$	−477692.	+	1.15325e6i	−0.601949	+	1.45323i	0.269623	+	0.962966i	$0.413101\pi$
$229$	−477692.	+	1.15325e6i	−0.601949	+	1.45323i	−0.871572	+	0.490267i	$0.836899\pi$
$230$	2.31433e6	−	1.10271e6i	2.88473	−	1.37449i
$231$	−386910.	+	155205.i	−0.477067	+	0.191371i
$232$	−218966.	−	358311.i	−0.267089	−	0.437059i
$233$	597085.	+	597085.i	0.720520	+	0.720520i	0.968711	−	0.248191i	$-0.0798360\pi$
$233$	597085.	+	597085.i	0.720520	+	0.720520i	−0.248191	+	0.968711i	$0.579836\pi$
$234$	−295173.	−	657043.i	−0.352401	−	0.784429i
$235$	831382.	−	2.00713e6i	0.982044	−	2.37086i
$236$	−413825.	+	1.39284e6i	−0.483657	+	1.62788i
$237$	−22550.8	−	252.824i	−0.0260790	−	0.000292379i
$238$	−34994.9	+	38833.6i	−0.0400463	+	0.0444391i
$239$			68223.8i			0.0772576i	0.999254	+	0.0386288i	$0.0122990\pi$
$239$			68223.8i			0.0772576i	−0.999254	+	0.0386288i	$0.987701\pi$
$240$	−1.73601e6	−	344890.i	−1.94546	−	0.386503i
$241$			989630.i			1.09756i	0.835965	+	0.548782i	$0.184908\pi$
$241$			989630.i			1.09756i	−0.835965	+	0.548782i	$0.815092\pi$
$242$	326612.	+	294326.i	0.358504	+	0.323065i
$243$	919037.	+	51569.8i	0.998429	+	0.0560247i
$244$	−599484.	+	324855.i	−0.644619	+	0.349313i
$245$	348979.	−	842511.i	0.371436	−	0.896727i
$246$	−828885.	−	763960.i	−0.873286	−	0.804883i
$247$	325957.	+	325957.i	0.339953	+	0.339953i
$248$	−40905.1	−	260343.i	−0.0422327	−	0.268792i
$249$	−563929.	−	1.40582e6i	−0.576402	−	1.43691i
$250$	1.63077e6	+	3.42261e6i	1.65023	+	3.46343i
$251$	−298654.	+	721014.i	−0.299215	+	0.722369i	0.700745	+	0.713412i	$0.252851\pi$
$251$	−298654.	+	721014.i	−0.299215	+	0.722369i	−0.999960	+	0.00895725i	$0.997149\pi$
$252$	−466243.	+	549156.i	−0.462499	+	0.544747i
$253$	1.09002e6	−	451502.i	1.07062	−	0.443464i
$254$	−40671.7	−	782216.i	−0.0395556	−	0.760750i
$255$	158539.	+	67761.0i	0.152681	+	0.0652574i
$256$	959320.	−	423341.i	0.914879	−	0.403729i
$257$			645214.i			0.609356i	0.952455	+	0.304678i	$0.0985488\pi$
$257$			645214.i			0.609356i	−0.952455	+	0.304678i	$0.901451\pi$
$258$	−476180.	+	1.29660e6i	−0.445371	+	1.21271i
$259$	99089.4	+	239223.i	0.0917863	+	0.221592i
$260$	−192823.	−	1.84922e6i	−0.176899	−	1.69650i
$261$	203988.	+	525496.i	0.185355	+	0.477494i
$262$	284318.	−	135469.i	0.255889	−	0.121923i
$263$	−784126.	−	784126.i	−0.699031	−	0.699031i	0.265170	−	0.964202i	$-0.414572\pi$
$263$	−784126.	−	784126.i	−0.699031	−	0.699031i	−0.964202	+	0.265170i	$0.914572\pi$
$264$	−789631.	−	199998.i	−0.697292	−	0.176610i
$265$	−249862.	+	249862.i	−0.218567	+	0.218567i
$266$	154073.	−	434521.i	0.133513	−	0.376536i
$267$	−1.26685e6	+	1.23876e6i	−1.08754	+	1.06343i
$268$	249191.	+	459854.i	0.211931	+	0.391095i
$269$	1.53143e6	−	634337.i	1.29037	−	0.534490i	0.371276	−	0.928522i	$-0.378920\pi$
$269$	1.53143e6	−	634337.i	1.29037	−	0.534490i	0.919097	+	0.394032i	$0.128920\pi$
$270$	2.21138e6	+	868883.i	1.84610	+	0.725357i
$271$	−106877.			−0.0884020			−0.0442010	−	0.999023i	$-0.514074\pi$
$271$	−106877.			−0.0884020			−0.0442010	+	0.999023i	$0.514074\pi$
$272$	−99946.5	+	21072.5i	−0.0819116	+	0.0172701i
$273$	−695842.	−	297409.i	−0.565072	−	0.241517i
$274$	−571182.	−	514720.i	−0.459619	−	0.414185i
$275$	1.01293e6	+	2.44543e6i	0.807695	+	1.94995i
$276$	1.30203e6	−	1.56889e6i	1.02884	−	1.23971i
$277$	−1.27887e6	−	529726.i	−1.00145	−	0.414812i	−0.179118	−	0.983828i	$-0.557324\pi$
$277$	−1.27887e6	−	529726.i	−1.00145	−	0.414812i	−0.822327	+	0.569015i	$0.807324\pi$
$278$	−297972.	+	840348.i	−0.231240	+	0.652149i
$279$	−7931.46	+	353683.i	−0.00610018	+	0.272021i
$280$	−1.58665e6	+	969610.i	−1.20945	+	0.739098i
$281$	471101.	−	471101.i	0.355917	−	0.355917i	−0.506389	−	0.862305i	$-0.669020\pi$
$281$	471101.	−	471101.i	0.355917	−	0.355917i	0.862305	+	0.506389i	$0.169020\pi$
$282$	−70366.0	−	1.72633e6i	−0.0526915	−	1.29271i
$283$	−746696.	−	309292.i	−0.554214	−	0.229563i	0.0879570	−	0.996124i	$-0.471966\pi$
$283$	−746696.	−	309292.i	−0.554214	−	0.229563i	−0.642171	+	0.766561i	$0.721966\pi$
$284$	397742.	+	322627.i	0.292621	+	0.237359i
$285$	−1.52045e6	−	17046.2i	−1.10882	−	0.0124313i
$286$	−44430.8	−	854513.i	−0.0321195	−	0.617737i
$287$	−1.18427e6			−0.848681
$288$	−1.36815e6	+	330929.i	−0.971971	+	0.235100i
$289$	−1.40991e6			−0.992992
$290$	75552.6	+	1.45306e6i	0.0527539	+	1.01459i
$291$	32857.3	+	368.372i	0.0227457	+	0.000255008i
$292$	1.56619e6	−	1.93083e6i	1.07495	−	1.32522i
$293$	536532.	+	222239.i	0.365112	+	0.151234i	0.557694	−	0.830046i	$-0.311686\pi$
$293$	536532.	+	222239.i	0.365112	+	0.151234i	−0.192582	+	0.981281i	$0.561686\pi$
$294$	−29536.7	−	724642.i	−0.0199294	−	0.488940i
$295$	3.56008e6	−	3.56008e6i	2.38180	−	2.38180i
$296$	−118718.	+	491821.i	−0.0787564	+	0.326270i
$297$	995593.	+	452187.i	0.654924	+	0.297459i
$298$	−409551.	+	1.15503e6i	−0.267157	+	0.753445i
$299$	1.97865e6	+	819585.i	1.27995	+	0.530171i
$300$	3.51976e6	+	2.92107e6i	2.25793	+	1.87387i
$301$	555329.	+	1.34068e6i	0.353292	+	0.852923i
$302$	−1.38174e6	−	1.24516e6i	−0.871786	−	0.785609i
$303$	2.04170e6	+	872644.i	1.27757	+	0.546048i
$304$	743237.	−	509015.i	0.461257	−	0.315898i
$305$	2.36260e6			1.45425
$306$	137058.	−	4048.09i	0.0836759	−	0.00247142i
$307$	−1.13823e6	+	471471.i	−0.689262	+	0.285502i	−0.699693	−	0.714444i	$-0.746680\pi$
$307$	−1.13823e6	+	471471.i	−0.689262	+	0.285502i	0.0104306	+	0.999946i	$0.496680\pi$
$308$	−752400.	+	407719.i	−0.451931	+	0.244897i
$309$	206426.	−	201848.i	0.122989	−	0.120262i
$310$	−305172.	+	860654.i	−0.180360	+	0.508656i
$311$	−782240.	+	782240.i	−0.458605	+	0.458605i	−0.898197	−	0.439592i	$-0.855123\pi$
$311$	−782240.	+	782240.i	−0.458605	+	0.458605i	0.439592	+	0.898197i	$0.355123\pi$
$312$	−756835.	−	1.27026e6i	−0.440164	−	0.738764i
$313$	830992.	+	830992.i	0.479442	+	0.479442i	0.904953	−	0.425511i	$-0.139906\pi$
$313$	830992.	+	830992.i	0.479442	+	0.479442i	−0.425511	+	0.904953i	$0.639906\pi$
$314$	−739218.	+	352216.i	−0.423105	+	0.201597i
$315$	2.32697e6	−	903288.i	1.32134	−	0.512920i
$316$	−46045.6	+	4801.31i	−0.0259400	+	0.00270484i
$317$	−454135.	−	1.09638e6i	−0.253826	−	0.612791i	0.744680	−	0.667421i	$-0.232602\pi$
$317$	−454135.	−	1.09638e6i	−0.253826	−	0.612791i	−0.998507	+	0.0546303i	$0.982602\pi$
$318$	−96879.1	+	263794.i	−0.0537233	+	0.146284i
$319$			669637.i			0.368436i
$320$	−3.62141e6	−	294003.i	−1.97698	−	0.160501i
$321$	1.91258e6	+	817457.i	1.03600	+	0.442795i
$322$	−111220.	−	2.13904e6i	−0.0597785	−	1.14969i
$323$	−81072.0	+	33581.1i	−0.0432379	+	0.0179097i
$324$	1.88627e6	−	111522.i	0.998257	−	0.0590198i
$325$	−1.83871e6	+	4.43904e6i	−0.965618	+	2.33121i
$326$	−24763.2	−	51972.0i	−0.0129051	−	0.0270848i
$327$	−617016.	−	1.53816e6i	−0.319100	−	0.795485i
$328$	−1.87040e6	−	1.36245e6i	−0.959951	−	0.699256i
$329$	−1.28351e6	−	1.28351e6i	−0.653749	−	0.653749i
$330$	2.07542e6	+	1.91285e6i	1.04911	+	0.966934i
$331$	291984.	−	704911.i	0.146484	−	0.353643i	−0.833559	−	0.552430i	$-0.813700\pi$
$331$	291984.	−	704911.i	0.146484	−	0.353643i	0.980043	+	0.198788i	$0.0637005\pi$
$332$	−1.48143e6	−	2.73381e6i	−0.737623	−	1.36120i
$333$	273914.	−	621496.i	0.135364	−	0.307134i
$334$	−1.28069e6	−	1.15409e6i	−0.628172	−	0.566077i
$335$		−	1.81231e6i		−	0.882306i
$336$	−821293.	+	1.22978e6i	−0.396872	+	0.594262i
$337$		−	691627.i		−	0.331740i	−0.986148	−	0.165870i	$-0.946957\pi$
$337$		−	691627.i		−	0.331740i	0.986148	−	0.165870i	$-0.0530431\pi$
$338$	−366253.	+	406429.i	−0.174377	+	0.193506i
$339$	−2.85753e6	−	32036.5i	−1.35049	−	0.0151407i
$340$	339271.	+	100800.i	0.159166	+	0.0472895i
$341$	−160825.	+	388266.i	−0.0748976	+	0.180819i
$342$	−1.10307e6	+	495551.i	−0.509964	+	0.229099i
$343$	−1.63976e6	−	1.63976e6i	−0.752565	−	0.752565i
$344$	−665331.	+	2.75632e6i	−0.303139	+	1.25584i
$345$	−6.55661e6	+	2.63012e6i	−2.96573	+	1.18967i
$346$	−3.07315e6	+	1.46426e6i	−1.38004	+	0.657551i
$347$	792581.	−	1.91346e6i	0.353362	−	0.853091i	−0.642838	−	0.766002i	$-0.722243\pi$
$347$	792581.	−	1.91346e6i	0.353362	−	0.853091i	0.996200	−	0.0870896i	$-0.0277567\pi$
$348$	539874.	+	1.02351e6i	0.238970	+	0.453046i
$349$	1.52394e6	−	631236.i	0.669736	−	0.277414i	−0.0217927	−	0.999763i	$-0.506937\pi$
$349$	1.52394e6	−	631236.i	0.669736	−	0.277414i	0.691529	+	0.722349i	$0.256937\pi$
$350$	4.79887e6	−	249519.i	2.09396	−	0.108877i
$351$	697500.	+	1.85833e6i	0.302187	+	0.805108i
$352$	−1.65738e6	−	221666.i	−0.712962	−	0.0953549i
$353$		−	3.87083e6i		−	1.65336i	−0.562672	−	0.826681i	$-0.690226\pi$
$353$		−	3.87083e6i		−	1.65336i	0.562672	−	0.826681i	$-0.309774\pi$
$354$	1.38035e6	−	3.75859e6i	0.585440	−	1.59411i
$355$	−679097.	−	1.63949e6i	−0.285997	−	0.690457i
$356$	−2.29131e6	+	2.82478e6i	−0.958206	+	1.18130i
$357$	102997.	−	100713.i	0.0427713	−	0.0418229i
$358$	492282.	+	1.03318e6i	0.203005	+	0.426060i
$359$	−1.94529e6	−	1.94529e6i	−0.796616	−	0.796616i	0.185945	−	0.982560i	$-0.440466\pi$
$359$	−1.94529e6	−	1.94529e6i	−0.796616	−	0.796616i	−0.982560	+	0.185945i	$0.940466\pi$
$360$	4.71434e6	+	1.25046e6i	1.91719	+	0.508525i
$361$	−1.20363e6	+	1.20363e6i	−0.486101	+	0.486101i
$362$	507141.	+	179823.i	0.203403	+	0.0721229i
$363$	−847050.	−	866258.i	−0.337398	−	0.345049i
$364$	−1.48909e6	−	442422.i	−0.589072	−	0.175018i
$365$	−7.95886e6	+	3.29667e6i	−3.12693	+	1.29522i
$366$	1.70519e6	−	789142.i	0.665382	−	0.307930i
$367$	877552.			0.340101			0.170050	−	0.985435i	$-0.445607\pi$
$367$	877552.			0.340101			0.170050	+	0.985435i	$0.445607\pi$
$368$	2.28522e6	−	3.50630e6i	0.879649	−	1.34967i
$369$	2.14671e6	+	2.24520e6i	0.820743	+	0.858398i
$370$	1.17359e6	−	1.30233e6i	0.445670	−	0.494557i
$371$	112982.	+	272763.i	0.0426162	+	0.102885i
$372$	67214.7	+	723105.i	0.0251830	+	0.270922i
$373$	−329435.	−	136456.i	−0.122602	−	0.0507834i	0.320539	−	0.947235i	$-0.396136\pi$
$373$	−329435.	−	136456.i	−0.122602	−	0.0507834i	−0.443141	+	0.896452i	$0.646136\pi$
$374$	153521.	+	54435.7i	0.0567530	+	0.0201236i
$375$	−3.88962e6	−	9.69643e6i	−1.42833	−	3.56069i
$376$	−550514.	−	3.50378e6i	−0.200816	−	1.27811i
$377$	−859525.	+	859525.i	−0.311462	+	0.311462i
$378$	1.37777e6	−	1.42919e6i	0.495960	−	0.514469i
$379$	799769.	+	331275.i	0.286000	+	0.118465i	0.521072	−	0.853513i	$-0.325532\pi$
$379$	799769.	+	331275.i	0.286000	+	0.118465i	−0.235071	+	0.971978i	$0.575532\pi$
$380$	−3.10455e6	+	323721.i	−1.10291	+	0.115004i
$381$	−24197.4	+	2.15831e6i	−0.00853997	+	0.761730i
$382$	−2.31833e6	+	120542.i	−0.812860	+	0.0422650i
$383$	−5.44760e6			−1.89762			−0.948808	−	0.315853i	$-0.897709\pi$
$383$	−5.44760e6			−1.89762			−0.948808	+	0.315853i	$0.897709\pi$
$384$	−2.71194e6	+	997408.i	−0.938537	+	0.345179i
$385$	2.96524e6			1.01955
$386$	495094.	−	25742.6i	0.169130	−	0.00879397i
$387$	1.53510e6	−	3.48306e6i	0.521026	−	1.18218i
$388$	67090.0	−	6995.66i	0.0226245	−	0.00235912i
$389$	2.24167e6	+	928529.i	0.751099	+	0.311116i	0.725190	−	0.688549i	$-0.241752\pi$
$389$	2.24167e6	+	928529.i	0.751099	+	0.311116i	0.0259093	+	0.999664i	$0.491752\pi$
$390$	208662.	+	5.11922e6i	0.0694674	+	1.70429i
$391$	−288283.	+	288283.i	−0.0953624	+	0.0953624i
$392$	−231083.	−	1.47074e6i	−0.0759542	−	0.483415i
$393$	−805488.	+	323113.i	−0.263074	+	0.105529i
$394$	2.72186e6	+	965120.i	0.883334	+	0.313214i
$395$	148203.	+	61387.6i	0.0477929	+	0.0197965i
$396$	2.13684e6	+	687373.i	0.684754	+	0.220270i
$397$	−1.27822e6	−	3.08591e6i	−0.407034	−	0.982667i	−0.985914	−	0.167254i	$-0.946510\pi$
$397$	−1.27822e6	−	3.08591e6i	−0.407034	−	0.982667i	0.578880	−	0.815413i	$-0.303490\pi$
$398$	2.10759e6	−	2.33878e6i	0.666926	−	0.740084i
$399$	−499305.	+	1.16821e6i	−0.157012	+	0.367358i
$400$	7.86626e6	+	5.12683e6i	2.45821	+	1.60213i
$401$	706214.			0.219319			0.109659	−	0.993969i	$-0.465024\pi$
$401$	706214.			0.219319			0.109659	+	0.993969i	$0.465024\pi$
$402$	−605337.	−	1.30802e6i	−0.186824	−	0.403692i
$403$	−704797.	+	291936.i	−0.216173	+	0.0895418i
$404$	4.36922e6	+	1.29813e6i	1.33184	+	0.395700i
$405$	−5.93058e6	−	2.77421e6i	−1.79663	−	0.840432i
$406$	1.14580e6	+	406279.i	0.344979	+	0.122323i
$407$	570508.	−	570508.i	0.170717	−	0.170717i
$408$	278536.	−	40569.4i	0.0828383	−	0.0120656i
$409$	1.40312e6	+	1.40312e6i	0.414751	+	0.414751i	0.883390	−	0.468639i	$-0.155255\pi$
$409$	1.40312e6	+	1.40312e6i	0.414751	+	0.414751i	−0.468639	+	0.883390i	$0.655255\pi$
$410$	3.44889e6	+	7.23841e6i	1.01326	+	2.12659i
$411$	1.48133e6	+	1.51492e6i	0.432560	+	0.442369i
$412$	373356.	−	460282.i	0.108363	−	0.133592i
$413$	−1.60979e6	−	3.88638e6i	−0.464402	−	1.12117i
$414$	−3.85371e6	+	4.08828e6i	−1.10504	+	1.17230i
$415$			1.07741e7i			3.07085i
$416$	−1.84284e6	−	2.41189e6i	−0.522101	−	0.683320i
$417$	965639.	−	2.25928e6i	0.271941	−	0.636254i
$418$	−1.43460e6	+	74592.5i	−0.401596	+	0.0208812i
$419$	−3.78991e6	+	1.56983e6i	−1.05462	+	0.436836i	−0.841537	−	0.540199i	$-0.818349\pi$
$419$	−3.78991e6	+	1.56983e6i	−1.05462	+	0.436836i	−0.213078	+	0.977035i	$0.568349\pi$
$420$	4.53222e6	−	2.39064e6i	1.25368	−	0.661287i
$421$	1.59359e6	−	3.84727e6i	0.438200	−	1.05791i	−0.538371	−	0.842708i	$-0.680960\pi$
$421$	1.59359e6	−	3.84727e6i	0.438200	−	1.05791i	0.976570	−	0.215199i	$-0.0690400\pi$
$422$	−1.40341e6	+	668683.i	−0.383621	+	0.182784i
$423$	−106744.	+	4.75997e6i	−0.0290063	+	1.29346i
$424$	−135362.	+	560775.i	−0.0365664	+	0.151487i
$425$	−646753.	−	646753.i	−0.173687	−	0.173687i
$426$	−1.03775e6	−	956462.i	−0.277056	−	0.255355i
$427$	755412.	−	1.82373e6i	0.200500	−	0.484049i
$428$	4.09291e6	+	1.21604e6i	1.08000	+	0.320876i
$429$	−26433.9	+	2.35779e6i	−0.00693454	+	0.618533i
$430$	6.57719e6	−	7.29867e6i	1.71541	−	1.90359i
$431$			6.84930e6i			1.77604i	0.459803	+	0.888021i	$0.347920\pi$
$431$			6.84930e6i			1.77604i	−0.459803	+	0.888021i	$0.652080\pi$
$432$	3.82023e6	−	672149.i	0.984872	−	0.173283i
$433$			3.06368e6i			0.785278i	0.919693	+	0.392639i	$0.128438\pi$
$433$			3.06368e6i			0.785278i	−0.919693	+	0.392639i	$0.871562\pi$
$434$	566778.	+	510751.i	0.144440	+	0.130162i
$435$	44949.7	−	4.00933e6i	0.0113895	−	1.01589i
$436$	−1.62089e6	−	2.99116e6i	−0.408353	−	0.753570i
$437$	1.37596e6	−	3.32186e6i	0.344669	−	0.832103i
$438$	−4.64313e6	+	5.03773e6i	−1.15645	+	1.25473i
$439$	4.02229e6	+	4.02229e6i	0.996122	+	0.996122i	0.999993	−	0.00387056i	$-0.00123204\pi$
$439$	4.02229e6	+	4.02229e6i	0.996122	+	0.996122i	−0.00387056	+	0.999993i	$0.501232\pi$
$440$	4.68322e6	+	3.41139e6i	1.15322	+	0.840040i
$441$	−44806.7	+	1.99804e6i	−0.0109710	+	0.489223i
$442$	127183.	+	266927.i	0.0309651	+	0.0649885i
$443$	−779995.	+	1.88308e6i	−0.188835	+	0.455888i	−0.989736	−	0.142909i	$-0.954354\pi$
$443$	−779995.	+	1.88308e6i	−0.188835	+	0.455888i	0.800901	+	0.598797i	$0.204354\pi$
$444$	412038.	−	1.33195e6i	0.0991927	−	0.320649i
$445$	1.16437e7	−	4.82298e6i	2.78734	−	1.15456i
$446$	−144760.	−	2.78409e6i	−0.0344597	−	0.662744i
$447$	1.32723e6	−	3.10530e6i	0.314180	−	0.735080i
$448$	−1.38485e6	+	2.70142e6i	−0.325992	+	0.635912i
$449$		−	7.68132e6i		−	1.79813i	−0.437819	−	0.899063i	$-0.644249\pi$
$449$		−	7.68132e6i		−	1.79813i	0.437819	−	0.899063i	$-0.355751\pi$
$450$	−9.17192e6	−	8.64566e6i	−2.13515	−	2.01264i
$451$	1.41214e6	+	3.40921e6i	0.326917	+	0.789246i
$452$	−5.83467e6	+	608397.i	−1.34329	+	0.140069i
$453$	3.58347e6	+	3.66473e6i	0.820462	+	0.839067i
$454$	−4.13925e6	+	1.97223e6i	−0.942502	+	0.449075i
$455$	3.80610e6	+	3.80610e6i	0.861889	+	0.861889i
$456$	−2.13257e6	+	1.27061e6i	−0.480276	+	0.286154i
$457$	−1.13919e6	+	1.13919e6i	−0.255156	+	0.255156i	−0.823081	−	0.567925i	$-0.807747\pi$
$457$	−1.13919e6	+	1.13919e6i	−0.255156	+	0.255156i	0.567925	+	0.823081i	$0.307747\pi$
$458$	2.35984e6	−	6.65529e6i	0.525677	−	1.48253i
$459$	−377638.	−	12705.7i	−0.0836650	−	0.00281492i
$460$	−1.27502e7	+	6.90924e6i	−2.80947	+	1.52242i
$461$	5.03268e6	−	2.08460e6i	1.10293	−	0.456847i	0.244431	−	0.969667i	$-0.421399\pi$
$461$	5.03268e6	−	2.08460e6i	1.10293	−	0.456847i	0.858496	+	0.512819i	$0.171399\pi$
$462$	2.14015e6	−	990435.i	0.466487	−	0.215884i
$463$	773117.			0.167607			0.0838036	−	0.996482i	$-0.473293\pi$
$463$	773117.			0.167607			0.0838036	+	0.996482i	$0.473293\pi$
$464$	1.34223e6	+	1.95986e6i	0.289423	+	0.422601i
$465$	988973.	−	2.31388e6i	0.212106	−	0.496258i
$466$	−3.54845e6	−	3.19768e6i	−0.756962	−	0.682135i
$467$	1.17632e6	+	2.83988e6i	0.249593	+	0.602570i	0.998170	−	0.0604779i	$-0.0192625\pi$
$467$	1.17632e6	+	2.83988e6i	0.249593	+	0.602570i	−0.748577	+	0.663048i	$0.769262\pi$
$468$	1.86050e6	+	3.62508e6i	0.392658	+	0.765073i
$469$	−1.39895e6	−	579463.i	−0.293676	−	0.121645i
$470$	−4.10710e6	+	1.15830e7i	−0.857612	+	2.41866i
$471$	2.09425e6	−	840084.i	0.434986	−	0.174490i
$472$	1.92867e6	−	7.99004e6i	0.398476	−	1.65080i
$473$	3.19731e6	−	3.19731e6i	0.657101	−	0.657101i
$474$	127469.	−	5195.68i	0.0260590	−	0.00106218i
$475$	7.45248e6	+	3.08692e6i	1.51554	+	0.627756i
$476$	186287.	−	229659.i	0.0376847	−	0.0464586i
$477$	312317.	−	708632.i	0.0628492	−	0.142602i
$478$	−20039.6	−	385411.i	−0.00401162	−	0.0771533i
$479$	4.92324e6			0.980421			0.490210	−	0.871604i	$-0.336920\pi$
$479$	4.92324e6			0.980421			0.490210	+	0.871604i	$0.336920\pi$
$480$	9.90839e6	+	1.43844e6i	1.96291	+	0.284963i
$481$	1.46457e6			0.288635
$482$	−290688.	−	5.59064e6i	−0.0569914	−	1.09608i
$483$	−66170.1	+	5.90210e6i	−0.0129061	+	1.15117i
$484$	−1.93156e6	−	1.56678e6i	−0.374796	−	0.304014i
$485$	−215936.	−	89443.6i	−0.0416841	−	0.0172661i
$486$	−5.20699e6	−	21376.8i	−0.999992	−	0.00410538i
$487$	−1.29540e6	+	1.29540e6i	−0.247503	+	0.247503i	−0.819945	−	0.572442i	$-0.805996\pi$
$487$	−1.29540e6	+	1.29540e6i	−0.247503	+	0.247503i	0.572442	+	0.819945i	$0.305996\pi$
$488$	3.29120e6	−	2.01127e6i	0.625611	−	0.382314i
$489$	59063.6	+	147240.i	0.0111699	+	0.0278453i
$490$	−1.72399e6	+	4.86204e6i	−0.324373	+	0.914804i
$491$	−7.22809e6	−	2.99397e6i	−1.35307	−	0.560459i	−0.415923	−	0.909400i	$-0.636541\pi$
$491$	−7.22809e6	−	2.99397e6i	−1.35307	−	0.560459i	−0.937145	+	0.348941i	$0.886541\pi$
$492$	4.90696e6	+	4.07231e6i	0.913902	+	0.758452i
$493$	−88550.9	−	213781.i	−0.0164088	−	0.0396143i
$494$	−1.93715e6	−	1.74566e6i	−0.357146	−	0.321842i
$495$	−5.37507e6	−	5.62167e6i	−0.985986	−	1.03122i
$496$	307554.	+	1.45872e6i	0.0561328	+	0.266237i
$497$	−1.48268e6			−0.269250
$498$	3.59869e6	+	7.77613e6i	0.650237	+	1.40504i
$499$	−1.02357e7	+	4.23975e6i	−1.84020	+	0.762234i	−0.885511	+	0.464619i	$0.846191\pi$
$499$	−1.02357e7	+	4.23975e6i	−1.84020	+	0.762234i	−0.954686	+	0.297616i	$0.903809\pi$
$500$	−1.02179e7	−	1.88561e7i	−1.82784	−	3.37307i
$501$	3.32140e6	+	3.39672e6i	0.591190	+	0.604597i
$502$	1.47538e6	−	4.16089e6i	0.261302	−	0.736932i
$503$	1.17143e6	−	1.17143e6i	0.206441	−	0.206441i	−0.596312	−	0.802753i	$-0.703368\pi$
$503$	1.17143e6	−	1.17143e6i	0.206441	−	0.206441i	0.802753	+	0.596312i	$0.203368\pi$
$504$	2.47260e6	−	3.23926e6i	0.433589	−	0.568027i
$505$	−1.11677e7	−	1.11677e7i	−1.94865	−	1.94865i
$506$	−6.02515e6	+	2.87081e6i	−1.04614	+	0.498458i
$507$	1.07795e6	−	1.05405e6i	0.186243	−	0.182113i
$508$	459526.	+	4.40696e6i	0.0790044	+	0.757670i
$509$	555266.	+	1.34053e6i	0.0949962	+	0.229341i	0.964234	−	0.265054i	$-0.0853897\pi$
$509$	555266.	+	1.34053e6i	0.0949962	+	0.229341i	−0.869237	+	0.494395i	$0.835390\pi$
$510$	−915525.	−	336229.i	−0.155864	−	0.0572413i
$511$			7.19763e6i			1.21938i
$512$	−5.29506e6	+	2.67333e6i	−0.892681	+	0.450690i
$513$	3.11985e6	−	1.17100e6i	0.523407	−	0.196454i
$514$	−189521.	−	3.64496e6i	−0.0316410	−	0.608534i
$515$	−1.89728e6	+	785877.i	−0.315219	+	0.130568i
$516$	2.30919e6	−	7.46466e6i	0.381800	−	1.23420i
$517$	−2.16443e6	+	5.22541e6i	−0.356138	+	0.859793i
$518$	−630046.	−	1.32232e6i	−0.103169	−	0.216527i
$519$	8.70639e6	−	3.49248e6i	1.41880	−	0.569135i
$520$	1.63248e6	+	1.03900e7i	0.264752	+	1.68503i
$521$	4.18805e6	+	4.18805e6i	0.675955	+	0.675955i	0.959082	−	0.283128i	$-0.0913720\pi$
$521$	4.18805e6	+	4.18805e6i	0.675955	+	0.675955i	−0.283128	+	0.959082i	$0.591372\pi$
$522$	−1.30673e6	−	2.90873e6i	−0.209899	−	0.467226i
$523$	1.40255e6	−	3.38605e6i	0.224214	−	0.541301i	−0.771240	−	0.636545i	$-0.780363\pi$
$523$	1.40255e6	−	3.38605e6i	0.224214	−	0.541301i	0.995454	+	0.0952438i	$0.0303631\pi$
$524$	−1.56638e6	+	848809.i	−0.249212	+	0.135046i
$525$	−1.32412e7	−	148450.i	−2.09666	−	0.0235062i
$526$	4.66003e6	+	4.19938e6i	0.734386	+	0.661791i
$527$		−	145221.i		−	0.0227773i
$528$	4.51955e6	+	897893.i	0.705521	+	0.140165i
$529$		−	1.02686e7i		−	1.59540i
$530$	1.33813e6	−	1.48492e6i	0.206923	−	0.229622i
$531$	−4.44996e6	+	1.00967e7i	−0.684888	+	1.55398i
$532$	−742759.	+	2.49996e6i	−0.113781	+	0.382961i
$533$	−2.56338e6	+	6.18854e6i	−0.390836	+	0.943562i
$534$	6.79284e6	−	7.37012e6i	1.03086	−	1.11846i
$535$	−1.04614e7	−	1.04614e7i	−1.58018	−	1.58018i
$536$	−1.54281e6	−	2.52462e6i	−0.231953	−	0.379563i
$537$	−1.17416e6	−	2.92707e6i	−0.175708	−	0.438023i
$538$	−8.46504e6	+	4.03334e6i	−1.26088	+	0.600772i
$539$	−908539.	+	2.19341e6i	−0.134701	+	0.325198i
$540$	−1.27478e7	−	4.25896e6i	−1.88127	−	0.628519i
$541$	6.32958e6	−	2.62180e6i	0.929784	−	0.385129i	0.134187	−	0.990956i	$-0.457158\pi$
$541$	6.32958e6	−	2.62180e6i	0.929784	−	0.385129i	0.795597	+	0.605827i	$0.207158\pi$
$542$	603773.	−	31393.5i	0.0882827	−	0.00459030i
$543$	−1.36345e6	−	582753.i	−0.198445	−	0.0848174i
$544$	558430.	−	148401.i	0.0809043	−	0.0215001i
$545$			1.17883e7i			1.70005i
$546$	4.01832e6	+	1.47574e6i	0.576851	+	0.211850i
$547$	−2.89372e6	−	6.98605e6i	−0.413512	−	0.998306i	−0.984187	−	0.177130i	$-0.943319\pi$
$547$	−2.89372e6	−	6.98605e6i	−0.413512	−	0.998306i	0.570676	−	0.821176i	$-0.306681\pi$
$548$	3.37793e6	+	2.73999e6i	0.480506	+	0.389761i
$549$	−4.82685e6	+	1.87370e6i	−0.683491	+	0.265319i
$550$	−6.44057e6	−	1.35172e7i	−0.907857	−	1.90538i
$551$	1.44301e6	+	1.44301e6i	0.202484	+	0.202484i
$552$	−6.89464e6	+	9.24548e6i	−0.963083	+	1.29146i
$553$	94772.0	−	94772.0i	0.0131785	−	0.0131785i
$554$	7.38022e6	+	2.61689e6i	1.02163	+	0.362252i
$555$	−3.45411e6	+	3.37752e6i	−0.475996	+	0.465441i
$556$	1.43647e6	−	4.83483e6i	0.197065	−	0.663277i
$557$	8.52091e6	−	3.52948e6i	1.16372	−	0.482028i	0.284607	−	0.958644i	$-0.408137\pi$
$557$	8.52091e6	−	3.52948e6i	1.16372	−	0.482028i	0.879112	+	0.476616i	$0.158137\pi$
$558$	−59081.9	−	2.00036e6i	−0.00803284	−	0.271971i
$559$	8.20794e6			1.11098
$560$	8.67853e6	−	5.94360e6i	1.16944	−	0.800902i
$561$	−412743.	−	176410.i	−0.0553697	−	0.0236655i
$562$	−2.52298e6	+	2.79973e6i	−0.336956	+	0.373918i
$563$	1.26476e6	+	3.05340e6i	0.168166	+	0.405988i	0.985386	−	0.170338i	$-0.0544859\pi$
$563$	1.26476e6	+	3.05340e6i	0.168166	+	0.405988i	−0.817220	+	0.576326i	$0.804486\pi$
$564$	904596.	+	9.73177e6i	0.119745	+	1.28823i
$565$	1.87795e7	+	7.77872e6i	2.47493	+	1.02515i
$566$	4.30910e6	+	1.52793e6i	0.565387	+	0.200476i
$567$	−4.03769e6	+	3.69088e6i	−0.527443	+	0.482139i
$568$	−2.34170e6	−	1.70576e6i	−0.304551	−	0.221844i
$569$	−1.88941e6	+	1.88941e6i	−0.244650	+	0.244650i	−0.818771	−	0.574121i	$-0.805344\pi$
$569$	−1.88941e6	+	1.88941e6i	−0.244650	+	0.244650i	0.574121	+	0.818771i	$0.305344\pi$
$570$	8.59439e6	−	350311.i	1.10797	−	0.0451613i
$571$	−6.62812e6	−	2.74546e6i	−0.850746	−	0.352390i	−0.0856644	−	0.996324i	$-0.527301\pi$
$571$	−6.62812e6	−	2.74546e6i	−0.850746	−	0.352390i	−0.765081	+	0.643934i	$0.777301\pi$
$572$	501999.	+	4.81428e6i	0.0641524	+	0.615236i
$573$	6.39678e6	+	71716.1i	0.813907	+	0.00912494i
$574$	6.69018e6	−	347859.i	0.847536	−	0.0440680i
$575$	3.74769e7			4.72709
$576$	7.63180e6	−	2.27136e6i	0.958452	−	0.285253i
$577$	4.50956e6			0.563891			0.281945	−	0.959430i	$-0.409020\pi$
$577$	4.50956e6			0.563891			0.281945	+	0.959430i	$0.409020\pi$
$578$	7.96488e6	−	414137.i	0.991653	−	0.0515614i
$579$	−1.36608e6	−	15315.5i	−0.169347	−	0.00189860i
$580$	−853627.	−	8.18648e6i	−0.105365	−	1.01048i
$581$	8.31667e6	+	3.44488e6i	1.02214	+	0.423383i
$582$	−185726.	+	7570.28i	−0.0227282	+	0.000926413i
$583$	650495.	−	650495.i	0.0792634	−	0.0792634i
$584$	−8.28059e6	+	1.13677e7i	−1.00468	+	1.37925i
$585$	316536.	−	1.41151e7i	0.0382414	−	1.70527i
$586$	−3.09627e6	−	1.09788e6i	−0.372472	−	0.132072i
$587$	408105.	+	169042.i	0.0488851	+	0.0202489i	0.406992	−	0.913432i	$-0.366578\pi$
$587$	408105.	+	169042.i	0.0488851	+	0.0202489i	−0.358107	+	0.933681i	$0.616578\pi$
$588$	379711.	+	4.08499e6i	0.0452908	+	0.487245i
$589$	490117.	+	1.18325e6i	0.0582119	+	0.140536i
$590$	−1.90660e7	+	2.11574e7i	−2.25491	+	2.50226i
$591$	−7.31774e6	−	3.12767e6i	−0.861803	−	0.368343i
$592$	526198.	−	2.81328e6i	0.0617084	−	0.329919i
$593$	−1.10667e7			−1.29235			−0.646177	−	0.763188i	$-0.723633\pi$
$593$	−1.10667e7			−1.29235			−0.646177	+	0.763188i	$0.723633\pi$
$594$	−5.75715e6	−	2.26206e6i	−0.669486	−	0.263050i
$595$	−946651.	+	392116.i	−0.109622	+	0.0454069i
$596$	1.97437e6	−	6.64530e6i	0.227674	−	0.766300i
$597$	−6.20303e6	+	6.06549e6i	−0.712309	+	0.696514i
$598$	−1.14186e7	−	4.04882e6i	−1.30575	−	0.462994i
$599$	−6.75384e6	+	6.75384e6i	−0.769101	+	0.769101i	−0.977948	−	0.208847i	$-0.933029\pi$
$599$	−6.75384e6	+	6.75384e6i	−0.769101	+	0.769101i	0.208847	+	0.977948i	$0.433029\pi$
$600$	−2.07419e7	−	1.54679e7i	−2.35218	−	1.75409i
$601$	−1.09622e7	−	1.09622e7i	−1.23797	−	1.23797i	−0.960827	−	0.277147i	$-0.910611\pi$
$601$	−1.09622e7	−	1.09622e7i	−1.23797	−	1.23797i	−0.277147	−	0.960827i	$-0.589389\pi$
$602$	−3.53098e6	−	7.41070e6i	−0.397104	−	0.833427i
$603$	1.43728e6	+	3.70259e6i	0.160971	+	0.414679i
$604$	8.17152e6	+	6.62830e6i	0.911403	+	0.739281i
$605$	3.29791e6	+	7.96185e6i	0.366311	+	0.884353i
$606$	−1.17904e7	−	4.33005e6i	−1.30421	−	0.478973i
$607$		−	6.00755e6i		−	0.661798i	−0.943666	−	0.330899i	$-0.892648\pi$
$607$		−	6.00755e6i		−	0.661798i	0.943666	−	0.330899i	$-0.107352\pi$
$608$	−4.04920e6	+	3.09385e6i	−0.444232	+	0.339422i
$609$	−3.08049e6	−	1.31663e6i	−0.336571	−	0.143854i
$610$	−1.33468e7	+	693975.i	−1.45229	+	0.0755125i
$611$	−9.48538e6	+	3.92897e6i	−1.02790	+	0.425771i
$612$	−773081.	+	63127.1i	−0.0834347	+	0.00681298i
$613$	4.79934e6	−	1.15866e7i	0.515859	−	1.24539i	−0.424568	−	0.905396i	$-0.639574\pi$
$613$	4.79934e6	−	1.15866e7i	0.515859	−	1.24539i	0.940427	−	0.339997i	$-0.110426\pi$
$614$	6.29163e6	−	2.99778e6i	0.673507	−	0.320907i
$615$	−8.22609e6	−	2.05068e7i	−0.877012	−	2.18630i
$616$	4.13071e6	−	2.52430e6i	0.438605	−	0.268033i
$617$	−1.21995e7	−	1.21995e7i	−1.29012	−	1.29012i	−0.934710	−	0.355411i	$-0.884341\pi$
$617$	−1.21995e7	−	1.21995e7i	−1.29012	−	1.29012i	−0.355411	−	0.934710i	$-0.615659\pi$
$618$	−1.10686e6	+	1.20092e6i	−0.116579	+	0.126486i
$619$	−3.38114e6	+	8.16279e6i	−0.354680	+	0.856272i	0.641350	+	0.767249i	$0.278375\pi$
$619$	−3.38114e6	+	8.16279e6i	−0.354680	+	0.856272i	−0.996030	+	0.0890237i	$0.971625\pi$
$620$	1.47118e6	−	4.95167e6i	0.153705	−	0.517335i
$621$	1.13095e7	−	1.05732e7i	1.17683	−	1.10022i
$622$	4.18928e6	−	4.64882e6i	0.434173	−	0.481800i
$623$		−	1.05300e7i		−	1.08695i
$624$	4.64865e6	+	6.95366e6i	0.477931	+	0.714911i
$625$			4.56582e7i			4.67540i
$626$	−4.93855e6	−	4.45037e6i	−0.503691	−	0.453900i
$627$	3.95838e6	+	44378.5i	0.402113	+	0.00450820i
$628$	4.07255e6	−	2.20688e6i	0.412067	−	0.223295i
$629$	−106692.	+	257577.i	−0.0107524	+	0.0259585i
$630$	−1.28802e7	+	5.78639e6i	−1.29292	+	0.580839i
$631$	6.58686e6	+	6.58686e6i	0.658574	+	0.658574i	0.955043	−	0.296468i	$-0.0958090\pi$
$631$	6.58686e6	+	6.58686e6i	0.658574	+	0.658574i	−0.296468	+	0.955043i	$0.595809\pi$
$632$	258712.	−	40648.8i	0.0257646	−	0.00404814i
$633$	3.97593e6	−	1.59490e6i	0.394393	−	0.158207i
$634$	2.88755e6	+	6.06029e6i	0.285303	+	0.598784i
$635$	5.87532e6	−	1.41843e7i	0.578225	−	1.39596i
$636$	469807.	−	1.51869e6i	0.0460549	−	0.148876i
$637$	−3.98156e6	+	1.64922e6i	−0.388781	+	0.161038i
$638$	−196695.	−	3.78293e6i	−0.0191312	−	0.367939i
$639$	2.68763e6	+	2.81094e6i	0.260386	+	0.272333i
$640$	2.05445e7	+	597160.i	1.98265	+	0.0576289i
$641$		−	6.20207e6i		−	0.596199i	−0.954535	−	0.298100i	$-0.903647\pi$
$641$		−	6.20207e6i		−	0.596199i	0.954535	−	0.298100i	$-0.0963528\pi$
$642$	−1.10447e7	−	4.05621e6i	−1.05759	−	0.388403i
$643$	−7.00260e6	−	1.69058e7i	−0.667932	−	1.61253i	−0.785065	−	0.619414i	$-0.787370\pi$
$643$	−7.00260e6	−	1.69058e7i	−0.667932	−	1.61253i	0.117133	−	0.993116i	$-0.462630\pi$
$644$	1.25662e6	+	1.20513e7i	0.119396	+	1.14503i
$645$	−1.93579e7	+	1.89287e7i	−1.83214	+	1.79152i
$646$	448130.	−	213521.i	0.0422496	−	0.0201307i
$647$	5.35123e6	+	5.35123e6i	0.502566	+	0.502566i	0.912234	−	0.409669i	$-0.134356\pi$
$647$	5.35123e6	+	5.35123e6i	0.502566	+	0.502566i	−0.409669	+	0.912234i	$0.634356\pi$
$648$	−1.06232e7	+	1.18407e6i	−0.993846	+	0.110775i
$649$	−9.26838e6	+	9.26838e6i	−0.863758	+	0.863758i
$650$	9.08340e6	−	2.56172e7i	0.843267	−	2.37820i
$651$	−1.46991e6	−	1.50324e6i	−0.135937	−	0.139019i
$652$	155159.	+	286328.i	0.0142941	+	0.0263782i
$653$	−5.52115e6	+	2.28694e6i	−0.506695	+	0.209880i	−0.621361	−	0.783524i	$-0.713420\pi$
$653$	−5.52115e6	+	2.28694e6i	−0.506695	+	0.209880i	0.114666	+	0.993404i	$0.463420\pi$
$654$	3.93747e6	+	8.50816e6i	0.359976	+	0.777842i
$655$	6.17319e6			0.562220
$656$	1.09665e7	+	7.14739e6i	0.994965	+	0.648467i
$657$	1.36457e7	−	1.30471e7i	1.23334	−	1.17923i
$658$	7.62787e6	+	6.87384e6i	0.686813	+	0.618921i
$659$	−1.61000e6	−	3.88689e6i	−0.144415	−	0.348649i	0.835076	−	0.550134i	$-0.185423\pi$
$659$	−1.61000e6	−	3.88689e6i	−0.144415	−	0.348649i	−0.979492	+	0.201485i	$0.935423\pi$
$660$	−1.22864e7	−	1.01965e7i	−1.09790	−	0.911154i
$661$	−5.87124e6	−	2.43195e6i	−0.522669	−	0.216496i	0.105720	−	0.994396i	$-0.466285\pi$
$661$	−5.87124e6	−	2.43195e6i	−0.522669	−	0.216496i	−0.628389	+	0.777899i	$0.716285\pi$
$662$	−1.44243e6	+	4.06797e6i	−0.127923	+	0.360772i
$663$	−303349.	−	756219.i	−0.0268015	−	0.0668134i
$664$	9.17192e6	+	1.50087e7i	0.807309	+	1.32106i
$665$	6.38986e6	−	6.38986e6i	0.560321	−	0.560321i
$666$	−1.36485e6	+	3.59143e6i	−0.119233	+	0.313749i
$667$	8.75949e6	+	3.62830e6i	0.762367	+	0.315783i
$668$	7.57392e6	+	6.14356e6i	0.656719	+	0.532695i
$669$	−86124.2	+	7.68193e6i	−0.00743978	+	0.663598i
$670$	532335.	+	1.02381e7i	0.0458140	+	0.881116i
$671$	−6.15082e6			−0.527384
$672$	4.27844e6	−	7.18852e6i	0.365479	−	0.614068i
$673$	−6.80867e6			−0.579462			−0.289731	−	0.957108i	$-0.593566\pi$
$673$	−6.80867e6			−0.579462			−0.289731	+	0.957108i	$0.593566\pi$
$674$	203154.	+	3.90716e6i	0.0172257	+	0.331292i
$675$	2.37207e7	+	2.53724e7i	2.00386	+	2.14340i
$676$	1.94967e6	−	2.40359e6i	0.164094	−	0.202299i
$677$	−3.29660e6	−	1.36549e6i	−0.276436	−	0.114503i	0.240159	−	0.970734i	$-0.422800\pi$
$677$	−3.29660e6	−	1.36549e6i	−0.276436	−	0.114503i	−0.516594	+	0.856230i	$0.672800\pi$
$678$	1.61522e7	−	658371.i	1.34945	−	0.0550043i
$679$	−138086.	+	138086.i	−0.0114941	+	0.0114941i
$680$	−1.94623e6	−	469788.i	−0.161407	−	0.0389609i
$681$	1.17267e7	−	4.70405e6i	0.968967	−	0.388691i
$682$	794490.	−	2.24064e6i	0.0654075	−	0.184464i
$683$	−6.87153e6	−	2.84628e6i	−0.563640	−	0.233467i	0.0826247	−	0.996581i	$-0.473670\pi$
$683$	−6.87153e6	−	2.84628e6i	−0.563640	−	0.233467i	−0.646265	+	0.763113i	$0.723670\pi$
$684$	6.08595e6	−	3.12349e6i	0.497380	−	0.255270i
$685$	−5.76741e6	−	1.39238e7i	−0.469628	−	1.13378i
$686$	9.74500e6	+	8.78170e6i	0.790627	+	0.712473i
$687$	−7.64756e6	+	1.78928e7i	−0.618203	+	1.44639i
$688$	2.94898e6	−	1.57665e7i	0.237520	−	1.26988i
$689$	1.66991e6			0.134012
$690$	3.62672e7	−	1.67840e7i	2.89996	−	1.34206i
$691$	−554453.	+	229662.i	−0.0441743	+	0.0182976i	−0.404661	−	0.914467i	$-0.632611\pi$
$691$	−554453.	+	229662.i	−0.0441743	+	0.0182976i	0.360487	+	0.932764i	$0.382611\pi$
$692$	1.69308e7	−	9.17465e6i	1.34404	−	0.728323i
$693$	−6.05807e6	+	2.35164e6i	−0.479183	+	0.186010i
$694$	−3.91542e6	+	1.10424e7i	−0.308588	+	0.870289i
$695$	−1.23578e7	+	1.23578e7i	−0.970460	+	0.970460i
$696$	−3.35051e6	−	5.62343e6i	−0.262173	−	0.440026i
$697$	−901649.	−	901649.i	−0.0703001	−	0.0703001i
$698$	−8.42365e6	+	4.01363e6i	−0.654428	+	0.311816i
$699$	9.20270e6	+	9.41139e6i	0.712398	+	0.728553i
$700$	−2.70366e7	+	2.81918e6i	−2.08548	+	0.217459i
$701$	−5.46546e6	−	1.31948e7i	−0.420080	−	1.01416i	−0.982324	−	0.187191i	$-0.940062\pi$
$701$	−5.46546e6	−	1.31948e7i	−0.420080	−	1.01416i	0.562244	−	0.826972i	$-0.309938\pi$
$702$	−4.48619e6	−	1.02932e7i	−0.343585	−	0.788331i
$703$		−	2.45880e6i		−	0.187644i
$704$	9.42803e6	+	765413.i	0.716951	+	0.0582055i
$705$	1.33099e7	−	3.11409e7i	1.00856	−	2.35971i
$706$	1.13699e6	+	2.18672e7i	0.0858513	+	1.65113i
$707$	−1.21912e7	+	5.04977e6i	−0.917273	+	0.379947i
$708$	−6.69390e6	+	2.16386e7i	−0.501876	+	1.62236i
$709$	−4.26740e6	+	1.03024e7i	−0.318821	+	0.769703i	0.680496	+	0.732752i	$0.261764\pi$
$709$	−4.26740e6	+	1.03024e7i	−0.318821	+	0.769703i	−0.999317	+	0.0369506i	$0.988236\pi$
$710$	4.31794e6	+	9.06234e6i	0.321463	+	0.674675i
$711$	−351466.	−	7881.77i	−0.0260741	−	0.000584722i
$712$	1.21144e7	−	1.66308e7i	0.895574	−	1.22946i
$713$	4.20749e6	+	4.20749e6i	0.309956	+	0.309956i
$714$	−552268.	+	599203.i	−0.0405420	+	0.0439874i
$715$	6.41835e6	−	1.54953e7i	0.469525	−	1.13353i
$716$	−3.08449e6	−	5.69209e6i	−0.224854	−	0.414944i
$717$	−11922.5	+	1.06344e6i	−0.000866102	+	0.0772527i
$718$	1.15608e7	+	1.04180e7i	0.836905	+	0.754176i
$719$		−	2.13793e7i		−	1.54231i	−0.636647	−	0.771155i	$-0.719679\pi$
$719$		−	2.13793e7i		−	1.54231i	0.636647	−	0.771155i	$-0.280321\pi$
$720$	−2.69997e7	−	5.67935e6i	−1.94101	−	0.408289i
$721$			1.71581e6i			0.122923i
$722$	6.44605e6	−	7.15314e6i	0.460204	−	0.510686i
$723$	−172943.	+	1.54258e7i	−0.0123043	+	1.09750i
$724$	−2.91777e6	−	866895.i	−0.206874	−	0.0614639i
$725$	−8.13998e6	+	1.96516e7i	−0.575146	+	1.38853i
$726$	5.03962e6	+	4.64488e6i	0.354860	+	0.327064i
$727$	−6.63662e6	−	6.63662e6i	−0.465705	−	0.465705i	0.434815	−	0.900520i	$-0.356814\pi$
$727$	−6.63662e6	−	6.63662e6i	−0.465705	−	0.465705i	−0.900520	+	0.434815i	$0.856814\pi$
$728$	8.54217e6	+	2.06194e6i	0.597365	+	0.144194i
$729$	1.43165e7	+	964450.i	0.997739	+	0.0672141i
$730$	4.39930e7	−	2.09614e7i	3.05546	−	1.45584i
$731$	−597935.	+	1.44354e6i	−0.0413866	+	0.0999162i
$732$	−9.40122e6	+	4.95891e6i	−0.648495	+	0.342065i
$733$	−2.67300e6	+	1.10719e6i	−0.183755	+	0.0761137i	−0.472664	−	0.881243i	$-0.656708\pi$
$733$	−2.67300e6	+	1.10719e6i	−0.183755	+	0.0761137i	0.288909	+	0.957357i	$0.406708\pi$
$734$	−4.95749e6	+	257767.i	−0.339642	+	0.0176598i
$735$	5.58694e6	−	1.30716e7i	0.381466	−	0.892507i
$736$	−1.18798e7	+	2.04791e7i	−0.808380	+	1.39353i
$737$			4.71819e6i			0.319968i
$738$	−1.27867e7	−	1.20531e7i	−0.864208	−	0.814623i
$739$	−1.05827e6	−	2.55489e6i	−0.0712830	−	0.172092i	0.884222	−	0.467066i	$-0.154689\pi$
$739$	−1.05827e6	−	2.55489e6i	−0.0712830	−	0.172092i	−0.955505	+	0.294974i	$0.904689\pi$
$740$	−6.24735e6	+	7.70187e6i	−0.419388	+	0.517031i
$741$	5.02389e6	+	5.13782e6i	0.336120	+	0.343742i
$742$	−718380.	−	1.50771e6i	−0.0479010	−	0.100533i
$743$	−8.31177e6	−	8.31177e6i	−0.552359	−	0.552359i	0.374762	−	0.927121i	$-0.377724\pi$
$743$	−8.31177e6	−	8.31177e6i	−0.552359	−	0.552359i	−0.927121	+	0.374762i	$0.877724\pi$
$744$	−592111.	−	4.06524e6i	−0.0392167	−	0.269249i
$745$	−1.69853e7	+	1.69853e7i	−1.12120	+	1.12120i
$746$	1.90113e6	+	674107.i	0.125074	+	0.0443488i
$747$	−8.54455e6	−	2.20117e7i	−0.560258	−	1.44328i
$748$	−883264.	−	262425.i	−0.0577214	−	0.0171495i
$749$	−1.14202e7	+	4.73041e6i	−0.743824	+	0.308102i
$750$	2.48215e7	+	5.36348e7i	1.61130	+	3.48172i
$751$	−4.64384e6			−0.300454			−0.150227	−	0.988652i	$-0.548000\pi$
$751$	−4.64384e6			−0.300454			−0.150227	+	0.988652i	$0.548000\pi$
$752$	4.13915e6	+	1.96319e7i	0.266911	+	1.26595i
$753$	−4.78126e6	+	1.11866e7i	−0.307295	+	0.718970i
$754$	4.60318e6	−	5.10812e6i	0.294869	−	0.327215i
$755$	−1.39519e7	−	3.36829e7i	−0.890771	−	2.15051i
$756$	−7.36351e6	+	8.47849e6i	−0.468577	+	0.539528i
$757$	837842.	+	347045.i	0.0531401	+	0.0220113i	0.409095	−	0.912492i	$-0.365844\pi$
$757$	837842.	+	347045.i	0.0531401	+	0.0220113i	−0.355955	+	0.934503i	$0.615844\pi$
$758$	−4.61538e6	−	1.63653e6i	−0.291766	−	0.103455i
$759$	1.70696e7	−	6.84729e6i	1.07552	−	0.431434i
$760$	1.74432e7	−	2.74068e6i	1.09545	−	0.172117i
$761$	5.26294e6	−	5.26294e6i	0.329433	−	0.329433i	−0.522938	−	0.852371i	$-0.675164\pi$
$761$	5.26294e6	−	5.26294e6i	0.329433	−	0.329433i	0.852371	+	0.522938i	$0.175164\pi$
$762$	−497272.	−	1.21999e7i	−0.0310246	−	0.761146i
$763$	9.09959e6	+	3.76917e6i	0.565862	+	0.234388i
$764$	1.30613e7	−	1.36194e6i	0.809569	−	0.0844160i
$765$	2.45938e6	+	1.08393e6i	0.151940	+	0.0669649i
$766$	3.07747e7	−	1.60015e6i	1.89506	−	0.0985343i
$767$	−2.37932e7			−1.46038
$768$	1.50274e7	−	6.43117e6i	0.919347	−	0.393447i
$769$	1.60802e7			0.980564			0.490282	−	0.871564i	$-0.336894\pi$
$769$	1.60802e7			0.980564			0.490282	+	0.871564i	$0.336894\pi$
$770$	−1.67513e7	+	870992.i	−1.01817	+	0.0529404i
$771$	−112755.	+	1.00573e7i	−0.00683123	+	0.609317i
$772$	−2.78934e6	+	290852.i	−0.168445	+	0.0175642i
$773$	1.86502e7	+	7.72517e6i	1.12263	+	0.465007i	0.865268	−	0.501309i	$-0.167148\pi$
$773$	1.86502e7	+	7.72517e6i	1.12263	+	0.465007i	0.257358	+	0.966316i	$0.417148\pi$
$774$	−7.64903e6	+	2.01275e7i	−0.458938	+	1.20764i
$775$	−9.43938e6	+	9.43938e6i	−0.564533	+	0.564533i
$776$	−376951.	+	59226.6i	−0.0224714	+	0.00353071i
$777$	1.50275e6	+	3.74620e6i	0.0892964	+	0.222607i
$778$	−1.29364e7	−	4.58702e6i	−0.766241	−	0.271695i
$779$	1.03896e7	+	4.30352e6i	0.613417	+	0.254086i
$780$	−2.68246e6	−	2.88583e7i	−0.157869	−	1.69838i
$781$	1.76797e6	+	4.26826e6i	0.103717	+	0.250394i
$782$	1.54390e6	−	1.71325e6i	0.0902820	−	0.100185i
$783$	3.08783e6	+	8.22681e6i	0.179990	+	0.479542i
$784$	1.73744e6	+	8.24065e6i	0.100953	+	0.478819i
$785$	−1.60501e7			−0.929617
$786$	4.45547e6	−	2.06194e6i	0.257239	−	0.119047i
$787$	−552070.	+	228675.i	−0.0317729	+	0.0131608i	−0.398513	−	0.917163i	$-0.630474\pi$
$787$	−552070.	+	228675.i	−0.0317729	+	0.0131608i	0.366740	+	0.930323i	$0.380474\pi$
$788$	−1.56599e7	−	4.65268e6i	−0.898406	−	0.266924i
$789$	−1.20855e7	−	1.23596e7i	−0.691151	−	0.706824i
$790$	−855262.	−	303260.i	−0.0487564	−	0.0172881i
$791$	1.20090e7	−	1.20090e7i	0.682444	−	0.682444i
$792$	−1.22734e7	−	3.25546e6i	−0.695268	−	0.184416i
$793$	−7.89501e6	−	7.89501e6i	−0.445831	−	0.445831i
$794$	8.12741e6	+	1.70575e7i	0.457510	+	0.960206i
$795$	−3.93838e6	+	3.85105e6i	−0.221004	+	0.216103i
$796$	−1.12192e7	+	1.38313e7i	−0.627597	+	0.773716i
$797$	−4.50171e6	−	1.08681e7i	−0.251034	−	0.606049i	0.747254	−	0.664538i	$-0.231372\pi$
$797$	−4.50171e6	−	1.08681e7i	−0.251034	−	0.606049i	−0.998288	+	0.0584893i	$0.981372\pi$
$798$	2.47754e6	−	6.74615e6i	0.137725	−	0.375015i
$799$		−	1.95442e6i		−	0.108306i
$800$	−4.59442e7	−	2.66520e7i	−2.53808	−	1.47233i
$801$	−1.99634e7	+	1.90877e7i	−1.09940	+	1.05117i
$802$	−3.98956e6	+	207439.i	−0.219023	+	0.0113882i
$803$	2.07202e7	−	8.58260e6i	1.13398	−	0.469710i
$804$	3.80389e6	+	7.21151e6i	0.207533	+	0.393447i
$805$	1.60666e7	−	3.87882e7i	0.873845	−	2.10965i
$806$	3.89580e6	−	1.85624e6i	0.211232	−	0.100646i
$807$	2.39819e7	−	9.62009e6i	1.29628	−	0.519991i
$808$	−2.50640e7	−	6.05005e6i	−1.35059	−	0.326010i
$809$	2.18344e7	+	2.18344e7i	1.17292	+	1.17292i	0.981509	+	0.191414i	$0.0613072\pi$
$809$	2.18344e7	+	2.18344e7i	1.17292	+	1.17292i	0.191414	+	0.981509i	$0.438693\pi$
$810$	3.43180e7	+	1.39301e7i	1.83785	+	0.746007i
$811$	−4.01959e6	+	9.70414e6i	−0.214600	+	0.518090i	−0.994120	−	0.108288i	$-0.965463\pi$
$811$	−4.01959e6	+	9.70414e6i	−0.214600	+	0.518090i	0.779520	+	0.626378i	$0.215463\pi$
$812$	−6.59221e6	−	1.95860e6i	−0.350866	−	0.104245i
$813$	−1.66595e6	−	18677.4i	−0.0883964	−	0.000991037i
$814$	−3.05535e6	+	3.39051e6i	−0.161622	+	0.179351i
$815$		−	1.12843e6i		−	0.0595088i
$816$	−1.56160e6	+	311001.i	−0.0821000	+	0.0163507i
$817$		−	1.37799e7i		−	0.722255i
$818$	−8.33870e6	−	7.51441e6i	−0.435728	−	0.392655i
$819$	−1.07944e7	−	4.75747e6i	−0.562329	−	0.247837i
$820$	−2.16097e7	−	3.98783e7i	−1.12231	−	2.07111i
$821$	−3.24473e6	+	7.83346e6i	−0.168004	+	0.405598i	−0.985349	−	0.170551i	$-0.945445\pi$
$821$	−3.24473e6	+	7.83346e6i	−0.168004	+	0.405598i	0.817345	+	0.576149i	$0.195445\pi$
$822$	−8.81334e6	−	8.12300e6i	−0.454947	−	0.419312i
$823$	8.73608e6	+	8.73608e6i	0.449591	+	0.449591i	0.895218	−	0.445628i	$-0.147019\pi$
$823$	8.73608e6	+	8.73608e6i	0.449591	+	0.449591i	−0.445628	+	0.895218i	$0.647019\pi$
$824$	−1.97397e6	+	2.70990e6i	−0.101280	+	0.139039i
$825$	1.53617e7	+	3.82951e7i	0.785784	+	1.95888i
$826$	1.02356e7	+	2.14822e7i	0.521993	+	1.09554i
$827$	−5.36759e6	+	1.29585e7i	−0.272907	+	0.658857i	−0.999605	−	0.0281005i	$-0.991054\pi$
$827$	−5.36759e6	+	1.29585e7i	−0.272907	+	0.658857i	0.726698	+	0.686957i	$0.241054\pi$
$828$	2.05696e7	−	2.42276e7i	1.04268	−	1.22810i
$829$	−3.10948e7	+	1.28799e7i	−1.57145	+	0.650917i	−0.987031	−	0.160532i	$-0.948679\pi$
$829$	−3.10948e7	+	1.28799e7i	−1.57145	+	0.650917i	−0.584423	+	0.811449i	$0.698679\pi$
$830$	−3.16471e6	−	6.08651e7i	−0.159455	−	3.06671i
$831$	−1.98418e7	−	8.48058e6i	−0.996732	−	0.426013i
$832$	1.11191e7	+	1.30840e7i	0.556879	+	0.655288i
$833$		−	820385.i		−	0.0409643i
$834$	−4.79148e6	+	1.30468e7i	−0.238536	+	0.649516i
$835$	−1.29316e7	−	3.12196e7i	−0.641852	−	1.54957i
$836$	8.08245e6	−	842779.i	0.399970	−	0.0417060i
$837$	−185440.	+	5.51163e6i	−0.00914932	+	0.271936i
$838$	2.09489e7	−	9.98156e6i	1.03051	−	0.491008i
$839$	289940.	+	289940.i	0.0142201	+	0.0142201i	0.714181	−	0.699961i	$-0.246799\pi$
$839$	289940.	+	289940.i	0.0142201	+	0.0142201i	−0.699961	+	0.714181i	$0.746799\pi$
$840$	−2.49013e7	+	1.48365e7i	−1.21765	+	0.725493i
$841$	1.06985e7	−	1.06985e7i	0.521592	−	0.521592i
$842$	−7.87248e6	+	2.22022e7i	−0.382676	+	1.07923i
$843$	7.42561e6	−	7.26095e6i	0.359884	−	0.351904i
$844$	7.73174e6	−	4.18976e6i	0.373612	−	0.202457i
$845$	−9.90756e6	+	4.10385e6i	−0.477337	+	0.197719i
$846$	−795143.	−	2.69215e7i	−0.0381961	−	1.29322i
$847$	7.20034e6			0.344862
$848$	599972.	−	3.20770e6i	0.0286511	−	0.153181i
$849$	−1.15851e7	−	4.95156e6i	−0.551606	−	0.235762i
$850$	3.84363e6	+	3.46368e6i	0.182471	+	0.164434i
$851$	−4.37160e6	−	1.05540e7i	−0.206927	−	0.499566i
$852$	6.14341e6	+	5.09845e6i	0.289942	+	0.240624i
$853$	−1.61264e7	−	6.67979e6i	−0.758867	−	0.314333i	−0.0305136	−	0.999534i	$-0.509714\pi$
$853$	−1.61264e7	−	6.67979e6i	−0.758867	−	0.314333i	−0.728354	+	0.685201i	$0.759714\pi$
$854$	−3.73180e6	+	1.05245e7i	−0.175095	+	0.493807i
$855$	−2.36971e7	−	531416.i	−1.10861	−	0.0248610i
$856$	−2.34789e7	−	5.66744e6i	−1.09520	−	0.264364i
$857$	−1.44904e7	+	1.44904e7i	−0.673951	+	0.673951i	−0.958624	−	0.284674i	$-0.908115\pi$
$857$	−1.44904e7	+	1.44904e7i	−0.673951	+	0.673951i	0.284674	+	0.958624i	$0.408115\pi$
$858$	−543233.	−	1.33275e7i	−0.0251923	−	0.618058i
$859$	−2.01462e7	−	8.34482e6i	−0.931558	−	0.385864i	−0.135289	−	0.990806i	$-0.543196\pi$
$859$	−2.01462e7	−	8.34482e6i	−0.931558	−	0.385864i	−0.796269	+	0.604942i	$0.793196\pi$
$860$	−3.50121e7	+	4.31638e7i	−1.61426	+	1.99009i
$861$	−1.84597e7	−	206957.i	−0.848628	−	0.00951421i
$862$	−2.01187e6	−	3.86932e7i	−0.0922215	−	1.77365i
$863$	−1.82134e7			−0.832463			−0.416232	−	0.909259i	$-0.636649\pi$
$863$	−1.82134e7			−0.832463			−0.416232	+	0.909259i	$0.636649\pi$
$864$	−2.13839e7	+	4.91925e6i	−0.974546	+	0.224189i
$865$	−6.67251e7			−3.03214
$866$	−899907.	−	1.73074e7i	−0.0407758	−	0.784219i
$867$	−2.19769e7	−	246389.i	−0.992930	−	0.0111320i
$868$	−3.35188e6	−	2.71886e6i	−0.151004	−	0.122487i
$869$	−385833.	−	159817.i	−0.0173321	−	0.00717918i
$870$	923744.	+	2.26628e7i	0.0413765	+	1.01511i
$871$	−6.05612e6	+	6.05612e6i	−0.270489	+	0.270489i
$872$	1.00353e7	+	1.64216e7i	0.446932	+	0.731350i
$873$	512098.	+	11484.0i	0.0227414	+	0.000509985i
$874$	−6.79735e6	+	1.91701e7i	−0.300996	+	0.848878i
$875$	5.73631e7	+	2.37606e7i	2.53287	+	1.04915i
$876$	2.47503e7	−	2.98231e7i	1.08973	−	1.31308i
$877$	1.28432e7	+	3.10063e7i	0.563866	+	1.36129i	0.906652	+	0.421879i	$0.138629\pi$
$877$	1.28432e7	+	3.10063e7i	0.563866	+	1.36129i	−0.342787	+	0.939413i	$0.611371\pi$
$878$	−2.39043e7	−	2.15414e7i	−1.04650	−	0.943054i
$879$	8.32434e6	+	3.55790e6i	0.363394	+	0.155318i
$880$	−2.74586e7	−	1.78961e7i	−1.19529	−	0.779026i
$881$	3.47033e7			1.50637			0.753184	−	0.657810i	$-0.228517\pi$
$881$	3.47033e7			1.50637			0.753184	+	0.657810i	$0.228517\pi$
$882$	−333768.	−	1.13005e7i	−0.0144468	−	0.489132i
$883$	1.39086e7	−	5.76112e6i	0.600317	−	0.248660i	−0.0617650	−	0.998091i	$-0.519673\pi$
$883$	1.39086e7	−	5.76112e6i	0.600317	−	0.248660i	0.662082	+	0.749431i	$0.269673\pi$
$884$	−796890.	−	1.47057e6i	−0.0342979	−	0.0632930i
$885$	5.61149e7	−	5.48706e7i	2.40835	−	2.35495i
$886$	3.85325e6	−	1.08670e7i	0.164908	−	0.465079i
$887$	2.04410e7	−	2.04410e7i	0.872357	−	0.872357i	−0.120372	−	0.992729i	$-0.538409\pi$
$887$	2.04410e7	−	2.04410e7i	0.872357	−	0.872357i	0.992729	+	0.120372i	$0.0384088\pi$
$888$	−1.93646e6	+	7.64549e6i	−0.0824091	+	0.325367i
$889$	−9.07050e6	−	9.07050e6i	−0.384926	−	0.384926i
$890$	−6.43611e7	+	3.06662e7i	−2.72363	+	1.29773i
$891$	1.54398e7	+	7.22244e6i	0.651548	+	0.304782i
$892$	1.63556e6	+	1.56854e7i	0.0688264	+	0.660061i
$893$	6.59615e6	+	1.59245e7i	0.276797	+	0.668247i
$894$	−6.58571e6	+	1.79324e7i	−0.275587	+	0.750402i
$895$			2.24328e7i			0.936108i
$896$	7.02981e6	−	1.56677e7i	0.292532	−	0.651981i
$897$	3.06990e7	+	1.31210e7i	1.27392	+	0.544487i
$898$	2.25627e6	+	4.33935e7i	0.0933683	+	1.79570i
$899$	−3.12013e6	+	1.29240e6i	−0.128758	+	0.0533333i
$900$	5.43537e7	+	4.61472e7i	2.23678	+	1.89906i
$901$	−121650.	+	293689.i	−0.00499230	+	0.0120525i
$902$	−8.97890e6	−	1.88446e7i	−0.367457	−	0.771206i
$903$	8.42189e6	+	2.09949e7i	0.343708	+	0.856830i
$904$	3.27826e7	−	5.15081e6i	1.33421	−	0.209631i
$905$	7.45778e6	+	7.45778e6i	0.302683	+	0.302683i
$906$	−2.13203e7	−	1.96503e7i	−0.862924	−	0.795333i
$907$	1.51471e6	−	3.65684e6i	0.0611380	−	0.147600i	−0.890358	−	0.455261i	$-0.849546\pi$
$907$	1.51471e6	−	3.65684e6i	0.0611380	−	0.147600i	0.951496	+	0.307660i	$0.0995461\pi$
$908$	2.28042e7	−	1.23574e7i	0.917912	−	0.497409i
$909$	3.16725e7	+	1.39591e7i	1.27137	+	0.560336i
$910$	−2.26195e7	−	2.03835e7i	−0.905480	−	0.815972i
$911$		−	7.35973e6i		−	0.293810i	−0.989151	−	0.146905i	$-0.953069\pi$
$911$		−	7.35973e6i		−	0.293810i	0.989151	−	0.146905i	$-0.0469311\pi$
$912$	1.16741e7	−	7.80437e6i	0.464770	−	0.310707i
$913$		−	2.80494e7i		−	1.11364i
$914$	6.10092e6	−	6.77016e6i	0.241563	−	0.268061i
$915$	3.68269e7	+	412877.i	1.45416	+	0.0163030i
$916$	−1.13764e7	+	3.82904e7i	−0.447987	+	1.50782i
$917$	1.97380e6	−	4.76518e6i	0.0775141	−	0.187136i
$918$	2.13709e6	−	39147.9i	0.0836983	−	0.00153321i
$919$	1.46184e7	+	1.46184e7i	0.570966	+	0.570966i	0.932398	−	0.361432i	$-0.117712\pi$
$919$	1.46184e7	+	1.46184e7i	0.570966	+	0.570966i	−0.361432	+	0.932398i	$0.617712\pi$
$920$	6.99995e7	−	4.27770e7i	2.72662	−	1.66625i
$921$	−1.78245e7	+	7.15013e6i	−0.692419	+	0.277757i
$922$	−2.78184e7	+	1.32547e7i	−1.07772	+	0.513501i
$923$	−3.20930e6	+	7.74793e6i	−0.123995	+	0.299352i
$924$	−1.17993e7	+	6.22382e6i	−0.454648	+	0.239815i
$925$	2.36775e7	−	9.80755e6i	0.909876	−	0.376883i
$926$	−4.36751e6	+	227091.i	−0.167381	+	0.00870306i
$927$	3.25293e6	−	3.11023e6i	0.124330	−	0.118876i
$928$	−8.15826e6	−	1.06774e7i	−0.310976	−	0.407002i
$929$		−	1.48589e7i		−	0.564869i	−0.959287	−	0.282434i	$-0.908858\pi$
$929$		−	1.48589e7i		−	0.564869i	0.959287	−	0.282434i	$-0.0911419\pi$
$930$	−4.90727e6	+	1.33621e7i	−0.186051	+	0.506603i
$931$	2.76879e6	+	6.68444e6i	0.104692	+	0.252750i
$932$	2.09853e7	+	1.70221e7i	0.791361	+	0.641910i
$933$	−1.23298e7	+	1.20564e7i	−0.463718	+	0.453435i
$934$	−7.47944e6	−	1.56976e7i	−0.280545	−	0.588797i
$935$	2.25761e6	+	2.25761e6i	0.0844539	+	0.0844539i
$936$	−1.15752e7	−	1.99324e7i	−0.431854	−	0.743652i
$937$	1.14093e7	−	1.14093e7i	0.424532	−	0.424532i	−0.462229	−	0.886761i	$-0.652950\pi$
$937$	1.14093e7	−	1.14093e7i	0.424532	−	0.424532i	0.886761	+	0.462229i	$0.152950\pi$
$938$	8.07317e6	+	2.86260e6i	0.299597	+	0.106231i
$939$	1.28079e7	+	1.30983e7i	0.474037	+	0.484787i
$940$	1.97996e7	−	6.66411e7i	0.730865	−	2.45993i
$941$	−8.25422e6	+	3.41901e6i	−0.303880	+	0.125871i	−0.529413	−	0.848364i	$-0.677588\pi$
$941$	−8.25422e6	+	3.41901e6i	−0.303880	+	0.125871i	0.225533	+	0.974236i	$0.427588\pi$
$942$	−1.15841e7	+	5.36097e6i	−0.425339	+	0.196841i
$943$	5.22472e7			1.91330
$944$	−8.54852e6	+	4.57040e7i	−0.312220	+	1.66926i
$945$	3.64294e7	−	1.36733e7i	1.32701	−	0.498075i
$946$	−1.71232e7	+	1.90015e7i	−0.622094	+	0.690334i
$947$	7.40910e6	+	1.78871e7i	0.268467	+	0.648136i	0.999412	−	0.0343005i	$-0.0109203\pi$
$947$	7.40910e6	+	1.78871e7i	0.268467	+	0.648136i	−0.730945	+	0.682437i	$0.760920\pi$
$948$	−718574.	+	66793.5i	−0.0259687	+	0.00241387i
$949$	3.76122e7	+	1.55795e7i	1.35570	+	0.561549i
$950$	−4.30074e7	−	1.52496e7i	−1.54609	−	0.548215i
$951$	−6.88722e6	−	1.71691e7i	−0.246941	−	0.615598i
$952$	−984919.	+	1.35211e6i	−0.0352215	+	0.0483527i
$953$	−2.17088e7	+	2.17088e7i	−0.774291	+	0.774291i	−0.978853	−	0.204563i	$-0.934423\pi$
$953$	−2.17088e7	+	2.17088e7i	−0.774291	+	0.774291i	0.204563	+	0.978853i	$0.434423\pi$
$954$	−1.55620e6	+	4.09496e6i	−0.0553598	+	0.145673i
$955$	−4.20393e7	−	1.74132e7i	−1.49158	−	0.617833i
$956$	226417.	+	2.17139e6i	0.00801242	+	0.0768410i
$957$	−117023.	+	1.04379e7i	−0.00413038	+	0.368413i
$958$	−2.78125e7	+	1.44612e6i	−0.979098	+	0.0509086i
$959$	−1.25920e7			−0.442129
$960$	−5.63972e7	−	5.21563e6i	−1.97506	−	0.182654i
$961$	2.65097e7			0.925967
$962$	−8.27371e6	+	430195.i	−0.288245	+	0.0149874i
$963$	2.96695e7	+	1.30763e7i	1.03097	+	0.454381i
$964$	3.28432e6	+	3.14974e7i	0.113829	+	1.09165i
$965$	8.97777e6	+	3.71872e6i	0.310349	+	0.128551i
$966$	−1.35984e6	−	3.33617e7i	−0.0468861	−	1.15028i
$967$	1.07906e6	−	1.07906e6i	0.0371090	−	0.0371090i	−0.688309	−	0.725418i	$-0.741647\pi$
$967$	1.07906e6	−	1.07906e6i	0.0371090	−	0.0371090i	0.725418	+	0.688309i	$0.241647\pi$
$968$	1.13720e7	+	8.28371e6i	0.390076	+	0.284143i
$969$	−1.26958e6	+	509277.i	−0.0434359	+	0.0174239i
$970$	1.24614e6	+	441859.i	0.0425245	+	0.0150784i
$971$	2.90777e6	+	1.20444e6i	0.0989718	+	0.0409954i	0.431620	−	0.902056i	$-0.357942\pi$
$971$	2.90777e6	+	1.20444e6i	0.0989718	+	0.0409954i	−0.332648	+	0.943051i	$0.607942\pi$
$972$	2.94217e7	−	1.40871e6i	0.998856	−	0.0478250i
$973$	5.58790e6	+	1.34904e7i	0.189220	+	0.456817i
$974$	6.93750e6	−	7.69850e6i	0.234318	−	0.260021i
$975$	−2.94366e7	+	6.88722e7i	−0.991692	+	2.32024i
$976$	−1.80019e7	+	1.23288e7i	−0.604916	+	0.414284i
$977$	−4.51890e7			−1.51459			−0.757297	−	0.653071i	$-0.773480\pi$
$977$	−4.51890e7			−1.51459			−0.757297	+	0.653071i	$0.773480\pi$
$978$	−376913.	−	814440.i	−0.0126007	−	0.0272278i
$979$	−3.03134e7	+	1.25562e7i	−1.01083	+	0.418699i
$980$	8.31105e6	−	2.79731e7i	0.276434	−	0.930413i
$981$	−9.34892e6	−	2.40838e7i	−0.310162	−	0.799012i
$982$	4.17125e7	+	1.47905e7i	1.38034	+	0.489445i
$983$	−2.24821e7	+	2.24821e7i	−0.742083	+	0.742083i	−0.972979	−	0.230895i	$-0.925835\pi$
$983$	−2.24821e7	+	2.24821e7i	−0.742083	+	0.742083i	0.230895	+	0.972979i	$0.425835\pi$
$984$	−2.89167e7	−	2.15640e7i	−0.952052	−	0.709974i
$985$	4.00264e7	+	4.00264e7i	1.31448	+	1.31448i
$986$	563039.	+	1.18169e6i	0.0184436	+	0.0387088i
$987$	−1.97824e7	−	2.02310e7i	−0.646379	−	0.661037i
$988$	1.14562e7	+	9.29262e6i	0.373376	+	0.302863i
$989$	−2.44999e7	−	5.91479e7i	−0.796477	−	1.92286i
$990$	3.20162e7	+	3.01792e7i	1.03820	+	0.978634i
$991$			1.83547e7i			0.593694i	0.954925	+	0.296847i	$0.0959351\pi$
$991$			1.83547e7i			0.593694i	−0.954925	+	0.296847i	$0.904065\pi$
$992$	−2.16591e6	−	8.15030e6i	−0.0698815	−	0.262963i
$993$	4.67448e6	−	1.09368e7i	0.150439	−	0.351978i
$994$	8.37598e6	−	435513.i	0.268887	−	0.0139809i
$995$	5.70126e7	−	2.36154e7i	1.82563	−	0.756201i
$996$	−2.26139e7	−	4.28720e7i	−0.722317	−	1.36939i
$997$	1.44236e7	−	3.48217e7i	0.459553	−	1.10946i	−0.509025	−	0.860752i	$-0.669994\pi$
$997$	1.44236e7	−	3.48217e7i	0.459553	−	1.10946i	0.968578	−	0.248708i	$-0.0800061\pi$
$998$	5.65781e7	−	2.69578e7i	1.79813	−	0.856759i
$999$	4.37824e6	−	9.63969e6i	0.138799	−	0.305597i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	96.6.o.a.11.2	✓	312
3.2	odd	2	inner	96.6.o.a.11.77	yes	312
32.3	odd	8	inner	96.6.o.a.35.77	yes	312
96.35	even	8	inner	96.6.o.a.35.2	yes	312

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.6.o.a.11.2	✓	312	1.1	even	1	trivial
96.6.o.a.11.77	yes	312	3.2	odd	2	inner
96.6.o.a.35.2	yes	312	96.35	even	8	inner
96.6.o.a.35.77	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+(-5.64922 + 0.293734i) q^{2} +(15.5875 + 0.174756i) q^{3} +(31.8274 - 3.31874i) q^{4} +(-102.440 - 42.4320i) q^{5} +(-88.1085 + 3.59134i) q^{6} +(-65.5079 + 65.5079i) q^{7} +(-178.825 + 28.0971i) q^{8} +(242.939 + 5.44800i) q^{9} +(591.170 + 209.618i) q^{10} +(266.694 + 110.468i) q^{11} +(496.689 - 46.1687i) q^{12} +(200.527 + 484.114i) q^{13} +(350.827 - 389.311i) q^{14} +(-1589.37 - 679.310i) q^{15} +(1001.97 - 211.254i) q^{16} -99.7498 q^{17} +(-1374.02 + 40.5824i) q^{18} +(812.754 - 336.654i) q^{19} +(-3401.22 - 1010.53i) q^{20} +(-1032.55 + 1009.65i) q^{21} +(-1539.06 - 545.723i) q^{22} +(2890.06 - 2890.06i) q^{23} +(-2792.35 + 406.712i) q^{24} +(6483.76 + 6483.76i) q^{25} +(-1275.02 - 2675.97i) q^{26} +(3785.85 + 127.375i) q^{27} +(-1867.54 + 2302.35i) q^{28} +(887.731 + 2143.17i) q^{29} +(9178.22 + 3370.72i) q^{30} +1455.85i q^{31} +(-5598.31 + 1487.73i) q^{32} +(4137.78 + 1768.53i) q^{33} +(563.509 - 29.2999i) q^{34} +(9490.26 - 3930.99i) q^{35} +(7750.20 - 632.854i) q^{36} +(1069.59 - 2582.23i) q^{37} +(-4492.54 + 2140.56i) q^{38} +(3041.10 + 7581.16i) q^{39} +(19511.1 + 4709.66i) q^{40} +(9039.11 + 9039.11i) q^{41} +(5536.54 - 6007.06i) q^{42} +(5994.35 - 14471.6i) q^{43} +(8854.80 + 2630.83i) q^{44} +(-24655.5 - 10866.5i) q^{45} +(-15477.7 + 17175.5i) q^{46} +19593.3i q^{47} +(15655.1 - 3117.81i) q^{48} +8224.43i q^{49} +(-38532.7 - 34723.7i) q^{50} +(-1554.85 - 17.4318i) q^{51} +(7988.89 + 14742.6i) q^{52} +(1219.55 - 2944.26i) q^{53} +(-21424.5 + 392.461i) q^{54} +(-22632.7 - 22632.7i) q^{55} +(9873.90 - 13555.1i) q^{56} +(12727.6 - 5105.55i) q^{57} +(-5644.51 - 11846.5i) q^{58} +(-17376.4 + 41950.4i) q^{59} +(-52839.9 - 16346.0i) q^{60} +(-19685.7 + 8154.08i) q^{61} +(-427.632 - 8224.42i) q^{62} +(-16271.3 + 15557.5i) q^{63} +(31189.1 - 10048.9i) q^{64} -58101.4i q^{65} +(-23894.7 - 8775.40i) q^{66} +(6254.85 + 15100.5i) q^{67} +(-3174.78 + 331.043i) q^{68} +(45553.8 - 44543.7i) q^{69} +(-52457.9 + 24994.7i) q^{70} +(11316.8 + 11316.8i) q^{71} +(-43596.7 + 5851.63i) q^{72} +(54937.2 - 54937.2i) q^{73} +(-5283.89 + 14901.8i) q^{74} +(99932.4 + 102199. i) q^{75} +(24750.6 - 13412.1i) q^{76} +(-24707.1 + 10234.0i) q^{77} +(-19406.7 - 41934.4i) q^{78} -1446.73 q^{79} +(-111606. - 20874.9i) q^{80} +(58989.6 + 2647.06i) q^{81} +(-53719.1 - 48408.9i) q^{82} +(-37184.8 - 89772.0i) q^{83} +(-29512.7 + 35561.5i) q^{84} +(10218.4 + 4232.58i) q^{85} +(-29612.6 + 83514.2i) q^{86} +(13463.0 + 33561.8i) q^{87} +(-50795.5 - 12261.2i) q^{88} +(-80372.3 + 80372.3i) q^{89} +(142476. + 54145.0i) q^{90} +(-44849.3 - 18577.2i) q^{91} +(82391.9 - 101575. i) q^{92} +(-254.418 + 22693.0i) q^{93} +(-5755.21 - 110687. i) q^{94} -97543.3 q^{95} +(-87523.5 + 22211.7i) q^{96} +2107.93 q^{97} +(-2415.79 - 46461.7i) q^{98} +(64188.5 + 28290.0i) 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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