LMFDB - Embedded newform 62.8.d.a.47.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,8,Mod(33,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.33"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	62.d (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,-80] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$19.3678715800$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			47.4
Character	$\chi$	$=$	62.47
Dual form			62.8.d.a.33.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-6.47214 + 4.70228i) q^{2} +(-27.0752 - 19.6713i) q^{3} +(19.7771 - 60.8676i) q^{4} +383.739 q^{5} +267.735 q^{6} +(-272.247 + 837.889i) q^{7} +(158.217 + 486.941i) q^{8} +(-329.712 - 1014.75i) q^{9} +(-2483.61 + 1804.45i) q^{10} +(-93.9530 + 289.158i) q^{11} +(-1732.81 + 1258.96i) q^{12} +(-4427.96 - 3217.10i) q^{13} +(-2177.97 - 6703.11i) q^{14} +(-10389.8 - 7548.64i) q^{15} +(-3313.73 - 2407.57i) q^{16} +(4193.41 + 12906.0i) q^{17} +(6905.59 + 5017.20i) q^{18} +(35610.4 - 25872.5i) q^{19} +(7589.23 - 23357.3i) q^{20} +(23853.5 - 17330.6i) q^{21} +(-751.624 - 2313.26i) q^{22} +(27727.3 + 85336.0i) q^{23} +(5295.01 - 16296.4i) q^{24} +69130.4 q^{25} +43786.1 q^{26} +(-33652.0 + 103570. i) q^{27} +(45616.1 + 33142.0i) q^{28} +(46108.6 - 33499.8i) q^{29} +102740. q^{30} +(28495.2 - 163403. i) q^{31} +32768.0 q^{32} +(8231.91 - 5980.83i) q^{33} +(-87827.8 - 63810.6i) q^{34} +(-104472. + 321530. i) q^{35} -68286.2 q^{36} +509355. q^{37} +(-108816. + 334900. i) q^{38} +(56603.5 + 174208. i) q^{39} +(60713.9 + 186858. i) q^{40} +(520621. - 378253. i) q^{41} +(-72889.9 + 224332. i) q^{42} +(390651. - 283824. i) q^{43} +(15742.2 + 11437.4i) q^{44} +(-126523. - 389399. i) q^{45} +(-580729. - 421924. i) q^{46} +(931817. + 677005. i) q^{47} +(42360.1 + 130371. i) q^{48} +(38320.3 + 27841.3i) q^{49} +(-447421. + 325070. i) q^{50} +(140340. - 431922. i) q^{51} +(-283389. + 205894. i) q^{52} +(-523048. - 1.60978e6i) q^{53} +(-269216. - 828561. i) q^{54} +(-36053.4 + 110961. i) q^{55} -451077. q^{56} -1.47311e6 q^{57} +(-140895. + 433631. i) q^{58} +(429264. + 311879. i) q^{59} +(-664948. + 483113. i) q^{60} -675428. q^{61} +(583944. + 1.19156e6i) q^{62} +940011. q^{63} +(-212079. + 154084. i) q^{64} +(-1.69918e6 - 1.23453e6i) q^{65} +(-25154.5 + 77417.5i) q^{66} -2.91568e6 q^{67} +868489. q^{68} +(927946. - 2.85592e6i) q^{69} +(-835773. - 2.57224e6i) q^{70} +(1.02800e6 + 3.16385e6i) q^{71} +(441957. - 321101. i) q^{72} +(-367159. + 1.13000e6i) q^{73} +(-3.29662e6 + 2.39513e6i) q^{74} +(-1.87172e6 - 1.35988e6i) q^{75} +(-870526. - 2.67920e6i) q^{76} +(-216704. - 157444. i) q^{77} +(-1.18552e6 - 861329. i) q^{78} +(1.36418e6 + 4.19852e6i) q^{79} +(-1.27161e6 - 923877. i) q^{80} +(1.06068e6 - 770630. i) q^{81} +(-1.59088e6 + 4.89621e6i) q^{82} +(3.10497e6 - 2.25589e6i) q^{83} +(-583119. - 1.79466e6i) q^{84} +(1.60917e6 + 4.95252e6i) q^{85} +(-1.19372e6 + 3.67390e6i) q^{86} -1.90739e6 q^{87} -155668. q^{88} +(390426. - 1.20161e6i) q^{89} +(2.64994e6 + 1.92529e6i) q^{90} +(3.90107e6 - 2.83429e6i) q^{91} +5.74256e6 q^{92} +(-3.98587e6 + 3.86364e6i) q^{93} -9.21432e6 q^{94} +(1.36651e7 - 9.92827e6i) q^{95} +(-887201. - 644589. i) q^{96} +(-893048. + 2.74852e6i) q^{97} -378932. q^{98} +324400. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 80 q^{2} + 28 q^{3} - 640 q^{4} + 168 q^{5} - 1936 q^{6} + 1402 q^{7} - 5120 q^{8} - 6164 q^{9} - 1496 q^{10} - 3402 q^{11} + 1792 q^{12} + 6413 q^{13} + 11216 q^{14} + 46465 q^{15} - 40960 q^{16}+ \cdots + 13336614 q^{99}+O(q^{100}) $ 40 * q - 80 * q^2 + 28 * q^3 - 640 * q^4 + 168 * q^5 - 1936 * q^6 + 1402 * q^7 - 5120 * q^8 - 6164 * q^9 - 1496 * q^10 - 3402 * q^11 + 1792 * q^12 + 6413 * q^13 + 11216 * q^14 + 46465 * q^15 - 40960 * q^16 + 17155 * q^17 - 98152 * q^18 + 67290 * q^19 + 6592 * q^20 + 16727 * q^21 - 27216 * q^22 + 2051 * q^23 + 47616 * q^24 + 787196 * q^25 - 214576 * q^26 + 603289 * q^27 - 62592 * q^28 + 95739 * q^29 - 369200 * q^30 + 540003 * q^31 + 1310720 * q^32 + 941656 * q^33 + 290520 * q^34 - 638364 * q^35 + 2359424 * q^36 + 843716 * q^37 - 169080 * q^38 + 827496 * q^39 + 52736 * q^40 + 175557 * q^41 + 1299656 * q^42 + 566562 * q^43 + 441152 * q^44 - 2450173 * q^45 + 484128 * q^46 - 2289258 * q^47 + 380928 * q^48 - 1290090 * q^49 - 2003912 * q^50 + 351796 * q^51 + 410432 * q^52 - 741339 * q^53 + 4826312 * q^54 - 755935 * q^55 - 434176 * q^56 - 8091472 * q^57 - 1476568 * q^58 - 8176986 * q^59 + 2973760 * q^60 - 10479540 * q^61 + 6613544 * q^62 - 10121022 * q^63 - 2621440 * q^64 + 9085330 * q^65 - 1581152 * q^66 + 7646158 * q^67 - 6844160 * q^68 - 5432460 * q^69 - 5106912 * q^70 - 24632815 * q^71 - 6281728 * q^72 - 11099311 * q^73 - 3436312 * q^74 + 11990582 * q^75 - 1352640 * q^76 + 8000688 * q^77 - 10937992 * q^78 + 10390986 * q^79 - 765952 * q^80 - 23584945 * q^81 + 2535096 * q^82 + 36507958 * q^83 + 10397248 * q^84 + 23914083 * q^85 + 5244176 * q^86 + 16619052 * q^87 - 3574784 * q^88 - 17387733 * q^89 - 2091344 * q^90 - 8973442 * q^91 - 8008576 * q^92 - 21404363 * q^93 - 137504 * q^94 - 12445576 * q^95 + 917504 * q^96 - 1428702 * q^97 + 92378560 * q^98 + 13336614 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−6.47214	+	4.70228i	−0.572061	+	0.415627i
$2$	−6.47214	+	4.70228i	−0.572061	+	0.415627i
$3$	−27.0752	−	19.6713i	−0.578959	−	0.420638i	0.259390	−	0.965773i	$-0.416479\pi$
$3$	−27.0752	−	19.6713i	−0.578959	−	0.420638i	−0.838349	+	0.545134i	$0.816479\pi$
$4$	19.7771	−	60.8676i	0.154508	−	0.475528i
$5$	383.739			1.37291			0.686453	−	0.727175i	$-0.259167\pi$
$5$	383.739			1.37291			0.686453	+	0.727175i	$0.259167\pi$
$6$	267.735			0.506029
$7$	−272.247	+	837.889i	−0.299999	+	0.923301i	0.681498	+	0.731820i	$0.261329\pi$
$7$	−272.247	+	837.889i	−0.299999	+	0.923301i	−0.981496	+	0.191481i	$0.938671\pi$
$8$	158.217	+	486.941i	0.109254	+	0.336249i
$9$	−329.712	−	1014.75i	−0.150760	−	0.463992i
$10$	−2483.61	+	1804.45i	−0.785386	+	0.570616i
$11$	−93.9530	+	289.158i	−0.0212832	+	0.0655029i	−0.961134	−	0.276082i	$-0.910964\pi$
$11$	−93.9530	+	289.158i	−0.0212832	+	0.0655029i	0.939851	+	0.341585i	$0.110964\pi$
$12$	−1732.81	+	1258.96i	−0.289479	+	0.210319i
$13$	−4427.96	−	3217.10i	−0.558987	−	0.406128i	0.272101	−	0.962269i	$-0.412282\pi$
$13$	−4427.96	−	3217.10i	−0.558987	−	0.406128i	−0.831088	+	0.556141i	$0.812282\pi$
$14$	−2177.97	−	6703.11i	−0.212131	−	0.652873i
$15$	−10389.8	−	7548.64i	−0.794856	−	0.577496i
$16$	−3313.73	−	2407.57i	−0.202254	−	0.146946i
$17$	4193.41	+	12906.0i	0.207012	+	0.637118i	0.999625	+	0.0273922i	$0.00872028\pi$
$17$	4193.41	+	12906.0i	0.207012	+	0.637118i	−0.792613	+	0.609725i	$0.791280\pi$
$18$	6905.59	+	5017.20i	0.279092	+	0.202772i
$19$	35610.4	−	25872.5i	1.19108	−	0.865367i	0.197699	−	0.980263i	$-0.436653\pi$
$19$	35610.4	−	25872.5i	1.19108	−	0.865367i	0.993378	+	0.114895i	$0.0366533\pi$
$20$	7589.23	−	23357.3i	0.212126	−	0.652855i
$21$	23853.5	−	17330.6i	0.562063	−	0.408363i
$22$	−751.624	−	2313.26i	−0.0150495	−	0.0463175i
$23$	27727.3	+	85336.0i	0.475183	+	1.46246i	0.845711	+	0.533641i	$0.179177\pi$
$23$	27727.3	+	85336.0i	0.475183	+	1.46246i	−0.370528	+	0.928821i	$0.620823\pi$
$24$	5295.01	−	16296.4i	0.0781857	−	0.240631i
$25$	69130.4			0.884869
$26$	43786.1			0.488573
$27$	−33652.0	+	103570.i	−0.329031	+	1.01265i
$28$	45616.1	+	33142.0i	0.392703	+	0.285316i
$29$	46108.6	−	33499.8i	0.351066	−	0.255064i	−0.398250	−	0.917277i	$-0.630382\pi$
$29$	46108.6	−	33499.8i	0.351066	−	0.255064i	0.749316	+	0.662213i	$0.230382\pi$
$30$	102740.			0.694729
$31$	28495.2	−	163403.i	0.171793	−	0.985133i
$31$	28495.2	−	163403.i	0.171793	−	0.985133i
$32$	32768.0			0.176777
$33$	8231.91	−	5980.83i	0.0398751	−	0.0289709i
$34$	−87827.8	−	63810.6i	−0.383227	−	0.278431i
$35$	−104472.	+	321530.i	−0.411870	+	1.26761i
$36$	−68286.2			−0.243935
$37$	509355.			1.65316			0.826580	−	0.562820i	$-0.190283\pi$
$37$	509355.			1.65316			0.826580	+	0.562820i	$0.190283\pi$
$38$	−108816.	+	334900.i	−0.321699	+	0.990087i
$39$	56603.5	+	174208.i	0.152798	+	0.470263i
$40$	60713.9	+	186858.i	0.149995	+	0.461638i
$41$	520621.	−	378253.i	1.17972	−	0.857115i	0.187577	−	0.982250i	$-0.439936\pi$
$41$	520621.	−	378253.i	1.17972	−	0.857115i	0.992140	+	0.125135i	$0.0399364\pi$
$42$	−72889.9	+	224332.i	−0.151808	+	0.467217i
$43$	390651.	−	283824.i	0.749289	−	0.544390i	−0.146318	−	0.989238i	$-0.546742\pi$
$43$	390651.	−	283824.i	0.749289	−	0.544390i	0.895606	+	0.444848i	$0.146742\pi$
$44$	15742.2	+	11437.4i	0.0278600	+	0.0202415i
$45$	−126523.	−	389399.i	−0.206979	−	0.637017i
$46$	−580729.	−	421924.i	−0.879673	−	0.639120i
$47$	931817.	+	677005.i	1.30915	+	0.951151i	1.00000		0.000136269i	$4.33758e-5\pi$
$47$	931817.	+	677005.i	1.30915	+	0.951151i	0.309147	+	0.951014i	$0.399957\pi$
$48$	42360.1	+	130371.i	0.0552857	+	0.170152i
$49$	38320.3	+	27841.3i	0.0465310	+	0.0338068i
$50$	−447421.	+	325070.i	−0.506199	+	0.367775i
$51$	140340.	−	431922.i	0.148145	−	0.455942i
$52$	−283389.	+	205894.i	−0.279494	+	0.203064i
$53$	−523048.	−	1.60978e6i	−0.482587	−	1.48525i	−0.835445	−	0.549574i	$-0.814790\pi$
$53$	−523048.	−	1.60978e6i	−0.482587	−	1.48525i	0.352857	−	0.935677i	$-0.385210\pi$
$54$	−269216.	−	828561.i	−0.232660	−	0.716055i
$55$	−36053.4	+	110961.i	−0.0292198	+	0.0899292i
$56$	−451077.			−0.343235
$57$	−1.47311e6			−1.05359
$58$	−140895.	+	433631.i	−0.0948196	+	0.291825i
$59$	429264.	+	311879.i	0.272109	+	0.197699i	0.715468	−	0.698645i	$-0.246213\pi$
$59$	429264.	+	311879.i	0.272109	+	0.197699i	−0.443359	+	0.896344i	$0.646213\pi$
$60$	−664948.	+	483113.i	−0.397428	+	0.288748i
$61$	−675428.			−0.381000			−0.190500	−	0.981687i	$-0.561011\pi$
$61$	−675428.			−0.381000			−0.190500	+	0.981687i	$0.561011\pi$
$62$	583944.	+	1.19156e6i	0.311172	+	0.634958i
$63$	940011.			0.473632
$64$	−212079.	+	154084.i	−0.101127	+	0.0734732i
$65$	−1.69918e6	−	1.23453e6i	−0.767437	−	0.557575i
$66$	−25154.5	+	77417.5i	−0.0107699	+	0.0331463i
$67$	−2.91568e6			−1.18435			−0.592173	−	0.805811i	$-0.701730\pi$
$67$	−2.91568e6			−1.18435			−0.592173	+	0.805811i	$0.701730\pi$
$68$	868489.			0.334953
$69$	927946.	−	2.85592e6i	0.340056	−	1.04659i
$70$	−835773.	−	2.57224e6i	−0.291236	−	0.896332i
$71$	1.02800e6	+	3.16385e6i	0.340869	+	1.04909i	0.963758	+	0.266777i	$0.0859587\pi$
$71$	1.02800e6	+	3.16385e6i	0.340869	+	1.04909i	−0.622889	+	0.782310i	$0.714041\pi$
$72$	441957.	−	321101.i	0.139546	−	0.101386i
$73$	−367159.	+	1.13000e6i	−0.110465	+	0.339976i	−0.990974	−	0.134053i	$-0.957201\pi$
$73$	−367159.	+	1.13000e6i	−0.110465	+	0.339976i	0.880509	+	0.474029i	$0.157201\pi$
$74$	−3.29662e6	+	2.39513e6i	−0.945709	+	0.687098i
$75$	−1.87172e6	−	1.35988e6i	−0.512303	−	0.372210i
$76$	−870526.	−	2.67920e6i	−0.227475	−	0.700097i
$77$	−216704.	−	157444.i	−0.0540939	−	0.0393016i
$78$	−1.18552e6	−	861329.i	−0.282864	−	0.205512i
$79$	1.36418e6	+	4.19852e6i	0.311299	+	0.958080i	0.977251	+	0.212085i	$0.0680255\pi$
$79$	1.36418e6	+	4.19852e6i	0.311299	+	0.958080i	−0.665952	+	0.745994i	$0.731975\pi$
$80$	−1.27161e6	−	923877.i	−0.277676	−	0.201743i
$81$	1.06068e6	−	770630.i	0.221762	−	0.161120i
$82$	−1.59088e6	+	4.89621e6i	−0.318631	+	0.980644i
$83$	3.10497e6	−	2.25589e6i	0.596052	−	0.433057i	−0.248423	−	0.968652i	$-0.579912\pi$
$83$	3.10497e6	−	2.25589e6i	0.596052	−	0.433057i	0.844475	+	0.535594i	$0.179912\pi$
$84$	−583119.	−	1.79466e6i	−0.107344	−	0.330372i
$85$	1.60917e6	+	4.95252e6i	0.284208	+	0.874702i
$86$	−1.19372e6	+	3.67390e6i	−0.202376	+	0.622849i
$87$	−1.90739e6			−0.310542
$88$	−155668.			−0.0243506
$89$	390426.	−	1.20161e6i	0.0587048	−	0.180675i	−0.917404	−	0.397957i	$-0.869719\pi$
$89$	390426.	−	1.20161e6i	0.0587048	−	0.180675i	0.976109	+	0.217282i	$0.0697193\pi$
$90$	2.64994e6	+	1.92529e6i	0.383166	+	0.278387i
$91$	3.90107e6	−	2.83429e6i	0.542674	−	0.394276i
$92$	5.74256e6			0.768862
$93$	−3.98587e6	+	3.86364e6i	−0.513846	+	0.498089i
$94$	−9.21432e6			−1.14424
$95$	1.36651e7	−	9.92827e6i	1.63523	−	1.18807i
$96$	−887201.	−	644589.i	−0.102346	−	0.0743590i
$97$	−893048.	+	2.74852e6i	−0.0993513	+	0.305772i	−0.988363	−	0.152112i	$-0.951393\pi$
$97$	−893048.	+	2.74852e6i	−0.0993513	+	0.305772i	0.889012	+	0.457884i	$0.151393\pi$
$98$	−378932.			−0.0406696
$99$	324400.			0.0336015
$100$	1.36720e6	−	4.20780e6i	0.136720	−	0.420780i
$101$	−1.34798e6	−	4.14865e6i	−0.130184	−	0.400665i	0.864626	−	0.502416i	$-0.167556\pi$
$101$	−1.34798e6	−	4.14865e6i	−0.130184	−	0.400665i	−0.994810	+	0.101751i	$0.967556\pi$
$102$	1.12272e6	+	3.45538e6i	0.104754	+	0.322400i
$103$	2.32576e6	−	1.68976e6i	0.209718	−	0.152369i	−0.477968	−	0.878377i	$-0.658627\pi$
$103$	2.32576e6	−	1.68976e6i	0.209718	−	0.152369i	0.687686	+	0.726008i	$0.258627\pi$
$104$	865961.	−	2.66515e6i	0.0754887	−	0.232330i
$105$	9.15352e6	−	6.65042e6i	0.771659	−	0.560643i
$106$	1.09549e7	+	7.95917e6i	0.893380	+	0.649079i
$107$	2.64391e6	+	8.13712e6i	0.208643	+	0.642137i	0.999544	+	0.0301930i	$0.00961218\pi$
$107$	2.64391e6	+	8.13712e6i	0.208643	+	0.642137i	−0.790901	+	0.611944i	$0.790388\pi$
$108$	5.63853e6	+	4.09663e6i	0.430708	+	0.312928i
$109$	−8.02419e6	−	5.82992e6i	−0.593483	−	0.431191i	0.250076	−	0.968226i	$-0.419544\pi$
$109$	−8.02419e6	−	5.82992e6i	−0.593483	−	0.431191i	−0.843560	+	0.537035i	$0.819544\pi$
$110$	−288427.	−	887688.i	−0.0206615	−	0.0635896i
$111$	−1.37909e7	−	1.00197e7i	−0.957112	−	0.695382i
$112$	2.91943e6	−	2.12109e6i	0.196352	−	0.142658i
$113$	4.00779e6	−	1.23347e7i	0.261295	−	0.804183i	−0.731229	−	0.682132i	$-0.761053\pi$
$113$	4.00779e6	−	1.23347e7i	0.261295	−	0.804183i	0.992524	−	0.122051i	$-0.0389470\pi$
$114$	9.53414e6	−	6.92696e6i	0.602719	−	0.437901i
$115$	1.06401e7	+	3.27467e7i	0.652381	+	2.00782i
$116$	−1.12716e6	−	3.46905e6i	−0.0670476	−	0.206351i
$117$	−1.80460e6	+	5.55399e6i	−0.104167	+	0.320594i
$118$	−4.24480e6			−0.237832
$119$	−1.19554e7			−0.650355
$120$	2.03190e6	−	6.25355e6i	0.107342	−	0.330363i
$121$	1.56907e7	+	1.13999e7i	0.805179	+	0.584997i
$122$	4.37146e6	−	3.17605e6i	0.217955	−	0.158354i
$123$	−2.15367e7			−1.04354
$124$	−9.38242e6	−	4.96607e6i	−0.441915	−	0.233904i
$125$	−3.45159e6			−0.158065
$126$	−6.08388e6	+	4.42020e6i	−0.270947	+	0.196854i
$127$	2.47323e6	+	1.79691e6i	0.107140	+	0.0778419i	0.640065	−	0.768321i	$-0.278907\pi$
$127$	2.47323e6	+	1.79691e6i	0.107140	+	0.0778419i	−0.532925	+	0.846162i	$0.678907\pi$
$128$	648056.	−	1.99451e6i	0.0273135	−	0.0840623i
$129$	−1.61602e7			−0.662799
$130$	1.68024e7			0.670764
$131$	1.19296e7	−	3.67155e7i	0.463635	−	1.42692i	−0.397057	−	0.917794i	$-0.629968\pi$
$131$	1.19296e7	−	3.67155e7i	0.463635	−	1.42692i	0.860692	−	0.509127i	$-0.170032\pi$
$132$	−201236.	−	619340.i	−0.00761546	−	0.0234380i
$133$	1.19835e7	+	3.68813e7i	0.441674	+	1.35933i
$134$	1.88707e7	−	1.37104e7i	0.677518	−	0.492246i
$135$	−1.29136e7	+	3.97439e7i	−0.451729	+	1.39028i
$136$	−5.62098e6	+	4.08388e6i	−0.191613	+	0.139215i
$137$	1.39808e7	+	1.01576e7i	0.464524	+	0.337497i	0.795304	−	0.606211i	$-0.207311\pi$
$137$	1.39808e7	+	1.01576e7i	0.464524	+	0.337497i	−0.330779	+	0.943708i	$0.607311\pi$
$138$	7.42357e6	+	2.28474e7i	0.240456	+	0.740048i
$139$	4.79120e6	+	3.48101e6i	0.151319	+	0.109939i	0.660869	−	0.750502i	$-0.270188\pi$
$139$	4.79120e6	+	3.48101e6i	0.151319	+	0.109939i	−0.509550	+	0.860441i	$0.670188\pi$
$140$	1.75046e7	+	1.27179e7i	0.539145	+	0.391712i
$141$	−1.19116e7	−	3.66601e7i	−0.357852	−	1.10135i
$142$	−2.15306e7	−	1.56429e7i	−0.631027	−	0.458468i
$143$	1.34627e6	−	978122.i	0.0384996	−	0.0279716i
$144$	−1.35050e6	+	4.15642e6i	−0.0376900	+	0.115998i
$145$	1.76936e7	−	1.28552e7i	0.481980	−	0.350179i
$146$	−2.93727e6	−	9.04000e6i	−0.0781105	−	0.240399i
$147$	−489855.	−	1.50762e6i	−0.0127191	−	0.0391454i
$148$	1.00736e7	−	3.10032e7i	0.255427	−	0.786124i
$149$	−2.62470e7			−0.650022			−0.325011	−	0.945710i	$-0.605368\pi$
$149$	−2.62470e7			−0.650022			−0.325011	+	0.945710i	$0.605368\pi$
$150$	1.85086e7			0.447769
$151$	−1.24014e7	+	3.81676e7i	−0.293124	+	0.902143i	0.690721	+	0.723121i	$0.257293\pi$
$151$	−1.24014e7	+	3.81676e7i	−0.293124	+	0.902143i	−0.983845	+	0.179022i	$0.942707\pi$
$152$	1.82325e7	+	1.32467e7i	0.421109	+	0.305954i
$153$	1.17137e7	−	8.51052e6i	0.264408	−	0.192104i
$154$	2.14288e6			0.0472798
$155$	1.09347e7	−	6.27042e7i	0.235855	−	1.35249i
$156$	1.17230e7			0.247232
$157$	−1.59424e7	+	1.15828e7i	−0.328780	+	0.238872i	−0.739913	−	0.672703i	$-0.765133\pi$
$157$	−1.59424e7	+	1.15828e7i	−0.328780	+	0.238872i	0.411133	+	0.911575i	$0.365133\pi$
$158$	−2.85718e7	−	2.07586e7i	−0.576286	−	0.418696i
$159$	−1.75048e7	+	5.38741e7i	−0.345355	+	1.06289i
$160$	1.25743e7			0.242698
$161$	−7.90508e7			−1.49285
$162$	−3.24115e6	+	9.97524e6i	−0.0598959	+	0.184341i
$163$	940991.	+	2.89607e6i	0.0170188	+	0.0523785i	0.959205	−	0.282711i	$-0.0912336\pi$
$163$	940991.	+	2.89607e6i	0.0170188	+	0.0523785i	−0.942186	+	0.335089i	$0.891234\pi$
$164$	−1.27270e7	−	3.91697e7i	−0.225306	−	0.693420i
$165$	3.15890e6	−	2.29508e6i	0.0547447	−	0.0397744i
$166$	−9.48795e6	+	2.92009e7i	−0.160988	+	0.495471i
$167$	−7.92260e7	+	5.75611e7i	−1.31632	+	0.956360i	−0.316346	+	0.948644i	$0.602456\pi$
$167$	−7.92260e7	+	5.75611e7i	−1.31632	+	0.956360i	−0.999970	+	0.00771580i	$0.997544\pi$
$168$	1.22130e7	+	8.87326e6i	0.198719	+	0.144378i
$169$	−1.01333e7	−	3.11870e7i	−0.161490	−	0.497016i
$170$	−3.37029e7	−	2.44866e7i	−0.526134	−	0.382259i
$171$	−3.79953e7	−	2.76052e7i	−0.581090	−	0.422187i
$172$	−9.54978e6	−	2.93912e7i	−0.143101	−	0.440421i
$173$	−8.19469e7	−	5.95379e7i	−1.20329	−	0.874243i	−0.208688	−	0.977982i	$-0.566919\pi$
$173$	−8.19469e7	−	5.95379e7i	−1.20329	−	0.874243i	−0.994605	+	0.103739i	$0.966919\pi$
$174$	1.23449e7	−	8.96906e6i	0.177649	−	0.129070i
$175$	−1.88205e7	+	5.79236e7i	−0.265459	+	0.817000i
$176$	1.00750e6	−	731993.i	0.0139300	−	0.0101207i
$177$	−5.48737e6	−	1.68884e7i	−0.0743802	−	0.228919i
$178$	3.12341e6	+	9.61286e6i	0.0415105	+	0.127756i
$179$	8.33498e6	−	2.56524e7i	0.108622	−	0.334305i	−0.881941	−	0.471359i	$-0.843763\pi$
$179$	8.33498e6	−	2.56524e7i	0.108622	−	0.334305i	0.990564	+	0.137054i	$0.0437635\pi$
$180$	−2.62040e7			−0.334900
$181$	−1.12346e8			−1.40826			−0.704129	−	0.710072i	$-0.748662\pi$
$181$	−1.12346e8			−1.40826			−0.704129	+	0.710072i	$0.748662\pi$
$182$	−1.19206e7	+	3.66879e7i	−0.146571	+	0.451100i
$183$	1.82874e7	+	1.32866e7i	0.220583	+	0.160263i
$184$	−3.71667e7	+	2.70032e7i	−0.439836	+	0.319560i
$185$	1.95459e8			2.26963
$186$	7.62914e6	−	4.37487e7i	0.0869321	−	0.498506i
$187$	−4.12584e6			−0.0461389
$188$	5.96363e7	−	4.33283e7i	0.654573	−	0.475575i
$189$	−7.76187e7	−	5.63933e7i	−0.836276	−	0.607590i
$190$	−4.17568e7	+	1.28514e8i	−0.441662	+	1.35930i
$191$	8.99985e7			0.934584			0.467292	−	0.884103i	$-0.345230\pi$
$191$	8.99985e7			0.934584			0.467292	+	0.884103i	$0.345230\pi$
$192$	8.77313e6			0.0894541
$193$	4.74470e7	−	1.46027e8i	0.475071	−	1.46212i	−0.370791	−	0.928716i	$-0.620913\pi$
$193$	4.74470e7	−	1.46027e8i	0.475071	−	1.46212i	0.845862	−	0.533402i	$-0.179087\pi$
$194$	−7.14438e6	−	2.19881e7i	−0.0702520	−	0.216213i
$195$	2.17209e7	+	6.68502e7i	0.209777	+	0.645626i
$196$	2.45250e6	−	1.78184e6i	0.0232655	−	0.0169034i
$197$	−2.63613e7	+	8.11317e7i	−0.245660	+	0.756064i	0.749867	+	0.661589i	$0.230117\pi$
$197$	−2.63613e7	+	8.11317e7i	−0.245660	+	0.756064i	−0.995527	+	0.0944757i	$0.969883\pi$
$198$	−2.09956e6	+	1.52542e6i	−0.0192221	+	0.0139657i
$199$	9.70989e7	+	7.05465e7i	0.873431	+	0.634585i	0.931505	−	0.363728i	$-0.118496\pi$
$199$	9.70989e7	+	7.05465e7i	0.873431	+	0.634585i	−0.0580745	+	0.998312i	$0.518496\pi$
$200$	1.09376e7	+	3.36624e7i	0.0966754	+	0.297536i
$201$	7.89427e7	+	5.73553e7i	0.685687	+	0.498181i
$202$	2.82324e7	+	2.05120e7i	0.241001	+	0.175097i
$203$	1.55162e7	+	4.77541e7i	0.130182	+	0.400658i
$204$	−2.35145e7	−	1.70843e7i	−0.193924	−	0.140894i
$205$	1.99782e8	−	1.45150e8i	1.61964	−	1.17674i
$206$	−7.10689e6	+	2.18728e7i	−0.0566428	+	0.174329i
$207$	7.74527e7	−	5.62727e7i	0.606932	−	0.440962i
$208$	6.92769e6	+	2.13212e7i	0.0533785	+	0.164282i
$209$	4.13552e6	+	1.27278e7i	0.0313342	+	0.0964367i
$210$	−2.79707e7	+	8.60848e7i	−0.208418	+	0.641445i
$211$	−9.65642e7			−0.707665			−0.353832	−	0.935309i	$-0.615122\pi$
$211$	−9.65642e7			−0.707665			−0.353832	+	0.935309i	$0.615122\pi$
$212$	−1.08328e8			−0.780843
$213$	3.44038e7	−	1.05884e8i	0.243937	−	0.750761i
$214$	−5.53748e7	−	4.02321e7i	−0.386246	−	0.280624i
$215$	1.49908e8	−	1.08914e8i	1.02870	−	0.747396i
$216$	−5.57569e7			−0.376452
$217$	1.29156e8	+	6.83618e7i	0.858037	+	0.454155i
$218$	7.93476e7			0.518724
$219$	3.21695e7	−	2.33725e7i	0.206962	−	0.150366i
$220$	6.04090e6	+	4.38897e6i	0.0382492	+	0.0277897i
$221$	2.29516e7	−	7.06378e7i	0.143034	−	0.440214i
$222$	1.36372e8			0.836546
$223$	−1.65803e8			−1.00121			−0.500604	−	0.865676i	$-0.666889\pi$
$223$	−1.65803e8			−1.00121			−0.500604	+	0.865676i	$0.666889\pi$
$224$	−8.92098e6	+	2.74560e7i	−0.0530328	+	0.163218i
$225$	−2.27931e7	−	7.01501e7i	−0.133403	−	0.410572i
$226$	3.20623e7	+	9.86777e7i	0.184763	+	0.568643i
$227$	3.39554e6	−	2.46701e6i	0.0192672	−	0.0139984i	−0.578110	−	0.815959i	$-0.696210\pi$
$227$	3.39554e6	−	2.46701e6i	0.0192672	−	0.0139984i	0.597377	+	0.801960i	$0.296210\pi$
$228$	−2.91337e7	+	8.96645e7i	−0.162789	+	0.501012i
$229$	−1.17240e8	+	8.51798e7i	−0.645136	+	0.468719i	−0.861611	−	0.507569i	$-0.830544\pi$
$229$	−1.17240e8	+	8.51798e7i	−0.645136	+	0.468719i	0.216475	+	0.976288i	$0.430544\pi$
$230$	−2.22848e8	−	1.61909e8i	−1.20771	−	0.877451i
$231$	2.77016e6	+	8.52569e6i	0.0147864	+	0.0455080i
$232$	2.36076e7	+	1.71519e7i	0.124121	+	0.0901788i
$233$	2.77529e8	+	2.01636e8i	1.43735	+	1.04430i	0.988588	+	0.150643i	$0.0481345\pi$
$233$	2.77529e8	+	2.01636e8i	1.43735	+	1.04430i	0.448761	+	0.893652i	$0.351866\pi$
$234$	−1.44368e7	−	4.44319e7i	−0.0736573	−	0.226694i
$235$	3.57574e8	+	2.59793e8i	1.79733	+	1.30584i
$236$	2.74729e7	−	1.99602e7i	0.136054	−	0.0988493i
$237$	4.56549e7	−	1.40511e8i	0.222776	−	0.685633i
$238$	7.73771e7	−	5.62177e7i	0.372043	−	0.270305i
$239$	6.67642e7	+	2.05479e8i	0.316338	+	0.973588i	0.975200	+	0.221324i	$0.0710379\pi$
$239$	6.67642e7	+	2.05479e8i	0.316338	+	0.973588i	−0.658862	+	0.752263i	$0.728962\pi$
$240$	1.62552e7	+	5.00284e7i	0.0759020	+	0.233602i
$241$	−9.44660e7	+	2.90737e8i	−0.434726	+	1.33795i	0.458640	+	0.888622i	$0.348337\pi$
$241$	−9.44660e7	+	2.90737e8i	−0.434726	+	1.33795i	−0.893367	+	0.449328i	$0.851663\pi$
$242$	−1.55158e8			−0.703753
$243$	1.94287e8			0.868604
$244$	−1.33580e7	+	4.11117e7i	−0.0588677	+	0.181176i
$245$	1.47050e7	+	1.06838e7i	0.0638827	+	0.0464135i
$246$	1.39388e8	−	1.01271e8i	0.596971	−	0.433725i
$247$	−2.40916e8			−1.01725
$248$	8.40762e7	−	1.19777e7i	0.350019	−	0.0498645i
$249$	−1.28444e8			−0.527250
$250$	2.23392e7	−	1.62304e7i	0.0904226	−	0.0656959i
$251$	−2.18046e8	−	1.58420e8i	−0.870342	−	0.632340i	0.0603370	−	0.998178i	$-0.480782\pi$
$251$	−2.18046e8	−	1.58420e8i	−0.870342	−	0.632340i	−0.930679	+	0.365838i	$0.880782\pi$
$252$	1.85907e7	−	5.72163e7i	0.0731802	−	0.225225i
$253$	−2.72806e7			−0.105909
$254$	−2.44567e7			−0.0936439
$255$	5.38539e7	−	1.65745e8i	0.203388	−	0.625965i
$256$	5.18444e6	+	1.59561e7i	0.0193136	+	0.0594410i
$257$	−1.25403e8	−	3.85950e8i	−0.460831	−	1.41829i	−0.864151	−	0.503232i	$-0.832144\pi$
$257$	−1.25403e8	−	3.85950e8i	−0.460831	−	1.41829i	0.403321	−	0.915059i	$-0.367856\pi$
$258$	1.04591e8	−	7.59896e7i	0.379162	−	0.275477i
$259$	−1.38670e8	+	4.26783e8i	−0.495946	+	1.52636i
$260$	−1.08747e8	+	7.90097e7i	−0.383718	+	0.278788i
$261$	−4.91965e7	−	3.57434e7i	−0.171274	−	0.124438i
$262$	9.54367e7	+	2.93724e8i	0.327839	+	1.00899i
$263$	−2.19111e8	−	1.59194e8i	−0.742710	−	0.539610i	0.150849	−	0.988557i	$-0.451799\pi$
$263$	−2.19111e8	−	1.59194e8i	−0.742710	−	0.539610i	−0.893559	+	0.448946i	$0.851799\pi$
$264$	4.21474e6	+	3.06219e6i	0.0140980	+	0.0102428i
$265$	−2.00714e8	−	6.17733e8i	−0.662547	−	2.03911i
$266$	−2.50985e8	−	1.82351e8i	−0.817639	−	0.594050i
$267$	−3.42080e7	+	2.48536e7i	−0.109986	+	0.0799098i
$268$	−5.76637e7	+	1.77471e8i	−0.182991	+	0.563190i
$269$	3.19298e8	−	2.31984e8i	1.00015	−	0.726649i	0.0380273	−	0.999277i	$-0.487893\pi$
$269$	3.19298e8	−	2.31984e8i	1.00015	−	0.726649i	0.962120	+	0.272627i	$0.0878926\pi$
$270$	−1.03309e8	−	3.17951e8i	−0.319421	−	0.983076i
$271$	−1.85163e7	−	5.69872e7i	−0.0565146	−	0.173934i	0.918815	−	0.394689i	$-0.129148\pi$
$271$	−1.85163e7	−	5.69872e7i	−0.0565146	−	0.173934i	−0.975329	+	0.220755i	$0.929148\pi$
$272$	1.71762e7	−	5.28629e7i	0.0517530	−	0.159279i
$273$	−1.61377e8			−0.480034
$274$	−1.38249e8			−0.406009
$275$	−6.49500e6	+	1.99896e7i	−0.0188328	+	0.0579614i
$276$	−1.55481e8	−	1.12964e8i	−0.445140	−	0.323413i
$277$	−6.27452e7	+	4.55871e7i	−0.177379	+	0.128873i	−0.672932	−	0.739704i	$-0.734965\pi$
$277$	−6.27452e7	+	4.55871e7i	−0.177379	+	0.128873i	0.495553	+	0.868578i	$0.334965\pi$
$278$	−4.73780e7			−0.132257
$279$	−1.75209e8	+	2.49606e7i	−0.482993	+	0.0688083i
$280$	−1.73095e8			−0.471230
$281$	−7.19153e7	+	5.22495e7i	−0.193352	+	0.140479i	−0.680250	−	0.732981i	$-0.738129\pi$
$281$	−7.19153e7	+	5.22495e7i	−0.193352	+	0.140479i	0.486897	+	0.873459i	$0.338129\pi$
$282$	2.49480e8	+	1.81258e8i	0.662466	+	0.481310i
$283$	−5.08006e7	+	1.56348e8i	−0.133234	+	0.410053i	−0.995311	−	0.0967242i	$-0.969164\pi$
$283$	−5.08006e7	+	1.56348e8i	−0.133234	+	0.410053i	0.862077	+	0.506778i	$0.169164\pi$
$284$	2.12907e8			0.551538
$285$	−5.65288e8			−1.44648
$286$	−4.11383e6	+	1.26611e7i	−0.0103984	+	0.0320029i
$287$	1.75197e8	+	5.39201e8i	0.437461	+	1.34637i
$288$	−1.08040e7	−	3.32513e7i	−0.0266509	−	0.0820230i
$289$	1.82991e8	−	1.32951e8i	0.445952	−	0.324003i
$290$	−5.40669e7	+	1.66401e8i	−0.130178	+	0.400648i
$291$	7.82464e7	−	5.68494e7i	0.186140	−	0.135238i
$292$	6.15190e7	+	4.46962e7i	0.144600	+	0.105058i
$293$	−1.60119e8	−	4.92794e8i	−0.371882	−	1.14453i	−0.945558	−	0.325453i	$-0.894483\pi$
$293$	−1.60119e8	−	4.92794e8i	−0.371882	−	1.14453i	0.573677	−	0.819082i	$-0.305517\pi$
$294$	1.02597e7	+	7.45408e6i	0.0235460	+	0.0171072i
$295$	1.64725e8	+	1.19680e8i	0.373580	+	0.271422i
$296$	8.05885e7	+	2.48026e8i	0.180614	+	0.555874i
$297$	−2.67864e7	−	1.94615e7i	−0.0593290	−	0.0431050i
$298$	1.69874e8	−	1.23421e8i	0.371853	−	0.270167i
$299$	1.51759e8	−	4.67066e8i	0.328326	−	1.01048i
$300$	−1.19790e8	+	8.70326e7i	−0.256151	+	0.186105i
$301$	1.31460e8	+	4.04592e8i	0.277850	+	0.855136i
$302$	−9.92112e7	−	3.05341e8i	−0.207270	−	0.637911i
$303$	−4.51125e7	+	1.38842e8i	−0.0931640	+	0.286729i
$304$	−1.80293e8			−0.368063
$305$	−2.59188e8			−0.523077
$306$	−3.57940e7	+	1.10162e8i	−0.0714142	+	0.219790i
$307$	5.38945e8	+	3.91567e8i	1.06307	+	0.772363i	0.974653	−	0.223721i	$-0.0718204\pi$
$307$	5.38945e8	+	3.91567e8i	1.06307	+	0.772363i	0.0884133	+	0.996084i	$0.471820\pi$
$308$	−1.38690e7	+	1.00764e7i	−0.0270470	+	0.0196508i
$309$	−9.62104e7			−0.185510
$310$	2.24082e8	+	4.57248e8i	0.427209	+	0.871738i
$311$	−6.56938e8			−1.23841			−0.619203	−	0.785231i	$-0.712544\pi$
$311$	−6.56938e8			−1.23841			−0.619203	+	0.785231i	$0.712544\pi$
$312$	−7.58732e7	+	5.51251e7i	−0.141432	+	0.102756i
$313$	2.13122e8	+	1.54842e8i	0.392847	+	0.285420i	0.766621	−	0.642100i	$-0.221936\pi$
$313$	2.13122e8	+	1.54842e8i	0.392847	+	0.285420i	−0.373774	+	0.927520i	$0.621936\pi$
$314$	4.87157e7	−	1.49931e8i	0.0888004	−	0.273299i
$315$	3.60719e8			0.650252
$316$	2.82534e8			0.503692
$317$	−4.82152e7	+	1.48391e8i	−0.0850114	+	0.261638i	−0.984522	−	0.175261i	$-0.943923\pi$
$317$	−4.82152e7	+	1.48391e8i	−0.0850114	+	0.261638i	0.899511	+	0.436899i	$0.143923\pi$
$318$	−1.40038e8	−	4.30993e8i	−0.244203	−	0.751580i
$319$	5.35469e6	+	1.64801e7i	0.00923564	+	0.0284244i
$320$	−8.13829e7	+	5.91281e7i	−0.138838	+	0.100872i
$321$	8.84833e7	−	2.72324e8i	0.149312	−	0.459534i
$322$	5.11627e8	−	3.71719e8i	0.854001	−	0.620468i
$323$	4.83239e8	+	3.51093e8i	0.797908	+	0.579714i
$324$	−2.59292e7	−	7.98019e7i	−0.0423528	−	0.130348i
$325$	−3.06106e8	−	2.22399e8i	−0.494630	−	0.359370i
$326$	−1.97084e7	−	1.43190e7i	−0.0315057	−	0.0228902i
$327$	1.02575e8	+	3.15693e8i	0.162227	+	0.499284i
$328$	2.66558e8	+	1.93666e8i	0.417093	+	0.303036i
$329$	−8.20939e8	+	5.96447e8i	−1.27094	+	0.923393i
$330$	−9.65274e6	+	2.97081e7i	−0.0147860	+	0.0455068i
$331$	−1.16572e8	+	8.46943e7i	−0.176683	+	0.128368i	−0.672612	−	0.739995i	$-0.734828\pi$
$331$	−1.16572e8	+	8.46943e7i	−0.176683	+	0.128368i	0.495929	+	0.868363i	$0.334828\pi$
$332$	−7.59036e7	−	2.33607e8i	−0.113836	−	0.350351i
$333$	−1.67941e8	−	5.16868e8i	−0.249231	−	0.767053i
$334$	2.42093e8	−	7.45086e8i	0.355525	−	1.09419i
$335$	−1.11886e9			−1.62599
$336$	−1.20769e8			−0.173687
$337$	−3.80182e8	+	1.17008e9i	−0.541112	+	1.66537i	0.188947	+	0.981987i	$0.439492\pi$
$337$	−3.80182e8	+	1.17008e9i	−0.541112	+	1.66537i	−0.730059	+	0.683384i	$0.760508\pi$
$338$	2.12234e8	+	1.54197e8i	0.298955	+	0.217204i
$339$	−3.51152e8	+	2.55127e8i	−0.489549	+	0.355678i
$340$	3.33273e8			0.459858
$341$	4.45721e7	+	2.35918e7i	0.0608727	+	0.0322197i
$342$	3.75718e8			0.507892
$343$	−6.20742e8	+	4.50995e8i	−0.830580	+	0.603452i
$344$	2.00013e8	+	1.45318e8i	0.264914	+	0.192471i
$345$	3.56089e8	−	1.09593e9i	0.466865	−	1.43686i
$346$	8.10336e8			1.05172
$347$	−3.02538e8			−0.388711			−0.194356	−	0.980931i	$-0.562262\pi$
$347$	−3.02538e8			−0.388711			−0.194356	+	0.980931i	$0.562262\pi$
$348$	−3.77225e7	+	1.16098e8i	−0.0479815	+	0.147672i
$349$	−2.00594e8	−	6.17366e8i	−0.252598	−	0.777417i	−0.994293	−	0.106680i	$-0.965978\pi$
$349$	−2.00594e8	−	6.17366e8i	−0.252598	−	0.777417i	0.741695	−	0.670737i	$-0.234022\pi$
$350$	−1.50564e8	−	4.63389e8i	−0.187708	−	0.577706i
$351$	4.82205e8	−	3.50343e8i	0.595192	−	0.432432i
$352$	−3.07865e6	+	9.47512e6i	−0.00376237	+	0.0115794i
$353$	1.21261e9	−	8.81016e8i	1.46727	−	1.06604i	0.485882	−	0.874024i	$-0.338498\pi$
$353$	1.21261e9	−	8.81016e8i	1.46727	−	1.06604i	0.981392	−	0.192013i	$-0.0615016\pi$
$354$	1.14929e8	+	8.35007e7i	0.137695	+	0.100041i
$355$	3.94482e8	+	1.21409e9i	0.467981	+	1.44030i
$356$	−6.54175e7	−	4.75286e7i	−0.0768456	−	0.0558316i
$357$	3.23696e8	+	2.35179e8i	0.376529	+	0.273564i
$358$	6.66798e7	+	2.05219e8i	0.0768076	+	0.236389i
$359$	1.30377e9	+	9.47246e8i	1.48721	+	1.08052i	0.975144	+	0.221570i	$0.0711181\pi$
$359$	1.30377e9	+	9.47246e8i	1.48721	+	1.08052i	0.512062	+	0.858949i	$0.328882\pi$
$360$	1.69596e8	−	1.23219e8i	0.191583	−	0.139193i
$361$	3.22495e8	−	9.92538e8i	0.360785	−	1.11038i
$362$	7.27118e8	−	5.28282e8i	0.805610	−	0.585310i
$363$	−2.00577e8	−	6.17312e8i	−0.220094	−	0.677379i
$364$	−9.53649e7	−	2.93503e8i	−0.103642	−	0.318976i
$365$	−1.40893e8	+	4.33624e8i	−0.151658	+	0.466755i
$366$	−1.80836e8			−0.192797
$367$	2.35876e8			0.249088			0.124544	−	0.992214i	$-0.460253\pi$
$367$	2.35876e8			0.249088			0.124544	+	0.992214i	$0.460253\pi$
$368$	1.13571e8	−	3.49536e8i	0.118796	−	0.365616i
$369$	−5.55487e8	−	4.03585e8i	−0.575549	−	0.418161i
$370$	−1.26504e9	+	9.19105e8i	−1.29837	+	0.943320i
$371$	1.49121e9			1.51611
$372$	1.56342e8	+	3.19022e8i	0.157462	+	0.321307i
$373$	1.19386e9			1.19116			0.595582	−	0.803294i	$-0.296921\pi$
$373$	1.19386e9			1.19116			0.595582	+	0.803294i	$0.296921\pi$
$374$	2.67030e7	−	1.94009e7i	0.0263943	−	0.0191766i
$375$	9.34527e7	+	6.78973e7i	0.0915129	+	0.0664880i
$376$	−1.82232e8	+	5.60853e8i	−0.176794	+	0.544117i
$377$	−3.11939e8			−0.299830
$378$	7.67536e8			0.730932
$379$	3.45900e8	−	1.06457e9i	0.326372	−	1.00447i	−0.644445	−	0.764651i	$-0.722912\pi$
$379$	3.45900e8	−	1.06457e9i	0.326372	−	1.00447i	0.970817	−	0.239820i	$-0.0770884\pi$
$380$	−3.34055e8	−	1.02811e9i	−0.312302	−	0.961167i
$381$	−3.16158e7	−	9.73035e7i	−0.0292865	−	0.0901345i
$382$	−5.82483e8	+	4.23198e8i	−0.534640	+	0.388438i
$383$	−1.21537e8	+	3.74052e8i	−0.110538	+	0.340202i	−0.990990	−	0.133933i	$-0.957239\pi$
$383$	−1.21537e8	+	3.74052e8i	−0.110538	+	0.340202i	0.880452	+	0.474135i	$0.157239\pi$
$384$	−5.67809e7	+	4.12537e7i	−0.0511732	+	0.0371795i
$385$	−8.31576e7	−	6.04175e7i	−0.0742659	−	0.0539573i
$386$	3.79576e8	+	1.16822e9i	0.335926	+	1.03387i
$387$	−4.16813e8	−	3.02833e8i	−0.365555	−	0.265592i
$388$	1.49634e8	+	1.08715e8i	0.130053	+	0.0944887i
$389$	4.90140e7	+	1.50850e8i	0.0422179	+	0.129933i	0.969944	−	0.243328i	$-0.0782393\pi$
$389$	4.90140e7	+	1.50850e8i	0.0422179	+	0.129933i	−0.927726	+	0.373262i	$0.878239\pi$
$390$	−4.54929e8	−	3.30525e8i	−0.388345	−	0.282149i
$391$	−9.85072e8	+	7.15697e8i	−0.833392	+	0.605495i
$392$	−7.49417e6	+	2.30647e7i	−0.00628380	+	0.0193395i
$393$	−1.04524e9	+	7.59410e8i	−0.868643	+	0.631106i
$394$	−2.10890e8	−	6.49054e8i	−0.173708	−	0.534618i
$395$	5.23490e8	+	1.61114e9i	0.427384	+	1.31535i
$396$	6.41569e6	−	1.97455e7i	0.00519171	−	0.0159784i
$397$	6.69329e8			0.536874			0.268437	−	0.963297i	$-0.413493\pi$
$397$	6.69329e8			0.536874			0.268437	+	0.963297i	$0.413493\pi$
$398$	−9.60167e8			−0.763407
$399$	4.01048e8	−	1.23430e9i	0.316076	−	0.972782i
$400$	−2.29080e8	−	1.66436e8i	−0.178968	−	0.130028i
$401$	2.79619e8	−	2.03155e8i	0.216552	−	0.157334i	−0.474221	−	0.880406i	$-0.657270\pi$
$401$	2.79619e8	−	2.03155e8i	0.216552	−	0.157334i	0.690773	+	0.723072i	$0.257270\pi$
$402$	−7.80629e8			−0.599313
$403$	−6.51860e8	+	6.31872e8i	−0.496120	+	0.480907i
$404$	−2.79177e8			−0.210642
$405$	4.07024e8	−	2.95720e8i	0.304458	−	0.221202i
$406$	−3.24976e8	−	2.36109e8i	−0.240996	−	0.175094i
$407$	−4.78555e7	+	1.47284e8i	−0.0351845	+	0.108287i
$408$	2.32525e8			0.169496
$409$	−1.99394e9			−1.44105			−0.720527	−	0.693427i	$-0.756100\pi$
$409$	−1.99394e9			−1.44105			−0.720527	+	0.693427i	$0.756100\pi$
$410$	−6.10480e8	+	1.87887e9i	−0.437450	+	1.34633i
$411$	−1.78719e8	−	5.50039e8i	−0.126977	−	0.390794i
$412$	−5.68552e7	−	1.74982e8i	−0.0400525	−	0.123269i
$413$	−3.78186e8	+	2.74768e8i	−0.264168	+	0.191929i
$414$	−2.36674e8	+	7.28409e8i	−0.163927	+	0.504515i
$415$	1.19150e9	−	8.65674e8i	0.818323	−	0.594547i
$416$	−1.45095e8	−	1.05418e8i	−0.0988159	−	0.0717940i
$417$	−6.12468e7	−	1.88498e8i	−0.0413626	−	0.127301i
$418$	−8.66155e7	−	6.29298e7i	−0.0580067	−	0.0421444i
$419$	−1.65036e9	−	1.19905e9i	−1.09605	−	0.796324i	−0.115636	−	0.993292i	$-0.536890\pi$
$419$	−1.65036e9	−	1.19905e9i	−1.09605	−	0.796324i	−0.980410	+	0.196968i	$0.936890\pi$
$420$	−2.23765e8	−	6.88679e8i	−0.147374	−	0.453570i
$421$	1.19347e9	+	8.67110e8i	0.779518	+	0.566353i	0.904834	−	0.425764i	$-0.139995\pi$
$421$	1.19347e9	+	8.67110e8i	0.779518	+	0.566353i	−0.125317	+	0.992117i	$0.539995\pi$
$422$	6.24977e8	−	4.54072e8i	0.404828	−	0.294125i
$423$	3.79759e8	−	1.16878e9i	0.243959	−	0.750829i
$424$	7.01111e8	−	5.09387e8i	0.446690	−	0.324539i
$425$	2.89892e8	+	8.92195e8i	0.183178	+	0.563765i
$426$	2.75230e8	+	8.47072e8i	0.172489	+	0.530868i
$427$	1.83883e8	−	5.65934e8i	0.114299	−	0.351778i
$428$	5.47576e8			0.337591
$429$	−5.56915e7			−0.0340556
$430$	−4.58078e8	+	1.40982e9i	−0.277843	+	0.855113i
$431$	−1.46165e9	−	1.06195e9i	−0.879375	−	0.638903i	0.0537112	−	0.998557i	$-0.482895\pi$
$431$	−1.46165e9	−	1.06195e9i	−0.879375	−	0.638903i	−0.933086	+	0.359653i	$0.882895\pi$
$432$	3.60866e8	−	2.62184e8i	0.215354	−	0.156464i
$433$	2.84413e9			1.68361			0.841805	−	0.539782i	$-0.181493\pi$
$433$	2.84413e9			1.68361			0.841805	+	0.539782i	$0.181493\pi$
$434$	−1.15737e9	+	1.64882e8i	−0.679609	+	0.0968185i
$435$	−7.31937e8			−0.426345
$436$	−5.13548e8	+	3.73115e8i	−0.296742	+	0.215595i
$437$	3.19524e9	+	2.32148e9i	1.83155	+	1.33070i
$438$	−9.83012e7	+	3.02540e8i	−0.0558984	+	0.172038i
$439$	−3.23791e9			−1.82658			−0.913290	−	0.407309i	$-0.866467\pi$
$439$	−3.23791e9			−1.82658			−0.913290	+	0.407309i	$0.866467\pi$
$440$	−5.97357e7			−0.0334310
$441$	1.56173e7	−	4.80651e7i	0.00867104	−	0.0266867i
$442$	1.83613e8	+	5.65102e8i	0.101140	+	0.311278i
$443$	−8.79508e8	−	2.70685e9i	−0.480647	−	1.47928i	−0.838187	−	0.545383i	$-0.816384\pi$
$443$	−8.79508e8	−	2.70685e9i	−0.480647	−	1.47928i	0.357540	−	0.933898i	$-0.383616\pi$
$444$	−8.82618e8	+	6.41260e8i	−0.478556	+	0.347691i
$445$	1.49821e8	−	4.61103e8i	0.0805961	−	0.248049i
$446$	1.07310e9	−	7.79651e8i	0.572753	−	0.416129i
$447$	7.10644e8	+	5.16313e8i	0.376336	+	0.273424i
$448$	−7.13678e7	−	2.19648e8i	−0.0374998	−	0.115413i
$449$	−2.78870e9	−	2.02611e9i	−1.45392	−	1.05633i	−0.984896	−	0.173145i	$-0.944607\pi$
$449$	−2.78870e9	−	2.02611e9i	−1.45392	−	1.05633i	−0.469021	−	0.883187i	$-0.655393\pi$
$450$	4.77386e8	+	3.46841e8i	0.246959	+	0.179426i
$451$	6.04609e7	+	1.86079e8i	0.0310353	+	0.0955170i
$452$	−6.71522e8	−	4.87890e8i	−0.342039	−	0.248506i
$453$	1.08658e9	−	7.89444e8i	0.549183	−	0.399004i
$454$	−1.03759e7	+	3.19336e7i	−0.00520390	+	0.0160159i
$455$	1.49699e9	−	1.08763e9i	0.745040	−	0.541303i
$456$	−2.33070e8	−	7.17316e8i	−0.115109	−	0.354269i
$457$	1.01229e9	+	3.11551e9i	0.496133	+	1.52694i	0.815184	+	0.579202i	$0.196636\pi$
$457$	1.01229e9	+	3.11551e9i	0.496133	+	1.52694i	−0.319051	+	0.947738i	$0.603364\pi$
$458$	3.58253e8	−	1.10259e9i	0.174245	−	0.536272i
$459$	−1.47779e9			−0.713294
$460$	2.20364e9			1.05557
$461$	−9.92202e8	+	3.05368e9i	−0.471679	+	1.45168i	0.378705	+	0.925518i	$0.376370\pi$
$461$	−9.92202e8	+	3.05368e9i	−0.471679	+	1.45168i	−0.850384	+	0.526162i	$0.823630\pi$
$462$	−5.80191e7	−	4.21533e7i	−0.0273731	−	0.0198877i
$463$	−2.35017e9	+	1.70750e9i	−1.10044	+	0.799514i	−0.981131	−	0.193343i	$-0.938067\pi$
$463$	−2.35017e9	+	1.70750e9i	−1.10044	+	0.799514i	−0.119306	+	0.992858i	$0.538067\pi$
$464$	−2.33445e8			−0.108485
$465$	−1.52953e9	+	1.48263e9i	−0.705461	+	0.683829i
$466$	−2.74436e9			−1.25629
$467$	1.93972e9	−	1.40929e9i	0.881314	−	0.640312i	−0.0522845	−	0.998632i	$-0.516650\pi$
$467$	1.93972e9	−	1.40929e9i	0.881314	−	0.640312i	0.933599	+	0.358320i	$0.116650\pi$
$468$	3.02369e8	+	2.19684e8i	0.136357	+	0.0990689i
$469$	7.93785e8	−	2.44302e9i	0.355302	−	1.09351i
$470$	−3.53589e9			−1.57093
$471$	6.59494e8			0.290829
$472$	−8.39498e7	+	2.58371e8i	−0.0367470	+	0.113096i
$473$	4.53672e7	+	1.39626e8i	0.0197119	+	0.0606669i
$474$	3.65239e8	+	1.12409e9i	0.157526	+	0.484816i
$475$	2.46176e9	−	1.78857e9i	1.05395	−	0.765736i
$476$	−2.36443e8	+	7.27698e8i	−0.100485	+	0.309262i
$477$	−1.46107e9	+	1.06153e9i	−0.616390	+	0.447833i
$478$	−1.39833e9	−	1.01594e9i	−0.585614	−	0.425473i
$479$	−4.55702e8	−	1.40251e9i	−0.189455	−	0.583083i	0.810541	−	0.585681i	$-0.199173\pi$
$479$	−4.55702e8	−	1.40251e9i	−0.189455	−	0.583083i	−0.999997	+	0.00259827i	$0.999173\pi$
$480$	−3.40453e8	−	2.47354e8i	−0.140512	−	0.102088i
$481$	−2.25541e9	−	1.63865e9i	−0.924095	−	0.671395i
$482$	−7.55728e8	−	2.32589e9i	−0.307398	−	0.946074i
$483$	2.14032e9	+	1.55503e9i	0.864298	+	0.627949i
$484$	1.00420e9	−	7.29596e8i	0.402590	−	0.292499i
$485$	−3.42697e8	+	1.05471e9i	−0.136400	+	0.419796i
$486$	−1.25745e9	+	9.13592e8i	−0.496895	+	0.361015i
$487$	−6.68830e8	−	2.05845e9i	−0.262400	−	0.807585i	−0.992281	−	0.124010i	$-0.960424\pi$
$487$	−6.68830e8	−	2.05845e9i	−0.262400	−	0.807585i	0.729881	−	0.683574i	$-0.239576\pi$
$488$	−1.06864e8	−	3.28894e8i	−0.0416258	−	0.128111i
$489$	3.14920e7	−	9.69223e7i	0.0121792	−	0.0374837i
$490$	−1.45411e8			−0.0558355
$491$	2.67240e9			1.01886			0.509431	−	0.860511i	$-0.329856\pi$
$491$	2.67240e9			1.01886			0.509431	+	0.860511i	$0.329856\pi$
$492$	−4.25932e8	+	1.31088e9i	−0.161236	+	0.496234i
$493$	6.25700e8	+	4.54598e8i	0.235181	+	0.170869i
$494$	1.55924e9	−	1.13285e9i	0.581927	−	0.422795i
$495$	1.24485e8			0.0461316
$496$	−4.87830e8	+	4.72871e8i	−0.179508	+	0.174003i
$497$	−2.93082e9			−1.07088
$498$	8.31309e8	−	6.03981e8i	0.301620	−	0.219139i
$499$	−3.51482e9	−	2.55367e9i	−1.26634	−	0.920051i	−0.267292	−	0.963616i	$-0.586129\pi$
$499$	−3.51482e9	−	2.55367e9i	−1.26634	−	0.920051i	−0.999051	+	0.0435642i	$0.986129\pi$
$500$	−6.82625e7	+	2.10090e8i	−0.0244223	+	0.0751642i
$501$	3.27736e9			1.16437
$502$	2.15616e9			0.760706
$503$	2.21071e8	−	6.80388e8i	0.0774541	−	0.238379i	−0.904831	−	0.425770i	$-0.860003\pi$
$503$	2.21071e8	−	6.80388e8i	0.0774541	−	0.238379i	0.982285	+	0.187391i	$0.0600032\pi$
$504$	1.48726e8	+	4.57730e8i	0.0517462	+	0.159258i
$505$	−5.17271e8	−	1.59200e9i	−0.178730	−	0.550076i
$506$	1.76564e8	−	1.28281e8i	0.0605864	−	0.0440186i
$507$	−3.39128e8	+	1.04373e9i	−0.115568	+	0.355681i
$508$	1.58287e8	−	1.15002e8i	0.0535701	−	0.0389209i
$509$	3.22902e9	+	2.34602e9i	1.08532	+	0.788532i	0.978603	−	0.205757i	$-0.0659656\pi$
$509$	3.22902e9	+	2.34602e9i	1.08532	+	0.788532i	0.106718	+	0.994289i	$0.465966\pi$
$510$	4.30831e8	+	1.32596e9i	0.143817	+	0.442624i
$511$	−8.46856e8	−	6.15277e8i	−0.280761	−	0.203985i
$512$	−1.08584e8	−	7.88912e7i	−0.0357538	−	0.0259767i
$513$	1.48126e9	+	4.55884e9i	0.484417	+	1.49088i
$514$	2.62647e9	+	1.90824e9i	0.853103	+	0.619816i
$515$	8.92485e8	−	6.48428e8i	0.287922	−	0.209188i
$516$	−3.19601e8	+	9.83630e8i	−0.102408	+	0.315180i
$517$	−2.83308e8	+	2.05835e8i	−0.0901659	+	0.0655093i
$518$	−1.10936e9	−	3.41427e9i	−0.350687	−	1.07930i
$519$	1.04754e9	+	3.22401e9i	0.328917	+	1.01230i
$520$	3.32303e8	−	1.02272e9i	0.103639	−	0.318967i
$521$	5.05636e9			1.56641			0.783207	−	0.621762i	$-0.213583\pi$
$521$	5.05636e9			1.56641			0.783207	+	0.621762i	$0.213583\pi$
$522$	4.86482e8			0.149699
$523$	4.86090e8	−	1.49603e9i	0.148580	−	0.457283i	−0.848874	−	0.528595i	$-0.822719\pi$
$523$	4.86090e8	−	1.49603e9i	0.148580	−	0.457283i	0.997454	+	0.0713128i	$0.0227189\pi$
$524$	−1.99885e9	−	1.45225e9i	−0.606906	−	0.440943i
$525$	1.64900e9	−	1.19807e9i	0.497352	−	0.361347i
$526$	2.16669e9			0.649152
$527$	2.22837e9	−	3.17458e8i	0.663209	−	0.0944821i
$528$	−4.16776e7			−0.0123221
$529$	−3.75886e9	+	2.73097e9i	−1.10398	+	0.802089i
$530$	4.20380e9	+	3.05424e9i	1.22653	+	0.891123i
$531$	1.74945e8	−	5.38426e8i	0.0507074	−	0.156061i
$532$	2.48187e9			0.714643
$533$	−3.52217e9			−1.00755
$534$	1.04530e8	−	3.21712e8i	0.0297063	−	0.0914266i
$535$	1.01457e9	+	3.12253e9i	0.286447	+	0.881593i
$536$	−4.61310e8	−	1.41976e9i	−0.129394	−	0.398235i
$537$	−7.30288e8	+	5.30586e8i	−0.203509	+	0.147858i
$538$	−9.75689e8	+	3.00286e9i	−0.270130	+	0.831376i
$539$	−1.16508e7	+	8.46483e6i	−0.00320477	+	0.00232840i
$540$	2.16372e9	+	1.57204e9i	0.591321	+	0.429620i
$541$	1.02081e9	+	3.14172e9i	0.277174	+	0.853054i	0.988636	+	0.150329i	$0.0480334\pi$
$541$	1.02081e9	+	3.14172e9i	0.277174	+	0.853054i	−0.711462	+	0.702725i	$0.751967\pi$
$542$	3.87810e8	+	2.81760e8i	0.104622	+	0.0760120i
$543$	3.04179e9	+	2.20999e9i	0.815323	+	0.592367i
$544$	1.37410e8	+	4.22903e8i	0.0365949	+	0.112628i
$545$	−3.07919e9	−	2.23716e9i	−0.814797	−	0.591984i
$546$	1.04445e9	−	7.58839e8i	0.274609	−	0.199515i
$547$	1.35418e8	−	4.16773e8i	0.0353769	−	0.108879i	−0.931809	−	0.362950i	$-0.881770\pi$
$547$	1.35418e8	−	4.16773e8i	0.0353769	−	0.108879i	0.967186	+	0.254071i	$0.0817696\pi$
$548$	8.94768e8	−	6.50087e8i	0.232262	−	0.168748i
$549$	2.22697e8	+	6.85391e8i	0.0574396	+	0.176781i
$550$	−5.19600e7	−	1.59917e8i	−0.0133168	−	0.0409849i
$551$	7.75221e8	−	2.38589e9i	0.197422	−	0.607602i
$552$	1.53748e9			0.389066
$553$	−3.88929e9			−0.977986
$554$	1.91732e8	−	5.90091e8i	0.0479083	−	0.147447i
$555$	−5.29211e9	−	3.84494e9i	−1.31402	−	0.954694i
$556$	3.06637e8	−	2.22785e8i	0.0756594	−	0.0549697i
$557$	3.08816e9			0.757192			0.378596	−	0.925562i	$-0.376407\pi$
$557$	3.08816e9			0.757192			0.378596	+	0.925562i	$0.376407\pi$
$558$	1.01660e9	−	9.85430e8i	0.247703	−	0.240108i
$559$	−2.64288e9			−0.639935
$560$	1.12030e9	−	8.13944e8i	0.269572	−	0.195856i
$561$	1.11708e8	+	8.11607e7i	0.0267125	+	0.0194078i
$562$	2.19754e8	−	6.76332e8i	0.0522226	−	0.160725i
$563$	2.93733e9			0.693702			0.346851	−	0.937920i	$-0.387251\pi$
$563$	2.93733e9			0.693702			0.346851	+	0.937920i	$0.387251\pi$
$564$	−2.46699e9			−0.579016
$565$	1.53794e9	−	4.73331e9i	0.358733	−	1.10407i
$566$	−4.06405e8	−	1.25079e9i	−0.0942110	−	0.289952i
$567$	3.56935e8	+	1.09853e9i	0.0822335	+	0.253089i
$568$	−1.37796e9	+	1.00115e9i	−0.315513	+	0.229234i
$569$	3.05355e8	−	9.39785e8i	0.0694883	−	0.213863i	−0.910282	−	0.413989i	$-0.864135\pi$
$569$	3.05355e8	−	9.39785e8i	0.0694883	−	0.213863i	0.979770	+	0.200126i	$0.0641352\pi$
$570$	3.65862e9	−	2.65814e9i	0.827476	−	0.601196i
$571$	3.31138e9	+	2.40586e9i	0.744359	+	0.540808i	0.894073	−	0.447921i	$-0.147835\pi$
$571$	3.31138e9	+	2.40586e9i	0.744359	+	0.540808i	−0.149715	+	0.988729i	$0.547835\pi$
$572$	−3.29107e7	−	1.01289e8i	−0.00735276	−	0.0226295i
$573$	−2.43673e9	−	1.77039e9i	−0.541086	−	0.393122i
$574$	−3.66937e9	−	2.66595e9i	−0.809841	−	0.588384i
$575$	1.91680e9	+	5.89931e9i	0.420474	+	1.29409i
$576$	2.26282e8	+	1.64404e8i	0.0493369	+	0.0358453i
$577$	1.90886e9	−	1.38687e9i	0.413674	−	0.300552i	−0.361414	−	0.932406i	$-0.617706\pi$
$577$	1.90886e9	−	1.38687e9i	0.413674	−	0.300552i	0.775087	+	0.631854i	$0.217706\pi$
$578$	−5.59172e8	+	1.72095e9i	−0.120448	+	0.370699i
$579$	−4.15718e9	+	3.02037e9i	−0.890070	+	0.646673i
$580$	−4.32536e8	−	1.33121e9i	−0.0920500	−	0.283301i
$581$	1.04487e9	+	3.21578e9i	0.221027	+	0.680253i
$582$	−2.39100e8	+	7.35873e8i	−0.0502746	+	0.154729i
$583$	5.14621e8			0.107559
$584$	−6.08334e8			−0.126385
$585$	−6.92495e8	+	2.13128e9i	−0.143012	+	0.440145i
$586$	3.35357e9	+	2.43651e9i	0.688439	+	0.500180i
$587$	−3.15277e8	+	2.29062e8i	−0.0643368	+	0.0467434i	−0.619489	−	0.785005i	$-0.712660\pi$
$587$	−3.15277e8	+	2.29062e8i	−0.0643368	+	0.0467434i	0.555152	+	0.831749i	$0.312660\pi$
$588$	−1.01453e8			−0.0205800
$589$	−3.21292e9	−	6.55610e9i	−0.647884	−	1.32203i
$590$	−1.62889e9			−0.326521
$591$	2.30970e9	−	1.67810e9i	0.460257	−	0.334396i
$592$	−1.68787e9	−	1.22631e9i	−0.334359	−	0.242926i
$593$	−1.73059e9	+	5.32620e9i	−0.340802	+	1.04888i	0.622991	+	0.782229i	$0.285917\pi$
$593$	−1.73059e9	+	5.32620e9i	−0.340802	+	1.04888i	−0.963793	+	0.266652i	$0.914083\pi$
$594$	2.64878e8			0.0518554
$595$	−4.58776e9			−0.892875
$596$	−5.19090e8	+	1.59759e9i	−0.100434	+	0.309104i
$597$	−1.24123e9	−	3.82012e9i	−0.238750	−	0.734797i
$598$	1.21407e9	+	3.73653e9i	0.232161	+	0.714520i
$599$	−2.64241e7	+	1.91982e7i	−0.00502350	+	0.00364979i	−0.590294	−	0.807188i	$-0.700988\pi$
$599$	−2.64241e7	+	1.91982e7i	−0.00502350	+	0.00364979i	0.585271	+	0.810838i	$0.300988\pi$
$600$	3.66046e8	−	1.12657e9i	0.0691841	−	0.212927i
$601$	2.95832e9	−	2.14935e9i	0.555885	−	0.403874i	−0.274066	−	0.961711i	$-0.588369\pi$
$601$	2.95832e9	−	2.14935e9i	0.555885	−	0.403874i	0.829951	+	0.557837i	$0.188369\pi$
$602$	−2.75333e9	−	2.00041e9i	−0.514365	−	0.373708i
$603$	9.61336e8	+	2.95869e9i	0.178552	+	0.549527i
$604$	2.07791e9	+	1.50969e9i	0.383704	+	0.278777i
$605$	6.02112e9	+	4.37460e9i	1.10543	+	0.803145i
$606$	−3.60900e8	−	1.11074e9i	−0.0658769	−	0.202748i
$607$	−7.93945e9	−	5.76835e9i	−1.44089	−	1.04687i	−0.987856	−	0.155370i	$-0.950343\pi$
$607$	−7.93945e9	−	5.76835e9i	−1.44089	−	1.04687i	−0.453030	−	0.891495i	$-0.649657\pi$
$608$	1.16688e9	−	8.47790e8i	0.210555	−	0.152977i
$609$	5.19279e8	−	1.59818e9i	0.0931624	−	0.286724i
$610$	1.67750e9	−	1.21877e9i	0.299232	−	0.217405i
$611$	−1.94806e9	−	5.99550e9i	−0.345507	−	1.06336i
$612$	−2.86352e8	−	8.81300e8i	−0.0504975	−	0.155415i
$613$	−8.81796e8	+	2.71389e9i	−0.154617	+	0.475861i	−0.998122	−	0.0612598i	$-0.980488\pi$
$613$	−8.81796e8	+	2.71389e9i	−0.154617	+	0.475861i	0.843505	+	0.537121i	$0.180488\pi$
$614$	−5.32939e9			−0.929154
$615$	−8.26445e9			−1.43269
$616$	4.23800e7	−	1.30432e8i	0.00730514	−	0.0224829i
$617$	−4.56272e9	−	3.31501e9i	−0.782034	−	0.568181i	0.123555	−	0.992338i	$-0.460571\pi$
$617$	−4.56272e9	−	3.31501e9i	−0.782034	−	0.568181i	−0.905589	+	0.424157i	$0.860571\pi$
$618$	6.22687e8	−	4.52408e8i	0.106123	−	0.0771030i
$619$	−6.21433e9			−1.05312			−0.526559	−	0.850138i	$-0.676518\pi$
$619$	−6.21433e9			−1.05312			−0.526559	+	0.850138i	$0.676518\pi$
$620$	−3.60040e9	−	1.90567e9i	−0.606708	−	0.321128i
$621$	−9.77134e9			−1.63732
$622$	4.25179e9	−	3.08911e9i	0.708444	−	0.514715i
$623$	9.00521e8	+	6.54267e8i	0.149206	+	0.108404i
$624$	2.31848e8	−	7.13554e8i	0.0381994	−	0.117566i
$625$	−6.72532e9			−1.10188
$626$	−2.10747e9			−0.343361
$627$	1.38403e8	−	4.25960e8i	0.0224238	−	0.0690132i
$628$	3.89725e8	+	1.19945e9i	0.0627913	+	0.193252i
$629$	2.13593e9	+	6.57373e9i	0.342224	+	1.05326i
$630$	−2.33462e9	+	1.69620e9i	−0.371984	+	0.270262i
$631$	2.48078e9	−	7.63505e9i	0.393084	−	1.20979i	−0.537360	−	0.843353i	$-0.680578\pi$
$631$	2.48078e9	−	7.63505e9i	0.393084	−	1.20979i	0.930444	−	0.366435i	$-0.119422\pi$
$632$	−1.82860e9	+	1.32855e9i	−0.288143	+	0.209348i
$633$	2.61450e9	+	1.89954e9i	0.409709	+	0.297671i
$634$	−3.85722e8	−	1.18713e9i	−0.0601121	−	0.185006i
$635$	9.49075e8	+	6.89544e8i	0.147093	+	0.106869i
$636$	2.93299e9	+	2.13095e9i	0.452076	+	0.328452i
$637$	−8.01124e7	−	2.46560e8i	−0.0122804	−	0.0377951i
$638$	−1.12150e8	−	8.14819e7i	−0.0170973	−	0.0124219i
$639$	2.87157e9	−	2.08632e9i	0.435378	−	0.316321i
$640$	2.48684e8	−	7.65371e8i	0.0374988	−	0.115410i
$641$	4.49398e8	−	3.26506e8i	0.0673950	−	0.0489653i	−0.553578	−	0.832798i	$-0.686738\pi$
$641$	4.49398e8	−	3.26506e8i	0.0673950	−	0.0489653i	0.620973	+	0.783832i	$0.286738\pi$
$642$	7.07866e8	+	2.17859e9i	0.105579	+	0.324940i
$643$	−9.24194e8	−	2.84438e9i	−0.137096	−	0.421938i	0.858814	−	0.512287i	$-0.171202\pi$
$643$	−9.24194e8	−	2.84438e9i	−0.137096	−	0.421938i	−0.995910	+	0.0903493i	$0.971202\pi$
$644$	−1.56339e9	+	4.81163e9i	−0.230658	+	0.709891i
$645$	−6.20128e9			−0.909960
$646$	−4.77853e9			−0.697397
$647$	−3.93284e9	+	1.21040e10i	−0.570875	+	1.75697i	0.0789394	+	0.996879i	$0.474847\pi$
$647$	−3.93284e9	+	1.21040e10i	−0.570875	+	1.75697i	−0.649814	+	0.760093i	$0.725153\pi$
$648$	5.43069e8	+	3.94562e8i	0.0784047	+	0.0569644i
$649$	−1.30513e8	+	9.48231e7i	−0.0187412	+	0.0136163i
$650$	3.02695e9			0.432323
$651$	−2.15217e9	−	4.39158e9i	−0.305733	−	0.623860i
$652$	1.94887e8			0.0275370
$653$	−5.43311e9	+	3.94738e9i	−0.763576	+	0.554770i	−0.900005	−	0.435880i	$-0.856437\pi$
$653$	−5.43311e9	+	3.94738e9i	−0.763576	+	0.554770i	0.136429	+	0.990650i	$0.456437\pi$
$654$	−2.14835e9	−	1.56087e9i	−0.300320	−	0.218195i
$655$	4.57784e9	−	1.40892e10i	0.636526	−	1.95903i
$656$	−2.63587e9			−0.364553
$657$	1.26772e9			0.174400
$658$	2.50857e9	−	7.72058e9i	0.343269	−	1.05647i
$659$	3.22469e9	+	9.92457e9i	0.438923	+	1.35087i	0.889012	+	0.457884i	$0.151392\pi$
$659$	3.22469e9	+	9.92457e9i	0.438923	+	1.35087i	−0.450089	+	0.892984i	$0.648608\pi$
$660$	−7.72219e7	−	2.37665e8i	−0.0104553	−	0.0321781i
$661$	1.13103e10	−	8.21744e9i	1.52325	−	1.10670i	0.563400	−	0.826184i	$-0.309493\pi$
$661$	1.13103e10	−	8.21744e9i	1.52325	−	1.10670i	0.959848	−	0.280520i	$-0.0905070\pi$
$662$	3.56211e8	−	1.09631e9i	0.0477205	−	0.146869i
$663$	−2.01096e9	+	1.46105e9i	−0.267982	+	0.194700i
$664$	1.58975e9	+	1.15502e9i	0.210736	+	0.153109i
$665$	4.59852e9	+	1.41528e10i	0.606376	+	1.86623i
$666$	3.51740e9	+	2.55554e9i	0.461383	+	0.335214i
$667$	4.13721e9	+	3.00586e9i	0.539842	+	0.392218i
$668$	1.93675e9	+	5.96069e9i	0.251394	+	0.773711i
$669$	4.48915e9	+	3.26156e9i	0.579659	+	0.421147i
$670$	7.24141e9	−	5.26119e9i	0.930168	−	0.675807i
$671$	6.34585e7	−	1.95305e8i	0.00810888	−	0.0249566i
$672$	7.81632e8	−	5.67889e8i	0.0993596	−	0.0721890i
$673$	−2.30506e9	−	7.09423e9i	−0.291493	−	0.897124i	−0.984377	−	0.176075i	$-0.943660\pi$
$673$	−2.30506e9	−	7.09423e9i	−0.291493	−	0.897124i	0.692884	−	0.721050i	$-0.256340\pi$
$674$	−3.04146e9	−	9.36064e9i	−0.382624	−	1.17760i
$675$	−2.32637e9	+	7.15984e9i	−0.291150	+	0.896066i
$676$	−2.09868e9			−0.261297
$677$	2.27064e9			0.281248			0.140624	−	0.990063i	$-0.455089\pi$
$677$	2.27064e9			0.281248			0.140624	+	0.990063i	$0.455089\pi$
$678$	1.07302e9	−	3.30243e9i	0.132223	−	0.406939i
$679$	−2.05982e9	−	1.49655e9i	−0.252514	−	0.183462i
$680$	−2.15699e9	+	1.56714e9i	−0.263067	+	0.191129i
$681$	−1.40464e8			−0.0170432
$682$	−3.99412e8	+	5.69011e7i	−0.0482143	+	0.00686871i
$683$	5.26043e9			0.631755			0.315877	−	0.948800i	$-0.397701\pi$
$683$	5.26043e9			0.631755			0.315877	+	0.948800i	$0.397701\pi$
$684$	−2.43170e9	+	1.76673e9i	−0.290545	+	0.211093i
$685$	5.36496e9	+	3.89787e9i	0.637748	+	0.463351i
$686$	1.89682e9	−	5.83780e9i	0.224332	−	0.690423i
$687$	4.84990e9			0.570668
$688$	−1.97784e9			−0.231543
$689$	−2.86278e9	+	8.81072e9i	−0.333442	+	1.02623i
$690$	2.84871e9	+	8.76743e9i	0.330124	+	1.01602i
$691$	−1.92021e8	−	5.90980e8i	−0.0221399	−	0.0681396i	0.939376	−	0.342888i	$-0.111405\pi$
$691$	−1.92021e8	−	5.90980e8i	−0.0221399	−	0.0681396i	−0.961516	+	0.274749i	$0.911405\pi$
$692$	−5.24460e9	+	3.81043e9i	−0.601646	+	0.437122i
$693$	−8.83169e7	+	2.71811e8i	−0.0100804	+	0.0310243i
$694$	1.95807e9	−	1.42262e9i	0.222367	−	0.161559i
$695$	1.83857e9	+	1.33580e9i	0.207746	+	0.150937i
$696$	−3.01780e8	−	9.28784e8i	−0.0339280	−	0.104420i
$697$	7.06490e9	+	5.13295e9i	0.790298	+	0.574185i
$698$	4.20131e9	+	3.05243e9i	0.467617	+	0.339744i
$699$	−3.54770e9	−	1.09187e10i	−0.392896	−	1.20921i
$700$	3.15346e9	+	2.29112e9i	0.347491	+	0.252467i
$701$	8.79561e8	−	6.39038e8i	0.0964390	−	0.0700671i	−0.538521	−	0.842612i	$-0.681017\pi$
$701$	8.79561e8	−	6.39038e8i	0.0964390	−	0.0700671i	0.634960	+	0.772545i	$0.281017\pi$
$702$	−1.47349e9	+	4.53493e9i	−0.160756	+	0.494756i
$703$	1.81384e10	−	1.31783e10i	1.96904	−	1.43059i
$704$	−2.46292e7	−	7.58009e7i	−0.00266040	−	0.00818786i
$705$	−4.57094e9	−	1.40679e10i	−0.491296	−	1.51206i
$706$	−3.70542e9	+	1.14041e10i	−0.396297	+	1.21968i
$707$	3.84309e9			0.408990
$708$	−1.13648e9			−0.120350
$709$	−5.39780e8	+	1.66127e9i	−0.0568794	+	0.175057i	−0.975460	−	0.220177i	$-0.929336\pi$
$709$	−5.39780e8	+	1.66127e9i	−0.0568794	+	0.175057i	0.918581	+	0.395234i	$0.129336\pi$
$710$	−8.26214e9	−	6.00280e9i	−0.866340	−	0.629433i
$711$	3.81066e9	−	2.76861e9i	0.397610	−	0.288880i
$712$	6.46883e8			0.0671655
$713$	1.47343e10	−	2.09908e9i	1.52235	−	0.216878i
$714$	−3.20088e9			−0.329098
$715$	5.16616e8	−	3.75343e8i	0.0528563	−	0.0384023i
$716$	−1.39656e9	−	1.01466e9i	−0.142188	−	0.103306i
$717$	2.23439e9	−	6.87674e9i	0.226382	−	0.696731i
$718$	−1.28924e10			−1.29987
$719$	1.24067e9			0.124481			0.0622407	−	0.998061i	$-0.480175\pi$
$719$	1.24067e9			0.124481			0.0622407	+	0.998061i	$0.480175\pi$
$720$	−5.18240e8	+	1.59498e9i	−0.0517448	+	0.159254i
$721$	7.82655e8	+	2.40876e9i	0.0777672	+	0.239343i
$722$	2.57996e9	+	7.94030e9i	0.255113	+	0.785158i
$723$	8.27686e9	−	6.01349e9i	0.814482	−	0.591756i
$724$	−2.22187e9	+	6.83823e9i	−0.217588	+	0.669666i
$725$	3.18750e9	−	2.31586e9i	0.310647	−	0.225698i
$726$	4.20093e9	+	3.05216e9i	0.407444	+	0.296025i
$727$	7.67884e8	+	2.36331e9i	0.0741183	+	0.228113i	0.981252	−	0.192730i	$-0.0617343\pi$
$727$	7.67884e8	+	2.36331e9i	0.0741183	+	0.228113i	−0.907133	+	0.420843i	$0.861734\pi$
$728$	1.99735e9	+	1.45116e9i	0.191864	+	0.139398i
$729$	−7.58008e9	−	5.50725e9i	−0.724648	−	0.526488i
$730$	−1.12715e9	−	3.46900e9i	−0.107238	−	0.330045i
$731$	5.30119e9	+	3.85154e9i	0.501952	+	0.364690i
$732$	1.17039e9	−	8.50340e8i	0.110292	−	0.0801316i
$733$	−4.26588e9	+	1.31290e10i	−0.400078	+	1.23131i	0.524858	+	0.851190i	$0.324118\pi$
$733$	−4.26588e9	+	1.31290e10i	−0.400078	+	1.23131i	−0.924936	+	0.380123i	$0.875882\pi$
$734$	−1.52662e9	+	1.10916e9i	−0.142494	+	0.103528i
$735$	−1.87976e8	−	5.78532e8i	−0.0174622	−	0.0537430i
$736$	9.08570e8	+	2.79629e9i	0.0840013	+	0.258529i
$737$	2.73937e8	−	8.43092e8i	0.0252066	−	0.0775780i
$738$	5.49296e9			0.503048
$739$	−1.21235e10			−1.10503			−0.552513	−	0.833504i	$-0.686331\pi$
$739$	−1.21235e10			−1.10503			−0.552513	+	0.833504i	$0.686331\pi$
$740$	3.86562e9	−	1.18971e10i	0.350677	−	1.07927i
$741$	6.52285e9	+	4.73913e9i	0.588944	+	0.427893i
$742$	−9.65133e9	+	7.01210e9i	−0.867308	+	0.630136i
$743$	−1.45022e10			−1.29710			−0.648549	−	0.761173i	$-0.724624\pi$
$743$	−1.45022e10			−1.29710			−0.648549	+	0.761173i	$0.724624\pi$
$744$	−2.51200e9	−	1.32959e9i	−0.223622	−	0.118362i
$745$	−1.00720e10			−0.892419
$746$	−7.72681e9	+	5.61386e9i	−0.681419	+	0.495080i
$747$	−3.31292e9	−	2.40698e9i	−0.290796	−	0.211276i
$748$	−8.15972e7	+	2.51130e8i	−0.00712885	+	0.0219403i
$749$	−7.53780e9			−0.655478
$750$	−9.24111e8			−0.0799852
$751$	6.13930e9	−	1.88948e10i	0.528907	−	1.62781i	−0.227552	−	0.973766i	$-0.573072\pi$
$751$	6.13930e9	−	1.88948e10i	0.528907	−	1.62781i	0.756459	−	0.654041i	$-0.226928\pi$
$752$	−1.45786e9	−	4.48683e9i	−0.125012	−	0.384749i
$753$	2.78732e9	+	8.57849e9i	0.237906	+	0.732198i
$754$	2.01891e9	−	1.46683e9i	0.171521	−	0.124617i
$755$	−4.75890e9	+	1.46464e10i	−0.402431	+	1.23856i
$756$	−4.96759e9	+	3.60917e9i	−0.418138	+	0.303795i
$757$	1.52890e10	+	1.11081e10i	1.28098	+	0.930688i	0.999582	−	0.0289032i	$-0.00920147\pi$
$757$	1.52890e10	+	1.11081e10i	1.28098	+	0.930688i	0.281399	+	0.959591i	$0.409201\pi$
$758$	2.76720e9	+	8.51656e9i	0.230780	+	0.710268i
$759$	7.38629e8	+	5.36645e8i	0.0613169	+	0.0445493i
$760$	6.99653e9	+	5.08328e9i	0.578143	+	0.420045i
$761$	−1.08259e9	−	3.33186e9i	−0.0890465	−	0.274057i	0.896610	−	0.442821i	$-0.146022\pi$
$761$	−1.08259e9	−	3.33186e9i	−0.0890465	−	0.274057i	−0.985656	+	0.168764i	$0.946022\pi$
$762$	6.62170e8	+	4.81095e8i	0.0542160	+	0.0393902i
$763$	7.06939e9	−	5.13621e9i	0.576164	−	0.418607i
$764$	1.77991e9	−	5.47799e9i	0.144401	−	0.444421i
$765$	4.49501e9	−	3.26582e9i	0.363007	−	0.263740i
$766$	−9.72296e8	−	2.99242e9i	−0.0781624	−	0.240559i
$767$	−8.97420e8	−	2.76197e9i	−0.0718144	−	0.221022i
$768$	1.73507e8	−	5.33999e8i	0.0138214	−	0.0425379i
$769$	1.03191e10			0.818274			0.409137	−	0.912473i	$-0.365830\pi$
$769$	1.03191e10			0.818274			0.409137	+	0.912473i	$0.365830\pi$
$770$	8.22307e8			0.0649107
$771$	−4.19683e9	+	1.29165e10i	−0.329785	+	1.01497i
$772$	−7.94995e9	−	5.77598e9i	−0.621876	−	0.451819i
$773$	9.36821e9	−	6.80641e9i	0.729505	−	0.530017i	−0.159902	−	0.987133i	$-0.551118\pi$
$773$	9.36821e9	−	6.80641e9i	0.729505	−	0.530017i	0.889407	+	0.457116i	$0.151118\pi$
$774$	4.12168e9			0.319507
$775$	1.96988e9	−	1.12961e10i	0.152014	−	0.871713i
$776$	−1.47966e9			−0.113670
$777$	1.21499e10	−	8.82743e9i	0.929180	−	0.675088i
$778$	−1.02656e9	−	7.45842e8i	−0.0781551	−	0.0567830i
$779$	8.75317e9	−	2.69395e10i	0.663414	−	2.04178i
$780$	4.49859e9			0.339426
$781$	−1.01143e9			−0.0759730
$782$	3.01011e9	−	9.26417e9i	0.225091	−	0.692760i
$783$	1.91794e9	+	5.90281e9i	0.142780	+	0.439433i
$784$	−5.99533e7	−	1.84517e8i	−0.00444332	−	0.0136751i
$785$	−6.11772e9	+	4.44478e9i	−0.451383	+	0.327949i
$786$	3.19396e9	−	9.83001e9i	0.234612	−	0.722063i
$787$	−8.56932e9	+	6.22598e9i	−0.626664	+	0.455298i	−0.855243	−	0.518227i	$-0.826592\pi$
$787$	−8.56932e9	+	6.22598e9i	−0.626664	+	0.455298i	0.228579	+	0.973525i	$0.426592\pi$
$788$	4.41694e9	+	3.20910e9i	0.321573	+	0.233637i
$789$	2.80094e9	+	8.62040e9i	0.203018	+	0.624825i
$790$	−1.09641e10	−	7.96589e9i	−0.791186	−	0.574830i
$791$	9.24402e9	+	6.71617e9i	0.664115	+	0.482508i
$792$	5.13255e7	+	1.57964e8i	0.00367109	+	0.0112985i
$793$	2.99077e9	+	2.17292e9i	0.212974	+	0.154735i
$794$	−4.33199e9	+	3.14737e9i	−0.307125	+	0.223139i
$795$	−6.71725e9	+	2.06736e10i	−0.474140	+	1.45925i
$796$	6.21433e9	−	4.51497e9i	0.436715	−	0.317292i
$797$	−6.19473e9	−	1.90654e10i	−0.433429	−	1.33396i	−0.894688	−	0.446692i	$-0.852602\pi$
$797$	−6.19473e9	−	1.90654e10i	−0.433429	−	1.33396i	0.461258	−	0.887266i	$-0.347398\pi$
$798$	3.20839e9	+	9.87440e9i	0.223499	+	0.687861i
$799$	−4.82992e9	+	1.48650e10i	−0.334986	+	1.03098i
$800$	2.26526e9			0.156424
$801$	−1.34806e9			−0.0926820
$802$	−8.54440e8	+	2.62970e9i	−0.0584886	+	0.180009i
$803$	−2.92252e8	−	2.12334e8i	−0.0199184	−	0.0144715i
$804$	5.05234e9	−	3.67074e9i	0.342844	−	0.249090i
$805$	−3.03348e10			−2.04954
$806$	1.24769e9	−	7.15479e9i	0.0839334	−	0.481309i
$807$	−1.32085e10			−0.884701
$808$	1.80687e9	−	1.31277e9i	0.120500	−	0.0875486i
$809$	−1.98390e10	−	1.44139e10i	−1.31735	−	0.957108i	−0.999961	−	0.00881061i	$-0.997195\pi$
$809$	−1.98390e10	−	1.44139e10i	−1.31735	−	0.957108i	−0.317384	−	0.948297i	$-0.602805\pi$
$810$	−1.24376e9	+	3.82789e9i	−0.0822313	+	0.253082i
$811$	9.69920e9			0.638503			0.319251	−	0.947670i	$-0.396569\pi$
$811$	9.69920e9			0.638503			0.319251	+	0.947670i	$0.396569\pi$
$812$	3.21354e9			0.210639
$813$	−6.19680e8	+	1.90718e9i	−0.0404437	+	0.124473i
$814$	−3.82844e8	−	1.17827e9i	−0.0248792	−	0.0765702i
$815$	3.61095e8	+	1.11133e9i	0.0233652	+	0.0719107i
$816$	−1.50493e9	+	1.09340e9i	−0.0969619	+	0.0704469i
$817$	6.56800e9	−	2.02142e10i	0.421362	−	1.29682i
$818$	1.29050e10	−	9.37607e9i	0.824372	−	0.598941i
$819$	−4.16233e9	−	3.02411e9i	−0.264754	−	0.192355i
$820$	−4.88384e9	−	1.50309e10i	−0.309324	−	0.952000i
$821$	−1.45043e10	−	1.05380e10i	−0.914733	−	0.664592i	0.0274745	−	0.999623i	$-0.491253\pi$
$821$	−1.45043e10	−	1.05380e10i	−0.914733	−	0.664592i	−0.942207	+	0.335030i	$0.891253\pi$
$822$	3.74313e9	+	2.71954e9i	0.235063	+	0.170783i
$823$	7.49052e9	+	2.30535e10i	0.468396	+	1.44157i	0.854661	+	0.519186i	$0.173765\pi$
$823$	7.49052e9	+	2.30535e10i	0.468396	+	1.44157i	−0.386266	+	0.922388i	$0.626235\pi$
$824$	1.19079e9	+	8.65159e8i	0.0741464	+	0.0538705i
$825$	5.69075e8	−	4.13457e8i	0.0352842	−	0.0256355i
$826$	1.15563e9	−	3.55667e9i	0.0713493	−	0.219590i
$827$	−1.74675e10	+	1.26909e10i	−1.07389	+	0.780229i	−0.976608	−	0.215028i	$-0.931016\pi$
$827$	−1.74675e10	+	1.26909e10i	−1.07389	+	0.780229i	−0.0972851	+	0.995257i	$0.531016\pi$
$828$	−1.89339e9	−	5.82727e9i	−0.115914	−	0.356746i
$829$	1.42519e9	+	4.38629e9i	0.0868825	+	0.267397i	0.985053	−	0.172250i	$-0.0551037\pi$
$829$	1.42519e9	+	4.38629e9i	0.0868825	+	0.267397i	−0.898171	+	0.439647i	$0.855104\pi$
$830$	−3.64089e9	+	1.12055e10i	−0.221022	+	0.680235i
$831$	2.59560e9			0.156904
$832$	1.43478e9			0.0863683
$833$	−1.98627e8	+	6.11311e8i	−0.0119064	+	0.0366441i
$834$	1.28277e9	+	9.31987e8i	0.0765716	+	0.0556325i
$835$	−3.04021e10	+	2.20884e10i	−1.80718	+	1.31299i
$836$	8.56501e8			0.0506997
$837$	1.59648e10	+	8.45009e9i	0.941074	+	0.498107i
$838$	1.63196e10			0.957979
$839$	7.46020e9	−	5.42015e9i	0.436097	−	0.316843i	−0.347985	−	0.937500i	$-0.613134\pi$
$839$	7.46020e9	−	5.42015e9i	0.436097	−	0.316843i	0.784082	+	0.620657i	$0.213134\pi$
$840$	4.68660e9	+	3.40501e9i	0.272823	+	0.198217i
$841$	−4.32674e9	+	1.33163e10i	−0.250828	+	0.771968i
$842$	−1.18017e10			−0.681323
$843$	2.97494e9			0.171034
$844$	−1.90976e9	+	5.87763e9i	−0.109340	+	0.336515i
$845$	−3.88853e9	−	1.19677e10i	−0.221711	−	0.682355i
$846$	3.03807e9	+	9.35023e9i	0.172505	+	0.530916i
$847$	−1.38236e10	+	1.00434e10i	−0.781681	+	0.567925i
$848$	−2.14240e9	+	6.59364e9i	−0.120647	+	0.371313i
$849$	4.45101e9	−	3.23385e9i	0.249621	−	0.181361i
$850$	−6.07157e9	−	4.41125e9i	−0.339105	−	0.246374i
$851$	1.41231e10	+	4.34663e10i	0.785553	+	2.41768i
$852$	−5.76450e9	−	4.18815e9i	−0.319318	−	0.231998i
$853$	−2.00597e10	−	1.45742e10i	−1.10663	−	0.804013i	−0.124499	−	0.992220i	$-0.539732\pi$
$853$	−2.00597e10	−	1.45742e10i	−1.10663	−	0.804013i	−0.982129	+	0.188207i	$0.939732\pi$
$854$	1.47106e9	+	4.52747e9i	0.0808219	+	0.248744i
$855$	−1.45803e10	−	1.05932e10i	−0.797782	−	0.579622i
$856$	−3.54399e9	+	2.57486e9i	−0.193123	+	0.140312i
$857$	1.50182e9	−	4.62211e9i	0.0815049	−	0.250846i	−0.901998	−	0.431741i	$-0.857899\pi$
$857$	1.50182e9	−	4.62211e9i	0.0815049	−	0.250846i	0.983502	+	0.180895i	$0.0578994\pi$
$858$	3.60443e8	−	2.61877e8i	0.0194819	−	0.0141544i
$859$	8.01316e8	+	2.46620e9i	0.0431348	+	0.132755i	0.970305	−	0.241886i	$-0.0777660\pi$
$859$	8.01316e8	+	2.46620e9i	0.0431348	+	0.132755i	−0.927170	+	0.374641i	$0.877766\pi$
$860$	−3.66462e9	−	1.12785e10i	−0.196465	−	0.604656i
$861$	5.86328e9	−	1.80453e10i	0.313062	−	0.963505i
$862$	1.44536e10			0.768602
$863$	−5.52986e9			−0.292871			−0.146436	−	0.989220i	$-0.546780\pi$
$863$	−5.52986e9			−0.292871			−0.146436	+	0.989220i	$0.546780\pi$
$864$	−1.10271e9	+	3.39379e9i	−0.0581651	+	0.179014i
$865$	−3.14462e10	−	2.28470e10i	−1.65201	−	1.20025i
$866$	−1.84076e10	+	1.33739e10i	−0.963128	+	0.699753i
$867$	−7.56986e9			−0.394476
$868$	6.71535e9	−	6.50943e9i	0.348538	−	0.337850i
$869$	−1.34220e9			−0.0693824
$870$	4.73720e9	−	3.44178e9i	0.243896	−	0.177201i
$871$	1.29105e10	+	9.38004e9i	0.662034	+	0.480996i
$872$	1.56926e9	−	4.82970e9i	0.0801472	−	0.246668i
$873$	3.08351e9			0.156854
$874$	−3.15962e10			−1.60083
$875$	9.39685e8	−	2.89205e9i	0.0474192	−	0.145941i
$876$	−7.86410e8	−	2.42032e9i	−0.0395261	−	0.121649i
$877$	8.79743e8	+	2.70757e9i	0.0440410	+	0.135544i	0.970659	−	0.240459i	$-0.0772980\pi$
$877$	8.79743e8	+	2.70757e9i	0.0440410	+	0.135544i	−0.926618	+	0.376004i	$0.877298\pi$
$878$	2.09562e10	−	1.52256e10i	1.04492	−	0.759176i
$879$	−5.35866e9	+	1.64923e10i	−0.266131	+	0.819066i
$880$	3.86617e8	−	2.80894e8i	0.0191246	−	0.0138948i
$881$	1.99232e9	+	1.44750e9i	0.0981620	+	0.0713188i	0.635784	−	0.771867i	$-0.280677\pi$
$881$	1.99232e9	+	1.44750e9i	0.0981620	+	0.0713188i	−0.537622	+	0.843186i	$0.680677\pi$
$882$	1.24939e8	+	3.84521e8i	0.00613135	+	0.0188704i
$883$	−5.96834e9	−	4.33625e9i	−0.291736	−	0.211959i	0.432284	−	0.901738i	$-0.357708\pi$
$883$	−5.96834e9	−	4.33625e9i	−0.291736	−	0.211959i	−0.724020	+	0.689779i	$0.757708\pi$
$884$	−3.84564e9	−	2.79402e9i	−0.187234	−	0.136034i
$885$	−2.10571e9	−	6.48072e9i	−0.102117	−	0.314284i
$886$	1.84206e10	+	1.33834e10i	0.889789	+	0.646469i
$887$	4.65029e9	−	3.37863e9i	0.223742	−	0.162558i	−0.470268	−	0.882524i	$-0.655843\pi$
$887$	4.65029e9	−	3.37863e9i	0.223742	−	0.162558i	0.694009	+	0.719966i	$0.255843\pi$
$888$	2.69704e9	−	8.30064e9i	0.129253	−	0.397801i
$889$	−2.17894e9	+	1.58309e9i	−0.104013	+	0.0755701i
$890$	1.19857e9	+	3.68882e9i	0.0569900	+	0.175397i
$891$	1.23179e8	+	3.79107e8i	0.00583399	+	0.0179552i
$892$	−3.27909e9	+	1.00920e10i	−0.154695	+	0.476103i
$893$	5.06982e10			2.38239
$894$	−7.02724e9			−0.328930
$895$	3.19845e9	−	9.84383e9i	0.149128	−	0.458969i
$896$	1.49475e9	+	1.08600e9i	0.0694208	+	0.0504372i
$897$	−1.32967e10	+	9.66062e9i	−0.615135	+	0.446922i
$898$	2.75762e10			1.27077
$899$	−4.16011e9	−	8.48887e9i	−0.190962	−	0.389665i
$900$	−4.72065e9			−0.215850
$901$	1.85824e10	−	1.35009e10i	0.846378	−	0.614930i
$902$	−1.26631e9	−	9.20027e8i	−0.0574535	−	0.0417424i
$903$	4.39955e9	−	1.35404e10i	0.198839	−	0.611963i
$904$	6.64038e9			0.298953
$905$	−4.31115e10			−1.93340
$906$	−3.32028e9	+	1.02188e10i	−0.148329	+	0.456510i
$907$	−2.42394e9	−	7.46012e9i	−0.107869	−	0.331987i	0.882524	−	0.470267i	$-0.155842\pi$
$907$	−2.42394e9	−	7.46012e9i	−0.107869	−	0.331987i	−0.990393	+	0.138281i	$0.955842\pi$
$908$	−8.30069e7	−	2.55469e8i	−0.00367971	−	0.0113250i
$909$	−3.76540e9	+	2.73572e9i	−0.166279	+	0.120809i
$910$	−4.57440e9	+	1.40786e10i	−0.201228	+	0.619317i
$911$	1.12891e10	−	8.20204e9i	0.494705	−	0.359424i	−0.312286	−	0.949988i	$-0.601095\pi$
$911$	1.12891e10	−	8.20204e9i	0.494705	−	0.359424i	0.806991	+	0.590564i	$0.201095\pi$
$912$	4.88148e9	+	3.54660e9i	0.213093	+	0.154821i
$913$	3.60588e8	+	1.10977e9i	0.0156806	+	0.0482600i
$914$	−2.12017e10	−	1.54039e10i	−0.918456	−	0.667297i
$915$	7.01757e9	+	5.09857e9i	0.302840	+	0.220026i
$916$	2.86603e9	+	8.82072e9i	0.123210	+	0.379202i
$917$	2.75157e10	+	1.99913e10i	1.17839	+	0.856149i
$918$	9.56446e9	−	6.94899e9i	0.408048	−	0.296464i
$919$	−7.70764e9	+	2.37217e10i	−0.327580	+	1.00819i	0.642683	+	0.766132i	$0.277821\pi$
$919$	−7.70764e9	+	2.37217e10i	−0.327580	+	1.00819i	−0.970263	+	0.242055i	$0.922179\pi$
$920$	−1.42623e10	+	1.03622e10i	−0.603854	+	0.438725i
$921$	−6.88944e9	−	2.12035e10i	−0.290586	−	0.894333i
$922$	−7.93762e9	−	2.44295e10i	−0.333528	−	1.02649i
$923$	5.62649e9	−	1.73166e10i	0.235522	−	0.724863i
$924$	5.73724e8			0.0239250
$925$	3.52119e10			1.46283
$926$	7.18147e9	−	2.21023e10i	0.297218	−	0.914742i
$927$	−2.48152e9	−	1.80293e9i	−0.102315	−	0.0743361i
$928$	1.51089e9	−	1.09772e9i	0.0620603	−	0.0450894i
$929$	−3.96930e10			−1.62427			−0.812135	−	0.583469i	$-0.801695\pi$
$929$	−3.96930e10			−1.62427			−0.812135	+	0.583469i	$0.801695\pi$
$930$	2.92760e9	−	1.67881e10i	0.119350	−	0.684401i
$931$	2.08493e9			0.0846772
$932$	1.77618e10	−	1.29047e10i	0.718674	−	0.522148i
$933$	1.77867e10	+	1.29228e10i	0.716986	+	0.520921i
$934$	−5.92727e9	+	1.82423e10i	−0.238035	+	0.732596i
$935$	−1.58325e9			−0.0633443
$936$	−2.98998e9			−0.119180
$937$	−5.65510e9	+	1.74046e10i	−0.224570	+	0.691155i	0.773765	+	0.633473i	$0.218371\pi$
$937$	−5.65510e9	+	1.74046e10i	−0.224570	+	0.691155i	−0.998335	+	0.0576824i	$0.981629\pi$
$938$	6.35028e9	+	1.95441e10i	0.251237	+	0.773226i
$939$	−2.72438e9	−	8.38479e9i	−0.107384	−	0.330493i
$940$	2.28848e10	−	1.66267e10i	0.898667	−	0.652920i
$941$	−9.61055e9	+	2.95782e10i	−0.375997	+	1.15720i	0.566806	+	0.823851i	$0.308179\pi$
$941$	−9.61055e9	+	2.95782e10i	−0.375997	+	1.15720i	−0.942804	+	0.333349i	$0.891821\pi$
$942$	−4.26833e9	+	3.10113e9i	−0.166372	+	0.120876i
$943$	4.67140e10	+	3.39397e10i	1.81408	+	1.31801i
$944$	−6.71598e8	−	2.06697e9i	−0.0259841	−	0.0799708i
$945$	−2.97853e10	−	2.16403e10i	−1.14813	−	0.834164i
$946$	−9.50183e8	−	6.90348e8i	−0.0364912	−	0.0265124i
$947$	−7.71408e9	−	2.37415e10i	−0.295161	−	0.908413i	−0.983167	−	0.182708i	$-0.941514\pi$
$947$	−7.71408e9	−	2.37415e10i	−0.295161	−	0.908413i	0.688006	−	0.725705i	$-0.258486\pi$
$948$	−7.64966e9	−	5.55781e9i	−0.291617	−	0.211872i
$949$	5.26109e9	−	3.82240e9i	0.199822	−	0.145179i
$950$	−7.52247e9	+	2.31518e10i	−0.284661	+	0.876097i
$951$	4.22449e9	−	3.06927e9i	0.159273	−	0.115719i
$952$	−1.89155e9	−	5.82158e9i	−0.0710539	−	0.218681i
$953$	−5.26515e9	−	1.62045e10i	−0.197054	−	0.606470i	−0.999946	−	0.0103461i	$-0.996707\pi$
$953$	−5.26515e9	−	1.62045e10i	−0.197054	−	0.606470i	0.802892	−	0.596124i	$-0.203293\pi$
$954$	4.46462e9	−	1.37407e10i	0.166481	−	0.512376i
$955$	3.45359e10			1.28310
$956$	1.38274e10			0.511845
$957$	1.79205e8	−	5.51535e8i	0.00660933	−	0.0203414i
$958$	9.54434e9	+	6.93437e9i	0.350725	+	0.254817i
$959$	−1.23172e10	+	8.94895e9i	−0.450968	+	0.327647i
$960$	3.36659e9			0.122812
$961$	−2.58887e10	−	9.31241e9i	−0.940974	−	0.338478i
$962$	2.23027e10			0.807689
$963$	7.38542e9	−	5.36582e9i	0.266491	−	0.193617i
$964$	1.58282e10	+	1.14998e10i	0.569064	+	0.413449i
$965$	1.82073e10	−	5.60362e10i	0.652227	−	2.00735i
$966$	−2.11646e10			−0.755424
$967$	1.27735e10			0.454272			0.227136	−	0.973863i	$-0.427064\pi$
$967$	1.27735e10			0.454272			0.227136	+	0.973863i	$0.427064\pi$
$968$	−3.06857e9	+	9.44409e9i	−0.108736	+	0.334654i
$969$	−6.17733e9	−	1.90119e10i	−0.218106	−	0.671261i
$970$	−2.74158e9	−	8.43770e9i	−0.0964493	−	0.296840i
$971$	−2.85282e10	+	2.07269e10i	−1.00002	+	0.726554i	−0.962091	−	0.272727i	$-0.912074\pi$
$971$	−2.85282e10	+	2.07269e10i	−1.00002	+	0.726554i	−0.0379239	+	0.999281i	$0.512074\pi$
$972$	3.84243e9	−	1.18258e10i	0.134207	−	0.413046i
$973$	−4.22109e9	+	3.06680e9i	−0.146903	+	0.106731i
$974$	1.40081e10	+	1.01775e10i	0.485763	+	0.352927i
$975$	3.91302e9	+	1.20430e10i	0.135206	+	0.416121i
$976$	2.23819e9	+	1.62614e9i	0.0770588	+	0.0559865i
$977$	−2.16341e10	−	1.57181e10i	−0.742178	−	0.539224i	0.151215	−	0.988501i	$-0.451682\pi$
$977$	−2.16341e10	−	1.57181e10i	−0.742178	−	0.539224i	−0.893392	+	0.449277i	$0.851682\pi$
$978$	2.51936e8	+	7.75379e8i	0.00861200	+	0.0265050i
$979$	3.10772e8	+	2.25789e8i	0.0105853	+	0.00769066i
$980$	9.41118e8	−	6.83762e8i	0.0319413	−	0.0232067i
$981$	−3.27024e9	+	1.00647e10i	−0.110596	+	0.340378i
$982$	−1.72961e10	+	1.25664e10i	−0.582852	+	0.423467i
$983$	1.48200e10	+	4.56111e10i	0.497634	+	1.53156i	0.812812	+	0.582526i	$0.197936\pi$
$983$	1.48200e10	+	4.56111e10i	0.497634	+	1.53156i	−0.315178	+	0.949032i	$0.602064\pi$
$984$	−3.40746e9	−	1.04871e10i	−0.114011	−	0.350891i
$985$	−1.01158e10	+	3.11334e10i	−0.337268	+	1.03800i
$986$	−6.18726e9			−0.205556
$987$	3.39600e10			1.12424
$988$	−4.76462e9	+	1.46640e10i	−0.157173	+	0.483729i
$989$	3.50522e10	+	2.54669e10i	1.15220	+	0.837122i
$990$	−8.05683e8	+	5.85363e8i	−0.0263901	+	0.0191735i
$991$	2.93290e10			0.957282			0.478641	−	0.878011i	$-0.341130\pi$
$991$	2.93290e10			0.957282			0.478641	+	0.878011i	$0.341130\pi$
$992$	9.33730e8	−	5.35440e9i	0.0303690	−	0.174149i
$993$	4.82225e9			0.156289
$994$	1.89687e10	−	1.37816e10i	0.612611	−	0.445088i
$995$	3.72606e10	+	2.70714e10i	1.19914	+	0.871225i
$996$	−2.54025e9	+	7.81809e9i	−0.0814647	+	0.250722i
$997$	−2.35448e10			−0.752422			−0.376211	−	0.926534i	$-0.622773\pi$
$997$	−2.35448e10			−0.752422			−0.376211	+	0.926534i	$0.622773\pi$
$998$	3.47564e10			1.10682
$999$	−1.71408e10	+	5.27540e10i	−0.543942	+	1.67408i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.8.d.a.47.4	yes	40
31.2	even	5	inner	62.8.d.a.33.4	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.8.d.a.33.4	✓	40	31.2	even	5	inner
62.8.d.a.47.4	yes	40	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	62.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.47214 + 4.70228i) q^{2} +(-27.0752 - 19.6713i) q^{3} +(19.7771 - 60.8676i) q^{4} +383.739 q^{5} +267.735 q^{6} +(-272.247 + 837.889i) q^{7} +(158.217 + 486.941i) q^{8} +(-329.712 - 1014.75i) q^{9} +(-2483.61 + 1804.45i) q^{10} +(-93.9530 + 289.158i) q^{11} +(-1732.81 + 1258.96i) q^{12} +(-4427.96 - 3217.10i) q^{13} +(-2177.97 - 6703.11i) q^{14} +(-10389.8 - 7548.64i) q^{15} +(-3313.73 - 2407.57i) q^{16} +(4193.41 + 12906.0i) q^{17} +(6905.59 + 5017.20i) q^{18} +(35610.4 - 25872.5i) q^{19} +(7589.23 - 23357.3i) q^{20} +(23853.5 - 17330.6i) q^{21} +(-751.624 - 2313.26i) q^{22} +(27727.3 + 85336.0i) q^{23} +(5295.01 - 16296.4i) q^{24} +69130.4 q^{25} +43786.1 q^{26} +(-33652.0 + 103570. i) q^{27} +(45616.1 + 33142.0i) q^{28} +(46108.6 - 33499.8i) q^{29} +102740. q^{30} +(28495.2 - 163403. i) q^{31} +32768.0 q^{32} +(8231.91 - 5980.83i) q^{33} +(-87827.8 - 63810.6i) q^{34} +(-104472. + 321530. i) q^{35} -68286.2 q^{36} +509355. q^{37} +(-108816. + 334900. i) q^{38} +(56603.5 + 174208. i) q^{39} +(60713.9 + 186858. i) q^{40} +(520621. - 378253. i) q^{41} +(-72889.9 + 224332. i) q^{42} +(390651. - 283824. i) q^{43} +(15742.2 + 11437.4i) q^{44} +(-126523. - 389399. i) q^{45} +(-580729. - 421924. i) q^{46} +(931817. + 677005. i) q^{47} +(42360.1 + 130371. i) q^{48} +(38320.3 + 27841.3i) q^{49} +(-447421. + 325070. i) q^{50} +(140340. - 431922. i) q^{51} +(-283389. + 205894. i) q^{52} +(-523048. - 1.60978e6i) q^{53} +(-269216. - 828561. i) q^{54} +(-36053.4 + 110961. i) q^{55} -451077. q^{56} -1.47311e6 q^{57} +(-140895. + 433631. i) q^{58} +(429264. + 311879. i) q^{59} +(-664948. + 483113. i) q^{60} -675428. q^{61} +(583944. + 1.19156e6i) q^{62} +940011. q^{63} +(-212079. + 154084. i) q^{64} +(-1.69918e6 - 1.23453e6i) q^{65} +(-25154.5 + 77417.5i) q^{66} -2.91568e6 q^{67} +868489. q^{68} +(927946. - 2.85592e6i) q^{69} +(-835773. - 2.57224e6i) q^{70} +(1.02800e6 + 3.16385e6i) q^{71} +(441957. - 321101. i) q^{72} +(-367159. + 1.13000e6i) q^{73} +(-3.29662e6 + 2.39513e6i) q^{74} +(-1.87172e6 - 1.35988e6i) q^{75} +(-870526. - 2.67920e6i) q^{76} +(-216704. - 157444. i) q^{77} +(-1.18552e6 - 861329. i) q^{78} +(1.36418e6 + 4.19852e6i) q^{79} +(-1.27161e6 - 923877. i) q^{80} +(1.06068e6 - 770630. i) q^{81} +(-1.59088e6 + 4.89621e6i) q^{82} +(3.10497e6 - 2.25589e6i) q^{83} +(-583119. - 1.79466e6i) q^{84} +(1.60917e6 + 4.95252e6i) q^{85} +(-1.19372e6 + 3.67390e6i) q^{86} -1.90739e6 q^{87} -155668. q^{88} +(390426. - 1.20161e6i) q^{89} +(2.64994e6 + 1.92529e6i) q^{90} +(3.90107e6 - 2.83429e6i) q^{91} +5.74256e6 q^{92} +(-3.98587e6 + 3.86364e6i) q^{93} -9.21432e6 q^{94} +(1.36651e7 - 9.92827e6i) q^{95} +(-887201. - 644589. i) q^{96} +(-893048. + 2.74852e6i) q^{97} -378932. q^{98} +324400. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 80 q^{2} + 28 q^{3} - 640 q^{4} + 168 q^{5} - 1936 q^{6} + 1402 q^{7} - 5120 q^{8} - 6164 q^{9} - 1496 q^{10} - 3402 q^{11} + 1792 q^{12} + 6413 q^{13} + 11216 q^{14} + 46465 q^{15} - 40960 q^{16}+ \cdots + 13336614 q^{99}+O(q^{100}) \) 40 * q - 80 * q^2 + 28 * q^3 - 640 * q^4 + 168 * q^5 - 1936 * q^6 + 1402 * q^7 - 5120 * q^8 - 6164 * q^9 - 1496 * q^10 - 3402 * q^11 + 1792 * q^12 + 6413 * q^13 + 11216 * q^14 + 46465 * q^15 - 40960 * q^16 + 17155 * q^17 - 98152 * q^18 + 67290 * q^19 + 6592 * q^20 + 16727 * q^21 - 27216 * q^22 + 2051 * q^23 + 47616 * q^24 + 787196 * q^25 - 214576 * q^26 + 603289 * q^27 - 62592 * q^28 + 95739 * q^29 - 369200 * q^30 + 540003 * q^31 + 1310720 * q^32 + 941656 * q^33 + 290520 * q^34 - 638364 * q^35 + 2359424 * q^36 + 843716 * q^37 - 169080 * q^38 + 827496 * q^39 + 52736 * q^40 + 175557 * q^41 + 1299656 * q^42 + 566562 * q^43 + 441152 * q^44 - 2450173 * q^45 + 484128 * q^46 - 2289258 * q^47 + 380928 * q^48 - 1290090 * q^49 - 2003912 * q^50 + 351796 * q^51 + 410432 * q^52 - 741339 * q^53 + 4826312 * q^54 - 755935 * q^55 - 434176 * q^56 - 8091472 * q^57 - 1476568 * q^58 - 8176986 * q^59 + 2973760 * q^60 - 10479540 * q^61 + 6613544 * q^62 - 10121022 * q^63 - 2621440 * q^64 + 9085330 * q^65 - 1581152 * q^66 + 7646158 * q^67 - 6844160 * q^68 - 5432460 * q^69 - 5106912 * q^70 - 24632815 * q^71 - 6281728 * q^72 - 11099311 * q^73 - 3436312 * q^74 + 11990582 * q^75 - 1352640 * q^76 + 8000688 * q^77 - 10937992 * q^78 + 10390986 * q^79 - 765952 * q^80 - 23584945 * q^81 + 2535096 * q^82 + 36507958 * q^83 + 10397248 * q^84 + 23914083 * q^85 + 5244176 * q^86 + 16619052 * q^87 - 3574784 * q^88 - 17387733 * q^89 - 2091344 * q^90 - 8973442 * q^91 - 8008576 * q^92 - 21404363 * q^93 - 137504 * q^94 - 12445576 * q^95 + 917504 * q^96 - 1428702 * q^97 + 92378560 * q^98 + 13336614 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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