LMFDB - Embedded newform 31.6.g.a.7.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [31,6,Mod(7,31)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([28])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("31.7"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	31.g (of order $15$, degree $8$, 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:	$4.97189841420$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			7.8
Character	$\chi$	$=$	31.7
Dual form			31.6.g.a.9.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.694022 + 2.13598i) q^{2} +(-29.5682 + 6.28491i) q^{3} +(21.8078 - 15.8443i) q^{4} +(21.0196 - 36.4070i) q^{5} +(-33.9454 - 58.7951i) q^{6} +(70.5928 + 31.4300i) q^{7} +(107.121 + 77.8282i) q^{8} +(612.785 - 272.829i) q^{9} +(92.3528 + 19.6302i) q^{10} +(-40.9531 - 389.643i) q^{11} +(-545.237 + 605.547i) q^{12} +(-314.512 - 349.301i) q^{13} +(-18.1408 + 172.598i) q^{14} +(-392.697 + 1208.60i) q^{15} +(174.660 - 537.548i) q^{16} +(147.399 - 1402.40i) q^{17} +(1008.04 + 1119.55i) q^{18} +(-61.5169 + 68.3214i) q^{19} +(-118.452 - 1127.00i) q^{20} +(-2284.83 - 485.657i) q^{21} +(803.847 - 357.896i) q^{22} +(3975.65 + 2888.48i) q^{23} +(-3656.52 - 1627.99i) q^{24} +(678.852 + 1175.81i) q^{25} +(527.821 - 914.213i) q^{26} +(-10461.5 + 7600.73i) q^{27} +(2037.46 - 433.075i) q^{28} +(-1069.29 - 3290.94i) q^{29} -2854.08 q^{30} +(-4542.94 - 2826.80i) q^{31} +5506.51 q^{32} +(3659.78 + 11263.6i) q^{33} +(3097.81 - 658.459i) q^{34} +(2628.11 - 1909.43i) q^{35} +(9040.70 - 15658.9i) q^{36} +(-2045.21 - 3542.40i) q^{37} +(-188.627 - 83.9822i) q^{38} +(11494.9 + 8351.50i) q^{39} +(5085.14 - 2264.05i) q^{40} +(4941.71 + 1050.39i) q^{41} +(-548.373 - 5217.42i) q^{42} +(-4231.26 + 4699.29i) q^{43} +(-7066.71 - 7848.38i) q^{44} +(2947.59 - 28044.4i) q^{45} +(-3410.54 + 10496.6i) q^{46} +(814.409 - 2506.49i) q^{47} +(-1785.93 + 16992.0i) q^{48} +(-7250.57 - 8052.58i) q^{49} +(-2040.36 + 2266.05i) q^{50} +(4455.67 + 42392.9i) q^{51} +(-12393.2 - 2634.26i) q^{52} +(602.912 - 268.434i) q^{53} +(-23495.5 - 17070.5i) q^{54} +(-15046.6 - 6699.16i) q^{55} +(5115.86 + 8860.93i) q^{56} +(1389.55 - 2406.77i) q^{57} +(6287.27 - 4567.97i) q^{58} +(13972.7 - 2969.99i) q^{59} +(10585.5 + 32578.8i) q^{60} +24009.8 q^{61} +(2885.09 - 11665.5i) q^{62} +51833.2 q^{63} +(-1767.48 - 5439.75i) q^{64} +(-19327.9 + 4108.28i) q^{65} +(-21518.9 + 15634.4i) q^{66} +(-28532.5 + 49419.7i) q^{67} +(-19005.7 - 32918.8i) q^{68} +(-135706. - 60420.4i) q^{69} +(5902.47 + 4288.39i) q^{70} +(-10736.3 + 4780.12i) q^{71} +(86876.1 + 18466.1i) q^{72} +(5672.03 + 53965.7i) q^{73} +(6147.09 - 6827.03i) q^{74} +(-27462.2 - 30499.9i) q^{75} +(-259.043 + 2464.63i) q^{76} +(9355.46 - 28793.1i) q^{77} +(-9860.96 + 30348.9i) q^{78} +(-6499.26 + 61836.3i) q^{79} +(-15899.2 - 17657.9i) q^{80} +(152490. - 169358. i) q^{81} +(1186.04 + 11284.4i) q^{82} +(45840.6 + 9743.73i) q^{83} +(-57522.1 + 25610.5i) q^{84} +(-47959.1 - 34844.3i) q^{85} +(-12974.2 - 5776.47i) q^{86} +(52300.2 + 90586.7i) q^{87} +(25938.2 - 44926.4i) q^{88} +(16209.9 - 11777.2i) q^{89} +(61948.1 - 13167.5i) q^{90} +(-11223.8 - 34543.2i) q^{91} +132466. q^{92} +(152093. + 55031.4i) q^{93} +5919.04 q^{94} +(1194.32 + 3675.74i) q^{95} +(-162817. + 34607.9i) q^{96} +(-103493. + 75191.9i) q^{97} +(12168.1 - 21075.7i) q^{98} +(-131401. - 227594. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 6 q^{2} - 20 q^{3} - 346 q^{4} - 33 q^{5} + 283 q^{6} - 66 q^{7} - 271 q^{8} + 658 q^{9} + 896 q^{10} + 41 q^{11} - 1169 q^{12} + 149 q^{13} - 2 q^{14} + 4906 q^{15} - 2450 q^{16} - 3152 q^{17} - 3 q^{18}+ \cdots + 674326 q^{99}+O(q^{100}) $ 96 * q - 6 * q^2 - 20 * q^3 - 346 * q^4 - 33 * q^5 + 283 * q^6 - 66 * q^7 - 271 * q^8 + 658 * q^9 + 896 * q^10 + 41 * q^11 - 1169 * q^12 + 149 * q^13 - 2 * q^14 + 4906 * q^15 - 2450 * q^16 - 3152 * q^17 - 3 * q^18 - 5216 * q^19 + 7943 * q^20 - 14003 * q^21 - 8471 * q^22 + 13925 * q^23 + 25478 * q^24 - 18843 * q^25 + 12637 * q^26 + 3409 * q^27 - 10560 * q^28 + 6386 * q^29 - 25530 * q^30 - 39101 * q^31 + 31482 * q^32 + 17969 * q^33 - 18136 * q^34 + 5943 * q^35 - 9713 * q^36 + 40836 * q^37 + 18746 * q^38 + 55889 * q^39 + 15841 * q^40 - 46266 * q^41 + 8917 * q^42 - 137449 * q^43 + 28951 * q^44 + 69269 * q^45 - 97978 * q^46 + 5774 * q^47 - 112102 * q^48 - 146686 * q^49 + 58913 * q^50 + 149254 * q^51 + 263153 * q^52 + 62548 * q^53 + 144508 * q^54 + 13077 * q^55 - 103466 * q^56 + 68345 * q^57 - 52881 * q^58 - 149116 * q^59 + 65951 * q^60 - 204972 * q^61 - 62393 * q^62 - 80326 * q^63 - 205193 * q^64 - 296504 * q^65 - 268720 * q^66 - 105499 * q^67 + 497808 * q^68 + 448358 * q^69 + 351230 * q^70 + 93454 * q^71 + 192637 * q^72 + 74644 * q^73 - 83209 * q^74 - 323995 * q^75 - 446776 * q^76 - 249590 * q^77 - 588829 * q^78 + 396670 * q^79 - 236822 * q^80 + 616675 * q^81 + 449670 * q^82 + 518776 * q^83 + 578676 * q^84 + 463509 * q^85 - 95508 * q^86 - 360817 * q^87 + 238379 * q^88 + 239175 * q^89 - 1232679 * q^90 - 178840 * q^91 - 1350224 * q^92 - 65783 * q^93 + 580620 * q^94 - 276050 * q^95 - 1587604 * q^96 - 611799 * q^97 + 200092 * q^98 + 674326 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{14}{15}\right)$

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 $

$2$	0.694022	+	2.13598i	0.122687	+	0.377592i	0.993473	−	0.114071i	$-0.0363893\pi$
$2$	0.694022	+	2.13598i	0.122687	+	0.377592i	−0.870786	+	0.491663i	$0.836389\pi$
$3$	−29.5682	+	6.28491i	−1.89680	+	0.403177i	−0.999285	−	0.0378099i	$-0.987962\pi$
$3$	−29.5682	+	6.28491i	−1.89680	+	0.403177i	−0.897514	+	0.440987i	$0.854629\pi$
$4$	21.8078	−	15.8443i	0.681494	−	0.495134i
$5$	21.0196	−	36.4070i	0.376010	−	0.651269i	−0.614467	−	0.788942i	$-0.710629\pi$
$5$	21.0196	−	36.4070i	0.376010	−	0.651269i	0.990478	+	0.137673i	$0.0439624\pi$
$6$	−33.9454	−	58.7951i	−0.384949	−	0.666750i
$7$	70.5928	+	31.4300i	0.544522	+	0.242437i	0.660515	−	0.750813i	$-0.270338\pi$
$7$	70.5928	+	31.4300i	0.544522	+	0.242437i	−0.115992	+	0.993250i	$0.537005\pi$
$8$	107.121	+	77.8282i	0.591767	+	0.429944i
$9$	612.785	−	272.829i	2.52175	−	1.12275i
$10$	92.3528	+	19.6302i	0.292045	+	0.0620761i
$11$	−40.9531	−	389.643i	−0.102048	−	0.970923i	−0.919011	−	0.394233i	$-0.871010\pi$
$11$	−40.9531	−	389.643i	−0.102048	−	0.970923i	0.816963	−	0.576691i	$-0.195656\pi$
$12$	−545.237	+	605.547i	−1.09303	+	1.21393i
$13$	−314.512	−	349.301i	−0.516153	−	0.573246i	0.427570	−	0.903982i	$-0.359370\pi$
$13$	−314.512	−	349.301i	−0.516153	−	0.573246i	−0.943723	+	0.330736i	$0.892703\pi$
$14$	−18.1408	+	172.598i	−0.0247364	+	0.235351i
$15$	−392.697	+	1208.60i	−0.450639	+	1.38692i
$16$	174.660	−	537.548i	0.170566	−	0.524949i
$17$	147.399	−	1402.40i	0.123700	−	1.17693i	−0.739887	−	0.672731i	$-0.765121\pi$
$17$	147.399	−	1402.40i	0.123700	−	1.17693i	0.863587	−	0.504199i	$-0.168212\pi$
$18$	1008.04	+	1119.55i	0.733328	+	0.814443i
$19$	−61.5169	+	68.3214i	−0.0390940	+	0.0434183i	−0.762375	−	0.647136i	$-0.775967\pi$
$19$	−61.5169	+	68.3214i	−0.0390940	+	0.0434183i	0.723281	+	0.690554i	$0.242633\pi$
$20$	−118.452	−	1127.00i	−0.0662169	−	0.630011i
$21$	−2284.83	−	485.657i	−1.13059	−	0.240315i
$22$	803.847	−	357.896i	0.354092	−	0.157652i
$23$	3975.65	+	2888.48i	1.56707	+	1.13854i	0.929896	+	0.367824i	$0.119897\pi$
$23$	3975.65	+	2888.48i	1.56707	+	1.13854i	0.637175	+	0.770720i	$0.280103\pi$
$24$	−3656.52	−	1627.99i	−1.29581	−	0.576930i
$25$	678.852	+	1175.81i	0.217233	+	0.376258i
$26$	527.821	−	914.213i	0.153128	−	0.265225i
$27$	−10461.5	+	7600.73i	−2.76175	+	2.00653i
$28$	2037.46	−	433.075i	0.491127	−	0.104392i
$29$	−1069.29	−	3290.94i	−0.236103	−	0.726650i	−0.996973	−	0.0777458i	$-0.975228\pi$
$29$	−1069.29	−	3290.94i	−0.236103	−	0.726650i	0.760870	−	0.648904i	$-0.224772\pi$
$30$	−2854.08			−0.578978
$31$	−4542.94	−	2826.80i	−0.849050	−	0.528313i
$31$	−4542.94	−	2826.80i	−0.849050	−	0.528313i
$32$	5506.51			0.950607
$33$	3659.78	+	11263.6i	0.585019	+	1.80050i
$34$	3097.81	−	658.459i	0.459575	−	0.0976858i
$35$	2628.11	−	1909.43i	0.362637	−	0.263472i
$36$	9040.70	−	15658.9i	1.16264	−	2.01375i
$37$	−2045.21	−	3542.40i	−0.245603	−	0.425396i	0.716698	−	0.697384i	$-0.245653\pi$
$37$	−2045.21	−	3542.40i	−0.245603	−	0.425396i	−0.962301	+	0.271987i	$0.912319\pi$
$38$	−188.627	−	83.9822i	−0.0211907	−	0.00943471i
$39$	11494.9	+	8351.50i	1.21016	+	0.879231i
$40$	5085.14	−	2264.05i	0.502520	−	0.223736i
$41$	4941.71	+	1050.39i	0.459111	+	0.0975870i	0.431660	−	0.902036i	$-0.357928\pi$
$41$	4941.71	+	1050.39i	0.459111	+	0.0975870i	0.0274503	+	0.999623i	$0.491261\pi$
$42$	−548.373	−	5217.42i	−0.0479681	−	0.456386i
$43$	−4231.26	+	4699.29i	−0.348978	+	0.387580i	−0.891922	−	0.452189i	$-0.850643\pi$
$43$	−4231.26	+	4699.29i	−0.348978	+	0.387580i	0.542944	+	0.839769i	$0.317310\pi$
$44$	−7066.71	−	7848.38i	−0.550282	−	0.611151i
$45$	2947.59	−	28044.4i	0.216988	−	2.06450i
$46$	−3410.54	+	10496.6i	−0.237645	+	0.731397i
$47$	814.409	−	2506.49i	0.0537772	−	0.165509i	−0.920561	−	0.390600i	$-0.872268\pi$
$47$	814.409	−	2506.49i	0.0537772	−	0.165509i	0.974338	+	0.225090i	$0.0722677\pi$
$48$	−1785.93	+	16992.0i	−0.111883	+	1.06449i
$49$	−7250.57	−	8052.58i	−0.431402	−	0.479120i
$50$	−2040.36	+	2266.05i	−0.115420	+	0.128187i
$51$	4455.67	+	42392.9i	0.239877	+	2.28227i
$52$	−12393.2	−	2634.26i	−0.635589	−	0.135099i
$53$	602.912	−	268.434i	0.0294825	−	0.0131264i	−0.391942	−	0.919990i	$-0.628197\pi$
$53$	602.912	−	268.434i	0.0294825	−	0.0131264i	0.421425	+	0.906863i	$0.361530\pi$
$54$	−23495.5	−	17070.5i	−1.09648	−	0.796639i
$55$	−15046.6	−	6699.16i	−0.670703	−	0.298616i
$56$	5115.86	+	8860.93i	0.217996	+	0.377580i
$57$	1389.55	−	2406.77i	0.0566482	−	0.0981175i
$58$	6287.27	−	4567.97i	0.245410	−	0.178301i
$59$	13972.7	−	2969.99i	0.522576	−	0.111077i	0.0609316	−	0.998142i	$-0.480593\pi$
$59$	13972.7	−	2969.99i	0.522576	−	0.111077i	0.461645	+	0.887065i	$0.347260\pi$
$60$	10585.5	+	32578.8i	0.379606	+	1.16831i
$61$	24009.8			0.826159			0.413079	−	0.910695i	$-0.364453\pi$
$61$	24009.8			0.826159			0.413079	+	0.910695i	$0.364453\pi$
$62$	2885.09	−	11665.5i	0.0953192	−	0.385411i
$63$	51833.2			1.64534
$64$	−1767.48	−	5439.75i	−0.0539392	−	0.166008i
$65$	−19327.9	+	4108.28i	−0.567416	+	0.120608i
$66$	−21518.9	+	15634.4i	−0.608080	+	0.441796i
$67$	−28532.5	+	49419.7i	−0.776520	+	1.34497i	0.157416	+	0.987532i	$0.449684\pi$
$67$	−28532.5	+	49419.7i	−0.776520	+	1.34497i	−0.933936	+	0.357440i	$0.883650\pi$
$68$	−19005.7	−	32918.8i	−0.498438	−	0.863319i
$69$	−135706.	−	60420.4i	−3.43145	−	1.52778i
$70$	5902.47	+	4288.39i	0.143976	+	0.104604i
$71$	−10736.3	+	4780.12i	−0.252761	+	0.112536i	−0.529206	−	0.848493i	$-0.677510\pi$
$71$	−10736.3	+	4780.12i	−0.252761	+	0.112536i	0.276445	+	0.961030i	$0.410844\pi$
$72$	86876.1	+	18466.1i	1.97501	+	0.419801i
$73$	5672.03	+	53965.7i	0.124575	+	1.18525i	0.860954	+	0.508683i	$0.169868\pi$
$73$	5672.03	+	53965.7i	0.124575	+	1.18525i	−0.736379	+	0.676570i	$0.763466\pi$
$74$	6147.09	−	6827.03i	0.130494	−	0.144928i
$75$	−27462.2	−	30499.9i	−0.563745	−	0.626102i
$76$	−259.043	+	2464.63i	−0.00514444	+	0.0489461i
$77$	9355.46	−	28793.1i	0.179820	−	0.553429i
$78$	−9860.96	+	30348.9i	−0.183520	+	0.564815i
$79$	−6499.26	+	61836.3i	−0.117164	+	1.11475i	0.765074	+	0.643943i	$0.222702\pi$
$79$	−6499.26	+	61836.3i	−0.117164	+	1.11475i	−0.882238	+	0.470803i	$0.843964\pi$
$80$	−15899.2	−	17657.9i	−0.277748	−	0.308471i
$81$	152490.	−	169358.i	2.58244	−	2.86809i
$82$	1186.04	+	11284.4i	0.0194789	+	0.185329i
$83$	45840.6	+	9743.73i	0.730391	+	0.155249i	0.558073	−	0.829792i	$-0.311541\pi$
$83$	45840.6	+	9743.73i	0.730391	+	0.155249i	0.172318	+	0.985041i	$0.444874\pi$
$84$	−57522.1	+	25610.5i	−0.889481	+	0.396022i
$85$	−47959.1	−	34844.3i	−0.719986	−	0.523100i
$86$	−12974.2	−	5776.47i	−0.189162	−	0.0842203i
$87$	52300.2	+	90586.7i	0.740808	+	1.28312i
$88$	25938.2	−	44926.4i	0.357054	−	0.618436i
$89$	16209.9	−	11777.2i	0.216923	−	0.157604i	−0.474017	−	0.880515i	$-0.657197\pi$
$89$	16209.9	−	11777.2i	0.216923	−	0.157604i	0.690941	+	0.722912i	$0.257197\pi$
$90$	61948.1	−	13167.5i	0.806160	−	0.171355i
$91$	−11223.8	−	34543.2i	−0.142081	−	0.437280i
$92$	132466.			1.63168
$93$	152093.	+	55031.4i	1.82348	+	0.659786i
$94$	5919.04			0.0690926
$95$	1194.32	+	3675.74i	0.0135772	+	0.0417864i
$96$	−162817.	+	34607.9i	−1.80311	+	0.383263i
$97$	−103493.	+	75191.9i	−1.11681	+	0.811412i	−0.983723	−	0.179692i	$-0.942490\pi$
$97$	−103493.	+	75191.9i	−1.11681	+	0.811412i	−0.133090	+	0.991104i	$0.542490\pi$
$98$	12168.1	−	21075.7i	0.127984	−	0.221676i
$99$	−131401.	−	227594.i	−1.34745	−	2.33385i
$100$	33434.1	+	14885.8i	0.334341	+	0.148858i
$101$	59191.9	+	43005.4i	0.577376	+	0.419488i	0.837777	−	0.546012i	$-0.183855\pi$
$101$	59191.9	+	43005.4i	0.577376	+	0.419488i	−0.260401	+	0.965501i	$0.583855\pi$
$102$	−87458.1	+	38938.8i	−0.832337	+	0.370580i
$103$	−27698.2	−	5887.44i	−0.257252	−	0.0546806i	0.0774803	−	0.996994i	$-0.475313\pi$
$103$	−27698.2	−	5887.44i	−0.257252	−	0.0546806i	−0.334732	+	0.942313i	$0.608646\pi$
$104$	−6505.47	−	61895.4i	−0.0589787	−	0.561145i
$105$	−65707.7	+	72975.8i	−0.581625	+	0.645960i
$106$	991.803	+	1101.51i	0.00857355	+	0.00952189i
$107$	19807.9	−	188459.i	0.167255	−	1.59132i	−0.513028	−	0.858372i	$-0.671476\pi$
$107$	19807.9	−	188459.i	0.167255	−	1.59132i	0.680283	−	0.732950i	$-0.261857\pi$
$108$	−107714.	+	331510.i	−0.888615	+	2.73488i
$109$	−41988.8	+	129228.i	−0.338507	+	1.04182i	0.626462	+	0.779452i	$0.284502\pi$
$109$	−41988.8	+	129228.i	−0.338507	+	1.04182i	−0.964969	+	0.262365i	$0.915498\pi$
$110$	3866.63	−	36788.5i	0.0304685	−	0.289888i
$111$	82736.7	+	91888.5i	0.637369	+	0.707870i
$112$	29224.8	−	32457.5i	0.220144	−	0.244495i
$113$	3411.28	+	32456.2i	0.0251317	+	0.239112i	0.999875	+	0.0157855i	$0.00502488\pi$
$113$	3411.28	+	32456.2i	0.0251317	+	0.239112i	−0.974744	+	0.223326i	$0.928308\pi$
$114$	6105.18	+	1297.70i	0.0439983	+	0.00935214i
$115$	188728.	−	84026.9i	1.33073	−	0.592480i
$116$	−75461.5	−	54826.0i	−0.520692	−	0.378305i
$117$	−288027.	−	128238.i	−1.94522	−	0.866069i
$118$	16041.2	+	27784.1i	0.106055	+	0.183693i
$119$	54482.8	−	94366.9i	0.352689	−	0.610875i
$120$	−136129.	+	98903.5i	−0.862974	+	0.626987i
$121$	7387.33	−	1570.23i	0.0458695	−	0.00974986i
$122$	16663.3	+	51284.4i	0.101359	+	0.311950i
$123$	−152719.			−0.910185
$124$	−143860.	+	10333.4i	−0.840208	+	0.0603516i
$125$	188449.			1.07875
$126$	35973.4	+	110715.i	0.201862	+	0.621268i
$127$	200317.	−	42578.8i	1.10207	−	0.234252i	0.379254	−	0.925292i	$-0.376181\pi$
$127$	200317.	−	42578.8i	1.10207	−	0.234252i	0.722816	+	0.691040i	$0.242847\pi$
$128$	152948.	−	111123.i	0.825123	−	0.599487i
$129$	95576.0	−	165542.i	0.505678	−	0.875861i
$130$	−22189.2	−	38432.8i	−0.115155	−	0.199454i
$131$	−228128.	−	101569.i	−1.16145	−	0.517110i	−0.266743	−	0.963768i	$-0.585948\pi$
$131$	−228128.	−	101569.i	−1.16145	−	0.517110i	−0.894705	+	0.446657i	$0.852614\pi$
$132$	258276.	+	187648.i	1.29018	+	0.937368i
$133$	−6489.99	+	2889.53i	−0.0318137	+	0.0141644i
$134$	−125362.	−	26646.5i	−0.603119	−	0.128197i
$135$	56823.2	+	540637.i	0.268344	+	2.55312i
$136$	124936.	−	138756.i	0.579216	−	0.643285i
$137$	−4038.16	−	4484.84i	−0.0183816	−	0.0204148i	0.733884	−	0.679275i	$-0.237706\pi$
$137$	−4038.16	−	4484.84i	−0.0183816	−	0.0204148i	−0.752266	+	0.658860i	$0.771039\pi$
$138$	34873.5	−	331799.i	0.155883	−	1.48313i
$139$	−118233.	+	363884.i	−0.519041	+	1.59744i	0.256766	+	0.966474i	$0.417343\pi$
$139$	−118233.	+	363884.i	−0.519041	+	1.59744i	−0.775807	+	0.630971i	$0.782657\pi$
$140$	27059.6	−	83281.0i	0.116681	−	0.359108i
$141$	−8327.50	+	79230.9i	−0.0352750	+	0.335619i
$142$	−17661.5	−	19615.1i	−0.0735032	−	0.0816336i
$143$	−123222.	+	136852.i	−0.503905	+	0.559644i
$144$	−39629.9	−	377053.i	−0.159264	−	1.51529i
$145$	−142289.	−	30244.6i	−0.562021	−	0.119461i
$146$	−111333.	+	49568.8i	−0.432258	+	0.192454i
$147$	264996.	+	192531.i	1.01145	+	0.734864i
$148$	−100728.	−	44847.2i	−0.378005	−	0.168299i
$149$	143431.	+	248429.i	0.529269	+	0.916721i	0.999417	+	0.0341332i	$0.0108670\pi$
$149$	143431.	+	248429.i	0.529269	+	0.916721i	−0.470148	+	0.882587i	$0.655800\pi$
$150$	46087.8	−	79826.4i	0.167247	−	0.289680i
$151$	359145.	−	260934.i	1.28182	−	0.931299i	0.282216	−	0.959351i	$-0.408930\pi$
$151$	359145.	−	260934.i	1.28182	−	0.931299i	0.999606	+	0.0280521i	$0.00893043\pi$
$152$	−11907.1	+	2530.93i	−0.0418020	+	0.00888529i
$153$	−292293.	−	899586.i	−1.00946	−	3.10681i
$154$	67994.5			0.231032
$155$	−198406.	+	105977.i	−0.663325	+	0.354309i
$156$	383001.			1.26005
$157$	−44131.5	−	135823.i	−0.142889	−	0.439768i	0.853844	−	0.520528i	$-0.174265\pi$
$157$	−44131.5	−	135823.i	−0.142889	−	0.439768i	−0.996734	+	0.0807608i	$0.974265\pi$
$158$	−136592.	+	29033.5i	−0.435293	+	0.0925244i
$159$	−16139.9	+	11726.3i	−0.0506301	+	0.0367849i
$160$	115745.	−	200476.i	0.357438	−	0.619101i
$161$	189868.	+	328860.i	0.577279	+	0.999877i
$162$	467576.	+	208178.i	1.39980	+	0.623229i
$163$	−147796.	−	107380.i	−0.435705	−	0.316558i	0.348221	−	0.937413i	$-0.386786\pi$
$163$	−147796.	−	107380.i	−0.435705	−	0.316558i	−0.783926	+	0.620854i	$0.786786\pi$
$164$	124410.	−	55391.1i	0.361200	−	0.160816i
$165$	487003.	+	103516.i	1.39258	+	0.296003i
$166$	11002.0	+	104677.i	0.0309886	+	0.294837i
$167$	−393809.	+	437369.i	−1.09268	+	1.21355i	−0.117285	+	0.993098i	$0.537419\pi$
$167$	−393809.	+	437369.i	−1.09268	+	1.21355i	−0.975398	+	0.220450i	$0.929248\pi$
$168$	−206957.	−	229849.i	−0.565726	−	0.628303i
$169$	15717.4	−	149541.i	0.0423314	−	0.402757i
$170$	41142.1	−	126622.i	0.109185	−	0.336038i
$171$	−19056.5	+	58649.9i	−0.0498371	+	0.153383i
$172$	−17817.5	+	169522.i	−0.0459226	+	0.436924i
$173$	−106576.	−	118365.i	−0.270735	−	0.300682i	0.592411	−	0.805636i	$-0.298176\pi$
$173$	−106576.	−	118365.i	−0.270735	−	0.300682i	−0.863146	+	0.504954i	$0.831509\pi$
$174$	−157194.	+	174581.i	−0.393607	+	0.437144i
$175$	10966.5	+	104340.i	0.0270692	+	0.257546i
$176$	−216604.	−	46040.7i	−0.527091	−	0.112037i
$177$	−394480.	+	175634.i	−0.946438	+	0.421382i
$178$	36405.9	+	26450.4i	0.0861235	+	0.0625724i
$179$	558346.	+	248592.i	1.30248	+	0.579901i	0.936482	−	0.350715i	$-0.114061\pi$
$179$	558346.	+	248592.i	1.30248	+	0.579901i	0.365997	+	0.930616i	$0.380728\pi$
$180$	−380064.	−	658290.i	−0.874330	−	1.51438i
$181$	−6694.70	+	11595.6i	−0.0151892	+	0.0263084i	−0.873520	−	0.486788i	$-0.838168\pi$
$181$	−6694.70	+	11595.6i	−0.0151892	+	0.0263084i	0.858331	+	0.513097i	$0.171502\pi$
$182$	65994.1	−	47947.5i	0.147682	−	0.107297i
$183$	−709925.	+	150899.i	−1.56706	+	0.333088i
$184$	201072.	+	618835.i	0.437831	+	1.34751i
$185$	−171958.			−0.369397
$186$	−11990.3	+	363060.i	−0.0254124	+	0.769478i
$187$	−552473.			−1.15533
$188$	−21953.2	−	67564.8i	−0.0453004	−	0.139420i
$189$	−977398.	+	207752.i	−1.99029	+	0.423050i
$190$	−7022.42	+	5102.08i	−0.0141125	+	0.0102533i
$191$	−234807.	+	406698.i	−0.465723	+	0.806656i	−0.999234	−	0.0391373i	$-0.987539\pi$
$191$	−234807.	+	406698.i	−0.465723	+	0.806656i	0.533511	+	0.845793i	$0.320872\pi$
$192$	86449.5	+	149735.i	0.169242	+	0.293136i
$193$	−109362.	−	48690.9i	−0.211335	−	0.0940925i	0.298339	−	0.954460i	$-0.403567\pi$
$193$	−109362.	−	48690.9i	−0.211335	−	0.0940925i	−0.509674	+	0.860367i	$0.670234\pi$
$194$	−232435.	−	168874.i	−0.443401	−	0.322149i
$195$	545671.	−	242948.i	1.02765	−	0.457538i
$196$	−285706.	−	60728.8i	−0.531227	−	0.112916i
$197$	51259.7	+	487704.i	0.0941045	+	0.895345i	0.935119	+	0.354333i	$0.115292\pi$
$197$	51259.7	+	487704.i	0.0941045	+	0.895345i	−0.841015	+	0.541012i	$0.818041\pi$
$198$	394941.	−	438626.i	0.715927	−	0.795118i
$199$	−21793.5	−	24204.2i	−0.0390117	−	0.0433269i	0.723323	−	0.690510i	$-0.242614\pi$
$199$	−21793.5	−	24204.2i	−0.0390117	−	0.0433269i	−0.762335	+	0.647183i	$0.775947\pi$
$200$	−18791.3	+	178788.i	−0.0332187	+	0.316055i
$201$	533055.	−	1.64058e6i	0.930641	−	2.86422i
$202$	−50778.3	+	156279.i	−0.0875587	+	0.269478i
$203$	27949.8	−	265925.i	0.0476035	−	0.452917i
$204$	768854.	+	853899.i	1.29351	+	1.43658i
$205$	142114.	−	157834.i	0.236186	−	0.262311i
$206$	−6647.72	−	63248.8i	−0.0109145	−	0.103845i
$207$	3.22428e6	+	685341.i	5.23006	+	1.11168i
$208$	−242698.	+	108056.i	−0.388963	+	0.173178i
$209$	29140.2	+	21171.6i	0.0461453	+	0.0335265i
$210$	−201477.	−	89703.5i	−0.315267	−	0.140366i
$211$	−503541.	−	872159.i	−0.778626	−	1.34862i	−0.932734	−	0.360566i	$-0.882583\pi$
$211$	−503541.	−	872159.i	−0.778626	−	1.34862i	0.154107	−	0.988054i	$-0.450750\pi$
$212$	8895.04	−	15406.7i	0.0135928	−	0.0235434i
$213$	287411.	−	208816.i	0.434064	−	0.315366i
$214$	416292.	−	88485.6i	0.621389	−	0.132080i
$215$	82147.8	+	252825.i	0.121199	+	0.373013i
$216$	−1.71220e6			−2.49701
$217$	−231853.	−	342337.i	−0.334244	−	0.493519i
$218$	−305170.			−0.434912
$219$	−506881.	−	1.56002e6i	−0.714161	−	2.19796i
$220$	−434276.	+	92308.2i	−0.604935	+	0.128583i
$221$	−536219.	+	389586.i	−0.738519	+	0.536566i
$222$	−138851.	+	240497.i	−0.189089	+	0.327511i
$223$	117779.	+	203999.i	0.158601	+	0.274705i	0.934364	−	0.356319i	$-0.115968\pi$
$223$	117779.	+	203999.i	0.158601	+	0.274705i	−0.775764	+	0.631024i	$0.782635\pi$
$224$	388720.	+	173069.i	0.517627	+	0.230462i
$225$	736784.	+	535305.i	0.970251	+	0.704928i
$226$	−66958.2	+	29811.7i	−0.0872033	+	0.0388254i
$227$	−23358.6	−	4965.02i	−0.0300872	−	0.00639523i	0.192844	−	0.981230i	$-0.438229\pi$
$227$	−23358.6	−	4965.02i	−0.0300872	−	0.00639523i	−0.222931	+	0.974834i	$0.571562\pi$
$228$	−7830.54	−	74502.7i	−0.00997596	−	0.0949149i
$229$	365803.	−	406265.i	0.460955	−	0.511942i	−0.467192	−	0.884156i	$-0.654734\pi$
$229$	365803.	−	406265.i	0.460955	−	0.511942i	0.928147	+	0.372213i	$0.121401\pi$
$230$	310461.	+	344802.i	0.386979	+	0.429784i
$231$	−95661.5	+	910158.i	−0.117953	+	1.12224i
$232$	141584.	−	435751.i	0.172701	−	0.531518i
$233$	−112238.	+	345434.i	−0.135441	+	0.416845i	−0.995658	−	0.0930826i	$-0.970328\pi$
$233$	−112238.	+	345434.i	−0.135441	+	0.416845i	0.860217	+	0.509928i	$0.170328\pi$
$234$	74016.6	−	704221.i	0.0883669	−	0.840755i
$235$	−74135.4	−	82335.8i	−0.0875702	−	0.0972565i
$236$	257656.	−	286156.i	0.301134	−	0.334444i
$237$	−196464.	−	1.86923e6i	−0.227202	−	2.16169i
$238$	239378.	+	50881.4i	0.273932	+	0.0582260i
$239$	−546291.	+	243225.i	−0.618628	+	0.275431i	−0.692027	−	0.721872i	$-0.743282\pi$
$239$	−546291.	+	243225.i	−0.618628	+	0.275431i	0.0733988	+	0.997303i	$0.476615\pi$
$240$	581090.	+	422186.i	0.651201	+	0.473125i
$241$	1.41896e6	+	631760.i	1.57372	+	0.700664i	0.993504	−	0.113801i	$-0.0363028\pi$
$241$	1.41896e6	+	631760.i	1.57372	+	0.700664i	0.580213	+	0.814465i	$0.302969\pi$
$242$	8480.94	+	14689.4i	0.00930905	+	0.0161238i
$243$	−1.87333e6	+	3.24470e6i	−2.03516	+	3.52500i
$244$	523600.	−	380418.i	0.563022	−	0.409059i
$245$	−445575.	+	94709.8i	−0.474248	+	0.100804i
$246$	−105990.	−	326204.i	−0.111668	−	0.343678i
$247$	43212.5			0.0450678
$248$	−266641.	−	656380.i	−0.275295	−	0.677682i
$249$	−1.41666e6			−1.44800
$250$	130788.	+	402524.i	0.132348	+	0.407326i
$251$	42973.1	−	9134.21i	0.0430539	−	0.00915138i	−0.186334	−	0.982486i	$-0.559661\pi$
$251$	42973.1	−	9134.21i	0.0430539	−	0.00915138i	0.229388	+	0.973335i	$0.426327\pi$
$252$	1.13037e6	−	821261.i	1.12129	−	0.814666i
$253$	962659.	−	1.66737e6i	0.945521	−	1.63769i
$254$	229972.	+	398323.i	0.223661	+	0.387393i
$255$	1.63706e6	+	728865.i	1.57657	+	0.701934i
$256$	195432.	+	141989.i	0.186378	+	0.135412i
$257$	438609.	−	195281.i	0.414233	−	0.184429i	−0.189029	−	0.981972i	$-0.560534\pi$
$257$	438609.	−	195281.i	0.414233	−	0.184429i	0.603262	+	0.797543i	$0.293867\pi$
$258$	419927.	+	89258.3i	0.392758	+	0.0834832i
$259$	−33039.4	−	314349.i	−0.0306043	−	0.291181i
$260$	−356407.	+	395830.i	−0.326973	+	0.363141i
$261$	−1.55311e6	−	1.72490e6i	−1.41124	−	1.56734i
$262$	58623.7	−	557768.i	0.0527619	−	0.501996i
$263$	210350.	−	647390.i	0.187522	−	0.577134i	−0.812461	−	0.583016i	$-0.801872\pi$
$263$	210350.	−	647390.i	0.187522	−	0.577134i	0.999983	+	0.00588239i	$0.00187243\pi$
$264$	−484588.	+	1.49141e6i	−0.427920	+	1.31700i
$265$	2900.10	−	27592.6i	0.00253687	−	0.0241367i
$266$	−10676.2	−	11857.1i	−0.00925148	−	0.0102748i
$267$	−405279.	+	450108.i	−0.347917	+	0.386401i
$268$	160790.	+	1.52981e6i	0.136748	+	1.30107i
$269$	−481474.	−	102340.i	−0.405688	−	0.0862317i	0.000547955	−	1.00000i	$-0.499826\pi$
$269$	−481474.	−	102340.i	−0.405688	−	0.0862317i	−0.406236	+	0.913768i	$0.633159\pi$
$270$	−1.11535e6	+	496587.i	−0.931114	+	0.414559i
$271$	470058.	+	341517.i	0.388802	+	0.282481i	0.764964	−	0.644072i	$-0.222756\pi$
$271$	470058.	+	341517.i	0.388802	+	0.282481i	−0.376162	+	0.926554i	$0.622756\pi$
$272$	−728115.	−	324178.i	−0.596730	−	0.265681i
$273$	548967.	+	950839.i	0.445800	+	0.772148i
$274$	6776.94	−	11738.0i	0.00545328	−	0.00944535i
$275$	430343.	−	312662.i	0.343149	−	0.249312i
$276$	−3.91678e6	+	832537.i	−3.09497	+	0.657856i
$277$	−47240.2	−	145390.i	−0.0369924	−	0.113851i	0.930855	−	0.365388i	$-0.119064\pi$
$277$	−47240.2	−	145390.i	−0.0369924	−	0.113851i	−0.967848	+	0.251537i	$0.919064\pi$
$278$	−859305.			−0.666861
$279$	−3.55508e6	−	492773.i	−2.73425	−	0.378998i
$280$	430134.			0.327875
$281$	272829.	+	839681.i	0.206122	+	0.634378i	0.999665	+	0.0258648i	$0.00823394\pi$
$281$	272829.	+	839681.i	0.206122	+	0.634378i	−0.793543	+	0.608514i	$0.791766\pi$
$282$	−175015.	+	37200.6i	−0.131055	+	0.0278565i
$283$	−638887.	+	464179.i	−0.474196	+	0.344524i	−0.799074	−	0.601232i	$-0.794677\pi$
$283$	−638887.	+	464179.i	−0.474196	+	0.344524i	0.324878	+	0.945756i	$0.394677\pi$
$284$	−158398.	+	274353.i	−0.116534	+	0.201843i
$285$	−58415.5	−	101179.i	−0.0426006	−	0.0737864i
$286$	−377832.	−	168222.i	−0.273139	−	0.121609i
$287$	315835.	+	229468.i	0.226337	+	0.164444i
$288$	3.37430e6	−	1.50234e6i	2.39719	−	1.06730i
$289$	−556181.	−	118220.i	−0.391716	−	0.0832619i
$290$	−34150.2	−	324918.i	−0.0238451	−	0.226871i
$291$	2.58752e6	−	2.87373e6i	1.79123	−	1.98936i
$292$	978744.	+	1.08700e6i	0.671756	+	0.746061i
$293$	−23358.3	+	222239.i	−0.0158954	+	0.151235i	−0.999591	−	0.0286086i	$-0.990892\pi$
$293$	−23358.3	+	222239.i	−0.0158954	+	0.151235i	0.983695	+	0.179843i	$0.0575590\pi$
$294$	−227329.	+	699646.i	−0.153386	+	0.472074i
$295$	185572.	−	571132.i	0.124153	−	0.382104i
$296$	56613.6	−	538642.i	0.0375570	−	0.357331i
$297$	3.39000e6	+	3.76498e6i	2.23002	+	2.47669i
$298$	−431096.	+	478780.i	−0.281212	+	0.312317i
$299$	−241441.	−	2.29716e6i	−0.156183	−	1.48598i
$300$	−1.08214e6	−	230016.i	−0.694193	−	0.147555i
$301$	−446395.	+	198748.i	−0.283990	+	0.126440i
$302$	806606.	+	586033.i	0.508913	+	0.369747i
$303$	−2.02048e6	−	899576.i	−1.26429	−	0.562900i
$304$	25981.5	+	45001.3i	0.0161243	+	0.0279281i
$305$	504676.	−	874125.i	0.310644	−	0.538051i
$306$	1.71864e6	−	1.24867e6i	1.04926	−	0.762329i
$307$	129899.	−	27610.8i	0.0786608	−	0.0167199i	−0.168413	−	0.985716i	$-0.553864\pi$
$307$	129899.	−	27610.8i	0.0786608	−	0.0167199i	0.247074	+	0.968997i	$0.420531\pi$
$308$	−252185.	−	776146.i	−0.151476	−	0.466194i
$309$	855987.			0.510001
$310$	−364063.	−	350242.i	−0.215165	−	0.206997i
$311$	1.90252e6			1.11539			0.557697	−	0.830045i	$-0.311685\pi$
$311$	1.90252e6			1.11539			0.557697	+	0.830045i	$0.311685\pi$
$312$	581362.	+	1.78925e6i	0.338112	+	1.04060i
$313$	−267358.	+	56828.7i	−0.154253	+	0.0327874i	−0.284391	−	0.958708i	$-0.591791\pi$
$313$	−267358.	+	56828.7i	−0.154253	+	0.0327874i	0.130138	+	0.991496i	$0.458458\pi$
$314$	259486.	−	188528.i	0.148522	−	0.107907i
$315$	1.08951e6	−	1.88709e6i	0.618666	−	1.07156i
$316$	838018.	+	1.45149e6i	0.472102	+	0.817704i
$317$	826932.	+	368174.i	0.462191	+	0.205781i	0.624603	−	0.780942i	$-0.285261\pi$
$317$	826932.	+	368174.i	0.462191	+	0.205781i	−0.162412	+	0.986723i	$0.551927\pi$
$318$	−36248.7	−	26336.2i	−0.0201013	−	0.0146045i
$319$	−1.23850e6	+	551416.i	−0.681427	+	0.303391i
$320$	−235197.	−	49992.6i	−0.128397	−	0.0272917i
$321$	598767.	+	5.69688e6i	0.324336	+	3.08585i
$322$	−570667.	+	633790.i	−0.306721	+	0.340648i
$323$	86746.7	+	96342.0i	0.0462644	+	0.0513818i
$324$	642126.	−	6.10942e6i	0.339827	−	3.23324i
$325$	197203.	−	606928.i	0.103563	−	0.318734i
$326$	126788.	−	390213.i	0.0660744	−	0.203356i
$327$	429344.	−	4.08494e6i	0.222043	−	2.11259i
$328$	447612.	+	497124.i	0.229730	+	0.255141i
$329$	136270.	−	151344.i	0.0694084	−	0.0770858i
$330$	116883.	+	1.11207e6i	0.0590837	+	0.562144i
$331$	−1.27221e6	−	270417.i	−0.638248	−	0.135664i	−0.122589	−	0.992458i	$-0.539120\pi$
$331$	−1.27221e6	−	270417.i	−0.638248	−	0.135664i	−0.515659	+	0.856794i	$0.672453\pi$
$332$	1.15407e6	−	513823.i	0.574626	−	0.255840i
$333$	−2.21974e6	−	1.61274e6i	−1.09696	−	0.796991i
$334$	−1.20752e6	−	537624.i	−0.592283	−	0.263702i
$335$	1.19948e6	+	2.07757e6i	0.583959	+	1.01145i
$336$	−660133.	+	1.14338e6i	−0.318994	+	0.552514i
$337$	−1.90075e6	+	1.38098e6i	−0.911698	+	0.662387i	−0.941444	−	0.337170i	$-0.890530\pi$
$337$	−1.90075e6	+	1.38098e6i	−0.911698	+	0.662387i	0.0297458	+	0.999557i	$0.490530\pi$
$338$	330324.	−	70212.6i	0.157271	−	0.0334290i
$339$	−304849.	−	938229.i	−0.144074	−	0.443414i
$340$	−1.59797e6			−0.749671
$341$	−915396.	+	1.88589e6i	−0.426307	+	0.878275i
$342$	−138501.			−0.0640304
$343$	−660078.	−	2.03151e6i	−0.302942	−	0.932360i
$344$	−818995.	+	174083.i	−0.373152	+	0.0793158i
$345$	−5.05223e6	+	3.67066e6i	−2.28526	+	1.66034i
$346$	178859.	−	309792.i	0.0803193	−	0.139117i
$347$	−1.35630e6	−	2.34919e6i	−0.604691	−	1.04736i	−0.992100	−	0.125448i	$-0.959963\pi$
$347$	−1.35630e6	−	2.34919e6i	−0.604691	−	1.04736i	0.387409	−	0.921908i	$-0.373370\pi$
$348$	2.57583e6	+	1.14684e6i	1.14017	+	0.507637i
$349$	1.44541e6	+	1.05015e6i	0.635225	+	0.461518i	0.858207	−	0.513305i	$-0.171579\pi$
$349$	1.44541e6	+	1.05015e6i	0.635225	+	0.461518i	−0.222981	+	0.974823i	$0.571579\pi$
$350$	−215257.	+	95838.4i	−0.0939261	+	0.0418186i
$351$	5.94521e6	+	1.26369e6i	2.57572	+	0.547487i
$352$	−225508.	−	2.14557e6i	−0.0970077	−	0.922967i
$353$	−61708.0	+	68533.7i	−0.0263575	+	0.0292730i	−0.756179	−	0.654364i	$-0.772936\pi$
$353$	−61708.0	+	68533.7i	−0.0263575	+	0.0292730i	0.729822	+	0.683637i	$0.239603\pi$
$354$	−648929.	−	720709.i	−0.275226	−	0.305669i
$355$	−51643.4	+	491354.i	−0.0217492	+	0.206930i
$356$	166901.	−	513670.i	0.0697967	−	0.214812i
$357$	−1.01787e6	+	3.13268e6i	−0.422689	+	1.30090i
$358$	−143482.	+	1.36514e6i	−0.0591686	+	0.562951i
$359$	−2.36921e6	−	2.63128e6i	−0.970214	−	1.07753i	−0.996962	−	0.0778900i	$-0.975182\pi$
$359$	−2.36921e6	−	2.63128e6i	−0.970214	−	1.07753i	0.0267476	−	0.999642i	$-0.491485\pi$
$360$	2.49840e6	−	2.77475e6i	1.01603	−	1.12841i
$361$	257939.	+	2.45413e6i	0.104172	+	0.991127i
$362$	−29414.1	−	6252.17i	−0.0117974	−	0.00250761i
$363$	−208561.	+	92857.4i	−0.0830743	+	0.0369871i
$364$	−792079.	−	575479.i	−0.313339	−	0.227654i
$365$	2.08396e6	+	927837.i	0.818760	+	0.364535i
$366$	−815021.	−	1.41166e6i	−0.318029	−	0.550842i
$367$	−2.08208e6	+	3.60626e6i	−0.806922	+	1.39763i	0.108064	+	0.994144i	$0.465535\pi$
$367$	−2.08208e6	+	3.60626e6i	−0.806922	+	1.39763i	−0.914986	+	0.403486i	$0.867798\pi$
$368$	2.24708e6	−	1.63260e6i	0.864967	−	0.628435i
$369$	3.31478e6	−	704578.i	1.26733	−	0.269379i
$370$	−119343.	−	367299.i	−0.0453201	−	0.139481i
$371$	50998.1			0.0192362
$372$	4.18874e6	−	1.20969e6i	1.56937	−	0.453227i
$373$	3.08500e6			1.14811			0.574054	−	0.818817i	$-0.305370\pi$
$373$	3.08500e6			1.14811			0.574054	+	0.818817i	$0.305370\pi$
$374$	−383428.	−	1.18007e6i	−0.141744	−	0.436244i
$375$	−5.57210e6	+	1.18439e6i	−2.04617	+	0.434926i
$376$	282316.	−	205115.i	0.102983	−	0.0748217i
$377$	−813223.	+	1.40854e6i	−0.294684	+	0.510407i
$378$	−1.12209e6	−	1.94352e6i	−0.403923	−	0.699615i
$379$	−2.93350e6	−	1.30608e6i	−1.04903	−	0.467059i	−0.191501	−	0.981492i	$-0.561336\pi$
$379$	−2.93350e6	−	1.30608e6i	−1.04903	−	0.467059i	−0.857530	+	0.514433i	$0.828002\pi$
$380$	84284.9	+	61236.6i	0.0299427	+	0.0217546i
$381$	−5.65542e6	+	2.51795e6i	−1.99596	+	0.888659i
$382$	−1.03166e6	−	219286.i	−0.361725	−	0.0768869i
$383$	−28012.8	−	266524.i	−0.00975798	−	0.0928410i	0.988559	−	0.150835i	$-0.0481962\pi$
$383$	−28012.8	−	266524.i	−0.00975798	−	0.0928410i	−0.998317	+	0.0579940i	$0.981530\pi$
$384$	−3.82399e6	+	4.24697e6i	−1.32339	+	1.46978i
$385$	−851625.	−	945825.i	−0.292817	−	0.325206i
$386$	28103.5	−	267387.i	0.00960046	−	0.0913423i
$387$	−1.31075e6	+	4.03406e6i	−0.444878	+	1.36919i
$388$	−1.06559e6	+	3.27954e6i	−0.359343	+	1.10594i
$389$	−231594.	+	2.20347e6i	−0.0775985	+	0.738301i	0.884673	+	0.466211i	$0.154381\pi$
$389$	−231594.	+	2.20347e6i	−0.0775985	+	0.738301i	−0.962272	+	0.272089i	$0.912285\pi$
$390$	897640.	+	996931.i	0.298841	+	0.331897i
$391$	4.63682e6	−	5.14971e6i	1.53383	−	1.70349i
$392$	−149973.	−	1.42690e6i	−0.0492946	−	0.469007i
$393$	7.38367e6	+	1.56945e6i	2.41152	+	0.512585i
$394$	−1.00615e6	+	447967.i	−0.326529	+	0.145380i
$395$	2.11466e6	+	1.53639e6i	0.681944	+	0.495461i
$396$	−6.47164e6	−	2.88136e6i	−2.07385	−	0.923335i
$397$	−608678.	−	1.05426e6i	−0.193826	−	0.335716i	0.752689	−	0.658376i	$-0.228756\pi$
$397$	−608678.	−	1.05426e6i	−0.193826	−	0.335716i	−0.946515	+	0.322660i	$0.895423\pi$
$398$	36574.4	−	63348.7i	0.0115736	−	0.0200461i
$399$	173737.	−	126227.i	0.0546335	−	0.0396936i
$400$	750620.	−	159549.i	0.234569	−	0.0498591i
$401$	−46201.8	−	142195.i	−0.0143482	−	0.0441593i	0.943626	−	0.331013i	$-0.107391\pi$
$401$	−46201.8	−	142195.i	−0.0143482	−	0.0441593i	−0.957974	+	0.286854i	$0.907391\pi$
$402$	3.87419e6			1.19568
$403$	441405.	+	2.47592e6i	0.135386	+	0.759405i
$404$	1.97224e6			0.601181
$405$	−2.96052e6	−	9.11155e6i	−0.896873	−	2.76029i
$406$	587407.	−	124857.i	0.176858	−	0.0375923i
$407$	−1.29651e6	+	941973.i	−0.387964	+	0.281872i
$408$	−2.82207e6	+	4.88796e6i	−0.839299	+	1.45371i
$409$	−1.22879e6	−	2.12832e6i	−0.363219	−	0.629113i	0.625270	−	0.780408i	$-0.284989\pi$
$409$	−1.22879e6	−	2.12832e6i	−0.363219	−	0.629113i	−0.988489	+	0.151296i	$0.951655\pi$
$410$	435761.	+	194013.i	0.128023	+	0.0569996i
$411$	147588.	+	107229.i	0.0430969	+	0.0313117i
$412$	−697319.	+	310467.i	−0.202390	+	0.0901097i
$413$	1.07972e6	+	229501.i	0.311484	+	0.0662079i
$414$	773844.	+	7.36264e6i	0.221898	+	2.11121i
$415$	1.31829e6	−	1.46411e6i	0.375744	−	0.417306i
$416$	−1.73186e6	−	1.92343e6i	−0.490659	−	0.544932i
$417$	1.20896e6	−	1.15025e7i	0.340464	−	3.23930i
$418$	−24998.2	+	76936.5i	−0.00699790	+	0.0215373i
$419$	786828.	−	2.42161e6i	0.218950	−	0.673858i	−0.779900	−	0.625905i	$-0.784730\pi$
$419$	786828.	−	2.42161e6i	0.218950	−	0.673858i	0.998850	−	0.0479539i	$-0.0152700\pi$
$420$	−276690.	+	2.63253e6i	−0.0765369	+	0.728200i
$421$	3.40790e6	+	3.78485e6i	0.937090	+	1.04074i	0.999089	+	0.0426673i	$0.0135856\pi$
$421$	3.40790e6	+	3.78485e6i	0.937090	+	1.04074i	−0.0619997	+	0.998076i	$0.519748\pi$
$422$	1.51345e6	−	1.68085e6i	0.413700	−	0.459461i
$423$	−184787.	−	1.75814e6i	−0.0502136	−	0.477751i
$424$	85476.4	+	18168.6i	0.0230904	+	0.00490802i
$425$	1.74902e6	−	778712.i	0.469701	−	0.209124i
$426$	645496.	+	468981.i	0.172334	+	0.125208i
$427$	1.69492e6	+	754626.i	0.449862	+	0.200291i
$428$	−2.55404e6	−	4.42372e6i	−0.673935	−	1.16729i
$429$	2.78335e6	−	4.82091e6i	0.730172	−	1.26469i
$430$	−483016.	+	350932.i	−0.125977	+	0.0915276i
$431$	3.64443e6	−	774647.i	0.945009	−	0.200868i	0.290460	−	0.956887i	$-0.406192\pi$
$431$	3.64443e6	−	774647.i	0.945009	−	0.200868i	0.654549	+	0.756019i	$0.272858\pi$
$432$	2.25855e6	+	6.95110e6i	0.582265	+	1.79203i
$433$	6.84597e6			1.75475			0.877375	−	0.479805i	$-0.159293\pi$
$433$	6.84597e6			1.75475			0.877375	+	0.479805i	$0.159293\pi$
$434$	570313.	−	732822.i	0.145341	−	0.186756i
$435$	4.39732e6			1.11421
$436$	1.13185e6	+	3.48347e6i	0.285149	+	0.877598i
$437$	−441914.	+	93931.8i	−0.110697	+	0.0235293i
$438$	2.98038e6	−	2.16538e6i	0.742313	−	0.539322i
$439$	−632277.	+	1.09514e6i	−0.156584	+	0.271211i	−0.933634	−	0.358227i	$-0.883381\pi$
$439$	−632277.	+	1.09514e6i	−0.156584	+	0.271211i	0.777051	+	0.629438i	$0.216715\pi$
$440$	−1.09042e6	−	1.88867e6i	−0.268512	−	0.465076i
$441$	−6.64002e6	−	2.95633e6i	−1.62582	−	0.723862i
$442$	−1.20430e6	−	874972.i	−0.293209	−	0.213029i
$443$	−4.33301e6	+	1.92918e6i	−1.04901	+	0.467050i	−0.857524	−	0.514445i	$-0.827998\pi$
$443$	−4.33301e6	+	1.92918e6i	−1.04901	+	0.467050i	−0.191488	+	0.981495i	$0.561331\pi$
$444$	3.26021e6	+	692980.i	0.784854	+	0.166826i
$445$	−88046.6	−	837707.i	−0.0210772	−	0.200536i
$446$	−353997.	+	393153.i	−0.0842679	+	0.0935890i
$447$	−5.80234e6	−	6.44415e6i	−1.37352	−	1.52545i
$448$	46199.5	−	439559.i	0.0108753	−	0.103472i
$449$	−140466.	+	432311.i	−0.0328819	+	0.101200i	−0.966150	−	0.257979i	$-0.916943\pi$
$449$	−140466.	+	432311.i	−0.0328819	+	0.101200i	0.933269	+	0.359179i	$0.116943\pi$
$450$	−632056.	+	1.94527e6i	−0.147138	+	0.452844i
$451$	206900.	−	1.96852e6i	0.0478981	−	0.455720i
$452$	588637.	+	653748.i	0.135519	+	0.150510i
$453$	−8.97932e6	+	9.97255e6i	−2.05588	+	2.28329i
$454$	−5606.18	−	53339.3i	−0.00127652	−	0.0121453i
$455$	−1.49354e6	−	317461.i	−0.338210	−	0.0718889i
$456$	336164.	−	149670.i	0.0757076	−	0.0337072i
$457$	−3.65977e6	−	2.65898e6i	−0.819717	−	0.595559i	0.0969146	−	0.995293i	$-0.469103\pi$
$457$	−3.65977e6	−	2.65898e6i	−0.819717	−	0.595559i	−0.916631	+	0.399734i	$0.869103\pi$
$458$	1.12165e6	+	499391.i	0.249858	+	0.111244i
$459$	9.11728e6	+	1.57916e7i	2.01992	+	3.49860i
$460$	2.78439e6	−	4.82270e6i	0.613529	−	1.06266i
$461$	−1.42008e6	+	1.03174e6i	−0.311214	+	0.226110i	−0.732417	−	0.680856i	$-0.761608\pi$
$461$	−1.42008e6	+	1.03174e6i	−0.311214	+	0.226110i	0.421203	+	0.906966i	$0.361608\pi$
$462$	−2.01047e6	+	427339.i	−0.438221	+	0.0931467i
$463$	−2.63836e6	−	8.12004e6i	−0.571981	−	1.76038i	−0.646236	−	0.763137i	$-0.723658\pi$
$463$	−2.63836e6	−	8.12004e6i	−0.571981	−	1.76038i	0.0742551	−	0.997239i	$-0.476342\pi$
$464$	−1.95580e6			−0.421725
$465$	5.20046e6	−	4.38051e6i	1.11535	−	0.939489i
$466$	−815735.			−0.174014
$467$	1.60589e6	+	4.94243e6i	0.340741	+	1.04869i	0.963824	+	0.266538i	$0.0858798\pi$
$467$	1.60589e6	+	4.94243e6i	0.340741	+	1.04869i	−0.623083	+	0.782156i	$0.714120\pi$
$468$	−8.31309e6	+	1.76700e6i	−1.75448	+	0.372926i
$469$	−3.56745e6	+	2.59190e6i	−0.748903	+	0.544110i
$470$	124416.	−	215495.i	0.0259795	−	0.0449979i
$471$	2.15852e6	+	3.73867e6i	0.448336	+	0.776541i
$472$	1.72792e6	+	769320.i	0.357001	+	0.158947i
$473$	2.00433e6	+	1.45623e6i	0.411923	+	0.299279i
$474$	3.85629e6	−	1.71693e6i	0.788359	−	0.351000i
$475$	−122093.	−	25951.8i	−0.0248290	−	0.00527756i
$476$	−307028.	−	2.92118e6i	−0.0621099	−	0.590936i
$477$	296219.	−	328984.i	0.0596096	−	0.0662032i
$478$	−898661.	−	998064.i	−0.179898	−	0.199797i
$479$	170952.	−	1.62650e6i	0.0340436	−	0.323903i	−0.964225	−	0.265085i	$-0.914600\pi$
$479$	170952.	−	1.62650e6i	0.0340436	−	0.323903i	0.998269	−	0.0588184i	$-0.0187333\pi$
$480$	−2.16239e6	+	6.65514e6i	−0.428381	+	1.31842i
$481$	−594122.	+	1.82852e6i	−0.117088	+	0.360360i
$482$	−364640.	+	3.46932e6i	−0.0714902	+	0.680184i
$483$	−7.68089e6	−	8.53049e6i	−1.49811	−	1.66382i
$484$	136222.	−	151290.i	0.0264323	−	0.0293560i
$485$	562136.	+	5.34837e6i	0.108514	+	1.03245i
$486$	−8.23075e6	−	1.74950e6i	−1.58070	−	0.335987i
$487$	−2.71541e6	+	1.20898e6i	−0.518815	+	0.230991i	−0.649402	−	0.760446i	$-0.724981\pi$
$487$	−2.71541e6	+	1.20898e6i	−0.518815	+	0.230991i	0.130587	+	0.991437i	$0.458314\pi$
$488$	2.57196e6	+	1.86864e6i	0.488894	+	0.355202i
$489$	5.04492e6	+	2.24614e6i	0.954074	+	0.424781i
$490$	−511537.	−	886008.i	−0.0962469	−	0.166705i
$491$	297000.	−	514419.i	0.0555971	−	0.0962971i	−0.836887	−	0.547375i	$-0.815627\pi$
$491$	297000.	−	514419.i	0.0555971	−	0.0962971i	0.892484	+	0.451078i	$0.148960\pi$
$492$	−3.33046e6	+	2.41972e6i	−0.620286	+	0.450664i
$493$	−4.77284e6	+	1.01450e6i	−0.884422	+	0.187990i
$494$	29990.4	+	92301.0i	0.00552924	+	0.0170172i
$495$	−1.10480e7			−2.02662
$496$	−2.31301e6	+	1.94832e6i	−0.422157	+	0.355595i
$497$	−908146.			−0.164917
$498$	−983195.	−	3.02596e6i	−0.177650	−	0.546752i
$499$	6.39178e6	−	1.35862e6i	1.14913	−	0.244256i	0.406305	−	0.913737i	$-0.366817\pi$
$499$	6.39178e6	−	1.35862e6i	1.14913	−	0.244256i	0.742829	+	0.669482i	$0.233484\pi$
$500$	4.10967e6	−	2.98585e6i	0.735159	−	0.534125i
$501$	8.89538e6	−	1.54073e7i	1.58333	−	2.74240i
$502$	49334.7	+	85450.3i	0.00873763	+	0.0151340i
$503$	1.35699e6	+	604170.i	0.239142	+	0.106473i	0.522809	−	0.852450i	$-0.324884\pi$
$503$	1.35699e6	+	604170.i	0.239142	+	0.106473i	−0.283667	+	0.958923i	$0.591551\pi$
$504$	5.55244e6	+	4.03409e6i	0.973661	+	0.707406i
$505$	2.80989e6	−	1.25104e6i	0.490299	−	0.218295i
$506$	4.22959e6	+	899026.i	0.734381	+	0.156098i
$507$	475116.	+	4.52043e6i	0.0820880	+	0.781015i
$508$	3.69385e6	−	4.10244e6i	0.635068	−	0.705314i
$509$	−3.27802e6	−	3.64061e6i	−0.560812	−	0.622845i	0.394339	−	0.918965i	$-0.370974\pi$
$509$	−3.27802e6	−	3.64061e6i	−0.560812	−	0.622845i	−0.955151	+	0.296120i	$0.904307\pi$
$510$	−420687.	+	4.00257e6i	−0.0716199	+	0.681418i
$511$	−1.29574e6	+	3.98787e6i	−0.219515	+	0.675598i
$512$	1.70182e6	−	5.23765e6i	0.286905	−	0.883002i
$513$	124267.	−	1.18232e6i	0.0208478	−	0.198354i
$514$	721522.	+	801331.i	0.120460	+	0.133784i
$515$	−796550.	+	884658.i	−0.132341	+	0.146980i
$516$	−538601.	−	5.12445e6i	−0.0890519	−	0.847272i
$517$	−1.00999e6	−	214680.i	−0.166185	−	0.0353236i
$518$	648513.	−	288737.i	0.106193	−	0.0472800i
$519$	3.89517e6	+	2.83001e6i	0.634758	+	0.461179i
$520$	−2.39017e6	−	1.06417e6i	−0.387633	−	0.172585i
$521$	863057.	+	1.49486e6i	0.139298	+	0.241271i	0.927231	−	0.374490i	$-0.122182\pi$
$521$	863057.	+	1.49486e6i	0.139298	+	0.241271i	−0.787933	+	0.615761i	$0.788849\pi$
$522$	2.60647e6	−	4.51453e6i	0.418674	−	0.725165i
$523$	2.57432e6	−	1.87036e6i	0.411537	−	0.298999i	−0.362687	−	0.931911i	$-0.618140\pi$
$523$	2.57432e6	−	1.87036e6i	0.411537	−	0.298999i	0.774224	+	0.632912i	$0.218140\pi$
$524$	−6.58426e6	+	1.39953e6i	−1.04756	+	0.222666i
$525$	−980026.	−	3.01621e6i	−0.155181	−	0.477599i
$526$	1.52880e6			0.240927
$527$	−4.63394e6	+	5.95438e6i	−0.726815	+	0.933920i
$528$	6.69396e6			1.04496
$529$	5.47354e6	+	1.68458e7i	0.850411	+	2.61730i
$530$	60950.0	−	12955.3i	0.00942506	−	0.00200336i
$531$	7.75195e6	−	5.63212e6i	1.19309	−	0.866833i
$532$	−95749.8	+	165844.i	−0.0146676	+	0.0254050i
$533$	−1.18732e6	−	2.05650e6i	−0.181030	−	0.313553i
$534$	−1.24269e6	−	553283.i	−0.188587	−	0.0839642i
$535$	−6.44489e6	−	4.68249e6i	−0.973489	−	0.707281i
$536$	−6.90269e6	+	3.07328e6i	−1.03778	+	0.462051i
$537$	−1.80716e7	−	3.84125e6i	−2.70434	−	0.574826i
$538$	−115556.	−	1.09945e6i	−0.0172123	−	0.163764i
$539$	−2.84069e6	+	3.15491e6i	−0.421165	+	0.467752i
$540$	9.80520e6	+	1.08898e7i	1.44701	+	1.60707i
$541$	−306072.	+	2.91208e6i	−0.0449605	+	0.427771i	0.948770	+	0.315968i	$0.102329\pi$
$541$	−306072.	+	2.91208e6i	−0.0449605	+	0.427771i	−0.993730	+	0.111803i	$0.964338\pi$
$542$	−403244.	+	1.24106e6i	−0.0589616	+	0.181465i
$543$	125073.	−	384935.i	0.0182039	−	0.0560258i
$544$	811651.	−	7.72235e6i	0.117590	−	1.11880i
$545$	3.82223e6	+	4.24502e6i	0.551221	+	0.612193i
$546$	−1.64998e6	+	1.83249e6i	−0.236863	+	0.263063i
$547$	−120704.	−	1.14842e6i	−0.0172485	−	0.164109i	0.982507	−	0.186226i	$-0.0596258\pi$
$547$	−120704.	−	1.14842e6i	−0.0172485	−	0.164109i	−0.999755	+	0.0221177i	$0.992959\pi$
$548$	−159123.	−	33822.5i	−0.0226350	−	0.00481122i
$549$	1.47128e7	−	6.55057e6i	2.08336	−	0.927573i
$550$	966508.	+	702209.i	0.136238	+	0.0989828i
$551$	290621.	+	129393.i	0.0407801	+	0.0181565i
$552$	−9.83464e6	−	1.70341e7i	−1.37376	−	2.37942i
$553$	−2.40231e6	+	4.16093e6i	−0.334054	+	0.578599i
$554$	277765.	−	201808.i	0.0384507	−	0.0279360i
$555$	5.08448e6	−	1.08074e6i	0.700671	−	0.148932i
$556$	3.18708e6	+	9.80882e6i	0.437226	+	1.34564i
$557$	−1.19710e7			−1.63490			−0.817451	−	0.575999i	$-0.804613\pi$
$557$	−1.19710e7			−1.63490			−0.817451	+	0.575999i	$0.804613\pi$
$558$	−1.41475e6	−	7.93558e6i	−0.192351	−	1.07893i
$559$	2.97225e6			0.402305
$560$	−567386.	−	1.74623e6i	−0.0764554	−	0.235306i
$561$	1.63356e7	−	3.47224e6i	2.19143	−	0.465804i
$562$	−1.60419e6	+	1.16551e6i	−0.214247	+	0.155660i
$563$	−5.41480e6	+	9.37871e6i	−0.719966	+	1.24702i	0.241047	+	0.970513i	$0.422509\pi$
$563$	−5.41480e6	+	9.37871e6i	−0.719966	+	1.24702i	−0.961013	+	0.276503i	$0.910824\pi$
$564$	1.07375e6	+	1.85979e6i	0.142137	+	0.246188i
$565$	1.25334e6	+	558021.i	0.165176	+	0.0735410i
$566$	−1.43488e6	−	1.04250e6i	−0.188267	−	0.136784i
$567$	1.60876e7	−	7.16267e6i	2.10152	−	0.935659i
$568$	−1.52212e6	−	323536.i	−0.197960	−	0.0420777i
$569$	−588203.	−	5.59637e6i	−0.0761634	−	0.724646i	−0.964254	−	0.264978i	$-0.914635\pi$
$569$	−588203.	−	5.59637e6i	−0.0761634	−	0.724646i	0.888091	−	0.459668i	$-0.152032\pi$
$570$	175574.	−	194994.i	0.0226346	−	0.0251383i
$571$	1.92798e6	+	2.14123e6i	0.247464	+	0.274836i	0.854061	−	0.520173i	$-0.174133\pi$
$571$	1.92798e6	+	2.14123e6i	0.247464	+	0.274836i	−0.606597	+	0.795009i	$0.707466\pi$
$572$	−518880.	+	4.93681e6i	−0.0663097	+	0.630894i
$573$	4.38676e6	−	1.35010e7i	0.558158	−	1.71783i
$574$	−270942.	+	833874.i	−0.0343239	+	0.105638i
$575$	−697413.	+	6.63544e6i	−0.0879671	+	0.836951i
$576$	−2.56721e6	−	2.85117e6i	−0.322407	−	0.358069i
$577$	6.65303e6	−	7.38893e6i	0.831916	−	0.923937i	−0.166150	−	0.986101i	$-0.553133\pi$
$577$	6.65303e6	−	7.38893e6i	0.831916	−	0.923937i	0.998066	+	0.0621639i	$0.0198002\pi$
$578$	−133486.	−	1.27004e6i	−0.0166195	−	0.158124i
$579$	3.53964e6	+	752374.i	0.438796	+	0.0932690i
$580$	−3.58222e6	+	1.59491e6i	−0.442163	+	0.196864i
$581$	2.92978e6	+	2.12861e6i	0.360076	+	0.261610i
$582$	7.93402e6	+	3.53245e6i	0.970925	+	0.432284i
$583$	−129284.	−	223927.i	−0.0157534	−	0.0272857i
$584$	−3.59246e6	+	6.22233e6i	−0.435873	+	0.754954i
$585$	−1.07230e7	+	7.79071e6i	−1.29547	+	0.941212i
$586$	−490909.	+	104346.i	−0.0590550	+	0.0125525i
$587$	−744187.	−	2.29037e6i	−0.0891429	−	0.274354i	0.896540	−	0.442963i	$-0.146073\pi$
$587$	−744187.	−	2.29037e6i	−0.0891429	−	0.274354i	−0.985683	+	0.168609i	$0.946073\pi$
$588$	8.82949e6			1.05315
$589$	472599.	−	136484.i	0.0561312	−	0.0162104i
$590$	1.34872e6			0.159511
$591$	−4.58083e6	−	1.40983e7i	−0.539480	−	1.66035i
$592$	−2.26143e6	+	480681.i	−0.265203	+	0.0563706i
$593$	−2.48528e6	+	1.80566e6i	−0.290228	+	0.210863i	−0.723366	−	0.690464i	$-0.757406\pi$
$593$	−2.48528e6	+	1.80566e6i	−0.290228	+	0.210863i	0.433138	+	0.901327i	$0.357406\pi$
$594$	−5.68918e6	+	9.85395e6i	−0.661582	+	1.14589i
$595$	−2.29041e6	−	3.96711e6i	−0.265229	−	0.459391i
$596$	7.06409e6	+	3.14514e6i	0.814593	+	0.362680i
$597$	796515.	+	578702.i	0.0914657	+	0.0664537i
$598$	4.73912e6	−	2.10999e6i	0.541932	−	0.241283i
$599$	−4.86892e6	−	1.03492e6i	−0.554454	−	0.117853i	−0.0778408	−	0.996966i	$-0.524803\pi$
$599$	−4.86892e6	−	1.03492e6i	−0.554454	−	0.117853i	−0.476614	+	0.879113i	$0.658136\pi$
$600$	−568038.	−	5.40452e6i	−0.0644169	−	0.612885i
$601$	−2.87777e6	+	3.19609e6i	−0.324990	+	0.360938i	−0.883394	−	0.468631i	$-0.844747\pi$
$601$	−2.87777e6	+	3.19609e6i	−0.324990	+	0.360938i	0.558404	+	0.829569i	$0.311414\pi$
$602$	−734329.	−	815555.i	−0.0825847	−	0.0917196i
$603$	−4.00113e6	+	3.80682e7i	−0.448114	+	4.26352i
$604$	3.69785e6	−	1.13808e7i	0.412436	−	1.26935i
$605$	98111.6	−	301956.i	0.0108976	−	0.0335394i
$606$	519218.	−	4.94003e6i	0.0574339	−	0.546447i
$607$	−5.55028e6	−	6.16421e6i	−0.611425	−	0.679057i	0.355336	−	0.934739i	$-0.384367\pi$
$607$	−5.55028e6	−	6.16421e6i	−0.611425	−	0.679057i	−0.966761	+	0.255682i	$0.917700\pi$
$608$	−338743.	+	376212.i	−0.0371630	+	0.0412737i
$609$	844887.	+	8.03856e6i	0.0923114	+	0.878284i
$610$	2.21737e6	+	471316.i	0.241276	+	0.0512847i
$611$	−1.13166e6	+	503848.i	−0.122635	+	0.0546005i
$612$	−2.06276e7	−	1.49868e7i	−2.22623	−	1.61745i
$613$	−2.58615e6	−	1.15143e6i	−0.277973	−	0.123761i	0.263016	−	0.964792i	$-0.415283\pi$
$613$	−2.58615e6	−	1.15143e6i	−0.277973	−	0.123761i	−0.540988	+	0.841030i	$0.681950\pi$
$614$	149129.	+	258298.i	0.0159639	+	0.0276503i
$615$	−3.21009e6	+	5.56004e6i	−0.342239	+	0.592775i
$616$	3.24309e6	−	2.35624e6i	0.344355	−	0.250189i
$617$	−7.32185e6	+	1.55631e6i	−0.774297	+	0.164582i	−0.578082	−	0.815979i	$-0.696199\pi$
$617$	−7.32185e6	+	1.55631e6i	−0.774297	+	0.164582i	−0.196215	+	0.980561i	$0.562865\pi$
$618$	594074.	+	1.82837e6i	0.0625704	+	0.192572i
$619$	9.94380e6			1.04310			0.521550	−	0.853221i	$-0.325354\pi$
$619$	9.94380e6			1.04310			0.521550	+	0.853221i	$0.325354\pi$
$620$	−2.64768e6	+	5.45473e6i	−0.276622	+	0.569894i
$621$	−6.35458e7			−6.61238
$622$	1.32039e6	+	4.06375e6i	0.136844	+	0.421163i
$623$	1.51446e6	−	321909.i	0.156328	−	0.0332286i
$624$	6.49702e6	−	4.72036e6i	0.667964	−	0.485304i
$625$	1.83972e6	−	3.18649e6i	0.188388	−	0.326297i
$626$	−306937.	−	531631.i	−0.0313050	−	0.0542219i
$627$	−994685.	−	442862.i	−0.101045	−	0.0449883i
$628$	−3.11443e6	−	2.26276e6i	−0.315122	−	0.228950i
$629$	−5.26934e6	+	2.34606e6i	−0.531043	+	0.236436i
$630$	4.78694e6	+	1.01750e6i	0.480515	+	0.102137i
$631$	−1.31632e6	−	1.25239e7i	−0.131609	−	1.25218i	−0.838518	−	0.544874i	$-0.816578\pi$
$631$	−1.31632e6	−	1.25239e7i	−0.131609	−	1.25218i	0.706909	−	0.707305i	$-0.250089\pi$
$632$	−5.50882e6	+	6.11816e6i	−0.548612	+	0.609296i
$633$	2.03702e7	+	2.26234e7i	2.02063	+	2.24414i
$634$	−212503.	+	2.02183e6i	−0.0209963	+	0.199766i
$635$	2.66043e6	−	8.18796e6i	0.261829	−	0.805826i
$636$	−166181.	+	511451.i	−0.0162906	+	0.0501373i
$637$	−532380.	+	5.06526e6i	−0.0519844	+	0.494599i
$638$	−2.03736e6	−	2.26272e6i	−0.198160	−	0.220079i
$639$	−5.27490e6	+	5.85837e6i	−0.511048	+	0.567577i
$640$	−830759.	−	7.90415e6i	−0.0801725	−	0.762790i
$641$	1.60047e7	+	3.40191e6i	1.53852	+	0.327022i	0.897678	−	0.440651i	$-0.145252\pi$
$641$	1.60047e7	+	3.40191e6i	1.53852	+	0.327022i	0.640841	+	0.767674i	$0.278586\pi$
$642$	−1.17529e7	+	5.23272e6i	−1.12540	+	0.501060i
$643$	3.31946e6	+	2.41173e6i	0.316621	+	0.230039i	0.734732	−	0.678357i	$-0.237308\pi$
$643$	3.31946e6	+	2.41173e6i	0.316621	+	0.230039i	−0.418111	+	0.908396i	$0.637308\pi$
$644$	9.35115e6	+	4.16340e6i	0.888486	+	0.395579i
$645$	−4.01794e6	−	6.95927e6i	−0.380281	−	0.658665i
$646$	−145580.	+	252153.i	−0.0137253	+	0.0237729i
$647$	1.20094e7	−	8.72531e6i	1.12787	−	0.819445i	0.142486	−	0.989797i	$-0.454490\pi$
$647$	1.20094e7	−	8.72531e6i	1.12787	−	0.819445i	0.985383	+	0.170351i	$0.0544903\pi$
$648$	2.95158e7	−	6.27377e6i	2.76132	−	0.586936i
$649$	−1.72946e6	−	5.32272e6i	−0.161175	−	0.496046i
$650$	1.43325e6			0.133057
$651$	9.00702e6	+	8.66509e6i	0.832969	+	0.801347i
$652$	−4.92446e6			−0.453669
$653$	−1.11722e6	−	3.43846e6i	−0.102531	−	0.315559i	0.886612	−	0.462514i	$-0.153053\pi$
$653$	−1.11722e6	−	3.43846e6i	−0.102531	−	0.315559i	−0.989143	+	0.146955i	$0.953053\pi$
$654$	9.02332e6	−	1.91797e6i	0.824940	−	0.175346i
$655$	−8.49299e6	+	6.17052e6i	−0.773494	+	0.561977i
$656$	1.42775e6	−	2.47294e6i	0.129537	−	0.224365i
$657$	1.81992e7	+	3.15219e7i	1.64489	+	2.84904i
$658$	417842.	+	186035.i	0.0376224	+	0.0167506i
$659$	−9.38572e6	−	6.81913e6i	−0.841888	−	0.611667i	0.0810096	−	0.996713i	$-0.474186\pi$
$659$	−9.38572e6	−	6.81913e6i	−0.841888	−	0.611667i	−0.922897	+	0.385046i	$0.874186\pi$
$660$	1.22606e7	−	5.45877e6i	1.09560	−	0.487792i
$661$	1.44365e7	+	3.06858e6i	1.28517	+	0.273170i	0.799336	−	0.600884i	$-0.205185\pi$
$661$	1.44365e7	+	3.06858e6i	1.28517	+	0.273170i	0.485829	+	0.874054i	$0.338518\pi$
$662$	−305338.	−	2.90510e6i	−0.0270792	−	0.257641i
$663$	1.34065e7	−	1.48894e7i	1.18449	−	1.31551i
$664$	4.15217e6	+	4.61146e6i	0.365473	+	0.405899i
$665$	−31217.8	+	297018.i	−0.00273747	+	0.0260453i
$666$	1.90423e6	−	5.86060e6i	0.166354	−	0.511985i
$667$	5.25468e6	−	1.61722e7i	0.457332	−	1.40752i
$668$	−1.65830e6	+	1.57777e7i	−0.143788	+	1.36805i
$669$	−4.76462e6	−	5.29165e6i	−0.411588	−	0.457115i
$670$	−3.60518e6	+	4.00395e6i	−0.310270	+	0.344589i
$671$	−983275.	−	9.35523e6i	−0.0843080	−	0.802137i
$672$	−1.25815e7	−	2.67427e6i	−1.07475	−	0.228445i
$673$	−1.47966e7	+	6.58788e6i	−1.25929	+	0.560671i	−0.924342	−	0.381566i	$-0.875385\pi$
$673$	−1.47966e7	+	6.58788e6i	−1.25929	+	0.560671i	−0.334947	+	0.942237i	$0.608718\pi$
$674$	−4.26891e6	−	3.10154e6i	−0.361965	−	0.262983i
$675$	−1.60388e7	−	7.14093e6i	−1.35492	−	0.603247i
$676$	−2.02661e6	−	3.51018e6i	−0.170570	−	0.295436i
$677$	8.71157e6	−	1.50889e7i	0.730507	−	1.26528i	−0.226159	−	0.974090i	$-0.572617\pi$
$677$	8.71157e6	−	1.50889e7i	0.730507	−	1.26528i	0.956667	−	0.291185i	$-0.0940497\pi$
$678$	1.79247e6	−	1.30230e6i	0.149754	−	0.108802i
$679$	−9.66912e6	+	2.05524e6i	−0.804846	+	0.171075i
$680$	−2.42557e6	−	7.46514e6i	−0.201160	−	0.619107i
$681$	721874.			0.0596477
$682$	−4.66353e6	−	646416.i	−0.383932	−	0.0532171i
$683$	2.12139e7			1.74008			0.870038	−	0.492985i	$-0.164094\pi$
$683$	2.12139e7			1.74008			0.870038	+	0.492985i	$0.164094\pi$
$684$	513686.	+	1.58096e6i	0.0419814	+	0.129206i
$685$	−248160.	+	52748.1i	−0.0202072	+	0.00429517i
$686$	3.88116e6	−	2.81983e6i	0.314884	−	0.228777i
$687$	−8.26278e6	+	1.43116e7i	−0.667935	+	1.15690i
$688$	1.78706e6	+	3.09528e6i	0.143936	+	0.249304i
$689$	−283387.	−	126172.i	−0.0227422	−	0.0101255i
$690$	−1.13468e7	−	8.24394e6i	−0.907300	−	0.659192i
$691$	−1.02762e7	+	4.57525e6i	−0.818723	+	0.364519i	−0.772977	−	0.634434i	$-0.781233\pi$
$691$	−1.02762e7	+	4.57525e6i	−0.818723	+	0.364519i	−0.0457460	+	0.998953i	$0.514566\pi$
$692$	−4.19960e6	−	892652.i	−0.333382	−	0.0708626i
$693$	−2.12273e6	−	2.01964e7i	−0.167904	−	1.59750i
$694$	4.07651e6	−	4.52743e6i	0.321285	−	0.356823i
$695$	1.07627e7	+	1.19532e7i	0.845201	+	0.938691i
$696$	−1.44773e6	+	1.37742e7i	−0.113283	+	1.07781i
$697$	2.20148e6	−	6.77544e6i	0.171645	−	0.528270i
$698$	−1.23996e6	+	3.81620e6i	−0.0963315	+	0.296478i
$699$	1.14766e6	−	1.09192e7i	0.0888423	−	0.845278i
$700$	1.89235e6	+	2.10166e6i	0.145967	+	0.162113i
$701$	5.45641e6	−	6.05996e6i	0.419384	−	0.465774i	−0.496019	−	0.868312i	$-0.665205\pi$
$701$	5.45641e6	−	6.05996e6i	0.419384	−	0.465774i	0.915403	+	0.402538i	$0.131872\pi$
$702$	1.42688e6	+	1.35759e7i	0.109281	+	1.03974i
$703$	367837.	+	78186.1i	0.0280716	+	0.00596680i
$704$	−2.04717e6	+	911461.i	−0.155677	+	0.0693116i
$705$	2.70952e6	+	1.96858e6i	0.205315	+	0.149170i
$706$	−189213.	−	84243.2i	−0.0142870	−	0.00636097i
$707$	2.82686e6	+	4.89627e6i	0.212695	+	0.368398i
$708$	−5.81995e6	+	1.00805e7i	−0.436351	+	0.755783i
$709$	−1.47193e6	+	1.06942e6i	−0.109969	+	0.0798973i	−0.641411	−	0.767198i	$-0.721651\pi$
$709$	−1.47193e6	+	1.06942e6i	−0.109969	+	0.0798973i	0.531442	+	0.847095i	$0.321651\pi$
$710$	−1.08536e6	+	230701.i	−0.0808034	+	0.0171753i
$711$	1.28881e7	+	3.96655e7i	0.956126	+	2.94265i
$712$	2.65303e6			0.196129
$713$	−9.89599e6	−	2.43606e7i	−0.729013	−	1.79458i
$714$	−7.39776e6			−0.543068
$715$	2.39230e6	+	7.36274e6i	0.175005	+	0.538610i
$716$	1.61151e7	−	3.42536e6i	1.17476	−	0.249703i
$717$	1.46242e7	−	1.06251e7i	1.06237	−	0.771854i
$718$	3.97607e6	−	6.88675e6i	0.287834	−	0.498544i
$719$	−997434.	−	1.72761e6i	−0.0719552	−	0.124630i	0.827803	−	0.561019i	$-0.189591\pi$
$719$	−997434.	−	1.72761e6i	−0.0719552	−	0.124630i	−0.899758	+	0.436389i	$0.856257\pi$
$720$	−1.45604e7	−	6.48271e6i	−1.04675	−	0.466042i
$721$	−1.77025e6	−	1.28616e6i	−0.126823	−	0.0921421i
$722$	−5.06295e6	+	2.25417e6i	−0.361461	+	0.160933i
$723$	−4.59265e7	−	9.76198e6i	−3.26751	−	0.694532i
$724$	37726.8	+	358946.i	0.00267487	+	0.0254497i
$725$	3.14362e6	−	3.49134e6i	0.222118	−	0.246687i
$726$	−343087.	−	381037.i	−0.0241581	−	0.0268303i
$727$	−302259.	+	2.87580e6i	−0.0212101	+	0.201801i	−0.999995	−	0.00308874i	$-0.999017\pi$
$727$	−302259.	+	2.87580e6i	−0.0212101	+	0.201801i	0.978785	+	0.204889i	$0.0656835\pi$
$728$	1.48613e6	−	4.57384e6i	0.103927	−	0.319855i
$729$	1.78855e7	−	5.50459e7i	1.24647	−	3.83624i
$730$	−535530.	+	5.09523e6i	−0.0371943	+	0.353880i
$731$	5.96662e6	+	6.62660e6i	0.412986	+	0.458667i
$732$	−1.30910e7	+	1.45390e7i	−0.903016	+	1.00290i
$733$	1.68658e6	+	1.60467e7i	0.115943	+	1.10313i	0.885529	+	0.464584i	$0.153796\pi$
$733$	1.68658e6	+	1.60467e7i	0.115943	+	1.10313i	−0.769586	+	0.638543i	$0.779537\pi$
$734$	−9.14791e6	−	1.94445e6i	−0.626732	−	0.133216i
$735$	1.25796e7	−	5.60079e6i	0.858910	−	0.382412i
$736$	2.18919e7	+	1.59054e7i	1.48967	+	1.08231i
$737$	2.04245e7	+	9.09359e6i	1.38511	+	0.616690i
$738$	3.80550e6	+	6.59131e6i	0.257200	+	0.445483i
$739$	3.39335e6	−	5.87745e6i	0.228569	−	0.395893i	−0.728815	−	0.684710i	$-0.759929\pi$
$739$	3.39335e6	−	5.87745e6i	0.228569	−	0.395893i	0.957384	+	0.288817i	$0.0932621\pi$
$740$	−3.75002e6	+	2.72455e6i	−0.251742	+	0.182901i
$741$	−1.27771e6	+	271586.i	−0.0854846	+	0.0181703i
$742$	35393.8	+	108931.i	0.00236003	+	0.00726343i
$743$	−1.40467e6			−0.0933476			−0.0466738	−	0.998910i	$-0.514862\pi$
$743$	−1.40467e6			−0.0933476			−0.0466738	+	0.998910i	$0.514862\pi$
$744$	1.20094e7	+	1.77321e7i	0.795405	+	1.17443i
$745$	1.20594e7			0.796042
$746$	2.14106e6	+	6.58950e6i	0.140858	+	0.433516i
$747$	3.07488e7	−	6.53586e6i	2.01617	−	0.428550i
$748$	−1.20482e7	+	8.75354e6i	−0.787352	+	0.572045i
$749$	7.32156e6	−	1.26813e7i	0.476869	−	0.825961i
$750$	−6.39699e6	−	1.10799e7i	−0.415262	−	0.719255i
$751$	−2.18179e6	−	971396.i	−0.141161	−	0.0628487i	0.334941	−	0.942239i	$-0.391284\pi$
$751$	−2.18179e6	−	971396.i	−0.141161	−	0.0628487i	−0.476101	+	0.879390i	$0.657950\pi$
$752$	−1.20512e6	−	875568.i	−0.0777113	−	0.0564606i
$753$	−1.21323e6	+	540163.i	−0.0779749	+	0.0347166i
$754$	−3.57302e6	−	759468.i	−0.228879	−	0.0486498i
$755$	−1.95075e6	−	1.85602e7i	−0.124547	−	1.18499i
$756$	−1.80232e7	+	2.00168e7i	−1.14691	+	1.27377i
$757$	−9.90736e6	−	1.10032e7i	−0.628374	−	0.697880i	0.341942	−	0.939721i	$-0.388915\pi$
$757$	−9.90736e6	−	1.10032e7i	−0.628374	−	0.697880i	−0.970316	+	0.241841i	$0.922249\pi$
$758$	753845.	−	7.17235e6i	0.0476551	−	0.453408i
$759$	−1.79848e7	+	5.53514e7i	−1.13318	+	3.48758i
$760$	−158139.	+	486701.i	−0.00993127	+	0.0305653i
$761$	−1.09653e6	+	1.04328e7i	−0.0686371	+	0.653039i	0.905074	+	0.425253i	$0.139815\pi$
$761$	−1.09653e6	+	1.04328e7i	−0.0686371	+	0.653039i	−0.973711	+	0.227785i	$0.926852\pi$
$762$	−9.30328e6	−	1.03323e7i	−0.580428	−	0.644631i
$763$	−7.02575e6	+	7.80288e6i	−0.436899	+	0.485226i
$764$	1.32321e6	+	1.25895e7i	0.0820156	+	0.780326i
$765$	−3.88952e7	−	8.26742e6i	−2.40294	−	0.510760i
$766$	549849.	−	244808.i	0.0338588	−	0.0150749i
$767$	−5.43199e6	−	3.94657e6i	−0.333404	−	0.242232i
$768$	−6.67095e6	−	2.97010e6i	−0.408117	−	0.181705i
$769$	−5.53798e6	−	9.59207e6i	−0.337704	−	0.584920i	0.646297	−	0.763086i	$-0.276317\pi$
$769$	−5.53798e6	−	9.59207e6i	−0.337704	−	0.584920i	−0.984000	+	0.178166i	$0.942983\pi$
$770$	1.42922e6	−	2.47548e6i	0.0868703	−	0.150464i
$771$	−1.17415e7	+	8.53073e6i	−0.711360	+	0.516833i
$772$	−3.15641e6	+	670916.i	−0.190612	+	0.0405158i
$773$	−7.88928e6	−	2.42807e7i	−0.474885	−	1.46155i	−0.846113	−	0.533004i	$-0.821063\pi$
$773$	−7.88928e6	−	2.42807e7i	−0.474885	−	1.46155i	0.371228	−	0.928542i	$-0.378937\pi$
$774$	−9.52637e6			−0.571577
$775$	239785.	−	7.26060e6i	0.0143406	−	0.434228i
$776$	−1.69383e7			−1.00976
$777$	2.95257e6	+	9.08708e6i	0.175448	+	0.539973i
$778$	−4.86730e6	+	1.03458e6i	−0.288296	+	0.0612793i
$779$	−375763.	+	273008.i	−0.0221855	+	0.0161187i
$780$	8.05054e6	−	1.39439e7i	0.473793	−	0.820633i
$781$	2.30222e6	+	3.98757e6i	0.135058	+	0.233927i
$782$	1.42177e7	+	6.33014e6i	0.831406	+	0.370166i
$783$	3.61999e7	+	2.63008e7i	2.11010	+	1.53308i
$784$	−5.59503e6	+	2.49107e6i	−0.325096	+	0.144742i
$785$	−5.87253e6	−	1.24824e6i	−0.340135	−	0.0722979i
$786$	1.77212e6	+	1.68606e7i	0.102314	+	0.973457i
$787$	−1.39825e7	+	1.55291e7i	−0.804725	+	0.893738i	−0.996141	−	0.0877713i	$-0.972026\pi$
$787$	−1.39825e7	+	1.55291e7i	−0.804725	+	0.893738i	0.191416	+	0.981509i	$0.438692\pi$
$788$	8.84518e6	+	9.82357e6i	0.507447	+	0.563577i
$789$	−2.15087e6	+	2.04642e7i	−0.123005	+	1.17031i
$790$	−1.81408e6	+	5.58317e6i	−0.103416	+	0.318283i
$791$	−779284.	+	2.39839e6i	−0.0442848	+	0.136294i
$792$	3.63733e6	−	3.46069e7i	0.206049	−	1.96042i
$793$	−7.55136e6	−	8.38663e6i	−0.426424	−	0.473592i
$794$	1.82944e6	−	2.03180e6i	0.102984	−	0.114375i
$795$	87666.3	+	834089.i	0.00491943	+	0.0468053i
$796$	−858766.	−	182536.i	−0.0480388	−	0.0102110i
$797$	−8.04624e6	+	3.58242e6i	−0.448691	+	0.199770i	−0.618627	−	0.785685i	$-0.712311\pi$
$797$	−8.04624e6	+	3.58242e6i	−0.448691	+	0.199770i	0.169936	+	0.985455i	$0.445644\pi$
$798$	390195.	+	283494.i	0.0216908	+	0.0157593i
$799$	−3.39507e6	−	1.51158e6i	−0.188141	−	0.0837656i
$800$	3.73810e6	+	6.47458e6i	0.206503	+	0.357673i
$801$	6.72003e6	−	1.16394e7i	0.370075	−	0.640989i
$802$	271660.	−	197372.i	0.0149138	−	0.0108355i
$803$	2.07951e7	−	4.42013e6i	1.13808	−	0.241906i
$804$	−1.43690e7	−	4.42232e7i	−0.783946	−	2.41274i
$805$	1.59638e7			0.868252
$806$	−4.98216e6	+	2.66117e6i	−0.270135	+	0.144290i
$807$	1.48795e7			0.804275
$808$	2.99368e6	+	9.21360e6i	0.161316	+	0.496479i
$809$	−2.44997e7	+	5.20757e6i	−1.31610	+	0.279746i	−0.811878	−	0.583827i	$-0.801555\pi$
$809$	−2.44997e7	+	5.20757e6i	−1.31610	+	0.279746i	−0.504224	+	0.863573i	$0.668221\pi$
$810$	1.74074e7	−	1.26472e7i	0.932228	−	0.677303i
$811$	8.80266e6	−	1.52466e7i	0.469961	−	0.813996i	−0.529449	−	0.848342i	$-0.677601\pi$
$811$	8.80266e6	−	1.52466e7i	0.469961	−	0.813996i	0.999410	+	0.0343456i	$0.0109347\pi$
$812$	−3.60386e6	−	6.24207e6i	−0.191813	−	0.332230i
$813$	−1.60452e7	−	7.14377e6i	−0.851369	−	0.379054i
$814$	−2.91185e6	−	2.11558e6i	−0.154031	−	0.111910i
$815$	−7.01599e6	+	3.12372e6i	−0.369994	+	0.164732i
$816$	2.35664e7	+	5.00920e6i	1.23899	+	0.263356i
$817$	−60768.2	−	578171.i	−0.00318509	−	0.0303041i
$818$	3.69324e6	−	4.10176e6i	0.192986	−	0.214332i
$819$	−1.63022e7	−	1.81054e7i	−0.849249	−	0.943187i
$820$	598434.	−	5.69372e6i	0.0310800	−	0.295707i
$821$	−1.17857e6	+	3.62726e6i	−0.0610235	+	0.187811i	−0.976921	−	0.213601i	$-0.931481\pi$
$821$	−1.17857e6	+	3.62726e6i	−0.0610235	+	0.187811i	0.915897	+	0.401413i	$0.131481\pi$
$822$	−126609.	+	389664.i	−0.00653562	+	0.0201146i
$823$	−1.95544e6	+	1.86048e7i	−0.100634	+	0.957469i	0.821398	+	0.570356i	$0.193195\pi$
$823$	−1.95544e6	+	1.86048e7i	−0.100634	+	0.957469i	−0.922032	+	0.387114i	$0.873472\pi$
$824$	−2.50886e6	−	2.78637e6i	−0.128724	−	0.142962i
$825$	−1.07594e7	+	1.19495e7i	−0.550368	+	0.611245i
$826$	259138.	+	2.46553e6i	0.0132154	+	0.125736i
$827$	−2.60775e7	−	5.54295e6i	−1.32587	−	0.281823i	−0.510061	−	0.860138i	$-0.670377\pi$
$827$	−2.60775e7	−	5.54295e6i	−1.32587	−	0.281823i	−0.815813	+	0.578315i	$0.803710\pi$
$828$	8.11732e7	−	3.61406e7i	4.11469	−	1.83198i
$829$	1.48554e7	+	1.07931e7i	0.750756	+	0.545456i	0.896061	−	0.443931i	$-0.146416\pi$
$829$	1.48554e7	+	1.07931e7i	0.750756	+	0.545456i	−0.145305	+	0.989387i	$0.546416\pi$
$830$	4.04224e6	+	1.79972e6i	0.203670	+	0.0906797i
$831$	2.31057e6	+	4.00203e6i	0.116069	+	0.201038i
$832$	−1.34421e6	+	2.32825e6i	−0.0673225	+	0.116606i
$833$	−1.23617e7	+	8.98129e6i	−0.617256	+	0.448463i
$834$	2.54081e7	−	5.40065e6i	1.26490	−	0.268863i
$835$	7.64560e6	+	2.35307e7i	0.379486	+	1.16794i
$836$	970934.			0.0480479
$837$	6.90118e7	−	4.95707e6i	3.40494	−	0.244575i
$838$	5.71858e6			0.281305
$839$	2.79632e6	+	8.60619e6i	0.137146	+	0.422091i	0.995918	−	0.0902671i	$-0.0287721\pi$
$839$	2.79632e6	+	8.60619e6i	0.137146	+	0.422091i	−0.858772	+	0.512358i	$0.828772\pi$
$840$	−1.27183e7	+	2.70335e6i	−0.621913	+	0.132192i
$841$	6.90696e6	−	5.01820e6i	0.336742	−	0.244657i
$842$	−5.71921e6	+	9.90597e6i	−0.278007	+	0.481523i
$843$	−1.33444e7	−	2.31131e7i	−0.646739	−	1.12018i
$844$	−2.47999e7	−	1.10416e7i	−1.19838	−	0.533552i
$845$	−5.11396e6	−	3.71551e6i	−0.246386	−	0.179010i
$846$	3.62710e6	−	1.61489e6i	0.174234	−	0.0775740i
$847$	570845.	+	121337.i	0.0273407	+	0.00581144i
$848$	−38991.4	−	370979.i	−0.00186200	−	0.0177157i
$849$	1.59734e7	−	1.77403e7i	0.760551	−	0.844677i
$850$	2.87717e6	+	3.19542e6i	0.136590	+	0.151698i
$851$	2.10113e6	−	1.99909e7i	0.0994554	−	0.946255i
$852$	2.95925e6	−	9.10764e6i	0.139663	−	0.429840i
$853$	−1.11863e7	+	3.44278e7i	−0.526396	+	1.62008i	0.235141	+	0.971961i	$0.424445\pi$
$853$	−1.11863e7	+	3.44278e7i	−0.526396	+	1.62008i	−0.761538	+	0.648121i	$0.775555\pi$
$854$	−435556.	+	4.14404e6i	−0.0204362	+	0.194437i
$855$	1.73471e6	+	1.92659e6i	0.0811543	+	0.0901309i
$856$	1.67893e7	−	1.86464e7i	0.783155	−	0.869782i
$857$	−2.79134e6	−	2.65578e7i	−0.129826	−	1.23521i	−0.844425	−	0.535674i	$-0.820058\pi$
$857$	−2.79134e6	−	2.65578e7i	−0.129826	−	1.23521i	0.714599	−	0.699534i	$-0.246609\pi$
$858$	1.22291e7	+	2.59937e6i	0.567120	+	0.120545i
$859$	−1.65226e7	+	7.35635e6i	−0.764005	+	0.340157i	−0.751472	−	0.659765i	$-0.770656\pi$
$859$	−1.65226e7	+	7.35635e6i	−0.764005	+	0.340157i	−0.0125325	+	0.999921i	$0.503989\pi$
$860$	5.79729e6	+	4.21198e6i	0.267288	+	0.194196i
$861$	−1.07809e7	−	4.79995e6i	−0.495616	−	0.220662i
$862$	4.18394e6	+	7.24680e6i	0.191786	+	0.332184i
$863$	2.02700e7	−	3.51086e7i	0.926459	−	1.60467i	0.137260	−	0.990535i	$-0.456170\pi$
$863$	2.02700e7	−	3.51086e7i	0.926459	−	1.60467i	0.789199	−	0.614138i	$-0.210496\pi$
$864$	−5.76063e7	+	4.18535e7i	−2.62534	+	1.90742i
$865$	−6.54950e6	+	1.39214e6i	−0.297624	+	0.0632619i
$866$	4.75126e6	+	1.46229e7i	0.215285	+	0.662579i
$867$	1.71883e7			0.776576
$868$	−1.04803e7	−	3.79206e6i	−0.472143	−	0.170835i
$869$	2.43602e7			1.09429
$870$	3.05184e6	+	9.39259e6i	0.136698	+	0.420714i
$871$	2.62362e7	−	5.57667e6i	1.17180	−	0.249075i
$872$	−1.45555e7	+	1.05752e7i	−0.648240	+	0.470974i
$873$	−4.29042e7	+	7.43123e7i	−1.90530	+	3.30008i
$874$	−507335.	−	878729.i	−0.0224655	−	0.0389114i
$875$	1.33032e7	+	5.92296e6i	0.587402	+	0.261528i
$876$	−3.57714e7	−	2.59894e7i	−1.57498	−	1.14429i
$877$	−3.79022e7	+	1.68752e7i	−1.66405	+	0.740882i	−0.999977	−	0.00678786i	$-0.997839\pi$
$877$	−3.79022e7	+	1.68752e7i	−1.66405	+	0.740882i	−0.664071	+	0.747670i	$0.731173\pi$
$878$	−2.77800e6	−	590483.i	−0.121618	−	0.0258506i
$879$	−706090.	−	6.71800e6i	−0.0308239	−	0.293270i
$880$	−6.22915e6	+	6.91817e6i	−0.271158	+	0.301151i
$881$	−2.16941e7	−	2.40938e7i	−0.941678	−	1.04584i	−0.998872	−	0.0474765i	$-0.984882\pi$
$881$	−2.16941e7	−	2.40938e7i	−0.941678	−	1.04584i	0.0571941	−	0.998363i	$-0.481785\pi$
$882$	1.70634e6	−	1.62347e7i	0.0738572	−	0.702705i
$883$	−261962.	+	806235.i	−0.0113067	+	0.0347985i	−0.956551	−	0.291566i	$-0.905824\pi$
$883$	−261962.	+	806235.i	−0.0113067	+	0.0347985i	0.945244	+	0.326365i	$0.105824\pi$
$884$	−5.52105e6	+	1.69920e7i	−0.237624	+	0.731332i
$885$	−1.89751e6	+	1.80536e7i	−0.0814379	+	0.774830i
$886$	−7.12790e6	−	7.91633e6i	−0.305054	−	0.338797i
$887$	2.32511e7	−	2.58229e7i	0.992279	−	1.10204i	−0.00250152	−	0.999997i	$-0.500796\pi$
$887$	2.32511e7	−	2.58229e7i	0.992279	−	1.10204i	0.994780	−	0.102040i	$-0.0325371\pi$
$888$	1.71136e6	+	1.62825e7i	0.0728296	+	0.692927i
$889$	1.54792e7	+	3.29021e6i	0.656893	+	0.139627i
$890$	1.72822e6	−	769453.i	0.0731348	−	0.0325617i
$891$	−7.22339e7	−	5.24810e7i	−3.04822	−	2.21466i
$892$	5.80072e6	+	2.58265e6i	0.244101	+	0.108681i
$893$	121147.	+	209833.i	0.00508376	+	0.00880533i
$894$	9.73762e6	−	1.68661e7i	0.407483	−	0.705781i
$895$	2.07867e7	−	1.51024e7i	0.867417	−	0.630215i
$896$	1.42896e7	−	3.03735e6i	0.594635	−	0.126394i
$897$	2.15764e7	+	6.64053e7i	0.895360	+	2.75563i
$898$	−1.02090e6			−0.0422465
$899$	−4.44511e6	+	1.79732e7i	−0.183435	+	0.741698i
$900$	2.45492e7			1.01025
$901$	−287584.	−	885093.i	−0.0118019	−	0.0363226i
$902$	4.34831e6	−	924261.i	0.177952	−	0.0378249i
$903$	1.19500e7	−	8.68216e6i	0.487694	−	0.354330i
$904$	−2.16058e6	+	3.74224e6i	−0.0879326	+	0.152304i
$905$	281440.	+	487468.i	0.0114226	+	0.0197845i
$906$	−2.75330e7	−	1.22585e7i	−1.11438	−	0.496154i
$907$	−9.97534e6	−	7.24751e6i	−0.402633	−	0.292530i	0.367979	−	0.929834i	$-0.380050\pi$
$907$	−9.97534e6	−	7.24751e6i	−0.402633	−	0.292530i	−0.770613	+	0.637304i	$0.780050\pi$
$908$	−588066.	+	261824.i	−0.0236707	+	0.0105389i
$909$	4.80050e7	+	1.02038e7i	1.92698	+	0.409592i
$910$	−358457.	−	3.41049e6i	−0.0143494	−	0.136525i
$911$	−1.84425e7	+	2.04824e7i	−0.736246	+	0.817685i	−0.988697	−	0.149925i	$-0.952097\pi$
$911$	−1.84425e7	+	2.04824e7i	−0.736246	+	0.817685i	0.252451	+	0.967610i	$0.418763\pi$
$912$	−1.05105e6	−	1.16731e6i	−0.0418444	−	0.0464730i
$913$	1.91926e6	−	1.82605e7i	0.0762002	−	0.724997i
$914$	3.13957e6	−	9.66260e6i	0.124310	−	0.382585i
$915$	−9.42855e6	+	2.90181e7i	−0.372299	+	1.14582i
$916$	1.54037e6	−	1.46556e7i	0.0606578	−	0.577120i
$917$	−1.29119e7	−	1.43401e7i	−0.507068	−	0.563156i
$918$	−2.74029e7	+	3.04341e7i	−1.07322	+	1.19194i
$919$	−3.24504e6	−	3.08745e7i	−0.126745	−	1.20590i	−0.854274	−	0.519823i	$-0.825998\pi$
$919$	−3.24504e6	−	3.08745e7i	−0.126745	−	1.20590i	0.727528	−	0.686078i	$-0.240669\pi$
$920$	2.67564e7	+	5.68725e6i	1.04222	+	0.221530i
$921$	−3.66733e6	+	1.63280e6i	−0.142463	+	0.0634284i
$922$	−3.18935e6	−	2.31720e6i	−0.123559	−	0.0897710i
$923$	5.04640e6	+	2.24680e6i	0.194974	+	0.0868081i
$924$	1.23347e7	+	2.13642e7i	0.475277	+	0.823204i
$925$	2.77679e6	−	4.80953e6i	0.106706	−	0.184820i
$926$	1.55132e7	−	1.12710e7i	0.594529	−	0.431950i
$927$	−1.85793e7	+	3.94915e6i	−0.710117	+	0.150940i
$928$	−5.88806e6	−	1.81216e7i	−0.224441	−	0.690758i
$929$	4.03759e7			1.53491			0.767455	−	0.641103i	$-0.221523\pi$
$929$	4.03759e7			1.53491			0.767455	+	0.641103i	$0.221523\pi$
$930$	1.29659e7	+	8.06791e6i	0.491582	+	0.305882i
$931$	996196.			0.0376678
$932$	3.02548e6	+	9.31148e6i	0.114092	+	0.351139i
$933$	−5.62540e7	+	1.19572e7i	−2.11568	+	0.449701i
$934$	−9.44241e6	+	6.86032e6i	−0.354173	+	0.257322i
$935$	−1.16128e7	+	2.01139e7i	−0.434417	+	0.752432i
$936$	−2.08733e7	−	3.61537e7i	−0.778758	−	1.34885i
$937$	−4.35607e6	−	1.93945e6i	−0.162086	−	0.0721654i	0.324090	−	0.946026i	$-0.394942\pi$
$937$	−4.35607e6	−	1.93945e6i	−0.162086	−	0.0721654i	−0.486176	+	0.873861i	$0.661609\pi$
$938$	−8.01215e6	−	5.82116e6i	−0.297332	−	0.216024i
$939$	7.54812e6	−	3.36064e6i	0.279367	−	0.124382i
$940$	−2.92128e6	−	620938.i	−0.107834	−	0.0229207i
$941$	−2.29556e6	−	2.18408e7i	−0.0845111	−	0.804070i	−0.951894	−	0.306428i	$-0.900866\pi$
$941$	−2.29556e6	−	2.18408e7i	−0.0845111	−	0.804070i	0.867383	−	0.497642i	$-0.165801\pi$
$942$	−6.48766e6	+	7.20527e6i	−0.238210	+	0.264559i
$943$	1.66125e7	+	1.84500e7i	0.608352	+	0.675643i
$944$	843958.	−	8.02972e6i	0.0308241	−	0.293272i
$945$	−1.29809e7	+	3.99510e7i	−0.472851	+	1.45529i
$946$	−1.71943e6	+	5.29186e6i	−0.0624678	+	0.192256i
$947$	−5.24877e6	+	4.99387e7i	−0.190188	+	1.80952i	0.317807	+	0.948156i	$0.397054\pi$
$947$	−5.24877e6	+	4.99387e7i	−0.190188	+	1.80952i	−0.507994	+	0.861360i	$0.669613\pi$
$948$	−3.39011e7	−	3.76510e7i	−1.22516	−	1.36068i
$949$	1.70664e7	−	1.89541e7i	0.615142	−	0.683184i
$950$	−29303.1	−	278800.i	−0.00105343	−	0.0100227i
$951$	−2.67648e7	−	5.68903e6i	−0.959650	−	0.203980i
$952$	1.31807e7	−	5.86842e6i	0.471352	−	0.209859i
$953$	7.70740e6	+	5.59975e6i	0.274901	+	0.199727i	0.716690	−	0.697392i	$-0.245656\pi$
$953$	7.70740e6	+	5.59975e6i	0.274901	+	0.199727i	−0.441790	+	0.897119i	$0.645656\pi$
$954$	908285.	+	404395.i	0.0323111	+	0.0143858i
$955$	9.87111e6	+	1.70973e7i	0.350233	+	0.606622i
$956$	−8.05969e6	+	1.39598e7i	−0.285216	+	0.494008i
$957$	3.31546e7	−	2.40882e7i	1.17021	−	0.850207i
$958$	3.59282e6	−	763677.i	0.126480	−	0.0268841i
$959$	−144107.	−	443517.i	−0.00505987	−	0.0155727i
$960$	7.26854e6			0.254548
$961$	1.26475e7	+	2.56840e7i	0.441771	+	0.897128i
$962$	−4.31802e6			−0.150434
$963$	−3.92792e7	−	1.20889e8i	−1.36489	−	4.20070i
$964$	4.09541e7	−	8.70506e6i	1.41940	−	0.301703i
$965$	−4.07143e6	+	2.95807e6i	−0.140744	+	0.102256i
$966$	1.28903e7	−	2.23266e7i	0.444446	−	0.769803i
$967$	−1.30139e7	−	2.25408e7i	−0.447550	−	0.775180i	0.550676	−	0.834719i	$-0.314370\pi$
$967$	−1.30139e7	−	2.25408e7i	−0.447550	−	0.775180i	−0.998226	+	0.0595396i	$0.981037\pi$
$968$	913548.	+	406738.i	0.0313360	+	0.0139517i
$969$	−3.17044e6	−	2.30346e6i	−0.108470	−	0.0788082i
$970$	−1.10339e7	+	4.91260e6i	−0.376529	+	0.167642i
$971$	8.26003e6	+	1.75572e6i	0.281147	+	0.0597596i	0.346327	−	0.938114i	$-0.387429\pi$
$971$	8.26003e6	+	1.75572e6i	0.281147	+	0.0597596i	−0.0651799	+	0.997874i	$0.520762\pi$
$972$	1.05568e7	+	1.00441e8i	0.358399	+	3.40994i
$973$	−1.97833e7	+	2.19715e7i	−0.669909	+	0.744009i
$974$	−4.46690e6	−	4.96100e6i	−0.150872	−	0.167561i
$975$	−2.01644e6	+	1.91851e7i	−0.0679319	+	0.646329i
$976$	4.19354e6	−	1.29064e7i	0.140915	−	0.433691i
$977$	1.38657e6	−	4.26742e6i	0.0464734	−	0.143031i	−0.925127	−	0.379657i	$-0.876042\pi$
$977$	1.38657e6	−	4.26742e6i	0.0464734	−	0.143031i	0.971601	+	0.236627i	$0.0760419\pi$
$978$	−1.29643e6	+	1.23347e7i	−0.0433413	+	0.412365i
$979$	−5.25275e6	−	5.83377e6i	−0.175158	−	0.194533i
$980$	−8.21639e6	+	9.12523e6i	−0.273285	+	0.303514i
$981$	9.52716e6	+	9.06449e7i	0.316076	+	3.00726i
$982$	1.30491e6	+	277368.i	0.0431820	+	0.00917862i
$983$	2.94709e6	−	1.31213e6i	0.0972769	−	0.0433105i	−0.357521	−	0.933905i	$-0.616378\pi$
$983$	2.94709e6	−	1.31213e6i	0.0972769	−	0.0433105i	0.454798	+	0.890595i	$0.349711\pi$
$984$	−1.63594e7	−	1.18858e7i	−0.538618	−	0.391329i
$985$	1.88333e7	+	8.38513e6i	0.618495	+	0.275372i
$986$	−5.47940e6	−	9.49061e6i	−0.179490	−	0.310886i
$987$	−3.07809e6	+	5.33140e6i	−0.100574	+	0.174200i
$988$	942369.	−	684671.i	0.0307135	−	0.0223146i
$989$	−3.03958e7	+	6.46082e6i	−0.988150	+	0.210038i
$990$	−7.66757e6	−	2.35984e7i	−0.248639	−	0.765233i
$991$	−2.22463e6			−0.0719572			−0.0359786	−	0.999353i	$-0.511455\pi$
$991$	−2.22463e6			−0.0719572			−0.0359786	+	0.999353i	$0.511455\pi$
$992$	−2.50157e7	−	1.55658e7i	−0.807113	−	0.502218i
$993$	3.93165e7			1.26532
$994$	−630274.	−	1.93978e6i	−0.0202331	−	0.0622712i
$995$	−1.33929e6	+	284675.i	−0.0428862	+	0.00911575i
$996$	−3.08943e7	+	2.24460e7i	−0.986801	+	0.716953i
$997$	1.27027e7	−	2.20016e7i	0.404722	−	0.700999i	−0.589567	−	0.807719i	$-0.700702\pi$
$997$	1.27027e7	−	2.20016e7i	0.404722	−	0.700999i	0.994289	+	0.106721i	$0.0340350\pi$
$998$	7.33801e6	+	1.27098e7i	0.233213	+	0.403936i
$999$	4.83208e7	+	2.15138e7i	1.53187	+	0.682030i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.6.g.a.7.8	✓	96
31.3	odd	30		961.6.a.k.1.28		48
31.9	even	15	inner	31.6.g.a.9.8	yes	96
31.28	even	15		961.6.a.j.1.28		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.6.g.a.7.8	✓	96	1.1	even	1	trivial
31.6.g.a.9.8	yes	96	31.9	even	15	inner
961.6.a.j.1.28		48	31.28	even	15
961.6.a.k.1.28		48	31.3	odd	30

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:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	31.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.694022 + 2.13598i) q^{2} +(-29.5682 + 6.28491i) q^{3} +(21.8078 - 15.8443i) q^{4} +(21.0196 - 36.4070i) q^{5} +(-33.9454 - 58.7951i) q^{6} +(70.5928 + 31.4300i) q^{7} +(107.121 + 77.8282i) q^{8} +(612.785 - 272.829i) q^{9} +(92.3528 + 19.6302i) q^{10} +(-40.9531 - 389.643i) q^{11} +(-545.237 + 605.547i) q^{12} +(-314.512 - 349.301i) q^{13} +(-18.1408 + 172.598i) q^{14} +(-392.697 + 1208.60i) q^{15} +(174.660 - 537.548i) q^{16} +(147.399 - 1402.40i) q^{17} +(1008.04 + 1119.55i) q^{18} +(-61.5169 + 68.3214i) q^{19} +(-118.452 - 1127.00i) q^{20} +(-2284.83 - 485.657i) q^{21} +(803.847 - 357.896i) q^{22} +(3975.65 + 2888.48i) q^{23} +(-3656.52 - 1627.99i) q^{24} +(678.852 + 1175.81i) q^{25} +(527.821 - 914.213i) q^{26} +(-10461.5 + 7600.73i) q^{27} +(2037.46 - 433.075i) q^{28} +(-1069.29 - 3290.94i) q^{29} -2854.08 q^{30} +(-4542.94 - 2826.80i) q^{31} +5506.51 q^{32} +(3659.78 + 11263.6i) q^{33} +(3097.81 - 658.459i) q^{34} +(2628.11 - 1909.43i) q^{35} +(9040.70 - 15658.9i) q^{36} +(-2045.21 - 3542.40i) q^{37} +(-188.627 - 83.9822i) q^{38} +(11494.9 + 8351.50i) q^{39} +(5085.14 - 2264.05i) q^{40} +(4941.71 + 1050.39i) q^{41} +(-548.373 - 5217.42i) q^{42} +(-4231.26 + 4699.29i) q^{43} +(-7066.71 - 7848.38i) q^{44} +(2947.59 - 28044.4i) q^{45} +(-3410.54 + 10496.6i) q^{46} +(814.409 - 2506.49i) q^{47} +(-1785.93 + 16992.0i) q^{48} +(-7250.57 - 8052.58i) q^{49} +(-2040.36 + 2266.05i) q^{50} +(4455.67 + 42392.9i) q^{51} +(-12393.2 - 2634.26i) q^{52} +(602.912 - 268.434i) q^{53} +(-23495.5 - 17070.5i) q^{54} +(-15046.6 - 6699.16i) q^{55} +(5115.86 + 8860.93i) q^{56} +(1389.55 - 2406.77i) q^{57} +(6287.27 - 4567.97i) q^{58} +(13972.7 - 2969.99i) q^{59} +(10585.5 + 32578.8i) q^{60} +24009.8 q^{61} +(2885.09 - 11665.5i) q^{62} +51833.2 q^{63} +(-1767.48 - 5439.75i) q^{64} +(-19327.9 + 4108.28i) q^{65} +(-21518.9 + 15634.4i) q^{66} +(-28532.5 + 49419.7i) q^{67} +(-19005.7 - 32918.8i) q^{68} +(-135706. - 60420.4i) q^{69} +(5902.47 + 4288.39i) q^{70} +(-10736.3 + 4780.12i) q^{71} +(86876.1 + 18466.1i) q^{72} +(5672.03 + 53965.7i) q^{73} +(6147.09 - 6827.03i) q^{74} +(-27462.2 - 30499.9i) q^{75} +(-259.043 + 2464.63i) q^{76} +(9355.46 - 28793.1i) q^{77} +(-9860.96 + 30348.9i) q^{78} +(-6499.26 + 61836.3i) q^{79} +(-15899.2 - 17657.9i) q^{80} +(152490. - 169358. i) q^{81} +(1186.04 + 11284.4i) q^{82} +(45840.6 + 9743.73i) q^{83} +(-57522.1 + 25610.5i) q^{84} +(-47959.1 - 34844.3i) q^{85} +(-12974.2 - 5776.47i) q^{86} +(52300.2 + 90586.7i) q^{87} +(25938.2 - 44926.4i) q^{88} +(16209.9 - 11777.2i) q^{89} +(61948.1 - 13167.5i) q^{90} +(-11223.8 - 34543.2i) q^{91} +132466. q^{92} +(152093. + 55031.4i) q^{93} +5919.04 q^{94} +(1194.32 + 3675.74i) q^{95} +(-162817. + 34607.9i) q^{96} +(-103493. + 75191.9i) q^{97} +(12168.1 - 21075.7i) q^{98} +(-131401. - 227594. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 6 q^{2} - 20 q^{3} - 346 q^{4} - 33 q^{5} + 283 q^{6} - 66 q^{7} - 271 q^{8} + 658 q^{9} + 896 q^{10} + 41 q^{11} - 1169 q^{12} + 149 q^{13} - 2 q^{14} + 4906 q^{15} - 2450 q^{16} - 3152 q^{17} - 3 q^{18}+ \cdots + 674326 q^{99}+O(q^{100}) \) 96 * q - 6 * q^2 - 20 * q^3 - 346 * q^4 - 33 * q^5 + 283 * q^6 - 66 * q^7 - 271 * q^8 + 658 * q^9 + 896 * q^10 + 41 * q^11 - 1169 * q^12 + 149 * q^13 - 2 * q^14 + 4906 * q^15 - 2450 * q^16 - 3152 * q^17 - 3 * q^18 - 5216 * q^19 + 7943 * q^20 - 14003 * q^21 - 8471 * q^22 + 13925 * q^23 + 25478 * q^24 - 18843 * q^25 + 12637 * q^26 + 3409 * q^27 - 10560 * q^28 + 6386 * q^29 - 25530 * q^30 - 39101 * q^31 + 31482 * q^32 + 17969 * q^33 - 18136 * q^34 + 5943 * q^35 - 9713 * q^36 + 40836 * q^37 + 18746 * q^38 + 55889 * q^39 + 15841 * q^40 - 46266 * q^41 + 8917 * q^42 - 137449 * q^43 + 28951 * q^44 + 69269 * q^45 - 97978 * q^46 + 5774 * q^47 - 112102 * q^48 - 146686 * q^49 + 58913 * q^50 + 149254 * q^51 + 263153 * q^52 + 62548 * q^53 + 144508 * q^54 + 13077 * q^55 - 103466 * q^56 + 68345 * q^57 - 52881 * q^58 - 149116 * q^59 + 65951 * q^60 - 204972 * q^61 - 62393 * q^62 - 80326 * q^63 - 205193 * q^64 - 296504 * q^65 - 268720 * q^66 - 105499 * q^67 + 497808 * q^68 + 448358 * q^69 + 351230 * q^70 + 93454 * q^71 + 192637 * q^72 + 74644 * q^73 - 83209 * q^74 - 323995 * q^75 - 446776 * q^76 - 249590 * q^77 - 588829 * q^78 + 396670 * q^79 - 236822 * q^80 + 616675 * q^81 + 449670 * q^82 + 518776 * q^83 + 578676 * q^84 + 463509 * q^85 - 95508 * q^86 - 360817 * q^87 + 238379 * q^88 + 239175 * q^89 - 1232679 * q^90 - 178840 * q^91 - 1350224 * q^92 - 65783 * q^93 + 580620 * q^94 - 276050 * q^95 - 1587604 * q^96 - 611799 * q^97 + 200092 * q^98 + 674326 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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