LMFDB - Embedded newform 62.6.g.b.41.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,6,Mod(7,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, 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("62.7"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	62.g (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [56,56] 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:	$9.94379682840$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			41.5
Character	$\chi$	$=$	62.41
Dual form			62.6.g.b.59.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.23607 + 2.35114i) q^{2} +(1.90823 + 18.1556i) q^{3} +(4.94427 + 15.2169i) q^{4} +(40.6803 + 70.4603i) q^{5} +(-36.5111 + 63.2392i) q^{6} +(-135.999 - 28.9075i) q^{7} +(-19.7771 + 60.8676i) q^{8} +(-88.2934 + 18.7673i) q^{9} +(-34.0180 + 323.660i) q^{10} +(415.393 - 461.341i) q^{11} +(-266.837 + 118.803i) q^{12} +(-246.472 - 109.736i) q^{13} +(-372.137 - 413.300i) q^{14} +(-1201.62 + 873.028i) q^{15} +(-207.108 + 150.473i) q^{16} +(936.006 + 1039.54i) q^{17} +(-329.848 - 146.858i) q^{18} +(-2227.00 + 991.522i) q^{19} +(-871.054 + 967.403i) q^{20} +(265.315 - 2524.30i) q^{21} +(2428.92 - 516.282i) q^{22} +(753.489 - 2319.00i) q^{23} +(-1142.83 - 242.915i) q^{24} +(-1747.27 + 3026.37i) q^{25} +(-539.595 - 934.606i) q^{26} +(861.616 + 2651.78i) q^{27} +(-232.534 - 2212.41i) q^{28} +(1905.13 + 1384.16i) q^{29} -5941.14 q^{30} +(5298.23 + 746.913i) q^{31} -1024.00 q^{32} +(9168.57 + 6661.36i) q^{33} +(584.874 + 5564.70i) q^{34} +(-3495.65 - 10758.5i) q^{35} +(-722.128 - 1250.76i) q^{36} +(-3990.35 + 6911.48i) q^{37} +(-9537.92 - 2027.35i) q^{38} +(1522.00 - 4684.24i) q^{39} +(-5093.29 + 1082.61i) q^{40} +(174.099 - 1656.44i) q^{41} +(6793.57 - 7545.02i) q^{42} +(12794.0 - 5696.27i) q^{43} +(9074.00 + 4040.00i) q^{44} +(-4914.16 - 5457.72i) q^{45} +(7890.64 - 5732.88i) q^{46} +(13609.9 - 9888.20i) q^{47} +(-3127.13 - 3473.03i) q^{48} +(2306.15 + 1026.76i) q^{49} +(-12769.7 + 5685.44i) q^{50} +(-17087.3 + 18977.4i) q^{51} +(451.224 - 4293.11i) q^{52} +(24572.3 - 5223.01i) q^{53} +(-3446.46 + 10607.1i) q^{54} +(49404.6 + 10501.3i) q^{55} +(4449.20 - 7706.23i) q^{56} +(-22251.3 - 38540.3i) q^{57} +(2910.78 + 8958.45i) q^{58} +(3467.37 + 32989.9i) q^{59} +(-19225.9 - 13968.5i) q^{60} -30580.8 q^{61} +(15389.3 + 14874.0i) q^{62} +12550.3 q^{63} +(-3313.73 - 2407.57i) q^{64} +(-2294.49 - 21830.6i) q^{65} +(14008.3 + 43113.2i) q^{66} +(-30660.3 - 53105.2i) q^{67} +(-11190.7 + 19382.9i) q^{68} +(43540.6 + 9254.84i) q^{69} +(13982.6 - 43034.0i) q^{70} +(45492.5 - 9669.74i) q^{71} +(603.863 - 5745.37i) q^{72} +(-26086.0 + 28971.4i) q^{73} +(-29162.9 + 12984.2i) q^{74} +(-58279.6 - 25947.7i) q^{75} +(-26098.8 - 28985.6i) q^{76} +(-69829.3 + 50734.0i) q^{77} +(15938.6 - 11580.1i) q^{78} +(-7240.15 - 8041.00i) q^{79} +(-19027.6 - 8471.64i) q^{80} +(-66538.7 + 29624.9i) q^{81} +(4457.91 - 4951.01i) q^{82} +(-4114.75 + 39149.3i) q^{83} +(39723.9 - 8443.57i) q^{84} +(-35169.3 + 108240. i) q^{85} +(54795.1 + 11647.1i) q^{86} +(-21494.7 + 37230.0i) q^{87} +(19865.5 + 34408.0i) q^{88} +(-25582.3 - 78734.2i) q^{89} +(-3070.67 - 29215.4i) q^{90} +(30347.8 + 22049.0i) q^{91} +39013.5 q^{92} +(-3450.40 + 97617.7i) q^{93} +67291.2 q^{94} +(-160458. - 116579. i) q^{95} +(-1954.02 - 18591.3i) q^{96} +(35677.1 + 109803. i) q^{97} +(5048.79 + 8744.76i) q^{98} +(-28018.3 + 48529.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 56 q^{2} - 7 q^{3} - 224 q^{4} + 91 q^{5} - 152 q^{6} - 94 q^{7} + 896 q^{8} + 896 q^{9} - 944 q^{10} - 31 q^{11} - 112 q^{12} - 1244 q^{13} + 856 q^{14} + 518 q^{15} - 3584 q^{16} + 1064 q^{17}+ \cdots - 625437 q^{99}+O(q^{100}) $ 56 * q + 56 * q^2 - 7 * q^3 - 224 * q^4 + 91 * q^5 - 152 * q^6 - 94 * q^7 + 896 * q^8 + 896 * q^9 - 944 * q^10 - 31 * q^11 - 112 * q^12 - 1244 * q^13 + 856 * q^14 + 518 * q^15 - 3584 * q^16 + 1064 * q^17 - 1724 * q^18 + 619 * q^19 - 1024 * q^20 + 9541 * q^21 + 124 * q^22 - 1717 * q^23 + 768 * q^24 - 24033 * q^25 - 1344 * q^26 + 22754 * q^27 + 1776 * q^28 + 11733 * q^29 + 13928 * q^30 + 57065 * q^31 - 57344 * q^32 - 11248 * q^33 - 10456 * q^34 - 7296 * q^35 - 42464 * q^36 - 1504 * q^37 - 29736 * q^38 - 19566 * q^39 + 4096 * q^40 + 35891 * q^41 + 40636 * q^42 + 66400 * q^43 + 23344 * q^44 - 27014 * q^45 - 7612 * q^46 + 36521 * q^47 - 3072 * q^48 + 121465 * q^49 - 13108 * q^50 - 236890 * q^51 - 19904 * q^52 - 143661 * q^53 - 91016 * q^54 + 106359 * q^55 + 5056 * q^56 + 13060 * q^57 + 59468 * q^58 + 230112 * q^59 + 8288 * q^60 - 49860 * q^61 + 26740 * q^62 + 66726 * q^63 - 57344 * q^64 + 201094 * q^65 - 30508 * q^66 + 74372 * q^67 - 4656 * q^68 - 599733 * q^69 + 29184 * q^70 + 23383 * q^71 - 27584 * q^72 - 66915 * q^73 + 186916 * q^74 + 553648 * q^75 - 152736 * q^76 + 120895 * q^77 + 142024 * q^78 - 452529 * q^79 - 50944 * q^80 - 365276 * q^81 - 14324 * q^82 - 469160 * q^83 - 50464 * q^84 - 127377 * q^85 + 215540 * q^86 + 217461 * q^87 + 39744 * q^88 - 155746 * q^89 + 820796 * q^90 - 142152 * q^91 - 5952 * q^92 + 342224 * q^93 + 29656 * q^94 + 756444 * q^95 + 7168 * q^96 + 325303 * q^97 + 533540 * q^98 - 625437 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{15}\right)$

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 $

$2$	3.23607	+	2.35114i	0.572061	+	0.415627i
$2$	3.23607	+	2.35114i	0.572061	+	0.415627i
$3$	1.90823	+	18.1556i	0.122413	+	1.16468i	0.867404	+	0.497605i	$0.165787\pi$
$3$	1.90823	+	18.1556i	0.122413	+	1.16468i	−0.744991	+	0.667075i	$0.767546\pi$
$4$	4.94427	+	15.2169i	0.154508	+	0.475528i
$5$	40.6803	+	70.4603i	0.727711	+	1.26043i	0.957848	+	0.287275i	$0.0927493\pi$
$5$	40.6803	+	70.4603i	0.727711	+	1.26043i	−0.230137	+	0.973158i	$0.573917\pi$
$6$	−36.5111	+	63.2392i	−0.414045	+	0.717147i
$7$	−135.999	−	28.9075i	−1.04904	−	0.222980i	−0.349027	−	0.937113i	$-0.613488\pi$
$7$	−135.999	−	28.9075i	−1.04904	−	0.222980i	−0.700010	+	0.714133i	$0.746821\pi$
$8$	−19.7771	+	60.8676i	−0.109254	+	0.336249i
$9$	−88.2934	+	18.7673i	−0.363347	+	0.0772319i
$10$	−34.0180	+	323.660i	−0.107574	+	1.02350i
$11$	415.393	−	461.341i	1.03509	−	1.14958i	0.0465039	−	0.998918i	$-0.485192\pi$
$11$	415.393	−	461.341i	1.03509	−	1.14958i	0.988585	−	0.150665i	$-0.0481413\pi$
$12$	−266.837	+	118.803i	−0.534925	+	0.238164i
$13$	−246.472	−	109.736i	−0.404492	−	0.180091i	0.194398	−	0.980923i	$-0.437725\pi$
$13$	−246.472	−	109.736i	−0.404492	−	0.180091i	−0.598890	+	0.800831i	$0.704391\pi$
$14$	−372.137	−	413.300i	−0.507437	−	0.563566i
$15$	−1201.62	+	873.028i	−1.37892	+	1.00184i
$16$	−207.108	+	150.473i	−0.202254	+	0.146946i
$17$	936.006	+	1039.54i	0.785518	+	0.872406i	0.994416	−	0.105531i	$-0.0336543\pi$
$17$	936.006	+	1039.54i	0.785518	+	0.872406i	−0.208898	+	0.977937i	$0.566988\pi$
$18$	−329.848	−	146.858i	−0.239957	−	0.106836i
$19$	−2227.00	+	991.522i	−1.41526	+	0.630113i	−0.964872	−	0.262721i	$-0.915380\pi$
$19$	−2227.00	+	991.522i	−1.41526	+	0.630113i	−0.450386	+	0.892834i	$0.648713\pi$
$20$	−871.054	+	967.403i	−0.486934	+	0.540795i
$21$	265.315	−	2524.30i	0.131284	−	1.24909i
$22$	2428.92	−	516.282i	1.06993	−	0.227421i
$23$	753.489	−	2319.00i	0.297001	−	0.914074i	−0.685542	−	0.728033i	$-0.740435\pi$
$23$	753.489	−	2319.00i	0.297001	−	0.914074i	0.982542	−	0.186040i	$-0.0595655\pi$
$24$	−1142.83	−	242.915i	−0.404997	−	0.0860848i
$25$	−1747.27	+	3026.37i	−0.559127	+	0.968437i
$26$	−539.595	−	934.606i	−0.156543	−	0.271141i
$27$	861.616	+	2651.78i	0.227460	+	0.700049i
$28$	−232.534	−	2212.41i	−0.0560520	−	0.533299i
$29$	1905.13	+	1384.16i	0.420658	+	0.305626i	0.777903	−	0.628385i	$-0.216284\pi$
$29$	1905.13	+	1384.16i	0.420658	+	0.305626i	−0.357244	+	0.934011i	$0.616284\pi$
$30$	−5941.14			−1.20522
$31$	5298.23	+	746.913i	0.990209	+	0.139594i
$31$	5298.23	+	746.913i	0.990209	+	0.139594i
$32$	−1024.00			−0.176777
$33$	9168.57	+	6661.36i	1.46560	+	1.06482i
$34$	584.874	+	5564.70i	0.0867690	+	0.825552i
$35$	−3495.65	−	10758.5i	−0.482345	−	1.48451i
$36$	−722.128	−	1250.76i	−0.0928662	−	0.160849i
$37$	−3990.35	+	6911.48i	−0.479189	+	0.829979i	−0.999715	−	0.0238666i	$-0.992402\pi$
$37$	−3990.35	+	6911.48i	−0.479189	+	0.829979i	0.520527	+	0.853845i	$0.325736\pi$
$38$	−9537.92	−	2027.35i	−1.07151	−	0.227756i
$39$	1522.00	−	4684.24i	0.160234	−	0.493149i
$40$	−5093.29	+	1082.61i	−0.503325	+	0.106985i
$41$	174.099	−	1656.44i	0.0161747	−	0.153892i	−0.983453	−	0.181161i	$-0.942014\pi$
$41$	174.099	−	1656.44i	0.0161747	−	0.153892i	0.999628	+	0.0272693i	$0.00868116\pi$
$42$	6793.57	−	7545.02i	0.594258	−	0.659990i
$43$	12794.0	−	5696.27i	1.05520	−	0.469807i	0.195556	−	0.980693i	$-0.437349\pi$
$43$	12794.0	−	5696.27i	1.05520	−	0.469807i	0.859649	+	0.510885i	$0.170682\pi$
$44$	9074.00	+	4040.00i	0.706589	+	0.314594i
$45$	−4914.16	−	5457.72i	−0.361758	−	0.401773i
$46$	7890.64	−	5732.88i	0.549816	−	0.399465i
$47$	13609.9	−	9888.20i	0.898693	−	0.652939i	−0.0394366	−	0.999222i	$-0.512556\pi$
$47$	13609.9	−	9888.20i	0.898693	−	0.652939i	0.938130	+	0.346283i	$0.112556\pi$
$48$	−3127.13	−	3473.03i	−0.195904	−	0.217573i
$49$	2306.15	+	1026.76i	0.137214	+	0.0610914i
$50$	−12769.7	+	5685.44i	−0.722364	+	0.321617i
$51$	−17087.3	+	18977.4i	−0.919917	+	1.02167i
$52$	451.224	−	4293.11i	0.0231411	−	0.220173i
$53$	24572.3	−	5223.01i	1.20159	−	0.255406i	0.436725	−	0.899595i	$-0.356138\pi$
$53$	24572.3	−	5223.01i	1.20159	−	0.255406i	0.764866	+	0.644189i	$0.222805\pi$
$54$	−3446.46	+	10607.1i	−0.160838	+	0.495009i
$55$	49404.6	+	10501.3i	2.20222	+	0.468096i
$56$	4449.20	−	7706.23i	0.189588	−	0.328377i
$57$	−22251.3	−	38540.3i	−0.907126	−	1.57119i
$58$	2910.78	+	8958.45i	0.113616	+	0.349674i
$59$	3467.37	+	32989.9i	0.129679	+	1.23382i	0.844903	+	0.534920i	$0.179658\pi$
$59$	3467.37	+	32989.9i	0.129679	+	1.23382i	−0.715223	+	0.698896i	$0.753675\pi$
$60$	−19225.9	−	13968.5i	−0.689460	−	0.500922i
$61$	−30580.8			−1.05226			−0.526132	−	0.850403i	$-0.676358\pi$
$61$	−30580.8			−1.05226			−0.526132	+	0.850403i	$0.676358\pi$
$62$	15389.3	+	14874.0i	0.508441	+	0.491414i
$63$	12550.3			0.398386
$64$	−3313.73	−	2407.57i	−0.101127	−	0.0734732i
$65$	−2294.49	−	21830.6i	−0.0673602	−	0.640889i
$66$	14008.3	+	43113.2i	0.395846	+	1.21829i
$67$	−30660.3	−	53105.2i	−0.834429	−	1.44527i	−0.894494	−	0.447079i	$-0.852464\pi$
$67$	−30660.3	−	53105.2i	−0.834429	−	1.44527i	0.0600652	−	0.998194i	$-0.480869\pi$
$68$	−11190.7	+	19382.9i	−0.293485	+	0.508330i
$69$	43540.6	+	9254.84i	1.10096	+	0.234016i
$70$	13982.6	−	43034.0i	0.341070	−	1.04970i
$71$	45492.5	−	9669.74i	1.07101	−	0.227651i	0.361520	−	0.932364i	$-0.382258\pi$
$71$	45492.5	−	9669.74i	1.07101	−	0.227651i	0.709492	+	0.704714i	$0.248925\pi$
$72$	603.863	−	5745.37i	0.0137280	−	0.130613i
$73$	−26086.0	+	28971.4i	−0.572928	+	0.636301i	−0.958062	−	0.286560i	$-0.907488\pi$
$73$	−26086.0	+	28971.4i	−0.572928	+	0.636301i	0.385135	+	0.922860i	$0.374155\pi$
$74$	−29162.9	+	12984.2i	−0.619087	+	0.275635i
$75$	−58279.6	−	25947.7i	−1.19636	−	0.532656i
$76$	−26098.8	−	28985.6i	−0.518306	−	0.575637i
$77$	−69829.3	+	50734.0i	−1.34218	+	0.975151i
$78$	15938.6	−	11580.1i	0.296630	−	0.215514i
$79$	−7240.15	−	8041.00i	−0.130521	−	0.144958i	0.674341	−	0.738420i	$-0.264428\pi$
$79$	−7240.15	−	8041.00i	−0.130521	−	0.144958i	−0.804862	+	0.593462i	$0.797761\pi$
$80$	−19027.6	−	8471.64i	−0.332399	−	0.147993i
$81$	−66538.7	+	29624.9i	−1.12684	+	0.501701i
$82$	4457.91	−	4951.01i	0.0732145	−	0.0813129i
$83$	−4114.75	+	39149.3i	−0.0655615	+	0.623776i	0.911571	+	0.411143i	$0.134870\pi$
$83$	−4114.75	+	39149.3i	−0.0655615	+	0.623776i	−0.977132	+	0.212632i	$0.931796\pi$
$84$	39723.9	−	8443.57i	0.614261	−	0.130565i
$85$	−35169.3	+	108240.i	−0.527979	+	1.62495i
$86$	54795.1	+	11647.1i	0.798906	+	0.169813i
$87$	−21494.7	+	37230.0i	−0.304463	+	0.527345i
$88$	19865.5	+	34408.0i	0.273459	+	0.473644i
$89$	−25582.3	−	78734.2i	−0.342345	−	1.05363i	−0.962990	−	0.269538i	$-0.913129\pi$
$89$	−25582.3	−	78734.2i	−0.342345	−	1.05363i	0.620644	−	0.784092i	$-0.286871\pi$
$90$	−3070.67	−	29215.4i	−0.0399601	−	0.380195i
$91$	30347.8	+	22049.0i	0.384170	+	0.279116i
$92$	39013.5			0.480557
$93$	−3450.40	+	97617.7i	−0.0413678	+	1.17036i
$94$	67291.2			0.785487
$95$	−160458.	−	116579.i	−1.82411	−	1.32530i
$96$	−1954.02	−	18591.3i	−0.0216397	−	0.205888i
$97$	35677.1	+	109803.i	0.385000	+	1.18491i	0.936480	+	0.350720i	$0.114063\pi$
$97$	35677.1	+	109803.i	0.385000	+	1.18491i	−0.551480	+	0.834188i	$0.685937\pi$
$98$	5048.79	+	8744.76i	0.0531033	+	0.0919777i
$99$	−28018.3	+	48529.2i	−0.287312	+	0.497640i
$100$	−54690.9	−	11624.9i	−0.546909	−	0.116249i
$101$	−16681.9	+	51341.7i	−0.162721	+	0.500803i	−0.998861	−	0.0477124i	$-0.984807\pi$
$101$	−16681.9	+	51341.7i	−0.162721	+	0.500803i	0.836140	+	0.548516i	$0.184807\pi$
$102$	−99914.2	+	21237.4i	−0.950883	+	0.202116i
$103$	16736.4	−	159236.i	0.155442	−	1.47893i	−0.587308	−	0.809364i	$-0.699812\pi$
$103$	16736.4	−	159236.i	0.155442	−	1.47893i	0.742750	−	0.669569i	$-0.233521\pi$
$104$	11553.9	−	12831.9i	0.104748	−	0.116334i
$105$	188656.	−	83995.2i	1.66993	−	0.743500i
$106$	91797.8	+	40871.0i	0.793537	+	0.353306i
$107$	40992.1	+	45526.4i	0.346131	+	0.384418i	0.890924	−	0.454153i	$-0.150058\pi$
$107$	40992.1	+	45526.4i	0.346131	+	0.384418i	−0.544792	+	0.838571i	$0.683391\pi$
$108$	−36091.8	+	26222.3i	−0.297749	+	0.216327i
$109$	30587.1	−	22222.8i	0.246588	−	0.179156i	−0.457625	−	0.889145i	$-0.651300\pi$
$109$	30587.1	−	22222.8i	0.246588	−	0.179156i	0.704213	+	0.709989i	$0.251300\pi$
$110$	135187.	+	150140.i	1.06525	+	1.18308i
$111$	−133096.	−	59258.3i	−1.02532	−	0.456501i
$112$	32516.3	−	14477.2i	0.244938	−	0.109054i
$113$	110969.	−	123244.i	0.817534	−	0.907963i	−0.179591	−	0.983741i	$-0.557477\pi$
$113$	110969.	−	123244.i	0.817534	−	0.907963i	0.997125	+	0.0757779i	$0.0241440\pi$
$114$	18607.1	−	177035.i	0.134096	−	1.27584i
$115$	194050.	−	41246.5i	1.36826	−	0.290832i
$116$	−11643.1	+	35833.8i	−0.0803386	+	0.247257i
$117$	23821.3	+	5063.38i	0.160880	+	0.0341961i
$118$	−66343.2	+	114910.i	−0.438623	+	0.759717i
$119$	−97245.4	−	168434.i	−0.629509	−	1.09034i
$120$	−29374.6	−	90405.7i	−0.186217	−	0.573116i
$121$	−23449.5	−	223107.i	−0.145603	−	1.38532i
$122$	−98961.6	−	71899.8i	−0.601959	−	0.437349i
$123$	30405.8			0.181215
$124$	14830.2	+	84315.6i	0.0866149	+	0.492441i
$125$	−30066.5			−0.172111
$126$	40613.8	+	29507.6i	0.227901	+	0.165580i
$127$	−23714.1	−	225625.i	−0.130466	−	1.24130i	−0.842322	−	0.538975i	$-0.818812\pi$
$127$	−23714.1	−	225625.i	−0.130466	−	1.24130i	0.711855	−	0.702326i	$-0.247855\pi$
$128$	−5062.93	−	15582.1i	−0.0273135	−	0.0840623i
$129$	127833.	+	221413.i	0.676346	+	1.17147i
$130$	43901.8	−	76040.1i	0.227837	−	0.394625i
$131$	−157167.	−	33406.8i	−0.800170	−	0.170081i	−0.210361	−	0.977624i	$-0.567464\pi$
$131$	−157167.	−	33406.8i	−0.800170	−	0.170081i	−0.589810	+	0.807542i	$0.700797\pi$
$132$	−56033.3	+	172453.i	−0.279906	+	0.861461i
$133$	331532.	−	70469.3i	1.62516	−	0.345438i
$134$	25639.0	−	243939.i	0.123350	−	1.17360i
$135$	−151795.	+	168585.i	−0.716840	+	0.796131i
$136$	−81785.8	+	36413.4i	−0.379167	+	0.168816i
$137$	135035.	+	60121.6i	0.614675	+	0.273671i	0.690366	−	0.723460i	$-0.257450\pi$
$137$	135035.	+	60121.6i	0.614675	+	0.273671i	−0.0756908	+	0.997131i	$0.524116\pi$
$138$	119141.	+	132319.i	0.532553	+	0.591460i
$139$	−119121.	+	86546.6i	−0.522940	+	0.379938i	−0.817710	−	0.575630i	$-0.804757\pi$
$139$	−119121.	+	86546.6i	−0.522940	+	0.379938i	0.294770	+	0.955568i	$0.404757\pi$
$140$	146428.	−	106386.i	0.631398	−	0.458738i
$141$	205497.	+	228227.i	0.870477	+	0.966762i
$142$	169952.	+	75667.4i	0.707302	+	0.314911i
$143$	−153009.	+	68123.9i	−0.625715	+	0.278586i
$144$	15462.3	−	17172.7i	0.0621396	−	0.0690130i
$145$	−20027.0	+	190544.i	−0.0791035	+	0.752619i
$146$	−152532.	+	32421.6i	−0.592213	+	0.125879i
$147$	−14240.8	+	43828.7i	−0.0543553	+	0.167288i
$148$	−124901.	−	26548.5i	−0.468717	−	0.0996289i
$149$	58108.7	−	100647.i	0.214425	−	0.371395i	−0.738669	−	0.674068i	$-0.764546\pi$
$149$	58108.7	−	100647.i	0.214425	−	0.371395i	0.953095	+	0.302673i	$0.0978789\pi$
$150$	−127590.	−	220992.i	−0.463008	−	0.801953i
$151$	−98420.8	−	302908.i	−0.351273	−	1.08111i	−0.958139	−	0.286302i	$-0.907574\pi$
$151$	−98420.8	−	302908.i	−0.351273	−	1.08111i	0.606867	−	0.794804i	$-0.292426\pi$
$152$	−16308.1	−	155161.i	−0.0572525	−	0.544722i
$153$	−102153.	−	74218.2i	−0.352793	−	0.256319i
$154$	−345255.			−1.17311
$155$	162906.	+	403700.i	0.544638	+	1.34968i
$156$	78804.9			0.259264
$157$	184556.	+	134088.i	0.597556	+	0.434149i	0.845010	−	0.534750i	$-0.179594\pi$
$157$	184556.	+	134088.i	0.597556	+	0.434149i	−0.247455	+	0.968899i	$0.579594\pi$
$158$	−4524.09	−	43043.9i	−0.0144175	−	0.137173i
$159$	141716.	+	436158.i	0.444557	+	1.36820i
$160$	−41656.6	−	72151.4i	−0.128642	−	0.222815i
$161$	−169510.	+	293600.i	−0.515384	+	0.892672i
$162$	−284976.	−	60573.6i	−0.853141	−	0.181341i
$163$	181094.	−	557352.i	0.533871	−	1.64309i	−0.212205	−	0.977225i	$-0.568065\pi$
$163$	181094.	−	557352.i	0.533871	−	1.64309i	0.746076	−	0.665860i	$-0.231935\pi$
$164$	26066.6	−	5540.63i	0.0756790	−	0.0160861i
$165$	−96381.3	+	917006.i	−0.275602	+	2.62218i
$166$	−105361.	+	117015.i	−0.296763	+	0.329589i
$167$	39148.3	−	17429.9i	0.108623	−	0.0483620i	−0.351706	−	0.936111i	$-0.614398\pi$
$167$	39148.3	−	17429.9i	0.108623	−	0.0483620i	0.460329	+	0.887749i	$0.347732\pi$
$168$	148401.	+	66072.4i	0.405662	+	0.180612i
$169$	−199737.	−	221830.i	−0.537950	−	0.597454i
$170$	−368298.	+	267584.i	−0.977411	+	0.710130i
$171$	178021.	−	129340.i	0.465565	−	0.338253i
$172$	149937.	+	166522.i	0.386445	+	0.429190i
$173$	36815.5	+	16391.3i	0.0935223	+	0.0416388i	0.452965	−	0.891528i	$-0.350366\pi$
$173$	36815.5	+	16391.3i	0.0935223	+	0.0416388i	−0.359442	+	0.933167i	$0.617033\pi$
$174$	−157091.	+	69941.6i	−0.393350	+	0.175131i
$175$	325112.	−	361074.i	0.802487	−	0.891253i
$176$	−16612.0	+	158053.i	−0.0404242	+	0.384610i
$177$	−592333.	+	125904.i	−1.42113	+	0.302070i
$178$	102329.	−	314937.i	0.242075	−	0.745029i
$179$	−624933.	−	132834.i	−1.45781	−	0.309867i	−0.590258	−	0.807215i	$-0.700974\pi$
$179$	−624933.	−	132834.i	−1.45781	−	0.309867i	−0.867551	+	0.497348i	$0.834307\pi$
$180$	58752.7	−	101763.i	0.135160	−	0.234103i
$181$	−278263.	−	481965.i	−0.631333	−	1.09350i	−0.987279	−	0.158995i	$-0.949175\pi$
$181$	−278263.	−	481965.i	−0.631333	−	1.09350i	0.355946	−	0.934507i	$-0.384159\pi$
$182$	46367.3	+	142704.i	0.103761	+	0.319343i
$183$	−58355.1	−	555212.i	−0.128810	−	1.22555i
$184$	126250.	+	91726.1i	0.274908	+	0.199732i
$185$	−649314.			−1.39484
$186$	−240679.	+	307785.i	−0.510100	+	0.652327i
$187$	868392.			1.81598
$188$	217759.	+	158211.i	0.449347	+	0.326470i
$189$	−40522.6	−	385547.i	−0.0825169	−	0.785096i
$190$	−245158.	−	754518.i	−0.492676	−	1.51630i
$191$	−123474.	−	213864.i	−0.244902	−	0.424183i	0.717202	−	0.696866i	$-0.245423\pi$
$191$	−123474.	−	213864.i	−0.244902	−	0.424183i	−0.962104	+	0.272682i	$0.912089\pi$
$192$	37387.4	−	64756.9i	0.0731935	−	0.126775i
$193$	912104.	+	193874.i	1.76259	+	0.374650i	0.971498	−	0.237049i	$-0.0761801\pi$
$193$	912104.	+	193874.i	1.76259	+	0.374650i	0.791091	+	0.611699i	$0.209513\pi$
$194$	−142709.	+	439212.i	−0.272236	+	0.837856i
$195$	391969.	−	83315.6i	0.738185	−	0.156906i
$196$	−4221.94	+	40169.0i	−0.00785003	+	0.0746881i
$197$	−152486.	+	169353.i	−0.279940	+	0.310905i	−0.866674	−	0.498875i	$-0.833747\pi$
$197$	−152486.	+	169353.i	−0.279940	+	0.310905i	0.586734	+	0.809780i	$0.300414\pi$
$198$	−204768.	+	91168.7i	−0.371193	+	0.165266i
$199$	−250843.	−	111683.i	−0.449024	−	0.199918i	0.169750	−	0.985487i	$-0.445704\pi$
$199$	−250843.	−	111683.i	−0.449024	−	0.199918i	−0.618774	+	0.785569i	$0.712371\pi$
$200$	−149652.	−	166205.i	−0.264549	−	0.293812i
$201$	905648.	−	657992.i	1.58114	−	1.14876i
$202$	−174696.	+	126924.i	−0.301234	+	0.218859i
$203$	−219083.	−	243317.i	−0.373138	−	0.414411i
$204$	−373261.	−	166187.i	−0.627968	−	0.279590i
$205$	123795.	−	55117.3i	0.205741	−	0.0916017i
$206$	428546.	−	475949.i	0.703607	−	0.781434i
$207$	−23006.6	+	218893.i	−0.0373187	+	0.355064i
$208$	67558.8	−	14360.1i	0.108274	−	0.0230143i
$209$	−467649.	+	1.43928e6i	−0.740550	+	2.27918i
$210$	807989.	+	171743.i	1.26432	+	0.268740i
$211$	−466172.	+	807433.i	−0.720841	+	1.24853i	0.239822	+	0.970817i	$0.422911\pi$
$211$	−466172.	+	807433.i	−0.720841	+	1.24853i	−0.960663	+	0.277717i	$0.910422\pi$
$212$	200970.	+	348091.i	0.307109	+	0.531928i
$213$	262370.	+	807491.i	0.396246	+	1.21952i
$214$	25614.4	+	243705.i	0.0382340	+	0.363772i
$215$	921827.	+	669746.i	1.36004	+	0.988130i
$216$	−178448.			−0.260242
$217$	−698963.	−	254738.i	−1.00764	−	0.367236i
$218$	151231.			0.215526
$219$	−575770.	−	418321.i	−0.811220	−	0.589386i
$220$	84472.8	+	803705.i	0.117669	+	1.11954i
$221$	−116624.	−	358932.i	−0.160623	−	0.494346i
$222$	−291384.	−	504692.i	−0.396811	−	0.687297i
$223$	464324.	−	804233.i	0.625258	−	1.08298i	−0.363233	−	0.931698i	$-0.618327\pi$
$223$	464324.	−	804233.i	0.625258	−	1.08298i	0.988491	−	0.151280i	$-0.0483394\pi$
$224$	139263.	+	29601.3i	0.185445	+	0.0394176i
$225$	97475.9	−	300000.i	0.128363	−	0.395062i
$226$	648867.	−	137921.i	0.845054	−	0.179622i
$227$	−146171.	+	1.39073e6i	−0.188277	+	1.79134i	0.338127	+	0.941100i	$0.390207\pi$
$227$	−146171.	+	1.39073e6i	−0.188277	+	1.79134i	−0.526404	+	0.850235i	$0.676460\pi$
$228$	476448.	−	529149.i	0.606986	−	0.674126i
$229$	−325058.	+	144725.i	−0.409611	+	0.182371i	−0.601189	−	0.799107i	$-0.705306\pi$
$229$	−325058.	+	144725.i	−0.409611	+	0.182371i	0.191578	+	0.981477i	$0.438640\pi$
$230$	724934.	+	322762.i	0.903606	+	0.402311i
$231$	−1.05435e6	−	1.17098e6i	−1.30004	−	1.44384i
$232$	−121928.	+	88586.1i	−0.148725	+	0.108055i
$233$	359073.	−	260882.i	0.433304	−	0.314814i	−0.349665	−	0.936875i	$-0.613705\pi$
$233$	359073.	−	260882.i	0.433304	−	0.314814i	0.782969	+	0.622061i	$0.213705\pi$
$234$	65182.7	+	72392.8i	0.0778203	+	0.0864282i
$235$	1.25038e6	+	556706.i	1.47698	+	0.657592i
$236$	−484860.	+	215874.i	−0.566678	+	0.252301i
$237$	132173.	−	146793.i	0.152852	−	0.169760i
$238$	81319.3	−	773702.i	0.0930575	−	0.885383i
$239$	1.43856e6	−	305775.i	1.62904	−	0.346264i	0.699402	−	0.714728i	$-0.253450\pi$
$239$	1.43856e6	−	305775.i	1.62904	−	0.346264i	0.929642	+	0.368464i	$0.120116\pi$
$240$	117498.	−	361623.i	0.131675	−	0.405254i
$241$	−713996.	−	151765.i	−0.791869	−	0.168317i	−0.205817	−	0.978590i	$-0.565985\pi$
$241$	−713996.	−	151765.i	−0.791869	−	0.168317i	−0.586052	+	0.810274i	$0.699319\pi$
$242$	448672.	−	777122.i	0.492482	−	0.853004i
$243$	−326056.	−	564746.i	−0.354223	−	0.613533i
$244$	−151200.	−	465345.i	−0.162584	−	0.500381i
$245$	21468.7	+	204261.i	0.0228502	+	0.217405i
$246$	98395.1	+	71488.3i	0.103666	+	0.0753177i
$247$	657699.			0.685938
$248$	−150246.	+	307719.i	−0.155123	+	0.317706i
$249$	−718629.			−0.734525
$250$	−97297.4	−	70690.7i	−0.0984580	−	0.0715339i
$251$	−132329.	−	1.25902e6i	−0.132577	−	1.26139i	−0.835247	−	0.549874i	$-0.814676\pi$
$251$	−132329.	−	1.25902e6i	−0.132577	−	1.26139i	0.702670	−	0.711516i	$-0.251991\pi$
$252$	62052.3	+	190977.i	0.0615540	+	0.189444i
$253$	−756855.	−	1.31091e6i	−0.743381	−	1.28757i
$254$	453735.	−	785892.i	0.441284	−	0.764326i
$255$	−2.03227e6	−	431972.i	−1.95718	−	0.416012i
$256$	20251.7	−	62328.4i	0.0193136	−	0.0594410i
$257$	−628768.	+	133649.i	−0.593824	+	0.126221i	−0.495014	−	0.868885i	$-0.664837\pi$
$257$	−628768.	+	133649.i	−0.593824	+	0.126221i	−0.0988102	+	0.995106i	$0.531504\pi$
$258$	−106898.	+	1.01706e6i	−0.0999812	+	0.951258i
$259$	742477.	−	824605.i	0.687755	−	0.763829i
$260$	320850.	−	142852.i	0.294353	−	0.131054i
$261$	−194187.	−	86457.8i	−0.176449	−	0.0785602i
$262$	−430058.	−	477628.i	−0.387056	−	0.429869i
$263$	−1.58455e6	+	1.15124e6i	−1.41259	+	1.02631i	−0.419649	+	0.907687i	$0.637847\pi$
$263$	−1.58455e6	+	1.15124e6i	−1.41259	+	1.02631i	−0.992940	+	0.118619i	$0.962153\pi$
$264$	−586788.	+	426327.i	−0.518169	+	0.376472i
$265$	1.36762e6	+	1.51890e6i	1.19633	+	1.32866i
$266$	1.23854e6	+	551435.i	1.07326	+	0.477848i
$267$	1.38065e6	−	614704.i	1.18524	−	0.527701i
$268$	656504.	−	729122.i	0.558342	−	0.620102i
$269$	−2146.64	+	20423.9i	−0.00180875	+	0.0172091i	−0.995389	−	0.0959200i	$-0.969421\pi$
$269$	−2146.64	+	20423.9i	−0.00180875	+	0.0172091i	0.993580	+	0.113129i	$0.0360874\pi$
$270$	−887585.	+	188662.i	−0.740970	+	0.157498i
$271$	−236694.	+	728469.i	−0.195778	+	0.602543i	0.804189	+	0.594374i	$0.202600\pi$
$271$	−236694.	+	728469.i	−0.195778	+	0.602543i	−0.999967	+	0.00816877i	$0.997400\pi$
$272$	−350277.	−	74453.7i	−0.287071	−	0.0610189i
$273$	−342401.	+	593056.i	−0.278053	+	0.481603i
$274$	295629.	+	512044.i	0.237887	+	0.412032i
$275$	670381.	+	2.06322e6i	0.534552	+	1.64518i
$276$	74446.5	+	708311.i	0.0588263	+	0.559695i
$277$	864822.	+	628330.i	0.677216	+	0.492026i	0.872433	−	0.488734i	$-0.162541\pi$
$277$	864822.	+	628330.i	0.677216	+	0.492026i	−0.195217	+	0.980760i	$0.562541\pi$
$278$	−588968.			−0.457067
$279$	−481817.	+	33486.3i	−0.370571	+	0.0257547i
$280$	723979.			0.551862
$281$	344042.	+	249961.i	0.259924	+	0.188846i	0.710113	−	0.704087i	$-0.248644\pi$
$281$	344042.	+	249961.i	0.259924	+	0.188846i	−0.450190	+	0.892933i	$0.648644\pi$
$282$	128407.	+	1.22171e6i	0.0961537	+	0.914841i
$283$	123384.	+	379737.i	0.0915784	+	0.281849i	0.986347	−	0.164681i	$-0.0526595\pi$
$283$	123384.	+	379737.i	0.0915784	+	0.281849i	−0.894768	+	0.446530i	$0.852659\pi$
$284$	372071.	+	644446.i	0.273735	+	0.474122i
$285$	1.81038e6	−	3.13566e6i	1.32025	−	2.28674i
$286$	−655316.	−	139292.i	−0.473735	−	0.100695i
$287$	−71560.7	+	220241.i	−0.0512826	+	0.157832i
$288$	90412.5	−	19217.8i	0.0642314	−	0.0136528i
$289$	−56120.5	+	533951.i	−0.0395255	+	0.376060i
$290$	−512804.	+	569527.i	−0.358061	+	0.397667i
$291$	−1.92545e6	+	857267.i	−1.33291	+	0.593450i
$292$	−569831.	−	253705.i	−0.391101	−	0.174129i
$293$	−1.41972e6	−	1.57676e6i	−0.966127	−	1.07299i	−0.997297	−	0.0734782i	$-0.976590\pi$
$293$	−1.41972e6	−	1.57676e6i	−0.966127	−	1.07299i	0.0311703	−	0.999514i	$-0.490077\pi$
$294$	−149132.	+	108351.i	−0.100624	+	0.0731077i
$295$	−2.18342e6	+	1.58635e6i	−1.46077	+	1.06131i
$296$	−341768.	−	379572.i	−0.226727	−	0.251805i
$297$	1.58128e6	+	704033.i	1.04020	+	0.463129i
$298$	424680.	−	189080.i	0.277026	−	0.123340i
$299$	−440193.	+	488884.i	−0.284751	+	0.316248i
$300$	106694.	−	1.01513e6i	0.0684444	−	0.651205i
$301$	−1.90464e6	+	404844.i	−1.21171	+	0.257556i
$302$	393683.	−	1.21163e6i	0.248387	−	0.764458i
$303$	−963971.	−	204898.i	−0.603195	−	0.128213i
$304$	312032.	−	540455.i	0.193649	−	0.335410i
$305$	−1.24404e6	−	2.15473e6i	−0.765744	−	1.32631i
$306$	−156075.	−	480350.i	−0.0952863	−	0.293261i
$307$	−137602.	−	1.30920e6i	−0.0833259	−	0.792793i	−0.953772	−	0.300530i	$-0.902837\pi$
$307$	−137602.	−	1.30920e6i	−0.0833259	−	0.792793i	0.870447	−	0.492263i	$-0.163830\pi$
$308$	−1.11727e6	−	811743.i	−0.671090	−	0.487576i
$309$	2.92296e6			1.74151
$310$	−421981.	+	1.68942e6i	−0.249395	+	0.998464i
$311$	−701095.			−0.411032			−0.205516	−	0.978654i	$-0.565887\pi$
$311$	−701095.			−0.411032			−0.205516	+	0.978654i	$0.565887\pi$
$312$	255018.	+	185281.i	0.148315	+	0.107757i
$313$	178541.	+	1.69870e6i	0.103009	+	0.980067i	0.916918	+	0.399075i	$0.130669\pi$
$313$	178541.	+	1.69870e6i	0.103009	+	0.980067i	−0.813909	+	0.580992i	$0.802665\pi$
$314$	281976.	+	867833.i	0.161394	+	0.496720i
$315$	510552.	+	884301.i	0.289910	+	0.502139i
$316$	86561.9	−	149930.i	0.0487651	−	0.0844636i
$317$	454777.	+	96665.9i	0.254185	+	0.0540288i	0.333242	−	0.942841i	$-0.391857\pi$
$317$	454777.	+	96665.9i	0.254185	+	0.0540288i	−0.0790565	+	0.996870i	$0.525191\pi$
$318$	−566865.	+	1.74463e6i	−0.314349	+	0.967467i
$319$	1.42995e6	−	303944.i	0.786761	−	0.167231i
$320$	34834.4	−	331427.i	0.0190166	−	0.180931i
$321$	−748335.	+	831110.i	−0.405353	+	0.450190i
$322$	−1.23884e6	+	551568.i	−0.665850	+	0.296456i
$323$	−3.11521e6	−	1.38698e6i	−1.66142	−	0.739714i
$324$	−779785.	−	866039.i	−0.412679	−	0.458327i
$325$	762757.	−	554175.i	0.400569	−	0.291031i
$326$	1.89645e6	−	1.37785e6i	0.988318	−	0.718055i
$327$	461835.	+	512919.i	0.238845	+	0.265265i
$328$	97380.2	+	43356.5i	0.0499788	+	0.0222520i
$329$	−2.13678e6	+	951357.i	−1.08835	+	0.484567i
$330$	−2.46791e6	+	2.74089e6i	−1.24751	+	1.38550i
$331$	−161046.	+	1.53225e6i	−0.0807940	+	0.768704i	0.876853	+	0.480759i	$0.159639\pi$
$331$	−161046.	+	1.53225e6i	−0.0807940	+	0.768704i	−0.957647	+	0.287945i	$0.907028\pi$
$332$	−616075.	+	130951.i	−0.306753	+	0.0652023i
$333$	222611.	−	685127.i	0.110011	−	0.338579i
$334$	167667.	+	35638.7i	0.0822396	+	0.0174806i
$335$	2.49454e6	−	4.32067e6i	1.21445	−	2.10348i
$336$	324891.	+	562727.i	0.156996	+	0.271925i
$337$	−652506.	−	2.00821e6i	−0.312975	−	0.963238i	−0.976580	−	0.215155i	$-0.930974\pi$
$337$	−652506.	−	2.00821e6i	−0.312975	−	0.963238i	0.663605	−	0.748083i	$-0.269026\pi$
$338$	−124808.	−	1.18747e6i	−0.0594225	−	0.565367i
$339$	2.44931e6	+	1.77953e6i	1.15756	+	0.841019i
$340$	−1.82097e6			−0.854288
$341$	2.54543e6	−	2.13403e6i	1.18543	−	0.993835i
$342$	880183.			0.406919
$343$	1.60656e6	+	1.16723e6i	0.737329	+	0.535701i
$344$	93689.8	+	891399.i	0.0426870	+	0.406140i
$345$	1.11915e6	+	3.44437e6i	0.506219	+	1.55798i
$346$	80599.1	+	139602.i	0.0361943	+	0.0626903i
$347$	−749363.	+	1.29794e6i	−0.334094	+	0.578668i	−0.983310	−	0.181936i	$-0.941764\pi$
$347$	−749363.	+	1.29794e6i	−0.334094	+	0.578668i	0.649216	+	0.760604i	$0.275097\pi$
$348$	−672801.	−	143008.i	−0.297809	−	0.0633014i
$349$	−525897.	+	1.61854e6i	−0.231120	+	0.711313i	0.766493	+	0.642253i	$0.222000\pi$
$349$	−525897.	+	1.61854e6i	−0.231120	+	0.711313i	−0.997612	+	0.0690603i	$0.978000\pi$
$350$	1.90102e6	−	404074.i	0.829501	−	0.176316i
$351$	78632.8	−	748141.i	0.0340672	−	0.324127i
$352$	−425363.	+	472413.i	−0.182980	+	0.203219i
$353$	1.93153e6	−	859974.i	0.825022	−	0.367323i	0.0496017	−	0.998769i	$-0.484205\pi$
$353$	1.93153e6	−	859974.i	0.825022	−	0.367323i	0.775420	+	0.631446i	$0.217538\pi$
$354$	−2.21285e6	−	985224.i	−0.938520	−	0.417856i
$355$	2.53198e6	+	2.81205e6i	1.06633	+	1.18427i
$356$	1.07160e6	−	778567.i	0.448136	−	0.325590i
$357$	2.87245e6	−	2.08696e6i	1.19284	−	0.866648i
$358$	−1.71001e6	−	1.89916e6i	−0.705167	−	0.783168i
$359$	−26248.8	−	11686.7i	−0.0107491	−	0.00478583i	0.401355	−	0.915923i	$-0.368539\pi$
$359$	−26248.8	−	11686.7i	−0.0107491	−	0.00478583i	−0.412104	+	0.911137i	$0.635206\pi$
$360$	429386.	−	191175.i	0.174619	−	0.0777455i
$361$	2.31956e6	−	2.57613e6i	0.936780	−	1.04040i
$362$	232691.	−	2.21391e6i	0.0933272	−	0.887949i
$363$	4.00589e6	−	851477.i	1.59563	−	0.339161i
$364$	−185469.	+	570815.i	−0.0733700	+	0.225809i
$365$	−3.10252e6	−	659461.i	−1.21894	−	0.259094i
$366$	1.11654e6	−	1.93390e6i	0.435684	−	0.754627i
$367$	1.54410e6	+	2.67446e6i	0.598427	+	1.03651i	0.993053	+	0.117664i	$0.0375406\pi$
$367$	1.54410e6	+	2.67446e6i	0.598427	+	1.03651i	−0.394627	+	0.918842i	$0.629126\pi$
$368$	192893.	+	593664.i	0.0742501	+	0.228518i
$369$	15715.2	+	149520.i	0.00600832	+	0.0571654i
$370$	−2.10122e6	−	1.52663e6i	−0.797936	−	0.579735i
$371$	−3.49280e6			−1.31746
$372$	−1.50250e6	+	430144.i	−0.562933	+	0.161160i
$373$	−3.42139e6			−1.27330			−0.636650	−	0.771153i	$-0.719680\pi$
$373$	−3.42139e6			−1.27330			−0.636650	+	0.771153i	$0.719680\pi$
$374$	2.81018e6	+	2.04171e6i	1.03885	+	0.754772i
$375$	−57373.8	−	545875.i	−0.0210686	−	0.200454i
$376$	332706.	+	1.02396e6i	0.121364	+	0.373521i
$377$	−317669.	−	550218.i	−0.115112	−	0.199380i
$378$	775341.	−	1.34293e6i	0.279102	−	0.483419i
$379$	−2.68047e6	−	569751.i	−0.958545	−	0.203745i	−0.298029	−	0.954557i	$-0.596329\pi$
$379$	−2.68047e6	−	569751.i	−0.958545	−	0.203745i	−0.660516	+	0.750812i	$0.729663\pi$
$380$	980631.	−	3.01807e6i	0.348375	−	1.07219i
$381$	4.05109e6	−	861086.i	1.42975	−	0.303902i
$382$	103253.	−	982383.i	0.0362028	−	0.344447i
$383$	2.04726e6	−	2.27372e6i	0.713143	−	0.792026i	−0.272267	−	0.962222i	$-0.587773\pi$
$383$	2.04726e6	−	2.27372e6i	0.713143	−	0.792026i	0.985410	+	0.170196i	$0.0544400\pi$
$384$	273241.	−	121655.i	0.0945622	−	0.0421018i
$385$	−6.41541e6	−	2.85632e6i	−2.20583	−	0.982100i
$386$	2.49581e6	+	2.77187e6i	0.852594	+	0.946902i
$387$	−1.02273e6	+	743054.i	−0.347122	+	0.252199i
$388$	−1.49446e6	+	1.08579e6i	−0.503971	+	0.366157i
$389$	3.17658e6	+	3.52795e6i	1.06435	+	1.18209i	0.982658	+	0.185428i	$0.0593673\pi$
$389$	3.17658e6	+	3.52795e6i	1.06435	+	1.18209i	0.0816970	+	0.996657i	$0.473966\pi$
$390$	1.46433e6	+	651960.i	0.487502	+	0.217050i
$391$	3.11596e6	−	1.38732e6i	1.03074	−	0.458916i
$392$	−108106.	+	120063.i	−0.0355331	+	0.0394635i
$393$	306610.	−	2.91720e6i	0.100139	−	0.952763i
$394$	−891630.	+	189522.i	−0.289364	+	0.0615062i
$395$	272040.	−	837254.i	0.0877285	−	0.270000i
$396$	−876994.	−	186411.i	−0.281034	−	0.0597356i
$397$	853382.	−	1.47810e6i	0.271748	−	0.470682i	−0.697561	−	0.716525i	$-0.745731\pi$
$397$	853382.	−	1.47810e6i	0.271748	−	0.470682i	0.969310	+	0.245843i	$0.0790648\pi$
$398$	−549164.	−	951180.i	−0.173778	−	0.300992i
$399$	1.91205e6	+	5.88468e6i	0.601266	+	1.85051i
$400$	−93511.6	−	889703.i	−0.0292224	−	0.278032i
$401$	2.99898e6	+	2.17889e6i	0.931349	+	0.676665i	0.946323	−	0.323223i	$-0.104766\pi$
$401$	2.99898e6	+	2.17889e6i	0.931349	+	0.676665i	−0.0149735	+	0.999888i	$0.504766\pi$
$402$	4.47777e6			1.38196
$403$	−1.22390e6	−	765503.i	−0.375392	−	0.234792i
$404$	−863743.			−0.263288
$405$	−4.79420e6	−	3.48319e6i	−1.45237	−	1.05521i
$406$	−136897.	−	1.30248e6i	−0.0412171	−	0.392155i
$407$	1.53099e6	+	4.71189e6i	0.458127	+	1.40997i
$408$	−817171.	−	1.41538e6i	−0.243032	−	0.420943i
$409$	−2.25759e6	+	3.91026e6i	−0.667323	+	1.15584i	0.311327	+	0.950303i	$0.399227\pi$
$409$	−2.25759e6	+	3.91026e6i	−0.667323	+	1.15584i	−0.978650	+	0.205535i	$0.934107\pi$
$410$	530199.	+	112697.i	0.155768	+	0.0331096i
$411$	−833863.	+	2.56637e6i	−0.243495	+	0.749401i
$412$	2.50583e6	−	532630.i	0.727291	−	0.154591i
$413$	482095.	−	4.58682e6i	0.139078	−	1.32323i
$414$	−589100.	+	654262.i	−0.168923	+	0.187608i
$415$	−2.92586e6	+	1.30268e6i	−0.833937	+	0.371293i
$416$	252388.	+	112370.i	0.0715047	+	0.0318359i
$417$	−1.79861e6	−	1.99756e6i	−0.506521	−	0.562549i
$418$	−4.89728e6	+	3.55809e6i	−1.37093	+	0.996037i
$419$	3.84371e6	−	2.79262e6i	1.06959	−	0.777100i	0.0937487	−	0.995596i	$-0.470115\pi$
$419$	3.84371e6	−	2.79262e6i	1.06959	−	0.777100i	0.975838	+	0.218496i	$0.0701150\pi$
$420$	2.21092e6	+	2.45547e6i	0.611574	+	0.679221i
$421$	−2.22602e6	−	991088.i	−0.612102	−	0.272525i	0.0771817	−	0.997017i	$-0.475408\pi$
$421$	−2.22602e6	−	991088.i	−0.612102	−	0.272525i	−0.689283	+	0.724492i	$0.742075\pi$
$422$	−3.40695e6	+	1.51687e6i	−0.931290	+	0.414637i
$423$	−1.01609e6	+	1.12849e6i	−0.276110	+	0.306651i
$424$	−168057.	+	1.59896e6i	−0.0453985	+	0.431938i
$425$	−4.78149e6	+	1.01634e6i	−1.28408	+	0.272939i
$426$	−1.04948e6	+	3.22996e6i	−0.280188	+	0.862330i
$427$	4.15896e6	+	884015.i	1.10386	+	0.234633i
$428$	−490094.	+	848868.i	−0.129321	+	0.223991i
$429$	−1.52880e6	−	2.64797e6i	−0.401059	−	0.694655i
$430$	1.40843e6	+	4.33469e6i	0.367336	+	1.13054i
$431$	−251230.	−	2.39029e6i	−0.0651446	−	0.619809i	−0.977576	−	0.210581i	$-0.932465\pi$
$431$	−251230.	−	2.39029e6i	−0.0651446	−	0.619809i	0.912432	−	0.409229i	$-0.134202\pi$
$432$	−577469.	−	419556.i	−0.148874	−	0.108163i
$433$	−4.27040e6			−1.09458			−0.547292	−	0.836942i	$-0.684341\pi$
$433$	−4.27040e6			−1.09458			−0.547292	+	0.836942i	$0.684341\pi$
$434$	−1.66297e6	−	2.46771e6i	−0.423799	−	0.628883i
$435$	−3.49765e6			−0.886244
$436$	489393.	+	355565.i	0.123294	+	0.0895782i
$437$	621324.	+	5.91150e6i	0.155638	+	1.48079i
$438$	−879698.	−	2.70743e6i	−0.219103	−	0.674330i
$439$	−2.56848e6	−	4.44873e6i	−0.636084	−	1.10173i	−0.986284	−	0.165055i	$-0.947220\pi$
$439$	−2.56848e6	−	4.44873e6i	−0.636084	−	1.10173i	0.350201	−	0.936675i	$-0.386113\pi$
$440$	−1.61626e6	+	2.79945e6i	−0.397998	+	0.689353i
$441$	−222887.	−	47376.2i	−0.0545744	−	0.0116001i
$442$	466496.	−	1.43573e6i	0.113577	−	0.349555i
$443$	−4.10083e6	+	871659.i	−0.992803	+	0.211027i	−0.675550	−	0.737314i	$-0.736094\pi$
$443$	−4.10083e6	+	871659.i	−0.992803	+	0.211027i	−0.317253	+	0.948341i	$0.602760\pi$
$444$	243664.	−	2.31830e6i	0.0586588	−	0.558101i
$445$	4.50694e6	−	5.00547e6i	1.07890	−	1.19824i
$446$	3.39345e6	−	1.51086e6i	0.807800	−	0.359656i
$447$	1.93819e6	+	862939.i	0.458805	+	0.204273i
$448$	381068.	+	423219.i	0.0897031	+	0.0996254i
$449$	−1.86907e6	+	1.35796e6i	−0.437533	+	0.317886i	−0.784654	−	0.619934i	$-0.787159\pi$
$449$	−1.86907e6	+	1.35796e6i	−0.437533	+	0.317886i	0.347121	+	0.937820i	$0.387159\pi$
$450$	1.02078e6	−	741641.i	0.237630	−	0.172648i
$451$	−691863.	−	768391.i	−0.160169	−	0.177886i
$452$	2.42405e6	+	1.07926e6i	0.558078	+	0.248472i
$453$	5.31166e6	−	2.36490e6i	1.21614	−	0.541462i
$454$	−3.74281e6	+	4.15681e6i	−0.852233	+	0.946501i
$455$	−319020.	+	3.03527e6i	−0.0722420	+	0.687336i
$456$	2.78592e6	−	592166.i	0.627418	−	0.133362i
$457$	−1.39160e6	+	4.28289e6i	−0.311690	+	0.959283i	0.665406	+	0.746482i	$0.268259\pi$
$457$	−1.39160e6	+	4.28289e6i	−0.311690	+	0.959283i	−0.977096	+	0.212801i	$0.931741\pi$
$458$	−1.39218e6	−	295917.i	−0.310121	−	0.0659183i
$459$	−1.95015e6	+	3.37777e6i	−0.432053	+	0.748338i
$460$	1.58708e6	+	2.74890e6i	0.349707	+	0.605710i
$461$	−588538.	−	1.81133e6i	−0.128980	−	0.396959i	0.865625	−	0.500692i	$-0.166921\pi$
$461$	−588538.	−	1.81133e6i	−0.128980	−	0.396959i	−0.994605	+	0.103733i	$0.966921\pi$
$462$	−658825.	−	6.26830e6i	−0.143604	−	1.36630i
$463$	5.82802e6	+	4.23430e6i	1.26348	+	0.917972i	0.998923	−	0.0463984i	$-0.0147744\pi$
$463$	5.82802e6	+	4.23430e6i	1.26348	+	0.917972i	0.264557	+	0.964370i	$0.414774\pi$
$464$	−602846.			−0.129991
$465$	−7.01854e6	+	3.72800e6i	−1.50527	+	0.799546i
$466$	1.77535e6			0.378721
$467$	−326066.	−	236901.i	−0.0691853	−	0.0502661i	0.552655	−	0.833410i	$-0.313615\pi$
$467$	−326066.	−	236901.i	−0.0691853	−	0.0502661i	−0.621840	+	0.783144i	$0.713615\pi$
$468$	40730.2	+	387522.i	0.00859610	+	0.0817865i
$469$	2.63463e6	+	8.10857e6i	0.553080	+	1.70221i
$470$	2.73743e6	+	4.74136e6i	0.571608	+	0.990054i
$471$	−2.08226e6	+	3.60658e6i	−0.432497	+	0.749107i
$472$	−2.07659e6	−	441393.i	−0.429038	−	0.0911948i
$473$	2.68663e6	−	8.26861e6i	0.552148	−	1.69934i
$474$	772853.	−	164275.i	0.157998	−	0.0335835i
$475$	890461.	−	8.47217e6i	0.181084	−	1.72290i
$476$	2.08224e6	−	2.31256e6i	0.421224	−	0.467816i
$477$	−2.07155e6	+	922315.i	−0.416869	+	0.185602i
$478$	5.37419e6	+	2.39275e6i	1.07583	+	0.478990i
$479$	−1.30920e6	−	1.45401e6i	−0.260715	−	0.289554i	0.598548	−	0.801087i	$-0.295744\pi$
$479$	−1.30920e6	−	1.45401e6i	−0.260715	−	0.289554i	−0.859264	+	0.511533i	$0.829078\pi$
$480$	1.23046e6	−	893981.i	0.243761	−	0.177103i
$481$	1.74195e6	−	1.26560e6i	0.343300	−	0.249422i
$482$	−1.95372e6	−	2.16983e6i	−0.383041	−	0.425410i
$483$	−5.65395e6	−	2.51730e6i	−1.10277	−	0.490984i
$484$	3.27906e6	−	1.45993e6i	0.636261	−	0.283282i
$485$	−6.28540e6	+	6.98064e6i	−1.21333	+	1.34754i
$486$	272657.	−	2.59416e6i	0.0523633	−	0.498203i
$487$	−1.00133e7	+	2.12839e6i	−1.91317	+	0.406657i	−1.00000		0.000919362i	$-0.999707\pi$
$487$	−1.00133e7	+	2.12839e6i	−1.91317	+	0.406657i	−0.913171	+	0.407576i	$0.866374\pi$
$488$	604799.	−	1.86138e6i	0.114964	−	0.353823i
$489$	1.04646e7	+	2.22432e6i	1.97902	+	0.420654i
$490$	−410772.	+	711479.i	−0.0772878	+	0.133866i
$491$	−1.29530e6	−	2.24353e6i	−0.242475	−	0.419979i	0.718944	−	0.695068i	$-0.244626\pi$
$491$	−1.29530e6	−	2.24353e6i	−0.242475	−	0.419979i	−0.961419	+	0.275089i	$0.911293\pi$
$492$	150334.	+	462682.i	0.0279992	+	0.0861727i
$493$	344325.	+	3.27604e6i	0.0638045	+	0.607060i
$494$	2.12836e6	+	1.54634e6i	0.392398	+	0.285094i
$495$	−4.55918e6			−0.836322
$496$	−1.20970e6	+	642549.i	−0.220787	+	0.117274i
$497$	−6.46647e6			−1.17429
$498$	−2.32553e6	−	1.68960e6i	−0.420193	−	0.305288i
$499$	86728.8	+	825169.i	0.0155924	+	0.148351i	0.999548	−	0.0300616i	$-0.00957035\pi$
$499$	86728.8	+	825169.i	0.0155924	+	0.148351i	−0.983956	+	0.178413i	$0.942904\pi$
$500$	−148657.	−	457520.i	−0.0265926	−	0.0818436i
$501$	391154.	+	677499.i	0.0696232	+	0.120591i
$502$	2.53192e6	−	4.38541e6i	0.448425	−	0.776695i
$503$	1.90518e6	+	404959.i	0.335751	+	0.0713660i	0.372702	−	0.927951i	$-0.378431\pi$
$503$	1.90518e6	+	404959.i	0.335751	+	0.0713660i	−0.0369514	+	0.999317i	$0.511765\pi$
$504$	−248209.	+	763909.i	−0.0435253	+	0.133957i
$505$	−4.29618e6	+	913182.i	−0.749643	+	0.159341i
$506$	632903.	−	6.02167e6i	0.109891	−	1.04554i
$507$	3.64631e6	−	4.04964e6i	0.629991	−	0.699676i
$508$	3.31606e6	−	1.47640e6i	0.570116	−	0.253832i
$509$	3.39497e6	+	1.51154e6i	0.580819	+	0.258597i	0.676047	−	0.736858i	$-0.263691\pi$
$509$	3.39497e6	+	1.51154e6i	0.580819	+	0.258597i	−0.0952282	+	0.995455i	$0.530358\pi$
$510$	−5.56094e6	−	6.17605e6i	−0.946722	−	1.05144i
$511$	4.38516e6	−	3.18600e6i	0.742904	−	0.539752i
$512$	212079.	−	154084.i	0.0357538	−	0.0259767i
$513$	−4.54812e6	−	5.05119e6i	−0.763024	−	0.847424i
$514$	−2.34896e6	−	1.04583e6i	−0.392165	−	0.174603i
$515$	1.19007e7	−	5.29852e6i	1.97721	−	0.880311i
$516$	−2.73718e6	+	3.03995e6i	−0.452564	+	0.502623i
$517$	1.09165e6	−	1.03863e7i	0.179620	−	1.70897i
$518$	4.34147e6	−	922808.i	0.710906	−	0.151108i
$519$	−227341.	+	699684.i	−0.0370476	+	0.114021i
$520$	1.37416e6	+	292086.i	0.222858	+	0.0473699i
$521$	2.18783e6	−	3.78942e6i	0.353117	−	0.611616i	−0.633677	−	0.773598i	$-0.718455\pi$
$521$	2.18783e6	−	3.78942e6i	0.353117	−	0.611616i	0.986794	+	0.161982i	$0.0517885\pi$
$522$	−425129.	−	736345.i	−0.0682880	−	0.118278i
$523$	1.09622e6	+	3.37383e6i	0.175245	+	0.539347i	0.999645	−	0.0266603i	$-0.00848724\pi$
$523$	1.09622e6	+	3.37383e6i	0.175245	+	0.539347i	−0.824400	+	0.566008i	$0.808487\pi$
$524$	−268727.	−	2.55676e6i	−0.0427546	−	0.406783i
$525$	7.17589e6	+	5.21359e6i	1.13626	+	0.825540i
$526$	−7.83443e6			−1.23465
$527$	4.18273e6	+	6.20684e6i	0.656045	+	0.973518i
$528$	−2.90124e6			−0.452897
$529$	397095.	+	288506.i	0.0616958	+	0.0448246i
$530$	854576.	+	8.13075e6i	0.132148	+	1.25731i
$531$	−925279.	−	2.84771e6i	−0.142409	−	0.438289i
$532$	2.71151e6	+	4.69647e6i	0.415367	+	0.719436i
$533$	−224682.	+	389161.i	−0.0342571	+	0.0593350i
$534$	5.91312e6	+	1.25687e6i	0.897354	+	0.190738i
$535$	−1.54023e6	+	4.74034e6i	−0.232649	+	0.716021i
$536$	3.83876e6	−	815953.i	0.577137	−	0.122674i
$537$	1.21915e6	−	1.15995e7i	0.182441	−	1.73581i
$538$	−54966.2	+	61046.2i	−0.00818729	+	0.00909291i
$539$	1.43165e6	−	637410.i	0.212258	−	0.0945033i
$540$	−3.31586e6	−	1.47631e6i	−0.489341	−	0.217868i
$541$	4.55081e6	+	5.05418e6i	0.668490	+	0.742434i	0.978033	−	0.208452i	$-0.0668424\pi$
$541$	4.55081e6	+	5.05418e6i	0.668490	+	0.742434i	−0.309542	+	0.950886i	$0.600176\pi$
$542$	−2.47869e6	+	1.80088e6i	−0.362430	+	0.263321i
$543$	8.21937e6	−	5.97172e6i	1.19630	−	0.869160i
$544$	−958470.	−	1.06449e6i	−0.138861	−	0.154221i
$545$	2.81012e6	+	1.25114e6i	0.405259	+	0.180433i
$546$	−2.50239e6	+	1.11414e6i	−0.359231	+	0.159940i
$547$	−3.09392e6	+	3.43614e6i	−0.442120	+	0.491024i	−0.922479	−	0.386048i	$-0.873840\pi$
$547$	−3.09392e6	+	3.43614e6i	−0.442120	+	0.491024i	0.480358	+	0.877072i	$0.340507\pi$
$548$	−247213.	+	2.35208e6i	−0.0351658	+	0.334580i
$549$	2.70008e6	−	573921.i	0.382337	−	0.0812682i
$550$	−2.68152e6	+	8.25288e6i	−0.377985	+	1.16332i
$551$	−5.61514e6	−	1.19353e6i	−0.787919	−	0.167477i
$552$	−1.42443e6	+	2.46718e6i	−0.198972	+	0.344630i
$553$	752209.	+	1.30286e6i	0.104599	+	0.181170i
$554$	1.32133e6	+	4.06664e6i	0.182910	+	0.562938i
$555$	−1.23904e6	−	1.17887e7i	−0.170747	−	1.62455i
$556$	−1.90594e6	−	1.38475e6i	−0.261470	−	0.189969i
$557$	−5.26273e6			−0.718742			−0.359371	−	0.933195i	$-0.617009\pi$
$557$	−5.26273e6			−0.718742			−0.359371	+	0.933195i	$0.617009\pi$
$558$	−1.63792e6	−	1.02446e6i	−0.222694	−	0.139286i
$559$	−3.77846e6			−0.511430
$560$	2.34284e6	+	1.70218e6i	0.315699	+	0.229369i
$561$	1.65709e6	+	1.57662e7i	0.222300	+	2.11504i
$562$	525650.	+	1.61778e6i	0.0702030	+	0.216063i
$563$	−6.63032e6	−	1.14840e7i	−0.881583	−	1.52695i	−0.849580	−	0.527459i	$-0.823145\pi$
$563$	−6.63032e6	−	1.14840e7i	−0.881583	−	1.52695i	−0.0320028	−	0.999488i	$-0.510189\pi$
$564$	−2.45688e6	+	4.25544e6i	−0.325227	+	0.563309i
$565$	1.31980e7	+	2.80533e6i	1.73936	+	0.369711i
$566$	−493536.	+	1.51895e6i	−0.0647557	+	0.199298i
$567$	9.90559e6	−	2.10550e6i	1.29397	−	0.275041i
$568$	−311136.	+	2.96026e6i	−0.0404650	+	0.384999i
$569$	−9.74053e6	+	1.08180e7i	−1.26125	+	1.40076i	−0.382171	+	0.924092i	$0.624823\pi$
$569$	−9.74053e6	+	1.08180e7i	−1.26125	+	1.40076i	−0.879082	+	0.476671i	$0.841843\pi$
$570$	1.32309e7	−	5.89077e6i	1.70570	−	0.759425i
$571$	4.53094e6	+	2.01731e6i	0.581565	+	0.258929i	0.676365	−	0.736567i	$-0.263554\pi$
$571$	4.53094e6	+	2.01731e6i	0.581565	+	0.258929i	−0.0947996	+	0.995496i	$0.530221\pi$
$572$	−1.79315e6	−	1.99150e6i	−0.229154	−	0.254501i
$573$	3.64720e6	−	2.64985e6i	0.464059	−	0.337158i
$574$	−749393.	+	544466.i	−0.0949358	+	0.0689749i
$575$	5.70159e6	+	6.33226e6i	0.719162	+	0.798710i
$576$	337765.	+	150382.i	0.0424187	+	0.0188860i
$577$	−2.14058e6	+	953049.i	−0.267666	+	0.119172i	−0.536181	−	0.844103i	$-0.680134\pi$
$577$	−2.14058e6	+	953049.i	−0.267666	+	0.119172i	0.268516	+	0.963275i	$0.413467\pi$
$578$	−1.43700e6	+	1.59595e6i	−0.178912	+	0.198701i
$579$	−1.77938e6	+	1.69297e7i	−0.220584	+	2.09871i
$580$	−2.99851e6	+	637353.i	−0.370114	+	0.0786701i
$581$	1.69131e6	−	5.20532e6i	0.207866	−	0.639745i
$582$	−8.24646e6	−	1.75284e6i	−1.00916	−	0.214504i
$583$	7.79759e6	−	1.35058e7i	0.950143	−	1.64570i
$584$	−1.24752e6	−	2.16076e6i	−0.151361	−	0.262165i
$585$	612291.	+	1.88444e6i	0.0739722	+	0.227663i
$586$	−887129.	−	8.44047e6i	−0.106719	−	1.01537i
$587$	−2.84354e6	−	2.06595e6i	−0.340615	−	0.247471i	0.404306	−	0.914624i	$-0.367513\pi$
$587$	−2.84354e6	−	2.06595e6i	−0.340615	−	0.247471i	−0.744921	+	0.667152i	$0.767513\pi$
$588$	−737348.			−0.0879487
$589$	−1.25397e7	+	3.58994e6i	−1.48936	+	0.426383i
$590$	−1.07954e7			−1.27676
$591$	−3.36568e6	−	2.44531e6i	−0.396374	−	0.287982i
$592$	−213558.	−	2.03187e6i	−0.0250444	−	0.238282i
$593$	−1.24612e6	−	3.83517e6i	−0.145520	−	0.447865i	0.851557	−	0.524262i	$-0.175659\pi$
$593$	−1.24612e6	−	3.83517e6i	−0.145520	−	0.447865i	−0.997078	+	0.0763963i	$0.975659\pi$
$594$	3.46186e6	+	5.99612e6i	0.402572	+	0.697275i
$595$	7.91195e6	−	1.37039e7i	0.916201	−	1.58691i
$596$	1.81884e6	+	386607.i	0.209739	+	0.0445815i
$597$	1.54899e6	−	4.76732e6i	0.177875	−	0.547442i
$598$	−2.57393e6	+	547106.i	−0.294336	+	0.0625631i
$599$	−1.49294e6	+	1.42044e7i	−0.170011	+	1.61754i	0.493754	+	0.869601i	$0.335624\pi$
$599$	−1.49294e6	+	1.42044e7i	−0.170011	+	1.61754i	−0.663765	+	0.747941i	$0.731042\pi$
$600$	2.73198e6	−	3.03417e6i	0.309813	−	0.344082i
$601$	−7.56024e6	+	3.36604e6i	−0.853787	+	0.380130i	−0.786490	−	0.617603i	$-0.788104\pi$
$601$	−7.56024e6	+	3.36604e6i	−0.853787	+	0.380130i	−0.0672966	+	0.997733i	$0.521437\pi$
$602$	−7.11540e6	−	3.16798e6i	−0.800218	−	0.356280i
$603$	3.70375e6	+	4.11343e6i	0.414809	+	0.460692i
$604$	4.12270e6	−	2.99532e6i	0.459822	−	0.334080i
$605$	1.47663e7	−	1.07283e7i	1.64014	−	1.19163i
$606$	−2.63773e6	−	2.92950e6i	−0.291776	−	0.324050i
$607$	−6.50546e6	−	2.89642e6i	−0.716649	−	0.319073i	0.0158184	−	0.999875i	$-0.494965\pi$
$607$	−6.50546e6	−	2.89642e6i	−0.716649	−	0.319073i	−0.732467	+	0.680802i	$0.761631\pi$
$608$	2.28044e6	−	1.01532e6i	0.250185	−	0.111389i
$609$	3.99949e6	−	4.44188e6i	0.436980	−	0.485315i
$610$	1.04030e6	−	9.89777e6i	0.113197	−	1.07699i
$611$	−4.43957e6	+	943659.i	−0.481103	+	0.102262i
$612$	624301.	−	1.92140e6i	0.0673776	−	0.207367i
$613$	4.51734e6	+	960191.i	0.485548	+	0.103206i	0.444180	−	0.895938i	$-0.353495\pi$
$613$	4.51734e6	+	960191.i	0.485548	+	0.103206i	0.0413679	+	0.999144i	$0.486828\pi$
$614$	2.63282e6	−	4.56018e6i	0.281838	−	0.488159i
$615$	1.23692e6	+	2.14240e6i	0.131872	+	0.228409i
$616$	−1.70703e6	−	5.25371e6i	−0.181255	−	0.557846i
$617$	−1.21956e6	−	1.16033e7i	−0.128970	−	1.22707i	−0.847205	−	0.531267i	$-0.821716\pi$
$617$	−1.21956e6	−	1.16033e7i	−0.128970	−	1.22707i	0.718235	−	0.695801i	$-0.244950\pi$
$618$	9.45889e6	+	6.87228e6i	0.996251	+	0.723819i
$619$	−3.21053e6			−0.336783			−0.168391	−	0.985720i	$-0.553857\pi$
$619$	−3.21053e6			−0.336783			−0.168391	+	0.985720i	$0.553857\pi$
$620$	−5.33761e6	+	4.47493e6i	−0.557658	+	0.467527i
$621$	6.79870e6			0.707452
$622$	−2.26879e6	−	1.64837e6i	−0.235136	−	0.170836i
$623$	1.20316e6	+	1.14473e7i	0.124195	+	1.18163i
$624$	389633.	+	1.19917e6i	0.0400584	+	0.123287i
$625$	4.23711e6	+	7.33890e6i	0.433880	+	0.751503i
$626$	−3.41611e6	+	5.91688e6i	−0.348415	+	0.603472i
$627$	−2.70232e7	−	5.74397e6i	−2.74517	−	0.583503i
$628$	−1.12790e6	+	3.47133e6i	−0.114123	+	0.351234i
$629$	−1.09197e7	+	2.32106e6i	−1.10049	+	0.233916i
$630$	−426937.	+	4.06204e6i	−0.0428561	+	0.407749i
$631$	−4.56941e6	+	5.07484e6i	−0.456864	+	0.507399i	−0.926931	−	0.375232i	$-0.877563\pi$
$631$	−4.56941e6	+	5.07484e6i	−0.456864	+	0.507399i	0.470067	+	0.882631i	$0.344230\pi$
$632$	632626.	−	281663.i	0.0630020	−	0.0280503i
$633$	−1.55490e7	−	6.92284e6i	−1.54238	−	0.686713i
$634$	1.24442e6	+	1.38206e6i	0.122954	+	0.136554i
$635$	1.49329e7	−	1.08494e7i	1.46964	−	1.06775i
$636$	−5.93629e6	+	4.31297e6i	−0.581932	+	0.422798i
$637$	−455728.	−	506137.i	−0.0444997	−	0.0494219i
$638$	5.34202e6	+	2.37842e6i	0.519581	+	0.231333i
$639$	−3.83522e6	+	1.70755e6i	−0.371567	+	0.165432i
$640$	891959.	−	990621.i	0.0860786	−	0.0955999i
$641$	−841596.	+	8.00725e6i	−0.0809018	+	0.769730i	0.876584	+	0.481249i	$0.159817\pi$
$641$	−841596.	+	8.00725e6i	−0.0809018	+	0.769730i	−0.957486	+	0.288481i	$0.906850\pi$
$642$	−4.37572e6	+	930088.i	−0.418998	+	0.0890607i
$643$	−5.65548e6	+	1.74058e7i	−0.539439	+	1.66022i	0.194418	+	0.980919i	$0.437718\pi$
$643$	−5.65548e6	+	1.74058e7i	−0.539439	+	1.66022i	−0.733857	+	0.679304i	$0.762282\pi$
$644$	−5.30579e6	−	1.12778e6i	−0.504122	−	0.107154i
$645$	−1.04006e7	+	1.80143e7i	−0.984369	+	1.70498i
$646$	−6.82004e6	−	1.18127e7i	−0.642992	−	1.11369i
$647$	457935.	+	1.40938e6i	0.0430074	+	0.132363i	0.970255	−	0.242086i	$-0.0778317\pi$
$647$	457935.	+	1.40938e6i	0.0430074	+	0.132363i	−0.927247	+	0.374449i	$0.877832\pi$
$648$	−487258.	−	4.63595e6i	−0.0455849	−	0.433712i
$649$	1.66599e7	+	1.21041e7i	1.55260	+	1.12803i
$650$	3.77128e6			0.350111
$651$	3.29113e6	−	1.31762e7i	0.304364	−	1.21853i
$652$	9.37655e6			0.863821
$653$	−913889.	−	663979.i	−0.0838707	−	0.0609357i	0.545060	−	0.838397i	$-0.316507\pi$
$653$	−913889.	−	663979.i	−0.0838707	−	0.0609357i	−0.628930	+	0.777462i	$0.716507\pi$
$654$	288583.	+	2.74568e6i	0.0263831	+	0.251018i
$655$	−4.03973e6	−	1.24330e7i	−0.367917	−	1.13233i
$656$	213192.	+	369259.i	0.0193424	+	0.0335021i
$657$	1.75950e6	−	3.04755e6i	0.159029	−	0.275446i
$658$	−9.15155e6	−	1.94522e6i	−0.824005	−	0.175148i
$659$	−6.58224e6	+	2.02581e7i	−0.590419	+	1.81712i	−0.0140967	+	0.999901i	$0.504487\pi$
$659$	−6.58224e6	+	2.02581e7i	−0.590419	+	1.81712i	−0.576322	+	0.817222i	$0.695513\pi$
$660$	−1.44305e7	+	3.06730e6i	−1.28950	+	0.274092i
$661$	1.84202e6	−	1.75256e7i	0.163980	−	1.56016i	−0.534895	−	0.844918i	$-0.679649\pi$
$661$	1.84202e6	−	1.75256e7i	0.163980	−	1.56016i	0.698875	−	0.715244i	$-0.253684\pi$
$662$	−4.12369e6	+	4.57982e6i	−0.365713	+	0.406166i
$663$	6.29406e6	−	2.80230e6i	0.556093	−	0.247588i
$664$	−2.30154e6	−	1.02471e6i	−0.202581	−	0.0901950i
$665$	1.84521e7	+	2.04931e7i	1.61805	+	1.79703i
$666$	2.33121e6	−	1.69373e6i	0.203656	−	0.147965i
$667$	4.64535e6	−	3.37505e6i	0.404300	−	0.293741i
$668$	458789.	+	509537.i	0.0397807	+	0.0441809i
$669$	1.54873e7	+	6.89541e6i	1.33786	+	0.595655i
$670$	1.82310e7	−	8.11697e6i	1.56900	−	0.698565i
$671$	−1.27031e7	+	1.41082e7i	−1.08919	+	1.20966i
$672$	−271682.	+	2.58489e6i	−0.0232080	+	0.220810i
$673$	6.52573e6	−	1.38709e6i	0.555381	−	0.118050i	0.0783333	−	0.996927i	$-0.475040\pi$
$673$	6.52573e6	−	1.38709e6i	0.555381	−	0.118050i	0.477048	+	0.878877i	$0.341707\pi$
$674$	2.61002e6	−	8.03283e6i	0.221307	−	0.681112i
$675$	−9.53074e6	−	2.02582e6i	−0.805132	−	0.171136i
$676$	2.38802e6	−	4.13617e6i	0.200988	−	0.348122i
$677$	1.51086e6	+	2.61689e6i	0.126693	+	0.219439i	0.922394	−	0.386251i	$-0.126230\pi$
$677$	1.51086e6	+	2.61689e6i	0.126693	+	0.219439i	−0.795700	+	0.605691i	$0.792897\pi$
$678$	3.74222e6	+	1.15174e7i	0.312647	+	0.962229i
$679$	−1.67793e6	−	1.59644e7i	−0.139669	−	1.32886i
$680$	−5.89277e6	−	4.28135e6i	−0.488705	−	0.355065i
$681$	−2.55283e7			−2.10938
$682$	1.32546e7	−	921194.i	1.09120	−	0.0758386i
$683$	9.13363e6			0.749190			0.374595	−	0.927189i	$-0.377782\pi$
$683$	9.13363e6			0.749190			0.374595	+	0.927189i	$0.377782\pi$
$684$	2.84833e6	+	2.06944e6i	0.232783	+	0.169126i
$685$	1.25709e6	+	1.19604e7i	0.102362	+	0.973910i
$686$	2.45460e6	+	7.55449e6i	0.199146	+	0.612908i
$687$	−3.24785e6	−	5.62544e6i	−0.262545	−	0.454742i
$688$	−1.79262e6	+	3.10490e6i	−0.144383	+	0.250079i
$689$	−6.62955e6	−	1.40915e6i	−0.532030	−	0.113086i
$690$	−4.47658e6	+	1.37775e7i	−0.357951	+	1.10166i
$691$	−1.24942e6	+	265573.i	−0.0995436	+	0.0211587i	−0.257414	−	0.966301i	$-0.582870\pi$
$691$	−1.24942e6	+	265573.i	−0.0995436	+	0.0211587i	0.157871	+	0.987460i	$0.449537\pi$
$692$	−67399.2	+	641261.i	−0.00535044	+	0.0509060i
$693$	5.21333e6	−	5.78998e6i	0.412365	−	0.457978i
$694$	−5.47662e6	+	2.43835e6i	−0.431632	+	0.192175i
$695$	−1.09440e7	−	4.87258e6i	−0.859437	−	0.382646i
$696$	−1.84100e6	−	2.04463e6i	−0.144056	−	0.159990i
$697$	1.88489e6	−	1.36945e6i	0.146962	−	0.106774i
$698$	−5.50726e6	+	4.00126e6i	−0.427856	+	0.310855i
$699$	5.42164e6	+	6.02135e6i	0.419699	+	0.466123i
$700$	7.10187e6	+	3.16196e6i	0.547807	+	0.243899i
$701$	7.66947e6	−	3.41467e6i	0.589481	−	0.262454i	−0.0902453	−	0.995920i	$-0.528765\pi$
$701$	7.66947e6	−	3.41467e6i	0.589481	−	0.262454i	0.679727	+	0.733466i	$0.262098\pi$
$702$	2.01345e6	−	2.23616e6i	0.154205	−	0.171262i
$703$	2.03360e6	−	1.93484e7i	0.155194	−	1.47658i
$704$	−2.48721e6	+	528673.i	−0.189139	+	0.0402027i
$705$	−7.72130e6	+	2.37637e7i	−0.585083	+	1.80070i
$706$	8.27249e6	+	1.75837e6i	0.624633	+	0.132770i
$707$	3.75289e6	−	6.50020e6i	0.282369	−	0.489078i
$708$	−4.84453e6	−	8.39097e6i	−0.363219	−	0.629114i
$709$	−5.81237e6	−	1.78886e7i	−0.434248	−	1.33648i	−0.893855	−	0.448356i	$-0.852010\pi$
$709$	−5.81237e6	−	1.78886e7i	−0.434248	−	1.33648i	0.459607	−	0.888122i	$-0.347990\pi$
$710$	1.58214e6	+	1.50530e7i	0.117787	+	1.12067i
$711$	790166.	+	574089.i	0.0586198	+	0.0425898i
$712$	5.29831e6			0.391685
$713$	5.72425e6	−	1.17238e7i	0.421691	−	0.863664i
$714$	1.42022e7			1.04258
$715$	−1.10245e7	−	8.00975e6i	−0.806479	−	0.585941i
$716$	−1.06852e6	−	1.01663e7i	−0.0778934	−	0.741106i
$717$	8.29662e6	+	2.55344e7i	0.602703	+	1.85493i
$718$	−57465.8	−	99533.8i	−0.00416005	−	0.00720542i
$719$	1.05572e7	−	1.82855e7i	0.761596	−	1.31912i	−0.180432	−	0.983587i	$-0.557750\pi$
$719$	1.05572e7	−	1.82855e7i	0.761596	−	1.31912i	0.942028	−	0.335535i	$-0.108917\pi$
$720$	1.83900e6	+	390892.i	0.132206	+	0.0281013i
$721$	−6.87925e6	+	2.11721e7i	−0.492836	+	1.51679i
$722$	1.35631e7	−	2.88293e6i	0.968314	−	0.205821i
$723$	1.39291e6	−	1.32526e7i	0.0991005	−	0.942878i
$724$	5.95821e6	−	6.61727e6i	0.422444	−	0.469172i
$725$	−7.51775e6	+	3.34712e6i	−0.531181	+	0.236497i
$726$	1.49653e7	+	6.66296e6i	1.05376	+	0.469165i
$727$	−1.30223e7	−	1.44628e7i	−0.913804	−	1.01488i	−0.999827	−	0.0185885i	$-0.994083\pi$
$727$	−1.30223e7	−	1.44628e7i	−0.913804	−	1.01488i	0.0860237	−	0.996293i	$-0.472584\pi$
$728$	−1.94226e6	+	1.41113e6i	−0.135825	+	0.0986824i
$729$	−4.68775e6	+	3.40585e6i	−0.326697	+	0.237359i
$730$	−8.48948e6	−	9.42852e6i	−0.589622	−	0.654842i
$731$	1.78968e7	+	7.96817e6i	1.23874	+	0.551525i
$732$	8.16008e6	−	3.63310e6i	0.562881	−	0.250611i
$733$	1.91241e7	−	2.12394e7i	1.31468	−	1.46010i	0.518448	−	0.855109i	$-0.326510\pi$
$733$	1.91241e7	−	2.12394e7i	1.31468	−	1.46010i	0.796232	−	0.604991i	$-0.206823\pi$
$734$	−1.29122e6	+	1.22852e7i	−0.0884628	+	0.841667i
$735$	−3.66751e6	+	779553.i	−0.250411	+	0.0532264i
$736$	−771573.	+	2.37466e6i	−0.0525028	+	0.161587i
$737$	−3.72357e7	−	7.91469e6i	−2.52517	−	0.536741i
$738$	−300687.	+	520805.i	−0.0203223	+	0.0351993i
$739$	9.14451e6	+	1.58388e7i	0.615956	+	1.06687i	0.990216	+	0.139543i	$0.0445634\pi$
$739$	9.14451e6	+	1.58388e7i	0.615956	+	1.06687i	−0.374260	+	0.927324i	$0.622103\pi$
$740$	−3.21039e6	−	9.88055e6i	−0.215515	−	0.663288i
$741$	1.25504e6	+	1.19409e7i	0.0839676	+	0.798898i
$742$	−1.13029e7	−	8.21206e6i	−0.753670	−	0.547574i
$743$	−3.47475e6			−0.230915			−0.115457	−	0.993312i	$-0.536833\pi$
$743$	−3.47475e6			−0.230915			−0.115457	+	0.993312i	$0.536833\pi$
$744$	−5.87352e6	−	2.14061e6i	−0.389015	−	0.141777i
$745$	9.45552e6			0.624158
$746$	−1.10718e7	−	8.04417e6i	−0.728405	−	0.529217i
$747$	−371422.	−	3.53385e6i	−0.0243538	−	0.231711i
$748$	4.29357e6	+	1.32142e7i	0.280585	+	0.863552i
$749$	−4.25884e6	−	7.37652e6i	−0.277387	−	0.480449i
$750$	1.09776e6	−	1.90138e6i	0.0712616	−	0.123429i
$751$	−2.00839e7	−	4.26896e6i	−1.29942	−	0.276199i	−0.494286	−	0.869299i	$-0.664571\pi$
$751$	−2.00839e7	−	4.26896e6i	−1.29942	−	0.276199i	−0.805129	+	0.593100i	$0.797904\pi$
$752$	−1.33082e6	+	4.09586e6i	−0.0858176	+	0.264119i
$753$	2.26058e7	−	4.80500e6i	1.45289	−	0.308821i
$754$	265643.	−	2.52743e6i	0.0170165	−	0.161901i
$755$	1.73392e7	−	1.92571e7i	1.10704	−	1.22949i
$756$	5.66648e6	−	2.52288e6i	0.360586	−	0.160543i
$757$	5.78343e6	+	2.57495e6i	0.366814	+	0.163316i	0.581862	−	0.813287i	$-0.302324\pi$
$757$	5.78343e6	+	2.57495e6i	0.366814	+	0.163316i	−0.215049	+	0.976603i	$0.568991\pi$
$758$	−7.33461e6	−	8.14591e6i	−0.463665	−	0.514952i
$759$	2.23561e7	−	1.62427e7i	1.40861	−	1.02342i
$760$	1.02693e7	−	7.46109e6i	0.644922	−	0.468563i
$761$	−1.23586e7	−	1.37257e7i	−0.773587	−	0.859155i	0.219612	−	0.975587i	$-0.429521\pi$
$761$	−1.23586e7	−	1.37257e7i	−0.773587	−	0.859155i	−0.993199	+	0.116432i	$0.962854\pi$
$762$	1.51341e7	+	6.73815e6i	0.944214	+	0.420391i
$763$	−4.80222e6	+	2.13808e6i	−0.298628	+	0.132958i
$764$	2.64385e6	−	2.93630e6i	0.163872	−	0.181998i
$765$	1.07384e6	−	1.02169e7i	0.0663417	−	0.631199i
$766$	1.19709e7	−	2.54450e6i	0.737149	−	0.156686i
$767$	2.76558e6	−	8.51158e6i	0.169745	−	0.522422i
$768$	1.17025e6	+	248745.i	0.0715940	+	0.0152178i
$769$	−5.46703e6	+	9.46917e6i	−0.333377	+	0.577426i	−0.983172	−	0.182684i	$-0.941522\pi$
$769$	−5.46703e6	+	9.46917e6i	−0.333377	+	0.577426i	0.649795	+	0.760110i	$0.274855\pi$
$770$	−1.40451e7	−	2.43268e7i	−0.853684	−	1.47862i
$771$	−3.62630e6	−	1.11606e7i	−0.219699	−	0.676164i
$772$	1.55953e6	+	1.48380e7i	0.0941784	+	0.896047i
$773$	7.86913e6	+	5.71726e6i	0.473673	+	0.344143i	0.798871	−	0.601503i	$-0.205431\pi$
$773$	7.86913e6	+	5.71726e6i	0.473673	+	0.344143i	−0.325198	+	0.945646i	$0.605431\pi$
$774$	−5.05663e6			−0.303396
$775$	−1.15179e7	+	1.47293e7i	−0.688841	+	0.880904i
$776$	−7.38903e6			−0.440487
$777$	1.63880e7	+	1.19066e7i	0.973807	+	0.707512i
$778$	1.98492e6	+	1.88853e7i	0.117570	+	1.11860i
$779$	1.25468e6	+	3.86150e6i	0.0740779	+	0.227988i
$780$	3.20581e6	+	5.55262e6i	0.188669	+	0.326785i
$781$	1.44362e7	−	2.50043e7i	0.846889	−	1.46686i
$782$	1.33452e7	+	2.83662e6i	0.780386	+	0.165876i
$783$	−2.02899e6	+	6.24460e6i	−0.118270	+	0.363999i
$784$	−632123.	+	134362.i	−0.0367292	+	0.00780703i
$785$	−1.94007e6	+	1.84586e7i	−0.112368	+	1.06911i
$786$	7.85096e6	−	8.71937e6i	0.453280	−	0.503418i
$787$	−1.41141e6	+	628400.i	−0.0812300	+	0.0361659i	−0.446949	−	0.894559i	$-0.647490\pi$
$787$	−1.41141e6	+	628400.i	−0.0812300	+	0.0361659i	0.365719	+	0.930725i	$0.380823\pi$
$788$	−3.33097e6	−	1.48304e6i	−0.191097	−	0.0850821i
$789$	−2.39251e7	−	2.65715e7i	−1.36824	−	1.51958i
$790$	2.84884e6	−	2.06981e6i	0.162406	−	0.117995i
$791$	−1.86544e7	+	1.35532e7i	−1.06008	+	0.770194i
$792$	−2.39973e6	−	2.66518e6i	−0.135941	−	0.150978i
$793$	7.53732e6	+	3.35583e6i	0.425632	+	0.189503i
$794$	6.23682e6	−	2.77681e6i	0.351085	−	0.156313i
$795$	−2.49668e7	+	2.77284e7i	−1.40102	+	1.55599i
$796$	459226.	−	4.36924e6i	0.0256888	−	0.244413i
$797$	1.63121e7	−	3.46724e6i	0.909628	−	0.193347i	0.270745	−	0.962651i	$-0.412730\pi$
$797$	1.63121e7	−	3.46724e6i	0.909628	−	0.193347i	0.638883	+	0.769304i	$0.279397\pi$
$798$	−7.64819e6	+	2.35387e7i	−0.425159	+	1.30851i
$799$	2.30182e7	+	4.89266e6i	1.27557	+	0.271130i
$800$	1.78921e6	−	3.09900e6i	0.0988407	−	0.171197i
$801$	3.73638e6	+	6.47160e6i	0.205764	+	0.356394i
$802$	4.58203e6	+	1.41020e7i	0.251549	+	0.774188i
$803$	2.52976e6	+	2.40690e7i	0.138449	+	1.31726i
$804$	1.44904e7	+	1.05279e7i	0.790568	+	0.574382i
$805$	−2.75829e7			−1.50020
$806$	−2.16083e6	−	5.35479e6i	−0.117161	−	0.290339i
$807$	−374905.			−0.0202645
$808$	−2.79513e6	−	2.03078e6i	−0.150617	−	0.109430i
$809$	−1.76429e6	−	1.67861e7i	−0.0947761	−	0.901734i	−0.933838	−	0.357697i	$-0.883562\pi$
$809$	−1.76429e6	−	1.67861e7i	−0.0947761	−	0.901734i	0.839061	−	0.544037i	$-0.183105\pi$
$810$	−7.32488e6	−	2.25437e7i	−0.392273	−	1.20729i
$811$	5.02991e6	+	8.71206e6i	0.268540	+	0.465124i	0.968485	−	0.249072i	$-0.0801257\pi$
$811$	5.02991e6	+	8.71206e6i	0.268540	+	0.465124i	−0.699945	+	0.714196i	$0.746792\pi$
$812$	2.61932e6	−	4.53679e6i	0.139411	−	0.241468i
$813$	−1.36774e7	−	2.90723e6i	−0.725736	−	0.154260i
$814$	−6.12395e6	+	1.88476e7i	−0.323944	+	0.996998i
$815$	4.66382e7	−	9.91325e6i	2.45950	−	0.522784i
$816$	683341.	−	6.50156e6i	0.0359263	−	0.341816i
$817$	−2.28443e7	+	2.53712e7i	−1.19735	+	1.32980i
$818$	−1.64993e7	+	7.34595e6i	−0.862147	+	0.383853i
$819$	−3.09331e6	−	1.37723e6i	−0.161144	−	0.0717459i
$820$	1.45079e6	+	1.61127e6i	0.0753479	+	0.0836823i
$821$	−2.23707e6	+	1.62532e6i	−0.115830	+	0.0841554i	−0.644192	−	0.764864i	$-0.722806\pi$
$821$	−2.23707e6	+	1.62532e6i	−0.115830	+	0.0841554i	0.528362	+	0.849019i	$0.322806\pi$
$822$	−8.73233e6	+	6.34441e6i	−0.450765	+	0.327500i
$823$	9.40883e6	+	1.04496e7i	0.484213	+	0.537773i	0.934901	−	0.354909i	$-0.115488\pi$
$823$	9.40883e6	+	1.04496e7i	0.484213	+	0.537773i	−0.450688	+	0.892681i	$0.648821\pi$
$824$	9.36132e6	+	4.16793e6i	0.480307	+	0.213847i
$825$	−3.61797e7	+	1.61082e7i	−1.85067	+	0.823973i
$826$	1.23444e7	−	1.37098e7i	0.629533	−	0.699167i
$827$	−510464.	+	4.85674e6i	−0.0259538	+	0.246934i	0.973851	+	0.227187i	$0.0729528\pi$
$827$	−510464.	+	4.85674e6i	−0.0259538	+	0.246934i	−0.999805	+	0.0197472i	$0.993714\pi$
$828$	−3.44463e6	+	732179.i	−0.174609	+	0.0371143i
$829$	6.84718e6	−	2.10735e7i	0.346039	−	1.06500i	−0.614986	−	0.788538i	$-0.710838\pi$
$829$	6.84718e6	−	2.10735e7i	0.346039	−	1.06500i	0.961025	−	0.276461i	$-0.0891618\pi$
$830$	−1.25311e7	−	2.66356e6i	−0.631383	−	0.134205i
$831$	−9.75741e6	+	1.69003e7i	−0.490153	+	0.848970i
$832$	552545.	+	957036.i	0.0276732	+	0.0479314i
$833$	1.09121e6	+	3.35839e6i	0.0544872	+	0.167694i
$834$	−1.12388e6	−	1.06930e7i	−0.0559508	−	0.532336i
$835$	2.82068e6	+	2.04935e6i	0.140003	+	0.101718i
$836$	−2.42135e7			−1.19823
$837$	2.58439e6	+	1.46933e7i	0.127510	+	0.724946i
$838$	1.90044e7			0.934853
$839$	−2.39283e7	−	1.73849e7i	−1.17356	−	0.852643i	−0.182132	−	0.983274i	$-0.558300\pi$
$839$	−2.39283e7	−	1.73849e7i	−1.17356	−	0.852643i	−0.991431	+	0.130631i	$0.958300\pi$
$840$	1.38152e6	+	1.31442e7i	0.0675550	+	0.642743i
$841$	−4.62467e6	−	1.42333e7i	−0.225471	−	0.693928i
$842$	−4.87336e6	−	8.44091e6i	−0.236891	−	0.410307i
$843$	−3.88168e6	+	6.72327e6i	−0.188127	+	0.325845i
$844$	−1.45915e7	−	3.10152e6i	−0.705089	−	0.149871i
$845$	7.50489e6	−	2.30977e7i	0.361578	−	1.11282i
$846$	−5.94137e6	+	1.26288e6i	−0.285405	+	0.0606646i
$847$	−3.26035e6	+	3.10202e7i	−0.156155	+	1.48572i
$848$	−4.30321e6	+	4.77920e6i	−0.205496	+	0.228226i
$849$	−6.65890e6	+	2.96473e6i	−0.317054	+	0.141162i
$850$	−1.78628e7	−	7.95301e6i	−0.848011	−	0.377559i
$851$	1.30211e7	+	1.44613e7i	0.616343	+	0.684518i
$852$	−1.09903e7	+	7.98491e6i	−0.518692	+	0.376852i
$853$	8.91545e6	−	6.47746e6i	0.419538	−	0.304812i	−0.357914	−	0.933754i	$-0.616512\pi$
$853$	8.91545e6	−	6.47746e6i	0.419538	−	0.304812i	0.777452	+	0.628943i	$0.216512\pi$
$854$	1.13802e7	+	1.26390e7i	0.533958	+	0.593020i
$855$	1.63553e7	+	7.28183e6i	0.765142	+	0.340663i
$856$	−3.58179e6	+	1.59471e6i	−0.167076	+	0.0743872i
$857$	−1.86384e7	+	2.07001e7i	−0.866877	+	0.962765i	−0.999597	−	0.0283890i	$-0.990962\pi$
$857$	−1.86384e7	+	2.07001e7i	−0.866877	+	0.962765i	0.132720	+	0.991154i	$0.457629\pi$
$858$	1.27843e6	−	1.21634e7i	0.0592868	−	0.564076i
$859$	2.41393e7	−	5.13096e6i	1.11620	−	0.237255i	0.387351	−	0.921932i	$-0.373390\pi$
$859$	2.41393e7	−	5.13096e6i	1.11620	−	0.237255i	0.728846	+	0.684677i	$0.240057\pi$
$860$	−5.63370e6	+	1.73388e7i	−0.259745	+	0.799414i
$861$	−4.13516e6	−	878955.i	−0.190101	−	0.0404072i
$862$	4.80692e6	−	8.32583e6i	0.220343	−	0.381645i
$863$	−7.95341e6	−	1.37757e7i	−0.363518	−	0.629632i	0.625019	−	0.780610i	$-0.285091\pi$
$863$	−7.95341e6	−	1.37757e7i	−0.363518	−	0.629632i	−0.988537	+	0.150978i	$0.951758\pi$
$864$	−882295.	−	2.71542e6i	−0.0402096	−	0.123752i
$865$	342728.	+	3.26083e6i	0.0155743	+	0.148180i
$866$	−1.38193e7	−	1.00403e7i	−0.626169	−	0.454938i
$867$	−9.80127e6			−0.442828
$868$	420461.	−	1.18956e7i	0.0189420	−	0.535902i
$869$	−6.71715e6			−0.301742
$870$	−1.13186e7	−	8.22347e6i	−0.506986	−	0.368347i
$871$	1.72933e6	+	1.64535e7i	0.0772384	+	0.734875i
$872$	747726.	+	2.30126e6i	0.0333005	+	0.102488i
$873$	−5.21077e6	−	9.02531e6i	−0.231401	−	0.400799i
$874$	−1.18881e7	+	2.05909e7i	−0.526423	+	0.911792i
$875$	4.08902e6	+	869149.i	0.180551	+	0.0383773i
$876$	3.51879e6	−	1.08297e7i	0.154929	−	0.476823i
$877$	1.65464e7	−	3.51704e6i	0.726447	−	0.154411i	0.170178	−	0.985413i	$-0.445566\pi$
$877$	1.65464e7	−	3.51704e6i	0.726447	−	0.154411i	0.556269	+	0.831002i	$0.312232\pi$
$878$	2.14783e6	−	2.04352e7i	0.0940294	−	0.894630i
$879$	2.59178e7	−	2.87847e7i	1.13143	−	1.25658i
$880$	−1.18123e7	+	5.25915e6i	−0.514193	+	0.228933i
$881$	−1.35410e7	−	6.02884e6i	−0.587775	−	0.261694i	0.0912278	−	0.995830i	$-0.470921\pi$
$881$	−1.35410e7	−	6.02884e6i	−0.587775	−	0.261694i	−0.679003	+	0.734136i	$0.737588\pi$
$882$	−609891.	−	677352.i	−0.0263986	−	0.0293186i
$883$	−9.87453e6	+	7.17426e6i	−0.426201	+	0.309653i	−0.780128	−	0.625620i	$-0.784846\pi$
$883$	−9.87453e6	+	7.17426e6i	−0.426201	+	0.309653i	0.353927	+	0.935273i	$0.384846\pi$
$884$	4.88521e6	−	3.54931e6i	0.210258	−	0.152761i
$885$	−3.29675e7	−	3.66142e7i	−1.41491	−	1.57142i
$886$	−1.53200e7	−	6.82089e6i	−0.655653	−	0.291915i
$887$	2.81033e7	−	1.25124e7i	1.19936	−	0.533989i	0.292842	−	0.956161i	$-0.405399\pi$
$887$	2.81033e7	−	1.25124e7i	1.19936	−	0.533989i	0.906516	+	0.422172i	$0.138732\pi$
$888$	6.23917e6	−	6.92930e6i	0.265518	−	0.294888i
$889$	−3.29715e6	+	3.13703e7i	−0.139921	+	1.33126i
$890$	2.63533e7	−	5.60157e6i	1.11522	−	0.237047i
$891$	−1.39725e7	+	4.30030e7i	−0.589632	+	1.81470i
$892$	1.45337e7	+	3.08923e6i	0.611594	+	0.129998i
$893$	−2.05049e7	+	3.55155e7i	−0.860457	+	1.49036i
$894$	4.24323e6	+	7.34949e6i	0.177563	+	0.307548i
$895$	−1.60629e7	−	4.94367e7i	−0.670298	−	2.06296i
$896$	238115.	+	2.26551e6i	0.00990869	+	0.0942748i
$897$	−9.71595e6	−	7.05905e6i	−0.403185	−	0.292931i
$898$	−9.24120e6			−0.382417
$899$	9.05997e6	+	8.75655e6i	0.373876	+	0.361355i
$900$	5.04702e6			0.207696
$901$	2.84294e7	+	2.06551e7i	1.16669	+	0.847649i
$902$	−432318.	−	4.11323e6i	−0.0176924	−	0.168332i
$903$	−1.09847e7	−	3.38073e7i	−0.448299	−	1.37972i
$904$	5.30690e6	+	9.19182e6i	0.215983	+	0.374094i
$905$	2.26396e7	−	3.92130e7i	0.918857	−	1.59151i
$906$	2.27491e7	+	4.83547e6i	0.920754	+	0.195712i
$907$	2.38053e6	−	7.32652e6i	0.0960850	−	0.295719i	−0.891450	−	0.453119i	$-0.850311\pi$
$907$	2.38053e6	−	7.32652e6i	0.0960850	−	0.295719i	0.987535	+	0.157400i	$0.0503112\pi$
$908$	−2.18852e7	+	4.65185e6i	−0.880921	+	0.187246i
$909$	509358.	−	4.84621e6i	0.0204462	−	0.194533i
$910$	−8.16873e6	+	9.07229e6i	−0.327002	+	0.363173i
$911$	1.24974e7	−	5.56421e6i	0.498913	−	0.222130i	−0.141822	−	0.989892i	$-0.545296\pi$
$911$	1.24974e7	−	5.56421e6i	0.498913	−	0.222130i	0.640735	+	0.767762i	$0.278630\pi$
$912$	1.04077e7	+	4.63381e6i	0.414350	+	0.184481i
$913$	1.63519e7	+	1.81606e7i	0.649220	+	0.721032i
$914$	−1.45730e7	+	1.05879e7i	−0.577009	+	0.419222i
$915$	3.67465e7	−	2.66979e7i	1.45099	−	1.05420i
$916$	−3.80944e6	−	4.23082e6i	−0.150011	−	0.166604i
$917$	2.04088e7	+	9.08660e6i	0.801484	+	0.356844i
$918$	−1.42524e7	+	6.34559e6i	−0.558190	+	0.248522i
$919$	−3.78948e6	+	4.20864e6i	−0.148010	+	0.164381i	−0.812591	−	0.582835i	$-0.801943\pi$
$919$	−3.78948e6	+	4.20864e6i	−0.148010	+	0.164381i	0.664581	+	0.747216i	$0.268610\pi$
$920$	−1.32716e6	+	1.26271e7i	−0.0516956	+	0.491851i
$921$	2.35067e7	−	4.99650e6i	0.913150	−	0.194096i
$922$	2.35415e6	−	7.24533e6i	0.0912025	−	0.280693i
$923$	−1.22738e7	−	2.60887e6i	−0.474213	−	0.100797i
$924$	1.26057e7	−	2.18336e7i	0.485720	−	0.841291i
$925$	−1.39445e7	−	2.41525e7i	−0.535855	−	0.928128i
$926$	8.90442e6	+	2.74050e7i	0.341254	+	1.05027i
$927$	1.51073e6	+	1.43736e7i	0.0577413	+	0.549371i
$928$	−1.95085e6	−	1.41738e6i	−0.0743626	−	0.0540276i
$929$	−2.98079e7			−1.13316			−0.566580	−	0.824007i	$-0.691734\pi$
$929$	−2.98079e7			−1.13316			−0.566580	+	0.824007i	$0.691734\pi$
$930$	−3.14775e7	−	4.43751e6i	−1.19342	−	0.168241i
$931$	−6.15384e6			−0.232687
$932$	5.74516e6	+	4.17410e6i	0.216652	+	0.157407i
$933$	−1.33785e6	−	1.27288e7i	−0.0503156	−	0.478721i
$934$	−498185.	−	1.53326e6i	−0.0186863	−	0.0575106i
$935$	3.53265e7	+	6.11872e7i	1.32151	+	2.28893i
$936$	−779313.	+	1.34981e6i	−0.0290752	+	0.0503596i
$937$	5.29950e6	+	1.12644e6i	0.197191	+	0.0419142i	0.305448	−	0.952209i	$-0.401194\pi$
$937$	5.29950e6	+	1.12644e6i	0.197191	+	0.0419142i	−0.108257	+	0.994123i	$0.534527\pi$
$938$	−1.05385e7	+	3.24343e7i	−0.391087	+	1.20364i
$939$	−3.05002e7	+	6.48301e6i	−1.12885	+	0.239946i
$940$	−2.28911e6	+	2.17795e7i	−0.0844982	+	0.803947i
$941$	1.65920e7	−	1.84272e7i	0.610835	−	0.678401i	−0.355799	−	0.934562i	$-0.615791\pi$
$941$	1.65920e7	−	1.84272e7i	0.610835	−	0.678401i	0.966634	+	0.256162i	$0.0824580\pi$
$942$	−1.52179e7	+	6.77546e6i	−0.558764	+	0.248778i
$943$	−3.71010e6	−	1.65184e6i	−0.135864	−	0.0604908i
$944$	−5.68221e6	−	6.31073e6i	−0.207533	−	0.230489i
$945$	2.55173e7	−	1.85394e7i	0.929512	−	0.675330i
$946$	2.81348e7	−	2.04411e7i	1.02215	−	0.742638i
$947$	2.57669e7	+	2.86170e7i	0.933656	+	1.03693i	0.999236	+	0.0390822i	$0.0124434\pi$
$947$	2.57669e7	+	2.86170e7i	0.933656	+	1.03693i	−0.0655805	+	0.997847i	$0.520890\pi$
$948$	2.88724e6	+	1.28548e6i	0.104343	+	0.0464563i
$949$	9.60868e6	−	4.27806e6i	0.346337	−	0.154199i
$950$	2.28008e7	−	2.53229e7i	0.819676	−	0.910342i
$951$	−887206.	+	8.44120e6i	−0.0318107	+	0.302659i
$952$	1.21754e7	−	2.58796e6i	0.435403	−	0.0925477i
$953$	1.51887e7	−	4.67459e7i	0.541736	−	1.66729i	−0.186891	−	0.982381i	$-0.559841\pi$
$953$	1.51887e7	−	4.67459e7i	0.541736	−	1.66729i	0.728627	−	0.684911i	$-0.240159\pi$
$954$	−8.87218e6	−	1.88584e6i	−0.315616	−	0.0670863i
$955$	1.00459e7	−	1.74001e7i	0.356437	−	0.617366i
$956$	1.17656e7	+	2.03786e7i	0.416359	+	0.721156i
$957$	8.24694e6	+	2.53815e7i	0.291081	+	0.895854i
$958$	−818067.	−	7.78339e6i	−0.0287988	−	0.274003i
$959$	−1.66267e7	−	1.20800e7i	−0.583794	−	0.424151i
$960$	6.08372e6			0.213055
$961$	2.75134e7	+	7.91464e6i	0.961027	+	0.276454i
$962$	8.61268e6			0.300055
$963$	−4.47374e6	−	3.25036e6i	−0.155455	−	0.112945i
$964$	−1.22080e6	−	1.16152e7i	−0.0423110	−	0.402563i
$965$	2.34443e7	+	7.21540e7i	0.810435	+	2.49426i
$966$	−1.23780e7	−	2.14394e7i	−0.426785	−	0.739212i
$967$	1.08011e7	−	1.87080e7i	0.371450	−	0.643371i	−0.618339	−	0.785912i	$-0.712194\pi$
$967$	1.08011e7	−	1.87080e7i	0.371450	−	0.643371i	0.989789	+	0.142541i	$0.0455273\pi$
$968$	1.40437e7	+	2.98509e6i	0.481720	+	0.102393i
$969$	1.92369e7	−	5.92050e7i	0.658150	−	2.02558i
$970$	−3.67524e7	+	7.81197e6i	−1.25417	+	0.266582i
$971$	−5.17131e6	+	4.92017e7i	−0.176016	+	1.67468i	0.448587	+	0.893739i	$0.351928\pi$
$971$	−5.17131e6	+	4.92017e7i	−0.176016	+	1.67468i	−0.624603	+	0.780943i	$0.714739\pi$
$972$	6.98158e6	−	7.75383e6i	0.237022	−	0.263239i
$973$	1.87022e7	−	8.32677e6i	0.633302	−	0.281964i
$974$	−3.74078e7	−	1.66550e7i	−1.26347	−	0.562533i
$975$	1.15169e7	+	1.27908e7i	0.387993	+	0.430909i
$976$	6.33354e6	−	4.60159e6i	0.212825	−	0.154626i
$977$	3.50161e7	−	2.54407e7i	1.17363	−	0.852691i	0.182190	−	0.983263i	$-0.441681\pi$
$977$	3.50161e7	−	2.54407e7i	1.17363	−	0.852691i	0.991439	+	0.130572i	$0.0416814\pi$
$978$	2.86345e7	+	3.18018e7i	0.957287	+	1.06317i
$979$	−4.69500e7	−	2.09035e7i	−1.56559	−	0.697047i
$980$	−3.00207e6	+	1.33661e6i	−0.0998519	+	0.0444569i
$981$	−2.28357e6	+	2.53616e6i	−0.0757604	+	0.0841405i
$982$	1.08317e6	−	1.03056e7i	0.0358440	−	0.341033i
$983$	−2.46586e7	+	5.24134e6i	−0.813924	+	0.173005i	−0.596024	−	0.802966i	$-0.703254\pi$
$983$	−2.46586e7	+	5.24134e6i	−0.813924	+	0.173005i	−0.217900	+	0.975971i	$0.569921\pi$
$984$	−601338.	+	1.85073e6i	−0.0197984	+	0.0609333i
$985$	−1.81359e7	−	3.85490e6i	−0.595591	−	0.126597i
$986$	−6.58816e6	+	1.14110e7i	−0.215810	+	0.373794i
$987$	−2.13499e7	−	3.69791e7i	−0.697594	−	1.20827i
$988$	3.25184e6	+	1.00081e7i	0.105983	+	0.326183i
$989$	−3.56949e6	−	3.39615e7i	−0.116042	−	1.10407i
$990$	−1.47538e7	−	1.07193e7i	−0.478428	−	0.347598i
$991$	−7.45957e6			−0.241285			−0.120642	−	0.992696i	$-0.538495\pi$
$991$	−7.45957e6			−0.241285			−0.120642	+	0.992696i	$0.538495\pi$
$992$	−5.42539e6	−	764839.i	−0.175046	−	0.0246769i
$993$	−2.81261e7			−0.905185
$994$	−2.09259e7	−	1.52036e7i	−0.671767	−	0.488068i
$995$	−2.33518e6	−	2.22178e7i	−0.0747761	−	0.711447i
$996$	−3.55310e6	−	1.09353e7i	−0.113490	−	0.349287i
$997$	−2.69752e7	−	4.67225e7i	−0.859463	−	1.48863i	−0.872442	−	0.488718i	$-0.837465\pi$
$997$	−2.69752e7	−	4.67225e7i	−0.859463	−	1.48863i	0.0129788	−	0.999916i	$-0.495869\pi$
$998$	−1.65943e6	+	2.87422e6i	−0.0527391	+	0.0913467i
$999$	−2.17659e7	−	4.62648e6i	−0.690022	−	0.146669i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.6.g.b.41.5	✓	56
31.28	even	15	inner	62.6.g.b.59.5	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.6.g.b.41.5	✓	56	1.1	even	1	trivial
62.6.g.b.59.5	yes	56	31.28	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	62.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(3.23607 + 2.35114i) q^{2} +(1.90823 + 18.1556i) q^{3} +(4.94427 + 15.2169i) q^{4} +(40.6803 + 70.4603i) q^{5} +(-36.5111 + 63.2392i) q^{6} +(-135.999 - 28.9075i) q^{7} +(-19.7771 + 60.8676i) q^{8} +(-88.2934 + 18.7673i) q^{9} +(-34.0180 + 323.660i) q^{10} +(415.393 - 461.341i) q^{11} +(-266.837 + 118.803i) q^{12} +(-246.472 - 109.736i) q^{13} +(-372.137 - 413.300i) q^{14} +(-1201.62 + 873.028i) q^{15} +(-207.108 + 150.473i) q^{16} +(936.006 + 1039.54i) q^{17} +(-329.848 - 146.858i) q^{18} +(-2227.00 + 991.522i) q^{19} +(-871.054 + 967.403i) q^{20} +(265.315 - 2524.30i) q^{21} +(2428.92 - 516.282i) q^{22} +(753.489 - 2319.00i) q^{23} +(-1142.83 - 242.915i) q^{24} +(-1747.27 + 3026.37i) q^{25} +(-539.595 - 934.606i) q^{26} +(861.616 + 2651.78i) q^{27} +(-232.534 - 2212.41i) q^{28} +(1905.13 + 1384.16i) q^{29} -5941.14 q^{30} +(5298.23 + 746.913i) q^{31} -1024.00 q^{32} +(9168.57 + 6661.36i) q^{33} +(584.874 + 5564.70i) q^{34} +(-3495.65 - 10758.5i) q^{35} +(-722.128 - 1250.76i) q^{36} +(-3990.35 + 6911.48i) q^{37} +(-9537.92 - 2027.35i) q^{38} +(1522.00 - 4684.24i) q^{39} +(-5093.29 + 1082.61i) q^{40} +(174.099 - 1656.44i) q^{41} +(6793.57 - 7545.02i) q^{42} +(12794.0 - 5696.27i) q^{43} +(9074.00 + 4040.00i) q^{44} +(-4914.16 - 5457.72i) q^{45} +(7890.64 - 5732.88i) q^{46} +(13609.9 - 9888.20i) q^{47} +(-3127.13 - 3473.03i) q^{48} +(2306.15 + 1026.76i) q^{49} +(-12769.7 + 5685.44i) q^{50} +(-17087.3 + 18977.4i) q^{51} +(451.224 - 4293.11i) q^{52} +(24572.3 - 5223.01i) q^{53} +(-3446.46 + 10607.1i) q^{54} +(49404.6 + 10501.3i) q^{55} +(4449.20 - 7706.23i) q^{56} +(-22251.3 - 38540.3i) q^{57} +(2910.78 + 8958.45i) q^{58} +(3467.37 + 32989.9i) q^{59} +(-19225.9 - 13968.5i) q^{60} -30580.8 q^{61} +(15389.3 + 14874.0i) q^{62} +12550.3 q^{63} +(-3313.73 - 2407.57i) q^{64} +(-2294.49 - 21830.6i) q^{65} +(14008.3 + 43113.2i) q^{66} +(-30660.3 - 53105.2i) q^{67} +(-11190.7 + 19382.9i) q^{68} +(43540.6 + 9254.84i) q^{69} +(13982.6 - 43034.0i) q^{70} +(45492.5 - 9669.74i) q^{71} +(603.863 - 5745.37i) q^{72} +(-26086.0 + 28971.4i) q^{73} +(-29162.9 + 12984.2i) q^{74} +(-58279.6 - 25947.7i) q^{75} +(-26098.8 - 28985.6i) q^{76} +(-69829.3 + 50734.0i) q^{77} +(15938.6 - 11580.1i) q^{78} +(-7240.15 - 8041.00i) q^{79} +(-19027.6 - 8471.64i) q^{80} +(-66538.7 + 29624.9i) q^{81} +(4457.91 - 4951.01i) q^{82} +(-4114.75 + 39149.3i) q^{83} +(39723.9 - 8443.57i) q^{84} +(-35169.3 + 108240. i) q^{85} +(54795.1 + 11647.1i) q^{86} +(-21494.7 + 37230.0i) q^{87} +(19865.5 + 34408.0i) q^{88} +(-25582.3 - 78734.2i) q^{89} +(-3070.67 - 29215.4i) q^{90} +(30347.8 + 22049.0i) q^{91} +39013.5 q^{92} +(-3450.40 + 97617.7i) q^{93} +67291.2 q^{94} +(-160458. - 116579. i) q^{95} +(-1954.02 - 18591.3i) q^{96} +(35677.1 + 109803. i) q^{97} +(5048.79 + 8744.76i) q^{98} +(-28018.3 + 48529.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 56 q^{2} - 7 q^{3} - 224 q^{4} + 91 q^{5} - 152 q^{6} - 94 q^{7} + 896 q^{8} + 896 q^{9} - 944 q^{10} - 31 q^{11} - 112 q^{12} - 1244 q^{13} + 856 q^{14} + 518 q^{15} - 3584 q^{16} + 1064 q^{17}+ \cdots - 625437 q^{99}+O(q^{100}) \) 56 * q + 56 * q^2 - 7 * q^3 - 224 * q^4 + 91 * q^5 - 152 * q^6 - 94 * q^7 + 896 * q^8 + 896 * q^9 - 944 * q^10 - 31 * q^11 - 112 * q^12 - 1244 * q^13 + 856 * q^14 + 518 * q^15 - 3584 * q^16 + 1064 * q^17 - 1724 * q^18 + 619 * q^19 - 1024 * q^20 + 9541 * q^21 + 124 * q^22 - 1717 * q^23 + 768 * q^24 - 24033 * q^25 - 1344 * q^26 + 22754 * q^27 + 1776 * q^28 + 11733 * q^29 + 13928 * q^30 + 57065 * q^31 - 57344 * q^32 - 11248 * q^33 - 10456 * q^34 - 7296 * q^35 - 42464 * q^36 - 1504 * q^37 - 29736 * q^38 - 19566 * q^39 + 4096 * q^40 + 35891 * q^41 + 40636 * q^42 + 66400 * q^43 + 23344 * q^44 - 27014 * q^45 - 7612 * q^46 + 36521 * q^47 - 3072 * q^48 + 121465 * q^49 - 13108 * q^50 - 236890 * q^51 - 19904 * q^52 - 143661 * q^53 - 91016 * q^54 + 106359 * q^55 + 5056 * q^56 + 13060 * q^57 + 59468 * q^58 + 230112 * q^59 + 8288 * q^60 - 49860 * q^61 + 26740 * q^62 + 66726 * q^63 - 57344 * q^64 + 201094 * q^65 - 30508 * q^66 + 74372 * q^67 - 4656 * q^68 - 599733 * q^69 + 29184 * q^70 + 23383 * q^71 - 27584 * q^72 - 66915 * q^73 + 186916 * q^74 + 553648 * q^75 - 152736 * q^76 + 120895 * q^77 + 142024 * q^78 - 452529 * q^79 - 50944 * q^80 - 365276 * q^81 - 14324 * q^82 - 469160 * q^83 - 50464 * q^84 - 127377 * q^85 + 215540 * q^86 + 217461 * q^87 + 39744 * q^88 - 155746 * q^89 + 820796 * q^90 - 142152 * q^91 - 5952 * q^92 + 342224 * q^93 + 29656 * q^94 + 756444 * q^95 + 7168 * q^96 + 325303 * q^97 + 533540 * q^98 - 625437 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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