LMFDB - Embedded newform 62.6.g.b.59.5

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)

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);

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")

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			59.5
Character	$\chi$	$=$	62.59
Dual form			62.6.g.b.41.5

$q$-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 $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{8}{15}\right)$

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	−0.744991	−	0.667075i	$-0.767546\pi$
$3$	1.90823	−	18.1556i	0.122413	−	1.16468i	0.867404	−	0.497605i	$-0.165787\pi$
$4$	4.94427	−	15.2169i	0.154508	−	0.475528i
$5$	40.6803	−	70.4603i	0.727711	−	1.26043i	−0.230137	−	0.973158i	$-0.573917\pi$
$5$	40.6803	−	70.4603i	0.727711	−	1.26043i	0.957848	−	0.287275i	$-0.0927493\pi$
$6$	−36.5111	−	63.2392i	−0.414045	−	0.717147i
$7$	−135.999	+	28.9075i	−1.04904	+	0.222980i	−0.700010	−	0.714133i	$-0.746821\pi$
$7$	−135.999	+	28.9075i	−1.04904	+	0.222980i	−0.349027	+	0.937113i	$0.613488\pi$
$8$	−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	0.988585	+	0.150665i	$0.0481413\pi$
$11$	415.393	+	461.341i	1.03509	+	1.14958i	0.0465039	+	0.998918i	$0.485192\pi$
$12$	−266.837	−	118.803i	−0.534925	−	0.238164i
$13$	−246.472	+	109.736i	−0.404492	+	0.180091i	−0.598890	−	0.800831i	$-0.704391\pi$
$13$	−246.472	+	109.736i	−0.404492	+	0.180091i	0.194398	+	0.980923i	$0.437725\pi$
$14$	−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	−0.208898	−	0.977937i	$-0.566988\pi$
$17$	936.006	−	1039.54i	0.785518	−	0.872406i	0.994416	+	0.105531i	$0.0336543\pi$
$18$	−329.848	+	146.858i	−0.239957	+	0.106836i
$19$	−2227.00	−	991.522i	−1.41526	−	0.630113i	−0.450386	−	0.892834i	$-0.648713\pi$
$19$	−2227.00	−	991.522i	−1.41526	−	0.630113i	−0.964872	+	0.262721i	$0.915380\pi$
$20$	−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	0.982542	+	0.186040i	$0.0595655\pi$
$23$	753.489	+	2319.00i	0.297001	+	0.914074i	−0.685542	+	0.728033i	$0.740435\pi$
$24$	−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	−0.357244	−	0.934011i	$-0.616284\pi$
$29$	1905.13	−	1384.16i	0.420658	−	0.305626i	0.777903	+	0.628385i	$0.216284\pi$
$30$	−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	0.520527	−	0.853845i	$-0.325736\pi$
$37$	−3990.35	−	6911.48i	−0.479189	−	0.829979i	−0.999715	+	0.0238666i	$0.992402\pi$
$38$	−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	0.999628	−	0.0272693i	$-0.00868116\pi$
$41$	174.099	+	1656.44i	0.0161747	+	0.153892i	−0.983453	+	0.181161i	$0.942014\pi$
$42$	6793.57	+	7545.02i	0.594258	+	0.659990i
$43$	12794.0	+	5696.27i	1.05520	+	0.469807i	0.859649	−	0.510885i	$-0.170682\pi$
$43$	12794.0	+	5696.27i	1.05520	+	0.469807i	0.195556	+	0.980693i	$0.437349\pi$
$44$	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	0.938130	−	0.346283i	$-0.112556\pi$
$47$	13609.9	+	9888.20i	0.898693	+	0.652939i	−0.0394366	+	0.999222i	$0.512556\pi$
$48$	−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	0.764866	−	0.644189i	$-0.222805\pi$
$53$	24572.3	+	5223.01i	1.20159	+	0.255406i	0.436725	+	0.899595i	$0.356138\pi$
$54$	−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	−0.715223	−	0.698896i	$-0.753675\pi$
$59$	3467.37	−	32989.9i	0.129679	−	1.23382i	0.844903	−	0.534920i	$-0.179658\pi$
$60$	−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	0.0600652	+	0.998194i	$0.480869\pi$
$67$	−30660.3	+	53105.2i	−0.834429	+	1.44527i	−0.894494	+	0.447079i	$0.852464\pi$
$68$	−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	0.709492	−	0.704714i	$-0.248925\pi$
$71$	45492.5	+	9669.74i	1.07101	+	0.227651i	0.361520	+	0.932364i	$0.382258\pi$
$72$	603.863	+	5745.37i	0.0137280	+	0.130613i
$73$	−26086.0	−	28971.4i	−0.572928	−	0.636301i	0.385135	−	0.922860i	$-0.374155\pi$
$73$	−26086.0	−	28971.4i	−0.572928	−	0.636301i	−0.958062	+	0.286560i	$0.907488\pi$
$74$	−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	−0.804862	−	0.593462i	$-0.797761\pi$
$79$	−7240.15	+	8041.00i	−0.130521	+	0.144958i	0.674341	+	0.738420i	$0.264428\pi$
$80$	−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	−0.977132	−	0.212632i	$-0.931796\pi$
$83$	−4114.75	−	39149.3i	−0.0655615	−	0.623776i	0.911571	−	0.411143i	$-0.134870\pi$
$84$	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	0.620644	+	0.784092i	$0.286871\pi$
$89$	−25582.3	+	78734.2i	−0.342345	+	1.05363i	−0.962990	+	0.269538i	$0.913129\pi$
$90$	−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	−0.551480	−	0.834188i	$-0.685937\pi$
$97$	35677.1	−	109803.i	0.385000	−	1.18491i	0.936480	−	0.350720i	$-0.114063\pi$
$98$	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	0.836140	−	0.548516i	$-0.184807\pi$
$101$	−16681.9	−	51341.7i	−0.162721	−	0.500803i	−0.998861	+	0.0477124i	$0.984807\pi$
$102$	−99914.2	−	21237.4i	−0.950883	−	0.202116i
$103$	16736.4	+	159236.i	0.155442	+	1.47893i	0.742750	+	0.669569i	$0.233521\pi$
$103$	16736.4	+	159236.i	0.155442	+	1.47893i	−0.587308	+	0.809364i	$0.699812\pi$
$104$	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	−0.544792	−	0.838571i	$-0.683391\pi$
$107$	40992.1	−	45526.4i	0.346131	−	0.384418i	0.890924	+	0.454153i	$0.150058\pi$
$108$	−36091.8	−	26222.3i	−0.297749	−	0.216327i
$109$	30587.1	+	22222.8i	0.246588	+	0.179156i	0.704213	−	0.709989i	$-0.251300\pi$
$109$	30587.1	+	22222.8i	0.246588	+	0.179156i	−0.457625	+	0.889145i	$0.651300\pi$
$110$	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	0.997125	−	0.0757779i	$-0.0241440\pi$
$113$	110969.	+	123244.i	0.817534	+	0.907963i	−0.179591	+	0.983741i	$0.557477\pi$
$114$	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	0.711855	+	0.702326i	$0.247855\pi$
$127$	−23714.1	+	225625.i	−0.130466	+	1.24130i	−0.842322	+	0.538975i	$0.818812\pi$
$128$	−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	−0.589810	−	0.807542i	$-0.700797\pi$
$131$	−157167.	+	33406.8i	−0.800170	+	0.170081i	−0.210361	+	0.977624i	$0.567464\pi$
$132$	−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	−0.0756908	−	0.997131i	$-0.524116\pi$
$137$	135035.	−	60121.6i	0.614675	−	0.273671i	0.690366	+	0.723460i	$0.257450\pi$
$138$	119141.	−	132319.i	0.532553	−	0.591460i
$139$	−119121.	−	86546.6i	−0.522940	−	0.379938i	0.294770	−	0.955568i	$-0.404757\pi$
$139$	−119121.	−	86546.6i	−0.522940	−	0.379938i	−0.817710	+	0.575630i	$0.804757\pi$
$140$	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	0.953095	−	0.302673i	$-0.0978789\pi$
$149$	58108.7	+	100647.i	0.214425	+	0.371395i	−0.738669	+	0.674068i	$0.764546\pi$
$150$	−127590.	+	220992.i	−0.463008	+	0.801953i
$151$	−98420.8	+	302908.i	−0.351273	+	1.08111i	0.606867	+	0.794804i	$0.292426\pi$
$151$	−98420.8	+	302908.i	−0.351273	+	1.08111i	−0.958139	+	0.286302i	$0.907574\pi$
$152$	−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	−0.247455	−	0.968899i	$-0.579594\pi$
$157$	184556.	−	134088.i	0.597556	−	0.434149i	0.845010	+	0.534750i	$0.179594\pi$
$158$	−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	0.746076	+	0.665860i	$0.231935\pi$
$163$	181094.	+	557352.i	0.533871	+	1.64309i	−0.212205	+	0.977225i	$0.568065\pi$
$164$	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	0.460329	−	0.887749i	$-0.347732\pi$
$167$	39148.3	+	17429.9i	0.108623	+	0.0483620i	−0.351706	+	0.936111i	$0.614398\pi$
$168$	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	−0.359442	−	0.933167i	$-0.617033\pi$
$173$	36815.5	−	16391.3i	0.0935223	−	0.0416388i	0.452965	+	0.891528i	$0.350366\pi$
$174$	−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	−0.867551	−	0.497348i	$-0.834307\pi$
$179$	−624933.	+	132834.i	−1.45781	+	0.309867i	−0.590258	+	0.807215i	$0.700974\pi$
$180$	58752.7	+	101763.i	0.135160	+	0.234103i
$181$	−278263.	+	481965.i	−0.631333	+	1.09350i	0.355946	+	0.934507i	$0.384159\pi$
$181$	−278263.	+	481965.i	−0.631333	+	1.09350i	−0.987279	+	0.158995i	$0.949175\pi$
$182$	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	−0.962104	−	0.272682i	$-0.912089\pi$
$191$	−123474.	+	213864.i	−0.244902	+	0.424183i	0.717202	+	0.696866i	$0.245423\pi$
$192$	37387.4	+	64756.9i	0.0731935	+	0.126775i
$193$	912104.	−	193874.i	1.76259	−	0.374650i	0.791091	−	0.611699i	$-0.209513\pi$
$193$	912104.	−	193874.i	1.76259	−	0.374650i	0.971498	+	0.237049i	$0.0761801\pi$
$194$	−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	0.586734	−	0.809780i	$-0.300414\pi$
$197$	−152486.	−	169353.i	−0.279940	−	0.310905i	−0.866674	+	0.498875i	$0.833747\pi$
$198$	−204768.	−	91168.7i	−0.371193	−	0.165266i
$199$	−250843.	+	111683.i	−0.449024	+	0.199918i	−0.618774	−	0.785569i	$-0.712371\pi$
$199$	−250843.	+	111683.i	−0.449024	+	0.199918i	0.169750	+	0.985487i	$0.445704\pi$
$200$	−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	−0.960663	−	0.277717i	$-0.910422\pi$
$211$	−466172.	−	807433.i	−0.720841	−	1.24853i	0.239822	−	0.970817i	$-0.422911\pi$
$212$	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	0.988491	+	0.151280i	$0.0483394\pi$
$223$	464324.	+	804233.i	0.625258	+	1.08298i	−0.363233	+	0.931698i	$0.618327\pi$
$224$	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	−0.526404	−	0.850235i	$-0.676460\pi$
$227$	−146171.	−	1.39073e6i	−0.188277	−	1.79134i	0.338127	−	0.941100i	$-0.390207\pi$
$228$	476448.	+	529149.i	0.606986	+	0.674126i
$229$	−325058.	−	144725.i	−0.409611	−	0.182371i	0.191578	−	0.981477i	$-0.438640\pi$
$229$	−325058.	−	144725.i	−0.409611	−	0.182371i	−0.601189	+	0.799107i	$0.705306\pi$
$230$	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	0.782969	−	0.622061i	$-0.213705\pi$
$233$	359073.	+	260882.i	0.433304	+	0.314814i	−0.349665	+	0.936875i	$0.613705\pi$
$234$	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	0.929642	−	0.368464i	$-0.120116\pi$
$239$	1.43856e6	+	305775.i	1.62904	+	0.346264i	0.699402	+	0.714728i	$0.253450\pi$
$240$	117498.	+	361623.i	0.131675	+	0.405254i
$241$	−713996.	+	151765.i	−0.791869	+	0.168317i	−0.586052	−	0.810274i	$-0.699319\pi$
$241$	−713996.	+	151765.i	−0.791869	+	0.168317i	−0.205817	+	0.978590i	$0.565985\pi$
$242$	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	0.702670	+	0.711516i	$0.251991\pi$
$251$	−132329.	+	1.25902e6i	−0.132577	+	1.26139i	−0.835247	+	0.549874i	$0.814676\pi$
$252$	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	−0.0988102	−	0.995106i	$-0.531504\pi$
$257$	−628768.	−	133649.i	−0.593824	−	0.126221i	−0.495014	+	0.868885i	$0.664837\pi$
$258$	−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	−0.992940	−	0.118619i	$-0.962153\pi$
$263$	−1.58455e6	−	1.15124e6i	−1.41259	−	1.02631i	−0.419649	−	0.907687i	$-0.637847\pi$
$264$	−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	0.993580	−	0.113129i	$-0.0360874\pi$
$269$	−2146.64	−	20423.9i	−0.00180875	−	0.0172091i	−0.995389	+	0.0959200i	$0.969421\pi$
$270$	−887585.	−	188662.i	−0.740970	−	0.157498i
$271$	−236694.	−	728469.i	−0.195778	−	0.602543i	−0.999967	−	0.00816877i	$-0.997400\pi$
$271$	−236694.	−	728469.i	−0.195778	−	0.602543i	0.804189	−	0.594374i	$-0.202600\pi$
$272$	−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	−0.195217	−	0.980760i	$-0.562541\pi$
$277$	864822.	−	628330.i	0.677216	−	0.492026i	0.872433	+	0.488734i	$0.162541\pi$
$278$	−588968.			−0.457067
$279$	−481817.	−	33486.3i	−0.370571	−	0.0257547i
$280$	723979.			0.551862
$281$	344042.	−	249961.i	0.259924	−	0.188846i	−0.450190	−	0.892933i	$-0.648644\pi$
$281$	344042.	−	249961.i	0.259924	−	0.188846i	0.710113	+	0.704087i	$0.248644\pi$
$282$	128407.	−	1.22171e6i	0.0961537	−	0.914841i
$283$	123384.	−	379737.i	0.0915784	−	0.281849i	−0.894768	−	0.446530i	$-0.852659\pi$
$283$	123384.	−	379737.i	0.0915784	−	0.281849i	0.986347	+	0.164681i	$0.0526595\pi$
$284$	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	0.0311703	+	0.999514i	$0.490077\pi$
$293$	−1.41972e6	+	1.57676e6i	−0.966127	+	1.07299i	−0.997297	+	0.0734782i	$0.976590\pi$
$294$	−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	0.870447	+	0.492263i	$0.163830\pi$
$307$	−137602.	+	1.30920e6i	−0.0833259	+	0.792793i	−0.953772	+	0.300530i	$0.902837\pi$
$308$	−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	−0.813909	−	0.580992i	$-0.802665\pi$
$313$	178541.	−	1.69870e6i	0.103009	−	0.980067i	0.916918	−	0.399075i	$-0.130669\pi$
$314$	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	−0.0790565	−	0.996870i	$-0.525191\pi$
$317$	454777.	−	96665.9i	0.254185	−	0.0540288i	0.333242	+	0.942841i	$0.391857\pi$
$318$	−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	−0.957647	−	0.287945i	$-0.907028\pi$
$331$	−161046.	−	1.53225e6i	−0.0807940	−	0.768704i	0.876853	−	0.480759i	$-0.159639\pi$
$332$	−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	0.663605	+	0.748083i	$0.269026\pi$
$337$	−652506.	+	2.00821e6i	−0.312975	+	0.963238i	−0.976580	+	0.215155i	$0.930974\pi$
$338$	−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	0.649216	−	0.760604i	$-0.275097\pi$
$347$	−749363.	−	1.29794e6i	−0.334094	−	0.578668i	−0.983310	+	0.181936i	$0.941764\pi$
$348$	−672801.	+	143008.i	−0.297809	+	0.0633014i
$349$	−525897.	−	1.61854e6i	−0.231120	−	0.711313i	−0.997612	−	0.0690603i	$-0.978000\pi$
$349$	−525897.	−	1.61854e6i	−0.231120	−	0.711313i	0.766493	−	0.642253i	$-0.222000\pi$
$350$	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	0.775420	−	0.631446i	$-0.217538\pi$
$353$	1.93153e6	+	859974.i	0.825022	+	0.367323i	0.0496017	+	0.998769i	$0.484205\pi$
$354$	−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	−0.412104	−	0.911137i	$-0.635206\pi$
$359$	−26248.8	+	11686.7i	−0.0107491	+	0.00478583i	0.401355	+	0.915923i	$0.368539\pi$
$360$	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	−0.394627	−	0.918842i	$-0.629126\pi$
$367$	1.54410e6	−	2.67446e6i	0.598427	−	1.03651i	0.993053	−	0.117664i	$-0.0375406\pi$
$368$	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	−0.660516	−	0.750812i	$-0.729663\pi$
$379$	−2.68047e6	+	569751.i	−0.958545	+	0.203745i	−0.298029	+	0.954557i	$0.596329\pi$
$380$	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	0.985410	−	0.170196i	$-0.0544400\pi$
$383$	2.04726e6	+	2.27372e6i	0.713143	+	0.792026i	−0.272267	+	0.962222i	$0.587773\pi$
$384$	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	0.0816970	−	0.996657i	$-0.473966\pi$
$389$	3.17658e6	−	3.52795e6i	1.06435	−	1.18209i	0.982658	−	0.185428i	$-0.0593673\pi$
$390$	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	0.969310	−	0.245843i	$-0.0790648\pi$
$397$	853382.	+	1.47810e6i	0.271748	+	0.470682i	−0.697561	+	0.716525i	$0.745731\pi$
$398$	−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	−0.0149735	−	0.999888i	$-0.504766\pi$
$401$	2.99898e6	−	2.17889e6i	0.931349	−	0.676665i	0.946323	+	0.323223i	$0.104766\pi$
$402$	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	−0.978650	−	0.205535i	$-0.934107\pi$
$409$	−2.25759e6	−	3.91026e6i	−0.667323	−	1.15584i	0.311327	−	0.950303i	$-0.399227\pi$
$410$	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	0.975838	−	0.218496i	$-0.0701150\pi$
$419$	3.84371e6	+	2.79262e6i	1.06959	+	0.777100i	0.0937487	+	0.995596i	$0.470115\pi$
$420$	2.21092e6	−	2.45547e6i	0.611574	−	0.679221i
$421$	−2.22602e6	+	991088.i	−0.612102	+	0.272525i	−0.689283	−	0.724492i	$-0.742075\pi$
$421$	−2.22602e6	+	991088.i	−0.612102	+	0.272525i	0.0771817	+	0.997017i	$0.475408\pi$
$422$	−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	0.912432	+	0.409229i	$0.134202\pi$
$431$	−251230.	+	2.39029e6i	−0.0651446	+	0.619809i	−0.977576	+	0.210581i	$0.932465\pi$
$432$	−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	0.350201	+	0.936675i	$0.386113\pi$
$439$	−2.56848e6	+	4.44873e6i	−0.636084	+	1.10173i	−0.986284	+	0.165055i	$0.947220\pi$
$440$	−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	−0.317253	−	0.948341i	$-0.602760\pi$
$443$	−4.10083e6	−	871659.i	−0.992803	−	0.211027i	−0.675550	+	0.737314i	$0.736094\pi$
$444$	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	0.347121	−	0.937820i	$-0.387159\pi$
$449$	−1.86907e6	−	1.35796e6i	−0.437533	−	0.317886i	−0.784654	+	0.619934i	$0.787159\pi$
$450$	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	−0.977096	−	0.212801i	$-0.931741\pi$
$457$	−1.39160e6	−	4.28289e6i	−0.311690	−	0.959283i	0.665406	−	0.746482i	$-0.268259\pi$
$458$	−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	−0.994605	−	0.103733i	$-0.966921\pi$
$461$	−588538.	+	1.81133e6i	−0.128980	+	0.396959i	0.865625	+	0.500692i	$0.166921\pi$
$462$	−658825.	+	6.26830e6i	−0.143604	+	1.36630i
$463$	5.82802e6	−	4.23430e6i	1.26348	−	0.917972i	0.264557	−	0.964370i	$-0.414774\pi$
$463$	5.82802e6	−	4.23430e6i	1.26348	−	0.917972i	0.998923	+	0.0463984i	$0.0147744\pi$
$464$	−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	−0.621840	−	0.783144i	$-0.713615\pi$
$467$	−326066.	+	236901.i	−0.0691853	+	0.0502661i	0.552655	+	0.833410i	$0.313615\pi$
$468$	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	−0.859264	−	0.511533i	$-0.829078\pi$
$479$	−1.30920e6	+	1.45401e6i	−0.260715	+	0.289554i	0.598548	+	0.801087i	$0.295744\pi$
$480$	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	−0.913171	−	0.407576i	$-0.866374\pi$
$487$	−1.00133e7	−	2.12839e6i	−1.91317	−	0.406657i	−1.00000		0.000919362i	$0.999707\pi$
$488$	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	−0.961419	−	0.275089i	$-0.911293\pi$
$491$	−1.29530e6	+	2.24353e6i	−0.242475	+	0.419979i	0.718944	+	0.695068i	$0.244626\pi$
$492$	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	−0.983956	−	0.178413i	$-0.942904\pi$
$499$	86728.8	−	825169.i	0.0155924	−	0.148351i	0.999548	+	0.0300616i	$0.00957035\pi$
$500$	−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	−0.0369514	−	0.999317i	$-0.511765\pi$
$503$	1.90518e6	−	404959.i	0.335751	−	0.0713660i	0.372702	+	0.927951i	$0.378431\pi$
$504$	−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	−0.0952282	−	0.995455i	$-0.530358\pi$
$509$	3.39497e6	−	1.51154e6i	0.580819	−	0.258597i	0.676047	+	0.736858i	$0.263691\pi$
$510$	−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	0.986794	−	0.161982i	$-0.0517885\pi$
$521$	2.18783e6	+	3.78942e6i	0.353117	+	0.611616i	−0.633677	+	0.773598i	$0.718455\pi$
$522$	−425129.	+	736345.i	−0.0682880	+	0.118278i
$523$	1.09622e6	−	3.37383e6i	0.175245	−	0.539347i	−0.824400	−	0.566008i	$-0.808487\pi$
$523$	1.09622e6	−	3.37383e6i	0.175245	−	0.539347i	0.999645	+	0.0266603i	$0.00848724\pi$
$524$	−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	−0.309542	−	0.950886i	$-0.600176\pi$
$541$	4.55081e6	−	5.05418e6i	0.668490	−	0.742434i	0.978033	+	0.208452i	$0.0668424\pi$
$542$	−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	0.480358	−	0.877072i	$-0.340507\pi$
$547$	−3.09392e6	−	3.43614e6i	−0.442120	−	0.491024i	−0.922479	+	0.386048i	$0.873840\pi$
$548$	−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	−0.0320028	+	0.999488i	$0.510189\pi$
$563$	−6.63032e6	+	1.14840e7i	−0.881583	+	1.52695i	−0.849580	+	0.527459i	$0.823145\pi$
$564$	−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	−0.879082	−	0.476671i	$-0.841843\pi$
$569$	−9.74053e6	−	1.08180e7i	−1.26125	−	1.40076i	−0.382171	−	0.924092i	$-0.624823\pi$
$570$	1.32309e7	+	5.89077e6i	1.70570	+	0.759425i
$571$	4.53094e6	−	2.01731e6i	0.581565	−	0.258929i	−0.0947996	−	0.995496i	$-0.530221\pi$
$571$	4.53094e6	−	2.01731e6i	0.581565	−	0.258929i	0.676365	+	0.736567i	$0.263554\pi$
$572$	−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	0.268516	−	0.963275i	$-0.413467\pi$
$577$	−2.14058e6	−	953049.i	−0.267666	−	0.119172i	−0.536181	+	0.844103i	$0.680134\pi$
$578$	−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	−0.744921	−	0.667152i	$-0.767513\pi$
$587$	−2.84354e6	+	2.06595e6i	−0.340615	+	0.247471i	0.404306	+	0.914624i	$0.367513\pi$
$588$	−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	−0.997078	−	0.0763963i	$-0.975659\pi$
$593$	−1.24612e6	+	3.83517e6i	−0.145520	+	0.447865i	0.851557	+	0.524262i	$0.175659\pi$
$594$	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	−0.663765	−	0.747941i	$-0.731042\pi$
$599$	−1.49294e6	−	1.42044e7i	−0.170011	−	1.61754i	0.493754	−	0.869601i	$-0.335624\pi$
$600$	2.73198e6	+	3.03417e6i	0.309813	+	0.344082i
$601$	−7.56024e6	−	3.36604e6i	−0.853787	−	0.380130i	−0.0672966	−	0.997733i	$-0.521437\pi$
$601$	−7.56024e6	−	3.36604e6i	−0.853787	−	0.380130i	−0.786490	+	0.617603i	$0.788104\pi$
$602$	−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	−0.732467	−	0.680802i	$-0.761631\pi$
$607$	−6.50546e6	+	2.89642e6i	−0.716649	+	0.319073i	0.0158184	+	0.999875i	$0.494965\pi$
$608$	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	0.0413679	−	0.999144i	$-0.486828\pi$
$613$	4.51734e6	−	960191.i	0.485548	−	0.103206i	0.444180	+	0.895938i	$0.353495\pi$
$614$	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	0.718235	+	0.695801i	$0.244950\pi$
$617$	−1.21956e6	+	1.16033e7i	−0.128970	+	1.22707i	−0.847205	+	0.531267i	$0.821716\pi$
$618$	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	0.470067	−	0.882631i	$-0.344230\pi$
$631$	−4.56941e6	−	5.07484e6i	−0.456864	−	0.507399i	−0.926931	+	0.375232i	$0.877563\pi$
$632$	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	−0.957486	−	0.288481i	$-0.906850\pi$
$641$	−841596.	−	8.00725e6i	−0.0809018	−	0.769730i	0.876584	−	0.481249i	$-0.159817\pi$
$642$	−4.37572e6	−	930088.i	−0.418998	−	0.0890607i
$643$	−5.65548e6	−	1.74058e7i	−0.539439	−	1.66022i	−0.733857	−	0.679304i	$-0.762282\pi$
$643$	−5.65548e6	−	1.74058e7i	−0.539439	−	1.66022i	0.194418	−	0.980919i	$-0.437718\pi$
$644$	−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	−0.927247	−	0.374449i	$-0.877832\pi$
$647$	457935.	−	1.40938e6i	0.0430074	−	0.132363i	0.970255	+	0.242086i	$0.0778317\pi$
$648$	−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	−0.628930	−	0.777462i	$-0.716507\pi$
$653$	−913889.	+	663979.i	−0.0838707	+	0.0609357i	0.545060	+	0.838397i	$0.316507\pi$
$654$	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	−0.576322	−	0.817222i	$-0.695513\pi$
$659$	−6.58224e6	−	2.02581e7i	−0.590419	−	1.81712i	−0.0140967	−	0.999901i	$-0.504487\pi$
$660$	−1.44305e7	−	3.06730e6i	−1.28950	−	0.274092i
$661$	1.84202e6	+	1.75256e7i	0.163980	+	1.56016i	0.698875	+	0.715244i	$0.253684\pi$
$661$	1.84202e6	+	1.75256e7i	0.163980	+	1.56016i	−0.534895	+	0.844918i	$0.679649\pi$
$662$	−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	0.477048	−	0.878877i	$-0.341707\pi$
$673$	6.52573e6	+	1.38709e6i	0.555381	+	0.118050i	0.0783333	+	0.996927i	$0.475040\pi$
$674$	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	−0.795700	−	0.605691i	$-0.792897\pi$
$677$	1.51086e6	−	2.61689e6i	0.126693	−	0.219439i	0.922394	+	0.386251i	$0.126230\pi$
$678$	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	0.157871	−	0.987460i	$-0.449537\pi$
$691$	−1.24942e6	−	265573.i	−0.0995436	−	0.0211587i	−0.257414	+	0.966301i	$0.582870\pi$
$692$	−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	0.679727	−	0.733466i	$-0.262098\pi$
$701$	7.66947e6	+	3.41467e6i	0.589481	+	0.262454i	−0.0902453	+	0.995920i	$0.528765\pi$
$702$	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	0.459607	+	0.888122i	$0.347990\pi$
$709$	−5.81237e6	+	1.78886e7i	−0.434248	+	1.33648i	−0.893855	+	0.448356i	$0.852010\pi$
$710$	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	0.942028	+	0.335535i	$0.108917\pi$
$719$	1.05572e7	+	1.82855e7i	0.761596	+	1.31912i	−0.180432	+	0.983587i	$0.557750\pi$
$720$	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	0.0860237	+	0.996293i	$0.472584\pi$
$727$	−1.30223e7	+	1.44628e7i	−0.913804	+	1.01488i	−0.999827	+	0.0185885i	$0.994083\pi$
$728$	−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	0.796232	+	0.604991i	$0.206823\pi$
$733$	1.91241e7	+	2.12394e7i	1.31468	+	1.46010i	0.518448	+	0.855109i	$0.326510\pi$
$734$	−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	−0.374260	−	0.927324i	$-0.622103\pi$
$739$	9.14451e6	−	1.58388e7i	0.615956	−	1.06687i	0.990216	−	0.139543i	$-0.0445634\pi$
$740$	−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	−0.805129	−	0.593100i	$-0.797904\pi$
$751$	−2.00839e7	+	4.26896e6i	−1.29942	+	0.276199i	−0.494286	+	0.869299i	$0.664571\pi$
$752$	−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	−0.215049	−	0.976603i	$-0.568991\pi$
$757$	5.78343e6	−	2.57495e6i	0.366814	−	0.163316i	0.581862	+	0.813287i	$0.302324\pi$
$758$	−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	−0.993199	−	0.116432i	$-0.962854\pi$
$761$	−1.23586e7	+	1.37257e7i	−0.773587	+	0.859155i	0.219612	+	0.975587i	$0.429521\pi$
$762$	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	0.649795	−	0.760110i	$-0.274855\pi$
$769$	−5.46703e6	−	9.46917e6i	−0.333377	−	0.577426i	−0.983172	+	0.182684i	$0.941522\pi$
$770$	−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	−0.325198	−	0.945646i	$-0.605431\pi$
$773$	7.86913e6	−	5.71726e6i	0.473673	−	0.344143i	0.798871	+	0.601503i	$0.205431\pi$
$774$	−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	0.365719	−	0.930725i	$-0.380823\pi$
$787$	−1.41141e6	−	628400.i	−0.0812300	−	0.0361659i	−0.446949	+	0.894559i	$0.647490\pi$
$788$	−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	0.638883	−	0.769304i	$-0.279397\pi$
$797$	1.63121e7	+	3.46724e6i	0.909628	+	0.193347i	0.270745	+	0.962651i	$0.412730\pi$
$798$	−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	0.839061	+	0.544037i	$0.183105\pi$
$809$	−1.76429e6	+	1.67861e7i	−0.0947761	+	0.901734i	−0.933838	+	0.357697i	$0.883562\pi$
$810$	−7.32488e6	+	2.25437e7i	−0.392273	+	1.20729i
$811$	5.02991e6	−	8.71206e6i	0.268540	−	0.465124i	−0.699945	−	0.714196i	$-0.746792\pi$
$811$	5.02991e6	−	8.71206e6i	0.268540	−	0.465124i	0.968485	+	0.249072i	$0.0801257\pi$
$812$	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	0.528362	−	0.849019i	$-0.322806\pi$
$821$	−2.23707e6	−	1.62532e6i	−0.115830	−	0.0841554i	−0.644192	+	0.764864i	$0.722806\pi$
$822$	−8.73233e6	−	6.34441e6i	−0.450765	−	0.327500i
$823$	9.40883e6	−	1.04496e7i	0.484213	−	0.537773i	−0.450688	−	0.892681i	$-0.648821\pi$
$823$	9.40883e6	−	1.04496e7i	0.484213	−	0.537773i	0.934901	+	0.354909i	$0.115488\pi$
$824$	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	−0.999805	−	0.0197472i	$-0.993714\pi$
$827$	−510464.	−	4.85674e6i	−0.0259538	−	0.246934i	0.973851	−	0.227187i	$-0.0729528\pi$
$828$	−3.44463e6	−	732179.i	−0.174609	−	0.0371143i
$829$	6.84718e6	+	2.10735e7i	0.346039	+	1.06500i	0.961025	+	0.276461i	$0.0891618\pi$
$829$	6.84718e6	+	2.10735e7i	0.346039	+	1.06500i	−0.614986	+	0.788538i	$0.710838\pi$
$830$	−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	−0.991431	−	0.130631i	$-0.958300\pi$
$839$	−2.39283e7	+	1.73849e7i	−1.17356	+	0.852643i	−0.182132	+	0.983274i	$0.558300\pi$
$840$	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	0.777452	−	0.628943i	$-0.216512\pi$
$853$	8.91545e6	+	6.47746e6i	0.419538	+	0.304812i	−0.357914	+	0.933754i	$0.616512\pi$
$854$	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	0.132720	−	0.991154i	$-0.457629\pi$
$857$	−1.86384e7	−	2.07001e7i	−0.866877	−	0.962765i	−0.999597	+	0.0283890i	$0.990962\pi$
$858$	1.27843e6	+	1.21634e7i	0.0592868	+	0.564076i
$859$	2.41393e7	+	5.13096e6i	1.11620	+	0.237255i	0.728846	−	0.684677i	$-0.240057\pi$
$859$	2.41393e7	+	5.13096e6i	1.11620	+	0.237255i	0.387351	+	0.921932i	$0.373390\pi$
$860$	−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	−0.988537	−	0.150978i	$-0.951758\pi$
$863$	−7.95341e6	+	1.37757e7i	−0.363518	+	0.629632i	0.625019	+	0.780610i	$0.285091\pi$
$864$	−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	0.556269	−	0.831002i	$-0.312232\pi$
$877$	1.65464e7	+	3.51704e6i	0.726447	+	0.154411i	0.170178	+	0.985413i	$0.445566\pi$
$878$	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	−0.679003	−	0.734136i	$-0.737588\pi$
$881$	−1.35410e7	+	6.02884e6i	−0.587775	+	0.261694i	0.0912278	+	0.995830i	$0.470921\pi$
$882$	−609891.	+	677352.i	−0.0263986	+	0.0293186i
$883$	−9.87453e6	−	7.17426e6i	−0.426201	−	0.309653i	0.353927	−	0.935273i	$-0.384846\pi$
$883$	−9.87453e6	−	7.17426e6i	−0.426201	−	0.309653i	−0.780128	+	0.625620i	$0.784846\pi$
$884$	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	0.906516	−	0.422172i	$-0.138732\pi$
$887$	2.81033e7	+	1.25124e7i	1.19936	+	0.533989i	0.292842	+	0.956161i	$0.405399\pi$
$888$	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	0.987535	−	0.157400i	$-0.0503112\pi$
$907$	2.38053e6	+	7.32652e6i	0.0960850	+	0.295719i	−0.891450	+	0.453119i	$0.850311\pi$
$908$	−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	0.640735	−	0.767762i	$-0.278630\pi$
$911$	1.24974e7	+	5.56421e6i	0.498913	+	0.222130i	−0.141822	+	0.989892i	$0.545296\pi$
$912$	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	0.664581	−	0.747216i	$-0.268610\pi$
$919$	−3.78948e6	−	4.20864e6i	−0.148010	−	0.164381i	−0.812591	+	0.582835i	$0.801943\pi$
$920$	−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	−0.108257	−	0.994123i	$-0.534527\pi$
$937$	5.29950e6	−	1.12644e6i	0.197191	−	0.0419142i	0.305448	+	0.952209i	$0.401194\pi$
$938$	−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	0.966634	−	0.256162i	$-0.0824580\pi$
$941$	1.65920e7	+	1.84272e7i	0.610835	+	0.678401i	−0.355799	+	0.934562i	$0.615791\pi$
$942$	−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	−0.0655805	−	0.997847i	$-0.520890\pi$
$947$	2.57669e7	−	2.86170e7i	0.933656	−	1.03693i	0.999236	−	0.0390822i	$-0.0124434\pi$
$948$	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	0.728627	+	0.684911i	$0.240159\pi$
$953$	1.51887e7	+	4.67459e7i	0.541736	+	1.66729i	−0.186891	+	0.982381i	$0.559841\pi$
$954$	−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	0.989789	−	0.142541i	$-0.0455273\pi$
$967$	1.08011e7	+	1.87080e7i	0.371450	+	0.643371i	−0.618339	+	0.785912i	$0.712194\pi$
$968$	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	−0.624603	−	0.780943i	$-0.714739\pi$
$971$	−5.17131e6	−	4.92017e7i	−0.176016	−	1.67468i	0.448587	−	0.893739i	$-0.351928\pi$
$972$	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	0.991439	−	0.130572i	$-0.0416814\pi$
$977$	3.50161e7	+	2.54407e7i	1.17363	+	0.852691i	0.182190	+	0.983263i	$0.441681\pi$
$978$	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	−0.217900	−	0.975971i	$-0.569921\pi$
$983$	−2.46586e7	−	5.24134e6i	−0.813924	−	0.173005i	−0.596024	+	0.802966i	$0.703254\pi$
$984$	−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	0.0129788	+	0.999916i	$0.495869\pi$
$997$	−2.69752e7	+	4.67225e7i	−0.859463	+	1.48863i	−0.872442	+	0.488718i	$0.837465\pi$
$998$	−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.59.5	yes	56
31.10	even	15	inner	62.6.g.b.41.5	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.6.g.b.41.5	✓	56	31.10	even	15	inner
62.6.g.b.59.5	yes	56	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 6 \)
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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