LMFDB - Embedded newform 62.8.d.a.47.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			47.5
Character	$\chi$	$=$	62.47
Dual form			62.8.d.a.33.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-6.47214 + 4.70228i) q^{2} +(6.77917 + 4.92536i) q^{3} +(19.7771 - 60.8676i) q^{4} +35.5870 q^{5} -67.0362 q^{6} +(-136.422 + 419.862i) q^{7} +(158.217 + 486.941i) q^{8} +(-654.122 - 2013.18i) q^{9} +(-230.324 + 167.340i) q^{10} +(-320.129 + 985.256i) q^{11} +(433.867 - 315.223i) q^{12} +(6315.92 + 4588.78i) q^{13} +(-1091.37 - 3358.90i) q^{14} +(241.251 + 175.279i) q^{15} +(-3313.73 - 2407.57i) q^{16} +(6664.29 + 20510.6i) q^{17} +(13700.1 + 9953.71i) q^{18} +(-12083.5 + 8779.15i) q^{19} +(703.807 - 2166.10i) q^{20} +(-2992.80 + 2174.40i) q^{21} +(-2561.03 - 7882.05i) q^{22} +(-10314.2 - 31743.8i) q^{23} +(-1325.78 + 4080.33i) q^{24} -76858.6 q^{25} -62455.2 q^{26} +(11144.3 - 34298.6i) q^{27} +(22858.0 + 16607.3i) q^{28} +(-175266. + 127338. i) q^{29} -2385.62 q^{30} +(-112272. + 122097. i) q^{31} +32768.0 q^{32} +(-7022.95 + 5102.47i) q^{33} +(-139579. - 101410. i) q^{34} +(-4854.84 + 14941.6i) q^{35} -135474. q^{36} -240162. q^{37} +(36923.8 - 113640. i) q^{38} +(20215.3 + 62216.3i) q^{39} +(5630.46 + 17328.8i) q^{40} +(-480297. + 348956. i) q^{41} +(9145.18 - 28146.0i) q^{42} +(-168032. + 122082. i) q^{43} +(53638.9 + 38971.0i) q^{44} +(-23278.3 - 71643.1i) q^{45} +(216023. + 156950. i) q^{46} +(-201054. - 146074. i) q^{47} +(-10606.2 - 32642.7i) q^{48} +(508587. + 369510. i) q^{49} +(497439. - 361411. i) q^{50} +(-55843.5 + 171869. i) q^{51} +(404219. - 293682. i) q^{52} +(-14972.3 - 46080.1i) q^{53} +(89154.2 + 274389. i) q^{54} +(-11392.4 + 35062.3i) q^{55} -226032. q^{56} -125156. q^{57} +(535564. - 1.64830e6i) q^{58} +(161647. + 117443. i) q^{59} +(15440.0 - 11217.8i) q^{60} +2.87849e6 q^{61} +(152502. - 1.31816e6i) q^{62} +934495. q^{63} +(-212079. + 154084. i) q^{64} +(224765. + 163301. i) q^{65} +(21460.2 - 66047.8i) q^{66} -1.57905e6 q^{67} +1.38023e6 q^{68} +(86428.0 - 265998. i) q^{69} +(-38838.7 - 119533. i) q^{70} +(1.77914e6 + 5.47562e6i) q^{71} +(876807. - 637038. i) q^{72} +(342373. - 1.05371e6i) q^{73} +(1.55436e6 - 1.12931e6i) q^{74} +(-521038. - 378556. i) q^{75} +(295390. + 909118. i) q^{76} +(-369999. - 268820. i) q^{77} +(-423395. - 307614. i) q^{78} +(-1.68287e6 - 5.17933e6i) q^{79} +(-117926. - 85678.2i) q^{80} +(-3.50079e6 + 2.54347e6i) q^{81} +(1.46766e6 - 4.51698e6i) q^{82} +(2.48379e6 - 1.80458e6i) q^{83} +(73161.4 + 225168. i) q^{84} +(237162. + 729910. i) q^{85} +(513460. - 1.58027e6i) q^{86} -1.81534e6 q^{87} -530411. q^{88} +(-956804. + 2.94474e6i) q^{89} +(487546. + 354223. i) q^{90} +(-2.78829e6 + 2.02581e6i) q^{91} -2.13616e6 q^{92} +(-1.36248e6 + 274739. i) q^{93} +1.98813e6 q^{94} +(-430014. + 312424. i) q^{95} +(222140. + 161394. i) q^{96} +(-49127.2 + 151198. i) q^{97} -5.02918e6 q^{98} +2.19290e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 80 q^{2} + 28 q^{3} - 640 q^{4} + 168 q^{5} - 1936 q^{6} + 1402 q^{7} - 5120 q^{8} - 6164 q^{9} - 1496 q^{10} - 3402 q^{11} + 1792 q^{12} + 6413 q^{13} + 11216 q^{14} + 46465 q^{15} - 40960 q^{16}+ \cdots + 13336614 q^{99}+O(q^{100}) $ 40 * q - 80 * q^2 + 28 * q^3 - 640 * q^4 + 168 * q^5 - 1936 * q^6 + 1402 * q^7 - 5120 * q^8 - 6164 * q^9 - 1496 * q^10 - 3402 * q^11 + 1792 * q^12 + 6413 * q^13 + 11216 * q^14 + 46465 * q^15 - 40960 * q^16 + 17155 * q^17 - 98152 * q^18 + 67290 * q^19 + 6592 * q^20 + 16727 * q^21 - 27216 * q^22 + 2051 * q^23 + 47616 * q^24 + 787196 * q^25 - 214576 * q^26 + 603289 * q^27 - 62592 * q^28 + 95739 * q^29 - 369200 * q^30 + 540003 * q^31 + 1310720 * q^32 + 941656 * q^33 + 290520 * q^34 - 638364 * q^35 + 2359424 * q^36 + 843716 * q^37 - 169080 * q^38 + 827496 * q^39 + 52736 * q^40 + 175557 * q^41 + 1299656 * q^42 + 566562 * q^43 + 441152 * q^44 - 2450173 * q^45 + 484128 * q^46 - 2289258 * q^47 + 380928 * q^48 - 1290090 * q^49 - 2003912 * q^50 + 351796 * q^51 + 410432 * q^52 - 741339 * q^53 + 4826312 * q^54 - 755935 * q^55 - 434176 * q^56 - 8091472 * q^57 - 1476568 * q^58 - 8176986 * q^59 + 2973760 * q^60 - 10479540 * q^61 + 6613544 * q^62 - 10121022 * q^63 - 2621440 * q^64 + 9085330 * q^65 - 1581152 * q^66 + 7646158 * q^67 - 6844160 * q^68 - 5432460 * q^69 - 5106912 * q^70 - 24632815 * q^71 - 6281728 * q^72 - 11099311 * q^73 - 3436312 * q^74 + 11990582 * q^75 - 1352640 * q^76 + 8000688 * q^77 - 10937992 * q^78 + 10390986 * q^79 - 765952 * q^80 - 23584945 * q^81 + 2535096 * q^82 + 36507958 * q^83 + 10397248 * q^84 + 23914083 * q^85 + 5244176 * q^86 + 16619052 * q^87 - 3574784 * q^88 - 17387733 * q^89 - 2091344 * q^90 - 8973442 * q^91 - 8008576 * q^92 - 21404363 * q^93 - 137504 * q^94 - 12445576 * q^95 + 917504 * q^96 - 1428702 * q^97 + 92378560 * q^98 + 13336614 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	−6.47214	+	4.70228i	−0.572061	+	0.415627i
$2$	−6.47214	+	4.70228i	−0.572061	+	0.415627i
$3$	6.77917	+	4.92536i	0.144961	+	0.105321i	0.657902	−	0.753103i	$-0.271444\pi$
$3$	6.77917	+	4.92536i	0.144961	+	0.105321i	−0.512941	+	0.858424i	$0.671444\pi$
$4$	19.7771	−	60.8676i	0.154508	−	0.475528i
$5$	35.5870			0.127320			0.0636600	−	0.997972i	$-0.479723\pi$
$5$	35.5870			0.127320			0.0636600	+	0.997972i	$0.479723\pi$
$6$	−67.0362			−0.126701
$7$	−136.422	+	419.862i	−0.150328	+	0.462662i	−0.997658	−	0.0684053i	$-0.978209\pi$
$7$	−136.422	+	419.862i	−0.150328	+	0.462662i	0.847330	+	0.531067i	$0.178209\pi$
$8$	158.217	+	486.941i	0.109254	+	0.336249i
$9$	−654.122	−	2013.18i	−0.299096	−	0.920522i
$10$	−230.324	+	167.340i	−0.0728348	+	0.0529176i
$11$	−320.129	+	985.256i	−0.0725188	+	0.223190i	−0.980746	−	0.195287i	$-0.937436\pi$
$11$	−320.129	+	985.256i	−0.0725188	+	0.223190i	0.908227	+	0.418477i	$0.137436\pi$
$12$	433.867	−	315.223i	0.0724807	−	0.0526603i
$13$	6315.92	+	4588.78i	0.797324	+	0.579290i	0.910128	−	0.414328i	$-0.135983\pi$
$13$	6315.92	+	4588.78i	0.797324	+	0.579290i	−0.112804	+	0.993617i	$0.535983\pi$
$14$	−1091.37	−	3358.90i	−0.106298	−	0.327151i
$15$	241.251	+	175.279i	0.0184565	+	0.0134094i
$16$	−3313.73	−	2407.57i	−0.202254	−	0.146946i
$17$	6664.29	+	20510.6i	0.328990	+	1.01253i	0.969607	+	0.244667i	$0.0786785\pi$
$17$	6664.29	+	20510.6i	0.328990	+	1.01253i	−0.640617	+	0.767860i	$0.721322\pi$
$18$	13700.1	+	9953.71i	0.553695	+	0.402283i
$19$	−12083.5	+	8779.15i	−0.404160	+	0.293640i	−0.771233	−	0.636552i	$-0.780360\pi$
$19$	−12083.5	+	8779.15i	−0.404160	+	0.293640i	0.367073	+	0.930192i	$0.380360\pi$
$20$	703.807	−	2166.10i	0.0196720	−	0.0605442i
$21$	−2992.80	+	2174.40i	−0.0705196	+	0.0512355i
$22$	−2561.03	−	7882.05i	−0.0512785	−	0.157819i
$23$	−10314.2	−	31743.8i	−0.176762	−	0.544016i	0.822948	−	0.568117i	$-0.192328\pi$
$23$	−10314.2	−	31743.8i	−0.176762	−	0.544016i	−0.999710	+	0.0241004i	$0.992328\pi$
$24$	−1325.78	+	4080.33i	−0.0195764	+	0.0602499i
$25$	−76858.6			−0.983790
$26$	−62455.2			−0.696887
$27$	11144.3	−	34298.6i	0.108963	−	0.335353i
$28$	22858.0	+	16607.3i	0.196782	+	0.142970i
$29$	−175266.	+	127338.i	−1.33445	+	0.969538i	−0.334826	+	0.942280i	$0.608677\pi$
$29$	−175266.	+	127338.i	−1.33445	+	0.969538i	−0.999628	+	0.0272577i	$0.991323\pi$
$30$	−2385.62			−0.0161316
$31$	−112272.	+	122097.i	−0.676868	+	0.736104i
$31$	−112272.	+	122097.i	−0.676868	+	0.736104i
$32$	32768.0			0.176777
$33$	−7022.95	+	5102.47i	−0.0340189	+	0.0247162i
$34$	−139579.	−	101410.i	−0.609036	−	0.442490i
$35$	−4854.84	+	14941.6i	−0.0191398	+	0.0589061i
$36$	−135474.			−0.483947
$37$	−240162.			−0.779467			−0.389733	−	0.920928i	$-0.627433\pi$
$37$	−240162.			−0.779467			−0.389733	+	0.920928i	$0.627433\pi$
$38$	36923.8	−	113640.i	0.109160	−	0.335960i
$39$	20215.3	+	62216.3i	0.0545700	+	0.167949i
$40$	5630.46	+	17328.8i	0.0139102	+	0.0428112i
$41$	−480297.	+	348956.i	−1.08834	+	0.790728i	−0.979119	−	0.203289i	$-0.934837\pi$
$41$	−480297.	+	348956.i	−1.08834	+	0.790728i	−0.109225	+	0.994017i	$0.534837\pi$
$42$	9145.18	−	28146.0i	0.0190467	−	0.0586197i
$43$	−168032.	+	122082.i	−0.322294	+	0.234160i	−0.737154	−	0.675725i	$-0.763831\pi$
$43$	−168032.	+	122082.i	−0.322294	+	0.234160i	0.414860	+	0.909885i	$0.363831\pi$
$44$	53638.9	+	38971.0i	0.0949283	+	0.0689695i
$45$	−23278.3	−	71643.1i	−0.0380808	−	0.117201i
$46$	216023.	+	156950.i	0.327226	+	0.237744i
$47$	−201054.	−	146074.i	−0.282468	−	0.205225i	0.437525	−	0.899206i	$-0.355855\pi$
$47$	−201054.	−	146074.i	−0.282468	−	0.205225i	−0.719993	+	0.693981i	$0.755855\pi$
$48$	−10606.2	−	32642.7i	−0.0138426	−	0.0426031i
$49$	508587.	+	369510.i	0.617559	+	0.448683i
$50$	497439.	−	361411.i	0.562788	−	0.408889i
$51$	−55843.5	+	171869.i	−0.0589491	+	0.181427i
$52$	404219.	−	293682.i	0.398662	−	0.289645i
$53$	−14972.3	−	46080.1i	−0.0138141	−	0.0425156i	0.943912	−	0.330198i	$-0.107115\pi$
$53$	−14972.3	−	46080.1i	−0.0138141	−	0.0425156i	−0.957726	+	0.287682i	$0.907115\pi$
$54$	89154.2	+	274389.i	0.0770484	+	0.237131i
$55$	−11392.4	+	35062.3i	−0.00923309	+	0.0284165i
$56$	−226032.			−0.171994
$57$	−125156.			−0.0895140
$58$	535564.	−	1.64830e6i	0.360424	−	1.10927i
$59$	161647.	+	117443.i	0.102467	+	0.0744467i	0.637839	−	0.770170i	$-0.279829\pi$
$59$	161647.	+	117443.i	0.102467	+	0.0744467i	−0.535372	+	0.844616i	$0.679829\pi$
$60$	15440.0	−	11217.8i	0.00922824	−	0.00670471i
$61$	2.87849e6			1.62372			0.811859	−	0.583854i	$-0.198456\pi$
$61$	2.87849e6			1.62372			0.811859	+	0.583854i	$0.198456\pi$
$62$	152502.	−	1.31816e6i	0.0812654	−	0.702421i
$63$	934495.			0.470853
$64$	−212079.	+	154084.i	−0.101127	+	0.0734732i
$65$	224765.	+	163301.i	0.101515	+	0.0737551i
$66$	21460.2	−	66047.8i	0.00918820	−	0.0282784i
$67$	−1.57905e6			−0.641407			−0.320704	−	0.947180i	$-0.603919\pi$
$67$	−1.57905e6			−0.641407			−0.320704	+	0.947180i	$0.603919\pi$
$68$	1.38023e6			0.532317
$69$	86428.0	−	265998.i	0.0316725	−	0.0974781i
$70$	−38838.7	−	119533.i	−0.0135339	−	0.0416529i
$71$	1.77914e6	+	5.47562e6i	0.589936	+	1.81564i	0.578473	+	0.815701i	$0.303649\pi$
$71$	1.77914e6	+	5.47562e6i	0.589936	+	1.81564i	0.0114626	+	0.999934i	$0.496351\pi$
$72$	876807.	−	637038.i	0.276847	−	0.201141i
$73$	342373.	−	1.05371e6i	0.103008	−	0.317025i	−0.886250	−	0.463207i	$-0.846699\pi$
$73$	342373.	−	1.05371e6i	0.103008	−	0.317025i	0.989258	+	0.146182i	$0.0466987\pi$
$74$	1.55436e6	−	1.12931e6i	0.445903	−	0.323967i
$75$	−521038.	−	378556.i	−0.142612	−	0.103613i
$76$	295390.	+	909118.i	0.0771878	+	0.237560i
$77$	−369999.	−	268820.i	−0.0923599	−	0.0671034i
$78$	−423395.	−	307614.i	−0.101022	−	0.0733965i
$79$	−1.68287e6	−	5.17933e6i	−0.384021	−	1.18189i	−0.937188	−	0.348825i	$-0.886581\pi$
$79$	−1.68287e6	−	5.17933e6i	−0.384021	−	1.18189i	0.553167	−	0.833070i	$-0.313419\pi$
$80$	−117926.	−	85678.2i	−0.0257510	−	0.0187092i
$81$	−3.50079e6	+	2.54347e6i	−0.731927	+	0.531776i
$82$	1.46766e6	−	4.51698e6i	0.293952	−	0.904690i
$83$	2.48379e6	−	1.80458e6i	0.476805	−	0.346419i	−0.323282	−	0.946303i	$-0.604786\pi$
$83$	2.48379e6	−	1.80458e6i	0.476805	−	0.346419i	0.800087	+	0.599883i	$0.204786\pi$
$84$	73161.4	+	225168.i	0.0134681	+	0.0414504i
$85$	237162.	+	729910.i	0.0418870	+	0.128915i
$86$	513460.	−	1.58027e6i	0.0870486	−	0.267908i
$87$	−1.81534e6			−0.295557
$88$	−530411.			−0.0829704
$89$	−956804.	+	2.94474e6i	−0.143866	+	0.442774i	−0.996863	−	0.0791412i	$-0.974782\pi$
$89$	−956804.	+	2.94474e6i	−0.143866	+	0.442774i	0.852997	+	0.521915i	$0.174782\pi$
$90$	487546.	+	354223.i	0.0704964	+	0.0512186i
$91$	−2.78829e6	+	2.02581e6i	−0.387875	+	0.281808i
$92$	−2.13616e6			−0.286006
$93$	−1.36248e6	+	274739.i	−0.175647	+	0.0354185i
$94$	1.98813e6			0.246886
$95$	−430014.	+	312424.i	−0.0514577	+	0.0373862i
$96$	222140.	+	161394.i	0.0256258	+	0.0186182i
$97$	−49127.2	+	151198.i	−0.00546538	+	0.0168207i	−0.953752	−	0.300595i	$-0.902815\pi$
$97$	−49127.2	+	151198.i	−0.00546538	+	0.0168207i	0.948287	+	0.317415i	$0.102815\pi$
$98$	−5.02918e6			−0.539767
$99$	2.19290e6			0.227141
$100$	−1.52004e6	+	4.67820e6i	−0.152004	+	0.467820i
$101$	−700893.	−	2.15713e6i	−0.0676904	−	0.208330i	0.911490	−	0.411323i	$-0.134933\pi$
$101$	−700893.	−	2.15713e6i	−0.0676904	−	0.208330i	−0.979180	+	0.202993i	$0.934933\pi$
$102$	−446748.	−	1.37495e6i	−0.0416833	−	0.128288i
$103$	4.87835e6	−	3.54433e6i	0.439889	−	0.319598i	−0.345702	−	0.938344i	$-0.612359\pi$
$103$	4.87835e6	−	3.54433e6i	0.439889	−	0.319598i	0.785591	+	0.618746i	$0.212359\pi$
$104$	−1.23518e6	+	3.80150e6i	−0.107675	+	0.331389i
$105$	−106505.	+	77380.2i	−0.00897856	+	0.00652330i
$106$	313585.	+	227833.i	0.0255731	+	0.0185800i
$107$	4.60021e6	+	1.41580e7i	0.363023	+	1.11727i	0.951210	+	0.308546i	$0.0998422\pi$
$107$	4.60021e6	+	1.41580e7i	0.363023	+	1.11727i	−0.588186	+	0.808726i	$0.700158\pi$
$108$	−1.86727e6	−	1.35665e6i	−0.142634	−	0.103630i
$109$	−1.04644e7	−	7.60284e6i	−0.773966	−	0.562319i	0.129196	−	0.991619i	$-0.458760\pi$
$109$	−1.04644e7	−	7.60284e6i	−0.773966	−	0.562319i	−0.903162	+	0.429300i	$0.858760\pi$
$110$	−91139.5	−	280498.i	−0.00652878	−	0.0200935i
$111$	−1.62810e6	−	1.18288e6i	−0.112993	−	0.0820939i
$112$	1.46291e6	−	1.06287e6i	0.0983910	−	0.0714852i
$113$	−6.39508e6	+	1.96820e7i	−0.416938	+	1.28320i	0.493568	+	0.869707i	$0.335692\pi$
$113$	−6.39508e6	+	1.96820e7i	−0.416938	+	1.28320i	−0.910506	+	0.413496i	$0.864308\pi$
$114$	810029.	−	588521.i	0.0512075	−	0.0372044i
$115$	−367052.	−	1.12967e6i	−0.0225053	−	0.0692642i
$116$	4.28451e6	+	1.31864e7i	0.254858	+	0.784373i
$117$	5.10667e6	−	1.57167e7i	0.294773	−	0.907217i
$118$	−1.59845e6			−0.0895596
$119$	−9.52077e6			−0.517914
$120$	−47180.6	+	145207.i	−0.00249246	+	0.00767101i
$121$	1.48972e7	+	1.08235e7i	0.764462	+	0.555414i
$122$	−1.86300e7	+	1.35355e7i	−0.928866	+	0.674861i
$123$	−4.97475e6			−0.241048
$124$	5.21135e6	+	9.24843e6i	0.245456	+	0.435604i
$125$	−5.51540e6			−0.252576
$126$	−6.04818e6	+	4.39426e6i	−0.269357	+	0.195699i
$127$	−2.30182e7	−	1.67237e7i	−0.997146	−	0.724469i	−0.0356715	−	0.999364i	$-0.511357\pi$
$127$	−2.30182e7	−	1.67237e7i	−0.997146	−	0.724469i	−0.961474	+	0.274895i	$0.911357\pi$
$128$	648056.	−	1.99451e6i	0.0273135	−	0.0840623i
$129$	−1.74042e6			−0.0713821
$130$	−2.22260e6			−0.0887276
$131$	1.17311e7	−	3.61045e7i	0.455919	−	1.40318i	−0.414133	−	0.910216i	$-0.635915\pi$
$131$	1.17311e7	−	3.61045e7i	0.455919	−	1.40318i	0.870052	−	0.492959i	$-0.164085\pi$
$132$	171682.	+	528382.i	0.00649704	+	0.0199958i
$133$	−2.03759e6	−	6.27106e6i	−0.0750993	−	0.231132i
$134$	1.02198e7	−	7.42513e6i	0.366924	−	0.266586i
$135$	396592.	−	1.22058e6i	0.0138732	−	0.0426972i
$136$	−8.93303e6	+	6.49023e6i	−0.304518	+	0.221245i
$137$	1.37968e7	+	1.00240e7i	0.458412	+	0.333056i	0.792908	−	0.609341i	$-0.208566\pi$
$137$	1.37968e7	+	1.00240e7i	0.458412	+	0.333056i	−0.334496	+	0.942397i	$0.608566\pi$
$138$	691424.	+	2.12799e6i	0.0223959	+	0.0689274i
$139$	1.87602e6	+	1.36301e6i	0.0592497	+	0.0430474i	0.617016	−	0.786951i	$-0.288341\pi$
$139$	1.87602e6	+	1.36301e6i	0.0592497	+	0.0430474i	−0.557766	+	0.829998i	$0.688341\pi$
$140$	813448.	+	591005.i	0.0250543	+	0.0182030i
$141$	−643510.	−	1.98052e6i	−0.0193325	−	0.0594994i
$142$	−3.72627e7	−	2.70729e7i	−1.09211	−	0.793462i
$143$	−6.54303e6	+	4.75379e6i	−0.187113	+	0.135945i
$144$	−2.67928e6	+	8.24599e6i	−0.0747739	+	0.230130i
$145$	−6.23718e6	+	4.53158e6i	−0.169903	+	0.123442i
$146$	2.73898e6	+	8.42971e6i	0.0728373	+	0.224170i
$147$	1.62783e6	+	5.00994e6i	0.0422667	+	0.130083i
$148$	−4.74970e6	+	1.46181e7i	−0.120434	+	0.370658i
$149$	4.31625e7			1.06894			0.534472	−	0.845186i	$-0.320511\pi$
$149$	4.31625e7			1.06894			0.534472	+	0.845186i	$0.320511\pi$
$150$	5.15230e6			0.124647
$151$	5.12533e6	−	1.57741e7i	0.121144	−	0.372843i	−0.872035	−	0.489444i	$-0.837200\pi$
$151$	5.12533e6	−	1.57741e7i	0.121144	−	0.372843i	0.993179	+	0.116601i	$0.0371998\pi$
$152$	−6.18673e6	−	4.49493e6i	−0.142892	−	0.103817i
$153$	3.69322e7	−	2.68328e7i	0.833653	−	0.605685i
$154$	3.65875e6			0.0807255
$155$	−3.99541e6	+	4.34507e6i	−0.0861788	+	0.0937208i
$156$	4.18676e6			0.0882962
$157$	1.48229e7	−	1.07695e7i	0.305693	−	0.222099i	−0.424353	−	0.905497i	$-0.639499\pi$
$157$	1.48229e7	−	1.07695e7i	0.305693	−	0.222099i	0.730046	+	0.683398i	$0.239499\pi$
$158$	3.52464e7	+	2.56080e7i	0.710911	+	0.516507i
$159$	125461.	−	386129.i	0.00247525	−	0.00761803i
$160$	1.16612e6			0.0225072
$161$	1.47351e7			0.278268
$162$	1.06975e7	−	3.29234e7i	0.197687	−	0.608418i
$163$	−2.10725e7	−	6.48546e7i	−0.381119	−	1.17296i	−0.939257	−	0.343215i	$-0.888484\pi$
$163$	−2.10725e7	−	6.48546e7i	−0.381119	−	1.17296i	0.558138	−	0.829748i	$-0.311516\pi$
$164$	1.17412e7	+	3.61358e7i	0.207855	+	0.639712i
$165$	−249926.	+	181582.i	−0.00433129	+	0.00314687i
$166$	−7.58977e6	+	2.33589e7i	−0.128781	+	0.396346i
$167$	4.54751e7	−	3.30396e7i	0.755554	−	0.548942i	−0.141989	−	0.989868i	$-0.545350\pi$
$167$	4.54751e7	−	3.30396e7i	0.755554	−	0.548942i	0.897544	+	0.440926i	$0.145350\pi$
$168$	−1.53231e6	−	1.11329e6i	−0.0249325	−	0.0181145i
$169$	−556468.	−	1.71263e6i	−0.00886822	−	0.0272936i
$170$	−4.96719e6	−	3.60887e6i	−0.0775424	−	0.0563379i
$171$	2.55781e7	+	1.85836e7i	0.391184	+	0.284212i
$172$	4.10768e6	+	1.26421e7i	0.0615526	+	0.189440i
$173$	5.39430e7	+	3.91919e7i	0.792089	+	0.575486i	0.908583	−	0.417705i	$-0.137166\pi$
$173$	5.39430e7	+	3.91919e7i	0.792089	+	0.575486i	−0.116494	+	0.993191i	$0.537166\pi$
$174$	1.17491e7	−	8.53625e6i	0.169077	−	0.122841i
$175$	1.04852e7	−	3.22700e7i	0.147891	−	0.455162i
$176$	3.43289e6	−	2.49414e6i	0.0474642	−	0.0344847i
$177$	517381.	+	1.59234e6i	0.00701300	+	0.0215838i
$178$	−7.65443e6	−	2.35579e7i	−0.101729	−	0.313088i
$179$	−1.09485e7	+	3.36962e7i	−0.142683	+	0.439132i	−0.996706	−	0.0811033i	$-0.974156\pi$
$179$	−1.09485e7	+	3.36962e7i	−0.142683	+	0.439132i	0.854023	+	0.520235i	$0.174156\pi$
$180$	−4.82112e6			−0.0616161
$181$	3.88858e7			0.487434			0.243717	−	0.969846i	$-0.421633\pi$
$181$	3.88858e7			0.487434			0.243717	+	0.969846i	$0.421633\pi$
$182$	8.52024e6	−	2.62226e7i	0.104762	−	0.322423i
$183$	1.95138e7	+	1.41776e7i	0.235376	+	0.171011i
$184$	1.38255e7	−	1.00448e7i	0.163613	−	0.118872i
$185$	−8.54663e6			−0.0992417
$186$	7.52626e6	−	8.18492e6i	0.0857598	−	0.0932651i
$187$	−2.23416e7			−0.249844
$188$	−1.28674e7	+	9.34873e6i	−0.141234	+	0.102612i
$189$	1.28804e7	+	9.35813e6i	0.138775	+	0.100826i
$190$	1.31401e6	−	4.04410e6i	0.0138982	−	0.0427744i
$191$	−8.01573e7			−0.832389			−0.416194	−	0.909276i	$-0.636636\pi$
$191$	−8.01573e7			−0.832389			−0.416194	+	0.909276i	$0.636636\pi$
$192$	−2.19664e6			−0.0223978
$193$	2.00597e6	−	6.17373e6i	0.0200851	−	0.0618154i	−0.940512	−	0.339761i	$-0.889654\pi$
$193$	2.00597e6	−	6.17373e6i	0.0200851	−	0.0618154i	0.960597	+	0.277946i	$0.0896536\pi$
$194$	−393017.	−	1.20958e6i	−0.00386461	−	0.0118940i
$195$	719402.	+	2.21409e6i	0.00694786	+	0.0213833i
$196$	3.25495e7	−	2.36486e7i	0.308780	−	0.224342i
$197$	−5.10967e7	+	1.57259e8i	−0.476169	+	1.46550i	0.368206	+	0.929744i	$0.379972\pi$
$197$	−5.10967e7	+	1.57259e8i	−0.476169	+	1.46550i	−0.844375	+	0.535753i	$0.820028\pi$
$198$	−1.41928e7	+	1.03116e7i	−0.129939	+	0.0944060i
$199$	−1.79079e7	−	1.30109e7i	−0.161087	−	0.117036i	0.504322	−	0.863516i	$-0.331743\pi$
$199$	−1.79079e7	−	1.30109e7i	−0.161087	−	0.117036i	−0.665408	+	0.746479i	$0.731743\pi$
$200$	−1.21603e7	−	3.74256e7i	−0.107483	−	0.330799i
$201$	−1.07046e7	−	7.77738e6i	−0.0929793	−	0.0675534i
$202$	1.46797e7	+	1.06654e7i	0.125310	+	0.0910434i
$203$	−2.95544e7	−	9.09591e7i	−0.247962	−	0.763150i
$204$	9.35682e6	+	6.79813e6i	0.0771654	+	0.0560639i
$205$	−1.70923e7	+	1.24183e7i	−0.138568	+	0.100675i
$206$	−1.49069e7	+	4.58788e7i	−0.118810	+	0.365659i
$207$	−5.71593e7	+	4.15287e7i	−0.447910	+	0.325426i
$208$	−9.88146e6	−	3.04120e7i	−0.0761377	−	0.234328i
$209$	−4.78144e6	−	1.47158e7i	−0.0362282	−	0.111499i
$210$	325450.	−	1.00163e6i	0.00242503	−	0.00746346i
$211$	−4.55408e7			−0.333743			−0.166871	−	0.985979i	$-0.553366\pi$
$211$	−4.55408e7			−0.333743			−0.166871	+	0.985979i	$0.553366\pi$
$212$	−3.10089e6			−0.0223517
$213$	−1.49083e7	+	4.58830e7i	−0.105706	+	0.325330i
$214$	−9.63481e7	−	7.00010e7i	−0.672040	−	0.488265i
$215$	−5.97975e6	+	4.34454e6i	−0.0410344	+	0.0298133i
$216$	1.84646e7			0.124667
$217$	−3.59477e7	−	6.37953e7i	−0.238815	−	0.423818i
$218$	1.03478e8			0.676471
$219$	7.51092e6	−	5.45701e6i	0.0483213	−	0.0351075i
$220$	1.90885e6	+	1.38686e6i	0.0120863	+	0.00878119i
$221$	−5.20275e7	+	1.60124e8i	−0.324235	+	0.997892i
$222$	1.60995e7			0.0987591
$223$	−2.68292e8			−1.62010			−0.810048	−	0.586364i	$-0.800559\pi$
$223$	−2.68292e8			−1.62010			−0.810048	+	0.586364i	$0.800559\pi$
$224$	−4.47026e6	+	1.37581e7i	−0.0265745	+	0.0817879i
$225$	5.02749e7	+	1.54730e8i	0.294247	+	0.905600i
$226$	−5.11606e7	−	1.57456e8i	−0.294820	−	0.907362i
$227$	−1.50893e8	+	1.09630e8i	−0.856207	+	0.622071i	−0.926850	−	0.375431i	$-0.877495\pi$
$227$	−1.50893e8	+	1.09630e8i	−0.856207	+	0.622071i	0.0706434	+	0.997502i	$0.477495\pi$
$228$	−2.47523e6	+	7.61797e6i	−0.0138307	+	0.0425664i
$229$	−1.96107e8	+	1.42480e8i	−1.07912	+	0.784023i	−0.977529	−	0.210803i	$-0.932392\pi$
$229$	−1.96107e8	+	1.42480e8i	−1.07912	+	0.784023i	−0.101587	+	0.994827i	$0.532392\pi$
$230$	7.68763e6	+	5.58539e6i	0.0416625	+	0.0302695i
$231$	−1.18425e6	−	3.64476e6i	−0.00632125	−	0.0194548i
$232$	−8.97360e7	−	6.51970e7i	−0.471801	−	0.342783i
$233$	1.82598e8	+	1.32665e8i	0.945695	+	0.687087i	0.949785	−	0.312904i	$-0.101302\pi$
$233$	1.82598e8	+	1.32665e8i	0.945695	+	0.687087i	−0.00409014	+	0.999992i	$0.501302\pi$
$234$	4.08533e7	+	1.25734e8i	0.208436	+	0.641499i
$235$	−7.15489e6	−	5.19833e6i	−0.0359638	−	0.0261292i
$236$	1.03454e7	−	7.51636e6i	0.0512336	−	0.0372234i
$237$	1.41016e7	−	4.34003e7i	0.0688097	−	0.211775i
$238$	6.16197e7	−	4.47694e7i	0.296279	−	0.215259i
$239$	−8.66501e7	−	2.66682e8i	−0.410560	−	1.26357i	−0.916162	−	0.400807i	$-0.868730\pi$
$239$	−8.66501e7	−	2.66682e8i	−0.410560	−	1.26357i	0.505602	−	0.862767i	$-0.331270\pi$
$240$	−377444.	−	1.16165e6i	−0.00176244	−	0.00542422i
$241$	2.63512e7	−	8.11008e7i	0.121267	−	0.373220i	−0.871936	−	0.489620i	$-0.837135\pi$
$241$	2.63512e7	−	8.11008e7i	0.121267	−	0.373220i	0.993202	+	0.116400i	$0.0371354\pi$
$242$	−1.47312e8			−0.668164
$243$	−1.15131e8			−0.514720
$244$	5.69282e7	−	1.75207e8i	0.250878	−	0.772123i
$245$	1.80991e7	+	1.31498e7i	0.0786276	+	0.0571263i
$246$	3.21972e7	−	2.33927e7i	0.137894	−	0.100186i
$247$	−1.16604e8			−0.492349
$248$	−7.72173e7	−	3.53519e7i	−0.321465	−	0.147174i
$249$	2.57262e7			0.105603
$250$	3.56964e7	−	2.59350e7i	0.144489	−	0.104977i
$251$	8.60427e7	+	6.25137e7i	0.343444	+	0.249527i	0.746114	−	0.665819i	$-0.231918\pi$
$251$	8.60427e7	+	6.25137e7i	0.343444	+	0.249527i	−0.402669	+	0.915345i	$0.631918\pi$
$252$	1.84816e7	−	5.68805e7i	0.0727508	−	0.223904i
$253$	3.45777e7			0.134238
$254$	2.27617e8			0.871537
$255$	−1.98730e6	+	6.11630e6i	−0.00750540	+	0.0230992i
$256$	5.18444e6	+	1.59561e7i	0.0193136	+	0.0594410i
$257$	2.49547e7	+	7.68026e7i	0.0917036	+	0.282235i	0.986381	−	0.164479i	$-0.0525943\pi$
$257$	2.49547e7	+	7.68026e7i	0.0917036	+	0.282235i	−0.894677	+	0.446714i	$0.852594\pi$
$258$	1.12642e7	−	8.18393e6i	0.0408349	−	0.0296683i
$259$	3.27632e7	−	1.00835e8i	0.117176	−	0.360630i
$260$	1.43849e7	−	1.04513e7i	0.0507576	−	0.0368776i
$261$	3.70999e8	+	2.69547e8i	1.29161	+	0.938410i
$262$	9.38486e7	+	2.88836e8i	0.322384	+	0.992195i
$263$	2.30053e8	+	1.67144e8i	0.779800	+	0.566558i	0.904919	−	0.425584i	$-0.139931\pi$
$263$	2.30053e8	+	1.67144e8i	0.779800	+	0.566558i	−0.125119	+	0.992142i	$0.539931\pi$
$264$	−3.59575e6	−	2.61246e6i	−0.0120275	−	0.00873850i
$265$	−532821.	−	1.63985e6i	−0.00175882	−	0.00541308i
$266$	4.26758e7	+	3.10058e7i	0.139026	+	0.101008i
$267$	−2.09902e7	+	1.52503e7i	−0.0674882	+	0.0490331i
$268$	−3.12290e7	+	9.61130e7i	−0.0991029	+	0.305007i
$269$	2.44255e8	−	1.77462e8i	0.765086	−	0.555867i	−0.135380	−	0.990794i	$-0.543226\pi$
$269$	2.44255e8	−	1.77462e8i	0.765086	−	0.555867i	0.900466	+	0.434926i	$0.143226\pi$
$270$	3.17273e6	+	9.76467e6i	0.00980980	+	0.0301915i
$271$	−2.43321e7	−	7.48866e7i	−0.0742656	−	0.228566i	0.907032	−	0.421061i	$-0.138342\pi$
$271$	−2.43321e7	−	7.48866e7i	−0.0742656	−	0.228566i	−0.981298	+	0.192495i	$0.938342\pi$
$272$	2.72969e7	−	8.40113e7i	0.0822475	−	0.253132i
$273$	−2.88801e7			−0.0859072
$274$	−1.36430e8			−0.400667
$275$	2.46047e7	−	7.57253e7i	0.0713432	−	0.219572i
$276$	−1.44814e7	−	1.05213e7i	−0.0414599	−	0.0301224i
$277$	4.09591e8	−	2.97585e8i	1.15790	−	0.841264i	0.168390	−	0.985721i	$-0.446143\pi$
$277$	4.09591e8	−	2.97585e8i	1.15790	−	0.841264i	0.989511	+	0.144456i	$0.0461434\pi$
$278$	−1.85511e7			−0.0517861
$279$	3.19243e8	+	1.46157e8i	0.880048	+	0.402906i
$280$	−8.04382e6			−0.0218982
$281$	−2.89649e8	+	2.10443e8i	−0.778754	+	0.565798i	−0.904605	−	0.426251i	$-0.859834\pi$
$281$	−2.89649e8	+	2.10443e8i	−0.778754	+	0.565798i	0.125851	+	0.992049i	$0.459834\pi$
$282$	1.34779e7	+	9.79224e6i	0.0357889	+	0.0260022i
$283$	2.08917e8	−	6.42980e8i	0.547925	−	1.68634i	−0.166006	−	0.986125i	$-0.553087\pi$
$283$	2.08917e8	−	6.42980e8i	0.547925	−	1.68634i	0.713931	−	0.700216i	$-0.246913\pi$
$284$	3.68474e8			0.954536
$285$	−4.45394e6			−0.0113969
$286$	1.99937e7	−	6.15344e7i	0.0505374	−	0.155538i
$287$	−8.09907e7	−	2.49264e8i	−0.202231	−	0.622404i
$288$	−2.14343e7	−	6.59679e7i	−0.0528731	−	0.162727i
$289$	−4.42998e7	+	3.21857e7i	−0.107959	+	0.0784369i
$290$	1.90591e7	−	5.86579e7i	0.0458891	−	0.141232i
$291$	−1.07775e6	+	783028.i	−0.00256384	+	0.00186274i
$292$	−5.73659e7	−	4.16788e7i	−0.134839	−	0.0979660i
$293$	3.92863e7	+	1.20911e8i	0.0912440	+	0.280820i	0.986257	−	0.165221i	$-0.0528336\pi$
$293$	3.92863e7	+	1.20911e8i	0.0912440	+	0.280820i	−0.895013	+	0.446041i	$0.852834\pi$
$294$	−3.40937e7	−	2.47705e7i	−0.0782453	−	0.0568486i
$295$	5.75252e6	+	4.17945e6i	0.0130461	+	0.00947856i
$296$	−3.79976e7	−	1.16945e8i	−0.0851598	−	0.262095i
$297$	3.02252e7	+	2.19599e7i	0.0669456	+	0.0486389i
$298$	−2.79354e8	+	2.02962e8i	−0.611502	+	0.444282i
$299$	8.05220e7	−	2.47821e8i	0.174207	−	0.536154i
$300$	−3.33464e7	+	2.42276e7i	−0.0713058	+	0.0518067i
$301$	−2.83346e7	−	8.72049e7i	−0.0598872	−	0.184314i
$302$	4.10026e7	+	1.26193e8i	0.0856618	+	0.263640i
$303$	5.87315e6	−	1.80757e7i	0.0121289	−	0.0373290i
$304$	6.11778e7			0.124892
$305$	1.02437e8			0.206732
$306$	−1.12855e8	+	3.47332e8i	−0.225162	+	0.692978i
$307$	−3.71290e8	−	2.69758e8i	−0.732367	−	0.532096i	0.157945	−	0.987448i	$-0.449513\pi$
$307$	−3.71290e8	−	2.69758e8i	−0.732367	−	0.532096i	−0.890311	+	0.455352i	$0.849513\pi$
$308$	−2.36800e7	+	1.72045e7i	−0.0461799	+	0.0335517i
$309$	5.05283e7			0.0974272
$310$	5.42710e6	−	4.69094e7i	0.0103467	−	0.0894323i
$311$	2.06736e7			0.0389723			0.0194861	−	0.999810i	$-0.493797\pi$
$311$	2.06736e7			0.0389723			0.0194861	+	0.999810i	$0.493797\pi$
$312$	−2.70973e7	+	1.96873e7i	−0.0505108	+	0.0366983i
$313$	3.37966e8	+	2.45547e8i	0.622971	+	0.452615i	0.853958	−	0.520342i	$-0.174195\pi$
$313$	3.37966e8	+	2.45547e8i	0.622971	+	0.452615i	−0.230987	+	0.972957i	$0.574195\pi$
$314$	−4.52948e7	+	1.39403e8i	−0.0825647	+	0.254108i
$315$	3.32559e7			0.0599490
$316$	−3.48536e8			−0.621359
$317$	4.07657e7	−	1.25464e8i	0.0718767	−	0.221214i	−0.908665	−	0.417527i	$-0.862897\pi$
$317$	4.07657e7	−	1.25464e8i	0.0718767	−	0.221214i	0.980541	+	0.196313i	$0.0628969\pi$
$318$	1.00369e6	+	3.08903e6i	0.00175026	+	0.00538676i
$319$	−6.93528e7	−	2.13446e8i	−0.119618	−	0.368146i
$320$	−7.54726e6	+	5.48340e6i	−0.0128755	+	0.00935460i
$321$	−3.85476e7	+	1.18637e8i	−0.0650473	+	0.200195i
$322$	−9.53677e7	+	6.92887e7i	−0.159186	+	0.115656i
$323$	−2.60593e8	−	1.89332e8i	−0.430283	−	0.312619i
$324$	8.55796e7	+	2.63387e8i	0.139786	+	0.430216i
$325$	−4.85432e8	−	3.52687e8i	−0.784399	−	0.569899i
$326$	4.41349e8	+	3.20659e8i	0.705538	+	0.512603i
$327$	−3.34933e7	−	1.03082e8i	−0.0529714	−	0.163029i
$328$	−2.45912e8	−	1.78665e8i	−0.384788	−	0.279565i
$329$	8.87590e7	−	6.44872e7i	0.137413	−	0.0998361i
$330$	763705.	−	2.35044e6i	0.00116984	−	0.00360040i
$331$	5.70148e7	−	4.14237e7i	0.0864152	−	0.0627843i	−0.543739	−	0.839255i	$-0.682992\pi$
$331$	5.70148e7	−	4.14237e7i	0.0864152	−	0.0627843i	0.630154	+	0.776470i	$0.282992\pi$
$332$	−6.07182e7	−	1.86871e8i	−0.0910616	−	0.280259i
$333$	1.57095e8	+	4.83489e8i	0.233135	+	0.717516i
$334$	−1.38959e8	+	4.27673e8i	−0.204068	+	0.628057i
$335$	−5.61936e7			−0.0816639
$336$	1.51523e7			0.0217918
$337$	4.67648e7	−	1.43927e8i	0.0665602	−	0.204851i	−0.912245	−	0.409645i	$-0.865652\pi$
$337$	4.67648e7	−	1.43927e8i	0.0665602	−	0.204851i	0.978805	+	0.204794i	$0.0656525\pi$
$338$	1.16548e7	+	8.46772e6i	0.0164171	+	0.0119277i
$339$	−1.40294e8	+	1.01930e8i	−0.195588	+	0.142103i
$340$	4.91183e7			0.0677746
$341$	−8.43554e7	−	1.49703e8i	−0.115205	−	0.204452i
$342$	−2.52930e8			−0.341908
$343$	−5.18659e8	+	3.76828e8i	−0.693989	+	0.504213i
$344$	−8.60323e7	−	6.25061e7i	−0.113948	−	0.0827881i
$345$	3.07572e6	−	9.46608e6i	0.00403255	−	0.0124109i
$346$	−5.33418e8			−0.692311
$347$	−7.70797e8			−0.990345			−0.495173	−	0.868795i	$-0.664895\pi$
$347$	−7.70797e8			−0.990345			−0.495173	+	0.868795i	$0.664895\pi$
$348$	−3.59022e7	+	1.10495e8i	−0.0456660	+	0.140546i
$349$	1.70300e8	+	5.24129e8i	0.214450	+	0.660008i	0.999192	+	0.0401865i	$0.0127952\pi$
$349$	1.70300e8	+	5.24129e8i	0.214450	+	0.660008i	−0.784742	+	0.619822i	$0.787205\pi$
$350$	8.38813e7	+	2.58160e8i	0.104575	+	0.321848i
$351$	2.27775e8	−	1.65488e8i	0.281146	−	0.204264i
$352$	−1.04900e7	+	3.22849e7i	−0.0128196	+	0.0394548i
$353$	1.31458e9	−	9.55098e8i	1.59065	−	1.15568i	0.687648	−	0.726044i	$-0.258643\pi$
$353$	1.31458e9	−	9.55098e8i	1.59065	−	1.15568i	0.903004	−	0.429633i	$-0.141357\pi$
$354$	−1.08362e7	−	7.87294e6i	−0.0129827	−	0.00943247i
$355$	6.33141e7	+	1.94861e8i	0.0751106	+	0.231167i
$356$	1.60317e8	+	1.16477e8i	0.188323	+	0.136825i
$357$	−6.45430e7	−	4.68932e7i	−0.0750776	−	0.0545470i
$358$	−8.75883e7	−	2.69569e8i	−0.100892	−	0.310513i
$359$	5.46690e8	+	3.97193e8i	0.623606	+	0.453076i	0.854179	−	0.519979i	$-0.174060\pi$
$359$	5.46690e8	+	3.97193e8i	0.623606	+	0.453076i	−0.230573	+	0.973055i	$0.574060\pi$
$360$	3.12029e7	−	2.26703e7i	0.0352482	−	0.0256093i
$361$	−2.07285e8	+	6.37957e8i	−0.231896	+	0.713701i
$362$	−2.51674e8	+	1.82852e8i	−0.278842	+	0.202591i
$363$	4.76814e7	+	1.46748e8i	0.0523209	+	0.161027i
$364$	6.81619e7	+	2.09781e8i	0.0740776	+	0.227987i
$365$	1.21840e7	−	3.74985e7i	0.0131149	−	0.0403636i
$366$	−1.92963e8			−0.205726
$367$	−8.96531e8			−0.946747			−0.473374	−	0.880862i	$-0.656964\pi$
$367$	−8.96531e8			−0.946747			−0.473374	+	0.880862i	$0.656964\pi$
$368$	−4.22470e7	+	1.30023e8i	−0.0441904	+	0.136004i
$369$	1.01668e9	+	7.38664e8i	1.05340	+	0.765341i
$370$	5.53150e7	−	4.01887e7i	0.0567723	−	0.0412475i
$371$	2.13899e7			0.0217470
$372$	−1.02232e7	+	8.83645e7i	−0.0102964	+	0.0889975i
$373$	−1.26100e9			−1.25816			−0.629079	−	0.777341i	$-0.716568\pi$
$373$	−1.26100e9			−1.25816			−0.629079	+	0.777341i	$0.716568\pi$
$374$	1.44598e8	−	1.05056e8i	0.142926	−	0.103842i
$375$	−3.73899e7	−	2.71653e7i	−0.0366138	−	0.0266015i
$376$	3.93194e7	−	1.21013e8i	0.0381460	−	0.117401i
$377$	−1.69129e9			−1.62564
$378$	−1.27368e8			−0.121294
$379$	4.76348e8	−	1.46605e9i	0.449456	−	1.38328i	−0.428067	−	0.903747i	$-0.640805\pi$
$379$	4.76348e8	−	1.46605e9i	0.449456	−	1.38328i	0.877523	−	0.479535i	$-0.159195\pi$
$380$	1.05121e7	+	3.23528e7i	0.00982755	+	0.0302461i
$381$	−7.36742e7	−	2.26746e8i	−0.0682462	−	0.210040i
$382$	5.18789e8	−	3.76922e8i	0.476178	−	0.345963i
$383$	−1.90973e8	+	5.87755e8i	−0.173691	+	0.534565i	−0.999571	−	0.0292801i	$-0.990679\pi$
$383$	−1.90973e8	+	5.87755e8i	−0.173691	+	0.534565i	0.825881	+	0.563845i	$0.190679\pi$
$384$	1.42170e7	−	1.03292e7i	0.0128129	−	0.00930912i
$385$	−1.31672e7	−	9.56651e6i	−0.0117593	−	0.00854360i
$386$	1.60477e7	+	4.93898e7i	0.0142023	+	0.0437101i
$387$	3.55687e8	+	2.58422e8i	0.311946	+	0.226642i
$388$	8.23146e6	+	5.98051e6i	0.00715428	+	0.00519789i
$389$	2.41579e8	+	7.43503e8i	0.208082	+	0.640411i	0.999573	+	0.0292298i	$0.00930546\pi$
$389$	2.41579e8	+	7.43503e8i	0.208082	+	0.640411i	−0.791490	+	0.611182i	$0.790695\pi$
$390$	−1.50674e7	−	1.09471e7i	−0.0128621	−	0.00934484i
$391$	5.82347e8	−	4.23100e8i	0.492678	−	0.357952i
$392$	−9.94626e7	+	3.06114e8i	−0.0833985	+	0.256674i
$393$	2.57355e8	−	1.86979e8i	0.213874	−	0.155389i
$394$	−4.08774e8	−	1.25808e9i	−0.336702	−	1.03626i
$395$	−5.98882e7	−	1.84317e8i	−0.0488935	−	0.150479i
$396$	4.33692e7	−	1.33477e8i	0.0350952	−	0.108012i
$397$	−3.70300e8			−0.297021			−0.148510	−	0.988911i	$-0.547448\pi$
$397$	−3.70300e8			−0.297021			−0.148510	+	0.988911i	$0.547448\pi$
$398$	1.77083e8			0.140795
$399$	1.70740e7	−	5.25485e7i	0.0134565	−	0.0414147i
$400$	2.54689e8	+	1.85042e8i	0.198976	+	0.144564i
$401$	−8.31853e8	+	6.04376e8i	−0.644230	+	0.468061i	−0.861301	−	0.508095i	$-0.830350\pi$
$401$	−8.31853e8	+	6.04376e8i	−0.644230	+	0.468061i	0.217071	+	0.976156i	$0.430350\pi$
$402$	1.05853e8			0.0812669
$403$	−1.26938e9	+	2.55965e8i	−0.966101	+	0.194811i
$404$	−1.45161e8			−0.109525
$405$	−1.24583e8	+	9.05145e7i	−0.0931890	+	0.0677058i
$406$	6.18995e8	+	4.49726e8i	0.459035	+	0.333509i
$407$	7.68827e7	−	2.36621e8i	0.0565260	−	0.173969i
$408$	−9.25253e7			−0.0674450
$409$	1.20380e9			0.870004			0.435002	−	0.900429i	$-0.356748\pi$
$409$	1.20380e9			0.870004			0.435002	+	0.900429i	$0.356748\pi$
$410$	5.22295e7	−	1.60746e8i	0.0374259	−	0.115185i
$411$	4.41593e7	+	1.35908e8i	0.0313744	+	0.0965605i
$412$	−1.19255e8	−	3.67030e8i	−0.0840113	−	0.258560i
$413$	−7.13621e7	+	5.18476e7i	−0.0498474	+	0.0362162i
$414$	1.74663e8	−	5.37559e8i	0.120976	−	0.372327i
$415$	8.83905e7	−	6.42195e7i	0.0607068	−	0.0441061i
$416$	2.06960e8	+	1.50365e8i	0.140948	+	0.102405i
$417$	6.00457e6	+	1.84802e7i	0.00405514	+	0.0124804i
$418$	1.00144e8	+	7.27587e7i	0.0670667	+	0.0487268i
$419$	1.42829e9	+	1.03771e9i	0.948566	+	0.689174i	0.950467	−	0.310824i	$-0.100605\pi$
$419$	1.42829e9	+	1.03771e9i	0.948566	+	0.689174i	−0.00190094	+	0.999998i	$0.500605\pi$
$420$	2.60360e6	+	8.01305e6i	0.00171475	+	0.00527746i
$421$	−2.19087e8	−	1.59176e8i	−0.143097	−	0.103966i	0.513934	−	0.857830i	$-0.328188\pi$
$421$	−2.19087e8	−	1.59176e8i	−0.143097	−	0.103966i	−0.657030	+	0.753864i	$0.728188\pi$
$422$	2.94746e8	−	2.14146e8i	0.190921	−	0.138713i
$423$	−1.62560e8	+	5.00307e8i	−0.104429	+	0.321400i
$424$	2.00694e7	−	1.45813e7i	0.0127866	−	0.00928999i
$425$	−5.12208e8	−	1.57641e9i	−0.323657	−	0.996113i
$426$	−1.19266e8	−	3.67064e8i	−0.0747454	−	0.230043i
$427$	−3.92688e8	+	1.20857e9i	−0.244090	+	0.751232i
$428$	9.52742e8			0.587384
$429$	−6.77705e7			−0.0414419
$430$	1.82725e7	−	5.62369e7i	0.0110830	−	0.0341100i
$431$	−1.81285e9	−	1.31711e9i	−1.09067	−	0.792415i	−0.111154	−	0.993803i	$-0.535455\pi$
$431$	−1.81285e9	−	1.31711e9i	−1.09067	−	0.792415i	−0.979512	+	0.201388i	$0.935455\pi$
$432$	−1.19505e8	+	8.68257e7i	−0.0713172	+	0.0518150i
$433$	2.51157e9			1.48675			0.743375	−	0.668875i	$-0.233224\pi$
$433$	2.51157e9			1.48675			0.743375	+	0.668875i	$0.233224\pi$
$434$	5.32642e8	+	2.43856e8i	0.312767	+	0.143192i
$435$	−6.46026e7			−0.0376303
$436$	−6.69722e8	+	4.86582e8i	−0.386983	+	0.281160i
$437$	4.03315e8	+	2.93026e8i	0.231185	+	0.167966i
$438$	−2.29513e7	+	7.06370e7i	−0.0130511	+	0.0401673i
$439$	1.43562e9			0.809868			0.404934	−	0.914346i	$-0.367294\pi$
$439$	1.43562e9			0.809868			0.404934	+	0.914346i	$0.367294\pi$
$440$	−1.88757e7			−0.0105638
$441$	4.11212e8	−	1.26558e9i	0.228313	−	0.702676i
$442$	−4.16220e8	−	1.28099e9i	−0.229269	−	0.705616i
$443$	2.37343e8	+	7.30465e8i	0.129707	+	0.399196i	0.994729	−	0.102537i	$-0.0326959\pi$
$443$	2.37343e8	+	7.30465e8i	0.129707	+	0.399196i	−0.865022	+	0.501733i	$0.832696\pi$
$444$	−1.04198e8	+	7.57044e7i	−0.0564963	+	0.0410470i
$445$	−3.40498e7	+	1.04795e8i	−0.0183170	+	0.0563740i
$446$	1.73642e9	−	1.26158e9i	0.926794	−	0.673355i
$447$	2.92606e8	+	2.12591e8i	0.154956	+	0.112582i
$448$	−3.57621e7	−	1.10064e8i	−0.0187910	−	0.0578328i
$449$	−1.27447e9	−	9.25956e8i	−0.664457	−	0.482756i	0.203708	−	0.979032i	$-0.434701\pi$
$449$	−1.27447e9	−	9.25956e8i	−0.664457	−	0.482756i	−0.868165	+	0.496275i	$0.834701\pi$
$450$	−1.05297e9	−	7.65028e8i	−0.544719	−	0.395762i
$451$	−1.90054e8	−	5.84926e8i	−0.0975571	−	0.300250i
$452$	1.07152e9	+	7.78507e8i	0.545779	+	0.396532i
$453$	1.12439e8	−	8.16915e7i	0.0568293	−	0.0412889i
$454$	4.61088e8	−	1.41908e9i	0.231254	−	0.711725i
$455$	−9.92267e7	+	7.20924e7i	−0.0493843	+	0.0358798i
$456$	−1.98018e7	−	6.09438e7i	−0.00977976	−	0.0300990i
$457$	9.32426e8	+	2.86971e9i	0.456991	+	1.40647i	0.868782	+	0.495195i	$0.164904\pi$
$457$	9.32426e8	+	2.86971e9i	0.456991	+	1.40647i	−0.411790	+	0.911279i	$0.635096\pi$
$458$	5.99248e8	−	1.84430e9i	0.291459	−	0.897019i
$459$	7.77752e8			0.375402
$460$	−7.60194e7			−0.0364143
$461$	−3.16594e8	+	9.74378e8i	−0.150505	+	0.463206i	−0.997678	−	0.0681112i	$-0.978303\pi$
$461$	−3.16594e8	+	9.74378e8i	−0.150505	+	0.463206i	0.847173	+	0.531317i	$0.178303\pi$
$462$	2.48033e7	+	1.80207e7i	0.0117021	+	0.00850206i
$463$	2.17593e8	−	1.58091e8i	0.101885	−	0.0740241i	−0.535676	−	0.844424i	$-0.679943\pi$
$463$	2.17593e8	−	1.58091e8i	0.101885	−	0.0740241i	0.637562	+	0.770399i	$0.279943\pi$
$464$	8.87358e8			0.412369
$465$	−4.84866e7	+	9.77715e6i	−0.0223633	+	0.00450949i
$466$	−1.80563e9			−0.826567
$467$	3.32913e8	−	2.41876e8i	0.151259	−	0.109896i	−0.509582	−	0.860422i	$-0.670200\pi$
$467$	3.32913e8	−	2.41876e8i	0.151259	−	0.109896i	0.660841	+	0.750526i	$0.270200\pi$
$468$	−8.55644e8	−	6.21661e8i	−0.385862	−	0.280345i
$469$	2.15416e8	−	6.62983e8i	0.0964215	−	0.296755i
$470$	7.07515e7			0.0314335
$471$	1.53531e8			0.0677052
$472$	−3.16127e7	+	9.72938e7i	−0.0138377	+	0.0425881i
$473$	−6.64904e7	−	2.04636e8i	−0.0288898	−	0.0889137i
$474$	1.12813e8	+	3.47203e8i	0.0486558	+	0.149747i
$475$	9.28718e8	−	6.74753e8i	0.397609	−	0.288880i
$476$	−1.88293e8	+	5.79507e8i	−0.0800221	+	0.246283i
$477$	−8.29738e7	+	6.02840e7i	−0.0350047	+	0.0254324i
$478$	1.81482e9	+	1.31855e9i	0.760041	+	0.552202i
$479$	1.30536e9	+	4.01748e9i	0.542694	+	1.67024i	0.726410	+	0.687262i	$0.241188\pi$
$479$	1.30536e9	+	4.01748e9i	0.542694	+	1.67024i	−0.183715	+	0.982979i	$0.558812\pi$
$480$	7.90530e6	+	5.74354e6i	0.00326268	+	0.00237047i
$481$	−1.51684e9	−	1.10205e9i	−0.621487	−	0.451537i
$482$	2.10810e8	+	6.48806e8i	0.0857484	+	0.263907i
$483$	9.98920e7	+	7.25758e7i	0.0403381	+	0.0293074i
$484$	9.53421e8	−	6.92701e8i	0.382231	−	0.277707i
$485$	−1.74829e6	+	5.38068e6i	−0.000695852	+	0.00214161i
$486$	7.45144e8	−	5.41379e8i	0.294451	−	0.213931i
$487$	−1.62077e8	−	4.98822e8i	−0.0635873	−	0.195702i	0.914216	−	0.405228i	$-0.132808\pi$
$487$	−1.62077e8	−	4.98822e8i	−0.0635873	−	0.195702i	−0.977803	+	0.209526i	$0.932808\pi$
$488$	4.55425e8	+	1.40165e9i	0.177398	+	0.545974i
$489$	1.76578e8	−	5.43450e8i	0.0682897	−	0.210174i
$490$	−1.78974e8			−0.0687231
$491$	1.95236e8			0.0744344			0.0372172	−	0.999307i	$-0.488151\pi$
$491$	1.95236e8			0.0744344			0.0372172	+	0.999307i	$0.488151\pi$
$492$	−9.83860e7	+	3.02801e8i	−0.0372439	+	0.114625i
$493$	−3.77979e9	−	2.74618e9i	−1.42070	−	1.03220i
$494$	7.54676e8	−	5.48304e8i	0.281654	−	0.204634i
$495$	7.80388e7			0.0289196
$496$	6.65995e8	−	1.34296e8i	0.245067	−	0.0494169i
$497$	−2.54172e9			−0.928710
$498$	−1.66503e8	+	1.20972e8i	−0.0604116	+	0.0438916i
$499$	2.34551e9	+	1.70411e9i	0.845056	+	0.613969i	0.923778	−	0.382928i	$-0.125084\pi$
$499$	2.34551e9	+	1.70411e9i	0.845056	+	0.613969i	−0.0787226	+	0.996897i	$0.525084\pi$
$500$	−1.09079e8	+	3.35709e8i	−0.0390251	+	0.120107i
$501$	4.71015e8			0.167341
$502$	−8.50837e8			−0.300181
$503$	−5.25763e8	+	1.61813e9i	−0.184205	+	0.566926i	−0.999934	−	0.0115094i	$-0.996336\pi$
$503$	−5.25763e8	+	1.61813e9i	−0.184205	+	0.566926i	0.815728	+	0.578435i	$0.196336\pi$
$504$	1.47853e8	+	4.55044e8i	0.0514426	+	0.158324i
$505$	−2.49427e7	−	7.67657e7i	−0.00861834	−	0.0265245i
$506$	−2.23791e8	+	1.62594e8i	−0.0767921	+	0.0557927i
$507$	4.66293e6	−	1.43510e7i	0.00158903	−	0.00489052i
$508$	−1.47317e9	+	1.07032e9i	−0.498573	+	0.362234i
$509$	1.34308e9	+	9.75802e8i	0.451428	+	0.327981i	0.790159	−	0.612902i	$-0.209998\pi$
$509$	1.34308e9	+	9.75802e8i	0.451428	+	0.327981i	−0.338731	+	0.940883i	$0.609998\pi$
$510$	−1.58984e7	−	4.89304e7i	−0.00530712	−	0.0163336i
$511$	3.95708e8	+	2.87499e8i	0.131190	+	0.0953153i
$512$	−1.08584e8	−	7.88912e7i	−0.0357538	−	0.0259767i
$513$	1.66451e8	+	5.12283e8i	0.0544346	+	0.167532i
$514$	−5.22658e8	−	3.79733e8i	−0.169764	−	0.123341i
$515$	1.73606e8	−	1.26132e8i	0.0560066	−	0.0406912i
$516$	−3.44204e7	+	1.05935e8i	−0.0110291	+	0.0339442i
$517$	2.08283e8	−	1.51327e8i	0.0662884	−	0.0481613i
$518$	2.62106e8	+	8.06679e8i	0.0828557	+	0.255004i
$519$	1.72655e8	+	5.31377e8i	0.0542117	+	0.166847i
$520$	−4.39565e7	+	1.35284e8i	−0.0137092	+	0.0421925i
$521$	−3.79223e9			−1.17480			−0.587399	−	0.809298i	$-0.699848\pi$
$521$	−3.79223e9			−1.17480			−0.587399	+	0.809298i	$0.699848\pi$
$522$	−3.66864e9			−1.12891
$523$	−1.44465e9	+	4.44617e9i	−0.441576	+	1.35903i	0.444619	+	0.895720i	$0.353339\pi$
$523$	−1.44465e9	+	4.44617e9i	−0.441576	+	1.35903i	−0.886195	+	0.463312i	$0.846661\pi$
$524$	−1.96559e9	−	1.42808e9i	−0.596806	−	0.433605i
$525$	2.30022e8	−	1.67121e8i	0.0693765	−	0.0504050i
$526$	−2.27489e9			−0.681571
$527$	−3.25249e9	−	1.48907e9i	−0.968008	−	0.443176i
$528$	3.55567e7			0.0105124
$529$	1.85327e9	−	1.34648e9i	0.544308	−	0.395463i
$530$	1.11595e7	+	8.10788e6i	0.00325597	+	0.00236560i
$531$	1.30698e8	−	4.02246e8i	0.0378824	−	0.116590i
$532$	−4.22002e8			−0.121513
$533$	−4.63480e9			−1.32582
$534$	6.41405e7	−	1.97404e8i	0.0182279	−	0.0560999i
$535$	1.63708e8	+	5.03841e8i	0.0462201	+	0.142251i
$536$	−2.49832e8	−	7.68904e8i	−0.0700763	−	0.215673i
$537$	−2.40188e8	+	1.74507e8i	−0.0669331	+	0.0486297i
$538$	−7.46376e8	+	2.29711e9i	−0.206643	+	0.635981i
$539$	−5.26875e8	+	3.82797e8i	−0.144926	+	0.105295i
$540$	−6.64506e7	−	4.82792e7i	−0.0181602	−	0.0131942i
$541$	−1.42186e7	−	4.37604e7i	−0.00386071	−	0.0118820i	0.949108	−	0.314952i	$-0.101988\pi$
$541$	−1.42186e7	−	4.37604e7i	−0.00386071	−	0.0118820i	−0.952968	+	0.303070i	$0.901988\pi$
$542$	5.09619e8	+	3.70260e8i	0.137483	+	0.0998870i
$543$	2.63613e8	+	1.91526e8i	0.0706591	+	0.0513369i
$544$	2.18375e8	+	6.72090e8i	0.0581577	+	0.178991i
$545$	−3.72397e8	−	2.70562e8i	−0.0985413	−	0.0715945i
$546$	1.86916e8	−	1.35802e8i	0.0491442	−	0.0357053i
$547$	9.71590e8	−	2.99025e9i	0.253821	−	0.781180i	−0.740239	−	0.672344i	$-0.765288\pi$
$547$	9.71590e8	−	2.99025e9i	0.253821	−	0.781180i	0.994060	−	0.108836i	$-0.0347124\pi$
$548$	8.82995e8	−	6.41533e8i	0.229206	−	0.166528i
$549$	−1.88288e9	−	5.79492e9i	−0.485647	−	1.49467i
$550$	1.96837e8	+	6.05803e8i	0.0504473	+	0.155261i
$551$	9.99897e8	−	3.07737e9i	0.254639	−	0.783698i
$552$	1.43200e8			0.0362373
$553$	2.40419e9			0.604547
$554$	−1.25160e9	+	3.85203e9i	−0.312738	+	0.962509i
$555$	−5.79391e7	−	4.20952e7i	−0.0143862	−	0.0104522i
$556$	1.20065e8	−	8.72326e7i	0.0296248	−	0.0215237i
$557$	−1.47115e9			−0.360714			−0.180357	−	0.983601i	$-0.557725\pi$
$557$	−1.47115e9			−0.360714			−0.180357	+	0.983601i	$0.557725\pi$
$558$	−2.75345e9	+	5.55224e8i	−0.670900	+	0.135285i
$559$	−1.62148e9			−0.392619
$560$	5.20607e7	−	3.78243e7i	0.0125271	−	0.00910150i
$561$	−1.51458e8	−	1.10040e8i	−0.0362177	−	0.0263137i
$562$	8.85090e8	−	2.72403e9i	0.210334	−	0.647342i
$563$	−2.80698e9			−0.662917			−0.331459	−	0.943470i	$-0.607541\pi$
$563$	−2.80698e9			−0.662917			−0.331459	+	0.943470i	$0.607541\pi$
$564$	−1.33276e8			−0.0312807
$565$	−2.27582e8	+	7.00425e8i	−0.0530845	+	0.163377i
$566$	1.67134e9	+	5.14384e9i	0.387442	+	1.19242i
$567$	−5.90325e8	−	1.81683e9i	−0.136004	−	0.418576i
$568$	−2.38481e9	+	1.73267e9i	−0.546053	+	0.396731i
$569$	4.69625e8	−	1.44536e9i	0.106871	−	0.328914i	−0.883294	−	0.468819i	$-0.844680\pi$
$569$	4.69625e8	−	1.44536e9i	0.106871	−	0.328914i	0.990165	+	0.139905i	$0.0446798\pi$
$570$	2.88265e7	−	2.09437e7i	0.00651974	−	0.00473687i
$571$	4.77930e9	+	3.47236e9i	1.07433	+	0.780547i	0.976686	−	0.214675i	$-0.0688692\pi$
$571$	4.77930e9	+	3.47236e9i	1.07433	+	0.780547i	0.0976446	+	0.995221i	$0.468869\pi$
$572$	1.59950e8	+	4.92275e8i	0.0357353	+	0.109982i
$573$	−5.43400e8	−	3.94803e8i	−0.120664	−	0.0876677i
$574$	1.69629e9	+	1.23243e9i	0.374376	+	0.272000i
$575$	7.92735e8	+	2.43979e9i	0.173896	+	0.535198i
$576$	4.48925e8	+	3.26163e8i	0.0978803	+	0.0711142i
$577$	3.10408e9	−	2.25524e9i	0.672694	−	0.488740i	−0.198232	−	0.980155i	$-0.563520\pi$
$577$	3.10408e9	−	2.25524e9i	0.672694	−	0.488740i	0.870926	+	0.491415i	$0.163520\pi$
$578$	1.35368e8	−	4.16620e8i	0.0291588	−	0.0897415i
$579$	4.40066e7	−	3.19727e7i	0.00942200	−	0.00684548i
$580$	1.52473e8	+	4.69264e8i	0.0324485	+	0.0998663i
$581$	4.18832e8	+	1.28903e9i	0.0885978	+	0.272676i
$582$	3.29330e6	−	1.01357e7i	0.000692469	−	0.00213120i
$583$	5.01938e7			0.0104908
$584$	5.67266e8			0.117853
$585$	1.81731e8	−	5.59311e8i	0.0375304	−	0.115507i
$586$	−8.22823e8	−	5.97816e8i	−0.168914	−	0.122723i
$587$	−8.02007e8	+	5.82692e8i	−0.163661	+	0.118907i	−0.666601	−	0.745415i	$-0.732252\pi$
$587$	−8.02007e8	+	5.82692e8i	−0.163661	+	0.118907i	0.502940	+	0.864321i	$0.332252\pi$
$588$	3.37137e8			0.0683889
$589$	2.84722e8	−	2.46101e9i	0.0574139	−	0.496260i
$590$	−5.68841e7			−0.0114027
$591$	−1.12095e9	+	8.14420e8i	−0.223373	+	0.162290i
$592$	7.95832e8	+	5.78205e8i	0.157650	+	0.114540i
$593$	1.46181e9	−	4.49898e9i	0.287871	−	0.885977i	−0.697652	−	0.716437i	$-0.745772\pi$
$593$	1.46181e9	−	4.49898e9i	0.287871	−	0.885977i	0.985523	−	0.169540i	$-0.0542282\pi$
$594$	−2.98884e8			−0.0585126
$595$	−3.38816e8			−0.0659408
$596$	8.53629e8	−	2.62720e9i	0.165161	−	0.508313i
$597$	−5.73178e7	−	1.76406e8i	−0.0110250	−	0.0339315i
$598$	6.44176e8	+	1.98257e9i	0.123183	+	0.379118i
$599$	7.40154e9	−	5.37753e9i	1.40711	−	1.02233i	0.413375	−	0.910561i	$-0.364350\pi$
$599$	7.40154e9	−	5.37753e9i	1.40711	−	1.02233i	0.993735	−	0.111764i	$-0.0356502\pi$
$600$	1.01898e8	−	3.13608e8i	0.0192590	−	0.0592732i
$601$	4.21781e9	−	3.06442e9i	0.792549	−	0.575820i	−0.116170	−	0.993229i	$-0.537062\pi$
$601$	4.21781e9	−	3.06442e9i	0.792549	−	0.575820i	0.908719	+	0.417409i	$0.137062\pi$
$602$	5.93447e8	+	4.31165e8i	0.110865	+	0.0805481i
$603$	1.03289e9	+	3.17891e9i	0.191842	+	0.590429i
$604$	−8.58770e8	−	6.23933e8i	−0.158580	−	0.115215i
$605$	5.30147e8	+	3.85174e8i	0.0973313	+	0.0707153i
$606$	4.69852e7	+	1.44606e8i	0.00857644	+	0.0263956i
$607$	7.57985e9	+	5.50708e9i	1.37563	+	0.999451i	0.997274	+	0.0737888i	$0.0235091\pi$
$607$	7.57985e9	+	5.50708e9i	1.37563	+	0.999451i	0.378352	+	0.925662i	$0.376491\pi$
$608$	−3.95951e8	+	2.87675e8i	−0.0714462	+	0.0519087i
$609$	2.47652e8	−	7.62193e8i	0.0444305	−	0.136743i
$610$	−6.62985e8	+	4.81687e8i	−0.118263	+	0.0859232i
$611$	−5.99536e8	−	1.84518e9i	−0.106334	−	0.327262i
$612$	−9.02839e8	−	2.77865e9i	−0.159214	−	0.490009i
$613$	−2.41627e9	+	7.43652e9i	−0.423676	+	1.30394i	0.480580	+	0.876951i	$0.340426\pi$
$613$	−2.41627e9	+	7.43652e9i	−0.423676	+	1.30394i	−0.904256	+	0.426990i	$0.859574\pi$
$614$	3.67151e9			0.640112
$615$	−1.77036e8			−0.0306902
$616$	7.23595e7	−	2.22700e8i	0.0124728	−	0.0383873i
$617$	−2.69635e9	−	1.95901e9i	−0.462145	−	0.335768i	0.332227	−	0.943199i	$-0.392200\pi$
$617$	−2.69635e9	−	1.95901e9i	−0.462145	−	0.335768i	−0.794372	+	0.607432i	$0.792200\pi$
$618$	−3.27026e8	+	2.37598e8i	−0.0557343	+	0.0404934i
$619$	1.02004e10			1.72861			0.864307	−	0.502965i	$-0.167757\pi$
$619$	1.02004e10			1.72861			0.864307	+	0.502965i	$0.167757\pi$
$620$	1.85456e8	+	3.29124e8i	0.0312515	+	0.0554611i
$621$	−1.20371e9			−0.201698
$622$	−1.33803e8	+	9.72133e7i	−0.0222945	+	0.0161979i
$623$	−1.10586e9	−	8.03452e8i	−0.183228	−	0.133123i
$624$	8.28019e7	−	2.54838e8i	0.0136425	−	0.0419873i
$625$	5.80830e9			0.951632
$626$	−3.34199e9			−0.544497
$627$	4.00662e7	−	1.23311e8i	0.00649145	−	0.0199786i
$628$	−3.62358e8	−	1.11522e9i	−0.0583821	−	0.179682i
$629$	−1.60051e9	−	4.92585e9i	−0.256437	−	0.789231i
$630$	−2.15237e8	+	1.56379e8i	−0.0342945	+	0.0249164i
$631$	−2.26964e9	+	6.98522e9i	−0.359628	+	1.10682i	0.593649	+	0.804724i	$0.297687\pi$
$631$	−2.26964e9	+	6.98522e9i	−0.359628	+	1.10682i	−0.953277	+	0.302097i	$0.902313\pi$
$632$	2.25577e9	−	1.63891e9i	0.355455	−	0.258254i
$633$	−3.08729e8	−	2.24305e8i	−0.0483798	−	0.0351500i
$634$	3.26126e8	+	1.00371e9i	0.0508245	+	0.156422i
$635$	−8.19150e8	−	5.95147e8i	−0.126957	−	0.0922394i
$636$	−2.10215e7	−	1.52730e7i	−0.00324014	−	0.00235410i
$637$	1.51659e9	+	4.66759e9i	0.232477	+	0.715491i
$638$	1.45254e9	+	1.05533e9i	0.221440	+	0.160886i
$639$	9.85963e9	−	7.16344e9i	1.49488	−	1.08610i
$640$	2.30624e7	−	7.09787e7i	0.00347755	−	0.0107028i
$641$	1.13531e8	−	8.24852e7i	0.0170260	−	0.0123701i	−0.579240	−	0.815157i	$-0.696650\pi$
$641$	1.13531e8	−	8.24852e7i	0.0170260	−	0.0123701i	0.596266	+	0.802787i	$0.296650\pi$
$642$	−3.08381e8	−	9.49098e8i	−0.0459954	−	0.141559i
$643$	−2.20907e9	−	6.79883e9i	−0.327696	−	1.00855i	−0.970209	−	0.242270i	$-0.922108\pi$
$643$	−2.20907e9	−	6.79883e9i	−0.327696	−	1.00855i	0.642512	−	0.766275i	$-0.277892\pi$
$644$	2.91418e8	−	8.96892e8i	0.0429948	−	0.132324i
$645$	−6.19362e7			−0.00908836
$646$	2.57689e9			0.376081
$647$	−1.04717e8	+	3.22285e8i	−0.0152003	+	0.0467816i	−0.958369	−	0.285533i	$-0.907829\pi$
$647$	−1.04717e8	+	3.22285e8i	−0.0152003	+	0.0467816i	0.943169	+	0.332314i	$0.107829\pi$
$648$	−1.79240e9	−	1.30226e9i	−0.258775	−	0.188011i
$649$	−1.67459e8	+	1.21666e8i	−0.0240466	+	0.0174708i
$650$	4.80022e9			0.685590
$651$	7.05191e7	−	6.09535e8i	0.0100178	−	0.0865895i
$652$	−4.36430e9			−0.616663
$653$	1.12426e9	−	8.16822e8i	0.158005	−	0.114797i	−0.505974	−	0.862549i	$-0.668867\pi$
$653$	1.12426e9	−	8.16822e8i	0.158005	−	0.114797i	0.663978	+	0.747752i	$0.268867\pi$
$654$	7.01494e8	+	5.09665e8i	0.0980622	+	0.0712464i
$655$	4.17474e8	−	1.28485e9i	0.0580476	−	0.178652i
$656$	2.43171e9			0.336317
$657$	−2.34527e9			−0.322637
$658$	−2.71223e8	+	8.34740e8i	−0.0371139	+	0.114225i
$659$	−1.67645e9	−	5.15959e9i	−0.228188	−	0.702289i	−0.997952	−	0.0639615i	$-0.979627\pi$
$659$	−1.67645e9	−	5.15959e9i	−0.228188	−	0.702289i	0.769765	−	0.638328i	$-0.220373\pi$
$660$	6.10964e6	+	1.88035e7i	0.000827203	+	0.00254587i
$661$	−8.35875e9	+	6.07299e9i	−1.12574	+	0.817895i	−0.985069	−	0.172162i	$-0.944925\pi$
$661$	−8.35875e9	+	6.07299e9i	−1.12574	+	0.817895i	−0.140667	+	0.990057i	$0.544925\pi$
$662$	−1.74222e8	+	5.36200e8i	−0.0233399	+	0.0718329i
$663$	−1.14137e9	+	8.29255e8i	−0.152100	+	0.110507i
$664$	1.27170e9	+	9.23943e8i	0.168576	+	0.122478i
$665$	−7.25118e7	−	2.23168e8i	−0.00956165	−	0.0294277i
$666$	−3.29024e9	−	2.39050e9i	−0.431586	−	0.313566i
$667$	5.84992e9	+	4.25021e9i	0.763325	+	0.554588i
$668$	−1.11168e9	−	3.42139e9i	−0.144298	−	0.444104i
$669$	−1.81880e9	−	1.32143e9i	−0.234851	−	0.170629i
$670$	3.63693e8	−	2.64238e8i	0.0467168	−	0.0339417i
$671$	−9.21488e8	+	2.83605e9i	−0.117750	+	0.362397i
$672$	−9.80680e7	+	7.12506e7i	−0.0124662	+	0.00905724i
$673$	−1.64879e9	−	5.07447e9i	−0.208504	−	0.641708i	−0.999551	−	0.0299538i	$-0.990464\pi$
$673$	−1.64879e9	−	5.07447e9i	−0.208504	−	0.641708i	0.791048	−	0.611755i	$-0.209536\pi$
$674$	3.74118e8	+	1.15142e9i	0.0470652	+	0.144852i
$675$	−8.56533e8	+	2.63614e9i	−0.107197	+	0.329917i
$676$	−1.15249e8			−0.0143491
$677$	−5.29519e9			−0.655875			−0.327937	−	0.944699i	$-0.606353\pi$
$677$	−5.29519e9			−0.655875			−0.327937	+	0.944699i	$0.606353\pi$
$678$	4.28702e8	−	1.31941e9i	0.0528264	−	0.162583i
$679$	−5.67803e7	−	4.12533e7i	−0.00696071	−	0.00505725i
$680$	−3.17900e8	+	2.30968e8i	−0.0387712	+	0.0281689i
$681$	−1.56290e9			−0.189634
$682$	1.24991e9	+	5.72236e8i	0.150880	+	0.0690764i
$683$	−1.54279e10			−1.85282			−0.926412	−	0.376510i	$-0.877124\pi$
$683$	−1.54279e10			−1.85282			−0.926412	+	0.376510i	$0.877124\pi$
$684$	1.63700e9	−	1.18935e9i	0.195592	−	0.142106i
$685$	4.90987e8	+	3.56723e8i	0.0583650	+	0.0424047i
$686$	1.58488e9	−	4.87776e9i	0.187440	−	0.576881i
$687$	−2.03120e9			−0.239004
$688$	8.50734e8			0.0995943
$689$	1.16888e8	−	3.59743e8i	0.0136145	−	0.0419011i
$690$	2.46057e7	+	7.57286e7i	0.00285144	+	0.00877583i
$691$	4.74071e9	+	1.45904e10i	0.546601	+	1.68226i	0.717153	+	0.696916i	$0.245445\pi$
$691$	4.74071e9	+	1.45904e10i	0.546601	+	1.68226i	−0.170552	+	0.985349i	$0.554555\pi$
$692$	3.45235e9	−	2.50828e9i	0.396044	−	0.287743i
$693$	−2.99159e8	+	9.20717e8i	−0.0341457	+	0.105090i
$694$	4.98870e9	−	3.62450e9i	0.566538	−	0.411614i
$695$	6.67620e7	+	4.85054e7i	0.00754366	+	0.00548079i
$696$	−2.87217e8	−	8.83964e8i	−0.0322908	−	0.0993807i
$697$	−1.03581e10	−	7.52561e9i	−1.15869	−	0.841835i
$698$	−3.56681e9	−	2.59144e9i	−0.396996	−	0.288434i
$699$	5.84441e8	+	1.79872e9i	0.0647247	+	0.199202i
$700$	−1.75683e9	−	1.27641e9i	−0.193592	−	0.140653i
$701$	−2.56632e9	+	1.86454e9i	−0.281383	+	0.204437i	−0.719521	−	0.694471i	$-0.755638\pi$
$701$	−2.56632e9	+	1.86454e9i	−0.281383	+	0.204437i	0.438137	+	0.898908i	$0.355638\pi$
$702$	−6.96019e8	+	2.14212e9i	−0.0759348	+	0.233703i
$703$	2.90198e9	−	2.10841e9i	0.315030	−	0.228882i
$704$	−8.39199e7	−	2.58279e8i	−0.00906485	−	0.0278987i
$705$	−2.29006e7	−	7.04808e7i	−0.00246142	−	0.00757546i
$706$	−4.01700e9	+	1.23630e10i	−0.429620	+	1.32224i
$707$	1.00131e9			0.106562
$708$	1.07154e8			0.0113473
$709$	−4.40925e9	+	1.35703e10i	−0.464625	+	1.42997i	0.394829	+	0.918755i	$0.370804\pi$
$709$	−4.40925e9	+	1.35703e10i	−0.464625	+	1.42997i	−0.859454	+	0.511214i	$0.829196\pi$
$710$	−1.32607e9	−	9.63445e8i	−0.139047	−	0.101024i
$711$	−9.32613e9	+	6.77583e9i	−0.973101	+	0.706999i
$712$	−1.58530e9			−0.164600
$713$	5.03382e9	+	2.30460e9i	0.520097	+	0.238112i
$714$	6.38236e8			0.0656202
$715$	−2.32847e8	+	1.69173e8i	−0.0238232	+	0.0173085i
$716$	1.83447e9	+	1.33282e9i	0.186774	+	0.135699i
$717$	7.26087e8	−	2.23467e9i	0.0735650	−	0.226410i
$718$	−5.40597e9			−0.545052
$719$	−7.76304e9			−0.778898			−0.389449	−	0.921048i	$-0.627335\pi$
$719$	−7.76304e9			−0.778898			−0.389449	+	0.921048i	$0.627335\pi$
$720$	−9.53477e7	+	2.93450e8i	−0.00952021	+	0.0293002i
$721$	8.22619e8	+	2.53176e9i	0.0817382	+	0.251564i
$722$	−1.65828e9	−	5.10366e9i	−0.163975	−	0.504663i
$723$	5.78090e8	−	4.20007e8i	0.0568868	−	0.0413307i
$724$	7.69047e8	−	2.36688e9i	0.0753127	−	0.231789i
$725$	1.34707e10	−	9.78701e9i	1.31282	−	0.953821i
$726$	−9.98652e8	−	7.25563e8i	−0.0968581	−	0.0703715i
$727$	5.47644e9	+	1.68547e10i	0.528601	+	1.62687i	0.757083	+	0.653318i	$0.226624\pi$
$727$	5.47644e9	+	1.68547e10i	0.528601	+	1.62687i	−0.228483	+	0.973548i	$0.573376\pi$
$728$	−1.42760e9	−	1.03721e9i	−0.137135	−	0.0996342i
$729$	6.87573e9	+	4.99551e9i	0.657313	+	0.477566i
$730$	9.74721e7	+	2.99988e8i	0.00927364	+	0.0285413i
$731$	−3.62379e9	−	2.63284e9i	−0.343125	−	0.249295i
$732$	1.24888e9	−	9.07366e8i	0.117688	−	0.0855055i
$733$	−1.63381e9	+	5.02836e9i	−0.153228	+	0.471587i	−0.997977	−	0.0635753i	$-0.979750\pi$
$733$	−1.63381e9	+	5.02836e9i	−0.153228	+	0.471587i	0.844749	+	0.535163i	$0.179750\pi$
$734$	5.80247e9	−	4.21574e9i	0.541598	−	0.393494i
$735$	5.79296e7	+	1.78289e8i	0.00538139	+	0.0165622i
$736$	−3.37976e8	−	1.04018e9i	−0.0312473	−	0.0961694i
$737$	5.05499e8	−	1.55577e9i	0.0465141	−	0.143156i
$738$	−1.00535e10			−0.920706
$739$	−1.73463e10			−1.58107			−0.790537	−	0.612414i	$-0.790199\pi$
$739$	−1.73463e10			−1.58107			−0.790537	+	0.612414i	$0.790199\pi$
$740$	−1.69028e8	+	5.20213e8i	−0.0153337	+	0.0471922i
$741$	−7.90477e8	−	5.74315e8i	−0.0713717	−	0.0518545i
$742$	−1.38438e8	+	1.00581e8i	−0.0124406	+	0.00903863i
$743$	−1.82342e10			−1.63090			−0.815449	−	0.578829i	$-0.803510\pi$
$743$	−1.82342e10			−1.63090			−0.815449	+	0.578829i	$0.803510\pi$
$744$	−3.49349e8	−	6.19979e8i	−0.0310996	−	0.0551915i
$745$	1.53603e9			0.136098
$746$	8.16138e9	−	5.92959e9i	0.719744	−	0.522924i
$747$	−5.25764e9	−	3.81990e9i	−0.461497	−	0.335297i
$748$	−4.41852e8	+	1.35988e9i	−0.0386030	+	0.118808i
$749$	−6.57198e9			−0.571492
$750$	3.69731e8			0.0320016
$751$	2.22928e9	−	6.86103e9i	0.192055	−	0.591084i	−0.807943	−	0.589260i	$-0.799419\pi$
$751$	2.22928e9	−	6.86103e9i	0.192055	−	0.591084i	0.999998	−	0.00182430i	$-0.000580693\pi$
$752$	3.14555e8	+	9.68100e8i	0.0269733	+	0.0830152i
$753$	2.75396e8	+	8.47583e8i	0.0235058	+	0.0723435i
$754$	1.09463e10	−	7.95292e9i	0.929963	−	0.675658i
$755$	1.82395e8	−	5.61354e8i	0.0154241	−	0.0474704i
$756$	8.24343e8	−	5.98920e8i	0.0693876	−	0.0504130i
$757$	4.10412e9	+	2.98182e9i	0.343862	+	0.249830i	0.746290	−	0.665621i	$-0.231833\pi$
$757$	4.10412e9	+	2.98182e9i	0.343862	+	0.249830i	−0.402427	+	0.915452i	$0.631833\pi$
$758$	3.81078e9	+	1.17284e10i	0.317813	+	0.978128i
$759$	2.34408e8	+	1.70307e8i	0.0194593	+	0.0141380i
$760$	−2.20167e8	−	1.59961e8i	−0.0181930	−	0.0132180i
$761$	1.27680e9	+	3.92960e9i	0.105021	+	0.323223i	0.989735	−	0.142911i	$-0.0456464\pi$
$761$	1.27680e9	+	3.92960e9i	0.105021	+	0.323223i	−0.884714	+	0.466134i	$0.845646\pi$
$762$	1.54305e9	+	1.12109e9i	0.126339	+	0.0917909i
$763$	4.61972e9	−	3.35642e9i	0.376513	−	0.273552i
$764$	−1.58528e9	+	4.87898e9i	−0.128611	+	0.395824i
$765$	1.31431e9	−	9.54900e8i	0.106141	−	0.0771157i
$766$	−1.52779e9	−	4.70204e9i	−0.122818	−	0.377995i
$767$	4.82026e8	+	1.48352e9i	0.0385733	+	0.118716i
$768$	−4.34432e7	+	1.33704e8i	−0.00346065	+	0.0106508i
$769$	1.58935e10			1.26031			0.630156	−	0.776469i	$-0.282991\pi$
$769$	1.58935e10			1.26031			0.630156	+	0.776469i	$0.282991\pi$
$770$	1.30204e8			0.0102780
$771$	−2.09108e8	+	6.43569e8i	−0.0164316	+	0.0505714i
$772$	−3.36108e8	−	2.44197e8i	−0.0262917	−	0.0191020i
$773$	−1.59146e10	+	1.15626e10i	−1.23927	+	0.900385i	−0.997550	−	0.0699604i	$-0.977713\pi$
$773$	−1.59146e10	+	1.15626e10i	−1.23927	+	0.900385i	−0.241724	+	0.970345i	$0.577713\pi$
$774$	−3.51723e9			−0.272651
$775$	8.62904e9	−	9.38421e9i	0.665896	−	0.724172i
$776$	−8.13972e7			−0.00625307
$777$	7.18755e8	−	5.22206e8i	0.0549677	−	0.0399364i
$778$	−5.05969e9	−	3.67608e9i	−0.385208	−	0.279870i
$779$	2.74011e9	−	8.43319e9i	0.207676	−	0.639162i
$780$	1.48994e8			0.0112419
$781$	−5.96443e9			−0.448013
$782$	−1.77950e9	+	5.47672e9i	−0.133068	+	0.409541i
$783$	2.41430e9	+	7.43045e9i	0.179732	+	0.553157i
$784$	−7.95701e8	−	2.44891e9i	−0.0589717	−	0.181496i
$785$	5.27503e8	−	3.83254e8i	0.0389208	−	0.0282776i
$786$	−7.86406e8	+	2.42031e9i	−0.0577654	+	0.177784i
$787$	−2.98066e9	+	2.16558e9i	−0.217972	+	0.158366i	−0.691413	−	0.722459i	$-0.743012\pi$
$787$	−2.98066e9	+	2.16558e9i	−0.217972	+	0.158366i	0.473441	+	0.880825i	$0.343012\pi$
$788$	8.56147e9	+	6.22027e9i	0.623313	+	0.452864i
$789$	7.36330e8	+	2.26619e9i	0.0533707	+	0.164258i
$790$	1.25431e9	+	9.11313e8i	0.0905132	+	0.0657617i
$791$	−7.39132e9	−	5.37011e9i	−0.531012	−	0.385803i
$792$	3.46954e8	+	1.06781e9i	0.0248161	+	0.0763761i
$793$	1.81803e10	+	1.32088e10i	1.29463	+	0.940602i
$794$	2.39663e9	−	1.74125e9i	0.169914	−	0.123450i
$795$	4.46478e6	−	1.37412e7i	0.000315148	−	0.000969927i
$796$	−1.14611e9	+	8.32696e8i	−0.0805434	+	0.0585182i
$797$	−1.87421e9	−	5.76822e9i	−0.131133	−	0.403587i	0.863835	−	0.503775i	$-0.168056\pi$
$797$	−1.87421e9	−	5.76822e9i	−0.131133	−	0.403587i	−0.994969	+	0.100187i	$0.968056\pi$
$798$	1.36592e8	+	4.20388e8i	0.00951516	+	0.0292846i
$799$	1.65618e9	−	5.09720e9i	0.114867	−	0.353523i
$800$	−2.51850e9			−0.173911
$801$	6.55416e9			0.450613
$802$	2.54192e9	−	7.82321e9i	0.174001	−	0.535519i
$803$	9.28575e8	+	6.74649e8i	0.0632867	+	0.0459805i
$804$	−6.85098e8	+	4.97753e8i	−0.0464896	+	0.0337767i
$805$	5.24379e8			0.0354291
$806$	7.01195e9	−	7.62560e9i	0.471700	−	0.512981i
$807$	2.52991e9			0.169452
$808$	9.39501e8	−	6.82587e8i	0.0626552	−	0.0455217i
$809$	1.72959e10	+	1.25662e10i	1.14848	+	0.834420i	0.988278	−	0.152664i	$-0.0487851\pi$
$809$	1.72959e10	+	1.25662e10i	1.14848	+	0.834420i	0.160203	+	0.987084i	$0.448785\pi$
$810$	3.80690e8	−	1.17164e9i	0.0251695	−	0.0774637i
$811$	−7.94777e8			−0.0523205			−0.0261603	−	0.999658i	$-0.508328\pi$
$811$	−7.94777e8			−0.0523205			−0.0261603	+	0.999658i	$0.508328\pi$
$812$	−6.12096e9			−0.401212
$813$	2.03892e8	−	6.27514e8i	0.0133071	−	0.0409550i
$814$	6.15061e8	+	1.89296e9i	0.0399699	+	0.123015i
$815$	−7.49908e8	−	2.30798e9i	−0.0485240	−	0.149342i
$816$	5.98836e8	−	4.35080e8i	0.0385827	−	0.0280320i
$817$	9.58628e8	−	2.95035e9i	0.0614997	−	0.189277i
$818$	−7.79113e9	+	5.66059e9i	−0.497696	+	0.361597i
$819$	5.90220e9	+	4.28820e9i	0.375422	+	0.272760i
$820$	4.17836e8	+	1.28597e9i	0.0264641	+	0.0814481i
$821$	−2.01808e10	−	1.46622e10i	−1.27273	−	0.924693i	−0.273423	−	0.961894i	$-0.588156\pi$
$821$	−2.01808e10	−	1.46622e10i	−1.27273	−	0.924693i	−0.999308	+	0.0372004i	$0.988156\pi$
$822$	−9.24884e8	−	6.71968e8i	−0.0580812	−	0.0421985i
$823$	−6.14359e9	−	1.89080e10i	−0.384169	−	1.18235i	−0.937081	−	0.349111i	$-0.886483\pi$
$823$	−6.14359e9	−	1.89080e10i	−0.384169	−	1.18235i	0.552912	−	0.833240i	$-0.313517\pi$
$824$	2.49772e9	+	1.81470e9i	0.155524	+	0.112995i
$825$	5.39774e8	−	3.92169e8i	0.0334675	−	0.0243155i
$826$	2.18063e8	−	6.71129e8i	0.0134633	−	0.0414358i
$827$	1.71618e10	−	1.24688e10i	1.05510	−	0.766577i	0.0819265	−	0.996638i	$-0.473893\pi$
$827$	1.71618e10	−	1.24688e10i	1.05510	−	0.766577i	0.973176	+	0.230061i	$0.0738927\pi$
$828$	1.39731e9	+	4.30047e9i	0.0855433	+	0.263275i
$829$	−2.61777e9	−	8.05666e9i	−0.159584	−	0.491150i	0.839012	−	0.544113i	$-0.183134\pi$
$829$	−2.61777e9	−	8.05666e9i	−0.159584	−	0.491150i	−0.998596	+	0.0529626i	$0.983134\pi$
$830$	−2.70097e8	+	8.31274e8i	−0.0163963	+	0.0504628i
$831$	4.24240e9			0.256453
$832$	−2.04653e9			−0.123193
$833$	−4.18949e9	+	1.28939e10i	−0.251133	+	0.772908i
$834$	−1.25761e8	−	9.13709e7i	−0.00750699	−	0.00545415i
$835$	1.61832e9	−	1.17578e9i	0.0961971	−	0.0698913i
$836$	−9.90276e8			−0.0586185
$837$	2.93657e9	+	5.21144e9i	0.173102	+	0.307198i
$838$	−1.41237e10			−0.829077
$839$	2.17073e10	−	1.57713e10i	1.26894	−	0.921936i	0.269776	−	0.962923i	$-0.413050\pi$
$839$	2.17073e10	−	1.57713e10i	1.26894	−	0.921936i	0.999160	+	0.0409869i	$0.0130502\pi$
$840$	−5.45304e7	−	3.96187e7i	−0.00317440	−	0.00230634i
$841$	9.17258e9	−	2.82303e10i	0.531748	−	1.63655i
$842$	2.16645e9			0.125071
$843$	−3.00009e9			−0.172480
$844$	−9.00664e8	+	2.77196e9i	−0.0515661	+	0.158704i
$845$	−1.98030e7	−	6.09474e7i	−0.00112910	−	0.00347502i
$846$	−1.30048e9	−	4.00246e9i	−0.0738425	−	0.227264i
$847$	−6.57666e9	+	4.77822e9i	−0.371889	+	0.270193i
$848$	−6.13267e7	+	1.88744e8i	−0.00345354	+	0.0106289i
$849$	4.58319e9	−	3.32989e9i	0.257034	−	0.186746i
$850$	1.07278e10	+	7.79421e9i	0.599163	+	0.435317i
$851$	2.47707e9	+	7.62365e9i	0.137780	+	0.424043i
$852$	2.49795e9	+	1.81487e9i	0.138371	+	0.100532i
$853$	−1.25642e10	−	9.12842e9i	−0.693127	−	0.503586i	0.184560	−	0.982821i	$-0.440914\pi$
$853$	−1.25642e10	−	9.12842e9i	−0.693127	−	0.503586i	−0.877687	+	0.479235i	$0.840914\pi$
$854$	−3.14151e9	−	9.66856e9i	−0.172598	−	0.531201i
$855$	9.10247e8	+	6.61333e8i	0.0498056	+	0.0361859i
$856$	−6.16628e9	+	4.48006e9i	−0.336020	+	0.244133i
$857$	−2.39907e9	+	7.38358e9i	−0.130200	+	0.400714i	−0.994813	−	0.101725i	$-0.967564\pi$
$857$	−2.39907e9	+	7.38358e9i	−0.130200	+	0.400714i	0.864613	+	0.502439i	$0.167564\pi$
$858$	4.38620e8	−	3.18676e8i	0.0237073	−	0.0172244i
$859$	2.10915e9	+	6.49129e9i	0.113535	+	0.349426i	0.991639	−	0.129045i	$-0.0411912\pi$
$859$	2.10915e9	+	6.49129e9i	0.113535	+	0.349426i	−0.878103	+	0.478471i	$0.841191\pi$
$860$	1.46180e8	+	4.49896e8i	0.00783688	+	0.0241194i
$861$	6.78663e8	−	2.08871e9i	0.0362362	−	0.111524i
$862$	1.79265e10			0.953277
$863$	−5.51788e9			−0.292236			−0.146118	−	0.989267i	$-0.546678\pi$
$863$	−5.51788e9			−0.292236			−0.146118	+	0.989267i	$0.546678\pi$
$864$	3.65176e8	−	1.12390e9i	0.0192621	−	0.0592827i
$865$	1.91967e9	+	1.39472e9i	0.100849	+	0.0732709i
$866$	−1.62552e10	+	1.18101e10i	−0.850513	+	0.617934i
$867$	−4.58842e8			−0.0239109
$868$	−4.59401e9	+	9.26366e8i	−0.238437	+	0.0480799i
$869$	5.64170e9			0.291636
$870$	4.18117e8	−	3.03779e8i	0.0215268	−	0.0156402i
$871$	−9.97314e9	−	7.24591e9i	−0.511409	−	0.371561i
$872$	2.04649e9	−	6.29844e9i	0.104521	−	0.321681i
$873$	3.36524e8			0.0171185
$874$	−3.98820e9			−0.202063
$875$	7.52420e8	−	2.31571e9i	0.0379693	−	0.116857i
$876$	−1.83611e8	−	5.65096e8i	−0.00922856	−	0.0284026i
$877$	7.94186e9	+	2.44425e10i	0.397579	+	1.22362i	0.926935	+	0.375222i	$0.122434\pi$
$877$	7.94186e9	+	2.44425e10i	0.397579	+	1.22362i	−0.529356	+	0.848400i	$0.677566\pi$
$878$	−9.29154e9	+	6.75070e9i	−0.463294	+	0.336603i
$879$	−3.29200e8	+	1.01317e9i	−0.0163493	+	0.0503180i
$880$	1.22166e8	−	8.87591e7i	0.00604314	−	0.00439060i
$881$	3.06311e10	+	2.22548e10i	1.50920	+	1.09650i	0.966530	+	0.256553i	$0.0825869\pi$
$881$	3.06311e10	+	2.22548e10i	1.50920	+	1.09650i	0.542671	+	0.839945i	$0.317413\pi$
$882$	3.28970e9	+	1.01247e10i	0.161442	+	0.496867i
$883$	−2.85180e10	−	2.07195e10i	−1.39398	−	1.01279i	−0.995415	−	0.0956464i	$-0.969508\pi$
$883$	−2.85180e10	−	2.07195e10i	−1.39398	−	1.01279i	−0.398565	−	0.917140i	$-0.630492\pi$
$884$	8.71742e9	+	6.33358e9i	0.424429	+	0.308366i
$885$	1.84120e7	+	5.66665e7i	0.000892896	+	0.00274805i
$886$	−4.97097e9	−	3.61162e9i	−0.240117	−	0.174455i
$887$	2.29201e10	−	1.66524e10i	1.10277	−	0.801206i	0.121256	−	0.992621i	$-0.461308\pi$
$887$	2.29201e10	−	1.66524e10i	1.10277	−	0.801206i	0.981509	+	0.191415i	$0.0613078\pi$
$888$	3.18401e8	−	9.79939e8i	0.0152591	−	0.0469628i
$889$	1.01618e10	−	7.38301e9i	0.485083	−	0.352434i
$890$	−2.72398e8	−	8.38356e8i	−0.0129521	−	0.0398624i
$891$	−1.38527e9	−	4.26341e9i	−0.0656086	−	0.201923i
$892$	−5.30603e9	+	1.63303e10i	−0.250318	+	0.770401i
$893$	3.71183e9			0.174425
$894$	−2.89345e9			−0.135436
$895$	−3.89626e8	+	1.19915e9i	−0.0181663	+	0.0559102i
$896$	7.49011e8	+	5.44188e8i	0.0347865	+	0.0252738i
$897$	1.76648e9	−	1.28342e9i	0.0817213	−	0.0593740i
$898$	1.26026e10			0.580757
$899$	4.12977e9	−	3.56959e10i	0.189569	−	1.63855i
$900$	1.04123e10			0.476102
$901$	8.45349e8	−	6.14182e8i	0.0385034	−	0.0279744i
$902$	3.98054e9	+	2.89203e9i	0.180601	+	0.131214i
$903$	2.37430e8	−	7.30735e8i	0.0107307	−	0.0330258i
$904$	−1.05958e10			−0.477028
$905$	1.38383e9			0.0620601
$906$	−3.43582e8	+	1.05744e9i	−0.0153491	+	0.0472396i
$907$	−1.05002e10	−	3.23163e10i	−0.467274	−	1.43812i	−0.856100	−	0.516811i	$-0.827119\pi$
$907$	−1.05002e10	−	3.23163e10i	−0.467274	−	1.43812i	0.388826	−	0.921311i	$-0.372881\pi$
$908$	3.68871e9	+	1.13527e10i	0.163521	+	0.503266i
$909$	−3.88422e9	+	2.82205e9i	−0.171526	+	0.124621i
$910$	3.03210e8	−	9.33184e8i	0.0133382	−	0.0410509i
$911$	−6.22558e9	+	4.52315e9i	−0.272813	+	0.198210i	−0.715777	−	0.698329i	$-0.753927\pi$
$911$	−6.22558e9	+	4.52315e9i	−0.272813	+	0.198210i	0.442963	+	0.896540i	$0.353927\pi$
$912$	4.14735e8	+	3.01323e8i	0.0181046	+	0.0131538i
$913$	9.82837e8	+	3.02486e9i	0.0427399	+	0.131540i
$914$	−1.95290e10	−	1.41886e10i	−0.845995	−	0.614652i
$915$	6.94437e8	+	5.04538e8i	0.0299681	+	0.0217731i
$916$	4.79399e9	+	1.47544e10i	0.206093	+	0.634288i
$917$	1.35586e10	+	9.85087e9i	0.580659	+	0.421873i
$918$	−5.03372e9	+	3.65721e9i	−0.214753	+	0.156027i
$919$	−2.26009e8	+	6.95585e8i	−0.00960554	+	0.0295628i	−0.955744	−	0.294198i	$-0.904947\pi$
$919$	−2.26009e8	+	6.95585e8i	−0.00960554	+	0.0295628i	0.946139	+	0.323761i	$0.104947\pi$
$920$	4.92008e8	−	3.57465e8i	0.0208312	−	0.0151348i
$921$	−1.18838e9	−	3.65747e9i	−0.0501243	−	0.154267i
$922$	−2.53276e9	−	7.79502e9i	−0.106423	−	0.327536i
$923$	−1.38895e10	+	4.27476e10i	−0.581409	+	1.78939i
$924$	−2.45269e8			−0.0102280
$925$	1.84585e10			0.766831
$926$	−6.64906e8	+	2.04637e9i	−0.0275183	+	0.0846927i
$927$	−1.03264e10	−	7.50258e9i	−0.425766	−	0.309337i
$928$	−5.74310e9	+	4.17261e9i	−0.235900	+	0.171392i
$929$	−1.02557e10			−0.419674			−0.209837	−	0.977736i	$-0.567293\pi$
$929$	−1.02557e10			−0.419674			−0.209837	+	0.977736i	$0.567293\pi$
$930$	2.67837e8	−	2.91277e8i	0.0109189	−	0.0118745i
$931$	−9.38947e9			−0.381344
$932$	1.16863e10	−	8.49058e9i	0.472847	−	0.343544i
$933$	1.40150e8	+	1.01825e8i	0.00564947	+	0.00410458i
$934$	−1.01729e9	+	3.13091e9i	−0.0408538	+	0.125735i
$935$	−7.95070e8			−0.0318101
$936$	8.46107e9			0.337256
$937$	−5.99065e9	+	1.84373e10i	−0.237895	+	0.732166i	0.758829	+	0.651290i	$0.225772\pi$
$937$	−5.99065e9	+	1.84373e10i	−0.237895	+	0.732166i	−0.996724	+	0.0808759i	$0.974228\pi$
$938$	1.72333e9	+	5.30387e9i	0.0681803	+	0.209837i
$939$	1.08173e9	+	3.32921e9i	0.0426371	+	0.131223i
$940$	−4.57913e8	+	3.32693e8i	−0.0179819	+	0.0130646i
$941$	−1.00626e10	+	3.09694e10i	−0.393682	+	1.21163i	0.536302	+	0.844026i	$0.319821\pi$
$941$	−1.00626e10	+	3.09694e10i	−0.393682	+	1.21163i	−0.929983	+	0.367601i	$0.880179\pi$
$942$	−9.93671e8	+	7.21945e8i	−0.0387315	+	0.0281401i
$943$	1.60311e10	+	1.16473e10i	0.622546	+	0.452306i
$944$	−2.52901e8	−	7.78351e8i	−0.00978474	−	0.0301143i
$945$	4.58373e8	+	3.33028e8i	0.0176688	+	0.0128372i
$946$	1.39259e9	+	1.01178e9i	0.0534817	+	0.0388567i
$947$	1.33261e10	+	4.10136e10i	0.509893	+	1.56929i	0.792387	+	0.610019i	$0.208838\pi$
$947$	1.33261e10	+	4.10136e10i	0.509893	+	1.56929i	−0.282494	+	0.959269i	$0.591162\pi$
$948$	−2.36278e9	−	1.71666e9i	−0.0900731	−	0.0654419i
$949$	6.99766e9	−	5.08410e9i	0.265779	−	0.193100i
$950$	−2.83791e9	+	8.73419e9i	−0.107390	+	0.330514i
$951$	8.94314e8	−	6.49757e8i	0.0337177	−	0.0244973i
$952$	−1.50635e9	−	4.63605e9i	−0.0565842	−	0.174148i
$953$	−1.25491e10	−	3.86221e10i	−0.469663	−	1.44547i	−0.853022	−	0.521875i	$-0.825233\pi$
$953$	−1.25491e10	−	3.86221e10i	−0.469663	−	1.44547i	0.383359	−	0.923600i	$-0.374767\pi$
$954$	2.53545e8	−	7.80333e8i	0.00945446	−	0.0290978i
$955$	−2.85256e9			−0.105980
$956$	−1.79460e10			−0.664300
$957$	5.81143e8	−	1.78858e9i	0.0214334	−	0.0659653i
$958$	−2.73398e10	−	1.98635e10i	−1.00465	−	0.729922i
$959$	−6.09086e9	+	4.42527e9i	−0.223005	+	0.162022i
$960$	−7.81719e7			−0.00285168
$961$	−2.30278e9	−	2.74161e10i	−0.0836990	−	0.996491i
$962$	1.49993e10			0.543200
$963$	2.54935e10	−	1.85221e10i	0.919894	−	0.668342i
$964$	−4.41526e9	−	3.20787e9i	−0.158740	−	0.115331i
$965$	7.13863e7	−	2.19705e8i	0.00255723	−	0.00787034i
$966$	−9.87786e8			−0.0352568
$967$	−5.07087e10			−1.80339			−0.901695	−	0.432372i	$-0.857677\pi$
$967$	−5.07087e10			−1.80339			−0.901695	+	0.432372i	$0.857677\pi$
$968$	−2.91340e9	+	8.96651e9i	−0.103237	+	0.317731i
$969$	−8.34078e8	−	2.56703e9i	−0.0294492	−	0.0906353i
$970$	−1.39863e7	−	4.30454e7i	−0.000492042	−	0.00151435i
$971$	−3.01751e10	+	2.19235e10i	−1.05774	+	0.768496i	−0.973670	−	0.227963i	$-0.926793\pi$
$971$	−3.01751e10	+	2.19235e10i	−1.05774	+	0.768496i	−0.0840749	+	0.996459i	$0.526793\pi$
$972$	−2.27696e9	+	7.00776e9i	−0.0795286	+	0.244764i
$973$	−8.28206e8	+	6.01727e8i	−0.0288233	+	0.0209413i
$974$	3.39459e9	+	2.46631e9i	0.117715	+	0.0855247i
$975$	−1.55372e9	−	4.78186e9i	−0.0536854	−	0.165227i
$976$	−9.53855e9	−	6.93016e9i	−0.328404	−	0.238599i
$977$	−3.17781e9	−	2.30882e9i	−0.109018	−	0.0792061i	0.531941	−	0.846782i	$-0.321463\pi$
$977$	−3.17781e9	−	2.30882e9i	−0.109018	−	0.0792061i	−0.640958	+	0.767576i	$0.721463\pi$
$978$	1.41262e9	+	4.34760e9i	0.0482881	+	0.148615i
$979$	−2.59502e9	−	1.88539e9i	−0.0883897	−	0.0642189i
$980$	1.15834e9	−	8.41584e8i	0.0393138	−	0.0285632i
$981$	−8.46089e9	+	2.60399e10i	−0.286137	+	0.880640i
$982$	−1.26359e9	+	9.18053e8i	−0.0425811	+	0.0309369i
$983$	−8.12064e9	−	2.49928e10i	−0.272680	−	0.839222i	−0.989824	−	0.142297i	$-0.954551\pi$
$983$	−8.12064e9	−	2.49928e10i	−0.272680	−	0.839222i	0.717144	−	0.696925i	$-0.245449\pi$
$984$	−7.87088e8	−	2.42241e9i	−0.0263354	−	0.0810521i
$985$	−1.81838e9	+	5.59639e9i	−0.0606258	+	0.186587i
$986$	3.73767e10			1.24174
$987$	9.19335e8			0.0304343
$988$	−2.30608e9	+	7.09739e9i	−0.0760721	+	0.234126i
$989$	5.60847e9	+	4.07479e9i	0.184356	+	0.133943i
$990$	−5.05078e8	+	3.66960e8i	−0.0165438	+	0.0120198i
$991$	−4.17016e10			−1.36112			−0.680558	−	0.732694i	$-0.738262\pi$
$991$	−4.17016e10			−1.36112			−0.680558	+	0.732694i	$0.738262\pi$
$992$	−3.67892e9	+	4.00088e9i	−0.119655	+	0.130126i
$993$	5.90540e8			0.0191393
$994$	1.64503e10	−	1.19519e10i	0.531279	−	0.385997i
$995$	−6.37290e8	−	4.63018e8i	−0.0205096	−	0.0149011i
$996$	5.08789e8	−	1.56589e9i	0.0163166	−	0.0502174i
$997$	−3.64166e10			−1.16377			−0.581884	−	0.813272i	$-0.697684\pi$
$997$	−3.64166e10			−1.16377			−0.581884	+	0.813272i	$0.697684\pi$
$998$	−2.31937e10			−0.738606
$999$	−2.67643e9	+	8.23720e9i	−0.0849330	+	0.261397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.8.d.a.47.5	yes	40
31.2	even	5	inner	62.8.d.a.33.5	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.8.d.a.33.5	✓	40	31.2	even	5	inner
62.8.d.a.47.5	yes	40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-6.47214 + 4.70228i) q^{2} +(6.77917 + 4.92536i) q^{3} +(19.7771 - 60.8676i) q^{4} +35.5870 q^{5} -67.0362 q^{6} +(-136.422 + 419.862i) q^{7} +(158.217 + 486.941i) q^{8} +(-654.122 - 2013.18i) q^{9} +(-230.324 + 167.340i) q^{10} +(-320.129 + 985.256i) q^{11} +(433.867 - 315.223i) q^{12} +(6315.92 + 4588.78i) q^{13} +(-1091.37 - 3358.90i) q^{14} +(241.251 + 175.279i) q^{15} +(-3313.73 - 2407.57i) q^{16} +(6664.29 + 20510.6i) q^{17} +(13700.1 + 9953.71i) q^{18} +(-12083.5 + 8779.15i) q^{19} +(703.807 - 2166.10i) q^{20} +(-2992.80 + 2174.40i) q^{21} +(-2561.03 - 7882.05i) q^{22} +(-10314.2 - 31743.8i) q^{23} +(-1325.78 + 4080.33i) q^{24} -76858.6 q^{25} -62455.2 q^{26} +(11144.3 - 34298.6i) q^{27} +(22858.0 + 16607.3i) q^{28} +(-175266. + 127338. i) q^{29} -2385.62 q^{30} +(-112272. + 122097. i) q^{31} +32768.0 q^{32} +(-7022.95 + 5102.47i) q^{33} +(-139579. - 101410. i) q^{34} +(-4854.84 + 14941.6i) q^{35} -135474. q^{36} -240162. q^{37} +(36923.8 - 113640. i) q^{38} +(20215.3 + 62216.3i) q^{39} +(5630.46 + 17328.8i) q^{40} +(-480297. + 348956. i) q^{41} +(9145.18 - 28146.0i) q^{42} +(-168032. + 122082. i) q^{43} +(53638.9 + 38971.0i) q^{44} +(-23278.3 - 71643.1i) q^{45} +(216023. + 156950. i) q^{46} +(-201054. - 146074. i) q^{47} +(-10606.2 - 32642.7i) q^{48} +(508587. + 369510. i) q^{49} +(497439. - 361411. i) q^{50} +(-55843.5 + 171869. i) q^{51} +(404219. - 293682. i) q^{52} +(-14972.3 - 46080.1i) q^{53} +(89154.2 + 274389. i) q^{54} +(-11392.4 + 35062.3i) q^{55} -226032. q^{56} -125156. q^{57} +(535564. - 1.64830e6i) q^{58} +(161647. + 117443. i) q^{59} +(15440.0 - 11217.8i) q^{60} +2.87849e6 q^{61} +(152502. - 1.31816e6i) q^{62} +934495. q^{63} +(-212079. + 154084. i) q^{64} +(224765. + 163301. i) q^{65} +(21460.2 - 66047.8i) q^{66} -1.57905e6 q^{67} +1.38023e6 q^{68} +(86428.0 - 265998. i) q^{69} +(-38838.7 - 119533. i) q^{70} +(1.77914e6 + 5.47562e6i) q^{71} +(876807. - 637038. i) q^{72} +(342373. - 1.05371e6i) q^{73} +(1.55436e6 - 1.12931e6i) q^{74} +(-521038. - 378556. i) q^{75} +(295390. + 909118. i) q^{76} +(-369999. - 268820. i) q^{77} +(-423395. - 307614. i) q^{78} +(-1.68287e6 - 5.17933e6i) q^{79} +(-117926. - 85678.2i) q^{80} +(-3.50079e6 + 2.54347e6i) q^{81} +(1.46766e6 - 4.51698e6i) q^{82} +(2.48379e6 - 1.80458e6i) q^{83} +(73161.4 + 225168. i) q^{84} +(237162. + 729910. i) q^{85} +(513460. - 1.58027e6i) q^{86} -1.81534e6 q^{87} -530411. q^{88} +(-956804. + 2.94474e6i) q^{89} +(487546. + 354223. i) q^{90} +(-2.78829e6 + 2.02581e6i) q^{91} -2.13616e6 q^{92} +(-1.36248e6 + 274739. i) q^{93} +1.98813e6 q^{94} +(-430014. + 312424. i) q^{95} +(222140. + 161394. i) q^{96} +(-49127.2 + 151198. i) q^{97} -5.02918e6 q^{98} +2.19290e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 80 q^{2} + 28 q^{3} - 640 q^{4} + 168 q^{5} - 1936 q^{6} + 1402 q^{7} - 5120 q^{8} - 6164 q^{9} - 1496 q^{10} - 3402 q^{11} + 1792 q^{12} + 6413 q^{13} + 11216 q^{14} + 46465 q^{15} - 40960 q^{16}+ \cdots + 13336614 q^{99}+O(q^{100}) \) 40 * q - 80 * q^2 + 28 * q^3 - 640 * q^4 + 168 * q^5 - 1936 * q^6 + 1402 * q^7 - 5120 * q^8 - 6164 * q^9 - 1496 * q^10 - 3402 * q^11 + 1792 * q^12 + 6413 * q^13 + 11216 * q^14 + 46465 * q^15 - 40960 * q^16 + 17155 * q^17 - 98152 * q^18 + 67290 * q^19 + 6592 * q^20 + 16727 * q^21 - 27216 * q^22 + 2051 * q^23 + 47616 * q^24 + 787196 * q^25 - 214576 * q^26 + 603289 * q^27 - 62592 * q^28 + 95739 * q^29 - 369200 * q^30 + 540003 * q^31 + 1310720 * q^32 + 941656 * q^33 + 290520 * q^34 - 638364 * q^35 + 2359424 * q^36 + 843716 * q^37 - 169080 * q^38 + 827496 * q^39 + 52736 * q^40 + 175557 * q^41 + 1299656 * q^42 + 566562 * q^43 + 441152 * q^44 - 2450173 * q^45 + 484128 * q^46 - 2289258 * q^47 + 380928 * q^48 - 1290090 * q^49 - 2003912 * q^50 + 351796 * q^51 + 410432 * q^52 - 741339 * q^53 + 4826312 * q^54 - 755935 * q^55 - 434176 * q^56 - 8091472 * q^57 - 1476568 * q^58 - 8176986 * q^59 + 2973760 * q^60 - 10479540 * q^61 + 6613544 * q^62 - 10121022 * q^63 - 2621440 * q^64 + 9085330 * q^65 - 1581152 * q^66 + 7646158 * q^67 - 6844160 * q^68 - 5432460 * q^69 - 5106912 * q^70 - 24632815 * q^71 - 6281728 * q^72 - 11099311 * q^73 - 3436312 * q^74 + 11990582 * q^75 - 1352640 * q^76 + 8000688 * q^77 - 10937992 * q^78 + 10390986 * q^79 - 765952 * q^80 - 23584945 * q^81 + 2535096 * q^82 + 36507958 * q^83 + 10397248 * q^84 + 23914083 * q^85 + 5244176 * q^86 + 16619052 * q^87 - 3574784 * q^88 - 17387733 * q^89 - 2091344 * q^90 - 8973442 * q^91 - 8008576 * q^92 - 21404363 * q^93 - 137504 * q^94 - 12445576 * q^95 + 917504 * q^96 - 1428702 * q^97 + 92378560 * q^98 + 13336614 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more