LMFDB - Embedded newform 91.8.h.a.16.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,Mod(16,91)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 2]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("91.16");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.h (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$28.4270373191$
Analytic rank:	$0$
Dimension:	$126$
Relative dimension:	$63$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.3
Character	$\chi$	$=$	91.16
Dual form			91.8.h.a.74.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-21.0975 q^{2} +(26.1888 - 45.3604i) q^{3} +317.105 q^{4} +(-66.6229 + 115.394i) q^{5} +(-552.519 + 956.990i) q^{6} +(658.312 - 624.634i) q^{7} -3989.64 q^{8} +(-278.208 - 481.870i) q^{9} +O(q^{10})$	\(q-21.0975 q^{2} +(26.1888 - 45.3604i) q^{3} +317.105 q^{4} +(-66.6229 + 115.394i) q^{5} +(-552.519 + 956.990i) q^{6} +(658.312 - 624.634i) q^{7} -3989.64 q^{8} +(-278.208 - 481.870i) q^{9} +(1405.58 - 2434.53i) q^{10} +(3155.65 - 5465.74i) q^{11} +(8304.60 - 14384.0i) q^{12} +(6921.73 + 3852.03i) q^{13} +(-13888.7 + 13178.2i) q^{14} +(3489.55 + 6044.07i) q^{15} +43582.0 q^{16} +14762.4 q^{17} +(5869.49 + 10166.3i) q^{18} +(3130.17 + 5421.61i) q^{19} +(-21126.4 + 36592.0i) q^{20} +(-11093.2 - 46219.7i) q^{21} +(-66576.3 + 115313. i) q^{22} -94762.2 q^{23} +(-104484. + 180971. i) q^{24} +(30185.3 + 52282.5i) q^{25} +(-146031. - 81268.1i) q^{26} +85406.1 q^{27} +(208754. - 198074. i) q^{28} +(127941. + 221601. i) q^{29} +(-73620.7 - 127515. i) q^{30} +(82331.7 + 142603. i) q^{31} -408798. q^{32} +(-165285. - 286282. i) q^{33} -311451. q^{34} +(28220.5 + 117580. i) q^{35} +(-88221.0 - 152803. i) q^{36} +414256. q^{37} +(-66038.8 - 114383. i) q^{38} +(356001. - 213092. i) q^{39} +(265801. - 460381. i) q^{40} +(-230611. - 399430. i) q^{41} +(234039. + 975121. i) q^{42} +(-138583. + 240032. i) q^{43} +(1.00067e6 - 1.73321e6i) q^{44} +74140.0 q^{45} +1.99925e6 q^{46} +(81843.4 - 141757. i) q^{47} +(1.14136e6 - 1.97690e6i) q^{48} +(43207.5 - 822409. i) q^{49} +(-636834. - 1.10303e6i) q^{50} +(386611. - 669630. i) q^{51} +(2.19491e6 + 1.22150e6i) q^{52} +(-250272. - 433484. i) q^{53} -1.80186e6 q^{54} +(420476. + 728286. i) q^{55} +(-2.62643e6 + 2.49206e6i) q^{56} +327902. q^{57} +(-2.69924e6 - 4.67523e6i) q^{58} -126109. q^{59} +(1.10655e6 + 1.91660e6i) q^{60} +(1.15399e6 + 1.99876e6i) q^{61} +(-1.73699e6 - 3.00856e6i) q^{62} +(-484140. - 143443. i) q^{63} +3.04612e6 q^{64} +(-905647. + 542095. i) q^{65} +(3.48711e6 + 6.03985e6i) q^{66} +(728468. - 1.26174e6i) q^{67} +4.68124e6 q^{68} +(-2.48171e6 + 4.29845e6i) q^{69} +(-595382. - 2.48065e6i) q^{70} +(861774. - 1.49264e6i) q^{71} +(1.10995e6 + 1.92249e6i) q^{72} +(-2.29255e6 - 3.97081e6i) q^{73} -8.73977e6 q^{74} +3.16207e6 q^{75} +(992592. + 1.71922e6i) q^{76} +(-1.33669e6 - 5.56929e6i) q^{77} +(-7.51074e6 + 4.49572e6i) q^{78} +(1.81287e6 - 3.13998e6i) q^{79} +(-2.90356e6 + 5.02911e6i) q^{80} +(2.84513e6 - 4.92790e6i) q^{81} +(4.86531e6 + 8.42697e6i) q^{82} +516028. q^{83} +(-3.51771e6 - 1.46565e7i) q^{84} +(-983516. + 1.70350e6i) q^{85} +(2.92375e6 - 5.06408e6i) q^{86} +1.34025e7 q^{87} +(-1.25899e7 + 2.18063e7i) q^{88} -7.63666e6 q^{89} -1.56417e6 q^{90} +(6.96277e6 - 1.78772e6i) q^{91} -3.00496e7 q^{92} +8.62467e6 q^{93} +(-1.72669e6 + 2.99072e6i) q^{94} -834164. q^{95} +(-1.07059e7 + 1.85432e7i) q^{96} +(3.03500e6 - 5.25677e6i) q^{97} +(-911570. + 1.73508e7i) q^{98} -3.51170e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 126 q - 2 q^{2} - 80 q^{3} + 7678 q^{4} - 2 q^{5} - 258 q^{6} + 953 q^{7} - 264 q^{8} - 41707 q^{9}+O(q^{10}) $ 126 * q - 2 * q^2 - 80 * q^3 + 7678 * q^4 - 2 * q^5 - 258 * q^6 + 953 * q^7 - 264 * q^8 - 41707 * q^9	\( 126 q - 2 q^{2} - 80 q^{3} + 7678 q^{4} - 2 q^{5} - 258 q^{6} + 953 q^{7} - 264 q^{8} - 41707 q^{9} - 4255 q^{10} + 7423 q^{11} - 18072 q^{12} - 1824 q^{13} - 15916 q^{14} + 11047 q^{15} + 410294 q^{16} + 99274 q^{17} - 21111 q^{18} - 4844 q^{19} + 36626 q^{20} + 73198 q^{21} - 43360 q^{22} + 34130 q^{23} - 130304 q^{24} - 810669 q^{25} + 390708 q^{26} + 416614 q^{27} + 69267 q^{28} + 191096 q^{29} + 70666 q^{30} + 183609 q^{31} + 695346 q^{32} + 178591 q^{33} - 742000 q^{34} + 579437 q^{35} - 1732409 q^{36} - 1362898 q^{37} - 877438 q^{38} + 459227 q^{39} - 1502882 q^{40} + 593701 q^{41} + 1442877 q^{42} - 592188 q^{43} + 1254066 q^{44} + 1954226 q^{45} - 1385452 q^{46} + 98278 q^{47} - 374916 q^{48} - 1497637 q^{49} + 289562 q^{50} - 281250 q^{51} - 8455 q^{52} - 1256681 q^{53} - 293814 q^{54} - 3015554 q^{55} - 1646151 q^{56} + 2743072 q^{57} + 1851469 q^{58} - 2279458 q^{59} + 1031485 q^{60} - 1127636 q^{61} - 7724680 q^{62} + 5142530 q^{63} + 11827496 q^{64} - 2789048 q^{65} + 435059 q^{66} + 4373348 q^{67} + 8737122 q^{68} - 7610377 q^{69} - 8084578 q^{70} - 60067 q^{71} - 11660951 q^{72} - 5060877 q^{73} + 1184002 q^{74} + 22637254 q^{75} + 637438 q^{76} + 21469082 q^{77} - 7230943 q^{78} - 2446486 q^{79} - 123568 q^{80} - 30756895 q^{81} + 8626952 q^{82} - 18679806 q^{83} + 11302461 q^{84} + 5330093 q^{85} - 8512356 q^{86} - 16508762 q^{87} - 6438219 q^{88} - 6176684 q^{89} + 53481084 q^{90} + 29236777 q^{91} + 2460546 q^{92} + 27682404 q^{93} - 17421794 q^{94} + 39553398 q^{95} + 26667066 q^{96} + 7705262 q^{97} + 14093080 q^{98} - 60531432 q^{99}+O(q^{100}) \) 126 * q - 2 * q^2 - 80 * q^3 + 7678 * q^4 - 2 * q^5 - 258 * q^6 + 953 * q^7 - 264 * q^8 - 41707 * q^9 - 4255 * q^10 + 7423 * q^11 - 18072 * q^12 - 1824 * q^13 - 15916 * q^14 + 11047 * q^15 + 410294 * q^16 + 99274 * q^17 - 21111 * q^18 - 4844 * q^19 + 36626 * q^20 + 73198 * q^21 - 43360 * q^22 + 34130 * q^23 - 130304 * q^24 - 810669 * q^25 + 390708 * q^26 + 416614 * q^27 + 69267 * q^28 + 191096 * q^29 + 70666 * q^30 + 183609 * q^31 + 695346 * q^32 + 178591 * q^33 - 742000 * q^34 + 579437 * q^35 - 1732409 * q^36 - 1362898 * q^37 - 877438 * q^38 + 459227 * q^39 - 1502882 * q^40 + 593701 * q^41 + 1442877 * q^42 - 592188 * q^43 + 1254066 * q^44 + 1954226 * q^45 - 1385452 * q^46 + 98278 * q^47 - 374916 * q^48 - 1497637 * q^49 + 289562 * q^50 - 281250 * q^51 - 8455 * q^52 - 1256681 * q^53 - 293814 * q^54 - 3015554 * q^55 - 1646151 * q^56 + 2743072 * q^57 + 1851469 * q^58 - 2279458 * q^59 + 1031485 * q^60 - 1127636 * q^61 - 7724680 * q^62 + 5142530 * q^63 + 11827496 * q^64 - 2789048 * q^65 + 435059 * q^66 + 4373348 * q^67 + 8737122 * q^68 - 7610377 * q^69 - 8084578 * q^70 - 60067 * q^71 - 11660951 * q^72 - 5060877 * q^73 + 1184002 * q^74 + 22637254 * q^75 + 637438 * q^76 + 21469082 * q^77 - 7230943 * q^78 - 2446486 * q^79 - 123568 * q^80 - 30756895 * q^81 + 8626952 * q^82 - 18679806 * q^83 + 11302461 * q^84 + 5330093 * q^85 - 8512356 * q^86 - 16508762 * q^87 - 6438219 * q^88 - 6176684 * q^89 + 53481084 * q^90 + 29236777 * q^91 + 2460546 * q^92 + 27682404 * q^93 - 17421794 * q^94 + 39553398 * q^95 + 26667066 * q^96 + 7705262 * q^97 + 14093080 * q^98 - 60531432 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−21.0975			−1.86477			−0.932387	−	0.361462i	$-0.882278\pi$
$2$	−21.0975			−1.86477			−0.932387	+	0.361462i	$0.882278\pi$
$3$	26.1888	−	45.3604i	0.560004	−	0.969956i	−0.437491	−	0.899223i	$-0.644133\pi$
$3$	26.1888	−	45.3604i	0.560004	−	0.969956i	0.997495	−	0.0707332i	$-0.0225339\pi$
$4$	317.105			2.47738
$5$	−66.6229	+	115.394i	−0.238357	+	0.412847i	−0.960243	−	0.279165i	$-0.909942\pi$
$5$	−66.6229	+	115.394i	−0.238357	+	0.412847i	0.721886	+	0.692012i	$0.243276\pi$
$6$	−552.519	+	956.990i	−1.04428	+	1.80875i
$7$	658.312	−	624.634i	0.725419	−	0.688308i
$7$	658.312	−	624.634i	0.725419	−	0.688308i
$8$	−3989.64			−2.75498
$9$	−278.208	−	481.870i	−0.127210	−	0.220334i
$10$	1405.58	−	2434.53i	0.444482	−	0.769866i
$11$	3155.65	−	5465.74i	0.714848	−	1.23815i	−0.248170	−	0.968717i	$-0.579829\pi$
$11$	3155.65	−	5465.74i	0.714848	−	1.23815i	0.963018	−	0.269437i	$-0.0868376\pi$
$12$	8304.60	−	14384.0i	1.38734	−	2.40295i
$13$	6921.73	+	3852.03i	0.873802	+	0.486281i
$13$	6921.73	+	3852.03i	0.873802	+	0.486281i
$14$	−13888.7	+	13178.2i	−1.35274	+	1.28354i
$15$	3489.55	+	6044.07i	0.266962	+	0.462392i
$16$	43582.0			2.66003
$17$	14762.4			0.728764			0.364382	−	0.931250i	$-0.381280\pi$
$17$	14762.4			0.728764			0.364382	+	0.931250i	$0.381280\pi$
$18$	5869.49	+	10166.3i	0.237218	+	0.410873i
$19$	3130.17	+	5421.61i	0.104696	+	0.181339i	0.913614	−	0.406583i	$-0.133280\pi$
$19$	3130.17	+	5421.61i	0.104696	+	0.181339i	−0.808918	+	0.587922i	$0.799946\pi$
$20$	−21126.4	+	36592.0i	−0.590502	+	1.02278i
$21$	−11093.2	−	46219.7i	−0.261390	−	1.08908i
$22$	−66576.3	+	115313.i	−1.33303	+	2.30888i
$23$	−94762.2			−1.62401			−0.812003	−	0.583653i	$-0.801623\pi$
$23$	−94762.2			−1.62401			−0.812003	+	0.583653i	$0.801623\pi$
$24$	−104484.	+	180971.i	−1.54280	+	2.67221i
$25$	30185.3	+	52282.5i	0.386372	+	0.669215i
$26$	−146031.	−	81268.1i	−1.62944	−	0.906804i
$27$	85406.1			0.835057
$28$	208754.	−	198074.i	1.79714	−	1.70520i
$29$	127941.	+	221601.i	0.974133	+	1.68725i	0.682768	+	0.730635i	$0.260776\pi$
$29$	127941.	+	221601.i	0.974133	+	1.68725i	0.291365	+	0.956612i	$0.405891\pi$
$30$	−73620.7	−	127515.i	−0.497824	−	0.862256i
$31$	82331.7	+	142603.i	0.496365	+	0.859729i	0.999991	−	0.00419253i	$-0.00133453\pi$
$31$	82331.7	+	142603.i	0.496365	+	0.859729i	−0.503626	+	0.863922i	$0.668001\pi$
$32$	−408798.			−2.20538
$33$	−165285.	−	286282.i	−0.800636	−	1.38674i
$34$	−311451.			−1.35898
$35$	28220.5	+	117580.i	0.111257	+	0.463550i
$36$	−88221.0	−	152803.i	−0.315147	−	0.545851i
$37$	414256.			1.34451			0.672253	−	0.740322i	$-0.265327\pi$
$37$	414256.			1.34451			0.672253	+	0.740322i	$0.265327\pi$
$38$	−66038.8	−	114383.i	−0.195234	−	0.338156i
$39$	356001.	−	213092.i	0.961005	−	0.575230i
$40$	265801.	−	460381.i	0.656669	−	1.13738i
$41$	−230611.	−	399430.i	−0.522560	−	0.905100i	−0.999655	−	0.0262488i	$-0.991644\pi$
$41$	−230611.	−	399430.i	−0.522560	−	0.905100i	0.477096	−	0.878851i	$-0.341690\pi$
$42$	234039.	+	975121.i	0.487434	+	2.03089i
$43$	−138583.	+	240032.i	−0.265809	+	0.460394i	−0.967775	−	0.251816i	$-0.918972\pi$
$43$	−138583.	+	240032.i	−0.265809	+	0.460394i	0.701967	+	0.712210i	$0.252306\pi$
$44$	1.00067e6	−	1.73321e6i	1.77095	−	3.06738i
$45$	74140.0			0.121285
$46$	1.99925e6			3.02841
$47$	81843.4	−	141757.i	0.114985	−	0.199160i	−0.802789	−	0.596264i	$-0.796651\pi$
$47$	81843.4	−	141757.i	0.114985	−	0.199160i	0.917774	+	0.397104i	$0.129985\pi$
$48$	1.14136e6	−	1.97690e6i	1.48963	−	2.58012i
$49$	43207.5	−	822409.i	0.0524654	−	0.998623i
$50$	−636834.	−	1.10303e6i	−0.720496	−	1.24794i
$51$	386611.	−	669630.i	0.408111	−	0.706869i
$52$	2.19491e6	+	1.22150e6i	2.16474	+	1.20470i
$53$	−250272.	−	433484.i	−0.230912	−	0.399952i	0.727165	−	0.686463i	$-0.240838\pi$
$53$	−250272.	−	433484.i	−0.230912	−	0.399952i	−0.958077	+	0.286512i	$0.907504\pi$
$54$	−1.80186e6			−1.55719
$55$	420476.	+	728286.i	0.340778	+	0.590246i
$56$	−2.62643e6	+	2.49206e6i	−1.99852	+	1.89627i
$57$	327902.			0.234521
$58$	−2.69924e6	−	4.67523e6i	−1.81654	−	3.14633i
$59$	−126109.			−0.0799399			−0.0399700	−	0.999201i	$-0.512726\pi$
$59$	−126109.			−0.0799399			−0.0399700	+	0.999201i	$0.512726\pi$
$60$	1.10655e6	+	1.91660e6i	0.661367	+	1.14552i
$61$	1.15399e6	+	1.99876e6i	0.650948	+	1.12747i	0.982893	+	0.184176i	$0.0589617\pi$
$61$	1.15399e6	+	1.99876e6i	0.650948	+	1.12747i	−0.331945	+	0.943299i	$0.607705\pi$
$62$	−1.73699e6	−	3.00856e6i	−0.925608	−	1.60320i
$63$	−484140.	−	143443.i	−0.243938	−	0.0722749i
$64$	3.04612e6			1.45250
$65$	−905647.	+	542095.i	−0.409037	+	0.244838i
$66$	3.48711e6	+	6.03985e6i	1.49301	+	2.58596i
$67$	728468.	−	1.26174e6i	0.295902	−	0.512518i	−0.679292	−	0.733868i	$-0.737713\pi$
$67$	728468.	−	1.26174e6i	0.295902	−	0.512518i	0.975194	+	0.221350i	$0.0710464\pi$
$68$	4.68124e6			1.80543
$69$	−2.48171e6	+	4.29845e6i	−0.909451	+	1.57522i
$70$	−595382.	−	2.48065e6i	−0.207469	−	0.864416i
$71$	861774.	−	1.49264e6i	0.285752	−	0.494937i	−0.687039	−	0.726620i	$-0.741090\pi$
$71$	861774.	−	1.49264e6i	0.285752	−	0.494937i	0.972791	+	0.231683i	$0.0744234\pi$
$72$	1.10995e6	+	1.92249e6i	0.350461	+	0.607016i
$73$	−2.29255e6	−	3.97081e6i	−0.689744	−	1.19467i	−0.971920	−	0.235309i	$-0.924390\pi$
$73$	−2.29255e6	−	3.97081e6i	−0.689744	−	1.19467i	0.282176	−	0.959363i	$-0.408944\pi$
$74$	−8.73977e6			−2.50720
$75$	3.16207e6			0.865479
$76$	992592.	+	1.71922e6i	0.259372	+	0.449245i
$77$	−1.33669e6	−	5.56929e6i	−0.333666	−	1.39022i
$78$	−7.51074e6	+	4.49572e6i	−1.79206	+	1.07267i
$79$	1.81287e6	−	3.13998e6i	0.413687	−	0.716527i	−0.581603	−	0.813473i	$-0.697574\pi$
$79$	1.81287e6	−	3.13998e6i	0.413687	−	0.716527i	0.995290	+	0.0969463i	$0.0309075\pi$
$80$	−2.90356e6	+	5.02911e6i	−0.634038	+	1.09819i
$81$	2.84513e6	−	4.92790e6i	0.594845	−	1.03030i
$82$	4.86531e6	+	8.42697e6i	0.974456	+	1.68781i
$83$	516028.			0.0990603			0.0495302	−	0.998773i	$-0.484228\pi$
$83$	516028.			0.0990603			0.0495302	+	0.998773i	$0.484228\pi$
$84$	−3.51771e6	−	1.46565e7i	−0.647563	−	2.69807i
$85$	−983516.	+	1.70350e6i	−0.173706	+	0.300868i
$86$	2.92375e6	−	5.06408e6i	0.495673	−	0.858530i
$87$	1.34025e7			2.18207
$88$	−1.25899e7	+	2.18063e7i	−1.96939	+	3.41109i
$89$	−7.63666e6			−1.14826			−0.574128	−	0.818766i	$-0.694659\pi$
$89$	−7.63666e6			−1.14826			−0.574128	+	0.818766i	$0.694659\pi$
$90$	−1.56417e6			−0.226170
$91$	6.96277e6	−	1.78772e6i	0.968584	−	0.248687i
$92$	−3.00496e7			−4.02328
$93$	8.62467e6			1.11187
$94$	−1.72669e6	+	2.99072e6i	−0.214421	+	0.371388i
$95$	−834164.			−0.0998202
$96$	−1.07059e7	+	1.85432e7i	−1.23502	+	2.13912i
$97$	3.03500e6	−	5.25677e6i	0.337643	−	0.584814i	−0.646346	−	0.763044i	$-0.723704\pi$
$97$	3.03500e6	−	5.25677e6i	0.337643	−	0.584814i	0.983989	+	0.178230i	$0.0570371\pi$
$98$	−911570.	+	1.73508e7i	−0.0978360	+	1.86221i
$99$	−3.51170e6			−0.363743
$100$	9.57190e6	+	1.65790e7i	0.957190	+	1.65790i
$101$	−3.09275e6	+	5.35680e6i	−0.298690	+	0.517345i	−0.975836	−	0.218502i	$-0.929883\pi$
$101$	−3.09275e6	+	5.35680e6i	−0.298690	+	0.517345i	0.677147	+	0.735848i	$0.263216\pi$
$102$	−8.15653e6	+	1.41275e7i	−0.761035	+	1.31815i
$103$	571795.	−	990379.i	0.0515597	−	0.0893040i	−0.839094	−	0.543987i	$-0.816914\pi$
$103$	571795.	−	990379.i	0.0515597	−	0.0893040i	0.890653	+	0.454683i	$0.150247\pi$
$104$	−2.76152e7	−	1.53682e7i	−2.40731	−	1.33970i
$105$	6.07255e6	+	1.79920e6i	0.511927	+	0.151676i
$106$	5.28012e6	+	9.14543e6i	0.430599	+	0.745819i
$107$	2.03576e7			1.60651			0.803253	−	0.595638i	$-0.203101\pi$
$107$	2.03576e7			1.60651			0.803253	+	0.595638i	$0.203101\pi$
$108$	2.70827e7			2.06875
$109$	−4.65918e6	−	8.06994e6i	−0.344601	−	0.596867i	0.640680	−	0.767808i	$-0.278653\pi$
$109$	−4.65918e6	−	8.06994e6i	−0.344601	−	0.596867i	−0.985281	+	0.170941i	$0.945319\pi$
$110$	−8.87100e6	−	1.53650e7i	−0.635475	−	1.10067i
$111$	1.08489e7	−	1.87908e7i	0.752929	−	1.30411i
$112$	2.86906e7	−	2.72228e7i	1.92964	−	1.83092i
$113$	4.65877e6	−	8.06923e6i	0.303737	−	0.526087i	−0.673243	−	0.739422i	$-0.735099\pi$
$113$	4.65877e6	−	8.06923e6i	0.303737	−	0.526087i	0.976979	+	0.213334i	$0.0684324\pi$
$114$	−6.91791e6			−0.437329
$115$	6.31333e6	−	1.09350e7i	0.387094	−	0.670466i
$116$	4.05708e7	+	7.02707e7i	2.41330	+	4.17995i
$117$	−69504.8	−	4.40704e6i	−0.00401203	−	0.254388i
$118$	2.66058e6			0.149070
$119$	9.71830e6	−	9.22113e6i	0.528659	−	0.501614i
$120$	−1.39220e7	−	2.41137e7i	−0.735476	−	1.27388i
$121$	−1.01726e7	−	1.76195e7i	−0.522016	−	0.904159i
$122$	−2.43462e7	−	4.21689e7i	−1.21387	−	2.10249i
$123$	−2.41577e7			−1.17054
$124$	2.61078e7	+	4.52200e7i	1.22968	+	2.12988i
$125$	−1.84539e7			−0.845092
$126$	1.02142e7	+	3.02629e6i	0.454889	+	0.134776i
$127$	−1.23741e6	−	2.14326e6i	−0.0536046	−	0.0928459i	0.837978	−	0.545704i	$-0.183738\pi$
$127$	−1.23741e6	−	2.14326e6i	−0.0536046	−	0.0928459i	−0.891583	+	0.452858i	$0.850404\pi$
$128$	−1.19394e7			−0.503208
$129$	7.25863e6	+	1.25723e7i	0.297708	+	0.515645i
$130$	1.91069e7	−	1.14369e7i	0.762761	−	0.456567i
$131$	−1.71101e7	+	2.96355e7i	−0.664970	+	1.15176i	0.314324	+	0.949316i	$0.398222\pi$
$131$	−1.71101e7	+	2.96355e7i	−0.664970	+	1.15176i	−0.979294	+	0.202445i	$0.935111\pi$
$132$	−5.24127e7	−	9.07815e7i	−1.98348	−	3.43549i
$133$	5.44715e6	+	1.61390e6i	0.200765	+	0.0594836i
$134$	−1.53688e7	+	2.66196e7i	−0.551791	+	0.955730i
$135$	−5.69000e6	+	9.85537e6i	−0.199042	+	0.344750i
$136$	−5.88968e7			−2.00773
$137$	1.94539e7			0.646374			0.323187	−	0.946335i	$-0.395246\pi$
$137$	1.94539e7			0.646374			0.323187	+	0.946335i	$0.395246\pi$
$138$	5.23579e7	−	9.06865e7i	1.69592	−	2.93742i
$139$	9.05723e6	−	1.56876e7i	0.286051	−	0.495455i	−0.686812	−	0.726835i	$-0.740991\pi$
$139$	9.05723e6	−	1.56876e7i	0.286051	−	0.495455i	0.972864	+	0.231380i	$0.0743239\pi$
$140$	8.94885e6	+	3.72853e7i	0.275625	+	1.14839i
$141$	−4.28676e6	−	7.42489e6i	−0.128784	−	0.223061i
$142$	−1.81813e7	+	3.14909e7i	−0.532863	+	0.922945i
$143$	4.28967e7	−	2.56768e7i	1.22673	−	0.734284i
$144$	−1.21249e7	−	2.10009e7i	−0.338382	−	0.586096i
$145$	−3.40953e7			−0.928766
$146$	4.83670e7	+	8.37741e7i	1.28622	+	2.22779i
$147$	−3.61732e7	−	2.34978e7i	−0.939239	−	0.610122i
$148$	1.31363e8			3.33085
$149$	1.27370e7	+	2.20611e7i	0.315438	+	0.546355i	0.979531	−	0.201296i	$-0.0645152\pi$
$149$	1.27370e7	+	2.20611e7i	0.315438	+	0.546355i	−0.664093	+	0.747650i	$0.731182\pi$
$150$	−6.67117e7			−1.61392
$151$	−1.66332e7	−	2.88095e7i	−0.393148	−	0.680952i	0.599715	−	0.800214i	$-0.295281\pi$
$151$	−1.66332e7	−	2.88095e7i	−0.393148	−	0.680952i	−0.992863	+	0.119262i	$0.961947\pi$
$152$	−1.24882e7	−	2.16303e7i	−0.288436	−	0.499585i
$153$	−4.10703e6	−	7.11358e6i	−0.0927060	−	0.160571i
$154$	2.82007e7	+	1.17498e8i	0.622212	+	2.59244i
$155$	−2.19407e7			−0.473248
$156$	1.12890e8	−	6.75726e7i	2.38077	−	1.42506i
$157$	−7.41200e6	−	1.28380e7i	−0.152858	−	0.264757i	0.779419	−	0.626503i	$-0.215514\pi$
$157$	−7.41200e6	−	1.28380e7i	−0.152858	−	0.264757i	−0.932277	+	0.361746i	$0.882181\pi$
$158$	−3.82470e7	+	6.62458e7i	−0.771432	+	1.33616i
$159$	−2.62173e7			−0.517247
$160$	2.72353e7	−	4.71729e7i	0.525669	−	0.910485i
$161$	−6.23832e7	+	5.91917e7i	−1.17809	+	1.11782i
$162$	−6.00251e7	+	1.03966e8i	−1.10925	+	1.92128i
$163$	1.48005e6	+	2.56353e6i	0.0267683	+	0.0463641i	0.879099	−	0.476639i	$-0.158145\pi$
$163$	1.48005e6	+	2.56353e6i	0.0267683	+	0.0463641i	−0.852331	+	0.523003i	$0.824812\pi$
$164$	−7.31278e7	−	1.26661e8i	−1.29458	−	2.24228i
$165$	4.40471e7			0.763350
$166$	−1.08869e7			−0.184725
$167$	−1.20973e6	−	2.09532e6i	−0.0200993	−	0.0348131i	0.855801	−	0.517306i	$-0.173065\pi$
$167$	−1.20973e6	−	2.09532e6i	−0.0200993	−	0.0348131i	−0.875900	+	0.482492i	$0.839732\pi$
$168$	4.42579e7	+	1.84400e8i	0.720125	+	3.00039i
$169$	3.30723e7	+	5.33254e7i	0.527061	+	0.849827i
$170$	2.07497e7	−	3.59396e7i	0.323923	−	0.561051i
$171$	1.74168e6	−	3.01667e6i	0.0266367	−	0.0461362i
$172$	−4.39452e7	+	7.61153e7i	−0.658509	+	1.14057i
$173$	−5.91692e7	−	1.02484e8i	−0.868828	−	1.50485i	−0.863195	−	0.504871i	$-0.831540\pi$
$173$	−5.91692e7	−	1.02484e8i	−0.868828	−	1.50485i	−0.00563344	−	0.999984i	$-0.501793\pi$
$174$	−2.82760e8			−4.06907
$175$	5.25288e7	+	1.55634e7i	0.740907	+	0.219519i
$176$	1.37529e8	−	2.38208e8i	1.90152	−	3.29353i
$177$	−3.30264e6	+	5.72034e6i	−0.0447667	+	0.0775382i
$178$	1.61114e8			2.14124
$179$	−6.86675e7	+	1.18936e8i	−0.894882	+	1.54998i	−0.0609317	+	0.998142i	$0.519407\pi$
$179$	−6.86675e7	+	1.18936e8i	−0.894882	+	1.54998i	−0.833950	+	0.551839i	$0.813926\pi$
$180$	2.35101e7			0.300470
$181$	−1.00434e8			−1.25894			−0.629469	−	0.777026i	$-0.716727\pi$
$181$	−1.00434e8			−1.25894			−0.629469	+	0.777026i	$0.716727\pi$
$182$	−1.46897e8	+	3.77163e7i	−1.80619	+	0.463745i
$183$	1.20886e8			1.45813
$184$	3.78067e8			4.47411
$185$	−2.75989e7	+	4.78027e7i	−0.320473	+	0.555075i
$186$	−1.81959e8			−2.07338
$187$	4.65851e7	−	8.06877e7i	0.520956	−	0.902322i
$188$	2.59529e7	−	4.49518e7i	0.284862	−	0.493395i
$189$	5.62239e7	−	5.33476e7i	0.605766	−	0.574776i
$190$	1.75988e7			0.186142
$191$	2.45220e7	+	4.24734e7i	0.254647	+	0.441062i	0.964800	−	0.262986i	$-0.0847073\pi$
$191$	2.45220e7	+	4.24734e7i	0.254647	+	0.441062i	−0.710152	+	0.704048i	$0.751374\pi$
$192$	7.97742e7	−	1.38173e8i	0.813408	−	1.40886i
$193$	2.19603e7	−	3.80364e7i	0.219881	−	0.380846i	−0.734890	−	0.678186i	$-0.762766\pi$
$193$	2.19603e7	−	3.80364e7i	0.219881	−	0.380846i	0.954771	+	0.297341i	$0.0960997\pi$
$194$	−6.40309e7	+	1.10905e8i	−0.629627	+	1.09055i
$195$	871796.	+	5.52773e7i	0.00841964	+	0.533858i
$196$	1.37013e7	−	2.60790e8i	0.129977	−	2.47397i
$197$	−5.04951e7	−	8.74600e7i	−0.470562	−	0.815038i	0.528871	−	0.848702i	$-0.322616\pi$
$197$	−5.04951e7	−	8.74600e7i	−0.470562	−	0.815038i	−0.999433	+	0.0336645i	$0.989282\pi$
$198$	7.40882e7			0.678298
$199$	1.60412e8			1.44295			0.721473	−	0.692442i	$-0.243465\pi$
$199$	1.60412e8			1.44295			0.721473	+	0.692442i	$0.243465\pi$
$200$	−1.20428e8	−	2.08588e8i	−1.06445	−	1.84368i
$201$	−3.81554e7	−	6.60871e7i	−0.331413	−	0.574025i
$202$	6.52493e7	−	1.13015e8i	0.556988	−	0.964732i
$203$	2.22645e8	+	6.59661e7i	1.86800	+	0.553458i
$204$	1.22596e8	−	2.12343e8i	1.01105	−	1.75118i
$205$	6.14558e7			0.498224
$206$	−1.20635e7	+	2.08945e7i	−0.0961472	+	0.166532i
$207$	2.63636e7	+	4.56631e7i	0.206590	+	0.357824i
$208$	3.01663e8	+	1.67879e8i	2.32434	+	1.29352i
$209$	3.95108e7			0.299367
$210$	−1.28116e8	−	3.79586e7i	−0.954629	−	0.282841i
$211$	−3.47884e7	−	6.02553e7i	−0.254945	−	0.441577i	0.709936	−	0.704266i	$-0.248724\pi$
$211$	−3.47884e7	−	6.02553e7i	−0.254945	−	0.441577i	−0.964880	+	0.262689i	$0.915391\pi$
$212$	−7.93624e7	−	1.37460e8i	−0.572057	−	0.990832i
$213$	−4.51377e7	−	7.81807e7i	−0.320045	−	0.554333i
$214$	−4.29494e8			−2.99577
$215$	−1.84655e7	−	3.19832e7i	−0.126715	−	0.219476i
$216$	−3.40740e8			−2.30056
$217$	1.43274e8	+	4.24499e7i	0.951830	+	0.282012i
$218$	9.82971e7	+	1.70256e8i	0.642603	+	1.11302i
$219$	−2.40156e8			−1.54504
$220$	1.33335e8	+	2.30943e8i	0.844238	+	1.46226i
$221$	1.02182e8	+	5.68653e7i	0.636796	+	0.354384i
$222$	−2.28884e8	+	3.96439e8i	−1.40404	+	2.43187i
$223$	1.58160e8	+	2.73941e8i	0.955056	+	1.65420i	0.734241	+	0.678889i	$0.237538\pi$
$223$	1.58160e8	+	2.73941e8i	0.955056	+	1.65420i	0.220815	+	0.975316i	$0.429128\pi$
$224$	−2.69117e8	+	2.55349e8i	−1.59983	+	1.51798i
$225$	1.67956e7	−	2.90908e7i	0.0983005	−	0.170262i
$226$	−9.82885e7	+	1.70241e8i	−0.566400	+	0.981034i
$227$	1.31526e8			0.746311			0.373156	−	0.927769i	$-0.378276\pi$
$227$	1.31526e8			0.746311			0.373156	+	0.927769i	$0.378276\pi$
$228$	1.03979e8			0.580998
$229$	−7.09414e7	+	1.22874e8i	−0.390369	+	0.676139i	−0.992498	−	0.122260i	$-0.960986\pi$
$229$	−7.09414e7	+	1.22874e8i	−0.390369	+	0.676139i	0.602129	+	0.798399i	$0.294319\pi$
$230$	−1.33196e8	+	2.30701e8i	−0.721842	+	1.25027i
$231$	−2.87631e8	−	8.52205e7i	−1.53530	−	0.454886i
$232$	−5.10440e8	−	8.84108e8i	−2.68372	−	4.64833i
$233$	6.04801e7	−	1.04755e8i	0.313232	−	0.542534i	−0.665828	−	0.746105i	$-0.731921\pi$
$233$	6.04801e7	−	1.04755e8i	0.313232	−	0.542534i	0.979060	+	0.203571i	$0.0652548\pi$
$234$	1.46638e6	+	9.29776e7i	0.00748153	+	0.474376i
$235$	1.09053e7	+	1.88885e7i	0.0548150	+	0.0949424i
$236$	−3.99897e7			−0.198042
$237$	−9.49538e7	−	1.64465e8i	−0.463333	−	0.802516i
$238$	−2.05032e8	+	1.94543e8i	−0.985830	+	0.935396i
$239$	−183236.			−0.000868197			−0.000434098	−	1.00000i	$-0.500138\pi$
$239$	−183236.			−0.000868197			−0.000434098		1.00000i	$0.500138\pi$
$240$	1.52081e8	+	2.63413e8i	0.710129	+	1.22998i
$241$	−3.40723e8			−1.56798			−0.783991	−	0.620772i	$-0.786819\pi$
$241$	−3.40723e8			−1.56798			−0.783991	+	0.620772i	$0.786819\pi$
$242$	2.14617e8	+	3.71727e8i	0.973442	+	1.68605i
$243$	−5.56293e7	−	9.63528e7i	−0.248703	−	0.430767i
$244$	3.65935e8	+	6.33817e8i	1.61265	+	2.79318i
$245$	9.20226e7	+	5.97771e7i	0.399773	+	0.259689i
$246$	5.09667e8			2.18280
$247$	782012.	+	4.95845e7i	0.00330198	+	0.209366i
$248$	−3.28474e8	−	5.68933e8i	−1.36748	−	2.36854i
$249$	1.35142e7	−	2.34072e7i	0.0554742	−	0.0960842i
$250$	3.89332e8			1.57591
$251$	2.39162e8	−	4.14241e8i	0.954628	−	1.65346i	0.219410	−	0.975633i	$-0.429587\pi$
$251$	2.39162e8	−	4.14241e8i	0.954628	−	1.65346i	0.735218	−	0.677831i	$-0.237080\pi$
$252$	−1.53523e8	−	4.54865e7i	−0.604327	−	0.179052i
$253$	−2.99036e8	+	5.17946e8i	−1.16092	+	2.01077i
$254$	2.61064e7	+	4.52175e7i	0.0999604	+	0.173137i
$255$	5.15142e7	+	8.92253e7i	0.194552	+	0.336975i
$256$	−1.38012e8			−0.514135
$257$	7.58178e7			0.278615			0.139308	−	0.990249i	$-0.455512\pi$
$257$	7.58178e7			0.278615			0.139308	+	0.990249i	$0.455512\pi$
$258$	−1.53139e8	−	2.65244e8i	−0.555158	−	0.961562i
$259$	2.72710e8	−	2.58758e8i	0.975330	−	0.925434i
$260$	−2.87185e8	+	1.71901e8i	−1.01334	+	0.606557i
$261$	7.11886e7	−	1.23302e8i	0.247838	−	0.429269i
$262$	3.60979e8	−	6.25235e8i	1.24002	−	2.14777i
$263$	−4.99173e7	+	8.64593e7i	−0.169202	+	0.293067i	−0.938140	−	0.346257i	$-0.887452\pi$
$263$	−4.99173e7	+	8.64593e7i	−0.169202	+	0.293067i	0.768937	+	0.639324i	$0.220786\pi$
$264$	6.59428e8	+	1.14216e9i	2.20574	+	3.82045i
$265$	6.66954e7			0.220158
$266$	−1.14921e8	−	3.40494e7i	−0.374382	−	0.110923i
$267$	−1.99995e8	+	3.46402e8i	−0.643028	+	1.11376i
$268$	2.31001e8	−	4.00105e8i	0.733063	−	1.26970i
$269$	2.27901e8			0.713860			0.356930	−	0.934131i	$-0.383824\pi$
$269$	2.27901e8			0.713860			0.356930	+	0.934131i	$0.383824\pi$
$270$	1.20045e8	−	2.07924e8i	0.371168	−	0.642881i
$271$	−1.58022e8			−0.482310			−0.241155	−	0.970487i	$-0.577526\pi$
$271$	−1.58022e8			−0.482310			−0.241155	+	0.970487i	$0.577526\pi$
$272$	6.43377e8			1.93854
$273$	1.01255e8	−	3.62652e8i	0.301196	−	1.07875i
$274$	−4.10428e8			−1.20534
$275$	3.81016e8			1.10479
$276$	−7.86962e8	+	1.36306e9i	−2.25306	+	3.90241i
$277$	1.66252e8			0.469990			0.234995	−	0.971997i	$-0.424493\pi$
$277$	1.66252e8			0.469990			0.234995	+	0.971997i	$0.424493\pi$
$278$	−1.91085e8	+	3.30969e8i	−0.533421	+	0.923912i
$279$	4.58106e7	−	7.93463e7i	0.126285	−	0.218732i
$280$	−1.12590e8	−	4.69103e8i	−0.306510	−	1.27707i
$281$	−7.29916e8			−1.96246			−0.981230	−	0.192841i	$-0.938230\pi$
$281$	−7.29916e8			−1.96246			−0.981230	+	0.192841i	$0.938230\pi$
$282$	9.04400e7	+	1.56647e8i	0.240153	+	0.415958i
$283$	−5.18676e7	+	8.98373e7i	−0.136033	+	0.235616i	−0.925992	−	0.377544i	$-0.876769\pi$
$283$	−5.18676e7	+	8.98373e7i	−0.136033	+	0.235616i	0.789959	+	0.613160i	$0.210102\pi$
$284$	2.73273e8	−	4.73322e8i	0.707916	−	1.22615i
$285$	−2.18458e7	+	3.78380e7i	−0.0558998	+	0.0968212i
$286$	−9.05014e8	+	5.41716e8i	−2.28757	+	1.36927i
$287$	−4.01311e8	−	1.18902e8i	−1.00206	−	0.296895i
$288$	1.13731e8	+	1.96988e8i	0.280546	+	0.485920i
$289$	−1.92409e8			−0.468903
$290$	7.19326e8			1.73194
$291$	−1.58966e8	−	2.75337e8i	−0.378163	−	0.654997i
$292$	−7.26977e8	−	1.25916e9i	−1.70876	−	2.95966i
$293$	−1.53368e7	+	2.65642e7i	−0.0356204	+	0.0616964i	−0.883286	−	0.468835i	$-0.844674\pi$
$293$	−1.53368e7	+	2.65642e7i	−0.0356204	+	0.0616964i	0.847666	+	0.530531i	$0.178007\pi$
$294$	7.63164e8	+	4.95745e8i	1.75147	+	1.13774i
$295$	8.40174e6	−	1.45522e7i	0.0190543	−	0.0330029i
$296$	−1.65273e9			−3.70409
$297$	2.69512e8	−	4.66808e8i	0.596939	−	1.03393i
$298$	−2.68718e8	−	4.65434e8i	−0.588220	−	1.01883i
$299$	−6.55919e8	−	3.65027e8i	−1.41906	−	0.789724i
$300$	1.00271e9			2.14412
$301$	5.87016e7	+	2.44579e8i	0.124070	+	0.516937i
$302$	3.50919e8	+	6.07809e8i	0.733132	+	1.26982i
$303$	1.61991e8	+	2.80576e8i	0.334535	+	0.579431i
$304$	1.36419e8	+	2.36285e8i	0.278495	+	0.482368i
$305$	−3.07527e8			−0.620632
$306$	8.66480e7	+	1.50079e8i	0.172876	+	0.299429i
$307$	6.78954e8			1.33923			0.669617	−	0.742707i	$-0.266458\pi$
$307$	6.78954e8			1.33923			0.669617	+	0.742707i	$0.266458\pi$
$308$	−4.23870e8	−	1.76605e9i	−0.826618	−	3.44409i
$309$	−2.99493e7	−	5.18737e7i	−0.0577473	−	0.100021i
$310$	4.62894e8			0.882501
$311$	−7.46382e7	−	1.29277e8i	−0.140702	−	0.243703i	0.787059	−	0.616877i	$-0.211603\pi$
$311$	−7.46382e7	−	1.29277e8i	−0.140702	−	0.243703i	−0.927761	+	0.373175i	$0.878269\pi$
$312$	−1.42032e9	+	8.50161e8i	−2.64755	+	1.58475i
$313$	2.81826e7	−	4.88137e7i	0.0519489	−	0.0899781i	−0.838882	−	0.544314i	$-0.816790\pi$
$313$	2.81826e7	−	4.88137e7i	0.0519489	−	0.0899781i	0.890830	+	0.454336i	$0.150123\pi$
$314$	1.56375e8	+	2.70849e8i	0.285045	+	0.493712i
$315$	4.88073e7	−	4.63104e7i	0.0879828	−	0.0834817i
$316$	5.74870e8	−	9.95703e8i	1.02486	−	1.77511i
$317$	−3.82092e8	+	6.61804e8i	−0.673691	+	1.16687i	0.303158	+	0.952940i	$0.401959\pi$
$317$	−3.82092e8	+	6.61804e8i	−0.673691	+	1.16687i	−0.976850	+	0.213928i	$0.931374\pi$
$318$	5.53120e8			0.964549
$319$	1.61495e9			2.78543
$320$	−2.02941e8	+	3.51504e8i	−0.346215	+	0.599661i
$321$	5.33140e8	−	9.23426e8i	0.899650	−	1.55824i
$322$	1.31613e9	−	1.24880e9i	2.19686	−	2.08447i
$323$	4.62090e7	+	8.00363e7i	0.0762987	+	0.132153i
$324$	9.02203e8	−	1.56266e9i	1.47366	−	2.55245i
$325$	7.54121e6	+	4.78160e8i	0.0121857	+	0.772647i
$326$	−3.12254e7	−	5.40840e7i	−0.0499168	−	0.0864585i
$327$	−4.88074e8			−0.771913
$328$	9.20053e8	+	1.59358e9i	1.43964	+	2.49353i
$329$	−3.46677e7	−	1.44443e8i	−0.0536709	−	0.223619i
$330$	−9.29284e8			−1.42347
$331$	3.29982e8	+	5.71546e8i	0.500141	+	0.866270i	1.00000		0.000163150i	$5.19321e-5\pi$
$331$	3.29982e8	+	5.71546e8i	0.500141	+	0.866270i	−0.499859	+	0.866107i	$0.666615\pi$
$332$	1.63635e8			0.245410
$333$	−1.15249e8	−	1.99618e8i	−0.171034	−	0.296240i
$334$	2.55223e7	+	4.42060e7i	0.0374807	+	0.0649185i
$335$	9.70652e7	+	1.68122e8i	0.141061	+	0.244325i
$336$	−4.83464e8	−	2.01435e9i	−0.695307	−	2.89699i
$337$	−1.05199e9			−1.49729			−0.748647	−	0.662969i	$-0.769296\pi$
$337$	−1.05199e9			−1.49729			−0.748647	+	0.662969i	$0.769296\pi$
$338$	−6.97743e8	−	1.12503e9i	−0.982850	−	1.58474i
$339$	−2.44016e8	−	4.22647e8i	−0.340188	−	0.589222i
$340$	−3.11878e8	+	5.40188e8i	−0.430336	+	0.745364i
$341$	1.03924e9			1.41930
$342$	−3.67450e7	+	6.36442e7i	−0.0496715	+	0.0860335i
$343$	−4.85261e8	−	5.68391e8i	−0.649300	−	0.760532i
$344$	5.52894e8	−	9.57641e8i	0.732297	−	1.26838i
$345$	−3.30677e8	−	5.72750e8i	−0.433548	−	0.750928i
$346$	1.24832e9	+	2.16216e9i	1.62017	+	2.80621i
$347$	−6.41490e8			−0.824208			−0.412104	−	0.911137i	$-0.635206\pi$
$347$	−6.41490e8			−0.824208			−0.412104	+	0.911137i	$0.635206\pi$
$348$	4.25001e9			5.40583
$349$	5.54537e8	+	9.60486e8i	0.698299	+	1.20949i	0.969056	+	0.246842i	$0.0793927\pi$
$349$	5.54537e8	+	9.60486e8i	0.698299	+	1.20949i	−0.270757	+	0.962648i	$0.587274\pi$
$350$	−1.10823e9	−	3.28350e8i	−1.38162	−	0.409353i
$351$	5.91159e8	+	3.28987e8i	0.729674	+	0.406072i
$352$	−1.29002e9	+	2.23438e9i	−1.57651	+	2.73060i
$353$	6.78340e8	−	1.17492e9i	0.820798	−	1.42166i	−0.0842916	−	0.996441i	$-0.526863\pi$
$353$	6.78340e8	−	1.17492e9i	0.820798	−	1.42166i	0.905089	−	0.425222i	$-0.139804\pi$
$354$	6.96775e7	−	1.20685e8i	0.0834798	−	0.144591i
$355$	1.14828e8	+	1.98887e8i	0.136222	+	0.235943i
$356$	−2.42162e9			−2.84466
$357$	−1.63763e8	−	6.82316e8i	−0.190492	−	0.793682i
$358$	1.44871e9	−	2.50925e9i	1.66875	−	2.89036i
$359$	1.35861e8	−	2.35318e8i	0.154976	−	0.268426i	−0.778074	−	0.628172i	$-0.783803\pi$
$359$	1.35861e8	−	2.35318e8i	0.154976	−	0.268426i	0.933050	+	0.359746i	$0.117137\pi$
$360$	−2.95792e8			−0.334139
$361$	4.27340e8	−	7.40174e8i	0.478077	−	0.828054i
$362$	2.11890e9			2.34763
$363$	−1.06564e9			−1.16933
$364$	2.20793e9	−	5.66893e8i	2.39955	−	0.616093i
$365$	6.10944e8			0.657622
$366$	−2.55040e9			−2.71909
$367$	−4.68396e8	+	8.11286e8i	−0.494632	+	0.856727i	−0.999981	−	0.00618779i	$-0.998030\pi$
$367$	−4.68396e8	+	8.11286e8i	−0.494632	+	0.856727i	0.505349	+	0.862915i	$0.331364\pi$
$368$	−4.12993e9			−4.31991
$369$	−1.28315e8	+	2.22249e8i	−0.132949	+	0.230275i
$370$	5.82268e8	−	1.00852e9i	0.597609	−	1.03509i
$371$	−4.35526e8	−	1.29039e8i	−0.442798	−	0.131194i
$372$	2.73492e9			2.75451
$373$	−2.67520e8	−	4.63358e8i	−0.266917	−	0.462313i	0.701147	−	0.713016i	$-0.252671\pi$
$373$	−2.67520e8	−	4.63358e8i	−0.266917	−	0.462313i	−0.968064	+	0.250703i	$0.919338\pi$
$374$	−9.82828e8	+	1.70231e9i	−0.971465	+	1.68263i
$375$	−4.83287e8	+	8.37077e8i	−0.473255	+	0.819702i
$376$	−3.26526e8	+	5.65559e8i	−0.316781	+	0.548681i
$377$	3.19637e7	+	2.02670e9i	0.0307229	+	1.94802i
$378$	−1.18618e9	+	1.12550e9i	−1.12962	+	1.07183i
$379$	−6.18429e8	−	1.07115e9i	−0.583515	−	1.01068i	−0.995059	−	0.0992882i	$-0.968343\pi$
$379$	−6.18429e8	−	1.07115e9i	−0.583515	−	1.01068i	0.411543	−	0.911390i	$-0.364990\pi$
$380$	−2.64517e8			−0.247293
$381$	−1.29626e8			−0.120075
$382$	−5.17353e8	−	8.96082e8i	−0.474860	−	0.822481i
$383$	8.19790e8	+	1.41992e9i	0.745602	+	1.29142i	0.949913	+	0.312514i	$0.101171\pi$
$383$	8.19790e8	+	1.41992e9i	0.745602	+	1.29142i	−0.204311	+	0.978906i	$0.565495\pi$
$384$	−3.12678e8	+	5.41575e8i	−0.281798	+	0.488089i
$385$	7.31717e8	+	2.16796e8i	0.653478	+	0.193615i
$386$	−4.63308e8	+	8.02473e8i	−0.410029	+	0.710191i
$387$	1.54219e8			0.135254
$388$	9.62412e8	−	1.66695e9i	0.836470	−	1.44881i
$389$	−3.72414e8	−	6.45039e8i	−0.320776	−	0.555600i	0.659872	−	0.751378i	$-0.270610\pi$
$389$	−3.72414e8	−	6.45039e8i	−0.320776	−	0.555600i	−0.980648	+	0.195777i	$0.937277\pi$
$390$	−1.83927e7	−	1.16621e9i	−0.0157007	−	0.995524i
$391$	−1.39892e9			−1.18352
$392$	−1.72382e8	+	3.28111e9i	−0.144541	+	2.75119i
$393$	8.96184e8	+	1.55224e9i	0.744772	+	1.28998i
$394$	1.06532e9	+	1.84519e9i	0.877492	+	1.51986i
$395$	2.41557e8	+	4.18389e8i	0.197210	+	0.341579i
$396$	−1.11358e9			−0.901130
$397$	6.60273e8	+	1.14363e9i	0.529611	+	0.917313i	0.999403	+	0.0345363i	$0.0109954\pi$
$397$	6.60273e8	+	1.14363e9i	0.529611	+	0.917313i	−0.469792	+	0.882777i	$0.655671\pi$
$398$	−3.38429e9			−2.69077
$399$	2.15862e8	−	2.04819e8i	0.170126	−	0.161423i
$400$	1.31554e9	+	2.27857e9i	1.02776	+	1.78014i
$401$	1.29574e8			0.100349			0.0501746	−	0.998740i	$-0.484022\pi$
$401$	1.29574e8			0.100349			0.0501746	+	0.998740i	$0.484022\pi$
$402$	8.04984e8	+	1.39427e9i	0.618011	+	1.07043i
$403$	2.05690e7	+	1.30420e9i	0.0156547	+	0.992606i
$404$	−9.80726e8	+	1.69867e9i	−0.739968	+	1.28166i
$405$	3.79101e8	+	6.56622e8i	0.283571	+	0.491160i
$406$	−4.69725e9	−	1.39172e9i	−3.48340	−	1.03207i
$407$	1.30725e9	−	2.26422e9i	0.961118	−	1.66470i
$408$	−1.54244e9	+	2.67158e9i	−1.12434	+	1.94741i
$409$	−2.21748e9			−1.60261			−0.801304	−	0.598257i	$-0.795860\pi$
$409$	−2.21748e9			−1.60261			−0.801304	+	0.598257i	$0.795860\pi$
$410$	−1.29656e9			−0.929074
$411$	5.09474e8	−	8.82434e8i	0.361972	−	0.626955i
$412$	1.81319e8	−	3.14054e8i	0.127733	−	0.221240i
$413$	−8.30191e7	+	7.87719e7i	−0.0579899	+	0.0550233i
$414$	−5.56206e8	−	9.63377e8i	−0.385243	−	0.667260i
$415$	−3.43793e7	+	5.95466e7i	−0.0236117	+	0.0408967i
$416$	−2.82959e9	−	1.57470e9i	−1.92707	−	1.07244i
$417$	−4.74396e8	−	8.21679e8i	−0.320380	−	0.554914i
$418$	−8.33580e8			−0.558252
$419$	5.44489e8	+	9.43083e8i	0.361610	+	0.626327i	0.988226	−	0.153001i	$-0.0488939\pi$
$419$	5.44489e8	+	9.43083e8i	0.361610	+	0.626327i	−0.626616	+	0.779328i	$0.715561\pi$
$420$	1.92563e9	+	5.70534e8i	1.26824	+	0.375759i
$421$	−2.03709e9			−1.33053			−0.665263	−	0.746609i	$-0.731680\pi$
$421$	−2.03709e9			−1.33053			−0.665263	+	0.746609i	$0.731680\pi$
$422$	7.33949e8	+	1.27124e9i	0.475414	+	0.823441i
$423$	−9.10779e7			−0.0585089
$424$	9.98495e8	+	1.72944e9i	0.636158	+	1.10186i
$425$	4.45609e8	+	7.71817e8i	0.281574	+	0.487700i
$426$	9.52292e8	+	1.64942e9i	0.596811	+	1.03371i
$427$	2.00818e9	+	5.94991e8i	1.24826	+	0.369839i
$428$	6.45548e9			3.97993
$429$	−4.12933e7	−	2.61825e9i	−0.0252510	−	1.60107i
$430$	3.89577e8	+	6.74767e8i	0.236294	+	0.409274i
$431$	1.76453e8	−	3.05625e8i	0.106159	−	0.183873i	−0.808052	−	0.589111i	$-0.799478\pi$
$431$	1.76453e8	−	3.05625e8i	0.106159	−	0.183873i	0.914211	+	0.405238i	$0.132811\pi$
$432$	3.72217e9			2.22128
$433$	5.35551e8	−	9.27601e8i	0.317025	−	0.549103i	−0.662841	−	0.748760i	$-0.730650\pi$
$433$	5.35551e8	−	9.27601e8i	0.317025	−	0.549103i	0.979866	+	0.199657i	$0.0639829\pi$
$434$	−3.02273e9	−	8.95587e8i	−1.77495	−	0.525889i
$435$	−8.92915e8	+	1.54657e9i	−0.520113	+	0.900862i
$436$	−1.47745e9	−	2.55902e9i	−0.853708	−	1.47867i
$437$	−2.96622e8	−	5.13764e8i	−0.170027	−	0.294496i
$438$	5.06670e9			2.88115
$439$	−2.44254e9			−1.37790			−0.688948	−	0.724810i	$-0.741927\pi$
$439$	−2.44254e9			−1.37790			−0.688948	+	0.724810i	$0.741927\pi$
$440$	−1.67755e9	−	2.90560e9i	−0.938838	−	1.62612i
$441$	−4.08315e8	+	2.07980e8i	−0.226705	+	0.115475i
$442$	−2.15578e9	−	1.19972e9i	−1.18748	−	0.660847i
$443$	−9.93435e8	+	1.72068e9i	−0.542908	+	0.940345i	0.455827	+	0.890068i	$0.349344\pi$
$443$	−9.93435e8	+	1.72068e9i	−0.542908	+	0.940345i	−0.998735	+	0.0502764i	$0.983990\pi$
$444$	3.44023e9	−	5.95865e9i	1.86529	−	3.23078i
$445$	5.08776e8	−	8.81226e8i	0.273695	−	0.474053i
$446$	−3.33677e9	−	5.77946e9i	−1.78096	−	3.08472i
$447$	1.33426e9			0.706587
$448$	2.00530e9	−	1.90271e9i	1.05367	−	0.999769i
$449$	−9.77996e8	+	1.69394e9i	−0.509888	+	0.883152i	0.490046	+	0.871697i	$0.336980\pi$
$449$	−9.77996e8	+	1.69394e9i	−0.509888	+	0.883152i	−0.999934	+	0.0114559i	$0.996353\pi$
$450$	−3.54345e8	+	6.13743e8i	−0.183308	+	0.317499i
$451$	−2.91090e9			−1.49420
$452$	1.47732e9	−	2.55879e9i	0.752471	−	1.30332i
$453$	−1.74241e9			−0.880658
$454$	−2.77486e9			−1.39170
$455$	−2.57588e8	+	9.22566e8i	−0.128199	+	0.459153i
$456$	−1.30821e9			−0.646101
$457$	−2.65165e9			−1.29960			−0.649799	−	0.760106i	$-0.725147\pi$
$457$	−2.65165e9			−1.29960			−0.649799	+	0.760106i	$0.725147\pi$
$458$	1.49669e9	−	2.59234e9i	0.727950	−	1.26085i
$459$	1.26080e9			0.608559
$460$	2.00199e9	−	3.46754e9i	0.958979	−	1.66100i
$461$	1.36803e9	−	2.36949e9i	0.650342	−	1.12642i	−0.332698	−	0.943033i	$-0.607959\pi$
$461$	1.36803e9	−	2.36949e9i	0.650342	−	1.12642i	0.983040	−	0.183391i	$-0.0587076\pi$
$462$	6.06830e9	+	1.79794e9i	2.86299	+	0.848259i
$463$	5.42792e8			0.254156			0.127078	−	0.991893i	$-0.459440\pi$
$463$	5.42792e8			0.254156			0.127078	+	0.991893i	$0.459440\pi$
$464$	5.57594e9	+	9.65782e9i	2.59123	+	4.48814i
$465$	−5.74600e8	+	9.95237e8i	−0.265021	+	0.459030i
$466$	−1.27598e9	+	2.21006e9i	−0.584107	+	1.01170i
$467$	−3.64861e8	+	6.31958e8i	−0.165775	+	0.287130i	−0.936930	−	0.349517i	$-0.886346\pi$
$467$	−3.64861e8	+	6.31958e8i	−0.165775	+	0.287130i	0.771155	+	0.636647i	$0.219679\pi$
$468$	−2.20403e7	−	1.39749e9i	−0.00993933	−	0.630216i
$469$	−3.08568e8	−	1.28565e9i	−0.138117	−	0.575462i
$470$	−2.30074e8	−	3.98500e8i	−0.102218	−	0.177046i
$471$	−7.76446e8			−0.342404
$472$	5.03129e8			0.220233
$473$	8.74635e8	+	1.51491e9i	0.380026	+	0.658224i
$474$	2.00329e9	+	3.46980e9i	0.864011	+	1.49651i
$475$	−1.88970e8	+	3.27306e8i	−0.0809032	+	0.140128i
$476$	3.08172e9	−	2.92406e9i	1.30969	−	1.24269i
$477$	−1.39255e8	+	2.41197e8i	−0.0587486	+	0.101756i
$478$	3.86582e6			0.00161899
$479$	−1.31522e9	+	2.27802e9i	−0.546793	+	0.947074i	0.451698	+	0.892171i	$0.350818\pi$
$479$	−1.31522e9	+	2.27802e9i	−0.546793	+	0.947074i	−0.998492	+	0.0549032i	$0.982515\pi$
$480$	−1.42652e9	−	2.47080e9i	−0.588753	−	1.01975i
$481$	2.86737e9	+	1.59572e9i	1.17483	+	0.653808i
$482$	7.18840e9			2.92393
$483$	1.05122e9	+	4.37988e9i	0.424500	+	1.76867i
$484$	−3.22579e9	−	5.58723e9i	−1.29323	−	2.23995i
$485$	4.04401e8	+	7.00442e8i	0.160959	+	0.278789i
$486$	1.17364e9	+	2.03280e9i	0.463776	+	0.803283i
$487$	−7.14542e8			−0.280335			−0.140167	−	0.990128i	$-0.544764\pi$
$487$	−7.14542e8			−0.280335			−0.140167	+	0.990128i	$0.544764\pi$
$488$	−4.60399e9	−	7.97434e9i	−1.79335	−	3.10617i
$489$	1.55043e8			0.0599615
$490$	−1.94145e9	−	1.26115e9i	−0.745486	−	0.484261i
$491$	1.63017e9	+	2.82353e9i	0.621508	+	1.07648i	0.989205	+	0.146538i	$0.0468131\pi$
$491$	1.63017e9	+	2.82353e9i	0.621508	+	1.07648i	−0.367697	+	0.929946i	$0.619854\pi$
$492$	−7.66052e9			−2.89988
$493$	1.88873e9	+	3.27137e9i	0.709913	+	1.22961i
$494$	−1.64985e7	−	1.04611e9i	−0.00615744	−	0.390420i
$495$	2.33960e8	−	4.05230e8i	0.0867007	−	0.150170i
$496$	3.58818e9	+	6.21491e9i	1.32035	+	2.28691i
$497$	−3.65035e8	−	1.52091e9i	−0.133379	−	0.555722i
$498$	−2.85115e8	+	4.93834e8i	−0.103447	+	0.179175i
$499$	1.09535e9	−	1.89719e9i	0.394638	−	0.683533i	−0.598417	−	0.801185i	$-0.704203\pi$
$499$	1.09535e9	−	1.89719e9i	0.394638	−	0.683533i	0.993055	+	0.117652i	$0.0375366\pi$
$500$	−5.85183e9			−2.09362
$501$	−1.26726e8			−0.0450228
$502$	−5.04572e9	+	8.73944e9i	−1.78016	+	3.08334i
$503$	1.58209e9	−	2.74026e9i	0.554297	−	0.960071i	−0.443661	−	0.896195i	$-0.646320\pi$
$503$	1.58209e9	−	2.74026e9i	0.554297	−	0.960071i	0.997958	−	0.0638762i	$-0.0203463\pi$
$504$	1.93154e9	+	5.72286e8i	0.672044	+	0.199116i
$505$	−4.12096e8	−	7.13771e8i	−0.142390	−	0.246626i
$506$	6.30892e9	−	1.09274e10i	2.16485	−	3.74963i
$507$	3.28498e9	−	1.03643e8i	1.11945	−	0.0353192i
$508$	−3.92390e8	−	6.79639e8i	−0.132799	−	0.230015i
$509$	1.08622e9			0.365095			0.182548	−	0.983197i	$-0.441566\pi$
$509$	1.08622e9			0.365095			0.182548	+	0.983197i	$0.441566\pi$
$510$	−1.08682e9	−	1.88243e9i	−0.362796	−	0.628382i
$511$	−3.98951e9	−	1.18203e9i	−1.32266	−	0.391882i
$512$	4.43995e9			1.46195
$513$	2.67336e8	+	4.63039e8i	0.0874271	+	0.151428i
$514$	−1.59957e9			−0.519555
$515$	7.61893e7	+	1.31964e8i	0.0245793	+	0.0425725i
$516$	2.30174e9	+	3.98674e9i	0.737536	+	1.27745i
$517$	−5.16538e8	−	8.94669e8i	−0.164394	−	0.284738i
$518$	−5.75350e9	+	5.45916e9i	−1.81877	+	1.72572i
$519$	−6.19828e9			−1.94619
$520$	3.61320e9	−	2.16276e9i	1.12689	−	0.674524i
$521$	9.16255e8	+	1.58700e9i	0.283847	+	0.491638i	0.972329	−	0.233616i	$-0.0750559\pi$
$521$	9.16255e8	+	1.58700e9i	0.283847	+	0.491638i	−0.688482	+	0.725254i	$0.741723\pi$
$522$	−1.50190e9	+	2.60137e9i	−0.462163	+	0.800489i
$523$	−2.50985e9			−0.767169			−0.383585	−	0.923506i	$-0.625311\pi$
$523$	−2.50985e9			−0.767169			−0.383585	+	0.923506i	$0.625311\pi$
$524$	−5.42568e9	+	9.39755e9i	−1.64738	+	2.85335i
$525$	2.08163e9	−	1.97514e9i	0.627835	−	0.595716i
$526$	1.05313e9	−	1.82407e9i	0.315524	−	0.546503i
$527$	1.21542e9	+	2.10516e9i	0.361733	+	0.626540i
$528$	−7.20346e9	−	1.24768e10i	−2.12972	−	3.68878i
$529$	5.57506e9			1.63740
$530$	−1.40711e9			−0.410545
$531$	3.50845e7	+	6.07681e7i	0.0101691	+	0.0176135i
$532$	1.72732e9	+	5.11777e8i	0.497372	+	0.147363i
$533$	−5.76136e7	−	3.65306e9i	−0.0164809	−	1.04499i
$534$	4.21940e9	−	7.30821e9i	1.19910	−	2.07690i
$535$	−1.35628e9	+	2.34914e9i	−0.382922	+	0.663241i
$536$	−2.90632e9	+	5.03390e9i	−0.815205	+	1.41198i
$537$	3.59664e9	+	6.22957e9i	1.00228	+	1.73599i
$538$	−4.80814e9			−1.33119
$539$	−4.35872e9	−	2.83139e9i	−1.19894	−	0.778824i
$540$	−1.80433e9	+	3.12518e9i	−0.493102	+	0.854078i
$541$	9.30782e8	−	1.61216e9i	0.252730	−	0.437742i	−0.711546	−	0.702639i	$-0.752005\pi$
$541$	9.30782e8	−	1.61216e9i	0.252730	−	0.437742i	0.964277	+	0.264897i	$0.0853381\pi$
$542$	3.33388e9			0.899398
$543$	−2.63024e9	+	4.55570e9i	−0.705010	+	1.22111i
$544$	−6.03486e9			−1.60720
$545$	1.24163e9			0.328553
$546$	−2.13623e9	+	7.65105e9i	−0.561661	+	2.01162i
$547$	−5.07018e9			−1.32455			−0.662274	−	0.749261i	$-0.730409\pi$
$547$	−5.07018e9			−1.32455			−0.662274	+	0.749261i	$0.730409\pi$
$548$	6.16891e9			1.60131
$549$	6.42096e8	−	1.11214e9i	0.165614	−	0.286852i
$550$	−8.03849e9			−2.06018
$551$	−8.00957e8	+	1.38730e9i	−0.203976	+	0.353296i
$552$	9.90113e9	−	1.71493e10i	2.50552	−	4.33969i
$553$	−7.67905e8	−	3.19947e9i	−0.193094	−	0.804526i
$554$	−3.50751e9			−0.876424
$555$	1.44557e9	+	2.50379e9i	0.358932	+	0.621689i
$556$	2.87209e9	−	4.97461e9i	0.708658	−	1.22743i
$557$	−3.40958e9	+	5.90556e9i	−0.836002	+	1.44800i	0.0572103	+	0.998362i	$0.481779\pi$
$557$	−3.40958e9	+	5.90556e9i	−0.836002	+	1.44800i	−0.893212	+	0.449636i	$0.851554\pi$
$558$	−9.66490e8	+	1.67401e9i	−0.235493	+	0.407886i
$559$	−1.88384e9	+	1.12761e9i	−0.456145	+	0.273036i
$560$	1.22991e9	+	5.12439e9i	0.295947	+	1.23306i
$561$	−2.44001e9	−	4.22623e9i	−0.583475	−	1.01061i
$562$	1.53994e10			3.65954
$563$	6.72369e9			1.58792			0.793960	−	0.607970i	$-0.208016\pi$
$563$	6.72369e9			1.58792			0.793960	+	0.607970i	$0.208016\pi$
$564$	−1.35935e9	−	2.35447e9i	−0.319047	−	0.552606i
$565$	6.20762e8	+	1.07519e9i	0.144796	+	0.250793i
$566$	1.09428e9	−	1.89534e9i	0.253670	−	0.439370i
$567$	−1.20515e9	−	5.02126e9i	−0.277653	−	1.15684i
$568$	−3.43817e9	+	5.95508e9i	−0.787241	+	1.36354i
$569$	−2.74269e9			−0.624143			−0.312071	−	0.950059i	$-0.601023\pi$
$569$	−2.74269e9			−0.624143			−0.312071	+	0.950059i	$0.601023\pi$
$570$	4.60891e8	−	7.98286e8i	0.104240	−	0.180550i
$571$	−2.44398e9	−	4.23310e9i	−0.549378	−	0.951551i	−0.998317	−	0.0579883i	$-0.981531\pi$
$571$	−2.44398e9	−	4.23310e9i	−0.549378	−	0.951551i	0.448939	−	0.893562i	$-0.351802\pi$
$572$	1.36028e10	−	8.14223e9i	3.03907	−	1.81910i
$573$	2.56881e9			0.570415
$574$	8.46667e9	+	2.50854e9i	1.86862	+	0.553642i
$575$	−2.86043e9	−	4.95440e9i	−0.627470	−	1.08681i
$576$	−8.47454e8	−	1.46783e9i	−0.184773	−	0.320036i
$577$	−1.13145e9	−	1.95972e9i	−0.245199	−	0.424697i	0.716989	−	0.697085i	$-0.245520\pi$
$577$	−1.13145e9	−	1.95972e9i	−0.245199	−	0.424697i	−0.962187	+	0.272388i	$0.912187\pi$
$578$	4.05935e9			0.874397
$579$	−1.15023e9	−	1.99226e9i	−0.246269	−	0.426550i
$580$	−1.08118e10			−2.30091
$581$	3.39708e8	−	3.22329e8i	0.0718602	−	0.0681840i
$582$	3.35379e9	+	5.80893e9i	0.705188	+	1.22142i
$583$	−3.15908e9			−0.660269
$584$	9.14643e9	+	1.58421e10i	1.90023	+	3.29130i
$585$	5.13178e8	+	2.85589e8i	0.105980	+	0.0589789i
$586$	3.23569e8	−	5.60438e8i	0.0664240	−	0.115050i
$587$	−2.85176e9	−	4.93940e9i	−0.581942	−	1.00795i	−0.995249	−	0.0973620i	$-0.968960\pi$
$587$	−2.85176e9	−	4.93940e9i	−0.581942	−	1.00795i	0.413307	−	0.910592i	$-0.364374\pi$
$588$	−1.14707e10	−	7.45127e9i	−2.32685	−	1.51150i
$589$	−5.15424e8	+	8.92741e8i	−0.103935	+	0.180020i
$590$	−1.77256e8	+	3.07016e8i	−0.0355319	+	0.0615430i
$591$	−5.28962e9			−1.05407
$592$	1.80541e10			3.57643
$593$	3.21616e9	−	5.57055e9i	0.633353	−	1.09700i	−0.353509	−	0.935431i	$-0.615012\pi$
$593$	3.21616e9	−	5.57055e9i	0.633353	−	1.09700i	0.986862	−	0.161568i	$-0.0516551\pi$
$594$	−5.68602e9	+	9.84848e9i	−1.11316	+	1.92804i
$595$	4.16603e8	+	1.73577e9i	0.0810799	+	0.337819i
$596$	4.03895e9	+	6.99567e9i	0.781460	+	1.35353i
$597$	4.20099e9	−	7.27633e9i	0.808056	−	1.39959i
$598$	1.38383e10	+	7.70115e9i	2.64623	+	1.47266i
$599$	3.69607e9	+	6.40178e9i	0.702662	+	1.21705i	0.967529	+	0.252761i	$0.0813388\pi$
$599$	3.69607e9	+	6.40178e9i	0.702662	+	1.21705i	−0.264867	+	0.964285i	$0.585328\pi$
$600$	−1.26155e10			−2.38438
$601$	6.79928e8	+	1.17767e9i	0.127762	+	0.221291i	0.922809	−	0.385257i	$-0.125887\pi$
$601$	6.79928e8	+	1.17767e9i	0.127762	+	0.221291i	−0.795047	+	0.606548i	$0.792554\pi$
$602$	−1.23846e9	−	5.16002e9i	−0.231363	−	0.963970i
$603$	−8.10662e8			−0.150567
$604$	−5.27446e9	−	9.13563e9i	−0.973977	−	1.68698i
$605$	2.71092e9			0.497705
$606$	−3.41760e9	−	5.91946e9i	−0.623832	−	1.08051i
$607$	2.75555e9	+	4.77275e9i	0.500089	+	0.866180i	1.00000		0.000102999i	$3.27858e-5\pi$
$607$	2.75555e9	+	4.77275e9i	0.500089	+	0.866180i	−0.499911	+	0.866077i	$0.666634\pi$
$608$	−1.27961e9	−	2.21634e9i	−0.230895	−	0.399921i
$609$	8.82305e9	−	8.37168e9i	1.58292	−	1.50194i
$610$	6.48806e9			1.15734
$611$	1.11255e9	−	6.65941e8i	0.197322	−	0.118111i
$612$	−1.30236e9	−	2.25575e9i	−0.229668	−	0.397797i
$613$	2.73436e9	−	4.73605e9i	0.479450	−	0.830432i	−0.520272	−	0.854001i	$-0.674169\pi$
$613$	2.73436e9	−	4.73605e9i	0.479450	−	0.830432i	0.999722	+	0.0235685i	$0.00750277\pi$
$614$	−1.43242e10			−2.49737
$615$	1.60945e9	−	2.78766e9i	0.279007	−	0.483255i
$616$	5.33289e9	+	2.22194e10i	0.919243	+	3.83002i
$617$	−7.28714e8	+	1.26217e9i	−0.124899	+	0.216332i	−0.921693	−	0.387919i	$-0.873194\pi$
$617$	−7.28714e8	+	1.26217e9i	−0.124899	+	0.216332i	0.796794	+	0.604250i	$0.206527\pi$
$618$	6.31855e8	+	1.09441e9i	0.107686	+	0.186517i
$619$	2.21886e9	+	3.84317e9i	0.376021	+	0.651288i	0.990479	−	0.137662i	$-0.0439587\pi$
$619$	2.21886e9	+	3.84317e9i	0.376021	+	0.651288i	−0.614458	+	0.788949i	$0.710625\pi$
$620$	−6.95749e9			−1.17242
$621$	−8.09328e9			−1.35614
$622$	1.57468e9	+	2.72743e9i	0.262377	+	0.454451i
$623$	−5.02731e9	+	4.77012e9i	−0.832966	+	0.790353i
$624$	1.55152e10	−	9.28699e9i	2.55631	−	1.53013i
$625$	−1.12877e9	+	1.95509e9i	−0.184938	+	0.320322i
$626$	−5.94583e8	+	1.02985e9i	−0.0968729	+	0.167789i
$627$	1.03474e9	−	1.79223e9i	0.167647	−	0.290373i
$628$	−2.35038e9	−	4.07098e9i	−0.378686	−	0.655904i
$629$	6.11543e9			0.979828
$630$	−1.02971e9	+	9.77034e8i	−0.164068	+	0.155675i
$631$	−2.43513e9	+	4.21777e9i	−0.385850	+	0.668313i	−0.991887	−	0.127124i	$-0.959425\pi$
$631$	−2.43513e9	+	4.21777e9i	−0.385850	+	0.668313i	0.606036	+	0.795437i	$0.292759\pi$
$632$	−7.23269e9	+	1.25274e10i	−1.13970	+	1.97402i
$633$	−3.64427e9			−0.571081
$634$	8.06120e9	−	1.39624e10i	1.25628	−	2.17594i
$635$	3.29760e8			0.0511082
$636$	−8.31363e9			−1.28142
$637$	3.46701e9	−	5.52606e9i	0.531456	−	0.847086i
$638$	−3.40714e10			−5.19419
$639$	−9.59009e8			−0.145402
$640$	7.95436e8	−	1.37774e9i	0.119943	−	0.207748i
$641$	−5.08797e8			−0.0763030			−0.0381515	−	0.999272i	$-0.512147\pi$
$641$	−5.08797e8			−0.0763030			−0.0381515	+	0.999272i	$0.512147\pi$
$642$	−1.12479e10	+	1.94820e10i	−1.67764	+	2.90577i
$643$	−1.13441e9	+	1.96486e9i	−0.168280	+	0.291469i	−0.937815	−	0.347135i	$-0.887155\pi$
$643$	−1.13441e9	+	1.96486e9i	−0.168280	+	0.291469i	0.769535	+	0.638604i	$0.220488\pi$
$644$	−1.97820e10	+	1.87700e10i	−2.91857	+	2.76926i
$645$	−1.93436e9			−0.283843
$646$	−9.74894e8	−	1.68857e9i	−0.142280	−	0.246436i
$647$	3.16605e9	−	5.48375e9i	0.459571	−	0.796000i	−0.539367	−	0.842071i	$-0.681337\pi$
$647$	3.16605e9	−	5.48375e9i	0.459571	−	0.796000i	0.998938	+	0.0460706i	$0.0146699\pi$
$648$	−1.13510e10	+	1.96605e10i	−1.63879	+	2.83846i
$649$	−3.97955e8	+	6.89278e8i	−0.0571449	+	0.0989779i
$650$	−1.59101e8	−	1.00880e10i	−0.0227235	−	1.44081i
$651$	5.67773e9	−	5.38727e9i	0.806569	−	0.765306i
$652$	4.69332e8	+	8.12907e8i	0.0663153	+	0.114861i
$653$	1.14449e10			1.60848			0.804239	−	0.594306i	$-0.202573\pi$
$653$	1.14449e10			1.60848			0.804239	+	0.594306i	$0.202573\pi$
$654$	1.02971e10			1.43944
$655$	−2.27984e9	−	3.94880e9i	−0.317001	−	0.549061i
$656$	−1.00505e10	−	1.74079e10i	−1.39003	−	2.40760i
$657$	−1.27561e9	+	2.20942e9i	−0.175484	+	0.303948i
$658$	7.31402e8	+	3.04738e9i	0.100084	+	0.416999i
$659$	−2.79659e9	+	4.84384e9i	−0.380654	+	0.659311i	−0.991156	−	0.132703i	$-0.957634\pi$
$659$	−2.79659e9	+	4.84384e9i	−0.380654	+	0.659311i	0.610502	+	0.792015i	$0.290968\pi$
$660$	1.39675e10			1.89111
$661$	7.02276e9	−	1.21638e10i	0.945808	−	1.63819i	0.191682	−	0.981457i	$-0.438606\pi$
$661$	7.02276e9	−	1.21638e10i	0.945808	−	1.63819i	0.754126	−	0.656730i	$-0.228061\pi$
$662$	−6.96180e9	−	1.20582e10i	−0.932650	−	1.61540i
$663$	5.25545e9	−	3.14576e9i	0.700346	−	0.419207i
$664$	−2.05876e9			−0.272909
$665$	−5.49140e8	+	5.21047e8i	−0.0724115	+	0.0687070i
$666$	2.43147e9	+	4.21143e9i	0.318940	+	0.552421i
$667$	−1.21240e10	−	2.09994e10i	−1.58200	−	2.74010i
$668$	−3.83612e8	−	6.64435e8i	−0.0497937	−	0.0862452i
$669$	1.65681e10			2.13934
$670$	−2.04783e9	−	3.54695e9i	−0.263047	−	0.455610i
$671$	1.45663e10			1.86132
$672$	4.53488e9	+	1.88945e10i	0.576465	+	2.40184i
$673$	1.31001e9	+	2.26901e9i	0.165662	+	0.286935i	0.936890	−	0.349624i	$-0.113691\pi$
$673$	1.31001e9	+	2.26901e9i	0.165662	+	0.286935i	−0.771228	+	0.636559i	$0.780357\pi$
$674$	2.21944e10			2.79211
$675$	2.57801e9	+	4.46524e9i	0.322642	+	0.558833i
$676$	1.04874e10	+	1.69097e10i	1.30573	+	2.10535i
$677$	3.61094e9	−	6.25434e9i	0.447260	−	0.774678i	−0.550946	−	0.834541i	$-0.685733\pi$
$677$	3.61094e9	−	6.25434e9i	0.447260	−	0.774678i	0.998207	+	0.0598631i	$0.0190664\pi$
$678$	5.14812e9	+	8.91680e9i	0.634373	+	1.09877i
$679$	−1.28558e9	−	5.35636e9i	−0.157600	−	0.656637i
$680$	3.92387e9	−	6.79635e9i	0.478557	−	0.828885i
$681$	3.44450e9	−	5.96605e9i	0.417938	−	0.723889i
$682$	−2.19253e10			−2.64668
$683$	7.59933e9			0.912647			0.456323	−	0.889814i	$-0.349166\pi$
$683$	7.59933e9			0.912647			0.456323	+	0.889814i	$0.349166\pi$
$684$	5.52294e8	−	9.56601e8i	0.0659893	−	0.114297i
$685$	−1.29607e9	+	2.24486e9i	−0.154068	+	0.266854i
$686$	1.02378e10	+	1.19916e10i	1.21080	+	1.41822i
$687$	3.71574e9	+	6.43585e9i	0.437217	+	0.757282i
$688$	−6.03971e9	+	1.04611e10i	−0.707060	+	1.22466i
$689$	−6.25256e7	−	3.96451e9i	−0.00728267	−	0.461767i
$690$	6.97647e9	+	1.20836e10i	0.808470	+	1.40031i
$691$	−3.91978e9			−0.451948			−0.225974	−	0.974133i	$-0.572556\pi$
$691$	−3.91978e9			−0.451948			−0.225974	+	0.974133i	$0.572556\pi$
$692$	−1.87628e10	−	3.24982e10i	−2.15242	−	3.72810i
$693$	−2.31180e9	+	2.19353e9i	−0.263866	+	0.250367i
$694$	1.35338e10			1.53696
$695$	1.20684e9	+	2.09030e9i	0.136365	+	0.236191i
$696$	−5.34713e10			−6.01157
$697$	−3.40438e9	−	5.89656e9i	−0.380823	−	0.659605i
$698$	−1.16993e10	−	2.02639e10i	−1.30217	−	2.25542i
$699$	−3.16780e9	−	5.48679e9i	−0.350823	−	0.607643i
$700$	1.66571e10	+	4.93524e9i	1.83551	+	0.543832i
$701$	−8.07267e9			−0.885124			−0.442562	−	0.896738i	$-0.645930\pi$
$701$	−8.07267e9			−0.885124			−0.442562	+	0.896738i	$0.645930\pi$
$702$	−1.24720e10	−	6.94080e9i	−1.36068	−	0.757233i
$703$	1.29669e9	+	2.24594e9i	0.140764	+	0.243811i
$704$	9.61247e9	−	1.66493e10i	1.03832	−	1.79842i
$705$	1.14239e9			0.122787
$706$	−1.43113e10	+	2.47879e10i	−1.53060	+	2.65108i
$707$	1.31004e9	+	5.45829e9i	0.139418	+	0.580882i
$708$	−1.04728e9	+	1.81395e9i	−0.110904	+	0.192092i
$709$	5.13897e9	+	8.90095e9i	0.541519	+	0.937939i	0.998817	+	0.0486254i	$0.0154840\pi$
$709$	5.13897e9	+	8.90095e9i	0.541519	+	0.937939i	−0.457298	+	0.889314i	$0.651183\pi$
$710$	−2.42258e9	−	4.19603e9i	−0.254023	−	0.439981i
$711$	−2.01742e9			−0.210500
$712$	3.04675e10			3.16342
$713$	−7.80193e9	−	1.35133e10i	−0.806100	−	1.39621i
$714$	3.45499e9	+	1.43952e10i	0.355224	+	1.48004i
$715$	1.05048e8	+	6.66069e9i	0.0107477	+	0.681472i
$716$	−2.17748e10	+	3.77151e10i	−2.21696	+	3.83989i
$717$	−4.79873e6	+	8.31165e6i	−0.000486194	+	0.000842113i
$718$	−2.86633e9	+	4.96463e9i	−0.288995	+	0.500555i
$719$	6.23904e9	+	1.08063e10i	0.625988	+	1.08424i	0.988349	+	0.152206i	$0.0486376\pi$
$719$	6.23904e9	+	1.08063e10i	0.625988	+	1.08424i	−0.362360	+	0.932038i	$0.618029\pi$
$720$	3.23117e9			0.322624
$721$	−2.42204e8	−	1.00914e9i	−0.0240662	−	0.100272i
$722$	−9.01581e9	+	1.56158e10i	−0.891506	+	1.54413i
$723$	−8.92312e9	+	1.54553e10i	−0.878077	+	1.52087i
$724$	−3.18480e10			−3.11887
$725$	−7.72390e9	+	1.33782e10i	−0.752755	+	1.30381i
$726$	2.24822e10			2.18053
$727$	2.87252e9			0.277264			0.138632	−	0.990344i	$-0.455730\pi$
$727$	2.87252e9			0.277264			0.138632	+	0.990344i	$0.455730\pi$
$728$	−2.77789e10	+	7.13234e9i	−2.66843	+	0.685128i
$729$	6.61712e9			0.632590
$730$	−1.28894e10			−1.22632
$731$	−2.04582e9	+	3.54346e9i	−0.193712	+	0.335519i
$732$	3.83336e10			3.61235
$733$	−2.40172e9	+	4.15991e9i	−0.225247	+	0.390140i	−0.956394	−	0.292081i	$-0.905652\pi$
$733$	−2.40172e9	+	4.15991e9i	−0.225247	+	0.390140i	0.731146	+	0.682221i	$0.238986\pi$
$734$	9.88199e9	−	1.71161e10i	0.922376	−	1.59760i
$735$	5.12147e9	−	2.60869e9i	0.475761	−	0.242335i
$736$	3.87386e10			3.58155
$737$	−4.59757e9	−	7.96323e9i	−0.423051	−	0.732745i
$738$	2.70714e9	−	4.68890e9i	0.247921	−	0.429411i
$739$	−3.02405e9	+	5.23781e9i	−0.275635	+	0.477413i	−0.970295	−	0.241925i	$-0.922221\pi$
$739$	−3.02405e9	+	5.23781e9i	−0.275635	+	0.477413i	0.694660	+	0.719338i	$0.255555\pi$
$740$	−8.75175e9	+	1.51585e10i	−0.793933	+	1.37513i
$741$	2.26965e9	+	1.26309e9i	0.204925	+	0.114043i
$742$	9.18851e9	+	2.72241e9i	0.825718	+	0.244647i
$743$	−4.75591e9	−	8.23748e9i	−0.425376	−	0.736772i	0.571080	−	0.820895i	$-0.306525\pi$
$743$	−4.75591e9	−	8.23748e9i	−0.425376	−	0.736772i	−0.996455	+	0.0841222i	$0.973191\pi$
$744$	−3.44093e10			−3.06317
$745$	−3.39429e9			−0.300748
$746$	5.64401e9	+	9.77571e9i	0.497739	+	0.862109i
$747$	−1.43563e8	−	2.48658e8i	−0.0126014	−	0.0218263i
$748$	1.47723e10	−	2.55864e10i	1.29061	−	2.23540i
$749$	1.34016e10	−	1.27160e10i	1.16539	−	1.10577i
$750$	1.01961e10	−	1.76602e10i	0.882514	−	1.52856i
$751$	−1.24048e9			−0.106869			−0.0534343	−	0.998571i	$-0.517017\pi$
$751$	−1.24048e9			−0.106869			−0.0534343	+	0.998571i	$0.517017\pi$
$752$	3.56690e9	−	6.17805e9i	0.305864	−	0.529772i
$753$	−1.25267e10	−	2.16969e10i	−1.06919	−	1.85189i
$754$	−6.74354e8	−	4.27583e10i	−0.0572912	−	3.63262i
$755$	4.43260e9			0.374839
$756$	1.78289e10	−	1.69168e10i	1.50071	−	1.42394i
$757$	−3.72354e9	−	6.44936e9i	−0.311975	−	0.540357i	0.666815	−	0.745224i	$-0.267657\pi$
$757$	−3.72354e9	−	6.44936e9i	−0.311975	−	0.540357i	−0.978790	+	0.204867i	$0.934324\pi$
$758$	1.30473e10	+	2.25986e10i	1.08812	+	1.88469i
$759$	1.56628e10	+	2.71288e10i	1.30024	+	2.25208i
$760$	3.32801e9			0.275003
$761$	−5.82259e9	−	1.00850e10i	−0.478927	−	0.829526i	0.520781	−	0.853690i	$-0.325641\pi$
$761$	−5.82259e9	−	1.00850e10i	−0.478927	−	0.829526i	−0.999708	+	0.0241641i	$0.992308\pi$
$762$	2.73478e9			0.223913
$763$	−8.10795e9	−	2.40226e9i	−0.660808	−	0.195787i
$764$	7.77604e9	+	1.34685e10i	0.630858	+	1.09268i
$765$	1.09449e9			0.0883885
$766$	−1.72955e10	−	2.99567e10i	−1.39038	−	2.40821i
$767$	−8.72892e8	−	4.85775e8i	−0.0698517	−	0.0388733i
$768$	−3.61437e9	+	6.26027e9i	−0.287918	+	0.498688i
$769$	1.18221e10	+	2.04764e10i	0.937456	+	1.62372i	0.770195	+	0.637808i	$0.220159\pi$
$769$	1.18221e10	+	2.04764e10i	0.937456	+	1.62372i	0.167261	+	0.985913i	$0.446508\pi$
$770$	−1.54374e10	−	4.57386e9i	−1.21859	−	0.361048i
$771$	1.98558e9	−	3.43912e9i	0.156026	−	0.270245i
$772$	6.96372e9	−	1.20615e10i	0.544730	−	0.943499i
$773$	1.19881e10			0.933519			0.466759	−	0.884384i	$-0.345421\pi$
$773$	1.19881e10			0.933519			0.466759	+	0.884384i	$0.345421\pi$
$774$	−3.25364e9			−0.252218
$775$	−4.97041e9	+	8.60900e9i	−0.383563	+	0.664350i
$776$	−1.21085e10	+	2.09726e10i	−0.930199	+	1.61115i
$777$	−4.59543e9	−	1.91468e10i	−0.351441	−	1.46427i
$778$	7.85700e9	+	1.36087e10i	0.598175	+	1.03607i
$779$	1.44370e9	−	2.50056e9i	0.109420	−	0.189521i
$780$	2.76451e8	+	1.75287e10i	0.0208587	+	1.32257i
$781$	−5.43891e9	−	9.42046e9i	−0.408538	−	0.707609i
$782$	2.95138e10			2.20699
$783$	1.09270e10	+	1.89261e10i	0.813456	+	1.40895i
$784$	1.88307e9	−	3.58422e10i	0.139560	−	2.65637i
$785$	1.97524e9			0.145739
$786$	−1.89072e10	−	3.27483e10i	−1.38883	−	2.40553i
$787$	2.09485e10			1.53194			0.765969	−	0.642877i	$-0.222259\pi$
$787$	2.09485e10			1.53194			0.765969	+	0.642877i	$0.222259\pi$
$788$	−1.60122e10	−	2.77340e10i	−1.16576	−	2.01916i
$789$	2.61455e9	+	4.52853e9i	0.189508	+	0.328237i
$790$	−5.09625e9	−	8.82697e9i	−0.367753	−	0.636967i
$791$	−1.97339e9	−	8.22211e9i	−0.141774	−	0.590698i
$792$	1.40104e10			1.00210
$793$	2.88301e8	+	1.82801e10i	0.0205301	+	1.30173i
$794$	−1.39301e10	−	2.41277e10i	−0.987605	−	1.71058i
$795$	1.74667e9	−	3.02532e9i	0.123290	−	0.213544i
$796$	5.08673e10			3.57473
$797$	−1.20420e10	+	2.08574e10i	−0.842549	+	1.45934i	0.0451839	+	0.998979i	$0.485613\pi$
$797$	−1.20420e10	+	2.08574e10i	−0.842549	+	1.45934i	−0.887733	+	0.460359i	$0.847721\pi$
$798$	−4.55415e9	+	4.32116e9i	−0.317246	+	0.301017i
$799$	1.20821e9	−	2.09268e9i	0.0837969	−	0.145141i
$800$	−1.23397e10	−	2.13730e10i	−0.852097	−	1.47588i
$801$	2.12458e9	+	3.67988e9i	0.146069	+	0.252999i
$802$	−2.73370e9			−0.187129
$803$	−2.89379e10			−1.97225
$804$	−1.20993e10	−	2.09565e10i	−0.821037	−	1.42208i
$805$	−2.67424e9	−	1.11422e10i	−0.180682	−	0.752808i
$806$	−4.33954e8	−	2.75154e10i	−0.0291925	−	1.85099i
$807$	5.96845e9	−	1.03377e10i	0.399765	−	0.692412i
$808$	1.23390e10	−	2.13717e10i	0.822884	−	1.42528i
$809$	−4.90976e9	+	8.50395e9i	−0.326017	+	0.564678i	−0.981718	−	0.190343i	$-0.939040\pi$
$809$	−4.90976e9	+	8.50395e9i	−0.326017	+	0.564678i	0.655701	+	0.755021i	$0.272373\pi$
$810$	−7.99808e9	−	1.38531e10i	−0.528796	−	0.915902i
$811$	−2.82294e8			−0.0185836			−0.00929179	−	0.999957i	$-0.502958\pi$
$811$	−2.82294e8			−0.0185836			−0.00929179	+	0.999957i	$0.502958\pi$
$812$	7.06018e10	+	2.09182e10i	4.62775	+	1.37113i
$813$	−4.13842e9	+	7.16795e9i	−0.270095	+	0.467819i
$814$	−2.75796e10	+	4.77693e10i	−1.79227	+	3.10430i
$815$	−3.94422e8			−0.0255217
$816$	1.68493e10	−	2.91838e10i	1.08559	−	1.88030i
$817$	−1.73515e9			−0.111316
$818$	4.67832e10			2.98850
$819$	−2.79854e9	−	2.85779e9i	−0.178008	−	0.181776i
$820$	1.94879e10			1.23429
$821$	−1.04984e10			−0.662099			−0.331050	−	0.943613i	$-0.607403\pi$
$821$	−1.04984e10			−0.662099			−0.331050	+	0.943613i	$0.607403\pi$
$822$	−1.07486e10	+	1.86172e10i	−0.674997	+	1.16913i
$823$	4.18424e9			0.261648			0.130824	−	0.991406i	$-0.458238\pi$
$823$	4.18424e9			0.261648			0.130824	+	0.991406i	$0.458238\pi$
$824$	−2.28126e9	+	3.95125e9i	−0.142046	+	0.246031i
$825$	9.97837e9	−	1.72830e10i	0.618686	−	1.07160i
$826$	1.75150e9	−	1.66189e9i	0.108138	−	0.102606i
$827$	−4.01543e9			−0.246867			−0.123433	−	0.992353i	$-0.539391\pi$
$827$	−4.01543e9			−0.246867			−0.123433	+	0.992353i	$0.539391\pi$
$828$	8.36002e9	+	1.44800e10i	0.511801	+	0.886466i
$829$	6.64809e9	−	1.15148e10i	0.405281	−	0.701967i	−0.589073	−	0.808080i	$-0.700507\pi$
$829$	6.64809e9	−	1.15148e10i	0.405281	−	0.701967i	0.994354	+	0.106113i	$0.0338404\pi$
$830$	7.25316e8	−	1.25628e9i	0.0440306	−	0.0762632i
$831$	4.35395e9	−	7.54126e9i	0.263196	−	0.455869i
$832$	2.10844e10	+	1.17337e10i	1.26920	+	0.706325i
$833$	6.37848e8	−	1.21408e10i	0.0382349	−	0.727761i
$834$	1.00086e10	+	1.73354e10i	0.597436	+	1.03479i
$835$	3.22383e8			0.0191633
$836$	1.25291e10			0.741647
$837$	7.03163e9	+	1.21791e10i	0.414493	+	0.717922i
$838$	−1.14874e10	−	1.98967e10i	−0.674320	−	1.16796i
$839$	2.72958e9	−	4.72777e9i	0.159562	−	0.276369i	−0.775149	−	0.631778i	$-0.782325\pi$
$839$	2.72958e9	−	4.72777e9i	0.159562	−	0.276369i	0.934711	+	0.355410i	$0.115659\pi$
$840$	−2.42273e10	−	7.17815e9i	−1.41035	−	0.417864i
$841$	−2.41131e10	+	4.17651e10i	−1.39787	+	2.42118i
$842$	4.29775e10			2.48113
$843$	−1.91156e10	+	3.31093e10i	−1.09899	+	1.90350i
$844$	−1.10316e10	−	1.91072e10i	−0.631595	−	1.09395i
$845$	−8.35681e9	+	2.63661e8i	−0.476477	+	0.0150331i
$846$	1.92152e9			0.109106
$847$	−1.77025e10	−	5.24497e9i	−1.00102	−	0.296586i
$848$	−1.09074e10	−	1.88921e10i	−0.614234	−	1.06388i
$849$	2.71670e9	+	4.70546e9i	0.152358	+	0.263892i
$850$	−9.40123e9	−	1.62834e10i	−0.525072	−	0.909451i
$851$	−3.92558e10			−2.18349
$852$	−1.43134e10	−	2.47915e10i	−0.792872	−	1.37330i
$853$	−3.21221e10			−1.77208			−0.886038	−	0.463613i	$-0.846553\pi$
$853$	−3.21221e10			−1.77208			−0.886038	+	0.463613i	$0.846553\pi$
$854$	−4.23676e10	−	1.25528e10i	−2.32772	−	0.689667i
$855$	2.32071e8	+	4.01959e8i	0.0126981	+	0.0219938i
$856$	−8.12193e10			−4.42589
$857$	1.35543e10	+	2.34768e10i	0.735606	+	1.27411i	0.954457	+	0.298348i	$0.0964357\pi$
$857$	1.35543e10	+	2.34768e10i	0.735606	+	1.27411i	−0.218851	+	0.975758i	$0.570231\pi$
$858$	8.71186e8	+	5.52386e10i	0.0470875	+	2.98564i
$859$	−2.12494e9	+	3.68051e9i	−0.114386	+	0.198122i	−0.917534	−	0.397657i	$-0.869823\pi$
$859$	−2.12494e9	+	3.68051e9i	−0.114386	+	0.198122i	0.803148	+	0.595779i	$0.203157\pi$
$860$	−5.85551e9	−	1.01420e10i	−0.313921	−	0.543727i
$861$	−1.59033e10	+	1.50897e10i	−0.849134	+	0.805694i
$862$	−3.72272e9	+	6.44793e9i	−0.197963	+	0.342882i
$863$	2.49992e9	−	4.32998e9i	0.132400	−	0.229323i	−0.792201	−	0.610260i	$-0.791065\pi$
$863$	2.49992e9	−	4.32998e9i	0.132400	−	0.229323i	0.924601	+	0.380936i	$0.124398\pi$
$864$	−3.49138e10			−1.84162
$865$	1.57681e10			0.828366
$866$	−1.12988e10	+	1.95701e10i	−0.591179	+	1.02395i
$867$	−5.03896e9	+	8.72774e9i	−0.262588	+	0.454815i
$868$	4.54330e10	+	1.34611e10i	2.35805	+	0.698651i
$869$	−1.14416e10	−	1.98173e10i	−0.591447	−	1.02442i
$870$	1.88383e10	−	3.26289e10i	0.969893	−	1.67990i
$871$	9.90253e9	−	5.92737e9i	0.507788	−	0.303948i
$872$	1.85884e10	+	3.21961e10i	0.949370	+	1.64436i
$873$	−3.37744e9			−0.171806
$874$	6.25798e9	+	1.08391e10i	0.317062	+	0.549168i
$875$	−1.21485e10	+	1.15270e10i	−0.613046	+	0.581683i
$876$	−7.61547e10			−3.82765
$877$	−6.74664e9	−	1.16855e10i	−0.337745	−	0.584991i	0.646263	−	0.763114i	$-0.276331\pi$
$877$	−6.74664e9	−	1.16855e10i	−0.337745	−	0.584991i	−0.984008	+	0.178123i	$0.942997\pi$
$878$	5.15316e10			2.56947
$879$	8.03307e8	+	1.39137e9i	0.0398952	+	0.0691005i
$880$	1.83252e10	+	3.17402e10i	0.906483	+	1.57007i
$881$	4.50855e9	+	7.80904e9i	0.222137	+	0.384753i	0.955457	−	0.295131i	$-0.0953634\pi$
$881$	4.50855e9	+	7.80904e9i	0.222137	+	0.384753i	−0.733320	+	0.679884i	$0.762030\pi$
$882$	8.61443e9	−	4.38786e9i	0.422753	−	0.215334i
$883$	1.47500e10			0.720990			0.360495	−	0.932761i	$-0.382608\pi$
$883$	1.47500e10			0.720990			0.360495	+	0.932761i	$0.382608\pi$
$884$	3.24023e10	+	1.80323e10i	1.57759	+	0.877945i
$885$	−4.40063e8	−	7.62211e8i	−0.0213409	−	0.0369636i
$886$	2.09590e10	−	3.63021e10i	1.01240	−	1.75353i
$887$	−4.49576e8			−0.0216307			−0.0108153	−	0.999942i	$-0.503443\pi$
$887$	−4.49576e8			−0.0216307			−0.0108153	+	0.999942i	$0.503443\pi$
$888$	−4.32831e10	+	7.49685e10i	−2.07431	+	3.59280i
$889$	−2.15336e9	−	6.38006e8i	−0.102792	−	0.0304557i
$890$	−1.07339e10	+	1.85917e10i	−0.510379	+	0.884002i
$891$	−1.79564e10	−	3.11014e10i	−0.850448	−	1.47302i
$892$	5.01532e10	+	8.68678e10i	2.36604	+	4.09810i
$893$	1.02474e9			0.0481539
$894$	−2.81496e10			−1.31762
$895$	−9.14966e9	−	1.58477e10i	−0.426603	−	0.738898i
$896$	−7.85985e9	+	7.45775e9i	−0.365036	+	0.346362i
$897$	−3.37355e10	+	2.01931e10i	−1.56068	+	0.934178i
$898$	2.06333e10	−	3.57379e10i	0.950826	−	1.64688i
$899$	−2.10673e10	+	3.64896e10i	−0.967050	+	1.67498i
$900$	5.32595e9	−	9.22482e9i	0.243528	−	0.421803i
$901$	−3.69463e9	−	6.39928e9i	−0.168281	−	0.291470i
$902$	6.14128e10			2.78635
$903$	1.26315e10	+	3.74252e9i	0.570885	+	0.169144i
$904$	−1.85868e10	+	3.21933e10i	−0.836788	+	1.44936i
$905$	6.69118e9	−	1.15895e10i	0.300077	−	0.519748i
$906$	3.67606e10			1.64223
$907$	−1.09854e10	+	1.90273e10i	−0.488867	+	0.846742i	−0.999918	−	0.0128079i	$-0.995923\pi$
$907$	−1.09854e10	+	1.90273e10i	−0.488867	+	0.846742i	0.511051	+	0.859550i	$0.329256\pi$
$908$	4.17074e10			1.84890
$909$	3.44171e9			0.151985
$910$	5.43446e9	−	1.94638e10i	0.239063	−	0.856217i
$911$	2.62711e10			1.15123			0.575617	−	0.817720i	$-0.304762\pi$
$911$	2.62711e10			1.15123			0.575617	+	0.817720i	$0.304762\pi$
$912$	1.42906e10			0.623834
$913$	1.62840e9	−	2.82047e9i	0.0708131	−	0.122652i
$914$	5.59432e10			2.42346
$915$	−8.05378e9	+	1.39496e10i	−0.347557	+	0.601986i
$916$	−2.24959e10	+	3.89640e10i	−0.967093	+	1.67505i
$917$	7.24757e9	+	3.01969e10i	0.310384	+	1.29321i
$918$	−2.65998e10			−1.13483
$919$	−4.15750e8	−	7.20101e8i	−0.0176697	−	0.0306048i	0.857055	−	0.515224i	$-0.172291\pi$
$919$	−4.15750e8	−	7.20101e8i	−0.0176697	−	0.0306048i	−0.874725	+	0.484620i	$0.838958\pi$
$920$	−2.51879e10	+	4.36267e10i	−1.06644	+	1.84712i
$921$	1.77810e10	−	3.07976e10i	0.749976	−	1.29900i
$922$	−2.88620e10	+	4.99904e10i	−1.21274	+	2.10053i
$923$	1.17146e10	−	7.01206e9i	0.490369	−	0.293521i
$924$	−9.12092e10	−	2.70238e10i	−3.80353	−	1.12692i
$925$	1.25044e10	+	2.16583e10i	0.519479	+	0.899764i
$926$	−1.14516e10			−0.473943
$927$	−6.36312e8			−0.0262356
$928$	−5.23022e10	−	9.05900e10i	−2.14833	−	3.72102i
$929$	2.68001e9	+	4.64191e9i	0.109668	+	0.189951i	0.915636	−	0.402009i	$-0.131688\pi$
$929$	2.68001e9	+	4.64191e9i	0.109668	+	0.189951i	−0.805968	+	0.591960i	$0.798355\pi$
$930$	1.21226e10	−	2.09970e10i	0.494205	−	0.855987i
$931$	4.59403e9	−	2.34003e9i	0.186582	−	0.0950379i
$932$	1.91785e10	−	3.32182e10i	0.775996	−	1.34406i
$933$	−7.81875e9			−0.315175
$934$	7.69766e9	−	1.33327e10i	0.309133	−	0.535433i
$935$	6.20726e9	+	1.07513e10i	0.248347	+	0.430150i
$936$	2.77299e8	+	1.75825e10i	0.0110531	+	0.700834i
$937$	3.39248e9			0.134719			0.0673595	−	0.997729i	$-0.478543\pi$
$937$	3.39248e9			0.134719			0.0673595	+	0.997729i	$0.478543\pi$
$938$	6.51002e9	+	2.71239e10i	0.257557	+	1.07311i
$939$	−1.47614e9	−	2.55675e9i	−0.0581832	−	0.100776i
$940$	3.45812e9	+	5.98963e9i	0.135798	+	0.235208i
$941$	3.43592e9	+	5.95120e9i	0.134425	+	0.232831i	0.925378	−	0.379046i	$-0.123748\pi$
$941$	3.43592e9	+	5.95120e9i	0.134425	+	0.232831i	−0.790953	+	0.611877i	$0.790415\pi$
$942$	1.63811e10			0.638505
$943$	2.18532e10	+	3.78508e10i	0.848641	+	1.46989i
$944$	−5.49608e9			−0.212643
$945$	2.41020e9	+	1.00421e10i	0.0929057	+	0.387090i
$946$	−1.84526e10	−	3.19609e10i	−0.708662	−	1.22744i
$947$	−3.73166e10			−1.42783			−0.713916	−	0.700231i	$-0.753080\pi$
$947$	−3.73166e10			−1.42783			−0.713916	+	0.700231i	$0.753080\pi$
$948$	−3.01103e10	−	5.21526e10i	−1.14785	−	1.98814i
$949$	−5.72748e8	−	3.63158e10i	−0.0217536	−	1.37932i
$950$	3.98680e9	−	6.90534e9i	0.150866	−	0.261308i
$951$	2.00131e10	+	3.46637e10i	0.754540	+	1.30690i
$952$	−3.87725e10	+	3.67890e10i	−1.45645	+	1.38194i
$953$	2.40314e10	−	4.16236e10i	0.899403	−	1.55781i	0.0711442	−	0.997466i	$-0.477335\pi$
$953$	2.40314e10	−	4.16236e10i	0.899403	−	1.55781i	0.828259	−	0.560346i	$-0.189332\pi$
$954$	2.93794e9	−	5.08866e9i	0.109553	−	0.189751i
$955$	−6.53490e9			−0.242788
$956$	−5.81050e7			−0.00215085
$957$	4.22937e10	−	7.32548e10i	1.55985	−	2.70174i
$958$	2.77478e10	−	4.80606e10i	1.01965	−	1.76608i
$959$	1.28067e10	−	1.21516e10i	0.468892	−	0.444904i
$960$	1.06296e10	+	1.84110e10i	0.387763	+	0.671626i
$961$	1.99302e8	−	3.45202e8i	0.00724404	−	0.0125470i
$962$	−6.04943e10	−	3.36658e10i	−2.19080	−	1.21920i
$963$	−5.66363e9	−	9.80970e9i	−0.204363	−	0.353968i
$964$	−1.08045e11			−3.88449
$965$	2.92612e9	+	5.06819e9i	0.104821	+	0.181555i
$966$	−2.21781e10	−	9.24046e10i	−0.791596	−	3.29817i
$967$	−1.89121e10			−0.672585			−0.336293	−	0.941758i	$-0.609173\pi$
$967$	−1.89121e10			−0.672585			−0.336293	+	0.941758i	$0.609173\pi$
$968$	4.05851e10	+	7.02954e10i	1.43814	+	2.49094i
$969$	4.84063e9			0.170911
$970$	−8.53184e9	−	1.47776e10i	−0.300152	−	0.519879i
$971$	3.21111e9	+	5.56181e9i	0.112561	+	0.194962i	0.916802	−	0.399342i	$-0.130761\pi$
$971$	3.21111e9	+	5.56181e9i	0.112561	+	0.194962i	−0.804241	+	0.594303i	$0.797428\pi$
$972$	−1.76403e10	−	3.05539e10i	−0.616133	−	1.06717i
$973$	−3.83651e9	−	1.59848e10i	−0.133519	−	0.556304i
$974$	1.50751e10			0.522760
$975$	2.18870e10	+	1.21804e10i	0.756258	+	0.420866i
$976$	5.02930e10	+	8.71101e10i	1.73154	+	2.99912i
$977$	1.27662e10	−	2.21117e10i	0.437956	−	0.758561i	−0.559576	−	0.828779i	$-0.689036\pi$
$977$	1.27662e10	−	2.21117e10i	0.437956	−	0.758561i	0.997532	+	0.0702176i	$0.0223693\pi$
$978$	−3.27103e9			−0.111815
$979$	−2.40986e10	+	4.17400e10i	−0.820828	+	1.42172i
$980$	2.91808e10	+	1.89556e10i	0.990389	+	0.643349i
$981$	−2.59244e9	+	4.49024e9i	−0.0876733	+	0.151855i
$982$	−3.43925e10	−	5.95695e10i	−1.15897	−	2.00740i
$983$	2.57749e10	+	4.46434e10i	0.865485	+	1.49906i	0.866565	+	0.499064i	$0.166323\pi$
$983$	2.57749e10	+	4.46434e10i	0.865485	+	1.49906i	−0.00107991	+	0.999999i	$0.500344\pi$
$984$	9.63804e10			3.22482
$985$	1.34565e10			0.448648
$986$	−3.98474e10	−	6.90178e10i	−1.32383	−	2.29294i
$987$	−7.45987e9	−	2.21024e9i	−0.246957	−	0.0731694i
$988$	2.47980e8	+	1.57235e10i	0.00818026	+	0.518680i
$989$	1.31324e10	−	2.27460e10i	0.431675	−	0.747683i
$990$	−4.93597e9	+	8.54934e9i	−0.161677	+	0.280033i
$991$	−1.61341e8	+	2.79451e8i	−0.00526607	+	0.00912110i	−0.868646	−	0.495433i	$-0.835010\pi$
$991$	−1.61341e8	+	2.79451e8i	−0.00526607	+	0.00912110i	0.863380	+	0.504554i	$0.168343\pi$
$992$	−3.36570e10	−	5.82957e10i	−1.09467	−	1.89603i
$993$	3.45674e10			1.12033
$994$	7.70133e9	+	3.20875e10i	0.248721	+	1.03630i
$995$	−1.06871e10	+	1.85106e10i	−0.343937	+	0.595716i
$996$	4.28540e9	−	7.42254e9i	0.137431	−	0.238037i
$997$	−7.88979e9			−0.252135			−0.126067	−	0.992022i	$-0.540236\pi$
$997$	−7.88979e9			−0.252135			−0.126067	+	0.992022i	$0.540236\pi$
$998$	−2.31091e10	+	4.00261e10i	−0.735911	+	1.27464i
$999$	3.53800e10			1.12274

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.h.a.16.3	yes	126
7.4	even	3		91.8.g.a.81.61	yes	126
13.9	even	3		91.8.g.a.9.61	✓	126
91.74	even	3	inner	91.8.h.a.74.3	yes	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.g.a.9.61	✓	126	13.9	even	3
91.8.g.a.81.61	yes	126	7.4	even	3
91.8.h.a.16.3	yes	126	1.1	even	1	trivial
91.8.h.a.74.3	yes	126	91.74	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-21.0975 q^{2} +(26.1888 - 45.3604i) q^{3} +317.105 q^{4} +(-66.6229 + 115.394i) q^{5} +(-552.519 + 956.990i) q^{6} +(658.312 - 624.634i) q^{7} -3989.64 q^{8} +(-278.208 - 481.870i) q^{9} +O(q^{10})\)	\(q-21.0975 q^{2} +(26.1888 - 45.3604i) q^{3} +317.105 q^{4} +(-66.6229 + 115.394i) q^{5} +(-552.519 + 956.990i) q^{6} +(658.312 - 624.634i) q^{7} -3989.64 q^{8} +(-278.208 - 481.870i) q^{9} +(1405.58 - 2434.53i) q^{10} +(3155.65 - 5465.74i) q^{11} +(8304.60 - 14384.0i) q^{12} +(6921.73 + 3852.03i) q^{13} +(-13888.7 + 13178.2i) q^{14} +(3489.55 + 6044.07i) q^{15} +43582.0 q^{16} +14762.4 q^{17} +(5869.49 + 10166.3i) q^{18} +(3130.17 + 5421.61i) q^{19} +(-21126.4 + 36592.0i) q^{20} +(-11093.2 - 46219.7i) q^{21} +(-66576.3 + 115313. i) q^{22} -94762.2 q^{23} +(-104484. + 180971. i) q^{24} +(30185.3 + 52282.5i) q^{25} +(-146031. - 81268.1i) q^{26} +85406.1 q^{27} +(208754. - 198074. i) q^{28} +(127941. + 221601. i) q^{29} +(-73620.7 - 127515. i) q^{30} +(82331.7 + 142603. i) q^{31} -408798. q^{32} +(-165285. - 286282. i) q^{33} -311451. q^{34} +(28220.5 + 117580. i) q^{35} +(-88221.0 - 152803. i) q^{36} +414256. q^{37} +(-66038.8 - 114383. i) q^{38} +(356001. - 213092. i) q^{39} +(265801. - 460381. i) q^{40} +(-230611. - 399430. i) q^{41} +(234039. + 975121. i) q^{42} +(-138583. + 240032. i) q^{43} +(1.00067e6 - 1.73321e6i) q^{44} +74140.0 q^{45} +1.99925e6 q^{46} +(81843.4 - 141757. i) q^{47} +(1.14136e6 - 1.97690e6i) q^{48} +(43207.5 - 822409. i) q^{49} +(-636834. - 1.10303e6i) q^{50} +(386611. - 669630. i) q^{51} +(2.19491e6 + 1.22150e6i) q^{52} +(-250272. - 433484. i) q^{53} -1.80186e6 q^{54} +(420476. + 728286. i) q^{55} +(-2.62643e6 + 2.49206e6i) q^{56} +327902. q^{57} +(-2.69924e6 - 4.67523e6i) q^{58} -126109. q^{59} +(1.10655e6 + 1.91660e6i) q^{60} +(1.15399e6 + 1.99876e6i) q^{61} +(-1.73699e6 - 3.00856e6i) q^{62} +(-484140. - 143443. i) q^{63} +3.04612e6 q^{64} +(-905647. + 542095. i) q^{65} +(3.48711e6 + 6.03985e6i) q^{66} +(728468. - 1.26174e6i) q^{67} +4.68124e6 q^{68} +(-2.48171e6 + 4.29845e6i) q^{69} +(-595382. - 2.48065e6i) q^{70} +(861774. - 1.49264e6i) q^{71} +(1.10995e6 + 1.92249e6i) q^{72} +(-2.29255e6 - 3.97081e6i) q^{73} -8.73977e6 q^{74} +3.16207e6 q^{75} +(992592. + 1.71922e6i) q^{76} +(-1.33669e6 - 5.56929e6i) q^{77} +(-7.51074e6 + 4.49572e6i) q^{78} +(1.81287e6 - 3.13998e6i) q^{79} +(-2.90356e6 + 5.02911e6i) q^{80} +(2.84513e6 - 4.92790e6i) q^{81} +(4.86531e6 + 8.42697e6i) q^{82} +516028. q^{83} +(-3.51771e6 - 1.46565e7i) q^{84} +(-983516. + 1.70350e6i) q^{85} +(2.92375e6 - 5.06408e6i) q^{86} +1.34025e7 q^{87} +(-1.25899e7 + 2.18063e7i) q^{88} -7.63666e6 q^{89} -1.56417e6 q^{90} +(6.96277e6 - 1.78772e6i) q^{91} -3.00496e7 q^{92} +8.62467e6 q^{93} +(-1.72669e6 + 2.99072e6i) q^{94} -834164. q^{95} +(-1.07059e7 + 1.85432e7i) q^{96} +(3.03500e6 - 5.25677e6i) q^{97} +(-911570. + 1.73508e7i) q^{98} -3.51170e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 126 q - 2 q^{2} - 80 q^{3} + 7678 q^{4} - 2 q^{5} - 258 q^{6} + 953 q^{7} - 264 q^{8} - 41707 q^{9}+O(q^{10}) \) 126 * q - 2 * q^2 - 80 * q^3 + 7678 * q^4 - 2 * q^5 - 258 * q^6 + 953 * q^7 - 264 * q^8 - 41707 * q^9	\( 126 q - 2 q^{2} - 80 q^{3} + 7678 q^{4} - 2 q^{5} - 258 q^{6} + 953 q^{7} - 264 q^{8} - 41707 q^{9} - 4255 q^{10} + 7423 q^{11} - 18072 q^{12} - 1824 q^{13} - 15916 q^{14} + 11047 q^{15} + 410294 q^{16} + 99274 q^{17} - 21111 q^{18} - 4844 q^{19} + 36626 q^{20} + 73198 q^{21} - 43360 q^{22} + 34130 q^{23} - 130304 q^{24} - 810669 q^{25} + 390708 q^{26} + 416614 q^{27} + 69267 q^{28} + 191096 q^{29} + 70666 q^{30} + 183609 q^{31} + 695346 q^{32} + 178591 q^{33} - 742000 q^{34} + 579437 q^{35} - 1732409 q^{36} - 1362898 q^{37} - 877438 q^{38} + 459227 q^{39} - 1502882 q^{40} + 593701 q^{41} + 1442877 q^{42} - 592188 q^{43} + 1254066 q^{44} + 1954226 q^{45} - 1385452 q^{46} + 98278 q^{47} - 374916 q^{48} - 1497637 q^{49} + 289562 q^{50} - 281250 q^{51} - 8455 q^{52} - 1256681 q^{53} - 293814 q^{54} - 3015554 q^{55} - 1646151 q^{56} + 2743072 q^{57} + 1851469 q^{58} - 2279458 q^{59} + 1031485 q^{60} - 1127636 q^{61} - 7724680 q^{62} + 5142530 q^{63} + 11827496 q^{64} - 2789048 q^{65} + 435059 q^{66} + 4373348 q^{67} + 8737122 q^{68} - 7610377 q^{69} - 8084578 q^{70} - 60067 q^{71} - 11660951 q^{72} - 5060877 q^{73} + 1184002 q^{74} + 22637254 q^{75} + 637438 q^{76} + 21469082 q^{77} - 7230943 q^{78} - 2446486 q^{79} - 123568 q^{80} - 30756895 q^{81} + 8626952 q^{82} - 18679806 q^{83} + 11302461 q^{84} + 5330093 q^{85} - 8512356 q^{86} - 16508762 q^{87} - 6438219 q^{88} - 6176684 q^{89} + 53481084 q^{90} + 29236777 q^{91} + 2460546 q^{92} + 27682404 q^{93} - 17421794 q^{94} + 39553398 q^{95} + 26667066 q^{96} + 7705262 q^{97} + 14093080 q^{98} - 60531432 q^{99}+O(q^{100}) \) 126 * q - 2 * q^2 - 80 * q^3 + 7678 * q^4 - 2 * q^5 - 258 * q^6 + 953 * q^7 - 264 * q^8 - 41707 * q^9 - 4255 * q^10 + 7423 * q^11 - 18072 * q^12 - 1824 * q^13 - 15916 * q^14 + 11047 * q^15 + 410294 * q^16 + 99274 * q^17 - 21111 * q^18 - 4844 * q^19 + 36626 * q^20 + 73198 * q^21 - 43360 * q^22 + 34130 * q^23 - 130304 * q^24 - 810669 * q^25 + 390708 * q^26 + 416614 * q^27 + 69267 * q^28 + 191096 * q^29 + 70666 * q^30 + 183609 * q^31 + 695346 * q^32 + 178591 * q^33 - 742000 * q^34 + 579437 * q^35 - 1732409 * q^36 - 1362898 * q^37 - 877438 * q^38 + 459227 * q^39 - 1502882 * q^40 + 593701 * q^41 + 1442877 * q^42 - 592188 * q^43 + 1254066 * q^44 + 1954226 * q^45 - 1385452 * q^46 + 98278 * q^47 - 374916 * q^48 - 1497637 * q^49 + 289562 * q^50 - 281250 * q^51 - 8455 * q^52 - 1256681 * q^53 - 293814 * q^54 - 3015554 * q^55 - 1646151 * q^56 + 2743072 * q^57 + 1851469 * q^58 - 2279458 * q^59 + 1031485 * q^60 - 1127636 * q^61 - 7724680 * q^62 + 5142530 * q^63 + 11827496 * q^64 - 2789048 * q^65 + 435059 * q^66 + 4373348 * q^67 + 8737122 * q^68 - 7610377 * q^69 - 8084578 * q^70 - 60067 * q^71 - 11660951 * q^72 - 5060877 * q^73 + 1184002 * q^74 + 22637254 * q^75 + 637438 * q^76 + 21469082 * q^77 - 7230943 * q^78 - 2446486 * q^79 - 123568 * q^80 - 30756895 * q^81 + 8626952 * q^82 - 18679806 * q^83 + 11302461 * q^84 + 5330093 * q^85 - 8512356 * q^86 - 16508762 * q^87 - 6438219 * q^88 - 6176684 * q^89 + 53481084 * q^90 + 29236777 * q^91 + 2460546 * q^92 + 27682404 * q^93 - 17421794 * q^94 + 39553398 * q^95 + 26667066 * q^96 + 7705262 * q^97 + 14093080 * q^98 - 60531432 * q^99

Introduction

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