LMFDB - Embedded newform 33.8.e.b.31.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [33,8,Mod(4,33)] 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("33.4"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(33, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	33.e (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,-6] 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:	$10.3087058410$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			31.4
Character	$\chi$	$=$	33.31
Dual form			33.8.e.b.16.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.970201 + 2.98597i) q^{2} +(-21.8435 + 15.8702i) q^{3} +(95.5794 + 69.4425i) q^{4} +(-100.399 - 308.998i) q^{5} +(-26.1954 - 80.6212i) q^{6} +(1340.18 + 973.701i) q^{7} +(-625.207 + 454.240i) q^{8} +(225.273 - 693.320i) q^{9} +1020.07 q^{10} +(-4300.99 + 994.308i) q^{11} -3189.85 q^{12} +(-1831.75 + 5637.55i) q^{13} +(-4207.69 + 3057.07i) q^{14} +(7096.93 + 5156.22i) q^{15} +(3923.27 + 12074.6i) q^{16} +(9048.40 + 27848.1i) q^{17} +(1851.67 + 1345.32i) q^{18} +(-26235.4 + 19061.1i) q^{19} +(11861.5 - 36505.8i) q^{20} -44727.1 q^{21} +(1203.85 - 13807.3i) q^{22} +10937.0 q^{23} +(6447.81 - 19844.3i) q^{24} +(-22195.0 + 16125.6i) q^{25} +(-15056.4 - 10939.1i) q^{26} +(6082.38 + 18719.6i) q^{27} +(60477.8 + 186132. i) q^{28} +(80959.3 + 58820.4i) q^{29} +(-22281.8 + 16188.6i) q^{30} +(66382.8 - 204305. i) q^{31} -138779. q^{32} +(78168.6 - 89976.7i) q^{33} -91932.4 q^{34} +(166318. - 511873. i) q^{35} +(69677.4 - 50623.6i) q^{36} +(-69002.9 - 50133.6i) q^{37} +(-31462.4 - 96831.3i) q^{38} +(-49457.3 - 152214. i) q^{39} +(203129. + 147582. i) q^{40} +(-281410. + 204456. i) q^{41} +(43394.3 - 133554. i) q^{42} +492042. q^{43} +(-480134. - 203636. i) q^{44} -236852. q^{45} +(-10611.1 + 32657.6i) q^{46} +(771628. - 560620. i) q^{47} +(-277324. - 201487. i) q^{48} +(593512. + 1.82664e6i) q^{49} +(-26617.1 - 81918.9i) q^{50} +(-639603. - 464699. i) q^{51} +(-566563. + 411632. i) q^{52} +(-195736. + 602415. i) q^{53} -61797.5 q^{54} +(739056. + 1.22917e6i) q^{55} -1.28019e6 q^{56} +(270568. - 832723. i) q^{57} +(-254183. + 184675. i) q^{58} +(-46100.6 - 33494.1i) q^{59} +(320259. + 985657. i) q^{60} +(-565216. - 1.73955e6i) q^{61} +(545645. + 396434. i) q^{62} +(976994. - 709828. i) q^{63} +(-367535. + 1.13116e6i) q^{64} +1.92590e6 q^{65} +(192829. + 320705. i) q^{66} -1.57940e6 q^{67} +(-1.06900e6 + 3.29005e6i) q^{68} +(-238902. + 173573. i) q^{69} +(1.36708e6 + 993239. i) q^{70} +(-613230. - 1.88733e6i) q^{71} +(174091. + 535797. i) q^{72} +(3.48048e6 + 2.52872e6i) q^{73} +(216644. - 157401. i) q^{74} +(228899. - 704479. i) q^{75} -3.83122e6 q^{76} +(-6.73228e6 - 2.85532e6i) q^{77} +502490. q^{78} +(352400. - 1.08457e6i) q^{79} +(3.33712e6 - 2.42456e6i) q^{80} +(-429945. - 312373. i) q^{81} +(-337476. - 1.03865e6i) q^{82} +(-1.72299e6 - 5.30280e6i) q^{83} +(-4.27499e6 - 3.10596e6i) q^{84} +(7.69654e6 - 5.59187e6i) q^{85} +(-477380. + 1.46922e6i) q^{86} -2.70192e6 q^{87} +(2.23736e6 - 2.57533e6i) q^{88} +1.21091e7 q^{89} +(229794. - 707232. i) q^{90} +(-7.94417e6 + 5.77178e6i) q^{91} +(1.04535e6 + 759494. i) q^{92} +(1.79234e6 + 5.51624e6i) q^{93} +(925362. + 2.84797e6i) q^{94} +(8.52387e6 + 6.19295e6i) q^{95} +(3.03141e6 - 2.20245e6i) q^{96} +(5.32748e6 - 1.63963e7i) q^{97} -6.03012e6 q^{98} +(-279525. + 3.20596e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 6 q^{2} - 189 q^{3} + 160 q^{4} + 773 q^{5} - 162 q^{6} + 1289 q^{7} + 2956 q^{8} - 5103 q^{9} - 10640 q^{10} + 13209 q^{11} + 45630 q^{12} + 13499 q^{13} - 3318 q^{14} - 22734 q^{15} - 113196 q^{16}+ \cdots - 6579954 q^{99}+O(q^{100}) $ 28 * q - 6 * q^2 - 189 * q^3 + 160 * q^4 + 773 * q^5 - 162 * q^6 + 1289 * q^7 + 2956 * q^8 - 5103 * q^9 - 10640 * q^10 + 13209 * q^11 + 45630 * q^12 + 13499 * q^13 - 3318 * q^14 - 22734 * q^15 - 113196 * q^16 + 30296 * q^17 + 21141 * q^18 - 6858 * q^19 + 76725 * q^20 - 177012 * q^21 - 48859 * q^22 - 166984 * q^23 + 44442 * q^24 + 99832 * q^25 + 340424 * q^26 - 137781 * q^27 + 657387 * q^28 + 192014 * q^29 - 184410 * q^30 + 396068 * q^31 - 303498 * q^32 + 168453 * q^33 - 1229124 * q^34 - 725859 * q^35 + 116640 * q^36 + 811053 * q^37 + 1548798 * q^38 + 364473 * q^39 - 1427263 * q^40 + 1041497 * q^41 + 300024 * q^42 - 5265288 * q^43 - 5341085 * q^44 + 100602 * q^45 + 1198651 * q^46 + 1667505 * q^47 + 730593 * q^48 + 2968140 * q^49 + 11247432 * q^50 + 340767 * q^51 + 2325763 * q^52 - 1625736 * q^53 - 905418 * q^54 - 8338690 * q^55 - 18201906 * q^56 + 1546479 * q^57 + 14965553 * q^58 - 2587454 * q^59 + 2071575 * q^60 + 5801619 * q^61 + 15631121 * q^62 + 939681 * q^63 - 3732846 * q^64 - 15368174 * q^65 - 235683 * q^66 - 7141262 * q^67 + 17394545 * q^68 - 5063553 * q^69 - 4329200 * q^70 + 3569199 * q^71 + 1199934 * q^72 + 125008 * q^73 - 13691530 * q^74 - 11794221 * q^75 - 19690428 * q^76 - 6038739 * q^77 + 12684438 * q^78 + 17075485 * q^79 + 26606436 * q^80 - 3720087 * q^81 + 19886007 * q^82 - 4645575 * q^83 + 1074519 * q^84 + 12002715 * q^85 - 12296287 * q^86 - 12259512 * q^87 - 50905990 * q^88 + 9601664 * q^89 + 8857350 * q^90 - 14129477 * q^91 - 90776021 * q^92 + 10693836 * q^93 + 1047679 * q^94 + 58935661 * q^95 + 26156304 * q^96 - 22170261 * q^97 + 140532178 * q^98 - 6579954 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.970201	+	2.98597i	−0.0857545	+	0.263925i	−0.984734	−	0.174065i	$-0.944310\pi$
$2$	−0.970201	+	2.98597i	−0.0857545	+	0.263925i	0.898980	+	0.437990i	$0.144310\pi$
$3$	−21.8435	+	15.8702i	−0.467086	+	0.339358i
$3$	−21.8435	+	15.8702i	−0.467086	+	0.339358i
$4$	95.5794	+	69.4425i	0.746714	+	0.542520i
$5$	−100.399	−	308.998i	−0.359200	−	1.10550i	−0.953534	−	0.301285i	$-0.902584\pi$
$5$	−100.399	−	308.998i	−0.359200	−	1.10550i	0.594334	−	0.804218i	$-0.297416\pi$
$6$	−26.1954	−	80.6212i	−0.0495104	−	0.152377i
$7$	1340.18	+	973.701i	1.47680	+	1.07296i	0.978571	+	0.205911i	$0.0660158\pi$
$7$	1340.18	+	973.701i	1.47680	+	1.07296i	0.498228	+	0.867046i	$0.333984\pi$
$8$	−625.207	+	454.240i	−0.431727	+	0.313668i
$9$	225.273	−	693.320i	0.103006	−	0.317019i
$10$	1020.07			0.322573
$11$	−4300.99	+	994.308i	−0.974303	+	0.225241i
$11$	−4300.99	+	994.308i	−0.974303	+	0.225241i
$12$	−3189.85			−0.532888
$13$	−1831.75	+	5637.55i	−0.231241	+	0.711686i	0.766357	+	0.642415i	$0.222067\pi$
$13$	−1831.75	+	5637.55i	−0.231241	+	0.711686i	−0.997598	+	0.0692712i	$0.977933\pi$
$14$	−4207.69	+	3057.07i	−0.409822	+	0.297753i
$15$	7096.93	+	5156.22i	0.542939	+	0.394468i
$16$	3923.27	+	12074.6i	0.239457	+	0.736973i
$17$	9048.40	+	27848.1i	0.446684	+	1.37475i	0.880626	+	0.473811i	$0.157122\pi$
$17$	9048.40	+	27848.1i	0.446684	+	1.37475i	−0.433942	+	0.900941i	$0.642878\pi$
$18$	1851.67	+	1345.32i	0.0748360	+	0.0543716i
$19$	−26235.4	+	19061.1i	−0.877506	+	0.637546i	−0.932591	−	0.360936i	$-0.882457\pi$
$19$	−26235.4	+	19061.1i	−0.877506	+	0.637546i	0.0550841	+	0.998482i	$0.482457\pi$
$20$	11861.5	−	36505.8i	0.331538	−	1.02037i
$21$	−44727.1			−1.05391
$22$	1203.85	−	13807.3i	0.0241042	−	0.276458i
$23$	10937.0			0.187435			0.0937177	−	0.995599i	$-0.470125\pi$
$23$	10937.0			0.187435			0.0937177	+	0.995599i	$0.470125\pi$
$24$	6447.81	−	19844.3i	0.0952079	−	0.293020i
$25$	−22195.0	+	16125.6i	−0.284096	+	0.206408i
$26$	−15056.4	−	10939.1i	−0.168002	−	0.122061i
$27$	6082.38	+	18719.6i	0.0594703	+	0.183031i
$28$	60477.8	+	186132.i	0.520646	+	1.60239i
$29$	80959.3	+	58820.4i	0.616416	+	0.447852i	0.851668	−	0.524082i	$-0.175592\pi$
$29$	80959.3	+	58820.4i	0.616416	+	0.447852i	−0.235252	+	0.971934i	$0.575592\pi$
$30$	−22281.8	+	16188.6i	−0.150669	+	0.109468i
$31$	66382.8	−	204305.i	0.400212	−	1.23172i	−0.524616	−	0.851339i	$-0.675791\pi$
$31$	66382.8	−	204305.i	0.400212	−	1.23172i	0.924828	−	0.380386i	$-0.124209\pi$
$32$	−138779.			−0.748684
$33$	78168.6	−	89976.7i	0.378646	−	0.435844i
$34$	−91932.4			−0.401137
$35$	166318.	−	511873.i	0.655692	−	2.01801i
$36$	69677.4	−	50623.6i	0.248905	−	0.180840i
$37$	−69002.9	−	50133.6i	−0.223955	−	0.162713i	0.470150	−	0.882587i	$-0.344200\pi$
$37$	−69002.9	−	50133.6i	−0.223955	−	0.162713i	−0.694105	+	0.719873i	$0.744200\pi$
$38$	−31462.4	−	96831.3i	−0.0930142	−	0.286268i
$39$	−49457.3	−	152214.i	−0.133507	−	0.410892i
$40$	203129.	+	147582.i	0.501837	+	0.364606i
$41$	−281410.	+	204456.i	−0.637670	+	0.463294i	−0.859049	−	0.511894i	$-0.828944\pi$
$41$	−281410.	+	204456.i	−0.637670	+	0.463294i	0.221379	+	0.975188i	$0.428944\pi$
$42$	43394.3	−	133554.i	0.0903774	−	0.278153i
$43$	492042.			0.943762			0.471881	−	0.881662i	$-0.343575\pi$
$43$	492042.			0.943762			0.471881	+	0.881662i	$0.343575\pi$
$44$	−480134.	−	203636.i	−0.849724	−	0.360388i
$45$	−236852.			−0.387465
$46$	−10611.1	+	32657.6i	−0.0160734	+	0.0494689i
$47$	771628.	−	560620.i	1.08409	−	0.787637i	0.105698	−	0.994398i	$-0.466292\pi$
$47$	771628.	−	560620.i	1.08409	−	0.787637i	0.978391	+	0.206761i	$0.0662922\pi$
$48$	−277324.	−	201487.i	−0.361945	−	0.262968i
$49$	593512.	+	1.82664e6i	0.720681	+	2.21803i
$50$	−26617.1	−	81918.9i	−0.0301138	−	0.0926806i
$51$	−639603.	−	464699.i	−0.675173	−	0.490542i
$52$	−566563.	+	411632.i	−0.558775	+	0.405974i
$53$	−195736.	+	602415.i	−0.180595	+	0.555815i	−0.999845	−	0.0176225i	$-0.994390\pi$
$53$	−195736.	+	602415.i	−0.180595	+	0.555815i	0.819250	+	0.573437i	$0.194390\pi$
$54$	−61797.5			−0.0534063
$55$	739056.	+	1.22917e6i	0.598974	+	0.996189i
$56$	−1.28019e6			−0.974126
$57$	270568.	−	832723.i	0.193515	−	0.595578i
$58$	−254183.	+	184675.i	−0.171060	+	0.124282i
$59$	−46100.6	−	33494.1i	−0.0292230	−	0.0212318i	0.573078	−	0.819501i	$-0.305749\pi$
$59$	−46100.6	−	33494.1i	−0.0292230	−	0.0212318i	−0.602301	+	0.798269i	$0.705749\pi$
$60$	320259.	+	985657.i	0.191413	+	0.589110i
$61$	−565216.	−	1.73955e6i	−0.318830	−	0.981259i	−0.974149	−	0.225906i	$-0.927466\pi$
$61$	−565216.	−	1.73955e6i	−0.318830	−	0.981259i	0.655319	−	0.755353i	$-0.272534\pi$
$62$	545645.	+	396434.i	0.290763	+	0.211252i
$63$	976994.	−	709828.i	0.492266	−	0.357652i
$64$	−367535.	+	1.13116e6i	−0.175254	+	0.539377i
$65$	1.92590e6			0.869833
$66$	192829.	+	320705.i	0.0825596	+	0.137310i
$67$	−1.57940e6			−0.641550			−0.320775	−	0.947155i	$-0.603943\pi$
$67$	−1.57940e6			−0.641550			−0.320775	+	0.947155i	$0.603943\pi$
$68$	−1.06900e6	+	3.29005e6i	−0.412285	+	1.26888i
$69$	−238902.	+	173573.i	−0.0875485	+	0.0636077i
$70$	1.36708e6	+	993239.i	0.476376	+	0.346107i
$71$	−613230.	−	1.88733e6i	−0.203338	−	0.625811i	−0.999778	−	0.0210924i	$-0.993286\pi$
$71$	−613230.	−	1.88733e6i	−0.203338	−	0.625811i	0.796439	−	0.604719i	$-0.206714\pi$
$72$	174091.	+	535797.i	0.0549683	+	0.169175i
$73$	3.48048e6	+	2.52872e6i	1.04715	+	0.760799i	0.971669	−	0.236348i	$-0.0759504\pi$
$73$	3.48048e6	+	2.52872e6i	1.04715	+	0.760799i	0.0754821	+	0.997147i	$0.475950\pi$
$74$	216644.	−	157401.i	0.0621493	−	0.0451541i
$75$	228899.	−	704479.i	0.0626513	−	0.192821i
$76$	−3.83122e6			−1.00113
$77$	−6.73228e6	−	2.85532e6i	−1.68052	−	0.712751i
$78$	502490.			0.119894
$79$	352400.	−	1.08457e6i	0.0804157	−	0.247494i	−0.902764	−	0.430137i	$-0.858465\pi$
$79$	352400.	−	1.08457e6i	0.0804157	−	0.247494i	0.983179	+	0.182643i	$0.0584653\pi$
$80$	3.33712e6	−	2.42456e6i	0.728714	−	0.529442i
$81$	−429945.	−	312373.i	−0.0898908	−	0.0653095i
$82$	−337476.	−	1.03865e6i	−0.0675919	−	0.208027i
$83$	−1.72299e6	−	5.30280e6i	−0.330756	−	1.01796i	−0.968775	−	0.247942i	$-0.920246\pi$
$83$	−1.72299e6	−	5.30280e6i	−0.330756	−	1.01796i	0.638018	−	0.770021i	$-0.279754\pi$
$84$	−4.27499e6	−	3.10596e6i	−0.786969	−	0.571766i
$85$	7.69654e6	−	5.59187e6i	1.35934	−	0.987621i
$86$	−477380.	+	1.46922e6i	−0.0809318	+	0.249083i
$87$	−2.70192e6			−0.439901
$88$	2.23736e6	−	2.57533e6i	0.349982	−	0.402850i
$89$	1.21091e7			1.82073			0.910364	−	0.413808i	$-0.135801\pi$
$89$	1.21091e7			1.82073			0.910364	+	0.413808i	$0.135801\pi$
$90$	229794.	−	707232.i	0.0332269	−	0.102262i
$91$	−7.94417e6	+	5.77178e6i	−1.10510	+	0.802906i
$92$	1.04535e6	+	759494.i	0.139961	+	0.101687i
$93$	1.79234e6	+	5.51624e6i	0.231062	+	0.711137i
$94$	925362.	+	2.84797e6i	0.114912	+	0.353662i
$95$	8.52387e6	+	6.19295e6i	1.02001	+	0.741080i
$96$	3.03141e6	−	2.20245e6i	0.349700	−	0.254072i
$97$	5.32748e6	−	1.63963e7i	0.592681	−	1.82408i	0.0267336	−	0.999643i	$-0.491489\pi$
$97$	5.32748e6	−	1.63963e7i	0.592681	−	1.82408i	0.565947	−	0.824441i	$-0.308511\pi$
$98$	−6.03012e6			−0.647195
$99$	−279525.	+	3.20596e6i	−0.0289532	+	0.332074i
$100$	−3.24119e6			−0.324119
$101$	−1.29723e6	+	3.99248e6i	−0.125283	+	0.385583i	−0.993953	−	0.109810i	$-0.964976\pi$
$101$	−1.29723e6	+	3.99248e6i	−0.125283	+	0.385583i	0.868669	+	0.495393i	$0.164976\pi$
$102$	2.00812e6	−	1.45899e6i	0.187365	−	0.136129i
$103$	−1.72853e7	−	1.25585e7i	−1.55864	−	1.13242i	−0.937111	−	0.349031i	$-0.886511\pi$
$103$	−1.72853e7	−	1.25585e7i	−1.55864	−	1.13242i	−0.621532	−	0.783389i	$-0.713489\pi$
$104$	−1.41557e6	−	4.35669e6i	−0.123400	−	0.379787i
$105$	4.49057e6	+	1.38206e7i	0.378564	+	1.16510i
$106$	−1.60889e6	−	1.16893e6i	−0.131207	−	0.0953272i
$107$	2.32411e6	−	1.68856e6i	0.183406	−	0.133252i	−0.492294	−	0.870429i	$-0.663842\pi$
$107$	2.32411e6	−	1.68856e6i	0.183406	−	0.133252i	0.675700	+	0.737177i	$0.263842\pi$
$108$	−718589.	+	2.21159e6i	−0.0548905	+	0.168936i
$109$	−2.68209e6			−0.198372			−0.0991862	−	0.995069i	$-0.531624\pi$
$109$	−2.68209e6			−0.198372			−0.0991862	+	0.995069i	$0.531624\pi$
$110$	−4.38729e6	+	1.01426e6i	−0.314284	+	0.0726566i
$111$	2.30289e6			0.159824
$112$	−6.49912e6	+	2.00022e7i	−0.437111	+	1.34529i
$113$	−3.91362e6	+	2.84341e6i	−0.255155	+	0.185381i	−0.708008	−	0.706204i	$-0.750406\pi$
$113$	−3.91362e6	+	2.84341e6i	−0.255155	+	0.185381i	0.452853	+	0.891585i	$0.350406\pi$
$114$	2.22398e6	+	1.61582e6i	0.140593	+	0.102147i
$115$	−1.09807e6	−	3.37951e6i	−0.0673268	−	0.207211i
$116$	3.65341e6	+	1.12440e7i	0.217318	+	0.668835i
$117$	3.49598e6	+	2.53998e6i	0.201799	+	0.146615i
$118$	144739.	−	105159.i	0.00810960	−	0.00589197i
$119$	−1.49892e7	+	4.61320e7i	−0.815388	+	2.50950i
$120$	−6.77921e6			−0.358133
$121$	1.75099e7	−	8.55302e6i	0.898533	−	0.438905i
$122$	5.74263e6			0.286320
$123$	2.90220e6	−	8.93206e6i	0.140624	−	0.432797i
$124$	2.05323e7	−	1.49176e7i	0.967079	−	0.702624i
$125$	−1.33239e7	−	9.68040e6i	−0.610165	−	0.443311i
$126$	1.17165e6	+	3.60595e6i	0.0521794	+	0.160592i
$127$	−1.39678e6	−	4.29886e6i	−0.0605084	−	0.186226i	0.916233	−	0.400645i	$-0.131214\pi$
$127$	−1.39678e6	−	4.29886e6i	−0.0605084	−	0.186226i	−0.976742	+	0.214419i	$0.931214\pi$
$128$	−1.73922e7	−	1.26361e7i	−0.733024	−	0.532573i
$129$	−1.07479e7	+	7.80881e6i	−0.440818	+	0.320273i
$130$	−1.86851e6	+	5.75067e6i	−0.0745921	+	0.229571i
$131$	2.18807e7			0.850376			0.425188	−	0.905105i	$-0.360208\pi$
$131$	2.18807e7			0.850376			0.425188	+	0.905105i	$0.360208\pi$
$132$	1.37195e7	−	3.17170e6i	0.519195	−	0.120028i
$133$	−5.37201e7			−1.97996
$134$	1.53234e6	−	4.71605e6i	0.0550158	−	0.169321i
$135$	5.17366e6	−	3.75888e6i	0.180980	−	0.131489i
$136$	−1.83068e7	−	1.33007e7i	−0.624061	−	0.453407i
$137$	1.07425e7	+	3.30621e7i	0.356931	+	1.09852i	0.954881	+	0.296988i	$0.0959821\pi$
$137$	1.07425e7	+	3.30621e7i	0.356931	+	1.09852i	−0.597950	+	0.801533i	$0.704018\pi$
$138$	−286500.	−	881756.i	−0.00928000	−	0.0285609i
$139$	4.04818e7	+	2.94118e7i	1.27852	+	0.928901i	0.999507	−	0.0313859i	$-0.00999208\pi$
$139$	4.04818e7	+	2.94118e7i	1.27852	+	0.928901i	0.279015	+	0.960287i	$0.409992\pi$
$140$	5.14423e7	−	3.73750e7i	1.58443	−	1.15115i
$141$	−7.95786e6	+	2.44918e7i	−0.239072	+	0.735789i
$142$	6.23046e6			0.182604
$143$	2.27288e6	−	2.60684e7i	0.0649981	−	0.745483i
$144$	9.25535e6			0.258300
$145$	1.00471e7	−	3.09218e7i	0.273686	−	0.842318i
$146$	−1.09274e7	+	7.93925e6i	−0.290592	+	0.211127i
$147$	−4.19535e7	−	3.04810e7i	−1.08933	−	0.791441i
$148$	−3.11386e6	−	9.58348e6i	−0.0789556	−	0.243000i
$149$	−5.44351e6	−	1.67534e7i	−0.134812	−	0.414908i	0.860749	−	0.509030i	$-0.169996\pi$
$149$	−5.44351e6	−	1.67534e7i	−0.134812	−	0.414908i	−0.995561	+	0.0941220i	$0.969996\pi$
$150$	1.88148e6	+	1.36697e6i	0.0455176	+	0.0330705i
$151$	1.94571e6	−	1.41364e6i	0.0459895	−	0.0334134i	−0.564553	−	0.825397i	$-0.690951\pi$
$151$	1.94571e6	−	1.41364e6i	0.0459895	−	0.0334134i	0.610543	+	0.791983i	$0.290951\pi$
$152$	7.74424e6	−	2.38343e7i	0.178865	−	0.550491i
$153$	2.13460e7			0.481833
$154$	1.50576e7	−	1.73322e7i	0.332225	−	0.382411i
$155$	−6.97946e7			−1.50543
$156$	5.84301e6	−	1.79829e7i	0.123226	−	0.379249i
$157$	4.50068e6	−	3.26994e6i	0.0928174	−	0.0674358i	−0.540409	−	0.841403i	$-0.681730\pi$
$157$	4.50068e6	−	3.26994e6i	0.0928174	−	0.0674358i	0.633226	+	0.773967i	$0.281730\pi$
$158$	2.89661e6	+	2.10451e6i	0.0584239	+	0.0424474i
$159$	−5.28488e6	−	1.62652e7i	−0.104267	−	0.320900i
$160$	1.39333e7	+	4.28824e7i	0.268927	+	0.827673i
$161$	1.46576e7	+	1.06494e7i	0.276804	+	0.201110i
$162$	1.34987e6	−	980738.i	0.0249453	−	0.0181239i
$163$	−1.32918e7	+	4.09079e7i	−0.240396	+	0.739862i	0.755964	+	0.654613i	$0.227168\pi$
$163$	−1.32918e7	+	4.09079e7i	−0.240396	+	0.739862i	−0.996360	+	0.0852485i	$0.972832\pi$
$164$	−4.10950e7			−0.727503
$165$	−3.56507e7	−	1.51203e7i	−0.617837	−	0.262040i
$166$	1.75057e7			0.297030
$167$	1.35277e7	−	4.16339e7i	0.224758	−	0.691734i	−0.773558	−	0.633725i	$-0.781525\pi$
$167$	1.35277e7	−	4.16339e7i	0.224758	−	0.691734i	0.998316	−	0.0580085i	$-0.0184750\pi$
$168$	2.79637e7	−	2.03168e7i	0.455001	−	0.330577i
$169$	2.23380e7	+	1.62295e7i	0.355992	+	0.258643i
$170$	9.22996e6	+	2.84069e7i	0.144088	+	0.443458i
$171$	7.30534e6	+	2.24835e7i	0.111726	+	0.343857i
$172$	4.70291e7	+	3.41686e7i	0.704721	+	0.512010i
$173$	8.37358e7	−	6.08376e7i	1.22956	−	0.893328i	0.232703	−	0.972548i	$-0.425243\pi$
$173$	8.37358e7	−	6.08376e7i	1.22956	−	0.893328i	0.996857	+	0.0792197i	$0.0252429\pi$
$174$	2.62141e6	−	8.06786e6i	0.0377235	−	0.116101i
$175$	−4.54470e7			−0.641020
$176$	−2.88798e7	−	4.80317e7i	−0.399300	−	0.664100i
$177$	1.53856e6			0.0208548
$178$	−1.17482e7	+	3.61573e7i	−0.156136	+	0.480536i
$179$	−1.12246e8	+	8.15513e7i	−1.46280	+	1.06279i	−0.480176	+	0.877172i	$0.659427\pi$
$179$	−1.12246e8	+	8.15513e7i	−1.46280	+	1.06279i	−0.982623	+	0.185613i	$0.940573\pi$
$180$	−2.26381e7	−	1.64476e7i	−0.289326	−	0.210207i
$181$	1.64341e7	+	5.05789e7i	0.206002	+	0.634008i	0.999671	+	0.0256581i	$0.00816812\pi$
$181$	1.64341e7	+	5.05789e7i	0.206002	+	0.634008i	−0.793669	+	0.608350i	$0.791832\pi$
$182$	−9.52692e6	−	2.93208e7i	−0.117139	−	0.360518i
$183$	3.99533e7	+	2.90278e7i	0.481919	+	0.350135i
$184$	−6.83790e6	+	4.96803e6i	−0.0809209	+	0.0587925i
$185$	−8.56330e6	+	2.63551e7i	−0.0994352	+	0.306030i
$186$	−1.82103e7			−0.207501
$187$	−6.66067e7	−	1.10778e8i	−0.744856	−	1.23881i
$188$	1.12683e8			1.23681
$189$	−1.00758e7	+	3.10102e7i	−0.108559	+	0.334109i
$190$	−2.67618e7	+	1.94436e7i	−0.283060	+	0.205655i
$191$	3.57348e7	+	2.59629e7i	0.371086	+	0.269610i	0.757661	−	0.652648i	$-0.226342\pi$
$191$	3.57348e7	+	2.59629e7i	0.371086	+	0.269610i	−0.386575	+	0.922258i	$0.626342\pi$
$192$	−9.92344e6	−	3.05412e7i	−0.101183	−	0.311409i
$193$	2.18219e7	+	6.71609e7i	0.218495	+	0.672459i	0.998887	+	0.0471681i	$0.0150196\pi$
$193$	2.18219e7	+	6.71609e7i	0.218495	+	0.672459i	−0.780392	+	0.625291i	$0.784980\pi$
$194$	4.37902e7	+	3.18154e7i	0.430597	+	0.312847i
$195$	−4.20682e7	+	3.05643e7i	−0.406287	+	0.295185i
$196$	−7.01191e7	+	2.15804e8i	−0.665181	+	2.04722i
$197$	−1.37664e8			−1.28289			−0.641444	−	0.767170i	$-0.721664\pi$
$197$	−1.37664e8			−1.28289			−0.641444	+	0.767170i	$0.721664\pi$
$198$	−9.30170e6	−	3.94507e6i	−0.0851597	−	0.0361183i
$199$	2.12879e7			0.191491			0.0957453	−	0.995406i	$-0.469477\pi$
$199$	2.12879e7			0.191491			0.0957453	+	0.995406i	$0.469477\pi$
$200$	6.55159e6	−	2.01637e7i	0.0579084	−	0.178224i
$201$	3.44996e7	−	2.50654e7i	0.299659	−	0.217715i
$202$	−1.06628e7	−	7.74701e6i	−0.0910213	−	0.0661309i
$203$	5.12269e7	+	1.57660e8i	0.429796	+	1.32278i
$204$	−2.88630e7	−	8.88313e7i	−0.238033	−	0.732589i
$205$	9.14299e7	+	6.64277e7i	0.741224	+	0.538531i
$206$	5.42696e7	−	3.94291e7i	0.432535	−	0.314255i
$207$	2.46382e6	−	7.58286e6i	0.0193069	−	0.0594206i
$208$	−7.52574e7			−0.579866
$209$	9.38856e7	−	1.08068e8i	0.711356	−	0.818813i
$210$	−4.56246e7			−0.339963
$211$	1.25717e7	−	3.86916e7i	0.0921307	−	0.283549i	−0.894365	−	0.447339i	$-0.852372\pi$
$211$	1.25717e7	−	3.86916e7i	0.0921307	−	0.283549i	0.986495	+	0.163790i	$0.0523719\pi$
$212$	−6.05416e7	+	4.39860e7i	−0.436393	+	0.317058i
$213$	4.33473e7	+	3.14937e7i	0.307350	+	0.223303i
$214$	2.78715e6	+	8.57796e6i	0.0194407	+	0.0598323i
$215$	−4.94007e7	−	1.52040e8i	−0.338999	−	1.04333i
$216$	−1.23060e7	−	8.94080e6i	−0.0830859	−	0.0603654i
$217$	2.87897e8	−	2.09170e8i	1.91262	−	1.38960i
$218$	2.60217e6	−	8.00865e6i	0.0170113	−	0.0523554i
$219$	−1.16157e8			−0.747293
$220$	−1.47180e7	+	1.68805e8i	−0.0931899	+	1.06882i
$221$	−1.73569e8			−1.08168
$222$	−2.23427e6	+	6.87637e6i	−0.0137057	+	0.0421817i
$223$	2.02736e8	−	1.47297e8i	1.22423	−	0.889458i	0.227790	−	0.973710i	$-0.426850\pi$
$223$	2.02736e8	−	1.47297e8i	1.22423	−	0.889458i	0.996444	+	0.0842522i	$0.0268501\pi$
$224$	−1.85989e8	−	1.35129e8i	−1.10566	−	0.803306i
$225$	6.18028e6	+	1.90209e7i	0.0361717	+	0.111325i
$226$	−4.69335e6	−	1.44446e7i	−0.0270460	−	0.0832391i
$227$	7.57563e7	+	5.50402e7i	0.429861	+	0.312313i	0.781593	−	0.623788i	$-0.214407\pi$
$227$	7.57563e7	+	5.50402e7i	0.429861	+	0.312313i	−0.351732	+	0.936101i	$0.614407\pi$
$228$	8.36871e7	−	6.08022e7i	0.467613	−	0.339741i
$229$	2.11959e7	−	6.52343e7i	0.116635	−	0.358965i	−0.875650	−	0.482947i	$-0.839566\pi$
$229$	2.11959e7	−	6.52343e7i	0.116635	−	0.358965i	0.992284	+	0.123982i	$0.0395665\pi$
$230$	1.11565e7			0.0604616
$231$	1.92371e8	−	4.44725e7i	1.02683	−	0.237383i
$232$	−7.73349e7			−0.406600
$233$	−4.02569e7	+	1.23898e8i	−0.208494	+	0.641680i	0.791057	+	0.611742i	$0.209531\pi$
$233$	−4.02569e7	+	1.23898e8i	−0.208494	+	0.641680i	−0.999552	+	0.0299377i	$0.990469\pi$
$234$	−1.09761e7	+	7.97461e6i	−0.0560006	+	0.0406868i
$235$	−2.50701e8	−	1.82145e8i	−1.26014	−	0.915546i
$236$	−2.08036e6	−	6.40269e6i	−0.0103026	−	0.0317081i
$237$	9.51479e6	+	2.92835e7i	0.0464280	+	0.142891i
$238$	−1.23206e8	−	8.95146e7i	−0.592398	−	0.430402i
$239$	−7.16510e7	+	5.20575e7i	−0.339492	+	0.246655i	−0.744447	−	0.667681i	$-0.767287\pi$
$239$	−7.16510e7	+	5.20575e7i	−0.339492	+	0.246655i	0.404956	+	0.914336i	$0.367287\pi$
$240$	−3.44160e7	+	1.05922e8i	−0.160702	+	0.494590i
$241$	−1.80384e8			−0.830114			−0.415057	−	0.909796i	$-0.636238\pi$
$241$	−1.80384e8			−0.830114			−0.415057	+	0.909796i	$0.636238\pi$
$242$	8.55099e6	+	6.05821e7i	0.0387849	+	0.274784i
$243$	1.43489e7			0.0641500
$244$	6.67761e7	−	2.05516e8i	0.294277	−	0.905692i
$245$	5.04840e8	−	3.66787e8i	2.19317	−	1.59343i
$246$	2.38552e7	+	1.73318e7i	0.102167	+	0.0742285i
$247$	−5.94014e7	−	1.82819e8i	−0.250817	−	0.771936i
$248$	5.13005e7	+	1.57887e8i	0.213570	+	0.657302i
$249$	1.21793e8	+	8.84874e7i	0.499946	+	0.363232i
$250$	4.18323e7	−	3.03929e7i	0.169325	−	0.123022i
$251$	−1.29024e8	+	3.97094e8i	−0.515005	+	1.58502i	0.268268	+	0.963344i	$0.413549\pi$
$251$	−1.29024e8	+	3.97094e8i	−0.515005	+	1.58502i	−0.783273	+	0.621678i	$0.786451\pi$
$252$	1.42673e8			0.561616
$253$	−4.70400e7	+	1.08748e7i	−0.182619	+	0.0422181i
$254$	1.41914e7			0.0543385
$255$	−7.93751e7	+	2.44291e8i	−0.299774	+	0.922609i
$256$	−6.85589e7	+	4.98110e7i	−0.255402	+	0.185560i
$257$	2.30147e7	+	1.67212e7i	0.0845745	+	0.0614469i	0.629269	−	0.777188i	$-0.283354\pi$
$257$	2.30147e7	+	1.67212e7i	0.0845745	+	0.0614469i	−0.544695	+	0.838635i	$0.683354\pi$
$258$	−1.28892e7	−	3.96690e7i	−0.0467260	−	0.143808i
$259$	−4.36616e7	−	1.34376e8i	−0.156153	−	0.480589i
$260$	1.84076e8	+	1.33739e8i	0.649517	+	0.471902i
$261$	5.90193e7	−	4.28800e7i	0.205472	−	0.149284i
$262$	−2.12287e7	+	6.53351e7i	−0.0729236	+	0.224436i
$263$	1.35098e8			0.457935			0.228968	−	0.973434i	$-0.426465\pi$
$263$	1.35098e8			0.457935			0.228968	+	0.973434i	$0.426465\pi$
$264$	−8.00060e6	+	9.17614e7i	−0.0267614	+	0.306935i
$265$	2.05797e8			0.679325
$266$	5.21193e7	−	1.60407e8i	0.169790	−	0.522561i
$267$	−2.64504e8	+	1.92173e8i	−0.850437	+	0.617879i
$268$	−1.50958e8	−	1.09678e8i	−0.479055	−	0.348054i
$269$	−6.31373e7	−	1.94317e8i	−0.197767	−	0.608664i	−0.999933	−	0.0115629i	$-0.996319\pi$
$269$	−6.31373e7	−	1.94317e8i	−0.197767	−	0.608664i	0.802166	−	0.597101i	$-0.203681\pi$
$270$	6.20443e6	+	1.90953e7i	0.0191835	+	0.0590409i
$271$	−1.01616e8	−	7.38286e7i	−0.310149	−	0.225337i	0.421811	−	0.906684i	$-0.361395\pi$
$271$	−1.01616e8	−	7.38286e7i	−0.310149	−	0.225337i	−0.731961	+	0.681347i	$0.761395\pi$
$272$	−3.00755e8	+	2.18511e8i	−0.906194	+	0.658388i
$273$	8.19289e7	−	2.52151e8i	0.243707	−	0.750052i
$274$	−1.09145e8			−0.320536
$275$	7.94268e7	−	9.14249e7i	0.230305	−	0.265094i
$276$	−3.48875e7			−0.0998822
$277$	3.48101e7	−	1.07135e8i	0.0984071	−	0.302866i	−0.889720	−	0.456508i	$-0.849100\pi$
$277$	3.48101e7	−	1.07135e8i	0.0984071	−	0.302866i	0.988127	+	0.153642i	$0.0491002\pi$
$278$	−1.27098e8	+	9.23423e7i	−0.354799	+	0.257777i
$279$	−1.26695e8	−	9.20491e7i	−0.349256	−	0.253749i
$280$	1.28530e8	+	3.95575e8i	0.349906	+	1.07690i
$281$	1.48625e8	+	4.57421e8i	0.399595	+	1.22983i	0.925325	+	0.379175i	$0.123792\pi$
$281$	1.48625e8	+	4.57421e8i	0.399595	+	1.22983i	−0.525730	+	0.850651i	$0.676208\pi$
$282$	−6.54110e7	−	4.75239e7i	−0.173692	−	0.126194i
$283$	1.24101e8	−	9.01645e7i	0.325478	−	0.236474i	−0.413031	−	0.910717i	$-0.635530\pi$
$283$	1.24101e8	−	9.01645e7i	0.325478	−	0.236474i	0.738510	+	0.674243i	$0.235530\pi$
$284$	7.24486e7	−	2.22974e8i	0.187679	−	0.577617i
$285$	−2.84474e8			−0.727924
$286$	7.56342e7	+	3.20783e7i	0.191178	+	0.0810831i
$287$	−5.76220e8			−1.43881
$288$	−3.12632e7	+	9.62182e7i	−0.0771187	+	0.237347i
$289$	−3.61672e8	+	2.62770e8i	−0.881399	+	0.640374i
$290$	8.25838e7	+	6.00006e7i	0.198839	+	0.144465i
$291$	1.43842e8	+	4.42700e8i	0.342184	+	1.05314i
$292$	1.57062e8	+	4.83387e8i	0.369174	+	1.13620i
$293$	4.14382e8	+	3.01066e8i	0.962418	+	0.699238i	0.953711	−	0.300725i	$-0.0972285\pi$
$293$	4.14382e8	+	3.01066e8i	0.962418	+	0.699238i	0.00870688	+	0.999962i	$0.497228\pi$
$294$	1.31719e8	−	9.56993e7i	0.302296	−	0.219631i
$295$	−5.72111e6	+	1.76078e7i	−0.0129749	+	0.0399326i
$296$	6.59138e7			0.147725
$297$	−4.47734e7	−	7.44653e7i	−0.0991681	−	0.164932i
$298$	5.53065e7			0.121065
$299$	−2.00339e7	+	6.16580e7i	−0.0433427	+	0.133395i
$300$	7.07989e7	−	5.14384e7i	0.151392	−	0.109993i
$301$	6.59427e8	+	4.79102e8i	1.39375	+	1.01262i
$302$	2.33336e6	+	7.18136e6i	0.00487482	+	0.0150031i
$303$	−3.50253e7	−	1.07797e8i	−0.0723324	−	0.222616i
$304$	−3.33084e8	−	2.41999e8i	−0.679980	−	0.494034i
$305$	−4.80771e8	+	3.49301e8i	−0.970261	+	0.704936i
$306$	−2.07099e7	+	6.37386e7i	−0.0413193	+	0.127168i
$307$	−1.33560e8			−0.263447			−0.131724	−	0.991286i	$-0.542051\pi$
$307$	−1.33560e8			−0.263447			−0.131724	+	0.991286i	$0.542051\pi$
$308$	−4.45187e8	−	7.40417e8i	−0.868190	−	1.44394i
$309$	5.76877e8			1.11232
$310$	6.77148e7	−	2.08405e8i	0.129097	−	0.397321i
$311$	9.83028e7	−	7.14212e7i	0.185312	−	0.134637i	−0.491261	−	0.871012i	$-0.663464\pi$
$311$	9.83028e7	−	7.14212e7i	0.185312	−	0.134637i	0.676574	+	0.736375i	$0.263464\pi$
$312$	1.00063e8	+	7.26997e7i	0.186522	+	0.135516i
$313$	−2.55959e8	−	7.87760e8i	−0.471807	−	1.45207i	−0.850215	−	0.526435i	$-0.823528\pi$
$313$	−2.55959e8	−	7.87760e8i	−0.471807	−	1.45207i	0.378408	−	0.925639i	$-0.376472\pi$
$314$	5.39737e6	+	1.66114e7i	0.00983849	+	0.0302798i
$315$	−3.17425e8	−	2.30623e8i	−0.572208	−	0.415733i
$316$	1.08998e8	−	7.91915e7i	0.194318	−	0.141180i
$317$	1.55872e8	−	4.79724e8i	0.274827	−	0.845832i	−0.714438	−	0.699699i	$-0.753317\pi$
$317$	1.55872e8	−	4.79724e8i	0.274827	−	0.845832i	0.989265	−	0.146133i	$-0.0466826\pi$
$318$	5.36948e7			0.0936348
$319$	−4.06691e8	−	1.72487e8i	−0.701450	−	0.297502i
$320$	3.86425e8			0.659234
$321$	−2.39687e7	+	7.37681e7i	−0.0404461	+	0.124480i
$322$	−4.60196e7	+	3.34352e7i	−0.0768152	+	0.0558095i
$323$	−7.68205e8	−	5.58134e8i	−1.26844	−	0.921572i
$324$	−1.94019e7	−	5.97129e7i	−0.0316911	−	0.0975350i
$325$	−5.02533e7	−	1.54664e8i	−0.0812031	−	0.249917i
$326$	−1.09254e8	−	7.93777e7i	−0.174653	−	0.126893i
$327$	5.85862e7	−	4.25654e7i	0.0926570	−	0.0673192i
$328$	8.30674e7	−	2.55655e8i	0.129979	−	0.400033i
$329$	1.58000e9			2.44608
$330$	7.97372e7	−	9.17822e7i	0.122141	−	0.140592i
$331$	3.62665e8			0.549676			0.274838	−	0.961490i	$-0.411376\pi$
$331$	3.62665e8			0.549676			0.274838	+	0.961490i	$0.411376\pi$
$332$	2.03558e8	−	6.26487e8i	0.305285	−	0.939570i
$333$	−5.03031e7	+	3.65474e7i	−0.0746518	+	0.0542377i
$334$	1.11193e8	+	8.07864e7i	0.163292	+	0.118639i
$335$	1.58571e8	+	4.88031e8i	0.230445	+	0.709236i
$336$	−1.75476e8	−	5.40060e8i	−0.252366	−	0.776703i
$337$	1.99086e8	+	1.44645e8i	0.283359	+	0.205872i	0.720381	−	0.693579i	$-0.243967\pi$
$337$	1.99086e8	+	1.44645e8i	0.283359	+	0.205872i	−0.437022	+	0.899451i	$0.643967\pi$
$338$	−7.01331e7	+	5.09547e7i	−0.0987904	+	0.0717754i
$339$	4.03615e7	−	1.24220e8i	0.0562689	−	0.173178i
$340$	1.12394e9			1.55085
$341$	−8.23694e7	+	9.44720e8i	−0.112493	+	1.29022i
$342$	−7.42228e7			−0.100333
$343$	−5.61611e8	+	1.72846e9i	−0.751461	+	2.31276i
$344$	−3.07628e8	+	2.23505e8i	−0.407447	+	0.296028i
$345$	7.76192e7	+	5.63937e7i	0.101766	+	0.0739373i
$346$	1.00419e8	+	3.09058e8i	0.130331	+	0.401119i
$347$	−4.07657e8	−	1.25464e9i	−0.523771	−	1.61200i	−0.766733	−	0.641966i	$-0.778119\pi$
$347$	−4.07657e8	−	1.25464e9i	−0.523771	−	1.61200i	0.242962	−	0.970036i	$-0.421881\pi$
$348$	−2.58248e8	−	1.87628e8i	−0.328481	−	0.238655i
$349$	4.14126e7	−	3.00880e7i	0.0521487	−	0.0378883i	−0.561406	−	0.827541i	$-0.689739\pi$
$349$	4.14126e7	−	3.00880e7i	0.0521487	−	0.0378883i	0.613554	+	0.789653i	$0.289739\pi$
$350$	4.40927e7	−	1.35703e8i	0.0549704	−	0.169181i
$351$	−1.16674e8			−0.144013
$352$	5.96887e8	−	1.37989e8i	0.729445	−	0.168634i
$353$	−6.46661e8			−0.782465			−0.391233	−	0.920292i	$-0.627951\pi$
$353$	−6.46661e8			−0.782465			−0.391233	+	0.920292i	$0.627951\pi$
$354$	−1.49271e6	+	4.59408e6i	−0.00178839	+	0.00550411i
$355$	−5.21612e8	+	3.78973e8i	−0.618797	+	0.449582i
$356$	1.15738e9	+	8.40883e8i	1.35956	+	0.987781i
$357$	−4.04708e8	−	1.24556e9i	−0.470764	−	1.44886i
$358$	−1.34609e8	−	4.14284e8i	−0.155054	−	0.477208i
$359$	−1.16042e9	−	8.43092e8i	−1.32368	−	0.961711i	−0.999879	−	0.0155865i	$-0.995038\pi$
$359$	−1.16042e9	−	8.43092e8i	−1.32368	−	0.961711i	−0.323803	−	0.946125i	$-0.604962\pi$
$360$	1.48081e8	−	1.07587e8i	0.167279	−	0.121535i
$361$	4.87482e7	−	1.50032e8i	0.0545360	−	0.167845i
$362$	−1.66972e8			−0.184996
$363$	−2.46738e8	+	4.64713e8i	−0.270746	+	0.509931i
$364$	−1.16011e9			−1.26079
$365$	4.31929e8	−	1.32934e9i	0.464930	−	1.43091i
$366$	−1.25439e8	+	9.11368e7i	−0.133736	+	0.0971650i
$367$	5.11930e8	+	3.71939e8i	0.540604	+	0.392772i	0.824309	−	0.566140i	$-0.191564\pi$
$367$	5.11930e8	+	3.71939e8i	0.540604	+	0.392772i	−0.283705	+	0.958912i	$0.591564\pi$
$368$	4.29089e7	+	1.32060e8i	0.0448828	+	0.138135i
$369$	7.83595e7	+	2.41166e8i	0.0811894	+	0.249875i
$370$	−7.03875e7	−	5.11395e7i	−0.0722420	−	0.0524869i
$371$	−8.48894e8	+	6.16758e8i	−0.863068	+	0.627056i
$372$	−2.11751e8	+	6.51704e8i	−0.213268	+	0.656372i
$373$	1.73311e8			0.172920			0.0864599	−	0.996255i	$-0.472445\pi$
$373$	1.73311e8			0.172920			0.0864599	+	0.996255i	$0.472445\pi$
$374$	3.95400e8	−	9.14092e7i	0.390829	−	0.0903523i
$375$	4.44671e8			0.435441
$376$	−2.27771e8	+	7.01008e8i	−0.220974	+	0.680088i
$377$	−4.79900e8	+	3.48668e8i	−0.461271	+	0.335133i
$378$	−8.28200e7	−	6.01722e7i	−0.0788704	−	0.0573027i
$379$	3.81941e7	+	1.17549e8i	0.0360379	+	0.110913i	0.967457	−	0.253035i	$-0.0814287\pi$
$379$	3.81941e7	+	1.17549e8i	0.0360379	+	0.110913i	−0.931419	+	0.363948i	$0.881429\pi$
$380$	3.84652e8	+	1.18384e9i	0.359605	+	1.10675i
$381$	9.87343e7	+	7.17347e7i	0.0914599	+	0.0664495i
$382$	−1.12194e8	+	8.15139e7i	−0.102979	+	0.0748187i
$383$	4.40443e7	−	1.35554e8i	0.0400584	−	0.123287i	−0.929027	−	0.370011i	$-0.879354\pi$
$383$	4.40443e7	−	1.35554e8i	0.0400584	−	0.123287i	0.969086	+	0.246724i	$0.0793540\pi$
$384$	5.80443e8			0.523119
$385$	−2.06371e8	+	2.36693e9i	−0.184304	+	2.11384i
$386$	−2.21712e8			−0.196216
$387$	1.10844e8	−	3.41143e8i	0.0972128	−	0.299190i
$388$	1.64780e9	−	1.19720e9i	1.43216	−	1.04053i
$389$	5.37636e8	+	3.90615e8i	0.463089	+	0.336454i	0.794742	−	0.606948i	$-0.207606\pi$
$389$	5.37636e8	+	3.90615e8i	0.463089	+	0.336454i	−0.331653	+	0.943401i	$0.607606\pi$
$390$	−5.04497e7	−	1.55268e8i	−0.0430658	−	0.132543i
$391$	9.89625e7	+	3.04575e8i	0.0837244	+	0.257677i
$392$	−1.20080e9	−	8.72433e8i	−1.00686	−	0.731527i
$393$	−4.77950e8	+	3.47251e8i	−0.397199	+	0.288582i
$394$	1.33562e8	−	4.11061e8i	0.110013	−	0.338587i
$395$	−3.70512e8			−0.302491
$396$	−2.49346e8	+	2.87012e8i	−0.201776	+	0.232256i
$397$	3.05049e8			0.244683			0.122341	−	0.992488i	$-0.460960\pi$
$397$	3.05049e8			0.244683			0.122341	+	0.992488i	$0.460960\pi$
$398$	−2.06536e7	+	6.35651e7i	−0.0164212	+	0.0505392i
$399$	1.17343e9	−	8.52550e8i	0.924812	−	0.671915i
$400$	−2.81787e8	−	2.04730e8i	−0.220146	−	0.159946i
$401$	5.14286e8	+	1.58281e9i	0.398290	+	1.22581i	0.926370	+	0.376616i	$0.122912\pi$
$401$	5.14286e8	+	1.58281e9i	0.398290	+	1.22581i	−0.528079	+	0.849195i	$0.677088\pi$
$402$	4.13731e7	+	1.27333e8i	0.0317634	+	0.0977576i
$403$	1.03018e9	+	7.48472e8i	0.784056	+	0.569650i
$404$	−4.01236e8	+	2.91515e8i	−0.302737	+	0.219951i
$405$	−5.33564e7	+	1.64214e8i	−0.0399111	+	0.122834i
$406$	−5.20469e8			−0.385971
$407$	3.46629e8	+	1.47014e8i	0.254850	+	0.108088i
$408$	6.10969e8			0.445357
$409$	−2.46435e8	+	7.58449e8i	−0.178103	+	0.548144i	−0.999762	−	0.0218354i	$-0.993049\pi$
$409$	−2.46435e8	+	7.58449e8i	−0.178103	+	0.548144i	0.821659	+	0.569980i	$0.193049\pi$
$410$	−2.87057e8	+	2.08559e8i	−0.205695	+	0.149446i
$411$	−7.59356e8	−	5.51705e8i	−0.539510	−	0.391977i
$412$	−7.80025e8	−	2.40067e9i	−0.549501	−	1.69119i
$413$	−2.91701e7	−	8.97765e7i	−0.0203757	−	0.0627101i
$414$	2.02518e7	+	1.47138e7i	0.0140269	+	0.0101912i
$415$	−1.46557e9	+	1.06480e9i	−1.00655	+	0.731305i
$416$	2.54208e8	−	7.82373e8i	0.173126	−	0.532828i
$417$	−1.35103e9			−0.912410
$418$	2.31600e8	+	3.85187e8i	0.155103	+	0.257962i
$419$	1.70754e9			1.13402			0.567010	−	0.823711i	$-0.308100\pi$
$419$	1.70754e9			1.13402			0.567010	+	0.823711i	$0.308100\pi$
$420$	−5.30528e8	+	1.63280e9i	−0.349411	+	1.07538i
$421$	−3.50337e7	+	2.54535e7i	−0.0228823	+	0.0166249i	−0.599168	−	0.800624i	$-0.704502\pi$
$421$	−3.50337e7	+	2.54535e7i	−0.0228823	+	0.0166249i	0.576285	+	0.817249i	$0.304502\pi$
$422$	1.03335e8	+	7.50773e7i	0.0669351	+	0.0486312i
$423$	−2.14862e8	−	6.61278e8i	−0.138028	−	0.424808i
$424$	−1.51265e8	−	4.65545e8i	−0.0963734	−	0.296607i
$425$	−6.49898e8	−	4.72178e8i	−0.410661	−	0.298363i
$426$	−1.36095e8	+	9.88787e7i	−0.0852920	+	0.0619683i
$427$	9.36313e8	−	2.88167e9i	0.582001	−	1.79121i
$428$	3.39395e8			0.209243
$429$	3.64063e8	+	6.05494e8i	0.222626	+	0.370262i
$430$	5.01915e8			0.304432
$431$	6.03722e8	−	1.85807e9i	0.363217	−	1.11787i	−0.587872	−	0.808954i	$-0.700034\pi$
$431$	6.03722e8	−	1.85807e9i	0.363217	−	1.11787i	0.951090	−	0.308915i	$-0.0999658\pi$
$432$	−2.02169e8	+	1.46884e8i	−0.120648	+	0.0876561i
$433$	5.61706e7	+	4.08103e7i	0.0332507	+	0.0241581i	0.604286	−	0.796767i	$-0.293458\pi$
$433$	5.61706e7	+	4.08103e7i	0.0332507	+	0.0241581i	−0.571036	+	0.820925i	$0.693458\pi$
$434$	3.45256e8	+	1.06259e9i	0.202735	+	0.623953i
$435$	2.71271e8	+	8.34887e8i	0.158013	+	0.486313i
$436$	−2.56353e8	−	1.86251e8i	−0.148127	−	0.107621i
$437$	−2.86937e8	+	2.08472e8i	−0.164476	+	0.119499i
$438$	1.12696e8	−	3.46841e8i	0.0640837	−	0.197229i
$439$	−2.35341e9			−1.32761			−0.663806	−	0.747904i	$-0.731060\pi$
$439$	−2.35341e9			−1.32761			−0.663806	+	0.747904i	$0.731060\pi$
$440$	−1.02040e9	−	4.32776e8i	−0.571066	−	0.242203i
$441$	1.40015e9			0.777391
$442$	1.68397e8	−	5.18273e8i	0.0927592	−	0.285483i
$443$	1.11895e9	−	8.12964e8i	0.611501	−	0.444282i	−0.238441	−	0.971157i	$-0.576637\pi$
$443$	1.11895e9	−	8.12964e8i	0.611501	−	0.444282i	0.849943	+	0.526875i	$0.176637\pi$
$444$	2.20109e8	+	1.59919e8i	0.119343	+	0.0867079i
$445$	−1.21574e9	−	3.74167e9i	−0.654005	−	2.01282i
$446$	2.43128e8	+	7.48272e8i	0.129767	+	0.399381i
$447$	3.84785e8	+	2.79563e8i	0.203771	+	0.148048i
$448$	−1.59397e9	+	1.15809e9i	−0.837544	+	0.608511i
$449$	8.42753e8	−	2.59373e9i	0.439378	−	1.35227i	−0.449156	−	0.893453i	$-0.648275\pi$
$449$	8.42753e8	−	2.59373e9i	0.439378	−	1.35227i	0.888533	−	0.458812i	$-0.151725\pi$
$450$	−6.27921e7			−0.0324834
$451$	1.00705e9	−	1.15917e9i	0.516931	−	0.595018i
$452$	−5.71516e8			−0.291101
$453$	−2.00663e7	+	6.17577e7i	−0.0101420	+	0.0312138i
$454$	−2.37847e8	+	1.72806e8i	−0.119290	+	0.0866690i
$455$	2.58105e9	+	1.87525e9i	1.28457	+	0.933294i
$456$	2.09095e8	+	6.43527e8i	0.103268	+	0.317826i
$457$	−4.84270e8	−	1.49043e9i	−0.237345	−	0.730473i	−0.996802	−	0.0799153i	$-0.974535\pi$
$457$	−4.84270e8	−	1.49043e9i	−0.237345	−	0.730473i	0.759456	−	0.650558i	$-0.225465\pi$
$458$	1.74223e8	+	1.26581e8i	0.0847378	+	0.0615657i
$459$	−4.66271e8	+	3.38766e8i	−0.225058	+	0.163514i
$460$	1.29729e8	−	3.99265e8i	0.0621419	−	0.191253i
$461$	2.51125e9			1.19381			0.596907	−	0.802311i	$-0.296396\pi$
$461$	2.51125e9			1.19381			0.596907	+	0.802311i	$0.296396\pi$
$462$	−5.38447e7	+	6.17561e8i	−0.0254036	+	0.291362i
$463$	2.26078e9			1.05858			0.529292	−	0.848440i	$-0.322458\pi$
$463$	2.26078e9			1.05858			0.529292	+	0.848440i	$0.322458\pi$
$464$	−3.92606e8	+	1.20832e9i	−0.182450	+	0.561523i
$465$	1.52456e9	−	1.10765e9i	0.703166	−	0.510880i
$466$	−3.30898e8	−	2.40412e8i	−0.151476	−	0.110054i
$467$	8.05456e8	+	2.47894e9i	0.365959	+	1.12631i	0.949378	+	0.314135i	$0.101715\pi$
$467$	8.05456e8	+	2.47894e9i	0.365959	+	1.12631i	−0.583419	+	0.812171i	$0.698285\pi$
$468$	1.57761e8	+	4.85540e8i	0.0711443	+	0.218960i
$469$	−2.11669e9	−	1.53786e9i	−0.947440	−	0.688356i
$470$	7.87111e8	−	5.71870e8i	0.349698	−	0.254071i
$471$	−4.64159e7	+	1.42853e8i	−0.0204689	+	0.0629967i
$472$	4.40368e7			0.0192761
$473$	−2.11627e9	+	4.89241e8i	−0.919510	+	0.212574i
$474$	−9.66710e7			−0.0416939
$475$	2.74923e8	−	8.46126e8i	0.117702	−	0.362249i
$476$	−4.63618e9	+	3.36838e9i	−1.97032	+	1.43152i
$477$	3.73572e8	+	2.71416e8i	0.157601	+	0.114504i
$478$	−8.59263e7	−	2.64454e8i	−0.0359856	−	0.110752i
$479$	−1.14085e9	−	3.51119e9i	−0.474303	−	1.45975i	−0.846896	−	0.531759i	$-0.821531\pi$
$479$	−1.14085e9	−	3.51119e9i	−0.474303	−	1.45975i	0.372593	−	0.927995i	$-0.378469\pi$
$480$	−9.84903e8	−	7.15574e8i	−0.406490	−	0.295332i
$481$	4.09027e8	−	2.97175e8i	0.167588	−	0.121760i
$482$	1.75008e8	−	5.38620e8i	0.0711859	−	0.219088i
$483$	−4.89181e8			−0.197540
$484$	2.26753e9	+	3.98437e8i	0.909063	+	0.159735i
$485$	−5.60129e9			−2.22942
$486$	−1.39213e7	+	4.28454e7i	−0.00550115	+	0.0169308i
$487$	3.70014e8	−	2.68831e8i	0.145167	−	0.105470i	−0.512831	−	0.858489i	$-0.671403\pi$
$487$	3.70014e8	−	2.68831e8i	0.145167	−	0.105470i	0.657998	+	0.753019i	$0.271403\pi$
$488$	1.14355e9	+	8.30839e8i	0.445437	+	0.323629i
$489$	−3.58878e8	−	1.10451e9i	−0.138792	−	0.427159i
$490$	6.05421e8	+	1.86329e9i	0.232472	+	0.715476i
$491$	2.17075e9	+	1.57714e9i	0.827609	+	0.601293i	0.918882	−	0.394533i	$-0.129094\pi$
$491$	2.17075e9	+	1.57714e9i	0.827609	+	0.601293i	−0.0912728	+	0.995826i	$0.529094\pi$
$492$	8.97656e8	−	6.52185e8i	0.339807	−	0.246884i
$493$	−9.05484e8	+	2.78679e9i	−0.340343	+	1.04747i
$494$	6.03523e8			0.225242
$495$	1.01870e9	−	2.35504e8i	0.377508	−	0.0872729i
$496$	2.72734e9			1.00358
$497$	1.01585e9	−	3.12647e9i	0.371179	−	1.14237i
$498$	−3.82384e8	+	2.77818e8i	−0.138739	+	0.100799i
$499$	1.51024e9	+	1.09725e9i	0.544119	+	0.395325i	0.825612	−	0.564238i	$-0.190830\pi$
$499$	1.51024e9	+	1.09725e9i	0.544119	+	0.395325i	−0.281494	+	0.959563i	$0.590830\pi$
$500$	−6.01262e8	−	1.85050e9i	−0.215114	−	0.662053i
$501$	3.65247e8	+	1.12411e9i	0.129764	+	0.399373i
$502$	−1.06053e9	−	7.70522e8i	−0.374163	−	0.271845i
$503$	−3.59844e9	+	2.61442e9i	−1.26074	+	0.915983i	−0.998794	−	0.0490985i	$-0.984365\pi$
$503$	−3.59844e9	+	2.61442e9i	−1.26074	+	0.915983i	−0.261949	+	0.965082i	$0.584365\pi$
$504$	−2.88392e8	+	8.87579e8i	−0.100340	+	0.308816i
$505$	1.36391e9			0.471265
$506$	1.31665e7	−	1.51011e8i	0.00451798	−	0.0518181i
$507$	−7.45504e8			−0.254052
$508$	1.65020e8	−	5.07878e8i	0.0558487	−	0.171885i
$509$	4.92883e8	−	3.58100e8i	0.165665	−	0.120363i	−0.501864	−	0.864947i	$-0.667352\pi$
$509$	4.92883e8	−	3.58100e8i	0.165665	−	0.120363i	0.667529	+	0.744584i	$0.267352\pi$
$510$	−6.52437e8	−	4.74023e8i	−0.217793	−	0.158236i
$511$	2.20227e9	+	6.77789e9i	0.730126	+	2.24710i
$512$	−9.32549e8	−	2.87009e9i	−0.307063	−	0.945041i
$513$	−5.16392e8	−	3.75181e8i	−0.168876	−	0.122696i
$514$	−7.22578e7	+	5.24983e7i	−0.0234700	+	0.0170520i
$515$	−2.14511e9	+	6.60198e9i	−0.692030	+	2.12985i
$516$	−1.56954e9			−0.502920
$517$	−2.76133e9	+	3.17846e9i	−0.878824	+	1.01158i
$518$	4.43605e8			0.140230
$519$	−8.63574e8	+	2.65781e9i	−0.271153	+	0.834522i
$520$	−1.20408e9	+	8.74818e8i	−0.375530	+	0.272839i
$521$	4.19028e9	+	3.04442e9i	1.29811	+	0.943132i	0.999935	−	0.0113792i	$-0.00362220\pi$
$521$	4.19028e9	+	3.04442e9i	1.29811	+	0.943132i	0.298175	+	0.954511i	$0.403622\pi$
$522$	7.07780e7	+	2.17832e8i	0.0217797	+	0.0670310i
$523$	−1.04981e9	−	3.23098e9i	−0.320889	−	0.987594i	−0.973262	−	0.229697i	$-0.926227\pi$
$523$	−1.04981e9	−	3.23098e9i	−0.320889	−	0.987594i	0.652373	−	0.757898i	$-0.273773\pi$
$524$	2.09134e9	+	1.51945e9i	0.634988	+	0.461346i
$525$	9.92719e8	−	7.21253e8i	0.299412	−	0.217535i
$526$	−1.31072e8	+	4.03399e8i	−0.0392700	+	0.120861i
$527$	6.29017e9			1.87208
$528$	1.39311e9	+	5.90850e8i	0.411875	+	0.174686i
$529$	−3.28521e9			−0.964868
$530$	−1.99664e8	+	6.14503e8i	−0.0582551	+	0.179291i
$531$	−3.36074e7	+	2.44172e7i	−0.00974100	+	0.00707725i
$532$	−5.13454e9	−	3.73046e9i	−1.47846	−	1.07417i
$533$	−6.37159e8	−	1.96097e9i	−0.182265	−	0.560953i
$534$	−3.17202e8	−	9.76247e8i	−0.0901449	−	0.277438i
$535$	−7.55100e8	−	5.48613e8i	−0.213190	−	0.154891i
$536$	9.87453e8	−	7.17426e8i	0.276974	−	0.201234i
$537$	1.15760e9	−	3.56273e9i	0.322588	−	0.992825i
$538$	6.41480e8			0.177601
$539$	−4.36893e9	−	7.26623e9i	−1.20175	−	1.99870i
$540$	7.55522e8			0.206476
$541$	−1.06044e9	+	3.26371e9i	−0.287937	+	0.886179i	0.697566	+	0.716521i	$0.254266\pi$
$541$	−1.06044e9	+	3.26371e9i	−0.287937	+	0.886179i	−0.985503	+	0.169659i	$0.945734\pi$
$542$	3.19038e8	−	2.31795e8i	0.0860687	−	0.0625326i
$543$	−1.16167e9	−	8.44006e8i	−0.311376	−	0.226228i
$544$	−1.25573e9	−	3.86473e9i	−0.334425	−	1.02925i
$545$	2.69281e8	+	8.28760e8i	0.0712553	+	0.219301i
$546$	6.73429e8	+	4.89274e8i	0.177059	+	0.128641i
$547$	6.18756e9	−	4.49553e9i	1.61646	−	1.17442i	0.782281	−	0.622926i	$-0.214056\pi$
$547$	6.18756e9	−	4.49553e9i	1.61646	−	1.17442i	0.834176	−	0.551498i	$-0.185944\pi$
$548$	−1.26915e9	+	3.90605e9i	−0.329444	+	1.01392i
$549$	−1.33340e9			−0.343919
$550$	1.95932e8	+	3.25867e8i	0.0502154	+	0.0835162i
$551$	−3.24518e9			−0.826435
$552$	7.05199e7	−	2.17038e8i	0.0178453	−	0.0549223i
$553$	1.52833e9	−	1.11040e9i	0.384308	−	0.279216i
$554$	2.86128e8	+	2.07884e8i	0.0714950	+	0.0519442i
$555$	−2.31209e8	−	7.11588e8i	−0.0574089	−	0.176687i
$556$	1.82680e9	+	5.62232e9i	0.450744	+	1.38725i
$557$	−1.99332e9	−	1.44823e9i	−0.488747	−	0.355096i	0.315955	−	0.948774i	$-0.397675\pi$
$557$	−1.99332e9	−	1.44823e9i	−0.488747	−	0.355096i	−0.804702	+	0.593678i	$0.797675\pi$
$558$	3.97775e8	−	2.89001e8i	0.0969210	−	0.0704173i
$559$	−9.01298e8	+	2.77391e9i	−0.218236	+	0.671662i
$560$	6.83315e9			1.64423
$561$	3.21298e9	+	1.36270e9i	0.768313	+	0.325860i
$562$	−1.51004e9			−0.358849
$563$	1.48486e9	−	4.56994e9i	0.350677	−	1.07927i	−0.607797	−	0.794093i	$-0.707946\pi$
$563$	1.48486e9	−	4.56994e9i	0.350677	−	1.07927i	0.958474	−	0.285181i	$-0.0920535\pi$
$564$	−2.46138e9	+	1.78830e9i	−0.577699	+	0.419723i
$565$	1.27153e9	+	9.23823e8i	0.296591	+	0.215486i
$566$	1.48826e8	+	4.58039e8i	0.0345002	+	0.106181i
$567$	−2.72047e8	−	8.37275e8i	−0.0626763	−	0.192898i
$568$	1.24069e9	+	9.01418e8i	0.284083	+	0.206399i
$569$	−1.54739e9	+	1.12425e9i	−0.352134	+	0.255840i	−0.749764	−	0.661706i	$-0.769833\pi$
$569$	−1.54739e9	+	1.12425e9i	−0.352134	+	0.255840i	0.397630	+	0.917546i	$0.369833\pi$
$570$	2.75997e8	−	8.49432e8i	0.0624227	−	0.192117i
$571$	−5.11420e9			−1.14961			−0.574806	−	0.818290i	$-0.694922\pi$
$571$	−5.11420e9			−1.14961			−0.574806	+	0.818290i	$0.694922\pi$
$572$	2.02749e9	−	2.33377e9i	0.452974	−	0.521400i
$573$	−1.19261e9			−0.264823
$574$	5.59050e8	−	1.72058e9i	0.123384	−	0.379737i
$575$	−2.42748e8	+	1.76366e8i	−0.0532497	+	0.0386882i
$576$	7.01457e8	+	5.09638e8i	0.152940	+	0.111118i
$577$	2.23072e9	+	6.86544e9i	0.483425	+	1.48783i	0.834249	+	0.551388i	$0.185902\pi$
$577$	2.23072e9	+	6.86544e9i	0.483425	+	1.48783i	−0.350824	+	0.936442i	$0.614098\pi$
$578$	−4.33730e8	−	1.33488e9i	−0.0934268	−	0.287538i
$579$	−1.54252e9	−	1.12071e9i	−0.330260	−	0.239948i
$580$	3.10758e9	−	2.25779e9i	0.661339	−	0.480491i
$581$	2.85423e9	−	8.78441e9i	0.603771	−	1.85821i
$582$	−1.46145e9			−0.307293
$583$	2.42874e8	−	2.78560e9i	0.0507624	−	0.582209i
$584$	−3.32466e9			−0.690721
$585$	4.33853e8	−	1.33526e9i	0.0895977	−	0.275753i
$586$	−1.30101e9	+	9.45237e8i	−0.267078	+	0.194044i
$587$	−4.52369e9	−	3.28666e9i	−0.923124	−	0.670688i	0.0211760	−	0.999776i	$-0.493259\pi$
$587$	−4.52369e9	−	3.28666e9i	−0.923124	−	0.670688i	−0.944300	+	0.329087i	$0.893259\pi$
$588$	−1.89321e9	−	5.82672e9i	−0.384042	−	1.18196i
$589$	2.15271e9	+	6.62537e9i	0.434093	+	1.33600i
$590$	−4.70257e7	−	3.41662e7i	−0.00942656	−	0.00684880i
$591$	3.00706e9	−	2.18476e9i	0.599220	−	0.435358i
$592$	3.34625e8	−	1.02987e9i	0.0662875	−	0.204012i
$593$	−6.64072e9			−1.30775			−0.653873	−	0.756604i	$-0.726857\pi$
$593$	−6.64072e9			−1.30775			−0.653873	+	0.756604i	$0.726857\pi$
$594$	2.65790e8	−	6.14457e7i	0.0520339	−	0.0120293i
$595$	1.57596e10			3.06715
$596$	6.43111e8	−	1.97929e9i	0.124430	−	0.382955i
$597$	−4.65002e8	+	3.37843e8i	−0.0894426	+	0.0649838i
$598$	−1.64672e8	−	1.19641e8i	−0.0314895	−	0.0228785i
$599$	1.54085e9	+	4.74226e9i	0.292933	+	0.901554i	0.983908	+	0.178676i	$0.0571813\pi$
$599$	1.54085e9	+	4.74226e9i	0.292933	+	0.901554i	−0.690975	+	0.722878i	$0.742819\pi$
$600$	1.76893e8	+	5.44421e8i	0.0334335	+	0.102898i
$601$	−1.61188e9	−	1.17110e9i	−0.302881	−	0.220056i	0.425955	−	0.904744i	$-0.359938\pi$
$601$	−1.61188e9	−	1.17110e9i	−0.302881	−	0.220056i	−0.728836	+	0.684689i	$0.759938\pi$
$602$	−2.07036e9	+	1.50421e9i	−0.386775	+	0.281008i
$603$	−3.55797e8	+	1.09503e9i	−0.0660833	+	0.203383i
$604$	2.84137e8			0.0524685
$605$	−4.40084e9	−	4.55179e9i	−0.807964	−	0.835677i
$606$	3.55860e8			0.0649568
$607$	−3.16323e8	+	9.73541e8i	−0.0574076	+	0.176683i	−0.975649	−	0.219340i	$-0.929610\pi$
$607$	−3.16323e8	+	9.73541e8i	−0.0574076	+	0.176683i	0.918241	+	0.396022i	$0.129610\pi$
$608$	3.64092e9	−	2.64528e9i	0.656975	−	0.477320i
$609$	−3.62107e9	−	2.63086e9i	−0.649646	−	0.471995i
$610$	−5.76557e8	−	1.77446e9i	−0.102846	−	0.316528i
$611$	1.74709e9	+	5.37700e9i	0.309865	+	0.953665i
$612$	2.04024e9	+	1.48232e9i	0.359792	+	0.261404i
$613$	−8.13267e9	+	5.90873e9i	−1.42601	+	1.03605i	−0.435263	+	0.900304i	$0.643344\pi$
$613$	−8.13267e9	+	5.90873e9i	−1.42601	+	1.03605i	−0.990743	+	0.135750i	$0.956656\pi$
$614$	1.29580e8	−	3.98808e8i	0.0225918	−	0.0695303i
$615$	−3.05137e9			−0.528970
$616$	5.50607e9	−	1.27290e9i	0.949094	−	0.219413i
$617$	−1.40682e9			−0.241124			−0.120562	−	0.992706i	$-0.538470\pi$
$617$	−1.40682e9			−0.241124			−0.120562	+	0.992706i	$0.538470\pi$
$618$	−5.59686e8	+	1.72254e9i	−0.0953861	+	0.293568i
$619$	5.53308e9	−	4.02002e9i	0.937669	−	0.681256i	−0.0101897	−	0.999948i	$-0.503244\pi$
$619$	5.53308e9	−	4.02002e9i	0.937669	−	0.681256i	0.947858	+	0.318692i	$0.103244\pi$
$620$	−6.67093e9	−	4.84672e9i	−1.12413	−	0.816726i
$621$	6.65231e7	+	2.04737e8i	0.0111468	+	0.0343065i
$622$	1.17888e8	+	3.62822e8i	0.0196428	+	0.0604544i
$623$	1.62284e10	+	1.17906e10i	2.68885	+	1.95356i
$624$	1.64388e9	−	1.19435e9i	0.270847	−	0.196782i
$625$	−2.31583e9	+	7.12739e9i	−0.379426	+	1.16775i
$626$	2.60056e9			0.423698
$627$	−3.35727e8	+	3.85056e9i	−0.0543939	+	0.623861i
$628$	6.57245e8			0.105893
$629$	7.71759e8	−	2.37523e9i	0.123653	−	0.380564i
$630$	9.96598e8	−	7.24071e8i	0.158792	−	0.115369i
$631$	−8.59712e9	−	6.24617e9i	−1.36223	−	0.989718i	−0.998300	−	0.0582913i	$-0.981435\pi$
$631$	−8.59712e9	−	6.24617e9i	−1.36223	−	0.989718i	−0.363930	−	0.931426i	$-0.618565\pi$
$632$	2.72334e8	+	8.38158e8i	0.0429133	+	0.132074i
$633$	3.39435e8	+	1.04467e9i	0.0531917	+	0.163707i
$634$	1.28122e9	+	9.30857e8i	0.199669	+	0.145068i
$635$	−1.18810e9	+	8.63205e8i	−0.184139	+	0.133785i
$636$	6.24370e8	−	1.92161e9i	0.0962370	−	0.296187i
$637$	−1.13849e10			−1.74519
$638$	9.09614e8	−	1.04702e9i	0.138671	−	0.159618i
$639$	−1.44667e9			−0.219339
$640$	−2.15837e9	+	6.64279e9i	−0.325459	+	1.00166i
$641$	−3.55150e9	+	2.58032e9i	−0.532610	+	0.386964i	−0.821333	−	0.570449i	$-0.806769\pi$
$641$	−3.55150e9	+	2.58032e9i	−0.532610	+	0.386964i	0.288723	+	0.957413i	$0.406769\pi$
$642$	−1.97015e8	−	1.43140e8i	−0.0293850	−	0.0213495i
$643$	−2.61934e9	−	8.06150e9i	−0.388556	−	1.19585i	−0.933868	−	0.357619i	$-0.883589\pi$
$643$	−2.61934e9	−	8.06150e9i	−0.388556	−	1.19585i	0.545312	−	0.838233i	$-0.316411\pi$
$644$	6.61447e8	+	2.03572e9i	0.0975876	+	0.300344i
$645$	3.49198e9	+	2.53708e9i	0.512405	+	0.372284i
$646$	2.41188e9	−	1.75234e9i	0.352000	−	0.255743i
$647$	−3.71726e8	+	1.14405e9i	−0.0539582	+	0.166066i	−0.974404	−	0.224804i	$-0.927826\pi$
$647$	−3.71726e8	+	1.14405e9i	−0.0539582	+	0.166066i	0.920446	+	0.390870i	$0.127826\pi$
$648$	4.10697e8			0.0592937
$649$	2.31582e8	+	9.82195e7i	0.0332543	+	0.0141040i
$650$	5.10577e8			0.0729230
$651$	−2.96911e9	+	9.13798e9i	−0.421787	+	1.29813i
$652$	−4.11117e9	+	2.98694e9i	−0.580896	+	0.422046i
$653$	2.67321e9	+	1.94220e9i	0.375696	+	0.272959i	0.759569	−	0.650427i	$-0.225410\pi$
$653$	2.67321e9	+	1.94220e9i	0.375696	+	0.272959i	−0.383873	+	0.923386i	$0.625410\pi$
$654$	7.02586e7	+	2.16234e8i	0.00982149	+	0.0302274i
$655$	−2.19681e9	−	6.76108e9i	−0.305455	−	0.940094i
$656$	−3.57277e9	−	2.59577e9i	−0.494130	−	0.359007i
$657$	2.53727e9	−	1.84343e9i	0.349050	−	0.253600i
$658$	−1.53292e9	+	4.71783e9i	−0.209763	+	0.645583i
$659$	−8.72843e9			−1.18806			−0.594028	−	0.804444i	$-0.702463\pi$
$659$	−8.72843e9			−1.18806			−0.594028	+	0.804444i	$0.702463\pi$
$660$	−2.35748e9	−	3.92086e9i	−0.319186	−	0.530858i
$661$	−1.07586e10			−1.44895			−0.724473	−	0.689303i	$-0.757917\pi$
$661$	−1.07586e10			−1.44895			−0.724473	+	0.689303i	$0.757917\pi$
$662$	−3.51858e8	+	1.08291e9i	−0.0471372	+	0.145073i
$663$	3.79136e9	−	2.75458e9i	0.505239	−	0.367078i
$664$	3.48597e9	+	2.53270e9i	0.462099	+	0.335734i
$665$	5.39347e9	+	1.65994e10i	0.711201	+	2.18885i
$666$	−6.03253e7	−	1.85662e8i	−0.00791297	−	0.0243536i
$667$	8.85454e8	+	6.43320e8i	0.115538	+	0.0839434i
$668$	4.18413e9	−	3.03995e9i	0.543109	−	0.394592i
$669$	−2.09084e9	+	6.43493e9i	−0.269978	+	0.830907i
$670$	−1.61109e9			−0.206947
$671$	4.16064e9	+	6.91981e9i	0.531657	+	0.884230i
$672$	6.20718e9			0.789045
$673$	−1.27663e9	+	3.92906e9i	−0.161440	+	0.496863i	−0.998756	−	0.0498567i	$-0.984124\pi$
$673$	−1.27663e9	+	3.92906e9i	−0.161440	+	0.496863i	0.837316	+	0.546719i	$0.184124\pi$
$674$	−6.25058e8	+	4.54131e8i	−0.0786341	+	0.0571310i
$675$	−4.36865e8	−	3.17401e8i	−0.0546744	−	0.0397233i
$676$	1.00803e9	+	3.10241e9i	0.125505	+	0.386266i
$677$	1.06938e9	+	3.29120e9i	0.132455	+	0.407656i	0.995186	−	0.0980086i	$-0.0312473\pi$
$677$	1.06938e9	+	3.29120e9i	0.132455	+	0.407656i	−0.862730	+	0.505665i	$0.831247\pi$
$678$	3.31758e8	+	2.41037e8i	0.0408807	+	0.0297015i
$679$	2.31049e10	−	1.67867e10i	2.83243	−	2.05788i
$680$	−2.27189e9	+	6.99215e9i	−0.277080	+	0.852765i
$681$	−2.52828e9			−0.306768
$682$	−2.74099e9	−	1.16252e9i	−0.330874	−	0.140332i
$683$	−1.30563e10			−1.56801			−0.784006	−	0.620753i	$-0.786827\pi$
$683$	−1.30563e10			−1.56801			−0.784006	+	0.620753i	$0.786827\pi$
$684$	−8.63072e8	+	2.65626e9i	−0.103122	+	0.317376i
$685$	9.13757e9	−	6.63883e9i	1.08621	−	0.789177i
$686$	−4.61626e9	−	3.35391e9i	−0.545954	−	0.396659i
$687$	5.72289e8	+	1.76133e9i	0.0673391	+	0.207248i
$688$	1.93041e9	+	5.94120e9i	0.225991	+	0.695528i
$689$	−3.03760e9	−	2.20695e9i	−0.353805	−	0.257054i
$690$	−2.43696e8	+	1.77056e8i	−0.0282408	+	0.0205181i
$691$	1.58038e9	−	4.86390e9i	0.182216	−	0.560804i	−0.817673	−	0.575683i	$-0.804736\pi$
$691$	1.58038e9	−	4.86390e9i	0.182216	−	0.560804i	0.999889	+	0.0148789i	$0.00473629\pi$
$692$	1.22281e10			1.40278
$693$	−3.49626e9	+	4.02440e9i	−0.399059	+	0.459340i
$694$	4.14182e9			0.470363
$695$	5.02382e9	−	1.54617e10i	0.567658	−	1.74707i
$696$	1.68926e9	−	1.22732e9i	0.189917	−	0.137983i
$697$	−8.24003e9	−	5.98673e9i	−0.921751	−	0.669692i
$698$	4.96634e7	+	1.52848e8i	0.00552768	+	0.0170124i
$699$	−1.08694e9	−	3.34524e9i	−0.120374	−	0.370474i
$700$	−4.34380e9	−	3.15595e9i	−0.478659	−	0.347766i
$701$	8.72402e9	−	6.33837e9i	0.956541	−	0.694968i	0.00419630	−	0.999991i	$-0.498664\pi$
$701$	8.72402e9	−	6.33837e9i	0.956541	−	0.694968i	0.952345	+	0.305023i	$0.0986643\pi$
$702$	1.13198e8	−	3.48386e8i	0.0123497	−	0.0380085i
$703$	2.76592e9			0.300259
$704$	4.56046e8	−	5.23053e9i	0.0492611	−	0.564991i
$705$	8.36686e9			0.899292
$706$	6.27391e8	−	1.93091e9i	0.0670999	−	0.206512i
$707$	−5.62601e9	+	4.08753e9i	−0.598732	+	0.435004i
$708$	1.47054e8	+	1.06841e8i	0.0155726	+	0.0113142i
$709$	−1.29005e9	−	3.97036e9i	−0.135939	−	0.418377i	0.859796	−	0.510638i	$-0.170591\pi$
$709$	−1.29005e9	−	3.97036e9i	−0.135939	−	0.418377i	−0.995735	+	0.0922607i	$0.970591\pi$
$710$	−6.25535e8	−	1.92520e9i	−0.0655915	−	0.201870i
$711$	−6.72571e8	−	4.88652e8i	−0.0701770	−	0.0509866i
$712$	−7.57067e9	+	5.50041e9i	−0.786057	+	0.571104i
$713$	7.26030e8	−	2.23449e9i	0.0750138	−	0.230869i
$714$	4.11187e9			0.422762
$715$	−8.28326e9	+	1.91493e9i	−0.847481	+	0.195922i
$716$	−1.63915e10			−1.66887
$717$	7.38942e8	−	2.27423e9i	0.0748675	−	0.230419i
$718$	3.64329e9	−	2.64700e9i	0.367331	−	0.266882i
$719$	2.85832e9	+	2.07669e9i	0.286787	+	0.208363i	0.721872	−	0.692026i	$-0.243282\pi$
$719$	2.85832e9	+	2.07669e9i	0.286787	+	0.208363i	−0.435085	+	0.900389i	$0.643282\pi$
$720$	−9.29232e8	−	2.85988e9i	−0.0927813	−	0.285551i
$721$	−1.09373e10	−	3.36614e10i	−1.08676	−	3.34471i
$722$	4.00694e8	+	2.91122e8i	0.0396217	+	0.0287869i
$723$	3.94020e9	−	2.86272e9i	0.387735	−	0.281706i
$724$	−1.94157e9	+	5.97553e9i	−0.190137	+	0.585183i
$725$	−2.74541e9			−0.267562
$726$	−1.14823e9	−	1.18762e9i	−0.111366	−	0.115186i
$727$	3.02429e9			0.291913			0.145957	−	0.989291i	$-0.453374\pi$
$727$	3.02429e9			0.291913			0.145957	+	0.989291i	$0.453374\pi$
$728$	2.34498e9	−	7.21711e9i	0.225258	−	0.693272i
$729$	−3.13430e8	+	2.27720e8i	−0.0299636	+	0.0217698i
$730$	3.55032e9	+	2.57946e9i	0.337783	+	0.245413i
$731$	4.45219e9	+	1.37024e10i	0.421563	+	1.29744i
$732$	1.80295e9	+	5.54892e9i	0.169901	+	0.522902i
$733$	1.65283e10	+	1.20085e10i	1.55012	+	1.12623i	0.943565	+	0.331187i	$0.107449\pi$
$733$	1.65283e10	+	1.20085e10i	1.55012	+	1.12623i	0.606556	+	0.795041i	$0.292551\pi$
$734$	−1.60727e9	+	1.16775e9i	−0.150022	+	0.108997i
$735$	−5.20645e9	+	1.60238e10i	−0.483656	+	1.48854i
$736$	−1.51783e9			−0.140330
$737$	6.79299e9	−	1.57041e9i	0.625064	−	0.144503i
$738$	−7.96138e8			−0.0729107
$739$	−2.43716e9	+	7.50079e9i	−0.222141	+	0.683678i	0.776429	+	0.630205i	$0.217029\pi$
$739$	−2.43716e9	+	7.50079e9i	−0.222141	+	0.683678i	−0.998569	+	0.0534732i	$0.982971\pi$
$740$	−2.64864e9	+	1.92435e9i	−0.240277	+	0.174571i
$741$	4.19890e9	+	3.05068e9i	0.379116	+	0.275444i
$742$	−1.01802e9	−	3.13315e9i	−0.0914838	−	0.281558i
$743$	−1.64126e8	−	5.05128e8i	−0.0146797	−	0.0451795i	0.943448	−	0.331520i	$-0.107561\pi$
$743$	−1.64126e8	−	5.05128e8i	−0.0146797	−	0.0451795i	−0.958128	+	0.286340i	$0.907561\pi$
$744$	−3.62628e9	−	2.63464e9i	−0.322816	−	0.234540i
$745$	−4.63024e9	+	3.36407e9i	−0.410257	+	0.298069i
$746$	−1.68146e8	+	5.17501e8i	−0.0148286	+	0.0456379i
$747$	−4.06468e9			−0.356783
$748$	1.32644e9	−	1.52134e10i	0.115887	−	1.32914i
$749$	4.75888e9			0.413827
$750$	−4.31420e8	+	1.32777e9i	−0.0373410	+	0.114924i
$751$	−2.05008e9	+	1.48947e9i	−0.176616	+	0.128319i	−0.672581	−	0.740023i	$-0.734814\pi$
$751$	−2.05008e9	+	1.48947e9i	−0.176616	+	0.128319i	0.495965	+	0.868343i	$0.334814\pi$
$752$	9.79655e9	+	7.11761e9i	0.840061	+	0.610340i
$753$	−3.48364e9	−	1.07215e10i	−0.297338	−	0.915113i
$754$	−5.75512e8	−	1.77124e9i	−0.0488939	−	0.150480i
$755$	−6.32160e8	−	4.59291e8i	−0.0534580	−	0.0388395i
$756$	−3.11647e9	+	2.26425e9i	−0.262323	+	0.190589i
$757$	3.47005e9	−	1.06797e10i	0.290737	−	0.894796i	−0.693884	−	0.720087i	$-0.744102\pi$
$757$	3.47005e9	−	1.06797e10i	0.290737	−	0.894796i	0.984620	−	0.174708i	$-0.0558983\pi$
$758$	−3.88055e8			−0.0323632
$759$	8.54932e8	−	9.84077e8i	0.0709717	−	0.0816927i
$760$	−8.14227e9			−0.672818
$761$	3.28297e9	−	1.01039e10i	0.270035	−	0.831083i	−0.720455	−	0.693501i	$-0.756067\pi$
$761$	3.28297e9	−	1.01039e10i	0.270035	−	0.831083i	0.990490	−	0.137581i	$-0.0439328\pi$
$762$	−3.09990e8	+	2.25221e8i	−0.0253808	+	0.0184402i
$763$	−3.59450e9	−	2.61156e9i	−0.292956	−	0.212845i
$764$	1.61259e9	+	4.96303e9i	0.130827	+	0.402643i
$765$	−2.14313e9	−	6.59587e9i	−0.173074	−	0.532668i
$766$	3.62030e8	+	2.63030e8i	0.0291034	+	0.0211448i
$767$	2.73269e8	−	1.98542e8i	0.0218679	−	0.0158880i
$768$	7.07054e8	−	2.17609e9i	0.0563233	−	0.173345i
$769$	6.21266e9			0.492646			0.246323	−	0.969188i	$-0.420778\pi$
$769$	6.21266e9			0.492646			0.246323	+	0.969188i	$0.420778\pi$
$770$	−6.86737e9	−	2.91262e9i	−0.542092	−	0.229914i
$771$	−7.68089e8			−0.0603561
$772$	−2.57810e9	+	7.93457e9i	−0.201669	+	0.620673i
$773$	1.41673e10	−	1.02932e10i	1.10321	−	0.801531i	0.121631	−	0.992575i	$-0.461187\pi$
$773$	1.41673e10	−	1.02932e10i	1.10321	−	0.801531i	0.981581	+	0.191044i	$0.0611875\pi$
$774$	9.11101e8	+	6.61954e8i	0.0706274	+	0.0513138i
$775$	1.82118e9	+	5.60503e9i	0.140539	+	0.432536i
$776$	4.11707e9	+	1.26710e10i	0.316280	+	0.973411i
$777$	3.08630e9	+	2.24233e9i	0.236029	+	0.171485i
$778$	−1.68798e9	+	1.22639e9i	−0.128511	+	0.0933684i
$779$	3.48574e9	−	1.07280e10i	0.264188	−	0.813087i
$780$	−6.14332e9			−0.463524
$781$	4.51408e9	+	7.50764e9i	0.339071	+	0.563930i
$782$	−1.00547e9			−0.0751872
$783$	−6.08671e8	+	1.87330e9i	−0.0453123	+	0.139457i
$784$	−1.97274e10	+	1.43328e10i	−1.46206	+	1.06225i
$785$	−1.46227e9	−	1.06240e9i	−0.107891	−	0.0783870i
$786$	−5.73174e8	−	1.76405e9i	−0.0421024	−	0.129578i
$787$	4.18761e9	+	1.28881e10i	0.306235	+	0.942494i	0.979213	+	0.202832i	$0.0650146\pi$
$787$	4.18761e9	+	1.28881e10i	0.306235	+	0.942494i	−0.672978	+	0.739662i	$0.734985\pi$
$788$	−1.31579e10	−	9.55974e9i	−0.957951	−	0.695992i
$789$	−2.95101e9	+	2.14403e9i	−0.213895	+	0.155404i
$790$	3.59471e8	−	1.10634e9i	0.0259399	−	0.0798349i
$791$	−8.01361e9			−0.575719
$792$	−1.28151e9	−	2.13136e9i	−0.0916609	−	0.152447i
$793$	1.08422e10			0.772075
$794$	−2.95959e8	+	9.10868e8i	−0.0209826	+	0.0645779i
$795$	−4.49531e9	+	3.26603e9i	−0.317303	+	0.230534i
$796$	2.03469e9	+	1.47829e9i	0.142989	+	0.103887i
$797$	2.65278e9	+	8.16441e9i	0.185608	+	0.571243i	0.999958	−	0.00913077i	$-0.00290645\pi$
$797$	2.65278e9	+	8.16441e9i	0.185608	+	0.571243i	−0.814350	+	0.580374i	$0.802906\pi$
$798$	1.40722e9	+	4.33098e9i	0.0980285	+	0.301701i
$799$	2.25942e10	+	1.64156e10i	1.56705	+	1.13853i
$800$	3.08020e9	−	2.23790e9i	0.212698	−	0.154534i
$801$	2.72785e9	−	8.39545e9i	0.187545	−	0.577205i
$802$	−5.22519e9			−0.357677
$803$	−1.74838e10	−	7.41532e9i	−1.19161	−	0.505388i
$804$	5.03806e9			0.341875
$805$	1.81902e9	−	5.59836e9i	0.122900	−	0.378247i
$806$	−3.23440e9	+	2.34993e9i	−0.217581	+	0.158082i
$807$	4.46298e9	+	3.24255e9i	0.298929	+	0.217185i
$808$	−1.00250e9	−	3.08538e9i	−0.0668567	−	0.205764i
$809$	6.07041e8	+	1.86828e9i	0.0403086	+	0.124057i	0.969186	−	0.246330i	$-0.0792248\pi$
$809$	6.07041e8	+	1.86828e9i	0.0403086	+	0.124057i	−0.928877	+	0.370388i	$0.879225\pi$
$810$	−4.38572e8	−	3.18641e8i	−0.0289963	−	0.0210671i
$811$	−1.93051e9	+	1.40260e9i	−0.127087	+	0.0923338i	−0.649513	−	0.760351i	$-0.725027\pi$
$811$	−1.93051e9	+	1.40260e9i	−0.127087	+	0.0923338i	0.522426	+	0.852685i	$0.325027\pi$
$812$	−6.05209e9	+	1.86264e10i	−0.396697	+	1.22091i
$813$	3.39133e9			0.221336
$814$	−7.75279e8	+	8.92392e8i	−0.0503817	+	0.0579923i
$815$	1.39749e10			0.904270
$816$	3.10171e9	−	9.54607e9i	0.199841	−	0.615048i
$817$	−1.29089e10	+	9.37888e9i	−0.828157	+	0.601692i
$818$	−2.02562e9	−	1.47170e9i	−0.129396	−	0.0940117i
$819$	2.21208e9	+	6.80808e9i	0.140704	+	0.433043i
$820$	4.12591e9	+	1.26982e10i	0.261319	+	0.804258i
$821$	3.54550e8	+	2.57595e8i	0.0223602	+	0.0162456i	0.598909	−	0.800817i	$-0.295601\pi$
$821$	3.54550e8	+	2.57595e8i	0.0223602	+	0.0162456i	−0.576549	+	0.817063i	$0.695601\pi$
$822$	2.38410e9	−	1.73215e9i	0.149718	−	0.108776i
$823$	4.61394e8	−	1.42003e9i	0.0288518	−	0.0887967i	−0.935594	−	0.353078i	$-0.885135\pi$
$823$	4.61394e8	−	1.42003e9i	0.0288518	−	0.0887967i	0.964446	+	0.264282i	$0.0851349\pi$
$824$	1.65115e10			1.02811
$825$	−2.84024e8	+	3.25756e9i	−0.0176103	+	0.201978i
$826$	2.96371e8			0.0182981
$827$	−8.49493e8	+	2.61447e9i	−0.0522264	+	0.160736i	−0.973768	−	0.227543i	$-0.926931\pi$
$827$	−8.49493e8	+	2.61447e9i	−0.0522264	+	0.160736i	0.921541	+	0.388280i	$0.126931\pi$
$828$	7.62063e8	−	5.53671e8i	0.0466536	−	0.0338958i
$829$	2.17074e9	+	1.57714e9i	0.132333	+	0.0961453i	0.651982	−	0.758234i	$-0.273938\pi$
$829$	2.17074e9	+	1.57714e9i	0.132333	+	0.0961453i	−0.519650	+	0.854379i	$0.673938\pi$
$830$	−1.75756e9	−	5.40921e9i	−0.106693	−	0.328368i
$831$	9.39873e8	+	2.89263e9i	0.0568153	+	0.174860i
$832$	−5.70371e9	−	4.14399e9i	−0.343341	−	0.249452i
$833$	−4.54982e10	+	3.30563e10i	−2.72732	+	1.98151i
$834$	1.31077e9	−	4.03415e9i	0.0782432	−	0.240808i
$835$	−1.42229e10			−0.845447
$836$	1.64780e10	−	3.80941e9i	0.975402	−	0.225495i
$837$	4.22829e9			0.249244
$838$	−1.65665e9	+	5.09866e9i	−0.0972473	+	0.299296i
$839$	−3.49133e9	+	2.53660e9i	−0.204091	+	0.148281i	−0.685136	−	0.728415i	$-0.740257\pi$
$839$	−3.49133e9	+	2.53660e9i	−0.204091	+	0.148281i	0.481045	+	0.876696i	$0.340257\pi$
$840$	−9.08539e9	−	6.60092e9i	−0.528891	−	0.384262i
$841$	−2.23593e9	−	6.88150e9i	−0.129620	−	0.398930i
$842$	−4.20136e7	−	1.29305e8i	−0.00242548	−	0.00746487i
$843$	−1.05058e10	−	7.63294e9i	−0.603997	−	0.438829i
$844$	3.88844e9	−	2.82511e9i	0.222626	−	0.161747i
$845$	2.77215e9	−	8.53182e9i	0.158059	−	0.486455i
$846$	2.18302e9			0.123954
$847$	3.17945e10	+	5.58675e9i	1.79788	+	0.315913i
$848$	−8.04183e9			−0.452865
$849$	−1.27986e9	+	3.93901e9i	−0.0717771	+	0.220907i
$850$	2.04044e9	−	1.48247e9i	0.113962	−	0.0827979i
$851$	−7.54687e8	−	5.48312e8i	−0.0419772	−	0.0304982i
$852$	1.95611e9	+	6.02030e9i	0.108357	+	0.333487i
$853$	6.11604e9	+	1.88232e10i	0.337403	+	1.03842i	0.965526	+	0.260306i	$0.0838234\pi$
$853$	6.11604e9	+	1.88232e10i	0.337403	+	1.03842i	−0.628123	+	0.778114i	$0.716177\pi$
$854$	7.69619e9	+	5.59161e9i	0.422837	+	0.307209i
$855$	6.21390e9	−	4.51466e9i	0.340003	−	0.247027i
$856$	−6.86036e8	+	2.11140e9i	−0.0373843	+	0.115057i
$857$	2.86789e9			0.155643			0.0778215	−	0.996967i	$-0.475204\pi$
$857$	2.86789e9			0.155643			0.0778215	+	0.996967i	$0.475204\pi$
$858$	−2.16120e9	+	4.99630e8i	−0.116813	+	0.0270049i
$859$	−3.50044e10			−1.88428			−0.942142	−	0.335215i	$-0.891191\pi$
$859$	−3.50044e10			−1.88428			−0.942142	+	0.335215i	$0.891191\pi$
$860$	5.83633e9	−	1.79624e10i	0.312893	−	0.962985i
$861$	1.25866e10	−	9.14473e9i	0.672046	−	0.488270i
$862$	4.96240e9	+	3.60540e9i	0.263886	+	0.191724i
$863$	−1.00024e10	−	3.07842e10i	−0.529744	−	1.63038i	−0.754740	−	0.656024i	$-0.772237\pi$
$863$	−1.00024e10	−	3.07842e10i	−0.529744	−	1.63038i	0.224997	−	0.974360i	$-0.427763\pi$
$864$	−8.44106e8	−	2.59789e9i	−0.0445245	−	0.137032i
$865$	−2.72057e10	−	1.97661e10i	−1.42924	−	1.03840i
$866$	−1.76355e8	+	1.28130e8i	−0.00922732	+	0.00670404i
$867$	3.72995e9	−	1.14796e10i	0.194373	−	0.598220i
$868$	4.20423e10			2.18207
$869$	−4.37266e8	+	5.01514e9i	−0.0226035	+	0.259247i
$870$	−2.75614e9			−0.141900
$871$	2.89307e9	−	8.90395e9i	0.148353	−	0.456582i
$872$	1.67686e9	−	1.21831e9i	0.0856426	−	0.0622230i
$873$	−1.01677e10	−	7.38730e9i	−0.517220	−	0.375782i
$874$	−3.44105e8	−	1.05905e9i	−0.0174342	−	0.0536568i
$875$	−8.43071e9	−	2.59470e10i	−0.425438	−	1.30936i
$876$	−1.11022e10	−	8.06623e9i	−0.558014	−	0.405421i
$877$	−1.10173e10	+	8.00455e9i	−0.551540	+	0.400718i	−0.828353	−	0.560206i	$-0.810722\pi$
$877$	−1.10173e10	+	8.00455e9i	−0.551540	+	0.400718i	0.276813	+	0.960924i	$0.410722\pi$
$878$	2.28328e9	−	7.02721e9i	0.113849	−	0.350390i
$879$	−1.38295e10			−0.686824
$880$	−1.19422e10	+	1.37461e10i	−0.590736	+	0.679972i
$881$	2.28881e10			1.12770			0.563851	−	0.825877i	$-0.309319\pi$
$881$	2.28881e10			1.12770			0.563851	+	0.825877i	$0.309319\pi$
$882$	−1.35843e9	+	4.18081e9i	−0.0666647	+	0.205173i
$883$	2.60704e10	−	1.89412e10i	1.27434	−	0.925861i	0.274972	−	0.961452i	$-0.411331\pi$
$883$	2.60704e10	−	1.89412e10i	1.27434	−	0.925861i	0.999366	+	0.0355911i	$0.0113314\pi$
$884$	−1.65897e10	−	1.20531e10i	−0.807708	−	0.586835i
$885$	−1.54470e8	−	4.75410e8i	−0.00749105	−	0.0230551i
$886$	1.34188e9	+	4.12989e9i	0.0648181	+	0.199490i
$887$	−9.95569e9	−	7.23324e9i	−0.479004	−	0.348017i	0.321936	−	0.946761i	$-0.395666\pi$
$887$	−9.95569e9	−	7.23324e9i	−0.479004	−	0.348017i	−0.800940	+	0.598745i	$0.795666\pi$
$888$	−1.43979e9	+	1.04607e9i	−0.0690005	+	0.0501318i
$889$	2.31385e9	−	7.12131e9i	0.110454	−	0.339941i
$890$	1.23520e10			0.587318
$891$	2.15978e9	+	9.16016e8i	0.102291	+	0.0433842i
$892$	2.96061e10			1.39670
$893$	−9.55791e9	+	2.94162e10i	−0.449141	+	1.38231i
$894$	−1.20809e9	+	8.77726e8i	−0.0565479	+	0.0410844i
$895$	3.64686e10	+	2.64960e10i	1.70035	+	1.23538i
$896$	−1.10049e10	−	3.38695e10i	−0.511101	−	1.57301i
$897$	−5.40915e8	−	1.66477e9i	−0.0250239	−	0.0770157i
$898$	6.92715e9	+	5.03287e9i	0.319218	+	0.231926i
$899$	1.73916e10	−	1.26357e10i	0.798327	−	0.580019i
$900$	−7.30155e8	+	2.24719e9i	−0.0333861	+	0.102752i
$901$	−1.85472e10			−0.844776
$902$	2.48422e9	+	4.13165e9i	0.112711	+	0.187457i
$903$	−2.20076e10			−0.994639
$904$	1.15523e9	−	3.55544e9i	0.0520092	−	0.160068i
$905$	1.39788e10	−	1.01562e10i	0.626902	−	0.455471i
$906$	−1.64938e8	−	1.19835e8i	−0.00736839	−	0.00535345i
$907$	−1.71130e9	−	5.26685e9i	−0.0761556	−	0.234383i	0.905731	−	0.423853i	$-0.139323\pi$
$907$	−1.71130e9	−	5.26685e9i	−0.0761556	−	0.234383i	−0.981886	+	0.189471i	$0.939323\pi$
$908$	3.41862e9	+	1.05214e10i	0.151548	+	0.466417i
$909$	2.47583e9	+	1.79880e9i	0.109332	+	0.0794344i
$910$	−8.10357e9	+	5.88759e9i	−0.356477	+	0.258996i
$911$	−4.88623e9	+	1.50383e10i	−0.214121	+	0.658998i	0.785094	+	0.619377i	$0.212615\pi$
$911$	−4.88623e9	+	1.50383e10i	−0.214121	+	0.658998i	−0.999215	+	0.0396203i	$0.987385\pi$
$912$	1.11163e10			0.485263
$913$	1.26832e10	+	2.10941e10i	0.551544	+	0.917305i
$914$	4.92022e9			0.213144
$915$	4.95823e9	−	1.52599e10i	0.213970	−	0.658532i
$916$	6.55593e9	−	4.76316e9i	0.281838	−	0.204767i
$917$	2.93241e10	+	2.13052e10i	1.25583	+	0.912417i
$918$	−5.59168e8	−	1.72094e9i	−0.0238557	−	0.0734204i
$919$	−3.87977e9	−	1.19407e10i	−0.164893	−	0.507488i	0.834136	−	0.551559i	$-0.185967\pi$
$919$	−3.87977e9	−	1.19407e10i	−0.164893	−	0.507488i	−0.999028	+	0.0440718i	$0.985967\pi$
$920$	2.22163e9	+	1.61411e9i	0.0940620	+	0.0683401i
$921$	2.91742e9	−	2.11963e9i	0.123052	−	0.0894029i
$922$	−2.43642e9	+	7.49852e9i	−0.102375	+	0.315077i
$923$	1.17632e10			0.492401
$924$	2.14750e10	+	9.10806e9i	0.895531	+	0.379816i
$925$	2.33996e9			0.0972103
$926$	−2.19341e9	+	6.75063e9i	−0.0907783	+	0.279387i
$927$	−1.26010e10	+	9.15515e9i	−0.519548	+	0.377473i
$928$	−1.12354e10	−	8.16303e9i	−0.461501	−	0.335300i
$929$	−1.87577e9	−	5.77302e9i	−0.0767581	−	0.236237i	0.905314	−	0.424743i	$-0.139636\pi$
$929$	−1.87577e9	−	5.77302e9i	−0.0767581	−	0.236237i	−0.982072	+	0.188506i	$0.939636\pi$
$930$	1.82830e9	+	5.62693e9i	0.0745345	+	0.229394i
$931$	−5.03889e10	−	3.66097e10i	−2.04650	−	1.48687i
$932$	−1.24515e10	+	9.04655e9i	−0.503810	+	0.366039i
$933$	−1.01380e9	+	3.12017e9i	−0.0408666	+	0.125775i
$934$	−8.18350e9			−0.328643
$935$	−2.75427e10	+	3.17033e10i	−1.10196	+	1.26842i
$936$	−3.33947e9			−0.133110
$937$	−1.30611e8	+	4.01979e8i	−0.00518670	+	0.0159630i	−0.953616	−	0.301025i	$-0.902671\pi$
$937$	−1.30611e8	+	4.01979e8i	−0.00518670	+	0.0159630i	0.948430	+	0.316988i	$0.102671\pi$
$938$	6.64563e9	−	4.82833e9i	0.262922	−	0.191024i
$939$	1.80929e10	+	1.31453e10i	0.713148	+	0.518132i
$940$	−1.13133e10	−	3.48187e10i	−0.444263	−	1.36730i
$941$	−1.11412e10	−	3.42892e10i	−0.435883	−	1.34151i	−0.892179	−	0.451682i	$-0.850824\pi$
$941$	−1.11412e10	−	3.42892e10i	−0.435883	−	1.34151i	0.456296	−	0.889828i	$-0.349176\pi$
$942$	−3.81524e8	−	2.77193e8i	−0.0148711	−	0.0108045i
$943$	−3.07779e9	+	2.23614e9i	−0.119522	+	0.0868377i
$944$	2.23562e8	−	6.88052e8i	0.00864958	−	0.0266207i
$945$	1.05937e10			0.408353
$946$	5.92344e8	−	6.79378e9i	0.0227486	−	0.260911i
$947$	−2.42390e10			−0.927449			−0.463724	−	0.885980i	$-0.653487\pi$
$947$	−2.42390e10			−0.927449			−0.463724	+	0.885980i	$0.653487\pi$
$948$	−1.12410e9	+	3.45963e9i	−0.0428526	+	0.131887i
$949$	−2.06311e10	+	1.49894e10i	−0.783594	+	0.569315i
$950$	2.25978e9	+	1.64182e9i	0.0855131	+	0.0621289i
$951$	4.20854e9	+	1.29525e10i	0.158672	+	0.488341i
$952$	−1.15836e10	−	3.56508e10i	−0.435126	−	1.33918i
$953$	1.67375e10	+	1.21605e10i	0.626418	+	0.455119i	0.855157	−	0.518368i	$-0.173460\pi$
$953$	1.67375e10	+	1.21605e10i	0.626418	+	0.455119i	−0.228740	+	0.973488i	$0.573460\pi$
$954$	−1.17288e9	+	8.52148e8i	−0.0437355	+	0.0317757i
$955$	4.43471e9	−	1.36486e10i	0.164761	−	0.507081i
$956$	−1.04634e10			−0.387319
$957$	1.16209e10	−	2.68654e9i	0.428597	−	0.0990837i
$958$	1.15912e10			0.425939
$959$	−1.77956e10	+	5.47693e10i	−0.651551	+	2.00527i
$960$	−8.44085e9	+	6.13264e9i	−0.307919	+	0.223716i
$961$	−1.50758e10	−	1.09532e10i	−0.547959	−	0.398116i
$962$	4.90519e8	+	1.50966e9i	0.0177641	+	0.0546722i
$963$	−6.47155e8	−	1.99174e9i	−0.0233516	−	0.0718688i
$964$	−1.72410e10	−	1.25263e10i	−0.619858	−	0.450353i
$965$	1.85616e10	−	1.34858e10i	0.664922	−	0.483094i
$966$	4.74604e8	−	1.46068e9i	0.0169399	−	0.0521357i
$967$	4.91299e9			0.174724			0.0873621	−	0.996177i	$-0.472156\pi$
$967$	4.91299e9			0.174724			0.0873621	+	0.996177i	$0.472156\pi$
$968$	−7.06218e9	+	1.33011e10i	−0.250250	+	0.471328i
$969$	2.56379e10			0.905211
$970$	5.43438e9	−	1.67253e10i	0.191183	−	0.588400i
$971$	−3.30304e10	+	2.39980e10i	−1.15783	+	0.841216i	−0.989503	−	0.144515i	$-0.953838\pi$
$971$	−3.30304e10	+	2.39980e10i	−1.15783	+	0.841216i	−0.168332	+	0.985730i	$0.553838\pi$
$972$	1.37146e9	+	9.96424e8i	0.0479017	+	0.0348027i
$973$	2.56148e10	+	7.88344e10i	0.891450	+	2.74360i
$974$	4.43734e8	+	1.36567e9i	0.0153874	+	0.0473577i
$975$	3.55225e9	+	2.58086e9i	0.122740	+	0.0891761i
$976$	1.87869e10	−	1.36495e10i	0.646816	−	0.469939i
$977$	9.98728e9	−	3.07377e10i	0.342623	−	1.05448i	−0.620221	−	0.784427i	$-0.712957\pi$
$977$	9.98728e9	−	3.07377e10i	0.342623	−	1.05448i	0.962844	−	0.270058i	$-0.0870428\pi$
$978$	3.64623e9			0.124640
$979$	−5.20809e10	+	1.20401e10i	−1.77394	+	0.410102i
$980$	7.37229e10			2.50214
$981$	−6.04204e8	+	1.85955e9i	−0.0204335	+	0.0628878i
$982$	−6.81538e9	+	4.95166e9i	−0.229668	+	0.166863i
$983$	2.77678e10	+	2.01745e10i	0.932402	+	0.677430i	0.946580	−	0.322469i	$-0.104513\pi$
$983$	2.77678e10	+	2.01745e10i	0.932402	+	0.677430i	−0.0141774	+	0.999899i	$0.504513\pi$
$984$	2.24282e9	+	6.90269e9i	0.0750432	+	0.230959i
$985$	1.38214e10	+	4.25379e10i	0.460813	+	1.41824i
$986$	−7.44278e9	−	5.40750e9i	−0.247267	−	0.179650i
$987$	−3.45127e10	+	2.50749e10i	−1.14253	+	0.830098i
$988$	7.01784e9	−	2.15987e10i	0.231502	−	0.712489i
$989$	5.38147e9			0.176894
$990$	−2.85134e8	+	3.27028e9i	−0.00933953	+	0.107118i
$991$	−1.89205e10			−0.617554			−0.308777	−	0.951134i	$-0.599920\pi$
$991$	−1.89205e10			−0.617554			−0.308777	+	0.951134i	$0.599920\pi$
$992$	−9.21253e9	+	2.83533e10i	−0.299632	+	0.922172i
$993$	−7.92185e9	+	5.75556e9i	−0.256746	+	0.186537i
$994$	8.34997e9	+	6.06661e9i	0.269670	+	0.195927i
$995$	−2.13729e9	−	6.57791e9i	−0.0687834	−	0.211693i
$996$	5.49607e9	+	1.69152e10i	0.176256	+	0.542461i
$997$	1.82403e10	+	1.32523e10i	0.582906	+	0.423506i	0.839770	−	0.542942i	$-0.182690\pi$
$997$	1.82403e10	+	1.32523e10i	0.582906	+	0.423506i	−0.256865	+	0.966447i	$0.582690\pi$
$998$	−4.74160e9	+	3.44497e9i	−0.150997	+	0.109706i
$999$	5.18780e8	−	1.59664e9i	0.0164628	−	0.0506674i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.8.e.b.31.4	yes	28
3.2	odd	2		99.8.f.b.64.4		28
11.4	even	5		363.8.a.o.1.7		14
11.5	even	5	inner	33.8.e.b.16.4	✓	28
11.7	odd	10		363.8.a.r.1.8		14
33.5	odd	10		99.8.f.b.82.4		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.8.e.b.16.4	✓	28	11.5	even	5	inner
33.8.e.b.31.4	yes	28	1.1	even	1	trivial
99.8.f.b.64.4		28	3.2	odd	2
99.8.f.b.82.4		28	33.5	odd	10
363.8.a.o.1.7		14	11.4	even	5
363.8.a.r.1.8		14	11.7	odd	10

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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	33.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.970201 + 2.98597i) q^{2} +(-21.8435 + 15.8702i) q^{3} +(95.5794 + 69.4425i) q^{4} +(-100.399 - 308.998i) q^{5} +(-26.1954 - 80.6212i) q^{6} +(1340.18 + 973.701i) q^{7} +(-625.207 + 454.240i) q^{8} +(225.273 - 693.320i) q^{9} +1020.07 q^{10} +(-4300.99 + 994.308i) q^{11} -3189.85 q^{12} +(-1831.75 + 5637.55i) q^{13} +(-4207.69 + 3057.07i) q^{14} +(7096.93 + 5156.22i) q^{15} +(3923.27 + 12074.6i) q^{16} +(9048.40 + 27848.1i) q^{17} +(1851.67 + 1345.32i) q^{18} +(-26235.4 + 19061.1i) q^{19} +(11861.5 - 36505.8i) q^{20} -44727.1 q^{21} +(1203.85 - 13807.3i) q^{22} +10937.0 q^{23} +(6447.81 - 19844.3i) q^{24} +(-22195.0 + 16125.6i) q^{25} +(-15056.4 - 10939.1i) q^{26} +(6082.38 + 18719.6i) q^{27} +(60477.8 + 186132. i) q^{28} +(80959.3 + 58820.4i) q^{29} +(-22281.8 + 16188.6i) q^{30} +(66382.8 - 204305. i) q^{31} -138779. q^{32} +(78168.6 - 89976.7i) q^{33} -91932.4 q^{34} +(166318. - 511873. i) q^{35} +(69677.4 - 50623.6i) q^{36} +(-69002.9 - 50133.6i) q^{37} +(-31462.4 - 96831.3i) q^{38} +(-49457.3 - 152214. i) q^{39} +(203129. + 147582. i) q^{40} +(-281410. + 204456. i) q^{41} +(43394.3 - 133554. i) q^{42} +492042. q^{43} +(-480134. - 203636. i) q^{44} -236852. q^{45} +(-10611.1 + 32657.6i) q^{46} +(771628. - 560620. i) q^{47} +(-277324. - 201487. i) q^{48} +(593512. + 1.82664e6i) q^{49} +(-26617.1 - 81918.9i) q^{50} +(-639603. - 464699. i) q^{51} +(-566563. + 411632. i) q^{52} +(-195736. + 602415. i) q^{53} -61797.5 q^{54} +(739056. + 1.22917e6i) q^{55} -1.28019e6 q^{56} +(270568. - 832723. i) q^{57} +(-254183. + 184675. i) q^{58} +(-46100.6 - 33494.1i) q^{59} +(320259. + 985657. i) q^{60} +(-565216. - 1.73955e6i) q^{61} +(545645. + 396434. i) q^{62} +(976994. - 709828. i) q^{63} +(-367535. + 1.13116e6i) q^{64} +1.92590e6 q^{65} +(192829. + 320705. i) q^{66} -1.57940e6 q^{67} +(-1.06900e6 + 3.29005e6i) q^{68} +(-238902. + 173573. i) q^{69} +(1.36708e6 + 993239. i) q^{70} +(-613230. - 1.88733e6i) q^{71} +(174091. + 535797. i) q^{72} +(3.48048e6 + 2.52872e6i) q^{73} +(216644. - 157401. i) q^{74} +(228899. - 704479. i) q^{75} -3.83122e6 q^{76} +(-6.73228e6 - 2.85532e6i) q^{77} +502490. q^{78} +(352400. - 1.08457e6i) q^{79} +(3.33712e6 - 2.42456e6i) q^{80} +(-429945. - 312373. i) q^{81} +(-337476. - 1.03865e6i) q^{82} +(-1.72299e6 - 5.30280e6i) q^{83} +(-4.27499e6 - 3.10596e6i) q^{84} +(7.69654e6 - 5.59187e6i) q^{85} +(-477380. + 1.46922e6i) q^{86} -2.70192e6 q^{87} +(2.23736e6 - 2.57533e6i) q^{88} +1.21091e7 q^{89} +(229794. - 707232. i) q^{90} +(-7.94417e6 + 5.77178e6i) q^{91} +(1.04535e6 + 759494. i) q^{92} +(1.79234e6 + 5.51624e6i) q^{93} +(925362. + 2.84797e6i) q^{94} +(8.52387e6 + 6.19295e6i) q^{95} +(3.03141e6 - 2.20245e6i) q^{96} +(5.32748e6 - 1.63963e7i) q^{97} -6.03012e6 q^{98} +(-279525. + 3.20596e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 6 q^{2} - 189 q^{3} + 160 q^{4} + 773 q^{5} - 162 q^{6} + 1289 q^{7} + 2956 q^{8} - 5103 q^{9} - 10640 q^{10} + 13209 q^{11} + 45630 q^{12} + 13499 q^{13} - 3318 q^{14} - 22734 q^{15} - 113196 q^{16}+ \cdots - 6579954 q^{99}+O(q^{100}) \) 28 * q - 6 * q^2 - 189 * q^3 + 160 * q^4 + 773 * q^5 - 162 * q^6 + 1289 * q^7 + 2956 * q^8 - 5103 * q^9 - 10640 * q^10 + 13209 * q^11 + 45630 * q^12 + 13499 * q^13 - 3318 * q^14 - 22734 * q^15 - 113196 * q^16 + 30296 * q^17 + 21141 * q^18 - 6858 * q^19 + 76725 * q^20 - 177012 * q^21 - 48859 * q^22 - 166984 * q^23 + 44442 * q^24 + 99832 * q^25 + 340424 * q^26 - 137781 * q^27 + 657387 * q^28 + 192014 * q^29 - 184410 * q^30 + 396068 * q^31 - 303498 * q^32 + 168453 * q^33 - 1229124 * q^34 - 725859 * q^35 + 116640 * q^36 + 811053 * q^37 + 1548798 * q^38 + 364473 * q^39 - 1427263 * q^40 + 1041497 * q^41 + 300024 * q^42 - 5265288 * q^43 - 5341085 * q^44 + 100602 * q^45 + 1198651 * q^46 + 1667505 * q^47 + 730593 * q^48 + 2968140 * q^49 + 11247432 * q^50 + 340767 * q^51 + 2325763 * q^52 - 1625736 * q^53 - 905418 * q^54 - 8338690 * q^55 - 18201906 * q^56 + 1546479 * q^57 + 14965553 * q^58 - 2587454 * q^59 + 2071575 * q^60 + 5801619 * q^61 + 15631121 * q^62 + 939681 * q^63 - 3732846 * q^64 - 15368174 * q^65 - 235683 * q^66 - 7141262 * q^67 + 17394545 * q^68 - 5063553 * q^69 - 4329200 * q^70 + 3569199 * q^71 + 1199934 * q^72 + 125008 * q^73 - 13691530 * q^74 - 11794221 * q^75 - 19690428 * q^76 - 6038739 * q^77 + 12684438 * q^78 + 17075485 * q^79 + 26606436 * q^80 - 3720087 * q^81 + 19886007 * q^82 - 4645575 * q^83 + 1074519 * q^84 + 12002715 * q^85 - 12296287 * q^86 - 12259512 * q^87 - 50905990 * q^88 + 9601664 * q^89 + 8857350 * q^90 - 14129477 * q^91 - 90776021 * q^92 + 10693836 * q^93 + 1047679 * q^94 + 58935661 * q^95 + 26156304 * q^96 - 22170261 * q^97 + 140532178 * q^98 - 6579954 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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