LMFDB - Embedded newform 76.8.f.a.27.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,8,Mod(27,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("76.27");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	76.f (of order $6$, 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:	$23.7412619368$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			27.2
Character	$\chi$	$=$	76.27
Dual form			76.8.f.a.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11.2846 - 0.811527i) q^{2} +(-19.0858 + 33.0575i) q^{3} +(126.683 + 18.3155i) q^{4} +(115.282 - 199.674i) q^{5} +(242.202 - 357.551i) q^{6} +1657.40i q^{7} +(-1414.70 - 309.489i) q^{8} +(364.967 + 632.141i) q^{9} +O(q^{10})$	\(q+(-11.2846 - 0.811527i) q^{2} +(-19.0858 + 33.0575i) q^{3} +(126.683 + 18.3155i) q^{4} +(115.282 - 199.674i) q^{5} +(242.202 - 357.551i) q^{6} +1657.40i q^{7} +(-1414.70 - 309.489i) q^{8} +(364.967 + 632.141i) q^{9} +(-1462.95 + 2159.68i) q^{10} -1726.43i q^{11} +(-3023.30 + 3838.26i) q^{12} +(9299.59 - 5369.12i) q^{13} +(1345.03 - 18703.0i) q^{14} +(4400.49 + 7621.87i) q^{15} +(15713.1 + 4640.51i) q^{16} +(14969.6 - 25928.1i) q^{17} +(-3605.49 - 7429.62i) q^{18} +(-8873.23 + 28550.6i) q^{19} +(18261.4 - 23183.9i) q^{20} +(-54789.5 - 31632.8i) q^{21} +(-1401.04 + 19482.0i) q^{22} +(31671.6 - 18285.6i) q^{23} +(37231.5 - 40859.6i) q^{24} +(12482.6 + 21620.6i) q^{25} +(-109299. + 53041.3i) q^{26} -111344. q^{27} +(-30356.1 + 209964. i) q^{28} +(-93745.0 + 54123.7i) q^{29} +(-43472.3 - 89580.6i) q^{30} +165306. q^{31} +(-173549. - 65117.7i) q^{32} +(57071.4 + 32950.2i) q^{33} +(-189967. + 280439. i) q^{34} +(330940. + 191068. i) q^{35} +(34657.1 + 86766.0i) q^{36} +339343. i q^{37} +(123300. - 314980. i) q^{38} +409895. i q^{39} +(-224886. + 246800. i) q^{40} +(237227. + 136963. i) q^{41} +(592605. + 401425. i) q^{42} +(147828. + 85348.7i) q^{43} +(31620.3 - 218709. i) q^{44} +168296. q^{45} +(-372239. + 180643. i) q^{46} +(-228774. + 132083. i) q^{47} +(-453300. + 430868. i) q^{48} -1.92343e6 q^{49} +(-123315. - 254109. i) q^{50} +(571412. + 989715. i) q^{51} +(1.27644e6 - 509849. i) q^{52} +(-1.57195e6 + 907568. i) q^{53} +(1.25647e6 + 90358.6i) q^{54} +(-344723. - 199026. i) q^{55} +(512947. - 2.34472e6i) q^{56} +(-774460. - 838237. i) q^{57} +(1.10179e6 - 534686. i) q^{58} +(84177.8 - 145800. i) q^{59} +(417868. + 1.04616e6i) q^{60} +(1.10995e6 + 1.92250e6i) q^{61} +(-1.86540e6 - 134150. i) q^{62} +(-1.04771e6 + 604896. i) q^{63} +(1.90559e6 + 875665. i) q^{64} -2.47585e6i q^{65} +(-617286. - 418144. i) q^{66} +(998568. + 1.72957e6i) q^{67} +(2.37128e6 - 3.01047e6i) q^{68} +1.39598e6i q^{69} +(-3.57946e6 - 2.42469e6i) q^{70} +(-1.87870e6 + 3.25401e6i) q^{71} +(-320677. - 1.00724e6i) q^{72} +(201940. - 349771. i) q^{73} +(275386. - 3.82934e6i) q^{74} -952963. q^{75} +(-1.64700e6 + 3.45436e6i) q^{76} +2.86138e6 q^{77} +(332641. - 4.62549e6i) q^{78} +(2.01867e6 - 3.49643e6i) q^{79} +(2.73803e6 - 2.60253e6i) q^{80} +(1.32690e6 - 2.29826e6i) q^{81} +(-2.56586e6 - 1.73809e6i) q^{82} +2.08663e6i q^{83} +(-6.36153e6 - 5.01082e6i) q^{84} +(-3.45145e6 - 5.97808e6i) q^{85} +(-1.59891e6 - 1.08309e6i) q^{86} -4.13197e6i q^{87} +(-534310. + 2.44237e6i) q^{88} +(9.56681e6 - 5.52340e6i) q^{89} +(-1.89915e6 - 136577. i) q^{90} +(8.89878e6 + 1.54131e7i) q^{91} +(4.34716e6 - 1.73639e6i) q^{92} +(-3.15499e6 + 5.46460e6i) q^{93} +(2.68880e6 - 1.30484e6i) q^{94} +(4.67790e6 + 5.06313e6i) q^{95} +(5.46496e6 - 4.49429e6i) q^{96} +(-1.01380e7 - 5.85317e6i) q^{97} +(2.17051e7 + 1.56092e6i) q^{98} +(1.09135e6 - 630089. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 3 q^{2} - 27 q^{4} - 2 q^{5} + 309 q^{6} - 45540 q^{9}+O(q^{10}) $ 136 * q - 3 * q^2 - 27 * q^4 - 2 * q^5 + 309 * q^6 - 45540 * q^9	$ 136 q - 3 q^{2} - 27 q^{4} - 2 q^{5} + 309 q^{6} - 45540 q^{9} - 19464 q^{10} - 10602 q^{13} + 13602 q^{14} + 6525 q^{16} - 23974 q^{17} - 91316 q^{20} + 54264 q^{21} + 381 q^{22} - 51631 q^{24} - 937502 q^{25} + 172188 q^{26} - 165428 q^{28} - 6 q^{29} - 454352 q^{30} + 573507 q^{32} - 182106 q^{33} - 629706 q^{34} - 277130 q^{36} - 759906 q^{38} - 627504 q^{40} - 1873020 q^{41} + 332080 q^{42} - 358069 q^{44} + 321240 q^{45} - 7221687 q^{48} - 15750664 q^{49} + 2848050 q^{52} - 1027650 q^{53} + 4352085 q^{54} - 137426 q^{57} + 10387724 q^{58} + 1607094 q^{60} + 5318582 q^{61} + 3394376 q^{62} - 1319538 q^{64} + 2439607 q^{66} - 87756 q^{68} - 17825238 q^{70} + 26155014 q^{72} + 299212 q^{73} + 1895842 q^{74} + 29672379 q^{76} + 907280 q^{77} + 7456734 q^{78} + 5489562 q^{80} - 11065208 q^{81} + 1288975 q^{82} + 6118214 q^{85} + 16831518 q^{86} - 17728542 q^{89} + 52167894 q^{90} + 10184840 q^{92} - 3299132 q^{93} - 68841730 q^{96} - 9435888 q^{97} - 35100021 q^{98}+O(q^{100}) $ 136 * q - 3 * q^2 - 27 * q^4 - 2 * q^5 + 309 * q^6 - 45540 * q^9 - 19464 * q^10 - 10602 * q^13 + 13602 * q^14 + 6525 * q^16 - 23974 * q^17 - 91316 * q^20 + 54264 * q^21 + 381 * q^22 - 51631 * q^24 - 937502 * q^25 + 172188 * q^26 - 165428 * q^28 - 6 * q^29 - 454352 * q^30 + 573507 * q^32 - 182106 * q^33 - 629706 * q^34 - 277130 * q^36 - 759906 * q^38 - 627504 * q^40 - 1873020 * q^41 + 332080 * q^42 - 358069 * q^44 + 321240 * q^45 - 7221687 * q^48 - 15750664 * q^49 + 2848050 * q^52 - 1027650 * q^53 + 4352085 * q^54 - 137426 * q^57 + 10387724 * q^58 + 1607094 * q^60 + 5318582 * q^61 + 3394376 * q^62 - 1319538 * q^64 + 2439607 * q^66 - 87756 * q^68 - 17825238 * q^70 + 26155014 * q^72 + 299212 * q^73 + 1895842 * q^74 + 29672379 * q^76 + 907280 * q^77 + 7456734 * q^78 + 5489562 * q^80 - 11065208 * q^81 + 1288975 * q^82 + 6118214 * q^85 + 16831518 * q^86 - 17728542 * q^89 + 52167894 * q^90 + 10184840 * q^92 - 3299132 * q^93 - 68841730 * q^96 - 9435888 * q^97 - 35100021 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−11.2846	−	0.811527i	−0.997424	−	0.0717295i
$2$	−11.2846	−	0.811527i	−0.997424	−	0.0717295i
$3$	−19.0858	+	33.0575i	−0.408118	+	0.706880i	−0.994679	−	0.103025i	$-0.967148\pi$
$3$	−19.0858	+	33.0575i	−0.408118	+	0.706880i	0.586561	+	0.809905i	$0.300481\pi$
$4$	126.683	+	18.3155i	0.989710	+	0.143090i
$5$	115.282	−	199.674i	0.412445	−	0.714376i	−0.582711	−	0.812679i	$-0.698008\pi$
$5$	115.282	−	199.674i	0.412445	−	0.714376i	0.995157	+	0.0983031i	$0.0313415\pi$
$6$	242.202	−	357.551i	0.457770	−	0.675785i
$7$			1657.40i			1.82635i	0.407566	+	0.913176i	$0.366378\pi$
$7$			1657.40i			1.82635i	−0.407566	+	0.913176i	$0.633622\pi$
$8$	−1414.70	−	309.489i	−0.976897	−	0.213712i
$9$	364.967	+	632.141i	0.166880	+	0.289045i
$10$	−1462.95	+	2159.68i	−0.462625	+	0.682952i
$11$		−	1726.43i		−	0.391088i	−0.980695	−	0.195544i	$-0.937353\pi$
$11$		−	1726.43i		−	0.391088i	0.980695	−	0.195544i	$-0.0626472\pi$
$12$	−3023.30	+	3838.26i	−0.505065	+	0.641209i
$13$	9299.59	−	5369.12i	1.17398	−	0.677800i	0.219368	−	0.975642i	$-0.429600\pi$
$13$	9299.59	−	5369.12i	1.17398	−	0.677800i	0.954615	+	0.297842i	$0.0962670\pi$
$14$	1345.03	−	18703.0i	0.131003	−	1.82165i
$15$	4400.49	+	7621.87i	0.336652	+	0.583099i
$16$	15713.1	+	4640.51i	0.959051	+	0.283234i
$17$	14969.6	−	25928.1i	0.738990	−	1.27997i	−0.213960	−	0.976842i	$-0.568636\pi$
$17$	14969.6	−	25928.1i	0.738990	−	1.27997i	0.952950	−	0.303126i	$-0.0980304\pi$
$18$	−3605.49	−	7429.62i	−0.145717	−	0.300271i
$19$	−8873.23	+	28550.6i	−0.296786	+	0.954944i
$19$	−8873.23	+	28550.6i	−0.296786	+	0.954944i
$20$	18261.4	−	23183.9i	0.510421	−	0.648008i
$21$	−54789.5	−	31632.8i	−1.29101	−	0.745366i
$22$	−1401.04	+	19482.0i	−0.0280525	+	0.390080i
$23$	31671.6	−	18285.6i	0.542778	−	0.313373i	−0.203426	−	0.979090i	$-0.565208\pi$
$23$	31671.6	−	18285.6i	0.542778	−	0.313373i	0.746204	+	0.665717i	$0.231874\pi$
$24$	37231.5	−	40859.6i	0.549758	−	0.603329i
$25$	12482.6	+	21620.6i	0.159778	+	0.276743i
$26$	−109299.	+	53041.3i	−1.21958	+	0.591844i
$27$	−111344.			−1.08866
$28$	−30356.1	+	209964.i	−0.261332	+	1.80756i
$29$	−93745.0	+	54123.7i	−0.713765	+	0.412092i	−0.812453	−	0.583026i	$-0.801869\pi$
$29$	−93745.0	+	54123.7i	−0.713765	+	0.412092i	0.0986886	+	0.995118i	$0.468535\pi$
$30$	−43472.3	−	89580.6i	−0.293960	−	0.605745i
$31$	165306.			0.996603			0.498302	−	0.867004i	$-0.333957\pi$
$31$	165306.			0.996603			0.498302	+	0.867004i	$0.333957\pi$
$32$	−173549.	−	65117.7i	−0.936264	−	0.351297i
$33$	57071.4	+	32950.2i	0.276452	+	0.159610i
$34$	−189967.	+	280439.i	−0.828898	+	1.22366i
$35$	330940.	+	191068.i	1.30470	+	0.753270i
$36$	34657.1	+	86766.0i	0.123804	+	0.309949i
$37$			339343.i			1.10137i	0.834714	+	0.550684i	$0.185633\pi$
$37$			339343.i			1.10137i	−0.834714	+	0.550684i	$0.814367\pi$
$38$	123300.	−	314980.i	0.364520	−	0.931196i
$39$			409895.i			1.10649i
$40$	−224886.	+	246800.i	−0.555587	+	0.609727i
$41$	237227.	+	136963.i	0.537553	+	0.310356i	0.744086	−	0.668083i	$-0.232885\pi$
$41$	237227.	+	136963.i	0.537553	+	0.310356i	−0.206534	+	0.978439i	$0.566218\pi$
$42$	592605.	+	401425.i	1.23422	+	0.836050i
$43$	147828.	+	85348.7i	0.283542	+	0.163703i	0.635026	−	0.772491i	$-0.280989\pi$
$43$	147828.	+	85348.7i	0.283542	+	0.163703i	−0.351484	+	0.936194i	$0.614323\pi$
$44$	31620.3	−	218709.i	0.0559606	−	0.387063i
$45$	168296.			0.275316
$46$	−372239.	+	180643.i	−0.563858	+	0.273633i
$47$	−228774.	+	132083.i	−0.321414	+	0.185568i	−0.652022	−	0.758200i	$-0.726079\pi$
$47$	−228774.	+	132083.i	−0.321414	+	0.185568i	0.330609	+	0.943768i	$0.392746\pi$
$48$	−453300.	+	430868.i	−0.591618	+	0.562341i
$49$	−1.92343e6			−2.33556
$50$	−123315.	−	254109.i	−0.139516	−	0.287491i
$51$	571412.	+	989715.i	0.603190	+	1.04476i
$52$	1.27644e6	−	509849.i	1.25889	−	0.502840i
$53$	−1.57195e6	+	907568.i	−1.45035	+	0.837363i	−0.998501	−	0.0547298i	$-0.982570\pi$
$53$	−1.57195e6	+	907568.i	−1.45035	+	0.837363i	−0.451853	+	0.892092i	$0.649237\pi$
$54$	1.25647e6	+	90358.6i	1.08586	+	0.0780892i
$55$	−344723.	−	199026.i	−0.279384	−	0.161302i
$56$	512947.	−	2.34472e6i	0.390314	−	1.78416i
$57$	−774460.	−	838237.i	−0.553907	−	0.599522i
$58$	1.10179e6	−	534686.i	0.741485	−	0.359833i
$59$	84177.8	−	145800.i	0.0533600	−	0.0924222i	−0.838112	−	0.545499i	$-0.816340\pi$
$59$	84177.8	−	145800.i	0.0533600	−	0.0924222i	0.891472	+	0.453077i	$0.149674\pi$
$60$	417868.	+	1.04616e6i	0.249753	+	0.625270i
$61$	1.10995e6	+	1.92250e6i	0.626110	+	1.08445i	0.988325	+	0.152360i	$0.0486874\pi$
$61$	1.10995e6	+	1.92250e6i	0.626110	+	1.08445i	−0.362215	+	0.932095i	$0.617979\pi$
$62$	−1.86540e6	−	134150.i	−0.994036	−	0.0714859i
$63$	−1.04771e6	+	604896.i	−0.527897	+	0.304782i
$64$	1.90559e6	+	875665.i	0.908654	+	0.417550i
$65$		−	2.47585e6i		−	1.11822i
$66$	−617286.	−	418144.i	−0.264291	−	0.179028i
$67$	998568.	+	1.72957e6i	0.405617	+	0.702549i	0.994393	−	0.105747i	$-0.0337234\pi$
$67$	998568.	+	1.72957e6i	0.405617	+	0.702549i	−0.588776	+	0.808296i	$0.700390\pi$
$68$	2.37128e6	−	3.01047e6i	0.914536	−	1.16106i
$69$			1.39598e6i			0.511572i
$70$	−3.57946e6	−	2.42469e6i	−1.24731	−	0.844915i
$71$	−1.87870e6	+	3.25401e6i	−0.622951	+	1.07898i	0.365982	+	0.930622i	$0.380733\pi$
$71$	−1.87870e6	+	3.25401e6i	−0.622951	+	1.07898i	−0.988933	+	0.148361i	$0.952600\pi$
$72$	−320677.	−	1.00724e6i	−0.101252	−	0.318031i
$73$	201940.	−	349771.i	0.0607566	−	0.105233i	−0.834047	−	0.551693i	$-0.813982\pi$
$73$	201940.	−	349771.i	0.0607566	−	0.105233i	0.894804	+	0.446460i	$0.147315\pi$
$74$	275386.	−	3.82934e6i	0.0790006	−	1.09853i
$75$	−952963.			−0.260832
$76$	−1.64700e6	+	3.45436e6i	−0.430375	+	0.902650i
$77$	2.86138e6			0.714263
$78$	332641.	−	4.62549e6i	0.0793679	−	1.10364i
$79$	2.01867e6	−	3.49643e6i	0.460648	−	0.797866i	−0.538345	−	0.842725i	$-0.680950\pi$
$79$	2.01867e6	−	3.49643e6i	0.460648	−	0.797866i	0.998993	+	0.0448583i	$0.0142836\pi$
$80$	2.73803e6	−	2.60253e6i	0.597892	−	0.568304i
$81$	1.32690e6	−	2.29826e6i	0.277422	−	0.480509i
$82$	−2.56586e6	−	1.73809e6i	−0.513906	−	0.348115i
$83$			2.08663e6i			0.400564i	0.979738	+	0.200282i	$0.0641858\pi$
$83$			2.08663e6i			0.400564i	−0.979738	+	0.200282i	$0.935814\pi$
$84$	−6.36153e6	−	5.01082e6i	−1.17107	−	0.922426i
$85$	−3.45145e6	−	5.97808e6i	−0.609586	−	1.05583i
$86$	−1.59891e6	−	1.08309e6i	−0.271070	−	0.183620i
$87$		−	4.13197e6i		−	0.672728i
$88$	−534310.	+	2.44237e6i	−0.0835803	+	0.382052i
$89$	9.56681e6	−	5.52340e6i	1.43847	−	0.830503i	0.440730	−	0.897640i	$-0.354720\pi$
$89$	9.56681e6	−	5.52340e6i	1.43847	−	0.830503i	0.997744	+	0.0671365i	$0.0213863\pi$
$90$	−1.89915e6	−	136577.i	−0.274607	−	0.0197483i
$91$	8.89878e6	+	1.54131e7i	1.23790	+	2.14411i
$92$	4.34716e6	−	1.73639e6i	0.582033	−	0.232483i
$93$	−3.15499e6	+	5.46460e6i	−0.406731	+	0.704479i
$94$	2.68880e6	−	1.30484e6i	0.333896	−	0.162035i
$95$	4.67790e6	+	5.06313e6i	0.559781	+	0.605879i
$96$	5.46496e6	−	4.49429e6i	0.630431	−	0.518456i
$97$	−1.01380e7	−	5.85317e6i	−1.12785	−	0.651163i	−0.184455	−	0.982841i	$-0.559052\pi$
$97$	−1.01380e7	−	5.85317e6i	−1.12785	−	0.651163i	−0.943393	+	0.331677i	$0.892385\pi$
$98$	2.17051e7	+	1.56092e6i	2.32954	+	0.167529i
$99$	1.09135e6	−	630089.i	0.113042	−	0.0652648i
$100$	1.18535e6	+	2.96758e6i	0.118535	+	0.296758i
$101$	7.67848e6	+	1.32995e7i	0.741567	+	1.28443i	0.951782	+	0.306776i	$0.0992502\pi$
$101$	7.67848e6	+	1.32995e7i	0.741567	+	1.28443i	−0.210215	+	0.977655i	$0.567416\pi$
$102$	−5.64496e6	−	1.16322e7i	−0.526696	−	1.08533i
$103$	−5.35428e6			−0.482804			−0.241402	−	0.970425i	$-0.577607\pi$
$103$	−5.35428e6			−0.482804			−0.241402	+	0.970425i	$0.577607\pi$
$104$	−1.48178e7	+	4.71756e6i	−1.29171	+	0.411245i
$105$	−1.26325e7	+	7.29337e6i	−1.06494	+	0.614845i
$106$	1.84753e7	−	8.96583e6i	1.50668	−	0.731172i
$107$	−2.18345e7			−1.72306			−0.861528	−	0.507710i	$-0.830492\pi$
$107$	−2.18345e7			−1.72306			−0.861528	+	0.507710i	$0.830492\pi$
$108$	−1.41054e7	−	2.03931e6i	−1.07746	−	0.155776i
$109$	−1.37580e7	−	7.94318e6i	−1.01757	−	0.587492i	−0.104168	−	0.994560i	$-0.533218\pi$
$109$	−1.37580e7	−	7.94318e6i	−1.01757	−	0.587492i	−0.913398	+	0.407068i	$0.866551\pi$
$110$	3.72854e6	+	2.52567e6i	0.267094	+	0.180927i
$111$	−1.12178e7	−	6.47662e6i	−0.778535	−	0.449488i
$112$	−7.69118e6	+	2.60429e7i	−0.517285	+	1.75156i
$113$			9.18597e6i			0.598895i	0.954113	+	0.299447i	$0.0968023\pi$
$113$			9.18597e6i			0.598895i	−0.954113	+	0.299447i	$0.903198\pi$
$114$	8.05919e6	+	1.00876e7i	0.509477	+	0.637709i
$115$		−	8.43200e6i		−	0.516997i
$116$	−1.28672e7	+	5.13956e6i	−0.765386	+	0.305720i
$117$	6.78808e6	+	3.91910e6i	0.391829	+	0.226223i
$118$	−1.06823e6	+	1.57698e6i	−0.0598519	+	0.0883567i
$119$	4.29732e7	+	2.48106e7i	2.33767	+	1.34966i
$120$	−3.86648e6	−	1.21445e7i	−0.204259	−	0.641574i
$121$	1.65066e7			0.847050
$122$	−1.09652e7	−	2.25953e7i	−0.546710	−	1.12657i
$123$	−9.05533e6	+	5.22810e6i	−0.438769	+	0.253324i
$124$	2.09414e7	+	3.02765e6i	0.986348	+	0.142604i
$125$	2.37689e7			1.08849
$126$	1.23139e7	−	5.97575e6i	0.548400	−	0.266131i
$127$	−1.37012e7	−	2.37312e7i	−0.593535	−	1.02803i	−0.993752	−	0.111612i	$-0.964399\pi$
$127$	−1.37012e7	−	2.37312e7i	−0.593535	−	1.02803i	0.400217	−	0.916420i	$-0.368935\pi$
$128$	−2.07931e7	−	1.14279e7i	−0.876363	−	0.481652i
$129$	−5.64283e6	+	3.25789e6i	−0.231437	+	0.133620i
$130$	−2.00922e6	+	2.79389e7i	−0.0802095	+	1.11534i
$131$	2.24021e7	+	1.29338e7i	0.870640	+	0.502664i	0.867561	−	0.497331i	$-0.165687\pi$
$131$	2.24021e7	+	1.29338e7i	0.870640	+	0.502664i	0.00307903	+	0.999995i	$0.499020\pi$
$132$	6.62647e6	+	5.21952e6i	0.250769	+	0.197525i
$133$	−4.73198e7	−	1.47065e7i	−1.74406	−	0.542036i
$134$	−9.86482e6	−	2.03278e7i	−0.354179	−	0.729834i
$135$	−1.28359e7	+	2.22325e7i	−0.449013	+	0.777714i
$136$	−2.92019e7	+	3.20475e7i	−0.995462	+	1.09247i
$137$	−7.93978e6	−	1.37521e7i	−0.263807	−	0.456927i	0.703443	−	0.710751i	$-0.251645\pi$
$137$	−7.93978e6	−	1.37521e7i	−0.263807	−	0.456927i	−0.967250	+	0.253824i	$0.918312\pi$
$138$	1.13288e6	−	1.57530e7i	0.0366949	−	0.510255i
$139$	1.64362e6	−	948943.i	0.0519097	−	0.0299701i	−0.473821	−	0.880621i	$-0.657125\pi$
$139$	1.64362e6	−	948943.i	0.0519097	−	0.0299701i	0.525730	+	0.850651i	$0.323792\pi$
$140$	3.84249e7	+	3.02664e7i	1.18349	+	0.932208i
$141$		−	1.00836e7i		−	0.302935i
$142$	2.38411e7	−	3.51955e7i	0.698741	−	1.03152i
$143$	−9.26940e6	−	1.60551e7i	−0.265079	−	0.459130i
$144$	2.80130e6	+	1.16265e7i	0.0781791	+	0.324475i
$145$			2.49579e7i			0.679862i
$146$	−2.56266e6	+	3.78313e6i	−0.0681484	+	0.100604i
$147$	3.67102e7	−	6.35839e7i	0.953183	−	1.65096i
$148$	−6.21522e6	+	4.29889e7i	−0.157594	+	1.09003i
$149$	−6.44095e6	+	1.11561e7i	−0.159514	+	0.276286i	−0.934693	−	0.355455i	$-0.884326\pi$
$149$	−6.44095e6	+	1.11561e7i	−0.159514	+	0.276286i	0.775180	+	0.631741i	$0.217659\pi$
$150$	1.07538e7	+	773355.i	0.260161	+	0.0187094i
$151$	−2.13743e7			−0.505212			−0.252606	−	0.967569i	$-0.581288\pi$
$151$	−2.13743e7			−0.505212			−0.252606	+	0.967569i	$0.581288\pi$
$152$	2.13890e7	−	3.76443e7i	0.494013	−	0.869455i
$153$	2.18536e7			0.493291
$154$	−3.22895e7	−	2.32209e6i	−0.712424	−	0.0512338i
$155$	1.90568e7	−	3.30073e7i	0.411044	−	0.711950i
$156$	−7.50742e6	+	5.19267e7i	−0.158327	+	1.09510i
$157$	−1.44488e7	+	2.50261e7i	−0.297978	+	0.516113i	−0.975673	−	0.219230i	$-0.929645\pi$
$157$	−1.44488e7	+	2.50261e7i	−0.297978	+	0.516113i	0.677695	+	0.735343i	$0.262979\pi$
$158$	−2.56172e7	+	3.78175e7i	−0.516692	+	0.762769i
$159$		−	6.92865e7i		−	1.36697i
$160$	−3.30095e7	+	2.71465e7i	−0.637116	+	0.523954i
$161$	3.03066e7	+	5.24925e7i	0.572330	+	0.991304i
$162$	−1.68386e7	+	2.48580e7i	−0.311174	+	0.459372i
$163$			7.20151e7i			1.30247i	0.758877	+	0.651233i	$0.225748\pi$
$163$			7.20151e7i			1.30247i	−0.758877	+	0.651233i	$0.774252\pi$
$164$	2.75441e7	+	2.16958e7i	0.487612	+	0.384081i
$165$	1.31586e7	−	7.59713e6i	0.228043	−	0.131661i
$166$	1.69335e6	−	2.35467e7i	0.0287322	−	0.399532i
$167$	−1.17199e7	−	2.02995e7i	−0.194723	−	0.337270i	0.752087	−	0.659064i	$-0.229048\pi$
$167$	−1.17199e7	−	2.02995e7i	−0.194723	−	0.337270i	−0.946810	+	0.321794i	$0.895714\pi$
$168$	6.77207e7	+	6.17075e7i	1.10189	+	1.00405i
$169$	2.62806e7	−	4.55194e7i	0.418825	−	0.725426i
$170$	3.40967e7	+	7.02610e7i	0.532281	+	1.09684i
$171$	−2.12865e7	+	4.81090e6i	−0.325549	+	0.0735766i
$172$	1.71641e7	+	1.35198e7i	0.257200	+	0.202591i
$173$	−3.67833e7	−	2.12369e7i	−0.540119	−	0.311838i	0.205008	−	0.978760i	$-0.434278\pi$
$173$	−3.67833e7	−	2.12369e7i	−0.540119	−	0.311838i	−0.745127	+	0.666922i	$0.767611\pi$
$174$	−3.35321e6	+	4.66275e7i	−0.0482545	+	0.670996i
$175$	−3.58339e7	+	2.06887e7i	−0.505430	+	0.291810i
$176$	8.01151e6	−	2.71275e7i	0.110769	−	0.375073i
$177$	3.21320e6	+	5.56542e6i	0.0435543	+	0.0754383i
$178$	−1.12440e8	+	5.45654e7i	−1.49434	+	0.725183i
$179$	2.61162e7			0.340349			0.170174	−	0.985414i	$-0.445567\pi$
$179$	2.61162e7			0.340349			0.170174	+	0.985414i	$0.445567\pi$
$180$	2.13203e7	+	3.08243e6i	0.272483	+	0.0393948i
$181$	5.53322e7	−	3.19461e7i	0.693591	−	0.400445i	−0.111365	−	0.993780i	$-0.535522\pi$
$181$	5.53322e7	−	3.19461e7i	0.693591	−	0.400445i	0.804956	+	0.593335i	$0.202189\pi$
$182$	−8.79107e7	−	1.81152e8i	−1.08092	−	2.22738i
$183$	−8.47374e7			−1.02211
$184$	−5.04649e7	+	1.60666e7i	−0.597210	+	0.190135i
$185$	6.77580e7	+	3.91201e7i	0.786791	+	0.454254i
$186$	4.00374e7	−	5.91053e7i	0.456216	−	0.673490i
$187$	−4.47630e7	−	2.58439e7i	−0.500580	−	0.289010i
$188$	−3.14009e7	+	1.25425e7i	−0.344659	+	0.137668i
$189$		−	1.84541e8i		−	1.98828i
$190$	−4.86792e7	−	6.09314e7i	−0.514880	−	0.644471i
$191$		−	1.25742e8i		−	1.30576i	−0.757463	−	0.652878i	$-0.773561\pi$
$191$		−	1.25742e8i		−	1.30576i	0.757463	−	0.652878i	$-0.226439\pi$
$192$	−6.53169e7	+	4.62812e7i	−0.665995	+	0.471900i
$193$	1.07171e8	+	6.18754e7i	1.07307	+	0.619538i	0.929019	−	0.370033i	$-0.120653\pi$
$193$	1.07171e8	+	6.18754e7i	1.07307	+	0.619538i	0.144052	+	0.989570i	$0.453987\pi$
$194$	1.09653e8	+	7.42777e7i	1.07824	+	0.730386i
$195$	8.18455e7	+	4.72535e7i	0.790449	+	0.456366i
$196$	−2.43666e8	−	3.52286e7i	−2.31153	−	0.334194i
$197$	9.20349e7			0.857671			0.428836	−	0.903382i	$-0.358924\pi$
$197$	9.20349e7			0.857671			0.428836	+	0.903382i	$0.358924\pi$
$198$	−1.28267e7	+	6.22462e6i	−0.117432	+	0.0569882i
$199$	5.60288e7	−	3.23483e7i	0.503994	−	0.290981i	−0.226367	−	0.974042i	$-0.572685\pi$
$199$	5.60288e7	−	3.23483e7i	0.503994	−	0.290981i	0.730362	+	0.683061i	$0.239352\pi$
$200$	−1.09678e7	−	3.44498e7i	−0.0969429	−	0.304496i
$201$	−7.62338e7			−0.662157
$202$	−7.58553e7	−	1.56310e8i	−0.647525	−	1.33431i
$203$	−8.97047e7	−	1.55373e8i	−0.752625	−	1.30359i
$204$	5.42610e7	+	1.35846e8i	0.447489	+	1.12031i
$205$	5.46960e7	−	3.15788e7i	0.443422	−	0.256010i
$206$	6.04208e7	+	4.34515e6i	0.481561	+	0.0346313i
$207$	2.31182e7	+	1.33473e7i	0.181158	+	0.104592i
$208$	1.71041e8	−	4.12106e7i	1.31789	−	0.317532i
$209$	4.92906e7	+	1.53190e7i	0.373467	+	0.116069i
$210$	1.48471e8	−	7.20509e7i	1.10630	−	0.536874i
$211$	−1.94954e7	+	3.37670e7i	−0.142871	+	0.247459i	−0.928576	−	0.371141i	$-0.878967\pi$
$211$	−1.94954e7	+	3.37670e7i	−0.142871	+	0.247459i	0.785706	+	0.618600i	$0.212300\pi$
$212$	−2.15762e8	+	8.61822e7i	−1.55525	+	0.621215i
$213$	−7.17130e7	−	1.24211e8i	−0.508475	−	0.880704i
$214$	2.46392e8	+	1.77193e7i	1.71862	+	0.123594i
$215$	3.40839e7	−	1.96783e7i	0.233891	−	0.135037i
$216$	1.57518e8	+	3.44597e7i	1.06351	+	0.232661i
$217$			2.73978e8i			1.82015i
$218$	1.48807e8	+	1.00800e8i	0.972804	+	0.658968i
$219$	7.70837e6	+	1.33513e7i	0.0495916	+	0.0858952i
$220$	−4.00253e7	−	3.15269e7i	−0.253428	−	0.199619i
$221$		−	3.21494e8i		−	2.00355i
$222$	1.21332e8	+	8.21894e7i	0.744288	+	0.504174i
$223$	1.28541e8	−	2.22640e8i	0.776204	−	1.34442i	−0.157911	−	0.987453i	$-0.550476\pi$
$223$	1.28541e8	−	2.22640e8i	0.776204	−	1.34442i	0.934115	−	0.356971i	$-0.116191\pi$
$224$	1.07926e8	−	2.87641e8i	0.641592	−	1.70995i
$225$	−9.11150e6	+	1.57816e7i	−0.0533275	+	0.0923659i
$226$	7.45467e6	−	1.03660e8i	0.0429585	−	0.597352i
$227$	−1.61787e8			−0.918023			−0.459011	−	0.888430i	$-0.651796\pi$
$227$	−1.61787e8			−0.918023			−0.459011	+	0.888430i	$0.651796\pi$
$228$	−8.27581e7	−	1.20375e8i	−0.462422	−	0.672611i
$229$	−3.39014e8			−1.86549			−0.932747	−	0.360531i	$-0.882595\pi$
$229$	−3.39014e8			−1.86549			−0.932747	+	0.360531i	$0.882595\pi$
$230$	−6.84280e6	+	9.51515e7i	−0.0370840	+	0.515666i
$231$	−5.46117e7	+	9.45902e7i	−0.291503	+	0.504899i
$232$	1.49371e8	−	4.75557e7i	0.785344	−	0.250031i
$233$	−2.31303e7	+	4.00628e7i	−0.119794	+	0.207489i	−0.919686	−	0.392655i	$-0.871557\pi$
$233$	−2.31303e7	+	4.00628e7i	−0.119794	+	0.207489i	0.799892	+	0.600144i	$0.204890\pi$
$234$	−7.34201e7	−	4.97341e7i	−0.374593	−	0.253746i
$235$			6.09070e7i			0.306147i
$236$	1.33343e7	−	1.69286e7i	0.0660356	−	0.0838359i
$237$	7.70556e7	+	1.33464e8i	0.375997	+	0.651246i
$238$	−4.64800e8	−	3.14851e8i	−2.23484	−	1.51386i
$239$			3.28552e8i			1.55672i	0.627817	+	0.778361i	$0.283949\pi$
$239$			3.28552e8i			1.55672i	−0.627817	+	0.778361i	$0.716051\pi$
$240$	3.37759e7	+	1.40184e8i	0.157713	+	0.654573i
$241$	5.96845e7	−	3.44588e7i	0.274664	−	0.158577i	−0.356341	−	0.934356i	$-0.615976\pi$
$241$	5.96845e7	−	3.44588e7i	0.274664	−	0.158577i	0.631005	+	0.775779i	$0.282643\pi$
$242$	−1.86270e8	−	1.33956e7i	−0.844869	−	0.0607585i
$243$	−7.11047e7	−	1.23157e8i	−0.317889	−	0.550601i
$244$	1.05401e8	+	2.63877e8i	0.464493	+	1.16289i
$245$	−2.21737e8	+	3.84060e8i	−0.963290	+	1.66847i
$246$	1.06428e8	−	5.16481e7i	0.455810	−	0.221198i
$247$	7.07743e7	+	3.13150e8i	0.298838	+	1.32225i
$248$	−2.33858e8	−	5.11603e7i	−0.973578	−	0.212986i
$249$	−6.89787e7	−	3.98249e7i	−0.283150	−	0.163477i
$250$	−2.68222e8	−	1.92891e7i	−1.08569	−	0.0780768i
$251$	4.71585e7	−	2.72270e7i	0.188236	−	0.108678i	−0.402921	−	0.915235i	$-0.632005\pi$
$251$	4.71585e7	−	2.72270e7i	0.188236	−	0.108678i	0.591156	+	0.806557i	$0.298672\pi$
$252$	−1.43806e8	+	5.74407e7i	−0.566076	+	0.226109i
$253$	−3.15688e7	−	5.46787e7i	−0.122556	−	0.212274i
$254$	1.35354e8	+	2.78915e8i	0.518266	+	1.06796i
$255$	2.63494e8			0.995131
$256$	2.25367e8	+	1.45833e8i	0.839557	+	0.543272i
$257$	3.34039e8	−	1.92858e8i	1.22753	−	0.708714i	0.261016	−	0.965334i	$-0.415942\pi$
$257$	3.34039e8	−	1.92858e8i	1.22753	−	0.708714i	0.966512	+	0.256621i	$0.0826091\pi$
$258$	6.63208e7	−	3.21846e7i	0.240426	−	0.116675i
$259$	−5.62427e8			−2.01149
$260$	4.53464e7	−	3.13648e8i	0.160006	−	1.10671i
$261$	−6.84276e7	−	3.95067e7i	−0.238226	−	0.137540i
$262$	−2.42301e8	−	1.64133e8i	−0.832341	−	0.563820i
$263$	1.52524e8	+	8.80597e7i	0.517003	+	0.298492i	0.735707	−	0.677299i	$-0.236850\pi$
$263$	1.52524e8	+	8.80597e7i	0.517003	+	0.298492i	−0.218705	+	0.975791i	$0.570183\pi$
$264$	−7.05411e7	−	6.42775e7i	−0.235955	−	0.215003i
$265$			4.18505e8i			1.38146i
$266$	5.22049e8	+	2.04358e8i	1.70069	+	0.665741i
$267$			4.21673e8i			1.35577i
$268$	9.48236e7	+	2.37396e8i	0.300916	+	0.753359i
$269$	1.24296e8	+	7.17623e7i	0.389336	+	0.224783i	0.681872	−	0.731471i	$-0.261166\pi$
$269$	1.24296e8	+	7.17623e7i	0.389336	+	0.224783i	−0.292537	+	0.956254i	$0.594499\pi$
$270$	1.62890e8	−	2.40467e8i	0.503642	−	0.743503i
$271$	5.29945e8	+	3.05964e8i	1.61748	+	0.933851i	0.987570	+	0.157181i	$0.0502406\pi$
$271$	5.29945e8	+	3.05964e8i	1.61748	+	0.933851i	0.629908	+	0.776670i	$0.283093\pi$
$272$	3.55538e8	−	3.37944e8i	1.07126	−	1.01825i
$273$	−6.79360e8			−2.02084
$274$	7.84368e7	+	1.61630e8i	0.230352	+	0.474673i
$275$	3.73263e7	−	2.15504e7i	0.108231	−	0.0624871i
$276$	−2.55680e7	+	1.76847e8i	−0.0732007	+	0.506308i
$277$	−5.01368e7			−0.141735			−0.0708676	−	0.997486i	$-0.522577\pi$
$277$	−5.01368e7			−0.141735			−0.0708676	+	0.997486i	$0.522577\pi$
$278$	−1.93176e7	+	9.37456e6i	−0.0539258	+	0.0261694i
$279$	6.03312e7	+	1.04497e8i	0.166313	+	0.288063i
$280$	−4.09047e8	−	3.72726e8i	−1.11358	−	1.01470i
$281$	−4.73709e7	+	2.73496e7i	−0.127362	+	0.0735325i	−0.562327	−	0.826915i	$-0.690094\pi$
$281$	−4.73709e7	+	2.73496e7i	−0.127362	+	0.0735325i	0.434965	+	0.900447i	$0.356761\pi$
$282$	−8.18312e6	+	1.13789e8i	−0.0217294	+	0.302154i
$283$	2.57034e8	+	1.48399e8i	0.674121	+	0.389204i	0.797636	−	0.603139i	$-0.206083\pi$
$283$	2.57034e8	+	1.48399e8i	0.674121	+	0.389204i	−0.123515	+	0.992343i	$0.539417\pi$
$284$	−2.97598e8	+	3.77818e8i	−0.770932	+	0.978742i
$285$	−2.56656e8	+	5.80061e7i	−0.656741	+	0.148428i
$286$	9.15720e7	+	1.88697e8i	0.231463	+	0.476962i
$287$	−2.27003e8	+	3.93180e8i	−0.566819	+	0.981760i
$288$	−2.21762e7	−	1.33474e8i	−0.0547033	−	0.329247i
$289$	−2.43008e8	−	4.20902e8i	−0.592213	−	1.02574i
$290$	2.02541e7	−	2.81640e8i	0.0487662	−	0.678111i
$291$	3.86983e8	−	2.23424e8i	0.920589	−	0.531502i
$292$	3.19886e7	−	4.06114e7i	0.0751892	−	0.0954569i
$293$			4.31050e8i			1.00113i	0.865699	+	0.500565i	$0.166875\pi$
$293$			4.31050e8i			1.00113i	−0.865699	+	0.500565i	$0.833125\pi$
$294$	−4.65859e8	+	6.87726e8i	−1.06915	+	1.57834i
$295$	−1.94084e7	−	3.36163e7i	−0.0440162	−	0.0762382i
$296$	1.05023e8	−	4.80067e8i	0.235376	−	1.07592i
$297$			1.92227e8i			0.425762i
$298$	8.17368e7	−	1.20664e8i	0.178921	−	0.264132i
$299$	1.96355e8	−	3.40097e8i	0.424809	−	0.735790i
$300$	−1.20724e8	−	1.74540e7i	−0.258148	−	0.0373224i
$301$	−1.41457e8	+	2.45011e8i	−0.298980	+	0.517848i
$302$	2.41200e8	+	1.73459e7i	0.503910	+	0.0362386i
$303$	−5.86198e8			−1.21059
$304$	−2.71915e8	+	4.07442e8i	−0.555106	+	0.831780i
$305$	5.11831e8			1.03294
$306$	−2.46609e8	−	1.77348e7i	−0.492021	−	0.0353836i
$307$	−1.86975e8	+	3.23850e8i	−0.368806	+	0.638791i	−0.989379	−	0.145357i	$-0.953567\pi$
$307$	−1.86975e8	+	3.23850e8i	−0.368806	+	0.638791i	0.620573	+	0.784149i	$0.286900\pi$
$308$	3.62488e8	+	5.24075e7i	0.706913	+	0.102204i
$309$	1.02191e8	−	1.76999e8i	0.197041	−	0.341285i
$310$	−2.41834e8	+	3.57008e8i	−0.461053	+	0.680632i
$311$		−	4.49770e8i		−	0.847870i	−0.905693	−	0.423935i	$-0.860648\pi$
$311$		−	4.49770e8i		−	0.847870i	0.905693	−	0.423935i	$-0.139352\pi$
$312$	1.26858e8	−	5.79878e8i	0.236470	−	1.08092i
$313$	−2.38966e8	−	4.13901e8i	−0.440485	−	0.762942i	0.557241	−	0.830351i	$-0.311860\pi$
$313$	−2.38966e8	−	4.13901e8i	−0.440485	−	0.762942i	−0.997725	+	0.0674092i	$0.978527\pi$
$314$	1.83358e8	−	2.70683e8i	0.334231	−	0.493409i
$315$			2.78935e8i			0.502823i
$316$	3.19769e8	−	4.05965e8i	0.570074	−	0.723742i
$317$	6.58420e8	−	3.80139e8i	1.16090	−	0.670247i	0.209382	−	0.977834i	$-0.432855\pi$
$317$	6.58420e8	−	3.80139e8i	1.16090	−	0.670247i	0.951520	+	0.307587i	$0.0995214\pi$
$318$	−5.62279e7	+	7.81868e8i	−0.0980521	+	1.36345i
$319$	9.34407e7	+	1.61844e8i	0.161164	+	0.279145i
$320$	3.94527e8	−	2.79548e8i	0.673058	−	0.476904i
$321$	4.16728e8	−	7.21793e8i	0.703209	−	1.21799i
$322$	−2.99397e8	−	6.16950e8i	−0.499750	−	1.02980i
$323$	6.07434e8	+	6.57457e8i	1.00298	+	1.08557i
$324$	2.10189e8	−	2.66847e8i	0.343323	−	0.435868i
$325$	2.32167e8	+	1.34042e8i	0.375153	+	0.216595i
$326$	5.84422e7	−	8.12659e8i	0.0934254	−	1.29911i
$327$	5.25164e8	−	3.03203e8i	0.830573	−	0.479531i
$328$	−2.93216e8	−	2.67181e8i	−0.458806	−	0.418068i
$329$	−2.18914e8	−	3.79170e8i	−0.338913	−	0.587014i
$330$	−1.54655e8	+	7.50517e7i	−0.236899	+	0.114964i
$331$	−8.38873e8			−1.27145			−0.635724	−	0.771917i	$-0.719298\pi$
$331$	−8.38873e8			−1.27145			−0.635724	+	0.771917i	$0.719298\pi$
$332$	−3.82175e7	+	2.64340e8i	−0.0573165	+	0.396442i
$333$	−2.14513e8	+	1.23849e8i	−0.318345	+	0.183796i
$334$	1.15781e8	+	2.38582e8i	0.170029	+	0.350369i
$335$	4.60468e8			0.669179
$336$	−7.14121e8	−	7.51300e8i	−1.02703	−	1.08050i
$337$	−1.03671e7	−	5.98548e6i	−0.0147555	−	0.00851911i	0.492604	−	0.870254i	$-0.336045\pi$
$337$	−1.03671e7	−	5.98548e6i	−0.0147555	−	0.00851911i	−0.507360	+	0.861734i	$0.669378\pi$
$338$	−3.33506e8	+	4.92339e8i	−0.469780	+	0.693515i
$339$	−3.03665e8	−	1.75321e8i	−0.423347	−	0.244420i
$340$	−3.27748e8	−	8.20535e8i	−0.452234	−	1.13219i
$341$		−	2.85389e8i		−	0.389759i
$342$	2.44113e8	−	3.70143e7i	0.329988	−	0.0500355i
$343$		−	1.82296e9i		−	2.43920i
$344$	−1.82718e8	−	1.66494e8i	−0.242006	−	0.220518i
$345$	2.78741e8	+	1.60931e8i	0.365455	+	0.210996i
$346$	3.97849e8	+	2.69499e8i	0.516360	+	0.349777i
$347$	−1.17769e9	−	6.79942e8i	−1.51314	−	0.873612i	−0.999882	−	0.0153782i	$-0.995105\pi$
$347$	−1.17769e9	−	6.79942e8i	−1.51314	−	0.873612i	−0.513259	−	0.858234i	$-0.671562\pi$
$348$	7.56789e7	−	5.23450e8i	0.0962604	−	0.665806i
$349$	1.14838e9			1.44610			0.723050	−	0.690796i	$-0.242740\pi$
$349$	1.14838e9			1.44610			0.723050	+	0.690796i	$0.242740\pi$
$350$	4.21160e8	−	2.04383e8i	0.525060	−	0.254804i
$351$	−1.03545e9	+	5.97818e8i	−1.27807	+	0.737895i
$352$	−1.12421e8	+	2.99621e8i	−0.137388	+	0.366161i
$353$	8.10565e8			0.980791			0.490396	−	0.871500i	$-0.336852\pi$
$353$	8.10565e8			0.980791			0.490396	+	0.871500i	$0.336852\pi$
$354$	−3.17430e7	−	6.54110e7i	−0.0380310	−	0.0783681i
$355$	4.33161e8	+	7.50257e8i	0.513866	+	0.890043i
$356$	1.31311e9	−	5.24499e8i	1.54251	−	0.616127i
$357$	−1.64035e9	+	9.47059e8i	−1.90809	+	1.10164i
$358$	−2.94710e8	−	2.11940e7i	−0.339472	−	0.0244131i
$359$	−1.88811e8	−	1.09010e8i	−0.215376	−	0.124347i	0.388431	−	0.921478i	$-0.373017\pi$
$359$	−1.88811e8	−	1.09010e8i	−0.215376	−	0.124347i	−0.603807	+	0.797130i	$0.706350\pi$
$360$	−2.38088e8	−	5.20858e7i	−0.268955	−	0.0588384i
$361$	−7.36403e8	−	5.06672e8i	−0.823836	−	0.566829i
$362$	−6.50325e8	+	3.15594e8i	−0.720528	+	0.349662i
$363$	−3.15041e8	+	5.45668e8i	−0.345696	+	0.598763i
$364$	8.45024e8	+	2.11557e9i	0.918363	+	2.29917i
$365$	−4.65602e7	−	8.06446e7i	−0.0501175	−	0.0868061i
$366$	9.56224e8	+	6.87667e7i	1.01947	+	0.0733152i
$367$	7.01210e8	−	4.04844e8i	0.740486	−	0.427520i	−0.0817599	−	0.996652i	$-0.526054\pi$
$367$	7.01210e8	−	4.04844e8i	0.740486	−	0.427520i	0.822246	+	0.569132i	$0.192721\pi$
$368$	5.82513e8	−	1.40351e8i	0.609310	−	0.146807i
$369$			1.99948e8i			0.207169i
$370$	−7.32872e8	−	4.96441e8i	−0.752181	−	0.509520i
$371$	−1.50420e9	−	2.60536e9i	−1.52932	−	2.64886i
$372$	−4.99770e8	+	6.34486e8i	−0.503350	+	0.639031i
$373$			5.27659e8i			0.526468i	0.964732	+	0.263234i	$0.0847892\pi$
$373$			5.27659e8i			0.526468i	−0.964732	+	0.263234i	$0.915211\pi$
$374$	4.84158e8	+	3.27964e8i	0.478560	+	0.324172i
$375$	−4.53648e8	+	7.85741e8i	−0.444231	+	0.769431i
$376$	3.64524e8	−	1.16054e8i	0.353646	−	0.112591i
$377$	−5.81193e8	+	1.00666e9i	−0.558632	+	0.967579i
$378$	−1.49760e8	+	2.08247e9i	−0.142618	+	1.98316i
$379$	1.43431e9			1.35334			0.676668	−	0.736288i	$-0.263423\pi$
$379$	1.43431e9			1.35334			0.676668	+	0.736288i	$0.263423\pi$
$380$	4.99876e8	+	7.27089e8i	0.467326	+	0.679743i
$381$	1.04599e9			0.968928
$382$	−1.02043e8	+	1.41894e9i	−0.0936613	+	1.30239i
$383$	−4.01538e8	+	6.95484e8i	−0.365200	+	0.632545i	−0.988808	−	0.149192i	$-0.952333\pi$
$383$	−4.01538e8	+	6.95484e8i	−0.365200	+	0.632545i	0.623608	+	0.781737i	$0.285666\pi$
$384$	7.74631e8	−	4.69257e8i	0.698129	−	0.422913i
$385$	3.29866e8	−	5.71344e8i	0.294595	−	0.510253i
$386$	−1.15917e9	−	7.85210e8i	−1.02587	−	0.694913i
$387$			1.24598e8i			0.109275i
$388$	−1.17711e9	−	9.27178e8i	−1.02307	−	0.805846i
$389$	4.82625e7	+	8.35931e7i	0.0415706	+	0.0720024i	0.886062	−	0.463567i	$-0.153431\pi$
$389$	4.82625e7	+	8.35931e7i	0.0415706	+	0.0720024i	−0.844491	+	0.535569i	$0.820097\pi$
$390$	−8.85243e8	−	5.99655e8i	−0.755678	−	0.511889i
$391$		−	1.09491e9i		−	0.926319i
$392$	2.72108e9	+	5.95281e8i	2.28160	+	0.499138i
$393$	−8.55121e8	+	4.93705e8i	−0.710647	+	0.410292i
$394$	−1.03857e9	−	7.46889e7i	−0.855462	−	0.0615204i
$395$	−4.65431e8	−	8.06151e8i	−0.379984	−	0.658152i
$396$	1.49795e8	−	5.98330e7i	0.121217	−	0.0484181i
$397$	6.71188e8	−	1.16253e9i	0.538366	−	0.932477i	−0.460627	−	0.887594i	$-0.652375\pi$
$397$	6.71188e8	−	1.16253e9i	0.538366	−	0.932477i	0.998992	−	0.0448827i	$-0.0142914\pi$
$398$	−6.58512e8	+	3.19567e8i	−0.523568	+	0.254080i
$399$	1.38929e9	−	1.28359e9i	1.09494	−	1.01163i
$400$	9.58103e7	+	3.97652e8i	0.0748518	+	0.310665i
$401$	4.00712e8	+	2.31351e8i	0.310332	+	0.179170i	0.647075	−	0.762426i	$-0.275992\pi$
$401$	4.00712e8	+	2.31351e8i	0.310332	+	0.179170i	−0.336743	+	0.941597i	$0.609325\pi$
$402$	8.60265e8	+	6.18658e7i	0.660452	+	0.0474963i
$403$	1.53728e9	−	8.87547e8i	1.17000	−	0.675497i
$404$	7.29144e8	+	1.82545e9i	0.550147	+	1.37732i
$405$	−3.05935e8	−	5.29896e8i	−0.228843	−	0.396367i
$406$	8.86189e8	+	1.82611e9i	0.657181	+	1.35421i
$407$	5.85851e8			0.430731
$408$	−5.02070e8	−	1.57699e9i	−0.365977	−	1.14953i
$409$	−2.04923e8	+	1.18312e8i	−0.148101	+	0.0855064i	−0.572219	−	0.820101i	$-0.693917\pi$
$409$	−2.04923e8	+	1.18312e8i	−0.148101	+	0.0855064i	0.424118	+	0.905607i	$0.360584\pi$
$410$	−6.42848e8	+	3.11965e8i	−0.460643	+	0.223544i
$411$	6.06147e8			0.430657
$412$	−6.78296e8	−	9.80662e7i	−0.477836	−	0.0690843i
$413$	2.41649e8	+	1.39516e8i	0.168795	+	0.0974541i
$414$	−2.50047e8	−	1.69379e8i	−0.173189	−	0.117316i
$415$	4.16645e8	+	2.40550e8i	0.286153	+	0.165211i
$416$	−1.96356e9	+	3.26240e8i	−1.33727	+	0.222183i
$417$			7.24452e7i			0.0489253i
$418$	−5.43791e8	−	2.12869e8i	−0.364179	−	0.142559i
$419$			2.72743e8i			0.181136i	0.995890	+	0.0905681i	$0.0288683\pi$
$419$			2.72743e8i			0.181136i	−0.995890	+	0.0905681i	$0.971132\pi$
$420$	−1.73390e9	+	6.92575e8i	−1.14196	+	0.456136i
$421$	9.76343e8	+	5.63692e8i	0.637698	+	0.368175i	0.783727	−	0.621105i	$-0.213316\pi$
$421$	9.76343e8	+	5.63692e8i	0.637698	+	0.368175i	−0.146029	+	0.989280i	$0.546649\pi$
$422$	2.47400e8	−	3.65225e8i	0.160253	−	0.236574i
$423$	−1.66990e8	−	9.64116e7i	−0.107275	−	0.0619353i
$424$	2.50472e9	−	7.97432e8i	1.59580	−	0.508058i
$425$	7.47440e8			0.472297
$426$	7.08450e8	+	1.45986e9i	0.443992	+	0.914908i
$427$	−3.18635e9	+	1.83964e9i	−1.98060	+	1.14350i
$428$	−2.76605e9	−	3.99908e8i	−1.70533	−	0.246551i
$429$	7.07654e8			0.432734
$430$	−4.00591e8	+	1.94401e8i	−0.242975	+	0.117912i
$431$	8.71440e8	+	1.50938e9i	0.524285	+	0.908088i	0.999600	+	0.0282723i	$0.00900054\pi$
$431$	8.71440e8	+	1.50938e9i	0.524285	+	0.908088i	−0.475316	+	0.879815i	$0.657666\pi$
$432$	−1.74956e9	−	5.16692e8i	−1.04408	−	0.308346i
$433$	1.51239e9	−	8.73176e8i	0.895272	−	0.516885i	0.0196085	−	0.999808i	$-0.493758\pi$
$433$	1.51239e9	−	8.73176e8i	0.895272	−	0.516885i	0.875663	+	0.482922i	$0.160425\pi$
$434$	2.22341e8	−	3.09172e9i	0.130558	−	1.81546i
$435$	−8.25048e8	−	4.76342e8i	−0.480581	−	0.277464i
$436$	−1.59742e9	−	1.25825e9i	−0.923030	−	0.727049i
$437$	2.41036e8	+	1.06650e9i	0.138165	+	0.611328i
$438$	−7.61507e7	−	1.56919e8i	−0.0433027	−	0.0892311i
$439$	5.25088e8	−	9.09479e8i	0.296215	−	0.513059i	−0.679052	−	0.734090i	$-0.737609\pi$
$439$	5.25088e8	−	9.09479e8i	0.296215	−	0.513059i	0.975267	+	0.221031i	$0.0709423\pi$
$440$	4.26083e8	+	3.88249e8i	0.238457	+	0.217283i
$441$	−7.01989e8	−	1.21588e9i	−0.389758	−	0.675081i
$442$	−2.60901e8	+	3.62792e9i	−0.143714	+	1.99839i
$443$	−6.45472e8	+	3.72664e8i	−0.352748	+	0.203659i	−0.665895	−	0.746046i	$-0.731950\pi$
$443$	−6.45472e8	+	3.72664e8i	−0.352748	+	0.203659i	0.313147	+	0.949705i	$0.398617\pi$
$444$	−1.30248e9	−	1.02594e9i	−0.706207	−	0.556263i
$445$		−	2.54699e9i		−	1.37015i
$446$	−1.63121e9	+	2.40808e9i	−0.870640	+	1.28528i
$447$	−2.45861e8	−	4.25844e8i	−0.130201	−	0.225514i
$448$	−1.45133e9	+	3.15832e9i	−0.762593	+	1.65952i
$449$			1.02129e9i			0.532461i	0.963909	+	0.266230i	$0.0857782\pi$
$449$			1.02129e9i			0.532461i	−0.963909	+	0.266230i	$0.914222\pi$
$450$	1.15626e8	−	1.70694e8i	0.0598155	−	0.0883028i
$451$	2.36457e8	−	4.09556e8i	0.121376	−	0.210230i
$452$	−1.68245e8	+	1.16371e9i	−0.0856956	+	0.592732i
$453$	4.07946e8	−	7.06583e8i	0.206186	−	0.357124i
$454$	1.82570e9	+	1.31295e8i	0.915658	+	0.0658494i
$455$	4.10348e9			2.04226
$456$	8.36202e8	+	1.42554e9i	0.412985	+	0.704048i
$457$	−2.50660e9			−1.22851			−0.614254	−	0.789108i	$-0.710543\pi$
$457$	−2.50660e9			−1.22851			−0.614254	+	0.789108i	$0.710543\pi$
$458$	3.82563e9	+	2.75119e8i	1.86069	+	0.133811i
$459$	−1.66677e9	+	2.88693e9i	−0.804511	+	1.39345i
$460$	1.54436e8	−	1.06819e9i	0.0739769	−	0.511677i
$461$	1.77041e8	−	3.06645e8i	0.0841631	−	0.145775i	−0.820871	−	0.571113i	$-0.806512\pi$
$461$	1.77041e8	−	3.06645e8i	0.0841631	−	0.145775i	0.905034	+	0.425339i	$0.139845\pi$
$462$	6.93032e8	−	1.02309e9i	0.326969	−	0.482689i
$463$		−	2.02196e9i		−	0.946758i	−0.880859	−	0.473379i	$-0.843034\pi$
$463$		−	2.02196e9i		−	0.946758i	0.880859	−	0.473379i	$-0.156966\pi$
$464$	−1.72419e9	+	4.15426e8i	−0.801255	+	0.193055i
$465$	7.27427e8	+	1.25994e9i	0.335509	+	0.581118i
$466$	2.93527e8	−	4.33320e8i	0.134368	−	0.198362i
$467$		−	1.37222e8i		−	0.0623470i	−0.999514	−	0.0311735i	$-0.990076\pi$
$467$		−	1.37222e8i		−	0.0623470i	0.999514	−	0.0311735i	$-0.00992444\pi$
$468$	7.88154e8	+	6.20810e8i	0.355427	+	0.279961i
$469$	−2.86659e9	+	1.65503e9i	−1.28310	+	0.740799i
$470$	4.94277e7	−	6.87309e8i	0.0219598	−	0.305358i
$471$	−5.51534e8	−	9.55285e8i	−0.243220	−	0.421269i
$472$	−1.64210e8	+	1.80211e8i	−0.0718790	+	0.0788833i
$473$	1.47348e8	−	2.55215e8i	0.0640223	−	0.110890i
$474$	−7.61229e8	−	1.56862e9i	−0.328315	−	0.676539i
$475$	−7.28042e8	+	1.64543e8i	−0.311694	+	0.0704452i
$476$	4.98955e9	+	3.93015e9i	2.12050	+	1.67026i
$477$	−1.14742e9	−	6.62464e8i	−0.484071	−	0.279478i
$478$	2.66629e8	−	3.70756e9i	0.111663	−	1.55271i
$479$	−2.70494e9	+	1.56170e9i	−1.12456	+	0.649266i	−0.942562	−	0.334032i	$-0.891591\pi$
$479$	−2.70494e9	+	1.56170e9i	−1.12456	+	0.649266i	−0.182000	+	0.983298i	$0.558257\pi$
$480$	−2.67384e8	−	1.60932e9i	−0.110355	−	0.664200i
$481$	1.82197e9	+	3.15575e9i	0.746507	+	1.29299i
$482$	−7.01478e8	+	3.40417e8i	−0.285331	+	0.138467i
$483$	−2.31370e9			−0.934311
$484$	2.09111e9	+	3.02326e8i	0.838334	+	0.121204i
$485$	−2.33745e9	+	1.34953e9i	−0.930351	+	0.537139i
$486$	7.02440e8	+	1.44748e9i	0.277576	+	0.571985i
$487$	1.39533e9			0.547428			0.273714	−	0.961811i	$-0.411748\pi$
$487$	1.39533e9			0.547428			0.273714	+	0.961811i	$0.411748\pi$
$488$	−9.75259e8	−	3.06327e9i	−0.379884	−	1.19321i
$489$	−2.38064e9	−	1.37446e9i	−0.920688	−	0.531560i
$490$	2.81388e9	−	4.15400e9i	1.08049	−	1.59507i
$491$	3.15936e9	+	1.82406e9i	1.20452	+	0.695430i	0.961557	−	0.274605i	$-0.0885471\pi$
$491$	3.15936e9	+	1.82406e9i	1.20452	+	0.695430i	0.242964	+	0.970035i	$0.421880\pi$
$492$	−1.24291e9	+	4.96458e8i	−0.470502	+	0.187934i
$493$			3.24084e9i			1.21813i
$494$	−5.44527e8	−	3.59120e9i	−0.203224	−	1.34028i
$495$		−	2.90552e8i		−	0.107673i
$496$	2.59747e9	+	7.67103e8i	0.955793	+	0.282272i
$497$	−5.39320e9	−	3.11376e9i	−1.97060	−	1.13773i
$498$	7.46076e8	+	5.05384e8i	0.270695	+	0.183366i
$499$	9.10343e7	+	5.25587e7i	0.0327984	+	0.0189362i	0.516310	−	0.856402i	$-0.327305\pi$
$499$	9.10343e7	+	5.25587e7i	0.0327984	+	0.0189362i	−0.483511	+	0.875338i	$0.660639\pi$
$500$	3.01111e9	+	4.35338e8i	1.07729	+	0.155751i
$501$	8.94736e8			0.317880
$502$	−5.54258e8	+	2.68974e8i	−0.195546	+	0.0948959i
$503$	3.58631e8	−	2.07056e8i	0.125649	−	0.0725436i	−0.435858	−	0.900015i	$-0.643555\pi$
$503$	3.58631e8	−	2.07056e8i	0.125649	−	0.0725436i	0.561507	+	0.827472i	$0.310222\pi$
$504$	1.66940e9	−	5.31491e8i	0.580837	−	0.184922i
$505$	3.54076e9			1.22342
$506$	3.11867e8	+	6.42645e8i	0.107014	+	0.220518i
$507$	1.00317e9	+	1.73755e9i	0.341860	+	0.592118i
$508$	−1.30106e9	−	3.25728e9i	−0.440326	−	1.10238i
$509$	2.98420e9	−	1.72293e9i	1.00303	−	0.579101i	0.0938887	−	0.995583i	$-0.470070\pi$
$509$	2.98420e9	−	1.72293e9i	1.00303	−	0.579101i	0.909144	+	0.416481i	$0.136737\pi$
$510$	−2.97342e9	−	2.13833e8i	−0.992568	−	0.0713803i
$511$	5.79711e8	+	3.34696e8i	0.192193	+	0.110963i
$512$	−2.42482e9	−	1.82856e9i	−0.798425	−	0.602094i
$513$	9.87979e8	−	3.17894e9i	0.323100	−	1.03961i
$514$	−3.92600e9	+	1.90523e9i	−1.27520	+	0.618838i
$515$	−6.17252e8	+	1.06911e9i	−0.199130	+	0.344904i
$516$	−7.74520e8	+	3.09368e8i	−0.248175	+	0.0991291i
$517$	2.28031e8	+	3.94962e8i	0.0725734	+	0.125701i
$518$	6.34674e9	+	4.56425e8i	2.00630	+	0.144283i
$519$	1.40408e9	−	8.10643e8i	0.440864	−	0.254533i
$520$	−7.66248e8	+	3.50258e9i	−0.238978	+	1.09239i
$521$			3.92049e9i			1.21453i	0.794499	+	0.607265i	$0.207733\pi$
$521$			3.92049e9i			1.21453i	−0.794499	+	0.607265i	$0.792267\pi$
$522$	7.40115e8	+	5.01347e8i	0.227747	+	0.154274i
$523$	−2.07562e8	−	3.59507e8i	−0.0634441	−	0.109888i	0.832559	−	0.553937i	$-0.186875\pi$
$523$	−2.07562e8	−	3.59507e8i	−0.0634441	−	0.109888i	−0.896003	+	0.444048i	$0.853542\pi$
$524$	2.60107e9	+	2.04880e9i	0.789755	+	0.622071i
$525$		−	1.57944e9i		−	0.476372i
$526$	−1.64970e9	−	1.11749e9i	−0.494260	−	0.334807i
$527$	2.47456e9	−	4.28607e9i	0.736480	−	1.27562i
$528$	7.43863e8	+	7.82590e8i	0.219925	+	0.231375i
$529$	−1.03369e9	+	1.79040e9i	−0.303594	+	0.525841i
$530$	3.39628e8	−	4.72264e9i	0.0990918	−	1.37791i
$531$	1.22888e8			0.0356189
$532$	−5.72525e9	−	2.72974e9i	−1.64856	−	0.786016i
$533$	2.94149e9			0.841437
$534$	3.42199e8	−	4.75840e9i	0.0972489	−	1.35228i
$535$	−2.51712e9	+	4.35978e9i	−0.710666	+	1.23091i
$536$	−8.77390e8	−	2.75587e9i	−0.246102	−	0.773003i
$537$	−4.98448e8	+	8.63336e8i	−0.138902	+	0.240586i
$538$	−1.34439e9	−	9.10676e8i	−0.372209	−	0.252131i
$539$			3.32067e9i			0.913408i
$540$	−2.03329e9	+	2.58138e9i	−0.555676	+	0.705462i
$541$	−8.58225e8	−	1.48649e9i	−0.233029	−	0.403619i	0.725669	−	0.688044i	$-0.241531\pi$
$541$	−8.58225e8	−	1.48649e9i	−0.233029	−	0.403619i	−0.958698	+	0.284425i	$0.908197\pi$
$542$	−5.73190e9	−	3.88273e9i	−1.54633	−	1.04747i
$543$			2.43886e9i			0.653714i
$544$	−4.28634e9	+	3.52502e9i	−1.14154	+	0.938784i
$545$	−3.17210e9	+	1.83141e9i	−0.839380	+	0.484616i
$546$	7.66629e9	+	5.51319e8i	2.01563	+	0.144954i
$547$	−8.51751e8	−	1.47528e9i	−0.222514	−	0.385405i	0.733057	−	0.680167i	$-0.238093\pi$
$547$	−8.51751e8	−	1.47528e9i	−0.222514	−	0.385405i	−0.955571	+	0.294762i	$0.904760\pi$
$548$	−7.53958e8	−	1.88758e9i	−0.195711	−	0.489974i
$549$	−8.10193e8	+	1.40330e9i	−0.208971	+	0.361948i
$550$	−4.38700e8	+	2.12895e8i	−0.112434	+	0.0545628i
$551$	−7.13444e8	−	3.15673e9i	−0.181689	−	0.803909i
$552$	4.32040e8	−	1.97489e9i	0.109329	−	0.499753i
$553$	5.79499e9	+	3.34574e9i	1.45718	+	0.841306i
$554$	5.65772e8	+	4.06874e7i	0.141370	+	0.0101666i
$555$	−2.58643e9	+	1.49327e9i	−0.642207	+	0.370778i
$556$	2.25598e8	−	9.01111e7i	0.0556640	−	0.0222340i
$557$	−3.32303e9	−	5.75566e9i	−0.814781	−	1.41124i	−0.909485	−	0.415737i	$-0.863524\pi$
$557$	−3.32303e9	−	5.75566e9i	−0.814781	−	1.41124i	0.0947036	−	0.995506i	$-0.469810\pi$
$558$	−5.96009e8	−	1.22816e9i	−0.145222	−	0.299251i
$559$	1.83299e9			0.443832
$560$	4.31344e9	+	4.53801e9i	1.03792	+	1.09196i
$561$	1.70867e9	−	9.86502e8i	0.408591	−	0.235900i
$562$	5.56755e8	−	2.70186e8i	0.132308	−	0.0642075i
$563$	−6.39223e9			−1.50964			−0.754819	−	0.655933i	$-0.772275\pi$
$563$	−6.39223e9			−1.50964			−0.754819	+	0.655933i	$0.772275\pi$
$564$	1.84686e8	−	1.27742e9i	0.0433468	−	0.299817i
$565$	1.83420e9	+	1.05898e9i	0.427836	+	0.247011i
$566$	−2.78009e9	−	1.88320e9i	−0.644467	−	0.436556i
$567$	3.80914e9	+	2.19921e9i	0.877578	+	0.506670i
$568$	3.66488e9	−	4.02200e9i	0.839151	−	0.920922i
$569$		−	5.33922e9i		−	1.21502i	−0.794310	−	0.607512i	$-0.792168\pi$
$569$		−	5.33922e9i		−	1.21502i	0.794310	−	0.607512i	$-0.207832\pi$
$570$	2.94332e9	−	4.46290e8i	0.665696	−	0.100938i
$571$		−	3.56091e8i		−	0.0800451i	−0.999199	−	0.0400225i	$-0.987257\pi$
$571$		−	3.56091e8i		−	0.0800451i	0.999199	−	0.0400225i	$-0.0127430\pi$
$572$	−8.80218e8	−	2.20368e9i	−0.196655	−	0.492336i
$573$	4.15670e9	+	2.39987e9i	0.923013	+	0.532902i
$574$	2.88071e9	−	4.25265e9i	0.635781	−	0.938573i
$575$	7.90690e8	+	4.56505e8i	0.173448	+	0.100140i
$576$	1.41931e8	+	1.52419e9i	0.0309457	+	0.332323i
$577$	−8.50967e9			−1.84415			−0.922077	−	0.387007i	$-0.873509\pi$
$577$	−8.50967e9			−1.84415			−0.922077	+	0.387007i	$0.873509\pi$
$578$	2.40067e9	+	4.94691e9i	0.517112	+	1.06558i
$579$	−4.09090e9	+	2.36188e9i	−0.875878	+	0.505688i
$580$	−4.57116e8	+	3.16174e9i	−0.0972812	+	0.672866i
$581$	−3.45838e9			−0.731570
$582$	−4.54824e9	+	2.20720e9i	−0.956342	+	0.464100i
$583$	1.56685e9	+	2.71386e9i	0.327482	+	0.567216i
$584$	−3.93935e8	+	4.32322e8i	−0.0818426	+	0.0898178i
$585$	1.56509e9	−	9.03603e8i	0.323216	−	0.186609i
$586$	3.49809e8	−	4.86421e9i	0.0718107	−	0.998552i
$587$	−2.20961e9	−	1.27572e9i	−0.450901	−	0.260328i	0.257310	−	0.966329i	$-0.417164\pi$
$587$	−2.20961e9	−	1.27572e9i	−0.450901	−	0.260328i	−0.708211	+	0.706001i	$0.750497\pi$
$588$	5.81512e9	−	7.38263e9i	1.17961	−	1.49758i
$589$	−1.46680e9	+	4.71958e9i	−0.295778	+	0.951700i
$590$	1.91735e8	+	3.95096e8i	0.0384342	+	0.0791991i
$591$	−1.75656e9	+	3.04245e9i	−0.350031	+	0.606271i
$592$	−1.57472e9	+	5.33212e9i	−0.311945	+	1.05627i
$593$	−2.23204e9	−	3.86600e9i	−0.439552	−	0.761326i	0.558103	−	0.829772i	$-0.311529\pi$
$593$	−2.23204e9	−	3.86600e9i	−0.439552	−	0.761326i	−0.997655	+	0.0684459i	$0.978196\pi$
$594$	1.55998e8	−	2.16920e9i	0.0305397	−	0.424666i
$595$	9.90808e9	−	5.72043e9i	1.92832	−	1.11332i
$596$	−1.02029e9	+	1.29531e9i	−0.197406	+	0.250618i
$597$			2.46957e9i			0.475018i
$598$	−2.49178e9	+	3.67850e9i	−0.476492	+	0.703423i
$599$	−3.83992e9	−	6.65093e9i	−0.730008	−	1.26441i	−0.956879	−	0.290487i	$-0.906183\pi$
$599$	−3.83992e9	−	6.65093e9i	−0.730008	−	1.26441i	0.226871	−	0.973925i	$-0.427150\pi$
$600$	1.34815e9	+	2.94931e8i	0.254806	+	0.0557431i
$601$		−	7.19146e9i		−	1.35131i	−0.737216	−	0.675657i	$-0.763860\pi$
$601$		−	7.19146e9i		−	1.35131i	0.737216	−	0.675657i	$-0.236140\pi$
$602$	1.79511e9	−	2.65004e9i	0.335354	−	0.495068i
$603$	−7.28889e8	+	1.26247e9i	−0.135379	+	0.234483i
$604$	−2.70776e9	−	3.91481e8i	−0.500013	−	0.0722905i
$605$	1.90292e9	−	3.29595e9i	0.349362	−	0.605113i
$606$	6.61499e9	+	4.75716e8i	1.20747	+	0.0868347i
$607$	7.19074e9			1.30501			0.652504	−	0.757785i	$-0.273719\pi$
$607$	7.19074e9			1.30501			0.652504	+	0.757785i	$0.273719\pi$
$608$	3.39910e9	−	4.37714e9i	0.613339	−	0.789820i
$609$	6.84833e9			1.22864
$610$	−5.77579e9	−	4.15365e8i	−1.03028	−	0.0740927i
$611$	−1.41834e9	+	2.45663e9i	−0.251556	+	0.435708i
$612$	2.76848e9	+	4.00259e8i	0.488215	+	0.0705848i
$613$	2.78562e9	−	4.82483e9i	0.488438	−	0.846000i	−0.511473	−	0.859299i	$-0.670900\pi$
$613$	2.78562e9	−	4.82483e9i	0.488438	−	0.846000i	0.999912	+	0.0132993i	$0.00423343\pi$
$614$	2.37274e9	−	3.50277e9i	0.413677	−	0.610692i
$615$			2.41082e9i			0.417928i
$616$	−4.04799e9	−	8.85565e8i	−0.697761	−	0.152647i
$617$	−2.34561e9	−	4.06271e9i	−0.402029	−	0.696335i	0.591942	−	0.805981i	$-0.298362\pi$
$617$	−2.34561e9	−	4.06271e9i	−0.402029	−	0.696335i	−0.993971	+	0.109646i	$0.965028\pi$
$618$	−1.29682e9	+	1.91443e9i	−0.221014	+	0.326272i
$619$		−	1.67964e9i		−	0.284642i	−0.989821	−	0.142321i	$-0.954544\pi$
$619$		−	1.67964e9i		−	0.284642i	0.989821	−	0.142321i	$-0.0454565\pi$
$620$	3.01871e9	−	3.83243e9i	0.508687	−	0.645807i
$621$	−3.52644e9	+	2.03599e9i	−0.590902	+	0.341158i
$622$	−3.65001e8	+	5.07546e9i	−0.0608173	+	0.845686i
$623$	9.15448e9	+	1.58560e10i	1.51679	+	2.62716i
$624$	−1.90212e9	+	6.44072e9i	−0.313395	+	1.06118i
$625$	1.76492e9	−	3.05693e9i	0.289164	−	0.500847i
$626$	2.36073e9	+	4.86462e9i	0.384625	+	0.792572i
$627$	−1.44716e9	+	1.33705e9i	−0.234466	+	0.216626i
$628$	−2.28878e9	+	2.90574e9i	−0.368762	+	0.468164i
$629$	8.79851e9	+	5.07982e9i	1.40972	+	0.813900i
$630$	2.26363e8	−	3.14765e9i	0.0360673	−	0.501528i
$631$	6.58993e9	−	3.80470e9i	1.04419	−	0.602861i	0.123170	−	0.992386i	$-0.460694\pi$
$631$	6.58993e9	−	3.80470e9i	1.04419	−	0.602861i	0.921016	+	0.389525i	$0.127361\pi$
$632$	−3.93791e9	+	4.32164e9i	−0.620520	+	0.680987i
$633$	−7.44168e8	−	1.28894e9i	−0.116616	−	0.201985i
$634$	−7.73848e9	+	3.75538e9i	−1.20599	+	0.585250i
$635$	−6.31801e9			−0.979203
$636$	1.26901e9	−	8.77741e9i	0.195599	−	1.35290i
$637$	−1.78871e10	+	1.03271e10i	−2.74191	+	1.58304i
$638$	−9.23097e8	−	1.90217e9i	−0.140726	−	0.289986i
$639$	−2.74266e9			−0.415833
$640$	−4.67893e9	+	2.83441e9i	−0.705532	+	0.427398i
$641$	4.32726e9	+	2.49835e9i	0.648949	+	0.374671i	0.788053	−	0.615607i	$-0.211089\pi$
$641$	4.32726e9	+	2.49835e9i	0.648949	+	0.374671i	−0.139105	+	0.990278i	$0.544422\pi$
$642$	−5.28834e9	+	7.80694e9i	−0.788764	+	1.16442i
$643$	−9.04003e9	−	5.21926e9i	−1.34101	−	0.774231i	−0.354053	−	0.935225i	$-0.615197\pi$
$643$	−9.04003e9	−	5.21926e9i	−1.34101	−	0.774231i	−0.986955	+	0.160994i	$0.948530\pi$
$644$	2.87790e9	+	7.20498e9i	0.424595	+	1.06300i
$645$			1.50230e9i			0.220444i
$646$	−6.32109e9	−	7.91206e9i	−0.922525	−	1.15472i
$647$			3.17281e9i			0.460553i	0.973125	+	0.230277i	$0.0739631\pi$
$647$			3.17281e9i			0.460553i	−0.973125	+	0.230277i	$0.926037\pi$
$648$	−2.58845e9	+	2.84068e9i	−0.373703	+	0.410119i
$649$	−2.51714e8	−	1.45327e8i	−0.0361452	−	0.0208684i
$650$	−2.51112e9	−	1.70101e9i	−0.358650	−	0.242946i
$651$	−9.05703e9	−	5.22908e9i	−1.28663	−	0.742834i
$652$	−1.31899e9	+	9.12307e9i	−0.186369	+	1.28906i
$653$	7.88817e9			1.10861			0.554307	−	0.832312i	$-0.312983\pi$
$653$	7.88817e9			1.10861			0.554307	+	0.832312i	$0.312983\pi$
$654$	−6.17230e9	+	2.99533e9i	−0.862830	+	0.418719i
$655$	5.16511e9	−	2.98208e9i	0.718183	−	0.414643i
$656$	3.09199e9	+	3.25297e9i	0.427637	+	0.449901i
$657$	2.94806e8			0.0405562
$658$	2.16264e9	+	4.45643e9i	0.295933	+	0.609812i
$659$	−1.63806e9	−	2.83720e9i	−0.222962	−	0.386182i	0.732744	−	0.680504i	$-0.238239\pi$
$659$	−1.63806e9	−	2.83720e9i	−0.222962	−	0.386182i	−0.955706	+	0.294323i	$0.904906\pi$
$660$	1.80612e9	−	7.21420e8i	0.244535	−	0.0976752i
$661$	2.19759e8	−	1.26878e8i	0.0295965	−	0.0170876i	−0.485129	−	0.874443i	$-0.661227\pi$
$661$	2.19759e8	−	1.26878e8i	0.0295965	−	0.0170876i	0.514725	+	0.857355i	$0.327894\pi$
$662$	9.46632e9	+	6.80768e8i	1.26817	+	0.0912003i
$663$	1.06278e10	+	6.13596e9i	1.41627	+	0.817684i
$664$	6.45787e8	−	2.95195e9i	0.0856054	−	0.391309i
$665$	−8.39163e9	+	7.75315e9i	−1.10655	+	1.02236i
$666$	2.52119e9	−	1.22350e9i	0.330708	−	0.160488i
$667$	−1.97937e9	+	3.42837e9i	−0.258277	+	0.447350i
$668$	−1.11292e9	−	2.78626e9i	−0.144460	−	0.361663i
$669$	4.90662e9	+	8.49852e9i	0.633565	+	1.09737i
$670$	−5.19618e9	−	3.73682e8i	−0.667455	−	0.0479999i
$671$	3.31905e9	−	1.91626e9i	0.424117	−	0.244864i
$672$	7.44884e9	+	9.05762e9i	0.946883	+	1.15139i
$673$			1.01208e10i			1.27986i	0.768433	+	0.639931i	$0.221037\pi$
$673$			1.01208e10i			1.27986i	−0.768433	+	0.639931i	$0.778963\pi$
$674$	1.12131e8	+	7.59567e7i	0.0141064	+	0.00955557i
$675$	−1.38986e9	−	2.40732e9i	−0.173944	−	0.301280i
$676$	4.16301e9	−	5.28519e9i	0.518316	−	0.658032i
$677$		−	4.91594e9i		−	0.608900i	−0.952528	−	0.304450i	$-0.901527\pi$
$677$		−	4.91594e9i		−	0.608900i	0.952528	−	0.304450i	$-0.0984727\pi$
$678$	3.28446e9	+	2.22486e9i	0.404724	+	0.274156i
$679$	9.70105e9	−	1.68027e10i	1.18925	−	2.05985i
$680$	3.03261e9	+	9.52536e9i	0.369858	+	1.16172i
$681$	3.08783e9	−	5.34828e9i	0.374661	−	0.648932i
$682$	−2.31601e8	+	3.22049e9i	−0.0279572	+	0.388755i
$683$	1.67836e9			0.201564			0.100782	−	0.994909i	$-0.467866\pi$
$683$	1.67836e9			0.201564			0.100782	+	0.994909i	$0.467866\pi$
$684$	−2.78474e9	+	2.19587e8i	−0.332727	+	0.0262367i
$685$	−3.66125e9			−0.435224
$686$	−1.47938e9	+	2.05713e10i	−0.174963	+	2.43292i
$687$	6.47035e9	−	1.12070e10i	0.761341	−	1.31868i
$688$	1.92678e9	+	2.02709e9i	0.225565	+	0.237309i
$689$	−9.74568e9	+	1.68800e10i	−1.13513	+	1.96610i
$690$	−3.01487e9	−	2.04224e9i	−0.349379	−	0.236666i
$691$		−	1.15436e10i		−	1.33097i	−0.746411	−	0.665485i	$-0.768225\pi$
$691$		−	1.15436e10i		−	1.33097i	0.746411	−	0.665485i	$-0.231775\pi$
$692$	−4.27085e9	−	3.36405e9i	−0.489940	−	0.385914i
$693$	1.04431e9	+	1.80880e9i	0.119196	+	0.206454i
$694$	1.27380e10	+	8.62858e9i	1.44658	+	0.979899i
$695$		−	4.37584e8i		−	0.0494441i
$696$	−1.27880e9	+	5.84549e9i	−0.143770	+	0.657186i
$697$	7.10239e9	−	4.10057e9i	0.794492	−	0.458700i
$698$	−1.29590e10	−	9.31945e8i	−1.44238	−	0.103728i
$699$	−8.82918e8	−	1.52926e9i	−0.0977800	−	0.169360i
$700$	−4.91847e9	+	1.96459e9i	−0.541984	+	0.216486i
$701$	−1.83417e9	+	3.17687e9i	−0.201106	+	0.348326i	−0.948885	−	0.315622i	$-0.897787\pi$
$701$	−1.83417e9	+	3.17687e9i	−0.201106	+	0.348326i	0.747779	+	0.663948i	$0.231120\pi$
$702$	1.21698e10	−	5.90582e9i	1.32771	−	0.644319i
$703$	−9.68844e9	−	3.01107e9i	−1.05174	−	0.326871i
$704$	1.51177e9	−	3.28986e9i	0.163299	−	0.355363i
$705$	−2.01344e9	−	1.16246e9i	−0.216409	−	0.124944i
$706$	−9.14688e9	−	6.57796e8i	−0.978265	−	0.0703517i
$707$	−2.20426e10	+	1.27263e10i	−2.34582	+	1.35436i
$708$	3.05124e8	+	7.63895e8i	0.0323117	+	0.0808941i
$709$	−3.33584e9	−	5.77784e9i	−0.351514	−	0.608841i	0.635001	−	0.772512i	$-0.281000\pi$
$709$	−3.33584e9	−	5.77784e9i	−0.351514	−	0.608841i	−0.986515	+	0.163671i	$0.947667\pi$
$710$	−4.27918e9	−	8.81785e9i	−0.448700	−	0.924610i
$711$	2.94698e9			0.307492
$712$	−1.52436e10	+	4.85312e9i	−1.58273	+	0.503896i
$713$	5.23550e9	−	3.02272e9i	0.540935	−	0.312309i
$714$	1.92792e10	−	9.35596e9i	1.98220	−	0.961932i
$715$	−4.27438e9			−0.437322
$716$	3.30847e9	+	4.78330e8i	0.336846	+	0.0487004i
$717$	−1.08611e10	−	6.27066e9i	−1.10042	−	0.635326i
$718$	2.04219e9	+	1.38336e9i	0.205902	+	0.139476i
$719$	−1.01812e10	−	5.87814e9i	−1.02153	−	0.589778i	−0.106980	−	0.994261i	$-0.534118\pi$
$719$	−1.01812e10	−	5.87814e9i	−1.02153	−	0.589778i	−0.914546	+	0.404483i	$0.867452\pi$
$720$	2.64446e9	+	7.80981e8i	0.264042	+	0.0779788i
$721$		−	8.87419e9i		−	0.881770i
$722$	7.89881e9	+	6.31519e9i	0.781055	+	0.624462i
$723$			2.63069e9i			0.258873i
$724$	7.59475e9	−	3.03358e9i	0.743753	−	0.297078i
$725$	−2.34037e9	−	1.35121e9i	−0.228088	−	0.131686i
$726$	3.99793e9	−	5.90196e9i	0.387755	−	0.572424i
$727$	2.03969e9	+	1.17762e9i	0.196877	+	0.113667i	0.595198	−	0.803579i	$-0.297074\pi$
$727$	2.03969e9	+	1.17762e9i	0.196877	+	0.113667i	−0.398321	+	0.917246i	$0.630407\pi$
$728$	−7.81889e9	−	2.45590e10i	−0.751079	−	2.35912i
$729$	1.12322e10			1.07379
$730$	4.59966e8	+	9.47824e8i	0.0437619	+	0.0901774i
$731$	4.42586e9	−	2.55527e9i	0.419070	−	0.241950i
$732$	−1.07348e10	−	1.55200e9i	−1.01159	−	0.146253i
$733$	1.77640e10			1.66600			0.833002	−	0.553269i	$-0.186620\pi$
$733$	1.77640e10			1.66600			0.833002	+	0.553269i	$0.186620\pi$
$734$	−8.24139e9	+	3.99944e9i	−0.769245	+	0.373304i
$735$	−8.46405e9	−	1.46602e10i	−0.786271	−	1.36186i
$736$	−6.68731e9	+	1.11107e9i	−0.618271	+	0.102724i
$737$	2.98598e9	−	1.72396e9i	0.274758	−	0.158632i
$738$	1.62263e8	−	2.25633e9i	0.0148601	−	0.206635i
$739$	1.39060e10	+	8.02866e9i	1.26750	+	0.731792i	0.974514	−	0.224325i	$-0.0720178\pi$
$739$	1.39060e10	+	8.02866e9i	1.26750	+	0.731792i	0.292986	+	0.956117i	$0.405351\pi$
$740$	7.86727e9	+	6.19686e9i	0.713696	+	0.562161i
$741$	−1.17028e10	−	3.63709e9i	−1.05663	−	0.328391i
$742$	1.48600e10	+	3.06210e10i	1.33538	+	2.75173i
$743$	−3.33999e9	+	5.78503e9i	−0.298734	+	0.517422i	−0.975847	−	0.218457i	$-0.929898\pi$
$743$	−3.33999e9	+	5.78503e9i	−0.298734	+	0.517422i	0.677113	+	0.735879i	$0.263231\pi$
$744$	6.15459e9	−	6.75432e9i	0.547890	−	0.601280i
$745$	1.48505e9	+	2.57218e9i	0.131581	+	0.227906i
$746$	4.28209e8	−	5.95440e9i	0.0377633	−	0.525112i
$747$	−1.31904e9	+	7.61550e8i	−0.115781	+	0.0668461i
$748$	−5.19736e9	−	4.09384e9i	−0.454074	−	0.357664i
$749$		−	3.61885e10i		−	3.14691i
$750$	5.75687e9	−	8.49860e9i	0.498278	−	0.735585i
$751$	1.42537e8	+	2.46881e8i	0.0122797	+	0.0212690i	0.872100	−	0.489328i	$-0.162758\pi$
$751$	1.42537e8	+	2.46881e8i	0.0122797	+	0.0212690i	−0.859820	+	0.510597i	$0.829424\pi$
$752$	−4.20768e9	+	1.01380e9i	−0.360811	+	0.0869340i
$753$			2.07859e9i			0.177413i
$754$	7.37544e9	−	1.08880e10i	0.626597	−	0.925016i
$755$	−2.46408e9	+	4.26790e9i	−0.208372	+	0.360911i
$756$	3.37996e9	−	2.33782e10i	0.284502	−	1.96782i
$757$	4.95710e9	−	8.58595e9i	0.415329	−	0.719371i	−0.580134	−	0.814521i	$-0.697000\pi$
$757$	4.95710e9	−	8.58595e9i	0.415329	−	0.719371i	0.995463	+	0.0951503i	$0.0303332\pi$
$758$	−1.61856e10	−	1.16398e9i	−1.34985	−	0.0970742i
$759$	2.41006e9			0.200070
$760$	−5.05083e9	−	8.61055e9i	−0.417364	−	0.711514i
$761$	6.71521e9			0.552349			0.276174	−	0.961108i	$-0.410933\pi$
$761$	6.71521e9			0.552349			0.276174	+	0.961108i	$0.410933\pi$
$762$	−1.18036e10	−	8.48852e8i	−0.966432	−	0.0695008i
$763$	1.31650e10	−	2.28025e10i	1.07297	−	1.85843i
$764$	2.30301e9	−	1.59293e10i	0.186840	−	1.29232i
$765$	2.51933e9	−	4.36360e9i	0.203456	−	0.352395i
$766$	5.09558e9	−	7.52237e9i	0.409631	−	0.604720i
$767$		−	1.80784e9i		−	0.144670i
$768$	−9.12219e9	+	4.66672e9i	−0.726666	+	0.371747i
$769$	8.99077e9	+	1.55725e10i	0.712943	+	1.23485i	0.963747	+	0.266816i	$0.0859716\pi$
$769$	8.99077e9	+	1.55725e10i	0.712943	+	1.23485i	−0.250804	+	0.968038i	$0.580695\pi$
$770$	−4.18605e9	+	6.17968e9i	−0.330436	+	0.487807i
$771$			1.47233e10i			1.15695i
$772$	1.24435e10	+	9.80145e9i	0.973379	+	0.766708i
$773$	7.21324e9	−	4.16457e9i	0.561697	−	0.324296i	−0.192129	−	0.981370i	$-0.561539\pi$
$773$	7.21324e9	−	4.16457e9i	0.561697	−	0.324296i	0.753827	+	0.657073i	$0.228206\pi$
$774$	1.01114e8	−	1.40603e9i	0.00783827	−	0.108994i
$775$	2.06345e9	+	3.57401e9i	0.159235	+	0.275803i
$776$	1.25307e10	+	1.14181e10i	0.962629	+	0.877155i
$777$	1.07343e10	−	1.85924e10i	0.820922	−	1.42188i
$778$	−4.76783e8	−	9.82478e8i	−0.0362988	−	0.0747988i
$779$	−6.01535e9	+	5.55768e9i	−0.455911	+	0.421223i
$780$	9.50295e9	+	7.48525e9i	0.717013	+	0.564774i
$781$	5.61781e9	+	3.24345e9i	0.421977	+	0.243628i
$782$	−8.88551e8	+	1.23556e10i	−0.0664444	+	0.923933i
$783$	1.04379e10	−	6.02634e9i	0.777049	−	0.448629i
$784$	−3.02231e10	−	8.92571e9i	−2.23992	−	0.661510i
$785$	3.33138e9	+	5.77012e9i	0.245799	+	0.425736i
$786$	1.00503e10	−	4.87729e9i	0.738246	−	0.358261i
$787$	8.35446e8			0.0610952			0.0305476	−	0.999533i	$-0.490275\pi$
$787$	8.35446e8			0.0610952			0.0305476	+	0.999533i	$0.490275\pi$
$788$	1.16592e10	+	1.68566e9i	0.848846	+	0.122724i
$789$	−5.82207e9	+	3.36137e9i	−0.421996	+	0.243639i
$790$	4.59798e9	+	9.47477e9i	0.331797	+	0.683713i
$791$	−1.52248e10			−1.09379
$792$	−1.73893e9	+	5.53626e8i	−0.124378	+	0.0395985i
$793$	2.06442e10	+	1.19190e10i	1.47009	+	0.848755i
$794$	−8.51749e9	+	1.25740e10i	−0.603865	+	0.891458i
$795$	−1.38347e10	−	7.98749e9i	−0.976530	−	0.563800i
$796$	7.69036e9	−	3.07178e9i	0.540445	−	0.215871i
$797$		−	5.79001e9i		−	0.405112i	−0.979271	−	0.202556i	$-0.935075\pi$
$797$		−	5.79001e9i		−	0.405112i	0.979271	−	0.202556i	$-0.0649248\pi$
$798$	−1.67193e10	+	1.33573e10i	−1.16468	+	0.930484i
$799$			7.90890e9i			0.548532i
$800$	−7.58473e8	−	4.56508e9i	−0.0523751	−	0.315234i
$801$	6.98313e9	+	4.03171e9i	0.480105	+	0.277189i
$802$	−4.33411e9	−	2.93589e9i	−0.296681	−	0.200969i
$803$	−6.03854e8	−	3.48635e8i	−0.0411555	−	0.0237611i
$804$	−9.65751e9	−	1.39626e9i	−0.655344	−	0.0947478i
$805$	1.39752e10			0.944219
$806$	−1.80678e10	+	8.76804e9i	−1.21544	+	0.589834i
$807$	−4.74457e9	+	2.73928e9i	−0.317789	+	0.183476i
$808$	−6.74667e9	−	2.11912e10i	−0.449935	−	1.41324i
$809$	−2.37604e10			−1.57773			−0.788867	−	0.614564i	$-0.789332\pi$
$809$	−2.37604e10			−1.57773			−0.788867	+	0.614564i	$0.789332\pi$
$810$	3.02232e9	+	6.22792e9i	0.199822	+	0.411761i
$811$	−8.19556e8	−	1.41951e9i	−0.0539518	−	0.0934472i	0.837788	−	0.545995i	$-0.183848\pi$
$811$	−8.19556e8	−	1.41951e9i	−0.0539518	−	0.0934472i	−0.891740	+	0.452548i	$0.850515\pi$
$812$	−8.51831e9	−	2.13261e10i	−0.558351	−	1.39786i
$813$	−2.02288e10	+	1.16791e10i	−1.32024	+	0.762242i
$814$	−6.61107e9	−	4.75434e8i	−0.429622	−	0.0308962i
$815$	1.43795e10	+	8.30204e9i	0.930451	+	0.537196i
$816$	4.38587e9	+	1.82031e10i	0.282579	+	1.17282i
$817$	−3.74847e9	+	3.46327e9i	−0.240479	+	0.222182i
$818$	2.40848e9	−	1.16880e9i	0.153853	−	0.0746629i
$819$	−6.49552e9	+	1.12506e10i	−0.413162	+	0.715618i
$820$	7.50743e9	−	2.99871e9i	0.475492	−	0.189926i
$821$	−6.12143e9	−	1.06026e10i	−0.386057	−	0.668671i	0.605858	−	0.795573i	$-0.292830\pi$
$821$	−6.12143e9	−	1.06026e10i	−0.386057	−	0.668671i	−0.991915	+	0.126902i	$0.959497\pi$
$822$	−6.84011e9	−	4.91905e8i	−0.429548	−	0.0308909i
$823$	1.99496e10	−	1.15179e10i	1.24749	−	0.720236i	0.276878	−	0.960905i	$-0.410700\pi$
$823$	1.99496e10	−	1.15179e10i	1.24749	−	0.720236i	0.970607	+	0.240669i	$0.0773669\pi$
$824$	7.57469e9	+	1.65709e9i	0.471650	+	0.103181i
$825$			1.64522e9i			0.102008i
$826$	−2.61369e9	−	1.77049e9i	−0.161370	−	0.109311i
$827$	−1.56755e9	−	2.71508e9i	−0.0963723	−	0.166922i	0.813808	−	0.581134i	$-0.197391\pi$
$827$	−1.56755e9	−	2.71508e9i	−0.0963723	−	0.166922i	−0.910181	+	0.414212i	$0.864057\pi$
$828$	2.68421e9	+	2.11429e9i	0.164328	+	0.129437i
$829$			6.48805e9i			0.395524i	0.980250	+	0.197762i	$0.0633674\pi$
$829$			6.48805e9i			0.395524i	−0.980250	+	0.197762i	$0.936633\pi$
$830$	−4.50645e9	−	3.05263e9i	−0.273565	−	0.185311i
$831$	9.56900e8	−	1.65740e9i	0.0578446	−	0.100190i
$832$	2.24227e10	−	2.08799e9i	1.34976	−	0.125689i
$833$	−2.87930e10	+	4.98710e10i	−1.72596	+	2.98944i
$834$	5.87912e7	−	8.17512e8i	0.00350939	−	0.0487993i
$835$	−5.40439e9			−0.321251
$836$	5.96370e9	+	2.84343e9i	0.353015	+	0.168314i
$837$	−1.84058e10			−1.08496
$838$	2.21339e8	−	3.07779e9i	0.0129928	−	0.180670i
$839$	6.36672e9	−	1.10275e10i	0.372176	−	0.644628i	−0.617724	−	0.786395i	$-0.711945\pi$
$839$	6.36672e9	−	1.10275e10i	0.372176	−	0.644628i	0.989900	+	0.141767i	$0.0452784\pi$
$840$	2.01284e10	−	6.40830e9i	1.17174	−	0.373049i
$841$	−2.76619e9	+	4.79118e9i	−0.160360	+	0.277751i
$842$	−1.05602e10	−	7.15335e9i	−0.609647	−	0.412969i
$843$		−	2.08795e9i		−	0.120040i
$844$	−3.08819e9	+	3.92063e9i	−0.176809	+	0.224470i
$845$	−6.05937e9	−	1.04951e10i	−0.345485	−	0.598397i
$846$	1.80617e9	+	1.22348e9i	0.102556	+	0.0694706i
$847$			2.73581e10i			1.54701i
$848$	−2.89118e10	+	6.96603e9i	−1.62813	+	0.392283i
$849$	−9.81138e9	+	5.66460e9i	−0.550241	+	0.317682i
$850$	−8.43454e9	−	6.06568e8i	−0.471080	−	0.0338776i
$851$	6.20509e9	+	1.07475e10i	0.345139	+	0.597799i
$852$	−6.80983e9	−	1.70488e10i	−0.377223	−	0.944398i
$853$	4.66697e9	−	8.08342e9i	0.257462	−	0.445937i	−0.708099	−	0.706113i	$-0.750447\pi$
$853$	4.66697e9	−	8.08342e9i	0.257462	−	0.445937i	0.965561	+	0.260176i	$0.0837804\pi$
$854$	3.74495e10	−	1.81737e10i	2.05752	−	0.998485i
$855$	−1.49333e9	+	4.80497e9i	−0.0817100	+	0.262911i
$856$	3.08892e10	+	6.75752e9i	1.68325	+	0.368238i
$857$	−6.80255e9	−	3.92746e9i	−0.369181	−	0.213147i	0.303920	−	0.952698i	$-0.401705\pi$
$857$	−6.80255e9	−	3.92746e9i	−0.369181	−	0.213147i	−0.673101	+	0.739551i	$0.735038\pi$
$858$	−7.98557e9	−	5.74281e8i	−0.431619	−	0.0310398i
$859$	7.60408e9	−	4.39022e9i	0.409327	−	0.236325i	−0.281173	−	0.959657i	$-0.590724\pi$
$859$	7.60408e9	−	4.39022e9i	0.409327	−	0.236325i	0.690501	+	0.723332i	$0.257390\pi$
$860$	4.67826e9	−	1.86864e9i	0.250807	−	0.100180i
$861$	−8.66505e9	−	1.50083e10i	−0.462658	−	0.801347i
$862$	−8.60892e9	−	1.77399e10i	−0.457797	−	0.943355i
$863$	−1.08983e10			−0.577192			−0.288596	−	0.957451i	$-0.593189\pi$
$863$	−1.08983e10			−0.577192			−0.288596	+	0.957451i	$0.593189\pi$
$864$	1.93237e10	+	7.25046e9i	1.01928	+	0.382444i
$865$	−8.48090e9	+	4.89645e9i	−0.445539	+	0.257232i
$866$	−1.77752e10	+	8.62607e9i	−0.930041	+	0.451336i
$867$	1.85520e10			0.966770
$868$	−5.01803e9	+	3.47083e10i	−0.260444	+	1.80142i
$869$	−6.03634e9	−	3.48508e9i	−0.312036	−	0.180154i
$870$	8.92374e9	+	6.04486e9i	0.459441	+	0.311221i
$871$	1.85726e10	+	1.07229e10i	0.952375	+	0.549854i
$872$	1.70051e10	+	1.54951e10i	0.868502	+	0.791385i
$873$		−	8.54485e9i		−	0.434665i
$874$	−1.85450e9	−	1.22305e10i	−0.0939584	−	0.619664i
$875$			3.93946e10i			1.98796i
$876$	7.31984e8	+	1.83256e9i	0.0367906	+	0.0921074i
$877$	1.67036e10	+	9.64381e9i	0.836201	+	0.482781i	0.855971	−	0.517024i	$-0.172960\pi$
$877$	1.67036e10	+	9.64381e9i	0.836201	+	0.482781i	−0.0197700	+	0.999805i	$0.506293\pi$
$878$	−6.66346e9	+	9.83696e9i	−0.332253	+	0.490490i
$879$	−1.42494e10	−	8.22692e9i	−0.707680	−	0.408579i
$880$	−4.49308e9	−	4.72700e9i	−0.222257	−	0.233828i
$881$	−3.05452e10			−1.50497			−0.752485	−	0.658609i	$-0.771145\pi$
$881$	−3.05452e10			−1.50497			−0.752485	+	0.658609i	$0.771145\pi$
$882$	6.93492e9	+	1.42904e10i	0.340331	+	0.701300i
$883$	4.57045e9	−	2.63875e9i	0.223407	−	0.128984i	−0.384120	−	0.923283i	$-0.625495\pi$
$883$	4.57045e9	−	2.63875e9i	0.223407	−	0.128984i	0.607527	+	0.794299i	$0.292162\pi$
$884$	5.88831e9	−	4.07278e10i	0.286687	−	1.98293i
$885$	1.48169e9			0.0718551
$886$	7.58630e9	−	3.68153e9i	0.366448	−	0.177832i
$887$	7.51254e9	+	1.30121e10i	0.361455	+	0.626058i	0.988201	−	0.153166i	$-0.0489468\pi$
$887$	7.51254e9	+	1.30121e10i	0.361455	+	0.626058i	−0.626746	+	0.779224i	$0.715613\pi$
$888$	1.38654e10	+	1.26342e10i	0.664488	+	0.605486i
$889$	3.93321e10	−	2.27084e10i	1.87755	−	1.08400i
$890$	−2.06695e9	+	2.87417e10i	−0.0982801	+	1.36662i
$891$	−3.96778e9	−	2.29080e9i	−0.187921	−	0.108496i
$892$	2.03617e10	−	2.58504e10i	0.960590	−	1.21952i
$893$	−1.74108e9	−	7.70364e9i	−0.0818160	−	0.362006i
$894$	2.42885e9	+	5.00498e9i	0.113689	+	0.234273i
$895$	3.01073e9	−	5.21473e9i	0.140375	−	0.243137i
$896$	1.89407e10	−	3.44625e10i	0.879665	−	1.60055i
$897$	7.49518e9	+	1.29820e10i	0.346744	+	0.600578i
$898$	8.28806e8	−	1.15248e10i	0.0381932	−	0.531089i
$899$	−1.54966e10	+	8.94697e9i	−0.711340	+	0.410693i
$900$	−1.44332e9	+	1.83237e9i	−0.0659953	+	0.0837848i
$901$			5.43437e10i			2.47521i
$902$	−3.00068e9	+	4.42977e9i	−0.136144	+	0.200982i
$903$	−5.39963e9	−	9.35243e9i	−0.244038	−	0.422686i
$904$	2.84295e9	−	1.29954e10i	0.127991	−	0.585058i
$905$		−	1.47312e10i		−	0.660646i
$906$	−5.17690e9	+	7.64242e9i	−0.231271	+	0.341415i
$907$	−2.18431e10	+	3.78334e10i	−0.972051	+	1.68364i	−0.282709	+	0.959206i	$0.591233\pi$
$907$	−2.18431e10	+	3.78334e10i	−0.972051	+	1.68364i	−0.689342	+	0.724436i	$0.742100\pi$
$908$	−2.04957e10	−	2.96321e9i	−0.908576	−	0.131359i
$909$	−5.60478e9	+	9.70776e9i	−0.247505	+	0.428692i
$910$	−4.63059e10	−	3.33008e9i	−2.03700	−	0.146491i
$911$	1.73813e10			0.761672			0.380836	−	0.924643i	$-0.375636\pi$
$911$	1.73813e10			0.761672			0.380836	+	0.924643i	$0.375636\pi$
$912$	−8.27931e9	−	1.67652e10i	−0.361420	−	0.731857i
$913$	3.60241e9			0.156655
$914$	2.82859e10	+	2.03417e9i	1.22534	+	0.0881203i
$915$	−9.76869e9	+	1.69199e10i	−0.421563	+	0.730168i
$916$	−4.29473e10	−	6.20921e9i	−1.84630	−	0.266933i
$917$	−2.14366e10	+	3.71292e10i	−0.918041	+	1.59009i
$918$	2.11516e10	−	3.12252e10i	0.902390	−	1.33216i
$919$		−	4.35180e9i		−	0.184954i	−0.995715	−	0.0924772i	$-0.970521\pi$
$919$		−	4.35180e9i		−	0.184954i	0.995715	−	0.0924772i	$-0.0294785\pi$
$920$	−2.60961e9	+	1.19287e10i	−0.110489	+	0.505053i
$921$	−7.13711e9	−	1.23618e10i	−0.301033	−	0.521404i
$922$	−2.24669e9	+	3.31668e9i	−0.0944027	+	0.139362i
$923$			4.03479e10i			1.68894i
$924$	−8.65083e9	+	1.09827e10i	−0.360750	+	0.457992i
$925$	−7.33678e9	+	4.23589e9i	−0.304796	+	0.175974i
$926$	−1.64087e9	+	2.28169e10i	−0.0679105	+	0.944319i
$927$	−1.95414e9	−	3.38466e9i	−0.0805705	−	0.139552i
$928$	1.97938e10	−	3.28868e9i	0.813039	−	0.135084i
$929$	2.07309e10	−	3.59070e10i	0.848327	−	1.46935i	−0.0343729	−	0.999409i	$-0.510943\pi$
$929$	2.07309e10	−	3.59070e10i	0.848327	−	1.46935i	0.882700	−	0.469937i	$-0.155723\pi$
$930$	−7.18622e9	−	1.48082e10i	−0.292961	−	0.603687i
$931$	1.70671e10	−	5.49152e10i	0.693162	−	2.23033i
$932$	−3.66398e9	+	4.65163e9i	−0.148251	+	0.188213i
$933$	1.48683e10	+	8.58421e9i	0.599343	+	0.346031i
$934$	−1.11360e8	+	1.54849e9i	−0.00447212	+	0.0621864i
$935$	−1.03207e10	+	5.95868e9i	−0.412924	+	0.238402i
$936$	−8.39017e9	−	7.64518e9i	−0.334430	−	0.304735i
$937$	−8.14449e9	−	1.41067e10i	−0.323426	−	0.560191i	0.657766	−	0.753222i	$-0.271501\pi$
$937$	−8.14449e9	−	1.41067e10i	−0.323426	−	0.560191i	−0.981193	+	0.193031i	$0.938168\pi$
$938$	3.36913e10	−	1.63500e10i	1.33293	−	0.646854i
$939$	1.82434e10			0.719078
$940$	−1.11554e9	+	7.71588e9i	−0.0438064	+	0.302997i
$941$	4.77516e9	−	2.75694e9i	0.186820	−	0.107861i	−0.403673	−	0.914903i	$-0.632267\pi$
$941$	4.77516e9	−	2.75694e9i	0.186820	−	0.107861i	0.590493	+	0.807043i	$0.298933\pi$
$942$	5.44858e9	+	1.12276e10i	0.212376	+	0.437630i
$943$	1.00178e10			0.389029
$944$	1.99928e9	−	1.90034e9i	0.0773521	−	0.0735242i
$945$	−3.68481e10	−	2.12743e10i	−1.42038	−	0.820056i
$946$	−1.86988e9	+	2.76041e9i	−0.0718115	+	0.106012i
$947$	2.78972e9	+	1.61064e9i	0.106742	+	0.0616275i	0.552421	−	0.833566i	$-0.313704\pi$
$947$	2.78972e9	+	1.61064e9i	0.106742	+	0.0616275i	−0.445679	+	0.895193i	$0.647038\pi$
$948$	7.31716e9	+	1.83189e10i	0.278942	+	0.698346i
$949$		−	4.33697e9i		−	0.164723i
$950$	8.34916e9	−	1.26597e9i	0.315944	−	0.0479060i
$951$			2.90210e10i			1.09416i
$952$	−5.31155e10	−	4.83992e10i	−1.99523	−	1.81806i
$953$	−7.57571e8	−	4.37384e8i	−0.0283529	−	0.0163696i	0.485757	−	0.874094i	$-0.338544\pi$
$953$	−7.57571e8	−	4.37384e8i	−0.0283529	−	0.0163696i	−0.514109	+	0.857725i	$0.671877\pi$
$954$	1.24106e10	+	8.40679e9i	0.462777	+	0.313481i
$955$	−2.51073e10	−	1.44957e10i	−0.932801	−	0.538553i
$956$	−6.01758e9	+	4.16219e10i	−0.222751	+	1.54070i
$957$	−7.13355e9			−0.263096
$958$	3.17914e10	−	1.54280e10i	1.16824	−	0.566929i
$959$	2.27927e10	−	1.31594e10i	0.834510	−	0.481805i
$960$	1.71130e9	+	1.83775e10i	0.0624276	+	0.670404i
$961$	−1.86589e8			−0.00678195
$962$	−1.79992e10	−	3.70898e10i	−0.651839	−	1.34320i
$963$	−7.96886e9	−	1.38025e10i	−0.287544	−	0.498040i
$964$	8.19213e9	−	3.27220e9i	0.294528	−	0.117644i
$965$	2.47099e10	−	1.42662e10i	0.885166	−	0.511051i
$966$	2.61091e10	+	1.87763e9i	0.931904	+	0.0670177i
$967$	6.54881e9	+	3.78096e9i	0.232900	+	0.134465i	0.611909	−	0.790928i	$-0.290402\pi$
$967$	6.54881e9	+	3.78096e9i	0.232900	+	0.134465i	−0.379009	+	0.925393i	$0.623735\pi$
$968$	−2.33519e10	−	5.10861e9i	−0.827481	−	0.181025i
$969$	−3.33272e10	+	7.53220e9i	−1.17670	+	0.265943i
$970$	2.74723e10	−	1.33319e10i	0.966484	−	0.469021i
$971$	1.27229e9	−	2.20366e9i	0.0445982	−	0.0772464i	−0.842865	−	0.538126i	$-0.819133\pi$
$971$	1.27229e9	−	2.20366e9i	0.0445982	−	0.0772464i	0.887463	+	0.460879i	$0.152466\pi$
$972$	−6.75207e9	−	1.69042e10i	−0.235833	−	0.590422i
$973$	1.57278e9	+	2.72413e9i	0.0547359	+	0.0948054i
$974$	−1.57457e10	−	1.13235e9i	−0.546018	−	0.0392667i
$975$	−8.86216e9	+	5.11657e9i	−0.306213	+	0.176792i
$976$	8.51945e9	+	3.53591e10i	0.293317	+	1.21738i
$977$			2.44915e10i			0.840205i	0.907477	+	0.420102i	$0.138006\pi$
$977$			2.44915e10i			0.840205i	−0.907477	+	0.420102i	$0.861994\pi$
$978$	2.57491e10	+	1.74422e10i	0.880188	+	0.596231i
$979$	−9.53575e9	−	1.65164e10i	−0.324800	−	0.562569i
$980$	−3.51245e10	+	4.45926e10i	−1.19212	+	1.51346i
$981$		−	1.15960e10i		−	0.392163i
$982$	−3.41718e10	−	2.31476e10i	−1.15154	−	0.780039i
$983$	5.61148e9	−	9.71937e9i	0.188426	−	0.326363i	−0.756300	−	0.654225i	$-0.772995\pi$
$983$	5.61148e9	−	9.71937e9i	0.188426	−	0.326363i	0.944726	+	0.327862i	$0.106328\pi$
$984$	1.44286e10	−	4.59365e9i	0.482771	−	0.153701i
$985$	1.06100e10	−	1.83770e10i	0.353743	−	0.612700i
$986$	2.63003e9	−	3.65715e10i	0.0873758	−	1.21499i
$987$	1.67126e10			0.553265
$988$	3.23040e9	+	4.09670e10i	0.106563	+	1.35140i
$989$	6.24261e9			0.205201
$990$	−2.35791e8	+	3.27875e9i	−0.00772330	+	0.107395i
$991$	−2.02966e10	+	3.51547e10i	−0.662468	+	1.14743i	0.317497	+	0.948259i	$0.397158\pi$
$991$	−2.02966e10	+	3.51547e10i	−0.662468	+	1.14743i	−0.979965	+	0.199169i	$0.936176\pi$
$992$	−2.86887e10	−	1.07643e10i	−0.933084	−	0.350104i
$993$	1.60105e10	−	2.77311e10i	0.518900	−	0.898761i
$994$	5.83330e10	+	3.95142e10i	1.88392	+	1.27615i
$995$		−	1.49167e10i		−	0.480055i
$996$	−8.00901e9	−	6.30850e9i	−0.256845	−	0.202311i
$997$	1.55081e10	+	2.68609e10i	0.495594	+	0.858395i	0.999987	−	0.00507974i	$-0.00161694\pi$
$997$	1.55081e10	+	2.68609e10i	0.495594	+	0.858395i	−0.504393	+	0.863474i	$0.668284\pi$
$998$	−9.84630e8	−	6.66979e8i	−0.0313557	−	0.0212400i
$999$		−	3.77837e10i		−	1.19902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.8.f.a.27.2	✓	136
4.3	odd	2	inner	76.8.f.a.27.23	yes	136
19.12	odd	6	inner	76.8.f.a.31.23	yes	136
76.31	even	6	inner	76.8.f.a.31.2	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.8.f.a.27.2	✓	136	1.1	even	1	trivial
76.8.f.a.27.23	yes	136	4.3	odd	2	inner
76.8.f.a.31.2	yes	136	76.31	even	6	inner
76.8.f.a.31.23	yes	136	19.12	odd	6	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	76.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-11.2846 - 0.811527i) q^{2} +(-19.0858 + 33.0575i) q^{3} +(126.683 + 18.3155i) q^{4} +(115.282 - 199.674i) q^{5} +(242.202 - 357.551i) q^{6} +1657.40i q^{7} +(-1414.70 - 309.489i) q^{8} +(364.967 + 632.141i) q^{9} +O(q^{10})\)	\(q+(-11.2846 - 0.811527i) q^{2} +(-19.0858 + 33.0575i) q^{3} +(126.683 + 18.3155i) q^{4} +(115.282 - 199.674i) q^{5} +(242.202 - 357.551i) q^{6} +1657.40i q^{7} +(-1414.70 - 309.489i) q^{8} +(364.967 + 632.141i) q^{9} +(-1462.95 + 2159.68i) q^{10} -1726.43i q^{11} +(-3023.30 + 3838.26i) q^{12} +(9299.59 - 5369.12i) q^{13} +(1345.03 - 18703.0i) q^{14} +(4400.49 + 7621.87i) q^{15} +(15713.1 + 4640.51i) q^{16} +(14969.6 - 25928.1i) q^{17} +(-3605.49 - 7429.62i) q^{18} +(-8873.23 + 28550.6i) q^{19} +(18261.4 - 23183.9i) q^{20} +(-54789.5 - 31632.8i) q^{21} +(-1401.04 + 19482.0i) q^{22} +(31671.6 - 18285.6i) q^{23} +(37231.5 - 40859.6i) q^{24} +(12482.6 + 21620.6i) q^{25} +(-109299. + 53041.3i) q^{26} -111344. q^{27} +(-30356.1 + 209964. i) q^{28} +(-93745.0 + 54123.7i) q^{29} +(-43472.3 - 89580.6i) q^{30} +165306. q^{31} +(-173549. - 65117.7i) q^{32} +(57071.4 + 32950.2i) q^{33} +(-189967. + 280439. i) q^{34} +(330940. + 191068. i) q^{35} +(34657.1 + 86766.0i) q^{36} +339343. i q^{37} +(123300. - 314980. i) q^{38} +409895. i q^{39} +(-224886. + 246800. i) q^{40} +(237227. + 136963. i) q^{41} +(592605. + 401425. i) q^{42} +(147828. + 85348.7i) q^{43} +(31620.3 - 218709. i) q^{44} +168296. q^{45} +(-372239. + 180643. i) q^{46} +(-228774. + 132083. i) q^{47} +(-453300. + 430868. i) q^{48} -1.92343e6 q^{49} +(-123315. - 254109. i) q^{50} +(571412. + 989715. i) q^{51} +(1.27644e6 - 509849. i) q^{52} +(-1.57195e6 + 907568. i) q^{53} +(1.25647e6 + 90358.6i) q^{54} +(-344723. - 199026. i) q^{55} +(512947. - 2.34472e6i) q^{56} +(-774460. - 838237. i) q^{57} +(1.10179e6 - 534686. i) q^{58} +(84177.8 - 145800. i) q^{59} +(417868. + 1.04616e6i) q^{60} +(1.10995e6 + 1.92250e6i) q^{61} +(-1.86540e6 - 134150. i) q^{62} +(-1.04771e6 + 604896. i) q^{63} +(1.90559e6 + 875665. i) q^{64} -2.47585e6i q^{65} +(-617286. - 418144. i) q^{66} +(998568. + 1.72957e6i) q^{67} +(2.37128e6 - 3.01047e6i) q^{68} +1.39598e6i q^{69} +(-3.57946e6 - 2.42469e6i) q^{70} +(-1.87870e6 + 3.25401e6i) q^{71} +(-320677. - 1.00724e6i) q^{72} +(201940. - 349771. i) q^{73} +(275386. - 3.82934e6i) q^{74} -952963. q^{75} +(-1.64700e6 + 3.45436e6i) q^{76} +2.86138e6 q^{77} +(332641. - 4.62549e6i) q^{78} +(2.01867e6 - 3.49643e6i) q^{79} +(2.73803e6 - 2.60253e6i) q^{80} +(1.32690e6 - 2.29826e6i) q^{81} +(-2.56586e6 - 1.73809e6i) q^{82} +2.08663e6i q^{83} +(-6.36153e6 - 5.01082e6i) q^{84} +(-3.45145e6 - 5.97808e6i) q^{85} +(-1.59891e6 - 1.08309e6i) q^{86} -4.13197e6i q^{87} +(-534310. + 2.44237e6i) q^{88} +(9.56681e6 - 5.52340e6i) q^{89} +(-1.89915e6 - 136577. i) q^{90} +(8.89878e6 + 1.54131e7i) q^{91} +(4.34716e6 - 1.73639e6i) q^{92} +(-3.15499e6 + 5.46460e6i) q^{93} +(2.68880e6 - 1.30484e6i) q^{94} +(4.67790e6 + 5.06313e6i) q^{95} +(5.46496e6 - 4.49429e6i) q^{96} +(-1.01380e7 - 5.85317e6i) q^{97} +(2.17051e7 + 1.56092e6i) q^{98} +(1.09135e6 - 630089. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 3 q^{2} - 27 q^{4} - 2 q^{5} + 309 q^{6} - 45540 q^{9}+O(q^{10}) \) 136 * q - 3 * q^2 - 27 * q^4 - 2 * q^5 + 309 * q^6 - 45540 * q^9	\( 136 q - 3 q^{2} - 27 q^{4} - 2 q^{5} + 309 q^{6} - 45540 q^{9} - 19464 q^{10} - 10602 q^{13} + 13602 q^{14} + 6525 q^{16} - 23974 q^{17} - 91316 q^{20} + 54264 q^{21} + 381 q^{22} - 51631 q^{24} - 937502 q^{25} + 172188 q^{26} - 165428 q^{28} - 6 q^{29} - 454352 q^{30} + 573507 q^{32} - 182106 q^{33} - 629706 q^{34} - 277130 q^{36} - 759906 q^{38} - 627504 q^{40} - 1873020 q^{41} + 332080 q^{42} - 358069 q^{44} + 321240 q^{45} - 7221687 q^{48} - 15750664 q^{49} + 2848050 q^{52} - 1027650 q^{53} + 4352085 q^{54} - 137426 q^{57} + 10387724 q^{58} + 1607094 q^{60} + 5318582 q^{61} + 3394376 q^{62} - 1319538 q^{64} + 2439607 q^{66} - 87756 q^{68} - 17825238 q^{70} + 26155014 q^{72} + 299212 q^{73} + 1895842 q^{74} + 29672379 q^{76} + 907280 q^{77} + 7456734 q^{78} + 5489562 q^{80} - 11065208 q^{81} + 1288975 q^{82} + 6118214 q^{85} + 16831518 q^{86} - 17728542 q^{89} + 52167894 q^{90} + 10184840 q^{92} - 3299132 q^{93} - 68841730 q^{96} - 9435888 q^{97} - 35100021 q^{98}+O(q^{100}) \) 136 * q - 3 * q^2 - 27 * q^4 - 2 * q^5 + 309 * q^6 - 45540 * q^9 - 19464 * q^10 - 10602 * q^13 + 13602 * q^14 + 6525 * q^16 - 23974 * q^17 - 91316 * q^20 + 54264 * q^21 + 381 * q^22 - 51631 * q^24 - 937502 * q^25 + 172188 * q^26 - 165428 * q^28 - 6 * q^29 - 454352 * q^30 + 573507 * q^32 - 182106 * q^33 - 629706 * q^34 - 277130 * q^36 - 759906 * q^38 - 627504 * q^40 - 1873020 * q^41 + 332080 * q^42 - 358069 * q^44 + 321240 * q^45 - 7221687 * q^48 - 15750664 * q^49 + 2848050 * q^52 - 1027650 * q^53 + 4352085 * q^54 - 137426 * q^57 + 10387724 * q^58 + 1607094 * q^60 + 5318582 * q^61 + 3394376 * q^62 - 1319538 * q^64 + 2439607 * q^66 - 87756 * q^68 - 17825238 * q^70 + 26155014 * q^72 + 299212 * q^73 + 1895842 * q^74 + 29672379 * q^76 + 907280 * q^77 + 7456734 * q^78 + 5489562 * q^80 - 11065208 * q^81 + 1288975 * q^82 + 6118214 * q^85 + 16831518 * q^86 - 17728542 * q^89 + 52167894 * q^90 + 10184840 * q^92 - 3299132 * q^93 - 68841730 * q^96 - 9435888 * q^97 - 35100021 * q^98

Introduction

L-functions

Modular forms

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