LMFDB - Embedded newform 37.9.d.a.6.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,9,Mod(6,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("37.6");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	37.d (of order $4$, 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:	$15.0730085723$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$25$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			6.7
Character	$\chi$	$=$	37.6
Dual form			37.9.d.a.31.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.4597 + 13.4597i) q^{2} -99.3332i q^{3} -106.325i q^{4} +(-869.321 - 869.321i) q^{5} +(1336.99 + 1336.99i) q^{6} -3726.79 q^{7} +(-2014.58 - 2014.58i) q^{8} -3306.09 q^{9} +O(q^{10})$	\(q+(-13.4597 + 13.4597i) q^{2} -99.3332i q^{3} -106.325i q^{4} +(-869.321 - 869.321i) q^{5} +(1336.99 + 1336.99i) q^{6} -3726.79 q^{7} +(-2014.58 - 2014.58i) q^{8} -3306.09 q^{9} +23401.5 q^{10} -10629.1i q^{11} -10561.6 q^{12} +(33046.0 + 33046.0i) q^{13} +(50161.3 - 50161.3i) q^{14} +(-86352.5 + 86352.5i) q^{15} +81450.2 q^{16} +(-21122.6 - 21122.6i) q^{17} +(44498.9 - 44498.9i) q^{18} +(-105342. - 105342. i) q^{19} +(-92430.2 + 92430.2i) q^{20} +370194. i q^{21} +(143064. + 143064. i) q^{22} +(13018.8 + 13018.8i) q^{23} +(-200115. + 200115. i) q^{24} +1.12081e6i q^{25} -889576. q^{26} -323320. i q^{27} +396249. i q^{28} +(42437.6 - 42437.6i) q^{29} -2.32455e6i q^{30} +(-269281. + 269281. i) q^{31} +(-580559. + 580559. i) q^{32} -1.05582e6 q^{33} +568607. q^{34} +(3.23977e6 + 3.23977e6i) q^{35} +351519. i q^{36} +(990242. - 1.59119e6i) q^{37} +2.83573e6 q^{38} +(3.28257e6 - 3.28257e6i) q^{39} +3.50263e6i q^{40} -754056. i q^{41} +(-4.98268e6 - 4.98268e6i) q^{42} +(-1.77761e6 - 1.77761e6i) q^{43} -1.13014e6 q^{44} +(2.87406e6 + 2.87406e6i) q^{45} -350457. q^{46} -4.74724e6 q^{47} -8.09071e6i q^{48} +8.12415e6 q^{49} +(-1.50857e7 - 1.50857e7i) q^{50} +(-2.09818e6 + 2.09818e6i) q^{51} +(3.51360e6 - 3.51360e6i) q^{52} +1.73942e6 q^{53} +(4.35178e6 + 4.35178e6i) q^{54} +(-9.24011e6 + 9.24011e6i) q^{55} +(7.50791e6 + 7.50791e6i) q^{56} +(-1.04640e7 + 1.04640e7i) q^{57} +1.14239e6i q^{58} +(7.08907e6 + 7.08907e6i) q^{59} +(9.18139e6 + 9.18139e6i) q^{60} +(-4.06536e6 + 4.06536e6i) q^{61} -7.24887e6i q^{62} +1.23211e7 q^{63} +5.22299e6i q^{64} -5.74552e7i q^{65} +(1.42110e7 - 1.42110e7i) q^{66} +2.38059e6i q^{67} +(-2.24586e6 + 2.24586e6i) q^{68} +(1.29320e6 - 1.29320e6i) q^{69} -8.72125e7 q^{70} +2.87133e7 q^{71} +(6.66038e6 + 6.66038e6i) q^{72} +1.15144e7i q^{73} +(8.08861e6 + 3.47452e7i) q^{74} +1.11334e8 q^{75} +(-1.12004e7 + 1.12004e7i) q^{76} +3.96125e7i q^{77} +8.83644e7i q^{78} +(-8.22003e6 - 8.22003e6i) q^{79} +(-7.08063e7 - 7.08063e7i) q^{80} -5.38077e7 q^{81} +(1.01493e7 + 1.01493e7i) q^{82} -2.92262e7 q^{83} +3.93607e7 q^{84} +3.67247e7i q^{85} +4.78522e7 q^{86} +(-4.21547e6 - 4.21547e6i) q^{87} +(-2.14132e7 + 2.14132e7i) q^{88} +(7.21615e7 - 7.21615e7i) q^{89} -7.73676e7 q^{90} +(-1.23155e8 - 1.23155e8i) q^{91} +(1.38422e6 - 1.38422e6i) q^{92} +(2.67486e7 + 2.67486e7i) q^{93} +(6.38962e7 - 6.38962e7i) q^{94} +1.83152e8i q^{95} +(5.76688e7 + 5.76688e7i) q^{96} +(-7.92086e7 - 7.92086e7i) q^{97} +(-1.09348e8 + 1.09348e8i) q^{98} +3.51408e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 4 q^{2} + 124 q^{5} + 510 q^{6} - 4 q^{7} - 5256 q^{8} - 93534 q^{9}+O(q^{10}) $ 50 * q + 4 * q^2 + 124 * q^5 + 510 * q^6 - 4 * q^7 - 5256 * q^8 - 93534 * q^9	\( 50 q + 4 q^{2} + 124 q^{5} + 510 q^{6} - 4 q^{7} - 5256 q^{8} - 93534 q^{9} - 10756 q^{10} - 45440 q^{12} + 63592 q^{13} - 80206 q^{14} - 124346 q^{15} - 639128 q^{16} - 178796 q^{17} - 45882 q^{18} + 264774 q^{19} + 469204 q^{20} + 714574 q^{22} - 654272 q^{23} - 1573644 q^{24} + 1841660 q^{26} - 1683686 q^{29} + 1766336 q^{31} - 4332632 q^{32} - 1438888 q^{33} - 5838452 q^{34} - 650482 q^{35} - 2870078 q^{37} - 2281528 q^{38} + 11036546 q^{39} - 7453902 q^{42} + 5097830 q^{43} - 14992464 q^{44} - 15078446 q^{45} + 28776464 q^{46} + 13992320 q^{47} + 4370314 q^{49} + 7603288 q^{50} + 19417938 q^{51} + 54318452 q^{52} + 28075952 q^{53} - 19197122 q^{54} - 6104306 q^{55} + 47803128 q^{56} + 17462426 q^{57} - 677072 q^{59} + 24953316 q^{60} + 4206386 q^{61} - 18098032 q^{63} - 56061730 q^{66} - 52579760 q^{68} + 88118984 q^{69} - 295493636 q^{70} - 37172476 q^{71} - 74582504 q^{72} - 224754524 q^{74} - 144364996 q^{75} + 189294548 q^{76} + 271163438 q^{79} - 312998084 q^{80} + 41535626 q^{81} - 177494710 q^{82} - 74250268 q^{83} - 82088924 q^{84} + 112964036 q^{86} - 142771908 q^{87} + 224951860 q^{88} + 84928780 q^{89} + 716592116 q^{90} - 40969098 q^{91} - 701292428 q^{92} - 83761576 q^{93} + 553881406 q^{94} - 7259376 q^{96} + 467792674 q^{97} + 538649310 q^{98}+O(q^{100}) \) 50 * q + 4 * q^2 + 124 * q^5 + 510 * q^6 - 4 * q^7 - 5256 * q^8 - 93534 * q^9 - 10756 * q^10 - 45440 * q^12 + 63592 * q^13 - 80206 * q^14 - 124346 * q^15 - 639128 * q^16 - 178796 * q^17 - 45882 * q^18 + 264774 * q^19 + 469204 * q^20 + 714574 * q^22 - 654272 * q^23 - 1573644 * q^24 + 1841660 * q^26 - 1683686 * q^29 + 1766336 * q^31 - 4332632 * q^32 - 1438888 * q^33 - 5838452 * q^34 - 650482 * q^35 - 2870078 * q^37 - 2281528 * q^38 + 11036546 * q^39 - 7453902 * q^42 + 5097830 * q^43 - 14992464 * q^44 - 15078446 * q^45 + 28776464 * q^46 + 13992320 * q^47 + 4370314 * q^49 + 7603288 * q^50 + 19417938 * q^51 + 54318452 * q^52 + 28075952 * q^53 - 19197122 * q^54 - 6104306 * q^55 + 47803128 * q^56 + 17462426 * q^57 - 677072 * q^59 + 24953316 * q^60 + 4206386 * q^61 - 18098032 * q^63 - 56061730 * q^66 - 52579760 * q^68 + 88118984 * q^69 - 295493636 * q^70 - 37172476 * q^71 - 74582504 * q^72 - 224754524 * q^74 - 144364996 * q^75 + 189294548 * q^76 + 271163438 * q^79 - 312998084 * q^80 + 41535626 * q^81 - 177494710 * q^82 - 74250268 * q^83 - 82088924 * q^84 + 112964036 * q^86 - 142771908 * q^87 + 224951860 * q^88 + 84928780 * q^89 + 716592116 * q^90 - 40969098 * q^91 - 701292428 * q^92 - 83761576 * q^93 + 553881406 * q^94 - 7259376 * q^96 + 467792674 * q^97 + 538649310 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−13.4597	+	13.4597i	−0.841228	+	0.841228i	−0.989019	−	0.147790i	$-0.952784\pi$
$2$	−13.4597	+	13.4597i	−0.841228	+	0.841228i	0.147790	+	0.989019i	$0.452784\pi$
$3$		−	99.3332i		−	1.22634i	−0.789952	−	0.613168i	$-0.789895\pi$
$3$		−	99.3332i		−	1.22634i	0.789952	−	0.613168i	$-0.210105\pi$
$4$		−	106.325i		−	0.415331i
$5$	−869.321	−	869.321i	−1.39091	−	1.39091i	−0.823285	−	0.567628i	$-0.807861\pi$
$5$	−869.321	−	869.321i	−1.39091	−	1.39091i	−0.567628	−	0.823285i	$-0.692139\pi$
$6$	1336.99	+	1336.99i	1.03163	+	1.03163i
$7$	−3726.79			−1.55218			−0.776091	−	0.630621i	$-0.782800\pi$
$7$	−3726.79			−1.55218			−0.776091	+	0.630621i	$0.782800\pi$
$8$	−2014.58	−	2014.58i	−0.491840	−	0.491840i
$9$	−3306.09			−0.503901
$10$	23401.5			2.34015
$11$		−	10629.1i		−	0.725983i	−0.931792	−	0.362991i	$-0.881755\pi$
$11$		−	10629.1i		−	0.725983i	0.931792	−	0.362991i	$-0.118245\pi$
$12$	−10561.6			−0.509335
$13$	33046.0	+	33046.0i	1.15703	+	1.15703i	0.985111	+	0.171922i	$0.0549976\pi$
$13$	33046.0	+	33046.0i	1.15703	+	1.15703i	0.171922	+	0.985111i	$0.445002\pi$
$14$	50161.3	−	50161.3i	1.30574	−	1.30574i
$15$	−86352.5	+	86352.5i	−1.70573	+	1.70573i
$16$	81450.2			1.24283
$17$	−21122.6	−	21122.6i	−0.252902	−	0.252902i	0.569257	−	0.822159i	$-0.307231\pi$
$17$	−21122.6	−	21122.6i	−0.252902	−	0.252902i	−0.822159	+	0.569257i	$0.807231\pi$
$18$	44498.9	−	44498.9i	0.423896	−	0.423896i
$19$	−105342.	−	105342.i	−0.808326	−	0.808326i	0.176054	−	0.984380i	$-0.443667\pi$
$19$	−105342.	−	105342.i	−0.808326	−	0.808326i	−0.984380	+	0.176054i	$0.943667\pi$
$20$	−92430.2	+	92430.2i	−0.577689	+	0.577689i
$21$			370194.i			1.90350i
$22$	143064.	+	143064.i	0.610717	+	0.610717i
$23$	13018.8	+	13018.8i	0.0465221	+	0.0465221i	0.729985	−	0.683463i	$-0.239527\pi$
$23$	13018.8	+	13018.8i	0.0465221	+	0.0465221i	−0.683463	+	0.729985i	$0.739527\pi$
$24$	−200115.	+	200115.i	−0.603162	+	0.603162i
$25$			1.12081e6i			2.86928i
$26$	−889576.			−1.94666
$27$		−	323320.i		−	0.608384i
$28$			396249.i			0.644669i
$29$	42437.6	−	42437.6i	0.0600011	−	0.0600011i	−0.676470	−	0.736471i	$-0.736491\pi$
$29$	42437.6	−	42437.6i	0.0600011	−	0.0600011i	0.736471	+	0.676470i	$0.236491\pi$
$30$		−	2.32455e6i		−	2.86981i
$31$	−269281.	+	269281.i	−0.291581	+	0.291581i	−0.837705	−	0.546123i	$-0.816103\pi$
$31$	−269281.	+	269281.i	−0.291581	+	0.291581i	0.546123	+	0.837705i	$0.316103\pi$
$32$	−580559.	+	580559.i	−0.553664	+	0.553664i
$33$	−1.05582e6			−0.890299
$34$	568607.			0.425497
$35$	3.23977e6	+	3.23977e6i	2.15895	+	2.15895i
$36$			351519.i			0.209285i
$37$	990242.	−	1.59119e6i	0.528366	−	0.849017i
$37$	990242.	−	1.59119e6i	0.528366	−	0.849017i
$38$	2.83573e6			1.35997
$39$	3.28257e6	−	3.28257e6i	1.41891	−	1.41891i
$40$			3.50263e6i			1.36821i
$41$		−	754056.i		−	0.266851i	−0.991059	−	0.133425i	$-0.957402\pi$
$41$		−	754056.i		−	0.266851i	0.991059	−	0.133425i	$-0.0425976\pi$
$42$	−4.98268e6	−	4.98268e6i	−1.60128	−	1.60128i
$43$	−1.77761e6	−	1.77761e6i	−0.519953	−	0.519953i	0.397604	−	0.917557i	$-0.369842\pi$
$43$	−1.77761e6	−	1.77761e6i	−0.519953	−	0.519953i	−0.917557	+	0.397604i	$0.869842\pi$
$44$	−1.13014e6			−0.301523
$45$	2.87406e6	+	2.87406e6i	0.700882	+	0.700882i
$46$	−350457.			−0.0782715
$47$	−4.74724e6			−0.972859			−0.486429	−	0.873720i	$-0.661701\pi$
$47$	−4.74724e6			−0.972859			−0.486429	+	0.873720i	$0.661701\pi$
$48$		−	8.09071e6i		−	1.52413i
$49$	8.12415e6			1.40927
$50$	−1.50857e7	−	1.50857e7i	−2.41372	−	2.41372i
$51$	−2.09818e6	+	2.09818e6i	−0.310143	+	0.310143i
$52$	3.51360e6	−	3.51360e6i	0.480551	−	0.480551i
$53$	1.73942e6			0.220445			0.110223	−	0.993907i	$-0.464844\pi$
$53$	1.73942e6			0.220445			0.110223	+	0.993907i	$0.464844\pi$
$54$	4.35178e6	+	4.35178e6i	0.511790	+	0.511790i
$55$	−9.24011e6	+	9.24011e6i	−1.00978	+	1.00978i
$56$	7.50791e6	+	7.50791e6i	0.763426	+	0.763426i
$57$	−1.04640e7	+	1.04640e7i	−0.991280	+	0.991280i
$58$			1.14239e6i			0.100949i
$59$	7.08907e6	+	7.08907e6i	0.585034	+	0.585034i	0.936282	−	0.351248i	$-0.114243\pi$
$59$	7.08907e6	+	7.08907e6i	0.585034	+	0.585034i	−0.351248	+	0.936282i	$0.614243\pi$
$60$	9.18139e6	+	9.18139e6i	0.708441	+	0.708441i
$61$	−4.06536e6	+	4.06536e6i	−0.293616	+	0.293616i	−0.838507	−	0.544891i	$-0.816571\pi$
$61$	−4.06536e6	+	4.06536e6i	−0.293616	+	0.293616i	0.544891	+	0.838507i	$0.316571\pi$
$62$		−	7.24887e6i		−	0.490573i
$63$	1.23211e7			0.782146
$64$			5.22299e6i			0.311315i
$65$		−	5.74552e7i		−	3.21866i
$66$	1.42110e7	−	1.42110e7i	0.748945	−	0.748945i
$67$			2.38059e6i			0.118137i	0.998254	+	0.0590685i	$0.0188130\pi$
$67$			2.38059e6i			0.118137i	−0.998254	+	0.0590685i	$0.981187\pi$
$68$	−2.24586e6	+	2.24586e6i	−0.105038	+	0.105038i
$69$	1.29320e6	−	1.29320e6i	0.0570518	−	0.0570518i
$70$	−8.72125e7			−3.63234
$71$	2.87133e7			1.12992			0.564962	−	0.825117i	$-0.308891\pi$
$71$	2.87133e7			1.12992			0.564962	+	0.825117i	$0.308891\pi$
$72$	6.66038e6	+	6.66038e6i	0.247839	+	0.247839i
$73$			1.15144e7i			0.405462i	0.979234	+	0.202731i	$0.0649818\pi$
$73$			1.15144e7i			0.405462i	−0.979234	+	0.202731i	$0.935018\pi$
$74$	8.08861e6	+	3.47452e7i	0.269741	+	1.15869i
$75$	1.11334e8			3.51870
$76$	−1.12004e7	+	1.12004e7i	−0.335723	+	0.335723i
$77$			3.96125e7i			1.12686i
$78$			8.83644e7i			2.38726i
$79$	−8.22003e6	−	8.22003e6i	−0.211040	−	0.211040i	0.593669	−	0.804709i	$-0.297679\pi$
$79$	−8.22003e6	−	8.22003e6i	−0.211040	−	0.211040i	−0.804709	+	0.593669i	$0.797679\pi$
$80$	−7.08063e7	−	7.08063e7i	−1.72867	−	1.72867i
$81$	−5.38077e7			−1.24998
$82$	1.01493e7	+	1.01493e7i	0.224482	+	0.224482i
$83$	−2.92262e7			−0.615828			−0.307914	−	0.951414i	$-0.599631\pi$
$83$	−2.92262e7			−0.615828			−0.307914	+	0.951414i	$0.599631\pi$
$84$	3.93607e7			0.790581
$85$			3.67247e7i			0.703529i
$86$	4.78522e7			0.874798
$87$	−4.21547e6	−	4.21547e6i	−0.0735815	−	0.0735815i
$88$	−2.14132e7	+	2.14132e7i	−0.357068	+	0.357068i
$89$	7.21615e7	−	7.21615e7i	1.15013	−	1.15013i	0.163599	−	0.986527i	$-0.447690\pi$
$89$	7.21615e7	−	7.21615e7i	1.15013	−	1.15013i	0.986527	−	0.163599i	$-0.0523103\pi$
$90$	−7.73676e7			−1.17920
$91$	−1.23155e8	−	1.23155e8i	−1.79592	−	1.79592i
$92$	1.38422e6	−	1.38422e6i	0.0193221	−	0.0193221i
$93$	2.67486e7	+	2.67486e7i	0.357577	+	0.357577i
$94$	6.38962e7	−	6.38962e7i	0.818396	−	0.818396i
$95$			1.83152e8i			2.24862i
$96$	5.76688e7	+	5.76688e7i	0.678979	+	0.678979i
$97$	−7.92086e7	−	7.92086e7i	−0.894717	−	0.894717i	0.100246	−	0.994963i	$-0.468037\pi$
$97$	−7.92086e7	−	7.92086e7i	−0.894717	−	0.894717i	−0.994963	+	0.100246i	$0.968037\pi$
$98$	−1.09348e8	+	1.09348e8i	−1.18552	+	1.18552i
$99$			3.51408e7i			0.365823i
$100$	1.19170e8			1.19170
$101$			9.54047e7i			0.916821i	0.888741	+	0.458410i	$0.151581\pi$
$101$			9.54047e7i			0.916821i	−0.888741	+	0.458410i	$0.848419\pi$
$102$		−	5.64815e7i		−	0.521802i
$103$	−7.75783e7	+	7.75783e7i	−0.689273	+	0.689273i	−0.962071	−	0.272798i	$-0.912051\pi$
$103$	−7.75783e7	+	7.75783e7i	−0.689273	+	0.689273i	0.272798	+	0.962071i	$0.412051\pi$
$104$		−	1.33148e8i		−	1.13815i
$105$	3.21817e8	−	3.21817e8i	2.64760	−	2.64760i
$106$	−2.34120e7	+	2.34120e7i	−0.185445	+	0.185445i
$107$	1.70416e8			1.30010			0.650048	−	0.759893i	$-0.274749\pi$
$107$	1.70416e8			1.30010			0.650048	+	0.759893i	$0.274749\pi$
$108$	−3.43769e7			−0.252681
$109$	1.47182e8	+	1.47182e8i	1.04267	+	1.04267i	0.999048	+	0.0436229i	$0.0138900\pi$
$109$	1.47182e8	+	1.47182e8i	1.04267	+	1.04267i	0.0436229	+	0.999048i	$0.486110\pi$
$110$		−	2.48737e8i		−	1.69891i
$111$	−1.58059e8	−	9.83640e7i	−1.04118	−	0.647954i
$112$	−3.03548e8			−1.92910
$113$	−1.65474e8	+	1.65474e8i	−1.01488	+	1.01488i	−0.0149927	+	0.999888i	$0.504773\pi$
$113$	−1.65474e8	+	1.65474e8i	−1.01488	+	1.01488i	−0.999888	+	0.0149927i	$0.995227\pi$
$114$		−	2.81682e8i		−	1.66779i
$115$		−	2.26350e7i		−	0.129417i
$116$	−4.51217e6	−	4.51217e6i	−0.0249203	−	0.0249203i
$117$	−1.09253e8	−	1.09253e8i	−0.583030	−	0.583030i
$118$	−1.90833e8			−0.984295
$119$	7.87196e7	+	7.87196e7i	0.392550	+	0.392550i
$120$	3.47928e8			1.67789
$121$	1.01381e8			0.472949
$122$		−	1.09437e8i		−	0.493996i
$123$	−7.49028e7			−0.327248
$124$	2.86312e7	+	2.86312e7i	0.121103	+	0.121103i
$125$	6.34767e8	−	6.34767e8i	2.60001	−	2.60001i
$126$	−1.65838e8	+	1.65838e8i	−0.657963	+	0.657963i
$127$	−4.17004e8			−1.60297			−0.801484	−	0.598016i	$-0.795956\pi$
$127$	−4.17004e8			−1.60297			−0.801484	+	0.598016i	$0.795956\pi$
$128$	−2.18923e8	−	2.18923e8i	−0.815551	−	0.815551i
$129$	−1.76576e8	+	1.76576e8i	−0.637637	+	0.637637i
$130$	7.73327e8	+	7.73327e8i	2.70763	+	2.70763i
$131$	1.50254e7	−	1.50254e7i	0.0510200	−	0.0510200i	−0.681136	−	0.732156i	$-0.738514\pi$
$131$	1.50254e7	−	1.50254e7i	0.0510200	−	0.0510200i	0.732156	+	0.681136i	$0.238514\pi$
$132$			1.12260e8i			0.369769i
$133$	3.92587e8	+	3.92587e8i	1.25467	+	1.25467i
$134$	−3.20420e7	−	3.20420e7i	−0.0993802	−	0.0993802i
$135$	−2.81069e8	+	2.81069e8i	−0.846210	+	0.846210i
$136$			8.51064e7i			0.248775i
$137$	−2.32860e8			−0.661017			−0.330509	−	0.943803i	$-0.607220\pi$
$137$	−2.32860e8			−0.661017			−0.330509	+	0.943803i	$0.607220\pi$
$138$			3.48121e7i			0.0959872i
$139$			1.52662e8i			0.408950i	0.978872	+	0.204475i	$0.0655487\pi$
$139$			1.52662e8i			0.408950i	−0.978872	+	0.204475i	$0.934451\pi$
$140$	3.44468e8	−	3.44468e8i	0.896678	−	0.896678i
$141$			4.71559e8i			1.19305i
$142$	−3.86471e8	+	3.86471e8i	−0.950524	+	0.950524i
$143$	3.51250e8	−	3.51250e8i	0.839986	−	0.839986i
$144$	−2.69282e8			−0.626264
$145$	−7.37839e7			−0.166913
$146$	−1.54980e8	−	1.54980e8i	−0.341087	−	0.341087i
$147$		−	8.06998e8i		−	1.72824i
$148$	−1.69183e8	−	1.05287e8i	−0.352623	−	0.219446i
$149$	−3.71792e8			−0.754318			−0.377159	−	0.926148i	$-0.623099\pi$
$149$	−3.71792e8			−0.754318			−0.377159	+	0.926148i	$0.623099\pi$
$150$	−1.49852e9	+	1.49852e9i	−2.96003	+	2.96003i
$151$			3.76230e8i			0.723679i	0.932240	+	0.361839i	$0.117851\pi$
$151$			3.76230e8i			0.723679i	−0.932240	+	0.361839i	$0.882149\pi$
$152$			4.24439e8i			0.795135i
$153$	6.98334e7	+	6.98334e7i	0.127438	+	0.127438i
$154$	−5.33170e8	−	5.33170e8i	−0.947944	−	0.947944i
$155$	4.68184e8			0.811128
$156$	−3.49018e8	−	3.49018e8i	−0.589317	−	0.589317i
$157$	3.49620e8			0.575437			0.287719	−	0.957715i	$-0.407103\pi$
$157$	3.49620e8			0.575437			0.287719	+	0.957715i	$0.407103\pi$
$158$	2.21277e8			0.355066
$159$		−	1.72782e8i		−	0.270340i
$160$	1.00938e9			1.54020
$161$	−4.85183e7	−	4.85183e7i	−0.0722108	−	0.0722108i
$162$	7.24234e8	−	7.24234e8i	1.05152	−	1.05152i
$163$	−5.19606e8	+	5.19606e8i	−0.736078	+	0.736078i	−0.971817	−	0.235738i	$-0.924249\pi$
$163$	−5.19606e8	+	5.19606e8i	−0.736078	+	0.736078i	0.235738	+	0.971817i	$0.424249\pi$
$164$	−8.01747e7			−0.110831
$165$	9.17850e8	+	9.17850e8i	1.23833	+	1.23833i
$166$	3.93374e8	−	3.93374e8i	0.518052	−	0.518052i
$167$	−6.30721e8	−	6.30721e8i	−0.810908	−	0.810908i	0.173862	−	0.984770i	$-0.444375\pi$
$167$	−6.30721e8	−	6.30721e8i	−0.810908	−	0.810908i	−0.984770	+	0.173862i	$0.944375\pi$
$168$	7.45785e8	−	7.45785e8i	0.936217	−	0.936217i
$169$			1.36835e9i			1.67745i
$170$	−4.94302e8	−	4.94302e8i	−0.591829	−	0.591829i
$171$	3.48270e8	+	3.48270e8i	0.407316	+	0.407316i
$172$	−1.89004e8	+	1.89004e8i	−0.215952	+	0.215952i
$173$			7.11281e8i			0.794066i	0.917804	+	0.397033i	$0.129960\pi$
$173$			7.11281e8i			0.794066i	−0.917804	+	0.397033i	$0.870040\pi$
$174$	1.13478e8			0.123798
$175$		−	4.17703e9i		−	4.45364i
$176$		−	8.65743e8i		−	0.902274i
$177$	7.04181e8	−	7.04181e8i	0.717449	−	0.717449i
$178$			1.94254e9i			1.93504i
$179$	−3.07041e8	+	3.07041e8i	−0.299077	+	0.299077i	−0.840652	−	0.541575i	$-0.817828\pi$
$179$	−3.07041e8	+	3.07041e8i	−0.299077	+	0.299077i	0.541575	+	0.840652i	$0.317828\pi$
$180$	3.05583e8	−	3.05583e8i	0.291098	−	0.291098i
$181$	9.62475e8			0.896757			0.448379	−	0.893844i	$-0.352002\pi$
$181$	9.62475e8			0.896757			0.448379	+	0.893844i	$0.352002\pi$
$182$	3.31526e9			3.02157
$183$	4.03825e8	+	4.03825e8i	0.360072	+	0.360072i
$184$		−	5.24548e7i		−	0.0457629i
$185$	−2.24410e9	+	5.22421e8i	−1.91582	+	0.445998i
$186$	−7.20054e8			−0.601607
$187$	−2.24515e8	+	2.24515e8i	−0.183602	+	0.183602i
$188$			5.04749e8i			0.404058i
$189$			1.20495e9i			0.944323i
$190$	−2.46516e9	−	2.46516e9i	−1.89161	−	1.89161i
$191$	−4.33396e8	−	4.33396e8i	−0.325650	−	0.325650i	0.525279	−	0.850930i	$-0.323961\pi$
$191$	−4.33396e8	−	4.33396e8i	−0.325650	−	0.325650i	−0.850930	+	0.525279i	$0.823961\pi$
$192$	5.18817e8			0.381776
$193$	−5.68496e7	−	5.68496e7i	−0.0409730	−	0.0409730i	0.686323	−	0.727296i	$-0.259223\pi$
$193$	−5.68496e7	−	5.68496e7i	−0.0409730	−	0.0409730i	−0.727296	+	0.686323i	$0.759223\pi$
$194$	2.13224e9			1.50532
$195$	−5.70721e9			−3.94716
$196$		−	8.63797e8i		−	0.585312i
$197$	−8.55145e8			−0.567773			−0.283887	−	0.958858i	$-0.591624\pi$
$197$	−8.55145e8			−0.567773			−0.283887	+	0.958858i	$0.591624\pi$
$198$	−4.72984e8	−	4.72984e8i	−0.307741	−	0.307741i
$199$	6.68034e8	−	6.68034e8i	0.425977	−	0.425977i	−0.461279	−	0.887255i	$-0.652609\pi$
$199$	6.68034e8	−	6.68034e8i	0.425977	−	0.425977i	0.887255	+	0.461279i	$0.152609\pi$
$200$	2.25796e9	−	2.25796e9i	1.41123	−	1.41123i
$201$	2.36472e8			0.144876
$202$	−1.28411e9	−	1.28411e9i	−0.771256	−	0.771256i
$203$	−1.58156e8	+	1.58156e8i	−0.0931326	+	0.0931326i
$204$	2.23088e8	+	2.23088e8i	0.128812	+	0.128812i
$205$	−6.55516e8	+	6.55516e8i	−0.371166	+	0.371166i
$206$		−	2.08836e9i		−	1.15967i
$207$	−4.30414e7	−	4.30414e7i	−0.0234425	−	0.0234425i
$208$	2.69160e9	+	2.69160e9i	1.43800	+	1.43800i
$209$	−1.11969e9	+	1.11969e9i	−0.586831	+	0.586831i
$210$			8.66310e9i			4.45447i
$211$	9.92507e8			0.500730			0.250365	−	0.968151i	$-0.419449\pi$
$211$	9.92507e8			0.500730			0.250365	+	0.968151i	$0.419449\pi$
$212$		−	1.84943e8i		−	0.0915577i
$213$		−	2.85218e9i		−	1.38567i
$214$	−2.29374e9	+	2.29374e9i	−1.09368	+	1.09368i
$215$			3.09063e9i			1.44642i
$216$	−6.51355e8	+	6.51355e8i	−0.299228	+	0.299228i
$217$	1.00355e9	−	1.00355e9i	0.452587	−	0.452587i
$218$	−3.96202e9			−1.75425
$219$	1.14376e9			0.497233
$220$	9.82452e8	+	9.82452e8i	0.419392	+	0.419392i
$221$		−	1.39604e9i		−	0.585232i
$222$	3.45136e9	−	8.03468e8i	1.42095	−	0.330793i
$223$	3.24471e9			1.31207			0.656033	−	0.754732i	$-0.272233\pi$
$223$	3.24471e9			1.31207			0.656033	+	0.754732i	$0.272233\pi$
$224$	2.16362e9	−	2.16362e9i	0.859388	−	0.859388i
$225$		−	3.70551e9i		−	1.44583i
$226$		−	4.45443e9i		−	1.70749i
$227$	−1.95220e9	−	1.95220e9i	−0.735226	−	0.735226i	0.236424	−	0.971650i	$-0.424024\pi$
$227$	−1.95220e9	−	1.95220e9i	−0.735226	−	0.735226i	−0.971650	+	0.236424i	$0.924024\pi$
$228$	1.11258e9	+	1.11258e9i	0.411709	+	0.411709i
$229$	−3.37215e9			−1.22621			−0.613105	−	0.790002i	$-0.710080\pi$
$229$	−3.37215e9			−1.22621			−0.613105	+	0.790002i	$0.710080\pi$
$230$	3.04660e8	+	3.04660e8i	0.108869	+	0.108869i
$231$	3.93483e9			1.38191
$232$	−1.70988e8			−0.0590220
$233$			2.32817e9i			0.789934i	0.918695	+	0.394967i	$0.129244\pi$
$233$			2.32817e9i			0.789934i	−0.918695	+	0.394967i	$0.870756\pi$
$234$	2.94102e9			0.980922
$235$	4.12687e9	+	4.12687e9i	1.35316	+	1.35316i
$236$	7.53743e8	−	7.53743e8i	0.242983	−	0.242983i
$237$	−8.16522e8	+	8.16522e8i	−0.258806	+	0.258806i
$238$	−2.11908e9			−0.660448
$239$	9.52524e8	+	9.52524e8i	0.291934	+	0.291934i	0.837844	−	0.545910i	$-0.183816\pi$
$239$	9.52524e8	+	9.52524e8i	0.291934	+	0.291934i	−0.545910	+	0.837844i	$0.683816\pi$
$240$	−7.03342e9	+	7.03342e9i	−2.11993	+	2.11993i
$241$	−4.13090e8	−	4.13090e8i	−0.122455	−	0.122455i	0.643223	−	0.765678i	$-0.277597\pi$
$241$	−4.13090e8	−	4.13090e8i	−0.122455	−	0.122455i	−0.765678	+	0.643223i	$0.777597\pi$
$242$	−1.36455e9	+	1.36455e9i	−0.397858	+	0.397858i
$243$			3.22359e9i			0.924517i
$244$	4.32248e8	+	4.32248e8i	0.121948	+	0.121948i
$245$	−7.06249e9	−	7.06249e9i	−1.96017	−	1.96017i
$246$	1.00817e9	−	1.00817e9i	0.275291	−	0.275291i
$247$		−	6.96226e9i		−	1.87052i
$248$	1.08498e9			0.286823
$249$			2.90313e9i			0.755213i
$250$			1.70875e10i			4.37440i
$251$	1.06821e9	−	1.06821e9i	0.269130	−	0.269130i	−0.559620	−	0.828749i	$-0.689053\pi$
$251$	1.06821e9	−	1.06821e9i	0.269130	−	0.269130i	0.828749	+	0.559620i	$0.189053\pi$
$252$		−	1.31004e9i		−	0.324849i
$253$	1.38378e8	−	1.38378e8i	0.0337743	−	0.0337743i
$254$	5.61273e9	−	5.61273e9i	1.34846	−	1.34846i
$255$	3.64798e9			0.862764
$256$	4.55617e9			1.06082
$257$	−5.02656e9	−	5.02656e9i	−1.15223	−	1.15223i	−0.986105	−	0.166122i	$-0.946876\pi$
$257$	−5.02656e9	−	5.02656e9i	−1.15223	−	1.15223i	−0.166122	−	0.986105i	$-0.553124\pi$
$258$		−	4.75331e9i		−	1.07280i
$259$	−3.69042e9	+	5.93005e9i	−0.820119	+	1.31783i
$260$	−6.10890e9			−1.33681
$261$	−1.40303e8	+	1.40303e8i	−0.0302346	+	0.0302346i
$262$			4.04473e8i			0.0858390i
$263$			4.31755e9i			0.902431i	0.892415	+	0.451216i	$0.149009\pi$
$263$			4.31755e9i			0.902431i	−0.892415	+	0.451216i	$0.850991\pi$
$264$	2.12704e9	+	2.12704e9i	0.437885	+	0.437885i
$265$	−1.51211e9	−	1.51211e9i	−0.306620	−	0.306620i
$266$	−1.05682e10			−2.11093
$267$	−7.16803e9	−	7.16803e9i	−1.41044	−	1.41044i
$268$	2.53116e8			0.0490659
$269$	8.58633e9			1.63983			0.819914	−	0.572487i	$-0.194021\pi$
$269$	8.58633e9			1.63983			0.819914	+	0.572487i	$0.194021\pi$
$270$		−	7.56619e9i		−	1.42371i
$271$	8.32771e9			1.54400			0.772002	−	0.635620i	$-0.219256\pi$
$271$	8.32771e9			1.54400			0.772002	+	0.635620i	$0.219256\pi$
$272$	−1.72044e9	−	1.72044e9i	−0.314314	−	0.314314i
$273$	−1.22334e10	+	1.22334e10i	−2.20241	+	2.20241i
$274$	3.13422e9	−	3.13422e9i	0.556067	−	0.556067i
$275$	1.19132e10			2.08305
$276$	−1.37499e8	−	1.37499e8i	−0.0236954	−	0.0236954i
$277$	−5.69920e9	+	5.69920e9i	−0.968043	+	0.968043i	−0.999505	−	0.0314620i	$-0.989984\pi$
$277$	−5.69920e9	+	5.69920e9i	−0.968043	+	0.968043i	0.0314620	+	0.999505i	$0.489984\pi$
$278$	−2.05477e9	−	2.05477e9i	−0.344021	−	0.344021i
$279$	8.90269e8	−	8.90269e8i	0.146928	−	0.146928i
$280$		−	1.30536e10i		−	2.12372i
$281$	−1.80788e9	−	1.80788e9i	−0.289964	−	0.289964i	0.547102	−	0.837066i	$-0.315731\pi$
$281$	−1.80788e9	−	1.80788e9i	−0.289964	−	0.289964i	−0.837066	+	0.547102i	$0.815731\pi$
$282$	−6.34702e9	−	6.34702e9i	−1.00363	−	1.00363i
$283$	7.34052e8	−	7.34052e8i	0.114441	−	0.114441i	−0.647567	−	0.762008i	$-0.724214\pi$
$283$	7.34052e8	−	7.34052e8i	0.114441	−	0.114441i	0.762008	+	0.647567i	$0.224214\pi$
$284$		−	3.05293e9i		−	0.469292i
$285$	1.81931e10			2.75757
$286$			9.45540e9i			1.41324i
$287$			2.81021e9i			0.414200i
$288$	1.91938e9	−	1.91938e9i	0.278992	−	0.278992i
$289$		−	6.08343e9i		−	0.872081i
$290$	9.93105e8	−	9.93105e8i	0.140412	−	0.140412i
$291$	−7.86805e9	+	7.86805e9i	−1.09722	+	1.09722i
$292$	1.22427e9			0.168401
$293$	7.57338e9			1.02759			0.513794	−	0.857913i	$-0.328239\pi$
$293$	7.57338e9			1.02759			0.513794	+	0.857913i	$0.328239\pi$
$294$	1.08619e10	+	1.08619e10i	1.45384	+	1.45384i
$295$		−	1.23254e10i		−	1.62746i
$296$	−5.20051e9	+	1.21067e9i	−0.677452	+	0.157709i
$297$	−3.43661e9			−0.441677
$298$	5.00419e9	−	5.00419e9i	0.634554	−	0.634554i
$299$			8.60439e8i			0.107655i
$300$		−	1.18375e10i		−	1.46142i
$301$	6.62479e9	+	6.62479e9i	0.807061	+	0.807061i
$302$	−5.06393e9	−	5.06393e9i	−0.608779	−	0.608779i
$303$	9.47686e9			1.12433
$304$	−8.58011e9	−	8.58011e9i	−1.00461	−	1.00461i
$305$	7.06820e9			0.816789
$306$	−1.87987e9			−0.214408
$307$		−	2.86993e9i		−	0.323086i	−0.986866	−	0.161543i	$-0.948353\pi$
$307$		−	2.86993e9i		−	0.323086i	0.986866	−	0.161543i	$-0.0516471\pi$
$308$	4.21178e9			0.468018
$309$	7.70611e9	+	7.70611e9i	0.845281	+	0.845281i
$310$	−6.30159e9	+	6.30159e9i	−0.682344	+	0.682344i
$311$	3.16255e9	−	3.16255e9i	0.338062	−	0.338062i	−0.517576	−	0.855638i	$-0.673165\pi$
$311$	3.16255e9	−	3.16255e9i	0.338062	−	0.338062i	0.855638	+	0.517576i	$0.173165\pi$
$312$	−1.32260e10			−1.39576
$313$	3.49503e9	+	3.49503e9i	0.364144	+	0.364144i	0.865336	−	0.501192i	$-0.167105\pi$
$313$	3.49503e9	+	3.49503e9i	0.364144	+	0.364144i	−0.501192	+	0.865336i	$0.667105\pi$
$314$	−4.70577e9	+	4.70577e9i	−0.484074	+	0.484074i
$315$	−1.07110e10	−	1.07110e10i	−1.08790	−	1.08790i
$316$	−8.73991e8	+	8.73991e8i	−0.0876514	+	0.0876514i
$317$			1.14833e10i			1.13718i	0.822622	+	0.568588i	$0.192510\pi$
$317$			1.14833e10i			1.13718i	−0.822622	+	0.568588i	$0.807490\pi$
$318$	2.32559e9	+	2.32559e9i	0.227418	+	0.227418i
$319$	−4.51075e8	−	4.51075e8i	−0.0435598	−	0.0435598i
$320$	4.54046e9	−	4.54046e9i	0.433012	−	0.433012i
$321$		−	1.69280e10i		−	1.59435i
$322$	1.30608e9			0.121492
$323$			4.45019e9i			0.408855i
$324$			5.72109e9i			0.519157i
$325$	−3.70384e10	+	3.70384e10i	−3.31985	+	3.31985i
$326$		−	1.39874e10i		−	1.23842i
$327$	1.46200e10	−	1.46200e10i	1.27867	−	1.27867i
$328$	−1.51910e9	+	1.51910e9i	−0.131248	+	0.131248i
$329$	1.76920e10			1.51005
$330$	−2.47079e10			−2.08344
$331$	−8.96810e9	−	8.96810e9i	−0.747116	−	0.747116i	0.226820	−	0.973937i	$-0.427167\pi$
$331$	−8.96810e9	−	8.96810e9i	−0.747116	−	0.747116i	−0.973937	+	0.226820i	$0.927167\pi$
$332$			3.10746e9i			0.255772i
$333$	−3.27383e9	+	5.26064e9i	−0.266244	+	0.427820i
$334$	1.69786e10			1.36432
$335$	2.06950e9	−	2.06950e9i	0.164318	−	0.164318i
$336$			3.01524e10i			2.36572i
$337$			1.19932e10i			0.929854i	0.885349	+	0.464927i	$0.153919\pi$
$337$			1.19932e10i			0.929854i	−0.885349	+	0.464927i	$0.846081\pi$
$338$	−1.84175e10	−	1.84175e10i	−1.41112	−	1.41112i
$339$	1.64370e10	+	1.64370e10i	1.24458	+	1.24458i
$340$	3.90474e9			0.292197
$341$	2.86222e9	+	2.86222e9i	0.211683	+	0.211683i
$342$	−9.37519e9			−0.685292
$343$	−8.79279e9			−0.635258
$344$			7.16229e9i			0.511467i
$345$	−2.24841e9			−0.158708
$346$	−9.57359e9	−	9.57359e9i	−0.667991	−	0.667991i
$347$	−1.99593e9	+	1.99593e9i	−0.137666	+	0.137666i	−0.772582	−	0.634915i	$-0.781035\pi$
$347$	−1.99593e9	+	1.99593e9i	−0.137666	+	0.137666i	0.634915	+	0.772582i	$0.281035\pi$
$348$	−4.48208e8	+	4.48208e8i	−0.0305607	+	0.0305607i
$349$	3.73462e9			0.251736			0.125868	−	0.992047i	$-0.459828\pi$
$349$	3.73462e9			0.251736			0.125868	+	0.992047i	$0.459828\pi$
$350$	5.62214e10	+	5.62214e10i	3.74653	+	3.74653i
$351$	1.06844e10	−	1.06844e10i	0.703921	−	0.703921i
$352$	6.17083e9	+	6.17083e9i	0.401951	+	0.401951i
$353$	−1.38609e10	+	1.38609e10i	−0.892671	+	0.892671i	−0.994774	−	0.102103i	$-0.967443\pi$
$353$	−1.38609e10	+	1.38609e10i	−0.892671	+	0.892671i	0.102103	+	0.994774i	$0.467443\pi$
$354$			1.89561e10i			1.20708i
$355$	−2.49610e10	−	2.49610e10i	−1.57163	−	1.57163i
$356$	−7.67254e9	−	7.67254e9i	−0.477683	−	0.477683i
$357$	7.81947e9	−	7.81947e9i	0.481398	−	0.481398i
$358$		−	8.26532e9i		−	0.503185i
$359$	2.62246e10			1.57882			0.789408	−	0.613869i	$-0.210388\pi$
$359$	2.62246e10			1.57882			0.789408	+	0.613869i	$0.210388\pi$
$360$		−	1.15800e10i		−	0.689445i
$361$			5.21026e9i			0.306782i
$362$	−1.29546e10	+	1.29546e10i	−0.754378	+	0.754378i
$363$		−	1.00705e10i		−	0.579994i
$364$	−1.30945e10	+	1.30945e10i	−0.745902	+	0.745902i
$365$	1.00097e10	−	1.00097e10i	0.563963	−	0.563963i
$366$	−1.08707e10			−0.605805
$367$	2.69830e9			0.148739			0.0743697	−	0.997231i	$-0.476306\pi$
$367$	2.69830e9			0.148739			0.0743697	+	0.997231i	$0.476306\pi$
$368$	1.06038e9	+	1.06038e9i	0.0578192	+	0.0578192i
$369$			2.49298e9i			0.134466i
$370$	2.31732e10	−	3.72364e10i	1.23646	−	1.98683i
$371$	−6.48245e9			−0.342171
$372$	2.84403e9	−	2.84403e9i	0.148513	−	0.148513i
$373$			2.24815e10i			1.16142i	0.814111	+	0.580710i	$0.197225\pi$
$373$			2.24815e10i			1.16142i	−0.814111	+	0.580710i	$0.802775\pi$
$374$		−	6.04378e9i		−	0.308903i
$375$	−6.30535e10	−	6.30535e10i	−3.18848	−	3.18848i
$376$	9.56369e9	+	9.56369e9i	0.478491	+	0.478491i
$377$	2.80479e9			0.138846
$378$	−1.62182e10	−	1.62182e10i	−0.794392	−	0.794392i
$379$	−1.25421e10			−0.607872			−0.303936	−	0.952692i	$-0.598301\pi$
$379$	−1.25421e10			−0.607872			−0.303936	+	0.952692i	$0.598301\pi$
$380$	1.94735e10			0.933922
$381$			4.14223e10i			1.96578i
$382$	1.16667e10			0.547893
$383$	−2.01853e10	−	2.01853e10i	−0.938079	−	0.938079i	0.0601130	−	0.998192i	$-0.480854\pi$
$383$	−2.01853e10	−	2.01853e10i	−0.938079	−	0.938079i	−0.998192	+	0.0601130i	$0.980854\pi$
$384$	−2.17463e10	+	2.17463e10i	−1.00014	+	1.00014i
$385$	3.44359e10	−	3.44359e10i	1.56736	−	1.56736i
$386$	1.53035e9			0.0689354
$387$	5.87696e9	+	5.87696e9i	0.262005	+	0.262005i
$388$	−8.42183e9	+	8.42183e9i	−0.371603	+	0.371603i
$389$	−1.29883e10	−	1.29883e10i	−0.567221	−	0.567221i	0.364128	−	0.931349i	$-0.381367\pi$
$389$	−1.29883e10	−	1.29883e10i	−0.567221	−	0.567221i	−0.931349	+	0.364128i	$0.881367\pi$
$390$	7.68170e10	−	7.68170e10i	3.32047	−	3.32047i
$391$		−	5.49983e8i		−	0.0235311i
$392$	−1.63667e10	−	1.63667e10i	−0.693135	−	0.693135i
$393$	−1.49252e9	−	1.49252e9i	−0.0625677	−	0.0625677i
$394$	1.15100e10	−	1.15100e10i	0.477627	−	0.477627i
$395$			1.42917e10i			0.587077i
$396$	3.73634e9			0.151938
$397$		−	3.00613e10i		−	1.21017i	−0.796162	−	0.605084i	$-0.793140\pi$
$397$		−	3.00613e10i		−	1.21017i	0.796162	−	0.605084i	$-0.206860\pi$
$398$			1.79830e10i			0.716688i
$399$	3.89969e10	−	3.89969e10i	1.53865	−	1.53865i
$400$			9.12904e10i			3.56603i
$401$	−1.51153e10	+	1.51153e10i	−0.584574	+	0.584574i	−0.936157	−	0.351583i	$-0.885643\pi$
$401$	−1.51153e10	+	1.51153e10i	−0.584574	+	0.584574i	0.351583	+	0.936157i	$0.385643\pi$
$402$	−3.18283e9	+	3.18283e9i	−0.121874	+	0.121874i
$403$	−1.77973e10			−0.674738
$404$	1.01439e10			0.380784
$405$	4.67762e10	+	4.67762e10i	1.73862	+	1.73862i
$406$		−	4.25745e9i		−	0.156692i
$407$	−1.69130e10	−	1.05254e10i	−0.616372	−	0.383584i
$408$	8.45389e9			0.305082
$409$	−1.20455e10	+	1.20455e10i	−0.430460	+	0.430460i	−0.888785	−	0.458325i	$-0.848450\pi$
$409$	−1.20455e10	+	1.20455e10i	−0.430460	+	0.430460i	0.458325	+	0.888785i	$0.348450\pi$
$410$		−	1.76460e10i		−	0.624471i
$411$			2.31307e10i			0.810629i
$412$	8.24849e9	+	8.24849e9i	0.286276	+	0.286276i
$413$	−2.64195e10	−	2.64195e10i	−0.908080	−	0.908080i
$414$	1.15864e9			0.0394411
$415$	2.54069e10	+	2.54069e10i	0.856564	+	0.856564i
$416$	−3.83703e10			−1.28122
$417$	1.51644e10			0.501510
$418$		−	3.01413e10i		−	0.987318i
$419$	−3.76569e10			−1.22177			−0.610884	−	0.791720i	$-0.709186\pi$
$419$	−3.76569e10			−1.22177			−0.610884	+	0.791720i	$0.709186\pi$
$420$	−3.42171e10	−	3.42171e10i	−1.09963	−	1.09963i
$421$	−8.58611e9	+	8.58611e9i	−0.273318	+	0.273318i	−0.830434	−	0.557117i	$-0.811908\pi$
$421$	−8.58611e9	+	8.58611e9i	−0.273318	+	0.273318i	0.557117	+	0.830434i	$0.311908\pi$
$422$	−1.33588e10	+	1.33588e10i	−0.421228	+	0.421228i
$423$	1.56948e10			0.490224
$424$	−3.50420e9	−	3.50420e9i	−0.108424	−	0.108424i
$425$	2.36745e10	−	2.36745e10i	0.725647	−	0.725647i
$426$	3.83894e10	+	3.83894e10i	1.16566	+	1.16566i
$427$	1.51507e10	−	1.51507e10i	0.455745	−	0.455745i
$428$		−	1.81194e10i		−	0.539970i
$429$	−3.48908e10	−	3.48908e10i	−1.03010	−	1.03010i
$430$	−4.15989e10	−	4.15989e10i	−1.21677	−	1.21677i
$431$	−1.32939e10	+	1.32939e10i	−0.385252	+	0.385252i	−0.872990	−	0.487738i	$-0.837822\pi$
$431$	−1.32939e10	+	1.32939e10i	−0.385252	+	0.385252i	0.487738	+	0.872990i	$0.337822\pi$
$432$		−	2.63345e10i		−	0.756119i
$433$	3.99877e10			1.13756			0.568780	−	0.822490i	$-0.307416\pi$
$433$	3.99877e10			1.13756			0.568780	+	0.822490i	$0.307416\pi$
$434$			2.70150e10i			0.761458i
$435$			7.32919e9i			0.204691i
$436$	1.56490e10	−	1.56490e10i	0.433053	−	0.433053i
$437$		−	2.74285e9i		−	0.0752101i
$438$	−1.53947e10	+	1.53947e10i	−0.418287	+	0.418287i
$439$	−1.68145e10	+	1.68145e10i	−0.452716	+	0.452716i	−0.896255	−	0.443539i	$-0.853723\pi$
$439$	−1.68145e10	+	1.68145e10i	−0.452716	+	0.452716i	0.443539	+	0.896255i	$0.353723\pi$
$440$	3.72299e10			0.993301
$441$	−2.68592e10			−0.710131
$442$	1.87902e10	+	1.87902e10i	0.492313	+	0.492313i
$443$		−	3.61509e10i		−	0.938651i	−0.883025	−	0.469326i	$-0.844497\pi$
$443$		−	3.61509e10i		−	0.938651i	0.883025	−	0.469326i	$-0.155503\pi$
$444$	−1.04585e10	+	1.68055e10i	−0.269115	+	0.432434i
$445$	−1.25463e11			−3.19945
$446$	−4.36726e10	+	4.36726e10i	−1.10375	+	1.10375i
$447$			3.69313e10i			0.925048i
$448$		−	1.94650e10i		−	0.483217i
$449$	1.73791e10	+	1.73791e10i	0.427605	+	0.427605i	0.887812	−	0.460207i	$-0.152225\pi$
$449$	1.73791e10	+	1.73791e10i	0.427605	+	0.427605i	−0.460207	+	0.887812i	$0.652225\pi$
$450$	4.98749e10	+	4.98749e10i	1.21628	+	1.21628i
$451$	−8.01495e9			−0.193729
$452$	1.75939e10	+	1.75939e10i	0.421511	+	0.421511i
$453$	3.73722e10			0.887474
$454$	5.25518e10			1.23699
$455$			2.14123e11i			4.99595i
$456$	4.21609e10			0.975103
$457$	8.23292e9	+	8.23292e9i	0.188751	+	0.188751i	0.795156	−	0.606405i	$-0.207389\pi$
$457$	8.23292e9	+	8.23292e9i	0.188751	+	0.188751i	−0.606405	+	0.795156i	$0.707389\pi$
$458$	4.53879e10	−	4.53879e10i	1.03152	−	1.03152i
$459$	−6.82938e9	+	6.82938e9i	−0.153862	+	0.153862i
$460$	−2.40666e9			−0.0537507
$461$	2.44527e10	+	2.44527e10i	0.541406	+	0.541406i	0.923941	−	0.382535i	$-0.124949\pi$
$461$	2.44527e10	+	2.44527e10i	0.541406	+	0.541406i	−0.382535	+	0.923941i	$0.624949\pi$
$462$	−5.29615e10	+	5.29615e10i	−1.16250	+	1.16250i
$463$	−2.53630e10	−	2.53630e10i	−0.551920	−	0.551920i	0.375074	−	0.926995i	$-0.377617\pi$
$463$	−2.53630e10	−	2.53630e10i	−0.551920	−	0.551920i	−0.926995	+	0.375074i	$0.877617\pi$
$464$	3.45655e9	−	3.45655e9i	0.0745713	−	0.0745713i
$465$		−	4.65062e10i		−	0.994716i
$466$	−3.13364e10	−	3.13364e10i	−0.664515	−	0.664515i
$467$	−3.22395e10	−	3.22395e10i	−0.677830	−	0.677830i	0.281678	−	0.959509i	$-0.409109\pi$
$467$	−3.22395e10	−	3.22395e10i	−0.677830	−	0.677830i	−0.959509	+	0.281678i	$0.909109\pi$
$468$	−1.16163e10	+	1.16163e10i	−0.242150	+	0.242150i
$469$		−	8.87196e9i		−	0.183370i
$470$	−1.11093e11			−2.27664
$471$		−	3.47289e10i		−	0.705680i
$472$		−	2.85630e10i		−	0.575487i
$473$	−1.88945e10	+	1.88945e10i	−0.377477	+	0.377477i
$474$		−	2.19802e10i		−	0.435430i
$475$	1.18068e11	−	1.18068e11i	2.31931	−	2.31931i
$476$	8.36983e9	−	8.36983e9i	0.163038	−	0.163038i
$477$	−5.75068e9			−0.111083
$478$	−2.56413e10			−0.491166
$479$	1.97362e10	+	1.97362e10i	0.374905	+	0.374905i	0.869260	−	0.494355i	$-0.164596\pi$
$479$	1.97362e10	+	1.97362e10i	0.374905	+	0.374905i	−0.494355	+	0.869260i	$0.664596\pi$
$480$		−	1.00265e11i		−	1.88880i
$481$	8.53062e10	−	1.98591e10i	1.59368	−	0.371004i
$482$	1.11201e10			0.206025
$483$	−4.81948e9	+	4.81948e9i	−0.0885547	+	0.0885547i
$484$		−	1.07793e10i		−	0.196430i
$485$			1.37715e11i			2.48895i
$486$	−4.33884e10	−	4.33884e10i	−0.777730	−	0.777730i
$487$	−6.02922e10	−	6.02922e10i	−1.07188	−	1.07188i	−0.997208	−	0.0746697i	$-0.976210\pi$
$487$	−6.02922e10	−	6.02922e10i	−1.07188	−	1.07188i	−0.0746697	−	0.997208i	$-0.523790\pi$
$488$	1.63800e10			0.288824
$489$	5.16142e10	+	5.16142e10i	0.902679	+	0.902679i
$490$	1.90117e11			3.29790
$491$	−3.32120e10			−0.571438			−0.285719	−	0.958313i	$-0.592232\pi$
$491$	−3.32120e10			−0.571438			−0.285719	+	0.958313i	$0.592232\pi$
$492$			7.96401e9i			0.135916i
$493$	−1.79279e9			−0.0303488
$494$	9.37096e10	+	9.37096e10i	1.57353	+	1.57353i
$495$	3.05487e10	−	3.05487e10i	0.508829	−	0.508829i
$496$	−2.19330e10	+	2.19330e10i	−0.362386	+	0.362386i
$497$	−1.07008e11			−1.75385
$498$	−3.90752e10	−	3.90752e10i	−0.635307	−	0.635307i
$499$	−8.56722e10	+	8.56722e10i	−1.38178	+	1.38178i	−0.540312	+	0.841465i	$0.681694\pi$
$499$	−8.56722e10	+	8.56722e10i	−1.38178	+	1.38178i	−0.841465	+	0.540312i	$0.818306\pi$
$500$	−6.74914e10	−	6.74914e10i	−1.07986	−	1.07986i
$501$	−6.26516e10	+	6.26516e10i	−0.994445	+	0.994445i
$502$			2.87555e10i			0.452799i
$503$	5.86203e10	+	5.86203e10i	0.915748	+	0.915748i	0.996717	−	0.0809685i	$-0.0258013\pi$
$503$	5.86203e10	+	5.86203e10i	0.915748	+	0.915748i	−0.0809685	+	0.996717i	$0.525801\pi$
$504$	−2.48218e10	−	2.48218e10i	−0.384691	−	0.384691i
$505$	8.29373e10	−	8.29373e10i	1.27522	−	1.27522i
$506$			3.72505e9i			0.0568238i
$507$	1.35922e11			2.05712
$508$			4.43378e10i			0.665762i
$509$		−	8.83642e8i		−	0.0131645i	−0.999978	−	0.00658226i	$-0.997905\pi$
$509$		−	8.83642e8i		−	0.0131645i	0.999978	−	0.00658226i	$-0.00209521\pi$
$510$	−4.91006e10	+	4.91006e10i	−0.725781	+	0.725781i
$511$		−	4.29118e10i		−	0.629351i
$512$	−5.28018e9	+	5.28018e9i	−0.0768367	+	0.0768367i
$513$	−3.40592e10	+	3.40592e10i	−0.491773	+	0.491773i
$514$	1.35311e11			1.93857
$515$	1.34881e11			1.91744
$516$	1.87744e10	+	1.87744e10i	0.264830	+	0.264830i
$517$			5.04590e10i			0.706279i
$518$	−3.01446e10	−	1.29488e11i	−0.418687	−	1.79850i
$519$	7.06538e10			0.973792
$520$	−1.15748e11	+	1.15748e11i	−1.58307	+	1.58307i
$521$			3.81863e8i			0.00518271i	0.999997	+	0.00259136i	$0.000824855\pi$
$521$			3.81863e8i			0.00518271i	−0.999997	+	0.00259136i	$0.999175\pi$
$522$		−	3.77686e9i		−	0.0508684i
$523$	−5.71662e10	−	5.71662e10i	−0.764069	−	0.764069i	0.212986	−	0.977055i	$-0.431681\pi$
$523$	−5.71662e10	−	5.71662e10i	−0.764069	−	0.764069i	−0.977055	+	0.212986i	$0.931681\pi$
$524$	−1.59757e9	−	1.59757e9i	−0.0211902	−	0.0211902i
$525$	−4.14918e11			−5.46166
$526$	−5.81127e10	−	5.81127e10i	−0.759151	−	0.759151i
$527$	1.13759e10			0.147483
$528$	−8.59971e10			−1.10649
$529$		−	7.79720e10i		−	0.995671i
$530$	4.07051e10			0.515876
$531$	−2.34371e10	−	2.34371e10i	−0.294799	−	0.294799i
$532$	4.17417e10	−	4.17417e10i	0.521103	−	0.521103i
$533$	2.49185e10	−	2.49185e10i	0.308755	−	0.308755i
$534$	1.92959e11			2.37301
$535$	−1.48146e11	−	1.48146e11i	−1.80832	−	1.80832i
$536$	4.79589e9	−	4.79589e9i	0.0581045	−	0.0581045i
$537$	3.04993e10	+	3.04993e10i	0.366770	+	0.366770i
$538$	−1.15569e11	+	1.15569e11i	−1.37947	+	1.37947i
$539$		−	8.63525e10i		−	1.02310i
$540$	2.98846e10	+	2.98846e10i	0.351457	+	0.351457i
$541$	9.36850e10	+	9.36850e10i	1.09366	+	1.09366i	0.995135	+	0.0985218i	$0.0314114\pi$
$541$	9.36850e10	+	9.36850e10i	1.09366	+	1.09366i	0.0985218	+	0.995135i	$0.468589\pi$
$542$	−1.12088e11	+	1.12088e11i	−1.29886	+	1.29886i
$543$		−	9.56057e10i		−	1.09973i
$544$	2.45259e10			0.280046
$545$		−	2.55896e11i		−	2.90053i
$546$		−	3.29315e11i		−	3.70546i
$547$	−1.52259e9	+	1.52259e9i	−0.0170072	+	0.0170072i	−0.715559	−	0.698552i	$-0.753828\pi$
$547$	−1.52259e9	+	1.52259e9i	−0.0170072	+	0.0170072i	0.698552	+	0.715559i	$0.253828\pi$
$548$			2.47588e10i			0.274541i
$549$	1.34405e10	−	1.34405e10i	0.147953	−	0.147953i
$550$	−1.60348e11	+	1.60348e11i	−1.75232	+	1.75232i
$551$	−8.94092e9			−0.0970009
$552$	−5.21051e9			−0.0561208
$553$	3.06343e10	+	3.06343e10i	0.327572	+	0.327572i
$554$		−	1.53418e11i		−	1.62869i
$555$	5.18937e10	+	2.22913e11i	0.546944	+	2.34944i
$556$	1.62317e10			0.169850
$557$	1.29842e10	−	1.29842e10i	0.134895	−	0.134895i	−0.636435	−	0.771330i	$-0.719592\pi$
$557$	1.29842e10	−	1.29842e10i	0.134895	−	0.134895i	0.771330	+	0.636435i	$0.219592\pi$
$558$			2.39654e10i			0.247200i
$559$		−	1.17486e11i		−	1.20320i
$560$	2.63880e11	+	2.63880e11i	2.68321	+	2.68321i
$561$	2.23018e10	+	2.23018e10i	0.225158	+	0.225158i
$562$	4.86668e10			0.487852
$563$	−1.14853e11	−	1.14853e11i	−1.14317	−	1.14317i	−0.987867	−	0.155301i	$-0.950365\pi$
$563$	−1.14853e11	−	1.14853e11i	−1.14317	−	1.14317i	−0.155301	−	0.987867i	$-0.549635\pi$
$564$	5.01383e10			0.495511
$565$	2.87699e11			2.82322
$566$			1.97602e10i			0.192542i
$567$	2.00530e11			1.94020
$568$	−5.78451e10	−	5.78451e10i	−0.555742	−	0.555742i
$569$	5.25714e10	−	5.25714e10i	0.501534	−	0.501534i	−0.410381	−	0.911914i	$-0.634604\pi$
$569$	5.25714e10	−	5.25714e10i	0.501534	−	0.501534i	0.911914	+	0.410381i	$0.134604\pi$
$570$	−2.44872e11	+	2.44872e11i	−2.31975	+	2.31975i
$571$	1.86681e11			1.75613			0.878065	−	0.478541i	$-0.158834\pi$
$571$	1.86681e11			1.75613			0.878065	+	0.478541i	$0.158834\pi$
$572$	−3.73465e10	−	3.73465e10i	−0.348872	−	0.348872i
$573$	−4.30506e10	+	4.30506e10i	−0.399357	+	0.399357i
$574$	−3.78244e10	−	3.78244e10i	−0.348437	−	0.348437i
$575$	−1.45916e10	+	1.45916e10i	−0.133485	+	0.133485i
$576$		−	1.72677e10i		−	0.156872i
$577$	5.14787e10	+	5.14787e10i	0.464434	+	0.464434i	0.900106	−	0.435672i	$-0.143489\pi$
$577$	5.14787e10	+	5.14787e10i	0.464434	+	0.464434i	−0.435672	+	0.900106i	$0.643489\pi$
$578$	8.18808e10	+	8.18808e10i	0.733620	+	0.733620i
$579$	−5.64705e9	+	5.64705e9i	−0.0502467	+	0.0502467i
$580$			7.84504e9i			0.0693240i
$581$	1.08920e11			0.955878
$582$		−	2.11802e11i		−	1.84603i
$583$		−	1.84885e10i		−	0.160040i
$584$	2.31967e10	−	2.31967e10i	0.199423	−	0.199423i
$585$			1.89952e11i			1.62189i
$586$	−1.01935e11	+	1.01935e11i	−0.864437	+	0.864437i
$587$	−1.12471e11	+	1.12471e11i	−0.947298	+	0.947298i	−0.998679	−	0.0513808i	$-0.983638\pi$
$587$	−1.12471e11	+	1.12471e11i	−0.947298	+	0.947298i	0.0513808	+	0.998679i	$0.483638\pi$
$588$	−8.58038e10			−0.717790
$589$	5.67332e10			0.471385
$590$	1.65895e11	+	1.65895e11i	1.36907	+	1.36907i
$591$			8.49443e10i			0.696281i
$592$	8.06554e10	−	1.29603e11i	0.656669	−	1.05518i
$593$	3.77490e10			0.305272			0.152636	−	0.988282i	$-0.451224\pi$
$593$	3.77490e10			0.305272			0.152636	+	0.988282i	$0.451224\pi$
$594$	4.62556e10	−	4.62556e10i	0.371551	−	0.371551i
$595$		−	1.36865e11i		−	1.09201i
$596$			3.95306e10i			0.313292i
$597$	−6.63579e10	−	6.63579e10i	−0.522391	−	0.522391i
$598$	−1.15812e10	−	1.15812e10i	−0.0905627	−	0.0905627i
$599$	−1.25548e11			−0.975217			−0.487608	−	0.873062i	$-0.662131\pi$
$599$	−1.25548e11			−0.975217			−0.487608	+	0.873062i	$0.662131\pi$
$600$	−2.24291e11	−	2.24291e11i	−1.73064	−	1.73064i
$601$	−5.12972e10			−0.393184			−0.196592	−	0.980485i	$-0.562987\pi$
$601$	−5.12972e10			−0.393184			−0.196592	+	0.980485i	$0.562987\pi$
$602$	−1.78335e11			−1.35785
$603$		−	7.87046e9i		−	0.0595293i
$604$	4.00025e10			0.300566
$605$	−8.81324e10	−	8.81324e10i	−0.657831	−	0.657831i
$606$	−1.27555e11	+	1.27555e11i	−0.945819	+	0.945819i
$607$	6.91794e10	−	6.91794e10i	0.509591	−	0.509591i	−0.404810	−	0.914401i	$-0.632662\pi$
$607$	6.91794e10	−	6.91794e10i	0.509591	−	0.509591i	0.914401	+	0.404810i	$0.132662\pi$
$608$	1.22314e11			0.895083
$609$	1.57102e10	+	1.57102e10i	0.114212	+	0.114212i
$610$	−9.51356e10	+	9.51356e10i	−0.687106	+	0.687106i
$611$	−1.56877e11	−	1.56877e11i	−1.12563	−	1.12563i
$612$	7.42501e9	−	7.42501e9i	0.0529287	−	0.0529287i
$613$			2.70234e11i			1.91381i	0.290405	+	0.956904i	$0.406210\pi$
$613$			2.70234e11i			1.91381i	−0.290405	+	0.956904i	$0.593790\pi$
$614$	3.86283e10	+	3.86283e10i	0.271789	+	0.271789i
$615$	6.51146e10	+	6.51146e10i	0.455174	+	0.455174i
$616$	7.98024e10	−	7.98024e10i	0.554234	−	0.554234i
$617$			5.45438e10i			0.376361i	0.982134	+	0.188181i	$0.0602591\pi$
$617$			5.45438e10i			0.376361i	−0.982134	+	0.188181i	$0.939741\pi$
$618$	−2.07443e11			−1.42215
$619$			2.37711e11i			1.61915i	0.587016	+	0.809575i	$0.300303\pi$
$619$			2.37711e11i			1.61915i	−0.587016	+	0.809575i	$0.699697\pi$
$620$		−	4.97795e10i		−	0.336886i
$621$	4.20925e9	−	4.20925e9i	0.0283034	−	0.0283034i
$622$			8.51338e10i			0.568775i
$623$	−2.68931e11	+	2.68931e11i	−1.78520	+	1.78520i
$624$	2.67366e11	−	2.67366e11i	1.76347	−	1.76347i
$625$	−6.65815e11			−4.36349
$626$	−9.40837e10			−0.612656
$627$	1.11223e11	+	1.11223e11i	0.719652	+	0.719652i
$628$		−	3.71733e10i		−	0.238997i
$629$	−5.45267e10	+	1.26937e10i	−0.348343	+	0.0810934i
$630$	2.88333e11			1.83034
$631$	−4.08411e10	+	4.08411e10i	−0.257620	+	0.257620i	−0.824085	−	0.566465i	$-0.808310\pi$
$631$	−4.08411e10	+	4.08411e10i	−0.257620	+	0.257620i	0.566465	+	0.824085i	$0.308310\pi$
$632$			3.31198e10i			0.207596i
$633$		−	9.85889e10i		−	0.614064i
$634$	−1.54561e11	−	1.54561e11i	−0.956625	−	0.956625i
$635$	3.62510e11	+	3.62510e11i	2.22959	+	2.22959i
$636$	−1.83710e10			−0.112281
$637$	2.68471e11	+	2.68471e11i	1.63057	+	1.63057i
$638$	1.21426e10			0.0732875
$639$	−9.49287e10			−0.569369
$640$			3.80628e11i			2.26872i
$641$	−3.17145e11			−1.87856			−0.939282	−	0.343147i	$-0.888507\pi$
$641$	−3.17145e11			−1.87856			−0.939282	+	0.343147i	$0.888507\pi$
$642$	2.27845e11	+	2.27845e11i	1.34122	+	1.34122i
$643$	1.45013e11	−	1.45013e11i	0.848325	−	0.848325i	−0.141599	−	0.989924i	$-0.545224\pi$
$643$	1.45013e11	−	1.45013e11i	0.848325	−	0.848325i	0.989924	+	0.141599i	$0.0452244\pi$
$644$	−5.15869e9	+	5.15869e9i	−0.0299914	+	0.0299914i
$645$	3.07003e11			1.77379
$646$	−5.98981e10	−	5.98981e10i	−0.343940	−	0.343940i
$647$	1.74146e10	−	1.74146e10i	0.0993797	−	0.0993797i	−0.655669	−	0.755049i	$-0.727613\pi$
$647$	1.74146e10	−	1.74146e10i	0.0993797	−	0.0993797i	0.755049	+	0.655669i	$0.227613\pi$
$648$	1.08400e11	+	1.08400e11i	0.614793	+	0.614793i
$649$	7.53506e10	−	7.53506e10i	0.424725	−	0.424725i
$650$		−	9.97047e11i		−	5.58550i
$651$	−9.96863e10	−	9.96863e10i	−0.555024	−	0.555024i
$652$	5.52470e10	+	5.52470e10i	0.305716	+	0.305716i
$653$	2.08117e11	−	2.08117e11i	1.14460	−	1.14460i	0.157007	−	0.987597i	$-0.449815\pi$
$653$	2.08117e11	−	2.08117e11i	1.14460	−	1.14460i	0.987597	−	0.157007i	$-0.0501846\pi$
$654$			3.93561e11i			2.15130i
$655$	−2.61238e10			−0.141929
$656$		−	6.14180e10i		−	0.331650i
$657$		−	3.80677e10i		−	0.204313i
$658$	−2.38128e11	+	2.38128e11i	−1.27030	+	1.27030i
$659$		−	2.20529e11i		−	1.16930i	−0.811287	−	0.584649i	$-0.801232\pi$
$659$		−	2.20529e11i		−	1.16930i	0.811287	−	0.584649i	$-0.198768\pi$
$660$	9.75901e10	−	9.75901e10i	0.514316	−	0.514316i
$661$	−2.78529e10	+	2.78529e10i	−0.145903	+	0.145903i	−0.776285	−	0.630382i	$-0.782898\pi$
$661$	−2.78529e10	+	2.78529e10i	−0.145903	+	0.145903i	0.630382	+	0.776285i	$0.282898\pi$
$662$	2.41415e11			1.25699
$663$	−1.38673e11			−0.717691
$664$	5.88785e10	+	5.88785e10i	0.302889	+	0.302889i
$665$		−	6.82568e11i		−	3.49027i
$666$	−2.67417e10	−	1.14871e11i	−0.135923	−	0.583866i
$667$	1.10497e9			0.00558276
$668$	−6.70612e10	+	6.70612e10i	−0.336795	+	0.336795i
$669$		−	3.22307e11i		−	1.60903i
$670$			5.57095e10i			0.276458i
$671$	4.32112e10	+	4.32112e10i	0.213160	+	0.213160i
$672$	−2.14920e11	−	2.14920e11i	−1.05390	−	1.05390i
$673$	1.02165e10			0.0498015			0.0249008	−	0.999690i	$-0.492073\pi$
$673$	1.02165e10			0.0498015			0.0249008	+	0.999690i	$0.492073\pi$
$674$	−1.61424e11	−	1.61424e11i	−0.782219	−	0.782219i
$675$	3.62382e11			1.74563
$676$	1.45489e11			0.696696
$677$			2.30951e11i			1.09942i	0.835355	+	0.549711i	$0.185262\pi$
$677$			2.30951e11i			1.09942i	−0.835355	+	0.549711i	$0.814738\pi$
$678$	−4.42473e11			−2.09396
$679$	2.95194e11	+	2.95194e11i	1.38876	+	1.38876i
$680$	7.39848e10	−	7.39848e10i	0.346024	−	0.346024i
$681$	−1.93918e11	+	1.93918e11i	−0.901634	+	0.901634i
$682$	−7.70491e10			−0.356147
$683$	1.83477e10	+	1.83477e10i	0.0843138	+	0.0843138i	0.748006	−	0.663692i	$-0.231011\pi$
$683$	1.83477e10	+	1.83477e10i	0.0843138	+	0.0843138i	−0.663692	+	0.748006i	$0.731011\pi$
$684$	3.70297e10	−	3.70297e10i	0.169171	−	0.169171i
$685$	2.02430e11	+	2.02430e11i	0.919418	+	0.919418i
$686$	1.18348e11	−	1.18348e11i	0.534397	−	0.534397i
$687$			3.34966e11i			1.50375i
$688$	−1.44787e11	−	1.44787e11i	−0.646213	−	0.646213i
$689$	5.74809e10	+	5.74809e10i	0.255062	+	0.255062i
$690$	3.02628e10	−	3.02628e10i	0.133510	−	0.133510i
$691$		−	3.41672e11i		−	1.49864i	−0.662209	−	0.749319i	$-0.730381\pi$
$691$		−	3.41672e11i		−	1.49864i	0.662209	−	0.749319i	$-0.269619\pi$
$692$	7.56267e10			0.329800
$693$		−	1.30962e11i		−	0.567824i
$694$		−	5.37292e10i		−	0.231618i
$695$	1.32712e11	−	1.32712e11i	0.568814	−	0.568814i
$696$			1.69848e10i			0.0723808i
$697$	−1.59276e10	+	1.59276e10i	−0.0674870	+	0.0674870i
$698$	−5.02668e10	+	5.02668e10i	−0.211767	+	0.211767i
$699$	2.31265e11			0.968725
$700$	−4.44121e11			−1.84973
$701$	−7.04771e10	−	7.04771e10i	−0.291861	−	0.291861i	0.545954	−	0.837815i	$-0.316167\pi$
$701$	−7.04771e10	−	7.04771e10i	−0.291861	−	0.291861i	−0.837815	+	0.545954i	$0.816167\pi$
$702$			2.87618e11i			1.18432i
$703$	−2.71933e11	+	6.33055e10i	−1.11337	+	0.259191i
$704$	5.55158e10			0.226009
$705$	4.09936e11	−	4.09936e11i	1.65943	−	1.65943i
$706$		−	3.73125e11i		−	1.50188i
$707$		−	3.55553e11i		−	1.42307i
$708$	−7.48717e10	−	7.48717e10i	−0.297979	−	0.297979i
$709$	−5.37735e10	−	5.37735e10i	−0.212806	−	0.212806i	0.592653	−	0.805458i	$-0.298081\pi$
$709$	−5.37735e10	−	5.37735e10i	−0.212806	−	0.212806i	−0.805458	+	0.592653i	$0.798081\pi$
$710$	6.71934e11			2.64419
$711$	2.71762e10	+	2.71762e10i	0.106343	+	0.106343i
$712$	−2.90750e11			−1.13136
$713$	−7.01144e9			−0.0271300
$714$			2.10495e11i			0.809932i
$715$	−6.10697e11			−2.33669
$716$	3.26460e10	+	3.26460e10i	0.124216	+	0.124216i
$717$	9.46173e10	−	9.46173e10i	0.358009	−	0.358009i
$718$	−3.52974e11	+	3.52974e11i	−1.32814	+	1.32814i
$719$	−2.12047e11			−0.793443			−0.396722	−	0.917939i	$-0.629852\pi$
$719$	−2.12047e11			−0.793443			−0.396722	+	0.917939i	$0.629852\pi$
$720$	2.34092e11	+	2.34092e11i	0.871078	+	0.871078i
$721$	2.89118e11	−	2.89118e11i	1.06988	−	1.06988i
$722$	−7.01283e10	−	7.01283e10i	−0.258074	−	0.258074i
$723$	−4.10336e10	+	4.10336e10i	−0.150171	+	0.150171i
$724$		−	1.02335e11i		−	0.372451i
$725$	4.75646e10	+	4.75646e10i	0.172160	+	0.172160i
$726$	1.35545e11	+	1.35545e11i	0.487908	+	0.487908i
$727$	−3.78278e10	+	3.78278e10i	−0.135417	+	0.135417i	−0.771566	−	0.636149i	$-0.780526\pi$
$727$	−3.78278e10	+	3.78278e10i	−0.135417	+	0.135417i	0.636149	+	0.771566i	$0.280526\pi$
$728$			4.96213e11i			1.76662i
$729$	−3.28227e10			−0.116216
$730$			2.69455e11i			0.948844i
$731$			7.50958e10i			0.262994i
$732$	4.29366e10	−	4.29366e10i	0.149549	−	0.149549i
$733$		−	3.33106e11i		−	1.15390i	−0.816781	−	0.576948i	$-0.804243\pi$
$733$		−	3.33106e11i		−	1.15390i	0.816781	−	0.576948i	$-0.195757\pi$
$734$	−3.63182e10	+	3.63182e10i	−0.125124	+	0.125124i
$735$	−7.01540e11	+	7.01540e11i	−2.40383	+	2.40383i
$736$	−1.51164e10			−0.0515153
$737$	2.53036e10			0.0857654
$738$	−3.35546e10	−	3.35546e10i	−0.113117	−	0.113117i
$739$			9.27219e10i			0.310889i	0.987845	+	0.155444i	$0.0496809\pi$
$739$			9.27219e10i			0.310889i	−0.987845	+	0.155444i	$0.950319\pi$
$740$	5.55462e10	+	2.38603e11i	0.185237	+	0.795699i
$741$	−6.91583e11			−2.29389
$742$	8.72515e10	−	8.72515e10i	0.287844	−	0.287844i
$743$			5.32350e11i			1.74679i	0.487008	+	0.873397i	$0.338088\pi$
$743$			5.32350e11i			1.74679i	−0.487008	+	0.873397i	$0.661912\pi$
$744$		−	1.07774e11i		−	0.351741i
$745$	3.23206e11	+	3.23206e11i	1.04919	+	1.04919i
$746$	−3.02593e11	−	3.02593e11i	−0.977020	−	0.977020i
$747$	9.66245e10			0.310316
$748$	2.38715e10	+	2.38715e10i	0.0762557	+	0.0762557i
$749$	−6.35104e11			−2.01798
$750$	1.69736e12			5.36448
$751$			3.11405e11i			0.978963i	0.872014	+	0.489482i	$0.162814\pi$
$751$			3.11405e11i			0.978963i	−0.872014	+	0.489482i	$0.837186\pi$
$752$	−3.86664e11			−1.20910
$753$	−1.06109e11	−	1.06109e11i	−0.330043	−	0.330043i
$754$	−3.77515e10	+	3.77515e10i	−0.116802	+	0.116802i
$755$	3.27065e11	−	3.27065e11i	1.00657	−	1.00657i
$756$	1.28116e11			0.392206
$757$	2.46264e11	+	2.46264e11i	0.749923	+	0.749923i	0.974465	−	0.224541i	$-0.0720884\pi$
$757$	2.46264e11	+	2.46264e11i	0.749923	+	0.749923i	−0.224541	+	0.974465i	$0.572088\pi$
$758$	1.68812e11	−	1.68812e11i	0.511359	−	0.511359i
$759$	−1.37456e10	−	1.37456e10i	−0.0414186	−	0.0414186i
$760$	3.68974e11	−	3.68974e11i	1.10596	−	1.10596i
$761$		−	2.23087e11i		−	0.665175i	−0.943072	−	0.332587i	$-0.892078\pi$
$761$		−	2.23087e11i		−	0.665175i	0.943072	−	0.332587i	$-0.107922\pi$
$762$	−5.57530e11	−	5.57530e11i	−1.65367	−	1.65367i
$763$	−5.48514e11	−	5.48514e11i	−1.61841	−	1.61841i
$764$	−4.60807e10	+	4.60807e10i	−0.135253	+	0.135253i
$765$		−	1.21415e11i		−	0.354509i
$766$	5.43373e11			1.57828
$767$			4.68531e11i			1.35381i
$768$		−	4.52579e11i		−	1.30092i
$769$	−3.73811e11	+	3.73811e11i	−1.06892	+	1.06892i	−0.0714805	+	0.997442i	$0.522772\pi$
$769$	−3.73811e11	+	3.73811e11i	−1.06892	+	1.06892i	−0.997442	+	0.0714805i	$0.977228\pi$
$770$			9.26992e11i			2.63702i
$771$	−4.99304e11	+	4.99304e11i	−1.41302	+	1.41302i
$772$	−6.04451e9	+	6.04451e9i	−0.0170174	+	0.0170174i
$773$	6.91180e10			0.193586			0.0967928	−	0.995305i	$-0.469142\pi$
$773$	6.91180e10			0.193586			0.0967928	+	0.995305i	$0.469142\pi$
$774$	−1.58204e11			−0.440811
$775$	−3.01814e11	−	3.01814e11i	−0.836628	−	0.836628i
$776$			3.19144e11i			0.880116i
$777$	5.89051e11	+	3.66582e11i	1.61610	+	1.00574i
$778$	3.49635e11			0.954325
$779$	−7.94337e10	+	7.94337e10i	−0.215702	+	0.215702i
$780$			6.06817e11i			1.63938i
$781$		−	3.05197e11i		−	0.820305i
$782$	7.40258e9	+	7.40258e9i	0.0197950	+	0.0197950i
$783$	−1.37210e10	−	1.37210e10i	−0.0365037	−	0.0365037i
$784$	6.61713e11			1.75148
$785$	−3.03932e11	−	3.03932e11i	−0.800383	−	0.800383i
$786$	4.01776e10			0.105267
$787$	−3.57760e10			−0.0932595			−0.0466298	−	0.998912i	$-0.514848\pi$
$787$	−3.57760e10			−0.0932595			−0.0466298	+	0.998912i	$0.514848\pi$
$788$			9.09230e10i			0.235814i
$789$	4.28876e11			1.10668
$790$	−1.92361e11	−	1.92361e11i	−0.493866	−	0.493866i
$791$	6.16685e11	−	6.16685e11i	1.57528	−	1.57528i
$792$	7.07940e10	−	7.07940e10i	0.179927	−	0.179927i
$793$	−2.68688e11			−0.679446
$794$	4.04615e11	+	4.04615e11i	1.01803	+	1.01803i
$795$	−1.50203e11	+	1.50203e11i	−0.376020	+	0.376020i
$796$	−7.10284e10	−	7.10284e10i	−0.176921	−	0.176921i
$797$	−3.18921e11	+	3.18921e11i	−0.790406	+	0.790406i	−0.981560	−	0.191154i	$-0.938777\pi$
$797$	−3.18921e11	+	3.18921e11i	−0.790406	+	0.790406i	0.191154	+	0.981560i	$0.438777\pi$
$798$			1.04977e12i			2.58871i
$799$	1.00274e11	+	1.00274e11i	0.246038	+	0.246038i
$800$	−6.50698e11	−	6.50698e11i	−1.58862	−	1.58862i
$801$	−2.38573e11	+	2.38573e11i	−0.579549	+	0.579549i
$802$		−	4.06893e11i		−	0.983520i
$803$	1.22388e11			0.294359
$804$		−	2.51428e10i		−	0.0601713i
$805$			8.43560e10i			0.200878i
$806$	2.39546e11	−	2.39546e11i	0.567609	−	0.567609i
$807$		−	8.52908e11i		−	2.01098i
$808$	1.92200e11	−	1.92200e11i	0.450929	−	0.450929i
$809$	−1.81843e11	+	1.81843e11i	−0.424525	+	0.424525i	−0.886758	−	0.462233i	$-0.847048\pi$
$809$	−1.81843e11	+	1.81843e11i	−0.424525	+	0.424525i	0.462233	+	0.886758i	$0.347048\pi$
$810$	−1.25918e12			−2.92515
$811$	9.45140e10			0.218481			0.109240	−	0.994015i	$-0.465158\pi$
$811$	9.45140e10			0.218481			0.109240	+	0.994015i	$0.465158\pi$
$812$	1.68159e10	+	1.68159e10i	0.0386808	+	0.0386808i
$813$		−	8.27218e11i		−	1.89347i
$814$	3.69311e11	−	8.59748e10i	0.841192	−	0.195827i
$815$	9.03409e11			2.04764
$816$	−1.70897e11	+	1.70897e11i	−0.385455	+	0.385455i
$817$			3.74514e11i			0.840583i
$818$		−	3.24257e11i		−	0.724230i
$819$	4.07163e11	+	4.07163e11i	0.904968	+	0.904968i
$820$	6.96976e10	+	6.96976e10i	0.154157	+	0.154157i
$821$	−3.63978e11			−0.801129			−0.400564	−	0.916269i	$-0.631186\pi$
$821$	−3.63978e11			−0.801129			−0.400564	+	0.916269i	$0.631186\pi$
$822$	−3.11332e11	−	3.11332e11i	−0.681925	−	0.681925i
$823$	3.70797e11			0.808233			0.404117	−	0.914707i	$-0.367579\pi$
$823$	3.70797e11			0.808233			0.404117	+	0.914707i	$0.367579\pi$
$824$	3.12575e11			0.678025
$825$		−	1.18338e12i		−	2.55452i
$826$	7.11194e11			1.52780
$827$	−5.46743e11	−	5.46743e11i	−1.16886	−	1.16886i	−0.982478	−	0.186378i	$-0.940325\pi$
$827$	−5.46743e11	−	5.46743e11i	−1.16886	−	1.16886i	−0.186378	−	0.982478i	$-0.559675\pi$
$828$	−4.57636e9	+	4.57636e9i	−0.00973641	+	0.00973641i
$829$	−3.72338e11	+	3.72338e11i	−0.788350	+	0.788350i	−0.981224	−	0.192874i	$-0.938219\pi$
$829$	−3.72338e11	+	3.72338e11i	−0.788350	+	0.788350i	0.192874	+	0.981224i	$0.438219\pi$
$830$	−6.83937e11			−1.44113
$831$	5.66120e11	+	5.66120e11i	1.18715	+	1.18715i
$832$	−1.72599e11	+	1.72599e11i	−0.360201	+	0.360201i
$833$	−1.71603e11	−	1.71603e11i	−0.356407	−	0.356407i
$834$	−2.04107e11	+	2.04107e11i	−0.421885	+	0.421885i
$835$			1.09660e12i			2.25580i
$836$	1.19051e11	+	1.19051e11i	0.243729	+	0.243729i
$837$	8.70642e10	+	8.70642e10i	0.177393	+	0.177393i
$838$	5.06849e11	−	5.06849e11i	1.02779	−	1.02779i
$839$		−	6.83665e11i		−	1.37973i	−0.723936	−	0.689867i	$-0.757669\pi$
$839$		−	6.83665e11i		−	1.37973i	0.723936	−	0.689867i	$-0.242331\pi$
$840$	−1.29665e12			−2.60439
$841$			4.96645e11i			0.992800i
$842$		−	2.31132e11i		−	0.459845i
$843$	−1.79582e11	+	1.79582e11i	−0.355593	+	0.355593i
$844$		−	1.05528e11i		−	0.207969i
$845$	1.18953e12	−	1.18953e12i	2.33318	−	2.33318i
$846$	−2.11247e11	+	2.11247e11i	−0.412391	+	0.412391i
$847$	−3.77825e11			−0.734103
$848$	1.41676e11			0.273976
$849$	−7.29158e10	−	7.29158e10i	−0.140343	−	0.140343i
$850$			6.37301e11i			1.22087i
$851$	3.36072e10	−	7.82368e9i	0.0640788	−	0.0149174i
$852$	−3.03257e11			−0.575510
$853$	6.28319e11	−	6.28319e11i	1.18682	−	1.18682i	0.208875	−	0.977942i	$-0.433020\pi$
$853$	6.28319e11	−	6.28319e11i	1.18682	−	1.18682i	0.977942	−	0.208875i	$-0.0669801\pi$
$854$			4.07847e11i			0.766772i
$855$		−	6.05517e11i		−	1.13308i
$856$	−3.43316e11	−	3.43316e11i	−0.639440	−	0.639440i
$857$	2.42701e11	+	2.42701e11i	0.449934	+	0.449934i	0.895332	−	0.445398i	$-0.146938\pi$
$857$	2.42701e11	+	2.42701e11i	0.449934	+	0.449934i	−0.445398	+	0.895332i	$0.646938\pi$
$858$	9.39236e11			1.73311
$859$	1.04728e11	+	1.04728e11i	0.192349	+	0.192349i	0.796710	−	0.604361i	$-0.206572\pi$
$859$	1.04728e11	+	1.04728e11i	0.192349	+	0.192349i	−0.604361	+	0.796710i	$0.706572\pi$
$860$	3.28611e11			0.600742
$861$	2.79147e11			0.507949
$862$		−	3.57864e11i		−	0.648169i
$863$	−6.58221e11			−1.18667			−0.593333	−	0.804957i	$-0.702188\pi$
$863$	−6.58221e11			−1.18667			−0.593333	+	0.804957i	$0.702188\pi$
$864$	1.87707e11	+	1.87707e11i	0.336841	+	0.336841i
$865$	6.18331e11	−	6.18331e11i	1.10448	−	1.10448i
$866$	−5.38220e11	+	5.38220e11i	−0.956948	+	0.956948i
$867$	−6.04287e11			−1.06946
$868$	−1.06703e11	−	1.06703e11i	−0.187973	−	0.187973i
$869$	−8.73716e10	+	8.73716e10i	−0.153211	+	0.153211i
$870$	−9.86484e10	−	9.86484e10i	−0.172192	−	0.172192i
$871$	−7.86691e10	+	7.86691e10i	−0.136688	+	0.136688i
$872$		−	5.93017e11i		−	1.02566i
$873$	2.61871e11	+	2.61871e11i	0.450848	+	0.450848i
$874$	3.69178e10	+	3.69178e10i	0.0632689	+	0.0632689i
$875$	−2.36564e12	+	2.36564e12i	−4.03568	+	4.03568i
$876$		−	1.21610e11i		−	0.206516i
$877$	4.24263e11			0.717194			0.358597	−	0.933493i	$-0.383255\pi$
$877$	4.24263e11			0.717194			0.358597	+	0.933493i	$0.383255\pi$
$878$		−	4.52635e11i		−	0.761675i
$879$		−	7.52289e11i		−	1.26017i
$880$	−7.52609e11	+	7.52609e11i	−1.25498	+	1.25498i
$881$			5.58690e11i			0.927400i	0.885992	+	0.463700i	$0.153478\pi$
$881$			5.58690e11i			0.927400i	−0.885992	+	0.463700i	$0.846522\pi$
$882$	3.61515e11	−	3.61515e11i	0.597383	−	0.597383i
$883$	6.03641e11	−	6.03641e11i	0.992969	−	0.992969i	−0.00700600	−	0.999975i	$-0.502230\pi$
$883$	6.03641e11	−	6.03641e11i	0.992969	−	0.992969i	0.999975	+	0.00700600i	$0.00223010\pi$
$884$	−1.48433e11			−0.243065
$885$	−1.22432e12			−1.99582
$886$	4.86579e11	+	4.86579e11i	0.789620	+	0.789620i
$887$			5.11599e11i			0.826485i	0.910621	+	0.413243i	$0.135604\pi$
$887$			5.11599e11i			0.826485i	−0.910621	+	0.413243i	$0.864396\pi$
$888$	1.20259e11	+	5.16583e11i	0.193405	+	0.830785i
$889$	1.55408e12			2.48810
$890$	1.68869e12	−	1.68869e12i	2.69147	−	2.69147i
$891$			5.71929e11i			0.907468i
$892$		−	3.44992e11i		−	0.544941i
$893$	5.00083e11	+	5.00083e11i	0.786387	+	0.786387i
$894$	−4.97082e11	−	4.97082e11i	−0.778177	−	0.778177i
$895$	5.33834e11			0.831982
$896$	8.15879e11	+	8.15879e11i	1.26588	+	1.26588i
$897$	8.54702e10			0.132022
$898$	−4.67834e11			−0.719426
$899$			2.28553e10i			0.0349904i
$900$	−3.93987e11			−0.600498
$901$	−3.67411e10	−	3.67411e10i	−0.0557511	−	0.0557511i
$902$	1.07878e11	−	1.07878e11i	0.162970	−	0.162970i
$903$	6.58062e11	−	6.58062e11i	0.989728	−	0.989728i
$904$	6.66719e11			0.998318
$905$	−8.36699e11	−	8.36699e11i	−1.24731	−	1.24731i
$906$	−5.03016e11	+	5.03016e11i	−0.746568	+	0.746568i
$907$	3.98059e11	+	3.98059e11i	0.588191	+	0.588191i	0.937141	−	0.348950i	$-0.113462\pi$
$907$	3.98059e11	+	3.98059e11i	0.588191	+	0.588191i	−0.348950	+	0.937141i	$0.613462\pi$
$908$	−2.07567e11	+	2.07567e11i	−0.305362	+	0.305362i
$909$		−	3.15417e11i		−	0.461987i
$910$	−2.88202e12	−	2.88202e12i	−4.20274	−	4.20274i
$911$	−7.34722e11	−	7.34722e11i	−1.06672	−	1.06672i	−0.997609	−	0.0691086i	$-0.977984\pi$
$911$	−7.34722e11	−	7.34722e11i	−1.06672	−	1.06672i	−0.0691086	−	0.997609i	$-0.522016\pi$
$912$	−8.52291e11	+	8.52291e11i	−1.23199	+	1.23199i
$913$			3.10648e11i			0.447081i
$914$	−2.21624e11			−0.317565
$915$		−	7.02107e11i		−	1.00166i
$916$			3.58542e11i			0.509282i
$917$	−5.59965e10	+	5.59965e10i	−0.0791924	+	0.0791924i
$918$		−	1.83842e11i		−	0.258866i
$919$	−6.98455e11	+	6.98455e11i	−0.979211	+	0.979211i	−0.999788	−	0.0205772i	$-0.993450\pi$
$919$	−6.98455e11	+	6.98455e11i	−0.979211	+	0.979211i	0.0205772	+	0.999788i	$0.493450\pi$
$920$	−4.56001e10	+	4.56001e10i	−0.0636523	+	0.0636523i
$921$	−2.85080e11			−0.396212
$922$	−6.58250e11			−0.910892
$923$	9.48858e11	+	9.48858e11i	1.30736	+	1.30736i
$924$		−	4.18370e11i		−	0.573948i
$925$	1.78343e12	+	1.10988e12i	2.43607	+	1.51603i
$926$	6.82754e11			0.928582
$927$	2.56481e11	−	2.56481e11i	0.347325	−	0.347325i
$928$			4.92751e10i			0.0664410i
$929$			3.06241e11i			0.411150i	0.978641	+	0.205575i	$0.0659064\pi$
$929$			3.06241e11i			0.411150i	−0.978641	+	0.205575i	$0.934094\pi$
$930$	6.25958e11	+	6.25958e11i	0.836784	+	0.836784i
$931$	−8.55813e11	−	8.55813e11i	−1.13915	−	1.13915i
$932$	2.47542e11			0.328084
$933$	−3.14147e11	−	3.14147e11i	−0.414578	−	0.414578i
$934$	8.67866e11			1.14042
$935$	3.90351e11			0.510750
$936$			4.40198e11i			0.573515i
$937$	−3.98650e11			−0.517170			−0.258585	−	0.965989i	$-0.583256\pi$
$937$	−3.98650e11			−0.517170			−0.258585	+	0.965989i	$0.583256\pi$
$938$	1.19414e11	+	1.19414e11i	0.154256	+	0.154256i
$939$	3.47172e11	−	3.47172e11i	0.446563	−	0.446563i
$940$	4.38789e11	−	4.38789e11i	0.562010	−	0.562010i
$941$	−1.38751e12			−1.76961			−0.884806	−	0.465960i	$-0.845709\pi$
$941$	−1.38751e12			−1.76961			−0.884806	+	0.465960i	$0.845709\pi$
$942$	4.67439e11	+	4.67439e11i	0.593638	+	0.593638i
$943$	9.81690e9	−	9.81690e9i	0.0124145	−	0.0124145i
$944$	5.77406e11	+	5.77406e11i	0.727099	+	0.727099i
$945$	1.04749e12	−	1.04749e12i	1.31347	−	1.31347i
$946$		−	5.08626e11i		−	0.635088i
$947$	−3.45878e10	−	3.45878e10i	−0.0430054	−	0.0430054i	0.685277	−	0.728282i	$-0.259681\pi$
$947$	−3.45878e10	−	3.45878e10i	−0.0430054	−	0.0430054i	−0.728282	+	0.685277i	$0.759681\pi$
$948$	8.68164e10	+	8.68164e10i	0.107490	+	0.107490i
$949$	−3.80506e11	+	3.80506e11i	−0.469133	+	0.469133i
$950$			3.17832e12i			3.90215i
$951$	1.14067e12			1.39456
$952$		−	3.17173e11i		−	0.386144i
$953$			9.88077e11i			1.19790i	0.800788	+	0.598948i	$0.204414\pi$
$953$			9.88077e11i			1.19790i	−0.800788	+	0.598948i	$0.795586\pi$
$954$	7.74022e10	−	7.74022e10i	0.0934458	−	0.0934458i
$955$			7.53520e11i			0.905903i
$956$	1.01277e11	−	1.01277e11i	0.121249	−	0.121249i
$957$	−4.48067e10	+	4.48067e10i	−0.0534189	+	0.0534189i
$958$	−5.31285e11			−0.630761
$959$	8.67820e11			1.02602
$960$	−4.51018e11	−	4.51018e11i	−0.531018	−	0.531018i
$961$			7.07866e11i			0.829961i
$962$	−8.80895e11	+	1.41549e12i	−1.02855	+	1.65275i
$963$	−5.63411e11			−0.655119
$964$	−4.39216e10	+	4.39216e10i	−0.0508593	+	0.0508593i
$965$			9.88410e10i			0.113980i
$966$		−	1.29737e11i		−	0.148990i
$967$	3.10049e11	+	3.10049e11i	0.354589	+	0.354589i	0.861814	−	0.507225i	$-0.169329\pi$
$967$	3.10049e11	+	3.10049e11i	0.354589	+	0.354589i	−0.507225	+	0.861814i	$0.669329\pi$
$968$	−2.04240e11	−	2.04240e11i	−0.232615	−	0.232615i
$969$	4.42052e11			0.501393
$970$	−1.85360e12	−	1.85360e12i	−2.09377	−	2.09377i
$971$	−1.32318e12			−1.48847			−0.744237	−	0.667915i	$-0.767187\pi$
$971$	−1.32318e12			−1.48847			−0.744237	+	0.667915i	$0.767187\pi$
$972$	3.42747e11			0.383980
$973$		−	5.68937e11i		−	0.634765i
$974$	1.62302e12			1.80339
$975$	3.67914e12	+	3.67914e12i	4.07125	+	4.07125i
$976$	−3.31124e11	+	3.31124e11i	−0.364915	+	0.364915i
$977$	3.08218e11	−	3.08218e11i	0.338282	−	0.338282i	−0.517438	−	0.855720i	$-0.673114\pi$
$977$	3.08218e11	−	3.08218e11i	0.338282	−	0.338282i	0.855720	+	0.517438i	$0.173114\pi$
$978$	−1.38942e12			−1.51872
$979$	−7.67013e11	−	7.67013e11i	−0.834972	−	0.834972i
$980$	−7.50917e11	+	7.50917e11i	−0.814118	+	0.814118i
$981$	−4.86596e11	−	4.86596e11i	−0.525403	−	0.525403i
$982$	4.47022e11	−	4.47022e11i	0.480710	−	0.480710i
$983$		−	6.91370e11i		−	0.740452i	−0.928942	−	0.370226i	$-0.879280\pi$
$983$		−	6.91370e11i		−	0.740452i	0.928942	−	0.370226i	$-0.120720\pi$
$984$	1.50898e11	+	1.50898e11i	0.160954	+	0.160954i
$985$	7.43395e11	+	7.43395e11i	0.789723	+	0.789723i
$986$	2.41303e10	−	2.41303e10i	0.0255303	−	0.0255303i
$987$		−	1.75740e12i		−	1.85183i
$988$	−7.40259e11			−0.776884
$989$		−	4.62848e10i		−	0.0483786i
$990$			8.22349e11i			0.856082i
$991$	1.30214e12	−	1.30214e12i	1.35009	−	1.35009i	0.464541	−	0.885552i	$-0.346219\pi$
$991$	1.30214e12	−	1.30214e12i	1.35009	−	1.35009i	0.885552	−	0.464541i	$-0.153781\pi$
$992$		−	3.12668e11i		−	0.322876i
$993$	−8.90830e11	+	8.90830e11i	−0.916216	+	0.916216i
$994$	1.44029e12	−	1.44029e12i	1.47539	−	1.47539i
$995$	−1.16147e12			−1.18499
$996$	3.08674e11			0.313663
$997$	−2.58802e11	−	2.58802e11i	−0.261931	−	0.261931i	0.563907	−	0.825838i	$-0.309298\pi$
$997$	−2.58802e11	−	2.58802e11i	−0.261931	−	0.261931i	−0.825838	+	0.563907i	$0.809298\pi$
$998$		−	2.30624e12i		−	2.32478i
$999$	−5.14466e11	−	3.20166e11i	−0.516529	−	0.321449i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.9.d.a.6.7	✓	50
37.31	odd	4	inner	37.9.d.a.31.7	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.9.d.a.6.7	✓	50	1.1	even	1	trivial
37.9.d.a.31.7	yes	50	37.31	odd	4	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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	37.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-13.4597 + 13.4597i) q^{2} -99.3332i q^{3} -106.325i q^{4} +(-869.321 - 869.321i) q^{5} +(1336.99 + 1336.99i) q^{6} -3726.79 q^{7} +(-2014.58 - 2014.58i) q^{8} -3306.09 q^{9} +O(q^{10})\)	\(q+(-13.4597 + 13.4597i) q^{2} -99.3332i q^{3} -106.325i q^{4} +(-869.321 - 869.321i) q^{5} +(1336.99 + 1336.99i) q^{6} -3726.79 q^{7} +(-2014.58 - 2014.58i) q^{8} -3306.09 q^{9} +23401.5 q^{10} -10629.1i q^{11} -10561.6 q^{12} +(33046.0 + 33046.0i) q^{13} +(50161.3 - 50161.3i) q^{14} +(-86352.5 + 86352.5i) q^{15} +81450.2 q^{16} +(-21122.6 - 21122.6i) q^{17} +(44498.9 - 44498.9i) q^{18} +(-105342. - 105342. i) q^{19} +(-92430.2 + 92430.2i) q^{20} +370194. i q^{21} +(143064. + 143064. i) q^{22} +(13018.8 + 13018.8i) q^{23} +(-200115. + 200115. i) q^{24} +1.12081e6i q^{25} -889576. q^{26} -323320. i q^{27} +396249. i q^{28} +(42437.6 - 42437.6i) q^{29} -2.32455e6i q^{30} +(-269281. + 269281. i) q^{31} +(-580559. + 580559. i) q^{32} -1.05582e6 q^{33} +568607. q^{34} +(3.23977e6 + 3.23977e6i) q^{35} +351519. i q^{36} +(990242. - 1.59119e6i) q^{37} +2.83573e6 q^{38} +(3.28257e6 - 3.28257e6i) q^{39} +3.50263e6i q^{40} -754056. i q^{41} +(-4.98268e6 - 4.98268e6i) q^{42} +(-1.77761e6 - 1.77761e6i) q^{43} -1.13014e6 q^{44} +(2.87406e6 + 2.87406e6i) q^{45} -350457. q^{46} -4.74724e6 q^{47} -8.09071e6i q^{48} +8.12415e6 q^{49} +(-1.50857e7 - 1.50857e7i) q^{50} +(-2.09818e6 + 2.09818e6i) q^{51} +(3.51360e6 - 3.51360e6i) q^{52} +1.73942e6 q^{53} +(4.35178e6 + 4.35178e6i) q^{54} +(-9.24011e6 + 9.24011e6i) q^{55} +(7.50791e6 + 7.50791e6i) q^{56} +(-1.04640e7 + 1.04640e7i) q^{57} +1.14239e6i q^{58} +(7.08907e6 + 7.08907e6i) q^{59} +(9.18139e6 + 9.18139e6i) q^{60} +(-4.06536e6 + 4.06536e6i) q^{61} -7.24887e6i q^{62} +1.23211e7 q^{63} +5.22299e6i q^{64} -5.74552e7i q^{65} +(1.42110e7 - 1.42110e7i) q^{66} +2.38059e6i q^{67} +(-2.24586e6 + 2.24586e6i) q^{68} +(1.29320e6 - 1.29320e6i) q^{69} -8.72125e7 q^{70} +2.87133e7 q^{71} +(6.66038e6 + 6.66038e6i) q^{72} +1.15144e7i q^{73} +(8.08861e6 + 3.47452e7i) q^{74} +1.11334e8 q^{75} +(-1.12004e7 + 1.12004e7i) q^{76} +3.96125e7i q^{77} +8.83644e7i q^{78} +(-8.22003e6 - 8.22003e6i) q^{79} +(-7.08063e7 - 7.08063e7i) q^{80} -5.38077e7 q^{81} +(1.01493e7 + 1.01493e7i) q^{82} -2.92262e7 q^{83} +3.93607e7 q^{84} +3.67247e7i q^{85} +4.78522e7 q^{86} +(-4.21547e6 - 4.21547e6i) q^{87} +(-2.14132e7 + 2.14132e7i) q^{88} +(7.21615e7 - 7.21615e7i) q^{89} -7.73676e7 q^{90} +(-1.23155e8 - 1.23155e8i) q^{91} +(1.38422e6 - 1.38422e6i) q^{92} +(2.67486e7 + 2.67486e7i) q^{93} +(6.38962e7 - 6.38962e7i) q^{94} +1.83152e8i q^{95} +(5.76688e7 + 5.76688e7i) q^{96} +(-7.92086e7 - 7.92086e7i) q^{97} +(-1.09348e8 + 1.09348e8i) q^{98} +3.51408e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 4 q^{2} + 124 q^{5} + 510 q^{6} - 4 q^{7} - 5256 q^{8} - 93534 q^{9}+O(q^{10}) \) 50 * q + 4 * q^2 + 124 * q^5 + 510 * q^6 - 4 * q^7 - 5256 * q^8 - 93534 * q^9	\( 50 q + 4 q^{2} + 124 q^{5} + 510 q^{6} - 4 q^{7} - 5256 q^{8} - 93534 q^{9} - 10756 q^{10} - 45440 q^{12} + 63592 q^{13} - 80206 q^{14} - 124346 q^{15} - 639128 q^{16} - 178796 q^{17} - 45882 q^{18} + 264774 q^{19} + 469204 q^{20} + 714574 q^{22} - 654272 q^{23} - 1573644 q^{24} + 1841660 q^{26} - 1683686 q^{29} + 1766336 q^{31} - 4332632 q^{32} - 1438888 q^{33} - 5838452 q^{34} - 650482 q^{35} - 2870078 q^{37} - 2281528 q^{38} + 11036546 q^{39} - 7453902 q^{42} + 5097830 q^{43} - 14992464 q^{44} - 15078446 q^{45} + 28776464 q^{46} + 13992320 q^{47} + 4370314 q^{49} + 7603288 q^{50} + 19417938 q^{51} + 54318452 q^{52} + 28075952 q^{53} - 19197122 q^{54} - 6104306 q^{55} + 47803128 q^{56} + 17462426 q^{57} - 677072 q^{59} + 24953316 q^{60} + 4206386 q^{61} - 18098032 q^{63} - 56061730 q^{66} - 52579760 q^{68} + 88118984 q^{69} - 295493636 q^{70} - 37172476 q^{71} - 74582504 q^{72} - 224754524 q^{74} - 144364996 q^{75} + 189294548 q^{76} + 271163438 q^{79} - 312998084 q^{80} + 41535626 q^{81} - 177494710 q^{82} - 74250268 q^{83} - 82088924 q^{84} + 112964036 q^{86} - 142771908 q^{87} + 224951860 q^{88} + 84928780 q^{89} + 716592116 q^{90} - 40969098 q^{91} - 701292428 q^{92} - 83761576 q^{93} + 553881406 q^{94} - 7259376 q^{96} + 467792674 q^{97} + 538649310 q^{98}+O(q^{100}) \) 50 * q + 4 * q^2 + 124 * q^5 + 510 * q^6 - 4 * q^7 - 5256 * q^8 - 93534 * q^9 - 10756 * q^10 - 45440 * q^12 + 63592 * q^13 - 80206 * q^14 - 124346 * q^15 - 639128 * q^16 - 178796 * q^17 - 45882 * q^18 + 264774 * q^19 + 469204 * q^20 + 714574 * q^22 - 654272 * q^23 - 1573644 * q^24 + 1841660 * q^26 - 1683686 * q^29 + 1766336 * q^31 - 4332632 * q^32 - 1438888 * q^33 - 5838452 * q^34 - 650482 * q^35 - 2870078 * q^37 - 2281528 * q^38 + 11036546 * q^39 - 7453902 * q^42 + 5097830 * q^43 - 14992464 * q^44 - 15078446 * q^45 + 28776464 * q^46 + 13992320 * q^47 + 4370314 * q^49 + 7603288 * q^50 + 19417938 * q^51 + 54318452 * q^52 + 28075952 * q^53 - 19197122 * q^54 - 6104306 * q^55 + 47803128 * q^56 + 17462426 * q^57 - 677072 * q^59 + 24953316 * q^60 + 4206386 * q^61 - 18098032 * q^63 - 56061730 * q^66 - 52579760 * q^68 + 88118984 * q^69 - 295493636 * q^70 - 37172476 * q^71 - 74582504 * q^72 - 224754524 * q^74 - 144364996 * q^75 + 189294548 * q^76 + 271163438 * q^79 - 312998084 * q^80 + 41535626 * q^81 - 177494710 * q^82 - 74250268 * q^83 - 82088924 * q^84 + 112964036 * q^86 - 142771908 * q^87 + 224951860 * q^88 + 84928780 * q^89 + 716592116 * q^90 - 40969098 * q^91 - 701292428 * q^92 - 83761576 * q^93 + 553881406 * q^94 - 7259376 * q^96 + 467792674 * q^97 + 538649310 * q^98

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