LMFDB - Embedded newform 37.9.d.a.6.4

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			6.4
Character	$\chi$	$=$	37.6
Dual form			37.9.d.a.31.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-17.3562 + 17.3562i) q^{2} +155.578i q^{3} -346.477i q^{4} +(713.128 + 713.128i) q^{5} +(-2700.25 - 2700.25i) q^{6} +792.085 q^{7} +(1570.34 + 1570.34i) q^{8} -17643.6 q^{9} +O(q^{10})$	\(q+(-17.3562 + 17.3562i) q^{2} +155.578i q^{3} -346.477i q^{4} +(713.128 + 713.128i) q^{5} +(-2700.25 - 2700.25i) q^{6} +792.085 q^{7} +(1570.34 + 1570.34i) q^{8} -17643.6 q^{9} -24754.4 q^{10} -9886.59i q^{11} +53904.3 q^{12} +(-16033.3 - 16033.3i) q^{13} +(-13747.6 + 13747.6i) q^{14} +(-110947. + 110947. i) q^{15} +34187.8 q^{16} +(-50353.3 - 50353.3i) q^{17} +(306227. - 306227. i) q^{18} +(84690.9 + 84690.9i) q^{19} +(247083. - 247083. i) q^{20} +123231. i q^{21} +(171594. + 171594. i) q^{22} +(-242423. - 242423. i) q^{23} +(-244311. + 244311. i) q^{24} +626479. i q^{25} +556557. q^{26} -1.72422e6i q^{27} -274439. i q^{28} +(145961. - 145961. i) q^{29} -3.85125e6i q^{30} +(-1.05963e6 + 1.05963e6i) q^{31} +(-995378. + 995378. i) q^{32} +1.53814e6 q^{33} +1.74789e6 q^{34} +(564858. + 564858. i) q^{35} +6.11311e6i q^{36} +(-277926. + 1.85344e6i) q^{37} -2.93983e6 q^{38} +(2.49444e6 - 2.49444e6i) q^{39} +2.23971e6i q^{40} +3.72680e6i q^{41} +(-2.13883e6 - 2.13883e6i) q^{42} +(2.13927e6 + 2.13927e6i) q^{43} -3.42548e6 q^{44} +(-1.25822e7 - 1.25822e7i) q^{45} +8.41511e6 q^{46} -5.38957e6 q^{47} +5.31889e6i q^{48} -5.13740e6 q^{49} +(-1.08733e7 - 1.08733e7i) q^{50} +(7.83388e6 - 7.83388e6i) q^{51} +(-5.55518e6 + 5.55518e6i) q^{52} -1.95759e6 q^{53} +(2.99259e7 + 2.99259e7i) q^{54} +(7.05041e6 - 7.05041e6i) q^{55} +(1.24384e6 + 1.24384e6i) q^{56} +(-1.31761e7 + 1.31761e7i) q^{57} +5.06666e6i q^{58} +(3.34771e6 + 3.34771e6i) q^{59} +(3.84407e7 + 3.84407e7i) q^{60} +(6.58547e6 - 6.58547e6i) q^{61} -3.67824e7i q^{62} -1.39753e7 q^{63} -2.57999e7i q^{64} -2.28677e7i q^{65} +(-2.66963e7 + 2.66963e7i) q^{66} -1.00587e7i q^{67} +(-1.74463e7 + 1.74463e7i) q^{68} +(3.77158e7 - 3.77158e7i) q^{69} -1.96076e7 q^{70} +1.49679e7 q^{71} +(-2.77065e7 - 2.77065e7i) q^{72} +3.40281e7i q^{73} +(-2.73450e7 - 3.69924e7i) q^{74} -9.74666e7 q^{75} +(2.93434e7 - 2.93434e7i) q^{76} -7.83102e6i q^{77} +8.65882e7i q^{78} +(1.54247e7 + 1.54247e7i) q^{79} +(2.43803e7 + 2.43803e7i) q^{80} +1.52491e8 q^{81} +(-6.46831e7 - 6.46831e7i) q^{82} -8.49703e7 q^{83} +4.26968e7 q^{84} -7.18167e7i q^{85} -7.42593e7 q^{86} +(2.27083e7 + 2.27083e7i) q^{87} +(1.55253e7 - 1.55253e7i) q^{88} +(-2.95034e7 + 2.95034e7i) q^{89} +4.36758e8 q^{90} +(-1.26998e7 - 1.26998e7i) q^{91} +(-8.39941e7 + 8.39941e7i) q^{92} +(-1.64856e8 - 1.64856e8i) q^{93} +(9.35425e7 - 9.35425e7i) q^{94} +1.20791e8i q^{95} +(-1.54859e8 - 1.54859e8i) q^{96} +(3.18200e7 + 3.18200e7i) q^{97} +(8.91659e7 - 8.91659e7i) q^{98} +1.74435e8i 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 $

$2$	−17.3562	+	17.3562i	−1.08476	+	1.08476i	−0.0887061	+	0.996058i	$0.528273\pi$
$2$	−17.3562	+	17.3562i	−1.08476	+	1.08476i	−0.996058	+	0.0887061i	$0.971727\pi$
$3$			155.578i			1.92072i	0.278761	+	0.960360i	$0.410076\pi$
$3$			155.578i			1.92072i	−0.278761	+	0.960360i	$0.589924\pi$
$4$		−	346.477i		−	1.35343i
$5$	713.128	+	713.128i	1.14101	+	1.14101i	0.988267	+	0.152739i	$0.0488093\pi$
$5$	713.128	+	713.128i	1.14101	+	1.14101i	0.152739	+	0.988267i	$0.451191\pi$
$6$	−2700.25	−	2700.25i	−2.08353	−	2.08353i
$7$	792.085			0.329898			0.164949	−	0.986302i	$-0.447254\pi$
$7$	792.085			0.329898			0.164949	+	0.986302i	$0.447254\pi$
$8$	1570.34	+	1570.34i	0.383383	+	0.383383i
$9$	−17643.6			−2.68917
$10$	−24754.4			−2.47544
$11$		−	9886.59i		−	0.675268i	−0.941278	−	0.337634i	$-0.890373\pi$
$11$		−	9886.59i		−	0.675268i	0.941278	−	0.337634i	$-0.109627\pi$
$12$	53904.3			2.59955
$13$	−16033.3	−	16033.3i	−0.561372	−	0.561372i	0.368325	−	0.929697i	$-0.379931\pi$
$13$	−16033.3	−	16033.3i	−0.561372	−	0.561372i	−0.929697	+	0.368325i	$0.879931\pi$
$14$	−13747.6	+	13747.6i	−0.357861	+	0.357861i
$15$	−110947.	+	110947.i	−2.19155	+	2.19155i
$16$	34187.8			0.521665
$17$	−50353.3	−	50353.3i	−0.602882	−	0.602882i	0.338194	−	0.941076i	$-0.390184\pi$
$17$	−50353.3	−	50353.3i	−0.602882	−	0.602882i	−0.941076	+	0.338194i	$0.890184\pi$
$18$	306227.	−	306227.i	2.91711	−	2.91711i
$19$	84690.9	+	84690.9i	0.649864	+	0.649864i	0.952960	−	0.303096i	$-0.0980204\pi$
$19$	84690.9	+	84690.9i	0.649864	+	0.649864i	−0.303096	+	0.952960i	$0.598020\pi$
$20$	247083.	−	247083.i	1.54427	−	1.54427i
$21$			123231.i			0.633642i
$22$	171594.	+	171594.i	0.732506	+	0.732506i
$23$	−242423.	−	242423.i	−0.866290	−	0.866290i	0.125770	−	0.992059i	$-0.459860\pi$
$23$	−242423.	−	242423.i	−0.866290	−	0.866290i	−0.992059	+	0.125770i	$0.959860\pi$
$24$	−244311.	+	244311.i	−0.736372	+	0.736372i
$25$			626479.i			1.60379i
$26$	556557.			1.21791
$27$		−	1.72422e6i		−	3.24442i
$28$		−	274439.i		−	0.446492i
$29$	145961.	−	145961.i	0.206369	−	0.206369i	−0.596353	−	0.802722i	$-0.703384\pi$
$29$	145961.	−	145961.i	0.206369	−	0.206369i	0.802722	+	0.596353i	$0.203384\pi$
$30$		−	3.85125e6i		−	4.75463i
$31$	−1.05963e6	+	1.05963e6i	−1.14738	+	1.14738i	−0.160315	+	0.987066i	$0.551251\pi$
$31$	−1.05963e6	+	1.05963e6i	−1.14738	+	1.14738i	−0.987066	+	0.160315i	$0.948749\pi$
$32$	−995378.	+	995378.i	−0.949266	+	0.949266i
$33$	1.53814e6			1.29700
$34$	1.74789e6			1.30797
$35$	564858.	+	564858.i	0.376415	+	0.376415i
$36$			6.11311e6i			3.63959i
$37$	−277926.	+	1.85344e6i	−0.148294	+	0.988943i
$37$	−277926.	+	1.85344e6i	−0.148294	+	0.988943i
$38$	−2.93983e6			−1.40990
$39$	2.49444e6	−	2.49444e6i	1.07824	−	1.07824i
$40$			2.23971e6i			0.874885i
$41$			3.72680e6i			1.31886i	0.751764	+	0.659432i	$0.229203\pi$
$41$			3.72680e6i			1.31886i	−0.751764	+	0.659432i	$0.770797\pi$
$42$	−2.13883e6	−	2.13883e6i	−0.687352	−	0.687352i
$43$	2.13927e6	+	2.13927e6i	0.625737	+	0.625737i	0.946993	−	0.321255i	$-0.104105\pi$
$43$	2.13927e6	+	2.13927e6i	0.625737	+	0.625737i	−0.321255	+	0.946993i	$0.604105\pi$
$44$	−3.42548e6			−0.913924
$45$	−1.25822e7	−	1.25822e7i	−3.06836	−	3.06836i
$46$	8.41511e6			1.87944
$47$	−5.38957e6			−1.10449			−0.552246	−	0.833681i	$-0.686229\pi$
$47$	−5.38957e6			−1.10449			−0.552246	+	0.833681i	$0.686229\pi$
$48$			5.31889e6i			1.00197i
$49$	−5.13740e6			−0.891167
$50$	−1.08733e7	−	1.08733e7i	−1.73973	−	1.73973i
$51$	7.83388e6	−	7.83388e6i	1.15797	−	1.15797i
$52$	−5.55518e6	+	5.55518e6i	−0.759775	+	0.759775i
$53$	−1.95759e6			−0.248096			−0.124048	−	0.992276i	$-0.539588\pi$
$53$	−1.95759e6			−0.248096			−0.124048	+	0.992276i	$0.539588\pi$
$54$	2.99259e7	+	2.99259e7i	3.51943	+	3.51943i
$55$	7.05041e6	−	7.05041e6i	0.770484	−	0.770484i
$56$	1.24384e6	+	1.24384e6i	0.126477	+	0.126477i
$57$	−1.31761e7	+	1.31761e7i	−1.24821	+	1.24821i
$58$			5.06666e6i			0.447723i
$59$	3.34771e6	+	3.34771e6i	0.276274	+	0.276274i	0.831620	−	0.555346i	$-0.187414\pi$
$59$	3.34771e6	+	3.34771e6i	0.276274	+	0.276274i	−0.555346	+	0.831620i	$0.687414\pi$
$60$	3.84407e7	+	3.84407e7i	2.96610	+	2.96610i
$61$	6.58547e6	−	6.58547e6i	0.475628	−	0.475628i	−0.428102	−	0.903730i	$-0.640818\pi$
$61$	6.58547e6	−	6.58547e6i	0.475628	−	0.475628i	0.903730	+	0.428102i	$0.140818\pi$
$62$		−	3.67824e7i		−	2.48928i
$63$	−1.39753e7			−0.887151
$64$		−	2.57999e7i		−	1.53780i
$65$		−	2.28677e7i		−	1.28106i
$66$	−2.66963e7	+	2.66963e7i	−1.40694	+	1.40694i
$67$		−	1.00587e7i		−	0.499163i	−0.968354	−	0.249581i	$-0.919707\pi$
$67$		−	1.00587e7i		−	0.499163i	0.968354	−	0.249581i	$-0.0802930\pi$
$68$	−1.74463e7	+	1.74463e7i	−0.815956	+	0.815956i
$69$	3.77158e7	−	3.77158e7i	1.66390	−	1.66390i
$70$	−1.96076e7			−0.816643
$71$	1.49679e7			0.589017			0.294509	−	0.955649i	$-0.404844\pi$
$71$	1.49679e7			0.589017			0.294509	+	0.955649i	$0.404844\pi$
$72$	−2.77065e7	−	2.77065e7i	−1.03098	−	1.03098i
$73$			3.40281e7i			1.19825i	0.800656	+	0.599124i	$0.204484\pi$
$73$			3.40281e7i			1.19825i	−0.800656	+	0.599124i	$0.795516\pi$
$74$	−2.73450e7	−	3.69924e7i	−0.911907	−	1.23363i
$75$	−9.74666e7			−3.08043
$76$	2.93434e7	−	2.93434e7i	0.879542	−	0.879542i
$77$		−	7.83102e6i		−	0.222769i
$78$			8.65882e7i			2.33927i
$79$	1.54247e7	+	1.54247e7i	0.396011	+	0.396011i	0.876824	−	0.480812i	$-0.159658\pi$
$79$	1.54247e7	+	1.54247e7i	0.396011	+	0.396011i	−0.480812	+	0.876824i	$0.659658\pi$
$80$	2.43803e7	+	2.43803e7i	0.595222	+	0.595222i
$81$	1.52491e8			3.54246
$82$	−6.46831e7	−	6.46831e7i	−1.43066	−	1.43066i
$83$	−8.49703e7			−1.79042			−0.895210	−	0.445645i	$-0.852974\pi$
$83$	−8.49703e7			−1.79042			−0.895210	+	0.445645i	$0.852974\pi$
$84$	4.26968e7			0.857587
$85$		−	7.18167e7i		−	1.37578i
$86$	−7.42593e7			−1.35755
$87$	2.27083e7	+	2.27083e7i	0.396377	+	0.396377i
$88$	1.55253e7	−	1.55253e7i	0.258886	−	0.258886i
$89$	−2.95034e7	+	2.95034e7i	−0.470231	+	0.470231i	−0.901989	−	0.431758i	$-0.857893\pi$
$89$	−2.95034e7	+	2.95034e7i	−0.470231	+	0.470231i	0.431758	+	0.901989i	$0.357893\pi$
$90$	4.36758e8			6.65688
$91$	−1.26998e7	−	1.26998e7i	−0.185195	−	0.185195i
$92$	−8.39941e7	+	8.39941e7i	−1.17246	+	1.17246i
$93$	−1.64856e8	−	1.64856e8i	−2.20380	−	2.20380i
$94$	9.35425e7	−	9.35425e7i	1.19811	−	1.19811i
$95$			1.20791e8i			1.48300i
$96$	−1.54859e8	−	1.54859e8i	−1.82328	−	1.82328i
$97$	3.18200e7	+	3.18200e7i	0.359429	+	0.359429i	0.863603	−	0.504173i	$-0.168203\pi$
$97$	3.18200e7	+	3.18200e7i	0.359429	+	0.359429i	−0.504173	+	0.863603i	$0.668203\pi$
$98$	8.91659e7	−	8.91659e7i	0.966706	−	0.966706i
$99$			1.74435e8i			1.81591i
$100$	2.17061e8			2.17061
$101$			1.30875e8i			1.25768i	0.777533	+	0.628842i	$0.216471\pi$
$101$			1.30875e8i			1.25768i	−0.777533	+	0.628842i	$0.783529\pi$
$102$			2.71933e8i			2.51224i
$103$	−8.04861e7	+	8.04861e7i	−0.715108	+	0.715108i	−0.967599	−	0.252491i	$-0.918750\pi$
$103$	−8.04861e7	+	8.04861e7i	−0.715108	+	0.715108i	0.252491	+	0.967599i	$0.418750\pi$
$104$		−	5.03555e7i		−	0.430441i
$105$	−8.78797e7	+	8.78797e7i	−0.722988	+	0.722988i
$106$	3.39764e7	−	3.39764e7i	0.269125	−	0.269125i
$107$	1.08120e8			0.824842			0.412421	−	0.910993i	$-0.364683\pi$
$107$	1.08120e8			0.824842			0.412421	+	0.910993i	$0.364683\pi$
$108$	−5.97402e8			−4.39108
$109$	1.14765e7	+	1.14765e7i	0.0813024	+	0.0813024i	0.746588	−	0.665286i	$-0.231690\pi$
$109$	1.14765e7	+	1.14765e7i	0.0813024	+	0.0813024i	−0.665286	+	0.746588i	$0.731690\pi$
$110$			2.44737e8i			1.67159i
$111$	−2.88355e8	−	4.32393e7i	−1.89948	−	0.284830i
$112$	2.70797e7			0.172096
$113$	8.97438e7	−	8.97438e7i	0.550415	−	0.550415i	−0.376145	−	0.926561i	$-0.622751\pi$
$113$	8.97438e7	−	8.97438e7i	0.550415	−	0.550415i	0.926561	+	0.376145i	$0.122751\pi$
$114$		−	4.57374e8i		−	2.70802i
$115$		−	3.45758e8i		−	1.97688i
$116$	−5.05721e7	−	5.05721e7i	−0.279305	−	0.279305i
$117$	2.82886e8	+	2.82886e8i	1.50962	+	1.50962i
$118$	−1.16207e8			−0.599385
$119$	−3.98841e7	−	3.98841e7i	−0.198889	−	0.198889i
$120$	−3.48450e8			−1.68041
$121$	1.16614e8			0.544014
$122$			2.28598e8i			1.03189i
$123$	−5.79809e8			−2.53317
$124$	3.67138e8	+	3.67138e8i	1.55290	+	1.55290i
$125$	−1.68194e8	+	1.68194e8i	−0.688923	+	0.688923i
$126$	2.42558e8	−	2.42558e8i	0.962349	−	0.962349i
$127$	−7.78734e7			−0.299347			−0.149673	−	0.988735i	$-0.547822\pi$
$127$	−7.78734e7			−0.299347			−0.149673	+	0.988735i	$0.547822\pi$
$128$	1.92972e8	+	1.92972e8i	0.718878	+	0.718878i
$129$	−3.32824e8	+	3.32824e8i	−1.20187	+	1.20187i
$130$	3.96896e8	+	3.96896e8i	1.38964	+	1.38964i
$131$	1.80699e7	−	1.80699e7i	0.0613578	−	0.0613578i	−0.675762	−	0.737120i	$-0.736185\pi$
$131$	1.80699e7	−	1.80699e7i	0.0613578	−	0.0613578i	0.737120	+	0.675762i	$0.236185\pi$
$132$		−	5.32930e8i		−	1.75539i
$133$	6.70824e7	+	6.70824e7i	0.214389	+	0.214389i
$134$	1.74581e8	+	1.74581e8i	0.541474	+	0.541474i
$135$	1.22959e9	−	1.22959e9i	3.70190	−	3.70190i
$136$		−	1.58143e8i		−	0.462270i
$137$	1.75079e7			0.0496993			0.0248497	−	0.999691i	$-0.492089\pi$
$137$	1.75079e7			0.0496993			0.0248497	+	0.999691i	$0.492089\pi$
$138$			1.30921e9i			3.60988i
$139$		−	3.22943e8i		−	0.865101i	−0.901610	−	0.432550i	$-0.857614\pi$
$139$		−	3.22943e8i		−	0.865101i	0.901610	−	0.432550i	$-0.142386\pi$
$140$	1.95710e8	−	1.95710e8i	0.509450	−	0.509450i
$141$		−	8.38500e8i		−	2.12142i
$142$	−2.59786e8	+	2.59786e8i	−0.638945	+	0.638945i
$143$	−1.58515e8	+	1.58515e8i	−0.379076	+	0.379076i
$144$	−6.03197e8			−1.40284
$145$	2.08178e8			0.470936
$146$	−5.90600e8	−	5.90600e8i	−1.29982	−	1.29982i
$147$		−	7.99269e8i		−	1.71168i
$148$	6.42174e8	+	9.62949e7i	1.33846	+	0.200704i
$149$	2.96633e8			0.601830			0.300915	−	0.953651i	$-0.402708\pi$
$149$	2.96633e8			0.601830			0.300915	+	0.953651i	$0.402708\pi$
$150$	1.69165e9	−	1.69165e9i	3.34153	−	3.34153i
$151$			9.11628e8i			1.75352i	0.480932	+	0.876758i	$0.340298\pi$
$151$			9.11628e8i			1.75352i	−0.480932	+	0.876758i	$0.659702\pi$
$152$			2.65987e8i			0.498294i
$153$	8.88415e8	+	8.88415e8i	1.62125	+	1.62125i
$154$	1.35917e8	+	1.35917e8i	0.241652	+	0.241652i
$155$	−1.51131e9			−2.61834
$156$	−8.64267e8	−	8.64267e8i	−1.45932	−	1.45932i
$157$	5.44809e8			0.896697			0.448349	−	0.893859i	$-0.352012\pi$
$157$	5.44809e8			0.896697			0.448349	+	0.893859i	$0.352012\pi$
$158$	−5.35428e8			−0.859157
$159$		−	3.04559e8i		−	0.476522i
$160$	−1.41966e9			−2.16624
$161$	−1.92020e8	−	1.92020e8i	−0.285787	−	0.285787i
$162$	−2.64667e9	+	2.64667e9i	−3.84273	+	3.84273i
$163$	1.14303e8	−	1.14303e8i	0.161923	−	0.161923i	−0.621495	−	0.783418i	$-0.713475\pi$
$163$	1.14303e8	−	1.14303e8i	0.161923	−	0.161923i	0.783418	+	0.621495i	$0.213475\pi$
$164$	1.29125e9			1.78498
$165$	1.09689e9	+	1.09689e9i	1.47988	+	1.47988i
$166$	1.47476e9	−	1.47476e9i	1.94218	−	1.94218i
$167$	−6.54511e8	−	6.54511e8i	−0.841494	−	0.841494i	0.147559	−	0.989053i	$-0.452858\pi$
$167$	−6.54511e8	−	6.54511e8i	−0.841494	−	0.841494i	−0.989053	+	0.147559i	$0.952858\pi$
$168$	−1.93515e8	+	1.93515e8i	−0.242928	+	0.242928i
$169$		−	3.01595e8i		−	0.369723i
$170$	1.24647e9	+	1.24647e9i	1.49240	+	1.49240i
$171$	−1.49426e9	−	1.49426e9i	−1.74759	−	1.74759i
$172$	7.41208e8	−	7.41208e8i	0.846889	−	0.846889i
$173$		−	6.90541e8i		−	0.770913i	−0.922726	−	0.385456i	$-0.874044\pi$
$173$		−	6.90541e8i		−	0.770913i	0.922726	−	0.385456i	$-0.125956\pi$
$174$	−7.88262e8			−0.859951
$175$			4.96224e8i			0.529086i
$176$		−	3.38001e8i		−	0.352263i
$177$	−5.20832e8	+	5.20832e8i	−0.530646	+	0.530646i
$178$		−	1.02413e9i		−	1.02018i
$179$	−9.88753e8	+	9.88753e8i	−0.963109	+	0.963109i	−0.999343	−	0.0362340i	$-0.988464\pi$
$179$	−9.88753e8	+	9.88753e8i	−0.963109	+	0.963109i	0.0362340	+	0.999343i	$0.488464\pi$
$180$	−4.35943e9	+	4.35943e9i	−4.15279	+	4.15279i
$181$	1.48698e9			1.38545			0.692725	−	0.721202i	$-0.256410\pi$
$181$	1.48698e9			1.38545			0.692725	+	0.721202i	$0.256410\pi$
$182$	4.40840e8			0.401787
$183$	1.02456e9	+	1.02456e9i	0.913549	+	0.913549i
$184$		−	7.61373e8i		−	0.664242i
$185$	−1.51994e9	+	1.12354e9i	−1.29759	+	0.959186i
$186$	5.72254e9			4.78120
$187$	−4.97823e8	+	4.97823e8i	−0.407107	+	0.407107i
$188$			1.86736e9i			1.49485i
$189$		−	1.36573e9i		−	1.07033i
$190$	−2.09647e9	−	2.09647e9i	−1.60870	−	1.60870i
$191$	3.48298e8	+	3.48298e8i	0.261708	+	0.261708i	0.825748	−	0.564039i	$-0.190753\pi$
$191$	3.48298e8	+	3.48298e8i	0.261708	+	0.261708i	−0.564039	+	0.825748i	$0.690753\pi$
$192$	4.01391e9			2.95368
$193$	−6.14316e8	−	6.14316e8i	−0.442754	−	0.442754i	0.450182	−	0.892937i	$-0.351359\pi$
$193$	−6.14316e8	−	6.14316e8i	−0.442754	−	0.442754i	−0.892937	+	0.450182i	$0.851359\pi$
$194$	−1.10455e9			−0.779792
$195$	3.55771e9			2.46055
$196$			1.77999e9i			1.20613i
$197$	4.09066e8			0.271599			0.135800	−	0.990736i	$-0.456640\pi$
$197$	4.09066e8			0.271599			0.135800	+	0.990736i	$0.456640\pi$
$198$	−3.02754e9	−	3.02754e9i	−1.96983	−	1.96983i
$199$	−4.38185e8	+	4.38185e8i	−0.279412	+	0.279412i	−0.832874	−	0.553462i	$-0.813306\pi$
$199$	−4.38185e8	+	4.38185e8i	−0.279412	+	0.279412i	0.553462	+	0.832874i	$0.313306\pi$
$200$	−9.83784e8	+	9.83784e8i	−0.614865	+	0.614865i
$201$	1.56491e9			0.958752
$202$	−2.27150e9	−	2.27150e9i	−1.36429	−	1.36429i
$203$	1.15613e8	−	1.15613e8i	0.0680807	−	0.0680807i
$204$	−2.71426e9	−	2.71426e9i	−1.56722	−	1.56722i
$205$	−2.65768e9	+	2.65768e9i	−1.50483	+	1.50483i
$206$		−	2.79387e9i		−	1.55145i
$207$	4.27723e9	+	4.27723e9i	2.32960	+	2.32960i
$208$	−5.48145e8	−	5.48145e8i	−0.292848	−	0.292848i
$209$	8.37304e8	−	8.37304e8i	0.438832	−	0.438832i
$210$		−	3.05052e9i		−	1.56854i
$211$	6.78475e8			0.342298			0.171149	−	0.985245i	$-0.445252\pi$
$211$	6.78475e8			0.342298			0.171149	+	0.985245i	$0.445252\pi$
$212$			6.78261e8i			0.335779i
$213$			2.32868e9i			1.13134i
$214$	−1.87656e9	+	1.87656e9i	−0.894759	+	0.894759i
$215$			3.05115e9i			1.42794i
$216$	2.70761e9	−	2.70761e9i	1.24386	−	1.24386i
$217$	−8.39317e8	+	8.39317e8i	−0.378519	+	0.378519i
$218$	−3.98377e8			−0.176388
$219$	−5.29404e9			−2.30150
$220$	−2.44280e9	−	2.44280e9i	−1.04279	−	1.04279i
$221$			1.61466e9i			0.676882i
$222$	5.75522e9	−	4.25428e9i	2.36947	−	1.75152i
$223$	1.42380e9			0.575746			0.287873	−	0.957669i	$-0.407052\pi$
$223$	1.42380e9			0.575746			0.287873	+	0.957669i	$0.407052\pi$
$224$	−7.88424e8	+	7.88424e8i	−0.313161	+	0.313161i
$225$		−	1.10534e10i		−	4.31285i
$226$			3.11523e9i			1.19414i
$227$	1.39091e9	+	1.39091e9i	0.523834	+	0.523834i	0.918727	−	0.394893i	$-0.129218\pi$
$227$	1.39091e9	+	1.39091e9i	0.523834	+	0.523834i	−0.394893	+	0.918727i	$0.629218\pi$
$228$	4.56521e9	+	4.56521e9i	1.68936	+	1.68936i
$229$	2.59467e9			0.943496			0.471748	−	0.881733i	$-0.343623\pi$
$229$	2.59467e9			0.943496			0.471748	+	0.881733i	$0.343623\pi$
$230$	6.00105e9	+	6.00105e9i	2.14445	+	2.14445i
$231$	1.21834e9			0.427878
$232$	4.58416e8			0.158237
$233$		−	3.78608e9i		−	1.28459i	−0.766456	−	0.642297i	$-0.777982\pi$
$233$		−	3.78608e9i		−	1.28459i	0.766456	−	0.642297i	$-0.222018\pi$
$234$	−9.81968e9			−3.27517
$235$	−3.84345e9	−	3.84345e9i	−1.26023	−	1.26023i
$236$	1.15991e9	−	1.15991e9i	0.373917	−	0.373917i
$237$	−2.39975e9	+	2.39975e9i	−0.760627	+	0.760627i
$238$	1.38447e9			0.431496
$239$	2.41941e8	+	2.41941e8i	0.0741513	+	0.0741513i	0.743210	−	0.669058i	$-0.233302\pi$
$239$	2.41941e8	+	2.41941e8i	0.0741513	+	0.0741513i	−0.669058	+	0.743210i	$0.733302\pi$
$240$	−3.79305e9	+	3.79305e9i	−1.14326	+	1.14326i
$241$	3.53919e9	+	3.53919e9i	1.04914	+	1.04914i	0.998728	+	0.0504160i	$0.0160547\pi$
$241$	3.53919e9	+	3.53919e9i	1.04914	+	1.04914i	0.0504160	+	0.998728i	$0.483945\pi$
$242$	−2.02398e9	+	2.02398e9i	−0.590126	+	0.590126i
$243$			1.24117e10i			3.55965i
$244$	−2.28172e9	−	2.28172e9i	−0.643728	−	0.643728i
$245$	−3.66363e9	−	3.66363e9i	−1.01683	−	1.01683i
$246$	1.00633e10	−	1.00633e10i	2.74789	−	2.74789i
$247$		−	2.71576e9i		−	0.729631i
$248$	−3.32796e9			−0.879774
$249$		−	1.32195e10i		−	3.43890i
$250$		−	5.83843e9i		−	1.49464i
$251$	−1.72397e9	+	1.72397e9i	−0.434345	+	0.434345i	−0.890104	−	0.455758i	$-0.849368\pi$
$251$	−1.72397e9	+	1.72397e9i	−0.434345	+	0.434345i	0.455758	+	0.890104i	$0.349368\pi$
$252$			4.84210e9i			1.20069i
$253$	−2.39674e9	+	2.39674e9i	−0.584977	+	0.584977i
$254$	1.35159e9	−	1.35159e9i	0.324721	−	0.324721i
$255$	1.11731e10			2.64249
$256$	−9.37650e7			−0.0218314
$257$	1.38053e9	+	1.38053e9i	0.316456	+	0.316456i	0.847404	−	0.530949i	$-0.178164\pi$
$257$	1.38053e9	+	1.38053e9i	0.316456	+	0.316456i	−0.530949	+	0.847404i	$0.678164\pi$
$258$		−	1.15531e10i		−	2.60748i
$259$	−2.20141e8	+	1.46808e9i	−0.0489217	+	0.326250i
$260$	−7.92312e9			−1.73381
$261$	−2.57528e9	+	2.57528e9i	−0.554961	+	0.554961i
$262$			6.27250e8i			0.133118i
$263$			4.16116e8i			0.0869743i	0.999054	+	0.0434872i	$0.0138468\pi$
$263$			4.16116e8i			0.0869743i	−0.999054	+	0.0434872i	$0.986153\pi$
$264$	2.41540e9	+	2.41540e9i	0.497248	+	0.497248i
$265$	−1.39602e9	−	1.39602e9i	−0.283078	−	0.283078i
$266$	−2.32859e9			−0.465122
$267$	−4.59008e9	−	4.59008e9i	−0.903183	−	0.903183i
$268$	−3.48510e9			−0.675579
$269$	8.21115e9			1.56818			0.784089	−	0.620649i	$-0.213131\pi$
$269$	8.21115e9			1.56818			0.784089	+	0.620649i	$0.213131\pi$
$270$			4.26820e10i			8.03138i
$271$	−2.23237e9			−0.413894			−0.206947	−	0.978352i	$-0.566353\pi$
$271$	−2.23237e9			−0.413894			−0.206947	+	0.978352i	$0.566353\pi$
$272$	−1.72147e9	−	1.72147e9i	−0.314502	−	0.314502i
$273$	1.97581e9	−	1.97581e9i	0.355709	−	0.355709i
$274$	−3.03870e8	+	3.03870e8i	−0.0539121	+	0.0539121i
$275$	6.19374e9			1.08298
$276$	−1.30677e10	−	1.30677e10i	−2.25197	−	2.25197i
$277$	2.72856e9	−	2.72856e9i	0.463463	−	0.463463i	−0.436326	−	0.899789i	$-0.643721\pi$
$277$	2.72856e9	−	2.72856e9i	0.463463	−	0.463463i	0.899789	+	0.436326i	$0.143721\pi$
$278$	5.60507e9	+	5.60507e9i	0.938430	+	0.938430i
$279$	1.86957e10	−	1.86957e10i	3.08550	−	3.08550i
$280$			1.77404e9i			0.288623i
$281$	−1.79756e9	−	1.79756e9i	−0.288309	−	0.288309i	0.548102	−	0.836411i	$-0.315350\pi$
$281$	−1.79756e9	−	1.79756e9i	−0.288309	−	0.288309i	−0.836411	+	0.548102i	$0.815350\pi$
$282$	1.45532e10	+	1.45532e10i	2.30124	+	2.30124i
$283$	−7.03014e9	+	7.03014e9i	−1.09602	+	1.09602i	−0.101147	+	0.994871i	$0.532251\pi$
$283$	−7.03014e9	+	7.03014e9i	−1.09602	+	1.09602i	−0.994871	+	0.101147i	$0.967749\pi$
$284$		−	5.18604e9i		−	0.797191i
$285$	−1.87925e10			−2.84842
$286$		−	5.50245e9i		−	0.822416i
$287$			2.95194e9i			0.435090i
$288$	1.75621e10	−	1.75621e10i	2.55274	−	2.55274i
$289$		−	1.90485e9i		−	0.273067i
$290$	−3.61318e9	+	3.61318e9i	−0.510855	+	0.510855i
$291$	−4.95051e9	+	4.95051e9i	−0.690363	+	0.690363i
$292$	1.17900e10			1.62174
$293$	−4.60109e9			−0.624295			−0.312148	−	0.950034i	$-0.601048\pi$
$293$	−4.60109e9			−0.624295			−0.312148	+	0.950034i	$0.601048\pi$
$294$	1.38723e10	+	1.38723e10i	1.85677	+	1.85677i
$295$			4.77470e9i			0.630461i
$296$	−3.34696e9	+	2.47409e9i	−0.435998	+	0.322291i
$297$	−1.70466e10			−2.19085
$298$	−5.14842e9	+	5.14842e9i	−0.652843	+	0.652843i
$299$			7.77372e9i			0.972622i
$300$			3.37699e10i			4.16913i
$301$	1.69448e9	+	1.69448e9i	0.206429	+	0.206429i
$302$	−1.58224e10	−	1.58224e10i	−1.90215	−	1.90215i
$303$	−2.03613e10			−2.41566
$304$	2.89540e9	+	2.89540e9i	0.339011	+	0.339011i
$305$	9.39258e9			1.08539
$306$	−3.08391e10			−3.51735
$307$			7.05241e9i			0.793933i	0.917833	+	0.396967i	$0.129937\pi$
$307$			7.05241e9i			0.793933i	−0.917833	+	0.396967i	$0.870063\pi$
$308$	−2.71327e9			−0.301502
$309$	−1.25219e10	−	1.25219e10i	−1.37352	−	1.37352i
$310$	2.62306e10	−	2.62306e10i	2.84028	−	2.84028i
$311$	−5.60435e9	+	5.60435e9i	−0.599078	+	0.599078i	−0.940067	−	0.340989i	$-0.889238\pi$
$311$	−5.60435e9	+	5.60435e9i	−0.599078	+	0.599078i	0.340989	+	0.940067i	$0.389238\pi$
$312$	7.83423e9			0.826757
$313$	−8.71715e7	−	8.71715e7i	−0.00908233	−	0.00908233i	0.702551	−	0.711633i	$-0.252044\pi$
$313$	−8.71715e7	−	8.71715e7i	−0.00908233	−	0.00908233i	−0.711633	+	0.702551i	$0.752044\pi$
$314$	−9.45583e9	+	9.45583e9i	−0.972705	+	0.972705i
$315$	−9.96615e9	−	9.96615e9i	−1.01224	−	1.01224i
$316$	5.34429e9	−	5.34429e9i	0.535972	−	0.535972i
$317$		−	9.13066e9i		−	0.904201i	−0.891967	−	0.452101i	$-0.850675\pi$
$317$		−	9.13066e9i		−	0.904201i	0.891967	−	0.452101i	$-0.149325\pi$
$318$	5.28600e9	+	5.28600e9i	0.516914	+	0.516914i
$319$	−1.44306e9	−	1.44306e9i	−0.139354	−	0.139354i
$320$	1.83987e10	−	1.83987e10i	1.75463	−	1.75463i
$321$			1.68211e10i			1.58429i
$322$	6.66548e9			0.620023
$323$		−	8.52893e9i		−	0.783582i
$324$		−	5.28347e10i		−	4.79445i
$325$	1.00446e10	−	1.00446e10i	0.900321	−	0.900321i
$326$			3.96774e9i			0.351296i
$327$	−1.78549e9	+	1.78549e9i	−0.156159	+	0.156159i
$328$	−5.85233e9	+	5.85233e9i	−0.505631	+	0.505631i
$329$	−4.26899e9			−0.364369
$330$	−3.80758e10			−3.21065
$331$	1.22648e9	+	1.22648e9i	0.102176	+	0.102176i	0.756347	−	0.654171i	$-0.226982\pi$
$331$	1.22648e9	+	1.22648e9i	0.102176	+	0.102176i	−0.654171	+	0.756347i	$0.726982\pi$
$332$			2.94403e10i			2.42320i
$333$	4.90362e9	−	3.27014e10i	0.398786	−	2.65944i
$334$	2.27197e10			1.82565
$335$	7.17313e9	−	7.17313e9i	0.569547	−	0.569547i
$336$			4.21301e9i			0.330549i
$337$			1.73952e10i			1.34868i	0.738420	+	0.674341i	$0.235572\pi$
$337$			1.73952e10i			1.34868i	−0.738420	+	0.674341i	$0.764428\pi$
$338$	5.23454e9	+	5.23454e9i	0.401062	+	0.401062i
$339$	1.39622e10	+	1.39622e10i	1.05719	+	1.05719i
$340$	−2.48828e10			−1.86202
$341$	1.04761e10	+	1.04761e10i	0.774789	+	0.774789i
$342$	5.18692e10			3.79145
$343$	−8.63547e9			−0.623892
$344$			6.71876e9i			0.479794i
$345$	5.37925e10			3.79704
$346$	1.19852e10	+	1.19852e10i	0.836258	+	0.836258i
$347$	9.09665e9	−	9.09665e9i	0.627427	−	0.627427i	−0.319993	−	0.947420i	$-0.603680\pi$
$347$	9.09665e9	−	9.09665e9i	0.627427	−	0.627427i	0.947420	+	0.319993i	$0.103680\pi$
$348$	7.86792e9	−	7.86792e9i	0.536467	−	0.536467i
$349$	1.83983e10			1.24015			0.620076	−	0.784542i	$-0.287102\pi$
$349$	1.83983e10			1.24015			0.620076	+	0.784542i	$0.287102\pi$
$350$	−8.61258e9	−	8.61258e9i	−0.573933	−	0.573933i
$351$	−2.76450e10	+	2.76450e10i	−1.82133	+	1.82133i
$352$	9.84090e9	+	9.84090e9i	0.641009	+	0.641009i
$353$	−3.02046e9	+	3.02046e9i	−0.194524	+	0.194524i	−0.797648	−	0.603123i	$-0.793923\pi$
$353$	−3.02046e9	+	3.02046e9i	−0.194524	+	0.194524i	0.603123	+	0.797648i	$0.293923\pi$
$354$		−	1.80794e10i		−	1.15125i
$355$	1.06740e10	+	1.06740e10i	0.672072	+	0.672072i
$356$	1.02222e10	+	1.02222e10i	0.636423	+	0.636423i
$357$	6.20510e9	−	6.20510e9i	0.382011	−	0.382011i
$358$		−	3.43220e10i		−	2.08949i
$359$	−1.24329e10			−0.748507			−0.374254	−	0.927326i	$-0.622101\pi$
$359$	−1.24329e10			−0.748507			−0.374254	+	0.927326i	$0.622101\pi$
$360$		−	3.95165e10i		−	2.35271i
$361$		−	2.63847e9i		−	0.155354i
$362$	−2.58084e10	+	2.58084e10i	−1.50289	+	1.50289i
$363$			1.81426e10i			1.04490i
$364$	−4.40018e9	+	4.40018e9i	−0.250648	+	0.250648i
$365$	−2.42664e10	+	2.42664e10i	−1.36721	+	1.36721i
$366$	−3.55649e10			−1.98197
$367$	2.46922e10			1.36112			0.680560	−	0.732693i	$-0.261737\pi$
$367$	2.46922e10			1.36112			0.680560	+	0.732693i	$0.261737\pi$
$368$	−8.28793e9	−	8.28793e9i	−0.451913	−	0.451913i
$369$		−	6.57542e10i		−	3.54665i
$370$	6.87990e9	−	4.58808e10i	0.367092	−	2.44807i
$371$	−1.55058e9			−0.0818462
$372$	−5.71187e10	+	5.71187e10i	−2.98268	+	2.98268i
$373$			3.12326e10i			1.61351i	0.590884	+	0.806756i	$0.298779\pi$
$373$			3.12326e10i			1.61351i	−0.590884	+	0.806756i	$0.701221\pi$
$374$		−	1.72806e10i		−	0.883229i
$375$	−2.61674e10	−	2.61674e10i	−1.32323	−	1.32323i
$376$	−8.46344e9	−	8.46344e9i	−0.423444	−	0.423444i
$377$	−4.68048e9			−0.231699
$378$	2.37039e10	+	2.37039e10i	1.16105	+	1.16105i
$379$	−3.12901e10			−1.51653			−0.758264	−	0.651948i	$-0.773952\pi$
$379$	−3.12901e10			−1.51653			−0.758264	+	0.651948i	$0.773952\pi$
$380$	4.18513e10			2.00712
$381$		−	1.21154e10i		−	0.574961i
$382$	−1.20903e10			−0.567784
$383$	−1.75785e10	−	1.75785e10i	−0.816931	−	0.816931i	0.168731	−	0.985662i	$-0.446033\pi$
$383$	−1.75785e10	−	1.75785e10i	−0.816931	−	0.816931i	−0.985662	+	0.168731i	$0.946033\pi$
$384$	−3.00223e10	+	3.00223e10i	−1.38076	+	1.38076i
$385$	5.58452e9	−	5.58452e9i	0.254181	−	0.254181i
$386$	2.13244e10			0.960567
$387$	−3.77445e10	−	3.77445e10i	−1.68271	−	1.68271i
$388$	1.10249e10	−	1.10249e10i	0.486461	−	0.486461i
$389$	−1.63831e10	−	1.63831e10i	−0.715482	−	0.715482i	0.252194	−	0.967677i	$-0.418848\pi$
$389$	−1.63831e10	−	1.63831e10i	−0.715482	−	0.715482i	−0.967677	+	0.252194i	$0.918848\pi$
$390$	−6.17485e10	+	6.17485e10i	−2.66912	+	2.66912i
$391$			2.44136e10i			1.04454i
$392$	−8.06746e9	−	8.06746e9i	−0.341659	−	0.341659i
$393$	2.81128e9	+	2.81128e9i	0.117851	+	0.117851i
$394$	−7.09984e9	+	7.09984e9i	−0.294621	+	0.294621i
$395$			2.19995e10i			0.903702i
$396$	6.04378e10			2.45770
$397$			3.18838e10i			1.28354i	0.766899	+	0.641768i	$0.221799\pi$
$397$			3.18838e10i			1.28354i	−0.766899	+	0.641768i	$0.778201\pi$
$398$		−	1.52105e10i		−	0.606192i
$399$	−1.04366e10	+	1.04366e10i	−0.411781	+	0.411781i
$400$			2.14180e10i			0.836639i
$401$	7.94942e9	−	7.94942e9i	0.307438	−	0.307438i	−0.536477	−	0.843915i	$-0.680245\pi$
$401$	7.94942e9	−	7.94942e9i	0.307438	−	0.307438i	0.843915	+	0.536477i	$0.180245\pi$
$402$	−2.71610e10	+	2.71610e10i	−1.04002	+	1.04002i
$403$	3.39788e10			1.28822
$404$	4.53452e10			1.70218
$405$	1.08746e11	+	1.08746e11i	4.04196	+	4.04196i
$406$			4.01322e9i			0.147703i
$407$	1.83242e10	+	2.74774e9i	0.667801	+	0.100138i
$408$	2.46037e10			0.887891
$409$	−2.67703e10	+	2.67703e10i	−0.956667	+	0.956667i	−0.999099	−	0.0424324i	$-0.986489\pi$
$409$	−2.67703e10	+	2.67703e10i	−0.956667	+	0.956667i	0.0424324	+	0.999099i	$0.486489\pi$
$410$		−	9.22547e10i		−	3.26477i
$411$			2.72384e9i			0.0954586i
$412$	2.78866e10	+	2.78866e10i	0.967846	+	0.967846i
$413$	2.65167e9	+	2.65167e9i	0.0911423	+	0.0911423i
$414$	−1.48473e11			−5.05413
$415$	−6.05947e10	−	6.05947e10i	−2.04288	−	2.04288i
$416$	3.19185e10			1.06578
$417$	5.02430e10			1.66162
$418$			2.90649e10i			0.952058i
$419$	−5.26880e9			−0.170945			−0.0854724	−	0.996341i	$-0.527240\pi$
$419$	−5.26880e9			−0.170945			−0.0854724	+	0.996341i	$0.527240\pi$
$420$	3.04483e10	+	3.04483e10i	0.978511	+	0.978511i
$421$	−3.27717e10	+	3.27717e10i	−1.04321	+	1.04321i	−0.0441844	+	0.999023i	$0.514069\pi$
$421$	−3.27717e10	+	3.27717e10i	−1.04321	+	1.04321i	−0.999023	+	0.0441844i	$0.985931\pi$
$422$	−1.17758e10	+	1.17758e10i	−0.371312	+	0.371312i
$423$	9.50916e10			2.97016
$424$	−3.07408e9	−	3.07408e9i	−0.0951157	−	0.0951157i
$425$	3.15453e10	−	3.15453e10i	0.966894	−	0.966894i
$426$	−4.04172e10	−	4.04172e10i	−1.22723	−	1.22723i
$427$	5.21625e9	−	5.21625e9i	0.156909	−	0.156909i
$428$		−	3.74611e10i		−	1.11636i
$429$	−2.46615e10	−	2.46615e10i	−0.728100	−	0.728100i
$430$	−5.29564e10	−	5.29564e10i	−1.54898	−	1.54898i
$431$	−1.34024e10	+	1.34024e10i	−0.388394	+	0.388394i	−0.874114	−	0.485720i	$-0.838557\pi$
$431$	−1.34024e10	+	1.34024e10i	−0.388394	+	0.388394i	0.485720	+	0.874114i	$0.338557\pi$
$432$		−	5.89473e10i		−	1.69250i
$433$	8.34940e9			0.237522			0.118761	−	0.992923i	$-0.462108\pi$
$433$	8.34940e9			0.237522			0.118761	+	0.992923i	$0.462108\pi$
$434$		−	2.91348e10i		−	0.821207i
$435$			3.23879e10i			0.904537i
$436$	3.97634e9	−	3.97634e9i	0.110037	−	0.110037i
$437$		−	4.10621e10i		−	1.12594i
$438$	9.18846e10	−	9.18846e10i	2.49658	−	2.49658i
$439$	2.43640e10	−	2.43640e10i	0.655980	−	0.655980i	−0.298446	−	0.954426i	$-0.596468\pi$
$439$	2.43640e10	−	2.43640e10i	0.655980	−	0.655980i	0.954426	+	0.298446i	$0.0964684\pi$
$440$	2.21431e10			0.590781
$441$	9.06424e10			2.39650
$442$	−2.80245e10	−	2.80245e10i	−0.734257	−	0.734257i
$443$		−	1.34804e10i		−	0.350017i	−0.984567	−	0.175009i	$-0.944005\pi$
$443$		−	1.34804e10i		−	0.350017i	0.984567	−	0.175009i	$-0.0559953\pi$
$444$	−1.49814e10	+	9.99084e10i	−0.385497	+	2.57081i
$445$	−4.20794e10			−1.07307
$446$	−2.47119e10	+	2.47119e10i	−0.624548	+	0.624548i
$447$			4.61496e10i			1.15595i
$448$		−	2.04357e10i		−	0.507315i
$449$	−3.54772e10	−	3.54772e10i	−0.872899	−	0.872899i	0.119889	−	0.992787i	$-0.461746\pi$
$449$	−3.54772e10	−	3.54772e10i	−0.872899	−	0.872899i	−0.992787	+	0.119889i	$0.961746\pi$
$450$	1.91845e11	+	1.91845e11i	4.67843	+	4.67843i
$451$	3.68453e10			0.890586
$452$	−3.10941e10	−	3.10941e10i	−0.744946	−	0.744946i
$453$	−1.41830e11			−3.36801
$454$	−4.82817e10			−1.13647
$455$		−	1.81131e10i		−	0.422618i
$456$	−4.13818e10			−0.957083
$457$	2.62271e10	+	2.62271e10i	0.601291	+	0.601291i	0.940655	−	0.339364i	$-0.110212\pi$
$457$	2.62271e10	+	2.62271e10i	0.601291	+	0.601291i	−0.339364	+	0.940655i	$0.610212\pi$
$458$	−4.50336e10	+	4.50336e10i	−1.02347	+	1.02347i
$459$	−8.68201e10	+	8.68201e10i	−1.95600	+	1.95600i
$460$	−1.19797e11			−2.67556
$461$	4.65285e10	+	4.65285e10i	1.03019	+	1.03019i	0.999530	+	0.0306559i	$0.00975962\pi$
$461$	4.65285e10	+	4.65285e10i	1.03019	+	1.03019i	0.0306559	+	0.999530i	$0.490240\pi$
$462$	−2.11457e10	+	2.11457e10i	−0.464146	+	0.464146i
$463$	−2.14458e10	−	2.14458e10i	−0.466679	−	0.466679i	0.434158	−	0.900837i	$-0.357046\pi$
$463$	−2.14458e10	−	2.14458e10i	−0.466679	−	0.466679i	−0.900837	+	0.434158i	$0.857046\pi$
$464$	4.99008e9	−	4.99008e9i	0.107655	−	0.107655i
$465$		−	2.35126e11i		−	5.02909i
$466$	6.57120e10	+	6.57120e10i	1.39348	+	1.39348i
$467$	8.95197e9	+	8.95197e9i	0.188214	+	0.188214i	0.794923	−	0.606710i	$-0.207511\pi$
$467$	8.95197e9	+	8.95197e9i	0.188214	+	0.188214i	−0.606710	+	0.794923i	$0.707511\pi$
$468$	9.80136e10	−	9.80136e10i	2.04316	−	2.04316i
$469$		−	7.96733e9i		−	0.164673i
$470$	1.33416e11			2.73411
$471$			8.47605e10i			1.72230i
$472$			1.05141e10i			0.211838i
$473$	2.11501e10	−	2.11501e10i	0.422540	−	0.422540i
$474$		−	8.33010e10i		−	1.65020i
$475$	−5.30571e10	+	5.30571e10i	−1.04224	+	1.04224i
$476$	−1.38189e10	+	1.38189e10i	−0.269182	+	0.269182i
$477$	3.45391e10			0.667171
$478$	−8.39838e9			−0.160873
$479$	−9.83675e9	−	9.83675e9i	−0.186857	−	0.186857i	0.607479	−	0.794336i	$-0.292181\pi$
$479$	−9.83675e9	−	9.83675e9i	−0.186857	−	0.186857i	−0.794336	+	0.607479i	$0.792181\pi$
$480$		−	2.20869e11i		−	4.16073i
$481$	3.41729e10	−	2.52607e10i	0.638413	−	0.471917i
$482$	−1.22854e11			−2.27615
$483$	2.98741e10	−	2.98741e10i	0.548917	−	0.548917i
$484$		−	4.04041e10i		−	0.736282i
$485$			4.53835e10i			0.820221i
$486$	−2.15421e11	−	2.15421e11i	−3.86138	−	3.86138i
$487$	−6.20588e10	−	6.20588e10i	−1.10328	−	1.10328i	−0.994012	−	0.109272i	$-0.965148\pi$
$487$	−6.20588e10	−	6.20588e10i	−1.10328	−	1.10328i	−0.109272	−	0.994012i	$-0.534852\pi$
$488$	2.06828e10			0.364696
$489$	1.77831e10	+	1.77831e10i	0.311008	+	0.311008i
$490$	1.27173e11			2.20603
$491$	5.91225e10			1.01725			0.508624	−	0.860989i	$-0.330154\pi$
$491$	5.91225e10			1.01725			0.508624	+	0.860989i	$0.330154\pi$
$492$			2.00890e11i			3.42846i
$493$	−1.46992e10			−0.248832
$494$	4.71353e10	+	4.71353e10i	0.791477	+	0.791477i
$495$	−1.24395e11	+	1.24395e11i	−2.07196	+	2.07196i
$496$	−3.62265e10	+	3.62265e10i	−0.598548	+	0.598548i
$497$	1.18559e10			0.194315
$498$	2.29441e11	+	2.29441e11i	3.73039	+	3.73039i
$499$	−2.76467e10	+	2.76467e10i	−0.445903	+	0.445903i	−0.893990	−	0.448087i	$-0.852106\pi$
$499$	−2.76467e10	+	2.76467e10i	−0.445903	+	0.445903i	0.448087	+	0.893990i	$0.352106\pi$
$500$	5.82754e10	+	5.82754e10i	0.932407	+	0.932407i
$501$	1.01828e11	−	1.01828e11i	1.61628	−	1.61628i
$502$		−	5.98433e10i		−	0.942324i
$503$	2.79691e9	+	2.79691e9i	0.0436925	+	0.0436925i	0.728615	−	0.684923i	$-0.240164\pi$
$503$	2.79691e9	+	2.79691e9i	0.0436925	+	0.0436925i	−0.684923	+	0.728615i	$0.740164\pi$
$504$	−2.19459e10	−	2.19459e10i	−0.340119	−	0.340119i
$505$	−9.33308e10	+	9.33308e10i	−1.43502	+	1.43502i
$506$		−	8.31968e10i		−	1.26912i
$507$	4.69216e10			0.710135
$508$			2.69814e10i			0.405143i
$509$			2.87792e10i			0.428753i	0.976751	+	0.214377i	$0.0687720\pi$
$509$			2.87792e10i			0.428753i	−0.976751	+	0.214377i	$0.931228\pi$
$510$	−1.93923e11	+	1.93923e11i	−2.86648	+	2.86648i
$511$			2.69532e10i			0.395299i
$512$	−4.77735e10	+	4.77735e10i	−0.695196	+	0.695196i
$513$	1.46026e11	−	1.46026e11i	2.10843	−	2.10843i
$514$	−4.79215e10			−0.686559
$515$	−1.14794e11			−1.63188
$516$	1.15316e11	+	1.15316e11i	1.62664	+	1.62664i
$517$			5.32845e10i			0.745828i
$518$	−2.16595e10	−	2.93012e10i	−0.300836	−	0.406973i
$519$	1.07433e11			1.48071
$520$	3.59100e10	−	3.59100e10i	0.491136	−	0.491136i
$521$		−	1.30112e11i		−	1.76589i	−0.469472	−	0.882947i	$-0.655556\pi$
$521$		−	1.30112e11i		−	1.76589i	0.469472	−	0.882947i	$-0.344444\pi$
$522$		−	8.93942e10i		−	1.20400i
$523$	−1.46169e10	−	1.46169e10i	−0.195366	−	0.195366i	0.602644	−	0.798010i	$-0.294114\pi$
$523$	−1.46169e10	−	1.46169e10i	−0.195366	−	0.195366i	−0.798010	+	0.602644i	$0.794114\pi$
$524$	−6.26080e9	−	6.26080e9i	−0.0830433	−	0.0830433i
$525$	−7.72018e10			−1.01623
$526$	−7.22220e9	−	7.22220e9i	−0.0943466	−	0.0943466i
$527$	1.06712e11			1.38347
$528$	5.25857e10			0.676599
$529$			3.92272e10i			0.500916i
$530$	4.84591e10			0.614146
$531$	−5.90658e10	−	5.90658e10i	−0.742948	−	0.742948i
$532$	2.32425e10	−	2.32425e10i	0.290159	−	0.290159i
$533$	5.97530e10	−	5.97530e10i	0.740373	−	0.740373i
$534$	1.59333e11			1.95948
$535$	7.71035e10	+	7.71035e10i	0.941150	+	0.941150i
$536$	1.57955e10	−	1.57955e10i	0.191371	−	0.191371i
$537$	−1.53829e11	−	1.53829e11i	−1.84986	−	1.84986i
$538$	−1.42515e11	+	1.42515e11i	−1.70110	+	1.70110i
$539$			5.07914e10i			0.601776i
$540$	−4.26024e11	−	4.26024e11i	−5.01025	−	5.01025i
$541$	6.48976e9	+	6.48976e9i	0.0757600	+	0.0757600i	0.743971	−	0.668211i	$-0.232940\pi$
$541$	6.48976e9	+	6.48976e9i	0.0757600	+	0.0757600i	−0.668211	+	0.743971i	$0.732940\pi$
$542$	3.87455e10	−	3.87455e10i	0.448977	−	0.448977i
$543$			2.31342e11i			2.66106i
$544$	1.00241e11			1.14459
$545$			1.63684e10i			0.185533i
$546$			6.85852e10i			0.771720i
$547$	9.55797e10	−	9.55797e10i	1.06762	−	1.06762i	0.0700776	−	0.997542i	$-0.477675\pi$
$547$	9.55797e10	−	9.55797e10i	1.06762	−	1.06762i	0.997542	−	0.0700776i	$-0.0223247\pi$
$548$		−	6.06607e9i		−	0.0672644i
$549$	−1.16192e11	+	1.16192e11i	−1.27904	+	1.27904i
$550$	−1.07500e11	+	1.07500e11i	−1.17478	+	1.17478i
$551$	2.47231e10			0.268223
$552$	1.18453e11			1.27582
$553$	1.22176e10	+	1.22176e10i	0.130643	+	0.130643i
$554$			9.47151e10i			1.00550i
$555$	−1.74799e11	−	2.36469e11i	−1.84233	−	2.49231i
$556$	−1.11892e11			−1.17085
$557$	−4.84935e10	+	4.84935e10i	−0.503806	+	0.503806i	−0.912618	−	0.408813i	$-0.865943\pi$
$557$	−4.84935e10	+	4.84935e10i	−0.503806	+	0.503806i	0.408813	+	0.912618i	$0.365943\pi$
$558$			6.48975e11i			6.69408i
$559$		−	6.85993e10i		−	0.702543i
$560$	1.93113e10	+	1.93113e10i	0.196363	+	0.196363i
$561$	−7.74504e10	−	7.74504e10i	−0.781938	−	0.781938i
$562$	6.23977e10			0.625494
$563$	−1.60551e10	−	1.60551e10i	−0.159801	−	0.159801i	0.622677	−	0.782479i	$-0.286045\pi$
$563$	−1.60551e10	−	1.60551e10i	−0.159801	−	0.159801i	−0.782479	+	0.622677i	$0.786045\pi$
$564$	−2.90521e11			−2.87118
$565$	1.27998e11			1.25605
$566$		−	2.44033e11i		−	2.37784i
$567$	1.20786e11			1.16865
$568$	2.35047e10	+	2.35047e10i	0.225819	+	0.225819i
$569$	−7.70848e10	+	7.70848e10i	−0.735393	+	0.735393i	−0.971683	−	0.236290i	$-0.924069\pi$
$569$	−7.70848e10	+	7.70848e10i	−0.735393	+	0.735393i	0.236290	+	0.971683i	$0.424069\pi$
$570$	3.26166e11	−	3.26166e11i	3.08986	−	3.08986i
$571$	1.74335e11			1.63999			0.819993	−	0.572374i	$-0.193977\pi$
$571$	1.74335e11			1.63999			0.819993	+	0.572374i	$0.193977\pi$
$572$	5.49218e10	+	5.49218e10i	0.513051	+	0.513051i
$573$	−5.41877e10	+	5.41877e10i	−0.502669	+	0.502669i
$574$	−5.12345e10	−	5.12345e10i	−0.471970	−	0.471970i
$575$	1.51873e11	−	1.51873e11i	1.38934	−	1.38934i
$576$			4.55204e11i			4.13539i
$577$	3.50348e10	+	3.50348e10i	0.316079	+	0.316079i	0.847259	−	0.531180i	$-0.178251\pi$
$577$	3.50348e10	+	3.50348e10i	0.316079	+	0.316079i	−0.531180	+	0.847259i	$0.678251\pi$
$578$	3.30610e10	+	3.30610e10i	0.296213	+	0.296213i
$579$	9.55743e10	−	9.55743e10i	0.850407	−	0.850407i
$580$		−	7.21287e10i		−	0.637377i
$581$	−6.73037e10			−0.590656
$582$		−	1.71844e11i		−	1.49776i
$583$			1.93539e10i			0.167531i
$584$	−5.34357e10	+	5.34357e10i	−0.459388	+	0.459388i
$585$			4.03469e11i			3.44498i
$586$	7.98575e10	−	7.98575e10i	0.677213	−	0.677213i
$587$	−1.50973e11	+	1.50973e11i	−1.27159	+	1.27159i	−0.326341	+	0.945252i	$0.605816\pi$
$587$	−1.50973e11	+	1.50973e11i	−1.27159	+	1.27159i	−0.945252	+	0.326341i	$0.894184\pi$
$588$	−2.76928e11			−2.31664
$589$	−1.79482e11			−1.49128
$590$	−8.28708e10	−	8.28708e10i	−0.683901	−	0.683901i
$591$			6.36418e10i			0.521666i
$592$	−9.50168e9	+	6.33651e10i	−0.0773595	+	0.515897i
$593$	−1.05546e11			−0.853538			−0.426769	−	0.904361i	$-0.640348\pi$
$593$	−1.05546e11			−0.853538			−0.426769	+	0.904361i	$0.640348\pi$
$594$	2.95865e11	−	2.95865e11i	2.37656	−	2.37656i
$595$		−	5.68849e10i		−	0.453868i
$596$		−	1.02776e11i		−	0.814532i
$597$	−6.81720e10	−	6.81720e10i	−0.536672	−	0.536672i
$598$	−1.34922e11	−	1.34922e11i	−1.05506	−	1.05506i
$599$	1.96854e11			1.52910			0.764552	−	0.644563i	$-0.222960\pi$
$599$	1.96854e11			1.52910			0.764552	+	0.644563i	$0.222960\pi$
$600$	−1.53055e11	−	1.53055e11i	−1.18098	−	1.18098i
$601$	1.27768e11			0.979318			0.489659	−	0.871914i	$-0.337121\pi$
$601$	1.27768e11			0.979318			0.489659	+	0.871914i	$0.337121\pi$
$602$	−5.88197e10			−0.447854
$603$			1.77472e11i			1.34233i
$604$	3.15858e11			2.37325
$605$	8.31609e10	+	8.31609e10i	0.620723	+	0.620723i
$606$	3.53396e11	−	3.53396e11i	2.62042	−	2.62042i
$607$	6.48043e10	−	6.48043e10i	0.477363	−	0.477363i	−0.426924	−	0.904287i	$-0.640403\pi$
$607$	6.48043e10	−	6.48043e10i	0.477363	−	0.477363i	0.904287	+	0.426924i	$0.140403\pi$
$608$	−1.68599e11			−1.23379
$609$	1.79869e10	+	1.79869e10i	0.130764	+	0.130764i
$610$	−1.63020e11	+	1.63020e11i	−1.17739	+	1.17739i
$611$	8.64128e10	+	8.64128e10i	0.620031	+	0.620031i
$612$	3.07815e11	−	3.07815e11i	2.19424	−	2.19424i
$613$		−	1.83662e11i		−	1.30070i	−0.759634	−	0.650351i	$-0.774622\pi$
$613$		−	1.83662e11i		−	1.30070i	0.759634	−	0.650351i	$-0.225378\pi$
$614$	−1.22403e11	−	1.22403e11i	−0.861230	−	0.861230i
$615$	−4.13478e11	−	4.13478e11i	−2.89036	−	2.89036i
$616$	1.22973e10	−	1.22973e10i	0.0854060	−	0.0854060i
$617$		−	1.54875e11i		−	1.06867i	−0.845274	−	0.534333i	$-0.820563\pi$
$617$		−	1.54875e11i		−	1.06867i	0.845274	−	0.534333i	$-0.179437\pi$
$618$	4.34665e11			2.97990
$619$		−	1.16462e11i		−	0.793271i	−0.917976	−	0.396636i	$-0.870178\pi$
$619$		−	1.16462e11i		−	0.793271i	0.917976	−	0.396636i	$-0.129822\pi$
$620$			5.23632e11i			3.54372i
$621$	−4.17991e11	+	4.17991e11i	−2.81061	+	2.81061i
$622$		−	1.94541e11i		−	1.29972i
$623$	−2.33692e10	+	2.33692e10i	−0.155128	+	0.155128i
$624$	8.52795e10	−	8.52795e10i	0.562479	−	0.562479i
$625$	4.83028e9			0.0316557
$626$	3.02594e9			0.0197044
$627$	1.30266e11	+	1.30266e11i	0.842874	+	0.842874i
$628$		−	1.88764e11i		−	1.21361i
$629$	1.07321e11	−	7.93323e10i	0.685620	−	0.506813i
$630$	3.45949e11			2.19609
$631$	−1.72895e11	+	1.72895e11i	−1.09060	+	1.09060i	−0.0951371	+	0.995464i	$0.530329\pi$
$631$	−1.72895e11	+	1.72895e11i	−1.09060	+	1.09060i	−0.995464	+	0.0951371i	$0.969671\pi$
$632$			4.84439e10i			0.303648i
$633$			1.05556e11i			0.657458i
$634$	1.58474e11	+	1.58474e11i	0.980845	+	0.980845i
$635$	−5.55338e10	−	5.55338e10i	−0.341556	−	0.341556i
$636$	−1.05523e11			−0.644937
$637$	8.23697e10	+	8.23697e10i	0.500276	+	0.500276i
$638$	5.00920e10			0.302333
$639$	−2.64088e11			−1.58397
$640$			2.75228e11i			1.64049i
$641$	2.36052e11			1.39822			0.699109	−	0.715015i	$-0.253580\pi$
$641$	2.36052e11			1.39822			0.699109	+	0.715015i	$0.253580\pi$
$642$	−2.91951e11	−	2.91951e11i	−1.71858	−	1.71858i
$643$	1.82332e11	−	1.82332e11i	1.06664	−	1.06664i	0.0690283	−	0.997615i	$-0.478010\pi$
$643$	1.82332e11	−	1.82332e11i	1.06664	−	1.06664i	0.997615	−	0.0690283i	$-0.0219899\pi$
$644$	−6.65305e10	+	6.65305e10i	−0.386792	+	0.386792i
$645$	−4.74693e11			−2.74267
$646$	1.48030e11	+	1.48030e11i	0.850002	+	0.850002i
$647$	−1.93705e11	+	1.93705e11i	−1.10541	+	1.10541i	−0.111668	+	0.993746i	$0.535619\pi$
$647$	−1.93705e11	+	1.93705e11i	−1.10541	+	1.10541i	−0.993746	+	0.111668i	$0.964381\pi$
$648$	2.39463e11	+	2.39463e11i	1.35812	+	1.35812i
$649$	3.30975e10	−	3.30975e10i	0.186559	−	0.186559i
$650$			3.48671e11i			1.95327i
$651$	−1.30580e11	−	1.30580e11i	−0.727028	−	0.727028i
$652$	−3.96034e10	−	3.96034e10i	−0.219150	−	0.219150i
$653$	−1.35825e10	+	1.35825e10i	−0.0747011	+	0.0747011i	−0.743470	−	0.668769i	$-0.766821\pi$
$653$	−1.35825e10	+	1.35825e10i	−0.0747011	+	0.0747011i	0.668769	+	0.743470i	$0.266821\pi$
$654$		−	6.19789e10i		−	0.338792i
$655$	2.57723e10			0.140019
$656$			1.27411e11i			0.688005i
$657$		−	6.00380e11i		−	3.22229i
$658$	7.40936e10	−	7.40936e10i	0.395255	−	0.395255i
$659$		−	1.98498e10i		−	0.105248i	−0.998614	−	0.0526240i	$-0.983242\pi$
$659$		−	1.98498e10i		−	0.105248i	0.998614	−	0.0526240i	$-0.0167585\pi$
$660$	3.80048e11	−	3.80048e11i	2.00291	−	2.00291i
$661$	2.36836e11	−	2.36836e11i	1.24063	−	1.24063i	0.280892	−	0.959739i	$-0.409370\pi$
$661$	2.36836e11	−	2.36836e11i	1.24063	−	1.24063i	0.959739	−	0.280892i	$-0.0906301\pi$
$662$	−4.25740e10			−0.221673
$663$	−2.51207e11			−1.30010
$664$	−1.33432e11	−	1.33432e11i	−0.686417	−	0.686417i
$665$			9.56767e10i			0.489237i
$666$	4.82464e11	+	6.52681e11i	2.45227	+	3.31745i
$667$	−7.07686e10			−0.357551
$668$	−2.26773e11	+	2.26773e11i	−1.13890	+	1.13890i
$669$			2.21513e11i			1.10585i
$670$			2.48997e11i			1.23565i
$671$	−6.51079e10	−	6.51079e10i	−0.321176	−	0.321176i
$672$	−1.22662e11	−	1.22662e11i	−0.601495	−	0.601495i
$673$	1.07398e10			0.0523522			0.0261761	−	0.999657i	$-0.491667\pi$
$673$	1.07398e10			0.0523522			0.0261761	+	0.999657i	$0.491667\pi$
$674$	−3.01915e11	−	3.01915e11i	−1.46300	−	1.46300i
$675$	1.08019e12			5.20336
$676$	−1.04496e11			−0.500393
$677$		−	1.83284e11i		−	0.872510i	−0.899823	−	0.436255i	$-0.856305\pi$
$677$		−	1.83284e11i		−	0.872510i	0.899823	−	0.436255i	$-0.143695\pi$
$678$	−4.84662e11			−2.29361
$679$	2.52041e10	+	2.52041e10i	0.118575	+	0.118575i
$680$	1.12777e11	−	1.12777e11i	0.527452	−	0.527452i
$681$	−2.16395e11	+	2.16395e11i	−1.00614	+	1.00614i
$682$	−3.63652e11			−1.68093
$683$	−4.11536e10	−	4.11536e10i	−0.189115	−	0.189115i	0.606199	−	0.795313i	$-0.292694\pi$
$683$	−4.11536e10	−	4.11536e10i	−0.189115	−	0.189115i	−0.795313	+	0.606199i	$0.792694\pi$
$684$	−5.17725e11	+	5.17725e11i	−2.36524	+	2.36524i
$685$	1.24853e10	+	1.24853e10i	0.0567072	+	0.0567072i
$686$	1.49879e11	−	1.49879e11i	0.676776	−	0.676776i
$687$			4.03674e11i			1.81219i
$688$	7.31370e10	+	7.31370e10i	0.326425	+	0.326425i
$689$	3.13868e10	+	3.13868e10i	0.139274	+	0.139274i
$690$	−9.33634e11	+	9.33634e11i	−4.11889	+	4.11889i
$691$		−	1.55823e11i		−	0.683472i	−0.939796	−	0.341736i	$-0.888985\pi$
$691$		−	1.55823e11i		−	0.683472i	0.939796	−	0.341736i	$-0.111015\pi$
$692$	−2.39257e11			−1.04337
$693$			1.38168e11i			0.599064i
$694$			3.15767e11i			1.36122i
$695$	2.30300e11	−	2.30300e11i	0.987085	−	0.987085i
$696$			7.13196e10i			0.303929i
$697$	1.87656e11	−	1.87656e11i	0.795119	−	0.795119i
$698$	−3.19324e11	+	3.19324e11i	−1.34527	+	1.34527i
$699$	5.89032e11			2.46735
$700$	1.71930e11			0.716078
$701$	−1.48533e11	−	1.48533e11i	−0.615108	−	0.615108i	0.329165	−	0.944273i	$-0.393233\pi$
$701$	−1.48533e11	−	1.48533e11i	−0.615108	−	0.615108i	−0.944273	+	0.329165i	$0.893233\pi$
$702$		−	9.59625e11i		−	3.95142i
$703$	−1.80507e11	+	1.33432e11i	−0.739049	+	0.546308i
$704$	−2.55073e11			−1.03842
$705$	5.97958e11	−	5.97958e11i	2.42055	−	2.42055i
$706$		−	1.04847e11i		−	0.422026i
$707$			1.03664e11i			0.414907i
$708$	1.80456e11	+	1.80456e11i	0.718189	+	0.718189i
$709$	6.51191e10	+	6.51191e10i	0.257706	+	0.257706i	0.824120	−	0.566415i	$-0.191670\pi$
$709$	6.51191e10	+	6.51191e10i	0.257706	+	0.257706i	−0.566415	+	0.824120i	$0.691670\pi$
$710$	−3.70522e11			−1.45808
$711$	−2.72147e11	−	2.72147e11i	−1.06494	−	1.06494i
$712$	−9.26605e10			−0.360557
$713$	5.13759e11			1.98793
$714$			2.15394e11i			0.828784i
$715$	−2.26083e11			−0.865056
$716$	3.42580e11	+	3.42580e11i	1.30350	+	1.30350i
$717$	−3.76408e10	+	3.76408e10i	−0.142424	+	0.142424i
$718$	2.15789e11	−	2.15789e11i	0.811954	−	0.811954i
$719$	2.59280e10			0.0970182			0.0485091	−	0.998823i	$-0.484553\pi$
$719$	2.59280e10			0.0970182			0.0485091	+	0.998823i	$0.484553\pi$
$720$	−4.30157e11	−	4.30157e11i	−1.60065	−	1.60065i
$721$	−6.37518e10	+	6.37518e10i	−0.235913	+	0.235913i
$722$	4.57938e10	+	4.57938e10i	0.168523	+	0.168523i
$723$	−5.50621e11	+	5.50621e11i	−2.01511	+	2.01511i
$724$		−	5.15205e11i		−	1.87510i
$725$	9.14414e10	+	9.14414e10i	0.330972	+	0.330972i
$726$	−3.14888e11	−	3.14888e11i	−1.13347	−	1.13347i
$727$	−2.03814e11	+	2.03814e11i	−0.729620	+	0.729620i	−0.970544	−	0.240924i	$-0.922550\pi$
$727$	−2.03814e11	+	2.03814e11i	−0.729620	+	0.729620i	0.240924	+	0.970544i	$0.422550\pi$
$728$		−	3.98859e10i		−	0.142002i
$729$	−9.30503e11			−3.29464
$730$		−	8.42347e11i		−	2.96619i
$731$		−	2.15439e11i		−	0.754491i
$732$	3.54986e11	−	3.54986e11i	1.23642	−	1.23642i
$733$			1.54335e11i			0.534623i	0.963610	+	0.267312i	$0.0861353\pi$
$733$			1.54335e11i			0.534623i	−0.963610	+	0.267312i	$0.913865\pi$
$734$	−4.28564e11	+	4.28564e11i	−1.47649	+	1.47649i
$735$	5.69981e11	−	5.69981e11i	1.95304	−	1.95304i
$736$	4.82606e11			1.64468
$737$	−9.94461e10			−0.337068
$738$	1.14124e12	+	1.14124e12i	3.84728	+	3.84728i
$739$		−	3.36813e11i		−	1.12931i	−0.825328	−	0.564653i	$-0.809010\pi$
$739$		−	3.36813e11i		−	1.12931i	0.825328	−	0.564653i	$-0.190990\pi$
$740$	3.89282e11	+	5.26623e11i	1.29819	+	1.75620i
$741$	4.22513e11			1.40142
$742$	2.69122e10	−	2.69122e10i	0.0887838	−	0.0887838i
$743$			9.30044e10i			0.305175i	0.988290	+	0.152587i	$0.0487605\pi$
$743$			9.30044e10i			0.305175i	−0.988290	+	0.152587i	$0.951239\pi$
$744$		−	5.17758e11i		−	1.68980i
$745$	2.11537e11	+	2.11537e11i	0.686691	+	0.686691i
$746$	−5.42080e11	−	5.42080e11i	−1.75028	−	1.75028i
$747$	1.49919e12			4.81474
$748$	1.72484e11	+	1.72484e11i	0.550988	+	0.550988i
$749$	8.56402e10			0.272114
$750$	9.08334e11			2.87078
$751$		−	4.41342e11i		−	1.38744i	−0.720243	−	0.693722i	$-0.755970\pi$
$751$		−	4.41342e11i		−	1.38744i	0.720243	−	0.693722i	$-0.244030\pi$
$752$	−1.84258e11			−0.576175
$753$	−2.68213e11	−	2.68213e11i	−0.834256	−	0.834256i
$754$	8.12355e10	−	8.12355e10i	0.251339	−	0.251339i
$755$	−6.50107e11	+	6.50107e11i	−2.00077	+	2.00077i
$756$	−4.73193e11			−1.44861
$757$	8.61513e10	+	8.61513e10i	0.262348	+	0.262348i	0.826007	−	0.563659i	$-0.190607\pi$
$757$	8.61513e10	+	8.61513e10i	0.262348	+	0.262348i	−0.563659	+	0.826007i	$0.690607\pi$
$758$	5.43078e11	−	5.43078e11i	1.64507	−	1.64507i
$759$	−3.72881e11	−	3.72881e11i	−1.12358	−	1.12358i
$760$	−1.89683e11	+	1.89683e11i	−0.568556	+	0.568556i
$761$			4.76613e11i			1.42111i	0.703642	+	0.710555i	$0.251556\pi$
$761$			4.76613e11i			1.42111i	−0.703642	+	0.710555i	$0.748444\pi$
$762$	2.10278e11	+	2.10278e11i	0.623697	+	0.623697i
$763$	9.09036e9	+	9.09036e9i	0.0268215	+	0.0268215i
$764$	1.20677e11	−	1.20677e11i	0.354203	−	0.354203i
$765$			1.26711e12i			3.69971i
$766$	6.10191e11			1.77236
$767$		−	1.07350e11i		−	0.310185i
$768$		−	1.45878e10i		−	0.0419319i
$769$	−3.68316e11	+	3.68316e11i	−1.05321	+	1.05321i	−0.0547074	+	0.998502i	$0.517423\pi$
$769$	−3.68316e11	+	3.68316e11i	−1.05321	+	1.05321i	−0.998502	+	0.0547074i	$0.982577\pi$
$770$			1.93852e11i			0.551453i
$771$	−2.14780e11	+	2.14780e11i	−0.607823	+	0.607823i
$772$	−2.12846e11	+	2.12846e11i	−0.599235	+	0.599235i
$773$	−6.33210e10			−0.177349			−0.0886747	−	0.996061i	$-0.528263\pi$
$773$	−6.33210e10			−0.177349			−0.0886747	+	0.996061i	$0.528263\pi$
$774$	1.31020e12			3.65069
$775$	−6.63836e11	−	6.63836e11i	−1.84015	−	1.84015i
$776$			9.99363e10i			0.275598i
$777$	−2.28402e11	−	3.42492e10i	−0.626636	−	0.0939649i
$778$	5.68699e11			1.55226
$779$	−3.15626e11	+	3.15626e11i	−0.857082	+	0.857082i
$780$		−	1.23267e12i		−	3.33017i
$781$		−	1.47982e11i		−	0.397744i
$782$	−4.23729e11	−	4.23729e11i	−1.13308	−	1.13308i
$783$	−2.51668e11	−	2.51668e11i	−0.669548	−	0.669548i
$784$	−1.75637e11			−0.464891
$785$	3.88519e11	+	3.88519e11i	1.02314	+	1.02314i
$786$	−9.75865e10			−0.255682
$787$	−1.31520e11			−0.342841			−0.171421	−	0.985198i	$-0.554836\pi$
$787$	−1.31520e11			−0.342841			−0.171421	+	0.985198i	$0.554836\pi$
$788$		−	1.41732e11i		−	0.367589i
$789$	−6.47386e10			−0.167053
$790$	−3.81829e11	−	3.81829e11i	−0.980303	−	0.980303i
$791$	7.10847e10	−	7.10847e10i	0.181581	−	0.181581i
$792$	−2.73923e11	+	2.73923e11i	−0.696189	+	0.696189i
$793$	−2.11174e11			−0.534009
$794$	−5.53383e11	−	5.53383e11i	−1.39233	−	1.39233i
$795$	2.17190e11	−	2.17190e11i	0.543714	−	0.543714i
$796$	1.51821e11	+	1.51821e11i	0.378163	+	0.378163i
$797$	3.34974e11	−	3.34974e11i	0.830192	−	0.830192i	−0.157351	−	0.987543i	$-0.550295\pi$
$797$	3.34974e11	−	3.34974e11i	0.830192	−	0.830192i	0.987543	+	0.157351i	$0.0502954\pi$
$798$		−	3.62279e11i		−	0.893370i
$799$	2.71383e11	+	2.71383e11i	0.665878	+	0.665878i
$800$	−6.23583e11	−	6.23583e11i	−1.52242	−	1.52242i
$801$	5.20546e11	−	5.20546e11i	1.26453	−	1.26453i
$802$			2.75944e11i			0.666996i
$803$	3.36422e11			0.809138
$804$		−	5.42207e11i		−	1.29760i
$805$		−	2.73870e11i		−	0.652169i
$806$	−5.89744e11	+	5.89744e11i	−1.39741	+	1.39741i
$807$			1.27748e12i			3.01203i
$808$	−2.05518e11	+	2.05518e11i	−0.482175	+	0.482175i
$809$	−3.02084e11	+	3.02084e11i	−0.705234	+	0.705234i	−0.965529	−	0.260295i	$-0.916180\pi$
$809$	−3.02084e11	+	3.02084e11i	−0.705234	+	0.705234i	0.260295	+	0.965529i	$0.416180\pi$
$810$	−3.77483e12			−8.76915
$811$	−3.27753e11			−0.757640			−0.378820	−	0.925470i	$-0.623670\pi$
$811$	−3.27753e11			−0.757640			−0.378820	+	0.925470i	$0.623670\pi$
$812$	−4.00574e10	−	4.00574e10i	−0.0921421	−	0.0921421i
$813$		−	3.47308e11i		−	0.794974i
$814$	−3.65729e11	+	2.70348e11i	−0.833033	+	0.615781i
$815$	1.63025e11			0.369509
$816$	2.67823e11	−	2.67823e11i	0.604071	−	0.604071i
$817$			3.62354e11i			0.813288i
$818$		−	9.29264e11i		−	2.07552i
$819$	2.24070e11	+	2.24070e11i	0.498022	+	0.498022i
$820$	9.20826e11	+	9.20826e11i	2.03668	+	2.03668i
$821$	1.85599e11			0.408510			0.204255	−	0.978918i	$-0.434523\pi$
$821$	1.85599e11			0.408510			0.204255	+	0.978918i	$0.434523\pi$
$822$	−4.72756e10	−	4.72756e10i	−0.103550	−	0.103550i
$823$	−7.07091e11			−1.54126			−0.770630	−	0.637283i	$-0.780058\pi$
$823$	−7.07091e11			−1.54126			−0.770630	+	0.637283i	$0.780058\pi$
$824$	−2.52781e11			−0.548321
$825$			9.63612e11i			2.08011i
$826$	−9.20461e10			−0.197736
$827$	4.39395e11	+	4.39395e11i	0.939363	+	0.939363i	0.998264	−	0.0589010i	$-0.0187596\pi$
$827$	4.39395e11	+	4.39395e11i	0.939363	+	0.939363i	−0.0589010	+	0.998264i	$0.518760\pi$
$828$	1.48196e12	−	1.48196e12i	3.15294	−	3.15294i
$829$	−1.16926e11	+	1.16926e11i	−0.247568	+	0.247568i	−0.819972	−	0.572404i	$-0.806011\pi$
$829$	−1.16926e11	+	1.16926e11i	−0.247568	+	0.247568i	0.572404	+	0.819972i	$0.306011\pi$
$830$	2.10339e12			4.43208
$831$	4.24505e11	+	4.24505e11i	0.890183	+	0.890183i
$832$	−4.13659e11	+	4.13659e11i	−0.863275	+	0.863275i
$833$	2.58685e11	+	2.58685e11i	0.537269	+	0.537269i
$834$	−8.72028e11	+	8.72028e11i	−1.80246	+	1.80246i
$835$		−	9.33501e11i		−	1.92030i
$836$	−2.90107e11	−	2.90107e11i	−0.593926	−	0.593926i
$837$	1.82703e12	+	1.82703e12i	3.72259	+	3.72259i
$838$	9.14465e10	−	9.14465e10i	0.185435	−	0.185435i
$839$		−	3.44610e11i		−	0.695473i	−0.937592	−	0.347737i	$-0.886950\pi$
$839$		−	3.44610e11i		−	0.695473i	0.937592	−	0.347737i	$-0.113050\pi$
$840$	−2.76002e11			−0.554363
$841$			4.57637e11i			0.914824i
$842$		−	1.13759e12i		−	2.26327i
$843$	2.79661e11	−	2.79661e11i	0.553761	−	0.553761i
$844$		−	2.35076e11i		−	0.463274i
$845$	2.15076e11	−	2.15076e11i	0.421856	−	0.421856i
$846$	−1.65043e12	+	1.65043e12i	−3.22193	+	3.22193i
$847$	9.23683e10			0.179469
$848$	−6.69258e10			−0.129423
$849$	−1.09374e12	−	1.09374e12i	−2.10515	−	2.10515i
$850$			1.09501e12i			2.09770i
$851$	5.16693e11	−	3.81941e11i	0.985177	−	0.728246i
$852$	8.06835e11			1.53118
$853$	−6.89872e11	+	6.89872e11i	−1.30308	+	1.30308i	−0.376782	+	0.926302i	$0.622970\pi$
$853$	−6.89872e11	+	6.89872e11i	−1.30308	+	1.30308i	−0.926302	+	0.376782i	$0.877030\pi$
$854$			1.81069e11i			0.340418i
$855$		−	2.13119e12i		−	3.98803i
$856$	1.69785e11	+	1.69785e11i	0.316231	+	0.316231i
$857$	2.79979e11	+	2.79979e11i	0.519041	+	0.519041i	0.917281	−	0.398240i	$-0.130379\pi$
$857$	2.79979e11	+	2.79979e11i	0.519041	+	0.519041i	−0.398240	+	0.917281i	$0.630379\pi$
$858$	8.56062e11			1.57963
$859$	−5.50685e11	−	5.50685e11i	−1.01142	−	1.01142i	−0.999934	−	0.0114837i	$-0.996345\pi$
$859$	−5.50685e11	−	5.50685e11i	−1.01142	−	1.01142i	−0.0114837	−	0.999934i	$-0.503655\pi$
$860$	1.05715e12			1.93261
$861$	−4.59258e11			−0.835687
$862$		−	4.65229e11i		−	0.842631i
$863$	3.38013e11			0.609384			0.304692	−	0.952451i	$-0.401447\pi$
$863$	3.38013e11			0.609384			0.304692	+	0.952451i	$0.401447\pi$
$864$	1.71625e12	+	1.71625e12i	3.07982	+	3.07982i
$865$	4.92445e11	−	4.92445e11i	0.879616	−	0.879616i
$866$	−1.44914e11	+	1.44914e11i	−0.257655	+	0.257655i
$867$	2.96353e11			0.524485
$868$	2.90804e11	+	2.90804e11i	0.512297	+	0.512297i
$869$	1.52497e11	−	1.52497e11i	0.267414	−	0.267414i
$870$	−5.62132e11	−	5.62132e11i	−0.981209	−	0.981209i
$871$	−1.61274e11	+	1.61274e11i	−0.280216	+	0.280216i
$872$			3.60439e10i			0.0623399i
$873$	−5.61421e11	−	5.61421e11i	−0.966566	−	0.966566i
$874$	7.12683e11	+	7.12683e11i	1.22138	+	1.22138i
$875$	−1.33224e11	+	1.33224e11i	−0.227274	+	0.227274i
$876$			1.83426e12i			3.11491i
$877$	−1.93988e11			−0.327927			−0.163963	−	0.986466i	$-0.552428\pi$
$877$	−1.93988e11			−0.327927			−0.163963	+	0.986466i	$0.552428\pi$
$878$			8.45734e11i			1.42317i
$879$		−	7.15830e11i		−	1.19910i
$880$	2.41038e11	−	2.41038e11i	0.401934	−	0.401934i
$881$		−	5.62372e10i		−	0.0933513i	−0.998910	−	0.0466756i	$-0.985137\pi$
$881$		−	5.62372e10i		−	0.0933513i	0.998910	−	0.0466756i	$-0.0148627\pi$
$882$	−1.57321e12	+	1.57321e12i	−2.59964	+	2.59964i
$883$	−5.16279e9	+	5.16279e9i	−0.00849262	+	0.00849262i	−0.711340	−	0.702848i	$-0.751912\pi$
$883$	−5.16279e9	+	5.16279e9i	−0.00849262	+	0.00849262i	0.702848	+	0.711340i	$0.251912\pi$
$884$	5.59444e11			0.916109
$885$	−7.42840e11			−1.21094
$886$	2.33970e11	+	2.33970e11i	0.379686	+	0.379686i
$887$			8.88996e11i			1.43617i	0.695956	+	0.718084i	$0.254981\pi$
$887$			8.88996e11i			1.43617i	−0.695956	+	0.718084i	$0.745019\pi$
$888$	−3.84915e11	−	5.20715e11i	−0.619031	−	0.837430i
$889$	−6.16824e10			−0.0987538
$890$	7.30339e11	−	7.30339e11i	1.16403	−	1.16403i
$891$		−	1.50762e12i		−	2.39211i
$892$		−	4.93315e11i		−	0.779229i
$893$	−4.56447e11	−	4.56447e11i	−0.717769	−	0.717769i
$894$	−8.00983e11	−	8.00983e11i	−1.25393	−	1.25393i
$895$	−1.41022e12			−2.19783
$896$	1.52851e11	+	1.52851e11i	0.237156	+	0.237156i
$897$	−1.20942e12			−1.86813
$898$	1.23150e12			1.89378
$899$			3.09329e11i			0.473568i
$900$	−3.82974e12			−5.83712
$901$	9.85713e10	+	9.85713e10i	0.149572	+	0.149572i
$902$	−6.39495e11	+	6.39495e11i	−0.966076	+	0.966076i
$903$	−2.63625e11	+	2.63625e11i	−0.396493	+	0.396493i
$904$	2.81856e11			0.422040
$905$	1.06041e12	+	1.06041e12i	1.58081	+	1.58081i
$906$	2.46162e12	−	2.46162e12i	3.65350	−	3.65350i
$907$	6.99339e11	+	6.99339e11i	1.03338	+	1.03338i	0.999423	+	0.0339530i	$0.0108097\pi$
$907$	6.99339e11	+	6.99339e11i	1.03338	+	1.03338i	0.0339530	+	0.999423i	$0.489190\pi$
$908$	4.81917e11	−	4.81917e11i	0.708971	−	0.708971i
$909$		−	2.30911e12i		−	3.38212i
$910$	3.14375e11	+	3.14375e11i	0.458441	+	0.458441i
$911$	−2.00860e10	−	2.00860e10i	−0.0291622	−	0.0291622i	0.692375	−	0.721538i	$-0.256564\pi$
$911$	−2.00860e10	−	2.00860e10i	−0.0291622	−	0.0291622i	−0.721538	+	0.692375i	$0.756564\pi$
$912$	−4.50461e11	+	4.50461e11i	−0.651146	+	0.651146i
$913$			8.40067e11i			1.20901i
$914$	−9.10406e11			−1.30452
$915$			1.46128e12i			2.08473i
$916$		−	8.98993e11i		−	1.27695i
$917$	1.43129e10	−	1.43129e10i	0.0202418	−	0.0202418i
$918$		−	3.01374e12i		−	4.24360i
$919$	−1.57102e11	+	1.57102e11i	−0.220252	+	0.220252i	−0.808604	−	0.588353i	$-0.799777\pi$
$919$	−1.57102e11	+	1.57102e11i	−0.220252	+	0.220252i	0.588353	+	0.808604i	$0.299777\pi$
$920$	5.42957e11	−	5.42957e11i	0.757904	−	0.757904i
$921$	−1.09720e12			−1.52492
$922$	−1.61512e12			−2.23502
$923$	−2.39986e11	−	2.39986e11i	−0.330658	−	0.330658i
$924$		−	4.22126e11i		−	0.579101i
$925$	−1.16114e12	−	1.74115e11i	−1.58605	−	0.237831i
$926$	7.44436e11			1.01247
$927$	1.42007e12	−	1.42007e12i	1.92305	−	1.92305i
$928$			2.90572e11i			0.391798i
$929$			1.19348e12i			1.60233i	0.598444	+	0.801165i	$0.295786\pi$
$929$			1.19348e12i			1.60233i	−0.598444	+	0.801165i	$0.704214\pi$
$930$	4.08091e12	+	4.08091e12i	5.45538	+	5.45538i
$931$	−4.35091e11	−	4.35091e11i	−0.579137	−	0.579137i
$932$	−1.31179e12			−1.73860
$933$	−8.71916e11	−	8.71916e11i	−1.15066	−	1.15066i
$934$	−3.10745e11			−0.408335
$935$	−7.10023e11			−0.929022
$936$			8.88455e11i			1.15753i
$937$	−5.51076e11			−0.714913			−0.357457	−	0.933930i	$-0.616356\pi$
$937$	−5.51076e11			−0.714913			−0.357457	+	0.933930i	$0.616356\pi$
$938$	1.38283e11	+	1.38283e11i	0.178631	+	0.178631i
$939$	1.35620e10	−	1.35620e10i	0.0174446	−	0.0174446i
$940$	−1.33167e12	+	1.33167e12i	−1.70563	+	1.70563i
$941$	7.14953e11			0.911841			0.455921	−	0.890020i	$-0.349310\pi$
$941$	7.14953e11			0.911841			0.455921	+	0.890020i	$0.349310\pi$
$942$	−1.47112e12	−	1.47112e12i	−1.86829	−	1.86829i
$943$	9.03462e11	−	9.03462e11i	1.14252	−	1.14252i
$944$	1.14451e11	+	1.14451e11i	0.144123	+	0.144123i
$945$	9.73938e11	−	9.73938e11i	1.22125	−	1.22125i
$946$			7.34172e11i			0.916712i
$947$	−3.00582e10	−	3.00582e10i	−0.0373735	−	0.0373735i	0.688173	−	0.725547i	$-0.258413\pi$
$947$	−3.00582e10	−	3.00582e10i	−0.0373735	−	0.0373735i	−0.725547	+	0.688173i	$0.758413\pi$
$948$	8.31456e11	+	8.31456e11i	1.02945	+	1.02945i
$949$	5.45585e11	−	5.45585e11i	0.672663	−	0.672663i
$950$		−	1.84174e12i		−	2.26117i
$951$	1.42053e12			1.73672
$952$		−	1.25263e11i		−	0.152502i
$953$			5.05527e11i			0.612876i	0.951891	+	0.306438i	$0.0991373\pi$
$953$			5.05527e11i			0.612876i	−0.951891	+	0.306438i	$0.900863\pi$
$954$	−5.99468e11	+	5.99468e11i	−0.723723	+	0.723723i
$955$			4.96762e11i			0.597221i
$956$	8.38271e10	−	8.38271e10i	0.100358	−	0.100358i
$957$	2.24508e11	−	2.24508e11i	0.267661	−	0.267661i
$958$	3.41458e11			0.405392
$959$	1.38677e10			0.0163957
$960$	2.86243e12	+	2.86243e12i	3.37016	+	3.37016i
$961$		−	1.39274e12i		−	1.63297i
$962$	−1.54681e11	+	1.03154e12i	−0.180608	+	1.20445i
$963$	−1.90763e12			−2.21814
$964$	1.22625e12	−	1.22625e12i	1.41994	−	1.41994i
$965$		−	8.76172e11i		−	1.01037i
$966$			1.03700e12i			1.19089i
$967$	−9.36813e11	−	9.36813e11i	−1.07139	−	1.07139i	−0.997248	−	0.0741403i	$-0.976379\pi$
$967$	−9.36813e11	−	9.36813e11i	−1.07139	−	1.07139i	−0.0741403	−	0.997248i	$-0.523621\pi$
$968$	1.83124e11	+	1.83124e11i	0.208566	+	0.208566i
$969$	1.32692e12			1.50504
$970$	−7.87686e11	−	7.87686e11i	−0.889747	−	0.889747i
$971$	−1.33003e12			−1.49618			−0.748089	−	0.663599i	$-0.769028\pi$
$971$	−1.33003e12			−1.49618			−0.748089	+	0.663599i	$0.769028\pi$
$972$	4.30038e12			4.81772
$973$		−	2.55798e11i		−	0.285395i
$974$	2.15421e12			2.39361
$975$	1.56272e12	+	1.56272e12i	1.72926	+	1.72926i
$976$	2.25143e11	−	2.25143e11i	0.248119	−	0.248119i
$977$	−1.03667e12	+	1.03667e12i	−1.13779	+	1.13779i	−0.148950	+	0.988845i	$0.547589\pi$
$977$	−1.03667e12	+	1.03667e12i	−1.13779	+	1.13779i	−0.988845	+	0.148950i	$0.952411\pi$
$978$	−6.17294e11			−0.674741
$979$	2.91688e11	+	2.91688e11i	0.317532	+	0.317532i
$980$	−1.26936e12	+	1.26936e12i	−1.37620	+	1.37620i
$981$	−2.02487e11	−	2.02487e11i	−0.218636	−	0.218636i
$982$	−1.02614e12	+	1.02614e12i	−1.10347	+	1.10347i
$983$			1.18543e12i			1.26958i	0.772683	+	0.634792i	$0.218914\pi$
$983$			1.18543e12i			1.26958i	−0.772683	+	0.634792i	$0.781086\pi$
$984$	−9.10496e11	−	9.10496e11i	−0.971175	−	0.971175i
$985$	2.91717e11	+	2.91717e11i	0.309896	+	0.309896i
$986$	2.55123e11	−	2.55123e11i	0.269924	−	0.269924i
$987$		−	6.64163e11i		−	0.699852i
$988$	−9.40947e11			−0.987501
$989$		−	1.03722e12i		−	1.08414i
$990$		−	4.31805e12i		−	4.49518i
$991$	1.13475e12	−	1.13475e12i	1.17653	−	1.17653i	0.195911	−	0.980622i	$-0.437234\pi$
$991$	1.13475e12	−	1.13475e12i	1.17653	−	1.17653i	0.980622	−	0.195911i	$-0.0627663\pi$
$992$		−	2.10947e12i		−	2.17834i
$993$	−1.90813e11	+	1.90813e11i	−0.196251	+	0.196251i
$994$	−2.05773e11	+	2.05773e11i	−0.210786	+	0.210786i
$995$	−6.24964e11			−0.637621
$996$	−4.58027e12			−4.65429
$997$	9.52638e10	+	9.52638e10i	0.0964156	+	0.0964156i	0.753669	−	0.657254i	$-0.228282\pi$
$997$	9.52638e10	+	9.52638e10i	0.0964156	+	0.0964156i	−0.657254	+	0.753669i	$0.728282\pi$
$998$		−	9.59683e11i		−	0.967399i
$999$	3.19573e12	+	4.79205e11i	3.20855	+	0.481126i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.9.d.a.6.4	✓	50
37.31	odd	4	inner	37.9.d.a.31.4	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.9.d.a.6.4	✓	50	1.1	even	1	trivial
37.9.d.a.31.4	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)

\(f(q)\)	\(=\)	\(q+(-17.3562 + 17.3562i) q^{2} +155.578i q^{3} -346.477i q^{4} +(713.128 + 713.128i) q^{5} +(-2700.25 - 2700.25i) q^{6} +792.085 q^{7} +(1570.34 + 1570.34i) q^{8} -17643.6 q^{9} +O(q^{10})\)	\(q+(-17.3562 + 17.3562i) q^{2} +155.578i q^{3} -346.477i q^{4} +(713.128 + 713.128i) q^{5} +(-2700.25 - 2700.25i) q^{6} +792.085 q^{7} +(1570.34 + 1570.34i) q^{8} -17643.6 q^{9} -24754.4 q^{10} -9886.59i q^{11} +53904.3 q^{12} +(-16033.3 - 16033.3i) q^{13} +(-13747.6 + 13747.6i) q^{14} +(-110947. + 110947. i) q^{15} +34187.8 q^{16} +(-50353.3 - 50353.3i) q^{17} +(306227. - 306227. i) q^{18} +(84690.9 + 84690.9i) q^{19} +(247083. - 247083. i) q^{20} +123231. i q^{21} +(171594. + 171594. i) q^{22} +(-242423. - 242423. i) q^{23} +(-244311. + 244311. i) q^{24} +626479. i q^{25} +556557. q^{26} -1.72422e6i q^{27} -274439. i q^{28} +(145961. - 145961. i) q^{29} -3.85125e6i q^{30} +(-1.05963e6 + 1.05963e6i) q^{31} +(-995378. + 995378. i) q^{32} +1.53814e6 q^{33} +1.74789e6 q^{34} +(564858. + 564858. i) q^{35} +6.11311e6i q^{36} +(-277926. + 1.85344e6i) q^{37} -2.93983e6 q^{38} +(2.49444e6 - 2.49444e6i) q^{39} +2.23971e6i q^{40} +3.72680e6i q^{41} +(-2.13883e6 - 2.13883e6i) q^{42} +(2.13927e6 + 2.13927e6i) q^{43} -3.42548e6 q^{44} +(-1.25822e7 - 1.25822e7i) q^{45} +8.41511e6 q^{46} -5.38957e6 q^{47} +5.31889e6i q^{48} -5.13740e6 q^{49} +(-1.08733e7 - 1.08733e7i) q^{50} +(7.83388e6 - 7.83388e6i) q^{51} +(-5.55518e6 + 5.55518e6i) q^{52} -1.95759e6 q^{53} +(2.99259e7 + 2.99259e7i) q^{54} +(7.05041e6 - 7.05041e6i) q^{55} +(1.24384e6 + 1.24384e6i) q^{56} +(-1.31761e7 + 1.31761e7i) q^{57} +5.06666e6i q^{58} +(3.34771e6 + 3.34771e6i) q^{59} +(3.84407e7 + 3.84407e7i) q^{60} +(6.58547e6 - 6.58547e6i) q^{61} -3.67824e7i q^{62} -1.39753e7 q^{63} -2.57999e7i q^{64} -2.28677e7i q^{65} +(-2.66963e7 + 2.66963e7i) q^{66} -1.00587e7i q^{67} +(-1.74463e7 + 1.74463e7i) q^{68} +(3.77158e7 - 3.77158e7i) q^{69} -1.96076e7 q^{70} +1.49679e7 q^{71} +(-2.77065e7 - 2.77065e7i) q^{72} +3.40281e7i q^{73} +(-2.73450e7 - 3.69924e7i) q^{74} -9.74666e7 q^{75} +(2.93434e7 - 2.93434e7i) q^{76} -7.83102e6i q^{77} +8.65882e7i q^{78} +(1.54247e7 + 1.54247e7i) q^{79} +(2.43803e7 + 2.43803e7i) q^{80} +1.52491e8 q^{81} +(-6.46831e7 - 6.46831e7i) q^{82} -8.49703e7 q^{83} +4.26968e7 q^{84} -7.18167e7i q^{85} -7.42593e7 q^{86} +(2.27083e7 + 2.27083e7i) q^{87} +(1.55253e7 - 1.55253e7i) q^{88} +(-2.95034e7 + 2.95034e7i) q^{89} +4.36758e8 q^{90} +(-1.26998e7 - 1.26998e7i) q^{91} +(-8.39941e7 + 8.39941e7i) q^{92} +(-1.64856e8 - 1.64856e8i) q^{93} +(9.35425e7 - 9.35425e7i) q^{94} +1.20791e8i q^{95} +(-1.54859e8 - 1.54859e8i) q^{96} +(3.18200e7 + 3.18200e7i) q^{97} +(8.91659e7 - 8.91659e7i) q^{98} +1.74435e8i 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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