LMFDB - Embedded newform 37.9.d.a.6.20

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			6.20
Character	$\chi$	$=$	37.6
Dual form			37.9.d.a.31.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(11.9313 - 11.9313i) q^{2} -129.954i q^{3} -28.7121i q^{4} +(-176.820 - 176.820i) q^{5} +(-1550.52 - 1550.52i) q^{6} -2761.63 q^{7} +(2711.84 + 2711.84i) q^{8} -10327.0 q^{9} +O(q^{10})$	\(q+(11.9313 - 11.9313i) q^{2} -129.954i q^{3} -28.7121i q^{4} +(-176.820 - 176.820i) q^{5} +(-1550.52 - 1550.52i) q^{6} -2761.63 q^{7} +(2711.84 + 2711.84i) q^{8} -10327.0 q^{9} -4219.39 q^{10} -5594.40i q^{11} -3731.25 q^{12} +(-20737.4 - 20737.4i) q^{13} +(-32949.8 + 32949.8i) q^{14} +(-22978.5 + 22978.5i) q^{15} +72061.9 q^{16} +(78871.9 + 78871.9i) q^{17} +(-123215. + 123215. i) q^{18} +(-31294.0 - 31294.0i) q^{19} +(-5076.88 + 5076.88i) q^{20} +358884. i q^{21} +(-66748.5 - 66748.5i) q^{22} +(-172818. - 172818. i) q^{23} +(352414. - 352414. i) q^{24} -328094. i q^{25} -494848. q^{26} +489407. i q^{27} +79292.1i q^{28} +(-576226. + 576226. i) q^{29} +548327. i q^{30} +(-306624. + 306624. i) q^{31} +(165561. - 165561. i) q^{32} -727014. q^{33} +1.88209e6 q^{34} +(488312. + 488312. i) q^{35} +296510. i q^{36} +(-144828. - 1.86856e6i) q^{37} -746758. q^{38} +(-2.69490e6 + 2.69490e6i) q^{39} -959017. i q^{40} -4.57629e6i q^{41} +(4.28195e6 + 4.28195e6i) q^{42} +(-1.73999e6 - 1.73999e6i) q^{43} -160627. q^{44} +(1.82602e6 + 1.82602e6i) q^{45} -4.12389e6 q^{46} +1.08422e6 q^{47} -9.36472e6i q^{48} +1.86178e6 q^{49} +(-3.91459e6 - 3.91459e6i) q^{50} +(1.02497e7 - 1.02497e7i) q^{51} +(-595414. + 595414. i) q^{52} +1.34938e7 q^{53} +(5.83927e6 + 5.83927e6i) q^{54} +(-989203. + 989203. i) q^{55} +(-7.48909e6 - 7.48909e6i) q^{56} +(-4.06678e6 + 4.06678e6i) q^{57} +1.37503e7i q^{58} +(-4.21692e6 - 4.21692e6i) q^{59} +(659761. + 659761. i) q^{60} +(9.22788e6 - 9.22788e6i) q^{61} +7.31685e6i q^{62} +2.85193e7 q^{63} +1.44971e7i q^{64} +7.33357e6i q^{65} +(-8.67422e6 + 8.67422e6i) q^{66} -1.69836e7i q^{67} +(2.26458e6 - 2.26458e6i) q^{68} +(-2.24584e7 + 2.24584e7i) q^{69} +1.16524e7 q^{70} -2.90292e7 q^{71} +(-2.80052e7 - 2.80052e7i) q^{72} +2.25693e7i q^{73} +(-2.40223e7 - 2.05663e7i) q^{74} -4.26371e7 q^{75} +(-898518. + 898518. i) q^{76} +1.54496e7i q^{77} +6.43074e7i q^{78} +(-1.42358e7 - 1.42358e7i) q^{79} +(-1.27420e7 - 1.27420e7i) q^{80} -4.15512e6 q^{81} +(-5.46011e7 - 5.46011e7i) q^{82} +4.36261e7 q^{83} +1.03043e7 q^{84} -2.78923e7i q^{85} -4.15208e7 q^{86} +(7.48829e7 + 7.48829e7i) q^{87} +(1.51711e7 - 1.51711e7i) q^{88} +(-5.77020e6 + 5.77020e6i) q^{89} +4.35737e7 q^{90} +(5.72688e7 + 5.72688e7i) q^{91} +(-4.96197e6 + 4.96197e6i) q^{92} +(3.98470e7 + 3.98470e7i) q^{93} +(1.29362e7 - 1.29362e7i) q^{94} +1.10668e7i q^{95} +(-2.15153e7 - 2.15153e7i) q^{96} +(5.99578e7 + 5.99578e7i) q^{97} +(2.22134e7 - 2.22134e7i) q^{98} +5.77734e7i 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 $

$2$	11.9313	−	11.9313i	0.745707	−	0.745707i	−0.227963	−	0.973670i	$-0.573207\pi$
$2$	11.9313	−	11.9313i	0.745707	−	0.745707i	0.973670	+	0.227963i	$0.0732066\pi$
$3$		−	129.954i		−	1.60437i	−0.597076	−	0.802184i	$-0.703671\pi$
$3$		−	129.954i		−	1.60437i	0.597076	−	0.802184i	$-0.296329\pi$
$4$		−	28.7121i		−	0.112157i
$5$	−176.820	−	176.820i	−0.282912	−	0.282912i	0.551357	−	0.834269i	$-0.314110\pi$
$5$	−176.820	−	176.820i	−0.282912	−	0.282912i	−0.834269	+	0.551357i	$0.814110\pi$
$6$	−1550.52	−	1550.52i	−1.19639	−	1.19639i
$7$	−2761.63			−1.15020			−0.575099	−	0.818084i	$-0.695037\pi$
$7$	−2761.63			−1.15020			−0.575099	+	0.818084i	$0.695037\pi$
$8$	2711.84	+	2711.84i	0.662071	+	0.662071i
$9$	−10327.0			−1.57400
$10$	−4219.39			−0.421939
$11$		−	5594.40i		−	0.382105i	−0.981580	−	0.191052i	$-0.938810\pi$
$11$		−	5594.40i		−	0.382105i	0.981580	−	0.191052i	$-0.0611901\pi$
$12$	−3731.25			−0.179941
$13$	−20737.4	−	20737.4i	−0.726073	−	0.726073i	0.243762	−	0.969835i	$-0.421618\pi$
$13$	−20737.4	−	20737.4i	−0.726073	−	0.726073i	−0.969835	+	0.243762i	$0.921618\pi$
$14$	−32949.8	+	32949.8i	−0.857710	+	0.857710i
$15$	−22978.5	+	22978.5i	−0.453896	+	0.453896i
$16$	72061.9			1.09958
$17$	78871.9	+	78871.9i	0.944336	+	0.944336i	0.998530	−	0.0541945i	$-0.0172591\pi$
$17$	78871.9	+	78871.9i	0.944336	+	0.944336i	−0.0541945	+	0.998530i	$0.517259\pi$
$18$	−123215.	+	123215.i	−1.17374	+	1.17374i
$19$	−31294.0	−	31294.0i	−0.240130	−	0.240130i	0.576774	−	0.816904i	$-0.304311\pi$
$19$	−31294.0	−	31294.0i	−0.240130	−	0.240130i	−0.816904	+	0.576774i	$0.804311\pi$
$20$	−5076.88	+	5076.88i	−0.0317305	+	0.0317305i
$21$			358884.i			1.84534i
$22$	−66748.5	−	66748.5i	−0.284938	−	0.284938i
$23$	−172818.	−	172818.i	−0.617558	−	0.617558i	0.327346	−	0.944904i	$-0.393846\pi$
$23$	−172818.	−	172818.i	−0.617558	−	0.617558i	−0.944904	+	0.327346i	$0.893846\pi$
$24$	352414.	−	352414.i	1.06221	−	1.06221i
$25$		−	328094.i		−	0.839921i
$26$	−494848.			−1.08287
$27$			489407.i			0.920906i
$28$			79292.1i			0.129002i
$29$	−576226.	+	576226.i	−0.814707	+	0.814707i	−0.985335	−	0.170629i	$-0.945420\pi$
$29$	−576226.	+	576226.i	−0.814707	+	0.814707i	0.170629	+	0.985335i	$0.445420\pi$
$30$			548327.i			0.676946i
$31$	−306624.	+	306624.i	−0.332016	+	0.332016i	−0.853352	−	0.521336i	$-0.825434\pi$
$31$	−306624.	+	306624.i	−0.332016	+	0.332016i	0.521336	+	0.853352i	$0.325434\pi$
$32$	165561.	−	165561.i	0.157892	−	0.157892i
$33$	−727014.			−0.613037
$34$	1.88209e6			1.40839
$35$	488312.	+	488312.i	0.325405	+	0.325405i
$36$			296510.i			0.176535i
$37$	−144828.	−	1.86856e6i	−0.0772761	−	0.997010i
$37$	−144828.	−	1.86856e6i	−0.0772761	−	0.997010i
$38$	−746758.			−0.358134
$39$	−2.69490e6	+	2.69490e6i	−1.16489	+	1.16489i
$40$		−	959017.i		−	0.374616i
$41$		−	4.57629e6i		−	1.61949i	−0.586783	−	0.809744i	$-0.699606\pi$
$41$		−	4.57629e6i		−	1.61949i	0.586783	−	0.809744i	$-0.300394\pi$
$42$	4.28195e6	+	4.28195e6i	1.37608	+	1.37608i
$43$	−1.73999e6	−	1.73999e6i	−0.508949	−	0.508949i	0.405255	−	0.914204i	$-0.367183\pi$
$43$	−1.73999e6	−	1.73999e6i	−0.508949	−	0.508949i	−0.914204	+	0.405255i	$0.867183\pi$
$44$	−160627.			−0.0428556
$45$	1.82602e6	+	1.82602e6i	0.445304	+	0.445304i
$46$	−4.12389e6			−0.921035
$47$	1.08422e6			0.222191			0.111096	−	0.993810i	$-0.464564\pi$
$47$	1.08422e6			0.222191			0.111096	+	0.993810i	$0.464564\pi$
$48$		−	9.36472e6i		−	1.76413i
$49$	1.86178e6			0.322956
$50$	−3.91459e6	−	3.91459e6i	−0.626335	−	0.626335i
$51$	1.02497e7	−	1.02497e7i	1.51506	−	1.51506i
$52$	−595414.	+	595414.i	−0.0814339	+	0.0814339i
$53$	1.34938e7			1.71014			0.855069	−	0.518514i	$-0.173514\pi$
$53$	1.34938e7			1.71014			0.855069	+	0.518514i	$0.173514\pi$
$54$	5.83927e6	+	5.83927e6i	0.686726	+	0.686726i
$55$	−989203.	+	989203.i	−0.108102	+	0.108102i
$56$	−7.48909e6	−	7.48909e6i	−0.761512	−	0.761512i
$57$	−4.06678e6	+	4.06678e6i	−0.385258	+	0.385258i
$58$			1.37503e7i			1.21506i
$59$	−4.21692e6	−	4.21692e6i	−0.348007	−	0.348007i	0.511360	−	0.859367i	$-0.329142\pi$
$59$	−4.21692e6	−	4.21692e6i	−0.348007	−	0.348007i	−0.859367	+	0.511360i	$0.829142\pi$
$60$	659761.	+	659761.i	0.0509075	+	0.0509075i
$61$	9.22788e6	−	9.22788e6i	0.666473	−	0.666473i	−0.290425	−	0.956898i	$-0.593797\pi$
$61$	9.22788e6	−	9.22788e6i	0.666473	−	0.666473i	0.956898	+	0.290425i	$0.0937965\pi$
$62$			7.31685e6i			0.495173i
$63$	2.85193e7			1.81041
$64$			1.44971e7i			0.864096i
$65$			7.33357e6i			0.410830i
$66$	−8.67422e6	+	8.67422e6i	−0.457146	+	0.457146i
$67$		−	1.69836e7i		−	0.842811i	−0.906872	−	0.421405i	$-0.861537\pi$
$67$		−	1.69836e7i		−	0.842811i	0.906872	−	0.421405i	$-0.138463\pi$
$68$	2.26458e6	−	2.26458e6i	0.105914	−	0.105914i
$69$	−2.24584e7	+	2.24584e7i	−0.990791	+	0.990791i
$70$	1.16524e7			0.485314
$71$	−2.90292e7			−1.14236			−0.571178	−	0.820826i	$-0.693513\pi$
$71$	−2.90292e7			−1.14236			−0.571178	+	0.820826i	$0.693513\pi$
$72$	−2.80052e7	−	2.80052e7i	−1.04210	−	1.04210i
$73$			2.25693e7i			0.794743i	0.917658	+	0.397372i	$0.130078\pi$
$73$			2.25693e7i			0.794743i	−0.917658	+	0.397372i	$0.869922\pi$
$74$	−2.40223e7	−	2.05663e7i	−0.801102	−	0.685851i
$75$	−4.26371e7			−1.34754
$76$	−898518.	+	898518.i	−0.0269322	+	0.0269322i
$77$			1.54496e7i			0.439496i
$78$			6.43074e7i			1.73733i
$79$	−1.42358e7	−	1.42358e7i	−0.365489	−	0.365489i	0.500340	−	0.865829i	$-0.333208\pi$
$79$	−1.42358e7	−	1.42358e7i	−0.365489	−	0.365489i	−0.865829	+	0.500340i	$0.833208\pi$
$80$	−1.27420e7	−	1.27420e7i	−0.311084	−	0.311084i
$81$	−4.15512e6			−0.0965257
$82$	−5.46011e7	−	5.46011e7i	−1.20766	−	1.20766i
$83$	4.36261e7			0.919251			0.459626	−	0.888113i	$-0.347984\pi$
$83$	4.36261e7			0.919251			0.459626	+	0.888113i	$0.347984\pi$
$84$	1.03043e7			0.206967
$85$		−	2.78923e7i		−	0.534329i
$86$	−4.15208e7			−0.759053
$87$	7.48829e7	+	7.48829e7i	1.30709	+	1.30709i
$88$	1.51711e7	−	1.51711e7i	0.252980	−	0.252980i
$89$	−5.77020e6	+	5.77020e6i	−0.0919667	+	0.0919667i	−0.751593	−	0.659627i	$-0.770714\pi$
$89$	−5.77020e6	+	5.77020e6i	−0.0919667	+	0.0919667i	0.659627	+	0.751593i	$0.270714\pi$
$90$	4.35737e7			0.664132
$91$	5.72688e7	+	5.72688e7i	0.835128	+	0.835128i
$92$	−4.96197e6	+	4.96197e6i	−0.0692633	+	0.0692633i
$93$	3.98470e7	+	3.98470e7i	0.532677	+	0.532677i
$94$	1.29362e7	−	1.29362e7i	0.165690	−	0.165690i
$95$			1.10668e7i			0.135872i
$96$	−2.15153e7	−	2.15153e7i	−0.253316	−	0.253316i
$97$	5.99578e7	+	5.99578e7i	0.677265	+	0.677265i	0.959380	−	0.282116i	$-0.0910362\pi$
$97$	5.99578e7	+	5.99578e7i	0.677265	+	0.677265i	−0.282116	+	0.959380i	$0.591036\pi$
$98$	2.22134e7	−	2.22134e7i	0.240830	−	0.240830i
$99$			5.77734e7i			0.601433i
$100$	−9.42027e6			−0.0942027
$101$			1.48289e8i			1.42503i	0.701656	+	0.712516i	$0.252444\pi$
$101$			1.48289e8i			1.42503i	−0.701656	+	0.712516i	$0.747556\pi$
$102$		−	2.44585e8i		−	2.25958i
$103$	9.11433e7	−	9.11433e7i	0.809796	−	0.809796i	−0.174807	−	0.984603i	$-0.555930\pi$
$103$	9.11433e7	−	9.11433e7i	0.809796	−	0.809796i	0.984603	+	0.174807i	$0.0559300\pi$
$104$		−	1.12473e8i		−	0.961423i
$105$	6.34580e7	−	6.34580e7i	0.522070	−	0.522070i
$106$	1.60999e8	−	1.60999e8i	1.27526	−	1.27526i
$107$	−1.83138e8			−1.39715			−0.698574	−	0.715538i	$-0.746182\pi$
$107$	−1.83138e8			−1.39715			−0.698574	+	0.715538i	$0.746182\pi$
$108$	1.40519e7			0.103286
$109$	3.18948e7	+	3.18948e7i	0.225951	+	0.225951i	0.810999	−	0.585048i	$-0.198924\pi$
$109$	3.18948e7	+	3.18948e7i	0.225951	+	0.225951i	−0.585048	+	0.810999i	$0.698924\pi$
$110$			2.36050e7i			0.161225i
$111$	−2.42826e8	+	1.88209e7i	−1.59957	+	0.123979i
$112$	−1.99008e8			−1.26473
$113$	1.51638e8	−	1.51638e8i	0.930026	−	0.930026i	−0.0676808	−	0.997707i	$-0.521560\pi$
$113$	1.51638e8	−	1.51638e8i	0.930026	−	0.930026i	0.997707	+	0.0676808i	$0.0215599\pi$
$114$			9.70441e7i			0.574579i
$115$			6.11155e7i			0.349430i
$116$	1.65447e7	+	1.65447e7i	0.0913748	+	0.0913748i
$117$	2.14155e8	+	2.14155e8i	1.14284	+	1.14284i
$118$	−1.00627e8			−0.519022
$119$	−2.17815e8	−	2.17815e8i	−1.08617	−	1.08617i
$120$	−1.24628e8			−0.601022
$121$	1.83062e8			0.853996
$122$		−	2.20201e8i		−	0.993987i
$123$	−5.94706e8			−2.59826
$124$	8.80382e6	+	8.80382e6i	0.0372378	+	0.0372378i
$125$	−1.27084e8	+	1.27084e8i	−0.520537	+	0.520537i
$126$	3.40273e8	−	3.40273e8i	1.35004	−	1.35004i
$127$	3.92480e8			1.50870			0.754350	−	0.656472i	$-0.227952\pi$
$127$	3.92480e8			1.50870			0.754350	+	0.656472i	$0.227952\pi$
$128$	2.15353e8	+	2.15353e8i	0.802254	+	0.802254i
$129$	−2.26119e8	+	2.26119e8i	−0.816541	+	0.816541i
$130$	8.74991e7	+	8.74991e7i	0.306359	+	0.306359i
$131$	2.96361e8	−	2.96361e8i	1.00632	−	1.00632i	0.00633803	−	0.999980i	$-0.497983\pi$
$131$	2.96361e8	−	2.96361e8i	1.00632	−	1.00632i	0.999980	−	0.00633803i	$-0.00201747\pi$
$132$			2.08741e7i			0.0687562i
$133$	8.64224e7	+	8.64224e7i	0.276198	+	0.276198i
$134$	−2.02636e8	−	2.02636e8i	−0.628490	−	0.628490i
$135$	8.65372e7	−	8.65372e7i	0.260536	−	0.260536i
$136$			4.27776e8i			1.25043i
$137$	3.95449e8			1.12256			0.561279	−	0.827627i	$-0.310310\pi$
$137$	3.95449e8			1.12256			0.561279	+	0.827627i	$0.310310\pi$
$138$			5.35916e8i			1.47768i
$139$			4.65701e8i			1.24752i	0.781616	+	0.623760i	$0.214396\pi$
$139$			4.65701e8i			1.24752i	−0.781616	+	0.623760i	$0.785604\pi$
$140$	1.40205e7	−	1.40205e7i	0.0364964	−	0.0364964i
$141$		−	1.40899e8i		−	0.356477i
$142$	−3.46356e8	+	3.46356e8i	−0.851862	+	0.851862i
$143$	−1.16013e8	+	1.16013e8i	−0.277436	+	0.277436i
$144$	−7.44184e8			−1.73073
$145$	2.03777e8			0.460981
$146$	2.69281e8	+	2.69281e8i	0.592645	+	0.592645i
$147$		−	2.41945e8i		−	0.518140i
$148$	−5.36502e7	+	4.15831e6i	−0.111821	+	0.00866703i
$149$	5.93888e8			1.20492			0.602462	−	0.798148i	$-0.294186\pi$
$149$	5.93888e8			1.20492			0.602462	+	0.798148i	$0.294186\pi$
$150$	−5.08716e8	+	5.08716e8i	−1.00487	+	1.00487i
$151$		−	6.38283e8i		−	1.22774i	−0.789408	−	0.613868i	$-0.789613\pi$
$151$		−	6.38283e8i		−	1.22774i	0.789408	−	0.613868i	$-0.210387\pi$
$152$		−	1.69729e8i		−	0.317967i
$153$	−8.14511e8	−	8.14511e8i	−1.48638	−	1.48638i
$154$	1.84334e8	+	1.84334e8i	0.327735	+	0.327735i
$155$	1.08435e8			0.187863
$156$	7.73763e7	+	7.73763e7i	0.130650	+	0.130650i
$157$	−6.38282e8			−1.05054			−0.525271	−	0.850935i	$-0.676036\pi$
$157$	−6.38282e8			−1.05054			−0.525271	+	0.850935i	$0.676036\pi$
$158$	−3.39704e8			−0.545095
$159$		−	1.75357e9i		−	2.74369i
$160$	−5.85492e7			−0.0893390
$161$	4.77259e8	+	4.77259e8i	0.710314	+	0.710314i
$162$	−4.95760e7	+	4.95760e7i	−0.0719799	+	0.0719799i
$163$	−6.04243e8	+	6.04243e8i	−0.855975	+	0.855975i	−0.990861	−	0.134886i	$-0.956933\pi$
$163$	−6.04243e8	+	6.04243e8i	−0.855975	+	0.855975i	0.134886	+	0.990861i	$0.456933\pi$
$164$	−1.31395e8			−0.181636
$165$	1.28551e8	+	1.28551e8i	0.173436	+	0.173436i
$166$	5.20517e8	−	5.20517e8i	0.685492	−	0.685492i
$167$	−5.19569e6	−	5.19569e6i	−0.00668002	−	0.00668002i	0.703759	−	0.710439i	$-0.251504\pi$
$167$	−5.19569e6	−	5.19569e6i	−0.00668002	−	0.00668002i	−0.710439	+	0.703759i	$0.751504\pi$
$168$	−9.73236e8	+	9.73236e8i	−1.22175	+	1.22175i
$169$			4.43461e7i			0.0543636i
$170$	−3.32792e8	−	3.32792e8i	−0.398453	−	0.398453i
$171$	3.23174e8	+	3.23174e8i	0.377965	+	0.377965i
$172$	−4.99589e7	+	4.99589e7i	−0.0570820	+	0.0570820i
$173$			1.42213e9i			1.58766i	0.608143	+	0.793828i	$0.291915\pi$
$173$			1.42213e9i			1.58766i	−0.608143	+	0.793828i	$0.708085\pi$
$174$	1.78690e9			1.94941
$175$			9.06073e8i			0.966076i
$176$		−	4.03143e8i		−	0.420154i
$177$	−5.48005e8	+	5.48005e8i	−0.558331	+	0.558331i
$178$			1.37692e8i			0.137160i
$179$	8.72570e8	−	8.72570e8i	0.849939	−	0.849939i	−0.140186	−	0.990125i	$-0.544770\pi$
$179$	8.72570e8	−	8.72570e8i	0.849939	−	0.849939i	0.990125	+	0.140186i	$0.0447700\pi$
$180$	5.24290e7	−	5.24290e7i	0.0499438	−	0.0499438i
$181$	3.62518e8			0.337765			0.168883	−	0.985636i	$-0.445984\pi$
$181$	3.62518e8			0.337765			0.168883	+	0.985636i	$0.445984\pi$
$182$	1.36658e9			1.24552
$183$	−1.19920e9	−	1.19920e9i	−1.06927	−	1.06927i
$184$		−	9.37311e8i		−	0.817734i
$185$	−3.04790e8	+	3.56007e8i	−0.260204	+	0.303929i
$186$	9.50853e8			0.794441
$187$	4.41241e8	−	4.41241e8i	0.360835	−	0.360835i
$188$		−	3.11303e7i		−	0.0249202i
$189$		−	1.35156e9i		−	1.05922i
$190$	1.32042e8	+	1.32042e8i	0.101321	+	0.101321i
$191$	−1.38965e9	−	1.38965e9i	−1.04417	−	1.04417i	−0.998978	−	0.0451901i	$-0.985611\pi$
$191$	−1.38965e9	−	1.38965e9i	−1.04417	−	1.04417i	−0.0451901	−	0.998978i	$-0.514389\pi$
$192$	1.88396e9			1.38633
$193$	−1.52923e9	−	1.52923e9i	−1.10216	−	1.10216i	−0.994150	−	0.108006i	$-0.965553\pi$
$193$	−1.52923e9	−	1.52923e9i	−1.10216	−	1.10216i	−0.108006	−	0.994150i	$-0.534447\pi$
$194$	1.43075e9			1.01008
$195$	9.53026e8			0.659123
$196$		−	5.34555e7i		−	0.0362217i
$197$	1.75627e8			0.116607			0.0583036	−	0.998299i	$-0.481431\pi$
$197$	1.75627e8			0.116607			0.0583036	+	0.998299i	$0.481431\pi$
$198$	6.89312e8	+	6.89312e8i	0.448493	+	0.448493i
$199$	−1.35091e9	+	1.35091e9i	−0.861418	+	0.861418i	−0.991503	−	0.130085i	$-0.958475\pi$
$199$	−1.35091e9	+	1.35091e9i	−0.861418	+	0.861418i	0.130085	+	0.991503i	$0.458475\pi$
$200$	8.89739e8	−	8.89739e8i	0.556087	−	0.556087i
$201$	−2.20708e9			−1.35218
$202$	1.76929e9	+	1.76929e9i	1.06266	+	1.06266i
$203$	1.59132e9	−	1.59132e9i	0.937074	−	0.937074i
$204$	−2.94291e8	−	2.94291e8i	−0.169924	−	0.169924i
$205$	−8.09180e8	+	8.09180e8i	−0.458173	+	0.458173i
$206$		−	2.17492e9i		−	1.20774i
$207$	1.78469e9	+	1.78469e9i	0.972036	+	0.972036i
$208$	−1.49437e9	−	1.49437e9i	−0.798373	−	0.798373i
$209$	−1.75071e8	+	1.75071e8i	−0.0917551	+	0.0917551i
$210$		−	1.51427e9i		−	0.778623i
$211$	−1.00128e9			−0.505157			−0.252579	−	0.967576i	$-0.581279\pi$
$211$	−1.00128e9			−0.505157			−0.252579	+	0.967576i	$0.581279\pi$
$212$		−	3.87436e8i		−	0.191803i
$213$			3.77245e9i			1.83276i
$214$	−2.18507e9	+	2.18507e9i	−1.04186	+	1.04186i
$215$			6.15332e8i			0.287976i
$216$	−1.32720e9	+	1.32720e9i	−0.609705	+	0.609705i
$217$	8.46781e8	−	8.46781e8i	0.381885	−	0.381885i
$218$	7.61094e8			0.336986
$219$	2.93297e9			1.27506
$220$	2.84021e7	+	2.84021e7i	0.0121244	+	0.0121244i
$221$		−	3.27119e9i		−	1.37131i
$222$	−2.67268e9	+	3.12179e9i	−1.10036	+	1.28526i
$223$	−2.60958e9			−1.05524			−0.527620	−	0.849481i	$-0.676915\pi$
$223$	−2.60958e9			−1.05524			−0.527620	+	0.849481i	$0.676915\pi$
$224$	−4.57218e8	+	4.57218e8i	−0.181607	+	0.181607i
$225$			3.38823e9i			1.32204i
$226$		−	3.61849e9i		−	1.38705i
$227$	2.70910e8	+	2.70910e8i	0.102029	+	0.102029i	0.756278	−	0.654250i	$-0.227016\pi$
$227$	2.70910e8	+	2.70910e8i	0.102029	+	0.102029i	−0.654250	+	0.756278i	$0.727016\pi$
$228$	1.16766e8	+	1.16766e8i	0.0432092	+	0.0432092i
$229$	−1.38963e9			−0.505310			−0.252655	−	0.967556i	$-0.581304\pi$
$229$	−1.38963e9			−0.505310			−0.252655	+	0.967556i	$0.581304\pi$
$230$	7.29188e8	+	7.29188e8i	0.260572	+	0.260572i
$231$	2.00774e9			0.705114
$232$	−3.12527e9			−1.07879
$233$		−	3.96395e8i		−	0.134494i	−0.997736	−	0.0672472i	$-0.978578\pi$
$233$		−	3.96395e8i		−	0.134494i	0.997736	−	0.0672472i	$-0.0214216\pi$
$234$	5.11030e9			1.70444
$235$	−1.91713e8	−	1.91713e8i	−0.0628607	−	0.0628607i
$236$	−1.21077e8	+	1.21077e8i	−0.0390313	+	0.0390313i
$237$	−1.85000e9	+	1.85000e9i	−0.586379	+	0.586379i
$238$	−5.19763e9			−1.61993
$239$	3.00410e8	+	3.00410e8i	0.0920709	+	0.0920709i	0.751642	−	0.659571i	$-0.229262\pi$
$239$	3.00410e8	+	3.00410e8i	0.0920709	+	0.0920709i	−0.659571	+	0.751642i	$0.729262\pi$
$240$	−1.65587e9	+	1.65587e9i	−0.499094	+	0.499094i
$241$	1.73573e8	+	1.73573e8i	0.0514533	+	0.0514533i	0.732365	−	0.680912i	$-0.238416\pi$
$241$	1.73573e8	+	1.73573e8i	0.0514533	+	0.0514533i	−0.680912	+	0.732365i	$0.738416\pi$
$242$	2.18416e9	−	2.18416e9i	0.636830	−	0.636830i
$243$			3.75098e9i			1.07577i
$244$	−2.64952e8	−	2.64952e8i	−0.0747494	−	0.0747494i
$245$	−3.29200e8	−	3.29200e8i	−0.0913682	−	0.0913682i
$246$	−7.09562e9	+	7.09562e9i	−1.93754	+	1.93754i
$247$			1.29791e9i			0.348704i
$248$	−1.66303e9			−0.439636
$249$		−	5.66938e9i		−	1.47482i
$250$			3.03256e9i			0.776335i
$251$	2.05074e9	−	2.05074e9i	0.516673	−	0.516673i	−0.399890	−	0.916563i	$-0.630952\pi$
$251$	2.05074e9	−	2.05074e9i	0.516673	−	0.516673i	0.916563	+	0.399890i	$0.130952\pi$
$252$		−	8.18850e8i		−	0.203050i
$253$	−9.66814e8	+	9.66814e8i	−0.235972	+	0.235972i
$254$	4.68280e9	−	4.68280e9i	1.12505	−	1.12505i
$255$	−3.62471e9			−0.857260
$256$	1.42763e9			0.332396
$257$	−2.10871e9	−	2.10871e9i	−0.483375	−	0.483375i	0.422833	−	0.906208i	$-0.361036\pi$
$257$	−2.10871e9	−	2.10871e9i	−0.483375	−	0.483375i	−0.906208	+	0.422833i	$0.861036\pi$
$258$			5.39579e9i			1.21780i
$259$	3.99960e8	+	5.16025e9i	0.0888828	+	1.14676i
$260$	2.10562e8			0.0460773
$261$	5.95070e9	−	5.95070e9i	1.28235	−	1.28235i
$262$		−	7.07194e9i		−	1.50084i
$263$		−	5.53988e9i		−	1.15792i	−0.815357	−	0.578959i	$-0.803459\pi$
$263$		−	5.53988e9i		−	1.15792i	0.815357	−	0.578959i	$-0.196541\pi$
$264$	−1.97155e9	−	1.97155e9i	−0.405874	−	0.405874i
$265$	−2.38598e9	−	2.38598e9i	−0.483820	−	0.483820i
$266$	2.06227e9			0.411925
$267$	7.49860e8	+	7.49860e8i	0.147549	+	0.147549i
$268$	−4.87634e8			−0.0945269
$269$	2.58659e9			0.493991			0.246995	−	0.969017i	$-0.420557\pi$
$269$	2.58659e9			0.493991			0.246995	+	0.969017i	$0.420557\pi$
$270$		−	2.06500e9i		−	0.388567i
$271$	1.06239e10			1.96973			0.984864	−	0.173328i	$-0.0554521\pi$
$271$	1.06239e10			1.96973			0.984864	+	0.173328i	$0.0554521\pi$
$272$	5.68366e9	+	5.68366e9i	1.03837	+	1.03837i
$273$	7.44231e9	−	7.44231e9i	1.33985	−	1.33985i
$274$	4.71823e9	−	4.71823e9i	0.837099	−	0.837099i
$275$	−1.83549e9			−0.320938
$276$	6.44828e8	+	6.44828e8i	0.111124	+	0.111124i
$277$	−6.71985e9	+	6.71985e9i	−1.14141	+	1.14141i	−0.153215	+	0.988193i	$0.548963\pi$
$277$	−6.71985e9	+	6.71985e9i	−1.14141	+	1.14141i	−0.988193	+	0.153215i	$0.951037\pi$
$278$	5.55642e9	+	5.55642e9i	0.930284	+	0.930284i
$279$	3.16651e9	−	3.16651e9i	0.522593	−	0.522593i
$280$			2.64845e9i			0.430883i
$281$	−7.80166e9	−	7.80166e9i	−1.25130	−	1.25130i	−0.955137	−	0.296164i	$-0.904293\pi$
$281$	−7.80166e9	−	7.80166e9i	−1.25130	−	1.25130i	−0.296164	−	0.955137i	$-0.595707\pi$
$282$	−1.68111e9	−	1.68111e9i	−0.265827	−	0.265827i
$283$	−7.15522e9	+	7.15522e9i	−1.11552	+	1.11552i	−0.123129	+	0.992391i	$0.539293\pi$
$283$	−7.15522e9	+	7.15522e9i	−1.11552	+	1.11552i	−0.992391	+	0.123129i	$0.960707\pi$
$284$			8.33489e8i			0.128123i
$285$	1.43818e9			0.217989
$286$			2.76838e9i			0.413772i
$287$			1.26380e10i			1.86273i
$288$	−1.70975e9	+	1.70975e9i	−0.248521	+	0.248521i
$289$			5.46579e9i			0.783540i
$290$	2.43133e9	−	2.43133e9i	0.343757	−	0.343757i
$291$	7.79174e9	−	7.79174e9i	1.08658	−	1.08658i
$292$	6.48013e8			0.0891358
$293$	−7.27897e9			−0.987641			−0.493821	−	0.869564i	$-0.664400\pi$
$293$	−7.27897e9			−0.987641			−0.493821	+	0.869564i	$0.664400\pi$
$294$	−2.88672e9	−	2.88672e9i	−0.386381	−	0.386381i
$295$			1.49127e9i			0.196911i
$296$	4.67448e9	−	5.45998e9i	0.608929	−	0.711253i
$297$	2.73794e9			0.351883
$298$	7.08586e9	−	7.08586e9i	0.898520	−	0.898520i
$299$			7.16759e9i			0.896785i
$300$			1.22420e9i			0.151136i
$301$	4.80521e9	+	4.80521e9i	0.585392	+	0.585392i
$302$	−7.61555e9	−	7.61555e9i	−0.915532	−	0.915532i
$303$	1.92708e10			2.28628
$304$	−2.25511e9	−	2.25511e9i	−0.264042	−	0.264042i
$305$	−3.26335e9			−0.377107
$306$	−1.94363e10			−2.21681
$307$		−	1.00919e10i		−	1.13611i	−0.822992	−	0.568053i	$-0.807697\pi$
$307$		−	1.00919e10i		−	1.13611i	0.822992	−	0.568053i	$-0.192303\pi$
$308$	4.43592e8			0.0492925
$309$	−1.18444e10	−	1.18444e10i	−1.29921	−	1.29921i
$310$	1.29377e9	−	1.29377e9i	0.140091	−	0.140091i
$311$	8.58804e9	−	8.58804e9i	0.918021	−	0.918021i	−0.0788641	−	0.996885i	$-0.525129\pi$
$311$	8.58804e9	−	8.58804e9i	0.918021	−	0.918021i	0.996885	+	0.0788641i	$0.0251293\pi$
$312$	−1.46163e10			−1.54248
$313$	−2.71448e9	−	2.71448e9i	−0.282820	−	0.282820i	0.551413	−	0.834233i	$-0.314089\pi$
$313$	−2.71448e9	−	2.71448e9i	−0.282820	−	0.282820i	−0.834233	+	0.551413i	$0.814089\pi$
$314$	−7.61553e9	+	7.61553e9i	−0.783397	+	0.783397i
$315$	−5.04280e9	−	5.04280e9i	−0.512188	−	0.512188i
$316$	−4.08740e8	+	4.08740e8i	−0.0409920	+	0.0409920i
$317$			1.94974e10i			1.93081i	0.260759	+	0.965404i	$0.416027\pi$
$317$			1.94974e10i			1.93081i	−0.260759	+	0.965404i	$0.583973\pi$
$318$	−2.09224e10	−	2.09224e10i	−2.04599	−	2.04599i
$319$	3.22364e9	+	3.22364e9i	0.311303	+	0.311303i
$320$	2.56339e9	−	2.56339e9i	0.244464	−	0.244464i
$321$			2.37994e10i			2.24154i
$322$	1.13886e10			1.05937
$323$		−	4.93644e9i		−	0.453528i
$324$			1.19302e8i			0.0108260i
$325$	−6.80381e9	+	6.80381e9i	−0.609844	+	0.609844i
$326$			1.44188e10i			1.27661i
$327$	4.14485e9	−	4.14485e9i	0.362509	−	0.362509i
$328$	1.24102e10	−	1.24102e10i	1.07222	−	1.07222i
$329$	−2.99422e9			−0.255564
$330$	3.06756e9			0.258665
$331$	1.33834e9	+	1.33834e9i	0.111495	+	0.111495i	0.760653	−	0.649158i	$-0.224879\pi$
$331$	1.33834e9	+	1.33834e9i	0.111495	+	0.111495i	−0.649158	+	0.760653i	$0.724879\pi$
$332$		−	1.25260e9i		−	0.103100i
$333$	1.49564e9	+	1.92966e10i	0.121633	+	1.56929i
$334$	−1.23983e8			−0.00996267
$335$	−3.00304e9	+	3.00304e9i	−0.238442	+	0.238442i
$336$			2.58619e10i			2.02910i
$337$			1.01286e10i			0.785286i	0.919691	+	0.392643i	$0.128439\pi$
$337$			1.01286e10i			0.785286i	−0.919691	+	0.392643i	$0.871561\pi$
$338$	5.29107e8	+	5.29107e8i	0.0405393	+	0.0405393i
$339$	−1.97060e10	−	1.97060e10i	−1.49211	−	1.49211i
$340$	−8.00847e8			−0.0599285
$341$	1.71538e9	+	1.71538e9i	0.126865	+	0.126865i
$342$	7.71177e9			0.563702
$343$	1.07787e10			0.778735
$344$		−	9.43717e9i		−	0.673920i
$345$	7.94220e9			0.560614
$346$	1.69679e10	+	1.69679e10i	1.18393	+	1.18393i
$347$	9.36006e9	−	9.36006e9i	0.645596	−	0.645596i	−0.306330	−	0.951925i	$-0.599101\pi$
$347$	9.36006e9	−	9.36006e9i	0.645596	−	0.645596i	0.951925	+	0.306330i	$0.0991010\pi$
$348$	2.15004e9	−	2.15004e9i	0.146599	−	0.146599i
$349$	−9.39521e9			−0.633293			−0.316646	−	0.948544i	$-0.602557\pi$
$349$	−9.39521e9			−0.633293			−0.316646	+	0.948544i	$0.602557\pi$
$350$	1.08106e10	+	1.08106e10i	0.720409	+	0.720409i
$351$	1.01490e10	−	1.01490e10i	0.668645	−	0.668645i
$352$	−9.26216e8	−	9.26216e8i	−0.0603312	−	0.0603312i
$353$	5.23084e9	−	5.23084e9i	0.336878	−	0.336878i	−0.518313	−	0.855191i	$-0.673440\pi$
$353$	5.23084e9	−	5.23084e9i	0.336878	−	0.336878i	0.855191	+	0.518313i	$0.173440\pi$
$354$			1.30768e10i			0.832702i
$355$	5.13295e9	+	5.13295e9i	0.323187	+	0.323187i
$356$	1.65675e8	+	1.65675e8i	0.0103147	+	0.0103147i
$357$	−2.83059e10	+	2.83059e10i	−1.74262	+	1.74262i
$358$		−	2.08218e10i		−	1.26761i
$359$	−1.43369e10			−0.863135			−0.431567	−	0.902081i	$-0.642039\pi$
$359$	−1.43369e10			−0.863135			−0.431567	+	0.902081i	$0.642039\pi$
$360$			9.90378e9i			0.589645i
$361$		−	1.50249e10i		−	0.884675i
$362$	4.32531e9	−	4.32531e9i	0.251874	−	0.251874i
$363$		−	2.37896e10i		−	1.37012i
$364$	1.64431e9	−	1.64431e9i	0.0936651	−	0.0936651i
$365$	3.99071e9	−	3.99071e9i	0.224843	−	0.224843i
$366$	−2.86160e10			−1.59472
$367$	1.14974e10			0.633778			0.316889	−	0.948463i	$-0.397362\pi$
$367$	1.14974e10			0.633778			0.316889	+	0.948463i	$0.397362\pi$
$368$	−1.24536e10	−	1.24536e10i	−0.679053	−	0.679053i
$369$			4.72594e10i			2.54907i
$370$	6.11086e8	+	7.88418e9i	0.0326058	+	0.420678i
$371$	−3.72649e10			−1.96700
$372$	1.14409e9	−	1.14409e9i	0.0597432	−	0.0597432i
$373$			2.05792e9i			0.106315i	0.998586	+	0.0531573i	$0.0169285\pi$
$373$			2.05792e9i			0.106315i	−0.998586	+	0.0531573i	$0.983072\pi$
$374$		−	1.05292e10i		−	0.538155i
$375$	1.65151e10	+	1.65151e10i	0.835133	+	0.835133i
$376$	2.94024e9	+	2.94024e9i	0.147106	+	0.147106i
$377$	2.38988e10			1.18307
$378$	−1.61259e10	−	1.61259e10i	−0.789871	−	0.789871i
$379$	1.35654e10			0.657470			0.328735	−	0.944422i	$-0.393378\pi$
$379$	1.35654e10			0.657470			0.328735	+	0.944422i	$0.393378\pi$
$380$	3.17752e8			0.0152389
$381$		−	5.10043e10i		−	2.42051i
$382$	−3.31606e10			−1.55729
$383$	4.62512e8	+	4.62512e8i	0.0214945	+	0.0214945i	0.717772	−	0.696278i	$-0.245162\pi$
$383$	4.62512e8	+	4.62512e8i	0.0214945	+	0.0214945i	−0.696278	+	0.717772i	$0.745162\pi$
$384$	2.79860e10	−	2.79860e10i	1.28711	−	1.28711i
$385$	2.73181e9	−	2.73181e9i	0.124339	−	0.124339i
$386$	−3.64914e10			−1.64377
$387$	1.79689e10	+	1.79689e10i	0.801085	+	0.801085i
$388$	1.72151e9	−	1.72151e9i	0.0759597	−	0.0759597i
$389$	7.07806e9	+	7.07806e9i	0.309112	+	0.309112i	0.844565	−	0.535453i	$-0.179859\pi$
$389$	7.07806e9	+	7.07806e9i	0.309112	+	0.309112i	−0.535453	+	0.844565i	$0.679859\pi$
$390$	1.13708e10	−	1.13708e10i	0.491512	−	0.491512i
$391$		−	2.72610e10i		−	1.16636i
$392$	5.04884e9	+	5.04884e9i	0.213820	+	0.213820i
$393$	−3.85132e10	−	3.85132e10i	−1.61451	−	1.61451i
$394$	2.09545e9	−	2.09545e9i	0.0869547	−	0.0869547i
$395$			5.03436e9i			0.206803i
$396$	1.65880e9			0.0674547
$397$			4.49198e10i			1.80832i	0.427192	+	0.904161i	$0.359503\pi$
$397$			4.49198e10i			1.80832i	−0.427192	+	0.904161i	$0.640497\pi$
$398$			3.22362e10i			1.28473i
$399$	1.12309e10	−	1.12309e10i	0.443123	−	0.443123i
$400$		−	2.36431e10i		−	0.923558i
$401$	−1.71926e10	+	1.71926e10i	−0.664912	+	0.664912i	−0.956534	−	0.291621i	$-0.905805\pi$
$401$	−1.71926e10	+	1.71926e10i	−0.664912	+	0.664912i	0.291621	+	0.956534i	$0.405805\pi$
$402$	−2.63334e10	+	2.63334e10i	−1.00833	+	1.00833i
$403$	1.27171e10			0.482136
$404$	4.25770e9			0.159827
$405$	7.34709e8	+	7.34709e8i	0.0273083	+	0.0273083i
$406$		−	3.79731e10i		−	1.39756i
$407$	−1.04535e10	+	8.10225e8i	−0.380962	+	0.0295276i
$408$	5.55912e10			2.00616
$409$	3.41590e10	−	3.41590e10i	1.22071	−	1.22071i	0.253329	−	0.967380i	$-0.418475\pi$
$409$	3.41590e10	−	3.41590e10i	1.22071	−	1.22071i	0.967380	−	0.253329i	$-0.0815255\pi$
$410$			1.93092e10i			0.683326i
$411$		−	5.13902e10i		−	1.80100i
$412$	−2.61692e9	−	2.61692e9i	−0.0908240	−	0.0908240i
$413$	1.16456e10	+	1.16456e10i	0.400276	+	0.400276i
$414$	4.25875e10			1.44971
$415$	−7.71398e9	−	7.71398e9i	−0.260068	−	0.260068i
$416$	−6.86661e9			−0.229282
$417$	6.05196e10			2.00148
$418$			4.17766e9i			0.136845i
$419$	−1.23560e10			−0.400887			−0.200444	−	0.979705i	$-0.564238\pi$
$419$	−1.23560e10			−0.400887			−0.200444	+	0.979705i	$0.564238\pi$
$420$	−1.82201e9	−	1.82201e9i	−0.0585537	−	0.0585537i
$421$	−1.94983e10	+	1.94983e10i	−0.620682	+	0.620682i	−0.945706	−	0.325024i	$-0.894628\pi$
$421$	−1.94983e10	+	1.94983e10i	−0.620682	+	0.620682i	0.325024	+	0.945706i	$0.394628\pi$
$422$	−1.19466e10	+	1.19466e10i	−0.376699	+	0.376699i
$423$	−1.11968e10			−0.349729
$424$	3.65931e10	+	3.65931e10i	1.13223	+	1.13223i
$425$	2.58774e10	−	2.58774e10i	0.793168	−	0.793168i
$426$	4.50103e10	+	4.50103e10i	1.36670	+	1.36670i
$427$	−2.54840e10	+	2.54840e10i	−0.766576	+	0.766576i
$428$			5.25827e9i			0.156700i
$429$	1.50764e10	+	1.50764e10i	0.445110	+	0.445110i
$430$	7.34172e9	+	7.34172e9i	0.214745	+	0.214745i
$431$	−4.22847e10	+	4.22847e10i	−1.22539	+	1.22539i	−0.259698	+	0.965690i	$0.583623\pi$
$431$	−4.22847e10	+	4.22847e10i	−1.22539	+	1.22539i	−0.965690	+	0.259698i	$0.916377\pi$
$432$			3.52676e10i			1.01261i
$433$	−9.40111e9			−0.267441			−0.133720	−	0.991019i	$-0.542692\pi$
$433$	−9.40111e9			−0.267441			−0.133720	+	0.991019i	$0.542692\pi$
$434$		−	2.02064e10i		−	0.569548i
$435$		−	2.64816e10i		−	0.739584i
$436$	9.15767e8	−	9.15767e8i	0.0253419	−	0.0253419i
$437$			1.08164e10i			0.296589i
$438$	3.49942e10	−	3.49942e10i	0.950822	−	0.950822i
$439$	−4.31585e9	+	4.31585e9i	−0.116201	+	0.116201i	−0.762816	−	0.646615i	$-0.776184\pi$
$439$	−4.31585e9	+	4.31585e9i	−0.116201	+	0.116201i	0.646615	+	0.762816i	$0.276184\pi$
$440$	−5.36512e9			−0.143143
$441$	−1.92266e10			−0.508332
$442$	−3.90296e10	−	3.90296e10i	−1.02260	−	1.02260i
$443$		−	2.94390e10i		−	0.764377i	−0.924084	−	0.382189i	$-0.875170\pi$
$443$		−	2.94390e10i		−	0.764377i	0.924084	−	0.382189i	$-0.124830\pi$
$444$	5.40389e8	+	6.97205e9i	0.0139051	+	0.179403i
$445$	2.04058e9			0.0520371
$446$	−3.11357e10	+	3.11357e10i	−0.786899	+	0.786899i
$447$		−	7.71781e10i		−	1.93314i
$448$		−	4.00356e10i		−	0.993882i
$449$	−2.16933e10	−	2.16933e10i	−0.533753	−	0.533753i	0.387934	−	0.921687i	$-0.373189\pi$
$449$	−2.16933e10	−	2.16933e10i	−0.533753	−	0.533753i	−0.921687	+	0.387934i	$0.873189\pi$
$450$	4.04260e10	+	4.04260e10i	0.985850	+	0.985850i
$451$	−2.56016e10			−0.618815
$452$	−4.35386e9	−	4.35386e9i	−0.104309	−	0.104309i
$453$	−8.29473e10			−1.96974
$454$	6.46462e9			0.152167
$455$		−	2.02526e10i		−	0.472536i
$456$	−2.20569e10			−0.510136
$457$	4.98293e10	+	4.98293e10i	1.14240	+	1.14240i	0.988009	+	0.154395i	$0.0493428\pi$
$457$	4.98293e10	+	4.98293e10i	1.14240	+	1.14240i	0.154395	+	0.988009i	$0.450657\pi$
$458$	−1.65801e10	+	1.65801e10i	−0.376813	+	0.376813i
$459$	−3.86005e10	+	3.86005e10i	−0.869645	+	0.869645i
$460$	1.75476e9			0.0391909
$461$	−3.47570e10	−	3.47570e10i	−0.769552	−	0.769552i	0.208475	−	0.978028i	$-0.433150\pi$
$461$	−3.47570e10	−	3.47570e10i	−0.769552	−	0.769552i	−0.978028	+	0.208475i	$0.933150\pi$
$462$	2.39550e10	−	2.39550e10i	0.525808	−	0.525808i
$463$	−3.02173e10	−	3.02173e10i	−0.657554	−	0.657554i	0.297247	−	0.954801i	$-0.403932\pi$
$463$	−3.02173e10	−	3.02173e10i	−0.657554	−	0.657554i	−0.954801	+	0.297247i	$0.903932\pi$
$464$	−4.15240e10	+	4.15240e10i	−0.895833	+	0.895833i
$465$		−	1.40915e10i		−	0.301402i
$466$	−4.72951e9	−	4.72951e9i	−0.100293	−	0.100293i
$467$	1.04320e10	+	1.04320e10i	0.219331	+	0.219331i	0.808216	−	0.588886i	$-0.200433\pi$
$467$	1.04320e10	+	1.04320e10i	0.219331	+	0.219331i	−0.588886	+	0.808216i	$0.700433\pi$
$468$	6.14884e9	−	6.14884e9i	0.128177	−	0.128177i
$469$			4.69023e10i			0.969400i
$470$	−4.57476e9			−0.0937513
$471$			8.29472e10i			1.68546i
$472$		−	2.28712e10i		−	0.460810i
$473$	−9.73422e9	+	9.73422e9i	−0.194472	+	0.194472i
$474$			4.41458e10i			0.874533i
$475$	−1.02674e10	+	1.02674e10i	−0.201691	+	0.201691i
$476$	−6.25392e9	+	6.25392e9i	−0.121822	+	0.121822i
$477$	−1.39351e11			−2.69176
$478$	7.16856e9			0.137316
$479$	1.82448e10	+	1.82448e10i	0.346575	+	0.346575i	0.858832	−	0.512257i	$-0.171191\pi$
$479$	1.82448e10	+	1.82448e10i	0.346575	+	0.346575i	−0.512257	+	0.858832i	$0.671191\pi$
$480$			7.60870e9i			0.143333i
$481$	−3.57456e10	+	4.17523e10i	−0.667794	+	0.780010i
$482$	4.14190e9			0.0767382
$483$	6.20217e10	−	6.20217e10i	1.13961	−	1.13961i
$484$		−	5.25608e9i		−	0.0957813i
$485$		−	2.12035e10i		−	0.383213i
$486$	4.47540e10	+	4.47540e10i	0.802208	+	0.802208i
$487$	−4.04718e10	−	4.04718e10i	−0.719509	−	0.719509i	0.248996	−	0.968505i	$-0.419900\pi$
$487$	−4.04718e10	−	4.04718e10i	−0.719509	−	0.719509i	−0.968505	+	0.248996i	$0.919900\pi$
$488$	5.00491e10			0.882505
$489$	7.85237e10	+	7.85237e10i	1.37330	+	1.37330i
$490$	−7.85557e9			−0.136268
$491$	7.85625e10			1.35173			0.675864	−	0.737026i	$-0.263771\pi$
$491$	7.85625e10			1.35173			0.675864	+	0.737026i	$0.263771\pi$
$492$			1.70753e10i			0.291412i
$493$	−9.08961e10			−1.53871
$494$	1.54858e10	+	1.54858e10i	0.260031	+	0.260031i
$495$	1.02155e10	−	1.02155e10i	0.170153	−	0.170153i
$496$	−2.20959e10	+	2.20959e10i	−0.365078	+	0.365078i
$497$	8.01677e10			1.31394
$498$	−6.76431e10	−	6.76431e10i	−1.09978	−	1.09978i
$499$	7.97551e10	−	7.97551e10i	1.28634	−	1.28634i	0.349350	−	0.936992i	$-0.386403\pi$
$499$	7.97551e10	−	7.97551e10i	1.28634	−	1.28634i	0.936992	−	0.349350i	$-0.113597\pi$
$500$	3.64885e9	+	3.64885e9i	0.0583817	+	0.0583817i
$501$	−6.75201e8	+	6.75201e8i	−0.0107172	+	0.0107172i
$502$		−	4.89360e10i		−	0.770573i
$503$	−2.26958e10	−	2.26958e10i	−0.354546	−	0.354546i	0.507252	−	0.861798i	$-0.330661\pi$
$503$	−2.26958e10	−	2.26958e10i	−0.354546	−	0.354546i	−0.861798	+	0.507252i	$0.830661\pi$
$504$	7.73399e10	+	7.73399e10i	1.19862	+	1.19862i
$505$	2.62206e10	−	2.62206e10i	0.403159	−	0.403159i
$506$			2.30707e10i			0.351932i
$507$	5.76295e9			0.0872193
$508$		−	1.12689e10i		−	0.169211i
$509$		−	3.49501e10i		−	0.520688i	−0.965516	−	0.260344i	$-0.916164\pi$
$509$		−	3.49501e10i		−	0.520688i	0.965516	−	0.260344i	$-0.0838360\pi$
$510$	−4.32475e10	+	4.32475e10i	−0.639265	+	0.639265i
$511$		−	6.23280e10i		−	0.914112i
$512$	−3.80970e10	+	3.80970e10i	−0.554384	+	0.554384i
$513$	1.53155e10	−	1.53155e10i	0.221138	−	0.221138i
$514$	−5.03193e10			−0.720912
$515$	−3.22320e10			−0.458203
$516$	6.49235e9	+	6.49235e9i	0.0915805	+	0.0915805i
$517$		−	6.06558e9i		−	0.0849004i
$518$	6.63406e10	+	5.67965e10i	0.921426	+	0.788865i
$519$	1.84812e11			2.54719
$520$	−1.98875e10	+	1.98875e10i	−0.271999	+	0.271999i
$521$		−	5.33725e10i		−	0.724380i	−0.932104	−	0.362190i	$-0.882029\pi$
$521$		−	5.33725e10i		−	0.724380i	0.932104	−	0.362190i	$-0.117971\pi$
$522$		−	1.41999e11i		−	1.91251i
$523$	5.17939e10	+	5.17939e10i	0.692264	+	0.692264i	0.962730	−	0.270466i	$-0.0871777\pi$
$523$	5.17939e10	+	5.17939e10i	0.692264	+	0.692264i	−0.270466	+	0.962730i	$0.587178\pi$
$524$	−8.50914e9	−	8.50914e9i	−0.112865	−	0.112865i
$525$	1.17748e11			1.54994
$526$	−6.60980e10	−	6.60980e10i	−0.863467	−	0.863467i
$527$	−4.83680e10			−0.627070
$528$	−5.23900e10			−0.674082
$529$		−	1.85788e10i		−	0.237243i
$530$	−5.69357e10			−0.721575
$531$	4.35482e10	+	4.35482e10i	0.547762	+	0.547762i
$532$	2.48137e9	−	2.48137e9i	0.0309774	−	0.0309774i
$533$	−9.49001e10	+	9.49001e10i	−1.17587	+	1.17587i
$534$	1.78936e10			0.220056
$535$	3.23825e10	+	3.23825e10i	0.395271	+	0.395271i
$536$	4.60568e10	−	4.60568e10i	0.558000	−	0.558000i
$537$	−1.13394e11	−	1.13394e11i	−1.36362	−	1.36362i
$538$	3.08614e10	−	3.08614e10i	0.368372	−	0.368372i
$539$		−	1.04155e10i		−	0.123403i
$540$	−2.48466e9	−	2.48466e9i	−0.0292208	−	0.0292208i
$541$	5.85862e10	+	5.85862e10i	0.683922	+	0.683922i	0.960882	−	0.276960i	$-0.0893268\pi$
$541$	5.85862e10	+	5.85862e10i	0.683922	+	0.683922i	−0.276960	+	0.960882i	$0.589327\pi$
$542$	1.26757e11	−	1.26757e11i	1.46884	−	1.46884i
$543$		−	4.71106e10i		−	0.541900i
$544$	2.61163e10			0.298205
$545$		−	1.12793e10i		−	0.127849i
$546$		−	1.77593e11i		−	1.99827i
$547$	5.53927e10	−	5.53927e10i	0.618732	−	0.618732i	−0.326474	−	0.945206i	$-0.605860\pi$
$547$	5.53927e10	−	5.53927e10i	0.618732	−	0.618732i	0.945206	+	0.326474i	$0.105860\pi$
$548$		−	1.13542e10i		−	0.125902i
$549$	−9.52964e10	+	9.52964e10i	−1.04903	+	1.04903i
$550$	−2.18998e10	+	2.18998e10i	−0.239326	+	0.239326i
$551$	3.60649e10			0.391272
$552$	−1.21807e11			−1.31195
$553$	3.93140e10	+	3.93140e10i	0.420385	+	0.420385i
$554$			1.60353e11i			1.70231i
$555$	4.62645e10	+	3.96087e10i	0.487614	+	0.417463i
$556$	1.33712e10			0.139918
$557$	8.39215e10	−	8.39215e10i	0.871872	−	0.871872i	−0.120804	−	0.992676i	$-0.538547\pi$
$557$	8.39215e10	−	8.39215e10i	0.871872	−	0.871872i	0.992676	+	0.120804i	$0.0385474\pi$
$558$		−	7.55612e10i		−	0.779403i
$559$			7.21658e10i			0.739067i
$560$	3.51887e10	+	3.51887e10i	0.357808	+	0.357808i
$561$	−5.73409e10	−	5.73409e10i	−0.578913	−	0.578913i
$562$	−1.86168e11			−1.86621
$563$	1.89446e9	+	1.89446e9i	0.0188561	+	0.0188561i	0.716472	−	0.697616i	$-0.245756\pi$
$563$	1.89446e9	+	1.89446e9i	0.0188561	+	0.0188561i	−0.697616	+	0.716472i	$0.745756\pi$
$564$	−4.04551e9			−0.0399813
$565$	−5.36255e10			−0.526232
$566$			1.70742e11i			1.66370i
$567$	1.14749e10			0.111024
$568$	−7.87225e10	−	7.87225e10i	−0.756320	−	0.756320i
$569$	1.11769e11	−	1.11769e11i	1.06628	−	1.06628i	0.0686399	−	0.997642i	$-0.478134\pi$
$569$	1.11769e11	−	1.11769e11i	1.06628	−	1.06628i	0.997642	−	0.0686399i	$-0.0218660\pi$
$570$	1.71594e10	−	1.71594e10i	0.162555	−	0.162555i
$571$	9.42031e10			0.886177			0.443089	−	0.896478i	$-0.353883\pi$
$571$	9.42031e10			0.886177			0.443089	+	0.896478i	$0.353883\pi$
$572$	3.33098e9	+	3.33098e9i	0.0311163	+	0.0311163i
$573$	−1.80590e11	+	1.80590e11i	−1.67523	+	1.67523i
$574$	1.50788e11	+	1.50788e11i	1.38905	+	1.38905i
$575$	−5.67006e10	+	5.67006e10i	−0.518700	+	0.518700i
$576$		−	1.49712e11i		−	1.36009i
$577$	1.33824e11	+	1.33824e11i	1.20735	+	1.20735i	0.971883	+	0.235464i	$0.0756611\pi$
$577$	1.33824e11	+	1.33824e11i	1.20735	+	1.20735i	0.235464	+	0.971883i	$0.424339\pi$
$578$	6.52140e10	+	6.52140e10i	0.584291	+	0.584291i
$579$	−1.98729e11	+	1.98729e11i	−1.76826	+	1.76826i
$580$		−	5.85087e9i		−	0.0517021i
$581$	−1.20479e11			−1.05732
$582$		−	1.85931e11i		−	1.62054i
$583$		−	7.54898e10i		−	0.653453i
$584$	−6.12044e10	+	6.12044e10i	−0.526176	+	0.526176i
$585$		−	7.57339e10i		−	0.646646i
$586$	−8.68476e10	+	8.68476e10i	−0.736491	+	0.736491i
$587$	−4.08341e10	+	4.08341e10i	−0.343931	+	0.343931i	−0.857843	−	0.513912i	$-0.828196\pi$
$587$	−4.08341e10	+	4.08341e10i	−0.343931	+	0.343931i	0.513912	+	0.857843i	$0.328196\pi$
$588$	−6.94675e9			−0.0581129
$589$	1.91910e10			0.159454
$590$	1.77928e10	+	1.77928e10i	0.146838	+	0.146838i
$591$		−	2.28234e10i		−	0.187081i
$592$	−1.04366e10	−	1.34652e11i	−0.0849711	−	1.09629i
$593$	−1.25284e11			−1.01315			−0.506577	−	0.862195i	$-0.669089\pi$
$593$	−1.25284e11			−1.01315			−0.506577	+	0.862195i	$0.669089\pi$
$594$	3.26672e10	−	3.26672e10i	0.262401	−	0.262401i
$595$			7.70281e10i			0.614584i
$596$		−	1.70518e10i		−	0.135140i
$597$	1.75556e11	+	1.75556e11i	1.38203	+	1.38203i
$598$	8.55187e10	+	8.55187e10i	0.668738	+	0.668738i
$599$	5.95089e8			0.00462248			0.00231124	−	0.999997i	$-0.499264\pi$
$599$	5.95089e8			0.00462248			0.00231124	+	0.999997i	$0.499264\pi$
$600$	−1.15625e11	−	1.15625e11i	−0.892169	−	0.892169i
$601$	1.47926e11			1.13382			0.566912	−	0.823778i	$-0.308138\pi$
$601$	1.47926e11			1.13382			0.566912	+	0.823778i	$0.308138\pi$
$602$	1.14665e11			0.873061
$603$			1.75390e11i			1.32658i
$604$	−1.83264e10			−0.137699
$605$	−3.23690e10	−	3.23690e10i	−0.241606	−	0.241606i
$606$	2.29926e11	−	2.29926e11i	1.70489	−	1.70489i
$607$	−1.71488e11	+	1.71488e11i	−1.26322	+	1.26322i	−0.313698	+	0.949523i	$0.601568\pi$
$607$	−1.71488e11	+	1.71488e11i	−1.26322	+	1.26322i	−0.949523	+	0.313698i	$0.898432\pi$
$608$	−1.03622e10			−0.0758292
$609$	−2.06798e11	−	2.06798e11i	−1.50341	−	1.50341i
$610$	−3.89361e10	+	3.89361e10i	−0.281211	+	0.281211i
$611$	−2.24839e10	−	2.24839e10i	−0.161327	−	0.161327i
$612$	−2.33863e10	+	2.33863e10i	−0.166708	+	0.166708i
$613$		−	7.19703e10i		−	0.509696i	−0.966981	−	0.254848i	$-0.917975\pi$
$613$		−	7.19703e10i		−	0.509696i	0.966981	−	0.254848i	$-0.0820254\pi$
$614$	−1.20409e11	−	1.20409e11i	−0.847202	−	0.847202i
$615$	1.05156e11	+	1.05156e11i	0.735079	+	0.735079i
$616$	−4.18970e10	+	4.18970e10i	−0.290978	+	0.290978i
$617$			2.77034e9i			0.0191158i	0.999954	+	0.00955789i	$0.00304242\pi$
$617$			2.77034e9i			0.0191158i	−0.999954	+	0.00955789i	$0.996958\pi$
$618$	−2.82639e11			−1.93766
$619$			1.59496e11i			1.08639i	0.839606	+	0.543196i	$0.182786\pi$
$619$			1.59496e11i			1.08639i	−0.839606	+	0.543196i	$0.817214\pi$
$620$		−	3.11339e9i		−	0.0210701i
$621$	8.45785e10	−	8.45785e10i	0.568713	−	0.568713i
$622$		−	2.04933e11i		−	1.36915i
$623$	1.59351e10	−	1.59351e10i	0.105780	−	0.105780i
$624$	−1.94200e11	+	1.94200e11i	−1.28089	+	1.28089i
$625$	−8.32197e10			−0.545388
$626$	−6.47747e10			−0.421801
$627$	2.27512e10	+	2.27512e10i	0.147209	+	0.147209i
$628$			1.83264e10i			0.117825i
$629$	1.35954e11	−	1.58799e11i	0.868537	−	1.01449i
$630$	−1.20334e11			−0.763884
$631$	−4.21790e8	+	4.21790e8i	−0.00266059	+	0.00266059i	−0.708436	−	0.705775i	$-0.750599\pi$
$631$	−4.21790e8	+	4.21790e8i	−0.00266059	+	0.00266059i	0.705775	+	0.708436i	$0.250599\pi$
$632$		−	7.72106e10i		−	0.483959i
$633$			1.30120e11i			0.810458i
$634$	2.32629e11	+	2.32629e11i	1.43982	+	1.43982i
$635$	−6.93985e10	−	6.93985e10i	−0.426830	−	0.426830i
$636$	−5.03488e10			−0.307723
$637$	−3.86083e10	−	3.86083e10i	−0.234489	−	0.234489i
$638$	7.69245e10			0.464282
$639$	2.99785e11			1.79807
$640$		−	7.61577e10i		−	0.453935i
$641$	1.48229e11			0.878016			0.439008	−	0.898483i	$-0.355330\pi$
$641$	1.48229e11			0.878016			0.439008	+	0.898483i	$0.355330\pi$
$642$	2.83958e11	+	2.83958e11i	1.67153	+	1.67153i
$643$	1.49816e11	−	1.49816e11i	0.876423	−	0.876423i	−0.116739	−	0.993163i	$-0.537244\pi$
$643$	1.49816e11	−	1.49816e11i	0.876423	−	0.876423i	0.993163	+	0.116739i	$0.0372442\pi$
$644$	1.37031e10	−	1.37031e10i	0.0796665	−	0.0796665i
$645$	7.99648e10			0.462019
$646$	−5.88982e10	−	5.88982e10i	−0.338199	−	0.338199i
$647$	5.25501e10	−	5.25501e10i	0.299886	−	0.299886i	−0.541083	−	0.840969i	$-0.681986\pi$
$647$	5.25501e10	−	5.25501e10i	0.299886	−	0.299886i	0.840969	+	0.541083i	$0.181986\pi$
$648$	−1.12680e10	−	1.12680e10i	−0.0639068	−	0.0639068i
$649$	−2.35911e10	+	2.35911e10i	−0.132975	+	0.132975i
$650$			1.62357e11i			0.909529i
$651$	−1.10042e11	−	1.10042e11i	−0.612684	−	0.612684i
$652$	1.73491e10	+	1.73491e10i	0.0960034	+	0.0960034i
$653$	6.90382e10	−	6.90382e10i	0.379697	−	0.379697i	−0.491296	−	0.870993i	$-0.663477\pi$
$653$	6.90382e10	−	6.90382e10i	0.379697	−	0.379697i	0.870993	+	0.491296i	$0.163477\pi$
$654$		−	9.89071e10i		−	0.540650i
$655$	−1.04805e11			−0.569400
$656$		−	3.29776e11i		−	1.78075i
$657$		−	2.33074e11i		−	1.25093i
$658$	−3.57249e10	+	3.57249e10i	−0.190576	+	0.190576i
$659$			3.72507e11i			1.97512i	0.157245	+	0.987560i	$0.449739\pi$
$659$			3.72507e11i			1.97512i	−0.157245	+	0.987560i	$0.550261\pi$
$660$	3.69096e9	−	3.69096e9i	0.0194520	−	0.0194520i
$661$	−1.00419e11	+	1.00419e11i	−0.526031	+	0.526031i	−0.919387	−	0.393355i	$-0.871314\pi$
$661$	−1.00419e11	+	1.00419e11i	−0.526031	+	0.526031i	0.393355	+	0.919387i	$0.371314\pi$
$662$	3.19364e10			0.166285
$663$	−4.25104e11			−2.20009
$664$	1.18307e11	+	1.18307e11i	0.608609	+	0.608609i
$665$		−	3.05625e10i		−	0.156280i
$666$	2.48079e11	+	2.12389e11i	1.26093	+	1.07953i
$667$	1.99165e11			1.00626
$668$	−1.49179e8	+	1.49179e8i	−0.000749209	+	0.000749209i
$669$			3.39125e11i			1.69299i
$670$			7.16604e10i			0.355615i
$671$	−5.16245e10	−	5.16245e10i	−0.254663	−	0.254663i
$672$	5.94173e10	+	5.94173e10i	0.291364	+	0.291364i
$673$	1.45932e11			0.711361			0.355680	−	0.934608i	$-0.384249\pi$
$673$	1.45932e11			0.711361			0.355680	+	0.934608i	$0.384249\pi$
$674$	1.20847e11	+	1.20847e11i	0.585593	+	0.585593i
$675$	1.60572e11			0.773489
$676$	1.27327e9			0.00609724
$677$			4.88555e10i			0.232573i	0.993216	+	0.116286i	$0.0370991\pi$
$677$			4.88555e10i			0.232573i	−0.993216	+	0.116286i	$0.962901\pi$
$678$	−4.70236e11			−2.22535
$679$	−1.65581e11	−	1.65581e11i	−0.778989	−	0.778989i
$680$	7.56395e10	−	7.56395e10i	0.353763	−	0.353763i
$681$	3.52058e10	−	3.52058e10i	0.163691	−	0.163691i
$682$	4.09334e10			0.189208
$683$	−2.43988e11	−	2.43988e11i	−1.12121	−	1.12121i	−0.991560	−	0.129648i	$-0.958615\pi$
$683$	−2.43988e11	−	2.43988e11i	−1.12121	−	1.12121i	−0.129648	−	0.991560i	$-0.541385\pi$
$684$	9.27900e9	−	9.27900e9i	0.0423913	−	0.0423913i
$685$	−6.99235e10	−	6.99235e10i	−0.317586	−	0.317586i
$686$	1.28604e11	−	1.28604e11i	0.580708	−	0.580708i
$687$			1.80588e11i			0.810703i
$688$	−1.25387e11	−	1.25387e11i	−0.559628	−	0.559628i
$689$	−2.79826e11	−	2.79826e11i	−1.24169	−	1.24169i
$690$	9.47608e10	−	9.47608e10i	0.418054	−	0.418054i
$691$		−	3.08910e11i		−	1.35494i	−0.735551	−	0.677469i	$-0.763077\pi$
$691$		−	3.08910e11i		−	1.35494i	0.735551	−	0.677469i	$-0.236923\pi$
$692$	4.08325e10			0.178066
$693$		−	1.59549e11i		−	0.691767i
$694$		−	2.23355e11i		−	0.962850i
$695$	8.23453e10	−	8.23453e10i	0.352939	−	0.352939i
$696$			4.06141e11i			1.73077i
$697$	3.60940e11	−	3.60940e11i	1.52934	−	1.52934i
$698$	−1.12097e11	+	1.12097e11i	−0.472251	+	0.472251i
$699$	−5.15130e10			−0.215779
$700$	2.60153e10			0.108352
$701$	−1.62752e11	−	1.62752e11i	−0.673992	−	0.673992i	0.284642	−	0.958634i	$-0.408125\pi$
$701$	−1.62752e11	−	1.62752e11i	−0.673992	−	0.673992i	−0.958634	+	0.284642i	$0.908125\pi$
$702$		−	2.42182e11i		−	0.997226i
$703$	−5.39425e10	+	6.30070e10i	−0.220856	+	0.257969i
$704$	8.11027e10			0.330175
$705$	−2.49138e10	+	2.49138e10i	−0.100852	+	0.100852i
$706$		−	1.24821e11i		−	0.502424i
$707$		−	4.09520e11i		−	1.63907i
$708$	1.57344e10	+	1.57344e10i	0.0626205	+	0.0626205i
$709$	−8.93480e9	−	8.93480e9i	−0.0353590	−	0.0353590i	0.689206	−	0.724565i	$-0.257959\pi$
$709$	−8.93480e9	−	8.93480e9i	−0.0353590	−	0.0353590i	−0.724565	+	0.689206i	$0.757959\pi$
$710$	1.22486e11			0.482005
$711$	1.47013e11	+	1.47013e11i	0.575279	+	0.575279i
$712$	−3.12957e10			−0.121777
$713$	1.05980e11			0.410079
$714$			6.75452e11i			2.59897i
$715$	4.10269e10			0.156980
$716$	−2.50533e10	−	2.50533e10i	−0.0953264	−	0.0953264i
$717$	3.90394e10	−	3.90394e10i	0.147716	−	0.147716i
$718$	−1.71058e11	+	1.71058e11i	−0.643645	+	0.643645i
$719$	6.95880e10			0.260387			0.130193	−	0.991489i	$-0.458440\pi$
$719$	6.95880e10			0.260387			0.130193	+	0.991489i	$0.458440\pi$
$720$	1.31587e11	+	1.31587e11i	0.489646	+	0.489646i
$721$	−2.51704e11	+	2.51704e11i	−0.931426	+	0.931426i
$722$	−1.79267e11	−	1.79267e11i	−0.659708	−	0.659708i
$723$	2.25565e10	−	2.25565e10i	0.0825501	−	0.0825501i
$724$		−	1.04086e10i		−	0.0378826i
$725$	1.89057e11	+	1.89057e11i	0.684289	+	0.684289i
$726$	−2.83841e11	−	2.83841e11i	−1.02171	−	1.02171i
$727$	−1.88767e11	+	1.88767e11i	−0.675752	+	0.675752i	−0.959036	−	0.283284i	$-0.908576\pi$
$727$	−1.88767e11	+	1.88767e11i	−0.675752	+	0.675752i	0.283284	+	0.959036i	$0.408576\pi$
$728$			3.10608e11i			1.10583i
$729$	4.60192e11			1.62940
$730$		−	9.52288e10i		−	0.335334i
$731$		−	2.74473e11i		−	0.961237i
$732$	−3.44315e10	+	3.44315e10i	−0.119926	+	0.119926i
$733$			2.11590e11i			0.732957i	0.930426	+	0.366479i	$0.119437\pi$
$733$			2.11590e11i			0.732957i	−0.930426	+	0.366479i	$0.880563\pi$
$734$	1.37179e11	−	1.37179e11i	0.472612	−	0.472612i
$735$	−4.27808e10	+	4.27808e10i	−0.146588	+	0.146588i
$736$	−5.72240e10			−0.195015
$737$	−9.50129e10			−0.322042
$738$	5.63866e11	+	5.63866e11i	1.90086	+	1.90086i
$739$		−	2.97139e11i		−	0.996283i	−0.867096	−	0.498141i	$-0.834016\pi$
$739$		−	2.97139e11i		−	0.996283i	0.867096	−	0.498141i	$-0.165984\pi$
$740$	1.02217e10	+	8.75117e9i	0.0340876	+	0.0291836i
$741$	1.68669e11			0.559451
$742$	−4.44619e11	+	4.44619e11i	−1.46680	+	1.46680i
$743$			9.04390e10i			0.296757i	0.988931	+	0.148378i	$0.0474054\pi$
$743$			9.04390e10i			0.296757i	−0.988931	+	0.148378i	$0.952595\pi$
$744$			2.16117e11i			0.705339i
$745$	−1.05012e11	−	1.05012e11i	−0.340888	−	0.340888i
$746$	2.45537e10	+	2.45537e10i	0.0792795	+	0.0792795i
$747$	−4.50527e11			−1.44690
$748$	−1.26690e10	−	1.26690e10i	−0.0404701	−	0.0404701i
$749$	5.05758e11			1.60700
$750$	3.94093e11			1.24553
$751$			1.56148e11i			0.490880i	0.969412	+	0.245440i	$0.0789325\pi$
$751$			1.56148e11i			0.490880i	−0.969412	+	0.245440i	$0.921068\pi$
$752$	7.81312e10			0.244317
$753$	−2.66502e11	−	2.66502e11i	−0.828934	−	0.828934i
$754$	2.85144e11	−	2.85144e11i	0.882225	−	0.882225i
$755$	−1.12861e11	+	1.12861e11i	−0.347342	+	0.347342i
$756$	−3.88061e10			−0.118799
$757$	2.30275e11	+	2.30275e11i	0.701235	+	0.701235i	0.964676	−	0.263440i	$-0.0848572\pi$
$757$	2.30275e11	+	2.30275e11i	0.701235	+	0.701235i	−0.263440	+	0.964676i	$0.584857\pi$
$758$	1.61853e11	−	1.61853e11i	0.490280	−	0.490280i
$759$	1.25641e11	+	1.25641e11i	0.378586	+	0.378586i
$760$	−3.00115e10	+	3.00115e10i	−0.0899567	+	0.0899567i
$761$		−	2.43985e11i		−	0.727486i	−0.931499	−	0.363743i	$-0.881499\pi$
$761$		−	2.43985e11i		−	0.727486i	0.931499	−	0.363743i	$-0.118501\pi$
$762$	−6.08548e11	−	6.08548e11i	−1.80499	−	1.80499i
$763$	−8.80815e10	−	8.80815e10i	−0.259888	−	0.259888i
$764$	−3.98997e10	+	3.98997e10i	−0.117110	+	0.117110i
$765$			2.88044e11i			0.841033i
$766$	1.10367e10			0.0320572
$767$			1.74896e11i			0.505356i
$768$		−	1.85526e11i		−	0.533285i
$769$	−1.07727e11	+	1.07727e11i	−0.308049	+	0.308049i	−0.844152	−	0.536103i	$-0.819896\pi$
$769$	−1.07727e11	+	1.07727e11i	−0.308049	+	0.308049i	0.536103	+	0.844152i	$0.319896\pi$
$770$		−	6.51881e10i		−	0.185441i
$771$	−2.74035e11	+	2.74035e11i	−0.775512	+	0.775512i
$772$	−4.39074e10	+	4.39074e10i	−0.123614	+	0.123614i
$773$	−1.35425e11			−0.379297			−0.189649	−	0.981852i	$-0.560735\pi$
$773$	−1.35425e11			−0.379297			−0.189649	+	0.981852i	$0.560735\pi$
$774$	4.28786e11			1.19475
$775$	1.00602e11	+	1.00602e11i	0.278867	+	0.278867i
$776$			3.25192e11i			0.896794i
$777$	6.70595e11	−	5.19764e10i	1.83982	−	0.142601i
$778$	1.68901e11			0.461014
$779$	−1.43211e11	+	1.43211e11i	−0.388889	+	0.388889i
$780$		−	2.73634e10i		−	0.0739250i
$781$			1.62401e11i			0.436500i
$782$	−3.25259e11	−	3.25259e11i	−0.869766	−	0.869766i
$783$	−2.82010e11	−	2.82010e11i	−0.750269	−	0.750269i
$784$	1.34163e11			0.355115
$785$	1.12861e11	+	1.12861e11i	0.297212	+	0.297212i
$786$	−9.19026e11			−2.40789
$787$	−1.88393e11			−0.491094			−0.245547	−	0.969385i	$-0.578968\pi$
$787$	−1.88393e11			−0.491094			−0.245547	+	0.969385i	$0.578968\pi$
$788$		−	5.04261e9i		−	0.0130783i
$789$	−7.19929e11			−1.85773
$790$	6.00665e10	+	6.00665e10i	0.154214	+	0.154214i
$791$	−4.18768e11	+	4.18768e11i	−1.06971	+	1.06971i
$792$	−1.56672e11	+	1.56672e11i	−0.398191	+	0.398191i
$793$	−3.82724e11			−0.967816
$794$	5.35952e11	+	5.35952e11i	1.34848	+	1.34848i
$795$	−3.10067e11	+	3.10067e11i	−0.776225	+	0.776225i
$796$	3.87875e10	+	3.87875e10i	0.0966138	+	0.0966138i
$797$	−9.13400e10	+	9.13400e10i	−0.226375	+	0.226375i	−0.811176	−	0.584802i	$-0.801172\pi$
$797$	−9.13400e10	+	9.13400e10i	−0.226375	+	0.226375i	0.584802	+	0.811176i	$0.301172\pi$
$798$		−	2.67999e11i		−	0.660879i
$799$	8.55147e10	+	8.55147e10i	0.209823	+	0.209823i
$800$	−5.43197e10	−	5.43197e10i	−0.132616	−	0.132616i
$801$	5.95889e10	−	5.95889e10i	0.144756	−	0.144756i
$802$			4.10261e11i			0.991659i
$803$	1.26262e11			0.303675
$804$			6.33700e10i			0.151656i
$805$		−	1.68778e11i		−	0.401914i
$806$	1.51732e11	−	1.51732e11i	0.359532	−	0.359532i
$807$		−	3.36138e11i		−	0.792543i
$808$	−4.02137e11	+	4.02137e11i	−0.943472	+	0.943472i
$809$	−4.63693e11	+	4.63693e11i	−1.08252	+	1.08252i	−0.0862475	+	0.996274i	$0.527488\pi$
$809$	−4.63693e11	+	4.63693e11i	−1.08252	+	1.08252i	−0.996274	+	0.0862475i	$0.972512\pi$
$810$	1.75321e10			0.0407280
$811$	−2.89735e11			−0.669757			−0.334878	−	0.942261i	$-0.608695\pi$
$811$	−2.89735e11			−0.669757			−0.334878	+	0.942261i	$0.608695\pi$
$812$	−4.56902e10	−	4.56902e10i	−0.105099	−	0.105099i
$813$		−	1.38062e12i		−	3.16017i
$814$	−1.15056e11	+	1.34390e11i	−0.262067	+	0.306105i
$815$	2.13685e11			0.484332
$816$	7.38613e11	−	7.38613e11i	1.66593	−	1.66593i
$817$			1.08903e11i			0.244428i
$818$		−	8.15123e11i		−	1.82058i
$819$	−5.91416e11	−	5.91416e11i	−1.31449	−	1.31449i
$820$	2.32333e10	+	2.32333e10i	0.0513872	+	0.0513872i
$821$	4.48561e10			0.0987300			0.0493650	−	0.998781i	$-0.484280\pi$
$821$	4.48561e10			0.0987300			0.0493650	+	0.998781i	$0.484280\pi$
$822$	−6.13152e11	−	6.13152e11i	−1.34301	−	1.34301i
$823$	6.69621e11			1.45959			0.729793	−	0.683668i	$-0.239617\pi$
$823$	6.69621e11			1.45959			0.729793	+	0.683668i	$0.239617\pi$
$824$	4.94332e11			1.07228
$825$			2.38529e11i			0.514903i
$826$	2.77893e11			0.596978
$827$	−1.17329e11	−	1.17329e11i	−0.250833	−	0.250833i	0.570479	−	0.821312i	$-0.306758\pi$
$827$	−1.17329e11	−	1.17329e11i	−0.250833	−	0.250833i	−0.821312	+	0.570479i	$0.806758\pi$
$828$	5.12423e10	−	5.12423e10i	0.109020	−	0.109020i
$829$	2.75939e10	−	2.75939e10i	0.0584244	−	0.0584244i	−0.677291	−	0.735715i	$-0.736846\pi$
$829$	2.75939e10	−	2.75939e10i	0.0584244	−	0.0584244i	0.735715	+	0.677291i	$0.236846\pi$
$830$	−1.84076e11			−0.387868
$831$	8.73271e11	+	8.73271e11i	1.83124	+	1.83124i
$832$	3.00632e11	−	3.00632e11i	0.627397	−	0.627397i
$833$	1.46842e11	+	1.46842e11i	0.304979	+	0.304979i
$834$	7.22078e11	−	7.22078e11i	1.49252	−	1.49252i
$835$			1.83741e9i			0.00377972i
$836$	5.02667e9	+	5.02667e9i	0.0102909	+	0.0102909i
$837$	−1.50064e11	−	1.50064e11i	−0.305756	−	0.305756i
$838$	−1.47423e11	+	1.47423e11i	−0.298944	+	0.298944i
$839$		−	8.33651e11i		−	1.68243i	−0.540703	−	0.841214i	$-0.681842\pi$
$839$		−	8.33651e11i		−	1.68243i	0.540703	−	0.841214i	$-0.318158\pi$
$840$	3.44176e11			0.691295
$841$		−	1.63828e11i		−	0.327494i
$842$			4.65282e11i			0.925694i
$843$	−1.01386e12	+	1.01386e12i	−2.00755	+	2.00755i
$844$			2.87489e10i			0.0566567i
$845$	7.84129e9	−	7.84129e9i	0.0153801	−	0.0153801i
$846$	−1.33592e11	+	1.33592e11i	−0.260795	+	0.260795i
$847$	−5.05548e11			−0.982264
$848$	9.72390e11			1.88043
$849$	9.29848e11	+	9.29848e11i	1.78970	+	1.78970i
$850$		−	6.17502e11i		−	1.18294i
$851$	−2.97892e11	+	3.47949e11i	−0.567989	+	0.663434i
$852$	1.08315e11			0.205556
$853$	3.00117e11	−	3.00117e11i	0.566885	−	0.566885i	−0.364369	−	0.931255i	$-0.618715\pi$
$853$	3.00117e11	−	3.00117e11i	0.566885	−	0.566885i	0.931255	+	0.364369i	$0.118715\pi$
$854$			6.08114e11i			1.14328i
$855$		−	1.14287e11i		−	0.213862i
$856$	−4.96640e11	−	4.96640e11i	−0.925011	−	0.925011i
$857$	7.32781e11	+	7.32781e11i	1.35847	+	1.35847i	0.875803	+	0.482669i	$0.160333\pi$
$857$	7.32781e11	+	7.32781e11i	1.35847	+	1.35847i	0.482669	+	0.875803i	$0.339667\pi$
$858$	3.59761e11			0.663843
$859$	−4.18137e11	−	4.18137e11i	−0.767974	−	0.767974i	0.209776	−	0.977750i	$-0.432727\pi$
$859$	−4.18137e11	−	4.18137e11i	−0.767974	−	0.767974i	−0.977750	+	0.209776i	$0.932727\pi$
$860$	1.76675e10			0.0322984
$861$	1.64236e12			2.98851
$862$			1.00902e12i			1.82756i
$863$	3.55139e11			0.640259			0.320130	−	0.947374i	$-0.396274\pi$
$863$	3.55139e11			0.640259			0.320130	+	0.947374i	$0.396274\pi$
$864$	8.10270e10	+	8.10270e10i	0.145403	+	0.145403i
$865$	2.51462e11	−	2.51462e11i	0.449168	−	0.449168i
$866$	−1.12167e11	+	1.12167e11i	−0.199432	+	0.199432i
$867$	7.10300e11			1.25709
$868$	−2.43129e10	−	2.43129e10i	−0.0428309	−	0.0428309i
$869$	−7.96408e10	+	7.96408e10i	−0.139655	+	0.139655i
$870$	−3.15960e11	−	3.15960e11i	−0.551513	−	0.551513i
$871$	−3.52195e11	+	3.52195e11i	−0.611942	+	0.611942i
$872$			1.72987e11i			0.299191i
$873$	−6.19184e11	−	6.19184e11i	−1.06601	−	1.06601i
$874$	1.29053e11	+	1.29053e11i	0.221169	+	0.221169i
$875$	3.50959e11	−	3.50959e11i	0.598720	−	0.598720i
$876$		−	8.42118e10i		−	0.143007i
$877$	7.10020e11			1.20025			0.600125	−	0.799906i	$-0.295117\pi$
$877$	7.10020e11			1.20025			0.600125	+	0.799906i	$0.295117\pi$
$878$			1.02987e11i			0.173303i
$879$			9.45930e11i			1.58454i
$880$	−7.12839e10	+	7.12839e10i	−0.118867	+	0.118867i
$881$		−	4.98158e11i		−	0.826920i	−0.910522	−	0.413460i	$-0.864320\pi$
$881$		−	4.98158e11i		−	0.826920i	0.910522	−	0.413460i	$-0.135680\pi$
$882$	−2.29398e11	+	2.29398e11i	−0.379067	+	0.379067i
$883$	4.44923e11	−	4.44923e11i	0.731884	−	0.731884i	−0.239108	−	0.970993i	$-0.576855\pi$
$883$	4.44923e11	−	4.44923e11i	0.731884	−	0.731884i	0.970993	+	0.239108i	$0.0768551\pi$
$884$	−9.39228e10			−0.153802
$885$	1.93797e11			0.315917
$886$	−3.51245e11	−	3.51245e11i	−0.570001	−	0.570001i
$887$		−	6.01168e11i		−	0.971184i	−0.874186	−	0.485592i	$-0.838604\pi$
$887$		−	6.01168e11i		−	0.971184i	0.874186	−	0.485592i	$-0.161396\pi$
$888$	−7.09545e11	−	6.07467e11i	−1.14111	−	0.976946i
$889$	−1.08388e12			−1.73530
$890$	2.43467e10	−	2.43467e10i	0.0388044	−	0.0388044i
$891$			2.32454e10i			0.0368830i
$892$			7.49265e10i			0.118352i
$893$	−3.39297e10	−	3.39297e10i	−0.0533549	−	0.0533549i
$894$	−9.20835e11	−	9.20835e11i	−1.44156	−	1.44156i
$895$	−3.08576e11			−0.480917
$896$	−5.94725e11	−	5.94725e11i	−0.922751	−	0.922751i
$897$	9.31456e11			1.43877
$898$	−5.17659e11			−0.796046
$899$		−	3.53370e11i		−	0.540992i
$900$	9.72833e10			0.148275
$901$	1.06428e12	+	1.06428e12i	1.61495	+	1.61495i
$902$	−3.05460e11	+	3.05460e11i	−0.461454	+	0.461454i
$903$	6.24456e11	−	6.24456e11i	0.939184	−	0.939184i
$904$	8.22438e11			1.23149
$905$	−6.41005e10	−	6.41005e10i	−0.0955580	−	0.0955580i
$906$	−9.89670e11	+	9.89670e11i	−1.46885	+	1.46885i
$907$	−2.09584e11	−	2.09584e11i	−0.309691	−	0.309691i	0.535098	−	0.844790i	$-0.320275\pi$
$907$	−2.09584e11	−	2.09584e11i	−0.309691	−	0.309691i	−0.844790	+	0.535098i	$0.820275\pi$
$908$	7.77840e9	−	7.77840e9i	0.0114432	−	0.0114432i
$909$		−	1.53139e12i		−	2.24300i
$910$	−2.41640e11	−	2.41640e11i	−0.352373	−	0.352373i
$911$	−5.99696e11	−	5.99696e11i	−0.870678	−	0.870678i	0.121868	−	0.992546i	$-0.461112\pi$
$911$	−5.99696e11	−	5.99696e11i	−0.870678	−	0.870678i	−0.992546	+	0.121868i	$0.961112\pi$
$912$	−2.93060e11	+	2.93060e11i	−0.423621	+	0.423621i
$913$		−	2.44062e11i		−	0.351250i
$914$	1.18906e12			1.70380
$915$			4.24086e11i			0.605019i
$916$			3.98992e10i			0.0566738i
$917$	−8.18437e11	+	8.18437e11i	−1.15747	+	1.15747i
$918$			9.21108e11i			1.29700i
$919$	4.01911e11	−	4.01911e11i	0.563466	−	0.563466i	−0.366824	−	0.930290i	$-0.619555\pi$
$919$	4.01911e11	−	4.01911e11i	0.563466	−	0.563466i	0.930290	+	0.366824i	$0.119555\pi$
$920$	−1.65736e11	+	1.65736e11i	−0.231347	+	0.231347i
$921$	−1.31148e12			−1.82273
$922$	−8.29392e11			−1.14772
$923$	6.01989e11	+	6.01989e11i	0.829434	+	0.829434i
$924$		−	5.76464e10i		−	0.0790833i
$925$	−6.13063e11	+	4.75172e10i	−0.837409	+	0.0649058i
$926$	−7.21063e11			−0.980685
$927$	−9.41237e11	+	9.41237e11i	−1.27462	+	1.27462i
$928$			1.90802e11i			0.257271i
$929$		−	3.85642e11i		−	0.517751i	−0.965911	−	0.258876i	$-0.916648\pi$
$929$		−	3.85642e11i		−	0.517751i	0.965911	−	0.258876i	$-0.0833520\pi$
$930$	−1.68130e11	−	1.68130e11i	−0.224757	−	0.224757i
$931$	−5.82625e10	−	5.82625e10i	−0.0775515	−	0.0775515i
$932$	−1.13813e10			−0.0150844
$933$	−1.11605e12	−	1.11605e12i	−1.47284	−	1.47284i
$934$	2.48935e11			0.327113
$935$	−1.56041e11			−0.204170
$936$			1.16151e12i			1.51328i
$937$	1.18169e12			1.53301			0.766504	−	0.642239i	$-0.221994\pi$
$937$	1.18169e12			1.53301			0.766504	+	0.642239i	$0.221994\pi$
$938$	5.59606e11	+	5.59606e11i	0.722888	+	0.722888i
$939$	−3.52758e11	+	3.52758e11i	−0.453748	+	0.453748i
$940$	−5.50447e9	+	5.50447e9i	−0.00705025	+	0.00705025i
$941$	−5.72144e11			−0.729704			−0.364852	−	0.931066i	$-0.618880\pi$
$941$	−5.72144e11			−0.729704			−0.364852	+	0.931066i	$0.618880\pi$
$942$	9.89668e11	+	9.89668e11i	1.25686	+	1.25686i
$943$	−7.90865e11	+	7.90865e11i	−1.00013	+	1.00013i
$944$	−3.03879e11	−	3.03879e11i	−0.382660	−	0.382660i
$945$	−2.38983e11	+	2.38983e11i	−0.299668	+	0.299668i
$946$			2.32284e11i			0.290038i
$947$	−2.33646e11	−	2.33646e11i	−0.290508	−	0.290508i	0.546773	−	0.837281i	$-0.315856\pi$
$947$	−2.33646e11	−	2.33646e11i	−0.290508	−	0.290508i	−0.837281	+	0.546773i	$0.815856\pi$
$948$	5.31174e10	+	5.31174e10i	0.0657663	+	0.0657663i
$949$	4.68028e11	−	4.68028e11i	0.577042	−	0.577042i
$950$			2.45007e11i			0.300804i
$951$	2.53376e12			3.09773
$952$		−	1.18136e12i		−	1.43825i
$953$			1.38887e11i			0.168379i	0.996450	+	0.0841896i	$0.0268302\pi$
$953$			1.38887e11i			0.168379i	−0.996450	+	0.0841896i	$0.973170\pi$
$954$	−1.66264e12	+	1.66264e12i	−2.00726	+	2.00726i
$955$			4.91435e11i			0.590817i
$956$	8.62540e9	−	8.62540e9i	0.0103264	−	0.0103264i
$957$	4.18925e11	−	4.18925e11i	0.499446	−	0.499446i
$958$	4.35369e11			0.516886
$959$	−1.09208e12			−1.29116
$960$	−3.33122e11	−	3.33122e11i	−0.392210	−	0.392210i
$961$			6.64854e11i			0.779530i
$962$	7.16677e10	+	9.24651e11i	0.0836803	+	1.07964i
$963$	1.89126e12			2.19911
$964$	4.98364e9	−	4.98364e9i	0.00577084	−	0.00577084i
$965$			5.40797e11i			0.623627i
$966$		−	1.48000e12i		−	1.69962i
$967$	7.57436e11	+	7.57436e11i	0.866243	+	0.866243i	0.992054	−	0.125811i	$-0.0401532\pi$
$967$	7.57436e11	+	7.57436e11i	0.866243	+	0.866243i	−0.125811	+	0.992054i	$0.540153\pi$
$968$	4.96434e11	+	4.96434e11i	0.565406	+	0.565406i
$969$	−6.41510e11			−0.727626
$970$	−2.52985e11	−	2.52985e11i	−0.285765	−	0.285765i
$971$	−7.63567e11			−0.858955			−0.429477	−	0.903078i	$-0.641302\pi$
$971$	−7.63567e11			−0.858955			−0.429477	+	0.903078i	$0.641302\pi$
$972$	1.07698e11			0.120655
$973$		−	1.28609e12i		−	1.43490i
$974$	−9.65762e11			−1.07309
$975$	8.84181e11	+	8.84181e11i	0.978415	+	0.978415i
$976$	6.64979e11	−	6.64979e11i	0.732839	−	0.732839i
$977$	−4.90903e11	+	4.90903e11i	−0.538788	+	0.538788i	−0.923173	−	0.384385i	$-0.874413\pi$
$977$	−4.90903e11	+	4.90903e11i	−0.538788	+	0.538788i	0.384385	+	0.923173i	$0.374413\pi$
$978$	1.87378e12			2.04816
$979$	3.22808e10	+	3.22808e10i	0.0351409	+	0.0351409i
$980$	−9.45202e9	+	9.45202e9i	−0.0102476	+	0.0102476i
$981$	−3.29378e11	−	3.29378e11i	−0.355647	−	0.355647i
$982$	9.37353e11	−	9.37353e11i	1.00799	−	1.00799i
$983$			5.54368e11i			0.593723i	0.954921	+	0.296862i	$0.0959400\pi$
$983$			5.54368e11i			0.593723i	−0.954921	+	0.296862i	$0.904060\pi$
$984$	−1.61275e12	−	1.61275e12i	−1.72023	−	1.72023i
$985$	−3.10543e10	−	3.10543e10i	−0.0329896	−	0.0329896i
$986$	−1.08451e12	+	1.08451e12i	−1.14743	+	1.14743i
$987$			3.89110e11i			0.410019i
$988$	3.72658e10			0.0391095
$989$			6.01405e11i			0.628611i
$990$		−	2.43769e11i		−	0.253768i
$991$	4.93971e10	−	4.93971e10i	0.0512161	−	0.0512161i	−0.681035	−	0.732251i	$-0.738470\pi$
$991$	4.93971e10	−	4.93971e10i	0.0512161	−	0.0512161i	0.732251	+	0.681035i	$0.238470\pi$
$992$			1.01530e11i			0.104845i
$993$	1.73923e11	−	1.73923e11i	0.178879	−	0.178879i
$994$	9.56506e11	−	9.56506e11i	0.979810	−	0.979810i
$995$	4.77736e11			0.487412
$996$	−1.62780e11			−0.165411
$997$	5.64619e11	+	5.64619e11i	0.571446	+	0.571446i	0.932532	−	0.361086i	$-0.117594\pi$
$997$	5.64619e11	+	5.64619e11i	0.571446	+	0.571446i	−0.361086	+	0.932532i	$0.617594\pi$
$998$		−	1.90317e12i		−	1.91847i
$999$	9.14486e11	−	7.08798e10i	0.918153	−	0.0711641i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.9.d.a.6.20	✓	50
37.31	odd	4	inner	37.9.d.a.31.20	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.9.d.a.6.20	✓	50	1.1	even	1	trivial
37.9.d.a.31.20	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)

\(f(q)\)	\(=\)	\(q+(11.9313 - 11.9313i) q^{2} -129.954i q^{3} -28.7121i q^{4} +(-176.820 - 176.820i) q^{5} +(-1550.52 - 1550.52i) q^{6} -2761.63 q^{7} +(2711.84 + 2711.84i) q^{8} -10327.0 q^{9} +O(q^{10})\)	\(q+(11.9313 - 11.9313i) q^{2} -129.954i q^{3} -28.7121i q^{4} +(-176.820 - 176.820i) q^{5} +(-1550.52 - 1550.52i) q^{6} -2761.63 q^{7} +(2711.84 + 2711.84i) q^{8} -10327.0 q^{9} -4219.39 q^{10} -5594.40i q^{11} -3731.25 q^{12} +(-20737.4 - 20737.4i) q^{13} +(-32949.8 + 32949.8i) q^{14} +(-22978.5 + 22978.5i) q^{15} +72061.9 q^{16} +(78871.9 + 78871.9i) q^{17} +(-123215. + 123215. i) q^{18} +(-31294.0 - 31294.0i) q^{19} +(-5076.88 + 5076.88i) q^{20} +358884. i q^{21} +(-66748.5 - 66748.5i) q^{22} +(-172818. - 172818. i) q^{23} +(352414. - 352414. i) q^{24} -328094. i q^{25} -494848. q^{26} +489407. i q^{27} +79292.1i q^{28} +(-576226. + 576226. i) q^{29} +548327. i q^{30} +(-306624. + 306624. i) q^{31} +(165561. - 165561. i) q^{32} -727014. q^{33} +1.88209e6 q^{34} +(488312. + 488312. i) q^{35} +296510. i q^{36} +(-144828. - 1.86856e6i) q^{37} -746758. q^{38} +(-2.69490e6 + 2.69490e6i) q^{39} -959017. i q^{40} -4.57629e6i q^{41} +(4.28195e6 + 4.28195e6i) q^{42} +(-1.73999e6 - 1.73999e6i) q^{43} -160627. q^{44} +(1.82602e6 + 1.82602e6i) q^{45} -4.12389e6 q^{46} +1.08422e6 q^{47} -9.36472e6i q^{48} +1.86178e6 q^{49} +(-3.91459e6 - 3.91459e6i) q^{50} +(1.02497e7 - 1.02497e7i) q^{51} +(-595414. + 595414. i) q^{52} +1.34938e7 q^{53} +(5.83927e6 + 5.83927e6i) q^{54} +(-989203. + 989203. i) q^{55} +(-7.48909e6 - 7.48909e6i) q^{56} +(-4.06678e6 + 4.06678e6i) q^{57} +1.37503e7i q^{58} +(-4.21692e6 - 4.21692e6i) q^{59} +(659761. + 659761. i) q^{60} +(9.22788e6 - 9.22788e6i) q^{61} +7.31685e6i q^{62} +2.85193e7 q^{63} +1.44971e7i q^{64} +7.33357e6i q^{65} +(-8.67422e6 + 8.67422e6i) q^{66} -1.69836e7i q^{67} +(2.26458e6 - 2.26458e6i) q^{68} +(-2.24584e7 + 2.24584e7i) q^{69} +1.16524e7 q^{70} -2.90292e7 q^{71} +(-2.80052e7 - 2.80052e7i) q^{72} +2.25693e7i q^{73} +(-2.40223e7 - 2.05663e7i) q^{74} -4.26371e7 q^{75} +(-898518. + 898518. i) q^{76} +1.54496e7i q^{77} +6.43074e7i q^{78} +(-1.42358e7 - 1.42358e7i) q^{79} +(-1.27420e7 - 1.27420e7i) q^{80} -4.15512e6 q^{81} +(-5.46011e7 - 5.46011e7i) q^{82} +4.36261e7 q^{83} +1.03043e7 q^{84} -2.78923e7i q^{85} -4.15208e7 q^{86} +(7.48829e7 + 7.48829e7i) q^{87} +(1.51711e7 - 1.51711e7i) q^{88} +(-5.77020e6 + 5.77020e6i) q^{89} +4.35737e7 q^{90} +(5.72688e7 + 5.72688e7i) q^{91} +(-4.96197e6 + 4.96197e6i) q^{92} +(3.98470e7 + 3.98470e7i) q^{93} +(1.29362e7 - 1.29362e7i) q^{94} +1.10668e7i q^{95} +(-2.15153e7 - 2.15153e7i) q^{96} +(5.99578e7 + 5.99578e7i) q^{97} +(2.22134e7 - 2.22134e7i) q^{98} +5.77734e7i 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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