LMFDB - Embedded newform 48.8.k.a.11.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,8,Mod(11,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

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

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

chi := DirichletCharacter("48.11");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	48.k (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:	$14.9944812232$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.17
Character	$\chi$	$=$	48.11
Dual form			48.8.k.a.35.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.86971 + 8.98928i) q^{2} +(34.0729 + 32.0318i) q^{3} +(-33.6142 - 123.507i) q^{4} +(201.123 - 201.123i) q^{5} +(-522.014 + 86.2416i) q^{6} -1025.82 q^{7} +(1341.16 + 546.292i) q^{8} +(134.926 + 2182.83i) q^{9} +O(q^{10})$	\(q+(-6.86971 + 8.98928i) q^{2} +(34.0729 + 32.0318i) q^{3} +(-33.6142 - 123.507i) q^{4} +(201.123 - 201.123i) q^{5} +(-522.014 + 86.2416i) q^{6} -1025.82 q^{7} +(1341.16 + 546.292i) q^{8} +(134.926 + 2182.83i) q^{9} +(426.294 + 3189.61i) q^{10} +(3756.76 + 3756.76i) q^{11} +(2810.83 - 5284.98i) q^{12} +(-4614.47 + 4614.47i) q^{13} +(7047.08 - 9221.38i) q^{14} +(13295.2 - 410.511i) q^{15} +(-14124.2 + 8303.21i) q^{16} +25813.8i q^{17} +(-20549.0 - 13782.5i) q^{18} +(7259.43 + 7259.43i) q^{19} +(-31600.8 - 18079.6i) q^{20} +(-34952.7 - 32858.9i) q^{21} +(-59578.4 + 7962.71i) q^{22} +7050.99i q^{23} +(28198.6 + 61573.6i) q^{24} -2775.87i q^{25} +(-9780.69 - 73180.8i) q^{26} +(-65322.8 + 78697.4i) q^{27} +(34482.1 + 126696. i) q^{28} +(-125449. - 125449. i) q^{29} +(-87643.8 + 122334. i) q^{30} +271011. i q^{31} +(22389.0 - 184007. i) q^{32} +(7667.89 + 248339. i) q^{33} +(-232048. - 177333. i) q^{34} +(-206316. + 206316. i) q^{35} +(265061. - 90038.6i) q^{36} +(-149832. - 149832. i) q^{37} +(-115127. + 15386.9i) q^{38} +(-305038. + 9418.56i) q^{39} +(379610. - 159867. i) q^{40} +369802. q^{41} +(535492. - 88468.3i) q^{42} +(690229. - 690229. i) q^{43} +(337707. - 590268. i) q^{44} +(466155. + 411881. i) q^{45} +(-63383.3 - 48438.2i) q^{46} +358611. q^{47} +(-747218. - 169508. i) q^{48} +228763. q^{49} +(24953.1 + 19069.4i) q^{50} +(-826863. + 879552. i) q^{51} +(725033. + 414809. i) q^{52} +(-738128. + 738128. i) q^{53} +(-258684. - 1.12783e6i) q^{54} +1.51114e6 q^{55} +(-1.37579e6 - 560398. i) q^{56} +(14817.2 + 479883. i) q^{57} +(1.98950e6 - 265899. i) q^{58} +(1.62939e6 + 1.62939e6i) q^{59} +(-497608. - 1.62825e6i) q^{60} +(-1.07174e6 + 1.07174e6i) q^{61} +(-2.43619e6 - 1.86177e6i) q^{62} +(-138410. - 2.23919e6i) q^{63} +(1.50028e6 + 1.46533e6i) q^{64} +1.85615e6i q^{65} +(-2.28507e6 - 1.63709e6i) q^{66} +(-958120. - 958120. i) q^{67} +(3.18820e6 - 867711. i) q^{68} +(-225856. + 240248. i) q^{69} +(-437301. - 3.27196e6i) q^{70} -413019. i q^{71} +(-1.01151e6 + 3.00124e6i) q^{72} +3.94535e6i q^{73} +(2.37619e6 - 317580. i) q^{74} +(88916.3 - 94582.1i) q^{75} +(652573. - 1.14061e6i) q^{76} +(-3.85376e6 - 3.85376e6i) q^{77} +(2.01086e6 - 2.80678e6i) q^{78} -3.80043e6i q^{79} +(-1.17073e6 + 4.51066e6i) q^{80} +(-4.74656e6 + 589042. i) q^{81} +(-2.54043e6 + 3.32425e6i) q^{82} +(539140. - 539140. i) q^{83} +(-2.88341e6 + 5.42144e6i) q^{84} +(5.19175e6 + 5.19175e6i) q^{85} +(1.46299e6 + 1.09463e7i) q^{86} +(-256054. - 8.29280e6i) q^{87} +(2.98613e6 + 7.09071e6i) q^{88} +5.01486e6 q^{89} +(-6.90486e6 + 1.36089e6i) q^{90} +(4.73361e6 - 4.73361e6i) q^{91} +(870849. - 237013. i) q^{92} +(-8.68097e6 + 9.23413e6i) q^{93} +(-2.46355e6 + 3.22366e6i) q^{94} +2.92008e6 q^{95} +(6.65693e6 - 5.55248e6i) q^{96} -1.16410e7 q^{97} +(-1.57154e6 + 2.05642e6i) q^{98} +(-7.69350e6 + 8.70726e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 2 q^{3} - 4 q^{4} + 172 q^{6} - 8 q^{7}+O(q^{10}) $ 108 * q - 2 * q^3 - 4 * q^4 + 172 * q^6 - 8 * q^7	$ 108 q - 2 q^{3} - 4 q^{4} + 172 q^{6} - 8 q^{7} - 6504 q^{10} + 12016 q^{12} - 4 q^{13} - 55280 q^{16} + 21172 q^{18} - 60588 q^{19} - 4376 q^{21} - 212744 q^{22} - 317304 q^{24} + 238042 q^{27} + 219736 q^{28} - 503852 q^{30} - 4 q^{33} - 364856 q^{34} + 867620 q^{36} - 4 q^{37} - 283948 q^{39} + 390392 q^{40} - 3022344 q^{42} + 752844 q^{43} - 156252 q^{45} - 1166824 q^{46} + 358320 q^{48} + 9882508 q^{49} + 1121592 q^{51} - 4458688 q^{52} + 203816 q^{54} + 4191000 q^{55} + 4975544 q^{58} - 4390240 q^{60} - 2279892 q^{61} + 4781432 q^{64} + 1457476 q^{66} + 1552540 q^{67} + 4372 q^{69} - 9366152 q^{70} - 1660280 q^{72} - 886066 q^{75} - 6569272 q^{76} - 13616772 q^{78} - 4 q^{81} + 11560256 q^{82} - 10944176 q^{84} + 7846496 q^{85} - 40789116 q^{87} + 24614816 q^{88} + 25746032 q^{90} - 1590680 q^{91} - 14495396 q^{93} - 6995856 q^{94} - 13927736 q^{96} - 8 q^{97} - 4701076 q^{99}+O(q^{100}) $ 108 * q - 2 * q^3 - 4 * q^4 + 172 * q^6 - 8 * q^7 - 6504 * q^10 + 12016 * q^12 - 4 * q^13 - 55280 * q^16 + 21172 * q^18 - 60588 * q^19 - 4376 * q^21 - 212744 * q^22 - 317304 * q^24 + 238042 * q^27 + 219736 * q^28 - 503852 * q^30 - 4 * q^33 - 364856 * q^34 + 867620 * q^36 - 4 * q^37 - 283948 * q^39 + 390392 * q^40 - 3022344 * q^42 + 752844 * q^43 - 156252 * q^45 - 1166824 * q^46 + 358320 * q^48 + 9882508 * q^49 + 1121592 * q^51 - 4458688 * q^52 + 203816 * q^54 + 4191000 * q^55 + 4975544 * q^58 - 4390240 * q^60 - 2279892 * q^61 + 4781432 * q^64 + 1457476 * q^66 + 1552540 * q^67 + 4372 * q^69 - 9366152 * q^70 - 1660280 * q^72 - 886066 * q^75 - 6569272 * q^76 - 13616772 * q^78 - 4 * q^81 + 11560256 * q^82 - 10944176 * q^84 + 7846496 * q^85 - 40789116 * q^87 + 24614816 * q^88 + 25746032 * q^90 - 1590680 * q^91 - 14495396 * q^93 - 6995856 * q^94 - 13927736 * q^96 - 8 * q^97 - 4701076 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−6.86971	+	8.98928i	−0.607202	+	0.794547i
$2$	−6.86971	+	8.98928i	−0.607202	+	0.794547i
$3$	34.0729	+	32.0318i	0.728593	+	0.684947i
$3$	34.0729	+	32.0318i	0.728593	+	0.684947i
$4$	−33.6142	−	123.507i	−0.262611	−	0.964902i
$5$	201.123	−	201.123i	0.719559	−	0.719559i	−0.248956	−	0.968515i	$-0.580087\pi$
$5$	201.123	−	201.123i	0.719559	−	0.719559i	0.968515	+	0.248956i	$0.0800873\pi$
$6$	−522.014	+	86.2416i	−0.986626	+	0.163000i
$7$	−1025.82			−1.13039			−0.565195	−	0.824958i	$-0.691199\pi$
$7$	−1025.82			−1.13039			−0.565195	+	0.824958i	$0.691199\pi$
$8$	1341.16	+	546.292i	0.926118	+	0.377233i
$9$	134.926	+	2182.83i	0.0616945	+	0.998095i
$10$	426.294	+	3189.61i	0.134806	+	1.00864i
$11$	3756.76	+	3756.76i	0.851018	+	0.851018i	0.990259	−	0.139240i	$-0.0444660\pi$
$11$	3756.76	+	3756.76i	0.851018	+	0.851018i	−0.139240	+	0.990259i	$0.544466\pi$
$12$	2810.83	−	5284.98i	0.469570	−	0.882895i
$13$	−4614.47	+	4614.47i	−0.582532	+	0.582532i	−0.935598	−	0.353066i	$-0.885139\pi$
$13$	−4614.47	+	4614.47i	−0.582532	+	0.582532i	0.353066	+	0.935598i	$0.385139\pi$
$14$	7047.08	−	9221.38i	0.686375	−	0.898148i
$15$	13295.2	−	410.511i	1.01713	−	0.0314054i
$16$	−14124.2	+	8303.21i	−0.862071	+	0.506788i
$17$			25813.8i			1.27433i	0.770728	+	0.637164i	$0.219893\pi$
$17$			25813.8i			1.27433i	−0.770728	+	0.637164i	$0.780107\pi$
$18$	−20549.0	−	13782.5i	−0.830495	−	0.557026i
$19$	7259.43	+	7259.43i	0.242809	+	0.242809i	0.818011	−	0.575202i	$-0.195077\pi$
$19$	7259.43	+	7259.43i	0.242809	+	0.242809i	−0.575202	+	0.818011i	$0.695077\pi$
$20$	−31600.8	−	18079.6i	−0.883268	−	0.505340i
$21$	−34952.7	−	32858.9i	−0.823593	−	0.774257i
$22$	−59578.4	+	7962.71i	−1.19291	+	0.159434i
$23$			7050.99i			0.120838i	0.998173	+	0.0604188i	$0.0192436\pi$
$23$			7050.99i			0.120838i	−0.998173	+	0.0604188i	$0.980756\pi$
$24$	28198.6	+	61573.6i	0.416378	+	0.909192i
$25$		−	2775.87i		−	0.0355312i
$26$	−9780.69	−	73180.8i	−0.109135	−	0.816564i
$27$	−65322.8	+	78697.4i	−0.638692	+	0.769462i
$28$	34482.1	+	126696.i	0.296853	+	1.09071i
$29$	−125449.	−	125449.i	−0.955159	−	0.955159i	0.0438781	−	0.999037i	$-0.486029\pi$
$29$	−125449.	−	125449.i	−0.955159	−	0.955159i	−0.999037	+	0.0438781i	$0.986029\pi$
$30$	−87643.8	+	122334.i	−0.592648	+	0.827224i
$31$			271011.i			1.63388i	0.576721	+	0.816941i	$0.304332\pi$
$31$			271011.i			1.63388i	−0.576721	+	0.816941i	$0.695668\pi$
$32$	22389.0	−	184007.i	0.120784	−	0.992679i
$33$	7667.89	+	248339.i	0.0371430	+	1.20295i
$34$	−232048.	−	177333.i	−1.01251	−	0.773774i
$35$	−206316.	+	206316.i	−0.813382	+	0.813382i
$36$	265061.	−	90038.6i	0.946862	−	0.321640i
$37$	−149832.	−	149832.i	−0.486294	−	0.486294i	0.420840	−	0.907135i	$-0.361735\pi$
$37$	−149832.	−	149832.i	−0.486294	−	0.486294i	−0.907135	+	0.420840i	$0.861735\pi$
$38$	−115127.	+	15386.9i	−0.340357	+	0.0454891i
$39$	−305038.	+	9418.56i	−0.823433	+	0.0254248i
$40$	379610.	−	159867.i	0.937839	−	0.394955i
$41$	369802.			0.837965			0.418982	−	0.907994i	$-0.362387\pi$
$41$	369802.			0.837965			0.418982	+	0.907994i	$0.362387\pi$
$42$	535492.	−	88468.3i	1.11527	−	0.184253i
$43$	690229.	−	690229.i	1.32390	−	1.32390i	0.413302	−	0.910594i	$-0.364375\pi$
$43$	690229.	−	690229.i	1.32390	−	1.32390i	0.910594	−	0.413302i	$-0.135625\pi$
$44$	337707.	−	590268.i	0.597662	−	1.04464i
$45$	466155.	+	411881.i	0.762581	+	0.673796i
$46$	−63383.3	−	48438.2i	−0.0960113	−	0.0733729i
$47$	358611.			0.503827			0.251914	−	0.967750i	$-0.418940\pi$
$47$	358611.			0.503827			0.251914	+	0.967750i	$0.418940\pi$
$48$	−747218.	−	169508.i	−0.975221	−	0.221231i
$49$	228763.			0.277779
$50$	24953.1	+	19069.4i	0.0282312	+	0.0215746i
$51$	−826863.	+	879552.i	−0.872847	+	0.928466i
$52$	725033.	+	414809.i	0.715066	+	0.409107i
$53$	−738128.	+	738128.i	−0.681030	+	0.681030i	−0.960232	−	0.279203i	$-0.909930\pi$
$53$	−738128.	+	738128.i	−0.681030	+	0.681030i	0.279203	+	0.960232i	$0.409930\pi$
$54$	−258684.	−	1.12783e6i	−0.223559	−	0.974690i
$55$	1.51114e6			1.22472
$56$	−1.37579e6	−	560398.i	−1.04687	−	0.426421i
$57$	14817.2	+	479883.i	0.0105975	+	0.343220i
$58$	1.98950e6	−	265899.i	1.33889	−	0.178944i
$59$	1.62939e6	+	1.62939e6i	1.03287	+	1.03287i	0.999441	+	0.0334253i	$0.0106416\pi$
$59$	1.62939e6	+	1.62939e6i	1.03287	+	1.03287i	0.0334253	+	0.999441i	$0.489358\pi$
$60$	−497608.	−	1.62825e6i	−0.297412	−	0.973179i
$61$	−1.07174e6	+	1.07174e6i	−0.604553	+	0.604553i	−0.941517	−	0.336964i	$-0.890600\pi$
$61$	−1.07174e6	+	1.07174e6i	−0.604553	+	0.604553i	0.336964	+	0.941517i	$0.390600\pi$
$62$	−2.43619e6	−	1.86177e6i	−1.29820	−	0.992097i
$63$	−138410.	−	2.23919e6i	−0.0697388	−	1.12824i
$64$	1.50028e6	+	1.46533e6i	0.715390	+	0.698726i
$65$			1.85615e6i			0.838333i
$66$	−2.28507e6	−	1.63709e6i	−0.978353	−	0.700921i
$67$	−958120.	−	958120.i	−0.389187	−	0.389187i	0.485211	−	0.874397i	$-0.338743\pi$
$67$	−958120.	−	958120.i	−0.389187	−	0.389187i	−0.874397	+	0.485211i	$0.838743\pi$
$68$	3.18820e6	−	867711.i	1.22960	−	0.334653i
$69$	−225856.	+	240248.i	−0.0827675	+	0.0880415i
$70$	−437301.	−	3.27196e6i	−0.152383	−	1.14016i
$71$		−	413019.i		−	0.136951i	−0.997653	−	0.0684756i	$-0.978186\pi$
$71$		−	413019.i		−	0.136951i	0.997653	−	0.0684756i	$-0.0218135\pi$
$72$	−1.01151e6	+	3.00124e6i	−0.319378	+	0.947627i
$73$			3.94535e6i			1.18701i	0.804829	+	0.593507i	$0.202257\pi$
$73$			3.94535e6i			1.18701i	−0.804829	+	0.593507i	$0.797743\pi$
$74$	2.37619e6	−	317580.i	0.681663	−	0.0911049i
$75$	88916.3	−	94582.1i	0.0243370	−	0.0258878i
$76$	652573.	−	1.14061e6i	0.170523	−	0.298051i
$77$	−3.85376e6	−	3.85376e6i	−0.961982	−	0.961982i
$78$	2.01086e6	−	2.80678e6i	0.479789	−	0.669694i
$79$		−	3.80043e6i		−	0.867237i	−0.901097	−	0.433618i	$-0.857237\pi$
$79$		−	3.80043e6i		−	0.867237i	0.901097	−	0.433618i	$-0.142763\pi$
$80$	−1.17073e6	+	4.51066e6i	−0.255647	+	0.984975i
$81$	−4.74656e6	+	589042.i	−0.992388	+	0.123154i
$82$	−2.54043e6	+	3.32425e6i	−0.508814	+	0.665803i
$83$	539140.	−	539140.i	0.103497	−	0.103497i	−0.653462	−	0.756959i	$-0.726684\pi$
$83$	539140.	−	539140.i	0.103497	−	0.103497i	0.756959	+	0.653462i	$0.226684\pi$
$84$	−2.88341e6	+	5.42144e6i	−0.530797	+	0.998015i
$85$	5.19175e6	+	5.19175e6i	0.916954	+	0.916954i
$86$	1.46299e6	+	1.09463e7i	0.248026	+	1.85577i
$87$	−256054.	−	8.29280e6i	−0.0416883	−	1.35016i
$88$	2.98613e6	+	7.09071e6i	0.467111	+	1.10918i
$89$	5.01486e6			0.754039			0.377020	−	0.926205i	$-0.376949\pi$
$89$	5.01486e6			0.754039			0.377020	+	0.926205i	$0.376949\pi$
$90$	−6.90486e6	+	1.36089e6i	−0.998404	+	0.196777i
$91$	4.73361e6	−	4.73361e6i	0.658488	−	0.658488i
$92$	870849.	−	237013.i	0.116597	−	0.0317333i
$93$	−8.68097e6	+	9.23413e6i	−1.11912	+	1.19044i
$94$	−2.46355e6	+	3.22366e6i	−0.305925	+	0.400314i
$95$	2.92008e6			0.349431
$96$	6.65693e6	−	5.55248e6i	0.767935	−	0.640528i
$97$	−1.16410e7			−1.29506			−0.647530	−	0.762040i	$-0.724198\pi$
$97$	−1.16410e7			−1.29506			−0.647530	+	0.762040i	$0.724198\pi$
$98$	−1.57154e6	+	2.05642e6i	−0.168668	+	0.220709i
$99$	−7.69350e6	+	8.70726e6i	−0.796894	+	0.901900i
$100$	−342841.	+	93308.8i	−0.0342841	+	0.00933088i
$101$	1.23377e7	−	1.23377e7i	1.19155	−	1.19155i	0.214913	−	0.976633i	$-0.431053\pi$
$101$	1.23377e7	−	1.23377e7i	1.19155	−	1.19155i	0.976633	−	0.214913i	$-0.0689468\pi$
$102$	−2.22623e6	−	1.34752e7i	−0.207715	−	1.25728i
$103$	1.34444e7			1.21230			0.606152	−	0.795349i	$-0.292712\pi$
$103$	1.34444e7			1.21230			0.606152	+	0.795349i	$0.292712\pi$
$104$	−8.70960e6	+	3.66790e6i	−0.759244	+	0.319743i
$105$	−1.36385e7	+	421110.i	−1.14975	+	0.0355004i
$106$	−1.56451e6	−	1.17060e7i	−0.127588	−	0.954633i
$107$	−5.48720e6	−	5.48720e6i	−0.433019	−	0.433019i	0.456635	−	0.889654i	$-0.349055\pi$
$107$	−5.48720e6	−	5.48720e6i	−0.433019	−	0.433019i	−0.889654	+	0.456635i	$0.849055\pi$
$108$	1.19155e7	+	5.42250e6i	0.910183	+	0.414206i
$109$	2.65634e6	−	2.65634e6i	0.196468	−	0.196468i	−0.602016	−	0.798484i	$-0.705636\pi$
$109$	2.65634e6	−	2.65634e6i	0.196468	−	0.196468i	0.798484	+	0.602016i	$0.205636\pi$
$110$	−1.03811e7	+	1.35841e7i	−0.743650	+	0.973095i
$111$	−305822.	−	9.90462e6i	−0.0212245	−	0.687397i
$112$	1.44889e7	−	8.51760e6i	0.974475	−	0.572867i
$113$		−	1.08827e7i		−	0.709518i	−0.934958	−	0.354759i	$-0.884563\pi$
$113$		−	1.08827e7i		−	0.709518i	0.934958	−	0.354759i	$-0.115437\pi$
$114$	−4.41559e6	−	3.16346e6i	−0.279140	−	0.199984i
$115$	1.41812e6	+	1.41812e6i	0.0869499	+	0.0869499i
$116$	−1.12770e7	+	1.97108e7i	−0.670799	+	1.17247i
$117$	−1.06952e7	−	9.45001e6i	−0.617362	−	0.545484i
$118$	−2.58405e7	+	3.45361e6i	−1.44782	+	0.193503i
$119$		−	2.64803e7i		−	1.44049i
$120$	1.80552e7	+	6.71249e6i	0.953826	+	0.354609i
$121$			8.73930e6i			0.448464i
$122$	−2.27162e6	−	1.69967e7i	−0.113260	−	0.847432i
$123$	1.26002e7	+	1.18454e7i	0.610535	+	0.573962i
$124$	3.34719e7	−	9.10982e6i	1.57654	−	0.429076i
$125$	1.51544e7	+	1.51544e7i	0.693993	+	0.693993i
$126$	2.10796e7	+	1.41384e7i	0.938782	+	0.629656i
$127$			6.86917e6i			0.297571i	0.988869	+	0.148786i	$0.0475365\pi$
$127$			6.86917e6i			0.297571i	−0.988869	+	0.148786i	$0.952464\pi$
$128$	−2.34788e7	+	3.42003e6i	−0.989557	+	0.144143i
$129$	4.56274e7	−	1.40882e6i	1.87138	−	0.0577820i
$130$	−1.66855e7	−	1.27512e7i	−0.666095	−	0.509038i
$131$	2.63354e7	−	2.63354e7i	1.02351	−	1.02351i	0.0237899	−	0.999717i	$-0.492427\pi$
$131$	2.63354e7	−	2.63354e7i	1.02351	−	1.02351i	0.999717	−	0.0237899i	$-0.00757326\pi$
$132$	3.04140e7	−	9.29478e6i	1.15097	−	0.351747i
$133$	−7.44687e6	−	7.44687e6i	−0.274469	−	0.274469i
$134$	1.51948e7	−	2.03080e6i	0.545542	−	0.0729123i
$135$	2.68994e6	+	2.89658e7i	0.0940967	+	1.01325i
$136$	−1.41019e7	+	3.46205e7i	−0.480719	+	1.18018i
$137$	−4.25440e7			−1.41357			−0.706784	−	0.707429i	$-0.749855\pi$
$137$	−4.25440e7			−1.41357			−0.706784	+	0.707429i	$0.749855\pi$
$138$	−608088.	−	3.68071e6i	−0.0196965	−	0.119222i
$139$	3.26077e7	−	3.26077e7i	1.02984	−	1.02984i	0.0302942	−	0.999541i	$-0.490356\pi$
$139$	3.26077e7	−	3.26077e7i	1.02984	−	1.02984i	0.999541	−	0.0302942i	$-0.00964441\pi$
$140$	3.24167e7	+	1.85464e7i	0.998437	+	0.571231i
$141$	1.22189e7	+	1.14870e7i	0.367085	+	0.345095i
$142$	3.71274e6	+	2.83732e6i	0.108814	+	0.0831571i
$143$	−3.46709e7			−0.991491
$144$	−2.00302e7	−	2.97104e7i	−0.559007	−	0.829163i
$145$	−5.04615e7			−1.37459
$146$	−3.54659e7	−	2.71034e7i	−0.943138	−	0.720757i
$147$	7.79463e6	+	7.32770e6i	0.202388	+	0.190264i
$148$	−1.34689e7	+	2.35419e7i	−0.341520	+	0.596933i
$149$	3.37821e7	−	3.37821e7i	0.836633	−	0.836633i	−0.151781	−	0.988414i	$-0.548501\pi$
$149$	3.37821e7	−	3.37821e7i	0.836633	−	0.836633i	0.988414	+	0.151781i	$0.0485009\pi$
$150$	239396.	+	1.44904e6i	0.00579158	+	0.0350560i
$151$	−1.47043e7			−0.347556			−0.173778	−	0.984785i	$-0.555598\pi$
$151$	−1.47043e7			−0.347556			−0.173778	+	0.984785i	$0.555598\pi$
$152$	5.77030e6	+	1.37018e7i	0.133274	+	0.316466i
$153$	−5.63473e7	+	3.48295e6i	−1.27190	+	0.0786190i
$154$	6.11167e7	−	8.16831e6i	1.34846	−	0.180223i
$155$	5.45065e7	+	5.45065e7i	1.17568	+	1.17568i
$156$	1.14169e7	+	3.73579e7i	0.240775	+	0.787855i
$157$	−3.78276e7	+	3.78276e7i	−0.780118	+	0.780118i	−0.979851	−	0.199732i	$-0.935993\pi$
$157$	−3.78276e7	+	3.78276e7i	−0.780118	+	0.780118i	0.199732	+	0.979851i	$0.435993\pi$
$158$	3.41631e7	+	2.61078e7i	0.689061	+	0.526588i
$159$	−4.87937e7	+	1.50659e6i	−0.962662	+	0.0297238i
$160$	−3.25050e7	−	4.15109e7i	−0.627380	−	0.801203i
$161$		−	7.23304e6i		−	0.136594i
$162$	2.73124e7	−	4.67147e7i	0.504728	−	0.863278i
$163$	−3.49433e7	−	3.49433e7i	−0.631985	−	0.631985i	0.316580	−	0.948566i	$-0.397465\pi$
$163$	−3.49433e7	−	3.49433e7i	−0.631985	−	0.631985i	−0.948566	+	0.316580i	$0.897465\pi$
$164$	−1.24306e7	−	4.56733e7i	−0.220059	−	0.808554i
$165$	5.14890e7	+	4.84046e7i	0.892319	+	0.838866i
$166$	1.14274e6	+	8.55022e6i	0.0193897	+	0.145077i
$167$		−	5.76117e7i		−	0.957201i	−0.878033	−	0.478600i	$-0.841144\pi$
$167$		−	5.76117e7i		−	0.957201i	0.878033	−	0.478600i	$-0.158856\pi$
$168$	−2.89266e7	−	6.31635e7i	−0.470669	−	1.02774i
$169$			2.01619e7i			0.321312i
$170$	−8.23359e7	+	1.10043e7i	−1.28534	+	0.171787i
$171$	−1.48666e7	+	1.68256e7i	−0.227367	+	0.257327i
$172$	−1.08450e8	−	6.20469e7i	−1.62510	−	0.929760i
$173$	9.32516e7	+	9.32516e7i	1.36929	+	1.36929i	0.861456	+	0.507833i	$0.169553\pi$
$173$	9.32516e7	+	9.32516e7i	1.36929	+	1.36929i	0.507833	+	0.861456i	$0.330447\pi$
$174$	7.63053e7	+	5.46674e7i	1.09808	+	0.786694i
$175$			2.84755e6i			0.0401641i
$176$	−8.42543e7	−	2.18679e7i	−1.16492	−	0.302352i
$177$	3.32575e6	+	1.07711e8i	0.0450799	+	1.46000i
$178$	−3.44506e7	+	4.50800e7i	−0.457854	+	0.599120i
$179$	−9.66728e7	+	9.66728e7i	−1.25985	+	1.25985i	−0.308685	+	0.951164i	$0.599889\pi$
$179$	−9.66728e7	+	9.66728e7i	−1.25985	+	1.25985i	−0.951164	+	0.308685i	$0.900111\pi$
$180$	3.52010e7	−	7.14186e7i	0.449884	−	0.912762i
$181$	−3.13535e7	−	3.13535e7i	−0.393017	−	0.393017i	0.482744	−	0.875761i	$-0.339640\pi$
$181$	−3.13535e7	−	3.13535e7i	−0.393017	−	0.393017i	−0.875761	+	0.482744i	$0.839640\pi$
$182$	1.00332e7	+	7.50703e7i	0.123365	+	0.923035i
$183$	−7.08470e7	+	2.18752e6i	−0.854560	+	0.0263860i
$184$	−3.85190e6	+	9.45652e6i	−0.0455840	+	0.111910i
$185$	−6.02694e7			−0.699835
$186$	−2.33724e7	−	1.41471e8i	−0.266323	−	1.61203i
$187$	−9.69763e7	+	9.69763e7i	−1.08448	+	1.08448i
$188$	−1.20544e7	−	4.42912e7i	−0.132311	−	0.486144i
$189$	6.70094e7	−	8.07294e7i	0.721971	−	0.869792i
$190$	−2.00601e7	+	2.62494e7i	−0.212175	+	0.277640i
$191$	1.17075e8			1.21576			0.607881	−	0.794028i	$-0.292020\pi$
$191$	1.17075e8			1.21576			0.607881	+	0.794028i	$0.292020\pi$
$192$	4.18164e6	+	9.79849e7i	0.0426376	+	0.999091i
$193$	5.99363e7			0.600122			0.300061	−	0.953920i	$-0.402993\pi$
$193$	5.99363e7			0.600122			0.300061	+	0.953920i	$0.402993\pi$
$194$	7.99703e7	−	1.04644e8i	0.786363	−	1.02899i
$195$	−5.94559e7	+	6.32445e7i	−0.574214	+	0.610803i
$196$	−7.68970e6	−	2.82540e7i	−0.0729479	−	0.268030i
$197$	9.57526e7	−	9.57526e7i	0.892316	−	0.892316i	−0.102424	−	0.994741i	$-0.532660\pi$
$197$	9.57526e7	−	9.57526e7i	0.892316	−	0.892316i	0.994741	+	0.102424i	$0.0326600\pi$
$198$	−2.54199e7	−	1.28975e8i	−0.232727	−	1.18081i
$199$	7.18233e7			0.646070			0.323035	−	0.946387i	$-0.395297\pi$
$199$	7.18233e7			0.646070			0.323035	+	0.946387i	$0.395297\pi$
$200$	1.51644e6	−	3.72290e6i	0.0134036	−	0.0329061i
$201$	−1.95561e6	−	6.33362e7i	−0.0169862	−	0.550131i
$202$	2.61507e7	+	1.95664e8i	0.223230	+	1.67025i
$203$	1.28688e8	+	1.28688e8i	1.07970	+	1.07970i
$204$	1.36426e8	+	7.25583e7i	1.12510	+	0.598386i
$205$	7.43757e7	−	7.43757e7i	0.602965	−	0.602965i
$206$	−9.23591e7	+	1.20855e8i	−0.736113	+	0.963232i
$207$	−1.53911e7	+	951360.i	−0.120608	+	0.00745502i
$208$	2.68606e7	−	1.03490e8i	0.206964	−	0.797404i
$209$			5.45439e7i			0.413270i
$210$	8.99067e7	−	1.25493e8i	0.669923	−	0.935085i
$211$	1.12262e8	+	1.12262e8i	0.822704	+	0.822704i	0.986495	−	0.163791i	$-0.0523722\pi$
$211$	1.12262e8	+	1.12262e8i	0.822704	+	0.822704i	−0.163791	+	0.986495i	$0.552372\pi$
$212$	1.15976e8	+	6.63527e7i	0.835972	+	0.478281i
$213$	1.32298e7	−	1.40728e7i	0.0938044	−	0.0997817i
$214$	8.70214e7	−	1.16305e7i	0.606985	−	0.0811241i
$215$		−	2.77642e8i		−	1.90524i
$216$	−1.30600e8	+	6.98607e7i	−0.881772	+	0.471677i
$217$		−	2.78008e8i		−	1.84692i
$218$	5.63030e6	+	4.21268e7i	0.0368073	+	0.275398i
$219$	−1.26377e8	+	1.34430e8i	−0.813042	+	0.864849i
$220$	−5.07958e7	−	1.86637e8i	−0.321624	−	1.18173i
$221$	−1.19117e8	−	1.19117e8i	−0.742337	−	0.742337i
$222$	9.11363e7	+	6.52927e7i	0.559057	+	0.400525i
$223$			1.07643e8i			0.650010i	0.945712	+	0.325005i	$0.105366\pi$
$223$			1.07643e8i			0.650010i	−0.945712	+	0.325005i	$0.894634\pi$
$224$	−2.29671e7	+	1.88758e8i	−0.136533	+	1.12211i
$225$	6.05927e6	−	374537.i	0.0354635	−	0.00219208i
$226$	9.78279e7	+	7.47612e7i	0.563745	+	0.430821i
$227$	−1.87575e7	+	1.87575e7i	−0.106435	+	0.106435i	−0.758319	−	0.651884i	$-0.773979\pi$
$227$	−1.87575e7	+	1.87575e7i	−0.106435	+	0.106435i	0.651884	+	0.758319i	$0.273979\pi$
$228$	5.87710e7	−	1.79609e7i	0.328391	−	0.100359i
$229$	1.16826e7	+	1.16826e7i	0.0642857	+	0.0642857i	0.738519	−	0.674233i	$-0.235526\pi$
$229$	1.16826e7	+	1.16826e7i	0.0642857	+	0.0642857i	−0.674233	+	0.738519i	$0.735526\pi$
$230$	−2.24899e7	+	3.00579e6i	−0.121882	+	0.0162896i
$231$	−7.86588e6	−	2.54752e8i	−0.0419861	−	1.35980i
$232$	−9.97159e7	−	2.36780e8i	−0.524272	−	1.24491i
$233$	−2.35871e8			−1.22160			−0.610800	−	0.791785i	$-0.709152\pi$
$233$	−2.35871e8			−1.22160			−0.610800	+	0.791785i	$0.709152\pi$
$234$	1.58422e8	−	3.12236e7i	0.808276	−	0.159304i
$235$	7.21250e7	−	7.21250e7i	0.362533	−	0.362533i
$236$	1.46471e8	−	2.56013e8i	0.725373	−	1.26786i
$237$	1.21735e8	−	1.29492e8i	0.594011	−	0.631862i
$238$	2.38039e8	+	1.81912e8i	1.14453	+	0.874666i
$239$	−1.81667e8			−0.860761			−0.430380	−	0.902648i	$-0.641621\pi$
$239$	−1.81667e8			−0.860761			−0.430380	+	0.902648i	$0.641621\pi$
$240$	−1.84375e8	+	1.16191e8i	−0.860919	+	0.542541i
$241$	2.69002e7			0.123793			0.0618965	−	0.998083i	$-0.480285\pi$
$241$	2.69002e7			0.123793			0.0618965	+	0.998083i	$0.480285\pi$
$242$	−7.85600e7	−	6.00365e7i	−0.356326	−	0.272309i
$243$	−1.80597e8	−	1.31971e8i	−0.807400	−	0.590004i
$244$	1.68393e8	+	9.63420e7i	0.742097	+	0.424572i
$245$	4.60095e7	−	4.60095e7i	0.199879	−	0.199879i
$246$	−1.93042e8	+	3.18923e7i	−0.826758	+	0.136588i
$247$	−6.69968e7			−0.282888
$248$	−1.48051e8	+	3.63470e8i	−0.616355	+	1.51317i
$249$	3.56397e7	−	1.10044e6i	0.146297	−	0.00451717i
$250$	−2.40334e8	+	3.21209e7i	−0.972804	+	0.130016i
$251$	4.96770e7	+	4.96770e7i	0.198288	+	0.198288i	0.799266	−	0.600978i	$-0.205222\pi$
$251$	4.96770e7	+	4.96770e7i	0.198288	+	0.198288i	−0.600978	+	0.799266i	$0.705222\pi$
$252$	−2.71905e8	+	9.23634e7i	−1.07032	+	0.363578i
$253$	−2.64889e7	+	2.64889e7i	−0.102835	+	0.102835i
$254$	−6.17489e7	−	4.71892e7i	−0.236435	−	0.180686i
$255$	1.05968e7	+	3.43199e8i	0.0400208	+	1.29615i
$256$	1.30549e8	−	2.34552e8i	0.486332	−	0.873774i
$257$		−	1.72877e8i		−	0.635291i	−0.948210	−	0.317645i	$-0.897108\pi$
$257$		−	1.72877e8i		−	0.635291i	0.948210	−	0.317645i	$-0.102892\pi$
$258$	−3.00783e8	+	4.19836e8i	−1.09040	+	1.52199i
$259$	1.53701e8	+	1.53701e8i	0.549702	+	0.549702i
$260$	2.29248e8	−	6.23931e7i	0.808909	−	0.220156i
$261$	2.56909e8	−	2.90762e8i	0.894411	−	1.01227i
$262$	5.58198e7	+	4.17653e8i	0.191749	+	1.43470i
$263$		−	2.64484e8i		−	0.896509i	−0.893906	−	0.448255i	$-0.852046\pi$
$263$		−	2.64484e8i		−	0.896509i	0.893906	−	0.448255i	$-0.147954\pi$
$264$	−1.25382e8	+	3.37252e8i	−0.419394	+	1.12808i
$265$			2.96909e8i			0.980082i
$266$	1.18100e8	−	1.57841e7i	0.384736	−	0.0514204i
$267$	1.70871e8	+	1.60635e8i	0.549388	+	0.516477i
$268$	−8.61285e7	+	1.50541e8i	−0.273322	+	0.477732i
$269$	1.27710e8	+	1.27710e8i	0.400029	+	0.400029i	0.878243	−	0.478214i	$-0.158716\pi$
$269$	1.27710e8	+	1.27710e8i	0.400029	+	0.400029i	−0.478214	+	0.878243i	$0.658716\pi$
$270$	−2.78860e8	−	1.74806e8i	−0.862211	−	0.540484i
$271$		−	1.61262e8i		−	0.492198i	−0.969245	−	0.246099i	$-0.920851\pi$
$271$		−	1.61262e8i		−	0.492198i	0.969245	−	0.246099i	$-0.0791488\pi$
$272$	−2.14338e8	−	3.64599e8i	−0.645814	−	1.09856i
$273$	3.12914e8	−	9.66174e6i	0.930799	−	0.0287400i
$274$	2.92265e8	−	3.82440e8i	0.858322	−	1.12315i
$275$	1.04283e7	−	1.04283e7i	0.0302377	−	0.0302377i
$276$	3.72643e7	+	1.98191e7i	0.106687	+	0.0567418i
$277$	−2.53694e8	−	2.53694e8i	−0.717184	−	0.717184i	0.250844	−	0.968028i	$-0.419292\pi$
$277$	−2.53694e8	−	2.53694e8i	−0.717184	−	0.717184i	−0.968028	+	0.250844i	$0.919292\pi$
$278$	6.91142e7	+	5.17124e8i	0.192935	+	1.44357i
$279$	−5.91572e8	+	3.65664e7i	−1.63077	+	0.100802i
$280$	−3.89412e8	+	1.63994e8i	−1.06012	+	0.446453i
$281$	3.20609e8			0.861991			0.430996	−	0.902354i	$-0.358162\pi$
$281$	3.20609e8			0.861991			0.430996	+	0.902354i	$0.358162\pi$
$282$	−1.87200e8	+	3.09272e7i	−0.497089	+	0.0821238i
$283$	6.41108e7	−	6.41108e7i	0.168143	−	0.168143i	−0.618020	−	0.786163i	$-0.712065\pi$
$283$	6.41108e7	−	6.41108e7i	0.168143	−	0.168143i	0.786163	+	0.618020i	$0.212065\pi$
$284$	−5.10109e7	+	1.38833e7i	−0.132144	+	0.0359649i
$285$	9.94955e7	+	9.35353e7i	0.254593	+	0.239342i
$286$	2.38179e8	−	3.11666e8i	0.602036	−	0.787787i
$287$	−3.79350e8			−0.947226
$288$	4.04677e8	+	2.40443e7i	0.998240	+	0.0593115i
$289$	−2.56015e8			−0.623911
$290$	3.46656e8	−	4.53612e8i	0.834652	−	1.09217i
$291$	−3.96643e8	−	3.72883e8i	−0.943571	−	0.887047i
$292$	4.87280e8	−	1.32620e8i	1.14535	−	0.311723i
$293$	−9.72507e7	+	9.72507e7i	−0.225869	+	0.225869i	−0.810964	−	0.585096i	$-0.801057\pi$
$293$	−9.72507e7	+	9.72507e7i	−0.225869	+	0.225869i	0.585096	+	0.810964i	$0.301057\pi$
$294$	−1.19418e8	+	1.97289e7i	−0.274064	+	0.0452780i
$295$	6.55417e8			1.48642
$296$	−1.19097e8	−	2.82802e8i	−0.266920	−	0.633813i
$297$	−5.41049e8	+	5.02452e7i	−1.19837	+	0.111288i
$298$	7.16035e7	+	5.35750e8i	0.156739	+	1.17275i
$299$	−3.25366e7	−	3.25366e7i	−0.0703919	−	0.0703919i
$300$	−1.46704e7	−	7.80252e6i	−0.0313703	−	0.0166844i
$301$	−7.08051e8	+	7.08051e8i	−1.49652	+	1.49652i
$302$	1.01014e8	−	1.32181e8i	0.211037	−	0.276150i
$303$	8.15583e8	−	2.51825e7i	1.68430	−	0.0520055i
$304$	−1.62810e8	−	4.22568e7i	−0.332371	−	0.0862659i
$305$			4.31102e8i			0.870024i
$306$	3.55780e8	−	5.30448e8i	0.709834	−	1.05832i
$307$	2.42023e8	+	2.42023e8i	0.477388	+	0.477388i	0.904295	−	0.426907i	$-0.140397\pi$
$307$	2.42023e8	+	2.42023e8i	0.477388	+	0.477388i	−0.426907	+	0.904295i	$0.640397\pi$
$308$	−3.46427e8	+	6.05509e8i	−0.675591	+	1.18085i
$309$	4.58090e8	+	4.30649e8i	0.883275	+	0.830364i
$310$	−8.64418e8	+	1.15530e8i	−1.64800	+	0.220257i
$311$			5.99065e8i			1.12931i	0.825328	+	0.564654i	$0.190990\pi$
$311$			5.99065e8i			1.12931i	−0.825328	+	0.564654i	$0.809010\pi$
$312$	−4.14251e8	−	1.54008e8i	−0.772187	−	0.287080i
$313$			4.39192e8i			0.809561i	0.914414	+	0.404780i	$0.132652\pi$
$313$			4.39192e8i			0.809561i	−0.914414	+	0.404780i	$0.867348\pi$
$314$	−8.01783e7	−	5.99908e8i	−0.146151	−	1.09353i
$315$	−4.78191e8	−	4.22516e8i	−0.862014	−	0.761651i
$316$	−4.69381e8	+	1.27748e8i	−0.836798	+	0.227746i
$317$	−5.76151e7	−	5.76151e7i	−0.101585	−	0.101585i	0.654488	−	0.756073i	$-0.272884\pi$
$317$	−5.76151e7	−	5.76151e7i	−0.101585	−	0.101585i	−0.756073	+	0.654488i	$0.772884\pi$
$318$	3.21656e8	−	4.48970e8i	0.560914	−	0.782929i
$319$		−	9.42566e8i		−	1.62572i
$320$	5.96453e8	−	7.02871e6i	1.01754	−	0.0119909i
$321$	−1.11999e7	−	3.62730e8i	−0.0188993	−	0.612090i
$322$	6.50198e7	+	4.96889e7i	0.108530	+	0.0829399i
$323$	−1.87394e8	+	1.87394e8i	−0.309418	+	0.309418i
$324$	2.32303e8	+	5.66435e8i	0.379443	+	0.925215i
$325$	1.28092e7	+	1.28092e7i	0.0206981	+	0.0206981i
$326$	5.54165e8	−	7.40647e7i	0.885885	−	0.118399i
$327$	1.75597e8	−	5.42184e6i	0.277715	−	0.00857490i
$328$	4.95964e8	+	2.02020e8i	0.776054	+	0.316108i
$329$	−3.67871e8			−0.569521
$330$	−7.88836e8	+	1.30323e8i	−1.20834	+	0.199629i
$331$	8.63280e8	−	8.63280e8i	1.30844	−	1.30844i	0.385898	−	0.922541i	$-0.373892\pi$
$331$	8.63280e8	−	8.63280e8i	1.30844	−	1.30844i	0.922541	−	0.385898i	$-0.126108\pi$
$332$	−8.47106e7	−	4.84650e7i	−0.127044	−	0.0726851i
$333$	3.06843e8	−	3.47275e8i	0.455366	−	0.515370i
$334$	5.17888e8	+	3.95776e8i	0.760542	+	0.581214i
$335$	−3.85400e8			−0.560086
$336$	7.66511e8	+	1.73885e8i	1.10238	+	0.250077i
$337$	−6.24407e8			−0.888716			−0.444358	−	0.895849i	$-0.646568\pi$
$337$	−6.24407e8			−0.888716			−0.444358	+	0.895849i	$0.646568\pi$
$338$	−1.81241e8	−	1.38506e8i	−0.255298	−	0.195102i
$339$	3.48594e8	−	3.70806e8i	0.485982	−	0.516949i
$340$	4.66703e8	−	8.15737e8i	0.643968	−	1.12557i
$341$	−1.01812e9	+	1.01812e9i	−1.39046	+	1.39046i
$342$	−4.91206e7	−	2.49227e8i	−0.0664006	−	0.336903i
$343$	6.10137e8			0.816390
$344$	1.30278e9	−	5.48643e8i	1.72550	−	0.726666i
$345$	2.89450e6	+	9.37441e7i	0.00379496	+	0.122907i
$346$	−1.47888e9	+	1.97653e8i	−1.91940	+	0.256530i
$347$	4.25648e8	+	4.25648e8i	0.546887	+	0.546887i	0.925539	−	0.378652i	$-0.123612\pi$
$347$	4.25648e8	+	4.25648e8i	0.546887	+	0.546887i	−0.378652	+	0.925539i	$0.623612\pi$
$348$	−1.01561e9	+	3.10380e8i	−1.29182	+	0.394791i
$349$	1.45088e8	−	1.45088e8i	0.182702	−	0.182702i	−0.609830	−	0.792532i	$-0.708762\pi$
$349$	1.45088e8	−	1.45088e8i	0.182702	−	0.182702i	0.792532	+	0.609830i	$0.208762\pi$
$350$	−2.55974e7	−	1.95618e7i	−0.0319122	−	0.0243877i
$351$	−6.17167e7	−	6.64577e8i	−0.0761777	−	0.820295i
$352$	7.75379e8	−	6.07159e8i	0.947578	−	0.741998i
$353$			1.47179e7i			0.0178088i	0.999960	+	0.00890440i	$0.00283440\pi$
$353$			1.47179e7i			0.0178088i	−0.999960	+	0.00890440i	$0.997166\pi$
$354$	−9.91088e8	−	7.10045e8i	−1.18741	−	0.850696i
$355$	−8.30676e7	−	8.30676e7i	−0.0985445	−	0.0985445i
$356$	−1.68571e8	−	6.19373e8i	−0.198019	−	0.727574i
$357$	8.48213e8	−	9.02262e8i	0.986657	−	1.04953i
$358$	−2.04905e8	−	1.53313e9i	−0.236027	−	1.76599i
$359$			1.66859e9i			1.90335i	0.307112	+	0.951673i	$0.400637\pi$
$359$			1.66859e9i			1.90335i	−0.307112	+	0.951673i	$0.599363\pi$
$360$	4.00181e8	+	8.07056e8i	0.452062	+	0.911686i
$361$		−	7.88473e8i		−	0.882088i
$362$	4.97235e8	−	6.64560e7i	0.550911	−	0.0736299i
$363$	−2.79936e8	+	2.97773e8i	−0.307174	+	0.326748i
$364$	−7.43753e8	−	4.25520e8i	−0.808303	−	0.462450i
$365$	7.93501e8	+	7.93501e8i	0.854127	+	0.854127i
$366$	4.67034e8	−	6.51891e8i	0.497926	−	0.695010i
$367$			1.05635e9i			1.11552i	0.830004	+	0.557758i	$0.188338\pi$
$367$			1.05635e9i			1.11552i	−0.830004	+	0.557758i	$0.811662\pi$
$368$	−5.85458e7	−	9.95893e7i	−0.0612391	−	0.104171i
$369$	4.98958e7	+	8.07216e8i	0.0516978	+	0.836368i
$370$	4.14033e8	−	5.41778e8i	0.424942	−	0.556052i
$371$	7.57186e8	−	7.57186e8i	0.769828	−	0.769828i
$372$	1.43229e9	+	7.61767e8i	1.44255	+	0.767223i
$373$	8.66843e7	+	8.66843e7i	0.0864887	+	0.0864887i	0.749028	−	0.662539i	$-0.230521\pi$
$373$	8.66843e7	+	8.66843e7i	0.0864887	+	0.0864887i	−0.662539	+	0.749028i	$0.730521\pi$
$374$	−2.05548e8	−	1.53795e9i	−0.203171	−	1.52016i
$375$	3.09316e7	+	1.00178e9i	0.0302896	+	0.980986i
$376$	4.80956e8	+	1.95907e8i	0.466603	+	0.190060i
$377$	1.15776e9			1.11282
$378$	2.65363e8	+	1.15695e9i	0.252708	+	1.10178i
$379$	−4.84686e8	+	4.84686e8i	−0.457323	+	0.457323i	−0.897776	−	0.440453i	$-0.854818\pi$
$379$	−4.84686e8	+	4.84686e8i	−0.457323	+	0.457323i	0.440453	+	0.897776i	$0.354818\pi$
$380$	−9.81561e7	−	3.60651e8i	−0.0917645	−	0.337167i
$381$	−2.20032e8	+	2.34053e8i	−0.203821	+	0.216808i
$382$	−8.04274e8	+	1.05242e9i	−0.738214	+	0.965981i
$383$	−5.69069e8			−0.517571			−0.258785	−	0.965935i	$-0.583322\pi$
$383$	−5.69069e8			−0.517571			−0.258785	+	0.965935i	$0.583322\pi$
$384$	−9.09540e8	−	6.35538e8i	−0.819714	−	0.572772i
$385$	−1.55016e9			−1.38441
$386$	−4.11745e8	+	5.38784e8i	−0.364395	+	0.476825i
$387$	1.59979e9	+	1.41353e9i	1.40305	+	1.23970i
$388$	3.91303e8	+	1.43775e9i	0.340097	+	1.24960i
$389$	−8.66762e8	+	8.66762e8i	−0.746579	+	0.746579i	−0.973835	−	0.227256i	$-0.927025\pi$
$389$	−8.66762e8	+	8.66762e8i	−0.746579	+	0.746579i	0.227256	+	0.973835i	$0.427025\pi$
$390$	−1.60077e8	−	9.68936e8i	−0.136648	−	0.827121i
$391$	−1.82013e8			−0.153987
$392$	3.06809e8	+	1.24972e8i	0.257257	+	0.104788i
$393$	1.74090e9	−	5.37530e7i	1.44677	−	0.0446714i
$394$	2.02954e8	+	1.51854e9i	0.167171	+	1.25080i
$395$	−7.64353e8	−	7.64353e8i	−0.624028	−	0.624028i
$396$	1.33402e9	+	6.57516e8i	1.07952	+	0.532075i
$397$	−9.84655e8	+	9.84655e8i	−0.789800	+	0.789800i	−0.981461	−	0.191661i	$-0.938613\pi$
$397$	−9.84655e8	+	9.84655e8i	−0.789800	+	0.789800i	0.191661	+	0.981461i	$0.438613\pi$
$398$	−4.93405e8	+	6.45640e8i	−0.392295	+	0.513333i
$399$	−1.51997e7	−	4.92273e8i	−0.0119793	−	0.387972i
$400$	2.30487e7	+	3.92069e7i	0.0180068	+	0.0306304i
$401$		−	2.35004e9i		−	1.82000i	−0.414613	−	0.909998i	$-0.636083\pi$
$401$		−	2.35004e9i		−	1.82000i	0.414613	−	0.909998i	$-0.363917\pi$
$402$	5.82781e8	+	4.17522e8i	0.447419	+	0.320544i
$403$	−1.25057e9	−	1.25057e9i	−0.951790	−	0.951790i
$404$	−1.93853e9	−	1.10908e9i	−1.46264	−	0.836812i
$405$	−8.36172e8	+	1.07311e9i	−0.625465	+	0.802698i
$406$	−2.04087e9	+	2.72764e8i	−1.51347	+	0.202277i
$407$		−	1.12577e9i		−	0.827691i
$408$	−1.58945e9	+	7.27913e8i	−1.15861	+	0.530602i
$409$			1.52907e9i			1.10509i	0.833484	+	0.552543i	$0.186343\pi$
$409$			1.52907e9i			1.10509i	−0.833484	+	0.552543i	$0.813657\pi$
$410$	1.57644e8	+	1.17952e9i	0.112963	+	0.845206i
$411$	−1.44960e9	−	1.36276e9i	−1.02992	−	0.968220i
$412$	−4.51923e8	−	1.66048e9i	−0.318364	−	1.16975i
$413$	−1.67147e9	−	1.67147e9i	−1.16754	−	1.16754i
$414$	9.71805e7	−	1.44891e8i	0.0673098	−	0.100355i
$415$		−	2.16867e8i		−	0.148945i
$416$	7.45780e8	+	9.52407e8i	0.507907	+	0.648628i
$417$	2.15552e9	−	6.65552e7i	1.45571	−	0.0449476i
$418$	−4.90310e8	−	3.74700e8i	−0.328363	−	0.250938i
$419$	1.22012e8	−	1.22012e8i	0.0810312	−	0.0810312i	−0.665430	−	0.746461i	$-0.731752\pi$
$419$	1.22012e8	−	1.22012e8i	0.0810312	−	0.0810312i	0.746461	+	0.665430i	$0.231752\pi$
$420$	5.10456e8	+	1.67030e9i	0.336191	+	1.10007i
$421$	−9.26958e8	−	9.26958e8i	−0.605442	−	0.605442i	0.336309	−	0.941752i	$-0.390821\pi$
$421$	−9.26958e8	−	9.26958e8i	−0.605442	−	0.605442i	−0.941752	+	0.336309i	$0.890821\pi$
$422$	−1.78036e9	+	2.37947e8i	−1.15323	+	0.154130i
$423$	4.83859e7	+	7.82789e8i	0.0310834	+	0.502867i
$424$	−1.39318e9	+	5.86715e8i	−0.887621	+	0.373807i
$425$	7.16559e7			0.0452784
$426$	3.56194e7	+	2.15602e8i	0.0223230	+	0.135120i
$427$	1.09941e9	−	1.09941e9i	0.683380	−	0.683380i
$428$	−4.93262e8	+	8.62157e8i	−0.304105	+	0.531537i
$429$	−1.18134e9	−	1.11057e9i	−0.722393	−	0.679119i
$430$	2.49580e9	+	1.90732e9i	1.51381	+	1.15687i
$431$	1.19537e9			0.719170			0.359585	−	0.933112i	$-0.382918\pi$
$431$	1.19537e9			0.719170			0.359585	+	0.933112i	$0.382918\pi$
$432$	2.69189e8	−	1.65392e9i	0.160644	−	0.987012i
$433$	3.22719e8			0.191037			0.0955183	−	0.995428i	$-0.469549\pi$
$433$	3.22719e8			0.191037			0.0955183	+	0.995428i	$0.469549\pi$
$434$	2.49909e9	+	1.90984e9i	1.46747	+	1.12146i
$435$	−1.71937e9	−	1.61637e9i	−1.00151	−	0.941519i
$436$	−4.17368e8	−	2.38787e8i	−0.241166	−	0.137977i
$437$	−5.11861e7	+	5.11861e7i	−0.0293405	+	0.0293405i
$438$	−3.40253e8	−	2.05953e9i	−0.193483	−	1.17114i
$439$	−7.30703e8			−0.412207			−0.206103	−	0.978530i	$-0.566078\pi$
$439$	−7.30703e8			−0.412207			−0.206103	+	0.978530i	$0.566078\pi$
$440$	2.02669e9	+	8.25525e8i	1.13423	+	0.462004i
$441$	3.08661e7	+	4.99352e8i	0.0171375	+	0.277250i
$442$	1.88908e9	−	2.52477e8i	1.04057	−	0.139073i
$443$	1.92658e8	+	1.92658e8i	0.105287	+	0.105287i	0.757788	−	0.652501i	$-0.226280\pi$
$443$	1.92658e8	+	1.92658e8i	0.105287	+	0.105287i	−0.652501	+	0.757788i	$0.726280\pi$
$444$	−1.21301e9	+	3.70707e8i	−0.657696	+	0.200998i
$445$	1.00860e9	−	1.00860e9i	0.542576	−	0.542576i
$446$	−9.67636e8	−	7.39478e8i	−0.516464	−	0.394688i
$447$	2.23316e9	−	6.89524e7i	1.18261	−	0.0365152i
$448$	−1.53902e9	−	1.50317e9i	−0.808669	−	0.789832i
$449$		−	2.02291e9i		−	1.05466i	−0.849660	−	0.527332i	$-0.823193\pi$
$449$		−	2.02291e9i		−	1.05466i	0.849660	−	0.527332i	$-0.176807\pi$
$450$	−3.82586e7	+	5.70414e7i	−0.0197918	+	0.0295085i
$451$	1.38926e9	+	1.38926e9i	0.713123	+	0.713123i
$452$	−1.34410e9	+	3.65814e8i	−0.684615	+	0.186327i
$453$	−5.01018e8	−	4.71005e8i	−0.253227	−	0.238058i
$454$	−3.97577e7	−	2.97474e8i	−0.0199400	−	0.149195i
$455$		−	1.90408e9i		−	0.947642i
$456$	−2.42284e8	+	6.51695e8i	−0.119660	+	0.321860i
$457$			4.18168e8i			0.204948i	0.994736	+	0.102474i	$0.0326759\pi$
$457$			4.18168e8i			0.204948i	−0.994736	+	0.102474i	$0.967324\pi$
$458$	−1.85274e8	+	2.47620e7i	−0.0901125	+	0.0120436i
$459$	−2.03148e9	−	1.68623e9i	−0.980547	−	0.813903i
$460$	1.27479e8	−	2.22817e8i	0.0610641	−	0.106732i
$461$	−9.53802e8	−	9.53802e8i	−0.453425	−	0.453425i	0.443065	−	0.896490i	$-0.353891\pi$
$461$	−9.53802e8	−	9.53802e8i	−0.453425	−	0.453425i	−0.896490	+	0.443065i	$0.853891\pi$
$462$	2.34407e9	+	1.67936e9i	1.10592	+	0.792313i
$463$			2.50715e9i			1.17394i	0.809608	+	0.586971i	$0.199680\pi$
$463$			2.50715e9i			1.17394i	−0.809608	+	0.586971i	$0.800320\pi$
$464$	2.81350e9	+	7.30236e8i	1.30748	+	0.339352i
$465$	1.11253e8	+	3.60314e9i	0.0513128	+	1.66186i
$466$	1.62037e9	−	2.12031e9i	0.741758	−	0.970619i
$467$	−6.36576e8	+	6.36576e8i	−0.289229	+	0.289229i	−0.836775	−	0.547546i	$-0.815562\pi$
$467$	−6.36576e8	+	6.36576e8i	−0.289229	+	0.289229i	0.547546	+	0.836775i	$0.315562\pi$
$468$	−8.07634e8	+	1.63860e9i	−0.364212	+	0.738943i
$469$	9.82858e8	+	9.82858e8i	0.439932	+	0.439932i
$470$	1.52874e8	+	1.14383e9i	0.0679189	+	0.508181i
$471$	−2.50059e9	+	7.72097e7i	−1.10273	+	0.0340486i
$472$	1.29516e9	+	3.07541e9i	0.566925	+	1.34619i
$473$	5.18605e9			2.25332
$474$	3.27755e8	+	1.98388e9i	0.141360	+	0.855638i
$475$	2.01513e7	−	2.01513e7i	0.00862729	−	0.00862729i
$476$	−3.27052e9	+	8.90116e8i	−1.38993	+	0.378288i
$477$	−1.71080e9	−	1.51162e9i	−0.721748	−	0.637716i
$478$	1.24800e9	−	1.63305e9i	0.522656	−	0.683915i
$479$	1.52624e9			0.634525			0.317263	−	0.948338i	$-0.397236\pi$
$479$	1.52624e9			0.634525			0.317263	+	0.948338i	$0.397236\pi$
$480$	2.22130e8	−	2.45559e9i	0.0916774	−	1.01347i
$481$	1.38279e9			0.566564
$482$	−1.84797e8	+	2.41814e8i	−0.0751674	+	0.0983594i
$483$	2.31687e8	−	2.46451e8i	0.0935594	−	0.0995211i
$484$	1.07937e9	−	2.93765e8i	0.432724	−	0.117772i
$485$	−2.34127e9	+	2.34127e9i	−0.931872	+	0.931872i
$486$	2.42697e9	−	7.16839e8i	0.959041	−	0.283266i
$487$	1.62848e9			0.638899			0.319449	−	0.947603i	$-0.396502\pi$
$487$	1.62848e9			0.638899			0.319449	+	0.947603i	$0.396502\pi$
$488$	−2.02286e9	+	8.51893e8i	−0.787945	+	0.331830i
$489$	−7.13225e7	−	2.30991e9i	−0.0275832	−	0.893336i
$490$	9.75204e7	+	7.29665e8i	0.0374463	+	0.280180i
$491$	5.65475e8	+	5.65475e8i	0.215590	+	0.215590i	0.806637	−	0.591047i	$-0.201285\pi$
$491$	5.65475e8	+	5.65475e8i	0.215590	+	0.215590i	−0.591047	+	0.806637i	$0.701285\pi$
$492$	1.03945e9	−	1.95440e9i	0.393483	−	0.739835i
$493$	3.23833e9	−	3.23833e9i	1.21719	−	1.21719i
$494$	4.60249e8	−	6.02253e8i	0.171770	−	0.224768i
$495$	2.03892e8	+	3.29857e9i	0.0755583	+	1.22238i
$496$	−2.25026e9	−	3.82780e9i	−0.828032	−	1.40852i
$497$			4.23683e8i			0.154808i
$498$	−2.34942e8	+	3.27935e8i	−0.0852430	+	0.118983i
$499$	−2.96013e8	−	2.96013e8i	−0.106649	−	0.106649i	0.651769	−	0.758418i	$-0.274027\pi$
$499$	−2.96013e8	−	2.96013e8i	−0.106649	−	0.106649i	−0.758418	+	0.651769i	$0.774027\pi$
$500$	1.36228e9	−	2.38109e9i	0.487384	−	0.851885i
$501$	1.84541e9	−	1.96300e9i	0.655632	−	0.697410i
$502$	−7.87827e8	+	1.05294e8i	−0.277951	+	0.0371484i
$503$			1.40293e9i			0.491526i	0.969330	+	0.245763i	$0.0790386\pi$
$503$			1.40293e9i			0.491526i	−0.969330	+	0.245763i	$0.920961\pi$
$504$	1.03763e9	−	3.07874e9i	0.361022	−	1.07119i
$505$		−	4.96281e9i		−	1.71478i
$506$	−5.61450e7	−	4.20086e8i	−0.0192657	−	0.144149i
$507$	−6.45821e8	+	6.86973e8i	−0.220082	+	0.234106i
$508$	8.48393e8	−	2.30902e8i	0.287127	−	0.0781455i
$509$	1.03778e9	+	1.03778e9i	0.348813	+	0.348813i	0.859667	−	0.510855i	$-0.170671\pi$
$509$	1.03778e9	+	1.03778e9i	0.348813	+	0.348813i	−0.510855	+	0.859667i	$0.670671\pi$
$510$	−3.15791e9	−	2.26242e9i	−1.05415	−	0.755227i
$511$		−	4.04722e9i		−	1.34179i
$512$	1.21162e9	+	2.78484e9i	0.398953	+	0.916971i
$513$	−1.04550e9	+	9.70920e7i	−0.341913	+	0.0317521i
$514$	1.55404e9	+	1.18762e9i	0.504768	+	0.385750i
$515$	2.70398e9	−	2.70398e9i	0.872324	−	0.872324i
$516$	−1.70773e9	−	5.58797e9i	−0.547199	−	1.79052i
$517$	1.34722e9	+	1.34722e9i	0.428766	+	0.428766i
$518$	−2.43754e9	+	3.25780e8i	−0.770544	+	0.102984i
$519$	1.90335e8	+	6.16437e9i	0.0597631	+	1.93554i
$520$	−1.01400e9	+	2.48940e9i	−0.316247	+	0.776395i
$521$	4.43846e9			1.37499			0.687496	−	0.726188i	$-0.258710\pi$
$521$	4.43846e9			1.37499			0.687496	+	0.726188i	$0.258710\pi$
$522$	8.48848e8	+	4.30687e9i	0.261206	+	1.32530i
$523$	−3.84539e9	+	3.84539e9i	−1.17540	+	1.17540i	−0.194493	+	0.980904i	$0.562306\pi$
$523$	−3.84539e9	+	3.84539e9i	−1.17540	+	1.17540i	−0.980904	+	0.194493i	$0.937694\pi$
$524$	−4.13786e9	−	2.36738e9i	−1.25637	−	0.718799i
$525$	−9.12121e7	+	9.70242e7i	−0.0275103	+	0.0292632i
$526$	2.37752e9	+	1.81693e9i	0.712319	+	0.544362i
$527$	−6.99583e9			−2.08210
$528$	−2.17032e9	−	3.44392e9i	−0.641659	−	1.01820i
$529$	3.35511e9			0.985398
$530$	−2.66900e9	−	2.03968e9i	−0.778722	−	0.595108i
$531$	−3.33685e9	+	3.77654e9i	−0.967177	+	1.09462i
$532$	−6.69423e8	+	1.17006e9i	−0.192757	+	0.336914i
$533$	−1.70644e9	+	1.70644e9i	−0.488141	+	0.488141i
$534$	−2.61783e9	+	4.32490e8i	−0.743955	+	0.122908i
$535$	−2.20720e9			−0.623166
$536$	−7.61581e8	−	1.80841e9i	−0.213619	−	0.507247i
$537$	−6.39053e9	+	1.97318e8i	−1.78085	+	0.0549866i
$538$	−2.02535e9	+	2.70690e8i	−0.560741	+	0.0749435i
$539$	8.59408e8	+	8.59408e8i	0.236395	+	0.236395i
$540$	3.48707e9	−	1.30589e9i	0.952977	−	0.356885i
$541$	4.50746e8	−	4.50746e8i	0.122389	−	0.122389i	−0.643260	−	0.765648i	$-0.722418\pi$
$541$	4.50746e8	−	4.50746e8i	0.122389	−	0.122389i	0.765648	+	0.643260i	$0.222418\pi$
$542$	1.44963e9	+	1.10782e9i	0.391075	+	0.298864i
$543$	−6.39955e7	−	2.07262e9i	−0.0171534	−	0.555545i
$544$	4.74992e9	+	5.77947e8i	1.26500	+	0.153919i
$545$		−	1.06850e9i		−	0.282740i
$546$	−2.06278e9	+	2.87925e9i	−0.542348	+	0.757015i
$547$	2.82710e9	+	2.82710e9i	0.738559	+	0.738559i	0.972299	−	0.233740i	$-0.0750964\pi$
$547$	2.82710e9	+	2.82710e9i	0.738559	+	0.738559i	−0.233740	+	0.972299i	$0.575096\pi$
$548$	1.43008e9	+	5.25451e9i	0.371219	+	1.36395i
$549$	−2.48403e9	−	2.19482e9i	−0.640699	−	0.566104i
$550$	2.21035e7	+	1.65382e8i	0.00566489	+	0.0423857i
$551$		−	1.82138e9i		−	0.463842i
$552$	−4.34155e8	+	1.98828e8i	−0.109865	+	0.0503141i
$553$			3.89855e9i			0.980315i
$554$	4.02332e9	−	5.37721e8i	1.00531	−	0.134361i
$555$	−2.05355e9	−	1.93054e9i	−0.509895	−	0.479350i
$556$	−5.12337e9	−	2.93121e9i	−1.26414	−	0.723244i
$557$	3.77801e9	+	3.77801e9i	0.926338	+	0.926338i	0.997467	−	0.0711287i	$-0.0226601\pi$
$557$	3.77801e9	+	3.77801e9i	0.926338	+	0.926338i	−0.0711287	+	0.997467i	$0.522660\pi$
$558$	3.73522e9	−	5.56900e9i	0.910116	−	1.35693i
$559$			6.37008e9i			1.54242i
$560$	1.20096e9	−	4.62712e9i	0.288981	−	1.11340i
$561$	−6.41059e9	+	1.97938e8i	−1.53295	+	0.0473324i
$562$	−2.20249e9	+	2.88204e9i	−0.523403	+	0.684893i
$563$	3.22291e9	−	3.22291e9i	0.761147	−	0.761147i	−0.215383	−	0.976530i	$-0.569100\pi$
$563$	3.22291e9	−	3.22291e9i	0.761147	−	0.761147i	0.976530	+	0.215383i	$0.0690999\pi$
$564$	1.00800e9	−	1.89525e9i	0.236582	−	0.444826i
$565$	−2.18877e9	−	2.18877e9i	−0.510540	−	0.510540i
$566$	1.35887e8	+	1.01673e9i	0.0315008	+	0.235694i
$567$	4.86911e9	−	6.04250e8i	1.12178	−	0.139212i
$568$	2.25629e8	−	5.53926e8i	0.0516626	−	0.126833i
$569$	−3.46765e9			−0.789120			−0.394560	−	0.918870i	$-0.629103\pi$
$569$	−3.46765e9			−0.789120			−0.394560	+	0.918870i	$0.629103\pi$
$570$	−1.52432e9	+	2.51832e8i	−0.344758	+	0.0569572i
$571$	−4.70112e9	+	4.70112e9i	−1.05676	+	1.05676i	−0.0584666	+	0.998289i	$0.518621\pi$
$571$	−4.70112e9	+	4.70112e9i	−1.05676	+	1.05676i	−0.998289	+	0.0584666i	$0.981379\pi$
$572$	1.16543e9	+	4.28211e9i	0.260377	+	0.956692i
$573$	3.98910e9	+	3.75014e9i	0.885796	+	0.832734i
$574$	2.60602e9	−	3.41008e9i	0.575158	−	0.752616i
$575$	1.95726e7			0.00429351
$576$	−2.99615e9	+	3.47258e9i	−0.653259	+	0.757135i
$577$	1.11265e7			0.00241127			0.00120563	−	0.999999i	$-0.499616\pi$
$577$	1.11265e7			0.00241127			0.00120563	+	0.999999i	$0.499616\pi$
$578$	1.75875e9	−	2.30139e9i	0.378840	−	0.495726i
$579$	2.04220e9	+	1.91987e9i	0.437244	+	0.411052i
$580$	1.69622e9	+	6.23237e9i	0.360982	+	1.32634i
$581$	−5.53061e8	+	5.53061e8i	−0.116992	+	0.116992i
$582$	6.07677e9	−	1.00394e9i	1.27774	−	0.211095i
$583$	−5.54594e9			−1.15914
$584$	−2.15532e9	+	5.29136e9i	−0.447781	+	1.09931i
$585$	−4.05167e9	+	2.50443e8i	−0.836736	+	0.0517205i
$586$	−2.06130e8	−	1.54230e9i	−0.0423154	−	0.316611i
$587$	5.00952e9	+	5.00952e9i	1.02226	+	1.02226i	0.999746	+	0.0225166i	$0.00716787\pi$
$587$	5.00952e9	+	5.00952e9i	1.02226	+	1.02226i	0.0225166	+	0.999746i	$0.492832\pi$
$588$	6.43015e8	−	1.20901e9i	0.130437	−	0.245250i
$589$	−1.96739e9	+	1.96739e9i	−0.396722	+	0.396722i
$590$	−4.50252e9	+	5.89173e9i	−0.902556	+	1.18103i
$591$	6.32970e9	−	1.95440e8i	1.26132	−	0.0389455i
$592$	3.36035e9	+	8.72167e8i	0.665668	+	0.172772i
$593$		−	9.22691e9i		−	1.81704i	−0.417840	−	0.908521i	$-0.637213\pi$
$593$		−	9.22691e9i		−	1.81704i	0.417840	−	0.908521i	$-0.362787\pi$
$594$	3.26518e9	−	5.20881e9i	0.639227	−	1.01973i
$595$	−5.32580e9	−	5.32580e9i	−1.03651	−	1.03651i
$596$	−5.30790e9	−	3.03678e9i	−1.02698	−	0.587560i
$597$	2.44723e9	+	2.30063e9i	0.470722	+	0.442524i
$598$	5.15997e8	−	6.89635e7i	0.0986718	−	0.0131876i
$599$			2.98675e9i			0.567813i	0.958852	+	0.283907i	$0.0916306\pi$
$599$			2.98675e9i			0.567813i	−0.958852	+	0.283907i	$0.908369\pi$
$600$	1.70921e8	−	7.82756e7i	0.0323047	−	0.0147944i
$601$		−	9.47746e9i		−	1.78087i	−0.455115	−	0.890433i	$-0.650402\pi$
$601$		−	9.47746e9i		−	1.78087i	0.455115	−	0.890433i	$-0.349598\pi$
$602$	−1.50076e9	−	1.12290e10i	−0.280365	−	2.09774i
$603$	1.96214e9	−	2.22069e9i	0.364435	−	0.412456i
$604$	4.94273e8	+	1.81609e9i	0.0912721	+	0.335357i
$605$	1.75767e9	+	1.75767e9i	0.322697	+	0.322697i
$606$	−5.37644e9	+	7.50450e9i	−0.981389	+	1.36983i
$607$		−	2.32136e9i		−	0.421290i	−0.977563	−	0.210645i	$-0.932444\pi$
$607$		−	2.32136e9i		−	0.421290i	0.977563	−	0.210645i	$-0.0675564\pi$
$608$	1.49832e9	−	1.17325e9i	0.270359	−	0.211704i
$609$	2.62665e8	+	8.50692e9i	0.0471240	+	1.52620i
$610$	−3.87530e9	−	2.96155e9i	−0.691275	−	0.528280i
$611$	−1.65480e9	+	1.65480e9i	−0.293496	+	0.293496i
$612$	2.32424e9	+	6.84223e9i	0.409875	+	1.20661i
$613$	5.48887e9	+	5.48887e9i	0.962434	+	0.962434i	0.999320	−	0.0368854i	$-0.0117436\pi$
$613$	5.48887e9	+	5.48887e9i	0.962434	+	0.962434i	−0.0368854	+	0.999320i	$0.511744\pi$
$614$	−3.83823e9	+	5.12984e8i	−0.669179	+	0.0894364i
$615$	4.91658e9	−	1.51808e8i	0.852315	−	0.0263167i
$616$	−3.06324e9	−	7.27379e9i	−0.528017	−	1.25380i
$617$	−3.98233e9			−0.682557			−0.341279	−	0.939962i	$-0.610860\pi$
$617$	−3.98233e9			−0.682557			−0.341279	+	0.939962i	$0.610860\pi$
$618$	−7.01816e9	+	1.15947e9i	−1.19609	+	0.197605i
$619$	7.67280e9	−	7.67280e9i	1.30028	−	1.30028i	0.372077	−	0.928202i	$-0.378646\pi$
$619$	7.67280e9	−	7.67280e9i	1.30028	−	1.30028i	0.928202	−	0.372077i	$-0.121354\pi$
$620$	4.89977e9	−	8.56415e9i	0.825666	−	1.44316i
$621$	−5.54894e8	−	4.60590e8i	−0.0929800	−	0.0771781i
$622$	−5.38516e9	−	4.11540e9i	−0.897289	−	0.685718i
$623$	−5.14435e9			−0.852358
$624$	4.23021e9	−	2.66583e9i	0.696972	−	0.439224i
$625$	6.31268e9			1.03427
$626$	−3.94802e9	−	3.01712e9i	−0.643234	−	0.491567i
$627$	−1.74714e9	+	1.85847e9i	−0.283068	+	0.301105i
$628$	5.94354e9	+	3.40045e9i	0.957605	+	0.547870i
$629$	3.86774e9	−	3.86774e9i	0.619698	−	0.619698i
$630$	7.08314e9	−	1.39603e9i	1.12858	−	0.222434i
$631$	−4.53085e9			−0.717921			−0.358961	−	0.933353i	$-0.616869\pi$
$631$	−4.53085e9			−0.717921			−0.358961	+	0.933353i	$0.616869\pi$
$632$	2.07615e9	−	5.09699e9i	0.327151	−	0.803164i
$633$	2.29137e8	+	7.42104e9i	0.0359073	+	1.16293i
$634$	9.13717e8	−	1.22119e8i	0.142396	−	0.0190314i
$635$	1.38155e9	+	1.38155e9i	0.214120	+	0.214120i
$636$	1.82624e9	+	5.97574e9i	0.281486	+	0.921069i
$637$	−1.05562e9	+	1.05562e9i	−0.161815	+	0.161815i
$638$	8.47299e9	+	6.47515e9i	1.29171	+	0.987138i
$639$	9.01552e8	−	5.57270e7i	0.136690	−	0.00844914i
$640$	−4.03428e9	+	5.40997e9i	−0.608325	+	0.815765i
$641$			6.67400e9i			1.00088i	0.865771	+	0.500441i	$0.166829\pi$
$641$			6.67400e9i			1.00088i	−0.865771	+	0.500441i	$0.833171\pi$
$642$	3.33762e9	+	2.39117e9i	0.497810	+	0.356646i
$643$	−1.17099e9	−	1.17099e9i	−0.173706	−	0.173706i	0.614899	−	0.788606i	$-0.289197\pi$
$643$	−1.17099e9	−	1.17099e9i	−0.173706	−	0.173706i	−0.788606	+	0.614899i	$0.789197\pi$
$644$	−8.93334e8	+	2.43133e8i	−0.131799	+	0.0358710i
$645$	8.89338e9	−	9.46007e9i	1.30499	−	1.38815i
$646$	−3.97194e8	−	2.97187e9i	−0.0579680	−	0.433727i
$647$		−	8.73215e9i		−	1.26752i	−0.773528	−	0.633762i	$-0.781510\pi$
$647$		−	8.73215e9i		−	1.26752i	0.773528	−	0.633762i	$-0.218490\pi$
$648$	−6.68770e9	−	1.80301e9i	−0.965526	−	0.260307i
$649$			1.22425e10i			1.75798i
$650$	−2.03141e8	+	2.71499e7i	−0.0290135	+	0.00387768i
$651$	8.90511e9	−	9.47255e9i	1.26505	−	1.34565i
$652$	−3.14116e9	+	5.49034e9i	−0.443837	+	0.775770i
$653$	−6.72583e9	−	6.72583e9i	−0.945256	−	0.945256i	0.0533210	−	0.998577i	$-0.483019\pi$
$653$	−6.72583e9	−	6.72583e9i	−0.945256	−	0.945256i	−0.998577	+	0.0533210i	$0.983019\pi$
$654$	−1.15756e9	+	1.61573e9i	−0.161816	+	0.225864i
$655$		−	1.05933e10i		−	1.47295i
$656$	−5.22314e9	+	3.07054e9i	−0.722385	+	0.424670i
$657$	−8.61205e9	+	5.32330e8i	−1.18475	+	0.0732322i
$658$	2.52716e9	−	3.30689e9i	0.345814	−	0.452511i
$659$	3.29812e9	−	3.29812e9i	0.448919	−	0.448919i	−0.446076	−	0.894995i	$-0.647179\pi$
$659$	3.29812e9	−	3.29812e9i	0.448919	−	0.448919i	0.894995	+	0.446076i	$0.147179\pi$
$660$	4.24756e9	−	7.98635e9i	0.575090	−	1.08130i
$661$	−6.63013e9	−	6.63013e9i	−0.892929	−	0.892929i	0.101869	−	0.994798i	$-0.467518\pi$
$661$	−6.63013e9	−	6.63013e9i	−0.892929	−	0.892929i	−0.994798	+	0.101869i	$0.967518\pi$
$662$	1.82978e9	+	1.36907e10i	0.245130	+	1.83410i
$663$	−2.43129e8	−	7.87420e9i	−0.0323996	−	1.04932i
$664$	1.01760e9	−	4.28546e8i	0.134893	−	0.0568080i
$665$	−2.99547e9			−0.394993
$666$	1.01383e9	+	5.14397e9i	0.132986	+	0.674744i
$667$	8.84542e8	−	8.84542e8i	0.115419	−	0.115419i
$668$	−7.11547e9	+	1.93657e9i	−0.923605	+	0.251372i
$669$	−3.44801e9	+	3.66772e9i	−0.445223	+	0.473593i
$670$	2.64758e9	−	3.46446e9i	0.340085	−	0.445015i
$671$	−8.05253e9			−1.02897
$672$	−6.82881e9	+	5.69585e9i	−0.868066	+	0.724045i
$673$	6.08079e9			0.768967			0.384483	−	0.923132i	$-0.374380\pi$
$673$	6.08079e9			0.768967			0.384483	+	0.923132i	$0.374380\pi$
$674$	4.28949e9	−	5.61297e9i	0.539630	−	0.706127i
$675$	2.18454e8	+	1.81328e8i	0.0273399	+	0.0226935i
$676$	2.49014e9	−	6.77725e8i	0.310035	−	0.0843802i
$677$	−1.82423e9	+	1.82423e9i	−0.225954	+	0.225954i	−0.811000	−	0.585046i	$-0.801076\pi$
$677$	−1.82423e9	+	1.82423e9i	−0.225954	+	0.225954i	0.585046	+	0.811000i	$0.301076\pi$
$678$	9.38544e8	+	5.68093e9i	0.115651	+	0.700029i
$679$	1.19416e10			1.46392
$680$	4.12677e9	+	9.79920e9i	0.503302	+	1.19511i
$681$	−1.23996e9	+	3.82857e7i	−0.150450	+	0.00464539i
$682$	−2.15798e9	−	1.61464e10i	−0.260497	−	1.94908i
$683$	5.02524e9	+	5.02524e9i	0.603510	+	0.603510i	0.941242	−	0.337732i	$-0.109660\pi$
$683$	5.02524e9	+	5.02524e9i	0.603510	+	0.603510i	−0.337732	+	0.941242i	$0.609660\pi$
$684$	2.57782e9	+	1.27056e9i	0.308004	+	0.151810i
$685$	−8.55658e9	+	8.55658e9i	−1.01715	+	1.01715i
$686$	−4.19146e9	+	5.48469e9i	−0.495714	+	0.648661i
$687$	2.38452e7	+	7.72274e8i	0.00280578	+	0.0908704i
$688$	−4.01780e9	+	1.54800e10i	−0.470358	+	1.81223i
$689$		−	6.81213e9i		−	0.793443i
$690$	−8.62576e8	−	6.17975e8i	−0.0999599	−	0.0716142i
$691$	−1.15505e9	−	1.15505e9i	−0.133177	−	0.133177i	0.637376	−	0.770553i	$-0.280020\pi$
$691$	−1.15505e9	−	1.15505e9i	−0.133177	−	0.133177i	−0.770553	+	0.637376i	$0.780020\pi$
$692$	8.38269e9	−	1.46518e10i	0.961638	−	1.68082i
$693$	7.89214e9	−	8.93208e9i	0.900800	−	1.01950i
$694$	−6.75035e9	+	9.02191e8i	−0.766599	+	0.102457i
$695$		−	1.31163e10i		−	1.48206i
$696$	4.18688e9	−	1.12619e10i	0.470715	−	1.26613i
$697$			9.54600e9i			1.06784i
$698$	3.07524e8	+	2.30095e9i	0.0342283	+	0.256102i
$699$	−8.03682e9	−	7.55538e9i	−0.890049	−	0.836732i
$700$	3.51693e8	−	9.57180e7i	0.0387544	−	0.0105475i
$701$	6.70615e9	+	6.70615e9i	0.735293	+	0.735293i	0.971663	−	0.236370i	$-0.0759578\pi$
$701$	6.70615e9	+	6.70615e9i	0.735293	+	0.735293i	−0.236370	+	0.971663i	$0.575958\pi$
$702$	6.39804e9	+	4.01066e9i	0.698019	+	0.437558i
$703$		−	2.17539e9i		−	0.236153i
$704$	1.31289e8	+	1.11411e10i	0.0141815	+	1.20344i
$705$	4.76780e9	−	1.47214e8i	0.512455	−	0.0158229i
$706$	−1.32303e8	−	1.01108e8i	−0.0141499	−	0.0108135i
$707$	−1.26563e10	+	1.26563e10i	−1.34691	+	1.34691i
$708$	1.31913e10	−	4.03136e9i	1.39692	−	0.426909i
$709$	−3.86791e8	−	3.86791e8i	−0.0407582	−	0.0407582i	0.686434	−	0.727192i	$-0.259175\pi$
$709$	−3.86791e8	−	3.86791e8i	−0.0407582	−	0.0407582i	−0.727192	+	0.686434i	$0.759175\pi$
$710$	1.31737e9	−	1.76068e8i	0.138135	−	0.0184618i
$711$	8.29570e9	−	5.12776e8i	0.865585	−	0.0535037i
$712$	6.72574e9	+	2.73958e9i	0.698330	+	0.284449i
$713$	−1.91089e9			−0.197435
$714$	2.28371e9	+	1.38231e10i	0.234799	+	1.42122i
$715$	−6.97311e9	+	6.97311e9i	−0.713437	+	0.713437i
$716$	1.51894e10	+	8.69023e9i	1.54648	+	0.884781i
$717$	−6.18991e9	−	5.81911e9i	−0.627144	−	0.589576i
$718$	−1.49994e10	−	1.14627e10i	−1.51230	−	1.15572i
$719$	8.03073e9			0.805757			0.402879	−	0.915253i	$-0.368010\pi$
$719$	8.03073e9			0.805757			0.402879	+	0.915253i	$0.368010\pi$
$720$	−1.00040e10	−	1.94690e9i	−0.998871	−	0.194393i
$721$	−1.37915e10			−1.37037
$722$	7.08780e9	+	5.41658e9i	0.700860	+	0.535605i
$723$	9.16569e8	+	8.61663e8i	0.0901947	+	0.0847917i
$724$	−2.81847e9	+	4.92632e9i	−0.276012	+	0.482433i
$725$	−3.48232e8	+	3.48232e8i	−0.0339379	+	0.0339379i
$726$	−7.53691e8	−	4.56204e9i	−0.0730997	−	0.442467i
$727$	−1.16813e10			−1.12751			−0.563754	−	0.825943i	$-0.690643\pi$
$727$	−1.16813e10			−1.12751			−0.563754	+	0.825943i	$0.690643\pi$
$728$	8.93448e9	−	3.76261e9i	0.858242	−	0.361434i
$729$	−1.92621e9	−	1.02815e10i	−0.184144	−	0.982899i
$730$	−1.25841e10	+	1.68188e9i	−1.19727	+	0.160017i
$731$	1.78175e10	+	1.78175e10i	1.68708	+	1.68708i
$732$	2.65164e9	+	8.67660e9i	0.249877	+	0.817637i
$733$	1.15395e10	−	1.15395e10i	1.08224	−	1.08224i	0.0859376	−	0.996301i	$-0.472611\pi$
$733$	1.15395e10	−	1.15395e10i	1.08224	−	1.08224i	0.996301	−	0.0859376i	$-0.0273886\pi$
$734$	−9.49580e9	−	7.25680e9i	−0.886330	−	0.677344i
$735$	3.04145e9	−	9.39097e7i	0.282537	−	0.00872379i
$736$	1.29743e9	+	1.57865e8i	0.119953	+	0.0145953i
$737$		−	7.19885e9i		−	0.662410i
$738$	−7.59906e9	−	5.09681e9i	−0.695925	−	0.466768i
$739$	2.17669e9	+	2.17669e9i	0.198400	+	0.198400i	0.799314	−	0.600914i	$-0.205197\pi$
$739$	2.17669e9	+	2.17669e9i	0.198400	+	0.198400i	−0.600914	+	0.799314i	$0.705197\pi$
$740$	2.02591e9	+	7.44372e9i	0.183785	+	0.675272i
$741$	−2.28278e9	−	2.14603e9i	−0.206110	−	0.193764i
$742$	1.60491e9	+	1.20082e10i	0.144224	+	1.07911i
$743$		−	1.89127e10i		−	1.69158i	−0.533516	−	0.845790i	$-0.679130\pi$
$743$		−	1.89127e10i		−	1.69158i	0.533516	−	0.845790i	$-0.320870\pi$
$744$	−1.66871e10	+	7.64212e9i	−1.48551	+	0.680313i
$745$		−	1.35887e10i		−	1.20401i
$746$	−1.37472e9	+	1.83733e8i	−0.121236	+	0.0162032i
$747$	1.24960e9	+	1.10411e9i	0.109685	+	0.0969148i
$748$	1.52371e10	+	8.71751e9i	1.33121	+	0.761617i
$749$	5.62888e9	+	5.62888e9i	0.489480	+	0.489480i
$750$	−9.21777e9	−	6.60388e9i	−0.797832	−	0.571590i
$751$			7.75275e9i			0.667907i	0.942590	+	0.333954i	$0.108383\pi$
$751$			7.75275e9i			0.667907i	−0.942590	+	0.333954i	$0.891617\pi$
$752$	−5.06509e9	+	2.97763e9i	−0.434335	+	0.255333i
$753$	1.01395e8	+	3.28388e9i	0.00865437	+	0.280288i
$754$	−7.95351e9	+	1.04075e10i	−0.675708	+	0.884190i
$755$	−2.95737e9	+	2.95737e9i	−0.250087	+	0.250087i
$756$	−1.22231e10	−	5.56251e9i	−1.02886	−	0.468214i
$757$	1.38572e10	+	1.38572e10i	1.16102	+	1.16102i	0.984252	+	0.176770i	$0.0565650\pi$
$757$	1.38572e10	+	1.38572e10i	1.16102	+	1.16102i	0.176770	+	0.984252i	$0.443435\pi$
$758$	−1.02733e9	−	7.68663e9i	−0.0856773	−	0.641053i
$759$	−1.75104e9	+	5.40662e7i	−0.145362	+	0.00448828i
$760$	3.91630e9	+	1.59522e9i	0.323614	+	0.131817i
$761$	−1.49913e10			−1.23309			−0.616544	−	0.787321i	$-0.711468\pi$
$761$	−1.49913e10			−1.23309			−0.616544	+	0.787321i	$0.711468\pi$
$762$	−5.92408e8	−	3.58580e9i	−0.0485041	−	0.293592i
$763$	−2.72493e9	+	2.72493e9i	−0.222085	+	0.222085i
$764$	−3.93540e9	−	1.44597e10i	−0.319273	−	1.17309i
$765$	−1.06322e10	+	1.20332e10i	−0.858636	+	0.971779i
$766$	3.90934e9	−	5.11552e9i	0.314270	−	0.411234i
$767$	−1.50376e10			−1.20336
$768$	1.19613e10	−	3.81015e9i	0.952827	−	0.303513i
$769$	−1.45170e10			−1.15116			−0.575581	−	0.817745i	$-0.695224\pi$
$769$	−1.45170e10			−1.15116			−0.575581	+	0.817745i	$0.695224\pi$
$770$	1.06491e10	−	1.39348e10i	0.840614	−	1.09998i
$771$	5.53758e9	−	5.89044e9i	0.435141	−	0.462868i
$772$	−2.01471e9	−	7.40258e9i	−0.157599	−	0.579058i
$773$	−1.40695e10	+	1.40695e10i	−1.09560	+	1.09560i	−0.100681	+	0.994919i	$0.532102\pi$
$773$	−1.40695e10	+	1.40695e10i	−1.09560	+	1.09560i	−0.994919	+	0.100681i	$0.967898\pi$
$774$	−2.36966e10	+	4.67041e9i	−1.83693	+	0.362044i
$775$	7.52292e8			0.0580538
$776$	−1.56125e10	−	6.35940e9i	−1.19938	−	0.488540i
$777$	3.13718e8	+	1.01604e10i	0.0239920	+	0.777026i
$778$	−1.83716e9	−	1.37460e10i	−0.139868	−	1.04652i
$779$	2.68455e9	+	2.68455e9i	0.203465	+	0.203465i
$780$	9.80972e9	+	5.21733e9i	0.740160	+	0.393656i
$781$	1.55161e9	−	1.55161e9i	0.116548	−	0.116548i
$782$	1.25038e9	−	1.63616e9i	0.0935011	−	0.122350i
$783$	1.80672e10	−	1.67784e9i	1.34501	−	0.124906i
$784$	−3.23109e9	+	1.89947e9i	−0.239466	+	0.140775i
$785$			1.52160e10i			1.12268i
$786$	−1.14762e10	+	1.60187e10i	−0.842987	+	1.17665i
$787$	1.28924e9	+	1.28924e9i	0.0942804	+	0.0942804i	0.752674	−	0.658394i	$-0.228764\pi$
$787$	1.28924e9	+	1.28924e9i	0.0942804	+	0.0942804i	−0.658394	+	0.752674i	$0.728764\pi$
$788$	−1.50448e10	−	8.60751e9i	−1.09533	−	0.626666i
$789$	8.47191e9	−	9.01175e9i	0.614062	−	0.653190i
$790$	1.21219e10	−	1.62010e9i	0.874731	−	0.116909i
$791$			1.11637e10i			0.802031i
$792$	−1.50749e10	+	7.47496e9i	−1.07825	+	0.534651i
$793$		−	9.89101e9i		−	0.704343i
$794$	−2.08704e9	−	1.56156e10i	−0.147965	−	1.10710i
$795$	−9.51053e9	+	1.01165e10i	−0.671305	+	0.714081i
$796$	−2.41428e9	−	8.87071e9i	−0.169665	−	0.623394i
$797$	1.73793e9	+	1.73793e9i	0.121599	+	0.121599i	0.765287	−	0.643689i	$-0.222597\pi$
$797$	1.73793e9	+	1.73793e9i	0.121599	+	0.121599i	−0.643689	+	0.765287i	$0.722597\pi$
$798$	4.52960e9	+	3.24514e9i	0.315536	+	0.226060i
$799$			9.25713e9i			0.642041i
$800$	−5.10779e8	−	6.21492e7i	−0.0352710	−	0.00429161i
$801$	6.76635e8	+	1.09466e10i	0.0465201	+	0.752603i
$802$	2.11252e10	+	1.61441e10i	1.44607	+	1.10511i
$803$	−1.48217e10	+	1.48217e10i	−1.01017	+	1.01017i
$804$	−7.75676e9	+	2.37053e9i	−0.526362	+	0.160860i
$805$	−1.45473e9	−	1.45473e9i	−0.0982872	−	0.0982872i
$806$	1.98328e10	−	2.65067e9i	1.33417	−	0.178313i
$807$	2.60668e8	+	8.44223e9i	0.0174594	+	0.565457i
$808$	2.32869e10	−	9.80690e9i	1.55300	−	0.654021i
$809$	2.22105e10			1.47482			0.737409	−	0.675447i	$-0.236049\pi$
$809$	2.22105e10			1.47482			0.737409	+	0.675447i	$0.236049\pi$
$810$	−3.90224e9	−	1.48885e10i	−0.257998	−	0.984362i
$811$	8.79667e9	−	8.79667e9i	0.579089	−	0.579089i	−0.355563	−	0.934652i	$-0.615711\pi$
$811$	8.79667e9	−	8.79667e9i	0.579089	−	0.579089i	0.934652	+	0.355563i	$0.115711\pi$
$812$	1.15682e10	−	2.02197e10i	0.758264	−	1.32535i
$813$	5.16552e9	−	5.49467e9i	0.337130	−	0.358612i
$814$	1.01198e10	+	7.73369e9i	0.657640	+	0.502576i
$815$	−1.40558e10			−0.909502
$816$	4.37565e9	−	1.92886e10i	0.281921	−	1.24275i
$817$	1.00213e10			0.642908
$818$	−1.37453e10	−	1.05043e10i	−0.878044	−	0.671011i
$819$	1.09714e10	+	9.69401e9i	0.697859	+	0.616609i
$820$	−1.16860e10	−	6.68587e9i	−0.740148	−	0.423457i
$821$	1.03142e9	−	1.03142e9i	0.0650481	−	0.0650481i	−0.673834	−	0.738882i	$-0.735354\pi$
$821$	1.03142e9	−	1.03142e9i	0.0650481	−	0.0650481i	0.738882	+	0.673834i	$0.235354\pi$
$822$	2.22086e10	−	3.66907e9i	1.39466	−	0.230412i
$823$	3.07511e9			0.192292			0.0961460	−	0.995367i	$-0.469348\pi$
$823$	3.07511e9			0.192292			0.0961460	+	0.995367i	$0.469348\pi$
$824$	1.80311e10	+	7.34458e9i	1.12274	+	0.457321i
$825$	6.89359e8	−	2.12851e7i	0.0427422	−	0.00131974i
$826$	2.65077e10	−	3.54279e9i	1.63660	−	0.218733i
$827$	−4.33180e9	−	4.33180e9i	−0.266317	−	0.266317i	0.561297	−	0.827614i	$-0.310303\pi$
$827$	−4.33180e9	−	4.33180e9i	−0.266317	−	0.266317i	−0.827614	+	0.561297i	$0.810303\pi$
$828$	6.34861e8	+	1.86894e9i	0.0388662	+	0.114417i
$829$	1.66414e10	−	1.66414e10i	1.01449	−	1.01449i	0.0145979	−	0.999893i	$-0.495353\pi$
$829$	1.66414e10	−	1.66414e10i	1.01449	−	1.01449i	0.999893	−	0.0145979i	$-0.00464682\pi$
$830$	1.94948e9	+	1.48981e9i	0.118344	+	0.0904395i
$831$	−5.17812e8	−	1.67703e10i	−0.0313018	−	1.01377i
$832$	−1.36847e10	+	1.61263e8i	−0.823768	+	0.00970743i
$833$			5.90525e9i			0.353982i
$834$	−1.42095e10	+	1.98338e10i	−0.848199	+	1.18393i
$835$	−1.15870e10	−	1.15870e10i	−0.688763	−	0.688763i
$836$	6.73657e9	−	1.83345e9i	0.398765	−	0.108529i
$837$	−2.13279e10	−	1.77032e10i	−1.25721	−	1.04355i
$838$	2.58612e8	+	1.93498e9i	0.0151808	+	0.113585i
$839$			6.92157e9i			0.404611i	0.979322	+	0.202305i	$0.0648434\pi$
$839$			6.92157e9i			0.404611i	−0.979322	+	0.202305i	$0.935157\pi$
$840$	−1.85214e10	−	6.88581e9i	−1.07819	−	0.400846i
$841$			1.42252e10i			0.824656i
$842$	1.47006e10	−	1.96475e9i	0.848679	−	0.113427i
$843$	1.09241e10	+	1.02697e10i	0.628041	+	0.590419i
$844$	1.00916e10	−	1.76388e10i	0.577778	−	1.00988i
$845$	4.05501e9	+	4.05501e9i	0.231203	+	0.231203i
$846$	−7.36910e9	−	4.94258e9i	−0.418426	−	0.280645i
$847$		−	8.96495e9i		−	0.506939i
$848$	4.29661e9	−	1.65543e10i	0.241958	−	0.932233i
$849$	4.23803e9	−	1.30856e8i	0.237677	−	0.00733866i
$850$	−4.92255e8	+	6.44135e8i	−0.0274931	+	0.0359758i
$851$	1.05647e9	−	1.05647e9i	0.0587627	−	0.0587627i
$852$	−2.18280e9	−	1.16093e9i	−0.120914	−	0.0643082i
$853$	9.43839e9	+	9.43839e9i	0.520687	+	0.520687i	0.917779	−	0.397092i	$-0.129981\pi$
$853$	9.43839e9	+	9.43839e9i	0.520687	+	0.520687i	−0.397092	+	0.917779i	$0.629981\pi$
$854$	2.33028e9	+	1.74355e10i	0.128028	+	0.957928i
$855$	3.93994e8	+	6.37404e9i	0.0215580	+	0.348765i
$856$	−4.36161e9	−	1.03568e10i	−0.237678	−	0.564376i
$857$	−7.97724e9			−0.432932			−0.216466	−	0.976290i	$-0.569453\pi$
$857$	−7.97724e9			−0.432932			−0.216466	+	0.976290i	$0.569453\pi$
$858$	1.80987e10	−	2.99007e9i	0.978231	−	0.161613i
$859$	−9.09516e9	+	9.09516e9i	−0.489592	+	0.489592i	−0.908177	−	0.418586i	$-0.862526\pi$
$859$	−9.09516e9	+	9.09516e9i	−0.489592	+	0.489592i	0.418586	+	0.908177i	$0.362526\pi$
$860$	−3.42908e10	+	9.33272e9i	−1.83837	+	0.500338i
$861$	−1.29256e10	−	1.21513e10i	−0.690142	−	0.648800i
$862$	−8.21184e9	+	1.07455e10i	−0.436682	+	0.571415i
$863$	1.39287e10			0.737691			0.368845	−	0.929491i	$-0.379753\pi$
$863$	1.39287e10			0.737691			0.368845	+	0.929491i	$0.379753\pi$
$864$	1.30183e10	+	1.37818e10i	0.686685	+	0.726955i
$865$	3.75101e10			1.97057
$866$	−2.21698e9	+	2.90101e9i	−0.115998	+	0.151788i
$867$	−8.72316e9	−	8.20061e9i	−0.454577	−	0.427346i
$868$	−3.43361e10	+	9.34504e9i	−1.78210	+	0.485023i
$869$	1.42773e10	−	1.42773e10i	0.738034	−	0.738034i
$870$	2.63416e10	−	4.35188e9i	1.35620	−	0.224058i
$871$	8.84243e9			0.453428
$872$	5.01372e9	−	2.11144e9i	0.256066	−	0.107838i
$873$	−1.57067e9	−	2.54104e10i	−0.0798980	−	1.29259i
$874$	−1.08493e8	−	8.11760e8i	−0.00549680	−	0.0411280i
$875$	−1.55457e10	−	1.55457e10i	−0.784482	−	0.784482i
$876$	2.08511e10	+	1.10897e10i	1.04801	+	0.557386i
$877$	−3.41952e9	+	3.41952e9i	−0.171185	+	0.171185i	−0.787500	−	0.616315i	$-0.788625\pi$
$877$	−3.41952e9	+	3.41952e9i	−0.171185	+	0.171185i	0.616315	+	0.787500i	$0.288625\pi$
$878$	5.01971e9	−	6.56849e9i	0.250293	−	0.327518i
$879$	−6.42873e9	+	1.98498e8i	−0.319274	+	0.00985813i
$880$	−2.13436e10	+	1.25473e10i	−1.05579	+	0.620671i
$881$		−	5.34536e9i		−	0.263367i	−0.991292	−	0.131684i	$-0.957962\pi$
$881$		−	5.34536e9i		−	0.263367i	0.991292	−	0.131684i	$-0.0420383\pi$
$882$	−4.70086e9	−	3.15294e9i	−0.230694	−	0.154730i
$883$	3.95752e9	+	3.95752e9i	0.193446	+	0.193446i	0.797183	−	0.603737i	$-0.206322\pi$
$883$	3.95752e9	+	3.95752e9i	0.193446	+	0.193446i	−0.603737	+	0.797183i	$0.706322\pi$
$884$	−1.07078e10	+	1.87159e10i	−0.521336	+	0.911228i
$885$	2.23320e10	+	2.09942e10i	1.08299	+	1.01812i
$886$	−3.05536e9	+	4.08352e8i	−0.147586	+	0.0197250i
$887$			2.00641e9i			0.0965356i	0.998834	+	0.0482678i	$0.0153701\pi$
$887$			2.00641e9i			0.0965356i	−0.998834	+	0.0482678i	$0.984630\pi$
$888$	5.00066e9	−	1.34508e10i	0.239653	−	0.644617i
$889$		−	7.04653e9i		−	0.336371i
$890$	2.13781e9	+	1.59954e10i	0.101649	+	0.760556i
$891$	−2.00446e10	−	1.56188e10i	−0.949346	−	0.739734i
$892$	1.32948e10	−	3.61835e9i	0.627196	−	0.170700i
$893$	2.60331e9	+	2.60331e9i	0.122334	+	0.122334i
$894$	−1.47213e10	+	2.05482e10i	−0.689073	+	0.961815i
$895$			3.88862e10i			1.81307i
$896$	2.40850e10	−	3.50833e9i	1.11858	−	0.162938i
$897$	−6.64101e7	−	2.15082e9i	−0.00307228	−	0.0995017i
$898$	1.81845e10	+	1.38968e10i	0.837980	+	0.640394i
$899$	3.39982e10	−	3.39982e10i	1.56062	−	1.56062i
$900$	−2.49936e8	−	7.35775e8i	−0.0114282	−	0.0336431i
$901$	−1.90539e10	−	1.90539e10i	−0.867855	−	0.867855i
$902$	−2.20322e10	+	2.94463e9i	−0.999620	+	0.133600i
$903$	−4.68055e10	+	1.44520e9i	−2.11539	+	0.0653161i
$904$	5.94515e9	−	1.45955e10i	0.267654	−	0.657097i
$905$	−1.26118e10			−0.565598
$906$	7.67585e9	−	1.26812e9i	0.342908	−	0.0566516i
$907$	3.01053e9	−	3.01053e9i	0.133973	−	0.133973i	−0.636940	−	0.770913i	$-0.719800\pi$
$907$	3.01053e9	−	3.01053e9i	0.133973	−	0.133973i	0.770913	+	0.636940i	$0.219800\pi$
$908$	2.94720e9	+	1.68617e9i	0.130650	+	0.0747481i
$909$	2.85959e10	+	2.52666e10i	1.26279	+	1.11576i
$910$	1.71163e10	+	1.30805e10i	0.752947	+	0.575411i
$911$	−2.03171e10			−0.890324			−0.445162	−	0.895450i	$-0.646854\pi$
$911$	−2.03171e10			−0.890324			−0.445162	+	0.895450i	$0.646854\pi$
$912$	−4.19385e9	−	6.65491e9i	−0.183076	−	0.290510i
$913$	4.05084e9			0.176156
$914$	−3.75903e9	−	2.87269e9i	−0.162841	−	0.124445i
$915$	−1.38090e10	+	1.46889e10i	−0.595920	+	0.633893i
$916$	1.05018e9	−	1.83559e9i	0.0451473	−	0.0789116i
$917$	−2.70154e10	+	2.70154e10i	−1.15696	+	1.15696i
$918$	2.91137e10	−	6.67763e9i	1.24207	−	0.284887i
$919$	−2.03532e10			−0.865026			−0.432513	−	0.901628i	$-0.642373\pi$
$919$	−2.03532e10			−0.865026			−0.432513	+	0.901628i	$0.642373\pi$
$920$	1.12722e9	+	2.67663e9i	0.0477255	+	0.113326i
$921$	4.93991e8	+	1.59988e10i	0.0208358	+	0.674807i
$922$	1.51263e10	−	2.02165e9i	0.635588	−	0.0849469i
$923$	1.90586e9	+	1.90586e9i	0.0797785	+	0.0797785i
$924$	−3.11993e10	+	9.53477e9i	−1.30105	+	0.397611i
$925$	−4.15915e8	+	4.15915e8i	−0.0172786	+	0.0172786i
$926$	−2.25375e10	−	1.72234e10i	−0.932753	−	0.712820i
$927$	1.81400e9	+	2.93469e10i	0.0747924	+	1.20999i
$928$	−2.58922e10	+	2.02748e10i	−1.06353	+	0.832798i
$929$		−	3.48906e10i		−	1.42775i	−0.700271	−	0.713877i	$-0.746938\pi$
$929$		−	3.48906e10i		−	1.42775i	0.700271	−	0.713877i	$-0.253062\pi$
$930$	−3.31539e10	−	2.37524e10i	−1.35159	−	0.968317i
$931$	1.66069e9	+	1.66069e9i	0.0674474	+	0.0674474i
$932$	7.92863e9	+	2.91318e10i	0.320806	+	1.17872i
$933$	−1.91891e10	+	2.04119e10i	−0.773516	+	0.822805i
$934$	−1.34927e9	−	1.00955e10i	−0.0541856	−	0.405426i
$935$			3.90083e10i			1.56069i
$936$	−9.18157e9	−	1.85167e10i	−0.365975	−	0.738072i
$937$			5.99394e9i			0.238026i	0.992893	+	0.119013i	$0.0379730\pi$
$937$			5.99394e9i			0.238026i	−0.992893	+	0.119013i	$0.962027\pi$
$938$	−1.55871e10	+	2.08324e9i	−0.616675	+	0.0824192i
$939$	−1.40681e10	+	1.49646e10i	−0.554506	+	0.589840i
$940$	−1.13324e10	−	6.48354e9i	−0.445014	−	0.254604i
$941$	−2.45166e10	−	2.45166e10i	−0.959174	−	0.959174i	0.0400247	−	0.999199i	$-0.487256\pi$
$941$	−2.45166e10	−	2.45166e10i	−0.959174	−	0.959174i	−0.999199	+	0.0400247i	$0.987256\pi$
$942$	1.64842e10	−	2.30089e10i	0.642526	−	0.896844i
$943$			2.60747e9i			0.101258i
$944$	−3.65430e10	−	9.48464e9i	−1.41385	−	0.366960i
$945$	−2.75939e9	−	2.97137e10i	−0.106366	−	1.14537i
$946$	−3.56267e10	+	4.66189e10i	−1.36822	+	1.79037i
$947$	3.08779e10	−	3.08779e10i	1.18147	−	1.18147i	0.202105	−	0.979364i	$-0.435222\pi$
$947$	3.08779e10	−	3.08779e10i	1.18147	−	1.18147i	0.979364	−	0.202105i	$-0.0647783\pi$
$948$	−2.00852e10	−	1.06824e10i	−0.765679	−	0.407229i
$949$	−1.82057e10	−	1.82057e10i	−0.691474	−	0.691474i
$950$	4.27120e7	+	3.19578e8i	0.00161628	+	0.0120933i
$951$	−1.17598e8	−	3.80863e9i	−0.00443371	−	0.143594i
$952$	1.44660e10	−	3.55144e10i	0.543400	−	1.33406i
$953$	3.72264e10			1.39324			0.696620	−	0.717440i	$-0.254686\pi$
$953$	3.72264e10			1.39324			0.696620	+	0.717440i	$0.254686\pi$
$954$	2.53411e10	−	4.99451e9i	0.944943	−	0.186240i
$955$	2.35466e10	−	2.35466e10i	0.874814	−	0.874814i
$956$	6.10658e9	+	2.24372e10i	0.226045	+	0.830550i
$957$	3.01921e10	−	3.21160e10i	1.11353	−	1.18448i
$958$	−1.04848e10	+	1.37198e10i	−0.385285	+	0.504160i
$959$	4.36425e10			1.59788
$960$	2.05480e10	+	1.88660e10i	0.749585	+	0.688225i
$961$	−4.59343e10			−1.66957
$962$	−9.49938e9	+	1.24303e10i	−0.344019	+	0.450162i
$963$	1.12373e10	−	1.27180e10i	0.405480	−	0.458909i
$964$	−9.04230e8	−	3.32238e9i	−0.0325094	−	0.119448i
$965$	1.20546e10	−	1.20546e10i	0.431823	−	0.431823i
$966$	6.23789e8	+	3.77575e9i	0.0222647	+	0.134767i
$967$	1.15979e10			0.412464			0.206232	−	0.978503i	$-0.433880\pi$
$967$	1.15979e10			0.412464			0.206232	+	0.978503i	$0.433880\pi$
$968$	−4.77421e9	+	1.17208e10i	−0.169176	+	0.415331i
$969$	−1.23876e10	+	3.82488e8i	−0.437375	+	0.0135047i
$970$	−4.96249e9	−	3.71302e10i	−0.174582	−	1.30625i
$971$	−2.49932e10	−	2.49932e10i	−0.876103	−	0.876103i	0.117025	−	0.993129i	$-0.462664\pi$
$971$	−2.49932e10	−	2.49932e10i	−0.876103	−	0.876103i	−0.993129	+	0.117025i	$0.962664\pi$
$972$	−1.02287e10	+	2.67412e10i	−0.357264	+	0.934004i
$973$	−3.34496e10	+	3.34496e10i	−1.16411	+	1.16411i
$974$	−1.11872e10	+	1.46389e10i	−0.387941	+	0.507635i
$975$	2.61447e7	+	8.46747e8i	0.000903375	+	0.0292575i
$976$	6.23854e9	−	2.40363e10i	0.214787	−	0.827548i
$977$		−	9.63092e9i		−	0.330398i	−0.986260	−	0.165199i	$-0.947173\pi$
$977$		−	9.63092e9i		−	0.330398i	0.986260	−	0.165199i	$-0.0528266\pi$
$978$	2.12544e10	+	1.52273e10i	0.726547	+	0.520520i
$979$	1.88396e10	+	1.88396e10i	0.641701	+	0.641701i
$980$	−7.22910e9	−	4.13595e9i	−0.245354	−	0.140373i
$981$	6.15676e9	+	5.43994e9i	0.208214	+	0.183972i
$982$	−8.96786e9	+	1.19856e9i	−0.302203	+	0.0403897i
$983$			2.68863e10i			0.902806i	0.892320	+	0.451403i	$0.149076\pi$
$983$			2.68863e10i			0.902806i	−0.892320	+	0.451403i	$0.850924\pi$
$984$	1.04279e10	+	2.27700e10i	0.348910	+	0.761870i
$985$		−	3.85161e10i		−	1.28415i
$986$	6.86386e9	+	5.13566e10i	0.228034	+	1.70619i
$987$	−1.25344e10	−	1.17836e10i	−0.414948	−	0.390092i
$988$	2.25205e9	+	8.27461e9i	0.0742896	+	0.272959i
$989$	4.86680e9	+	4.86680e9i	0.159977	+	0.159977i
$990$	−3.10524e10	−	2.08274e10i	−1.01712	−	0.682199i
$991$		−	1.94023e10i		−	0.633279i	−0.948546	−	0.316639i	$-0.897445\pi$
$991$		−	1.94023e10i		−	0.633279i	0.948546	−	0.316639i	$-0.102555\pi$
$992$	4.98678e10	+	6.06768e9i	1.62192	+	0.197348i
$993$	5.70669e10	−	1.76203e9i	1.84953	−	0.0571074i
$994$	−3.80861e9	−	2.91058e9i	−0.123002	−	0.0939999i
$995$	1.44453e10	−	1.44453e10i	0.464886	−	0.464886i
$996$	−1.33391e9	−	4.36478e9i	−0.0427779	−	0.139976i
$997$	−5.54457e9	−	5.54457e9i	−0.177188	−	0.177188i	0.612941	−	0.790129i	$-0.289986\pi$
$997$	−5.54457e9	−	5.54457e9i	−0.177188	−	0.177188i	−0.790129	+	0.612941i	$0.789986\pi$
$998$	4.69446e9	−	6.27420e8i	0.149496	−	0.0199803i
$999$	2.15789e10	−	2.00395e9i	0.684778	−	0.0635927i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.8.k.a.11.17	✓	108
3.2	odd	2	inner	48.8.k.a.11.38	yes	108
16.3	odd	4	inner	48.8.k.a.35.38	yes	108
48.35	even	4	inner	48.8.k.a.35.17	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.8.k.a.11.17	✓	108	1.1	even	1	trivial
48.8.k.a.11.38	yes	108	3.2	odd	2	inner
48.8.k.a.35.17	yes	108	48.35	even	4	inner
48.8.k.a.35.38	yes	108	16.3	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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	48.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.86971 + 8.98928i) q^{2} +(34.0729 + 32.0318i) q^{3} +(-33.6142 - 123.507i) q^{4} +(201.123 - 201.123i) q^{5} +(-522.014 + 86.2416i) q^{6} -1025.82 q^{7} +(1341.16 + 546.292i) q^{8} +(134.926 + 2182.83i) q^{9} +O(q^{10})\)	\(q+(-6.86971 + 8.98928i) q^{2} +(34.0729 + 32.0318i) q^{3} +(-33.6142 - 123.507i) q^{4} +(201.123 - 201.123i) q^{5} +(-522.014 + 86.2416i) q^{6} -1025.82 q^{7} +(1341.16 + 546.292i) q^{8} +(134.926 + 2182.83i) q^{9} +(426.294 + 3189.61i) q^{10} +(3756.76 + 3756.76i) q^{11} +(2810.83 - 5284.98i) q^{12} +(-4614.47 + 4614.47i) q^{13} +(7047.08 - 9221.38i) q^{14} +(13295.2 - 410.511i) q^{15} +(-14124.2 + 8303.21i) q^{16} +25813.8i q^{17} +(-20549.0 - 13782.5i) q^{18} +(7259.43 + 7259.43i) q^{19} +(-31600.8 - 18079.6i) q^{20} +(-34952.7 - 32858.9i) q^{21} +(-59578.4 + 7962.71i) q^{22} +7050.99i q^{23} +(28198.6 + 61573.6i) q^{24} -2775.87i q^{25} +(-9780.69 - 73180.8i) q^{26} +(-65322.8 + 78697.4i) q^{27} +(34482.1 + 126696. i) q^{28} +(-125449. - 125449. i) q^{29} +(-87643.8 + 122334. i) q^{30} +271011. i q^{31} +(22389.0 - 184007. i) q^{32} +(7667.89 + 248339. i) q^{33} +(-232048. - 177333. i) q^{34} +(-206316. + 206316. i) q^{35} +(265061. - 90038.6i) q^{36} +(-149832. - 149832. i) q^{37} +(-115127. + 15386.9i) q^{38} +(-305038. + 9418.56i) q^{39} +(379610. - 159867. i) q^{40} +369802. q^{41} +(535492. - 88468.3i) q^{42} +(690229. - 690229. i) q^{43} +(337707. - 590268. i) q^{44} +(466155. + 411881. i) q^{45} +(-63383.3 - 48438.2i) q^{46} +358611. q^{47} +(-747218. - 169508. i) q^{48} +228763. q^{49} +(24953.1 + 19069.4i) q^{50} +(-826863. + 879552. i) q^{51} +(725033. + 414809. i) q^{52} +(-738128. + 738128. i) q^{53} +(-258684. - 1.12783e6i) q^{54} +1.51114e6 q^{55} +(-1.37579e6 - 560398. i) q^{56} +(14817.2 + 479883. i) q^{57} +(1.98950e6 - 265899. i) q^{58} +(1.62939e6 + 1.62939e6i) q^{59} +(-497608. - 1.62825e6i) q^{60} +(-1.07174e6 + 1.07174e6i) q^{61} +(-2.43619e6 - 1.86177e6i) q^{62} +(-138410. - 2.23919e6i) q^{63} +(1.50028e6 + 1.46533e6i) q^{64} +1.85615e6i q^{65} +(-2.28507e6 - 1.63709e6i) q^{66} +(-958120. - 958120. i) q^{67} +(3.18820e6 - 867711. i) q^{68} +(-225856. + 240248. i) q^{69} +(-437301. - 3.27196e6i) q^{70} -413019. i q^{71} +(-1.01151e6 + 3.00124e6i) q^{72} +3.94535e6i q^{73} +(2.37619e6 - 317580. i) q^{74} +(88916.3 - 94582.1i) q^{75} +(652573. - 1.14061e6i) q^{76} +(-3.85376e6 - 3.85376e6i) q^{77} +(2.01086e6 - 2.80678e6i) q^{78} -3.80043e6i q^{79} +(-1.17073e6 + 4.51066e6i) q^{80} +(-4.74656e6 + 589042. i) q^{81} +(-2.54043e6 + 3.32425e6i) q^{82} +(539140. - 539140. i) q^{83} +(-2.88341e6 + 5.42144e6i) q^{84} +(5.19175e6 + 5.19175e6i) q^{85} +(1.46299e6 + 1.09463e7i) q^{86} +(-256054. - 8.29280e6i) q^{87} +(2.98613e6 + 7.09071e6i) q^{88} +5.01486e6 q^{89} +(-6.90486e6 + 1.36089e6i) q^{90} +(4.73361e6 - 4.73361e6i) q^{91} +(870849. - 237013. i) q^{92} +(-8.68097e6 + 9.23413e6i) q^{93} +(-2.46355e6 + 3.22366e6i) q^{94} +2.92008e6 q^{95} +(6.65693e6 - 5.55248e6i) q^{96} -1.16410e7 q^{97} +(-1.57154e6 + 2.05642e6i) q^{98} +(-7.69350e6 + 8.70726e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 2 q^{3} - 4 q^{4} + 172 q^{6} - 8 q^{7}+O(q^{10}) \) 108 * q - 2 * q^3 - 4 * q^4 + 172 * q^6 - 8 * q^7	\( 108 q - 2 q^{3} - 4 q^{4} + 172 q^{6} - 8 q^{7} - 6504 q^{10} + 12016 q^{12} - 4 q^{13} - 55280 q^{16} + 21172 q^{18} - 60588 q^{19} - 4376 q^{21} - 212744 q^{22} - 317304 q^{24} + 238042 q^{27} + 219736 q^{28} - 503852 q^{30} - 4 q^{33} - 364856 q^{34} + 867620 q^{36} - 4 q^{37} - 283948 q^{39} + 390392 q^{40} - 3022344 q^{42} + 752844 q^{43} - 156252 q^{45} - 1166824 q^{46} + 358320 q^{48} + 9882508 q^{49} + 1121592 q^{51} - 4458688 q^{52} + 203816 q^{54} + 4191000 q^{55} + 4975544 q^{58} - 4390240 q^{60} - 2279892 q^{61} + 4781432 q^{64} + 1457476 q^{66} + 1552540 q^{67} + 4372 q^{69} - 9366152 q^{70} - 1660280 q^{72} - 886066 q^{75} - 6569272 q^{76} - 13616772 q^{78} - 4 q^{81} + 11560256 q^{82} - 10944176 q^{84} + 7846496 q^{85} - 40789116 q^{87} + 24614816 q^{88} + 25746032 q^{90} - 1590680 q^{91} - 14495396 q^{93} - 6995856 q^{94} - 13927736 q^{96} - 8 q^{97} - 4701076 q^{99}+O(q^{100}) \) 108 * q - 2 * q^3 - 4 * q^4 + 172 * q^6 - 8 * q^7 - 6504 * q^10 + 12016 * q^12 - 4 * q^13 - 55280 * q^16 + 21172 * q^18 - 60588 * q^19 - 4376 * q^21 - 212744 * q^22 - 317304 * q^24 + 238042 * q^27 + 219736 * q^28 - 503852 * q^30 - 4 * q^33 - 364856 * q^34 + 867620 * q^36 - 4 * q^37 - 283948 * q^39 + 390392 * q^40 - 3022344 * q^42 + 752844 * q^43 - 156252 * q^45 - 1166824 * q^46 + 358320 * q^48 + 9882508 * q^49 + 1121592 * q^51 - 4458688 * q^52 + 203816 * q^54 + 4191000 * q^55 + 4975544 * q^58 - 4390240 * q^60 - 2279892 * q^61 + 4781432 * q^64 + 1457476 * q^66 + 1552540 * q^67 + 4372 * q^69 - 9366152 * q^70 - 1660280 * q^72 - 886066 * q^75 - 6569272 * q^76 - 13616772 * q^78 - 4 * q^81 + 11560256 * q^82 - 10944176 * q^84 + 7846496 * q^85 - 40789116 * q^87 + 24614816 * q^88 + 25746032 * q^90 - 1590680 * q^91 - 14495396 * q^93 - 6995856 * q^94 - 13927736 * q^96 - 8 * q^97 - 4701076 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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