LMFDB - Embedded newform 177.8.a.c.1.7

Newspace parameters

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$55.2921495107$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
Defining polynomial:	$x^{17} - 2 x^{16} - 1669 x^{15} + 2385 x^{14} + 1108684 x^{13} - 848131 x^{12} - 377920980 x^{11} + 12724944 x^{10} + 71331230512 x^{9} + 50741131904 x^{8} - 7480805165760 x^{7} - 10751966150272 x^{6} + 413177144536320 x^{5} + 886760582981376 x^{4} - 10454479722123264 x^{3} - 29180140031461376 x^{2} + 79787300207378432 x + 248723246810300416$
Coefficient ring:	$\Z[a_1, \ldots, a_{31}]$
Coefficient ring index:	multiple of $ 2^{10}\cdot 3^{5} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-5.66556$ of defining polynomial
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q-5.66556 q^{2} -27.0000 q^{3} -95.9014 q^{4} +117.894 q^{5} +152.970 q^{6} +1197.66 q^{7} +1268.53 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-5.66556 q^{2} -27.0000 q^{3} -95.9014 q^{4} +117.894 q^{5} +152.970 q^{6} +1197.66 q^{7} +1268.53 q^{8} +729.000 q^{9} -667.937 q^{10} -6536.63 q^{11} +2589.34 q^{12} +11916.5 q^{13} -6785.43 q^{14} -3183.14 q^{15} +5088.45 q^{16} +29402.4 q^{17} -4130.20 q^{18} +3457.38 q^{19} -11306.2 q^{20} -32336.9 q^{21} +37033.7 q^{22} -37722.6 q^{23} -34250.2 q^{24} -64225.9 q^{25} -67514.0 q^{26} -19683.0 q^{27} -114857. q^{28} -207751. q^{29} +18034.3 q^{30} +111488. q^{31} -191200. q^{32} +176489. q^{33} -166581. q^{34} +141197. q^{35} -69912.1 q^{36} -49565.3 q^{37} -19588.0 q^{38} -321747. q^{39} +149552. q^{40} +112884. q^{41} +183207. q^{42} -38995.6 q^{43} +626872. q^{44} +85944.9 q^{45} +213720. q^{46} +1.22368e6 q^{47} -137388. q^{48} +610852. q^{49} +363876. q^{50} -793865. q^{51} -1.14281e6 q^{52} -475269. q^{53} +111515. q^{54} -770631. q^{55} +1.51927e6 q^{56} -93349.3 q^{57} +1.17702e6 q^{58} -205379. q^{59} +305268. q^{60} +699413. q^{61} -631640. q^{62} +873096. q^{63} +431937. q^{64} +1.40489e6 q^{65} -999909. q^{66} -3.23969e6 q^{67} -2.81973e6 q^{68} +1.01851e6 q^{69} -799963. q^{70} +5.13542e6 q^{71} +924757. q^{72} +5.08296e6 q^{73} +280816. q^{74} +1.73410e6 q^{75} -331568. q^{76} -7.82867e6 q^{77} +1.82288e6 q^{78} +7.01416e6 q^{79} +599899. q^{80} +531441. q^{81} -639551. q^{82} +6.20880e6 q^{83} +3.10115e6 q^{84} +3.46637e6 q^{85} +220932. q^{86} +5.60927e6 q^{87} -8.29189e6 q^{88} +1.44794e6 q^{89} -486926. q^{90} +1.42720e7 q^{91} +3.61765e6 q^{92} -3.01017e6 q^{93} -6.93283e6 q^{94} +407605. q^{95} +5.16241e6 q^{96} -1.19209e7 q^{97} -3.46082e6 q^{98} -4.76520e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17q + 2q^{2} - 459q^{3} + 1166q^{4} - 318q^{5} - 54q^{6} + 3145q^{7} + 2355q^{8} + 12393q^{9} + O(q^{10}) $	\( 17q + 2q^{2} - 459q^{3} + 1166q^{4} - 318q^{5} - 54q^{6} + 3145q^{7} + 2355q^{8} + 12393q^{9} + 6521q^{10} - 1764q^{11} - 31482q^{12} + 18192q^{13} - 7827q^{14} + 8586q^{15} + 139226q^{16} - 15507q^{17} + 1458q^{18} + 52083q^{19} + 721q^{20} - 84915q^{21} - 234434q^{22} + 63823q^{23} - 63585q^{24} + 202153q^{25} - 367956q^{26} - 334611q^{27} + 182306q^{28} - 502955q^{29} - 176067q^{30} + 347531q^{31} - 243908q^{32} + 47628q^{33} - 330872q^{34} + 92641q^{35} + 850014q^{36} + 447615q^{37} + 775669q^{38} - 491184q^{39} + 2203270q^{40} + 940335q^{41} + 211329q^{42} + 478562q^{43} - 596924q^{44} - 231822q^{45} - 3078663q^{46} + 703121q^{47} - 3759102q^{48} + 1895082q^{49} - 876967q^{50} + 418689q^{51} + 6278296q^{52} - 1005974q^{53} - 39366q^{54} + 5212846q^{55} + 3425294q^{56} - 1406241q^{57} + 6710166q^{58} - 3491443q^{59} - 19467q^{60} + 11510749q^{61} + 5996234q^{62} + 2292705q^{63} + 29496941q^{64} + 11094180q^{65} + 6329718q^{66} + 14007144q^{67} + 19688159q^{68} - 1723221q^{69} + 30909708q^{70} + 5229074q^{71} + 1716795q^{72} + 5452211q^{73} + 12819662q^{74} - 5458131q^{75} + 41929340q^{76} + 9930777q^{77} + 9934812q^{78} + 15275654q^{79} + 36576105q^{80} + 9034497q^{81} + 32025935q^{82} + 7826609q^{83} - 4922262q^{84} + 11836945q^{85} + 51649136q^{86} + 13579785q^{87} + 30223741q^{88} - 6436185q^{89} + 4753809q^{90} + 11633535q^{91} + 43357972q^{92} - 9383337q^{93} - 4494252q^{94} + 23741055q^{95} + 6585516q^{96} + 26377540q^{97} + 26517816q^{98} - 1285956q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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 $

$2$	−5.66556	−0.500770	−0.250385	−	0.968146i	$-0.580557\pi$
$2$	−5.66556	−0.500770	−0.250385	+	0.968146i	$0.580557\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	−95.9014	−0.749230
$5$	117.894	0.421791	0.210896	−	0.977509i	$-0.432362\pi$
$5$	117.894	0.421791	0.210896	+	0.977509i	$0.432362\pi$
$6$	152.970	0.289120
$7$	1197.66	1.31975	0.659874	−	0.751376i	$-0.270609\pi$
$7$	1197.66	1.31975	0.659874	+	0.751376i	$0.270609\pi$
$8$	1268.53	0.875961
$9$	729.000	0.333333
$10$	−667.937	−0.211220
$11$	−6536.63	−1.48074	−0.740371	−	0.672199i	$-0.765350\pi$
$11$	−6536.63	−1.48074	−0.740371	+	0.672199i	$0.765350\pi$
$12$	2589.34	0.432568
$13$	11916.5	1.50435	0.752175	−	0.658964i	$-0.229005\pi$
$13$	11916.5	1.50435	0.752175	+	0.658964i	$0.229005\pi$
$14$	−6785.43	−0.660890
$15$	−3183.14	−0.243521
$16$	5088.45	0.310574
$17$	29402.4	1.45148	0.725741	−	0.687968i	$-0.241497\pi$
$17$	29402.4	1.45148	0.725741	+	0.687968i	$0.241497\pi$
$18$	−4130.20	−0.166923
$19$	3457.38	0.115640	0.0578202	−	0.998327i	$-0.481585\pi$
$19$	3457.38	0.115640	0.0578202	+	0.998327i	$0.481585\pi$
$20$	−11306.2	−0.316018
$21$	−32336.9	−0.761957
$22$	37033.7	0.741511
$23$	−37722.6	−0.646479	−0.323239	−	0.946317i	$-0.604772\pi$
$23$	−37722.6	−0.646479	−0.323239	+	0.946317i	$0.604772\pi$
$24$	−34250.2	−0.505737
$25$	−64225.9	−0.822092
$26$	−67514.0	−0.753333
$27$	−19683.0	−0.192450
$28$	−114857.	−0.988795
$29$	−207751.	−1.58179	−0.790896	−	0.611951i	$-0.790385\pi$
$29$	−207751.	−1.58179	−0.790896	+	0.611951i	$0.790385\pi$
$30$	18034.3	0.121948
$31$	111488.	0.672141	0.336071	−	0.941837i	$-0.390902\pi$
$31$	111488.	0.672141	0.336071	+	0.941837i	$0.390902\pi$
$32$	−191200.	−1.03149
$33$	176489.	0.854907
$34$	−166581.	−0.726858
$35$	141197.	0.556658
$36$	−69912.1	−0.249743
$37$	−49565.3	−0.160869	−0.0804344	−	0.996760i	$-0.525631\pi$
$37$	−49565.3	−0.160869	−0.0804344	+	0.996760i	$0.525631\pi$
$38$	−19588.0	−0.0579092
$39$	−321747.	−0.868536
$40$	149552.	0.369473
$41$	112884.	0.255793	0.127896	−	0.991788i	$-0.459177\pi$
$41$	112884.	0.255793	0.127896	+	0.991788i	$0.459177\pi$
$42$	183207.	0.381565
$43$	−38995.6	−0.0747956	−0.0373978	−	0.999300i	$-0.511907\pi$
$43$	−38995.6	−0.0747956	−0.0373978	+	0.999300i	$0.511907\pi$
$44$	626872.	1.10942
$45$	85944.9	0.140597
$46$	213720.	0.323737
$47$	1.22368e6	1.71919	0.859597	−	0.510972i	$-0.170715\pi$
$47$	1.22368e6	1.71919	0.859597	+	0.510972i	$0.170715\pi$
$48$	−137388.	−0.179310
$49$	610852.	0.741737
$50$	363876.	0.411679
$51$	−793865.	−0.838013
$52$	−1.14281e6	−1.12710
$53$	−475269.	−0.438504	−0.219252	−	0.975668i	$-0.570362\pi$
$53$	−475269.	−0.438504	−0.219252	+	0.975668i	$0.570362\pi$
$54$	111515.	0.0963732
$55$	−770631.	−0.624564
$56$	1.51927e6	1.15605
$57$	−93349.3	−0.0667650
$58$	1.17702e6	0.792114
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	305268.	0.182453
$61$	699413.	0.394529	0.197265	−	0.980350i	$-0.436794\pi$
$61$	699413.	0.394529	0.197265	+	0.980350i	$0.436794\pi$
$62$	−631640.	−0.336588
$63$	873096.	0.439916
$64$	431937.	0.205964
$65$	1.40489e6	0.634521
$66$	−999909.	−0.428111
$67$	−3.23969e6	−1.31596	−0.657979	−	0.753036i	$-0.728589\pi$
$67$	−3.23969e6	−1.31596	−0.657979	+	0.753036i	$0.728589\pi$
$68$	−2.81973e6	−1.08749
$69$	1.01851e6	0.373245
$70$	−799963.	−0.278758
$71$	5.13542e6	1.70283	0.851417	−	0.524490i	$-0.175744\pi$
$71$	5.13542e6	1.70283	0.851417	+	0.524490i	$0.175744\pi$
$72$	924757.	0.291987
$73$	5.08296e6	1.52928	0.764639	−	0.644459i	$-0.222917\pi$
$73$	5.08296e6	1.52928	0.764639	+	0.644459i	$0.222917\pi$
$74$	280816.	0.0805583
$75$	1.73410e6	0.474635
$76$	−331568.	−0.0866412
$77$	−7.82867e6	−1.95421
$78$	1.82288e6	0.434937
$79$	7.01416e6	1.60059	0.800296	−	0.599605i	$-0.204675\pi$
$79$	7.01416e6	1.60059	0.800296	+	0.599605i	$0.204675\pi$
$80$	599899.	0.130998
$81$	531441.	0.111111
$82$	−639551.	−0.128093
$83$	6.20880e6	1.19188	0.595942	−	0.803027i	$-0.296779\pi$
$83$	6.20880e6	1.19188	0.595942	+	0.803027i	$0.296779\pi$
$84$	3.10115e6	0.570881
$85$	3.46637e6	0.612222
$86$	220932.	0.0374554
$87$	5.60927e6	0.913248
$88$	−8.29189e6	−1.29707
$89$	1.44794e6	0.217714	0.108857	−	0.994057i	$-0.465281\pi$
$89$	1.44794e6	0.217714	0.108857	+	0.994057i	$0.465281\pi$
$90$	−486926.	−0.0704068
$91$	1.42720e7	1.98536
$92$	3.61765e6	0.484361
$93$	−3.01017e6	−0.388061
$94$	−6.93283e6	−0.860921
$95$	407605.	0.0487761
$96$	5.16241e6	0.595530
$97$	−1.19209e7	−1.32620	−0.663098	−	0.748532i	$-0.730759\pi$
$97$	−1.19209e7	−1.32620	−0.663098	+	0.748532i	$0.730759\pi$
$98$	−3.46082e6	−0.371439
$99$	−4.76520e6	−0.493581
$100$	6.15936e6	0.615936
$101$	−1.33614e7	−1.29041	−0.645205	−	0.764009i	$-0.723228\pi$
$101$	−1.33614e7	−1.29041	−0.645205	+	0.764009i	$0.723228\pi$
$102$	4.49769e6	0.419652
$103$	2.58316e6	0.232928	0.116464	−	0.993195i	$-0.462844\pi$
$103$	2.58316e6	0.232928	0.116464	+	0.993195i	$0.462844\pi$
$104$	1.51165e7	1.31775
$105$	−3.81233e6	−0.321387
$106$	2.69266e6	0.219590
$107$	−4.52462e6	−0.357058	−0.178529	−	0.983935i	$-0.557134\pi$
$107$	−4.52462e6	−0.357058	−0.178529	+	0.983935i	$0.557134\pi$
$108$	1.88763e6	0.144189
$109$	−312613.	−0.0231214	−0.0115607	−	0.999933i	$-0.503680\pi$
$109$	−312613.	−0.0231214	−0.0115607	+	0.999933i	$0.503680\pi$
$110$	4.36606e6	0.312763
$111$	1.33826e6	0.0928777
$112$	6.09425e6	0.409880
$113$	4.97336e6	0.324246	0.162123	−	0.986771i	$-0.448166\pi$
$113$	4.97336e6	0.324246	0.162123	+	0.986771i	$0.448166\pi$
$114$	528876.	0.0334339
$115$	−4.44728e6	−0.272679
$116$	1.99236e7	1.18513
$117$	8.68716e6	0.501450
$118$	1.16359e6	0.0651947
$119$	3.52141e7	1.91559
$120$	−4.03791e6	−0.213315
$121$	2.32403e7	1.19260
$122$	−3.96257e6	−0.197568
$123$	−3.04786e6	−0.147682
$124$	−1.06918e7	−0.503588
$125$	−1.67824e7	−0.768543
$126$	−4.94658e6	−0.220297
$127$	4.34322e7	1.88148	0.940738	−	0.339134i	$-0.110134\pi$
$127$	4.34322e7	1.88148	0.940738	+	0.339134i	$0.110134\pi$
$128$	2.20265e7	0.928347
$129$	1.05288e6	0.0431833
$130$	−7.95951e6	−0.317749
$131$	−3.43447e7	−1.33478	−0.667391	−	0.744707i	$-0.732589\pi$
$131$	−3.43447e7	−1.33478	−0.667391	+	0.744707i	$0.732589\pi$
$132$	−1.69255e7	−0.640521
$133$	4.14077e6	0.152616
$134$	1.83547e7	0.658992
$135$	−2.32051e6	−0.0811738
$136$	3.72978e7	1.27144
$137$	−5.15704e7	−1.71348	−0.856738	−	0.515752i	$-0.827513\pi$
$137$	−5.15704e7	−1.71348	−0.856738	+	0.515752i	$0.827513\pi$
$138$	−5.77044e6	−0.186910
$139$	6.25955e7	1.97693	0.988466	−	0.151444i	$-0.0483924\pi$
$139$	6.25955e7	1.97693	0.988466	+	0.151444i	$0.0483924\pi$
$140$	−1.35410e7	−0.417065
$141$	−3.30393e7	−0.992577
$142$	−2.90951e7	−0.852728
$143$	−7.78940e7	−2.22755
$144$	3.70948e6	0.103525
$145$	−2.44926e7	−0.667186
$146$	−2.87978e7	−0.765816
$147$	−1.64930e7	−0.428242
$148$	4.75338e6	0.120528
$149$	−4.84710e6	−0.120041	−0.0600206	−	0.998197i	$-0.519117\pi$
$149$	−4.84710e6	−0.120041	−0.0600206	+	0.998197i	$0.519117\pi$
$150$	−9.82466e6	−0.237683
$151$	7.66941e7	1.81277	0.906385	−	0.422452i	$-0.138831\pi$
$151$	7.66941e7	1.81277	0.906385	+	0.422452i	$0.138831\pi$
$152$	4.38578e6	0.101297
$153$	2.14344e7	0.483827
$154$	4.43538e7	0.978608
$155$	1.31437e7	0.283503
$156$	3.08560e7	0.650733
$157$	−4.97181e6	−0.102534	−0.0512668	−	0.998685i	$-0.516326\pi$
$157$	−4.97181e6	−0.102534	−0.0512668	+	0.998685i	$0.516326\pi$
$158$	−3.97392e7	−0.801529
$159$	1.28323e7	0.253170
$160$	−2.25414e7	−0.435073
$161$	−4.51790e7	−0.853190
$162$	−3.01091e6	−0.0556411
$163$	1.80568e7	0.326577	0.163288	−	0.986578i	$-0.447790\pi$
$163$	1.80568e7	0.326577	0.163288	+	0.986578i	$0.447790\pi$
$164$	−1.08257e7	−0.191648
$165$	2.08070e7	0.360592
$166$	−3.51763e7	−0.596860
$167$	−3.89288e7	−0.646790	−0.323395	−	0.946264i	$-0.604824\pi$
$167$	−3.89288e7	−0.646790	−0.323395	+	0.946264i	$0.604824\pi$
$168$	−4.10202e7	−0.667445
$169$	7.92556e7	1.26307
$170$	−1.96390e7	−0.306582
$171$	2.52043e6	0.0385468
$172$	3.73973e6	0.0560391
$173$	9.04299e7	1.32786	0.663928	−	0.747797i	$-0.268888\pi$
$173$	9.04299e7	1.32786	0.663928	+	0.747797i	$0.268888\pi$
$174$	−3.17797e7	−0.457327
$175$	−7.69210e7	−1.08496
$176$	−3.32613e7	−0.459881
$177$	5.54523e6	0.0751646
$178$	−8.20342e6	−0.109025
$179$	1.14493e7	0.149208	0.0746042	−	0.997213i	$-0.476231\pi$
$179$	1.14493e7	0.149208	0.0746042	+	0.997213i	$0.476231\pi$
$180$	−8.24223e6	−0.105339
$181$	−9.25112e7	−1.15963	−0.579815	−	0.814748i	$-0.696875\pi$
$181$	−9.25112e7	−1.15963	−0.579815	+	0.814748i	$0.696875\pi$
$182$	−8.08589e7	−0.994210
$183$	−1.88841e7	−0.227781
$184$	−4.78522e7	−0.566291
$185$	−5.84347e6	−0.0678531
$186$	1.70543e7	0.194329
$187$	−1.92193e8	−2.14927
$188$	−1.17353e8	−1.28807
$189$	−2.35736e7	−0.253986
$190$	−2.30931e6	−0.0244256
$191$	2.78323e7	0.289023	0.144511	−	0.989503i	$-0.453839\pi$
$191$	2.78323e7	0.289023	0.144511	+	0.989503i	$0.453839\pi$
$192$	−1.16623e7	−0.118913
$193$	−3.52675e7	−0.353122	−0.176561	−	0.984290i	$-0.556497\pi$
$193$	−3.52675e7	−0.353122	−0.176561	+	0.984290i	$0.556497\pi$
$194$	6.75386e7	0.664119
$195$	−3.79321e7	−0.366341
$196$	−5.85816e7	−0.555731
$197$	1.76100e8	1.64107	0.820536	−	0.571595i	$-0.193675\pi$
$197$	1.76100e8	1.64107	0.820536	+	0.571595i	$0.193675\pi$
$198$	2.69976e7	0.247170
$199$	1.94813e8	1.75239	0.876196	−	0.481954i	$-0.160073\pi$
$199$	1.94813e8	1.75239	0.876196	+	0.481954i	$0.160073\pi$
$200$	−8.14724e7	−0.720121
$201$	8.74717e7	0.759769
$202$	7.57000e7	0.646199
$203$	−2.48815e8	−2.08757
$204$	7.61327e7	0.627864
$205$	1.33084e7	0.107891
$206$	−1.46351e7	−0.116643
$207$	−2.74998e7	−0.215493
$208$	6.06368e7	0.467212
$209$	−2.25996e7	−0.171234
$210$	2.15990e7	0.160941
$211$	9.43223e7	0.691235	0.345617	−	0.938376i	$-0.387670\pi$
$211$	9.43223e7	0.691235	0.345617	+	0.938376i	$0.387670\pi$
$212$	4.55789e7	0.328540
$213$	−1.38656e8	−0.983131
$214$	2.56345e7	0.178804
$215$	−4.59736e6	−0.0315481
$216$	−2.49684e7	−0.168579
$217$	1.33525e8	0.887058
$218$	1.77113e6	0.0115785
$219$	−1.37240e8	−0.882929
$220$	7.39045e7	0.467942
$221$	3.50375e8	2.18354
$222$	−7.58202e6	−0.0465103
$223$	−3.04202e8	−1.83694	−0.918470	−	0.395492i	$-0.870574\pi$
$223$	−3.04202e8	−1.83694	−0.918470	+	0.395492i	$0.870574\pi$
$224$	−2.28994e8	−1.36130
$225$	−4.68207e7	−0.274031
$226$	−2.81769e7	−0.162373
$227$	1.54534e8	0.876866	0.438433	−	0.898764i	$-0.355534\pi$
$227$	1.54534e8	0.876866	0.438433	+	0.898764i	$0.355534\pi$
$228$	8.95232e6	0.0500223
$229$	1.18030e8	0.649485	0.324742	−	0.945803i	$-0.394722\pi$
$229$	1.18030e8	0.649485	0.324742	+	0.945803i	$0.394722\pi$
$230$	2.51963e7	0.136550
$231$	2.11374e8	1.12826
$232$	−2.63537e8	−1.38559
$233$	−6.82032e7	−0.353231	−0.176615	−	0.984280i	$-0.556515\pi$
$233$	−6.82032e7	−0.353231	−0.176615	+	0.984280i	$0.556515\pi$
$234$	−4.92177e7	−0.251111
$235$	1.44265e8	0.725141
$236$	1.96961e7	0.0975414
$237$	−1.89382e8	−0.924103
$238$	−1.99508e8	−0.959270
$239$	−8.01024e7	−0.379536	−0.189768	−	0.981829i	$-0.560774\pi$
$239$	−8.01024e7	−0.379536	−0.189768	+	0.981829i	$0.560774\pi$
$240$	−1.61973e7	−0.0756315
$241$	9.44904e7	0.434839	0.217419	−	0.976078i	$-0.430236\pi$
$241$	9.44904e7	0.434839	0.217419	+	0.976078i	$0.430236\pi$
$242$	−1.31670e8	−0.597216
$243$	−1.43489e7	−0.0641500
$244$	−6.70746e7	−0.295593
$245$	7.20159e7	0.312858
$246$	1.72679e7	0.0739547
$247$	4.12000e7	0.173964
$248$	1.41425e8	0.588770
$249$	−1.67638e8	−0.688135
$250$	9.50815e7	0.384863
$251$	−2.37800e8	−0.949191	−0.474596	−	0.880204i	$-0.657406\pi$
$251$	−2.37800e8	−0.949191	−0.474596	+	0.880204i	$0.657406\pi$
$252$	−8.37311e7	−0.329598
$253$	2.46579e8	0.957268
$254$	−2.46068e8	−0.942187
$255$	−9.35921e7	−0.353467
$256$	−1.80080e8	−0.670852
$257$	673684.	0.00247566	0.00123783	−	0.999999i	$-0.499606\pi$
$257$	673684.	0.00247566	0.00123783	+	0.999999i	$0.499606\pi$
$258$	−5.96517e6	−0.0216249
$259$	−5.93625e7	−0.212307
$260$	−1.34731e8	−0.475402
$261$	−1.51450e8	−0.527264
$262$	1.94582e8	0.668419
$263$	−3.23561e7	−0.109676	−0.0548380	−	0.998495i	$-0.517464\pi$
$263$	−3.23561e7	−0.109676	−0.0548380	+	0.998495i	$0.517464\pi$
$264$	2.23881e8	0.748865
$265$	−5.60314e7	−0.184957
$266$	−2.34598e7	−0.0764256
$267$	−3.90945e7	−0.125697
$268$	3.10691e8	0.985955
$269$	2.61753e8	0.819896	0.409948	−	0.912109i	$-0.365547\pi$
$269$	2.61753e8	0.819896	0.409948	+	0.912109i	$0.365547\pi$
$270$	1.31470e7	0.0406494
$271$	6.21861e8	1.89802	0.949011	−	0.315244i	$-0.102086\pi$
$271$	6.21861e8	1.89802	0.949011	+	0.315244i	$0.102086\pi$
$272$	1.49613e8	0.450793
$273$	−3.85344e8	−1.14625
$274$	2.92175e8	0.858057
$275$	4.19821e8	1.21731
$276$	−9.76766e7	−0.279646
$277$	2.81765e8	0.796541	0.398270	−	0.917268i	$-0.369611\pi$
$277$	2.81765e8	0.796541	0.398270	+	0.917268i	$0.369611\pi$
$278$	−3.54639e8	−0.989988
$279$	8.12745e7	0.224047
$280$	1.79113e8	0.487611
$281$	2.34019e8	0.629186	0.314593	−	0.949227i	$-0.398132\pi$
$281$	2.34019e8	0.629186	0.314593	+	0.949227i	$0.398132\pi$
$282$	1.87186e8	0.497053
$283$	−3.59081e8	−0.941759	−0.470879	−	0.882198i	$-0.656063\pi$
$283$	−3.59081e8	−0.941759	−0.470879	+	0.882198i	$0.656063\pi$
$284$	−4.92494e8	−1.27581
$285$	−1.10053e7	−0.0281609
$286$	4.41314e8	1.11549
$287$	1.35197e8	0.337582
$288$	−1.39385e8	−0.343829
$289$	4.54163e8	1.10680
$290$	1.38764e8	0.334107
$291$	3.21864e8	0.765680
$292$	−4.87463e8	−1.14578
$293$	2.48310e8	0.576711	0.288355	−	0.957523i	$-0.406892\pi$
$293$	2.48310e8	0.576711	0.288355	+	0.957523i	$0.406892\pi$
$294$	9.34422e7	0.214451
$295$	−2.42130e7	−0.0549125
$296$	−6.28750e7	−0.140915
$297$	1.28660e8	0.284969
$298$	2.74616e7	0.0601130
$299$	−4.49523e8	−0.972530
$300$	−1.66303e8	−0.355611
$301$	−4.67036e7	−0.0987114
$302$	−4.34516e8	−0.907781
$303$	3.60758e8	0.745019
$304$	1.75927e7	0.0359150
$305$	8.24567e7	0.166409
$306$	−1.21438e8	−0.242286
$307$	1.92429e8	0.379566	0.189783	−	0.981826i	$-0.439222\pi$
$307$	1.92429e8	0.379566	0.189783	+	0.981826i	$0.439222\pi$
$308$	7.50780e8	1.46415
$309$	−6.97454e7	−0.134481
$310$	−7.44667e7	−0.141970
$311$	−4.80733e8	−0.906238	−0.453119	−	0.891450i	$-0.649689\pi$
$311$	−4.80733e8	−0.906238	−0.453119	+	0.891450i	$0.649689\pi$
$312$	−4.08145e8	−0.760804
$313$	7.85937e8	1.44871	0.724357	−	0.689425i	$-0.242137\pi$
$313$	7.85937e8	1.44871	0.724357	+	0.689425i	$0.242137\pi$
$314$	2.81681e7	0.0513457
$315$	1.02933e8	0.185553
$316$	−6.72668e8	−1.19921
$317$	−2.09039e8	−0.368570	−0.184285	−	0.982873i	$-0.558997\pi$
$317$	−2.09039e8	−0.368570	−0.184285	+	0.982873i	$0.558997\pi$
$318$	−7.27019e7	−0.126780
$319$	1.35799e9	2.34222
$320$	5.09229e7	0.0868736
$321$	1.22165e8	0.206148
$322$	2.55964e8	0.427252
$323$	1.01655e8	0.167850
$324$	−5.09659e7	−0.0832477
$325$	−7.65351e8	−1.23671
$326$	−1.02302e8	−0.163540
$327$	8.44054e6	0.0133491
$328$	1.43196e8	0.224065
$329$	1.46555e9	2.26890
$330$	−1.17884e8	−0.180574
$331$	7.95790e8	1.20615	0.603074	−	0.797685i	$-0.293942\pi$
$331$	7.95790e8	1.20615	0.603074	+	0.797685i	$0.293942\pi$
$332$	−5.95432e8	−0.892995
$333$	−3.61331e7	−0.0536230
$334$	2.20554e8	0.323893
$335$	−3.81941e8	−0.555060
$336$	−1.64545e8	−0.236644
$337$	2.75834e8	0.392593	0.196297	−	0.980545i	$-0.437108\pi$
$337$	2.75834e8	0.392593	0.196297	+	0.980545i	$0.437108\pi$
$338$	−4.49027e8	−0.632506
$339$	−1.34281e8	−0.187204
$340$	−3.32430e8	−0.458695
$341$	−7.28753e8	−0.995268
$342$	−1.42797e7	−0.0193031
$343$	−2.54732e8	−0.340843
$344$	−4.94670e7	−0.0655181
$345$	1.20077e8	0.157431
$346$	−5.12337e8	−0.664950
$347$	4.81631e8	0.618816	0.309408	−	0.950929i	$-0.399869\pi$
$347$	4.81631e8	0.618816	0.309408	+	0.950929i	$0.399869\pi$
$348$	−5.37936e8	−0.684232
$349$	−3.21673e8	−0.405066	−0.202533	−	0.979275i	$-0.564917\pi$
$349$	−3.21673e8	−0.405066	−0.202533	+	0.979275i	$0.564917\pi$
$350$	4.35801e8	0.543313
$351$	−2.34553e8	−0.289512
$352$	1.24981e9	1.52737
$353$	1.17516e9	1.42195	0.710977	−	0.703216i	$-0.248253\pi$
$353$	1.17516e9	1.42195	0.710977	+	0.703216i	$0.248253\pi$
$354$	−3.14169e7	−0.0376402
$355$	6.05437e8	0.718240
$356$	−1.38860e8	−0.163118
$357$	−9.50782e8	−1.10597
$358$	−6.48668e7	−0.0747191
$359$	3.28816e8	0.375079	0.187539	−	0.982257i	$-0.439949\pi$
$359$	3.28816e8	0.375079	0.187539	+	0.982257i	$0.439949\pi$
$360$	1.09023e8	0.123158
$361$	−8.81918e8	−0.986627
$362$	5.24128e8	0.580707
$363$	−6.27489e8	−0.688546
$364$	−1.36870e9	−1.48749
$365$	5.99251e8	0.645036
$366$	1.06989e8	0.114066
$367$	−6.95555e8	−0.734515	−0.367257	−	0.930119i	$-0.619703\pi$
$367$	−6.95555e8	−0.734515	−0.367257	+	0.930119i	$0.619703\pi$
$368$	−1.91950e8	−0.200780
$369$	8.22923e7	0.0852643
$370$	3.31065e7	0.0339788
$371$	−5.69211e8	−0.578715
$372$	2.88679e8	0.290747
$373$	1.04776e9	1.04540	0.522699	−	0.852517i	$-0.324925\pi$
$373$	1.04776e9	1.04540	0.522699	+	0.852517i	$0.324925\pi$
$374$	1.08888e9	1.07629
$375$	4.53124e8	0.443718
$376$	1.55227e9	1.50595
$377$	−2.47567e9	−2.37957
$378$	1.33558e8	0.127188
$379$	9.05666e8	0.854537	0.427268	−	0.904125i	$-0.359476\pi$
$379$	9.05666e8	0.854537	0.427268	+	0.904125i	$0.359476\pi$
$380$	−3.90899e7	−0.0365445
$381$	−1.17267e9	−1.08627
$382$	−1.57686e8	−0.144734
$383$	1.13004e9	1.02777	0.513887	−	0.857858i	$-0.328205\pi$
$383$	1.13004e9	1.02777	0.513887	+	0.857858i	$0.328205\pi$
$384$	−5.94715e8	−0.535982
$385$	−9.22955e8	−0.824267
$386$	1.99810e8	0.176833
$387$	−2.84278e7	−0.0249319
$388$	1.14323e9	0.993626
$389$	−9.69975e8	−0.835482	−0.417741	−	0.908566i	$-0.637178\pi$
$389$	−9.69975e8	−0.835482	−0.417741	+	0.908566i	$0.637178\pi$
$390$	2.14907e8	0.183453
$391$	−1.10914e9	−0.938352
$392$	7.74883e8	0.649733
$393$	9.27307e8	0.770637
$394$	−9.97706e8	−0.821799
$395$	8.26929e8	0.675116
$396$	4.56989e8	0.369805
$397$	−1.37378e9	−1.10192	−0.550961	−	0.834531i	$-0.685739\pi$
$397$	−1.37378e9	−1.10192	−0.550961	+	0.834531i	$0.685739\pi$
$398$	−1.10372e9	−0.877546
$399$	−1.11801e8	−0.0881130
$400$	−3.26811e8	−0.255321
$401$	5.72339e8	0.443249	0.221625	−	0.975132i	$-0.428864\pi$
$401$	5.72339e8	0.443249	0.221625	+	0.975132i	$0.428864\pi$
$402$	−4.95577e8	−0.380469
$403$	1.32855e9	1.01114
$404$	1.28138e9	0.966813
$405$	6.26538e7	0.0468657
$406$	1.40968e9	1.04539
$407$	3.23990e8	0.238205
$408$	−1.00704e9	−0.734067
$409$	1.07412e8	0.0776286	0.0388143	−	0.999246i	$-0.487642\pi$
$409$	1.07412e8	0.0776286	0.0388143	+	0.999246i	$0.487642\pi$
$410$	−7.53994e7	−0.0540287
$411$	1.39240e9	0.989276
$412$	−2.47729e8	−0.174516
$413$	−2.45975e8	−0.171817
$414$	1.55802e8	0.107912
$415$	7.31982e8	0.502727
$416$	−2.27845e9	−1.55172
$417$	−1.69008e9	−1.14138
$418$	1.28040e8	0.0857486
$419$	4.96522e8	0.329753	0.164877	−	0.986314i	$-0.447277\pi$
$419$	4.96522e8	0.329753	0.164877	+	0.986314i	$0.447277\pi$
$420$	3.65608e8	0.240793
$421$	2.13271e9	1.39298	0.696490	−	0.717566i	$-0.254744\pi$
$421$	2.13271e9	1.39298	0.696490	+	0.717566i	$0.254744\pi$
$422$	−5.34389e8	−0.346150
$423$	8.92062e8	0.573065
$424$	−6.02891e8	−0.384113
$425$	−1.88840e9	−1.19325
$426$	7.85567e8	0.492323
$427$	8.37660e8	0.520679
$428$	4.33918e8	0.267519
$429$	2.10314e9	1.28608
$430$	2.60466e7	0.0157984
$431$	−2.75546e8	−0.165777	−0.0828885	−	0.996559i	$-0.526415\pi$
$431$	−2.75546e8	−0.165777	−0.0828885	+	0.996559i	$0.526415\pi$
$432$	−1.00156e8	−0.0597701
$433$	1.42964e9	0.846289	0.423144	−	0.906062i	$-0.360926\pi$
$433$	1.42964e9	0.846289	0.423144	+	0.906062i	$0.360926\pi$
$434$	−7.56492e8	−0.444212
$435$	6.61300e8	0.385200
$436$	2.99800e7	0.0173232
$437$	−1.30421e8	−0.0747591
$438$	7.77541e8	0.442144
$439$	−2.29794e9	−1.29632	−0.648161	−	0.761503i	$-0.724462\pi$
$439$	−2.29794e9	−1.29632	−0.648161	+	0.761503i	$0.724462\pi$
$440$	−9.77566e8	−0.547094
$441$	4.45311e8	0.247246
$442$	−1.98507e9	−1.09345
$443$	−5.72726e8	−0.312992	−0.156496	−	0.987679i	$-0.550020\pi$
$443$	−5.72726e8	−0.312992	−0.156496	+	0.987679i	$0.550020\pi$
$444$	−1.28341e8	−0.0695867
$445$	1.70704e8	0.0918300
$446$	1.72347e9	0.919884
$447$	1.30872e8	0.0693058
$448$	5.17315e8	0.271820
$449$	−2.51611e9	−1.31180	−0.655899	−	0.754848i	$-0.727710\pi$
$449$	−2.51611e9	−1.31180	−0.655899	+	0.754848i	$0.727710\pi$
$450$	2.65266e8	0.137226
$451$	−7.37880e8	−0.378763
$452$	−4.76952e8	−0.242935
$453$	−2.07074e9	−1.04660
$454$	−8.75521e8	−0.439108
$455$	1.68259e9	0.837409
$456$	−1.18416e8	−0.0584836
$457$	−9.31683e8	−0.456627	−0.228314	−	0.973588i	$-0.573321\pi$
$457$	−9.31683e8	−0.456627	−0.228314	+	0.973588i	$0.573321\pi$
$458$	−6.68708e8	−0.325242
$459$	−5.78727e8	−0.279338
$460$	4.26500e8	0.204299
$461$	−2.12369e8	−0.100957	−0.0504786	−	0.998725i	$-0.516075\pi$
$461$	−2.12369e8	−0.100957	−0.0504786	+	0.998725i	$0.516075\pi$
$462$	−1.19755e9	−0.565000
$463$	3.14522e9	1.47271	0.736355	−	0.676596i	$-0.236545\pi$
$463$	3.14522e9	1.47271	0.736355	+	0.676596i	$0.236545\pi$
$464$	−1.05713e9	−0.491264
$465$	−3.54881e8	−0.163681
$466$	3.86409e8	0.176887
$467$	3.87688e9	1.76146	0.880732	−	0.473615i	$-0.157051\pi$
$467$	3.87688e9	1.76146	0.880732	+	0.473615i	$0.157051\pi$
$468$	−8.33111e8	−0.375701
$469$	−3.88006e9	−1.73673
$470$	−8.17341e8	−0.363129
$471$	1.34239e8	0.0591978
$472$	−2.60529e8	−0.114040
$473$	2.54900e8	0.110753
$474$	1.07296e9	0.462763
$475$	−2.22054e8	−0.0950671
$476$	−3.37709e9	−1.43522
$477$	−3.46471e8	−0.146168
$478$	4.53825e8	0.190060
$479$	−3.88318e9	−1.61441	−0.807205	−	0.590272i	$-0.799021\pi$
$479$	−3.88318e9	−1.61441	−0.807205	+	0.590272i	$0.799021\pi$
$480$	6.08619e8	0.251189
$481$	−5.90648e8	−0.242003
$482$	−5.35342e8	−0.217754
$483$	1.21983e9	0.492589
$484$	−2.22878e9	−0.893528
$485$	−1.40541e9	−0.559378
$486$	8.12947e7	0.0321244
$487$	−1.79849e9	−0.705597	−0.352799	−	0.935699i	$-0.614770\pi$
$487$	−1.79849e9	−0.705597	−0.352799	+	0.935699i	$0.614770\pi$
$488$	8.87224e8	0.345592
$489$	−4.87535e8	−0.188549
$490$	−4.08011e8	−0.156670
$491$	−1.24531e9	−0.474780	−0.237390	−	0.971414i	$-0.576292\pi$
$491$	−1.24531e9	−0.474780	−0.237390	+	0.971414i	$0.576292\pi$
$492$	2.92294e8	0.110648
$493$	−6.10837e9	−2.29594
$494$	−2.33421e8	−0.0871157
$495$	−5.61790e8	−0.208188
$496$	5.67299e8	0.208750
$497$	6.15051e9	2.24731
$498$	9.49761e8	0.344597
$499$	3.02782e9	1.09088	0.545442	−	0.838148i	$-0.316362\pi$
$499$	3.02782e9	1.09088	0.545442	+	0.838148i	$0.316362\pi$
$500$	1.60945e9	0.575815
$501$	1.05108e9	0.373424
$502$	1.34727e9	0.475326
$503$	−3.67205e9	−1.28653	−0.643267	−	0.765642i	$-0.722421\pi$
$503$	−3.67205e9	−1.28653	−0.643267	+	0.765642i	$0.722421\pi$
$504$	1.10755e9	0.385350
$505$	−1.57523e9	−0.544284
$506$	−1.39701e9	−0.479371
$507$	−2.13990e9	−0.729232
$508$	−4.16521e9	−1.40966
$509$	−7.51140e8	−0.252469	−0.126235	−	0.992000i	$-0.540289\pi$
$509$	−7.51140e8	−0.252469	−0.126235	+	0.992000i	$0.540289\pi$
$510$	5.30252e8	0.177005
$511$	6.08767e9	2.01826
$512$	−1.79913e9	−0.592405
$513$	−6.80516e7	−0.0222550
$514$	−3.81680e6	−0.00123973
$515$	3.04540e8	0.0982469
$516$	−1.00973e8	−0.0323542
$517$	−7.99873e9	−2.54568
$518$	3.36322e8	0.106317
$519$	−2.44161e9	−0.766638
$520$	1.78214e9	0.555816
$521$	2.30813e9	0.715036	0.357518	−	0.933906i	$-0.383623\pi$
$521$	2.30813e9	0.715036	0.357518	+	0.933906i	$0.383623\pi$
$522$	8.58051e8	0.264038
$523$	−9.93626e8	−0.303716	−0.151858	−	0.988402i	$-0.548526\pi$
$523$	−9.93626e8	−0.303716	−0.151858	+	0.988402i	$0.548526\pi$
$524$	3.29371e9	1.00006
$525$	2.07687e9	0.626399
$526$	1.83316e8	0.0549224
$527$	3.27800e9	0.975601
$528$	8.98055e8	0.265512
$529$	−1.98183e9	−0.582065
$530$	3.17450e8	0.0926210
$531$	−1.49721e8	−0.0433963
$532$	−3.97106e8	−0.114345
$533$	1.34519e9	0.384802
$534$	2.21492e8	0.0629455
$535$	−5.33427e8	−0.150604
$536$	−4.10964e9	−1.15273
$537$	−3.09131e8	−0.0861456
$538$	−1.48298e9	−0.410579
$539$	−3.99291e9	−1.09832
$540$	2.22540e8	0.0608178
$541$	−7.57542e8	−0.205691	−0.102846	−	0.994697i	$-0.532795\pi$
$541$	−7.57542e8	−0.205691	−0.102846	+	0.994697i	$0.532795\pi$
$542$	−3.52320e9	−0.950472
$543$	2.49780e9	0.669512
$544$	−5.62175e9	−1.49719
$545$	−3.68552e7	−0.00975240
$546$	2.18319e9	0.574007
$547$	−7.20248e9	−1.88160	−0.940798	−	0.338969i	$-0.889922\pi$
$547$	−7.20248e9	−1.88160	−0.940798	+	0.338969i	$0.889922\pi$
$548$	4.94567e9	1.28379
$549$	5.09872e8	0.131510
$550$	−2.37852e9	−0.609590
$551$	−7.18273e8	−0.182919
$552$	1.29201e9	0.326948
$553$	8.40060e9	2.11238
$554$	−1.59636e9	−0.398884
$555$	1.57774e8	0.0391750
$556$	−6.00300e9	−1.48118
$557$	−2.72425e9	−0.667966	−0.333983	−	0.942579i	$-0.608393\pi$
$557$	−2.72425e9	−0.667966	−0.333983	+	0.942579i	$0.608393\pi$
$558$	−4.60466e8	−0.112196
$559$	−4.64693e8	−0.112519
$560$	7.18477e8	0.172884
$561$	5.18920e9	1.24088
$562$	−1.32585e9	−0.315077
$563$	4.08861e9	0.965599	0.482799	−	0.875731i	$-0.339620\pi$
$563$	4.08861e9	0.965599	0.482799	+	0.875731i	$0.339620\pi$
$564$	3.16852e9	0.743668
$565$	5.86330e8	0.136764
$566$	2.03440e9	0.471604
$567$	6.36487e8	0.146639
$568$	6.51443e9	1.49162
$569$	−6.62224e9	−1.50699	−0.753497	−	0.657451i	$-0.771635\pi$
$569$	−6.62224e9	−1.50699	−0.753497	+	0.657451i	$0.771635\pi$
$570$	6.23515e7	0.0141021
$571$	1.73743e9	0.390555	0.195277	−	0.980748i	$-0.437439\pi$
$571$	1.73743e9	0.390555	0.195277	+	0.980748i	$0.437439\pi$
$572$	7.47014e9	1.66895
$573$	−7.51472e8	−0.166867
$574$	−7.65966e8	−0.169051
$575$	2.42277e9	0.531465
$576$	3.14882e8	0.0686545
$577$	3.85948e9	0.836399	0.418200	−	0.908355i	$-0.362661\pi$
$577$	3.85948e9	0.836399	0.418200	+	0.908355i	$0.362661\pi$
$578$	−2.57309e9	−0.554252
$579$	9.52223e8	0.203875
$580$	2.34887e9	0.499875
$581$	7.43604e9	1.57299
$582$	−1.82354e9	−0.383430
$583$	3.10665e9	0.649311
$584$	6.44787e9	1.33959
$585$	1.02417e9	0.211507
$586$	−1.40682e9	−0.288799
$587$	−2.98276e9	−0.608674	−0.304337	−	0.952564i	$-0.598435\pi$
$587$	−2.98276e9	−0.608674	−0.304337	+	0.952564i	$0.598435\pi$
$588$	1.58170e9	0.320852
$589$	3.85455e8	0.0777267
$590$	1.37180e8	0.0274985
$591$	−4.75470e9	−0.947473
$592$	−2.52211e8	−0.0499618
$593$	2.61405e9	0.514781	0.257390	−	0.966308i	$-0.417137\pi$
$593$	2.61405e9	0.514781	0.257390	+	0.966308i	$0.417137\pi$
$594$	−7.28934e8	−0.142704
$595$	4.15155e9	0.807980
$596$	4.64844e8	0.0899384
$597$	−5.25994e9	−1.01174
$598$	2.54680e9	0.487014
$599$	−2.42519e8	−0.0461054	−0.0230527	−	0.999734i	$-0.507339\pi$
$599$	−2.42519e8	−0.0461054	−0.0230527	+	0.999734i	$0.507339\pi$
$600$	2.19975e9	0.415762
$601$	6.57764e9	1.23597	0.617987	−	0.786188i	$-0.287948\pi$
$601$	6.57764e9	1.23597	0.617987	+	0.786188i	$0.287948\pi$
$602$	2.64602e8	0.0494317
$603$	−2.36174e9	−0.438653
$604$	−7.35507e9	−1.35818
$605$	2.73990e9	0.503027
$606$	−2.04390e9	−0.373083
$607$	3.79055e9	0.687927	0.343963	−	0.938983i	$-0.388230\pi$
$607$	3.79055e9	0.687927	0.343963	+	0.938983i	$0.388230\pi$
$608$	−6.61053e8	−0.119282
$609$	6.71801e9	1.20526
$610$	−4.67164e8	−0.0833326
$611$	1.45820e10	2.58627
$612$	−2.05558e9	−0.362498
$613$	−5.87144e9	−1.02952	−0.514758	−	0.857336i	$-0.672118\pi$
$613$	−5.87144e9	−1.02952	−0.514758	+	0.857336i	$0.672118\pi$
$614$	−1.09022e9	−0.190075
$615$	−3.59326e8	−0.0622910
$616$	−9.93089e9	−1.71181
$617$	−4.89410e9	−0.838832	−0.419416	−	0.907794i	$-0.637765\pi$
$617$	−4.89410e9	−0.838832	−0.419416	+	0.907794i	$0.637765\pi$
$618$	3.95147e8	0.0673440
$619$	9.45629e9	1.60252	0.801260	−	0.598316i	$-0.204163\pi$
$619$	9.45629e9	1.60252	0.801260	+	0.598316i	$0.204163\pi$
$620$	−1.26050e9	−0.212409
$621$	7.42494e8	0.124415
$622$	2.72362e9	0.453817
$623$	1.73415e9	0.287328
$624$	−1.63719e9	−0.269745
$625$	3.03911e9	0.497928
$626$	−4.45278e9	−0.725473
$627$	6.10189e8	0.0988617
$628$	4.76804e8	0.0768212
$629$	−1.45734e9	−0.233498
$630$	−5.83173e8	−0.0929193
$631$	2.37404e9	0.376171	0.188086	−	0.982153i	$-0.439772\pi$
$631$	2.37404e9	0.376171	0.188086	+	0.982153i	$0.439772\pi$
$632$	8.89766e9	1.40206
$633$	−2.54670e9	−0.399085
$634$	1.18432e9	0.184569
$635$	5.12041e9	0.793590
$636$	−1.23063e9	−0.189683
$637$	7.27925e9	1.11583
$638$	−7.69377e9	−1.17292
$639$	3.74372e9	0.567611
$640$	2.59680e9	0.391569
$641$	1.19471e10	1.79168	0.895841	−	0.444375i	$-0.146574\pi$
$641$	1.19471e10	1.79168	0.895841	+	0.444375i	$0.146574\pi$
$642$	−6.92133e8	−0.103233
$643$	3.95645e9	0.586904	0.293452	−	0.955974i	$-0.405196\pi$
$643$	3.95645e9	0.586904	0.293452	+	0.955974i	$0.405196\pi$
$644$	4.33272e9	0.639235
$645$	1.24129e8	0.0182143
$646$	−5.75935e8	−0.0840542
$647$	8.69167e9	1.26165	0.630824	−	0.775926i	$-0.282717\pi$
$647$	8.69167e9	1.26165	0.630824	+	0.775926i	$0.282717\pi$
$648$	6.74148e8	0.0973290
$649$	1.34249e9	0.192776
$650$	4.33615e9	0.619309
$651$	−3.60516e9	−0.512143
$652$	−1.73168e9	−0.244681
$653$	2.95452e9	0.415231	0.207616	−	0.978210i	$-0.433430\pi$
$653$	2.95452e9	0.415231	0.207616	+	0.978210i	$0.433430\pi$
$654$	−4.78204e7	−0.00668485
$655$	−4.04904e9	−0.562999
$656$	5.74404e8	0.0794427
$657$	3.70548e9	0.509759
$658$	−8.30319e9	−1.13620
$659$	−6.81330e9	−0.927382	−0.463691	−	0.885997i	$-0.653475\pi$
$659$	−6.81330e9	−0.927382	−0.463691	+	0.885997i	$0.653475\pi$
$660$	−1.99542e9	−0.270166
$661$	−9.65769e9	−1.30067	−0.650336	−	0.759646i	$-0.725372\pi$
$661$	−9.65769e9	−1.30067	−0.650336	+	0.759646i	$0.725372\pi$
$662$	−4.50860e9	−0.604003
$663$	−9.46013e9	−1.26066
$664$	7.87603e9	1.04404
$665$	4.88173e8	0.0643722
$666$	2.04715e8	0.0268528
$667$	7.83690e9	1.02259
$668$	3.73332e9	0.484594
$669$	8.21345e9	1.06056
$670$	2.16391e9	0.277957
$671$	−4.57180e9	−0.584196
$672$	6.18283e9	0.785950
$673$	−5.74382e9	−0.726354	−0.363177	−	0.931720i	$-0.618308\pi$
$673$	−5.74382e9	−0.726354	−0.363177	+	0.931720i	$0.618308\pi$
$674$	−1.56275e9	−0.196599
$675$	1.26416e9	0.158212
$676$	−7.60072e9	−0.946327
$677$	−6.39314e9	−0.791870	−0.395935	−	0.918279i	$-0.629579\pi$
$677$	−6.39314e9	−0.791870	−0.395935	+	0.918279i	$0.629579\pi$
$678$	7.60776e8	0.0937460
$679$	−1.42772e10	−1.75025
$680$	4.39719e9	0.536283
$681$	−4.17241e9	−0.506259
$682$	4.12880e9	0.498400
$683$	−1.10711e10	−1.32959	−0.664794	−	0.747027i	$-0.731481\pi$
$683$	−1.10711e10	−1.32959	−0.664794	+	0.747027i	$0.731481\pi$
$684$	−2.41713e8	−0.0288804
$685$	−6.07985e9	−0.722729
$686$	1.44320e9	0.170684
$687$	−3.18681e9	−0.374980
$688$	−1.98427e8	−0.0232296
$689$	−5.66356e9	−0.659663
$690$	−6.80301e8	−0.0788369
$691$	1.01541e10	1.17077	0.585383	−	0.810757i	$-0.300944\pi$
$691$	1.01541e10	1.17077	0.585383	+	0.810757i	$0.300944\pi$
$692$	−8.67236e9	−0.994869
$693$	−5.70710e9	−0.651402
$694$	−2.72871e9	−0.309884
$695$	7.37965e9	0.833852
$696$	7.11551e9	0.799970
$697$	3.31906e9	0.371279
$698$	1.82246e9	0.202845
$699$	1.84149e9	0.203938
$700$	7.37683e9	0.812880
$701$	6.42013e9	0.703933	0.351966	−	0.936013i	$-0.385513\pi$
$701$	6.42013e9	0.703933	0.351966	+	0.936013i	$0.385513\pi$
$702$	1.32888e9	0.144979
$703$	−1.71366e8	−0.0186029
$704$	−2.82341e9	−0.304979
$705$	−3.89515e9	−0.418660
$706$	−6.65794e9	−0.712071
$707$	−1.60025e10	−1.70302
$708$	−5.31796e8	−0.0563155
$709$	−1.49237e10	−1.57259	−0.786293	−	0.617854i	$-0.788002\pi$
$709$	−1.49237e10	−1.57259	−0.786293	+	0.617854i	$0.788002\pi$
$710$	−3.43014e9	−0.359673
$711$	5.11332e9	0.533531
$712$	1.83676e9	0.190709
$713$	−4.20560e9	−0.434525
$714$	5.38672e9	0.553835
$715$	−9.18326e9	−0.939562
$716$	−1.09800e9	−0.111791
$717$	2.16276e9	0.219125
$718$	−1.86293e9	−0.187828
$719$	−3.46295e9	−0.347452	−0.173726	−	0.984794i	$-0.555581\pi$
$719$	−3.46295e9	−0.347452	−0.173726	+	0.984794i	$0.555581\pi$
$720$	4.37326e8	0.0436659
$721$	3.09376e9	0.307406
$722$	4.99656e9	0.494073
$723$	−2.55124e9	−0.251054
$724$	8.87195e9	0.868828
$725$	1.33430e10	1.30038
$726$	3.55508e9	0.344803
$727$	−1.19482e10	−1.15327	−0.576637	−	0.817000i	$-0.695635\pi$
$727$	−1.19482e10	−1.15327	−0.576637	+	0.817000i	$0.695635\pi$
$728$	1.81044e10	1.73910
$729$	3.87420e8	0.0370370
$730$	−3.39510e9	−0.323015
$731$	−1.14656e9	−0.108564
$732$	1.81102e9	0.170661
$733$	−4.90087e9	−0.459631	−0.229815	−	0.973234i	$-0.573812\pi$
$733$	−4.90087e9	−0.459631	−0.229815	+	0.973234i	$0.573812\pi$
$734$	3.94071e9	0.367823
$735$	−1.94443e9	−0.180629
$736$	7.21258e9	0.666835
$737$	2.11767e10	1.94859
$738$	−4.66233e8	−0.0426978
$739$	−1.16073e10	−1.05797	−0.528986	−	0.848631i	$-0.677428\pi$
$739$	−1.16073e10	−1.05797	−0.528986	+	0.848631i	$0.677428\pi$
$740$	5.60397e8	0.0508375
$741$	−1.11240e9	−0.100438
$742$	3.22490e9	0.289803
$743$	−1.83926e10	−1.64506	−0.822531	−	0.568720i	$-0.807439\pi$
$743$	−1.83926e10	−1.64506	−0.822531	+	0.568720i	$0.807439\pi$
$744$	−3.81848e9	−0.339926
$745$	−5.71445e8	−0.0506323
$746$	−5.93617e9	−0.523504
$747$	4.52621e9	0.397295
$748$	1.84315e10	1.61030
$749$	−5.41897e9	−0.471227
$750$	−2.56720e9	−0.222201
$751$	−1.54442e10	−1.33054	−0.665268	−	0.746604i	$-0.731683\pi$
$751$	−1.54442e10	−1.33054	−0.665268	+	0.746604i	$0.731683\pi$
$752$	6.22663e9	0.533938
$753$	6.42060e9	0.548016
$754$	1.40261e10	1.19162
$755$	9.04180e9	0.764611
$756$	2.26074e9	0.190294
$757$	−1.95008e10	−1.63387	−0.816933	−	0.576732i	$-0.804328\pi$
$757$	−1.95008e10	−1.63387	−0.816933	+	0.576732i	$0.804328\pi$
$758$	−5.13111e9	−0.427926
$759$	−6.65762e9	−0.552679
$760$	5.17059e8	0.0427260
$761$	−9.37201e9	−0.770880	−0.385440	−	0.922733i	$-0.625950\pi$
$761$	−9.37201e9	−0.770880	−0.385440	+	0.922733i	$0.625950\pi$
$762$	6.64383e9	0.543972
$763$	−3.74405e8	−0.0305144
$764$	−2.66916e9	−0.216544
$765$	2.52699e9	0.204074
$766$	−6.40231e9	−0.514679
$767$	−2.44741e9	−0.195850
$768$	4.86217e9	0.387317
$769$	−1.02340e10	−0.811528	−0.405764	−	0.913978i	$-0.632994\pi$
$769$	−1.02340e10	−0.811528	−0.405764	+	0.913978i	$0.632994\pi$
$770$	5.22906e9	0.412768
$771$	−1.81895e7	−0.00142932
$772$	3.38220e9	0.264569
$773$	2.44487e10	1.90383	0.951913	−	0.306367i	$-0.0991135\pi$
$773$	2.44487e10	1.90383	0.951913	+	0.306367i	$0.0991135\pi$
$774$	1.61060e8	0.0124851
$775$	−7.16040e9	−0.552562
$776$	−1.51220e10	−1.16170
$777$	1.60279e9	0.122575
$778$	5.49546e9	0.418384
$779$	3.90283e8	0.0295800
$780$	3.63774e9	0.274474
$781$	−3.35684e10	−2.52146
$782$	6.28388e9	0.469899
$783$	4.08915e9	0.304416
$784$	3.10829e9	0.230364
$785$	−5.86148e8	−0.0432478
$786$	−5.25372e9	−0.385912
$787$	−3.61895e8	−0.0264649	−0.0132325	−	0.999912i	$-0.504212\pi$
$787$	−3.61895e8	−0.0264649	−0.0132325	+	0.999912i	$0.504212\pi$
$788$	−1.68882e10	−1.22954
$789$	8.73615e8	0.0633214
$790$	−4.68502e9	−0.338078
$791$	5.95640e9	0.427924
$792$	−6.04479e9	−0.432358
$793$	8.33458e9	0.593510
$794$	7.78325e9	0.551810
$795$	1.51285e9	0.106785
$796$	−1.86828e10	−1.31294
$797$	−5.22352e9	−0.365476	−0.182738	−	0.983162i	$-0.558496\pi$
$797$	−5.22352e9	−0.365476	−0.182738	+	0.983162i	$0.558496\pi$
$798$	6.33415e8	0.0441244
$799$	3.59791e10	2.49538
$800$	1.22800e10	0.847978
$801$	1.05555e9	0.0725714
$802$	−3.24262e9	−0.221966
$803$	−3.32254e10	−2.26447
$804$	−8.38866e9	−0.569241
$805$	−5.32634e9	−0.359868
$806$	−7.52697e9	−0.506346
$807$	−7.06733e9	−0.473367
$808$	−1.69493e10	−1.13035
$809$	−2.37703e10	−1.57839	−0.789194	−	0.614144i	$-0.789502\pi$
$809$	−2.37703e10	−1.57839	−0.789194	+	0.614144i	$0.789502\pi$
$810$	−3.54969e8	−0.0234689
$811$	1.74347e10	1.14774	0.573868	−	0.818948i	$-0.305442\pi$
$811$	1.74347e10	1.14774	0.573868	+	0.818948i	$0.305442\pi$
$812$	2.38617e10	1.56407
$813$	−1.67903e10	−1.09582
$814$	−1.83559e9	−0.119286
$815$	2.12880e9	0.137747
$816$	−4.03954e9	−0.260266
$817$	−1.34823e8	−0.00864940
$818$	−6.08550e8	−0.0388741
$819$	1.04043e10	0.661788
$820$	−1.27629e9	−0.0808353
$821$	−2.87309e9	−0.181196	−0.0905978	−	0.995888i	$-0.528878\pi$
$821$	−2.87309e9	−0.181196	−0.0905978	+	0.995888i	$0.528878\pi$
$822$	−7.88873e9	−0.495400
$823$	6.48563e9	0.405558	0.202779	−	0.979225i	$-0.435003\pi$
$823$	6.48563e9	0.405558	0.202779	+	0.979225i	$0.435003\pi$
$824$	3.27681e9	0.204036
$825$	−1.13352e10	−0.702812
$826$	1.39359e9	0.0860406
$827$	−1.45803e10	−0.896388	−0.448194	−	0.893936i	$-0.647933\pi$
$827$	−1.45803e10	−0.896388	−0.448194	+	0.893936i	$0.647933\pi$
$828$	2.63727e9	0.161454
$829$	2.97207e9	0.181183	0.0905916	−	0.995888i	$-0.471124\pi$
$829$	2.97207e9	0.181183	0.0905916	+	0.995888i	$0.471124\pi$
$830$	−4.14709e9	−0.251750
$831$	−7.60766e9	−0.459883
$832$	5.14720e9	0.309841
$833$	1.79605e10	1.07662
$834$	9.57526e9	0.571570
$835$	−4.58948e9	−0.272810
$836$	2.16733e9	0.128293
$837$	−2.19441e9	−0.129354
$838$	−2.81307e9	−0.165130
$839$	−1.23558e10	−0.722276	−0.361138	−	0.932512i	$-0.617612\pi$
$839$	−1.23558e10	−0.722276	−0.361138	+	0.932512i	$0.617612\pi$
$840$	−4.83605e9	−0.281523
$841$	2.59104e10	1.50206
$842$	−1.20830e10	−0.697562
$843$	−6.31851e9	−0.363261
$844$	−9.04564e9	−0.517894
$845$	9.34377e9	0.532750
$846$	−5.05403e9	−0.286974
$847$	2.78341e10	1.57393
$848$	−2.41838e9	−0.136188
$849$	9.69518e9	0.543725
$850$	1.06988e10	0.597545
$851$	1.86973e9	0.103998
$852$	1.32973e10	0.736591
$853$	−3.00088e9	−0.165549	−0.0827746	−	0.996568i	$-0.526378\pi$
$853$	−3.00088e9	−0.165549	−0.0827746	+	0.996568i	$0.526378\pi$
$854$	−4.74582e9	−0.260741
$855$	2.97144e8	0.0162587
$856$	−5.73961e9	−0.312769
$857$	6.68872e9	0.363003	0.181502	−	0.983391i	$-0.441904\pi$
$857$	6.68872e9	0.363003	0.181502	+	0.983391i	$0.441904\pi$
$858$	−1.19155e10	−0.644029
$859$	9.56843e9	0.515068	0.257534	−	0.966269i	$-0.417090\pi$
$859$	9.56843e9	0.515068	0.257534	+	0.966269i	$0.417090\pi$
$860$	4.40893e8	0.0236368
$861$	−3.65031e9	−0.194903
$862$	1.56113e9	0.0830161
$863$	3.10651e10	1.64526	0.822632	−	0.568575i	$-0.192505\pi$
$863$	3.10651e10	1.64526	0.822632	+	0.568575i	$0.192505\pi$
$864$	3.76340e9	0.198510
$865$	1.06612e10	0.560078
$866$	−8.09971e9	−0.423796
$867$	−1.22624e10	−0.639011
$868$	−1.28052e10	−0.664610
$869$	−4.58490e10	−2.37006
$870$	−3.74664e9	−0.192897
$871$	−3.86060e10	−1.97966
$872$	−3.96558e8	−0.0202534
$873$	−8.69034e9	−0.442066
$874$	7.38911e8	0.0374371
$875$	−2.00996e10	−1.01428
$876$	1.31615e10	0.661516
$877$	−3.23289e10	−1.61843	−0.809213	−	0.587515i	$-0.800106\pi$
$877$	−3.23289e10	−1.61843	−0.809213	+	0.587515i	$0.800106\pi$
$878$	1.30191e10	0.649159
$879$	−6.70438e9	−0.332964
$880$	−3.92132e9	−0.193974
$881$	1.05719e10	0.520881	0.260440	−	0.965490i	$-0.416132\pi$
$881$	1.05719e10	0.520881	0.260440	+	0.965490i	$0.416132\pi$
$882$	−2.52294e9	−0.123813
$883$	1.62742e10	0.795493	0.397746	−	0.917495i	$-0.369792\pi$
$883$	1.62742e10	0.795493	0.397746	+	0.917495i	$0.369792\pi$
$884$	−3.36015e10	−1.63597
$885$	6.53751e8	0.0317038
$886$	3.24481e9	0.156737
$887$	−5.54686e9	−0.266879	−0.133440	−	0.991057i	$-0.542602\pi$
$887$	−5.54686e9	−0.266879	−0.133440	+	0.991057i	$0.542602\pi$
$888$	1.69763e9	0.0813573
$889$	5.20171e10	2.48308
$890$	−9.67136e8	−0.0459857
$891$	−3.47383e9	−0.164527
$892$	2.91734e10	1.37629
$893$	4.23072e9	0.198808
$894$	−7.41462e8	−0.0347062
$895$	1.34981e9	0.0629348
$896$	2.63803e10	1.22519
$897$	1.21371e10	0.561490
$898$	1.42552e10	0.656909
$899$	−2.31616e10	−1.06319
$900$	4.49017e9	0.205312
$901$	−1.39740e10	−0.636481
$902$	4.18051e9	0.189673
$903$	1.26100e9	0.0569911
$904$	6.30884e9	0.284027
$905$	−1.09065e10	−0.489121
$906$	1.17319e10	0.524107
$907$	2.33401e10	1.03867	0.519335	−	0.854571i	$-0.326180\pi$
$907$	2.33401e10	1.03867	0.519335	+	0.854571i	$0.326180\pi$
$908$	−1.48200e10	−0.656974
$909$	−9.74047e9	−0.430137
$910$	−9.53280e9	−0.419349
$911$	1.77936e10	0.779740	0.389870	−	0.920870i	$-0.372520\pi$
$911$	1.77936e10	0.779740	0.389870	+	0.920870i	$0.372520\pi$
$912$	−4.75003e8	−0.0207355
$913$	−4.05846e10	−1.76487
$914$	5.27851e9	0.228665
$915$	−2.22633e9	−0.0960762
$916$	−1.13193e10	−0.486613
$917$	−4.11334e10	−1.76158
$918$	3.27882e9	0.139884
$919$	2.41659e10	1.02706	0.513532	−	0.858070i	$-0.328337\pi$
$919$	2.41659e10	1.02706	0.513532	+	0.858070i	$0.328337\pi$
$920$	−5.64150e9	−0.238856
$921$	−5.19559e9	−0.219142
$922$	1.20319e9	0.0505563
$923$	6.11965e10	2.56166
$924$	−2.02711e10	−0.845327
$925$	3.18338e9	0.132249
$926$	−1.78194e10	−0.737489
$927$	1.88313e9	0.0776426
$928$	3.97220e10	1.63160
$929$	−2.78712e10	−1.14052	−0.570258	−	0.821466i	$-0.693157\pi$
$929$	−2.78712e10	−1.14052	−0.570258	+	0.821466i	$0.693157\pi$
$930$	2.01060e9	0.0819664
$931$	2.11195e9	0.0857747
$932$	6.54078e9	0.264651
$933$	1.29798e10	0.523217
$934$	−2.19647e10	−0.882088
$935$	−2.26584e10	−0.906543
$936$	1.10199e10	0.439251
$937$	1.83113e10	0.727162	0.363581	−	0.931563i	$-0.381554\pi$
$937$	1.83113e10	0.727162	0.363581	+	0.931563i	$0.381554\pi$
$938$	2.19827e10	0.869704
$939$	−2.12203e10	−0.836416
$940$	−1.38352e10	−0.543297
$941$	3.20558e9	0.125413	0.0627066	−	0.998032i	$-0.480027\pi$
$941$	3.20558e9	0.125413	0.0627066	+	0.998032i	$0.480027\pi$
$942$	−7.60540e8	−0.0296445
$943$	−4.25828e9	−0.165365
$944$	−1.04506e9	−0.0404333
$945$	−2.77919e9	−0.107129
$946$	−1.44415e9	−0.0554618
$947$	1.13660e10	0.434895	0.217448	−	0.976072i	$-0.430227\pi$
$947$	1.13660e10	0.434895	0.217448	+	0.976072i	$0.430227\pi$
$948$	1.81620e10	0.692365
$949$	6.05713e10	2.30057
$950$	1.25806e9	0.0476067
$951$	5.64405e9	0.212794
$952$	4.46701e10	1.67798
$953$	−2.26241e10	−0.846732	−0.423366	−	0.905959i	$-0.639152\pi$
$953$	−2.26241e10	−0.846732	−0.423366	+	0.905959i	$0.639152\pi$
$954$	1.96295e9	0.0731965
$955$	3.28127e9	0.121907
$956$	7.68193e9	0.284359
$957$	−3.66657e10	−1.35228
$958$	2.20004e10	0.808447
$959$	−6.17639e10	−2.26136
$960$	−1.37492e9	−0.0501565
$961$	−1.50831e10	−0.548226
$962$	3.34635e9	0.121188
$963$	−3.29845e9	−0.119019
$964$	−9.06176e9	−0.325794
$965$	−4.15784e9	−0.148944
$966$	−6.91104e9	−0.246674
$967$	4.77814e10	1.69928	0.849642	−	0.527359i	$-0.176818\pi$
$967$	4.77814e10	1.69928	0.849642	+	0.527359i	$0.176818\pi$
$968$	2.94810e10	1.04467
$969$	−2.74469e9	−0.0969082
$970$	7.96242e9	0.280120
$971$	2.36126e9	0.0827707	0.0413854	−	0.999143i	$-0.486823\pi$
$971$	2.36126e9	0.0827707	0.0413854	+	0.999143i	$0.486823\pi$
$972$	1.37608e9	0.0480631
$973$	7.49683e10	2.60905
$974$	1.01895e10	0.353342
$975$	2.06645e10	0.714017
$976$	3.55893e9	0.122531
$977$	−2.09178e10	−0.717604	−0.358802	−	0.933414i	$-0.616815\pi$
$977$	−2.09178e10	−0.717604	−0.358802	+	0.933414i	$0.616815\pi$
$978$	2.76216e9	0.0944197
$979$	−9.46467e9	−0.322379
$980$	−6.90643e9	−0.234403
$981$	−2.27895e8	−0.00770713
$982$	7.05538e9	0.237755
$983$	−5.00358e9	−0.168013	−0.0840066	−	0.996465i	$-0.526772\pi$
$983$	−5.00358e9	−0.168013	−0.0840066	+	0.996465i	$0.526772\pi$
$984$	−3.86630e9	−0.129364
$985$	2.07612e10	0.692190
$986$	3.46073e10	1.14974
$987$	−3.95700e10	−1.30995
$988$	−3.95114e9	−0.130339
$989$	1.47102e9	0.0483538
$990$	3.18286e9	0.104254
$991$	2.88517e10	0.941702	0.470851	−	0.882213i	$-0.343947\pi$
$991$	2.88517e10	0.941702	0.470851	+	0.882213i	$0.343947\pi$
$992$	−2.13165e10	−0.693306
$993$	−2.14863e10	−0.696370
$994$	−3.48461e10	−1.12539
$995$	2.29673e10	0.739144
$996$	1.60767e10	0.515571
$997$	−4.64145e10	−1.48327	−0.741636	−	0.670802i	$-0.765950\pi$
$997$	−4.64145e10	−1.48327	−0.741636	+	0.670802i	$0.765950\pi$
$998$	−1.71543e10	−0.546282
$999$	9.75595e8	0.0309592

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.c.1.7	✓	17
3.2	odd	2		531.8.a.c.1.11		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.c.1.7	✓	17	1.1	even	1	trivial
531.8.a.c.1.11		17	3.2	odd	2

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-5.66556 q^{2} -27.0000 q^{3} -95.9014 q^{4} +117.894 q^{5} +152.970 q^{6} +1197.66 q^{7} +1268.53 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-5.66556 q^{2} -27.0000 q^{3} -95.9014 q^{4} +117.894 q^{5} +152.970 q^{6} +1197.66 q^{7} +1268.53 q^{8} +729.000 q^{9} -667.937 q^{10} -6536.63 q^{11} +2589.34 q^{12} +11916.5 q^{13} -6785.43 q^{14} -3183.14 q^{15} +5088.45 q^{16} +29402.4 q^{17} -4130.20 q^{18} +3457.38 q^{19} -11306.2 q^{20} -32336.9 q^{21} +37033.7 q^{22} -37722.6 q^{23} -34250.2 q^{24} -64225.9 q^{25} -67514.0 q^{26} -19683.0 q^{27} -114857. q^{28} -207751. q^{29} +18034.3 q^{30} +111488. q^{31} -191200. q^{32} +176489. q^{33} -166581. q^{34} +141197. q^{35} -69912.1 q^{36} -49565.3 q^{37} -19588.0 q^{38} -321747. q^{39} +149552. q^{40} +112884. q^{41} +183207. q^{42} -38995.6 q^{43} +626872. q^{44} +85944.9 q^{45} +213720. q^{46} +1.22368e6 q^{47} -137388. q^{48} +610852. q^{49} +363876. q^{50} -793865. q^{51} -1.14281e6 q^{52} -475269. q^{53} +111515. q^{54} -770631. q^{55} +1.51927e6 q^{56} -93349.3 q^{57} +1.17702e6 q^{58} -205379. q^{59} +305268. q^{60} +699413. q^{61} -631640. q^{62} +873096. q^{63} +431937. q^{64} +1.40489e6 q^{65} -999909. q^{66} -3.23969e6 q^{67} -2.81973e6 q^{68} +1.01851e6 q^{69} -799963. q^{70} +5.13542e6 q^{71} +924757. q^{72} +5.08296e6 q^{73} +280816. q^{74} +1.73410e6 q^{75} -331568. q^{76} -7.82867e6 q^{77} +1.82288e6 q^{78} +7.01416e6 q^{79} +599899. q^{80} +531441. q^{81} -639551. q^{82} +6.20880e6 q^{83} +3.10115e6 q^{84} +3.46637e6 q^{85} +220932. q^{86} +5.60927e6 q^{87} -8.29189e6 q^{88} +1.44794e6 q^{89} -486926. q^{90} +1.42720e7 q^{91} +3.61765e6 q^{92} -3.01017e6 q^{93} -6.93283e6 q^{94} +407605. q^{95} +5.16241e6 q^{96} -1.19209e7 q^{97} -3.46082e6 q^{98} -4.76520e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17q + 2q^{2} - 459q^{3} + 1166q^{4} - 318q^{5} - 54q^{6} + 3145q^{7} + 2355q^{8} + 12393q^{9} + O(q^{10}) \)	\( 17q + 2q^{2} - 459q^{3} + 1166q^{4} - 318q^{5} - 54q^{6} + 3145q^{7} + 2355q^{8} + 12393q^{9} + 6521q^{10} - 1764q^{11} - 31482q^{12} + 18192q^{13} - 7827q^{14} + 8586q^{15} + 139226q^{16} - 15507q^{17} + 1458q^{18} + 52083q^{19} + 721q^{20} - 84915q^{21} - 234434q^{22} + 63823q^{23} - 63585q^{24} + 202153q^{25} - 367956q^{26} - 334611q^{27} + 182306q^{28} - 502955q^{29} - 176067q^{30} + 347531q^{31} - 243908q^{32} + 47628q^{33} - 330872q^{34} + 92641q^{35} + 850014q^{36} + 447615q^{37} + 775669q^{38} - 491184q^{39} + 2203270q^{40} + 940335q^{41} + 211329q^{42} + 478562q^{43} - 596924q^{44} - 231822q^{45} - 3078663q^{46} + 703121q^{47} - 3759102q^{48} + 1895082q^{49} - 876967q^{50} + 418689q^{51} + 6278296q^{52} - 1005974q^{53} - 39366q^{54} + 5212846q^{55} + 3425294q^{56} - 1406241q^{57} + 6710166q^{58} - 3491443q^{59} - 19467q^{60} + 11510749q^{61} + 5996234q^{62} + 2292705q^{63} + 29496941q^{64} + 11094180q^{65} + 6329718q^{66} + 14007144q^{67} + 19688159q^{68} - 1723221q^{69} + 30909708q^{70} + 5229074q^{71} + 1716795q^{72} + 5452211q^{73} + 12819662q^{74} - 5458131q^{75} + 41929340q^{76} + 9930777q^{77} + 9934812q^{78} + 15275654q^{79} + 36576105q^{80} + 9034497q^{81} + 32025935q^{82} + 7826609q^{83} - 4922262q^{84} + 11836945q^{85} + 51649136q^{86} + 13579785q^{87} + 30223741q^{88} - 6436185q^{89} + 4753809q^{90} + 11633535q^{91} + 43357972q^{92} - 9383337q^{93} - 4494252q^{94} + 23741055q^{95} + 6585516q^{96} + 26377540q^{97} + 26517816q^{98} - 1285956q^{99} + O(q^{100}) \)

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