LMFDB - Embedded newform 62.8.a.c.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,8,Mod(1,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.1"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	62.a (trivial)

Newform invariants

comment:select newform

sage:traces = [5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$19.3678715800$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 2617x^{3} - 17755x^{2} + 1742092x + 24429360 $ x^5 - x^4 - 2617x^3 - 17755x^2 + 1742092*x + 24429360
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$36.5857$ of defining polynomial
Character	$\chi$	$=$	62.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-8.00000 q^{2} -40.7973 q^{3} +64.0000 q^{4} -417.873 q^{5} +326.379 q^{6} -620.990 q^{7} -512.000 q^{8} -522.579 q^{9} +3342.99 q^{10} -7918.03 q^{11} -2611.03 q^{12} -1388.81 q^{13} +4967.92 q^{14} +17048.1 q^{15} +4096.00 q^{16} -34612.0 q^{17} +4180.63 q^{18} -6526.03 q^{19} -26743.9 q^{20} +25334.7 q^{21} +63344.2 q^{22} -9798.60 q^{23} +20888.2 q^{24} +96493.2 q^{25} +11110.5 q^{26} +110544. q^{27} -39743.4 q^{28} +103706. q^{29} -136385. q^{30} -29791.0 q^{31} -32768.0 q^{32} +323034. q^{33} +276896. q^{34} +259495. q^{35} -33445.1 q^{36} +299797. q^{37} +52208.2 q^{38} +56659.8 q^{39} +213951. q^{40} -525636. q^{41} -202678. q^{42} -385253. q^{43} -506754. q^{44} +218372. q^{45} +78388.8 q^{46} +228977. q^{47} -167106. q^{48} -437914. q^{49} -771945. q^{50} +1.41208e6 q^{51} -88884.0 q^{52} -7199.71 q^{53} -884348. q^{54} +3.30873e6 q^{55} +317947. q^{56} +266244. q^{57} -829646. q^{58} -1.73512e6 q^{59} +1.09108e6 q^{60} -2.62421e6 q^{61} +238328. q^{62} +324517. q^{63} +262144. q^{64} +580348. q^{65} -2.58427e6 q^{66} -2.22379e6 q^{67} -2.21517e6 q^{68} +399757. q^{69} -2.07596e6 q^{70} -2.06785e6 q^{71} +267561. q^{72} -2.92917e6 q^{73} -2.39837e6 q^{74} -3.93666e6 q^{75} -417666. q^{76} +4.91702e6 q^{77} -453278. q^{78} +5.93317e6 q^{79} -1.71161e6 q^{80} -3.36700e6 q^{81} +4.20509e6 q^{82} -9.72743e6 q^{83} +1.62142e6 q^{84} +1.44634e7 q^{85} +3.08202e6 q^{86} -4.23092e6 q^{87} +4.05403e6 q^{88} +5.66978e6 q^{89} -1.74698e6 q^{90} +862439. q^{91} -627110. q^{92} +1.21539e6 q^{93} -1.83182e6 q^{94} +2.72705e6 q^{95} +1.33685e6 q^{96} +1.33640e7 q^{97} +3.50331e6 q^{98} +4.13780e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 40 q^{2} + 28 q^{3} + 320 q^{4} + 152 q^{5} - 224 q^{6} - 132 q^{7} - 2560 q^{8} + 9149 q^{9} - 1216 q^{10} - 4218 q^{11} + 1792 q^{12} - 7014 q^{13} + 1056 q^{14} - 30666 q^{15} + 20480 q^{16} - 30180 q^{17}+ \cdots + 36785690 q^{99}+O(q^{100}) $ 5 * q - 40 * q^2 + 28 * q^3 + 320 * q^4 + 152 * q^5 - 224 * q^6 - 132 * q^7 - 2560 * q^8 + 9149 * q^9 - 1216 * q^10 - 4218 * q^11 + 1792 * q^12 - 7014 * q^13 + 1056 * q^14 - 30666 * q^15 + 20480 * q^16 - 30180 * q^17 - 73192 * q^18 - 8320 * q^19 + 9728 * q^20 + 117298 * q^21 + 33744 * q^22 + 67130 * q^23 - 14336 * q^24 + 374909 * q^25 + 56112 * q^26 + 522556 * q^27 - 8448 * q^28 + 290034 * q^29 + 245328 * q^30 - 148955 * q^31 - 163840 * q^32 + 1406308 * q^33 + 241440 * q^34 + 617080 * q^35 + 585536 * q^36 + 682400 * q^37 + 66560 * q^38 + 890040 * q^39 - 77824 * q^40 + 197844 * q^41 - 938384 * q^42 + 2333288 * q^43 - 269952 * q^44 + 420684 * q^45 - 537040 * q^46 - 405160 * q^47 + 114688 * q^48 + 18911 * q^49 - 2999272 * q^50 - 2221952 * q^51 - 448896 * q^52 + 1029596 * q^53 - 4180448 * q^54 + 1893688 * q^55 + 67584 * q^56 + 1816438 * q^57 - 2320272 * q^58 - 400004 * q^59 - 1962624 * q^60 - 4933754 * q^61 + 1191640 * q^62 - 2215816 * q^63 + 1310720 * q^64 - 12557830 * q^65 - 11250464 * q^66 + 2699572 * q^67 - 1931520 * q^68 - 5447084 * q^69 - 4936640 * q^70 - 613944 * q^71 - 4684288 * q^72 + 7894998 * q^73 - 5459200 * q^74 + 1100718 * q^75 - 532480 * q^76 + 13071604 * q^77 - 7120320 * q^78 + 10463774 * q^79 + 622592 * q^80 + 4221713 * q^81 - 1582752 * q^82 - 12217942 * q^83 + 7507072 * q^84 + 9681846 * q^85 - 18666304 * q^86 + 10112196 * q^87 + 2159616 * q^88 + 22649884 * q^89 - 3365472 * q^90 - 3100110 * q^91 + 4296320 * q^92 - 834148 * q^93 + 3241280 * q^94 - 22084956 * q^95 - 917504 * q^96 - 7610048 * q^97 - 151288 * q^98 + 36785690 * q^99

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 $

$2$	−8.00000	−0.707107
$2$	−8.00000	−0.707107
$3$	−40.7973	−0.872383	−0.436191	−	0.899854i	$-0.643673\pi$
$3$	−40.7973	−0.872383	−0.436191	+	0.899854i	$0.643673\pi$
$4$	64.0000	0.500000
$5$	−417.873	−1.49503	−0.747515	−	0.664245i	$-0.768753\pi$
$5$	−417.873	−1.49503	−0.747515	+	0.664245i	$0.768753\pi$
$6$	326.379	0.616868
$7$	−620.990	−0.684292	−0.342146	−	0.939647i	$-0.611154\pi$
$7$	−620.990	−0.684292	−0.342146	+	0.939647i	$0.611154\pi$
$8$	−512.000	−0.353553
$9$	−522.579	−0.238948
$10$	3342.99	1.05715
$11$	−7918.03	−1.79367	−0.896835	−	0.442365i	$-0.854140\pi$
$11$	−7918.03	−1.79367	−0.896835	+	0.442365i	$0.854140\pi$
$12$	−2611.03	−0.436191
$13$	−1388.81	−0.175324	−0.0876621	−	0.996150i	$-0.527940\pi$
$13$	−1388.81	−0.175324	−0.0876621	+	0.996150i	$0.527940\pi$
$14$	4967.92	0.483868
$15$	17048.1	1.30424
$16$	4096.00	0.250000
$17$	−34612.0	−1.70866	−0.854329	−	0.519733i	$-0.826032\pi$
$17$	−34612.0	−1.70866	−0.854329	+	0.519733i	$0.826032\pi$
$18$	4180.63	0.168962
$19$	−6526.03	−0.218279	−0.109139	−	0.994026i	$-0.534809\pi$
$19$	−6526.03	−0.218279	−0.109139	+	0.994026i	$0.534809\pi$
$20$	−26743.9	−0.747515
$21$	25334.7	0.596965
$22$	63344.2	1.26832
$23$	−9798.60	−0.167925	−0.0839627	−	0.996469i	$-0.526758\pi$
$23$	−9798.60	−0.167925	−0.0839627	+	0.996469i	$0.526758\pi$
$24$	20888.2	0.308434
$25$	96493.2	1.23511
$26$	11110.5	0.123973
$27$	110544.	1.08084
$28$	−39743.4	−0.342146
$29$	103706.	0.789605	0.394803	−	0.918766i	$-0.370813\pi$
$29$	103706.	0.789605	0.394803	+	0.918766i	$0.370813\pi$
$30$	−136385.	−0.922236
$31$	−29791.0	−0.179605
$31$	−29791.0	−0.179605
$32$	−32768.0	−0.176777
$33$	323034.	1.56477
$34$	276896.	1.20820
$35$	259495.	1.02304
$36$	−33445.1	−0.119474
$37$	299797.	0.973018	0.486509	−	0.873676i	$-0.338270\pi$
$37$	299797.	0.973018	0.486509	+	0.873676i	$0.338270\pi$
$38$	52208.2	0.154346
$39$	56659.8	0.152950
$40$	213951.	0.528573
$41$	−525636.	−1.19108	−0.595541	−	0.803325i	$-0.703062\pi$
$41$	−525636.	−1.19108	−0.595541	+	0.803325i	$0.703062\pi$
$42$	−202678.	−0.422118
$43$	−385253.	−0.738935	−0.369468	−	0.929244i	$-0.620460\pi$
$43$	−385253.	−0.738935	−0.369468	+	0.929244i	$0.620460\pi$
$44$	−506754.	−0.896835
$45$	218372.	0.357234
$46$	78388.8	0.118741
$47$	228977.	0.321699	0.160849	−	0.986979i	$-0.448577\pi$
$47$	228977.	0.321699	0.160849	+	0.986979i	$0.448577\pi$
$48$	−167106.	−0.218096
$49$	−437914.	−0.531744
$50$	−771945.	−0.873357
$51$	1.41208e6	1.49060
$52$	−88884.0	−0.0876621
$53$	−7199.71	−0.00664277	−0.00332139	−	0.999994i	$-0.501057\pi$
$53$	−7199.71	−0.00664277	−0.00332139	+	0.999994i	$0.501057\pi$
$54$	−884348.	−0.764267
$55$	3.30873e6	2.68159
$56$	317947.	0.241934
$57$	266244.	0.190423
$58$	−829646.	−0.558335
$59$	−1.73512e6	−1.09988	−0.549942	−	0.835203i	$-0.685350\pi$
$59$	−1.73512e6	−1.09988	−0.549942	+	0.835203i	$0.685350\pi$
$60$	1.09108e6	0.652119
$61$	−2.62421e6	−1.48028	−0.740140	−	0.672452i	$-0.765241\pi$
$61$	−2.62421e6	−1.48028	−0.740140	+	0.672452i	$0.765241\pi$
$62$	238328.	0.127000
$63$	324517.	0.163510
$64$	262144.	0.125000
$65$	580348.	0.262115
$66$	−2.58427e6	−1.10646
$67$	−2.22379e6	−0.903298	−0.451649	−	0.892196i	$-0.649164\pi$
$67$	−2.22379e6	−0.903298	−0.451649	+	0.892196i	$0.649164\pi$
$68$	−2.21517e6	−0.854329
$69$	399757.	0.146495
$70$	−2.07596e6	−0.723397
$71$	−2.06785e6	−0.685670	−0.342835	−	0.939396i	$-0.611387\pi$
$71$	−2.06785e6	−0.685670	−0.342835	+	0.939396i	$0.611387\pi$
$72$	267561.	0.0844808
$73$	−2.92917e6	−0.881281	−0.440640	−	0.897684i	$-0.645249\pi$
$73$	−2.92917e6	−0.881281	−0.440640	+	0.897684i	$0.645249\pi$
$74$	−2.39837e6	−0.688028
$75$	−3.93666e6	−1.07749
$76$	−417666.	−0.109139
$77$	4.91702e6	1.22740
$78$	−453278.	−0.108152
$79$	5.93317e6	1.35392	0.676959	−	0.736021i	$-0.263298\pi$
$79$	5.93317e6	1.35392	0.676959	+	0.736021i	$0.263298\pi$
$80$	−1.71161e6	−0.373757
$81$	−3.36700e6	−0.703956
$82$	4.20509e6	0.842222
$83$	−9.72743e6	−1.86735	−0.933673	−	0.358126i	$-0.883416\pi$
$83$	−9.72743e6	−1.86735	−0.933673	+	0.358126i	$0.883416\pi$
$84$	1.62142e6	0.298483
$85$	1.44634e7	2.55449
$86$	3.08202e6	0.522506
$87$	−4.23092e6	−0.688838
$88$	4.05403e6	0.634158
$89$	5.66978e6	0.852513	0.426257	−	0.904602i	$-0.359832\pi$
$89$	5.66978e6	0.852513	0.426257	+	0.904602i	$0.359832\pi$
$90$	−1.74698e6	−0.252603
$91$	862439.	0.119973
$92$	−627110.	−0.0839627
$93$	1.21539e6	0.156685
$94$	−1.83182e6	−0.227475
$95$	2.72705e6	0.326333
$96$	1.33685e6	0.154217
$97$	1.33640e7	1.48674	0.743372	−	0.668879i	$-0.233225\pi$
$97$	1.33640e7	1.48674	0.743372	+	0.668879i	$0.233225\pi$
$98$	3.50331e6	0.376000
$99$	4.13780e6	0.428594
$100$	6.17556e6	0.617556
$101$	−3.37263e6	−0.325719	−0.162860	−	0.986649i	$-0.552072\pi$
$101$	−3.37263e6	−0.325719	−0.162860	+	0.986649i	$0.552072\pi$
$102$	−1.12966e7	−1.05402
$103$	5.53317e6	0.498934	0.249467	−	0.968383i	$-0.419745\pi$
$103$	5.53317e6	0.498934	0.249467	+	0.968383i	$0.419745\pi$
$104$	711072.	0.0619864
$105$	−1.05867e7	−0.892480
$106$	57597.7	0.00469715
$107$	−1.12749e7	−0.889751	−0.444875	−	0.895592i	$-0.646752\pi$
$107$	−1.12749e7	−0.889751	−0.444875	+	0.895592i	$0.646752\pi$
$108$	7.07479e6	0.540419
$109$	−2.34093e7	−1.73139	−0.865697	−	0.500569i	$-0.833124\pi$
$109$	−2.34093e7	−1.73139	−0.865697	+	0.500569i	$0.833124\pi$
$110$	−2.64699e7	−1.89617
$111$	−1.22309e7	−0.848844
$112$	−2.54358e6	−0.171073
$113$	2.16946e7	1.41441	0.707206	−	0.707007i	$-0.249955\pi$
$113$	2.16946e7	1.41441	0.707206	+	0.707007i	$0.249955\pi$
$114$	−2.12996e6	−0.134649
$115$	4.09457e6	0.251053
$116$	6.63717e6	0.394803
$117$	725764.	0.0418933
$118$	1.38809e7	0.777735
$119$	2.14937e7	1.16922
$120$	−8.72863e6	−0.461118
$121$	4.32080e7	2.21725
$122$	2.09937e7	1.04672
$123$	2.14445e7	1.03908
$124$	−1.90662e6	−0.0898027
$125$	−7.67557e6	−0.351500
$126$	−2.59613e6	−0.115619
$127$	−3.01075e7	−1.30425	−0.652126	−	0.758110i	$-0.726123\pi$
$127$	−3.01075e7	−1.30425	−0.652126	+	0.758110i	$0.726123\pi$
$128$	−2.09715e6	−0.0883883
$129$	1.57173e7	0.644635
$130$	−4.64278e6	−0.185343
$131$	−1.68742e7	−0.655802	−0.327901	−	0.944712i	$-0.606341\pi$
$131$	−1.68742e7	−0.655802	−0.327901	+	0.944712i	$0.606341\pi$
$132$	2.06742e7	0.782384
$133$	4.05260e6	0.149366
$134$	1.77903e7	0.638728
$135$	−4.61932e7	−1.61588
$136$	1.77213e7	0.604102
$137$	8.80817e6	0.292660	0.146330	−	0.989236i	$-0.453254\pi$
$137$	8.80817e6	0.292660	0.146330	+	0.989236i	$0.453254\pi$
$138$	−3.19805e6	−0.103588
$139$	−4.92255e7	−1.55467	−0.777335	−	0.629087i	$-0.783429\pi$
$139$	−4.92255e7	−1.55467	−0.777335	+	0.629087i	$0.783429\pi$
$140$	1.66077e7	0.511519
$141$	−9.34165e6	−0.280645
$142$	1.65428e7	0.484842
$143$	1.09967e7	0.314474
$144$	−2.14048e6	−0.0597370
$145$	−4.33359e7	−1.18048
$146$	2.34333e7	0.623160
$147$	1.78657e7	0.463884
$148$	1.91870e7	0.486509
$149$	−2.96829e7	−0.735114	−0.367557	−	0.930001i	$-0.619806\pi$
$149$	−2.96829e7	−0.735114	−0.367557	+	0.930001i	$0.619806\pi$
$150$	3.14933e7	0.761901
$151$	−5.81968e7	−1.37556	−0.687781	−	0.725919i	$-0.741415\pi$
$151$	−5.81968e7	−1.37556	−0.687781	+	0.725919i	$0.741415\pi$
$152$	3.34133e6	0.0771732
$153$	1.80875e7	0.408280
$154$	−3.93362e7	−0.867899
$155$	1.24489e7	0.268515
$156$	3.62623e6	0.0764749
$157$	5.32105e7	1.09736	0.548679	−	0.836033i	$-0.315131\pi$
$157$	5.32105e7	1.09736	0.548679	+	0.836033i	$0.315131\pi$
$158$	−4.74654e7	−0.957364
$159$	293729.	0.00579504
$160$	1.36929e7	0.264286
$161$	6.08484e6	0.114910
$162$	2.69360e7	0.497772
$163$	2.57846e7	0.466341	0.233171	−	0.972436i	$-0.425090\pi$
$163$	2.57846e7	0.466341	0.233171	+	0.972436i	$0.425090\pi$
$164$	−3.36407e7	−0.595541
$165$	−1.34987e8	−2.33937
$166$	7.78194e7	1.32041
$167$	−2.82779e7	−0.469829	−0.234914	−	0.972016i	$-0.575481\pi$
$167$	−2.82779e7	−0.469829	−0.234914	+	0.972016i	$0.575481\pi$
$168$	−1.29714e7	−0.211059
$169$	−6.08197e7	−0.969261
$170$	−1.15707e8	−1.80630
$171$	3.41037e6	0.0521572
$172$	−2.46562e7	−0.369468
$173$	6.35962e7	0.933834	0.466917	−	0.884301i	$-0.345365\pi$
$173$	6.35962e7	0.933834	0.466917	+	0.884301i	$0.345365\pi$
$174$	3.38473e7	0.487082
$175$	−5.99213e7	−0.845178
$176$	−3.24322e7	−0.448418
$177$	7.07881e7	0.959520
$178$	−4.53582e7	−0.602818
$179$	−9.56662e7	−1.24673	−0.623365	−	0.781931i	$-0.714235\pi$
$179$	−9.56662e7	−1.24673	−0.623365	+	0.781931i	$0.714235\pi$
$180$	1.39758e7	0.178617
$181$	−6.58091e7	−0.824918	−0.412459	−	0.910976i	$-0.635330\pi$
$181$	−6.58091e7	−0.824918	−0.412459	+	0.910976i	$0.635330\pi$
$182$	−6.89951e6	−0.0848337
$183$	1.07061e8	1.29137
$184$	5.01688e6	0.0593706
$185$	−1.25277e8	−1.45469
$186$	−9.72314e6	−0.110793
$187$	2.74059e8	3.06477
$188$	1.46545e7	0.160849
$189$	−6.86465e7	−0.739609
$190$	−2.18164e7	−0.230752
$191$	−9.41465e7	−0.977659	−0.488829	−	0.872379i	$-0.662576\pi$
$191$	−9.41465e7	−0.977659	−0.488829	+	0.872379i	$0.662576\pi$
$192$	−1.06948e7	−0.109048
$193$	1.01005e8	1.01133	0.505665	−	0.862730i	$-0.331247\pi$
$193$	1.01005e8	1.01133	0.505665	+	0.862730i	$0.331247\pi$
$194$	−1.06912e8	−1.05129
$195$	−2.36766e7	−0.228664
$196$	−2.80265e7	−0.265872
$197$	−1.39459e8	−1.29962	−0.649810	−	0.760097i	$-0.725151\pi$
$197$	−1.39459e8	−1.29962	−0.649810	+	0.760097i	$0.725151\pi$
$198$	−3.31024e7	−0.303062
$199$	2.11768e8	1.90491	0.952456	−	0.304677i	$-0.0985485\pi$
$199$	2.11768e8	1.90491	0.952456	+	0.304677i	$0.0985485\pi$
$200$	−4.94045e7	−0.436678
$201$	9.07245e7	0.788022
$202$	2.69810e7	0.230318
$203$	−6.44003e7	−0.540321
$204$	9.03728e7	0.745302
$205$	2.19649e8	1.78070
$206$	−4.42653e7	−0.352800
$207$	5.12054e6	0.0401254
$208$	−5.68857e6	−0.0438310
$209$	5.16733e7	0.391520
$210$	8.46937e7	0.631079
$211$	−8.66123e6	−0.0634733	−0.0317367	−	0.999496i	$-0.510104\pi$
$211$	−8.66123e6	−0.0634733	−0.0317367	+	0.999496i	$0.510104\pi$
$212$	−460781.	−0.00332139
$213$	8.43627e7	0.598166
$214$	9.01990e7	0.629149
$215$	1.60987e8	1.10473
$216$	−5.65983e7	−0.382134
$217$	1.84999e7	0.122903
$218$	1.87274e8	1.22428
$219$	1.19502e8	0.768814
$220$	2.11759e8	1.34079
$221$	4.80695e7	0.299569
$222$	9.78472e7	0.600224
$223$	−7.80335e7	−0.471210	−0.235605	−	0.971849i	$-0.575707\pi$
$223$	−7.80335e7	−0.471210	−0.235605	+	0.971849i	$0.575707\pi$
$224$	2.03486e7	0.120967
$225$	−5.04253e7	−0.295128
$226$	−1.73556e8	−1.00014
$227$	−6.01021e7	−0.341035	−0.170517	−	0.985355i	$-0.554544\pi$
$227$	−6.01021e7	−0.341035	−0.170517	+	0.985355i	$0.554544\pi$
$228$	1.70396e7	0.0952113
$229$	1.94222e8	1.06874	0.534372	−	0.845250i	$-0.320548\pi$
$229$	1.94222e8	1.06874	0.534372	+	0.845250i	$0.320548\pi$
$230$	−3.27566e7	−0.177522
$231$	−2.00601e8	−1.07076
$232$	−5.30974e7	−0.279168
$233$	2.75094e8	1.42474	0.712369	−	0.701805i	$-0.247622\pi$
$233$	2.75094e8	1.42474	0.712369	+	0.701805i	$0.247622\pi$
$234$	−5.80611e6	−0.0296231
$235$	−9.56834e7	−0.480949
$236$	−1.11047e8	−0.549942
$237$	−2.42057e8	−1.18113
$238$	−1.71950e8	−0.826765
$239$	1.08680e7	0.0514939	0.0257469	−	0.999668i	$-0.491804\pi$
$239$	1.08680e7	0.0514939	0.0257469	+	0.999668i	$0.491804\pi$
$240$	6.98291e7	0.326060
$241$	3.16267e8	1.45544	0.727720	−	0.685874i	$-0.240580\pi$
$241$	3.16267e8	1.45544	0.727720	+	0.685874i	$0.240580\pi$
$242$	−3.45664e8	−1.56783
$243$	−1.04394e8	−0.466718
$244$	−1.67949e8	−0.740140
$245$	1.82993e8	0.794973
$246$	−1.71556e8	−0.734740
$247$	9.06342e6	0.0382695
$248$	1.52530e7	0.0635001
$249$	3.96853e8	1.62904
$250$	6.14046e7	0.248548
$251$	−8.90394e7	−0.355406	−0.177703	−	0.984084i	$-0.556867\pi$
$251$	−8.90394e7	−0.355406	−0.177703	+	0.984084i	$0.556867\pi$
$252$	2.07691e7	0.0817551
$253$	7.75856e7	0.301203
$254$	2.40860e8	0.922246
$255$	−5.90069e8	−2.22850
$256$	1.67772e7	0.0625000
$257$	1.91926e8	0.705291	0.352646	−	0.935757i	$-0.385282\pi$
$257$	1.91926e8	0.705291	0.352646	+	0.935757i	$0.385282\pi$
$258$	−1.25738e8	−0.455826
$259$	−1.86171e8	−0.665829
$260$	3.71422e7	0.131057
$261$	−5.41945e7	−0.188675
$262$	1.34993e8	0.463722
$263$	2.64672e7	0.0897146	0.0448573	−	0.998993i	$-0.485717\pi$
$263$	2.64672e7	0.0897146	0.0448573	+	0.998993i	$0.485717\pi$
$264$	−1.65394e8	−0.553229
$265$	3.00857e6	0.00993114
$266$	−3.24208e7	−0.105618
$267$	−2.31312e8	−0.743718
$268$	−1.42322e8	−0.451649
$269$	−4.26555e8	−1.33611	−0.668054	−	0.744113i	$-0.732873\pi$
$269$	−4.26555e8	−1.33611	−0.668054	+	0.744113i	$0.732873\pi$
$270$	3.69546e8	1.14260
$271$	7.25746e7	0.221509	0.110755	−	0.993848i	$-0.464673\pi$
$271$	7.25746e7	0.221509	0.110755	+	0.993848i	$0.464673\pi$
$272$	−1.41771e8	−0.427165
$273$	−3.51852e7	−0.104662
$274$	−7.04653e7	−0.206942
$275$	−7.64036e8	−2.21538
$276$	2.55844e7	0.0732477
$277$	5.83878e8	1.65060	0.825302	−	0.564692i	$-0.191005\pi$
$277$	5.83878e8	1.65060	0.825302	+	0.564692i	$0.191005\pi$
$278$	3.93804e8	1.09932
$279$	1.55682e7	0.0429163
$280$	−1.32862e8	−0.361698
$281$	2.37499e7	0.0638542	0.0319271	−	0.999490i	$-0.489836\pi$
$281$	2.37499e7	0.0638542	0.0319271	+	0.999490i	$0.489836\pi$
$282$	7.47332e7	0.198446
$283$	−6.75972e8	−1.77287	−0.886434	−	0.462856i	$-0.846825\pi$
$283$	−6.75972e8	−1.77287	−0.886434	+	0.462856i	$0.846825\pi$
$284$	−1.32342e8	−0.342835
$285$	−1.11256e8	−0.284687
$286$	−8.79732e7	−0.222366
$287$	3.26415e8	0.815048
$288$	1.71239e7	0.0422404
$289$	7.87650e8	1.91951
$290$	3.46687e8	0.834727
$291$	−5.45216e8	−1.29701
$292$	−1.87467e8	−0.440640
$293$	−4.12692e8	−0.958494	−0.479247	−	0.877680i	$-0.659090\pi$
$293$	−4.12692e8	−0.958494	−0.479247	+	0.877680i	$0.659090\pi$
$294$	−1.42926e8	−0.328016
$295$	7.25059e8	1.64436
$296$	−1.53496e8	−0.344014
$297$	−8.75287e8	−1.93867
$298$	2.37463e8	0.519804
$299$	1.36084e7	0.0294414
$300$	−2.51946e8	−0.538746
$301$	2.39238e8	0.505648
$302$	4.65575e8	0.972669
$303$	1.37594e8	0.284152
$304$	−2.67306e7	−0.0545697
$305$	1.09659e9	2.21306
$306$	−1.44700e8	−0.288698
$307$	−1.72022e8	−0.339312	−0.169656	−	0.985503i	$-0.554266\pi$
$307$	−1.72022e8	−0.339312	−0.169656	+	0.985503i	$0.554266\pi$
$308$	3.14689e8	0.613698
$309$	−2.25738e8	−0.435262
$310$	−9.95909e7	−0.189869
$311$	−9.15845e8	−1.72648	−0.863238	−	0.504797i	$-0.831567\pi$
$311$	−9.15845e8	−1.72648	−0.863238	+	0.504797i	$0.831567\pi$
$312$	−2.90098e7	−0.0540759
$313$	−5.11090e8	−0.942090	−0.471045	−	0.882109i	$-0.656123\pi$
$313$	−5.11090e8	−0.942090	−0.471045	+	0.882109i	$0.656123\pi$
$314$	−4.25684e8	−0.775949
$315$	−1.35607e8	−0.244453
$316$	3.79723e8	0.676959
$317$	−2.00927e8	−0.354267	−0.177134	−	0.984187i	$-0.556683\pi$
$317$	−2.00927e8	−0.354267	−0.177134	+	0.984187i	$0.556683\pi$
$318$	−2.34983e6	−0.00409771
$319$	−8.21145e8	−1.41629
$320$	−1.09543e8	−0.186879
$321$	4.59985e8	0.776204
$322$	−4.86787e7	−0.0812537
$323$	2.25879e8	0.372964
$324$	−2.15488e8	−0.351978
$325$	−1.34011e8	−0.216545
$326$	−2.06277e8	−0.329753
$327$	9.55037e8	1.51044
$328$	2.69126e8	0.421111
$329$	−1.42193e8	−0.220136
$330$	1.07990e9	1.65419
$331$	1.72587e8	0.261584	0.130792	−	0.991410i	$-0.458248\pi$
$331$	1.72587e8	0.261584	0.130792	+	0.991410i	$0.458248\pi$
$332$	−6.22556e8	−0.933673
$333$	−1.56668e8	−0.232501
$334$	2.26223e8	0.332219
$335$	9.29261e8	1.35046
$336$	1.03771e8	0.149241
$337$	−2.35763e8	−0.335560	−0.167780	−	0.985824i	$-0.553660\pi$
$337$	−2.35763e8	−0.335560	−0.167780	+	0.985824i	$0.553660\pi$
$338$	4.86558e8	0.685371
$339$	−8.85080e8	−1.23391
$340$	9.25659e8	1.27725
$341$	2.35886e8	0.322153
$342$	−2.72829e7	−0.0368807
$343$	7.83353e8	1.04816
$344$	1.97250e8	0.261253
$345$	−1.67048e8	−0.219015
$346$	−5.08769e8	−0.660320
$347$	1.06453e9	1.36774	0.683871	−	0.729603i	$-0.260295\pi$
$347$	1.06453e9	1.36774	0.683871	+	0.729603i	$0.260295\pi$
$348$	−2.70779e8	−0.344419
$349$	−3.71468e8	−0.467770	−0.233885	−	0.972264i	$-0.575144\pi$
$349$	−3.71468e8	−0.467770	−0.233885	+	0.972264i	$0.575144\pi$
$350$	4.79371e8	0.597631
$351$	−1.53524e8	−0.189497
$352$	2.59458e8	0.317079
$353$	2.53889e8	0.307208	0.153604	−	0.988133i	$-0.450912\pi$
$353$	2.53889e8	0.307208	0.153604	+	0.988133i	$0.450912\pi$
$354$	−5.66305e8	−0.678483
$355$	8.64100e8	1.02510
$356$	3.62866e8	0.426257
$357$	−8.76885e8	−1.02001
$358$	7.65329e8	0.881572
$359$	−1.19177e9	−1.35945	−0.679723	−	0.733469i	$-0.737900\pi$
$359$	−1.19177e9	−1.35945	−0.679723	+	0.733469i	$0.737900\pi$
$360$	−1.11806e8	−0.126301
$361$	−8.51283e8	−0.952354
$362$	5.26473e8	0.583305
$363$	−1.76277e9	−1.93429
$364$	5.51961e7	0.0599865
$365$	1.22402e9	1.31754
$366$	−8.56486e8	−0.913138
$367$	6.96395e8	0.735402	0.367701	−	0.929944i	$-0.380145\pi$
$367$	6.96395e8	0.735402	0.367701	+	0.929944i	$0.380145\pi$
$368$	−4.01351e7	−0.0419814
$369$	2.74686e8	0.284606
$370$	1.00222e9	1.02862
$371$	4.47095e6	0.00454560
$372$	7.77851e7	0.0783423
$373$	4.53131e8	0.452109	0.226055	−	0.974115i	$-0.427417\pi$
$373$	4.53131e8	0.452109	0.226055	+	0.974115i	$0.427417\pi$
$374$	−2.19247e9	−2.16712
$375$	3.13143e8	0.306643
$376$	−1.17236e8	−0.113738
$377$	−1.44028e8	−0.138437
$378$	5.49172e8	0.522982
$379$	−3.55064e8	−0.335019	−0.167509	−	0.985871i	$-0.553572\pi$
$379$	−3.55064e8	−0.335019	−0.167509	+	0.985871i	$0.553572\pi$
$380$	1.74531e8	0.163167
$381$	1.22831e9	1.13781
$382$	7.53172e8	0.691309
$383$	1.56851e9	1.42656	0.713282	−	0.700877i	$-0.247208\pi$
$383$	1.56851e9	1.42656	0.713282	+	0.700877i	$0.247208\pi$
$384$	8.55582e7	0.0771085
$385$	−2.05469e9	−1.83499
$386$	−8.08041e8	−0.715118
$387$	2.01325e8	0.176567
$388$	8.55297e8	0.743372
$389$	1.37865e9	1.18749	0.593747	−	0.804652i	$-0.297648\pi$
$389$	1.37865e9	1.18749	0.593747	+	0.804652i	$0.297648\pi$
$390$	1.89413e8	0.161690
$391$	3.39149e8	0.286927
$392$	2.24212e8	0.188000
$393$	6.88420e8	0.572110
$394$	1.11568e9	0.918970
$395$	−2.47931e9	−2.02415
$396$	2.64819e8	0.214297
$397$	−7.58780e8	−0.608624	−0.304312	−	0.952572i	$-0.598427\pi$
$397$	−7.58780e8	−0.608624	−0.304312	+	0.952572i	$0.598427\pi$
$398$	−1.69414e9	−1.34698
$399$	−1.65335e8	−0.130305
$400$	3.95236e8	0.308778
$401$	1.87069e9	1.44876	0.724378	−	0.689403i	$-0.242127\pi$
$401$	1.87069e9	1.44876	0.724378	+	0.689403i	$0.242127\pi$
$402$	−7.25796e8	−0.557216
$403$	4.13741e7	0.0314891
$404$	−2.15848e8	−0.162860
$405$	1.40698e9	1.05243
$406$	5.15202e8	0.382065
$407$	−2.37380e9	−1.74527
$408$	−7.22983e8	−0.527008
$409$	−2.45944e9	−1.77748	−0.888741	−	0.458410i	$-0.848419\pi$
$409$	−2.45944e9	−1.77748	−0.888741	+	0.458410i	$0.848419\pi$
$410$	−1.75719e9	−1.25915
$411$	−3.59350e8	−0.255312
$412$	3.54123e8	0.249467
$413$	1.07749e9	0.752642
$414$	−4.09643e7	−0.0283730
$415$	4.06483e9	2.79174
$416$	4.55086e7	0.0309932
$417$	2.00827e9	1.35627
$418$	−4.13386e8	−0.276846
$419$	−1.23723e9	−0.821675	−0.410838	−	0.911708i	$-0.634764\pi$
$419$	−1.23723e9	−0.821675	−0.410838	+	0.911708i	$0.634764\pi$
$420$	−6.77550e8	−0.446240
$421$	3.37838e8	0.220659	0.110329	−	0.993895i	$-0.464809\pi$
$421$	3.37838e8	0.220659	0.110329	+	0.993895i	$0.464809\pi$
$422$	6.92899e7	0.0448824
$423$	−1.19659e8	−0.0768693
$424$	3.68625e6	0.00234857
$425$	−3.33982e9	−2.11039
$426$	−6.74902e8	−0.422968
$427$	1.62961e9	1.01294
$428$	−7.21592e8	−0.444875
$429$	−4.48634e8	−0.274341
$430$	−1.28790e9	−0.781162
$431$	−8.25702e8	−0.496767	−0.248384	−	0.968662i	$-0.579899\pi$
$431$	−8.25702e8	−0.496767	−0.248384	+	0.968662i	$0.579899\pi$
$432$	4.52786e8	0.270209
$433$	−1.16907e9	−0.692042	−0.346021	−	0.938227i	$-0.612467\pi$
$433$	−1.16907e9	−0.692042	−0.346021	+	0.938227i	$0.612467\pi$
$434$	−1.47999e8	−0.0869052
$435$	1.76799e9	1.02983
$436$	−1.49820e9	−0.865697
$437$	6.39459e7	0.0366545
$438$	−9.56018e8	−0.543634
$439$	−1.13018e9	−0.637560	−0.318780	−	0.947829i	$-0.603273\pi$
$439$	−1.13018e9	−0.637560	−0.318780	+	0.947829i	$0.603273\pi$
$440$	−1.69407e9	−0.948085
$441$	2.28845e8	0.127059
$442$	−3.84556e8	−0.211827
$443$	3.45470e9	1.88798	0.943990	−	0.329973i	$-0.107040\pi$
$443$	3.45470e9	1.88798	0.943990	+	0.329973i	$0.107040\pi$
$444$	−7.82778e8	−0.424422
$445$	−2.36925e9	−1.27453
$446$	6.24268e8	0.333196
$447$	1.21098e9	0.641301
$448$	−1.62789e8	−0.0855366
$449$	−1.14401e9	−0.596443	−0.298221	−	0.954497i	$-0.596393\pi$
$449$	−1.14401e9	−0.596443	−0.298221	+	0.954497i	$0.596393\pi$
$450$	4.03403e8	0.208687
$451$	4.16200e9	2.13641
$452$	1.38845e9	0.707206
$453$	2.37427e9	1.20002
$454$	4.80817e8	0.241148
$455$	−3.60390e8	−0.179363
$456$	−1.36317e8	−0.0673246
$457$	−1.71386e9	−0.839979	−0.419989	−	0.907529i	$-0.637966\pi$
$457$	−1.71386e9	−0.839979	−0.419989	+	0.907529i	$0.637966\pi$
$458$	−1.55377e9	−0.755716
$459$	−3.82613e9	−1.84678
$460$	2.62053e8	0.125527
$461$	6.08702e8	0.289368	0.144684	−	0.989478i	$-0.453783\pi$
$461$	6.08702e8	0.289368	0.144684	+	0.989478i	$0.453783\pi$
$462$	1.60481e9	0.757141
$463$	−1.89787e9	−0.888655	−0.444327	−	0.895864i	$-0.646557\pi$
$463$	−1.89787e9	−0.888655	−0.444327	+	0.895864i	$0.646557\pi$
$464$	4.24779e8	0.197401
$465$	−5.07880e8	−0.234248
$466$	−2.20075e9	−1.00744
$467$	−8.08808e8	−0.367482	−0.183741	−	0.982975i	$-0.558821\pi$
$467$	−8.08808e8	−0.367482	−0.183741	+	0.982975i	$0.558821\pi$
$468$	4.64489e7	0.0209467
$469$	1.38095e9	0.618120
$470$	7.65467e8	0.340082
$471$	−2.17084e9	−0.957317
$472$	8.88380e8	0.388868
$473$	3.05044e9	1.32541
$474$	1.93646e9	0.835188
$475$	−6.29717e8	−0.269599
$476$	1.37560e9	0.584611
$477$	3.76242e6	0.00158728
$478$	−8.69437e7	−0.0364117
$479$	2.02860e9	0.843376	0.421688	−	0.906741i	$-0.361438\pi$
$479$	2.02860e9	0.843376	0.421688	+	0.906741i	$0.361438\pi$
$480$	−5.58633e8	−0.230559
$481$	−4.16361e8	−0.170594
$482$	−2.53014e9	−1.02915
$483$	−2.48245e8	−0.100246
$484$	2.76531e9	1.10863
$485$	−5.58447e9	−2.22272
$486$	8.35154e8	0.330019
$487$	9.87432e8	0.387396	0.193698	−	0.981061i	$-0.437952\pi$
$487$	9.87432e8	0.387396	0.193698	+	0.981061i	$0.437952\pi$
$488$	1.34360e9	0.523358
$489$	−1.05194e9	−0.406828
$490$	−1.46394e9	−0.562130
$491$	4.09396e9	1.56084	0.780420	−	0.625256i	$-0.215005\pi$
$491$	4.09396e9	1.56084	0.780420	+	0.625256i	$0.215005\pi$
$492$	1.37245e9	0.519540
$493$	−3.58946e9	−1.34917
$494$	−7.25074e7	−0.0270606
$495$	−1.72907e9	−0.640760
$496$	−1.22024e8	−0.0449013
$497$	1.28412e9	0.469199
$498$	−3.17482e9	−1.15191
$499$	−5.51368e7	−0.0198650	−0.00993252	−	0.999951i	$-0.503162\pi$
$499$	−5.51368e7	−0.0198650	−0.00993252	+	0.999951i	$0.503162\pi$
$500$	−4.91237e8	−0.175750
$501$	1.15366e9	0.409871
$502$	7.12315e8	0.251310
$503$	1.91196e8	0.0669871	0.0334935	−	0.999439i	$-0.489337\pi$
$503$	1.91196e8	0.0669871	0.0334935	+	0.999439i	$0.489337\pi$
$504$	−1.66153e8	−0.0578096
$505$	1.40933e9	0.486960
$506$	−6.20685e8	−0.212983
$507$	2.48128e9	0.845567
$508$	−1.92688e9	−0.652126
$509$	−4.53511e9	−1.52432	−0.762158	−	0.647391i	$-0.775860\pi$
$509$	−4.53511e9	−1.52432	−0.762158	+	0.647391i	$0.775860\pi$
$510$	4.72055e9	1.57579
$511$	1.81899e9	0.603054
$512$	−1.34218e8	−0.0441942
$513$	−7.21410e8	−0.235924
$514$	−1.53541e9	−0.498716
$515$	−2.31216e9	−0.745921
$516$	1.00591e9	0.322317
$517$	−1.81305e9	−0.577022
$518$	1.48937e9	0.470812
$519$	−2.59455e9	−0.814661
$520$	−2.97138e8	−0.0926715
$521$	3.62476e9	1.12292	0.561458	−	0.827505i	$-0.310241\pi$
$521$	3.62476e9	1.12292	0.561458	+	0.827505i	$0.310241\pi$
$522$	4.33556e8	0.133413
$523$	−4.09293e9	−1.25106	−0.625530	−	0.780200i	$-0.715117\pi$
$523$	−4.09293e9	−1.25106	−0.625530	+	0.780200i	$0.715117\pi$
$524$	−1.07995e9	−0.327901
$525$	2.44463e9	0.737319
$526$	−2.11738e8	−0.0634378
$527$	1.03113e9	0.306884
$528$	1.32315e9	0.391192
$529$	−3.30881e9	−0.971801
$530$	−2.40685e7	−0.00702238
$531$	9.06736e8	0.262815
$532$	2.59366e8	0.0746832
$533$	7.30009e8	0.208825
$534$	1.85049e9	0.525888
$535$	4.71147e9	1.33020
$536$	1.13858e9	0.319364
$537$	3.90292e9	1.08763
$538$	3.41244e9	0.944771
$539$	3.46741e9	0.953773
$540$	−2.95637e9	−0.807942
$541$	2.72975e9	0.741194	0.370597	−	0.928794i	$-0.379153\pi$
$541$	2.72975e9	0.741194	0.370597	+	0.928794i	$0.379153\pi$
$542$	−5.80597e8	−0.156631
$543$	2.68483e9	0.719645
$544$	1.13417e9	0.302051
$545$	9.78212e9	2.58848
$546$	2.81482e8	0.0740075
$547$	3.30606e9	0.863683	0.431842	−	0.901949i	$-0.357864\pi$
$547$	3.30606e9	0.863683	0.431842	+	0.901949i	$0.357864\pi$
$548$	5.63723e8	0.146330
$549$	1.37136e9	0.353710
$550$	6.11229e9	1.56651
$551$	−6.76787e8	−0.172354
$552$	−2.04675e8	−0.0517939
$553$	−3.68444e9	−0.926475
$554$	−4.67102e9	−1.16715
$555$	5.11097e9	1.26905
$556$	−3.15043e9	−0.777335
$557$	8.14341e8	0.199670	0.0998350	−	0.995004i	$-0.468168\pi$
$557$	8.14341e8	0.199670	0.0998350	+	0.995004i	$0.468168\pi$
$558$	−1.24545e8	−0.0303464
$559$	5.35044e8	0.129553
$560$	1.06289e9	0.255759
$561$	−1.11809e10	−2.67365
$562$	−1.89999e8	−0.0451517
$563$	−3.55944e9	−0.840626	−0.420313	−	0.907379i	$-0.638080\pi$
$563$	−3.55944e9	−0.840626	−0.420313	+	0.907379i	$0.638080\pi$
$564$	−5.97865e8	−0.140322
$565$	−9.06558e9	−2.11459
$566$	5.40778e9	1.25361
$567$	2.09087e9	0.481712
$568$	1.05874e9	0.242421
$569$	2.88158e9	0.655748	0.327874	−	0.944721i	$-0.393668\pi$
$569$	2.88158e9	0.655748	0.327874	+	0.944721i	$0.393668\pi$
$570$	8.90052e8	0.201304
$571$	5.68986e9	1.27901	0.639507	−	0.768785i	$-0.279138\pi$
$571$	5.68986e9	1.27901	0.639507	+	0.768785i	$0.279138\pi$
$572$	7.03786e8	0.157237
$573$	3.84092e9	0.852893
$574$	−2.61132e9	−0.576326
$575$	−9.45498e8	−0.207407
$576$	−1.36991e8	−0.0298685
$577$	−3.28049e9	−0.710925	−0.355462	−	0.934691i	$-0.615677\pi$
$577$	−3.28049e9	−0.710925	−0.355462	+	0.934691i	$0.615677\pi$
$578$	−6.30120e9	−1.35730
$579$	−4.12074e9	−0.882267
$580$	−2.77350e9	−0.590241
$581$	6.04064e9	1.27781
$582$	4.36173e9	0.917124
$583$	5.70075e7	0.0119149
$584$	1.49973e9	0.311580
$585$	−3.03277e8	−0.0626318
$586$	3.30154e9	0.677757
$587$	3.57385e9	0.729295	0.364648	−	0.931146i	$-0.381189\pi$
$587$	3.57385e9	0.729295	0.364648	+	0.931146i	$0.381189\pi$
$588$	1.14341e9	0.231942
$589$	1.94417e8	0.0392040
$590$	−5.80047e9	−1.16274
$591$	5.68957e9	1.13377
$592$	1.22797e9	0.243254
$593$	−2.16031e8	−0.0425426	−0.0212713	−	0.999774i	$-0.506771\pi$
$593$	−2.16031e8	−0.0425426	−0.0212713	+	0.999774i	$0.506771\pi$
$594$	7.00230e9	1.37084
$595$	−8.98165e9	−1.74802
$596$	−1.89971e9	−0.367557
$597$	−8.63957e9	−1.66181
$598$	−1.08867e8	−0.0208182
$599$	−6.35978e9	−1.20906	−0.604531	−	0.796582i	$-0.706639\pi$
$599$	−6.35978e9	−1.20906	−0.604531	+	0.796582i	$0.706639\pi$
$600$	2.01557e9	0.380951
$601$	−6.72076e9	−1.26287	−0.631434	−	0.775430i	$-0.717533\pi$
$601$	−6.72076e9	−1.26287	−0.631434	+	0.775430i	$0.717533\pi$
$602$	−1.91391e9	−0.357547
$603$	1.16210e9	0.215841
$604$	−3.72460e9	−0.687781
$605$	−1.80555e10	−3.31486
$606$	−1.10075e9	−0.200926
$607$	−5.74452e9	−1.04254	−0.521270	−	0.853392i	$-0.674542\pi$
$607$	−5.74452e9	−1.04254	−0.521270	+	0.853392i	$0.674542\pi$
$608$	2.13845e8	0.0385866
$609$	2.62736e9	0.471367
$610$	−8.77270e9	−1.56487
$611$	−3.18006e8	−0.0564016
$612$	1.15760e9	0.204140
$613$	7.35937e9	1.29041	0.645207	−	0.764008i	$-0.276771\pi$
$613$	7.35937e9	1.29041	0.645207	+	0.764008i	$0.276771\pi$
$614$	1.37618e9	0.239930
$615$	−8.96110e9	−1.55345
$616$	−2.51751e9	−0.433950
$617$	−6.91278e9	−1.18483	−0.592413	−	0.805634i	$-0.701825\pi$
$617$	−6.91278e9	−1.18483	−0.592413	+	0.805634i	$0.701825\pi$
$618$	1.80591e9	0.307777
$619$	−8.46739e9	−1.43494	−0.717468	−	0.696592i	$-0.754699\pi$
$619$	−8.46739e9	−1.43494	−0.717468	+	0.696592i	$0.754699\pi$
$620$	7.96727e8	0.134258
$621$	−1.08317e9	−0.181500
$622$	7.32676e9	1.22080
$623$	−3.52088e9	−0.583369
$624$	2.32079e8	0.0382374
$625$	−4.33111e9	−0.709609
$626$	4.08872e9	0.666158
$627$	−2.10813e9	−0.341555
$628$	3.40547e9	0.548679
$629$	−1.03766e10	−1.66255
$630$	1.08485e9	0.172854
$631$	−4.28026e8	−0.0678215	−0.0339108	−	0.999425i	$-0.510796\pi$
$631$	−4.28026e8	−0.0678215	−0.0339108	+	0.999425i	$0.510796\pi$
$632$	−3.03778e9	−0.478682
$633$	3.53355e8	0.0553730
$634$	1.60742e9	0.250505
$635$	1.25811e10	1.94990
$636$	1.87986e7	0.00289752
$637$	6.08180e8	0.0932275
$638$	6.56916e9	1.00147
$639$	1.08062e9	0.163839
$640$	8.76344e8	0.132143
$641$	9.78813e9	1.46790	0.733950	−	0.679203i	$-0.237674\pi$
$641$	9.78813e9	1.46790	0.733950	+	0.679203i	$0.237674\pi$
$642$	−3.67988e9	−0.548859
$643$	5.90503e9	0.875958	0.437979	−	0.898985i	$-0.355694\pi$
$643$	5.90503e9	0.875958	0.437979	+	0.898985i	$0.355694\pi$
$644$	3.89430e8	0.0574551
$645$	−6.56784e9	−0.963748
$646$	−1.80703e9	−0.263725
$647$	−4.45052e9	−0.646019	−0.323010	−	0.946396i	$-0.604695\pi$
$647$	−4.45052e9	−0.646019	−0.323010	+	0.946396i	$0.604695\pi$
$648$	1.72390e9	0.248886
$649$	1.37387e10	1.97283
$650$	1.07209e9	0.153120
$651$	−7.54747e8	−0.107218
$652$	1.65021e9	0.233171
$653$	1.04534e10	1.46914	0.734568	−	0.678535i	$-0.237385\pi$
$653$	1.04534e10	1.46914	0.734568	+	0.678535i	$0.237385\pi$
$654$	−7.64029e9	−1.06804
$655$	7.05126e9	0.980443
$656$	−2.15300e9	−0.297770
$657$	1.53072e9	0.210580
$658$	1.13754e9	0.155660
$659$	5.54564e9	0.754837	0.377418	−	0.926043i	$-0.376812\pi$
$659$	5.54564e9	0.754837	0.377418	+	0.926043i	$0.376812\pi$
$660$	−8.63920e9	−1.16969
$661$	−1.05040e10	−1.41466	−0.707329	−	0.706885i	$-0.750100\pi$
$661$	−1.05040e10	−1.41466	−0.707329	+	0.706885i	$0.750100\pi$
$662$	−1.38070e9	−0.184968
$663$	−1.96111e9	−0.261339
$664$	4.98044e9	0.660207
$665$	−1.69347e9	−0.223307
$666$	1.25334e9	0.164403
$667$	−1.01617e9	−0.132595
$668$	−1.80979e9	−0.234914
$669$	3.18356e9	0.411075
$670$	−7.43409e9	−0.954917
$671$	2.07786e10	2.65514
$672$	−8.30169e8	−0.105530
$673$	1.01223e10	1.28005	0.640023	−	0.768356i	$-0.278925\pi$
$673$	1.01223e10	1.28005	0.640023	+	0.768356i	$0.278925\pi$
$674$	1.88610e9	0.237277
$675$	1.06667e10	1.33496
$676$	−3.89246e9	−0.484631
$677$	−5.53216e8	−0.0685226	−0.0342613	−	0.999413i	$-0.510908\pi$
$677$	−5.53216e8	−0.0685226	−0.0342613	+	0.999413i	$0.510908\pi$
$678$	7.08064e9	0.872506
$679$	−8.29893e9	−1.01737
$680$	−7.40527e9	−0.903150
$681$	2.45200e9	0.297513
$682$	−1.88709e9	−0.227796
$683$	−4.69427e9	−0.563761	−0.281881	−	0.959449i	$-0.590958\pi$
$683$	−4.69427e9	−0.563761	−0.281881	+	0.959449i	$0.590958\pi$
$684$	2.18263e8	0.0260786
$685$	−3.68070e9	−0.437536
$686$	−6.26682e9	−0.741162
$687$	−7.92372e9	−0.932353
$688$	−1.57800e9	−0.184734
$689$	9.99904e6	0.00116464
$690$	1.33638e9	0.154867
$691$	−1.07481e10	−1.23925	−0.619623	−	0.784899i	$-0.712715\pi$
$691$	−1.07481e10	−1.23925	−0.619623	+	0.784899i	$0.712715\pi$
$692$	4.07015e9	0.466917
$693$	−2.56953e9	−0.293284
$694$	−8.51623e9	−0.967140
$695$	2.05700e10	2.32428
$696$	2.16623e9	0.243541
$697$	1.81933e10	2.03515
$698$	2.97174e9	0.330763
$699$	−1.12231e10	−1.24292
$700$	−3.83497e9	−0.422589
$701$	1.50160e10	1.64642	0.823211	−	0.567735i	$-0.192180\pi$
$701$	1.50160e10	1.64642	0.823211	+	0.567735i	$0.192180\pi$
$702$	1.22819e9	0.133994
$703$	−1.95648e9	−0.212389
$704$	−2.07566e9	−0.224209
$705$	3.90363e9	0.419572
$706$	−2.03111e9	−0.217229
$707$	2.09437e9	0.222887
$708$	4.53044e9	0.479760
$709$	−1.14211e10	−1.20350	−0.601750	−	0.798685i	$-0.705530\pi$
$709$	−1.14211e10	−1.20350	−0.601750	+	0.798685i	$0.705530\pi$
$710$	−6.91280e9	−0.724852
$711$	−3.10055e9	−0.323516
$712$	−2.90293e9	−0.301409
$713$	2.91910e8	0.0301603
$714$	7.01508e9	0.721255
$715$	−4.59521e9	−0.470147
$716$	−6.12263e9	−0.623365
$717$	−4.43384e8	−0.0449224
$718$	9.53416e9	0.961273
$719$	2.40273e9	0.241076	0.120538	−	0.992709i	$-0.461538\pi$
$719$	2.40273e9	0.241076	0.120538	+	0.992709i	$0.461538\pi$
$720$	8.94451e8	0.0893085
$721$	−3.43604e9	−0.341417
$722$	6.81026e9	0.673416
$723$	−1.29029e10	−1.26970
$724$	−4.21178e9	−0.412459
$725$	1.00069e10	0.975251
$726$	1.41022e10	1.36775
$727$	1.34707e10	1.30023	0.650115	−	0.759836i	$-0.274721\pi$
$727$	1.34707e10	1.30023	0.650115	+	0.759836i	$0.274721\pi$
$728$	−4.41569e8	−0.0424169
$729$	1.16226e10	1.11111
$730$	−9.79217e9	−0.931642
$731$	1.33344e10	1.26259
$732$	6.85188e9	0.645686
$733$	−1.98292e10	−1.85969	−0.929845	−	0.367952i	$-0.880059\pi$
$733$	−1.98292e10	−1.85969	−0.929845	+	0.367952i	$0.880059\pi$
$734$	−5.57116e9	−0.520007
$735$	−7.46561e9	−0.693521
$736$	3.21080e8	0.0296853
$737$	1.76080e10	1.62022
$738$	−2.19749e9	−0.201247
$739$	−5.34582e9	−0.487258	−0.243629	−	0.969869i	$-0.578338\pi$
$739$	−5.34582e9	−0.487258	−0.243629	+	0.969869i	$0.578338\pi$
$740$	−8.01773e9	−0.727345
$741$	−3.69763e8	−0.0333857
$742$	−3.57676e7	−0.00321422
$743$	−5.70628e9	−0.510378	−0.255189	−	0.966891i	$-0.582138\pi$
$743$	−5.70628e9	−0.510378	−0.255189	+	0.966891i	$0.582138\pi$
$744$	−6.22281e8	−0.0553964
$745$	1.24037e10	1.09902
$746$	−3.62505e9	−0.319689
$747$	5.08335e9	0.446199
$748$	1.75397e10	1.53238
$749$	7.00159e9	0.608850
$750$	−2.50514e9	−0.216829
$751$	2.55448e9	0.220071	0.110035	−	0.993928i	$-0.464904\pi$
$751$	2.55448e9	0.220071	0.110035	+	0.993928i	$0.464904\pi$
$752$	9.37890e8	0.0804247
$753$	3.63257e9	0.310050
$754$	1.15222e9	0.0978896
$755$	2.43189e10	2.05650
$756$	−4.39338e9	−0.369804
$757$	−6.09090e9	−0.510324	−0.255162	−	0.966898i	$-0.582129\pi$
$757$	−6.09090e9	−0.510324	−0.255162	+	0.966898i	$0.582129\pi$
$758$	2.84051e9	0.236894
$759$	−3.16528e9	−0.262764
$760$	−1.39625e9	−0.115376
$761$	−1.56404e9	−0.128647	−0.0643236	−	0.997929i	$-0.520489\pi$
$761$	−1.56404e9	−0.128647	−0.0643236	+	0.997929i	$0.520489\pi$
$762$	−9.82644e9	−0.804552
$763$	1.45370e10	1.18478
$764$	−6.02537e9	−0.488829
$765$	−7.55828e9	−0.610391
$766$	−1.25481e10	−1.00873
$767$	2.40975e9	0.192836
$768$	−6.84465e8	−0.0545239
$769$	−1.81491e10	−1.43918	−0.719588	−	0.694402i	$-0.755669\pi$
$769$	−1.81491e10	−1.43918	−0.719588	+	0.694402i	$0.755669\pi$
$770$	1.64375e10	1.29754
$771$	−7.83008e9	−0.615284
$772$	6.46433e9	0.505665
$773$	−2.07867e10	−1.61867	−0.809335	−	0.587347i	$-0.800172\pi$
$773$	−2.07867e10	−1.61867	−0.809335	+	0.587347i	$0.800172\pi$
$774$	−1.61060e9	−0.124852
$775$	−2.87463e9	−0.221833
$776$	−6.84238e9	−0.525643
$777$	7.59527e9	0.580858
$778$	−1.10292e10	−0.839685
$779$	3.43031e9	0.259988
$780$	−1.51530e9	−0.114332
$781$	1.63733e10	1.22987
$782$	−2.71319e9	−0.202888
$783$	1.14640e10	0.853435
$784$	−1.79370e9	−0.132936
$785$	−2.22352e10	−1.64058
$786$	−5.50736e9	−0.404543
$787$	−2.25373e10	−1.64813	−0.824064	−	0.566497i	$-0.808298\pi$
$787$	−2.25373e10	−1.64813	−0.824064	+	0.566497i	$0.808298\pi$
$788$	−8.92540e9	−0.649810
$789$	−1.07979e9	−0.0782655
$790$	1.98345e10	1.43129
$791$	−1.34721e10	−0.967872
$792$	−2.11855e9	−0.151531
$793$	3.64453e9	0.259529
$794$	6.07024e9	0.430362
$795$	−1.22741e8	−0.00866376
$796$	1.35532e10	0.952456
$797$	−1.48826e10	−1.04129	−0.520647	−	0.853772i	$-0.674309\pi$
$797$	−1.48826e10	−1.04129	−0.520647	+	0.853772i	$0.674309\pi$
$798$	1.32268e9	0.0921394
$799$	−7.92535e9	−0.549673
$800$	−3.16189e9	−0.218339
$801$	−2.96291e9	−0.203706
$802$	−1.49655e10	−1.02443
$803$	2.31932e10	1.58073
$804$	5.80637e9	0.394011
$805$	−2.54269e9	−0.171794
$806$	−3.30993e8	−0.0222662
$807$	1.74023e10	1.16560
$808$	1.72679e9	0.115159
$809$	−1.45923e10	−0.968955	−0.484477	−	0.874804i	$-0.660990\pi$
$809$	−1.45923e10	−0.968955	−0.484477	+	0.874804i	$0.660990\pi$
$810$	−1.12558e10	−0.744184
$811$	1.55759e9	0.102537	0.0512685	−	0.998685i	$-0.483674\pi$
$811$	1.55759e9	0.102537	0.0512685	+	0.998685i	$0.483674\pi$
$812$	−4.12162e9	−0.270160
$813$	−2.96085e9	−0.193241
$814$	1.89904e10	1.23409
$815$	−1.07747e10	−0.697194
$816$	5.78386e9	0.372651
$817$	2.51417e9	0.161294
$818$	1.96755e10	1.25687
$819$	−4.50693e8	−0.0286673
$820$	1.40575e10	0.890351
$821$	1.10726e9	0.0698313	0.0349157	−	0.999390i	$-0.488884\pi$
$821$	1.10726e9	0.0698313	0.0349157	+	0.999390i	$0.488884\pi$
$822$	2.87480e9	0.180533
$823$	−1.28442e10	−0.803171	−0.401586	−	0.915821i	$-0.631541\pi$
$823$	−1.28442e10	−0.803171	−0.401586	+	0.915821i	$0.631541\pi$
$824$	−2.83298e9	−0.176400
$825$	3.11706e10	1.93266
$826$	−8.61993e9	−0.532198
$827$	7.20214e9	0.442785	0.221392	−	0.975185i	$-0.428940\pi$
$827$	7.20214e9	0.442785	0.221392	+	0.975185i	$0.428940\pi$
$828$	3.27715e8	0.0200627
$829$	−3.36146e9	−0.204921	−0.102461	−	0.994737i	$-0.532672\pi$
$829$	−3.36146e9	−0.204921	−0.102461	+	0.994737i	$0.532672\pi$
$830$	−3.25187e10	−1.97406
$831$	−2.38206e10	−1.43996
$832$	−3.64069e8	−0.0219155
$833$	1.51571e10	0.908568
$834$	−1.60661e10	−0.959025
$835$	1.18166e10	0.702408
$836$	3.30709e9	0.195760
$837$	−3.29320e9	−0.194124
$838$	9.89782e9	0.581012
$839$	−4.51585e9	−0.263981	−0.131990	−	0.991251i	$-0.542137\pi$
$839$	−4.51585e9	−0.263981	−0.131990	+	0.991251i	$0.542137\pi$
$840$	5.42040e9	0.315539
$841$	−6.49499e9	−0.376524
$842$	−2.70271e9	−0.156029
$843$	−9.68931e8	−0.0557053
$844$	−5.54319e8	−0.0317367
$845$	2.54149e10	1.44907
$846$	9.57269e8	0.0543548
$847$	−2.68318e10	−1.51725
$848$	−2.94900e7	−0.00166069
$849$	2.75778e10	1.54662
$850$	2.67186e10	1.49227
$851$	−2.93759e9	−0.163394
$852$	5.39922e9	0.299083
$853$	1.43396e10	0.791070	0.395535	−	0.918451i	$-0.370559\pi$
$853$	1.43396e10	0.791070	0.395535	+	0.918451i	$0.370559\pi$
$854$	−1.30369e10	−0.716260
$855$	−1.42510e9	−0.0779766
$856$	5.77274e9	0.314574
$857$	−2.38691e9	−0.129540	−0.0647698	−	0.997900i	$-0.520631\pi$
$857$	−2.38691e9	−0.129540	−0.0647698	+	0.997900i	$0.520631\pi$
$858$	3.58907e9	0.193989
$859$	−1.84668e10	−0.994065	−0.497032	−	0.867732i	$-0.665577\pi$
$859$	−1.84668e10	−0.994065	−0.497032	+	0.867732i	$0.665577\pi$
$860$	1.03032e10	0.552365
$861$	−1.33168e10	−0.711034
$862$	6.60562e9	0.351267
$863$	−1.90229e10	−1.00748	−0.503742	−	0.863854i	$-0.668044\pi$
$863$	−1.90229e10	−1.00748	−0.503742	+	0.863854i	$0.668044\pi$
$864$	−3.62229e9	−0.191067
$865$	−2.65751e10	−1.39611
$866$	9.35256e9	0.489348
$867$	−3.21340e10	−1.67455
$868$	1.18400e9	0.0614513
$869$	−4.69790e10	−2.42848
$870$	−1.41439e10	−0.728202
$871$	3.08842e9	0.158370
$872$	1.19856e10	0.612140
$873$	−6.98376e9	−0.355254
$874$	−5.11567e8	−0.0259187
$875$	4.76646e9	0.240529
$876$	7.64814e9	0.384407
$877$	−3.63551e10	−1.81998	−0.909989	−	0.414632i	$-0.863910\pi$
$877$	−3.63551e10	−1.81998	−0.909989	+	0.414632i	$0.863910\pi$
$878$	9.04142e9	0.450823
$879$	1.68367e10	0.836174
$880$	1.35526e10	0.670397
$881$	−1.67922e10	−0.827357	−0.413679	−	0.910423i	$-0.635756\pi$
$881$	−1.67922e10	−0.827357	−0.413679	+	0.910423i	$0.635756\pi$
$882$	−1.83076e9	−0.0898443
$883$	−9.20607e9	−0.449999	−0.225000	−	0.974359i	$-0.572238\pi$
$883$	−9.20607e9	−0.449999	−0.225000	+	0.974359i	$0.572238\pi$
$884$	3.07645e9	0.149784
$885$	−2.95805e10	−1.43451
$886$	−2.76376e10	−1.33500
$887$	−3.69325e10	−1.77695	−0.888477	−	0.458922i	$-0.848236\pi$
$887$	−3.69325e10	−1.77695	−0.888477	+	0.458922i	$0.848236\pi$
$888$	6.26222e9	0.300112
$889$	1.86965e10	0.892490
$890$	1.89540e10	0.901231
$891$	2.66600e10	1.26266
$892$	−4.99415e9	−0.235605
$893$	−1.49431e9	−0.0702200
$894$	−9.68787e9	−0.453468
$895$	3.99763e10	1.86390
$896$	1.30231e9	0.0604835
$897$	−5.55187e8	−0.0256842
$898$	9.15210e9	0.421749
$899$	−3.08950e9	−0.141817
$900$	−3.22722e9	−0.147564
$901$	2.49196e8	0.0113502
$902$	−3.32960e10	−1.51067
$903$	−9.76029e9	−0.441119
$904$	−1.11076e10	−0.500070
$905$	2.74999e10	1.23328
$906$	−1.89942e10	−0.848540
$907$	5.40746e9	0.240640	0.120320	−	0.992735i	$-0.461608\pi$
$907$	5.40746e9	0.240640	0.120320	+	0.992735i	$0.461608\pi$
$908$	−3.84653e9	−0.170517
$909$	1.76246e9	0.0778300
$910$	2.88312e9	0.126829
$911$	4.05406e10	1.77654	0.888271	−	0.459319i	$-0.151906\pi$
$911$	4.05406e10	1.77654	0.888271	+	0.459319i	$0.151906\pi$
$912$	1.09054e9	0.0476057
$913$	7.70221e10	3.34940
$914$	1.37109e10	0.593955
$915$	−4.47378e10	−1.93064
$916$	1.24302e10	0.534372
$917$	1.04787e10	0.448760
$918$	3.06090e10	1.30587
$919$	−4.00001e10	−1.70003	−0.850015	−	0.526758i	$-0.823407\pi$
$919$	−4.00001e10	−1.70003	−0.850015	+	0.526758i	$0.823407\pi$
$920$	−2.09642e9	−0.0887608
$921$	7.01804e9	0.296010
$922$	−4.86961e9	−0.204614
$923$	2.87185e9	0.120214
$924$	−1.28385e10	−0.535379
$925$	2.89283e10	1.20179
$926$	1.51830e10	0.628374
$927$	−2.89152e9	−0.119219
$928$	−3.39823e9	−0.139584
$929$	1.46712e10	0.600360	0.300180	−	0.953883i	$-0.402953\pi$
$929$	1.46712e10	0.600360	0.300180	+	0.953883i	$0.402953\pi$
$930$	4.06304e9	0.165638
$931$	2.85784e9	0.116068
$932$	1.76060e10	0.712369
$933$	3.73640e10	1.50615
$934$	6.47047e9	0.259849
$935$	−1.14522e11	−4.58192
$936$	−3.71591e8	−0.0148115
$937$	3.16419e9	0.125653	0.0628267	−	0.998024i	$-0.479988\pi$
$937$	3.16419e9	0.125653	0.0628267	+	0.998024i	$0.479988\pi$
$938$	−1.10476e10	−0.437077
$939$	2.08511e10	0.821863
$940$	−6.12374e9	−0.240475
$941$	9.23936e9	0.361475	0.180738	−	0.983531i	$-0.442152\pi$
$941$	9.23936e9	0.361475	0.180738	+	0.983531i	$0.442152\pi$
$942$	1.73668e10	0.676925
$943$	5.15049e9	0.200013
$944$	−7.10704e9	−0.274971
$945$	2.86855e10	1.10574
$946$	−2.44036e10	−0.937204
$947$	2.22265e10	0.850445	0.425222	−	0.905089i	$-0.360196\pi$
$947$	2.22265e10	0.850445	0.425222	+	0.905089i	$0.360196\pi$
$948$	−1.54917e10	−0.590567
$949$	4.06806e9	0.154510
$950$	5.03774e9	0.190635
$951$	8.19729e9	0.309057
$952$	−1.10048e10	−0.413382
$953$	1.34511e10	0.503423	0.251711	−	0.967802i	$-0.419007\pi$
$953$	1.34511e10	0.503423	0.251711	+	0.967802i	$0.419007\pi$
$954$	−3.00993e7	−0.00112237
$955$	3.93413e10	1.46163
$956$	6.95550e8	0.0257469
$957$	3.35005e10	1.23555
$958$	−1.62288e10	−0.596357
$959$	−5.46979e9	−0.200265
$960$	4.46906e9	0.163030
$961$	8.87504e8	0.0322581
$962$	3.33089e9	0.120628
$963$	5.89201e9	0.212604
$964$	2.02411e10	0.727720
$965$	−4.22074e10	−1.51197
$966$	1.98596e9	0.0708844
$967$	2.76468e10	0.983224	0.491612	−	0.870814i	$-0.336408\pi$
$967$	2.76468e10	0.983224	0.491612	+	0.870814i	$0.336408\pi$
$968$	−2.21225e10	−0.783917
$969$	−9.21525e9	−0.325367
$970$	4.46757e10	1.57170
$971$	7.45508e9	0.261327	0.130664	−	0.991427i	$-0.458289\pi$
$971$	7.45508e9	0.261327	0.130664	+	0.991427i	$0.458289\pi$
$972$	−6.68123e9	−0.233359
$973$	3.05685e10	1.06385
$974$	−7.89945e9	−0.273931
$975$	5.46728e9	0.188910
$976$	−1.07488e10	−0.370070
$977$	−2.64244e10	−0.906514	−0.453257	−	0.891380i	$-0.649738\pi$
$977$	−2.64244e10	−0.906514	−0.453257	+	0.891380i	$0.649738\pi$
$978$	8.41554e9	0.287671
$979$	−4.48935e10	−1.52913
$980$	1.17115e10	0.397486
$981$	1.22332e10	0.413713
$982$	−3.27517e10	−1.10368
$983$	1.18942e10	0.399390	0.199695	−	0.979858i	$-0.436005\pi$
$983$	1.18942e10	0.399390	0.199695	+	0.979858i	$0.436005\pi$
$984$	−1.09796e10	−0.367370
$985$	5.82764e10	1.94297
$986$	2.87157e10	0.954004
$987$	5.80107e9	0.192043
$988$	5.80059e8	0.0191348
$989$	3.77494e9	0.124086
$990$	1.38326e10	0.453086
$991$	−9.57215e9	−0.312429	−0.156215	−	0.987723i	$-0.549929\pi$
$991$	−9.57215e9	−0.312429	−0.156215	+	0.987723i	$0.549929\pi$
$992$	9.76191e8	0.0317500
$993$	−7.04109e9	−0.228201
$994$	−1.02729e10	−0.331773
$995$	−8.84923e10	−2.84790
$996$	2.53986e10	0.814521
$997$	−6.04369e10	−1.93139	−0.965694	−	0.259684i	$-0.916382\pi$
$997$	−6.04369e10	−1.93139	−0.965694	+	0.259684i	$0.916382\pi$
$998$	4.41094e8	0.0140467
$999$	3.31406e10	1.05167

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.8.a.c.1.2	✓	5
3.2	odd	2		558.8.a.m.1.4		5
4.3	odd	2		496.8.a.c.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.8.a.c.1.2	✓	5	1.1	even	1	trivial
496.8.a.c.1.4		5	4.3	odd	2
558.8.a.m.1.4		5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	62.a (trivial)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} -40.7973 q^{3} +64.0000 q^{4} -417.873 q^{5} +326.379 q^{6} -620.990 q^{7} -512.000 q^{8} -522.579 q^{9} +3342.99 q^{10} -7918.03 q^{11} -2611.03 q^{12} -1388.81 q^{13} +4967.92 q^{14} +17048.1 q^{15} +4096.00 q^{16} -34612.0 q^{17} +4180.63 q^{18} -6526.03 q^{19} -26743.9 q^{20} +25334.7 q^{21} +63344.2 q^{22} -9798.60 q^{23} +20888.2 q^{24} +96493.2 q^{25} +11110.5 q^{26} +110544. q^{27} -39743.4 q^{28} +103706. q^{29} -136385. q^{30} -29791.0 q^{31} -32768.0 q^{32} +323034. q^{33} +276896. q^{34} +259495. q^{35} -33445.1 q^{36} +299797. q^{37} +52208.2 q^{38} +56659.8 q^{39} +213951. q^{40} -525636. q^{41} -202678. q^{42} -385253. q^{43} -506754. q^{44} +218372. q^{45} +78388.8 q^{46} +228977. q^{47} -167106. q^{48} -437914. q^{49} -771945. q^{50} +1.41208e6 q^{51} -88884.0 q^{52} -7199.71 q^{53} -884348. q^{54} +3.30873e6 q^{55} +317947. q^{56} +266244. q^{57} -829646. q^{58} -1.73512e6 q^{59} +1.09108e6 q^{60} -2.62421e6 q^{61} +238328. q^{62} +324517. q^{63} +262144. q^{64} +580348. q^{65} -2.58427e6 q^{66} -2.22379e6 q^{67} -2.21517e6 q^{68} +399757. q^{69} -2.07596e6 q^{70} -2.06785e6 q^{71} +267561. q^{72} -2.92917e6 q^{73} -2.39837e6 q^{74} -3.93666e6 q^{75} -417666. q^{76} +4.91702e6 q^{77} -453278. q^{78} +5.93317e6 q^{79} -1.71161e6 q^{80} -3.36700e6 q^{81} +4.20509e6 q^{82} -9.72743e6 q^{83} +1.62142e6 q^{84} +1.44634e7 q^{85} +3.08202e6 q^{86} -4.23092e6 q^{87} +4.05403e6 q^{88} +5.66978e6 q^{89} -1.74698e6 q^{90} +862439. q^{91} -627110. q^{92} +1.21539e6 q^{93} -1.83182e6 q^{94} +2.72705e6 q^{95} +1.33685e6 q^{96} +1.33640e7 q^{97} +3.50331e6 q^{98} +4.13780e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 40 q^{2} + 28 q^{3} + 320 q^{4} + 152 q^{5} - 224 q^{6} - 132 q^{7} - 2560 q^{8} + 9149 q^{9} - 1216 q^{10} - 4218 q^{11} + 1792 q^{12} - 7014 q^{13} + 1056 q^{14} - 30666 q^{15} + 20480 q^{16} - 30180 q^{17}+ \cdots + 36785690 q^{99}+O(q^{100}) \) 5 * q - 40 * q^2 + 28 * q^3 + 320 * q^4 + 152 * q^5 - 224 * q^6 - 132 * q^7 - 2560 * q^8 + 9149 * q^9 - 1216 * q^10 - 4218 * q^11 + 1792 * q^12 - 7014 * q^13 + 1056 * q^14 - 30666 * q^15 + 20480 * q^16 - 30180 * q^17 - 73192 * q^18 - 8320 * q^19 + 9728 * q^20 + 117298 * q^21 + 33744 * q^22 + 67130 * q^23 - 14336 * q^24 + 374909 * q^25 + 56112 * q^26 + 522556 * q^27 - 8448 * q^28 + 290034 * q^29 + 245328 * q^30 - 148955 * q^31 - 163840 * q^32 + 1406308 * q^33 + 241440 * q^34 + 617080 * q^35 + 585536 * q^36 + 682400 * q^37 + 66560 * q^38 + 890040 * q^39 - 77824 * q^40 + 197844 * q^41 - 938384 * q^42 + 2333288 * q^43 - 269952 * q^44 + 420684 * q^45 - 537040 * q^46 - 405160 * q^47 + 114688 * q^48 + 18911 * q^49 - 2999272 * q^50 - 2221952 * q^51 - 448896 * q^52 + 1029596 * q^53 - 4180448 * q^54 + 1893688 * q^55 + 67584 * q^56 + 1816438 * q^57 - 2320272 * q^58 - 400004 * q^59 - 1962624 * q^60 - 4933754 * q^61 + 1191640 * q^62 - 2215816 * q^63 + 1310720 * q^64 - 12557830 * q^65 - 11250464 * q^66 + 2699572 * q^67 - 1931520 * q^68 - 5447084 * q^69 - 4936640 * q^70 - 613944 * q^71 - 4684288 * q^72 + 7894998 * q^73 - 5459200 * q^74 + 1100718 * q^75 - 532480 * q^76 + 13071604 * q^77 - 7120320 * q^78 + 10463774 * q^79 + 622592 * q^80 + 4221713 * q^81 - 1582752 * q^82 - 12217942 * q^83 + 7507072 * q^84 + 9681846 * q^85 - 18666304 * q^86 + 10112196 * q^87 + 2159616 * q^88 + 22649884 * q^89 - 3365472 * q^90 - 3100110 * q^91 + 4296320 * q^92 - 834148 * q^93 + 3241280 * q^94 - 22084956 * q^95 - 917504 * q^96 - 7610048 * q^97 - 151288 * q^98 + 36785690 * q^99

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