LMFDB - Embedded newform 3.32.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,32,Mod(1,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 32, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 32);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 32 $
Character orbit:	$[\chi]$	$=$	3.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$18.2631398457$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 2875320 $ x^2 - x - 2875320
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{3}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1695.18$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+20932.2 q^{2} +1.43489e7 q^{3} -1.70932e9 q^{4} +4.40531e10 q^{5} +3.00355e11 q^{6} -1.09681e13 q^{7} -8.07317e13 q^{8} +2.05891e14 q^{9} +O(q^{10})$	\(q+20932.2 q^{2} +1.43489e7 q^{3} -1.70932e9 q^{4} +4.40531e10 q^{5} +3.00355e11 q^{6} -1.09681e13 q^{7} -8.07317e13 q^{8} +2.05891e14 q^{9} +9.22129e14 q^{10} -1.20825e16 q^{11} -2.45269e16 q^{12} +6.41891e16 q^{13} -2.29587e17 q^{14} +6.32113e17 q^{15} +1.98085e18 q^{16} -1.57894e19 q^{17} +4.30976e18 q^{18} -1.01444e20 q^{19} -7.53010e19 q^{20} -1.57380e20 q^{21} -2.52914e20 q^{22} -1.16552e21 q^{23} -1.15841e21 q^{24} -2.71594e21 q^{25} +1.34362e21 q^{26} +2.95431e21 q^{27} +1.87480e22 q^{28} -1.53466e22 q^{29} +1.32315e22 q^{30} +2.39613e23 q^{31} +2.14834e23 q^{32} -1.73371e23 q^{33} -3.30509e23 q^{34} -4.83178e23 q^{35} -3.51935e23 q^{36} -5.11449e22 q^{37} -2.12345e24 q^{38} +9.21043e23 q^{39} -3.55648e24 q^{40} -1.02794e24 q^{41} -3.29432e24 q^{42} +9.54950e24 q^{43} +2.06529e25 q^{44} +9.07013e24 q^{45} -2.43969e25 q^{46} +1.30600e26 q^{47} +2.84231e25 q^{48} -3.74764e25 q^{49} -5.68507e25 q^{50} -2.26561e26 q^{51} -1.09720e26 q^{52} -3.91027e26 q^{53} +6.18404e25 q^{54} -5.32271e26 q^{55} +8.85472e26 q^{56} -1.45561e27 q^{57} -3.21239e26 q^{58} +5.34202e27 q^{59} -1.08049e27 q^{60} +1.24697e27 q^{61} +5.01564e27 q^{62} -2.25823e27 q^{63} +2.43103e26 q^{64} +2.82773e27 q^{65} -3.62904e27 q^{66} -3.44146e28 q^{67} +2.69893e28 q^{68} -1.67239e28 q^{69} -1.01140e28 q^{70} +3.70520e28 q^{71} -1.66219e28 q^{72} -1.06906e29 q^{73} -1.07058e27 q^{74} -3.89708e28 q^{75} +1.73400e29 q^{76} +1.32522e29 q^{77} +1.92795e28 q^{78} +2.48482e29 q^{79} +8.72626e28 q^{80} +4.23912e28 q^{81} -2.15170e28 q^{82} -8.38577e29 q^{83} +2.69014e29 q^{84} -6.95574e29 q^{85} +1.99893e29 q^{86} -2.20207e29 q^{87} +9.75440e29 q^{88} -3.06538e30 q^{89} +1.89858e29 q^{90} -7.04032e29 q^{91} +1.99225e30 q^{92} +3.43818e30 q^{93} +2.73375e30 q^{94} -4.46891e30 q^{95} +3.08263e30 q^{96} +2.89967e30 q^{97} -7.84466e29 q^{98} -2.48768e30 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 39528 q^{2} + 28697814 q^{3} - 201366976 q^{4} - 7930517220 q^{5} - 567183595896 q^{6} - 10488874236176 q^{7} - 42065768434176 q^{8} + 411782264189298 q^{9}+O(q^{10}) $ 2 * q - 39528 * q^2 + 28697814 * q^3 - 201366976 * q^4 - 7930517220 * q^5 - 567183595896 * q^6 - 10488874236176 * q^7 - 42065768434176 * q^8 + 411782264189298 * q^9	$ 2 q - 39528 q^{2} + 28697814 q^{3} - 201366976 q^{4} - 7930517220 q^{5} - 567183595896 q^{6} - 10488874236176 q^{7} - 42065768434176 q^{8} + 411782264189298 q^{9} + 40\!\cdots\!40 q^{10}+ \cdots + 22\!\cdots\!92 q^{99}+O(q^{100}) $ 2 * q - 39528 * q^2 + 28697814 * q^3 - 201366976 * q^4 - 7930517220 * q^5 - 567183595896 * q^6 - 10488874236176 * q^7 - 42065768434176 * q^8 + 411782264189298 * q^9 + 4065069087861840 * q^10 + 10782060500929608 * q^11 - 2889396011495232 * q^12 - 91686777034056308 * q^13 - 258560108208609984 * q^14 - 113794254051678540 * q^15 - 3595212242257899520 * q^16 - 16595285055794710812 * q^17 - 8138464669437285672 * q^18 - 82480245798578318024 * q^19 - 153690009762588577920 * q^20 - 150503880949585459632 * q^21 - 1635310640344066149024 * q^22 - 3510229760731757537712 * q^23 - 603597799145527045632 * q^24 - 4670262053173672152850 * q^25 + 10767915474742339649424 * q^26 + 5908625413101667397286 * q^27 + 19470658220602184146432 * q^28 + 27292102645387535397612 * q^29 + 58329298290304371008880 * q^30 + 32627031656431162883392 * q^31 + 468929434910304216121344 * q^32 + 154710783396212358738456 * q^33 - 281787665552204278707792 * q^34 - 508089050110930039768800 * q^35 - 41459674655116014911424 * q^36 - 3583146918713545401630116 * q^37 - 3269981889193482397514592 * q^38 - 1315605036791409796255356 * q^39 - 5566467832741725214510080 * q^40 - 3797899216135385210632908 * q^41 - 3710054946595281259687488 * q^42 + 26575294422425069121661960 * q^43 + 55131699398690171610853632 * q^44 - 1632823168521908564355780 * q^45 + 117364920594432004467352512 * q^46 + 35525358464593824073372320 * q^47 - 51587366109420070227824640 * q^48 - 195022162059991348175701230 * q^49 + 61307978112283866795340200 * q^50 - 238124201904088116533282484 * q^51 - 344774229920038676879368832 * q^52 + 209333823893552605529106108 * q^53 - 116778072664541354439960504 * q^54 - 1720852397107481929939963920 * q^55 + 904001217638747705093836800 * q^56 - 1183501376300941017542799768 * q^57 - 2899187104604865887521185264 * q^58 + 8315016058044372283987872744 * q^59 - 2205283656912475583836333440 * q^60 + 4363691539370591264432189740 * q^61 + 17530048836377045276588782848 * q^62 - 2159566190884673448811822224 * q^63 - 3145087146211331732110311424 * q^64 + 10930710572477042656631722920 * q^65 - 23464920294407453174193516768 * q^66 - 42369284190160751303828837672 * q^67 + 25774131672494516419161284736 * q^68 - 50367960385372240855178480784 * q^69 - 8607856574006081326444406400 * q^70 - 16546316342864021533760545296 * q^71 - 8660968685343847043758324224 * q^72 - 119663167384814660837541194252 * q^73 + 212475132055045059714085448016 * q^74 - 67013155866618076569734434950 * q^75 + 201996400191863673719694589696 * q^76 + 143478912022010782926074993088 * q^77 + 154507817730938680591997579568 * q^78 - 111310025088680432366828160800 * q^79 + 377126313405184879658681425920 * q^80 + 84782316550432407028588866402 * q^81 + 145955621212388339389027195248 * q^82 - 1258094410515212478889159597896 * q^83 + 279382664036206224314027149824 * q^84 - 653683338582772611056270015880 * q^85 - 829491133742090715106836469152 * q^86 + 391611842693119724379542610084 * q^87 + 1859518717097362129166224103424 * q^88 - 4692098539351208698917605954604 * q^89 + 836961676542836421299915294160 * q^90 - 778729510605845448339936789088 * q^91 - 1543476723048531611525136139776 * q^92 + 468162242924186708115643652544 * q^93 + 8481973556486642845766202739584 * q^94 - 5454695816719667916384315579120 * q^95 + 6728624851090508538833065771008 * q^96 + 9654846058153613483749893797188 * q^97 + 8740788233364983573968509908568 * q^98 + 2219930642849395287788742467592 * q^99

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 $

$2$	20932.2	0.451701	0.225850	−	0.974162i	$-0.427484\pi$
$2$	20932.2	0.451701	0.225850	+	0.974162i	$0.427484\pi$
$3$	1.43489e7	0.577350
$3$	1.43489e7	0.577350
$4$	−1.70932e9	−0.795966
$5$	4.40531e10	0.645566	0.322783	−	0.946473i	$-0.395382\pi$
$5$	4.40531e10	0.645566	0.322783	+	0.946473i	$0.395382\pi$
$6$	3.00355e11	0.260790
$7$	−1.09681e13	−0.873195	−0.436598	−	0.899657i	$-0.643817\pi$
$7$	−1.09681e13	−0.873195	−0.436598	+	0.899657i	$0.643817\pi$
$8$	−8.07317e13	−0.811240
$9$	2.05891e14	0.333333
$10$	9.22129e14	0.291603
$11$	−1.20825e16	−0.872108	−0.436054	−	0.899921i	$-0.643624\pi$
$11$	−1.20825e16	−0.872108	−0.436054	+	0.899921i	$0.643624\pi$
$12$	−2.45269e16	−0.459551
$13$	6.41891e16	0.347808	0.173904	−	0.984763i	$-0.444362\pi$
$13$	6.41891e16	0.347808	0.173904	+	0.984763i	$0.444362\pi$
$14$	−2.29587e17	−0.394423
$15$	6.32113e17	0.372718
$16$	1.98085e18	0.429529
$17$	−1.57894e19	−1.33785	−0.668927	−	0.743328i	$-0.733246\pi$
$17$	−1.57894e19	−1.33785	−0.668927	+	0.743328i	$0.733246\pi$
$18$	4.30976e18	0.150567
$19$	−1.01444e20	−1.53301	−0.766504	−	0.642240i	$-0.778005\pi$
$19$	−1.01444e20	−1.53301	−0.766504	+	0.642240i	$0.778005\pi$
$20$	−7.53010e19	−0.513849
$21$	−1.57380e20	−0.504139
$22$	−2.52914e20	−0.393932
$23$	−1.16552e21	−0.911460	−0.455730	−	0.890118i	$-0.650622\pi$
$23$	−1.16552e21	−0.911460	−0.455730	+	0.890118i	$0.650622\pi$
$24$	−1.15841e21	−0.468369
$25$	−2.71594e21	−0.583244
$26$	1.34362e21	0.157105
$27$	2.95431e21	0.192450
$28$	1.87480e22	0.695034
$29$	−1.53466e22	−0.330251	−0.165125	−	0.986273i	$-0.552803\pi$
$29$	−1.53466e22	−0.330251	−0.165125	+	0.986273i	$0.552803\pi$
$30$	1.32315e22	0.168357
$31$	2.39613e23	1.83402	0.917010	−	0.398865i	$-0.130596\pi$
$31$	2.39613e23	1.83402	0.917010	+	0.398865i	$0.130596\pi$
$32$	2.14834e23	1.00526
$33$	−1.73371e23	−0.503512
$34$	−3.30509e23	−0.604310
$35$	−4.83178e23	−0.563706
$36$	−3.51935e23	−0.265322
$37$	−5.11449e22	−0.0252160	−0.0126080	−	0.999921i	$-0.504013\pi$
$37$	−5.11449e22	−0.0252160	−0.0126080	+	0.999921i	$0.504013\pi$
$38$	−2.12345e24	−0.692461
$39$	9.21043e23	0.200807
$40$	−3.55648e24	−0.523709
$41$	−1.02794e24	−0.103232	−0.0516162	−	0.998667i	$-0.516437\pi$
$41$	−1.02794e24	−0.103232	−0.0516162	+	0.998667i	$0.516437\pi$
$42$	−3.29432e24	−0.227720
$43$	9.54950e24	0.458374	0.229187	−	0.973382i	$-0.426393\pi$
$43$	9.54950e24	0.458374	0.229187	+	0.973382i	$0.426393\pi$
$44$	2.06529e25	0.694168
$45$	9.07013e24	0.215189
$46$	−2.43969e25	−0.411707
$47$	1.30600e26	1.57916	0.789579	−	0.613648i	$-0.210299\pi$
$47$	1.30600e26	1.57916	0.789579	+	0.613648i	$0.210299\pi$
$48$	2.84231e25	0.247989
$49$	−3.74764e25	−0.237530
$50$	−5.68507e25	−0.263452
$51$	−2.26561e26	−0.772410
$52$	−1.09720e26	−0.276843
$53$	−3.91027e26	−0.734397	−0.367199	−	0.930143i	$-0.619683\pi$
$53$	−3.91027e26	−0.734397	−0.367199	+	0.930143i	$0.619683\pi$
$54$	6.18404e25	0.0869299
$55$	−5.32271e26	−0.563003
$56$	8.85472e26	0.708370
$57$	−1.45561e27	−0.885083
$58$	−3.21239e26	−0.149175
$59$	5.34202e27	1.90327	0.951633	−	0.307237i	$-0.0994046\pi$
$59$	5.34202e27	1.90327	0.951633	+	0.307237i	$0.0994046\pi$
$60$	−1.08049e27	−0.296671
$61$	1.24697e27	0.264998	0.132499	−	0.991183i	$-0.457700\pi$
$61$	1.24697e27	0.264998	0.132499	+	0.991183i	$0.457700\pi$
$62$	5.01564e27	0.828428
$63$	−2.25823e27	−0.291065
$64$	2.43103e26	0.0245471
$65$	2.82773e27	0.224533
$66$	−3.62904e27	−0.227437
$67$	−3.44146e28	−1.70838	−0.854189	−	0.519963i	$-0.825946\pi$
$67$	−3.44146e28	−1.70838	−0.854189	+	0.519963i	$0.825946\pi$
$68$	2.69893e28	1.06489
$69$	−1.67239e28	−0.526232
$70$	−1.01140e28	−0.254626
$71$	3.70520e28	0.748698	0.374349	−	0.927288i	$-0.377866\pi$
$71$	3.70520e28	0.748698	0.374349	+	0.927288i	$0.377866\pi$
$72$	−1.66219e28	−0.270413
$73$	−1.06906e29	−1.40442	−0.702212	−	0.711968i	$-0.747804\pi$
$73$	−1.06906e29	−1.40442	−0.702212	+	0.711968i	$0.747804\pi$
$74$	−1.07058e27	−0.0113901
$75$	−3.89708e28	−0.336736
$76$	1.73400e29	1.22022
$77$	1.32522e29	0.761520
$78$	1.92795e28	0.0907047
$79$	2.48482e29	0.959568	0.479784	−	0.877387i	$-0.340715\pi$
$79$	2.48482e29	0.959568	0.479784	+	0.877387i	$0.340715\pi$
$80$	8.72626e28	0.277289
$81$	4.23912e28	0.111111
$82$	−2.15170e28	−0.0466302
$83$	−8.38577e29	−1.50603	−0.753014	−	0.658005i	$-0.771401\pi$
$83$	−8.38577e29	−1.50603	−0.753014	+	0.658005i	$0.771401\pi$
$84$	2.69014e29	0.401278
$85$	−6.95574e29	−0.863674
$86$	1.99893e29	0.207048
$87$	−2.20207e29	−0.190670
$88$	9.75440e29	0.707488
$89$	−3.06538e30	−1.86612	−0.933060	−	0.359722i	$-0.882872\pi$
$89$	−3.06538e30	−1.86612	−0.933060	+	0.359722i	$0.882872\pi$
$90$	1.89858e29	0.0972010
$91$	−7.04032e29	−0.303704
$92$	1.99225e30	0.725491
$93$	3.43818e30	1.05887
$94$	2.73375e30	0.713307
$95$	−4.46891e30	−0.989659
$96$	3.08263e30	0.580386
$97$	2.89967e30	0.464929	0.232465	−	0.972605i	$-0.425321\pi$
$97$	2.89967e30	0.464929	0.232465	+	0.972605i	$0.425321\pi$
$98$	−7.84466e29	−0.107293
$99$	−2.48768e30	−0.290703
$100$	4.64243e30	0.464243
$101$	4.94438e30	0.423770	0.211885	−	0.977295i	$-0.432040\pi$
$101$	4.94438e30	0.423770	0.211885	+	0.977295i	$0.432040\pi$
$102$	−4.74244e30	−0.348898
$103$	−8.87935e30	−0.561570	−0.280785	−	0.959771i	$-0.590595\pi$
$103$	−8.87935e30	−0.561570	−0.280785	+	0.959771i	$0.590595\pi$
$104$	−5.18209e30	−0.282155
$105$	−6.93307e30	−0.325456
$106$	−8.18508e30	−0.331728
$107$	−1.22838e30	−0.0430411	−0.0215205	−	0.999768i	$-0.506851\pi$
$107$	−1.22838e30	−0.0430411	−0.0215205	+	0.999768i	$0.506851\pi$
$108$	−5.04988e30	−0.153184
$109$	−2.77269e30	−0.0729107	−0.0364553	−	0.999335i	$-0.511607\pi$
$109$	−2.77269e30	−0.0729107	−0.0364553	+	0.999335i	$0.511607\pi$
$110$	−1.11416e31	−0.254309
$111$	−7.33874e29	−0.0145585
$112$	−2.17262e31	−0.375062
$113$	1.32016e32	1.98569	0.992844	−	0.119420i	$-0.0381035\pi$
$113$	1.32016e32	1.98569	0.992844	+	0.119420i	$0.0381035\pi$
$114$	−3.04691e31	−0.399793
$115$	−5.13446e31	−0.588408
$116$	2.62324e31	0.262869
$117$	1.32160e31	0.115936
$118$	1.11821e32	0.859707
$119$	1.73180e32	1.16821
$120$	−5.10316e31	−0.302364
$121$	−4.59567e31	−0.239428
$122$	2.61018e31	0.119700
$123$	−1.47498e31	−0.0596013
$124$	−4.09576e32	−1.45982
$125$	−3.24784e32	−1.02209
$126$	−4.72699e31	−0.131474
$127$	2.17026e32	0.534015	0.267008	−	0.963694i	$-0.413965\pi$
$127$	2.17026e32	0.534015	0.267008	+	0.963694i	$0.413965\pi$
$128$	−4.56263e32	−0.994170
$129$	1.37025e32	0.264642
$130$	5.91907e31	0.101422
$131$	3.39782e31	0.0517006	0.0258503	−	0.999666i	$-0.491771\pi$
$131$	3.39782e31	0.0517006	0.0258503	+	0.999666i	$0.491771\pi$
$132$	2.96347e32	0.400778
$133$	1.11264e33	1.33862
$134$	−7.20376e32	−0.771676
$135$	1.30147e32	0.124239
$136$	1.27471e33	1.08532
$137$	1.29517e31	0.00984371	0.00492186	−	0.999988i	$-0.498433\pi$
$137$	1.29517e31	0.00984371	0.00492186	+	0.999988i	$0.498433\pi$
$138$	−3.50069e32	−0.237699
$139$	−1.97605e33	−1.19969	−0.599845	−	0.800116i	$-0.704771\pi$
$139$	−1.97605e33	−1.19969	−0.599845	+	0.800116i	$0.704771\pi$
$140$	8.25908e32	0.448691
$141$	1.87396e33	0.911728
$142$	7.75581e32	0.338188
$143$	−7.75565e32	−0.303326
$144$	4.07840e32	0.143176
$145$	−6.76066e32	−0.213199
$146$	−2.23779e33	−0.634380
$147$	−5.37746e32	−0.137138
$148$	8.74233e31	0.0200711
$149$	−6.33803e33	−1.31089	−0.655446	−	0.755242i	$-0.727520\pi$
$149$	−6.33803e33	−1.31089	−0.655446	+	0.755242i	$0.727520\pi$
$150$	−8.15746e32	−0.152104
$151$	−3.99156e33	−0.671428	−0.335714	−	0.941964i	$-0.608978\pi$
$151$	−3.99156e33	−0.671428	−0.335714	+	0.941964i	$0.608978\pi$
$152$	8.18972e33	1.24364
$153$	−3.25091e33	−0.445951
$154$	2.77398e33	0.343979
$155$	1.05557e34	1.18398
$156$	−1.57436e33	−0.159836
$157$	−9.28666e33	−0.853916	−0.426958	−	0.904272i	$-0.640415\pi$
$157$	−9.28666e33	−0.853916	−0.426958	+	0.904272i	$0.640415\pi$
$158$	5.20129e33	0.433437
$159$	−5.61081e33	−0.424004
$160$	9.46408e33	0.648961
$161$	1.27835e34	0.795882
$162$	8.87342e32	0.0501890
$163$	1.77973e34	0.915055	0.457527	−	0.889196i	$-0.348735\pi$
$163$	1.77973e34	0.915055	0.457527	+	0.889196i	$0.348735\pi$
$164$	1.75708e33	0.0821696
$165$	−7.63751e33	−0.325050
$166$	−1.75533e34	−0.680274
$167$	−1.36885e33	−0.0483338	−0.0241669	−	0.999708i	$-0.507693\pi$
$167$	−1.36885e33	−0.0483338	−0.0241669	+	0.999708i	$0.507693\pi$
$168$	1.27056e34	0.408978
$169$	−2.99397e34	−0.879030
$170$	−1.45599e34	−0.390122
$171$	−2.08864e34	−0.511003
$172$	−1.63232e34	−0.364850
$173$	−2.49091e34	−0.508913	−0.254456	−	0.967084i	$-0.581897\pi$
$173$	−2.49091e34	−0.508913	−0.254456	+	0.967084i	$0.581897\pi$
$174$	−4.60943e33	−0.0861260
$175$	2.97887e34	0.509286
$176$	−2.39336e34	−0.374595
$177$	7.66522e34	1.09885
$178$	−6.41653e34	−0.842928
$179$	3.63508e34	0.437816	0.218908	−	0.975745i	$-0.429750\pi$
$179$	3.63508e34	0.437816	0.218908	+	0.975745i	$0.429750\pi$
$180$	−1.55038e34	−0.171283
$181$	1.10473e35	1.12005	0.560027	−	0.828474i	$-0.310791\pi$
$181$	1.10473e35	1.12005	0.560027	+	0.828474i	$0.310791\pi$
$182$	−1.47370e34	−0.137183
$183$	1.78926e34	0.152997
$184$	9.40942e34	0.739412
$185$	−2.25309e33	−0.0162786
$186$	7.19689e34	0.478293
$187$	1.90776e35	1.16675
$188$	−2.23238e35	−1.25696
$189$	−3.24032e34	−0.168046
$190$	−9.35442e34	−0.447030
$191$	−2.47010e35	−1.08817	−0.544086	−	0.839029i	$-0.683124\pi$
$191$	−2.47010e35	−1.08817	−0.544086	+	0.839029i	$0.683124\pi$
$192$	3.48826e33	0.0141723
$193$	−9.61543e34	−0.360438	−0.180219	−	0.983627i	$-0.557681\pi$
$193$	−9.61543e34	−0.360438	−0.180219	+	0.983627i	$0.557681\pi$
$194$	6.06966e34	0.210009
$195$	4.05748e34	0.129634
$196$	6.40594e34	0.189066
$197$	3.10929e35	0.848075	0.424038	−	0.905645i	$-0.360612\pi$
$197$	3.10929e35	0.848075	0.424038	+	0.905645i	$0.360612\pi$
$198$	−5.20727e34	−0.131311
$199$	−6.54172e35	−1.52570	−0.762851	−	0.646575i	$-0.776201\pi$
$199$	−6.54172e35	−1.52570	−0.762851	+	0.646575i	$0.776201\pi$
$200$	2.19262e35	0.473151
$201$	−4.93813e35	−0.986332
$202$	1.03497e35	0.191417
$203$	1.68323e35	0.288373
$204$	3.87267e35	0.614813
$205$	−4.52837e34	−0.0666434
$206$	−1.85865e35	−0.253662
$207$	−2.39970e35	−0.303820
$208$	1.27149e35	0.149393
$209$	1.22569e36	1.33695
$210$	−1.45125e35	−0.147009
$211$	6.05990e35	0.570279	0.285140	−	0.958486i	$-0.407960\pi$
$211$	6.05990e35	0.570279	0.285140	+	0.958486i	$0.407960\pi$
$212$	6.68392e35	0.584555
$213$	5.31655e35	0.432261
$214$	−2.57127e34	−0.0194417
$215$	4.20685e35	0.295911
$216$	−2.38507e35	−0.156123
$217$	−2.62809e36	−1.60146
$218$	−5.80387e34	−0.0329338
$219$	−1.53399e36	−0.810845
$220$	9.09824e35	0.448132
$221$	−1.01351e36	−0.465316
$222$	−1.53616e34	−0.00657607
$223$	2.61681e35	0.104483	0.0522417	−	0.998634i	$-0.483363\pi$
$223$	2.61681e35	0.104483	0.0522417	+	0.998634i	$0.483363\pi$
$224$	−2.35631e36	−0.877786
$225$	−5.59188e35	−0.194415
$226$	2.76339e36	0.896937
$227$	−2.75682e36	−0.835617	−0.417809	−	0.908535i	$-0.637202\pi$
$227$	−2.75682e36	−0.835617	−0.417809	+	0.908535i	$0.637202\pi$
$228$	2.48810e36	0.704496
$229$	−2.25667e36	−0.597060	−0.298530	−	0.954400i	$-0.596496\pi$
$229$	−2.25667e36	−0.597060	−0.298530	+	0.954400i	$0.596496\pi$
$230$	−1.07476e36	−0.265784
$231$	1.90154e36	0.439664
$232$	1.23896e36	0.267912
$233$	4.62445e36	0.935500	0.467750	−	0.883861i	$-0.345065\pi$
$233$	4.62445e36	0.935500	0.467750	+	0.883861i	$0.345065\pi$
$234$	2.76640e35	0.0523684
$235$	5.75332e36	1.01945
$236$	−9.13125e36	−1.51494
$237$	3.56545e36	0.554007
$238$	3.62505e36	0.527680
$239$	7.91195e36	1.07923	0.539617	−	0.841910i	$-0.318569\pi$
$239$	7.91195e36	1.07923	0.539617	+	0.841910i	$0.318569\pi$
$240$	1.25212e36	0.160093
$241$	−5.03968e36	−0.604142	−0.302071	−	0.953285i	$-0.597678\pi$
$241$	−5.03968e36	−0.604142	−0.302071	+	0.953285i	$0.597678\pi$
$242$	−9.61976e35	−0.108150
$243$	6.08267e35	0.0641500
$244$	−2.13147e36	−0.210930
$245$	−1.65095e36	−0.153342
$246$	−3.08746e35	−0.0269220
$247$	−6.51158e36	−0.533192
$248$	−1.93443e37	−1.48783
$249$	−1.20327e37	−0.869505
$250$	−6.79845e36	−0.461679
$251$	2.03833e37	1.30116	0.650580	−	0.759438i	$-0.274526\pi$
$251$	2.03833e37	1.30116	0.650580	+	0.759438i	$0.274526\pi$
$252$	3.86005e36	0.231678
$253$	1.40824e37	0.794891
$254$	4.54284e36	0.241215
$255$	−9.98072e36	−0.498642
$256$	−1.00727e37	−0.473615
$257$	9.61306e35	0.0425499	0.0212749	−	0.999774i	$-0.493227\pi$
$257$	9.61306e35	0.0425499	0.0212749	+	0.999774i	$0.493227\pi$
$258$	2.86824e36	0.119539
$259$	5.60962e35	0.0220185
$260$	−4.83350e36	−0.178721
$261$	−3.15973e36	−0.110084
$262$	7.11241e35	0.0233532
$263$	3.80962e37	1.17915	0.589573	−	0.807715i	$-0.299296\pi$
$263$	3.80962e37	1.17915	0.589573	+	0.807715i	$0.299296\pi$
$264$	1.39965e37	0.408469
$265$	−1.72259e37	−0.474102
$266$	2.32901e37	0.604654
$267$	−4.39849e37	−1.07740
$268$	5.88258e37	1.35981
$269$	4.04473e37	0.882529	0.441265	−	0.897377i	$-0.354530\pi$
$269$	4.04473e37	0.882529	0.441265	+	0.897377i	$0.354530\pi$
$270$	2.72426e36	0.0561190
$271$	−5.05688e37	−0.983691	−0.491845	−	0.870682i	$-0.663678\pi$
$271$	−5.05688e37	−0.983691	−0.491845	+	0.870682i	$0.663678\pi$
$272$	−3.12766e37	−0.574647
$273$	−1.01021e37	−0.175344
$274$	2.71109e35	0.00444641
$275$	3.28154e37	0.508651
$276$	2.85866e37	0.418863
$277$	−7.39462e37	−1.02442	−0.512211	−	0.858859i	$-0.671174\pi$
$277$	−7.39462e37	−1.02442	−0.512211	+	0.858859i	$0.671174\pi$
$278$	−4.13632e37	−0.541901
$279$	4.93342e37	0.611340
$280$	3.90077e37	0.457300
$281$	−1.72462e38	−1.91313	−0.956566	−	0.291517i	$-0.905840\pi$
$281$	−1.72462e38	−1.91313	−0.956566	+	0.291517i	$0.905840\pi$
$282$	3.92263e37	0.411828
$283$	−1.80265e37	−0.179152	−0.0895759	−	0.995980i	$-0.528551\pi$
$283$	−1.80265e37	−0.179152	−0.0895759	+	0.995980i	$0.528551\pi$
$284$	−6.33338e37	−0.595938
$285$	−6.41239e37	−0.571380
$286$	−1.62343e37	−0.137013
$287$	1.12745e37	0.0901421
$288$	4.42323e37	0.335086
$289$	1.10018e38	0.789853
$290$	−1.41516e37	−0.0963021
$291$	4.16071e37	0.268427
$292$	1.82737e38	1.11787
$293$	1.11111e38	0.644629	0.322314	−	0.946633i	$-0.395539\pi$
$293$	1.11111e38	0.644629	0.322314	+	0.946633i	$0.395539\pi$
$294$	−1.12562e37	−0.0619454
$295$	2.35332e38	1.22868
$296$	4.12902e36	0.0204562
$297$	−3.56955e37	−0.167837
$298$	−1.32669e38	−0.592131
$299$	−7.48136e37	−0.317013
$300$	6.66137e37	0.268031
$301$	−1.04740e38	−0.400250
$302$	−8.35522e37	−0.303285
$303$	7.09464e37	0.244664
$304$	−2.00945e38	−0.658471
$305$	5.49328e37	0.171074
$306$	−6.80488e37	−0.201437
$307$	−1.01205e38	−0.284812	−0.142406	−	0.989808i	$-0.545484\pi$
$307$	−1.01205e38	−0.284812	−0.142406	+	0.989808i	$0.545484\pi$
$308$	−2.26523e38	−0.606144
$309$	−1.27409e38	−0.324223
$310$	2.20954e38	0.534805
$311$	4.83177e38	1.11255	0.556276	−	0.830997i	$-0.312230\pi$
$311$	4.83177e38	1.11255	0.556276	+	0.830997i	$0.312230\pi$
$312$	−7.43574e37	−0.162903
$313$	−5.34051e38	−1.11338	−0.556692	−	0.830719i	$-0.687930\pi$
$313$	−5.34051e38	−1.11338	−0.556692	+	0.830719i	$0.687930\pi$
$314$	−1.94391e38	−0.385714
$315$	−9.94820e37	−0.187902
$316$	−4.24737e38	−0.763783
$317$	3.94290e38	0.675145	0.337572	−	0.941300i	$-0.390394\pi$
$317$	3.94290e38	0.675145	0.337572	+	0.941300i	$0.390394\pi$
$318$	−1.17447e38	−0.191523
$319$	1.85426e38	0.288014
$320$	1.07094e37	0.0158468
$321$	−1.76259e37	−0.0248498
$322$	2.67588e38	0.359501
$323$	1.60174e39	2.05094
$324$	−7.24603e37	−0.0884407
$325$	−1.74334e38	−0.202857
$326$	3.72538e38	0.413331
$327$	−3.97851e37	−0.0420950
$328$	8.29870e37	0.0837463
$329$	−1.43243e39	−1.37891
$330$	−1.59870e38	−0.146825
$331$	1.06627e39	0.934405	0.467202	−	0.884150i	$-0.345262\pi$
$331$	1.06627e39	0.934405	0.467202	+	0.884150i	$0.345262\pi$
$332$	1.43340e39	1.19875
$333$	−1.05303e37	−0.00840533
$334$	−2.86531e37	−0.0218324
$335$	−1.51607e39	−1.10287
$336$	−3.11747e38	−0.216542
$337$	−1.56150e39	−1.03580	−0.517902	−	0.855440i	$-0.673287\pi$
$337$	−1.56150e39	−1.03580	−0.517902	+	0.855440i	$0.673287\pi$
$338$	−6.26705e38	−0.397058
$339$	1.89429e39	1.14644
$340$	1.18896e39	0.687455
$341$	−2.89512e39	−1.59946
$342$	−4.37199e38	−0.230820
$343$	2.14154e39	1.08061
$344$	−7.70947e38	−0.371851
$345$	−7.36739e38	−0.339718
$346$	−5.21403e38	−0.229876
$347$	2.10545e38	0.0887642	0.0443821	−	0.999015i	$-0.485868\pi$
$347$	2.10545e38	0.0887642	0.0443821	+	0.999015i	$0.485868\pi$
$348$	3.76406e38	0.151767
$349$	−1.93616e39	−0.746700	−0.373350	−	0.927690i	$-0.621791\pi$
$349$	−1.93616e39	−0.746700	−0.373350	+	0.927690i	$0.621791\pi$
$350$	6.23544e38	0.230045
$351$	1.89635e38	0.0669356
$352$	−2.59573e39	−0.876693
$353$	−2.49692e39	−0.807042	−0.403521	−	0.914970i	$-0.632214\pi$
$353$	−2.49692e39	−0.807042	−0.403521	+	0.914970i	$0.632214\pi$
$354$	1.60450e39	0.496352
$355$	1.63225e39	0.483334
$356$	5.23973e39	1.48537
$357$	2.48494e39	0.674465
$358$	7.60904e38	0.197762
$359$	−1.04431e39	−0.259936	−0.129968	−	0.991518i	$-0.541487\pi$
$359$	−1.04431e39	−0.259936	−0.129968	+	0.991518i	$0.541487\pi$
$360$	−7.32247e38	−0.174570
$361$	5.91196e39	1.35011
$362$	2.31245e39	0.505930
$363$	−6.59428e38	−0.138234
$364$	1.20342e39	0.241738
$365$	−4.70954e39	−0.906649
$366$	3.74533e38	0.0691088
$367$	1.66771e38	0.0294982	0.0147491	−	0.999891i	$-0.495305\pi$
$367$	1.66771e38	0.0294982	0.0147491	+	0.999891i	$0.495305\pi$
$368$	−2.30872e39	−0.391498
$369$	−2.11643e38	−0.0344108
$370$	−4.71622e37	−0.00735305
$371$	4.28882e39	0.641272
$372$	−5.87697e39	−0.842826
$373$	−1.10143e40	−1.51520	−0.757600	−	0.652719i	$-0.773628\pi$
$373$	−1.10143e40	−1.51520	−0.757600	+	0.652719i	$0.773628\pi$
$374$	3.99337e39	0.527023
$375$	−4.66029e39	−0.590103
$376$	−1.05435e40	−1.28108
$377$	−9.85086e38	−0.114864
$378$	−6.78271e38	−0.0759067
$379$	7.20739e39	0.774230	0.387115	−	0.922031i	$-0.373472\pi$
$379$	7.20739e39	0.774230	0.387115	+	0.922031i	$0.373472\pi$
$380$	7.63881e39	0.787735
$381$	3.11408e39	0.308314
$382$	−5.17048e39	−0.491529
$383$	1.74574e39	0.159367	0.0796837	−	0.996820i	$-0.474609\pi$
$383$	1.74574e39	0.159367	0.0796837	+	0.996820i	$0.474609\pi$
$384$	−6.54687e39	−0.573984
$385$	5.83799e39	0.491612
$386$	−2.01273e39	−0.162810
$387$	1.96616e39	0.152791
$388$	−4.95648e39	−0.370068
$389$	7.84444e39	0.562786	0.281393	−	0.959593i	$-0.409204\pi$
$389$	7.84444e39	0.562786	0.281393	+	0.959593i	$0.409204\pi$
$390$	8.49321e38	0.0585559
$391$	1.84029e40	1.21940
$392$	3.02553e39	0.192694
$393$	4.87550e38	0.0298494
$394$	6.50844e39	0.383076
$395$	1.09464e40	0.619465
$396$	4.25225e39	0.231389
$397$	−1.97611e40	−1.03409	−0.517046	−	0.855958i	$-0.672968\pi$
$397$	−1.97611e40	−1.03409	−0.517046	+	0.855958i	$0.672968\pi$
$398$	−1.36933e40	−0.689161
$399$	1.59652e40	0.772850
$400$	−5.37988e39	−0.250520
$401$	−1.38849e40	−0.622022	−0.311011	−	0.950406i	$-0.600668\pi$
$401$	−1.38849e40	−0.622022	−0.311011	+	0.950406i	$0.600668\pi$
$402$	−1.03366e40	−0.445527
$403$	1.53805e40	0.637886
$404$	−8.45155e39	−0.337307
$405$	1.86746e39	0.0717296
$406$	3.52338e39	0.130258
$407$	6.17958e38	0.0219910
$408$	1.82907e40	0.626610
$409$	−1.19387e40	−0.393774	−0.196887	−	0.980426i	$-0.563083\pi$
$409$	−1.19387e40	−0.393774	−0.196887	+	0.980426i	$0.563083\pi$
$410$	−9.47890e38	−0.0301029
$411$	1.85843e38	0.00568327
$412$	1.51777e40	0.446991
$413$	−5.85918e40	−1.66192
$414$	−5.02311e39	−0.137236
$415$	−3.69419e40	−0.972241
$416$	1.37900e40	0.349637
$417$	−2.83542e40	−0.692642
$418$	2.56565e40	0.603901
$419$	−5.60824e40	−1.27206	−0.636032	−	0.771662i	$-0.719426\pi$
$419$	−5.60824e40	−1.27206	−0.636032	+	0.771662i	$0.719426\pi$
$420$	1.18509e40	0.259052
$421$	4.20899e40	0.886759	0.443379	−	0.896334i	$-0.353779\pi$
$421$	4.20899e40	0.886759	0.443379	+	0.896334i	$0.353779\pi$
$422$	1.26847e40	0.257596
$423$	2.68893e40	0.526386
$424$	3.15683e40	0.595772
$425$	4.28832e40	0.780295
$426$	1.11287e40	0.195253
$427$	−1.36769e40	−0.231395
$428$	2.09969e39	0.0342592
$429$	−1.11285e40	−0.175125
$430$	8.80588e39	0.133663
$431$	4.29537e40	0.628931	0.314466	−	0.949269i	$-0.398175\pi$
$431$	4.29537e40	0.628931	0.314466	+	0.949269i	$0.398175\pi$
$432$	5.85206e39	0.0826629
$433$	1.09938e40	0.149825	0.0749127	−	0.997190i	$-0.476132\pi$
$433$	1.09938e40	0.149825	0.0749127	+	0.997190i	$0.476132\pi$
$434$	−5.50119e40	−0.723379
$435$	−9.70080e39	−0.123090
$436$	4.73943e39	0.0580344
$437$	1.18235e41	1.39728
$438$	−3.21098e40	−0.366259
$439$	−1.20983e41	−1.33207	−0.666033	−	0.745922i	$-0.732009\pi$
$439$	−1.20983e41	−1.33207	−0.666033	+	0.745922i	$0.732009\pi$
$440$	4.29711e40	0.456731
$441$	−7.71606e39	−0.0791767
$442$	−2.12151e40	−0.210184
$443$	1.23606e41	1.18245	0.591225	−	0.806507i	$-0.298644\pi$
$443$	1.23606e41	1.18245	0.591225	+	0.806507i	$0.298644\pi$
$444$	1.25443e39	0.0115880
$445$	−1.35039e41	−1.20470
$446$	5.47758e39	0.0471952
$447$	−9.09438e40	−0.756844
$448$	−2.66638e39	−0.0214344
$449$	−1.71928e40	−0.133514	−0.0667571	−	0.997769i	$-0.521265\pi$
$449$	−1.71928e40	−0.133514	−0.0667571	+	0.997769i	$0.521265\pi$
$450$	−1.17051e40	−0.0878173
$451$	1.24200e40	0.0900299
$452$	−2.25658e41	−1.58054
$453$	−5.72745e40	−0.387649
$454$	−5.77064e40	−0.377449
$455$	−3.10147e40	−0.196061
$456$	1.17514e41	0.718014
$457$	1.45034e41	0.856580	0.428290	−	0.903641i	$-0.359116\pi$
$457$	1.45034e41	0.856580	0.428290	+	0.903641i	$0.359116\pi$
$458$	−4.72372e40	−0.269693
$459$	−4.66470e40	−0.257470
$460$	8.77647e40	0.468353
$461$	3.35312e41	1.73015	0.865076	−	0.501641i	$-0.167270\pi$
$461$	3.35312e41	1.73015	0.865076	+	0.501641i	$0.167270\pi$
$462$	3.98036e40	0.198597
$463$	−5.88828e40	−0.284108	−0.142054	−	0.989859i	$-0.545371\pi$
$463$	−5.88828e40	−0.284108	−0.142054	+	0.989859i	$0.545371\pi$
$464$	−3.03994e40	−0.141852
$465$	1.51462e41	0.683572
$466$	9.68002e40	0.422566
$467$	−2.49301e40	−0.105272	−0.0526358	−	0.998614i	$-0.516762\pi$
$467$	−2.49301e40	−0.105272	−0.0526358	+	0.998614i	$0.516762\pi$
$468$	−2.25904e40	−0.0922811
$469$	3.77463e41	1.49175
$470$	1.20430e41	0.460487
$471$	−1.33253e41	−0.493009
$472$	−4.31270e41	−1.54400
$473$	−1.15382e41	−0.399751
$474$	7.46329e40	0.250245
$475$	2.75515e41	0.894118
$476$	−2.96021e41	−0.929854
$477$	−8.05090e40	−0.244799
$478$	1.65615e41	0.487491
$479$	−5.31387e41	−1.51430	−0.757148	−	0.653244i	$-0.773408\pi$
$479$	−5.31387e41	−1.51430	−0.757148	+	0.653244i	$0.773408\pi$
$480$	1.35799e41	0.374678
$481$	−3.28295e39	−0.00877031
$482$	−1.05492e41	−0.272891
$483$	1.83429e41	0.459503
$484$	7.85549e40	0.190577
$485$	1.27739e41	0.300143
$486$	1.27324e40	0.0289766
$487$	−8.56525e41	−1.88817	−0.944086	−	0.329701i	$-0.893052\pi$
$487$	−8.56525e41	−1.88817	−0.944086	+	0.329701i	$0.893052\pi$
$488$	−1.00670e41	−0.214977
$489$	2.55372e41	0.528307
$490$	−3.45581e40	−0.0692645
$491$	1.41318e41	0.274432	0.137216	−	0.990541i	$-0.456185\pi$
$491$	1.41318e41	0.274432	0.137216	+	0.990541i	$0.456185\pi$
$492$	2.52121e40	0.0474406
$493$	2.42315e41	0.441827
$494$	−1.36302e41	−0.240843
$495$	−1.09590e41	−0.187668
$496$	4.74638e41	0.787764
$497$	−4.06389e41	−0.653760
$498$	−2.51871e41	−0.392756
$499$	−7.12950e41	−1.07771	−0.538854	−	0.842399i	$-0.681142\pi$
$499$	−7.12950e41	−1.07771	−0.538854	+	0.842399i	$0.681142\pi$
$500$	5.55161e41	0.813549
$501$	−1.96415e40	−0.0279055
$502$	4.26667e41	0.587735
$503$	6.23756e41	0.833127	0.416563	−	0.909107i	$-0.363234\pi$
$503$	6.23756e41	0.833127	0.416563	+	0.909107i	$0.363234\pi$
$504$	1.82311e41	0.236123
$505$	2.17815e41	0.273572
$506$	2.94776e41	0.359053
$507$	−4.29602e41	−0.507508
$508$	−3.70968e41	−0.425058
$509$	6.57401e41	0.730642	0.365321	−	0.930882i	$-0.380959\pi$
$509$	6.57401e41	0.730642	0.365321	+	0.930882i	$0.380959\pi$
$510$	−2.08919e41	−0.225237
$511$	1.17256e42	1.22634
$512$	7.68974e41	0.780238
$513$	−2.99696e41	−0.295028
$514$	2.01223e40	0.0192198
$515$	−3.91162e41	−0.362531
$516$	−2.34220e41	−0.210646
$517$	−1.57797e42	−1.37720
$518$	1.17422e40	0.00994576
$519$	−3.57418e41	−0.293821
$520$	−2.28287e41	−0.182150
$521$	1.43485e42	1.11128	0.555640	−	0.831423i	$-0.312473\pi$
$521$	1.43485e42	1.11128	0.555640	+	0.831423i	$0.312473\pi$
$522$	−6.61403e40	−0.0497249
$523$	−6.04761e41	−0.441375	−0.220687	−	0.975345i	$-0.570830\pi$
$523$	−6.04761e41	−0.441375	−0.220687	+	0.975345i	$0.570830\pi$
$524$	−5.80798e40	−0.0411519
$525$	4.27435e41	0.294036
$526$	7.97440e41	0.532622
$527$	−3.78336e42	−2.45365
$528$	−3.43422e41	−0.216273
$529$	−2.76737e41	−0.169241
$530$	−3.60578e41	−0.214152
$531$	1.09987e42	0.634422
$532$	−1.90187e42	−1.06549
$533$	−6.59823e40	−0.0359051
$534$	−9.20702e41	−0.486665
$535$	−5.41138e40	−0.0277859
$536$	2.77835e42	1.38590
$537$	5.21594e41	0.252773
$538$	8.46653e41	0.398639
$539$	4.52809e41	0.207152
$540$	−2.22463e41	−0.0988903
$541$	3.68602e42	1.59221	0.796104	−	0.605160i	$-0.206891\pi$
$541$	3.68602e42	1.59221	0.796104	+	0.605160i	$0.206891\pi$
$542$	−1.05852e42	−0.444334
$543$	1.58517e42	0.646664
$544$	−3.39210e42	−1.34489
$545$	−1.22146e41	−0.0470687
$546$	−2.11459e41	−0.0792029
$547$	4.18759e42	1.52462	0.762308	−	0.647214i	$-0.224066\pi$
$547$	4.18759e42	1.52462	0.762308	+	0.647214i	$0.224066\pi$
$548$	−2.21387e40	−0.00783526
$549$	2.56740e41	0.0883327
$550$	6.86899e41	0.229758
$551$	1.55682e42	0.506277
$552$	1.35015e42	0.426900
$553$	−2.72538e42	−0.837890
$554$	−1.54786e42	−0.462733
$555$	−3.23294e40	−0.00939845
$556$	3.37772e42	0.954913
$557$	−6.56584e42	−1.80524	−0.902620	−	0.430438i	$-0.858359\pi$
$557$	−6.56584e42	−1.80524	−0.902620	+	0.430438i	$0.858359\pi$
$558$	1.03267e42	0.276143
$559$	6.12974e41	0.159426
$560$	−9.57104e41	−0.242128
$561$	2.73743e42	0.673625
$562$	−3.61001e42	−0.864163
$563$	−1.48105e42	−0.344898	−0.172449	−	0.985018i	$-0.555168\pi$
$563$	−1.48105e42	−0.344898	−0.172449	+	0.985018i	$0.555168\pi$
$564$	−3.20321e42	−0.725705
$565$	5.81571e42	1.28189
$566$	−3.77335e41	−0.0809230
$567$	−4.64950e41	−0.0970217
$568$	−2.99127e42	−0.607373
$569$	−2.38083e42	−0.470423	−0.235211	−	0.971944i	$-0.575578\pi$
$569$	−2.38083e42	−0.470423	−0.235211	+	0.971944i	$0.575578\pi$
$570$	−1.34226e42	−0.258093
$571$	−6.63013e42	−1.24069	−0.620344	−	0.784330i	$-0.713007\pi$
$571$	−6.63013e42	−1.24069	−0.620344	+	0.784330i	$0.713007\pi$
$572$	1.32569e42	0.241437
$573$	−3.54433e42	−0.628257
$574$	2.36001e41	0.0407173
$575$	3.16548e42	0.531604
$576$	5.00528e40	0.00818238
$577$	2.51858e42	0.400803	0.200402	−	0.979714i	$-0.435775\pi$
$577$	2.51858e42	0.400803	0.200402	+	0.979714i	$0.435775\pi$
$578$	2.30292e42	0.356777
$579$	−1.37971e42	−0.208099
$580$	1.15562e42	0.169699
$581$	9.19759e42	1.31506
$582$	8.70930e41	0.121249
$583$	4.72459e42	0.640473
$584$	8.63071e42	1.13932
$585$	5.82204e41	0.0748443
$586$	2.32581e42	0.291179
$587$	2.11545e38	2.57936e−5 0	1.28968e−5	−	1.00000i	$-0.499996\pi$
$587$	2.11545e38	2.57936e−5 0	1.28968e−5		1.00000i	$0.499996\pi$
$588$	9.19182e41	0.109157
$589$	−2.43072e43	−2.81157
$590$	4.92603e42	0.554998
$591$	4.46149e42	0.489636
$592$	−1.01311e41	−0.0108310
$593$	−1.24398e43	−1.29559	−0.647794	−	0.761816i	$-0.724308\pi$
$593$	−1.24398e43	−1.29559	−0.647794	+	0.761816i	$0.724308\pi$
$594$	−7.47187e41	−0.0758122
$595$	7.62911e42	0.754156
$596$	1.08338e43	1.04343
$597$	−9.38666e42	−0.880864
$598$	−1.56602e42	−0.143195
$599$	7.23451e42	0.644605	0.322302	−	0.946637i	$-0.395543\pi$
$599$	7.23451e42	0.644605	0.322302	+	0.946637i	$0.395543\pi$
$600$	3.14618e42	0.273174
$601$	1.57661e43	1.33404	0.667022	−	0.745038i	$-0.267569\pi$
$601$	1.57661e43	1.33404	0.667022	+	0.745038i	$0.267569\pi$
$602$	−2.19244e42	−0.180793
$603$	−7.08567e42	−0.569459
$604$	6.82286e42	0.534434
$605$	−2.02453e42	−0.154567
$606$	1.48507e42	0.110515
$607$	−2.24806e43	−1.63073	−0.815367	−	0.578945i	$-0.803465\pi$
$607$	−2.24806e43	−1.63073	−0.815367	+	0.578945i	$0.803465\pi$
$608$	−2.17935e43	−1.54107
$609$	2.41525e42	0.166492
$610$	1.14987e42	0.0772742
$611$	8.38308e42	0.549244
$612$	5.55686e42	0.354962
$613$	−5.88645e42	−0.366620	−0.183310	−	0.983055i	$-0.558681\pi$
$613$	−5.88645e42	−0.366620	−0.183310	+	0.983055i	$0.558681\pi$
$614$	−2.11845e42	−0.128650
$615$	−6.49772e41	−0.0384766
$616$	−1.06987e43	−0.617775
$617$	−2.16755e43	−1.22053	−0.610264	−	0.792198i	$-0.708937\pi$
$617$	−2.16755e43	−1.22053	−0.610264	+	0.792198i	$0.708937\pi$
$618$	−2.66695e42	−0.146452
$619$	1.57517e43	0.843571	0.421786	−	0.906696i	$-0.361403\pi$
$619$	1.57517e43	0.843571	0.421786	+	0.906696i	$0.361403\pi$
$620$	−1.80431e43	−0.942409
$621$	−3.44331e42	−0.175411
$622$	1.01140e43	0.502541
$623$	3.36214e43	1.62949
$624$	1.82445e42	0.0862523
$625$	−1.66062e42	−0.0765826
$626$	−1.11789e43	−0.502917
$627$	1.75874e43	0.771887
$628$	1.58739e43	0.679688
$629$	8.07550e41	0.0337353
$630$	−2.08238e42	−0.0848754
$631$	3.31927e43	1.32004	0.660021	−	0.751248i	$-0.270548\pi$
$631$	3.31927e43	1.32004	0.660021	+	0.751248i	$0.270548\pi$
$632$	−2.00604e43	−0.778439
$633$	8.69530e42	0.329251
$634$	8.25337e42	0.304963
$635$	9.56065e42	0.344742
$636$	9.59070e42	0.337493
$637$	−2.40558e42	−0.0826149
$638$	3.88137e42	0.130096
$639$	7.62867e42	0.249566
$640$	−2.00998e43	−0.641803
$641$	−1.08239e43	−0.337352	−0.168676	−	0.985672i	$-0.553949\pi$
$641$	−1.08239e43	−0.337352	−0.168676	+	0.985672i	$0.553949\pi$
$642$	−3.68949e41	−0.0112247
$643$	−8.97741e42	−0.266613	−0.133306	−	0.991075i	$-0.542559\pi$
$643$	−8.97741e42	−0.266613	−0.133306	+	0.991075i	$0.542559\pi$
$644$	−2.18512e43	−0.633496
$645$	6.03637e42	0.170844
$646$	3.35280e43	0.926412
$647$	5.58409e40	0.00150638	0.000753192	−	1.00000i	$-0.499760\pi$
$647$	5.58409e40	0.00150638	0.000753192		1.00000i	$0.499760\pi$
$648$	−3.42231e42	−0.0901377
$649$	−6.45450e43	−1.65985
$650$	−3.64920e42	−0.0916306
$651$	−3.77103e43	−0.924601
$652$	−3.04214e43	−0.728353
$653$	6.57643e43	1.53757	0.768787	−	0.639505i	$-0.220861\pi$
$653$	6.57643e43	1.53757	0.768787	+	0.639505i	$0.220861\pi$
$654$	−8.32792e41	−0.0190143
$655$	1.49684e42	0.0333762
$656$	−2.03619e42	−0.0443413
$657$	−2.20110e43	−0.468141
$658$	−2.99840e43	−0.622857
$659$	−1.78454e43	−0.362079	−0.181039	−	0.983476i	$-0.557946\pi$
$659$	−1.78454e43	−0.362079	−0.181039	+	0.983476i	$0.557946\pi$
$660$	1.30550e43	0.258729
$661$	−5.28302e43	−1.02273	−0.511363	−	0.859365i	$-0.670859\pi$
$661$	−5.28302e43	−1.02273	−0.511363	+	0.859365i	$0.670859\pi$
$662$	2.23195e43	0.422072
$663$	−1.45428e43	−0.268650
$664$	6.76998e43	1.22175
$665$	4.90154e43	0.864165
$666$	−2.20423e41	−0.00379669
$667$	1.78868e43	0.301010
$668$	2.33981e42	0.0384721
$669$	3.75484e42	0.0603235
$670$	−3.17348e43	−0.498168
$671$	−1.50665e43	−0.231107
$672$	−3.38105e43	−0.506790
$673$	1.13410e44	1.66118	0.830589	−	0.556885i	$-0.188004\pi$
$673$	1.13410e44	1.66118	0.830589	+	0.556885i	$0.188004\pi$
$674$	−3.26856e43	−0.467873
$675$	−8.02374e42	−0.112245
$676$	5.11767e43	0.699678
$677$	6.88221e43	0.919610	0.459805	−	0.888020i	$-0.347919\pi$
$677$	6.88221e43	0.919610	0.459805	+	0.888020i	$0.347919\pi$
$678$	3.96517e43	0.517847
$679$	−3.18038e43	−0.405974
$680$	5.61548e43	0.700646
$681$	−3.95573e43	−0.482444
$682$	−6.06014e43	−0.722478
$683$	−3.40632e43	−0.396976	−0.198488	−	0.980103i	$-0.563603\pi$
$683$	−3.40632e43	−0.396976	−0.198488	+	0.980103i	$0.563603\pi$
$684$	3.57016e43	0.406741
$685$	5.70563e41	0.00635477
$686$	4.48272e43	0.488110
$687$	−3.23807e43	−0.344713
$688$	1.89161e43	0.196885
$689$	−2.50997e43	−0.255429
$690$	−1.54216e43	−0.153451
$691$	−1.10287e44	−1.07304	−0.536519	−	0.843888i	$-0.680261\pi$
$691$	−1.10287e44	−1.07304	−0.536519	+	0.843888i	$0.680261\pi$
$692$	4.25777e43	0.405077
$693$	2.72851e43	0.253840
$694$	4.40718e42	0.0400949
$695$	−8.70512e43	−0.774480
$696$	1.77777e43	0.154679
$697$	1.62305e43	0.138110
$698$	−4.05281e43	−0.337285
$699$	6.63558e43	0.540111
$700$	−5.09185e43	−0.405374
$701$	−1.65580e44	−1.28937	−0.644686	−	0.764447i	$-0.723012\pi$
$701$	−1.65580e44	−1.28937	−0.644686	+	0.764447i	$0.723012\pi$
$702$	3.96948e42	0.0302349
$703$	5.18833e42	0.0386563
$704$	−2.93729e42	−0.0214077
$705$	8.25539e43	0.588581
$706$	−5.22661e43	−0.364541
$707$	−5.42304e43	−0.370034
$708$	−1.31023e44	−0.874648
$709$	1.12924e44	0.737516	0.368758	−	0.929525i	$-0.379783\pi$
$709$	1.12924e44	0.737516	0.368758	+	0.929525i	$0.379783\pi$
$710$	3.41667e43	0.218323
$711$	5.11603e43	0.319856
$712$	2.47473e44	1.51387
$713$	−2.79273e44	−1.67164
$714$	5.20155e43	0.304656
$715$	−3.41660e43	−0.195817
$716$	−6.21353e43	−0.348487
$717$	1.13528e44	0.623096
$718$	−2.18598e43	−0.117413
$719$	2.26669e44	1.19150	0.595750	−	0.803170i	$-0.296855\pi$
$719$	2.26669e44	1.19150	0.595750	+	0.803170i	$0.296855\pi$
$720$	1.79666e43	0.0924298
$721$	9.73894e43	0.490360
$722$	1.23751e44	0.609847
$723$	−7.23139e43	−0.348802
$724$	−1.88835e44	−0.891526
$725$	4.16805e43	0.192617
$726$	−1.38033e43	−0.0624404
$727$	1.21876e44	0.539678	0.269839	−	0.962905i	$-0.413030\pi$
$727$	1.21876e44	0.539678	0.269839	+	0.962905i	$0.413030\pi$
$728$	5.68376e43	0.246377
$729$	8.72796e42	0.0370370
$730$	−9.85813e43	−0.409534
$731$	−1.50781e44	−0.613237
$732$	−3.05843e43	−0.121780
$733$	4.47746e44	1.74550	0.872750	−	0.488168i	$-0.162335\pi$
$733$	4.47746e44	1.74550	0.872750	+	0.488168i	$0.162335\pi$
$734$	3.49089e42	0.0133244
$735$	−2.36893e43	−0.0885318
$736$	−2.50392e44	−0.916252
$737$	4.15815e44	1.48989
$738$	−4.43016e42	−0.0155434
$739$	−3.11363e43	−0.106974	−0.0534871	−	0.998569i	$-0.517034\pi$
$739$	−3.11363e43	−0.106974	−0.0534871	+	0.998569i	$0.517034\pi$
$740$	3.85126e42	0.0129572
$741$	−9.34341e43	−0.307839
$742$	8.97747e43	0.289663
$743$	−9.87276e43	−0.311969	−0.155985	−	0.987759i	$-0.549855\pi$
$743$	−9.87276e43	−0.311969	−0.155985	+	0.987759i	$0.549855\pi$
$744$	−2.77570e44	−0.858998
$745$	−2.79210e44	−0.846269
$746$	−2.30554e44	−0.684417
$747$	−1.72656e44	−0.502009
$748$	−3.26098e44	−0.928696
$749$	1.34729e43	0.0375833
$750$	−9.75503e43	−0.266550
$751$	−4.84816e44	−1.29765	−0.648825	−	0.760938i	$-0.724739\pi$
$751$	−4.84816e44	−1.29765	−0.648825	+	0.760938i	$0.724739\pi$
$752$	2.58699e44	0.678294
$753$	2.92477e44	0.751225
$754$	−2.06201e43	−0.0518841
$755$	−1.75840e44	−0.433451
$756$	5.53875e43	0.133759
$757$	−1.03752e44	−0.245477	−0.122739	−	0.992439i	$-0.539168\pi$
$757$	−1.03752e44	−0.245477	−0.122739	+	0.992439i	$0.539168\pi$
$758$	1.50867e44	0.349720
$759$	2.02067e44	0.458931
$760$	3.60782e44	0.802850
$761$	2.07194e44	0.451768	0.225884	−	0.974154i	$-0.427473\pi$
$761$	2.07194e44	0.451768	0.225884	+	0.974154i	$0.427473\pi$
$762$	6.51848e43	0.139266
$763$	3.04111e43	0.0636652
$764$	4.22221e44	0.866149
$765$	−1.43212e44	−0.287891
$766$	3.65423e43	0.0719864
$767$	3.42900e44	0.661971
$768$	−1.44532e44	−0.273442
$769$	7.00403e44	1.29864	0.649321	−	0.760514i	$-0.275053\pi$
$769$	7.00403e44	1.29864	0.649321	+	0.760514i	$0.275053\pi$
$770$	1.22202e44	0.222062
$771$	1.37937e43	0.0245662
$772$	1.64359e44	0.286896
$773$	−3.48386e44	−0.596044	−0.298022	−	0.954559i	$-0.596327\pi$
$773$	−3.48386e44	−0.596044	−0.298022	+	0.954559i	$0.596327\pi$
$774$	4.11561e43	0.0690159
$775$	−6.50774e44	−1.06968
$776$	−2.34095e44	−0.377169
$777$	8.04919e42	0.0127124
$778$	1.64202e44	0.254211
$779$	1.04278e44	0.158256
$780$	−6.93555e43	−0.103184
$781$	−4.47680e44	−0.652945
$782$	3.85214e44	0.550804
$783$	−4.53387e43	−0.0635568
$784$	−7.42352e43	−0.102026
$785$	−4.09106e44	−0.551259
$786$	1.02055e43	0.0134830
$787$	1.26285e45	1.63585	0.817926	−	0.575323i	$-0.195124\pi$
$787$	1.26285e45	1.63585	0.817926	+	0.575323i	$0.195124\pi$
$788$	−5.31478e44	−0.675039
$789$	5.46639e44	0.680781
$790$	2.29133e44	0.279813
$791$	−1.44796e45	−1.73389
$792$	2.00834e44	0.235829
$793$	8.00418e43	0.0921684
$794$	−4.13645e44	−0.467100
$795$	−2.47173e44	−0.273723
$796$	1.11819e45	1.21441
$797$	−1.39768e45	−1.48869	−0.744346	−	0.667794i	$-0.767239\pi$
$797$	−1.39768e45	−1.48869	−0.744346	+	0.667794i	$0.767239\pi$
$798$	3.34188e44	0.349097
$799$	−2.06210e45	−2.11268
$800$	−5.83475e44	−0.586311
$801$	−6.31135e44	−0.622040
$802$	−2.90643e44	−0.280968
$803$	1.29169e45	1.22481
$804$	8.44086e44	0.785087
$805$	5.63153e44	0.513795
$806$	3.21949e44	0.288134
$807$	5.80375e44	0.509529
$808$	−3.99168e44	−0.343779
$809$	6.93401e44	0.585844	0.292922	−	0.956136i	$-0.405372\pi$
$809$	6.93401e44	0.585844	0.292922	+	0.956136i	$0.405372\pi$
$810$	3.90901e43	0.0324003
$811$	8.57913e44	0.697622	0.348811	−	0.937193i	$-0.386586\pi$
$811$	8.57913e44	0.697622	0.348811	+	0.937193i	$0.386586\pi$
$812$	−2.87719e44	−0.229535
$813$	−7.25607e44	−0.567934
$814$	1.29353e43	0.00993338
$815$	7.84027e44	0.590729
$816$	−4.48784e44	−0.331772
$817$	−9.68737e44	−0.702690
$818$	−2.49904e44	−0.177868
$819$	−1.44954e44	−0.101235
$820$	7.74046e43	0.0530459
$821$	1.31358e45	0.883358	0.441679	−	0.897173i	$-0.354383\pi$
$821$	1.31358e45	0.883358	0.441679	+	0.897173i	$0.354383\pi$
$822$	3.89011e42	0.00256714
$823$	2.06901e45	1.33988	0.669940	−	0.742415i	$-0.266320\pi$
$823$	2.06901e45	1.33988	0.669940	+	0.742415i	$0.266320\pi$
$824$	7.16844e44	0.455568
$825$	4.70864e44	0.293670
$826$	−1.22646e45	−0.750692
$827$	1.35815e45	0.815853	0.407926	−	0.913015i	$-0.366252\pi$
$827$	1.35815e45	0.815853	0.407926	+	0.913015i	$0.366252\pi$
$828$	4.10186e44	0.241830
$829$	−2.28248e44	−0.132072	−0.0660361	−	0.997817i	$-0.521035\pi$
$829$	−2.28248e44	−0.132072	−0.0660361	+	0.997817i	$0.521035\pi$
$830$	−7.73277e44	−0.439162
$831$	−1.06105e45	−0.591451
$832$	1.56046e43	0.00853768
$833$	5.91732e44	0.317781
$834$	−5.93517e44	−0.312867
$835$	−6.03021e43	−0.0312027
$836$	−2.09511e45	−1.06417
$837$	7.07891e44	0.352957
$838$	−1.17393e45	−0.574593
$839$	2.94578e45	1.41543	0.707717	−	0.706496i	$-0.249725\pi$
$839$	2.94578e45	1.41543	0.707717	+	0.706496i	$0.249725\pi$
$840$	5.59719e44	0.264022
$841$	−1.92391e45	−0.890934
$842$	8.81036e44	0.400550
$843$	−2.47464e45	−1.10455
$844$	−1.03583e45	−0.453923
$845$	−1.31894e45	−0.567472
$846$	5.62854e44	0.237769
$847$	5.04057e44	0.209068
$848$	−7.74567e44	−0.315445
$849$	−2.58660e44	−0.103433
$850$	8.97642e44	0.352460
$851$	5.96103e43	0.0229834
$852$	−9.08771e44	−0.344065
$853$	−7.40047e44	−0.275137	−0.137569	−	0.990492i	$-0.543929\pi$
$853$	−7.40047e44	−0.275137	−0.137569	+	0.990492i	$0.543929\pi$
$854$	−2.86287e44	−0.104521
$855$	−9.20108e44	−0.329886
$856$	9.91689e43	0.0349166
$857$	−2.79291e45	−0.965726	−0.482863	−	0.875696i	$-0.660403\pi$
$857$	−2.79291e45	−0.965726	−0.482863	+	0.875696i	$0.660403\pi$
$858$	−2.32945e44	−0.0791042
$859$	1.54735e45	0.516054	0.258027	−	0.966138i	$-0.416928\pi$
$859$	1.54735e45	0.516054	0.258027	+	0.966138i	$0.416928\pi$
$860$	−7.19087e44	−0.235535
$861$	1.61777e44	0.0520436
$862$	8.99118e44	0.284089
$863$	6.13273e45	1.90321	0.951605	−	0.307323i	$-0.0994332\pi$
$863$	6.13273e45	1.90321	0.951605	+	0.307323i	$0.0994332\pi$
$864$	6.34686e44	0.193462
$865$	−1.09732e45	−0.328537
$866$	2.30125e44	0.0676763
$867$	1.57864e45	0.456022
$868$	4.49227e45	1.27471
$869$	−3.00229e45	−0.836846
$870$	−2.03060e44	−0.0556000
$871$	−2.20905e45	−0.594187
$872$	2.23844e44	0.0591480
$873$	5.97016e44	0.154976
$874$	2.47491e45	0.631150
$875$	3.56225e45	0.892483
$876$	2.62208e45	0.645405
$877$	7.87430e44	0.190422	0.0952112	−	0.995457i	$-0.469647\pi$
$877$	7.87430e44	0.190422	0.0952112	+	0.995457i	$0.469647\pi$
$878$	−2.53245e45	−0.601695
$879$	1.59432e45	0.372177
$880$	−1.05435e45	−0.241826
$881$	−1.72113e45	−0.387870	−0.193935	−	0.981014i	$-0.562125\pi$
$881$	−1.72113e45	−0.387870	−0.193935	+	0.981014i	$0.562125\pi$
$882$	−1.61515e44	−0.0357642
$883$	−2.08592e45	−0.453844	−0.226922	−	0.973913i	$-0.572866\pi$
$883$	−2.08592e45	−0.453844	−0.226922	+	0.973913i	$0.572866\pi$
$884$	1.73242e45	0.370376
$885$	3.37676e45	0.709381
$886$	2.58736e45	0.534114
$887$	−5.27733e45	−1.07053	−0.535265	−	0.844684i	$-0.679788\pi$
$887$	−5.27733e45	−1.07053	−0.535265	+	0.844684i	$0.679788\pi$
$888$	5.92469e43	0.0118104
$889$	−2.38036e45	−0.466300
$890$	−2.82668e45	−0.544166
$891$	−5.12191e44	−0.0969009
$892$	−4.47298e44	−0.0831653
$893$	−1.32485e46	−2.42086
$894$	−1.90366e45	−0.341867
$895$	1.60136e45	0.282640
$896$	5.00433e45	0.868104
$897$	−1.07349e45	−0.183027
$898$	−3.59883e44	−0.0603084
$899$	−3.67725e45	−0.605686
$900$	9.55834e44	0.154748
$901$	6.17410e45	0.982516
$902$	2.59979e44	0.0406666
$903$	−1.50290e45	−0.231084
$904$	−1.06579e46	−1.61087
$905$	4.86669e45	0.723070
$906$	−1.19888e45	−0.175101
$907$	−3.17856e45	−0.456371	−0.228185	−	0.973618i	$-0.573279\pi$
$907$	−3.17856e45	−0.456371	−0.228185	+	0.973618i	$0.573279\pi$
$908$	4.71230e45	0.665123
$909$	1.01800e45	0.141257
$910$	−6.49208e44	−0.0885610
$911$	6.98227e45	0.936400	0.468200	−	0.883622i	$-0.344903\pi$
$911$	6.98227e45	0.936400	0.468200	+	0.883622i	$0.344903\pi$
$912$	−2.88334e45	−0.380168
$913$	1.01321e46	1.31342
$914$	3.03588e45	0.386918
$915$	7.88225e44	0.0987696
$916$	3.85738e45	0.475240
$917$	−3.72676e44	−0.0451447
$918$	−9.76426e44	−0.116299
$919$	−9.49719e45	−1.11226	−0.556128	−	0.831097i	$-0.687714\pi$
$919$	−9.49719e45	−1.11226	−0.556128	+	0.831097i	$0.687714\pi$
$920$	4.14514e45	0.477340
$921$	−1.45218e45	−0.164436
$922$	7.01883e45	0.781511
$923$	2.37833e45	0.260403
$924$	−3.25036e45	−0.349958
$925$	1.38907e44	0.0147071
$926$	−1.23255e45	−0.128332
$927$	−1.82818e45	−0.187190
$928$	−3.29697e45	−0.331987
$929$	−1.87466e45	−0.185643	−0.0928214	−	0.995683i	$-0.529589\pi$
$929$	−1.87466e45	−0.185643	−0.0928214	+	0.995683i	$0.529589\pi$
$930$	3.17045e45	0.308770
$931$	3.80175e45	0.364136
$932$	−7.90469e45	−0.744626
$933$	6.93307e45	0.642332
$934$	−5.21842e44	−0.0475513
$935$	8.40427e45	0.753216
$936$	−1.06695e45	−0.0940518
$937$	−1.18309e44	−0.0102578	−0.00512888	−	0.999987i	$-0.501633\pi$
$937$	−1.18309e44	−0.0102578	−0.00512888	+	0.999987i	$0.501633\pi$
$938$	7.90115e45	0.673823
$939$	−7.66304e45	−0.642813
$940$	−9.83429e45	−0.811449
$941$	1.34234e46	1.08949	0.544744	−	0.838602i	$-0.316627\pi$
$941$	1.34234e46	1.08949	0.544744	+	0.838602i	$0.316627\pi$
$942$	−2.78929e45	−0.222692
$943$	1.19808e45	0.0940923
$944$	1.05818e46	0.817507
$945$	−1.42746e45	−0.108485
$946$	−2.41520e45	−0.180568
$947$	−1.18925e46	−0.874676	−0.437338	−	0.899297i	$-0.644079\pi$
$947$	−1.18925e46	−0.874676	−0.437338	+	0.899297i	$0.644079\pi$
$948$	−6.09451e45	−0.440971
$949$	−6.86221e45	−0.488470
$950$	5.76715e45	0.403874
$951$	5.65763e45	0.389795
$952$	−1.39811e46	−0.947696
$953$	−2.01182e46	−1.34168	−0.670841	−	0.741601i	$-0.734067\pi$
$953$	−2.01182e46	−1.34168	−0.670841	+	0.741601i	$0.734067\pi$
$954$	−1.68523e45	−0.110576
$955$	−1.08816e46	−0.702488
$956$	−1.35241e46	−0.859034
$957$	2.66065e45	0.166285
$958$	−1.11231e46	−0.684009
$959$	−1.42056e44	−0.00859548
$960$	1.53669e44	0.00914916
$961$	4.03451e46	2.36363
$962$	−6.87194e43	−0.00396156
$963$	−2.52912e44	−0.0143470
$964$	8.61445e45	0.480877
$965$	−4.23589e45	−0.232687
$966$	3.83959e45	0.207558
$967$	−2.20337e46	−1.17214	−0.586068	−	0.810262i	$-0.699325\pi$
$967$	−2.20337e46	−1.17214	−0.586068	+	0.810262i	$0.699325\pi$
$968$	3.71016e45	0.194234
$969$	2.29832e46	1.18411
$970$	2.67387e45	0.135575
$971$	2.07400e46	1.03493	0.517463	−	0.855705i	$-0.326876\pi$
$971$	2.07400e46	1.03493	0.517463	+	0.855705i	$0.326876\pi$
$972$	−1.03973e45	−0.0510613
$973$	2.16735e46	1.04756
$974$	−1.79290e46	−0.852888
$975$	−2.50150e45	−0.117119
$976$	2.47006e45	0.113824
$977$	−2.59772e46	−1.17822	−0.589110	−	0.808053i	$-0.700521\pi$
$977$	−2.59772e46	−1.17822	−0.589110	+	0.808053i	$0.700521\pi$
$978$	5.34552e45	0.238637
$979$	3.70375e46	1.62746
$980$	2.82201e45	0.122055
$981$	−5.70873e44	−0.0243036
$982$	2.95811e45	0.123961
$983$	−2.17544e46	−0.897361	−0.448680	−	0.893692i	$-0.648106\pi$
$983$	−2.17544e46	−0.897361	−0.448680	+	0.893692i	$0.648106\pi$
$984$	1.19077e45	0.0483509
$985$	1.36974e46	0.547489
$986$	5.07219e45	0.199574
$987$	−2.05538e46	−0.796116
$988$	1.11304e46	0.424403
$989$	−1.11301e46	−0.417789
$990$	−2.29396e45	−0.0847697
$991$	1.88235e45	0.0684792	0.0342396	−	0.999414i	$-0.489099\pi$
$991$	1.88235e45	0.0684792	0.0342396	+	0.999414i	$0.489099\pi$
$992$	5.14769e46	1.84366
$993$	1.52999e46	0.539479
$994$	−8.50664e45	−0.295304
$995$	−2.88183e46	−0.984942
$996$	2.05677e46	0.692097
$997$	−4.41026e46	−1.46113	−0.730566	−	0.682842i	$-0.760744\pi$
$997$	−4.41026e46	−1.46113	−0.730566	+	0.682842i	$0.760744\pi$
$998$	−1.49237e46	−0.486801
$999$	−1.51098e44	−0.00485282

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.32.a.a.1.2	✓	2
3.2	odd	2		9.32.a.b.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.32.a.a.1.2	✓	2	1.1	even	1	trivial
9.32.a.b.1.1		2	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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 32 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q+20932.2 q^{2} +1.43489e7 q^{3} -1.70932e9 q^{4} +4.40531e10 q^{5} +3.00355e11 q^{6} -1.09681e13 q^{7} -8.07317e13 q^{8} +2.05891e14 q^{9} +O(q^{10})\)	\(q+20932.2 q^{2} +1.43489e7 q^{3} -1.70932e9 q^{4} +4.40531e10 q^{5} +3.00355e11 q^{6} -1.09681e13 q^{7} -8.07317e13 q^{8} +2.05891e14 q^{9} +9.22129e14 q^{10} -1.20825e16 q^{11} -2.45269e16 q^{12} +6.41891e16 q^{13} -2.29587e17 q^{14} +6.32113e17 q^{15} +1.98085e18 q^{16} -1.57894e19 q^{17} +4.30976e18 q^{18} -1.01444e20 q^{19} -7.53010e19 q^{20} -1.57380e20 q^{21} -2.52914e20 q^{22} -1.16552e21 q^{23} -1.15841e21 q^{24} -2.71594e21 q^{25} +1.34362e21 q^{26} +2.95431e21 q^{27} +1.87480e22 q^{28} -1.53466e22 q^{29} +1.32315e22 q^{30} +2.39613e23 q^{31} +2.14834e23 q^{32} -1.73371e23 q^{33} -3.30509e23 q^{34} -4.83178e23 q^{35} -3.51935e23 q^{36} -5.11449e22 q^{37} -2.12345e24 q^{38} +9.21043e23 q^{39} -3.55648e24 q^{40} -1.02794e24 q^{41} -3.29432e24 q^{42} +9.54950e24 q^{43} +2.06529e25 q^{44} +9.07013e24 q^{45} -2.43969e25 q^{46} +1.30600e26 q^{47} +2.84231e25 q^{48} -3.74764e25 q^{49} -5.68507e25 q^{50} -2.26561e26 q^{51} -1.09720e26 q^{52} -3.91027e26 q^{53} +6.18404e25 q^{54} -5.32271e26 q^{55} +8.85472e26 q^{56} -1.45561e27 q^{57} -3.21239e26 q^{58} +5.34202e27 q^{59} -1.08049e27 q^{60} +1.24697e27 q^{61} +5.01564e27 q^{62} -2.25823e27 q^{63} +2.43103e26 q^{64} +2.82773e27 q^{65} -3.62904e27 q^{66} -3.44146e28 q^{67} +2.69893e28 q^{68} -1.67239e28 q^{69} -1.01140e28 q^{70} +3.70520e28 q^{71} -1.66219e28 q^{72} -1.06906e29 q^{73} -1.07058e27 q^{74} -3.89708e28 q^{75} +1.73400e29 q^{76} +1.32522e29 q^{77} +1.92795e28 q^{78} +2.48482e29 q^{79} +8.72626e28 q^{80} +4.23912e28 q^{81} -2.15170e28 q^{82} -8.38577e29 q^{83} +2.69014e29 q^{84} -6.95574e29 q^{85} +1.99893e29 q^{86} -2.20207e29 q^{87} +9.75440e29 q^{88} -3.06538e30 q^{89} +1.89858e29 q^{90} -7.04032e29 q^{91} +1.99225e30 q^{92} +3.43818e30 q^{93} +2.73375e30 q^{94} -4.46891e30 q^{95} +3.08263e30 q^{96} +2.89967e30 q^{97} -7.84466e29 q^{98} -2.48768e30 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 39528 q^{2} + 28697814 q^{3} - 201366976 q^{4} - 7930517220 q^{5} - 567183595896 q^{6} - 10488874236176 q^{7} - 42065768434176 q^{8} + 411782264189298 q^{9}+O(q^{10}) \) 2 * q - 39528 * q^2 + 28697814 * q^3 - 201366976 * q^4 - 7930517220 * q^5 - 567183595896 * q^6 - 10488874236176 * q^7 - 42065768434176 * q^8 + 411782264189298 * q^9	\( 2 q - 39528 q^{2} + 28697814 q^{3} - 201366976 q^{4} - 7930517220 q^{5} - 567183595896 q^{6} - 10488874236176 q^{7} - 42065768434176 q^{8} + 411782264189298 q^{9} + 40\!\cdots\!40 q^{10}+ \cdots + 22\!\cdots\!92 q^{99}+O(q^{100}) \) 2 * q - 39528 * q^2 + 28697814 * q^3 - 201366976 * q^4 - 7930517220 * q^5 - 567183595896 * q^6 - 10488874236176 * q^7 - 42065768434176 * q^8 + 411782264189298 * q^9 + 4065069087861840 * q^10 + 10782060500929608 * q^11 - 2889396011495232 * q^12 - 91686777034056308 * q^13 - 258560108208609984 * q^14 - 113794254051678540 * q^15 - 3595212242257899520 * q^16 - 16595285055794710812 * q^17 - 8138464669437285672 * q^18 - 82480245798578318024 * q^19 - 153690009762588577920 * q^20 - 150503880949585459632 * q^21 - 1635310640344066149024 * q^22 - 3510229760731757537712 * q^23 - 603597799145527045632 * q^24 - 4670262053173672152850 * q^25 + 10767915474742339649424 * q^26 + 5908625413101667397286 * q^27 + 19470658220602184146432 * q^28 + 27292102645387535397612 * q^29 + 58329298290304371008880 * q^30 + 32627031656431162883392 * q^31 + 468929434910304216121344 * q^32 + 154710783396212358738456 * q^33 - 281787665552204278707792 * q^34 - 508089050110930039768800 * q^35 - 41459674655116014911424 * q^36 - 3583146918713545401630116 * q^37 - 3269981889193482397514592 * q^38 - 1315605036791409796255356 * q^39 - 5566467832741725214510080 * q^40 - 3797899216135385210632908 * q^41 - 3710054946595281259687488 * q^42 + 26575294422425069121661960 * q^43 + 55131699398690171610853632 * q^44 - 1632823168521908564355780 * q^45 + 117364920594432004467352512 * q^46 + 35525358464593824073372320 * q^47 - 51587366109420070227824640 * q^48 - 195022162059991348175701230 * q^49 + 61307978112283866795340200 * q^50 - 238124201904088116533282484 * q^51 - 344774229920038676879368832 * q^52 + 209333823893552605529106108 * q^53 - 116778072664541354439960504 * q^54 - 1720852397107481929939963920 * q^55 + 904001217638747705093836800 * q^56 - 1183501376300941017542799768 * q^57 - 2899187104604865887521185264 * q^58 + 8315016058044372283987872744 * q^59 - 2205283656912475583836333440 * q^60 + 4363691539370591264432189740 * q^61 + 17530048836377045276588782848 * q^62 - 2159566190884673448811822224 * q^63 - 3145087146211331732110311424 * q^64 + 10930710572477042656631722920 * q^65 - 23464920294407453174193516768 * q^66 - 42369284190160751303828837672 * q^67 + 25774131672494516419161284736 * q^68 - 50367960385372240855178480784 * q^69 - 8607856574006081326444406400 * q^70 - 16546316342864021533760545296 * q^71 - 8660968685343847043758324224 * q^72 - 119663167384814660837541194252 * q^73 + 212475132055045059714085448016 * q^74 - 67013155866618076569734434950 * q^75 + 201996400191863673719694589696 * q^76 + 143478912022010782926074993088 * q^77 + 154507817730938680591997579568 * q^78 - 111310025088680432366828160800 * q^79 + 377126313405184879658681425920 * q^80 + 84782316550432407028588866402 * q^81 + 145955621212388339389027195248 * q^82 - 1258094410515212478889159597896 * q^83 + 279382664036206224314027149824 * q^84 - 653683338582772611056270015880 * q^85 - 829491133742090715106836469152 * q^86 + 391611842693119724379542610084 * q^87 + 1859518717097362129166224103424 * q^88 - 4692098539351208698917605954604 * q^89 + 836961676542836421299915294160 * q^90 - 778729510605845448339936789088 * q^91 - 1543476723048531611525136139776 * q^92 + 468162242924186708115643652544 * q^93 + 8481973556486642845766202739584 * q^94 - 5454695816719667916384315579120 * q^95 + 6728624851090508538833065771008 * q^96 + 9654846058153613483749893797188 * q^97 + 8740788233364983573968509908568 * q^98 + 2219930642849395287788742467592 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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