LMFDB - Embedded newform 3.32.a.a.1.1

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			1.1
Root			$1696.18$ 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)

$f(q)$	$=$	$q-60460.2 q^{2} +1.43489e7 q^{3} +1.50796e9 q^{4} -5.19836e10 q^{5} -8.67538e11 q^{6} +4.79214e11 q^{7} +3.86659e13 q^{8} +2.05891e14 q^{9} +O(q^{10})$	\(q-60460.2 q^{2} +1.43489e7 q^{3} +1.50796e9 q^{4} -5.19836e10 q^{5} -8.67538e11 q^{6} +4.79214e11 q^{7} +3.86659e13 q^{8} +2.05891e14 q^{9} +3.14294e15 q^{10} +2.28646e16 q^{11} +2.16375e16 q^{12} -1.55876e17 q^{13} -2.89734e16 q^{14} -7.45907e17 q^{15} -5.57606e18 q^{16} -8.05835e17 q^{17} -1.24482e19 q^{18} +1.89635e19 q^{19} -7.83890e19 q^{20} +6.87619e18 q^{21} -1.38240e21 q^{22} -2.34471e21 q^{23} +5.54813e20 q^{24} -1.95432e21 q^{25} +9.42429e21 q^{26} +2.95431e21 q^{27} +7.22634e20 q^{28} +4.26387e22 q^{29} +4.50977e22 q^{30} -2.06986e23 q^{31} +2.54096e23 q^{32} +3.28081e23 q^{33} +4.87210e22 q^{34} -2.49112e22 q^{35} +3.10475e23 q^{36} -3.53200e24 q^{37} -1.14654e24 q^{38} -2.23665e24 q^{39} -2.00999e24 q^{40} -2.76996e24 q^{41} -4.15736e23 q^{42} +1.70258e25 q^{43} +3.44788e25 q^{44} -1.07030e25 q^{45} +1.41762e26 q^{46} -9.50745e25 q^{47} -8.00104e25 q^{48} -1.57546e26 q^{49} +1.18159e26 q^{50} -1.15629e25 q^{51} -2.35054e26 q^{52} +6.00361e26 q^{53} -1.78618e26 q^{54} -1.18858e27 q^{55} +1.85292e25 q^{56} +2.72105e26 q^{57} -2.57795e27 q^{58} +2.97299e27 q^{59} -1.12480e27 q^{60} +3.11672e27 q^{61} +1.25144e28 q^{62} +9.86659e25 q^{63} -3.38819e27 q^{64} +8.10298e27 q^{65} -1.98359e28 q^{66} -7.95464e27 q^{67} -1.21517e27 q^{68} -3.36440e28 q^{69} +1.50614e27 q^{70} -5.35983e28 q^{71} +7.96096e27 q^{72} -1.27570e28 q^{73} +2.13546e29 q^{74} -2.80424e28 q^{75} +2.85961e28 q^{76} +1.09570e28 q^{77} +1.35228e29 q^{78} -3.59792e29 q^{79} +2.89864e29 q^{80} +4.23912e28 q^{81} +1.67473e29 q^{82} -4.19517e29 q^{83} +1.03690e28 q^{84} +4.18902e28 q^{85} -1.02938e30 q^{86} +6.11819e29 q^{87} +8.84079e29 q^{88} -1.62672e30 q^{89} +6.47103e29 q^{90} -7.46979e28 q^{91} -3.53573e30 q^{92} -2.97002e30 q^{93} +5.74823e30 q^{94} -9.85790e29 q^{95} +3.64600e30 q^{96} +6.75518e30 q^{97} +9.52525e30 q^{98} +4.70761e30 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−60460.2	−1.30468	−0.652341	−	0.757925i	$-0.726213\pi$
$2$	−60460.2	−1.30468	−0.652341	+	0.757925i	$0.726213\pi$
$3$	1.43489e7	0.577350
$3$	1.43489e7	0.577350
$4$	1.50796e9	0.702198
$5$	−5.19836e10	−0.761783	−0.380891	−	0.924620i	$-0.624383\pi$
$5$	−5.19836e10	−0.761783	−0.380891	+	0.924620i	$0.624383\pi$
$6$	−8.67538e11	−0.753259
$7$	4.79214e11	0.0381513	0.0190757	−	0.999818i	$-0.493928\pi$
$7$	4.79214e11	0.0381513	0.0190757	+	0.999818i	$0.493928\pi$
$8$	3.86659e13	0.388538
$9$	2.05891e14	0.333333
$10$	3.14294e15	0.993885
$11$	2.28646e16	1.65035	0.825175	−	0.564877i	$-0.191076\pi$
$11$	2.28646e16	1.65035	0.825175	+	0.564877i	$0.191076\pi$
$12$	2.16375e16	0.405414
$13$	−1.55876e17	−0.844611	−0.422306	−	0.906453i	$-0.638779\pi$
$13$	−1.55876e17	−0.844611	−0.422306	+	0.906453i	$0.638779\pi$
$14$	−2.89734e16	−0.0497754
$15$	−7.45907e17	−0.439815
$16$	−5.57606e18	−1.20912
$17$	−8.05835e17	−0.0682791	−0.0341396	−	0.999417i	$-0.510869\pi$
$17$	−8.05835e17	−0.0682791	−0.0341396	+	0.999417i	$0.510869\pi$
$18$	−1.24482e19	−0.434894
$19$	1.89635e19	0.286574	0.143287	−	0.989681i	$-0.454233\pi$
$19$	1.89635e19	0.286574	0.143287	+	0.989681i	$0.454233\pi$
$20$	−7.83890e19	−0.534922
$21$	6.87619e18	0.0220267
$22$	−1.38240e21	−2.15318
$23$	−2.34471e21	−1.83361	−0.916807	−	0.399330i	$-0.869243\pi$
$23$	−2.34471e21	−1.83361	−0.916807	+	0.399330i	$0.869243\pi$
$24$	5.54813e20	0.224322
$25$	−1.95432e21	−0.419687
$26$	9.42429e21	1.10195
$27$	2.95431e21	0.192450
$28$	7.22634e20	0.0267898
$29$	4.26387e22	0.917562	0.458781	−	0.888549i	$-0.348286\pi$
$29$	4.26387e22	0.917562	0.458781	+	0.888549i	$0.348286\pi$
$30$	4.50977e22	0.573820
$31$	−2.06986e23	−1.58429	−0.792144	−	0.610334i	$-0.791035\pi$
$31$	−2.06986e23	−1.58429	−0.792144	+	0.610334i	$0.791035\pi$
$32$	2.54096e23	1.18898
$33$	3.28081e23	0.952830
$34$	4.87210e22	0.0890826
$35$	−2.49112e22	−0.0290630
$36$	3.10475e23	0.234066
$37$	−3.53200e24	−1.74138	−0.870691	−	0.491830i	$-0.836328\pi$
$37$	−3.53200e24	−1.74138	−0.870691	+	0.491830i	$0.836328\pi$
$38$	−1.14654e24	−0.373889
$39$	−2.23665e24	−0.487637
$40$	−2.00999e24	−0.295981
$41$	−2.76996e24	−0.278179	−0.139089	−	0.990280i	$-0.544418\pi$
$41$	−2.76996e24	−0.278179	−0.139089	+	0.990280i	$0.544418\pi$
$42$	−4.15736e23	−0.0287378
$43$	1.70258e25	0.817234	0.408617	−	0.912706i	$-0.366011\pi$
$43$	1.70258e25	0.817234	0.408617	+	0.912706i	$0.366011\pi$
$44$	3.44788e25	1.15887
$45$	−1.07030e25	−0.253928
$46$	1.41762e26	2.39229
$47$	−9.50745e25	−1.14960	−0.574800	−	0.818294i	$-0.694920\pi$
$47$	−9.50745e25	−1.14960	−0.574800	+	0.818294i	$0.694920\pi$
$48$	−8.00104e25	−0.698084
$49$	−1.57546e26	−0.998544
$50$	1.18159e26	0.547559
$51$	−1.15629e25	−0.0394210
$52$	−2.35054e26	−0.593084
$53$	6.00361e26	1.12755	0.563776	−	0.825928i	$-0.309348\pi$
$53$	6.00361e26	1.12755	0.563776	+	0.825928i	$0.309348\pi$
$54$	−1.78618e26	−0.251086
$55$	−1.18858e27	−1.25721
$56$	1.85292e25	0.0148232
$57$	2.72105e26	0.165454
$58$	−2.57795e27	−1.19713
$59$	2.97299e27	1.05922	0.529612	−	0.848240i	$-0.322337\pi$
$59$	2.97299e27	1.05922	0.529612	+	0.848240i	$0.322337\pi$
$60$	−1.12480e27	−0.308837
$61$	3.11672e27	0.662347	0.331174	−	0.943570i	$-0.392555\pi$
$61$	3.11672e27	0.662347	0.331174	+	0.943570i	$0.392555\pi$
$62$	1.25144e28	2.06699
$63$	9.86659e25	0.0127171
$64$	−3.38819e27	−0.342120
$65$	8.10298e27	0.643410
$66$	−1.98359e28	−1.24314
$67$	−7.95464e27	−0.394876	−0.197438	−	0.980315i	$-0.563262\pi$
$67$	−7.95464e27	−0.394876	−0.197438	+	0.980315i	$0.563262\pi$
$68$	−1.21517e27	−0.0479454
$69$	−3.36440e28	−1.05864
$70$	1.50614e27	0.0379180
$71$	−5.35983e28	−1.08304	−0.541522	−	0.840686i	$-0.682152\pi$
$71$	−5.35983e28	−1.08304	−0.541522	+	0.840686i	$0.682152\pi$
$72$	7.96096e27	0.129513
$73$	−1.27570e28	−0.167589	−0.0837943	−	0.996483i	$-0.526704\pi$
$73$	−1.27570e28	−0.167589	−0.0837943	+	0.996483i	$0.526704\pi$
$74$	2.13546e29	2.27195
$75$	−2.80424e28	−0.242307
$76$	2.85961e28	0.201232
$77$	1.09570e28	0.0629631
$78$	1.35228e29	0.636211
$79$	−3.59792e29	−1.38941	−0.694707	−	0.719292i	$-0.744466\pi$
$79$	−3.59792e29	−1.38941	−0.694707	+	0.719292i	$0.744466\pi$
$80$	2.89864e29	0.921084
$81$	4.23912e28	0.111111
$82$	1.67473e29	0.362935
$83$	−4.19517e29	−0.753423	−0.376712	−	0.926331i	$-0.622945\pi$
$83$	−4.19517e29	−0.753423	−0.376712	+	0.926331i	$0.622945\pi$
$84$	1.03690e28	0.0154671
$85$	4.18902e28	0.0520138
$86$	−1.02938e30	−1.06623
$87$	6.11819e29	0.529754
$88$	8.84079e29	0.641224
$89$	−1.62672e30	−0.990300	−0.495150	−	0.868807i	$-0.664887\pi$
$89$	−1.62672e30	−0.990300	−0.495150	+	0.868807i	$0.664887\pi$
$90$	6.47103e29	0.331295
$91$	−7.46979e28	−0.0322231
$92$	−3.53573e30	−1.28756
$93$	−2.97002e30	−0.914690
$94$	5.74823e30	1.49986
$95$	−9.85790e29	−0.218307
$96$	3.64600e30	0.686455
$97$	6.75518e30	1.08312	0.541558	−	0.840664i	$-0.317835\pi$
$97$	6.75518e30	1.08312	0.541558	+	0.840664i	$0.317835\pi$
$98$	9.52525e30	1.30278
$99$	4.70761e30	0.550117
$100$	−2.94703e30	−0.294703
$101$	−8.80255e30	−0.754444	−0.377222	−	0.926123i	$-0.623121\pi$
$101$	−8.80255e30	−0.754444	−0.377222	+	0.926123i	$0.623121\pi$
$102$	6.99093e29	0.0514319
$103$	−2.47783e31	−1.56709	−0.783547	−	0.621332i	$-0.786592\pi$
$103$	−2.47783e31	−1.56709	−0.783547	+	0.621332i	$0.786592\pi$
$104$	−6.02708e30	−0.328163
$105$	−3.57449e29	−0.0167795
$106$	−3.62980e31	−1.47110
$107$	2.55144e30	0.0894000	0.0447000	−	0.999000i	$-0.485767\pi$
$107$	2.55144e30	0.0894000	0.0447000	+	0.999000i	$0.485767\pi$
$108$	4.45498e30	0.135138
$109$	1.92531e31	0.506280	0.253140	−	0.967430i	$-0.418537\pi$
$109$	1.92531e31	0.506280	0.253140	+	0.967430i	$0.418537\pi$
$110$	7.18619e31	1.64026
$111$	−5.06804e31	−1.00539
$112$	−2.67213e30	−0.0461294
$113$	2.22133e31	0.334116	0.167058	−	0.985947i	$-0.446573\pi$
$113$	2.22133e31	0.334116	0.167058	+	0.985947i	$0.446573\pi$
$114$	−1.64515e31	−0.215865
$115$	1.21886e32	1.39682
$116$	6.42974e31	0.644310
$117$	−3.20935e31	−0.281537
$118$	−1.79748e32	−1.38195
$119$	−3.86167e29	−0.00260494
$120$	−2.88412e31	−0.170885
$121$	3.30845e32	1.72366
$122$	−1.88438e32	−0.864153
$123$	−3.97459e31	−0.160607
$124$	−3.12126e32	−1.11248
$125$	3.43660e32	1.08149
$126$	−5.96536e30	−0.0165918
$127$	−1.08865e32	−0.267874	−0.133937	−	0.990990i	$-0.542762\pi$
$127$	−1.08865e32	−0.267874	−0.133937	+	0.990990i	$0.542762\pi$
$128$	−3.40816e32	−0.742618
$129$	2.44302e32	0.471830
$130$	−4.89908e32	−0.839446
$131$	−4.59959e32	−0.699865	−0.349933	−	0.936775i	$-0.613795\pi$
$131$	−4.59959e32	−0.699865	−0.349933	+	0.936775i	$0.613795\pi$
$132$	4.94733e32	0.669075
$133$	9.08756e30	0.0109332
$134$	4.80939e32	0.515188
$135$	−1.53576e32	−0.146605
$136$	−3.11583e31	−0.0265290
$137$	−8.55279e32	−0.650039	−0.325019	−	0.945707i	$-0.605371\pi$
$137$	−8.55279e32	−0.650039	−0.325019	+	0.945707i	$0.605371\pi$
$138$	2.03413e33	1.38119
$139$	3.23712e33	1.96531	0.982653	−	0.185456i	$-0.0593762\pi$
$139$	3.23712e33	1.96531	0.982653	+	0.185456i	$0.0593762\pi$
$140$	−3.75651e31	−0.0204080
$141$	−1.36421e33	−0.663722
$142$	3.24056e33	1.41303
$143$	−3.56403e33	−1.39390
$144$	−1.14806e33	−0.403039
$145$	−2.21651e33	−0.698983
$146$	7.71292e32	0.218650
$147$	−2.26061e33	−0.576510
$148$	−5.32611e33	−1.22279
$149$	−2.51506e33	−0.520188	−0.260094	−	0.965583i	$-0.583754\pi$
$149$	−2.51506e33	−0.520188	−0.260094	+	0.965583i	$0.583754\pi$
$150$	1.69545e33	0.316133
$151$	−6.45384e32	−0.108561	−0.0542807	−	0.998526i	$-0.517287\pi$
$151$	−6.45384e32	−0.108561	−0.0542807	+	0.998526i	$0.517287\pi$
$152$	7.33240e32	0.111345
$153$	−1.65914e32	−0.0227597
$154$	−6.62464e32	−0.0821468
$155$	1.07599e34	1.20688
$156$	−3.37277e33	−0.342417
$157$	8.57470e33	0.788450	0.394225	−	0.919014i	$-0.371013\pi$
$157$	8.57470e33	0.788450	0.394225	+	0.919014i	$0.371013\pi$
$158$	2.17531e34	1.81275
$159$	8.61452e33	0.650992
$160$	−1.32088e34	−0.905741
$161$	−1.12362e33	−0.0699548
$162$	−2.56298e33	−0.144965
$163$	−3.43001e34	−1.76355	−0.881774	−	0.471671i	$-0.843651\pi$
$163$	−3.43001e34	−1.76355	−0.881774	+	0.471671i	$0.843651\pi$
$164$	−4.17699e33	−0.195337
$165$	−1.70548e34	−0.725850
$166$	2.53641e34	0.982979
$167$	2.56900e34	0.907109	0.453555	−	0.891229i	$-0.350156\pi$
$167$	2.56900e34	0.907109	0.453555	+	0.891229i	$0.350156\pi$
$168$	2.65874e32	0.00855820
$169$	−9.76266e33	−0.286632
$170$	−2.53269e33	−0.0678616
$171$	3.90441e33	0.0955248
$172$	2.56742e34	0.573860
$173$	−3.22167e34	−0.658212	−0.329106	−	0.944293i	$-0.606747\pi$
$173$	−3.22167e34	−0.658212	−0.329106	+	0.944293i	$0.606747\pi$
$174$	−3.69907e34	−0.691162
$175$	−9.36538e32	−0.0160116
$176$	−1.27494e35	−1.99547
$177$	4.26592e34	0.611543
$178$	9.83517e34	1.29203
$179$	−2.52883e34	−0.304577	−0.152289	−	0.988336i	$-0.548664\pi$
$179$	−2.52883e34	−0.304577	−0.152289	+	0.988336i	$0.548664\pi$
$180$	−1.61396e34	−0.178307
$181$	5.78234e34	0.586254	0.293127	−	0.956073i	$-0.405304\pi$
$181$	5.78234e34	0.586254	0.293127	+	0.956073i	$0.405304\pi$
$182$	4.51625e33	0.0420409
$183$	4.47216e34	0.382406
$184$	−9.06604e34	−0.712428
$185$	1.83606e35	1.32656
$186$	1.79568e35	1.19338
$187$	−1.84251e34	−0.112684
$188$	−1.43368e35	−0.807247
$189$	1.41575e33	0.00734223
$190$	5.96011e34	0.284822
$191$	2.13459e35	0.940366	0.470183	−	0.882569i	$-0.344188\pi$
$191$	2.13459e35	0.940366	0.470183	+	0.882569i	$0.344188\pi$
$192$	−4.86168e34	−0.197523
$193$	−1.98036e35	−0.742344	−0.371172	−	0.928564i	$-0.621044\pi$
$193$	−1.98036e35	−0.742344	−0.371172	+	0.928564i	$0.621044\pi$
$194$	−4.08420e35	−1.41312
$195$	1.16269e35	0.371473
$196$	−2.37572e35	−0.701175
$197$	−1.28212e35	−0.349705	−0.174853	−	0.984595i	$-0.555945\pi$
$197$	−1.28212e35	−0.349705	−0.174853	+	0.984595i	$0.555945\pi$
$198$	−2.84623e35	−0.717728
$199$	−1.20737e35	−0.281591	−0.140795	−	0.990039i	$-0.544966\pi$
$199$	−1.20737e35	−0.281591	−0.140795	+	0.990039i	$0.544966\pi$
$200$	−7.55656e34	−0.163064
$201$	−1.14140e35	−0.227982
$202$	5.32204e35	0.984311
$203$	2.04331e34	0.0350062
$204$	−1.74363e34	−0.0276813
$205$	1.43993e35	0.211912
$206$	1.49810e36	2.04456
$207$	−4.82755e35	−0.611205
$208$	8.69174e35	1.02123
$209$	4.33592e35	0.472948
$210$	2.16115e34	0.0218920
$211$	−9.25697e35	−0.871146	−0.435573	−	0.900153i	$-0.643454\pi$
$211$	−9.25697e35	−0.871146	−0.435573	+	0.900153i	$0.643454\pi$
$212$	9.05319e35	0.791764
$213$	−7.69077e35	−0.625296
$214$	−1.54261e35	−0.116639
$215$	−8.85062e35	−0.622554
$216$	1.14231e35	0.0747741
$217$	−9.91905e34	−0.0604427
$218$	−1.16405e36	−0.660535
$219$	−1.83049e35	−0.0967574
$220$	−1.79233e36	−0.882809
$221$	1.25610e35	0.0576693
$222$	3.06415e36	1.31171
$223$	−1.87403e36	−0.748259	−0.374130	−	0.927376i	$-0.622059\pi$
$223$	−1.87403e36	−0.748259	−0.374130	+	0.927376i	$0.622059\pi$
$224$	1.21766e35	0.0453610
$225$	−4.02377e35	−0.139896
$226$	−1.34302e36	−0.435916
$227$	4.14939e36	1.25772	0.628859	−	0.777519i	$-0.283522\pi$
$227$	4.14939e36	1.25772	0.628859	+	0.777519i	$0.283522\pi$
$228$	4.10323e35	0.116181
$229$	3.40911e36	0.901967	0.450983	−	0.892532i	$-0.351073\pi$
$229$	3.40911e36	0.901967	0.450983	+	0.892532i	$0.351073\pi$
$230$	−7.36929e36	−1.82240
$231$	1.57221e35	0.0363517
$232$	1.64866e36	0.356507
$233$	−6.95380e36	−1.40671	−0.703357	−	0.710837i	$-0.748316\pi$
$233$	−6.95380e36	−1.40671	−0.703357	+	0.710837i	$0.748316\pi$
$234$	1.94038e36	0.367317
$235$	4.94231e36	0.875746
$236$	4.48315e36	0.743785
$237$	−5.16263e36	−0.802179
$238$	2.33478e34	0.00339862
$239$	7.57580e36	1.03338	0.516691	−	0.856172i	$-0.327163\pi$
$239$	7.57580e36	1.03338	0.516691	+	0.856172i	$0.327163\pi$
$240$	4.15923e36	0.531788
$241$	1.49114e37	1.78753	0.893765	−	0.448535i	$-0.148054\pi$
$241$	1.49114e37	1.78753	0.893765	+	0.448535i	$0.148054\pi$
$242$	−2.00029e37	−2.24883
$243$	6.08267e35	0.0641500
$244$	4.69989e36	0.465099
$245$	8.18979e36	0.760674
$246$	2.40305e36	0.209541
$247$	−2.95595e36	−0.242044
$248$	−8.00329e36	−0.615556
$249$	−6.01961e36	−0.434989
$250$	−2.07778e37	−1.41101
$251$	5.26166e35	0.0335877	0.0167938	−	0.999859i	$-0.494654\pi$
$251$	5.26166e35	0.0335877	0.0167938	+	0.999859i	$0.494654\pi$
$252$	1.48784e35	0.00892992
$253$	−5.36108e37	−3.02611
$254$	6.58201e36	0.349491
$255$	6.01078e35	0.0300302
$256$	2.78819e37	1.31100
$257$	2.83031e37	1.25277	0.626383	−	0.779515i	$-0.284535\pi$
$257$	2.83031e37	1.25277	0.626383	+	0.779515i	$0.284535\pi$
$258$	−1.47705e37	−0.615589
$259$	−1.69258e36	−0.0664361
$260$	1.22190e37	0.451801
$261$	8.77894e36	0.305854
$262$	2.78093e37	0.913102
$263$	5.51705e37	1.70763	0.853813	−	0.520579i	$-0.174284\pi$
$263$	5.51705e37	1.70763	0.853813	+	0.520579i	$0.174284\pi$
$264$	1.26856e37	0.370211
$265$	−3.12089e37	−0.858949
$266$	−5.49436e35	−0.0142643
$267$	−2.33416e37	−0.571750
$268$	−1.19953e37	−0.277281
$269$	−1.75709e37	−0.383384	−0.191692	−	0.981455i	$-0.561398\pi$
$269$	−1.75709e37	−0.383384	−0.191692	+	0.981455i	$0.561398\pi$
$270$	9.28523e36	0.191273
$271$	2.76113e37	0.537110	0.268555	−	0.963264i	$-0.413454\pi$
$271$	2.76113e37	0.537110	0.268555	+	0.963264i	$0.413454\pi$
$272$	4.49339e36	0.0825574
$273$	−1.07183e36	−0.0186040
$274$	5.17104e37	0.848094
$275$	−4.46847e37	−0.692631
$276$	−5.07338e37	−0.743373
$277$	−1.31159e37	−0.181703	−0.0908515	−	0.995864i	$-0.528959\pi$
$277$	−1.31159e37	−0.181703	−0.0908515	+	0.995864i	$0.528959\pi$
$278$	−1.95717e38	−2.56410
$279$	−4.26165e37	−0.528096
$280$	−9.63216e35	−0.0112921
$281$	1.47067e38	1.63143	0.815714	−	0.578455i	$-0.196344\pi$
$281$	1.47067e38	1.63143	0.815714	+	0.578455i	$0.196344\pi$
$282$	8.24808e37	0.865947
$283$	−4.84440e37	−0.481449	−0.240724	−	0.970593i	$-0.577385\pi$
$283$	−4.84440e37	−0.481449	−0.240724	+	0.970593i	$0.577385\pi$
$284$	−8.08239e37	−0.760511
$285$	−1.41450e37	−0.126040
$286$	2.15482e38	1.81860
$287$	−1.32740e36	−0.0106129
$288$	5.23161e37	0.396325
$289$	−1.38640e38	−0.995338
$290$	1.34011e38	0.911951
$291$	9.69294e37	0.625337
$292$	−1.92370e37	−0.117680
$293$	−2.49385e38	−1.44684	−0.723421	−	0.690407i	$-0.757432\pi$
$293$	−2.49385e38	−1.44684	−0.723421	+	0.690407i	$0.757432\pi$
$294$	1.36677e38	0.752163
$295$	−1.54547e38	−0.806899
$296$	−1.36568e38	−0.676593
$297$	6.75491e37	0.317610
$298$	1.52061e38	0.678680
$299$	3.65484e38	1.54869
$300$	−4.22867e37	−0.170147
$301$	8.15900e36	0.0311786
$302$	3.90201e37	0.141638
$303$	−1.26307e38	−0.435579
$304$	−1.05742e38	−0.346502
$305$	−1.62018e38	−0.504565
$306$	1.00312e37	0.0296942
$307$	6.63440e38	1.86706	0.933528	−	0.358506i	$-0.116714\pi$
$307$	6.63440e38	1.86706	0.933528	+	0.358506i	$0.116714\pi$
$308$	1.65227e37	0.0442125
$309$	−3.55542e38	−0.904763
$310$	−6.50544e38	−1.57460
$311$	3.07486e38	0.708009	0.354004	−	0.935244i	$-0.384820\pi$
$311$	3.07486e38	0.708009	0.354004	+	0.935244i	$0.384820\pi$
$312$	−8.64820e37	−0.189465
$313$	−2.72740e38	−0.568606	−0.284303	−	0.958734i	$-0.591762\pi$
$313$	−2.72740e38	−0.568606	−0.284303	+	0.958734i	$0.591762\pi$
$314$	−5.18429e38	−1.02868
$315$	−5.12901e36	−0.00968767
$316$	−5.42552e38	−0.975644
$317$	2.25948e38	0.386893	0.193446	−	0.981111i	$-0.438033\pi$
$317$	2.25948e38	0.386893	0.193446	+	0.981111i	$0.438033\pi$
$318$	−5.20836e38	−0.849339
$319$	9.74916e38	1.51430
$320$	1.76130e38	0.260621
$321$	3.66104e37	0.0516151
$322$	6.79342e37	0.0912689
$323$	−1.52814e37	−0.0195670
$324$	6.39241e37	0.0780219
$325$	3.04631e38	0.354473
$326$	2.07379e39	2.30087
$327$	2.76261e38	0.292301
$328$	−1.07103e38	−0.108083
$329$	−4.55610e37	−0.0438588
$330$	1.03114e39	0.947004
$331$	5.39155e38	0.472476	0.236238	−	0.971695i	$-0.424085\pi$
$331$	5.39155e38	0.472476	0.236238	+	0.971695i	$0.424085\pi$
$332$	−6.32614e38	−0.529052
$333$	−7.27208e38	−0.580461
$334$	−1.55323e39	−1.18349
$335$	4.13510e38	0.300810
$336$	−3.83421e37	−0.0266328
$337$	−2.34616e39	−1.55631	−0.778153	−	0.628075i	$-0.783843\pi$
$337$	−2.34616e39	−1.55631	−0.778153	+	0.628075i	$0.783843\pi$
$338$	5.90253e38	0.373963
$339$	3.18737e38	0.192902
$340$	6.31686e37	0.0365240
$341$	−4.73264e39	−2.61463
$342$	−2.36062e38	−0.124630
$343$	−1.51106e38	−0.0762471
$344$	6.58318e38	0.317526
$345$	1.74894e39	0.806452
$346$	1.94783e39	0.858758
$347$	−1.51527e39	−0.638829	−0.319414	−	0.947615i	$-0.603486\pi$
$347$	−1.51527e39	−0.638829	−0.319414	+	0.947615i	$0.603486\pi$
$348$	9.22597e38	0.371992
$349$	6.79258e38	0.261963	0.130982	−	0.991385i	$-0.458187\pi$
$349$	6.79258e38	0.261963	0.130982	+	0.991385i	$0.458187\pi$
$350$	5.66233e37	0.0208901
$351$	−4.60506e38	−0.162546
$352$	5.80979e39	1.96223
$353$	−2.08479e39	−0.673837	−0.336918	−	0.941534i	$-0.609385\pi$
$353$	−2.08479e39	−0.673837	−0.336918	+	0.941534i	$0.609385\pi$
$354$	−2.57919e39	−0.797870
$355$	2.78623e39	0.825045
$356$	−2.45302e39	−0.695387
$357$	−5.54108e36	−0.00150396
$358$	1.52894e39	0.397377
$359$	4.27759e39	1.06472	0.532360	−	0.846518i	$-0.321305\pi$
$359$	4.27759e39	1.06472	0.532360	+	0.846518i	$0.321305\pi$
$360$	−4.13839e38	−0.0986604
$361$	−4.01925e39	−0.917875
$362$	−3.49602e39	−0.764876
$363$	4.74726e39	0.995154
$364$	−1.12641e38	−0.0226269
$365$	6.63155e38	0.127666
$366$	−2.70388e39	−0.498919
$367$	−1.53779e39	−0.272003	−0.136002	−	0.990709i	$-0.543425\pi$
$367$	−1.53779e39	−0.272003	−0.136002	+	0.990709i	$0.543425\pi$
$368$	1.30743e40	2.21705
$369$	−5.70311e38	−0.0927263
$370$	−1.11009e40	−1.73073
$371$	2.87701e38	0.0430176
$372$	−4.47867e39	−0.642293
$373$	3.20755e39	0.441252	0.220626	−	0.975358i	$-0.429190\pi$
$373$	3.20755e39	0.441252	0.220626	+	0.975358i	$0.429190\pi$
$374$	1.11398e39	0.147018
$375$	4.93114e39	0.624400
$376$	−3.67614e39	−0.446663
$377$	−6.64635e39	−0.774983
$378$	−8.55964e37	−0.00957928
$379$	−2.17776e39	−0.233939	−0.116969	−	0.993136i	$-0.537318\pi$
$379$	−2.17776e39	−0.233939	−0.116969	+	0.993136i	$0.537318\pi$
$380$	−1.48653e39	−0.153295
$381$	−1.56209e39	−0.154657
$382$	−1.29058e40	−1.22688
$383$	1.00334e40	0.915941	0.457970	−	0.888967i	$-0.348577\pi$
$383$	1.00334e40	0.915941	0.457970	+	0.888967i	$0.348577\pi$
$384$	−4.89033e39	−0.428750
$385$	−5.69585e38	−0.0479642
$386$	1.19733e40	0.968523
$387$	3.50546e39	0.272411
$388$	1.01865e40	0.760561
$389$	−9.60716e39	−0.689249	−0.344625	−	0.938741i	$-0.611994\pi$
$389$	−9.60716e39	−0.689249	−0.344625	+	0.938741i	$0.611994\pi$
$390$	−7.02965e39	−0.484655
$391$	1.88945e39	0.125198
$392$	−6.09165e39	−0.387972
$393$	−6.59991e39	−0.404067
$394$	7.75173e39	0.456255
$395$	1.87033e40	1.05843
$396$	7.09888e39	0.386291
$397$	1.81559e40	0.950088	0.475044	−	0.879962i	$-0.342432\pi$
$397$	1.81559e40	0.950088	0.475044	+	0.879962i	$0.342432\pi$
$398$	7.29980e39	0.367387
$399$	1.30397e38	0.00631228
$400$	1.08974e40	0.507451
$401$	−3.26830e39	−0.146414	−0.0732072	−	0.997317i	$-0.523323\pi$
$401$	−3.26830e39	−0.146414	−0.0732072	+	0.997317i	$0.523323\pi$
$402$	6.90095e39	0.297444
$403$	3.22641e40	1.33811
$404$	−1.32739e40	−0.529769
$405$	−2.20364e39	−0.0846425
$406$	−1.23539e39	−0.0456720
$407$	−8.07577e40	−2.87389
$408$	−4.47088e38	−0.0153165
$409$	−4.69622e40	−1.54895	−0.774474	−	0.632606i	$-0.781985\pi$
$409$	−4.69622e40	−1.54895	−0.774474	+	0.632606i	$0.781985\pi$
$410$	−8.70583e39	−0.276478
$411$	−1.22723e40	−0.375300
$412$	−3.73647e40	−1.10041
$413$	1.42470e39	0.0404108
$414$	2.91875e40	0.797428
$415$	2.18080e40	0.573945
$416$	−3.96074e40	−1.00422
$417$	4.64492e40	1.13467
$418$	−2.62151e40	−0.617047
$419$	5.66404e40	1.28472	0.642360	−	0.766403i	$-0.277955\pi$
$419$	5.66404e40	1.28472	0.642360	+	0.766403i	$0.277955\pi$
$420$	−5.39018e38	−0.0117826
$421$	6.21251e38	0.0130886	0.00654432	−	0.999979i	$-0.497917\pi$
$421$	6.21251e38	0.0130886	0.00654432	+	0.999979i	$0.497917\pi$
$422$	5.59679e40	1.13657
$423$	−1.95750e40	−0.383200
$424$	2.32135e40	0.438096
$425$	1.57486e39	0.0286559
$426$	4.64986e40	0.815813
$427$	1.49358e39	0.0252694
$428$	3.84747e39	0.0627764
$429$	−5.11400e40	−0.804771
$430$	5.35110e40	0.812236
$431$	5.70544e40	0.835394	0.417697	−	0.908586i	$-0.362837\pi$
$431$	5.70544e40	0.835394	0.417697	+	0.908586i	$0.362837\pi$
$432$	−1.64734e40	−0.232695
$433$	−5.10678e40	−0.695961	−0.347981	−	0.937502i	$-0.613132\pi$
$433$	−5.10678e40	−0.695961	−0.347981	+	0.937502i	$0.613132\pi$
$434$	5.99708e39	0.0788586
$435$	−3.18045e40	−0.403558
$436$	2.90329e40	0.355508
$437$	−4.44639e40	−0.525467
$438$	1.10672e40	0.126238
$439$	−6.28099e39	−0.0691557	−0.0345778	−	0.999402i	$-0.511009\pi$
$439$	−6.28099e39	−0.0691557	−0.0345778	+	0.999402i	$0.511009\pi$
$440$	−4.59576e40	−0.488473
$441$	−3.24373e40	−0.332848
$442$	−7.59443e39	−0.0752402
$443$	−9.35324e40	−0.894755	−0.447377	−	0.894345i	$-0.647642\pi$
$443$	−9.35324e40	−0.894755	−0.447377	+	0.894345i	$0.647642\pi$
$444$	−7.64239e40	−0.705981
$445$	8.45626e40	0.754394
$446$	1.13305e41	0.976241
$447$	−3.60883e40	−0.300331
$448$	−1.62367e39	−0.0130523
$449$	1.52510e41	1.18435	0.592173	−	0.805811i	$-0.298270\pi$
$449$	1.52510e41	1.18435	0.592173	+	0.805811i	$0.298270\pi$
$450$	2.43278e40	0.182520
$451$	−6.33340e40	−0.459093
$452$	3.34967e40	0.234615
$453$	−9.26056e39	−0.0626780
$454$	−2.50873e41	−1.64092
$455$	3.88306e39	0.0245470
$456$	1.05212e40	0.0642850
$457$	−3.69792e40	−0.218402	−0.109201	−	0.994020i	$-0.534829\pi$
$457$	−3.69792e40	−0.218402	−0.109201	+	0.994020i	$0.534829\pi$
$458$	−2.06115e41	−1.17678
$459$	−2.38069e39	−0.0131403
$460$	1.83800e41	0.980840
$461$	3.37827e41	1.74313	0.871566	−	0.490279i	$-0.163105\pi$
$461$	3.37827e41	1.74313	0.871566	+	0.490279i	$0.163105\pi$
$462$	−9.50563e39	−0.0474275
$463$	−3.45609e41	−1.66755	−0.833776	−	0.552103i	$-0.813826\pi$
$463$	−3.45609e41	−1.66755	−0.833776	+	0.552103i	$0.813826\pi$
$464$	−2.37756e41	−1.10944
$465$	1.54392e41	0.696795
$466$	4.20429e41	1.83532
$467$	1.85054e41	0.781424	0.390712	−	0.920513i	$-0.372229\pi$
$467$	1.85054e41	0.781424	0.390712	+	0.920513i	$0.372229\pi$
$468$	−4.83956e40	−0.197695
$469$	−3.81197e39	−0.0150651
$470$	−2.98813e41	−1.14257
$471$	1.23038e41	0.455212
$472$	1.14954e41	0.411549
$473$	3.89287e41	1.34872
$474$	3.12134e41	1.04659
$475$	−3.70607e40	−0.120272
$476$	−5.82324e38	−0.00182918
$477$	1.23609e41	0.375851
$478$	−4.58035e41	−1.34824
$479$	−2.59635e41	−0.739882	−0.369941	−	0.929055i	$-0.620622\pi$
$479$	−2.59635e41	−0.739882	−0.369941	+	0.929055i	$0.620622\pi$
$480$	−1.89532e41	−0.522930
$481$	5.50554e41	1.47079
$482$	−9.01545e41	−2.33216
$483$	−1.61227e40	−0.0403884
$484$	4.98900e41	1.21035
$485$	−3.51158e41	−0.825099
$486$	−3.67760e40	−0.0836954
$487$	−2.12708e41	−0.468906	−0.234453	−	0.972127i	$-0.575330\pi$
$487$	−2.12708e41	−0.468906	−0.234453	+	0.972127i	$0.575330\pi$
$488$	1.20511e41	0.257347
$489$	−4.92169e41	−1.01819
$490$	−4.95157e41	−0.992438
$491$	−8.52273e40	−0.165507	−0.0827534	−	0.996570i	$-0.526371\pi$
$491$	−8.52273e40	−0.165507	−0.0827534	+	0.996570i	$0.526371\pi$
$492$	−5.99352e40	−0.112778
$493$	−3.43598e40	−0.0626503
$494$	1.78717e41	0.315791
$495$	−2.44718e41	−0.419069
$496$	1.15417e42	1.91559
$497$	−2.56850e40	−0.0413196
$498$	3.63947e41	0.567523
$499$	−5.54432e41	−0.838088	−0.419044	−	0.907966i	$-0.637635\pi$
$499$	−5.54432e41	−0.838088	−0.419044	+	0.907966i	$0.637635\pi$
$500$	5.18225e41	0.759422
$501$	3.68624e41	0.523720
$502$	−3.18121e40	−0.0438213
$503$	−1.21211e42	−1.61897	−0.809487	−	0.587138i	$-0.800255\pi$
$503$	−1.21211e42	−1.61897	−0.809487	+	0.587138i	$0.800255\pi$
$504$	3.81500e39	0.00494108
$505$	4.57588e41	0.574723
$506$	3.24132e42	3.94811
$507$	−1.40083e41	−0.165487
$508$	−1.64164e41	−0.188101
$509$	3.93073e41	0.436865	0.218433	−	0.975852i	$-0.429906\pi$
$509$	3.93073e41	0.436865	0.218433	+	0.975852i	$0.429906\pi$
$510$	−3.63413e40	−0.0391799
$511$	−6.11334e39	−0.00639373
$512$	−9.53850e41	−0.967822
$513$	5.60241e40	0.0551513
$514$	−1.71121e42	−1.63446
$515$	1.28807e42	1.19379
$516$	3.68396e41	0.331318
$517$	−2.17384e42	−1.89724
$518$	1.02334e41	0.0866780
$519$	−4.62274e41	−0.380019
$520$	3.13309e41	0.249989
$521$	−1.20516e42	−0.933381	−0.466691	−	0.884421i	$-0.654554\pi$
$521$	−1.20516e42	−0.933381	−0.466691	+	0.884421i	$0.654554\pi$
$522$	−5.30777e41	−0.399042
$523$	1.48284e42	1.08222	0.541112	−	0.840951i	$-0.318004\pi$
$523$	1.48284e42	1.08222	0.541112	+	0.840951i	$0.318004\pi$
$524$	−6.93599e41	−0.491444
$525$	−1.34383e40	−0.00924432
$526$	−3.33562e42	−2.22791
$527$	1.66796e41	0.108174
$528$	−1.82940e42	−1.15208
$529$	3.86250e42	2.36214
$530$	1.88690e42	1.12066
$531$	6.12113e41	0.353075
$532$	1.37037e40	0.00767726
$533$	4.31770e41	0.234953
$534$	1.41124e42	0.745953
$535$	−1.32633e41	−0.0681033
$536$	−3.07573e41	−0.153424
$537$	−3.62859e41	−0.175848
$538$	1.06234e42	0.500195
$539$	−3.60221e42	−1.64795
$540$	−2.31586e41	−0.102946
$541$	2.79718e42	1.20827	0.604134	−	0.796883i	$-0.293519\pi$
$541$	2.79718e42	1.20827	0.604134	+	0.796883i	$0.293519\pi$
$542$	−1.66939e42	−0.700758
$543$	8.29703e41	0.338474
$544$	−2.04759e41	−0.0811822
$545$	−1.00085e42	−0.385675
$546$	6.48033e40	0.0242723
$547$	−6.52472e41	−0.237552	−0.118776	−	0.992921i	$-0.537897\pi$
$547$	−6.52472e41	−0.237552	−0.118776	+	0.992921i	$0.537897\pi$
$548$	−1.28972e42	−0.456455
$549$	6.41706e41	0.220782
$550$	2.70165e42	0.903664
$551$	8.08579e41	0.262950
$552$	−1.30088e42	−0.411321
$553$	−1.72417e41	−0.0530080
$554$	7.92992e41	0.237065
$555$	2.63455e42	0.765887
$556$	4.88145e42	1.38003
$557$	1.97916e42	0.544158	0.272079	−	0.962275i	$-0.412289\pi$
$557$	1.97916e42	0.544158	0.272079	+	0.962275i	$0.412289\pi$
$558$	2.57661e42	0.688998
$559$	−2.65391e42	−0.690245
$560$	1.38907e41	0.0351406
$561$	−2.64380e41	−0.0650584
$562$	−8.89172e42	−2.12850
$563$	−1.27770e42	−0.297541	−0.148771	−	0.988872i	$-0.547532\pi$
$563$	−1.27770e42	−0.297541	−0.148771	+	0.988872i	$0.547532\pi$
$564$	−2.05718e42	−0.466064
$565$	−1.15473e42	−0.254524
$566$	2.92894e42	0.628138
$567$	2.03144e40	0.00423904
$568$	−2.07243e42	−0.420804
$569$	−6.39443e42	−1.26346	−0.631730	−	0.775188i	$-0.717655\pi$
$569$	−6.39443e42	−1.26346	−0.631730	+	0.775188i	$0.717655\pi$
$570$	8.55210e41	0.164442
$571$	4.90473e41	0.0917815	0.0458908	−	0.998946i	$-0.485387\pi$
$571$	4.90473e41	0.0917815	0.0458908	+	0.998946i	$0.485387\pi$
$572$	−5.37441e42	−0.978797
$573$	3.06290e42	0.542921
$574$	8.02552e40	0.0138465
$575$	4.58232e42	0.769544
$576$	−6.97598e41	−0.114040
$577$	−9.68937e42	−1.54195	−0.770975	−	0.636865i	$-0.780231\pi$
$577$	−9.68937e42	−1.54195	−0.770975	+	0.636865i	$0.780231\pi$
$578$	8.38218e42	1.29860
$579$	−2.84160e42	−0.428592
$580$	−3.34241e42	−0.490824
$581$	−2.01038e41	−0.0287441
$582$	−5.86037e42	−0.815867
$583$	1.37270e43	1.86086
$584$	−4.93261e41	−0.0651145
$585$	1.66833e42	0.214470
$586$	1.50778e43	1.88767
$587$	9.44167e41	0.115122	0.0575610	−	0.998342i	$-0.481668\pi$
$587$	9.44167e41	0.115122	0.0575610	+	0.998342i	$0.481668\pi$
$588$	−3.40890e42	−0.404824
$589$	−3.92517e42	−0.454016
$590$	9.34394e42	1.05275
$591$	−1.83970e42	−0.201902
$592$	1.96947e43	2.10553
$593$	9.82369e42	1.02312	0.511560	−	0.859247i	$-0.329068\pi$
$593$	9.82369e42	1.02312	0.511560	+	0.859247i	$0.329068\pi$
$594$	−4.08403e42	−0.414380
$595$	2.00744e40	0.00198440
$596$	−3.79260e42	−0.365275
$597$	−1.73245e42	−0.162576
$598$	−2.20972e43	−2.02055
$599$	2.87453e42	0.256125	0.128062	−	0.991766i	$-0.459124\pi$
$599$	2.87453e42	0.256125	0.128062	+	0.991766i	$0.459124\pi$
$600$	−1.08428e42	−0.0941452
$601$	−1.59224e43	−1.34727	−0.673636	−	0.739063i	$-0.735269\pi$
$601$	−1.59224e43	−1.34727	−0.673636	+	0.739063i	$0.735269\pi$
$602$	−4.93295e41	−0.0406781
$603$	−1.63779e42	−0.131625
$604$	−9.73212e41	−0.0762316
$605$	−1.71985e43	−1.31305
$606$	7.63655e42	0.568292
$607$	−1.17991e43	−0.855903	−0.427951	−	0.903802i	$-0.640765\pi$
$607$	−1.17991e43	−0.855903	−0.427951	+	0.903802i	$0.640765\pi$
$608$	4.81854e42	0.340730
$609$	2.93192e41	0.0202108
$610$	9.79567e42	0.658297
$611$	1.48198e43	0.970966
$612$	−2.50192e41	−0.0159818
$613$	−4.70661e42	−0.293137	−0.146569	−	0.989200i	$-0.546823\pi$
$613$	−4.70661e42	−0.293137	−0.146569	+	0.989200i	$0.546823\pi$
$614$	−4.01118e43	−2.43591
$615$	2.06614e42	0.122347
$616$	4.23663e41	0.0244635
$617$	−8.20513e42	−0.462025	−0.231013	−	0.972951i	$-0.574204\pi$
$617$	−8.20513e42	−0.462025	−0.231013	+	0.972951i	$0.574204\pi$
$618$	2.14962e43	1.18043
$619$	2.39708e43	1.28374	0.641872	−	0.766812i	$-0.278158\pi$
$619$	2.39708e43	1.28374	0.641872	+	0.766812i	$0.278158\pi$
$620$	1.62254e43	0.847471
$621$	−6.92701e42	−0.352879
$622$	−1.85907e43	−0.923727
$623$	−7.79545e41	−0.0377813
$624$	1.24717e43	0.589609
$625$	−8.76416e42	−0.404175
$626$	1.64899e43	0.741851
$627$	6.22157e42	0.273057
$628$	1.29303e43	0.553648
$629$	2.84621e42	0.118900
$630$	3.10101e41	0.0126393
$631$	3.15158e43	1.25335	0.626675	−	0.779280i	$-0.284415\pi$
$631$	3.15158e43	1.25335	0.626675	+	0.779280i	$0.284415\pi$
$632$	−1.39117e43	−0.539840
$633$	−1.32827e43	−0.502956
$634$	−1.36609e43	−0.504772
$635$	5.65919e42	0.204062
$636$	1.29903e43	0.457125
$637$	2.45576e43	0.843382
$638$	−5.89436e43	−1.97568
$639$	−1.10354e43	−0.361015
$640$	1.77168e43	0.565713
$641$	1.37405e43	0.428256	0.214128	−	0.976806i	$-0.431309\pi$
$641$	1.37405e43	0.428256	0.214128	+	0.976806i	$0.431309\pi$
$642$	−2.21348e42	−0.0673413
$643$	−3.47044e43	−1.03066	−0.515329	−	0.856993i	$-0.672330\pi$
$643$	−3.47044e43	−1.03066	−0.515329	+	0.856993i	$0.672330\pi$
$644$	−1.69437e42	−0.0491221
$645$	−1.26997e43	−0.359432
$646$	9.23920e41	0.0255288
$647$	2.34842e43	0.633519	0.316760	−	0.948506i	$-0.397405\pi$
$647$	2.34842e43	0.633519	0.316760	+	0.948506i	$0.397405\pi$
$648$	1.63909e42	0.0431709
$649$	6.79762e43	1.74809
$650$	−1.84181e43	−0.462474
$651$	−1.42327e42	−0.0348966
$652$	−5.17231e43	−1.23836
$653$	−1.50734e43	−0.352417	−0.176208	−	0.984353i	$-0.556383\pi$
$653$	−1.50734e43	−0.352417	−0.176208	+	0.984353i	$0.556383\pi$
$654$	−1.67028e43	−0.381360
$655$	2.39103e43	0.533145
$656$	1.54455e43	0.336351
$657$	−2.62656e42	−0.0558629
$658$	2.75463e42	0.0572218
$659$	2.48853e43	0.504916	0.252458	−	0.967608i	$-0.418761\pi$
$659$	2.48853e43	0.504916	0.252458	+	0.967608i	$0.418761\pi$
$660$	−2.57180e43	−0.509690
$661$	−3.54490e43	−0.686249	−0.343125	−	0.939290i	$-0.611485\pi$
$661$	−3.54490e43	−0.686249	−0.343125	+	0.939290i	$0.611485\pi$
$662$	−3.25975e43	−0.616432
$663$	1.80237e42	0.0332954
$664$	−1.62210e43	−0.292733
$665$	−4.72404e41	−0.00832872
$666$	4.39672e43	0.757317
$667$	−9.99755e43	−1.68245
$668$	3.87395e43	0.636970
$669$	−2.68903e43	−0.432008
$670$	−2.50009e43	−0.392461
$671$	7.12625e43	1.09311
$672$	1.74721e42	0.0261892
$673$	−8.53660e43	−1.25041	−0.625204	−	0.780462i	$-0.714984\pi$
$673$	−8.53660e43	−1.25041	−0.625204	+	0.780462i	$0.714984\pi$
$674$	1.41850e44	2.03049
$675$	−5.77368e42	−0.0807688
$676$	−1.47217e43	−0.201272
$677$	6.94791e43	0.928388	0.464194	−	0.885734i	$-0.346344\pi$
$677$	6.94791e43	0.928388	0.464194	+	0.885734i	$0.346344\pi$
$678$	−1.92709e43	−0.251676
$679$	3.23717e42	0.0413223
$680$	1.61972e42	0.0202093
$681$	5.95392e43	0.726144
$682$	2.86137e44	3.41127
$683$	−4.30146e43	−0.501297	−0.250648	−	0.968078i	$-0.580644\pi$
$683$	−4.30146e43	−0.501297	−0.250648	+	0.968078i	$0.580644\pi$
$684$	5.88769e42	0.0670773
$685$	4.44605e43	0.495188
$686$	9.13592e42	0.0994783
$687$	4.89169e43	0.520751
$688$	−9.49369e43	−0.988131
$689$	−9.35818e43	−0.952343
$690$	−1.05741e44	−1.05216
$691$	−1.10490e44	−1.07501	−0.537506	−	0.843260i	$-0.680633\pi$
$691$	−1.10490e44	−1.07501	−0.537506	+	0.843260i	$0.680633\pi$
$692$	−4.85814e43	−0.462195
$693$	2.25595e42	0.0209877
$694$	9.16138e43	0.833469
$695$	−1.68277e44	−1.49714
$696$	2.36565e43	0.205830
$697$	2.23213e42	0.0189938
$698$	−4.10681e43	−0.341779
$699$	−9.97795e43	−0.812166
$700$	−1.41226e42	−0.0112433
$701$	−1.54392e44	−1.20225	−0.601127	−	0.799154i	$-0.705281\pi$
$701$	−1.54392e44	−1.20225	−0.601127	+	0.799154i	$0.705281\pi$
$702$	2.78423e43	0.212070
$703$	−6.69791e43	−0.499036
$704$	−7.74695e43	−0.564618
$705$	7.09168e43	0.505612
$706$	1.26047e44	0.879143
$707$	−4.21830e42	−0.0287831
$708$	6.43283e43	0.429424
$709$	1.68117e44	1.09798	0.548990	−	0.835829i	$-0.315013\pi$
$709$	1.68117e44	1.09798	0.548990	+	0.835829i	$0.315013\pi$
$710$	−1.68456e44	−1.07642
$711$	−7.40780e43	−0.463138
$712$	−6.28985e43	−0.384769
$713$	4.85322e44	2.90497
$714$	3.35015e41	0.00196219
$715$	1.85271e44	1.06185
$716$	−3.81337e43	−0.213873
$717$	1.08704e44	0.596624
$718$	−2.58624e44	−1.38912
$719$	−1.87213e44	−0.984099	−0.492049	−	0.870567i	$-0.663752\pi$
$719$	−1.87213e44	−0.984099	−0.492049	+	0.870567i	$0.663752\pi$
$720$	5.96804e43	0.307028
$721$	−1.18741e43	−0.0597868
$722$	2.43005e44	1.19754
$723$	2.13962e44	1.03203
$724$	8.71953e43	0.411666
$725$	−8.33298e43	−0.385089
$726$	−2.87020e44	−1.29836
$727$	1.67518e44	0.741786	0.370893	−	0.928676i	$-0.379052\pi$
$727$	1.67518e44	0.741786	0.370893	+	0.928676i	$0.379052\pi$
$728$	−2.88826e42	−0.0125199
$729$	8.72796e42	0.0370370
$730$	−4.00945e43	−0.166564
$731$	−1.37200e43	−0.0558000
$732$	6.74382e43	0.268525
$733$	1.03836e42	0.00404795	0.00202398	−	0.999998i	$-0.499356\pi$
$733$	1.03836e42	0.00404795	0.00202398	+	0.999998i	$0.499356\pi$
$734$	9.29753e43	0.354878
$735$	1.17515e44	0.439175
$736$	−5.95781e44	−2.18012
$737$	−1.81879e44	−0.651684
$738$	3.44811e43	0.120978
$739$	−2.27325e44	−0.781013	−0.390506	−	0.920600i	$-0.627700\pi$
$739$	−2.27325e44	−0.781013	−0.390506	+	0.920600i	$0.627700\pi$
$740$	2.76870e44	0.931504
$741$	−4.24146e43	−0.139744
$742$	−1.73945e43	−0.0561243
$743$	1.80441e44	0.570175	0.285088	−	0.958501i	$-0.407977\pi$
$743$	1.80441e44	0.570175	0.285088	+	0.958501i	$0.407977\pi$
$744$	−1.14838e44	−0.355391
$745$	1.30742e44	0.396270
$746$	−1.93929e44	−0.575694
$747$	−8.63748e43	−0.251141
$748$	−2.77842e43	−0.0791268
$749$	1.22269e42	0.00341073
$750$	−2.98138e44	−0.814644
$751$	−2.36337e44	−0.632577	−0.316288	−	0.948663i	$-0.602437\pi$
$751$	−2.36337e44	−0.632577	−0.316288	+	0.948663i	$0.602437\pi$
$752$	5.30141e44	1.39000
$753$	7.54990e42	0.0193919
$754$	4.01840e44	1.01111
$755$	3.35494e43	0.0827002
$756$	2.13489e42	0.00515569
$757$	4.32773e44	1.02394	0.511970	−	0.859003i	$-0.328916\pi$
$757$	4.32773e44	1.02394	0.511970	+	0.859003i	$0.328916\pi$
$758$	1.31668e44	0.305216
$759$	−7.69256e44	−1.74712
$760$	−3.81164e43	−0.0848206
$761$	−6.80240e44	−1.48320	−0.741600	−	0.670842i	$-0.765933\pi$
$761$	−6.80240e44	−1.48320	−0.741600	+	0.670842i	$0.765933\pi$
$762$	9.44446e43	0.201779
$763$	9.22637e42	0.0193152
$764$	3.21887e44	0.660323
$765$	8.62482e42	0.0173379
$766$	−6.06622e44	−1.19501
$767$	−4.63418e44	−0.894633
$768$	4.00075e44	0.756906
$769$	9.20391e44	1.70653	0.853265	−	0.521477i	$-0.174619\pi$
$769$	9.20391e44	1.70653	0.853265	+	0.521477i	$0.174619\pi$
$770$	3.44372e43	0.0625780
$771$	4.06118e44	0.723285
$772$	−2.98629e44	−0.521272
$773$	5.85357e44	1.00147	0.500736	−	0.865600i	$-0.333063\pi$
$773$	5.85357e44	1.00147	0.500736	+	0.865600i	$0.333063\pi$
$774$	−2.11941e44	−0.355410
$775$	4.04517e44	0.664906
$776$	2.61195e44	0.420831
$777$	−2.42867e43	−0.0383569
$778$	5.80852e44	0.899252
$779$	−5.25281e43	−0.0797189
$780$	1.75329e44	0.260847
$781$	−1.22550e45	−1.78740
$782$	−1.14237e44	−0.163343
$783$	1.25968e44	0.176585
$784$	8.78485e44	1.20736
$785$	−4.45744e44	−0.600628
$786$	3.99032e44	0.527180
$787$	−2.17858e44	−0.282205	−0.141103	−	0.989995i	$-0.545065\pi$
$787$	−2.17858e44	−0.282205	−0.141103	+	0.989995i	$0.545065\pi$
$788$	−1.93338e44	−0.245562
$789$	7.91636e44	0.985899
$790$	−1.13081e45	−1.38092
$791$	1.06449e43	0.0127470
$792$	1.82024e44	0.213741
$793$	−4.85822e44	−0.559426
$794$	−1.09771e45	−1.23956
$795$	−4.47814e44	−0.495915
$796$	−1.82067e44	−0.197732
$797$	6.99196e44	0.744724	0.372362	−	0.928088i	$-0.378548\pi$
$797$	6.99196e44	0.744724	0.372362	+	0.928088i	$0.378548\pi$
$798$	−7.88381e42	−0.00823553
$799$	7.66143e43	0.0784937
$800$	−4.96585e44	−0.498998
$801$	−3.34927e44	−0.330100
$802$	1.97602e44	0.191024
$803$	−2.91683e44	−0.276580
$804$	−1.72119e44	−0.160088
$805$	5.84097e43	0.0532904
$806$	−1.95070e45	−1.74581
$807$	−2.52124e44	−0.221347
$808$	−3.40358e44	−0.293130
$809$	−2.96018e44	−0.250102	−0.125051	−	0.992150i	$-0.539909\pi$
$809$	−2.96018e44	−0.250102	−0.125051	+	0.992150i	$0.539909\pi$
$810$	1.33233e44	0.110432
$811$	−6.73556e44	−0.547709	−0.273855	−	0.961771i	$-0.588299\pi$
$811$	−6.73556e44	−0.547709	−0.273855	+	0.961771i	$0.588299\pi$
$812$	3.08122e43	0.0245813
$813$	3.96192e44	0.310101
$814$	4.88263e45	3.74952
$815$	1.78304e45	1.34344
$816$	6.44752e43	0.0476645
$817$	3.22868e44	0.234198
$818$	2.83934e45	2.02089
$819$	−1.53796e43	−0.0107410
$820$	2.17135e44	0.148804
$821$	−1.24266e45	−0.835667	−0.417833	−	0.908524i	$-0.637210\pi$
$821$	−1.24266e45	−0.835667	−0.417833	+	0.908524i	$0.637210\pi$
$822$	7.41988e44	0.489647
$823$	−5.23353e44	−0.338920	−0.169460	−	0.985537i	$-0.554202\pi$
$823$	−5.23353e44	−0.338920	−0.169460	+	0.985537i	$0.554202\pi$
$824$	−9.58077e44	−0.608876
$825$	−6.41176e44	−0.399891
$826$	−8.61377e43	−0.0527233
$827$	2.38140e45	1.43053	0.715266	−	0.698853i	$-0.246306\pi$
$827$	2.38140e45	1.43053	0.715266	+	0.698853i	$0.246306\pi$
$828$	−7.27975e44	−0.429186
$829$	−4.25365e44	−0.246131	−0.123066	−	0.992399i	$-0.539273\pi$
$829$	−4.25365e44	−0.246131	−0.123066	+	0.992399i	$0.539273\pi$
$830$	−1.31852e45	−0.748816
$831$	−1.88199e44	−0.104906
$832$	5.28137e44	0.288958
$833$	1.26956e44	0.0681797
$834$	−2.80833e45	−1.48038
$835$	−1.33546e45	−0.691020
$836$	6.53838e44	0.332103
$837$	−6.11501e44	−0.304897
$838$	−3.42449e45	−1.67615
$839$	6.06364e44	0.291355	0.145678	−	0.989332i	$-0.453464\pi$
$839$	6.06364e44	0.291355	0.145678	+	0.989332i	$0.453464\pi$
$840$	−1.38211e43	−0.00651949
$841$	−3.41363e44	−0.158081
$842$	−3.75610e43	−0.0170765
$843$	2.11025e45	0.941906
$844$	−1.39591e45	−0.611717
$845$	5.07498e44	0.218351
$846$	1.18351e45	0.499955
$847$	1.58545e44	0.0657598
$848$	−3.34765e45	−1.36334
$849$	−6.95118e44	−0.277965
$850$	−9.52165e43	−0.0373868
$851$	8.28153e45	3.19302
$852$	−1.15974e45	−0.439081
$853$	−3.44147e45	−1.27948	−0.639741	−	0.768591i	$-0.720958\pi$
$853$	−3.44147e45	−1.27948	−0.639741	+	0.768591i	$0.720958\pi$
$854$	−9.03020e43	−0.0329686
$855$	−2.02965e44	−0.0727691
$856$	9.86538e43	0.0347353
$857$	−5.71917e44	−0.197756	−0.0988781	−	0.995100i	$-0.531525\pi$
$857$	−5.71917e44	−0.197756	−0.0988781	+	0.995100i	$0.531525\pi$
$858$	3.09194e45	1.04997
$859$	4.01393e45	1.33868	0.669338	−	0.742958i	$-0.266578\pi$
$859$	4.01393e45	1.33868	0.669338	+	0.742958i	$0.266578\pi$
$860$	−1.33464e45	−0.437156
$861$	−1.90468e43	−0.00612736
$862$	−3.44952e45	−1.08992
$863$	−1.64027e45	−0.509035	−0.254517	−	0.967068i	$-0.581917\pi$
$863$	−1.64027e45	−0.509035	−0.254517	+	0.967068i	$0.581917\pi$
$864$	7.50679e44	0.228818
$865$	1.67474e45	0.501415
$866$	3.08757e45	0.908008
$867$	−1.98933e45	−0.574659
$868$	−1.49575e44	−0.0424427
$869$	−8.22649e45	−2.29302
$870$	1.92291e45	0.526515
$871$	1.23994e45	0.333517
$872$	7.44439e44	0.196709
$873$	1.39083e45	0.361039
$874$	2.68830e45	0.685567
$875$	1.64687e44	0.0412604
$876$	−2.76030e44	−0.0679428
$877$	6.35255e45	1.53622	0.768112	−	0.640316i	$-0.221197\pi$
$877$	6.35255e45	1.53622	0.768112	+	0.640316i	$0.221197\pi$
$878$	3.79750e44	0.0902262
$879$	−3.57840e45	−0.835335
$880$	6.62761e45	1.52011
$881$	−3.22548e45	−0.726888	−0.363444	−	0.931616i	$-0.618399\pi$
$881$	−3.22548e45	−0.726888	−0.363444	+	0.931616i	$0.618399\pi$
$882$	1.96117e45	0.434261
$883$	−5.42514e45	−1.18038	−0.590188	−	0.807266i	$-0.700946\pi$
$883$	−5.42514e45	−1.18038	−0.590188	+	0.807266i	$0.700946\pi$
$884$	1.89415e44	0.0404953
$885$	−2.21758e45	−0.465863
$886$	5.65499e45	1.16737
$887$	2.29821e45	0.466202	0.233101	−	0.972453i	$-0.425113\pi$
$887$	2.29821e45	0.466202	0.233101	+	0.972453i	$0.425113\pi$
$888$	−1.95960e45	−0.390631
$889$	−5.21696e43	−0.0102198
$890$	−5.11267e45	−0.984245
$891$	9.69255e44	0.183372
$892$	−2.82596e45	−0.525426
$893$	−1.80294e45	−0.329446
$894$	2.18191e45	0.391836
$895$	1.31458e45	0.232022
$896$	−1.63324e44	−0.0283319
$897$	5.24430e45	0.894137
$898$	−9.22077e45	−1.54520
$899$	−8.82561e45	−1.45368
$900$	−6.06768e44	−0.0982344
$901$	−4.83792e44	−0.0769882
$902$	3.82919e45	0.598970
$903$	1.17073e44	0.0180009
$904$	8.58897e44	0.129817
$905$	−3.00587e45	−0.446598
$906$	5.59896e44	0.0817749
$907$	−4.35319e45	−0.625021	−0.312510	−	0.949914i	$-0.601170\pi$
$907$	−4.35319e45	−0.625021	−0.312510	+	0.949914i	$0.601170\pi$
$908$	6.25710e45	0.883167
$909$	−1.81237e45	−0.251481
$910$	−2.34771e44	−0.0320260
$911$	−7.55541e44	−0.101327	−0.0506633	−	0.998716i	$-0.516134\pi$
$911$	−7.55541e44	−0.101327	−0.0506633	+	0.998716i	$0.516134\pi$
$912$	−1.51728e45	−0.200053
$913$	−9.59207e45	−1.24341
$914$	2.23577e45	0.284945
$915$	−2.32479e45	−0.291311
$916$	5.14079e45	0.633359
$917$	−2.20419e44	−0.0267008
$918$	1.43937e44	0.0171440
$919$	1.18945e46	1.39302	0.696509	−	0.717548i	$-0.254735\pi$
$919$	1.18945e46	1.39302	0.696509	+	0.717548i	$0.254735\pi$
$920$	4.71285e45	0.542716
$921$	9.51965e45	1.07794
$922$	−2.04251e46	−2.27423
$923$	8.35468e45	0.914752
$924$	2.37083e44	0.0255261
$925$	6.90267e45	0.730836
$926$	2.08956e46	2.17563
$927$	−5.10164e45	−0.522365
$928$	1.08343e46	1.09096
$929$	1.77410e46	1.75685	0.878427	−	0.477877i	$-0.158594\pi$
$929$	1.77410e46	1.75685	0.878427	+	0.477877i	$0.158594\pi$
$930$	−9.33459e45	−0.909096
$931$	−2.98762e45	−0.286157
$932$	−1.04860e46	−0.987791
$933$	4.41208e45	0.408769
$934$	−1.11884e46	−1.01951
$935$	9.57801e44	0.0858411
$936$	−1.24092e45	−0.109388
$937$	5.42429e45	0.470305	0.235152	−	0.971959i	$-0.424441\pi$
$937$	5.42429e45	0.470305	0.235152	+	0.971959i	$0.424441\pi$
$938$	2.30473e44	0.0196551
$939$	−3.91352e45	−0.328285
$940$	7.45280e45	0.614947
$941$	−1.40330e46	−1.13896	−0.569482	−	0.822004i	$-0.692856\pi$
$941$	−1.40330e46	−1.13896	−0.569482	+	0.822004i	$0.692856\pi$
$942$	−7.43888e45	−0.593907
$943$	6.49476e45	0.510073
$944$	−1.65776e46	−1.28073
$945$	−7.35956e43	−0.00559318
$946$	−2.35364e46	−1.75965
$947$	2.62358e45	0.192961	0.0964805	−	0.995335i	$-0.469241\pi$
$947$	2.62358e45	0.192961	0.0964805	+	0.995335i	$0.469241\pi$
$948$	−7.78502e45	−0.563288
$949$	1.98851e45	0.141547
$950$	2.24070e45	0.156916
$951$	3.24211e45	0.223373
$952$	−1.49315e43	−0.00101212
$953$	−2.10226e46	−1.40200	−0.700999	−	0.713162i	$-0.747262\pi$
$953$	−2.10226e46	−1.40200	−0.700999	+	0.713162i	$0.747262\pi$
$954$	−7.47343e45	−0.490366
$955$	−1.10964e46	−0.716355
$956$	1.14240e46	0.725639
$957$	1.39890e46	0.874281
$958$	1.56976e46	0.965311
$959$	−4.09862e44	−0.0247998
$960$	2.52728e45	0.150470
$961$	2.57740e46	1.50997
$962$	−3.32866e46	−1.91892
$963$	5.25320e44	0.0298000
$964$	2.24857e46	1.25520
$965$	1.02946e46	0.565505
$966$	9.74782e44	0.0526941
$967$	−2.60069e46	−1.38349	−0.691747	−	0.722140i	$-0.743159\pi$
$967$	−2.60069e46	−1.38349	−0.691747	+	0.722140i	$0.743159\pi$
$968$	1.27924e46	0.669706
$969$	−2.19272e44	−0.0112970
$970$	2.12311e46	1.07649
$971$	1.01344e46	0.505707	0.252854	−	0.967505i	$-0.418631\pi$
$971$	1.01344e46	0.505707	0.252854	+	0.967505i	$0.418631\pi$
$972$	9.17241e44	0.0450460
$973$	1.55127e45	0.0749790
$974$	1.28604e46	0.611773
$975$	4.37113e45	0.204655
$976$	−1.73790e46	−0.800855
$977$	−1.12179e46	−0.508800	−0.254400	−	0.967099i	$-0.581878\pi$
$977$	−1.12179e46	−0.508800	−0.254400	+	0.967099i	$0.581878\pi$
$978$	2.97567e46	1.32841
$979$	−3.71942e46	−1.63434
$980$	1.23499e46	0.534143
$981$	3.96405e45	0.168760
$982$	5.15287e45	0.215934
$983$	1.04662e46	0.431726	0.215863	−	0.976424i	$-0.430743\pi$
$983$	1.04662e46	0.431726	0.215863	+	0.976424i	$0.430743\pi$
$984$	−1.53681e45	−0.0624018
$985$	6.66492e45	0.266399
$986$	2.07740e45	0.0817388
$987$	−6.53751e44	−0.0253219
$988$	−4.45745e45	−0.169963
$989$	−3.99206e46	−1.49849
$990$	1.47957e46	0.546753
$991$	−2.02353e46	−0.736151	−0.368076	−	0.929796i	$-0.619983\pi$
$991$	−2.02353e46	−0.736151	−0.368076	+	0.929796i	$0.619983\pi$
$992$	−5.25942e46	−1.88368
$993$	7.73629e45	0.272784
$994$	1.55292e45	0.0539090
$995$	6.27635e45	0.214511
$996$	−9.07732e45	−0.305448
$997$	3.13226e46	1.03772	0.518862	−	0.854858i	$-0.326356\pi$
$997$	3.13226e46	1.03772	0.518862	+	0.854858i	$0.326356\pi$
$998$	3.35211e46	1.09344
$999$	−1.04346e46	−0.335129

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.32.a.a.1.1	✓	2	1.1	even	1	trivial
9.32.a.b.1.2		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)

\(f(q)\)	\(=\)	\(q-60460.2 q^{2} +1.43489e7 q^{3} +1.50796e9 q^{4} -5.19836e10 q^{5} -8.67538e11 q^{6} +4.79214e11 q^{7} +3.86659e13 q^{8} +2.05891e14 q^{9} +O(q^{10})\)	\(q-60460.2 q^{2} +1.43489e7 q^{3} +1.50796e9 q^{4} -5.19836e10 q^{5} -8.67538e11 q^{6} +4.79214e11 q^{7} +3.86659e13 q^{8} +2.05891e14 q^{9} +3.14294e15 q^{10} +2.28646e16 q^{11} +2.16375e16 q^{12} -1.55876e17 q^{13} -2.89734e16 q^{14} -7.45907e17 q^{15} -5.57606e18 q^{16} -8.05835e17 q^{17} -1.24482e19 q^{18} +1.89635e19 q^{19} -7.83890e19 q^{20} +6.87619e18 q^{21} -1.38240e21 q^{22} -2.34471e21 q^{23} +5.54813e20 q^{24} -1.95432e21 q^{25} +9.42429e21 q^{26} +2.95431e21 q^{27} +7.22634e20 q^{28} +4.26387e22 q^{29} +4.50977e22 q^{30} -2.06986e23 q^{31} +2.54096e23 q^{32} +3.28081e23 q^{33} +4.87210e22 q^{34} -2.49112e22 q^{35} +3.10475e23 q^{36} -3.53200e24 q^{37} -1.14654e24 q^{38} -2.23665e24 q^{39} -2.00999e24 q^{40} -2.76996e24 q^{41} -4.15736e23 q^{42} +1.70258e25 q^{43} +3.44788e25 q^{44} -1.07030e25 q^{45} +1.41762e26 q^{46} -9.50745e25 q^{47} -8.00104e25 q^{48} -1.57546e26 q^{49} +1.18159e26 q^{50} -1.15629e25 q^{51} -2.35054e26 q^{52} +6.00361e26 q^{53} -1.78618e26 q^{54} -1.18858e27 q^{55} +1.85292e25 q^{56} +2.72105e26 q^{57} -2.57795e27 q^{58} +2.97299e27 q^{59} -1.12480e27 q^{60} +3.11672e27 q^{61} +1.25144e28 q^{62} +9.86659e25 q^{63} -3.38819e27 q^{64} +8.10298e27 q^{65} -1.98359e28 q^{66} -7.95464e27 q^{67} -1.21517e27 q^{68} -3.36440e28 q^{69} +1.50614e27 q^{70} -5.35983e28 q^{71} +7.96096e27 q^{72} -1.27570e28 q^{73} +2.13546e29 q^{74} -2.80424e28 q^{75} +2.85961e28 q^{76} +1.09570e28 q^{77} +1.35228e29 q^{78} -3.59792e29 q^{79} +2.89864e29 q^{80} +4.23912e28 q^{81} +1.67473e29 q^{82} -4.19517e29 q^{83} +1.03690e28 q^{84} +4.18902e28 q^{85} -1.02938e30 q^{86} +6.11819e29 q^{87} +8.84079e29 q^{88} -1.62672e30 q^{89} +6.47103e29 q^{90} -7.46979e28 q^{91} -3.53573e30 q^{92} -2.97002e30 q^{93} +5.74823e30 q^{94} -9.85790e29 q^{95} +3.64600e30 q^{96} +6.75518e30 q^{97} +9.52525e30 q^{98} +4.70761e30 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 39528 q^{2} + 28697814 q^{3} - 201366976 q^{4} - 7930517220 q^{5} - 567183595896 q^{6} - 10488874236176 q^{7} - 42065768434176 q^{8} + 411782264189298 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more