LMFDB - Embedded newform 25.34.a.d.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,34,Mod(1,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 34, names="a")

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

chi := DirichletCharacter("25.1");

S:= CuspForms(chi, 34);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 34 $
Character orbit:	$[\chi]$	$=$	25.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:	$172.457072203$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - x^{10} - 71909733210 x^{9} - 392361971317440 x^{8} + \cdots + 13\!\cdots\!48 $ x^11 - x^10 - 71909733210x^9 - 392361971317440x^8 + 1789020862523351140800x^7 + 15057968169589785919302432x^6 - 18240376108577281349602470726592x^5 - 118793082389247521352101537474727680x^4 + 70339384981314044531499864093672157167360x^3 - 93184212295829066424280494839341830566058240x^2 - 66043164692761651440492767327962940420438352419328*x + 13944892725752680722269718925910686764312949634715648
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{47}\cdot 3^{12}\cdot 5^{30}\cdot 7^{2}\cdot 11^{3} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-99441.3$ of defining polynomial
Character	$\chi$	$=$	25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-100295. q^{2} -1.18201e8 q^{3} +1.46921e9 q^{4} +1.18550e13 q^{6} -1.07417e13 q^{7} +7.14175e14 q^{8} +8.41244e15 q^{9} +O(q^{10})$	\(q-100295. q^{2} -1.18201e8 q^{3} +1.46921e9 q^{4} +1.18550e13 q^{6} -1.07417e13 q^{7} +7.14175e14 q^{8} +8.41244e15 q^{9} +2.38218e17 q^{11} -1.73662e17 q^{12} +1.09650e18 q^{13} +1.07734e18 q^{14} -8.42488e19 q^{16} -2.82710e20 q^{17} -8.43728e20 q^{18} +4.67870e20 q^{19} +1.26968e21 q^{21} -2.38922e22 q^{22} +1.10068e21 q^{23} -8.44163e22 q^{24} -1.09973e23 q^{26} -3.37272e23 q^{27} -1.57817e22 q^{28} +1.88825e24 q^{29} -7.01821e24 q^{31} +2.31504e24 q^{32} -2.81577e25 q^{33} +2.83544e25 q^{34} +1.23596e25 q^{36} -6.16972e25 q^{37} -4.69252e25 q^{38} -1.29607e26 q^{39} +2.46253e25 q^{41} -1.27343e26 q^{42} -2.92621e25 q^{43} +3.49992e26 q^{44} -1.10393e26 q^{46} +4.02156e27 q^{47} +9.95830e27 q^{48} -7.61561e27 q^{49} +3.34166e28 q^{51} +1.61098e27 q^{52} -4.79966e28 q^{53} +3.38268e28 q^{54} -7.67144e27 q^{56} -5.53028e28 q^{57} -1.89382e29 q^{58} +1.22509e29 q^{59} +7.09485e28 q^{61} +7.03894e29 q^{62} -9.03637e28 q^{63} +4.91504e29 q^{64} +2.82408e30 q^{66} +4.28703e29 q^{67} -4.15359e29 q^{68} -1.30102e29 q^{69} +6.98564e30 q^{71} +6.00795e30 q^{72} -5.69333e30 q^{73} +6.18794e30 q^{74} +6.87398e29 q^{76} -2.55887e30 q^{77} +1.29990e31 q^{78} +2.53634e31 q^{79} -6.89932e30 q^{81} -2.46981e30 q^{82} -6.16471e31 q^{83} +1.86542e30 q^{84} +2.93485e30 q^{86} -2.23193e32 q^{87} +1.70130e32 q^{88} +1.29871e32 q^{89} -1.17782e31 q^{91} +1.61713e30 q^{92} +8.29560e32 q^{93} -4.03344e32 q^{94} -2.73640e32 q^{96} -4.34255e32 q^{97} +7.63810e32 q^{98} +2.00400e33 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 9393 q^{2} - 80330849 q^{3} + 49338206677 q^{4} - 17783977676723 q^{6} - 21344025107658 q^{7} + 970199832420105 q^{8} + 24\!\cdots\!58 q^{9}+O(q^{10}) $ 11 * q - 9393 * q^2 - 80330849 * q^3 + 49338206677 * q^4 - 17783977676723 * q^6 - 21344025107658 * q^7 + 970199832420105 * q^8 + 24299637974625658 * q^9	$ 11 q - 9393 q^{2} - 80330849 q^{3} + 49338206677 q^{4} - 17783977676723 q^{6} - 21344025107658 q^{7} + 970199832420105 q^{8} + 24\!\cdots\!58 q^{9}+ \cdots + 13\!\cdots\!06 q^{99}+O(q^{100}) $ 11 * q - 9393 * q^2 - 80330849 * q^3 + 49338206677 * q^4 - 17783977676723 * q^6 - 21344025107658 * q^7 + 970199832420105 * q^8 + 24299637974625658 * q^9 - 194487534567113523 * q^11 - 1128411534853252093 * q^12 - 5151173641795199804 * q^13 + 9695004297667451034 * q^14 + 287795879559665379601 * q^16 - 217450883530375665663 * q^17 + 883205358438912773746 * q^18 - 2304421397121542404315 * q^19 + 3951679538424255448062 * q^21 - 65697936516541243081001 * q^22 - 39745489889804460665334 * q^23 - 202096278074290714435545 * q^24 + 232341332678498439460092 * q^26 - 215757396930304201071995 * q^27 + 1844234528929870945073094 * q^28 + 1675632286595729558796840 * q^29 - 1879684496680578139929438 * q^31 + 22333622446463598116694177 * q^32 + 36653442436454147951147057 * q^33 - 44873360881289881717450051 * q^34 + 193677686753165783059502006 * q^36 - 180277972113296426057413198 * q^37 - 216179528860395412757129505 * q^38 - 359172746626046600427282844 * q^39 + 549519804753897528529573167 * q^41 - 2593357144102832185922898306 * q^42 - 50270064758017307324647244 * q^43 - 2976543624086726877274410711 * q^44 + 1688362231334867471013357582 * q^46 - 10903258570108047175558188228 * q^47 - 28193416941275907016447196209 * q^48 - 2501658924474402528580483073 * q^49 + 66317965316246498072666600557 * q^51 - 155672232460399094184759234028 * q^52 - 33298643916770080171872677874 * q^53 - 213393152239696124781888030065 * q^54 + 339537122636968128125815064910 * q^56 - 159006470550216362740785378215 * q^57 - 62377017575001287720537209120 * q^58 - 67706990548480155796584121920 * q^59 - 344769258471797286249471450898 * q^61 + 1319517422843123577963573948294 * q^62 + 699283498025109144495841661076 * q^63 + 1420026267960910564014627900737 * q^64 - 160016657586606697551149537011 * q^66 + 1671796054942808947714198855437 * q^67 - 3088683653934580261727419953441 * q^68 + 7218504661993692063958711761426 * q^69 - 5525905608449961693610592189868 * q^71 + 21423093069732612399854192774190 * q^72 - 1280933432508086429255473349609 * q^73 + 8483102027446485651051216797154 * q^74 - 3794387798301159395171650466255 * q^76 + 25187595245022035764699127942394 * q^77 + 56671274702179561872150030862772 * q^78 + 28416813573575354189758739594190 * q^79 - 4511447703484319172258978381029 * q^81 - 94213252968905060003342215055821 * q^82 - 127792566726367853829683612248839 * q^83 - 299946577157245367261151073271766 * q^84 + 455910432123816097591159189088412 * q^86 - 485010641407021414487926087945160 * q^87 - 5212296644003692182363473725515 * q^88 - 24030870261451879999370600550555 * q^89 - 346687858887153608395037323300248 * q^91 - 535778496942575427226503821168238 * q^92 - 789528086332099641022541300872758 * q^93 + 232538212076560959503267655560444 * q^94 - 1842110282591420302371913525952353 * q^96 + 674692794164529660649398963528122 * q^97 + 2571899453674006542996540156918099 * q^98 + 1300949547786735016969037553636806 * 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 $

$2$	−100295.	−1.08215	−0.541073	−	0.840976i	$-0.681982\pi$
$2$	−100295.	−1.08215	−0.541073	+	0.840976i	$0.681982\pi$
$3$	−1.18201e8	−1.58533	−0.792667	−	0.609655i	$-0.791308\pi$
$3$	−1.18201e8	−1.58533	−0.792667	+	0.609655i	$0.791308\pi$
$4$	1.46921e9	0.171038
$5$	0	0
$5$	0	0
$6$	1.18550e13	1.71556
$7$	−1.07417e13	−0.122167	−0.0610836	−	0.998133i	$-0.519456\pi$
$7$	−1.07417e13	−0.122167	−0.0610836	+	0.998133i	$0.519456\pi$
$8$	7.14175e14	0.897057
$9$	8.41244e15	1.51328
$10$	0	0
$11$	2.38218e17	1.56313	0.781567	−	0.623822i	$-0.214421\pi$
$11$	2.38218e17	1.56313	0.781567	+	0.623822i	$0.214421\pi$
$12$	−1.73662e17	−0.271153
$13$	1.09650e18	0.457027	0.228514	−	0.973541i	$-0.426613\pi$
$13$	1.09650e18	0.457027	0.228514	+	0.973541i	$0.426613\pi$
$14$	1.07734e18	0.132203
$15$	0	0
$16$	−8.42488e19	−1.14178
$17$	−2.82710e20	−1.40907	−0.704536	−	0.709668i	$-0.748845\pi$
$17$	−2.82710e20	−1.40907	−0.704536	+	0.709668i	$0.748845\pi$
$18$	−8.43728e20	−1.63759
$19$	4.67870e20	0.372127	0.186063	−	0.982538i	$-0.440427\pi$
$19$	4.67870e20	0.372127	0.186063	+	0.982538i	$0.440427\pi$
$20$	0	0
$21$	1.26968e21	0.193676
$22$	−2.38922e22	−1.69154
$23$	1.10068e21	0.0374241	0.0187121	−	0.999825i	$-0.494043\pi$
$23$	1.10068e21	0.0374241	0.0187121	+	0.999825i	$0.494043\pi$
$24$	−8.44163e22	−1.42214
$25$	0	0
$26$	−1.09973e23	−0.494570
$27$	−3.37272e23	−0.813726
$28$	−1.57817e22	−0.0208952
$29$	1.88825e24	1.40117	0.700587	−	0.713567i	$-0.252922\pi$
$29$	1.88825e24	1.40117	0.700587	+	0.713567i	$0.252922\pi$
$30$	0	0
$31$	−7.01821e24	−1.73284	−0.866420	−	0.499315i	$-0.833585\pi$
$31$	−7.01821e24	−1.73284	−0.866420	+	0.499315i	$0.833585\pi$
$32$	2.31504e24	0.338519
$33$	−2.81577e25	−2.47809
$34$	2.83544e25	1.52482
$35$	0	0
$36$	1.23596e25	0.258829
$37$	−6.16972e25	−0.822124	−0.411062	−	0.911607i	$-0.634842\pi$
$37$	−6.16972e25	−0.822124	−0.411062	+	0.911607i	$0.634842\pi$
$38$	−4.69252e25	−0.402695
$39$	−1.29607e26	−0.724540
$40$	0	0
$41$	2.46253e25	0.0603182	0.0301591	−	0.999545i	$-0.490399\pi$
$41$	2.46253e25	0.0603182	0.0301591	+	0.999545i	$0.490399\pi$
$42$	−1.27343e26	−0.209585
$43$	−2.92621e25	−0.0326645	−0.0163322	−	0.999867i	$-0.505199\pi$
$43$	−2.92621e25	−0.0326645	−0.0163322	+	0.999867i	$0.505199\pi$
$44$	3.49992e26	0.267355
$45$	0	0
$46$	−1.10393e26	−0.0404983
$47$	4.02156e27	1.03462	0.517309	−	0.855799i	$-0.326934\pi$
$47$	4.02156e27	1.03462	0.517309	+	0.855799i	$0.326934\pi$
$48$	9.95830e27	1.81011
$49$	−7.61561e27	−0.985075
$50$	0	0
$51$	3.34166e28	2.23385
$52$	1.61098e27	0.0781691
$53$	−4.79966e28	−1.70082	−0.850410	−	0.526121i	$-0.823646\pi$
$53$	−4.79966e28	−1.70082	−0.850410	+	0.526121i	$0.823646\pi$
$54$	3.38268e28	0.880570
$55$	0	0
$56$	−7.67144e27	−0.109591
$57$	−5.53028e28	−0.589946
$58$	−1.89382e29	−1.51627
$59$	1.22509e29	0.739790	0.369895	−	0.929074i	$-0.379394\pi$
$59$	1.22509e29	0.739790	0.369895	+	0.929074i	$0.379394\pi$
$60$	0	0
$61$	7.09485e28	0.247173	0.123586	−	0.992334i	$-0.460560\pi$
$61$	7.09485e28	0.247173	0.123586	+	0.992334i	$0.460560\pi$
$62$	7.03894e29	1.87518
$63$	−9.03637e28	−0.184874
$64$	4.91504e29	0.775457
$65$	0	0
$66$	2.82408e30	2.68165
$67$	4.28703e29	0.317630	0.158815	−	0.987308i	$-0.449233\pi$
$67$	4.28703e29	0.317630	0.158815	+	0.987308i	$0.449233\pi$
$68$	−4.15359e29	−0.241005
$69$	−1.30102e29	−0.0593298
$70$	0	0
$71$	6.98564e30	1.98812	0.994061	−	0.108822i	$-0.0347078\pi$
$71$	6.98564e30	1.98812	0.994061	+	0.108822i	$0.0347078\pi$
$72$	6.00795e30	1.35750
$73$	−5.69333e30	−1.02456	−0.512282	−	0.858817i	$-0.671200\pi$
$73$	−5.69333e30	−1.02456	−0.512282	+	0.858817i	$0.671200\pi$
$74$	6.18794e30	0.889657
$75$	0	0
$76$	6.87398e29	0.0636479
$77$	−2.55887e30	−0.190964
$78$	1.29990e31	0.784058
$79$	2.53634e31	1.23983	0.619913	−	0.784671i	$-0.287168\pi$
$79$	2.53634e31	1.23983	0.619913	+	0.784671i	$0.287168\pi$
$80$	0	0
$81$	−6.89932e30	−0.223256
$82$	−2.46981e30	−0.0652731
$83$	−6.16471e31	−1.33390	−0.666951	−	0.745102i	$-0.732401\pi$
$83$	−6.16471e31	−1.33390	−0.666951	+	0.745102i	$0.732401\pi$
$84$	1.86542e30	0.0331259
$85$	0	0
$86$	2.93485e30	0.0353477
$87$	−2.23193e32	−2.22133
$88$	1.70130e32	1.40222
$89$	1.29871e32	0.888337	0.444168	−	0.895943i	$-0.353499\pi$
$89$	1.29871e32	0.888337	0.444168	+	0.895943i	$0.353499\pi$
$90$	0	0
$91$	−1.17782e31	−0.0558337
$92$	1.61713e30	0.00640095
$93$	8.29560e32	2.74713
$94$	−4.03344e32	−1.11961
$95$	0	0
$96$	−2.73640e32	−0.536666
$97$	−4.34255e32	−0.717812	−0.358906	−	0.933374i	$-0.616850\pi$
$97$	−4.34255e32	−0.717812	−0.358906	+	0.933374i	$0.616850\pi$
$98$	7.63810e32	1.06599
$99$	2.00400e33	2.36546
$100$	0	0
$101$	−2.04084e33	−1.73183	−0.865917	−	0.500187i	$-0.833264\pi$
$101$	−2.04084e33	−1.73183	−0.865917	+	0.500187i	$0.833264\pi$
$102$	−3.35153e33	−2.41735
$103$	−1.31588e33	−0.807982	−0.403991	−	0.914763i	$-0.632377\pi$
$103$	−1.31588e33	−0.807982	−0.403991	+	0.914763i	$0.632377\pi$
$104$	7.83091e32	0.409979
$105$	0	0
$106$	4.81383e33	1.84053
$107$	1.85120e33	0.606207	0.303104	−	0.952958i	$-0.401977\pi$
$107$	1.85120e33	0.606207	0.303104	+	0.952958i	$0.401977\pi$
$108$	−4.95522e32	−0.139178
$109$	6.95162e33	1.67706	0.838531	−	0.544855i	$-0.183415\pi$
$109$	6.95162e33	1.67706	0.838531	+	0.544855i	$0.183415\pi$
$110$	0	0
$111$	7.29268e33	1.30334
$112$	9.04974e32	0.139489
$113$	1.10974e34	1.47716	0.738581	−	0.674164i	$-0.235496\pi$
$113$	1.10974e34	1.47716	0.738581	+	0.674164i	$0.235496\pi$
$114$	5.54661e33	0.638407
$115$	0	0
$116$	2.77422e33	0.239654
$117$	9.22421e33	0.691612
$118$	−1.22870e34	−0.800560
$119$	3.03678e33	0.172142
$120$	0	0
$121$	3.35229e34	1.44339
$122$	−7.11579e33	−0.267477
$123$	−2.91074e33	−0.0956245
$124$	−1.03112e34	−0.296382
$125$	0	0
$126$	9.06305e33	0.200060
$127$	−9.12271e32	−0.0176751	−0.00883757	−	0.999961i	$-0.502813\pi$
$127$	−9.12271e32	−0.0176751	−0.00883757	+	0.999961i	$0.502813\pi$
$128$	−6.91816e34	−1.17768
$129$	3.45881e33	0.0517841
$130$	0	0
$131$	−1.56684e35	−1.81990	−0.909950	−	0.414718i	$-0.863880\pi$
$131$	−1.56684e35	−1.81990	−0.909950	+	0.414718i	$0.863880\pi$
$132$	−4.13694e34	−0.423848
$133$	−5.02571e33	−0.0454617
$134$	−4.29969e34	−0.343722
$135$	0	0
$136$	−2.01904e35	−1.26402
$137$	2.80790e35	1.55773	0.778865	−	0.627191i	$-0.215796\pi$
$137$	2.80790e35	1.55773	0.778865	+	0.627191i	$0.215796\pi$
$138$	1.30486e34	0.0642034
$139$	−3.00000e35	−1.31032	−0.655160	−	0.755490i	$-0.727399\pi$
$139$	−3.00000e35	−1.31032	−0.655160	+	0.755490i	$0.727399\pi$
$140$	0	0
$141$	−4.75353e35	−1.64022
$142$	−7.00626e35	−2.15144
$143$	2.61206e35	0.714394
$144$	−7.08738e35	−1.72784
$145$	0	0
$146$	5.71015e35	1.10873
$147$	9.00173e35	1.56167
$148$	−9.06460e34	−0.140615
$149$	9.25696e33	0.0128498	0.00642488	−	0.999979i	$-0.497955\pi$
$149$	9.25696e33	0.0128498	0.00642488	+	0.999979i	$0.497955\pi$
$150$	0	0
$151$	−4.37112e35	−0.486938	−0.243469	−	0.969909i	$-0.578285\pi$
$151$	−4.37112e35	−0.486938	−0.243469	+	0.969909i	$0.578285\pi$
$152$	3.34141e35	0.333819
$153$	−2.37828e36	−2.13233
$154$	2.56642e35	0.206650
$155$	0	0
$156$	−1.90420e35	−0.123924
$157$	−5.98664e35	−0.350622	−0.175311	−	0.984513i	$-0.556093\pi$
$157$	−5.98664e35	−0.350622	−0.175311	+	0.984513i	$0.556093\pi$
$158$	−2.54383e36	−1.34167
$159$	5.67325e36	2.69637
$160$	0	0
$161$	−1.18232e34	−0.00457200
$162$	6.91969e35	0.241596
$163$	−7.06844e35	−0.222961	−0.111480	−	0.993767i	$-0.535559\pi$
$163$	−7.06844e35	−0.222961	−0.111480	+	0.993767i	$0.535559\pi$
$164$	3.61797e34	0.0103167
$165$	0	0
$166$	6.18291e36	1.44348
$167$	−3.67014e36	−0.775999	−0.387999	−	0.921660i	$-0.626834\pi$
$167$	−3.67014e36	−0.775999	−0.387999	+	0.921660i	$0.626834\pi$
$168$	9.06773e35	0.173738
$169$	−4.55383e36	−0.791126
$170$	0	0
$171$	3.93593e36	0.563134
$172$	−4.29920e34	−0.00558687
$173$	6.08763e36	0.718931	0.359466	−	0.933158i	$-0.382959\pi$
$173$	6.08763e36	0.718931	0.359466	+	0.933158i	$0.382959\pi$
$174$	2.23852e37	2.40380
$175$	0	0
$176$	−2.00696e37	−1.78476
$177$	−1.44806e37	−1.17281
$178$	−1.30255e37	−0.961309
$179$	1.93784e37	1.30390	0.651948	−	0.758264i	$-0.273952\pi$
$179$	1.93784e37	1.30390	0.651948	+	0.758264i	$0.273952\pi$
$180$	0	0
$181$	−1.38808e36	−0.0777529	−0.0388765	−	0.999244i	$-0.512378\pi$
$181$	−1.38808e36	−0.0777529	−0.0388765	+	0.999244i	$0.512378\pi$
$182$	1.18130e36	0.0604202
$183$	−8.38618e36	−0.391851
$184$	7.86078e35	0.0335716
$185$	0	0
$186$	−8.32010e37	−2.97279
$187$	−6.73466e37	−2.20257
$188$	5.90851e36	0.176959
$189$	3.62287e36	0.0994106
$190$	0	0
$191$	−5.84448e36	−0.134802	−0.0674008	−	0.997726i	$-0.521471\pi$
$191$	−5.84448e36	−0.134802	−0.0674008	+	0.997726i	$0.521471\pi$
$192$	−5.80964e37	−1.22936
$193$	−6.95190e37	−1.35023	−0.675115	−	0.737712i	$-0.735906\pi$
$193$	−6.95190e37	−1.35023	−0.675115	+	0.737712i	$0.735906\pi$
$194$	4.35537e37	0.776777
$195$	0	0
$196$	−1.11889e37	−0.168485
$197$	4.77416e37	0.661004	0.330502	−	0.943805i	$-0.392782\pi$
$197$	4.77416e37	0.661004	0.330502	+	0.943805i	$0.392782\pi$
$198$	−2.00991e38	−2.55978
$199$	−4.17107e37	−0.488846	−0.244423	−	0.969669i	$-0.578599\pi$
$199$	−4.17107e37	−0.488846	−0.244423	+	0.969669i	$0.578599\pi$
$200$	0	0
$201$	−5.06731e37	−0.503550
$202$	2.04687e38	1.87410
$203$	−2.02829e37	−0.171177
$204$	4.90959e37	0.382074
$205$	0	0
$206$	1.31976e38	0.874354
$207$	9.25940e36	0.0566333
$208$	−9.23785e37	−0.521826
$209$	1.11455e38	0.581684
$210$	0	0
$211$	−1.72498e38	−0.769348	−0.384674	−	0.923052i	$-0.625686\pi$
$211$	−1.72498e38	−0.769348	−0.384674	+	0.923052i	$0.625686\pi$
$212$	−7.05169e37	−0.290905
$213$	−8.25710e38	−3.15184
$214$	−1.85667e38	−0.656004
$215$	0	0
$216$	−2.40871e38	−0.729959
$217$	7.53874e37	0.211696
$218$	−6.97215e38	−1.81482
$219$	6.72958e38	1.62428
$220$	0	0
$221$	−3.09990e38	−0.643984
$222$	−7.31421e38	−1.41040
$223$	5.99984e37	0.107426	0.0537130	−	0.998556i	$-0.482894\pi$
$223$	5.99984e37	0.107426	0.0537130	+	0.998556i	$0.482894\pi$
$224$	−2.48674e37	−0.0413559
$225$	0	0
$226$	−1.11302e39	−1.59850
$227$	−3.73826e38	−0.499164	−0.249582	−	0.968354i	$-0.580293\pi$
$227$	−3.73826e38	−0.499164	−0.249582	+	0.968354i	$0.580293\pi$
$228$	−8.12512e37	−0.100903
$229$	8.71546e38	1.00694	0.503472	−	0.864012i	$-0.332056\pi$
$229$	8.71546e38	1.00694	0.503472	+	0.864012i	$0.332056\pi$
$230$	0	0
$231$	3.02461e38	0.302741
$232$	1.34854e39	1.25693
$233$	2.14446e39	1.86185	0.930925	−	0.365210i	$-0.119003\pi$
$233$	2.14446e39	1.86185	0.930925	+	0.365210i	$0.119003\pi$
$234$	−9.25144e38	−0.748424
$235$	0	0
$236$	1.79990e38	0.126532
$237$	−2.99798e39	−1.96554
$238$	−3.04574e38	−0.186283
$239$	7.11923e38	0.406320	0.203160	−	0.979146i	$-0.434879\pi$
$239$	7.11923e38	0.406320	0.203160	+	0.979146i	$0.434879\pi$
$240$	0	0
$241$	−1.59013e39	−0.790957	−0.395478	−	0.918475i	$-0.629421\pi$
$241$	−1.59013e39	−0.790957	−0.395478	+	0.918475i	$0.629421\pi$
$242$	−3.36218e39	−1.56195
$243$	2.69042e39	1.16766
$244$	1.04238e38	0.0422760
$245$	0	0
$246$	2.91934e38	0.103480
$247$	5.13018e38	0.170072
$248$	−5.01223e39	−1.55446
$249$	7.28675e39	2.11468
$250$	0	0
$251$	1.75524e39	0.446395	0.223198	−	0.974773i	$-0.428351\pi$
$251$	1.75524e39	0.446395	0.223198	+	0.974773i	$0.428351\pi$
$252$	−1.32763e38	−0.0316204
$253$	2.62202e38	0.0584989
$254$	9.14965e37	0.0191271
$255$	0	0
$256$	2.71659e39	0.498960
$257$	9.54443e39	1.64382	0.821909	−	0.569619i	$-0.192909\pi$
$257$	9.54443e39	1.64382	0.821909	+	0.569619i	$0.192909\pi$
$258$	−3.46902e38	−0.0560379
$259$	6.62732e38	0.100437
$260$	0	0
$261$	1.58848e40	2.12037
$262$	1.57146e40	1.96940
$263$	9.19136e39	1.08171	0.540854	−	0.841117i	$-0.318101\pi$
$263$	9.19136e39	1.08171	0.540854	+	0.841117i	$0.318101\pi$
$264$	−2.01095e40	−2.22299
$265$	0	0
$266$	5.04055e38	0.0491962
$267$	−1.53509e40	−1.40831
$268$	6.29853e38	0.0543269
$269$	7.25506e39	0.588475	0.294238	−	0.955732i	$-0.404934\pi$
$269$	7.25506e39	0.588475	0.294238	+	0.955732i	$0.404934\pi$
$270$	0	0
$271$	7.67052e39	0.550594	0.275297	−	0.961359i	$-0.411224\pi$
$271$	7.67052e39	0.550594	0.275297	+	0.961359i	$0.411224\pi$
$272$	2.38179e40	1.60886
$273$	1.39220e39	0.0885151
$274$	−2.81619e40	−1.68569
$275$	0	0
$276$	−1.91146e38	−0.0101477
$277$	−2.75284e40	−1.37678	−0.688389	−	0.725341i	$-0.741682\pi$
$277$	−2.75284e40	−1.37678	−0.688389	+	0.725341i	$0.741682\pi$
$278$	3.00886e40	1.41796
$279$	−5.90403e40	−2.62228
$280$	0	0
$281$	−2.80354e40	−1.10676	−0.553379	−	0.832930i	$-0.686662\pi$
$281$	−2.80354e40	−1.10676	−0.553379	+	0.832930i	$0.686662\pi$
$282$	4.76757e40	1.77495
$283$	2.01665e40	0.708196	0.354098	−	0.935208i	$-0.384788\pi$
$283$	2.01665e40	0.708196	0.354098	+	0.935208i	$0.384788\pi$
$284$	1.02633e40	0.340045
$285$	0	0
$286$	−2.61977e40	−0.773078
$287$	−2.64517e38	−0.00736891
$288$	1.94751e40	0.512275
$289$	3.96703e40	0.985486
$290$	0	0
$291$	5.13294e40	1.13797
$292$	−8.36468e39	−0.175240
$293$	−1.20254e40	−0.238113	−0.119057	−	0.992887i	$-0.537987\pi$
$293$	−1.20254e40	−0.238113	−0.119057	+	0.992887i	$0.537987\pi$
$294$	−9.02831e40	−1.68996
$295$	0	0
$296$	−4.40626e40	−0.737492
$297$	−8.03444e40	−1.27196
$298$	−9.28430e38	−0.0139053
$299$	1.20689e39	0.0171038
$300$	0	0
$301$	3.14324e38	0.00399053
$302$	4.38403e40	0.526937
$303$	2.41230e41	2.74554
$304$	−3.94175e40	−0.424889
$305$	0	0
$306$	2.38530e41	2.30749
$307$	1.15318e41	1.05709	0.528547	−	0.848904i	$-0.322737\pi$
$307$	1.15318e41	1.05709	0.528547	+	0.848904i	$0.322737\pi$
$308$	−3.75950e39	−0.0326621
$309$	1.55538e41	1.28092
$310$	0	0
$311$	1.68995e41	1.25120	0.625600	−	0.780144i	$-0.284854\pi$
$311$	1.68995e41	1.25120	0.625600	+	0.780144i	$0.284854\pi$
$312$	−9.25622e40	−0.649954
$313$	1.81722e41	1.21039	0.605197	−	0.796076i	$-0.293094\pi$
$313$	1.81722e41	1.21039	0.605197	+	0.796076i	$0.293094\pi$
$314$	6.00431e40	0.379424
$315$	0	0
$316$	3.72641e40	0.212058
$317$	2.26568e41	1.22383	0.611916	−	0.790923i	$-0.290399\pi$
$317$	2.26568e41	1.22383	0.611916	+	0.790923i	$0.290399\pi$
$318$	−5.69000e41	−2.91786
$319$	4.49815e41	2.19022
$320$	0	0
$321$	−2.18814e41	−0.961041
$322$	1.18581e39	0.00494757
$323$	−1.32271e41	−0.524354
$324$	−1.01365e40	−0.0381853
$325$	0	0
$326$	7.08931e40	0.241276
$327$	−8.21689e41	−2.65870
$328$	1.75868e40	0.0541089
$329$	−4.31983e40	−0.126396
$330$	0	0
$331$	−1.08689e41	−0.287755	−0.143877	−	0.989596i	$-0.545957\pi$
$331$	−1.08689e41	−0.287755	−0.143877	+	0.989596i	$0.545957\pi$
$332$	−9.05723e40	−0.228148
$333$	−5.19024e41	−1.24411
$334$	3.68098e41	0.839743
$335$	0	0
$336$	−1.06969e41	−0.221136
$337$	5.97224e41	1.17556	0.587779	−	0.809022i	$-0.300003\pi$
$337$	5.97224e41	1.17556	0.587779	+	0.809022i	$0.300003\pi$
$338$	4.56727e41	0.856114
$339$	−1.31173e42	−2.34180
$340$	0	0
$341$	−1.67187e42	−2.70866
$342$	−3.94755e41	−0.609392
$343$	1.64848e41	0.242511
$344$	−2.08983e40	−0.0293019
$345$	0	0
$346$	−6.10560e41	−0.777988
$347$	−2.05995e41	−0.250277	−0.125138	−	0.992139i	$-0.539938\pi$
$347$	−2.05995e41	−0.250277	−0.125138	+	0.992139i	$0.539938\pi$
$348$	−3.27916e41	−0.379932
$349$	1.68049e41	0.185702	0.0928510	−	0.995680i	$-0.470402\pi$
$349$	1.68049e41	0.185702	0.0928510	+	0.995680i	$0.470402\pi$
$350$	0	0
$351$	−3.69818e41	−0.371895
$352$	5.51484e41	0.529150
$353$	−1.30886e42	−1.19842	−0.599211	−	0.800591i	$-0.704519\pi$
$353$	−1.30886e42	−1.19842	−0.599211	+	0.800591i	$0.704519\pi$
$354$	1.45234e42	1.26915
$355$	0	0
$356$	1.90808e41	0.151939
$357$	−3.58950e41	−0.272903
$358$	−1.94356e42	−1.41100
$359$	−1.19927e42	−0.831494	−0.415747	−	0.909480i	$-0.636480\pi$
$359$	−1.19927e42	−0.831494	−0.415747	+	0.909480i	$0.636480\pi$
$360$	0	0
$361$	−1.36187e42	−0.861522
$362$	1.39217e41	0.0841400
$363$	−3.96244e42	−2.28825
$364$	−1.73046e40	−0.00954969
$365$	0	0
$366$	8.41095e41	0.424040
$367$	−1.58763e42	−0.765172	−0.382586	−	0.923920i	$-0.624966\pi$
$367$	−1.58763e42	−0.765172	−0.382586	+	0.923920i	$0.624966\pi$
$368$	−9.27310e40	−0.0427303
$369$	2.07159e41	0.0912786
$370$	0	0
$371$	5.15564e41	0.207784
$372$	1.21880e42	0.469864
$373$	2.64106e42	0.974052	0.487026	−	0.873387i	$-0.338082\pi$
$373$	2.64106e42	0.974052	0.487026	+	0.873387i	$0.338082\pi$
$374$	6.75455e42	2.38350
$375$	0	0
$376$	2.87210e42	0.928112
$377$	2.07046e42	0.640374
$378$	−3.63357e41	−0.107577
$379$	−4.63222e42	−1.31293	−0.656466	−	0.754355i	$-0.727950\pi$
$379$	−4.63222e42	−1.31293	−0.656466	+	0.754355i	$0.727950\pi$
$380$	0	0
$381$	1.07831e41	0.0280210
$382$	5.86174e41	0.145875
$383$	6.48790e41	0.154641	0.0773205	−	0.997006i	$-0.475364\pi$
$383$	6.48790e41	0.154641	0.0773205	+	0.997006i	$0.475364\pi$
$384$	8.17734e42	1.86701
$385$	0	0
$386$	6.97243e42	1.46115
$387$	−2.46165e41	−0.0494306
$388$	−6.38010e41	−0.122773
$389$	−3.80740e42	−0.702199	−0.351100	−	0.936338i	$-0.614192\pi$
$389$	−3.80740e42	−0.702199	−0.351100	+	0.936338i	$0.614192\pi$
$390$	0	0
$391$	−3.11173e41	−0.0527333
$392$	−5.43888e42	−0.883669
$393$	1.85202e43	2.88515
$394$	−4.78826e42	−0.715302
$395$	0	0
$396$	2.94429e42	0.404585
$397$	−4.78435e42	−0.630638	−0.315319	−	0.948986i	$-0.602111\pi$
$397$	−4.78435e42	−0.630638	−0.315319	+	0.948986i	$0.602111\pi$
$398$	4.18339e42	0.529002
$399$	5.94045e41	0.0720720
$400$	0	0
$401$	−7.89830e42	−0.882372	−0.441186	−	0.897416i	$-0.645442\pi$
$401$	−7.89830e42	−0.882372	−0.441186	+	0.897416i	$0.645442\pi$
$402$	5.08228e42	0.544914
$403$	−7.69544e42	−0.791955
$404$	−2.99842e42	−0.296210
$405$	0	0
$406$	2.03428e42	0.185239
$407$	−1.46974e43	−1.28509
$408$	2.38653e43	2.00389
$409$	3.31586e41	0.0267400	0.0133700	−	0.999911i	$-0.495744\pi$
$409$	3.31586e41	0.0267400	0.0133700	+	0.999911i	$0.495744\pi$
$410$	0	0
$411$	−3.31897e43	−2.46952
$412$	−1.93330e42	−0.138196
$413$	−1.31595e42	−0.0903780
$414$	−9.28674e41	−0.0612855
$415$	0	0
$416$	2.53843e42	0.154712
$417$	3.54604e43	2.07730
$418$	−1.11784e43	−0.629467
$419$	−2.00047e43	−1.08293	−0.541466	−	0.840723i	$-0.682131\pi$
$419$	−2.00047e43	−1.08293	−0.541466	+	0.840723i	$0.682131\pi$
$420$	0	0
$421$	2.36083e43	1.18144	0.590719	−	0.806878i	$-0.298844\pi$
$421$	2.36083e43	1.18144	0.590719	+	0.806878i	$0.298844\pi$
$422$	1.73007e43	0.832547
$423$	3.38311e43	1.56567
$424$	−3.42780e43	−1.52573
$425$	0	0
$426$	8.28148e43	3.41075
$427$	−7.62106e41	−0.0301964
$428$	2.71980e42	0.103685
$429$	−3.08748e43	−1.13255
$430$	0	0
$431$	9.17533e42	0.311707	0.155854	−	0.987780i	$-0.450187\pi$
$431$	9.17533e42	0.311707	0.155854	+	0.987780i	$0.450187\pi$
$432$	2.84148e43	0.929100
$433$	1.77198e43	0.557711	0.278856	−	0.960333i	$-0.410045\pi$
$433$	1.77198e43	0.557711	0.278856	+	0.960333i	$0.410045\pi$
$434$	−7.56100e42	−0.229086
$435$	0	0
$436$	1.02134e43	0.286841
$437$	5.14976e41	0.0139265
$438$	−6.74945e43	−1.75770
$439$	1.15735e43	0.290270	0.145135	−	0.989412i	$-0.453638\pi$
$439$	1.15735e43	0.290270	0.145135	+	0.989412i	$0.453638\pi$
$440$	0	0
$441$	−6.40658e43	−1.49070
$442$	3.10905e43	0.696885
$443$	−4.45699e43	−0.962454	−0.481227	−	0.876596i	$-0.659809\pi$
$443$	−4.45699e43	−0.962454	−0.481227	+	0.876596i	$0.659809\pi$
$444$	1.07145e43	0.222921
$445$	0	0
$446$	−6.01755e42	−0.116250
$447$	−1.09418e42	−0.0203712
$448$	−5.27958e42	−0.0947354
$449$	4.27285e43	0.739015	0.369508	−	0.929228i	$-0.379526\pi$
$449$	4.27285e43	0.739015	0.369508	+	0.929228i	$0.379526\pi$
$450$	0	0
$451$	5.86621e42	0.0942854
$452$	1.63044e43	0.252651
$453$	5.16671e43	0.771959
$454$	3.74930e43	0.540168
$455$	0	0
$456$	−3.94959e43	−0.529215
$457$	−1.01564e44	−1.31257	−0.656284	−	0.754514i	$-0.727873\pi$
$457$	−1.01564e44	−1.31257	−0.656284	+	0.754514i	$0.727873\pi$
$458$	−8.74120e43	−1.08966
$459$	9.53501e43	1.14660
$460$	0	0
$461$	6.03006e43	0.674926	0.337463	−	0.941339i	$-0.390431\pi$
$461$	6.03006e43	0.674926	0.337463	+	0.941339i	$0.390431\pi$
$462$	−3.03354e43	−0.327610
$463$	1.59773e44	1.66501	0.832504	−	0.554019i	$-0.186906\pi$
$463$	1.59773e44	1.66501	0.832504	+	0.554019i	$0.186906\pi$
$464$	−1.59083e44	−1.59984
$465$	0	0
$466$	−2.15079e44	−2.01479
$467$	−1.57317e44	−1.42248	−0.711240	−	0.702949i	$-0.751866\pi$
$467$	−1.57317e44	−1.42248	−0.711240	+	0.702949i	$0.751866\pi$
$468$	1.35523e43	0.118292
$469$	−4.60499e42	−0.0388040
$470$	0	0
$471$	7.07627e43	0.555852
$472$	8.74926e43	0.663634
$473$	−6.97077e42	−0.0510589
$474$	3.00684e44	2.12700
$475$	0	0
$476$	4.46165e42	0.0294429
$477$	−4.03768e44	−2.57382
$478$	−7.14025e43	−0.439697
$479$	9.07529e43	0.539914	0.269957	−	0.962872i	$-0.412990\pi$
$479$	9.07529e43	0.539914	0.269957	+	0.962872i	$0.412990\pi$
$480$	0	0
$481$	−6.76508e43	−0.375733
$482$	1.59483e44	0.855930
$483$	1.39751e42	0.00724815
$484$	4.92520e43	0.246874
$485$	0	0
$486$	−2.69837e44	−1.26358
$487$	8.20051e43	0.371204	0.185602	−	0.982625i	$-0.440576\pi$
$487$	8.20051e43	0.371204	0.185602	+	0.982625i	$0.440576\pi$
$488$	5.06696e43	0.221728
$489$	8.35498e43	0.353467
$490$	0	0
$491$	−4.35053e44	−1.72067	−0.860334	−	0.509731i	$-0.829745\pi$
$491$	−4.35053e44	−1.72067	−0.860334	+	0.509731i	$0.829745\pi$
$492$	−4.27648e42	−0.0163554
$493$	−5.33826e44	−1.97435
$494$	−5.14533e43	−0.184043
$495$	0	0
$496$	5.91276e44	1.97853
$497$	−7.50375e43	−0.242883
$498$	−7.30827e44	−2.28839
$499$	3.20750e44	0.971645	0.485822	−	0.874058i	$-0.338520\pi$
$499$	3.20750e44	0.971645	0.485822	+	0.874058i	$0.338520\pi$
$500$	0	0
$501$	4.33815e44	1.23022
$502$	−1.76042e44	−0.483064
$503$	−1.94904e44	−0.517547	−0.258773	−	0.965938i	$-0.583318\pi$
$503$	−1.94904e44	−0.517547	−0.258773	+	0.965938i	$0.583318\pi$
$504$	−6.45355e43	−0.165842
$505$	0	0
$506$	−2.62976e43	−0.0633043
$507$	5.38267e44	1.25420
$508$	−1.34031e42	−0.00302312
$509$	3.82784e44	0.835814	0.417907	−	0.908490i	$-0.362764\pi$
$509$	3.82784e44	0.835814	0.417907	+	0.908490i	$0.362764\pi$
$510$	0	0
$511$	6.11560e43	0.125168
$512$	3.21804e44	0.637730
$513$	−1.57800e44	−0.302809
$514$	−9.57261e44	−1.77885
$515$	0	0
$516$	5.08171e42	0.00885706
$517$	9.58010e44	1.61725
$518$	−6.64689e43	−0.108687
$519$	−7.19564e44	−1.13975
$520$	0	0
$521$	−6.73383e44	−1.00101	−0.500507	−	0.865733i	$-0.666853\pi$
$521$	−6.73383e44	−1.00101	−0.500507	+	0.865733i	$0.666853\pi$
$522$	−1.59317e45	−2.29455
$523$	4.48155e44	0.625389	0.312694	−	0.949854i	$-0.398768\pi$
$523$	4.48155e44	0.625389	0.312694	+	0.949854i	$0.398768\pi$
$524$	−2.30201e44	−0.311272
$525$	0	0
$526$	−9.21850e44	−1.17056
$527$	1.98412e45	2.44170
$528$	2.37225e45	2.82944
$529$	−8.63793e44	−0.998599
$530$	0	0
$531$	1.03060e45	1.11951
$532$	−7.38381e42	−0.00777568
$533$	2.70016e43	0.0275671
$534$	1.53962e45	1.52400
$535$	0	0
$536$	3.06169e44	0.284933
$537$	−2.29055e45	−2.06711
$538$	−7.27648e44	−0.636816
$539$	−1.81418e45	−1.53980
$540$	0	0
$541$	−1.24268e45	−0.992214	−0.496107	−	0.868261i	$-0.665238\pi$
$541$	−1.24268e45	−0.992214	−0.496107	+	0.868261i	$0.665238\pi$
$542$	−7.69317e44	−0.595823
$543$	1.64072e44	0.123264
$544$	−6.54483e44	−0.476998
$545$	0	0
$546$	−1.39631e44	−0.0957861
$547$	−2.79714e44	−0.186176	−0.0930878	−	0.995658i	$-0.529674\pi$
$547$	−2.79714e44	−0.186176	−0.0930878	+	0.995658i	$0.529674\pi$
$548$	4.12539e44	0.266431
$549$	5.96849e44	0.374043
$550$	0	0
$551$	8.83455e44	0.521414
$552$	−9.29153e43	−0.0532222
$553$	−2.72446e44	−0.151466
$554$	2.76096e45	1.48987
$555$	0	0
$556$	−4.40762e44	−0.224115
$557$	7.31187e44	0.360926	0.180463	−	0.983582i	$-0.442240\pi$
$557$	7.31187e44	0.360926	0.180463	+	0.983582i	$0.442240\pi$
$558$	5.92146e45	2.83769
$559$	−3.20858e43	−0.0149285
$560$	0	0
$561$	7.96045e45	3.49181
$562$	2.81182e45	1.19767
$563$	1.17142e45	0.484535	0.242268	−	0.970209i	$-0.422109\pi$
$563$	1.17142e45	0.484535	0.242268	+	0.970209i	$0.422109\pi$
$564$	−6.98392e44	−0.280539
$565$	0	0
$566$	−2.02260e45	−0.766371
$567$	7.41103e43	0.0272746
$568$	4.98897e45	1.78346
$569$	−3.31218e45	−1.15017	−0.575085	−	0.818094i	$-0.695031\pi$
$569$	−3.31218e45	−1.15017	−0.575085	+	0.818094i	$0.695031\pi$
$570$	0	0
$571$	2.01622e45	0.660756	0.330378	−	0.943849i	$-0.392824\pi$
$571$	2.01622e45	0.660756	0.330378	+	0.943849i	$0.392824\pi$
$572$	3.83765e44	0.122189
$573$	6.90824e44	0.213706
$574$	2.65299e43	0.00797423
$575$	0	0
$576$	4.13475e45	1.17349
$577$	5.76715e45	1.59060	0.795299	−	0.606217i	$-0.207314\pi$
$577$	5.76715e45	1.59060	0.795299	+	0.606217i	$0.207314\pi$
$578$	−3.97874e45	−1.06644
$579$	8.21722e45	2.14057
$580$	0	0
$581$	6.62193e44	0.162959
$582$	−5.14809e45	−1.23145
$583$	−1.14337e46	−2.65861
$584$	−4.06604e45	−0.919093
$585$	0	0
$586$	1.20609e45	0.257673
$587$	−5.34761e45	−1.11079	−0.555394	−	0.831588i	$-0.687432\pi$
$587$	−5.34761e45	−1.11079	−0.555394	+	0.831588i	$0.687432\pi$
$588$	1.32254e45	0.267106
$589$	−3.28361e45	−0.644837
$590$	0	0
$591$	−5.64311e45	−1.04791
$592$	5.19792e45	0.938688
$593$	−2.76974e45	−0.486449	−0.243224	−	0.969970i	$-0.578205\pi$
$593$	−2.76974e45	−0.486449	−0.243224	+	0.969970i	$0.578205\pi$
$594$	8.05816e45	1.37645
$595$	0	0
$596$	1.36004e43	0.00219780
$597$	4.93025e45	0.774984
$598$	−1.21046e44	−0.0185088
$599$	−1.07144e46	−1.59376	−0.796882	−	0.604135i	$-0.793519\pi$
$599$	−1.07144e46	−1.59376	−0.796882	+	0.604135i	$0.793519\pi$
$600$	0	0
$601$	−7.75480e45	−1.09180	−0.545898	−	0.837851i	$-0.683812\pi$
$601$	−7.75480e45	−1.09180	−0.545898	+	0.837851i	$0.683812\pi$
$602$	−3.15252e43	−0.00431833
$603$	3.60643e45	0.480665
$604$	−6.42208e44	−0.0832849
$605$	0	0
$606$	−2.41942e46	−2.97107
$607$	−9.69667e45	−1.15880	−0.579401	−	0.815043i	$-0.696713\pi$
$607$	−9.69667e45	−1.15880	−0.579401	+	0.815043i	$0.696713\pi$
$608$	1.08314e45	0.125972
$609$	2.39747e45	0.271373
$610$	0	0
$611$	4.40963e45	0.472849
$612$	−3.49418e45	−0.364709
$613$	−4.57708e45	−0.465040	−0.232520	−	0.972592i	$-0.574697\pi$
$613$	−4.57708e45	−0.465040	−0.232520	+	0.972592i	$0.574697\pi$
$614$	−1.15658e46	−1.14393
$615$	0	0
$616$	−1.82748e45	−0.171305
$617$	9.88010e45	0.901688	0.450844	−	0.892603i	$-0.351123\pi$
$617$	9.88010e45	0.901688	0.450844	+	0.892603i	$0.351123\pi$
$618$	−1.55998e46	−1.38614
$619$	−1.00856e46	−0.872584	−0.436292	−	0.899805i	$-0.643709\pi$
$619$	−1.00856e46	−0.872584	−0.436292	+	0.899805i	$0.643709\pi$
$620$	0	0
$621$	−3.71229e44	−0.0304530
$622$	−1.69494e46	−1.35398
$623$	−1.39503e45	−0.108526
$624$	1.09192e46	0.827269
$625$	0	0
$626$	−1.82259e46	−1.30982
$627$	−1.31741e46	−0.922164
$628$	−8.79561e44	−0.0599697
$629$	1.74424e46	1.15843
$630$	0	0
$631$	1.57860e46	0.994918	0.497459	−	0.867487i	$-0.334266\pi$
$631$	1.57860e46	0.994918	0.497459	+	0.867487i	$0.334266\pi$
$632$	1.81139e46	1.11219
$633$	2.03894e46	1.21967
$634$	−2.27237e46	−1.32436
$635$	0	0
$636$	8.33517e45	0.461182
$637$	−8.35049e45	−0.450206
$638$	−4.51143e46	−2.37014
$639$	5.87662e46	3.00859
$640$	0	0
$641$	−1.18505e45	−0.0576206	−0.0288103	−	0.999585i	$-0.509172\pi$
$641$	−1.18505e45	−0.0576206	−0.0288103	+	0.999585i	$0.509172\pi$
$642$	2.19460e46	1.03999
$643$	−3.16044e46	−1.45971	−0.729855	−	0.683602i	$-0.760413\pi$
$643$	−3.16044e46	−1.45971	−0.729855	+	0.683602i	$0.760413\pi$
$644$	−1.73706e43	−0.000781986 0
$645$	0	0
$646$	1.32662e46	0.567427
$647$	−4.20047e45	−0.175137	−0.0875683	−	0.996159i	$-0.527910\pi$
$647$	−4.20047e45	−0.175137	−0.0875683	+	0.996159i	$0.527910\pi$
$648$	−4.92732e45	−0.200273
$649$	2.91838e46	1.15639
$650$	0	0
$651$	−8.91087e45	−0.335609
$652$	−1.03850e45	−0.0381348
$653$	1.95321e46	0.699327	0.349664	−	0.936875i	$-0.386296\pi$
$653$	1.95321e46	0.699327	0.349664	+	0.936875i	$0.386296\pi$
$654$	8.24115e46	2.87710
$655$	0	0
$656$	−2.07466e45	−0.0688704
$657$	−4.78948e46	−1.55046
$658$	4.33259e45	0.136779
$659$	−4.47813e46	−1.37876	−0.689378	−	0.724402i	$-0.742116\pi$
$659$	−4.47813e46	−1.37876	−0.689378	+	0.724402i	$0.742116\pi$
$660$	0	0
$661$	3.41637e45	0.100056	0.0500278	−	0.998748i	$-0.484069\pi$
$661$	3.41637e45	0.100056	0.0500278	+	0.998748i	$0.484069\pi$
$662$	1.09010e46	0.311392
$663$	3.66412e46	1.02093
$664$	−4.40268e46	−1.19659
$665$	0	0
$666$	5.20557e46	1.34630
$667$	2.07836e45	0.0524377
$668$	−5.39220e45	−0.132725
$669$	−7.09187e45	−0.170306
$670$	0	0
$671$	1.69012e46	0.386364
$672$	2.93935e45	0.0655629
$673$	−2.58526e46	−0.562674	−0.281337	−	0.959609i	$-0.590778\pi$
$673$	−2.58526e46	−0.562674	−0.281337	+	0.959609i	$0.590778\pi$
$674$	−5.98987e46	−1.27212
$675$	0	0
$676$	−6.69051e45	−0.135313
$677$	−5.00348e46	−0.987550	−0.493775	−	0.869590i	$-0.664383\pi$
$677$	−5.00348e46	−0.987550	−0.493775	+	0.869590i	$0.664383\pi$
$678$	1.31560e47	2.53416
$679$	4.66463e45	0.0876931
$680$	0	0
$681$	4.41867e46	0.791341
$682$	1.67680e47	2.93116
$683$	7.27991e46	1.24218	0.621090	−	0.783739i	$-0.286690\pi$
$683$	7.27991e46	1.24218	0.621090	+	0.783739i	$0.286690\pi$
$684$	5.78269e45	0.0963173
$685$	0	0
$686$	−1.65335e46	−0.262432
$687$	−1.03018e47	−1.59634
$688$	2.46529e45	0.0372958
$689$	−5.26281e46	−0.777321
$690$	0	0
$691$	−1.10753e47	−1.55944	−0.779720	−	0.626129i	$-0.784638\pi$
$691$	−1.10753e47	−1.55944	−0.779720	+	0.626129i	$0.784638\pi$
$692$	8.94398e45	0.122965
$693$	−2.15263e46	−0.288982
$694$	2.06603e46	0.270836
$695$	0	0
$696$	−1.59399e47	−1.99266
$697$	−6.96182e45	−0.0849928
$698$	−1.68545e46	−0.200957
$699$	−2.53477e47	−2.95165
$700$	0	0
$701$	−6.39910e46	−0.710839	−0.355420	−	0.934707i	$-0.615662\pi$
$701$	−6.39910e46	−0.710839	−0.355420	+	0.934707i	$0.615662\pi$
$702$	3.70910e46	0.402444
$703$	−2.88663e46	−0.305934
$704$	1.17085e47	1.21214
$705$	0	0
$706$	1.31272e47	1.29687
$707$	2.19221e46	0.211573
$708$	−2.12751e46	−0.200596
$709$	−1.32785e47	−1.22317	−0.611585	−	0.791179i	$-0.709468\pi$
$709$	−1.32785e47	−1.22317	−0.611585	+	0.791179i	$0.709468\pi$
$710$	0	0
$711$	2.13368e47	1.87621
$712$	9.27508e46	0.796889
$713$	−7.72481e45	−0.0648501
$714$	3.60010e46	0.295321
$715$	0	0
$716$	2.84709e46	0.223016
$717$	−8.41501e46	−0.644152
$718$	1.20281e47	0.899797
$719$	−4.87360e46	−0.356306	−0.178153	−	0.984003i	$-0.557012\pi$
$719$	−4.87360e46	−0.356306	−0.178153	+	0.984003i	$0.557012\pi$
$720$	0	0
$721$	1.41348e46	0.0987089
$722$	1.36589e47	0.932291
$723$	1.87956e47	1.25393
$724$	−2.03937e45	−0.0132987
$725$	0	0
$726$	3.97414e47	2.47622
$727$	3.19850e47	1.94818	0.974090	−	0.226159i	$-0.0726171\pi$
$727$	3.19850e47	1.94818	0.974090	+	0.226159i	$0.0726171\pi$
$728$	−8.41171e45	−0.0500860
$729$	−2.79657e47	−1.62788
$730$	0	0
$731$	8.27267e45	0.0460266
$732$	−1.23210e46	−0.0670215
$733$	−2.08452e47	−1.10864	−0.554319	−	0.832304i	$-0.687021\pi$
$733$	−2.08452e47	−1.10864	−0.554319	+	0.832304i	$0.687021\pi$
$734$	1.59232e47	0.828027
$735$	0	0
$736$	2.54811e45	0.0126688
$737$	1.02125e47	0.496499
$738$	−2.07771e46	−0.0987767
$739$	3.11658e47	1.44892	0.724461	−	0.689316i	$-0.242089\pi$
$739$	3.11658e47	1.44892	0.724461	+	0.689316i	$0.242089\pi$
$740$	0	0
$741$	−6.06393e46	−0.269621
$742$	−5.17086e46	−0.224853
$743$	1.10806e46	0.0471246	0.0235623	−	0.999722i	$-0.492499\pi$
$743$	1.10806e46	0.0471246	0.0235623	+	0.999722i	$0.492499\pi$
$744$	5.92452e47	2.46433
$745$	0	0
$746$	−2.64886e47	−1.05407
$747$	−5.18602e47	−2.01857
$748$	−9.89461e46	−0.376723
$749$	−1.98850e46	−0.0740586
$750$	0	0
$751$	−3.90356e46	−0.139124	−0.0695620	−	0.997578i	$-0.522160\pi$
$751$	−3.90356e46	−0.139124	−0.0695620	+	0.997578i	$0.522160\pi$
$752$	−3.38812e47	−1.18131
$753$	−2.07471e47	−0.707685
$754$	−2.07657e47	−0.692978
$755$	0	0
$756$	5.32274e45	0.0170030
$757$	−4.61535e47	−1.44252	−0.721261	−	0.692663i	$-0.756437\pi$
$757$	−4.61535e47	−1.44252	−0.721261	+	0.692663i	$0.756437\pi$
$758$	4.64590e47	1.42078
$759$	−3.09926e46	−0.0927403
$760$	0	0
$761$	−1.37335e47	−0.393490	−0.196745	−	0.980455i	$-0.563037\pi$
$761$	−1.37335e47	−0.393490	−0.196745	+	0.980455i	$0.563037\pi$
$762$	−1.08150e46	−0.0303228
$763$	−7.46721e46	−0.204882
$764$	−8.58675e45	−0.0230562
$765$	0	0
$766$	−6.50706e46	−0.167344
$767$	1.34330e47	0.338104
$768$	−3.21104e47	−0.791018
$769$	6.07971e47	1.46588	0.732939	−	0.680294i	$-0.238148\pi$
$769$	6.07971e47	1.46588	0.732939	+	0.680294i	$0.238148\pi$
$770$	0	0
$771$	−1.12816e48	−2.60600
$772$	−1.02138e47	−0.230941
$773$	−2.01842e47	−0.446736	−0.223368	−	0.974734i	$-0.571705\pi$
$773$	−2.01842e47	−0.446736	−0.223368	+	0.974734i	$0.571705\pi$
$774$	2.46892e46	0.0534911
$775$	0	0
$776$	−3.10134e47	−0.643919
$777$	−7.83356e46	−0.159225
$778$	3.81864e47	0.759881
$779$	1.15215e46	0.0224460
$780$	0	0
$781$	1.66411e48	3.10770
$782$	3.12092e46	0.0570651
$783$	−6.36853e47	−1.14017
$784$	6.41606e47	1.12474
$785$	0	0
$786$	−1.85749e48	−3.12215
$787$	−3.53259e47	−0.581447	−0.290723	−	0.956807i	$-0.593896\pi$
$787$	−3.53259e47	−0.581447	−0.290723	+	0.956807i	$0.593896\pi$
$788$	7.01423e46	0.113057
$789$	−1.08643e48	−1.71487
$790$	0	0
$791$	−1.19205e47	−0.180461
$792$	1.43121e48	2.12196
$793$	7.77947e46	0.112965
$794$	4.79848e47	0.682441
$795$	0	0
$796$	−6.12817e46	−0.0836113
$797$	−7.65249e47	−1.02268	−0.511341	−	0.859378i	$-0.670851\pi$
$797$	−7.65249e47	−1.02268	−0.511341	+	0.859378i	$0.670851\pi$
$798$	−5.95799e46	−0.0779923
$799$	−1.13693e48	−1.45785
$800$	0	0
$801$	1.09253e48	1.34431
$802$	7.92162e47	0.954854
$803$	−1.35626e48	−1.60153
$804$	−7.44493e46	−0.0861263
$805$	0	0
$806$	7.71817e47	0.857010
$807$	−8.57556e47	−0.932930
$808$	−1.45752e48	−1.55355
$809$	−1.19928e47	−0.125248	−0.0626238	−	0.998037i	$-0.519947\pi$
$809$	−1.19928e47	−0.125248	−0.0626238	+	0.998037i	$0.519947\pi$
$810$	0	0
$811$	1.18185e48	1.18500	0.592502	−	0.805569i	$-0.298140\pi$
$811$	1.18185e48	1.18500	0.592502	+	0.805569i	$0.298140\pi$
$812$	−2.97998e46	−0.0292779
$813$	−9.06664e47	−0.872876
$814$	1.47408e48	1.39065
$815$	0	0
$816$	−2.81531e48	−2.55058
$817$	−1.36909e46	−0.0121553
$818$	−3.32565e46	−0.0289366
$819$	−9.90834e46	−0.0844922
$820$	0	0
$821$	−3.09842e47	−0.253792	−0.126896	−	0.991916i	$-0.540501\pi$
$821$	−3.09842e47	−0.253792	−0.126896	+	0.991916i	$0.540501\pi$
$822$	3.32877e48	2.67238
$823$	−9.72259e47	−0.765041	−0.382521	−	0.923947i	$-0.624944\pi$
$823$	−9.72259e47	−0.765041	−0.382521	+	0.923947i	$0.624944\pi$
$824$	−9.39769e47	−0.724806
$825$	0	0
$826$	1.31983e47	0.0978021
$827$	−1.72721e48	−1.25460	−0.627298	−	0.778779i	$-0.715839\pi$
$827$	−1.72721e48	−1.25460	−0.627298	+	0.778779i	$0.715839\pi$
$828$	1.36040e46	0.00968646
$829$	2.30502e48	1.60889	0.804444	−	0.594029i	$-0.202464\pi$
$829$	2.30502e48	1.60889	0.804444	+	0.594029i	$0.202464\pi$
$830$	0	0
$831$	3.25388e48	2.18265
$832$	5.38933e47	0.354405
$833$	2.15301e48	1.38804
$834$	−3.55651e48	−2.24794
$835$	0	0
$836$	1.63751e47	0.0994902
$837$	2.36705e48	1.41006
$838$	2.00638e48	1.17189
$839$	4.09990e47	0.234801	0.117401	−	0.993085i	$-0.462544\pi$
$839$	4.09990e47	0.234801	0.117401	+	0.993085i	$0.462544\pi$
$840$	0	0
$841$	1.74940e48	0.963286
$842$	−2.36780e48	−1.27849
$843$	3.31381e48	1.75458
$844$	−2.53435e47	−0.131588
$845$	0	0
$846$	−3.39310e48	−1.69428
$847$	−3.60092e47	−0.176334
$848$	4.04365e48	1.94197
$849$	−2.38370e48	−1.12273
$850$	0	0
$851$	−6.79089e46	−0.0307673
$852$	−1.21314e48	−0.539085
$853$	7.10700e47	0.309761	0.154881	−	0.987933i	$-0.450501\pi$
$853$	7.10700e47	0.309761	0.154881	+	0.987933i	$0.450501\pi$
$854$	7.64356e46	0.0326769
$855$	0	0
$856$	1.32208e48	0.543803
$857$	−2.71615e48	−1.09590	−0.547949	−	0.836511i	$-0.684591\pi$
$857$	−2.71615e48	−1.09590	−0.547949	+	0.836511i	$0.684591\pi$
$858$	3.09660e48	1.22559
$859$	−4.17849e47	−0.162230	−0.0811152	−	0.996705i	$-0.525848\pi$
$859$	−4.17849e47	−0.162230	−0.0811152	+	0.996705i	$0.525848\pi$
$860$	0	0
$861$	3.12663e46	0.0116822
$862$	−9.20242e47	−0.337312
$863$	1.36178e48	0.489697	0.244849	−	0.969561i	$-0.421262\pi$
$863$	1.36178e48	0.489697	0.244849	+	0.969561i	$0.421262\pi$
$864$	−7.80797e47	−0.275462
$865$	0	0
$866$	−1.77722e48	−0.603524
$867$	−4.68907e48	−1.56233
$868$	1.10760e47	0.0362081
$869$	6.04203e48	1.93801
$870$	0	0
$871$	4.70071e47	0.145166
$872$	4.96468e48	1.50442
$873$	−3.65314e48	−1.08625
$874$	−5.16496e46	−0.0150705
$875$	0	0
$876$	9.88715e47	0.277813
$877$	4.09886e48	1.13024	0.565119	−	0.825009i	$-0.308830\pi$
$877$	4.09886e48	1.13024	0.565119	+	0.825009i	$0.308830\pi$
$878$	−1.16077e48	−0.314114
$879$	1.42141e48	0.377489
$880$	0	0
$881$	2.24659e48	0.574674	0.287337	−	0.957830i	$-0.407230\pi$
$881$	2.24659e48	0.574674	0.287337	+	0.957830i	$0.407230\pi$
$882$	6.42550e48	1.61315
$883$	−1.41582e48	−0.348863	−0.174432	−	0.984669i	$-0.555809\pi$
$883$	−1.41582e48	−0.348863	−0.174432	+	0.984669i	$0.555809\pi$
$884$	−4.55439e47	−0.110146
$885$	0	0
$886$	4.47015e48	1.04152
$887$	−5.80717e48	−1.32808	−0.664041	−	0.747696i	$-0.731160\pi$
$887$	−5.80717e48	−1.32808	−0.664041	+	0.747696i	$0.731160\pi$
$888$	5.20825e48	1.16917
$889$	9.79933e45	0.00215932
$890$	0	0
$891$	−1.64354e48	−0.348979
$892$	8.81500e46	0.0183739
$893$	1.88157e48	0.385009
$894$	1.09741e47	0.0220446
$895$	0	0
$896$	7.43126e47	0.143873
$897$	−1.42656e47	−0.0271153
$898$	−4.28547e48	−0.799722
$899$	−1.32521e49	−2.42801
$900$	0	0
$901$	1.35691e49	2.39658
$902$	−5.88353e47	−0.102031
$903$	−3.71534e46	−0.00632632
$904$	7.92551e48	1.32510
$905$	0	0
$906$	−5.18197e48	−0.835371
$907$	9.51843e48	1.50676	0.753382	−	0.657583i	$-0.228421\pi$
$907$	9.51843e48	1.50676	0.753382	+	0.657583i	$0.228421\pi$
$908$	−5.49228e47	−0.0853760
$909$	−1.71684e49	−2.62076
$910$	0	0
$911$	2.66104e47	0.0391740	0.0195870	−	0.999808i	$-0.493765\pi$
$911$	2.66104e47	0.0391740	0.0195870	+	0.999808i	$0.493765\pi$
$912$	4.65919e48	0.673590
$913$	−1.46855e49	−2.08507
$914$	1.01864e49	1.42039
$915$	0	0
$916$	1.28048e48	0.172226
$917$	1.68305e48	0.222332
$918$	−9.56316e48	−1.24079
$919$	1.65505e48	0.210914	0.105457	−	0.994424i	$-0.466369\pi$
$919$	1.65505e48	0.210914	0.105457	+	0.994424i	$0.466369\pi$
$920$	0	0
$921$	−1.36307e49	−1.67585
$922$	−6.04787e48	−0.730368
$923$	7.65972e48	0.908626
$924$	4.44377e47	0.0517803
$925$	0	0
$926$	−1.60245e49	−1.80178
$927$	−1.10698e49	−1.22271
$928$	4.37136e48	0.474324
$929$	1.12664e49	1.20095	0.600477	−	0.799642i	$-0.294978\pi$
$929$	1.12664e49	1.20095	0.600477	+	0.799642i	$0.294978\pi$
$930$	0	0
$931$	−3.56312e48	−0.366573
$932$	3.15065e48	0.318447
$933$	−1.99754e49	−1.98357
$934$	1.57781e49	1.53933
$935$	0	0
$936$	6.58770e48	0.620415
$937$	9.05198e48	0.837607	0.418804	−	0.908077i	$-0.362450\pi$
$937$	9.05198e48	0.837607	0.418804	+	0.908077i	$0.362450\pi$
$938$	4.61858e47	0.0419916
$939$	−2.14798e49	−1.91888
$940$	0	0
$941$	−2.06615e49	−1.78211	−0.891054	−	0.453898i	$-0.850033\pi$
$941$	−2.06615e49	−1.78211	−0.891054	+	0.453898i	$0.850033\pi$
$942$	−7.09717e48	−0.601513
$943$	2.71046e46	0.00225736
$944$	−1.03212e49	−0.844680
$945$	0	0
$946$	6.99135e47	0.0552532
$947$	−1.01046e49	−0.784774	−0.392387	−	0.919800i	$-0.628351\pi$
$947$	−1.01046e49	−0.784774	−0.392387	+	0.919800i	$0.628351\pi$
$948$	−4.40466e48	−0.336182
$949$	−6.24272e48	−0.468254
$950$	0	0
$951$	−2.67806e49	−1.94018
$952$	2.16879e48	0.154422
$953$	−3.11277e48	−0.217828	−0.108914	−	0.994051i	$-0.534737\pi$
$953$	−3.11277e48	−0.217828	−0.108914	+	0.994051i	$0.534737\pi$
$954$	4.04960e49	2.78525
$955$	0	0
$956$	1.04596e48	0.0694962
$957$	−5.31686e49	−3.47223
$958$	−9.10209e48	−0.584266
$959$	−3.01616e48	−0.190304
$960$	0	0
$961$	3.28518e49	2.00274
$962$	6.78506e48	0.406597
$963$	1.55731e49	0.917364
$964$	−2.33624e48	−0.135284
$965$	0	0
$966$	−1.40164e47	−0.00784355
$967$	−6.39561e48	−0.351840	−0.175920	−	0.984404i	$-0.556290\pi$
$967$	−6.39561e48	−0.351840	−0.175920	+	0.984404i	$0.556290\pi$
$968$	2.39412e49	1.29480
$969$	1.56346e49	0.831276
$970$	0	0
$971$	−2.23630e49	−1.14924	−0.574622	−	0.818419i	$-0.694851\pi$
$971$	−2.23630e49	−1.14924	−0.574622	+	0.818419i	$0.694851\pi$
$972$	3.95279e48	0.199715
$973$	3.22251e48	0.160078
$974$	−8.22473e48	−0.401697
$975$	0	0
$976$	−5.97732e48	−0.282218
$977$	2.33703e49	1.08493	0.542467	−	0.840077i	$-0.317490\pi$
$977$	2.33703e49	1.08493	0.542467	+	0.840077i	$0.317490\pi$
$978$	−8.37965e48	−0.382503
$979$	3.09377e49	1.38859
$980$	0	0
$981$	5.84801e49	2.53787
$982$	4.36337e49	1.86201
$983$	−6.12527e48	−0.257035	−0.128518	−	0.991707i	$-0.541022\pi$
$983$	−6.12527e48	−0.257035	−0.128518	+	0.991707i	$0.541022\pi$
$984$	−2.07878e48	−0.0857807
$985$	0	0
$986$	5.35402e49	2.13654
$987$	5.10609e48	0.200381
$988$	7.53730e47	0.0290888
$989$	−3.22082e46	−0.00122244
$990$	0	0
$991$	−2.52500e49	−0.926929	−0.463465	−	0.886115i	$-0.653394\pi$
$991$	−2.52500e49	−0.926929	−0.463465	+	0.886115i	$0.653394\pi$
$992$	−1.62474e49	−0.586600
$993$	1.28471e49	0.456187
$994$	7.52590e48	0.262835
$995$	0	0
$996$	1.07057e49	0.361691
$997$	1.64715e49	0.547349	0.273674	−	0.961822i	$-0.411761\pi$
$997$	1.64715e49	0.547349	0.273674	+	0.961822i	$0.411761\pi$
$998$	−3.21697e49	−1.05146
$999$	2.08088e49	0.668984

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.a.d.1.4	✓	11
5.2	odd	4		25.34.b.d.24.7		22
5.3	odd	4		25.34.b.d.24.16		22
5.4	even	2		25.34.a.e.1.8	yes	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.34.a.d.1.4	✓	11	1.1	even	1	trivial
25.34.a.e.1.8	yes	11	5.4	even	2
25.34.b.d.24.7		22	5.2	odd	4
25.34.b.d.24.16		22	5.3	odd	4

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 34 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

\(f(q)\)	\(=\)	\(q-100295. q^{2} -1.18201e8 q^{3} +1.46921e9 q^{4} +1.18550e13 q^{6} -1.07417e13 q^{7} +7.14175e14 q^{8} +8.41244e15 q^{9} +O(q^{10})\)	\(q-100295. q^{2} -1.18201e8 q^{3} +1.46921e9 q^{4} +1.18550e13 q^{6} -1.07417e13 q^{7} +7.14175e14 q^{8} +8.41244e15 q^{9} +2.38218e17 q^{11} -1.73662e17 q^{12} +1.09650e18 q^{13} +1.07734e18 q^{14} -8.42488e19 q^{16} -2.82710e20 q^{17} -8.43728e20 q^{18} +4.67870e20 q^{19} +1.26968e21 q^{21} -2.38922e22 q^{22} +1.10068e21 q^{23} -8.44163e22 q^{24} -1.09973e23 q^{26} -3.37272e23 q^{27} -1.57817e22 q^{28} +1.88825e24 q^{29} -7.01821e24 q^{31} +2.31504e24 q^{32} -2.81577e25 q^{33} +2.83544e25 q^{34} +1.23596e25 q^{36} -6.16972e25 q^{37} -4.69252e25 q^{38} -1.29607e26 q^{39} +2.46253e25 q^{41} -1.27343e26 q^{42} -2.92621e25 q^{43} +3.49992e26 q^{44} -1.10393e26 q^{46} +4.02156e27 q^{47} +9.95830e27 q^{48} -7.61561e27 q^{49} +3.34166e28 q^{51} +1.61098e27 q^{52} -4.79966e28 q^{53} +3.38268e28 q^{54} -7.67144e27 q^{56} -5.53028e28 q^{57} -1.89382e29 q^{58} +1.22509e29 q^{59} +7.09485e28 q^{61} +7.03894e29 q^{62} -9.03637e28 q^{63} +4.91504e29 q^{64} +2.82408e30 q^{66} +4.28703e29 q^{67} -4.15359e29 q^{68} -1.30102e29 q^{69} +6.98564e30 q^{71} +6.00795e30 q^{72} -5.69333e30 q^{73} +6.18794e30 q^{74} +6.87398e29 q^{76} -2.55887e30 q^{77} +1.29990e31 q^{78} +2.53634e31 q^{79} -6.89932e30 q^{81} -2.46981e30 q^{82} -6.16471e31 q^{83} +1.86542e30 q^{84} +2.93485e30 q^{86} -2.23193e32 q^{87} +1.70130e32 q^{88} +1.29871e32 q^{89} -1.17782e31 q^{91} +1.61713e30 q^{92} +8.29560e32 q^{93} -4.03344e32 q^{94} -2.73640e32 q^{96} -4.34255e32 q^{97} +7.63810e32 q^{98} +2.00400e33 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 9393 q^{2} - 80330849 q^{3} + 49338206677 q^{4} - 17783977676723 q^{6} - 21344025107658 q^{7} + 970199832420105 q^{8} + 24\!\cdots\!58 q^{9}+O(q^{10}) \) 11 * q - 9393 * q^2 - 80330849 * q^3 + 49338206677 * q^4 - 17783977676723 * q^6 - 21344025107658 * q^7 + 970199832420105 * q^8 + 24299637974625658 * q^9	\( 11 q - 9393 q^{2} - 80330849 q^{3} + 49338206677 q^{4} - 17783977676723 q^{6} - 21344025107658 q^{7} + 970199832420105 q^{8} + 24\!\cdots\!58 q^{9}+ \cdots + 13\!\cdots\!06 q^{99}+O(q^{100}) \) 11 * q - 9393 * q^2 - 80330849 * q^3 + 49338206677 * q^4 - 17783977676723 * q^6 - 21344025107658 * q^7 + 970199832420105 * q^8 + 24299637974625658 * q^9 - 194487534567113523 * q^11 - 1128411534853252093 * q^12 - 5151173641795199804 * q^13 + 9695004297667451034 * q^14 + 287795879559665379601 * q^16 - 217450883530375665663 * q^17 + 883205358438912773746 * q^18 - 2304421397121542404315 * q^19 + 3951679538424255448062 * q^21 - 65697936516541243081001 * q^22 - 39745489889804460665334 * q^23 - 202096278074290714435545 * q^24 + 232341332678498439460092 * q^26 - 215757396930304201071995 * q^27 + 1844234528929870945073094 * q^28 + 1675632286595729558796840 * q^29 - 1879684496680578139929438 * q^31 + 22333622446463598116694177 * q^32 + 36653442436454147951147057 * q^33 - 44873360881289881717450051 * q^34 + 193677686753165783059502006 * q^36 - 180277972113296426057413198 * q^37 - 216179528860395412757129505 * q^38 - 359172746626046600427282844 * q^39 + 549519804753897528529573167 * q^41 - 2593357144102832185922898306 * q^42 - 50270064758017307324647244 * q^43 - 2976543624086726877274410711 * q^44 + 1688362231334867471013357582 * q^46 - 10903258570108047175558188228 * q^47 - 28193416941275907016447196209 * q^48 - 2501658924474402528580483073 * q^49 + 66317965316246498072666600557 * q^51 - 155672232460399094184759234028 * q^52 - 33298643916770080171872677874 * q^53 - 213393152239696124781888030065 * q^54 + 339537122636968128125815064910 * q^56 - 159006470550216362740785378215 * q^57 - 62377017575001287720537209120 * q^58 - 67706990548480155796584121920 * q^59 - 344769258471797286249471450898 * q^61 + 1319517422843123577963573948294 * q^62 + 699283498025109144495841661076 * q^63 + 1420026267960910564014627900737 * q^64 - 160016657586606697551149537011 * q^66 + 1671796054942808947714198855437 * q^67 - 3088683653934580261727419953441 * q^68 + 7218504661993692063958711761426 * q^69 - 5525905608449961693610592189868 * q^71 + 21423093069732612399854192774190 * q^72 - 1280933432508086429255473349609 * q^73 + 8483102027446485651051216797154 * q^74 - 3794387798301159395171650466255 * q^76 + 25187595245022035764699127942394 * q^77 + 56671274702179561872150030862772 * q^78 + 28416813573575354189758739594190 * q^79 - 4511447703484319172258978381029 * q^81 - 94213252968905060003342215055821 * q^82 - 127792566726367853829683612248839 * q^83 - 299946577157245367261151073271766 * q^84 + 455910432123816097591159189088412 * q^86 - 485010641407021414487926087945160 * q^87 - 5212296644003692182363473725515 * q^88 - 24030870261451879999370600550555 * q^89 - 346687858887153608395037323300248 * q^91 - 535778496942575427226503821168238 * q^92 - 789528086332099641022541300872758 * q^93 + 232538212076560959503267655560444 * q^94 - 1842110282591420302371913525952353 * q^96 + 674692794164529660649398963528122 * q^97 + 2571899453674006542996540156918099 * q^98 + 1300949547786735016969037553636806 * q^99

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