LMFDB - Embedded newform 25.34.a.e.1.2

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:	$0$
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			1.2
Root			$154848.$ 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)

$f(q)$	$=$	$q-153994. q^{2} -7.94763e7 q^{3} +1.51243e10 q^{4} +1.22389e13 q^{6} +4.85062e13 q^{7} -1.00626e15 q^{8} +7.57418e14 q^{9} +O(q^{10})$	\(q-153994. q^{2} -7.94763e7 q^{3} +1.51243e10 q^{4} +1.22389e13 q^{6} +4.85062e13 q^{7} -1.00626e15 q^{8} +7.57418e14 q^{9} -1.47532e17 q^{11} -1.20203e18 q^{12} +2.08598e18 q^{13} -7.46967e18 q^{14} +2.50413e19 q^{16} -2.59222e20 q^{17} -1.16638e20 q^{18} -1.93050e21 q^{19} -3.85509e21 q^{21} +2.27191e22 q^{22} -2.85728e22 q^{23} +7.99737e22 q^{24} -3.21229e23 q^{26} +3.81617e23 q^{27} +7.33623e23 q^{28} -3.23015e22 q^{29} -2.36311e24 q^{31} +4.78749e24 q^{32} +1.17253e25 q^{33} +3.99187e25 q^{34} +1.14554e25 q^{36} +3.95398e25 q^{37} +2.97286e26 q^{38} -1.65786e26 q^{39} -1.88559e26 q^{41} +5.93662e26 q^{42} -1.41754e27 q^{43} -2.23132e27 q^{44} +4.40005e27 q^{46} +5.67475e27 q^{47} -1.99019e27 q^{48} -5.37815e27 q^{49} +2.06020e28 q^{51} +3.15490e28 q^{52} +3.48052e28 q^{53} -5.87668e28 q^{54} -4.88098e28 q^{56} +1.53429e29 q^{57} +4.97424e27 q^{58} +1.09273e29 q^{59} -4.19695e29 q^{61} +3.63905e29 q^{62} +3.67395e28 q^{63} -9.52349e29 q^{64} -1.80563e30 q^{66} -2.51440e30 q^{67} -3.92056e30 q^{68} +2.27086e30 q^{69} +1.38382e30 q^{71} -7.62159e29 q^{72} -6.30166e30 q^{73} -6.08891e30 q^{74} -2.91975e31 q^{76} -7.15620e30 q^{77} +2.55301e31 q^{78} -1.34248e31 q^{79} -3.45400e31 q^{81} +2.90370e31 q^{82} +4.79505e31 q^{83} -5.83056e31 q^{84} +2.18294e32 q^{86} +2.56720e30 q^{87} +1.48455e32 q^{88} -1.97781e32 q^{89} +1.01183e32 q^{91} -4.32144e32 q^{92} +1.87811e32 q^{93} -8.73879e32 q^{94} -3.80492e32 q^{96} -6.00782e32 q^{97} +8.28204e32 q^{98} -1.11743e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−153994.	−1.66154	−0.830768	−	0.556619i	$-0.812098\pi$
$2$	−153994.	−1.66154	−0.830768	+	0.556619i	$0.812098\pi$
$3$	−7.94763e7	−1.06595	−0.532975	−	0.846131i	$-0.678926\pi$
$3$	−7.94763e7	−1.06595	−0.532975	+	0.846131i	$0.678926\pi$
$4$	1.51243e10	1.76070
$5$	0	0
$5$	0	0
$6$	1.22389e13	1.77111
$7$	4.85062e13	0.551670	0.275835	−	0.961205i	$-0.411046\pi$
$7$	4.85062e13	0.551670	0.275835	+	0.961205i	$0.411046\pi$
$8$	−1.00626e15	−1.26394
$9$	7.57418e14	0.136249
$10$	0	0
$11$	−1.47532e17	−0.968069	−0.484034	−	0.875049i	$-0.660829\pi$
$11$	−1.47532e17	−0.968069	−0.484034	+	0.875049i	$0.660829\pi$
$12$	−1.20203e18	−1.87682
$13$	2.08598e18	0.869449	0.434724	−	0.900564i	$-0.356846\pi$
$13$	2.08598e18	0.869449	0.434724	+	0.900564i	$0.356846\pi$
$14$	−7.46967e18	−0.916620
$15$	0	0
$16$	2.50413e19	0.339372
$17$	−2.59222e20	−1.29201	−0.646003	−	0.763335i	$-0.723561\pi$
$17$	−2.59222e20	−1.29201	−0.646003	+	0.763335i	$0.723561\pi$
$18$	−1.16638e20	−0.226383
$19$	−1.93050e21	−1.53545	−0.767725	−	0.640780i	$-0.778611\pi$
$19$	−1.93050e21	−1.53545	−0.767725	+	0.640780i	$0.778611\pi$
$20$	0	0
$21$	−3.85509e21	−0.588052
$22$	2.27191e22	1.60848
$23$	−2.85728e22	−0.971501	−0.485751	−	0.874097i	$-0.661454\pi$
$23$	−2.85728e22	−0.971501	−0.485751	+	0.874097i	$0.661454\pi$
$24$	7.99737e22	1.34729
$25$	0	0
$26$	−3.21229e23	−1.44462
$27$	3.81617e23	0.920715
$28$	7.33623e23	0.971327
$29$	−3.23015e22	−0.0239693	−0.0119846	−	0.999928i	$-0.503815\pi$
$29$	−3.23015e22	−0.0239693	−0.0119846	+	0.999928i	$0.503815\pi$
$30$	0	0
$31$	−2.36311e24	−0.583466	−0.291733	−	0.956500i	$-0.594232\pi$
$31$	−2.36311e24	−0.583466	−0.291733	+	0.956500i	$0.594232\pi$
$32$	4.78749e24	0.700057
$33$	1.17253e25	1.03191
$34$	3.99187e25	2.14671
$35$	0	0
$36$	1.14554e25	0.239895
$37$	3.95398e25	0.526874	0.263437	−	0.964677i	$-0.415144\pi$
$37$	3.95398e25	0.526874	0.263437	+	0.964677i	$0.415144\pi$
$38$	2.97286e26	2.55121
$39$	−1.65786e26	−0.926789
$40$	0	0
$41$	−1.88559e26	−0.461863	−0.230932	−	0.972970i	$-0.574177\pi$
$41$	−1.88559e26	−0.461863	−0.230932	+	0.972970i	$0.574177\pi$
$42$	5.93662e26	0.977071
$43$	−1.41754e27	−1.58237	−0.791183	−	0.611579i	$-0.790535\pi$
$43$	−1.41754e27	−1.58237	−0.791183	+	0.611579i	$0.790535\pi$
$44$	−2.23132e27	−1.70448
$45$	0	0
$46$	4.40005e27	1.61418
$47$	5.67475e27	1.45993	0.729965	−	0.683485i	$-0.239536\pi$
$47$	5.67475e27	1.45993	0.729965	+	0.683485i	$0.239536\pi$
$48$	−1.99019e27	−0.361754
$49$	−5.37815e27	−0.695660
$50$	0	0
$51$	2.06020e28	1.37721
$52$	3.15490e28	1.53084
$53$	3.48052e28	1.23337	0.616683	−	0.787211i	$-0.288476\pi$
$53$	3.48052e28	1.23337	0.616683	+	0.787211i	$0.288476\pi$
$54$	−5.87668e28	−1.52980
$55$	0	0
$56$	−4.88098e28	−0.697275
$57$	1.53429e29	1.63671
$58$	4.97424e27	0.0398258
$59$	1.09273e29	0.659864	0.329932	−	0.944005i	$-0.392974\pi$
$59$	1.09273e29	0.659864	0.329932	+	0.944005i	$0.392974\pi$
$60$	0	0
$61$	−4.19695e29	−1.46215	−0.731075	−	0.682297i	$-0.760981\pi$
$61$	−4.19695e29	−1.46215	−0.731075	+	0.682297i	$0.760981\pi$
$62$	3.63905e29	0.969450
$63$	3.67395e28	0.0751647
$64$	−9.52349e29	−1.50254
$65$	0	0
$66$	−1.80563e30	−1.71456
$67$	−2.51440e30	−1.86294	−0.931471	−	0.363815i	$-0.881474\pi$
$67$	−2.51440e30	−1.86294	−0.931471	+	0.363815i	$0.881474\pi$
$68$	−3.92056e30	−2.27484
$69$	2.27086e30	1.03557
$70$	0	0
$71$	1.38382e30	0.393836	0.196918	−	0.980420i	$-0.436907\pi$
$71$	1.38382e30	0.393836	0.196918	+	0.980420i	$0.436907\pi$
$72$	−7.62159e29	−0.172210
$73$	−6.30166e30	−1.13404	−0.567019	−	0.823705i	$-0.691904\pi$
$73$	−6.30166e30	−1.13404	−0.567019	+	0.823705i	$0.691904\pi$
$74$	−6.08891e30	−0.875420
$75$	0	0
$76$	−2.91975e31	−2.70347
$77$	−7.15620e30	−0.534054
$78$	2.55301e31	1.53989
$79$	−1.34248e31	−0.656236	−0.328118	−	0.944637i	$-0.606414\pi$
$79$	−1.34248e31	−0.656236	−0.328118	+	0.944637i	$0.606414\pi$
$80$	0	0
$81$	−3.45400e31	−1.11769
$82$	2.90370e31	0.767402
$83$	4.79505e31	1.03754	0.518770	−	0.854914i	$-0.326390\pi$
$83$	4.79505e31	1.03754	0.518770	+	0.854914i	$0.326390\pi$
$84$	−5.83056e31	−1.03539
$85$	0	0
$86$	2.18294e32	2.62916
$87$	2.56720e30	0.0255501
$88$	1.48455e32	1.22358
$89$	−1.97781e32	−1.35285	−0.676425	−	0.736511i	$-0.736472\pi$
$89$	−1.97781e32	−1.35285	−0.676425	+	0.736511i	$0.736472\pi$
$90$	0	0
$91$	1.01183e32	0.479649
$92$	−4.32144e32	−1.71053
$93$	1.87811e32	0.621946
$94$	−8.73879e32	−2.42573
$95$	0	0
$96$	−3.80492e32	−0.746225
$97$	−6.00782e32	−0.993077	−0.496539	−	0.868015i	$-0.665396\pi$
$97$	−6.00782e32	−0.993077	−0.496539	+	0.868015i	$0.665396\pi$
$98$	8.28204e32	1.15586
$99$	−1.11743e32	−0.131899
$100$	0	0
$101$	−4.96197e32	−0.421067	−0.210534	−	0.977587i	$-0.567520\pi$
$101$	−4.96197e32	−0.421067	−0.210534	+	0.977587i	$0.567520\pi$
$102$	−3.17259e33	−2.28829
$103$	1.75960e33	1.08044	0.540219	−	0.841524i	$-0.318341\pi$
$103$	1.75960e33	1.08044	0.540219	+	0.841524i	$0.318341\pi$
$104$	−2.09903e33	−1.09893
$105$	0	0
$106$	−5.35980e33	−2.04928
$107$	−4.28967e33	−1.40473	−0.702363	−	0.711819i	$-0.747872\pi$
$107$	−4.28967e33	−1.40473	−0.702363	+	0.711819i	$0.747872\pi$
$108$	5.77169e33	1.62111
$109$	−5.32871e32	−0.128554	−0.0642769	−	0.997932i	$-0.520474\pi$
$109$	−5.32871e32	−0.128554	−0.0642769	+	0.997932i	$0.520474\pi$
$110$	0	0
$111$	−3.14248e33	−0.561621
$112$	1.21466e33	0.187221
$113$	−4.53951e33	−0.604247	−0.302124	−	0.953269i	$-0.597696\pi$
$113$	−4.53951e33	−0.604247	−0.302124	+	0.953269i	$0.597696\pi$
$114$	−2.36272e34	−2.71946
$115$	0	0
$116$	−4.88538e32	−0.0422028
$117$	1.57996e33	0.118462
$118$	−1.68274e34	−1.09639
$119$	−1.25739e34	−0.712761
$120$	0	0
$121$	−1.45953e33	−0.0628426
$122$	6.46307e34	2.42941
$123$	1.49860e34	0.492323
$124$	−3.57404e34	−1.02731
$125$	0	0
$126$	−5.65767e33	−0.124889
$127$	−8.27877e34	−1.60400	−0.802000	−	0.597324i	$-0.796231\pi$
$127$	−8.27877e34	−1.60400	−0.802000	+	0.597324i	$0.796231\pi$
$128$	1.05532e35	1.79647
$129$	1.12661e35	1.68672
$130$	0	0
$131$	2.50694e34	0.291184	0.145592	−	0.989345i	$-0.453491\pi$
$131$	2.50694e34	0.291184	0.145592	+	0.989345i	$0.453491\pi$
$132$	1.77337e35	1.81689
$133$	−9.36412e34	−0.847061
$134$	3.87203e35	3.09535
$135$	0	0
$136$	2.60844e35	1.63301
$137$	−1.86641e35	−1.03542	−0.517711	−	0.855556i	$-0.673216\pi$
$137$	−1.86641e35	−1.03542	−0.517711	+	0.855556i	$0.673216\pi$
$138$	−3.49699e35	−1.72064
$139$	2.43117e35	1.06187	0.530934	−	0.847413i	$-0.321841\pi$
$139$	2.43117e35	1.06187	0.530934	+	0.847413i	$0.321841\pi$
$140$	0	0
$141$	−4.51008e35	−1.55621
$142$	−2.13100e35	−0.654373
$143$	−3.07748e35	−0.841686
$144$	1.89667e34	0.0462392
$145$	0	0
$146$	9.70420e35	1.88425
$147$	4.27435e35	0.741539
$148$	5.98013e35	0.927668
$149$	9.65442e35	1.34015	0.670074	−	0.742294i	$-0.266262\pi$
$149$	9.65442e35	1.34015	0.670074	+	0.742294i	$0.266262\pi$
$150$	0	0
$151$	7.53600e35	0.839501	0.419751	−	0.907639i	$-0.362118\pi$
$151$	7.53600e35	0.839501	0.419751	+	0.907639i	$0.362118\pi$
$152$	1.94258e36	1.94071
$153$	−1.96339e35	−0.176035
$154$	1.10201e36	0.887351
$155$	0	0
$156$	−2.50740e36	−1.63180
$157$	3.49186e35	0.204509	0.102254	−	0.994758i	$-0.467394\pi$
$157$	3.49186e35	0.204509	0.102254	+	0.994758i	$0.467394\pi$
$158$	2.06734e36	1.09036
$159$	−2.76619e36	−1.31471
$160$	0	0
$161$	−1.38596e36	−0.535948
$162$	5.31897e36	1.85708
$163$	1.89269e36	0.597013	0.298506	−	0.954408i	$-0.403512\pi$
$163$	1.89269e36	0.597013	0.298506	+	0.954408i	$0.403512\pi$
$164$	−2.85183e36	−0.813204
$165$	0	0
$166$	−7.38411e36	−1.72391
$167$	−2.61460e36	−0.552819	−0.276409	−	0.961040i	$-0.589145\pi$
$167$	−2.61460e36	−0.552819	−0.276409	+	0.961040i	$0.589145\pi$
$168$	3.87922e36	0.743261
$169$	−1.40483e36	−0.244059
$170$	0	0
$171$	−1.46220e36	−0.209204
$172$	−2.14394e37	−2.78608
$173$	−2.88353e36	−0.340536	−0.170268	−	0.985398i	$-0.554463\pi$
$173$	−2.88353e36	−0.340536	−0.170268	+	0.985398i	$0.554463\pi$
$174$	−3.95334e35	−0.0424524
$175$	0	0
$176$	−3.69438e36	−0.328536
$177$	−8.68460e36	−0.703382
$178$	3.04572e37	2.24781
$179$	−1.17579e37	−0.791140	−0.395570	−	0.918436i	$-0.629453\pi$
$179$	−1.17579e37	−0.791140	−0.395570	+	0.918436i	$0.629453\pi$
$180$	0	0
$181$	−1.55363e37	−0.870267	−0.435133	−	0.900366i	$-0.643299\pi$
$181$	−1.55363e37	−0.870267	−0.435133	+	0.900366i	$0.643299\pi$
$182$	−1.55816e37	−0.796954
$183$	3.33558e37	1.55858
$184$	2.87516e37	1.22792
$185$	0	0
$186$	−2.89218e37	−1.03339
$187$	3.82435e37	1.25075
$188$	8.58267e37	2.57050
$189$	1.85108e37	0.507931
$190$	0	0
$191$	4.40286e37	1.01551	0.507755	−	0.861502i	$-0.330476\pi$
$191$	4.40286e37	1.01551	0.507755	+	0.861502i	$0.330476\pi$
$192$	7.56891e37	1.60163
$193$	−2.70522e36	−0.0525421	−0.0262710	−	0.999655i	$-0.508363\pi$
$193$	−2.70522e36	−0.0525421	−0.0262710	+	0.999655i	$0.508363\pi$
$194$	9.25170e37	1.65003
$195$	0	0
$196$	−8.13408e37	−1.22485
$197$	7.21384e37	0.998789	0.499395	−	0.866375i	$-0.333556\pi$
$197$	7.21384e37	0.998789	0.499395	+	0.866375i	$0.333556\pi$
$198$	1.72078e37	0.219155
$199$	−1.45920e38	−1.71017	−0.855087	−	0.518484i	$-0.826497\pi$
$199$	−1.45920e38	−1.71017	−0.855087	+	0.518484i	$0.826497\pi$
$200$	0	0
$201$	1.99835e38	1.98580
$202$	7.64115e37	0.699618
$203$	−1.56682e36	−0.0132231
$204$	3.11591e38	2.42486
$205$	0	0
$206$	−2.70969e38	−1.79519
$207$	−2.16416e37	−0.132366
$208$	5.22355e37	0.295067
$209$	2.84810e38	1.48642
$210$	0	0
$211$	−3.48527e38	−1.55445	−0.777223	−	0.629226i	$-0.783372\pi$
$211$	−3.48527e38	−1.55445	−0.777223	+	0.629226i	$0.783372\pi$
$212$	5.26405e38	2.17159
$213$	−1.09981e38	−0.419810
$214$	6.60585e38	2.33400
$215$	0	0
$216$	−3.84005e38	−1.16372
$217$	−1.14625e38	−0.321881
$218$	8.20591e37	0.213597
$219$	5.00833e38	1.20883
$220$	0	0
$221$	−5.40731e38	−1.12333
$222$	4.83924e38	0.933154
$223$	6.93713e38	1.24208	0.621040	−	0.783779i	$-0.286711\pi$
$223$	6.93713e38	1.24208	0.621040	+	0.783779i	$0.286711\pi$
$224$	2.32223e38	0.386200
$225$	0	0
$226$	6.99059e38	1.00398
$227$	−1.29992e39	−1.73577	−0.867883	−	0.496769i	$-0.834520\pi$
$227$	−1.29992e39	−1.73577	−0.867883	+	0.496769i	$0.834520\pi$
$228$	2.32051e39	2.88176
$229$	−1.68587e39	−1.94778	−0.973888	−	0.227031i	$-0.927098\pi$
$229$	−1.68587e39	−1.94778	−0.973888	+	0.227031i	$0.927098\pi$
$230$	0	0
$231$	5.68748e38	0.569275
$232$	3.25036e37	0.0302956
$233$	−8.48734e38	−0.736884	−0.368442	−	0.929651i	$-0.620109\pi$
$233$	−8.48734e38	−0.736884	−0.368442	+	0.929651i	$0.620109\pi$
$234$	−2.43304e38	−0.196829
$235$	0	0
$236$	1.65268e39	1.16182
$237$	1.06695e39	0.699515
$238$	1.93630e39	1.18428
$239$	2.78161e38	0.158756	0.0793780	−	0.996845i	$-0.474707\pi$
$239$	2.78161e38	0.158756	0.0793780	+	0.996845i	$0.474707\pi$
$240$	0	0
$241$	−2.03318e39	−1.01133	−0.505667	−	0.862728i	$-0.668754\pi$
$241$	−2.03318e39	−1.01133	−0.505667	+	0.862728i	$0.668754\pi$
$242$	2.24759e38	0.104415
$243$	6.23681e38	0.270682
$244$	−6.34761e39	−2.57441
$245$	0	0
$246$	−2.30775e39	−0.818013
$247$	−4.02698e39	−1.33499
$248$	2.37790e39	0.737464
$249$	−3.81093e39	−1.10597
$250$	0	0
$251$	−6.66369e38	−0.169472	−0.0847361	−	0.996403i	$-0.527005\pi$
$251$	−6.66369e38	−0.169472	−0.0847361	+	0.996403i	$0.527005\pi$
$252$	5.55660e38	0.132343
$253$	4.21539e39	0.940480
$254$	1.27488e40	2.66510
$255$	0	0
$256$	−8.07074e39	−1.48236
$257$	−6.33375e39	−1.09085	−0.545424	−	0.838160i	$-0.683631\pi$
$257$	−6.33375e39	−1.09085	−0.545424	+	0.838160i	$0.683631\pi$
$258$	−1.73492e40	−2.80255
$259$	1.91793e39	0.290660
$260$	0	0
$261$	−2.44657e37	−0.00326580
$262$	−3.86055e39	−0.483814
$263$	3.70638e39	0.436194	0.218097	−	0.975927i	$-0.430015\pi$
$263$	3.70638e39	0.436194	0.218097	+	0.975927i	$0.430015\pi$
$264$	−1.17987e40	−1.30427
$265$	0	0
$266$	1.44202e40	1.40742
$267$	1.57189e40	1.44207
$268$	−3.80285e40	−3.28009
$269$	−1.85776e40	−1.50688	−0.753438	−	0.657519i	$-0.771606\pi$
$269$	−1.85776e40	−1.50688	−0.753438	+	0.657519i	$0.771606\pi$
$270$	0	0
$271$	4.93293e39	0.354088	0.177044	−	0.984203i	$-0.443346\pi$
$271$	4.93293e39	0.354088	0.177044	+	0.984203i	$0.443346\pi$
$272$	−6.49124e39	−0.438471
$273$	−8.04163e39	−0.511282
$274$	2.87416e40	1.72039
$275$	0	0
$276$	3.43452e40	1.82333
$277$	2.39957e39	0.120010	0.0600049	−	0.998198i	$-0.480888\pi$
$277$	2.39957e39	0.120010	0.0600049	+	0.998198i	$0.480888\pi$
$278$	−3.74386e40	−1.76433
$279$	−1.78986e39	−0.0794969
$280$	0	0
$281$	2.01128e40	0.793998	0.396999	−	0.917819i	$-0.370052\pi$
$281$	2.01128e40	0.793998	0.396999	+	0.917819i	$0.370052\pi$
$282$	6.94527e40	2.58570
$283$	3.20203e40	1.12447	0.562237	−	0.826976i	$-0.309941\pi$
$283$	3.20203e40	1.12447	0.562237	+	0.826976i	$0.309941\pi$
$284$	2.09293e40	0.693429
$285$	0	0
$286$	4.73914e40	1.39849
$287$	−9.14627e39	−0.254796
$288$	3.62613e39	0.0953822
$289$	2.69415e40	0.669279
$290$	0	0
$291$	4.77479e40	1.05857
$292$	−9.53084e40	−1.99671
$293$	6.86133e39	0.135860	0.0679301	−	0.997690i	$-0.478361\pi$
$293$	6.86133e39	0.135860	0.0679301	+	0.997690i	$0.478361\pi$
$294$	−6.58226e40	−1.23209
$295$	0	0
$296$	−3.97873e40	−0.665935
$297$	−5.63006e40	−0.891316
$298$	−1.48673e41	−2.22670
$299$	−5.96022e40	−0.844671
$300$	0	0
$301$	−6.87596e40	−0.872944
$302$	−1.16050e41	−1.39486
$303$	3.94359e40	0.448837
$304$	−4.83422e40	−0.521089
$305$	0	0
$306$	3.02352e40	0.292489
$307$	−3.72649e40	−0.341599	−0.170799	−	0.985306i	$-0.554635\pi$
$307$	−3.72649e40	−0.341599	−0.170799	+	0.985306i	$0.554635\pi$
$308$	−1.08233e41	−0.940311
$309$	−1.39847e41	−1.15169
$310$	0	0
$311$	−2.02072e41	−1.49610	−0.748048	−	0.663645i	$-0.769009\pi$
$311$	−2.02072e41	−1.49610	−0.748048	+	0.663645i	$0.769009\pi$
$312$	1.66823e41	1.17140
$313$	−1.38444e41	−0.922132	−0.461066	−	0.887366i	$-0.652533\pi$
$313$	−1.38444e41	−0.922132	−0.461066	+	0.887366i	$0.652533\pi$
$314$	−5.37726e40	−0.339799
$315$	0	0
$316$	−2.03041e41	−1.15544
$317$	−2.67920e41	−1.44720	−0.723598	−	0.690221i	$-0.757513\pi$
$317$	−2.67920e41	−1.44720	−0.723598	+	0.690221i	$0.757513\pi$
$318$	4.25977e41	2.18443
$319$	4.76549e39	0.0232039
$320$	0	0
$321$	3.40927e41	1.49737
$322$	2.13429e41	0.890497
$323$	5.00428e41	1.98381
$324$	−5.22394e41	−1.96791
$325$	0	0
$326$	−2.91463e41	−0.991958
$327$	4.23506e40	0.137032
$328$	1.89739e41	0.583765
$329$	2.75260e41	0.805399
$330$	0	0
$331$	−4.10070e40	−0.108566	−0.0542832	−	0.998526i	$-0.517287\pi$
$331$	−4.10070e40	−0.108566	−0.0542832	+	0.998526i	$0.517287\pi$
$332$	7.25219e41	1.82680
$333$	2.99482e40	0.0717862
$334$	4.02633e41	0.918529
$335$	0	0
$336$	−9.65363e40	−0.199569
$337$	1.26373e41	0.248749	0.124374	−	0.992235i	$-0.460308\pi$
$337$	1.26373e41	0.248749	0.124374	+	0.992235i	$0.460308\pi$
$338$	2.16336e41	0.405512
$339$	3.60783e41	0.644097
$340$	0	0
$341$	3.48633e41	0.564835
$342$	2.25170e41	0.347600
$343$	−6.35874e41	−0.935445
$344$	1.42642e42	2.00001
$345$	0	0
$346$	4.44047e41	0.565814
$347$	−1.12726e42	−1.36958	−0.684788	−	0.728742i	$-0.740105\pi$
$347$	−1.12726e42	−1.36958	−0.684788	+	0.728742i	$0.740105\pi$
$348$	3.88272e40	0.0449861
$349$	1.04813e42	1.15823	0.579115	−	0.815246i	$-0.303398\pi$
$349$	1.04813e42	1.15823	0.579115	+	0.815246i	$0.303398\pi$
$350$	0	0
$351$	7.96043e41	0.800515
$352$	−7.06307e41	−0.677703
$353$	1.23093e41	0.112707	0.0563536	−	0.998411i	$-0.482053\pi$
$353$	1.23093e41	0.112707	0.0563536	+	0.998411i	$0.482053\pi$
$354$	1.33738e42	1.16869
$355$	0	0
$356$	−2.99131e42	−2.38197
$357$	9.99324e41	0.759767
$358$	1.81064e42	1.31451
$359$	1.86856e42	1.29553	0.647765	−	0.761840i	$-0.275704\pi$
$359$	1.86856e42	1.29553	0.647765	+	0.761840i	$0.275704\pi$
$360$	0	0
$361$	2.14606e42	1.35761
$362$	2.39251e42	1.44598
$363$	1.15998e41	0.0669871
$364$	1.53032e42	0.844519
$365$	0	0
$366$	−5.13661e42	−2.58963
$367$	1.81182e42	0.873221	0.436611	−	0.899651i	$-0.356179\pi$
$367$	1.81182e42	0.873221	0.436611	+	0.899651i	$0.356179\pi$
$368$	−7.15498e41	−0.329701
$369$	−1.42818e41	−0.0629286
$370$	0	0
$371$	1.68827e42	0.680411
$372$	2.84051e42	1.09506
$373$	4.68096e42	1.72639	0.863196	−	0.504870i	$-0.168459\pi$
$373$	4.68096e42	1.72639	0.863196	+	0.504870i	$0.168459\pi$
$374$	−5.88928e42	−2.07817
$375$	0	0
$376$	−5.71027e42	−1.84526
$377$	−6.73801e40	−0.0208401
$378$	−2.85055e42	−0.843945
$379$	−5.78002e42	−1.63826	−0.819129	−	0.573609i	$-0.805543\pi$
$379$	−5.78002e42	−1.63826	−0.819129	+	0.573609i	$0.805543\pi$
$380$	0	0
$381$	6.57966e42	1.70978
$382$	−6.78015e42	−1.68731
$383$	3.17369e42	0.756458	0.378229	−	0.925712i	$-0.376533\pi$
$383$	3.17369e42	0.756458	0.378229	+	0.925712i	$0.376533\pi$
$384$	−8.38730e42	−1.91495
$385$	0	0
$386$	4.16589e41	0.0873005
$387$	−1.07367e42	−0.215596
$388$	−9.08642e42	−1.74851
$389$	8.34650e42	1.53935	0.769673	−	0.638439i	$-0.220419\pi$
$389$	8.34650e42	1.53935	0.769673	+	0.638439i	$0.220419\pi$
$390$	0	0
$391$	7.40669e42	1.25519
$392$	5.41181e42	0.879270
$393$	−1.99243e42	−0.310388
$394$	−1.11089e43	−1.65952
$395$	0	0
$396$	−1.69004e42	−0.232235
$397$	−1.12772e43	−1.48647	−0.743237	−	0.669028i	$-0.766711\pi$
$397$	−1.12772e43	−1.48647	−0.743237	+	0.669028i	$0.766711\pi$
$398$	2.24709e43	2.84152
$399$	7.44225e42	0.902925
$400$	0	0
$401$	−1.45087e43	−1.62086	−0.810429	−	0.585837i	$-0.800766\pi$
$401$	−1.45087e43	−1.62086	−0.810429	+	0.585837i	$0.800766\pi$
$402$	−3.07734e43	−3.29948
$403$	−4.92939e42	−0.507294
$404$	−7.50464e42	−0.741374
$405$	0	0
$406$	2.41281e41	0.0219707
$407$	−5.83338e42	−0.510050
$408$	−2.07309e43	−1.74071
$409$	−1.68080e42	−0.135544	−0.0677722	−	0.997701i	$-0.521589\pi$
$409$	−1.68080e42	−0.135544	−0.0677722	+	0.997701i	$0.521589\pi$
$410$	0	0
$411$	1.48335e43	1.10371
$412$	2.66128e43	1.90233
$413$	5.30041e42	0.364027
$414$	3.33268e42	0.219932
$415$	0	0
$416$	9.98659e42	0.608663
$417$	−1.93220e43	−1.13190
$418$	−4.38592e43	−2.46974
$419$	2.32710e43	1.25975	0.629873	−	0.776698i	$-0.283107\pi$
$419$	2.32710e43	1.25975	0.629873	+	0.776698i	$0.283107\pi$
$420$	0	0
$421$	2.99141e43	1.49700	0.748498	−	0.663137i	$-0.230775\pi$
$421$	2.99141e43	1.49700	0.748498	+	0.663137i	$0.230775\pi$
$422$	5.36711e43	2.58277
$423$	4.29816e42	0.198914
$424$	−3.50230e43	−1.55890
$425$	0	0
$426$	1.69364e43	0.697529
$427$	−2.03578e43	−0.806624
$428$	−6.48784e43	−2.47331
$429$	2.44586e43	0.897196
$430$	0	0
$431$	3.30702e43	1.12347	0.561736	−	0.827317i	$-0.310134\pi$
$431$	3.30702e43	1.12347	0.561736	+	0.827317i	$0.310134\pi$
$432$	9.55616e42	0.312465
$433$	1.80699e43	0.568728	0.284364	−	0.958716i	$-0.408218\pi$
$433$	1.80699e43	0.568728	0.284364	+	0.958716i	$0.408218\pi$
$434$	1.76516e43	0.534816
$435$	0	0
$436$	−8.05931e42	−0.226345
$437$	5.51598e43	1.49169
$438$	−7.71254e43	−2.00851
$439$	−4.94471e43	−1.24016	−0.620078	−	0.784540i	$-0.712899\pi$
$439$	−4.94471e43	−1.24016	−0.620078	+	0.784540i	$0.712899\pi$
$440$	0	0
$441$	−4.07351e42	−0.0947833
$442$	8.32695e43	1.86646
$443$	8.63707e43	1.86511	0.932556	−	0.361024i	$-0.117573\pi$
$443$	8.63707e43	1.86511	0.932556	+	0.361024i	$0.117573\pi$
$444$	−4.75279e43	−0.988848
$445$	0	0
$446$	−1.06828e44	−2.06376
$447$	−7.67297e43	−1.42853
$448$	−4.61948e43	−0.828907
$449$	6.46553e43	1.11825	0.559126	−	0.829083i	$-0.311137\pi$
$449$	6.46553e43	1.11825	0.559126	+	0.829083i	$0.311137\pi$
$450$	0	0
$451$	2.78184e43	0.447115
$452$	−6.86570e43	−1.06390
$453$	−5.98933e43	−0.894867
$454$	2.00181e44	2.88404
$455$	0	0
$456$	−1.54389e44	−2.06870
$457$	−1.20092e43	−0.155201	−0.0776007	−	0.996985i	$-0.524726\pi$
$457$	−1.20092e43	−0.155201	−0.0776007	+	0.996985i	$0.524726\pi$
$458$	2.59615e44	3.23630
$459$	−9.89234e43	−1.18957
$460$	0	0
$461$	8.81590e43	0.986737	0.493369	−	0.869820i	$-0.335765\pi$
$461$	8.81590e43	0.986737	0.493369	+	0.869820i	$0.335765\pi$
$462$	−8.75840e43	−0.945872
$463$	2.97743e43	0.310281	0.155140	−	0.987892i	$-0.450417\pi$
$463$	2.97743e43	0.310281	0.155140	+	0.987892i	$0.450417\pi$
$464$	−8.08869e41	−0.00813451
$465$	0	0
$466$	1.30700e44	1.22436
$467$	−1.44667e44	−1.30810	−0.654048	−	0.756453i	$-0.726931\pi$
$467$	−1.44667e44	−1.30810	−0.654048	+	0.756453i	$0.726931\pi$
$468$	2.38958e43	0.208576
$469$	−1.21964e44	−1.02773
$470$	0	0
$471$	−2.77520e43	−0.217996
$472$	−1.09957e44	−0.834025
$473$	2.09133e44	1.53184
$474$	−1.64305e44	−1.16227
$475$	0	0
$476$	−1.90171e44	−1.25496
$477$	2.63621e43	0.168045
$478$	−4.28352e43	−0.263779
$479$	−3.04182e41	−0.00180966	−0.000904832	−	1.00000i	$-0.500288\pi$
$479$	−3.04182e41	−0.00180966	−0.000904832		1.00000i	$0.500288\pi$
$480$	0	0
$481$	8.24792e43	0.458090
$482$	3.13098e44	1.68037
$483$	1.10151e44	0.571294
$484$	−2.20744e43	−0.110647
$485$	0	0
$486$	−9.60434e43	−0.449748
$487$	2.01757e44	0.913274	0.456637	−	0.889653i	$-0.349054\pi$
$487$	2.01757e44	0.913274	0.456637	+	0.889653i	$0.349054\pi$
$488$	4.22322e44	1.84806
$489$	−1.50424e44	−0.636386
$490$	0	0
$491$	−3.24218e44	−1.28231	−0.641154	−	0.767412i	$-0.721544\pi$
$491$	−3.24218e44	−1.28231	−0.641154	+	0.767412i	$0.721544\pi$
$492$	2.26652e44	0.866835
$493$	8.37324e42	0.0309685
$494$	6.20132e44	2.21814
$495$	0	0
$496$	−5.91752e43	−0.198012
$497$	6.71236e43	0.217268
$498$	5.86861e44	1.83760
$499$	−1.93911e42	−0.00587412	−0.00293706	−	0.999996i	$-0.500935\pi$
$499$	−1.93911e42	−0.00587412	−0.00293706	+	0.999996i	$0.500935\pi$
$500$	0	0
$501$	2.07798e44	0.589277
$502$	1.02617e44	0.281584
$503$	3.71840e43	0.0987380	0.0493690	−	0.998781i	$-0.484279\pi$
$503$	3.71840e43	0.0987380	0.0493690	+	0.998781i	$0.484279\pi$
$504$	−3.69694e43	−0.0950033
$505$	0	0
$506$	−6.49147e44	−1.56264
$507$	1.11651e44	0.260154
$508$	−1.25211e45	−2.82417
$509$	4.92599e44	1.07560	0.537799	−	0.843073i	$-0.319256\pi$
$509$	4.92599e44	1.07560	0.537799	+	0.843073i	$0.319256\pi$
$510$	0	0
$511$	−3.05669e44	−0.625615
$512$	3.36334e44	0.666524
$513$	−7.36711e44	−1.41371
$514$	9.75361e44	1.81248
$515$	0	0
$516$	1.70392e45	2.96982
$517$	−8.37206e44	−1.41331
$518$	−2.95350e44	−0.482943
$519$	2.29172e44	0.362995
$520$	0	0
$521$	−5.36473e44	−0.797491	−0.398745	−	0.917062i	$-0.630554\pi$
$521$	−5.36473e44	−0.797491	−0.398745	+	0.917062i	$0.630554\pi$
$522$	3.76758e42	0.00542624
$523$	−1.04429e45	−1.45728	−0.728638	−	0.684899i	$-0.759846\pi$
$523$	−1.04429e45	−1.45728	−0.728638	+	0.684899i	$0.759846\pi$
$524$	3.79158e44	0.512689
$525$	0	0
$526$	−5.70761e44	−0.724752
$527$	6.12569e44	0.753842
$528$	2.93616e44	0.350203
$529$	−4.86004e43	−0.0561852
$530$	0	0
$531$	8.27653e43	0.0899060
$532$	−1.41626e45	−1.49142
$533$	−3.93329e44	−0.401566
$534$	−2.42062e45	−2.39605
$535$	0	0
$536$	2.53013e45	2.35464
$537$	9.34471e44	0.843316
$538$	2.86085e45	2.50373
$539$	7.93447e44	0.673447
$540$	0	0
$541$	−8.69308e43	−0.0694095	−0.0347047	−	0.999398i	$-0.511049\pi$
$541$	−8.69308e43	−0.0694095	−0.0347047	+	0.999398i	$0.511049\pi$
$542$	−7.59643e44	−0.588330
$543$	1.23477e45	0.927661
$544$	−1.24102e45	−0.904477
$545$	0	0
$546$	1.23836e45	0.849513
$547$	1.58048e45	1.05196	0.525980	−	0.850497i	$-0.323699\pi$
$547$	1.58048e45	1.05196	0.525980	+	0.850497i	$0.323699\pi$
$548$	−2.82282e45	−1.82307
$549$	−3.17885e44	−0.199217
$550$	0	0
$551$	6.23580e43	0.0368036
$552$	−2.28507e45	−1.30890
$553$	−6.51185e44	−0.362026
$554$	−3.69519e44	−0.199400
$555$	0	0
$556$	3.67698e45	1.86963
$557$	9.88087e44	0.487736	0.243868	−	0.969808i	$-0.421584\pi$
$557$	9.88087e44	0.487736	0.243868	+	0.969808i	$0.421584\pi$
$558$	2.75629e44	0.132087
$559$	−2.95696e45	−1.37579
$560$	0	0
$561$	−3.03945e45	−1.33324
$562$	−3.09726e45	−1.31926
$563$	−3.48748e44	−0.144252	−0.0721262	−	0.997396i	$-0.522978\pi$
$563$	−3.48748e44	−0.144252	−0.0721262	+	0.997396i	$0.522978\pi$
$564$	−6.82119e45	−2.74003
$565$	0	0
$566$	−4.93095e45	−1.86835
$567$	−1.67540e45	−0.616593
$568$	−1.39248e45	−0.497784
$569$	−3.00628e45	−1.04394	−0.521972	−	0.852963i	$-0.674804\pi$
$569$	−3.00628e45	−1.04394	−0.521972	+	0.852963i	$0.674804\pi$
$570$	0	0
$571$	−1.47037e45	−0.481873	−0.240936	−	0.970541i	$-0.577454\pi$
$571$	−1.47037e45	−0.481873	−0.240936	+	0.970541i	$0.577454\pi$
$572$	−4.65448e45	−1.48196
$573$	−3.49923e45	−1.08248
$574$	1.40847e45	0.423353
$575$	0	0
$576$	−7.21327e44	−0.204720
$577$	5.76995e45	1.59137	0.795686	−	0.605710i	$-0.207111\pi$
$577$	5.76995e45	1.59137	0.795686	+	0.605710i	$0.207111\pi$
$578$	−4.14884e45	−1.11203
$579$	2.15001e44	0.0560072
$580$	0	0
$581$	2.32590e45	0.572379
$582$	−7.35291e45	−1.75885
$583$	−5.13487e45	−1.19398
$584$	6.34110e45	1.43335
$585$	0	0
$586$	−1.05661e45	−0.225737
$587$	1.02684e45	0.213293	0.106646	−	0.994297i	$-0.465989\pi$
$587$	1.02684e45	0.213293	0.106646	+	0.994297i	$0.465989\pi$
$588$	6.46467e45	1.30563
$589$	4.56198e45	0.895883
$590$	0	0
$591$	−5.73329e45	−1.06466
$592$	9.90127e44	0.178806
$593$	7.75566e45	1.36212	0.681062	−	0.732226i	$-0.261519\pi$
$593$	7.75566e45	1.36212	0.681062	+	0.732226i	$0.261519\pi$
$594$	8.66997e45	1.48095
$595$	0	0
$596$	1.46017e46	2.35960
$597$	1.15972e46	1.82296
$598$	9.17840e45	1.40345
$599$	−4.30236e45	−0.639976	−0.319988	−	0.947422i	$-0.603679\pi$
$599$	−4.30236e45	−0.639976	−0.319988	+	0.947422i	$0.603679\pi$
$600$	0	0
$601$	−1.28830e45	−0.181379	−0.0906896	−	0.995879i	$-0.528907\pi$
$601$	−1.28830e45	−0.181379	−0.0906896	+	0.995879i	$0.528907\pi$
$602$	1.05886e46	1.45043
$603$	−1.90445e45	−0.253825
$604$	1.13977e46	1.47811
$605$	0	0
$606$	−6.07290e45	−0.745758
$607$	1.14010e46	1.36248	0.681239	−	0.732061i	$-0.261442\pi$
$607$	1.14010e46	1.36248	0.681239	+	0.732061i	$0.261442\pi$
$608$	−9.24225e45	−1.07490
$609$	1.24525e44	0.0140952
$610$	0	0
$611$	1.18374e46	1.26933
$612$	−2.96950e45	−0.309945
$613$	−7.53365e45	−0.765434	−0.382717	−	0.923866i	$-0.625012\pi$
$613$	−7.53365e45	−0.765434	−0.382717	+	0.923866i	$0.625012\pi$
$614$	5.73858e45	0.567579
$615$	0	0
$616$	7.20099e45	0.675011
$617$	−1.68713e46	−1.53973	−0.769864	−	0.638208i	$-0.779676\pi$
$617$	−1.68713e46	−1.53973	−0.769864	+	0.638208i	$0.779676\pi$
$618$	2.15356e46	1.91358
$619$	6.32455e45	0.547185	0.273592	−	0.961846i	$-0.411788\pi$
$619$	6.32455e45	0.547185	0.273592	+	0.961846i	$0.411788\pi$
$620$	0	0
$621$	−1.09039e46	−0.894476
$622$	3.11179e46	2.48582
$623$	−9.59360e45	−0.746327
$624$	−4.15148e45	−0.314526
$625$	0	0
$626$	2.13196e46	1.53216
$627$	−2.26357e46	−1.58445
$628$	5.28120e45	0.360079
$629$	−1.02496e46	−0.680724
$630$	0	0
$631$	−7.80043e44	−0.0491625	−0.0245813	−	0.999698i	$-0.507825\pi$
$631$	−7.80043e44	−0.0491625	−0.0245813	+	0.999698i	$0.507825\pi$
$632$	1.35088e46	0.829441
$633$	2.76996e46	1.65696
$634$	4.12582e46	2.40457
$635$	0	0
$636$	−4.18367e46	−2.31481
$637$	−1.12187e46	−0.604841
$638$	−7.33859e44	−0.0385542
$639$	1.04813e45	0.0536599
$640$	0	0
$641$	−2.79223e46	−1.35767	−0.678835	−	0.734291i	$-0.737515\pi$
$641$	−2.79223e46	−1.35767	−0.678835	+	0.734291i	$0.737515\pi$
$642$	−5.25008e46	−2.48793
$643$	2.34324e46	1.08227	0.541135	−	0.840936i	$-0.317995\pi$
$643$	2.34324e46	1.08227	0.541135	+	0.840936i	$0.317995\pi$
$644$	−2.09617e46	−0.943645
$645$	0	0
$646$	−7.70631e46	−3.29617
$647$	1.63952e46	0.683592	0.341796	−	0.939774i	$-0.388965\pi$
$647$	1.63952e46	0.683592	0.341796	+	0.939774i	$0.388965\pi$
$648$	3.47562e46	1.41268
$649$	−1.61212e46	−0.638793
$650$	0	0
$651$	9.10999e45	0.343109
$652$	2.86256e46	1.05116
$653$	−2.70944e46	−0.970091	−0.485046	−	0.874489i	$-0.661197\pi$
$653$	−2.70944e46	−0.970091	−0.485046	+	0.874489i	$0.661197\pi$
$654$	−6.52175e45	−0.227683
$655$	0	0
$656$	−4.72175e45	−0.156744
$657$	−4.77299e45	−0.154512
$658$	−4.23885e46	−1.33820
$659$	−1.00285e46	−0.308763	−0.154381	−	0.988011i	$-0.549338\pi$
$659$	−1.00285e46	−0.308763	−0.154381	+	0.988011i	$0.549338\pi$
$660$	0	0
$661$	4.37969e46	1.28268	0.641341	−	0.767256i	$-0.278379\pi$
$661$	4.37969e46	1.28268	0.641341	+	0.767256i	$0.278379\pi$
$662$	6.31484e45	0.180387
$663$	4.29753e46	1.19742
$664$	−4.82506e46	−1.31138
$665$	0	0
$666$	−4.61185e45	−0.119275
$667$	9.22943e44	0.0232862
$668$	−3.95440e46	−0.973350
$669$	−5.51337e46	−1.32399
$670$	0	0
$671$	6.19184e46	1.41546
$672$	−1.84562e46	−0.411670
$673$	7.40237e46	1.61110	0.805550	−	0.592528i	$-0.201870\pi$
$673$	7.40237e46	1.61110	0.805550	+	0.592528i	$0.201870\pi$
$674$	−1.94607e46	−0.413305
$675$	0	0
$676$	−2.12472e46	−0.429715
$677$	−3.05580e46	−0.603131	−0.301566	−	0.953445i	$-0.597509\pi$
$677$	−3.05580e46	−0.603131	−0.301566	+	0.953445i	$0.597509\pi$
$678$	−5.55586e46	−1.07019
$679$	−2.91416e46	−0.547851
$680$	0	0
$681$	1.03313e47	1.85024
$682$	−5.36876e46	−0.938494
$683$	3.55003e45	0.0605746	0.0302873	−	0.999541i	$-0.490358\pi$
$683$	3.55003e45	0.0605746	0.0302873	+	0.999541i	$0.490358\pi$
$684$	−2.21147e46	−0.368346
$685$	0	0
$686$	9.79210e46	1.55428
$687$	1.33987e47	2.07623
$688$	−3.54971e46	−0.537011
$689$	7.26028e46	1.07235
$690$	0	0
$691$	−1.59202e46	−0.224162	−0.112081	−	0.993699i	$-0.535752\pi$
$691$	−1.59202e46	−0.224162	−0.112081	+	0.993699i	$0.535752\pi$
$692$	−4.36114e46	−0.599583
$693$	−5.42024e45	−0.0727646
$694$	1.73591e47	2.27560
$695$	0	0
$696$	−2.58327e45	−0.0322936
$697$	4.88786e46	0.596730
$698$	−1.61406e47	−1.92444
$699$	6.74542e46	0.785481
$700$	0	0
$701$	5.22500e46	0.580415	0.290208	−	0.956964i	$-0.406276\pi$
$701$	5.22500e46	0.580415	0.290208	+	0.956964i	$0.406276\pi$
$702$	−1.22586e47	−1.33008
$703$	−7.63317e46	−0.808988
$704$	1.40502e47	1.45456
$705$	0	0
$706$	−1.89557e46	−0.187267
$707$	−2.40686e46	−0.232290
$708$	−1.31349e47	−1.23845
$709$	−8.21967e46	−0.757167	−0.378583	−	0.925567i	$-0.623589\pi$
$709$	−8.21967e46	−0.757167	−0.378583	+	0.925567i	$0.623589\pi$
$710$	0	0
$711$	−1.01682e46	−0.0894118
$712$	1.99019e47	1.70992
$713$	6.75206e46	0.566838
$714$	−1.53890e47	−1.26238
$715$	0	0
$716$	−1.77830e47	−1.39296
$717$	−2.21072e46	−0.169226
$718$	−2.87747e47	−2.15257
$719$	1.29211e47	0.944653	0.472327	−	0.881424i	$-0.343414\pi$
$719$	1.29211e47	0.944653	0.472327	+	0.881424i	$0.343414\pi$
$720$	0	0
$721$	8.53515e46	0.596045
$722$	−3.30482e47	−2.25571
$723$	1.61590e47	1.07803
$724$	−2.34977e47	−1.53228
$725$	0	0
$726$	−1.78630e46	−0.111301
$727$	−2.40458e47	−1.46461	−0.732303	−	0.680978i	$-0.761555\pi$
$727$	−2.40458e47	−1.46461	−0.732303	+	0.680978i	$0.761555\pi$
$728$	−1.01816e47	−0.606245
$729$	1.42442e47	0.829152
$730$	0	0
$731$	3.67459e47	2.04443
$732$	5.04484e47	2.74419
$733$	−1.95548e47	−1.04001	−0.520006	−	0.854163i	$-0.674070\pi$
$733$	−1.95548e47	−1.04001	−0.520006	+	0.854163i	$0.674070\pi$
$734$	−2.79010e47	−1.45089
$735$	0	0
$736$	−1.36792e47	−0.680106
$737$	3.70953e47	1.80346
$738$	2.19932e46	0.104558
$739$	−9.86918e46	−0.458826	−0.229413	−	0.973329i	$-0.573681\pi$
$739$	−9.86918e46	−0.458826	−0.229413	+	0.973329i	$0.573681\pi$
$740$	0	0
$741$	3.20049e47	1.42304
$742$	−2.59983e47	−1.13053
$743$	1.87477e47	0.797318	0.398659	−	0.917099i	$-0.369476\pi$
$743$	1.87477e47	0.797318	0.398659	+	0.917099i	$0.369476\pi$
$744$	−1.88987e47	−0.786099
$745$	0	0
$746$	−7.20841e47	−2.86846
$747$	3.63186e46	0.141364
$748$	5.78407e47	2.20220
$749$	−2.08075e47	−0.774945
$750$	0	0
$751$	−2.76323e47	−0.984824	−0.492412	−	0.870362i	$-0.663885\pi$
$751$	−2.76323e47	−0.984824	−0.492412	+	0.870362i	$0.663885\pi$
$752$	1.42103e47	0.495460
$753$	5.29606e46	0.180649
$754$	1.03761e46	0.0346265
$755$	0	0
$756$	2.79963e47	0.894315
$757$	1.68577e47	0.526887	0.263443	−	0.964675i	$-0.415142\pi$
$757$	1.68577e47	0.526887	0.263443	+	0.964675i	$0.415142\pi$
$758$	8.90091e47	2.72203
$759$	−3.35024e47	−1.00250
$760$	0	0
$761$	−4.07016e47	−1.16618	−0.583088	−	0.812409i	$-0.698156\pi$
$761$	−4.07016e47	−1.16618	−0.583088	+	0.812409i	$0.698156\pi$
$762$	−1.01323e48	−2.84087
$763$	−2.58475e46	−0.0709192
$764$	6.65902e47	1.78801
$765$	0	0
$766$	−4.88730e47	−1.25688
$767$	2.27941e47	0.573718
$768$	6.41432e47	1.58012
$769$	3.30672e47	0.797283	0.398642	−	0.917107i	$-0.369482\pi$
$769$	3.30672e47	0.797283	0.398642	+	0.917107i	$0.369482\pi$
$770$	0	0
$771$	5.03383e47	1.16279
$772$	−4.09146e46	−0.0925110
$773$	4.00465e47	0.886345	0.443173	−	0.896436i	$-0.353853\pi$
$773$	4.00465e47	0.886345	0.443173	+	0.896436i	$0.353853\pi$
$774$	1.65340e47	0.358221
$775$	0	0
$776$	6.04542e47	1.25519
$777$	−1.52430e47	−0.309829
$778$	−1.28531e48	−2.55768
$779$	3.64013e47	0.709168
$780$	0	0
$781$	−2.04157e47	−0.381261
$782$	−1.14059e48	−2.08554
$783$	−1.23268e46	−0.0220689
$784$	−1.34675e47	−0.236088
$785$	0	0
$786$	3.06822e47	0.515721
$787$	2.46231e47	0.405284	0.202642	−	0.979253i	$-0.435047\pi$
$787$	2.46231e47	0.405284	0.202642	+	0.979253i	$0.435047\pi$
$788$	1.09104e48	1.75857
$789$	−2.94569e47	−0.464961
$790$	0	0
$791$	−2.20194e47	−0.333345
$792$	1.12443e47	0.166712
$793$	−8.75474e47	−1.27126
$794$	1.73662e48	2.46983
$795$	0	0
$796$	−2.20695e48	−3.01111
$797$	8.51467e47	1.13790	0.568952	−	0.822371i	$-0.307349\pi$
$797$	8.51467e47	1.13790	0.568952	+	0.822371i	$0.307349\pi$
$798$	−1.14606e48	−1.50024
$799$	−1.47102e48	−1.88624
$800$	0	0
$801$	−1.49803e47	−0.184325
$802$	2.23425e48	2.69311
$803$	9.29695e47	1.09783
$804$	3.02237e48	3.49641
$805$	0	0
$806$	7.59098e47	0.842887
$807$	1.47648e48	1.60625
$808$	4.99303e47	0.532202
$809$	−1.00045e48	−1.04483	−0.522414	−	0.852692i	$-0.674968\pi$
$809$	−1.00045e48	−1.04483	−0.522414	+	0.852692i	$0.674968\pi$
$810$	0	0
$811$	1.42802e48	1.43182	0.715912	−	0.698190i	$-0.246011\pi$
$811$	1.42802e48	1.43182	0.715912	+	0.698190i	$0.246011\pi$
$812$	−2.36971e46	−0.0232820
$813$	−3.92051e47	−0.377440
$814$	8.98308e47	0.847467
$815$	0	0
$816$	5.15900e47	0.467388
$817$	2.73657e48	2.42964
$818$	2.58834e47	0.225212
$819$	7.66376e46	0.0653518
$820$	0	0
$821$	−5.90143e47	−0.483387	−0.241694	−	0.970353i	$-0.577703\pi$
$821$	−5.90143e47	−0.483387	−0.241694	+	0.970353i	$0.577703\pi$
$822$	−2.28428e48	−1.83385
$823$	−8.62995e47	−0.679064	−0.339532	−	0.940594i	$-0.610269\pi$
$823$	−8.62995e47	−0.679064	−0.339532	+	0.940594i	$0.610269\pi$
$824$	−1.77061e48	−1.36561
$825$	0	0
$826$	−8.16233e47	−0.604844
$827$	1.08862e48	0.790747	0.395373	−	0.918521i	$-0.370615\pi$
$827$	1.08862e48	0.790747	0.395373	+	0.918521i	$0.370615\pi$
$828$	−3.27314e47	−0.233058
$829$	−6.28606e47	−0.438762	−0.219381	−	0.975639i	$-0.570404\pi$
$829$	−6.28606e47	−0.438762	−0.219381	+	0.975639i	$0.570404\pi$
$830$	0	0
$831$	−1.90709e47	−0.127924
$832$	−1.98658e48	−1.30638
$833$	1.39413e48	0.898797
$834$	2.97548e48	1.88069
$835$	0	0
$836$	4.30756e48	2.61715
$837$	−9.01801e47	−0.537206
$838$	−3.58360e48	−2.09311
$839$	−1.96775e48	−1.12693	−0.563465	−	0.826140i	$-0.690532\pi$
$839$	−1.96775e48	−1.12693	−0.563465	+	0.826140i	$0.690532\pi$
$840$	0	0
$841$	−1.81503e48	−0.999425
$842$	−4.60660e48	−2.48731
$843$	−1.59849e48	−0.846362
$844$	−5.27123e48	−2.73692
$845$	0	0
$846$	−6.61892e47	−0.330504
$847$	−7.07961e46	−0.0346684
$848$	8.71565e47	0.418570
$849$	−2.54486e48	−1.19863
$850$	0	0
$851$	−1.12976e48	−0.511859
$852$	−1.66338e48	−0.739160
$853$	2.75837e48	1.20225	0.601123	−	0.799156i	$-0.294720\pi$
$853$	2.75837e48	1.20225	0.601123	+	0.799156i	$0.294720\pi$
$854$	3.13499e48	1.34023
$855$	0	0
$856$	4.31652e48	1.77548
$857$	−6.56727e46	−0.0264973	−0.0132486	−	0.999912i	$-0.504217\pi$
$857$	−6.56727e46	−0.0264973	−0.0132486	+	0.999912i	$0.504217\pi$
$858$	−3.76649e48	−1.49072
$859$	−1.54196e48	−0.598668	−0.299334	−	0.954148i	$-0.596765\pi$
$859$	−1.54196e48	−0.598668	−0.299334	+	0.954148i	$0.596765\pi$
$860$	0	0
$861$	7.26911e47	0.271600
$862$	−5.09263e48	−1.86669
$863$	2.09589e47	0.0753684	0.0376842	−	0.999290i	$-0.488002\pi$
$863$	2.09589e47	0.0753684	0.0376842	+	0.999290i	$0.488002\pi$
$864$	1.82699e48	0.644553
$865$	0	0
$866$	−2.78266e48	−0.944962
$867$	−2.14121e48	−0.713418
$868$	−1.73363e48	−0.566736
$869$	1.98058e48	0.635282
$870$	0	0
$871$	−5.24497e48	−1.61973
$872$	5.36206e47	0.162484
$873$	−4.55043e47	−0.135306
$874$	−8.49430e48	−2.47850
$875$	0	0
$876$	7.57475e48	2.12839
$877$	3.55305e48	0.979734	0.489867	−	0.871797i	$-0.337045\pi$
$877$	3.55305e48	0.979734	0.489867	+	0.871797i	$0.337045\pi$
$878$	7.61457e48	2.06056
$879$	−5.45313e47	−0.144820
$880$	0	0
$881$	7.23829e48	1.85154	0.925771	−	0.378084i	$-0.123417\pi$
$881$	7.23829e48	1.85154	0.925771	+	0.378084i	$0.123417\pi$
$882$	6.27297e47	0.157486
$883$	4.54962e48	1.12105	0.560523	−	0.828139i	$-0.310600\pi$
$883$	4.54962e48	1.12105	0.560523	+	0.828139i	$0.310600\pi$
$884$	−8.17819e48	−1.97786
$885$	0	0
$886$	−1.33006e49	−3.09895
$887$	−2.68828e48	−0.614801	−0.307400	−	0.951580i	$-0.599459\pi$
$887$	−2.68828e48	−0.614801	−0.307400	+	0.951580i	$0.599459\pi$
$888$	3.16215e48	0.709853
$889$	−4.01571e48	−0.884879
$890$	0	0
$891$	5.09575e48	1.08200
$892$	1.04919e49	2.18693
$893$	−1.09551e49	−2.24165
$894$	1.18159e49	2.37356
$895$	0	0
$896$	5.11896e48	0.991059
$897$	4.73696e48	0.900377
$898$	−9.95655e48	−1.85802
$899$	7.63318e46	0.0139853
$900$	0	0
$901$	−9.02227e48	−1.59352
$902$	−4.28388e48	−0.742898
$903$	5.46476e48	0.930515
$904$	4.56792e48	0.763730
$905$	0	0
$906$	9.22324e48	1.48685
$907$	1.19492e49	1.89155	0.945776	−	0.324819i	$-0.105303\pi$
$907$	1.19492e49	1.89155	0.945776	+	0.324819i	$0.105303\pi$
$908$	−1.96605e49	−3.05617
$909$	−3.75829e47	−0.0573701
$910$	0	0
$911$	9.36081e48	1.37804	0.689018	−	0.724745i	$-0.258042\pi$
$911$	9.36081e48	1.37804	0.689018	+	0.724745i	$0.258042\pi$
$912$	3.84205e48	0.555455
$913$	−7.07422e48	−1.00441
$914$	1.84934e48	0.257873
$915$	0	0
$916$	−2.54977e49	−3.42945
$917$	1.21602e48	0.160638
$918$	1.52336e49	1.97651
$919$	9.33447e48	1.18955	0.594777	−	0.803891i	$-0.297241\pi$
$919$	9.33447e48	1.18955	0.594777	+	0.803891i	$0.297241\pi$
$920$	0	0
$921$	2.96167e48	0.364127
$922$	−1.35760e49	−1.63950
$923$	2.88661e48	0.342420
$924$	8.60193e48	1.00232
$925$	0	0
$926$	−4.58507e48	−0.515543
$927$	1.33275e48	0.147209
$928$	−1.54643e47	−0.0167799
$929$	8.55507e48	0.911936	0.455968	−	0.889996i	$-0.349293\pi$
$929$	8.55507e48	0.911936	0.455968	+	0.889996i	$0.349293\pi$
$930$	0	0
$931$	1.03825e49	1.06815
$932$	−1.28365e49	−1.29743
$933$	1.60599e49	1.59476
$934$	2.22778e49	2.17345
$935$	0	0
$936$	−1.58985e48	−0.149728
$937$	6.77538e48	0.626946	0.313473	−	0.949597i	$-0.398507\pi$
$937$	6.77538e48	0.626946	0.313473	+	0.949597i	$0.398507\pi$
$938$	1.87817e49	1.70761
$939$	1.10030e49	0.982946
$940$	0	0
$941$	5.06011e48	0.436446	0.218223	−	0.975899i	$-0.429974\pi$
$941$	5.06011e48	0.436446	0.218223	+	0.975899i	$0.429974\pi$
$942$	4.27365e48	0.362209
$943$	5.38765e48	0.448701
$944$	2.73633e48	0.223939
$945$	0	0
$946$	−3.22053e49	−2.54521
$947$	−9.56627e47	−0.0742965	−0.0371482	−	0.999310i	$-0.511827\pi$
$947$	−9.56627e47	−0.0742965	−0.0371482	+	0.999310i	$0.511827\pi$
$948$	1.61369e49	1.23164
$949$	−1.31451e49	−0.985989
$950$	0	0
$951$	2.12933e49	1.54264
$952$	1.26526e49	0.900884
$953$	−3.82690e48	−0.267802	−0.133901	−	0.990995i	$-0.542750\pi$
$953$	−3.82690e48	−0.267802	−0.133901	+	0.990995i	$0.542750\pi$
$954$	−4.05961e48	−0.279213
$955$	0	0
$956$	4.20699e48	0.279522
$957$	−3.78743e47	−0.0247342
$958$	4.68423e46	0.00300682
$959$	−9.05323e48	−0.571211
$960$	0	0
$961$	−1.08192e49	−0.659567
$962$	−1.27013e49	−0.761133
$963$	−3.24908e48	−0.191393
$964$	−3.07505e49	−1.78066
$965$	0	0
$966$	−1.69626e49	−0.949225
$967$	1.01112e48	0.0556243	0.0278122	−	0.999613i	$-0.491146\pi$
$967$	1.01112e48	0.0556243	0.0278122	+	0.999613i	$0.491146\pi$
$968$	1.46866e48	0.0794290
$969$	−3.97722e49	−2.11464
$970$	0	0
$971$	2.85606e49	1.46775	0.733873	−	0.679287i	$-0.237711\pi$
$971$	2.85606e49	1.46775	0.733873	+	0.679287i	$0.237711\pi$
$972$	9.43276e48	0.476590
$973$	1.17927e49	0.585801
$974$	−3.10695e49	−1.51744
$975$	0	0
$976$	−1.05097e49	−0.496213
$977$	−2.45925e49	−1.14167	−0.570837	−	0.821064i	$-0.693381\pi$
$977$	−2.45925e49	−1.14167	−0.570837	+	0.821064i	$0.693381\pi$
$978$	2.31644e49	1.05738
$979$	2.91790e49	1.30965
$980$	0	0
$981$	−4.03606e47	−0.0175154
$982$	4.99277e49	2.13060
$983$	3.62125e49	1.51959	0.759794	−	0.650164i	$-0.225300\pi$
$983$	3.62125e49	1.51959	0.759794	+	0.650164i	$0.225300\pi$
$984$	−1.50798e49	−0.622265
$985$	0	0
$986$	−1.28943e48	−0.0514552
$987$	−2.18767e49	−0.858515
$988$	−6.09053e49	−2.35053
$989$	4.05032e49	1.53727
$990$	0	0
$991$	−1.09969e48	−0.0403698	−0.0201849	−	0.999796i	$-0.506425\pi$
$991$	−1.09969e48	−0.0403698	−0.0201849	+	0.999796i	$0.506425\pi$
$992$	−1.13134e49	−0.408459
$993$	3.25908e48	0.115726
$994$	−1.03367e49	−0.360998
$995$	0	0
$996$	−5.76377e49	−1.94728
$997$	1.76019e48	0.0584909	0.0292455	−	0.999572i	$-0.490690\pi$
$997$	1.76019e48	0.0584909	0.0292455	+	0.999572i	$0.490690\pi$
$998$	2.98612e47	0.00976006
$999$	1.50891e49	0.485101

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.a.e.1.2	yes	11
5.2	odd	4		25.34.b.d.24.3		22
5.3	odd	4		25.34.b.d.24.20		22
5.4	even	2		25.34.a.d.1.10	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.34.a.d.1.10	✓	11	5.4	even	2
25.34.a.e.1.2	yes	11	1.1	even	1	trivial
25.34.b.d.24.3		22	5.2	odd	4
25.34.b.d.24.20		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)

\(f(q)\)	\(=\)	\(q-153994. q^{2} -7.94763e7 q^{3} +1.51243e10 q^{4} +1.22389e13 q^{6} +4.85062e13 q^{7} -1.00626e15 q^{8} +7.57418e14 q^{9} +O(q^{10})\)	\(q-153994. q^{2} -7.94763e7 q^{3} +1.51243e10 q^{4} +1.22389e13 q^{6} +4.85062e13 q^{7} -1.00626e15 q^{8} +7.57418e14 q^{9} -1.47532e17 q^{11} -1.20203e18 q^{12} +2.08598e18 q^{13} -7.46967e18 q^{14} +2.50413e19 q^{16} -2.59222e20 q^{17} -1.16638e20 q^{18} -1.93050e21 q^{19} -3.85509e21 q^{21} +2.27191e22 q^{22} -2.85728e22 q^{23} +7.99737e22 q^{24} -3.21229e23 q^{26} +3.81617e23 q^{27} +7.33623e23 q^{28} -3.23015e22 q^{29} -2.36311e24 q^{31} +4.78749e24 q^{32} +1.17253e25 q^{33} +3.99187e25 q^{34} +1.14554e25 q^{36} +3.95398e25 q^{37} +2.97286e26 q^{38} -1.65786e26 q^{39} -1.88559e26 q^{41} +5.93662e26 q^{42} -1.41754e27 q^{43} -2.23132e27 q^{44} +4.40005e27 q^{46} +5.67475e27 q^{47} -1.99019e27 q^{48} -5.37815e27 q^{49} +2.06020e28 q^{51} +3.15490e28 q^{52} +3.48052e28 q^{53} -5.87668e28 q^{54} -4.88098e28 q^{56} +1.53429e29 q^{57} +4.97424e27 q^{58} +1.09273e29 q^{59} -4.19695e29 q^{61} +3.63905e29 q^{62} +3.67395e28 q^{63} -9.52349e29 q^{64} -1.80563e30 q^{66} -2.51440e30 q^{67} -3.92056e30 q^{68} +2.27086e30 q^{69} +1.38382e30 q^{71} -7.62159e29 q^{72} -6.30166e30 q^{73} -6.08891e30 q^{74} -2.91975e31 q^{76} -7.15620e30 q^{77} +2.55301e31 q^{78} -1.34248e31 q^{79} -3.45400e31 q^{81} +2.90370e31 q^{82} +4.79505e31 q^{83} -5.83056e31 q^{84} +2.18294e32 q^{86} +2.56720e30 q^{87} +1.48455e32 q^{88} -1.97781e32 q^{89} +1.01183e32 q^{91} -4.32144e32 q^{92} +1.87811e32 q^{93} -8.73879e32 q^{94} -3.80492e32 q^{96} -6.00782e32 q^{97} +8.28204e32 q^{98} -1.11743e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 9393 q^{2} + 80330849 q^{3} + 49338206677 q^{4} - 17783977676723 q^{6} + 21344025107658 q^{7} - 970199832420105 q^{8} + 24\!\cdots\!58 q^{9}+O(q^{10}) \) 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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