LMFDB - Embedded newform 25.34.a.e.1.3

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			1.3
Root			$110093.$ 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)

$f(q)$	$=$	$q-109239. q^{2} +1.96178e7 q^{3} +3.34318e9 q^{4} -2.14302e12 q^{6} -7.24227e12 q^{7} +5.73150e14 q^{8} -5.17420e15 q^{9} +O(q^{10})$	\(q-109239. q^{2} +1.96178e7 q^{3} +3.34318e9 q^{4} -2.14302e12 q^{6} -7.24227e12 q^{7} +5.73150e14 q^{8} -5.17420e15 q^{9} +1.80998e17 q^{11} +6.55856e16 q^{12} -1.38383e18 q^{13} +7.91136e17 q^{14} -9.13278e19 q^{16} +6.46344e19 q^{17} +5.65224e20 q^{18} +1.46370e21 q^{19} -1.42077e20 q^{21} -1.97720e22 q^{22} -7.51392e21 q^{23} +1.12439e22 q^{24} +1.51168e23 q^{26} -2.10563e23 q^{27} -2.42122e22 q^{28} -3.42626e23 q^{29} +1.13942e24 q^{31} +5.05322e24 q^{32} +3.55077e24 q^{33} -7.06058e24 q^{34} -1.72983e25 q^{36} -2.61955e25 q^{37} -1.59893e26 q^{38} -2.71476e25 q^{39} +1.74813e26 q^{41} +1.55203e25 q^{42} +1.37416e27 q^{43} +6.05108e26 q^{44} +8.20811e26 q^{46} +3.57221e27 q^{47} -1.79165e27 q^{48} -7.67854e27 q^{49} +1.26798e27 q^{51} -4.62639e27 q^{52} +3.47129e27 q^{53} +2.30016e28 q^{54} -4.15090e27 q^{56} +2.87146e28 q^{57} +3.74280e28 q^{58} -1.06805e29 q^{59} +3.27030e29 q^{61} -1.24468e29 q^{62} +3.74730e28 q^{63} +2.32492e29 q^{64} -3.87882e29 q^{66} -5.06936e29 q^{67} +2.16084e29 q^{68} -1.47406e29 q^{69} -2.35556e30 q^{71} -2.96559e30 q^{72} +2.40851e30 q^{73} +2.86157e30 q^{74} +4.89342e30 q^{76} -1.31083e30 q^{77} +2.96557e30 q^{78} -2.85259e31 q^{79} +2.46330e31 q^{81} -1.90963e31 q^{82} +1.04315e31 q^{83} -4.74988e29 q^{84} -1.50111e32 q^{86} -6.72154e30 q^{87} +1.03739e32 q^{88} -2.05429e32 q^{89} +1.00221e31 q^{91} -2.51204e31 q^{92} +2.23528e31 q^{93} -3.90224e32 q^{94} +9.91329e31 q^{96} -7.08500e32 q^{97} +8.38795e32 q^{98} -9.36520e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−109239.	−1.17864	−0.589321	−	0.807899i	$-0.700605\pi$
$2$	−109239.	−1.17864	−0.589321	+	0.807899i	$0.700605\pi$
$3$	1.96178e7	0.263117	0.131558	−	0.991308i	$-0.458002\pi$
$3$	1.96178e7	0.263117	0.131558	+	0.991308i	$0.458002\pi$
$4$	3.34318e9	0.389197
$5$	0	0
$5$	0	0
$6$	−2.14302e12	−0.310120
$7$	−7.24227e12	−0.0823677	−0.0411838	−	0.999152i	$-0.513113\pi$
$7$	−7.24227e12	−0.0823677	−0.0411838	+	0.999152i	$0.513113\pi$
$8$	5.73150e14	0.719918
$9$	−5.17420e15	−0.930770
$10$	0	0
$11$	1.80998e17	1.18767	0.593833	−	0.804589i	$-0.297614\pi$
$11$	1.80998e17	1.18767	0.593833	+	0.804589i	$0.297614\pi$
$12$	6.55856e16	0.102404
$13$	−1.38383e18	−0.576790	−0.288395	−	0.957512i	$-0.593122\pi$
$13$	−1.38383e18	−0.576790	−0.288395	+	0.957512i	$0.593122\pi$
$14$	7.91136e17	0.0970820
$15$	0	0
$16$	−9.13278e19	−1.23772
$17$	6.46344e19	0.322149	0.161074	−	0.986942i	$-0.448504\pi$
$17$	6.46344e19	0.322149	0.161074	+	0.986942i	$0.448504\pi$
$18$	5.65224e20	1.09704
$19$	1.46370e21	1.16418	0.582088	−	0.813126i	$-0.302236\pi$
$19$	1.46370e21	1.16418	0.582088	+	0.813126i	$0.302236\pi$
$20$	0	0
$21$	−1.42077e20	−0.0216723
$22$	−1.97720e22	−1.39983
$23$	−7.51392e21	−0.255480	−0.127740	−	0.991808i	$-0.540772\pi$
$23$	−7.51392e21	−0.255480	−0.127740	+	0.991808i	$0.540772\pi$
$24$	1.12439e22	0.189423
$25$	0	0
$26$	1.51168e23	0.679829
$27$	−2.10563e23	−0.508018
$28$	−2.42122e22	−0.0320572
$29$	−3.42626e23	−0.254245	−0.127123	−	0.991887i	$-0.540574\pi$
$29$	−3.42626e23	−0.254245	−0.127123	+	0.991887i	$0.540574\pi$
$30$	0	0
$31$	1.13942e24	0.281329	0.140665	−	0.990057i	$-0.455076\pi$
$31$	1.13942e24	0.281329	0.140665	+	0.990057i	$0.455076\pi$
$32$	5.05322e24	0.738914
$33$	3.55077e24	0.312495
$34$	−7.06058e24	−0.379698
$35$	0	0
$36$	−1.72983e25	−0.362253
$37$	−2.61955e25	−0.349059	−0.174529	−	0.984652i	$-0.555840\pi$
$37$	−2.61955e25	−0.349059	−0.174529	+	0.984652i	$0.555840\pi$
$38$	−1.59893e26	−1.37215
$39$	−2.71476e25	−0.151763
$40$	0	0
$41$	1.74813e26	0.428193	0.214096	−	0.976813i	$-0.431319\pi$
$41$	1.74813e26	0.428193	0.214096	+	0.976813i	$0.431319\pi$
$42$	1.55203e25	0.0255439
$43$	1.37416e27	1.53393	0.766966	−	0.641687i	$-0.221765\pi$
$43$	1.37416e27	1.53393	0.766966	+	0.641687i	$0.221765\pi$
$44$	6.05108e26	0.462236
$45$	0	0
$46$	8.20811e26	0.301120
$47$	3.57221e27	0.919015	0.459508	−	0.888174i	$-0.348026\pi$
$47$	3.57221e27	0.919015	0.459508	+	0.888174i	$0.348026\pi$
$48$	−1.79165e27	−0.325666
$49$	−7.67854e27	−0.993216
$50$	0	0
$51$	1.26798e27	0.0847627
$52$	−4.62639e27	−0.224485
$53$	3.47129e27	0.123010	0.0615049	−	0.998107i	$-0.480410\pi$
$53$	3.47129e27	0.123010	0.0615049	+	0.998107i	$0.480410\pi$
$54$	2.30016e28	0.598771
$55$	0	0
$56$	−4.15090e27	−0.0592980
$57$	2.87146e28	0.306314
$58$	3.74280e28	0.299664
$59$	−1.06805e29	−0.644958	−0.322479	−	0.946577i	$-0.604516\pi$
$59$	−1.06805e29	−0.644958	−0.322479	+	0.946577i	$0.604516\pi$
$60$	0	0
$61$	3.27030e29	1.13932	0.569660	−	0.821880i	$-0.307075\pi$
$61$	3.27030e29	1.13932	0.569660	+	0.821880i	$0.307075\pi$
$62$	−1.24468e29	−0.331586
$63$	3.74730e28	0.0766653
$64$	2.32492e29	0.366808
$65$	0	0
$66$	−3.87882e29	−0.368319
$67$	−5.06936e29	−0.375594	−0.187797	−	0.982208i	$-0.560135\pi$
$67$	−5.06936e29	−0.375594	−0.187797	+	0.982208i	$0.560135\pi$
$68$	2.16084e29	0.125379
$69$	−1.47406e29	−0.0672211
$70$	0	0
$71$	−2.35556e30	−0.670396	−0.335198	−	0.942148i	$-0.608803\pi$
$71$	−2.35556e30	−0.670396	−0.335198	+	0.942148i	$0.608803\pi$
$72$	−2.96559e30	−0.670078
$73$	2.40851e30	0.433432	0.216716	−	0.976235i	$-0.430465\pi$
$73$	2.40851e30	0.433432	0.216716	+	0.976235i	$0.430465\pi$
$74$	2.86157e30	0.411415
$75$	0	0
$76$	4.89342e30	0.453094
$77$	−1.31083e30	−0.0978252
$78$	2.96557e30	0.178874
$79$	−2.85259e31	−1.39441	−0.697207	−	0.716870i	$-0.745574\pi$
$79$	−2.85259e31	−1.39441	−0.697207	+	0.716870i	$0.745574\pi$
$80$	0	0
$81$	2.46330e31	0.797102
$82$	−1.90963e31	−0.504686
$83$	1.04315e31	0.225715	0.112857	−	0.993611i	$-0.464000\pi$
$83$	1.04315e31	0.225715	0.112857	+	0.993611i	$0.464000\pi$
$84$	−4.74988e29	−0.00843480
$85$	0	0
$86$	−1.50111e32	−1.80796
$87$	−6.72154e30	−0.0668962
$88$	1.03739e32	0.855022
$89$	−2.05429e32	−1.40516	−0.702581	−	0.711603i	$-0.747969\pi$
$89$	−2.05429e32	−1.40516	−0.702581	+	0.711603i	$0.747969\pi$
$90$	0	0
$91$	1.00221e31	0.0475088
$92$	−2.51204e31	−0.0994321
$93$	2.23528e31	0.0740224
$94$	−3.90224e32	−1.08319
$95$	0	0
$96$	9.91329e31	0.194421
$97$	−7.08500e32	−1.17113	−0.585566	−	0.810624i	$-0.699128\pi$
$97$	−7.08500e32	−1.17113	−0.585566	+	0.810624i	$0.699128\pi$
$98$	8.38795e32	1.17065
$99$	−9.36520e32	−1.10544
$100$	0	0
$101$	−1.86281e33	−1.58076	−0.790380	−	0.612617i	$-0.790117\pi$
$101$	−1.86281e33	−1.58076	−0.790380	+	0.612617i	$0.790117\pi$
$102$	−1.38513e32	−0.0999049
$103$	7.41307e32	0.455181	0.227590	−	0.973757i	$-0.426915\pi$
$103$	7.41307e32	0.455181	0.227590	+	0.973757i	$0.426915\pi$
$104$	−7.93142e32	−0.415241
$105$	0	0
$106$	−3.79200e32	−0.144984
$107$	−5.76499e33	−1.88785	−0.943923	−	0.330166i	$-0.892895\pi$
$107$	−5.76499e33	−1.88785	−0.943923	+	0.330166i	$0.892895\pi$
$108$	−7.03948e32	−0.197719
$109$	−6.57177e33	−1.58542	−0.792711	−	0.609598i	$-0.791331\pi$
$109$	−6.57177e33	−1.58542	−0.792711	+	0.609598i	$0.791331\pi$
$110$	0	0
$111$	−5.13897e32	−0.0918432
$112$	6.61420e32	0.101948
$113$	8.95137e33	1.19150	0.595751	−	0.803169i	$-0.296854\pi$
$113$	8.95137e33	1.19150	0.595751	+	0.803169i	$0.296854\pi$
$114$	−3.13675e33	−0.361035
$115$	0	0
$116$	−1.14546e33	−0.0989515
$117$	7.16022e33	0.536858
$118$	1.16672e34	0.760175
$119$	−4.68099e32	−0.0265346
$120$	0	0
$121$	9.53505e33	0.410549
$122$	−3.57244e34	−1.34285
$123$	3.42943e33	0.112665
$124$	3.80927e33	0.109492
$125$	0	0
$126$	−4.09350e33	−0.0903610
$127$	7.07774e34	1.37130	0.685651	−	0.727930i	$-0.259518\pi$
$127$	7.07774e34	1.37130	0.685651	+	0.727930i	$0.259518\pi$
$128$	−6.88040e34	−1.17125
$129$	2.69578e34	0.403603
$130$	0	0
$131$	−1.14692e34	−0.133216	−0.0666079	−	0.997779i	$-0.521218\pi$
$131$	−1.14692e34	−0.133216	−0.0666079	+	0.997779i	$0.521218\pi$
$132$	1.18708e34	0.121622
$133$	−1.06005e34	−0.0958905
$134$	5.53770e34	0.442691
$135$	0	0
$136$	3.70452e34	0.231921
$137$	8.29417e34	0.460133	0.230067	−	0.973175i	$-0.426106\pi$
$137$	8.29417e34	0.460133	0.230067	+	0.973175i	$0.426106\pi$
$138$	1.61025e34	0.0792296
$139$	3.40975e35	1.48929	0.744643	−	0.667463i	$-0.232620\pi$
$139$	3.40975e35	1.48929	0.744643	+	0.667463i	$0.232620\pi$
$140$	0	0
$141$	7.00788e34	0.241808
$142$	2.57319e35	0.790157
$143$	−2.50470e35	−0.685033
$144$	4.72549e35	1.15203
$145$	0	0
$146$	−2.63103e35	−0.510861
$147$	−1.50636e35	−0.261332
$148$	−8.75762e34	−0.135853
$149$	1.79313e35	0.248908	0.124454	−	0.992225i	$-0.460282\pi$
$149$	1.79313e35	0.248908	0.124454	+	0.992225i	$0.460282\pi$
$150$	0	0
$151$	2.78845e35	0.310630	0.155315	−	0.987865i	$-0.450361\pi$
$151$	2.78845e35	0.310630	0.155315	+	0.987865i	$0.450361\pi$
$152$	8.38921e35	0.838112
$153$	−3.34431e35	−0.299846
$154$	1.43194e35	0.115301
$155$	0	0
$156$	−9.07593e34	−0.0590657
$157$	1.75653e36	1.02875	0.514376	−	0.857565i	$-0.328024\pi$
$157$	1.75653e36	1.02875	0.514376	+	0.857565i	$0.328024\pi$
$158$	3.11613e36	1.64352
$159$	6.80990e34	0.0323659
$160$	0	0
$161$	5.44178e34	0.0210433
$162$	−2.69087e36	−0.939497
$163$	2.40082e36	0.757295	0.378647	−	0.925541i	$-0.376389\pi$
$163$	2.40082e36	0.757295	0.378647	+	0.925541i	$0.376389\pi$
$164$	5.84430e35	0.166651
$165$	0	0
$166$	−1.13953e36	−0.266037
$167$	−4.72050e36	−0.998081	−0.499041	−	0.866579i	$-0.666314\pi$
$167$	−4.72050e36	−0.998081	−0.499041	+	0.866579i	$0.666314\pi$
$168$	−8.14314e34	−0.0156023
$169$	−3.84114e36	−0.667314
$170$	0	0
$171$	−7.57350e36	−1.08358
$172$	4.59404e36	0.597002
$173$	1.39436e37	1.64670	0.823350	−	0.567534i	$-0.192102\pi$
$173$	1.39436e37	1.64670	0.823350	+	0.567534i	$0.192102\pi$
$174$	7.34253e35	0.0788467
$175$	0	0
$176$	−1.65301e37	−1.47000
$177$	−2.09526e36	−0.169699
$178$	2.24408e37	1.65618
$179$	−1.33795e35	−0.00900255	−0.00450128	−	0.999990i	$-0.501433\pi$
$179$	−1.33795e35	−0.00900255	−0.00450128	+	0.999990i	$0.501433\pi$
$180$	0	0
$181$	−6.42440e36	−0.359862	−0.179931	−	0.983679i	$-0.557587\pi$
$181$	−6.42440e36	−0.359862	−0.179931	+	0.983679i	$0.557587\pi$
$182$	−1.09480e36	−0.0559959
$183$	6.41560e36	0.299774
$184$	−4.30660e36	−0.183925
$185$	0	0
$186$	−2.44179e36	−0.0872459
$187$	1.16987e37	0.382605
$188$	1.19425e37	0.357678
$189$	1.52495e36	0.0418443
$190$	0	0
$191$	−4.06643e37	−0.937914	−0.468957	−	0.883221i	$-0.655370\pi$
$191$	−4.06643e37	−0.937914	−0.468957	+	0.883221i	$0.655370\pi$
$192$	4.56097e36	0.0965133
$193$	6.26368e37	1.21656	0.608281	−	0.793722i	$-0.291859\pi$
$193$	6.26368e37	1.21656	0.608281	+	0.793722i	$0.291859\pi$
$194$	7.73957e37	1.38035
$195$	0	0
$196$	−2.56707e37	−0.386556
$197$	5.72700e37	0.792930	0.396465	−	0.918050i	$-0.370237\pi$
$197$	5.72700e37	0.792930	0.396465	+	0.918050i	$0.370237\pi$
$198$	1.02304e38	1.30292
$199$	1.51928e38	1.78058	0.890289	−	0.455396i	$-0.150502\pi$
$199$	1.51928e38	1.78058	0.890289	+	0.455396i	$0.150502\pi$
$200$	0	0
$201$	−9.94494e36	−0.0988250
$202$	2.03491e38	1.86315
$203$	2.48139e36	0.0209416
$204$	4.23908e36	0.0329894
$205$	0	0
$206$	−8.09795e37	−0.536495
$207$	3.88786e37	0.237793
$208$	1.26382e38	0.713906
$209$	2.64927e38	1.38265
$210$	0	0
$211$	7.89682e36	0.0352202	0.0176101	−	0.999845i	$-0.494394\pi$
$211$	7.89682e36	0.0352202	0.0176101	+	0.999845i	$0.494394\pi$
$212$	1.16051e37	0.0478750
$213$	−4.62108e37	−0.176392
$214$	6.29761e38	2.22509
$215$	0	0
$216$	−1.20684e38	−0.365731
$217$	−8.25196e36	−0.0231724
$218$	7.17892e38	1.86864
$219$	4.72495e37	0.114043
$220$	0	0
$221$	−8.94430e37	−0.185812
$222$	5.61375e37	0.108250
$223$	−5.86319e36	−0.0104979	−0.00524896	−	0.999986i	$-0.501671\pi$
$223$	−5.86319e36	−0.0104979	−0.00524896	+	0.999986i	$0.501671\pi$
$224$	−3.65968e37	−0.0608626
$225$	0	0
$226$	−9.77836e38	−1.40436
$227$	9.99903e38	1.33515	0.667577	−	0.744541i	$-0.267331\pi$
$227$	9.99903e38	1.33515	0.667577	+	0.744541i	$0.267331\pi$
$228$	9.59979e37	0.119217
$229$	1.69123e38	0.195396	0.0976982	−	0.995216i	$-0.468852\pi$
$229$	1.69123e38	0.195396	0.0976982	+	0.995216i	$0.468852\pi$
$230$	0	0
$231$	−2.57156e37	−0.0257395
$232$	−1.96376e38	−0.183036
$233$	1.96054e39	1.70217	0.851086	−	0.525026i	$-0.175944\pi$
$233$	1.96054e39	1.70217	0.851086	+	0.525026i	$0.175944\pi$
$234$	−7.82174e38	−0.632764
$235$	0	0
$236$	−3.57066e38	−0.251016
$237$	−5.59613e38	−0.366894
$238$	5.11346e37	0.0312748
$239$	−2.20476e39	−1.25833	−0.629166	−	0.777271i	$-0.716604\pi$
$239$	−2.20476e39	−1.25833	−0.629166	+	0.777271i	$0.716604\pi$
$240$	0	0
$241$	−9.40073e38	−0.467606	−0.233803	−	0.972284i	$-0.575117\pi$
$241$	−9.40073e38	−0.467606	−0.233803	+	0.972284i	$0.575117\pi$
$242$	−1.04160e39	−0.483890
$243$	1.65377e39	0.717749
$244$	1.09332e39	0.443420
$245$	0	0
$246$	−3.74627e38	−0.132791
$247$	−2.02552e39	−0.671485
$248$	6.53056e38	0.202534
$249$	2.04643e38	0.0593894
$250$	0	0
$251$	−1.27323e39	−0.323810	−0.161905	−	0.986806i	$-0.551764\pi$
$251$	−1.27323e39	−0.323810	−0.161905	+	0.986806i	$0.551764\pi$
$252$	1.25279e38	0.0298379
$253$	−1.36000e39	−0.303425
$254$	−7.73164e39	−1.61627
$255$	0	0
$256$	5.51897e39	1.01368
$257$	−1.83336e39	−0.315755	−0.157878	−	0.987459i	$-0.550465\pi$
$257$	−1.83336e39	−0.315755	−0.157878	+	0.987459i	$0.550465\pi$
$258$	−2.94484e39	−0.475704
$259$	1.89715e38	0.0287512
$260$	0	0
$261$	1.77281e39	0.236644
$262$	1.25288e39	0.157014
$263$	−1.40189e40	−1.64984	−0.824922	−	0.565247i	$-0.808781\pi$
$263$	−1.40189e40	−1.64984	−0.824922	+	0.565247i	$0.808781\pi$
$264$	2.03512e39	0.224971
$265$	0	0
$266$	1.15799e39	0.113021
$267$	−4.03006e39	−0.369722
$268$	−1.69477e39	−0.146180
$269$	1.72452e40	1.39880	0.699399	−	0.714732i	$-0.253451\pi$
$269$	1.72452e40	1.39880	0.699399	+	0.714732i	$0.253451\pi$
$270$	0	0
$271$	1.59037e40	1.14158	0.570788	−	0.821098i	$-0.306638\pi$
$271$	1.59037e40	1.14158	0.570788	+	0.821098i	$0.306638\pi$
$272$	−5.90291e39	−0.398731
$273$	1.96610e38	0.0125004
$274$	−9.06045e39	−0.542332
$275$	0	0
$276$	−4.92805e38	−0.0261623
$277$	2.65726e40	1.32898	0.664489	−	0.747298i	$-0.268649\pi$
$277$	2.65726e40	1.32898	0.664489	+	0.747298i	$0.268649\pi$
$278$	−3.72477e40	−1.75533
$279$	−5.89557e39	−0.261853
$280$	0	0
$281$	3.55370e40	1.40290	0.701450	−	0.712719i	$-0.252537\pi$
$281$	3.55370e40	1.40290	0.701450	+	0.712719i	$0.252537\pi$
$282$	−7.65532e39	−0.285005
$283$	−5.38426e40	−1.89082	−0.945410	−	0.325884i	$-0.894338\pi$
$283$	−5.38426e40	−1.89082	−0.945410	+	0.325884i	$0.894338\pi$
$284$	−7.87505e39	−0.260916
$285$	0	0
$286$	2.73611e40	0.807409
$287$	−1.26604e39	−0.0352693
$288$	−2.61464e40	−0.687758
$289$	−3.60769e40	−0.896220
$290$	0	0
$291$	−1.38992e40	−0.308145
$292$	8.05207e39	0.168690
$293$	1.19080e40	0.235789	0.117895	−	0.993026i	$-0.462385\pi$
$293$	1.19080e40	0.235789	0.117895	+	0.993026i	$0.462385\pi$
$294$	1.64553e40	0.308016
$295$	0	0
$296$	−1.50140e40	−0.251294
$297$	−3.81114e40	−0.603355
$298$	−1.95880e40	−0.293374
$299$	1.03980e40	0.147358
$300$	0	0
$301$	−9.95200e39	−0.126346
$302$	−3.04607e40	−0.366122
$303$	−3.65442e40	−0.415925
$304$	−1.33677e41	−1.44093
$305$	0	0
$306$	3.65329e40	0.353411
$307$	−1.92332e41	−1.76307	−0.881533	−	0.472123i	$-0.843488\pi$
$307$	−1.92332e41	−1.76307	−0.881533	+	0.472123i	$0.843488\pi$
$308$	−4.38235e39	−0.0380733
$309$	1.45428e40	0.119766
$310$	0	0
$311$	7.59201e40	0.562096	0.281048	−	0.959694i	$-0.409318\pi$
$311$	7.59201e40	0.562096	0.281048	+	0.959694i	$0.409318\pi$
$312$	−1.55597e40	−0.109257
$313$	2.38953e41	1.59159	0.795795	−	0.605566i	$-0.207053\pi$
$313$	2.38953e41	1.59159	0.795795	+	0.605566i	$0.207053\pi$
$314$	−1.91881e41	−1.21253
$315$	0	0
$316$	−9.53670e40	−0.542702
$317$	1.87224e41	1.01131	0.505655	−	0.862736i	$-0.331251\pi$
$317$	1.87224e41	1.01131	0.505655	+	0.862736i	$0.331251\pi$
$318$	−7.43905e39	−0.0381478
$319$	−6.20145e40	−0.301958
$320$	0	0
$321$	−1.13096e41	−0.496724
$322$	−5.94453e39	−0.0248025
$323$	9.46056e40	0.375038
$324$	8.23523e40	0.310229
$325$	0	0
$326$	−2.62263e41	−0.892579
$327$	−1.28923e41	−0.417151
$328$	1.00194e41	0.308264
$329$	−2.58709e40	−0.0756972
$330$	0	0
$331$	1.81289e41	0.479965	0.239983	−	0.970777i	$-0.422858\pi$
$331$	1.81289e41	0.479965	0.239983	+	0.970777i	$0.422858\pi$
$332$	3.48745e40	0.0878475
$333$	1.35541e41	0.324893
$334$	5.15661e41	1.17638
$335$	0	0
$336$	1.29756e40	0.0268243
$337$	2.06387e41	0.406246	0.203123	−	0.979153i	$-0.434891\pi$
$337$	2.06387e41	0.406246	0.203123	+	0.979153i	$0.434891\pi$
$338$	4.19602e41	0.786524
$339$	1.75606e41	0.313504
$340$	0	0
$341$	2.06232e41	0.334125
$342$	8.27320e41	1.27715
$343$	1.11600e41	0.164177
$344$	7.87597e41	1.10431
$345$	0	0
$346$	−1.52318e42	−1.94087
$347$	2.42023e41	0.294050	0.147025	−	0.989133i	$-0.453030\pi$
$347$	2.42023e41	0.294050	0.147025	+	0.989133i	$0.453030\pi$
$348$	−2.24713e40	−0.0260358
$349$	9.38948e41	1.03758	0.518790	−	0.854902i	$-0.326383\pi$
$349$	9.38948e41	1.03758	0.518790	+	0.854902i	$0.326383\pi$
$350$	0	0
$351$	2.91383e41	0.293019
$352$	9.14622e41	0.877582
$353$	6.44457e41	0.590081	0.295040	−	0.955485i	$-0.404667\pi$
$353$	6.44457e41	0.590081	0.295040	+	0.955485i	$0.404667\pi$
$354$	2.28884e41	0.200015
$355$	0	0
$356$	−6.86785e41	−0.546885
$357$	−9.18305e39	−0.00698171
$358$	1.46156e40	0.0106108
$359$	2.55980e42	1.77479	0.887397	−	0.461005i	$-0.152511\pi$
$359$	2.55980e42	1.77479	0.887397	+	0.461005i	$0.152511\pi$
$360$	0	0
$361$	5.61659e41	0.355307
$362$	7.01794e41	0.424149
$363$	1.87056e41	0.108022
$364$	3.35055e40	0.0184903
$365$	0	0
$366$	−7.00832e41	−0.353326
$367$	−1.65759e42	−0.798890	−0.399445	−	0.916757i	$-0.630797\pi$
$367$	−1.65759e42	−0.798890	−0.399445	+	0.916757i	$0.630797\pi$
$368$	6.86230e41	0.316214
$369$	−9.04517e41	−0.398549
$370$	0	0
$371$	−2.51400e40	−0.0101320
$372$	7.47293e40	0.0288093
$373$	1.60280e42	0.591131	0.295566	−	0.955322i	$-0.404492\pi$
$373$	1.60280e42	0.591131	0.295566	+	0.955322i	$0.404492\pi$
$374$	−1.27795e42	−0.450954
$375$	0	0
$376$	2.04741e42	0.661616
$377$	4.74136e41	0.146646
$378$	−1.66584e41	−0.0493194
$379$	−7.63887e41	−0.216512	−0.108256	−	0.994123i	$-0.534527\pi$
$379$	−7.63887e41	−0.216512	−0.108256	+	0.994123i	$0.534527\pi$
$380$	0	0
$381$	1.38849e42	0.360813
$382$	4.44212e42	1.10546
$383$	6.89316e42	1.64300	0.821502	−	0.570206i	$-0.193136\pi$
$383$	6.89316e42	1.64300	0.821502	+	0.570206i	$0.193136\pi$
$384$	−1.34978e42	−0.308175
$385$	0	0
$386$	−6.84237e42	−1.43389
$387$	−7.11016e42	−1.42774
$388$	−2.36864e42	−0.455801
$389$	−6.00537e42	−1.10757	−0.553785	−	0.832660i	$-0.686817\pi$
$389$	−6.00537e42	−1.10757	−0.553785	+	0.832660i	$0.686817\pi$
$390$	0	0
$391$	−4.85657e41	−0.0823026
$392$	−4.40095e42	−0.715034
$393$	−2.25000e41	−0.0350513
$394$	−6.25611e42	−0.934580
$395$	0	0
$396$	−3.13095e42	−0.430235
$397$	−6.47973e42	−0.854110	−0.427055	−	0.904226i	$-0.640449\pi$
$397$	−6.47973e42	−0.854110	−0.427055	+	0.904226i	$0.640449\pi$
$398$	−1.65964e43	−2.09866
$399$	−2.07959e41	−0.0252304
$400$	0	0
$401$	1.49165e43	1.66642	0.833211	−	0.552956i	$-0.186500\pi$
$401$	1.49165e43	1.66642	0.833211	+	0.552956i	$0.186500\pi$
$402$	1.08637e42	0.116479
$403$	−1.57676e42	−0.162268
$404$	−6.22770e42	−0.615227
$405$	0	0
$406$	−2.71064e41	−0.0246826
$407$	−4.74133e42	−0.414565
$408$	7.26743e41	0.0610222
$409$	−1.52685e42	−0.123130	−0.0615648	−	0.998103i	$-0.519609\pi$
$409$	−1.52685e42	−0.123130	−0.0615648	+	0.998103i	$0.519609\pi$
$410$	0	0
$411$	1.62713e42	0.121069
$412$	2.47832e42	0.177155
$413$	7.73507e41	0.0531237
$414$	−4.24705e42	−0.280273
$415$	0	0
$416$	−6.99280e42	−0.426198
$417$	6.68916e42	0.391856
$418$	−2.89403e43	−1.62965
$419$	9.92998e42	0.537547	0.268774	−	0.963203i	$-0.413382\pi$
$419$	9.92998e42	0.537547	0.268774	+	0.963203i	$0.413382\pi$
$420$	0	0
$421$	3.76712e43	1.88519	0.942596	−	0.333936i	$-0.108377\pi$
$421$	3.76712e43	1.88519	0.942596	+	0.333936i	$0.108377\pi$
$422$	−8.62639e41	−0.0415120
$423$	−1.84834e43	−0.855391
$424$	1.98957e42	0.0885569
$425$	0	0
$426$	5.04801e42	0.207904
$427$	−2.36844e42	−0.0938432
$428$	−1.92734e43	−0.734744
$429$	−4.91366e42	−0.180244
$430$	0	0
$431$	1.57215e43	0.534097	0.267048	−	0.963683i	$-0.413952\pi$
$431$	1.57215e43	0.534097	0.267048	+	0.963683i	$0.413952\pi$
$432$	1.92302e43	0.628785
$433$	−2.48284e43	−0.781446	−0.390723	−	0.920508i	$-0.627775\pi$
$433$	−2.48284e43	−0.781446	−0.390723	+	0.920508i	$0.627775\pi$
$434$	9.01434e41	0.0273120
$435$	0	0
$436$	−2.19706e43	−0.617041
$437$	−1.09982e43	−0.297424
$438$	−5.16148e42	−0.134416
$439$	4.21958e43	1.05829	0.529145	−	0.848531i	$-0.322513\pi$
$439$	4.21958e43	1.05829	0.529145	+	0.848531i	$0.322513\pi$
$440$	0	0
$441$	3.97304e43	0.924455
$442$	9.77064e42	0.219006
$443$	4.28416e43	0.925133	0.462567	−	0.886585i	$-0.346929\pi$
$443$	4.28416e43	0.925133	0.462567	+	0.886585i	$0.346929\pi$
$444$	−1.71805e42	−0.0357451
$445$	0	0
$446$	6.40488e41	0.0123733
$447$	3.51773e42	0.0654919
$448$	−1.68377e42	−0.0302131
$449$	4.10901e43	0.710678	0.355339	−	0.934737i	$-0.384365\pi$
$449$	4.10901e43	0.710678	0.355339	+	0.934737i	$0.384365\pi$
$450$	0	0
$451$	3.16407e43	0.508550
$452$	2.99260e43	0.463729
$453$	5.47032e42	0.0817321
$454$	−1.09228e44	−1.57367
$455$	0	0
$456$	1.64577e43	0.220521
$457$	−1.07321e44	−1.38697	−0.693485	−	0.720471i	$-0.743925\pi$
$457$	−1.07321e44	−1.38697	−0.693485	+	0.720471i	$0.743925\pi$
$458$	−1.84748e43	−0.230302
$459$	−1.36096e43	−0.163657
$460$	0	0
$461$	−1.65449e44	−1.85182	−0.925910	−	0.377744i	$-0.876700\pi$
$461$	−1.65449e44	−1.85182	−0.925910	+	0.377744i	$0.876700\pi$
$462$	2.80914e42	0.0303376
$463$	7.01897e43	0.731454	0.365727	−	0.930722i	$-0.380820\pi$
$463$	7.01897e43	0.731454	0.365727	+	0.930722i	$0.380820\pi$
$464$	3.12912e43	0.314685
$465$	0	0
$466$	−2.14167e44	−2.00625
$467$	6.51752e43	0.589324	0.294662	−	0.955602i	$-0.404793\pi$
$467$	6.51752e43	0.589324	0.294662	+	0.955602i	$0.404793\pi$
$468$	2.39379e43	0.208944
$469$	3.67136e42	0.0309368
$470$	0	0
$471$	3.44591e43	0.270682
$472$	−6.12150e43	−0.464317
$473$	2.48719e44	1.82180
$474$	6.11315e43	0.432436
$475$	0	0
$476$	−1.56494e42	−0.0103272
$477$	−1.79612e43	−0.114494
$478$	2.40845e44	1.48312
$479$	−1.66158e44	−0.988519	−0.494259	−	0.869314i	$-0.664561\pi$
$479$	−1.66158e44	−0.988519	−0.494259	+	0.869314i	$0.664561\pi$
$480$	0	0
$481$	3.62502e43	0.201334
$482$	1.02692e44	0.551140
$483$	1.06756e42	0.00553685
$484$	3.18774e43	0.159784
$485$	0	0
$486$	−1.80656e44	−0.845969
$487$	1.12846e44	0.510809	0.255404	−	0.966834i	$-0.417791\pi$
$487$	1.12846e44	0.510809	0.255404	+	0.966834i	$0.417791\pi$
$488$	1.87437e44	0.820217
$489$	4.70988e43	0.199257
$490$	0	0
$491$	1.02544e44	0.405568	0.202784	−	0.979223i	$-0.435001\pi$
$491$	1.02544e44	0.405568	0.202784	+	0.979223i	$0.435001\pi$
$492$	1.14652e43	0.0438488
$493$	−2.21454e43	−0.0819048
$494$	2.21265e44	0.791441
$495$	0	0
$496$	−1.04060e44	−0.348207
$497$	1.70596e43	0.0552190
$498$	−2.23550e43	−0.0699988
$499$	7.84092e43	0.237524	0.118762	−	0.992923i	$-0.462107\pi$
$499$	7.84092e43	0.237524	0.118762	+	0.992923i	$0.462107\pi$
$500$	0	0
$501$	−9.26055e43	−0.262612
$502$	1.39086e44	0.381656
$503$	−1.09015e44	−0.289478	−0.144739	−	0.989470i	$-0.546234\pi$
$503$	−1.09015e44	−0.289478	−0.144739	+	0.989470i	$0.546234\pi$
$504$	2.14776e43	0.0551928
$505$	0	0
$506$	1.48565e44	0.357629
$507$	−7.53546e43	−0.175581
$508$	2.36621e44	0.533707
$509$	8.09488e44	1.76753	0.883766	−	0.467930i	$-0.155000\pi$
$509$	8.09488e44	1.76753	0.883766	+	0.467930i	$0.155000\pi$
$510$	0	0
$511$	−1.74431e43	−0.0357008
$512$	−1.18640e43	−0.0235112
$513$	−3.08201e44	−0.591422
$514$	2.00274e44	0.372163
$515$	0	0
$516$	9.01248e43	0.157081
$517$	6.46563e44	1.09148
$518$	−2.07242e43	−0.0338873
$519$	2.73542e44	0.433274
$520$	0	0
$521$	−6.34148e44	−0.942688	−0.471344	−	0.881950i	$-0.656231\pi$
$521$	−6.34148e44	−0.942688	−0.471344	+	0.881950i	$0.656231\pi$
$522$	−1.93660e44	−0.278918
$523$	−3.63034e44	−0.506605	−0.253303	−	0.967387i	$-0.581517\pi$
$523$	−3.63034e44	−0.506605	−0.253303	+	0.967387i	$0.581517\pi$
$524$	−3.83435e43	−0.0518472
$525$	0	0
$526$	1.53140e45	1.94457
$527$	7.36455e43	0.0906298
$528$	−3.24284e44	−0.386782
$529$	−8.08546e44	−0.934730
$530$	0	0
$531$	5.52628e44	0.600307
$532$	−3.54395e43	−0.0373203
$533$	−2.41911e44	−0.246977
$534$	4.40238e44	0.435770
$535$	0	0
$536$	−2.90550e44	−0.270397
$537$	−2.62476e42	−0.00236872
$538$	−1.88384e45	−1.64868
$539$	−1.38980e45	−1.17961
$540$	0	0
$541$	−4.70277e44	−0.375490	−0.187745	−	0.982218i	$-0.560118\pi$
$541$	−4.70277e44	−0.375490	−0.187745	+	0.982218i	$0.560118\pi$
$542$	−1.73730e45	−1.34551
$543$	−1.26032e44	−0.0946857
$544$	3.26612e44	0.238040
$545$	0	0
$546$	−2.14775e43	−0.0147335
$547$	5.18112e44	0.344852	0.172426	−	0.985022i	$-0.444839\pi$
$547$	5.18112e44	0.344852	0.172426	+	0.985022i	$0.444839\pi$
$548$	2.77289e44	0.179082
$549$	−1.69212e45	−1.06044
$550$	0	0
$551$	−5.01502e44	−0.295986
$552$	−8.44858e43	−0.0483937
$553$	2.06592e44	0.114855
$554$	−2.90276e45	−1.56639
$555$	0	0
$556$	1.13994e45	0.579625
$557$	2.37652e44	0.117309	0.0586543	−	0.998278i	$-0.481319\pi$
$557$	2.37652e44	0.117309	0.0586543	+	0.998278i	$0.481319\pi$
$558$	6.44025e44	0.308630
$559$	−1.90160e45	−0.884757
$560$	0	0
$561$	2.29502e44	0.100670
$562$	−3.88202e45	−1.65352
$563$	−1.99820e45	−0.826515	−0.413258	−	0.910614i	$-0.635609\pi$
$563$	−1.99820e45	−0.826515	−0.413258	+	0.910614i	$0.635609\pi$
$564$	2.34286e44	0.0941110
$565$	0	0
$566$	5.88170e45	2.22860
$567$	−1.78398e44	−0.0656554
$568$	−1.35009e45	−0.482630
$569$	−1.93847e45	−0.673143	−0.336572	−	0.941658i	$-0.609267\pi$
$569$	−1.93847e45	−0.673143	−0.336572	+	0.941658i	$0.609267\pi$
$570$	0	0
$571$	−3.94735e45	−1.29363	−0.646814	−	0.762648i	$-0.723899\pi$
$571$	−3.94735e45	−1.29363	−0.646814	+	0.762648i	$0.723899\pi$
$572$	−8.37366e44	−0.266613
$573$	−7.97743e44	−0.246781
$574$	1.38301e44	0.0415698
$575$	0	0
$576$	−1.20296e45	−0.341414
$577$	−3.00897e45	−0.829884	−0.414942	−	0.909848i	$-0.636198\pi$
$577$	−3.00897e45	−0.829884	−0.414942	+	0.909848i	$0.636198\pi$
$578$	3.94100e45	1.05632
$579$	1.22879e45	0.320098
$580$	0	0
$581$	−7.55480e43	−0.0185916
$582$	1.51833e45	0.363192
$583$	6.28296e44	0.146094
$584$	1.38044e45	0.312036
$585$	0	0
$586$	−1.30082e45	−0.277911
$587$	1.28524e45	0.266966	0.133483	−	0.991051i	$-0.457384\pi$
$587$	1.28524e45	0.266966	0.133483	+	0.991051i	$0.457384\pi$
$588$	−5.03602e44	−0.101709
$589$	1.66777e45	0.327517
$590$	0	0
$591$	1.12351e45	0.208633
$592$	2.39238e45	0.432038
$593$	−9.50883e45	−1.67003	−0.835016	−	0.550226i	$-0.814542\pi$
$593$	−9.50883e45	−1.67003	−0.835016	+	0.550226i	$0.814542\pi$
$594$	4.16324e45	0.711140
$595$	0	0
$596$	5.99476e44	0.0968743
$597$	2.98048e45	0.468500
$598$	−1.13586e45	−0.173683
$599$	−1.27061e44	−0.0189004	−0.00945019	−	0.999955i	$-0.503008\pi$
$599$	−1.27061e44	−0.0189004	−0.00945019	+	0.999955i	$0.503008\pi$
$600$	0	0
$601$	1.36330e45	0.191939	0.0959693	−	0.995384i	$-0.469405\pi$
$601$	1.36330e45	0.191939	0.0959693	+	0.995384i	$0.469405\pi$
$602$	1.08714e45	0.148917
$603$	2.62299e45	0.349591
$604$	9.32229e44	0.120896
$605$	0	0
$606$	3.99204e45	0.490226
$607$	1.10280e46	1.31790	0.658950	−	0.752187i	$-0.271001\pi$
$607$	1.10280e46	1.31790	0.658950	+	0.752187i	$0.271001\pi$
$608$	7.39642e45	0.860226
$609$	4.86792e43	0.00551008
$610$	0	0
$611$	−4.94334e45	−0.530079
$612$	−1.11806e45	−0.116699
$613$	1.31076e46	1.33176	0.665878	−	0.746061i	$-0.268057\pi$
$613$	1.31076e46	1.33176	0.665878	+	0.746061i	$0.268057\pi$
$614$	2.10101e46	2.07802
$615$	0	0
$616$	−7.51304e44	−0.0704262
$617$	1.57052e46	1.43330	0.716652	−	0.697431i	$-0.245674\pi$
$617$	1.57052e46	1.43330	0.716652	+	0.697431i	$0.245674\pi$
$618$	−1.58863e45	−0.141161
$619$	1.19014e46	1.02968	0.514839	−	0.857287i	$-0.327852\pi$
$619$	1.19014e46	1.02968	0.514839	+	0.857287i	$0.327852\pi$
$620$	0	0
$621$	1.58215e45	0.129788
$622$	−8.29342e45	−0.662510
$623$	1.48777e45	0.115740
$624$	2.47933e45	0.187841
$625$	0	0
$626$	−2.61030e46	−1.87592
$627$	5.19728e45	0.363799
$628$	5.87238e45	0.400387
$629$	−1.69313e45	−0.112449
$630$	0	0
$631$	−1.38247e46	−0.871305	−0.435653	−	0.900115i	$-0.643482\pi$
$631$	−1.38247e46	−0.871305	−0.435653	+	0.900115i	$0.643482\pi$
$632$	−1.63496e46	−1.00386
$633$	1.54918e44	0.00926702
$634$	−2.04521e46	−1.19197
$635$	0	0
$636$	2.27667e44	0.0125967
$637$	1.06258e46	0.572877
$638$	6.77439e45	0.355901
$639$	1.21882e46	0.623984
$640$	0	0
$641$	2.51084e46	1.22085	0.610424	−	0.792075i	$-0.290999\pi$
$641$	2.51084e46	1.22085	0.610424	+	0.792075i	$0.290999\pi$
$642$	1.23545e46	0.585459
$643$	2.27110e46	1.04895	0.524474	−	0.851426i	$-0.324262\pi$
$643$	2.27110e46	1.04895	0.524474	+	0.851426i	$0.324262\pi$
$644$	1.81928e44	0.00818999
$645$	0	0
$646$	−1.03346e46	−0.442035
$647$	−3.85605e46	−1.60776	−0.803882	−	0.594788i	$-0.797236\pi$
$647$	−3.85605e46	−1.60776	−0.803882	+	0.594788i	$0.797236\pi$
$648$	1.41184e46	0.573848
$649$	−1.93314e46	−0.765994
$650$	0	0
$651$	−1.61885e44	−0.00609705
$652$	8.02638e45	0.294737
$653$	2.29880e46	0.823065	0.411533	−	0.911395i	$-0.364994\pi$
$653$	2.29880e46	0.823065	0.411533	+	0.911395i	$0.364994\pi$
$654$	1.40834e46	0.491672
$655$	0	0
$656$	−1.59653e46	−0.529984
$657$	−1.24621e46	−0.403425
$658$	2.82611e45	0.0892198
$659$	−4.66885e46	−1.43748	−0.718738	−	0.695281i	$-0.755280\pi$
$659$	−4.66885e46	−1.43748	−0.718738	+	0.695281i	$0.755280\pi$
$660$	0	0
$661$	−1.75754e46	−0.514731	−0.257366	−	0.966314i	$-0.582854\pi$
$661$	−1.75754e46	−0.514731	−0.257366	+	0.966314i	$0.582854\pi$
$662$	−1.98038e46	−0.565707
$663$	−1.75467e45	−0.0488903
$664$	5.97883e45	0.162496
$665$	0	0
$666$	−1.48063e46	−0.382933
$667$	2.57446e45	0.0649546
$668$	−1.57814e46	−0.388450
$669$	−1.15023e44	−0.00276218
$670$	0	0
$671$	5.91918e46	1.35313
$672$	−7.17947e44	−0.0160140
$673$	−6.04589e45	−0.131587	−0.0657933	−	0.997833i	$-0.520958\pi$
$673$	−6.04589e45	−0.131587	−0.0657933	+	0.997833i	$0.520958\pi$
$674$	−2.25454e46	−0.478818
$675$	0	0
$676$	−1.28416e46	−0.259716
$677$	3.42156e46	0.675323	0.337662	−	0.941268i	$-0.390364\pi$
$677$	3.42156e46	0.675323	0.337662	+	0.941268i	$0.390364\pi$
$678$	−1.91830e46	−0.369509
$679$	5.13114e45	0.0964635
$680$	0	0
$681$	1.96159e46	0.351301
$682$	−2.25285e46	−0.393813
$683$	−2.32228e46	−0.396253	−0.198127	−	0.980176i	$-0.563486\pi$
$683$	−2.32228e46	−0.396253	−0.198127	+	0.980176i	$0.563486\pi$
$684$	−2.53196e46	−0.421726
$685$	0	0
$686$	−1.21910e46	−0.193505
$687$	3.31781e45	0.0514121
$688$	−1.25499e47	−1.89858
$689$	−4.80368e45	−0.0709507
$690$	0	0
$691$	8.01402e46	1.12840	0.564199	−	0.825638i	$-0.309185\pi$
$691$	8.01402e46	1.12840	0.564199	+	0.825638i	$0.309185\pi$
$692$	4.66159e46	0.640890
$693$	6.78253e45	0.0910527
$694$	−2.64383e46	−0.346580
$695$	0	0
$696$	−3.85245e45	−0.0481598
$697$	1.12989e46	0.137942
$698$	−1.02569e47	−1.22294
$699$	3.84614e46	0.447870
$700$	0	0
$701$	1.00753e47	1.11921	0.559605	−	0.828760i	$-0.310953\pi$
$701$	1.00753e47	1.11921	0.559605	+	0.828760i	$0.310953\pi$
$702$	−3.18303e46	−0.345365
$703$	−3.83425e46	−0.406366
$704$	4.20806e46	0.435645
$705$	0	0
$706$	−7.03997e46	−0.695494
$707$	1.34910e46	0.130204
$708$	−7.00484e45	−0.0660464
$709$	1.27253e47	1.17220	0.586102	−	0.810237i	$-0.300662\pi$
$709$	1.27253e47	1.17220	0.586102	+	0.810237i	$0.300662\pi$
$710$	0	0
$711$	1.47599e47	1.29788
$712$	−1.17742e47	−1.01160
$713$	−8.56148e45	−0.0718740
$714$	1.00315e45	0.00822893
$715$	0	0
$716$	−4.47301e44	−0.00350377
$717$	−4.32524e46	−0.331088
$718$	−2.79630e47	−2.09185
$719$	−1.16194e47	−0.849490	−0.424745	−	0.905313i	$-0.639636\pi$
$719$	−1.16194e47	−0.849490	−0.424745	+	0.905313i	$0.639636\pi$
$720$	0	0
$721$	−5.36874e45	−0.0374922
$722$	−6.13549e46	−0.418780
$723$	−1.84421e46	−0.123035
$724$	−2.14779e46	−0.140057
$725$	0	0
$726$	−2.04338e46	−0.127319
$727$	2.67321e47	1.62823	0.814114	−	0.580705i	$-0.197223\pi$
$727$	2.67321e47	1.62823	0.814114	+	0.580705i	$0.197223\pi$
$728$	5.74414e45	0.0342025
$729$	−1.04493e47	−0.608250
$730$	0	0
$731$	8.88177e46	0.494154
$732$	2.14485e46	0.116671
$733$	2.06440e47	1.09794	0.548968	−	0.835843i	$-0.315021\pi$
$733$	2.06440e47	1.09794	0.548968	+	0.835843i	$0.315021\pi$
$734$	1.81073e47	0.941606
$735$	0	0
$736$	−3.79695e46	−0.188778
$737$	−9.17542e46	−0.446080
$738$	9.88083e46	0.469746
$739$	−3.44156e47	−1.60001	−0.800004	−	0.599994i	$-0.795169\pi$
$739$	−3.44156e47	−1.60001	−0.800004	+	0.599994i	$0.795169\pi$
$740$	0	0
$741$	−3.97361e46	−0.176679
$742$	2.74627e45	0.0119420
$743$	3.56403e47	1.51575	0.757873	−	0.652402i	$-0.226239\pi$
$743$	3.56403e47	1.51575	0.757873	+	0.652402i	$0.226239\pi$
$744$	1.28115e46	0.0532901
$745$	0	0
$746$	−1.75088e47	−0.696732
$747$	−5.39749e46	−0.210088
$748$	3.91107e46	0.148909
$749$	4.17516e46	0.155497
$750$	0	0
$751$	−3.38219e46	−0.120542	−0.0602710	−	0.998182i	$-0.519196\pi$
$751$	−3.38219e46	−0.120542	−0.0602710	+	0.998182i	$0.519196\pi$
$752$	−3.26242e47	−1.13749
$753$	−2.49779e46	−0.0851999
$754$	−5.17940e46	−0.172843
$755$	0	0
$756$	5.09818e45	0.0162857
$757$	1.03676e47	0.324038	0.162019	−	0.986788i	$-0.448199\pi$
$757$	1.03676e47	0.324038	0.162019	+	0.986788i	$0.448199\pi$
$758$	8.34461e46	0.255190
$759$	−2.66802e46	−0.0798362
$760$	0	0
$761$	1.98844e47	0.569726	0.284863	−	0.958568i	$-0.408052\pi$
$761$	1.98844e47	0.569726	0.284863	+	0.958568i	$0.408052\pi$
$762$	−1.51677e47	−0.425269
$763$	4.75945e46	0.130588
$764$	−1.35948e47	−0.365033
$765$	0	0
$766$	−7.53000e47	−1.93651
$767$	1.47799e47	0.372005
$768$	1.08270e47	0.266715
$769$	−4.79063e47	−1.15507	−0.577534	−	0.816367i	$-0.695985\pi$
$769$	−4.79063e47	−1.15507	−0.577534	+	0.816367i	$0.695985\pi$
$770$	0	0
$771$	−3.59664e46	−0.0830805
$772$	2.09406e47	0.473482
$773$	3.87609e47	0.857891	0.428946	−	0.903330i	$-0.358885\pi$
$773$	3.87609e47	0.857891	0.428946	+	0.903330i	$0.358885\pi$
$774$	7.76705e47	1.68279
$775$	0	0
$776$	−4.06076e47	−0.843120
$777$	3.72178e45	0.00756491
$778$	6.56019e47	1.30543
$779$	2.55874e47	0.498492
$780$	0	0
$781$	−4.26351e47	−0.796206
$782$	5.30526e46	0.0970053
$783$	7.21441e46	0.129161
$784$	7.01265e47	1.22933
$785$	0	0
$786$	2.45787e46	0.0413130
$787$	1.12069e48	1.84461	0.922304	−	0.386465i	$-0.126304\pi$
$787$	1.12069e48	1.84461	0.922304	+	0.386465i	$0.126304\pi$
$788$	1.91464e47	0.308606
$789$	−2.75018e47	−0.434101
$790$	0	0
$791$	−6.48282e46	−0.0981413
$792$	−5.36766e47	−0.795828
$793$	−4.52555e47	−0.657148
$794$	7.07838e47	1.00669
$795$	0	0
$796$	5.07921e47	0.692995
$797$	9.96509e47	1.33174	0.665869	−	0.746069i	$-0.268061\pi$
$797$	9.96509e47	1.33174	0.665869	+	0.746069i	$0.268061\pi$
$798$	2.27171e46	0.0297376
$799$	2.30888e47	0.296059
$800$	0	0
$801$	1.06293e48	1.30788
$802$	−1.62946e48	−1.96411
$803$	4.35935e47	0.514772
$804$	−3.32477e46	−0.0384624
$805$	0	0
$806$	1.72243e47	0.191256
$807$	3.38311e47	0.368047
$808$	−1.06767e48	−1.13802
$809$	9.98570e47	1.04286	0.521432	−	0.853293i	$-0.325398\pi$
$809$	9.98570e47	1.04286	0.521432	+	0.853293i	$0.325398\pi$
$810$	0	0
$811$	−1.14204e48	−1.14509	−0.572544	−	0.819874i	$-0.694043\pi$
$811$	−1.14204e48	−1.14509	−0.572544	+	0.819874i	$0.694043\pi$
$812$	8.29571e45	0.00815040
$813$	3.11995e47	0.300368
$814$	5.17937e47	0.488624
$815$	0	0
$816$	−1.15802e47	−0.104913
$817$	2.01136e48	1.78577
$818$	1.66791e47	0.145126
$819$	−5.18562e46	−0.0442198
$820$	0	0
$821$	1.20008e48	0.982989	0.491495	−	0.870881i	$-0.336451\pi$
$821$	1.20008e48	0.982989	0.491495	+	0.870881i	$0.336451\pi$
$822$	−1.77746e47	−0.142697
$823$	−8.31615e47	−0.654372	−0.327186	−	0.944960i	$-0.606100\pi$
$823$	−8.31615e47	−0.654372	−0.327186	+	0.944960i	$0.606100\pi$
$824$	4.24880e47	0.327693
$825$	0	0
$826$	−8.44969e46	−0.0626138
$827$	7.47488e47	0.542955	0.271477	−	0.962445i	$-0.412488\pi$
$827$	7.47488e47	0.542955	0.271477	+	0.962445i	$0.412488\pi$
$828$	1.29978e47	0.0925484
$829$	−2.01484e48	−1.40634	−0.703171	−	0.711020i	$-0.748233\pi$
$829$	−2.01484e48	−1.40634	−0.703171	+	0.711020i	$0.748233\pi$
$830$	0	0
$831$	5.21294e47	0.349676
$832$	−3.21730e47	−0.211571
$833$	−4.96298e47	−0.319963
$834$	−7.30716e47	−0.461858
$835$	0	0
$836$	8.85698e47	0.538124
$837$	−2.39918e47	−0.142920
$838$	−1.08474e48	−0.633576
$839$	−6.19222e47	−0.354629	−0.177314	−	0.984154i	$-0.556741\pi$
$839$	−6.19222e47	−0.354629	−0.177314	+	0.984154i	$0.556741\pi$
$840$	0	0
$841$	−1.69868e48	−0.935359
$842$	−4.11516e48	−2.22197
$843$	6.97156e47	0.369126
$844$	2.64005e46	0.0137076
$845$	0	0
$846$	2.01910e48	1.00820
$847$	−6.90554e46	−0.0338159
$848$	−3.17026e47	−0.152252
$849$	−1.05627e48	−0.497506
$850$	0	0
$851$	1.96831e47	0.0891776
$852$	−1.54491e47	−0.0686514
$853$	−3.53602e48	−1.54119	−0.770594	−	0.637327i	$-0.780040\pi$
$853$	−3.53602e48	−1.54119	−0.770594	+	0.637327i	$0.780040\pi$
$854$	2.58726e47	0.110607
$855$	0	0
$856$	−3.30420e48	−1.35909
$857$	−9.74863e47	−0.393333	−0.196666	−	0.980470i	$-0.563012\pi$
$857$	−9.74863e47	−0.393333	−0.196666	+	0.980470i	$0.563012\pi$
$858$	5.36763e47	0.212443
$859$	−4.20702e48	−1.63338	−0.816690	−	0.577076i	$-0.804194\pi$
$859$	−4.20702e48	−1.63338	−0.816690	+	0.577076i	$0.804194\pi$
$860$	0	0
$861$	−2.48369e46	−0.00927993
$862$	−1.71740e48	−0.629509
$863$	−6.84409e46	−0.0246115	−0.0123057	−	0.999924i	$-0.503917\pi$
$863$	−6.84409e46	−0.0246115	−0.0123057	+	0.999924i	$0.503917\pi$
$864$	−1.06402e48	−0.375381
$865$	0	0
$866$	2.71223e48	0.921045
$867$	−7.07748e47	−0.235811
$868$	−2.75877e46	−0.00901863
$869$	−5.16312e48	−1.65610
$870$	0	0
$871$	7.01513e47	0.216639
$872$	−3.76660e48	−1.14137
$873$	3.66592e48	1.09005
$874$	1.20142e48	0.350556
$875$	0	0
$876$	1.57963e47	0.0443853
$877$	6.44909e48	1.77830	0.889150	−	0.457615i	$-0.151296\pi$
$877$	6.44909e48	1.77830	0.889150	+	0.457615i	$0.151296\pi$
$878$	−4.60942e48	−1.24735
$879$	2.33609e47	0.0620402
$880$	0	0
$881$	3.47493e48	0.888882	0.444441	−	0.895808i	$-0.353402\pi$
$881$	3.47493e48	0.888882	0.444441	+	0.895808i	$0.353402\pi$
$882$	−4.34010e48	−1.08960
$883$	−4.36520e48	−1.07560	−0.537802	−	0.843071i	$-0.680745\pi$
$883$	−4.36520e48	−1.07560	−0.537802	+	0.843071i	$0.680745\pi$
$884$	−2.99024e47	−0.0723175
$885$	0	0
$886$	−4.67996e48	−1.09040
$887$	4.94841e48	1.13168	0.565842	−	0.824513i	$-0.308551\pi$
$887$	4.94841e48	1.13168	0.565842	+	0.824513i	$0.308551\pi$
$888$	−2.94540e47	−0.0661196
$889$	−5.12589e47	−0.112951
$890$	0	0
$891$	4.45851e48	0.946690
$892$	−1.96017e46	−0.00408576
$893$	5.22866e48	1.06990
$894$	−3.84272e47	−0.0771915
$895$	0	0
$896$	4.98297e47	0.0964731
$897$	2.03985e47	0.0387725
$898$	−4.48864e48	−0.837635
$899$	−3.90393e47	−0.0715266
$900$	0	0
$901$	2.24365e47	0.0396274
$902$	−3.45639e48	−0.599398
$903$	−1.95236e47	−0.0332439
$904$	5.13047e48	0.857785
$905$	0	0
$906$	−5.97571e47	−0.0963328
$907$	3.55400e48	0.562596	0.281298	−	0.959620i	$-0.409235\pi$
$907$	3.55400e48	0.562596	0.281298	+	0.959620i	$0.409235\pi$
$908$	3.34285e48	0.519638
$909$	9.63856e48	1.47132
$910$	0	0
$911$	4.07509e48	0.599908	0.299954	−	0.953954i	$-0.403029\pi$
$911$	4.07509e48	0.599908	0.299954	+	0.953954i	$0.403029\pi$
$912$	−2.62244e48	−0.379132
$913$	1.88809e48	0.268074
$914$	1.17236e49	1.63474
$915$	0	0
$916$	5.65407e47	0.0760477
$917$	8.30629e46	0.0109727
$918$	1.48669e48	0.192893
$919$	6.75427e47	0.0860740	0.0430370	−	0.999073i	$-0.486297\pi$
$919$	6.75427e47	0.0860740	0.0430370	+	0.999073i	$0.486297\pi$
$920$	0	0
$921$	−3.77312e48	−0.463892
$922$	1.80734e49	2.18263
$923$	3.25970e48	0.386678
$924$	−8.59718e46	−0.0100177
$925$	0	0
$926$	−7.66744e48	−0.862122
$927$	−3.83567e48	−0.423668
$928$	−1.73136e48	−0.187865
$929$	3.55712e48	0.379174	0.189587	−	0.981864i	$-0.439285\pi$
$929$	3.55712e48	0.379174	0.189587	+	0.981864i	$0.439285\pi$
$930$	0	0
$931$	−1.12391e49	−1.15628
$932$	6.55444e48	0.662480
$933$	1.48938e48	0.147897
$934$	−7.11966e48	−0.694602
$935$	0	0
$936$	4.10388e48	0.386494
$937$	5.42233e48	0.501744	0.250872	−	0.968020i	$-0.419283\pi$
$937$	5.42233e48	0.501744	0.250872	+	0.968020i	$0.419283\pi$
$938$	−4.01055e47	−0.0364634
$939$	4.68773e48	0.418774
$940$	0	0
$941$	1.76662e49	1.52375	0.761877	−	0.647722i	$-0.224278\pi$
$941$	1.76662e49	1.52375	0.761877	+	0.647722i	$0.224278\pi$
$942$	−3.76427e48	−0.319037
$943$	−1.31353e48	−0.109395
$944$	9.75422e48	0.798279
$945$	0	0
$946$	−2.71698e49	−2.14725
$947$	−9.85410e48	−0.765318	−0.382659	−	0.923890i	$-0.624992\pi$
$947$	−9.85410e48	−0.765318	−0.382659	+	0.923890i	$0.624992\pi$
$948$	−1.87089e48	−0.142794
$949$	−3.33297e48	−0.249999
$950$	0	0
$951$	3.67292e48	0.266092
$952$	−2.68291e47	−0.0191028
$953$	1.89853e49	1.32857	0.664284	−	0.747480i	$-0.268737\pi$
$953$	1.89853e49	1.32857	0.664284	+	0.747480i	$0.268737\pi$
$954$	1.96206e48	0.134947
$955$	0	0
$956$	−7.37089e48	−0.489739
$957$	−1.21658e48	−0.0794503
$958$	1.81509e49	1.16511
$959$	−6.00686e47	−0.0379001
$960$	0	0
$961$	−1.51052e49	−0.920854
$962$	−3.95992e48	−0.237300
$963$	2.98293e49	1.75715
$964$	−3.14283e48	−0.181991
$965$	0	0
$966$	−1.16618e47	−0.00652596
$967$	1.65793e49	0.912070	0.456035	−	0.889962i	$-0.349269\pi$
$967$	1.65793e49	0.912070	0.456035	+	0.889962i	$0.349269\pi$
$968$	5.46501e48	0.295561
$969$	1.85595e48	0.0986787
$970$	0	0
$971$	1.44525e49	0.742723	0.371361	−	0.928488i	$-0.378891\pi$
$971$	1.44525e49	0.742723	0.371361	+	0.928488i	$0.378891\pi$
$972$	5.52885e48	0.279346
$973$	−2.46943e48	−0.122669
$974$	−1.23272e49	−0.602061
$975$	0	0
$976$	−2.98670e49	−1.41016
$977$	−1.83197e49	−0.850467	−0.425234	−	0.905084i	$-0.639808\pi$
$977$	−1.83197e49	−0.850467	−0.425234	+	0.905084i	$0.639808\pi$
$978$	−5.14501e48	−0.234853
$979$	−3.71822e49	−1.66886
$980$	0	0
$981$	3.40037e49	1.47566
$982$	−1.12017e49	−0.478020
$983$	−9.70579e48	−0.407285	−0.203642	−	0.979045i	$-0.565278\pi$
$983$	−9.70579e48	−0.407285	−0.203642	+	0.979045i	$0.565278\pi$
$984$	1.96558e48	0.0811094
$985$	0	0
$986$	2.41914e48	0.0965364
$987$	−5.07529e47	−0.0199172
$988$	−6.77166e48	−0.261340
$989$	−1.03253e49	−0.391889
$990$	0	0
$991$	−1.33593e49	−0.490421	−0.245210	−	0.969470i	$-0.578857\pi$
$991$	−1.33593e49	−0.490421	−0.245210	+	0.969470i	$0.578857\pi$
$992$	5.75772e48	0.207878
$993$	3.55648e48	0.126287
$994$	−1.86357e48	−0.0650834
$995$	0	0
$996$	6.84159e47	0.0231142
$997$	−3.08053e49	−1.02366	−0.511829	−	0.859088i	$-0.671032\pi$
$997$	−3.08053e49	−1.02366	−0.511829	+	0.859088i	$0.671032\pi$
$998$	−8.56533e48	−0.279956
$999$	5.51580e48	0.177328

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.a.e.1.3	yes	11
5.2	odd	4		25.34.b.d.24.5		22
5.3	odd	4		25.34.b.d.24.18		22
5.4	even	2		25.34.a.d.1.9	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.34.a.d.1.9	✓	11	5.4	even	2
25.34.a.e.1.3	yes	11	1.1	even	1	trivial
25.34.b.d.24.5		22	5.2	odd	4
25.34.b.d.24.18		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)

\(f(q)\)	\(=\)	\(q-109239. q^{2} +1.96178e7 q^{3} +3.34318e9 q^{4} -2.14302e12 q^{6} -7.24227e12 q^{7} +5.73150e14 q^{8} -5.17420e15 q^{9} +O(q^{10})\)	\(q-109239. q^{2} +1.96178e7 q^{3} +3.34318e9 q^{4} -2.14302e12 q^{6} -7.24227e12 q^{7} +5.73150e14 q^{8} -5.17420e15 q^{9} +1.80998e17 q^{11} +6.55856e16 q^{12} -1.38383e18 q^{13} +7.91136e17 q^{14} -9.13278e19 q^{16} +6.46344e19 q^{17} +5.65224e20 q^{18} +1.46370e21 q^{19} -1.42077e20 q^{21} -1.97720e22 q^{22} -7.51392e21 q^{23} +1.12439e22 q^{24} +1.51168e23 q^{26} -2.10563e23 q^{27} -2.42122e22 q^{28} -3.42626e23 q^{29} +1.13942e24 q^{31} +5.05322e24 q^{32} +3.55077e24 q^{33} -7.06058e24 q^{34} -1.72983e25 q^{36} -2.61955e25 q^{37} -1.59893e26 q^{38} -2.71476e25 q^{39} +1.74813e26 q^{41} +1.55203e25 q^{42} +1.37416e27 q^{43} +6.05108e26 q^{44} +8.20811e26 q^{46} +3.57221e27 q^{47} -1.79165e27 q^{48} -7.67854e27 q^{49} +1.26798e27 q^{51} -4.62639e27 q^{52} +3.47129e27 q^{53} +2.30016e28 q^{54} -4.15090e27 q^{56} +2.87146e28 q^{57} +3.74280e28 q^{58} -1.06805e29 q^{59} +3.27030e29 q^{61} -1.24468e29 q^{62} +3.74730e28 q^{63} +2.32492e29 q^{64} -3.87882e29 q^{66} -5.06936e29 q^{67} +2.16084e29 q^{68} -1.47406e29 q^{69} -2.35556e30 q^{71} -2.96559e30 q^{72} +2.40851e30 q^{73} +2.86157e30 q^{74} +4.89342e30 q^{76} -1.31083e30 q^{77} +2.96557e30 q^{78} -2.85259e31 q^{79} +2.46330e31 q^{81} -1.90963e31 q^{82} +1.04315e31 q^{83} -4.74988e29 q^{84} -1.50111e32 q^{86} -6.72154e30 q^{87} +1.03739e32 q^{88} -2.05429e32 q^{89} +1.00221e31 q^{91} -2.51204e31 q^{92} +2.23528e31 q^{93} -3.90224e32 q^{94} +9.91329e31 q^{96} -7.08500e32 q^{97} +8.38795e32 q^{98} -9.36520e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 9393 q^{2} + 80330849 q^{3} + 49338206677 q^{4} - 17783977676723 q^{6} + 21344025107658 q^{7} - 970199832420105 q^{8} + 24\!\cdots\!58 q^{9}+O(q^{10}) \) 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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