LMFDB - Embedded newform 25.34.a.d.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("25.1");

S:= CuspForms(chi, 34);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1.9
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	$-0.299395\pi$
$2$	109239.	1.17864	0.589321	+	0.807899i	$0.299395\pi$
$3$	−1.96178e7	−0.263117	−0.131558	−	0.991308i	$-0.541998\pi$
$3$	−1.96178e7	−0.263117	−0.131558	+	0.991308i	$0.541998\pi$
$4$	3.34318e9	0.389197
$5$	0	0
$5$	0	0
$6$	−2.14302e12	−0.310120
$7$	7.24227e12	0.0823677	0.0411838	−	0.999152i	$-0.486887\pi$
$7$	7.24227e12	0.0823677	0.0411838	+	0.999152i	$0.486887\pi$
$8$	−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	$-0.406878\pi$
$13$	1.38383e18	0.576790	0.288395	+	0.957512i	$0.406878\pi$
$14$	7.91136e17	0.0970820
$15$	0	0
$16$	−9.13278e19	−1.23772
$17$	−6.46344e19	−0.322149	−0.161074	−	0.986942i	$-0.551496\pi$
$17$	−6.46344e19	−0.322149	−0.161074	+	0.986942i	$0.551496\pi$
$18$	−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	$-0.459228\pi$
$23$	7.51392e21	0.255480	0.127740	+	0.991808i	$0.459228\pi$
$24$	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	$-0.444160\pi$
$37$	2.61955e25	0.349059	0.174529	+	0.984652i	$0.444160\pi$
$38$	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	$-0.778235\pi$
$43$	−1.37416e27	−1.53393	−0.766966	+	0.641687i	$0.778235\pi$
$44$	6.05108e26	0.462236
$45$	0	0
$46$	8.20811e26	0.301120
$47$	−3.57221e27	−0.919015	−0.459508	−	0.888174i	$-0.651974\pi$
$47$	−3.57221e27	−0.919015	−0.459508	+	0.888174i	$0.651974\pi$
$48$	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	$-0.519590\pi$
$53$	−3.47129e27	−0.123010	−0.0615049	+	0.998107i	$0.519590\pi$
$54$	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	$-0.439865\pi$
$67$	5.06936e29	0.375594	0.187797	+	0.982208i	$0.439865\pi$
$68$	−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	$-0.569535\pi$
$73$	−2.40851e30	−0.433432	−0.216716	+	0.976235i	$0.569535\pi$
$74$	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	$-0.536000\pi$
$83$	−1.04315e31	−0.225715	−0.112857	+	0.993611i	$0.536000\pi$
$84$	−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	$-0.300872\pi$
$97$	7.08500e32	1.17113	0.585566	+	0.810624i	$0.300872\pi$
$98$	−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	$-0.573085\pi$
$103$	−7.41307e32	−0.455181	−0.227590	+	0.973757i	$0.573085\pi$
$104$	−7.93142e32	−0.415241
$105$	0	0
$106$	−3.79200e32	−0.144984
$107$	5.76499e33	1.88785	0.943923	−	0.330166i	$-0.107105\pi$
$107$	5.76499e33	1.88785	0.943923	+	0.330166i	$0.107105\pi$
$108$	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	$-0.703146\pi$
$113$	−8.95137e33	−1.19150	−0.595751	+	0.803169i	$0.703146\pi$
$114$	−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	$-0.740482\pi$
$127$	−7.07774e34	−1.37130	−0.685651	+	0.727930i	$0.740482\pi$
$128$	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	$-0.573894\pi$
$137$	−8.29417e34	−0.460133	−0.230067	+	0.973175i	$0.573894\pi$
$138$	−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	$-0.671976\pi$
$157$	−1.75653e36	−1.02875	−0.514376	+	0.857565i	$0.671976\pi$
$158$	−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	$-0.623611\pi$
$163$	−2.40082e36	−0.757295	−0.378647	+	0.925541i	$0.623611\pi$
$164$	5.84430e35	0.166651
$165$	0	0
$166$	−1.13953e36	−0.266037
$167$	4.72050e36	0.998081	0.499041	−	0.866579i	$-0.333686\pi$
$167$	4.72050e36	0.998081	0.499041	+	0.866579i	$0.333686\pi$
$168$	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	$-0.807898\pi$
$173$	−1.39436e37	−1.64670	−0.823350	+	0.567534i	$0.807898\pi$
$174$	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	$-0.708141\pi$
$193$	−6.26368e37	−1.21656	−0.608281	+	0.793722i	$0.708141\pi$
$194$	7.73957e37	1.38035
$195$	0	0
$196$	−2.56707e37	−0.386556
$197$	−5.72700e37	−0.792930	−0.396465	−	0.918050i	$-0.629763\pi$
$197$	−5.72700e37	−0.792930	−0.396465	+	0.918050i	$0.629763\pi$
$198$	−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	$-0.498329\pi$
$223$	5.86319e36	0.0104979	0.00524896	+	0.999986i	$0.498329\pi$
$224$	−3.65968e37	−0.0608626
$225$	0	0
$226$	−9.77836e38	−1.40436
$227$	−9.99903e38	−1.33515	−0.667577	−	0.744541i	$-0.732669\pi$
$227$	−9.99903e38	−1.33515	−0.667577	+	0.744541i	$0.732669\pi$
$228$	−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	$-0.824056\pi$
$233$	−1.96054e39	−1.70217	−0.851086	+	0.525026i	$0.824056\pi$
$234$	−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	$-0.449535\pi$
$257$	1.83336e39	0.315755	0.157878	+	0.987459i	$0.449535\pi$
$258$	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	$-0.191219\pi$
$263$	1.40189e40	1.64984	0.824922	+	0.565247i	$0.191219\pi$
$264$	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	$-0.731351\pi$
$277$	−2.65726e40	−1.32898	−0.664489	+	0.747298i	$0.731351\pi$
$278$	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	$-0.105662\pi$
$283$	5.38426e40	1.89082	0.945410	+	0.325884i	$0.105662\pi$
$284$	−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	$-0.537615\pi$
$293$	−1.19080e40	−0.235789	−0.117895	+	0.993026i	$0.537615\pi$
$294$	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	$-0.156512\pi$
$307$	1.92332e41	1.76307	0.881533	+	0.472123i	$0.156512\pi$
$308$	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	$-0.792947\pi$
$313$	−2.38953e41	−1.59159	−0.795795	+	0.605566i	$0.792947\pi$
$314$	−1.91881e41	−1.21253
$315$	0	0
$316$	−9.53670e40	−0.542702
$317$	−1.87224e41	−1.01131	−0.505655	−	0.862736i	$-0.668749\pi$
$317$	−1.87224e41	−1.01131	−0.505655	+	0.862736i	$0.668749\pi$
$318$	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	$-0.565109\pi$
$337$	−2.06387e41	−0.406246	−0.203123	+	0.979153i	$0.565109\pi$
$338$	−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	$-0.546970\pi$
$347$	−2.42023e41	−0.294050	−0.147025	+	0.989133i	$0.546970\pi$
$348$	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	$-0.595333\pi$
$353$	−6.44457e41	−0.590081	−0.295040	+	0.955485i	$0.595333\pi$
$354$	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	$-0.369203\pi$
$367$	1.65759e42	0.798890	0.399445	+	0.916757i	$0.369203\pi$
$368$	−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	$-0.595508\pi$
$373$	−1.60280e42	−0.591131	−0.295566	+	0.955322i	$0.595508\pi$
$374$	−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	$-0.806864\pi$
$383$	−6.89316e42	−1.64300	−0.821502	+	0.570206i	$0.806864\pi$
$384$	−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	$-0.359551\pi$
$397$	6.47973e42	0.854110	0.427055	+	0.904226i	$0.359551\pi$
$398$	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	$-0.372225\pi$
$433$	2.48284e43	0.781446	0.390723	+	0.920508i	$0.372225\pi$
$434$	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	$-0.653071\pi$
$443$	−4.28416e43	−0.925133	−0.462567	+	0.886585i	$0.653071\pi$
$444$	−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	$-0.256075\pi$
$457$	1.07321e44	1.38697	0.693485	+	0.720471i	$0.256075\pi$
$458$	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	$-0.619180\pi$
$463$	−7.01897e43	−0.731454	−0.365727	+	0.930722i	$0.619180\pi$
$464$	3.12912e43	0.314685
$465$	0	0
$466$	−2.14167e44	−2.00625
$467$	−6.51752e43	−0.589324	−0.294662	−	0.955602i	$-0.595207\pi$
$467$	−6.51752e43	−0.589324	−0.294662	+	0.955602i	$0.595207\pi$
$468$	−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	$-0.582209\pi$
$487$	−1.12846e44	−0.510809	−0.255404	+	0.966834i	$0.582209\pi$
$488$	−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	$-0.453766\pi$
$503$	1.09015e44	0.289478	0.144739	+	0.989470i	$0.453766\pi$
$504$	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	$-0.418483\pi$
$523$	3.63034e44	0.506605	0.253303	+	0.967387i	$0.418483\pi$
$524$	−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	$-0.555161\pi$
$547$	−5.18112e44	−0.344852	−0.172426	+	0.985022i	$0.555161\pi$
$548$	−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	$-0.518681\pi$
$557$	−2.37652e44	−0.117309	−0.0586543	+	0.998278i	$0.518681\pi$
$558$	−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	$-0.364391\pi$
$563$	1.99820e45	0.826515	0.413258	+	0.910614i	$0.364391\pi$
$564$	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	$-0.363802\pi$
$577$	3.00897e45	0.829884	0.414942	+	0.909848i	$0.363802\pi$
$578$	−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	$-0.542616\pi$
$587$	−1.28524e45	−0.266966	−0.133483	+	0.991051i	$0.542616\pi$
$588$	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	$-0.185458\pi$
$593$	9.50883e45	1.67003	0.835016	+	0.550226i	$0.185458\pi$
$594$	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	$-0.728999\pi$
$607$	−1.10280e46	−1.31790	−0.658950	+	0.752187i	$0.728999\pi$
$608$	−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	$-0.731943\pi$
$613$	−1.31076e46	−1.33176	−0.665878	+	0.746061i	$0.731943\pi$
$614$	2.10101e46	2.07802
$615$	0	0
$616$	−7.51304e44	−0.0704262
$617$	−1.57052e46	−1.43330	−0.716652	−	0.697431i	$-0.754326\pi$
$617$	−1.57052e46	−1.43330	−0.716652	+	0.697431i	$0.754326\pi$
$618$	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	$-0.675738\pi$
$643$	−2.27110e46	−1.04895	−0.524474	+	0.851426i	$0.675738\pi$
$644$	1.81928e44	0.00818999
$645$	0	0
$646$	−1.03346e46	−0.442035
$647$	3.85605e46	1.60776	0.803882	−	0.594788i	$-0.202764\pi$
$647$	3.85605e46	1.60776	0.803882	+	0.594788i	$0.202764\pi$
$648$	−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	$-0.635006\pi$
$653$	−2.29880e46	−0.823065	−0.411533	+	0.911395i	$0.635006\pi$
$654$	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	$-0.479042\pi$
$673$	6.04589e45	0.131587	0.0657933	+	0.997833i	$0.479042\pi$
$674$	−2.25454e46	−0.478818
$675$	0	0
$676$	−1.28416e46	−0.259716
$677$	−3.42156e46	−0.675323	−0.337662	−	0.941268i	$-0.609636\pi$
$677$	−3.42156e46	−0.675323	−0.337662	+	0.941268i	$0.609636\pi$
$678$	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	$-0.436514\pi$
$683$	2.32228e46	0.396253	0.198127	+	0.980176i	$0.436514\pi$
$684$	−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	$-0.802777\pi$
$727$	−2.67321e47	−1.62823	−0.814114	+	0.580705i	$0.802777\pi$
$728$	−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	$-0.684979\pi$
$733$	−2.06440e47	−1.09794	−0.548968	+	0.835843i	$0.684979\pi$
$734$	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	$-0.773761\pi$
$743$	−3.56403e47	−1.51575	−0.757873	+	0.652402i	$0.773761\pi$
$744$	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	$-0.551801\pi$
$757$	−1.03676e47	−0.324038	−0.162019	+	0.986788i	$0.551801\pi$
$758$	−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	$-0.641115\pi$
$773$	−3.87609e47	−0.857891	−0.428946	+	0.903330i	$0.641115\pi$
$774$	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	$-0.873696\pi$
$787$	−1.12069e48	−1.84461	−0.922304	+	0.386465i	$0.873696\pi$
$788$	−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	$-0.731939\pi$
$797$	−9.96509e47	−1.33174	−0.665869	+	0.746069i	$0.731939\pi$
$798$	−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	$-0.393900\pi$
$823$	8.31615e47	0.654372	0.327186	+	0.944960i	$0.393900\pi$
$824$	4.24880e47	0.327693
$825$	0	0
$826$	−8.44969e46	−0.0626138
$827$	−7.47488e47	−0.542955	−0.271477	−	0.962445i	$-0.587512\pi$
$827$	−7.47488e47	−0.542955	−0.271477	+	0.962445i	$0.587512\pi$
$828$	−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	$-0.219960\pi$
$853$	3.53602e48	1.54119	0.770594	+	0.637327i	$0.219960\pi$
$854$	2.58726e47	0.110607
$855$	0	0
$856$	−3.30420e48	−1.35909
$857$	9.74863e47	0.393333	0.196666	−	0.980470i	$-0.436988\pi$
$857$	9.74863e47	0.393333	0.196666	+	0.980470i	$0.436988\pi$
$858$	−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	$-0.496083\pi$
$863$	6.84409e46	0.0246115	0.0123057	+	0.999924i	$0.496083\pi$
$864$	−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	$-0.848704\pi$
$877$	−6.44909e48	−1.77830	−0.889150	+	0.457615i	$0.848704\pi$
$878$	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	$-0.319255\pi$
$883$	4.36520e48	1.07560	0.537802	+	0.843071i	$0.319255\pi$
$884$	−2.99024e47	−0.0723175
$885$	0	0
$886$	−4.67996e48	−1.09040
$887$	−4.94841e48	−1.13168	−0.565842	−	0.824513i	$-0.691449\pi$
$887$	−4.94841e48	−1.13168	−0.565842	+	0.824513i	$0.691449\pi$
$888$	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	$-0.590765\pi$
$907$	−3.55400e48	−0.562596	−0.281298	+	0.959620i	$0.590765\pi$
$908$	−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	$-0.580717\pi$
$937$	−5.42233e48	−0.501744	−0.250872	+	0.968020i	$0.580717\pi$
$938$	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	$-0.375008\pi$
$947$	9.85410e48	0.765318	0.382659	+	0.923890i	$0.375008\pi$
$948$	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	$-0.731263\pi$
$953$	−1.89853e49	−1.32857	−0.664284	+	0.747480i	$0.731263\pi$
$954$	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	$-0.650731\pi$
$967$	−1.65793e49	−0.912070	−0.456035	+	0.889962i	$0.650731\pi$
$968$	−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	$-0.360192\pi$
$977$	1.83197e49	0.850467	0.425234	+	0.905084i	$0.360192\pi$
$978$	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	$-0.434722\pi$
$983$	9.70579e48	0.407285	0.203642	+	0.979045i	$0.434722\pi$
$984$	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	$-0.328968\pi$
$997$	3.08053e49	1.02366	0.511829	+	0.859088i	$0.328968\pi$
$998$	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.d.1.9	✓	11
5.2	odd	4		25.34.b.d.24.18		22
5.3	odd	4		25.34.b.d.24.5		22
5.4	even	2		25.34.a.e.1.3	yes	11

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