LMFDB - Embedded newform 25.34.a.d.1.11

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			1.11
Root			$178021.$ 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)

$f(q)$	$=$	$q+177167. q^{2} -1.20911e8 q^{3} +2.27982e10 q^{4} -2.14214e13 q^{6} +1.11259e14 q^{7} +2.51723e15 q^{8} +9.06036e15 q^{9} +O(q^{10})$	\(q+177167. q^{2} -1.20911e8 q^{3} +2.27982e10 q^{4} -2.14214e13 q^{6} +1.11259e14 q^{7} +2.51723e15 q^{8} +9.06036e15 q^{9} -1.24906e17 q^{11} -2.75655e18 q^{12} -2.26681e18 q^{13} +1.97114e19 q^{14} +2.50136e20 q^{16} -3.98383e20 q^{17} +1.60520e21 q^{18} +3.39897e20 q^{19} -1.34524e22 q^{21} -2.21292e22 q^{22} -1.96795e22 q^{23} -3.04361e23 q^{24} -4.01605e23 q^{26} -4.23345e23 q^{27} +2.53650e24 q^{28} -1.40974e23 q^{29} +3.85660e24 q^{31} +2.26929e25 q^{32} +1.51025e25 q^{33} -7.05803e25 q^{34} +2.06560e26 q^{36} +5.90970e24 q^{37} +6.02185e25 q^{38} +2.74082e26 q^{39} -8.25921e24 q^{41} -2.38332e27 q^{42} +6.30947e26 q^{43} -2.84763e27 q^{44} -3.48656e27 q^{46} -3.36586e27 q^{47} -3.02441e28 q^{48} +4.64754e27 q^{49} +4.81688e28 q^{51} -5.16793e28 q^{52} +5.10657e27 q^{53} -7.50028e28 q^{54} +2.80065e29 q^{56} -4.10972e28 q^{57} -2.49760e28 q^{58} -2.91603e29 q^{59} -3.91923e29 q^{61} +6.83262e29 q^{62} +1.00805e30 q^{63} +1.87178e30 q^{64} +2.67566e30 q^{66} +1.32177e30 q^{67} -9.08241e30 q^{68} +2.37946e30 q^{69} -4.98102e30 q^{71} +2.28071e31 q^{72} -3.33107e30 q^{73} +1.04700e30 q^{74} +7.74904e30 q^{76} -1.38969e31 q^{77} +4.85583e31 q^{78} +1.93342e31 q^{79} +8.19892e29 q^{81} -1.46326e30 q^{82} -6.11641e31 q^{83} -3.06690e32 q^{84} +1.11783e32 q^{86} +1.70453e31 q^{87} -3.14418e32 q^{88} -7.66849e31 q^{89} -2.52203e32 q^{91} -4.48657e32 q^{92} -4.66305e32 q^{93} -5.96319e32 q^{94} -2.74382e33 q^{96} -2.66508e32 q^{97} +8.23390e32 q^{98} -1.13169e33 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	177167.	1.91156	0.955780	−	0.294084i	$-0.0950144\pi$
$2$	177167.	1.91156	0.955780	+	0.294084i	$0.0950144\pi$
$3$	−1.20911e8	−1.62168	−0.810839	−	0.585270i	$-0.800989\pi$
$3$	−1.20911e8	−1.62168	−0.810839	+	0.585270i	$0.800989\pi$
$4$	2.27982e10	2.65406
$5$	0	0
$5$	0	0
$6$	−2.14214e13	−3.09993
$7$	1.11259e14	1.26537	0.632684	−	0.774410i	$-0.281953\pi$
$7$	1.11259e14	1.26537	0.632684	+	0.774410i	$0.281953\pi$
$8$	2.51723e15	3.16183
$9$	9.06036e15	1.62984
$10$	0	0
$11$	−1.24906e17	−0.819604	−0.409802	−	0.912174i	$-0.634402\pi$
$11$	−1.24906e17	−0.819604	−0.409802	+	0.912174i	$0.634402\pi$
$12$	−2.75655e18	−4.30403
$13$	−2.26681e18	−0.944823	−0.472412	−	0.881378i	$-0.656616\pi$
$13$	−2.26681e18	−0.944823	−0.472412	+	0.881378i	$0.656616\pi$
$14$	1.97114e19	2.41883
$15$	0	0
$16$	2.50136e20	3.38997
$17$	−3.98383e20	−1.98561	−0.992804	−	0.119754i	$-0.961789\pi$
$17$	−3.98383e20	−1.98561	−0.992804	+	0.119754i	$0.961789\pi$
$18$	1.60520e21	3.11553
$19$	3.39897e20	0.270342	0.135171	−	0.990822i	$-0.456842\pi$
$19$	3.39897e20	0.270342	0.135171	+	0.990822i	$0.456842\pi$
$20$	0	0
$21$	−1.34524e22	−2.05202
$22$	−2.21292e22	−1.56672
$23$	−1.96795e22	−0.669121	−0.334561	−	0.942374i	$-0.608588\pi$
$23$	−1.96795e22	−0.669121	−0.334561	+	0.942374i	$0.608588\pi$
$24$	−3.04361e23	−5.12747
$25$	0	0
$26$	−4.01605e23	−1.80609
$27$	−4.23345e23	−1.02139
$28$	2.53650e24	3.35836
$29$	−1.40974e23	−0.104610	−0.0523050	−	0.998631i	$-0.516657\pi$
$29$	−1.40974e23	−0.104610	−0.0523050	+	0.998631i	$0.516657\pi$
$30$	0	0
$31$	3.85660e24	0.952219	0.476109	−	0.879386i	$-0.342047\pi$
$31$	3.85660e24	0.952219	0.476109	+	0.879386i	$0.342047\pi$
$32$	2.26929e25	3.31830
$33$	1.51025e25	1.32913
$34$	−7.05803e25	−3.79561
$35$	0	0
$36$	2.06560e26	4.32568
$37$	5.90970e24	0.0787475	0.0393738	−	0.999225i	$-0.487464\pi$
$37$	5.90970e24	0.0787475	0.0393738	+	0.999225i	$0.487464\pi$
$38$	6.02185e25	0.516774
$39$	2.74082e26	1.53220
$40$	0	0
$41$	−8.25921e24	−0.0202304	−0.0101152	−	0.999949i	$-0.503220\pi$
$41$	−8.25921e24	−0.0202304	−0.0101152	+	0.999949i	$0.503220\pi$
$42$	−2.38332e27	−3.92256
$43$	6.30947e26	0.704309	0.352154	−	0.935942i	$-0.385449\pi$
$43$	6.30947e26	0.704309	0.352154	+	0.935942i	$0.385449\pi$
$44$	−2.84763e27	−2.17528
$45$	0	0
$46$	−3.48656e27	−1.27906
$47$	−3.36586e27	−0.865927	−0.432964	−	0.901411i	$-0.642532\pi$
$47$	−3.36586e27	−0.865927	−0.432964	+	0.901411i	$0.642532\pi$
$48$	−3.02441e28	−5.49744
$49$	4.64754e27	0.601157
$50$	0	0
$51$	4.81688e28	3.22001
$52$	−5.16793e28	−2.50762
$53$	5.10657e27	0.180958	0.0904790	−	0.995898i	$-0.471160\pi$
$53$	5.10657e27	0.180958	0.0904790	+	0.995898i	$0.471160\pi$
$54$	−7.50028e28	−1.95245
$55$	0	0
$56$	2.80065e29	4.00088
$57$	−4.10972e28	−0.438407
$58$	−2.49760e28	−0.199968
$59$	−2.91603e29	−1.76089	−0.880447	−	0.474144i	$-0.842757\pi$
$59$	−2.91603e29	−1.76089	−0.880447	+	0.474144i	$0.842757\pi$
$60$	0	0
$61$	−3.91923e29	−1.36540	−0.682699	−	0.730700i	$-0.739194\pi$
$61$	−3.91923e29	−1.36540	−0.682699	+	0.730700i	$0.739194\pi$
$62$	6.83262e29	1.82022
$63$	1.00805e30	2.06234
$64$	1.87178e30	2.95315
$65$	0	0
$66$	2.67566e30	2.54072
$67$	1.32177e30	0.979313	0.489657	−	0.871915i	$-0.337122\pi$
$67$	1.32177e30	0.979313	0.489657	+	0.871915i	$0.337122\pi$
$68$	−9.08241e30	−5.26992
$69$	2.37946e30	1.08510
$70$	0	0
$71$	−4.98102e30	−1.41761	−0.708803	−	0.705407i	$-0.750764\pi$
$71$	−4.98102e30	−1.41761	−0.708803	+	0.705407i	$0.750764\pi$
$72$	2.28071e31	5.15327
$73$	−3.33107e30	−0.599454	−0.299727	−	0.954025i	$-0.596896\pi$
$73$	−3.33107e30	−0.599454	−0.299727	+	0.954025i	$0.596896\pi$
$74$	1.04700e30	0.150531
$75$	0	0
$76$	7.74904e30	0.717503
$77$	−1.38969e31	−1.03710
$78$	4.85583e31	2.92889
$79$	1.93342e31	0.945103	0.472552	−	0.881303i	$-0.343333\pi$
$79$	1.93342e31	0.945103	0.472552	+	0.881303i	$0.343333\pi$
$80$	0	0
$81$	8.19892e29	0.0265310
$82$	−1.46326e30	−0.0386716
$83$	−6.11641e31	−1.32345	−0.661726	−	0.749746i	$-0.730176\pi$
$83$	−6.11641e31	−1.32345	−0.661726	+	0.749746i	$0.730176\pi$
$84$	−3.06690e32	−5.44618
$85$	0	0
$86$	1.11783e32	1.34633
$87$	1.70453e31	0.169644
$88$	−3.14418e32	−2.59145
$89$	−7.66849e31	−0.524535	−0.262268	−	0.964995i	$-0.584470\pi$
$89$	−7.66849e31	−0.524535	−0.262268	+	0.964995i	$0.584470\pi$
$90$	0	0
$91$	−2.52203e32	−1.19555
$92$	−4.48657e32	−1.77589
$93$	−4.66305e32	−1.54419
$94$	−5.96319e32	−1.65527
$95$	0	0
$96$	−2.74382e33	−5.38121
$97$	−2.66508e32	−0.440530	−0.220265	−	0.975440i	$-0.570692\pi$
$97$	−2.66508e32	−0.440530	−0.220265	+	0.975440i	$0.570692\pi$
$98$	8.23390e32	1.14915
$99$	−1.13169e33	−1.33582
$100$	0	0
$101$	4.53257e32	0.384629	0.192314	−	0.981333i	$-0.438401\pi$
$101$	4.53257e32	0.384629	0.192314	+	0.981333i	$0.438401\pi$
$102$	8.53392e33	6.15525
$103$	1.94880e33	1.19661	0.598304	−	0.801269i	$-0.295841\pi$
$103$	1.94880e33	1.19661	0.598304	+	0.801269i	$0.295841\pi$
$104$	−5.70610e33	−2.98737
$105$	0	0
$106$	9.04716e32	0.345912
$107$	−4.03797e33	−1.32230	−0.661150	−	0.750253i	$-0.729931\pi$
$107$	−4.03797e33	−1.32230	−0.661150	+	0.750253i	$0.729931\pi$
$108$	−9.65150e33	−2.71083
$109$	3.32000e33	0.800941	0.400471	−	0.916310i	$-0.368847\pi$
$109$	3.32000e33	0.800941	0.400471	+	0.916310i	$0.368847\pi$
$110$	0	0
$111$	−7.14546e32	−0.127703
$112$	2.78298e34	4.28956
$113$	−5.18771e33	−0.690528	−0.345264	−	0.938506i	$-0.612211\pi$
$113$	−5.18771e33	−0.690528	−0.345264	+	0.938506i	$0.612211\pi$
$114$	−7.28107e33	−0.838041
$115$	0	0
$116$	−3.21396e33	−0.277641
$117$	−2.05382e34	−1.53991
$118$	−5.16624e34	−3.36605
$119$	−4.43236e34	−2.51252
$120$	0	0
$121$	−7.62363e33	−0.328249
$122$	−6.94359e34	−2.61004
$123$	9.98627e32	0.0328072
$124$	8.79235e34	2.52725
$125$	0	0
$126$	1.78592e35	3.94229
$127$	−4.26706e34	−0.826738	−0.413369	−	0.910564i	$-0.635648\pi$
$127$	−4.26706e34	−0.826738	−0.413369	+	0.910564i	$0.635648\pi$
$128$	1.36688e35	2.32683
$129$	−7.62883e34	−1.14216
$130$	0	0
$131$	9.51459e34	1.10513	0.552566	−	0.833469i	$-0.313649\pi$
$131$	9.51459e34	1.10513	0.552566	+	0.833469i	$0.313649\pi$
$132$	3.44310e35	3.52760
$133$	3.78166e34	0.342082
$134$	2.34174e35	1.87202
$135$	0	0
$136$	−1.00282e36	−6.27816
$137$	−3.09831e35	−1.71884	−0.859420	−	0.511270i	$-0.829175\pi$
$137$	−3.09831e35	−1.71884	−0.859420	+	0.511270i	$0.829175\pi$
$138$	4.21562e35	2.07423
$139$	−3.67774e34	−0.160634	−0.0803169	−	0.996769i	$-0.525593\pi$
$139$	−3.67774e34	−0.160634	−0.0803169	+	0.996769i	$0.525593\pi$
$140$	0	0
$141$	4.06969e35	1.40425
$142$	−8.82472e35	−2.70984
$143$	2.83139e35	0.774381
$144$	2.26632e36	5.52510
$145$	0	0
$146$	−5.90155e35	−1.14589
$147$	−5.61938e35	−0.974882
$148$	1.34730e35	0.209001
$149$	−1.01479e35	−0.140865	−0.0704326	−	0.997517i	$-0.522438\pi$
$149$	−1.01479e35	−0.140865	−0.0704326	+	0.997517i	$0.522438\pi$
$150$	0	0
$151$	1.09661e36	1.22161	0.610803	−	0.791782i	$-0.290847\pi$
$151$	1.09661e36	1.22161	0.610803	+	0.791782i	$0.290847\pi$
$152$	8.55601e35	0.854775
$153$	−3.60949e36	−3.23622
$154$	−2.46207e36	−1.98248
$155$	0	0
$156$	6.24858e36	4.06655
$157$	−1.18915e36	−0.696453	−0.348227	−	0.937410i	$-0.613216\pi$
$157$	−1.18915e36	−0.696453	−0.348227	+	0.937410i	$0.613216\pi$
$158$	3.42538e36	1.80662
$159$	−6.17440e35	−0.293455
$160$	0	0
$161$	−2.18952e36	−0.846685
$162$	1.45258e35	0.0507156
$163$	3.11032e36	0.981093	0.490547	−	0.871415i	$-0.336797\pi$
$163$	3.11032e36	0.981093	0.490547	+	0.871415i	$0.336797\pi$
$164$	−1.88295e35	−0.0536927
$165$	0	0
$166$	−1.08363e37	−2.52986
$167$	−1.39555e36	−0.295069	−0.147535	−	0.989057i	$-0.547134\pi$
$167$	−1.39555e36	−0.295069	−0.147535	+	0.989057i	$0.547134\pi$
$168$	−3.38628e37	−6.48814
$169$	−6.17684e35	−0.107309
$170$	0	0
$171$	3.07959e36	0.440613
$172$	1.43844e37	1.86928
$173$	1.01617e36	0.120007	0.0600034	−	0.998198i	$-0.480889\pi$
$173$	1.01617e36	0.120007	0.0600034	+	0.998198i	$0.480889\pi$
$174$	3.01987e36	0.324284
$175$	0	0
$176$	−3.12435e37	−2.77843
$177$	3.52579e37	2.85560
$178$	−1.35860e37	−1.00268
$179$	2.10377e37	1.41555	0.707773	−	0.706440i	$-0.249700\pi$
$179$	2.10377e37	1.41555	0.707773	+	0.706440i	$0.249700\pi$
$180$	0	0
$181$	−7.67214e36	−0.429754	−0.214877	−	0.976641i	$-0.568935\pi$
$181$	−7.67214e36	−0.429754	−0.214877	+	0.976641i	$0.568935\pi$
$182$	−4.46821e37	−2.28536
$183$	4.73878e37	2.21423
$184$	−4.95379e37	−2.11565
$185$	0	0
$186$	−8.26138e37	−2.95181
$187$	4.97604e37	1.62741
$188$	−7.67355e37	−2.29822
$189$	−4.71009e37	−1.29244
$190$	0	0
$191$	2.89689e37	0.668162	0.334081	−	0.942544i	$-0.391574\pi$
$191$	2.89689e37	0.668162	0.334081	+	0.942544i	$0.391574\pi$
$192$	−2.26319e38	−4.78906
$193$	1.08652e37	0.211030	0.105515	−	0.994418i	$-0.466351\pi$
$193$	1.08652e37	0.211030	0.105515	+	0.994418i	$0.466351\pi$
$194$	−4.72163e37	−0.842100
$195$	0	0
$196$	1.05956e38	1.59551
$197$	−8.66891e37	−1.20025	−0.600125	−	0.799906i	$-0.704883\pi$
$197$	−8.66891e37	−1.20025	−0.600125	+	0.799906i	$0.704883\pi$
$198$	−2.00499e38	−2.55350
$199$	1.33609e38	1.56588	0.782941	−	0.622096i	$-0.213719\pi$
$199$	1.33609e38	1.56588	0.782941	+	0.622096i	$0.213719\pi$
$200$	0	0
$201$	−1.59816e38	−1.58813
$202$	8.03022e37	0.735241
$203$	−1.56846e37	−0.132370
$204$	1.09816e39	8.54611
$205$	0	0
$206$	3.45262e38	2.28739
$207$	−1.78303e38	−1.09056
$208$	−5.67011e38	−3.20292
$209$	−4.24552e37	−0.221573
$210$	0	0
$211$	−1.06827e38	−0.476454	−0.238227	−	0.971210i	$-0.576566\pi$
$211$	−1.06827e38	−0.476454	−0.238227	+	0.971210i	$0.576566\pi$
$212$	1.16421e38	0.480273
$213$	6.02259e38	2.29890
$214$	−7.15394e38	−2.52766
$215$	0	0
$216$	−1.06566e39	−3.22947
$217$	4.29081e38	1.20491
$218$	5.88194e38	1.53105
$219$	4.02762e38	0.972121
$220$	0	0
$221$	9.03060e38	1.87605
$222$	−1.26594e38	−0.244112
$223$	−8.53641e38	−1.52843	−0.764214	−	0.644962i	$-0.776873\pi$
$223$	−8.53641e38	−1.52843	−0.764214	+	0.644962i	$0.776873\pi$
$224$	2.52479e39	4.19887
$225$	0	0
$226$	−9.19091e38	−1.31999
$227$	−9.76166e38	−1.30346	−0.651729	−	0.758452i	$-0.725956\pi$
$227$	−9.76166e38	−1.30346	−0.651729	+	0.758452i	$0.725956\pi$
$228$	−9.36943e38	−1.16356
$229$	−1.17399e39	−1.35638	−0.678188	−	0.734888i	$-0.737235\pi$
$229$	−1.17399e39	−1.35638	−0.678188	+	0.734888i	$0.737235\pi$
$230$	0	0
$231$	1.68029e39	1.68184
$232$	−3.54865e38	−0.330759
$233$	−3.61332e38	−0.313714	−0.156857	−	0.987621i	$-0.550136\pi$
$233$	−3.61332e38	−0.313714	−0.156857	+	0.987621i	$0.550136\pi$
$234$	−3.63868e39	−2.94363
$235$	0	0
$236$	−6.64801e39	−4.67352
$237$	−2.33771e39	−1.53265
$238$	−7.85268e39	−4.80284
$239$	−2.97191e38	−0.169617	−0.0848087	−	0.996397i	$-0.527028\pi$
$239$	−2.97191e38	−0.169617	−0.0848087	+	0.996397i	$0.527028\pi$
$240$	0	0
$241$	8.15459e37	0.0405621	0.0202811	−	0.999794i	$-0.493544\pi$
$241$	8.15459e37	0.0405621	0.0202811	+	0.999794i	$0.493544\pi$
$242$	−1.35066e39	−0.627467
$243$	2.25427e39	0.978367
$244$	−8.93515e39	−3.62384
$245$	0	0
$246$	1.76924e38	0.0627129
$247$	−7.70484e38	−0.255425
$248$	9.70797e39	3.01076
$249$	7.39540e39	2.14621
$250$	0	0
$251$	3.98247e39	1.01283	0.506414	−	0.862290i	$-0.330971\pi$
$251$	3.98247e39	1.01283	0.506414	+	0.862290i	$0.330971\pi$
$252$	2.29816e40	5.47358
$253$	2.45809e39	0.548415
$254$	−7.55983e39	−1.58036
$255$	0	0
$256$	8.13803e39	1.49472
$257$	−1.37695e39	−0.237149	−0.118574	−	0.992945i	$-0.537832\pi$
$257$	−1.37695e39	−0.237149	−0.118574	+	0.992945i	$0.537832\pi$
$258$	−1.35158e40	−2.18331
$259$	6.57506e38	0.0996446
$260$	0	0
$261$	−1.27728e39	−0.170497
$262$	1.68567e40	2.11252
$263$	−4.06217e39	−0.478066	−0.239033	−	0.971011i	$-0.576830\pi$
$263$	−4.06217e39	−0.478066	−0.239033	+	0.971011i	$0.576830\pi$
$264$	3.80165e40	4.20250
$265$	0	0
$266$	6.69985e39	0.653910
$267$	9.27203e39	0.850627
$268$	3.01340e40	2.59916
$269$	9.40208e39	0.762625	0.381313	−	0.924446i	$-0.375472\pi$
$269$	9.40208e39	0.762625	0.381313	+	0.924446i	$0.375472\pi$
$270$	0	0
$271$	−8.74843e39	−0.627967	−0.313984	−	0.949428i	$-0.601664\pi$
$271$	−8.74843e39	−0.627967	−0.313984	+	0.949428i	$0.601664\pi$
$272$	−9.96498e40	−6.73115
$273$	3.04941e40	1.93880
$274$	−5.48918e40	−3.28567
$275$	0	0
$276$	5.42475e40	2.87992
$277$	−1.79091e40	−0.895691	−0.447845	−	0.894111i	$-0.647808\pi$
$277$	−1.79091e40	−0.895691	−0.447845	+	0.894111i	$0.647808\pi$
$278$	−6.51574e39	−0.307061
$279$	3.49422e40	1.55196
$280$	0	0
$281$	−3.07657e40	−1.21454	−0.607271	−	0.794495i	$-0.707736\pi$
$281$	−3.07657e40	−1.21454	−0.607271	+	0.794495i	$0.707736\pi$
$282$	7.21014e40	2.68432
$283$	−1.98938e40	−0.698622	−0.349311	−	0.937007i	$-0.613584\pi$
$283$	−1.98938e40	−0.698622	−0.349311	+	0.937007i	$0.613584\pi$
$284$	−1.13558e41	−3.76241
$285$	0	0
$286$	5.01628e40	1.48028
$287$	−9.18910e38	−0.0255989
$288$	2.05606e41	5.40829
$289$	1.18454e41	2.94264
$290$	0	0
$291$	3.22236e40	0.714398
$292$	−7.59423e40	−1.59099
$293$	3.51689e40	0.696375	0.348187	−	0.937425i	$-0.386797\pi$
$293$	3.51689e40	0.696375	0.348187	+	0.937425i	$0.386797\pi$
$294$	−9.95568e40	−1.86355
$295$	0	0
$296$	1.48761e40	0.248986
$297$	5.28784e40	0.837137
$298$	−1.79788e40	−0.269272
$299$	4.46098e40	0.632201
$300$	0	0
$301$	7.01984e40	0.891210
$302$	1.94283e41	2.33517
$303$	−5.48037e40	−0.623744
$304$	8.50204e40	0.916451
$305$	0	0
$306$	−6.39483e41	−6.18622
$307$	−2.17720e41	−1.99579	−0.997895	−	0.0648506i	$-0.979343\pi$
$307$	−2.17720e41	−1.99579	−0.997895	+	0.0648506i	$0.979343\pi$
$308$	−3.16824e41	−2.75253
$309$	−2.35630e41	−1.94051
$310$	0	0
$311$	7.47866e40	0.553703	0.276852	−	0.960913i	$-0.410709\pi$
$311$	7.47866e40	0.553703	0.276852	+	0.960913i	$0.410709\pi$
$312$	6.89929e41	4.84455
$313$	−1.94316e40	−0.129428	−0.0647139	−	0.997904i	$-0.520613\pi$
$313$	−1.94316e40	−0.129428	−0.0647139	+	0.997904i	$0.520613\pi$
$314$	−2.10678e41	−1.33131
$315$	0	0
$316$	4.40785e41	2.50836
$317$	2.89155e41	1.56190	0.780949	−	0.624595i	$-0.214736\pi$
$317$	2.89155e41	1.56190	0.780949	+	0.624595i	$0.214736\pi$
$318$	−1.09390e41	−0.560957
$319$	1.76085e40	0.0857388
$320$	0	0
$321$	4.88234e41	2.14434
$322$	−3.87910e41	−1.61849
$323$	−1.35409e41	−0.536793
$324$	1.86920e40	0.0704148
$325$	0	0
$326$	5.51047e41	1.87542
$327$	−4.01424e41	−1.29887
$328$	−2.07904e40	−0.0639652
$329$	−3.74482e41	−1.09572
$330$	0	0
$331$	4.23132e41	1.12025	0.560124	−	0.828409i	$-0.310753\pi$
$331$	4.23132e41	1.12025	0.560124	+	0.828409i	$0.310753\pi$
$332$	−1.39443e42	−3.51252
$333$	5.35440e40	0.128346
$334$	−2.47246e41	−0.564043
$335$	0	0
$336$	−3.36493e42	−6.95628
$337$	1.90258e41	0.374498	0.187249	−	0.982312i	$-0.440043\pi$
$337$	1.90258e41	0.374498	0.187249	+	0.982312i	$0.440043\pi$
$338$	−1.09433e41	−0.205127
$339$	6.27250e41	1.11981
$340$	0	0
$341$	−4.81713e41	−0.780443
$342$	5.45602e41	0.842258
$343$	−3.43062e41	−0.504684
$344$	1.58824e42	2.22691
$345$	0	0
$346$	1.80032e41	0.229400
$347$	−7.85300e41	−0.954112	−0.477056	−	0.878873i	$-0.658296\pi$
$347$	−7.85300e41	−0.954112	−0.477056	+	0.878873i	$0.658296\pi$
$348$	3.88602e41	0.450244
$349$	1.51475e42	1.67387	0.836937	−	0.547300i	$-0.184344\pi$
$349$	1.51475e42	1.67387	0.836937	+	0.547300i	$0.184344\pi$
$350$	0	0
$351$	9.59645e41	0.965035
$352$	−2.83448e42	−2.71969
$353$	−2.12379e42	−1.94459	−0.972297	−	0.233751i	$-0.924900\pi$
$353$	−2.12379e42	−1.94459	−0.972297	+	0.233751i	$0.924900\pi$
$354$	6.24654e42	5.45865
$355$	0	0
$356$	−1.74828e42	−1.39215
$357$	5.35920e42	4.07450
$358$	3.72719e42	2.70590
$359$	−2.70737e42	−1.87711	−0.938553	−	0.345135i	$-0.887833\pi$
$359$	−2.70737e42	−1.87711	−0.938553	+	0.345135i	$0.887833\pi$
$360$	0	0
$361$	−1.46524e42	−0.926915
$362$	−1.35925e42	−0.821500
$363$	9.21779e41	0.532314
$364$	−5.74978e42	−3.17306
$365$	0	0
$366$	8.39555e42	4.23264
$367$	1.95306e42	0.941295	0.470648	−	0.882321i	$-0.344020\pi$
$367$	1.95306e42	0.941295	0.470648	+	0.882321i	$0.344020\pi$
$368$	−4.92255e42	−2.26830
$369$	−7.48314e40	−0.0329723
$370$	0	0
$371$	5.68151e41	0.228978
$372$	−1.06309e43	−4.09838
$373$	3.00107e42	1.10683	0.553413	−	0.832907i	$-0.313325\pi$
$373$	3.00107e42	1.10683	0.553413	+	0.832907i	$0.313325\pi$
$374$	8.81590e42	3.11089
$375$	0	0
$376$	−8.47266e42	−2.73792
$377$	3.19563e41	0.0988379
$378$	−8.34472e42	−2.47057
$379$	−2.42202e42	−0.686485	−0.343242	−	0.939247i	$-0.611525\pi$
$379$	−2.42202e42	−0.686485	−0.343242	+	0.939247i	$0.611525\pi$
$380$	0	0
$381$	5.15934e42	1.34070
$382$	5.13234e42	1.27723
$383$	−5.11408e42	−1.21895	−0.609477	−	0.792804i	$-0.708621\pi$
$383$	−5.11408e42	−1.21895	−0.609477	+	0.792804i	$0.708621\pi$
$384$	−1.65270e43	−3.77337
$385$	0	0
$386$	1.92496e42	0.403395
$387$	5.71660e42	1.14791
$388$	−6.07589e42	−1.16919
$389$	4.84726e42	0.893980	0.446990	−	0.894539i	$-0.352496\pi$
$389$	4.84726e42	0.893980	0.446990	+	0.894539i	$0.352496\pi$
$390$	0	0
$391$	7.83997e42	1.32861
$392$	1.16989e43	1.90076
$393$	−1.15042e43	−1.79217
$394$	−1.53584e43	−2.29435
$395$	0	0
$396$	−2.58006e43	−3.54535
$397$	1.26339e43	1.66531	0.832656	−	0.553791i	$-0.186819\pi$
$397$	1.26339e43	1.66531	0.832656	+	0.553791i	$0.186819\pi$
$398$	2.36711e43	2.99328
$399$	−4.57243e42	−0.554746
$400$	0	0
$401$	−4.14706e42	−0.463296	−0.231648	−	0.972800i	$-0.574412\pi$
$401$	−4.14706e42	−0.463296	−0.231648	+	0.972800i	$0.574412\pi$
$402$	−2.83142e43	−3.03580
$403$	−8.74220e42	−0.899679
$404$	1.03334e43	1.02083
$405$	0	0
$406$	−2.77880e42	−0.253033
$407$	−7.38157e41	−0.0645418
$408$	1.21252e44	10.1811
$409$	2.91139e42	0.234782	0.117391	−	0.993086i	$-0.462547\pi$
$409$	2.91139e42	0.234782	0.117391	+	0.993086i	$0.462547\pi$
$410$	0	0
$411$	3.74619e43	2.78740
$412$	4.44290e43	3.17587
$413$	−3.24434e43	−2.22818
$414$	−3.15895e43	−2.08467
$415$	0	0
$416$	−5.14406e43	−3.13521
$417$	4.44679e42	0.260496
$418$	−7.52166e42	−0.423550
$419$	2.78455e43	1.50738	0.753691	−	0.657229i	$-0.228271\pi$
$419$	2.78455e43	1.50738	0.753691	+	0.657229i	$0.228271\pi$
$420$	0	0
$421$	6.27307e42	0.313925	0.156962	−	0.987605i	$-0.449830\pi$
$421$	6.27307e42	0.313925	0.156962	+	0.987605i	$0.449830\pi$
$422$	−1.89262e43	−0.910769
$423$	−3.04959e43	−1.41132
$424$	1.28544e43	0.572159
$425$	0	0
$426$	1.06700e44	4.39448
$427$	−4.36050e43	−1.72773
$428$	−9.20583e43	−3.50946
$429$	−3.42345e43	−1.25580
$430$	0	0
$431$	2.59418e43	0.881302	0.440651	−	0.897678i	$-0.354748\pi$
$431$	2.59418e43	0.881302	0.440651	+	0.897678i	$0.354748\pi$
$432$	−1.05894e44	−3.46249
$433$	5.37170e43	1.69068	0.845341	−	0.534227i	$-0.179397\pi$
$433$	5.37170e43	1.69068	0.845341	+	0.534227i	$0.179397\pi$
$434$	7.60190e43	2.30325
$435$	0	0
$436$	7.56900e43	2.12575
$437$	−6.68901e42	−0.180891
$438$	7.13561e43	1.85827
$439$	5.32504e43	1.33554	0.667772	−	0.744365i	$-0.267248\pi$
$439$	5.32504e43	1.33554	0.667772	+	0.744365i	$0.267248\pi$
$440$	0	0
$441$	4.21084e43	0.979787
$442$	1.59992e44	3.58618
$443$	3.70109e43	0.799224	0.399612	−	0.916684i	$-0.369145\pi$
$443$	3.70109e43	0.799224	0.399612	+	0.916684i	$0.369145\pi$
$444$	−1.62904e43	−0.338931
$445$	0	0
$446$	−1.51237e44	−2.92168
$447$	1.22699e43	0.228438
$448$	2.08253e44	3.73683
$449$	−3.12899e43	−0.541178	−0.270589	−	0.962695i	$-0.587218\pi$
$449$	−3.12899e43	−0.541178	−0.270589	+	0.962695i	$0.587218\pi$
$450$	0	0
$451$	1.03162e42	0.0165809
$452$	−1.18270e44	−1.83270
$453$	−1.32592e44	−1.98105
$454$	−1.72944e44	−2.49164
$455$	0	0
$456$	−1.03451e44	−1.38617
$457$	1.28166e44	1.65636	0.828179	−	0.560463i	$-0.189377\pi$
$457$	1.28166e44	1.65636	0.828179	+	0.560463i	$0.189377\pi$
$458$	−2.07993e44	−2.59279
$459$	1.68653e44	2.02808
$460$	0	0
$461$	−7.43569e42	−0.0832254	−0.0416127	−	0.999134i	$-0.513250\pi$
$461$	−7.43569e42	−0.0832254	−0.0416127	+	0.999134i	$0.513250\pi$
$462$	2.97691e44	3.21494
$463$	1.76967e44	1.84419	0.922094	−	0.386966i	$-0.126477\pi$
$463$	1.76967e44	1.84419	0.922094	+	0.386966i	$0.126477\pi$
$464$	−3.52627e43	−0.354625
$465$	0	0
$466$	−6.40161e43	−0.599683
$467$	1.54998e44	1.40152	0.700759	−	0.713398i	$-0.252845\pi$
$467$	1.54998e44	1.40152	0.700759	+	0.713398i	$0.252845\pi$
$468$	−4.68233e44	−4.08701
$469$	1.47059e44	1.23919
$470$	0	0
$471$	1.43781e44	1.12942
$472$	−7.34032e44	−5.56765
$473$	−7.88091e43	−0.577255
$474$	−4.14166e44	−2.92976
$475$	0	0
$476$	−1.01050e45	−6.66839
$477$	4.62674e43	0.294932
$478$	−5.26525e43	−0.324234
$479$	1.90950e44	1.13602	0.568008	−	0.823023i	$-0.307714\pi$
$479$	1.90950e44	1.13602	0.568008	+	0.823023i	$0.307714\pi$
$480$	0	0
$481$	−1.33962e43	−0.0744025
$482$	1.44472e43	0.0775369
$483$	2.64736e44	1.37305
$484$	−1.73805e44	−0.871192
$485$	0	0
$486$	3.99382e44	1.87021
$487$	−9.86519e43	−0.446558	−0.223279	−	0.974755i	$-0.571676\pi$
$487$	−9.86519e43	−0.446558	−0.223279	+	0.974755i	$0.571676\pi$
$488$	−9.86563e44	−4.31716
$489$	−3.76072e44	−1.59102
$490$	0	0
$491$	9.91478e43	0.392138	0.196069	−	0.980590i	$-0.437182\pi$
$491$	9.91478e43	0.392138	0.196069	+	0.980590i	$0.437182\pi$
$492$	2.27669e43	0.0870722
$493$	5.61617e43	0.207714
$494$	−1.36504e44	−0.488260
$495$	0	0
$496$	9.64674e44	3.22799
$497$	−5.54182e44	−1.79379
$498$	1.31022e45	4.10261
$499$	2.18397e44	0.661588	0.330794	−	0.943703i	$-0.392684\pi$
$499$	2.18397e44	0.661588	0.330794	+	0.943703i	$0.392684\pi$
$500$	0	0
$501$	1.68737e44	0.478507
$502$	7.05561e44	1.93608
$503$	−4.26115e44	−1.13150	−0.565750	−	0.824577i	$-0.691413\pi$
$503$	−4.26115e44	−1.13150	−0.565750	+	0.824577i	$0.691413\pi$
$504$	2.53749e45	6.52079
$505$	0	0
$506$	4.35492e44	1.04833
$507$	7.46846e43	0.174020
$508$	−9.72814e44	−2.19421
$509$	−4.45432e44	−0.972607	−0.486304	−	0.873790i	$-0.661655\pi$
$509$	−4.45432e44	−0.972607	−0.486304	+	0.873790i	$0.661655\pi$
$510$	0	0
$511$	−3.70611e44	−0.758530
$512$	2.67653e44	0.530417
$513$	−1.43894e44	−0.276125
$514$	−2.43950e44	−0.453324
$515$	0	0
$516$	−1.73923e45	−3.03136
$517$	4.20416e44	0.709718
$518$	1.16488e44	0.190477
$519$	−1.22866e44	−0.194612
$520$	0	0
$521$	7.95638e44	1.18275	0.591375	−	0.806397i	$-0.298585\pi$
$521$	7.95638e44	1.18275	0.591375	+	0.806397i	$0.298585\pi$
$522$	−2.26292e44	−0.325915
$523$	5.07858e43	0.0708703	0.0354352	−	0.999372i	$-0.488718\pi$
$523$	5.07858e43	0.0708703	0.0354352	+	0.999372i	$0.488718\pi$
$524$	2.16916e45	2.93308
$525$	0	0
$526$	−7.19682e44	−0.913852
$527$	−1.53640e45	−1.89073
$528$	3.77767e45	4.50572
$529$	−4.77722e44	−0.552277
$530$	0	0
$531$	−2.64203e45	−2.86997
$532$	8.62150e44	0.907906
$533$	1.87221e43	0.0191142
$534$	1.64270e45	1.62602
$535$	0	0
$536$	3.32720e45	3.09642
$537$	−2.54369e45	−2.29556
$538$	1.66574e45	1.45780
$539$	−5.80506e44	−0.492711
$540$	0	0
$541$	5.77848e44	0.461380	0.230690	−	0.973027i	$-0.425902\pi$
$541$	5.77848e44	0.461380	0.230690	+	0.973027i	$0.425902\pi$
$542$	−1.54993e45	−1.20040
$543$	9.27644e44	0.696922
$544$	−9.04046e45	−6.58884
$545$	0	0
$546$	5.40254e45	3.70612
$547$	1.52755e45	1.01673	0.508363	−	0.861143i	$-0.330251\pi$
$547$	1.52755e45	1.01673	0.508363	+	0.861143i	$0.330251\pi$
$548$	−7.06359e45	−4.56190
$549$	−3.55097e45	−2.22537
$550$	0	0
$551$	−4.79168e43	−0.0282804
$552$	5.98967e45	3.43090
$553$	2.15110e45	1.19590
$554$	−3.17290e45	−1.71217
$555$	0	0
$556$	−8.38459e44	−0.426332
$557$	2.40408e45	1.18669	0.593345	−	0.804948i	$-0.297807\pi$
$557$	2.40408e45	1.18669	0.593345	+	0.804948i	$0.297807\pi$
$558$	6.19060e45	2.96667
$559$	−1.43024e45	−0.665447
$560$	0	0
$561$	−6.01657e45	−2.63914
$562$	−5.45066e45	−2.32167
$563$	−6.97447e44	−0.288485	−0.144242	−	0.989542i	$-0.546074\pi$
$563$	−6.97447e44	−0.288485	−0.144242	+	0.989542i	$0.546074\pi$
$564$	9.27816e45	3.72697
$565$	0	0
$566$	−3.52453e45	−1.33546
$567$	9.12202e43	0.0335715
$568$	−1.25384e46	−4.48223
$569$	3.28369e45	1.14028	0.570138	−	0.821549i	$-0.306890\pi$
$569$	3.28369e45	1.14028	0.570138	+	0.821549i	$0.306890\pi$
$570$	0	0
$571$	−4.65773e45	−1.52644	−0.763218	−	0.646141i	$-0.776382\pi$
$571$	−4.65773e45	−1.52644	−0.763218	+	0.646141i	$0.776382\pi$
$572$	6.45505e45	2.05525
$573$	−3.50266e45	−1.08354
$574$	−1.62800e44	−0.0489338
$575$	0	0
$576$	1.69590e46	4.81316
$577$	5.19987e45	1.43414	0.717070	−	0.697001i	$-0.245483\pi$
$577$	5.19987e45	1.43414	0.717070	+	0.697001i	$0.245483\pi$
$578$	2.09862e46	5.62502
$579$	−1.31372e45	−0.342222
$580$	0	0
$581$	−6.80505e45	−1.67465
$582$	5.70896e45	1.36561
$583$	−6.37842e44	−0.148314
$584$	−8.38507e45	−1.89537
$585$	0	0
$586$	6.23077e45	1.33116
$587$	−1.42187e45	−0.295346	−0.147673	−	0.989036i	$-0.547178\pi$
$587$	−1.42187e45	−0.295346	−0.147673	+	0.989036i	$0.547178\pi$
$588$	−1.28112e46	−2.58740
$589$	1.31085e45	0.257424
$590$	0	0
$591$	1.04817e46	1.94642
$592$	1.47823e45	0.266952
$593$	1.86285e44	0.0327171	0.0163586	−	0.999866i	$-0.494793\pi$
$593$	1.86285e44	0.0327171	0.0163586	+	0.999866i	$0.494793\pi$
$594$	9.36830e45	1.60024
$595$	0	0
$596$	−2.31354e45	−0.373864
$597$	−1.61547e46	−2.53936
$598$	7.90338e45	1.20849
$599$	−1.86132e45	−0.276871	−0.138436	−	0.990371i	$-0.544207\pi$
$599$	−1.86132e45	−0.276871	−0.138436	+	0.990371i	$0.544207\pi$
$600$	0	0
$601$	−7.31474e45	−1.02984	−0.514921	−	0.857238i	$-0.672179\pi$
$601$	−7.31474e45	−1.02984	−0.514921	+	0.857238i	$0.672179\pi$
$602$	1.24368e46	1.70360
$603$	1.19757e46	1.59612
$604$	2.50007e46	3.24222
$605$	0	0
$606$	−9.70940e45	−1.19232
$607$	−1.20958e46	−1.44551	−0.722755	−	0.691104i	$-0.757125\pi$
$607$	−1.20958e46	−1.44551	−0.722755	+	0.691104i	$0.757125\pi$
$608$	7.71326e45	0.897075
$609$	1.89644e45	0.214662
$610$	0	0
$611$	7.62978e45	0.818148
$612$	−8.22899e46	−8.58911
$613$	4.67729e45	0.475222	0.237611	−	0.971360i	$-0.423636\pi$
$613$	4.67729e45	0.475222	0.237611	+	0.971360i	$0.423636\pi$
$614$	−3.85728e46	−3.81507
$615$	0	0
$616$	−3.49818e46	−3.27914
$617$	7.40374e45	0.675687	0.337844	−	0.941202i	$-0.390303\pi$
$617$	7.40374e45	0.675687	0.337844	+	0.941202i	$0.390303\pi$
$618$	−4.17459e46	−3.70940
$619$	−5.69692e45	−0.492884	−0.246442	−	0.969158i	$-0.579261\pi$
$619$	−5.69692e45	−0.492884	−0.246442	+	0.969158i	$0.579261\pi$
$620$	0	0
$621$	8.33122e45	0.683435
$622$	1.32497e46	1.05844
$623$	−8.53187e45	−0.663730
$624$	6.85578e46	5.19411
$625$	0	0
$626$	−3.44264e45	−0.247409
$627$	5.13329e45	0.359320
$628$	−2.71105e46	−1.84843
$629$	−2.35432e45	−0.156362
$630$	0	0
$631$	1.42939e46	0.900877	0.450439	−	0.892807i	$-0.351268\pi$
$631$	1.42939e46	0.900877	0.450439	+	0.892807i	$0.351268\pi$
$632$	4.86687e46	2.98826
$633$	1.29165e46	0.772654
$634$	5.12287e46	2.98566
$635$	0	0
$636$	−1.40765e46	−0.778848
$637$	−1.05351e46	−0.567987
$638$	3.11965e45	0.163895
$639$	−4.51298e46	−2.31047
$640$	0	0
$641$	3.81314e46	1.85407	0.927034	−	0.374978i	$-0.122350\pi$
$641$	3.81314e46	1.85407	0.927034	+	0.374978i	$0.122350\pi$
$642$	8.64989e46	4.09904
$643$	8.01593e44	0.0370231	0.0185116	−	0.999829i	$-0.494107\pi$
$643$	8.01593e44	0.0370231	0.0185116	+	0.999829i	$0.494107\pi$
$644$	−4.99171e46	−2.24715
$645$	0	0
$646$	−2.39900e46	−1.02611
$647$	−4.41584e46	−1.84116	−0.920582	−	0.390548i	$-0.872285\pi$
$647$	−4.41584e46	−1.84116	−0.920582	+	0.390548i	$0.872285\pi$
$648$	2.06386e45	0.0838866
$649$	3.64229e46	1.44324
$650$	0	0
$651$	−5.18805e46	−1.95397
$652$	7.09098e46	2.60388
$653$	4.02818e46	1.44225	0.721127	−	0.692803i	$-0.243625\pi$
$653$	4.02818e46	1.44225	0.721127	+	0.692803i	$0.243625\pi$
$654$	−7.11190e46	−2.48286
$655$	0	0
$656$	−2.06592e45	−0.0685805
$657$	−3.01807e46	−0.977012
$658$	−6.63458e46	−2.09453
$659$	2.34159e46	0.720942	0.360471	−	0.932770i	$-0.382616\pi$
$659$	2.34159e46	0.720942	0.360471	+	0.932770i	$0.382616\pi$
$660$	0	0
$661$	5.49451e45	0.160918	0.0804591	−	0.996758i	$-0.474361\pi$
$661$	5.49451e45	0.160918	0.0804591	+	0.996758i	$0.474361\pi$
$662$	7.49651e46	2.14142
$663$	−1.09190e47	−3.04234
$664$	−1.53964e47	−4.18453
$665$	0	0
$666$	9.48623e45	0.245340
$667$	2.77430e45	0.0699967
$668$	−3.18161e46	−0.783132
$669$	1.03214e47	2.47862
$670$	0	0
$671$	4.89536e46	1.11909
$672$	−3.05274e47	−6.80921
$673$	−6.08553e45	−0.132449	−0.0662247	−	0.997805i	$-0.521095\pi$
$673$	−6.08553e45	−0.132449	−0.0662247	+	0.997805i	$0.521095\pi$
$674$	3.37074e46	0.715875
$675$	0	0
$676$	−1.40821e46	−0.284804
$677$	4.63043e46	0.913920	0.456960	−	0.889487i	$-0.348938\pi$
$677$	4.63043e46	0.913920	0.456960	+	0.889487i	$0.348938\pi$
$678$	1.11128e47	2.14059
$679$	−2.96513e46	−0.557433
$680$	0	0
$681$	1.18029e47	2.11379
$682$	−8.53436e46	−1.49186
$683$	3.95290e46	0.674488	0.337244	−	0.941417i	$-0.390505\pi$
$683$	3.95290e46	0.674488	0.337244	+	0.941417i	$0.390505\pi$
$684$	7.02091e46	1.16941
$685$	0	0
$686$	−6.07792e46	−0.964732
$687$	1.41948e47	2.19960
$688$	1.57822e47	2.38759
$689$	−1.15756e46	−0.170973
$690$	0	0
$691$	−1.31488e46	−0.185139	−0.0925694	−	0.995706i	$-0.529508\pi$
$691$	−1.31488e46	−0.185139	−0.0925694	+	0.995706i	$0.529508\pi$
$692$	2.31668e46	0.318505
$693$	−1.25911e47	−1.69031
$694$	−1.39129e47	−1.82384
$695$	0	0
$696$	4.29071e46	0.536385
$697$	3.29033e45	0.0401696
$698$	2.68364e47	3.19971
$699$	4.36889e46	0.508743
$700$	0	0
$701$	−1.78515e46	−0.198303	−0.0991513	−	0.995072i	$-0.531613\pi$
$701$	−1.78515e46	−0.198303	−0.0991513	+	0.995072i	$0.531613\pi$
$702$	1.70017e47	1.84472
$703$	2.00869e45	0.0212887
$704$	−2.33797e47	−2.42042
$705$	0	0
$706$	−3.76265e47	−3.71721
$707$	5.04289e46	0.486697
$708$	8.03817e47	7.57894
$709$	−1.04358e47	−0.961309	−0.480655	−	0.876910i	$-0.659601\pi$
$709$	−1.04358e47	−0.961309	−0.480655	+	0.876910i	$0.659601\pi$
$710$	0	0
$711$	1.75175e47	1.54036
$712$	−1.93034e47	−1.65849
$713$	−7.58960e46	−0.637150
$714$	9.49474e47	7.78865
$715$	0	0
$716$	4.79623e47	3.75694
$717$	3.59336e46	0.275065
$718$	−4.79656e47	−3.58820
$719$	1.34958e47	0.986667	0.493334	−	0.869840i	$-0.335778\pi$
$719$	1.34958e47	0.986667	0.493334	+	0.869840i	$0.335778\pi$
$720$	0	0
$721$	2.16821e47	1.51415
$722$	−2.59592e47	−1.77185
$723$	−9.85978e45	−0.0657787
$724$	−1.74911e47	−1.14059
$725$	0	0
$726$	1.63309e47	1.01755
$727$	−1.33195e47	−0.811279	−0.405639	−	0.914033i	$-0.632951\pi$
$727$	−1.33195e47	−0.811279	−0.405639	+	0.914033i	$0.632951\pi$
$728$	−6.34854e47	−3.78013
$729$	−2.77123e47	−1.61313
$730$	0	0
$731$	−2.51358e47	−1.39848
$732$	1.08036e48	5.87671
$733$	−1.24873e47	−0.664131	−0.332065	−	0.943256i	$-0.607745\pi$
$733$	−1.24873e47	−0.664131	−0.332065	+	0.943256i	$0.607745\pi$
$734$	3.46018e47	1.79934
$735$	0	0
$736$	−4.46585e47	−2.22034
$737$	−1.65097e47	−0.802649
$738$	−1.32576e46	−0.0630284
$739$	−1.60801e47	−0.747578	−0.373789	−	0.927514i	$-0.621942\pi$
$739$	−1.60801e47	−0.747578	−0.373789	+	0.927514i	$0.621942\pi$
$740$	0	0
$741$	9.31598e46	0.414217
$742$	1.00658e47	0.437706
$743$	−2.88596e47	−1.22737	−0.613683	−	0.789552i	$-0.710313\pi$
$743$	−2.88596e47	−1.22737	−0.613683	+	0.789552i	$0.710313\pi$
$744$	−1.17380e48	−4.88247
$745$	0	0
$746$	5.31690e47	2.11577
$747$	−5.54169e47	−2.15701
$748$	1.13445e48	4.31925
$749$	−4.49259e47	−1.67320
$750$	0	0
$751$	4.31988e47	1.53962	0.769809	−	0.638274i	$-0.220351\pi$
$751$	4.31988e47	1.53962	0.769809	+	0.638274i	$0.220351\pi$
$752$	−8.41922e47	−2.93547
$753$	−4.81523e47	−1.64248
$754$	5.66159e46	0.188935
$755$	0	0
$756$	−1.07382e48	−3.43020
$757$	−3.86378e47	−1.20762	−0.603810	−	0.797128i	$-0.706351\pi$
$757$	−3.86378e47	−1.20762	−0.603810	+	0.797128i	$0.706351\pi$
$758$	−4.29102e47	−1.31226
$759$	−2.97210e47	−0.889351
$760$	0	0
$761$	−1.73723e47	−0.497750	−0.248875	−	0.968536i	$-0.580061\pi$
$761$	−1.73723e47	−0.497750	−0.248875	+	0.968536i	$0.580061\pi$
$762$	9.14065e47	2.56283
$763$	3.69379e47	1.01349
$764$	6.60440e47	1.77334
$765$	0	0
$766$	−9.06045e47	−2.33010
$767$	6.61009e47	1.66373
$768$	−9.83976e47	−2.42395
$769$	−5.01555e47	−1.20930	−0.604649	−	0.796492i	$-0.706687\pi$
$769$	−5.01555e47	−1.20930	−0.604649	+	0.796492i	$0.706687\pi$
$770$	0	0
$771$	1.66488e47	0.384579
$772$	2.47708e47	0.560085
$773$	−2.46977e47	−0.546633	−0.273316	−	0.961924i	$-0.588121\pi$
$773$	−2.46977e47	−0.546633	−0.273316	+	0.961924i	$0.588121\pi$
$774$	1.01279e48	2.19430
$775$	0	0
$776$	−6.70862e47	−1.39288
$777$	−7.94996e46	−0.161591
$778$	8.58774e47	1.70890
$779$	−2.80728e45	−0.00546912
$780$	0	0
$781$	6.22159e47	1.16188
$782$	1.38898e48	2.53972
$783$	5.96808e46	0.106848
$784$	1.16252e48	2.03790
$785$	0	0
$786$	−2.03816e48	−3.42583
$787$	−3.46347e47	−0.570069	−0.285035	−	0.958517i	$-0.592005\pi$
$787$	−3.46347e47	−0.570069	−0.285035	+	0.958517i	$0.592005\pi$
$788$	−1.97636e48	−3.18554
$789$	4.91160e47	0.775269
$790$	0	0
$791$	−5.77179e47	−0.873773
$792$	−2.84874e48	−4.22364
$793$	8.88418e47	1.29006
$794$	2.23832e48	3.18334
$795$	0	0
$796$	3.04604e48	4.15594
$797$	−1.83743e47	−0.245555	−0.122778	−	0.992434i	$-0.539180\pi$
$797$	−1.83743e47	−0.245555	−0.122778	+	0.992434i	$0.539180\pi$
$798$	−8.10084e47	−1.06043
$799$	1.34090e48	1.71939
$800$	0	0
$801$	−6.94793e47	−0.854907
$802$	−7.34723e47	−0.885618
$803$	4.16070e47	0.491315
$804$	−3.64352e48	−4.21499
$805$	0	0
$806$	−1.54883e48	−1.71979
$807$	−1.13681e48	−1.23673
$808$	1.14095e48	1.21613
$809$	−4.02171e47	−0.420011	−0.210005	−	0.977700i	$-0.567348\pi$
$809$	−4.02171e47	−0.420011	−0.210005	+	0.977700i	$0.567348\pi$
$810$	0	0
$811$	−1.31777e48	−1.32128	−0.660640	−	0.750703i	$-0.729715\pi$
$811$	−1.31777e48	−1.32128	−0.660640	+	0.750703i	$0.729715\pi$
$812$	−3.57582e47	−0.351318
$813$	1.05778e48	1.01836
$814$	−1.30777e47	−0.123375
$815$	0	0
$816$	1.20487e49	10.9158
$817$	2.14457e47	0.190404
$818$	5.15802e47	0.448800
$819$	−2.28505e48	−1.94855
$820$	0	0
$821$	7.93981e47	0.650352	0.325176	−	0.945654i	$-0.394577\pi$
$821$	7.93981e47	0.650352	0.325176	+	0.945654i	$0.394577\pi$
$822$	6.63701e48	5.32829
$823$	2.50063e47	0.196767	0.0983836	−	0.995149i	$-0.468633\pi$
$823$	2.50063e47	0.196767	0.0983836	+	0.995149i	$0.468633\pi$
$824$	4.90557e48	3.78348
$825$	0	0
$826$	−5.74789e48	−4.25930
$827$	−2.45832e48	−1.78566	−0.892829	−	0.450395i	$-0.851283\pi$
$827$	−2.45832e48	−1.78566	−0.892829	+	0.450395i	$0.851283\pi$
$828$	−4.06500e48	−2.89441
$829$	3.63215e47	0.253521	0.126760	−	0.991933i	$-0.459542\pi$
$829$	3.63215e47	0.253521	0.126760	+	0.991933i	$0.459542\pi$
$830$	0	0
$831$	2.16541e48	1.45252
$832$	−4.24299e48	−2.79021
$833$	−1.85150e48	−1.19366
$834$	7.87824e47	0.497954
$835$	0	0
$836$	−9.67902e47	−0.588069
$837$	−1.63267e48	−0.972588
$838$	4.93330e48	2.88145
$839$	−6.95183e46	−0.0398132	−0.0199066	−	0.999802i	$-0.506337\pi$
$839$	−6.95183e46	−0.0398132	−0.0199066	+	0.999802i	$0.506337\pi$
$840$	0	0
$841$	−1.79620e48	−0.989057
$842$	1.11138e48	0.600086
$843$	3.71990e48	1.96959
$844$	−2.43546e48	−1.26454
$845$	0	0
$846$	−5.40287e48	−2.69782
$847$	−8.48196e47	−0.415356
$848$	1.27734e48	0.613442
$849$	2.40538e48	1.13294
$850$	0	0
$851$	−1.16300e47	−0.0526916
$852$	1.37304e49	6.10141
$853$	−1.76186e48	−0.767913	−0.383957	−	0.923351i	$-0.625439\pi$
$853$	−1.76186e48	−0.767913	−0.383957	+	0.923351i	$0.625439\pi$
$854$	−7.72536e48	−3.30266
$855$	0	0
$856$	−1.01645e49	−4.18089
$857$	−1.03657e48	−0.418229	−0.209114	−	0.977891i	$-0.567058\pi$
$857$	−1.03657e48	−0.418229	−0.209114	+	0.977891i	$0.567058\pi$
$858$	−6.06523e48	−2.40053
$859$	−1.92702e48	−0.748168	−0.374084	−	0.927395i	$-0.622043\pi$
$859$	−1.92702e48	−0.748168	−0.374084	+	0.927395i	$0.622043\pi$
$860$	0	0
$861$	1.11106e47	0.0415132
$862$	4.59603e48	1.68466
$863$	1.63147e48	0.586681	0.293341	−	0.956008i	$-0.405233\pi$
$863$	1.63147e48	0.586681	0.293341	+	0.956008i	$0.405233\pi$
$864$	−9.60693e48	−3.38928
$865$	0	0
$866$	9.51689e48	3.23184
$867$	−1.43224e49	−4.77201
$868$	9.78227e48	3.19790
$869$	−2.41496e48	−0.774610
$870$	0	0
$871$	−2.99621e48	−0.925278
$872$	8.35721e48	2.53244
$873$	−2.41465e48	−0.717993
$874$	−1.18507e48	−0.345785
$875$	0	0
$876$	9.18224e48	2.58007
$877$	2.98707e48	0.823668	0.411834	−	0.911259i	$-0.364888\pi$
$877$	2.98707e48	0.823668	0.411834	+	0.911259i	$0.364888\pi$
$878$	9.43422e48	2.55297
$879$	−4.25230e48	−1.12930
$880$	0	0
$881$	3.94938e48	1.01025	0.505123	−	0.863047i	$-0.331447\pi$
$881$	3.94938e48	1.01025	0.505123	+	0.863047i	$0.331447\pi$
$882$	7.46021e48	1.87292
$883$	−5.17634e48	−1.27547	−0.637736	−	0.770255i	$-0.720129\pi$
$883$	−5.17634e48	−1.27547	−0.637736	+	0.770255i	$0.720129\pi$
$884$	2.05881e49	4.97914
$885$	0	0
$886$	6.55712e48	1.52776
$887$	7.45605e47	0.170518	0.0852588	−	0.996359i	$-0.472828\pi$
$887$	7.45605e47	0.170518	0.0852588	+	0.996359i	$0.472828\pi$
$888$	−1.79868e48	−0.403776
$889$	−4.74749e48	−1.04613
$890$	0	0
$891$	−1.02409e47	−0.0217449
$892$	−1.94615e49	−4.05654
$893$	−1.14405e48	−0.234096
$894$	2.17383e48	0.436672
$895$	0	0
$896$	1.52077e49	2.94430
$897$	−5.39380e48	−1.02523
$898$	−5.54354e48	−1.03449
$899$	−5.43682e47	−0.0996116
$900$	0	0
$901$	−2.03437e48	−0.359311
$902$	1.82770e47	0.0316954
$903$	−8.48775e48	−1.44525
$904$	−1.30587e49	−2.18334
$905$	0	0
$906$	−2.34909e49	−3.78690
$907$	−2.76026e48	−0.436948	−0.218474	−	0.975843i	$-0.570108\pi$
$907$	−2.76026e48	−0.436948	−0.218474	+	0.975843i	$0.570108\pi$
$908$	−2.22548e49	−3.45946
$909$	4.10667e48	0.626882
$910$	0	0
$911$	−1.69247e48	−0.249155	−0.124577	−	0.992210i	$-0.539757\pi$
$911$	−1.69247e48	−0.249155	−0.124577	+	0.992210i	$0.539757\pi$
$912$	−1.02799e49	−1.48619
$913$	7.63977e48	1.08471
$914$	2.27067e49	3.16623
$915$	0	0
$916$	−2.67649e49	−3.59990
$917$	1.05858e49	1.39840
$918$	2.98798e49	3.87680
$919$	−1.77855e48	−0.226652	−0.113326	−	0.993558i	$-0.536150\pi$
$919$	−1.77855e48	−0.226652	−0.113326	+	0.993558i	$0.536150\pi$
$920$	0	0
$921$	2.63247e49	3.23653
$922$	−1.31736e48	−0.159090
$923$	1.12910e49	1.33939
$924$	3.83075e49	4.46371
$925$	0	0
$926$	3.13526e49	3.52527
$927$	1.76568e49	1.95028
$928$	−3.19912e48	−0.347127
$929$	−1.77834e48	−0.189564	−0.0947818	−	0.995498i	$-0.530215\pi$
$929$	−1.77834e48	−0.189564	−0.0947818	+	0.995498i	$0.530215\pi$
$930$	0	0
$931$	1.57969e48	0.162518
$932$	−8.23772e48	−0.832615
$933$	−9.04250e48	−0.897928
$934$	2.74606e49	2.67909
$935$	0	0
$936$	−5.16993e49	−4.86893
$937$	1.51116e49	1.39832	0.699162	−	0.714964i	$-0.253557\pi$
$937$	1.51116e49	1.39832	0.699162	+	0.714964i	$0.253557\pi$
$938$	2.60539e49	2.36879
$939$	2.34949e48	0.209890
$940$	0	0
$941$	1.64231e49	1.41654	0.708268	−	0.705944i	$-0.249477\pi$
$941$	1.64231e49	1.41654	0.708268	+	0.705944i	$0.249477\pi$
$942$	2.54732e49	2.15896
$943$	1.62537e47	0.0135366
$944$	−7.29402e49	−5.96938
$945$	0	0
$946$	−1.39624e49	−1.10346
$947$	7.47638e48	0.580653	0.290326	−	0.956928i	$-0.406236\pi$
$947$	7.47638e48	0.580653	0.290326	+	0.956928i	$0.406236\pi$
$948$	−5.32956e49	−4.06775
$949$	7.55091e48	0.566378
$950$	0	0
$951$	−3.49619e49	−2.53289
$952$	−1.11573e50	−7.94418
$953$	−4.85671e48	−0.339867	−0.169934	−	0.985456i	$-0.554355\pi$
$953$	−4.85671e48	−0.339867	−0.169934	+	0.985456i	$0.554355\pi$
$954$	8.19705e48	0.563780
$955$	0	0
$956$	−6.77542e48	−0.450175
$957$	−2.12906e48	−0.139041
$958$	3.38301e49	2.17156
$959$	−3.44714e49	−2.17497
$960$	0	0
$961$	−1.53011e48	−0.0932794
$962$	−2.37336e48	−0.142225
$963$	−3.65854e49	−2.15513
$964$	1.85910e48	0.107654
$965$	0	0
$966$	4.69026e49	2.62467
$967$	−1.05832e49	−0.582208	−0.291104	−	0.956691i	$-0.594023\pi$
$967$	−1.05832e49	−0.582208	−0.291104	+	0.956691i	$0.594023\pi$
$968$	−1.91905e49	−1.03787
$969$	1.63724e49	0.870504
$970$	0	0
$971$	1.10262e49	0.566644	0.283322	−	0.959025i	$-0.408564\pi$
$971$	1.10262e49	0.566644	0.283322	+	0.959025i	$0.408564\pi$
$972$	5.13932e49	2.59664
$973$	−4.09181e48	−0.203261
$974$	−1.74778e49	−0.853621
$975$	0	0
$976$	−9.80341e49	−4.62866
$977$	−1.02152e49	−0.474227	−0.237114	−	0.971482i	$-0.576201\pi$
$977$	−1.02152e49	−0.474227	−0.237114	+	0.971482i	$0.576201\pi$
$978$	−6.66275e49	−3.04132
$979$	9.57841e48	0.429911
$980$	0	0
$981$	3.00804e49	1.30540
$982$	1.75657e49	0.749594
$983$	−1.94073e49	−0.814388	−0.407194	−	0.913342i	$-0.633493\pi$
$983$	−1.94073e49	−0.814388	−0.407194	+	0.913342i	$0.633493\pi$
$984$	2.51378e48	0.103731
$985$	0	0
$986$	9.95000e48	0.397058
$987$	4.52789e49	1.77690
$988$	−1.75656e49	−0.677914
$989$	−1.24167e49	−0.471268
$990$	0	0
$991$	9.24952e48	0.339550	0.169775	−	0.985483i	$-0.445696\pi$
$991$	9.24952e48	0.339550	0.169775	+	0.985483i	$0.445696\pi$
$992$	8.75175e49	3.15975
$993$	−5.11613e49	−1.81668
$994$	−9.81828e49	−3.42894
$995$	0	0
$996$	1.68602e50	5.69617
$997$	−4.80545e49	−1.59685	−0.798424	−	0.602095i	$-0.794333\pi$
$997$	−4.80545e49	−1.59685	−0.798424	+	0.602095i	$0.794333\pi$
$998$	3.86927e49	1.26466
$999$	−2.50184e48	−0.0804321

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.a.d.1.11	✓	11
5.2	odd	4		25.34.b.d.24.22		22
5.3	odd	4		25.34.b.d.24.1		22
5.4	even	2		25.34.a.e.1.1	yes	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.34.a.d.1.11	✓	11	1.1	even	1	trivial
25.34.a.e.1.1	yes	11	5.4	even	2
25.34.b.d.24.1		22	5.3	odd	4
25.34.b.d.24.22		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)

\(f(q)\)	\(=\)	\(q+177167. q^{2} -1.20911e8 q^{3} +2.27982e10 q^{4} -2.14214e13 q^{6} +1.11259e14 q^{7} +2.51723e15 q^{8} +9.06036e15 q^{9} +O(q^{10})\)	\(q+177167. q^{2} -1.20911e8 q^{3} +2.27982e10 q^{4} -2.14214e13 q^{6} +1.11259e14 q^{7} +2.51723e15 q^{8} +9.06036e15 q^{9} -1.24906e17 q^{11} -2.75655e18 q^{12} -2.26681e18 q^{13} +1.97114e19 q^{14} +2.50136e20 q^{16} -3.98383e20 q^{17} +1.60520e21 q^{18} +3.39897e20 q^{19} -1.34524e22 q^{21} -2.21292e22 q^{22} -1.96795e22 q^{23} -3.04361e23 q^{24} -4.01605e23 q^{26} -4.23345e23 q^{27} +2.53650e24 q^{28} -1.40974e23 q^{29} +3.85660e24 q^{31} +2.26929e25 q^{32} +1.51025e25 q^{33} -7.05803e25 q^{34} +2.06560e26 q^{36} +5.90970e24 q^{37} +6.02185e25 q^{38} +2.74082e26 q^{39} -8.25921e24 q^{41} -2.38332e27 q^{42} +6.30947e26 q^{43} -2.84763e27 q^{44} -3.48656e27 q^{46} -3.36586e27 q^{47} -3.02441e28 q^{48} +4.64754e27 q^{49} +4.81688e28 q^{51} -5.16793e28 q^{52} +5.10657e27 q^{53} -7.50028e28 q^{54} +2.80065e29 q^{56} -4.10972e28 q^{57} -2.49760e28 q^{58} -2.91603e29 q^{59} -3.91923e29 q^{61} +6.83262e29 q^{62} +1.00805e30 q^{63} +1.87178e30 q^{64} +2.67566e30 q^{66} +1.32177e30 q^{67} -9.08241e30 q^{68} +2.37946e30 q^{69} -4.98102e30 q^{71} +2.28071e31 q^{72} -3.33107e30 q^{73} +1.04700e30 q^{74} +7.74904e30 q^{76} -1.38969e31 q^{77} +4.85583e31 q^{78} +1.93342e31 q^{79} +8.19892e29 q^{81} -1.46326e30 q^{82} -6.11641e31 q^{83} -3.06690e32 q^{84} +1.11783e32 q^{86} +1.70453e31 q^{87} -3.14418e32 q^{88} -7.66849e31 q^{89} -2.52203e32 q^{91} -4.48657e32 q^{92} -4.66305e32 q^{93} -5.96319e32 q^{94} -2.74382e33 q^{96} -2.66508e32 q^{97} +8.23390e32 q^{98} -1.13169e33 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 9393 q^{2} - 80330849 q^{3} + 49338206677 q^{4} - 17783977676723 q^{6} - 21344025107658 q^{7} + 970199832420105 q^{8} + 24\!\cdots\!58 q^{9}+O(q^{10}) \) 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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