LMFDB - Embedded newform 25.34.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("25.1");

S:= CuspForms(chi, 34);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$172.457072203$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - x^{10} - 71909733210 x^{9} - 392361971317440 x^{8} + \cdots + 13\!\cdots\!48 $ x^11 - x^10 - 71909733210x^9 - 392361971317440x^8 + 1789020862523351140800x^7 + 15057968169589785919302432x^6 - 18240376108577281349602470726592x^5 - 118793082389247521352101537474727680x^4 + 70339384981314044531499864093672157167360x^3 - 93184212295829066424280494839341830566058240x^2 - 66043164692761651440492767327962940420438352419328*x + 13944892725752680722269718925910686764312949634715648
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{47}\cdot 3^{12}\cdot 5^{30}\cdot 7^{2}\cdot 11^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$62096.8$ 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)

$f(q)$	$=$	$q-61242.8 q^{2} +1.16397e8 q^{3} -4.83925e9 q^{4} -7.12847e12 q^{6} +1.52684e14 q^{7} +8.22441e14 q^{8} +7.98915e15 q^{9} +O(q^{10})$	\(q-61242.8 q^{2} +1.16397e8 q^{3} -4.83925e9 q^{4} -7.12847e12 q^{6} +1.52684e14 q^{7} +8.22441e14 q^{8} +7.98915e15 q^{9} -2.70714e17 q^{11} -5.63273e17 q^{12} -3.01712e18 q^{13} -9.35077e18 q^{14} -8.79981e18 q^{16} -5.13465e19 q^{17} -4.89278e20 q^{18} -2.04320e21 q^{19} +1.77719e22 q^{21} +1.65793e22 q^{22} +2.04394e22 q^{23} +9.57295e22 q^{24} +1.84777e23 q^{26} +2.82855e23 q^{27} -7.38874e23 q^{28} +1.42015e24 q^{29} +5.31617e24 q^{31} -6.52579e24 q^{32} -3.15102e25 q^{33} +3.14460e24 q^{34} -3.86615e25 q^{36} +5.96668e25 q^{37} +1.25131e26 q^{38} -3.51183e26 q^{39} +2.10328e26 q^{41} -1.08840e27 q^{42} +3.53517e26 q^{43} +1.31005e27 q^{44} -1.25177e27 q^{46} -1.08480e27 q^{47} -1.02427e27 q^{48} +1.55813e28 q^{49} -5.97656e27 q^{51} +1.46006e28 q^{52} +1.51399e28 q^{53} -1.73228e28 q^{54} +1.25573e29 q^{56} -2.37822e29 q^{57} -8.69743e28 q^{58} -3.91155e28 q^{59} +1.55030e29 q^{61} -3.25577e29 q^{62} +1.21981e30 q^{63} +4.75248e29 q^{64} +1.92977e30 q^{66} -5.34638e29 q^{67} +2.48478e29 q^{68} +2.37908e30 q^{69} +4.86501e30 q^{71} +6.57061e30 q^{72} +5.33567e30 q^{73} -3.65416e30 q^{74} +9.88755e30 q^{76} -4.13335e31 q^{77} +2.15074e31 q^{78} +2.81314e30 q^{79} -1.14888e31 q^{81} -1.28811e31 q^{82} -2.25113e31 q^{83} -8.60025e31 q^{84} -2.16504e31 q^{86} +1.65301e32 q^{87} -2.22646e32 q^{88} +5.60122e31 q^{89} -4.60664e32 q^{91} -9.89113e31 q^{92} +6.18785e32 q^{93} +6.64360e31 q^{94} -7.59581e32 q^{96} -2.05217e32 q^{97} -9.54241e32 q^{98} -2.16277e33 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−61242.8	−0.660785	−0.330393	−	0.943844i	$-0.607181\pi$
$2$	−61242.8	−0.660785	−0.330393	+	0.943844i	$0.607181\pi$
$3$	1.16397e8	1.56113	0.780567	−	0.625072i	$-0.214930\pi$
$3$	1.16397e8	1.56113	0.780567	+	0.625072i	$0.214930\pi$
$4$	−4.83925e9	−0.563363
$5$	0	0
$5$	0	0
$6$	−7.12847e12	−1.03157
$7$	1.52684e14	1.73650	0.868249	−	0.496128i	$-0.165245\pi$
$7$	1.52684e14	1.73650	0.868249	+	0.496128i	$0.165245\pi$
$8$	8.22441e14	1.03305
$9$	7.98915e15	1.43714
$10$	0	0
$11$	−2.70714e17	−1.77636	−0.888180	−	0.459497i	$-0.848030\pi$
$11$	−2.70714e17	−1.77636	−0.888180	+	0.459497i	$0.848030\pi$
$12$	−5.63273e17	−0.879485
$13$	−3.01712e18	−1.25755	−0.628777	−	0.777586i	$-0.716444\pi$
$13$	−3.01712e18	−1.25755	−0.628777	+	0.777586i	$0.716444\pi$
$14$	−9.35077e18	−1.14745
$15$	0	0
$16$	−8.79981e18	−0.119260
$17$	−5.13465e19	−0.255920	−0.127960	−	0.991779i	$-0.540843\pi$
$17$	−5.13465e19	−0.255920	−0.127960	+	0.991779i	$0.540843\pi$
$18$	−4.89278e20	−0.949641
$19$	−2.04320e21	−1.62509	−0.812543	−	0.582901i	$-0.801918\pi$
$19$	−2.04320e21	−1.62509	−0.812543	+	0.582901i	$0.801918\pi$
$20$	0	0
$21$	1.77719e22	2.71091
$22$	1.65793e22	1.17379
$23$	2.04394e22	0.694958	0.347479	−	0.937688i	$-0.387038\pi$
$23$	2.04394e22	0.694958	0.347479	+	0.937688i	$0.387038\pi$
$24$	9.57295e22	1.61273
$25$	0	0
$26$	1.84777e23	0.830973
$27$	2.82855e23	0.682435
$28$	−7.38874e23	−0.978279
$29$	1.42015e24	1.05383	0.526913	−	0.849919i	$-0.323349\pi$
$29$	1.42015e24	1.05383	0.526913	+	0.849919i	$0.323349\pi$
$30$	0	0
$31$	5.31617e24	1.31260	0.656298	−	0.754502i	$-0.272122\pi$
$31$	5.31617e24	1.31260	0.656298	+	0.754502i	$0.272122\pi$
$32$	−6.52579e24	−0.954242
$33$	−3.15102e25	−2.77314
$34$	3.14460e24	0.169108
$35$	0	0
$36$	−3.86615e25	−0.809631
$37$	5.96668e25	0.795068	0.397534	−	0.917587i	$-0.369866\pi$
$37$	5.96668e25	0.795068	0.397534	+	0.917587i	$0.369866\pi$
$38$	1.25131e26	1.07383
$39$	−3.51183e26	−1.96321
$40$	0	0
$41$	2.10328e26	0.515186	0.257593	−	0.966253i	$-0.417071\pi$
$41$	2.10328e26	0.515186	0.257593	+	0.966253i	$0.417071\pi$
$42$	−1.08840e27	−1.79133
$43$	3.53517e26	0.394621	0.197311	−	0.980341i	$-0.436779\pi$
$43$	3.53517e26	0.394621	0.197311	+	0.980341i	$0.436779\pi$
$44$	1.31005e27	1.00073
$45$	0	0
$46$	−1.25177e27	−0.459218
$47$	−1.08480e27	−0.279083	−0.139541	−	0.990216i	$-0.544563\pi$
$47$	−1.08480e27	−0.279083	−0.139541	+	0.990216i	$0.544563\pi$
$48$	−1.02427e27	−0.186180
$49$	1.55813e28	2.01543
$50$	0	0
$51$	−5.97656e27	−0.399525
$52$	1.46006e28	0.708459
$53$	1.51399e28	0.536502	0.268251	−	0.963349i	$-0.413554\pi$
$53$	1.51399e28	0.536502	0.268251	+	0.963349i	$0.413554\pi$
$54$	−1.73228e28	−0.450943
$55$	0	0
$56$	1.25573e29	1.79389
$57$	−2.37822e29	−2.53698
$58$	−8.69743e28	−0.696352
$59$	−3.91155e28	−0.236206	−0.118103	−	0.993001i	$-0.537681\pi$
$59$	−3.91155e28	−0.236206	−0.118103	+	0.993001i	$0.537681\pi$
$60$	0	0
$61$	1.55030e29	0.540097	0.270049	−	0.962847i	$-0.412960\pi$
$61$	1.55030e29	0.540097	0.270049	+	0.962847i	$0.412960\pi$
$62$	−3.25577e29	−0.867344
$63$	1.21981e30	2.49559
$64$	4.75248e29	0.749809
$65$	0	0
$66$	1.92977e30	1.83245
$67$	−5.34638e29	−0.396119	−0.198060	−	0.980190i	$-0.563464\pi$
$67$	−5.34638e29	−0.396119	−0.198060	+	0.980190i	$0.563464\pi$
$68$	2.48478e29	0.144176
$69$	2.37908e30	1.08492
$70$	0	0
$71$	4.86501e30	1.38459	0.692295	−	0.721615i	$-0.256600\pi$
$71$	4.86501e30	1.38459	0.692295	+	0.721615i	$0.256600\pi$
$72$	6.57061e30	1.48463
$73$	5.33567e30	0.960200	0.480100	−	0.877214i	$-0.340600\pi$
$73$	5.33567e30	0.960200	0.480100	+	0.877214i	$0.340600\pi$
$74$	−3.65416e30	−0.525369
$75$	0	0
$76$	9.88755e30	0.915513
$77$	−4.13335e31	−3.08465
$78$	2.15074e31	1.29726
$79$	2.81314e30	0.137513	0.0687566	−	0.997633i	$-0.478097\pi$
$79$	2.81314e30	0.137513	0.0687566	+	0.997633i	$0.478097\pi$
$80$	0	0
$81$	−1.14888e31	−0.371768
$82$	−1.28811e31	−0.340428
$83$	−2.25113e31	−0.487092	−0.243546	−	0.969889i	$-0.578311\pi$
$83$	−2.25113e31	−0.487092	−0.243546	+	0.969889i	$0.578311\pi$
$84$	−8.60025e31	−1.52722
$85$	0	0
$86$	−2.16504e31	−0.260760
$87$	1.65301e32	1.64516
$88$	−2.22646e32	−1.83506
$89$	5.60122e31	0.383131	0.191566	−	0.981480i	$-0.438644\pi$
$89$	5.60122e31	0.383131	0.191566	+	0.981480i	$0.438644\pi$
$90$	0	0
$91$	−4.60664e32	−2.18374
$92$	−9.89113e31	−0.391513
$93$	6.18785e32	2.04914
$94$	6.64360e31	0.184414
$95$	0	0
$96$	−7.59581e32	−1.48970
$97$	−2.05217e32	−0.339218	−0.169609	−	0.985511i	$-0.554251\pi$
$97$	−2.05217e32	−0.339218	−0.169609	+	0.985511i	$0.554251\pi$
$98$	−9.54241e32	−1.33177
$99$	−2.16277e33	−2.55288
$100$	0	0
$101$	5.72611e32	0.485911	0.242956	−	0.970037i	$-0.421883\pi$
$101$	5.72611e32	0.485911	0.242956	+	0.970037i	$0.421883\pi$
$102$	3.66022e32	0.264000
$103$	1.61083e33	0.989087	0.494544	−	0.869153i	$-0.335335\pi$
$103$	1.61083e33	0.989087	0.494544	+	0.869153i	$0.335335\pi$
$104$	−2.48140e33	−1.29911
$105$	0	0
$106$	−9.27210e32	−0.354512
$107$	−7.00011e32	−0.229231	−0.114615	−	0.993410i	$-0.536564\pi$
$107$	−7.00011e32	−0.229231	−0.114615	+	0.993410i	$0.536564\pi$
$108$	−1.36880e33	−0.384458
$109$	3.40209e32	0.0820745	0.0410372	−	0.999158i	$-0.486934\pi$
$109$	3.40209e32	0.0820745	0.0410372	+	0.999158i	$0.486934\pi$
$110$	0	0
$111$	6.94502e33	1.24121
$112$	−1.34359e33	−0.207094
$113$	1.31038e34	1.74423	0.872115	−	0.489302i	$-0.162748\pi$
$113$	1.31038e34	1.74423	0.872115	+	0.489302i	$0.162748\pi$
$114$	1.45649e34	1.67640
$115$	0	0
$116$	−6.87248e33	−0.593686
$117$	−2.41042e34	−1.80728
$118$	2.39554e33	0.156081
$119$	−7.83976e33	−0.444404
$120$	0	0
$121$	5.00607e34	2.15545
$122$	−9.49445e33	−0.356888
$123$	2.44816e34	0.804275
$124$	−2.57263e34	−0.739467
$125$	0	0
$126$	−7.47047e34	−1.64905
$127$	−4.66720e33	−0.0904264	−0.0452132	−	0.998977i	$-0.514397\pi$
$127$	−4.66720e33	−0.0904264	−0.0452132	+	0.998977i	$0.514397\pi$
$128$	2.69506e34	0.458779
$129$	4.11482e34	0.616057
$130$	0	0
$131$	1.00302e34	0.116502	0.0582512	−	0.998302i	$-0.481448\pi$
$131$	1.00302e34	0.116502	0.0582512	+	0.998302i	$0.481448\pi$
$132$	1.52486e35	1.56228
$133$	−3.11963e35	−2.82196
$134$	3.27428e34	0.261750
$135$	0	0
$136$	−4.22295e34	−0.264377
$137$	2.30007e35	1.27600	0.638001	−	0.770036i	$-0.279762\pi$
$137$	2.30007e35	1.27600	0.638001	+	0.770036i	$0.279762\pi$
$138$	−1.45702e35	−0.716901
$139$	2.21338e35	0.966745	0.483372	−	0.875415i	$-0.339412\pi$
$139$	2.21338e35	0.966745	0.483372	+	0.875415i	$0.339412\pi$
$140$	0	0
$141$	−1.26267e35	−0.435686
$142$	−2.97947e35	−0.914917
$143$	8.16774e35	2.23387
$144$	−7.03030e34	−0.171393
$145$	0	0
$146$	−3.26772e35	−0.634486
$147$	1.81361e36	3.14635
$148$	−2.88742e35	−0.447912
$149$	−6.94142e35	−0.963551	−0.481776	−	0.876295i	$-0.660008\pi$
$149$	−6.94142e35	−0.963551	−0.481776	+	0.876295i	$0.660008\pi$
$150$	0	0
$151$	−6.93068e35	−0.772070	−0.386035	−	0.922484i	$-0.626156\pi$
$151$	−6.93068e35	−0.772070	−0.386035	+	0.922484i	$0.626156\pi$
$152$	−1.68041e36	−1.67879
$153$	−4.10215e35	−0.367792
$154$	2.53138e36	2.03829
$155$	0	0
$156$	1.69946e36	1.10600
$157$	−2.71872e36	−1.59229	−0.796143	−	0.605109i	$-0.793130\pi$
$157$	−2.71872e36	−1.59229	−0.796143	+	0.605109i	$0.793130\pi$
$158$	−1.72285e35	−0.0908667
$159$	1.76224e36	0.837551
$160$	0	0
$161$	3.12076e36	1.20679
$162$	7.03607e35	0.245659
$163$	3.97714e36	1.25451	0.627257	−	0.778812i	$-0.284178\pi$
$163$	3.97714e36	1.25451	0.627257	+	0.778812i	$0.284178\pi$
$164$	−1.01783e36	−0.290237
$165$	0	0
$166$	1.37865e36	0.321863
$167$	3.59469e36	0.760046	0.380023	−	0.924977i	$-0.375916\pi$
$167$	3.59469e36	0.760046	0.380023	+	0.924977i	$0.375916\pi$
$168$	1.46163e37	2.80050
$169$	3.34686e36	0.581443
$170$	0	0
$171$	−1.63234e37	−2.33548
$172$	−1.71076e36	−0.222315
$173$	4.00036e36	0.472431	0.236216	−	0.971701i	$-0.424093\pi$
$173$	4.00036e36	0.472431	0.236216	+	0.971701i	$0.424093\pi$
$174$	−1.01235e37	−1.08710
$175$	0	0
$176$	2.38223e36	0.211848
$177$	−4.55292e36	−0.368749
$178$	−3.43035e36	−0.253168
$179$	−8.79988e36	−0.592109	−0.296055	−	0.955171i	$-0.595671\pi$
$179$	−8.79988e36	−0.592109	−0.296055	+	0.955171i	$0.595671\pi$
$180$	0	0
$181$	−3.29934e37	−1.84812	−0.924061	−	0.382246i	$-0.875151\pi$
$181$	−3.29934e37	−1.84812	−0.924061	+	0.382246i	$0.875151\pi$
$182$	2.82124e37	1.44298
$183$	1.80449e37	0.843165
$184$	1.68102e37	0.717924
$185$	0	0
$186$	−3.78961e37	−1.35404
$187$	1.39002e37	0.454605
$188$	5.24960e36	0.157225
$189$	4.31872e37	1.18505
$190$	0	0
$191$	2.42443e37	0.559189	0.279595	−	0.960118i	$-0.409800\pi$
$191$	2.42443e37	0.559189	0.279595	+	0.960118i	$0.409800\pi$
$192$	5.53173e37	1.17055
$193$	5.35430e36	0.103994	0.0519969	−	0.998647i	$-0.483441\pi$
$193$	5.35430e36	0.103994	0.0519969	+	0.998647i	$0.483441\pi$
$194$	1.25681e37	0.224151
$195$	0	0
$196$	−7.54016e37	−1.13542
$197$	−5.10097e37	−0.706252	−0.353126	−	0.935576i	$-0.614881\pi$
$197$	−5.10097e37	−0.706252	−0.353126	+	0.935576i	$0.614881\pi$
$198$	1.32454e38	1.68690
$199$	8.02061e37	0.940008	0.470004	−	0.882664i	$-0.344253\pi$
$199$	8.02061e37	0.940008	0.470004	+	0.882664i	$0.344253\pi$
$200$	0	0
$201$	−6.22302e37	−0.618395
$202$	−3.50683e37	−0.321083
$203$	2.16834e38	1.82997
$204$	2.89221e37	0.225077
$205$	0	0
$206$	−9.86516e37	−0.653574
$207$	1.63293e38	0.998752
$208$	2.65501e37	0.149976
$209$	5.53122e38	2.88674
$210$	0	0
$211$	3.04681e38	1.35889	0.679445	−	0.733726i	$-0.262220\pi$
$211$	3.04681e38	1.35889	0.679445	+	0.733726i	$0.262220\pi$
$212$	−7.32657e37	−0.302245
$213$	5.66272e38	2.16153
$214$	4.28707e37	0.151472
$215$	0	0
$216$	2.32631e38	0.704987
$217$	8.11691e38	2.27932
$218$	−2.08353e37	−0.0542336
$219$	6.21055e38	1.49900
$220$	0	0
$221$	1.54918e38	0.321833
$222$	−4.25333e38	−0.820172
$223$	−4.72155e38	−0.845385	−0.422692	−	0.906273i	$-0.638915\pi$
$223$	−4.72155e38	−0.845385	−0.422692	+	0.906273i	$0.638915\pi$
$224$	−9.96381e38	−1.65704
$225$	0	0
$226$	−8.02515e38	−1.15256
$227$	−2.32476e38	−0.310421	−0.155211	−	0.987881i	$-0.549606\pi$
$227$	−2.32476e38	−0.310421	−0.155211	+	0.987881i	$0.549606\pi$
$228$	1.15088e39	1.42924
$229$	−1.88914e38	−0.218262	−0.109131	−	0.994027i	$-0.534807\pi$
$229$	−1.88914e38	−0.218262	−0.109131	+	0.994027i	$0.534807\pi$
$230$	0	0
$231$	−4.81109e39	−4.81555
$232$	1.16799e39	1.08865
$233$	1.00706e39	0.874345	0.437172	−	0.899378i	$-0.355980\pi$
$233$	1.00706e39	0.874345	0.437172	+	0.899378i	$0.355980\pi$
$234$	1.47621e39	1.19423
$235$	0	0
$236$	1.89290e38	0.133070
$237$	3.27441e38	0.214677
$238$	4.80129e38	0.293656
$239$	−1.09777e39	−0.626534	−0.313267	−	0.949665i	$-0.601423\pi$
$239$	−1.09777e39	−0.626534	−0.313267	+	0.949665i	$0.601423\pi$
$240$	0	0
$241$	3.35837e39	1.67050	0.835251	−	0.549869i	$-0.185322\pi$
$241$	3.35837e39	1.67050	0.835251	+	0.549869i	$0.185322\pi$
$242$	−3.06586e39	−1.42429
$243$	−2.90967e39	−1.26281
$244$	−7.50226e38	−0.304271
$245$	0	0
$246$	−1.49932e39	−0.531453
$247$	6.16457e39	2.04363
$248$	4.37224e39	1.35597
$249$	−2.62024e39	−0.760416
$250$	0	0
$251$	5.63657e39	1.43350	0.716751	−	0.697329i	$-0.245628\pi$
$251$	5.63657e39	1.43350	0.716751	+	0.697329i	$0.245628\pi$
$252$	−5.90297e39	−1.40592
$253$	−5.53322e39	−1.23449
$254$	2.85833e38	0.0597524
$255$	0	0
$256$	−5.73288e39	−1.05296
$257$	−8.42092e39	−1.45032	−0.725159	−	0.688582i	$-0.758234\pi$
$257$	−8.42092e39	−1.45032	−0.725159	+	0.688582i	$0.758234\pi$
$258$	−2.52003e39	−0.407081
$259$	9.11013e39	1.38063
$260$	0	0
$261$	1.13458e40	1.51450
$262$	−6.14281e38	−0.0769831
$263$	1.45121e40	1.70789	0.853943	−	0.520366i	$-0.174205\pi$
$263$	1.45121e40	1.70789	0.853943	+	0.520366i	$0.174205\pi$
$264$	−2.59153e40	−2.86478
$265$	0	0
$266$	1.91055e40	1.86471
$267$	6.51964e39	0.598119
$268$	2.58725e39	0.223159
$269$	1.80369e40	1.46302	0.731508	−	0.681832i	$-0.238817\pi$
$269$	1.80369e40	1.46302	0.731508	+	0.681832i	$0.238817\pi$
$270$	0	0
$271$	8.00345e37	0.00574492	0.00287246	−	0.999996i	$-0.499086\pi$
$271$	8.00345e37	0.00574492	0.00287246	+	0.999996i	$0.499086\pi$
$272$	4.51840e38	0.0305209
$273$	−5.36198e40	−3.40911
$274$	−1.40863e40	−0.843163
$275$	0	0
$276$	−1.15130e40	−0.611205
$277$	−1.33035e40	−0.665348	−0.332674	−	0.943042i	$-0.607951\pi$
$277$	−1.33035e40	−0.665348	−0.332674	+	0.943042i	$0.607951\pi$
$278$	−1.35554e40	−0.638811
$279$	4.24717e40	1.88638
$280$	0	0
$281$	3.66368e40	1.44631	0.723157	−	0.690684i	$-0.242690\pi$
$281$	3.66368e40	1.44631	0.723157	+	0.690684i	$0.242690\pi$
$282$	7.73293e39	0.287895
$283$	−3.20197e40	−1.12445	−0.562226	−	0.826983i	$-0.690055\pi$
$283$	−3.20197e40	−1.12445	−0.562226	+	0.826983i	$0.690055\pi$
$284$	−2.35430e40	−0.780026
$285$	0	0
$286$	−5.00216e40	−1.47611
$287$	3.21137e40	0.894620
$288$	−5.21355e40	−1.37138
$289$	−3.76180e40	−0.934505
$290$	0	0
$291$	−2.38866e40	−0.529565
$292$	−2.58206e40	−0.540941
$293$	−8.52126e40	−1.68728	−0.843641	−	0.536907i	$-0.819593\pi$
$293$	−8.52126e40	−1.68728	−0.843641	+	0.536907i	$0.819593\pi$
$294$	−1.11071e41	−2.07906
$295$	0	0
$296$	4.90724e40	0.821343
$297$	−7.65726e40	−1.21225
$298$	4.25112e40	0.636701
$299$	−6.16680e40	−0.873947
$300$	0	0
$301$	5.39762e40	0.685260
$302$	4.24455e40	0.510172
$303$	6.66500e40	0.758572
$304$	1.79798e40	0.193807
$305$	0	0
$306$	2.51227e40	0.243032
$307$	1.30196e41	1.19348	0.596740	−	0.802434i	$-0.296462\pi$
$307$	1.30196e41	1.19348	0.596740	+	0.802434i	$0.296462\pi$
$308$	2.00023e41	1.73777
$309$	1.87495e41	1.54410
$310$	0	0
$311$	1.69188e41	1.25263	0.626314	−	0.779571i	$-0.284563\pi$
$311$	1.69188e41	1.25263	0.626314	+	0.779571i	$0.284563\pi$
$312$	−2.88827e41	−2.02809
$313$	−8.13687e40	−0.541971	−0.270985	−	0.962583i	$-0.587350\pi$
$313$	−8.13687e40	−0.541971	−0.270985	+	0.962583i	$0.587350\pi$
$314$	1.66502e41	1.05216
$315$	0	0
$316$	−1.36135e40	−0.0774698
$317$	−3.44270e40	−0.185961	−0.0929805	−	0.995668i	$-0.529639\pi$
$317$	−3.44270e40	−0.185961	−0.0929805	+	0.995668i	$0.529639\pi$
$318$	−1.07924e41	−0.553442
$319$	−3.84455e41	−1.87197
$320$	0	0
$321$	−8.14790e40	−0.357860
$322$	−1.91124e41	−0.797431
$323$	1.04911e41	0.415891
$324$	5.55972e40	0.209440
$325$	0	0
$326$	−2.43571e41	−0.828965
$327$	3.95992e40	0.128129
$328$	1.72983e41	0.532212
$329$	−1.65630e41	−0.484627
$330$	0	0
$331$	1.77844e41	0.470845	0.235422	−	0.971893i	$-0.424353\pi$
$331$	1.77844e41	0.470845	0.235422	+	0.971893i	$0.424353\pi$
$332$	1.08938e41	0.274410
$333$	4.76687e41	1.14262
$334$	−2.20149e41	−0.502228
$335$	0	0
$336$	−1.56389e41	−0.323302
$337$	3.38563e41	0.666417	0.333208	−	0.942853i	$-0.391869\pi$
$337$	3.38563e41	0.666417	0.333208	+	0.942853i	$0.391869\pi$
$338$	−2.04971e41	−0.384209
$339$	1.52524e42	2.72298
$340$	0	0
$341$	−1.43916e42	−2.33164
$342$	9.99693e41	1.54325
$343$	1.19861e42	1.76329
$344$	2.90747e41	0.407662
$345$	0	0
$346$	−2.44994e41	−0.312176
$347$	2.23211e41	0.271193	0.135596	−	0.990764i	$-0.456705\pi$
$347$	2.23211e41	0.271193	0.135596	+	0.990764i	$0.456705\pi$
$348$	−7.99935e41	−0.926824
$349$	7.47321e41	0.825824	0.412912	−	0.910771i	$-0.364512\pi$
$349$	7.47321e41	0.825824	0.412912	+	0.910771i	$0.364512\pi$
$350$	0	0
$351$	−8.53405e41	−0.858199
$352$	1.76662e42	1.69508
$353$	−1.59110e42	−1.45685	−0.728426	−	0.685124i	$-0.759748\pi$
$353$	−1.59110e42	−1.45685	−0.728426	+	0.685124i	$0.759748\pi$
$354$	2.78834e41	0.243664
$355$	0	0
$356$	−2.71057e41	−0.215842
$357$	−9.12523e41	−0.693774
$358$	5.38930e41	0.391257
$359$	−1.91809e42	−1.32988	−0.664938	−	0.746899i	$-0.731542\pi$
$359$	−1.91809e42	−1.32988	−0.664938	+	0.746899i	$0.731542\pi$
$360$	0	0
$361$	2.59390e42	1.64091
$362$	2.02061e42	1.22121
$363$	5.82690e42	3.36495
$364$	2.22927e42	1.23024
$365$	0	0
$366$	−1.10512e42	−0.557151
$367$	−2.05163e42	−0.988800	−0.494400	−	0.869235i	$-0.664612\pi$
$367$	−2.05163e42	−0.988800	−0.494400	+	0.869235i	$0.664612\pi$
$368$	−1.79863e41	−0.0828805
$369$	1.68035e42	0.740395
$370$	0	0
$371$	2.31161e42	0.931635
$372$	−2.99445e42	−1.15441
$373$	1.79481e42	0.661945	0.330972	−	0.943640i	$-0.392623\pi$
$373$	1.79481e42	0.661945	0.330972	+	0.943640i	$0.392623\pi$
$374$	−8.51287e41	−0.300396
$375$	0	0
$376$	−8.92181e41	−0.288306
$377$	−4.28477e42	−1.32524
$378$	−2.64491e42	−0.783062
$379$	−7.45789e41	−0.211382	−0.105691	−	0.994399i	$-0.533706\pi$
$379$	−7.45789e41	−0.211382	−0.105691	+	0.994399i	$0.533706\pi$
$380$	0	0
$381$	−5.43247e41	−0.141168
$382$	−1.48479e42	−0.369504
$383$	−7.50246e39	−0.00178823	−0.000894117	−	1.00000i	$-0.500285\pi$
$383$	−7.50246e39	−0.00178823	−0.000894117		1.00000i	$0.500285\pi$
$384$	3.13696e42	0.716216
$385$	0	0
$386$	−3.27913e41	−0.0687176
$387$	2.82430e42	0.567126
$388$	9.93095e41	0.191103
$389$	1.60222e41	0.0295498	0.0147749	−	0.999891i	$-0.495297\pi$
$389$	1.60222e41	0.0295498	0.0147749	+	0.999891i	$0.495297\pi$
$390$	0	0
$391$	−1.04949e42	−0.177853
$392$	1.28147e43	2.08203
$393$	1.16749e42	0.181876
$394$	3.12398e42	0.466681
$395$	0	0
$396$	1.04662e43	1.43820
$397$	−8.68103e42	−1.14427	−0.572134	−	0.820160i	$-0.693884\pi$
$397$	−8.68103e42	−1.14427	−0.572134	+	0.820160i	$0.693884\pi$
$398$	−4.91205e42	−0.621143
$399$	−3.63115e43	−4.40546
$400$	0	0
$401$	−1.74844e43	−1.95330	−0.976650	−	0.214835i	$-0.931079\pi$
$401$	−1.74844e43	−1.95330	−0.976650	+	0.214835i	$0.931079\pi$
$402$	3.81115e42	0.408627
$403$	−1.60395e43	−1.65066
$404$	−2.77101e42	−0.273744
$405$	0	0
$406$	−1.32795e43	−1.20922
$407$	−1.61526e43	−1.41233
$408$	−4.91537e42	−0.412728
$409$	4.63147e42	0.373495	0.186747	−	0.982408i	$-0.440205\pi$
$409$	4.63147e42	0.373495	0.186747	+	0.982408i	$0.440205\pi$
$410$	0	0
$411$	2.67720e43	1.99201
$412$	−7.79519e42	−0.557215
$413$	−5.97229e42	−0.410171
$414$	−1.00005e43	−0.659961
$415$	0	0
$416$	1.96891e43	1.20001
$417$	2.57630e43	1.50922
$418$	−3.38748e43	−1.90751
$419$	−1.92258e42	−0.104077	−0.0520383	−	0.998645i	$-0.516572\pi$
$419$	−1.92258e42	−0.104077	−0.0520383	+	0.998645i	$0.516572\pi$
$420$	0	0
$421$	1.19695e43	0.598994	0.299497	−	0.954097i	$-0.403181\pi$
$421$	1.19695e43	0.598994	0.299497	+	0.954097i	$0.403181\pi$
$422$	−1.86595e43	−0.897935
$423$	−8.66660e42	−0.401081
$424$	1.24517e43	0.554232
$425$	0	0
$426$	−3.46801e43	−1.42831
$427$	2.36705e43	0.937879
$428$	3.38753e42	0.129140
$429$	9.50699e43	3.48737
$430$	0	0
$431$	3.20269e43	1.08803	0.544013	−	0.839076i	$-0.316904\pi$
$431$	3.20269e43	1.08803	0.544013	+	0.839076i	$0.316904\pi$
$432$	−2.48907e42	−0.0813870
$433$	3.85334e43	1.21279	0.606397	−	0.795162i	$-0.292614\pi$
$433$	3.85334e43	1.21279	0.606397	+	0.795162i	$0.292614\pi$
$434$	−4.97103e43	−1.50614
$435$	0	0
$436$	−1.64635e42	−0.0462377
$437$	−4.17617e43	−1.12937
$438$	−3.80352e43	−0.990518
$439$	−4.54949e43	−1.14103	−0.570516	−	0.821287i	$-0.693257\pi$
$439$	−4.54949e43	−1.14103	−0.570516	+	0.821287i	$0.693257\pi$
$440$	0	0
$441$	1.24481e44	2.89645
$442$	−9.48764e42	−0.212662
$443$	−1.02820e43	−0.222033	−0.111017	−	0.993819i	$-0.535411\pi$
$443$	−1.02820e43	−0.222033	−0.111017	+	0.993819i	$0.535411\pi$
$444$	−3.36087e43	−0.699250
$445$	0	0
$446$	2.89161e43	0.558618
$447$	−8.07959e43	−1.50423
$448$	7.25625e43	1.30204
$449$	5.57673e43	0.964529	0.482264	−	0.876026i	$-0.339814\pi$
$449$	5.57673e43	0.964529	0.482264	+	0.876026i	$0.339814\pi$
$450$	0	0
$451$	−5.69388e43	−0.915156
$452$	−6.34126e43	−0.982634
$453$	−8.06709e43	−1.20530
$454$	1.42375e43	0.205122
$455$	0	0
$456$	−1.95595e44	−2.62082
$457$	1.36752e44	1.76733	0.883663	−	0.468123i	$-0.155070\pi$
$457$	1.36752e44	1.76733	0.883663	+	0.468123i	$0.155070\pi$
$458$	1.15696e43	0.144224
$459$	−1.45236e43	−0.174648
$460$	0	0
$461$	9.55770e43	1.06976	0.534882	−	0.844927i	$-0.320356\pi$
$461$	9.55770e43	1.06976	0.534882	+	0.844927i	$0.320356\pi$
$462$	2.94645e44	3.18204
$463$	8.83617e43	0.920826	0.460413	−	0.887705i	$-0.347701\pi$
$463$	8.83617e43	0.920826	0.460413	+	0.887705i	$0.347701\pi$
$464$	−1.24971e43	−0.125679
$465$	0	0
$466$	−6.16752e43	−0.577754
$467$	−3.90426e43	−0.353029	−0.176514	−	0.984298i	$-0.556482\pi$
$467$	−3.90426e43	−0.353029	−0.176514	+	0.984298i	$0.556482\pi$
$468$	1.16646e44	1.01816
$469$	−8.16305e43	−0.687861
$470$	0	0
$471$	−3.16451e44	−2.48577
$472$	−3.21702e43	−0.244012
$473$	−9.57018e43	−0.700989
$474$	−2.00534e43	−0.141855
$475$	0	0
$476$	3.79386e43	0.250361
$477$	1.20955e44	0.771028
$478$	6.72303e43	0.414005
$479$	2.78662e44	1.65784	0.828918	−	0.559370i	$-0.188957\pi$
$479$	2.78662e44	1.65784	0.828918	+	0.559370i	$0.188957\pi$
$480$	0	0
$481$	−1.80022e44	−0.999841
$482$	−2.05676e44	−1.10384
$483$	3.63246e44	1.88397
$484$	−2.42256e44	−1.21430
$485$	0	0
$486$	1.78196e44	0.834449
$487$	−3.84992e44	−1.74271	−0.871353	−	0.490656i	$-0.836757\pi$
$487$	−3.84992e44	−1.74271	−0.871353	+	0.490656i	$0.836757\pi$
$488$	1.27503e44	0.557946
$489$	4.62926e44	1.95847
$490$	0	0
$491$	−2.78220e44	−1.10038	−0.550191	−	0.835039i	$-0.685445\pi$
$491$	−2.78220e44	−1.10038	−0.550191	+	0.835039i	$0.685445\pi$
$492$	−1.18472e44	−0.453099
$493$	−7.29199e43	−0.269695
$494$	−3.77536e44	−1.35040
$495$	0	0
$496$	−4.67813e43	−0.156540
$497$	7.42807e44	2.40434
$498$	1.60471e44	0.502472
$499$	5.63211e43	0.170613	0.0853065	−	0.996355i	$-0.472813\pi$
$499$	5.63211e43	0.170613	0.0853065	+	0.996355i	$0.472813\pi$
$500$	0	0
$501$	4.18411e44	1.18653
$502$	−3.45199e44	−0.947237
$503$	3.86793e44	1.02709	0.513543	−	0.858064i	$-0.328333\pi$
$503$	3.86793e44	1.02709	0.513543	+	0.858064i	$0.328333\pi$
$504$	1.00322e45	2.57806
$505$	0	0
$506$	3.38870e44	0.815736
$507$	3.89564e44	0.907710
$508$	2.25858e43	0.0509429
$509$	−4.99727e44	−1.09116	−0.545582	−	0.838058i	$-0.683691\pi$
$509$	−4.99727e44	−1.09116	−0.545582	+	0.838058i	$0.683691\pi$
$510$	0	0
$511$	8.14669e44	1.66739
$512$	1.19594e44	0.237004
$513$	−5.77929e44	−1.10902
$514$	5.15721e44	0.958349
$515$	0	0
$516$	−1.99126e44	−0.347064
$517$	2.93669e44	0.495752
$518$	−5.57930e44	−0.912303
$519$	4.65629e44	0.737529
$520$	0	0
$521$	−3.45348e44	−0.513374	−0.256687	−	0.966495i	$-0.582631\pi$
$521$	−3.45348e44	−0.513374	−0.256687	+	0.966495i	$0.582631\pi$
$522$	−6.94851e44	−1.00076
$523$	9.61952e44	1.34238	0.671190	−	0.741285i	$-0.265783\pi$
$523$	9.61952e44	1.34238	0.671190	+	0.741285i	$0.265783\pi$
$524$	−4.85388e43	−0.0656331
$525$	0	0
$526$	−8.88759e44	−1.12855
$527$	−2.72967e44	−0.335919
$528$	2.77284e44	0.330723
$529$	−4.47237e44	−0.517034
$530$	0	0
$531$	−3.12500e44	−0.339461
$532$	1.50967e45	1.58979
$533$	−6.34585e44	−0.647875
$534$	−3.99281e44	−0.395228
$535$	0	0
$536$	−4.39709e44	−0.409210
$537$	−1.02428e45	−0.924362
$538$	−1.10463e45	−0.966740
$539$	−4.21806e45	−3.58012
$540$	0	0
$541$	4.75196e44	0.379418	0.189709	−	0.981840i	$-0.439245\pi$
$541$	4.75196e44	0.379418	0.189709	+	0.981840i	$0.439245\pi$
$542$	−4.90154e42	−0.00379616
$543$	−3.84032e45	−2.88517
$544$	3.35076e44	0.244209
$545$	0	0
$546$	3.28383e45	2.25269
$547$	−1.24806e45	−0.830699	−0.415350	−	0.909662i	$-0.636341\pi$
$547$	−1.24806e45	−0.830699	−0.415350	+	0.909662i	$0.636341\pi$
$548$	−1.11306e45	−0.718852
$549$	1.23855e45	0.776196
$550$	0	0
$551$	−2.90166e45	−1.71256
$552$	1.95665e45	1.12078
$553$	4.29520e44	0.238792
$554$	8.14743e44	0.439653
$555$	0	0
$556$	−1.07111e45	−0.544628
$557$	−1.39942e45	−0.690777	−0.345389	−	0.938460i	$-0.612253\pi$
$557$	−1.39942e45	−0.690777	−0.345389	+	0.938460i	$0.612253\pi$
$558$	−2.60109e45	−1.24649
$559$	−1.06660e45	−0.496258
$560$	0	0
$561$	1.61794e45	0.709700
$562$	−2.24374e45	−0.955703
$563$	2.98083e45	1.23296	0.616479	−	0.787371i	$-0.288559\pi$
$563$	2.98083e45	1.23296	0.616479	+	0.787371i	$0.288559\pi$
$564$	6.11036e44	0.245449
$565$	0	0
$566$	1.96098e45	0.743022
$567$	−1.75415e45	−0.645575
$568$	4.00119e45	1.43035
$569$	−3.72006e45	−1.29181	−0.645904	−	0.763419i	$-0.723519\pi$
$569$	−3.72006e45	−1.29181	−0.645904	+	0.763419i	$0.723519\pi$
$570$	0	0
$571$	4.39952e45	1.44181	0.720907	−	0.693032i	$-0.243725\pi$
$571$	4.39952e45	1.44181	0.720907	+	0.693032i	$0.243725\pi$
$572$	−3.95257e45	−1.25848
$573$	2.82196e45	0.872970
$574$	−1.96673e45	−0.591152
$575$	0	0
$576$	3.79683e45	1.07758
$577$	3.96283e44	0.109296	0.0546480	−	0.998506i	$-0.482596\pi$
$577$	3.96283e44	0.109296	0.0546480	+	0.998506i	$0.482596\pi$
$578$	2.30384e45	0.617507
$579$	6.23224e44	0.162348
$580$	0	0
$581$	−3.43710e45	−0.845835
$582$	1.46288e45	0.349929
$583$	−4.09858e45	−0.953020
$584$	4.38828e45	0.991932
$585$	0	0
$586$	5.21866e45	1.11493
$587$	3.03944e45	0.631343	0.315672	−	0.948868i	$-0.397770\pi$
$587$	3.03944e45	0.631343	0.315672	+	0.948868i	$0.397770\pi$
$588$	−8.77651e45	−1.77254
$589$	−1.08620e46	−2.13308
$590$	0	0
$591$	−5.93736e45	−1.10255
$592$	−5.25057e44	−0.0948196
$593$	−1.87676e45	−0.329614	−0.164807	−	0.986326i	$-0.552700\pi$
$593$	−1.87676e45	−0.329614	−0.164807	+	0.986326i	$0.552700\pi$
$594$	4.68952e45	0.801037
$595$	0	0
$596$	3.35913e45	0.542829
$597$	9.33573e45	1.46748
$598$	3.77672e45	0.577491
$599$	1.10721e46	1.64698	0.823490	−	0.567330i	$-0.192024\pi$
$599$	1.10721e46	1.64698	0.823490	+	0.567330i	$0.192024\pi$
$600$	0	0
$601$	−9.12305e45	−1.28443	−0.642216	−	0.766524i	$-0.721985\pi$
$601$	−9.12305e45	−1.28443	−0.642216	+	0.766524i	$0.721985\pi$
$602$	−3.30566e45	−0.452809
$603$	−4.27131e45	−0.569279
$604$	3.35393e45	0.434955
$605$	0	0
$606$	−4.08184e45	−0.501254
$607$	5.35422e45	0.639857	0.319928	−	0.947442i	$-0.396341\pi$
$607$	5.35422e45	0.639857	0.319928	+	0.947442i	$0.396341\pi$
$608$	1.33335e46	1.55073
$609$	2.52388e46	2.85682
$610$	0	0
$611$	3.27296e45	0.350962
$612$	1.98513e45	0.207200
$613$	1.25482e44	0.0127492	0.00637459	−	0.999980i	$-0.497971\pi$
$613$	1.25482e44	0.0127492	0.00637459	+	0.999980i	$0.497971\pi$
$614$	−7.97359e45	−0.788635
$615$	0	0
$616$	−3.39944e46	−3.18658
$617$	−8.06814e45	−0.736323	−0.368162	−	0.929762i	$-0.620013\pi$
$617$	−8.06814e45	−0.736323	−0.368162	+	0.929762i	$0.620013\pi$
$618$	−1.14827e46	−1.02032
$619$	−2.05474e46	−1.77771	−0.888856	−	0.458186i	$-0.848499\pi$
$619$	−2.05474e46	−1.77771	−0.888856	+	0.458186i	$0.848499\pi$
$620$	0	0
$621$	5.78137e45	0.474263
$622$	−1.03615e46	−0.827718
$623$	8.55214e45	0.665307
$624$	3.09034e45	0.234132
$625$	0	0
$626$	4.98325e45	0.358126
$627$	6.43816e46	4.50658
$628$	1.31566e46	0.897034
$629$	−3.06368e45	−0.203473
$630$	0	0
$631$	1.16488e45	0.0734170	0.0367085	−	0.999326i	$-0.488313\pi$
$631$	1.16488e45	0.0734170	0.0367085	+	0.999326i	$0.488313\pi$
$632$	2.31364e45	0.142058
$633$	3.54639e46	2.12141
$634$	2.10841e45	0.122880
$635$	0	0
$636$	−8.52790e45	−0.471845
$637$	−4.70105e46	−2.53451
$638$	2.35451e46	1.23697
$639$	3.88673e46	1.98985
$640$	0	0
$641$	−9.00359e45	−0.437783	−0.218891	−	0.975749i	$-0.570244\pi$
$641$	−9.00359e45	−0.437783	−0.218891	+	0.975749i	$0.570244\pi$
$642$	4.99001e45	0.236468
$643$	−3.03445e46	−1.40152	−0.700759	−	0.713398i	$-0.747155\pi$
$643$	−3.03445e46	−1.40152	−0.700759	+	0.713398i	$0.747155\pi$
$644$	−1.51021e46	−0.679862
$645$	0	0
$646$	−6.42506e45	−0.274815
$647$	−3.19654e46	−1.33278	−0.666392	−	0.745602i	$-0.732162\pi$
$647$	−3.19654e46	−1.33278	−0.666392	+	0.745602i	$0.732162\pi$
$648$	−9.44887e45	−0.384054
$649$	1.05891e46	0.419587
$650$	0	0
$651$	9.44783e46	3.55832
$652$	−1.92464e46	−0.706747
$653$	2.96852e46	1.06285	0.531426	−	0.847105i	$-0.321656\pi$
$653$	2.96852e46	1.06285	0.531426	+	0.847105i	$0.321656\pi$
$654$	−2.42517e45	−0.0846659
$655$	0	0
$656$	−1.85085e45	−0.0614410
$657$	4.26275e46	1.37994
$658$	1.01437e46	0.320235
$659$	7.90933e45	0.243518	0.121759	−	0.992560i	$-0.461147\pi$
$659$	7.90933e45	0.243518	0.121759	+	0.992560i	$0.461147\pi$
$660$	0	0
$661$	−5.80040e45	−0.169877	−0.0849384	−	0.996386i	$-0.527069\pi$
$661$	−5.80040e45	−0.169877	−0.0849384	+	0.996386i	$0.527069\pi$
$662$	−1.08917e46	−0.311127
$663$	1.80320e46	0.502424
$664$	−1.85142e46	−0.503189
$665$	0	0
$666$	−2.91937e46	−0.755029
$667$	2.90271e46	0.732364
$668$	−1.73956e46	−0.428182
$669$	−5.49573e46	−1.31976
$670$	0	0
$671$	−4.19686e46	−0.959407
$672$	−1.15976e47	−2.58686
$673$	4.73930e46	1.03149	0.515745	−	0.856742i	$-0.327515\pi$
$673$	4.73930e46	1.03149	0.515745	+	0.856742i	$0.327515\pi$
$674$	−2.07346e46	−0.440359
$675$	0	0
$676$	−1.61963e46	−0.327563
$677$	3.10009e46	0.611874	0.305937	−	0.952052i	$-0.401030\pi$
$677$	3.10009e46	0.611874	0.305937	+	0.952052i	$0.401030\pi$
$678$	−9.34102e46	−1.79930
$679$	−3.13332e46	−0.589052
$680$	0	0
$681$	−2.70594e46	−0.484609
$682$	8.81382e46	1.54071
$683$	1.45608e46	0.248453	0.124227	−	0.992254i	$-0.460355\pi$
$683$	1.45608e46	0.248453	0.124227	+	0.992254i	$0.460355\pi$
$684$	7.89931e46	1.31572
$685$	0	0
$686$	−7.34061e46	−1.16516
$687$	−2.19889e46	−0.340736
$688$	−3.11088e45	−0.0470624
$689$	−4.56788e46	−0.674680
$690$	0	0
$691$	2.89366e46	0.407436	0.203718	−	0.979030i	$-0.434697\pi$
$691$	2.89366e46	0.407436	0.203718	+	0.979030i	$0.434697\pi$
$692$	−1.93588e46	−0.266150
$693$	−3.30220e47	−4.43307
$694$	−1.36700e46	−0.179200
$695$	0	0
$696$	1.35951e47	1.69953
$697$	−1.07996e46	−0.131846
$698$	−4.57681e46	−0.545693
$699$	1.17219e47	1.36497
$700$	0	0
$701$	7.65232e46	0.850052	0.425026	−	0.905181i	$-0.360265\pi$
$701$	7.65232e46	0.850052	0.425026	+	0.905181i	$0.360265\pi$
$702$	5.22650e46	0.567085
$703$	−1.21911e47	−1.29205
$704$	−1.28656e47	−1.33193
$705$	0	0
$706$	9.74437e46	0.962667
$707$	8.74282e46	0.843784
$708$	2.20327e46	0.207740
$709$	−1.52586e47	−1.40557	−0.702784	−	0.711403i	$-0.748060\pi$
$709$	−1.52586e47	−1.40557	−0.702784	+	0.711403i	$0.748060\pi$
$710$	0	0
$711$	2.24746e46	0.197626
$712$	4.60668e46	0.395793
$713$	1.08659e47	0.912198
$714$	5.58855e46	0.458436
$715$	0	0
$716$	4.25848e46	0.333572
$717$	−1.27777e47	−0.978104
$718$	1.17469e47	0.878762
$719$	6.69791e46	0.489680	0.244840	−	0.969563i	$-0.421265\pi$
$719$	6.69791e46	0.489680	0.244840	+	0.969563i	$0.421265\pi$
$720$	0	0
$721$	2.45947e47	1.71755
$722$	−1.58858e47	−1.08429
$723$	3.90903e47	2.60788
$724$	1.59663e47	1.04116
$725$	0	0
$726$	−3.56856e47	−2.22351
$727$	−9.79650e46	−0.596696	−0.298348	−	0.954457i	$-0.596436\pi$
$727$	−9.79650e46	−0.596696	−0.298348	+	0.954457i	$0.596436\pi$
$728$	−3.78869e47	−2.25591
$729$	−2.74809e47	−1.59966
$730$	0	0
$731$	−1.81518e46	−0.100991
$732$	−8.73239e46	−0.475008
$733$	6.92215e45	0.0368150	0.0184075	−	0.999831i	$-0.494140\pi$
$733$	6.92215e45	0.0368150	0.0184075	+	0.999831i	$0.494140\pi$
$734$	1.25647e47	0.653384
$735$	0	0
$736$	−1.33383e47	−0.663158
$737$	1.44734e47	0.703650
$738$	−1.02909e47	−0.489242
$739$	−1.98349e47	−0.922140	−0.461070	−	0.887364i	$-0.652534\pi$
$739$	−1.98349e47	−0.922140	−0.461070	+	0.887364i	$0.652534\pi$
$740$	0	0
$741$	7.17536e47	3.19039
$742$	−1.41570e47	−0.615611
$743$	8.20980e45	0.0349154	0.0174577	−	0.999848i	$-0.494443\pi$
$743$	8.20980e45	0.0349154	0.0174577	+	0.999848i	$0.494443\pi$
$744$	5.08914e47	2.11686
$745$	0	0
$746$	−1.09919e47	−0.437403
$747$	−1.79846e47	−0.700020
$748$	−6.72665e46	−0.256108
$749$	−1.06880e47	−0.398059
$750$	0	0
$751$	−3.70104e47	−1.31906	−0.659531	−	0.751677i	$-0.729245\pi$
$751$	−3.70104e47	−1.31906	−0.659531	+	0.751677i	$0.729245\pi$
$752$	9.54600e45	0.0332834
$753$	6.56078e47	2.23789
$754$	2.62412e47	0.875701
$755$	0	0
$756$	−2.08994e47	−0.667611
$757$	4.25190e47	1.32893	0.664463	−	0.747321i	$-0.268660\pi$
$757$	4.25190e47	1.32893	0.664463	+	0.747321i	$0.268660\pi$
$758$	4.56742e46	0.139678
$759$	−6.44049e47	−1.92721
$760$	0	0
$761$	−8.75693e46	−0.250903	−0.125451	−	0.992100i	$-0.540038\pi$
$761$	−8.75693e46	−0.250903	−0.125451	+	0.992100i	$0.540038\pi$
$762$	3.32700e46	0.0932816
$763$	5.19443e46	0.142522
$764$	−1.17324e47	−0.315027
$765$	0	0
$766$	4.59472e44	0.00118164
$767$	1.18016e47	0.297042
$768$	−6.67289e47	−1.64382
$769$	2.32456e47	0.560475	0.280237	−	0.959931i	$-0.409587\pi$
$769$	2.32456e47	0.560475	0.280237	+	0.959931i	$0.409587\pi$
$770$	0	0
$771$	−9.80168e47	−2.26414
$772$	−2.59108e46	−0.0585862
$773$	8.67662e47	1.92039	0.960194	−	0.279333i	$-0.0901134\pi$
$773$	8.67662e47	1.92039	0.960194	+	0.279333i	$0.0901134\pi$
$774$	−1.72968e47	−0.374749
$775$	0	0
$776$	−1.68779e47	−0.350429
$777$	1.06039e48	2.15536
$778$	−9.81246e45	−0.0195261
$779$	−4.29743e47	−0.837222
$780$	0	0
$781$	−1.31703e48	−2.45953
$782$	6.42738e46	0.117523
$783$	4.01697e47	0.719167
$784$	−1.37112e47	−0.240359
$785$	0	0
$786$	−7.15003e46	−0.120181
$787$	1.53515e47	0.252678	0.126339	−	0.991987i	$-0.459677\pi$
$787$	1.53515e47	0.252678	0.126339	+	0.991987i	$0.459677\pi$
$788$	2.46848e47	0.397876
$789$	1.68916e48	2.66624
$790$	0	0
$791$	2.00074e48	3.02885
$792$	−1.77875e48	−2.63724
$793$	−4.67742e47	−0.679202
$794$	5.31651e47	0.756116
$795$	0	0
$796$	−3.88137e47	−0.529565
$797$	1.58622e47	0.211983	0.105991	−	0.994367i	$-0.466198\pi$
$797$	1.58622e47	0.211983	0.105991	+	0.994367i	$0.466198\pi$
$798$	2.22382e48	2.91106
$799$	5.57004e46	0.0714228
$800$	0	0
$801$	4.47490e47	0.550613
$802$	1.07080e48	1.29071
$803$	−1.44444e48	−1.70566
$804$	3.01147e47	0.348381
$805$	0	0
$806$	9.82304e47	1.09073
$807$	2.09944e48	2.28397
$808$	4.70939e47	0.501969
$809$	1.81233e48	1.89272	0.946359	−	0.323116i	$-0.104731\pi$
$809$	1.81233e48	1.89272	0.946359	+	0.323116i	$0.104731\pi$
$810$	0	0
$811$	−2.40110e47	−0.240750	−0.120375	−	0.992728i	$-0.538410\pi$
$811$	−2.40110e47	−0.240750	−0.120375	+	0.992728i	$0.538410\pi$
$812$	−1.04931e48	−1.03094
$813$	9.31576e45	0.00896859
$814$	9.89232e47	0.933244
$815$	0	0
$816$	5.25927e46	0.0476472
$817$	−7.22306e47	−0.641294
$818$	−2.83645e47	−0.246800
$819$	−3.68031e48	−3.13834
$820$	0	0
$821$	1.95200e48	1.59889	0.799444	−	0.600741i	$-0.205128\pi$
$821$	1.95200e48	1.59889	0.799444	+	0.600741i	$0.205128\pi$
$822$	−1.63960e48	−1.31629
$823$	−1.52141e48	−1.19715	−0.598574	−	0.801068i	$-0.704266\pi$
$823$	−1.52141e48	−1.19715	−0.598574	+	0.801068i	$0.704266\pi$
$824$	1.32481e48	1.02177
$825$	0	0
$826$	3.65760e47	0.271035
$827$	−1.82790e48	−1.32774	−0.663869	−	0.747849i	$-0.731087\pi$
$827$	−1.82790e48	−1.32774	−0.663869	+	0.747849i	$0.731087\pi$
$828$	−7.90217e47	−0.562660
$829$	−7.69592e47	−0.537169	−0.268585	−	0.963256i	$-0.586556\pi$
$829$	−7.69592e47	−0.537169	−0.268585	+	0.963256i	$0.586556\pi$
$830$	0	0
$831$	−1.54848e48	−1.03870
$832$	−1.43388e48	−0.942925
$833$	−8.00043e47	−0.515788
$834$	−1.57780e48	−0.997270
$835$	0	0
$836$	−2.67670e48	−1.62628
$837$	1.50370e48	0.895761
$838$	1.17744e47	0.0687722
$839$	2.04370e48	1.17043	0.585215	−	0.810878i	$-0.301010\pi$
$839$	2.04370e48	1.17043	0.585215	+	0.810878i	$0.301010\pi$
$840$	0	0
$841$	2.00764e47	0.110548
$842$	−7.33048e47	−0.395806
$843$	4.26440e48	2.25789
$844$	−1.47443e48	−0.765549
$845$	0	0
$846$	5.30767e47	0.265029
$847$	7.64344e48	3.74294
$848$	−1.33228e47	−0.0639831
$849$	−3.72699e48	−1.75542
$850$	0	0
$851$	1.21955e48	0.552539
$852$	−2.74033e48	−1.21773
$853$	−2.79059e48	−1.21629	−0.608145	−	0.793826i	$-0.708086\pi$
$853$	−2.79059e48	−1.21629	−0.608145	+	0.793826i	$0.708086\pi$
$854$	−1.44965e48	−0.619736
$855$	0	0
$856$	−5.75718e47	−0.236806
$857$	2.78683e48	1.12441	0.562207	−	0.826997i	$-0.309952\pi$
$857$	2.78683e48	1.12441	0.562207	+	0.826997i	$0.309952\pi$
$858$	−5.82235e48	−2.30440
$859$	1.23473e48	0.479384	0.239692	−	0.970849i	$-0.422953\pi$
$859$	1.23473e48	0.479384	0.239692	+	0.970849i	$0.422953\pi$
$860$	0	0
$861$	3.73793e48	1.39662
$862$	−1.96142e48	−0.718952
$863$	−1.65114e48	−0.593755	−0.296877	−	0.954916i	$-0.595945\pi$
$863$	−1.65114e48	−0.593755	−0.296877	+	0.954916i	$0.595945\pi$
$864$	−1.84585e48	−0.651208
$865$	0	0
$866$	−2.35989e48	−0.801396
$867$	−4.37862e48	−1.45889
$868$	−3.92798e48	−1.28408
$869$	−7.61556e47	−0.244273
$870$	0	0
$871$	1.61307e48	0.498141
$872$	2.79802e47	0.0847868
$873$	−1.63951e48	−0.487504
$874$	2.55761e48	0.746269
$875$	0	0
$876$	−3.00544e48	−0.844481
$877$	−1.37890e48	−0.380223	−0.190111	−	0.981763i	$-0.560885\pi$
$877$	−1.37890e48	−0.380223	−0.190111	+	0.981763i	$0.560885\pi$
$878$	2.78623e48	0.753977
$879$	−9.91847e48	−2.63408
$880$	0	0
$881$	−5.43818e46	−0.0139108	−0.00695538	−	0.999976i	$-0.502214\pi$
$881$	−5.43818e46	−0.0139108	−0.00695538	+	0.999976i	$0.502214\pi$
$882$	−7.62357e48	−1.91393
$883$	−5.86213e47	−0.144445	−0.0722227	−	0.997389i	$-0.523009\pi$
$883$	−5.86213e47	−0.144445	−0.0722227	+	0.997389i	$0.523009\pi$
$884$	−7.49688e47	−0.181309
$885$	0	0
$886$	6.29701e47	0.146716
$887$	1.66488e48	0.380753	0.190377	−	0.981711i	$-0.439029\pi$
$887$	1.66488e48	0.380753	0.190377	+	0.981711i	$0.439029\pi$
$888$	5.71187e48	1.28223
$889$	−7.12605e47	−0.157025
$890$	0	0
$891$	3.11017e48	0.660393
$892$	2.28488e48	0.476258
$893$	2.21645e48	0.453534
$894$	4.94817e48	0.993975
$895$	0	0
$896$	4.11491e48	0.796670
$897$	−7.17796e48	−1.36435
$898$	−3.41535e48	−0.637346
$899$	7.54978e48	1.38325
$900$	0	0
$901$	−7.77380e47	−0.137301
$902$	3.48709e48	0.604722
$903$	6.28266e48	1.06978
$904$	1.07771e49	1.80187
$905$	0	0
$906$	4.94052e48	0.796447
$907$	8.00665e48	1.26745	0.633724	−	0.773559i	$-0.281525\pi$
$907$	8.00665e48	1.26745	0.633724	+	0.773559i	$0.281525\pi$
$908$	1.12501e48	0.174880
$909$	4.57467e48	0.698322
$910$	0	0
$911$	1.44015e48	0.212009	0.106004	−	0.994366i	$-0.466194\pi$
$911$	1.44015e48	0.212009	0.106004	+	0.994366i	$0.466194\pi$
$912$	2.09279e48	0.302559
$913$	6.09410e48	0.865251
$914$	−8.37509e48	−1.16782
$915$	0	0
$916$	9.14200e47	0.122961
$917$	1.53145e48	0.202306
$918$	8.89466e47	0.115405
$919$	−2.47134e48	−0.314939	−0.157469	−	0.987524i	$-0.550334\pi$
$919$	−2.47134e48	−0.314939	−0.157469	+	0.987524i	$0.550334\pi$
$920$	0	0
$921$	1.51544e49	1.86318
$922$	−5.85341e48	−0.706885
$923$	−1.46783e49	−1.74120
$924$	2.32820e49	2.71290
$925$	0	0
$926$	−5.41152e48	−0.608468
$927$	1.28691e49	1.42146
$928$	−9.26763e48	−1.00560
$929$	−9.81639e48	−1.04639	−0.523194	−	0.852214i	$-0.675260\pi$
$929$	−9.81639e48	−1.04639	−0.523194	+	0.852214i	$0.675260\pi$
$930$	0	0
$931$	−3.18356e49	−3.27525
$932$	−4.87342e48	−0.492573
$933$	1.96929e49	1.95552
$934$	2.39108e48	0.233276
$935$	0	0
$936$	−1.98243e49	−1.86701
$937$	4.76155e48	0.440601	0.220300	−	0.975432i	$-0.429296\pi$
$937$	4.76155e48	0.440601	0.220300	+	0.975432i	$0.429296\pi$
$938$	4.99928e48	0.454528
$939$	−9.47106e48	−0.846089
$940$	0	0
$941$	−7.34573e48	−0.633587	−0.316793	−	0.948495i	$-0.602606\pi$
$941$	−7.34573e48	−0.633587	−0.316793	+	0.948495i	$0.602606\pi$
$942$	1.93803e49	1.64256
$943$	4.29898e48	0.358033
$944$	3.44209e47	0.0281699
$945$	0	0
$946$	5.86105e48	0.463203
$947$	1.77230e49	1.37646	0.688229	−	0.725493i	$-0.258388\pi$
$947$	1.77230e49	1.37646	0.688229	+	0.725493i	$0.258388\pi$
$948$	−1.58457e48	−0.120941
$949$	−1.60983e49	−1.20750
$950$	0	0
$951$	−4.00720e48	−0.290310
$952$	−6.44774e48	−0.459090
$953$	1.70424e49	1.19261	0.596306	−	0.802757i	$-0.296635\pi$
$953$	1.70424e49	1.19261	0.596306	+	0.802757i	$0.296635\pi$
$954$	−7.40762e48	−0.509484
$955$	0	0
$956$	5.31237e48	0.352966
$957$	−4.47493e49	−2.92240
$958$	−1.70660e49	−1.09547
$959$	3.51182e49	2.21578
$960$	0	0
$961$	1.18582e49	0.722906
$962$	1.10250e49	0.660680
$963$	−5.59249e48	−0.329436
$964$	−1.62520e49	−0.941099
$965$	0	0
$966$	−2.22462e49	−1.24490
$967$	5.35097e48	0.294371	0.147186	−	0.989109i	$-0.452979\pi$
$967$	5.35097e48	0.294371	0.147186	+	0.989109i	$0.452979\pi$
$968$	4.11720e49	2.22668
$969$	1.22113e49	0.649262
$970$	0	0
$971$	−4.10947e48	−0.211187	−0.105594	−	0.994409i	$-0.533674\pi$
$971$	−4.10947e48	−0.211187	−0.105594	+	0.994409i	$0.533674\pi$
$972$	1.40806e49	0.711423
$973$	3.37947e49	1.67875
$974$	2.35780e49	1.15155
$975$	0	0
$976$	−1.36423e48	−0.0644119
$977$	−1.88993e49	−0.877376	−0.438688	−	0.898639i	$-0.644557\pi$
$977$	−1.88993e49	−0.877376	−0.438688	+	0.898639i	$0.644557\pi$
$978$	−2.83509e49	−1.29413
$979$	−1.51633e49	−0.680579
$980$	0	0
$981$	2.71798e48	0.117953
$982$	1.70390e49	0.727117
$983$	4.64069e48	0.194737	0.0973687	−	0.995248i	$-0.468957\pi$
$983$	4.64069e48	0.194737	0.0973687	+	0.995248i	$0.468957\pi$
$984$	2.01346e49	0.830854
$985$	0	0
$986$	4.46582e48	0.178210
$987$	−1.92789e49	−0.756568
$988$	−2.98319e49	−1.15131
$989$	7.22567e48	0.274245
$990$	0	0
$991$	−1.20728e49	−0.443193	−0.221596	−	0.975138i	$-0.571127\pi$
$991$	−1.20728e49	−0.443193	−0.221596	+	0.975138i	$0.571127\pi$
$992$	−3.46922e49	−1.25253
$993$	2.07005e49	0.735052
$994$	−4.54916e49	−1.58875
$995$	0	0
$996$	1.26800e49	0.428390
$997$	2.20246e47	0.00731876	0.00365938	−	0.999993i	$-0.498835\pi$
$997$	2.20246e47	0.00731876	0.00365938	+	0.999993i	$0.498835\pi$
$998$	−3.44926e48	−0.112739
$999$	1.68770e49	0.542582

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.a.e.1.4	yes	11
5.2	odd	4		25.34.b.d.24.8		22
5.3	odd	4		25.34.b.d.24.15		22
5.4	even	2		25.34.a.d.1.8	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.34.a.d.1.8	✓	11	5.4	even	2
25.34.a.e.1.4	yes	11	1.1	even	1	trivial
25.34.b.d.24.8		22	5.2	odd	4
25.34.b.d.24.15		22	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-61242.8 q^{2} +1.16397e8 q^{3} -4.83925e9 q^{4} -7.12847e12 q^{6} +1.52684e14 q^{7} +8.22441e14 q^{8} +7.98915e15 q^{9} +O(q^{10})\)	\(q-61242.8 q^{2} +1.16397e8 q^{3} -4.83925e9 q^{4} -7.12847e12 q^{6} +1.52684e14 q^{7} +8.22441e14 q^{8} +7.98915e15 q^{9} -2.70714e17 q^{11} -5.63273e17 q^{12} -3.01712e18 q^{13} -9.35077e18 q^{14} -8.79981e18 q^{16} -5.13465e19 q^{17} -4.89278e20 q^{18} -2.04320e21 q^{19} +1.77719e22 q^{21} +1.65793e22 q^{22} +2.04394e22 q^{23} +9.57295e22 q^{24} +1.84777e23 q^{26} +2.82855e23 q^{27} -7.38874e23 q^{28} +1.42015e24 q^{29} +5.31617e24 q^{31} -6.52579e24 q^{32} -3.15102e25 q^{33} +3.14460e24 q^{34} -3.86615e25 q^{36} +5.96668e25 q^{37} +1.25131e26 q^{38} -3.51183e26 q^{39} +2.10328e26 q^{41} -1.08840e27 q^{42} +3.53517e26 q^{43} +1.31005e27 q^{44} -1.25177e27 q^{46} -1.08480e27 q^{47} -1.02427e27 q^{48} +1.55813e28 q^{49} -5.97656e27 q^{51} +1.46006e28 q^{52} +1.51399e28 q^{53} -1.73228e28 q^{54} +1.25573e29 q^{56} -2.37822e29 q^{57} -8.69743e28 q^{58} -3.91155e28 q^{59} +1.55030e29 q^{61} -3.25577e29 q^{62} +1.21981e30 q^{63} +4.75248e29 q^{64} +1.92977e30 q^{66} -5.34638e29 q^{67} +2.48478e29 q^{68} +2.37908e30 q^{69} +4.86501e30 q^{71} +6.57061e30 q^{72} +5.33567e30 q^{73} -3.65416e30 q^{74} +9.88755e30 q^{76} -4.13335e31 q^{77} +2.15074e31 q^{78} +2.81314e30 q^{79} -1.14888e31 q^{81} -1.28811e31 q^{82} -2.25113e31 q^{83} -8.60025e31 q^{84} -2.16504e31 q^{86} +1.65301e32 q^{87} -2.22646e32 q^{88} +5.60122e31 q^{89} -4.60664e32 q^{91} -9.89113e31 q^{92} +6.18785e32 q^{93} +6.64360e31 q^{94} -7.59581e32 q^{96} -2.05217e32 q^{97} -9.54241e32 q^{98} -2.16277e33 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 9393 q^{2} + 80330849 q^{3} + 49338206677 q^{4} - 17783977676723 q^{6} + 21344025107658 q^{7} - 970199832420105 q^{8} + 24\!\cdots\!58 q^{9}+O(q^{10}) \) 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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