LMFDB - Embedded newform 45.22.a.i.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,22,Mod(1,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("45.1");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	45.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:	$125.764804929$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 11485586 x^{5} + 1293459480 x^{4} + 34165285911360 x^{3} + \cdots + 25\!\cdots\!88 $ x^7 - x^6 - 11485586x^5 + 1293459480x^4 + 34165285911360x^3 - 2076902713733328x^2 - 21801632220745600032*x + 2582404532579746533888
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{17}\cdot 5^{7}\cdot 7^{2} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-997.261$ of defining polynomial
Character	$\chi$	$=$	45.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-915.261 q^{2} -1.25945e6 q^{4} -9.76562e6 q^{5} -9.67247e8 q^{7} +3.07217e9 q^{8} +O(q^{10})$	\(q-915.261 q^{2} -1.25945e6 q^{4} -9.76562e6 q^{5} -9.67247e8 q^{7} +3.07217e9 q^{8} +8.93809e9 q^{10} +5.85592e10 q^{11} -8.35652e11 q^{13} +8.85283e11 q^{14} -1.70575e11 q^{16} -2.88103e12 q^{17} -1.26372e13 q^{19} +1.22993e13 q^{20} -5.35969e13 q^{22} +3.44241e14 q^{23} +9.53674e13 q^{25} +7.64839e14 q^{26} +1.21820e15 q^{28} -1.05067e15 q^{29} +2.70800e15 q^{31} -6.28668e15 q^{32} +2.63689e15 q^{34} +9.44577e15 q^{35} +3.58723e15 q^{37} +1.15663e16 q^{38} -3.00016e16 q^{40} +8.22978e16 q^{41} +3.16163e16 q^{43} -7.37523e16 q^{44} -3.15070e17 q^{46} +4.88337e17 q^{47} +3.77020e17 q^{49} -8.72861e16 q^{50} +1.05246e18 q^{52} +2.17151e17 q^{53} -5.71867e17 q^{55} -2.97154e18 q^{56} +9.61640e17 q^{58} -3.50397e18 q^{59} -5.82465e18 q^{61} -2.47853e18 q^{62} +6.11167e18 q^{64} +8.16066e18 q^{65} +2.95753e19 q^{67} +3.62851e18 q^{68} -8.64534e18 q^{70} +2.20469e19 q^{71} +3.95169e19 q^{73} -3.28325e18 q^{74} +1.59159e19 q^{76} -5.66412e19 q^{77} -1.49205e19 q^{79} +1.66577e18 q^{80} -7.53239e19 q^{82} +8.63032e19 q^{83} +2.81350e19 q^{85} -2.89372e19 q^{86} +1.79904e20 q^{88} +8.04804e19 q^{89} +8.08282e20 q^{91} -4.33554e20 q^{92} -4.46956e20 q^{94} +1.23410e20 q^{95} -5.75262e19 q^{97} -3.45072e20 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 575 q^{2} + 8338341 q^{4} - 68359375 q^{5} + 59286610 q^{7} - 602858175 q^{8}+O(q^{10}) $ 7 * q + 575 * q^2 + 8338341 * q^4 - 68359375 * q^5 + 59286610 * q^7 - 602858175 * q^8	$ 7 q + 575 q^{2} + 8338341 q^{4} - 68359375 q^{5} + 59286610 q^{7} - 602858175 q^{8} - 5615234375 q^{10} - 140355265750 q^{11} - 208991867340 q^{13} + 1796874777750 q^{14} + 12803748698673 q^{16} + 1128139963850 q^{17} - 15344485652652 q^{19} - 81429111328125 q^{20} - 2813591285650 q^{22} + 112588829920200 q^{23} + 667572021484375 q^{25} - 261343603553500 q^{26} + 45\!\cdots\!30 q^{28}+ \cdots + 10\!\cdots\!75 q^{98}+O(q^{100}) $ 7 * q + 575 * q^2 + 8338341 * q^4 - 68359375 * q^5 + 59286610 * q^7 - 602858175 * q^8 - 5615234375 * q^10 - 140355265750 * q^11 - 208991867340 * q^13 + 1796874777750 * q^14 + 12803748698673 * q^16 + 1128139963850 * q^17 - 15344485652652 * q^19 - 81429111328125 * q^20 - 2813591285650 * q^22 + 112588829920200 * q^23 + 667572021484375 * q^25 - 261343603553500 * q^26 + 4575704582134330 * q^28 - 4510314655295750 * q^29 + 9307677897566716 * q^31 - 18986436031637975 * q^32 + 19110615925476890 * q^34 - 578970800781250 * q^35 - 3659765919950920 * q^37 - 148014269948202700 * q^38 + 5887286865234375 * q^40 - 229063383838346000 * q^41 + 267726514729849560 * q^43 - 528752916336974750 * q^44 - 1150803639936246720 * q^46 + 199817668629879800 * q^47 - 626984501359908149 * q^49 + 54836273193359375 * q^50 - 1938845750001596020 * q^52 - 313454513779361350 * q^53 + 1370656892089843750 * q^55 + 4764746750564345250 * q^56 + 4780338115165635850 * q^58 + 5389196037389518250 * q^59 + 1868229488329518174 * q^61 + 24558299772652382100 * q^62 + 6017351694526520689 * q^64 + 2040936204492187500 * q^65 + 30280970729577023260 * q^67 - 26296226809433348450 * q^68 - 17547605251464843750 * q^70 + 26220232923451409500 * q^71 - 89207100808924659270 * q^73 - 72106964934167693000 * q^74 - 6514482616986768676 * q^76 - 153387195834733012500 * q^77 - 77958551277728196308 * q^79 - 125036608385478515625 * q^80 - 238268753859115035200 * q^82 - 325542858541808727900 * q^83 - 11016991834472656250 * q^85 - 326607069085333441000 * q^86 - 44497535431219080150 * q^88 + 370010788821361177500 * q^89 + 249148676379154429400 * q^91 - 172959882955623644400 * q^92 + 196640777968603613120 * q^94 + 149848492701679687500 * q^95 + 913937589584017744910 * q^97 + 1008191498872893333475 * q^98

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 $

$2$	−915.261	−0.632019	−0.316009	−	0.948756i	$-0.602343\pi$
$2$	−915.261	−0.632019	−0.316009	+	0.948756i	$0.602343\pi$
$3$	0	0
$3$	0	0
$4$	−1.25945e6	−0.600552
$5$	−9.76562e6	−0.447214
$5$	−9.76562e6	−0.447214
$6$	0	0
$7$	−9.67247e8	−1.29422	−0.647110	−	0.762397i	$-0.724022\pi$
$7$	−9.67247e8	−1.29422	−0.647110	+	0.762397i	$0.724022\pi$
$8$	3.07217e9	1.01158
$9$	0	0
$10$	8.93809e9	0.282647
$11$	5.85592e10	0.680725	0.340363	−	0.940294i	$-0.389450\pi$
$11$	5.85592e10	0.680725	0.340363	+	0.940294i	$0.389450\pi$
$12$	0	0
$13$	−8.35652e11	−1.68120	−0.840602	−	0.541654i	$-0.817798\pi$
$13$	−8.35652e11	−1.68120	−0.840602	+	0.541654i	$0.817798\pi$
$14$	8.85283e11	0.817971
$15$	0	0
$16$	−1.70575e11	−0.0387843
$17$	−2.88103e12	−0.346604	−0.173302	−	0.984869i	$-0.555444\pi$
$17$	−2.88103e12	−0.346604	−0.173302	+	0.984869i	$0.555444\pi$
$18$	0	0
$19$	−1.26372e13	−0.472865	−0.236432	−	0.971648i	$-0.575978\pi$
$19$	−1.26372e13	−0.472865	−0.236432	+	0.971648i	$0.575978\pi$
$20$	1.22993e13	0.268575
$21$	0	0
$22$	−5.35969e13	−0.430231
$23$	3.44241e14	1.73269	0.866343	−	0.499449i	$-0.166464\pi$
$23$	3.44241e14	1.73269	0.866343	+	0.499449i	$0.166464\pi$
$24$	0	0
$25$	9.53674e13	0.200000
$26$	7.64839e14	1.06255
$27$	0	0
$28$	1.21820e15	0.777247
$29$	−1.05067e15	−0.463755	−0.231878	−	0.972745i	$-0.574487\pi$
$29$	−1.05067e15	−0.463755	−0.231878	+	0.972745i	$0.574487\pi$
$30$	0	0
$31$	2.70800e15	0.593405	0.296703	−	0.954970i	$-0.404113\pi$
$31$	2.70800e15	0.593405	0.296703	+	0.954970i	$0.404113\pi$
$32$	−6.28668e15	−0.987067
$33$	0	0
$34$	2.63689e15	0.219060
$35$	9.44577e15	0.578792
$36$	0	0
$37$	3.58723e15	0.122643	0.0613213	−	0.998118i	$-0.480469\pi$
$37$	3.58723e15	0.122643	0.0613213	+	0.998118i	$0.480469\pi$
$38$	1.15663e16	0.298859
$39$	0	0
$40$	−3.00016e16	−0.452392
$41$	8.22978e16	0.957542	0.478771	−	0.877940i	$-0.341082\pi$
$41$	8.22978e16	0.957542	0.478771	+	0.877940i	$0.341082\pi$
$42$	0	0
$43$	3.16163e16	0.223097	0.111548	−	0.993759i	$-0.464419\pi$
$43$	3.16163e16	0.223097	0.111548	+	0.993759i	$0.464419\pi$
$44$	−7.37523e16	−0.408811
$45$	0	0
$46$	−3.15070e17	−1.09509
$47$	4.88337e17	1.35423	0.677115	−	0.735877i	$-0.263230\pi$
$47$	4.88337e17	1.35423	0.677115	+	0.735877i	$0.263230\pi$
$48$	0	0
$49$	3.77020e17	0.675004
$50$	−8.72861e16	−0.126404
$51$	0	0
$52$	1.05246e18	1.00965
$53$	2.17151e17	0.170555	0.0852775	−	0.996357i	$-0.472822\pi$
$53$	2.17151e17	0.170555	0.0852775	+	0.996357i	$0.472822\pi$
$54$	0	0
$55$	−5.71867e17	−0.304430
$56$	−2.97154e18	−1.30920
$57$	0	0
$58$	9.61640e17	0.293102
$59$	−3.50397e18	−0.892512	−0.446256	−	0.894905i	$-0.647243\pi$
$59$	−3.50397e18	−0.892512	−0.446256	+	0.894905i	$0.647243\pi$
$60$	0	0
$61$	−5.82465e18	−1.04546	−0.522729	−	0.852499i	$-0.675086\pi$
$61$	−5.82465e18	−1.04546	−0.522729	+	0.852499i	$0.675086\pi$
$62$	−2.47853e18	−0.375043
$63$	0	0
$64$	6.11167e18	0.662629
$65$	8.16066e18	0.751857
$66$	0	0
$67$	2.95753e19	1.98218	0.991090	−	0.133191i	$-0.0425223\pi$
$67$	2.95753e19	1.98218	0.991090	+	0.133191i	$0.0425223\pi$
$68$	3.62851e18	0.208154
$69$	0	0
$70$	−8.64534e18	−0.365808
$71$	2.20469e19	0.803775	0.401887	−	0.915689i	$-0.368354\pi$
$71$	2.20469e19	0.803775	0.401887	+	0.915689i	$0.368354\pi$
$72$	0	0
$73$	3.95169e19	1.07620	0.538100	−	0.842881i	$-0.319142\pi$
$73$	3.95169e19	1.07620	0.538100	+	0.842881i	$0.319142\pi$
$74$	−3.28325e18	−0.0775125
$75$	0	0
$76$	1.59159e19	0.283980
$77$	−5.66412e19	−0.881008
$78$	0	0
$79$	−1.49205e19	−0.177296	−0.0886482	−	0.996063i	$-0.528255\pi$
$79$	−1.49205e19	−0.177296	−0.0886482	+	0.996063i	$0.528255\pi$
$80$	1.66577e18	0.0173449
$81$	0	0
$82$	−7.53239e19	−0.605184
$83$	8.63032e19	0.610530	0.305265	−	0.952267i	$-0.401255\pi$
$83$	8.63032e19	0.610530	0.305265	+	0.952267i	$0.401255\pi$
$84$	0	0
$85$	2.81350e19	0.155006
$86$	−2.89372e19	−0.141001
$87$	0	0
$88$	1.79904e20	0.688607
$89$	8.04804e19	0.273587	0.136793	−	0.990600i	$-0.456320\pi$
$89$	8.04804e19	0.273587	0.136793	+	0.990600i	$0.456320\pi$
$90$	0	0
$91$	8.08282e20	2.17585
$92$	−4.33554e20	−1.04057
$93$	0	0
$94$	−4.46956e20	−0.855899
$95$	1.23410e20	0.211471
$96$	0	0
$97$	−5.75262e19	−0.0792067	−0.0396034	−	0.999215i	$-0.512609\pi$
$97$	−5.75262e19	−0.0792067	−0.0396034	+	0.999215i	$0.512609\pi$
$98$	−3.45072e20	−0.426615
$99$	0	0
$100$	−1.20110e20	−0.120110
$101$	1.76126e21	1.58653	0.793266	−	0.608876i	$-0.208379\pi$
$101$	1.76126e21	1.58653	0.793266	+	0.608876i	$0.208379\pi$
$102$	0	0
$103$	1.37927e21	1.01125	0.505624	−	0.862754i	$-0.331262\pi$
$103$	1.37927e21	1.01125	0.505624	+	0.862754i	$0.331262\pi$
$104$	−2.56726e21	−1.70067
$105$	0	0
$106$	−1.98749e20	−0.107794
$107$	−2.14582e21	−1.05454	−0.527271	−	0.849697i	$-0.676785\pi$
$107$	−2.14582e21	−1.05454	−0.527271	+	0.849697i	$0.676785\pi$
$108$	0	0
$109$	−4.68807e21	−1.89677	−0.948387	−	0.317116i	$-0.897285\pi$
$109$	−4.68807e21	−1.89677	−0.948387	+	0.317116i	$0.897285\pi$
$110$	5.23407e20	0.192405
$111$	0	0
$112$	1.64988e20	0.0501954
$113$	−6.02042e21	−1.66841	−0.834206	−	0.551453i	$-0.814074\pi$
$113$	−6.02042e21	−1.66841	−0.834206	+	0.551453i	$0.814074\pi$
$114$	0	0
$115$	−3.36173e21	−0.774881
$116$	1.32327e21	0.278509
$117$	0	0
$118$	3.20705e21	0.564084
$119$	2.78666e21	0.448581
$120$	0	0
$121$	−3.97107e21	−0.536613
$122$	5.33107e21	0.660749
$123$	0	0
$124$	−3.41059e21	−0.356371
$125$	−9.31323e20	−0.0894427
$126$	0	0
$127$	3.44130e21	0.279758	0.139879	−	0.990169i	$-0.455329\pi$
$127$	3.44130e21	0.279758	0.139879	+	0.990169i	$0.455329\pi$
$128$	7.59035e21	0.568273
$129$	0	0
$130$	−7.46913e21	−0.475188
$131$	−2.92284e22	−1.71576	−0.857880	−	0.513849i	$-0.828219\pi$
$131$	−2.92284e22	−1.71576	−0.857880	+	0.513849i	$0.828219\pi$
$132$	0	0
$133$	1.22233e22	0.611991
$134$	−2.70691e22	−1.25278
$135$	0	0
$136$	−8.85099e21	−0.350617
$137$	−4.43501e22	−1.62678	−0.813390	−	0.581718i	$-0.802381\pi$
$137$	−4.43501e22	−1.62678	−0.813390	+	0.581718i	$0.802381\pi$
$138$	0	0
$139$	−7.52470e21	−0.237047	−0.118523	−	0.992951i	$-0.537816\pi$
$139$	−7.52470e21	−0.237047	−0.118523	+	0.992951i	$0.537816\pi$
$140$	−1.18965e22	−0.347595
$141$	0	0
$142$	−2.01786e22	−0.508001
$143$	−4.89351e22	−1.14444
$144$	0	0
$145$	1.02605e22	0.207398
$146$	−3.61683e22	−0.680178
$147$	0	0
$148$	−4.51794e21	−0.0736534
$149$	−5.46937e21	−0.0830771	−0.0415385	−	0.999137i	$-0.513226\pi$
$149$	−5.46937e21	−0.0830771	−0.0415385	+	0.999137i	$0.513226\pi$
$150$	0	0
$151$	1.27229e23	1.68007	0.840037	−	0.542529i	$-0.182533\pi$
$151$	1.27229e23	1.68007	0.840037	+	0.542529i	$0.182533\pi$
$152$	−3.88235e22	−0.478340
$153$	0	0
$154$	5.18414e22	0.556813
$155$	−2.64453e22	−0.265379
$156$	0	0
$157$	−9.51376e22	−0.834461	−0.417230	−	0.908801i	$-0.636999\pi$
$157$	−9.51376e22	−0.834461	−0.417230	+	0.908801i	$0.636999\pi$
$158$	1.36562e22	0.112055
$159$	0	0
$160$	6.13933e22	0.441430
$161$	−3.32966e23	−2.24248
$162$	0	0
$163$	−6.39927e22	−0.378582	−0.189291	−	0.981921i	$-0.560619\pi$
$163$	−6.39927e22	−0.378582	−0.189291	+	0.981921i	$0.560619\pi$
$164$	−1.03650e23	−0.575054
$165$	0	0
$166$	−7.89899e22	−0.385866
$167$	1.65557e23	0.759319	0.379660	−	0.925126i	$-0.376041\pi$
$167$	1.65557e23	0.759319	0.379660	+	0.925126i	$0.376041\pi$
$168$	0	0
$169$	4.51250e23	1.82644
$170$	−2.57509e22	−0.0979667
$171$	0	0
$172$	−3.98192e22	−0.133981
$173$	−4.55954e23	−1.44357	−0.721784	−	0.692119i	$-0.756677\pi$
$173$	−4.55954e23	−1.44357	−0.721784	+	0.692119i	$0.756677\pi$
$174$	0	0
$175$	−9.22438e22	−0.258844
$176$	−9.98874e21	−0.0264014
$177$	0	0
$178$	−7.36605e22	−0.172912
$179$	−5.39064e23	−1.19312	−0.596559	−	0.802569i	$-0.703466\pi$
$179$	−5.39064e23	−1.19312	−0.596559	+	0.802569i	$0.703466\pi$
$180$	0	0
$181$	−5.81397e23	−1.14511	−0.572555	−	0.819866i	$-0.694048\pi$
$181$	−5.81397e23	−1.14511	−0.572555	+	0.819866i	$0.694048\pi$
$182$	−7.39788e23	−1.37517
$183$	0	0
$184$	1.05756e24	1.75275
$185$	−3.50316e22	−0.0548475
$186$	0	0
$187$	−1.68711e23	−0.235942
$188$	−6.15036e23	−0.813286
$189$	0	0
$190$	−1.12952e23	−0.133654
$191$	1.29385e24	1.44888	0.724440	−	0.689338i	$-0.242098\pi$
$191$	1.29385e24	1.44888	0.724440	+	0.689338i	$0.242098\pi$
$192$	0	0
$193$	−2.85192e23	−0.286276	−0.143138	−	0.989703i	$-0.545719\pi$
$193$	−2.85192e23	−0.286276	−0.143138	+	0.989703i	$0.545719\pi$
$194$	5.26514e22	0.0500601
$195$	0	0
$196$	−4.74838e23	−0.405375
$197$	−9.53116e23	−0.771348	−0.385674	−	0.922635i	$-0.626031\pi$
$197$	−9.53116e23	−0.771348	−0.385674	+	0.922635i	$0.626031\pi$
$198$	0	0
$199$	−1.70629e24	−1.24193	−0.620965	−	0.783839i	$-0.713259\pi$
$199$	−1.70629e24	−1.24193	−0.620965	+	0.783839i	$0.713259\pi$
$200$	2.92985e23	0.202316
$201$	0	0
$202$	−1.61201e24	−1.00272
$203$	1.01626e24	0.600201
$204$	0	0
$205$	−8.03689e23	−0.428226
$206$	−1.26239e24	−0.639127
$207$	0	0
$208$	1.42541e23	0.0652043
$209$	−7.40022e23	−0.321891
$210$	0	0
$211$	2.10894e24	0.830037	0.415019	−	0.909813i	$-0.363775\pi$
$211$	2.10894e24	0.830037	0.415019	+	0.909813i	$0.363775\pi$
$212$	−2.73490e23	−0.102427
$213$	0	0
$214$	1.96399e24	0.666490
$215$	−3.08753e23	−0.0997718
$216$	0	0
$217$	−2.61931e24	−0.767997
$218$	4.29080e24	1.19880
$219$	0	0
$220$	7.20238e23	0.182826
$221$	2.40753e24	0.582712
$222$	0	0
$223$	7.71265e24	1.69825	0.849127	−	0.528189i	$-0.177129\pi$
$223$	7.71265e24	1.69825	0.849127	+	0.528189i	$0.177129\pi$
$224$	6.08077e24	1.27748
$225$	0	0
$226$	5.51026e24	1.05447
$227$	7.45871e24	1.36268	0.681338	−	0.731969i	$-0.261399\pi$
$227$	7.45871e24	1.36268	0.681338	+	0.731969i	$0.261399\pi$
$228$	0	0
$229$	−7.12934e24	−1.18789	−0.593946	−	0.804505i	$-0.702431\pi$
$229$	−7.12934e24	−1.18789	−0.593946	+	0.804505i	$0.702431\pi$
$230$	3.07686e24	0.489739
$231$	0	0
$232$	−3.22784e24	−0.469125
$233$	−5.61256e23	−0.0779694	−0.0389847	−	0.999240i	$-0.512412\pi$
$233$	−5.61256e23	−0.0779694	−0.0389847	+	0.999240i	$0.512412\pi$
$234$	0	0
$235$	−4.76892e24	−0.605630
$236$	4.41307e24	0.536001
$237$	0	0
$238$	−2.55052e24	−0.283512
$239$	−9.22281e23	−0.0981037	−0.0490518	−	0.998796i	$-0.515620\pi$
$239$	−9.22281e23	−0.0981037	−0.0490518	+	0.998796i	$0.515620\pi$
$240$	0	0
$241$	2.27261e24	0.221485	0.110743	−	0.993849i	$-0.464677\pi$
$241$	2.27261e24	0.221485	0.110743	+	0.993849i	$0.464677\pi$
$242$	3.63457e24	0.339150
$243$	0	0
$244$	7.33585e24	0.627852
$245$	−3.68184e24	−0.301871
$246$	0	0
$247$	1.05603e25	0.794982
$248$	8.31943e24	0.600276
$249$	0	0
$250$	8.52403e23	0.0565295
$251$	6.34616e23	0.0403586	0.0201793	−	0.999796i	$-0.493576\pi$
$251$	6.34616e23	0.0403586	0.0201793	+	0.999796i	$0.493576\pi$
$252$	0	0
$253$	2.01585e25	1.17948
$254$	−3.14968e24	−0.176812
$255$	0	0
$256$	−1.97643e25	−1.02179
$257$	3.08026e25	1.52859	0.764294	−	0.644868i	$-0.223088\pi$
$257$	3.08026e25	1.52859	0.764294	+	0.644868i	$0.223088\pi$
$258$	0	0
$259$	−3.46974e24	−0.158727
$260$	−1.02779e25	−0.451530
$261$	0	0
$262$	2.67516e25	1.08439
$263$	1.89440e25	0.737797	0.368899	−	0.929470i	$-0.379735\pi$
$263$	1.89440e25	0.737797	0.368899	+	0.929470i	$0.379735\pi$
$264$	0	0
$265$	−2.12061e24	−0.0762745
$266$	−1.11875e25	−0.386789
$267$	0	0
$268$	−3.72486e25	−1.19040
$269$	4.78265e25	1.46984	0.734919	−	0.678155i	$-0.237220\pi$
$269$	4.78265e25	1.46984	0.734919	+	0.678155i	$0.237220\pi$
$270$	0	0
$271$	−2.20632e25	−0.627323	−0.313661	−	0.949535i	$-0.601556\pi$
$271$	−2.20632e25	−0.627323	−0.313661	+	0.949535i	$0.601556\pi$
$272$	4.91431e23	0.0134428
$273$	0	0
$274$	4.05919e25	1.02816
$275$	5.58464e24	0.136145
$276$	0	0
$277$	−3.34497e25	−0.755709	−0.377854	−	0.925865i	$-0.623338\pi$
$277$	−3.34497e25	−0.755709	−0.377854	+	0.925865i	$0.623338\pi$
$278$	6.88706e24	0.149818
$279$	0	0
$280$	2.90190e25	0.585494
$281$	6.54750e25	1.27250	0.636252	−	0.771481i	$-0.280484\pi$
$281$	6.54750e25	1.27250	0.636252	+	0.771481i	$0.280484\pi$
$282$	0	0
$283$	−7.97442e25	−1.43861	−0.719303	−	0.694697i	$-0.755539\pi$
$283$	−7.97442e25	−1.43861	−0.719303	+	0.694697i	$0.755539\pi$
$284$	−2.77669e25	−0.482709
$285$	0	0
$286$	4.47884e25	0.723306
$287$	−7.96023e25	−1.23927
$288$	0	0
$289$	−6.07916e25	−0.879866
$290$	−9.39102e24	−0.131079
$291$	0	0
$292$	−4.97696e25	−0.646315
$293$	−5.34915e25	−0.670154	−0.335077	−	0.942191i	$-0.608762\pi$
$293$	−5.34915e25	−0.670154	−0.335077	+	0.942191i	$0.608762\pi$
$294$	0	0
$295$	3.42185e25	0.399144
$296$	1.10206e25	0.124063
$297$	0	0
$298$	5.00590e24	0.0525062
$299$	−2.87665e26	−2.91300
$300$	0	0
$301$	−3.05808e25	−0.288736
$302$	−1.16448e26	−1.06184
$303$	0	0
$304$	2.15559e24	0.0183397
$305$	5.68813e25	0.467543
$306$	0	0
$307$	6.45179e25	0.495139	0.247570	−	0.968870i	$-0.420368\pi$
$307$	6.45179e25	0.495139	0.247570	+	0.968870i	$0.420368\pi$
$308$	7.13367e25	0.529091
$309$	0	0
$310$	2.42044e25	0.167724
$311$	−2.04121e26	−1.36743	−0.683713	−	0.729751i	$-0.739636\pi$
$311$	−2.04121e26	−1.36743	−0.683713	+	0.729751i	$0.739636\pi$
$312$	0	0
$313$	−5.01579e25	−0.314140	−0.157070	−	0.987587i	$-0.550205\pi$
$313$	−5.01579e25	−0.314140	−0.157070	+	0.987587i	$0.550205\pi$
$314$	8.70757e25	0.527395
$315$	0	0
$316$	1.87917e25	0.106476
$317$	9.08402e25	0.497916	0.248958	−	0.968514i	$-0.419912\pi$
$317$	9.08402e25	0.497916	0.248958	+	0.968514i	$0.419912\pi$
$318$	0	0
$319$	−6.15266e25	−0.315690
$320$	−5.96843e25	−0.296337
$321$	0	0
$322$	3.04751e26	1.41729
$323$	3.64080e25	0.163897
$324$	0	0
$325$	−7.96940e25	−0.336241
$326$	5.85700e25	0.239271
$327$	0	0
$328$	2.52832e26	0.968629
$329$	−4.72343e26	−1.75267
$330$	0	0
$331$	−1.59672e26	−0.555950	−0.277975	−	0.960588i	$-0.589663\pi$
$331$	−1.59672e26	−0.555950	−0.277975	+	0.960588i	$0.589663\pi$
$332$	−1.08695e26	−0.366655
$333$	0	0
$334$	−1.51528e26	−0.479904
$335$	−2.88821e26	−0.886458
$336$	0	0
$337$	2.69981e26	0.778431	0.389215	−	0.921147i	$-0.372746\pi$
$337$	2.69981e26	0.778431	0.389215	+	0.921147i	$0.372746\pi$
$338$	−4.13011e26	−1.15435
$339$	0	0
$340$	−3.54346e25	−0.0930892
$341$	1.58578e26	0.403946
$342$	0	0
$343$	1.75580e26	0.420617
$344$	9.71307e25	0.225680
$345$	0	0
$346$	4.17317e26	0.912362
$347$	−1.62844e26	−0.345392	−0.172696	−	0.984975i	$-0.555248\pi$
$347$	−1.62844e26	−0.345392	−0.172696	+	0.984975i	$0.555248\pi$
$348$	0	0
$349$	1.04064e26	0.207794	0.103897	−	0.994588i	$-0.466869\pi$
$349$	1.04064e26	0.207794	0.103897	+	0.994588i	$0.466869\pi$
$350$	8.44272e25	0.163594
$351$	0	0
$352$	−3.68143e26	−0.671921
$353$	8.99929e26	1.59431	0.797157	−	0.603772i	$-0.206336\pi$
$353$	8.99929e26	1.59431	0.797157	+	0.603772i	$0.206336\pi$
$354$	0	0
$355$	−2.15302e26	−0.359459
$356$	−1.01361e26	−0.164303
$357$	0	0
$358$	4.93384e26	0.754073
$359$	−3.74893e26	−0.556436	−0.278218	−	0.960518i	$-0.589744\pi$
$359$	−3.74893e26	−0.556436	−0.278218	+	0.960518i	$0.589744\pi$
$360$	0	0
$361$	−5.54512e26	−0.776399
$362$	5.32130e26	0.723731
$363$	0	0
$364$	−1.01799e27	−1.30671
$365$	−3.85907e26	−0.481291
$366$	0	0
$367$	−5.37842e26	−0.633375	−0.316688	−	0.948530i	$-0.602571\pi$
$367$	−5.37842e26	−0.633375	−0.316688	+	0.948530i	$0.602571\pi$
$368$	−5.87189e25	−0.0672010
$369$	0	0
$370$	3.20630e25	0.0346646
$371$	−2.10038e26	−0.220735
$372$	0	0
$373$	−6.42062e26	−0.637726	−0.318863	−	0.947801i	$-0.603301\pi$
$373$	−6.42062e26	−0.637726	−0.318863	+	0.947801i	$0.603301\pi$
$374$	1.54414e26	0.149120
$375$	0	0
$376$	1.50025e27	1.36991
$377$	8.77997e26	0.779667
$378$	0	0
$379$	8.21546e26	0.690113	0.345056	−	0.938582i	$-0.387860\pi$
$379$	8.21546e26	0.690113	0.345056	+	0.938582i	$0.387860\pi$
$380$	−1.55428e26	−0.127000
$381$	0	0
$382$	−1.18421e27	−0.915719
$383$	2.13865e27	1.60899	0.804493	−	0.593962i	$-0.202437\pi$
$383$	2.13865e27	1.60899	0.804493	+	0.593962i	$0.202437\pi$
$384$	0	0
$385$	5.53136e26	0.393999
$386$	2.61025e26	0.180932
$387$	0	0
$388$	7.24513e25	0.0475678
$389$	−8.91956e26	−0.569997	−0.284999	−	0.958528i	$-0.591993\pi$
$389$	−8.91956e26	−0.569997	−0.284999	+	0.958528i	$0.591993\pi$
$390$	0	0
$391$	−9.91767e26	−0.600556
$392$	1.15827e27	0.682819
$393$	0	0
$394$	8.72349e26	0.487506
$395$	1.45708e26	0.0792894
$396$	0	0
$397$	−5.44289e26	−0.280886	−0.140443	−	0.990089i	$-0.544853\pi$
$397$	−5.44289e26	−0.280886	−0.140443	+	0.990089i	$0.544853\pi$
$398$	1.56170e27	0.784922
$399$	0	0
$400$	−1.62673e25	−0.00775686
$401$	3.58409e27	1.66481	0.832403	−	0.554171i	$-0.186965\pi$
$401$	3.58409e27	1.66481	0.832403	+	0.554171i	$0.186965\pi$
$402$	0	0
$403$	−2.26295e27	−0.997635
$404$	−2.21822e27	−0.952795
$405$	0	0
$406$	−9.30143e26	−0.379338
$407$	2.10065e26	0.0834860
$408$	0	0
$409$	4.35423e27	1.64368	0.821840	−	0.569719i	$-0.192948\pi$
$409$	4.35423e27	1.64368	0.821840	+	0.569719i	$0.192948\pi$
$410$	7.35585e26	0.270647
$411$	0	0
$412$	−1.73712e27	−0.607307
$413$	3.38920e27	1.15511
$414$	0	0
$415$	−8.42805e26	−0.273037
$416$	5.25347e27	1.65946
$417$	0	0
$418$	6.77313e26	0.203441
$419$	−2.45864e26	−0.0720190	−0.0360095	−	0.999351i	$-0.511465\pi$
$419$	−2.45864e26	−0.0720190	−0.0360095	+	0.999351i	$0.511465\pi$
$420$	0	0
$421$	−6.28135e27	−1.75021	−0.875107	−	0.483929i	$-0.839209\pi$
$421$	−6.28135e27	−1.75021	−0.875107	+	0.483929i	$0.839209\pi$
$422$	−1.93023e27	−0.524599
$423$	0	0
$424$	6.67122e26	0.172530
$425$	−2.74756e26	−0.0693208
$426$	0	0
$427$	5.63387e27	1.35305
$428$	2.70255e27	0.633308
$429$	0	0
$430$	2.82590e26	0.0630576
$431$	−1.82173e26	−0.0396710	−0.0198355	−	0.999803i	$-0.506314\pi$
$431$	−1.82173e26	−0.0396710	−0.0198355	+	0.999803i	$0.506314\pi$
$432$	0	0
$433$	6.57490e27	1.36385	0.681924	−	0.731423i	$-0.261143\pi$
$433$	6.57490e27	1.36385	0.681924	+	0.731423i	$0.261143\pi$
$434$	2.39735e27	0.485388
$435$	0	0
$436$	5.90438e27	1.13911
$437$	−4.35023e27	−0.819326
$438$	0	0
$439$	4.72073e27	0.847485	0.423742	−	0.905783i	$-0.360716\pi$
$439$	4.72073e27	0.847485	0.423742	+	0.905783i	$0.360716\pi$
$440$	−1.75687e27	−0.307955
$441$	0	0
$442$	−2.20352e27	−0.368285
$443$	−8.10360e27	−1.32263	−0.661315	−	0.750108i	$-0.730002\pi$
$443$	−8.10360e27	−1.32263	−0.661315	+	0.750108i	$0.730002\pi$
$444$	0	0
$445$	−7.85941e26	−0.122352
$446$	−7.05909e27	−1.07333
$447$	0	0
$448$	−5.91149e27	−0.857587
$449$	−1.19439e28	−1.69262	−0.846311	−	0.532690i	$-0.821181\pi$
$449$	−1.19439e28	−1.69262	−0.846311	+	0.532690i	$0.821181\pi$
$450$	0	0
$451$	4.81929e27	0.651823
$452$	7.58242e27	1.00197
$453$	0	0
$454$	−6.82667e27	−0.861236
$455$	−7.89338e27	−0.973068
$456$	0	0
$457$	−7.18815e26	−0.0846247	−0.0423124	−	0.999104i	$-0.513472\pi$
$457$	−7.18815e26	−0.0846247	−0.0423124	+	0.999104i	$0.513472\pi$
$458$	6.52521e27	0.750770
$459$	0	0
$460$	4.23393e27	0.465357
$461$	3.30441e27	0.355005	0.177502	−	0.984120i	$-0.443198\pi$
$461$	3.30441e27	0.355005	0.177502	+	0.984120i	$0.443198\pi$
$462$	0	0
$463$	1.06575e28	1.09409	0.547046	−	0.837103i	$-0.315752\pi$
$463$	1.06575e28	1.09409	0.547046	+	0.837103i	$0.315752\pi$
$464$	1.79219e26	0.0179864
$465$	0	0
$466$	5.13696e26	0.0492781
$467$	2.56955e27	0.241007	0.120504	−	0.992713i	$-0.461549\pi$
$467$	2.56955e27	0.241007	0.120504	+	0.992713i	$0.461549\pi$
$468$	0	0
$469$	−2.86066e28	−2.56538
$470$	4.36480e27	0.382769
$471$	0	0
$472$	−1.07648e28	−0.902847
$473$	1.85143e27	0.151867
$474$	0	0
$475$	−1.20517e27	−0.0945729
$476$	−3.50966e27	−0.269397
$477$	0	0
$478$	8.44127e26	0.0620033
$479$	−1.21419e28	−0.872499	−0.436249	−	0.899826i	$-0.643693\pi$
$479$	−1.21419e28	−0.872499	−0.436249	+	0.899826i	$0.643693\pi$
$480$	0	0
$481$	−2.99768e27	−0.206187
$482$	−2.08003e27	−0.139983
$483$	0	0
$484$	5.00137e27	0.322264
$485$	5.61779e26	0.0354223
$486$	0	0
$487$	1.63175e28	0.985372	0.492686	−	0.870207i	$-0.336015\pi$
$487$	1.63175e28	0.985372	0.492686	+	0.870207i	$0.336015\pi$
$488$	−1.78943e28	−1.05756
$489$	0	0
$490$	3.36984e27	0.190788
$491$	−2.49249e28	−1.38127	−0.690634	−	0.723205i	$-0.742668\pi$
$491$	−2.49249e28	−1.38127	−0.690634	+	0.723205i	$0.742668\pi$
$492$	0	0
$493$	3.02702e27	0.160739
$494$	−9.66540e27	−0.502443
$495$	0	0
$496$	−4.61918e26	−0.0230148
$497$	−2.13248e28	−1.04026
$498$	0	0
$499$	−5.97808e27	−0.279580	−0.139790	−	0.990181i	$-0.544643\pi$
$499$	−5.97808e27	−0.279580	−0.139790	+	0.990181i	$0.544643\pi$
$500$	1.17295e27	0.0537150
$501$	0	0
$502$	−5.80839e26	−0.0255074
$503$	1.88655e28	0.811345	0.405672	−	0.914019i	$-0.367037\pi$
$503$	1.88655e28	0.811345	0.405672	+	0.914019i	$0.367037\pi$
$504$	0	0
$505$	−1.71998e28	−0.709518
$506$	−1.84502e28	−0.745456
$507$	0	0
$508$	−4.33414e27	−0.168010
$509$	−7.15931e27	−0.271853	−0.135927	−	0.990719i	$-0.543401\pi$
$509$	−7.15931e27	−0.271853	−0.135927	+	0.990719i	$0.543401\pi$
$510$	0	0
$511$	−3.82226e28	−1.39284
$512$	2.17133e27	0.0775160
$513$	0	0
$514$	−2.81925e28	−0.966096
$515$	−1.34694e28	−0.452244
$516$	0	0
$517$	2.85966e28	0.921858
$518$	3.17572e27	0.100318
$519$	0	0
$520$	2.50709e28	0.760563
$521$	−1.13976e26	−0.00338858	−0.00169429	−	0.999999i	$-0.500539\pi$
$521$	−1.13976e26	−0.00338858	−0.00169429	+	0.999999i	$0.500539\pi$
$522$	0	0
$523$	3.18787e28	0.910402	0.455201	−	0.890389i	$-0.349567\pi$
$523$	3.18787e28	0.910402	0.455201	+	0.890389i	$0.349567\pi$
$524$	3.68117e28	1.03040
$525$	0	0
$526$	−1.73387e28	−0.466301
$527$	−7.80183e27	−0.205677
$528$	0	0
$529$	7.90301e28	2.00220
$530$	1.94091e27	0.0482069
$531$	0	0
$532$	−1.53946e28	−0.367532
$533$	−6.87723e28	−1.60982
$534$	0	0
$535$	2.09553e28	0.471605
$536$	9.08601e28	2.00513
$537$	0	0
$538$	−4.37737e28	−0.928965
$539$	2.20780e28	0.459492
$540$	0	0
$541$	−1.04081e28	−0.208353	−0.104176	−	0.994559i	$-0.533221\pi$
$541$	−1.04081e28	−0.208353	−0.104176	+	0.994559i	$0.533221\pi$
$542$	2.01936e28	0.396480
$543$	0	0
$544$	1.81121e28	0.342121
$545$	4.57819e28	0.848263
$546$	0	0
$547$	2.31815e28	0.413309	0.206654	−	0.978414i	$-0.433742\pi$
$547$	2.31815e28	0.413309	0.206654	+	0.978414i	$0.433742\pi$
$548$	5.58568e28	0.976967
$549$	0	0
$550$	−5.11140e27	−0.0860462
$551$	1.32775e28	0.219293
$552$	0	0
$553$	1.44318e28	0.229461
$554$	3.06152e28	0.477622
$555$	0	0
$556$	9.47698e27	0.142359
$557$	−5.84547e28	−0.861668	−0.430834	−	0.902431i	$-0.641781\pi$
$557$	−5.84547e28	−0.861668	−0.430834	+	0.902431i	$0.641781\pi$
$558$	0	0
$559$	−2.64203e28	−0.375071
$560$	−1.61121e27	−0.0224481
$561$	0	0
$562$	−5.99267e28	−0.804246
$563$	−1.32370e28	−0.174362	−0.0871811	−	0.996192i	$-0.527786\pi$
$563$	−1.32370e28	−0.174362	−0.0871811	+	0.996192i	$0.527786\pi$
$564$	0	0
$565$	5.87932e28	0.746136
$566$	7.29868e28	0.909225
$567$	0	0
$568$	6.77317e28	0.813082
$569$	−6.62293e27	−0.0780497	−0.0390249	−	0.999238i	$-0.512425\pi$
$569$	−6.62293e27	−0.0780497	−0.0390249	+	0.999238i	$0.512425\pi$
$570$	0	0
$571$	−7.96200e26	−0.00904363	−0.00452182	−	0.999990i	$-0.501439\pi$
$571$	−7.96200e26	−0.00904363	−0.00452182	+	0.999990i	$0.501439\pi$
$572$	6.16313e28	0.687295
$573$	0	0
$574$	7.28568e28	0.783241
$575$	3.28294e28	0.346537
$576$	0	0
$577$	−1.68060e29	−1.71048	−0.855242	−	0.518229i	$-0.826591\pi$
$577$	−1.68060e29	−1.71048	−0.855242	+	0.518229i	$0.826591\pi$
$578$	5.56402e28	0.556092
$579$	0	0
$580$	−1.29226e28	−0.124553
$581$	−8.34765e28	−0.790159
$582$	0	0
$583$	1.27162e28	0.116101
$584$	1.21403e29	1.08866
$585$	0	0
$586$	4.89586e28	0.423550
$587$	2.26546e29	1.92511	0.962555	−	0.271088i	$-0.0873833\pi$
$587$	2.26546e29	1.92511	0.962555	+	0.271088i	$0.0873833\pi$
$588$	0	0
$589$	−3.42215e28	−0.280600
$590$	−3.13188e28	−0.252266
$591$	0	0
$592$	−6.11893e26	−0.00475661
$593$	−1.73244e29	−1.32307	−0.661537	−	0.749913i	$-0.730095\pi$
$593$	−1.73244e29	−1.32307	−0.661537	+	0.749913i	$0.730095\pi$
$594$	0	0
$595$	−2.72135e28	−0.200612
$596$	6.88839e27	0.0498921
$597$	0	0
$598$	2.63289e29	1.84107
$599$	2.58736e29	1.77777	0.888883	−	0.458134i	$-0.151482\pi$
$599$	2.58736e29	1.77777	0.888883	+	0.458134i	$0.151482\pi$
$600$	0	0
$601$	−2.10826e29	−1.39876	−0.699379	−	0.714751i	$-0.746540\pi$
$601$	−2.10826e29	−1.39876	−0.699379	+	0.714751i	$0.746540\pi$
$602$	2.79894e28	0.182486
$603$	0	0
$604$	−1.60239e29	−1.00897
$605$	3.87800e28	0.239981
$606$	0	0
$607$	−8.56906e28	−0.512214	−0.256107	−	0.966648i	$-0.582440\pi$
$607$	−8.56906e28	−0.512214	−0.256107	+	0.966648i	$0.582440\pi$
$608$	7.94458e28	0.466749
$609$	0	0
$610$	−5.20612e28	−0.295496
$611$	−4.08080e29	−2.27674
$612$	0	0
$613$	9.13834e28	0.492643	0.246322	−	0.969188i	$-0.420778\pi$
$613$	9.13834e28	0.492643	0.246322	+	0.969188i	$0.420778\pi$
$614$	−5.90507e28	−0.312937
$615$	0	0
$616$	−1.74011e29	−0.891209
$617$	−2.97590e29	−1.49839	−0.749195	−	0.662350i	$-0.769559\pi$
$617$	−2.97590e29	−1.49839	−0.749195	+	0.662350i	$0.769559\pi$
$618$	0	0
$619$	4.94443e28	0.240638	0.120319	−	0.992735i	$-0.461608\pi$
$619$	4.94443e28	0.240638	0.120319	+	0.992735i	$0.461608\pi$
$620$	3.33066e28	0.159374
$621$	0	0
$622$	1.86824e29	0.864239
$623$	−7.78444e28	−0.354081
$624$	0	0
$625$	9.09495e27	0.0400000
$626$	4.59076e28	0.198543
$627$	0	0
$628$	1.19821e29	0.501138
$629$	−1.03349e28	−0.0425084
$630$	0	0
$631$	−3.44009e29	−1.36855	−0.684276	−	0.729223i	$-0.739882\pi$
$631$	−3.44009e29	−1.36855	−0.684276	+	0.729223i	$0.739882\pi$
$632$	−4.58384e28	−0.179349
$633$	0	0
$634$	−8.31425e28	−0.314692
$635$	−3.36064e28	−0.125112
$636$	0	0
$637$	−3.15058e29	−1.13482
$638$	5.63129e28	0.199522
$639$	0	0
$640$	−7.41245e28	−0.254139
$641$	1.38110e29	0.465818	0.232909	−	0.972499i	$-0.425176\pi$
$641$	1.38110e29	0.465818	0.232909	+	0.972499i	$0.425176\pi$
$642$	0	0
$643$	4.35372e29	1.42117	0.710584	−	0.703613i	$-0.248431\pi$
$643$	4.35372e29	1.42117	0.710584	+	0.703613i	$0.248431\pi$
$644$	4.19354e29	1.34672
$645$	0	0
$646$	−3.33228e28	−0.103586
$647$	−1.40465e29	−0.429609	−0.214804	−	0.976657i	$-0.568911\pi$
$647$	−1.40465e29	−0.429609	−0.214804	+	0.976657i	$0.568911\pi$
$648$	0	0
$649$	−2.05190e29	−0.607556
$650$	7.29408e28	0.212510
$651$	0	0
$652$	8.05956e28	0.227359
$653$	−4.87058e29	−1.35205	−0.676024	−	0.736880i	$-0.736298\pi$
$653$	−4.87058e29	−1.35205	−0.676024	+	0.736880i	$0.736298\pi$
$654$	0	0
$655$	2.85434e29	0.767312
$656$	−1.40380e28	−0.0371376
$657$	0	0
$658$	4.32317e29	1.10772
$659$	−6.21241e29	−1.56662	−0.783310	−	0.621632i	$-0.786470\pi$
$659$	−6.21241e29	−1.56662	−0.783310	+	0.621632i	$0.786470\pi$
$660$	0	0
$661$	6.03932e29	1.47527	0.737637	−	0.675198i	$-0.235942\pi$
$661$	6.03932e29	1.47527	0.737637	+	0.675198i	$0.235942\pi$
$662$	1.46142e29	0.351370
$663$	0	0
$664$	2.65138e29	0.617599
$665$	−1.19368e29	−0.273690
$666$	0	0
$667$	−3.61685e29	−0.803543
$668$	−2.08511e29	−0.456011
$669$	0	0
$670$	2.64347e29	0.560258
$671$	−3.41087e29	−0.711669
$672$	0	0
$673$	3.02543e29	0.611827	0.305913	−	0.952059i	$-0.401038\pi$
$673$	3.02543e29	0.611827	0.305913	+	0.952059i	$0.401038\pi$
$674$	−2.47103e29	−0.491983
$675$	0	0
$676$	−5.68326e29	−1.09688
$677$	−5.25623e29	−0.998834	−0.499417	−	0.866362i	$-0.666452\pi$
$677$	−5.25623e29	−0.998834	−0.499417	+	0.866362i	$0.666452\pi$
$678$	0	0
$679$	5.56420e28	0.102511
$680$	8.64354e28	0.156801
$681$	0	0
$682$	−1.45141e29	−0.255301
$683$	−9.04320e29	−1.56641	−0.783204	−	0.621765i	$-0.786416\pi$
$683$	−9.04320e29	−1.56641	−0.783204	+	0.621765i	$0.786416\pi$
$684$	0	0
$685$	4.33107e29	0.727518
$686$	−1.60701e29	−0.265838
$687$	0	0
$688$	−5.39296e27	−0.00865264
$689$	−1.81462e29	−0.286738
$690$	0	0
$691$	−8.14627e29	−1.24865	−0.624323	−	0.781166i	$-0.714625\pi$
$691$	−8.14627e29	−1.24865	−0.624323	+	0.781166i	$0.714625\pi$
$692$	5.74251e29	0.866938
$693$	0	0
$694$	1.49045e29	0.218294
$695$	7.34834e28	0.106011
$696$	0	0
$697$	−2.37102e29	−0.331888
$698$	−9.52456e28	−0.131330
$699$	0	0
$700$	1.16176e29	0.155449
$701$	3.91879e29	0.516551	0.258275	−	0.966071i	$-0.416846\pi$
$701$	3.91879e29	0.516551	0.258275	+	0.966071i	$0.416846\pi$
$702$	0	0
$703$	−4.53325e28	−0.0579934
$704$	3.57894e29	0.451068
$705$	0	0
$706$	−8.23670e29	−1.00764
$707$	−1.70357e30	−2.05332
$708$	0	0
$709$	−2.89513e29	−0.338753	−0.169376	−	0.985551i	$-0.554175\pi$
$709$	−2.89513e29	−0.338753	−0.169376	+	0.985551i	$0.554175\pi$
$710$	1.97057e29	0.227185
$711$	0	0
$712$	2.47249e29	0.276754
$713$	9.32205e29	1.02819
$714$	0	0
$715$	4.77882e29	0.511808
$716$	6.78924e29	0.716530
$717$	0	0
$718$	3.43125e29	0.351678
$719$	−7.17610e29	−0.724829	−0.362414	−	0.932017i	$-0.618047\pi$
$719$	−7.17610e29	−0.724829	−0.362414	+	0.932017i	$0.618047\pi$
$720$	0	0
$721$	−1.33409e30	−1.30878
$722$	5.07523e29	0.490699
$723$	0	0
$724$	7.32240e29	0.687699
$725$	−1.00200e29	−0.0927510
$726$	0	0
$727$	7.02397e29	0.631643	0.315821	−	0.948819i	$-0.397720\pi$
$727$	7.02397e29	0.631643	0.315821	+	0.948819i	$0.397720\pi$
$728$	2.48318e30	2.20104
$729$	0	0
$730$	3.53206e29	0.304185
$731$	−9.10875e28	−0.0773261
$732$	0	0
$733$	2.24336e30	1.85057	0.925287	−	0.379268i	$-0.123824\pi$
$733$	2.24336e30	1.85057	0.925287	+	0.379268i	$0.123824\pi$
$734$	4.92266e29	0.400305
$735$	0	0
$736$	−2.16413e30	−1.71028
$737$	1.73190e30	1.34932
$738$	0	0
$739$	−1.67883e30	−1.27127	−0.635637	−	0.771988i	$-0.719263\pi$
$739$	−1.67883e30	−1.27127	−0.635637	+	0.771988i	$0.719263\pi$
$740$	4.41205e28	0.0329388
$741$	0	0
$742$	1.92240e29	0.139509
$743$	−1.09413e29	−0.0782866	−0.0391433	−	0.999234i	$-0.512463\pi$
$743$	−1.09413e29	−0.0782866	−0.0391433	+	0.999234i	$0.512463\pi$
$744$	0	0
$745$	5.34118e28	0.0371532
$746$	5.87654e29	0.403055
$747$	0	0
$748$	2.12482e29	0.141696
$749$	2.07554e30	1.36481
$750$	0	0
$751$	−6.00380e29	−0.383890	−0.191945	−	0.981406i	$-0.561480\pi$
$751$	−6.00380e29	−0.383890	−0.191945	+	0.981406i	$0.561480\pi$
$752$	−8.32982e28	−0.0525228
$753$	0	0
$754$	−8.03597e29	−0.492764
$755$	−1.24247e30	−0.751352
$756$	0	0
$757$	−3.10310e30	−1.82511	−0.912555	−	0.408954i	$-0.865894\pi$
$757$	−3.10310e30	−1.82511	−0.912555	+	0.408954i	$0.865894\pi$
$758$	−7.51929e29	−0.436164
$759$	0	0
$760$	3.79135e29	0.213920
$761$	−2.20443e30	−1.22675	−0.613376	−	0.789791i	$-0.710189\pi$
$761$	−2.20443e30	−1.22675	−0.613376	+	0.789791i	$0.710189\pi$
$762$	0	0
$763$	4.53452e30	2.45484
$764$	−1.62953e30	−0.870129
$765$	0	0
$766$	−1.95742e30	−1.01691
$767$	2.92810e30	1.50049
$768$	0	0
$769$	−1.33161e30	−0.663972	−0.331986	−	0.943284i	$-0.607719\pi$
$769$	−1.33161e30	−0.663972	−0.331986	+	0.943284i	$0.607719\pi$
$770$	−5.06264e29	−0.249014
$771$	0	0
$772$	3.59184e29	0.171924
$773$	2.59159e30	1.22372	0.611858	−	0.790967i	$-0.290422\pi$
$773$	2.59159e30	1.22372	0.611858	+	0.790967i	$0.290422\pi$
$774$	0	0
$775$	2.58255e29	0.118681
$776$	−1.76730e29	−0.0801239
$777$	0	0
$778$	8.16372e29	0.360249
$779$	−1.04001e30	−0.452788
$780$	0	0
$781$	1.29105e30	0.547150
$782$	9.07725e29	0.379563
$783$	0	0
$784$	−6.43103e28	−0.0261795
$785$	9.29078e29	0.373182
$786$	0	0
$787$	−1.53600e30	−0.600699	−0.300350	−	0.953829i	$-0.597103\pi$
$787$	−1.53600e30	−0.600699	−0.300350	+	0.953829i	$0.597103\pi$
$788$	1.20040e30	0.463235
$789$	0	0
$790$	−1.33361e29	−0.0501124
$791$	5.82323e30	2.15929
$792$	0	0
$793$	4.86738e30	1.75763
$794$	4.98166e29	0.177525
$795$	0	0
$796$	2.14899e30	0.745844
$797$	4.14430e29	0.141951	0.0709755	−	0.997478i	$-0.477389\pi$
$797$	4.14430e29	0.141951	0.0709755	+	0.997478i	$0.477389\pi$
$798$	0	0
$799$	−1.40691e30	−0.469381
$800$	−5.99544e29	−0.197413
$801$	0	0
$802$	−3.28038e30	−1.05219
$803$	2.31408e30	0.732596
$804$	0	0
$805$	3.25162e30	1.00287
$806$	2.07119e30	0.630524
$807$	0	0
$808$	5.41088e30	1.60490
$809$	−5.69445e30	−1.66722	−0.833609	−	0.552355i	$-0.813729\pi$
$809$	−5.69445e30	−1.66722	−0.833609	+	0.552355i	$0.813729\pi$
$810$	0	0
$811$	−5.82741e30	−1.66248	−0.831241	−	0.555913i	$-0.812369\pi$
$811$	−5.82741e30	−1.66248	−0.831241	+	0.555913i	$0.812369\pi$
$812$	−1.27993e30	−0.360452
$813$	0	0
$814$	−1.92265e29	−0.0527647
$815$	6.24929e29	0.169307
$816$	0	0
$817$	−3.99541e29	−0.105494
$818$	−3.98526e30	−1.03884
$819$	0	0
$820$	1.01221e30	0.257172
$821$	−2.09582e30	−0.525715	−0.262857	−	0.964835i	$-0.584665\pi$
$821$	−2.09582e30	−0.525715	−0.262857	+	0.964835i	$0.584665\pi$
$822$	0	0
$823$	4.51355e30	1.10362	0.551810	−	0.833970i	$-0.313937\pi$
$823$	4.51355e30	1.10362	0.551810	+	0.833970i	$0.313937\pi$
$824$	4.23734e30	1.02296
$825$	0	0
$826$	−3.10200e30	−0.730049
$827$	−6.73591e30	−1.56527	−0.782634	−	0.622482i	$-0.786124\pi$
$827$	−6.73591e30	−1.56527	−0.782634	+	0.622482i	$0.786124\pi$
$828$	0	0
$829$	5.22443e30	1.18363	0.591816	−	0.806073i	$-0.298411\pi$
$829$	5.22443e30	1.18363	0.591816	+	0.806073i	$0.298411\pi$
$830$	7.71386e29	0.172565
$831$	0	0
$832$	−5.10723e30	−1.11401
$833$	−1.08621e30	−0.233959
$834$	0	0
$835$	−1.61677e30	−0.339578
$836$	9.32021e29	0.193312
$837$	0	0
$838$	2.25029e29	0.0455174
$839$	−5.77623e30	−1.15384	−0.576918	−	0.816802i	$-0.695745\pi$
$839$	−5.77623e30	−1.15384	−0.576918	+	0.816802i	$0.695745\pi$
$840$	0	0
$841$	−4.02893e30	−0.784931
$842$	5.74908e30	1.10617
$843$	0	0
$844$	−2.65610e30	−0.498481
$845$	−4.40673e30	−0.816811
$846$	0	0
$847$	3.84101e30	0.694495
$848$	−3.70405e28	−0.00661485
$849$	0	0
$850$	2.51473e29	0.0438120
$851$	1.23487e30	0.212501
$852$	0	0
$853$	5.69670e30	0.956441	0.478221	−	0.878240i	$-0.341282\pi$
$853$	5.69670e30	0.956441	0.478221	+	0.878240i	$0.341282\pi$
$854$	−5.15646e30	−0.855153
$855$	0	0
$856$	−6.59232e30	−1.06675
$857$	−4.61068e30	−0.736998	−0.368499	−	0.929628i	$-0.620128\pi$
$857$	−4.61068e30	−0.736998	−0.368499	+	0.929628i	$0.620128\pi$
$858$	0	0
$859$	1.02106e31	1.59266	0.796330	−	0.604862i	$-0.206772\pi$
$859$	1.02106e31	1.59266	0.796330	+	0.604862i	$0.206772\pi$
$860$	3.88859e29	0.0599182
$861$	0	0
$862$	1.66736e29	0.0250728
$863$	9.94622e30	1.47756	0.738779	−	0.673947i	$-0.235403\pi$
$863$	9.94622e30	1.47756	0.738779	+	0.673947i	$0.235403\pi$
$864$	0	0
$865$	4.45268e30	0.645583
$866$	−6.01774e30	−0.861977
$867$	0	0
$868$	3.29889e30	0.461222
$869$	−8.73735e29	−0.120690
$870$	0	0
$871$	−2.47146e31	−3.33245
$872$	−1.44025e31	−1.91874
$873$	0	0
$874$	3.98159e30	0.517829
$875$	9.00819e29	0.115758
$876$	0	0
$877$	−1.39556e31	−1.75087	−0.875435	−	0.483336i	$-0.839425\pi$
$877$	−1.39556e31	−1.75087	−0.875435	+	0.483336i	$0.839425\pi$
$878$	−4.32070e30	−0.535626
$879$	0	0
$880$	9.75463e28	0.0118071
$881$	−6.73449e30	−0.805486	−0.402743	−	0.915313i	$-0.631943\pi$
$881$	−6.73449e30	−0.805486	−0.402743	+	0.915313i	$0.631943\pi$
$882$	0	0
$883$	−5.35750e30	−0.625712	−0.312856	−	0.949800i	$-0.601286\pi$
$883$	−5.35750e30	−0.625712	−0.312856	+	0.949800i	$0.601286\pi$
$884$	−3.03217e30	−0.349949
$885$	0	0
$886$	7.41690e30	0.835927
$887$	3.83803e30	0.427474	0.213737	−	0.976891i	$-0.431436\pi$
$887$	3.83803e30	0.427474	0.213737	+	0.976891i	$0.431436\pi$
$888$	0	0
$889$	−3.32858e30	−0.362069
$890$	7.19341e29	0.0773285
$891$	0	0
$892$	−9.71370e30	−1.01989
$893$	−6.17120e30	−0.640367
$894$	0	0
$895$	5.26430e30	0.533579
$896$	−7.34174e30	−0.735470
$897$	0	0
$898$	1.09318e31	1.06977
$899$	−2.84523e30	−0.275195
$900$	0	0
$901$	−6.25616e29	−0.0591150
$902$	−4.41091e30	−0.411964
$903$	0	0
$904$	−1.84957e31	−1.68773
$905$	5.67770e30	0.512109
$906$	0	0
$907$	8.18425e30	0.721278	0.360639	−	0.932706i	$-0.382559\pi$
$907$	8.18425e30	0.721278	0.360639	+	0.932706i	$0.382559\pi$
$908$	−9.39388e30	−0.818358
$909$	0	0
$910$	7.22450e30	0.614997
$911$	1.35023e31	1.13623	0.568114	−	0.822950i	$-0.307673\pi$
$911$	1.35023e31	1.13623	0.568114	+	0.822950i	$0.307673\pi$
$912$	0	0
$913$	5.05384e30	0.415603
$914$	6.57903e29	0.0534844
$915$	0	0
$916$	8.97905e30	0.713391
$917$	2.82711e31	2.22057
$918$	0	0
$919$	6.76946e30	0.519686	0.259843	−	0.965651i	$-0.416329\pi$
$919$	6.76946e30	0.519686	0.259843	+	0.965651i	$0.416329\pi$
$920$	−1.03278e31	−0.783853
$921$	0	0
$922$	−3.02440e30	−0.224370
$923$	−1.84235e31	−1.35131
$924$	0	0
$925$	3.42105e29	0.0245285
$926$	−9.75436e30	−0.691486
$927$	0	0
$928$	6.60525e30	0.457757
$929$	2.15858e31	1.47912	0.739561	−	0.673090i	$-0.235033\pi$
$929$	2.15858e31	1.47912	0.739561	+	0.673090i	$0.235033\pi$
$930$	0	0
$931$	−4.76447e30	−0.319185
$932$	7.06874e29	0.0468247
$933$	0	0
$934$	−2.35181e30	−0.152321
$935$	1.64756e30	0.105516
$936$	0	0
$937$	5.93425e30	0.371621	0.185810	−	0.982586i	$-0.440509\pi$
$937$	5.93425e30	0.371621	0.185810	+	0.982586i	$0.440509\pi$
$938$	2.61825e31	1.62137
$939$	0	0
$940$	6.00621e30	0.363713
$941$	−1.78030e30	−0.106611	−0.0533054	−	0.998578i	$-0.516976\pi$
$941$	−1.78030e30	−0.106611	−0.0533054	+	0.998578i	$0.516976\pi$
$942$	0	0
$943$	2.83303e31	1.65912
$944$	5.97690e29	0.0346155
$945$	0	0
$946$	−1.69454e30	−0.0959830
$947$	1.38682e31	0.776866	0.388433	−	0.921477i	$-0.373017\pi$
$947$	1.38682e31	0.776866	0.388433	+	0.921477i	$0.373017\pi$
$948$	0	0
$949$	−3.30224e31	−1.80931
$950$	1.10305e30	0.0597719
$951$	0	0
$952$	8.56109e30	0.453776
$953$	1.08134e31	0.566877	0.283438	−	0.958990i	$-0.408525\pi$
$953$	1.08134e31	0.566877	0.283438	+	0.958990i	$0.408525\pi$
$954$	0	0
$955$	−1.26352e31	−0.647959
$956$	1.16157e30	0.0589164
$957$	0	0
$958$	1.11130e31	0.551435
$959$	4.28975e31	2.10541
$960$	0	0
$961$	−1.34922e31	−0.647870
$962$	2.74366e30	0.130314
$963$	0	0
$964$	−2.86223e30	−0.133014
$965$	2.78507e30	0.128027
$966$	0	0
$967$	5.21987e30	0.234791	0.117396	−	0.993085i	$-0.462545\pi$
$967$	5.21987e30	0.234791	0.117396	+	0.993085i	$0.462545\pi$
$968$	−1.21998e31	−0.542827
$969$	0	0
$970$	−5.14174e29	−0.0223876
$971$	9.44324e30	0.406742	0.203371	−	0.979102i	$-0.434810\pi$
$971$	9.44324e30	0.406742	0.203371	+	0.979102i	$0.434810\pi$
$972$	0	0
$973$	7.27824e30	0.306790
$974$	−1.49348e31	−0.622773
$975$	0	0
$976$	9.93540e29	0.0405473
$977$	−3.14485e31	−1.26972	−0.634858	−	0.772628i	$-0.718942\pi$
$977$	−3.14485e31	−1.26972	−0.634858	+	0.772628i	$0.718942\pi$
$978$	0	0
$979$	4.71286e30	0.186237
$980$	4.63709e30	0.181289
$981$	0	0
$982$	2.28128e31	0.872987
$983$	−1.31474e31	−0.497768	−0.248884	−	0.968533i	$-0.580064\pi$
$983$	−1.31474e31	−0.497768	−0.248884	+	0.968533i	$0.580064\pi$
$984$	0	0
$985$	9.30777e30	0.344957
$986$	−2.77051e30	−0.101590
$987$	0	0
$988$	−1.33001e31	−0.477428
$989$	1.08836e31	0.386556
$990$	0	0
$991$	−2.92159e31	−1.01589	−0.507944	−	0.861390i	$-0.669594\pi$
$991$	−2.92159e31	−1.01589	−0.507944	+	0.861390i	$0.669594\pi$
$992$	−1.70243e31	−0.585731
$993$	0	0
$994$	1.95177e31	0.657464
$995$	1.66630e31	0.555408
$996$	0	0
$997$	−1.22592e30	−0.0400095	−0.0200047	−	0.999800i	$-0.506368\pi$
$997$	−1.22592e30	−0.0400095	−0.0200047	+	0.999800i	$0.506368\pi$
$998$	5.47150e30	0.176700
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.22.a.i.1.3	yes	7
3.2	odd	2		45.22.a.h.1.5	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.22.a.h.1.5	✓	7	3.2	odd	2
45.22.a.i.1.3	yes	7	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	45.a (trivial)

\(f(q)\)	\(=\)	\(q-915.261 q^{2} -1.25945e6 q^{4} -9.76562e6 q^{5} -9.67247e8 q^{7} +3.07217e9 q^{8} +O(q^{10})\)	\(q-915.261 q^{2} -1.25945e6 q^{4} -9.76562e6 q^{5} -9.67247e8 q^{7} +3.07217e9 q^{8} +8.93809e9 q^{10} +5.85592e10 q^{11} -8.35652e11 q^{13} +8.85283e11 q^{14} -1.70575e11 q^{16} -2.88103e12 q^{17} -1.26372e13 q^{19} +1.22993e13 q^{20} -5.35969e13 q^{22} +3.44241e14 q^{23} +9.53674e13 q^{25} +7.64839e14 q^{26} +1.21820e15 q^{28} -1.05067e15 q^{29} +2.70800e15 q^{31} -6.28668e15 q^{32} +2.63689e15 q^{34} +9.44577e15 q^{35} +3.58723e15 q^{37} +1.15663e16 q^{38} -3.00016e16 q^{40} +8.22978e16 q^{41} +3.16163e16 q^{43} -7.37523e16 q^{44} -3.15070e17 q^{46} +4.88337e17 q^{47} +3.77020e17 q^{49} -8.72861e16 q^{50} +1.05246e18 q^{52} +2.17151e17 q^{53} -5.71867e17 q^{55} -2.97154e18 q^{56} +9.61640e17 q^{58} -3.50397e18 q^{59} -5.82465e18 q^{61} -2.47853e18 q^{62} +6.11167e18 q^{64} +8.16066e18 q^{65} +2.95753e19 q^{67} +3.62851e18 q^{68} -8.64534e18 q^{70} +2.20469e19 q^{71} +3.95169e19 q^{73} -3.28325e18 q^{74} +1.59159e19 q^{76} -5.66412e19 q^{77} -1.49205e19 q^{79} +1.66577e18 q^{80} -7.53239e19 q^{82} +8.63032e19 q^{83} +2.81350e19 q^{85} -2.89372e19 q^{86} +1.79904e20 q^{88} +8.04804e19 q^{89} +8.08282e20 q^{91} -4.33554e20 q^{92} -4.46956e20 q^{94} +1.23410e20 q^{95} -5.75262e19 q^{97} -3.45072e20 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 575 q^{2} + 8338341 q^{4} - 68359375 q^{5} + 59286610 q^{7} - 602858175 q^{8}+O(q^{10}) \) 7 * q + 575 * q^2 + 8338341 * q^4 - 68359375 * q^5 + 59286610 * q^7 - 602858175 * q^8	\( 7 q + 575 q^{2} + 8338341 q^{4} - 68359375 q^{5} + 59286610 q^{7} - 602858175 q^{8} - 5615234375 q^{10} - 140355265750 q^{11} - 208991867340 q^{13} + 1796874777750 q^{14} + 12803748698673 q^{16} + 1128139963850 q^{17} - 15344485652652 q^{19} - 81429111328125 q^{20} - 2813591285650 q^{22} + 112588829920200 q^{23} + 667572021484375 q^{25} - 261343603553500 q^{26} + 45\!\cdots\!30 q^{28}+ \cdots + 10\!\cdots\!75 q^{98}+O(q^{100}) \) 7 * q + 575 * q^2 + 8338341 * q^4 - 68359375 * q^5 + 59286610 * q^7 - 602858175 * q^8 - 5615234375 * q^10 - 140355265750 * q^11 - 208991867340 * q^13 + 1796874777750 * q^14 + 12803748698673 * q^16 + 1128139963850 * q^17 - 15344485652652 * q^19 - 81429111328125 * q^20 - 2813591285650 * q^22 + 112588829920200 * q^23 + 667572021484375 * q^25 - 261343603553500 * q^26 + 4575704582134330 * q^28 - 4510314655295750 * q^29 + 9307677897566716 * q^31 - 18986436031637975 * q^32 + 19110615925476890 * q^34 - 578970800781250 * q^35 - 3659765919950920 * q^37 - 148014269948202700 * q^38 + 5887286865234375 * q^40 - 229063383838346000 * q^41 + 267726514729849560 * q^43 - 528752916336974750 * q^44 - 1150803639936246720 * q^46 + 199817668629879800 * q^47 - 626984501359908149 * q^49 + 54836273193359375 * q^50 - 1938845750001596020 * q^52 - 313454513779361350 * q^53 + 1370656892089843750 * q^55 + 4764746750564345250 * q^56 + 4780338115165635850 * q^58 + 5389196037389518250 * q^59 + 1868229488329518174 * q^61 + 24558299772652382100 * q^62 + 6017351694526520689 * q^64 + 2040936204492187500 * q^65 + 30280970729577023260 * q^67 - 26296226809433348450 * q^68 - 17547605251464843750 * q^70 + 26220232923451409500 * q^71 - 89207100808924659270 * q^73 - 72106964934167693000 * q^74 - 6514482616986768676 * q^76 - 153387195834733012500 * q^77 - 77958551277728196308 * q^79 - 125036608385478515625 * q^80 - 238268753859115035200 * q^82 - 325542858541808727900 * q^83 - 11016991834472656250 * q^85 - 326607069085333441000 * q^86 - 44497535431219080150 * q^88 + 370010788821361177500 * q^89 + 249148676379154429400 * q^91 - 172959882955623644400 * q^92 + 196640777968603613120 * q^94 + 149848492701679687500 * q^95 + 913937589584017744910 * q^97 + 1008191498872893333475 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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