LMFDB - Embedded newform 45.28.a.d.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,28,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, 28, names="a")

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

chi := DirichletCharacter("45.1");

S:= CuspForms(chi, 28);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 28 $
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:	$207.835008677$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 105406182x^{3} - 8285617904x^{2} + 1593173725628800x - 1939393055148057600 $ x^5 - 2x^4 - 105406182x^3 - 8285617904x^2 + 1593173725628800x - 1939393055148057600
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{9}\cdot 5^{4}\cdot 7 $
Twist minimal:	no (minimal twist has level 5)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$9540.66$ 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)

$f(q)$	$=$	$q+15097.3 q^{2} +9.37113e7 q^{4} +1.22070e9 q^{5} +2.87369e11 q^{7} -6.11538e11 q^{8} +O(q^{10})$	\(q+15097.3 q^{2} +9.37113e7 q^{4} +1.22070e9 q^{5} +2.87369e11 q^{7} -6.11538e11 q^{8} +1.84293e13 q^{10} +1.77257e14 q^{11} -5.40271e14 q^{13} +4.33850e15 q^{14} -2.18103e16 q^{16} -5.58399e15 q^{17} +1.87919e17 q^{19} +1.14394e17 q^{20} +2.67611e18 q^{22} +1.25303e18 q^{23} +1.49012e18 q^{25} -8.15664e18 q^{26} +2.69297e19 q^{28} -5.09124e19 q^{29} +2.57384e20 q^{31} -2.47198e20 q^{32} -8.43033e19 q^{34} +3.50792e20 q^{35} -6.56249e20 q^{37} +2.83707e21 q^{38} -7.46507e20 q^{40} -4.64407e20 q^{41} +7.04216e21 q^{43} +1.66110e22 q^{44} +1.89174e22 q^{46} +7.81638e21 q^{47} +1.68684e22 q^{49} +2.24968e22 q^{50} -5.06295e22 q^{52} -3.58001e23 q^{53} +2.16379e23 q^{55} -1.75737e23 q^{56} -7.68640e23 q^{58} +1.07015e24 q^{59} +2.22872e24 q^{61} +3.88580e24 q^{62} -8.04695e23 q^{64} -6.59510e23 q^{65} +1.96786e23 q^{67} -5.23283e23 q^{68} +5.29602e24 q^{70} -1.57561e25 q^{71} +5.36070e24 q^{73} -9.90760e24 q^{74} +1.76101e25 q^{76} +5.09382e25 q^{77} -5.98177e25 q^{79} -2.66239e25 q^{80} -7.01130e24 q^{82} -1.26229e25 q^{83} -6.81640e24 q^{85} +1.06318e26 q^{86} -1.08400e26 q^{88} -4.25414e25 q^{89} -1.55257e26 q^{91} +1.17423e26 q^{92} +1.18006e26 q^{94} +2.29393e26 q^{95} +1.03333e27 q^{97} +2.54668e26 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 19916 q^{2} + 251490240 q^{4} + 6103515625 q^{5} + 155646348206 q^{7} - 4844427693600 q^{8}+O(q^{10}) $ 5 * q - 19916 * q^2 + 251490240 * q^4 + 6103515625 * q^5 + 155646348206 * q^7 - 4844427693600 * q^8	$ 5 q - 19916 q^{2} + 251490240 q^{4} + 6103515625 q^{5} + 155646348206 q^{7} - 4844427693600 q^{8} - 24311523437500 q^{10} + 34307841041440 q^{11} + 12\!\cdots\!22 q^{13}+ \cdots + 24\!\cdots\!12 q^{98}+O(q^{100}) $ 5 * q - 19916 * q^2 + 251490240 * q^4 + 6103515625 * q^5 + 155646348206 * q^7 - 4844427693600 * q^8 - 24311523437500 * q^10 + 34307841041440 * q^11 + 1264965428684322 * q^13 + 1494481038585720 * q^14 + 50480141682449280 * q^16 - 11381432659133186 * q^17 - 177889284152803500 * q^19 + 306994921875000000 * q^20 + 1661117755714509952 * q^22 - 5314231426153528362 * q^23 + 7450580596923828125 * q^25 - 64194207115665583160 * q^26 + 74243491650979261568 * q^28 - 142675767255557016550 * q^29 + 490757140558660526660 * q^31 - 709255558573159910656 * q^32 - 823451155892216853320 * q^34 + 189997983649902343750 * q^35 - 1594690133202798011054 * q^37 + 8102840491936976962000 * q^38 - 5913608024414062500000 * q^40 + 14453824011731896105490 * q^41 - 6456338188721923591758 * q^43 + 61776067586935488773120 * q^44 + 41662242513049160161560 * q^46 - 19960747396802751518726 * q^47 + 64529931934369352760065 * q^49 - 29677152633666992187500 * q^50 + 694364047806293961951616 * q^52 - 203485571063020242199082 * q^53 + 41879688771289062500000 * q^55 + 514718506150627561339200 * q^56 - 568257469475936639738200 * q^58 + 1753694580358227494398300 * q^59 - 1715799924029775655491390 * q^61 - 856653132512718918087792 * q^62 + 2825791291455308901232640 * q^64 + 1544147251811916503906250 * q^65 - 52283413307813388053914 * q^67 + 18798756173665084661988992 * q^68 + 1824317674054833984375000 * q^70 - 13737346388576400396156460 * q^71 + 52785881484144679283287962 * q^73 - 44617246831379823508169080 * q^74 - 50943444226830794465542400 * q^76 - 40527442829187717880256832 * q^77 - 18659027886608771061377800 * q^79 + 61621266702208593750000000 * q^80 - 233045910890443727506605688 * q^82 + 49391953045615520178004398 * q^83 - 13893350413980939941406250 * q^85 + 246095687260751641221151240 * q^86 - 662199546636275930413900800 * q^88 - 180573322691431536135373650 * q^89 + 317295677016426969579588460 * q^91 + 379021343242797571985691264 * q^92 - 34623503302055809185576920 * q^94 - 217150005069340209960937500 * q^95 + 1118012018325586896775804426 * q^97 + 243326561625995319625007012 * 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 $

$2$	15097.3	1.30315	0.651576	−	0.758584i	$-0.274108\pi$
$2$	15097.3	1.30315	0.651576	+	0.758584i	$0.274108\pi$
$3$	0	0
$3$	0	0
$4$	9.37113e7	0.698204
$5$	1.22070e9	0.447214
$5$	1.22070e9	0.447214
$6$	0	0
$7$	2.87369e11	1.12103	0.560513	−	0.828145i	$-0.310604\pi$
$7$	2.87369e11	1.12103	0.560513	+	0.828145i	$0.310604\pi$
$8$	−6.11538e11	−0.393286
$9$	0	0
$10$	1.84293e13	0.582787
$11$	1.77257e14	1.54812	0.774058	−	0.633115i	$-0.218224\pi$
$11$	1.77257e14	1.54812	0.774058	+	0.633115i	$0.218224\pi$
$12$	0	0
$13$	−5.40271e14	−0.494739	−0.247370	−	0.968921i	$-0.579566\pi$
$13$	−5.40271e14	−0.494739	−0.247370	+	0.968921i	$0.579566\pi$
$14$	4.33850e15	1.46087
$15$	0	0
$16$	−2.18103e16	−1.21072
$17$	−5.58399e15	−0.136736	−0.0683682	−	0.997660i	$-0.521779\pi$
$17$	−5.58399e15	−0.136736	−0.0683682	+	0.997660i	$0.521779\pi$
$18$	0	0
$19$	1.87919e17	1.02517	0.512586	−	0.858636i	$-0.328688\pi$
$19$	1.87919e17	1.02517	0.512586	+	0.858636i	$0.328688\pi$
$20$	1.14394e17	0.312246
$21$	0	0
$22$	2.67611e18	2.01743
$23$	1.25303e18	0.518366	0.259183	−	0.965828i	$-0.416547\pi$
$23$	1.25303e18	0.518366	0.259183	+	0.965828i	$0.416547\pi$
$24$	0	0
$25$	1.49012e18	0.200000
$26$	−8.15664e18	−0.644720
$27$	0	0
$28$	2.69297e19	0.782705
$29$	−5.09124e19	−0.921404	−0.460702	−	0.887555i	$-0.652402\pi$
$29$	−5.09124e19	−0.921404	−0.460702	+	0.887555i	$0.652402\pi$
$30$	0	0
$31$	2.57384e20	1.89321	0.946604	−	0.322399i	$-0.104489\pi$
$31$	2.57384e20	1.89321	0.946604	+	0.322399i	$0.104489\pi$
$32$	−2.47198e20	−1.18446
$33$	0	0
$34$	−8.43033e19	−0.178188
$35$	3.50792e20	0.501338
$36$	0	0
$37$	−6.56249e20	−0.442941	−0.221470	−	0.975167i	$-0.571086\pi$
$37$	−6.56249e20	−0.442941	−0.221470	+	0.975167i	$0.571086\pi$
$38$	2.83707e21	1.33595
$39$	0	0
$40$	−7.46507e20	−0.175883
$41$	−4.64407e20	−0.0784001	−0.0392001	−	0.999231i	$-0.512481\pi$
$41$	−4.64407e20	−0.0784001	−0.0392001	+	0.999231i	$0.512481\pi$
$42$	0	0
$43$	7.04216e21	0.625003	0.312501	−	0.949917i	$-0.398833\pi$
$43$	7.04216e21	0.625003	0.312501	+	0.949917i	$0.398833\pi$
$44$	1.66110e22	1.08090
$45$	0	0
$46$	1.89174e22	0.675509
$47$	7.81638e21	0.208778	0.104389	−	0.994537i	$-0.466711\pi$
$47$	7.81638e21	0.208778	0.104389	+	0.994537i	$0.466711\pi$
$48$	0	0
$49$	1.68684e22	0.256701
$50$	2.24968e22	0.260630
$51$	0	0
$52$	−5.06295e22	−0.345429
$53$	−3.58001e23	−1.88868	−0.944342	−	0.328964i	$-0.893301\pi$
$53$	−3.58001e23	−1.88868	−0.944342	+	0.328964i	$0.893301\pi$
$54$	0	0
$55$	2.16379e23	0.692338
$56$	−1.75737e23	−0.440885
$57$	0	0
$58$	−7.68640e23	−1.20073
$59$	1.07015e24	1.32722	0.663609	−	0.748080i	$-0.269024\pi$
$59$	1.07015e24	1.32722	0.663609	+	0.748080i	$0.269024\pi$
$60$	0	0
$61$	2.22872e24	1.76240	0.881198	−	0.472747i	$-0.156738\pi$
$61$	2.22872e24	1.76240	0.881198	+	0.472747i	$0.156738\pi$
$62$	3.88580e24	2.46714
$63$	0	0
$64$	−8.04695e23	−0.332814
$65$	−6.59510e23	−0.221254
$66$	0	0
$67$	1.96786e23	0.0438516	0.0219258	−	0.999760i	$-0.493020\pi$
$67$	1.96786e23	0.0438516	0.0219258	+	0.999760i	$0.493020\pi$
$68$	−5.23283e23	−0.0954699
$69$	0	0
$70$	5.29602e24	0.653320
$71$	−1.57561e25	−1.60495	−0.802476	−	0.596684i	$-0.796485\pi$
$71$	−1.57561e25	−1.60495	−0.802476	+	0.596684i	$0.796485\pi$
$72$	0	0
$73$	5.36070e24	0.375287	0.187643	−	0.982237i	$-0.439915\pi$
$73$	5.36070e24	0.375287	0.187643	+	0.982237i	$0.439915\pi$
$74$	−9.90760e24	−0.577219
$75$	0	0
$76$	1.76101e25	0.715778
$77$	5.09382e25	1.73548
$78$	0	0
$79$	−5.98177e25	−1.44166	−0.720831	−	0.693110i	$-0.756240\pi$
$79$	−5.98177e25	−1.44166	−0.720831	+	0.693110i	$0.756240\pi$
$80$	−2.66239e25	−0.541448
$81$	0	0
$82$	−7.01130e24	−0.102167
$83$	−1.26229e25	−0.156173	−0.0780865	−	0.996947i	$-0.524881\pi$
$83$	−1.26229e25	−0.156173	−0.0780865	+	0.996947i	$0.524881\pi$
$84$	0	0
$85$	−6.81640e24	−0.0611504
$86$	1.06318e26	0.814473
$87$	0	0
$88$	−1.08400e26	−0.608853
$89$	−4.25414e25	−0.205138	−0.102569	−	0.994726i	$-0.532706\pi$
$89$	−4.25414e25	−0.205138	−0.102569	+	0.994726i	$0.532706\pi$
$90$	0	0
$91$	−1.55257e26	−0.554616
$92$	1.17423e26	0.361925
$93$	0	0
$94$	1.18006e26	0.272069
$95$	2.29393e26	0.458471
$96$	0	0
$97$	1.03333e27	1.55890	0.779451	−	0.626463i	$-0.215498\pi$
$97$	1.03333e27	1.55890	0.779451	+	0.626463i	$0.215498\pi$
$98$	2.54668e26	0.334520
$99$	0	0
$100$	1.39641e26	0.139641
$101$	1.55113e26	0.135615	0.0678076	−	0.997698i	$-0.478400\pi$
$101$	1.55113e26	0.135615	0.0678076	+	0.997698i	$0.478400\pi$
$102$	0	0
$103$	2.35098e27	1.57742	0.788708	−	0.614769i	$-0.210751\pi$
$103$	2.35098e27	1.57742	0.788708	+	0.614769i	$0.210751\pi$
$104$	3.30396e26	0.194574
$105$	0	0
$106$	−5.40485e27	−2.46124
$107$	2.44047e26	0.0979023	0.0489511	−	0.998801i	$-0.484412\pi$
$107$	2.44047e26	0.0979023	0.0489511	+	0.998801i	$0.484412\pi$
$108$	0	0
$109$	3.61017e27	1.12790	0.563950	−	0.825809i	$-0.309281\pi$
$109$	3.61017e27	1.12790	0.563950	+	0.825809i	$0.309281\pi$
$110$	3.26674e27	0.902221
$111$	0	0
$112$	−6.26760e27	−1.35724
$113$	5.56378e27	1.06859	0.534295	−	0.845298i	$-0.320577\pi$
$113$	5.56378e27	1.06859	0.534295	+	0.845298i	$0.320577\pi$
$114$	0	0
$115$	1.52958e27	0.231820
$116$	−4.77106e27	−0.643328
$117$	0	0
$118$	1.61564e28	1.72957
$119$	−1.60466e27	−0.153285
$120$	0	0
$121$	1.83102e28	1.39666
$122$	3.36478e28	2.29667
$123$	0	0
$124$	2.41198e28	1.32184
$125$	1.81899e27	0.0894427
$126$	0	0
$127$	−2.95605e28	−1.17317	−0.586586	−	0.809887i	$-0.699528\pi$
$127$	−2.95605e28	−1.17317	−0.586586	+	0.809887i	$0.699528\pi$
$128$	2.10296e28	0.750752
$129$	0	0
$130$	−9.95684e27	−0.288328
$131$	−1.44057e27	−0.0376159	−0.0188079	−	0.999823i	$-0.505987\pi$
$131$	−1.44057e27	−0.0376159	−0.0188079	+	0.999823i	$0.505987\pi$
$132$	0	0
$133$	5.40020e28	1.14924
$134$	2.97095e27	0.0571452
$135$	0	0
$136$	3.41483e27	0.0537766
$137$	1.27731e29	1.82208	0.911042	−	0.412314i	$-0.135279\pi$
$137$	1.27731e29	1.82208	0.911042	+	0.412314i	$0.135279\pi$
$138$	0	0
$139$	8.34835e28	0.979266	0.489633	−	0.871929i	$-0.337131\pi$
$139$	8.34835e28	0.979266	0.489633	+	0.871929i	$0.337131\pi$
$140$	3.28732e28	0.350036
$141$	0	0
$142$	−2.37876e29	−2.09150
$143$	−9.57671e28	−0.765913
$144$	0	0
$145$	−6.21489e28	−0.412065
$146$	8.09322e28	0.489055
$147$	0	0
$148$	−6.14980e28	−0.309263
$149$	3.11164e28	0.142881	0.0714405	−	0.997445i	$-0.477240\pi$
$149$	3.11164e28	0.142881	0.0714405	+	0.997445i	$0.477240\pi$
$150$	0	0
$151$	−4.70383e28	−0.180411	−0.0902055	−	0.995923i	$-0.528752\pi$
$151$	−4.70383e28	−0.180411	−0.0902055	+	0.995923i	$0.528752\pi$
$152$	−1.14920e29	−0.403186
$153$	0	0
$154$	7.69031e29	2.26159
$155$	3.14189e29	0.846668
$156$	0	0
$157$	6.83044e29	1.54812	0.774058	−	0.633115i	$-0.218224\pi$
$157$	6.83044e29	1.54812	0.774058	+	0.633115i	$0.218224\pi$
$158$	−9.03086e29	−1.87871
$159$	0	0
$160$	−3.01755e29	−0.529706
$161$	3.60082e29	0.581102
$162$	0	0
$163$	−7.19695e29	−0.983142	−0.491571	−	0.870838i	$-0.663577\pi$
$163$	−7.19695e29	−0.983142	−0.491571	+	0.870838i	$0.663577\pi$
$164$	−4.35202e28	−0.0547393
$165$	0	0
$166$	−1.90572e29	−0.203517
$167$	1.55012e30	1.52649	0.763243	−	0.646112i	$-0.223606\pi$
$167$	1.55012e30	1.52649	0.763243	+	0.646112i	$0.223606\pi$
$168$	0	0
$169$	−9.00641e29	−0.755233
$170$	−1.02909e29	−0.0796882
$171$	0	0
$172$	6.59930e29	0.436379
$173$	−2.49989e29	−0.152862	−0.0764308	−	0.997075i	$-0.524352\pi$
$173$	−2.49989e29	−0.152862	−0.0764308	+	0.997075i	$0.524352\pi$
$174$	0	0
$175$	4.28213e29	0.224205
$176$	−3.86604e30	−1.87433
$177$	0	0
$178$	−6.42261e29	−0.267326
$179$	−5.35930e29	−0.206820	−0.103410	−	0.994639i	$-0.532975\pi$
$179$	−5.35930e29	−0.206820	−0.103410	+	0.994639i	$0.532975\pi$
$180$	0	0
$181$	1.06765e30	0.354623	0.177312	−	0.984155i	$-0.443260\pi$
$181$	1.06765e30	0.354623	0.177312	+	0.984155i	$0.443260\pi$
$182$	−2.34396e30	−0.722748
$183$	0	0
$184$	−7.66277e29	−0.203866
$185$	−8.01085e29	−0.198089
$186$	0	0
$187$	−9.89804e29	−0.211684
$188$	7.32483e29	0.145770
$189$	0	0
$190$	3.46322e30	0.597457
$191$	−9.45195e30	−1.51905	−0.759523	−	0.650480i	$-0.774568\pi$
$191$	−9.45195e30	−1.51905	−0.759523	+	0.650480i	$0.774568\pi$
$192$	0	0
$193$	−5.25368e30	−0.733567	−0.366784	−	0.930306i	$-0.619541\pi$
$193$	−5.25368e30	−0.733567	−0.366784	+	0.930306i	$0.619541\pi$
$194$	1.56005e31	2.03149
$195$	0	0
$196$	1.58076e30	0.179229
$197$	−1.39226e31	−1.47376	−0.736881	−	0.676023i	$-0.763702\pi$
$197$	−1.39226e31	−1.47376	−0.736881	+	0.676023i	$0.763702\pi$
$198$	0	0
$199$	5.72042e30	0.528337	0.264169	−	0.964477i	$-0.414902\pi$
$199$	5.72042e30	0.528337	0.264169	+	0.964477i	$0.414902\pi$
$200$	−9.11263e29	−0.0786573
$201$	0	0
$202$	2.34178e30	0.176727
$203$	−1.46306e31	−1.03292
$204$	0	0
$205$	−5.66903e29	−0.0350616
$206$	3.54935e31	2.05561
$207$	0	0
$208$	1.17835e31	0.598988
$209$	3.33100e31	1.58708
$210$	0	0
$211$	−2.51790e31	−1.05493	−0.527466	−	0.849576i	$-0.676858\pi$
$211$	−2.51790e31	−1.05493	−0.527466	+	0.849576i	$0.676858\pi$
$212$	−3.35487e31	−1.31869
$213$	0	0
$214$	3.68446e30	0.127582
$215$	8.59639e30	0.279510
$216$	0	0
$217$	7.39640e31	2.12234
$218$	5.45039e31	1.46982
$219$	0	0
$220$	2.02771e31	0.483393
$221$	3.01687e30	0.0676489
$222$	0	0
$223$	6.27350e31	1.24565	0.622823	−	0.782363i	$-0.285986\pi$
$223$	6.27350e31	1.24565	0.622823	+	0.782363i	$0.285986\pi$
$224$	−7.10369e31	−1.32781
$225$	0	0
$226$	8.39982e31	1.39253
$227$	1.05511e32	1.64797	0.823986	−	0.566610i	$-0.191745\pi$
$227$	1.05511e32	1.64797	0.823986	+	0.566610i	$0.191745\pi$
$228$	0	0
$229$	−1.85493e31	−0.257365	−0.128682	−	0.991686i	$-0.541075\pi$
$229$	−1.85493e31	−0.257365	−0.128682	+	0.991686i	$0.541075\pi$
$230$	2.30926e31	0.302097
$231$	0	0
$232$	3.11349e31	0.362376
$233$	1.31699e32	1.44636	0.723182	−	0.690657i	$-0.242679\pi$
$233$	1.31699e32	1.44636	0.723182	+	0.690657i	$0.242679\pi$
$234$	0	0
$235$	9.54148e30	0.0933683
$236$	1.00285e32	0.926668
$237$	0	0
$238$	−2.42261e31	−0.199754
$239$	9.69261e31	0.755212	0.377606	−	0.925966i	$-0.376747\pi$
$239$	9.69261e31	0.755212	0.377606	+	0.925966i	$0.376747\pi$
$240$	0	0
$241$	1.77783e32	1.23783	0.618913	−	0.785460i	$-0.287573\pi$
$241$	1.77783e32	1.23783	0.618913	+	0.785460i	$0.287573\pi$
$242$	2.76435e32	1.82006
$243$	0	0
$244$	2.08857e32	1.23051
$245$	2.05913e31	0.114800
$246$	0	0
$247$	−1.01527e32	−0.507193
$248$	−1.57400e32	−0.744573
$249$	0	0
$250$	2.74619e31	0.116557
$251$	−3.33859e32	−1.34267	−0.671333	−	0.741156i	$-0.734278\pi$
$251$	−3.33859e32	−1.34267	−0.671333	+	0.741156i	$0.734278\pi$
$252$	0	0
$253$	2.22109e32	0.802490
$254$	−4.46284e32	−1.52882
$255$	0	0
$256$	4.25495e32	1.31116
$257$	3.75072e32	1.09652	0.548261	−	0.836308i	$-0.315290\pi$
$257$	3.75072e32	1.09652	0.548261	+	0.836308i	$0.315290\pi$
$258$	0	0
$259$	−1.88585e32	−0.496548
$260$	−6.18036e31	−0.154480
$261$	0	0
$262$	−2.17487e31	−0.0490192
$263$	−2.40881e32	−0.515704	−0.257852	−	0.966184i	$-0.583015\pi$
$263$	−2.40881e32	−0.515704	−0.257852	+	0.966184i	$0.583015\pi$
$264$	0	0
$265$	−4.37012e32	−0.844646
$266$	8.15285e32	1.49764
$267$	0	0
$268$	1.84411e31	0.0306173
$269$	−2.39271e32	−0.377775	−0.188888	−	0.981999i	$-0.560488\pi$
$269$	−2.39271e32	−0.377775	−0.188888	+	0.981999i	$0.560488\pi$
$270$	0	0
$271$	−7.45798e31	−0.106546	−0.0532728	−	0.998580i	$-0.516965\pi$
$271$	−7.45798e31	−0.106546	−0.0532728	+	0.998580i	$0.516965\pi$
$272$	1.21789e32	0.165549
$273$	0	0
$274$	1.92839e33	2.37445
$275$	2.64134e32	0.309623
$276$	0	0
$277$	9.78299e32	1.03991	0.519954	−	0.854194i	$-0.325949\pi$
$277$	9.78299e32	1.03991	0.519954	+	0.854194i	$0.325949\pi$
$278$	1.26038e33	1.27613
$279$	0	0
$280$	−2.14523e32	−0.197170
$281$	9.49277e31	0.0831491	0.0415746	−	0.999135i	$-0.486763\pi$
$281$	9.49277e31	0.0831491	0.0415746	+	0.999135i	$0.486763\pi$
$282$	0	0
$283$	1.26463e33	1.00658	0.503289	−	0.864118i	$-0.332123\pi$
$283$	1.26463e33	1.00658	0.503289	+	0.864118i	$0.332123\pi$
$284$	−1.47653e33	−1.12058
$285$	0	0
$286$	−1.44583e33	−0.998101
$287$	−1.33456e32	−0.0878886
$288$	0	0
$289$	−1.63653e33	−0.981303
$290$	−9.38281e32	−0.536983
$291$	0	0
$292$	5.02358e32	0.262026
$293$	−3.27505e33	−1.63119	−0.815595	−	0.578623i	$-0.803590\pi$
$293$	−3.27505e33	−1.63119	−0.815595	+	0.578623i	$0.803590\pi$
$294$	0	0
$295$	1.30633e33	0.593550
$296$	4.01322e32	0.174202
$297$	0	0
$298$	4.69774e32	0.186196
$299$	−6.76977e32	−0.256456
$300$	0	0
$301$	2.02370e33	0.700645
$302$	−7.10152e32	−0.235103
$303$	0	0
$304$	−4.09857e33	−1.24119
$305$	2.72061e33	0.788167
$306$	0	0
$307$	1.52157e33	0.403576	0.201788	−	0.979429i	$-0.435325\pi$
$307$	1.52157e33	0.403576	0.201788	+	0.979429i	$0.435325\pi$
$308$	4.77349e33	1.21172
$309$	0	0
$310$	4.74341e33	1.10334
$311$	−6.05603e33	−1.34872	−0.674361	−	0.738401i	$-0.735581\pi$
$311$	−6.05603e33	−1.34872	−0.674361	+	0.738401i	$0.735581\pi$
$312$	0	0
$313$	−4.61245e33	−0.942070	−0.471035	−	0.882115i	$-0.656119\pi$
$313$	−4.61245e33	−0.942070	−0.471035	+	0.882115i	$0.656119\pi$
$314$	1.03121e34	2.01743
$315$	0	0
$316$	−5.60559e33	−1.00657
$317$	4.71631e33	0.811525	0.405762	−	0.913979i	$-0.367006\pi$
$317$	4.71631e33	0.811525	0.405762	+	0.913979i	$0.367006\pi$
$318$	0	0
$319$	−9.02460e33	−1.42644
$320$	−9.82294e32	−0.148839
$321$	0	0
$322$	5.43628e33	0.757264
$323$	−1.04934e33	−0.140178
$324$	0	0
$325$	−8.05067e32	−0.0989479
$326$	−1.08655e34	−1.28118
$327$	0	0
$328$	2.84003e32	0.0308337
$329$	2.24618e33	0.234046
$330$	0	0
$331$	4.55532e33	0.437362	0.218681	−	0.975796i	$-0.429825\pi$
$331$	4.55532e33	0.437362	0.218681	+	0.975796i	$0.429825\pi$
$332$	−1.18291e33	−0.109041
$333$	0	0
$334$	2.34026e34	1.98924
$335$	2.40218e32	0.0196110
$336$	0	0
$337$	1.35057e34	1.01745	0.508724	−	0.860929i	$-0.330117\pi$
$337$	1.35057e34	1.01745	0.508724	+	0.860929i	$0.330117\pi$
$338$	−1.35973e34	−0.984183
$339$	0	0
$340$	−6.38773e32	−0.0426954
$341$	4.56232e34	2.93090
$342$	0	0
$343$	−1.40362e34	−0.833258
$344$	−4.30655e33	−0.245805
$345$	0	0
$346$	−3.77416e33	−0.199202
$347$	1.00035e34	0.507815	0.253907	−	0.967229i	$-0.418284\pi$
$347$	1.00035e34	0.507815	0.253907	+	0.967229i	$0.418284\pi$
$348$	0	0
$349$	−1.49380e34	−0.701694	−0.350847	−	0.936433i	$-0.614106\pi$
$349$	−1.49380e34	−0.701694	−0.350847	+	0.936433i	$0.614106\pi$
$350$	6.46486e33	0.292173
$351$	0	0
$352$	−4.38177e34	−1.83368
$353$	−1.51465e34	−0.610033	−0.305017	−	0.952347i	$-0.598662\pi$
$353$	−1.51465e34	−0.610033	−0.305017	+	0.952347i	$0.598662\pi$
$354$	0	0
$355$	−1.92336e34	−0.717757
$356$	−3.98661e33	−0.143228
$357$	0	0
$358$	−8.09111e33	−0.269518
$359$	−5.09141e34	−1.63329	−0.816644	−	0.577142i	$-0.804168\pi$
$359$	−5.09141e34	−1.63329	−0.816644	+	0.577142i	$0.804168\pi$
$360$	0	0
$361$	1.71285e33	0.0509766
$362$	1.61186e34	0.462128
$363$	0	0
$364$	−1.45493e34	−0.387235
$365$	6.54382e33	0.167833
$366$	0	0
$367$	−1.50646e34	−0.358894	−0.179447	−	0.983768i	$-0.557431\pi$
$367$	−1.50646e34	−0.358894	−0.179447	+	0.983768i	$0.557431\pi$
$368$	−2.73290e34	−0.627594
$369$	0	0
$370$	−1.20942e34	−0.258140
$371$	−1.02878e35	−2.11727
$372$	0	0
$373$	−6.81098e34	−1.30359	−0.651794	−	0.758396i	$-0.725984\pi$
$373$	−6.81098e34	−1.30359	−0.651794	+	0.758396i	$0.725984\pi$
$374$	−1.49434e34	−0.275856
$375$	0	0
$376$	−4.78002e33	−0.0821095
$377$	2.75065e34	0.455855
$378$	0	0
$379$	7.11379e34	1.09767	0.548835	−	0.835931i	$-0.315072\pi$
$379$	7.11379e34	1.09767	0.548835	+	0.835931i	$0.315072\pi$
$380$	2.14967e34	0.320106
$381$	0	0
$382$	−1.42699e35	−1.97955
$383$	−3.51669e34	−0.470923	−0.235462	−	0.971884i	$-0.575660\pi$
$383$	−3.51669e34	−0.470923	−0.235462	+	0.971884i	$0.575660\pi$
$384$	0	0
$385$	6.21805e34	0.776129
$386$	−7.93165e34	−0.955949
$387$	0	0
$388$	9.68343e34	1.08843
$389$	−7.65694e34	−0.831257	−0.415629	−	0.909534i	$-0.636438\pi$
$389$	−7.65694e34	−0.831257	−0.415629	+	0.909534i	$0.636438\pi$
$390$	0	0
$391$	−6.99692e33	−0.0708795
$392$	−1.03157e34	−0.100957
$393$	0	0
$394$	−2.10194e35	−1.92053
$395$	−7.30196e34	−0.644731
$396$	0	0
$397$	−1.21681e34	−0.100358	−0.0501788	−	0.998740i	$-0.515979\pi$
$397$	−1.21681e34	−0.100358	−0.0501788	+	0.998740i	$0.515979\pi$
$398$	8.63630e34	0.688504
$399$	0	0
$400$	−3.24999e34	−0.242143
$401$	6.96921e34	0.502036	0.251018	−	0.967982i	$-0.419235\pi$
$401$	6.96921e34	0.502036	0.251018	+	0.967982i	$0.419235\pi$
$402$	0	0
$403$	−1.39057e35	−0.936644
$404$	1.45358e34	0.0946870
$405$	0	0
$406$	−2.20883e35	−1.34605
$407$	−1.16325e35	−0.685723
$408$	0	0
$409$	−5.80856e34	−0.320482	−0.160241	−	0.987078i	$-0.551227\pi$
$409$	−5.80856e34	−0.320482	−0.160241	+	0.987078i	$0.551227\pi$
$410$	−8.55872e33	−0.0456906
$411$	0	0
$412$	2.20313e35	1.10136
$413$	3.07527e35	1.48785
$414$	0	0
$415$	−1.54088e34	−0.0698427
$416$	1.33554e35	0.585998
$417$	0	0
$418$	5.02892e35	2.06821
$419$	−1.98341e35	−0.789811	−0.394906	−	0.918722i	$-0.629223\pi$
$419$	−1.98341e35	−0.789811	−0.394906	+	0.918722i	$0.629223\pi$
$420$	0	0
$421$	6.83497e34	0.255228	0.127614	−	0.991824i	$-0.459268\pi$
$421$	6.83497e34	0.255228	0.127614	+	0.991824i	$0.459268\pi$
$422$	−3.80135e35	−1.37474
$423$	0	0
$424$	2.18931e35	0.742794
$425$	−8.32080e33	−0.0273473
$426$	0	0
$427$	6.40465e35	1.97569
$428$	2.28700e34	0.0683557
$429$	0	0
$430$	1.29782e35	0.364243
$431$	−4.62647e34	−0.125837	−0.0629183	−	0.998019i	$-0.520041\pi$
$431$	−4.62647e34	−0.125837	−0.0629183	+	0.998019i	$0.520041\pi$
$432$	0	0
$433$	−5.70094e35	−1.45667	−0.728333	−	0.685223i	$-0.759705\pi$
$433$	−5.70094e35	−1.45667	−0.728333	+	0.685223i	$0.759705\pi$
$434$	1.11666e36	2.76573
$435$	0	0
$436$	3.38314e35	0.787503
$437$	2.35468e35	0.531414
$438$	0	0
$439$	9.22423e34	0.195731	0.0978654	−	0.995200i	$-0.468799\pi$
$439$	9.22423e34	0.195731	0.0978654	+	0.995200i	$0.468799\pi$
$440$	−1.32324e35	−0.272287
$441$	0	0
$442$	4.55466e34	0.0881568
$443$	−3.35418e35	−0.629704	−0.314852	−	0.949141i	$-0.601955\pi$
$443$	−3.35418e35	−0.629704	−0.314852	+	0.949141i	$0.601955\pi$
$444$	0	0
$445$	−5.19305e34	−0.0917407
$446$	9.47130e35	1.62326
$447$	0	0
$448$	−2.31244e35	−0.373093
$449$	8.56132e35	1.34034	0.670171	−	0.742207i	$-0.266221\pi$
$449$	8.56132e35	1.34034	0.670171	+	0.742207i	$0.266221\pi$
$450$	0	0
$451$	−8.23196e34	−0.121372
$452$	5.21389e35	0.746093
$453$	0	0
$454$	1.59294e36	2.14756
$455$	−1.89523e35	−0.248032
$456$	0	0
$457$	−1.28712e36	−1.58763	−0.793816	−	0.608158i	$-0.791909\pi$
$457$	−1.28712e36	−1.58763	−0.793816	+	0.608158i	$0.791909\pi$
$458$	−2.80045e35	−0.335385
$459$	0	0
$460$	1.43339e35	0.161858
$461$	−1.21700e36	−1.33453	−0.667264	−	0.744821i	$-0.732535\pi$
$461$	−1.21700e36	−1.33453	−0.667264	+	0.744821i	$0.732535\pi$
$462$	0	0
$463$	−3.33793e35	−0.345250	−0.172625	−	0.984988i	$-0.555225\pi$
$463$	−3.33793e35	−0.345250	−0.172625	+	0.984988i	$0.555225\pi$
$464$	1.11041e36	1.11556
$465$	0	0
$466$	1.98830e36	1.88483
$467$	−1.19656e36	−1.10194	−0.550969	−	0.834526i	$-0.685742\pi$
$467$	−1.19656e36	−1.10194	−0.550969	+	0.834526i	$0.685742\pi$
$468$	0	0
$469$	5.65502e34	0.0491588
$470$	1.44051e35	0.121673
$471$	0	0
$472$	−6.54438e35	−0.521977
$473$	1.24828e36	0.967576
$474$	0	0
$475$	2.80021e35	0.205034
$476$	−1.50375e35	−0.107024
$477$	0	0
$478$	1.46332e36	0.984156
$479$	−1.18973e36	−0.777890	−0.388945	−	0.921261i	$-0.627160\pi$
$479$	−1.18973e36	−0.777890	−0.388945	+	0.921261i	$0.627160\pi$
$480$	0	0
$481$	3.54552e35	0.219140
$482$	2.68404e36	1.61307
$483$	0	0
$484$	1.71587e36	0.975154
$485$	1.26138e36	0.697163
$486$	0	0
$487$	2.01778e36	1.05495	0.527477	−	0.849569i	$-0.323138\pi$
$487$	2.01778e36	1.05495	0.527477	+	0.849569i	$0.323138\pi$
$488$	−1.36295e36	−0.693126
$489$	0	0
$490$	3.10873e35	0.149602
$491$	−8.76148e35	−0.410183	−0.205091	−	0.978743i	$-0.565749\pi$
$491$	−8.76148e35	−0.410183	−0.205091	+	0.978743i	$0.565749\pi$
$492$	0	0
$493$	2.84294e35	0.125990
$494$	−1.53279e36	−0.660949
$495$	0	0
$496$	−5.61362e36	−2.29214
$497$	−4.52782e36	−1.79919
$498$	0	0
$499$	9.64898e35	0.363182	0.181591	−	0.983374i	$-0.441875\pi$
$499$	9.64898e35	0.363182	0.181591	+	0.983374i	$0.441875\pi$
$500$	1.70460e35	0.0624492
$501$	0	0
$502$	−5.04038e36	−1.74970
$503$	−3.79863e36	−1.28369	−0.641844	−	0.766835i	$-0.721830\pi$
$503$	−3.79863e36	−1.28369	−0.641844	+	0.766835i	$0.721830\pi$
$504$	0	0
$505$	1.89346e35	0.0606490
$506$	3.35326e36	1.04577
$507$	0	0
$508$	−2.77015e36	−0.819113
$509$	6.13116e35	0.176544	0.0882719	−	0.996096i	$-0.471866\pi$
$509$	6.13116e35	0.176544	0.0882719	+	0.996096i	$0.471866\pi$
$510$	0	0
$511$	1.54050e36	0.420706
$512$	3.60129e36	0.957885
$513$	0	0
$514$	5.66258e36	1.42893
$515$	2.86985e36	0.705441
$516$	0	0
$517$	1.38551e36	0.323212
$518$	−2.84713e36	−0.647077
$519$	0	0
$520$	4.03316e35	0.0870162
$521$	−6.24114e36	−1.31206	−0.656031	−	0.754734i	$-0.727766\pi$
$521$	−6.24114e36	−1.31206	−0.656031	+	0.754734i	$0.727766\pi$
$522$	0	0
$523$	−2.68065e36	−0.535140	−0.267570	−	0.963538i	$-0.586221\pi$
$523$	−2.68065e36	−0.535140	−0.267570	+	0.963538i	$0.586221\pi$
$524$	−1.34997e35	−0.0262635
$525$	0	0
$526$	−3.63666e36	−0.672040
$527$	−1.43723e36	−0.258871
$528$	0	0
$529$	−4.27312e36	−0.731297
$530$	−6.59772e36	−1.10070
$531$	0	0
$532$	5.06059e36	0.802407
$533$	2.50906e35	0.0387876
$534$	0	0
$535$	2.97909e35	0.0437832
$536$	−1.20342e35	−0.0172462
$537$	0	0
$538$	−3.61235e36	−0.492299
$539$	2.99005e36	0.397402
$540$	0	0
$541$	−6.28935e36	−0.795138	−0.397569	−	0.917572i	$-0.630146\pi$
$541$	−6.28935e36	−0.795138	−0.397569	+	0.917572i	$0.630146\pi$
$542$	−1.12596e36	−0.138845
$543$	0	0
$544$	1.38035e36	0.161959
$545$	4.40695e36	0.504412
$546$	0	0
$547$	−1.06223e37	−1.15715	−0.578574	−	0.815630i	$-0.696391\pi$
$547$	−1.06223e37	−1.15715	−0.578574	+	0.815630i	$0.696391\pi$
$548$	1.19698e37	1.27219
$549$	0	0
$550$	3.98772e36	0.403486
$551$	−9.56739e36	−0.944597
$552$	0	0
$553$	−1.71897e37	−1.61614
$554$	1.47697e37	1.35516
$555$	0	0
$556$	7.82334e36	0.683727
$557$	2.66321e36	0.227175	0.113588	−	0.993528i	$-0.463766\pi$
$557$	2.66321e36	0.227175	0.113588	+	0.993528i	$0.463766\pi$
$558$	0	0
$559$	−3.80468e36	−0.309213
$560$	−7.65088e36	−0.606978
$561$	0	0
$562$	1.43315e36	0.108356
$563$	9.52111e36	0.702788	0.351394	−	0.936228i	$-0.385708\pi$
$563$	9.52111e36	0.702788	0.351394	+	0.936228i	$0.385708\pi$
$564$	0	0
$565$	6.79172e36	0.477888
$566$	1.90926e37	1.31172
$567$	0	0
$568$	9.63549e36	0.631206
$569$	−9.18092e36	−0.587314	−0.293657	−	0.955911i	$-0.594872\pi$
$569$	−9.18092e36	−0.587314	−0.293657	+	0.955911i	$0.594872\pi$
$570$	0	0
$571$	5.22581e36	0.318835	0.159418	−	0.987211i	$-0.449038\pi$
$571$	5.22581e36	0.318835	0.159418	+	0.987211i	$0.449038\pi$
$572$	−8.97446e36	−0.534764
$573$	0	0
$574$	−2.01483e36	−0.114532
$575$	1.86716e36	0.103673
$576$	0	0
$577$	3.25301e37	1.72350	0.861752	−	0.507329i	$-0.169367\pi$
$577$	3.25301e37	1.72350	0.861752	+	0.507329i	$0.169367\pi$
$578$	−2.47072e37	−1.27879
$579$	0	0
$580$	−5.82405e36	−0.287705
$581$	−3.62743e36	−0.175074
$582$	0	0
$583$	−6.34583e37	−2.92390
$584$	−3.27827e36	−0.147595
$585$	0	0
$586$	−4.94444e37	−2.12569
$587$	−5.54641e36	−0.233022	−0.116511	−	0.993189i	$-0.537171\pi$
$587$	−5.54641e36	−0.233022	−0.116511	+	0.993189i	$0.537171\pi$
$588$	0	0
$589$	4.83672e37	1.94086
$590$	1.97222e37	0.773485
$591$	0	0
$592$	1.43130e37	0.536275
$593$	−2.73539e37	−1.00180	−0.500899	−	0.865506i	$-0.666997\pi$
$593$	−2.73539e37	−1.00180	−0.500899	+	0.865506i	$0.666997\pi$
$594$	0	0
$595$	−1.95882e36	−0.0685512
$596$	2.91596e36	0.0997601
$597$	0	0
$598$	−1.02205e37	−0.334201
$599$	−1.30808e37	−0.418188	−0.209094	−	0.977896i	$-0.567051\pi$
$599$	−1.30808e37	−0.418188	−0.209094	+	0.977896i	$0.567051\pi$
$600$	0	0
$601$	−4.39124e35	−0.0134209	−0.00671046	−	0.999977i	$-0.502136\pi$
$601$	−4.39124e35	−0.0134209	−0.00671046	+	0.999977i	$0.502136\pi$
$602$	3.05524e37	0.913046
$603$	0	0
$604$	−4.40802e36	−0.125964
$605$	2.23513e37	0.624606
$606$	0	0
$607$	−3.87422e37	−1.03547	−0.517734	−	0.855541i	$-0.673224\pi$
$607$	−3.87422e37	−1.03547	−0.517734	+	0.855541i	$0.673224\pi$
$608$	−4.64531e37	−1.21427
$609$	0	0
$610$	4.10739e37	1.02710
$611$	−4.22296e36	−0.103291
$612$	0	0
$613$	−2.14418e37	−0.501815	−0.250908	−	0.968011i	$-0.580729\pi$
$613$	−2.14418e37	−0.501815	−0.250908	+	0.968011i	$0.580729\pi$
$614$	2.29717e37	0.525920
$615$	0	0
$616$	−3.11507e37	−0.682540
$617$	4.89663e36	0.104966	0.0524828	−	0.998622i	$-0.483287\pi$
$617$	4.89663e36	0.104966	0.0524828	+	0.998622i	$0.483287\pi$
$618$	0	0
$619$	7.29135e37	1.49618	0.748091	−	0.663596i	$-0.230971\pi$
$619$	7.29135e37	1.49618	0.748091	+	0.663596i	$0.230971\pi$
$620$	2.94431e37	0.591147
$621$	0	0
$622$	−9.14298e37	−1.75759
$623$	−1.22251e37	−0.229966
$624$	0	0
$625$	2.22045e36	0.0400000
$626$	−6.96356e37	−1.22766
$627$	0	0
$628$	6.40089e37	1.08090
$629$	3.66449e36	0.0605661
$630$	0	0
$631$	−5.13396e36	−0.0812936	−0.0406468	−	0.999174i	$-0.512942\pi$
$631$	−5.13396e36	−0.0812936	−0.0406468	+	0.999174i	$0.512942\pi$
$632$	3.65808e37	0.566986
$633$	0	0
$634$	7.12036e37	1.05754
$635$	−3.60846e37	−0.524658
$636$	0	0
$637$	−9.11351e36	−0.127000
$638$	−1.36247e38	−1.85887
$639$	0	0
$640$	2.56709e37	0.335746
$641$	−1.22726e38	−1.57164	−0.785822	−	0.618453i	$-0.787760\pi$
$641$	−1.22726e38	−1.57164	−0.785822	+	0.618453i	$0.787760\pi$
$642$	0	0
$643$	−1.15541e38	−1.41869	−0.709345	−	0.704862i	$-0.751009\pi$
$643$	−1.15541e38	−1.41869	−0.709345	+	0.704862i	$0.751009\pi$
$644$	3.37438e37	0.405727
$645$	0	0
$646$	−1.58422e37	−0.182674
$647$	−4.75539e37	−0.537005	−0.268503	−	0.963279i	$-0.586529\pi$
$647$	−4.75539e37	−0.537005	−0.268503	+	0.963279i	$0.586529\pi$
$648$	0	0
$649$	1.89692e38	2.05469
$650$	−1.21543e37	−0.128944
$651$	0	0
$652$	−6.74436e37	−0.686433
$653$	1.21109e38	1.20739	0.603696	−	0.797215i	$-0.293694\pi$
$653$	1.21109e38	1.20739	0.603696	+	0.797215i	$0.293694\pi$
$654$	0	0
$655$	−1.75851e36	−0.0168223
$656$	1.01289e37	0.0949202
$657$	0	0
$658$	3.39113e37	0.304997
$659$	1.57953e38	1.39180	0.695898	−	0.718141i	$-0.255007\pi$
$659$	1.57953e38	1.39180	0.695898	+	0.718141i	$0.255007\pi$
$660$	0	0
$661$	1.17794e38	0.996329	0.498165	−	0.867082i	$-0.334007\pi$
$661$	1.17794e38	0.996329	0.498165	+	0.867082i	$0.334007\pi$
$662$	6.87731e37	0.569949
$663$	0	0
$664$	7.71941e36	0.0614207
$665$	6.59204e37	0.513958
$666$	0	0
$667$	−6.37948e37	−0.477625
$668$	1.45264e38	1.06580
$669$	0	0
$670$	3.62664e36	0.0255561
$671$	3.95058e38	2.72839
$672$	0	0
$673$	−2.67318e37	−0.177348	−0.0886738	−	0.996061i	$-0.528263\pi$
$673$	−2.67318e37	−0.177348	−0.0886738	+	0.996061i	$0.528263\pi$
$674$	2.03899e38	1.32589
$675$	0	0
$676$	−8.44002e37	−0.527306
$677$	−2.91501e38	−1.78522	−0.892612	−	0.450826i	$-0.851130\pi$
$677$	−2.91501e38	−1.78522	−0.892612	+	0.450826i	$0.851130\pi$
$678$	0	0
$679$	2.96946e38	1.74757
$680$	4.16849e36	0.0240496
$681$	0	0
$682$	6.88788e38	3.81941
$683$	−4.50429e37	−0.244876	−0.122438	−	0.992476i	$-0.539071\pi$
$683$	−4.50429e37	−0.244876	−0.122438	+	0.992476i	$0.539071\pi$
$684$	0	0
$685$	1.55921e38	0.814861
$686$	−2.11909e38	−1.08586
$687$	0	0
$688$	−1.53592e38	−0.756700
$689$	1.93417e38	0.934407
$690$	0	0
$691$	−1.26775e38	−0.588952	−0.294476	−	0.955659i	$-0.595145\pi$
$691$	−1.26775e38	−0.588952	−0.294476	+	0.955659i	$0.595145\pi$
$692$	−2.34268e37	−0.106729
$693$	0	0
$694$	1.51027e38	0.661760
$695$	1.01909e38	0.437941
$696$	0	0
$697$	2.59325e36	0.0107202
$698$	−2.25523e38	−0.914413
$699$	0	0
$700$	4.01284e37	0.156541
$701$	2.52684e38	0.966907	0.483453	−	0.875370i	$-0.339382\pi$
$701$	2.52684e38	0.966907	0.483453	+	0.875370i	$0.339382\pi$
$702$	0	0
$703$	−1.23322e38	−0.454090
$704$	−1.42638e38	−0.515235
$705$	0	0
$706$	−2.28671e38	−0.794966
$707$	4.45745e37	0.152028
$708$	0	0
$709$	−4.72340e38	−1.55071	−0.775355	−	0.631525i	$-0.782429\pi$
$709$	−4.72340e38	−1.55071	−0.775355	+	0.631525i	$0.782429\pi$
$710$	−2.90375e38	−0.935346
$711$	0	0
$712$	2.60157e37	0.0806781
$713$	3.22510e38	0.981374
$714$	0	0
$715$	−1.16903e38	−0.342527
$716$	−5.02227e37	−0.144402
$717$	0	0
$718$	−7.68666e38	−2.12842
$719$	2.60664e38	0.708338	0.354169	−	0.935181i	$-0.384764\pi$
$719$	2.60664e38	0.708338	0.354169	+	0.935181i	$0.384764\pi$
$720$	0	0
$721$	6.75597e38	1.76832
$722$	2.58594e37	0.0664302
$723$	0	0
$724$	1.00051e38	0.247599
$725$	−7.58653e37	−0.184281
$726$	0	0
$727$	5.67336e37	0.132778	0.0663890	−	0.997794i	$-0.478852\pi$
$727$	5.67336e37	0.132778	0.0663890	+	0.997794i	$0.478852\pi$
$728$	9.49456e37	0.218123
$729$	0	0
$730$	9.87942e37	0.218712
$731$	−3.93234e37	−0.0854607
$732$	0	0
$733$	6.56173e38	1.37441	0.687203	−	0.726466i	$-0.258838\pi$
$733$	6.56173e38	1.37441	0.687203	+	0.726466i	$0.258838\pi$
$734$	−2.27435e38	−0.467693
$735$	0	0
$736$	−3.09747e38	−0.613983
$737$	3.48818e37	0.0678873
$738$	0	0
$739$	3.82217e38	0.717150	0.358575	−	0.933501i	$-0.383263\pi$
$739$	3.82217e38	0.717150	0.358575	+	0.933501i	$0.383263\pi$
$740$	−7.50707e37	−0.138306
$741$	0	0
$742$	−1.55318e39	−2.75912
$743$	−4.43270e38	−0.773249	−0.386625	−	0.922237i	$-0.626359\pi$
$743$	−4.43270e38	−0.773249	−0.386625	+	0.922237i	$0.626359\pi$
$744$	0	0
$745$	3.79839e37	0.0638983
$746$	−1.02828e39	−1.69877
$747$	0	0
$748$	−9.27559e37	−0.147798
$749$	7.01315e37	0.109751
$750$	0	0
$751$	−5.14037e37	−0.0775988	−0.0387994	−	0.999247i	$-0.512353\pi$
$751$	−5.14037e37	−0.0775988	−0.0387994	+	0.999247i	$0.512353\pi$
$752$	−1.70478e38	−0.252771
$753$	0	0
$754$	4.15274e38	0.594048
$755$	−5.74198e37	−0.0806822
$756$	0	0
$757$	−8.77449e38	−1.18967	−0.594836	−	0.803847i	$-0.702783\pi$
$757$	−8.77449e38	−1.18967	−0.594836	+	0.803847i	$0.702783\pi$
$758$	1.07399e39	1.43043
$759$	0	0
$760$	−1.40283e38	−0.180310
$761$	−5.25859e38	−0.664013	−0.332006	−	0.943277i	$-0.607726\pi$
$761$	−5.25859e38	−0.664013	−0.332006	+	0.943277i	$0.607726\pi$
$762$	0	0
$763$	1.03745e39	1.26441
$764$	−8.85755e38	−1.06060
$765$	0	0
$766$	−5.30926e38	−0.613685
$767$	−5.78171e38	−0.656627
$768$	0	0
$769$	1.76825e38	0.193883	0.0969413	−	0.995290i	$-0.469094\pi$
$769$	1.76825e38	0.193883	0.0969413	+	0.995290i	$0.469094\pi$
$770$	9.38758e38	1.01141
$771$	0	0
$772$	−4.92329e38	−0.512179
$773$	−1.64719e39	−1.68392	−0.841960	−	0.539540i	$-0.818598\pi$
$773$	−1.64719e39	−1.68392	−0.841960	+	0.539540i	$0.818598\pi$
$774$	0	0
$775$	3.83532e38	0.378642
$776$	−6.31919e38	−0.613095
$777$	0	0
$778$	−1.15599e39	−1.08325
$779$	−8.72708e37	−0.0803736
$780$	0	0
$781$	−2.79289e39	−2.48465
$782$	−1.05635e38	−0.0923668
$783$	0	0
$784$	−3.67905e38	−0.310791
$785$	8.33794e38	0.692338
$786$	0	0
$787$	1.28441e38	0.103050	0.0515248	−	0.998672i	$-0.483592\pi$
$787$	1.28441e38	0.103050	0.0515248	+	0.998672i	$0.483592\pi$
$788$	−1.30471e39	−1.02899
$789$	0	0
$790$	−1.10240e39	−0.840182
$791$	1.59886e39	1.19792
$792$	0	0
$793$	−1.20411e39	−0.871926
$794$	−1.83706e38	−0.130781
$795$	0	0
$796$	5.36068e38	0.368887
$797$	1.77034e39	1.19776	0.598880	−	0.800839i	$-0.295613\pi$
$797$	1.77034e39	1.19776	0.598880	+	0.800839i	$0.295613\pi$
$798$	0	0
$799$	−4.36466e37	−0.0285476
$800$	−3.68354e38	−0.236892
$801$	0	0
$802$	1.05216e39	0.654228
$803$	9.50224e38	0.580987
$804$	0	0
$805$	4.39553e38	0.259877
$806$	−2.09939e39	−1.22059
$807$	0	0
$808$	−9.48573e37	−0.0533356
$809$	−9.17218e37	−0.0507186	−0.0253593	−	0.999678i	$-0.508073\pi$
$809$	−9.17218e37	−0.0507186	−0.0253593	+	0.999678i	$0.508073\pi$
$810$	0	0
$811$	2.06324e39	1.10349	0.551746	−	0.834012i	$-0.313962\pi$
$811$	2.06324e39	1.10349	0.551746	+	0.834012i	$0.313962\pi$
$812$	−1.37105e39	−0.721188
$813$	0	0
$814$	−1.75620e39	−0.893601
$815$	−8.78535e38	−0.439674
$816$	0	0
$817$	1.32335e39	0.640735
$818$	−8.76936e38	−0.417636
$819$	0	0
$820$	−5.31252e37	−0.0244801
$821$	2.42576e39	1.09955	0.549776	−	0.835312i	$-0.314713\pi$
$821$	2.42576e39	1.09955	0.549776	+	0.835312i	$0.314713\pi$
$822$	0	0
$823$	2.22813e39	0.977332	0.488666	−	0.872471i	$-0.337484\pi$
$823$	2.22813e39	0.977332	0.488666	+	0.872471i	$0.337484\pi$
$824$	−1.43771e39	−0.620376
$825$	0	0
$826$	4.64284e39	1.93889
$827$	3.06088e39	1.25754	0.628770	−	0.777592i	$-0.283559\pi$
$827$	3.06088e39	1.25754	0.628770	+	0.777592i	$0.283559\pi$
$828$	0	0
$829$	−3.10133e39	−1.23328	−0.616640	−	0.787245i	$-0.711506\pi$
$829$	−3.10133e39	−1.23328	−0.616640	+	0.787245i	$0.711506\pi$
$830$	−2.32632e38	−0.0910156
$831$	0	0
$832$	4.34753e38	0.164656
$833$	−9.41930e37	−0.0351003
$834$	0	0
$835$	1.89224e39	0.682665
$836$	3.12152e39	1.10811
$837$	0	0
$838$	−2.99442e39	−1.02924
$839$	1.27631e39	0.431686	0.215843	−	0.976428i	$-0.430750\pi$
$839$	1.27631e39	0.431686	0.215843	+	0.976428i	$0.430750\pi$
$840$	0	0
$841$	−4.61066e38	−0.151014
$842$	1.03190e39	0.332601
$843$	0	0
$844$	−2.35955e39	−0.736558
$845$	−1.09941e39	−0.337750
$846$	0	0
$847$	5.26178e39	1.56569
$848$	7.80810e39	2.28666
$849$	0	0
$850$	−1.25622e38	−0.0356377
$851$	−8.22301e38	−0.229605
$852$	0	0
$853$	2.49006e39	0.673594	0.336797	−	0.941577i	$-0.390656\pi$
$853$	2.49006e39	0.673594	0.336797	+	0.941577i	$0.390656\pi$
$854$	9.66931e39	2.57463
$855$	0	0
$856$	−1.49244e38	−0.0385036
$857$	−2.09615e39	−0.532330	−0.266165	−	0.963927i	$-0.585757\pi$
$857$	−2.09615e39	−0.532330	−0.266165	+	0.963927i	$0.585757\pi$
$858$	0	0
$859$	−4.85233e38	−0.119411	−0.0597053	−	0.998216i	$-0.519016\pi$
$859$	−4.85233e38	−0.119411	−0.0597053	+	0.998216i	$0.519016\pi$
$860$	8.05579e38	0.195155
$861$	0	0
$862$	−6.98474e38	−0.163984
$863$	1.74729e39	0.403850	0.201925	−	0.979401i	$-0.435280\pi$
$863$	1.74729e39	0.403850	0.201925	+	0.979401i	$0.435280\pi$
$864$	0	0
$865$	−3.05162e38	−0.0683618
$866$	−8.60689e39	−1.89826
$867$	0	0
$868$	6.93126e39	1.48182
$869$	−1.06031e40	−2.23186
$870$	0	0
$871$	−1.06318e38	−0.0216951
$872$	−2.20776e39	−0.443588
$873$	0	0
$874$	3.55494e39	0.692513
$875$	5.22721e38	0.100268
$876$	0	0
$877$	2.09575e39	0.389802	0.194901	−	0.980823i	$-0.437561\pi$
$877$	2.09575e39	0.389802	0.194901	+	0.980823i	$0.437561\pi$
$878$	1.39261e39	0.255067
$879$	0	0
$880$	−4.71929e39	−0.838224
$881$	6.05411e39	1.05895	0.529475	−	0.848326i	$-0.322389\pi$
$881$	6.05411e39	1.05895	0.529475	+	0.848326i	$0.322389\pi$
$882$	0	0
$883$	1.03091e40	1.74884	0.874422	−	0.485166i	$-0.161241\pi$
$883$	1.03091e40	1.74884	0.874422	+	0.485166i	$0.161241\pi$
$884$	2.82715e38	0.0472327
$885$	0	0
$886$	−5.06391e39	−0.820599
$887$	1.43539e38	0.0229087	0.0114543	−	0.999934i	$-0.496354\pi$
$887$	1.43539e38	0.0229087	0.0114543	+	0.999934i	$0.496354\pi$
$888$	0	0
$889$	−8.49477e39	−1.31516
$890$	−7.84011e38	−0.119552
$891$	0	0
$892$	5.87898e39	0.869714
$893$	1.46884e39	0.214033
$894$	0	0
$895$	−6.54212e38	−0.0924927
$896$	6.04325e39	0.841613
$897$	0	0
$898$	1.29253e40	1.74667
$899$	−1.31040e40	−1.74441
$900$	0	0
$901$	1.99907e39	0.258252
$902$	−1.24281e39	−0.158167
$903$	0	0
$904$	−3.40247e39	−0.420262
$905$	1.30328e39	0.158592
$906$	0	0
$907$	−8.83389e39	−1.04341	−0.521703	−	0.853127i	$-0.674703\pi$
$907$	−8.83389e39	−1.04341	−0.521703	+	0.853127i	$0.674703\pi$
$908$	9.88760e39	1.15062
$909$	0	0
$910$	−2.86128e39	−0.323223
$911$	−5.82734e39	−0.648593	−0.324296	−	0.945956i	$-0.605128\pi$
$911$	−5.82734e39	−0.648593	−0.324296	+	0.945956i	$0.605128\pi$
$912$	0	0
$913$	−2.23751e39	−0.241774
$914$	−1.94320e40	−2.06892
$915$	0	0
$916$	−1.73828e39	−0.179693
$917$	−4.13974e38	−0.0421684
$918$	0	0
$919$	2.55020e39	0.252240	0.126120	−	0.992015i	$-0.459747\pi$
$919$	2.55020e39	0.252240	0.126120	+	0.992015i	$0.459747\pi$
$920$	−9.35397e38	−0.0911718
$921$	0	0
$922$	−1.83734e40	−1.73909
$923$	8.51259e39	0.794033
$924$	0	0
$925$	−9.77887e38	−0.0885881
$926$	−5.03938e39	−0.449913
$927$	0	0
$928$	1.25854e40	1.09137
$929$	8.08006e39	0.690561	0.345281	−	0.938499i	$-0.387784\pi$
$929$	8.08006e39	0.690561	0.345281	+	0.938499i	$0.387784\pi$
$930$	0	0
$931$	3.16989e39	0.263162
$932$	1.23417e40	1.00986
$933$	0	0
$934$	−1.80649e40	−1.43599
$935$	−1.20826e39	−0.0946679
$936$	0	0
$937$	4.71436e39	0.358871	0.179435	−	0.983770i	$-0.442573\pi$
$937$	4.71436e39	0.358871	0.179435	+	0.983770i	$0.442573\pi$
$938$	8.53757e38	0.0640613
$939$	0	0
$940$	8.94144e38	0.0651901
$941$	−5.60593e39	−0.402891	−0.201446	−	0.979500i	$-0.564564\pi$
$941$	−5.60593e39	−0.402891	−0.201446	+	0.979500i	$0.564564\pi$
$942$	0	0
$943$	−5.81917e38	−0.0406400
$944$	−2.33403e40	−1.60688
$945$	0	0
$946$	1.88456e40	1.26090
$947$	−1.23604e40	−0.815280	−0.407640	−	0.913143i	$-0.633648\pi$
$947$	−1.23604e40	−0.815280	−0.407640	+	0.913143i	$0.633648\pi$
$948$	0	0
$949$	−2.89623e39	−0.185669
$950$	4.22756e39	0.267191
$951$	0	0
$952$	9.81314e38	0.0602850
$953$	−9.22351e39	−0.558653	−0.279326	−	0.960196i	$-0.590111\pi$
$953$	−9.22351e39	−0.558653	−0.279326	+	0.960196i	$0.590111\pi$
$954$	0	0
$955$	−1.15380e40	−0.679338
$956$	9.08307e39	0.527292
$957$	0	0
$958$	−1.79617e40	−1.01371
$959$	3.67059e40	2.04260
$960$	0	0
$961$	4.77637e40	2.58423
$962$	5.35279e39	0.285573
$963$	0	0
$964$	1.66603e40	0.864254
$965$	−6.41319e39	−0.328061
$966$	0	0
$967$	9.98254e39	0.496573	0.248287	−	0.968687i	$-0.420132\pi$
$967$	9.98254e39	0.496573	0.248287	+	0.968687i	$0.420132\pi$
$968$	−1.11974e40	−0.549288
$969$	0	0
$970$	1.90435e40	0.908508
$971$	−1.32713e39	−0.0624386	−0.0312193	−	0.999513i	$-0.509939\pi$
$971$	−1.32713e39	−0.0624386	−0.0312193	+	0.999513i	$0.509939\pi$
$972$	0	0
$973$	2.39905e40	1.09778
$974$	3.04631e40	1.37476
$975$	0	0
$976$	−4.86092e40	−2.13376
$977$	1.28166e40	0.554875	0.277438	−	0.960744i	$-0.410515\pi$
$977$	1.28166e40	0.554875	0.277438	+	0.960744i	$0.410515\pi$
$978$	0	0
$979$	−7.54079e39	−0.317578
$980$	1.92964e39	0.0801537
$981$	0	0
$982$	−1.32275e40	−0.534530
$983$	4.10358e40	1.63565	0.817825	−	0.575466i	$-0.195179\pi$
$983$	4.10358e40	1.63565	0.817825	+	0.575466i	$0.195179\pi$
$984$	0	0
$985$	−1.69954e40	−0.659086
$986$	4.29208e39	0.164184
$987$	0	0
$988$	−9.51423e39	−0.354124
$989$	8.82406e39	0.323980
$990$	0	0
$991$	−2.58154e40	−0.922325	−0.461162	−	0.887316i	$-0.652567\pi$
$991$	−2.58154e40	−0.922325	−0.461162	+	0.887316i	$0.652567\pi$
$992$	−6.36247e40	−2.24243
$993$	0	0
$994$	−6.83580e40	−2.34462
$995$	6.98293e39	0.236280
$996$	0	0
$997$	−2.25475e39	−0.0742531	−0.0371265	−	0.999311i	$-0.511820\pi$
$997$	−2.25475e39	−0.0742531	−0.0371265	+	0.999311i	$0.511820\pi$
$998$	1.45674e40	0.473281
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.28.a.d.1.5		5
3.2	odd	2		5.28.a.b.1.1	✓	5
15.2	even	4		25.28.b.c.24.2		10
15.8	even	4		25.28.b.c.24.9		10
15.14	odd	2		25.28.a.c.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.28.a.b.1.1	✓	5	3.2	odd	2
25.28.a.c.1.5		5	15.14	odd	2
25.28.b.c.24.2		10	15.2	even	4
25.28.b.c.24.9		10	15.8	even	4
45.28.a.d.1.5		5	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:	\( k \)	\(=\)	\( 28 \)
Character orbit:	\([\chi]\)	\(=\)	45.a (trivial)

\(f(q)\)	\(=\)	\(q+15097.3 q^{2} +9.37113e7 q^{4} +1.22070e9 q^{5} +2.87369e11 q^{7} -6.11538e11 q^{8} +O(q^{10})\)	\(q+15097.3 q^{2} +9.37113e7 q^{4} +1.22070e9 q^{5} +2.87369e11 q^{7} -6.11538e11 q^{8} +1.84293e13 q^{10} +1.77257e14 q^{11} -5.40271e14 q^{13} +4.33850e15 q^{14} -2.18103e16 q^{16} -5.58399e15 q^{17} +1.87919e17 q^{19} +1.14394e17 q^{20} +2.67611e18 q^{22} +1.25303e18 q^{23} +1.49012e18 q^{25} -8.15664e18 q^{26} +2.69297e19 q^{28} -5.09124e19 q^{29} +2.57384e20 q^{31} -2.47198e20 q^{32} -8.43033e19 q^{34} +3.50792e20 q^{35} -6.56249e20 q^{37} +2.83707e21 q^{38} -7.46507e20 q^{40} -4.64407e20 q^{41} +7.04216e21 q^{43} +1.66110e22 q^{44} +1.89174e22 q^{46} +7.81638e21 q^{47} +1.68684e22 q^{49} +2.24968e22 q^{50} -5.06295e22 q^{52} -3.58001e23 q^{53} +2.16379e23 q^{55} -1.75737e23 q^{56} -7.68640e23 q^{58} +1.07015e24 q^{59} +2.22872e24 q^{61} +3.88580e24 q^{62} -8.04695e23 q^{64} -6.59510e23 q^{65} +1.96786e23 q^{67} -5.23283e23 q^{68} +5.29602e24 q^{70} -1.57561e25 q^{71} +5.36070e24 q^{73} -9.90760e24 q^{74} +1.76101e25 q^{76} +5.09382e25 q^{77} -5.98177e25 q^{79} -2.66239e25 q^{80} -7.01130e24 q^{82} -1.26229e25 q^{83} -6.81640e24 q^{85} +1.06318e26 q^{86} -1.08400e26 q^{88} -4.25414e25 q^{89} -1.55257e26 q^{91} +1.17423e26 q^{92} +1.18006e26 q^{94} +2.29393e26 q^{95} +1.03333e27 q^{97} +2.54668e26 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 19916 q^{2} + 251490240 q^{4} + 6103515625 q^{5} + 155646348206 q^{7} - 4844427693600 q^{8}+O(q^{10}) \) 5 * q - 19916 * q^2 + 251490240 * q^4 + 6103515625 * q^5 + 155646348206 * q^7 - 4844427693600 * q^8	\( 5 q - 19916 q^{2} + 251490240 q^{4} + 6103515625 q^{5} + 155646348206 q^{7} - 4844427693600 q^{8} - 24311523437500 q^{10} + 34307841041440 q^{11} + 12\!\cdots\!22 q^{13}+ \cdots + 24\!\cdots\!12 q^{98}+O(q^{100}) \) 5 * q - 19916 * q^2 + 251490240 * q^4 + 6103515625 * q^5 + 155646348206 * q^7 - 4844427693600 * q^8 - 24311523437500 * q^10 + 34307841041440 * q^11 + 1264965428684322 * q^13 + 1494481038585720 * q^14 + 50480141682449280 * q^16 - 11381432659133186 * q^17 - 177889284152803500 * q^19 + 306994921875000000 * q^20 + 1661117755714509952 * q^22 - 5314231426153528362 * q^23 + 7450580596923828125 * q^25 - 64194207115665583160 * q^26 + 74243491650979261568 * q^28 - 142675767255557016550 * q^29 + 490757140558660526660 * q^31 - 709255558573159910656 * q^32 - 823451155892216853320 * q^34 + 189997983649902343750 * q^35 - 1594690133202798011054 * q^37 + 8102840491936976962000 * q^38 - 5913608024414062500000 * q^40 + 14453824011731896105490 * q^41 - 6456338188721923591758 * q^43 + 61776067586935488773120 * q^44 + 41662242513049160161560 * q^46 - 19960747396802751518726 * q^47 + 64529931934369352760065 * q^49 - 29677152633666992187500 * q^50 + 694364047806293961951616 * q^52 - 203485571063020242199082 * q^53 + 41879688771289062500000 * q^55 + 514718506150627561339200 * q^56 - 568257469475936639738200 * q^58 + 1753694580358227494398300 * q^59 - 1715799924029775655491390 * q^61 - 856653132512718918087792 * q^62 + 2825791291455308901232640 * q^64 + 1544147251811916503906250 * q^65 - 52283413307813388053914 * q^67 + 18798756173665084661988992 * q^68 + 1824317674054833984375000 * q^70 - 13737346388576400396156460 * q^71 + 52785881484144679283287962 * q^73 - 44617246831379823508169080 * q^74 - 50943444226830794465542400 * q^76 - 40527442829187717880256832 * q^77 - 18659027886608771061377800 * q^79 + 61621266702208593750000000 * q^80 - 233045910890443727506605688 * q^82 + 49391953045615520178004398 * q^83 - 13893350413980939941406250 * q^85 + 246095687260751641221151240 * q^86 - 662199546636275930413900800 * q^88 - 180573322691431536135373650 * q^89 + 317295677016426969579588460 * q^91 + 379021343242797571985691264 * q^92 - 34623503302055809185576920 * q^94 - 217150005069340209960937500 * q^95 + 1118012018325586896775804426 * q^97 + 243326561625995319625007012 * q^98

Introduction

L-functions

Modular forms

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Groups

Database

Properties

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