LMFDB - Embedded newform 9.28.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,28,Mod(1,9)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 28, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 28);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 28 $
Character orbit:	$[\chi]$	$=$	9.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:	$41.5670017354$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{18209}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4552 $ x^2 - x - 4552
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{3}\cdot 3^{3} $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-66.9704$ of defining polynomial
Character	$\chi$	$=$	9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+18713.6 q^{2} +2.15981e8 q^{4} -5.76560e8 q^{5} -1.96873e11 q^{7} +1.53009e12 q^{8} +O(q^{10})$	\(q+18713.6 q^{2} +2.15981e8 q^{4} -5.76560e8 q^{5} -1.96873e11 q^{7} +1.53009e12 q^{8} -1.07895e13 q^{10} -2.06714e14 q^{11} -1.66656e14 q^{13} -3.68421e15 q^{14} -3.55072e14 q^{16} +5.47219e15 q^{17} +1.61471e17 q^{19} -1.24526e17 q^{20} -3.86837e18 q^{22} -2.80341e18 q^{23} -7.11816e18 q^{25} -3.11874e18 q^{26} -4.25209e19 q^{28} +2.99842e18 q^{29} +9.09190e19 q^{31} -2.12009e20 q^{32} +1.02404e20 q^{34} +1.13509e20 q^{35} +1.50001e21 q^{37} +3.02171e21 q^{38} -8.82187e20 q^{40} -5.47146e21 q^{41} -6.81035e21 q^{43} -4.46463e22 q^{44} -5.24619e22 q^{46} +9.41657e21 q^{47} -2.69532e22 q^{49} -1.33206e23 q^{50} -3.59946e22 q^{52} +5.35936e22 q^{53} +1.19183e23 q^{55} -3.01233e23 q^{56} +5.61113e22 q^{58} -9.16258e23 q^{59} +1.47362e24 q^{61} +1.70142e24 q^{62} -3.91980e24 q^{64} +9.60874e22 q^{65} -3.21915e24 q^{67} +1.18189e24 q^{68} +2.12417e24 q^{70} -3.38255e24 q^{71} +1.32172e25 q^{73} +2.80705e25 q^{74} +3.48748e25 q^{76} +4.06965e25 q^{77} +4.66230e25 q^{79} +2.04720e23 q^{80} -1.02391e26 q^{82} -7.14690e25 q^{83} -3.15505e24 q^{85} -1.27446e26 q^{86} -3.16290e26 q^{88} +1.40708e26 q^{89} +3.28102e25 q^{91} -6.05484e26 q^{92} +1.76218e26 q^{94} -9.30980e25 q^{95} +3.77568e26 q^{97} -5.04391e26 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8280 q^{2} + 190623296 q^{4} - 5443587900 q^{5} - 175391963600 q^{7} + 3195032348160 q^{8}+O(q^{10}) $ 2 * q + 8280 * q^2 + 190623296 * q^4 - 5443587900 * q^5 - 175391963600 * q^7 + 3195032348160 * q^8	$ 2 q + 8280 q^{2} + 190623296 q^{4} - 5443587900 q^{5} - 175391963600 q^{7} + 3195032348160 q^{8} + 39991096148400 q^{10} - 138167337691944 q^{11} - 753433801271060 q^{13} - 39\!\cdots\!12 q^{14}+ \cdots + 17\!\cdots\!40 q^{98}+O(q^{100}) $ 2 * q + 8280 * q^2 + 190623296 * q^4 - 5443587900 * q^5 - 175391963600 * q^7 + 3195032348160 * q^8 + 39991096148400 * q^10 - 138167337691944 * q^11 - 753433801271060 * q^13 - 3908340052811712 * q^14 - 14322995785166848 * q^16 + 29753620331011740 * q^17 + 404565810372684760 * q^19 - 1109219331427200 * q^20 - 4583556785578779360 * q^22 - 2929078923121218960 * q^23 + 9119218786673228750 * q^25 + 3003459254146640016 * q^26 - 43065656535315868160 * q^28 + 15546679995448558260 * q^29 + 28544554594467385024 * q^31 - 289738949030869893120 * q^32 - 150938335185934859568 * q^34 + 8958395384765013600 * q^35 + 1867697204682824566780 * q^37 + 485361223888169521440 * q^38 - 8985527186071883904000 * q^40 - 9081343698046512254964 * q^41 + 5145612605801421773800 * q^43 - 46384541037574305299712 * q^44 - 51150723570313970279616 * q^46 + 1150251488862201070560 * q^47 - 92204113217840907690414 * q^49 - 302620649115949014735000 * q^50 - 21115266673184124022400 * q^52 - 106953735591470060758620 * q^53 - 214436254091483969701200 * q^55 - 265467760964859260989440 * q^56 - 74812163717162466470160 * q^58 - 2009620977624026488631880 * q^59 + 147857426692448940370444 * q^61 + 2352212714010270811080960 * q^62 - 1234057803938137445761024 * q^64 + 2951949350200452960922200 * q^65 + 3051578535738098902157560 * q^67 + 566166870324676171716480 * q^68 + 3215012724032159046326400 * q^70 + 13175198820369338598286416 * q^71 + 5284260812951286572116660 * q^73 + 24234145145448525537787728 * q^74 + 28710432717942786872615680 * q^76 + 42169025756092787413646400 * q^77 + 62814351035720719918179040 * q^79 + 68186991639088251432345600 * q^80 - 64726649726985190956760560 * q^82 - 171806873410054757883176280 * q^83 - 121333441005595565089302600 * q^85 - 252189883901197432712215584 * q^86 - 202163623954874235550955520 * q^88 + 313473438761105539763494380 * q^89 + 20205365125040878536694304 * q^91 - 602296848225491467788034560 * q^92 + 262465434750720041893579392 * q^94 - 1276245244260479145691314000 * q^95 - 653202933397052842883888060 * q^97 + 176410316250092689584969240 * 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 $

$2$	18713.6	1.61530	0.807648	−	0.589664i	$-0.200740\pi$
$2$	18713.6	1.61530	0.807648	+	0.589664i	$0.200740\pi$
$3$	0	0
$3$	0	0
$4$	2.15981e8	1.60918
$5$	−5.76560e8	−0.211227	−0.105614	−	0.994407i	$-0.533681\pi$
$5$	−5.76560e8	−0.211227	−0.105614	+	0.994407i	$0.533681\pi$
$6$	0	0
$7$	−1.96873e11	−0.768004	−0.384002	−	0.923332i	$-0.625454\pi$
$7$	−1.96873e11	−0.768004	−0.384002	+	0.923332i	$0.625454\pi$
$8$	1.53009e12	0.984013
$9$	0	0
$10$	−1.07895e13	−0.341194
$11$	−2.06714e14	−1.80538	−0.902691	−	0.430290i	$-0.858411\pi$
$11$	−2.06714e14	−1.80538	−0.902691	+	0.430290i	$0.858411\pi$
$12$	0	0
$13$	−1.66656e14	−0.152611	−0.0763057	−	0.997084i	$-0.524312\pi$
$13$	−1.66656e14	−0.152611	−0.0763057	+	0.997084i	$0.524312\pi$
$14$	−3.68421e15	−1.24055
$15$	0	0
$16$	−3.55072e14	−0.0197105
$17$	5.47219e15	0.133999	0.0669994	−	0.997753i	$-0.478657\pi$
$17$	5.47219e15	0.133999	0.0669994	+	0.997753i	$0.478657\pi$
$18$	0	0
$19$	1.61471e17	0.880891	0.440445	−	0.897779i	$-0.354821\pi$
$19$	1.61471e17	0.880891	0.440445	+	0.897779i	$0.354821\pi$
$20$	−1.24526e17	−0.339903
$21$	0	0
$22$	−3.86837e18	−2.91623
$23$	−2.80341e18	−1.15974	−0.579870	−	0.814709i	$-0.696897\pi$
$23$	−2.80341e18	−1.15974	−0.579870	+	0.814709i	$0.696897\pi$
$24$	0	0
$25$	−7.11816e18	−0.955383
$26$	−3.11874e18	−0.246513
$27$	0	0
$28$	−4.25209e19	−1.23586
$29$	2.99842e18	0.0542650	0.0271325	−	0.999632i	$-0.491362\pi$
$29$	2.99842e18	0.0542650	0.0271325	+	0.999632i	$0.491362\pi$
$30$	0	0
$31$	9.09190e19	0.668763	0.334381	−	0.942438i	$-0.391473\pi$
$31$	9.09190e19	0.668763	0.334381	+	0.942438i	$0.391473\pi$
$32$	−2.12009e20	−1.01585
$33$	0	0
$34$	1.02404e20	0.216448
$35$	1.13509e20	0.162223
$36$	0	0
$37$	1.50001e21	1.01244	0.506220	−	0.862404i	$-0.331042\pi$
$37$	1.50001e21	1.01244	0.506220	+	0.862404i	$0.331042\pi$
$38$	3.02171e21	1.42290
$39$	0	0
$40$	−8.82187e20	−0.207850
$41$	−5.47146e21	−0.923679	−0.461840	−	0.886963i	$-0.652810\pi$
$41$	−5.47146e21	−0.923679	−0.461840	+	0.886963i	$0.652810\pi$
$42$	0	0
$43$	−6.81035e21	−0.604429	−0.302215	−	0.953240i	$-0.597726\pi$
$43$	−6.81035e21	−0.604429	−0.302215	+	0.953240i	$0.597726\pi$
$44$	−4.46463e22	−2.90519
$45$	0	0
$46$	−5.24619e22	−1.87333
$47$	9.41657e21	0.251520	0.125760	−	0.992061i	$-0.459863\pi$
$47$	9.41657e21	0.251520	0.125760	+	0.992061i	$0.459863\pi$
$48$	0	0
$49$	−2.69532e22	−0.410169
$50$	−1.33206e23	−1.54323
$51$	0	0
$52$	−3.59946e22	−0.245580
$53$	5.35936e22	0.282741	0.141370	−	0.989957i	$-0.454849\pi$
$53$	5.35936e22	0.282741	0.141370	+	0.989957i	$0.454849\pi$
$54$	0	0
$55$	1.19183e23	0.381346
$56$	−3.01233e23	−0.755726
$57$	0	0
$58$	5.61113e22	0.0876541
$59$	−9.16258e23	−1.13636	−0.568180	−	0.822904i	$-0.692352\pi$
$59$	−9.16258e23	−1.13636	−0.568180	+	0.822904i	$0.692352\pi$
$60$	0	0
$61$	1.47362e24	1.16529	0.582643	−	0.812728i	$-0.302019\pi$
$61$	1.47362e24	1.16529	0.582643	+	0.812728i	$0.302019\pi$
$62$	1.70142e24	1.08025
$63$	0	0
$64$	−3.91980e24	−1.62119
$65$	9.60874e22	0.0322356
$66$	0	0
$67$	−3.21915e24	−0.717349	−0.358675	−	0.933463i	$-0.616771\pi$
$67$	−3.21915e24	−0.717349	−0.358675	+	0.933463i	$0.616771\pi$
$68$	1.18189e24	0.215629
$69$	0	0
$70$	2.12417e24	0.262039
$71$	−3.38255e24	−0.344554	−0.172277	−	0.985049i	$-0.555112\pi$
$71$	−3.38255e24	−0.344554	−0.172277	+	0.985049i	$0.555112\pi$
$72$	0	0
$73$	1.32172e25	0.925295	0.462648	−	0.886542i	$-0.346900\pi$
$73$	1.32172e25	0.925295	0.462648	+	0.886542i	$0.346900\pi$
$74$	2.80705e25	1.63539
$75$	0	0
$76$	3.48748e25	1.41752
$77$	4.06965e25	1.38654
$78$	0	0
$79$	4.66230e25	1.12366	0.561830	−	0.827253i	$-0.310098\pi$
$79$	4.66230e25	1.12366	0.561830	+	0.827253i	$0.310098\pi$
$80$	2.04720e23	0.00416338
$81$	0	0
$82$	−1.02391e26	−1.49202
$83$	−7.14690e25	−0.884226	−0.442113	−	0.896959i	$-0.645771\pi$
$83$	−7.14690e25	−0.884226	−0.442113	+	0.896959i	$0.645771\pi$
$84$	0	0
$85$	−3.15505e24	−0.0283042
$86$	−1.27446e26	−0.976332
$87$	0	0
$88$	−3.16290e26	−1.77652
$89$	1.40708e26	0.678504	0.339252	−	0.940696i	$-0.389826\pi$
$89$	1.40708e26	0.678504	0.339252	+	0.940696i	$0.389826\pi$
$90$	0	0
$91$	3.28102e25	0.117206
$92$	−6.05484e26	−1.86624
$93$	0	0
$94$	1.76218e26	0.406279
$95$	−9.30980e25	−0.186068
$96$	0	0
$97$	3.77568e26	0.569609	0.284805	−	0.958586i	$-0.408071\pi$
$97$	3.77568e26	0.569609	0.284805	+	0.958586i	$0.408071\pi$
$98$	−5.04391e26	−0.662545
$99$	0	0
$100$	−1.53739e27	−1.53739
$101$	1.82546e27	1.59600	0.798002	−	0.602654i	$-0.205890\pi$
$101$	1.82546e27	1.59600	0.798002	+	0.602654i	$0.205890\pi$
$102$	0	0
$103$	2.87048e27	1.92598	0.962991	−	0.269534i	$-0.0868695\pi$
$103$	2.87048e27	1.92598	0.962991	+	0.269534i	$0.0868695\pi$
$104$	−2.54999e26	−0.150172
$105$	0	0
$106$	1.00293e27	0.456710
$107$	1.31331e27	0.526849	0.263425	−	0.964680i	$-0.415148\pi$
$107$	1.31331e27	0.526849	0.263425	+	0.964680i	$0.415148\pi$
$108$	0	0
$109$	−3.16013e27	−0.987296	−0.493648	−	0.869662i	$-0.664337\pi$
$109$	−3.16013e27	−0.987296	−0.493648	+	0.869662i	$0.664337\pi$
$110$	2.23035e27	0.615986
$111$	0	0
$112$	6.99043e25	0.0151377
$113$	−3.68033e27	−0.706851	−0.353425	−	0.935463i	$-0.614983\pi$
$113$	−3.68033e27	−0.706851	−0.353425	+	0.935463i	$0.614983\pi$
$114$	0	0
$115$	1.61633e27	0.244969
$116$	6.47603e26	0.0873224
$117$	0	0
$118$	−1.71465e28	−1.83556
$119$	−1.07733e27	−0.102912
$120$	0	0
$121$	2.96208e28	2.25940
$122$	2.75767e28	1.88228
$123$	0	0
$124$	1.96368e28	1.07616
$125$	8.39976e27	0.413030
$126$	0	0
$127$	−2.69227e28	−1.06849	−0.534243	−	0.845331i	$-0.679403\pi$
$127$	−2.69227e28	−1.06849	−0.534243	+	0.845331i	$0.679403\pi$
$128$	−4.48982e28	−1.60285
$129$	0	0
$130$	1.79814e27	0.0520701
$131$	−3.17810e28	−0.829860	−0.414930	−	0.909853i	$-0.636194\pi$
$131$	−3.17810e28	−0.829860	−0.414930	+	0.909853i	$0.636194\pi$
$132$	0	0
$133$	−3.17894e28	−0.676528
$134$	−6.02418e28	−1.15873
$135$	0	0
$136$	8.37292e27	0.131857
$137$	−2.13194e28	−0.304122	−0.152061	−	0.988371i	$-0.548591\pi$
$137$	−2.13194e28	−0.304122	−0.152061	+	0.988371i	$0.548591\pi$
$138$	0	0
$139$	−1.15969e29	−1.36032	−0.680161	−	0.733062i	$-0.738090\pi$
$139$	−1.15969e29	−1.36032	−0.680161	+	0.733062i	$0.738090\pi$
$140$	2.45159e28	0.261047
$141$	0	0
$142$	−6.32998e28	−0.556557
$143$	3.44502e28	0.275522
$144$	0	0
$145$	−1.72877e27	−0.0114622
$146$	2.47341e29	1.49463
$147$	0	0
$148$	3.23973e29	1.62920
$149$	−2.70481e29	−1.24200	−0.621000	−	0.783810i	$-0.713273\pi$
$149$	−2.70481e29	−1.24200	−0.621000	+	0.783810i	$0.713273\pi$
$150$	0	0
$151$	6.43669e28	0.246873	0.123437	−	0.992352i	$-0.460608\pi$
$151$	6.43669e28	0.246873	0.123437	+	0.992352i	$0.460608\pi$
$152$	2.47065e29	0.866808
$153$	0	0
$154$	7.61579e29	2.23968
$155$	−5.24203e28	−0.141261
$156$	0	0
$157$	−7.36476e29	−1.66922	−0.834609	−	0.550842i	$-0.814307\pi$
$157$	−7.36476e29	−1.66922	−0.834609	+	0.550842i	$0.814307\pi$
$158$	8.72484e29	1.81504
$159$	0	0
$160$	1.22236e29	0.214575
$161$	5.51917e29	0.890686
$162$	0	0
$163$	4.91659e29	0.671632	0.335816	−	0.941928i	$-0.390988\pi$
$163$	4.91659e29	0.671632	0.335816	+	0.941928i	$0.390988\pi$
$164$	−1.18173e30	−1.48637
$165$	0	0
$166$	−1.33744e30	−1.42829
$167$	−6.37427e29	−0.627709	−0.313854	−	0.949471i	$-0.601620\pi$
$167$	−6.37427e29	−0.627709	−0.313854	+	0.949471i	$0.601620\pi$
$168$	0	0
$169$	−1.16476e30	−0.976710
$170$	−5.90423e28	−0.0457196
$171$	0	0
$172$	−1.47091e30	−0.972638
$173$	−2.71145e30	−1.65798	−0.828989	−	0.559265i	$-0.811083\pi$
$173$	−2.71145e30	−1.65798	−0.828989	+	0.559265i	$0.811083\pi$
$174$	0	0
$175$	1.40138e30	0.733738
$176$	7.33984e28	0.0355849
$177$	0	0
$178$	2.63315e30	1.09599
$179$	1.65055e30	0.636961	0.318481	−	0.947929i	$-0.396827\pi$
$179$	1.65055e30	0.636961	0.318481	+	0.947929i	$0.396827\pi$
$180$	0	0
$181$	4.30260e30	1.42913	0.714563	−	0.699571i	$-0.246626\pi$
$181$	4.30260e30	1.42913	0.714563	+	0.699571i	$0.246626\pi$
$182$	6.13997e29	0.189323
$183$	0	0
$184$	−4.28946e30	−1.14120
$185$	−8.64843e29	−0.213855
$186$	0	0
$187$	−1.13118e30	−0.241919
$188$	2.03380e30	0.404741
$189$	0	0
$190$	−1.74220e30	−0.300555
$191$	−5.35850e30	−0.861177	−0.430589	−	0.902548i	$-0.641694\pi$
$191$	−5.35850e30	−0.861177	−0.430589	+	0.902548i	$0.641694\pi$
$192$	0	0
$193$	2.47114e30	0.345044	0.172522	−	0.985006i	$-0.444808\pi$
$193$	2.47114e30	0.345044	0.172522	+	0.985006i	$0.444808\pi$
$194$	7.06566e30	0.920088
$195$	0	0
$196$	−5.82138e30	−0.660038
$197$	4.41349e30	0.467185	0.233592	−	0.972335i	$-0.424952\pi$
$197$	4.41349e30	0.467185	0.233592	+	0.972335i	$0.424952\pi$
$198$	0	0
$199$	−1.58034e31	−1.45960	−0.729802	−	0.683658i	$-0.760388\pi$
$199$	−1.58034e31	−1.45960	−0.729802	+	0.683658i	$0.760388\pi$
$200$	−1.08914e31	−0.940110
$201$	0	0
$202$	3.41610e31	2.57802
$203$	−5.90310e29	−0.0416758
$204$	0	0
$205$	3.15463e30	0.195106
$206$	5.37170e31	3.11103
$207$	0	0
$208$	5.91750e28	0.00300804
$209$	−3.33784e31	−1.59034
$210$	0	0
$211$	−1.50086e31	−0.628820	−0.314410	−	0.949287i	$-0.601807\pi$
$211$	−1.50086e31	−0.628820	−0.314410	+	0.949287i	$0.601807\pi$
$212$	1.15752e31	0.454982
$213$	0	0
$214$	2.45768e31	0.851018
$215$	3.92658e30	0.127672
$216$	0	0
$217$	−1.78995e31	−0.513613
$218$	−5.91374e31	−1.59478
$219$	0	0
$220$	2.57413e31	0.613655
$221$	−9.11975e29	−0.0204497
$222$	0	0
$223$	−1.04534e31	−0.207559	−0.103779	−	0.994600i	$-0.533094\pi$
$223$	−1.04534e31	−0.207559	−0.103779	+	0.994600i	$0.533094\pi$
$224$	4.17390e31	0.780178
$225$	0	0
$226$	−6.88722e31	−1.14177
$227$	−9.45028e31	−1.47603	−0.738016	−	0.674783i	$-0.764237\pi$
$227$	−9.45028e31	−1.47603	−0.738016	+	0.674783i	$0.764237\pi$
$228$	0	0
$229$	−6.26689e31	−0.869508	−0.434754	−	0.900549i	$-0.643165\pi$
$229$	−6.26689e31	−0.869508	−0.434754	+	0.900549i	$0.643165\pi$
$230$	3.02474e31	0.395697
$231$	0	0
$232$	4.58785e30	0.0533975
$233$	−7.87335e31	−0.864678	−0.432339	−	0.901711i	$-0.642312\pi$
$233$	−7.87335e31	−0.864678	−0.432339	+	0.901711i	$0.642312\pi$
$234$	0	0
$235$	−5.42922e30	−0.0531277
$236$	−1.97894e32	−1.82861
$237$	0	0
$238$	−2.01607e31	−0.166233
$239$	5.65108e30	0.0440311	0.0220156	−	0.999758i	$-0.492992\pi$
$239$	5.65108e30	0.0440311	0.0220156	+	0.999758i	$0.492992\pi$
$240$	0	0
$241$	−4.42939e31	−0.308400	−0.154200	−	0.988040i	$-0.549280\pi$
$241$	−4.42939e31	−0.308400	−0.154200	+	0.988040i	$0.549280\pi$
$242$	5.54311e32	3.64961
$243$	0	0
$244$	3.18274e32	1.87516
$245$	1.55401e31	0.0866389
$246$	0	0
$247$	−2.69102e31	−0.134434
$248$	1.39114e32	0.658071
$249$	0	0
$250$	1.57190e32	0.667166
$251$	3.28116e32	1.31957	0.659785	−	0.751454i	$-0.270647\pi$
$251$	3.28116e32	1.31957	0.659785	+	0.751454i	$0.270647\pi$
$252$	0	0
$253$	5.79505e32	2.09377
$254$	−5.03822e32	−1.72592
$255$	0	0
$256$	−3.14099e32	−0.967894
$257$	−3.48288e31	−0.101822	−0.0509109	−	0.998703i	$-0.516212\pi$
$257$	−3.48288e31	−0.101822	−0.0509109	+	0.998703i	$0.516212\pi$
$258$	0	0
$259$	−2.95311e32	−0.777559
$260$	2.07531e31	0.0518731
$261$	0	0
$262$	−5.94736e32	−1.34047
$263$	−3.82694e31	−0.0819311	−0.0409656	−	0.999161i	$-0.513043\pi$
$263$	−3.82694e31	−0.0819311	−0.0409656	+	0.999161i	$0.513043\pi$
$264$	0	0
$265$	−3.08999e31	−0.0597225
$266$	−5.94895e32	−1.09279
$267$	0	0
$268$	−6.95274e32	−1.15435
$269$	4.44965e31	0.0702539	0.0351269	−	0.999383i	$-0.488816\pi$
$269$	4.44965e31	0.0702539	0.0351269	+	0.999383i	$0.488816\pi$
$270$	0	0
$271$	3.62870e32	0.518401	0.259200	−	0.965824i	$-0.416541\pi$
$271$	3.62870e32	0.518401	0.259200	+	0.965824i	$0.416541\pi$
$272$	−1.94302e30	−0.00264118
$273$	0	0
$274$	−3.98963e32	−0.491247
$275$	1.47142e33	1.72483
$276$	0	0
$277$	1.40758e33	1.49622	0.748111	−	0.663574i	$-0.230961\pi$
$277$	1.40758e33	1.49622	0.748111	+	0.663574i	$0.230961\pi$
$278$	−2.17020e33	−2.19733
$279$	0	0
$280$	1.73679e32	0.159630
$281$	−3.59534e32	−0.314924	−0.157462	−	0.987525i	$-0.550331\pi$
$281$	−3.59534e32	−0.314924	−0.157462	+	0.987525i	$0.550331\pi$
$282$	0	0
$283$	−3.59177e32	−0.285885	−0.142943	−	0.989731i	$-0.545656\pi$
$283$	−3.59177e32	−0.285885	−0.142943	+	0.989731i	$0.545656\pi$
$284$	−7.30568e32	−0.554451
$285$	0	0
$286$	6.44688e32	0.445049
$287$	1.07719e33	0.709390
$288$	0	0
$289$	−1.63777e33	−0.982044
$290$	−3.23515e31	−0.0185149
$291$	0	0
$292$	2.85466e33	1.48897
$293$	−3.51312e32	−0.174976	−0.0874882	−	0.996166i	$-0.527884\pi$
$293$	−3.51312e32	−0.174976	−0.0874882	+	0.996166i	$0.527884\pi$
$294$	0	0
$295$	5.28278e32	0.240030
$296$	2.29514e33	0.996255
$297$	0	0
$298$	−5.06167e33	−2.00620
$299$	4.67206e32	0.176990
$300$	0	0
$301$	1.34078e33	0.464204
$302$	1.20454e33	0.398773
$303$	0	0
$304$	−5.73340e31	−0.0173628
$305$	−8.49630e32	−0.246140
$306$	0	0
$307$	−6.75654e32	−0.179208	−0.0896038	−	0.995977i	$-0.528560\pi$
$307$	−6.75654e32	−0.179208	−0.0896038	+	0.995977i	$0.528560\pi$
$308$	8.78968e33	2.23120
$309$	0	0
$310$	−9.80972e32	−0.228178
$311$	−5.16690e33	−1.15071	−0.575354	−	0.817905i	$-0.695136\pi$
$311$	−5.16690e33	−1.15071	−0.575354	+	0.817905i	$0.695136\pi$
$312$	0	0
$313$	−1.10679e33	−0.226056	−0.113028	−	0.993592i	$-0.536055\pi$
$313$	−1.10679e33	−0.226056	−0.113028	+	0.993592i	$0.536055\pi$
$314$	−1.37821e34	−2.69628
$315$	0	0
$316$	1.00697e34	1.80817
$317$	9.49991e33	1.63463	0.817315	−	0.576191i	$-0.195461\pi$
$317$	9.49991e33	1.63463	0.817315	+	0.576191i	$0.195461\pi$
$318$	0	0
$319$	−6.19817e32	−0.0979691
$320$	2.26000e33	0.342440
$321$	0	0
$322$	1.03284e34	1.43872
$323$	8.83602e32	0.118038
$324$	0	0
$325$	1.18629e33	0.145802
$326$	9.20072e33	1.08489
$327$	0	0
$328$	−8.37180e33	−0.908913
$329$	−1.85387e33	−0.193168
$330$	0	0
$331$	−1.25351e34	−1.20351	−0.601757	−	0.798679i	$-0.705533\pi$
$331$	−1.25351e34	−1.20351	−0.601757	+	0.798679i	$0.705533\pi$
$332$	−1.54359e34	−1.42288
$333$	0	0
$334$	−1.19286e34	−1.01394
$335$	1.85603e33	0.151524
$336$	0	0
$337$	−3.36740e33	−0.253683	−0.126842	−	0.991923i	$-0.540484\pi$
$337$	−3.36740e33	−0.253683	−0.126842	+	0.991923i	$0.540484\pi$
$338$	−2.17968e34	−1.57768
$339$	0	0
$340$	−6.81430e32	−0.0455466
$341$	−1.87943e34	−1.20737
$342$	0	0
$343$	1.82434e34	1.08302
$344$	−1.04204e34	−0.594766
$345$	0	0
$346$	−5.07409e34	−2.67813
$347$	1.91545e34	0.972353	0.486177	−	0.873861i	$-0.338391\pi$
$347$	1.91545e34	0.972353	0.486177	+	0.873861i	$0.338391\pi$
$348$	0	0
$349$	1.45433e34	0.683158	0.341579	−	0.939853i	$-0.389038\pi$
$349$	1.45433e34	0.683158	0.341579	+	0.939853i	$0.389038\pi$
$350$	2.62248e34	1.18521
$351$	0	0
$352$	4.38253e34	1.83400
$353$	4.39359e33	0.176954	0.0884772	−	0.996078i	$-0.471800\pi$
$353$	4.39359e33	0.176954	0.0884772	+	0.996078i	$0.471800\pi$
$354$	0	0
$355$	1.95025e33	0.0727791
$356$	3.03902e34	1.09184
$357$	0	0
$358$	3.08877e34	1.02888
$359$	−2.60550e34	−0.835828	−0.417914	−	0.908487i	$-0.637239\pi$
$359$	−2.60550e34	−0.835828	−0.417914	+	0.908487i	$0.637239\pi$
$360$	0	0
$361$	−7.52760e33	−0.224032
$362$	8.05172e34	2.30846
$363$	0	0
$364$	7.08639e33	0.188606
$365$	−7.62050e33	−0.195447
$366$	0	0
$367$	3.50053e34	0.833953	0.416977	−	0.908917i	$-0.363090\pi$
$367$	3.50053e34	0.833953	0.416977	+	0.908917i	$0.363090\pi$
$368$	9.95413e32	0.0228590
$369$	0	0
$370$	−1.61843e34	−0.345439
$371$	−1.05512e34	−0.217146
$372$	0	0
$373$	−2.06100e34	−0.394464	−0.197232	−	0.980357i	$-0.563195\pi$
$373$	−2.06100e34	−0.394464	−0.197232	+	0.980357i	$0.563195\pi$
$374$	−2.11684e34	−0.390771
$375$	0	0
$376$	1.44082e34	0.247499
$377$	−4.99707e32	−0.00828146
$378$	0	0
$379$	−3.69120e34	−0.569559	−0.284779	−	0.958593i	$-0.591920\pi$
$379$	−3.69120e34	−0.569559	−0.284779	+	0.958593i	$0.591920\pi$
$380$	−2.01074e34	−0.299418
$381$	0	0
$382$	−1.00277e35	−1.39106
$383$	−6.12833e34	−0.820652	−0.410326	−	0.911939i	$-0.634585\pi$
$383$	−6.12833e34	−0.820652	−0.410326	+	0.911939i	$0.634585\pi$
$384$	0	0
$385$	−2.34640e34	−0.292875
$386$	4.62439e34	0.557348
$387$	0	0
$388$	8.15476e34	0.916606
$389$	−5.65060e34	−0.613444	−0.306722	−	0.951799i	$-0.599232\pi$
$389$	−5.65060e34	−0.613444	−0.306722	+	0.951799i	$0.599232\pi$
$390$	0	0
$391$	−1.53408e34	−0.155404
$392$	−4.12407e34	−0.403612
$393$	0	0
$394$	8.25924e34	0.754642
$395$	−2.68810e34	−0.237347
$396$	0	0
$397$	−2.20649e35	−1.81983	−0.909915	−	0.414794i	$-0.863854\pi$
$397$	−2.20649e35	−1.81983	−0.909915	+	0.414794i	$0.863854\pi$
$398$	−2.95739e35	−2.35769
$399$	0	0
$400$	2.52746e33	0.0188310
$401$	1.87612e35	1.35148	0.675741	−	0.737139i	$-0.263824\pi$
$401$	1.87612e35	1.35148	0.675741	+	0.737139i	$0.263824\pi$
$402$	0	0
$403$	−1.51522e34	−0.102061
$404$	3.94265e35	2.56827
$405$	0	0
$406$	−1.10468e34	−0.0673188
$407$	−3.10072e35	−1.82784
$408$	0	0
$409$	2.22853e35	1.22957	0.614786	−	0.788694i	$-0.289242\pi$
$409$	2.22853e35	1.22957	0.614786	+	0.788694i	$0.289242\pi$
$410$	5.90344e34	0.315154
$411$	0	0
$412$	6.19970e35	3.09926
$413$	1.80387e35	0.872729
$414$	0	0
$415$	4.12062e34	0.186773
$416$	3.53327e34	0.155030
$417$	0	0
$418$	−6.24631e35	−2.56888
$419$	5.47879e34	0.218170	0.109085	−	0.994032i	$-0.465208\pi$
$419$	5.47879e34	0.218170	0.109085	+	0.994032i	$0.465208\pi$
$420$	0	0
$421$	−1.97758e35	−0.738458	−0.369229	−	0.929338i	$-0.620378\pi$
$421$	−1.97758e35	−0.738458	−0.369229	+	0.929338i	$0.620378\pi$
$422$	−2.80864e35	−1.01573
$423$	0	0
$424$	8.20028e34	0.278221
$425$	−3.89519e34	−0.128020
$426$	0	0
$427$	−2.90116e35	−0.894945
$428$	2.83650e35	0.847798
$429$	0	0
$430$	7.34804e34	0.206228
$431$	4.94928e35	1.34617	0.673083	−	0.739567i	$-0.264970\pi$
$431$	4.94928e35	1.34617	0.673083	+	0.739567i	$0.264970\pi$
$432$	0	0
$433$	3.12882e35	0.799454	0.399727	−	0.916634i	$-0.369105\pi$
$433$	3.12882e35	0.799454	0.399727	+	0.916634i	$0.369105\pi$
$434$	−3.34965e35	−0.829637
$435$	0	0
$436$	−6.82528e35	−1.58874
$437$	−4.52671e35	−1.02160
$438$	0	0
$439$	7.22790e35	1.53370	0.766852	−	0.641824i	$-0.221822\pi$
$439$	7.22790e35	1.53370	0.766852	+	0.641824i	$0.221822\pi$
$440$	1.82361e35	0.375249
$441$	0	0
$442$	−1.70663e34	−0.0330324
$443$	7.68142e35	1.44209	0.721043	−	0.692891i	$-0.243663\pi$
$443$	7.68142e35	1.44209	0.721043	+	0.692891i	$0.243663\pi$
$444$	0	0
$445$	−8.11264e34	−0.143318
$446$	−1.95620e35	−0.335269
$447$	0	0
$448$	7.71705e35	1.24508
$449$	6.52536e35	1.02160	0.510798	−	0.859701i	$-0.329350\pi$
$449$	6.52536e35	1.02160	0.510798	+	0.859701i	$0.329350\pi$
$450$	0	0
$451$	1.13103e36	1.66759
$452$	−7.94881e35	−1.13745
$453$	0	0
$454$	−1.76849e36	−2.38423
$455$	−1.89171e34	−0.0247571
$456$	0	0
$457$	6.21081e35	0.766090	0.383045	−	0.923730i	$-0.374875\pi$
$457$	6.21081e35	0.766090	0.383045	+	0.923730i	$0.374875\pi$
$458$	−1.17276e36	−1.40451
$459$	0	0
$460$	3.49098e35	0.394200
$461$	−1.02161e36	−1.12027	−0.560133	−	0.828402i	$-0.689250\pi$
$461$	−1.02161e36	−1.12027	−0.560133	+	0.828402i	$0.689250\pi$
$462$	0	0
$463$	−1.10341e36	−1.14129	−0.570643	−	0.821199i	$-0.693306\pi$
$463$	−1.10341e36	−1.14129	−0.570643	+	0.821199i	$0.693306\pi$
$464$	−1.06466e33	−0.00106959
$465$	0	0
$466$	−1.47339e36	−1.39671
$467$	−8.66440e35	−0.797922	−0.398961	−	0.916968i	$-0.630629\pi$
$467$	−8.66440e35	−0.797922	−0.398961	+	0.916968i	$0.630629\pi$
$468$	0	0
$469$	6.33764e35	0.550927
$470$	−1.01600e35	−0.0858171
$471$	0	0
$472$	−1.40195e36	−1.11819
$473$	1.40780e36	1.09123
$474$	0	0
$475$	−1.14938e36	−0.841588
$476$	−2.32683e35	−0.165604
$477$	0	0
$478$	1.05752e35	0.0711234
$479$	2.57345e36	1.68262	0.841311	−	0.540552i	$-0.181785\pi$
$479$	2.57345e36	1.68262	0.841311	+	0.540552i	$0.181785\pi$
$480$	0	0
$481$	−2.49985e35	−0.154510
$482$	−8.28899e35	−0.498157
$483$	0	0
$484$	6.39752e36	3.63580
$485$	−2.17691e35	−0.120317
$486$	0	0
$487$	−2.28927e36	−1.19690	−0.598448	−	0.801162i	$-0.704216\pi$
$487$	−2.28927e36	−1.19690	−0.598448	+	0.801162i	$0.704216\pi$
$488$	2.25476e36	1.14666
$489$	0	0
$490$	2.90812e35	0.139948
$491$	−1.74114e36	−0.815142	−0.407571	−	0.913174i	$-0.633624\pi$
$491$	−1.74114e36	−0.815142	−0.407571	+	0.913174i	$0.633624\pi$
$492$	0	0
$493$	1.64079e34	0.00727145
$494$	−5.03587e35	−0.217151
$495$	0	0
$496$	−3.22828e34	−0.0131816
$497$	6.65935e35	0.264619
$498$	0	0
$499$	2.80174e36	1.05456	0.527278	−	0.849693i	$-0.323213\pi$
$499$	2.80174e36	1.05456	0.527278	+	0.849693i	$0.323213\pi$
$500$	1.81419e36	0.664641
$501$	0	0
$502$	6.14024e36	2.13150
$503$	−3.44032e36	−1.16260	−0.581301	−	0.813688i	$-0.697456\pi$
$503$	−3.44032e36	−1.16260	−0.581301	+	0.813688i	$0.697456\pi$
$504$	0	0
$505$	−1.05249e36	−0.337119
$506$	1.08446e37	3.38207
$507$	0	0
$508$	−5.81480e36	−1.71939
$509$	−1.50719e35	−0.0433989	−0.0216995	−	0.999765i	$-0.506908\pi$
$509$	−1.50719e35	−0.0433989	−0.0216995	+	0.999765i	$0.506908\pi$
$510$	0	0
$511$	−2.60211e36	−0.710631
$512$	1.48198e35	0.0394183
$513$	0	0
$514$	−6.51772e35	−0.164473
$515$	−1.65501e36	−0.406820
$516$	0	0
$517$	−1.94654e36	−0.454089
$518$	−5.52634e36	−1.25599
$519$	0	0
$520$	1.47022e35	0.0317203
$521$	−8.14778e36	−1.71289	−0.856446	−	0.516236i	$-0.827333\pi$
$521$	−8.14778e36	−1.71289	−0.856446	+	0.516236i	$0.827333\pi$
$522$	0	0
$523$	−4.14380e36	−0.827229	−0.413615	−	0.910452i	$-0.635734\pi$
$523$	−4.14380e36	−0.827229	−0.413615	+	0.910452i	$0.635734\pi$
$524$	−6.86409e36	−1.33540
$525$	0	0
$526$	−7.16158e35	−0.132343
$527$	4.97526e35	0.0896133
$528$	0	0
$529$	2.01590e36	0.344999
$530$	−5.78249e35	−0.0964696
$531$	0	0
$532$	−6.86591e36	−1.08866
$533$	9.11854e35	0.140964
$534$	0	0
$535$	−7.57203e35	−0.111285
$536$	−4.92557e36	−0.705881
$537$	0	0
$538$	8.32690e35	0.113481
$539$	5.57161e36	0.740512
$540$	0	0
$541$	1.06017e37	1.34033	0.670163	−	0.742214i	$-0.266224\pi$
$541$	1.06017e37	1.34033	0.670163	+	0.742214i	$0.266224\pi$
$542$	6.79060e36	0.837371
$543$	0	0
$544$	−1.16016e36	−0.136123
$545$	1.82201e36	0.208544
$546$	0	0
$547$	8.42305e36	0.917573	0.458786	−	0.888547i	$-0.348284\pi$
$547$	8.42305e36	0.917573	0.458786	+	0.888547i	$0.348284\pi$
$548$	−4.60459e36	−0.489388
$549$	0	0
$550$	2.75356e37	2.78611
$551$	4.84160e35	0.0478016
$552$	0	0
$553$	−9.17883e36	−0.862975
$554$	2.63409e37	2.41684
$555$	0	0
$556$	−2.50471e37	−2.18901
$557$	5.59363e36	0.477143	0.238571	−	0.971125i	$-0.423321\pi$
$557$	5.59363e36	0.477143	0.238571	+	0.971125i	$0.423321\pi$
$558$	0	0
$559$	1.13499e36	0.0922427
$560$	−4.03040e34	−0.00319750
$561$	0	0
$562$	−6.72818e36	−0.508695
$563$	−2.06136e37	−1.52157	−0.760783	−	0.649006i	$-0.775185\pi$
$563$	−2.06136e37	−1.52157	−0.760783	+	0.649006i	$0.775185\pi$
$564$	0	0
$565$	2.12193e36	0.149306
$566$	−6.72150e36	−0.461790
$567$	0	0
$568$	−5.17560e36	−0.339046
$569$	−4.96854e36	−0.317844	−0.158922	−	0.987291i	$-0.550802\pi$
$569$	−4.96854e36	−0.317844	−0.158922	+	0.987291i	$0.550802\pi$
$570$	0	0
$571$	1.02940e36	0.0628055	0.0314028	−	0.999507i	$-0.490003\pi$
$571$	1.02940e36	0.0628055	0.0314028	+	0.999507i	$0.490003\pi$
$572$	7.44060e36	0.443365
$573$	0	0
$574$	2.01580e37	1.14587
$575$	1.99551e37	1.10800
$576$	0	0
$577$	−4.63258e36	−0.245442	−0.122721	−	0.992441i	$-0.539162\pi$
$577$	−4.63258e36	−0.245442	−0.122721	+	0.992441i	$0.539162\pi$
$578$	−3.06485e37	−1.58629
$579$	0	0
$580$	−3.73382e35	−0.0184449
$581$	1.40703e37	0.679090
$582$	0	0
$583$	−1.10786e37	−0.510455
$584$	2.02234e37	0.910503
$585$	0	0
$586$	−6.57430e36	−0.282639
$587$	−2.64137e36	−0.110972	−0.0554862	−	0.998459i	$-0.517671\pi$
$587$	−2.64137e36	−0.110972	−0.0554862	+	0.998459i	$0.517671\pi$
$588$	0	0
$589$	1.46808e37	0.589107
$590$	9.88599e36	0.387720
$591$	0	0
$592$	−5.32610e35	−0.0199557
$593$	3.52090e37	1.28948	0.644741	−	0.764401i	$-0.276965\pi$
$593$	3.52090e37	1.28948	0.644741	+	0.764401i	$0.276965\pi$
$594$	0	0
$595$	6.21145e35	0.0217377
$596$	−5.84187e37	−1.99861
$597$	0	0
$598$	8.74311e36	0.285891
$599$	−4.76915e37	−1.52468	−0.762341	−	0.647176i	$-0.775950\pi$
$599$	−4.76915e37	−1.52468	−0.762341	+	0.647176i	$0.775950\pi$
$600$	0	0
$601$	−2.39124e37	−0.730831	−0.365416	−	0.930844i	$-0.619073\pi$
$601$	−2.39124e37	−0.730831	−0.365416	+	0.930844i	$0.619073\pi$
$602$	2.50908e37	0.749827
$603$	0	0
$604$	1.39020e37	0.397264
$605$	−1.70782e37	−0.477247
$606$	0	0
$607$	3.35424e37	0.896493	0.448246	−	0.893910i	$-0.352049\pi$
$607$	3.35424e37	0.896493	0.448246	+	0.893910i	$0.352049\pi$
$608$	−3.42334e37	−0.894854
$609$	0	0
$610$	−1.58996e37	−0.397589
$611$	−1.56933e36	−0.0383847
$612$	0	0
$613$	−6.25036e37	−1.46281	−0.731407	−	0.681942i	$-0.761136\pi$
$613$	−6.25036e37	−1.46281	−0.731407	+	0.681942i	$0.761136\pi$
$614$	−1.26439e37	−0.289474
$615$	0	0
$616$	6.22692e37	1.36437
$617$	6.57455e37	1.40934	0.704671	−	0.709534i	$-0.251094\pi$
$617$	6.57455e37	1.40934	0.704671	+	0.709534i	$0.251094\pi$
$618$	0	0
$619$	2.39694e37	0.491851	0.245926	−	0.969289i	$-0.420908\pi$
$619$	2.39694e37	0.491851	0.245926	+	0.969289i	$0.420908\pi$
$620$	−1.13218e37	−0.227315
$621$	0	0
$622$	−9.66913e37	−1.85873
$623$	−2.77016e37	−0.521094
$624$	0	0
$625$	4.81915e37	0.868140
$626$	−2.07120e37	−0.365148
$627$	0	0
$628$	−1.59065e38	−2.68608
$629$	8.20831e36	0.135666
$630$	0	0
$631$	−2.72032e37	−0.430748	−0.215374	−	0.976532i	$-0.569097\pi$
$631$	−2.72032e37	−0.430748	−0.215374	+	0.976532i	$0.569097\pi$
$632$	7.13372e37	1.10570
$633$	0	0
$634$	1.77778e38	2.64041
$635$	1.55226e37	0.225693
$636$	0	0
$637$	4.49192e36	0.0625965
$638$	−1.15990e37	−0.158249
$639$	0	0
$640$	2.58865e37	0.338566
$641$	−6.03099e37	−0.772334	−0.386167	−	0.922429i	$-0.626201\pi$
$641$	−6.03099e37	−0.772334	−0.386167	+	0.922429i	$0.626201\pi$
$642$	0	0
$643$	−1.01937e38	−1.25165	−0.625823	−	0.779965i	$-0.715237\pi$
$643$	−1.01937e38	−1.25165	−0.625823	+	0.779965i	$0.715237\pi$
$644$	1.19204e38	1.43328
$645$	0	0
$646$	1.65354e37	0.190667
$647$	−1.38190e36	−0.0156052	−0.00780260	−	0.999970i	$-0.502484\pi$
$647$	−1.38190e36	−0.0156052	−0.00780260	+	0.999970i	$0.502484\pi$
$648$	0	0
$649$	1.89404e38	2.05156
$650$	2.21997e37	0.235514
$651$	0	0
$652$	1.06189e38	1.08078
$653$	1.67383e38	1.66872	0.834358	−	0.551224i	$-0.185839\pi$
$653$	1.67383e38	1.66872	0.834358	+	0.551224i	$0.185839\pi$
$654$	0	0
$655$	1.83236e37	0.175289
$656$	1.94276e36	0.0182061
$657$	0	0
$658$	−3.46926e37	−0.312024
$659$	1.83021e38	1.61268	0.806339	−	0.591454i	$-0.201446\pi$
$659$	1.83021e38	1.61268	0.806339	+	0.591454i	$0.201446\pi$
$660$	0	0
$661$	6.09366e37	0.515417	0.257708	−	0.966223i	$-0.417033\pi$
$661$	6.09366e37	0.515417	0.257708	+	0.966223i	$0.417033\pi$
$662$	−2.34578e38	−1.94403
$663$	0	0
$664$	−1.09354e38	−0.870090
$665$	1.83285e37	0.142901
$666$	0	0
$667$	−8.40581e36	−0.0629334
$668$	−1.37672e38	−1.01010
$669$	0	0
$670$	3.47330e37	0.244756
$671$	−3.04618e38	−2.10379
$672$	0	0
$673$	−6.36340e37	−0.422168	−0.211084	−	0.977468i	$-0.567699\pi$
$673$	−6.36340e37	−0.422168	−0.211084	+	0.977468i	$0.567699\pi$
$674$	−6.30163e37	−0.409774
$675$	0	0
$676$	−2.51566e38	−1.57171
$677$	5.37104e37	0.328936	0.164468	−	0.986382i	$-0.447409\pi$
$677$	5.37104e37	0.328936	0.164468	+	0.986382i	$0.447409\pi$
$678$	0	0
$679$	−7.43332e37	−0.437462
$680$	−4.82749e36	−0.0278517
$681$	0	0
$682$	−3.51708e38	−1.95026
$683$	−1.59190e38	−0.865437	−0.432718	−	0.901529i	$-0.642446\pi$
$683$	−1.59190e38	−0.865437	−0.432718	+	0.901529i	$0.642446\pi$
$684$	0	0
$685$	1.22919e37	0.0642387
$686$	3.41399e38	1.74939
$687$	0	0
$688$	2.41817e36	0.0119136
$689$	−8.93171e36	−0.0431495
$690$	0	0
$691$	−1.11503e38	−0.518006	−0.259003	−	0.965877i	$-0.583394\pi$
$691$	−1.11503e38	−0.518006	−0.259003	+	0.965877i	$0.583394\pi$
$692$	−5.85621e38	−2.66799
$693$	0	0
$694$	3.58451e38	1.57064
$695$	6.68631e37	0.287337
$696$	0	0
$697$	−2.99409e37	−0.123772
$698$	2.72158e38	1.10350
$699$	0	0
$700$	3.02671e38	1.18072
$701$	−9.04824e37	−0.346235	−0.173117	−	0.984901i	$-0.555384\pi$
$701$	−9.04824e37	−0.346235	−0.173117	+	0.984901i	$0.555384\pi$
$702$	0	0
$703$	2.42208e38	0.891849
$704$	8.10278e38	2.92687
$705$	0	0
$706$	8.22199e37	0.285834
$707$	−3.59385e38	−1.22574
$708$	0	0
$709$	2.52263e38	0.828190	0.414095	−	0.910234i	$-0.364098\pi$
$709$	2.52263e38	0.828190	0.414095	+	0.910234i	$0.364098\pi$
$710$	3.64961e37	0.117560
$711$	0	0
$712$	2.15295e38	0.667657
$713$	−2.54883e38	−0.775591
$714$	0	0
$715$	−1.98626e37	−0.0581976
$716$	3.56488e38	1.02499
$717$	0	0
$718$	−4.87584e38	−1.35011
$719$	2.15368e38	0.585249	0.292624	−	0.956227i	$-0.405471\pi$
$719$	2.15368e38	0.585249	0.292624	+	0.956227i	$0.405471\pi$
$720$	0	0
$721$	−5.65122e38	−1.47916
$722$	−1.40869e38	−0.361878
$723$	0	0
$724$	9.29280e38	2.29973
$725$	−2.13433e37	−0.0518439
$726$	0	0
$727$	−6.18554e38	−1.44765	−0.723824	−	0.689985i	$-0.757617\pi$
$727$	−6.18554e38	−1.44765	−0.723824	+	0.689985i	$0.757617\pi$
$728$	5.02025e37	0.115332
$729$	0	0
$730$	−1.42607e38	−0.315706
$731$	−3.72675e37	−0.0809927
$732$	0	0
$733$	−5.13013e36	−0.0107455	−0.00537273	−	0.999986i	$-0.501710\pi$
$733$	−5.13013e36	−0.0107455	−0.00537273	+	0.999986i	$0.501710\pi$
$734$	6.55075e38	1.34708
$735$	0	0
$736$	5.94349e38	1.17812
$737$	6.65443e38	1.29509
$738$	0	0
$739$	−5.22466e38	−0.980298	−0.490149	−	0.871639i	$-0.663058\pi$
$739$	−5.22466e38	−0.980298	−0.490149	+	0.871639i	$0.663058\pi$
$740$	−1.86790e38	−0.344132
$741$	0	0
$742$	−1.97450e38	−0.350756
$743$	−1.00984e39	−1.76158	−0.880789	−	0.473509i	$-0.842987\pi$
$743$	−1.00984e39	−1.76158	−0.880789	+	0.473509i	$0.842987\pi$
$744$	0	0
$745$	1.55948e38	0.262344
$746$	−3.85686e38	−0.637177
$747$	0	0
$748$	−2.44313e38	−0.389292
$749$	−2.58556e38	−0.404622
$750$	0	0
$751$	−4.44629e38	−0.671210	−0.335605	−	0.942003i	$-0.608941\pi$
$751$	−4.44629e38	−0.671210	−0.335605	+	0.942003i	$0.608941\pi$
$752$	−3.34356e36	−0.00495757
$753$	0	0
$754$	−9.35131e36	−0.0133770
$755$	−3.71114e37	−0.0521463
$756$	0	0
$757$	8.24934e38	1.11847	0.559235	−	0.829009i	$-0.311095\pi$
$757$	8.24934e38	1.11847	0.559235	+	0.829009i	$0.311095\pi$
$758$	−6.90757e38	−0.920007
$759$	0	0
$760$	−1.42448e38	−0.183093
$761$	5.69669e38	0.719333	0.359666	−	0.933081i	$-0.382891\pi$
$761$	5.69669e38	0.719333	0.359666	+	0.933081i	$0.382891\pi$
$762$	0	0
$763$	6.22146e38	0.758248
$764$	−1.15733e39	−1.38579
$765$	0	0
$766$	−1.14683e39	−1.32560
$767$	1.52700e38	0.173421
$768$	0	0
$769$	1.47938e39	1.62209	0.811043	−	0.584986i	$-0.198900\pi$
$769$	1.47938e39	1.62209	0.811043	+	0.584986i	$0.198900\pi$
$770$	−4.39096e38	−0.473080
$771$	0	0
$772$	5.33720e38	0.555239
$773$	1.83758e39	1.87855	0.939277	−	0.343160i	$-0.111497\pi$
$773$	1.83758e39	1.87855	0.939277	+	0.343160i	$0.111497\pi$
$774$	0	0
$775$	−6.47176e38	−0.638924
$776$	5.77712e38	0.560503
$777$	0	0
$778$	−1.05743e39	−0.990894
$779$	−8.83484e38	−0.813660
$780$	0	0
$781$	6.99222e38	0.622051
$782$	−2.87081e38	−0.251023
$783$	0	0
$784$	9.57033e36	0.00808463
$785$	4.24623e38	0.352584
$786$	0	0
$787$	−3.93218e38	−0.315482	−0.157741	−	0.987481i	$-0.550421\pi$
$787$	−3.93218e38	−0.315482	−0.157741	+	0.987481i	$0.550421\pi$
$788$	9.53231e38	0.751786
$789$	0	0
$790$	−5.03040e38	−0.383386
$791$	7.24559e38	0.542864
$792$	0	0
$793$	−2.45588e38	−0.177836
$794$	−4.12914e39	−2.93957
$795$	0	0
$796$	−3.41324e39	−2.34877
$797$	1.32458e39	0.896168	0.448084	−	0.893991i	$-0.352107\pi$
$797$	1.32458e39	0.896168	0.448084	+	0.893991i	$0.352107\pi$
$798$	0	0
$799$	5.15293e37	0.0337033
$800$	1.50912e39	0.970527
$801$	0	0
$802$	3.51089e39	2.18305
$803$	−2.73218e39	−1.67051
$804$	0	0
$805$	−3.18213e38	−0.188137
$806$	−2.83553e38	−0.164858
$807$	0	0
$808$	2.79311e39	1.57049
$809$	2.19258e39	1.21241	0.606206	−	0.795308i	$-0.292691\pi$
$809$	2.19258e39	1.21241	0.606206	+	0.795308i	$0.292691\pi$
$810$	0	0
$811$	2.76373e39	1.47813	0.739066	−	0.673633i	$-0.235267\pi$
$811$	2.76373e39	1.47813	0.739066	+	0.673633i	$0.235267\pi$
$812$	−1.27496e38	−0.0670640
$813$	0	0
$814$	−5.80257e39	−2.95251
$815$	−2.83471e38	−0.141867
$816$	0	0
$817$	−1.09968e39	−0.532436
$818$	4.17038e39	1.98612
$819$	0	0
$820$	6.81340e38	0.313962
$821$	9.42212e38	0.427087	0.213543	−	0.976934i	$-0.431500\pi$
$821$	9.42212e38	0.427087	0.213543	+	0.976934i	$0.431500\pi$
$822$	0	0
$823$	2.17900e39	0.955782	0.477891	−	0.878419i	$-0.341401\pi$
$823$	2.17900e39	0.955782	0.477891	+	0.878419i	$0.341401\pi$
$824$	4.39208e39	1.89519
$825$	0	0
$826$	3.37569e39	1.40972
$827$	8.15484e38	0.335036	0.167518	−	0.985869i	$-0.446425\pi$
$827$	8.15484e38	0.335036	0.167518	+	0.985869i	$0.446425\pi$
$828$	0	0
$829$	1.51577e39	0.602763	0.301382	−	0.953504i	$-0.402552\pi$
$829$	1.51577e39	0.602763	0.301382	+	0.953504i	$0.402552\pi$
$830$	7.71116e38	0.301693
$831$	0	0
$832$	6.53260e38	0.247412
$833$	−1.47493e38	−0.0549622
$834$	0	0
$835$	3.67515e38	0.132589
$836$	−7.20911e39	−2.55916
$837$	0	0
$838$	1.02528e39	0.352409
$839$	−3.04177e39	−1.02882	−0.514410	−	0.857544i	$-0.671989\pi$
$839$	−3.04177e39	−1.02882	−0.514410	+	0.857544i	$0.671989\pi$
$840$	0	0
$841$	−3.04414e39	−0.997055
$842$	−3.70077e39	−1.19283
$843$	0	0
$844$	−3.24157e39	−1.01189
$845$	6.71554e38	0.206308
$846$	0	0
$847$	−5.83154e39	−1.73523
$848$	−1.90296e37	−0.00557295
$849$	0	0
$850$	−7.28931e38	−0.206791
$851$	−4.20513e39	−1.17417
$852$	0	0
$853$	−9.78044e38	−0.264574	−0.132287	−	0.991211i	$-0.542232\pi$
$853$	−9.78044e38	−0.264574	−0.132287	+	0.991211i	$0.542232\pi$
$854$	−5.42912e39	−1.44560
$855$	0	0
$856$	2.00948e39	0.518427
$857$	6.93851e39	1.76208	0.881039	−	0.473044i	$-0.156845\pi$
$857$	6.93851e39	1.76208	0.881039	+	0.473044i	$0.156845\pi$
$858$	0	0
$859$	−6.79141e39	−1.67129	−0.835646	−	0.549268i	$-0.814907\pi$
$859$	−6.79141e39	−1.67129	−0.835646	+	0.549268i	$0.814907\pi$
$860$	8.48066e38	0.205447
$861$	0	0
$862$	9.26188e39	2.17446
$863$	5.27048e38	0.121816	0.0609080	−	0.998143i	$-0.480600\pi$
$863$	5.27048e38	0.121816	0.0609080	+	0.998143i	$0.480600\pi$
$864$	0	0
$865$	1.56331e39	0.350210
$866$	5.85514e39	1.29136
$867$	0	0
$868$	−3.86596e39	−0.826497
$869$	−9.63764e39	−2.02863
$870$	0	0
$871$	5.36491e38	0.109476
$872$	−4.83527e39	−0.971512
$873$	0	0
$874$	−8.47110e39	−1.65019
$875$	−1.65369e39	−0.317209
$876$	0	0
$877$	3.42049e39	0.636200	0.318100	−	0.948057i	$-0.396955\pi$
$877$	3.42049e39	0.636200	0.318100	+	0.948057i	$0.396955\pi$
$878$	1.35260e40	2.47739
$879$	0	0
$880$	−4.23186e37	−0.00751650
$881$	7.31752e39	1.27994	0.639969	−	0.768401i	$-0.278947\pi$
$881$	7.31752e39	1.27994	0.639969	+	0.768401i	$0.278947\pi$
$882$	0	0
$883$	−2.06213e39	−0.349821	−0.174910	−	0.984584i	$-0.555964\pi$
$883$	−2.06213e39	−0.349821	−0.174910	+	0.984584i	$0.555964\pi$
$884$	−1.96969e38	−0.0329074
$885$	0	0
$886$	1.43747e40	2.32940
$887$	−6.98969e39	−1.11555	−0.557775	−	0.829992i	$-0.688345\pi$
$887$	−6.98969e39	−1.11555	−0.557775	+	0.829992i	$0.688345\pi$
$888$	0	0
$889$	5.30037e39	0.820602
$890$	−1.51817e39	−0.231502
$891$	0	0
$892$	−2.25773e39	−0.334000
$893$	1.52051e39	0.221561
$894$	0	0
$895$	−9.51642e38	−0.134543
$896$	8.83926e39	1.23100
$897$	0	0
$898$	1.22113e40	1.65018
$899$	2.72614e38	0.0362904
$900$	0	0
$901$	2.93274e38	0.0378869
$902$	2.11656e40	2.69366
$903$	0	0
$904$	−5.63122e39	−0.695550
$905$	−2.48071e39	−0.301870
$906$	0	0
$907$	−2.28488e39	−0.269876	−0.134938	−	0.990854i	$-0.543084\pi$
$907$	−2.28488e39	−0.269876	−0.134938	+	0.990854i	$0.543084\pi$
$908$	−2.04108e40	−2.37521
$909$	0	0
$910$	−3.54006e38	−0.0399901
$911$	−7.51662e39	−0.836612	−0.418306	−	0.908306i	$-0.637376\pi$
$911$	−7.51662e39	−0.836612	−0.418306	+	0.908306i	$0.637376\pi$
$912$	0	0
$913$	1.47737e40	1.59637
$914$	1.16227e40	1.23746
$915$	0	0
$916$	−1.35353e40	−1.39920
$917$	6.25683e39	0.637336
$918$	0	0
$919$	5.26405e39	0.520668	0.260334	−	0.965519i	$-0.416167\pi$
$919$	5.26405e39	0.520668	0.260334	+	0.965519i	$0.416167\pi$
$920$	2.47313e39	0.241052
$921$	0	0
$922$	−1.91179e40	−1.80956
$923$	5.63724e38	0.0525828
$924$	0	0
$925$	−1.06773e40	−0.967269
$926$	−2.06488e40	−1.84351
$927$	0	0
$928$	−6.35694e38	−0.0551252
$929$	2.48177e39	0.212104	0.106052	−	0.994361i	$-0.466179\pi$
$929$	2.48177e39	0.212104	0.106052	+	0.994361i	$0.466179\pi$
$930$	0	0
$931$	−4.35217e39	−0.361314
$932$	−1.70049e40	−1.39143
$933$	0	0
$934$	−1.62142e40	−1.28888
$935$	6.52193e38	0.0510998
$936$	0	0
$937$	−2.96211e39	−0.225485	−0.112742	−	0.993624i	$-0.535963\pi$
$937$	−2.96211e39	−0.225485	−0.112742	+	0.993624i	$0.535963\pi$
$938$	1.18600e40	0.889911
$939$	0	0
$940$	−1.17261e39	−0.0854923
$941$	−1.23582e40	−0.888168	−0.444084	−	0.895985i	$-0.646471\pi$
$941$	−1.23582e40	−0.888168	−0.444084	+	0.895985i	$0.646471\pi$
$942$	0	0
$943$	1.53388e40	1.07123
$944$	3.25338e38	0.0223982
$945$	0	0
$946$	2.63449e40	1.76265
$947$	−3.62546e39	−0.239132	−0.119566	−	0.992826i	$-0.538150\pi$
$947$	−3.62546e39	−0.239132	−0.119566	+	0.992826i	$0.538150\pi$
$948$	0	0
$949$	−2.20273e39	−0.141210
$950$	−2.15090e40	−1.35941
$951$	0	0
$952$	−1.64841e39	−0.101266
$953$	2.05559e40	1.24504	0.622519	−	0.782605i	$-0.286109\pi$
$953$	2.05559e40	1.24504	0.622519	+	0.782605i	$0.286109\pi$
$954$	0	0
$955$	3.08950e39	0.181904
$956$	1.22053e39	0.0708542
$957$	0	0
$958$	4.81585e40	2.71793
$959$	4.19722e39	0.233567
$960$	0	0
$961$	−1.02164e40	−0.552757
$962$	−4.67813e39	−0.249579
$963$	0	0
$964$	−9.56665e39	−0.496272
$965$	−1.42476e39	−0.0728825
$966$	0	0
$967$	−2.81961e40	−1.40259	−0.701296	−	0.712871i	$-0.747395\pi$
$967$	−2.81961e40	−1.40259	−0.701296	+	0.712871i	$0.747395\pi$
$968$	4.53223e40	2.22328
$969$	0	0
$970$	−4.07378e39	−0.194348
$971$	1.81766e40	0.855170	0.427585	−	0.903975i	$-0.359364\pi$
$971$	1.81766e40	0.855170	0.427585	+	0.903975i	$0.359364\pi$
$972$	0	0
$973$	2.28312e40	1.04473
$974$	−4.28405e40	−1.93334
$975$	0	0
$976$	−5.23241e38	−0.0229683
$977$	−2.03258e40	−0.879974	−0.439987	−	0.898004i	$-0.645017\pi$
$977$	−2.03258e40	−0.879974	−0.439987	+	0.898004i	$0.645017\pi$
$978$	0	0
$979$	−2.90863e40	−1.22496
$980$	3.35638e39	0.139418
$981$	0	0
$982$	−3.25830e40	−1.31670
$983$	−7.72807e39	−0.308034	−0.154017	−	0.988068i	$-0.549221\pi$
$983$	−7.72807e39	−0.308034	−0.154017	+	0.988068i	$0.549221\pi$
$984$	0	0
$985$	−2.54465e39	−0.0986820
$986$	3.07052e38	0.0117455
$987$	0	0
$988$	−5.81210e39	−0.216329
$989$	1.90922e40	0.700981
$990$	0	0
$991$	1.25885e40	0.449758	0.224879	−	0.974387i	$-0.427801\pi$
$991$	1.25885e40	0.449758	0.224879	+	0.974387i	$0.427801\pi$
$992$	−1.92757e40	−0.679364
$993$	0	0
$994$	1.24620e40	0.427438
$995$	9.11164e39	0.308308
$996$	0	0
$997$	4.50833e40	1.48467	0.742336	−	0.670028i	$-0.233718\pi$
$997$	4.50833e40	1.48467	0.742336	+	0.670028i	$0.233718\pi$
$998$	5.24306e40	1.70342
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.28.a.d.1.2		2
3.2	odd	2		1.28.a.a.1.1	✓	2
12.11	even	2		16.28.a.d.1.2		2
15.2	even	4		25.28.b.a.24.1		4
15.8	even	4		25.28.b.a.24.4		4
15.14	odd	2		25.28.a.a.1.2		2
21.20	even	2		49.28.a.b.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.28.a.a.1.1	✓	2	3.2	odd	2
9.28.a.d.1.2		2	1.1	even	1	trivial
16.28.a.d.1.2		2	12.11	even	2
25.28.a.a.1.2		2	15.14	odd	2
25.28.b.a.24.1		4	15.2	even	4
25.28.b.a.24.4		4	15.8	even	4
49.28.a.b.1.1		2	21.20	even	2

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:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 28 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q+18713.6 q^{2} +2.15981e8 q^{4} -5.76560e8 q^{5} -1.96873e11 q^{7} +1.53009e12 q^{8} +O(q^{10})\)	\(q+18713.6 q^{2} +2.15981e8 q^{4} -5.76560e8 q^{5} -1.96873e11 q^{7} +1.53009e12 q^{8} -1.07895e13 q^{10} -2.06714e14 q^{11} -1.66656e14 q^{13} -3.68421e15 q^{14} -3.55072e14 q^{16} +5.47219e15 q^{17} +1.61471e17 q^{19} -1.24526e17 q^{20} -3.86837e18 q^{22} -2.80341e18 q^{23} -7.11816e18 q^{25} -3.11874e18 q^{26} -4.25209e19 q^{28} +2.99842e18 q^{29} +9.09190e19 q^{31} -2.12009e20 q^{32} +1.02404e20 q^{34} +1.13509e20 q^{35} +1.50001e21 q^{37} +3.02171e21 q^{38} -8.82187e20 q^{40} -5.47146e21 q^{41} -6.81035e21 q^{43} -4.46463e22 q^{44} -5.24619e22 q^{46} +9.41657e21 q^{47} -2.69532e22 q^{49} -1.33206e23 q^{50} -3.59946e22 q^{52} +5.35936e22 q^{53} +1.19183e23 q^{55} -3.01233e23 q^{56} +5.61113e22 q^{58} -9.16258e23 q^{59} +1.47362e24 q^{61} +1.70142e24 q^{62} -3.91980e24 q^{64} +9.60874e22 q^{65} -3.21915e24 q^{67} +1.18189e24 q^{68} +2.12417e24 q^{70} -3.38255e24 q^{71} +1.32172e25 q^{73} +2.80705e25 q^{74} +3.48748e25 q^{76} +4.06965e25 q^{77} +4.66230e25 q^{79} +2.04720e23 q^{80} -1.02391e26 q^{82} -7.14690e25 q^{83} -3.15505e24 q^{85} -1.27446e26 q^{86} -3.16290e26 q^{88} +1.40708e26 q^{89} +3.28102e25 q^{91} -6.05484e26 q^{92} +1.76218e26 q^{94} -9.30980e25 q^{95} +3.77568e26 q^{97} -5.04391e26 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8280 q^{2} + 190623296 q^{4} - 5443587900 q^{5} - 175391963600 q^{7} + 3195032348160 q^{8}+O(q^{10}) \) 2 * q + 8280 * q^2 + 190623296 * q^4 - 5443587900 * q^5 - 175391963600 * q^7 + 3195032348160 * q^8	\( 2 q + 8280 q^{2} + 190623296 q^{4} - 5443587900 q^{5} - 175391963600 q^{7} + 3195032348160 q^{8} + 39991096148400 q^{10} - 138167337691944 q^{11} - 753433801271060 q^{13} - 39\!\cdots\!12 q^{14}+ \cdots + 17\!\cdots\!40 q^{98}+O(q^{100}) \) 2 * q + 8280 * q^2 + 190623296 * q^4 - 5443587900 * q^5 - 175391963600 * q^7 + 3195032348160 * q^8 + 39991096148400 * q^10 - 138167337691944 * q^11 - 753433801271060 * q^13 - 3908340052811712 * q^14 - 14322995785166848 * q^16 + 29753620331011740 * q^17 + 404565810372684760 * q^19 - 1109219331427200 * q^20 - 4583556785578779360 * q^22 - 2929078923121218960 * q^23 + 9119218786673228750 * q^25 + 3003459254146640016 * q^26 - 43065656535315868160 * q^28 + 15546679995448558260 * q^29 + 28544554594467385024 * q^31 - 289738949030869893120 * q^32 - 150938335185934859568 * q^34 + 8958395384765013600 * q^35 + 1867697204682824566780 * q^37 + 485361223888169521440 * q^38 - 8985527186071883904000 * q^40 - 9081343698046512254964 * q^41 + 5145612605801421773800 * q^43 - 46384541037574305299712 * q^44 - 51150723570313970279616 * q^46 + 1150251488862201070560 * q^47 - 92204113217840907690414 * q^49 - 302620649115949014735000 * q^50 - 21115266673184124022400 * q^52 - 106953735591470060758620 * q^53 - 214436254091483969701200 * q^55 - 265467760964859260989440 * q^56 - 74812163717162466470160 * q^58 - 2009620977624026488631880 * q^59 + 147857426692448940370444 * q^61 + 2352212714010270811080960 * q^62 - 1234057803938137445761024 * q^64 + 2951949350200452960922200 * q^65 + 3051578535738098902157560 * q^67 + 566166870324676171716480 * q^68 + 3215012724032159046326400 * q^70 + 13175198820369338598286416 * q^71 + 5284260812951286572116660 * q^73 + 24234145145448525537787728 * q^74 + 28710432717942786872615680 * q^76 + 42169025756092787413646400 * q^77 + 62814351035720719918179040 * q^79 + 68186991639088251432345600 * q^80 - 64726649726985190956760560 * q^82 - 171806873410054757883176280 * q^83 - 121333441005595565089302600 * q^85 - 252189883901197432712215584 * q^86 - 202163623954874235550955520 * q^88 + 313473438761105539763494380 * q^89 + 20205365125040878536694304 * q^91 - 602296848225491467788034560 * q^92 + 262465434750720041893579392 * q^94 - 1276245244260479145691314000 * q^95 - 653202933397052842883888060 * q^97 + 176410316250092689584969240 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more