LMFDB - Embedded newform 9.34.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,34,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, 34, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 34);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 34 $
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:	$62.0845459929$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 589050 $ x^2 - x - 589050
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-766.996$ 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)

$f(q)$	$=$	$q+171359. q^{2} +2.07741e10 q^{4} +2.01492e11 q^{5} +5.50153e13 q^{7} +2.08788e15 q^{8} +O(q^{10})$	\(q+171359. q^{2} +2.07741e10 q^{4} +2.01492e11 q^{5} +5.50153e13 q^{7} +2.08788e15 q^{8} +3.45276e16 q^{10} +8.18909e16 q^{11} -1.90399e18 q^{13} +9.42739e18 q^{14} +1.79329e20 q^{16} +3.33893e20 q^{17} -1.40494e20 q^{19} +4.18583e21 q^{20} +1.40328e22 q^{22} -3.12767e22 q^{23} -7.58162e22 q^{25} -3.26267e23 q^{26} +1.14289e24 q^{28} +1.50979e24 q^{29} +5.18762e23 q^{31} +1.27950e25 q^{32} +5.72158e25 q^{34} +1.10852e25 q^{35} -3.01507e25 q^{37} -2.40749e25 q^{38} +4.20691e26 q^{40} +2.18887e26 q^{41} +1.76701e27 q^{43} +1.70121e27 q^{44} -5.35955e27 q^{46} -3.25654e27 q^{47} -4.70431e27 q^{49} -1.29918e28 q^{50} -3.95538e28 q^{52} -9.17652e27 q^{53} +1.65004e28 q^{55} +1.14865e29 q^{56} +2.58716e29 q^{58} +1.18267e29 q^{59} -9.92930e27 q^{61} +8.88948e28 q^{62} +6.52116e29 q^{64} -3.83640e29 q^{65} +1.11293e30 q^{67} +6.93634e30 q^{68} +1.89955e30 q^{70} -7.58425e29 q^{71} -6.06835e30 q^{73} -5.16661e30 q^{74} -2.91863e30 q^{76} +4.50525e30 q^{77} -5.57890e30 q^{79} +3.61334e31 q^{80} +3.75083e31 q^{82} -4.13746e31 q^{83} +6.72769e31 q^{85} +3.02793e32 q^{86} +1.70978e32 q^{88} -6.21572e31 q^{89} -1.04749e32 q^{91} -6.49745e32 q^{92} -5.58039e32 q^{94} -2.83084e31 q^{95} +4.04003e32 q^{97} -8.06129e32 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 121680 q^{2} + 14652233984 q^{4} + 181061536500 q^{5} - 67153080066800 q^{7} + 28\!\cdots\!40 q^{8}+O(q^{10}) $ 2 * q + 121680 * q^2 + 14652233984 * q^4 + 181061536500 * q^5 - 67153080066800 * q^7 + 2818750585098240 * q^8	$ 2 q + 121680 q^{2} + 14652233984 q^{4} + 181061536500 q^{5} - 67153080066800 q^{7} + 28\!\cdots\!40 q^{8}+ \cdots - 11\!\cdots\!40 q^{98}+O(q^{100}) $ 2 * q + 121680 * q^2 + 14652233984 * q^4 + 181061536500 * q^5 - 67153080066800 * q^7 + 2818750585098240 * q^8 + 35542592216532000 * q^10 - 133871815441914264 * q^11 - 2981610478259443940 * q^13 + 15496641262468340352 * q^14 + 195605979111894351872 * q^16 + 79361149261175525340 * q^17 - 1360696443041697171800 * q^19 + 4310900037459183168000 * q^20 + 24751741840613395122240 * q^22 - 26163854053674631579440 * q^23 - 191814088084783724781250 * q^25 - 272731683634642092710304 * q^26 + 1890794991723644827125760 * q^28 + 1674519971630399929109700 * q^29 - 6238301225723632337095616 * q^31 + 5708163006744585940500480 * q^32 + 69860790536166916073075808 * q^34 + 13581143663546216842308000 * q^35 - 104802741516758180098173620 * q^37 + 36544090911856460663722560 * q^38 + 405758480738092701742080000 * q^40 - 277566613022002182732188244 * q^41 + 1567661189367072113768291800 * q^43 + 3022085914387766085808346112 * q^44 - 5613550634763385681470869376 * q^46 - 5421061461431251260476972640 * q^47 + 2489799365888888933444851314 * q^49 - 7229107516344249428363250000 * q^50 - 32956722688372988680703091200 * q^52 + 26867414785542903092975171220 * q^53 + 20908570805489145209222682000 * q^55 + 25575237795171758759822131200 * q^56 + 250532370716581201796821222560 * q^58 + 305786409635298433026663995400 * q^59 - 5745893983413264859067362436 * q^61 + 424581887479352364037004290560 * q^62 + 864365322360380859973709594624 * q^64 - 361623311364964256200313721000 * q^65 + 1598906337224495341750209565960 * q^67 + 8494558579722382470601861086720 * q^68 + 1775546165763388432770973344000 * q^70 + 2669761937956104715736810084976 * q^71 + 946314321191998870965166536340 * q^73 - 1457936998080019494211346192928 * q^74 + 4551314657470802548563162035200 * q^76 + 30864620292716415864215760033600 * q^77 - 8535199972765636469730106191200 * q^79 + 35800819471604723635001769984000 * q^80 + 62171822095602398237444019107040 * q^82 - 29072605803747945444403983322920 * q^83 + 72477213859794605306963311287000 * q^85 + 312696885737578501917214826406336 * q^86 + 13282372192867492753038509752320 * q^88 - 132719467655604316264938597726900 * q^89 + 26902102147452358410548887211744 * q^91 - 681044992402323869436382557788160 * q^92 - 450506433888867898835049561530112 * q^94 - 3378716387067841884487537110000 * q^95 - 367787330930535727150839877856060 * q^97 - 1163527978168280943548587223169840 * 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 $

$2$	171359.	1.84890	0.924449	−	0.381305i	$-0.124525\pi$
$2$	171359.	1.84890	0.924449	+	0.381305i	$0.124525\pi$
$3$	0	0
$3$	0	0
$4$	2.07741e10	2.41843
$5$	2.01492e11	0.590545	0.295273	−	0.955413i	$-0.404589\pi$
$5$	2.01492e11	0.590545	0.295273	+	0.955413i	$0.404589\pi$
$6$	0	0
$7$	5.50153e13	0.625699	0.312850	−	0.949803i	$-0.398716\pi$
$7$	5.50153e13	0.625699	0.312850	+	0.949803i	$0.398716\pi$
$8$	2.08788e15	2.62253
$9$	0	0
$10$	3.45276e16	1.09186
$11$	8.18909e16	0.537349	0.268674	−	0.963231i	$-0.413414\pi$
$11$	8.18909e16	0.537349	0.268674	+	0.963231i	$0.413414\pi$
$12$	0	0
$13$	−1.90399e18	−0.793597	−0.396798	−	0.917906i	$-0.629879\pi$
$13$	−1.90399e18	−0.793597	−0.396798	+	0.917906i	$0.629879\pi$
$14$	9.42739e18	1.15685
$15$	0	0
$16$	1.79329e20	2.43036
$17$	3.33893e20	1.66418	0.832090	−	0.554640i	$-0.187144\pi$
$17$	3.33893e20	1.66418	0.832090	+	0.554640i	$0.187144\pi$
$18$	0	0
$19$	−1.40494e20	−0.111743	−0.0558717	−	0.998438i	$-0.517794\pi$
$19$	−1.40494e20	−0.111743	−0.0558717	+	0.998438i	$0.517794\pi$
$20$	4.18583e21	1.42819
$21$	0	0
$22$	1.40328e22	0.993503
$23$	−3.12767e22	−1.06344	−0.531718	−	0.846922i	$-0.678453\pi$
$23$	−3.12767e22	−1.06344	−0.531718	+	0.846922i	$0.678453\pi$
$24$	0	0
$25$	−7.58162e22	−0.651256
$26$	−3.26267e23	−1.46728
$27$	0	0
$28$	1.14289e24	1.51321
$29$	1.50979e24	1.12034	0.560168	−	0.828379i	$-0.310736\pi$
$29$	1.50979e24	1.12034	0.560168	+	0.828379i	$0.310736\pi$
$30$	0	0
$31$	5.18762e23	0.128086	0.0640428	−	0.997947i	$-0.479601\pi$
$31$	5.18762e23	0.128086	0.0640428	+	0.997947i	$0.479601\pi$
$32$	1.27950e25	1.87096
$33$	0	0
$34$	5.72158e25	3.07690
$35$	1.10852e25	0.369504
$36$	0	0
$37$	−3.01507e25	−0.401762	−0.200881	−	0.979616i	$-0.564380\pi$
$37$	−3.01507e25	−0.401762	−0.200881	+	0.979616i	$0.564380\pi$
$38$	−2.40749e25	−0.206602
$39$	0	0
$40$	4.20691e26	1.54872
$41$	2.18887e26	0.536149	0.268075	−	0.963398i	$-0.413613\pi$
$41$	2.18887e26	0.536149	0.268075	+	0.963398i	$0.413613\pi$
$42$	0	0
$43$	1.76701e27	1.97246	0.986232	−	0.165369i	$-0.0528817\pi$
$43$	1.76701e27	1.97246	0.986232	+	0.165369i	$0.0528817\pi$
$44$	1.70121e27	1.29954
$45$	0	0
$46$	−5.35955e27	−1.96618
$47$	−3.25654e27	−0.837802	−0.418901	−	0.908032i	$-0.637585\pi$
$47$	−3.25654e27	−0.837802	−0.418901	+	0.908032i	$0.637585\pi$
$48$	0	0
$49$	−4.70431e27	−0.608500
$50$	−1.29918e28	−1.20411
$51$	0	0
$52$	−3.95538e28	−1.91926
$53$	−9.17652e27	−0.325182	−0.162591	−	0.986694i	$-0.551985\pi$
$53$	−9.17652e27	−0.325182	−0.162591	+	0.986694i	$0.551985\pi$
$54$	0	0
$55$	1.65004e28	0.317329
$56$	1.14865e29	1.64091
$57$	0	0
$58$	2.58716e29	2.07139
$59$	1.18267e29	0.714174	0.357087	−	0.934071i	$-0.383770\pi$
$59$	1.18267e29	0.714174	0.357087	+	0.934071i	$0.383770\pi$
$60$	0	0
$61$	−9.92930e27	−0.0345920	−0.0172960	−	0.999850i	$-0.505506\pi$
$61$	−9.92930e27	−0.0345920	−0.0172960	+	0.999850i	$0.505506\pi$
$62$	8.88948e28	0.236817
$63$	0	0
$64$	6.52116e29	1.02886
$65$	−3.83640e29	−0.468655
$66$	0	0
$67$	1.11293e30	0.824583	0.412291	−	0.911052i	$-0.364729\pi$
$67$	1.11293e30	0.824583	0.412291	+	0.911052i	$0.364729\pi$
$68$	6.93634e30	4.02470
$69$	0	0
$70$	1.89955e30	0.683175
$71$	−7.58425e29	−0.215849	−0.107924	−	0.994159i	$-0.534420\pi$
$71$	−7.58425e29	−0.215849	−0.107924	+	0.994159i	$0.534420\pi$
$72$	0	0
$73$	−6.06835e30	−1.09205	−0.546026	−	0.837768i	$-0.683860\pi$
$73$	−6.06835e30	−1.09205	−0.546026	+	0.837768i	$0.683860\pi$
$74$	−5.16661e30	−0.742818
$75$	0	0
$76$	−2.91863e30	−0.270243
$77$	4.50525e30	0.336219
$78$	0	0
$79$	−5.57890e30	−0.272711	−0.136355	−	0.990660i	$-0.543539\pi$
$79$	−5.57890e30	−0.272711	−0.136355	+	0.990660i	$0.543539\pi$
$80$	3.61334e31	1.43524
$81$	0	0
$82$	3.75083e31	0.991286
$83$	−4.13746e31	−0.895252	−0.447626	−	0.894221i	$-0.647730\pi$
$83$	−4.13746e31	−0.895252	−0.447626	+	0.894221i	$0.647730\pi$
$84$	0	0
$85$	6.72769e31	0.982775
$86$	3.02793e32	3.64688
$87$	0	0
$88$	1.70978e32	1.40921
$89$	−6.21572e31	−0.425164	−0.212582	−	0.977143i	$-0.568187\pi$
$89$	−6.21572e31	−0.425164	−0.212582	+	0.977143i	$0.568187\pi$
$90$	0	0
$91$	−1.04749e32	−0.496553
$92$	−6.49745e32	−2.57184
$93$	0	0
$94$	−5.58039e32	−1.54901
$95$	−2.83084e31	−0.0659896
$96$	0	0
$97$	4.04003e32	0.667808	0.333904	−	0.942607i	$-0.391634\pi$
$97$	4.04003e32	0.667808	0.333904	+	0.942607i	$0.391634\pi$
$98$	−8.06129e32	−1.12506
$99$	0	0
$100$	−1.57501e33	−1.57501
$101$	1.20576e33	1.02319	0.511596	−	0.859226i	$-0.329054\pi$
$101$	1.20576e33	1.02319	0.511596	+	0.859226i	$0.329054\pi$
$102$	0	0
$103$	−1.69378e33	−1.04002	−0.520011	−	0.854159i	$-0.674072\pi$
$103$	−1.69378e33	−1.04002	−0.520011	+	0.854159i	$0.674072\pi$
$104$	−3.97530e33	−2.08123
$105$	0	0
$106$	−1.57248e33	−0.601228
$107$	−7.07121e32	−0.231559	−0.115780	−	0.993275i	$-0.536937\pi$
$107$	−7.07121e32	−0.231559	−0.115780	+	0.993275i	$0.536937\pi$
$108$	0	0
$109$	4.42814e33	1.06828	0.534139	−	0.845397i	$-0.320636\pi$
$109$	4.42814e33	1.06828	0.534139	+	0.845397i	$0.320636\pi$
$110$	2.82750e33	0.586709
$111$	0	0
$112$	9.86582e33	1.52067
$113$	−1.36496e34	−1.81687	−0.908437	−	0.418023i	$-0.862723\pi$
$113$	−1.36496e34	−1.81687	−0.908437	+	0.418023i	$0.862723\pi$
$114$	0	0
$115$	−6.30200e33	−0.628007
$116$	3.13645e34	2.70945
$117$	0	0
$118$	2.02661e34	1.32043
$119$	1.83692e34	1.04128
$120$	0	0
$121$	−1.65190e34	−0.711256
$122$	−1.70148e33	−0.0639572
$123$	0	0
$124$	1.07768e34	0.309766
$125$	−3.87332e34	−0.975142
$126$	0	0
$127$	−7.12185e34	−1.37985	−0.689925	−	0.723881i	$-0.742356\pi$
$127$	−7.12185e34	−1.37985	−0.689925	+	0.723881i	$0.742356\pi$
$128$	1.83832e33	0.0312936
$129$	0	0
$130$	−6.57403e34	−0.866496
$131$	2.95217e34	0.342898	0.171449	−	0.985193i	$-0.445155\pi$
$131$	2.95217e34	0.342898	0.171449	+	0.985193i	$0.445155\pi$
$132$	0	0
$133$	−7.72929e33	−0.0699178
$134$	1.90711e35	1.52457
$135$	0	0
$136$	6.97128e35	4.36436
$137$	−8.90834e34	−0.494205	−0.247103	−	0.968989i	$-0.579479\pi$
$137$	−8.90834e34	−0.494205	−0.247103	+	0.968989i	$0.579479\pi$
$138$	0	0
$139$	−3.61707e35	−1.57984	−0.789920	−	0.613210i	$-0.789878\pi$
$139$	−3.61707e35	−1.57984	−0.789920	+	0.613210i	$0.789878\pi$
$140$	2.30284e35	0.893618
$141$	0	0
$142$	−1.29963e35	−0.399083
$143$	−1.55920e35	−0.426438
$144$	0	0
$145$	3.04210e35	0.661610
$146$	−1.03987e36	−2.01909
$147$	0	0
$148$	−6.26354e35	−0.971632
$149$	−1.73500e35	−0.240839	−0.120419	−	0.992723i	$-0.538424\pi$
$149$	−1.73500e35	−0.240839	−0.120419	+	0.992723i	$0.538424\pi$
$150$	0	0
$151$	−1.35744e36	−1.51217	−0.756085	−	0.654473i	$-0.772891\pi$
$151$	−1.35744e36	−1.51217	−0.756085	+	0.654473i	$0.772891\pi$
$152$	−2.93333e35	−0.293050
$153$	0	0
$154$	7.72017e35	0.621634
$155$	1.04527e35	0.0756404
$156$	0	0
$157$	−2.78049e36	−1.62846	−0.814229	−	0.580543i	$-0.802840\pi$
$157$	−2.78049e36	−1.62846	−0.814229	+	0.580543i	$0.802840\pi$
$158$	−9.55998e35	−0.504214
$159$	0	0
$160$	2.57809e36	1.10489
$161$	−1.72069e36	−0.665390
$162$	0	0
$163$	2.81381e36	0.887565	0.443782	−	0.896135i	$-0.353636\pi$
$163$	2.81381e36	0.887565	0.443782	+	0.896135i	$0.353636\pi$
$164$	4.54718e36	1.29664
$165$	0	0
$166$	−7.08993e36	−1.65523
$167$	−6.77893e36	−1.43331	−0.716653	−	0.697430i	$-0.754327\pi$
$167$	−6.77893e36	−1.43331	−0.716653	+	0.697430i	$0.754327\pi$
$168$	0	0
$169$	−2.13094e36	−0.370204
$170$	1.15285e37	1.81705
$171$	0	0
$172$	3.67080e37	4.77026
$173$	1.42570e37	1.68370	0.841852	−	0.539708i	$-0.181465\pi$
$173$	1.42570e37	1.68370	0.841852	+	0.539708i	$0.181465\pi$
$174$	0	0
$175$	−4.17105e36	−0.407490
$176$	1.46854e37	1.30595
$177$	0	0
$178$	−1.06512e37	−0.786085
$179$	−7.37934e36	−0.496527	−0.248263	−	0.968693i	$-0.579860\pi$
$179$	−7.37934e36	−0.496527	−0.248263	+	0.968693i	$0.579860\pi$
$180$	0	0
$181$	2.39313e36	0.134051	0.0670254	−	0.997751i	$-0.478649\pi$
$181$	2.39313e36	0.134051	0.0670254	+	0.997751i	$0.478649\pi$
$182$	−1.79497e37	−0.918076
$183$	0	0
$184$	−6.53018e37	−2.78889
$185$	−6.07513e36	−0.237259
$186$	0	0
$187$	2.73428e37	0.894245
$188$	−6.76517e37	−2.02616
$189$	0	0
$190$	−4.85091e36	−0.122008
$191$	6.98026e35	0.0160998	0.00804991	−	0.999968i	$-0.497438\pi$
$191$	6.98026e35	0.0160998	0.00804991	+	0.999968i	$0.497438\pi$
$192$	0	0
$193$	6.67098e36	0.129567	0.0647835	−	0.997899i	$-0.479364\pi$
$193$	6.67098e36	0.129567	0.0647835	+	0.997899i	$0.479364\pi$
$194$	6.92298e37	1.23471
$195$	0	0
$196$	−9.77280e37	−1.47161
$197$	8.89563e37	1.23164	0.615821	−	0.787886i	$-0.288825\pi$
$197$	8.89563e37	1.23164	0.615821	+	0.787886i	$0.288825\pi$
$198$	0	0
$199$	1.05106e38	1.23183	0.615916	−	0.787812i	$-0.288786\pi$
$199$	1.05106e38	1.23183	0.615916	+	0.787812i	$0.288786\pi$
$200$	−1.58295e38	−1.70794
$201$	0	0
$202$	2.06618e38	1.89178
$203$	8.30613e37	0.700994
$204$	0	0
$205$	4.41040e37	0.316621
$206$	−2.90245e38	−1.92290
$207$	0	0
$208$	−3.41441e38	−1.92873
$209$	−1.15051e37	−0.0600452
$210$	0	0
$211$	−5.59870e37	−0.249705	−0.124852	−	0.992175i	$-0.539846\pi$
$211$	−5.59870e37	−0.249705	−0.124852	+	0.992175i	$0.539846\pi$
$212$	−1.90634e38	−0.786428
$213$	0	0
$214$	−1.21172e38	−0.428129
$215$	3.56038e38	1.16483
$216$	0	0
$217$	2.85398e37	0.0801431
$218$	7.58804e38	1.97514
$219$	0	0
$220$	3.42781e38	0.767436
$221$	−6.35730e38	−1.32069
$222$	0	0
$223$	4.65676e38	0.833784	0.416892	−	0.908956i	$-0.363119\pi$
$223$	4.65676e38	0.833784	0.416892	+	0.908956i	$0.363119\pi$
$224$	7.03919e38	1.17066
$225$	0	0
$226$	−2.33898e39	−3.35921
$227$	2.61802e38	0.349580	0.174790	−	0.984606i	$-0.444075\pi$
$227$	2.61802e38	0.349580	0.174790	+	0.984606i	$0.444075\pi$
$228$	0	0
$229$	9.20963e38	1.06404	0.532018	−	0.846733i	$-0.321434\pi$
$229$	9.20963e38	1.06404	0.532018	+	0.846733i	$0.321434\pi$
$230$	−1.07991e39	−1.16112
$231$	0	0
$232$	3.15225e39	2.93811
$233$	−7.13755e37	−0.0619693	−0.0309847	−	0.999520i	$-0.509864\pi$
$233$	−7.13755e37	−0.0619693	−0.0309847	+	0.999520i	$0.509864\pi$
$234$	0	0
$235$	−6.56167e38	−0.494760
$236$	2.45688e39	1.72718
$237$	0	0
$238$	3.14774e39	1.92522
$239$	1.83178e39	1.04546	0.522731	−	0.852498i	$-0.324913\pi$
$239$	1.83178e39	1.04546	0.522731	+	0.852498i	$0.324913\pi$
$240$	0	0
$241$	−3.05313e39	−1.51867	−0.759336	−	0.650698i	$-0.774476\pi$
$241$	−3.05313e39	−1.51867	−0.759336	+	0.650698i	$0.774476\pi$
$242$	−2.83069e39	−1.31504
$243$	0	0
$244$	−2.06272e38	−0.0836583
$245$	−9.47883e38	−0.359347
$246$	0	0
$247$	2.67499e38	0.0886793
$248$	1.08311e39	0.335908
$249$	0	0
$250$	−6.63729e39	−1.80294
$251$	−3.03407e39	−0.771631	−0.385815	−	0.922576i	$-0.626080\pi$
$251$	−3.03407e39	−0.771631	−0.385815	+	0.922576i	$0.626080\pi$
$252$	0	0
$253$	−2.56127e39	−0.571435
$254$	−1.22040e40	−2.55120
$255$	0	0
$256$	−5.28662e39	−0.970999
$257$	2.91186e39	0.501503	0.250752	−	0.968051i	$-0.419322\pi$
$257$	2.91186e39	0.501503	0.250752	+	0.968051i	$0.419322\pi$
$258$	0	0
$259$	−1.65875e39	−0.251382
$260$	−7.96978e39	−1.13341
$261$	0	0
$262$	5.05883e39	0.633984
$263$	5.62907e39	0.662471	0.331236	−	0.943548i	$-0.392534\pi$
$263$	5.62907e39	0.662471	0.331236	+	0.943548i	$0.392534\pi$
$264$	0	0
$265$	−1.84900e39	−0.192035
$266$	−1.32449e39	−0.129271
$267$	0	0
$268$	2.31202e40	1.99419
$269$	9.77080e39	0.792533	0.396266	−	0.918136i	$-0.370306\pi$
$269$	9.77080e39	0.792533	0.396266	+	0.918136i	$0.370306\pi$
$270$	0	0
$271$	2.38779e40	1.71397	0.856985	−	0.515342i	$-0.172335\pi$
$271$	2.38779e40	1.71397	0.856985	+	0.515342i	$0.172335\pi$
$272$	5.98767e40	4.04456
$273$	0	0
$274$	−1.52653e40	−0.913736
$275$	−6.20865e39	−0.349952
$276$	0	0
$277$	−1.39835e40	−0.699358	−0.349679	−	0.936870i	$-0.613709\pi$
$277$	−1.39835e40	−0.699358	−0.349679	+	0.936870i	$0.613709\pi$
$278$	−6.19820e40	−2.92096
$279$	0	0
$280$	2.31444e40	0.969033
$281$	2.89927e40	1.14455	0.572274	−	0.820062i	$-0.306061\pi$
$281$	2.89927e40	1.14455	0.572274	+	0.820062i	$0.306061\pi$
$282$	0	0
$283$	−1.50945e40	−0.530081	−0.265040	−	0.964237i	$-0.585385\pi$
$283$	−1.50945e40	−0.530081	−0.265040	+	0.964237i	$0.585385\pi$
$284$	−1.57556e40	−0.522015
$285$	0	0
$286$	−2.67183e40	−0.788441
$287$	1.20421e40	0.335468
$288$	0	0
$289$	7.12303e40	1.76950
$290$	5.21293e40	1.22325
$291$	0	0
$292$	−1.26065e41	−2.64105
$293$	1.40305e40	0.277816	0.138908	−	0.990305i	$-0.455641\pi$
$293$	1.40305e40	0.277816	0.138908	+	0.990305i	$0.455641\pi$
$294$	0	0
$295$	2.38298e40	0.421752
$296$	−6.29509e40	−1.05363
$297$	0	0
$298$	−2.97309e40	−0.445286
$299$	5.95505e40	0.843939
$300$	0	0
$301$	9.72124e40	1.23417
$302$	−2.32610e41	−2.79585
$303$	0	0
$304$	−2.51945e40	−0.271577
$305$	−2.00068e39	−0.0204282
$306$	0	0
$307$	−2.92194e40	−0.267848	−0.133924	−	0.990992i	$-0.542758\pi$
$307$	−2.92194e40	−0.267848	−0.133924	+	0.990992i	$0.542758\pi$
$308$	9.35926e40	0.813120
$309$	0	0
$310$	1.79116e40	0.139851
$311$	2.24927e41	1.66531	0.832653	−	0.553794i	$-0.186821\pi$
$311$	2.24927e41	1.66531	0.832653	+	0.553794i	$0.186821\pi$
$312$	0	0
$313$	1.17836e41	0.784868	0.392434	−	0.919780i	$-0.371633\pi$
$313$	1.17836e41	0.784868	0.392434	+	0.919780i	$0.371633\pi$
$314$	−4.76463e41	−3.01086
$315$	0	0
$316$	−1.15897e41	−0.659530
$317$	9.02704e40	0.487604	0.243802	−	0.969825i	$-0.421605\pi$
$317$	9.02704e40	0.487604	0.243802	+	0.969825i	$0.421605\pi$
$318$	0	0
$319$	1.23638e41	0.602012
$320$	1.31396e41	0.607588
$321$	0	0
$322$	−2.94857e41	−1.23024
$323$	−4.69099e40	−0.185961
$324$	0	0
$325$	1.44353e41	0.516835
$326$	4.82174e41	1.64102
$327$	0	0
$328$	4.57008e41	1.40607
$329$	−1.79159e41	−0.524212
$330$	0	0
$331$	−2.91394e41	−0.771469	−0.385734	−	0.922610i	$-0.626052\pi$
$331$	−2.91394e41	−0.771469	−0.385734	+	0.922610i	$0.626052\pi$
$332$	−8.59521e41	−2.16510
$333$	0	0
$334$	−1.16163e42	−2.65004
$335$	2.24247e41	0.486954
$336$	0	0
$337$	−5.69474e41	−1.12094	−0.560468	−	0.828176i	$-0.689379\pi$
$337$	−5.69474e41	−1.12094	−0.560468	+	0.828176i	$0.689379\pi$
$338$	−3.65157e41	−0.684470
$339$	0	0
$340$	1.39762e42	2.37677
$341$	4.24819e40	0.0688266
$342$	0	0
$343$	−6.84132e41	−1.00644
$344$	3.68929e42	5.17284
$345$	0	0
$346$	2.44306e42	3.11300
$347$	−4.85020e41	−0.589283	−0.294641	−	0.955608i	$-0.595200\pi$
$347$	−4.85020e41	−0.589283	−0.294641	+	0.955608i	$0.595200\pi$
$348$	0	0
$349$	5.38533e41	0.595104	0.297552	−	0.954706i	$-0.403830\pi$
$349$	5.38533e41	0.595104	0.297552	+	0.954706i	$0.403830\pi$
$350$	−7.14748e41	−0.753408
$351$	0	0
$352$	1.04779e42	1.00536
$353$	9.77578e41	0.895094	0.447547	−	0.894260i	$-0.352298\pi$
$353$	9.77578e41	0.895094	0.447547	+	0.894260i	$0.352298\pi$
$354$	0	0
$355$	−1.52817e41	−0.127469
$356$	−1.29126e42	−1.02823
$357$	0	0
$358$	−1.26452e42	−0.918027
$359$	−1.18143e42	−0.819124	−0.409562	−	0.912282i	$-0.634318\pi$
$359$	−1.18143e42	−0.819124	−0.409562	+	0.912282i	$0.634318\pi$
$360$	0	0
$361$	−1.56103e42	−0.987513
$362$	4.10085e41	0.247846
$363$	0	0
$364$	−2.17606e42	−1.20088
$365$	−1.22273e42	−0.644907
$366$	0	0
$367$	7.16875e41	0.345504	0.172752	−	0.984965i	$-0.444734\pi$
$367$	7.16875e41	0.345504	0.172752	+	0.984965i	$0.444734\pi$
$368$	−5.60881e42	−2.58453
$369$	0	0
$370$	−1.04103e42	−0.438668
$371$	−5.04849e41	−0.203466
$372$	0	0
$373$	−6.80691e41	−0.251047	−0.125523	−	0.992091i	$-0.540061\pi$
$373$	−6.80691e41	−0.251047	−0.125523	+	0.992091i	$0.540061\pi$
$374$	4.68545e42	1.65337
$375$	0	0
$376$	−6.79925e42	−2.19716
$377$	−2.87462e42	−0.889096
$378$	0	0
$379$	5.14200e42	1.45742	0.728711	−	0.684821i	$-0.240120\pi$
$379$	5.14200e42	1.45742	0.728711	+	0.684821i	$0.240120\pi$
$380$	−5.88082e41	−0.159591
$381$	0	0
$382$	1.19613e41	0.0297669
$383$	6.82496e42	1.62675	0.813375	−	0.581740i	$-0.197628\pi$
$383$	6.82496e42	1.62675	0.813375	+	0.581740i	$0.197628\pi$
$384$	0	0
$385$	9.07773e41	0.198552
$386$	1.14314e42	0.239556
$387$	0	0
$388$	8.39281e42	1.61504
$389$	−3.03602e42	−0.559933	−0.279966	−	0.960010i	$-0.590323\pi$
$389$	−3.03602e42	−0.559933	−0.279966	+	0.960010i	$0.590323\pi$
$390$	0	0
$391$	−1.04431e43	−1.76975
$392$	−9.82202e42	−1.59581
$393$	0	0
$394$	1.52435e43	2.27718
$395$	−1.12411e42	−0.161048
$396$	0	0
$397$	8.54761e42	1.12668	0.563341	−	0.826225i	$-0.309516\pi$
$397$	8.54761e42	1.12668	0.563341	+	0.826225i	$0.309516\pi$
$398$	1.80109e43	2.27753
$399$	0	0
$400$	−1.35960e43	−1.58279
$401$	−4.64638e42	−0.519078	−0.259539	−	0.965733i	$-0.583571\pi$
$401$	−4.64638e42	−0.519078	−0.259539	+	0.965733i	$0.583571\pi$
$402$	0	0
$403$	−9.87719e41	−0.101648
$404$	2.50486e43	2.47452
$405$	0	0
$406$	1.42333e43	1.29607
$407$	−2.46907e42	−0.215886
$408$	0	0
$409$	1.73477e43	1.39897	0.699483	−	0.714649i	$-0.253414\pi$
$409$	1.73477e43	1.39897	0.699483	+	0.714649i	$0.253414\pi$
$410$	7.55763e42	0.585399
$411$	0	0
$412$	−3.51868e43	−2.51522
$413$	6.50647e42	0.446858
$414$	0	0
$415$	−8.33667e42	−0.528687
$416$	−2.43615e43	−1.48479
$417$	0	0
$418$	−1.97151e42	−0.111017
$419$	−1.59552e43	−0.863717	−0.431858	−	0.901941i	$-0.642142\pi$
$419$	−1.59552e43	−0.863717	−0.431858	+	0.901941i	$0.642142\pi$
$420$	0	0
$421$	−2.07154e43	−1.03667	−0.518333	−	0.855179i	$-0.673447\pi$
$421$	−2.07154e43	−1.03667	−0.518333	+	0.855179i	$0.673447\pi$
$422$	−9.59390e42	−0.461679
$423$	0	0
$424$	−1.91594e43	−0.852797
$425$	−2.53145e43	−1.08381
$426$	0	0
$427$	−5.46263e41	−0.0216442
$428$	−1.46898e43	−0.560008
$429$	0	0
$430$	6.10105e43	2.15365
$431$	2.15255e43	0.731272	0.365636	−	0.930758i	$-0.380851\pi$
$431$	2.15255e43	0.731272	0.365636	+	0.930758i	$0.380851\pi$
$432$	0	0
$433$	−2.62411e43	−0.825908	−0.412954	−	0.910752i	$-0.635503\pi$
$433$	−2.62411e43	−0.825908	−0.412954	+	0.910752i	$0.635503\pi$
$434$	4.89057e42	0.148176
$435$	0	0
$436$	9.19908e43	2.58355
$437$	4.39417e42	0.118832
$438$	0	0
$439$	1.50091e43	0.376434	0.188217	−	0.982127i	$-0.439729\pi$
$439$	1.50091e43	0.376434	0.188217	+	0.982127i	$0.439729\pi$
$440$	3.44507e43	0.832203
$441$	0	0
$442$	−1.08938e44	−2.44182
$443$	−1.03686e43	−0.223902	−0.111951	−	0.993714i	$-0.535710\pi$
$443$	−1.03686e43	−0.223902	−0.111951	+	0.993714i	$0.535710\pi$
$444$	0	0
$445$	−1.25242e43	−0.251079
$446$	7.97979e43	1.54158
$447$	0	0
$448$	3.58764e43	0.643756
$449$	3.05007e42	0.0527528	0.0263764	−	0.999652i	$-0.491603\pi$
$449$	3.05007e42	0.0527528	0.0263764	+	0.999652i	$0.491603\pi$
$450$	0	0
$451$	1.79248e43	0.288099
$452$	−2.83558e44	−4.39397
$453$	0	0
$454$	4.48623e43	0.646338
$455$	−2.11061e43	−0.293237
$456$	0	0
$457$	−8.15124e43	−1.05343	−0.526716	−	0.850042i	$-0.676577\pi$
$457$	−8.15124e43	−1.05343	−0.526716	+	0.850042i	$0.676577\pi$
$458$	1.57816e44	1.96730
$459$	0	0
$460$	−1.30919e44	−1.51879
$461$	−9.49311e43	−1.06253	−0.531267	−	0.847204i	$-0.678284\pi$
$461$	−9.49311e43	−1.06253	−0.531267	+	0.847204i	$0.678284\pi$
$462$	0	0
$463$	−6.84730e43	−0.713564	−0.356782	−	0.934188i	$-0.616126\pi$
$463$	−6.84730e43	−0.713564	−0.356782	+	0.934188i	$0.616126\pi$
$464$	2.70748e44	2.72282
$465$	0	0
$466$	−1.22309e43	−0.114575
$467$	−1.13867e44	−1.02961	−0.514803	−	0.857308i	$-0.672135\pi$
$467$	−1.13867e44	−1.02961	−0.514803	+	0.857308i	$0.672135\pi$
$468$	0	0
$469$	6.12282e43	0.515941
$470$	−1.12440e44	−0.914762
$471$	0	0
$472$	2.46926e44	1.87294
$473$	1.44702e44	1.05990
$474$	0	0
$475$	1.06517e43	0.0727736
$476$	3.81605e44	2.51825
$477$	0	0
$478$	3.13893e44	1.93295
$479$	2.43710e44	1.44990	0.724948	−	0.688804i	$-0.241864\pi$
$479$	2.43710e44	1.44990	0.724948	+	0.688804i	$0.241864\pi$
$480$	0	0
$481$	5.74067e43	0.318837
$482$	−5.23183e44	−2.80787
$483$	0	0
$484$	−3.43169e44	−1.72012
$485$	8.14036e43	0.394371
$486$	0	0
$487$	−1.55812e44	−0.705300	−0.352650	−	0.935755i	$-0.614719\pi$
$487$	−1.55812e44	−0.705300	−0.352650	+	0.935755i	$0.614719\pi$
$488$	−2.07311e43	−0.0907185
$489$	0	0
$490$	−1.62429e44	−0.664397
$491$	2.64492e43	0.104609	0.0523044	−	0.998631i	$-0.483343\pi$
$491$	2.64492e43	0.104609	0.0523044	+	0.998631i	$0.483343\pi$
$492$	0	0
$493$	5.04108e44	1.86444
$494$	4.58384e43	0.163959
$495$	0	0
$496$	9.30290e43	0.311294
$497$	−4.17250e43	−0.135057
$498$	0	0
$499$	3.31565e44	1.00441	0.502203	−	0.864750i	$-0.332523\pi$
$499$	3.31565e44	1.00441	0.502203	+	0.864750i	$0.332523\pi$
$500$	−8.04647e44	−2.35831
$501$	0	0
$502$	−5.19917e44	−1.42667
$503$	4.39485e44	1.16700	0.583502	−	0.812112i	$-0.301682\pi$
$503$	4.39485e44	1.16700	0.583502	+	0.812112i	$0.301682\pi$
$504$	0	0
$505$	2.42951e44	0.604242
$506$	−4.38898e44	−1.05653
$507$	0	0
$508$	−1.47950e45	−3.33706
$509$	7.37330e44	1.60997	0.804986	−	0.593294i	$-0.202173\pi$
$509$	7.37330e44	1.60997	0.804986	+	0.593294i	$0.202173\pi$
$510$	0	0
$511$	−3.33852e44	−0.683296
$512$	−9.21704e44	−1.82657
$513$	0	0
$514$	4.98975e44	0.927229
$515$	−3.41284e44	−0.614181
$516$	0	0
$517$	−2.66681e44	−0.450192
$518$	−2.84242e44	−0.464780
$519$	0	0
$520$	−8.00992e44	−1.22906
$521$	−1.67201e43	−0.0248552	−0.0124276	−	0.999923i	$-0.503956\pi$
$521$	−1.67201e43	−0.0248552	−0.0124276	+	0.999923i	$0.503956\pi$
$522$	0	0
$523$	1.06261e45	1.48284	0.741420	−	0.671041i	$-0.234153\pi$
$523$	1.06261e45	1.48284	0.741420	+	0.671041i	$0.234153\pi$
$524$	6.13288e44	0.829275
$525$	0	0
$526$	9.64595e44	1.22484
$527$	1.73211e44	0.213158
$528$	0	0
$529$	1.13224e44	0.130894
$530$	−3.16843e44	−0.355052
$531$	0	0
$532$	−1.60569e44	−0.169091
$533$	−4.16759e44	−0.425486
$534$	0	0
$535$	−1.42480e44	−0.136746
$536$	2.32366e45	2.16249
$537$	0	0
$538$	1.67432e45	1.46531
$539$	−3.85240e44	−0.326977
$540$	0	0
$541$	−1.73107e45	−1.38217	−0.691084	−	0.722774i	$-0.742867\pi$
$541$	−1.73107e45	−1.38217	−0.691084	+	0.722774i	$0.742867\pi$
$542$	4.09171e45	3.16896
$543$	0	0
$544$	4.27216e45	3.11362
$545$	8.92237e44	0.630867
$546$	0	0
$547$	1.88809e45	1.25670	0.628350	−	0.777931i	$-0.283731\pi$
$547$	1.88809e45	1.25670	0.628350	+	0.777931i	$0.283731\pi$
$548$	−1.85063e45	−1.19520
$549$	0	0
$550$	−1.06391e45	−0.647025
$551$	−2.12115e44	−0.125190
$552$	0	0
$553$	−3.06925e44	−0.170635
$554$	−2.39620e45	−1.29304
$555$	0	0
$556$	−7.51415e45	−3.82073
$557$	−1.82254e45	−0.899636	−0.449818	−	0.893120i	$-0.648511\pi$
$557$	−1.82254e45	−0.899636	−0.449818	+	0.893120i	$0.648511\pi$
$558$	0	0
$559$	−3.36437e45	−1.56534
$560$	1.98789e45	0.898027
$561$	0	0
$562$	4.96817e45	2.11615
$563$	−3.54966e45	−1.46824	−0.734122	−	0.679018i	$-0.762406\pi$
$563$	−3.54966e45	−1.46824	−0.734122	+	0.679018i	$0.762406\pi$
$564$	0	0
$565$	−2.75028e45	−1.07295
$566$	−2.58658e45	−0.980066
$567$	0	0
$568$	−1.58350e45	−0.566070
$569$	3.23817e45	1.12447	0.562234	−	0.826978i	$-0.309942\pi$
$569$	3.23817e45	1.12447	0.562234	+	0.826978i	$0.309942\pi$
$570$	0	0
$571$	1.75221e45	0.574237	0.287118	−	0.957895i	$-0.407303\pi$
$571$	1.75221e45	0.574237	0.287118	+	0.957895i	$0.407303\pi$
$572$	−3.23909e45	−1.03131
$573$	0	0
$574$	2.06353e45	0.620247
$575$	2.37128e45	0.692569
$576$	0	0
$577$	−2.22828e45	−0.614566	−0.307283	−	0.951618i	$-0.599420\pi$
$577$	−2.22828e45	−0.614566	−0.307283	+	0.951618i	$0.599420\pi$
$578$	1.22060e46	3.27162
$579$	0	0
$580$	6.31970e45	1.60005
$581$	−2.27624e45	−0.560159
$582$	0	0
$583$	−7.51473e44	−0.174736
$584$	−1.26700e46	−2.86394
$585$	0	0
$586$	2.40426e45	0.513654
$587$	−1.91072e45	−0.396889	−0.198444	−	0.980112i	$-0.563589\pi$
$587$	−1.91072e45	−0.396889	−0.198444	+	0.980112i	$0.563589\pi$
$588$	0	0
$589$	−7.28827e43	−0.0143127
$590$	4.08346e45	0.779777
$591$	0	0
$592$	−5.40689e45	−0.976426
$593$	−8.87275e45	−1.55832	−0.779158	−	0.626827i	$-0.784353\pi$
$593$	−8.87275e45	−1.55832	−0.779158	+	0.626827i	$0.784353\pi$
$594$	0	0
$595$	3.70126e45	0.614921
$596$	−3.60431e45	−0.582451
$597$	0	0
$598$	1.02045e46	1.56036
$599$	1.96939e45	0.292947	0.146474	−	0.989215i	$-0.453208\pi$
$599$	1.96939e45	0.292947	0.146474	+	0.989215i	$0.453208\pi$
$600$	0	0
$601$	6.49113e45	0.913885	0.456942	−	0.889496i	$-0.348945\pi$
$601$	6.49113e45	0.913885	0.456942	+	0.889496i	$0.348945\pi$
$602$	1.66583e46	2.28185
$603$	0	0
$604$	−2.81996e46	−3.65707
$605$	−3.32846e45	−0.420029
$606$	0	0
$607$	−1.08656e46	−1.29849	−0.649247	−	0.760577i	$-0.724916\pi$
$607$	−1.08656e46	−1.29849	−0.649247	+	0.760577i	$0.724916\pi$
$608$	−1.79761e45	−0.209068
$609$	0	0
$610$	−3.42835e44	−0.0377696
$611$	6.20043e45	0.664877
$612$	0	0
$613$	8.70542e45	0.884488	0.442244	−	0.896895i	$-0.354182\pi$
$613$	8.70542e45	0.884488	0.442244	+	0.896895i	$0.354182\pi$
$614$	−5.00703e45	−0.495224
$615$	0	0
$616$	9.40640e45	0.881742
$617$	1.12685e46	1.02840	0.514199	−	0.857671i	$-0.328089\pi$
$617$	1.12685e46	1.02840	0.514199	+	0.857671i	$0.328089\pi$
$618$	0	0
$619$	−1.07685e46	−0.931663	−0.465831	−	0.884874i	$-0.654245\pi$
$619$	−1.07685e46	−0.931663	−0.465831	+	0.884874i	$0.654245\pi$
$620$	2.17145e45	0.182931
$621$	0	0
$622$	3.85433e46	3.07898
$623$	−3.41959e45	−0.266025
$624$	0	0
$625$	1.02173e45	0.0753905
$626$	2.01923e46	1.45114
$627$	0	0
$628$	−5.77622e46	−3.93831
$629$	−1.00671e46	−0.668605
$630$	0	0
$631$	2.47581e46	1.56039	0.780196	−	0.625535i	$-0.215119\pi$
$631$	2.47581e46	1.56039	0.780196	+	0.625535i	$0.215119\pi$
$632$	−1.16481e46	−0.715190
$633$	0	0
$634$	1.54687e46	0.901531
$635$	−1.43500e46	−0.814864
$636$	0	0
$637$	8.95698e45	0.482904
$638$	2.11865e46	1.11306
$639$	0	0
$640$	3.70407e44	0.0184803
$641$	6.66844e45	0.324240	0.162120	−	0.986771i	$-0.448167\pi$
$641$	6.66844e45	0.324240	0.162120	+	0.986771i	$0.448167\pi$
$642$	0	0
$643$	−8.88748e42	−0.000410485 0	−0.000205243	−	1.00000i	$-0.500065\pi$
$643$	−8.88748e42	−0.000410485 0	−0.000205243		1.00000i	$0.500065\pi$
$644$	−3.57459e46	−1.60920
$645$	0	0
$646$	−8.03845e45	−0.343824
$647$	1.36920e46	0.570884	0.285442	−	0.958396i	$-0.407860\pi$
$647$	1.36920e46	0.570884	0.285442	+	0.958396i	$0.407860\pi$
$648$	0	0
$649$	9.68495e45	0.383760
$650$	2.47363e46	0.955575
$651$	0	0
$652$	5.84545e46	2.14651
$653$	1.32140e46	0.473115	0.236557	−	0.971618i	$-0.423981\pi$
$653$	1.32140e46	0.473115	0.236557	+	0.971618i	$0.423981\pi$
$654$	0	0
$655$	5.94840e45	0.202497
$656$	3.92527e46	1.30304
$657$	0	0
$658$	−3.07007e46	−0.969215
$659$	−3.14029e46	−0.966852	−0.483426	−	0.875385i	$-0.660608\pi$
$659$	−3.14029e46	−0.966852	−0.483426	+	0.875385i	$0.660608\pi$
$660$	0	0
$661$	−5.62366e46	−1.64701	−0.823503	−	0.567313i	$-0.807983\pi$
$661$	−5.62366e46	−1.64701	−0.823503	+	0.567313i	$0.807983\pi$
$662$	−4.99331e46	−1.42637
$663$	0	0
$664$	−8.63851e46	−2.34782
$665$	−1.55739e45	−0.0412896
$666$	0	0
$667$	−4.72211e46	−1.19141
$668$	−1.40826e47	−3.46635
$669$	0	0
$670$	3.84269e46	0.900328
$671$	−8.13119e44	−0.0185880
$672$	0	0
$673$	1.86687e45	0.0406317	0.0203159	−	0.999794i	$-0.493533\pi$
$673$	1.86687e45	0.0406317	0.0203159	+	0.999794i	$0.493533\pi$
$674$	−9.75848e46	−2.07250
$675$	0	0
$676$	−4.42685e46	−0.895311
$677$	3.19535e46	0.630674	0.315337	−	0.948980i	$-0.397882\pi$
$677$	3.19535e46	0.630674	0.315337	+	0.948980i	$0.397882\pi$
$678$	0	0
$679$	2.22264e46	0.417847
$680$	1.40466e47	2.57735
$681$	0	0
$682$	7.27967e45	0.127253
$683$	9.67204e46	1.65035	0.825176	−	0.564876i	$-0.191076\pi$
$683$	9.67204e46	1.65035	0.825176	+	0.564876i	$0.191076\pi$
$684$	0	0
$685$	−1.79496e46	−0.291851
$686$	−1.17232e47	−1.86080
$687$	0	0
$688$	3.16875e47	4.79379
$689$	1.74720e46	0.258063
$690$	0	0
$691$	−4.21417e46	−0.593368	−0.296684	−	0.954976i	$-0.595881\pi$
$691$	−4.21417e46	−0.593368	−0.296684	+	0.954976i	$0.595881\pi$
$692$	2.96176e47	4.07192
$693$	0	0
$694$	−8.31128e46	−1.08952
$695$	−7.28813e46	−0.932968
$696$	0	0
$697$	7.30848e46	0.892249
$698$	9.22827e46	1.10029
$699$	0	0
$700$	−8.66499e46	−0.985485
$701$	−1.07382e47	−1.19284	−0.596422	−	0.802671i	$-0.703411\pi$
$701$	−1.07382e47	−1.19284	−0.596422	+	0.802671i	$0.703411\pi$
$702$	0	0
$703$	4.23598e45	0.0448943
$704$	5.34024e46	0.552856
$705$	0	0
$706$	1.67517e47	1.65494
$707$	6.63351e46	0.640211
$708$	0	0
$709$	9.99645e46	0.920837	0.460419	−	0.887702i	$-0.347699\pi$
$709$	9.99645e46	0.920837	0.460419	+	0.887702i	$0.347699\pi$
$710$	−2.61866e46	−0.235677
$711$	0	0
$712$	−1.29776e47	−1.11500
$713$	−1.62251e46	−0.136211
$714$	0	0
$715$	−3.14166e46	−0.251831
$716$	−1.53299e47	−1.20081
$717$	0	0
$718$	−2.02449e47	−1.51448
$719$	7.93598e46	0.580195	0.290097	−	0.956997i	$-0.406312\pi$
$719$	7.93598e46	0.580195	0.290097	+	0.956997i	$0.406312\pi$
$720$	0	0
$721$	−9.31838e46	−0.650741
$722$	−2.67498e47	−1.82581
$723$	0	0
$724$	4.97151e46	0.324192
$725$	−1.14466e47	−0.729626
$726$	0	0
$727$	1.33485e47	0.813046	0.406523	−	0.913641i	$-0.366741\pi$
$727$	1.33485e47	0.813046	0.406523	+	0.913641i	$0.366741\pi$
$728$	−2.18702e47	−1.30222
$729$	0	0
$730$	−2.09526e47	−1.19237
$731$	5.89992e47	3.28254
$732$	0	0
$733$	8.41792e46	0.447702	0.223851	−	0.974623i	$-0.428137\pi$
$733$	8.41792e46	0.447702	0.223851	+	0.974623i	$0.428137\pi$
$734$	1.22843e47	0.638802
$735$	0	0
$736$	−4.00184e47	−1.98965
$737$	9.11389e46	0.443088
$738$	0	0
$739$	2.39720e47	1.11448	0.557239	−	0.830352i	$-0.311861\pi$
$739$	2.39720e47	1.11448	0.557239	+	0.830352i	$0.311861\pi$
$740$	−1.26206e47	−0.573793
$741$	0	0
$742$	−8.65106e46	−0.376188
$743$	−4.51636e47	−1.92076	−0.960380	−	0.278695i	$-0.910098\pi$
$743$	−4.51636e47	−1.92076	−0.960380	+	0.278695i	$0.910098\pi$
$744$	0	0
$745$	−3.49589e46	−0.142226
$746$	−1.16643e47	−0.464160
$747$	0	0
$748$	5.68023e47	2.16267
$749$	−3.89025e46	−0.144886
$750$	0	0
$751$	−2.31769e46	−0.0826030	−0.0413015	−	0.999147i	$-0.513150\pi$
$751$	−2.31769e46	−0.0826030	−0.0413015	+	0.999147i	$0.513150\pi$
$752$	−5.83991e47	−2.03616
$753$	0	0
$754$	−4.92594e47	−1.64385
$755$	−2.73514e47	−0.893006
$756$	0	0
$757$	−6.14297e46	−0.191998	−0.0959989	−	0.995381i	$-0.530605\pi$
$757$	−6.14297e46	−0.191998	−0.0959989	+	0.995381i	$0.530605\pi$
$758$	8.81131e47	2.69463
$759$	0	0
$760$	−5.91044e46	−0.173059
$761$	4.18126e47	1.19801	0.599004	−	0.800746i	$-0.295563\pi$
$761$	4.18126e47	1.19801	0.599004	+	0.800746i	$0.295563\pi$
$762$	0	0
$763$	2.43616e47	0.668421
$764$	1.45009e46	0.0389362
$765$	0	0
$766$	1.16952e48	3.00769
$767$	−2.25179e47	−0.566766
$768$	0	0
$769$	−2.07493e47	−0.500286	−0.250143	−	0.968209i	$-0.580478\pi$
$769$	−2.07493e47	−0.500286	−0.250143	+	0.968209i	$0.580478\pi$
$770$	1.55555e47	0.367103
$771$	0	0
$772$	1.38584e47	0.313348
$773$	3.82656e47	0.846930	0.423465	−	0.905912i	$-0.360814\pi$
$773$	3.82656e47	0.846930	0.423465	+	0.905912i	$0.360814\pi$
$774$	0	0
$775$	−3.93306e46	−0.0834165
$776$	8.43509e47	1.75134
$777$	0	0
$778$	−5.20250e47	−1.03526
$779$	−3.07522e46	−0.0599112
$780$	0	0
$781$	−6.21081e46	−0.115986
$782$	−1.78952e48	−3.27209
$783$	0	0
$784$	−8.43619e47	−1.47887
$785$	−5.60247e47	−0.961679
$786$	0	0
$787$	−6.26036e47	−1.03043	−0.515213	−	0.857062i	$-0.672287\pi$
$787$	−6.26036e47	−1.03043	−0.515213	+	0.857062i	$0.672287\pi$
$788$	1.84799e48	2.97863
$789$	0	0
$790$	−1.92626e47	−0.297761
$791$	−7.50935e47	−1.13682
$792$	0	0
$793$	1.89053e46	0.0274521
$794$	1.46471e48	2.08312
$795$	0	0
$796$	2.18348e48	2.97910
$797$	−1.56391e47	−0.209002	−0.104501	−	0.994525i	$-0.533325\pi$
$797$	−1.56391e47	−0.209002	−0.104501	+	0.994525i	$0.533325\pi$
$798$	0	0
$799$	−1.08734e48	−1.39425
$800$	−9.70066e47	−1.21847
$801$	0	0
$802$	−7.96201e47	−0.959722
$803$	−4.96943e47	−0.586813
$804$	0	0
$805$	−3.46706e47	−0.392943
$806$	−1.69255e47	−0.187937
$807$	0	0
$808$	2.51747e48	2.68335
$809$	−4.01144e47	−0.418938	−0.209469	−	0.977815i	$-0.567174\pi$
$809$	−4.01144e47	−0.418938	−0.209469	+	0.977815i	$0.567174\pi$
$810$	0	0
$811$	2.34209e47	0.234833	0.117417	−	0.993083i	$-0.462539\pi$
$811$	2.34209e47	0.234833	0.117417	+	0.993083i	$0.462539\pi$
$812$	1.72553e48	1.69530
$813$	0	0
$814$	−4.23098e47	−0.399152
$815$	5.66962e47	0.524147
$816$	0	0
$817$	−2.48253e47	−0.220410
$818$	2.97269e48	2.58655
$819$	0	0
$820$	9.16221e47	0.765723
$821$	−4.03504e47	−0.330510	−0.165255	−	0.986251i	$-0.552845\pi$
$821$	−4.03504e47	−0.330510	−0.165255	+	0.986251i	$0.552845\pi$
$822$	0	0
$823$	1.82505e48	1.43608	0.718039	−	0.696002i	$-0.245040\pi$
$823$	1.82505e48	1.43608	0.718039	+	0.696002i	$0.245040\pi$
$824$	−3.53640e48	−2.72749
$825$	0	0
$826$	1.11494e48	0.826195
$827$	−7.52706e47	−0.546744	−0.273372	−	0.961908i	$-0.588139\pi$
$827$	−7.52706e47	−0.546744	−0.273372	+	0.961908i	$0.588139\pi$
$828$	0	0
$829$	−2.19354e48	−1.53107	−0.765537	−	0.643392i	$-0.777526\pi$
$829$	−2.19354e48	−1.53107	−0.765537	+	0.643392i	$0.777526\pi$
$830$	−1.42857e48	−0.977489
$831$	0	0
$832$	−1.24162e48	−0.816499
$833$	−1.57074e48	−1.01265
$834$	0	0
$835$	−1.36590e48	−0.846433
$836$	−2.39009e47	−0.145215
$837$	0	0
$838$	−2.73408e48	−1.59693
$839$	2.86394e48	1.64018	0.820091	−	0.572233i	$-0.193923\pi$
$839$	2.86394e48	1.64018	0.820091	+	0.572233i	$0.193923\pi$
$840$	0	0
$841$	4.63381e47	0.255155
$842$	−3.54978e48	−1.91669
$843$	0	0
$844$	−1.16308e48	−0.603892
$845$	−4.29368e47	−0.218622
$846$	0	0
$847$	−9.08800e47	−0.445033
$848$	−1.64561e48	−0.790308
$849$	0	0
$850$	−4.33788e48	−2.00385
$851$	9.43013e47	0.427248
$852$	0	0
$853$	4.28657e48	1.86832	0.934158	−	0.356859i	$-0.116152\pi$
$853$	4.28657e48	1.86832	0.934158	+	0.356859i	$0.116152\pi$
$854$	−9.36073e46	−0.0400180
$855$	0	0
$856$	−1.47638e48	−0.607270
$857$	8.64522e47	0.348813	0.174406	−	0.984674i	$-0.444199\pi$
$857$	8.64522e47	0.348813	0.174406	+	0.984674i	$0.444199\pi$
$858$	0	0
$859$	2.35883e48	0.915817	0.457909	−	0.888999i	$-0.348599\pi$
$859$	2.35883e48	0.915817	0.457909	+	0.888999i	$0.348599\pi$
$860$	7.39639e48	2.81705
$861$	0	0
$862$	3.68860e48	1.35205
$863$	6.27316e46	0.0225584	0.0112792	−	0.999936i	$-0.496410\pi$
$863$	6.27316e46	0.0225584	0.0112792	+	0.999936i	$0.496410\pi$
$864$	0	0
$865$	2.87267e48	0.994304
$866$	−4.49666e48	−1.52702
$867$	0	0
$868$	5.92890e47	0.193820
$869$	−4.56861e47	−0.146541
$870$	0	0
$871$	−2.11901e48	−0.654386
$872$	9.24541e48	2.80159
$873$	0	0
$874$	7.52982e47	0.219708
$875$	−2.13092e48	−0.610145
$876$	0	0
$877$	−2.00783e48	−0.553647	−0.276823	−	0.960921i	$-0.589282\pi$
$877$	−2.00783e48	−0.553647	−0.276823	+	0.960921i	$0.589282\pi$
$878$	2.57194e48	0.695988
$879$	0	0
$880$	2.95899e48	0.771223
$881$	4.20296e48	1.07511	0.537555	−	0.843229i	$-0.319348\pi$
$881$	4.20296e48	1.07511	0.537555	+	0.843229i	$0.319348\pi$
$882$	0	0
$883$	7.94997e48	1.95891	0.979453	−	0.201672i	$-0.0646376\pi$
$883$	7.94997e48	1.95891	0.979453	+	0.201672i	$0.0646376\pi$
$884$	−1.32067e49	−3.19399
$885$	0	0
$886$	−1.77675e48	−0.413971
$887$	7.43922e48	1.70133	0.850664	−	0.525710i	$-0.176200\pi$
$887$	7.43922e48	1.70133	0.850664	+	0.525710i	$0.176200\pi$
$888$	0	0
$889$	−3.91811e48	−0.863371
$890$	−2.14614e48	−0.464219
$891$	0	0
$892$	9.67400e48	2.01644
$893$	4.57523e47	0.0936189
$894$	0	0
$895$	−1.48688e48	−0.293222
$896$	1.01136e47	0.0195804
$897$	0	0
$898$	5.22659e47	0.0975345
$899$	7.83220e47	0.143499
$900$	0	0
$901$	−3.06398e48	−0.541161
$902$	3.07159e48	0.532666
$903$	0	0
$904$	−2.84986e49	−4.76480
$905$	4.82197e47	0.0791631
$906$	0	0
$907$	8.96944e48	1.41986	0.709929	−	0.704273i	$-0.248727\pi$
$907$	8.96944e48	1.41986	0.709929	+	0.704273i	$0.248727\pi$
$908$	5.43871e48	0.845433
$909$	0	0
$910$	−3.61672e48	−0.542166
$911$	−2.25421e48	−0.331850	−0.165925	−	0.986138i	$-0.553061\pi$
$911$	−2.25421e48	−0.331850	−0.165925	+	0.986138i	$0.553061\pi$
$912$	0	0
$913$	−3.38820e48	−0.481063
$914$	−1.39679e49	−1.94769
$915$	0	0
$916$	1.91322e49	2.57329
$917$	1.62415e48	0.214551
$918$	0	0
$919$	−7.04277e48	−0.897507	−0.448754	−	0.893656i	$-0.648132\pi$
$919$	−7.04277e48	−0.897507	−0.448754	+	0.893656i	$0.648132\pi$
$920$	−1.31578e49	−1.64696
$921$	0	0
$922$	−1.62673e49	−1.96452
$923$	1.44404e48	0.171297
$924$	0	0
$925$	2.28591e48	0.261650
$926$	−1.17335e49	−1.31931
$927$	0	0
$928$	1.93177e49	2.09611
$929$	−1.56732e49	−1.67070	−0.835348	−	0.549721i	$-0.814734\pi$
$929$	−1.56732e49	−1.67070	−0.835348	+	0.549721i	$0.814734\pi$
$930$	0	0
$931$	6.60926e47	0.0679959
$932$	−1.48276e48	−0.149868
$933$	0	0
$934$	−1.95123e49	−1.90364
$935$	5.50937e48	0.528093
$936$	0	0
$937$	4.17295e48	0.386136	0.193068	−	0.981185i	$-0.438156\pi$
$937$	4.17295e48	0.386136	0.193068	+	0.981185i	$0.438156\pi$
$938$	1.04920e49	0.953922
$939$	0	0
$940$	−1.36313e49	−1.19654
$941$	5.21719e48	0.449995	0.224998	−	0.974359i	$-0.427763\pi$
$941$	5.21719e48	0.449995	0.224998	+	0.974359i	$0.427763\pi$
$942$	0	0
$943$	−6.84604e48	−0.570160
$944$	2.12086e49	1.73570
$945$	0	0
$946$	2.47960e49	1.95965
$947$	1.05918e49	0.822616	0.411308	−	0.911496i	$-0.365072\pi$
$947$	1.05918e49	0.822616	0.411308	+	0.911496i	$0.365072\pi$
$948$	0	0
$949$	1.15541e49	0.866650
$950$	1.82527e48	0.134551
$951$	0	0
$952$	3.83527e49	2.73078
$953$	−1.49599e49	−1.04688	−0.523438	−	0.852064i	$-0.675351\pi$
$953$	−1.49599e49	−1.04688	−0.523438	+	0.852064i	$0.675351\pi$
$954$	0	0
$955$	1.40647e47	0.00950767
$956$	3.80536e49	2.52837
$957$	0	0
$958$	4.17619e49	2.68071
$959$	−4.90095e48	−0.309224
$960$	0	0
$961$	−1.61344e49	−0.983594
$962$	9.83718e48	0.589498
$963$	0	0
$964$	−6.34261e49	−3.67280
$965$	1.34415e48	0.0765152
$966$	0	0
$967$	−2.39619e49	−1.31821	−0.659106	−	0.752050i	$-0.729065\pi$
$967$	−2.39619e49	−1.31821	−0.659106	+	0.752050i	$0.729065\pi$
$968$	−3.44897e49	−1.86529
$969$	0	0
$970$	1.39493e49	0.729151
$971$	1.35152e47	0.00694552	0.00347276	−	0.999994i	$-0.498895\pi$
$971$	1.35152e47	0.00694552	0.00347276	+	0.999994i	$0.498895\pi$
$972$	0	0
$973$	−1.98994e49	−0.988505
$974$	−2.66999e49	−1.30403
$975$	0	0
$976$	−1.78061e48	−0.0840711
$977$	−1.84460e48	−0.0856333	−0.0428166	−	0.999083i	$-0.513633\pi$
$977$	−1.84460e48	−0.0856333	−0.0428166	+	0.999083i	$0.513633\pi$
$978$	0	0
$979$	−5.09011e48	−0.228461
$980$	−1.96914e49	−0.869055
$981$	0	0
$982$	4.53233e48	0.193411
$983$	6.69809e48	0.281072	0.140536	−	0.990076i	$-0.455117\pi$
$983$	6.69809e48	0.281072	0.140536	+	0.990076i	$0.455117\pi$
$984$	0	0
$985$	1.79240e49	0.727340
$986$	8.63836e49	3.44717
$987$	0	0
$988$	5.55705e48	0.214464
$989$	−5.52661e49	−2.09759
$990$	0	0
$991$	1.17168e49	0.430123	0.215062	−	0.976600i	$-0.431005\pi$
$991$	1.17168e49	0.430123	0.215062	+	0.976600i	$0.431005\pi$
$992$	6.63755e48	0.239643
$993$	0	0
$994$	−7.14997e48	−0.249706
$995$	2.11780e49	0.727453
$996$	0	0
$997$	2.44007e49	0.810834	0.405417	−	0.914132i	$-0.367126\pi$
$997$	2.44007e49	0.810834	0.405417	+	0.914132i	$0.367126\pi$
$998$	5.68168e49	1.85705
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.34.a.b.1.2		2
3.2	odd	2		1.34.a.a.1.1	✓	2
12.11	even	2		16.34.a.b.1.1		2
15.2	even	4		25.34.b.a.24.1		4
15.8	even	4		25.34.b.a.24.4		4
15.14	odd	2		25.34.a.a.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.34.a.a.1.1	✓	2	3.2	odd	2
9.34.a.b.1.2		2	1.1	even	1	trivial
16.34.a.b.1.1		2	12.11	even	2
25.34.a.a.1.2		2	15.14	odd	2
25.34.b.a.24.1		4	15.2	even	4
25.34.b.a.24.4		4	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 34 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q+171359. q^{2} +2.07741e10 q^{4} +2.01492e11 q^{5} +5.50153e13 q^{7} +2.08788e15 q^{8} +O(q^{10})\)	\(q+171359. q^{2} +2.07741e10 q^{4} +2.01492e11 q^{5} +5.50153e13 q^{7} +2.08788e15 q^{8} +3.45276e16 q^{10} +8.18909e16 q^{11} -1.90399e18 q^{13} +9.42739e18 q^{14} +1.79329e20 q^{16} +3.33893e20 q^{17} -1.40494e20 q^{19} +4.18583e21 q^{20} +1.40328e22 q^{22} -3.12767e22 q^{23} -7.58162e22 q^{25} -3.26267e23 q^{26} +1.14289e24 q^{28} +1.50979e24 q^{29} +5.18762e23 q^{31} +1.27950e25 q^{32} +5.72158e25 q^{34} +1.10852e25 q^{35} -3.01507e25 q^{37} -2.40749e25 q^{38} +4.20691e26 q^{40} +2.18887e26 q^{41} +1.76701e27 q^{43} +1.70121e27 q^{44} -5.35955e27 q^{46} -3.25654e27 q^{47} -4.70431e27 q^{49} -1.29918e28 q^{50} -3.95538e28 q^{52} -9.17652e27 q^{53} +1.65004e28 q^{55} +1.14865e29 q^{56} +2.58716e29 q^{58} +1.18267e29 q^{59} -9.92930e27 q^{61} +8.88948e28 q^{62} +6.52116e29 q^{64} -3.83640e29 q^{65} +1.11293e30 q^{67} +6.93634e30 q^{68} +1.89955e30 q^{70} -7.58425e29 q^{71} -6.06835e30 q^{73} -5.16661e30 q^{74} -2.91863e30 q^{76} +4.50525e30 q^{77} -5.57890e30 q^{79} +3.61334e31 q^{80} +3.75083e31 q^{82} -4.13746e31 q^{83} +6.72769e31 q^{85} +3.02793e32 q^{86} +1.70978e32 q^{88} -6.21572e31 q^{89} -1.04749e32 q^{91} -6.49745e32 q^{92} -5.58039e32 q^{94} -2.83084e31 q^{95} +4.04003e32 q^{97} -8.06129e32 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 121680 q^{2} + 14652233984 q^{4} + 181061536500 q^{5} - 67153080066800 q^{7} + 28\!\cdots\!40 q^{8}+O(q^{10}) \) 2 * q + 121680 * q^2 + 14652233984 * q^4 + 181061536500 * q^5 - 67153080066800 * q^7 + 2818750585098240 * q^8	\( 2 q + 121680 q^{2} + 14652233984 q^{4} + 181061536500 q^{5} - 67153080066800 q^{7} + 28\!\cdots\!40 q^{8}+ \cdots - 11\!\cdots\!40 q^{98}+O(q^{100}) \) 2 * q + 121680 * q^2 + 14652233984 * q^4 + 181061536500 * q^5 - 67153080066800 * q^7 + 2818750585098240 * q^8 + 35542592216532000 * q^10 - 133871815441914264 * q^11 - 2981610478259443940 * q^13 + 15496641262468340352 * q^14 + 195605979111894351872 * q^16 + 79361149261175525340 * q^17 - 1360696443041697171800 * q^19 + 4310900037459183168000 * q^20 + 24751741840613395122240 * q^22 - 26163854053674631579440 * q^23 - 191814088084783724781250 * q^25 - 272731683634642092710304 * q^26 + 1890794991723644827125760 * q^28 + 1674519971630399929109700 * q^29 - 6238301225723632337095616 * q^31 + 5708163006744585940500480 * q^32 + 69860790536166916073075808 * q^34 + 13581143663546216842308000 * q^35 - 104802741516758180098173620 * q^37 + 36544090911856460663722560 * q^38 + 405758480738092701742080000 * q^40 - 277566613022002182732188244 * q^41 + 1567661189367072113768291800 * q^43 + 3022085914387766085808346112 * q^44 - 5613550634763385681470869376 * q^46 - 5421061461431251260476972640 * q^47 + 2489799365888888933444851314 * q^49 - 7229107516344249428363250000 * q^50 - 32956722688372988680703091200 * q^52 + 26867414785542903092975171220 * q^53 + 20908570805489145209222682000 * q^55 + 25575237795171758759822131200 * q^56 + 250532370716581201796821222560 * q^58 + 305786409635298433026663995400 * q^59 - 5745893983413264859067362436 * q^61 + 424581887479352364037004290560 * q^62 + 864365322360380859973709594624 * q^64 - 361623311364964256200313721000 * q^65 + 1598906337224495341750209565960 * q^67 + 8494558579722382470601861086720 * q^68 + 1775546165763388432770973344000 * q^70 + 2669761937956104715736810084976 * q^71 + 946314321191998870965166536340 * q^73 - 1457936998080019494211346192928 * q^74 + 4551314657470802548563162035200 * q^76 + 30864620292716415864215760033600 * q^77 - 8535199972765636469730106191200 * q^79 + 35800819471604723635001769984000 * q^80 + 62171822095602398237444019107040 * q^82 - 29072605803747945444403983322920 * q^83 + 72477213859794605306963311287000 * q^85 + 312696885737578501917214826406336 * q^86 + 13282372192867492753038509752320 * q^88 - 132719467655604316264938597726900 * q^89 + 26902102147452358410548887211744 * q^91 - 681044992402323869436382557788160 * q^92 - 450506433888867898835049561530112 * q^94 - 3378716387067841884487537110000 * q^95 - 367787330930535727150839877856060 * q^97 - 1163527978168280943548587223169840 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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