LMFDB - Embedded newform 81.9.b.b.80.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,9,Mod(80,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("81.80");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	81.b (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$32.9976674150$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 1024 x^{14} + 419701 x^{12} + 88203292 x^{10} + 10121979748 x^{8} + 629108384896 x^{6} + \cdots + 16\!\cdots\!24 $ x^16 + 1024x^14 + 419701x^12 + 88203292x^10 + 10121979748x^8 + 629108384896x^6 + 20221245756928x^4 + 305638522445824*x^2 + 1623834669236224
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{84} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			80.1
Root			$-17.2054i$ of defining polynomial
Character	$\chi$	$=$	81.80
Dual form			81.9.b.b.80.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-29.8006i q^{2} -632.074 q^{4} +177.778i q^{5} +3390.81 q^{7} +11207.2i q^{8} +5297.89 q^{10} -22713.7i q^{11} +48777.1 q^{13} -101048. i q^{14} +172170. q^{16} +36661.7i q^{17} -81528.6 q^{19} -112369. i q^{20} -676882. q^{22} -44680.0i q^{23} +359020. q^{25} -1.45359e6i q^{26} -2.14324e6 q^{28} -307029. i q^{29} -377888. q^{31} -2.26173e6i q^{32} +1.09254e6 q^{34} +602813. i q^{35} +1.82114e6 q^{37} +2.42960e6i q^{38} -1.99240e6 q^{40} -2.56535e6i q^{41} -859529. q^{43} +1.43568e7i q^{44} -1.33149e6 q^{46} -3.14001e6i q^{47} +5.73282e6 q^{49} -1.06990e7i q^{50} -3.08307e7 q^{52} -1.04587e7i q^{53} +4.03801e6 q^{55} +3.80016e7i q^{56} -9.14964e6 q^{58} +2.01171e7i q^{59} -1.06653e7 q^{61} +1.12613e7i q^{62} -2.33251e7 q^{64} +8.67151e6i q^{65} -3.37493e7 q^{67} -2.31729e7i q^{68} +1.79642e7 q^{70} -387108. i q^{71} +1.74105e7 q^{73} -5.42711e7i q^{74} +5.15321e7 q^{76} -7.70180e7i q^{77} +1.30586e7 q^{79} +3.06081e7i q^{80} -7.64487e7 q^{82} -6.25273e7i q^{83} -6.51766e6 q^{85} +2.56144e7i q^{86} +2.54558e8 q^{88} -6.33977e7i q^{89} +1.65394e8 q^{91} +2.82411e7i q^{92} -9.35740e7 q^{94} -1.44940e7i q^{95} -6.53962e7 q^{97} -1.70841e8i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2048 q^{4} + 3692 q^{7} + 10752 q^{10} + 63860 q^{13} + 95116 q^{16} + 185108 q^{19} - 691980 q^{22} - 541712 q^{25} - 997132 q^{28} + 571136 q^{31} + 1027656 q^{34} + 4354268 q^{37} - 2973768 q^{40}+ \cdots - 133878688 q^{97}+O(q^{100}) $ 16 * q - 2048 * q^4 + 3692 * q^7 + 10752 * q^10 + 63860 * q^13 + 95116 * q^16 + 185108 * q^19 - 691980 * q^22 - 541712 * q^25 - 997132 * q^28 + 571136 * q^31 + 1027656 * q^34 + 4354268 * q^37 - 2973768 * q^40 + 5453084 * q^43 - 4234044 * q^46 + 14602560 * q^49 - 25384960 * q^52 - 14452572 * q^55 + 1213068 * q^58 + 31037996 * q^61 + 24253000 * q^64 - 62356828 * q^67 + 11075124 * q^70 - 21273664 * q^73 + 69593876 * q^76 - 151045036 * q^79 - 40201140 * q^82 + 160995564 * q^85 + 366976068 * q^88 + 373680796 * q^91 - 544741584 * q^94 - 133878688 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$	− 29.8006i	− 1.86254i	−0.364336	−	0.931268i	$-0.618704\pi$
$2$	− 29.8006i	− 1.86254i	0.364336	−	0.931268i	$-0.381296\pi$
$3$	0	0
$3$	0	0
$4$	−632.074	−2.46904
$5$	177.778i	0.284445i	0.989835	+	0.142223i	$0.0454249\pi$
$5$	177.778i	0.284445i	−0.989835	+	0.142223i	$0.954575\pi$
$6$	0	0
$7$	3390.81	1.41225	0.706125	−	0.708087i	$-0.250441\pi$
$7$	3390.81	1.41225	0.706125	+	0.708087i	$0.250441\pi$
$8$	11207.2i	2.73614i
$9$	0	0
$10$	5297.89	0.529789
$11$	− 22713.7i	− 1.55138i	−0.631115	−	0.775689i	$-0.717402\pi$
$11$	− 22713.7i	− 1.55138i	0.631115	−	0.775689i	$-0.282598\pi$
$12$	0	0
$13$	48777.1	1.70782	0.853911	−	0.520419i	$-0.174224\pi$
$13$	48777.1	1.70782	0.853911	+	0.520419i	$0.174224\pi$
$14$	− 101048.i	− 2.63037i
$15$	0	0
$16$	172170.	2.62711
$17$	36661.7i	0.438952i	0.975618	+	0.219476i	$0.0704348\pi$
$17$	36661.7i	0.438952i	−0.975618	+	0.219476i	$0.929565\pi$
$18$	0	0
$19$	−81528.6	−0.625598	−0.312799	−	0.949819i	$-0.601267\pi$
$19$	−81528.6	−0.625598	−0.312799	+	0.949819i	$0.601267\pi$
$20$	− 112369.i	− 0.702306i
$21$	0	0
$22$	−676882.	−2.88950
$23$	− 44680.0i	− 0.159662i	−0.996808	−	0.0798311i	$-0.974562\pi$
$23$	− 44680.0i	− 0.159662i	0.996808	−	0.0798311i	$-0.0254381\pi$
$24$	0	0
$25$	359020.	0.919091
$26$	− 1.45359e6i	− 3.18088i
$27$	0	0
$28$	−2.14324e6	−3.48690
$29$	− 307029.i	− 0.434098i	−0.976161	−	0.217049i	$-0.930357\pi$
$29$	− 307029.i	− 0.434098i	0.976161	−	0.217049i	$-0.0696431\pi$
$30$	0	0
$31$	−377888.	−0.409182	−0.204591	−	0.978848i	$-0.565586\pi$
$31$	−377888.	−0.409182	−0.204591	+	0.978848i	$0.565586\pi$
$32$	− 2.26173e6i	− 2.15695i
$33$	0	0
$34$	1.09254e6	0.817564
$35$	602813.i	0.401708i
$36$	0	0
$37$	1.82114e6	0.971711	0.485856	−	0.874039i	$-0.338508\pi$
$37$	1.82114e6	0.971711	0.485856	+	0.874039i	$0.338508\pi$
$38$	2.42960e6i	1.16520i
$39$	0	0
$40$	−1.99240e6	−0.778280
$41$	− 2.56535e6i	− 0.907842i	−0.891042	−	0.453921i	$-0.850025\pi$
$41$	− 2.56535e6i	− 0.907842i	0.891042	−	0.453921i	$-0.149975\pi$
$42$	0	0
$43$	−859529.	−0.251412	−0.125706	−	0.992068i	$-0.540120\pi$
$43$	−859529.	−0.251412	−0.125706	+	0.992068i	$0.540120\pi$
$44$	1.43568e7i	3.83041i
$45$	0	0
$46$	−1.33149e6	−0.297377
$47$	− 3.14001e6i	− 0.643487i	−0.946827	−	0.321743i	$-0.895731\pi$
$47$	− 3.14001e6i	− 0.643487i	0.946827	−	0.321743i	$-0.104269\pi$
$48$	0	0
$49$	5.73282e6	0.994453
$50$	− 1.06990e7i	− 1.71184i
$51$	0	0
$52$	−3.08307e7	−4.21668
$53$	− 1.04587e7i	− 1.32548i	−0.748848	−	0.662742i	$-0.769393\pi$
$53$	− 1.04587e7i	− 1.32548i	0.748848	−	0.662742i	$-0.230607\pi$
$54$	0	0
$55$	4.03801e6	0.441282
$56$	3.80016e7i	3.86411i
$57$	0	0
$58$	−9.14964e6	−0.808523
$59$	2.01171e7i	1.66019i	0.557625	+	0.830093i	$0.311713\pi$
$59$	2.01171e7i	1.66019i	−0.557625	+	0.830093i	$0.688287\pi$
$60$	0	0
$61$	−1.06653e7	−0.770286	−0.385143	−	0.922857i	$-0.625848\pi$
$61$	−1.06653e7	−0.770286	−0.385143	+	0.922857i	$0.625848\pi$
$62$	1.12613e7i	0.762115i
$63$	0	0
$64$	−2.33251e7	−1.39029
$65$	8.67151e6i	0.485782i
$66$	0	0
$67$	−3.37493e7	−1.67481	−0.837404	−	0.546585i	$-0.815928\pi$
$67$	−3.37493e7	−1.67481	−0.837404	+	0.546585i	$0.815928\pi$
$68$	− 2.31729e7i	− 1.08379i
$69$	0	0
$70$	1.79642e7	0.748195
$71$	− 387108.i	− 0.0152335i	−0.999971	−	0.00761673i	$-0.997575\pi$
$71$	− 387108.i	− 0.0152335i	0.999971	−	0.00761673i	$-0.00242450\pi$
$72$	0	0
$73$	1.74105e7	0.613083	0.306542	−	0.951857i	$-0.400828\pi$
$73$	1.74105e7	0.613083	0.306542	+	0.951857i	$0.400828\pi$
$74$	− 5.42711e7i	− 1.80985i
$75$	0	0
$76$	5.15321e7	1.54463
$77$	− 7.70180e7i	− 2.19094i
$78$	0	0
$79$	1.30586e7	0.335266	0.167633	−	0.985850i	$-0.446388\pi$
$79$	1.30586e7	0.335266	0.167633	+	0.985850i	$0.446388\pi$
$80$	3.06081e7i	0.747269i
$81$	0	0
$82$	−7.64487e7	−1.69089
$83$	− 6.25273e7i	− 1.31752i	−0.752353	−	0.658761i	$-0.771081\pi$
$83$	− 6.25273e7i	− 1.31752i	0.752353	−	0.658761i	$-0.228919\pi$
$84$	0	0
$85$	−6.51766e6	−0.124858
$86$	2.56144e7i	0.468264i
$87$	0	0
$88$	2.54558e8	4.24478
$89$	− 6.33977e7i	− 1.01045i	−0.862988	−	0.505224i	$-0.831410\pi$
$89$	− 6.33977e7i	− 1.01045i	0.862988	−	0.505224i	$-0.168590\pi$
$90$	0	0
$91$	1.65394e8	2.41187
$92$	2.82411e7i	0.394212i
$93$	0	0
$94$	−9.35740e7	−1.19852
$95$	− 1.44940e7i	− 0.177948i
$96$	0	0
$97$	−6.53962e7	−0.738696	−0.369348	−	0.929291i	$-0.620419\pi$
$97$	−6.53962e7	−0.738696	−0.369348	+	0.929291i	$0.620419\pi$
$98$	− 1.70841e8i	− 1.85220i
$99$	0	0
$100$	−2.26927e8	−2.26927
$101$	− 1.34466e7i	− 0.129219i	−0.997911	−	0.0646094i	$-0.979420\pi$
$101$	− 1.34466e7i	− 0.129219i	0.997911	−	0.0646094i	$-0.0205802\pi$
$102$	0	0
$103$	−2.87838e7	−0.255740	−0.127870	−	0.991791i	$-0.540814\pi$
$103$	−2.87838e7	−0.255740	−0.127870	+	0.991791i	$0.540814\pi$
$104$	5.46655e8i	4.67283i
$105$	0	0
$106$	−3.11675e8	−2.46876
$107$	− 7.10303e7i	− 0.541886i	−0.962595	−	0.270943i	$-0.912664\pi$
$107$	− 7.10303e7i	− 0.541886i	0.962595	−	0.270943i	$-0.0873356\pi$
$108$	0	0
$109$	5.37568e7	0.380827	0.190413	−	0.981704i	$-0.439017\pi$
$109$	5.37568e7	0.380827	0.190413	+	0.981704i	$0.439017\pi$
$110$	− 1.20335e8i	− 0.821903i
$111$	0	0
$112$	5.83798e8	3.71014
$113$	− 2.06482e8i	− 1.26639i	−0.773992	−	0.633195i	$-0.781743\pi$
$113$	− 2.06482e8i	− 1.26639i	0.773992	−	0.633195i	$-0.218257\pi$
$114$	0	0
$115$	7.94314e6	0.0454152
$116$	1.94065e8i	1.07180i
$117$	0	0
$118$	5.99500e8	3.09216
$119$	1.24313e8i	0.619910i
$120$	0	0
$121$	−3.01555e8	−1.40677
$122$	3.17831e8i	1.43468i
$123$	0	0
$124$	2.38853e8	1.01029
$125$	1.33271e8i	0.545876i
$126$	0	0
$127$	3.63640e8	1.39784	0.698918	−	0.715201i	$-0.253665\pi$
$127$	3.63640e8	1.39784	0.698918	+	0.715201i	$0.253665\pi$
$128$	1.16100e8i	0.432508i
$129$	0	0
$130$	2.58416e8	0.904786
$131$	1.38241e7i	0.0469408i	0.999725	+	0.0234704i	$0.00747154\pi$
$131$	1.38241e7i	0.0469408i	−0.999725	+	0.0234704i	$0.992528\pi$
$132$	0	0
$133$	−2.76448e8	−0.883502
$134$	1.00575e9i	3.11939i
$135$	0	0
$136$	−4.10876e8	−1.20103
$137$	− 2.27263e7i	− 0.0645130i	−0.999480	−	0.0322565i	$-0.989731\pi$
$137$	− 2.27263e7i	− 0.0645130i	0.999480	−	0.0322565i	$-0.0102693\pi$
$138$	0	0
$139$	5.08013e8	1.36087	0.680434	−	0.732809i	$-0.261791\pi$
$139$	5.08013e8	1.36087	0.680434	+	0.732809i	$0.261791\pi$
$140$	− 3.81022e8i	− 0.991832i
$141$	0	0
$142$	−1.15360e7	−0.0283728
$143$	− 1.10791e9i	− 2.64948i
$144$	0	0
$145$	5.45831e7	0.123477
$146$	− 5.18842e8i	− 1.14189i
$147$	0	0
$148$	−1.15110e9	−2.39919
$149$	− 3.67381e8i	− 0.745370i	−0.927958	−	0.372685i	$-0.878437\pi$
$149$	− 3.67381e8i	− 0.745370i	0.927958	−	0.372685i	$-0.121563\pi$
$150$	0	0
$151$	2.15381e7	0.0414286	0.0207143	−	0.999785i	$-0.493406\pi$
$151$	2.15381e7	0.0414286	0.0207143	+	0.999785i	$0.493406\pi$
$152$	− 9.13708e8i	− 1.71172i
$153$	0	0
$154$	−2.29518e9	−4.08069
$155$	− 6.71802e7i	− 0.116390i
$156$	0	0
$157$	−5.17571e8	−0.851866	−0.425933	−	0.904755i	$-0.640054\pi$
$157$	−5.17571e8	−0.851866	−0.425933	+	0.904755i	$0.640054\pi$
$158$	− 3.89154e8i	− 0.624444i
$159$	0	0
$160$	4.02086e8	0.613534
$161$	− 1.51502e8i	− 0.225483i
$162$	0	0
$163$	1.46155e8	0.207045	0.103522	−	0.994627i	$-0.466989\pi$
$163$	1.46155e8	0.207045	0.103522	+	0.994627i	$0.466989\pi$
$164$	1.62149e9i	2.24150i
$165$	0	0
$166$	−1.86335e9	−2.45393
$167$	2.78172e8i	0.357642i	0.983882	+	0.178821i	$0.0572283\pi$
$167$	2.78172e8i	0.357642i	−0.983882	+	0.178821i	$0.942772\pi$
$168$	0	0
$169$	1.56348e9	1.91666
$170$	1.94230e8i	0.232552i
$171$	0	0
$172$	5.43285e8	0.620747
$173$	1.39445e9i	1.55675i	0.627800	+	0.778374i	$0.283955\pi$
$173$	1.39445e9i	1.55675i	−0.627800	+	0.778374i	$0.716045\pi$
$174$	0	0
$175$	1.21737e9	1.29799
$176$	− 3.91063e9i	− 4.07564i
$177$	0	0
$178$	−1.88929e9	−1.88199
$179$	1.59335e9i	1.55203i	0.630717	+	0.776013i	$0.282761\pi$
$179$	1.59335e9i	1.55203i	−0.630717	+	0.776013i	$0.717239\pi$
$180$	0	0
$181$	4.20532e8	0.391818	0.195909	−	0.980622i	$-0.437234\pi$
$181$	4.20532e8	0.391818	0.195909	+	0.980622i	$0.437234\pi$
$182$	− 4.92884e9i	− 4.49220i
$183$	0	0
$184$	5.00739e8	0.436857
$185$	3.23760e8i	0.276399i
$186$	0	0
$187$	8.32724e8	0.680981
$188$	1.98472e9i	1.58879i
$189$	0	0
$190$	−4.31930e8	−0.331435
$191$	1.22642e9i	0.921524i	0.887524	+	0.460762i	$0.152424\pi$
$191$	1.22642e9i	0.921524i	−0.887524	+	0.460762i	$0.847576\pi$
$192$	0	0
$193$	1.96083e9	1.41322	0.706612	−	0.707601i	$-0.250223\pi$
$193$	1.96083e9	1.41322	0.706612	+	0.707601i	$0.250223\pi$
$194$	1.94884e9i	1.37585i
$195$	0	0
$196$	−3.62357e9	−2.45534
$197$	− 4.53495e7i	− 0.0301098i	−0.999887	−	0.0150549i	$-0.995208\pi$
$197$	− 4.53495e7i	− 0.0301098i	0.999887	−	0.0150549i	$-0.00479231\pi$
$198$	0	0
$199$	−1.93844e9	−1.23606	−0.618029	−	0.786155i	$-0.712069\pi$
$199$	−1.93844e9	−1.23606	−0.618029	+	0.786155i	$0.712069\pi$
$200$	4.02361e9i	2.51476i
$201$	0	0
$202$	−4.00715e8	−0.240675
$203$	− 1.04108e9i	− 0.613055i
$204$	0	0
$205$	4.56063e8	0.258231
$206$	8.57774e8i	0.476325i
$207$	0	0
$208$	8.39797e9	4.48664
$209$	1.85182e9i	0.970539i
$210$	0	0
$211$	−5.65952e8	−0.285529	−0.142764	−	0.989757i	$-0.545599\pi$
$211$	−5.65952e8	−0.285529	−0.142764	+	0.989757i	$0.545599\pi$
$212$	6.61067e9i	3.27267i
$213$	0	0
$214$	−2.11674e9	−1.00928
$215$	− 1.52805e8i	− 0.0715130i
$216$	0	0
$217$	−1.28135e9	−0.577867
$218$	− 1.60198e9i	− 0.709304i
$219$	0	0
$220$	−2.55232e9	−1.08954
$221$	1.78825e9i	0.749652i
$222$	0	0
$223$	−1.96590e9	−0.794954	−0.397477	−	0.917612i	$-0.630114\pi$
$223$	−1.96590e9	−0.794954	−0.397477	+	0.917612i	$0.630114\pi$
$224$	− 7.66910e9i	− 3.04616i
$225$	0	0
$226$	−6.15327e9	−2.35870
$227$	3.46174e9i	1.30374i	0.758330	+	0.651870i	$0.226015\pi$
$227$	3.46174e9i	1.30374i	−0.758330	+	0.651870i	$0.773985\pi$
$228$	0	0
$229$	5.09464e9	1.85256	0.926278	−	0.376842i	$-0.122990\pi$
$229$	5.09464e9	1.85256	0.926278	+	0.376842i	$0.122990\pi$
$230$	− 2.36710e8i	− 0.0845873i
$231$	0	0
$232$	3.44094e9	1.18775
$233$	− 4.76326e9i	− 1.61615i	−0.589083	−	0.808073i	$-0.700511\pi$
$233$	− 4.76326e9i	− 1.61615i	0.589083	−	0.808073i	$-0.299489\pi$
$234$	0	0
$235$	5.58225e8	0.183037
$236$	− 1.27155e10i	− 4.09906i
$237$	0	0
$238$	3.70460e9	1.15461
$239$	1.69940e9i	0.520839i	0.965496	+	0.260419i	$0.0838608\pi$
$239$	1.69940e9i	0.520839i	−0.965496	+	0.260419i	$0.916139\pi$
$240$	0	0
$241$	5.48403e9	1.62567	0.812833	−	0.582497i	$-0.197924\pi$
$241$	5.48403e9	1.62567	0.812833	+	0.582497i	$0.197924\pi$
$242$	8.98650e9i	2.62017i
$243$	0	0
$244$	6.74123e9	1.90186
$245$	1.01917e9i	0.282867i
$246$	0	0
$247$	−3.97673e9	−1.06841
$248$	− 4.23507e9i	− 1.11958i
$249$	0	0
$250$	3.97154e9	1.01671
$251$	2.82808e9i	0.712520i	0.934387	+	0.356260i	$0.115948\pi$
$251$	2.82808e9i	0.712520i	−0.934387	+	0.356260i	$0.884052\pi$
$252$	0	0
$253$	−1.01485e9	−0.247697
$254$	− 1.08367e10i	− 2.60352i
$255$	0	0
$256$	−2.51138e9	−0.584726
$257$	− 3.86210e9i	− 0.885301i	−0.896694	−	0.442651i	$-0.854038\pi$
$257$	− 3.86210e9i	− 0.885301i	0.896694	−	0.442651i	$-0.145962\pi$
$258$	0	0
$259$	6.17516e9	1.37230
$260$	− 5.48103e9i	− 1.19941i
$261$	0	0
$262$	4.11965e8	0.0874289
$263$	7.12622e9i	1.48948i	0.667352	+	0.744742i	$0.267428\pi$
$263$	7.12622e9i	1.48948i	−0.667352	+	0.744742i	$0.732572\pi$
$264$	0	0
$265$	1.85933e9	0.377028
$266$	8.23831e9i	1.64555i
$267$	0	0
$268$	2.13320e10	4.13516
$269$	4.73081e9i	0.903496i	0.892146	+	0.451748i	$0.149199\pi$
$269$	4.73081e9i	0.903496i	−0.892146	+	0.451748i	$0.850801\pi$
$270$	0	0
$271$	−4.16250e9	−0.771751	−0.385875	−	0.922551i	$-0.626100\pi$
$271$	−4.16250e9	−0.771751	−0.385875	+	0.922551i	$0.626100\pi$
$272$	6.31206e9i	1.15318i
$273$	0	0
$274$	−6.77257e8	−0.120158
$275$	− 8.15468e9i	− 1.42586i
$276$	0	0
$277$	−9.20052e9	−1.56276	−0.781382	−	0.624053i	$-0.785485\pi$
$277$	−9.20052e9	−1.56276	−0.781382	+	0.624053i	$0.785485\pi$
$278$	− 1.51391e10i	− 2.53466i
$279$	0	0
$280$	−6.75585e9	−1.09913
$281$	− 5.59520e9i	− 0.897409i	−0.893680	−	0.448705i	$-0.851886\pi$
$281$	− 5.59520e9i	− 0.897409i	0.893680	−	0.448705i	$-0.148114\pi$
$282$	0	0
$283$	6.72360e9	1.04823	0.524114	−	0.851648i	$-0.324396\pi$
$283$	6.72360e9	1.04823	0.524114	+	0.851648i	$0.324396\pi$
$284$	2.44681e8i	0.0376120i
$285$	0	0
$286$	−3.30163e10	−4.93475
$287$	− 8.69861e9i	− 1.28210i
$288$	0	0
$289$	5.63168e9	0.807321
$290$	− 1.62661e9i	− 0.229980i
$291$	0	0
$292$	−1.10047e10	−1.51373
$293$	8.45955e9i	1.14783i	0.818916	+	0.573914i	$0.194576\pi$
$293$	8.45955e9i	1.14783i	−0.818916	+	0.573914i	$0.805424\pi$
$294$	0	0
$295$	−3.57638e9	−0.472232
$296$	2.04099e10i	2.65873i
$297$	0	0
$298$	−1.09482e10	−1.38828
$299$	− 2.17936e9i	− 0.272675i
$300$	0	0
$301$	−2.91450e9	−0.355057
$302$	− 6.41848e8i	− 0.0771622i
$303$	0	0
$304$	−1.40368e10	−1.64352
$305$	− 1.89605e9i	− 0.219104i
$306$	0	0
$307$	1.52537e10	1.71721	0.858604	−	0.512639i	$-0.171332\pi$
$307$	1.52537e10	1.71721	0.858604	+	0.512639i	$0.171332\pi$
$308$	4.86811e10i	5.40950i
$309$	0	0
$310$	−2.00201e9	−0.216780
$311$	2.26328e8i	0.0241934i	0.999927	+	0.0120967i	$0.00385059\pi$
$311$	2.26328e8i	0.0241934i	−0.999927	+	0.0120967i	$0.996149\pi$
$312$	0	0
$313$	9.53020e9	0.992944	0.496472	−	0.868053i	$-0.334629\pi$
$313$	9.53020e9	0.992944	0.496472	+	0.868053i	$0.334629\pi$
$314$	1.54239e10i	1.58663i
$315$	0	0
$316$	−8.25401e9	−0.827784
$317$	− 1.07299e10i	− 1.06257i	−0.847192	−	0.531286i	$-0.821709\pi$
$317$	− 1.07299e10i	− 1.06257i	0.847192	−	0.531286i	$-0.178291\pi$
$318$	0	0
$319$	−6.97378e9	−0.673450
$320$	− 4.14670e9i	− 0.395460i
$321$	0	0
$322$	−4.51484e9	−0.419970
$323$	− 2.98898e9i	− 0.274608i
$324$	0	0
$325$	1.75120e10	1.56964
$326$	− 4.35551e9i	− 0.385628i
$327$	0	0
$328$	2.87504e10	2.48398
$329$	− 1.06472e10i	− 0.908764i
$330$	0	0
$331$	−4.58004e9	−0.381555	−0.190778	−	0.981633i	$-0.561101\pi$
$331$	−4.58004e9	−0.381555	−0.190778	+	0.981633i	$0.561101\pi$
$332$	3.95219e10i	3.25301i
$333$	0	0
$334$	8.28970e9	0.666120
$335$	− 5.99988e9i	− 0.476391i
$336$	0	0
$337$	−1.92192e10	−1.49010	−0.745051	−	0.667008i	$-0.767575\pi$
$337$	−1.92192e10	−1.49010	−0.745051	+	0.667008i	$0.767575\pi$
$338$	− 4.65925e10i	− 3.56984i
$339$	0	0
$340$	4.11964e9	0.308279
$341$	8.58324e9i	0.634796i
$342$	0	0
$343$	−1.08437e8	−0.00783431
$344$	− 9.63292e9i	− 0.687898i
$345$	0	0
$346$	4.15554e10	2.89950
$347$	8.34109e7i	0.00575314i	0.999996	+	0.00287657i	$0.000915642\pi$
$347$	8.34109e7i	0.00575314i	−0.999996	+	0.00287657i	$0.999084\pi$
$348$	0	0
$349$	−2.14746e10	−1.44752	−0.723759	−	0.690053i	$-0.757587\pi$
$349$	−2.14746e10	−1.44752	−0.723759	+	0.690053i	$0.757587\pi$
$350$	− 3.62783e10i	− 2.41755i
$351$	0	0
$352$	−5.13723e10	−3.34625
$353$	1.88260e10i	1.21244i	0.795297	+	0.606220i	$0.207315\pi$
$353$	1.88260e10i	1.21244i	−0.795297	+	0.606220i	$0.792685\pi$
$354$	0	0
$355$	6.88193e7	0.00433308
$356$	4.00720e10i	2.49483i
$357$	0	0
$358$	4.74827e10	2.89070
$359$	− 1.82528e10i	− 1.09888i	−0.835532	−	0.549442i	$-0.814840\pi$
$359$	− 1.82528e10i	− 1.09888i	0.835532	−	0.549442i	$-0.185160\pi$
$360$	0	0
$361$	−1.03367e10	−0.608627
$362$	− 1.25321e10i	− 0.729775i
$363$	0	0
$364$	−1.04541e11	−5.95501
$365$	3.09521e9i	0.174389i
$366$	0	0
$367$	−4.76601e9	−0.262719	−0.131359	−	0.991335i	$-0.541934\pi$
$367$	−4.76601e9	−0.262719	−0.131359	+	0.991335i	$0.541934\pi$
$368$	− 7.69258e9i	− 0.419450i
$369$	0	0
$370$	9.64822e9	0.514802
$371$	− 3.54635e10i	− 1.87192i
$372$	0	0
$373$	−1.20517e10	−0.622607	−0.311303	−	0.950311i	$-0.600766\pi$
$373$	−1.20517e10	−0.622607	−0.311303	+	0.950311i	$0.600766\pi$
$374$	− 2.48157e10i	− 1.26835i
$375$	0	0
$376$	3.51907e10	1.76067
$377$	− 1.49760e10i	− 0.741362i
$378$	0	0
$379$	−1.49538e10	−0.724759	−0.362380	−	0.932031i	$-0.618036\pi$
$379$	−1.49538e10	−0.724759	−0.362380	+	0.932031i	$0.618036\pi$
$380$	9.16128e9i	0.439361i
$381$	0	0
$382$	3.65481e10	1.71637
$383$	1.45100e10i	0.674332i	0.941445	+	0.337166i	$0.109468\pi$
$383$	1.45100e10i	0.674332i	−0.941445	+	0.337166i	$0.890532\pi$
$384$	0	0
$385$	1.36921e10	0.623201
$386$	− 5.84339e10i	− 2.63218i
$387$	0	0
$388$	4.13352e10	1.82387
$389$	− 4.99907e9i	− 0.218319i	−0.994024	−	0.109159i	$-0.965184\pi$
$389$	− 4.99907e9i	− 0.218319i	0.994024	−	0.109159i	$-0.0348159\pi$
$390$	0	0
$391$	1.63805e9	0.0700841
$392$	6.42489e10i	2.72096i
$393$	0	0
$394$	−1.35144e9	−0.0560806
$395$	2.32154e9i	0.0953647i
$396$	0	0
$397$	−4.71797e9	−0.189930	−0.0949649	−	0.995481i	$-0.530274\pi$
$397$	−4.71797e9	−0.189930	−0.0949649	+	0.995481i	$0.530274\pi$
$398$	5.77665e10i	2.30220i
$399$	0	0
$400$	6.18126e10	2.41455
$401$	− 4.33203e10i	− 1.67538i	−0.546143	−	0.837692i	$-0.683904\pi$
$401$	− 4.33203e10i	− 1.67538i	0.546143	−	0.837692i	$-0.316096\pi$
$402$	0	0
$403$	−1.84323e10	−0.698810
$404$	8.49922e9i	0.319046i
$405$	0	0
$406$	−3.10247e10	−1.14184
$407$	− 4.13650e10i	− 1.50749i
$408$	0	0
$409$	1.78697e10	0.638592	0.319296	−	0.947655i	$-0.396554\pi$
$409$	1.78697e10	0.638592	0.319296	+	0.947655i	$0.396554\pi$
$410$	− 1.35909e10i	− 0.480965i
$411$	0	0
$412$	1.81935e10	0.631433
$413$	6.82133e10i	2.34460i
$414$	0	0
$415$	1.11160e10	0.374763
$416$	− 1.10321e11i	− 3.68369i
$417$	0	0
$418$	5.51852e10	1.80766
$419$	4.40651e10i	1.42968i	0.699288	+	0.714840i	$0.253500\pi$
$419$	4.40651e10i	1.42968i	−0.699288	+	0.714840i	$0.746500\pi$
$420$	0	0
$421$	−1.84667e10	−0.587842	−0.293921	−	0.955830i	$-0.594960\pi$
$421$	−1.84667e10	−0.587842	−0.293921	+	0.955830i	$0.594960\pi$
$422$	1.68657e10i	0.531807i
$423$	0	0
$424$	1.17213e11	3.62670
$425$	1.31623e10i	0.403437i
$426$	0	0
$427$	−3.61639e10	−1.08784
$428$	4.48964e10i	1.33794i
$429$	0	0
$430$	−4.55369e9	−0.133196
$431$	3.36109e10i	0.974026i	0.873395	+	0.487013i	$0.161914\pi$
$431$	3.36109e10i	0.974026i	−0.873395	+	0.487013i	$0.838086\pi$
$432$	0	0
$433$	1.68004e10	0.477933	0.238966	−	0.971028i	$-0.423191\pi$
$433$	1.68004e10	0.477933	0.238966	+	0.971028i	$0.423191\pi$
$434$	3.81849e10i	1.07630i
$435$	0	0
$436$	−3.39783e10	−0.940276
$437$	3.64270e9i	0.0998844i
$438$	0	0
$439$	2.40634e10	0.647887	0.323944	−	0.946076i	$-0.394991\pi$
$439$	2.40634e10	0.647887	0.323944	+	0.946076i	$0.394991\pi$
$440$	4.52548e10i	1.20741i
$441$	0	0
$442$	5.32909e10	1.39625
$443$	4.06896e10i	1.05650i	0.849090	+	0.528249i	$0.177151\pi$
$443$	4.06896e10i	1.05650i	−0.849090	+	0.528249i	$0.822849\pi$
$444$	0	0
$445$	1.12707e10	0.287417
$446$	5.85850e10i	1.48063i
$447$	0	0
$448$	−7.90912e10	−1.96343
$449$	2.01989e10i	0.496983i	0.968634	+	0.248492i	$0.0799349\pi$
$449$	2.01989e10i	0.496983i	−0.968634	+	0.248492i	$0.920065\pi$
$450$	0	0
$451$	−5.82686e10	−1.40841
$452$	1.30512e11i	3.12677i
$453$	0	0
$454$	1.03162e11	2.42826
$455$	2.94035e10i	0.686046i
$456$	0	0
$457$	2.89357e9	0.0663391	0.0331695	−	0.999450i	$-0.489440\pi$
$457$	2.89357e9	0.0663391	0.0331695	+	0.999450i	$0.489440\pi$
$458$	− 1.51823e11i	− 3.45045i
$459$	0	0
$460$	−5.02065e9	−0.112132
$461$	− 9.00677e10i	− 1.99418i	−0.0762042	−	0.997092i	$-0.524280\pi$
$461$	− 9.00677e10i	− 1.99418i	0.0762042	−	0.997092i	$-0.475720\pi$
$462$	0	0
$463$	5.64711e9	0.122886	0.0614430	−	0.998111i	$-0.480430\pi$
$463$	5.64711e9	0.122886	0.0614430	+	0.998111i	$0.480430\pi$
$464$	− 5.28613e10i	− 1.14042i
$465$	0	0
$466$	−1.41948e11	−3.01013
$467$	− 3.24590e10i	− 0.682445i	−0.939983	−	0.341223i	$-0.889159\pi$
$467$	− 3.24590e10i	− 0.682445i	0.939983	−	0.341223i	$-0.110841\pi$
$468$	0	0
$469$	−1.14437e11	−2.36525
$470$	− 1.66354e10i	− 0.340912i
$471$	0	0
$472$	−2.25456e11	−4.54249
$473$	1.95231e10i	0.390036i
$474$	0	0
$475$	−2.92704e10	−0.574982
$476$	− 7.85750e10i	− 1.53058i
$477$	0	0
$478$	5.06430e10	0.970080
$479$	9.77923e10i	1.85764i	0.370526	+	0.928822i	$0.379178\pi$
$479$	9.77923e10i	1.85764i	−0.370526	+	0.928822i	$0.620822\pi$
$480$	0	0
$481$	8.88301e10	1.65951
$482$	− 1.63427e11i	− 3.02786i
$483$	0	0
$484$	1.90605e11	3.47338
$485$	− 1.16260e10i	− 0.210119i
$486$	0	0
$487$	−5.47177e10	−0.972774	−0.486387	−	0.873743i	$-0.661685\pi$
$487$	−5.47177e10	−0.972774	−0.486387	+	0.873743i	$0.661685\pi$
$488$	− 1.19528e11i	− 2.10761i
$489$	0	0
$490$	3.03719e10	0.526850
$491$	9.79400e9i	0.168513i	0.996444	+	0.0842566i	$0.0268516\pi$
$491$	9.79400e9i	0.168513i	−0.996444	+	0.0842566i	$0.973148\pi$
$492$	0	0
$493$	1.12562e10	0.190548
$494$	1.18509e11i	1.98995i
$495$	0	0
$496$	−6.50611e10	−1.07497
$497$	− 1.31261e9i	− 0.0215135i
$498$	0	0
$499$	−2.61258e10	−0.421373	−0.210687	−	0.977554i	$-0.567570\pi$
$499$	−2.61258e10	−0.421373	−0.210687	+	0.977554i	$0.567570\pi$
$500$	− 8.42368e10i	− 1.34779i
$501$	0	0
$502$	8.42784e10	1.32709
$503$	7.49906e10i	1.17148i	0.810499	+	0.585740i	$0.199196\pi$
$503$	7.49906e10i	1.17148i	−0.810499	+	0.585740i	$0.800804\pi$
$504$	0	0
$505$	2.39051e9	0.0367557
$506$	3.02431e10i	0.461344i
$507$	0	0
$508$	−2.29847e11	−3.45131
$509$	1.01569e11i	1.51317i	0.653894	+	0.756586i	$0.273134\pi$
$509$	1.01569e11i	1.51317i	−0.653894	+	0.756586i	$0.726866\pi$
$510$	0	0
$511$	5.90357e10	0.865827
$512$	1.04562e11i	1.52158i
$513$	0	0
$514$	−1.15093e11	−1.64890
$515$	− 5.11713e9i	− 0.0727441i
$516$	0	0
$517$	−7.13213e10	−0.998291
$518$	− 1.84023e11i	− 2.55596i
$519$	0	0
$520$	−9.71834e10	−1.32916
$521$	3.32430e10i	0.451179i	0.974222	+	0.225590i	$0.0724309\pi$
$521$	3.32430e10i	0.451179i	−0.974222	+	0.225590i	$0.927569\pi$
$522$	0	0
$523$	1.23700e10	0.165334	0.0826669	−	0.996577i	$-0.473656\pi$
$523$	1.23700e10	0.165334	0.0826669	+	0.996577i	$0.473656\pi$
$524$	− 8.73782e9i	− 0.115899i
$525$	0	0
$526$	2.12365e11	2.77422
$527$	− 1.38540e10i	− 0.179611i
$528$	0	0
$529$	7.63147e10	0.974508
$530$	− 5.54091e10i	− 0.702227i
$531$	0	0
$532$	1.74736e11	2.18140
$533$	− 1.25130e11i	− 1.55043i
$534$	0	0
$535$	1.26276e10	0.154137
$536$	− 3.78235e11i	− 4.58250i
$537$	0	0
$538$	1.40981e11	1.68279
$539$	− 1.30214e11i	− 1.54277i
$540$	0	0
$541$	6.00939e10	0.701522	0.350761	−	0.936465i	$-0.385923\pi$
$541$	6.00939e10	0.701522	0.350761	+	0.936465i	$0.385923\pi$
$542$	1.24045e11i	1.43741i
$543$	0	0
$544$	8.29188e10	0.946798
$545$	9.55679e9i	0.108324i
$546$	0	0
$547$	−7.31649e10	−0.817248	−0.408624	−	0.912703i	$-0.633991\pi$
$547$	−7.31649e10	−0.817248	−0.408624	+	0.912703i	$0.633991\pi$
$548$	1.43647e10i	0.159285i
$549$	0	0
$550$	−2.43014e11	−2.65571
$551$	2.50317e10i	0.271571i
$552$	0	0
$553$	4.42794e10	0.473479
$554$	2.74181e11i	2.91070i
$555$	0	0
$556$	−3.21102e11	−3.36003
$557$	1.00228e11i	1.04128i	0.853775	+	0.520642i	$0.174308\pi$
$557$	1.00228e11i	1.04128i	−0.853775	+	0.520642i	$0.825692\pi$
$558$	0	0
$559$	−4.19253e10	−0.429368
$560$	1.03787e11i	1.05533i
$561$	0	0
$562$	−1.66740e11	−1.67146
$563$	1.05362e10i	0.104870i	0.998624	+	0.0524350i	$0.0166982\pi$
$563$	1.05362e10i	0.104870i	−0.998624	+	0.0524350i	$0.983302\pi$
$564$	0	0
$565$	3.67079e10	0.360219
$566$	− 2.00367e11i	− 1.95236i
$567$	0	0
$568$	4.33840e9	0.0416808
$569$	1.14538e11i	1.09270i	0.837556	+	0.546351i	$0.183984\pi$
$569$	1.14538e11i	1.09270i	−0.837556	+	0.546351i	$0.816016\pi$
$570$	0	0
$571$	−3.37288e10	−0.317290	−0.158645	−	0.987336i	$-0.550713\pi$
$571$	−3.37288e10	−0.317290	−0.158645	+	0.987336i	$0.550713\pi$
$572$	7.00281e11i	6.54166i
$573$	0	0
$574$	−2.59223e11	−2.38796
$575$	− 1.60410e10i	− 0.146744i
$576$	0	0
$577$	1.77096e11	1.59773	0.798867	−	0.601508i	$-0.205433\pi$
$577$	1.77096e11	1.59773	0.798867	+	0.601508i	$0.205433\pi$
$578$	− 1.67827e11i	− 1.50366i
$579$	0	0
$580$	−3.45006e10	−0.304870
$581$	− 2.12019e11i	− 1.86067i
$582$	0	0
$583$	−2.37556e11	−2.05633
$584$	1.95123e11i	1.67748i
$585$	0	0
$586$	2.52099e11	2.13787
$587$	1.00900e11i	0.849841i	0.905231	+	0.424920i	$0.139698\pi$
$587$	1.00900e11i	0.849841i	−0.905231	+	0.424920i	$0.860302\pi$
$588$	0	0
$589$	3.08087e10	0.255983
$590$	1.06578e11i	0.879549i
$591$	0	0
$592$	3.13547e11	2.55279
$593$	− 2.10071e10i	− 0.169882i	−0.996386	−	0.0849410i	$-0.972930\pi$
$593$	− 2.10071e10i	− 0.169882i	0.996386	−	0.0849410i	$-0.0270702\pi$
$594$	0	0
$595$	−2.21002e10	−0.176331
$596$	2.32212e11i	1.84035i
$597$	0	0
$598$	−6.49463e10	−0.507866
$599$	− 1.88088e11i	− 1.46101i	−0.682908	−	0.730505i	$-0.739285\pi$
$599$	− 1.88088e11i	− 1.46101i	0.682908	−	0.730505i	$-0.260715\pi$
$600$	0	0
$601$	9.67891e10	0.741871	0.370936	−	0.928659i	$-0.379037\pi$
$601$	9.67891e10	0.741871	0.370936	+	0.928659i	$0.379037\pi$
$602$	8.68538e10i	0.661307i
$603$	0	0
$604$	−1.36137e10	−0.102289
$605$	− 5.36098e10i	− 0.400150i
$606$	0	0
$607$	6.56597e10	0.483664	0.241832	−	0.970318i	$-0.422252\pi$
$607$	6.56597e10	0.483664	0.241832	+	0.970318i	$0.422252\pi$
$608$	1.84395e11i	1.34938i
$609$	0	0
$610$	−5.65034e10	−0.408089
$611$	− 1.53161e11i	− 1.09896i
$612$	0	0
$613$	1.95329e10	0.138333	0.0691665	−	0.997605i	$-0.477966\pi$
$613$	1.95329e10	0.138333	0.0691665	+	0.997605i	$0.477966\pi$
$614$	− 4.54570e11i	− 3.19836i
$615$	0	0
$616$	8.63157e11	5.99469
$617$	8.36525e10i	0.577216i	0.957447	+	0.288608i	$0.0931924\pi$
$617$	8.36525e10i	0.577216i	−0.957447	+	0.288608i	$0.906808\pi$
$618$	0	0
$619$	−3.10110e10	−0.211229	−0.105614	−	0.994407i	$-0.533681\pi$
$619$	−3.10110e10	−0.211229	−0.105614	+	0.994407i	$0.533681\pi$
$620$	4.24629e10i	0.287371i
$621$	0	0
$622$	6.74470e9	0.0450610
$623$	− 2.14970e11i	− 1.42701i
$624$	0	0
$625$	1.16550e11	0.763819
$626$	− 2.84005e11i	− 1.84939i
$627$	0	0
$628$	3.27143e11	2.10329
$629$	6.67662e10i	0.426535i
$630$	0	0
$631$	9.80750e10	0.618644	0.309322	−	0.950957i	$-0.399898\pi$
$631$	9.80750e10	0.618644	0.309322	+	0.950957i	$0.399898\pi$
$632$	1.46351e11i	0.917332i
$633$	0	0
$634$	−3.19757e11	−1.97908
$635$	6.46472e10i	0.397608i
$636$	0	0
$637$	2.79630e11	1.69835
$638$	2.07823e11i	1.25432i
$639$	0	0
$640$	−2.06401e10	−0.123025
$641$	1.32995e11i	0.787774i	0.919159	+	0.393887i	$0.128870\pi$
$641$	1.32995e11i	0.787774i	−0.919159	+	0.393887i	$0.871130\pi$
$642$	0	0
$643$	−2.49007e11	−1.45669	−0.728346	−	0.685210i	$-0.759711\pi$
$643$	−2.49007e11	−1.45669	−0.728346	+	0.685210i	$0.759711\pi$
$644$	9.57603e10i	0.556726i
$645$	0	0
$646$	−8.90732e10	−0.511466
$647$	− 2.38080e11i	− 1.35864i	−0.733840	−	0.679322i	$-0.762274\pi$
$647$	− 2.38080e11i	− 1.35864i	0.733840	−	0.679322i	$-0.237726\pi$
$648$	0	0
$649$	4.56934e11	2.57558
$650$	− 5.21866e11i	− 2.92352i
$651$	0	0
$652$	−9.23810e10	−0.511202
$653$	− 1.87979e11i	− 1.03385i	−0.856031	−	0.516925i	$-0.827077\pi$
$653$	− 1.87979e11i	− 1.03385i	0.856031	−	0.516925i	$-0.172923\pi$
$654$	0	0
$655$	−2.45762e9	−0.0133521
$656$	− 4.41676e11i	− 2.38500i
$657$	0	0
$658$	−3.17292e11	−1.69261
$659$	2.06881e11i	1.09693i	0.836173	+	0.548466i	$0.184788\pi$
$659$	2.06881e11i	1.09693i	−0.836173	+	0.548466i	$0.815212\pi$
$660$	0	0
$661$	−1.68874e11	−0.884623	−0.442312	−	0.896861i	$-0.645841\pi$
$661$	−1.68874e11	−0.884623	−0.442312	+	0.896861i	$0.645841\pi$
$662$	1.36488e11i	0.710660i
$663$	0	0
$664$	7.00757e11	3.60492
$665$	− 4.91465e10i	− 0.251308i
$666$	0	0
$667$	−1.37181e10	−0.0693090
$668$	− 1.75826e11i	− 0.883031i
$669$	0	0
$670$	−1.78800e11	−0.887295
$671$	2.42248e11i	1.19500i
$672$	0	0
$673$	−3.26072e11	−1.58947	−0.794736	−	0.606955i	$-0.792391\pi$
$673$	−3.26072e11	−1.58947	−0.794736	+	0.606955i	$0.792391\pi$
$674$	5.72743e11i	2.77537i
$675$	0	0
$676$	−9.88232e11	−4.73230
$677$	− 3.62544e9i	− 0.0172586i	−0.999963	−	0.00862930i	$-0.997253\pi$
$677$	− 3.62544e9i	− 0.0172586i	0.999963	−	0.00862930i	$-0.00274683\pi$
$678$	0	0
$679$	−2.21747e11	−1.04322
$680$	− 7.30447e10i	− 0.341628i
$681$	0	0
$682$	2.55785e11	1.18233
$683$	− 2.50569e11i	− 1.15145i	−0.817644	−	0.575724i	$-0.804720\pi$
$683$	− 2.50569e11i	− 1.15145i	0.817644	−	0.575724i	$-0.195280\pi$
$684$	0	0
$685$	4.04025e9	0.0183504
$686$	3.23148e9i	0.0145917i
$687$	0	0
$688$	−1.47985e11	−0.660488
$689$	− 5.10146e11i	− 2.26369i
$690$	0	0
$691$	−7.90594e10	−0.346770	−0.173385	−	0.984854i	$-0.555470\pi$
$691$	−7.90594e10	−0.346770	−0.173385	+	0.984854i	$0.555470\pi$
$692$	− 8.81395e11i	− 3.84367i
$693$	0	0
$694$	2.48569e9	0.0107154
$695$	9.03137e10i	0.387092i
$696$	0	0
$697$	9.40500e10	0.398499
$698$	6.39956e11i	2.69605i
$699$	0	0
$700$	−7.69467e11	−3.20478
$701$	− 1.92497e11i	− 0.797173i	−0.917131	−	0.398587i	$-0.869501\pi$
$701$	− 1.92497e11i	− 0.797173i	0.917131	−	0.398587i	$-0.130499\pi$
$702$	0	0
$703$	−1.48475e11	−0.607901
$704$	5.29801e11i	2.15686i
$705$	0	0
$706$	5.61027e11	2.25821
$707$	− 4.55948e10i	− 0.182489i
$708$	0	0
$709$	8.03148e10	0.317842	0.158921	−	0.987291i	$-0.449199\pi$
$709$	8.03148e10	0.317842	0.158921	+	0.987291i	$0.449199\pi$
$710$	− 2.05085e9i	− 0.00807052i
$711$	0	0
$712$	7.10512e11	2.76472
$713$	1.68840e10i	0.0653309i
$714$	0	0
$715$	1.96962e11	0.753631
$716$	− 1.00711e12i	− 3.83201i
$717$	0	0
$718$	−5.43944e11	−2.04671
$719$	− 2.23610e11i	− 0.836712i	−0.908283	−	0.418356i	$-0.862607\pi$
$719$	− 2.23610e11i	− 0.836712i	0.908283	−	0.418356i	$-0.137393\pi$
$720$	0	0
$721$	−9.76005e10	−0.361170
$722$	3.08038e11i	1.13359i
$723$	0	0
$724$	−2.65807e11	−0.967414
$725$	− 1.10230e11i	− 0.398975i
$726$	0	0
$727$	3.67423e11	1.31531	0.657656	−	0.753318i	$-0.271548\pi$
$727$	3.67423e11	1.31531	0.657656	+	0.753318i	$0.271548\pi$
$728$	1.85361e12i	6.59921i
$729$	0	0
$730$	9.22389e10	0.324805
$731$	− 3.15118e10i	− 0.110358i
$732$	0	0
$733$	4.29526e11	1.48790	0.743950	−	0.668235i	$-0.232950\pi$
$733$	4.29526e11	1.48790	0.743950	+	0.668235i	$0.232950\pi$
$734$	1.42030e11i	0.489323i
$735$	0	0
$736$	−1.01054e11	−0.344384
$737$	7.66571e11i	2.59826i
$738$	0	0
$739$	5.45040e11	1.82747	0.913736	−	0.406309i	$-0.133184\pi$
$739$	5.45040e11	1.82747	0.913736	+	0.406309i	$0.133184\pi$
$740$	− 2.04640e11i	− 0.682439i
$741$	0	0
$742$	−1.05683e12	−3.48651
$743$	5.96208e11i	1.95633i	0.207824	+	0.978166i	$0.433362\pi$
$743$	5.96208e11i	1.95633i	−0.207824	+	0.978166i	$0.566638\pi$
$744$	0	0
$745$	6.53124e10	0.212017
$746$	3.59148e11i	1.15963i
$747$	0	0
$748$	−5.26343e11	−1.68137
$749$	− 2.40850e11i	− 0.765280i
$750$	0	0
$751$	2.63816e11	0.829356	0.414678	−	0.909968i	$-0.363894\pi$
$751$	2.63816e11	0.829356	0.414678	+	0.909968i	$0.363894\pi$
$752$	− 5.40616e11i	− 1.69051i
$753$	0	0
$754$	−4.46293e11	−1.38081
$755$	3.82901e9i	0.0117842i
$756$	0	0
$757$	−6.45369e10	−0.196528	−0.0982641	−	0.995160i	$-0.531329\pi$
$757$	−6.45369e10	−0.196528	−0.0982641	+	0.995160i	$0.531329\pi$
$758$	4.45631e11i	1.34989i
$759$	0	0
$760$	1.62437e11	0.486891
$761$	− 4.40862e10i	− 0.131451i	−0.997838	−	0.0657256i	$-0.979064\pi$
$761$	− 4.40862e10i	− 0.131451i	0.997838	−	0.0657256i	$-0.0209362\pi$
$762$	0	0
$763$	1.82279e11	0.537823
$764$	− 7.75190e11i	− 2.27528i
$765$	0	0
$766$	4.32407e11	1.25597
$767$	9.81253e11i	2.83530i
$768$	0	0
$769$	1.64096e11	0.469238	0.234619	−	0.972087i	$-0.424616\pi$
$769$	1.64096e11	0.469238	0.234619	+	0.972087i	$0.424616\pi$
$770$	− 4.08033e11i	− 1.16073i
$771$	0	0
$772$	−1.23939e12	−3.48930
$773$	6.54118e11i	1.83205i	0.401116	+	0.916027i	$0.368622\pi$
$773$	6.54118e11i	1.83205i	−0.401116	+	0.916027i	$0.631378\pi$
$774$	0	0
$775$	−1.35669e11	−0.376075
$776$	− 7.32909e11i	− 2.02117i
$777$	0	0
$778$	−1.48975e11	−0.406626
$779$	2.09149e11i	0.567944i
$780$	0	0
$781$	−8.79266e9	−0.0236328
$782$	− 4.88147e10i	− 0.130534i
$783$	0	0
$784$	9.87022e11	2.61254
$785$	− 9.20128e10i	− 0.242309i
$786$	0	0
$787$	−1.17983e11	−0.307554	−0.153777	−	0.988106i	$-0.549144\pi$
$787$	−1.17983e11	−0.307554	−0.153777	+	0.988106i	$0.549144\pi$
$788$	2.86643e10i	0.0743423i
$789$	0	0
$790$	6.91832e10	0.177620
$791$	− 7.00141e11i	− 1.78846i
$792$	0	0
$793$	−5.20220e11	−1.31551
$794$	1.40598e11i	0.353751i
$795$	0	0
$796$	1.22523e12	3.05188
$797$	− 4.89318e10i	− 0.121271i	−0.998160	−	0.0606356i	$-0.980687\pi$
$797$	− 4.89318e10i	− 0.121271i	0.998160	−	0.0606356i	$-0.0193128\pi$
$798$	0	0
$799$	1.15118e11	0.282460
$800$	− 8.12005e11i	− 1.98243i
$801$	0	0
$802$	−1.29097e12	−3.12046
$803$	− 3.95457e11i	− 0.951124i
$804$	0	0
$805$	2.69337e10	0.0641376
$806$	5.49292e11i	1.30156i
$807$	0	0
$808$	1.50698e11	0.353560
$809$	− 8.81881e10i	− 0.205881i	−0.994688	−	0.102940i	$-0.967175\pi$
$809$	− 8.81881e10i	− 0.205881i	0.994688	−	0.102940i	$-0.0328251\pi$
$810$	0	0
$811$	−7.58870e11	−1.75422	−0.877110	−	0.480290i	$-0.840532\pi$
$811$	−7.58870e11	−1.75422	−0.877110	+	0.480290i	$0.840532\pi$
$812$	6.58039e11i	1.51366i
$813$	0	0
$814$	−1.23270e12	−2.80776
$815$	2.59833e10i	0.0588929i
$816$	0	0
$817$	7.00761e10	0.157283
$818$	− 5.32527e11i	− 1.18940i
$819$	0	0
$820$	−2.88265e11	−0.637583
$821$	4.29292e11i	0.944888i	0.881361	+	0.472444i	$0.156628\pi$
$821$	4.29292e11i	0.944888i	−0.881361	+	0.472444i	$0.843372\pi$
$822$	0	0
$823$	−5.63516e11	−1.22831	−0.614154	−	0.789187i	$-0.710502\pi$
$823$	−5.63516e11	−1.22831	−0.614154	+	0.789187i	$0.710502\pi$
$824$	− 3.22586e11i	− 0.699740i
$825$	0	0
$826$	2.03279e12	4.36690
$827$	2.13022e11i	0.455410i	0.973730	+	0.227705i	$0.0731221\pi$
$827$	2.13022e11i	0.455410i	−0.973730	+	0.227705i	$0.926878\pi$
$828$	0	0
$829$	5.16375e11	1.09332	0.546660	−	0.837355i	$-0.315899\pi$
$829$	5.16375e11	1.09332	0.546660	+	0.837355i	$0.315899\pi$
$830$	− 3.31263e11i	− 0.698008i
$831$	0	0
$832$	−1.13773e12	−2.37436
$833$	2.10175e11i	0.436517i
$834$	0	0
$835$	−4.94530e10	−0.101729
$836$	− 1.17049e12i	− 2.39630i
$837$	0	0
$838$	1.31317e12	2.66283
$839$	− 6.87922e10i	− 0.138833i	−0.997588	−	0.0694163i	$-0.977886\pi$
$839$	− 6.87922e10i	− 0.138833i	0.997588	−	0.0694163i	$-0.0221137\pi$
$840$	0	0
$841$	4.05979e11	0.811559
$842$	5.50318e11i	1.09488i
$843$	0	0
$844$	3.57723e11	0.704981
$845$	2.77952e11i	0.545184i
$846$	0	0
$847$	−1.02252e12	−1.98672
$848$	− 1.80068e12i	− 3.48219i
$849$	0	0
$850$	3.92244e11	0.751415
$851$	− 8.13688e10i	− 0.155146i
$852$	0	0
$853$	2.33984e11	0.441967	0.220984	−	0.975278i	$-0.429073\pi$
$853$	2.33984e11	0.441967	0.220984	+	0.975278i	$0.429073\pi$
$854$	1.07770e12i	2.02613i
$855$	0	0
$856$	7.96051e11	1.48267
$857$	− 8.48896e11i	− 1.57373i	−0.617123	−	0.786867i	$-0.711702\pi$
$857$	− 8.48896e11i	− 1.57373i	0.617123	−	0.786867i	$-0.288298\pi$
$858$	0	0
$859$	1.16729e11	0.214390	0.107195	−	0.994238i	$-0.465813\pi$
$859$	1.16729e11	0.214390	0.107195	+	0.994238i	$0.465813\pi$
$860$	9.65843e10i	0.176568i
$861$	0	0
$862$	1.00162e12	1.81416
$863$	− 5.73876e11i	− 1.03461i	−0.855803	−	0.517303i	$-0.826936\pi$
$863$	− 5.73876e11i	− 1.03461i	0.855803	−	0.517303i	$-0.173064\pi$
$864$	0	0
$865$	−2.47903e11	−0.442810
$866$	− 5.00660e11i	− 0.890167i
$867$	0	0
$868$	8.09906e11	1.42678
$869$	− 2.96610e11i	− 0.520124i
$870$	0	0
$871$	−1.64619e12	−2.86027
$872$	6.02464e11i	1.04199i
$873$	0	0
$874$	1.08555e11	0.186038
$875$	4.51896e11i	0.770914i
$876$	0	0
$877$	7.33529e11	1.23999	0.619996	−	0.784605i	$-0.287134\pi$
$877$	7.33529e11	1.23999	0.619996	+	0.784605i	$0.287134\pi$
$878$	− 7.17104e11i	− 1.20671i
$879$	0	0
$880$	6.95225e11	1.15930
$881$	1.09657e12i	1.82026i	0.414327	+	0.910128i	$0.364017\pi$
$881$	1.09657e12i	1.82026i	−0.414327	+	0.910128i	$0.635983\pi$
$882$	0	0
$883$	−3.36234e11	−0.553093	−0.276547	−	0.961001i	$-0.589190\pi$
$883$	−3.36234e11	−0.553093	−0.276547	+	0.961001i	$0.589190\pi$
$884$	− 1.13031e12i	− 1.85092i
$885$	0	0
$886$	1.21257e12	1.96776
$887$	5.92998e11i	0.957985i	0.877819	+	0.478993i	$0.158998\pi$
$887$	5.92998e11i	0.957985i	−0.877819	+	0.478993i	$0.841002\pi$
$888$	0	0
$889$	1.23304e12	1.97410
$890$	− 3.35874e11i	− 0.535324i
$891$	0	0
$892$	1.24259e12	1.96277
$893$	2.56000e11i	0.402564i
$894$	0	0
$895$	−2.83263e11	−0.441466
$896$	3.93675e11i	0.610809i
$897$	0	0
$898$	6.01938e11	0.925649
$899$	1.16023e11i	0.177625i
$900$	0	0
$901$	3.83434e11	0.581824
$902$	1.73644e12i	2.62321i
$903$	0	0
$904$	2.31408e12	3.46502
$905$	7.47614e10i	0.111451i
$906$	0	0
$907$	−3.25524e11	−0.481010	−0.240505	−	0.970648i	$-0.577313\pi$
$907$	−3.25524e11	−0.481010	−0.240505	+	0.970648i	$0.577313\pi$
$908$	− 2.18808e12i	− 3.21899i
$909$	0	0
$910$	8.76240e11	1.27778
$911$	1.14396e11i	0.166088i	0.996546	+	0.0830441i	$0.0264642\pi$
$911$	1.14396e11i	0.166088i	−0.996546	+	0.0830441i	$0.973536\pi$
$912$	0	0
$913$	−1.42023e12	−2.04397
$914$	− 8.62301e10i	− 0.123559i
$915$	0	0
$916$	−3.22019e12	−4.57403
$917$	4.68748e10i	0.0662922i
$918$	0	0
$919$	−5.33897e11	−0.748506	−0.374253	−	0.927327i	$-0.622101\pi$
$919$	−5.33897e11	−0.748506	−0.374253	+	0.927327i	$0.622101\pi$
$920$	8.90204e10i	0.124262i
$921$	0	0
$922$	−2.68407e12	−3.71424
$923$	− 1.88820e10i	− 0.0260160i
$924$	0	0
$925$	6.53827e11	0.893091
$926$	− 1.68287e11i	− 0.228879i
$927$	0	0
$928$	−6.94416e11	−0.936328
$929$	− 2.79883e11i	− 0.375763i	−0.982192	−	0.187882i	$-0.939838\pi$
$929$	− 2.79883e11i	− 0.375763i	0.982192	−	0.187882i	$-0.0601621\pi$
$930$	0	0
$931$	−4.67389e11	−0.622128
$932$	3.01073e12i	3.99032i
$933$	0	0
$934$	−9.67297e11	−1.27108
$935$	1.48040e11i	0.193702i
$936$	0	0
$937$	9.25694e11	1.20091	0.600453	−	0.799660i	$-0.294987\pi$
$937$	9.25694e11	1.20091	0.600453	+	0.799660i	$0.294987\pi$
$938$	3.41030e12i	4.40536i
$939$	0	0
$940$	−3.52840e11	−0.451924
$941$	1.24170e12i	1.58364i	0.610754	+	0.791820i	$0.290866\pi$
$941$	1.24170e12i	1.58364i	−0.610754	+	0.791820i	$0.709134\pi$
$942$	0	0
$943$	−1.14620e11	−0.144948
$944$	3.46356e12i	4.36149i
$945$	0	0
$946$	5.81799e11	0.726455
$947$	− 1.34995e12i	− 1.67849i	−0.543757	−	0.839243i	$-0.682999\pi$
$947$	− 1.34995e12i	− 1.67849i	0.543757	−	0.839243i	$-0.317001\pi$
$948$	0	0
$949$	8.49233e11	1.04704
$950$	8.72274e11i	1.07092i
$951$	0	0
$952$	−1.39320e12	−1.69616
$953$	6.09272e11i	0.738651i	0.929300	+	0.369326i	$0.120411\pi$
$953$	6.09272e11i	0.738651i	−0.929300	+	0.369326i	$0.879589\pi$
$954$	0	0
$955$	−2.18031e11	−0.262123
$956$	− 1.07414e12i	− 1.28597i
$957$	0	0
$958$	2.91427e12	3.45993
$959$	− 7.70607e10i	− 0.0911085i
$960$	0	0
$961$	−7.10092e11	−0.832570
$962$	− 2.64719e12i	− 3.09090i
$963$	0	0
$964$	−3.46631e12	−4.01383
$965$	3.48593e11i	0.401985i
$966$	0	0
$967$	−3.43524e11	−0.392872	−0.196436	−	0.980517i	$-0.562937\pi$
$967$	−3.43524e11	−0.392872	−0.196436	+	0.980517i	$0.562937\pi$
$968$	− 3.37959e12i	− 3.84912i
$969$	0	0
$970$	−3.46462e11	−0.391353
$971$	− 8.09302e11i	− 0.910403i	−0.890388	−	0.455202i	$-0.849567\pi$
$971$	− 8.09302e11i	− 0.910403i	0.890388	−	0.455202i	$-0.150433\pi$
$972$	0	0
$973$	1.72258e12	1.92189
$974$	1.63062e12i	1.81183i
$975$	0	0
$976$	−1.83624e12	−2.02363
$977$	− 1.12752e12i	− 1.23750i	−0.785586	−	0.618752i	$-0.787639\pi$
$977$	− 1.12752e12i	− 1.23750i	0.785586	−	0.618752i	$-0.212361\pi$
$978$	0	0
$979$	−1.44000e12	−1.56759
$980$	− 6.44191e11i	− 0.698410i
$981$	0	0
$982$	2.91867e11	0.313862
$983$	− 6.57547e11i	− 0.704228i	−0.935957	−	0.352114i	$-0.885463\pi$
$983$	− 6.57547e11i	− 0.704228i	0.935957	−	0.352114i	$-0.114537\pi$
$984$	0	0
$985$	8.06216e9	0.00856459
$986$	− 3.35442e11i	− 0.354903i
$987$	0	0
$988$	2.51359e12	2.63795
$989$	3.84038e10i	0.0401411i
$990$	0	0
$991$	3.09933e11	0.321347	0.160673	−	0.987008i	$-0.448633\pi$
$991$	3.09933e11	0.321347	0.160673	+	0.987008i	$0.448633\pi$
$992$	8.54679e11i	0.882585i
$993$	0	0
$994$	−3.91165e10	−0.0400696
$995$	− 3.44612e11i	− 0.351591i
$996$	0	0
$997$	−8.26093e11	−0.836081	−0.418040	−	0.908428i	$-0.637283\pi$
$997$	−8.26093e11	−0.836081	−0.418040	+	0.908428i	$0.637283\pi$
$998$	7.78563e11i	0.784823i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.9.b.b.80.1	✓	16
3.2	odd	2	inner	81.9.b.b.80.16	yes	16
9.2	odd	6		81.9.d.g.53.16		32
9.4	even	3		81.9.d.g.26.16		32
9.5	odd	6		81.9.d.g.26.1		32
9.7	even	3		81.9.d.g.53.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.9.b.b.80.1	✓	16	1.1	even	1	trivial
81.9.b.b.80.16	yes	16	3.2	odd	2	inner
81.9.d.g.26.1		32	9.5	odd	6
81.9.d.g.26.16		32	9.4	even	3
81.9.d.g.53.1		32	9.7	even	3
81.9.d.g.53.16		32	9.2	odd	6

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	81.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-29.8006i q^{2} -632.074 q^{4} +177.778i q^{5} +3390.81 q^{7} +11207.2i q^{8} +5297.89 q^{10} -22713.7i q^{11} +48777.1 q^{13} -101048. i q^{14} +172170. q^{16} +36661.7i q^{17} -81528.6 q^{19} -112369. i q^{20} -676882. q^{22} -44680.0i q^{23} +359020. q^{25} -1.45359e6i q^{26} -2.14324e6 q^{28} -307029. i q^{29} -377888. q^{31} -2.26173e6i q^{32} +1.09254e6 q^{34} +602813. i q^{35} +1.82114e6 q^{37} +2.42960e6i q^{38} -1.99240e6 q^{40} -2.56535e6i q^{41} -859529. q^{43} +1.43568e7i q^{44} -1.33149e6 q^{46} -3.14001e6i q^{47} +5.73282e6 q^{49} -1.06990e7i q^{50} -3.08307e7 q^{52} -1.04587e7i q^{53} +4.03801e6 q^{55} +3.80016e7i q^{56} -9.14964e6 q^{58} +2.01171e7i q^{59} -1.06653e7 q^{61} +1.12613e7i q^{62} -2.33251e7 q^{64} +8.67151e6i q^{65} -3.37493e7 q^{67} -2.31729e7i q^{68} +1.79642e7 q^{70} -387108. i q^{71} +1.74105e7 q^{73} -5.42711e7i q^{74} +5.15321e7 q^{76} -7.70180e7i q^{77} +1.30586e7 q^{79} +3.06081e7i q^{80} -7.64487e7 q^{82} -6.25273e7i q^{83} -6.51766e6 q^{85} +2.56144e7i q^{86} +2.54558e8 q^{88} -6.33977e7i q^{89} +1.65394e8 q^{91} +2.82411e7i q^{92} -9.35740e7 q^{94} -1.44940e7i q^{95} -6.53962e7 q^{97} -1.70841e8i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2048 q^{4} + 3692 q^{7} + 10752 q^{10} + 63860 q^{13} + 95116 q^{16} + 185108 q^{19} - 691980 q^{22} - 541712 q^{25} - 997132 q^{28} + 571136 q^{31} + 1027656 q^{34} + 4354268 q^{37} - 2973768 q^{40}+ \cdots - 133878688 q^{97}+O(q^{100}) \) 16 * q - 2048 * q^4 + 3692 * q^7 + 10752 * q^10 + 63860 * q^13 + 95116 * q^16 + 185108 * q^19 - 691980 * q^22 - 541712 * q^25 - 997132 * q^28 + 571136 * q^31 + 1027656 * q^34 + 4354268 * q^37 - 2973768 * q^40 + 5453084 * q^43 - 4234044 * q^46 + 14602560 * q^49 - 25384960 * q^52 - 14452572 * q^55 + 1213068 * q^58 + 31037996 * q^61 + 24253000 * q^64 - 62356828 * q^67 + 11075124 * q^70 - 21273664 * q^73 + 69593876 * q^76 - 151045036 * q^79 - 40201140 * q^82 + 160995564 * q^85 + 366976068 * q^88 + 373680796 * q^91 - 544741584 * q^94 - 133878688 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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