LMFDB - Embedded newform 320.9.h.f.319.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,9,Mod(319,320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(320, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("320.319");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	320.h (of order $2$, degree $1$, not 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:	$130.361155220$
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} - 1394 x^{14} + 1332306 x^{12} - 657883370 x^{10} + 233333110300 x^{8} - 45644912663250 x^{6} + \cdots + 23\!\cdots\!00 $ x^16 - 1394x^14 + 1332306x^12 - 657883370x^10 + 233333110300x^8 - 45644912663250x^6 + 6418092533338125x^4 - 470478785036343750*x^2 + 23585385849201562500
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{99}\cdot 3^{9}\cdot 5^{10} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			319.15
Root			$17.5505 + 10.1328i$ of defining polynomial
Character	$\chi$	$=$	320.319
Dual form			320.9.h.f.319.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+125.551 q^{3} +(-388.104 - 489.899i) q^{5} -4128.49 q^{7} +9202.10 q^{9} +O(q^{10})$	\(q+125.551 q^{3} +(-388.104 - 489.899i) q^{5} -4128.49 q^{7} +9202.10 q^{9} -26931.1i q^{11} -8363.02i q^{13} +(-48726.9 - 61507.3i) q^{15} +72177.0i q^{17} -137394. i q^{19} -518337. q^{21} +46245.1 q^{23} +(-89376.1 + 380263. i) q^{25} +331593. q^{27} +975477. q^{29} -809697. i q^{31} -3.38123e6i q^{33} +(1.60228e6 + 2.02254e6i) q^{35} +1.67084e6i q^{37} -1.04999e6i q^{39} -2.35248e6 q^{41} +252943. q^{43} +(-3.57137e6 - 4.50809e6i) q^{45} -5.36666e6 q^{47} +1.12796e7 q^{49} +9.06191e6i q^{51} -799223. i q^{53} +(-1.31935e7 + 1.04521e7i) q^{55} -1.72499e7i q^{57} +1.84911e7i q^{59} -1.40817e7 q^{61} -3.79907e7 q^{63} +(-4.09703e6 + 3.24572e6i) q^{65} -1.89960e7 q^{67} +5.80613e6 q^{69} +2.68339e7i q^{71} +4.89281e7i q^{73} +(-1.12213e7 + 4.77424e7i) q^{75} +1.11185e8i q^{77} -1.02508e7i q^{79} -1.87431e7 q^{81} -8.40601e6 q^{83} +(3.53594e7 - 2.80122e7i) q^{85} +1.22472e8 q^{87} -5.91263e7 q^{89} +3.45266e7i q^{91} -1.01658e8i q^{93} +(-6.73090e7 + 5.33230e7i) q^{95} -4.66897e7i q^{97} -2.47822e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 600 q^{5} + 42176 q^{9}+O(q^{10}) $ 16 * q - 600 * q^5 + 42176 * q^9	$ 16 q - 600 q^{5} + 42176 q^{9} - 619344 q^{21} + 1137040 q^{25} + 3497568 q^{29} - 2169168 q^{41} + 1930760 q^{45} + 26174912 q^{49} - 22772656 q^{61} + 12524160 q^{65} - 8461392 q^{69} - 224999456 q^{81} + 18124800 q^{85} - 94250976 q^{89}+O(q^{100}) $ 16 * q - 600 * q^5 + 42176 * q^9 - 619344 * q^21 + 1137040 * q^25 + 3497568 * q^29 - 2169168 * q^41 + 1930760 * q^45 + 26174912 * q^49 - 22772656 * q^61 + 12524160 * q^65 - 8461392 * q^69 - 224999456 * q^81 + 18124800 * q^85 - 94250976 * q^89

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	125.551			1.55001			0.775007	−	0.631952i	$-0.217746\pi$
$3$	125.551			1.55001			0.775007	+	0.631952i	$0.217746\pi$
$4$		0			0
$5$	−388.104	−	489.899i	−0.620966	−	0.783838i
$5$	−388.104	−	489.899i	−0.620966	−	0.783838i
$6$		0			0
$7$	−4128.49			−1.71949			−0.859743	−	0.510726i	$-0.829377\pi$
$7$	−4128.49			−1.71949			−0.859743	+	0.510726i	$0.829377\pi$
$8$		0			0
$9$	9202.10			1.40254
$10$		0			0
$11$		−	26931.1i		−	1.83943i	−0.392588	−	0.919715i	$-0.628420\pi$
$11$		−	26931.1i		−	1.83943i	0.392588	−	0.919715i	$-0.371580\pi$
$12$		0			0
$13$		−	8363.02i		−	0.292813i	−0.989225	−	0.146406i	$-0.953229\pi$
$13$		−	8363.02i		−	0.292813i	0.989225	−	0.146406i	$-0.0467707\pi$
$14$		0			0
$15$	−48726.9	−	61507.3i	−0.962506	−	1.21496i
$16$		0			0
$17$			72177.0i			0.864178i	0.901831	+	0.432089i	$0.142223\pi$
$17$			72177.0i			0.864178i	−0.901831	+	0.432089i	$0.857777\pi$
$18$		0			0
$19$		−	137394.i		−	1.05427i	−0.849781	−	0.527136i	$-0.823266\pi$
$19$		−	137394.i		−	1.05427i	0.849781	−	0.527136i	$-0.176734\pi$
$20$		0			0
$21$	−518337.			−2.66523
$22$		0			0
$23$	46245.1			0.165255			0.0826275	−	0.996581i	$-0.473669\pi$
$23$	46245.1			0.165255			0.0826275	+	0.996581i	$0.473669\pi$
$24$		0			0
$25$	−89376.1	+	380263.i	−0.228803	+	0.973473i
$26$		0			0
$27$	331593.			0.623950
$28$		0			0
$29$	975477.			1.37919			0.689596	−	0.724194i	$-0.257788\pi$
$29$	975477.			1.37919			0.689596	+	0.724194i	$0.257788\pi$
$30$		0			0
$31$		−	809697.i		−	0.876749i	−0.898792	−	0.438375i	$-0.855554\pi$
$31$		−	809697.i		−	0.876749i	0.898792	−	0.438375i	$-0.144446\pi$
$32$		0			0
$33$		−	3.38123e6i		−	2.85114i
$34$		0			0
$35$	1.60228e6	+	2.02254e6i	1.06774	+	1.34780i
$36$		0			0
$37$			1.67084e6i			0.891514i	0.895154	+	0.445757i	$0.147066\pi$
$37$			1.67084e6i			0.891514i	−0.895154	+	0.445757i	$0.852934\pi$
$38$		0			0
$39$		−	1.04999e6i		−	0.453864i
$40$		0			0
$41$	−2.35248e6			−0.832513			−0.416256	−	0.909247i	$-0.636658\pi$
$41$	−2.35248e6			−0.832513			−0.416256	+	0.909247i	$0.636658\pi$
$42$		0			0
$43$	252943.			0.0739858			0.0369929	−	0.999316i	$-0.488222\pi$
$43$	252943.			0.0739858			0.0369929	+	0.999316i	$0.488222\pi$
$44$		0			0
$45$	−3.57137e6	−	4.50809e6i	−0.870932	−	1.09937i
$46$		0			0
$47$	−5.36666e6			−1.09980			−0.549898	−	0.835232i	$-0.685334\pi$
$47$	−5.36666e6			−1.09980			−0.549898	+	0.835232i	$0.685334\pi$
$48$		0			0
$49$	1.12796e7			1.95664
$50$		0			0
$51$			9.06191e6i			1.33949i
$52$		0			0
$53$		−	799223.i		−	0.101290i	−0.998717	−	0.0506448i	$-0.983872\pi$
$53$		−	799223.i		−	0.101290i	0.998717	−	0.0506448i	$-0.0161276\pi$
$54$		0			0
$55$	−1.31935e7	+	1.04521e7i	−1.44181	+	1.14222i
$56$		0			0
$57$		−	1.72499e7i		−	1.63414i
$58$		0			0
$59$			1.84911e7i			1.52600i	0.646400	+	0.762999i	$0.276274\pi$
$59$			1.84911e7i			1.52600i	−0.646400	+	0.762999i	$0.723726\pi$
$60$		0			0
$61$	−1.40817e7			−1.01703			−0.508516	−	0.861053i	$-0.669806\pi$
$61$	−1.40817e7			−1.01703			−0.508516	+	0.861053i	$0.669806\pi$
$62$		0			0
$63$	−3.79907e7			−2.41166
$64$		0			0
$65$	−4.09703e6	+	3.24572e6i	−0.229517	+	0.181827i
$66$		0			0
$67$	−1.89960e7			−0.942677			−0.471339	−	0.881952i	$-0.656229\pi$
$67$	−1.89960e7			−0.942677			−0.471339	+	0.881952i	$0.656229\pi$
$68$		0			0
$69$	5.80613e6			0.256148
$70$		0			0
$71$			2.68339e7i			1.05597i	0.849254	+	0.527984i	$0.177052\pi$
$71$			2.68339e7i			1.05597i	−0.849254	+	0.527984i	$0.822948\pi$
$72$		0			0
$73$			4.89281e7i			1.72293i	0.507818	+	0.861464i	$0.330452\pi$
$73$			4.89281e7i			1.72293i	−0.507818	+	0.861464i	$0.669548\pi$
$74$		0			0
$75$	−1.12213e7	+	4.77424e7i	−0.354648	+	1.50890i
$76$		0			0
$77$			1.11185e8i			3.16287i
$78$		0			0
$79$		−	1.02508e7i		−	0.263179i	−0.991304	−	0.131590i	$-0.957992\pi$
$79$		−	1.02508e7i		−	0.263179i	0.991304	−	0.131590i	$-0.0420081\pi$
$80$		0			0
$81$	−1.87431e7			−0.435413
$82$		0			0
$83$	−8.40601e6			−0.177124			−0.0885620	−	0.996071i	$-0.528227\pi$
$83$	−8.40601e6			−0.177124			−0.0885620	+	0.996071i	$0.528227\pi$
$84$		0			0
$85$	3.53594e7	−	2.80122e7i	0.677375	−	0.536625i
$86$		0			0
$87$	1.22472e8			2.13777
$88$		0			0
$89$	−5.91263e7			−0.942369			−0.471184	−	0.882035i	$-0.656173\pi$
$89$	−5.91263e7			−0.942369			−0.471184	+	0.882035i	$0.656173\pi$
$90$		0			0
$91$			3.45266e7i			0.503487i
$92$		0			0
$93$		−	1.01658e8i		−	1.35897i
$94$		0			0
$95$	−6.73090e7	+	5.33230e7i	−0.826378	+	0.654667i
$96$		0			0
$97$		−	4.66897e7i		−	0.527393i	−0.964606	−	0.263696i	$-0.915058\pi$
$97$		−	4.66897e7i		−	0.527393i	0.964606	−	0.263696i	$-0.0849417\pi$
$98$		0			0
$99$		−	2.47822e8i		−	2.57988i
$100$		0			0
$101$	−1.59823e7			−0.153586			−0.0767932	−	0.997047i	$-0.524468\pi$
$101$	−1.59823e7			−0.153586			−0.0767932	+	0.997047i	$0.524468\pi$
$102$		0			0
$103$	4.27251e7			0.379607			0.189803	−	0.981822i	$-0.439215\pi$
$103$	4.27251e7			0.379607			0.189803	+	0.981822i	$0.439215\pi$
$104$		0			0
$105$	2.01168e8	+	2.53932e8i	1.65502	+	2.08911i
$106$		0			0
$107$	−2.09351e7			−0.159713			−0.0798566	−	0.996806i	$-0.525446\pi$
$107$	−2.09351e7			−0.159713			−0.0798566	+	0.996806i	$0.525446\pi$
$108$		0			0
$109$	−8.66263e7			−0.613683			−0.306841	−	0.951761i	$-0.599272\pi$
$109$	−8.66263e7			−0.613683			−0.306841	+	0.951761i	$0.599272\pi$
$110$		0			0
$111$			2.09776e8i			1.38186i
$112$		0			0
$113$		−	2.94712e7i		−	0.180752i	−0.995908	−	0.0903761i	$-0.971193\pi$
$113$		−	2.94712e7i		−	0.180752i	0.995908	−	0.0903761i	$-0.0288069\pi$
$114$		0			0
$115$	−1.79479e7	−	2.26554e7i	−0.102618	−	0.129533i
$116$		0			0
$117$		−	7.69573e7i		−	0.410683i
$118$		0			0
$119$		−	2.97982e8i		−	1.48594i
$120$		0			0
$121$	−5.10924e8			−2.38350
$122$		0			0
$123$	−2.95357e8			−1.29041
$124$		0			0
$125$	2.20977e8	−	1.03796e8i	0.905123	−	0.425149i
$126$		0			0
$127$	4.56705e8			1.75558			0.877790	−	0.479046i	$-0.159017\pi$
$127$	4.56705e8			1.75558			0.877790	+	0.479046i	$0.159017\pi$
$128$		0			0
$129$	3.17572e7			0.114679
$130$		0			0
$131$		−	3.02837e8i		−	1.02831i	−0.857698	−	0.514154i	$-0.828106\pi$
$131$		−	3.02837e8i		−	1.02831i	0.857698	−	0.514154i	$-0.171894\pi$
$132$		0			0
$133$			5.67229e8i			1.81281i
$134$		0			0
$135$	−1.28692e8	−	1.62447e8i	−0.387452	−	0.489076i
$136$		0			0
$137$			3.14396e7i			0.0892471i	0.999004	+	0.0446236i	$0.0142088\pi$
$137$			3.14396e7i			0.0892471i	−0.999004	+	0.0446236i	$0.985791\pi$
$138$		0			0
$139$			3.38385e8i			0.906466i	0.891392	+	0.453233i	$0.149729\pi$
$139$			3.38385e8i			0.906466i	−0.891392	+	0.453233i	$0.850271\pi$
$140$		0			0
$141$	−6.73790e8			−1.70470
$142$		0			0
$143$	−2.25225e8			−0.538608
$144$		0			0
$145$	−3.78586e8	−	4.77885e8i	−0.856431	−	1.08106i
$146$		0			0
$147$	1.41617e9			3.03281
$148$		0			0
$149$	1.43182e8			0.290498			0.145249	−	0.989395i	$-0.453602\pi$
$149$	1.43182e8			0.290498			0.145249	+	0.989395i	$0.453602\pi$
$150$		0			0
$151$		−	1.83795e8i		−	0.353529i	−0.984253	−	0.176765i	$-0.943437\pi$
$151$		−	1.83795e8i		−	0.353529i	0.984253	−	0.176765i	$-0.0565631\pi$
$152$		0			0
$153$			6.64180e8i			1.21205i
$154$		0			0
$155$	−3.96669e8	+	3.14246e8i	−0.687229	+	0.544431i
$156$		0			0
$157$		−	7.22291e7i		−	0.118881i	−0.998232	−	0.0594407i	$-0.981068\pi$
$157$		−	7.22291e7i		−	0.118881i	0.998232	−	0.0594407i	$-0.0189317\pi$
$158$		0			0
$159$		−	1.00343e8i		−	0.157000i
$160$		0			0
$161$	−1.90922e8			−0.284154
$162$		0			0
$163$	5.59052e8			0.791958			0.395979	−	0.918260i	$-0.370405\pi$
$163$	5.59052e8			0.791958			0.395979	+	0.918260i	$0.370405\pi$
$164$		0			0
$165$	−1.65646e9	+	1.31227e9i	−2.23483	+	1.77046i
$166$		0			0
$167$	1.00985e8			0.129835			0.0649175	−	0.997891i	$-0.479322\pi$
$167$	1.00985e8			0.129835			0.0649175	+	0.997891i	$0.479322\pi$
$168$		0			0
$169$	7.45791e8			0.914261
$170$		0			0
$171$		−	1.26431e9i		−	1.47866i
$172$		0			0
$173$			1.77453e8i			0.198107i	0.995082	+	0.0990533i	$0.0315814\pi$
$173$			1.77453e8i			0.198107i	−0.995082	+	0.0990533i	$0.968419\pi$
$174$		0			0
$175$	3.68988e8	−	1.56991e9i	0.393424	−	1.67387i
$176$		0			0
$177$			2.32158e9i			2.36532i
$178$		0			0
$179$			5.13003e8i			0.499698i	0.968285	+	0.249849i	$0.0803809\pi$
$179$			5.13003e8i			0.499698i	−0.968285	+	0.249849i	$0.919619\pi$
$180$		0			0
$181$	1.17102e9			1.09107			0.545533	−	0.838090i	$-0.316327\pi$
$181$	1.17102e9			1.09107			0.545533	+	0.838090i	$0.316327\pi$
$182$		0			0
$183$	−1.76797e9			−1.57641
$184$		0			0
$185$	8.18543e8	−	6.48460e8i	0.698802	−	0.553600i
$186$		0			0
$187$	1.94381e9			1.58959
$188$		0			0
$189$	−1.36898e9			−1.07287
$190$		0			0
$191$		−	5.35659e8i		−	0.402490i	−0.979541	−	0.201245i	$-0.935501\pi$
$191$		−	5.35659e8i		−	0.402490i	0.979541	−	0.201245i	$-0.0644987\pi$
$192$		0			0
$193$		−	7.43350e8i		−	0.535752i	−0.963453	−	0.267876i	$-0.913678\pi$
$193$		−	7.43350e8i		−	0.535752i	0.963453	−	0.267876i	$-0.0863218\pi$
$194$		0			0
$195$	−5.14387e8	+	4.07504e8i	−0.355755	+	0.281834i
$196$		0			0
$197$			1.39520e9i			0.926344i	0.886268	+	0.463172i	$0.153289\pi$
$197$			1.39520e9i			0.926344i	−0.886268	+	0.463172i	$0.846711\pi$
$198$		0			0
$199$			1.33050e9i			0.848402i	0.905568	+	0.424201i	$0.139445\pi$
$199$			1.33050e9i			0.848402i	−0.905568	+	0.424201i	$0.860555\pi$
$200$		0			0
$201$	−2.38497e9			−1.46116
$202$		0			0
$203$	−4.02724e9			−2.37150
$204$		0			0
$205$	9.13007e8	+	1.15248e9i	0.516962	+	0.652555i
$206$		0			0
$207$	4.25552e8			0.231778
$208$		0			0
$209$	−3.70016e9			−1.93926
$210$		0			0
$211$		−	1.66921e9i		−	0.842135i	−0.907029	−	0.421067i	$-0.861656\pi$
$211$		−	1.66921e9i		−	0.842135i	0.907029	−	0.421067i	$-0.138344\pi$
$212$		0			0
$213$			3.36903e9i			1.63677i
$214$		0			0
$215$	−9.81680e7	−	1.23916e8i	−0.0459426	−	0.0579928i
$216$		0			0
$217$			3.34282e9i			1.50756i
$218$		0			0
$219$			6.14299e9i			2.67056i
$220$		0			0
$221$	6.03618e8			0.253042
$222$		0			0
$223$	7.80751e8			0.315714			0.157857	−	0.987462i	$-0.449542\pi$
$223$	7.80751e8			0.315714			0.157857	+	0.987462i	$0.449542\pi$
$224$		0			0
$225$	−8.22448e8	+	3.49921e9i	−0.320906	+	1.36534i
$226$		0			0
$227$	−3.31543e9			−1.24864			−0.624318	−	0.781170i	$-0.714623\pi$
$227$	−3.31543e9			−1.24864			−0.624318	+	0.781170i	$0.714623\pi$
$228$		0			0
$229$	−5.30253e9			−1.92815			−0.964076	−	0.265625i	$-0.914422\pi$
$229$	−5.30253e9			−1.92815			−0.964076	+	0.265625i	$0.914422\pi$
$230$		0			0
$231$			1.39594e10i			4.90250i
$232$		0			0
$233$			3.46329e9i			1.17507i	0.809198	+	0.587537i	$0.199902\pi$
$233$			3.46329e9i			1.17507i	−0.809198	+	0.587537i	$0.800098\pi$
$234$		0			0
$235$	2.08282e9	+	2.62912e9i	0.682936	+	0.862062i
$236$		0			0
$237$		−	1.28701e9i		−	0.407931i
$238$		0			0
$239$			4.56691e8i			0.139969i	0.997548	+	0.0699843i	$0.0222949\pi$
$239$			4.56691e8i			0.139969i	−0.997548	+	0.0699843i	$0.977705\pi$
$240$		0			0
$241$	9.88765e8			0.293106			0.146553	−	0.989203i	$-0.453182\pi$
$241$	9.88765e8			0.293106			0.146553	+	0.989203i	$0.453182\pi$
$242$		0			0
$243$	−4.52880e9			−1.29885
$244$		0			0
$245$	−4.37766e9	−	5.52587e9i	−1.21500	−	1.53368i
$246$		0			0
$247$	−1.14903e9			−0.308704
$248$		0			0
$249$	−1.05538e9			−0.274545
$250$		0			0
$251$		−	4.36714e9i		−	1.10028i	−0.835073	−	0.550139i	$-0.814575\pi$
$251$		−	4.36714e9i		−	1.10028i	0.835073	−	0.550139i	$-0.185425\pi$
$252$		0			0
$253$		−	1.24543e9i		−	0.303975i
$254$		0			0
$255$	4.43942e9	−	3.51696e9i	1.04994	−	0.831777i
$256$		0			0
$257$		−	6.90439e9i		−	1.58268i	−0.611378	−	0.791339i	$-0.709384\pi$
$257$		−	6.90439e9i		−	1.58268i	0.611378	−	0.791339i	$-0.290616\pi$
$258$		0			0
$259$		−	6.89805e9i		−	1.53295i
$260$		0			0
$261$	8.97643e9			1.93438
$262$		0			0
$263$	−9.20662e9			−1.92432			−0.962160	−	0.272484i	$-0.912155\pi$
$263$	−9.20662e9			−1.92432			−0.962160	+	0.272484i	$0.912155\pi$
$264$		0			0
$265$	−3.91538e8	+	3.10181e8i	−0.0793946	+	0.0628974i
$266$		0			0
$267$	−7.42338e9			−1.46068
$268$		0			0
$269$	−2.15978e8			−0.0412477			−0.0206239	−	0.999787i	$-0.506565\pi$
$269$	−2.15978e8			−0.0412477			−0.0206239	+	0.999787i	$0.506565\pi$
$270$		0			0
$271$		−	7.47527e9i		−	1.38596i	−0.720959	−	0.692978i	$-0.756298\pi$
$271$		−	7.47527e9i		−	1.38596i	0.720959	−	0.692978i	$-0.243702\pi$
$272$		0			0
$273$			4.33486e9i			0.780413i
$274$		0			0
$275$	1.02409e10	+	2.40700e9i	1.79063	+	0.420867i
$276$		0			0
$277$			1.09118e10i			1.85344i	0.375750	+	0.926721i	$0.377385\pi$
$277$			1.09118e10i			1.85344i	−0.375750	+	0.926721i	$0.622615\pi$
$278$		0			0
$279$		−	7.45090e9i		−	1.22968i
$280$		0			0
$281$	−8.49127e9			−1.36191			−0.680954	−	0.732327i	$-0.738434\pi$
$281$	−8.49127e9			−1.36191			−0.680954	+	0.732327i	$0.738434\pi$
$282$		0			0
$283$	1.94100e9			0.302607			0.151304	−	0.988487i	$-0.451653\pi$
$283$	1.94100e9			0.302607			0.151304	+	0.988487i	$0.451653\pi$
$284$		0			0
$285$	−8.45072e9	+	6.69477e9i	−1.28090	+	1.01474i
$286$		0			0
$287$	9.71219e9			1.43149
$288$		0			0
$289$	1.76624e9			0.253196
$290$		0			0
$291$		−	5.86195e9i		−	0.817467i
$292$		0			0
$293$		−	9.95487e9i		−	1.35072i	−0.737489	−	0.675360i	$-0.763988\pi$
$293$		−	9.95487e9i		−	1.35072i	0.737489	−	0.675360i	$-0.236012\pi$
$294$		0			0
$295$	9.05875e9	−	7.17645e9i	1.19613	−	0.947593i
$296$		0			0
$297$		−	8.93015e9i		−	1.14771i
$298$		0			0
$299$		−	3.86749e8i		−	0.0483887i
$300$		0			0
$301$	−1.04427e9			−0.127218
$302$		0			0
$303$	−2.00659e9			−0.238061
$304$		0			0
$305$	5.46514e9	+	6.89858e9i	0.631542	+	0.797188i
$306$		0			0
$307$	1.21820e10			1.37140			0.685701	−	0.727884i	$-0.259496\pi$
$307$	1.21820e10			1.37140			0.685701	+	0.727884i	$0.259496\pi$
$308$		0			0
$309$	5.36419e9			0.588396
$310$		0			0
$311$			1.44725e10i			1.54704i	0.633773	+	0.773519i	$0.281505\pi$
$311$			1.44725e10i			1.54704i	−0.633773	+	0.773519i	$0.718495\pi$
$312$		0			0
$313$		−	1.15621e9i		−	0.120464i	−0.998184	−	0.0602322i	$-0.980816\pi$
$313$		−	1.15621e9i		−	0.120464i	0.998184	−	0.0602322i	$-0.0191841\pi$
$314$		0			0
$315$	1.47443e10	+	1.86116e10i	1.49756	+	1.89035i
$316$		0			0
$317$			1.18409e10i			1.17259i	0.810096	+	0.586297i	$0.199415\pi$
$317$			1.18409e10i			1.17259i	−0.810096	+	0.586297i	$0.800585\pi$
$318$		0			0
$319$		−	2.62706e10i		−	2.53693i
$320$		0			0
$321$	−2.62843e9			−0.247558
$322$		0			0
$323$	9.91667e9			0.911079
$324$		0			0
$325$	3.18014e9	+	7.47454e8i	0.285045	+	0.0669963i
$326$		0			0
$327$	−1.08760e10			−0.951217
$328$		0			0
$329$	2.21562e10			1.89109
$330$		0			0
$331$		−	1.43655e10i		−	1.19676i	−0.801212	−	0.598381i	$-0.795811\pi$
$331$		−	1.43655e10i		−	1.19676i	0.801212	−	0.598381i	$-0.204189\pi$
$332$		0			0
$333$			1.53752e10i			1.25039i
$334$		0			0
$335$	7.37242e9	+	9.30611e9i	0.585370	+	0.738906i
$336$		0			0
$337$			1.63216e10i			1.26545i	0.774378	+	0.632723i	$0.218063\pi$
$337$			1.63216e10i			1.26545i	−0.774378	+	0.632723i	$0.781937\pi$
$338$		0			0
$339$		−	3.70014e9i		−	0.280169i
$340$		0			0
$341$	−2.18060e10			−1.61272
$342$		0			0
$343$	−2.27678e10			−1.64492
$344$		0			0
$345$	−2.25338e9	−	2.84441e9i	−0.159059	−	0.200778i
$346$		0			0
$347$	−3.22160e9			−0.222205			−0.111103	−	0.993809i	$-0.535438\pi$
$347$	−3.22160e9			−0.222205			−0.111103	+	0.993809i	$0.535438\pi$
$348$		0			0
$349$	−1.26613e10			−0.853448			−0.426724	−	0.904382i	$-0.640332\pi$
$349$	−1.26613e10			−0.853448			−0.426724	+	0.904382i	$0.640332\pi$
$350$		0			0
$351$		−	2.77312e9i		−	0.182700i
$352$		0			0
$353$		−	7.62759e9i		−	0.491234i	−0.969367	−	0.245617i	$-0.921009\pi$
$353$		−	7.62759e9i		−	0.491234i	0.969367	−	0.245617i	$-0.0789905\pi$
$354$		0			0
$355$	1.31459e10	−	1.04143e10i	0.827707	−	0.655720i
$356$		0			0
$357$		−	3.74120e10i		−	2.30323i
$358$		0			0
$359$			4.07390e9i			0.245263i	0.992452	+	0.122632i	$0.0391333\pi$
$359$			4.07390e9i			0.245263i	−0.992452	+	0.122632i	$0.960867\pi$
$360$		0			0
$361$	−1.89349e9			−0.111489
$362$		0			0
$363$	−6.41471e10			−3.69446
$364$		0			0
$365$	2.39698e10	−	1.89892e10i	1.35050	−	1.06988i
$366$		0			0
$367$	−1.81115e10			−0.998369			−0.499184	−	0.866496i	$-0.666367\pi$
$367$	−1.81115e10			−0.998369			−0.499184	+	0.866496i	$0.666367\pi$
$368$		0			0
$369$	−2.16478e10			−1.16764
$370$		0			0
$371$			3.29958e9i			0.174166i
$372$		0			0
$373$			1.81722e10i			0.938799i	0.882986	+	0.469400i	$0.155530\pi$
$373$			1.81722e10i			0.938799i	−0.882986	+	0.469400i	$0.844470\pi$
$374$		0			0
$375$	2.77440e10	−	1.30317e10i	1.40295	−	0.658987i
$376$		0			0
$377$		−	8.15793e9i		−	0.403845i
$378$		0			0
$379$			2.72054e10i			1.31856i	0.751899	+	0.659278i	$0.229138\pi$
$379$			2.72054e10i			1.31856i	−0.751899	+	0.659278i	$0.770862\pi$
$380$		0			0
$381$	5.73398e10			2.72117
$382$		0			0
$383$	1.35362e10			0.629073			0.314536	−	0.949245i	$-0.398151\pi$
$383$	1.35362e10			0.629073			0.314536	+	0.949245i	$0.398151\pi$
$384$		0			0
$385$	5.44692e10	−	4.31512e10i	2.47918	−	1.96404i
$386$		0			0
$387$	2.32760e9			0.103768
$388$		0			0
$389$	2.53028e10			1.10502			0.552510	−	0.833507i	$-0.313670\pi$
$389$	2.53028e10			1.10502			0.552510	+	0.833507i	$0.313670\pi$
$390$		0			0
$391$			3.33783e9i			0.142810i
$392$		0			0
$393$		−	3.80215e10i		−	1.59389i
$394$		0			0
$395$	−5.02187e9	+	3.97839e9i	−0.206290	+	0.163425i
$396$		0			0
$397$		−	3.85005e10i		−	1.54990i	−0.632021	−	0.774951i	$-0.717775\pi$
$397$		−	3.85005e10i		−	1.54990i	0.632021	−	0.774951i	$-0.282225\pi$
$398$		0			0
$399$			7.12162e10i			2.80988i
$400$		0			0
$401$	−2.50131e10			−0.967365			−0.483683	−	0.875243i	$-0.660701\pi$
$401$	−2.50131e10			−0.967365			−0.483683	+	0.875243i	$0.660701\pi$
$402$		0			0
$403$	−6.77151e9			−0.256723
$404$		0			0
$405$	7.27427e9	+	9.18222e9i	0.270377	+	0.341293i
$406$		0			0
$407$	4.49976e10			1.63988
$408$		0			0
$409$	−6.46135e9			−0.230903			−0.115452	−	0.993313i	$-0.536832\pi$
$409$	−6.46135e9			−0.230903			−0.115452	+	0.993313i	$0.536832\pi$
$410$		0			0
$411$			3.94727e9i			0.138334i
$412$		0			0
$413$		−	7.63402e10i		−	2.62393i
$414$		0			0
$415$	3.26240e9	+	4.11809e9i	0.109988	+	0.138836i
$416$		0			0
$417$			4.24846e10i			1.40504i
$418$		0			0
$419$		−	2.24097e10i		−	0.727077i	−0.931579	−	0.363539i	$-0.881568\pi$
$419$		−	2.24097e10i		−	0.727077i	0.931579	−	0.363539i	$-0.118432\pi$
$420$		0			0
$421$	−4.83624e10			−1.53950			−0.769749	−	0.638347i	$-0.779619\pi$
$421$	−4.83624e10			−1.53950			−0.769749	+	0.638347i	$0.779619\pi$
$422$		0			0
$423$	−4.93845e10			−1.54251
$424$		0			0
$425$	−2.74462e10	−	6.45090e9i	−0.841254	−	0.197726i
$426$		0			0
$427$	5.81359e10			1.74877
$428$		0			0
$429$	−2.82773e10			−0.834850
$430$		0			0
$431$			2.02951e9i			0.0588141i	0.999568	+	0.0294071i	$0.00936191\pi$
$431$			2.02951e9i			0.0588141i	−0.999568	+	0.0294071i	$0.990638\pi$
$432$		0			0
$433$			1.80685e10i			0.514008i	0.966410	+	0.257004i	$0.0827354\pi$
$433$			1.80685e10i			0.514008i	−0.966410	+	0.257004i	$0.917265\pi$
$434$		0			0
$435$	−4.75319e10	−	5.99990e10i	−1.32748	−	1.67566i
$436$		0			0
$437$		−	6.35379e9i		−	0.174224i
$438$		0			0
$439$			1.23470e10i			0.332432i	0.986089	+	0.166216i	$0.0531549\pi$
$439$			1.23470e10i			0.332432i	−0.986089	+	0.166216i	$0.946845\pi$
$440$		0			0
$441$	1.03796e11			2.74427
$442$		0			0
$443$	−4.95796e10			−1.28732			−0.643662	−	0.765310i	$-0.722586\pi$
$443$	−4.95796e10			−1.28732			−0.643662	+	0.765310i	$0.722586\pi$
$444$		0			0
$445$	2.29471e10	+	2.89659e10i	0.585179	+	0.738664i
$446$		0			0
$447$	1.79766e10			0.450275
$448$		0			0
$449$	3.53853e9			0.0870637			0.0435318	−	0.999052i	$-0.486139\pi$
$449$	3.53853e9			0.0870637			0.0435318	+	0.999052i	$0.486139\pi$
$450$		0			0
$451$			6.33549e10i			1.53135i
$452$		0			0
$453$		−	2.30756e10i		−	0.547975i
$454$		0			0
$455$	1.69145e10	−	1.33999e10i	0.394652	−	0.312648i
$456$		0			0
$457$		−	6.84805e10i		−	1.57001i	−0.619490	−	0.785005i	$-0.712661\pi$
$457$		−	6.84805e10i		−	1.57001i	0.619490	−	0.785005i	$-0.287339\pi$
$458$		0			0
$459$			2.39334e10i			0.539204i
$460$		0			0
$461$	2.12617e10			0.470754			0.235377	−	0.971904i	$-0.424368\pi$
$461$	2.12617e10			0.470754			0.235377	+	0.971904i	$0.424368\pi$
$462$		0			0
$463$	−7.78078e10			−1.69316			−0.846582	−	0.532258i	$-0.821344\pi$
$463$	−7.78078e10			−1.69316			−0.846582	+	0.532258i	$0.821344\pi$
$464$		0			0
$465$	−4.98023e10	+	3.94540e10i	−1.06522	+	0.843877i
$466$		0			0
$467$	−1.63809e10			−0.344405			−0.172202	−	0.985062i	$-0.555088\pi$
$467$	−1.63809e10			−0.344405			−0.172202	+	0.985062i	$0.555088\pi$
$468$		0			0
$469$	7.84248e10			1.62092
$470$		0			0
$471$		−	9.06845e9i		−	0.184268i
$472$		0			0
$473$		−	6.81202e9i		−	0.136092i
$474$		0			0
$475$	5.22457e10	+	1.22797e10i	1.02631	+	0.241220i
$476$		0			0
$477$		−	7.35453e9i		−	0.142063i
$478$		0			0
$479$		−	4.06791e10i		−	0.772732i	−0.922346	−	0.386366i	$-0.873730\pi$
$479$		−	4.06791e10i		−	0.772732i	0.922346	−	0.386366i	$-0.126270\pi$
$480$		0			0
$481$	1.39733e10			0.261047
$482$		0			0
$483$	−2.39705e10			−0.440442
$484$		0			0
$485$	−2.28732e10	+	1.81204e10i	−0.413390	+	0.327493i
$486$		0			0
$487$	3.28304e10			0.583661			0.291830	−	0.956470i	$-0.405736\pi$
$487$	3.28304e10			0.583661			0.291830	+	0.956470i	$0.405736\pi$
$488$		0			0
$489$	7.01897e10			1.22755
$490$		0			0
$491$		−	6.70457e9i		−	0.115357i	−0.998335	−	0.0576786i	$-0.981630\pi$
$491$		−	6.70457e9i		−	0.115357i	0.998335	−	0.0576786i	$-0.0183699\pi$
$492$		0			0
$493$			7.04070e10i			1.19187i
$494$		0			0
$495$	−1.21408e11	+	9.61808e10i	−2.02221	+	1.60202i
$496$		0			0
$497$		−	1.10784e11i		−	1.81572i
$498$		0			0
$499$			9.58349e10i			1.54569i	0.634596	+	0.772844i	$0.281166\pi$
$499$			9.58349e10i			1.54569i	−0.634596	+	0.772844i	$0.718834\pi$
$500$		0			0
$501$	1.26788e10			0.201246
$502$		0			0
$503$	−1.81609e10			−0.283703			−0.141852	−	0.989888i	$-0.545306\pi$
$503$	−1.81609e10			−0.283703			−0.141852	+	0.989888i	$0.545306\pi$
$504$		0			0
$505$	6.20278e9	+	7.82969e9i	0.0953719	+	0.120387i
$506$		0			0
$507$	9.36349e10			1.41712
$508$		0			0
$509$	−1.27124e10			−0.189389			−0.0946945	−	0.995506i	$-0.530187\pi$
$509$	−1.27124e10			−0.189389			−0.0946945	+	0.995506i	$0.530187\pi$
$510$		0			0
$511$		−	2.01999e11i		−	2.96255i
$512$		0			0
$513$		−	4.55588e10i		−	0.657813i
$514$		0			0
$515$	−1.65818e10	−	2.09310e10i	−0.235723	−	0.297550i
$516$		0			0
$517$			1.44530e11i			2.02300i
$518$		0			0
$519$			2.22794e10i			0.307068i
$520$		0			0
$521$	1.83379e10			0.248886			0.124443	−	0.992227i	$-0.460286\pi$
$521$	1.83379e10			0.248886			0.124443	+	0.992227i	$0.460286\pi$
$522$		0			0
$523$	7.82825e10			1.04630			0.523152	−	0.852239i	$-0.324756\pi$
$523$	7.82825e10			1.04630			0.523152	+	0.852239i	$0.324756\pi$
$524$		0			0
$525$	4.63269e10	−	1.97104e11i	0.609812	−	2.59453i
$526$		0			0
$527$	5.84415e10			0.757668
$528$		0			0
$529$	−7.61724e10			−0.972691
$530$		0			0
$531$			1.70157e11i			2.14028i
$532$		0			0
$533$			1.96738e10i			0.243770i
$534$		0			0
$535$	8.12501e9	+	1.02561e10i	0.0991765	+	0.125189i
$536$		0			0
$537$			6.44081e10i			0.774539i
$538$		0			0
$539$		−	3.03772e11i		−	3.59909i
$540$		0			0
$541$	−4.54928e10			−0.531072			−0.265536	−	0.964101i	$-0.585549\pi$
$541$	−4.54928e10			−0.531072			−0.265536	+	0.964101i	$0.585549\pi$
$542$		0			0
$543$	1.47023e11			1.69117
$544$		0			0
$545$	3.36200e10	+	4.24381e10i	0.381076	+	0.481028i
$546$		0			0
$547$	−4.13465e10			−0.461837			−0.230919	−	0.972973i	$-0.574173\pi$
$547$	−4.13465e10			−0.461837			−0.230919	+	0.972973i	$0.574173\pi$
$548$		0			0
$549$	−1.29581e11			−1.42643
$550$		0			0
$551$		−	1.34024e11i		−	1.45404i
$552$		0			0
$553$			4.23205e10i			0.452533i
$554$		0			0
$555$	1.02769e11	−	8.14149e10i	1.08315	−	0.858088i
$556$		0			0
$557$		−	7.11799e10i		−	0.739497i	−0.929132	−	0.369749i	$-0.879444\pi$
$557$		−	7.11799e10i		−	0.739497i	0.929132	−	0.369749i	$-0.120556\pi$
$558$		0			0
$559$		−	2.11536e9i		−	0.0216640i
$560$		0			0
$561$	2.44047e11			2.46389
$562$		0			0
$563$	1.66853e11			1.66074			0.830369	−	0.557214i	$-0.188130\pi$
$563$	1.66853e11			1.66074			0.830369	+	0.557214i	$0.188130\pi$
$564$		0			0
$565$	−1.44379e10	+	1.14379e10i	−0.141680	+	0.112241i
$566$		0			0
$567$	7.73807e10			0.748687
$568$		0			0
$569$	−1.76721e11			−1.68593			−0.842965	−	0.537969i	$-0.819192\pi$
$569$	−1.76721e11			−1.68593			−0.842965	+	0.537969i	$0.819192\pi$
$570$		0			0
$571$		−	1.16865e11i		−	1.09936i	−0.835375	−	0.549680i	$-0.814750\pi$
$571$		−	1.16865e11i		−	1.09936i	0.835375	−	0.549680i	$-0.185250\pi$
$572$		0			0
$573$		−	6.72526e10i		−	0.623865i
$574$		0			0
$575$	−4.13321e9	+	1.75853e10i	−0.0378108	+	0.160871i
$576$		0			0
$577$		−	8.96099e10i		−	0.808449i	−0.914660	−	0.404224i	$-0.867541\pi$
$577$		−	8.96099e10i		−	0.808449i	0.914660	−	0.404224i	$-0.132459\pi$
$578$		0			0
$579$		−	9.33285e10i		−	0.830424i
$580$		0			0
$581$	3.47041e10			0.304562
$582$		0			0
$583$	−2.15239e10			−0.186315
$584$		0			0
$585$	−3.77013e10	+	2.98674e10i	−0.321909	+	0.255020i
$586$		0			0
$587$	1.63831e10			0.137989			0.0689943	−	0.997617i	$-0.478021\pi$
$587$	1.63831e10			0.137989			0.0689943	+	0.997617i	$0.478021\pi$
$588$		0			0
$589$	−1.11247e11			−0.924332
$590$		0			0
$591$			1.75169e11i			1.43585i
$592$		0			0
$593$			1.69196e11i			1.36827i	0.729357	+	0.684134i	$0.239820\pi$
$593$			1.69196e11i			1.36827i	−0.729357	+	0.684134i	$0.760180\pi$
$594$		0			0
$595$	−1.45981e11	+	1.15648e11i	−1.16474	+	0.922720i
$596$		0			0
$597$			1.67045e11i			1.31503i
$598$		0			0
$599$		−	2.08068e11i		−	1.61621i	−0.589038	−	0.808105i	$-0.700493\pi$
$599$		−	2.08068e11i		−	1.61621i	0.589038	−	0.808105i	$-0.299507\pi$
$600$		0			0
$601$	−3.46399e10			−0.265509			−0.132754	−	0.991149i	$-0.542382\pi$
$601$	−3.46399e10			−0.265509			−0.132754	+	0.991149i	$0.542382\pi$
$602$		0			0
$603$	−1.74803e11			−1.32215
$604$		0			0
$605$	1.98292e11	+	2.50301e11i	1.48007	+	1.86828i
$606$		0			0
$607$	−1.07146e11			−0.789262			−0.394631	−	0.918840i	$-0.629128\pi$
$607$	−1.07146e11			−0.789262			−0.394631	+	0.918840i	$0.629128\pi$
$608$		0			0
$609$	−5.05625e11			−3.67586
$610$		0			0
$611$			4.48815e10i			0.322034i
$612$		0			0
$613$		−	1.16695e11i		−	0.826435i	−0.910632	−	0.413217i	$-0.864405\pi$
$613$		−	1.16695e11i		−	0.826435i	0.910632	−	0.413217i	$-0.135595\pi$
$614$		0			0
$615$	1.14629e11	+	1.44695e11i	0.801298	+	1.01147i
$616$		0			0
$617$			1.81450e11i			1.25204i	0.779808	+	0.626018i	$0.215317\pi$
$617$			1.81450e11i			1.25204i	−0.779808	+	0.626018i	$0.784683\pi$
$618$		0			0
$619$			1.63974e10i			0.111690i	0.998439	+	0.0558448i	$0.0177852\pi$
$619$			1.63974e10i			0.111690i	−0.998439	+	0.0558448i	$0.982215\pi$
$620$		0			0
$621$	1.53345e10			0.103111
$622$		0			0
$623$	2.44102e11			1.62039
$624$		0			0
$625$	−1.36612e11	−	6.79728e10i	−0.895299	−	0.445467i
$626$		0			0
$627$	−4.64560e11			−3.00588
$628$		0			0
$629$	−1.20596e11			−0.770427
$630$		0			0
$631$		−	8.37197e10i		−	0.528093i	−0.964510	−	0.264046i	$-0.914943\pi$
$631$		−	8.37197e10i		−	0.528093i	0.964510	−	0.264046i	$-0.0850572\pi$
$632$		0			0
$633$		−	2.09572e11i		−	1.30532i
$634$		0			0
$635$	−1.77249e11	−	2.23739e11i	−1.09016	−	1.37609i
$636$		0			0
$637$		−	9.43316e10i		−	0.572927i
$638$		0			0
$639$			2.46928e11i			1.48104i
$640$		0			0
$641$	−1.06246e11			−0.629333			−0.314667	−	0.949202i	$-0.601893\pi$
$641$	−1.06246e11			−0.629333			−0.314667	+	0.949202i	$0.601893\pi$
$642$		0			0
$643$	2.90084e11			1.69699			0.848496	−	0.529202i	$-0.177509\pi$
$643$	2.90084e11			1.69699			0.848496	+	0.529202i	$0.177509\pi$
$644$		0			0
$645$	−1.23251e10	−	1.55578e10i	−0.0712118	−	0.0898897i
$646$		0			0
$647$	−2.39567e11			−1.36713			−0.683565	−	0.729890i	$-0.739571\pi$
$647$	−2.39567e11			−1.36713			−0.683565	+	0.729890i	$0.739571\pi$
$648$		0			0
$649$	4.97984e11			2.80697
$650$		0			0
$651$			4.19695e11i			2.33674i
$652$		0			0
$653$		−	6.34483e9i		−	0.0348953i	−0.999848	−	0.0174477i	$-0.994446\pi$
$653$		−	6.34483e9i		−	0.0348953i	0.999848	−	0.0174477i	$-0.00555404\pi$
$654$		0			0
$655$	−1.48359e11	+	1.17532e11i	−0.806027	+	0.638544i
$656$		0			0
$657$			4.50241e11i			2.41648i
$658$		0			0
$659$			1.20888e11i			0.640975i	0.947253	+	0.320487i	$0.103847\pi$
$659$			1.20888e11i			0.640975i	−0.947253	+	0.320487i	$0.896153\pi$
$660$		0			0
$661$	−1.57538e11			−0.825237			−0.412618	−	0.910904i	$-0.635386\pi$
$661$	−1.57538e11			−0.825237			−0.412618	+	0.910904i	$0.635386\pi$
$662$		0			0
$663$	7.57849e10			0.392219
$664$		0			0
$665$	2.77884e11	−	2.20143e11i	1.42095	−	1.12569i
$666$		0			0
$667$	4.51110e10			0.227918
$668$		0			0
$669$	9.80242e10			0.489361
$670$		0			0
$671$			3.79234e11i			1.87076i
$672$		0			0
$673$			4.09629e11i			1.99678i	0.0566966	+	0.998391i	$0.481943\pi$
$673$			4.09629e11i			1.99678i	−0.0566966	+	0.998391i	$0.518057\pi$
$674$		0			0
$675$	−2.96365e10	+	1.26092e11i	−0.142762	+	0.607398i
$676$		0			0
$677$		−	2.57704e11i		−	1.22678i	−0.789780	−	0.613390i	$-0.789805\pi$
$677$		−	2.57704e11i		−	1.22678i	0.789780	−	0.613390i	$-0.210195\pi$
$678$		0			0
$679$			1.92758e11i			0.906845i
$680$		0			0
$681$	−4.16256e11			−1.93540
$682$		0			0
$683$	7.29875e10			0.335402			0.167701	−	0.985838i	$-0.446366\pi$
$683$	7.29875e10			0.335402			0.167701	+	0.985838i	$0.446366\pi$
$684$		0			0
$685$	1.54022e10	−	1.22018e10i	0.0699552	−	0.0554194i
$686$		0			0
$687$	−6.65739e11			−2.98866
$688$		0			0
$689$	−6.68392e9			−0.0296588
$690$		0			0
$691$		−	2.75836e11i		−	1.20987i	−0.796274	−	0.604936i	$-0.793199\pi$
$691$		−	2.75836e11i		−	1.20987i	0.796274	−	0.604936i	$-0.206801\pi$
$692$		0			0
$693$			1.02313e12i			4.43607i
$694$		0			0
$695$	1.65774e11	−	1.31328e11i	0.710522	−	0.562884i
$696$		0			0
$697$		−	1.69795e11i		−	0.719439i
$698$		0			0
$699$			4.34820e11i			1.82138i
$700$		0			0
$701$	−2.82711e11			−1.17077			−0.585384	−	0.810756i	$-0.699056\pi$
$701$	−2.82711e11			−1.17077			−0.585384	+	0.810756i	$0.699056\pi$
$702$		0			0
$703$	2.29563e11			0.939899
$704$		0			0
$705$	2.61500e11	+	3.30089e11i	1.05856	+	1.33621i
$706$		0			0
$707$	6.59826e10			0.264090
$708$		0			0
$709$	−2.58013e11			−1.02107			−0.510537	−	0.859856i	$-0.670553\pi$
$709$	−2.58013e11			−1.02107			−0.510537	+	0.859856i	$0.670553\pi$
$710$		0			0
$711$		−	9.43293e10i		−	0.369120i
$712$		0			0
$713$		−	3.74445e10i		−	0.144887i
$714$		0			0
$715$	8.74107e10	+	1.10337e11i	0.334457	+	0.422181i
$716$		0			0
$717$			5.73380e10i			0.216953i
$718$		0			0
$719$			3.77413e10i			0.141222i	0.997504	+	0.0706108i	$0.0224948\pi$
$719$			3.77413e10i			0.141222i	−0.997504	+	0.0706108i	$0.977505\pi$
$720$		0			0
$721$	−1.76390e11			−0.652729
$722$		0			0
$723$	1.24141e11			0.454319
$724$		0			0
$725$	−8.71843e10	+	3.70937e11i	−0.315563	+	1.34261i
$726$		0			0
$727$	−1.42925e11			−0.511646			−0.255823	−	0.966724i	$-0.582346\pi$
$727$	−1.42925e11			−0.511646			−0.255823	+	0.966724i	$0.582346\pi$
$728$		0			0
$729$	−4.45622e11			−1.57782
$730$		0			0
$731$			1.82566e10i			0.0639369i
$732$		0			0
$733$		−	7.74861e10i		−	0.268416i	−0.990953	−	0.134208i	$-0.957151\pi$
$733$		−	7.74861e10i		−	0.268416i	0.990953	−	0.134208i	$-0.0428490\pi$
$734$		0			0
$735$	−5.49620e11	−	6.93779e11i	−1.88327	−	2.37723i
$736$		0			0
$737$			5.11583e11i			1.73399i
$738$		0			0
$739$		−	1.24212e11i		−	0.416471i	−0.978079	−	0.208236i	$-0.933228\pi$
$739$		−	1.24212e11i		−	0.416471i	0.978079	−	0.208236i	$-0.0667721\pi$
$740$		0			0
$741$	−1.44262e11			−0.478496
$742$		0			0
$743$	2.81616e11			0.924062			0.462031	−	0.886864i	$-0.347121\pi$
$743$	2.81616e11			0.924062			0.462031	+	0.886864i	$0.347121\pi$
$744$		0			0
$745$	−5.55693e10	−	7.01445e10i	−0.180389	−	0.227703i
$746$		0			0
$747$	−7.73529e10			−0.248424
$748$		0			0
$749$	8.64305e10			0.274625
$750$		0			0
$751$		−	4.83852e11i		−	1.52108i	−0.649289	−	0.760542i	$-0.724933\pi$
$751$		−	4.83852e11i		−	1.52108i	0.649289	−	0.760542i	$-0.275067\pi$
$752$		0			0
$753$		−	5.48300e11i		−	1.70545i
$754$		0			0
$755$	−9.00407e10	+	7.13314e10i	−0.277109	+	0.219529i
$756$		0			0
$757$			2.80068e11i			0.852866i	0.904519	+	0.426433i	$0.140230\pi$
$757$			2.80068e11i			0.852866i	−0.904519	+	0.426433i	$0.859770\pi$
$758$		0			0
$759$		−	1.56365e11i		−	0.471165i
$760$		0			0
$761$	6.23909e11			1.86030			0.930150	−	0.367180i	$-0.119677\pi$
$761$	6.23909e11			1.86030			0.930150	+	0.367180i	$0.119677\pi$
$762$		0			0
$763$	3.57636e11			1.05522
$764$		0			0
$765$	3.25381e11	−	2.57771e11i	0.950049	−	0.752641i
$766$		0			0
$767$	1.54641e11			0.446831
$768$		0			0
$769$	−3.36450e11			−0.962088			−0.481044	−	0.876696i	$-0.659742\pi$
$769$	−3.36450e11			−0.962088			−0.481044	+	0.876696i	$0.659742\pi$
$770$		0			0
$771$		−	8.66854e11i		−	2.45317i
$772$		0			0
$773$		−	3.73322e11i		−	1.04560i	−0.852455	−	0.522800i	$-0.824887\pi$
$773$		−	3.73322e11i		−	1.04560i	0.852455	−	0.522800i	$-0.175113\pi$
$774$		0			0
$775$	3.07897e11	+	7.23675e10i	0.853492	+	0.200603i
$776$		0			0
$777$		−	8.66058e11i		−	2.37609i
$778$		0			0
$779$			3.23216e11i			0.877695i
$780$		0			0
$781$	7.22666e11			1.94238
$782$		0			0
$783$	3.23461e11			0.860547
$784$		0			0
$785$	−3.53849e10	+	2.80324e10i	−0.0931837	+	0.0738213i
$786$		0			0
$787$	−2.89749e11			−0.755306			−0.377653	−	0.925947i	$-0.623269\pi$
$787$	−2.89749e11			−0.755306			−0.377653	+	0.925947i	$0.623269\pi$
$788$		0			0
$789$	−1.15590e12			−2.98272
$790$		0			0
$791$			1.21671e11i			0.310801i
$792$		0			0
$793$			1.17765e11i			0.297800i
$794$		0			0
$795$	−4.91581e10	+	3.89436e10i	−0.123063	+	0.0974918i
$796$		0			0
$797$			3.31880e11i			0.822522i	0.911518	+	0.411261i	$0.134911\pi$
$797$			3.31880e11i			0.822522i	−0.911518	+	0.411261i	$0.865089\pi$
$798$		0			0
$799$		−	3.87349e11i		−	0.950420i
$800$		0			0
$801$	−5.44086e11			−1.32171
$802$		0			0
$803$	1.31769e12			3.16921
$804$		0			0
$805$	7.40977e10	+	9.35326e10i	0.176450	+	0.222730i
$806$		0			0
$807$	−2.71163e10			−0.0639345
$808$		0			0
$809$	−1.83647e11			−0.428736			−0.214368	−	0.976753i	$-0.568769\pi$
$809$	−1.83647e11			−0.428736			−0.214368	+	0.976753i	$0.568769\pi$
$810$		0			0
$811$		−	6.99407e11i		−	1.61676i	−0.588658	−	0.808382i	$-0.700343\pi$
$811$		−	6.99407e11i		−	1.61676i	0.588658	−	0.808382i	$-0.299657\pi$
$812$		0			0
$813$		−	9.38529e11i		−	2.14825i
$814$		0			0
$815$	−2.16970e11	−	2.73879e11i	−0.491779	−	0.620766i
$816$		0			0
$817$		−	3.47527e10i		−	0.0780011i
$818$		0			0
$819$			3.17717e11i			0.706163i
$820$		0			0
$821$	5.98773e11			1.31792			0.658961	−	0.752177i	$-0.270996\pi$
$821$	5.98773e11			1.31792			0.658961	+	0.752177i	$0.270996\pi$
$822$		0			0
$823$	−2.41855e11			−0.527175			−0.263588	−	0.964635i	$-0.584906\pi$
$823$	−2.41855e11			−0.527175			−0.263588	+	0.964635i	$0.584906\pi$
$824$		0			0
$825$	1.28576e12	+	3.02201e11i	2.77551	+	0.652349i
$826$		0			0
$827$	6.35373e10			0.135833			0.0679167	−	0.997691i	$-0.478365\pi$
$827$	6.35373e10			0.135833			0.0679167	+	0.997691i	$0.478365\pi$
$828$		0			0
$829$	−3.72983e11			−0.789715			−0.394858	−	0.918742i	$-0.629206\pi$
$829$	−3.72983e11			−0.789715			−0.394858	+	0.918742i	$0.629206\pi$
$830$		0			0
$831$			1.36999e12i			2.87286i
$832$		0			0
$833$			8.14129e11i			1.69088i
$834$		0			0
$835$	−3.91927e10	−	4.94725e10i	−0.0806230	−	0.101769i
$836$		0			0
$837$		−	2.68489e11i		−	0.547048i
$838$		0			0
$839$			3.38956e11i			0.684063i	0.939689	+	0.342031i	$0.111115\pi$
$839$			3.38956e11i			0.684063i	−0.939689	+	0.342031i	$0.888885\pi$
$840$		0			0
$841$	4.51308e11			0.902172
$842$		0			0
$843$	−1.06609e12			−2.11098
$844$		0			0
$845$	−2.89444e11	−	3.65362e11i	−0.567725	−	0.716632i
$846$		0			0
$847$	2.10935e12			4.09840
$848$		0			0
$849$	2.43694e11			0.469045
$850$		0			0
$851$			7.72683e10i			0.147327i
$852$		0			0
$853$		−	7.44937e11i		−	1.40710i	−0.710648	−	0.703548i	$-0.751598\pi$
$853$		−	7.44937e11i		−	1.40710i	0.710648	−	0.703548i	$-0.248402\pi$
$854$		0			0
$855$	−6.19384e11	+	4.90684e11i	−1.15903	+	0.918200i
$856$		0			0
$857$		−	7.35573e11i		−	1.36365i	−0.731516	−	0.681824i	$-0.761187\pi$
$857$		−	7.35573e11i		−	1.36365i	0.731516	−	0.681824i	$-0.238813\pi$
$858$		0			0
$859$		−	7.93849e11i		−	1.45803i	−0.684499	−	0.729013i	$-0.739979\pi$
$859$		−	7.93849e11i		−	1.45803i	0.684499	−	0.729013i	$-0.260021\pi$
$860$		0			0
$861$	1.21938e12			2.21884
$862$		0			0
$863$	4.58222e9			0.00826100			0.00413050	−	0.999991i	$-0.498685\pi$
$863$	4.58222e9			0.00826100			0.00413050	+	0.999991i	$0.498685\pi$
$864$		0			0
$865$	8.69340e10	−	6.88702e10i	0.155283	−	0.123017i
$866$		0			0
$867$	2.21753e11			0.392458
$868$		0			0
$869$	−2.76066e11			−0.484099
$870$		0			0
$871$			1.58864e11i			0.276028i
$872$		0			0
$873$		−	4.29643e11i		−	0.739692i
$874$		0			0
$875$	−9.12302e11	+	4.28521e11i	−1.55635	+	0.731038i
$876$		0			0
$877$			2.35551e11i			0.398187i	0.979980	+	0.199094i	$0.0637998\pi$
$877$			2.35551e11i			0.398187i	−0.979980	+	0.199094i	$0.936200\pi$
$878$		0			0
$879$		−	1.24985e12i		−	2.09363i
$880$		0			0
$881$	−3.93280e11			−0.652827			−0.326414	−	0.945227i	$-0.605840\pi$
$881$	−3.93280e11			−0.652827			−0.326414	+	0.945227i	$0.605840\pi$
$882$		0			0
$883$	−8.63680e11			−1.42072			−0.710362	−	0.703836i	$-0.751469\pi$
$883$	−8.63680e11			−1.42072			−0.710362	+	0.703836i	$0.751469\pi$
$884$		0			0
$885$	1.13734e12	−	9.01012e11i	1.85403	−	1.46878i
$886$		0			0
$887$	−4.28074e11			−0.691551			−0.345775	−	0.938317i	$-0.612384\pi$
$887$	−4.28074e11			−0.691551			−0.345775	+	0.938317i	$0.612384\pi$
$888$		0			0
$889$	−1.88550e12			−3.01870
$890$		0			0
$891$			5.04772e11i			0.800911i
$892$		0			0
$893$			7.37345e11i			1.15948i
$894$		0			0
$895$	2.51319e11	−	1.99098e11i	0.391682	−	0.310295i
$896$		0			0
$897$		−	4.85568e10i		−	0.0750032i
$898$		0			0
$899$		−	7.89840e11i		−	1.20921i
$900$		0			0
$901$	5.76856e10			0.0875322
$902$		0			0
$903$	−1.31109e11			−0.197189
$904$		0			0
$905$	−4.54478e11	−	5.73682e11i	−0.677514	−	0.855218i
$906$		0			0
$907$	2.57651e11			0.380717			0.190359	−	0.981715i	$-0.439035\pi$
$907$	2.57651e11			0.380717			0.190359	+	0.981715i	$0.439035\pi$
$908$		0			0
$909$	−1.47070e11			−0.215412
$910$		0			0
$911$		−	7.93863e10i		−	0.115258i	−0.998338	−	0.0576291i	$-0.981646\pi$
$911$		−	7.93863e10i		−	0.115258i	0.998338	−	0.0576291i	$-0.0183541\pi$
$912$		0			0
$913$			2.26383e11i			0.325807i
$914$		0			0
$915$	6.86155e11	+	8.66125e11i	0.978899	+	1.23565i
$916$		0			0
$917$			1.25026e12i			1.76816i
$918$		0			0
$919$			1.96749e11i			0.275835i	0.990444	+	0.137918i	$0.0440409\pi$
$919$			1.96749e11i			0.275835i	−0.990444	+	0.137918i	$0.955959\pi$
$920$		0			0
$921$	1.52946e12			2.12569
$922$		0			0
$923$	2.24413e11			0.309201
$924$		0			0
$925$	−6.35359e11	−	1.49333e11i	−0.867865	−	0.203981i
$926$		0			0
$927$	3.93160e11			0.532416
$928$		0			0
$929$	4.52675e11			0.607748			0.303874	−	0.952712i	$-0.401720\pi$
$929$	4.52675e11			0.607748			0.303874	+	0.952712i	$0.401720\pi$
$930$		0			0
$931$		−	1.54975e12i		−	2.06283i
$932$		0			0
$933$			1.81703e12i			2.39793i
$934$		0			0
$935$	−7.54398e11	−	9.52267e11i	−0.987084	−	1.24598i
$936$		0			0
$937$			1.30394e12i			1.69161i	0.533495	+	0.845803i	$0.320878\pi$
$937$			1.30394e12i			1.69161i	−0.533495	+	0.845803i	$0.679122\pi$
$938$		0			0
$939$		−	1.45163e11i		−	0.186722i
$940$		0			0
$941$	9.07118e11			1.15693			0.578463	−	0.815709i	$-0.303653\pi$
$941$	9.07118e11			1.15693			0.578463	+	0.815709i	$0.303653\pi$
$942$		0			0
$943$	−1.08791e11			−0.137577
$944$		0			0
$945$	5.31305e11	+	6.70660e11i	0.666218	+	0.840959i
$946$		0			0
$947$	−3.44441e11			−0.428267			−0.214134	−	0.976804i	$-0.568693\pi$
$947$	−3.44441e11			−0.428267			−0.214134	+	0.976804i	$0.568693\pi$
$948$		0			0
$949$	4.09187e11			0.504495
$950$		0			0
$951$			1.48664e12i			1.81754i
$952$		0			0
$953$		−	7.98379e11i		−	0.967916i	−0.875091	−	0.483958i	$-0.839199\pi$
$953$		−	7.98379e11i		−	0.967916i	0.875091	−	0.483958i	$-0.160801\pi$
$954$		0			0
$955$	−2.62418e11	+	2.07891e11i	−0.315487	+	0.249932i
$956$		0			0
$957$		−	3.29831e12i		−	3.93227i
$958$		0			0
$959$		−	1.29798e11i		−	0.153459i
$960$		0			0
$961$	1.97283e11			0.231310
$962$		0			0
$963$	−1.92647e11			−0.224005
$964$		0			0
$965$	−3.64166e11	+	2.88497e11i	−0.419943	+	0.332684i
$966$		0			0
$967$	−1.02530e12			−1.17258			−0.586292	−	0.810100i	$-0.699413\pi$
$967$	−1.02530e12			−1.17258			−0.586292	+	0.810100i	$0.699413\pi$
$968$		0			0
$969$	1.24505e12			1.41219
$970$		0			0
$971$			1.42530e12i			1.60335i	0.597760	+	0.801675i	$0.296058\pi$
$971$			1.42530e12i			1.60335i	−0.597760	+	0.801675i	$0.703942\pi$
$972$		0			0
$973$		−	1.39702e12i		−	1.55866i
$974$		0			0
$975$	3.99271e11	+	9.38437e10i	0.441824	+	0.103845i
$976$		0			0
$977$		−	1.21551e12i		−	1.33408i	−0.745024	−	0.667038i	$-0.767562\pi$
$977$		−	1.21551e12i		−	1.33408i	0.745024	−	0.667038i	$-0.232438\pi$
$978$		0			0
$979$			1.59234e12i			1.73342i
$980$		0			0
$981$	−7.97144e11			−0.860718
$982$		0			0
$983$	−5.83215e11			−0.624619			−0.312309	−	0.949980i	$-0.601103\pi$
$983$	−5.83215e11			−0.624619			−0.312309	+	0.949980i	$0.601103\pi$
$984$		0			0
$985$	6.83508e11	−	5.41483e11i	0.726103	−	0.575228i
$986$		0			0
$987$	2.78173e12			2.93121
$988$		0			0
$989$	1.16974e10			0.0122265
$990$		0			0
$991$		−	4.26175e11i		−	0.441868i	−0.975289	−	0.220934i	$-0.929089\pi$
$991$		−	4.26175e11i		−	0.441868i	0.975289	−	0.220934i	$-0.0709106\pi$
$992$		0			0
$993$		−	1.80360e12i		−	1.85500i
$994$		0			0
$995$	6.51808e11	−	5.16371e11i	0.665009	−	0.526828i
$996$		0			0
$997$		−	9.27605e10i		−	0.0938820i	−0.998898	−	0.0469410i	$-0.985053\pi$
$997$		−	9.27605e10i		−	0.0938820i	0.998898	−	0.0469410i	$-0.0149473\pi$
$998$		0			0
$999$			5.54039e11i			0.556260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.9.h.f.319.15		16
4.3	odd	2	inner	320.9.h.f.319.1		16
5.4	even	2	inner	320.9.h.f.319.2		16
8.3	odd	2		80.9.h.d.79.16	yes	16
8.5	even	2		80.9.h.d.79.2	yes	16
20.19	odd	2	inner	320.9.h.f.319.16		16
40.3	even	4		400.9.b.m.351.15		16
40.13	odd	4		400.9.b.m.351.2		16
40.19	odd	2		80.9.h.d.79.1	✓	16
40.27	even	4		400.9.b.m.351.1		16
40.29	even	2		80.9.h.d.79.15	yes	16
40.37	odd	4		400.9.b.m.351.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.9.h.d.79.1	✓	16	40.19	odd	2
80.9.h.d.79.2	yes	16	8.5	even	2
80.9.h.d.79.15	yes	16	40.29	even	2
80.9.h.d.79.16	yes	16	8.3	odd	2
320.9.h.f.319.1		16	4.3	odd	2	inner
320.9.h.f.319.2		16	5.4	even	2	inner
320.9.h.f.319.15		16	1.1	even	1	trivial
320.9.h.f.319.16		16	20.19	odd	2	inner
400.9.b.m.351.1		16	40.27	even	4
400.9.b.m.351.2		16	40.13	odd	4
400.9.b.m.351.15		16	40.3	even	4
400.9.b.m.351.16		16	40.37	odd	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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	320.h (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+125.551 q^{3} +(-388.104 - 489.899i) q^{5} -4128.49 q^{7} +9202.10 q^{9} +O(q^{10})\)	\(q+125.551 q^{3} +(-388.104 - 489.899i) q^{5} -4128.49 q^{7} +9202.10 q^{9} -26931.1i q^{11} -8363.02i q^{13} +(-48726.9 - 61507.3i) q^{15} +72177.0i q^{17} -137394. i q^{19} -518337. q^{21} +46245.1 q^{23} +(-89376.1 + 380263. i) q^{25} +331593. q^{27} +975477. q^{29} -809697. i q^{31} -3.38123e6i q^{33} +(1.60228e6 + 2.02254e6i) q^{35} +1.67084e6i q^{37} -1.04999e6i q^{39} -2.35248e6 q^{41} +252943. q^{43} +(-3.57137e6 - 4.50809e6i) q^{45} -5.36666e6 q^{47} +1.12796e7 q^{49} +9.06191e6i q^{51} -799223. i q^{53} +(-1.31935e7 + 1.04521e7i) q^{55} -1.72499e7i q^{57} +1.84911e7i q^{59} -1.40817e7 q^{61} -3.79907e7 q^{63} +(-4.09703e6 + 3.24572e6i) q^{65} -1.89960e7 q^{67} +5.80613e6 q^{69} +2.68339e7i q^{71} +4.89281e7i q^{73} +(-1.12213e7 + 4.77424e7i) q^{75} +1.11185e8i q^{77} -1.02508e7i q^{79} -1.87431e7 q^{81} -8.40601e6 q^{83} +(3.53594e7 - 2.80122e7i) q^{85} +1.22472e8 q^{87} -5.91263e7 q^{89} +3.45266e7i q^{91} -1.01658e8i q^{93} +(-6.73090e7 + 5.33230e7i) q^{95} -4.66897e7i q^{97} -2.47822e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 600 q^{5} + 42176 q^{9}+O(q^{10}) \) 16 * q - 600 * q^5 + 42176 * q^9	\( 16 q - 600 q^{5} + 42176 q^{9} - 619344 q^{21} + 1137040 q^{25} + 3497568 q^{29} - 2169168 q^{41} + 1930760 q^{45} + 26174912 q^{49} - 22772656 q^{61} + 12524160 q^{65} - 8461392 q^{69} - 224999456 q^{81} + 18124800 q^{85} - 94250976 q^{89}+O(q^{100}) \) 16 * q - 600 * q^5 + 42176 * q^9 - 619344 * q^21 + 1137040 * q^25 + 3497568 * q^29 - 2169168 * q^41 + 1930760 * q^45 + 26174912 * q^49 - 22772656 * q^61 + 12524160 * q^65 - 8461392 * q^69 - 224999456 * q^81 + 18124800 * q^85 - 94250976 * q^89

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more