LMFDB - Embedded newform 162.7.b.b.161.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,7,Mod(161,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("162.161");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	162.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:	$37.2687615464$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 1382x^{6} - 288x^{5} + 716245x^{4} + 201312x^{3} - 164876604x^{2} - 33576768x + 14252103396 $ x^8 - 1382x^6 - 288x^5 + 716245x^4 + 201312x^3 - 164876604x^2 - 33576768x + 14252103396
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			161.4
Root			$-18.8398 + 1.41421i$ of defining polynomial
Character	$\chi$	$=$	162.161
Dual form			162.7.b.b.161.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.65685i q^{2} -32.0000 q^{4} +153.557i q^{5} +672.272 q^{7} +181.019i q^{8} +O(q^{10})$	\(q-5.65685i q^{2} -32.0000 q^{4} +153.557i q^{5} +672.272 q^{7} +181.019i q^{8} +868.648 q^{10} +2559.91i q^{11} -1770.09 q^{13} -3802.95i q^{14} +1024.00 q^{16} -3978.79i q^{17} -7767.58 q^{19} -4913.81i q^{20} +14481.0 q^{22} -2613.58i q^{23} -7954.65 q^{25} +10013.1i q^{26} -21512.7 q^{28} +14470.1i q^{29} -44412.0 q^{31} -5792.62i q^{32} -22507.4 q^{34} +103232. i q^{35} -39519.1 q^{37} +43940.1i q^{38} -27796.7 q^{40} +16317.7i q^{41} +55205.5 q^{43} -81917.0i q^{44} -14784.6 q^{46} +119316. i q^{47} +334301. q^{49} +44998.3i q^{50} +56642.9 q^{52} +5933.28i q^{53} -393091. q^{55} +121694. i q^{56} +81855.3 q^{58} -7429.46i q^{59} +54532.1 q^{61} +251232. i q^{62} -32768.0 q^{64} -271809. i q^{65} -223540. q^{67} +127321. i q^{68} +583968. q^{70} +72415.7i q^{71} -317041. q^{73} +223554. i q^{74} +248563. q^{76} +1.72095e6i q^{77} +172861. q^{79} +157242. i q^{80} +92306.7 q^{82} -14663.9i q^{83} +610970. q^{85} -312290. i q^{86} -463392. q^{88} +800260. i q^{89} -1.18998e6 q^{91} +83634.4i q^{92} +674955. q^{94} -1.19276e6i q^{95} -167846. q^{97} -1.89109e6i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 256 q^{4} + 964 q^{7}+O(q^{10}) $ 8 * q - 256 * q^4 + 964 * q^7	$ 8 q - 256 q^{4} + 964 q^{7} - 768 q^{10} + 4540 q^{13} + 8192 q^{16} - 23684 q^{19} + 27072 q^{22} - 32392 q^{25} - 30848 q^{28} + 77056 q^{31} - 52608 q^{34} - 11348 q^{37} + 24576 q^{40} - 226604 q^{43} - 162720 q^{46} + 1298088 q^{49} - 145280 q^{52} - 1460916 q^{55} + 867456 q^{58} - 327476 q^{61} - 262144 q^{64} + 1713292 q^{67} - 176352 q^{70} - 2189216 q^{73} + 757888 q^{76} - 1326884 q^{79} - 1158816 q^{82} + 3483180 q^{85} - 866304 q^{88} + 1130324 q^{91} - 26400 q^{94} - 2200064 q^{97}+O(q^{100}) $ 8 * q - 256 * q^4 + 964 * q^7 - 768 * q^10 + 4540 * q^13 + 8192 * q^16 - 23684 * q^19 + 27072 * q^22 - 32392 * q^25 - 30848 * q^28 + 77056 * q^31 - 52608 * q^34 - 11348 * q^37 + 24576 * q^40 - 226604 * q^43 - 162720 * q^46 + 1298088 * q^49 - 145280 * q^52 - 1460916 * q^55 + 867456 * q^58 - 327476 * q^61 - 262144 * q^64 + 1713292 * q^67 - 176352 * q^70 - 2189216 * q^73 + 757888 * q^76 - 1326884 * q^79 - 1158816 * q^82 + 3483180 * q^85 - 866304 * q^88 + 1130324 * q^91 - 26400 * q^94 - 2200064 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$-1$

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 $

$2$	− 5.65685i	− 0.707107i
$2$	− 5.65685i	− 0.707107i
$3$	0	0
$3$	0	0
$4$	−32.0000	−0.500000
$5$	153.557i	1.22845i	0.789130	+	0.614227i	$0.210532\pi$
$5$	153.557i	1.22845i	−0.789130	+	0.614227i	$0.789468\pi$
$6$	0	0
$7$	672.272	1.95998	0.979989	−	0.199053i	$-0.0637867\pi$
$7$	672.272	1.95998	0.979989	+	0.199053i	$0.0637867\pi$
$8$	181.019i	0.353553i
$9$	0	0
$10$	868.648	0.868648
$11$	2559.91i	1.92329i	0.274289	+	0.961647i	$0.411558\pi$
$11$	2559.91i	1.92329i	−0.274289	+	0.961647i	$0.588442\pi$
$12$	0	0
$13$	−1770.09	−0.805685	−0.402843	−	0.915269i	$-0.631978\pi$
$13$	−1770.09	−0.805685	−0.402843	+	0.915269i	$0.631978\pi$
$14$	− 3802.95i	− 1.38591i
$15$	0	0
$16$	1024.00	0.250000
$17$	− 3978.79i	− 0.809850i	−0.914350	−	0.404925i	$-0.867298\pi$
$17$	− 3978.79i	− 0.809850i	0.914350	−	0.404925i	$-0.132702\pi$
$18$	0	0
$19$	−7767.58	−1.13247	−0.566233	−	0.824245i	$-0.691600\pi$
$19$	−7767.58	−1.13247	−0.566233	+	0.824245i	$0.691600\pi$
$20$	− 4913.81i	− 0.614227i
$21$	0	0
$22$	14481.0	1.35997
$23$	− 2613.58i	− 0.214809i	−0.994215	−	0.107404i	$-0.965746\pi$
$23$	− 2613.58i	− 0.214809i	0.994215	−	0.107404i	$-0.0342539\pi$
$24$	0	0
$25$	−7954.65	−0.509098
$26$	10013.1i	0.569706i
$27$	0	0
$28$	−21512.7	−0.979989
$29$	14470.1i	0.593305i	0.954985	+	0.296652i	$0.0958703\pi$
$29$	14470.1i	0.593305i	−0.954985	+	0.296652i	$0.904130\pi$
$30$	0	0
$31$	−44412.0	−1.49079	−0.745394	−	0.666625i	$-0.767738\pi$
$31$	−44412.0	−1.49079	−0.745394	+	0.666625i	$0.767738\pi$
$32$	− 5792.62i	− 0.176777i
$33$	0	0
$34$	−22507.4	−0.572650
$35$	103232.i	2.40774i
$36$	0	0
$37$	−39519.1	−0.780193	−0.390097	−	0.920774i	$-0.627558\pi$
$37$	−39519.1	−0.780193	−0.390097	+	0.920774i	$0.627558\pi$
$38$	43940.1i	0.800774i
$39$	0	0
$40$	−27796.7	−0.434324
$41$	16317.7i	0.236759i	0.992968	+	0.118380i	$0.0377700\pi$
$41$	16317.7i	0.236759i	−0.992968	+	0.118380i	$0.962230\pi$
$42$	0	0
$43$	55205.5	0.694348	0.347174	−	0.937801i	$-0.387141\pi$
$43$	55205.5	0.694348	0.347174	+	0.937801i	$0.387141\pi$
$44$	− 81917.0i	− 0.961647i
$45$	0	0
$46$	−14784.6	−0.151893
$47$	119316.i	1.14923i	0.818425	+	0.574614i	$0.194848\pi$
$47$	119316.i	1.14923i	−0.818425	+	0.574614i	$0.805152\pi$
$48$	0	0
$49$	334301.	2.84151
$50$	44998.3i	0.359986i
$51$	0	0
$52$	56642.9	0.402843
$53$	5933.28i	0.0398536i	0.999801	+	0.0199268i	$0.00634331\pi$
$53$	5933.28i	0.0398536i	−0.999801	+	0.0199268i	$0.993657\pi$
$54$	0	0
$55$	−393091.	−2.36268
$56$	121694.i	0.692957i
$57$	0	0
$58$	81855.3	0.419530
$59$	− 7429.46i	− 0.0361744i	−0.999836	−	0.0180872i	$-0.994242\pi$
$59$	− 7429.46i	− 0.0361744i	0.999836	−	0.0180872i	$-0.00575764\pi$
$60$	0	0
$61$	54532.1	0.240250	0.120125	−	0.992759i	$-0.461671\pi$
$61$	54532.1	0.240250	0.120125	+	0.992759i	$0.461671\pi$
$62$	251232.i	1.05415i
$63$	0	0
$64$	−32768.0	−0.125000
$65$	− 271809.i	− 0.989747i
$66$	0	0
$67$	−223540.	−0.743242	−0.371621	−	0.928385i	$-0.621198\pi$
$67$	−223540.	−0.743242	−0.371621	+	0.928385i	$0.621198\pi$
$68$	127321.i	0.404925i
$69$	0	0
$70$	583968.	1.70253
$71$	72415.7i	0.202329i	0.994870	+	0.101164i	$0.0322568\pi$
$71$	72415.7i	0.202329i	−0.994870	+	0.101164i	$0.967743\pi$
$72$	0	0
$73$	−317041.	−0.814979	−0.407489	−	0.913210i	$-0.633596\pi$
$73$	−317041.	−0.814979	−0.407489	+	0.913210i	$0.633596\pi$
$74$	223554.i	0.551680i
$75$	0	0
$76$	248563.	0.566233
$77$	1.72095e6i	3.76961i
$78$	0	0
$79$	172861.	0.350604	0.175302	−	0.984515i	$-0.443910\pi$
$79$	172861.	0.350604	0.175302	+	0.984515i	$0.443910\pi$
$80$	157242.i	0.307113i
$81$	0	0
$82$	92306.7	0.167414
$83$	− 14663.9i	− 0.0256457i	−0.999918	−	0.0128229i	$-0.995918\pi$
$83$	− 14663.9i	− 0.0256457i	0.999918	−	0.0128229i	$-0.00408175\pi$
$84$	0	0
$85$	610970.	0.994863
$86$	− 312290.i	− 0.490978i
$87$	0	0
$88$	−463392.	−0.679987
$89$	800260.i	1.13517i	0.823315	+	0.567585i	$0.192122\pi$
$89$	800260.i	1.13517i	−0.823315	+	0.567585i	$0.807878\pi$
$90$	0	0
$91$	−1.18998e6	−1.57913
$92$	83634.4i	0.107404i
$93$	0	0
$94$	674955.	0.812627
$95$	− 1.19276e6i	− 1.39118i
$96$	0	0
$97$	−167846.	−0.183906	−0.0919529	−	0.995763i	$-0.529311\pi$
$97$	−167846.	−0.183906	−0.0919529	+	0.995763i	$0.529311\pi$
$98$	− 1.89109e6i	− 2.00925i
$99$	0	0
$100$	254549.	0.254549
$101$	256097.i	0.248565i	0.992247	+	0.124283i	$0.0396630\pi$
$101$	256097.i	0.248565i	−0.992247	+	0.124283i	$0.960337\pi$
$102$	0	0
$103$	80614.1	0.0737733	0.0368866	−	0.999319i	$-0.488256\pi$
$103$	80614.1	0.0737733	0.0368866	+	0.999319i	$0.488256\pi$
$104$	− 320421.i	− 0.284853i
$105$	0	0
$106$	33563.7	0.0281807
$107$	991514.i	0.809371i	0.914456	+	0.404685i	$0.132619\pi$
$107$	991514.i	0.809371i	−0.914456	+	0.404685i	$0.867381\pi$
$108$	0	0
$109$	2.01080e6	1.55270	0.776352	−	0.630300i	$-0.217068\pi$
$109$	2.01080e6	1.55270	0.776352	+	0.630300i	$0.217068\pi$
$110$	2.22366e6i	1.67067i
$111$	0	0
$112$	688407.	0.489994
$113$	275062.i	0.190632i	0.995447	+	0.0953159i	$0.0303861\pi$
$113$	275062.i	0.190632i	−0.995447	+	0.0953159i	$0.969614\pi$
$114$	0	0
$115$	401332.	0.263882
$116$	− 463044.i	− 0.296652i
$117$	0	0
$118$	−42027.4	−0.0255791
$119$	− 2.67483e6i	− 1.58729i
$120$	0	0
$121$	−4.78155e6	−2.69906
$122$	− 308480.i	− 0.169882i
$123$	0	0
$124$	1.42119e6	0.745394
$125$	1.17783e6i	0.603051i
$126$	0	0
$127$	−864483.	−0.422032	−0.211016	−	0.977483i	$-0.567677\pi$
$127$	−864483.	−0.422032	−0.211016	+	0.977483i	$0.567677\pi$
$128$	185364.i	0.0883883i
$129$	0	0
$130$	−1.53759e6	−0.699857
$131$	− 1.19953e6i	− 0.533577i	−0.963755	−	0.266788i	$-0.914038\pi$
$131$	− 1.19953e6i	− 0.533577i	0.963755	−	0.266788i	$-0.0859625\pi$
$132$	0	0
$133$	−5.22193e6	−2.21961
$134$	1.26453e6i	0.525551i
$135$	0	0
$136$	720238.	0.286325
$137$	− 2.50425e6i	− 0.973905i	−0.873429	−	0.486952i	$-0.838109\pi$
$137$	− 2.50425e6i	− 0.973905i	0.873429	−	0.486952i	$-0.161891\pi$
$138$	0	0
$139$	−2.14546e6	−0.798869	−0.399434	−	0.916762i	$-0.630793\pi$
$139$	−2.14546e6	−0.798869	−0.399434	+	0.916762i	$0.630793\pi$
$140$	− 3.30342e6i	− 1.20387i
$141$	0	0
$142$	409645.	0.143068
$143$	− 4.53126e6i	− 1.54957i
$144$	0	0
$145$	−2.22198e6	−0.728847
$146$	1.79345e6i	0.576277i
$147$	0	0
$148$	1.26461e6	0.390097
$149$	− 3.67677e6i	− 1.11150i	−0.831351	−	0.555748i	$-0.812432\pi$
$149$	− 3.67677e6i	− 1.11150i	0.831351	−	0.555748i	$-0.187568\pi$
$150$	0	0
$151$	−3.62130e6	−1.05180	−0.525901	−	0.850546i	$-0.676272\pi$
$151$	−3.62130e6	−1.05180	−0.525901	+	0.850546i	$0.676272\pi$
$152$	− 1.40608e6i	− 0.400387i
$153$	0	0
$154$	9.73518e6	2.66552
$155$	− 6.81977e6i	− 1.83136i
$156$	0	0
$157$	4.26280e6	1.10153	0.550765	−	0.834661i	$-0.314336\pi$
$157$	4.26280e6	1.10153	0.550765	+	0.834661i	$0.314336\pi$
$158$	− 977851.i	− 0.247914i
$159$	0	0
$160$	889495.	0.217162
$161$	− 1.75703e6i	− 0.421020i
$162$	0	0
$163$	6.80481e6	1.57128	0.785639	−	0.618685i	$-0.212334\pi$
$163$	6.80481e6	1.57128	0.785639	+	0.618685i	$0.212334\pi$
$164$	− 522166.i	− 0.118380i
$165$	0	0
$166$	−82951.5	−0.0181343
$167$	7.57793e6i	1.62705i	0.581529	+	0.813526i	$0.302455\pi$
$167$	7.57793e6i	1.62705i	−0.581529	+	0.813526i	$0.697545\pi$
$168$	0	0
$169$	−1.69359e6	−0.350871
$170$	− 3.45617e6i	− 0.703474i
$171$	0	0
$172$	−1.76658e6	−0.347174
$173$	4.17954e6i	0.807217i	0.914932	+	0.403608i	$0.132244\pi$
$173$	4.17954e6i	0.807217i	−0.914932	+	0.403608i	$0.867756\pi$
$174$	0	0
$175$	−5.34769e6	−0.997820
$176$	2.62134e6i	0.480824i
$177$	0	0
$178$	4.52695e6	0.802687
$179$	5.42321e6i	0.945578i	0.881176	+	0.472789i	$0.156753\pi$
$179$	5.42321e6i	0.945578i	−0.881176	+	0.472789i	$0.843247\pi$
$180$	0	0
$181$	4.86015e6	0.819623	0.409812	−	0.912170i	$-0.365594\pi$
$181$	4.86015e6	0.819623	0.409812	+	0.912170i	$0.365594\pi$
$182$	6.73156e6i	1.11661i
$183$	0	0
$184$	473108.	0.0759463
$185$	− 6.06842e6i	− 0.958431i
$186$	0	0
$187$	1.01853e7	1.55758
$188$	− 3.81812e6i	− 0.574614i
$189$	0	0
$190$	−6.74729e6	−0.983714
$191$	− 3.18037e6i	− 0.456433i	−0.973610	−	0.228216i	$-0.926711\pi$
$191$	− 3.18037e6i	− 0.456433i	0.973610	−	0.228216i	$-0.0732894\pi$
$192$	0	0
$193$	−6.68693e6	−0.930154	−0.465077	−	0.885270i	$-0.653973\pi$
$193$	−6.68693e6	−0.930154	−0.465077	+	0.885270i	$0.653973\pi$
$194$	949480.i	0.130041i
$195$	0	0
$196$	−1.06976e7	−1.42076
$197$	− 1.54760e6i	− 0.202423i	−0.994865	−	0.101212i	$-0.967728\pi$
$197$	− 1.54760e6i	− 0.202423i	0.994865	−	0.101212i	$-0.0322719\pi$
$198$	0	0
$199$	1.08352e7	1.37493	0.687463	−	0.726219i	$-0.258724\pi$
$199$	1.08352e7	1.37493	0.687463	+	0.726219i	$0.258724\pi$
$200$	− 1.43995e6i	− 0.179993i
$201$	0	0
$202$	1.44870e6	0.175762
$203$	9.72786e6i	1.16286i
$204$	0	0
$205$	−2.50569e6	−0.290848
$206$	− 456022.i	− 0.0521656i
$207$	0	0
$208$	−1.81257e6	−0.201421
$209$	− 1.98843e7i	− 2.17807i
$210$	0	0
$211$	1.37945e7	1.46845	0.734226	−	0.678905i	$-0.237545\pi$
$211$	1.37945e7	1.46845	0.734226	+	0.678905i	$0.237545\pi$
$212$	− 189865.i	− 0.0199268i
$213$	0	0
$214$	5.60885e6	0.572311
$215$	8.47718e6i	0.852974i
$216$	0	0
$217$	−2.98570e7	−2.92191
$218$	− 1.13748e7i	− 1.09793i
$219$	0	0
$220$	1.25789e7	1.18134
$221$	7.04282e6i	0.652484i
$222$	0	0
$223$	−507240.	−0.0457402	−0.0228701	−	0.999738i	$-0.507280\pi$
$223$	−507240.	−0.0457402	−0.0228701	+	0.999738i	$0.507280\pi$
$224$	− 3.89422e6i	− 0.346478i
$225$	0	0
$226$	1.55599e6	0.134797
$227$	2.01699e7i	1.72436i	0.506605	+	0.862178i	$0.330900\pi$
$227$	2.01699e7i	1.72436i	−0.506605	+	0.862178i	$0.669100\pi$
$228$	0	0
$229$	−3.59898e6	−0.299691	−0.149845	−	0.988709i	$-0.547878\pi$
$229$	−3.59898e6	−0.299691	−0.149845	+	0.988709i	$0.547878\pi$
$230$	− 2.27028e6i	− 0.186593i
$231$	0	0
$232$	−2.61937e6	−0.209765
$233$	− 4.20593e6i	− 0.332502i	−0.986083	−	0.166251i	$-0.946834\pi$
$233$	− 4.20593e6i	− 0.332502i	0.986083	−	0.166251i	$-0.0531662\pi$
$234$	0	0
$235$	−1.83218e7	−1.41177
$236$	237743.i	0.0180872i
$237$	0	0
$238$	−1.51311e7	−1.12238
$239$	− 1.69035e7i	− 1.23818i	−0.785320	−	0.619090i	$-0.787502\pi$
$239$	− 1.69035e7i	− 1.23818i	0.785320	−	0.619090i	$-0.212498\pi$
$240$	0	0
$241$	2.16041e7	1.54342	0.771712	−	0.635972i	$-0.219401\pi$
$241$	2.16041e7	1.54342	0.771712	+	0.635972i	$0.219401\pi$
$242$	2.70486e7i	1.90853i
$243$	0	0
$244$	−1.74503e6	−0.120125
$245$	5.13341e7i	3.49066i
$246$	0	0
$247$	1.37493e7	0.912411
$248$	− 8.03944e6i	− 0.527073i
$249$	0	0
$250$	6.66283e6	0.426421
$251$	9.17726e6i	0.580352i	0.956973	+	0.290176i	$0.0937139\pi$
$251$	9.17726e6i	0.580352i	−0.956973	+	0.290176i	$0.906286\pi$
$252$	0	0
$253$	6.69051e6	0.413140
$254$	4.89025e6i	0.298422i
$255$	0	0
$256$	1.04858e6	0.0625000
$257$	1.92913e7i	1.13648i	0.822863	+	0.568240i	$0.192376\pi$
$257$	1.92913e7i	1.13648i	−0.822863	+	0.568240i	$0.807624\pi$
$258$	0	0
$259$	−2.65676e7	−1.52916
$260$	8.69790e6i	0.494873i
$261$	0	0
$262$	−6.78556e6	−0.377296
$263$	1.93699e7i	1.06478i	0.846499	+	0.532390i	$0.178706\pi$
$263$	1.93699e7i	1.06478i	−0.846499	+	0.532390i	$0.821294\pi$
$264$	0	0
$265$	−911095.	−0.0489583
$266$	2.95397e7i	1.56950i
$267$	0	0
$268$	7.15327e6	0.371621
$269$	− 2.18670e7i	− 1.12340i	−0.827343	−	0.561698i	$-0.810148\pi$
$269$	− 2.18670e7i	− 1.12340i	0.827343	−	0.561698i	$-0.189852\pi$
$270$	0	0
$271$	−8.52403e6	−0.428289	−0.214145	−	0.976802i	$-0.568696\pi$
$271$	−8.52403e6	−0.428289	−0.214145	+	0.976802i	$0.568696\pi$
$272$	− 4.07428e6i	− 0.202462i
$273$	0	0
$274$	−1.41662e7	−0.688655
$275$	− 2.03632e7i	− 0.979145i
$276$	0	0
$277$	2.42684e7	1.14183	0.570914	−	0.821010i	$-0.306589\pi$
$277$	2.42684e7	1.14183	0.570914	+	0.821010i	$0.306589\pi$
$278$	1.21365e7i	0.564886i
$279$	0	0
$280$	−1.86870e7	−0.851265
$281$	− 4.16687e7i	− 1.87798i	−0.343943	−	0.938990i	$-0.611763\pi$
$281$	− 4.16687e7i	− 1.87798i	0.343943	−	0.938990i	$-0.388237\pi$
$282$	0	0
$283$	3.35099e7	1.47847	0.739237	−	0.673445i	$-0.235186\pi$
$283$	3.35099e7	1.47847	0.739237	+	0.673445i	$0.235186\pi$
$284$	− 2.31730e6i	− 0.101164i
$285$	0	0
$286$	−2.56327e7	−1.09571
$287$	1.09699e7i	0.464043i
$288$	0	0
$289$	8.30679e6	0.344143
$290$	1.25694e7i	0.515373i
$291$	0	0
$292$	1.01453e7	0.407489
$293$	− 1.17171e7i	− 0.465818i	−0.972498	−	0.232909i	$-0.925175\pi$
$293$	− 1.17171e7i	− 0.465818i	0.972498	−	0.232909i	$-0.0748245\pi$
$294$	0	0
$295$	1.14084e6	0.0444385
$296$	− 7.15372e6i	− 0.275840i
$297$	0	0
$298$	−2.07989e7	−0.785946
$299$	4.62627e6i	0.173068i
$300$	0	0
$301$	3.71132e7	1.36091
$302$	2.04852e7i	0.743736i
$303$	0	0
$304$	−7.95400e6	−0.283116
$305$	8.37377e6i	0.295136i
$306$	0	0
$307$	−1.61170e7	−0.557019	−0.278510	−	0.960433i	$-0.589840\pi$
$307$	−1.61170e7	−0.557019	−0.278510	+	0.960433i	$0.589840\pi$
$308$	− 5.50705e7i	− 1.88481i
$309$	0	0
$310$	−3.85784e7	−1.29497
$311$	− 3.47969e7i	− 1.15680i	−0.815753	−	0.578401i	$-0.803677\pi$
$311$	− 3.47969e7i	− 1.15680i	0.815753	−	0.578401i	$-0.196323\pi$
$312$	0	0
$313$	1.20378e6	0.0392568	0.0196284	−	0.999807i	$-0.493752\pi$
$313$	1.20378e6	0.0392568	0.0196284	+	0.999807i	$0.493752\pi$
$314$	− 2.41140e7i	− 0.778899i
$315$	0	0
$316$	−5.53156e6	−0.175302
$317$	4.36912e7i	1.37157i	0.727806	+	0.685783i	$0.240540\pi$
$317$	4.36912e7i	1.37157i	−0.727806	+	0.685783i	$0.759460\pi$
$318$	0	0
$319$	−3.70421e7	−1.14110
$320$	− 5.03174e6i	− 0.153557i
$321$	0	0
$322$	−9.93929e6	−0.297706
$323$	3.09056e7i	0.917127i
$324$	0	0
$325$	1.40805e7	0.410173
$326$	− 3.84938e7i	− 1.11106i
$327$	0	0
$328$	−2.95382e6	−0.0837070
$329$	8.02130e7i	2.25246i
$330$	0	0
$331$	5.60586e7	1.54582	0.772908	−	0.634518i	$-0.218801\pi$
$331$	5.60586e7	1.54582	0.772908	+	0.634518i	$0.218801\pi$
$332$	469244.i	0.0128229i
$333$	0	0
$334$	4.28673e7	1.15050
$335$	− 3.43260e7i	− 0.913038i
$336$	0	0
$337$	−4.86582e7	−1.27135	−0.635676	−	0.771956i	$-0.719279\pi$
$337$	−4.86582e7	−1.27135	−0.635676	+	0.771956i	$0.719279\pi$
$338$	9.58038e6i	0.248103i
$339$	0	0
$340$	−1.95510e7	−0.497431
$341$	− 1.13691e8i	− 2.86722i
$342$	0	0
$343$	1.45649e8	3.60932
$344$	9.99327e6i	0.245489i
$345$	0	0
$346$	2.36431e7	0.570789
$347$	− 668450.i	− 0.0159985i	−0.999968	−	0.00799927i	$-0.997454\pi$
$347$	− 668450.i	− 0.0159985i	0.999968	−	0.00799927i	$-0.00254627\pi$
$348$	0	0
$349$	6.61894e6	0.155708	0.0778542	−	0.996965i	$-0.475193\pi$
$349$	6.61894e6	0.155708	0.0778542	+	0.996965i	$0.475193\pi$
$350$	3.02511e7i	0.705565i
$351$	0	0
$352$	1.48286e7	0.339994
$353$	3.86266e7i	0.878138i	0.898453	+	0.439069i	$0.144692\pi$
$353$	3.86266e7i	0.878138i	−0.898453	+	0.439069i	$0.855308\pi$
$354$	0	0
$355$	−1.11199e7	−0.248552
$356$	− 2.56083e7i	− 0.567585i
$357$	0	0
$358$	3.06783e7	0.668625
$359$	− 4.14923e7i	− 0.896776i	−0.893839	−	0.448388i	$-0.851998\pi$
$359$	− 4.14923e7i	− 0.896776i	0.893839	−	0.448388i	$-0.148002\pi$
$360$	0	0
$361$	1.32895e7	0.282479
$362$	− 2.74932e7i	− 0.579561i
$363$	0	0
$364$	3.80795e7	0.789563
$365$	− 4.86837e7i	− 1.00116i
$366$	0	0
$367$	2.44254e7	0.494132	0.247066	−	0.968999i	$-0.420534\pi$
$367$	2.44254e7	0.494132	0.247066	+	0.968999i	$0.420534\pi$
$368$	− 2.67630e6i	− 0.0537022i
$369$	0	0
$370$	−3.43282e7	−0.677713
$371$	3.98878e6i	0.0781121i
$372$	0	0
$373$	2.52224e7	0.486027	0.243013	−	0.970023i	$-0.421864\pi$
$373$	2.52224e7	0.486027	0.243013	+	0.970023i	$0.421864\pi$
$374$	− 5.76169e7i	− 1.10138i
$375$	0	0
$376$	−2.15986e7	−0.406313
$377$	− 2.56134e7i	− 0.478017i
$378$	0	0
$379$	−6.95718e6	−0.127795	−0.0638977	−	0.997956i	$-0.520353\pi$
$379$	−6.95718e6	−0.127795	−0.0638977	+	0.997956i	$0.520353\pi$
$380$	3.81685e7i	0.695591i
$381$	0	0
$382$	−1.79909e7	−0.322747
$383$	− 3.59728e7i	− 0.640292i	−0.947368	−	0.320146i	$-0.896268\pi$
$383$	− 3.59728e7i	− 0.640292i	0.947368	−	0.320146i	$-0.103732\pi$
$384$	0	0
$385$	−2.64264e8	−4.63079
$386$	3.78270e7i	0.657718i
$387$	0	0
$388$	5.37107e6	0.0919529
$389$	− 5.02727e7i	− 0.854050i	−0.904240	−	0.427025i	$-0.859562\pi$
$389$	− 5.02727e7i	− 0.854050i	0.904240	−	0.427025i	$-0.140438\pi$
$390$	0	0
$391$	−1.03989e7	−0.173963
$392$	6.05149e7i	1.00463i
$393$	0	0
$394$	−8.75455e6	−0.143135
$395$	2.65440e7i	0.430700i
$396$	0	0
$397$	2.70307e7	0.432002	0.216001	−	0.976393i	$-0.430699\pi$
$397$	2.70307e7	0.432002	0.216001	+	0.976393i	$0.430699\pi$
$398$	− 6.12934e7i	− 0.972219i
$399$	0	0
$400$	−8.14556e6	−0.127274
$401$	− 8.09253e7i	− 1.25502i	−0.778608	−	0.627511i	$-0.784074\pi$
$401$	− 8.09253e7i	− 1.25502i	0.778608	−	0.627511i	$-0.215926\pi$
$402$	0	0
$403$	7.86134e7	1.20111
$404$	− 8.19511e6i	− 0.124283i
$405$	0	0
$406$	5.50291e7	0.822269
$407$	− 1.01165e8i	− 1.50054i
$408$	0	0
$409$	−6.43480e7	−0.940514	−0.470257	−	0.882530i	$-0.655839\pi$
$409$	−6.43480e7	−0.940514	−0.470257	+	0.882530i	$0.655839\pi$
$410$	1.41743e7i	0.205660i
$411$	0	0
$412$	−2.57965e6	−0.0368866
$413$	− 4.99462e6i	− 0.0709009i
$414$	0	0
$415$	2.25174e6	0.0315046
$416$	1.02535e7i	0.142426i
$417$	0	0
$418$	−1.12482e8	−1.54012
$419$	5.55006e7i	0.754493i	0.926113	+	0.377247i	$0.123129\pi$
$419$	5.55006e7i	0.754493i	−0.926113	+	0.377247i	$0.876871\pi$
$420$	0	0
$421$	2.75269e7	0.368902	0.184451	−	0.982842i	$-0.440949\pi$
$421$	2.75269e7	0.368902	0.184451	+	0.982842i	$0.440949\pi$
$422$	− 7.80337e7i	− 1.03835i
$423$	0	0
$424$	−1.07404e6	−0.0140904
$425$	3.16499e7i	0.412293i
$426$	0	0
$427$	3.66604e7	0.470884
$428$	− 3.17284e7i	− 0.404685i
$429$	0	0
$430$	4.79542e7	0.603144
$431$	1.36305e8i	1.70248i	0.524779	+	0.851238i	$0.324148\pi$
$431$	1.36305e8i	1.70248i	−0.524779	+	0.851238i	$0.675852\pi$
$432$	0	0
$433$	−1.06153e8	−1.30758	−0.653792	−	0.756675i	$-0.726823\pi$
$433$	−1.06153e8	−1.30758	−0.653792	+	0.756675i	$0.726823\pi$
$434$	1.68897e8i	2.06610i
$435$	0	0
$436$	−6.43455e7	−0.776352
$437$	2.03012e7i	0.243263i
$438$	0	0
$439$	6.31295e7	0.746171	0.373086	−	0.927797i	$-0.378300\pi$
$439$	6.31295e7	0.746171	0.373086	+	0.927797i	$0.378300\pi$
$440$	− 7.11570e7i	− 0.835333i
$441$	0	0
$442$	3.98402e7	0.461376
$443$	− 4.74799e7i	− 0.546133i	−0.961995	−	0.273066i	$-0.911962\pi$
$443$	− 4.74799e7i	− 0.546133i	0.961995	−	0.273066i	$-0.0880379\pi$
$444$	0	0
$445$	−1.22885e8	−1.39450
$446$	2.86938e6i	0.0323432i
$447$	0	0
$448$	−2.20290e7	−0.244997
$449$	1.11141e8i	1.22782i	0.789376	+	0.613910i	$0.210404\pi$
$449$	1.11141e8i	1.22782i	−0.789376	+	0.613910i	$0.789596\pi$
$450$	0	0
$451$	−4.17717e7	−0.455358
$452$	− 8.80199e6i	− 0.0953159i
$453$	0	0
$454$	1.14098e8	1.21930
$455$	− 1.82730e8i	− 1.93988i
$456$	0	0
$457$	−8.81213e7	−0.923278	−0.461639	−	0.887068i	$-0.652738\pi$
$457$	−8.81213e7	−0.923278	−0.461639	+	0.887068i	$0.652738\pi$
$458$	2.03589e7i	0.211913i
$459$	0	0
$460$	−1.28426e7	−0.131941
$461$	1.39975e8i	1.42873i	0.699775	+	0.714363i	$0.253283\pi$
$461$	1.39975e8i	1.42873i	−0.699775	+	0.714363i	$0.746717\pi$
$462$	0	0
$463$	1.31217e8	1.32205	0.661024	−	0.750365i	$-0.270122\pi$
$463$	1.31217e8	1.32205	0.661024	+	0.750365i	$0.270122\pi$
$464$	1.48174e7i	0.148326i
$465$	0	0
$466$	−2.37924e7	−0.235115
$467$	− 8.32231e7i	− 0.817134i	−0.912728	−	0.408567i	$-0.866029\pi$
$467$	− 8.32231e7i	− 0.817134i	0.912728	−	0.408567i	$-0.133971\pi$
$468$	0	0
$469$	−1.50280e8	−1.45674
$470$	1.03644e8i	0.998274i
$471$	0	0
$472$	1.34488e6	0.0127896
$473$	1.41321e8i	1.33544i
$474$	0	0
$475$	6.17884e7	0.576536
$476$	8.55946e7i	0.793644i
$477$	0	0
$478$	−9.56208e7	−0.875525
$479$	− 1.48496e8i	− 1.35116i	−0.737287	−	0.675580i	$-0.763893\pi$
$479$	− 1.48496e8i	− 1.35116i	0.737287	−	0.675580i	$-0.236107\pi$
$480$	0	0
$481$	6.99524e7	0.628590
$482$	− 1.22211e8i	− 1.09137i
$483$	0	0
$484$	1.53010e8	1.34953
$485$	− 2.57739e7i	− 0.225920i
$486$	0	0
$487$	1.02978e8	0.891571	0.445785	−	0.895140i	$-0.352924\pi$
$487$	1.02978e8	0.891571	0.445785	+	0.895140i	$0.352924\pi$
$488$	9.87137e6i	0.0849411i
$489$	0	0
$490$	2.90390e8	2.46827
$491$	1.30669e8i	1.10390i	0.833879	+	0.551948i	$0.186115\pi$
$491$	1.30669e8i	1.10390i	−0.833879	+	0.551948i	$0.813885\pi$
$492$	0	0
$493$	5.75736e7	0.480488
$494$	− 7.77779e7i	− 0.645172i
$495$	0	0
$496$	−4.54779e7	−0.372697
$497$	4.86831e7i	0.396560i
$498$	0	0
$499$	1.48296e8	1.19351	0.596757	−	0.802422i	$-0.296456\pi$
$499$	1.48296e8	1.19351	0.596757	+	0.802422i	$0.296456\pi$
$500$	− 3.76907e7i	− 0.301525i
$501$	0	0
$502$	5.19144e7	0.410371
$503$	− 4.70389e6i	− 0.0369618i	−0.999829	−	0.0184809i	$-0.994117\pi$
$503$	− 4.70389e6i	− 0.0369618i	0.999829	−	0.0184809i	$-0.00588300\pi$
$504$	0	0
$505$	−3.93254e7	−0.305351
$506$	− 3.78472e7i	− 0.292134i
$507$	0	0
$508$	2.76635e7	0.211016
$509$	2.30644e8i	1.74899i	0.485032	+	0.874496i	$0.338808\pi$
$509$	2.30644e8i	1.74899i	−0.485032	+	0.874496i	$0.661192\pi$
$510$	0	0
$511$	−2.13138e8	−1.59734
$512$	− 5.93164e6i	− 0.0441942i
$513$	0	0
$514$	1.09128e8	0.803613
$515$	1.23788e7i	0.0906270i
$516$	0	0
$517$	−3.05438e8	−2.21030
$518$	1.50289e8i	1.08128i
$519$	0	0
$520$	4.92027e7	0.349928
$521$	− 1.23094e8i	− 0.870413i	−0.900331	−	0.435207i	$-0.856675\pi$
$521$	− 1.23094e8i	− 0.870413i	0.900331	−	0.435207i	$-0.143325\pi$
$522$	0	0
$523$	−2.36329e8	−1.65201	−0.826004	−	0.563664i	$-0.809391\pi$
$523$	−2.36329e8	−1.65201	−0.826004	+	0.563664i	$0.809391\pi$
$524$	3.83849e7i	0.266788i
$525$	0	0
$526$	1.09573e8	0.752914
$527$	1.76706e8i	1.20731i
$528$	0	0
$529$	1.41205e8	0.953857
$530$	5.15393e6i	0.0346187i
$531$	0	0
$532$	1.67102e8	1.10980
$533$	− 2.88838e7i	− 0.190753i
$534$	0	0
$535$	−1.52254e8	−0.994274
$536$	− 4.04650e7i	− 0.262776i
$537$	0	0
$538$	−1.23698e8	−0.794360
$539$	8.55779e8i	5.46506i
$540$	0	0
$541$	−2.15827e8	−1.36306	−0.681529	−	0.731791i	$-0.738685\pi$
$541$	−2.15827e8	−1.36306	−0.681529	+	0.731791i	$0.738685\pi$
$542$	4.82192e7i	0.302846i
$543$	0	0
$544$	−2.30476e7	−0.143163
$545$	3.08771e8i	1.90742i
$546$	0	0
$547$	1.65636e8	1.01203	0.506015	−	0.862525i	$-0.331118\pi$
$547$	1.65636e8	1.01203	0.506015	+	0.862525i	$0.331118\pi$
$548$	8.01361e7i	0.486952i
$549$	0	0
$550$	−1.15191e8	−0.692360
$551$	− 1.12398e8i	− 0.671898i
$552$	0	0
$553$	1.16210e8	0.687175
$554$	− 1.37283e8i	− 0.807395i
$555$	0	0
$556$	6.86546e7	0.399434
$557$	− 3.30976e8i	− 1.91527i	−0.287979	−	0.957637i	$-0.592983\pi$
$557$	− 3.30976e8i	− 1.91527i	0.287979	−	0.957637i	$-0.407017\pi$
$558$	0	0
$559$	−9.77188e7	−0.559426
$560$	1.05709e8i	0.601935i
$561$	0	0
$562$	−2.35714e8	−1.32793
$563$	− 2.53188e8i	− 1.41879i	−0.704811	−	0.709395i	$-0.748968\pi$
$563$	− 2.53188e8i	− 1.41879i	0.704811	−	0.709395i	$-0.251032\pi$
$564$	0	0
$565$	−4.22376e7	−0.234182
$566$	− 1.89561e8i	− 1.04544i
$567$	0	0
$568$	−1.31087e7	−0.0715341
$569$	2.25334e7i	0.122318i	0.998128	+	0.0611589i	$0.0194796\pi$
$569$	2.25334e7i	0.122318i	−0.998128	+	0.0611589i	$0.980520\pi$
$570$	0	0
$571$	2.37279e8	1.27453	0.637266	−	0.770644i	$-0.280065\pi$
$571$	2.37279e8	1.27453	0.637266	+	0.770644i	$0.280065\pi$
$572$	1.45000e8i	0.774785i
$573$	0	0
$574$	6.20553e7	0.328128
$575$	2.07901e7i	0.109359i
$576$	0	0
$577$	1.32757e8	0.691085	0.345542	−	0.938403i	$-0.387695\pi$
$577$	1.32757e8	0.691085	0.345542	+	0.938403i	$0.387695\pi$
$578$	− 4.69903e7i	− 0.243346i
$579$	0	0
$580$	7.11034e7	0.364424
$581$	− 9.85812e6i	− 0.0502650i
$582$	0	0
$583$	−1.51886e7	−0.0766502
$584$	− 5.73905e7i	− 0.288139i
$585$	0	0
$586$	−6.62818e7	−0.329383
$587$	8.46294e7i	0.418415i	0.977871	+	0.209207i	$0.0670884\pi$
$587$	8.46294e7i	0.418415i	−0.977871	+	0.209207i	$0.932912\pi$
$588$	0	0
$589$	3.44974e8	1.68827
$590$	− 6.45358e6i	− 0.0314228i
$591$	0	0
$592$	−4.04676e7	−0.195048
$593$	− 2.84449e8i	− 1.36408i	−0.731313	−	0.682042i	$-0.761092\pi$
$593$	− 2.84449e8i	− 1.36408i	0.731313	−	0.682042i	$-0.238908\pi$
$594$	0	0
$595$	4.10738e8	1.94991
$596$	1.17657e8i	0.555748i
$597$	0	0
$598$	2.61701e7	0.122378
$599$	− 4.12035e8i	− 1.91714i	−0.284858	−	0.958570i	$-0.591946\pi$
$599$	− 4.12035e8i	− 1.91714i	0.284858	−	0.958570i	$-0.408054\pi$
$600$	0	0
$601$	1.61253e8	0.742820	0.371410	−	0.928469i	$-0.378874\pi$
$601$	1.61253e8	0.742820	0.371410	+	0.928469i	$0.378874\pi$
$602$	− 2.09944e8i	− 0.962306i
$603$	0	0
$604$	1.15882e8	0.525901
$605$	− 7.34240e8i	− 3.31567i
$606$	0	0
$607$	−4.70745e7	−0.210484	−0.105242	−	0.994447i	$-0.533562\pi$
$607$	−4.70745e7	−0.210484	−0.105242	+	0.994447i	$0.533562\pi$
$608$	4.49946e7i	0.200194i
$609$	0	0
$610$	4.73692e7	0.208692
$611$	− 2.11201e8i	− 0.925916i
$612$	0	0
$613$	−2.39685e8	−1.04054	−0.520271	−	0.854002i	$-0.674169\pi$
$613$	−2.39685e8	−1.04054	−0.520271	+	0.854002i	$0.674169\pi$
$614$	9.11717e7i	0.393872i
$615$	0	0
$616$	−3.11526e8	−1.33276
$617$	− 4.02430e8i	− 1.71330i	−0.515895	−	0.856652i	$-0.672540\pi$
$617$	− 4.02430e8i	− 1.71330i	0.515895	−	0.856652i	$-0.327460\pi$
$618$	0	0
$619$	−2.91856e8	−1.23054	−0.615271	−	0.788316i	$-0.710953\pi$
$619$	−2.91856e8	−1.23054	−0.615271	+	0.788316i	$0.710953\pi$
$620$	2.18233e8i	0.915681i
$621$	0	0
$622$	−1.96841e8	−0.817982
$623$	5.37992e8i	2.22491i
$624$	0	0
$625$	−3.05156e8	−1.24992
$626$	− 6.80962e6i	− 0.0277588i
$627$	0	0
$628$	−1.36410e8	−0.550765
$629$	1.57238e8i	0.631839i
$630$	0	0
$631$	2.90786e8	1.15740	0.578702	−	0.815539i	$-0.303559\pi$
$631$	2.90786e8	1.15740	0.578702	+	0.815539i	$0.303559\pi$
$632$	3.12912e7i	0.123957i
$633$	0	0
$634$	2.47155e8	0.969843
$635$	− 1.32747e8i	− 0.518447i
$636$	0	0
$637$	−5.91743e8	−2.28936
$638$	2.09542e8i	0.806880i
$639$	0	0
$640$	−2.84638e7	−0.108581
$641$	3.49131e8i	1.32561i	0.748794	+	0.662803i	$0.230633\pi$
$641$	3.49131e8i	1.32561i	−0.748794	+	0.662803i	$0.769367\pi$
$642$	0	0
$643$	−3.75425e8	−1.41218	−0.706091	−	0.708121i	$-0.749543\pi$
$643$	−3.75425e8	−1.41218	−0.706091	+	0.708121i	$0.749543\pi$
$644$	5.62251e7i	0.210510i
$645$	0	0
$646$	1.74828e8	0.648507
$647$	3.70870e8i	1.36933i	0.728856	+	0.684667i	$0.240052\pi$
$647$	3.70870e8i	1.36933i	−0.728856	+	0.684667i	$0.759948\pi$
$648$	0	0
$649$	1.90187e7	0.0695740
$650$	− 7.96511e7i	− 0.290036i
$651$	0	0
$652$	−2.17754e8	−0.785639
$653$	1.30340e8i	0.468100i	0.972225	+	0.234050i	$0.0751979\pi$
$653$	1.30340e8i	0.468100i	−0.972225	+	0.234050i	$0.924802\pi$
$654$	0	0
$655$	1.84196e8	0.655474
$656$	1.67093e7i	0.0591898i
$657$	0	0
$658$	4.53753e8	1.59273
$659$	− 1.96154e8i	− 0.685394i	−0.939446	−	0.342697i	$-0.888660\pi$
$659$	− 1.96154e8i	− 0.685394i	0.939446	−	0.342697i	$-0.111340\pi$
$660$	0	0
$661$	−3.42741e8	−1.18676	−0.593378	−	0.804924i	$-0.702206\pi$
$661$	−3.42741e8	−1.18676	−0.593378	+	0.804924i	$0.702206\pi$
$662$	− 3.17115e8i	− 1.09306i
$663$	0	0
$664$	2.65445e6	0.00906713
$665$	− 8.01862e8i	− 2.72668i
$666$	0	0
$667$	3.78187e7	0.127447
$668$	− 2.42494e8i	− 0.813526i
$669$	0	0
$670$	−1.94177e8	−0.645615
$671$	1.39597e8i	0.462071i
$672$	0	0
$673$	3.10020e8	1.01706	0.508528	−	0.861045i	$-0.330190\pi$
$673$	3.10020e8	1.01706	0.508528	+	0.861045i	$0.330190\pi$
$674$	2.75252e8i	0.898982i
$675$	0	0
$676$	5.41948e7	0.175436
$677$	2.55949e8i	0.824874i	0.910986	+	0.412437i	$0.135322\pi$
$677$	2.55949e8i	0.824874i	−0.910986	+	0.412437i	$0.864678\pi$
$678$	0	0
$679$	−1.12838e8	−0.360451
$680$	1.10597e8i	0.351737i
$681$	0	0
$682$	−6.43131e8	−2.02743
$683$	− 4.96369e7i	− 0.155791i	−0.996962	−	0.0778955i	$-0.975180\pi$
$683$	− 4.96369e7i	− 0.155791i	0.996962	−	0.0778955i	$-0.0248200\pi$
$684$	0	0
$685$	3.84545e8	1.19640
$686$	− 8.23916e8i	− 2.55217i
$687$	0	0
$688$	5.65305e7	0.173587
$689$	− 1.05024e7i	− 0.0321094i
$690$	0	0
$691$	−3.24420e7	−0.0983273	−0.0491636	−	0.998791i	$-0.515656\pi$
$691$	−3.24420e7	−0.0983273	−0.0491636	+	0.998791i	$0.515656\pi$
$692$	− 1.33745e8i	− 0.403608i
$693$	0	0
$694$	−3.78132e6	−0.0113127
$695$	− 3.29449e8i	− 0.981373i
$696$	0	0
$697$	6.49247e7	0.191739
$698$	− 3.74424e7i	− 0.110103i
$699$	0	0
$700$	1.71126e8	0.498910
$701$	2.92826e8i	0.850071i	0.905177	+	0.425035i	$0.139738\pi$
$701$	2.92826e8i	0.850071i	−0.905177	+	0.425035i	$0.860262\pi$
$702$	0	0
$703$	3.06968e8	0.883542
$704$	− 8.38830e7i	− 0.240412i
$705$	0	0
$706$	2.18505e8	0.620937
$707$	1.72167e8i	0.487182i
$708$	0	0
$709$	−4.84608e8	−1.35973	−0.679863	−	0.733339i	$-0.737961\pi$
$709$	−4.84608e8	−1.35973	−0.679863	+	0.733339i	$0.737961\pi$
$710$	6.29038e7i	0.175753i
$711$	0	0
$712$	−1.44862e8	−0.401343
$713$	1.16074e8i	0.320234i
$714$	0	0
$715$	6.95806e8	1.90358
$716$	− 1.73543e8i	− 0.472789i
$717$	0	0
$718$	−2.34716e8	−0.634116
$719$	− 2.30795e8i	− 0.620927i	−0.950585	−	0.310463i	$-0.899516\pi$
$719$	− 2.30795e8i	− 0.620927i	0.950585	−	0.310463i	$-0.100484\pi$
$720$	0	0
$721$	5.41946e7	0.144594
$722$	− 7.51766e7i	− 0.199743i
$723$	0	0
$724$	−1.55525e8	−0.409812
$725$	− 1.15105e8i	− 0.302050i
$726$	0	0
$727$	−3.46793e7	−0.0902541	−0.0451271	−	0.998981i	$-0.514369\pi$
$727$	−3.46793e7	−0.0902541	−0.0451271	+	0.998981i	$0.514369\pi$
$728$	− 2.15410e8i	− 0.558305i
$729$	0	0
$730$	−2.75397e8	−0.707929
$731$	− 2.19651e8i	− 0.562318i
$732$	0	0
$733$	−4.55712e8	−1.15712	−0.578560	−	0.815640i	$-0.696385\pi$
$733$	−4.55712e8	−1.15712	−0.578560	+	0.815640i	$0.696385\pi$
$734$	− 1.38171e8i	− 0.349404i
$735$	0	0
$736$	−1.51395e7	−0.0379732
$737$	− 5.72240e8i	− 1.42947i
$738$	0	0
$739$	4.45251e8	1.10324	0.551621	−	0.834095i	$-0.314009\pi$
$739$	4.45251e8	1.10324	0.551621	+	0.834095i	$0.314009\pi$
$740$	1.94190e8i	0.479215i
$741$	0	0
$742$	2.25639e7	0.0552336
$743$	− 5.85277e8i	− 1.42691i	−0.700704	−	0.713453i	$-0.747130\pi$
$743$	− 5.85277e8i	− 1.42691i	0.700704	−	0.713453i	$-0.252870\pi$
$744$	0	0
$745$	5.64592e8	1.36542
$746$	− 1.42679e8i	− 0.343673i
$747$	0	0
$748$	−3.25931e8	−0.778790
$749$	6.66567e8i	1.58635i
$750$	0	0
$751$	3.83614e8	0.905679	0.452840	−	0.891592i	$-0.350411\pi$
$751$	3.83614e8	0.905679	0.452840	+	0.891592i	$0.350411\pi$
$752$	1.22180e8i	0.287307i
$753$	0	0
$754$	−1.44891e8	−0.338009
$755$	− 5.56075e8i	− 1.29209i
$756$	0	0
$757$	−7.52012e7	−0.173355	−0.0866777	−	0.996236i	$-0.527625\pi$
$757$	−7.52012e7	−0.173355	−0.0866777	+	0.996236i	$0.527625\pi$
$758$	3.93557e7i	0.0903650i
$759$	0	0
$760$	2.15913e8	0.491857
$761$	− 1.72125e8i	− 0.390561i	−0.980747	−	0.195281i	$-0.937438\pi$
$761$	− 1.72125e8i	− 0.390561i	0.980747	−	0.195281i	$-0.0625618\pi$
$762$	0	0
$763$	1.35180e9	3.04326
$764$	1.01772e8i	0.228216i
$765$	0	0
$766$	−2.03493e8	−0.452755
$767$	1.31508e7i	0.0291452i
$768$	0	0
$769$	1.19958e8	0.263786	0.131893	−	0.991264i	$-0.457895\pi$
$769$	1.19958e8	0.263786	0.131893	+	0.991264i	$0.457895\pi$
$770$	1.49490e9i	3.27447i
$771$	0	0
$772$	2.13982e8	0.465077
$773$	7.73357e8i	1.67433i	0.546949	+	0.837166i	$0.315789\pi$
$773$	7.73357e8i	1.67433i	−0.546949	+	0.837166i	$0.684211\pi$
$774$	0	0
$775$	3.53282e8	0.758956
$776$	− 3.03834e7i	− 0.0650205i
$777$	0	0
$778$	−2.84385e8	−0.603905
$779$	− 1.26749e8i	− 0.268122i
$780$	0	0
$781$	−1.85377e8	−0.389138
$782$	5.88249e7i	0.123010i
$783$	0	0
$784$	3.42324e8	0.710378
$785$	6.54581e8i	1.35318i
$786$	0	0
$787$	1.47659e8	0.302924	0.151462	−	0.988463i	$-0.451602\pi$
$787$	1.47659e8	0.302924	0.151462	+	0.988463i	$0.451602\pi$
$788$	4.95232e7i	0.101212i
$789$	0	0
$790$	1.50156e8	0.304551
$791$	1.84917e8i	0.373634i
$792$	0	0
$793$	−9.65268e7	−0.193566
$794$	− 1.52909e8i	− 0.305472i
$795$	0	0
$796$	−3.46728e8	−0.687463
$797$	1.00935e9i	1.99374i	0.0790530	+	0.996870i	$0.474810\pi$
$797$	1.00935e9i	1.99374i	−0.0790530	+	0.996870i	$0.525190\pi$
$798$	0	0
$799$	4.74735e8	0.930702
$800$	4.60783e7i	0.0899966i
$801$	0	0
$802$	−4.57783e8	−0.887435
$803$	− 8.11594e8i	− 1.56744i
$804$	0	0
$805$	2.69804e8	0.517203
$806$	− 4.44704e8i	− 0.849310i
$807$	0	0
$808$	−4.63585e7	−0.0878811
$809$	3.05870e8i	0.577686i	0.957376	+	0.288843i	$0.0932705\pi$
$809$	3.05870e8i	0.577686i	−0.957376	+	0.288843i	$0.906729\pi$
$810$	0	0
$811$	−2.24649e8	−0.421156	−0.210578	−	0.977577i	$-0.567535\pi$
$811$	−2.24649e8	−0.421156	−0.210578	+	0.977577i	$0.567535\pi$
$812$	− 3.11291e8i	− 0.581432i
$813$	0	0
$814$	−5.72277e8	−1.06104
$815$	1.04492e9i	1.93024i
$816$	0	0
$817$	−4.28814e8	−0.786326
$818$	3.64007e8i	0.665044i
$819$	0	0
$820$	8.01820e7	0.145424
$821$	1.91182e8i	0.345475i	0.984968	+	0.172738i	$0.0552613\pi$
$821$	1.91182e8i	0.345475i	−0.984968	+	0.172738i	$0.944739\pi$
$822$	0	0
$823$	6.08837e8	1.09220	0.546099	−	0.837720i	$-0.316112\pi$
$823$	6.08837e8	1.09220	0.546099	+	0.837720i	$0.316112\pi$
$824$	1.45927e7i	0.0260828i
$825$	0	0
$826$	−2.82538e7	−0.0501345
$827$	4.70812e7i	0.0832398i	0.999134	+	0.0416199i	$0.0132519\pi$
$827$	4.70812e7i	0.0832398i	−0.999134	+	0.0416199i	$0.986748\pi$
$828$	0	0
$829$	1.01177e8	0.177589	0.0887947	−	0.996050i	$-0.471698\pi$
$829$	1.01177e8	0.177589	0.0887947	+	0.996050i	$0.471698\pi$
$830$	− 1.27378e7i	− 0.0222771i
$831$	0	0
$832$	5.80023e7	0.100711
$833$	− 1.33011e9i	− 2.30120i
$834$	0	0
$835$	−1.16364e9	−1.99876
$836$	6.36297e8i	1.08903i
$837$	0	0
$838$	3.13959e8	0.533507
$839$	4.17131e8i	0.706295i	0.935568	+	0.353148i	$0.114889\pi$
$839$	4.17131e8i	0.706295i	−0.935568	+	0.353148i	$0.885111\pi$
$840$	0	0
$841$	3.85439e8	0.647989
$842$	− 1.55715e8i	− 0.260853i
$843$	0	0
$844$	−4.41425e8	−0.734226
$845$	− 2.60062e8i	− 0.431029i
$846$	0	0
$847$	−3.21451e9	−5.29010
$848$	6.07568e6i	0.00996339i
$849$	0	0
$850$	1.79039e8	0.291535
$851$	1.03286e8i	0.167592i
$852$	0	0
$853$	−4.65353e7	−0.0749782	−0.0374891	−	0.999297i	$-0.511936\pi$
$853$	−4.65353e7	−0.0749782	−0.0374891	+	0.999297i	$0.511936\pi$
$854$	− 2.07383e8i	− 0.332965i
$855$	0	0
$856$	−1.79483e8	−0.286156
$857$	4.52688e8i	0.719211i	0.933104	+	0.359606i	$0.117089\pi$
$857$	4.52688e8i	0.719211i	−0.933104	+	0.359606i	$0.882911\pi$
$858$	0	0
$859$	1.55301e8	0.245015	0.122508	−	0.992468i	$-0.460906\pi$
$859$	1.55301e8	0.245015	0.122508	+	0.992468i	$0.460906\pi$
$860$	− 2.71270e8i	− 0.426487i
$861$	0	0
$862$	7.71060e8	1.20383
$863$	− 3.43497e7i	− 0.0534430i	−0.999643	−	0.0267215i	$-0.991493\pi$
$863$	− 3.43497e7i	− 0.0534430i	0.999643	−	0.0267215i	$-0.00850672\pi$
$864$	0	0
$865$	−6.41796e8	−0.991628
$866$	6.00493e8i	0.924601i
$867$	0	0
$868$	9.55423e8	1.46095
$869$	4.42508e8i	0.674314i
$870$	0	0
$871$	3.95686e8	0.598819
$872$	3.63993e8i	0.548963i
$873$	0	0
$874$	1.14841e8	0.172013
$875$	7.91825e8i	1.18197i
$876$	0	0
$877$	4.99097e8	0.739922	0.369961	−	0.929047i	$-0.379371\pi$
$877$	4.99097e8	0.739922	0.369961	+	0.929047i	$0.379371\pi$
$878$	− 3.57114e8i	− 0.527623i
$879$	0	0
$880$	−4.02525e8	−0.590669
$881$	9.97853e8i	1.45928i	0.683831	+	0.729640i	$0.260312\pi$
$881$	9.97853e8i	1.45928i	−0.683831	+	0.729640i	$0.739688\pi$
$882$	0	0
$883$	5.39800e8	0.784062	0.392031	−	0.919952i	$-0.371773\pi$
$883$	5.39800e8	0.784062	0.392031	+	0.919952i	$0.371773\pi$
$884$	− 2.25370e8i	− 0.326242i
$885$	0	0
$886$	−2.68587e8	−0.386174
$887$	− 1.81280e8i	− 0.259764i	−0.991529	−	0.129882i	$-0.958540\pi$
$887$	− 1.81280e8i	− 0.259764i	0.991529	−	0.129882i	$-0.0414598\pi$
$888$	0	0
$889$	−5.81168e8	−0.827173
$890$	6.95144e8i	0.986063i
$891$	0	0
$892$	1.62317e7	0.0228701
$893$	− 9.26799e8i	− 1.30146i
$894$	0	0
$895$	−8.32770e8	−1.16160
$896$	1.24615e8i	0.173239i
$897$	0	0
$898$	6.28707e8	0.868200
$899$	− 6.42647e8i	− 0.884492i
$900$	0	0
$901$	2.36073e7	0.0322754
$902$	2.36297e8i	0.321987i
$903$	0	0
$904$	−4.97916e7	−0.0673985
$905$	7.46309e8i	1.00687i
$906$	0	0
$907$	1.02564e9	1.37458	0.687292	−	0.726381i	$-0.258799\pi$
$907$	1.02564e9	1.37458	0.687292	+	0.726381i	$0.258799\pi$
$908$	− 6.45438e8i	− 0.862178i
$909$	0	0
$910$	−1.03368e9	−1.37170
$911$	9.19267e8i	1.21587i	0.793987	+	0.607934i	$0.208002\pi$
$911$	9.19267e8i	1.21587i	−0.793987	+	0.607934i	$0.791998\pi$
$912$	0	0
$913$	3.75382e7	0.0493243
$914$	4.98489e8i	0.652856i
$915$	0	0
$916$	1.15167e8	0.149845
$917$	− 8.06410e8i	− 1.04580i
$918$	0	0
$919$	1.20573e9	1.55347	0.776737	−	0.629826i	$-0.216874\pi$
$919$	1.20573e9	1.55347	0.776737	+	0.629826i	$0.216874\pi$
$920$	7.26489e7i	0.0932965i
$921$	0	0
$922$	7.91821e8	1.01026
$923$	− 1.28182e8i	− 0.163013i
$924$	0	0
$925$	3.14361e8	0.397194
$926$	− 7.42275e8i	− 0.934829i
$927$	0	0
$928$	8.38199e7	0.104882
$929$	− 1.02285e8i	− 0.127574i	−0.997964	−	0.0637872i	$-0.979682\pi$
$929$	− 1.02285e8i	− 0.127574i	0.997964	−	0.0637872i	$-0.0203179\pi$
$930$	0	0
$931$	−2.59671e9	−3.21791
$932$	1.34590e8i	0.166251i
$933$	0	0
$934$	−4.70781e8	−0.577801
$935$	1.56403e9i	1.91341i
$936$	0	0
$937$	4.70010e8	0.571332	0.285666	−	0.958329i	$-0.407785\pi$
$937$	4.70010e8	0.571332	0.285666	+	0.958329i	$0.407785\pi$
$938$	8.50109e8i	1.03007i
$939$	0	0
$940$	5.86298e8	0.705886
$941$	− 8.91011e8i	− 1.06934i	−0.845062	−	0.534668i	$-0.820437\pi$
$941$	− 8.91011e8i	− 1.06934i	0.845062	−	0.534668i	$-0.179563\pi$
$942$	0	0
$943$	4.26475e7	0.0508579
$944$	− 7.60776e6i	− 0.00904359i
$945$	0	0
$946$	7.99432e8	0.944296
$947$	8.94200e8i	1.05289i	0.850208	+	0.526447i	$0.176476\pi$
$947$	8.94200e8i	1.05289i	−0.850208	+	0.526447i	$0.823524\pi$
$948$	0	0
$949$	5.61191e8	0.656617
$950$	− 3.49528e8i	− 0.407672i
$951$	0	0
$952$	4.84196e8	0.561191
$953$	1.03289e9i	1.19337i	0.802476	+	0.596684i	$0.203516\pi$
$953$	1.03289e9i	1.19337i	−0.802476	+	0.596684i	$0.796484\pi$
$954$	0	0
$955$	4.88366e8	0.560707
$956$	5.40913e8i	0.619090i
$957$	0	0
$958$	−8.40018e8	−0.955415
$959$	− 1.68354e9i	− 1.90883i
$960$	0	0
$961$	1.08493e9	1.22245
$962$	− 3.95711e8i	− 0.444480i
$963$	0	0
$964$	−6.91332e8	−0.771712
$965$	− 1.02682e9i	− 1.14265i
$966$	0	0
$967$	3.08670e8	0.341362	0.170681	−	0.985326i	$-0.445403\pi$
$967$	3.08670e8	0.341362	0.170681	+	0.985326i	$0.445403\pi$
$968$	− 8.65554e8i	− 0.954263i
$969$	0	0
$970$	−1.45799e8	−0.159749
$971$	2.10002e8i	0.229386i	0.993401	+	0.114693i	$0.0365884\pi$
$971$	2.10002e8i	0.229386i	−0.993401	+	0.114693i	$0.963412\pi$
$972$	0	0
$973$	−1.44233e9	−1.56576
$974$	− 5.82529e8i	− 0.630436i
$975$	0	0
$976$	5.58409e7	0.0600624
$977$	1.32934e9i	1.42545i	0.701443	+	0.712725i	$0.252539\pi$
$977$	1.32934e9i	1.42545i	−0.701443	+	0.712725i	$0.747461\pi$
$978$	0	0
$979$	−2.04859e9	−2.18327
$980$	− 1.64269e9i	− 1.74533i
$981$	0	0
$982$	7.39175e8	0.780572
$983$	− 1.30790e9i	− 1.37694i	−0.725266	−	0.688469i	$-0.758283\pi$
$983$	− 1.30790e9i	− 1.37694i	0.725266	−	0.688469i	$-0.241717\pi$
$984$	0	0
$985$	2.37644e8	0.248667
$986$	− 3.25685e8i	− 0.339756i
$987$	0	0
$988$	−4.39978e8	−0.456206
$989$	− 1.44284e8i	− 0.149152i
$990$	0	0
$991$	−6.02119e8	−0.618673	−0.309337	−	0.950953i	$-0.600107\pi$
$991$	−6.02119e8	−0.618673	−0.309337	+	0.950953i	$0.600107\pi$
$992$	2.57262e8i	0.263536i
$993$	0	0
$994$	2.75393e8	0.280410
$995$	1.66382e9i	1.68903i
$996$	0	0
$997$	8.17590e8	0.824992	0.412496	−	0.910959i	$-0.364657\pi$
$997$	8.17590e8	0.824992	0.412496	+	0.910959i	$0.364657\pi$
$998$	− 8.38888e8i	− 0.843942i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.7.b.b.161.4	✓	8
3.2	odd	2	inner	162.7.b.b.161.5	yes	8
9.2	odd	6		162.7.d.g.53.8		16
9.4	even	3		162.7.d.g.107.8		16
9.5	odd	6		162.7.d.g.107.1		16
9.7	even	3		162.7.d.g.53.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.7.b.b.161.4	✓	8	1.1	even	1	trivial
162.7.b.b.161.5	yes	8	3.2	odd	2	inner
162.7.d.g.53.1		16	9.7	even	3
162.7.d.g.53.8		16	9.2	odd	6
162.7.d.g.107.1		16	9.5	odd	6
162.7.d.g.107.8		16	9.4	even	3

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	162.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.65685i q^{2} -32.0000 q^{4} +153.557i q^{5} +672.272 q^{7} +181.019i q^{8} +O(q^{10})\)	\(q-5.65685i q^{2} -32.0000 q^{4} +153.557i q^{5} +672.272 q^{7} +181.019i q^{8} +868.648 q^{10} +2559.91i q^{11} -1770.09 q^{13} -3802.95i q^{14} +1024.00 q^{16} -3978.79i q^{17} -7767.58 q^{19} -4913.81i q^{20} +14481.0 q^{22} -2613.58i q^{23} -7954.65 q^{25} +10013.1i q^{26} -21512.7 q^{28} +14470.1i q^{29} -44412.0 q^{31} -5792.62i q^{32} -22507.4 q^{34} +103232. i q^{35} -39519.1 q^{37} +43940.1i q^{38} -27796.7 q^{40} +16317.7i q^{41} +55205.5 q^{43} -81917.0i q^{44} -14784.6 q^{46} +119316. i q^{47} +334301. q^{49} +44998.3i q^{50} +56642.9 q^{52} +5933.28i q^{53} -393091. q^{55} +121694. i q^{56} +81855.3 q^{58} -7429.46i q^{59} +54532.1 q^{61} +251232. i q^{62} -32768.0 q^{64} -271809. i q^{65} -223540. q^{67} +127321. i q^{68} +583968. q^{70} +72415.7i q^{71} -317041. q^{73} +223554. i q^{74} +248563. q^{76} +1.72095e6i q^{77} +172861. q^{79} +157242. i q^{80} +92306.7 q^{82} -14663.9i q^{83} +610970. q^{85} -312290. i q^{86} -463392. q^{88} +800260. i q^{89} -1.18998e6 q^{91} +83634.4i q^{92} +674955. q^{94} -1.19276e6i q^{95} -167846. q^{97} -1.89109e6i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 256 q^{4} + 964 q^{7}+O(q^{10}) \) 8 * q - 256 * q^4 + 964 * q^7	\( 8 q - 256 q^{4} + 964 q^{7} - 768 q^{10} + 4540 q^{13} + 8192 q^{16} - 23684 q^{19} + 27072 q^{22} - 32392 q^{25} - 30848 q^{28} + 77056 q^{31} - 52608 q^{34} - 11348 q^{37} + 24576 q^{40} - 226604 q^{43} - 162720 q^{46} + 1298088 q^{49} - 145280 q^{52} - 1460916 q^{55} + 867456 q^{58} - 327476 q^{61} - 262144 q^{64} + 1713292 q^{67} - 176352 q^{70} - 2189216 q^{73} + 757888 q^{76} - 1326884 q^{79} - 1158816 q^{82} + 3483180 q^{85} - 866304 q^{88} + 1130324 q^{91} - 26400 q^{94} - 2200064 q^{97}+O(q^{100}) \) 8 * q - 256 * q^4 + 964 * q^7 - 768 * q^10 + 4540 * q^13 + 8192 * q^16 - 23684 * q^19 + 27072 * q^22 - 32392 * q^25 - 30848 * q^28 + 77056 * q^31 - 52608 * q^34 - 11348 * q^37 + 24576 * q^40 - 226604 * q^43 - 162720 * q^46 + 1298088 * q^49 - 145280 * q^52 - 1460916 * q^55 + 867456 * q^58 - 327476 * q^61 - 262144 * q^64 + 1713292 * q^67 - 176352 * q^70 - 2189216 * q^73 + 757888 * q^76 - 1326884 * q^79 - 1158816 * q^82 + 3483180 * q^85 - 866304 * q^88 + 1130324 * q^91 - 26400 * q^94 - 2200064 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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