LMFDB - Embedded newform 162.9.b.a.161.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,9,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, 9, names="a")

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

chi := DirichletCharacter("162.161");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 9 $
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:	$65.9953348299$
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} + 3364x^{6} + 4188433x^{4} + 2287495488x^{2} + 462682923264 $ x^8 + 3364x^6 + 4188433x^4 + 2287495488*x^2 + 462682923264
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			161.1
Root			$-32.5932i$ of defining polynomial
Character	$\chi$	$=$	162.161
Dual form			162.9.b.a.161.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-11.3137i q^{2} -128.000 q^{4} -724.855i q^{5} -1954.36 q^{7} +1448.15i q^{8} +O(q^{10})$	\(q-11.3137i q^{2} -128.000 q^{4} -724.855i q^{5} -1954.36 q^{7} +1448.15i q^{8} -8200.80 q^{10} -25108.4i q^{11} -6033.17 q^{13} +22111.1i q^{14} +16384.0 q^{16} -146810. i q^{17} -59531.5 q^{19} +92781.5i q^{20} -284069. q^{22} +168478. i q^{23} -134790. q^{25} +68257.5i q^{26} +250158. q^{28} -876106. i q^{29} -714041. q^{31} -185364. i q^{32} -1.66096e6 q^{34} +1.41663e6i q^{35} -534900. q^{37} +673522. i q^{38} +1.04970e6 q^{40} -1.96481e6i q^{41} +6.10848e6 q^{43} +3.21388e6i q^{44} +1.90611e6 q^{46} -2.83764e6i q^{47} -1.94527e6 q^{49} +1.52498e6i q^{50} +772246. q^{52} +9.99763e6i q^{53} -1.82000e7 q^{55} -2.83022e6i q^{56} -9.91201e6 q^{58} +4.50322e6i q^{59} -1.83395e7 q^{61} +8.07845e6i q^{62} -2.09715e6 q^{64} +4.37318e6i q^{65} -2.60895e7 q^{67} +1.87917e7i q^{68} +1.60273e7 q^{70} -2.94857e6i q^{71} +2.60882e7 q^{73} +6.05170e6i q^{74} +7.62003e6 q^{76} +4.90709e7i q^{77} +6.66226e7 q^{79} -1.18760e7i q^{80} -2.22292e7 q^{82} +4.64347e7i q^{83} -1.06416e8 q^{85} -6.91095e7i q^{86} +3.63609e7 q^{88} +9.06184e7i q^{89} +1.17910e7 q^{91} -2.15651e7i q^{92} -3.21043e7 q^{94} +4.31517e7i q^{95} +1.49962e8 q^{97} +2.20083e7i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 1024 q^{4} - 8876 q^{7}+O(q^{10}) $ 8 * q - 1024 * q^4 - 8876 * q^7	$ 8 q - 1024 q^{4} - 8876 q^{7} + 8448 q^{10} - 117380 q^{13} + 131072 q^{16} + 270220 q^{19} - 210816 q^{22} - 1801672 q^{25} + 1136128 q^{28} - 393344 q^{31} - 691968 q^{34} + 1830988 q^{37} - 1081344 q^{40} + 11135236 q^{43} + 5296320 q^{46} - 13586328 q^{49} + 15024640 q^{52} - 1579716 q^{55} - 32988672 q^{58} + 12184204 q^{61} - 16777216 q^{64} - 80355716 q^{67} - 18723264 q^{70} + 197085760 q^{73} - 34588160 q^{76} + 84451852 q^{79} + 144639168 q^{82} - 582634548 q^{85} + 26984448 q^{88} + 373079588 q^{91} - 210121536 q^{94} + 341136928 q^{97}+O(q^{100}) $ 8 * q - 1024 * q^4 - 8876 * q^7 + 8448 * q^10 - 117380 * q^13 + 131072 * q^16 + 270220 * q^19 - 210816 * q^22 - 1801672 * q^25 + 1136128 * q^28 - 393344 * q^31 - 691968 * q^34 + 1830988 * q^37 - 1081344 * q^40 + 11135236 * q^43 + 5296320 * q^46 - 13586328 * q^49 + 15024640 * q^52 - 1579716 * q^55 - 32988672 * q^58 + 12184204 * q^61 - 16777216 * q^64 - 80355716 * q^67 - 18723264 * q^70 + 197085760 * q^73 - 34588160 * q^76 + 84451852 * q^79 + 144639168 * q^82 - 582634548 * q^85 + 26984448 * q^88 + 373079588 * q^91 - 210121536 * q^94 + 341136928 * 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 $

$2$	− 11.3137i	− 0.707107i
$2$	− 11.3137i	− 0.707107i
$3$	0	0
$3$	0	0
$4$	−128.000	−0.500000
$5$	− 724.855i	− 1.15977i	−0.814699	−	0.579884i	$-0.803098\pi$
$5$	− 724.855i	− 1.15977i	0.814699	−	0.579884i	$-0.196902\pi$
$6$	0	0
$7$	−1954.36	−0.813978	−0.406989	−	0.913433i	$-0.633421\pi$
$7$	−1954.36	−0.813978	−0.406989	+	0.913433i	$0.633421\pi$
$8$	1448.15i	0.353553i
$9$	0	0
$10$	−8200.80	−0.820080
$11$	− 25108.4i	− 1.71494i	−0.514535	−	0.857469i	$-0.672035\pi$
$11$	− 25108.4i	− 1.71494i	0.514535	−	0.857469i	$-0.327965\pi$
$12$	0	0
$13$	−6033.17	−0.211238	−0.105619	−	0.994407i	$-0.533682\pi$
$13$	−6033.17	−0.211238	−0.105619	+	0.994407i	$0.533682\pi$
$14$	22111.1i	0.575569i
$15$	0	0
$16$	16384.0	0.250000
$17$	− 146810.i	− 1.75776i	−0.477043	−	0.878880i	$-0.658292\pi$
$17$	− 146810.i	− 1.75776i	0.477043	−	0.878880i	$-0.341708\pi$
$18$	0	0
$19$	−59531.5	−0.456807	−0.228403	−	0.973567i	$-0.573350\pi$
$19$	−59531.5	−0.456807	−0.228403	+	0.973567i	$0.573350\pi$
$20$	92781.5i	0.579884i
$21$	0	0
$22$	−284069.	−1.21264
$23$	168478.i	0.602048i	0.953617	+	0.301024i	$0.0973284\pi$
$23$	168478.i	0.602048i	−0.953617	+	0.301024i	$0.902672\pi$
$24$	0	0
$25$	−134790.	−0.345063
$26$	68257.5i	0.149368i
$27$	0	0
$28$	250158.	0.406989
$29$	− 876106.i	− 1.23870i	−0.785117	−	0.619348i	$-0.787397\pi$
$29$	− 876106.i	− 1.23870i	0.785117	−	0.619348i	$-0.212603\pi$
$30$	0	0
$31$	−714041.	−0.773172	−0.386586	−	0.922253i	$-0.626346\pi$
$31$	−714041.	−0.773172	−0.386586	+	0.922253i	$0.626346\pi$
$32$	− 185364.i	− 0.176777i
$33$	0	0
$34$	−1.66096e6	−1.24292
$35$	1.41663e6i	0.944026i
$36$	0	0
$37$	−534900.	−0.285408	−0.142704	−	0.989765i	$-0.545580\pi$
$37$	−534900.	−0.285408	−0.142704	+	0.989765i	$0.545580\pi$
$38$	673522.i	0.323011i
$39$	0	0
$40$	1.04970e6	0.410040
$41$	− 1.96481e6i	− 0.695319i	−0.937621	−	0.347660i	$-0.886977\pi$
$41$	− 1.96481e6i	− 0.695319i	0.937621	−	0.347660i	$-0.113023\pi$
$42$	0	0
$43$	6.10848e6	1.78673	0.893365	−	0.449331i	$-0.148338\pi$
$43$	6.10848e6	1.78673	0.893365	+	0.449331i	$0.148338\pi$
$44$	3.21388e6i	0.857469i
$45$	0	0
$46$	1.90611e6	0.425712
$47$	− 2.83764e6i	− 0.581522i	−0.956796	−	0.290761i	$-0.906091\pi$
$47$	− 2.83764e6i	− 0.581522i	0.956796	−	0.290761i	$-0.0939085\pi$
$48$	0	0
$49$	−1.94527e6	−0.337440
$50$	1.52498e6i	0.243997i
$51$	0	0
$52$	772246.	0.105619
$53$	9.99763e6i	1.26705i	0.773722	+	0.633525i	$0.218392\pi$
$53$	9.99763e6i	1.26705i	−0.773722	+	0.633525i	$0.781608\pi$
$54$	0	0
$55$	−1.82000e7	−1.98893
$56$	− 2.83022e6i	− 0.287785i
$57$	0	0
$58$	−9.91201e6	−0.875890
$59$	4.50322e6i	0.371634i	0.982584	+	0.185817i	$0.0594932\pi$
$59$	4.50322e6i	0.371634i	−0.982584	+	0.185817i	$0.940507\pi$
$60$	0	0
$61$	−1.83395e7	−1.32455	−0.662276	−	0.749260i	$-0.730409\pi$
$61$	−1.83395e7	−1.32455	−0.662276	+	0.749260i	$0.730409\pi$
$62$	8.07845e6i	0.546715i
$63$	0	0
$64$	−2.09715e6	−0.125000
$65$	4.37318e6i	0.244987i
$66$	0	0
$67$	−2.60895e7	−1.29469	−0.647345	−	0.762197i	$-0.724121\pi$
$67$	−2.60895e7	−1.29469	−0.647345	+	0.762197i	$0.724121\pi$
$68$	1.87917e7i	0.878880i
$69$	0	0
$70$	1.60273e7	0.667527
$71$	− 2.94857e6i	− 0.116032i	−0.998316	−	0.0580160i	$-0.981523\pi$
$71$	− 2.94857e6i	− 0.116032i	0.998316	−	0.0580160i	$-0.0184775\pi$
$72$	0	0
$73$	2.60882e7	0.918655	0.459328	−	0.888267i	$-0.348090\pi$
$73$	2.60882e7	0.918655	0.459328	+	0.888267i	$0.348090\pi$
$74$	6.05170e6i	0.201814i
$75$	0	0
$76$	7.62003e6	0.228403
$77$	4.90709e7i	1.39592i
$78$	0	0
$79$	6.66226e7	1.71046	0.855230	−	0.518248i	$-0.173416\pi$
$79$	6.66226e7	1.71046	0.855230	+	0.518248i	$0.173416\pi$
$80$	− 1.18760e7i	− 0.289942i
$81$	0	0
$82$	−2.22292e7	−0.491665
$83$	4.64347e7i	0.978431i	0.872163	+	0.489215i	$0.162717\pi$
$83$	4.64347e7i	0.978431i	−0.872163	+	0.489215i	$0.837283\pi$
$84$	0	0
$85$	−1.06416e8	−2.03859
$86$	− 6.91095e7i	− 1.26341i
$87$	0	0
$88$	3.63609e7	0.606322
$89$	9.06184e7i	1.44430i	0.691739	+	0.722148i	$0.256845\pi$
$89$	9.06184e7i	1.44430i	−0.691739	+	0.722148i	$0.743155\pi$
$90$	0	0
$91$	1.17910e7	0.171943
$92$	− 2.15651e7i	− 0.301024i
$93$	0	0
$94$	−3.21043e7	−0.411198
$95$	4.31517e7i	0.529790i
$96$	0	0
$97$	1.49962e8	1.69392	0.846962	−	0.531654i	$-0.178429\pi$
$97$	1.49962e8	1.69392	0.846962	+	0.531654i	$0.178429\pi$
$98$	2.20083e7i	0.238606i
$99$	0	0
$100$	1.72532e7	0.172532
$101$	1.06361e8i	1.02211i	0.859547	+	0.511056i	$0.170746\pi$
$101$	1.06361e8i	1.02211i	−0.859547	+	0.511056i	$0.829254\pi$
$102$	0	0
$103$	8.17182e7	0.726056	0.363028	−	0.931778i	$-0.381743\pi$
$103$	8.17182e7	0.726056	0.363028	+	0.931778i	$0.381743\pi$
$104$	− 8.73696e6i	− 0.0746839i
$105$	0	0
$106$	1.13110e8	0.895939
$107$	− 7.42292e7i	− 0.566291i	−0.959077	−	0.283146i	$-0.908622\pi$
$107$	− 7.42292e7i	− 0.566291i	0.959077	−	0.283146i	$-0.0913779\pi$
$108$	0	0
$109$	7.93457e7	0.562105	0.281052	−	0.959692i	$-0.409317\pi$
$109$	7.93457e7	0.562105	0.281052	+	0.959692i	$0.409317\pi$
$110$	2.05909e8i	1.40639i
$111$	0	0
$112$	−3.20203e7	−0.203494
$113$	1.64898e8i	1.01135i	0.862724	+	0.505674i	$0.168756\pi$
$113$	1.64898e8i	1.01135i	−0.862724	+	0.505674i	$0.831244\pi$
$114$	0	0
$115$	1.22122e8	0.698236
$116$	1.12142e8i	0.619348i
$117$	0	0
$118$	5.09482e7	0.262785
$119$	2.86919e8i	1.43078i
$120$	0	0
$121$	−4.16074e8	−1.94102
$122$	2.07488e8i	0.936599i
$123$	0	0
$124$	9.13972e7	0.386586
$125$	− 1.85443e8i	− 0.759575i
$126$	0	0
$127$	−3.48082e8	−1.33803	−0.669016	−	0.743248i	$-0.733284\pi$
$127$	−3.48082e8	−1.33803	−0.669016	+	0.743248i	$0.733284\pi$
$128$	2.37266e7i	0.0883883i
$129$	0	0
$130$	4.94768e7	0.173232
$131$	5.12466e8i	1.74012i	0.492942	+	0.870062i	$0.335921\pi$
$131$	5.12466e8i	1.74012i	−0.492942	+	0.870062i	$0.664079\pi$
$132$	0	0
$133$	1.16346e8	0.371830
$134$	2.95169e8i	0.915484i
$135$	0	0
$136$	2.12603e8	0.621462
$137$	− 3.56143e8i	− 1.01098i	−0.862833	−	0.505489i	$-0.831312\pi$
$137$	− 3.56143e8i	− 1.01098i	0.862833	−	0.505489i	$-0.168688\pi$
$138$	0	0
$139$	−1.72193e8	−0.461272	−0.230636	−	0.973040i	$-0.574081\pi$
$139$	−1.72193e8	−0.461272	−0.230636	+	0.973040i	$0.574081\pi$
$140$	− 1.81329e8i	− 0.472013i
$141$	0	0
$142$	−3.33593e7	−0.0820471
$143$	1.51483e8i	0.362260i
$144$	0	0
$145$	−6.35050e8	−1.43660
$146$	− 2.95154e8i	− 0.649587i
$147$	0	0
$148$	6.84672e7	0.142704
$149$	− 5.53392e8i	− 1.12276i	−0.827557	−	0.561382i	$-0.810270\pi$
$149$	− 5.53392e8i	− 1.12276i	0.827557	−	0.561382i	$-0.189730\pi$
$150$	0	0
$151$	3.04226e8	0.585179	0.292590	−	0.956238i	$-0.405483\pi$
$151$	3.04226e8	0.585179	0.292590	+	0.956238i	$0.405483\pi$
$152$	− 8.62108e7i	− 0.161505i
$153$	0	0
$154$	5.55174e8	0.987066
$155$	5.17576e8i	0.896701i
$156$	0	0
$157$	−5.60432e8	−0.922411	−0.461205	−	0.887293i	$-0.652583\pi$
$157$	−5.60432e8	−0.922411	−0.461205	+	0.887293i	$0.652583\pi$
$158$	− 7.53748e8i	− 1.20948i
$159$	0	0
$160$	−1.34362e8	−0.205020
$161$	− 3.29266e8i	− 0.490054i
$162$	0	0
$163$	6.12889e8	0.868223	0.434112	−	0.900859i	$-0.357062\pi$
$163$	6.12889e8	0.868223	0.434112	+	0.900859i	$0.357062\pi$
$164$	2.51495e8i	0.347660i
$165$	0	0
$166$	5.25348e8	0.691855
$167$	6.37360e8i	0.819444i	0.912211	+	0.409722i	$0.134374\pi$
$167$	6.37360e8i	0.819444i	−0.912211	+	0.409722i	$0.865626\pi$
$168$	0	0
$169$	−7.79332e8	−0.955378
$170$	1.20396e9i	1.44150i
$171$	0	0
$172$	−7.81885e8	−0.893365
$173$	− 1.75191e9i	− 1.95581i	−0.209051	−	0.977905i	$-0.567038\pi$
$173$	− 1.75191e9i	− 1.95581i	0.209051	−	0.977905i	$-0.432962\pi$
$174$	0	0
$175$	2.63429e8	0.280874
$176$	− 4.11376e8i	− 0.428735i
$177$	0	0
$178$	1.02523e9	1.02127
$179$	7.90306e8i	0.769810i	0.922956	+	0.384905i	$0.125766\pi$
$179$	7.90306e8i	0.769810i	−0.922956	+	0.384905i	$0.874234\pi$
$180$	0	0
$181$	5.85613e8	0.545628	0.272814	−	0.962067i	$-0.412046\pi$
$181$	5.85613e8	0.545628	0.272814	+	0.962067i	$0.412046\pi$
$182$	− 1.33400e8i	− 0.121582i
$183$	0	0
$184$	−2.43982e8	−0.212856
$185$	3.87725e8i	0.331007i
$186$	0	0
$187$	−3.68616e9	−3.01445
$188$	3.63218e8i	0.290761i
$189$	0	0
$190$	4.88206e8	0.374618
$191$	− 1.04588e9i	− 0.785865i	−0.919567	−	0.392933i	$-0.871461\pi$
$191$	− 1.04588e9i	− 0.785865i	0.919567	−	0.392933i	$-0.128539\pi$
$192$	0	0
$193$	5.58989e8	0.402878	0.201439	−	0.979501i	$-0.435438\pi$
$193$	5.58989e8	0.402878	0.201439	+	0.979501i	$0.435438\pi$
$194$	− 1.69662e9i	− 1.19778i
$195$	0	0
$196$	2.48995e8	0.168720
$197$	− 2.83826e9i	− 1.88446i	−0.334963	−	0.942231i	$-0.608724\pi$
$197$	− 2.83826e9i	− 1.88446i	0.334963	−	0.942231i	$-0.391276\pi$
$198$	0	0
$199$	−2.90112e9	−1.84992	−0.924960	−	0.380064i	$-0.875902\pi$
$199$	−2.90112e9	−1.84992	−0.924960	+	0.380064i	$0.875902\pi$
$200$	− 1.95197e8i	− 0.121998i
$201$	0	0
$202$	1.20334e9	0.722743
$203$	1.71223e9i	1.00827i
$204$	0	0
$205$	−1.42420e9	−0.806409
$206$	− 9.24536e8i	− 0.513399i
$207$	0	0
$208$	−9.88475e7	−0.0528095
$209$	1.49474e9i	0.783395i
$210$	0	0
$211$	3.07710e9	1.55243	0.776215	−	0.630468i	$-0.217137\pi$
$211$	3.07710e9	1.55243	0.776215	+	0.630468i	$0.217137\pi$
$212$	− 1.27970e9i	− 0.633525i
$213$	0	0
$214$	−8.39808e8	−0.400428
$215$	− 4.42776e9i	− 2.07219i
$216$	0	0
$217$	1.39549e9	0.629345
$218$	− 8.97694e8i	− 0.397468i
$219$	0	0
$220$	2.32960e9	0.994466
$221$	8.85729e8i	0.371306i
$222$	0	0
$223$	−3.62038e8	−0.146398	−0.0731989	−	0.997317i	$-0.523321\pi$
$223$	−3.62038e8	−0.146398	−0.0731989	+	0.997317i	$0.523321\pi$
$224$	3.62268e8i	0.143892i
$225$	0	0
$226$	1.86560e9	0.715131
$227$	− 8.86169e8i	− 0.333744i	−0.985979	−	0.166872i	$-0.946633\pi$
$227$	− 8.86169e8i	− 0.333744i	0.985979	−	0.166872i	$-0.0533666\pi$
$228$	0	0
$229$	−2.28253e9	−0.829992	−0.414996	−	0.909823i	$-0.636217\pi$
$229$	−2.28253e9	−0.829992	−0.414996	+	0.909823i	$0.636217\pi$
$230$	− 1.38165e9i	− 0.493728i
$231$	0	0
$232$	1.26874e9	0.437945
$233$	− 4.45321e8i	− 0.151095i	−0.997142	−	0.0755473i	$-0.975930\pi$
$233$	− 4.45321e8i	− 0.151095i	0.997142	−	0.0755473i	$-0.0240704\pi$
$234$	0	0
$235$	−2.05688e9	−0.674431
$236$	− 5.76413e8i	− 0.185817i
$237$	0	0
$238$	3.24612e9	1.01171
$239$	− 4.30907e9i	− 1.32066i	−0.750975	−	0.660331i	$-0.770416\pi$
$239$	− 4.30907e9i	− 1.32066i	0.750975	−	0.660331i	$-0.229584\pi$
$240$	0	0
$241$	−2.37226e9	−0.703226	−0.351613	−	0.936146i	$-0.614367\pi$
$241$	−2.37226e9	−0.703226	−0.351613	+	0.936146i	$0.614367\pi$
$242$	4.70734e9i	1.37251i
$243$	0	0
$244$	2.34746e9	0.662276
$245$	1.41004e9i	0.391352i
$246$	0	0
$247$	3.59164e8	0.0964949
$248$	− 1.03404e9i	− 0.273358i
$249$	0	0
$250$	−2.09805e9	−0.537101
$251$	− 2.58894e9i	− 0.652269i	−0.945323	−	0.326135i	$-0.894254\pi$
$251$	− 2.58894e9i	− 0.652269i	0.945323	−	0.326135i	$-0.105746\pi$
$252$	0	0
$253$	4.23021e9	1.03248
$254$	3.93810e9i	0.946132i
$255$	0	0
$256$	2.68435e8	0.0625000
$257$	5.35494e8i	0.122750i	0.998115	+	0.0613751i	$0.0195486\pi$
$257$	5.35494e8i	0.122750i	−0.998115	+	0.0613751i	$0.980451\pi$
$258$	0	0
$259$	1.04539e9	0.232316
$260$	− 5.59767e8i	− 0.122494i
$261$	0	0
$262$	5.79790e9	1.23045
$263$	− 5.55561e9i	− 1.16120i	−0.814188	−	0.580602i	$-0.802817\pi$
$263$	− 5.55561e9i	− 1.16120i	0.814188	−	0.580602i	$-0.197183\pi$
$264$	0	0
$265$	7.24684e9	1.46948
$266$	− 1.31630e9i	− 0.262924i
$267$	0	0
$268$	3.33945e9	0.647345
$269$	− 9.05318e9i	− 1.72899i	−0.502643	−	0.864494i	$-0.667639\pi$
$269$	− 9.05318e9i	− 1.72899i	0.502643	−	0.864494i	$-0.332361\pi$
$270$	0	0
$271$	−1.03696e9	−0.192257	−0.0961287	−	0.995369i	$-0.530646\pi$
$271$	−1.03696e9	−0.192257	−0.0961287	+	0.995369i	$0.530646\pi$
$272$	− 2.40533e9i	− 0.439440i
$273$	0	0
$274$	−4.02929e9	−0.714869
$275$	3.38437e9i	0.591763i
$276$	0	0
$277$	−9.85725e8	−0.167431	−0.0837157	−	0.996490i	$-0.526679\pi$
$277$	−9.85725e8	−0.167431	−0.0837157	+	0.996490i	$0.526679\pi$
$278$	1.94815e9i	0.326169i
$279$	0	0
$280$	−2.05150e9	−0.333764
$281$	3.59070e9i	0.575909i	0.957644	+	0.287955i	$0.0929752\pi$
$281$	3.59070e9i	0.575909i	−0.957644	+	0.287955i	$0.907025\pi$
$282$	0	0
$283$	−5.47939e9	−0.854252	−0.427126	−	0.904192i	$-0.640474\pi$
$283$	−5.47939e9	−0.854252	−0.427126	+	0.904192i	$0.640474\pi$
$284$	3.77417e8i	0.0580160i
$285$	0	0
$286$	1.71384e9	0.256157
$287$	3.83994e9i	0.565974i
$288$	0	0
$289$	−1.45774e10	−2.08972
$290$	7.18477e9i	1.01583i
$291$	0	0
$292$	−3.33929e9	−0.459328
$293$	4.67021e9i	0.633674i	0.948480	+	0.316837i	$0.102621\pi$
$293$	4.67021e9i	0.633674i	−0.948480	+	0.316837i	$0.897379\pi$
$294$	0	0
$295$	3.26419e9	0.431010
$296$	− 7.74618e8i	− 0.100907i
$297$	0	0
$298$	−6.26092e9	−0.793913
$299$	− 1.01645e9i	− 0.127175i
$300$	0	0
$301$	−1.19382e10	−1.45436
$302$	− 3.44193e9i	− 0.413784i
$303$	0	0
$304$	−9.75364e8	−0.114202
$305$	1.32935e10i	1.53617i
$306$	0	0
$307$	6.11231e9	0.688101	0.344050	−	0.938951i	$-0.388201\pi$
$307$	6.11231e9	0.688101	0.344050	+	0.938951i	$0.388201\pi$
$308$	− 6.28108e9i	− 0.697961i
$309$	0	0
$310$	5.85571e9	0.634063
$311$	1.44526e10i	1.54492i	0.635066	+	0.772458i	$0.280973\pi$
$311$	1.44526e10i	1.54492i	−0.635066	+	0.772458i	$0.719027\pi$
$312$	0	0
$313$	3.16546e9	0.329807	0.164903	−	0.986310i	$-0.447269\pi$
$313$	3.16546e9	0.329807	0.164903	+	0.986310i	$0.447269\pi$
$314$	6.34057e9i	0.652243i
$315$	0	0
$316$	−8.52769e9	−0.855230
$317$	− 3.73711e9i	− 0.370083i	−0.982731	−	0.185041i	$-0.940758\pi$
$317$	− 3.73711e9i	− 0.370083i	0.982731	−	0.185041i	$-0.0592419\pi$
$318$	0	0
$319$	−2.19976e10	−2.12429
$320$	1.52013e9i	0.144971i
$321$	0	0
$322$	−3.72522e9	−0.346520
$323$	8.73981e9i	0.802956i
$324$	0	0
$325$	8.13213e8	0.0728905
$326$	− 6.93405e9i	− 0.613927i
$327$	0	0
$328$	2.84534e9	0.245832
$329$	5.54578e9i	0.473346i
$330$	0	0
$331$	7.57421e9	0.630994	0.315497	−	0.948927i	$-0.397829\pi$
$331$	7.57421e9	0.630994	0.315497	+	0.948927i	$0.397829\pi$
$332$	− 5.94364e9i	− 0.489215i
$333$	0	0
$334$	7.21091e9	0.579434
$335$	1.89111e10i	1.50154i
$336$	0	0
$337$	1.76446e10	1.36802	0.684010	−	0.729472i	$-0.260234\pi$
$337$	1.76446e10	1.36802	0.684010	+	0.729472i	$0.260234\pi$
$338$	8.81713e9i	0.675555i
$339$	0	0
$340$	1.36212e10	1.01930
$341$	1.79284e10i	1.32594i
$342$	0	0
$343$	1.50683e10	1.08865
$344$	8.84602e9i	0.631705i
$345$	0	0
$346$	−1.98206e10	−1.38297
$347$	− 1.59804e10i	− 1.10223i	−0.834430	−	0.551113i	$-0.814203\pi$
$347$	− 1.59804e10i	− 1.10223i	0.834430	−	0.551113i	$-0.185797\pi$
$348$	0	0
$349$	8.15215e9	0.549503	0.274752	−	0.961515i	$-0.411404\pi$
$349$	8.15215e9	0.549503	0.274752	+	0.961515i	$0.411404\pi$
$350$	− 2.98036e9i	− 0.198608i
$351$	0	0
$352$	−4.65419e9	−0.303161
$353$	1.49531e10i	0.963012i	0.876443	+	0.481506i	$0.159910\pi$
$353$	1.49531e10i	0.963012i	−0.876443	+	0.481506i	$0.840090\pi$
$354$	0	0
$355$	−2.13729e9	−0.134570
$356$	− 1.15992e10i	− 0.722148i
$357$	0	0
$358$	8.94130e9	0.544338
$359$	1.47438e10i	0.887627i	0.896119	+	0.443814i	$0.146375\pi$
$359$	1.47438e10i	0.887627i	−0.896119	+	0.443814i	$0.853625\pi$
$360$	0	0
$361$	−1.34396e10	−0.791328
$362$	− 6.62545e9i	− 0.385817i
$363$	0	0
$364$	−1.50925e9	−0.0859716
$365$	− 1.89102e10i	− 1.06543i
$366$	0	0
$367$	3.56912e9	0.196742	0.0983709	−	0.995150i	$-0.468637\pi$
$367$	3.56912e9	0.196742	0.0983709	+	0.995150i	$0.468637\pi$
$368$	2.76034e9i	0.150512i
$369$	0	0
$370$	4.38661e9	0.234057
$371$	− 1.95390e10i	− 1.03135i
$372$	0	0
$373$	−3.48963e10	−1.80279	−0.901393	−	0.433001i	$-0.857455\pi$
$373$	−3.48963e10	−1.80279	−0.901393	+	0.433001i	$0.857455\pi$
$374$	4.17042e10i	2.13154i
$375$	0	0
$376$	4.10935e9	0.205599
$377$	5.28570e9i	0.261660i
$378$	0	0
$379$	1.86839e10	0.905548	0.452774	−	0.891625i	$-0.350434\pi$
$379$	1.86839e10	0.905548	0.452774	+	0.891625i	$0.350434\pi$
$380$	− 5.52342e9i	− 0.264895i
$381$	0	0
$382$	−1.18328e10	−0.555690
$383$	2.81144e9i	0.130657i	0.997864	+	0.0653286i	$0.0208096\pi$
$383$	2.81144e9i	0.130657i	−0.997864	+	0.0653286i	$0.979190\pi$
$384$	0	0
$385$	3.55693e10	1.61895
$386$	− 6.32424e9i	− 0.284878i
$387$	0	0
$388$	−1.91951e10	−0.846962
$389$	1.92834e9i	0.0842140i	0.999113	+	0.0421070i	$0.0134070\pi$
$389$	1.92834e9i	0.0842140i	−0.999113	+	0.0421070i	$0.986593\pi$
$390$	0	0
$391$	2.47342e10	1.05826
$392$	− 2.81706e9i	− 0.119303i
$393$	0	0
$394$	−3.21113e10	−1.33252
$395$	− 4.82917e10i	− 1.98374i
$396$	0	0
$397$	−2.60079e10	−1.04699	−0.523495	−	0.852029i	$-0.675372\pi$
$397$	−2.60079e10	−1.04699	−0.523495	+	0.852029i	$0.675372\pi$
$398$	3.28224e10i	1.30809i
$399$	0	0
$400$	−2.20841e9	−0.0862658
$401$	2.67223e9i	0.103347i	0.998664	+	0.0516734i	$0.0164555\pi$
$401$	2.67223e9i	0.103347i	−0.998664	+	0.0516734i	$0.983545\pi$
$402$	0	0
$403$	4.30793e9	0.163323
$404$	− 1.36143e10i	− 0.511056i
$405$	0	0
$406$	1.93716e10	0.712955
$407$	1.34305e10i	0.489457i
$408$	0	0
$409$	1.67495e10	0.598560	0.299280	−	0.954165i	$-0.403253\pi$
$409$	1.67495e10	0.598560	0.299280	+	0.954165i	$0.403253\pi$
$410$	1.61130e10i	0.570217i
$411$	0	0
$412$	−1.04599e10	−0.363028
$413$	− 8.80093e9i	− 0.302502i
$414$	0	0
$415$	3.36584e10	1.13475
$416$	1.11833e9i	0.0373420i
$417$	0	0
$418$	1.69111e10	0.553944
$419$	− 1.09485e10i	− 0.355221i	−0.984101	−	0.177611i	$-0.943163\pi$
$419$	− 1.09485e10i	− 0.355221i	0.984101	−	0.177611i	$-0.0568367\pi$
$420$	0	0
$421$	−1.14603e10	−0.364812	−0.182406	−	0.983223i	$-0.558389\pi$
$421$	−1.14603e10	−0.364812	−0.182406	+	0.983223i	$0.558389\pi$
$422$	− 3.48134e10i	− 1.09773i
$423$	0	0
$424$	−1.44781e10	−0.447970
$425$	1.97886e10i	0.606538i
$426$	0	0
$427$	3.58421e10	1.07816
$428$	9.50134e9i	0.283146i
$429$	0	0
$430$	−5.00944e10	−1.46526
$431$	1.09427e10i	0.317114i	0.987350	+	0.158557i	$0.0506841\pi$
$431$	1.09427e10i	0.317114i	−0.987350	+	0.158557i	$0.949316\pi$
$432$	0	0
$433$	3.11908e10	0.887308	0.443654	−	0.896198i	$-0.353682\pi$
$433$	3.11908e10	0.887308	0.443654	+	0.896198i	$0.353682\pi$
$434$	− 1.57882e10i	− 0.445014i
$435$	0	0
$436$	−1.01562e10	−0.281052
$437$	− 1.00297e10i	− 0.275019i
$438$	0	0
$439$	4.30604e10	1.15937	0.579683	−	0.814842i	$-0.303177\pi$
$439$	4.30604e10	1.15937	0.579683	+	0.814842i	$0.303177\pi$
$440$	− 2.63564e10i	− 0.703194i
$441$	0	0
$442$	1.00209e10	0.262553
$443$	− 2.65467e10i	− 0.689279i	−0.938735	−	0.344640i	$-0.888001\pi$
$443$	− 2.65467e10i	− 0.689279i	0.938735	−	0.344640i	$-0.111999\pi$
$444$	0	0
$445$	6.56852e10	1.67505
$446$	4.09599e9i	0.103519i
$447$	0	0
$448$	4.09859e9	0.101747
$449$	7.44995e10i	1.83302i	0.400008	+	0.916512i	$0.369007\pi$
$449$	7.44995e10i	1.83302i	−0.400008	+	0.916512i	$0.630993\pi$
$450$	0	0
$451$	−4.93332e10	−1.19243
$452$	− 2.11069e10i	− 0.505674i
$453$	0	0
$454$	−1.00259e10	−0.235992
$455$	− 8.54677e9i	− 0.199414i
$456$	0	0
$457$	−8.22913e10	−1.88664	−0.943320	−	0.331885i	$-0.892315\pi$
$457$	−8.22913e10	−1.88664	−0.943320	+	0.331885i	$0.892315\pi$
$458$	2.58238e10i	0.586893i
$459$	0	0
$460$	−1.56316e10	−0.349118
$461$	− 1.07428e10i	− 0.237856i	−0.992903	−	0.118928i	$-0.962054\pi$
$461$	− 1.07428e10i	− 0.237856i	0.992903	−	0.118928i	$-0.0379458\pi$
$462$	0	0
$463$	1.01613e10	0.221118	0.110559	−	0.993870i	$-0.464736\pi$
$463$	1.01613e10	0.221118	0.110559	+	0.993870i	$0.464736\pi$
$464$	− 1.43541e10i	− 0.309674i
$465$	0	0
$466$	−5.03823e9	−0.106840
$467$	1.27531e10i	0.268131i	0.990972	+	0.134066i	$0.0428033\pi$
$467$	1.27531e10i	0.268131i	−0.990972	+	0.134066i	$0.957197\pi$
$468$	0	0
$469$	5.09882e10	1.05385
$470$	2.32710e10i	0.476895i
$471$	0	0
$472$	−6.52137e9	−0.131393
$473$	− 1.53374e11i	− 3.06413i
$474$	0	0
$475$	8.02427e9	0.157627
$476$	− 3.67257e10i	− 0.715389i
$477$	0	0
$478$	−4.87515e10	−0.933849
$479$	− 6.12176e10i	− 1.16288i	−0.813590	−	0.581439i	$-0.802490\pi$
$479$	− 6.12176e10i	− 1.16288i	0.813590	−	0.581439i	$-0.197510\pi$
$480$	0	0
$481$	3.22714e9	0.0602890
$482$	2.68391e10i	0.497256i
$483$	0	0
$484$	5.32575e10	0.970508
$485$	− 1.08701e11i	− 1.96456i
$486$	0	0
$487$	4.91420e9	0.0873649	0.0436824	−	0.999045i	$-0.486091\pi$
$487$	4.91420e9	0.0873649	0.0436824	+	0.999045i	$0.486091\pi$
$488$	− 2.65585e10i	− 0.468300i
$489$	0	0
$490$	1.59528e10	0.276728
$491$	− 6.49799e10i	− 1.11803i	−0.829158	−	0.559015i	$-0.811179\pi$
$491$	− 6.49799e10i	− 1.11803i	0.829158	−	0.559015i	$-0.188821\pi$
$492$	0	0
$493$	−1.28621e11	−2.17733
$494$	− 4.06347e9i	− 0.0682322i
$495$	0	0
$496$	−1.16988e10	−0.193293
$497$	5.76257e9i	0.0944476i
$498$	0	0
$499$	1.02300e11	1.64996	0.824982	−	0.565159i	$-0.191185\pi$
$499$	1.02300e11	1.64996	0.824982	+	0.565159i	$0.191185\pi$
$500$	2.37367e10i	0.379787i
$501$	0	0
$502$	−2.92905e10	−0.461224
$503$	7.51856e10i	1.17453i	0.809396	+	0.587263i	$0.199795\pi$
$503$	7.51856e10i	1.17453i	−0.809396	+	0.587263i	$0.800205\pi$
$504$	0	0
$505$	7.70967e10	1.18541
$506$	− 4.78593e10i	− 0.730070i
$507$	0	0
$508$	4.45545e10	0.669016
$509$	6.30144e10i	0.938790i	0.882988	+	0.469395i	$0.155528\pi$
$509$	6.30144e10i	0.938790i	−0.882988	+	0.469395i	$0.844472\pi$
$510$	0	0
$511$	−5.09857e10	−0.747765
$512$	− 3.03700e9i	− 0.0441942i
$513$	0	0
$514$	6.05842e9	0.0867974
$515$	− 5.92339e10i	− 0.842057i
$516$	0	0
$517$	−7.12487e10	−0.997275
$518$	− 1.18272e10i	− 0.164272i
$519$	0	0
$520$	−6.33304e9	−0.0866161
$521$	− 1.57912e10i	− 0.214321i	−0.994242	−	0.107161i	$-0.965824\pi$
$521$	− 1.57912e10i	− 0.214321i	0.994242	−	0.107161i	$-0.0341759\pi$
$522$	0	0
$523$	−3.18186e10	−0.425279	−0.212640	−	0.977131i	$-0.568206\pi$
$523$	−3.18186e10	−0.425279	−0.212640	+	0.977131i	$0.568206\pi$
$524$	− 6.55957e10i	− 0.870062i
$525$	0	0
$526$	−6.28545e10	−0.821095
$527$	1.04828e11i	1.35905i
$528$	0	0
$529$	4.99263e10	0.637538
$530$	− 8.19886e10i	− 1.03908i
$531$	0	0
$532$	−1.48923e10	−0.185915
$533$	1.18540e10i	0.146878i
$534$	0	0
$535$	−5.38054e10	−0.656767
$536$	− 3.77816e10i	− 0.457742i
$537$	0	0
$538$	−1.02425e11	−1.22258
$539$	4.88427e10i	0.578689i
$540$	0	0
$541$	−8.64637e10	−1.00936	−0.504679	−	0.863307i	$-0.668389\pi$
$541$	−8.64637e10	−1.00936	−0.504679	+	0.863307i	$0.668389\pi$
$542$	1.17318e10i	0.135947i
$543$	0	0
$544$	−2.72132e10	−0.310731
$545$	− 5.75141e10i	− 0.651911i
$546$	0	0
$547$	−1.34564e11	−1.50307	−0.751534	−	0.659695i	$-0.770686\pi$
$547$	−1.34564e11	−1.50307	−0.751534	+	0.659695i	$0.770686\pi$
$548$	4.55863e10i	0.505489i
$549$	0	0
$550$	3.82898e10	0.418439
$551$	5.21559e10i	0.565844i
$552$	0	0
$553$	−1.30205e11	−1.39228
$554$	1.11522e10i	0.118392i
$555$	0	0
$556$	2.20408e10	0.230636
$557$	3.61911e10i	0.375994i	0.982170	+	0.187997i	$0.0601995\pi$
$557$	3.61911e10i	0.375994i	−0.982170	+	0.187997i	$0.939800\pi$
$558$	0	0
$559$	−3.68535e10	−0.377425
$560$	2.32101e10i	0.236007i
$561$	0	0
$562$	4.06242e10	0.407229
$563$	1.28121e11i	1.27523i	0.770357	+	0.637613i	$0.220078\pi$
$563$	1.28121e11i	1.27523i	−0.770357	+	0.637613i	$0.779922\pi$
$564$	0	0
$565$	1.19527e11	1.17293
$566$	6.19922e10i	0.604048i
$567$	0	0
$568$	4.26999e9	0.0410235
$569$	− 4.93793e10i	− 0.471081i	−0.971865	−	0.235540i	$-0.924314\pi$
$569$	− 4.93793e10i	− 0.471081i	0.971865	−	0.235540i	$-0.0756860\pi$
$570$	0	0
$571$	1.62562e11	1.52924	0.764620	−	0.644482i	$-0.222927\pi$
$571$	1.62562e11	1.52924	0.764620	+	0.644482i	$0.222927\pi$
$572$	− 1.93899e10i	− 0.181130i
$573$	0	0
$574$	4.34440e10	0.400204
$575$	− 2.27092e10i	− 0.207745i
$576$	0	0
$577$	−6.12916e10	−0.552965	−0.276483	−	0.961019i	$-0.589169\pi$
$577$	−6.12916e10	−0.552965	−0.276483	+	0.961019i	$0.589169\pi$
$578$	1.64924e11i	1.47765i
$579$	0	0
$580$	8.12864e10	0.718300
$581$	− 9.07501e10i	− 0.796421i
$582$	0	0
$583$	2.51025e11	2.17291
$584$	3.77797e10i	0.324794i
$585$	0	0
$586$	5.28374e10	0.448075
$587$	− 4.63088e10i	− 0.390042i	−0.980799	−	0.195021i	$-0.937523\pi$
$587$	− 4.63088e10i	− 0.390042i	0.980799	−	0.195021i	$-0.0624774\pi$
$588$	0	0
$589$	4.25079e10	0.353190
$590$	− 3.69301e10i	− 0.304770i
$591$	0	0
$592$	−8.76380e9	−0.0713519
$593$	− 2.12824e11i	− 1.72108i	−0.509381	−	0.860541i	$-0.670126\pi$
$593$	− 2.12824e11i	− 1.72108i	0.509381	−	0.860541i	$-0.329874\pi$
$594$	0	0
$595$	2.07975e11	1.65937
$596$	7.08342e10i	0.561382i
$597$	0	0
$598$	−1.14999e10	−0.0899266
$599$	5.14803e10i	0.399884i	0.979808	+	0.199942i	$0.0640754\pi$
$599$	5.14803e10i	0.399884i	−0.979808	+	0.199942i	$0.935925\pi$
$600$	0	0
$601$	1.67400e11	1.28309	0.641546	−	0.767084i	$-0.278293\pi$
$601$	1.67400e11	1.28309	0.641546	+	0.767084i	$0.278293\pi$
$602$	1.35065e11i	1.02839i
$603$	0	0
$604$	−3.89410e10	−0.292590
$605$	3.01593e11i	2.25113i
$606$	0	0
$607$	−2.92997e10	−0.215828	−0.107914	−	0.994160i	$-0.534417\pi$
$607$	−2.92997e10	−0.215828	−0.107914	+	0.994160i	$0.534417\pi$
$608$	1.10350e10i	0.0807527i
$609$	0	0
$610$	1.50399e11	1.08624
$611$	1.71200e10i	0.122840i
$612$	0	0
$613$	−1.71922e11	−1.21756	−0.608780	−	0.793339i	$-0.708341\pi$
$613$	−1.71922e11	−1.21756	−0.608780	+	0.793339i	$0.708341\pi$
$614$	− 6.91529e10i	− 0.486561i
$615$	0	0
$616$	−7.10623e10	−0.493533
$617$	− 4.57706e10i	− 0.315825i	−0.987453	−	0.157912i	$-0.949524\pi$
$617$	− 4.57706e10i	− 0.315825i	0.987453	−	0.157912i	$-0.0504764\pi$
$618$	0	0
$619$	−1.69440e11	−1.15412	−0.577062	−	0.816700i	$-0.695801\pi$
$619$	−1.69440e11	−1.15412	−0.577062	+	0.816700i	$0.695801\pi$
$620$	− 6.62498e10i	− 0.448350i
$621$	0	0
$622$	1.63513e11	1.09242
$623$	− 1.77101e11i	− 1.17563i
$624$	0	0
$625$	−1.87072e11	−1.22599
$626$	− 3.58131e10i	− 0.233209i
$627$	0	0
$628$	7.17353e10	0.461205
$629$	7.85286e10i	0.501678i
$630$	0	0
$631$	−1.46027e11	−0.921116	−0.460558	−	0.887630i	$-0.652351\pi$
$631$	−1.46027e11	−0.921116	−0.460558	+	0.887630i	$0.652351\pi$
$632$	9.64798e10i	0.604739i
$633$	0	0
$634$	−4.22806e10	−0.261688
$635$	2.52309e11i	1.55181i
$636$	0	0
$637$	1.17362e10	0.0712801
$638$	2.48875e11i	1.50210i
$639$	0	0
$640$	1.71983e10	0.102510
$641$	1.44147e11i	0.853836i	0.904290	+	0.426918i	$0.140401\pi$
$641$	1.44147e11i	0.853836i	−0.904290	+	0.426918i	$0.859599\pi$
$642$	0	0
$643$	−1.17950e11	−0.690010	−0.345005	−	0.938601i	$-0.612123\pi$
$643$	−1.17950e11	−0.690010	−0.345005	+	0.938601i	$0.612123\pi$
$644$	4.21461e10i	0.245027i
$645$	0	0
$646$	9.88796e10	0.567776
$647$	3.46876e9i	0.0197951i	0.999951	+	0.00989753i	$0.00315053\pi$
$647$	3.46876e9i	0.0197951i	−0.999951	+	0.00989753i	$0.996849\pi$
$648$	0	0
$649$	1.13069e11	0.637330
$650$	− 9.20046e9i	− 0.0515414i
$651$	0	0
$652$	−7.84498e10	−0.434112
$653$	1.66200e11i	0.914065i	0.889450	+	0.457033i	$0.151088\pi$
$653$	1.66200e11i	0.914065i	−0.889450	+	0.457033i	$0.848912\pi$
$654$	0	0
$655$	3.71464e11	2.01814
$656$	− 3.21914e10i	− 0.173830i
$657$	0	0
$658$	6.27433e10	0.334706
$659$	1.81389e11i	0.961765i	0.876785	+	0.480883i	$0.159684\pi$
$659$	1.81389e11i	0.961765i	−0.876785	+	0.480883i	$0.840316\pi$
$660$	0	0
$661$	−2.20363e11	−1.15434	−0.577169	−	0.816625i	$-0.695843\pi$
$661$	−2.20363e11	−1.15434	−0.577169	+	0.816625i	$0.695843\pi$
$662$	− 8.56924e10i	− 0.446180i
$663$	0	0
$664$	−6.72446e10	−0.345928
$665$	− 8.43340e10i	− 0.431237i
$666$	0	0
$667$	1.47604e11	0.745754
$668$	− 8.15821e10i	− 0.409722i
$669$	0	0
$670$	2.13955e11	1.06175
$671$	4.60477e11i	2.27153i
$672$	0	0
$673$	−2.54483e11	−1.24050	−0.620252	−	0.784403i	$-0.712970\pi$
$673$	−2.54483e11	−1.24050	−0.620252	+	0.784403i	$0.712970\pi$
$674$	− 1.99626e11i	− 0.967336i
$675$	0	0
$676$	9.97544e10	0.477689
$677$	1.61144e11i	0.767112i	0.923518	+	0.383556i	$0.125301\pi$
$677$	1.61144e11i	0.767112i	−0.923518	+	0.383556i	$0.874699\pi$
$678$	0	0
$679$	−2.93080e11	−1.37882
$680$	− 1.54107e11i	− 0.720752i
$681$	0	0
$682$	2.02837e11	0.937583
$683$	− 2.49823e11i	− 1.14802i	−0.818848	−	0.574010i	$-0.805387\pi$
$683$	− 2.49823e11i	− 1.14802i	0.818848	−	0.574010i	$-0.194613\pi$
$684$	0	0
$685$	−2.58152e11	−1.17250
$686$	− 1.70478e11i	− 0.769789i
$687$	0	0
$688$	1.00081e11	0.446683
$689$	− 6.03174e10i	− 0.267649i
$690$	0	0
$691$	3.49484e10	0.153291	0.0766453	−	0.997058i	$-0.475579\pi$
$691$	3.49484e10	0.153291	0.0766453	+	0.997058i	$0.475579\pi$
$692$	2.24244e11i	0.977905i
$693$	0	0
$694$	−1.80798e11	−0.779392
$695$	1.24815e11i	0.534969i
$696$	0	0
$697$	−2.88453e11	−1.22220
$698$	− 9.22310e10i	− 0.388557i
$699$	0	0
$700$	−3.37189e10	−0.140437
$701$	− 5.97829e10i	− 0.247574i	−0.992309	−	0.123787i	$-0.960496\pi$
$701$	− 5.97829e10i	− 0.247574i	0.992309	−	0.123787i	$-0.0395040\pi$
$702$	0	0
$703$	3.18434e10	0.130376
$704$	5.26562e10i	0.214367i
$705$	0	0
$706$	1.69175e11	0.680953
$707$	− 2.07869e11i	− 0.831977i
$708$	0	0
$709$	−4.44232e11	−1.75802	−0.879012	−	0.476799i	$-0.841797\pi$
$709$	−4.44232e11	−1.75802	−0.879012	+	0.476799i	$0.841797\pi$
$710$	2.41806e10i	0.0951556i
$711$	0	0
$712$	−1.31229e11	−0.510636
$713$	− 1.20300e11i	− 0.465487i
$714$	0	0
$715$	1.09804e11	0.420138
$716$	− 1.01159e11i	− 0.384905i
$717$	0	0
$718$	1.66807e11	0.627647
$719$	1.62667e11i	0.608674i	0.952564	+	0.304337i	$0.0984349\pi$
$719$	1.62667e11i	0.608674i	−0.952564	+	0.304337i	$0.901565\pi$
$720$	0	0
$721$	−1.59707e11	−0.590993
$722$	1.52051e11i	0.559553i
$723$	0	0
$724$	−7.49584e10	−0.272814
$725$	1.18091e11i	0.427429i
$726$	0	0
$727$	3.60109e11	1.28913	0.644565	−	0.764549i	$-0.277038\pi$
$727$	3.60109e11	1.28913	0.644565	+	0.764549i	$0.277038\pi$
$728$	1.70752e10i	0.0607911i
$729$	0	0
$730$	−2.13944e11	−0.753371
$731$	− 8.96784e11i	− 3.14064i
$732$	0	0
$733$	3.07905e11	1.06660	0.533299	−	0.845927i	$-0.320952\pi$
$733$	3.07905e11	1.06660	0.533299	+	0.845927i	$0.320952\pi$
$734$	− 4.03800e10i	− 0.139117i
$735$	0	0
$736$	3.12297e10	0.106428
$737$	6.55065e11i	2.22032i
$738$	0	0
$739$	1.69448e11	0.568145	0.284072	−	0.958803i	$-0.408314\pi$
$739$	1.69448e11	0.568145	0.284072	+	0.958803i	$0.408314\pi$
$740$	− 4.96288e10i	− 0.165504i
$741$	0	0
$742$	−2.21058e11	−0.729275
$743$	1.84146e11i	0.604236i	0.953270	+	0.302118i	$0.0976937\pi$
$743$	1.84146e11i	0.604236i	−0.953270	+	0.302118i	$0.902306\pi$
$744$	0	0
$745$	−4.01130e11	−1.30215
$746$	3.94807e11i	1.27476i
$747$	0	0
$748$	4.71829e11	1.50723
$749$	1.45071e11i	0.460948i
$750$	0	0
$751$	1.76885e11	0.556072	0.278036	−	0.960571i	$-0.410317\pi$
$751$	1.76885e11	0.556072	0.278036	+	0.960571i	$0.410317\pi$
$752$	− 4.64920e10i	− 0.145381i
$753$	0	0
$754$	5.98008e10	0.185021
$755$	− 2.20520e11i	− 0.678672i
$756$	0	0
$757$	−3.46881e11	−1.05632	−0.528161	−	0.849144i	$-0.677118\pi$
$757$	−3.46881e11	−1.05632	−0.528161	+	0.849144i	$0.677118\pi$
$758$	− 2.11385e11i	− 0.640319i
$759$	0	0
$760$	−6.24904e10	−0.187309
$761$	− 3.66921e11i	− 1.09404i	−0.837119	−	0.547021i	$-0.815762\pi$
$761$	− 3.66921e11i	− 1.09404i	0.837119	−	0.547021i	$-0.184238\pi$
$762$	0	0
$763$	−1.55070e11	−0.457541
$764$	1.33873e11i	0.392933i
$765$	0	0
$766$	3.18078e10	0.0923886
$767$	− 2.71687e10i	− 0.0785033i
$768$	0	0
$769$	3.55240e11	1.01582	0.507910	−	0.861410i	$-0.330418\pi$
$769$	3.55240e11	1.01582	0.507910	+	0.861410i	$0.330418\pi$
$770$	− 4.02421e11i	− 1.14477i
$771$	0	0
$772$	−7.15506e10	−0.201439
$773$	− 2.00470e10i	− 0.0561475i	−0.999606	−	0.0280738i	$-0.991063\pi$
$773$	− 2.00470e10i	− 0.0561475i	0.999606	−	0.0280738i	$-0.00893733\pi$
$774$	0	0
$775$	9.62458e10	0.266793
$776$	2.17168e11i	0.598892i
$777$	0	0
$778$	2.18166e10	0.0595483
$779$	1.16968e11i	0.317626i
$780$	0	0
$781$	−7.40339e10	−0.198988
$782$	− 2.79835e11i	− 0.748299i
$783$	0	0
$784$	−3.18714e10	−0.0843600
$785$	4.06232e11i	1.06978i
$786$	0	0
$787$	3.93335e11	1.02533	0.512665	−	0.858589i	$-0.328658\pi$
$787$	3.93335e11	1.02533	0.512665	+	0.858589i	$0.328658\pi$
$788$	3.63298e11i	0.942231i
$789$	0	0
$790$	−5.46359e11	−1.40271
$791$	− 3.22270e11i	− 0.823216i
$792$	0	0
$793$	1.10646e11	0.279796
$794$	2.94245e11i	0.740334i
$795$	0	0
$796$	3.71343e11	0.924960
$797$	− 2.19380e11i	− 0.543706i	−0.962339	−	0.271853i	$-0.912364\pi$
$797$	− 2.19380e11i	− 0.543706i	0.962339	−	0.271853i	$-0.0876364\pi$
$798$	0	0
$799$	−4.16594e11	−1.02218
$800$	2.49853e10i	0.0609992i
$801$	0	0
$802$	3.02329e10	0.0730772
$803$	− 6.55033e11i	− 1.57544i
$804$	0	0
$805$	−2.38670e11	−0.568349
$806$	− 4.87387e10i	− 0.115487i
$807$	0	0
$808$	−1.54028e11	−0.361371
$809$	− 7.99208e11i	− 1.86580i	−0.360131	−	0.932902i	$-0.617268\pi$
$809$	− 7.99208e11i	− 1.86580i	0.360131	−	0.932902i	$-0.382732\pi$
$810$	0	0
$811$	−4.25096e10	−0.0982661	−0.0491331	−	0.998792i	$-0.515646\pi$
$811$	−4.25096e10	−0.0982661	−0.0491331	+	0.998792i	$0.515646\pi$
$812$	− 2.19165e11i	− 0.504136i
$813$	0	0
$814$	1.51949e11	0.346098
$815$	− 4.44256e11i	− 1.00694i
$816$	0	0
$817$	−3.63647e11	−0.816190
$818$	− 1.89499e11i	− 0.423246i
$819$	0	0
$820$	1.82298e11	0.403205
$821$	− 2.25537e10i	− 0.0496415i	−0.999692	−	0.0248207i	$-0.992099\pi$
$821$	− 2.25537e10i	− 0.0496415i	0.999692	−	0.0248207i	$-0.00790150\pi$
$822$	0	0
$823$	−1.44899e11	−0.315840	−0.157920	−	0.987452i	$-0.550479\pi$
$823$	−1.44899e11	−0.315840	−0.157920	+	0.987452i	$0.550479\pi$
$824$	1.18341e11i	0.256699i
$825$	0	0
$826$	−9.95711e10	−0.213901
$827$	− 5.86919e11i	− 1.25475i	−0.778719	−	0.627373i	$-0.784130\pi$
$827$	− 5.86919e11i	− 1.25475i	0.778719	−	0.627373i	$-0.215870\pi$
$828$	0	0
$829$	−2.57431e11	−0.545059	−0.272529	−	0.962147i	$-0.587860\pi$
$829$	−2.57431e11	−0.545059	−0.272529	+	0.962147i	$0.587860\pi$
$830$	− 3.80802e11i	− 0.802392i
$831$	0	0
$832$	1.26525e10	0.0264048
$833$	2.85585e11i	0.593138i
$834$	0	0
$835$	4.61994e11	0.950365
$836$	− 1.91327e11i	− 0.391698i
$837$	0	0
$838$	−1.23868e11	−0.251179
$839$	− 9.44521e11i	− 1.90618i	−0.302688	−	0.953090i	$-0.597884\pi$
$839$	− 9.44521e11i	− 1.90618i	0.302688	−	0.953090i	$-0.402116\pi$
$840$	0	0
$841$	−2.67316e11	−0.534368
$842$	1.29659e11i	0.257961i
$843$	0	0
$844$	−3.93869e11	−0.776215
$845$	5.64903e11i	1.10802i
$846$	0	0
$847$	8.13159e11	1.57994
$848$	1.63801e11i	0.316762i
$849$	0	0
$850$	2.23882e11	0.428887
$851$	− 9.01187e10i	− 0.171829i
$852$	0	0
$853$	−1.64562e11	−0.310837	−0.155419	−	0.987849i	$-0.549673\pi$
$853$	−1.64562e11	−0.310837	−0.155419	+	0.987849i	$0.549673\pi$
$854$	− 4.05507e11i	− 0.762371i
$855$	0	0
$856$	1.07495e11	0.200214
$857$	9.58876e11i	1.77762i	0.458274	+	0.888811i	$0.348468\pi$
$857$	9.58876e11i	1.77762i	−0.458274	+	0.888811i	$0.651532\pi$
$858$	0	0
$859$	9.96658e11	1.83052	0.915258	−	0.402869i	$-0.131987\pi$
$859$	9.96658e11	1.83052	0.915258	+	0.402869i	$0.131987\pi$
$860$	5.66753e11i	1.03610i
$861$	0	0
$862$	1.23802e11	0.224233
$863$	− 2.58156e10i	− 0.0465413i	−0.999729	−	0.0232706i	$-0.992592\pi$
$863$	− 2.58156e10i	− 0.0465413i	0.999729	−	0.0232706i	$-0.00740795\pi$
$864$	0	0
$865$	−1.26988e12	−2.26829
$866$	− 3.52883e11i	− 0.627422i
$867$	0	0
$868$	−1.78623e11	−0.314673
$869$	− 1.67279e12i	− 2.93333i
$870$	0	0
$871$	1.57402e11	0.273488
$872$	1.14905e11i	0.198734i
$873$	0	0
$874$	−1.13473e11	−0.194468
$875$	3.62423e11i	0.618277i
$876$	0	0
$877$	2.32514e10	0.0393052	0.0196526	−	0.999807i	$-0.493744\pi$
$877$	2.32514e10	0.0393052	0.0196526	+	0.999807i	$0.493744\pi$
$878$	− 4.87173e11i	− 0.819795i
$879$	0	0
$880$	−2.98188e11	−0.497233
$881$	− 4.50262e11i	− 0.747415i	−0.927547	−	0.373708i	$-0.878086\pi$
$881$	− 4.50262e11i	− 0.747415i	0.927547	−	0.373708i	$-0.121914\pi$
$882$	0	0
$883$	4.70736e11	0.774345	0.387173	−	0.922007i	$-0.373452\pi$
$883$	4.70736e11	0.774345	0.387173	+	0.922007i	$0.373452\pi$
$884$	− 1.13373e11i	− 0.185653i
$885$	0	0
$886$	−3.00341e11	−0.487394
$887$	9.97354e11i	1.61122i	0.592446	+	0.805610i	$0.298162\pi$
$887$	9.97354e11i	1.61122i	−0.592446	+	0.805610i	$0.701838\pi$
$888$	0	0
$889$	6.80278e11	1.08913
$890$	− 7.43143e11i	− 1.18444i
$891$	0	0
$892$	4.63409e10	0.0731989
$893$	1.68929e11i	0.265643i
$894$	0	0
$895$	5.72858e11	0.892801
$896$	− 4.63703e10i	− 0.0719462i
$897$	0	0
$898$	8.42866e11	1.29614
$899$	6.25576e11i	0.957725i
$900$	0	0
$901$	1.46775e12	2.22717
$902$	5.58141e11i	0.843175i
$903$	0	0
$904$	−2.38797e11	−0.357566
$905$	− 4.24485e11i	− 0.632802i
$906$	0	0
$907$	−9.86539e11	−1.45776	−0.728879	−	0.684643i	$-0.759958\pi$
$907$	−9.86539e11	−1.45776	−0.728879	+	0.684643i	$0.759958\pi$
$908$	1.13430e11i	0.166872i
$909$	0	0
$910$	−9.66956e10	−0.141007
$911$	2.94621e11i	0.427751i	0.976861	+	0.213875i	$0.0686086\pi$
$911$	2.94621e11i	0.427751i	−0.976861	+	0.213875i	$0.931391\pi$
$912$	0	0
$913$	1.16590e12	1.67795
$914$	9.31019e11i	1.33406i
$915$	0	0
$916$	2.92163e11	0.414996
$917$	− 1.00154e12i	− 1.41642i
$918$	0	0
$919$	1.09311e12	1.53250	0.766252	−	0.642540i	$-0.222119\pi$
$919$	1.09311e12	1.53250	0.766252	+	0.642540i	$0.222119\pi$
$920$	1.76851e11i	0.246864i
$921$	0	0
$922$	−1.21541e11	−0.168190
$923$	1.77892e10i	0.0245104i
$924$	0	0
$925$	7.20994e10	0.0984838
$926$	− 1.14962e11i	− 0.156354i
$927$	0	0
$928$	−1.62398e11	−0.218973
$929$	5.36626e11i	0.720458i	0.932864	+	0.360229i	$0.117302\pi$
$929$	5.36626e11i	0.720458i	−0.932864	+	0.360229i	$0.882698\pi$
$930$	0	0
$931$	1.15805e11	0.154145
$932$	5.70010e10i	0.0755473i
$933$	0	0
$934$	1.44285e11	0.189598
$935$	2.67194e12i	3.49607i
$936$	0	0
$937$	−2.36202e11	−0.306426	−0.153213	−	0.988193i	$-0.548962\pi$
$937$	−2.36202e11	−0.306426	−0.153213	+	0.988193i	$0.548962\pi$
$938$	− 5.76866e11i	− 0.745184i
$939$	0	0
$940$	2.63281e11	0.337216
$941$	− 9.00493e11i	− 1.14848i	−0.818688	−	0.574238i	$-0.805298\pi$
$941$	− 9.00493e11i	− 1.14848i	0.818688	−	0.574238i	$-0.194702\pi$
$942$	0	0
$943$	3.31026e11	0.418615
$944$	7.37808e10i	0.0929085i
$945$	0	0
$946$	−1.73523e12	−2.16667
$947$	− 6.90632e11i	− 0.858710i	−0.903136	−	0.429355i	$-0.858741\pi$
$947$	− 6.90632e11i	− 0.858710i	0.903136	−	0.429355i	$-0.141259\pi$
$948$	0	0
$949$	−1.57394e11	−0.194055
$950$	− 9.07843e10i	− 0.111459i
$951$	0	0
$952$	−4.15504e11	−0.505856
$953$	6.18684e11i	0.750062i	0.927012	+	0.375031i	$0.122368\pi$
$953$	6.18684e11i	0.750062i	−0.927012	+	0.375031i	$0.877632\pi$
$954$	0	0
$955$	−7.58111e11	−0.911422
$956$	5.51561e11i	0.660331i
$957$	0	0
$958$	−6.92598e11	−0.822278
$959$	6.96031e11i	0.822914i
$960$	0	0
$961$	−3.43037e11	−0.402205
$962$	− 3.65110e10i	− 0.0426308i
$963$	0	0
$964$	3.03650e11	0.351613
$965$	− 4.05186e11i	− 0.467246i
$966$	0	0
$967$	−1.49456e12	−1.70926	−0.854631	−	0.519236i	$-0.826216\pi$
$967$	−1.49456e12	−1.70926	−0.854631	+	0.519236i	$0.826216\pi$
$968$	− 6.02539e11i	− 0.686253i
$969$	0	0
$970$	−1.22981e12	−1.38915
$971$	2.58703e11i	0.291022i	0.989357	+	0.145511i	$0.0464826\pi$
$971$	2.58703e11i	0.291022i	−0.989357	+	0.145511i	$0.953517\pi$
$972$	0	0
$973$	3.36528e11	0.375465
$974$	− 5.55978e10i	− 0.0617763i
$975$	0	0
$976$	−3.00475e11	−0.331138
$977$	− 2.98819e11i	− 0.327966i	−0.986463	−	0.163983i	$-0.947566\pi$
$977$	− 2.98819e11i	− 0.327966i	0.986463	−	0.163983i	$-0.0524343\pi$
$978$	0	0
$979$	2.27528e12	2.47688
$980$	− 1.80485e11i	− 0.195676i
$981$	0	0
$982$	−7.35164e11	−0.790566
$983$	1.07496e12i	1.15128i	0.817705	+	0.575638i	$0.195246\pi$
$983$	1.07496e12i	1.15128i	−0.817705	+	0.575638i	$0.804754\pi$
$984$	0	0
$985$	−2.05733e12	−2.18554
$986$	1.45518e12i	1.53960i
$987$	0	0
$988$	−4.59729e10	−0.0482475
$989$	1.02914e12i	1.07570i
$990$	0	0
$991$	−5.51000e11	−0.571290	−0.285645	−	0.958335i	$-0.592208\pi$
$991$	−5.51000e11	−0.571290	−0.285645	+	0.958335i	$0.592208\pi$
$992$	1.32357e11i	0.136679i
$993$	0	0
$994$	6.51961e10	0.0667845
$995$	2.10289e12i	2.14548i
$996$	0	0
$997$	9.18894e11	0.930004	0.465002	−	0.885310i	$-0.346054\pi$
$997$	9.18894e11	0.930004	0.465002	+	0.885310i	$0.346054\pi$
$998$	− 1.15740e12i	− 1.16670i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.9.b.a.161.1	✓	8
3.2	odd	2	inner	162.9.b.a.161.8	yes	8
9.2	odd	6		162.9.d.h.53.5		16
9.4	even	3		162.9.d.h.107.5		16
9.5	odd	6		162.9.d.h.107.4		16
9.7	even	3		162.9.d.h.53.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.9.b.a.161.1	✓	8	1.1	even	1	trivial
162.9.b.a.161.8	yes	8	3.2	odd	2	inner
162.9.d.h.53.4		16	9.7	even	3
162.9.d.h.53.5		16	9.2	odd	6
162.9.d.h.107.4		16	9.5	odd	6
162.9.d.h.107.5		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:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	162.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-11.3137i q^{2} -128.000 q^{4} -724.855i q^{5} -1954.36 q^{7} +1448.15i q^{8} +O(q^{10})\)	\(q-11.3137i q^{2} -128.000 q^{4} -724.855i q^{5} -1954.36 q^{7} +1448.15i q^{8} -8200.80 q^{10} -25108.4i q^{11} -6033.17 q^{13} +22111.1i q^{14} +16384.0 q^{16} -146810. i q^{17} -59531.5 q^{19} +92781.5i q^{20} -284069. q^{22} +168478. i q^{23} -134790. q^{25} +68257.5i q^{26} +250158. q^{28} -876106. i q^{29} -714041. q^{31} -185364. i q^{32} -1.66096e6 q^{34} +1.41663e6i q^{35} -534900. q^{37} +673522. i q^{38} +1.04970e6 q^{40} -1.96481e6i q^{41} +6.10848e6 q^{43} +3.21388e6i q^{44} +1.90611e6 q^{46} -2.83764e6i q^{47} -1.94527e6 q^{49} +1.52498e6i q^{50} +772246. q^{52} +9.99763e6i q^{53} -1.82000e7 q^{55} -2.83022e6i q^{56} -9.91201e6 q^{58} +4.50322e6i q^{59} -1.83395e7 q^{61} +8.07845e6i q^{62} -2.09715e6 q^{64} +4.37318e6i q^{65} -2.60895e7 q^{67} +1.87917e7i q^{68} +1.60273e7 q^{70} -2.94857e6i q^{71} +2.60882e7 q^{73} +6.05170e6i q^{74} +7.62003e6 q^{76} +4.90709e7i q^{77} +6.66226e7 q^{79} -1.18760e7i q^{80} -2.22292e7 q^{82} +4.64347e7i q^{83} -1.06416e8 q^{85} -6.91095e7i q^{86} +3.63609e7 q^{88} +9.06184e7i q^{89} +1.17910e7 q^{91} -2.15651e7i q^{92} -3.21043e7 q^{94} +4.31517e7i q^{95} +1.49962e8 q^{97} +2.20083e7i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 1024 q^{4} - 8876 q^{7}+O(q^{10}) \) 8 * q - 1024 * q^4 - 8876 * q^7	\( 8 q - 1024 q^{4} - 8876 q^{7} + 8448 q^{10} - 117380 q^{13} + 131072 q^{16} + 270220 q^{19} - 210816 q^{22} - 1801672 q^{25} + 1136128 q^{28} - 393344 q^{31} - 691968 q^{34} + 1830988 q^{37} - 1081344 q^{40} + 11135236 q^{43} + 5296320 q^{46} - 13586328 q^{49} + 15024640 q^{52} - 1579716 q^{55} - 32988672 q^{58} + 12184204 q^{61} - 16777216 q^{64} - 80355716 q^{67} - 18723264 q^{70} + 197085760 q^{73} - 34588160 q^{76} + 84451852 q^{79} + 144639168 q^{82} - 582634548 q^{85} + 26984448 q^{88} + 373079588 q^{91} - 210121536 q^{94} + 341136928 q^{97}+O(q^{100}) \) 8 * q - 1024 * q^4 - 8876 * q^7 + 8448 * q^10 - 117380 * q^13 + 131072 * q^16 + 270220 * q^19 - 210816 * q^22 - 1801672 * q^25 + 1136128 * q^28 - 393344 * q^31 - 691968 * q^34 + 1830988 * q^37 - 1081344 * q^40 + 11135236 * q^43 + 5296320 * q^46 - 13586328 * q^49 + 15024640 * q^52 - 1579716 * q^55 - 32988672 * q^58 + 12184204 * q^61 - 16777216 * q^64 - 80355716 * q^67 - 18723264 * q^70 + 197085760 * q^73 - 34588160 * q^76 + 84451852 * q^79 + 144639168 * q^82 - 582634548 * q^85 + 26984448 * q^88 + 373079588 * q^91 - 210121536 * q^94 + 341136928 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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