LMFDB - Embedded newform 162.7.b.c.161.3

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 370x^{10} + 51793x^{8} + 3491832x^{6} + 117603792x^{4} + 1832032512x^{2} + 10453017600 $ x^12 + 370x^10 + 51793x^8 + 3491832x^6 + 117603792x^4 + 1832032512*x^2 + 10453017600
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{42} $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			161.3
Root			$3.87527i$ of defining polynomial
Character	$\chi$	$=$	162.161
Dual form			162.7.b.c.161.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.65685i q^{2} -32.0000 q^{4} +1.84488i q^{5} -12.6882 q^{7} +181.019i q^{8} +O(q^{10})$	\(q-5.65685i q^{2} -32.0000 q^{4} +1.84488i q^{5} -12.6882 q^{7} +181.019i q^{8} +10.4362 q^{10} +57.5134i q^{11} +2822.35 q^{13} +71.7754i q^{14} +1024.00 q^{16} -7221.17i q^{17} -10648.3 q^{19} -59.0360i q^{20} +325.345 q^{22} +13364.4i q^{23} +15621.6 q^{25} -15965.6i q^{26} +406.023 q^{28} -35559.1i q^{29} -17315.7 q^{31} -5792.62i q^{32} -40849.1 q^{34} -23.4082i q^{35} -60441.2 q^{37} +60236.1i q^{38} -333.958 q^{40} -87106.4i q^{41} -75864.3 q^{43} -1840.43i q^{44} +75600.6 q^{46} -71472.0i q^{47} -117488. q^{49} -88369.1i q^{50} -90315.2 q^{52} +147761. i q^{53} -106.105 q^{55} -2296.81i q^{56} -201153. q^{58} +115728. i q^{59} -40277.3 q^{61} +97952.2i q^{62} -32768.0 q^{64} +5206.88i q^{65} -181767. q^{67} +231077. i q^{68} -132.417 q^{70} -301066. i q^{71} -612635. q^{73} +341907. i q^{74} +340747. q^{76} -729.742i q^{77} -343302. q^{79} +1889.15i q^{80} -492748. q^{82} +151937. i q^{83} +13322.1 q^{85} +429153. i q^{86} -10411.0 q^{88} -102435. i q^{89} -35810.6 q^{91} -427662. i q^{92} -404306. q^{94} -19644.9i q^{95} -495764. q^{97} +664613. i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 384 q^{4} - 480 q^{7}+O(q^{10}) $ 12 * q - 384 * q^4 - 480 * q^7	$ 12 q - 384 q^{4} - 480 q^{7} - 3360 q^{13} + 12288 q^{16} - 2820 q^{19} + 7200 q^{22} - 16188 q^{25} + 15360 q^{28} - 42960 q^{31} + 54720 q^{34} - 25536 q^{37} - 142860 q^{43} - 135072 q^{46} + 271908 q^{49} + 107520 q^{52} + 580392 q^{55} - 318528 q^{58} - 271488 q^{61} - 393216 q^{64} + 579876 q^{67} - 311904 q^{70} - 977700 q^{73} + 90240 q^{76} + 1529592 q^{79} + 1073088 q^{82} - 3239136 q^{85} - 230400 q^{88} + 355584 q^{91} + 1473696 q^{94} + 77748 q^{97}+O(q^{100}) $ 12 * q - 384 * q^4 - 480 * q^7 - 3360 * q^13 + 12288 * q^16 - 2820 * q^19 + 7200 * q^22 - 16188 * q^25 + 15360 * q^28 - 42960 * q^31 + 54720 * q^34 - 25536 * q^37 - 142860 * q^43 - 135072 * q^46 + 271908 * q^49 + 107520 * q^52 + 580392 * q^55 - 318528 * q^58 - 271488 * q^61 - 393216 * q^64 + 579876 * q^67 - 311904 * q^70 - 977700 * q^73 + 90240 * q^76 + 1529592 * q^79 + 1073088 * q^82 - 3239136 * q^85 - 230400 * q^88 + 355584 * q^91 + 1473696 * q^94 + 77748 * 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
$5$	1.84488i	0.0147590i	0.999973	+	0.00737950i	$0.00234899\pi$
$5$	1.84488i	0.0147590i	−0.999973	+	0.00737950i	$0.997651\pi$
$6$	0	0
$7$	−12.6882	−0.0369919	−0.0184959	−	0.999829i	$-0.505888\pi$
$7$	−12.6882	−0.0369919	−0.0184959	+	0.999829i	$0.505888\pi$
$8$	181.019i	0.353553i
$9$	0	0
$10$	10.4362	0.0104362
$11$	57.5134i	0.0432106i	0.999767	+	0.0216053i	$0.00687772\pi$
$11$	57.5134i	0.0432106i	−0.999767	+	0.0216053i	$0.993122\pi$
$12$	0	0
$13$	2822.35	1.28464	0.642319	−	0.766437i	$-0.277972\pi$
$13$	2822.35	1.28464	0.642319	+	0.766437i	$0.277972\pi$
$14$	71.7754i	0.0261572i
$15$	0	0
$16$	1024.00	0.250000
$17$	− 7221.17i	− 1.46981i	−0.678171	−	0.734904i	$-0.737227\pi$
$17$	− 7221.17i	− 1.46981i	0.678171	−	0.734904i	$-0.262773\pi$
$18$	0	0
$19$	−10648.3	−1.55246	−0.776231	−	0.630449i	$-0.782871\pi$
$19$	−10648.3	−1.55246	−0.776231	+	0.630449i	$0.782871\pi$
$20$	− 59.0360i	− 0.00737950i
$21$	0	0
$22$	325.345	0.0305545
$23$	13364.4i	1.09842i	0.835686	+	0.549208i	$0.185070\pi$
$23$	13364.4i	1.09842i	−0.835686	+	0.549208i	$0.814930\pi$
$24$	0	0
$25$	15621.6	0.999782
$26$	− 15965.6i	− 0.908376i
$27$	0	0
$28$	406.023	0.0184959
$29$	− 35559.1i	− 1.45800i	−0.684514	−	0.729000i	$-0.739986\pi$
$29$	− 35559.1i	− 1.45800i	0.684514	−	0.729000i	$-0.260014\pi$
$30$	0	0
$31$	−17315.7	−0.581238	−0.290619	−	0.956839i	$-0.593861\pi$
$31$	−17315.7	−0.581238	−0.290619	+	0.956839i	$0.593861\pi$
$32$	− 5792.62i	− 0.176777i
$33$	0	0
$34$	−40849.1	−1.03931
$35$	− 23.4082i	0 0.000545963i
$36$	0	0
$37$	−60441.2	−1.19324	−0.596620	−	0.802524i	$-0.703490\pi$
$37$	−60441.2	−1.19324	−0.596620	+	0.802524i	$0.703490\pi$
$38$	60236.1i	1.09776i
$39$	0	0
$40$	−333.958	−0.00521810
$41$	− 87106.4i	− 1.26386i	−0.775026	−	0.631929i	$-0.782263\pi$
$41$	− 87106.4i	− 1.26386i	0.775026	−	0.631929i	$-0.217737\pi$
$42$	0	0
$43$	−75864.3	−0.954184	−0.477092	−	0.878853i	$-0.658309\pi$
$43$	−75864.3	−0.954184	−0.477092	+	0.878853i	$0.658309\pi$
$44$	− 1840.43i	− 0.0216053i
$45$	0	0
$46$	75600.6	0.776697
$47$	− 71472.0i	− 0.688402i	−0.938896	−	0.344201i	$-0.888150\pi$
$47$	− 71472.0i	− 0.688402i	0.938896	−	0.344201i	$-0.111850\pi$
$48$	0	0
$49$	−117488.	−0.998632
$50$	− 88369.1i	− 0.706953i
$51$	0	0
$52$	−90315.2	−0.642319
$53$	147761.i	0.992505i	0.868178	+	0.496252i	$0.165291\pi$
$53$	147761.i	0.992505i	−0.868178	+	0.496252i	$0.834709\pi$
$54$	0	0
$55$	−106.105	−0.000637746 0
$56$	− 2296.81i	− 0.0130786i
$57$	0	0
$58$	−201153.	−1.03096
$59$	115728.i	0.563486i	0.959490	+	0.281743i	$0.0909126\pi$
$59$	115728.i	0.563486i	−0.959490	+	0.281743i	$0.909087\pi$
$60$	0	0
$61$	−40277.3	−0.177448	−0.0887239	−	0.996056i	$-0.528279\pi$
$61$	−40277.3	−0.177448	−0.0887239	+	0.996056i	$0.528279\pi$
$62$	97952.2i	0.410998i
$63$	0	0
$64$	−32768.0	−0.125000
$65$	5206.88i	0.0189600i
$66$	0	0
$67$	−181767.	−0.604354	−0.302177	−	0.953252i	$-0.597713\pi$
$67$	−181767.	−0.604354	−0.302177	+	0.953252i	$0.597713\pi$
$68$	231077.i	0.734904i
$69$	0	0
$70$	−132.417	−0.000386054 0
$71$	− 301066.i	− 0.841175i	−0.907252	−	0.420588i	$-0.861824\pi$
$71$	− 301066.i	− 0.841175i	0.907252	−	0.420588i	$-0.138176\pi$
$72$	0	0
$73$	−612635.	−1.57483	−0.787415	−	0.616424i	$-0.788581\pi$
$73$	−612635.	−1.57483	−0.787415	+	0.616424i	$0.788581\pi$
$74$	341907.i	0.843748i
$75$	0	0
$76$	340747.	0.776231
$77$	− 729.742i	− 0.00159844i
$78$	0	0
$79$	−343302.	−0.696298	−0.348149	−	0.937439i	$-0.613190\pi$
$79$	−343302.	−0.696298	−0.348149	+	0.937439i	$0.613190\pi$
$80$	1889.15i	0.00368975i
$81$	0	0
$82$	−492748.	−0.893683
$83$	151937.i	0.265723i	0.991135	+	0.132862i	$0.0424166\pi$
$83$	151937.i	0.265723i	−0.991135	+	0.132862i	$0.957583\pi$
$84$	0	0
$85$	13322.1	0.0216929
$86$	429153.i	0.674710i
$87$	0	0
$88$	−10411.0	−0.0152773
$89$	− 102435.i	− 0.145304i	−0.997357	−	0.0726520i	$-0.976854\pi$
$89$	− 102435.i	− 0.145304i	0.997357	−	0.0726520i	$-0.0231462\pi$
$90$	0	0
$91$	−35810.6	−0.0475212
$92$	− 427662.i	− 0.549208i
$93$	0	0
$94$	−404306.	−0.486774
$95$	− 19644.9i	− 0.0229128i
$96$	0	0
$97$	−495764.	−0.543200	−0.271600	−	0.962410i	$-0.587553\pi$
$97$	−495764.	−0.543200	−0.271600	+	0.962410i	$0.587553\pi$
$98$	664613.i	0.706139i
$99$	0	0
$100$	−499891.	−0.499891
$101$	− 78700.0i	− 0.0763854i	−0.999270	−	0.0381927i	$-0.987840\pi$
$101$	− 78700.0i	− 0.0763854i	0.999270	−	0.0381927i	$-0.0121601\pi$
$102$	0	0
$103$	−653628.	−0.598163	−0.299081	−	0.954228i	$-0.596680\pi$
$103$	−653628.	−0.598163	−0.299081	+	0.954228i	$0.596680\pi$
$104$	510900.i	0.454188i
$105$	0	0
$106$	835863.	0.701807
$107$	− 1.53176e6i	− 1.25037i	−0.780476	−	0.625186i	$-0.785023\pi$
$107$	− 1.53176e6i	− 1.25037i	0.780476	−	0.625186i	$-0.214977\pi$
$108$	0	0
$109$	863246.	0.666584	0.333292	−	0.942824i	$-0.391840\pi$
$109$	863246.	0.666584	0.333292	+	0.942824i	$0.391840\pi$
$110$	600.221i	0 0.000450955i
$111$	0	0
$112$	−12992.7	−0.00924797
$113$	− 1.74523e6i	− 1.20953i	−0.796404	−	0.604765i	$-0.793267\pi$
$113$	− 1.74523e6i	− 1.20953i	0.796404	−	0.604765i	$-0.206733\pi$
$114$	0	0
$115$	−24655.7	−0.0162115
$116$	1.13789e6i	0.729000i
$117$	0	0
$118$	654658.	0.398445
$119$	91623.7i	0.0543709i
$120$	0	0
$121$	1.76825e6	0.998133
$122$	227843.i	0.125475i
$123$	0	0
$124$	554101.	0.290619
$125$	57646.1i	0.0295148i
$126$	0	0
$127$	3.20463e6	1.56447	0.782234	−	0.622985i	$-0.214080\pi$
$127$	3.20463e6	1.56447	0.782234	+	0.622985i	$0.214080\pi$
$128$	185364.i	0.0883883i
$129$	0	0
$130$	29454.6	0.0134067
$131$	− 3.04826e6i	− 1.35593i	−0.735092	−	0.677967i	$-0.762861\pi$
$131$	− 3.04826e6i	− 1.35593i	0.735092	−	0.677967i	$-0.237139\pi$
$132$	0	0
$133$	135108.	0.0574285
$134$	1.02823e6i	0.427343i
$135$	0	0
$136$	1.30717e6	0.519656
$137$	− 4.09772e6i	− 1.59360i	−0.604240	−	0.796802i	$-0.706523\pi$
$137$	− 4.09772e6i	− 1.59360i	0.604240	−	0.796802i	$-0.293477\pi$
$138$	0	0
$139$	−1.11292e6	−0.414400	−0.207200	−	0.978299i	$-0.566435\pi$
$139$	−1.11292e6	−0.414400	−0.207200	+	0.978299i	$0.566435\pi$
$140$	749.061i	0 0.000272982i
$141$	0	0
$142$	−1.70309e6	−0.594801
$143$	162323.i	0.0555100i
$144$	0	0
$145$	65602.2	0.0215186
$146$	3.46559e6i	1.11357i
$147$	0	0
$148$	1.93412e6	0.596620
$149$	− 508285.i	− 0.153656i	−0.997044	−	0.0768278i	$-0.975521\pi$
$149$	− 508285.i	− 0.153656i	0.997044	−	0.0768278i	$-0.0244792\pi$
$150$	0	0
$151$	5.63502e6	1.63668	0.818341	−	0.574733i	$-0.194894\pi$
$151$	5.63502e6	1.63668	0.818341	+	0.574733i	$0.194894\pi$
$152$	− 1.92756e6i	− 0.548878i
$153$	0	0
$154$	−4128.04	−0.00113027
$155$	− 31945.3i	− 0.00857850i
$156$	0	0
$157$	5.36252e6	1.38570	0.692852	−	0.721080i	$-0.256354\pi$
$157$	5.36252e6	1.38570	0.692852	+	0.721080i	$0.256354\pi$
$158$	1.94201e6i	0.492357i
$159$	0	0
$160$	10686.7	0.00260905
$161$	− 169571.i	− 0.0406324i
$162$	0	0
$163$	−2.42021e6	−0.558844	−0.279422	−	0.960168i	$-0.590143\pi$
$163$	−2.42021e6	−0.558844	−0.279422	+	0.960168i	$0.590143\pi$
$164$	2.78740e6i	0.631929i
$165$	0	0
$166$	859487.	0.187895
$167$	8.26872e6i	1.77537i	0.460452	+	0.887685i	$0.347687\pi$
$167$	8.26872e6i	1.77537i	−0.460452	+	0.887685i	$0.652313\pi$
$168$	0	0
$169$	3.13885e6	0.650294
$170$	− 75361.5i	− 0.0153392i
$171$	0	0
$172$	2.42766e6	0.477092
$173$	− 2.62489e6i	− 0.506958i	−0.967341	−	0.253479i	$-0.918425\pi$
$173$	− 2.62489e6i	− 0.506958i	0.967341	−	0.253479i	$-0.0815749\pi$
$174$	0	0
$175$	−198210.	−0.0369838
$176$	58893.7i	0.0108027i
$177$	0	0
$178$	−579459.	−0.102745
$179$	− 7.60442e6i	− 1.32589i	−0.748669	−	0.662944i	$-0.769307\pi$
$179$	− 7.60442e6i	− 1.32589i	0.748669	−	0.662944i	$-0.230693\pi$
$180$	0	0
$181$	−9.89440e6	−1.66861	−0.834303	−	0.551306i	$-0.814130\pi$
$181$	−9.89440e6	−1.66861	−0.834303	+	0.551306i	$0.814130\pi$
$182$	202575.i	0.0336025i
$183$	0	0
$184$	−2.41922e6	−0.388349
$185$	− 111506.i	− 0.0176110i
$186$	0	0
$187$	415314.	0.0635113
$188$	2.28710e6i	0.344201i
$189$	0	0
$190$	−111128.	−0.0162018
$191$	1.26507e6i	0.181558i	0.995871	+	0.0907791i	$0.0289357\pi$
$191$	1.26507e6i	0.181558i	−0.995871	+	0.0907791i	$0.971064\pi$
$192$	0	0
$193$	1.30997e6	0.182218	0.0911089	−	0.995841i	$-0.470959\pi$
$193$	1.30997e6	0.182218	0.0911089	+	0.995841i	$0.470959\pi$
$194$	2.80447e6i	0.384101i
$195$	0	0
$196$	3.75962e6	0.499316
$197$	9.83234e6i	1.28605i	0.765845	+	0.643025i	$0.222321\pi$
$197$	9.83234e6i	1.28605i	−0.765845	+	0.643025i	$0.777679\pi$
$198$	0	0
$199$	1.36283e7	1.72934	0.864672	−	0.502336i	$-0.167526\pi$
$199$	1.36283e7	1.72934	0.864672	+	0.502336i	$0.167526\pi$
$200$	2.82781e6i	0.353476i
$201$	0	0
$202$	−445194.	−0.0540126
$203$	451182.i	0.0539341i
$204$	0	0
$205$	160700.	0.0186533
$206$	3.69748e6i	0.422965i
$207$	0	0
$208$	2.89009e6	0.321159
$209$	− 612422.i	− 0.0670829i
$210$	0	0
$211$	−3.11280e6	−0.331363	−0.165682	−	0.986179i	$-0.552982\pi$
$211$	−3.11280e6	−0.331363	−0.165682	+	0.986179i	$0.552982\pi$
$212$	− 4.72836e6i	− 0.496252i
$213$	0	0
$214$	−8.66493e6	−0.884146
$215$	− 139960.i	− 0.0140828i
$216$	0	0
$217$	219705.	0.0215011
$218$	− 4.88326e6i	− 0.471346i
$219$	0	0
$220$	3395.36	0.000318873 0
$221$	− 2.03807e7i	− 1.88817i
$222$	0	0
$223$	−2.00998e7	−1.81250	−0.906248	−	0.422747i	$-0.861066\pi$
$223$	−2.00998e7	−1.81250	−0.906248	+	0.422747i	$0.861066\pi$
$224$	73498.0i	0.00653930i
$225$	0	0
$226$	−9.87249e6	−0.855267
$227$	1.19038e7i	1.01767i	0.860864	+	0.508835i	$0.169924\pi$
$227$	1.19038e7i	1.01767i	−0.860864	+	0.508835i	$0.830076\pi$
$228$	0	0
$229$	−3.10348e6	−0.258430	−0.129215	−	0.991617i	$-0.541246\pi$
$229$	−3.10348e6	−0.258430	−0.129215	+	0.991617i	$0.541246\pi$
$230$	139474.i	0.0114633i
$231$	0	0
$232$	6.43689e6	0.515481
$233$	9.36024e6i	0.739979i	0.929036	+	0.369989i	$0.120639\pi$
$233$	9.36024e6i	0.739979i	−0.929036	+	0.369989i	$0.879361\pi$
$234$	0	0
$235$	131857.	0.0101601
$236$	− 3.70330e6i	− 0.281743i
$237$	0	0
$238$	518302.	0.0384461
$239$	6.99405e6i	0.512313i	0.966635	+	0.256156i	$0.0824562\pi$
$239$	6.99405e6i	0.512313i	−0.966635	+	0.256156i	$0.917544\pi$
$240$	0	0
$241$	−4.13545e6	−0.295442	−0.147721	−	0.989029i	$-0.547194\pi$
$241$	−4.13545e6	−0.295442	−0.147721	+	0.989029i	$0.547194\pi$
$242$	− 1.00028e7i	− 0.705786i
$243$	0	0
$244$	1.28887e6	0.0887239
$245$	− 216751.i	− 0.0147388i
$246$	0	0
$247$	−3.00533e7	−1.99435
$248$	− 3.13447e6i	− 0.205499i
$249$	0	0
$250$	326095.	0.0208701
$251$	− 6.15130e6i	− 0.388997i	−0.980903	−	0.194498i	$-0.937692\pi$
$251$	− 6.15130e6i	− 0.388997i	0.980903	−	0.194498i	$-0.0623079\pi$
$252$	0	0
$253$	−768633.	−0.0474633
$254$	− 1.81281e7i	− 1.10625i
$255$	0	0
$256$	1.04858e6	0.0625000
$257$	7.64854e6i	0.450588i	0.974291	+	0.225294i	$0.0723342\pi$
$257$	7.64854e6i	0.450588i	−0.974291	+	0.225294i	$0.927666\pi$
$258$	0	0
$259$	766891.	0.0441402
$260$	− 166620.i	− 0.00947999i
$261$	0	0
$262$	−1.72436e7	−0.958790
$263$	− 8.36828e6i	− 0.460012i	−0.973189	−	0.230006i	$-0.926125\pi$
$263$	− 8.36828e6i	− 0.460012i	0.973189	−	0.230006i	$-0.0738745\pi$
$264$	0	0
$265$	−272601.	−0.0146484
$266$	− 764288.i	− 0.0406081i
$267$	0	0
$268$	5.81656e6	0.302177
$269$	− 2.26505e7i	− 1.16364i	−0.813316	−	0.581822i	$-0.802340\pi$
$269$	− 2.26505e7i	− 1.16364i	0.813316	−	0.581822i	$-0.197660\pi$
$270$	0	0
$271$	−1.56983e7	−0.788758	−0.394379	−	0.918948i	$-0.629040\pi$
$271$	−1.56983e7	−0.788758	−0.394379	+	0.918948i	$0.629040\pi$
$272$	− 7.39447e6i	− 0.367452i
$273$	0	0
$274$	−2.31802e7	−1.12685
$275$	898451.i	0.0432012i
$276$	0	0
$277$	−1.90332e7	−0.895513	−0.447756	−	0.894156i	$-0.647777\pi$
$277$	−1.90332e7	−0.895513	−0.447756	+	0.894156i	$0.647777\pi$
$278$	6.29562e6i	0.293025i
$279$	0	0
$280$	4237.33	0.000193027 0
$281$	1.29524e7i	0.583758i	0.956455	+	0.291879i	$0.0942805\pi$
$281$	1.29524e7i	0.583758i	−0.956455	+	0.291879i	$0.905720\pi$
$282$	0	0
$283$	3.34938e7	1.47777	0.738883	−	0.673834i	$-0.235354\pi$
$283$	3.34938e7	1.47777	0.738883	+	0.673834i	$0.235354\pi$
$284$	9.63411e6i	0.420588i
$285$	0	0
$286$	918237.	0.0392515
$287$	1.10522e6i	0.0467525i
$288$	0	0
$289$	−2.80077e7	−1.16033
$290$	− 371102.i	− 0.0152160i
$291$	0	0
$292$	1.96043e7	0.787415
$293$	1.51346e7i	0.601682i	0.953674	+	0.300841i	$0.0972673\pi$
$293$	1.51346e7i	0.601682i	−0.953674	+	0.300841i	$0.902733\pi$
$294$	0	0
$295$	−213504.	−0.00831649
$296$	− 1.09410e7i	− 0.421874i
$297$	0	0
$298$	−2.87529e6	−0.108651
$299$	3.77191e7i	1.41107i
$300$	0	0
$301$	962583.	0.0352971
$302$	− 3.18765e7i	− 1.15731i
$303$	0	0
$304$	−1.09039e7	−0.388116
$305$	− 74306.5i	− 0.00261895i
$306$	0	0
$307$	−5.41823e6	−0.187259	−0.0936294	−	0.995607i	$-0.529847\pi$
$307$	−5.41823e6	−0.187259	−0.0936294	+	0.995607i	$0.529847\pi$
$308$	23351.7i	0 0.000799221i
$309$	0	0
$310$	−180710.	−0.00606591
$311$	2.73648e7i	0.909728i	0.890561	+	0.454864i	$0.150312\pi$
$311$	2.73648e7i	0.909728i	−0.890561	+	0.454864i	$0.849688\pi$
$312$	0	0
$313$	2.27790e7	0.742851	0.371426	−	0.928463i	$-0.378869\pi$
$313$	2.27790e7	0.742851	0.371426	+	0.928463i	$0.378869\pi$
$314$	− 3.03350e7i	− 0.979840i
$315$	0	0
$316$	1.09857e7	0.348149
$317$	− 2.64462e7i	− 0.830205i	−0.909775	−	0.415103i	$-0.863746\pi$
$317$	− 2.64462e7i	− 0.830205i	0.909775	−	0.415103i	$-0.136254\pi$
$318$	0	0
$319$	2.04513e6	0.0630011
$320$	− 60452.9i	− 0.00184488i
$321$	0	0
$322$	−959236.	−0.0287315
$323$	7.68934e7i	2.28182i
$324$	0	0
$325$	4.40896e7	1.28436
$326$	1.36908e7i	0.395162i
$327$	0	0
$328$	1.57679e7	0.446841
$329$	906851.i	0.0254653i
$330$	0	0
$331$	4.51271e7	1.24438	0.622190	−	0.782866i	$-0.286243\pi$
$331$	4.51271e7	1.24438	0.622190	+	0.782866i	$0.286243\pi$
$332$	− 4.86199e6i	− 0.132862i
$333$	0	0
$334$	4.67749e7	1.25538
$335$	− 335338.i	− 0.00891967i
$336$	0	0
$337$	−3.13832e7	−0.819989	−0.409994	−	0.912088i	$-0.634469\pi$
$337$	−3.13832e7	−0.819989	−0.409994	+	0.912088i	$0.634469\pi$
$338$	− 1.77560e7i	− 0.459828i
$339$	0	0
$340$	−426309.	−0.0108464
$341$	− 995883.i	− 0.0251157i
$342$	0	0
$343$	2.98347e6	0.0739331
$344$	− 1.37329e7i	− 0.337355i
$345$	0	0
$346$	−1.48486e7	−0.358474
$347$	1.10007e7i	0.263288i	0.991297	+	0.131644i	$0.0420255\pi$
$347$	1.10007e7i	0.263288i	−0.991297	+	0.131644i	$0.957974\pi$
$348$	0	0
$349$	−3.47811e6	−0.0818214	−0.0409107	−	0.999163i	$-0.513026\pi$
$349$	−3.47811e6	−0.0818214	−0.0409107	+	0.999163i	$0.513026\pi$
$350$	1.12125e6i	0.0261515i
$351$	0	0
$352$	333153.	0.00763864
$353$	− 2.69670e7i	− 0.613067i	−0.951860	−	0.306534i	$-0.900831\pi$
$353$	− 2.69670e7i	− 0.613067i	0.951860	−	0.306534i	$-0.0991692\pi$
$354$	0	0
$355$	555429.	0.0124149
$356$	3.27791e6i	0.0726520i
$357$	0	0
$358$	−4.30171e7	−0.937545
$359$	8.82517e7i	1.90739i	0.300775	+	0.953695i	$0.402755\pi$
$359$	8.82517e7i	1.90739i	−0.300775	+	0.953695i	$0.597245\pi$
$360$	0	0
$361$	6.63412e7	1.41014
$362$	5.59712e7i	1.17988i
$363$	0	0
$364$	1.14594e6	0.0237606
$365$	− 1.13024e6i	− 0.0232429i
$366$	0	0
$367$	3.00564e7	0.608048	0.304024	−	0.952664i	$-0.401670\pi$
$367$	3.00564e7	0.608048	0.304024	+	0.952664i	$0.401670\pi$
$368$	1.36852e7i	0.274604i
$369$	0	0
$370$	−630776.	−0.0124529
$371$	− 1.87482e6i	− 0.0367146i
$372$	0	0
$373$	3.91846e7	0.755074	0.377537	−	0.925995i	$-0.376771\pi$
$373$	3.91846e7	0.755074	0.377537	+	0.925995i	$0.376771\pi$
$374$	− 2.34937e6i	− 0.0449093i
$375$	0	0
$376$	1.29378e7	0.243387
$377$	− 1.00360e8i	− 1.87300i
$378$	0	0
$379$	−3.94927e7	−0.725436	−0.362718	−	0.931899i	$-0.618151\pi$
$379$	−3.94927e7	−0.725436	−0.362718	+	0.931899i	$0.618151\pi$
$380$	628635.i	0.0114564i
$381$	0	0
$382$	7.15634e6	0.128381
$383$	− 6.80692e7i	− 1.21159i	−0.795622	−	0.605793i	$-0.792856\pi$
$383$	− 6.80692e7i	− 1.21159i	0.795622	−	0.605793i	$-0.207144\pi$
$384$	0	0
$385$	1346.28	2.35914e−5 0
$386$	− 7.41034e6i	− 0.128847i
$387$	0	0
$388$	1.58645e7	0.271600
$389$	7.94946e7i	1.35048i	0.737597	+	0.675241i	$0.235960\pi$
$389$	7.94946e7i	1.35048i	−0.737597	+	0.675241i	$0.764040\pi$
$390$	0	0
$391$	9.65067e7	1.61446
$392$	− 2.12676e7i	− 0.353070i
$393$	0	0
$394$	5.56201e7	0.909375
$395$	− 633349.i	− 0.0102767i
$396$	0	0
$397$	−4.50639e6	−0.0720206	−0.0360103	−	0.999351i	$-0.511465\pi$
$397$	−4.50639e6	−0.0720206	−0.0360103	+	0.999351i	$0.511465\pi$
$398$	− 7.70931e7i	− 1.22283i
$399$	0	0
$400$	1.59965e7	0.249946
$401$	3.99909e7i	0.620194i	0.950705	+	0.310097i	$0.100362\pi$
$401$	3.99909e7i	0.620194i	−0.950705	+	0.310097i	$0.899638\pi$
$402$	0	0
$403$	−4.88709e7	−0.746681
$404$	2.51840e6i	0.0381927i
$405$	0	0
$406$	2.55227e6	0.0381372
$407$	− 3.47618e6i	− 0.0515607i
$408$	0	0
$409$	−4.01126e7	−0.586287	−0.293144	−	0.956068i	$-0.594701\pi$
$409$	−4.01126e7	−0.586287	−0.293144	+	0.956068i	$0.594701\pi$
$410$	− 909059.i	− 0.0131899i
$411$	0	0
$412$	2.09161e7	0.299081
$413$	− 1.46838e6i	− 0.0208444i
$414$	0	0
$415$	−280305.	−0.00392181
$416$	− 1.63488e7i	− 0.227094i
$417$	0	0
$418$	−3.46438e6	−0.0474348
$419$	8.89458e7i	1.20916i	0.796545	+	0.604579i	$0.206659\pi$
$419$	8.89458e7i	1.20916i	−0.796545	+	0.604579i	$0.793341\pi$
$420$	0	0
$421$	4.63373e7	0.620990	0.310495	−	0.950575i	$-0.399505\pi$
$421$	4.63373e7	0.620990	0.310495	+	0.950575i	$0.399505\pi$
$422$	1.76087e7i	0.234309i
$423$	0	0
$424$	−2.67476e7	−0.350903
$425$	− 1.12806e8i	− 1.46949i
$426$	0	0
$427$	511046.	0.00656412
$428$	4.90163e7i	0.625186i
$429$	0	0
$430$	−791735.	−0.00995805
$431$	− 1.17075e8i	− 1.46228i	−0.682227	−	0.731140i	$-0.738988\pi$
$431$	− 1.17075e8i	− 1.46228i	0.682227	−	0.731140i	$-0.261012\pi$
$432$	0	0
$433$	1.81236e7	0.223244	0.111622	−	0.993751i	$-0.464395\pi$
$433$	1.81236e7	0.223244	0.111622	+	0.993751i	$0.464395\pi$
$434$	− 1.24284e6i	− 0.0152036i
$435$	0	0
$436$	−2.76239e7	−0.333292
$437$	− 1.42309e8i	− 1.70525i
$438$	0	0
$439$	6.05281e6	0.0715425	0.0357712	−	0.999360i	$-0.488611\pi$
$439$	6.05281e6	0.0715425	0.0357712	+	0.999360i	$0.488611\pi$
$440$	− 19207.1i	0 0.000225477i
$441$	0	0
$442$	−1.15290e8	−1.33514
$443$	− 4.86530e6i	− 0.0559626i	−0.999608	−	0.0279813i	$-0.991092\pi$
$443$	− 4.86530e6i	− 0.0559626i	0.999608	−	0.0279813i	$-0.00890789\pi$
$444$	0	0
$445$	188979.	0.00214454
$446$	1.13702e8i	1.28163i
$447$	0	0
$448$	415767.	0.00462398
$449$	− 1.43332e8i	− 1.58345i	−0.610877	−	0.791725i	$-0.709183\pi$
$449$	− 1.43332e8i	− 1.58345i	0.610877	−	0.791725i	$-0.290817\pi$
$450$	0	0
$451$	5.00978e6	0.0546121
$452$	5.58473e7i	0.604765i
$453$	0	0
$454$	6.73379e7	0.719601
$455$	− 66066.0i	0 0.000701365i
$456$	0	0
$457$	9.74706e7	1.02123	0.510617	−	0.859808i	$-0.329417\pi$
$457$	9.74706e7	1.02123	0.510617	+	0.859808i	$0.329417\pi$
$458$	1.75559e7i	0.182738i
$459$	0	0
$460$	788982.	0.00810576
$461$	5.34701e7i	0.545769i	0.962047	+	0.272884i	$0.0879776\pi$
$461$	5.34701e7i	0.545769i	−0.962047	+	0.272884i	$0.912022\pi$
$462$	0	0
$463$	3.07780e7	0.310097	0.155048	−	0.987907i	$-0.450447\pi$
$463$	3.07780e7	0.310097	0.155048	+	0.987907i	$0.450447\pi$
$464$	− 3.64126e7i	− 0.364500i
$465$	0	0
$466$	5.29495e7	0.523244
$467$	1.10305e8i	1.08304i	0.840688	+	0.541519i	$0.182151\pi$
$467$	1.10305e8i	1.08304i	−0.840688	+	0.541519i	$0.817849\pi$
$468$	0	0
$469$	2.30630e6	0.0223562
$470$	− 745895.i	− 0.00718429i
$471$	0	0
$472$	−2.09490e7	−0.199222
$473$	− 4.36321e6i	− 0.0412309i
$474$	0	0
$475$	−1.66344e8	−1.55212
$476$	− 2.93196e6i	− 0.0271855i
$477$	0	0
$478$	3.95643e7	0.362260
$479$	8.44412e6i	0.0768330i	0.999262	+	0.0384165i	$0.0122314\pi$
$479$	8.44412e6i	0.0768330i	−0.999262	+	0.0384165i	$0.987769\pi$
$480$	0	0
$481$	−1.70586e8	−1.53288
$482$	2.33936e7i	0.208909i
$483$	0	0
$484$	−5.65841e7	−0.499066
$485$	− 914623.i	− 0.00801710i
$486$	0	0
$487$	−3.58999e7	−0.310818	−0.155409	−	0.987850i	$-0.549669\pi$
$487$	−3.58999e7	−0.310818	−0.155409	+	0.987850i	$0.549669\pi$
$488$	− 7.29096e6i	− 0.0627373i
$489$	0	0
$490$	−1.22613e6	−0.0104219
$491$	− 8.07050e7i	− 0.681798i	−0.940100	−	0.340899i	$-0.889269\pi$
$491$	− 8.07050e7i	− 0.681798i	0.940100	−	0.340899i	$-0.110731\pi$
$492$	0	0
$493$	−2.56778e8	−2.14298
$494$	1.70007e8i	1.41022i
$495$	0	0
$496$	−1.77312e7	−0.145310
$497$	3.81999e6i	0.0311166i
$498$	0	0
$499$	−9.72065e7	−0.782337	−0.391169	−	0.920319i	$-0.627929\pi$
$499$	−9.72065e7	−0.782337	−0.391169	+	0.920319i	$0.627929\pi$
$500$	− 1.84467e6i	− 0.0147574i
$501$	0	0
$502$	−3.47970e7	−0.275062
$503$	1.31021e8i	1.02952i	0.857333	+	0.514762i	$0.172120\pi$
$503$	1.31021e8i	1.02952i	−0.857333	+	0.514762i	$0.827880\pi$
$504$	0	0
$505$	145192.	0.00112737
$506$	4.34805e6i	0.0335616i
$507$	0	0
$508$	−1.02548e8	−0.782234
$509$	− 1.89694e8i	− 1.43847i	−0.694766	−	0.719236i	$-0.744492\pi$
$509$	− 1.89694e8i	− 1.43847i	0.694766	−	0.719236i	$-0.255508\pi$
$510$	0	0
$511$	7.77325e6	0.0582559
$512$	− 5.93164e6i	− 0.0441942i
$513$	0	0
$514$	4.32667e7	0.318614
$515$	− 1.20586e6i	− 0.00882828i
$516$	0	0
$517$	4.11059e6	0.0297463
$518$	− 4.33819e6i	− 0.0312118i
$519$	0	0
$520$	−942546.	−0.00670336
$521$	3.24426e7i	0.229405i	0.993400	+	0.114702i	$0.0365914\pi$
$521$	3.24426e7i	0.229405i	−0.993400	+	0.114702i	$0.963409\pi$
$522$	0	0
$523$	8.16094e7	0.570473	0.285237	−	0.958457i	$-0.407928\pi$
$523$	8.16094e7	0.570473	0.285237	+	0.958457i	$0.407928\pi$
$524$	9.75444e7i	0.677967i
$525$	0	0
$526$	−4.73381e7	−0.325277
$527$	1.25039e8i	0.854309i
$528$	0	0
$529$	−3.05720e7	−0.206517
$530$	1.54206e6i	0.0103580i
$531$	0	0
$532$	−4.32347e6	−0.0287142
$533$	− 2.45845e8i	− 1.62360i
$534$	0	0
$535$	2.82590e6	0.0184542
$536$	− 3.29034e7i	− 0.213672i
$537$	0	0
$538$	−1.28130e8	−0.822821
$539$	− 6.75713e6i	− 0.0431515i
$540$	0	0
$541$	−1.52147e8	−0.960884	−0.480442	−	0.877027i	$-0.659524\pi$
$541$	−1.52147e8	−0.960884	−0.480442	+	0.877027i	$0.659524\pi$
$542$	8.88028e7i	0.557736i
$543$	0	0
$544$	−4.18295e7	−0.259828
$545$	1.59258e6i	0.00983812i
$546$	0	0
$547$	1.71287e8	1.04656	0.523279	−	0.852161i	$-0.324709\pi$
$547$	1.71287e8	1.04656	0.523279	+	0.852161i	$0.324709\pi$
$548$	1.31127e8i	0.796802i
$549$	0	0
$550$	5.08240e6	0.0305479
$551$	3.78646e8i	2.26349i
$552$	0	0
$553$	4.35589e6	0.0257574
$554$	1.07668e8i	0.633223i
$555$	0	0
$556$	3.56134e7	0.207200
$557$	− 2.71640e8i	− 1.57191i	−0.618283	−	0.785956i	$-0.712171\pi$
$557$	− 2.71640e8i	− 1.57191i	0.618283	−	0.785956i	$-0.287829\pi$
$558$	0	0
$559$	−2.14116e8	−1.22578
$560$	− 23970.0i	0 0.000136491i
$561$	0	0
$562$	7.32701e7	0.412779
$563$	2.62132e8i	1.46891i	0.678658	+	0.734454i	$0.262562\pi$
$563$	2.62132e8i	1.46891i	−0.678658	+	0.734454i	$0.737438\pi$
$564$	0	0
$565$	3.21973e6	0.0178515
$566$	− 1.89470e8i	− 1.04494i
$567$	0	0
$568$	5.44987e7	0.297400
$569$	− 2.77186e8i	− 1.50465i	−0.658793	−	0.752324i	$-0.728933\pi$
$569$	− 2.77186e8i	− 1.50465i	0.658793	−	0.752324i	$-0.271067\pi$
$570$	0	0
$571$	−7.07499e7	−0.380030	−0.190015	−	0.981781i	$-0.560854\pi$
$571$	−7.07499e7	−0.380030	−0.190015	+	0.981781i	$0.560854\pi$
$572$	− 5.19433e6i	− 0.0277550i
$573$	0	0
$574$	6.25209e6	0.0330590
$575$	2.08774e8i	1.09818i
$576$	0	0
$577$	−1.69497e8	−0.882336	−0.441168	−	0.897425i	$-0.645436\pi$
$577$	−1.69497e8	−0.882336	−0.441168	+	0.897425i	$0.645436\pi$
$578$	1.58435e8i	0.820481i
$579$	0	0
$580$	−2.09927e6	−0.0107593
$581$	− 1.92781e6i	− 0.00982961i
$582$	0	0
$583$	−8.49824e6	−0.0428868
$584$	− 1.10899e8i	− 0.556786i
$585$	0	0
$586$	8.56140e7	0.425453
$587$	− 2.88623e8i	− 1.42698i	−0.700667	−	0.713489i	$-0.747114\pi$
$587$	− 2.88623e8i	− 1.42698i	0.700667	−	0.713489i	$-0.252886\pi$
$588$	0	0
$589$	1.84383e8	0.902351
$590$	1.20776e6i	0.00588065i
$591$	0	0
$592$	−6.18918e7	−0.298310
$593$	− 1.14093e8i	− 0.547135i	−0.961853	−	0.273567i	$-0.911796\pi$
$593$	− 1.14093e8i	− 0.547135i	0.961853	−	0.273567i	$-0.0882037\pi$
$594$	0	0
$595$	−169034.	−0.000802461 0
$596$	1.62651e7i	0.0768278i
$597$	0	0
$598$	2.13371e8	0.997775
$599$	− 9.69560e7i	− 0.451122i	−0.974229	−	0.225561i	$-0.927578\pi$
$599$	− 9.69560e7i	− 0.451122i	0.974229	−	0.225561i	$-0.0724215\pi$
$600$	0	0
$601$	4.11177e8	1.89411	0.947056	−	0.321068i	$-0.104042\pi$
$601$	4.11177e8	1.89411	0.947056	+	0.321068i	$0.104042\pi$
$602$	− 5.44519e6i	− 0.0249588i
$603$	0	0
$604$	−1.80321e8	−0.818341
$605$	3.26221e6i	0.0147314i
$606$	0	0
$607$	−1.08672e8	−0.485905	−0.242952	−	0.970038i	$-0.578116\pi$
$607$	−1.08672e8	−0.485905	−0.242952	+	0.970038i	$0.578116\pi$
$608$	6.16818e7i	0.274439i
$609$	0	0
$610$	−420341.	−0.00185188
$611$	− 2.01719e8i	− 0.884347i
$612$	0	0
$613$	2.58460e8	1.12205	0.561025	−	0.827799i	$-0.310407\pi$
$613$	2.58460e8	1.12205	0.561025	+	0.827799i	$0.310407\pi$
$614$	3.06501e7i	0.132412i
$615$	0	0
$616$	132097.	0.000565135 0
$617$	1.21801e8i	0.518557i	0.965803	+	0.259278i	$0.0834848\pi$
$617$	1.21801e8i	0.518557i	−0.965803	+	0.259278i	$0.916515\pi$
$618$	0	0
$619$	1.26249e8	0.532300	0.266150	−	0.963932i	$-0.414248\pi$
$619$	1.26249e8	0.532300	0.266150	+	0.963932i	$0.414248\pi$
$620$	1.02225e6i	0.00428925i
$621$	0	0
$622$	1.54799e8	0.643275
$623$	1.29971e6i	0.00537507i
$624$	0	0
$625$	2.43981e8	0.999347
$626$	− 1.28858e8i	− 0.525275i
$627$	0	0
$628$	−1.71601e8	−0.692852
$629$	4.36456e8i	1.75383i
$630$	0	0
$631$	1.13561e6	0.00452003	0.00226002	−	0.999997i	$-0.499281\pi$
$631$	1.13561e6	0.00452003	0.00226002	+	0.999997i	$0.499281\pi$
$632$	− 6.21443e7i	− 0.246179i
$633$	0	0
$634$	−1.49602e8	−0.587044
$635$	5.91214e6i	0.0230900i
$636$	0	0
$637$	−3.31592e8	−1.28288
$638$	− 1.15690e7i	− 0.0445485i
$639$	0	0
$640$	−341973.	−0.00130452
$641$	1.12730e7i	0.0428022i	0.999771	+	0.0214011i	$0.00681270\pi$
$641$	1.12730e7i	0.0428022i	−0.999771	+	0.0214011i	$0.993187\pi$
$642$	0	0
$643$	−3.22689e7	−0.121381	−0.0606905	−	0.998157i	$-0.519330\pi$
$643$	−3.22689e7	−0.121381	−0.0606905	+	0.998157i	$0.519330\pi$
$644$	5.42626e6i	0.0203162i
$645$	0	0
$646$	4.34975e8	1.61349
$647$	− 4.30138e8i	− 1.58816i	−0.607812	−	0.794081i	$-0.707952\pi$
$647$	− 4.30138e8i	− 1.58816i	0.607812	−	0.794081i	$-0.292048\pi$
$648$	0	0
$649$	−6.65592e6	−0.0243486
$650$	− 2.49408e8i	− 0.908178i
$651$	0	0
$652$	7.74468e7	0.279422
$653$	− 5.19891e8i	− 1.86712i	−0.358420	−	0.933561i	$-0.616684\pi$
$653$	− 5.19891e8i	− 1.86712i	0.358420	−	0.933561i	$-0.383316\pi$
$654$	0	0
$655$	5.62367e6	0.0200122
$656$	− 8.91969e7i	− 0.315965i
$657$	0	0
$658$	5.12993e6	0.0180067
$659$	4.15162e8i	1.45064i	0.688409	+	0.725322i	$0.258309\pi$
$659$	4.15162e8i	1.45064i	−0.688409	+	0.725322i	$0.741691\pi$
$660$	0	0
$661$	4.23215e8	1.46540	0.732700	−	0.680552i	$-0.238260\pi$
$661$	4.23215e8	1.46540	0.732700	+	0.680552i	$0.238260\pi$
$662$	− 2.55277e8i	− 0.879910i
$663$	0	0
$664$	−2.75036e7	−0.0939474
$665$	249258.i	0 0.000847587i
$666$	0	0
$667$	4.75227e8	1.60149
$668$	− 2.64599e8i	− 0.887685i
$669$	0	0
$670$	−1.89696e6	−0.00630716
$671$	− 2.31648e6i	− 0.00766763i
$672$	0	0
$673$	−1.72579e6	−0.00566163	−0.00283082	−	0.999996i	$-0.500901\pi$
$673$	−1.72579e6	−0.00566163	−0.00283082	+	0.999996i	$0.500901\pi$
$674$	1.77530e8i	0.579820i
$675$	0	0
$676$	−1.00443e8	−0.325147
$677$	1.87512e8i	0.604315i	0.953258	+	0.302158i	$0.0977069\pi$
$677$	1.87512e8i	0.604315i	−0.953258	+	0.302158i	$0.902293\pi$
$678$	0	0
$679$	6.29036e6	0.0200940
$680$	2.41157e6i	0.00766960i
$681$	0	0
$682$	−5.63356e6	−0.0177595
$683$	3.29781e8i	1.03506i	0.855666	+	0.517528i	$0.173148\pi$
$683$	3.29781e8i	1.03506i	−0.855666	+	0.517528i	$0.826852\pi$
$684$	0	0
$685$	7.55978e6	0.0235200
$686$	− 1.68770e7i	− 0.0522786i
$687$	0	0
$688$	−7.76851e7	−0.238546
$689$	4.17034e8i	1.27501i
$690$	0	0
$691$	−1.58936e8	−0.481714	−0.240857	−	0.970561i	$-0.577429\pi$
$691$	−1.58936e8	−0.481714	−0.240857	+	0.970561i	$0.577429\pi$
$692$	8.39964e7i	0.253479i
$693$	0	0
$694$	6.22291e7	0.186172
$695$	− 2.05320e6i	− 0.00611612i
$696$	0	0
$697$	−6.29010e8	−1.85763
$698$	1.96752e7i	0.0578565i
$699$	0	0
$700$	6.34272e6	0.0184919
$701$	1.13256e8i	0.328780i	0.986395	+	0.164390i	$0.0525656\pi$
$701$	1.13256e8i	0.328780i	−0.986395	+	0.164390i	$0.947434\pi$
$702$	0	0
$703$	6.43598e8	1.85246
$704$	− 1.88460e6i	− 0.00540133i
$705$	0	0
$706$	−1.52548e8	−0.433504
$707$	998562.i	0.00282564i
$708$	0	0
$709$	5.90478e7	0.165678	0.0828390	−	0.996563i	$-0.473601\pi$
$709$	5.90478e7	0.165678	0.0828390	+	0.996563i	$0.473601\pi$
$710$	− 3.14198e6i	− 0.00877866i
$711$	0	0
$712$	1.85427e7	0.0513727
$713$	− 2.31414e8i	− 0.638441i
$714$	0	0
$715$	−299465.	−0.000819273 0
$716$	2.43342e8i	0.662944i
$717$	0	0
$718$	4.99227e8	1.34873
$719$	1.17775e8i	0.316860i	0.987370	+	0.158430i	$0.0506433\pi$
$719$	1.17775e8i	0.316860i	−0.987370	+	0.158430i	$0.949357\pi$
$720$	0	0
$721$	8.29337e6	0.0221272
$722$	− 3.75283e8i	− 0.997119i
$723$	0	0
$724$	3.16621e8	0.834303
$725$	− 5.55491e8i	− 1.45768i
$726$	0	0
$727$	2.16642e8	0.563818	0.281909	−	0.959441i	$-0.409032\pi$
$727$	2.16642e8	0.563818	0.281909	+	0.959441i	$0.409032\pi$
$728$	− 6.48240e6i	− 0.0168013i
$729$	0	0
$730$	−6.39358e6	−0.0164352
$731$	5.47829e8i	1.40247i
$732$	0	0
$733$	5.09661e8	1.29410	0.647052	−	0.762446i	$-0.276002\pi$
$733$	5.09661e8	1.29410	0.647052	+	0.762446i	$0.276002\pi$
$734$	− 1.70024e8i	− 0.429955i
$735$	0	0
$736$	7.74150e7	0.194174
$737$	− 1.04541e7i	− 0.0261145i
$738$	0	0
$739$	1.66066e8	0.411479	0.205740	−	0.978607i	$-0.434040\pi$
$739$	1.66066e8	0.411479	0.205740	+	0.978607i	$0.434040\pi$
$740$	3.56821e6i	0.00880552i
$741$	0	0
$742$	−1.06056e7	−0.0259612
$743$	7.45706e8i	1.81803i	0.416762	+	0.909016i	$0.363165\pi$
$743$	7.45706e8i	1.81803i	−0.416762	+	0.909016i	$0.636835\pi$
$744$	0	0
$745$	937722.	0.00226780
$746$	− 2.21662e8i	− 0.533918i
$747$	0	0
$748$	−1.32900e7	−0.0317557
$749$	1.94353e7i	0.0462536i
$750$	0	0
$751$	−1.04621e8	−0.247002	−0.123501	−	0.992344i	$-0.539412\pi$
$751$	−1.04621e8	−0.247002	−0.123501	+	0.992344i	$0.539412\pi$
$752$	− 7.31873e7i	− 0.172100i
$753$	0	0
$754$	−5.67724e8	−1.32441
$755$	1.03959e7i	0.0241558i
$756$	0	0
$757$	−5.24396e8	−1.20885	−0.604424	−	0.796663i	$-0.706597\pi$
$757$	−5.24396e8	−1.20885	−0.604424	+	0.796663i	$0.706597\pi$
$758$	2.23405e8i	0.512961i
$759$	0	0
$760$	3.55610e6	0.00810090
$761$	− 2.72694e8i	− 0.618759i	−0.950939	−	0.309380i	$-0.899879\pi$
$761$	− 2.72694e8i	− 0.618759i	0.950939	−	0.309380i	$-0.100121\pi$
$762$	0	0
$763$	−1.09530e7	−0.0246582
$764$	− 4.04824e7i	− 0.0907791i
$765$	0	0
$766$	−3.85057e8	−0.856720
$767$	3.26625e8i	0.723876i
$768$	0	0
$769$	−1.43121e7	−0.0314719	−0.0157360	−	0.999876i	$-0.505009\pi$
$769$	−1.43121e7	−0.0314719	−0.0157360	+	0.999876i	$0.505009\pi$
$770$	− 7615.72i	0 1.66817e-5i
$771$	0	0
$772$	−4.19192e7	−0.0911089
$773$	3.91457e8i	0.847512i	0.905776	+	0.423756i	$0.139289\pi$
$773$	3.91457e8i	0.847512i	−0.905776	+	0.423756i	$0.860711\pi$
$774$	0	0
$775$	−2.70498e8	−0.581112
$776$	− 8.97429e7i	− 0.192050i
$777$	0	0
$778$	4.49689e8	0.954935
$779$	9.27538e8i	1.96209i
$780$	0	0
$781$	1.73153e7	0.0363477
$782$	− 5.45924e8i	− 1.14160i
$783$	0	0
$784$	−1.20308e8	−0.249658
$785$	9.89319e6i	0.0204516i
$786$	0	0
$787$	4.13691e8	0.848695	0.424348	−	0.905499i	$-0.360503\pi$
$787$	4.13691e8	0.848695	0.424348	+	0.905499i	$0.360503\pi$
$788$	− 3.14635e8i	− 0.643025i
$789$	0	0
$790$	−3.58277e6	−0.00726670
$791$	2.21438e7i	0.0447428i
$792$	0	0
$793$	−1.13677e8	−0.227956
$794$	2.54920e7i	0.0509263i
$795$	0	0
$796$	−4.36105e8	−0.864672
$797$	4.89600e7i	0.0967088i	0.998830	+	0.0483544i	$0.0153977\pi$
$797$	4.89600e7i	0.0967088i	−0.998830	+	0.0483544i	$0.984602\pi$
$798$	0	0
$799$	−5.16111e8	−1.01182
$800$	− 9.04900e7i	− 0.176738i
$801$	0	0
$802$	2.26222e8	0.438543
$803$	− 3.52347e7i	− 0.0680494i
$804$	0	0
$805$	312837.	0.000599694 0
$806$	2.76455e8i	0.527983i
$807$	0	0
$808$	1.42462e7	0.0270063
$809$	− 2.59106e8i	− 0.489364i	−0.969603	−	0.244682i	$-0.921316\pi$
$809$	− 2.59106e8i	− 0.489364i	0.969603	−	0.244682i	$-0.0786836\pi$
$810$	0	0
$811$	−9.21052e8	−1.72672	−0.863359	−	0.504590i	$-0.831644\pi$
$811$	−9.21052e8	−1.72672	−0.863359	+	0.504590i	$0.831644\pi$
$812$	− 1.44378e7i	− 0.0269671i
$813$	0	0
$814$	−1.96642e7	−0.0364589
$815$	− 4.46499e6i	− 0.00824798i
$816$	0	0
$817$	8.07829e8	1.48134
$818$	2.26911e8i	0.414568i
$819$	0	0
$820$	−5.14241e6	−0.00932664
$821$	3.48579e8i	0.629899i	0.949108	+	0.314950i	$0.101988\pi$
$821$	3.48579e8i	0.629899i	−0.949108	+	0.314950i	$0.898012\pi$
$822$	0	0
$823$	−4.13774e8	−0.742272	−0.371136	−	0.928578i	$-0.621032\pi$
$823$	−4.13774e8	−0.742272	−0.371136	+	0.928578i	$0.621032\pi$
$824$	− 1.18319e8i	− 0.211482i
$825$	0	0
$826$	−8.30643e6	−0.0147392
$827$	− 3.10912e8i	− 0.549693i	−0.961488	−	0.274847i	$-0.911373\pi$
$827$	− 3.10912e8i	− 0.549693i	0.961488	−	0.274847i	$-0.0886271\pi$
$828$	0	0
$829$	−2.87241e8	−0.504177	−0.252089	−	0.967704i	$-0.581117\pi$
$829$	−2.87241e8	−0.504177	−0.252089	+	0.967704i	$0.581117\pi$
$830$	1.58565e6i	0.00277314i
$831$	0	0
$832$	−9.24827e7	−0.160580
$833$	8.48400e8i	1.46780i
$834$	0	0
$835$	−1.52548e7	−0.0262027
$836$	1.95975e7i	0.0335414i
$837$	0	0
$838$	5.03153e8	0.855004
$839$	− 8.52887e8i	− 1.44413i	−0.691827	−	0.722064i	$-0.743194\pi$
$839$	− 8.52887e8i	− 1.44413i	0.691827	−	0.722064i	$-0.256806\pi$
$840$	0	0
$841$	−6.69629e8	−1.12576
$842$	− 2.62124e8i	− 0.439106i
$843$	0	0
$844$	9.96097e7	0.165682
$845$	5.79078e6i	0.00959770i
$846$	0	0
$847$	−2.24360e7	−0.0369228
$848$	1.51307e8i	0.248126i
$849$	0	0
$850$	−6.38128e8	−1.03908
$851$	− 8.07762e8i	− 1.31067i
$852$	0	0
$853$	−7.50303e8	−1.20890	−0.604449	−	0.796644i	$-0.706607\pi$
$853$	−7.50303e8	−1.20890	−0.604449	+	0.796644i	$0.706607\pi$
$854$	− 2.89092e6i	− 0.00464154i
$855$	0	0
$856$	2.77278e8	0.442073
$857$	− 9.88975e8i	− 1.57124i	−0.618708	−	0.785621i	$-0.712344\pi$
$857$	− 9.88975e8i	− 1.57124i	0.618708	−	0.785621i	$-0.287656\pi$
$858$	0	0
$859$	−8.15987e8	−1.28737	−0.643685	−	0.765290i	$-0.722595\pi$
$859$	−8.15987e8	−1.28737	−0.643685	+	0.765290i	$0.722595\pi$
$860$	4.47873e6i	0.00704140i
$861$	0	0
$862$	−6.62274e8	−1.03399
$863$	2.87047e8i	0.446603i	0.974749	+	0.223301i	$0.0716834\pi$
$863$	2.87047e8i	0.446603i	−0.974749	+	0.223301i	$0.928317\pi$
$864$	0	0
$865$	4.84259e6	0.00748220
$866$	− 1.02522e8i	− 0.157857i
$867$	0	0
$868$	−7.03056e6	−0.0107505
$869$	− 1.97445e7i	− 0.0300875i
$870$	0	0
$871$	−5.13011e8	−0.776376
$872$	1.56264e8i	0.235673i
$873$	0	0
$874$	−8.05021e8	−1.20579
$875$	− 731426.i	− 0.00109181i
$876$	0	0
$877$	2.34428e8	0.347545	0.173772	−	0.984786i	$-0.444404\pi$
$877$	2.34428e8	0.347545	0.173772	+	0.984786i	$0.444404\pi$
$878$	− 3.42399e7i	− 0.0505882i
$879$	0	0
$880$	−108652.	−0.000159437 0
$881$	− 6.01503e6i	− 0.00879651i	−0.999990	−	0.00439825i	$-0.998600\pi$
$881$	− 6.01503e6i	− 0.00879651i	0.999990	−	0.00439825i	$-0.00140001\pi$
$882$	0	0
$883$	−5.07079e8	−0.736535	−0.368267	−	0.929720i	$-0.620049\pi$
$883$	−5.07079e8	−0.736535	−0.368267	+	0.929720i	$0.620049\pi$
$884$	6.52181e8i	0.944085i
$885$	0	0
$886$	−2.75223e7	−0.0395715
$887$	− 1.14307e9i	− 1.63795i	−0.573826	−	0.818977i	$-0.694542\pi$
$887$	− 1.14307e9i	− 1.63795i	0.573826	−	0.818977i	$-0.305458\pi$
$888$	0	0
$889$	−4.06610e7	−0.0578726
$890$	− 1.06903e6i	− 0.00151642i
$891$	0	0
$892$	6.43193e8	0.906248
$893$	7.61058e8i	1.06872i
$894$	0	0
$895$	1.40292e7	0.0195688
$896$	− 2.35193e6i	− 0.00326965i
$897$	0	0
$898$	−8.10809e8	−1.11967
$899$	6.15730e8i	0.847445i
$900$	0	0
$901$	1.06701e9	1.45879
$902$	− 2.83396e7i	− 0.0386166i
$903$	0	0
$904$	3.15920e8	0.427633
$905$	− 1.82539e7i	− 0.0246270i
$906$	0	0
$907$	4.81570e8	0.645413	0.322707	−	0.946499i	$-0.395407\pi$
$907$	4.81570e8	0.645413	0.322707	+	0.946499i	$0.395407\pi$
$908$	− 3.80920e8i	− 0.508835i
$909$	0	0
$910$	−373726.	−0.000495940 0
$911$	− 7.24532e8i	− 0.958303i	−0.877732	−	0.479151i	$-0.840945\pi$
$911$	− 7.24532e8i	− 0.958303i	0.877732	−	0.479151i	$-0.159055\pi$
$912$	0	0
$913$	−8.73842e6	−0.0114821
$914$	− 5.51377e8i	− 0.722121i
$915$	0	0
$916$	9.93114e7	0.129215
$917$	3.86770e7i	0.0501585i
$918$	0	0
$919$	1.45033e7	0.0186862	0.00934311	−	0.999956i	$-0.497026\pi$
$919$	1.45033e7	0.0186862	0.00934311	+	0.999956i	$0.497026\pi$
$920$	− 4.46316e6i	− 0.00573164i
$921$	0	0
$922$	3.02473e8	0.385917
$923$	− 8.49713e8i	− 1.08061i
$924$	0	0
$925$	−9.44188e8	−1.19298
$926$	− 1.74107e8i	− 0.219272i
$927$	0	0
$928$	−2.05981e8	−0.257740
$929$	4.70497e8i	0.586826i	0.955986	+	0.293413i	$0.0947911\pi$
$929$	4.70497e8i	0.586826i	−0.955986	+	0.293413i	$0.905209\pi$
$930$	0	0
$931$	1.25105e9	1.55034
$932$	− 2.99528e8i	− 0.369989i
$933$	0	0
$934$	6.23978e8	0.765824
$935$	766202.i	0 0.000937364i
$936$	0	0
$937$	1.72677e8	0.209902	0.104951	−	0.994477i	$-0.466531\pi$
$937$	1.72677e8	0.209902	0.104951	+	0.994477i	$0.466531\pi$
$938$	− 1.30464e7i	− 0.0158082i
$939$	0	0
$940$	−4.21942e6	−0.00508006
$941$	1.87833e8i	0.225426i	0.993628	+	0.112713i	$0.0359540\pi$
$941$	1.87833e8i	0.225426i	−0.993628	+	0.112713i	$0.964046\pi$
$942$	0	0
$943$	1.16413e9	1.38824
$944$	1.18506e8i	0.140872i
$945$	0	0
$946$	−2.46821e7	−0.0291547
$947$	6.42687e7i	0.0756745i	0.999284	+	0.0378373i	$0.0120468\pi$
$947$	6.42687e7i	0.0756745i	−0.999284	+	0.0378373i	$0.987953\pi$
$948$	0	0
$949$	−1.72907e9	−2.02309
$950$	9.40984e8i	1.09752i
$951$	0	0
$952$	−1.65857e7	−0.0192230
$953$	− 8.06493e8i	− 0.931798i	−0.884838	−	0.465899i	$-0.845731\pi$
$953$	− 8.06493e8i	− 0.931798i	0.884838	−	0.465899i	$-0.154269\pi$
$954$	0	0
$955$	−2.33390e6	−0.00267962
$956$	− 2.23810e8i	− 0.256156i
$957$	0	0
$958$	4.77672e7	0.0543291
$959$	5.19927e7i	0.0589504i
$960$	0	0
$961$	−5.87671e8	−0.662162
$962$	9.64981e8i	1.08391i
$963$	0	0
$964$	1.32334e8	0.147721
$965$	2.41674e6i	0.00268935i
$966$	0	0
$967$	2.62029e8	0.289781	0.144890	−	0.989448i	$-0.453717\pi$
$967$	2.62029e8	0.289781	0.144890	+	0.989448i	$0.453717\pi$
$968$	3.20088e8i	0.352893i
$969$	0	0
$970$	−5.17389e6	−0.00566894
$971$	6.14354e8i	0.671060i	0.942030	+	0.335530i	$0.108915\pi$
$971$	6.14354e8i	0.671060i	−0.942030	+	0.335530i	$0.891085\pi$
$972$	0	0
$973$	1.41210e7	0.0153294
$974$	2.03080e8i	0.219781i
$975$	0	0
$976$	−4.12439e7	−0.0443619
$977$	8.39851e8i	0.900572i	0.892884	+	0.450286i	$0.148678\pi$
$977$	8.39851e8i	0.900572i	−0.892884	+	0.450286i	$0.851322\pi$
$978$	0	0
$979$	5.89137e6	0.00627868
$980$	6.93602e6i	0.00736940i
$981$	0	0
$982$	−4.56536e8	−0.482104
$983$	− 1.24834e9i	− 1.31423i	−0.753791	−	0.657114i	$-0.771777\pi$
$983$	− 1.24834e9i	− 1.31423i	0.753791	−	0.657114i	$-0.228223\pi$
$984$	0	0
$985$	−1.81394e7	−0.0189808
$986$	1.45256e9i	1.51531i
$987$	0	0
$988$	9.61707e8	0.997176
$989$	− 1.01388e9i	− 1.04809i
$990$	0	0
$991$	1.60725e8	0.165144	0.0825719	−	0.996585i	$-0.473687\pi$
$991$	1.60725e8	0.165144	0.0825719	+	0.996585i	$0.473687\pi$
$992$	1.00303e8i	0.102749i
$993$	0	0
$994$	2.16091e7	0.0220028
$995$	2.51425e7i	0.0255234i
$996$	0	0
$997$	6.87346e8	0.693569	0.346785	−	0.937945i	$-0.387273\pi$
$997$	6.87346e8	0.693569	0.346785	+	0.937945i	$0.387273\pi$
$998$	5.49883e8i	0.553196i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.7.b.c.161.3		12
3.2	odd	2	inner	162.7.b.c.161.10		12
9.2	odd	6		18.7.d.a.5.6	✓	12
9.4	even	3		18.7.d.a.11.6	yes	12
9.5	odd	6		54.7.d.a.35.2		12
9.7	even	3		54.7.d.a.17.2		12
36.7	odd	6		432.7.q.b.17.3		12
36.11	even	6		144.7.q.c.113.2		12
36.23	even	6		432.7.q.b.305.3		12
36.31	odd	6		144.7.q.c.65.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.7.d.a.5.6	✓	12	9.2	odd	6
18.7.d.a.11.6	yes	12	9.4	even	3
54.7.d.a.17.2		12	9.7	even	3
54.7.d.a.35.2		12	9.5	odd	6
144.7.q.c.65.2		12	36.31	odd	6
144.7.q.c.113.2		12	36.11	even	6
162.7.b.c.161.3		12	1.1	even	1	trivial
162.7.b.c.161.10		12	3.2	odd	2	inner
432.7.q.b.17.3		12	36.7	odd	6
432.7.q.b.305.3		12	36.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-5.65685i q^{2} -32.0000 q^{4} +1.84488i q^{5} -12.6882 q^{7} +181.019i q^{8} +O(q^{10})\)	\(q-5.65685i q^{2} -32.0000 q^{4} +1.84488i q^{5} -12.6882 q^{7} +181.019i q^{8} +10.4362 q^{10} +57.5134i q^{11} +2822.35 q^{13} +71.7754i q^{14} +1024.00 q^{16} -7221.17i q^{17} -10648.3 q^{19} -59.0360i q^{20} +325.345 q^{22} +13364.4i q^{23} +15621.6 q^{25} -15965.6i q^{26} +406.023 q^{28} -35559.1i q^{29} -17315.7 q^{31} -5792.62i q^{32} -40849.1 q^{34} -23.4082i q^{35} -60441.2 q^{37} +60236.1i q^{38} -333.958 q^{40} -87106.4i q^{41} -75864.3 q^{43} -1840.43i q^{44} +75600.6 q^{46} -71472.0i q^{47} -117488. q^{49} -88369.1i q^{50} -90315.2 q^{52} +147761. i q^{53} -106.105 q^{55} -2296.81i q^{56} -201153. q^{58} +115728. i q^{59} -40277.3 q^{61} +97952.2i q^{62} -32768.0 q^{64} +5206.88i q^{65} -181767. q^{67} +231077. i q^{68} -132.417 q^{70} -301066. i q^{71} -612635. q^{73} +341907. i q^{74} +340747. q^{76} -729.742i q^{77} -343302. q^{79} +1889.15i q^{80} -492748. q^{82} +151937. i q^{83} +13322.1 q^{85} +429153. i q^{86} -10411.0 q^{88} -102435. i q^{89} -35810.6 q^{91} -427662. i q^{92} -404306. q^{94} -19644.9i q^{95} -495764. q^{97} +664613. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 384 q^{4} - 480 q^{7}+O(q^{10}) \) 12 * q - 384 * q^4 - 480 * q^7	\( 12 q - 384 q^{4} - 480 q^{7} - 3360 q^{13} + 12288 q^{16} - 2820 q^{19} + 7200 q^{22} - 16188 q^{25} + 15360 q^{28} - 42960 q^{31} + 54720 q^{34} - 25536 q^{37} - 142860 q^{43} - 135072 q^{46} + 271908 q^{49} + 107520 q^{52} + 580392 q^{55} - 318528 q^{58} - 271488 q^{61} - 393216 q^{64} + 579876 q^{67} - 311904 q^{70} - 977700 q^{73} + 90240 q^{76} + 1529592 q^{79} + 1073088 q^{82} - 3239136 q^{85} - 230400 q^{88} + 355584 q^{91} + 1473696 q^{94} + 77748 q^{97}+O(q^{100}) \) 12 * q - 384 * q^4 - 480 * q^7 - 3360 * q^13 + 12288 * q^16 - 2820 * q^19 + 7200 * q^22 - 16188 * q^25 + 15360 * q^28 - 42960 * q^31 + 54720 * q^34 - 25536 * q^37 - 142860 * q^43 - 135072 * q^46 + 271908 * q^49 + 107520 * q^52 + 580392 * q^55 - 318528 * q^58 - 271488 * q^61 - 393216 * q^64 + 579876 * q^67 - 311904 * q^70 - 977700 * q^73 + 90240 * q^76 + 1529592 * q^79 + 1073088 * q^82 - 3239136 * q^85 - 230400 * q^88 + 355584 * q^91 + 1473696 * q^94 + 77748 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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