LMFDB - Embedded newform 162.7.b.c.161.6

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			161.6
Root			$-8.88570i$ of defining polynomial
Character	$\chi$	$=$	162.161
Dual form			162.7.b.c.161.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.65685i q^{2} -32.0000 q^{4} +233.541i q^{5} -191.150 q^{7} +181.019i q^{8} +O(q^{10})$	\(q-5.65685i q^{2} -32.0000 q^{4} +233.541i q^{5} -191.150 q^{7} +181.019i q^{8} +1321.11 q^{10} +777.202i q^{11} -91.1604 q^{13} +1081.31i q^{14} +1024.00 q^{16} +7047.39i q^{17} +2731.10 q^{19} -7473.32i q^{20} +4396.52 q^{22} -19894.3i q^{23} -38916.6 q^{25} +515.681i q^{26} +6116.81 q^{28} -31297.4i q^{29} -12349.0 q^{31} -5792.62i q^{32} +39866.1 q^{34} -44641.5i q^{35} -27972.0 q^{37} -15449.4i q^{38} -42275.5 q^{40} -43218.3i q^{41} -38512.1 q^{43} -24870.5i q^{44} -112539. q^{46} +166012. i q^{47} -81110.5 q^{49} +220145. i q^{50} +2917.13 q^{52} -54741.5i q^{53} -181509. q^{55} -34601.9i q^{56} -177045. q^{58} -16283.7i q^{59} -58887.4 q^{61} +69856.5i q^{62} -32768.0 q^{64} -21289.7i q^{65} +295997. q^{67} -225517. i q^{68} -252530. q^{70} +157251. i q^{71} +80297.0 q^{73} +158234. i q^{74} -87395.0 q^{76} -148563. i q^{77} -376849. q^{79} +239146. i q^{80} -244480. q^{82} -847541. i q^{83} -1.64586e6 q^{85} +217857. i q^{86} -140689. q^{88} +1128.91i q^{89} +17425.3 q^{91} +636617. i q^{92} +939108. q^{94} +637824. i q^{95} -1.35030e6 q^{97} +458831. i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	233.541i	1.86833i	0.356841	+	0.934165i	$0.383854\pi$
$5$	233.541i	1.86833i	−0.356841	+	0.934165i	$0.616146\pi$
$6$	0	0
$7$	−191.150	−0.557290	−0.278645	−	0.960394i	$-0.589885\pi$
$7$	−191.150	−0.557290	−0.278645	+	0.960394i	$0.589885\pi$
$8$	181.019i	0.353553i
$9$	0	0
$10$	1321.11	1.32111
$11$	777.202i	0.583924i	0.956430	+	0.291962i	$0.0943080\pi$
$11$	777.202i	0.583924i	−0.956430	+	0.291962i	$0.905692\pi$
$12$	0	0
$13$	−91.1604	−0.0414931	−0.0207466	−	0.999785i	$-0.506604\pi$
$13$	−91.1604	−0.0414931	−0.0207466	+	0.999785i	$0.506604\pi$
$14$	1081.31i	0.394063i
$15$	0	0
$16$	1024.00	0.250000
$17$	7047.39i	1.43444i	0.696848	+	0.717219i	$0.254585\pi$
$17$	7047.39i	1.43444i	−0.696848	+	0.717219i	$0.745415\pi$
$18$	0	0
$19$	2731.10	0.398177	0.199088	−	0.979982i	$-0.436202\pi$
$19$	2731.10	0.398177	0.199088	+	0.979982i	$0.436202\pi$
$20$	− 7473.32i	− 0.934165i
$21$	0	0
$22$	4396.52	0.412896
$23$	− 19894.3i	− 1.63510i	−0.575857	−	0.817550i	$-0.695332\pi$
$23$	− 19894.3i	− 1.63510i	0.575857	−	0.817550i	$-0.304668\pi$
$24$	0	0
$25$	−38916.6	−2.49066
$26$	515.681i	0.0293401i
$27$	0	0
$28$	6116.81	0.278645
$29$	− 31297.4i	− 1.28326i	−0.767015	−	0.641629i	$-0.778259\pi$
$29$	− 31297.4i	− 1.28326i	0.767015	−	0.641629i	$-0.221741\pi$
$30$	0	0
$31$	−12349.0	−0.414521	−0.207261	−	0.978286i	$-0.566455\pi$
$31$	−12349.0	−0.414521	−0.207261	+	0.978286i	$0.566455\pi$
$32$	− 5792.62i	− 0.176777i
$33$	0	0
$34$	39866.1	1.01430
$35$	− 44641.5i	− 1.04120i
$36$	0	0
$37$	−27972.0	−0.552228	−0.276114	−	0.961125i	$-0.589047\pi$
$37$	−27972.0	−0.552228	−0.276114	+	0.961125i	$0.589047\pi$
$38$	− 15449.4i	− 0.281554i
$39$	0	0
$40$	−42275.5	−0.660555
$41$	− 43218.3i	− 0.627070i	−0.949577	−	0.313535i	$-0.898487\pi$
$41$	− 43218.3i	− 0.627070i	0.949577	−	0.313535i	$-0.101513\pi$
$42$	0	0
$43$	−38512.1	−0.484386	−0.242193	−	0.970228i	$-0.577867\pi$
$43$	−38512.1	−0.484386	−0.242193	+	0.970228i	$0.577867\pi$
$44$	− 24870.5i	− 0.291962i
$45$	0	0
$46$	−112539.	−1.15619
$47$	166012.i	1.59899i	0.600670	+	0.799497i	$0.294901\pi$
$47$	166012.i	1.59899i	−0.600670	+	0.799497i	$0.705099\pi$
$48$	0	0
$49$	−81110.5	−0.689428
$50$	220145.i	1.76116i
$51$	0	0
$52$	2917.13	0.0207466
$53$	− 54741.5i	− 0.367696i	−0.982955	−	0.183848i	$-0.941145\pi$
$53$	− 54741.5i	− 0.367696i	0.982955	−	0.183848i	$-0.0588554\pi$
$54$	0	0
$55$	−181509.	−1.09096
$56$	− 34601.9i	− 0.197032i
$57$	0	0
$58$	−177045.	−0.907400
$59$	− 16283.7i	− 0.0792860i	−0.999214	−	0.0396430i	$-0.987378\pi$
$59$	− 16283.7i	− 0.0792860i	0.999214	−	0.0396430i	$-0.0126221\pi$
$60$	0	0
$61$	−58887.4	−0.259438	−0.129719	−	0.991551i	$-0.541407\pi$
$61$	−58887.4	−0.259438	−0.129719	+	0.991551i	$0.541407\pi$
$62$	69856.5i	0.293111i
$63$	0	0
$64$	−32768.0	−0.125000
$65$	− 21289.7i	− 0.0775229i
$66$	0	0
$67$	295997.	0.984152	0.492076	−	0.870552i	$-0.336238\pi$
$67$	295997.	0.984152	0.492076	+	0.870552i	$0.336238\pi$
$68$	− 225517.i	− 0.717219i
$69$	0	0
$70$	−252530.	−0.736240
$71$	157251.i	0.439358i	0.975572	+	0.219679i	$0.0705010\pi$
$71$	157251.i	0.439358i	−0.975572	+	0.219679i	$0.929499\pi$
$72$	0	0
$73$	80297.0	0.206410	0.103205	−	0.994660i	$-0.467090\pi$
$73$	80297.0	0.206410	0.103205	+	0.994660i	$0.467090\pi$
$74$	158234.i	0.390484i
$75$	0	0
$76$	−87395.0	−0.199088
$77$	− 148563.i	− 0.325415i
$78$	0	0
$79$	−376849.	−0.764338	−0.382169	−	0.924092i	$-0.624823\pi$
$79$	−376849.	−0.764338	−0.382169	+	0.924092i	$0.624823\pi$
$80$	239146.i	0.467083i
$81$	0	0
$82$	−244480.	−0.443406
$83$	− 847541.i	− 1.48227i	−0.671358	−	0.741134i	$-0.734289\pi$
$83$	− 847541.i	− 1.48227i	0.671358	−	0.741134i	$-0.265711\pi$
$84$	0	0
$85$	−1.64586e6	−2.68000
$86$	217857.i	0.342513i
$87$	0	0
$88$	−140689.	−0.206448
$89$	1128.91i	0.00160136i	1.00000		0.000800679i	$0.000254864\pi$
$89$	1128.91i	0.00160136i	−1.00000		0.000800679i	$0.999745\pi$
$90$	0	0
$91$	17425.3	0.0231237
$92$	636617.i	0.817550i
$93$	0	0
$94$	939108.	1.13066
$95$	637824.i	0.743926i
$96$	0	0
$97$	−1.35030e6	−1.47951	−0.739753	−	0.672879i	$-0.765057\pi$
$97$	−1.35030e6	−1.47951	−0.739753	+	0.672879i	$0.765057\pi$
$98$	458831.i	0.487499i
$99$	0	0
$100$	1.24533e6	1.24533
$101$	158837.i	0.154166i	0.997025	+	0.0770828i	$0.0245606\pi$
$101$	158837.i	0.154166i	−0.997025	+	0.0770828i	$0.975439\pi$
$102$	0	0
$103$	497228.	0.455034	0.227517	−	0.973774i	$-0.426939\pi$
$103$	497228.	0.455034	0.227517	+	0.973774i	$0.426939\pi$
$104$	− 16501.8i	− 0.0146700i
$105$	0	0
$106$	−309664.	−0.260000
$107$	207159.i	0.169103i	0.996419	+	0.0845516i	$0.0269458\pi$
$107$	207159.i	0.169103i	−0.996419	+	0.0845516i	$0.973054\pi$
$108$	0	0
$109$	−2.30287e6	−1.77824	−0.889120	−	0.457673i	$-0.848683\pi$
$109$	−2.30287e6	−1.77824	−0.889120	+	0.457673i	$0.848683\pi$
$110$	1.02677e6i	0.771427i
$111$	0	0
$112$	−195738.	−0.139322
$113$	− 782361.i	− 0.542216i	−0.962549	−	0.271108i	$-0.912610\pi$
$113$	− 782361.i	− 0.542216i	0.962549	−	0.271108i	$-0.0873900\pi$
$114$	0	0
$115$	4.64613e6	3.05491
$116$	1.00152e6i	0.641629i
$117$	0	0
$118$	−92114.4	−0.0560637
$119$	− 1.34711e6i	− 0.799397i
$120$	0	0
$121$	1.16752e6	0.659033
$122$	333118.i	0.183450i
$123$	0	0
$124$	395168.	0.207261
$125$	− 5.43954e6i	− 2.78504i
$126$	0	0
$127$	1.19415e6	0.582970	0.291485	−	0.956575i	$-0.405851\pi$
$127$	1.19415e6	0.582970	0.291485	+	0.956575i	$0.405851\pi$
$128$	185364.i	0.0883883i
$129$	0	0
$130$	−120433.	−0.0548170
$131$	− 2.51197e6i	− 1.11738i	−0.829377	−	0.558689i	$-0.811305\pi$
$131$	− 2.51197e6i	− 1.11738i	0.829377	−	0.558689i	$-0.188695\pi$
$132$	0	0
$133$	−522050.	−0.221900
$134$	− 1.67441e6i	− 0.695901i
$135$	0	0
$136$	−1.27571e6	−0.507150
$137$	− 812489.i	− 0.315977i	−0.987441	−	0.157989i	$-0.949499\pi$
$137$	− 812489.i	− 0.315977i	0.987441	−	0.157989i	$-0.0505009\pi$
$138$	0	0
$139$	701110.	0.261061	0.130530	−	0.991444i	$-0.458332\pi$
$139$	701110.	0.261061	0.130530	+	0.991444i	$0.458332\pi$
$140$	1.42853e6i	0.520601i
$141$	0	0
$142$	889546.	0.310673
$143$	− 70850.1i	− 0.0242288i
$144$	0	0
$145$	7.30923e6	2.39755
$146$	− 454228.i	− 0.145954i
$147$	0	0
$148$	895105.	0.276114
$149$	306150.i	0.0925498i	0.998929	+	0.0462749i	$0.0147350\pi$
$149$	306150.i	0.0925498i	−0.998929	+	0.0462749i	$0.985265\pi$
$150$	0	0
$151$	1.84757e6	0.536623	0.268312	−	0.963332i	$-0.413534\pi$
$151$	1.84757e6	0.536623	0.268312	+	0.963332i	$0.413534\pi$
$152$	494381.i	0.140777i
$153$	0	0
$154$	−840396.	−0.230103
$155$	− 2.88400e6i	− 0.774463i
$156$	0	0
$157$	3.15065e6	0.814144	0.407072	−	0.913396i	$-0.366550\pi$
$157$	3.15065e6	0.814144	0.407072	+	0.913396i	$0.366550\pi$
$158$	2.13178e6i	0.540469i
$159$	0	0
$160$	1.35282e6	0.330277
$161$	3.80280e6i	0.911225i
$162$	0	0
$163$	−1.29782e6	−0.299676	−0.149838	−	0.988711i	$-0.547875\pi$
$163$	−1.29782e6	−0.299676	−0.149838	+	0.988711i	$0.547875\pi$
$164$	1.38299e6i	0.313535i
$165$	0	0
$166$	−4.79442e6	−1.04812
$167$	− 1.63454e6i	− 0.350952i	−0.984484	−	0.175476i	$-0.943854\pi$
$167$	− 1.63454e6i	− 0.350952i	0.984484	−	0.175476i	$-0.0561464\pi$
$168$	0	0
$169$	−4.81850e6	−0.998278
$170$	9.31038e6i	1.89505i
$171$	0	0
$172$	1.23239e6	0.242193
$173$	9.48257e6i	1.83142i	0.401840	+	0.915710i	$0.368371\pi$
$173$	9.48257e6i	1.83142i	−0.401840	+	0.915710i	$0.631629\pi$
$174$	0	0
$175$	7.43891e6	1.38802
$176$	795855.i	0.145981i
$177$	0	0
$178$	6386.07	0.00113233
$179$	9.23510e6i	1.61021i	0.593133	+	0.805105i	$0.297891\pi$
$179$	9.23510e6i	1.61021i	−0.593133	+	0.805105i	$0.702109\pi$
$180$	0	0
$181$	4.59474e6	0.774864	0.387432	−	0.921898i	$-0.373362\pi$
$181$	4.59474e6	0.774864	0.387432	+	0.921898i	$0.373362\pi$
$182$	− 98572.6i	− 0.0163509i
$183$	0	0
$184$	3.60125e6	0.578095
$185$	− 6.53262e6i	− 1.03175i
$186$	0	0
$187$	−5.47725e6	−0.837602
$188$	− 5.31240e6i	− 0.799497i
$189$	0	0
$190$	3.60808e6	0.526035
$191$	− 7.84494e6i	− 1.12587i	−0.826500	−	0.562936i	$-0.809672\pi$
$191$	− 7.84494e6i	− 1.12587i	0.826500	−	0.562936i	$-0.190328\pi$
$192$	0	0
$193$	−5.43784e6	−0.756406	−0.378203	−	0.925723i	$-0.623458\pi$
$193$	−5.43784e6	−0.756406	−0.378203	+	0.925723i	$0.623458\pi$
$194$	7.63848e6i	1.04617i
$195$	0	0
$196$	2.59554e6	0.344714
$197$	− 1.01096e7i	− 1.32232i	−0.750246	−	0.661159i	$-0.770065\pi$
$197$	− 1.01096e7i	− 1.32232i	0.750246	−	0.661159i	$-0.229935\pi$
$198$	0	0
$199$	−6.91799e6	−0.877851	−0.438925	−	0.898523i	$-0.644641\pi$
$199$	−6.91799e6	−0.877851	−0.438925	+	0.898523i	$0.644641\pi$
$200$	− 7.04465e6i	− 0.880581i
$201$	0	0
$202$	898518.	0.109012
$203$	5.98250e6i	0.715146i
$204$	0	0
$205$	1.00933e7	1.17157
$206$	− 2.81275e6i	− 0.321758i
$207$	0	0
$208$	−93348.3	−0.0103733
$209$	2.12261e6i	0.232505i
$210$	0	0
$211$	−8.55191e6	−0.910366	−0.455183	−	0.890398i	$-0.650426\pi$
$211$	−8.55191e6	−0.910366	−0.455183	+	0.890398i	$0.650426\pi$
$212$	1.75173e6i	0.183848i
$213$	0	0
$214$	1.17187e6	0.119574
$215$	− 8.99417e6i	− 0.904994i
$216$	0	0
$217$	2.36052e6	0.231008
$218$	1.30270e7i	1.25741i
$219$	0	0
$220$	5.80828e6	0.545481
$221$	− 642443.i	− 0.0595193i
$222$	0	0
$223$	−5.25865e6	−0.474198	−0.237099	−	0.971485i	$-0.576197\pi$
$223$	−5.25865e6	−0.474198	−0.237099	+	0.971485i	$0.576197\pi$
$224$	1.10726e6i	0.0985158i
$225$	0	0
$226$	−4.42570e6	−0.383404
$227$	8.08649e6i	0.691326i	0.938359	+	0.345663i	$0.112346\pi$
$227$	8.08649e6i	0.691326i	−0.938359	+	0.345663i	$0.887654\pi$
$228$	0	0
$229$	−1.22011e7	−1.01600	−0.508001	−	0.861357i	$-0.669615\pi$
$229$	−1.22011e7	−1.01600	−0.508001	+	0.861357i	$0.669615\pi$
$230$	− 2.62825e7i	− 2.16015i
$231$	0	0
$232$	5.66543e6	0.453700
$233$	− 5.57473e6i	− 0.440713i	−0.975419	−	0.220357i	$-0.929278\pi$
$233$	− 5.57473e6i	− 0.440713i	0.975419	−	0.220357i	$-0.0707221\pi$
$234$	0	0
$235$	−3.87708e7	−2.98745
$236$	521078.i	0.0396430i
$237$	0	0
$238$	−7.62041e6	−0.565259
$239$	1.64693e7i	1.20637i	0.797601	+	0.603185i	$0.206102\pi$
$239$	1.64693e7i	1.20637i	−0.797601	+	0.603185i	$0.793898\pi$
$240$	0	0
$241$	4.60541e6	0.329016	0.164508	−	0.986376i	$-0.447396\pi$
$241$	4.60541e6	0.329016	0.164508	+	0.986376i	$0.447396\pi$
$242$	− 6.60448e6i	− 0.466007i
$243$	0	0
$244$	1.88440e6	0.129719
$245$	− 1.89427e7i	− 1.28808i
$246$	0	0
$247$	−248968.	−0.0165216
$248$	− 2.23541e6i	− 0.146555i
$249$	0	0
$250$	−3.07707e7	−1.96932
$251$	1.58119e7i	0.999913i	0.866051	+	0.499956i	$0.166651\pi$
$251$	1.58119e7i	0.999913i	−0.866051	+	0.499956i	$0.833349\pi$
$252$	0	0
$253$	1.54619e7	0.954774
$254$	− 6.75511e6i	− 0.412222i
$255$	0	0
$256$	1.04858e6	0.0625000
$257$	1.87763e7i	1.10614i	0.833134	+	0.553071i	$0.186544\pi$
$257$	1.87763e7i	1.10614i	−0.833134	+	0.553071i	$0.813456\pi$
$258$	0	0
$259$	5.34686e6	0.307751
$260$	681271.i	0.0387614i
$261$	0	0
$262$	−1.42098e7	−0.790106
$263$	8.52830e6i	0.468808i	0.972139	+	0.234404i	$0.0753139\pi$
$263$	8.52830e6i	0.468808i	−0.972139	+	0.234404i	$0.924686\pi$
$264$	0	0
$265$	1.27844e7	0.686977
$266$	2.95316e6i	0.156907i
$267$	0	0
$268$	−9.47189e6	−0.492076
$269$	1.62898e7i	0.836871i	0.908247	+	0.418436i	$0.137421\pi$
$269$	1.62898e7i	0.836871i	−0.908247	+	0.418436i	$0.862579\pi$
$270$	0	0
$271$	2.43919e7	1.22557	0.612785	−	0.790250i	$-0.290049\pi$
$271$	2.43919e7	1.22557	0.612785	+	0.790250i	$0.290049\pi$
$272$	7.21653e6i	0.358609i
$273$	0	0
$274$	−4.59613e6	−0.223430
$275$	− 3.02460e7i	− 1.45435i
$276$	0	0
$277$	−3.31231e7	−1.55845	−0.779223	−	0.626747i	$-0.784386\pi$
$277$	−3.31231e7	−1.55845	−0.779223	+	0.626747i	$0.784386\pi$
$278$	− 3.96608e6i	− 0.184598i
$279$	0	0
$280$	8.08098e6	0.368120
$281$	3.61709e6i	0.163020i	0.996673	+	0.0815098i	$0.0259742\pi$
$281$	3.61709e6i	0.163020i	−0.996673	+	0.0815098i	$0.974026\pi$
$282$	0	0
$283$	−3.23856e7	−1.42887	−0.714435	−	0.699702i	$-0.753316\pi$
$283$	−3.23856e7	−1.42887	−0.714435	+	0.699702i	$0.753316\pi$
$284$	− 5.03203e6i	− 0.219679i
$285$	0	0
$286$	−400789.	−0.0171324
$287$	8.26120e6i	0.349460i
$288$	0	0
$289$	−2.55282e7	−1.05761
$290$	− 4.13473e7i	− 1.69532i
$291$	0	0
$292$	−2.56950e6	−0.103205
$293$	− 1.67427e7i	− 0.665612i	−0.942995	−	0.332806i	$-0.892005\pi$
$293$	− 1.67427e7i	− 0.665612i	0.942995	−	0.332806i	$-0.107995\pi$
$294$	0	0
$295$	3.80291e6	0.148132
$296$	− 5.06348e6i	− 0.195242i
$297$	0	0
$298$	1.73185e6	0.0654426
$299$	1.81357e6i	0.0678455i
$300$	0	0
$301$	7.36160e6	0.269944
$302$	− 1.04514e7i	− 0.379450i
$303$	0	0
$304$	2.79664e6	0.0995442
$305$	− 1.37527e7i	− 0.484716i
$306$	0	0
$307$	1.09311e7	0.377790	0.188895	−	0.981997i	$-0.439509\pi$
$307$	1.09311e7	0.377790	0.188895	+	0.981997i	$0.439509\pi$
$308$	4.75400e6i	0.162707i
$309$	0	0
$310$	−1.63144e7	−0.547628
$311$	5.08738e7i	1.69127i	0.533761	+	0.845635i	$0.320778\pi$
$311$	5.08738e7i	1.69127i	−0.533761	+	0.845635i	$0.679222\pi$
$312$	0	0
$313$	2.39868e7	0.782240	0.391120	−	0.920340i	$-0.372088\pi$
$313$	2.39868e7	0.782240	0.391120	+	0.920340i	$0.372088\pi$
$314$	− 1.78228e7i	− 0.575687i
$315$	0	0
$316$	1.20592e7	0.382169
$317$	− 2.23516e7i	− 0.701668i	−0.936438	−	0.350834i	$-0.885898\pi$
$317$	− 2.23516e7i	− 0.701668i	0.936438	−	0.350834i	$-0.114102\pi$
$318$	0	0
$319$	2.43244e7	0.749325
$320$	− 7.65268e6i	− 0.233541i
$321$	0	0
$322$	2.15119e7	0.644333
$323$	1.92471e7i	0.571160i
$324$	0	0
$325$	3.54765e6	0.103345
$326$	7.34159e6i	0.211903i
$327$	0	0
$328$	7.82335e6	0.221703
$329$	− 3.17333e7i	− 0.891103i
$330$	0	0
$331$	−4.40210e7	−1.21388	−0.606941	−	0.794747i	$-0.707603\pi$
$331$	−4.40210e7	−1.21388	−0.606941	+	0.794747i	$0.707603\pi$
$332$	2.71213e7i	0.741134i
$333$	0	0
$334$	−9.24638e6	−0.248160
$335$	6.91274e7i	1.83872i
$336$	0	0
$337$	4.88756e7	1.27703	0.638516	−	0.769608i	$-0.279548\pi$
$337$	4.88756e7	1.27703	0.638516	+	0.769608i	$0.279548\pi$
$338$	2.72575e7i	0.705889i
$339$	0	0
$340$	5.26674e7	1.34000
$341$	− 9.59768e6i	− 0.242049i
$342$	0	0
$343$	3.79930e7	0.941501
$344$	− 6.97144e6i	− 0.171256i
$345$	0	0
$346$	5.36415e7	1.29501
$347$	5.51286e7i	1.31944i	0.751513	+	0.659719i	$0.229325\pi$
$347$	5.51286e7i	1.31944i	−0.751513	+	0.659719i	$0.770675\pi$
$348$	0	0
$349$	1.99417e7	0.469122	0.234561	−	0.972101i	$-0.424635\pi$
$349$	1.99417e7	0.469122	0.234561	+	0.972101i	$0.424635\pi$
$350$	− 4.20808e7i	− 0.981477i
$351$	0	0
$352$	4.50204e6	0.103224
$353$	7.53984e7i	1.71411i	0.515227	+	0.857054i	$0.327708\pi$
$353$	7.53984e7i	1.71411i	−0.515227	+	0.857054i	$0.672292\pi$
$354$	0	0
$355$	−3.67246e7	−0.820866
$356$	− 36125.0i	0 0.000800679i
$357$	0	0
$358$	5.22416e7	1.13859
$359$	5.29978e7i	1.14545i	0.819749	+	0.572723i	$0.194113\pi$
$359$	5.29978e7i	1.14545i	−0.819749	+	0.572723i	$0.805887\pi$
$360$	0	0
$361$	−3.95870e7	−0.841455
$362$	− 2.59918e7i	− 0.547912i
$363$	0	0
$364$	−557611.	−0.0115618
$365$	1.87527e7i	0.385642i
$366$	0	0
$367$	4.07906e7	0.825204	0.412602	−	0.910911i	$-0.364620\pi$
$367$	4.07906e7	0.825204	0.412602	+	0.910911i	$0.364620\pi$
$368$	− 2.03717e7i	− 0.408775i
$369$	0	0
$370$	−3.69541e7	−0.729554
$371$	1.04638e7i	0.204913i
$372$	0	0
$373$	−4.29016e7	−0.826698	−0.413349	−	0.910573i	$-0.635641\pi$
$373$	−4.29016e7	−0.826698	−0.413349	+	0.910573i	$0.635641\pi$
$374$	3.09840e7i	0.592274i
$375$	0	0
$376$	−3.00515e7	−0.565330
$377$	2.85308e6i	0.0532464i
$378$	0	0
$379$	−3.56353e6	−0.0654579	−0.0327290	−	0.999464i	$-0.510420\pi$
$379$	−3.56353e6	−0.0654579	−0.0327290	+	0.999464i	$0.510420\pi$
$380$	− 2.04104e7i	− 0.371963i
$381$	0	0
$382$	−4.43777e7	−0.796112
$383$	− 5.89075e7i	− 1.04851i	−0.851560	−	0.524257i	$-0.824343\pi$
$383$	− 5.89075e7i	− 1.04851i	0.851560	−	0.524257i	$-0.175657\pi$
$384$	0	0
$385$	3.46955e7	0.607982
$386$	3.07611e7i	0.534860i
$387$	0	0
$388$	4.32097e7	0.739753
$389$	− 4.40520e7i	− 0.748370i	−0.927354	−	0.374185i	$-0.877922\pi$
$389$	− 4.40520e7i	− 0.748370i	0.927354	−	0.374185i	$-0.122078\pi$
$390$	0	0
$391$	1.40203e8	2.34545
$392$	− 1.46826e7i	− 0.243750i
$393$	0	0
$394$	−5.71886e7	−0.935020
$395$	− 8.80097e7i	− 1.42804i
$396$	0	0
$397$	2.93968e6	0.0469818	0.0234909	−	0.999724i	$-0.492522\pi$
$397$	2.93968e6	0.0469818	0.0234909	+	0.999724i	$0.492522\pi$
$398$	3.91341e7i	0.620734i
$399$	0	0
$400$	−3.98505e7	−0.622665
$401$	− 1.60458e7i	− 0.248844i	−0.992229	−	0.124422i	$-0.960292\pi$
$401$	− 1.60458e7i	− 0.248844i	0.992229	−	0.124422i	$-0.0397077\pi$
$402$	0	0
$403$	1.12574e6	0.0171998
$404$	− 5.08278e6i	− 0.0770828i
$405$	0	0
$406$	3.38422e7	0.505685
$407$	− 2.17399e7i	− 0.322459i
$408$	0	0
$409$	−1.80856e7	−0.264340	−0.132170	−	0.991227i	$-0.542195\pi$
$409$	−1.80856e7	−0.264340	−0.132170	+	0.991227i	$0.542195\pi$
$410$	− 5.70961e7i	− 0.828428i
$411$	0	0
$412$	−1.59113e7	−0.227517
$413$	3.11263e6i	0.0441853i
$414$	0	0
$415$	1.97936e8	2.76937
$416$	528058.i	0.00733502i
$417$	0	0
$418$	1.20073e7	0.164406
$419$	− 7.46218e6i	− 0.101443i	−0.998713	−	0.0507217i	$-0.983848\pi$
$419$	− 7.46218e6i	− 0.101443i	0.998713	−	0.0507217i	$-0.0161521\pi$
$420$	0	0
$421$	−2.33546e7	−0.312987	−0.156494	−	0.987679i	$-0.550019\pi$
$421$	−2.33546e7	−0.312987	−0.156494	+	0.987679i	$0.550019\pi$
$422$	4.83769e7i	0.643726i
$423$	0	0
$424$	9.90926e6	0.130000
$425$	− 2.74260e8i	− 3.57270i
$426$	0	0
$427$	1.12564e7	0.144582
$428$	− 6.62907e6i	− 0.0845516i
$429$	0	0
$430$	−5.08787e7	−0.639927
$431$	− 7.00387e7i	− 0.874795i	−0.899268	−	0.437397i	$-0.855900\pi$
$431$	− 7.00387e7i	− 0.874795i	0.899268	−	0.437397i	$-0.144100\pi$
$432$	0	0
$433$	−8.83901e7	−1.08878	−0.544390	−	0.838832i	$-0.683239\pi$
$433$	−8.83901e7	−1.08878	−0.544390	+	0.838832i	$0.683239\pi$
$434$	− 1.33531e7i	− 0.163348i
$435$	0	0
$436$	7.36920e7	0.889120
$437$	− 5.43331e7i	− 0.651059i
$438$	0	0
$439$	1.02345e8	1.20968	0.604842	−	0.796346i	$-0.293236\pi$
$439$	1.02345e8	1.20968	0.604842	+	0.796346i	$0.293236\pi$
$440$	− 3.28566e7i	− 0.385713i
$441$	0	0
$442$	−3.63421e6	−0.0420865
$443$	1.27620e8i	1.46794i	0.679183	+	0.733969i	$0.262334\pi$
$443$	1.27620e8i	1.46794i	−0.679183	+	0.733969i	$0.737666\pi$
$444$	0	0
$445$	−263647.	−0.00299187
$446$	2.97474e7i	0.335309i
$447$	0	0
$448$	6.26361e6	0.0696612
$449$	1.44858e8i	1.60031i	0.599795	+	0.800154i	$0.295249\pi$
$449$	1.44858e8i	1.60031i	−0.599795	+	0.800154i	$0.704751\pi$
$450$	0	0
$451$	3.35894e7	0.366161
$452$	2.50356e7i	0.271108i
$453$	0	0
$454$	4.57441e7	0.488841
$455$	4.06954e6i	0.0432027i
$456$	0	0
$457$	−1.01826e8	−1.06687	−0.533433	−	0.845842i	$-0.679098\pi$
$457$	−1.01826e8	−1.06687	−0.533433	+	0.845842i	$0.679098\pi$
$458$	6.90201e7i	0.718421i
$459$	0	0
$460$	−1.48676e8	−1.52745
$461$	− 6.90837e7i	− 0.705136i	−0.935786	−	0.352568i	$-0.885308\pi$
$461$	− 6.90837e7i	− 0.705136i	0.935786	−	0.352568i	$-0.114692\pi$
$462$	0	0
$463$	−1.34932e8	−1.35948	−0.679741	−	0.733452i	$-0.737908\pi$
$463$	−1.34932e8	−1.35948	−0.679741	+	0.733452i	$0.737908\pi$
$464$	− 3.20485e7i	− 0.320814i
$465$	0	0
$466$	−3.15354e7	−0.311631
$467$	1.23430e8i	1.21191i	0.795500	+	0.605954i	$0.207208\pi$
$467$	1.23430e8i	1.21191i	−0.795500	+	0.605954i	$0.792792\pi$
$468$	0	0
$469$	−5.65798e7	−0.548458
$470$	2.19320e8i	2.11245i
$471$	0	0
$472$	2.94766e6	0.0280318
$473$	− 2.99317e7i	− 0.282845i
$474$	0	0
$475$	−1.06285e8	−0.991723
$476$	4.31076e7i	0.399699i
$477$	0	0
$478$	9.31642e7	0.853032
$479$	6.94017e7i	0.631485i	0.948845	+	0.315743i	$0.102254\pi$
$479$	6.94017e7i	0.631485i	−0.948845	+	0.315743i	$0.897746\pi$
$480$	0	0
$481$	2.54994e6	0.0229137
$482$	− 2.60521e7i	− 0.232649i
$483$	0	0
$484$	−3.73606e7	−0.329517
$485$	− 3.15352e8i	− 2.76420i
$486$	0	0
$487$	−2.01197e8	−1.74195	−0.870973	−	0.491331i	$-0.836511\pi$
$487$	−2.01197e8	−1.74195	−0.870973	+	0.491331i	$0.836511\pi$
$488$	− 1.06598e7i	− 0.0917251i
$489$	0	0
$490$	−1.07156e8	−0.910810
$491$	1.99368e8i	1.68427i	0.539267	+	0.842135i	$0.318701\pi$
$491$	1.99368e8i	1.68427i	−0.539267	+	0.842135i	$0.681299\pi$
$492$	0	0
$493$	2.20565e8	1.84075
$494$	1.40837e6i	0.0116825i
$495$	0	0
$496$	−1.26454e7	−0.103630
$497$	− 3.00586e7i	− 0.244850i
$498$	0	0
$499$	−8.77347e7	−0.706106	−0.353053	−	0.935603i	$-0.614856\pi$
$499$	−8.77347e7	−0.706106	−0.353053	+	0.935603i	$0.614856\pi$
$500$	1.74065e8i	1.39252i
$501$	0	0
$502$	8.94455e7	0.707045
$503$	− 1.53094e8i	− 1.20297i	−0.798885	−	0.601484i	$-0.794576\pi$
$503$	− 1.53094e8i	− 1.20297i	0.798885	−	0.601484i	$-0.205424\pi$
$504$	0	0
$505$	−3.70950e7	−0.288032
$506$	− 8.74656e7i	− 0.675127i
$507$	0	0
$508$	−3.82127e7	−0.291485
$509$	1.21788e8i	0.923528i	0.887003	+	0.461764i	$0.152783\pi$
$509$	1.21788e8i	0.923528i	−0.887003	+	0.461764i	$0.847217\pi$
$510$	0	0
$511$	−1.53488e7	−0.115030
$512$	− 5.93164e6i	− 0.0441942i
$513$	0	0
$514$	1.06215e8	0.782160
$515$	1.16123e8i	0.850154i
$516$	0	0
$517$	−1.29025e8	−0.933691
$518$	− 3.02464e7i	− 0.217613i
$519$	0	0
$520$	3.85385e6	0.0274085
$521$	1.44805e8i	1.02393i	0.859006	+	0.511965i	$0.171082\pi$
$521$	1.44805e8i	1.02393i	−0.859006	+	0.511965i	$0.828918\pi$
$522$	0	0
$523$	−2.14387e8	−1.49863	−0.749313	−	0.662216i	$-0.769616\pi$
$523$	−2.14387e8	−1.49863	−0.749313	+	0.662216i	$0.769616\pi$
$524$	8.03830e7i	0.558689i
$525$	0	0
$526$	4.82433e7	0.331497
$527$	− 8.70283e7i	− 0.594605i
$528$	0	0
$529$	−2.47746e8	−1.67355
$530$	− 7.23194e7i	− 0.485766i
$531$	0	0
$532$	1.67056e7	0.110950
$533$	3.93980e6i	0.0260191i
$534$	0	0
$535$	−4.83801e7	−0.315940
$536$	5.35811e7i	0.347950i
$537$	0	0
$538$	9.21489e7	0.591757
$539$	− 6.30393e7i	− 0.402573i
$540$	0	0
$541$	3.66711e7	0.231596	0.115798	−	0.993273i	$-0.463057\pi$
$541$	3.66711e7	0.231596	0.115798	+	0.993273i	$0.463057\pi$
$542$	− 1.37982e8i	− 0.866609i
$543$	0	0
$544$	4.08229e7	0.253575
$545$	− 5.37816e8i	− 3.32234i
$546$	0	0
$547$	−3.00421e8	−1.83556	−0.917780	−	0.397089i	$-0.870021\pi$
$547$	−3.00421e8	−1.83556	−0.917780	+	0.397089i	$0.870021\pi$
$548$	2.59996e7i	0.157989i
$549$	0	0
$550$	−1.71097e8	−1.02838
$551$	− 8.54761e7i	− 0.510964i
$552$	0	0
$553$	7.20347e7	0.425958
$554$	1.87373e8i	1.10199i
$555$	0	0
$556$	−2.24355e7	−0.130530
$557$	− 2.64642e8i	− 1.53141i	−0.643190	−	0.765707i	$-0.722389\pi$
$557$	− 2.64642e8i	− 1.53141i	0.643190	−	0.765707i	$-0.277611\pi$
$558$	0	0
$559$	3.51078e6	0.0200987
$560$	− 4.57129e7i	− 0.260300i
$561$	0	0
$562$	2.04613e7	0.115272
$563$	− 6.90928e7i	− 0.387175i	−0.981083	−	0.193588i	$-0.937988\pi$
$563$	− 6.90928e7i	− 0.387175i	0.981083	−	0.193588i	$-0.0620124\pi$
$564$	0	0
$565$	1.82714e8	1.01304
$566$	1.83201e8i	1.01036i
$567$	0	0
$568$	−2.84655e7	−0.155336
$569$	1.39811e8i	0.758934i	0.925205	+	0.379467i	$0.123893\pi$
$569$	1.39811e8i	0.758934i	−0.925205	+	0.379467i	$0.876107\pi$
$570$	0	0
$571$	2.04986e8	1.10107	0.550537	−	0.834811i	$-0.314423\pi$
$571$	2.04986e8	1.10107	0.550537	+	0.834811i	$0.314423\pi$
$572$	2.26720e6i	0.0121144i
$573$	0	0
$574$	4.67324e7	0.247105
$575$	7.74216e8i	4.07248i
$576$	0	0
$577$	1.77665e8	0.924854	0.462427	−	0.886657i	$-0.346979\pi$
$577$	1.77665e8	0.924854	0.462427	+	0.886657i	$0.346979\pi$
$578$	1.44409e8i	0.747844i
$579$	0	0
$580$	−2.33895e8	−1.19877
$581$	1.62008e8i	0.826052i
$582$	0	0
$583$	4.25452e7	0.214706
$584$	1.45353e7i	0.0729769i
$585$	0	0
$586$	−9.47107e7	−0.470659
$587$	− 3.37655e8i	− 1.66940i	−0.550708	−	0.834698i	$-0.685642\pi$
$587$	− 3.37655e8i	− 1.66940i	0.550708	−	0.834698i	$-0.314358\pi$
$588$	0	0
$589$	−3.37263e7	−0.165053
$590$	− 2.15125e7i	− 0.104745i
$591$	0	0
$592$	−2.86433e7	−0.138057
$593$	− 1.84023e8i	− 0.882488i	−0.897387	−	0.441244i	$-0.854537\pi$
$593$	− 1.84023e8i	− 0.882488i	0.897387	−	0.441244i	$-0.145463\pi$
$594$	0	0
$595$	3.14606e8	1.49354
$596$	− 9.79680e6i	− 0.0462749i
$597$	0	0
$598$	1.02591e7	0.0479740
$599$	1.63223e8i	0.759453i	0.925099	+	0.379726i	$0.123982\pi$
$599$	1.63223e8i	0.759453i	−0.925099	+	0.379726i	$0.876018\pi$
$600$	0	0
$601$	−1.71572e8	−0.790354	−0.395177	−	0.918605i	$-0.629317\pi$
$601$	−1.71572e8	−0.790354	−0.395177	+	0.918605i	$0.629317\pi$
$602$	− 4.16435e7i	− 0.190879i
$603$	0	0
$604$	−5.91222e7	−0.268312
$605$	2.72664e8i	1.23129i
$606$	0	0
$607$	1.85305e7	0.0828554	0.0414277	−	0.999142i	$-0.486809\pi$
$607$	1.85305e7	0.0828554	0.0414277	+	0.999142i	$0.486809\pi$
$608$	− 1.58202e7i	− 0.0703884i
$609$	0	0
$610$	−7.77967e7	−0.342746
$611$	− 1.51338e7i	− 0.0663473i
$612$	0	0
$613$	3.64689e8	1.58322	0.791609	−	0.611028i	$-0.209244\pi$
$613$	3.64689e8	1.58322	0.791609	+	0.611028i	$0.209244\pi$
$614$	− 6.18358e7i	− 0.267138i
$615$	0	0
$616$	2.68927e7	0.115051
$617$	− 7.51485e7i	− 0.319937i	−0.987122	−	0.159969i	$-0.948861\pi$
$617$	− 7.51485e7i	− 0.319937i	0.987122	−	0.159969i	$-0.0511393\pi$
$618$	0	0
$619$	−2.85725e6	−0.0120469	−0.00602345	−	0.999982i	$-0.501917\pi$
$619$	−2.85725e6	−0.0120469	−0.00602345	+	0.999982i	$0.501917\pi$
$620$	9.22881e7i	0.387231i
$621$	0	0
$622$	2.87786e8	1.19591
$623$	− 215791.i	0 0.000892420i
$624$	0	0
$625$	6.62286e8	2.71272
$626$	− 1.35690e8i	− 0.553127i
$627$	0	0
$628$	−1.00821e8	−0.407072
$629$	− 1.97130e8i	− 0.792137i
$630$	0	0
$631$	−9.87283e7	−0.392965	−0.196482	−	0.980507i	$-0.562952\pi$
$631$	−9.87283e7	−0.392965	−0.196482	+	0.980507i	$0.562952\pi$
$632$	− 6.82169e7i	− 0.270234i
$633$	0	0
$634$	−1.26440e8	−0.496154
$635$	2.78883e8i	1.08918i
$636$	0	0
$637$	7.39407e6	0.0286065
$638$	− 1.37600e8i	− 0.529853i
$639$	0	0
$640$	−4.32901e7	−0.165139
$641$	− 4.64299e8i	− 1.76288i	−0.472292	−	0.881442i	$-0.656573\pi$
$641$	− 4.64299e8i	− 1.76288i	0.472292	−	0.881442i	$-0.343427\pi$
$642$	0	0
$643$	−3.97653e8	−1.49579	−0.747897	−	0.663815i	$-0.768936\pi$
$643$	−3.97653e8	−1.49579	−0.747897	+	0.663815i	$0.768936\pi$
$644$	− 1.21689e8i	− 0.455612i
$645$	0	0
$646$	1.08878e8	0.403871
$647$	− 1.29737e8i	− 0.479017i	−0.970894	−	0.239509i	$-0.923014\pi$
$647$	− 1.29737e8i	− 0.479017i	0.970894	−	0.239509i	$-0.0769863\pi$
$648$	0	0
$649$	1.26557e7	0.0462970
$650$	− 2.00685e7i	− 0.0730761i
$651$	0	0
$652$	4.15303e7	0.149838
$653$	− 3.58550e8i	− 1.28769i	−0.765157	−	0.643844i	$-0.777339\pi$
$653$	− 3.58550e8i	− 1.28769i	0.765157	−	0.643844i	$-0.222661\pi$
$654$	0	0
$655$	5.86648e8	2.08763
$656$	− 4.42556e7i	− 0.156768i
$657$	0	0
$658$	−1.79511e8	−0.630105
$659$	4.20076e8i	1.46782i	0.679249	+	0.733908i	$0.262306\pi$
$659$	4.20076e8i	1.46782i	−0.679249	+	0.733908i	$0.737694\pi$
$660$	0	0
$661$	−4.12214e8	−1.42731	−0.713655	−	0.700498i	$-0.752961\pi$
$661$	−4.12214e8	−1.42731	−0.713655	+	0.700498i	$0.752961\pi$
$662$	2.49021e8i	0.858344i
$663$	0	0
$664$	1.53421e8	0.524061
$665$	− 1.21920e8i	− 0.414582i
$666$	0	0
$667$	−6.22638e8	−2.09826
$668$	5.23054e7i	0.175476i
$669$	0	0
$670$	3.91044e8	1.30017
$671$	− 4.57675e7i	− 0.151492i
$672$	0	0
$673$	4.71674e8	1.54738	0.773690	−	0.633565i	$-0.218409\pi$
$673$	4.71674e8	1.54738	0.773690	+	0.633565i	$0.218409\pi$
$674$	− 2.76482e8i	− 0.902999i
$675$	0	0
$676$	1.54192e8	0.499139
$677$	− 7.58667e7i	− 0.244504i	−0.992499	−	0.122252i	$-0.960988\pi$
$677$	− 7.58667e7i	− 0.244504i	0.992499	−	0.122252i	$-0.0390116\pi$
$678$	0	0
$679$	2.58111e8	0.824513
$680$	− 2.97932e8i	− 0.947524i
$681$	0	0
$682$	−5.42927e7	−0.171154
$683$	2.50625e8i	0.786616i	0.919407	+	0.393308i	$0.128669\pi$
$683$	2.50625e8i	0.786616i	−0.919407	+	0.393308i	$0.871331\pi$
$684$	0	0
$685$	1.89750e8	0.590350
$686$	− 2.14921e8i	− 0.665742i
$687$	0	0
$688$	−3.94364e7	−0.121097
$689$	4.99025e6i	0.0152569i
$690$	0	0
$691$	1.84793e8	0.560082	0.280041	−	0.959988i	$-0.409652\pi$
$691$	1.84793e8	0.560082	0.280041	+	0.959988i	$0.409652\pi$
$692$	− 3.03442e8i	− 0.915710i
$693$	0	0
$694$	3.11855e8	0.932983
$695$	1.63738e8i	0.487748i
$696$	0	0
$697$	3.04576e8	0.899493
$698$	− 1.12807e8i	− 0.331719i
$699$	0	0
$700$	−2.38045e8	−0.694009
$701$	− 1.48993e8i	− 0.432525i	−0.976335	−	0.216262i	$-0.930613\pi$
$701$	− 1.48993e8i	− 0.432525i	0.976335	−	0.216262i	$-0.0693866\pi$
$702$	0	0
$703$	−7.63942e7	−0.219885
$704$	− 2.54674e7i	− 0.0729905i
$705$	0	0
$706$	4.26518e8	1.21206
$707$	− 3.03617e7i	− 0.0859149i
$708$	0	0
$709$	−3.53594e8	−0.992126	−0.496063	−	0.868287i	$-0.665221\pi$
$709$	−3.53594e8	−0.992126	−0.496063	+	0.868287i	$0.665221\pi$
$710$	2.07746e8i	0.580440i
$711$	0	0
$712$	−204354.	−0.000566166 0
$713$	2.45674e8i	0.677784i
$714$	0	0
$715$	1.65464e7	0.0452674
$716$	− 2.95523e8i	− 0.805105i
$717$	0	0
$718$	2.99801e8	0.809953
$719$	− 1.15532e8i	− 0.310824i	−0.987850	−	0.155412i	$-0.950330\pi$
$719$	− 1.15532e8i	− 0.310824i	0.987850	−	0.155412i	$-0.0496705\pi$
$720$	0	0
$721$	−9.50453e7	−0.253586
$722$	2.23938e8i	0.594999i
$723$	0	0
$724$	−1.47032e8	−0.387432
$725$	1.21799e9i	3.19616i
$726$	0	0
$727$	−8.58299e7	−0.223375	−0.111688	−	0.993743i	$-0.535626\pi$
$727$	−8.58299e7	−0.223375	−0.111688	+	0.993743i	$0.535626\pi$
$728$	3.15432e6i	0.00817546i
$729$	0	0
$730$	1.06081e8	0.272690
$731$	− 2.71410e8i	− 0.694822i
$732$	0	0
$733$	−3.31619e8	−0.842029	−0.421014	−	0.907054i	$-0.638326\pi$
$733$	−3.31619e8	−0.842029	−0.421014	+	0.907054i	$0.638326\pi$
$734$	− 2.30746e8i	− 0.583508i
$735$	0	0
$736$	−1.15240e8	−0.289048
$737$	2.30049e8i	0.574670i
$738$	0	0
$739$	−4.32705e7	−0.107216	−0.0536079	−	0.998562i	$-0.517072\pi$
$739$	−4.32705e7	−0.107216	−0.0536079	+	0.998562i	$0.517072\pi$
$740$	2.09044e8i	0.515873i
$741$	0	0
$742$	5.91925e7	0.144895
$743$	5.67260e8i	1.38298i	0.722386	+	0.691490i	$0.243045\pi$
$743$	5.67260e8i	1.38298i	−0.722386	+	0.691490i	$0.756955\pi$
$744$	0	0
$745$	−7.14987e7	−0.172914
$746$	2.42688e8i	0.584564i
$747$	0	0
$748$	1.75272e8	0.418801
$749$	− 3.95984e7i	− 0.0942394i
$750$	0	0
$751$	−6.04175e7	−0.142640	−0.0713202	−	0.997453i	$-0.522721\pi$
$751$	−6.04175e7	−0.142640	−0.0713202	+	0.997453i	$0.522721\pi$
$752$	1.69997e8i	0.399749i
$753$	0	0
$754$	1.61395e7	0.0376509
$755$	4.31484e8i	1.00259i
$756$	0	0
$757$	2.57979e8	0.594697	0.297349	−	0.954769i	$-0.403898\pi$
$757$	2.57979e8	0.594697	0.297349	+	0.954769i	$0.403898\pi$
$758$	2.01583e7i	0.0462857i
$759$	0	0
$760$	−1.15458e8	−0.263018
$761$	− 2.99842e8i	− 0.680360i	−0.940360	−	0.340180i	$-0.889512\pi$
$761$	− 2.99842e8i	− 0.680360i	0.940360	−	0.340180i	$-0.110488\pi$
$762$	0	0
$763$	4.40195e8	0.990995
$764$	2.51038e8i	0.562936i
$765$	0	0
$766$	−3.33231e8	−0.741412
$767$	1.48443e6i	0.00328982i
$768$	0	0
$769$	−4.35019e8	−0.956597	−0.478299	−	0.878197i	$-0.658746\pi$
$769$	−4.35019e8	−0.956597	−0.478299	+	0.878197i	$0.658746\pi$
$770$	− 1.96267e8i	− 0.429908i
$771$	0	0
$772$	1.74011e8	0.378203
$773$	5.68247e8i	1.23027i	0.788423	+	0.615133i	$0.210898\pi$
$773$	5.68247e8i	1.23027i	−0.788423	+	0.615133i	$0.789102\pi$
$774$	0	0
$775$	4.80581e8	1.03243
$776$	− 2.44431e8i	− 0.523084i
$777$	0	0
$778$	−2.49196e8	−0.529178
$779$	− 1.18033e8i	− 0.249685i
$780$	0	0
$781$	−1.22216e8	−0.256552
$782$	− 7.93106e8i	− 1.65848i
$783$	0	0
$784$	−8.30572e7	−0.172357
$785$	7.35807e8i	1.52109i
$786$	0	0
$787$	8.22512e8	1.68740	0.843700	−	0.536815i	$-0.180373\pi$
$787$	8.22512e8	1.68740	0.843700	+	0.536815i	$0.180373\pi$
$788$	3.23507e8i	0.661159i
$789$	0	0
$790$	−4.97858e8	−1.00977
$791$	1.49549e8i	0.302171i
$792$	0	0
$793$	5.36820e6	0.0107649
$794$	− 1.66294e7i	− 0.0332211i
$795$	0	0
$796$	2.21376e8	0.438925
$797$	− 5.01123e8i	− 0.989851i	−0.868935	−	0.494925i	$-0.835195\pi$
$797$	− 5.01123e8i	− 0.989851i	0.868935	−	0.494925i	$-0.164805\pi$
$798$	0	0
$799$	−1.16995e9	−2.29366
$800$	2.25429e8i	0.440291i
$801$	0	0
$802$	−9.07686e7	−0.175959
$803$	6.24070e7i	0.120528i
$804$	0	0
$805$	−8.88110e8	−1.70247
$806$	− 6.36815e6i	− 0.0121621i
$807$	0	0
$808$	−2.87526e7	−0.0545058
$809$	4.25261e8i	0.803174i	0.915821	+	0.401587i	$0.131541\pi$
$809$	4.25261e8i	0.803174i	−0.915821	+	0.401587i	$0.868459\pi$
$810$	0	0
$811$	3.17254e8	0.594763	0.297381	−	0.954759i	$-0.403887\pi$
$811$	3.17254e8	0.594763	0.297381	+	0.954759i	$0.403887\pi$
$812$	− 1.91440e8i	− 0.357573i
$813$	0	0
$814$	−1.22980e8	−0.228013
$815$	− 3.03095e8i	− 0.559894i
$816$	0	0
$817$	−1.05180e8	−0.192871
$818$	1.02308e8i	0.186917i
$819$	0	0
$820$	−3.22984e8	−0.585787
$821$	− 2.38760e7i	− 0.0431452i	−0.999767	−	0.0215726i	$-0.993133\pi$
$821$	− 2.38760e7i	− 0.0431452i	0.999767	−	0.0215726i	$-0.00686731\pi$
$822$	0	0
$823$	1.05266e9	1.88838	0.944189	−	0.329406i	$-0.106848\pi$
$823$	1.05266e9	1.88838	0.944189	+	0.329406i	$0.106848\pi$
$824$	9.00079e7i	0.160879i
$825$	0	0
$826$	1.76077e7	0.0312437
$827$	1.79106e8i	0.316660i	0.987386	+	0.158330i	$0.0506109\pi$
$827$	1.79106e8i	0.316660i	−0.987386	+	0.158330i	$0.949389\pi$
$828$	0	0
$829$	−1.21964e8	−0.214076	−0.107038	−	0.994255i	$-0.534137\pi$
$829$	−1.21964e8	−0.214076	−0.107038	+	0.994255i	$0.534137\pi$
$830$	− 1.11969e9i	− 1.95824i
$831$	0	0
$832$	2.98714e6	0.00518664
$833$	− 5.71618e8i	− 0.988942i
$834$	0	0
$835$	3.81734e8	0.655694
$836$	− 6.79236e7i	− 0.116252i
$837$	0	0
$838$	−4.22125e7	−0.0717313
$839$	− 5.67200e8i	− 0.960395i	−0.877160	−	0.480198i	$-0.840565\pi$
$839$	− 5.67200e8i	− 0.960395i	0.877160	−	0.480198i	$-0.159435\pi$
$840$	0	0
$841$	−3.84702e8	−0.646751
$842$	1.32114e8i	0.221316i
$843$	0	0
$844$	2.73661e8	0.455183
$845$	− 1.12532e9i	− 1.86511i
$846$	0	0
$847$	−2.23171e8	−0.367272
$848$	− 5.60552e7i	− 0.0919240i
$849$	0	0
$850$	−1.55145e9	−2.52628
$851$	5.56483e8i	0.902949i
$852$	0	0
$853$	−9.19888e8	−1.48214	−0.741068	−	0.671430i	$-0.765680\pi$
$853$	−9.19888e8	−1.48214	−0.741068	+	0.671430i	$0.765680\pi$
$854$	− 6.36756e7i	− 0.102235i
$855$	0	0
$856$	−3.74997e7	−0.0597870
$857$	− 5.89322e8i	− 0.936290i	−0.883652	−	0.468145i	$-0.844923\pi$
$857$	− 5.89322e8i	− 0.936290i	0.883652	−	0.468145i	$-0.155077\pi$
$858$	0	0
$859$	−1.02147e8	−0.161157	−0.0805783	−	0.996748i	$-0.525677\pi$
$859$	−1.02147e8	−0.161157	−0.0805783	+	0.996748i	$0.525677\pi$
$860$	2.87813e8i	0.452497i
$861$	0	0
$862$	−3.96199e8	−0.618573
$863$	− 8.24326e8i	− 1.28253i	−0.767321	−	0.641264i	$-0.778410\pi$
$863$	− 8.24326e8i	− 1.28253i	0.767321	−	0.641264i	$-0.221590\pi$
$864$	0	0
$865$	−2.21457e9	−3.42170
$866$	5.00010e8i	0.769884i
$867$	0	0
$868$	−7.55365e7	−0.115504
$869$	− 2.92888e8i	− 0.446315i
$870$	0	0
$871$	−2.69832e7	−0.0408356
$872$	− 4.16865e8i	− 0.628703i
$873$	0	0
$874$	−3.07355e8	−0.460368
$875$	1.03977e9i	1.55208i
$876$	0	0
$877$	7.11429e8	1.05471	0.527355	−	0.849645i	$-0.323184\pi$
$877$	7.11429e8	1.05471	0.527355	+	0.849645i	$0.323184\pi$
$878$	− 5.78949e8i	− 0.855375i
$879$	0	0
$880$	−1.85865e8	−0.272741
$881$	− 1.35023e8i	− 0.197460i	−0.995114	−	0.0987302i	$-0.968522\pi$
$881$	− 1.35023e8i	− 0.197460i	0.995114	−	0.0987302i	$-0.0314781\pi$
$882$	0	0
$883$	4.91077e8	0.713293	0.356646	−	0.934239i	$-0.383920\pi$
$883$	4.91077e8	0.713293	0.356646	+	0.934239i	$0.383920\pi$
$884$	2.05582e7i	0.0297597i
$885$	0	0
$886$	7.21928e8	1.03799
$887$	− 9.37763e8i	− 1.34376i	−0.740659	−	0.671881i	$-0.765487\pi$
$887$	− 9.37763e8i	− 1.34376i	0.740659	−	0.671881i	$-0.234513\pi$
$888$	0	0
$889$	−2.28262e8	−0.324883
$890$	1.49141e6i	0.00211557i
$891$	0	0
$892$	1.68277e8	0.237099
$893$	4.53396e8i	0.636683i
$894$	0	0
$895$	−2.15678e9	−3.00840
$896$	− 3.54324e7i	− 0.0492579i
$897$	0	0
$898$	8.19440e8	1.13159
$899$	3.86491e8i	0.531938i
$900$	0	0
$901$	3.85784e8	0.527437
$902$	− 1.90010e8i	− 0.258915i
$903$	0	0
$904$	1.41623e8	0.191702
$905$	1.07306e9i	1.44770i
$906$	0	0
$907$	7.17999e8	0.962281	0.481140	−	0.876644i	$-0.340223\pi$
$907$	7.17999e8	0.962281	0.481140	+	0.876644i	$0.340223\pi$
$908$	− 2.58768e8i	− 0.345663i
$909$	0	0
$910$	2.30208e7	0.0305489
$911$	7.59779e8i	1.00492i	0.864600	+	0.502461i	$0.167572\pi$
$911$	7.59779e8i	1.00492i	−0.864600	+	0.502461i	$0.832428\pi$
$912$	0	0
$913$	6.58711e8	0.865531
$914$	5.76014e8i	0.754388i
$915$	0	0
$916$	3.90437e8	0.508001
$917$	4.80163e8i	0.622703i
$918$	0	0
$919$	−9.15355e8	−1.17935	−0.589676	−	0.807640i	$-0.700744\pi$
$919$	−9.15355e8	−1.17935	−0.589676	+	0.807640i	$0.700744\pi$
$920$	8.41040e8i	1.08007i
$921$	0	0
$922$	−3.90797e8	−0.498607
$923$	− 1.43351e7i	− 0.0182303i
$924$	0	0
$925$	1.08857e9	1.37541
$926$	7.63293e8i	0.961299i
$927$	0	0
$928$	−1.81294e8	−0.226850
$929$	− 4.95116e8i	− 0.617532i	−0.951138	−	0.308766i	$-0.900084\pi$
$929$	− 4.95116e8i	− 0.617532i	0.951138	−	0.308766i	$-0.0999160\pi$
$930$	0	0
$931$	−2.21521e8	−0.274514
$932$	1.78391e8i	0.220357i
$933$	0	0
$934$	6.98225e8	0.856948
$935$	− 1.27916e9i	− 1.56492i
$936$	0	0
$937$	5.39309e8	0.655570	0.327785	−	0.944752i	$-0.393698\pi$
$937$	5.39309e8	0.655570	0.327785	+	0.944752i	$0.393698\pi$
$938$	3.20064e8i	0.387818i
$939$	0	0
$940$	1.24066e9	1.49372
$941$	8.81713e8i	1.05818i	0.848567	+	0.529088i	$0.177466\pi$
$941$	8.81713e8i	1.05818i	−0.848567	+	0.529088i	$0.822534\pi$
$942$	0	0
$943$	−8.59797e8	−1.02532
$944$	− 1.66745e7i	− 0.0198215i
$945$	0	0
$946$	−1.69319e8	−0.200001
$947$	− 8.91278e8i	− 1.04945i	−0.851271	−	0.524727i	$-0.824168\pi$
$947$	− 8.91278e8i	− 1.04945i	0.851271	−	0.524727i	$-0.175832\pi$
$948$	0	0
$949$	−7.31991e6	−0.00856460
$950$	6.01238e8i	0.701254i
$951$	0	0
$952$	2.43853e8	0.282630
$953$	2.13491e8i	0.246661i	0.992366	+	0.123331i	$0.0393576\pi$
$953$	2.13491e8i	0.246661i	−0.992366	+	0.123331i	$0.960642\pi$
$954$	0	0
$955$	1.83212e9	2.10350
$956$	− 5.27016e8i	− 0.603185i
$957$	0	0
$958$	3.92595e8	0.446528
$959$	1.55307e8i	0.176091i
$960$	0	0
$961$	−7.35006e8	−0.828172
$962$	− 1.44246e7i	− 0.0162024i
$963$	0	0
$964$	−1.47373e8	−0.164508
$965$	− 1.26996e9i	− 1.41322i
$966$	0	0
$967$	−1.21296e9	−1.34143	−0.670716	−	0.741714i	$-0.734013\pi$
$967$	−1.21296e9	−1.34143	−0.670716	+	0.741714i	$0.734013\pi$
$968$	2.11343e8i	0.233003i
$969$	0	0
$970$	−1.78390e9	−1.95459
$971$	− 4.38734e8i	− 0.479230i	−0.970868	−	0.239615i	$-0.922979\pi$
$971$	− 4.38734e8i	− 0.479230i	0.970868	−	0.239615i	$-0.0770212\pi$
$972$	0	0
$973$	−1.34017e8	−0.145486
$974$	1.13814e9i	1.23174i
$975$	0	0
$976$	−6.03007e7	−0.0648594
$977$	− 1.19123e9i	− 1.27736i	−0.769473	−	0.638679i	$-0.779481\pi$
$977$	− 1.19123e9i	− 1.27736i	0.769473	−	0.638679i	$-0.220519\pi$
$978$	0	0
$979$	−877390.	−0.000935071 0
$980$	6.06165e8i	0.644040i
$981$	0	0
$982$	1.12780e9	1.19096
$983$	− 4.81948e8i	− 0.507388i	−0.967285	−	0.253694i	$-0.918354\pi$
$983$	− 4.81948e8i	− 0.507388i	0.967285	−	0.253694i	$-0.0816456\pi$
$984$	0	0
$985$	2.36101e9	2.47053
$986$	− 1.24770e9i	− 1.30161i
$987$	0	0
$988$	7.96697e6	0.00826080
$989$	7.66170e8i	0.792021i
$990$	0	0
$991$	−8.26440e8	−0.849162	−0.424581	−	0.905390i	$-0.639579\pi$
$991$	−8.26440e8	−0.849162	−0.424581	+	0.905390i	$0.639579\pi$
$992$	7.15331e7i	0.0732777i
$993$	0	0
$994$	−1.70037e8	−0.173135
$995$	− 1.61564e9i	− 1.64012i
$996$	0	0
$997$	1.30036e9	1.31214	0.656068	−	0.754702i	$-0.272219\pi$
$997$	1.30036e9	1.31214	0.656068	+	0.754702i	$0.272219\pi$
$998$	4.96303e8i	0.499292i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.7.b.c.161.6		12
3.2	odd	2	inner	162.7.b.c.161.7		12
9.2	odd	6		18.7.d.a.5.5	✓	12
9.4	even	3		18.7.d.a.11.5	yes	12
9.5	odd	6		54.7.d.a.35.1		12
9.7	even	3		54.7.d.a.17.1		12
36.7	odd	6		432.7.q.b.17.1		12
36.11	even	6		144.7.q.c.113.4		12
36.23	even	6		432.7.q.b.305.1		12
36.31	odd	6		144.7.q.c.65.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.7.d.a.5.5	✓	12	9.2	odd	6
18.7.d.a.11.5	yes	12	9.4	even	3
54.7.d.a.17.1		12	9.7	even	3
54.7.d.a.35.1		12	9.5	odd	6
144.7.q.c.65.4		12	36.31	odd	6
144.7.q.c.113.4		12	36.11	even	6
162.7.b.c.161.6		12	1.1	even	1	trivial
162.7.b.c.161.7		12	3.2	odd	2	inner
432.7.q.b.17.1		12	36.7	odd	6
432.7.q.b.305.1		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)

\(f(q)\)	\(=\)	\(q-5.65685i q^{2} -32.0000 q^{4} +233.541i q^{5} -191.150 q^{7} +181.019i q^{8} +O(q^{10})\)	\(q-5.65685i q^{2} -32.0000 q^{4} +233.541i q^{5} -191.150 q^{7} +181.019i q^{8} +1321.11 q^{10} +777.202i q^{11} -91.1604 q^{13} +1081.31i q^{14} +1024.00 q^{16} +7047.39i q^{17} +2731.10 q^{19} -7473.32i q^{20} +4396.52 q^{22} -19894.3i q^{23} -38916.6 q^{25} +515.681i q^{26} +6116.81 q^{28} -31297.4i q^{29} -12349.0 q^{31} -5792.62i q^{32} +39866.1 q^{34} -44641.5i q^{35} -27972.0 q^{37} -15449.4i q^{38} -42275.5 q^{40} -43218.3i q^{41} -38512.1 q^{43} -24870.5i q^{44} -112539. q^{46} +166012. i q^{47} -81110.5 q^{49} +220145. i q^{50} +2917.13 q^{52} -54741.5i q^{53} -181509. q^{55} -34601.9i q^{56} -177045. q^{58} -16283.7i q^{59} -58887.4 q^{61} +69856.5i q^{62} -32768.0 q^{64} -21289.7i q^{65} +295997. q^{67} -225517. i q^{68} -252530. q^{70} +157251. i q^{71} +80297.0 q^{73} +158234. i q^{74} -87395.0 q^{76} -148563. i q^{77} -376849. q^{79} +239146. i q^{80} -244480. q^{82} -847541. i q^{83} -1.64586e6 q^{85} +217857. i q^{86} -140689. q^{88} +1128.91i q^{89} +17425.3 q^{91} +636617. i q^{92} +939108. q^{94} +637824. i q^{95} -1.35030e6 q^{97} +458831. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 384 q^{4} - 480 q^{7}+O(q^{10}) \) 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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