LMFDB - Embedded newform 162.7.b.b.161.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("162.161");

S:= CuspForms(chi, 7);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$37.2687615464$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 1382x^{6} - 288x^{5} + 716245x^{4} + 201312x^{3} - 164876604x^{2} - 33576768x + 14252103396 $ x^8 - 1382x^6 - 288x^5 + 716245x^4 + 201312x^3 - 164876604x^2 - 33576768x + 14252103396
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			161.1
Root			$-18.3354 + 1.41421i$ of defining polynomial
Character	$\chi$	$=$	162.161
Dual form			162.7.b.b.161.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.65685i q^{2} -32.0000 q^{4} -171.064i q^{5} +560.839 q^{7} +181.019i q^{8} +O(q^{10})$	\(q-5.65685i q^{2} -32.0000 q^{4} -171.064i q^{5} +560.839 q^{7} +181.019i q^{8} -967.683 q^{10} +220.351i q^{11} +3781.00 q^{13} -3172.58i q^{14} +1024.00 q^{16} +2662.46i q^{17} +10334.0 q^{19} +5474.04i q^{20} +1246.49 q^{22} +14785.7i q^{23} -13637.8 q^{25} -21388.5i q^{26} -17946.8 q^{28} +14872.9i q^{29} +15831.0 q^{31} -5792.62i q^{32} +15061.2 q^{34} -95939.2i q^{35} +26550.4 q^{37} -58457.9i q^{38} +30965.8 q^{40} -113942. i q^{41} -52098.9 q^{43} -7051.22i q^{44} +83640.6 q^{46} +11558.4i q^{47} +196891. q^{49} +77147.0i q^{50} -120992. q^{52} +137651. i q^{53} +37694.0 q^{55} +101523. i q^{56} +84133.6 q^{58} -291382. i q^{59} -282218. q^{61} -89553.8i q^{62} -32768.0 q^{64} -646791. i q^{65} +377914. q^{67} -85198.8i q^{68} -542714. q^{70} -521287. i q^{71} -611614. q^{73} -150192. i q^{74} -330688. q^{76} +123581. i q^{77} -175575. q^{79} -175169. i q^{80} -644556. q^{82} -362996. i q^{83} +455451. q^{85} +294716. i q^{86} -39887.7 q^{88} +1.23323e6i q^{89} +2.12053e6 q^{91} -473143. i q^{92} +65384.1 q^{94} -1.76777e6i q^{95} -1.24829e6 q^{97} -1.11378e6i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 256 q^{4} + 964 q^{7}+O(q^{10}) $ 8 * q - 256 * q^4 + 964 * q^7	$ 8 q - 256 q^{4} + 964 q^{7} - 768 q^{10} + 4540 q^{13} + 8192 q^{16} - 23684 q^{19} + 27072 q^{22} - 32392 q^{25} - 30848 q^{28} + 77056 q^{31} - 52608 q^{34} - 11348 q^{37} + 24576 q^{40} - 226604 q^{43} - 162720 q^{46} + 1298088 q^{49} - 145280 q^{52} - 1460916 q^{55} + 867456 q^{58} - 327476 q^{61} - 262144 q^{64} + 1713292 q^{67} - 176352 q^{70} - 2189216 q^{73} + 757888 q^{76} - 1326884 q^{79} - 1158816 q^{82} + 3483180 q^{85} - 866304 q^{88} + 1130324 q^{91} - 26400 q^{94} - 2200064 q^{97}+O(q^{100}) $ 8 * q - 256 * q^4 + 964 * q^7 - 768 * q^10 + 4540 * q^13 + 8192 * q^16 - 23684 * q^19 + 27072 * q^22 - 32392 * q^25 - 30848 * q^28 + 77056 * q^31 - 52608 * q^34 - 11348 * q^37 + 24576 * q^40 - 226604 * q^43 - 162720 * q^46 + 1298088 * q^49 - 145280 * q^52 - 1460916 * q^55 + 867456 * q^58 - 327476 * q^61 - 262144 * q^64 + 1713292 * q^67 - 176352 * q^70 - 2189216 * q^73 + 757888 * q^76 - 1326884 * q^79 - 1158816 * q^82 + 3483180 * q^85 - 866304 * q^88 + 1130324 * q^91 - 26400 * q^94 - 2200064 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	− 5.65685i	− 0.707107i
$2$	− 5.65685i	− 0.707107i
$3$	0	0
$3$	0	0
$4$	−32.0000	−0.500000
$5$	− 171.064i	− 1.36851i	−0.729243	−	0.684255i	$-0.760128\pi$
$5$	− 171.064i	− 1.36851i	0.729243	−	0.684255i	$-0.239872\pi$
$6$	0	0
$7$	560.839	1.63510	0.817549	−	0.575859i	$-0.195332\pi$
$7$	560.839	1.63510	0.817549	+	0.575859i	$0.195332\pi$
$8$	181.019i	0.353553i
$9$	0	0
$10$	−967.683	−0.967683
$11$	220.351i	0.165553i	0.996568	+	0.0827764i	$0.0263787\pi$
$11$	220.351i	0.165553i	−0.996568	+	0.0827764i	$0.973621\pi$
$12$	0	0
$13$	3781.00	1.72098	0.860491	−	0.509466i	$-0.170157\pi$
$13$	3781.00	1.72098	0.860491	+	0.509466i	$0.170157\pi$
$14$	− 3172.58i	− 1.15619i
$15$	0	0
$16$	1024.00	0.250000
$17$	2662.46i	0.541922i	0.962590	+	0.270961i	$0.0873415\pi$
$17$	2662.46i	0.541922i	−0.962590	+	0.270961i	$0.912659\pi$
$18$	0	0
$19$	10334.0	1.50663	0.753317	−	0.657658i	$-0.228453\pi$
$19$	10334.0	1.50663	0.753317	+	0.657658i	$0.228453\pi$
$20$	5474.04i	0.684255i
$21$	0	0
$22$	1246.49	0.117063
$23$	14785.7i	1.21523i	0.794231	+	0.607615i	$0.207874\pi$
$23$	14785.7i	1.21523i	−0.794231	+	0.607615i	$0.792126\pi$
$24$	0	0
$25$	−13637.8	−0.872819
$26$	− 21388.5i	− 1.21692i
$27$	0	0
$28$	−17946.8	−0.817549
$29$	14872.9i	0.609818i	0.952381	+	0.304909i	$0.0986261\pi$
$29$	14872.9i	0.609818i	−0.952381	+	0.304909i	$0.901374\pi$
$30$	0	0
$31$	15831.0	0.531403	0.265701	−	0.964055i	$-0.414396\pi$
$31$	15831.0	0.531403	0.265701	+	0.964055i	$0.414396\pi$
$32$	− 5792.62i	− 0.176777i
$33$	0	0
$34$	15061.2	0.383197
$35$	− 95939.2i	− 2.23765i
$36$	0	0
$37$	26550.4	0.524162	0.262081	−	0.965046i	$-0.415591\pi$
$37$	26550.4	0.524162	0.262081	+	0.965046i	$0.415591\pi$
$38$	− 58457.9i	− 1.06535i
$39$	0	0
$40$	30965.8	0.483841
$41$	− 113942.i	− 1.65323i	−0.562766	−	0.826616i	$-0.690263\pi$
$41$	− 113942.i	− 1.65323i	0.562766	−	0.826616i	$-0.309737\pi$
$42$	0	0
$43$	−52098.9	−0.655275	−0.327637	−	0.944804i	$-0.606252\pi$
$43$	−52098.9	−0.655275	−0.327637	+	0.944804i	$0.606252\pi$
$44$	− 7051.22i	− 0.0827764i
$45$	0	0
$46$	83640.6	0.859298
$47$	11558.4i	0.111328i	0.998450	+	0.0556639i	$0.0177275\pi$
$47$	11558.4i	0.111328i	−0.998450	+	0.0556639i	$0.982272\pi$
$48$	0	0
$49$	196891.	1.67355
$50$	77147.0i	0.617176i
$51$	0	0
$52$	−120992.	−0.860491
$53$	137651.i	0.924595i	0.886725	+	0.462298i	$0.152975\pi$
$53$	137651.i	0.924595i	−0.886725	+	0.462298i	$0.847025\pi$
$54$	0	0
$55$	37694.0	0.226561
$56$	101523.i	0.578094i
$57$	0	0
$58$	84133.6	0.431207
$59$	− 291382.i	− 1.41875i	−0.704830	−	0.709377i	$-0.748977\pi$
$59$	− 291382.i	− 1.41875i	0.704830	−	0.709377i	$-0.251023\pi$
$60$	0	0
$61$	−282218.	−1.24336	−0.621678	−	0.783273i	$-0.713549\pi$
$61$	−282218.	−1.24336	−0.621678	+	0.783273i	$0.713549\pi$
$62$	− 89553.8i	− 0.375759i
$63$	0	0
$64$	−32768.0	−0.125000
$65$	− 646791.i	− 2.35518i
$66$	0	0
$67$	377914.	1.25652	0.628258	−	0.778005i	$-0.283768\pi$
$67$	377914.	1.25652	0.628258	+	0.778005i	$0.283768\pi$
$68$	− 85198.8i	− 0.270961i
$69$	0	0
$70$	−542714.	−1.58226
$71$	− 521287.i	− 1.45647i	−0.685328	−	0.728235i	$-0.740341\pi$
$71$	− 521287.i	− 1.45647i	0.685328	−	0.728235i	$-0.259659\pi$
$72$	0	0
$73$	−611614.	−1.57221	−0.786103	−	0.618096i	$-0.787904\pi$
$73$	−611614.	−1.57221	−0.786103	+	0.618096i	$0.787904\pi$
$74$	− 150192.i	− 0.370639i
$75$	0	0
$76$	−330688.	−0.753317
$77$	123581.i	0.270695i
$78$	0	0
$79$	−175575.	−0.356107	−0.178054	−	0.984021i	$-0.556980\pi$
$79$	−175575.	−0.356107	−0.178054	+	0.984021i	$0.556980\pi$
$80$	− 175169.i	− 0.342127i
$81$	0	0
$82$	−644556.	−1.16901
$83$	− 362996.i	− 0.634845i	−0.948284	−	0.317422i	$-0.897183\pi$
$83$	− 362996.i	− 0.634845i	0.948284	−	0.317422i	$-0.102817\pi$
$84$	0	0
$85$	455451.	0.741626
$86$	294716.i	0.463349i
$87$	0	0
$88$	−39887.7	−0.0585317
$89$	1.23323e6i	1.74934i	0.484719	+	0.874670i	$0.338922\pi$
$89$	1.23323e6i	1.74934i	−0.484719	+	0.874670i	$0.661078\pi$
$90$	0	0
$91$	2.12053e6	2.81397
$92$	− 473143.i	− 0.607615i
$93$	0	0
$94$	65384.1	0.0787206
$95$	− 1.76777e6i	− 2.06184i
$96$	0	0
$97$	−1.24829e6	−1.36773	−0.683863	−	0.729610i	$-0.739702\pi$
$97$	−1.24829e6	−1.36773	−0.683863	+	0.729610i	$0.739702\pi$
$98$	− 1.11378e6i	− 1.18338i
$99$	0	0
$100$	436410.	0.436410
$101$	1.05683e6i	1.02575i	0.858464	+	0.512874i	$0.171419\pi$
$101$	1.05683e6i	1.02575i	−0.858464	+	0.512874i	$0.828581\pi$
$102$	0	0
$103$	−289590.	−0.265016	−0.132508	−	0.991182i	$-0.542303\pi$
$103$	−289590.	−0.265016	−0.132508	+	0.991182i	$0.542303\pi$
$104$	684433.i	0.608459i
$105$	0	0
$106$	778672.	0.653788
$107$	811508.i	0.662432i	0.943555	+	0.331216i	$0.107459\pi$
$107$	811508.i	0.662432i	−0.943555	+	0.331216i	$0.892541\pi$
$108$	0	0
$109$	−595882.	−0.460130	−0.230065	−	0.973175i	$-0.573894\pi$
$109$	−595882.	−0.460130	−0.230065	+	0.973175i	$0.573894\pi$
$110$	− 213230.i	− 0.160203i
$111$	0	0
$112$	574299.	0.408775
$113$	− 643790.i	− 0.446179i	−0.974798	−	0.223089i	$-0.928386\pi$
$113$	− 643790.i	− 0.446179i	0.974798	−	0.223089i	$-0.0716142\pi$
$114$	0	0
$115$	2.52930e6	1.66306
$116$	− 475931.i	− 0.304909i
$117$	0	0
$118$	−1.64831e6	−1.00321
$119$	1.49321e6i	0.886096i
$120$	0	0
$121$	1.72301e6	0.972592
$122$	1.59647e6i	0.879185i
$123$	0	0
$124$	−506593.	−0.265701
$125$	− 339938.i	− 0.174048i
$126$	0	0
$127$	−53251.0	−0.0259966	−0.0129983	−	0.999916i	$-0.504138\pi$
$127$	−53251.0	−0.0259966	−0.0129983	+	0.999916i	$0.504138\pi$
$128$	185364.i	0.0883883i
$129$	0	0
$130$	−3.65880e6	−1.66536
$131$	1.73510e6i	0.771812i	0.922538	+	0.385906i	$0.126111\pi$
$131$	1.73510e6i	0.771812i	−0.922538	+	0.385906i	$0.873889\pi$
$132$	0	0
$133$	5.79570e6	2.46349
$134$	− 2.13780e6i	− 0.888491i
$135$	0	0
$136$	−481957.	−0.191598
$137$	2.12467e6i	0.826284i	0.910667	+	0.413142i	$0.135569\pi$
$137$	2.12467e6i	0.826284i	−0.910667	+	0.413142i	$0.864431\pi$
$138$	0	0
$139$	−2.98597e6	−1.11184	−0.555918	−	0.831237i	$-0.687633\pi$
$139$	−2.98597e6	−1.11184	−0.555918	+	0.831237i	$0.687633\pi$
$140$	3.07005e6i	1.11882i
$141$	0	0
$142$	−2.94884e6	−1.02988
$143$	833145.i	0.284913i
$144$	0	0
$145$	2.54421e6	0.834542
$146$	3.45981e6i	1.11172i
$147$	0	0
$148$	−849612.	−0.262081
$149$	1.58531e6i	0.479242i	0.970867	+	0.239621i	$0.0770232\pi$
$149$	1.58531e6i	0.479242i	−0.970867	+	0.239621i	$0.922977\pi$
$150$	0	0
$151$	200648.	0.0582780	0.0291390	−	0.999575i	$-0.490723\pi$
$151$	200648.	0.0582780	0.0291390	+	0.999575i	$0.490723\pi$
$152$	1.87065e6i	0.532675i
$153$	0	0
$154$	699081.	0.191410
$155$	− 2.70811e6i	− 0.727230i
$156$	0	0
$157$	1.05045e6	0.271441	0.135721	−	0.990747i	$-0.456665\pi$
$157$	1.05045e6	0.271441	0.135721	+	0.990747i	$0.456665\pi$
$158$	993201.i	0.251806i
$159$	0	0
$160$	−990907.	−0.241921
$161$	8.29240e6i	1.98702i
$162$	0	0
$163$	−2.04370e6	−0.471905	−0.235953	−	0.971765i	$-0.575821\pi$
$163$	−2.04370e6	−0.471905	−0.235953	+	0.971765i	$0.575821\pi$
$164$	3.64616e6i	0.826616i
$165$	0	0
$166$	−2.05342e6	−0.448903
$167$	− 6.84327e6i	− 1.46931i	−0.678439	−	0.734657i	$-0.737343\pi$
$167$	− 6.84327e6i	− 1.46931i	0.678439	−	0.734657i	$-0.262657\pi$
$168$	0	0
$169$	9.46912e6	1.96178
$170$	− 2.57642e6i	− 0.524409i
$171$	0	0
$172$	1.66717e6	0.327637
$173$	1.25762e6i	0.242891i	0.992598	+	0.121445i	$0.0387529\pi$
$173$	1.25762e6i	0.242891i	−0.992598	+	0.121445i	$0.961247\pi$
$174$	0	0
$175$	−7.64861e6	−1.42715
$176$	225639.i	0.0413882i
$177$	0	0
$178$	6.97620e6	1.23697
$179$	8.25586e6i	1.43947i	0.694248	+	0.719736i	$0.255737\pi$
$179$	8.25586e6i	1.43947i	−0.694248	+	0.719736i	$0.744263\pi$
$180$	0	0
$181$	2.62711e6	0.443040	0.221520	−	0.975156i	$-0.428898\pi$
$181$	2.62711e6	0.443040	0.221520	+	0.975156i	$0.428898\pi$
$182$	− 1.19955e7i	− 1.98978i
$183$	0	0
$184$	−2.67650e6	−0.429649
$185$	− 4.54181e6i	− 0.717321i
$186$	0	0
$187$	−586676.	−0.0897167
$188$	− 369868.i	− 0.0556639i
$189$	0	0
$190$	−1.00000e7	−1.45794
$191$	1.46940e6i	0.210882i	0.994426	+	0.105441i	$0.0336253\pi$
$191$	1.46940e6i	0.210882i	−0.994426	+	0.105441i	$0.966375\pi$
$192$	0	0
$193$	−163198.	−0.0227008	−0.0113504	−	0.999936i	$-0.503613\pi$
$193$	−163198.	−0.0227008	−0.0113504	+	0.999936i	$0.503613\pi$
$194$	7.06138e6i	0.967129i
$195$	0	0
$196$	−6.30051e6	−0.836773
$197$	− 1.03528e7i	− 1.35413i	−0.735923	−	0.677065i	$-0.763252\pi$
$197$	− 1.03528e7i	− 1.35413i	0.735923	−	0.677065i	$-0.236748\pi$
$198$	0	0
$199$	−6.96701e6	−0.884071	−0.442035	−	0.896998i	$-0.645743\pi$
$199$	−6.96701e6	−0.884071	−0.442035	+	0.896998i	$0.645743\pi$
$200$	− 2.46871e6i	− 0.308588i
$201$	0	0
$202$	5.97833e6	0.725314
$203$	8.34127e6i	0.997112i
$204$	0	0
$205$	−1.94914e7	−2.26246
$206$	1.63817e6i	0.187395i
$207$	0	0
$208$	3.87174e6	0.430245
$209$	2.27710e6i	0.249427i
$210$	0	0
$211$	1.21726e7	1.29580	0.647900	−	0.761726i	$-0.275648\pi$
$211$	1.21726e7	1.29580	0.647900	+	0.761726i	$0.275648\pi$
$212$	− 4.40483e6i	− 0.462298i
$213$	0	0
$214$	4.59058e6	0.468410
$215$	8.91224e6i	0.896750i
$216$	0	0
$217$	8.87865e6	0.868896
$218$	3.37082e6i	0.325361i
$219$	0	0
$220$	−1.20621e6	−0.113280
$221$	1.00668e7i	0.932638i
$222$	0	0
$223$	−1.57172e7	−1.41729	−0.708647	−	0.705563i	$-0.750694\pi$
$223$	−1.57172e7	−1.41729	−0.708647	+	0.705563i	$0.750694\pi$
$224$	− 3.24872e6i	− 0.289047i
$225$	0	0
$226$	−3.64183e6	−0.315496
$227$	150520.i	0.0128681i	0.999979	+	0.00643407i	$0.00204804\pi$
$227$	150520.i	0.0128681i	−0.999979	+	0.00643407i	$0.997952\pi$
$228$	0	0
$229$	−1.26143e7	−1.05040	−0.525201	−	0.850978i	$-0.676010\pi$
$229$	−1.26143e7	−1.05040	−0.525201	+	0.850978i	$0.676010\pi$
$230$	− 1.43079e7i	− 1.17596i
$231$	0	0
$232$	−2.69227e6	−0.215603
$233$	− 1.73833e7i	− 1.37425i	−0.726542	−	0.687123i	$-0.758874\pi$
$233$	− 1.73833e7i	− 1.37425i	0.726542	−	0.687123i	$-0.241126\pi$
$234$	0	0
$235$	1.97722e6	0.152353
$236$	9.32423e6i	0.709377i
$237$	0	0
$238$	8.44689e6	0.626564
$239$	− 1.26812e7i	− 0.928893i	−0.885601	−	0.464447i	$-0.846253\pi$
$239$	− 1.26812e7i	− 0.928893i	0.885601	−	0.464447i	$-0.153747\pi$
$240$	0	0
$241$	9.98976e6	0.713681	0.356840	−	0.934165i	$-0.383854\pi$
$241$	9.98976e6	0.713681	0.356840	+	0.934165i	$0.383854\pi$
$242$	− 9.74680e6i	− 0.687727i
$243$	0	0
$244$	9.03098e6	0.621678
$245$	− 3.36809e7i	− 2.29026i
$246$	0	0
$247$	3.90728e7	2.59289
$248$	2.86572e6i	0.187879i
$249$	0	0
$250$	−1.92298e6	−0.123071
$251$	− 1.92884e7i	− 1.21976i	−0.792493	−	0.609881i	$-0.791217\pi$
$251$	− 1.92884e7i	− 1.21976i	0.792493	−	0.609881i	$-0.208783\pi$
$252$	0	0
$253$	−3.25804e6	−0.201185
$254$	301233.i	0.0183824i
$255$	0	0
$256$	1.04858e6	0.0625000
$257$	− 1.52948e7i	− 0.901041i	−0.892766	−	0.450520i	$-0.851238\pi$
$257$	− 1.52948e7i	− 0.901041i	0.892766	−	0.450520i	$-0.148762\pi$
$258$	0	0
$259$	1.48905e7	0.857057
$260$	2.06973e7i	1.17759i
$261$	0	0
$262$	9.81523e6	0.545754
$263$	2.20312e7i	1.21107i	0.795817	+	0.605537i	$0.207042\pi$
$263$	2.20312e7i	1.21107i	−0.795817	+	0.605537i	$0.792958\pi$
$264$	0	0
$265$	2.35471e7	1.26532
$266$	− 3.27855e7i	− 1.74195i
$267$	0	0
$268$	−1.20932e7	−0.628258
$269$	− 1.44503e7i	− 0.742368i	−0.928559	−	0.371184i	$-0.878952\pi$
$269$	− 1.44503e7i	− 0.742368i	0.928559	−	0.371184i	$-0.121048\pi$
$270$	0	0
$271$	−8.83074e6	−0.443700	−0.221850	−	0.975081i	$-0.571209\pi$
$271$	−8.83074e6	−0.443700	−0.221850	+	0.975081i	$0.571209\pi$
$272$	2.72636e6i	0.135481i
$273$	0	0
$274$	1.20189e7	0.584271
$275$	− 3.00510e6i	− 0.144498i
$276$	0	0
$277$	−2.45816e7	−1.15657	−0.578283	−	0.815836i	$-0.696277\pi$
$277$	−2.45816e7	−1.15657	−0.578283	+	0.815836i	$0.696277\pi$
$278$	1.68912e7i	0.786187i
$279$	0	0
$280$	1.73668e7	0.791128
$281$	− 3.31584e7i	− 1.49443i	−0.664584	−	0.747213i	$-0.731391\pi$
$281$	− 3.31584e7i	− 1.49443i	0.664584	−	0.747213i	$-0.268609\pi$
$282$	0	0
$283$	−3.81470e7	−1.68307	−0.841533	−	0.540206i	$-0.818346\pi$
$283$	−3.81470e7	−1.68307	−0.841533	+	0.540206i	$0.818346\pi$
$284$	1.66812e7i	0.728235i
$285$	0	0
$286$	4.71298e6	0.201464
$287$	− 6.39033e7i	− 2.70320i
$288$	0	0
$289$	1.70489e7	0.706320
$290$	− 1.43922e7i	− 0.590110i
$291$	0	0
$292$	1.95717e7	0.786103
$293$	3.46678e7i	1.37824i	0.724649	+	0.689118i	$0.242002\pi$
$293$	3.46678e7i	1.37824i	−0.724649	+	0.689118i	$0.757998\pi$
$294$	0	0
$295$	−4.98449e7	−1.94158
$296$	4.80613e6i	0.185319i
$297$	0	0
$298$	8.96786e6	0.338875
$299$	5.59047e7i	2.09139i
$300$	0	0
$301$	−2.92191e7	−1.07144
$302$	− 1.13504e6i	− 0.0412088i
$303$	0	0
$304$	1.05820e7	0.376658
$305$	4.82773e7i	1.70154i
$306$	0	0
$307$	−4.85387e7	−1.67754	−0.838770	−	0.544486i	$-0.816725\pi$
$307$	−4.85387e7	−1.67754	−0.838770	+	0.544486i	$0.816725\pi$
$308$	− 3.95460e6i	− 0.135348i
$309$	0	0
$310$	−1.53194e7	−0.514229
$311$	3.09343e7i	1.02839i	0.857672	+	0.514197i	$0.171910\pi$
$311$	3.09343e7i	1.02839i	−0.857672	+	0.514197i	$0.828090\pi$
$312$	0	0
$313$	719494.	0.0234636	0.0117318	−	0.999931i	$-0.496266\pi$
$313$	719494.	0.0234636	0.0117318	+	0.999931i	$0.496266\pi$
$314$	− 5.94224e6i	− 0.191938i
$315$	0	0
$316$	5.61839e6	0.178054
$317$	− 7.46097e6i	− 0.234217i	−0.993119	−	0.117108i	$-0.962638\pi$
$317$	− 7.46097e6i	− 0.234217i	0.993119	−	0.117108i	$-0.0373625\pi$
$318$	0	0
$319$	−3.27724e6	−0.100957
$320$	5.60542e6i	0.171064i
$321$	0	0
$322$	4.69089e7	1.40504
$323$	2.75139e7i	0.816478i
$324$	0	0
$325$	−5.15645e7	−1.50211
$326$	1.15609e7i	0.333687i
$327$	0	0
$328$	2.06258e7	0.584506
$329$	6.48239e6i	0.182032i
$330$	0	0
$331$	1.48457e6	0.0409371	0.0204685	−	0.999790i	$-0.493484\pi$
$331$	1.48457e6	0.0409371	0.0204685	+	0.999790i	$0.493484\pi$
$332$	1.16159e7i	0.317422i
$333$	0	0
$334$	−3.87114e7	−1.03896
$335$	− 6.46473e7i	− 1.71956i
$336$	0	0
$337$	7.86515e6	0.205503	0.102751	−	0.994707i	$-0.467235\pi$
$337$	7.86515e6	0.205503	0.102751	+	0.994707i	$0.467235\pi$
$338$	− 5.35654e7i	− 1.38718i
$339$	0	0
$340$	−1.45744e7	−0.370813
$341$	3.48838e6i	0.0879752i
$342$	0	0
$343$	4.44420e7	1.10131
$344$	− 9.43091e6i	− 0.231675i
$345$	0	0
$346$	7.11417e6	0.171750
$347$	− 1.83359e7i	− 0.438847i	−0.975630	−	0.219423i	$-0.929582\pi$
$347$	− 1.83359e7i	− 0.438847i	0.975630	−	0.219423i	$-0.0704176\pi$
$348$	0	0
$349$	6.43300e7	1.51334	0.756672	−	0.653795i	$-0.226824\pi$
$349$	6.43300e7	1.51334	0.756672	+	0.653795i	$0.226824\pi$
$350$	4.32670e7i	1.00914i
$351$	0	0
$352$	1.27641e6	0.0292659
$353$	2.38431e7i	0.542049i	0.962572	+	0.271025i	$0.0873625\pi$
$353$	2.38431e7i	0.542049i	−0.962572	+	0.271025i	$0.912637\pi$
$354$	0	0
$355$	−8.91732e7	−1.99319
$356$	− 3.94634e7i	− 0.874670i
$357$	0	0
$358$	4.67022e7	1.01786
$359$	1.50510e7i	0.325298i	0.986684	+	0.162649i	$0.0520038\pi$
$359$	1.50510e7i	0.325298i	−0.986684	+	0.162649i	$0.947996\pi$
$360$	0	0
$361$	5.97456e7	1.26994
$362$	− 1.48612e7i	− 0.313276i
$363$	0	0
$364$	−6.78569e7	−1.40699
$365$	1.04625e8i	2.15158i
$366$	0	0
$367$	1.79478e7	0.363090	0.181545	−	0.983383i	$-0.441890\pi$
$367$	1.79478e7	0.363090	0.181545	+	0.983383i	$0.441890\pi$
$368$	1.51406e7i	0.303808i
$369$	0	0
$370$	−2.56923e7	−0.507223
$371$	7.72000e7i	1.51180i
$372$	0	0
$373$	−8.66801e6	−0.167029	−0.0835147	−	0.996507i	$-0.526615\pi$
$373$	−8.66801e6	−0.167029	−0.0835147	+	0.996507i	$0.526615\pi$
$374$	3.31874e6i	0.0634393i
$375$	0	0
$376$	−2.09229e6	−0.0393603
$377$	5.62342e7i	1.04949i
$378$	0	0
$379$	−1.03648e7	−0.190390	−0.0951950	−	0.995459i	$-0.530347\pi$
$379$	−1.03648e7	−0.190390	−0.0951950	+	0.995459i	$0.530347\pi$
$380$	5.65687e7i	1.03092i
$381$	0	0
$382$	8.31215e6	0.149116
$383$	− 2.50515e6i	− 0.0445900i	−0.999751	−	0.0222950i	$-0.992903\pi$
$383$	− 2.50515e6i	− 0.0445900i	0.999751	−	0.0222950i	$-0.00709730\pi$
$384$	0	0
$385$	2.11403e7	0.370449
$386$	923185.i	0.0160519i
$387$	0	0
$388$	3.99452e7	0.683863
$389$	− 2.45954e6i	− 0.0417835i	−0.999782	−	0.0208917i	$-0.993349\pi$
$389$	− 2.45954e6i	− 0.0417835i	0.999782	−	0.0208917i	$-0.00665053\pi$
$390$	0	0
$391$	−3.93664e7	−0.658561
$392$	3.56411e7i	0.591688i
$393$	0	0
$394$	−5.85644e7	−0.957514
$395$	3.00345e7i	0.487336i
$396$	0	0
$397$	1.17180e6	0.0187275	0.00936376	−	0.999956i	$-0.497019\pi$
$397$	1.17180e6	0.0187275	0.00936376	+	0.999956i	$0.497019\pi$
$398$	3.94113e7i	0.625132i
$399$	0	0
$400$	−1.39651e7	−0.218205
$401$	1.76040e7i	0.273009i	0.990639	+	0.136505i	$0.0435868\pi$
$401$	1.76040e7i	0.273009i	−0.990639	+	0.136505i	$0.956413\pi$
$402$	0	0
$403$	5.98570e7	0.914534
$404$	− 3.38186e7i	− 0.512874i
$405$	0	0
$406$	4.71854e7	0.705065
$407$	5.85040e6i	0.0867765i
$408$	0	0
$409$	6.45297e7	0.943170	0.471585	−	0.881821i	$-0.343682\pi$
$409$	6.45297e7	0.943170	0.471585	+	0.881821i	$0.343682\pi$
$410$	1.10260e8i	1.59980i
$411$	0	0
$412$	9.26689e6	0.132508
$413$	− 1.63418e8i	− 2.31980i
$414$	0	0
$415$	−6.20954e7	−0.868791
$416$	− 2.19019e7i	− 0.304229i
$417$	0	0
$418$	1.28812e7	0.176372
$419$	− 1.10734e8i	− 1.50536i	−0.658386	−	0.752681i	$-0.728760\pi$
$419$	− 1.10734e8i	− 1.50536i	0.658386	−	0.752681i	$-0.271240\pi$
$420$	0	0
$421$	3.16902e7	0.424697	0.212348	−	0.977194i	$-0.431889\pi$
$421$	3.16902e7	0.424697	0.212348	+	0.977194i	$0.431889\pi$
$422$	− 6.88589e7i	− 0.916268i
$423$	0	0
$424$	−2.49175e7	−0.326894
$425$	− 3.63101e7i	− 0.473000i
$426$	0	0
$427$	−1.58279e8	−2.03301
$428$	− 2.59682e7i	− 0.331216i
$429$	0	0
$430$	5.04152e7	0.634098
$431$	− 9.48759e6i	− 0.118502i	−0.998243	−	0.0592508i	$-0.981129\pi$
$431$	− 9.48759e6i	− 0.118502i	0.998243	−	0.0592508i	$-0.0188712\pi$
$432$	0	0
$433$	−1.03139e8	−1.27045	−0.635225	−	0.772327i	$-0.719092\pi$
$433$	−1.03139e8	−1.27045	−0.635225	+	0.772327i	$0.719092\pi$
$434$	− 5.02252e7i	− 0.614402i
$435$	0	0
$436$	1.90682e7	0.230065
$437$	1.52796e8i	1.83091i
$438$	0	0
$439$	−4.62794e7	−0.547009	−0.273504	−	0.961871i	$-0.588183\pi$
$439$	−4.62794e7	−0.547009	−0.273504	+	0.961871i	$0.588183\pi$
$440$	6.82335e6i	0.0801013i
$441$	0	0
$442$	5.69462e7	0.659475
$443$	7.26342e7i	0.835468i	0.908569	+	0.417734i	$0.137176\pi$
$443$	7.26342e7i	0.835468i	−0.908569	+	0.417734i	$0.862824\pi$
$444$	0	0
$445$	2.10961e8	2.39399
$446$	8.89098e7i	1.00218i
$447$	0	0
$448$	−1.83776e7	−0.204387
$449$	1.26263e7i	0.139488i	0.997565	+	0.0697439i	$0.0222182\pi$
$449$	1.26263e7i	0.139488i	−0.997565	+	0.0697439i	$0.977782\pi$
$450$	0	0
$451$	2.51073e7	0.273697
$452$	2.06013e7i	0.223089i
$453$	0	0
$454$	851468.	0.00909915
$455$	− 3.62745e8i	− 3.85095i
$456$	0	0
$457$	1.48235e8	1.55311	0.776555	−	0.630049i	$-0.216965\pi$
$457$	1.48235e8	1.55311	0.776555	+	0.630049i	$0.216965\pi$
$458$	7.13571e7i	0.742747i
$459$	0	0
$460$	−8.09376e7	−0.831528
$461$	1.20256e8i	1.22745i	0.789521	+	0.613723i	$0.210329\pi$
$461$	1.20256e8i	1.22745i	−0.789521	+	0.613723i	$0.789671\pi$
$462$	0	0
$463$	1.25442e8	1.26387	0.631934	−	0.775022i	$-0.282261\pi$
$463$	1.25442e8	1.26387	0.631934	+	0.775022i	$0.282261\pi$
$464$	1.52298e7i	0.152455i
$465$	0	0
$466$	−9.83347e7	−0.971738
$467$	7.20089e7i	0.707027i	0.935429	+	0.353513i	$0.115013\pi$
$467$	7.20089e7i	0.707027i	−0.935429	+	0.353513i	$0.884987\pi$
$468$	0	0
$469$	2.11949e8	2.05453
$470$	− 1.11848e7i	− 0.107730i
$471$	0	0
$472$	5.27458e7	0.501605
$473$	− 1.14800e7i	− 0.108483i
$474$	0	0
$475$	−1.40933e8	−1.31502
$476$	− 4.77828e7i	− 0.443048i
$477$	0	0
$478$	−7.17356e7	−0.656827
$479$	− 4.25691e7i	− 0.387336i	−0.981067	−	0.193668i	$-0.937962\pi$
$479$	− 4.25691e7i	− 0.387336i	0.981067	−	0.193668i	$-0.0620384\pi$
$480$	0	0
$481$	1.00387e8	0.902073
$482$	− 5.65106e7i	− 0.504648i
$483$	0	0
$484$	−5.51362e7	−0.486296
$485$	2.13537e8i	1.87175i
$486$	0	0
$487$	9.50256e7	0.822723	0.411362	−	0.911472i	$-0.365053\pi$
$487$	9.50256e7	0.822723	0.411362	+	0.911472i	$0.365053\pi$
$488$	− 5.10869e7i	− 0.439593i
$489$	0	0
$490$	−1.90528e8	−1.61946
$491$	1.34186e8i	1.13361i	0.823852	+	0.566805i	$0.191821\pi$
$491$	1.34186e8i	1.13361i	−0.823852	+	0.566805i	$0.808179\pi$
$492$	0	0
$493$	−3.95984e7	−0.330474
$494$	− 2.21029e8i	− 1.83345i
$495$	0	0
$496$	1.62110e7	0.132851
$497$	− 2.92358e8i	− 2.38147i
$498$	0	0
$499$	3.06221e6	0.0246452	0.0123226	−	0.999924i	$-0.496077\pi$
$499$	3.06221e6	0.0246452	0.0123226	+	0.999924i	$0.496077\pi$
$500$	1.08780e7i	0.0870241i
$501$	0	0
$502$	−1.09112e8	−0.862503
$503$	− 6.21612e7i	− 0.488445i	−0.969719	−	0.244223i	$-0.921467\pi$
$503$	− 6.21612e7i	− 0.488445i	0.969719	−	0.244223i	$-0.0785327\pi$
$504$	0	0
$505$	1.80785e8	1.40375
$506$	1.84303e7i	0.142259i
$507$	0	0
$508$	1.70403e6	0.0129983
$509$	− 2.59187e8i	− 1.96544i	−0.185095	−	0.982721i	$-0.559259\pi$
$509$	− 2.59187e8i	− 1.96544i	0.185095	−	0.982721i	$-0.440741\pi$
$510$	0	0
$511$	−3.43017e8	−2.57071
$512$	− 5.93164e6i	− 0.0441942i
$513$	0	0
$514$	−8.65204e7	−0.637132
$515$	4.95384e7i	0.362677i
$516$	0	0
$517$	−2.54690e6	−0.0184306
$518$	− 8.42333e7i	− 0.606031i
$519$	0	0
$520$	1.17082e8	0.832682
$521$	− 6.34248e7i	− 0.448483i	−0.974534	−	0.224241i	$-0.928010\pi$
$521$	− 6.34248e7i	− 0.448483i	0.974534	−	0.224241i	$-0.0719904\pi$
$522$	0	0
$523$	−2.12228e8	−1.48353	−0.741766	−	0.670659i	$-0.766011\pi$
$523$	−2.12228e8	−1.48353	−0.741766	+	0.670659i	$0.766011\pi$
$524$	− 5.55233e7i	− 0.385906i
$525$	0	0
$526$	1.24627e8	0.856359
$527$	4.21495e7i	0.287979i
$528$	0	0
$529$	−7.05815e7	−0.476786
$530$	− 1.33202e8i	− 0.894715i
$531$	0	0
$532$	−1.85463e8	−1.23175
$533$	− 4.30816e8i	− 2.84518i
$534$	0	0
$535$	1.38820e8	0.906545
$536$	6.84097e7i	0.444246i
$537$	0	0
$538$	−8.17431e7	−0.524934
$539$	4.33851e7i	0.277060i
$540$	0	0
$541$	960703.	0.00606733	0.00303366	−	0.999995i	$-0.499034\pi$
$541$	960703.	0.00606733	0.00303366	+	0.999995i	$0.499034\pi$
$542$	4.99542e7i	0.313743i
$543$	0	0
$544$	1.54226e7	0.0957992
$545$	1.01934e8i	0.629693i
$546$	0	0
$547$	2.57947e8	1.57604	0.788021	−	0.615648i	$-0.211106\pi$
$547$	2.57947e8	1.57604	0.788021	+	0.615648i	$0.211106\pi$
$548$	− 6.79894e7i	− 0.413142i
$549$	0	0
$550$	−1.69994e7	−0.102175
$551$	1.53696e8i	0.918772i
$552$	0	0
$553$	−9.84691e7	−0.582270
$554$	1.39054e8i	0.817815i
$555$	0	0
$556$	9.55511e7	0.555918
$557$	7.25922e7i	0.420073i	0.977694	+	0.210036i	$0.0673583\pi$
$557$	7.25922e7i	0.420073i	−0.977694	+	0.210036i	$0.932642\pi$
$558$	0	0
$559$	−1.96986e8	−1.12772
$560$	− 9.82417e7i	− 0.559412i
$561$	0	0
$562$	−1.87572e8	−1.05672
$563$	− 1.62390e8i	− 0.909983i	−0.890496	−	0.454991i	$-0.849642\pi$
$563$	− 1.62390e8i	− 0.909983i	0.890496	−	0.454991i	$-0.150358\pi$
$564$	0	0
$565$	−1.10129e8	−0.610600
$566$	2.15792e8i	1.19011i
$567$	0	0
$568$	9.43629e7	0.514940
$569$	1.56368e8i	0.848812i	0.905472	+	0.424406i	$0.139517\pi$
$569$	1.56368e8i	0.848812i	−0.905472	+	0.424406i	$0.860483\pi$
$570$	0	0
$571$	1.54583e7	0.0830333	0.0415166	−	0.999138i	$-0.486781\pi$
$571$	1.54583e7	0.0830333	0.0415166	+	0.999138i	$0.486781\pi$
$572$	− 2.66606e7i	− 0.142457i
$573$	0	0
$574$	−3.61492e8	−1.91145
$575$	− 2.01645e8i	− 1.06068i
$576$	0	0
$577$	8.55108e7	0.445137	0.222568	−	0.974917i	$-0.428556\pi$
$577$	8.55108e7	0.445137	0.222568	+	0.974917i	$0.428556\pi$
$578$	− 9.64429e7i	− 0.499444i
$579$	0	0
$580$	−8.14146e7	−0.417271
$581$	− 2.03582e8i	− 1.03803i
$582$	0	0
$583$	−3.03315e7	−0.153069
$584$	− 1.10714e8i	− 0.555858i
$585$	0	0
$586$	1.96111e8	0.974561
$587$	3.20228e8i	1.58323i	0.611018	+	0.791617i	$0.290760\pi$
$587$	3.20228e8i	1.58323i	−0.611018	+	0.791617i	$0.709240\pi$
$588$	0	0
$589$	1.63598e8	0.800629
$590$	2.81965e8i	1.37290i
$591$	0	0
$592$	2.71876e7	0.131041
$593$	2.07242e8i	0.993832i	0.867799	+	0.496916i	$0.165534\pi$
$593$	2.07242e8i	0.993832i	−0.867799	+	0.496916i	$0.834466\pi$
$594$	0	0
$595$	2.55435e8	1.21263
$596$	− 5.07299e7i	− 0.239621i
$597$	0	0
$598$	3.16245e8	1.47884
$599$	− 2.81509e8i	− 1.30982i	−0.755706	−	0.654911i	$-0.772706\pi$
$599$	− 2.81509e8i	− 1.30982i	0.755706	−	0.654911i	$-0.227294\pi$
$600$	0	0
$601$	9.15921e7	0.421924	0.210962	−	0.977494i	$-0.432340\pi$
$601$	9.15921e7	0.421924	0.210962	+	0.977494i	$0.432340\pi$
$602$	1.65288e8i	0.757621i
$603$	0	0
$604$	−6.42075e6	−0.0291390
$605$	− 2.94744e8i	− 1.33100i
$606$	0	0
$607$	1.29041e8	0.576980	0.288490	−	0.957483i	$-0.406847\pi$
$607$	1.29041e8	0.576980	0.288490	+	0.957483i	$0.406847\pi$
$608$	− 5.98609e7i	− 0.266338i
$609$	0	0
$610$	2.73098e8	1.20317
$611$	4.37022e7i	0.191593i
$612$	0	0
$613$	−3.34072e7	−0.145030	−0.0725151	−	0.997367i	$-0.523103\pi$
$613$	−3.34072e7	−0.145030	−0.0725151	+	0.997367i	$0.523103\pi$
$614$	2.74576e8i	1.18620i
$615$	0	0
$616$	−2.23706e7	−0.0957051
$617$	4.12753e8i	1.75726i	0.477508	+	0.878628i	$0.341540\pi$
$617$	4.12753e8i	1.75726i	−0.477508	+	0.878628i	$0.658460\pi$
$618$	0	0
$619$	3.93806e7	0.166039	0.0830196	−	0.996548i	$-0.473544\pi$
$619$	3.93806e7	0.166039	0.0830196	+	0.996548i	$0.473544\pi$
$620$	8.66596e7i	0.363615i
$621$	0	0
$622$	1.74991e8	0.727185
$623$	6.91643e8i	2.86034i
$624$	0	0
$625$	−2.71242e8	−1.11101
$626$	− 4.07007e6i	− 0.0165913i
$627$	0	0
$628$	−3.36144e7	−0.135721
$629$	7.06894e7i	0.284055i
$630$	0	0
$631$	−3.58330e8	−1.42625	−0.713124	−	0.701038i	$-0.752720\pi$
$631$	−3.58330e8	−1.42625	−0.713124	+	0.701038i	$0.752720\pi$
$632$	− 3.17824e7i	− 0.125903i
$633$	0	0
$634$	−4.22056e7	−0.165616
$635$	9.10932e6i	0.0355766i
$636$	0	0
$637$	7.44444e8	2.88014
$638$	1.85389e7i	0.0713874i
$639$	0	0
$640$	3.17090e7	0.120960
$641$	− 2.95815e8i	− 1.12317i	−0.827418	−	0.561586i	$-0.810191\pi$
$641$	− 2.95815e8i	− 1.12317i	0.827418	−	0.561586i	$-0.189809\pi$
$642$	0	0
$643$	−6.90523e7	−0.259744	−0.129872	−	0.991531i	$-0.541457\pi$
$643$	−6.90523e7	−0.259744	−0.129872	+	0.991531i	$0.541457\pi$
$644$	− 2.65357e8i	− 0.993511i
$645$	0	0
$646$	1.55642e8	0.577337
$647$	7.16195e7i	0.264435i	0.991221	+	0.132217i	$0.0422097\pi$
$647$	7.16195e7i	0.264435i	−0.991221	+	0.132217i	$0.957790\pi$
$648$	0	0
$649$	6.42063e7	0.234879
$650$	2.91693e8i	1.06215i
$651$	0	0
$652$	6.53985e7	0.235953
$653$	5.01498e8i	1.80107i	0.434788	+	0.900533i	$0.356823\pi$
$653$	5.01498e8i	1.80107i	−0.434788	+	0.900533i	$0.643177\pi$
$654$	0	0
$655$	2.96813e8	1.05623
$656$	− 1.16677e8i	− 0.413308i
$657$	0	0
$658$	3.66699e7	0.128716
$659$	− 3.59634e8i	− 1.25662i	−0.777963	−	0.628310i	$-0.783747\pi$
$659$	− 3.59634e8i	− 1.25662i	0.777963	−	0.628310i	$-0.216253\pi$
$660$	0	0
$661$	−3.91271e8	−1.35480	−0.677398	−	0.735617i	$-0.736892\pi$
$661$	−3.91271e8	−1.35480	−0.677398	+	0.735617i	$0.736892\pi$
$662$	− 8.39799e6i	− 0.0289469i
$663$	0	0
$664$	6.57093e7	0.224451
$665$	− 9.91435e8i	− 3.37131i
$666$	0	0
$667$	−2.19906e8	−0.741070
$668$	2.18985e8i	0.734657i
$669$	0	0
$670$	−3.65701e8	−1.21591
$671$	− 6.21870e7i	− 0.205841i
$672$	0	0
$673$	−3.01730e8	−0.989858	−0.494929	−	0.868933i	$-0.664806\pi$
$673$	−3.01730e8	−0.989858	−0.494929	+	0.868933i	$0.664806\pi$
$674$	− 4.44920e7i	− 0.145312i
$675$	0	0
$676$	−3.03012e8	−0.980888
$677$	5.62027e7i	0.181130i	0.995891	+	0.0905652i	$0.0288673\pi$
$677$	5.62027e7i	0.181130i	−0.995891	+	0.0905652i	$0.971133\pi$
$678$	0	0
$679$	−7.00088e8	−2.23637
$680$	8.24454e7i	0.262204i
$681$	0	0
$682$	1.97332e7	0.0622079
$683$	1.47922e8i	0.464270i	0.972684	+	0.232135i	$0.0745711\pi$
$683$	1.47922e8i	0.464270i	−0.972684	+	0.232135i	$0.925429\pi$
$684$	0	0
$685$	3.63454e8	1.13078
$686$	− 2.51402e8i	− 0.778746i
$687$	0	0
$688$	−5.33493e7	−0.163819
$689$	5.20458e8i	1.59121i
$690$	0	0
$691$	−2.27233e7	−0.0688711	−0.0344355	−	0.999407i	$-0.510963\pi$
$691$	−2.27233e7	−0.0688711	−0.0344355	+	0.999407i	$0.510963\pi$
$692$	− 4.02438e7i	− 0.121445i
$693$	0	0
$694$	−1.03723e8	−0.310311
$695$	5.10791e8i	1.52156i
$696$	0	0
$697$	3.03367e8	0.895923
$698$	− 3.63906e8i	− 1.07010i
$699$	0	0
$700$	2.44755e8	0.713573
$701$	5.55648e8i	1.61304i	0.591205	+	0.806521i	$0.298652\pi$
$701$	5.55648e8i	1.61304i	−0.591205	+	0.806521i	$0.701348\pi$
$702$	0	0
$703$	2.74372e8	0.789720
$704$	− 7.22045e6i	− 0.0206941i
$705$	0	0
$706$	1.34877e8	0.383287
$707$	5.92711e8i	1.67720i
$708$	0	0
$709$	−6.80430e7	−0.190917	−0.0954585	−	0.995433i	$-0.530432\pi$
$709$	−6.80430e7	−0.190917	−0.0954585	+	0.995433i	$0.530432\pi$
$710$	5.04440e8i	1.40940i
$711$	0	0
$712$	−2.23239e8	−0.618485
$713$	2.34073e8i	0.645777i
$714$	0	0
$715$	1.42521e8	0.389906
$716$	− 2.64188e8i	− 0.719736i
$717$	0	0
$718$	8.51412e7	0.230020
$719$	1.29526e8i	0.348474i	0.984704	+	0.174237i	$0.0557459\pi$
$719$	1.29526e8i	0.348474i	−0.984704	+	0.174237i	$0.944254\pi$
$720$	0	0
$721$	−1.62413e8	−0.433327
$722$	− 3.37972e8i	− 0.897986i
$723$	0	0
$724$	−8.40675e7	−0.221520
$725$	− 2.02833e8i	− 0.532261i
$726$	0	0
$727$	−6.10700e8	−1.58937	−0.794684	−	0.607023i	$-0.792364\pi$
$727$	−6.10700e8	−1.58937	−0.794684	+	0.607023i	$0.792364\pi$
$728$	3.83857e8i	0.994890i
$729$	0	0
$730$	5.91849e8	1.52140
$731$	− 1.38711e8i	− 0.355108i
$732$	0	0
$733$	−1.09869e8	−0.278975	−0.139487	−	0.990224i	$-0.544545\pi$
$733$	−1.09869e8	−0.278975	−0.139487	+	0.990224i	$0.544545\pi$
$734$	− 1.01528e8i	− 0.256743i
$735$	0	0
$736$	8.56480e7	0.214825
$737$	8.32736e7i	0.208020i
$738$	0	0
$739$	−3.13732e8	−0.777366	−0.388683	−	0.921372i	$-0.627070\pi$
$739$	−3.13732e8	−0.777366	−0.388683	+	0.921372i	$0.627070\pi$
$740$	1.45338e8i	0.358661i
$741$	0	0
$742$	4.36709e8	1.06901
$743$	3.10615e8i	0.757280i	0.925544	+	0.378640i	$0.123608\pi$
$743$	3.10615e8i	0.757280i	−0.925544	+	0.378640i	$0.876392\pi$
$744$	0	0
$745$	2.71189e8	0.655847
$746$	4.90336e7i	0.118108i
$747$	0	0
$748$	1.87736e7	0.0448584
$749$	4.55125e8i	1.08314i
$750$	0	0
$751$	−5.57362e8	−1.31588	−0.657942	−	0.753069i	$-0.728573\pi$
$751$	−5.57362e8	−1.31588	−0.657942	+	0.753069i	$0.728573\pi$
$752$	1.18358e7i	0.0278319i
$753$	0	0
$754$	3.18109e8	0.742098
$755$	− 3.43237e7i	− 0.0797541i
$756$	0	0
$757$	1.72743e7	0.0398210	0.0199105	−	0.999802i	$-0.493662\pi$
$757$	1.72743e7	0.0398210	0.0199105	+	0.999802i	$0.493662\pi$
$758$	5.86323e7i	0.134626i
$759$	0	0
$760$	3.20001e8	0.728971
$761$	− 3.79607e7i	− 0.0861351i	−0.999072	−	0.0430675i	$-0.986287\pi$
$761$	− 3.79607e7i	− 0.0861351i	0.999072	−	0.0430675i	$-0.0137131\pi$
$762$	0	0
$763$	−3.34194e8	−0.752358
$764$	− 4.70206e7i	− 0.105441i
$765$	0	0
$766$	−1.41713e7	−0.0315299
$767$	− 1.10171e9i	− 2.44165i
$768$	0	0
$769$	−1.43966e8	−0.316577	−0.158289	−	0.987393i	$-0.550598\pi$
$769$	−1.43966e8	−0.316577	−0.158289	+	0.987393i	$0.550598\pi$
$770$	− 1.19587e8i	− 0.261947i
$771$	0	0
$772$	5.22232e6	0.0113504
$773$	2.81284e8i	0.608984i	0.952515	+	0.304492i	$0.0984867\pi$
$773$	2.81284e8i	0.608984i	−0.952515	+	0.304492i	$0.901513\pi$
$774$	0	0
$775$	−2.15900e8	−0.463819
$776$	− 2.25964e8i	− 0.483564i
$777$	0	0
$778$	−1.39132e7	−0.0295454
$779$	− 1.17748e9i	− 2.49081i
$780$	0	0
$781$	1.14866e8	0.241123
$782$	2.22690e8i	0.465673i
$783$	0	0
$784$	2.01616e8	0.418386
$785$	− 1.79694e8i	− 0.371470i
$786$	0	0
$787$	−2.81779e8	−0.578076	−0.289038	−	0.957318i	$-0.593335\pi$
$787$	−2.81779e8	−0.578076	−0.289038	+	0.957318i	$0.593335\pi$
$788$	3.31290e8i	0.677065i
$789$	0	0
$790$	1.69901e8	0.344599
$791$	− 3.61062e8i	− 0.729546i
$792$	0	0
$793$	−1.06707e9	−2.13979
$794$	− 6.62868e6i	− 0.0132424i
$795$	0	0
$796$	2.22944e8	0.442035
$797$	− 1.91957e8i	− 0.379167i	−0.981865	−	0.189583i	$-0.939286\pi$
$797$	− 1.91957e8i	− 0.379167i	0.981865	−	0.189583i	$-0.0607137\pi$
$798$	0	0
$799$	−3.07738e7	−0.0603310
$800$	7.89986e7i	0.154294i
$801$	0	0
$802$	9.95830e7	0.193047
$803$	− 1.34770e8i	− 0.260283i
$804$	0	0
$805$	1.41853e9	2.71926
$806$	− 3.38602e8i	− 0.646673i
$807$	0	0
$808$	−1.91307e8	−0.362657
$809$	− 3.02304e8i	− 0.570950i	−0.958386	−	0.285475i	$-0.907849\pi$
$809$	− 3.02304e8i	− 0.570950i	0.958386	−	0.285475i	$-0.0921513\pi$
$810$	0	0
$811$	−4.85058e8	−0.909351	−0.454675	−	0.890657i	$-0.650245\pi$
$811$	−4.85058e8	−0.909351	−0.454675	+	0.890657i	$0.650245\pi$
$812$	− 2.66921e8i	− 0.498556i
$813$	0	0
$814$	3.30948e7	0.0613603
$815$	3.49603e8i	0.645807i
$816$	0	0
$817$	−5.38390e8	−0.987259
$818$	− 3.65035e8i	− 0.666922i
$819$	0	0
$820$	6.23725e8	1.13123
$821$	9.11768e7i	0.164761i	0.996601	+	0.0823806i	$0.0262523\pi$
$821$	9.11768e7i	0.164761i	−0.996601	+	0.0823806i	$0.973748\pi$
$822$	0	0
$823$	9.37492e7	0.168178	0.0840888	−	0.996458i	$-0.473202\pi$
$823$	9.37492e7	0.168178	0.0840888	+	0.996458i	$0.473202\pi$
$824$	− 5.24214e7i	− 0.0936973i
$825$	0	0
$826$	−9.24434e8	−1.64035
$827$	− 7.81578e8i	− 1.38183i	−0.722934	−	0.690917i	$-0.757207\pi$
$827$	− 7.81578e8i	− 1.38183i	0.722934	−	0.690917i	$-0.242793\pi$
$828$	0	0
$829$	5.47882e8	0.961663	0.480832	−	0.876813i	$-0.340335\pi$
$829$	5.47882e8	0.961663	0.480832	+	0.876813i	$0.340335\pi$
$830$	3.51265e8i	0.614328i
$831$	0	0
$832$	−1.23896e8	−0.215123
$833$	5.24215e8i	0.906932i
$834$	0	0
$835$	−1.17064e9	−2.01077
$836$	− 7.28673e7i	− 0.124714i
$837$	0	0
$838$	−6.26409e8	−1.06445
$839$	− 5.35404e7i	− 0.0906559i	−0.998972	−	0.0453279i	$-0.985567\pi$
$839$	− 5.35404e7i	− 0.0906559i	0.998972	−	0.0453279i	$-0.0144333\pi$
$840$	0	0
$841$	3.73622e8	0.628122
$842$	− 1.79267e8i	− 0.300306i
$843$	0	0
$844$	−3.89525e8	−0.647900
$845$	− 1.61982e9i	− 2.68471i
$846$	0	0
$847$	9.66329e8	1.59028
$848$	1.40955e8i	0.231149i
$849$	0	0
$850$	−2.05401e8	−0.334462
$851$	3.92566e8i	0.636978i
$852$	0	0
$853$	−2.58793e8	−0.416970	−0.208485	−	0.978026i	$-0.566853\pi$
$853$	−2.58793e8	−0.416970	−0.208485	+	0.978026i	$0.566853\pi$
$854$	8.95360e8i	1.43755i
$855$	0	0
$856$	−1.46899e8	−0.234205
$857$	− 6.67612e8i	− 1.06067i	−0.847787	−	0.530337i	$-0.822065\pi$
$857$	− 6.67612e8i	− 1.06067i	0.847787	−	0.530337i	$-0.177935\pi$
$858$	0	0
$859$	−1.14305e9	−1.80338	−0.901690	−	0.432382i	$-0.857673\pi$
$859$	−1.14305e9	−1.80338	−0.901690	+	0.432382i	$0.857673\pi$
$860$	− 2.85192e8i	− 0.448375i
$861$	0	0
$862$	−5.36699e7	−0.0837933
$863$	− 1.78293e8i	− 0.277396i	−0.990335	−	0.138698i	$-0.955708\pi$
$863$	− 1.78293e8i	− 0.277396i	0.990335	−	0.138698i	$-0.0442918\pi$
$864$	0	0
$865$	2.15133e8	0.332398
$866$	5.83440e8i	0.898343i
$867$	0	0
$868$	−2.84117e8	−0.434448
$869$	− 3.86880e7i	− 0.0589545i
$870$	0	0
$871$	1.42889e9	2.16244
$872$	− 1.07866e8i	− 0.162681i
$873$	0	0
$874$	8.64342e8	1.29465
$875$	− 1.90650e8i	− 0.284586i
$876$	0	0
$877$	9.29840e8	1.37851	0.689254	−	0.724519i	$-0.257938\pi$
$877$	9.29840e8	1.37851	0.689254	+	0.724519i	$0.257938\pi$
$878$	2.61796e8i	0.386794i
$879$	0	0
$880$	3.85987e7	0.0566401
$881$	5.01442e8i	0.733319i	0.930355	+	0.366660i	$0.119499\pi$
$881$	5.01442e8i	0.733319i	−0.930355	+	0.366660i	$0.880501\pi$
$882$	0	0
$883$	8.14295e8	1.18277	0.591384	−	0.806390i	$-0.298582\pi$
$883$	8.14295e8	1.18277	0.591384	+	0.806390i	$0.298582\pi$
$884$	− 3.22136e8i	− 0.466319i
$885$	0	0
$886$	4.10881e8	0.590765
$887$	− 3.96753e8i	− 0.568525i	−0.958746	−	0.284262i	$-0.908251\pi$
$887$	− 3.96753e8i	− 0.568525i	0.958746	−	0.284262i	$-0.0917487\pi$
$888$	0	0
$889$	−2.98652e7	−0.0425070
$890$	− 1.19338e9i	− 1.69281i
$891$	0	0
$892$	5.02950e8	0.708647
$893$	1.19444e8i	0.167730i
$894$	0	0
$895$	1.41228e9	1.96993
$896$	1.03959e8i	0.144524i
$897$	0	0
$898$	7.14250e7	0.0986328
$899$	2.35453e8i	0.324059i
$900$	0	0
$901$	−3.66491e8	−0.501059
$902$	− 1.42028e8i	− 0.193533i
$903$	0	0
$904$	1.16538e8	0.157748
$905$	− 4.49403e8i	− 0.606304i
$906$	0	0
$907$	−8.80068e8	−1.17949	−0.589745	−	0.807589i	$-0.700772\pi$
$907$	−8.80068e8	−1.17949	−0.589745	+	0.807589i	$0.700772\pi$
$908$	− 4.81663e6i	− 0.00643407i
$909$	0	0
$910$	−2.05200e9	−2.72303
$911$	5.05211e8i	0.668217i	0.942535	+	0.334109i	$0.108435\pi$
$911$	5.05211e8i	0.668217i	−0.942535	+	0.334109i	$0.891565\pi$
$912$	0	0
$913$	7.99864e7	0.105100
$914$	− 8.38544e8i	− 1.09821i
$915$	0	0
$916$	4.03657e8	0.525201
$917$	9.73114e8i	1.26199i
$918$	0	0
$919$	−2.68525e8	−0.345969	−0.172985	−	0.984925i	$-0.555341\pi$
$919$	−2.68525e8	−0.345969	−0.172985	+	0.984925i	$0.555341\pi$
$920$	4.57852e8i	0.587979i
$921$	0	0
$922$	6.80268e8	0.867935
$923$	− 1.97098e9i	− 2.50656i
$924$	0	0
$925$	−3.62089e8	−0.457499
$926$	− 7.09610e8i	− 0.893690i
$927$	0	0
$928$	8.61528e7	0.107802
$929$	7.01488e8i	0.874929i	0.899236	+	0.437465i	$0.144123\pi$
$929$	7.01488e8i	0.874929i	−0.899236	+	0.437465i	$0.855877\pi$
$930$	0	0
$931$	2.03467e9	2.52142
$932$	5.56265e8i	0.687123i
$933$	0	0
$934$	4.07344e8	0.499943
$935$	1.00359e8i	0.122778i
$936$	0	0
$937$	5.16722e8	0.628114	0.314057	−	0.949404i	$-0.398312\pi$
$937$	5.16722e8	0.628114	0.314057	+	0.949404i	$0.398312\pi$
$938$	− 1.19896e9i	− 1.45277i
$939$	0	0
$940$	−6.32710e7	−0.0761765
$941$	− 8.26999e7i	− 0.0992513i	−0.998768	−	0.0496256i	$-0.984197\pi$
$941$	− 8.26999e7i	− 0.0992513i	0.998768	−	0.0496256i	$-0.0158028\pi$
$942$	0	0
$943$	1.68472e9	2.00906
$944$	− 2.98375e8i	− 0.354688i
$945$	0	0
$946$	−6.49409e7	−0.0767087
$947$	− 4.72216e8i	− 0.556020i	−0.960578	−	0.278010i	$-0.910325\pi$
$947$	− 4.72216e8i	− 0.556020i	0.960578	−	0.278010i	$-0.0896748\pi$
$948$	0	0
$949$	−2.31251e9	−2.70574
$950$	7.97237e8i	0.929858i
$951$	0	0
$952$	−2.70300e8	−0.313282
$953$	9.55129e8i	1.10353i	0.834000	+	0.551764i	$0.186045\pi$
$953$	9.55129e8i	1.10353i	−0.834000	+	0.551764i	$0.813955\pi$
$954$	0	0
$955$	2.51360e8	0.288593
$956$	4.05798e8i	0.464447i
$957$	0	0
$958$	−2.40807e8	−0.273888
$959$	1.19160e9i	1.35106i
$960$	0	0
$961$	−6.36882e8	−0.717611
$962$	− 5.67874e8i	− 0.637862i
$963$	0	0
$964$	−3.19672e8	−0.356840
$965$	2.79172e7i	0.0310663i
$966$	0	0
$967$	9.13723e7	0.101050	0.0505249	−	0.998723i	$-0.483911\pi$
$967$	9.13723e7	0.101050	0.0505249	+	0.998723i	$0.483911\pi$
$968$	3.11898e8i	0.343863i
$969$	0	0
$970$	1.20795e9	1.32353
$971$	− 1.09426e8i	− 0.119526i	−0.998213	−	0.0597630i	$-0.980966\pi$
$971$	− 1.09426e8i	− 0.119526i	0.998213	−	0.0597630i	$-0.0190345\pi$
$972$	0	0
$973$	−1.67465e9	−1.81796
$974$	− 5.37546e8i	− 0.581753i
$975$	0	0
$976$	−2.88991e8	−0.310839
$977$	− 5.90806e8i	− 0.633521i	−0.948506	−	0.316760i	$-0.897405\pi$
$977$	− 5.90806e8i	− 0.633521i	0.948506	−	0.316760i	$-0.102595\pi$
$978$	0	0
$979$	−2.71743e8	−0.289608
$980$	1.07779e9i	1.14513i
$981$	0	0
$982$	7.59072e8	0.801584
$983$	1.55583e9i	1.63796i	0.573824	+	0.818978i	$0.305459\pi$
$983$	1.55583e9i	1.63796i	−0.573824	+	0.818978i	$0.694541\pi$
$984$	0	0
$985$	−1.77099e9	−1.85314
$986$	2.24003e8i	0.233680i
$987$	0	0
$988$	−1.25033e9	−1.29644
$989$	− 7.70320e8i	− 0.796310i
$990$	0	0
$991$	1.71185e9	1.75891	0.879456	−	0.475979i	$-0.157906\pi$
$991$	1.71185e9	1.75891	0.879456	+	0.475979i	$0.157906\pi$
$992$	− 9.17031e7i	− 0.0939396i
$993$	0	0
$994$	−1.65382e9	−1.68395
$995$	1.19180e9i	1.20986i
$996$	0	0
$997$	−7.14024e8	−0.720489	−0.360244	−	0.932858i	$-0.617307\pi$
$997$	−7.14024e8	−0.720489	−0.360244	+	0.932858i	$0.617307\pi$
$998$	− 1.73225e7i	− 0.0174268i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.7.b.b.161.1	✓	8
3.2	odd	2	inner	162.7.b.b.161.8	yes	8
9.2	odd	6		162.7.d.g.53.5		16
9.4	even	3		162.7.d.g.107.5		16
9.5	odd	6		162.7.d.g.107.4		16
9.7	even	3		162.7.d.g.53.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.7.b.b.161.1	✓	8	1.1	even	1	trivial
162.7.b.b.161.8	yes	8	3.2	odd	2	inner
162.7.d.g.53.4		16	9.7	even	3
162.7.d.g.53.5		16	9.2	odd	6
162.7.d.g.107.4		16	9.5	odd	6
162.7.d.g.107.5		16	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-5.65685i q^{2} -32.0000 q^{4} -171.064i q^{5} +560.839 q^{7} +181.019i q^{8} +O(q^{10})\)	\(q-5.65685i q^{2} -32.0000 q^{4} -171.064i q^{5} +560.839 q^{7} +181.019i q^{8} -967.683 q^{10} +220.351i q^{11} +3781.00 q^{13} -3172.58i q^{14} +1024.00 q^{16} +2662.46i q^{17} +10334.0 q^{19} +5474.04i q^{20} +1246.49 q^{22} +14785.7i q^{23} -13637.8 q^{25} -21388.5i q^{26} -17946.8 q^{28} +14872.9i q^{29} +15831.0 q^{31} -5792.62i q^{32} +15061.2 q^{34} -95939.2i q^{35} +26550.4 q^{37} -58457.9i q^{38} +30965.8 q^{40} -113942. i q^{41} -52098.9 q^{43} -7051.22i q^{44} +83640.6 q^{46} +11558.4i q^{47} +196891. q^{49} +77147.0i q^{50} -120992. q^{52} +137651. i q^{53} +37694.0 q^{55} +101523. i q^{56} +84133.6 q^{58} -291382. i q^{59} -282218. q^{61} -89553.8i q^{62} -32768.0 q^{64} -646791. i q^{65} +377914. q^{67} -85198.8i q^{68} -542714. q^{70} -521287. i q^{71} -611614. q^{73} -150192. i q^{74} -330688. q^{76} +123581. i q^{77} -175575. q^{79} -175169. i q^{80} -644556. q^{82} -362996. i q^{83} +455451. q^{85} +294716. i q^{86} -39887.7 q^{88} +1.23323e6i q^{89} +2.12053e6 q^{91} -473143. i q^{92} +65384.1 q^{94} -1.76777e6i q^{95} -1.24829e6 q^{97} -1.11378e6i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 256 q^{4} + 964 q^{7}+O(q^{10}) \) 8 * q - 256 * q^4 + 964 * q^7	\( 8 q - 256 q^{4} + 964 q^{7} - 768 q^{10} + 4540 q^{13} + 8192 q^{16} - 23684 q^{19} + 27072 q^{22} - 32392 q^{25} - 30848 q^{28} + 77056 q^{31} - 52608 q^{34} - 11348 q^{37} + 24576 q^{40} - 226604 q^{43} - 162720 q^{46} + 1298088 q^{49} - 145280 q^{52} - 1460916 q^{55} + 867456 q^{58} - 327476 q^{61} - 262144 q^{64} + 1713292 q^{67} - 176352 q^{70} - 2189216 q^{73} + 757888 q^{76} - 1326884 q^{79} - 1158816 q^{82} + 3483180 q^{85} - 866304 q^{88} + 1130324 q^{91} - 26400 q^{94} - 2200064 q^{97}+O(q^{100}) \) 8 * q - 256 * q^4 + 964 * q^7 - 768 * q^10 + 4540 * q^13 + 8192 * q^16 - 23684 * q^19 + 27072 * q^22 - 32392 * q^25 - 30848 * q^28 + 77056 * q^31 - 52608 * q^34 - 11348 * q^37 + 24576 * q^40 - 226604 * q^43 - 162720 * q^46 + 1298088 * q^49 - 145280 * q^52 - 1460916 * q^55 + 867456 * q^58 - 327476 * q^61 - 262144 * q^64 + 1713292 * q^67 - 176352 * q^70 - 2189216 * q^73 + 757888 * q^76 - 1326884 * q^79 - 1158816 * q^82 + 3483180 * q^85 - 866304 * q^88 + 1130324 * q^91 - 26400 * q^94 - 2200064 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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