LMFDB - Embedded newform 162.7.b.b.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:	$8$
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			161.6
Root			$16.6034 - 1.41421i$ of defining polynomial
Character	$\chi$	$=$	162.161
Dual form			162.7.b.b.161.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.65685i q^{2} -32.0000 q^{4} -85.6833i q^{5} -564.058 q^{7} -181.019i q^{8} +O(q^{10})$	\(q+5.65685i q^{2} -32.0000 q^{4} -85.6833i q^{5} -564.058 q^{7} -181.019i q^{8} +484.698 q^{10} -1453.72i q^{11} +840.623 q^{13} -3190.79i q^{14} +1024.00 q^{16} +5090.31i q^{17} -6688.88 q^{19} +2741.87i q^{20} +8223.51 q^{22} +11850.8i q^{23} +8283.37 q^{25} +4755.28i q^{26} +18049.9 q^{28} -15431.8i q^{29} +33082.2 q^{31} +5792.62i q^{32} -28795.1 q^{34} +48330.3i q^{35} +84382.4 q^{37} -37838.0i q^{38} -15510.3 q^{40} +16156.3i q^{41} -66110.9 q^{43} +46519.2i q^{44} -67038.2 q^{46} +159085. i q^{47} +200512. q^{49} +46857.8i q^{50} -26899.9 q^{52} +150118. i q^{53} -124560. q^{55} +102105. i q^{56} +87295.3 q^{58} +192083. i q^{59} -382488. q^{61} +187141. i q^{62} -32768.0 q^{64} -72027.4i q^{65} +237549. q^{67} -162890. i q^{68} -273398. q^{70} -688359. i q^{71} +379634. q^{73} +477339. i q^{74} +214044. q^{76} +819985. i q^{77} -770991. q^{79} -87739.7i q^{80} -91394.1 q^{82} +755560. i q^{83} +436155. q^{85} -373980. i q^{86} -263152. q^{88} +871169. i q^{89} -474160. q^{91} -379226. i q^{92} -899918. q^{94} +573125. i q^{95} +1.21326e6 q^{97} +1.13427e6i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	− 85.6833i	− 0.685467i	−0.939433	−	0.342733i	$-0.888647\pi$
$5$	− 85.6833i	− 0.685467i	0.939433	−	0.342733i	$-0.111353\pi$
$6$	0	0
$7$	−564.058	−1.64448	−0.822242	−	0.569138i	$-0.807277\pi$
$7$	−564.058	−1.64448	−0.822242	+	0.569138i	$0.807277\pi$
$8$	− 181.019i	− 0.353553i
$9$	0	0
$10$	484.698	0.484698
$11$	− 1453.72i	− 1.09220i	−0.837718	−	0.546102i	$-0.816111\pi$
$11$	− 1453.72i	− 1.09220i	0.837718	−	0.546102i	$-0.183889\pi$
$12$	0	0
$13$	840.623	0.382623	0.191312	−	0.981529i	$-0.438726\pi$
$13$	840.623	0.382623	0.191312	+	0.981529i	$0.438726\pi$
$14$	− 3190.79i	− 1.16283i
$15$	0	0
$16$	1024.00	0.250000
$17$	5090.31i	1.03609i	0.855353	+	0.518045i	$0.173340\pi$
$17$	5090.31i	1.03609i	−0.855353	+	0.518045i	$0.826660\pi$
$18$	0	0
$19$	−6688.88	−0.975198	−0.487599	−	0.873068i	$-0.662127\pi$
$19$	−6688.88	−0.975198	−0.487599	+	0.873068i	$0.662127\pi$
$20$	2741.87i	0.342733i
$21$	0	0
$22$	8223.51	0.772305
$23$	11850.8i	0.974012i	0.873399	+	0.487006i	$0.161911\pi$
$23$	11850.8i	0.974012i	−0.873399	+	0.487006i	$0.838089\pi$
$24$	0	0
$25$	8283.37	0.530136
$26$	4755.28i	0.270555i
$27$	0	0
$28$	18049.9	0.822242
$29$	− 15431.8i	− 0.632735i	−0.948637	−	0.316367i	$-0.897537\pi$
$29$	− 15431.8i	− 0.632735i	0.948637	−	0.316367i	$-0.102463\pi$
$30$	0	0
$31$	33082.2	1.11048	0.555239	−	0.831691i	$-0.312627\pi$
$31$	33082.2	1.11048	0.555239	+	0.831691i	$0.312627\pi$
$32$	5792.62i	0.176777i
$33$	0	0
$34$	−28795.1	−0.732626
$35$	48330.3i	1.12724i
$36$	0	0
$37$	84382.4	1.66589	0.832945	−	0.553355i	$-0.186653\pi$
$37$	84382.4	1.66589	0.832945	+	0.553355i	$0.186653\pi$
$38$	− 37838.0i	− 0.689569i
$39$	0	0
$40$	−15510.3	−0.242349
$41$	16156.3i	0.234418i	0.993107	+	0.117209i	$0.0373948\pi$
$41$	16156.3i	0.234418i	−0.993107	+	0.117209i	$0.962605\pi$
$42$	0	0
$43$	−66110.9	−0.831510	−0.415755	−	0.909477i	$-0.636483\pi$
$43$	−66110.9	−0.831510	−0.415755	+	0.909477i	$0.636483\pi$
$44$	46519.2i	0.546102i
$45$	0	0
$46$	−67038.2	−0.688730
$47$	159085.i	1.53227i	0.642681	+	0.766134i	$0.277822\pi$
$47$	159085.i	1.53227i	−0.642681	+	0.766134i	$0.722178\pi$
$48$	0	0
$49$	200512.	1.70433
$50$	46857.8i	0.374862i
$51$	0	0
$52$	−26899.9	−0.191312
$53$	150118.i	1.00834i	0.863606	+	0.504168i	$0.168201\pi$
$53$	150118.i	1.00834i	−0.863606	+	0.504168i	$0.831799\pi$
$54$	0	0
$55$	−124560.	−0.748670
$56$	102105.i	0.581413i
$57$	0	0
$58$	87295.3	0.447411
$59$	192083.i	0.935263i	0.883924	+	0.467631i	$0.154892\pi$
$59$	192083.i	0.935263i	−0.883924	+	0.467631i	$0.845108\pi$
$60$	0	0
$61$	−382488.	−1.68511	−0.842554	−	0.538611i	$-0.818949\pi$
$61$	−382488.	−1.68511	−0.842554	+	0.538611i	$0.818949\pi$
$62$	187141.i	0.785226i
$63$	0	0
$64$	−32768.0	−0.125000
$65$	− 72027.4i	− 0.262275i
$66$	0	0
$67$	237549.	0.789820	0.394910	−	0.918720i	$-0.370776\pi$
$67$	237549.	0.789820	0.394910	+	0.918720i	$0.370776\pi$
$68$	− 162890.i	− 0.518045i
$69$	0	0
$70$	−273398.	−0.797078
$71$	− 688359.i	− 1.92327i	−0.274334	−	0.961635i	$-0.588457\pi$
$71$	− 688359.i	− 1.92327i	0.274334	−	0.961635i	$-0.411543\pi$
$72$	0	0
$73$	379634.	0.975880	0.487940	−	0.872877i	$-0.337749\pi$
$73$	379634.	0.975880	0.487940	+	0.872877i	$0.337749\pi$
$74$	477339.i	1.17796i
$75$	0	0
$76$	214044.	0.487599
$77$	819985.i	1.79611i
$78$	0	0
$79$	−770991.	−1.56375	−0.781877	−	0.623433i	$-0.785737\pi$
$79$	−770991.	−1.56375	−0.781877	+	0.623433i	$0.785737\pi$
$80$	− 87739.7i	− 0.171367i
$81$	0	0
$82$	−91394.1	−0.165759
$83$	755560.i	1.32140i	0.750649	+	0.660701i	$0.229741\pi$
$83$	755560.i	1.32140i	−0.750649	+	0.660701i	$0.770259\pi$
$84$	0	0
$85$	436155.	0.710205
$86$	− 373980.i	− 0.587967i
$87$	0	0
$88$	−263152.	−0.386153
$89$	871169.i	1.23575i	0.786274	+	0.617877i	$0.212007\pi$
$89$	871169.i	1.23575i	−0.786274	+	0.617877i	$0.787993\pi$
$90$	0	0
$91$	−474160.	−0.629217
$92$	− 379226.i	− 0.487006i
$93$	0	0
$94$	−899918.	−1.08348
$95$	573125.i	0.668465i
$96$	0	0
$97$	1.21326e6	1.32935	0.664675	−	0.747133i	$-0.268570\pi$
$97$	1.21326e6	1.32935	0.664675	+	0.747133i	$0.268570\pi$
$98$	1.13427e6i	1.20514i
$99$	0	0
$100$	−265068.	−0.265068
$101$	798017.i	0.774547i	0.921965	+	0.387274i	$0.126583\pi$
$101$	798017.i	0.774547i	−0.921965	+	0.387274i	$0.873417\pi$
$102$	0	0
$103$	743896.	0.680770	0.340385	−	0.940286i	$-0.389443\pi$
$103$	743896.	0.680770	0.340385	+	0.940286i	$0.389443\pi$
$104$	− 152169.i	− 0.135278i
$105$	0	0
$106$	−849196.	−0.713001
$107$	− 1.02594e6i	− 0.837474i	−0.908108	−	0.418737i	$-0.862473\pi$
$107$	− 1.02594e6i	− 0.837474i	0.908108	−	0.418737i	$-0.137527\pi$
$108$	0	0
$109$	1.09355e6	0.844421	0.422210	−	0.906498i	$-0.361254\pi$
$109$	1.09355e6	0.844421	0.422210	+	0.906498i	$0.361254\pi$
$110$	− 704617.i	− 0.529389i
$111$	0	0
$112$	−577595.	−0.411121
$113$	− 364476.i	− 0.252600i	−0.991992	−	0.126300i	$-0.959690\pi$
$113$	− 364476.i	− 0.252600i	0.991992	−	0.126300i	$-0.0403102\pi$
$114$	0	0
$115$	1.01542e6	0.667652
$116$	493817.i	0.316367i
$117$	0	0
$118$	−1.08659e6	−0.661330
$119$	− 2.87123e6i	− 1.70383i
$120$	0	0
$121$	−341754.	−0.192911
$122$	− 2.16368e6i	− 1.19155i
$123$	0	0
$124$	−1.05863e6	−0.555239
$125$	− 2.04855e6i	− 1.04886i
$126$	0	0
$127$	2.27969e6	1.11292	0.556461	−	0.830874i	$-0.312159\pi$
$127$	2.27969e6	1.11292	0.556461	+	0.830874i	$0.312159\pi$
$128$	− 185364.i	− 0.0883883i
$129$	0	0
$130$	407448.	0.185457
$131$	152500.i	0.0678351i	0.999425	+	0.0339176i	$0.0107984\pi$
$131$	152500.i	0.0678351i	−0.999425	+	0.0339176i	$0.989202\pi$
$132$	0	0
$133$	3.77292e6	1.60370
$134$	1.34378e6i	0.558487i
$135$	0	0
$136$	921444.	0.366313
$137$	− 3.05911e6i	− 1.18969i	−0.803841	−	0.594844i	$-0.797214\pi$
$137$	− 3.05911e6i	− 1.18969i	0.803841	−	0.594844i	$-0.202786\pi$
$138$	0	0
$139$	622018.	0.231611	0.115805	−	0.993272i	$-0.463055\pi$
$139$	622018.	0.231611	0.115805	+	0.993272i	$0.463055\pi$
$140$	− 1.54657e6i	− 0.563619i
$141$	0	0
$142$	3.89395e6	1.35996
$143$	− 1.22203e6i	− 0.417903i
$144$	0	0
$145$	−1.32225e6	−0.433719
$146$	2.14753e6i	0.690051i
$147$	0	0
$148$	−2.70024e6	−0.832945
$149$	3.82058e6i	1.15497i	0.816402	+	0.577484i	$0.195966\pi$
$149$	3.82058e6i	1.15497i	−0.816402	+	0.577484i	$0.804034\pi$
$150$	0	0
$151$	4.85930e6	1.41138	0.705688	−	0.708522i	$-0.250638\pi$
$151$	4.85930e6	1.41138	0.705688	+	0.708522i	$0.250638\pi$
$152$	1.21082e6i	0.344784i
$153$	0	0
$154$	−4.63853e6	−1.27004
$155$	− 2.83459e6i	− 0.761195i
$156$	0	0
$157$	−5.39974e6	−1.39532	−0.697660	−	0.716429i	$-0.745775\pi$
$157$	−5.39974e6	−1.39532	−0.697660	+	0.716429i	$0.745775\pi$
$158$	− 4.36139e6i	− 1.10574i
$159$	0	0
$160$	496331.	0.121175
$161$	− 6.68454e6i	− 1.60175i
$162$	0	0
$163$	−1.13788e6	−0.262744	−0.131372	−	0.991333i	$-0.541938\pi$
$163$	−1.13788e6	−0.262744	−0.131372	+	0.991333i	$0.541938\pi$
$164$	− 517003.i	− 0.117209i
$165$	0	0
$166$	−4.27409e6	−0.934372
$167$	− 1.53256e6i	− 0.329055i	−0.986373	−	0.164527i	$-0.947390\pi$
$167$	− 1.53256e6i	− 0.329055i	0.986373	−	0.164527i	$-0.0526099\pi$
$168$	0	0
$169$	−4.12016e6	−0.853600
$170$	2.46726e6i	0.502191i
$171$	0	0
$172$	2.11555e6	0.415755
$173$	6.37589e6i	1.23141i	0.787977	+	0.615704i	$0.211128\pi$
$173$	6.37589e6i	1.23141i	−0.787977	+	0.615704i	$0.788872\pi$
$174$	0	0
$175$	−4.67230e6	−0.871799
$176$	− 1.48861e6i	− 0.273051i
$177$	0	0
$178$	−4.92808e6	−0.873811
$179$	719446.i	0.125441i	0.998031	+	0.0627204i	$0.0199776\pi$
$179$	719446.i	0.125441i	−0.998031	+	0.0627204i	$0.980022\pi$
$180$	0	0
$181$	7.41982e6	1.25129	0.625645	−	0.780108i	$-0.284836\pi$
$181$	7.41982e6	1.25129	0.625645	+	0.780108i	$0.284836\pi$
$182$	− 2.68225e6i	− 0.444924i
$183$	0	0
$184$	2.14522e6	0.344365
$185$	− 7.23016e6i	− 1.14191i
$186$	0	0
$187$	7.39991e6	1.13162
$188$	− 5.09071e6i	− 0.766134i
$189$	0	0
$190$	−3.24209e6	−0.472676
$191$	− 2.04203e6i	− 0.293063i	−0.989206	−	0.146532i	$-0.953189\pi$
$191$	− 2.04203e6i	− 0.293063i	0.989206	−	0.146532i	$-0.0468110\pi$
$192$	0	0
$193$	4.20898e6	0.585471	0.292735	−	0.956194i	$-0.405435\pi$
$193$	4.20898e6	0.585471	0.292735	+	0.956194i	$0.405435\pi$
$194$	6.86325e6i	0.939992i
$195$	0	0
$196$	−6.41639e6	−0.852163
$197$	− 1.06745e7i	− 1.39621i	−0.715995	−	0.698105i	$-0.754027\pi$
$197$	− 1.06745e7i	− 1.39621i	0.715995	−	0.698105i	$-0.245973\pi$
$198$	0	0
$199$	−3.53584e6	−0.448676	−0.224338	−	0.974511i	$-0.572022\pi$
$199$	−3.53584e6	−0.448676	−0.224338	+	0.974511i	$0.572022\pi$
$200$	− 1.49945e6i	− 0.187431i
$201$	0	0
$202$	−4.51427e6	−0.547688
$203$	8.70441e6i	1.04052i
$204$	0	0
$205$	1.38433e6	0.160686
$206$	4.20811e6i	0.481377i
$207$	0	0
$208$	860798.	0.0956558
$209$	9.72379e6i	1.06512i
$210$	0	0
$211$	7.20482e6	0.766965	0.383483	−	0.923548i	$-0.374725\pi$
$211$	7.20482e6	0.766965	0.383483	+	0.923548i	$0.374725\pi$
$212$	− 4.80378e6i	− 0.504168i
$213$	0	0
$214$	5.80360e6	0.592184
$215$	5.66460e6i	0.569973i
$216$	0	0
$217$	−1.86603e7	−1.82616
$218$	6.18605e6i	0.597096i
$219$	0	0
$220$	3.98592e6	0.374335
$221$	4.27903e6i	0.396432i
$222$	0	0
$223$	−1.30991e7	−1.18121	−0.590603	−	0.806962i	$-0.701110\pi$
$223$	−1.30991e7	−1.18121	−0.590603	+	0.806962i	$0.701110\pi$
$224$	− 3.26737e6i	− 0.290706i
$225$	0	0
$226$	2.06179e6	0.178615
$227$	3.62456e6i	0.309869i	0.987925	+	0.154934i	$0.0495166\pi$
$227$	3.62456e6i	0.309869i	−0.987925	+	0.154934i	$0.950483\pi$
$228$	0	0
$229$	1.32984e7	1.10737	0.553683	−	0.832727i	$-0.313222\pi$
$229$	1.32984e7	1.10737	0.553683	+	0.832727i	$0.313222\pi$
$230$	5.74406e6i	0.472102i
$231$	0	0
$232$	−2.79345e6	−0.223706
$233$	2.32921e7i	1.84137i	0.390308	+	0.920684i	$0.372369\pi$
$233$	2.32921e7i	1.84137i	−0.390308	+	0.920684i	$0.627631\pi$
$234$	0	0
$235$	1.36309e7	1.05032
$236$	− 6.14666e6i	− 0.467631i
$237$	0	0
$238$	1.62421e7	1.20479
$239$	1.61394e7i	1.18220i	0.806597	+	0.591102i	$0.201307\pi$
$239$	1.61394e7i	1.18220i	−0.806597	+	0.591102i	$0.798693\pi$
$240$	0	0
$241$	−1.11953e7	−0.799809	−0.399904	−	0.916557i	$-0.630957\pi$
$241$	−1.11953e7	−0.799809	−0.399904	+	0.916557i	$0.630957\pi$
$242$	− 1.93325e6i	− 0.136409i
$243$	0	0
$244$	1.22396e7	0.842554
$245$	− 1.71806e7i	− 1.16826i
$246$	0	0
$247$	−5.62283e6	−0.373133
$248$	− 5.98852e6i	− 0.392613i
$249$	0	0
$250$	1.15883e7	0.741654
$251$	1.76943e7i	1.11896i	0.828845	+	0.559478i	$0.188998\pi$
$251$	1.76943e7i	1.11896i	−0.828845	+	0.559478i	$0.811002\pi$
$252$	0	0
$253$	1.72278e7	1.06382
$254$	1.28959e7i	0.786954i
$255$	0	0
$256$	1.04858e6	0.0625000
$257$	− 2.81347e7i	− 1.65746i	−0.559648	−	0.828730i	$-0.689064\pi$
$257$	− 2.81347e7i	− 1.65746i	0.559648	−	0.828730i	$-0.310936\pi$
$258$	0	0
$259$	−4.75965e7	−2.73953
$260$	2.30488e6i	0.131138i
$261$	0	0
$262$	−862668.	−0.0479667
$263$	2.71927e6i	0.149480i	0.997203	+	0.0747402i	$0.0238128\pi$
$263$	2.71927e6i	0.149480i	−0.997203	+	0.0747402i	$0.976187\pi$
$264$	0	0
$265$	1.28626e7	0.691180
$266$	2.13428e7i	1.13398i
$267$	0	0
$268$	−7.60156e6	−0.394910
$269$	2.04116e7i	1.04863i	0.851525	+	0.524314i	$0.175678\pi$
$269$	2.04116e7i	1.04863i	−0.851525	+	0.524314i	$0.824322\pi$
$270$	0	0
$271$	−1.14647e7	−0.576044	−0.288022	−	0.957624i	$-0.592998\pi$
$271$	−1.14647e7	−0.576044	−0.288022	+	0.957624i	$0.592998\pi$
$272$	5.21248e6i	0.259022i
$273$	0	0
$274$	1.73049e7	0.841237
$275$	− 1.20417e7i	− 0.579017i
$276$	0	0
$277$	2.12684e7	1.00068	0.500340	−	0.865829i	$-0.333208\pi$
$277$	2.12684e7	1.00068	0.500340	+	0.865829i	$0.333208\pi$
$278$	3.51866e6i	0.163773i
$279$	0	0
$280$	8.74873e6	0.398539
$281$	1.50482e7i	0.678213i	0.940748	+	0.339107i	$0.110125\pi$
$281$	1.50482e7i	0.678213i	−0.940748	+	0.339107i	$0.889875\pi$
$282$	0	0
$283$	−1.70775e7	−0.753470	−0.376735	−	0.926321i	$-0.622953\pi$
$283$	−1.70775e7	−0.753470	−0.376735	+	0.926321i	$0.622953\pi$
$284$	2.20275e7i	0.961635i
$285$	0	0
$286$	6.91287e6	0.295502
$287$	− 9.11311e6i	− 0.385497i
$288$	0	0
$289$	−1.77368e6	−0.0734822
$290$	− 7.47975e6i	− 0.306685i
$291$	0	0
$292$	−1.21483e7	−0.487940
$293$	2.81002e7i	1.11714i	0.829458	+	0.558569i	$0.188649\pi$
$293$	2.81002e7i	1.11714i	−0.829458	+	0.558569i	$0.811351\pi$
$294$	0	0
$295$	1.64583e7	0.641091
$296$	− 1.52748e7i	− 0.588981i
$297$	0	0
$298$	−2.16125e7	−0.816686
$299$	9.96205e6i	0.372679i
$300$	0	0
$301$	3.72904e7	1.36740
$302$	2.74884e7i	0.997994i
$303$	0	0
$304$	−6.84941e6	−0.243799
$305$	3.27728e7i	1.15509i
$306$	0	0
$307$	−2.48453e7	−0.858676	−0.429338	−	0.903144i	$-0.641253\pi$
$307$	−2.48453e7	−0.858676	−0.429338	+	0.903144i	$0.641253\pi$
$308$	− 2.62395e7i	− 0.898056i
$309$	0	0
$310$	1.60349e7	0.538246
$311$	− 2.54535e7i	− 0.846188i	−0.906086	−	0.423094i	$-0.860944\pi$
$311$	− 2.54535e7i	− 0.846188i	0.906086	−	0.423094i	$-0.139056\pi$
$312$	0	0
$313$	−1.80377e7	−0.588233	−0.294116	−	0.955770i	$-0.595025\pi$
$313$	−1.80377e7	−0.588233	−0.294116	+	0.955770i	$0.595025\pi$
$314$	− 3.05455e7i	− 0.986641i
$315$	0	0
$316$	2.46717e7	0.781877
$317$	2.48387e7i	0.779744i	0.920869	+	0.389872i	$0.127481\pi$
$317$	2.48387e7i	0.779744i	−0.920869	+	0.389872i	$0.872519\pi$
$318$	0	0
$319$	−2.24335e7	−0.691076
$320$	2.80767e6i	0.0856833i
$321$	0	0
$322$	3.78134e7	1.13261
$323$	− 3.40485e7i	− 1.01039i
$324$	0	0
$325$	6.96319e6	0.202842
$326$	− 6.43680e6i	− 0.185788i
$327$	0	0
$328$	2.92461e6	0.0828794
$329$	− 8.97329e7i	− 2.51979i
$330$	0	0
$331$	−3.19747e7	−0.881702	−0.440851	−	0.897580i	$-0.645323\pi$
$331$	−3.19747e7	−0.881702	−0.440851	+	0.897580i	$0.645323\pi$
$332$	− 2.41779e7i	− 0.660701i
$333$	0	0
$334$	8.66947e6	0.232677
$335$	− 2.03540e7i	− 0.541395i
$336$	0	0
$337$	−7.03435e7	−1.83795	−0.918977	−	0.394312i	$-0.870983\pi$
$337$	−7.03435e7	−1.83795	−0.918977	+	0.394312i	$0.870983\pi$
$338$	− 2.33072e7i	− 0.603586i
$339$	0	0
$340$	−1.39569e7	−0.355102
$341$	− 4.80924e7i	− 1.21287i
$342$	0	0
$343$	−4.67397e7	−1.15825
$344$	1.19673e7i	0.293983i
$345$	0	0
$346$	−3.60675e7	−0.870737
$347$	4.91231e7i	1.17570i	0.808969	+	0.587851i	$0.200026\pi$
$347$	4.91231e7i	1.17570i	−0.808969	+	0.587851i	$0.799974\pi$
$348$	0	0
$349$	3.49390e7	0.821928	0.410964	−	0.911652i	$-0.365192\pi$
$349$	3.49390e7	0.821928	0.410964	+	0.911652i	$0.365192\pi$
$350$	− 2.64305e7i	− 0.616455i
$351$	0	0
$352$	8.42087e6	0.193076
$353$	− 7.49168e6i	− 0.170316i	−0.996367	−	0.0851579i	$-0.972861\pi$
$353$	− 7.49168e6i	− 0.170316i	0.996367	−	0.0851579i	$-0.0271395\pi$
$354$	0	0
$355$	−5.89809e7	−1.31834
$356$	− 2.78774e7i	− 0.617877i
$357$	0	0
$358$	−4.06980e6	−0.0887001
$359$	3.14246e7i	0.679183i	0.940573	+	0.339592i	$0.110289\pi$
$359$	3.14246e7i	0.679183i	−0.940573	+	0.339592i	$0.889711\pi$
$360$	0	0
$361$	−2.30477e6	−0.0489898
$362$	4.19729e7i	0.884795i
$363$	0	0
$364$	1.51731e7	0.314609
$365$	− 3.25283e7i	− 0.668933i
$366$	0	0
$367$	4.63284e7	0.937237	0.468618	−	0.883401i	$-0.344752\pi$
$367$	4.63284e7	0.937237	0.468618	+	0.883401i	$0.344752\pi$
$368$	1.21352e7i	0.243503i
$369$	0	0
$370$	4.09000e7	0.807454
$371$	− 8.46752e7i	− 1.65819i
$372$	0	0
$373$	−7.28264e6	−0.140334	−0.0701669	−	0.997535i	$-0.522353\pi$
$373$	−7.28264e6	−0.140334	−0.0701669	+	0.997535i	$0.522353\pi$
$374$	4.18602e7i	0.800178i
$375$	0	0
$376$	2.87974e7	0.541738
$377$	− 1.29723e7i	− 0.242099i
$378$	0	0
$379$	−6.01546e7	−1.10497	−0.552486	−	0.833522i	$-0.686321\pi$
$379$	−6.01546e7	−1.10497	−0.552486	+	0.833522i	$0.686321\pi$
$380$	− 1.83400e7i	− 0.334233i
$381$	0	0
$382$	1.15515e7	0.207227
$383$	8.58659e6i	0.152836i	0.997076	+	0.0764178i	$0.0243483\pi$
$383$	8.58659e6i	0.152836i	−0.997076	+	0.0764178i	$0.975652\pi$
$384$	0	0
$385$	7.02590e7	1.23118
$386$	2.38096e7i	0.413990i
$387$	0	0
$388$	−3.88244e7	−0.664675
$389$	7.66723e7i	1.30254i	0.758848	+	0.651268i	$0.225763\pi$
$389$	7.66723e7i	1.30254i	−0.758848	+	0.651268i	$0.774237\pi$
$390$	0	0
$391$	−6.03242e7	−1.00916
$392$	− 3.62966e7i	− 0.602570i
$393$	0	0
$394$	6.03844e7	0.987270
$395$	6.60611e7i	1.07190i
$396$	0	0
$397$	6.57190e7	1.05031	0.525157	−	0.851005i	$-0.324006\pi$
$397$	6.57190e7	1.05031	0.525157	+	0.851005i	$0.324006\pi$
$398$	− 2.00017e7i	− 0.317262i
$399$	0	0
$400$	8.48217e6	0.132534
$401$	− 1.62827e7i	− 0.252519i	−0.991997	−	0.126260i	$-0.959703\pi$
$401$	− 1.62827e7i	− 0.252519i	0.991997	−	0.126260i	$-0.0402972\pi$
$402$	0	0
$403$	2.78097e7	0.424894
$404$	− 2.55365e7i	− 0.387274i
$405$	0	0
$406$	−4.92396e7	−0.735760
$407$	− 1.22669e8i	− 1.81949i
$408$	0	0
$409$	−4.61848e7	−0.675039	−0.337519	−	0.941319i	$-0.609588\pi$
$409$	−4.61848e7	−0.675039	−0.337519	+	0.941319i	$0.609588\pi$
$410$	7.83095e6i	0.113622i
$411$	0	0
$412$	−2.38047e7	−0.340385
$413$	− 1.08346e8i	− 1.53802i
$414$	0	0
$415$	6.47389e7	0.905777
$416$	4.86941e6i	0.0676389i
$417$	0	0
$418$	−5.50061e7	−0.753150
$419$	2.23089e7i	0.303274i	0.988436	+	0.151637i	$0.0484545\pi$
$419$	2.23089e7i	0.303274i	−0.988436	+	0.151637i	$0.951545\pi$
$420$	0	0
$421$	−4.79778e6	−0.0642974	−0.0321487	−	0.999483i	$-0.510235\pi$
$421$	−4.79778e6	−0.0642974	−0.0321487	+	0.999483i	$0.510235\pi$
$422$	4.07566e7i	0.542326i
$423$	0	0
$424$	2.71743e7	0.356501
$425$	4.21649e7i	0.549268i
$426$	0	0
$427$	2.15745e8	2.77113
$428$	3.28301e7i	0.418737i
$429$	0	0
$430$	−3.20438e7	−0.403031
$431$	− 1.04853e8i	− 1.30963i	−0.755791	−	0.654813i	$-0.772747\pi$
$431$	− 1.04853e8i	− 1.30963i	0.755791	−	0.654813i	$-0.227253\pi$
$432$	0	0
$433$	1.10290e8	1.35854	0.679270	−	0.733889i	$-0.262297\pi$
$433$	1.10290e8	1.35854	0.679270	+	0.733889i	$0.262297\pi$
$434$	− 1.05559e8i	− 1.29129i
$435$	0	0
$436$	−3.49936e7	−0.422210
$437$	− 7.92686e7i	− 0.949854i
$438$	0	0
$439$	−9.35146e6	−0.110531	−0.0552657	−	0.998472i	$-0.517601\pi$
$439$	−9.35146e6	−0.110531	−0.0552657	+	0.998472i	$0.517601\pi$
$440$	2.25478e7i	0.264695i
$441$	0	0
$442$	−2.42059e7	−0.280320
$443$	− 1.94364e7i	− 0.223566i	−0.993733	−	0.111783i	$-0.964344\pi$
$443$	− 1.94364e7i	− 0.223566i	0.993733	−	0.111783i	$-0.0356561\pi$
$444$	0	0
$445$	7.46446e7	0.847069
$446$	− 7.40995e7i	− 0.835239i
$447$	0	0
$448$	1.84830e7	0.205560
$449$	1.24211e8i	1.37221i	0.727503	+	0.686105i	$0.240681\pi$
$449$	1.24211e8i	1.37221i	−0.727503	+	0.686105i	$0.759319\pi$
$450$	0	0
$451$	2.34869e7	0.256033
$452$	1.16632e7i	0.126300i
$453$	0	0
$454$	−2.05036e7	−0.219110
$455$	4.06276e7i	0.431307i
$456$	0	0
$457$	−1.75216e7	−0.183580	−0.0917902	−	0.995778i	$-0.529259\pi$
$457$	−1.75216e7	−0.183580	−0.0917902	+	0.995778i	$0.529259\pi$
$458$	7.52268e7i	0.783026i
$459$	0	0
$460$	−3.24933e7	−0.333826
$461$	3.53923e7i	0.361249i	0.983552	+	0.180624i	$0.0578118\pi$
$461$	3.53923e7i	0.361249i	−0.983552	+	0.180624i	$0.942188\pi$
$462$	0	0
$463$	−3.08613e6	−0.0310936	−0.0155468	−	0.999879i	$-0.504949\pi$
$463$	−3.08613e6	−0.0310936	−0.0155468	+	0.999879i	$0.504949\pi$
$464$	− 1.58021e7i	− 0.158184i
$465$	0	0
$466$	−1.31760e8	−1.30204
$467$	1.08045e8i	1.06085i	0.847731	+	0.530427i	$0.177968\pi$
$467$	1.08045e8i	1.06085i	−0.847731	+	0.530427i	$0.822032\pi$
$468$	0	0
$469$	−1.33991e8	−1.29885
$470$	7.71080e7i	0.742687i
$471$	0	0
$472$	3.47708e7	0.330665
$473$	9.61070e7i	0.908179i
$474$	0	0
$475$	−5.54065e7	−0.516987
$476$	9.18793e7i	0.851916i
$477$	0	0
$478$	−9.12980e7	−0.835944
$479$	− 1.31304e8i	− 1.19474i	−0.801967	−	0.597368i	$-0.796213\pi$
$479$	− 1.31304e8i	− 1.19474i	0.801967	−	0.597368i	$-0.203787\pi$
$480$	0	0
$481$	7.09338e7	0.637408
$482$	− 6.33304e7i	− 0.565550i
$483$	0	0
$484$	1.09361e7	0.0964555
$485$	− 1.03956e8i	− 0.911225i
$486$	0	0
$487$	−4.65915e7	−0.403385	−0.201692	−	0.979449i	$-0.564644\pi$
$487$	−4.65915e7	−0.403385	−0.201692	+	0.979449i	$0.564644\pi$
$488$	6.92377e7i	0.595776i
$489$	0	0
$490$	9.71879e7	0.826083
$491$	2.19500e8i	1.85435i	0.374632	+	0.927173i	$0.377769\pi$
$491$	2.19500e8i	1.85435i	−0.374632	+	0.927173i	$0.622231\pi$
$492$	0	0
$493$	7.85525e7	0.655570
$494$	− 3.18075e7i	− 0.263845i
$495$	0	0
$496$	3.38762e7	0.277619
$497$	3.88274e8i	3.16278i
$498$	0	0
$499$	−1.33446e8	−1.07400	−0.537001	−	0.843581i	$-0.680443\pi$
$499$	−1.33446e8	−1.07400	−0.537001	+	0.843581i	$0.680443\pi$
$500$	6.55535e7i	0.524428i
$501$	0	0
$502$	−1.00094e8	−0.791221
$503$	1.81087e7i	0.142293i	0.997466	+	0.0711463i	$0.0226657\pi$
$503$	1.81087e7i	0.142293i	−0.997466	+	0.0711463i	$0.977334\pi$
$504$	0	0
$505$	6.83767e7	0.530926
$506$	9.74551e7i	0.752234i
$507$	0	0
$508$	−7.29501e7	−0.556461
$509$	1.34559e8i	1.02037i	0.860064	+	0.510187i	$0.170424\pi$
$509$	1.34559e8i	1.02037i	−0.860064	+	0.510187i	$0.829576\pi$
$510$	0	0
$511$	−2.14135e8	−1.60482
$512$	5.93164e6i	0.0441942i
$513$	0	0
$514$	1.59154e8	1.17200
$515$	− 6.37395e7i	− 0.466645i
$516$	0	0
$517$	2.31265e8	1.67355
$518$	− 2.69247e8i	− 1.93714i
$519$	0	0
$520$	−1.30383e7	−0.0927283
$521$	− 6.97595e7i	− 0.493276i	−0.969108	−	0.246638i	$-0.920674\pi$
$521$	− 6.97595e7i	− 0.493276i	0.969108	−	0.246638i	$-0.0793259\pi$
$522$	0	0
$523$	−1.49134e7	−0.104249	−0.0521245	−	0.998641i	$-0.516599\pi$
$523$	−1.49134e7	−0.104249	−0.0521245	+	0.998641i	$0.516599\pi$
$524$	− 4.87999e6i	− 0.0339176i
$525$	0	0
$526$	−1.53825e7	−0.105699
$527$	1.68399e8i	1.15055i
$528$	0	0
$529$	7.59444e6	0.0513013
$530$	7.27619e7i	0.488738i
$531$	0	0
$532$	−1.20733e8	−0.801848
$533$	1.35814e7i	0.0896938i
$534$	0	0
$535$	−8.79061e7	−0.574061
$536$	− 4.30009e7i	− 0.279244i
$537$	0	0
$538$	−1.15466e8	−0.741492
$539$	− 2.91490e8i	− 1.86147i
$540$	0	0
$541$	2.00053e8	1.26344	0.631718	−	0.775198i	$-0.282350\pi$
$541$	2.00053e8	1.26344	0.631718	+	0.775198i	$0.282350\pi$
$542$	− 6.48542e7i	− 0.407324i
$543$	0	0
$544$	−2.94862e7	−0.183157
$545$	− 9.36989e7i	− 0.578822i
$546$	0	0
$547$	−2.59236e8	−1.58392	−0.791962	−	0.610571i	$-0.790940\pi$
$547$	−2.59236e8	−1.58392	−0.791962	+	0.610571i	$0.790940\pi$
$548$	9.78915e7i	0.594844i
$549$	0	0
$550$	6.81183e7	0.409427
$551$	1.03221e8i	0.617041i
$552$	0	0
$553$	4.34884e8	2.57157
$554$	1.20312e8i	0.707587i
$555$	0	0
$556$	−1.99046e7	−0.115805
$557$	2.08528e8i	1.20670i	0.797477	+	0.603349i	$0.206167\pi$
$557$	2.08528e8i	1.20670i	−0.797477	+	0.603349i	$0.793833\pi$
$558$	0	0
$559$	−5.55743e7	−0.318155
$560$	4.94903e7i	0.281810i
$561$	0	0
$562$	−8.51256e7	−0.479569
$563$	3.10432e8i	1.73957i	0.493431	+	0.869785i	$0.335742\pi$
$563$	3.10432e8i	1.73957i	−0.493431	+	0.869785i	$0.664258\pi$
$564$	0	0
$565$	−3.12295e7	−0.173149
$566$	− 9.66051e7i	− 0.532783i
$567$	0	0
$568$	−1.24606e8	−0.679978
$569$	− 1.85571e8i	− 1.00734i	−0.863897	−	0.503668i	$-0.831984\pi$
$569$	− 1.85571e8i	− 1.00734i	0.863897	−	0.503668i	$-0.168016\pi$
$570$	0	0
$571$	−8.04718e7	−0.432250	−0.216125	−	0.976366i	$-0.569342\pi$
$571$	−8.04718e7	−0.432250	−0.216125	+	0.976366i	$0.569342\pi$
$572$	3.91051e7i	0.208951i
$573$	0	0
$574$	5.15515e7	0.272588
$575$	9.81645e7i	0.516358i
$576$	0	0
$577$	8.84457e7	0.460415	0.230207	−	0.973142i	$-0.426060\pi$
$577$	8.84457e7	0.460415	0.230207	+	0.973142i	$0.426060\pi$
$578$	− 1.00335e7i	− 0.0519597i
$579$	0	0
$580$	4.23119e7	0.216859
$581$	− 4.26180e8i	− 2.17302i
$582$	0	0
$583$	2.18230e8	1.10131
$584$	− 6.87211e7i	− 0.345026i
$585$	0	0
$586$	−1.58959e8	−0.789936
$587$	3.13917e8i	1.55203i	0.630715	+	0.776015i	$0.282762\pi$
$587$	3.13917e8i	1.55203i	−0.630715	+	0.776015i	$0.717238\pi$
$588$	0	0
$589$	−2.21283e8	−1.08293
$590$	9.31024e7i	0.453320i
$591$	0	0
$592$	8.64075e7	0.416473
$593$	− 3.05107e8i	− 1.46315i	−0.681762	−	0.731574i	$-0.738786\pi$
$593$	− 3.05107e8i	− 1.46315i	0.681762	−	0.731574i	$-0.261214\pi$
$594$	0	0
$595$	−2.46016e8	−1.16792
$596$	− 1.22258e8i	− 0.577484i
$597$	0	0
$598$	−5.63539e7	−0.263524
$599$	− 6.17896e7i	− 0.287498i	−0.989614	−	0.143749i	$-0.954084\pi$
$599$	− 6.17896e7i	− 0.287498i	0.989614	−	0.143749i	$-0.0459158\pi$
$600$	0	0
$601$	3.79901e8	1.75004	0.875019	−	0.484089i	$-0.160849\pi$
$601$	3.79901e8	1.75004	0.875019	+	0.484089i	$0.160849\pi$
$602$	2.10946e8i	0.966901i
$603$	0	0
$604$	−1.55498e8	−0.705688
$605$	2.92826e7i	0.132234i
$606$	0	0
$607$	5.41765e7	0.242239	0.121120	−	0.992638i	$-0.461352\pi$
$607$	5.41765e7	0.242239	0.121120	+	0.992638i	$0.461352\pi$
$608$	− 3.87461e7i	− 0.172392i
$609$	0	0
$610$	−1.85391e8	−0.816769
$611$	1.33730e8i	0.586281i
$612$	0	0
$613$	4.26874e7	0.185318	0.0926592	−	0.995698i	$-0.470463\pi$
$613$	4.26874e7	0.185318	0.0926592	+	0.995698i	$0.470463\pi$
$614$	− 1.40546e8i	− 0.607176i
$615$	0	0
$616$	1.48433e8	0.635022
$617$	− 5.20036e7i	− 0.221400i	−0.993854	−	0.110700i	$-0.964691\pi$
$617$	− 5.20036e7i	− 0.221400i	0.993854	−	0.110700i	$-0.0353093\pi$
$618$	0	0
$619$	−6.47486e7	−0.272997	−0.136499	−	0.990640i	$-0.543585\pi$
$619$	−6.47486e7	−0.272997	−0.136499	+	0.990640i	$0.543585\pi$
$620$	9.07070e7i	0.380597i
$621$	0	0
$622$	1.43987e8	0.598345
$623$	− 4.91390e8i	− 2.03218i
$624$	0	0
$625$	−4.60988e7	−0.188821
$626$	− 1.02037e8i	− 0.415944i
$627$	0	0
$628$	1.72792e8	0.697660
$629$	4.29532e8i	1.72601i
$630$	0	0
$631$	4.62024e7	0.183898	0.0919489	−	0.995764i	$-0.470690\pi$
$631$	4.62024e7	0.183898	0.0919489	+	0.995764i	$0.470690\pi$
$632$	1.39564e8i	0.552870i
$633$	0	0
$634$	−1.40509e8	−0.551362
$635$	− 1.95331e8i	− 0.762871i
$636$	0	0
$637$	1.68555e8	0.652114
$638$	− 1.26903e8i	− 0.488665i
$639$	0	0
$640$	−1.58826e7	−0.0605873
$641$	− 2.58548e8i	− 0.981674i	−0.871251	−	0.490837i	$-0.836691\pi$
$641$	− 2.58548e8i	− 0.981674i	0.871251	−	0.490837i	$-0.163309\pi$
$642$	0	0
$643$	−2.24134e8	−0.843090	−0.421545	−	0.906808i	$-0.638512\pi$
$643$	−2.24134e8	−0.843090	−0.421545	+	0.906808i	$0.638512\pi$
$644$	2.13905e8i	0.800873i
$645$	0	0
$646$	1.92607e8	0.714455
$647$	− 2.73001e8i	− 1.00798i	−0.863709	−	0.503990i	$-0.831865\pi$
$647$	− 2.73001e8i	− 1.00798i	0.863709	−	0.503990i	$-0.168135\pi$
$648$	0	0
$649$	2.79236e8	1.02150
$650$	3.93898e7i	0.143431i
$651$	0	0
$652$	3.64120e7	0.131372
$653$	− 4.93887e8i	− 1.77373i	−0.462025	−	0.886867i	$-0.652877\pi$
$653$	− 4.93887e8i	− 1.77373i	0.462025	−	0.886867i	$-0.347123\pi$
$654$	0	0
$655$	1.30667e7	0.0464987
$656$	1.65441e7i	0.0586046i
$657$	0	0
$658$	5.07606e8	1.78176
$659$	− 3.51067e8i	− 1.22669i	−0.789817	−	0.613343i	$-0.789824\pi$
$659$	− 3.51067e8i	− 1.22669i	0.789817	−	0.613343i	$-0.210176\pi$
$660$	0	0
$661$	−1.15905e7	−0.0401326	−0.0200663	−	0.999799i	$-0.506388\pi$
$661$	−1.15905e7	−0.0401326	−0.0200663	+	0.999799i	$0.506388\pi$
$662$	− 1.80876e8i	− 0.623458i
$663$	0	0
$664$	1.36771e8	0.467186
$665$	− 3.23276e8i	− 1.09928i
$666$	0	0
$667$	1.82879e8	0.616291
$668$	4.90419e7i	0.164527i
$669$	0	0
$670$	1.15139e8	0.382824
$671$	5.56032e8i	1.84048i
$672$	0	0
$673$	−1.25203e8	−0.410742	−0.205371	−	0.978684i	$-0.565840\pi$
$673$	−1.25203e8	−0.410742	−0.205371	+	0.978684i	$0.565840\pi$
$674$	− 3.97923e8i	− 1.29963i
$675$	0	0
$676$	1.31845e8	0.426800
$677$	1.35196e8i	0.435709i	0.975981	+	0.217854i	$0.0699058\pi$
$677$	1.35196e8i	0.435709i	−0.975981	+	0.217854i	$0.930094\pi$
$678$	0	0
$679$	−6.84350e8	−2.18609
$680$	− 7.89524e7i	− 0.251095i
$681$	0	0
$682$	2.72052e8	0.857627
$683$	1.53606e8i	0.482110i	0.970511	+	0.241055i	$0.0774935\pi$
$683$	1.53606e8i	0.482110i	−0.970511	+	0.241055i	$0.922507\pi$
$684$	0	0
$685$	−2.62115e8	−0.815492
$686$	− 2.64399e8i	− 0.819008i
$687$	0	0
$688$	−6.76976e7	−0.207878
$689$	1.26193e8i	0.385813i
$690$	0	0
$691$	3.17865e8	0.963404	0.481702	−	0.876335i	$-0.340019\pi$
$691$	3.17865e8	0.963404	0.481702	+	0.876335i	$0.340019\pi$
$692$	− 2.04028e8i	− 0.615704i
$693$	0	0
$694$	−2.77882e8	−0.831346
$695$	− 5.32966e7i	− 0.158761i
$696$	0	0
$697$	−8.22408e7	−0.242878
$698$	1.97645e8i	0.581191i
$699$	0	0
$700$	1.49514e8	0.435900
$701$	1.74451e8i	0.506431i	0.967410	+	0.253215i	$0.0814881\pi$
$701$	1.74451e8i	0.506431i	−0.967410	+	0.253215i	$0.918512\pi$
$702$	0	0
$703$	−5.64424e8	−1.62457
$704$	4.76356e7i	0.136526i
$705$	0	0
$706$	4.23793e7	0.120432
$707$	− 4.50128e8i	− 1.27373i
$708$	0	0
$709$	7.84585e7	0.220141	0.110071	−	0.993924i	$-0.464892\pi$
$709$	7.84585e7	0.220141	0.110071	+	0.993924i	$0.464892\pi$
$710$	− 3.33646e8i	− 0.932205i
$711$	0	0
$712$	1.57698e8	0.436905
$713$	3.92051e8i	1.08162i
$714$	0	0
$715$	−1.04708e8	−0.286458
$716$	− 2.30223e7i	− 0.0627204i
$717$	0	0
$718$	−1.77765e8	−0.480255
$719$	6.02172e8i	1.62007i	0.586382	+	0.810035i	$0.300552\pi$
$719$	6.02172e8i	1.62007i	−0.586382	+	0.810035i	$0.699448\pi$
$720$	0	0
$721$	−4.19600e8	−1.11952
$722$	− 1.30377e7i	− 0.0346410i
$723$	0	0
$724$	−2.37434e8	−0.625645
$725$	− 1.27827e8i	− 0.335435i
$726$	0	0
$727$	1.88838e8	0.491459	0.245729	−	0.969338i	$-0.420973\pi$
$727$	1.88838e8	0.491459	0.245729	+	0.969338i	$0.420973\pi$
$728$	8.58321e7i	0.222462i
$729$	0	0
$730$	1.84008e8	0.473007
$731$	− 3.36525e8i	− 0.861519i
$732$	0	0
$733$	−2.66823e8	−0.677503	−0.338752	−	0.940876i	$-0.610005\pi$
$733$	−2.66823e8	−0.677503	−0.338752	+	0.940876i	$0.610005\pi$
$734$	2.62073e8i	0.662726i
$735$	0	0
$736$	−6.86472e7	−0.172183
$737$	− 3.45330e8i	− 0.862645i
$738$	0	0
$739$	−6.75150e7	−0.167289	−0.0836444	−	0.996496i	$-0.526656\pi$
$739$	−6.75150e7	−0.167289	−0.0836444	+	0.996496i	$0.526656\pi$
$740$	2.31365e8i	0.570956i
$741$	0	0
$742$	4.78995e8	1.17252
$743$	− 4.38858e8i	− 1.06994i	−0.844872	−	0.534968i	$-0.820324\pi$
$743$	− 4.38858e8i	− 1.06994i	0.844872	−	0.534968i	$-0.179676\pi$
$744$	0	0
$745$	3.27360e8	0.791692
$746$	− 4.11968e7i	− 0.0992310i
$747$	0	0
$748$	−2.36797e8	−0.565811
$749$	5.78691e8i	1.37721i
$750$	0	0
$751$	3.42114e8	0.807701	0.403851	−	0.914825i	$-0.367672\pi$
$751$	3.42114e8	0.807701	0.403851	+	0.914825i	$0.367672\pi$
$752$	1.62903e8i	0.383067i
$753$	0	0
$754$	7.33824e7	0.171190
$755$	− 4.16361e8i	− 0.967452i
$756$	0	0
$757$	8.84203e7	0.203828	0.101914	−	0.994793i	$-0.467503\pi$
$757$	8.84203e7	0.203828	0.101914	+	0.994793i	$0.467503\pi$
$758$	− 3.40286e8i	− 0.781333i
$759$	0	0
$760$	1.03747e8	0.236338
$761$	− 3.90287e8i	− 0.885584i	−0.896624	−	0.442792i	$-0.853988\pi$
$761$	− 3.90287e8i	− 0.885584i	0.896624	−	0.442792i	$-0.146012\pi$
$762$	0	0
$763$	−6.16825e8	−1.38864
$764$	6.53449e7i	0.146532i
$765$	0	0
$766$	−4.85731e7	−0.108071
$767$	1.61470e8i	0.357853i
$768$	0	0
$769$	1.37049e8	0.301368	0.150684	−	0.988582i	$-0.451852\pi$
$769$	1.37049e8	0.301368	0.150684	+	0.988582i	$0.451852\pi$
$770$	3.97445e8i	0.870572i
$771$	0	0
$772$	−1.34687e8	−0.292735
$773$	1.98181e6i	0.00429065i	0.999998	+	0.00214533i	$0.000682879\pi$
$773$	1.98181e6i	0.00429065i	−0.999998	+	0.00214533i	$0.999317\pi$
$774$	0	0
$775$	2.74032e8	0.588703
$776$	− 2.19624e8i	− 0.469996i
$777$	0	0
$778$	−4.33724e8	−0.921032
$779$	− 1.08068e8i	− 0.228604i
$780$	0	0
$781$	−1.00068e9	−2.10060
$782$	− 3.41245e8i	− 0.713586i
$783$	0	0
$784$	2.05325e8	0.426081
$785$	4.62668e8i	0.956446i
$786$	0	0
$787$	−1.21733e8	−0.249738	−0.124869	−	0.992173i	$-0.539851\pi$
$787$	−1.21733e8	−0.249738	−0.124869	+	0.992173i	$0.539851\pi$
$788$	3.41586e8i	0.698105i
$789$	0	0
$790$	−3.73698e8	−0.757948
$791$	2.05585e8i	0.415396i
$792$	0	0
$793$	−3.21528e8	−0.644762
$794$	3.71763e8i	0.742685i
$795$	0	0
$796$	1.13147e8	0.224338
$797$	− 3.61504e8i	− 0.714065i	−0.934092	−	0.357033i	$-0.883789\pi$
$797$	− 3.61504e8i	− 0.714065i	0.934092	−	0.357033i	$-0.116211\pi$
$798$	0	0
$799$	−8.09790e8	−1.58757
$800$	4.79824e7i	0.0937156i
$801$	0	0
$802$	9.21090e7	0.178558
$803$	− 5.51883e8i	− 1.06586i
$804$	0	0
$805$	−5.72753e8	−1.09794
$806$	1.57315e8i	0.300446i
$807$	0	0
$808$	1.44457e8	0.273844
$809$	2.16174e8i	0.408279i	0.978942	+	0.204140i	$0.0654396\pi$
$809$	2.16174e8i	0.408279i	−0.978942	+	0.204140i	$0.934560\pi$
$810$	0	0
$811$	−4.81616e6	−0.00902897	−0.00451449	−	0.999990i	$-0.501437\pi$
$811$	−4.81616e6	−0.00902897	−0.00451449	+	0.999990i	$0.501437\pi$
$812$	− 2.78541e8i	− 0.520261i
$813$	0	0
$814$	6.93919e8	1.28658
$815$	9.74970e7i	0.180102i
$816$	0	0
$817$	4.42208e8	0.810887
$818$	− 2.61260e8i	− 0.477325i
$819$	0	0
$820$	−4.42985e7	−0.0803429
$821$	6.91066e8i	1.24879i	0.781108	+	0.624396i	$0.214655\pi$
$821$	6.91066e8i	1.24879i	−0.781108	+	0.624396i	$0.785345\pi$
$822$	0	0
$823$	1.01432e9	1.81959	0.909795	−	0.415058i	$-0.136239\pi$
$823$	1.01432e9	1.81959	0.909795	+	0.415058i	$0.136239\pi$
$824$	− 1.34660e8i	− 0.240689i
$825$	0	0
$826$	6.12898e8	1.08755
$827$	3.47789e8i	0.614892i	0.951566	+	0.307446i	$0.0994743\pi$
$827$	3.47789e8i	0.614892i	−0.951566	+	0.307446i	$0.900526\pi$
$828$	0	0
$829$	5.07108e8	0.890096	0.445048	−	0.895507i	$-0.353187\pi$
$829$	5.07108e8	0.890096	0.445048	+	0.895507i	$0.353187\pi$
$830$	3.66219e8i	0.640481i
$831$	0	0
$832$	−2.75455e7	−0.0478279
$833$	1.02067e9i	1.76583i
$834$	0	0
$835$	−1.31315e8	−0.225556
$836$	− 3.11161e8i	− 0.532558i
$837$	0	0
$838$	−1.26198e8	−0.214447
$839$	− 1.74329e8i	− 0.295178i	−0.989049	−	0.147589i	$-0.952849\pi$
$839$	− 1.74329e8i	− 0.295178i	0.989049	−	0.147589i	$-0.0471513\pi$
$840$	0	0
$841$	3.56684e8	0.599647
$842$	− 2.71403e7i	− 0.0454651i
$843$	0	0
$844$	−2.30554e8	−0.383483
$845$	3.53029e8i	0.585114i
$846$	0	0
$847$	1.92769e8	0.317239
$848$	1.53721e8i	0.252084i
$849$	0	0
$850$	−2.38521e8	−0.388391
$851$	9.99999e8i	1.62260i
$852$	0	0
$853$	−3.14584e8	−0.506862	−0.253431	−	0.967354i	$-0.581559\pi$
$853$	−3.14584e8	−0.506862	−0.253431	+	0.967354i	$0.581559\pi$
$854$	1.22044e9i	1.95949i
$855$	0	0
$856$	−1.85715e8	−0.296092
$857$	− 6.87822e8i	− 1.09278i	−0.837530	−	0.546391i	$-0.816001\pi$
$857$	− 6.87822e8i	− 1.09278i	0.837530	−	0.546391i	$-0.183999\pi$
$858$	0	0
$859$	7.88341e8	1.24375	0.621877	−	0.783115i	$-0.286370\pi$
$859$	7.88341e8	1.24375	0.621877	+	0.783115i	$0.286370\pi$
$860$	− 1.81267e8i	− 0.284986i
$861$	0	0
$862$	5.93136e8	0.926045
$863$	9.95858e8i	1.54941i	0.632326	+	0.774703i	$0.282101\pi$
$863$	9.95858e8i	1.54941i	−0.632326	+	0.774703i	$0.717899\pi$
$864$	0	0
$865$	5.46307e8	0.844089
$866$	6.23894e8i	0.960632i
$867$	0	0
$868$	5.97129e8	0.913081
$869$	1.12081e9i	1.70794i
$870$	0	0
$871$	1.99689e8	0.302204
$872$	− 1.97954e8i	− 0.298548i
$873$	0	0
$874$	4.48411e8	0.671648
$875$	1.15550e9i	1.72483i
$876$	0	0
$877$	−2.19092e8	−0.324808	−0.162404	−	0.986724i	$-0.551925\pi$
$877$	−2.19092e8	−0.324808	−0.162404	+	0.986724i	$0.551925\pi$
$878$	− 5.28999e7i	− 0.0781576i
$879$	0	0
$880$	−1.27549e8	−0.187167
$881$	4.82715e8i	0.705932i	0.935636	+	0.352966i	$0.114827\pi$
$881$	4.82715e8i	0.705932i	−0.935636	+	0.352966i	$0.885173\pi$
$882$	0	0
$883$	−7.75993e8	−1.12713	−0.563567	−	0.826070i	$-0.690571\pi$
$883$	−7.75993e8	−1.12713	−0.563567	+	0.826070i	$0.690571\pi$
$884$	− 1.36929e8i	− 0.198216i
$885$	0	0
$886$	1.09949e8	0.158085
$887$	− 9.51645e8i	− 1.36365i	−0.731514	−	0.681827i	$-0.761186\pi$
$887$	− 9.51645e8i	− 1.36365i	0.731514	−	0.681827i	$-0.238814\pi$
$888$	0	0
$889$	−1.28588e9	−1.83018
$890$	4.22254e8i	0.598968i
$891$	0	0
$892$	4.19170e8	0.590603
$893$	− 1.06410e9i	− 1.49426i
$894$	0	0
$895$	6.16445e7	0.0859855
$896$	1.04556e8i	0.145353i
$897$	0	0
$898$	−7.02642e8	−0.970298
$899$	− 5.10517e8i	− 0.702638i
$900$	0	0
$901$	−7.64147e8	−1.04473
$902$	1.32862e8i	0.181042i
$903$	0	0
$904$	−6.59771e7	−0.0893075
$905$	− 6.35755e8i	− 0.857717i
$906$	0	0
$907$	4.93579e8	0.661508	0.330754	−	0.943717i	$-0.392697\pi$
$907$	4.93579e8	0.661508	0.330754	+	0.943717i	$0.392697\pi$
$908$	− 1.15986e8i	− 0.154934i
$909$	0	0
$910$	−2.29824e8	−0.304980
$911$	1.67733e8i	0.221851i	0.993829	+	0.110926i	$0.0353816\pi$
$911$	1.67733e8i	0.221851i	−0.993829	+	0.110926i	$0.964618\pi$
$912$	0	0
$913$	1.09838e9	1.44324
$914$	− 9.91174e7i	− 0.129811i
$915$	0	0
$916$	−4.25547e8	−0.553683
$917$	− 8.60186e7i	− 0.111554i
$918$	0	0
$919$	7.11908e8	0.917227	0.458614	−	0.888636i	$-0.348346\pi$
$919$	7.11908e8	0.917227	0.458614	+	0.888636i	$0.348346\pi$
$920$	− 1.83810e8i	− 0.236051i
$921$	0	0
$922$	−2.00209e8	−0.255441
$923$	− 5.78651e8i	− 0.735887i
$924$	0	0
$925$	6.98970e8	0.883148
$926$	− 1.74578e7i	− 0.0219865i
$927$	0	0
$928$	8.93904e7	0.111853
$929$	− 5.56076e8i	− 0.693565i	−0.937946	−	0.346783i	$-0.887274\pi$
$929$	− 5.56076e8i	− 0.693565i	0.937946	−	0.346783i	$-0.112726\pi$
$930$	0	0
$931$	−1.34120e9	−1.66205
$932$	− 7.45347e8i	− 0.920684i
$933$	0	0
$934$	−6.11197e8	−0.750137
$935$	− 6.34049e8i	− 0.775689i
$936$	0	0
$937$	1.14269e9	1.38902	0.694509	−	0.719484i	$-0.255622\pi$
$937$	1.14269e9	1.38902	0.694509	+	0.719484i	$0.255622\pi$
$938$	− 7.57969e8i	− 0.918423i
$939$	0	0
$940$	−4.36189e8	−0.525159
$941$	− 1.34486e8i	− 0.161401i	−0.996738	−	0.0807006i	$-0.974284\pi$
$941$	− 1.34486e8i	− 0.161401i	0.996738	−	0.0807006i	$-0.0257158\pi$
$942$	0	0
$943$	−1.91466e8	−0.228326
$944$	1.96693e8i	0.233816i
$945$	0	0
$946$	−5.43663e8	−0.642180
$947$	5.89972e8i	0.694674i	0.937740	+	0.347337i	$0.112914\pi$
$947$	5.89972e8i	0.694674i	−0.937740	+	0.347337i	$0.887086\pi$
$948$	0	0
$949$	3.19129e8	0.373394
$950$	− 3.13426e8i	− 0.365565i
$951$	0	0
$952$	−5.19748e8	−0.602396
$953$	4.97962e8i	0.575331i	0.957731	+	0.287665i	$0.0928791\pi$
$953$	4.97962e8i	0.575331i	−0.957731	+	0.287665i	$0.907121\pi$
$954$	0	0
$955$	−1.74968e8	−0.200885
$956$	− 5.16459e8i	− 0.591102i
$957$	0	0
$958$	7.42769e8	0.844806
$959$	1.72551e9i	1.95642i
$960$	0	0
$961$	2.06930e8	0.233159
$962$	4.01262e8i	0.450716i
$963$	0	0
$964$	3.58251e8	0.399904
$965$	− 3.60639e8i	− 0.401320i
$966$	0	0
$967$	1.65997e9	1.83579	0.917893	−	0.396828i	$-0.129889\pi$
$967$	1.65997e9	1.83579	0.917893	+	0.396828i	$0.129889\pi$
$968$	6.18640e7i	0.0682044i
$969$	0	0
$970$	5.88066e8	0.644333
$971$	− 1.02684e9i	− 1.12162i	−0.827944	−	0.560810i	$-0.810490\pi$
$971$	− 1.02684e9i	− 1.12162i	0.827944	−	0.560810i	$-0.189510\pi$
$972$	0	0
$973$	−3.50854e8	−0.380880
$974$	− 2.63561e8i	− 0.285236i
$975$	0	0
$976$	−3.91667e8	−0.421277
$977$	− 2.80695e8i	− 0.300990i	−0.988611	−	0.150495i	$-0.951913\pi$
$977$	− 2.80695e8i	− 0.300990i	0.988611	−	0.150495i	$-0.0480867\pi$
$978$	0	0
$979$	1.26644e9	1.34970
$980$	5.49778e8i	0.584129i
$981$	0	0
$982$	−1.24168e9	−1.31122
$983$	2.30006e8i	0.242147i	0.992644	+	0.121073i	$0.0386337\pi$
$983$	2.30006e8i	0.242147i	−0.992644	+	0.121073i	$0.961366\pi$
$984$	0	0
$985$	−9.14631e8	−0.957055
$986$	4.44360e8i	0.463558i
$987$	0	0
$988$	1.79930e8	0.186567
$989$	− 7.83467e8i	− 0.809901i
$990$	0	0
$991$	8.95079e7	0.0919688	0.0459844	−	0.998942i	$-0.485358\pi$
$991$	8.95079e7	0.0919688	0.0459844	+	0.998942i	$0.485358\pi$
$992$	1.91633e8i	0.196306i
$993$	0	0
$994$	−2.19641e9	−2.23643
$995$	3.02962e8i	0.307553i
$996$	0	0
$997$	1.24466e9	1.25593	0.627963	−	0.778243i	$-0.283889\pi$
$997$	1.24466e9	1.25593	0.627963	+	0.778243i	$0.283889\pi$
$998$	− 7.54887e8i	− 0.759435i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.7.b.b.161.6	yes	8
3.2	odd	2	inner	162.7.b.b.161.3	✓	8
9.2	odd	6		162.7.d.g.53.2		16
9.4	even	3		162.7.d.g.107.2		16
9.5	odd	6		162.7.d.g.107.7		16
9.7	even	3		162.7.d.g.53.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.7.b.b.161.3	✓	8	3.2	odd	2	inner
162.7.b.b.161.6	yes	8	1.1	even	1	trivial
162.7.d.g.53.2		16	9.2	odd	6
162.7.d.g.53.7		16	9.7	even	3
162.7.d.g.107.2		16	9.4	even	3
162.7.d.g.107.7		16	9.5	odd	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)

\(f(q)\)	\(=\)	\(q+5.65685i q^{2} -32.0000 q^{4} -85.6833i q^{5} -564.058 q^{7} -181.019i q^{8} +O(q^{10})\)	\(q+5.65685i q^{2} -32.0000 q^{4} -85.6833i q^{5} -564.058 q^{7} -181.019i q^{8} +484.698 q^{10} -1453.72i q^{11} +840.623 q^{13} -3190.79i q^{14} +1024.00 q^{16} +5090.31i q^{17} -6688.88 q^{19} +2741.87i q^{20} +8223.51 q^{22} +11850.8i q^{23} +8283.37 q^{25} +4755.28i q^{26} +18049.9 q^{28} -15431.8i q^{29} +33082.2 q^{31} +5792.62i q^{32} -28795.1 q^{34} +48330.3i q^{35} +84382.4 q^{37} -37838.0i q^{38} -15510.3 q^{40} +16156.3i q^{41} -66110.9 q^{43} +46519.2i q^{44} -67038.2 q^{46} +159085. i q^{47} +200512. q^{49} +46857.8i q^{50} -26899.9 q^{52} +150118. i q^{53} -124560. q^{55} +102105. i q^{56} +87295.3 q^{58} +192083. i q^{59} -382488. q^{61} +187141. i q^{62} -32768.0 q^{64} -72027.4i q^{65} +237549. q^{67} -162890. i q^{68} -273398. q^{70} -688359. i q^{71} +379634. q^{73} +477339. i q^{74} +214044. q^{76} +819985. i q^{77} -770991. q^{79} -87739.7i q^{80} -91394.1 q^{82} +755560. i q^{83} +436155. q^{85} -373980. i q^{86} -263152. q^{88} +871169. i q^{89} -474160. q^{91} -379226. i q^{92} -899918. q^{94} +573125. i q^{95} +1.21326e6 q^{97} +1.13427e6i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 256 q^{4} + 964 q^{7}+O(q^{10}) \) 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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