LMFDB - Embedded newform 8619.2.a.bn.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8619,2,Mod(1,8619)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8619, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("8619.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8619 = 3 \cdot 13^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8619.a (trivial)

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:	yes
Analytic conductor:	$68.8230615021$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 20x^{14} + 156x^{12} - 602x^{10} + 1212x^{8} - 1259x^{6} + 665x^{4} - 168x^{2} + 16 $ x^16 - 20x^14 + 156x^12 - 602x^10 + 1212x^8 - 1259x^6 + 665x^4 - 168*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 663)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.96679$ of defining polynomial
Character	$\chi$	$=$	8619.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.96679 q^{2} +1.00000 q^{3} +1.86826 q^{4} -0.562071 q^{5} -1.96679 q^{6} +3.08512 q^{7} +0.259096 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.96679 q^{2} +1.00000 q^{3} +1.86826 q^{4} -0.562071 q^{5} -1.96679 q^{6} +3.08512 q^{7} +0.259096 q^{8} +1.00000 q^{9} +1.10548 q^{10} -6.04044 q^{11} +1.86826 q^{12} -6.06779 q^{14} -0.562071 q^{15} -4.24612 q^{16} -1.00000 q^{17} -1.96679 q^{18} +3.95727 q^{19} -1.05010 q^{20} +3.08512 q^{21} +11.8803 q^{22} -8.16527 q^{23} +0.259096 q^{24} -4.68408 q^{25} +1.00000 q^{27} +5.76383 q^{28} -4.22613 q^{29} +1.10548 q^{30} +6.39872 q^{31} +7.83303 q^{32} -6.04044 q^{33} +1.96679 q^{34} -1.73406 q^{35} +1.86826 q^{36} -0.741352 q^{37} -7.78312 q^{38} -0.145630 q^{40} +8.97787 q^{41} -6.06779 q^{42} +8.54447 q^{43} -11.2851 q^{44} -0.562071 q^{45} +16.0594 q^{46} +5.29432 q^{47} -4.24612 q^{48} +2.51799 q^{49} +9.21260 q^{50} -1.00000 q^{51} +7.35907 q^{53} -1.96679 q^{54} +3.39516 q^{55} +0.799343 q^{56} +3.95727 q^{57} +8.31192 q^{58} -5.98304 q^{59} -1.05010 q^{60} -4.94978 q^{61} -12.5849 q^{62} +3.08512 q^{63} -6.91370 q^{64} +11.8803 q^{66} +7.77935 q^{67} -1.86826 q^{68} -8.16527 q^{69} +3.41053 q^{70} -9.81696 q^{71} +0.259096 q^{72} -8.70107 q^{73} +1.45808 q^{74} -4.68408 q^{75} +7.39323 q^{76} -18.6355 q^{77} +16.8289 q^{79} +2.38662 q^{80} +1.00000 q^{81} -17.6576 q^{82} +4.52040 q^{83} +5.76383 q^{84} +0.562071 q^{85} -16.8052 q^{86} -4.22613 q^{87} -1.56505 q^{88} +5.32147 q^{89} +1.10548 q^{90} -15.2549 q^{92} +6.39872 q^{93} -10.4128 q^{94} -2.22427 q^{95} +7.83303 q^{96} +7.70576 q^{97} -4.95236 q^{98} -6.04044 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{3} + 8 q^{4} + 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^3 + 8 * q^4 + 16 * q^9	$ 16 q + 16 q^{3} + 8 q^{4} + 16 q^{9} + 2 q^{10} + 8 q^{12} - 26 q^{14} - 16 q^{17} - 2 q^{22} - 42 q^{23} - 14 q^{25} + 16 q^{27} - 58 q^{29} + 2 q^{30} - 30 q^{35} + 8 q^{36} - 62 q^{38} + 4 q^{40} - 26 q^{42} - 6 q^{43} + 4 q^{49} - 16 q^{51} - 26 q^{53} - 18 q^{55} - 74 q^{56} - 58 q^{61} - 40 q^{62} - 36 q^{64} - 2 q^{66} - 8 q^{68} - 42 q^{69} - 34 q^{74} - 14 q^{75} + 8 q^{77} - 14 q^{79} + 16 q^{81} - 6 q^{82} - 58 q^{87} - 10 q^{88} + 2 q^{90} - 64 q^{92} + 50 q^{94} - 54 q^{95}+O(q^{100}) $ 16 * q + 16 * q^3 + 8 * q^4 + 16 * q^9 + 2 * q^10 + 8 * q^12 - 26 * q^14 - 16 * q^17 - 2 * q^22 - 42 * q^23 - 14 * q^25 + 16 * q^27 - 58 * q^29 + 2 * q^30 - 30 * q^35 + 8 * q^36 - 62 * q^38 + 4 * q^40 - 26 * q^42 - 6 * q^43 + 4 * q^49 - 16 * q^51 - 26 * q^53 - 18 * q^55 - 74 * q^56 - 58 * q^61 - 40 * q^62 - 36 * q^64 - 2 * q^66 - 8 * q^68 - 42 * q^69 - 34 * q^74 - 14 * q^75 + 8 * q^77 - 14 * q^79 + 16 * q^81 - 6 * q^82 - 58 * q^87 - 10 * q^88 + 2 * q^90 - 64 * q^92 + 50 * q^94 - 54 * q^95

Display 100 coefficients 10 coefficients

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 $

$2$	−1.96679	−1.39073	−0.695365	−	0.718656i	$-0.744757\pi$
$2$	−1.96679	−1.39073	−0.695365	+	0.718656i	$0.744757\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.86826	0.934132
$5$	−0.562071	−0.251366	−0.125683	−	0.992070i	$-0.540112\pi$
$5$	−0.562071	−0.251366	−0.125683	+	0.992070i	$0.540112\pi$
$6$	−1.96679	−0.802939
$7$	3.08512	1.16607	0.583034	−	0.812448i	$-0.301866\pi$
$7$	3.08512	1.16607	0.583034	+	0.812448i	$0.301866\pi$
$8$	0.259096	0.0916042
$9$	1.00000	0.333333
$10$	1.10548	0.349582
$11$	−6.04044	−1.82126	−0.910630	−	0.413222i	$-0.864403\pi$
$11$	−6.04044	−1.82126	−0.910630	+	0.413222i	$0.864403\pi$
$12$	1.86826	0.539322
$13$	0	0
$13$	0	0
$14$	−6.06779	−1.62169
$15$	−0.562071	−0.145126
$16$	−4.24612	−1.06153
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.96679	−0.463577
$19$	3.95727	0.907860	0.453930	−	0.891037i	$-0.350022\pi$
$19$	3.95727	0.907860	0.453930	+	0.891037i	$0.350022\pi$
$20$	−1.05010	−0.234809
$21$	3.08512	0.673229
$22$	11.8803	2.53288
$23$	−8.16527	−1.70258	−0.851288	−	0.524699i	$-0.824178\pi$
$23$	−8.16527	−1.70258	−0.851288	+	0.524699i	$0.824178\pi$
$24$	0.259096	0.0528877
$25$	−4.68408	−0.936815
$26$	0	0
$27$	1.00000	0.192450
$28$	5.76383	1.08926
$29$	−4.22613	−0.784773	−0.392387	−	0.919800i	$-0.628350\pi$
$29$	−4.22613	−0.784773	−0.392387	+	0.919800i	$0.628350\pi$
$30$	1.10548	0.201831
$31$	6.39872	1.14924	0.574622	−	0.818419i	$-0.305149\pi$
$31$	6.39872	1.14924	0.574622	+	0.818419i	$0.305149\pi$
$32$	7.83303	1.38470
$33$	−6.04044	−1.05151
$34$	1.96679	0.337302
$35$	−1.73406	−0.293110
$36$	1.86826	0.311377
$37$	−0.741352	−0.121878	−0.0609388	−	0.998142i	$-0.519409\pi$
$37$	−0.741352	−0.121878	−0.0609388	+	0.998142i	$0.519409\pi$
$38$	−7.78312	−1.26259
$39$	0	0
$40$	−0.145630	−0.0230262
$41$	8.97787	1.40211	0.701054	−	0.713108i	$-0.252713\pi$
$41$	8.97787	1.40211	0.701054	+	0.713108i	$0.252713\pi$
$42$	−6.06779	−0.936281
$43$	8.54447	1.30302	0.651510	−	0.758640i	$-0.274136\pi$
$43$	8.54447	1.30302	0.651510	+	0.758640i	$0.274136\pi$
$44$	−11.2851	−1.70130
$45$	−0.562071	−0.0837886
$46$	16.0594	2.36782
$47$	5.29432	0.772257	0.386128	−	0.922445i	$-0.373812\pi$
$47$	5.29432	0.772257	0.386128	+	0.922445i	$0.373812\pi$
$48$	−4.24612	−0.612874
$49$	2.51799	0.359713
$50$	9.21260	1.30286
$51$	−1.00000	−0.140028
$52$	0	0
$53$	7.35907	1.01085	0.505423	−	0.862872i	$-0.331336\pi$
$53$	7.35907	1.01085	0.505423	+	0.862872i	$0.331336\pi$
$54$	−1.96679	−0.267646
$55$	3.39516	0.457803
$56$	0.799343	0.106817
$57$	3.95727	0.524153
$58$	8.31192	1.09141
$59$	−5.98304	−0.778925	−0.389463	−	0.921042i	$-0.627339\pi$
$59$	−5.98304	−0.778925	−0.389463	+	0.921042i	$0.627339\pi$
$60$	−1.05010	−0.135567
$61$	−4.94978	−0.633755	−0.316877	−	0.948466i	$-0.602634\pi$
$61$	−4.94978	−0.633755	−0.316877	+	0.948466i	$0.602634\pi$
$62$	−12.5849	−1.59829
$63$	3.08512	0.388689
$64$	−6.91370	−0.864212
$65$	0	0
$66$	11.8803	1.46236
$67$	7.77935	0.950398	0.475199	−	0.879878i	$-0.342376\pi$
$67$	7.77935	0.950398	0.475199	+	0.879878i	$0.342376\pi$
$68$	−1.86826	−0.226560
$69$	−8.16527	−0.982983
$70$	3.41053	0.407636
$71$	−9.81696	−1.16506	−0.582529	−	0.812810i	$-0.697937\pi$
$71$	−9.81696	−1.16506	−0.582529	+	0.812810i	$0.697937\pi$
$72$	0.259096	0.0305347
$73$	−8.70107	−1.01838	−0.509191	−	0.860653i	$-0.670055\pi$
$73$	−8.70107	−1.01838	−0.509191	+	0.860653i	$0.670055\pi$
$74$	1.45808	0.169499
$75$	−4.68408	−0.540871
$76$	7.39323	0.848061
$77$	−18.6355	−2.12371
$78$	0	0
$79$	16.8289	1.89340	0.946702	−	0.322111i	$-0.104392\pi$
$79$	16.8289	1.89340	0.946702	+	0.322111i	$0.104392\pi$
$80$	2.38662	0.266832
$81$	1.00000	0.111111
$82$	−17.6576	−1.94996
$83$	4.52040	0.496179	0.248089	−	0.968737i	$-0.420197\pi$
$83$	4.52040	0.496179	0.248089	+	0.968737i	$0.420197\pi$
$84$	5.76383	0.628885
$85$	0.562071	0.0609652
$86$	−16.8052	−1.81215
$87$	−4.22613	−0.453089
$88$	−1.56505	−0.166835
$89$	5.32147	0.564075	0.282037	−	0.959403i	$-0.408990\pi$
$89$	5.32147	0.564075	0.282037	+	0.959403i	$0.408990\pi$
$90$	1.10548	0.116527
$91$	0	0
$92$	−15.2549	−1.59043
$93$	6.39872	0.663516
$94$	−10.4128	−1.07400
$95$	−2.22427	−0.228205
$96$	7.83303	0.799455
$97$	7.70576	0.782401	0.391201	−	0.920305i	$-0.372060\pi$
$97$	7.70576	0.782401	0.391201	+	0.920305i	$0.372060\pi$
$98$	−4.95236	−0.500264
$99$	−6.04044	−0.607087
$100$	−8.75109	−0.875109
$101$	−10.7781	−1.07246	−0.536232	−	0.844071i	$-0.680153\pi$
$101$	−10.7781	−1.07246	−0.536232	+	0.844071i	$0.680153\pi$
$102$	1.96679	0.194741
$103$	−15.9795	−1.57451	−0.787254	−	0.616629i	$-0.788498\pi$
$103$	−15.9795	−1.57451	−0.787254	+	0.616629i	$0.788498\pi$
$104$	0	0
$105$	−1.73406	−0.169227
$106$	−14.4738	−1.40582
$107$	2.30365	0.222703	0.111351	−	0.993781i	$-0.464482\pi$
$107$	2.30365	0.222703	0.111351	+	0.993781i	$0.464482\pi$
$108$	1.86826	0.179774
$109$	4.13594	0.396151	0.198075	−	0.980187i	$-0.436531\pi$
$109$	4.13594	0.396151	0.198075	+	0.980187i	$0.436531\pi$
$110$	−6.67756	−0.636680
$111$	−0.741352	−0.0703660
$112$	−13.0998	−1.23781
$113$	10.7776	1.01387	0.506936	−	0.861984i	$-0.330778\pi$
$113$	10.7776	1.01387	0.506936	+	0.861984i	$0.330778\pi$
$114$	−7.78312	−0.728956
$115$	4.58946	0.427969
$116$	−7.89554	−0.733082
$117$	0	0
$118$	11.7674	1.08328
$119$	−3.08512	−0.282813
$120$	−0.145630	−0.0132942
$121$	25.4869	2.31699
$122$	9.73519	0.881383
$123$	8.97787	0.809508
$124$	11.9545	1.07355
$125$	5.44314	0.486849
$126$	−6.06779	−0.540562
$127$	−15.1396	−1.34343	−0.671713	−	0.740812i	$-0.734441\pi$
$127$	−15.1396	−1.34343	−0.671713	+	0.740812i	$0.734441\pi$
$128$	−2.06827	−0.182811
$129$	8.54447	0.752298
$130$	0	0
$131$	−13.5864	−1.18705	−0.593524	−	0.804816i	$-0.702264\pi$
$131$	−13.5864	−1.18705	−0.593524	+	0.804816i	$0.702264\pi$
$132$	−11.2851	−0.982245
$133$	12.2087	1.05863
$134$	−15.3003	−1.32175
$135$	−0.562071	−0.0483754
$136$	−0.259096	−0.0222173
$137$	−19.2248	−1.64248	−0.821241	−	0.570582i	$-0.806718\pi$
$137$	−19.2248	−1.64248	−0.821241	+	0.570582i	$0.806718\pi$
$138$	16.0594	1.36706
$139$	−15.8544	−1.34475	−0.672377	−	0.740208i	$-0.734727\pi$
$139$	−15.8544	−1.34475	−0.672377	+	0.740208i	$0.734727\pi$
$140$	−3.23968	−0.273803
$141$	5.29432	0.445863
$142$	19.3079	1.62028
$143$	0	0
$144$	−4.24612	−0.353843
$145$	2.37539	0.197265
$146$	17.1132	1.41630
$147$	2.51799	0.207680
$148$	−1.38504	−0.113850
$149$	−8.07196	−0.661281	−0.330640	−	0.943757i	$-0.607265\pi$
$149$	−8.07196	−0.661281	−0.330640	+	0.943757i	$0.607265\pi$
$150$	9.21260	0.752205
$151$	−15.9640	−1.29914	−0.649568	−	0.760304i	$-0.725050\pi$
$151$	−15.9640	−1.29914	−0.649568	+	0.760304i	$0.725050\pi$
$152$	1.02531	0.0831638
$153$	−1.00000	−0.0808452
$154$	36.6521	2.95351
$155$	−3.59653	−0.288881
$156$	0	0
$157$	−16.2504	−1.29692	−0.648461	−	0.761247i	$-0.724587\pi$
$157$	−16.2504	−1.29692	−0.648461	+	0.761247i	$0.724587\pi$
$158$	−33.0990	−2.63322
$159$	7.35907	0.583612
$160$	−4.40272	−0.348066
$161$	−25.1909	−1.98532
$162$	−1.96679	−0.154526
$163$	1.25670	0.0984325	0.0492162	−	0.998788i	$-0.484328\pi$
$163$	1.25670	0.0984325	0.0492162	+	0.998788i	$0.484328\pi$
$164$	16.7730	1.30975
$165$	3.39516	0.264313
$166$	−8.89068	−0.690051
$167$	−0.919963	−0.0711889	−0.0355944	−	0.999366i	$-0.511332\pi$
$167$	−0.919963	−0.0711889	−0.0355944	+	0.999366i	$0.511332\pi$
$168$	0.799343	0.0616706
$169$	0	0
$170$	−1.10548	−0.0847862
$171$	3.95727	0.302620
$172$	15.9633	1.21719
$173$	14.1127	1.07297	0.536483	−	0.843911i	$-0.319752\pi$
$173$	14.1127	1.07297	0.536483	+	0.843911i	$0.319752\pi$
$174$	8.31192	0.630125
$175$	−14.4510	−1.09239
$176$	25.6484	1.93332
$177$	−5.98304	−0.449713
$178$	−10.4662	−0.784476
$179$	5.70954	0.426751	0.213376	−	0.976970i	$-0.431554\pi$
$179$	5.70954	0.426751	0.213376	+	0.976970i	$0.431554\pi$
$180$	−1.05010	−0.0782697
$181$	−19.4796	−1.44791	−0.723955	−	0.689847i	$-0.757678\pi$
$181$	−19.4796	−1.44791	−0.723955	+	0.689847i	$0.757678\pi$
$182$	0	0
$183$	−4.94978	−0.365899
$184$	−2.11559	−0.155963
$185$	0.416693	0.0306358
$186$	−12.5849	−0.922772
$187$	6.04044	0.441721
$188$	9.89120	0.721390
$189$	3.08512	0.224410
$190$	4.37467	0.317372
$191$	−2.55926	−0.185181	−0.0925907	−	0.995704i	$-0.529515\pi$
$191$	−2.55926	−0.185181	−0.0925907	+	0.995704i	$0.529515\pi$
$192$	−6.91370	−0.498953
$193$	12.3724	0.890587	0.445294	−	0.895385i	$-0.353099\pi$
$193$	12.3724	0.890587	0.445294	+	0.895385i	$0.353099\pi$
$194$	−15.1556	−1.08811
$195$	0	0
$196$	4.70427	0.336019
$197$	−10.0989	−0.719518	−0.359759	−	0.933045i	$-0.617141\pi$
$197$	−10.0989	−0.719518	−0.359759	+	0.933045i	$0.617141\pi$
$198$	11.8803	0.844294
$199$	−7.98297	−0.565898	−0.282949	−	0.959135i	$-0.591313\pi$
$199$	−7.98297	−0.565898	−0.282949	+	0.959135i	$0.591313\pi$
$200$	−1.21362	−0.0858162
$201$	7.77935	0.548713
$202$	21.1983	1.49151
$203$	−13.0381	−0.915099
$204$	−1.86826	−0.130805
$205$	−5.04620	−0.352442
$206$	31.4283	2.18972
$207$	−8.16527	−0.567525
$208$	0	0
$209$	−23.9036	−1.65345
$210$	3.41053	0.235349
$211$	−13.3331	−0.917891	−0.458946	−	0.888464i	$-0.651773\pi$
$211$	−13.3331	−0.917891	−0.458946	+	0.888464i	$0.651773\pi$
$212$	13.7487	0.944264
$213$	−9.81696	−0.672647
$214$	−4.53081	−0.309719
$215$	−4.80260	−0.327535
$216$	0.259096	0.0176292
$217$	19.7408	1.34010
$218$	−8.13452	−0.550939
$219$	−8.70107	−0.587964
$220$	6.34305	0.427648
$221$	0	0
$222$	1.45808	0.0978602
$223$	−27.3756	−1.83321	−0.916604	−	0.399796i	$-0.869081\pi$
$223$	−27.3756	−1.83321	−0.916604	+	0.399796i	$0.869081\pi$
$224$	24.1659	1.61465
$225$	−4.68408	−0.312272
$226$	−21.1973	−1.41002
$227$	−19.0770	−1.26618	−0.633092	−	0.774076i	$-0.718215\pi$
$227$	−19.0770	−1.26618	−0.633092	+	0.774076i	$0.718215\pi$
$228$	7.39323	0.489628
$229$	17.1978	1.13646	0.568230	−	0.822870i	$-0.307628\pi$
$229$	17.1978	1.13646	0.568230	+	0.822870i	$0.307628\pi$
$230$	−9.02651	−0.595190
$231$	−18.6355	−1.22613
$232$	−1.09497	−0.0718885
$233$	9.94963	0.651822	0.325911	−	0.945400i	$-0.394329\pi$
$233$	9.94963	0.651822	0.325911	+	0.945400i	$0.394329\pi$
$234$	0	0
$235$	−2.97579	−0.194119
$236$	−11.1779	−0.727619
$237$	16.8289	1.09316
$238$	6.06779	0.393317
$239$	27.2630	1.76350	0.881749	−	0.471719i	$-0.156366\pi$
$239$	27.2630	1.76350	0.881749	+	0.471719i	$0.156366\pi$
$240$	2.38662	0.154056
$241$	−3.05756	−0.196955	−0.0984774	−	0.995139i	$-0.531397\pi$
$241$	−3.05756	−0.196955	−0.0984774	+	0.995139i	$0.531397\pi$
$242$	−50.1274	−3.22231
$243$	1.00000	0.0641500
$244$	−9.24751	−0.592011
$245$	−1.41529	−0.0904195
$246$	−17.6576	−1.12581
$247$	0	0
$248$	1.65788	0.105276
$249$	4.52040	0.286469
$250$	−10.7055	−0.677076
$251$	11.1255	0.702237	0.351119	−	0.936331i	$-0.385801\pi$
$251$	11.1255	0.702237	0.351119	+	0.936331i	$0.385801\pi$
$252$	5.76383	0.363087
$253$	49.3218	3.10083
$254$	29.7765	1.86834
$255$	0.562071	0.0351983
$256$	17.8952	1.11845
$257$	3.24747	0.202571	0.101286	−	0.994857i	$-0.467704\pi$
$257$	3.24747	0.202571	0.101286	+	0.994857i	$0.467704\pi$
$258$	−16.8052	−1.04624
$259$	−2.28716	−0.142117
$260$	0	0
$261$	−4.22613	−0.261591
$262$	26.7216	1.65086
$263$	−30.6388	−1.88927	−0.944634	−	0.328125i	$-0.893583\pi$
$263$	−30.6388	−1.88927	−0.944634	+	0.328125i	$0.893583\pi$
$264$	−1.56505	−0.0963223
$265$	−4.13632	−0.254092
$266$	−24.0119	−1.47226
$267$	5.32147	0.325669
$268$	14.5339	0.887798
$269$	7.44447	0.453897	0.226949	−	0.973907i	$-0.427125\pi$
$269$	7.44447	0.453897	0.226949	+	0.973907i	$0.427125\pi$
$270$	1.10548	0.0672771
$271$	10.2116	0.620310	0.310155	−	0.950686i	$-0.399619\pi$
$271$	10.2116	0.620310	0.310155	+	0.950686i	$0.399619\pi$
$272$	4.24612	0.257459
$273$	0	0
$274$	37.8111	2.28425
$275$	28.2939	1.70618
$276$	−15.2549	−0.918236
$277$	−24.7769	−1.48870	−0.744350	−	0.667790i	$-0.767240\pi$
$277$	−24.7769	−1.48870	−0.744350	+	0.667790i	$0.767240\pi$
$278$	31.1823	1.87019
$279$	6.39872	0.383081
$280$	−0.449287	−0.0268501
$281$	−18.8029	−1.12169	−0.560843	−	0.827922i	$-0.689523\pi$
$281$	−18.8029	−1.12169	−0.560843	+	0.827922i	$0.689523\pi$
$282$	−10.4128	−0.620075
$283$	−3.60478	−0.214282	−0.107141	−	0.994244i	$-0.534170\pi$
$283$	−3.60478	−0.214282	−0.107141	+	0.994244i	$0.534170\pi$
$284$	−18.3407	−1.08832
$285$	−2.22427	−0.131754
$286$	0	0
$287$	27.6979	1.63495
$288$	7.83303	0.461566
$289$	1.00000	0.0588235
$290$	−4.67189	−0.274343
$291$	7.70576	0.451719
$292$	−16.2559	−0.951304
$293$	−9.00209	−0.525908	−0.262954	−	0.964808i	$-0.584697\pi$
$293$	−9.00209	−0.525908	−0.262954	+	0.964808i	$0.584697\pi$
$294$	−4.95236	−0.288827
$295$	3.36289	0.195795
$296$	−0.192081	−0.0111645
$297$	−6.04044	−0.350502
$298$	15.8758	0.919663
$299$	0	0
$300$	−8.75109	−0.505245
$301$	26.3607	1.51941
$302$	31.3979	1.80675
$303$	−10.7781	−0.619187
$304$	−16.8030	−0.963720
$305$	2.78213	0.159304
$306$	1.96679	0.112434
$307$	−4.04928	−0.231105	−0.115552	−	0.993301i	$-0.536864\pi$
$307$	−4.04928	−0.231105	−0.115552	+	0.993301i	$0.536864\pi$
$308$	−34.8160	−1.98383
$309$	−15.9795	−0.909042
$310$	7.07363	0.401755
$311$	−1.39386	−0.0790388	−0.0395194	−	0.999219i	$-0.512583\pi$
$311$	−1.39386	−0.0790388	−0.0395194	+	0.999219i	$0.512583\pi$
$312$	0	0
$313$	−1.24637	−0.0704491	−0.0352246	−	0.999379i	$-0.511215\pi$
$313$	−1.24637	−0.0704491	−0.0352246	+	0.999379i	$0.511215\pi$
$314$	31.9611	1.80367
$315$	−1.73406	−0.0977032
$316$	31.4409	1.76869
$317$	−22.7068	−1.27534	−0.637670	−	0.770310i	$-0.720102\pi$
$317$	−22.7068	−1.27534	−0.637670	+	0.770310i	$0.720102\pi$
$318$	−14.4738	−0.811648
$319$	25.5277	1.42928
$320$	3.88599	0.217233
$321$	2.30365	0.128577
$322$	49.5451	2.76104
$323$	−3.95727	−0.220188
$324$	1.86826	0.103792
$325$	0	0
$326$	−2.47167	−0.136893
$327$	4.13594	0.228718
$328$	2.32613	0.128439
$329$	16.3336	0.900503
$330$	−6.67756	−0.367588
$331$	−1.42852	−0.0785187	−0.0392593	−	0.999229i	$-0.512500\pi$
$331$	−1.42852	−0.0785187	−0.0392593	+	0.999229i	$0.512500\pi$
$332$	8.44531	0.463496
$333$	−0.741352	−0.0406258
$334$	1.80937	0.0990046
$335$	−4.37255	−0.238898
$336$	−13.0998	−0.714652
$337$	−19.7837	−1.07769	−0.538843	−	0.842406i	$-0.681138\pi$
$337$	−19.7837	−1.07769	−0.538843	+	0.842406i	$0.681138\pi$
$338$	0	0
$339$	10.7776	0.585359
$340$	1.05010	0.0569495
$341$	−38.6511	−2.09307
$342$	−7.78312	−0.420863
$343$	−13.8276	−0.746618
$344$	2.21384	0.119362
$345$	4.58946	0.247088
$346$	−27.7567	−1.49221
$347$	−7.16826	−0.384812	−0.192406	−	0.981315i	$-0.561629\pi$
$347$	−7.16826	−0.384812	−0.192406	+	0.981315i	$0.561629\pi$
$348$	−7.89554	−0.423245
$349$	2.72048	0.145624	0.0728120	−	0.997346i	$-0.476803\pi$
$349$	2.72048	0.145624	0.0728120	+	0.997346i	$0.476803\pi$
$350$	28.4220	1.51922
$351$	0	0
$352$	−47.3149	−2.52189
$353$	0.700200	0.0372679	0.0186339	−	0.999826i	$-0.494068\pi$
$353$	0.700200	0.0372679	0.0186339	+	0.999826i	$0.494068\pi$
$354$	11.7674	0.625429
$355$	5.51783	0.292856
$356$	9.94191	0.526920
$357$	−3.08512	−0.163282
$358$	−11.2295	−0.593496
$359$	−2.63317	−0.138973	−0.0694866	−	0.997583i	$-0.522136\pi$
$359$	−2.63317	−0.138973	−0.0694866	+	0.997583i	$0.522136\pi$
$360$	−0.145630	−0.00767539
$361$	−3.34002	−0.175791
$362$	38.3124	2.01365
$363$	25.4869	1.33771
$364$	0	0
$365$	4.89062	0.255987
$366$	9.73519	0.508866
$367$	−4.41653	−0.230541	−0.115271	−	0.993334i	$-0.536773\pi$
$367$	−4.41653	−0.230541	−0.115271	+	0.993334i	$0.536773\pi$
$368$	34.6707	1.80733
$369$	8.97787	0.467369
$370$	−0.819547	−0.0426062
$371$	22.7037	1.17871
$372$	11.9545	0.619812
$373$	13.1003	0.678309	0.339155	−	0.940731i	$-0.389859\pi$
$373$	13.1003	0.678309	0.339155	+	0.940731i	$0.389859\pi$
$374$	−11.8803	−0.614314
$375$	5.44314	0.281083
$376$	1.37174	0.0707420
$377$	0	0
$378$	−6.06779	−0.312094
$379$	−11.1265	−0.571530	−0.285765	−	0.958300i	$-0.592248\pi$
$379$	−11.1265	−0.571530	−0.285765	+	0.958300i	$0.592248\pi$
$380$	−4.15552	−0.213174
$381$	−15.1396	−0.775627
$382$	5.03352	0.257537
$383$	6.29283	0.321549	0.160774	−	0.986991i	$-0.448601\pi$
$383$	6.29283	0.321549	0.160774	+	0.986991i	$0.448601\pi$
$384$	−2.06827	−0.105546
$385$	10.4745	0.533829
$386$	−24.3340	−1.23857
$387$	8.54447	0.434340
$388$	14.3964	0.730866
$389$	−22.4981	−1.14070	−0.570349	−	0.821403i	$-0.693192\pi$
$389$	−22.4981	−1.14070	−0.570349	+	0.821403i	$0.693192\pi$
$390$	0	0
$391$	8.16527	0.412935
$392$	0.652401	0.0329512
$393$	−13.5864	−0.685343
$394$	19.8625	1.00066
$395$	−9.45906	−0.475937
$396$	−11.2851	−0.567099
$397$	−6.09072	−0.305684	−0.152842	−	0.988251i	$-0.548843\pi$
$397$	−6.09072	−0.305684	−0.152842	+	0.988251i	$0.548843\pi$
$398$	15.7008	0.787011
$399$	12.2087	0.611198
$400$	19.8891	0.994457
$401$	36.0160	1.79855	0.899277	−	0.437380i	$-0.144094\pi$
$401$	36.0160	1.79855	0.899277	+	0.437380i	$0.144094\pi$
$402$	−15.3003	−0.763112
$403$	0	0
$404$	−20.1364	−1.00182
$405$	−0.562071	−0.0279295
$406$	25.6433	1.27266
$407$	4.47809	0.221971
$408$	−0.259096	−0.0128272
$409$	−6.24154	−0.308624	−0.154312	−	0.988022i	$-0.549316\pi$
$409$	−6.24154	−0.308624	−0.154312	+	0.988022i	$0.549316\pi$
$410$	9.92483	0.490152
$411$	−19.2248	−0.948287
$412$	−29.8539	−1.47080
$413$	−18.4584	−0.908279
$414$	16.0594	0.789275
$415$	−2.54079	−0.124722
$416$	0	0
$417$	−15.8544	−0.776395
$418$	47.0134	2.29950
$419$	25.6818	1.25464	0.627319	−	0.778762i	$-0.284152\pi$
$419$	25.6818	1.25464	0.627319	+	0.778762i	$0.284152\pi$
$420$	−3.23968	−0.158080
$421$	3.69748	0.180204	0.0901020	−	0.995933i	$-0.471281\pi$
$421$	3.69748	0.180204	0.0901020	+	0.995933i	$0.471281\pi$
$422$	26.2235	1.27654
$423$	5.29432	0.257419
$424$	1.90670	0.0925978
$425$	4.68408	0.227211
$426$	19.3079	0.935471
$427$	−15.2707	−0.739001
$428$	4.30384	0.208034
$429$	0	0
$430$	9.44571	0.455512
$431$	−19.3305	−0.931117	−0.465558	−	0.885017i	$-0.654146\pi$
$431$	−19.3305	−0.931117	−0.465558	+	0.885017i	$0.654146\pi$
$432$	−4.24612	−0.204291
$433$	−33.4638	−1.60817	−0.804084	−	0.594515i	$-0.797344\pi$
$433$	−33.4638	−1.60817	−0.804084	+	0.594515i	$0.797344\pi$
$434$	−38.8261	−1.86371
$435$	2.37539	0.113891
$436$	7.72702	0.370057
$437$	−32.3122	−1.54570
$438$	17.1132	0.817699
$439$	33.6697	1.60697	0.803483	−	0.595328i	$-0.202978\pi$
$439$	33.6697	1.60697	0.803483	+	0.595328i	$0.202978\pi$
$440$	0.879671	0.0419367
$441$	2.51799	0.119904
$442$	0	0
$443$	−37.0256	−1.75914	−0.879569	−	0.475771i	$-0.842169\pi$
$443$	−37.0256	−1.75914	−0.879569	+	0.475771i	$0.842169\pi$
$444$	−1.38504	−0.0657312
$445$	−2.99104	−0.141789
$446$	53.8422	2.54950
$447$	−8.07196	−0.381790
$448$	−21.3296	−1.00773
$449$	−26.7583	−1.26280	−0.631402	−	0.775456i	$-0.717520\pi$
$449$	−26.7583	−1.26280	−0.631402	+	0.775456i	$0.717520\pi$
$450$	9.21260	0.434286
$451$	−54.2303	−2.55360
$452$	20.1354	0.947090
$453$	−15.9640	−0.750056
$454$	37.5204	1.76092
$455$	0	0
$456$	1.02531	0.0480146
$457$	17.9259	0.838537	0.419269	−	0.907862i	$-0.362287\pi$
$457$	17.9259	0.838537	0.419269	+	0.907862i	$0.362287\pi$
$458$	−33.8244	−1.58051
$459$	−1.00000	−0.0466760
$460$	8.57433	0.399780
$461$	−21.2476	−0.989599	−0.494800	−	0.869007i	$-0.664759\pi$
$461$	−21.2476	−0.989599	−0.494800	+	0.869007i	$0.664759\pi$
$462$	36.6521	1.70521
$463$	−7.65201	−0.355619	−0.177809	−	0.984065i	$-0.556901\pi$
$463$	−7.65201	−0.355619	−0.177809	+	0.984065i	$0.556901\pi$
$464$	17.9447	0.833060
$465$	−3.59653	−0.166785
$466$	−19.5688	−0.906509
$467$	26.0658	1.20618	0.603091	−	0.797672i	$-0.293935\pi$
$467$	26.0658	1.20618	0.603091	+	0.797672i	$0.293935\pi$
$468$	0	0
$469$	24.0002	1.10823
$470$	5.85275	0.269967
$471$	−16.2504	−0.748779
$472$	−1.55018	−0.0713528
$473$	−51.6123	−2.37314
$474$	−33.0990	−1.52029
$475$	−18.5361	−0.850497
$476$	−5.76383	−0.264185
$477$	7.35907	0.336949
$478$	−53.6207	−2.45255
$479$	26.2639	1.20003	0.600014	−	0.799989i	$-0.295162\pi$
$479$	26.2639	1.20003	0.600014	+	0.799989i	$0.295162\pi$
$480$	−4.40272	−0.200956
$481$	0	0
$482$	6.01358	0.273911
$483$	−25.1909	−1.14622
$484$	47.6163	2.16438
$485$	−4.33118	−0.196669
$486$	−1.96679	−0.0892154
$487$	23.9026	1.08313	0.541564	−	0.840659i	$-0.317832\pi$
$487$	23.9026	1.08313	0.541564	+	0.840659i	$0.317832\pi$
$488$	−1.28247	−0.0580546
$489$	1.25670	0.0568300
$490$	2.78358	0.125749
$491$	16.1493	0.728809	0.364404	−	0.931241i	$-0.381273\pi$
$491$	16.1493	0.728809	0.364404	+	0.931241i	$0.381273\pi$
$492$	16.7730	0.756187
$493$	4.22613	0.190336
$494$	0	0
$495$	3.39516	0.152601
$496$	−27.1697	−1.21996
$497$	−30.2865	−1.35854
$498$	−8.89068	−0.398401
$499$	−14.7230	−0.659091	−0.329546	−	0.944140i	$-0.606896\pi$
$499$	−14.7230	−0.659091	−0.329546	+	0.944140i	$0.606896\pi$
$500$	10.1692	0.454782
$501$	−0.919963	−0.0411009
$502$	−21.8816	−0.976623
$503$	−31.6338	−1.41048	−0.705240	−	0.708968i	$-0.749161\pi$
$503$	−31.6338	−1.41048	−0.705240	+	0.708968i	$0.749161\pi$
$504$	0.799343	0.0356056
$505$	6.05808	0.269581
$506$	−97.0056	−4.31243
$507$	0	0
$508$	−28.2849	−1.25494
$509$	−7.45932	−0.330629	−0.165314	−	0.986241i	$-0.552864\pi$
$509$	−7.45932	−0.330629	−0.165314	+	0.986241i	$0.552864\pi$
$510$	−1.10548	−0.0489513
$511$	−26.8439	−1.18750
$512$	−31.0597	−1.37266
$513$	3.95727	0.174718
$514$	−6.38709	−0.281722
$515$	8.98162	0.395778
$516$	15.9633	0.702746
$517$	−31.9800	−1.40648
$518$	4.49837	0.197647
$519$	14.1127	0.619478
$520$	0	0
$521$	−13.0678	−0.572511	−0.286256	−	0.958153i	$-0.592411\pi$
$521$	−13.0678	−0.572511	−0.286256	+	0.958153i	$0.592411\pi$
$522$	8.31192	0.363803
$523$	24.0924	1.05349	0.526744	−	0.850024i	$-0.323413\pi$
$523$	24.0924	1.05349	0.526744	+	0.850024i	$0.323413\pi$
$524$	−25.3830	−1.10886
$525$	−14.4510	−0.630691
$526$	60.2601	2.62746
$527$	−6.39872	−0.278732
$528$	25.6484	1.11620
$529$	43.6716	1.89876
$530$	8.13528	0.353374
$531$	−5.98304	−0.259642
$532$	22.8090	0.988896
$533$	0	0
$534$	−10.4662	−0.452917
$535$	−1.29482	−0.0559799
$536$	2.01560	0.0870605
$537$	5.70954	0.246385
$538$	−14.6417	−0.631249
$539$	−15.2098	−0.655131
$540$	−1.05010	−0.0451890
$541$	6.66483	0.286543	0.143272	−	0.989683i	$-0.454238\pi$
$541$	6.66483	0.286543	0.143272	+	0.989683i	$0.454238\pi$
$542$	−20.0841	−0.862685
$543$	−19.4796	−0.835951
$544$	−7.83303	−0.335838
$545$	−2.32469	−0.0995788
$546$	0	0
$547$	28.6141	1.22345	0.611725	−	0.791070i	$-0.290476\pi$
$547$	28.6141	1.22345	0.611725	+	0.791070i	$0.290476\pi$
$548$	−35.9169	−1.53430
$549$	−4.94978	−0.211252
$550$	−55.6481	−2.37284
$551$	−16.7239	−0.712464
$552$	−2.11559	−0.0900453
$553$	51.9194	2.20784
$554$	48.7310	2.07038
$555$	0.416693	0.0176876
$556$	−29.6203	−1.25618
$557$	−17.2596	−0.731311	−0.365656	−	0.930750i	$-0.619155\pi$
$557$	−17.2596	−0.731311	−0.365656	+	0.930750i	$0.619155\pi$
$558$	−12.5849	−0.532763
$559$	0	0
$560$	7.36302	0.311144
$561$	6.04044	0.255027
$562$	36.9813	1.55996
$563$	−26.3297	−1.10967	−0.554833	−	0.831962i	$-0.687218\pi$
$563$	−26.3297	−1.10967	−0.554833	+	0.831962i	$0.687218\pi$
$564$	9.89120	0.416495
$565$	−6.05778	−0.254853
$566$	7.08985	0.298009
$567$	3.08512	0.129563
$568$	−2.54353	−0.106724
$569$	−39.1628	−1.64179	−0.820895	−	0.571080i	$-0.806525\pi$
$569$	−39.1628	−1.64179	−0.820895	+	0.571080i	$0.806525\pi$
$570$	4.37467	0.183235
$571$	−29.3757	−1.22934	−0.614668	−	0.788786i	$-0.710710\pi$
$571$	−29.3757	−1.22934	−0.614668	+	0.788786i	$0.710710\pi$
$572$	0	0
$573$	−2.55926	−0.106915
$574$	−54.4759	−2.27378
$575$	38.2467	1.59500
$576$	−6.91370	−0.288071
$577$	14.9551	0.622588	0.311294	−	0.950314i	$-0.399238\pi$
$577$	14.9551	0.622588	0.311294	+	0.950314i	$0.399238\pi$
$578$	−1.96679	−0.0818077
$579$	12.3724	0.514181
$580$	4.43785	0.184272
$581$	13.9460	0.578578
$582$	−15.1556	−0.628220
$583$	−44.4520	−1.84101
$584$	−2.25441	−0.0932882
$585$	0	0
$586$	17.7052	0.731396
$587$	−29.4234	−1.21443	−0.607217	−	0.794536i	$-0.707714\pi$
$587$	−29.4234	−1.21443	−0.607217	+	0.794536i	$0.707714\pi$
$588$	4.70427	0.194001
$589$	25.3214	1.04335
$590$	−6.61411	−0.272298
$591$	−10.0989	−0.415414
$592$	3.14787	0.129377
$593$	−5.44237	−0.223491	−0.111746	−	0.993737i	$-0.535644\pi$
$593$	−5.44237	−0.223491	−0.111746	+	0.993737i	$0.535644\pi$
$594$	11.8803	0.487454
$595$	1.73406	0.0710895
$596$	−15.0806	−0.617724
$597$	−7.98297	−0.326721
$598$	0	0
$599$	22.9249	0.936684	0.468342	−	0.883547i	$-0.344851\pi$
$599$	22.9249	0.936684	0.468342	+	0.883547i	$0.344851\pi$
$600$	−1.21362	−0.0495460
$601$	10.1779	0.415164	0.207582	−	0.978218i	$-0.433441\pi$
$601$	10.1779	0.415164	0.207582	+	0.978218i	$0.433441\pi$
$602$	−51.8461	−2.11309
$603$	7.77935	0.316799
$604$	−29.8251	−1.21356
$605$	−14.3254	−0.582412
$606$	21.1983	0.861123
$607$	19.8809	0.806941	0.403470	−	0.914993i	$-0.367804\pi$
$607$	19.8809	0.806941	0.403470	+	0.914993i	$0.367804\pi$
$608$	30.9974	1.25711
$609$	−13.0381	−0.528332
$610$	−5.47187	−0.221550
$611$	0	0
$612$	−1.86826	−0.0755201
$613$	9.44265	0.381385	0.190692	−	0.981650i	$-0.438927\pi$
$613$	9.44265	0.381385	0.190692	+	0.981650i	$0.438927\pi$
$614$	7.96409	0.321404
$615$	−5.04620	−0.203483
$616$	−4.82838	−0.194541
$617$	41.5469	1.67261	0.836307	−	0.548261i	$-0.184710\pi$
$617$	41.5469	1.67261	0.836307	+	0.548261i	$0.184710\pi$
$618$	31.4283	1.26423
$619$	−14.8723	−0.597767	−0.298883	−	0.954290i	$-0.596614\pi$
$619$	−14.8723	−0.597767	−0.298883	+	0.954290i	$0.596614\pi$
$620$	−6.71928	−0.269853
$621$	−8.16527	−0.327661
$622$	2.74144	0.109922
$623$	16.4174	0.657749
$624$	0	0
$625$	20.3609	0.814438
$626$	2.45135	0.0979758
$627$	−23.9036	−0.954619
$628$	−30.3600	−1.21150
$629$	0.741352	0.0295596
$630$	3.41053	0.135879
$631$	15.9012	0.633017	0.316508	−	0.948590i	$-0.397489\pi$
$631$	15.9012	0.633017	0.316508	+	0.948590i	$0.397489\pi$
$632$	4.36031	0.173444
$633$	−13.3331	−0.529945
$634$	44.6595	1.77365
$635$	8.50955	0.337691
$636$	13.7487	0.545171
$637$	0	0
$638$	−50.2076	−1.98774
$639$	−9.81696	−0.388353
$640$	1.16252	0.0459524
$641$	9.80513	0.387279	0.193640	−	0.981073i	$-0.437971\pi$
$641$	9.80513	0.387279	0.193640	+	0.981073i	$0.437971\pi$
$642$	−4.53081	−0.178817
$643$	−23.5189	−0.927496	−0.463748	−	0.885967i	$-0.653496\pi$
$643$	−23.5189	−0.927496	−0.463748	+	0.885967i	$0.653496\pi$
$644$	−47.0632	−1.85455
$645$	−4.80260	−0.189102
$646$	7.78312	0.306223
$647$	25.9839	1.02153	0.510766	−	0.859720i	$-0.329362\pi$
$647$	25.9839	1.02153	0.510766	+	0.859720i	$0.329362\pi$
$648$	0.259096	0.0101782
$649$	36.1402	1.41863
$650$	0	0
$651$	19.7408	0.773704
$652$	2.34785	0.0919489
$653$	−14.2376	−0.557161	−0.278581	−	0.960413i	$-0.589864\pi$
$653$	−14.2376	−0.557161	−0.278581	+	0.960413i	$0.589864\pi$
$654$	−8.13452	−0.318085
$655$	7.63652	0.298383
$656$	−38.1211	−1.48838
$657$	−8.70107	−0.339461
$658$	−32.1249	−1.25236
$659$	−15.5512	−0.605788	−0.302894	−	0.953024i	$-0.597953\pi$
$659$	−15.5512	−0.605788	−0.302894	+	0.953024i	$0.597953\pi$
$660$	6.34305	0.246903
$661$	9.77803	0.380321	0.190161	−	0.981753i	$-0.439099\pi$
$661$	9.77803	0.380321	0.190161	+	0.981753i	$0.439099\pi$
$662$	2.80960	0.109198
$663$	0	0
$664$	1.17122	0.0454520
$665$	−6.86214	−0.266102
$666$	1.45808	0.0564996
$667$	34.5075	1.33614
$668$	−1.71873	−0.0664998
$669$	−27.3756	−1.05840
$670$	8.59988	0.332242
$671$	29.8989	1.15423
$672$	24.1659	0.932219
$673$	5.28038	0.203544	0.101772	−	0.994808i	$-0.467549\pi$
$673$	5.28038	0.203544	0.101772	+	0.994808i	$0.467549\pi$
$674$	38.9103	1.49877
$675$	−4.68408	−0.180290
$676$	0	0
$677$	−29.5267	−1.13480	−0.567401	−	0.823441i	$-0.692051\pi$
$677$	−29.5267	−1.13480	−0.567401	+	0.823441i	$0.692051\pi$
$678$	−21.1973	−0.814077
$679$	23.7732	0.912332
$680$	0.145630	0.00558467
$681$	−19.0770	−0.731032
$682$	76.0185	2.91090
$683$	26.6474	1.01963	0.509817	−	0.860283i	$-0.329713\pi$
$683$	26.6474	1.01963	0.509817	+	0.860283i	$0.329713\pi$
$684$	7.39323	0.282687
$685$	10.8057	0.412864
$686$	27.1959	1.03834
$687$	17.1978	0.656135
$688$	−36.2808	−1.38319
$689$	0	0
$690$	−9.02651	−0.343633
$691$	3.28553	0.124987	0.0624937	−	0.998045i	$-0.480095\pi$
$691$	3.28553	0.124987	0.0624937	+	0.998045i	$0.480095\pi$
$692$	26.3662	1.00229
$693$	−18.6355	−0.707904
$694$	14.0985	0.535170
$695$	8.91132	0.338026
$696$	−1.09497	−0.0415049
$697$	−8.97787	−0.340061
$698$	−5.35061	−0.202524
$699$	9.94963	0.376330
$700$	−26.9982	−1.02044
$701$	26.0823	0.985116	0.492558	−	0.870280i	$-0.336062\pi$
$701$	26.0823	0.985116	0.492558	+	0.870280i	$0.336062\pi$
$702$	0	0
$703$	−2.93373	−0.110648
$704$	41.7617	1.57395
$705$	−2.97579	−0.112075
$706$	−1.37715	−0.0518296
$707$	−33.2519	−1.25056
$708$	−11.1779	−0.420091
$709$	−32.2385	−1.21074	−0.605372	−	0.795943i	$-0.706976\pi$
$709$	−32.2385	−1.21074	−0.605372	+	0.795943i	$0.706976\pi$
$710$	−10.8524	−0.407284
$711$	16.8289	0.631135
$712$	1.37877	0.0516716
$713$	−52.2472	−1.95667
$714$	6.06779	0.227081
$715$	0	0
$716$	10.6669	0.398642
$717$	27.2630	1.01816
$718$	5.17888	0.193274
$719$	15.1113	0.563556	0.281778	−	0.959480i	$-0.409076\pi$
$719$	15.1113	0.563556	0.281778	+	0.959480i	$0.409076\pi$
$720$	2.38662	0.0889441
$721$	−49.2988	−1.83598
$722$	6.56913	0.244478
$723$	−3.05756	−0.113712
$724$	−36.3931	−1.35254
$725$	19.7955	0.735188
$726$	−50.1274	−1.86040
$727$	12.1366	0.450120	0.225060	−	0.974345i	$-0.427742\pi$
$727$	12.1366	0.450120	0.225060	+	0.974345i	$0.427742\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−9.61882	−0.356009
$731$	−8.54447	−0.316029
$732$	−9.24751	−0.341798
$733$	33.8030	1.24854	0.624271	−	0.781207i	$-0.285396\pi$
$733$	33.8030	1.24854	0.624271	+	0.781207i	$0.285396\pi$
$734$	8.68639	0.320621
$735$	−1.41529	−0.0522037
$736$	−63.9588	−2.35755
$737$	−46.9907	−1.73092
$738$	−17.6576	−0.649985
$739$	−35.2527	−1.29679	−0.648396	−	0.761303i	$-0.724560\pi$
$739$	−35.2527	−1.29679	−0.648396	+	0.761303i	$0.724560\pi$
$740$	0.778492	0.0286179
$741$	0	0
$742$	−44.6533	−1.63928
$743$	−23.7391	−0.870902	−0.435451	−	0.900213i	$-0.643411\pi$
$743$	−23.7391	−0.870902	−0.435451	+	0.900213i	$0.643411\pi$
$744$	1.65788	0.0607809
$745$	4.53701	0.166223
$746$	−25.7656	−0.943346
$747$	4.52040	0.165393
$748$	11.2851	0.412625
$749$	7.10706	0.259686
$750$	−10.7055	−0.390910
$751$	−44.6624	−1.62975	−0.814877	−	0.579634i	$-0.803196\pi$
$751$	−44.6624	−1.62975	−0.814877	+	0.579634i	$0.803196\pi$
$752$	−22.4803	−0.819773
$753$	11.1255	0.405437
$754$	0	0
$755$	8.97293	0.326558
$756$	5.76383	0.209628
$757$	9.07166	0.329715	0.164858	−	0.986317i	$-0.447284\pi$
$757$	9.07166	0.329715	0.164858	+	0.986317i	$0.447284\pi$
$758$	21.8835	0.794844
$759$	49.3218	1.79027
$760$	−0.576298	−0.0209045
$761$	24.7150	0.895917	0.447959	−	0.894054i	$-0.352151\pi$
$761$	24.7150	0.895917	0.447959	+	0.894054i	$0.352151\pi$
$762$	29.7765	1.07869
$763$	12.7599	0.461939
$764$	−4.78137	−0.172984
$765$	0.562071	0.0203217
$766$	−12.3767	−0.447188
$767$	0	0
$768$	17.8952	0.645739
$769$	−46.3877	−1.67278	−0.836392	−	0.548132i	$-0.815339\pi$
$769$	−46.3877	−1.67278	−0.836392	+	0.548132i	$0.815339\pi$
$770$	−20.6011	−0.742412
$771$	3.24747	0.116955
$772$	23.1150	0.831926
$773$	−48.1734	−1.73268	−0.866338	−	0.499459i	$-0.833532\pi$
$773$	−48.1734	−1.73268	−0.866338	+	0.499459i	$0.833532\pi$
$774$	−16.8052	−0.604050
$775$	−29.9721	−1.07663
$776$	1.99653	0.0716712
$777$	−2.28716	−0.0820515
$778$	44.2490	1.58640
$779$	35.5279	1.27292
$780$	0	0
$781$	59.2987	2.12188
$782$	−16.0594	−0.574282
$783$	−4.22613	−0.151030
$784$	−10.6917	−0.381846
$785$	9.13388	0.326002
$786$	26.7216	0.953127
$787$	−27.7635	−0.989661	−0.494830	−	0.868990i	$-0.664770\pi$
$787$	−27.7635	−0.989661	−0.494830	+	0.868990i	$0.664770\pi$
$788$	−18.8675	−0.672125
$789$	−30.6388	−1.09077
$790$	18.6040	0.661900
$791$	33.2502	1.18224
$792$	−1.56505	−0.0556117
$793$	0	0
$794$	11.9792	0.425125
$795$	−4.13632	−0.146700
$796$	−14.9143	−0.528623
$797$	13.7497	0.487039	0.243519	−	0.969896i	$-0.421698\pi$
$797$	13.7497	0.487039	0.243519	+	0.969896i	$0.421698\pi$
$798$	−24.0119	−0.850011
$799$	−5.29432	−0.187300
$800$	−36.6905	−1.29721
$801$	5.32147	0.188025
$802$	−70.8359	−2.50130
$803$	52.5583	1.85474
$804$	14.5339	0.512570
$805$	14.1591	0.499041
$806$	0	0
$807$	7.44447	0.262058
$808$	−2.79257	−0.0982422
$809$	27.9241	0.981758	0.490879	−	0.871228i	$-0.336676\pi$
$809$	27.9241	0.981758	0.490879	+	0.871228i	$0.336676\pi$
$810$	1.10548	0.0388425
$811$	0.352736	0.0123862	0.00619312	−	0.999981i	$-0.498029\pi$
$811$	0.352736	0.0123862	0.00619312	+	0.999981i	$0.498029\pi$
$812$	−24.3587	−0.854823
$813$	10.2116	0.358136
$814$	−8.80747	−0.308701
$815$	−0.706356	−0.0247426
$816$	4.24612	0.148644
$817$	33.8128	1.18296
$818$	12.2758	0.429213
$819$	0	0
$820$	−9.42764	−0.329228
$821$	6.30618	0.220087	0.110044	−	0.993927i	$-0.464901\pi$
$821$	6.30618	0.220087	0.110044	+	0.993927i	$0.464901\pi$
$822$	37.8111	1.31881
$823$	−11.2909	−0.393575	−0.196787	−	0.980446i	$-0.563051\pi$
$823$	−11.2909	−0.393575	−0.196787	+	0.980446i	$0.563051\pi$
$824$	−4.14022	−0.144232
$825$	28.2939	0.985066
$826$	36.3038	1.26317
$827$	−33.2092	−1.15480	−0.577399	−	0.816462i	$-0.695932\pi$
$827$	−33.2092	−1.15480	−0.577399	+	0.816462i	$0.695932\pi$
$828$	−15.2549	−0.530144
$829$	11.9060	0.413513	0.206757	−	0.978392i	$-0.433709\pi$
$829$	11.9060	0.413513	0.206757	+	0.978392i	$0.433709\pi$
$830$	4.99720	0.173455
$831$	−24.7769	−0.859501
$832$	0	0
$833$	−2.51799	−0.0872432
$834$	31.1823	1.07976
$835$	0.517085	0.0178945
$836$	−44.6583	−1.54454
$837$	6.39872	0.221172
$838$	−50.5107	−1.74486
$839$	−7.82667	−0.270207	−0.135103	−	0.990832i	$-0.543137\pi$
$839$	−7.82667	−0.270207	−0.135103	+	0.990832i	$0.543137\pi$
$840$	−0.449287	−0.0155019
$841$	−11.1398	−0.384131
$842$	−7.27216	−0.250615
$843$	−18.8029	−0.647605
$844$	−24.9098	−0.857432
$845$	0	0
$846$	−10.4128	−0.358000
$847$	78.6302	2.70177
$848$	−31.2475	−1.07304
$849$	−3.60478	−0.123716
$850$	−9.21260	−0.315989
$851$	6.05334	0.207506
$852$	−18.3407	−0.628341
$853$	7.47045	0.255784	0.127892	−	0.991788i	$-0.459179\pi$
$853$	7.47045	0.255784	0.127892	+	0.991788i	$0.459179\pi$
$854$	30.0343	1.02775
$855$	−2.22427	−0.0760683
$856$	0.596867	0.0204005
$857$	−38.9743	−1.33134	−0.665668	−	0.746248i	$-0.731853\pi$
$857$	−38.9743	−1.33134	−0.665668	+	0.746248i	$0.731853\pi$
$858$	0	0
$859$	11.0228	0.376092	0.188046	−	0.982160i	$-0.439785\pi$
$859$	11.0228	0.376092	0.188046	+	0.982160i	$0.439785\pi$
$860$	−8.97253	−0.305961
$861$	27.6979	0.943940
$862$	38.0190	1.29493
$863$	29.4909	1.00388	0.501941	−	0.864902i	$-0.332619\pi$
$863$	29.4909	1.00388	0.501941	+	0.864902i	$0.332619\pi$
$864$	7.83303	0.266485
$865$	−7.93233	−0.269707
$866$	65.8163	2.23653
$867$	1.00000	0.0339618
$868$	36.8811	1.25183
$869$	−101.654	−3.44838
$870$	−4.67189	−0.158392
$871$	0	0
$872$	1.07160	0.0362891
$873$	7.70576	0.260800
$874$	63.5512	2.14965
$875$	16.7928	0.567699
$876$	−16.2559	−0.549236
$877$	−12.0028	−0.405305	−0.202653	−	0.979251i	$-0.564956\pi$
$877$	−12.0028	−0.405305	−0.202653	+	0.979251i	$0.564956\pi$
$878$	−66.2212	−2.23486
$879$	−9.00209	−0.303633
$880$	−14.4162	−0.485971
$881$	−0.432480	−0.0145706	−0.00728530	−	0.999973i	$-0.502319\pi$
$881$	−0.432480	−0.0145706	−0.00728530	+	0.999973i	$0.502319\pi$
$882$	−4.95236	−0.166755
$883$	40.1105	1.34983	0.674913	−	0.737898i	$-0.264181\pi$
$883$	40.1105	1.34983	0.674913	+	0.737898i	$0.264181\pi$
$884$	0	0
$885$	3.36289	0.113042
$886$	72.8216	2.44649
$887$	−54.2453	−1.82138	−0.910690	−	0.413091i	$-0.864449\pi$
$887$	−54.2453	−1.82138	−0.910690	+	0.413091i	$0.864449\pi$
$888$	−0.192081	−0.00644582
$889$	−46.7077	−1.56652
$890$	5.88276	0.197190
$891$	−6.04044	−0.202362
$892$	−51.1449	−1.71246
$893$	20.9511	0.701101
$894$	15.8758	0.530968
$895$	−3.20917	−0.107271
$896$	−6.38087	−0.213170
$897$	0	0
$898$	52.6280	1.75622
$899$	−27.0418	−0.901896
$900$	−8.75109	−0.291703
$901$	−7.35907	−0.245166
$902$	106.660	3.55138
$903$	26.3607	0.877231
$904$	2.79243	0.0928749
$905$	10.9489	0.363955
$906$	31.3979	1.04313
$907$	22.6243	0.751227	0.375613	−	0.926776i	$-0.377432\pi$
$907$	22.6243	0.751227	0.375613	+	0.926776i	$0.377432\pi$
$908$	−35.6409	−1.18278
$909$	−10.7781	−0.357488
$910$	0	0
$911$	−13.7628	−0.455981	−0.227990	−	0.973663i	$-0.573215\pi$
$911$	−13.7628	−0.455981	−0.227990	+	0.973663i	$0.573215\pi$
$912$	−16.8030	−0.556404
$913$	−27.3052	−0.903670
$914$	−35.2565	−1.16618
$915$	2.78213	0.0919744
$916$	32.1300	1.06160
$917$	−41.9157	−1.38418
$918$	1.96679	0.0649138
$919$	−16.6604	−0.549576	−0.274788	−	0.961505i	$-0.588608\pi$
$919$	−16.6604	−0.549576	−0.274788	+	0.961505i	$0.588608\pi$
$920$	1.18911	0.0392038
$921$	−4.04928	−0.133428
$922$	41.7896	1.37627
$923$	0	0
$924$	−34.8160	−1.14536
$925$	3.47255	0.114177
$926$	15.0499	0.494570
$927$	−15.9795	−0.524836
$928$	−33.1034	−1.08667
$929$	19.4777	0.639044	0.319522	−	0.947579i	$-0.396478\pi$
$929$	19.4777	0.639044	0.319522	+	0.947579i	$0.396478\pi$
$930$	7.07363	0.231953
$931$	9.96436	0.326569
$932$	18.5885	0.608888
$933$	−1.39386	−0.0456331
$934$	−51.2660	−1.67748
$935$	−3.39516	−0.111033
$936$	0	0
$937$	23.4402	0.765757	0.382879	−	0.923799i	$-0.374933\pi$
$937$	23.4402	0.765757	0.382879	+	0.923799i	$0.374933\pi$
$938$	−47.2035	−1.54125
$939$	−1.24637	−0.0406738
$940$	−5.55956	−0.181333
$941$	6.19102	0.201822	0.100911	−	0.994895i	$-0.467824\pi$
$941$	6.19102	0.201822	0.100911	+	0.994895i	$0.467824\pi$
$942$	31.9611	1.04135
$943$	−73.3067	−2.38720
$944$	25.4047	0.826852
$945$	−1.73406	−0.0564090
$946$	101.511	3.30040
$947$	−39.8530	−1.29505	−0.647525	−	0.762045i	$-0.724196\pi$
$947$	−39.8530	−1.29505	−0.647525	+	0.762045i	$0.724196\pi$
$948$	31.4409	1.02115
$949$	0	0
$950$	36.4567	1.18281
$951$	−22.7068	−0.736318
$952$	−0.799343	−0.0259068
$953$	16.5030	0.534586	0.267293	−	0.963615i	$-0.413871\pi$
$953$	16.5030	0.534586	0.267293	+	0.963615i	$0.413871\pi$
$954$	−14.4738	−0.468605
$955$	1.43849	0.0465483
$956$	50.9345	1.64734
$957$	25.5277	0.825193
$958$	−51.6556	−1.66892
$959$	−59.3108	−1.91524
$960$	3.88599	0.125420
$961$	9.94358	0.320761
$962$	0	0
$963$	2.30365	0.0742342
$964$	−5.71234	−0.183982
$965$	−6.95419	−0.223863
$966$	49.5451	1.59409
$967$	−18.6447	−0.599573	−0.299786	−	0.954006i	$-0.596915\pi$
$967$	−18.6447	−0.599573	−0.299786	+	0.954006i	$0.596915\pi$
$968$	6.60355	0.212246
$969$	−3.95727	−0.127126
$970$	8.51853	0.273514
$971$	36.1738	1.16087	0.580435	−	0.814306i	$-0.302882\pi$
$971$	36.1738	1.16087	0.580435	+	0.814306i	$0.302882\pi$
$972$	1.86826	0.0599246
$973$	−48.9129	−1.56807
$974$	−47.0114	−1.50634
$975$	0	0
$976$	21.0174	0.672749
$977$	−9.18599	−0.293886	−0.146943	−	0.989145i	$-0.546943\pi$
$977$	−9.18599	−0.293886	−0.146943	+	0.989145i	$0.546943\pi$
$978$	−2.47167	−0.0790352
$979$	−32.1440	−1.02733
$980$	−2.64414	−0.0844638
$981$	4.13594	0.132050
$982$	−31.7623	−1.01358
$983$	9.47337	0.302154	0.151077	−	0.988522i	$-0.451726\pi$
$983$	9.47337	0.302154	0.151077	+	0.988522i	$0.451726\pi$
$984$	2.32613	0.0741543
$985$	5.67631	0.180862
$986$	−8.31192	−0.264705
$987$	16.3336	0.519906
$988$	0	0
$989$	−69.7679	−2.21849
$990$	−6.67756	−0.212227
$991$	−23.3313	−0.741143	−0.370572	−	0.928804i	$-0.620838\pi$
$991$	−23.3313	−0.741143	−0.370572	+	0.928804i	$0.620838\pi$
$992$	50.1213	1.59135
$993$	−1.42852	−0.0453328
$994$	59.5673	1.88936
$995$	4.48700	0.142247
$996$	8.44531	0.267600
$997$	−13.2407	−0.419337	−0.209669	−	0.977772i	$-0.567239\pi$
$997$	−13.2407	−0.419337	−0.209669	+	0.977772i	$0.567239\pi$
$998$	28.9570	0.916619
$999$	−0.741352	−0.0234553

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8619.2.a.bn.1.3		16
13.2	odd	12		663.2.z.d.511.2	yes	16
13.7	odd	12		663.2.z.d.205.2	✓	16
13.12	even	2	inner	8619.2.a.bn.1.14		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
663.2.z.d.205.2	✓	16	13.7	odd	12
663.2.z.d.511.2	yes	16	13.2	odd	12
8619.2.a.bn.1.3		16	1.1	even	1	trivial
8619.2.a.bn.1.14		16	13.12	even	2	inner

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:	\( N \)	\(=\)	\( 8619 = 3 \cdot 13^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8619.a (trivial)

\(f(q)\)	\(=\)	\(q-1.96679 q^{2} +1.00000 q^{3} +1.86826 q^{4} -0.562071 q^{5} -1.96679 q^{6} +3.08512 q^{7} +0.259096 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.96679 q^{2} +1.00000 q^{3} +1.86826 q^{4} -0.562071 q^{5} -1.96679 q^{6} +3.08512 q^{7} +0.259096 q^{8} +1.00000 q^{9} +1.10548 q^{10} -6.04044 q^{11} +1.86826 q^{12} -6.06779 q^{14} -0.562071 q^{15} -4.24612 q^{16} -1.00000 q^{17} -1.96679 q^{18} +3.95727 q^{19} -1.05010 q^{20} +3.08512 q^{21} +11.8803 q^{22} -8.16527 q^{23} +0.259096 q^{24} -4.68408 q^{25} +1.00000 q^{27} +5.76383 q^{28} -4.22613 q^{29} +1.10548 q^{30} +6.39872 q^{31} +7.83303 q^{32} -6.04044 q^{33} +1.96679 q^{34} -1.73406 q^{35} +1.86826 q^{36} -0.741352 q^{37} -7.78312 q^{38} -0.145630 q^{40} +8.97787 q^{41} -6.06779 q^{42} +8.54447 q^{43} -11.2851 q^{44} -0.562071 q^{45} +16.0594 q^{46} +5.29432 q^{47} -4.24612 q^{48} +2.51799 q^{49} +9.21260 q^{50} -1.00000 q^{51} +7.35907 q^{53} -1.96679 q^{54} +3.39516 q^{55} +0.799343 q^{56} +3.95727 q^{57} +8.31192 q^{58} -5.98304 q^{59} -1.05010 q^{60} -4.94978 q^{61} -12.5849 q^{62} +3.08512 q^{63} -6.91370 q^{64} +11.8803 q^{66} +7.77935 q^{67} -1.86826 q^{68} -8.16527 q^{69} +3.41053 q^{70} -9.81696 q^{71} +0.259096 q^{72} -8.70107 q^{73} +1.45808 q^{74} -4.68408 q^{75} +7.39323 q^{76} -18.6355 q^{77} +16.8289 q^{79} +2.38662 q^{80} +1.00000 q^{81} -17.6576 q^{82} +4.52040 q^{83} +5.76383 q^{84} +0.562071 q^{85} -16.8052 q^{86} -4.22613 q^{87} -1.56505 q^{88} +5.32147 q^{89} +1.10548 q^{90} -15.2549 q^{92} +6.39872 q^{93} -10.4128 q^{94} -2.22427 q^{95} +7.83303 q^{96} +7.70576 q^{97} -4.95236 q^{98} -6.04044 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{3} + 8 q^{4} + 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^3 + 8 * q^4 + 16 * q^9	\( 16 q + 16 q^{3} + 8 q^{4} + 16 q^{9} + 2 q^{10} + 8 q^{12} - 26 q^{14} - 16 q^{17} - 2 q^{22} - 42 q^{23} - 14 q^{25} + 16 q^{27} - 58 q^{29} + 2 q^{30} - 30 q^{35} + 8 q^{36} - 62 q^{38} + 4 q^{40} - 26 q^{42} - 6 q^{43} + 4 q^{49} - 16 q^{51} - 26 q^{53} - 18 q^{55} - 74 q^{56} - 58 q^{61} - 40 q^{62} - 36 q^{64} - 2 q^{66} - 8 q^{68} - 42 q^{69} - 34 q^{74} - 14 q^{75} + 8 q^{77} - 14 q^{79} + 16 q^{81} - 6 q^{82} - 58 q^{87} - 10 q^{88} + 2 q^{90} - 64 q^{92} + 50 q^{94} - 54 q^{95}+O(q^{100}) \) 16 * q + 16 * q^3 + 8 * q^4 + 16 * q^9 + 2 * q^10 + 8 * q^12 - 26 * q^14 - 16 * q^17 - 2 * q^22 - 42 * q^23 - 14 * q^25 + 16 * q^27 - 58 * q^29 + 2 * q^30 - 30 * q^35 + 8 * q^36 - 62 * q^38 + 4 * q^40 - 26 * q^42 - 6 * q^43 + 4 * q^49 - 16 * q^51 - 26 * q^53 - 18 * q^55 - 74 * q^56 - 58 * q^61 - 40 * q^62 - 36 * q^64 - 2 * q^66 - 8 * q^68 - 42 * q^69 - 34 * q^74 - 14 * q^75 + 8 * q^77 - 14 * q^79 + 16 * q^81 - 6 * q^82 - 58 * q^87 - 10 * q^88 + 2 * q^90 - 64 * q^92 + 50 * q^94 - 54 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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