LMFDB - Embedded newform 8470.2.a.dd.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8470,2,Mod(1,8470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8470, 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("8470.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8470.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:	$67.6332905120$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.745749504.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 18x^{4} - 4x^{3} + 81x^{2} + 36x - 44 $ x^6 - 18x^4 - 4x^3 + 81x^2 + 36x - 44
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-2.23874$ of defining polynomial
Character	$\chi$	$=$	8470.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.23874 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.23874 q^{6} -1.00000 q^{7} +1.00000 q^{8} +2.01195 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.23874 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.23874 q^{6} -1.00000 q^{7} +1.00000 q^{8} +2.01195 q^{9} -1.00000 q^{10} +2.23874 q^{12} +5.12829 q^{13} -1.00000 q^{14} -2.23874 q^{15} +1.00000 q^{16} -6.65568 q^{17} +2.01195 q^{18} -1.15751 q^{19} -1.00000 q^{20} -2.23874 q^{21} +3.87761 q^{23} +2.23874 q^{24} +1.00000 q^{25} +5.12829 q^{26} -2.21199 q^{27} -1.00000 q^{28} +5.89442 q^{29} -2.23874 q^{30} -6.64373 q^{31} +1.00000 q^{32} -6.65568 q^{34} +1.00000 q^{35} +2.01195 q^{36} +11.8944 q^{37} -1.15751 q^{38} +11.4809 q^{39} -1.00000 q^{40} +10.4700 q^{41} -2.23874 q^{42} +1.77464 q^{43} -2.01195 q^{45} +3.87761 q^{46} +8.71479 q^{47} +2.23874 q^{48} +1.00000 q^{49} +1.00000 q^{50} -14.9003 q^{51} +5.12829 q^{52} +8.28476 q^{53} -2.21199 q^{54} -1.00000 q^{56} -2.59135 q^{57} +5.89442 q^{58} -10.2614 q^{59} -2.23874 q^{60} -12.8132 q^{61} -6.64373 q^{62} -2.01195 q^{63} +1.00000 q^{64} -5.12829 q^{65} +14.9682 q^{67} -6.65568 q^{68} +8.68095 q^{69} +1.00000 q^{70} +7.76716 q^{71} +2.01195 q^{72} -2.54037 q^{73} +11.8944 q^{74} +2.23874 q^{75} -1.15751 q^{76} +11.4809 q^{78} +10.2605 q^{79} -1.00000 q^{80} -10.9879 q^{81} +10.4700 q^{82} -6.86423 q^{83} -2.23874 q^{84} +6.65568 q^{85} +1.77464 q^{86} +13.1961 q^{87} +15.1923 q^{89} -2.01195 q^{90} -5.12829 q^{91} +3.87761 q^{92} -14.8736 q^{93} +8.71479 q^{94} +1.15751 q^{95} +2.23874 q^{96} -0.406766 q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 6 q^{7} + 6 q^{8} + 18 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 - 6 * q^7 + 6 * q^8 + 18 * q^9	$ 6 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 6 q^{7} + 6 q^{8} + 18 q^{9} - 6 q^{10} - 6 q^{14} + 6 q^{16} - 6 q^{17} + 18 q^{18} - 6 q^{20} + 6 q^{25} - 12 q^{27} - 6 q^{28} - 12 q^{29} + 6 q^{32} - 6 q^{34} + 6 q^{35} + 18 q^{36} + 24 q^{37} + 24 q^{39} - 6 q^{40} - 12 q^{41} + 18 q^{43} - 18 q^{45} + 24 q^{47} + 6 q^{49} + 6 q^{50} + 12 q^{51} + 36 q^{53} - 12 q^{54} - 6 q^{56} + 12 q^{57} - 12 q^{58} + 30 q^{59} - 36 q^{61} - 18 q^{63} + 6 q^{64} - 12 q^{67} - 6 q^{68} + 6 q^{70} + 6 q^{71} + 18 q^{72} + 6 q^{73} + 24 q^{74} + 24 q^{78} + 24 q^{79} - 6 q^{80} + 54 q^{81} - 12 q^{82} - 24 q^{83} + 6 q^{85} + 18 q^{86} + 24 q^{87} + 36 q^{89} - 18 q^{90} + 24 q^{94} + 6 q^{98}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 - 6 * q^7 + 6 * q^8 + 18 * q^9 - 6 * q^10 - 6 * q^14 + 6 * q^16 - 6 * q^17 + 18 * q^18 - 6 * q^20 + 6 * q^25 - 12 * q^27 - 6 * q^28 - 12 * q^29 + 6 * q^32 - 6 * q^34 + 6 * q^35 + 18 * q^36 + 24 * q^37 + 24 * q^39 - 6 * q^40 - 12 * q^41 + 18 * q^43 - 18 * q^45 + 24 * q^47 + 6 * q^49 + 6 * q^50 + 12 * q^51 + 36 * q^53 - 12 * q^54 - 6 * q^56 + 12 * q^57 - 12 * q^58 + 30 * q^59 - 36 * q^61 - 18 * q^63 + 6 * q^64 - 12 * q^67 - 6 * q^68 + 6 * q^70 + 6 * q^71 + 18 * q^72 + 6 * q^73 + 24 * q^74 + 24 * q^78 + 24 * q^79 - 6 * q^80 + 54 * q^81 - 12 * q^82 - 24 * q^83 + 6 * q^85 + 18 * q^86 + 24 * q^87 + 36 * q^89 - 18 * q^90 + 24 * q^94 + 6 * q^98

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.23874	1.29254	0.646268	−	0.763111i	$-0.276329\pi$
$3$	2.23874	1.29254	0.646268	+	0.763111i	$0.276329\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.23874	0.913961
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	2.01195	0.670649
$10$	−1.00000	−0.316228
$11$	0	0
$11$	0	0
$12$	2.23874	0.646268
$13$	5.12829	1.42233	0.711167	−	0.703024i	$-0.248167\pi$
$13$	5.12829	1.42233	0.711167	+	0.703024i	$0.248167\pi$
$14$	−1.00000	−0.267261
$15$	−2.23874	−0.578040
$16$	1.00000	0.250000
$17$	−6.65568	−1.61424	−0.807119	−	0.590388i	$-0.798975\pi$
$17$	−6.65568	−1.61424	−0.807119	+	0.590388i	$0.798975\pi$
$18$	2.01195	0.474221
$19$	−1.15751	−0.265550	−0.132775	−	0.991146i	$-0.542389\pi$
$19$	−1.15751	−0.265550	−0.132775	+	0.991146i	$0.542389\pi$
$20$	−1.00000	−0.223607
$21$	−2.23874	−0.488533
$22$	0	0
$23$	3.87761	0.808537	0.404269	−	0.914640i	$-0.367526\pi$
$23$	3.87761	0.808537	0.404269	+	0.914640i	$0.367526\pi$
$24$	2.23874	0.456981
$25$	1.00000	0.200000
$26$	5.12829	1.00574
$27$	−2.21199	−0.425697
$28$	−1.00000	−0.188982
$29$	5.89442	1.09457	0.547283	−	0.836948i	$-0.315662\pi$
$29$	5.89442	1.09457	0.547283	+	0.836948i	$0.315662\pi$
$30$	−2.23874	−0.408736
$31$	−6.64373	−1.19325	−0.596624	−	0.802521i	$-0.703492\pi$
$31$	−6.64373	−1.19325	−0.596624	+	0.802521i	$0.703492\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−6.65568	−1.14144
$35$	1.00000	0.169031
$36$	2.01195	0.335325
$37$	11.8944	1.95543	0.977715	−	0.209937i	$-0.0673259\pi$
$37$	11.8944	1.95543	0.977715	+	0.209937i	$0.0673259\pi$
$38$	−1.15751	−0.187772
$39$	11.4809	1.83842
$40$	−1.00000	−0.158114
$41$	10.4700	1.63514	0.817570	−	0.575829i	$-0.195321\pi$
$41$	10.4700	1.63514	0.817570	+	0.575829i	$0.195321\pi$
$42$	−2.23874	−0.345445
$43$	1.77464	0.270630	0.135315	−	0.990803i	$-0.456795\pi$
$43$	1.77464	0.270630	0.135315	+	0.990803i	$0.456795\pi$
$44$	0	0
$45$	−2.01195	−0.299924
$46$	3.87761	0.571722
$47$	8.71479	1.27118	0.635591	−	0.772026i	$-0.280756\pi$
$47$	8.71479	1.27118	0.635591	+	0.772026i	$0.280756\pi$
$48$	2.23874	0.323134
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	−14.9003	−2.08646
$52$	5.12829	0.711167
$53$	8.28476	1.13800	0.568999	−	0.822338i	$-0.307331\pi$
$53$	8.28476	1.13800	0.568999	+	0.822338i	$0.307331\pi$
$54$	−2.21199	−0.301014
$55$	0	0
$56$	−1.00000	−0.133631
$57$	−2.59135	−0.343233
$58$	5.89442	0.773975
$59$	−10.2614	−1.33593	−0.667963	−	0.744194i	$-0.732834\pi$
$59$	−10.2614	−1.33593	−0.667963	+	0.744194i	$0.732834\pi$
$60$	−2.23874	−0.289020
$61$	−12.8132	−1.64056	−0.820280	−	0.571962i	$-0.806182\pi$
$61$	−12.8132	−1.64056	−0.820280	+	0.571962i	$0.806182\pi$
$62$	−6.64373	−0.843754
$63$	−2.01195	−0.253482
$64$	1.00000	0.125000
$65$	−5.12829	−0.636087
$66$	0	0
$67$	14.9682	1.82865	0.914327	−	0.404977i	$-0.132720\pi$
$67$	14.9682	1.82865	0.914327	+	0.404977i	$0.132720\pi$
$68$	−6.65568	−0.807119
$69$	8.68095	1.04506
$70$	1.00000	0.119523
$71$	7.76716	0.921793	0.460896	−	0.887454i	$-0.347528\pi$
$71$	7.76716	0.921793	0.460896	+	0.887454i	$0.347528\pi$
$72$	2.01195	0.237110
$73$	−2.54037	−0.297328	−0.148664	−	0.988888i	$-0.547497\pi$
$73$	−2.54037	−0.297328	−0.148664	+	0.988888i	$0.547497\pi$
$74$	11.8944	1.38270
$75$	2.23874	0.258507
$76$	−1.15751	−0.132775
$77$	0	0
$78$	11.4809	1.29996
$79$	10.2605	1.15439	0.577197	−	0.816605i	$-0.304146\pi$
$79$	10.2605	1.15439	0.577197	+	0.816605i	$0.304146\pi$
$80$	−1.00000	−0.111803
$81$	−10.9879	−1.22088
$82$	10.4700	1.15622
$83$	−6.86423	−0.753448	−0.376724	−	0.926326i	$-0.622949\pi$
$83$	−6.86423	−0.753448	−0.376724	+	0.926326i	$0.622949\pi$
$84$	−2.23874	−0.244266
$85$	6.65568	0.721910
$86$	1.77464	0.191364
$87$	13.1961	1.41477
$88$	0	0
$89$	15.1923	1.61038	0.805188	−	0.593019i	$-0.202064\pi$
$89$	15.1923	1.61038	0.805188	+	0.593019i	$0.202064\pi$
$90$	−2.01195	−0.212078
$91$	−5.12829	−0.537591
$92$	3.87761	0.404269
$93$	−14.8736	−1.54232
$94$	8.71479	0.898862
$95$	1.15751	0.118758
$96$	2.23874	0.228490
$97$	−0.406766	−0.0413008	−0.0206504	−	0.999787i	$-0.506574\pi$
$97$	−0.406766	−0.0413008	−0.0206504	+	0.999787i	$0.506574\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	0.964155	0.0959370	0.0479685	−	0.998849i	$-0.484725\pi$
$101$	0.964155	0.0959370	0.0479685	+	0.998849i	$0.484725\pi$
$102$	−14.9003	−1.47535
$103$	12.4021	1.22202	0.611010	−	0.791623i	$-0.290764\pi$
$103$	12.4021	1.22202	0.611010	+	0.791623i	$0.290764\pi$
$104$	5.12829	0.502871
$105$	2.23874	0.218478
$106$	8.28476	0.804687
$107$	11.3466	1.09691	0.548457	−	0.836179i	$-0.315215\pi$
$107$	11.3466	1.09691	0.548457	+	0.836179i	$0.315215\pi$
$108$	−2.21199	−0.212849
$109$	−9.81672	−0.940271	−0.470135	−	0.882594i	$-0.655795\pi$
$109$	−9.81672	−0.940271	−0.470135	+	0.882594i	$0.655795\pi$
$110$	0	0
$111$	26.6285	2.52746
$112$	−1.00000	−0.0944911
$113$	−15.4263	−1.45118	−0.725591	−	0.688126i	$-0.758433\pi$
$113$	−15.4263	−1.45118	−0.725591	+	0.688126i	$0.758433\pi$
$114$	−2.59135	−0.242702
$115$	−3.87761	−0.361589
$116$	5.89442	0.547283
$117$	10.3179	0.953887
$118$	−10.2614	−0.944643
$119$	6.65568	0.610125
$120$	−2.23874	−0.204368
$121$	0	0
$122$	−12.8132	−1.16005
$123$	23.4396	2.11348
$124$	−6.64373	−0.596624
$125$	−1.00000	−0.0894427
$126$	−2.01195	−0.179239
$127$	15.5058	1.37592	0.687961	−	0.725748i	$-0.258506\pi$
$127$	15.5058	1.37592	0.687961	+	0.725748i	$0.258506\pi$
$128$	1.00000	0.0883883
$129$	3.97295	0.349798
$130$	−5.12829	−0.449781
$131$	−16.5157	−1.44299	−0.721493	−	0.692421i	$-0.756544\pi$
$131$	−16.5157	−1.44299	−0.721493	+	0.692421i	$0.756544\pi$
$132$	0	0
$133$	1.15751	0.100368
$134$	14.9682	1.29305
$135$	2.21199	0.190378
$136$	−6.65568	−0.570720
$137$	13.8267	1.18129	0.590646	−	0.806931i	$-0.298873\pi$
$137$	13.8267	1.18129	0.590646	+	0.806931i	$0.298873\pi$
$138$	8.68095	0.738971
$139$	1.19890	0.101689	0.0508445	−	0.998707i	$-0.483809\pi$
$139$	1.19890	0.101689	0.0508445	+	0.998707i	$0.483809\pi$
$140$	1.00000	0.0845154
$141$	19.5101	1.64305
$142$	7.76716	0.651806
$143$	0	0
$144$	2.01195	0.167662
$145$	−5.89442	−0.489505
$146$	−2.54037	−0.210243
$147$	2.23874	0.184648
$148$	11.8944	0.977715
$149$	−5.37555	−0.440382	−0.220191	−	0.975457i	$-0.570668\pi$
$149$	−5.37555	−0.440382	−0.220191	+	0.975457i	$0.570668\pi$
$150$	2.23874	0.182792
$151$	1.95930	0.159445	0.0797226	−	0.996817i	$-0.474597\pi$
$151$	1.95930	0.159445	0.0797226	+	0.996817i	$0.474597\pi$
$152$	−1.15751	−0.0938861
$153$	−13.3909	−1.08259
$154$	0	0
$155$	6.64373	0.533637
$156$	11.4809	0.919208
$157$	13.1054	1.04593	0.522964	−	0.852355i	$-0.324826\pi$
$157$	13.1054	1.04593	0.522964	+	0.852355i	$0.324826\pi$
$158$	10.2605	0.816280
$159$	18.5474	1.47090
$160$	−1.00000	−0.0790569
$161$	−3.87761	−0.305598
$162$	−10.9879	−0.863292
$163$	−21.5818	−1.69041	−0.845207	−	0.534438i	$-0.820523\pi$
$163$	−21.5818	−1.69041	−0.845207	+	0.534438i	$0.820523\pi$
$164$	10.4700	0.817570
$165$	0	0
$166$	−6.86423	−0.532768
$167$	0.900461	0.0696797	0.0348399	−	0.999393i	$-0.488908\pi$
$167$	0.900461	0.0696797	0.0348399	+	0.999393i	$0.488908\pi$
$168$	−2.23874	−0.172722
$169$	13.2994	1.02303
$170$	6.65568	0.510467
$171$	−2.32884	−0.178091
$172$	1.77464	0.135315
$173$	−14.9963	−1.14015	−0.570075	−	0.821592i	$-0.693086\pi$
$173$	−14.9963	−1.14015	−0.570075	+	0.821592i	$0.693086\pi$
$174$	13.1961	1.00039
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	−22.9727	−1.72673
$178$	15.1923	1.13871
$179$	10.7148	0.800861	0.400430	−	0.916327i	$-0.368861\pi$
$179$	10.7148	0.800861	0.400430	+	0.916327i	$0.368861\pi$
$180$	−2.01195	−0.149962
$181$	−6.20078	−0.460900	−0.230450	−	0.973084i	$-0.574020\pi$
$181$	−6.20078	−0.460900	−0.230450	+	0.973084i	$0.574020\pi$
$182$	−5.12829	−0.380134
$183$	−28.6854	−2.12048
$184$	3.87761	0.285861
$185$	−11.8944	−0.874495
$186$	−14.8736	−1.09058
$187$	0	0
$188$	8.71479	0.635591
$189$	2.21199	0.160899
$190$	1.15751	0.0839743
$191$	−0.133153	−0.00963464	−0.00481732	−	0.999988i	$-0.501533\pi$
$191$	−0.133153	−0.00963464	−0.00481732	+	0.999988i	$0.501533\pi$
$192$	2.23874	0.161567
$193$	−12.7468	−0.917531	−0.458766	−	0.888557i	$-0.651708\pi$
$193$	−12.7468	−0.917531	−0.458766	+	0.888557i	$0.651708\pi$
$194$	−0.406766	−0.0292041
$195$	−11.4809	−0.822165
$196$	1.00000	0.0714286
$197$	4.39162	0.312890	0.156445	−	0.987687i	$-0.449997\pi$
$197$	4.39162	0.312890	0.156445	+	0.987687i	$0.449997\pi$
$198$	0	0
$199$	−0.430314	−0.0305041	−0.0152521	−	0.999884i	$-0.504855\pi$
$199$	−0.430314	−0.0305041	−0.0152521	+	0.999884i	$0.504855\pi$
$200$	1.00000	0.0707107
$201$	33.5098	2.36360
$202$	0.964155	0.0678377
$203$	−5.89442	−0.413707
$204$	−14.9003	−1.04323
$205$	−10.4700	−0.731257
$206$	12.4021	0.864098
$207$	7.80155	0.542245
$208$	5.12829	0.355583
$209$	0	0
$210$	2.23874	0.154488
$211$	−8.33737	−0.573968	−0.286984	−	0.957935i	$-0.592653\pi$
$211$	−8.33737	−0.573968	−0.286984	+	0.957935i	$0.592653\pi$
$212$	8.28476	0.568999
$213$	17.3886	1.19145
$214$	11.3466	0.775635
$215$	−1.77464	−0.121029
$216$	−2.21199	−0.150507
$217$	6.64373	0.451006
$218$	−9.81672	−0.664872
$219$	−5.68723	−0.384308
$220$	0	0
$221$	−34.1323	−2.29599
$222$	26.6285	1.78719
$223$	1.13218	0.0758166	0.0379083	−	0.999281i	$-0.487931\pi$
$223$	1.13218	0.0758166	0.0379083	+	0.999281i	$0.487931\pi$
$224$	−1.00000	−0.0668153
$225$	2.01195	0.134130
$226$	−15.4263	−1.02614
$227$	−10.2741	−0.681915	−0.340957	−	0.940079i	$-0.610751\pi$
$227$	−10.2741	−0.681915	−0.340957	+	0.940079i	$0.610751\pi$
$228$	−2.59135	−0.171616
$229$	−9.23127	−0.610019	−0.305010	−	0.952349i	$-0.598660\pi$
$229$	−9.23127	−0.610019	−0.305010	+	0.952349i	$0.598660\pi$
$230$	−3.87761	−0.255682
$231$	0	0
$232$	5.89442	0.386987
$233$	−6.68548	−0.437980	−0.218990	−	0.975727i	$-0.570276\pi$
$233$	−6.68548	−0.437980	−0.218990	+	0.975727i	$0.570276\pi$
$234$	10.3179	0.674500
$235$	−8.71479	−0.568490
$236$	−10.2614	−0.667963
$237$	22.9705	1.49210
$238$	6.65568	0.431423
$239$	−22.4534	−1.45239	−0.726193	−	0.687490i	$-0.758712\pi$
$239$	−22.4534	−1.45239	−0.726193	+	0.687490i	$0.758712\pi$
$240$	−2.23874	−0.144510
$241$	−28.6046	−1.84258	−0.921292	−	0.388872i	$-0.872865\pi$
$241$	−28.6046	−1.84258	−0.921292	+	0.388872i	$0.872865\pi$
$242$	0	0
$243$	−17.9631	−1.15233
$244$	−12.8132	−0.820280
$245$	−1.00000	−0.0638877
$246$	23.4396	1.49445
$247$	−5.93603	−0.377701
$248$	−6.64373	−0.421877
$249$	−15.3672	−0.973858
$250$	−1.00000	−0.0632456
$251$	25.4351	1.60545	0.802725	−	0.596349i	$-0.203383\pi$
$251$	25.4351	1.60545	0.802725	+	0.596349i	$0.203383\pi$
$252$	−2.01195	−0.126741
$253$	0	0
$254$	15.5058	0.972924
$255$	14.9003	0.933094
$256$	1.00000	0.0625000
$257$	−24.9567	−1.55676	−0.778379	−	0.627795i	$-0.783958\pi$
$257$	−24.9567	−1.55676	−0.778379	+	0.627795i	$0.783958\pi$
$258$	3.97295	0.247345
$259$	−11.8944	−0.739083
$260$	−5.12829	−0.318043
$261$	11.8593	0.734070
$262$	−16.5157	−1.02035
$263$	−0.333627	−0.0205723	−0.0102862	−	0.999947i	$-0.503274\pi$
$263$	−0.333627	−0.0205723	−0.0102862	+	0.999947i	$0.503274\pi$
$264$	0	0
$265$	−8.28476	−0.508929
$266$	1.15751	0.0709712
$267$	34.0115	2.08147
$268$	14.9682	0.914327
$269$	1.82597	0.111331	0.0556656	−	0.998449i	$-0.482272\pi$
$269$	1.82597	0.111331	0.0556656	+	0.998449i	$0.482272\pi$
$270$	2.21199	0.134617
$271$	13.3284	0.809642	0.404821	−	0.914396i	$-0.367334\pi$
$271$	13.3284	0.809642	0.404821	+	0.914396i	$0.367334\pi$
$272$	−6.65568	−0.403560
$273$	−11.4809	−0.694856
$274$	13.8267	0.835299
$275$	0	0
$276$	8.68095	0.522532
$277$	−15.4834	−0.930306	−0.465153	−	0.885230i	$-0.654001\pi$
$277$	−15.4834	−0.930306	−0.465153	+	0.885230i	$0.654001\pi$
$278$	1.19890	0.0719050
$279$	−13.3668	−0.800252
$280$	1.00000	0.0597614
$281$	28.3105	1.68886	0.844432	−	0.535663i	$-0.179938\pi$
$281$	28.3105	1.68886	0.844432	+	0.535663i	$0.179938\pi$
$282$	19.5101	1.16181
$283$	13.5891	0.807791	0.403895	−	0.914805i	$-0.367656\pi$
$283$	13.5891	0.807791	0.403895	+	0.914805i	$0.367656\pi$
$284$	7.76716	0.460896
$285$	2.59135	0.153498
$286$	0	0
$287$	−10.4700	−0.618025
$288$	2.01195	0.118555
$289$	27.2980	1.60577
$290$	−5.89442	−0.346132
$291$	−0.910642	−0.0533828
$292$	−2.54037	−0.148664
$293$	1.83423	0.107157	0.0535785	−	0.998564i	$-0.482937\pi$
$293$	1.83423	0.107157	0.0535785	+	0.998564i	$0.482937\pi$
$294$	2.23874	0.130566
$295$	10.2614	0.597445
$296$	11.8944	0.691349
$297$	0	0
$298$	−5.37555	−0.311397
$299$	19.8855	1.15001
$300$	2.23874	0.129254
$301$	−1.77464	−0.102288
$302$	1.95930	0.112745
$303$	2.15849	0.124002
$304$	−1.15751	−0.0663875
$305$	12.8132	0.733681
$306$	−13.3909	−0.765506
$307$	8.45358	0.482471	0.241236	−	0.970467i	$-0.422447\pi$
$307$	8.45358	0.482471	0.241236	+	0.970467i	$0.422447\pi$
$308$	0	0
$309$	27.7652	1.57950
$310$	6.64373	0.377338
$311$	16.9898	0.963402	0.481701	−	0.876336i	$-0.340019\pi$
$311$	16.9898	0.963402	0.481701	+	0.876336i	$0.340019\pi$
$312$	11.4809	0.649978
$313$	18.0862	1.02230	0.511148	−	0.859493i	$-0.329221\pi$
$313$	18.0862	1.02230	0.511148	+	0.859493i	$0.329221\pi$
$314$	13.1054	0.739583
$315$	2.01195	0.113360
$316$	10.2605	0.577197
$317$	−0.393194	−0.0220840	−0.0110420	−	0.999939i	$-0.503515\pi$
$317$	−0.393194	−0.0220840	−0.0110420	+	0.999939i	$0.503515\pi$
$318$	18.5474	1.04009
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	25.4020	1.41780
$322$	−3.87761	−0.216091
$323$	7.70398	0.428661
$324$	−10.9879	−0.610439
$325$	5.12829	0.284467
$326$	−21.5818	−1.19530
$327$	−21.9771	−1.21533
$328$	10.4700	0.578109
$329$	−8.71479	−0.480462
$330$	0	0
$331$	−34.5395	−1.89846	−0.949232	−	0.314577i	$-0.898137\pi$
$331$	−34.5395	−1.89846	−0.949232	+	0.314577i	$0.898137\pi$
$332$	−6.86423	−0.376724
$333$	23.9309	1.31141
$334$	0.900461	0.0492710
$335$	−14.9682	−0.817799
$336$	−2.23874	−0.122133
$337$	2.36075	0.128598	0.0642991	−	0.997931i	$-0.479519\pi$
$337$	2.36075	0.128598	0.0642991	+	0.997931i	$0.479519\pi$
$338$	13.2994	0.723392
$339$	−34.5354	−1.87570
$340$	6.65568	0.360955
$341$	0	0
$342$	−2.32884	−0.125929
$343$	−1.00000	−0.0539949
$344$	1.77464	0.0956820
$345$	−8.68095	−0.467367
$346$	−14.9963	−0.806208
$347$	−6.85646	−0.368074	−0.184037	−	0.982919i	$-0.558917\pi$
$347$	−6.85646	−0.368074	−0.184037	+	0.982919i	$0.558917\pi$
$348$	13.1961	0.707383
$349$	−8.34033	−0.446448	−0.223224	−	0.974767i	$-0.571658\pi$
$349$	−8.34033	−0.446448	−0.223224	+	0.974767i	$0.571658\pi$
$350$	−1.00000	−0.0534522
$351$	−11.3437	−0.605484
$352$	0	0
$353$	19.7691	1.05220	0.526101	−	0.850422i	$-0.323653\pi$
$353$	19.7691	1.05220	0.526101	+	0.850422i	$0.323653\pi$
$354$	−22.9727	−1.22098
$355$	−7.76716	−0.412238
$356$	15.1923	0.805188
$357$	14.9003	0.788608
$358$	10.7148	0.566294
$359$	0.257703	0.0136010	0.00680051	−	0.999977i	$-0.497835\pi$
$359$	0.257703	0.0136010	0.00680051	+	0.999977i	$0.497835\pi$
$360$	−2.01195	−0.106039
$361$	−17.6602	−0.929483
$362$	−6.20078	−0.325906
$363$	0	0
$364$	−5.12829	−0.268796
$365$	2.54037	0.132969
$366$	−28.6854	−1.49941
$367$	25.6755	1.34025	0.670125	−	0.742248i	$-0.266241\pi$
$367$	25.6755	1.34025	0.670125	+	0.742248i	$0.266241\pi$
$368$	3.87761	0.202134
$369$	21.0651	1.09661
$370$	−11.8944	−0.618361
$371$	−8.28476	−0.430123
$372$	−14.8736	−0.771159
$373$	−5.70957	−0.295631	−0.147815	−	0.989015i	$-0.547224\pi$
$373$	−5.70957	−0.295631	−0.147815	+	0.989015i	$0.547224\pi$
$374$	0	0
$375$	−2.23874	−0.115608
$376$	8.71479	0.449431
$377$	30.2283	1.55684
$378$	2.21199	0.113772
$379$	2.16686	0.111304	0.0556520	−	0.998450i	$-0.482276\pi$
$379$	2.16686	0.111304	0.0556520	+	0.998450i	$0.482276\pi$
$380$	1.15751	0.0593788
$381$	34.7135	1.77843
$382$	−0.133153	−0.00681272
$383$	10.3043	0.526523	0.263262	−	0.964725i	$-0.415202\pi$
$383$	10.3043	0.526523	0.263262	+	0.964725i	$0.415202\pi$
$384$	2.23874	0.114245
$385$	0	0
$386$	−12.7468	−0.648793
$387$	3.57048	0.181498
$388$	−0.406766	−0.0206504
$389$	5.86030	0.297129	0.148564	−	0.988903i	$-0.452535\pi$
$389$	5.86030	0.297129	0.148564	+	0.988903i	$0.452535\pi$
$390$	−11.4809	−0.581358
$391$	−25.8081	−1.30517
$392$	1.00000	0.0505076
$393$	−36.9744	−1.86511
$394$	4.39162	0.221246
$395$	−10.2605	−0.516261
$396$	0	0
$397$	−9.65824	−0.484733	−0.242367	−	0.970185i	$-0.577924\pi$
$397$	−9.65824	−0.484733	−0.242367	+	0.970185i	$0.577924\pi$
$398$	−0.430314	−0.0215697
$399$	2.59135	0.129730
$400$	1.00000	0.0500000
$401$	−3.76869	−0.188199	−0.0940996	−	0.995563i	$-0.529997\pi$
$401$	−3.76869	−0.188199	−0.0940996	+	0.995563i	$0.529997\pi$
$402$	33.5098	1.67132
$403$	−34.0710	−1.69720
$404$	0.964155	0.0479685
$405$	10.9879	0.545994
$406$	−5.89442	−0.292535
$407$	0	0
$408$	−14.9003	−0.737676
$409$	7.59552	0.375575	0.187787	−	0.982210i	$-0.439868\pi$
$409$	7.59552	0.375575	0.187787	+	0.982210i	$0.439868\pi$
$410$	−10.4700	−0.517077
$411$	30.9543	1.52686
$412$	12.4021	0.611010
$413$	10.2614	0.504933
$414$	7.80155	0.383425
$415$	6.86423	0.336952
$416$	5.12829	0.251435
$417$	2.68401	0.131437
$418$	0	0
$419$	−10.0288	−0.489937	−0.244968	−	0.969531i	$-0.578778\pi$
$419$	−10.0288	−0.489937	−0.244968	+	0.969531i	$0.578778\pi$
$420$	2.23874	0.109239
$421$	−4.21566	−0.205459	−0.102729	−	0.994709i	$-0.532758\pi$
$421$	−4.21566	−0.205459	−0.102729	+	0.994709i	$0.532758\pi$
$422$	−8.33737	−0.405857
$423$	17.5337	0.852518
$424$	8.28476	0.402343
$425$	−6.65568	−0.322848
$426$	17.3886	0.842483
$427$	12.8132	0.620073
$428$	11.3466	0.548457
$429$	0	0
$430$	−1.77464	−0.0855806
$431$	−23.7780	−1.14534	−0.572672	−	0.819784i	$-0.694093\pi$
$431$	−23.7780	−1.14534	−0.572672	+	0.819784i	$0.694093\pi$
$432$	−2.21199	−0.106424
$433$	−33.5935	−1.61440	−0.807199	−	0.590279i	$-0.799018\pi$
$433$	−33.5935	−1.61440	−0.807199	+	0.590279i	$0.799018\pi$
$434$	6.64373	0.318909
$435$	−13.1961	−0.632702
$436$	−9.81672	−0.470135
$437$	−4.48835	−0.214707
$438$	−5.68723	−0.271747
$439$	−27.7198	−1.32299	−0.661496	−	0.749949i	$-0.730078\pi$
$439$	−27.7198	−1.32299	−0.661496	+	0.749949i	$0.730078\pi$
$440$	0	0
$441$	2.01195	0.0958071
$442$	−34.1323	−1.62351
$443$	28.5238	1.35521	0.677603	−	0.735427i	$-0.263019\pi$
$443$	28.5238	1.35521	0.677603	+	0.735427i	$0.263019\pi$
$444$	26.6285	1.26373
$445$	−15.1923	−0.720182
$446$	1.13218	0.0536104
$447$	−12.0344	−0.569210
$448$	−1.00000	−0.0472456
$449$	−0.982968	−0.0463891	−0.0231946	−	0.999731i	$-0.507384\pi$
$449$	−0.982968	−0.0463891	−0.0231946	+	0.999731i	$0.507384\pi$
$450$	2.01195	0.0948442
$451$	0	0
$452$	−15.4263	−0.725591
$453$	4.38635	0.206089
$454$	−10.2741	−0.482187
$455$	5.12829	0.240418
$456$	−2.59135	−0.121351
$457$	4.98742	0.233302	0.116651	−	0.993173i	$-0.462784\pi$
$457$	4.98742	0.233302	0.116651	+	0.993173i	$0.462784\pi$
$458$	−9.23127	−0.431349
$459$	14.7223	0.687177
$460$	−3.87761	−0.180794
$461$	1.28781	0.0599791	0.0299896	−	0.999550i	$-0.490453\pi$
$461$	1.28781	0.0599791	0.0299896	+	0.999550i	$0.490453\pi$
$462$	0	0
$463$	−17.4015	−0.808717	−0.404358	−	0.914601i	$-0.632505\pi$
$463$	−17.4015	−0.808717	−0.404358	+	0.914601i	$0.632505\pi$
$464$	5.89442	0.273641
$465$	14.8736	0.689745
$466$	−6.68548	−0.309699
$467$	6.97072	0.322566	0.161283	−	0.986908i	$-0.448437\pi$
$467$	6.97072	0.322566	0.161283	+	0.986908i	$0.448437\pi$
$468$	10.3179	0.476943
$469$	−14.9682	−0.691166
$470$	−8.71479	−0.401983
$471$	29.3397	1.35190
$472$	−10.2614	−0.472321
$473$	0	0
$474$	22.9705	1.05507
$475$	−1.15751	−0.0531100
$476$	6.65568	0.305062
$477$	16.6685	0.763198
$478$	−22.4534	−1.02699
$479$	−26.7035	−1.22011	−0.610056	−	0.792358i	$-0.708853\pi$
$479$	−26.7035	−1.22011	−0.610056	+	0.792358i	$0.708853\pi$
$480$	−2.23874	−0.102184
$481$	60.9981	2.78127
$482$	−28.6046	−1.30290
$483$	−8.68095	−0.394997
$484$	0	0
$485$	0.406766	0.0184703
$486$	−17.9631	−0.814822
$487$	4.32910	0.196170	0.0980851	−	0.995178i	$-0.468728\pi$
$487$	4.32910	0.196170	0.0980851	+	0.995178i	$0.468728\pi$
$488$	−12.8132	−0.580026
$489$	−48.3159	−2.18492
$490$	−1.00000	−0.0451754
$491$	12.8945	0.581923	0.290961	−	0.956735i	$-0.406025\pi$
$491$	12.8945	0.581923	0.290961	+	0.956735i	$0.406025\pi$
$492$	23.4396	1.05674
$493$	−39.2313	−1.76689
$494$	−5.93603	−0.267075
$495$	0	0
$496$	−6.64373	−0.298312
$497$	−7.76716	−0.348405
$498$	−15.3672	−0.688622
$499$	−3.01676	−0.135049	−0.0675243	−	0.997718i	$-0.521510\pi$
$499$	−3.01676	−0.135049	−0.0675243	+	0.997718i	$0.521510\pi$
$500$	−1.00000	−0.0447214
$501$	2.01590	0.0900636
$502$	25.4351	1.13523
$503$	−6.17711	−0.275424	−0.137712	−	0.990472i	$-0.543975\pi$
$503$	−6.17711	−0.275424	−0.137712	+	0.990472i	$0.543975\pi$
$504$	−2.01195	−0.0896193
$505$	−0.964155	−0.0429043
$506$	0	0
$507$	29.7739	1.32230
$508$	15.5058	0.687961
$509$	33.6703	1.49241	0.746205	−	0.665717i	$-0.231874\pi$
$509$	33.6703	1.49241	0.746205	+	0.665717i	$0.231874\pi$
$510$	14.9003	0.659797
$511$	2.54037	0.112380
$512$	1.00000	0.0441942
$513$	2.56039	0.113044
$514$	−24.9567	−1.10079
$515$	−12.4021	−0.546504
$516$	3.97295	0.174899
$517$	0	0
$518$	−11.8944	−0.522611
$519$	−33.5729	−1.47369
$520$	−5.12829	−0.224891
$521$	24.5687	1.07637	0.538187	−	0.842826i	$-0.319110\pi$
$521$	24.5687	1.07637	0.538187	+	0.842826i	$0.319110\pi$
$522$	11.8593	0.519066
$523$	44.4679	1.94444	0.972222	−	0.234059i	$-0.0752010\pi$
$523$	44.4679	1.94444	0.972222	+	0.234059i	$0.0752010\pi$
$524$	−16.5157	−0.721493
$525$	−2.23874	−0.0977065
$526$	−0.333627	−0.0145468
$527$	44.2185	1.92619
$528$	0	0
$529$	−7.96415	−0.346268
$530$	−8.28476	−0.359867
$531$	−20.6455	−0.895939
$532$	1.15751	0.0501842
$533$	53.6933	2.32571
$534$	34.0115	1.47182
$535$	−11.3466	−0.490555
$536$	14.9682	0.646527
$537$	23.9876	1.03514
$538$	1.82597	0.0787231
$539$	0	0
$540$	2.21199	0.0951888
$541$	−1.30850	−0.0562569	−0.0281284	−	0.999604i	$-0.508955\pi$
$541$	−1.30850	−0.0562569	−0.0281284	+	0.999604i	$0.508955\pi$
$542$	13.3284	0.572503
$543$	−13.8819	−0.595730
$544$	−6.65568	−0.285360
$545$	9.81672	0.420502
$546$	−11.4809	−0.491338
$547$	−17.4553	−0.746335	−0.373168	−	0.927764i	$-0.621728\pi$
$547$	−17.4553	−0.746335	−0.373168	+	0.927764i	$0.621728\pi$
$548$	13.8267	0.590646
$549$	−25.7795	−1.10024
$550$	0	0
$551$	−6.82282	−0.290662
$552$	8.68095	0.369486
$553$	−10.2605	−0.436320
$554$	−15.4834	−0.657826
$555$	−26.6285	−1.13032
$556$	1.19890	0.0508445
$557$	−0.219818	−0.00931400	−0.00465700	−	0.999989i	$-0.501482\pi$
$557$	−0.219818	−0.00931400	−0.00465700	+	0.999989i	$0.501482\pi$
$558$	−13.3668	−0.565863
$559$	9.10086	0.384925
$560$	1.00000	0.0422577
$561$	0	0
$562$	28.3105	1.19421
$563$	22.4246	0.945084	0.472542	−	0.881308i	$-0.343336\pi$
$563$	22.4246	0.945084	0.472542	+	0.881308i	$0.343336\pi$
$564$	19.5101	0.821525
$565$	15.4263	0.648988
$566$	13.5891	0.571194
$567$	10.9879	0.461449
$568$	7.76716	0.325903
$569$	3.86730	0.162126	0.0810629	−	0.996709i	$-0.474169\pi$
$569$	3.86730	0.162126	0.0810629	+	0.996709i	$0.474169\pi$
$570$	2.59135	0.108540
$571$	25.4899	1.06672	0.533360	−	0.845888i	$-0.320929\pi$
$571$	25.4899	1.06672	0.533360	+	0.845888i	$0.320929\pi$
$572$	0	0
$573$	−0.298095	−0.0124531
$574$	−10.4700	−0.437010
$575$	3.87761	0.161707
$576$	2.01195	0.0838312
$577$	−33.6011	−1.39883	−0.699415	−	0.714716i	$-0.746556\pi$
$577$	−33.6011	−1.39883	−0.699415	+	0.714716i	$0.746556\pi$
$578$	27.2980	1.13545
$579$	−28.5366	−1.18594
$580$	−5.89442	−0.244752
$581$	6.86423	0.284776
$582$	−0.910642	−0.0377473
$583$	0	0
$584$	−2.54037	−0.105121
$585$	−10.3179	−0.426591
$586$	1.83423	0.0757715
$587$	38.8396	1.60308	0.801542	−	0.597939i	$-0.204013\pi$
$587$	38.8396	1.60308	0.801542	+	0.597939i	$0.204013\pi$
$588$	2.23874	0.0923240
$589$	7.69015	0.316867
$590$	10.2614	0.422457
$591$	9.83168	0.404421
$592$	11.8944	0.488857
$593$	−29.8393	−1.22535	−0.612677	−	0.790333i	$-0.709907\pi$
$593$	−29.8393	−1.22535	−0.612677	+	0.790333i	$0.709907\pi$
$594$	0	0
$595$	−6.65568	−0.272856
$596$	−5.37555	−0.220191
$597$	−0.963359	−0.0394277
$598$	19.8855	0.813179
$599$	26.4186	1.07944	0.539718	−	0.841846i	$-0.318531\pi$
$599$	26.4186	1.07944	0.539718	+	0.841846i	$0.318531\pi$
$600$	2.23874	0.0913961
$601$	−31.2101	−1.27309	−0.636543	−	0.771241i	$-0.719636\pi$
$601$	−31.2101	−1.27309	−0.636543	+	0.771241i	$0.719636\pi$
$602$	−1.77464	−0.0723288
$603$	30.1152	1.22639
$604$	1.95930	0.0797226
$605$	0	0
$606$	2.15849	0.0876827
$607$	−29.3084	−1.18959	−0.594795	−	0.803878i	$-0.702767\pi$
$607$	−29.3084	−1.18959	−0.594795	+	0.803878i	$0.702767\pi$
$608$	−1.15751	−0.0469431
$609$	−13.1961	−0.534731
$610$	12.8132	0.518791
$611$	44.6920	1.80804
$612$	−13.3909	−0.541294
$613$	−20.1964	−0.815725	−0.407863	−	0.913043i	$-0.633726\pi$
$613$	−20.1964	−0.815725	−0.407863	+	0.913043i	$0.633726\pi$
$614$	8.45358	0.341159
$615$	−23.4396	−0.945176
$616$	0	0
$617$	−2.08426	−0.0839091	−0.0419546	−	0.999120i	$-0.513358\pi$
$617$	−2.08426	−0.0839091	−0.0419546	+	0.999120i	$0.513358\pi$
$618$	27.7652	1.11688
$619$	−3.03990	−0.122184	−0.0610919	−	0.998132i	$-0.519458\pi$
$619$	−3.03990	−0.122184	−0.0610919	+	0.998132i	$0.519458\pi$
$620$	6.64373	0.266819
$621$	−8.57723	−0.344192
$622$	16.9898	0.681228
$623$	−15.1923	−0.608665
$624$	11.4809	0.459604
$625$	1.00000	0.0400000
$626$	18.0862	0.722872
$627$	0	0
$628$	13.1054	0.522964
$629$	−79.1654	−3.15653
$630$	2.01195	0.0801579
$631$	−11.3562	−0.452081	−0.226041	−	0.974118i	$-0.572578\pi$
$631$	−11.3562	−0.452081	−0.226041	+	0.974118i	$0.572578\pi$
$632$	10.2605	0.408140
$633$	−18.6652	−0.741874
$634$	−0.393194	−0.0156157
$635$	−15.5058	−0.615331
$636$	18.5474	0.735452
$637$	5.12829	0.203190
$638$	0	0
$639$	15.6271	0.618200
$640$	−1.00000	−0.0395285
$641$	−34.4272	−1.35979	−0.679896	−	0.733308i	$-0.737975\pi$
$641$	−34.4272	−1.35979	−0.679896	+	0.733308i	$0.737975\pi$
$642$	25.4020	1.00254
$643$	−31.4442	−1.24004	−0.620020	−	0.784586i	$-0.712875\pi$
$643$	−31.4442	−1.24004	−0.620020	+	0.784586i	$0.712875\pi$
$644$	−3.87761	−0.152799
$645$	−3.97295	−0.156435
$646$	7.70398	0.303109
$647$	−48.9448	−1.92422	−0.962110	−	0.272662i	$-0.912096\pi$
$647$	−48.9448	−1.92422	−0.962110	+	0.272662i	$0.912096\pi$
$648$	−10.9879	−0.431646
$649$	0	0
$650$	5.12829	0.201148
$651$	14.8736	0.582941
$652$	−21.5818	−0.845207
$653$	−17.0563	−0.667463	−0.333732	−	0.942668i	$-0.608308\pi$
$653$	−17.0563	−0.667463	−0.333732	+	0.942668i	$0.608308\pi$
$654$	−21.9771	−0.859371
$655$	16.5157	0.645323
$656$	10.4700	0.408785
$657$	−5.11110	−0.199403
$658$	−8.71479	−0.339738
$659$	39.3755	1.53385	0.766926	−	0.641736i	$-0.221786\pi$
$659$	39.3755	1.53385	0.766926	+	0.641736i	$0.221786\pi$
$660$	0	0
$661$	−47.5548	−1.84967	−0.924833	−	0.380374i	$-0.875795\pi$
$661$	−47.5548	−1.84967	−0.924833	+	0.380374i	$0.875795\pi$
$662$	−34.5395	−1.34242
$663$	−76.4132	−2.96764
$664$	−6.86423	−0.266384
$665$	−1.15751	−0.0448861
$666$	23.9309	0.927305
$667$	22.8562	0.884997
$668$	0.900461	0.0348399
$669$	2.53466	0.0979956
$670$	−14.9682	−0.578271
$671$	0	0
$672$	−2.23874	−0.0863612
$673$	30.7041	1.18356	0.591779	−	0.806100i	$-0.298426\pi$
$673$	30.7041	1.18356	0.591779	+	0.806100i	$0.298426\pi$
$674$	2.36075	0.0909326
$675$	−2.21199	−0.0851395
$676$	13.2994	0.511516
$677$	−30.7722	−1.18267	−0.591335	−	0.806426i	$-0.701399\pi$
$677$	−30.7722	−1.18267	−0.591335	+	0.806426i	$0.701399\pi$
$678$	−34.5354	−1.32632
$679$	0.406766	0.0156102
$680$	6.65568	0.255234
$681$	−23.0010	−0.881400
$682$	0	0
$683$	−10.3871	−0.397451	−0.198726	−	0.980055i	$-0.563680\pi$
$683$	−10.3871	−0.397451	−0.198726	+	0.980055i	$0.563680\pi$
$684$	−2.32884	−0.0890455
$685$	−13.8267	−0.528289
$686$	−1.00000	−0.0381802
$687$	−20.6664	−0.788472
$688$	1.77464	0.0676574
$689$	42.4867	1.61861
$690$	−8.68095	−0.330478
$691$	20.9815	0.798175	0.399088	−	0.916913i	$-0.369327\pi$
$691$	20.9815	0.798175	0.399088	+	0.916913i	$0.369327\pi$
$692$	−14.9963	−0.570075
$693$	0	0
$694$	−6.85646	−0.260267
$695$	−1.19890	−0.0454767
$696$	13.1961	0.500195
$697$	−69.6850	−2.63951
$698$	−8.34033	−0.315686
$699$	−14.9670	−0.566105
$700$	−1.00000	−0.0377964
$701$	30.6295	1.15686	0.578431	−	0.815731i	$-0.303665\pi$
$701$	30.6295	1.15686	0.578431	+	0.815731i	$0.303665\pi$
$702$	−11.3437	−0.428142
$703$	−13.7679	−0.519264
$704$	0	0
$705$	−19.5101	−0.734794
$706$	19.7691	0.744019
$707$	−0.964155	−0.0362608
$708$	−22.9727	−0.863367
$709$	41.2618	1.54962	0.774810	−	0.632194i	$-0.217845\pi$
$709$	41.2618	1.54962	0.774810	+	0.632194i	$0.217845\pi$
$710$	−7.76716	−0.291496
$711$	20.6436	0.774194
$712$	15.1923	0.569354
$713$	−25.7618	−0.964786
$714$	14.9003	0.557630
$715$	0	0
$716$	10.7148	0.400430
$717$	−50.2672	−1.87726
$718$	0.257703	0.00961738
$719$	26.9646	1.00561	0.502804	−	0.864400i	$-0.332302\pi$
$719$	26.9646	1.00561	0.502804	+	0.864400i	$0.332302\pi$
$720$	−2.01195	−0.0749809
$721$	−12.4021	−0.461880
$722$	−17.6602	−0.657244
$723$	−64.0382	−2.38161
$724$	−6.20078	−0.230450
$725$	5.89442	0.218913
$726$	0	0
$727$	−29.0208	−1.07632	−0.538161	−	0.842842i	$-0.680881\pi$
$727$	−29.0208	−1.07632	−0.538161	+	0.842842i	$0.680881\pi$
$728$	−5.12829	−0.190067
$729$	−7.25091	−0.268552
$730$	2.54037	0.0940235
$731$	−11.8114	−0.436861
$732$	−28.6854	−1.06024
$733$	28.4461	1.05068	0.525339	−	0.850893i	$-0.323938\pi$
$733$	28.4461	1.05068	0.525339	+	0.850893i	$0.323938\pi$
$734$	25.6755	0.947700
$735$	−2.23874	−0.0825771
$736$	3.87761	0.142931
$737$	0	0
$738$	21.0651	0.775417
$739$	−24.4968	−0.901128	−0.450564	−	0.892744i	$-0.648777\pi$
$739$	−24.4968	−0.901128	−0.450564	+	0.892744i	$0.648777\pi$
$740$	−11.8944	−0.437247
$741$	−13.2892	−0.488192
$742$	−8.28476	−0.304143
$743$	−6.04973	−0.221943	−0.110972	−	0.993824i	$-0.535396\pi$
$743$	−6.04973	−0.221943	−0.110972	+	0.993824i	$0.535396\pi$
$744$	−14.8736	−0.545291
$745$	5.37555	0.196945
$746$	−5.70957	−0.209042
$747$	−13.8105	−0.505299
$748$	0	0
$749$	−11.3466	−0.414595
$750$	−2.23874	−0.0817472
$751$	5.08525	0.185564	0.0927818	−	0.995686i	$-0.470424\pi$
$751$	5.08525	0.185564	0.0927818	+	0.995686i	$0.470424\pi$
$752$	8.71479	0.317796
$753$	56.9426	2.07510
$754$	30.2283	1.10085
$755$	−1.95930	−0.0713061
$756$	2.21199	0.0804493
$757$	25.4296	0.924254	0.462127	−	0.886814i	$-0.347086\pi$
$757$	25.4296	0.924254	0.462127	+	0.886814i	$0.347086\pi$
$758$	2.16686	0.0787039
$759$	0	0
$760$	1.15751	0.0419871
$761$	41.6911	1.51130	0.755650	−	0.654976i	$-0.227321\pi$
$761$	41.6911	1.51130	0.755650	+	0.654976i	$0.227321\pi$
$762$	34.7135	1.25754
$763$	9.81672	0.355389
$764$	−0.133153	−0.00481732
$765$	13.3909	0.484148
$766$	10.3043	0.372308
$767$	−52.6237	−1.90013
$768$	2.23874	0.0807835
$769$	−14.8389	−0.535106	−0.267553	−	0.963543i	$-0.586215\pi$
$769$	−14.8389	−0.535106	−0.267553	+	0.963543i	$0.586215\pi$
$770$	0	0
$771$	−55.8716	−2.01216
$772$	−12.7468	−0.458766
$773$	25.3422	0.911497	0.455749	−	0.890109i	$-0.349372\pi$
$773$	25.3422	0.911497	0.455749	+	0.890109i	$0.349372\pi$
$774$	3.57048	0.128338
$775$	−6.64373	−0.238650
$776$	−0.406766	−0.0146020
$777$	−26.6285	−0.955291
$778$	5.86030	0.210102
$779$	−12.1191	−0.434211
$780$	−11.4809	−0.411082
$781$	0	0
$782$	−25.8081	−0.922896
$783$	−13.0384	−0.465954
$784$	1.00000	0.0357143
$785$	−13.1054	−0.467753
$786$	−36.9744	−1.31883
$787$	17.7718	0.633496	0.316748	−	0.948510i	$-0.397409\pi$
$787$	17.7718	0.633496	0.316748	+	0.948510i	$0.397409\pi$
$788$	4.39162	0.156445
$789$	−0.746903	−0.0265905
$790$	−10.2605	−0.365051
$791$	15.4263	0.548495
$792$	0	0
$793$	−65.7098	−2.33342
$794$	−9.65824	−0.342758
$795$	−18.5474	−0.657808
$796$	−0.430314	−0.0152521
$797$	−3.36014	−0.119022	−0.0595112	−	0.998228i	$-0.518954\pi$
$797$	−3.36014	−0.119022	−0.0595112	+	0.998228i	$0.518954\pi$
$798$	2.59135	0.0917329
$799$	−58.0028	−2.05199
$800$	1.00000	0.0353553
$801$	30.5661	1.08000
$802$	−3.76869	−0.133077
$803$	0	0
$804$	33.5098	1.18180
$805$	3.87761	0.136668
$806$	−34.0710	−1.20010
$807$	4.08787	0.143900
$808$	0.964155	0.0339189
$809$	−17.3076	−0.608502	−0.304251	−	0.952592i	$-0.598406\pi$
$809$	−17.3076	−0.608502	−0.304251	+	0.952592i	$0.598406\pi$
$810$	10.9879	0.386076
$811$	−12.3583	−0.433960	−0.216980	−	0.976176i	$-0.569621\pi$
$811$	−12.3583	−0.433960	−0.216980	+	0.976176i	$0.569621\pi$
$812$	−5.89442	−0.206853
$813$	29.8388	1.04649
$814$	0	0
$815$	21.5818	0.755977
$816$	−14.9003	−0.521615
$817$	−2.05415	−0.0718657
$818$	7.59552	0.265571
$819$	−10.3179	−0.360535
$820$	−10.4700	−0.365628
$821$	−5.55685	−0.193935	−0.0969677	−	0.995288i	$-0.530914\pi$
$821$	−5.55685	−0.193935	−0.0969677	+	0.995288i	$0.530914\pi$
$822$	30.9543	1.07965
$823$	−52.8246	−1.84135	−0.920676	−	0.390329i	$-0.872361\pi$
$823$	−52.8246	−1.84135	−0.920676	+	0.390329i	$0.872361\pi$
$824$	12.4021	0.432049
$825$	0	0
$826$	10.2614	0.357041
$827$	−49.4908	−1.72097	−0.860483	−	0.509480i	$-0.829838\pi$
$827$	−49.4908	−1.72097	−0.860483	+	0.509480i	$0.829838\pi$
$828$	7.80155	0.271123
$829$	−48.2163	−1.67462	−0.837311	−	0.546727i	$-0.815873\pi$
$829$	−48.2163	−1.67462	−0.837311	+	0.546727i	$0.815873\pi$
$830$	6.86423	0.238261
$831$	−34.6632	−1.20245
$832$	5.12829	0.177792
$833$	−6.65568	−0.230606
$834$	2.68401	0.0929398
$835$	−0.900461	−0.0311617
$836$	0	0
$837$	14.6959	0.507963
$838$	−10.0288	−0.346438
$839$	22.3658	0.772154	0.386077	−	0.922467i	$-0.373830\pi$
$839$	22.3658	0.772154	0.386077	+	0.922467i	$0.373830\pi$
$840$	2.23874	0.0772438
$841$	5.74413	0.198073
$842$	−4.21566	−0.145281
$843$	63.3798	2.18292
$844$	−8.33737	−0.286984
$845$	−13.2994	−0.457513
$846$	17.5337	0.602821
$847$	0	0
$848$	8.28476	0.284500
$849$	30.4225	1.04410
$850$	−6.65568	−0.228288
$851$	46.1219	1.58104
$852$	17.3886	0.595725
$853$	24.9471	0.854173	0.427087	−	0.904211i	$-0.359540\pi$
$853$	24.9471	0.854173	0.427087	+	0.904211i	$0.359540\pi$
$854$	12.8132	0.438458
$855$	2.32884	0.0796447
$856$	11.3466	0.387818
$857$	−19.7163	−0.673496	−0.336748	−	0.941595i	$-0.609327\pi$
$857$	−19.7163	−0.673496	−0.336748	+	0.941595i	$0.609327\pi$
$858$	0	0
$859$	15.4209	0.526156	0.263078	−	0.964775i	$-0.415262\pi$
$859$	15.4209	0.526156	0.263078	+	0.964775i	$0.415262\pi$
$860$	−1.77464	−0.0605146
$861$	−23.4396	−0.798819
$862$	−23.7780	−0.809881
$863$	−14.2128	−0.483810	−0.241905	−	0.970300i	$-0.577772\pi$
$863$	−14.2128	−0.483810	−0.241905	+	0.970300i	$0.577772\pi$
$864$	−2.21199	−0.0752534
$865$	14.9963	0.509891
$866$	−33.5935	−1.14155
$867$	61.1132	2.07551
$868$	6.64373	0.225503
$869$	0	0
$870$	−13.1961	−0.447388
$871$	76.7612	2.60095
$872$	−9.81672	−0.332436
$873$	−0.818392	−0.0276984
$874$	−4.48835	−0.151821
$875$	1.00000	0.0338062
$876$	−5.68723	−0.192154
$877$	6.27739	0.211972	0.105986	−	0.994368i	$-0.466200\pi$
$877$	6.27739	0.211972	0.105986	+	0.994368i	$0.466200\pi$
$878$	−27.7198	−0.935496
$879$	4.10637	0.138504
$880$	0	0
$881$	0.955481	0.0321910	0.0160955	−	0.999870i	$-0.494876\pi$
$881$	0.955481	0.0321910	0.0160955	+	0.999870i	$0.494876\pi$
$882$	2.01195	0.0677458
$883$	8.50497	0.286215	0.143107	−	0.989707i	$-0.454291\pi$
$883$	8.50497	0.286215	0.143107	+	0.989707i	$0.454291\pi$
$884$	−34.1323	−1.14799
$885$	22.9727	0.772219
$886$	28.5238	0.958276
$887$	−2.18620	−0.0734056	−0.0367028	−	0.999326i	$-0.511685\pi$
$887$	−2.18620	−0.0734056	−0.0367028	+	0.999326i	$0.511685\pi$
$888$	26.6285	0.893593
$889$	−15.5058	−0.520049
$890$	−15.1923	−0.509246
$891$	0	0
$892$	1.13218	0.0379083
$893$	−10.0874	−0.337563
$894$	−12.0344	−0.402492
$895$	−10.7148	−0.358156
$896$	−1.00000	−0.0334077
$897$	44.5185	1.48643
$898$	−0.982968	−0.0328021
$899$	−39.1609	−1.30609
$900$	2.01195	0.0670649
$901$	−55.1407	−1.83700
$902$	0	0
$903$	−3.97295	−0.132211
$904$	−15.4263	−0.513070
$905$	6.20078	0.206121
$906$	4.38635	0.145727
$907$	0.266857	0.00886082	0.00443041	−	0.999990i	$-0.498590\pi$
$907$	0.266857	0.00886082	0.00443041	+	0.999990i	$0.498590\pi$
$908$	−10.2741	−0.340957
$909$	1.93983	0.0643401
$910$	5.12829	0.170001
$911$	−20.3552	−0.674397	−0.337198	−	0.941434i	$-0.609479\pi$
$911$	−20.3552	−0.674397	−0.337198	+	0.941434i	$0.609479\pi$
$912$	−2.59135	−0.0858082
$913$	0	0
$914$	4.98742	0.164969
$915$	28.6854	0.948309
$916$	−9.23127	−0.305010
$917$	16.5157	0.545398
$918$	14.7223	0.485908
$919$	8.19185	0.270224	0.135112	−	0.990830i	$-0.456861\pi$
$919$	8.19185	0.270224	0.135112	+	0.990830i	$0.456861\pi$
$920$	−3.87761	−0.127841
$921$	18.9254	0.623612
$922$	1.28781	0.0424116
$923$	39.8323	1.31110
$924$	0	0
$925$	11.8944	0.391086
$926$	−17.4015	−0.571849
$927$	24.9525	0.819547
$928$	5.89442	0.193494
$929$	−36.0873	−1.18398	−0.591992	−	0.805943i	$-0.701658\pi$
$929$	−36.0873	−1.18398	−0.591992	+	0.805943i	$0.701658\pi$
$930$	14.8736	0.487724
$931$	−1.15751	−0.0379357
$932$	−6.68548	−0.218990
$933$	38.0357	1.24523
$934$	6.97072	0.228089
$935$	0	0
$936$	10.3179	0.337250
$937$	42.0240	1.37286	0.686432	−	0.727194i	$-0.259176\pi$
$937$	42.0240	1.37286	0.686432	+	0.727194i	$0.259176\pi$
$938$	−14.9682	−0.488728
$939$	40.4904	1.32135
$940$	−8.71479	−0.284245
$941$	−57.0071	−1.85838	−0.929189	−	0.369605i	$-0.879493\pi$
$941$	−57.0071	−1.85838	−0.929189	+	0.369605i	$0.879493\pi$
$942$	29.3397	0.955938
$943$	40.5986	1.32207
$944$	−10.2614	−0.333982
$945$	−2.21199	−0.0719560
$946$	0	0
$947$	42.6517	1.38599	0.692997	−	0.720940i	$-0.256290\pi$
$947$	42.6517	1.38599	0.692997	+	0.720940i	$0.256290\pi$
$948$	22.9705	0.746048
$949$	−13.0278	−0.422900
$950$	−1.15751	−0.0375544
$951$	−0.880257	−0.0285443
$952$	6.65568	0.215712
$953$	−11.5905	−0.375453	−0.187726	−	0.982221i	$-0.560112\pi$
$953$	−11.5905	−0.375453	−0.187726	+	0.982221i	$0.560112\pi$
$954$	16.6685	0.539663
$955$	0.133153	0.00430874
$956$	−22.4534	−0.726193
$957$	0	0
$958$	−26.7035	−0.862750
$959$	−13.8267	−0.446486
$960$	−2.23874	−0.0722550
$961$	13.1391	0.423843
$962$	60.9981	1.96666
$963$	22.8287	0.735645
$964$	−28.6046	−0.921292
$965$	12.7468	0.410332
$966$	−8.68095	−0.279305
$967$	−38.6220	−1.24200	−0.621000	−	0.783811i	$-0.713273\pi$
$967$	−38.6220	−1.24200	−0.621000	+	0.783811i	$0.713273\pi$
$968$	0	0
$969$	17.2472	0.554060
$970$	0.406766	0.0130605
$971$	−53.2173	−1.70782	−0.853912	−	0.520418i	$-0.825776\pi$
$971$	−53.2173	−1.70782	−0.853912	+	0.520418i	$0.825776\pi$
$972$	−17.9631	−0.576166
$973$	−1.19890	−0.0384348
$974$	4.32910	0.138713
$975$	11.4809	0.367683
$976$	−12.8132	−0.410140
$977$	3.80768	0.121819	0.0609093	−	0.998143i	$-0.480600\pi$
$977$	3.80768	0.121819	0.0609093	+	0.998143i	$0.480600\pi$
$978$	−48.3159	−1.54497
$979$	0	0
$980$	−1.00000	−0.0319438
$981$	−19.7507	−0.630592
$982$	12.8945	0.411481
$983$	27.5427	0.878474	0.439237	−	0.898371i	$-0.355249\pi$
$983$	27.5427	0.878474	0.439237	+	0.898371i	$0.355249\pi$
$984$	23.4396	0.747227
$985$	−4.39162	−0.139929
$986$	−39.2313	−1.24938
$987$	−19.5101	−0.621014
$988$	−5.93603	−0.188850
$989$	6.88134	0.218814
$990$	0	0
$991$	−59.3959	−1.88677	−0.943386	−	0.331697i	$-0.892379\pi$
$991$	−59.3959	−1.88677	−0.943386	+	0.331697i	$0.892379\pi$
$992$	−6.64373	−0.210939
$993$	−77.3249	−2.45383
$994$	−7.76716	−0.246360
$995$	0.430314	0.0136419
$996$	−15.3672	−0.486929
$997$	32.6231	1.03318	0.516592	−	0.856232i	$-0.327201\pi$
$997$	32.6231	1.03318	0.516592	+	0.856232i	$0.327201\pi$
$998$	−3.01676	−0.0954937
$999$	−26.3103	−0.832422

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.dd.1.5	yes	6
11.10	odd	2		8470.2.a.cx.1.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8470.2.a.cx.1.5	✓	6	11.10	odd	2
8470.2.a.dd.1.5	yes	6	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8470.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.23874 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.23874 q^{6} -1.00000 q^{7} +1.00000 q^{8} +2.01195 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.23874 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.23874 q^{6} -1.00000 q^{7} +1.00000 q^{8} +2.01195 q^{9} -1.00000 q^{10} +2.23874 q^{12} +5.12829 q^{13} -1.00000 q^{14} -2.23874 q^{15} +1.00000 q^{16} -6.65568 q^{17} +2.01195 q^{18} -1.15751 q^{19} -1.00000 q^{20} -2.23874 q^{21} +3.87761 q^{23} +2.23874 q^{24} +1.00000 q^{25} +5.12829 q^{26} -2.21199 q^{27} -1.00000 q^{28} +5.89442 q^{29} -2.23874 q^{30} -6.64373 q^{31} +1.00000 q^{32} -6.65568 q^{34} +1.00000 q^{35} +2.01195 q^{36} +11.8944 q^{37} -1.15751 q^{38} +11.4809 q^{39} -1.00000 q^{40} +10.4700 q^{41} -2.23874 q^{42} +1.77464 q^{43} -2.01195 q^{45} +3.87761 q^{46} +8.71479 q^{47} +2.23874 q^{48} +1.00000 q^{49} +1.00000 q^{50} -14.9003 q^{51} +5.12829 q^{52} +8.28476 q^{53} -2.21199 q^{54} -1.00000 q^{56} -2.59135 q^{57} +5.89442 q^{58} -10.2614 q^{59} -2.23874 q^{60} -12.8132 q^{61} -6.64373 q^{62} -2.01195 q^{63} +1.00000 q^{64} -5.12829 q^{65} +14.9682 q^{67} -6.65568 q^{68} +8.68095 q^{69} +1.00000 q^{70} +7.76716 q^{71} +2.01195 q^{72} -2.54037 q^{73} +11.8944 q^{74} +2.23874 q^{75} -1.15751 q^{76} +11.4809 q^{78} +10.2605 q^{79} -1.00000 q^{80} -10.9879 q^{81} +10.4700 q^{82} -6.86423 q^{83} -2.23874 q^{84} +6.65568 q^{85} +1.77464 q^{86} +13.1961 q^{87} +15.1923 q^{89} -2.01195 q^{90} -5.12829 q^{91} +3.87761 q^{92} -14.8736 q^{93} +8.71479 q^{94} +1.15751 q^{95} +2.23874 q^{96} -0.406766 q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 6 q^{7} + 6 q^{8} + 18 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 - 6 * q^7 + 6 * q^8 + 18 * q^9	\( 6 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 6 q^{7} + 6 q^{8} + 18 q^{9} - 6 q^{10} - 6 q^{14} + 6 q^{16} - 6 q^{17} + 18 q^{18} - 6 q^{20} + 6 q^{25} - 12 q^{27} - 6 q^{28} - 12 q^{29} + 6 q^{32} - 6 q^{34} + 6 q^{35} + 18 q^{36} + 24 q^{37} + 24 q^{39} - 6 q^{40} - 12 q^{41} + 18 q^{43} - 18 q^{45} + 24 q^{47} + 6 q^{49} + 6 q^{50} + 12 q^{51} + 36 q^{53} - 12 q^{54} - 6 q^{56} + 12 q^{57} - 12 q^{58} + 30 q^{59} - 36 q^{61} - 18 q^{63} + 6 q^{64} - 12 q^{67} - 6 q^{68} + 6 q^{70} + 6 q^{71} + 18 q^{72} + 6 q^{73} + 24 q^{74} + 24 q^{78} + 24 q^{79} - 6 q^{80} + 54 q^{81} - 12 q^{82} - 24 q^{83} + 6 q^{85} + 18 q^{86} + 24 q^{87} + 36 q^{89} - 18 q^{90} + 24 q^{94} + 6 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 - 6 * q^7 + 6 * q^8 + 18 * q^9 - 6 * q^10 - 6 * q^14 + 6 * q^16 - 6 * q^17 + 18 * q^18 - 6 * q^20 + 6 * q^25 - 12 * q^27 - 6 * q^28 - 12 * q^29 + 6 * q^32 - 6 * q^34 + 6 * q^35 + 18 * q^36 + 24 * q^37 + 24 * q^39 - 6 * q^40 - 12 * q^41 + 18 * q^43 - 18 * q^45 + 24 * q^47 + 6 * q^49 + 6 * q^50 + 12 * q^51 + 36 * q^53 - 12 * q^54 - 6 * q^56 + 12 * q^57 - 12 * q^58 + 30 * q^59 - 36 * q^61 - 18 * q^63 + 6 * q^64 - 12 * q^67 - 6 * q^68 + 6 * q^70 + 6 * q^71 + 18 * q^72 + 6 * q^73 + 24 * q^74 + 24 * q^78 + 24 * q^79 - 6 * q^80 + 54 * q^81 - 12 * q^82 - 24 * q^83 + 6 * q^85 + 18 * q^86 + 24 * q^87 + 36 * q^89 - 18 * q^90 + 24 * q^94 + 6 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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