LMFDB - Embedded newform 8470.2.a.de.1.4

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:	6.6.13298000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 10x^{4} + 3x^{3} + 26x^{2} + 13x - 1 $ x^6 - x^5 - 10x^4 + 3x^3 + 26x^2 + 13x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 770)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.42266$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.17142 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.17142 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.62777 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.17142 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.17142 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.62777 q^{9} +1.00000 q^{10} +1.17142 q^{12} +2.71483 q^{13} +1.00000 q^{14} +1.17142 q^{15} +1.00000 q^{16} -5.34260 q^{17} -1.62777 q^{18} +3.97605 q^{19} +1.00000 q^{20} +1.17142 q^{21} +5.49704 q^{23} +1.17142 q^{24} +1.00000 q^{25} +2.71483 q^{26} -5.42107 q^{27} +1.00000 q^{28} -4.99939 q^{29} +1.17142 q^{30} -2.87010 q^{31} +1.00000 q^{32} -5.34260 q^{34} +1.00000 q^{35} -1.62777 q^{36} +0.0405417 q^{37} +3.97605 q^{38} +3.18021 q^{39} +1.00000 q^{40} +5.13012 q^{41} +1.17142 q^{42} +12.2705 q^{43} -1.62777 q^{45} +5.49704 q^{46} +9.89983 q^{47} +1.17142 q^{48} +1.00000 q^{49} +1.00000 q^{50} -6.25844 q^{51} +2.71483 q^{52} +4.55880 q^{53} -5.42107 q^{54} +1.00000 q^{56} +4.65762 q^{57} -4.99939 q^{58} -0.584705 q^{59} +1.17142 q^{60} +7.25963 q^{61} -2.87010 q^{62} -1.62777 q^{63} +1.00000 q^{64} +2.71483 q^{65} -14.4148 q^{67} -5.34260 q^{68} +6.43935 q^{69} +1.00000 q^{70} +8.20815 q^{71} -1.62777 q^{72} +14.5897 q^{73} +0.0405417 q^{74} +1.17142 q^{75} +3.97605 q^{76} +3.18021 q^{78} +6.75342 q^{79} +1.00000 q^{80} -1.46704 q^{81} +5.13012 q^{82} -15.5794 q^{83} +1.17142 q^{84} -5.34260 q^{85} +12.2705 q^{86} -5.85640 q^{87} +2.73408 q^{89} -1.62777 q^{90} +2.71483 q^{91} +5.49704 q^{92} -3.36210 q^{93} +9.89983 q^{94} +3.97605 q^{95} +1.17142 q^{96} -1.32780 q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + q^{3} + 6 q^{4} + 6 q^{5} + q^{6} + 6 q^{7} + 6 q^{8} + 15 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + q^3 + 6 * q^4 + 6 * q^5 + q^6 + 6 * q^7 + 6 * q^8 + 15 * q^9	$ 6 q + 6 q^{2} + q^{3} + 6 q^{4} + 6 q^{5} + q^{6} + 6 q^{7} + 6 q^{8} + 15 q^{9} + 6 q^{10} + q^{12} + 2 q^{13} + 6 q^{14} + q^{15} + 6 q^{16} + 7 q^{17} + 15 q^{18} + 11 q^{19} + 6 q^{20} + q^{21} - 6 q^{23} + q^{24} + 6 q^{25} + 2 q^{26} + 4 q^{27} + 6 q^{28} + 2 q^{29} + q^{30} + 6 q^{32} + 7 q^{34} + 6 q^{35} + 15 q^{36} - 14 q^{37} + 11 q^{38} + 20 q^{39} + 6 q^{40} + 13 q^{41} + q^{42} + 19 q^{43} + 15 q^{45} - 6 q^{46} + 22 q^{47} + q^{48} + 6 q^{49} + 6 q^{50} - 14 q^{51} + 2 q^{52} - 10 q^{53} + 4 q^{54} + 6 q^{56} + 32 q^{57} + 2 q^{58} - 7 q^{59} + q^{60} + 22 q^{61} + 15 q^{63} + 6 q^{64} + 2 q^{65} + 5 q^{67} + 7 q^{68} - 36 q^{69} + 6 q^{70} + 8 q^{71} + 15 q^{72} + 13 q^{73} - 14 q^{74} + q^{75} + 11 q^{76} + 20 q^{78} - 16 q^{79} + 6 q^{80} + 18 q^{81} + 13 q^{82} - 5 q^{83} + q^{84} + 7 q^{85} + 19 q^{86} + 14 q^{87} + q^{89} + 15 q^{90} + 2 q^{91} - 6 q^{92} - 42 q^{93} + 22 q^{94} + 11 q^{95} + q^{96} - 3 q^{97} + 6 q^{98}+O(q^{100}) $ 6 * q + 6 * q^2 + q^3 + 6 * q^4 + 6 * q^5 + q^6 + 6 * q^7 + 6 * q^8 + 15 * q^9 + 6 * q^10 + q^12 + 2 * q^13 + 6 * q^14 + q^15 + 6 * q^16 + 7 * q^17 + 15 * q^18 + 11 * q^19 + 6 * q^20 + q^21 - 6 * q^23 + q^24 + 6 * q^25 + 2 * q^26 + 4 * q^27 + 6 * q^28 + 2 * q^29 + q^30 + 6 * q^32 + 7 * q^34 + 6 * q^35 + 15 * q^36 - 14 * q^37 + 11 * q^38 + 20 * q^39 + 6 * q^40 + 13 * q^41 + q^42 + 19 * q^43 + 15 * q^45 - 6 * q^46 + 22 * q^47 + q^48 + 6 * q^49 + 6 * q^50 - 14 * q^51 + 2 * q^52 - 10 * q^53 + 4 * q^54 + 6 * q^56 + 32 * q^57 + 2 * q^58 - 7 * q^59 + q^60 + 22 * q^61 + 15 * q^63 + 6 * q^64 + 2 * q^65 + 5 * q^67 + 7 * q^68 - 36 * q^69 + 6 * q^70 + 8 * q^71 + 15 * q^72 + 13 * q^73 - 14 * q^74 + q^75 + 11 * q^76 + 20 * q^78 - 16 * q^79 + 6 * q^80 + 18 * q^81 + 13 * q^82 - 5 * q^83 + q^84 + 7 * q^85 + 19 * q^86 + 14 * q^87 + q^89 + 15 * q^90 + 2 * q^91 - 6 * q^92 - 42 * q^93 + 22 * q^94 + 11 * q^95 + q^96 - 3 * q^97 + 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
$3$	1.17142	0.676320	0.338160	−	0.941089i	$-0.390195\pi$
$3$	1.17142	0.676320	0.338160	+	0.941089i	$0.390195\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.17142	0.478231
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−1.62777	−0.542591
$10$	1.00000	0.316228
$11$	0	0
$11$	0	0
$12$	1.17142	0.338160
$13$	2.71483	0.752958	0.376479	−	0.926425i	$-0.377135\pi$
$13$	2.71483	0.752958	0.376479	+	0.926425i	$0.377135\pi$
$14$	1.00000	0.267261
$15$	1.17142	0.302460
$16$	1.00000	0.250000
$17$	−5.34260	−1.29577	−0.647885	−	0.761738i	$-0.724346\pi$
$17$	−5.34260	−1.29577	−0.647885	+	0.761738i	$0.724346\pi$
$18$	−1.62777	−0.383670
$19$	3.97605	0.912167	0.456084	−	0.889937i	$-0.349252\pi$
$19$	3.97605	0.912167	0.456084	+	0.889937i	$0.349252\pi$
$20$	1.00000	0.223607
$21$	1.17142	0.255625
$22$	0	0
$23$	5.49704	1.14621	0.573106	−	0.819481i	$-0.305738\pi$
$23$	5.49704	1.14621	0.573106	+	0.819481i	$0.305738\pi$
$24$	1.17142	0.239115
$25$	1.00000	0.200000
$26$	2.71483	0.532422
$27$	−5.42107	−1.04329
$28$	1.00000	0.188982
$29$	−4.99939	−0.928364	−0.464182	−	0.885740i	$-0.653652\pi$
$29$	−4.99939	−0.928364	−0.464182	+	0.885740i	$0.653652\pi$
$30$	1.17142	0.213871
$31$	−2.87010	−0.515485	−0.257743	−	0.966214i	$-0.582979\pi$
$31$	−2.87010	−0.515485	−0.257743	+	0.966214i	$0.582979\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−5.34260	−0.916248
$35$	1.00000	0.169031
$36$	−1.62777	−0.271295
$37$	0.0405417	0.00666501	0.00333251	−	0.999994i	$-0.498939\pi$
$37$	0.0405417	0.00666501	0.00333251	+	0.999994i	$0.498939\pi$
$38$	3.97605	0.645000
$39$	3.18021	0.509241
$40$	1.00000	0.158114
$41$	5.13012	0.801191	0.400595	−	0.916255i	$-0.368803\pi$
$41$	5.13012	0.801191	0.400595	+	0.916255i	$0.368803\pi$
$42$	1.17142	0.180754
$43$	12.2705	1.87123	0.935617	−	0.353017i	$-0.114844\pi$
$43$	12.2705	1.87123	0.935617	+	0.353017i	$0.114844\pi$
$44$	0	0
$45$	−1.62777	−0.242654
$46$	5.49704	0.810495
$47$	9.89983	1.44404	0.722019	−	0.691873i	$-0.243214\pi$
$47$	9.89983	1.44404	0.722019	+	0.691873i	$0.243214\pi$
$48$	1.17142	0.169080
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	−6.25844	−0.876356
$52$	2.71483	0.376479
$53$	4.55880	0.626199	0.313100	−	0.949720i	$-0.398633\pi$
$53$	4.55880	0.626199	0.313100	+	0.949720i	$0.398633\pi$
$54$	−5.42107	−0.737714
$55$	0	0
$56$	1.00000	0.133631
$57$	4.65762	0.616917
$58$	−4.99939	−0.656453
$59$	−0.584705	−0.0761221	−0.0380610	−	0.999275i	$-0.512118\pi$
$59$	−0.584705	−0.0761221	−0.0380610	+	0.999275i	$0.512118\pi$
$60$	1.17142	0.151230
$61$	7.25963	0.929500	0.464750	−	0.885442i	$-0.346144\pi$
$61$	7.25963	0.929500	0.464750	+	0.885442i	$0.346144\pi$
$62$	−2.87010	−0.364503
$63$	−1.62777	−0.205080
$64$	1.00000	0.125000
$65$	2.71483	0.336733
$66$	0	0
$67$	−14.4148	−1.76105	−0.880526	−	0.473998i	$-0.842811\pi$
$67$	−14.4148	−1.76105	−0.880526	+	0.473998i	$0.842811\pi$
$68$	−5.34260	−0.647885
$69$	6.43935	0.775207
$70$	1.00000	0.119523
$71$	8.20815	0.974128	0.487064	−	0.873366i	$-0.338068\pi$
$71$	8.20815	0.974128	0.487064	+	0.873366i	$0.338068\pi$
$72$	−1.62777	−0.191835
$73$	14.5897	1.70760	0.853801	−	0.520600i	$-0.174292\pi$
$73$	14.5897	1.70760	0.853801	+	0.520600i	$0.174292\pi$
$74$	0.0405417	0.00471288
$75$	1.17142	0.135264
$76$	3.97605	0.456084
$77$	0	0
$78$	3.18021	0.360088
$79$	6.75342	0.759819	0.379910	−	0.925024i	$-0.375955\pi$
$79$	6.75342	0.759819	0.379910	+	0.925024i	$0.375955\pi$
$80$	1.00000	0.111803
$81$	−1.46704	−0.163005
$82$	5.13012	0.566527
$83$	−15.5794	−1.71006	−0.855031	−	0.518577i	$-0.826462\pi$
$83$	−15.5794	−1.71006	−0.855031	+	0.518577i	$0.826462\pi$
$84$	1.17142	0.127813
$85$	−5.34260	−0.579486
$86$	12.2705	1.32316
$87$	−5.85640	−0.627872
$88$	0	0
$89$	2.73408	0.289812	0.144906	−	0.989445i	$-0.453712\pi$
$89$	2.73408	0.289812	0.144906	+	0.989445i	$0.453712\pi$
$90$	−1.62777	−0.171582
$91$	2.71483	0.284591
$92$	5.49704	0.573106
$93$	−3.36210	−0.348633
$94$	9.89983	1.02109
$95$	3.97605	0.407934
$96$	1.17142	0.119558
$97$	−1.32780	−0.134818	−0.0674088	−	0.997725i	$-0.521473\pi$
$97$	−1.32780	−0.134818	−0.0674088	+	0.997725i	$0.521473\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	12.9533	1.28890	0.644449	−	0.764647i	$-0.277087\pi$
$101$	12.9533	1.28890	0.644449	+	0.764647i	$0.277087\pi$
$102$	−6.25844	−0.619678
$103$	9.24014	0.910458	0.455229	−	0.890374i	$-0.349557\pi$
$103$	9.24014	0.910458	0.455229	+	0.890374i	$0.349557\pi$
$104$	2.71483	0.266211
$105$	1.17142	0.114319
$106$	4.55880	0.442790
$107$	10.0022	0.966947	0.483473	−	0.875359i	$-0.339375\pi$
$107$	10.0022	0.966947	0.483473	+	0.875359i	$0.339375\pi$
$108$	−5.42107	−0.521643
$109$	−0.535064	−0.0512498	−0.0256249	−	0.999672i	$-0.508158\pi$
$109$	−0.535064	−0.0512498	−0.0256249	+	0.999672i	$0.508158\pi$
$110$	0	0
$111$	0.0474914	0.00450768
$112$	1.00000	0.0944911
$113$	−1.55217	−0.146016	−0.0730078	−	0.997331i	$-0.523260\pi$
$113$	−1.55217	−0.146016	−0.0730078	+	0.997331i	$0.523260\pi$
$114$	4.65762	0.436226
$115$	5.49704	0.512602
$116$	−4.99939	−0.464182
$117$	−4.41912	−0.408548
$118$	−0.584705	−0.0538264
$119$	−5.34260	−0.489755
$120$	1.17142	0.106936
$121$	0	0
$122$	7.25963	0.657256
$123$	6.00954	0.541862
$124$	−2.87010	−0.257743
$125$	1.00000	0.0894427
$126$	−1.62777	−0.145013
$127$	−17.2777	−1.53315	−0.766575	−	0.642155i	$-0.778041\pi$
$127$	−17.2777	−1.53315	−0.766575	+	0.642155i	$0.778041\pi$
$128$	1.00000	0.0883883
$129$	14.3739	1.26555
$130$	2.71483	0.238106
$131$	11.0180	0.962651	0.481325	−	0.876542i	$-0.340156\pi$
$131$	11.0180	0.962651	0.481325	+	0.876542i	$0.340156\pi$
$132$	0	0
$133$	3.97605	0.344767
$134$	−14.4148	−1.24525
$135$	−5.42107	−0.466572
$136$	−5.34260	−0.458124
$137$	9.48971	0.810760	0.405380	−	0.914148i	$-0.367139\pi$
$137$	9.48971	0.810760	0.405380	+	0.914148i	$0.367139\pi$
$138$	6.43935	0.548154
$139$	−10.8603	−0.921162	−0.460581	−	0.887618i	$-0.652359\pi$
$139$	−10.8603	−0.921162	−0.460581	+	0.887618i	$0.652359\pi$
$140$	1.00000	0.0845154
$141$	11.5969	0.976633
$142$	8.20815	0.688813
$143$	0	0
$144$	−1.62777	−0.135648
$145$	−4.99939	−0.415177
$146$	14.5897	1.20746
$147$	1.17142	0.0966172
$148$	0.0405417	0.00333251
$149$	12.3315	1.01024	0.505118	−	0.863050i	$-0.331449\pi$
$149$	12.3315	1.01024	0.505118	+	0.863050i	$0.331449\pi$
$150$	1.17142	0.0956462
$151$	−8.70759	−0.708613	−0.354307	−	0.935129i	$-0.615283\pi$
$151$	−8.70759	−0.708613	−0.354307	+	0.935129i	$0.615283\pi$
$152$	3.97605	0.322500
$153$	8.69653	0.703073
$154$	0	0
$155$	−2.87010	−0.230532
$156$	3.18021	0.254620
$157$	−19.1275	−1.52654	−0.763269	−	0.646081i	$-0.776407\pi$
$157$	−19.1275	−1.52654	−0.763269	+	0.646081i	$0.776407\pi$
$158$	6.75342	0.537273
$159$	5.34028	0.423511
$160$	1.00000	0.0790569
$161$	5.49704	0.433228
$162$	−1.46704	−0.115262
$163$	−18.6244	−1.45878	−0.729389	−	0.684099i	$-0.760195\pi$
$163$	−18.6244	−1.45878	−0.729389	+	0.684099i	$0.760195\pi$
$164$	5.13012	0.400595
$165$	0	0
$166$	−15.5794	−1.20920
$167$	1.66091	0.128525	0.0642624	−	0.997933i	$-0.479531\pi$
$167$	1.66091	0.128525	0.0642624	+	0.997933i	$0.479531\pi$
$168$	1.17142	0.0903771
$169$	−5.62971	−0.433054
$170$	−5.34260	−0.409759
$171$	−6.47209	−0.494933
$172$	12.2705	0.935617
$173$	−10.4055	−0.791115	−0.395557	−	0.918441i	$-0.629449\pi$
$173$	−10.4055	−0.791115	−0.395557	+	0.918441i	$0.629449\pi$
$174$	−5.85640	−0.443972
$175$	1.00000	0.0755929
$176$	0	0
$177$	−0.684935	−0.0514829
$178$	2.73408	0.204928
$179$	−25.4215	−1.90010	−0.950048	−	0.312104i	$-0.898966\pi$
$179$	−25.4215	−1.90010	−0.950048	+	0.312104i	$0.898966\pi$
$180$	−1.62777	−0.121327
$181$	−9.34641	−0.694713	−0.347357	−	0.937733i	$-0.612921\pi$
$181$	−9.34641	−0.694713	−0.347357	+	0.937733i	$0.612921\pi$
$182$	2.71483	0.201236
$183$	8.50409	0.628640
$184$	5.49704	0.405247
$185$	0.0405417	0.00298068
$186$	−3.36210	−0.246521
$187$	0	0
$188$	9.89983	0.722019
$189$	−5.42107	−0.394325
$190$	3.97605	0.288453
$191$	4.55912	0.329886	0.164943	−	0.986303i	$-0.447256\pi$
$191$	4.55912	0.329886	0.164943	+	0.986303i	$0.447256\pi$
$192$	1.17142	0.0845401
$193$	15.8146	1.13836	0.569181	−	0.822212i	$-0.307260\pi$
$193$	15.8146	1.13836	0.569181	+	0.822212i	$0.307260\pi$
$194$	−1.32780	−0.0953304
$195$	3.18021	0.227739
$196$	1.00000	0.0714286
$197$	14.6162	1.04136	0.520679	−	0.853753i	$-0.325679\pi$
$197$	14.6162	1.04136	0.520679	+	0.853753i	$0.325679\pi$
$198$	0	0
$199$	16.4255	1.16438	0.582188	−	0.813054i	$-0.302197\pi$
$199$	16.4255	1.16438	0.582188	+	0.813054i	$0.302197\pi$
$200$	1.00000	0.0707107
$201$	−16.8858	−1.19104
$202$	12.9533	0.911389
$203$	−4.99939	−0.350889
$204$	−6.25844	−0.438178
$205$	5.13012	0.358303
$206$	9.24014	0.643791
$207$	−8.94793	−0.621924
$208$	2.71483	0.188239
$209$	0	0
$210$	1.17142	0.0808358
$211$	−4.78958	−0.329728	−0.164864	−	0.986316i	$-0.552719\pi$
$211$	−4.78958	−0.329728	−0.164864	+	0.986316i	$0.552719\pi$
$212$	4.55880	0.313100
$213$	9.61520	0.658823
$214$	10.0022	0.683735
$215$	12.2705	0.836841
$216$	−5.42107	−0.368857
$217$	−2.87010	−0.194835
$218$	−0.535064	−0.0362391
$219$	17.0907	1.15489
$220$	0	0
$221$	−14.5042	−0.975661
$222$	0.0474914	0.00318741
$223$	−23.2488	−1.55685	−0.778426	−	0.627737i	$-0.783981\pi$
$223$	−23.2488	−1.55685	−0.778426	+	0.627737i	$0.783981\pi$
$224$	1.00000	0.0668153
$225$	−1.62777	−0.108518
$226$	−1.55217	−0.103249
$227$	−17.0503	−1.13167	−0.565834	−	0.824519i	$-0.691446\pi$
$227$	−17.0503	−1.13167	−0.565834	+	0.824519i	$0.691446\pi$
$228$	4.65762	0.308459
$229$	10.5051	0.694196	0.347098	−	0.937829i	$-0.387167\pi$
$229$	10.5051	0.694196	0.347098	+	0.937829i	$0.387167\pi$
$230$	5.49704	0.362464
$231$	0	0
$232$	−4.99939	−0.328226
$233$	21.0739	1.38060	0.690300	−	0.723523i	$-0.257479\pi$
$233$	21.0739	1.38060	0.690300	+	0.723523i	$0.257479\pi$
$234$	−4.41912	−0.288887
$235$	9.89983	0.645794
$236$	−0.584705	−0.0380610
$237$	7.91110	0.513881
$238$	−5.34260	−0.346309
$239$	1.21833	0.0788074	0.0394037	−	0.999223i	$-0.487454\pi$
$239$	1.21833	0.0788074	0.0394037	+	0.999223i	$0.487454\pi$
$240$	1.17142	0.0756149
$241$	−1.70364	−0.109741	−0.0548706	−	0.998493i	$-0.517475\pi$
$241$	−1.70364	−0.109741	−0.0548706	+	0.998493i	$0.517475\pi$
$242$	0	0
$243$	14.5447	0.933042
$244$	7.25963	0.464750
$245$	1.00000	0.0638877
$246$	6.00954	0.383154
$247$	10.7943	0.686824
$248$	−2.87010	−0.182252
$249$	−18.2500	−1.15655
$250$	1.00000	0.0632456
$251$	−19.2825	−1.21710	−0.608551	−	0.793515i	$-0.708249\pi$
$251$	−19.2825	−1.21710	−0.608551	+	0.793515i	$0.708249\pi$
$252$	−1.62777	−0.102540
$253$	0	0
$254$	−17.2777	−1.08410
$255$	−6.25844	−0.391918
$256$	1.00000	0.0625000
$257$	−9.96978	−0.621898	−0.310949	−	0.950427i	$-0.600647\pi$
$257$	−9.96978	−0.621898	−0.310949	+	0.950427i	$0.600647\pi$
$258$	14.3739	0.894881
$259$	0.0405417	0.00251914
$260$	2.71483	0.168367
$261$	8.13787	0.503722
$262$	11.0180	0.680697
$263$	15.3900	0.948985	0.474493	−	0.880260i	$-0.342632\pi$
$263$	15.3900	0.948985	0.474493	+	0.880260i	$0.342632\pi$
$264$	0	0
$265$	4.55880	0.280045
$266$	3.97605	0.243787
$267$	3.20276	0.196006
$268$	−14.4148	−0.880526
$269$	−16.6521	−1.01530	−0.507649	−	0.861564i	$-0.669485\pi$
$269$	−16.6521	−1.01530	−0.507649	+	0.861564i	$0.669485\pi$
$270$	−5.42107	−0.329916
$271$	−2.85449	−0.173398	−0.0866989	−	0.996235i	$-0.527632\pi$
$271$	−2.85449	−0.173398	−0.0866989	+	0.996235i	$0.527632\pi$
$272$	−5.34260	−0.323943
$273$	3.18021	0.192475
$274$	9.48971	0.573294
$275$	0	0
$276$	6.43935	0.387603
$277$	25.0469	1.50492	0.752462	−	0.658636i	$-0.228866\pi$
$277$	25.0469	1.50492	0.752462	+	0.658636i	$0.228866\pi$
$278$	−10.8603	−0.651360
$279$	4.67187	0.279698
$280$	1.00000	0.0597614
$281$	4.37825	0.261184	0.130592	−	0.991436i	$-0.458312\pi$
$281$	4.37825	0.261184	0.130592	+	0.991436i	$0.458312\pi$
$282$	11.5969	0.690584
$283$	−7.46206	−0.443573	−0.221787	−	0.975095i	$-0.571189\pi$
$283$	−7.46206	−0.443573	−0.221787	+	0.975095i	$0.571189\pi$
$284$	8.20815	0.487064
$285$	4.65762	0.275894
$286$	0	0
$287$	5.13012	0.302822
$288$	−1.62777	−0.0959174
$289$	11.5434	0.679022
$290$	−4.99939	−0.293575
$291$	−1.55541	−0.0911799
$292$	14.5897	0.853801
$293$	5.85672	0.342153	0.171077	−	0.985258i	$-0.445275\pi$
$293$	5.85672	0.342153	0.171077	+	0.985258i	$0.445275\pi$
$294$	1.17142	0.0683187
$295$	−0.584705	−0.0340428
$296$	0.0405417	0.00235644
$297$	0	0
$298$	12.3315	0.714344
$299$	14.9235	0.863050
$300$	1.17142	0.0676320
$301$	12.2705	0.707260
$302$	−8.70759	−0.501065
$303$	15.1737	0.871709
$304$	3.97605	0.228042
$305$	7.25963	0.415685
$306$	8.69653	0.497148
$307$	34.7874	1.98542	0.992712	−	0.120513i	$-0.0384540\pi$
$307$	34.7874	1.98542	0.992712	+	0.120513i	$0.0384540\pi$
$308$	0	0
$309$	10.8241	0.615761
$310$	−2.87010	−0.163011
$311$	19.5779	1.11016	0.555082	−	0.831796i	$-0.312687\pi$
$311$	19.5779	1.11016	0.555082	+	0.831796i	$0.312687\pi$
$312$	3.18021	0.180044
$313$	−12.3630	−0.698796	−0.349398	−	0.936974i	$-0.613614\pi$
$313$	−12.3630	−0.698796	−0.349398	+	0.936974i	$0.613614\pi$
$314$	−19.1275	−1.07942
$315$	−1.62777	−0.0917146
$316$	6.75342	0.379910
$317$	5.15560	0.289568	0.144784	−	0.989463i	$-0.453751\pi$
$317$	5.15560	0.289568	0.144784	+	0.989463i	$0.453751\pi$
$318$	5.34028	0.299468
$319$	0	0
$320$	1.00000	0.0559017
$321$	11.7168	0.653966
$322$	5.49704	0.306338
$323$	−21.2424	−1.18196
$324$	−1.46704	−0.0815024
$325$	2.71483	0.150592
$326$	−18.6244	−1.03151
$327$	−0.626785	−0.0346613
$328$	5.13012	0.283264
$329$	9.89983	0.545795
$330$	0	0
$331$	−32.5061	−1.78670	−0.893349	−	0.449364i	$-0.851651\pi$
$331$	−32.5061	−1.78670	−0.893349	+	0.449364i	$0.851651\pi$
$332$	−15.5794	−0.855031
$333$	−0.0659926	−0.00361637
$334$	1.66091	0.0908807
$335$	−14.4148	−0.787566
$336$	1.17142	0.0639063
$337$	−27.1277	−1.47774	−0.738870	−	0.673848i	$-0.764640\pi$
$337$	−27.1277	−1.47774	−0.738870	+	0.673848i	$0.764640\pi$
$338$	−5.62971	−0.306216
$339$	−1.81824	−0.0987534
$340$	−5.34260	−0.289743
$341$	0	0
$342$	−6.47209	−0.349971
$343$	1.00000	0.0539949
$344$	12.2705	0.661581
$345$	6.43935	0.346683
$346$	−10.4055	−0.559403
$347$	11.1959	0.601027	0.300514	−	0.953778i	$-0.402842\pi$
$347$	11.1959	0.601027	0.300514	+	0.953778i	$0.402842\pi$
$348$	−5.85640	−0.313936
$349$	−28.5841	−1.53007	−0.765035	−	0.643989i	$-0.777278\pi$
$349$	−28.5841	−1.53007	−0.765035	+	0.643989i	$0.777278\pi$
$350$	1.00000	0.0534522
$351$	−14.7173	−0.785550
$352$	0	0
$353$	4.00343	0.213081	0.106541	−	0.994308i	$-0.466023\pi$
$353$	4.00343	0.213081	0.106541	+	0.994308i	$0.466023\pi$
$354$	−0.684935	−0.0364039
$355$	8.20815	0.435643
$356$	2.73408	0.144906
$357$	−6.25844	−0.331232
$358$	−25.4215	−1.34357
$359$	−9.77677	−0.515998	−0.257999	−	0.966145i	$-0.583063\pi$
$359$	−9.77677	−0.515998	−0.257999	+	0.966145i	$0.583063\pi$
$360$	−1.62777	−0.0857911
$361$	−3.19107	−0.167951
$362$	−9.34641	−0.491237
$363$	0	0
$364$	2.71483	0.142296
$365$	14.5897	0.763662
$366$	8.50409	0.444516
$367$	−13.1201	−0.684865	−0.342432	−	0.939543i	$-0.611251\pi$
$367$	−13.1201	−0.684865	−0.342432	+	0.939543i	$0.611251\pi$
$368$	5.49704	0.286553
$369$	−8.35067	−0.434719
$370$	0.0405417	0.00210766
$371$	4.55880	0.236681
$372$	−3.36210	−0.174317
$373$	−15.2552	−0.789886	−0.394943	−	0.918706i	$-0.629236\pi$
$373$	−15.2552	−0.789886	−0.394943	+	0.918706i	$0.629236\pi$
$374$	0	0
$375$	1.17142	0.0604919
$376$	9.89983	0.510545
$377$	−13.5725	−0.699019
$378$	−5.42107	−0.278830
$379$	26.6376	1.36828	0.684141	−	0.729349i	$-0.260177\pi$
$379$	26.6376	1.36828	0.684141	+	0.729349i	$0.260177\pi$
$380$	3.97605	0.203967
$381$	−20.2395	−1.03690
$382$	4.55912	0.233265
$383$	6.81998	0.348485	0.174242	−	0.984703i	$-0.444252\pi$
$383$	6.81998	0.348485	0.174242	+	0.984703i	$0.444252\pi$
$384$	1.17142	0.0597788
$385$	0	0
$386$	15.8146	0.804944
$387$	−19.9736	−1.01531
$388$	−1.32780	−0.0674088
$389$	23.0806	1.17023	0.585117	−	0.810949i	$-0.301048\pi$
$389$	23.0806	1.17023	0.585117	+	0.810949i	$0.301048\pi$
$390$	3.18021	0.161036
$391$	−29.3685	−1.48523
$392$	1.00000	0.0505076
$393$	12.9068	0.651060
$394$	14.6162	0.736351
$395$	6.75342	0.339801
$396$	0	0
$397$	−15.6435	−0.785123	−0.392561	−	0.919726i	$-0.628411\pi$
$397$	−15.6435	−0.785123	−0.392561	+	0.919726i	$0.628411\pi$
$398$	16.4255	0.823338
$399$	4.65762	0.233173
$400$	1.00000	0.0500000
$401$	−1.51369	−0.0755900	−0.0377950	−	0.999286i	$-0.512033\pi$
$401$	−1.51369	−0.0755900	−0.0377950	+	0.999286i	$0.512033\pi$
$402$	−16.8858	−0.842189
$403$	−7.79183	−0.388139
$404$	12.9533	0.644449
$405$	−1.46704	−0.0728980
$406$	−4.99939	−0.248116
$407$	0	0
$408$	−6.25844	−0.309839
$409$	−14.2110	−0.702689	−0.351345	−	0.936246i	$-0.614275\pi$
$409$	−14.2110	−0.702689	−0.351345	+	0.936246i	$0.614275\pi$
$410$	5.13012	0.253359
$411$	11.1164	0.548334
$412$	9.24014	0.455229
$413$	−0.584705	−0.0287714
$414$	−8.94793	−0.439767
$415$	−15.5794	−0.764763
$416$	2.71483	0.133105
$417$	−12.7220	−0.623001
$418$	0	0
$419$	6.61451	0.323140	0.161570	−	0.986861i	$-0.448344\pi$
$419$	6.61451	0.323140	0.161570	+	0.986861i	$0.448344\pi$
$420$	1.17142	0.0571595
$421$	−38.2913	−1.86620	−0.933101	−	0.359614i	$-0.882908\pi$
$421$	−38.2913	−1.86620	−0.933101	+	0.359614i	$0.882908\pi$
$422$	−4.78958	−0.233153
$423$	−16.1147	−0.783522
$424$	4.55880	0.221395
$425$	−5.34260	−0.259154
$426$	9.61520	0.465858
$427$	7.25963	0.351318
$428$	10.0022	0.483473
$429$	0	0
$430$	12.2705	0.591736
$431$	6.73123	0.324232	0.162116	−	0.986772i	$-0.448168\pi$
$431$	6.73123	0.324232	0.162116	+	0.986772i	$0.448168\pi$
$432$	−5.42107	−0.260821
$433$	−25.7699	−1.23842	−0.619212	−	0.785224i	$-0.712548\pi$
$433$	−25.7699	−1.23842	−0.619212	+	0.785224i	$0.712548\pi$
$434$	−2.87010	−0.137769
$435$	−5.85640	−0.280793
$436$	−0.535064	−0.0256249
$437$	21.8565	1.04554
$438$	17.0907	0.816627
$439$	13.8131	0.659262	0.329631	−	0.944110i	$-0.393076\pi$
$439$	13.8131	0.659262	0.329631	+	0.944110i	$0.393076\pi$
$440$	0	0
$441$	−1.62777	−0.0775129
$442$	−14.5042	−0.689896
$443$	−28.1206	−1.33605	−0.668025	−	0.744139i	$-0.732860\pi$
$443$	−28.1206	−1.33605	−0.668025	+	0.744139i	$0.732860\pi$
$444$	0.0474914	0.00225384
$445$	2.73408	0.129608
$446$	−23.2488	−1.10086
$447$	14.4454	0.683243
$448$	1.00000	0.0472456
$449$	27.8576	1.31468	0.657341	−	0.753593i	$-0.271681\pi$
$449$	27.8576	1.31468	0.657341	+	0.753593i	$0.271681\pi$
$450$	−1.62777	−0.0767339
$451$	0	0
$452$	−1.55217	−0.0730078
$453$	−10.2003	−0.479250
$454$	−17.0503	−0.800210
$455$	2.71483	0.127273
$456$	4.65762	0.218113
$457$	−38.0839	−1.78149	−0.890745	−	0.454504i	$-0.849817\pi$
$457$	−38.0839	−1.78149	−0.890745	+	0.454504i	$0.849817\pi$
$458$	10.5051	0.490871
$459$	28.9626	1.35186
$460$	5.49704	0.256301
$461$	13.9251	0.648556	0.324278	−	0.945962i	$-0.394879\pi$
$461$	13.9251	0.648556	0.324278	+	0.945962i	$0.394879\pi$
$462$	0	0
$463$	−2.93872	−0.136574	−0.0682870	−	0.997666i	$-0.521753\pi$
$463$	−2.93872	−0.136574	−0.0682870	+	0.997666i	$0.521753\pi$
$464$	−4.99939	−0.232091
$465$	−3.36210	−0.155914
$466$	21.0739	0.976231
$467$	−31.8095	−1.47197	−0.735985	−	0.676998i	$-0.763280\pi$
$467$	−31.8095	−1.47197	−0.735985	+	0.676998i	$0.763280\pi$
$468$	−4.41912	−0.204274
$469$	−14.4148	−0.665615
$470$	9.89983	0.456645
$471$	−22.4063	−1.03243
$472$	−0.584705	−0.0269132
$473$	0	0
$474$	7.91110	0.363369
$475$	3.97605	0.182433
$476$	−5.34260	−0.244878
$477$	−7.42069	−0.339770
$478$	1.21833	0.0557252
$479$	37.7725	1.72587	0.862936	−	0.505314i	$-0.168623\pi$
$479$	37.7725	1.72587	0.862936	+	0.505314i	$0.168623\pi$
$480$	1.17142	0.0534678
$481$	0.110064	0.00501847
$482$	−1.70364	−0.0775988
$483$	6.43935	0.293001
$484$	0	0
$485$	−1.32780	−0.0602922
$486$	14.5447	0.659760
$487$	−9.53146	−0.431912	−0.215956	−	0.976403i	$-0.569287\pi$
$487$	−9.53146	−0.431912	−0.215956	+	0.976403i	$0.569287\pi$
$488$	7.25963	0.328628
$489$	−21.8170	−0.986601
$490$	1.00000	0.0451754
$491$	−22.2193	−1.00274	−0.501371	−	0.865232i	$-0.667171\pi$
$491$	−22.2193	−1.00274	−0.501371	+	0.865232i	$0.667171\pi$
$492$	6.00954	0.270931
$493$	26.7098	1.20295
$494$	10.7943	0.485658
$495$	0	0
$496$	−2.87010	−0.128871
$497$	8.20815	0.368186
$498$	−18.2500	−0.817804
$499$	−10.8366	−0.485112	−0.242556	−	0.970137i	$-0.577986\pi$
$499$	−10.8366	−0.485112	−0.242556	+	0.970137i	$0.577986\pi$
$500$	1.00000	0.0447214
$501$	1.94562	0.0869239
$502$	−19.2825	−0.860621
$503$	−12.2494	−0.546173	−0.273087	−	0.961989i	$-0.588045\pi$
$503$	−12.2494	−0.546173	−0.273087	+	0.961989i	$0.588045\pi$
$504$	−1.62777	−0.0725067
$505$	12.9533	0.576413
$506$	0	0
$507$	−6.59476	−0.292884
$508$	−17.2777	−0.766575
$509$	−0.295071	−0.0130788	−0.00653939	−	0.999979i	$-0.502082\pi$
$509$	−0.295071	−0.0130788	−0.00653939	+	0.999979i	$0.502082\pi$
$510$	−6.25844	−0.277128
$511$	14.5897	0.645413
$512$	1.00000	0.0441942
$513$	−21.5544	−0.951651
$514$	−9.96978	−0.439748
$515$	9.24014	0.407169
$516$	14.3739	0.632777
$517$	0	0
$518$	0.0405417	0.00178130
$519$	−12.1892	−0.535047
$520$	2.71483	0.119053
$521$	27.5697	1.20785	0.603925	−	0.797041i	$-0.293603\pi$
$521$	27.5697	1.20785	0.603925	+	0.797041i	$0.293603\pi$
$522$	8.13787	0.356185
$523$	24.2495	1.06036	0.530178	−	0.847887i	$-0.322125\pi$
$523$	24.2495	1.06036	0.530178	+	0.847887i	$0.322125\pi$
$524$	11.0180	0.481325
$525$	1.17142	0.0511250
$526$	15.3900	0.671034
$527$	15.3338	0.667951
$528$	0	0
$529$	7.21747	0.313803
$530$	4.55880	0.198022
$531$	0.951766	0.0413031
$532$	3.97605	0.172383
$533$	13.9274	0.603263
$534$	3.20276	0.138597
$535$	10.0022	0.432432
$536$	−14.4148	−0.622626
$537$	−29.7793	−1.28507
$538$	−16.6521	−0.717924
$539$	0	0
$540$	−5.42107	−0.233286
$541$	19.6382	0.844310	0.422155	−	0.906524i	$-0.361274\pi$
$541$	19.6382	0.844310	0.422155	+	0.906524i	$0.361274\pi$
$542$	−2.85449	−0.122611
$543$	−10.9486	−0.469849
$544$	−5.34260	−0.229062
$545$	−0.535064	−0.0229196
$546$	3.18021	0.136100
$547$	−0.502119	−0.0214691	−0.0107345	−	0.999942i	$-0.503417\pi$
$547$	−0.502119	−0.0214691	−0.0107345	+	0.999942i	$0.503417\pi$
$548$	9.48971	0.405380
$549$	−11.8170	−0.504338
$550$	0	0
$551$	−19.8778	−0.846823
$552$	6.43935	0.274077
$553$	6.75342	0.287185
$554$	25.0469	1.06414
$555$	0.0474914	0.00201590
$556$	−10.8603	−0.460581
$557$	2.50897	0.106308	0.0531541	−	0.998586i	$-0.483073\pi$
$557$	2.50897	0.106308	0.0531541	+	0.998586i	$0.483073\pi$
$558$	4.67187	0.197776
$559$	33.3123	1.40896
$560$	1.00000	0.0422577
$561$	0	0
$562$	4.37825	0.184685
$563$	−17.3706	−0.732086	−0.366043	−	0.930598i	$-0.619288\pi$
$563$	−17.3706	−0.732086	−0.366043	+	0.930598i	$0.619288\pi$
$564$	11.5969	0.488317
$565$	−1.55217	−0.0653002
$566$	−7.46206	−0.313654
$567$	−1.46704	−0.0616100
$568$	8.20815	0.344406
$569$	−31.7612	−1.33150	−0.665750	−	0.746175i	$-0.731888\pi$
$569$	−31.7612	−1.33150	−0.665750	+	0.746175i	$0.731888\pi$
$570$	4.65762	0.195086
$571$	7.43290	0.311057	0.155529	−	0.987831i	$-0.450292\pi$
$571$	7.43290	0.311057	0.155529	+	0.987831i	$0.450292\pi$
$572$	0	0
$573$	5.34065	0.223109
$574$	5.13012	0.214127
$575$	5.49704	0.229243
$576$	−1.62777	−0.0678238
$577$	−18.4342	−0.767426	−0.383713	−	0.923452i	$-0.625355\pi$
$577$	−18.4342	−0.767426	−0.383713	+	0.923452i	$0.625355\pi$
$578$	11.5434	0.480141
$579$	18.5256	0.769898
$580$	−4.99939	−0.207589
$581$	−15.5794	−0.646343
$582$	−1.55541	−0.0644739
$583$	0	0
$584$	14.5897	0.603728
$585$	−4.41912	−0.182708
$586$	5.85672	0.241939
$587$	10.1616	0.419413	0.209707	−	0.977764i	$-0.432749\pi$
$587$	10.1616	0.419413	0.209707	+	0.977764i	$0.432749\pi$
$588$	1.17142	0.0483086
$589$	−11.4117	−0.470209
$590$	−0.584705	−0.0240719
$591$	17.1217	0.704292
$592$	0.0405417	0.00166625
$593$	−22.2216	−0.912532	−0.456266	−	0.889844i	$-0.650813\pi$
$593$	−22.2216	−0.912532	−0.456266	+	0.889844i	$0.650813\pi$
$594$	0	0
$595$	−5.34260	−0.219025
$596$	12.3315	0.505118
$597$	19.2412	0.787491
$598$	14.9235	0.610268
$599$	9.45290	0.386235	0.193117	−	0.981176i	$-0.438140\pi$
$599$	9.45290	0.386235	0.193117	+	0.981176i	$0.438140\pi$
$600$	1.17142	0.0478231
$601$	26.9039	1.09743	0.548716	−	0.836009i	$-0.315117\pi$
$601$	26.9039	1.09743	0.548716	+	0.836009i	$0.315117\pi$
$602$	12.2705	0.500108
$603$	23.4641	0.955530
$604$	−8.70759	−0.354307
$605$	0	0
$606$	15.1737	0.616391
$607$	−17.1534	−0.696237	−0.348118	−	0.937451i	$-0.613179\pi$
$607$	−17.1534	−0.696237	−0.348118	+	0.937451i	$0.613179\pi$
$608$	3.97605	0.161250
$609$	−5.85640	−0.237313
$610$	7.25963	0.293934
$611$	26.8763	1.08730
$612$	8.69653	0.351537
$613$	37.6479	1.52059	0.760293	−	0.649580i	$-0.225055\pi$
$613$	37.6479	1.52059	0.760293	+	0.649580i	$0.225055\pi$
$614$	34.7874	1.40391
$615$	6.00954	0.242328
$616$	0	0
$617$	22.0199	0.886488	0.443244	−	0.896401i	$-0.353828\pi$
$617$	22.0199	0.886488	0.443244	+	0.896401i	$0.353828\pi$
$618$	10.8241	0.435409
$619$	30.3761	1.22092	0.610459	−	0.792047i	$-0.290985\pi$
$619$	30.3761	1.22092	0.610459	+	0.792047i	$0.290985\pi$
$620$	−2.87010	−0.115266
$621$	−29.7999	−1.19583
$622$	19.5779	0.785004
$623$	2.73408	0.109539
$624$	3.18021	0.127310
$625$	1.00000	0.0400000
$626$	−12.3630	−0.494123
$627$	0	0
$628$	−19.1275	−0.763269
$629$	−0.216598	−0.00863633
$630$	−1.62777	−0.0648520
$631$	46.9052	1.86727	0.933634	−	0.358229i	$-0.116619\pi$
$631$	46.9052	1.86727	0.933634	+	0.358229i	$0.116619\pi$
$632$	6.75342	0.268637
$633$	−5.61062	−0.223002
$634$	5.15560	0.204755
$635$	−17.2777	−0.685645
$636$	5.34028	0.211756
$637$	2.71483	0.107565
$638$	0	0
$639$	−13.3610	−0.528553
$640$	1.00000	0.0395285
$641$	−25.1252	−0.992385	−0.496192	−	0.868213i	$-0.665269\pi$
$641$	−25.1252	−0.992385	−0.496192	+	0.868213i	$0.665269\pi$
$642$	11.7168	0.462424
$643$	−24.8911	−0.981608	−0.490804	−	0.871270i	$-0.663297\pi$
$643$	−24.8911	−0.981608	−0.490804	+	0.871270i	$0.663297\pi$
$644$	5.49704	0.216614
$645$	14.3739	0.565973
$646$	−21.2424	−0.835772
$647$	40.7004	1.60010	0.800049	−	0.599934i	$-0.204807\pi$
$647$	40.7004	1.60010	0.800049	+	0.599934i	$0.204807\pi$
$648$	−1.46704	−0.0576309
$649$	0	0
$650$	2.71483	0.106484
$651$	−3.36210	−0.131771
$652$	−18.6244	−0.729389
$653$	−13.3072	−0.520752	−0.260376	−	0.965507i	$-0.583847\pi$
$653$	−13.3072	−0.520752	−0.260376	+	0.965507i	$0.583847\pi$
$654$	−0.626785	−0.0245093
$655$	11.0180	0.430510
$656$	5.13012	0.200298
$657$	−23.7488	−0.926528
$658$	9.89983	0.385936
$659$	−17.1669	−0.668726	−0.334363	−	0.942444i	$-0.608521\pi$
$659$	−17.1669	−0.668726	−0.334363	+	0.942444i	$0.608521\pi$
$660$	0	0
$661$	1.82979	0.0711705	0.0355853	−	0.999367i	$-0.488670\pi$
$661$	1.82979	0.0711705	0.0355853	+	0.999367i	$0.488670\pi$
$662$	−32.5061	−1.26339
$663$	−16.9906	−0.659859
$664$	−15.5794	−0.604598
$665$	3.97605	0.154184
$666$	−0.0659926	−0.00255716
$667$	−27.4819	−1.06410
$668$	1.66091	0.0642624
$669$	−27.2341	−1.05293
$670$	−14.4148	−0.556894
$671$	0	0
$672$	1.17142	0.0451886
$673$	−19.8563	−0.765402	−0.382701	−	0.923872i	$-0.625006\pi$
$673$	−19.8563	−0.765402	−0.382701	+	0.923872i	$0.625006\pi$
$674$	−27.1277	−1.04492
$675$	−5.42107	−0.208657
$676$	−5.62971	−0.216527
$677$	−24.8180	−0.953835	−0.476918	−	0.878948i	$-0.658246\pi$
$677$	−24.8180	−0.953835	−0.476918	+	0.878948i	$0.658246\pi$
$678$	−1.81824	−0.0698292
$679$	−1.32780	−0.0509562
$680$	−5.34260	−0.204879
$681$	−19.9731	−0.765370
$682$	0	0
$683$	7.25911	0.277762	0.138881	−	0.990309i	$-0.455649\pi$
$683$	7.25911	0.277762	0.138881	+	0.990309i	$0.455649\pi$
$684$	−6.47209	−0.247467
$685$	9.48971	0.362583
$686$	1.00000	0.0381802
$687$	12.3059	0.469499
$688$	12.2705	0.467808
$689$	12.3764	0.471502
$690$	6.43935	0.245142
$691$	−20.0175	−0.761500	−0.380750	−	0.924678i	$-0.624334\pi$
$691$	−20.0175	−0.761500	−0.380750	+	0.924678i	$0.624334\pi$
$692$	−10.4055	−0.395557
$693$	0	0
$694$	11.1959	0.424990
$695$	−10.8603	−0.411956
$696$	−5.85640	−0.221986
$697$	−27.4082	−1.03816
$698$	−28.5841	−1.08192
$699$	24.6865	0.933728
$700$	1.00000	0.0377964
$701$	−41.0871	−1.55184	−0.775920	−	0.630831i	$-0.782714\pi$
$701$	−41.0871	−1.55184	−0.775920	+	0.630831i	$0.782714\pi$
$702$	−14.7173	−0.555468
$703$	0.161196	0.00607961
$704$	0	0
$705$	11.5969	0.436764
$706$	4.00343	0.150671
$707$	12.9533	0.487158
$708$	−0.684935	−0.0257415
$709$	−14.8981	−0.559510	−0.279755	−	0.960071i	$-0.590253\pi$
$709$	−14.8981	−0.559510	−0.279755	+	0.960071i	$0.590253\pi$
$710$	8.20815	0.308046
$711$	−10.9930	−0.412271
$712$	2.73408	0.102464
$713$	−15.7771	−0.590856
$714$	−6.25844	−0.234216
$715$	0	0
$716$	−25.4215	−0.950048
$717$	1.42718	0.0532990
$718$	−9.77677	−0.364866
$719$	35.3705	1.31910	0.659548	−	0.751662i	$-0.270748\pi$
$719$	35.3705	1.31910	0.659548	+	0.751662i	$0.270748\pi$
$720$	−1.62777	−0.0606635
$721$	9.24014	0.344121
$722$	−3.19107	−0.118759
$723$	−1.99568	−0.0742203
$724$	−9.34641	−0.347357
$725$	−4.99939	−0.185673
$726$	0	0
$727$	1.10139	0.0408482	0.0204241	−	0.999791i	$-0.493498\pi$
$727$	1.10139	0.0408482	0.0204241	+	0.999791i	$0.493498\pi$
$728$	2.71483	0.100618
$729$	21.4391	0.794040
$730$	14.5897	0.539991
$731$	−65.5564	−2.42469
$732$	8.50409	0.314320
$733$	12.9270	0.477471	0.238735	−	0.971085i	$-0.423267\pi$
$733$	12.9270	0.477471	0.238735	+	0.971085i	$0.423267\pi$
$734$	−13.1201	−0.484272
$735$	1.17142	0.0432085
$736$	5.49704	0.202624
$737$	0	0
$738$	−8.35067	−0.307392
$739$	−32.1959	−1.18435	−0.592173	−	0.805810i	$-0.701730\pi$
$739$	−32.1959	−1.18435	−0.592173	+	0.805810i	$0.701730\pi$
$740$	0.0405417	0.00149034
$741$	12.6447	0.464513
$742$	4.55880	0.167359
$743$	26.4833	0.971577	0.485788	−	0.874077i	$-0.338533\pi$
$743$	26.4833	0.971577	0.485788	+	0.874077i	$0.338533\pi$
$744$	−3.36210	−0.123260
$745$	12.3315	0.451791
$746$	−15.2552	−0.558534
$747$	25.3597	0.927864
$748$	0	0
$749$	10.0022	0.365472
$750$	1.17142	0.0427743
$751$	−38.6078	−1.40882	−0.704409	−	0.709795i	$-0.748788\pi$
$751$	−38.6078	−1.40882	−0.704409	+	0.709795i	$0.748788\pi$
$752$	9.89983	0.361010
$753$	−22.5879	−0.823151
$754$	−13.5725	−0.494281
$755$	−8.70759	−0.316902
$756$	−5.42107	−0.197162
$757$	−38.9080	−1.41413	−0.707067	−	0.707146i	$-0.749982\pi$
$757$	−38.9080	−1.41413	−0.707067	+	0.707146i	$0.749982\pi$
$758$	26.6376	0.967522
$759$	0	0
$760$	3.97605	0.144226
$761$	9.88051	0.358168	0.179084	−	0.983834i	$-0.442687\pi$
$761$	9.88051	0.358168	0.179084	+	0.983834i	$0.442687\pi$
$762$	−20.2395	−0.733199
$763$	−0.535064	−0.0193706
$764$	4.55912	0.164943
$765$	8.69653	0.314424
$766$	6.81998	0.246416
$767$	−1.58737	−0.0573167
$768$	1.17142	0.0422700
$769$	−20.8801	−0.752955	−0.376478	−	0.926426i	$-0.622865\pi$
$769$	−20.8801	−0.752955	−0.376478	+	0.926426i	$0.622865\pi$
$770$	0	0
$771$	−11.6788	−0.420602
$772$	15.8146	0.569181
$773$	−37.3833	−1.34459	−0.672293	−	0.740286i	$-0.734690\pi$
$773$	−37.3833	−1.34459	−0.672293	+	0.740286i	$0.734690\pi$
$774$	−19.9736	−0.717935
$775$	−2.87010	−0.103097
$776$	−1.32780	−0.0476652
$777$	0.0474914	0.00170374
$778$	23.0806	0.827481
$779$	20.3976	0.730820
$780$	3.18021	0.113870
$781$	0	0
$782$	−29.3685	−1.05022
$783$	27.1021	0.968549
$784$	1.00000	0.0357143
$785$	−19.1275	−0.682688
$786$	12.9068	0.460369
$787$	−16.4247	−0.585477	−0.292739	−	0.956193i	$-0.594567\pi$
$787$	−16.4247	−0.585477	−0.292739	+	0.956193i	$0.594567\pi$
$788$	14.6162	0.520679
$789$	18.0281	0.641818
$790$	6.75342	0.240276
$791$	−1.55217	−0.0551887
$792$	0	0
$793$	19.7086	0.699875
$794$	−15.6435	−0.555166
$795$	5.34028	0.189400
$796$	16.4255	0.582188
$797$	31.5634	1.11803	0.559016	−	0.829157i	$-0.311179\pi$
$797$	31.5634	1.11803	0.559016	+	0.829157i	$0.311179\pi$
$798$	4.65762	0.164878
$799$	−52.8908	−1.87114
$800$	1.00000	0.0353553
$801$	−4.45046	−0.157249
$802$	−1.51369	−0.0534502
$803$	0	0
$804$	−16.8858	−0.595518
$805$	5.49704	0.193745
$806$	−7.79183	−0.274456
$807$	−19.5067	−0.686667
$808$	12.9533	0.455695
$809$	−6.30494	−0.221670	−0.110835	−	0.993839i	$-0.535353\pi$
$809$	−6.30494	−0.221670	−0.110835	+	0.993839i	$0.535353\pi$
$810$	−1.46704	−0.0515466
$811$	28.7394	1.00918	0.504588	−	0.863361i	$-0.331645\pi$
$811$	28.7394	1.00918	0.504588	+	0.863361i	$0.331645\pi$
$812$	−4.99939	−0.175444
$813$	−3.34381	−0.117273
$814$	0	0
$815$	−18.6244	−0.652385
$816$	−6.25844	−0.219089
$817$	48.7881	1.70688
$818$	−14.2110	−0.496876
$819$	−4.41912	−0.154417
$820$	5.13012	0.179152
$821$	40.1131	1.39996	0.699978	−	0.714165i	$-0.253193\pi$
$821$	40.1131	1.39996	0.699978	+	0.714165i	$0.253193\pi$
$822$	11.1164	0.387731
$823$	−16.7750	−0.584739	−0.292370	−	0.956305i	$-0.594444\pi$
$823$	−16.7750	−0.584739	−0.292370	+	0.956305i	$0.594444\pi$
$824$	9.24014	0.321895
$825$	0	0
$826$	−0.584705	−0.0203445
$827$	7.08065	0.246218	0.123109	−	0.992393i	$-0.460713\pi$
$827$	7.08065	0.246218	0.123109	+	0.992393i	$0.460713\pi$
$828$	−8.94793	−0.310962
$829$	−17.7789	−0.617485	−0.308743	−	0.951146i	$-0.599908\pi$
$829$	−17.7789	−0.617485	−0.308743	+	0.951146i	$0.599908\pi$
$830$	−15.5794	−0.540769
$831$	29.3405	1.01781
$832$	2.71483	0.0941197
$833$	−5.34260	−0.185110
$834$	−12.7220	−0.440528
$835$	1.66091	0.0574780
$836$	0	0
$837$	15.5590	0.537798
$838$	6.61451	0.228494
$839$	−7.03094	−0.242735	−0.121368	−	0.992608i	$-0.538728\pi$
$839$	−7.03094	−0.242735	−0.121368	+	0.992608i	$0.538728\pi$
$840$	1.17142	0.0404179
$841$	−4.00606	−0.138140
$842$	−38.2913	−1.31960
$843$	5.12877	0.176644
$844$	−4.78958	−0.164864
$845$	−5.62971	−0.193668
$846$	−16.1147	−0.554034
$847$	0	0
$848$	4.55880	0.156550
$849$	−8.74121	−0.299998
$850$	−5.34260	−0.183250
$851$	0.222859	0.00763952
$852$	9.61520	0.329411
$853$	48.2865	1.65330	0.826648	−	0.562719i	$-0.190245\pi$
$853$	48.2865	1.65330	0.826648	+	0.562719i	$0.190245\pi$
$854$	7.25963	0.248419
$855$	−6.47209	−0.221341
$856$	10.0022	0.341867
$857$	−30.6816	−1.04806	−0.524032	−	0.851699i	$-0.675573\pi$
$857$	−30.6816	−1.04806	−0.524032	+	0.851699i	$0.675573\pi$
$858$	0	0
$859$	12.1328	0.413965	0.206983	−	0.978345i	$-0.433636\pi$
$859$	12.1328	0.413965	0.206983	+	0.978345i	$0.433636\pi$
$860$	12.2705	0.418421
$861$	6.00954	0.204804
$862$	6.73123	0.229267
$863$	−42.0830	−1.43252	−0.716261	−	0.697832i	$-0.754148\pi$
$863$	−42.0830	−1.43252	−0.716261	+	0.697832i	$0.754148\pi$
$864$	−5.42107	−0.184429
$865$	−10.4055	−0.353797
$866$	−25.7699	−0.875697
$867$	13.5222	0.459237
$868$	−2.87010	−0.0974176
$869$	0	0
$870$	−5.85640	−0.198550
$871$	−39.1338	−1.32600
$872$	−0.535064	−0.0181196
$873$	2.16135	0.0731507
$874$	21.8565	0.739307
$875$	1.00000	0.0338062
$876$	17.0907	0.577443
$877$	−34.3045	−1.15838	−0.579190	−	0.815193i	$-0.696631\pi$
$877$	−34.3045	−1.15838	−0.579190	+	0.815193i	$0.696631\pi$
$878$	13.8131	0.466169
$879$	6.86069	0.231405
$880$	0	0
$881$	0.874683	0.0294688	0.0147344	−	0.999891i	$-0.495310\pi$
$881$	0.874683	0.0294688	0.0147344	+	0.999891i	$0.495310\pi$
$882$	−1.62777	−0.0548099
$883$	49.3208	1.65978	0.829888	−	0.557930i	$-0.188404\pi$
$883$	49.3208	1.65978	0.829888	+	0.557930i	$0.188404\pi$
$884$	−14.5042	−0.487830
$885$	−0.684935	−0.0230239
$886$	−28.1206	−0.944730
$887$	10.2517	0.344218	0.172109	−	0.985078i	$-0.444942\pi$
$887$	10.2517	0.344218	0.172109	+	0.985078i	$0.444942\pi$
$888$	0.0474914	0.00159371
$889$	−17.2777	−0.579476
$890$	2.73408	0.0916466
$891$	0	0
$892$	−23.2488	−0.778426
$893$	39.3622	1.31721
$894$	14.4454	0.483126
$895$	−25.4215	−0.849749
$896$	1.00000	0.0334077
$897$	17.4817	0.583698
$898$	27.8576	0.929621
$899$	14.3488	0.478558
$900$	−1.62777	−0.0542591
$901$	−24.3558	−0.811411
$902$	0	0
$903$	14.3739	0.478334
$904$	−1.55217	−0.0516243
$905$	−9.34641	−0.310685
$906$	−10.2003	−0.338881
$907$	54.0073	1.79328	0.896642	−	0.442757i	$-0.146000\pi$
$907$	54.0073	1.79328	0.896642	+	0.442757i	$0.146000\pi$
$908$	−17.0503	−0.565834
$909$	−21.0850	−0.699344
$910$	2.71483	0.0899957
$911$	−21.9362	−0.726779	−0.363390	−	0.931637i	$-0.618381\pi$
$911$	−21.9362	−0.726779	−0.363390	+	0.931637i	$0.618381\pi$
$912$	4.65762	0.154229
$913$	0	0
$914$	−38.0839	−1.25970
$915$	8.50409	0.281136
$916$	10.5051	0.347098
$917$	11.0180	0.363848
$918$	28.9626	0.955909
$919$	−32.5378	−1.07332	−0.536662	−	0.843798i	$-0.680315\pi$
$919$	−32.5378	−1.07332	−0.536662	+	0.843798i	$0.680315\pi$
$920$	5.49704	0.181232
$921$	40.7507	1.34278
$922$	13.9251	0.458598
$923$	22.2837	0.733478
$924$	0	0
$925$	0.0405417	0.00133300
$926$	−2.93872	−0.0965725
$927$	−15.0408	−0.494006
$928$	−4.99939	−0.164113
$929$	1.52103	0.0499034	0.0249517	−	0.999689i	$-0.492057\pi$
$929$	1.52103	0.0499034	0.0249517	+	0.999689i	$0.492057\pi$
$930$	−3.36210	−0.110248
$931$	3.97605	0.130310
$932$	21.0739	0.690300
$933$	22.9340	0.750826
$934$	−31.8095	−1.04084
$935$	0	0
$936$	−4.41912	−0.144443
$937$	35.3146	1.15368	0.576839	−	0.816858i	$-0.304286\pi$
$937$	35.3146	1.15368	0.576839	+	0.816858i	$0.304286\pi$
$938$	−14.4148	−0.470661
$939$	−14.4822	−0.472610
$940$	9.89983	0.322897
$941$	17.8323	0.581316	0.290658	−	0.956827i	$-0.406126\pi$
$941$	17.8323	0.581316	0.290658	+	0.956827i	$0.406126\pi$
$942$	−22.4063	−0.730037
$943$	28.2005	0.918335
$944$	−0.584705	−0.0190305
$945$	−5.42107	−0.176347
$946$	0	0
$947$	−26.5867	−0.863953	−0.431977	−	0.901885i	$-0.642184\pi$
$947$	−26.5867	−0.863953	−0.431977	+	0.901885i	$0.642184\pi$
$948$	7.91110	0.256941
$949$	39.6087	1.28575
$950$	3.97605	0.129000
$951$	6.03939	0.195840
$952$	−5.34260	−0.173155
$953$	12.9284	0.418791	0.209396	−	0.977831i	$-0.432850\pi$
$953$	12.9284	0.418791	0.209396	+	0.977831i	$0.432850\pi$
$954$	−7.42069	−0.240254
$955$	4.55912	0.147530
$956$	1.21833	0.0394037
$957$	0	0
$958$	37.7725	1.22038
$959$	9.48971	0.306439
$960$	1.17142	0.0378075
$961$	−22.7625	−0.734275
$962$	0.110064	0.00354860
$963$	−16.2813	−0.524656
$964$	−1.70364	−0.0548706
$965$	15.8146	0.509091
$966$	6.43935	0.207183
$967$	6.45564	0.207599	0.103800	−	0.994598i	$-0.466900\pi$
$967$	6.45564	0.207599	0.103800	+	0.994598i	$0.466900\pi$
$968$	0	0
$969$	−24.8838	−0.799384
$970$	−1.32780	−0.0426331
$971$	16.5435	0.530907	0.265454	−	0.964124i	$-0.414478\pi$
$971$	16.5435	0.530907	0.265454	+	0.964124i	$0.414478\pi$
$972$	14.5447	0.466521
$973$	−10.8603	−0.348167
$974$	−9.53146	−0.305408
$975$	3.18021	0.101848
$976$	7.25963	0.232375
$977$	−24.7794	−0.792762	−0.396381	−	0.918086i	$-0.629734\pi$
$977$	−24.7794	−0.792762	−0.396381	+	0.918086i	$0.629734\pi$
$978$	−21.8170	−0.697632
$979$	0	0
$980$	1.00000	0.0319438
$981$	0.870962	0.0278077
$982$	−22.2193	−0.709046
$983$	−46.4963	−1.48300	−0.741501	−	0.670952i	$-0.765886\pi$
$983$	−46.4963	−1.48300	−0.741501	+	0.670952i	$0.765886\pi$
$984$	6.00954	0.191577
$985$	14.6162	0.465709
$986$	26.7098	0.850612
$987$	11.5969	0.369133
$988$	10.7943	0.343412
$989$	67.4514	2.14483
$990$	0	0
$991$	47.0722	1.49530	0.747649	−	0.664094i	$-0.231182\pi$
$991$	47.0722	1.49530	0.747649	+	0.664094i	$0.231182\pi$
$992$	−2.87010	−0.0911258
$993$	−38.0784	−1.20838
$994$	8.20815	0.260347
$995$	16.4255	0.520725
$996$	−18.2500	−0.578275
$997$	56.2531	1.78155	0.890776	−	0.454442i	$-0.150161\pi$
$997$	56.2531	1.78155	0.890776	+	0.454442i	$0.150161\pi$
$998$	−10.8366	−0.343026
$999$	−0.219779	−0.00695351

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.de.1.4		6
11.5	even	5		770.2.n.i.421.2	✓	12
11.9	even	5		770.2.n.i.631.2	yes	12
11.10	odd	2		8470.2.a.cy.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.i.421.2	✓	12	11.5	even	5
770.2.n.i.631.2	yes	12	11.9	even	5
8470.2.a.cy.1.4		6	11.10	odd	2
8470.2.a.de.1.4		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.17142 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.17142 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.62777 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.17142 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.17142 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.62777 q^{9} +1.00000 q^{10} +1.17142 q^{12} +2.71483 q^{13} +1.00000 q^{14} +1.17142 q^{15} +1.00000 q^{16} -5.34260 q^{17} -1.62777 q^{18} +3.97605 q^{19} +1.00000 q^{20} +1.17142 q^{21} +5.49704 q^{23} +1.17142 q^{24} +1.00000 q^{25} +2.71483 q^{26} -5.42107 q^{27} +1.00000 q^{28} -4.99939 q^{29} +1.17142 q^{30} -2.87010 q^{31} +1.00000 q^{32} -5.34260 q^{34} +1.00000 q^{35} -1.62777 q^{36} +0.0405417 q^{37} +3.97605 q^{38} +3.18021 q^{39} +1.00000 q^{40} +5.13012 q^{41} +1.17142 q^{42} +12.2705 q^{43} -1.62777 q^{45} +5.49704 q^{46} +9.89983 q^{47} +1.17142 q^{48} +1.00000 q^{49} +1.00000 q^{50} -6.25844 q^{51} +2.71483 q^{52} +4.55880 q^{53} -5.42107 q^{54} +1.00000 q^{56} +4.65762 q^{57} -4.99939 q^{58} -0.584705 q^{59} +1.17142 q^{60} +7.25963 q^{61} -2.87010 q^{62} -1.62777 q^{63} +1.00000 q^{64} +2.71483 q^{65} -14.4148 q^{67} -5.34260 q^{68} +6.43935 q^{69} +1.00000 q^{70} +8.20815 q^{71} -1.62777 q^{72} +14.5897 q^{73} +0.0405417 q^{74} +1.17142 q^{75} +3.97605 q^{76} +3.18021 q^{78} +6.75342 q^{79} +1.00000 q^{80} -1.46704 q^{81} +5.13012 q^{82} -15.5794 q^{83} +1.17142 q^{84} -5.34260 q^{85} +12.2705 q^{86} -5.85640 q^{87} +2.73408 q^{89} -1.62777 q^{90} +2.71483 q^{91} +5.49704 q^{92} -3.36210 q^{93} +9.89983 q^{94} +3.97605 q^{95} +1.17142 q^{96} -1.32780 q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + q^{3} + 6 q^{4} + 6 q^{5} + q^{6} + 6 q^{7} + 6 q^{8} + 15 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + q^3 + 6 * q^4 + 6 * q^5 + q^6 + 6 * q^7 + 6 * q^8 + 15 * q^9	\( 6 q + 6 q^{2} + q^{3} + 6 q^{4} + 6 q^{5} + q^{6} + 6 q^{7} + 6 q^{8} + 15 q^{9} + 6 q^{10} + q^{12} + 2 q^{13} + 6 q^{14} + q^{15} + 6 q^{16} + 7 q^{17} + 15 q^{18} + 11 q^{19} + 6 q^{20} + q^{21} - 6 q^{23} + q^{24} + 6 q^{25} + 2 q^{26} + 4 q^{27} + 6 q^{28} + 2 q^{29} + q^{30} + 6 q^{32} + 7 q^{34} + 6 q^{35} + 15 q^{36} - 14 q^{37} + 11 q^{38} + 20 q^{39} + 6 q^{40} + 13 q^{41} + q^{42} + 19 q^{43} + 15 q^{45} - 6 q^{46} + 22 q^{47} + q^{48} + 6 q^{49} + 6 q^{50} - 14 q^{51} + 2 q^{52} - 10 q^{53} + 4 q^{54} + 6 q^{56} + 32 q^{57} + 2 q^{58} - 7 q^{59} + q^{60} + 22 q^{61} + 15 q^{63} + 6 q^{64} + 2 q^{65} + 5 q^{67} + 7 q^{68} - 36 q^{69} + 6 q^{70} + 8 q^{71} + 15 q^{72} + 13 q^{73} - 14 q^{74} + q^{75} + 11 q^{76} + 20 q^{78} - 16 q^{79} + 6 q^{80} + 18 q^{81} + 13 q^{82} - 5 q^{83} + q^{84} + 7 q^{85} + 19 q^{86} + 14 q^{87} + q^{89} + 15 q^{90} + 2 q^{91} - 6 q^{92} - 42 q^{93} + 22 q^{94} + 11 q^{95} + q^{96} - 3 q^{97} + 6 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 + q^3 + 6 * q^4 + 6 * q^5 + q^6 + 6 * q^7 + 6 * q^8 + 15 * q^9 + 6 * q^10 + q^12 + 2 * q^13 + 6 * q^14 + q^15 + 6 * q^16 + 7 * q^17 + 15 * q^18 + 11 * q^19 + 6 * q^20 + q^21 - 6 * q^23 + q^24 + 6 * q^25 + 2 * q^26 + 4 * q^27 + 6 * q^28 + 2 * q^29 + q^30 + 6 * q^32 + 7 * q^34 + 6 * q^35 + 15 * q^36 - 14 * q^37 + 11 * q^38 + 20 * q^39 + 6 * q^40 + 13 * q^41 + q^42 + 19 * q^43 + 15 * q^45 - 6 * q^46 + 22 * q^47 + q^48 + 6 * q^49 + 6 * q^50 - 14 * q^51 + 2 * q^52 - 10 * q^53 + 4 * q^54 + 6 * q^56 + 32 * q^57 + 2 * q^58 - 7 * q^59 + q^60 + 22 * q^61 + 15 * q^63 + 6 * q^64 + 2 * q^65 + 5 * q^67 + 7 * q^68 - 36 * q^69 + 6 * q^70 + 8 * q^71 + 15 * q^72 + 13 * q^73 - 14 * q^74 + q^75 + 11 * q^76 + 20 * q^78 - 16 * q^79 + 6 * q^80 + 18 * q^81 + 13 * q^82 - 5 * q^83 + q^84 + 7 * q^85 + 19 * q^86 + 14 * q^87 + q^89 + 15 * q^90 + 2 * q^91 - 6 * q^92 - 42 * q^93 + 22 * q^94 + 11 * q^95 + q^96 - 3 * q^97 + 6 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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