LMFDB - Embedded newform 8470.2.a.da.1.1

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:	$1$
Dimension:	$6$
Coefficient field:	6.6.38498000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 12x^{4} + 5x^{3} + 38x^{2} - x - 19 $ x^6 - x^5 - 12x^4 + 5x^3 + 38*x^2 - x - 19
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			1.1
Root			$-2.29803$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -3.29803 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.29803 q^{6} +1.00000 q^{7} +1.00000 q^{8} +7.87703 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.29803 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.29803 q^{6} +1.00000 q^{7} +1.00000 q^{8} +7.87703 q^{9} -1.00000 q^{10} -3.29803 q^{12} +1.08609 q^{13} +1.00000 q^{14} +3.29803 q^{15} +1.00000 q^{16} +0.971513 q^{17} +7.87703 q^{18} -1.04489 q^{19} -1.00000 q^{20} -3.29803 q^{21} +2.42388 q^{23} -3.29803 q^{24} +1.00000 q^{25} +1.08609 q^{26} -16.0846 q^{27} +1.00000 q^{28} -8.23533 q^{29} +3.29803 q^{30} -4.17984 q^{31} +1.00000 q^{32} +0.971513 q^{34} -1.00000 q^{35} +7.87703 q^{36} +6.08312 q^{37} -1.04489 q^{38} -3.58197 q^{39} -1.00000 q^{40} -8.53772 q^{41} -3.29803 q^{42} -3.06122 q^{43} -7.87703 q^{45} +2.42388 q^{46} -12.3941 q^{47} -3.29803 q^{48} +1.00000 q^{49} +1.00000 q^{50} -3.20408 q^{51} +1.08609 q^{52} -0.323543 q^{53} -16.0846 q^{54} +1.00000 q^{56} +3.44609 q^{57} -8.23533 q^{58} +11.8882 q^{59} +3.29803 q^{60} +13.1507 q^{61} -4.17984 q^{62} +7.87703 q^{63} +1.00000 q^{64} -1.08609 q^{65} +8.03278 q^{67} +0.971513 q^{68} -7.99404 q^{69} -1.00000 q^{70} +4.18166 q^{71} +7.87703 q^{72} -9.94125 q^{73} +6.08312 q^{74} -3.29803 q^{75} -1.04489 q^{76} -3.58197 q^{78} -11.4402 q^{79} -1.00000 q^{80} +29.4165 q^{81} -8.53772 q^{82} -0.382041 q^{83} -3.29803 q^{84} -0.971513 q^{85} -3.06122 q^{86} +27.1604 q^{87} -11.2206 q^{89} -7.87703 q^{90} +1.08609 q^{91} +2.42388 q^{92} +13.7852 q^{93} -12.3941 q^{94} +1.04489 q^{95} -3.29803 q^{96} +14.8572 q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 5 q^{3} + 6 q^{4} - 6 q^{5} - 5 q^{6} + 6 q^{7} + 6 q^{8} + 11 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 - 5 * q^3 + 6 * q^4 - 6 * q^5 - 5 * q^6 + 6 * q^7 + 6 * q^8 + 11 * q^9	$ 6 q + 6 q^{2} - 5 q^{3} + 6 q^{4} - 6 q^{5} - 5 q^{6} + 6 q^{7} + 6 q^{8} + 11 q^{9} - 6 q^{10} - 5 q^{12} + 6 q^{14} + 5 q^{15} + 6 q^{16} - 15 q^{17} + 11 q^{18} - 13 q^{19} - 6 q^{20} - 5 q^{21} - 2 q^{23} - 5 q^{24} + 6 q^{25} - 26 q^{27} + 6 q^{28} - 4 q^{29} + 5 q^{30} - 2 q^{31} + 6 q^{32} - 15 q^{34} - 6 q^{35} + 11 q^{36} - 13 q^{38} - 30 q^{39} - 6 q^{40} - 17 q^{41} - 5 q^{42} + 15 q^{43} - 11 q^{45} - 2 q^{46} - 18 q^{47} - 5 q^{48} + 6 q^{49} + 6 q^{50} + 6 q^{51} + 22 q^{53} - 26 q^{54} + 6 q^{56} - 2 q^{57} - 4 q^{58} - 7 q^{59} + 5 q^{60} - 20 q^{61} - 2 q^{62} + 11 q^{63} + 6 q^{64} - 29 q^{67} - 15 q^{68} + 12 q^{69} - 6 q^{70} - 2 q^{71} + 11 q^{72} + q^{73} - 5 q^{75} - 13 q^{76} - 30 q^{78} - 12 q^{79} - 6 q^{80} + 22 q^{81} - 17 q^{82} - 35 q^{83} - 5 q^{84} + 15 q^{85} + 15 q^{86} - 29 q^{89} - 11 q^{90} - 2 q^{92} + 8 q^{93} - 18 q^{94} + 13 q^{95} - 5 q^{96} - 19 q^{97} + 6 q^{98}+O(q^{100}) $ 6 * q + 6 * q^2 - 5 * q^3 + 6 * q^4 - 6 * q^5 - 5 * q^6 + 6 * q^7 + 6 * q^8 + 11 * q^9 - 6 * q^10 - 5 * q^12 + 6 * q^14 + 5 * q^15 + 6 * q^16 - 15 * q^17 + 11 * q^18 - 13 * q^19 - 6 * q^20 - 5 * q^21 - 2 * q^23 - 5 * q^24 + 6 * q^25 - 26 * q^27 + 6 * q^28 - 4 * q^29 + 5 * q^30 - 2 * q^31 + 6 * q^32 - 15 * q^34 - 6 * q^35 + 11 * q^36 - 13 * q^38 - 30 * q^39 - 6 * q^40 - 17 * q^41 - 5 * q^42 + 15 * q^43 - 11 * q^45 - 2 * q^46 - 18 * q^47 - 5 * q^48 + 6 * q^49 + 6 * q^50 + 6 * q^51 + 22 * q^53 - 26 * q^54 + 6 * q^56 - 2 * q^57 - 4 * q^58 - 7 * q^59 + 5 * q^60 - 20 * q^61 - 2 * q^62 + 11 * q^63 + 6 * q^64 - 29 * q^67 - 15 * q^68 + 12 * q^69 - 6 * q^70 - 2 * q^71 + 11 * q^72 + q^73 - 5 * q^75 - 13 * q^76 - 30 * q^78 - 12 * q^79 - 6 * q^80 + 22 * q^81 - 17 * q^82 - 35 * q^83 - 5 * q^84 + 15 * q^85 + 15 * q^86 - 29 * q^89 - 11 * q^90 - 2 * q^92 + 8 * q^93 - 18 * q^94 + 13 * q^95 - 5 * q^96 - 19 * 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
$3$	−3.29803	−1.90412	−0.952060	−	0.305910i	$-0.901039\pi$
$3$	−3.29803	−1.90412	−0.952060	+	0.305910i	$0.901039\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.29803	−1.34642
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	7.87703	2.62568
$10$	−1.00000	−0.316228
$11$	0	0
$11$	0	0
$12$	−3.29803	−0.952060
$13$	1.08609	0.301228	0.150614	−	0.988593i	$-0.451875\pi$
$13$	1.08609	0.301228	0.150614	+	0.988593i	$0.451875\pi$
$14$	1.00000	0.267261
$15$	3.29803	0.851549
$16$	1.00000	0.250000
$17$	0.971513	0.235627	0.117813	−	0.993036i	$-0.462412\pi$
$17$	0.971513	0.235627	0.117813	+	0.993036i	$0.462412\pi$
$18$	7.87703	1.85663
$19$	−1.04489	−0.239715	−0.119857	−	0.992791i	$-0.538244\pi$
$19$	−1.04489	−0.239715	−0.119857	+	0.992791i	$0.538244\pi$
$20$	−1.00000	−0.223607
$21$	−3.29803	−0.719690
$22$	0	0
$23$	2.42388	0.505414	0.252707	−	0.967543i	$-0.418679\pi$
$23$	2.42388	0.505414	0.252707	+	0.967543i	$0.418679\pi$
$24$	−3.29803	−0.673208
$25$	1.00000	0.200000
$26$	1.08609	0.213000
$27$	−16.0846	−3.09548
$28$	1.00000	0.188982
$29$	−8.23533	−1.52926	−0.764631	−	0.644468i	$-0.777079\pi$
$29$	−8.23533	−1.52926	−0.764631	+	0.644468i	$0.777079\pi$
$30$	3.29803	0.602136
$31$	−4.17984	−0.750721	−0.375360	−	0.926879i	$-0.622481\pi$
$31$	−4.17984	−0.750721	−0.375360	+	0.926879i	$0.622481\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	0.971513	0.166613
$35$	−1.00000	−0.169031
$36$	7.87703	1.31284
$37$	6.08312	1.00006	0.500029	−	0.866009i	$-0.333323\pi$
$37$	6.08312	1.00006	0.500029	+	0.866009i	$0.333323\pi$
$38$	−1.04489	−0.169504
$39$	−3.58197	−0.573575
$40$	−1.00000	−0.158114
$41$	−8.53772	−1.33337	−0.666684	−	0.745341i	$-0.732287\pi$
$41$	−8.53772	−1.33337	−0.666684	+	0.745341i	$0.732287\pi$
$42$	−3.29803	−0.508898
$43$	−3.06122	−0.466832	−0.233416	−	0.972377i	$-0.574990\pi$
$43$	−3.06122	−0.466832	−0.233416	+	0.972377i	$0.574990\pi$
$44$	0	0
$45$	−7.87703	−1.17424
$46$	2.42388	0.357382
$47$	−12.3941	−1.80786	−0.903930	−	0.427681i	$-0.859331\pi$
$47$	−12.3941	−1.80786	−0.903930	+	0.427681i	$0.859331\pi$
$48$	−3.29803	−0.476030
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	−3.20408	−0.448661
$52$	1.08609	0.150614
$53$	−0.323543	−0.0444421	−0.0222211	−	0.999753i	$-0.507074\pi$
$53$	−0.323543	−0.0444421	−0.0222211	+	0.999753i	$0.507074\pi$
$54$	−16.0846	−2.18884
$55$	0	0
$56$	1.00000	0.133631
$57$	3.44609	0.456446
$58$	−8.23533	−1.08135
$59$	11.8882	1.54771	0.773857	−	0.633360i	$-0.218325\pi$
$59$	11.8882	1.54771	0.773857	+	0.633360i	$0.218325\pi$
$60$	3.29803	0.425774
$61$	13.1507	1.68377	0.841884	−	0.539658i	$-0.181446\pi$
$61$	13.1507	1.68377	0.841884	+	0.539658i	$0.181446\pi$
$62$	−4.17984	−0.530840
$63$	7.87703	0.992412
$64$	1.00000	0.125000
$65$	−1.08609	−0.134713
$66$	0	0
$67$	8.03278	0.981361	0.490680	−	0.871340i	$-0.336748\pi$
$67$	8.03278	0.981361	0.490680	+	0.871340i	$0.336748\pi$
$68$	0.971513	0.117813
$69$	−7.99404	−0.962370
$70$	−1.00000	−0.119523
$71$	4.18166	0.496272	0.248136	−	0.968725i	$-0.420182\pi$
$71$	4.18166	0.496272	0.248136	+	0.968725i	$0.420182\pi$
$72$	7.87703	0.928317
$73$	−9.94125	−1.16354	−0.581768	−	0.813355i	$-0.697639\pi$
$73$	−9.94125	−1.16354	−0.581768	+	0.813355i	$0.697639\pi$
$74$	6.08312	0.707148
$75$	−3.29803	−0.380824
$76$	−1.04489	−0.119857
$77$	0	0
$78$	−3.58197	−0.405579
$79$	−11.4402	−1.28712	−0.643562	−	0.765394i	$-0.722544\pi$
$79$	−11.4402	−1.28712	−0.643562	+	0.765394i	$0.722544\pi$
$80$	−1.00000	−0.111803
$81$	29.4165	3.26850
$82$	−8.53772	−0.942834
$83$	−0.382041	−0.0419344	−0.0209672	−	0.999780i	$-0.506675\pi$
$83$	−0.382041	−0.0419344	−0.0209672	+	0.999780i	$0.506675\pi$
$84$	−3.29803	−0.359845
$85$	−0.971513	−0.105375
$86$	−3.06122	−0.330100
$87$	27.1604	2.91190
$88$	0	0
$89$	−11.2206	−1.18938	−0.594692	−	0.803954i	$-0.702726\pi$
$89$	−11.2206	−1.18938	−0.594692	+	0.803954i	$0.702726\pi$
$90$	−7.87703	−0.830312
$91$	1.08609	0.113854
$92$	2.42388	0.252707
$93$	13.7852	1.42946
$94$	−12.3941	−1.27835
$95$	1.04489	0.107204
$96$	−3.29803	−0.336604
$97$	14.8572	1.50852	0.754262	−	0.656573i	$-0.227995\pi$
$97$	14.8572	1.50852	0.754262	+	0.656573i	$0.227995\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	5.85686	0.582779	0.291390	−	0.956604i	$-0.405882\pi$
$101$	5.85686	0.582779	0.291390	+	0.956604i	$0.405882\pi$
$102$	−3.20408	−0.317252
$103$	−11.1086	−1.09456	−0.547280	−	0.836949i	$-0.684337\pi$
$103$	−11.1086	−1.09456	−0.547280	+	0.836949i	$0.684337\pi$
$104$	1.08609	0.106500
$105$	3.29803	0.321855
$106$	−0.323543	−0.0314253
$107$	7.35576	0.711108	0.355554	−	0.934656i	$-0.384292\pi$
$107$	7.35576	0.711108	0.355554	+	0.934656i	$0.384292\pi$
$108$	−16.0846	−1.54774
$109$	−1.17544	−0.112587	−0.0562933	−	0.998414i	$-0.517928\pi$
$109$	−1.17544	−0.112587	−0.0562933	+	0.998414i	$0.517928\pi$
$110$	0	0
$111$	−20.0623	−1.90423
$112$	1.00000	0.0944911
$113$	11.3045	1.06344	0.531720	−	0.846920i	$-0.321546\pi$
$113$	11.3045	1.06344	0.531720	+	0.846920i	$0.321546\pi$
$114$	3.44609	0.322756
$115$	−2.42388	−0.226028
$116$	−8.23533	−0.764631
$117$	8.55519	0.790928
$118$	11.8882	1.09440
$119$	0.971513	0.0890585
$120$	3.29803	0.301068
$121$	0	0
$122$	13.1507	1.19060
$123$	28.1577	2.53889
$124$	−4.17984	−0.375360
$125$	−1.00000	−0.0894427
$126$	7.87703	0.701742
$127$	6.94515	0.616282	0.308141	−	0.951341i	$-0.400293\pi$
$127$	6.94515	0.616282	0.308141	+	0.951341i	$0.400293\pi$
$128$	1.00000	0.0883883
$129$	10.0960	0.888905
$130$	−1.08609	−0.0952567
$131$	−4.83817	−0.422713	−0.211356	−	0.977409i	$-0.567788\pi$
$131$	−4.83817	−0.422713	−0.211356	+	0.977409i	$0.567788\pi$
$132$	0	0
$133$	−1.04489	−0.0906037
$134$	8.03278	0.693927
$135$	16.0846	1.38434
$136$	0.971513	0.0833066
$137$	−16.9448	−1.44769	−0.723846	−	0.689962i	$-0.757627\pi$
$137$	−16.9448	−1.44769	−0.723846	+	0.689962i	$0.757627\pi$
$138$	−7.99404	−0.680498
$139$	−9.81201	−0.832244	−0.416122	−	0.909309i	$-0.636611\pi$
$139$	−9.81201	−0.832244	−0.416122	+	0.909309i	$0.636611\pi$
$140$	−1.00000	−0.0845154
$141$	40.8760	3.44238
$142$	4.18166	0.350917
$143$	0	0
$144$	7.87703	0.656419
$145$	8.23533	0.683907
$146$	−9.94125	−0.822744
$147$	−3.29803	−0.272017
$148$	6.08312	0.500029
$149$	−17.2573	−1.41377	−0.706885	−	0.707328i	$-0.749900\pi$
$149$	−17.2573	−1.41377	−0.706885	+	0.707328i	$0.749900\pi$
$150$	−3.29803	−0.269283
$151$	15.6657	1.27485	0.637426	−	0.770511i	$-0.279999\pi$
$151$	15.6657	1.27485	0.637426	+	0.770511i	$0.279999\pi$
$152$	−1.04489	−0.0847520
$153$	7.65264	0.618679
$154$	0	0
$155$	4.17984	0.335732
$156$	−3.58197	−0.286787
$157$	9.25792	0.738862	0.369431	−	0.929258i	$-0.379553\pi$
$157$	9.25792	0.738862	0.369431	+	0.929258i	$0.379553\pi$
$158$	−11.4402	−0.910135
$159$	1.06706	0.0846232
$160$	−1.00000	−0.0790569
$161$	2.42388	0.191029
$162$	29.4165	2.31118
$163$	−7.31437	−0.572905	−0.286453	−	0.958094i	$-0.592476\pi$
$163$	−7.31437	−0.572905	−0.286453	+	0.958094i	$0.592476\pi$
$164$	−8.53772	−0.666684
$165$	0	0
$166$	−0.382041	−0.0296521
$167$	−12.6498	−0.978870	−0.489435	−	0.872040i	$-0.662797\pi$
$167$	−12.6498	−0.978870	−0.489435	+	0.872040i	$0.662797\pi$
$168$	−3.29803	−0.254449
$169$	−11.8204	−0.909262
$170$	−0.971513	−0.0745117
$171$	−8.23066	−0.629414
$172$	−3.06122	−0.233416
$173$	1.01451	0.0771316	0.0385658	−	0.999256i	$-0.487721\pi$
$173$	1.01451	0.0771316	0.0385658	+	0.999256i	$0.487721\pi$
$174$	27.1604	2.05902
$175$	1.00000	0.0755929
$176$	0	0
$177$	−39.2078	−2.94704
$178$	−11.2206	−0.841021
$179$	−17.1959	−1.28528	−0.642641	−	0.766167i	$-0.722162\pi$
$179$	−17.1959	−1.28528	−0.642641	+	0.766167i	$0.722162\pi$
$180$	−7.87703	−0.587119
$181$	20.3704	1.51412	0.757059	−	0.653346i	$-0.226635\pi$
$181$	20.3704	1.51412	0.757059	+	0.653346i	$0.226635\pi$
$182$	1.08609	0.0805066
$183$	−43.3713	−3.20610
$184$	2.42388	0.178691
$185$	−6.08312	−0.447240
$186$	13.7852	1.01078
$187$	0	0
$188$	−12.3941	−0.903930
$189$	−16.0846	−1.16998
$190$	1.04489	0.0758045
$191$	−6.42615	−0.464980	−0.232490	−	0.972599i	$-0.574687\pi$
$191$	−6.42615	−0.464980	−0.232490	+	0.972599i	$0.574687\pi$
$192$	−3.29803	−0.238015
$193$	14.0142	1.00876	0.504382	−	0.863480i	$-0.331720\pi$
$193$	14.0142	1.00876	0.504382	+	0.863480i	$0.331720\pi$
$194$	14.8572	1.06669
$195$	3.58197	0.256510
$196$	1.00000	0.0714286
$197$	21.3383	1.52029	0.760147	−	0.649752i	$-0.225127\pi$
$197$	21.3383	1.52029	0.760147	+	0.649752i	$0.225127\pi$
$198$	0	0
$199$	−26.4689	−1.87633	−0.938166	−	0.346186i	$-0.887477\pi$
$199$	−26.4689	−1.87633	−0.938166	+	0.346186i	$0.887477\pi$
$200$	1.00000	0.0707107
$201$	−26.4924	−1.86863
$202$	5.85686	0.412087
$203$	−8.23533	−0.578007
$204$	−3.20408	−0.224331
$205$	8.53772	0.596300
$206$	−11.1086	−0.773971
$207$	19.0930	1.32705
$208$	1.08609	0.0753070
$209$	0	0
$210$	3.29803	0.227586
$211$	12.6514	0.870955	0.435477	−	0.900200i	$-0.356580\pi$
$211$	12.6514	0.870955	0.435477	+	0.900200i	$0.356580\pi$
$212$	−0.323543	−0.0222211
$213$	−13.7913	−0.944961
$214$	7.35576	0.502830
$215$	3.06122	0.208774
$216$	−16.0846	−1.09442
$217$	−4.17984	−0.283746
$218$	−1.17544	−0.0796107
$219$	32.7866	2.21551
$220$	0	0
$221$	1.05515	0.0709773
$222$	−20.0623	−1.34650
$223$	−19.2003	−1.28575	−0.642873	−	0.765973i	$-0.722258\pi$
$223$	−19.2003	−1.28575	−0.642873	+	0.765973i	$0.722258\pi$
$224$	1.00000	0.0668153
$225$	7.87703	0.525135
$226$	11.3045	0.751966
$227$	2.24667	0.149116	0.0745582	−	0.997217i	$-0.476245\pi$
$227$	2.24667	0.149116	0.0745582	+	0.997217i	$0.476245\pi$
$228$	3.44609	0.228223
$229$	−4.78822	−0.316414	−0.158207	−	0.987406i	$-0.550571\pi$
$229$	−4.78822	−0.316414	−0.158207	+	0.987406i	$0.550571\pi$
$230$	−2.42388	−0.159826
$231$	0	0
$232$	−8.23533	−0.540676
$233$	12.7428	0.834807	0.417404	−	0.908721i	$-0.362940\pi$
$233$	12.7428	0.834807	0.417404	+	0.908721i	$0.362940\pi$
$234$	8.55519	0.559270
$235$	12.3941	0.808499
$236$	11.8882	0.773857
$237$	37.7302	2.45084
$238$	0.971513	0.0629738
$239$	−2.25974	−0.146170	−0.0730851	−	0.997326i	$-0.523284\pi$
$239$	−2.25974	−0.146170	−0.0730851	+	0.997326i	$0.523284\pi$
$240$	3.29803	0.212887
$241$	1.94631	0.125373	0.0626865	−	0.998033i	$-0.480033\pi$
$241$	1.94631	0.125373	0.0626865	+	0.998033i	$0.480033\pi$
$242$	0	0
$243$	−48.7628	−3.12814
$244$	13.1507	0.841884
$245$	−1.00000	−0.0638877
$246$	28.1577	1.79527
$247$	−1.13485	−0.0722089
$248$	−4.17984	−0.265420
$249$	1.25998	0.0798482
$250$	−1.00000	−0.0632456
$251$	−15.8786	−1.00225	−0.501125	−	0.865375i	$-0.667080\pi$
$251$	−15.8786	−1.00225	−0.501125	+	0.865375i	$0.667080\pi$
$252$	7.87703	0.496206
$253$	0	0
$254$	6.94515	0.435777
$255$	3.20408	0.200648
$256$	1.00000	0.0625000
$257$	−7.07546	−0.441355	−0.220677	−	0.975347i	$-0.570827\pi$
$257$	−7.07546	−0.441355	−0.220677	+	0.975347i	$0.570827\pi$
$258$	10.0960	0.628551
$259$	6.08312	0.377986
$260$	−1.08609	−0.0673567
$261$	−64.8699	−4.01535
$262$	−4.83817	−0.298903
$263$	−26.1468	−1.61228	−0.806139	−	0.591726i	$-0.798447\pi$
$263$	−26.1468	−1.61228	−0.806139	+	0.591726i	$0.798447\pi$
$264$	0	0
$265$	0.323543	0.0198751
$266$	−1.04489	−0.0640665
$267$	37.0060	2.26473
$268$	8.03278	0.490680
$269$	17.5426	1.06959	0.534796	−	0.844981i	$-0.320388\pi$
$269$	17.5426	1.06959	0.534796	+	0.844981i	$0.320388\pi$
$270$	16.0846	0.978878
$271$	−27.3246	−1.65985	−0.829927	−	0.557873i	$-0.811618\pi$
$271$	−27.3246	−1.65985	−0.829927	+	0.557873i	$0.811618\pi$
$272$	0.971513	0.0589066
$273$	−3.58197	−0.216791
$274$	−16.9448	−1.02367
$275$	0	0
$276$	−7.99404	−0.481185
$277$	−4.29659	−0.258157	−0.129079	−	0.991634i	$-0.541202\pi$
$277$	−4.29659	−0.258157	−0.129079	+	0.991634i	$0.541202\pi$
$278$	−9.81201	−0.588485
$279$	−32.9247	−1.97115
$280$	−1.00000	−0.0597614
$281$	−25.8683	−1.54317	−0.771586	−	0.636125i	$-0.780536\pi$
$281$	−25.8683	−1.54317	−0.771586	+	0.636125i	$0.780536\pi$
$282$	40.8760	2.43413
$283$	27.1448	1.61359	0.806795	−	0.590831i	$-0.201200\pi$
$283$	27.1448	1.61359	0.806795	+	0.590831i	$0.201200\pi$
$284$	4.18166	0.248136
$285$	−3.44609	−0.204129
$286$	0	0
$287$	−8.53772	−0.503966
$288$	7.87703	0.464158
$289$	−16.0562	−0.944480
$290$	8.23533	0.483595
$291$	−48.9997	−2.87241
$292$	−9.94125	−0.581768
$293$	−28.7674	−1.68061	−0.840304	−	0.542115i	$-0.817624\pi$
$293$	−28.7674	−1.68061	−0.840304	+	0.542115i	$0.817624\pi$
$294$	−3.29803	−0.192345
$295$	−11.8882	−0.692159
$296$	6.08312	0.353574
$297$	0	0
$298$	−17.2573	−0.999686
$299$	2.63256	0.152245
$300$	−3.29803	−0.190412
$301$	−3.06122	−0.176446
$302$	15.6657	0.901457
$303$	−19.3161	−1.10968
$304$	−1.04489	−0.0599287
$305$	−13.1507	−0.753004
$306$	7.65264	0.437472
$307$	−22.6960	−1.29533	−0.647666	−	0.761924i	$-0.724255\pi$
$307$	−22.6960	−1.29533	−0.647666	+	0.761924i	$0.724255\pi$
$308$	0	0
$309$	36.6365	2.08418
$310$	4.17984	0.237399
$311$	0.759043	0.0430414	0.0215207	−	0.999768i	$-0.493149\pi$
$311$	0.759043	0.0430414	0.0215207	+	0.999768i	$0.493149\pi$
$312$	−3.58197	−0.202789
$313$	21.6267	1.22241	0.611207	−	0.791471i	$-0.290684\pi$
$313$	21.6267	1.22241	0.611207	+	0.791471i	$0.290684\pi$
$314$	9.25792	0.522454
$315$	−7.87703	−0.443820
$316$	−11.4402	−0.643562
$317$	0.0857876	0.00481831	0.00240916	−	0.999997i	$-0.499233\pi$
$317$	0.0857876	0.00481831	0.00240916	+	0.999997i	$0.499233\pi$
$318$	1.06706	0.0598376
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	−24.2596	−1.35404
$322$	2.42388	0.135078
$323$	−1.01513	−0.0564832
$324$	29.4165	1.63425
$325$	1.08609	0.0602456
$326$	−7.31437	−0.405105
$327$	3.87663	0.214378
$328$	−8.53772	−0.471417
$329$	−12.3941	−0.683307
$330$	0	0
$331$	−22.6026	−1.24235	−0.621177	−	0.783670i	$-0.713345\pi$
$331$	−22.6026	−1.24235	−0.621177	+	0.783670i	$0.713345\pi$
$332$	−0.382041	−0.0209672
$333$	47.9169	2.62583
$334$	−12.6498	−0.692165
$335$	−8.03278	−0.438878
$336$	−3.29803	−0.179923
$337$	15.2690	0.831753	0.415876	−	0.909421i	$-0.363475\pi$
$337$	15.2690	0.831753	0.415876	+	0.909421i	$0.363475\pi$
$338$	−11.8204	−0.642945
$339$	−37.2827	−2.02492
$340$	−0.971513	−0.0526877
$341$	0	0
$342$	−8.23066	−0.445063
$343$	1.00000	0.0539949
$344$	−3.06122	−0.165050
$345$	7.99404	0.430385
$346$	1.01451	0.0545402
$347$	5.89915	0.316683	0.158342	−	0.987384i	$-0.449385\pi$
$347$	5.89915	0.316683	0.158342	+	0.987384i	$0.449385\pi$
$348$	27.1604	1.45595
$349$	16.9015	0.904718	0.452359	−	0.891836i	$-0.350583\pi$
$349$	16.9015	0.904718	0.452359	+	0.891836i	$0.350583\pi$
$350$	1.00000	0.0534522
$351$	−17.4694	−0.932447
$352$	0	0
$353$	−17.3914	−0.925648	−0.462824	−	0.886450i	$-0.653164\pi$
$353$	−17.3914	−0.925648	−0.462824	+	0.886450i	$0.653164\pi$
$354$	−39.2078	−2.08387
$355$	−4.18166	−0.221939
$356$	−11.2206	−0.594692
$357$	−3.20408	−0.169578
$358$	−17.1959	−0.908832
$359$	22.4481	1.18476	0.592382	−	0.805657i	$-0.298188\pi$
$359$	22.4481	1.18476	0.592382	+	0.805657i	$0.298188\pi$
$360$	−7.87703	−0.415156
$361$	−17.9082	−0.942537
$362$	20.3704	1.07064
$363$	0	0
$364$	1.08609	0.0569268
$365$	9.94125	0.520349
$366$	−43.3713	−2.26705
$367$	−4.81275	−0.251224	−0.125612	−	0.992079i	$-0.540089\pi$
$367$	−4.81275	−0.251224	−0.125612	+	0.992079i	$0.540089\pi$
$368$	2.42388	0.126354
$369$	−67.2519	−3.50099
$370$	−6.08312	−0.316246
$371$	−0.323543	−0.0167975
$372$	13.7852	0.714731
$373$	−6.77161	−0.350621	−0.175310	−	0.984513i	$-0.556093\pi$
$373$	−6.77161	−0.350621	−0.175310	+	0.984513i	$0.556093\pi$
$374$	0	0
$375$	3.29803	0.170310
$376$	−12.3941	−0.639175
$377$	−8.94433	−0.460657
$378$	−16.0846	−0.827303
$379$	−35.5405	−1.82559	−0.912797	−	0.408413i	$-0.866082\pi$
$379$	−35.5405	−1.82559	−0.912797	+	0.408413i	$0.866082\pi$
$380$	1.04489	0.0536019
$381$	−22.9053	−1.17348
$382$	−6.42615	−0.328790
$383$	21.0463	1.07542	0.537709	−	0.843131i	$-0.319290\pi$
$383$	21.0463	1.07542	0.537709	+	0.843131i	$0.319290\pi$
$384$	−3.29803	−0.168302
$385$	0	0
$386$	14.0142	0.713304
$387$	−24.1134	−1.22575
$388$	14.8572	0.754262
$389$	35.1161	1.78046	0.890230	−	0.455512i	$-0.150544\pi$
$389$	35.1161	1.78046	0.890230	+	0.455512i	$0.150544\pi$
$390$	3.58197	0.181380
$391$	2.35483	0.119089
$392$	1.00000	0.0505076
$393$	15.9564	0.804896
$394$	21.3383	1.07501
$395$	11.4402	0.575620
$396$	0	0
$397$	10.4987	0.526914	0.263457	−	0.964671i	$-0.415137\pi$
$397$	10.4987	0.526914	0.263457	+	0.964671i	$0.415137\pi$
$398$	−26.4689	−1.32677
$399$	3.44609	0.172520
$400$	1.00000	0.0500000
$401$	−21.9027	−1.09377	−0.546884	−	0.837208i	$-0.684186\pi$
$401$	−21.9027	−1.09377	−0.546884	+	0.837208i	$0.684186\pi$
$402$	−26.4924	−1.32132
$403$	−4.53969	−0.226138
$404$	5.85686	0.291390
$405$	−29.4165	−1.46172
$406$	−8.23533	−0.408712
$407$	0	0
$408$	−3.20408	−0.158626
$409$	9.24769	0.457269	0.228634	−	0.973512i	$-0.426574\pi$
$409$	9.24769	0.457269	0.228634	+	0.973512i	$0.426574\pi$
$410$	8.53772	0.421648
$411$	55.8845	2.75658
$412$	−11.1086	−0.547280
$413$	11.8882	0.584981
$414$	19.0930	0.938369
$415$	0.382041	0.0187536
$416$	1.08609	0.0532501
$417$	32.3603	1.58469
$418$	0	0
$419$	2.02744	0.0990469	0.0495235	−	0.998773i	$-0.484230\pi$
$419$	2.02744	0.0990469	0.0495235	+	0.998773i	$0.484230\pi$
$420$	3.29803	0.160928
$421$	9.29834	0.453173	0.226587	−	0.973991i	$-0.427243\pi$
$421$	9.29834	0.453173	0.226587	+	0.973991i	$0.427243\pi$
$422$	12.6514	0.615858
$423$	−97.6284	−4.74685
$424$	−0.323543	−0.0157127
$425$	0.971513	0.0471253
$426$	−13.7913	−0.668189
$427$	13.1507	0.636405
$428$	7.35576	0.355554
$429$	0	0
$430$	3.06122	0.147625
$431$	−18.1249	−0.873048	−0.436524	−	0.899693i	$-0.643791\pi$
$431$	−18.1249	−0.873048	−0.436524	+	0.899693i	$0.643791\pi$
$432$	−16.0846	−0.773871
$433$	−33.4904	−1.60945	−0.804723	−	0.593650i	$-0.797686\pi$
$433$	−33.4904	−1.60945	−0.804723	+	0.593650i	$0.797686\pi$
$434$	−4.17984	−0.200639
$435$	−27.1604	−1.30224
$436$	−1.17544	−0.0562933
$437$	−2.53270	−0.121155
$438$	32.7866	1.56660
$439$	−39.7487	−1.89710	−0.948551	−	0.316623i	$-0.897451\pi$
$439$	−39.7487	−1.89710	−0.948551	+	0.316623i	$0.897451\pi$
$440$	0	0
$441$	7.87703	0.375097
$442$	1.05515	0.0501886
$443$	36.0159	1.71117	0.855584	−	0.517665i	$-0.173198\pi$
$443$	36.0159	1.71117	0.855584	+	0.517665i	$0.173198\pi$
$444$	−20.0623	−0.952116
$445$	11.2206	0.531909
$446$	−19.2003	−0.909160
$447$	56.9150	2.69199
$448$	1.00000	0.0472456
$449$	5.64047	0.266190	0.133095	−	0.991103i	$-0.457508\pi$
$449$	5.64047	0.266190	0.133095	+	0.991103i	$0.457508\pi$
$450$	7.87703	0.371327
$451$	0	0
$452$	11.3045	0.531720
$453$	−51.6659	−2.42747
$454$	2.24667	0.105441
$455$	−1.08609	−0.0509168
$456$	3.44609	0.161378
$457$	−21.2353	−0.993345	−0.496673	−	0.867938i	$-0.665445\pi$
$457$	−21.2353	−0.993345	−0.496673	+	0.867938i	$0.665445\pi$
$458$	−4.78822	−0.223739
$459$	−15.6264	−0.729378
$460$	−2.42388	−0.113014
$461$	−36.7740	−1.71273	−0.856367	−	0.516367i	$-0.827284\pi$
$461$	−36.7740	−1.71273	−0.856367	+	0.516367i	$0.827284\pi$
$462$	0	0
$463$	21.8388	1.01494	0.507469	−	0.861670i	$-0.330581\pi$
$463$	21.8388	1.01494	0.507469	+	0.861670i	$0.330581\pi$
$464$	−8.23533	−0.382315
$465$	−13.7852	−0.639275
$466$	12.7428	0.590298
$467$	34.4719	1.59517	0.797584	−	0.603208i	$-0.206111\pi$
$467$	34.4719	1.59517	0.797584	+	0.603208i	$0.206111\pi$
$468$	8.55519	0.395464
$469$	8.03278	0.370920
$470$	12.3941	0.571695
$471$	−30.5329	−1.40688
$472$	11.8882	0.547200
$473$	0	0
$474$	37.7302	1.73301
$475$	−1.04489	−0.0479430
$476$	0.971513	0.0445292
$477$	−2.54856	−0.116691
$478$	−2.25974	−0.103358
$479$	−5.73461	−0.262021	−0.131010	−	0.991381i	$-0.541822\pi$
$479$	−5.73461	−0.262021	−0.131010	+	0.991381i	$0.541822\pi$
$480$	3.29803	0.150534
$481$	6.60683	0.301246
$482$	1.94631	0.0886521
$483$	−7.99404	−0.363742
$484$	0	0
$485$	−14.8572	−0.674633
$486$	−48.7628	−2.21193
$487$	6.98339	0.316448	0.158224	−	0.987403i	$-0.449423\pi$
$487$	6.98339	0.316448	0.158224	+	0.987403i	$0.449423\pi$
$488$	13.1507	0.595302
$489$	24.1230	1.09088
$490$	−1.00000	−0.0451754
$491$	−42.0589	−1.89809	−0.949045	−	0.315139i	$-0.897949\pi$
$491$	−42.0589	−1.89809	−0.949045	+	0.315139i	$0.897949\pi$
$492$	28.1577	1.26945
$493$	−8.00073	−0.360335
$494$	−1.13485	−0.0510594
$495$	0	0
$496$	−4.17984	−0.187680
$497$	4.18166	0.187573
$498$	1.25998	0.0564612
$499$	−19.9215	−0.891808	−0.445904	−	0.895081i	$-0.647118\pi$
$499$	−19.9215	−0.891808	−0.445904	+	0.895081i	$0.647118\pi$
$500$	−1.00000	−0.0447214
$501$	41.7194	1.86389
$502$	−15.8786	−0.708698
$503$	8.42225	0.375530	0.187765	−	0.982214i	$-0.439876\pi$
$503$	8.42225	0.375530	0.187765	+	0.982214i	$0.439876\pi$
$504$	7.87703	0.350871
$505$	−5.85686	−0.260627
$506$	0	0
$507$	38.9841	1.73134
$508$	6.94515	0.308141
$509$	−7.87220	−0.348929	−0.174465	−	0.984663i	$-0.555819\pi$
$509$	−7.87220	−0.348929	−0.174465	+	0.984663i	$0.555819\pi$
$510$	3.20408	0.141879
$511$	−9.94125	−0.439775
$512$	1.00000	0.0441942
$513$	16.8067	0.742034
$514$	−7.07546	−0.312085
$515$	11.1086	0.489502
$516$	10.0960	0.444453
$517$	0	0
$518$	6.08312	0.267277
$519$	−3.34588	−0.146868
$520$	−1.08609	−0.0476283
$521$	23.4996	1.02953	0.514767	−	0.857330i	$-0.327878\pi$
$521$	23.4996	1.02953	0.514767	+	0.857330i	$0.327878\pi$
$522$	−64.8699	−2.83928
$523$	−8.57857	−0.375115	−0.187557	−	0.982254i	$-0.560057\pi$
$523$	−8.57857	−0.375115	−0.187557	+	0.982254i	$0.560057\pi$
$524$	−4.83817	−0.211356
$525$	−3.29803	−0.143938
$526$	−26.1468	−1.14005
$527$	−4.06077	−0.176890
$528$	0	0
$529$	−17.1248	−0.744556
$530$	0.323543	0.0140538
$531$	93.6439	4.06380
$532$	−1.04489	−0.0453019
$533$	−9.27276	−0.401648
$534$	37.0060	1.60141
$535$	−7.35576	−0.318017
$536$	8.03278	0.346963
$537$	56.7127	2.44733
$538$	17.5426	0.756316
$539$	0	0
$540$	16.0846	0.692171
$541$	−18.8588	−0.810804	−0.405402	−	0.914139i	$-0.632868\pi$
$541$	−18.8588	−0.810804	−0.405402	+	0.914139i	$0.632868\pi$
$542$	−27.3246	−1.17369
$543$	−67.1822	−2.88306
$544$	0.971513	0.0416533
$545$	1.17544	0.0503502
$546$	−3.58197	−0.153294
$547$	32.1205	1.37338	0.686688	−	0.726953i	$-0.259064\pi$
$547$	32.1205	1.37338	0.686688	+	0.726953i	$0.259064\pi$
$548$	−16.9448	−0.723846
$549$	103.588	4.42103
$550$	0	0
$551$	8.60504	0.366587
$552$	−7.99404	−0.340249
$553$	−11.4402	−0.486487
$554$	−4.29659	−0.182545
$555$	20.0623	0.851598
$556$	−9.81201	−0.416122
$557$	−24.7492	−1.04866	−0.524329	−	0.851516i	$-0.675684\pi$
$557$	−24.7492	−1.04866	−0.524329	+	0.851516i	$0.675684\pi$
$558$	−32.9247	−1.39381
$559$	−3.32478	−0.140623
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	−25.8683	−1.09119
$563$	4.50739	0.189964	0.0949820	−	0.995479i	$-0.469721\pi$
$563$	4.50739	0.189964	0.0949820	+	0.995479i	$0.469721\pi$
$564$	40.8760	1.72119
$565$	−11.3045	−0.475585
$566$	27.1448	1.14098
$567$	29.4165	1.23538
$568$	4.18166	0.175459
$569$	−35.3172	−1.48058	−0.740288	−	0.672290i	$-0.765311\pi$
$569$	−35.3172	−1.48058	−0.740288	+	0.672290i	$0.765311\pi$
$570$	−3.44609	−0.144341
$571$	−21.6537	−0.906179	−0.453089	−	0.891465i	$-0.649678\pi$
$571$	−21.6537	−0.906179	−0.453089	+	0.891465i	$0.649678\pi$
$572$	0	0
$573$	21.1937	0.885378
$574$	−8.53772	−0.356358
$575$	2.42388	0.101083
$576$	7.87703	0.328210
$577$	−6.00586	−0.250027	−0.125014	−	0.992155i	$-0.539897\pi$
$577$	−6.00586	−0.250027	−0.125014	+	0.992155i	$0.539897\pi$
$578$	−16.0562	−0.667848
$579$	−46.2193	−1.92081
$580$	8.23533	0.341953
$581$	−0.382041	−0.0158497
$582$	−48.9997	−2.03110
$583$	0	0
$584$	−9.94125	−0.411372
$585$	−8.55519	−0.353714
$586$	−28.7674	−1.18837
$587$	5.77309	0.238281	0.119140	−	0.992877i	$-0.461986\pi$
$587$	5.77309	0.238281	0.119140	+	0.992877i	$0.461986\pi$
$588$	−3.29803	−0.136009
$589$	4.36748	0.179959
$590$	−11.8882	−0.489430
$591$	−70.3745	−2.89482
$592$	6.08312	0.250015
$593$	10.5859	0.434710	0.217355	−	0.976093i	$-0.430257\pi$
$593$	10.5859	0.434710	0.217355	+	0.976093i	$0.430257\pi$
$594$	0	0
$595$	−0.971513	−0.0398282
$596$	−17.2573	−0.706885
$597$	87.2954	3.57276
$598$	2.63256	0.107653
$599$	−21.4656	−0.877062	−0.438531	−	0.898716i	$-0.644501\pi$
$599$	−21.4656	−0.877062	−0.438531	+	0.898716i	$0.644501\pi$
$600$	−3.29803	−0.134642
$601$	21.6912	0.884801	0.442401	−	0.896818i	$-0.354127\pi$
$601$	21.6912	0.884801	0.442401	+	0.896818i	$0.354127\pi$
$602$	−3.06122	−0.124766
$603$	63.2745	2.57674
$604$	15.6657	0.637426
$605$	0	0
$606$	−19.3161	−0.784664
$607$	3.63740	0.147637	0.0738187	−	0.997272i	$-0.476481\pi$
$607$	3.63740	0.147637	0.0738187	+	0.997272i	$0.476481\pi$
$608$	−1.04489	−0.0423760
$609$	27.1604	1.10059
$610$	−13.1507	−0.532454
$611$	−13.4611	−0.544578
$612$	7.65264	0.309340
$613$	−33.4826	−1.35235	−0.676174	−	0.736742i	$-0.736363\pi$
$613$	−33.4826	−1.35235	−0.676174	+	0.736742i	$0.736363\pi$
$614$	−22.6960	−0.915938
$615$	−28.1577	−1.13543
$616$	0	0
$617$	19.6244	0.790048	0.395024	−	0.918671i	$-0.370736\pi$
$617$	19.6244	0.790048	0.395024	+	0.918671i	$0.370736\pi$
$618$	36.6365	1.47374
$619$	4.83357	0.194278	0.0971389	−	0.995271i	$-0.469031\pi$
$619$	4.83357	0.194278	0.0971389	+	0.995271i	$0.469031\pi$
$620$	4.17984	0.167866
$621$	−38.9872	−1.56450
$622$	0.759043	0.0304348
$623$	−11.2206	−0.449545
$624$	−3.58197	−0.143394
$625$	1.00000	0.0400000
$626$	21.6267	0.864377
$627$	0	0
$628$	9.25792	0.369431
$629$	5.90983	0.235640
$630$	−7.87703	−0.313828
$631$	10.2621	0.408528	0.204264	−	0.978916i	$-0.434520\pi$
$631$	10.2621	0.408528	0.204264	+	0.978916i	$0.434520\pi$
$632$	−11.4402	−0.455067
$633$	−41.7246	−1.65840
$634$	0.0857876	0.00340706
$635$	−6.94515	−0.275610
$636$	1.06706	0.0423116
$637$	1.08609	0.0430326
$638$	0	0
$639$	32.9391	1.30305
$640$	−1.00000	−0.0395285
$641$	−10.9243	−0.431485	−0.215742	−	0.976450i	$-0.569217\pi$
$641$	−10.9243	−0.431485	−0.215742	+	0.976450i	$0.569217\pi$
$642$	−24.2596	−0.957448
$643$	−3.61607	−0.142604	−0.0713020	−	0.997455i	$-0.522715\pi$
$643$	−3.61607	−0.142604	−0.0713020	+	0.997455i	$0.522715\pi$
$644$	2.42388	0.0955143
$645$	−10.0960	−0.397531
$646$	−1.01513	−0.0399397
$647$	−15.1540	−0.595766	−0.297883	−	0.954602i	$-0.596281\pi$
$647$	−15.1540	−0.595766	−0.297883	+	0.954602i	$0.596281\pi$
$648$	29.4165	1.15559
$649$	0	0
$650$	1.08609	0.0426001
$651$	13.7852	0.540286
$652$	−7.31437	−0.286453
$653$	−10.3572	−0.405307	−0.202654	−	0.979250i	$-0.564957\pi$
$653$	−10.3572	−0.405307	−0.202654	+	0.979250i	$0.564957\pi$
$654$	3.87663	0.151588
$655$	4.83817	0.189043
$656$	−8.53772	−0.333342
$657$	−78.3075	−3.05507
$658$	−12.3941	−0.483171
$659$	−36.6439	−1.42744	−0.713722	−	0.700429i	$-0.752992\pi$
$659$	−36.6439	−1.42744	−0.713722	+	0.700429i	$0.752992\pi$
$660$	0	0
$661$	−23.5064	−0.914292	−0.457146	−	0.889392i	$-0.651128\pi$
$661$	−23.5064	−0.914292	−0.457146	+	0.889392i	$0.651128\pi$
$662$	−22.6026	−0.878477
$663$	−3.47993	−0.135149
$664$	−0.382041	−0.0148261
$665$	1.04489	0.0405192
$666$	47.9169	1.85674
$667$	−19.9615	−0.772911
$668$	−12.6498	−0.489435
$669$	63.3232	2.44822
$670$	−8.03278	−0.310334
$671$	0	0
$672$	−3.29803	−0.127224
$673$	2.53720	0.0978020	0.0489010	−	0.998804i	$-0.484428\pi$
$673$	2.53720	0.0978020	0.0489010	+	0.998804i	$0.484428\pi$
$674$	15.2690	0.588138
$675$	−16.0846	−0.619097
$676$	−11.8204	−0.454631
$677$	−28.9289	−1.11183	−0.555913	−	0.831240i	$-0.687631\pi$
$677$	−28.9289	−1.11183	−0.555913	+	0.831240i	$0.687631\pi$
$678$	−37.2827	−1.43183
$679$	14.8572	0.570169
$680$	−0.971513	−0.0372558
$681$	−7.40958	−0.283936
$682$	0	0
$683$	−5.90465	−0.225935	−0.112968	−	0.993599i	$-0.536036\pi$
$683$	−5.90465	−0.225935	−0.112968	+	0.993599i	$0.536036\pi$
$684$	−8.23066	−0.314707
$685$	16.9448	0.647427
$686$	1.00000	0.0381802
$687$	15.7917	0.602491
$688$	−3.06122	−0.116708
$689$	−0.351398	−0.0133872
$690$	7.99404	0.304328
$691$	−47.9809	−1.82528	−0.912639	−	0.408766i	$-0.865959\pi$
$691$	−47.9809	−1.82528	−0.912639	+	0.408766i	$0.865959\pi$
$692$	1.01451	0.0385658
$693$	0	0
$694$	5.89915	0.223929
$695$	9.81201	0.372191
$696$	27.1604	1.02951
$697$	−8.29451	−0.314177
$698$	16.9015	0.639732
$699$	−42.0261	−1.58957
$700$	1.00000	0.0377964
$701$	−31.0997	−1.17462	−0.587310	−	0.809362i	$-0.699813\pi$
$701$	−31.0997	−1.17462	−0.587310	+	0.809362i	$0.699813\pi$
$702$	−17.4694	−0.659340
$703$	−6.35621	−0.239729
$704$	0	0
$705$	−40.8760	−1.53948
$706$	−17.3914	−0.654532
$707$	5.85686	0.220270
$708$	−39.2078	−1.47352
$709$	1.54403	0.0579872	0.0289936	−	0.999580i	$-0.490770\pi$
$709$	1.54403	0.0579872	0.0289936	+	0.999580i	$0.490770\pi$
$710$	−4.18166	−0.156935
$711$	−90.1149	−3.37957
$712$	−11.2206	−0.420511
$713$	−10.1314	−0.379425
$714$	−3.20408	−0.119910
$715$	0	0
$716$	−17.1959	−0.642641
$717$	7.45269	0.278326
$718$	22.4481	0.837754
$719$	−27.9067	−1.04074	−0.520371	−	0.853940i	$-0.674207\pi$
$719$	−27.9067	−1.04074	−0.520371	+	0.853940i	$0.674207\pi$
$720$	−7.87703	−0.293560
$721$	−11.1086	−0.413705
$722$	−17.9082	−0.666474
$723$	−6.41901	−0.238725
$724$	20.3704	0.757059
$725$	−8.23533	−0.305852
$726$	0	0
$727$	19.3666	0.718267	0.359133	−	0.933286i	$-0.383072\pi$
$727$	19.3666	0.718267	0.359133	+	0.933286i	$0.383072\pi$
$728$	1.08609	0.0402533
$729$	72.5719	2.68785
$730$	9.94125	0.367942
$731$	−2.97402	−0.109998
$732$	−43.3713	−1.60305
$733$	−5.23132	−0.193223	−0.0966116	−	0.995322i	$-0.530800\pi$
$733$	−5.23132	−0.193223	−0.0966116	+	0.995322i	$0.530800\pi$
$734$	−4.81275	−0.177642
$735$	3.29803	0.121650
$736$	2.42388	0.0893455
$737$	0	0
$738$	−67.2519	−2.47558
$739$	10.9383	0.402373	0.201187	−	0.979553i	$-0.435520\pi$
$739$	10.9383	0.402373	0.201187	+	0.979553i	$0.435520\pi$
$740$	−6.08312	−0.223620
$741$	3.74278	0.137494
$742$	−0.323543	−0.0118777
$743$	32.0747	1.17671	0.588353	−	0.808604i	$-0.299776\pi$
$743$	32.0747	1.17671	0.588353	+	0.808604i	$0.299776\pi$
$744$	13.7852	0.505391
$745$	17.2573	0.632257
$746$	−6.77161	−0.247926
$747$	−3.00935	−0.110106
$748$	0	0
$749$	7.35576	0.268774
$750$	3.29803	0.120427
$751$	2.29206	0.0836383	0.0418192	−	0.999125i	$-0.486685\pi$
$751$	2.29206	0.0836383	0.0418192	+	0.999125i	$0.486685\pi$
$752$	−12.3941	−0.451965
$753$	52.3683	1.90841
$754$	−8.94433	−0.325733
$755$	−15.6657	−0.570132
$756$	−16.0846	−0.584992
$757$	49.1920	1.78791	0.893956	−	0.448155i	$-0.147919\pi$
$757$	49.1920	1.78791	0.893956	+	0.448155i	$0.147919\pi$
$758$	−35.5405	−1.29089
$759$	0	0
$760$	1.04489	0.0379023
$761$	−32.2555	−1.16926	−0.584630	−	0.811300i	$-0.698760\pi$
$761$	−32.2555	−1.16926	−0.584630	+	0.811300i	$0.698760\pi$
$762$	−22.9053	−0.829773
$763$	−1.17544	−0.0425537
$764$	−6.42615	−0.232490
$765$	−7.65264	−0.276682
$766$	21.0463	0.760435
$767$	12.9117	0.466215
$768$	−3.29803	−0.119008
$769$	36.9722	1.33325	0.666625	−	0.745393i	$-0.267738\pi$
$769$	36.9722	1.33325	0.666625	+	0.745393i	$0.267738\pi$
$770$	0	0
$771$	23.3351	0.840393
$772$	14.0142	0.504382
$773$	−44.1296	−1.58723	−0.793616	−	0.608419i	$-0.791804\pi$
$773$	−44.1296	−1.58723	−0.793616	+	0.608419i	$0.791804\pi$
$774$	−24.1134	−0.866737
$775$	−4.17984	−0.150144
$776$	14.8572	0.533344
$777$	−20.0623	−0.719732
$778$	35.1161	1.25897
$779$	8.92101	0.319628
$780$	3.58197	0.128255
$781$	0	0
$782$	2.35483	0.0842087
$783$	132.462	4.73381
$784$	1.00000	0.0357143
$785$	−9.25792	−0.330429
$786$	15.9564	0.569148
$787$	−27.4346	−0.977938	−0.488969	−	0.872301i	$-0.662627\pi$
$787$	−27.4346	−0.977938	−0.488969	+	0.872301i	$0.662627\pi$
$788$	21.3383	0.760147
$789$	86.2329	3.06997
$790$	11.4402	0.407025
$791$	11.3045	0.401943
$792$	0	0
$793$	14.2828	0.507198
$794$	10.4987	0.372584
$795$	−1.06706	−0.0378446
$796$	−26.4689	−0.938166
$797$	−3.49222	−0.123701	−0.0618505	−	0.998085i	$-0.519700\pi$
$797$	−3.49222	−0.123701	−0.0618505	+	0.998085i	$0.519700\pi$
$798$	3.44609	0.121990
$799$	−12.0410	−0.425980
$800$	1.00000	0.0353553
$801$	−88.3852	−3.12294
$802$	−21.9027	−0.773411
$803$	0	0
$804$	−26.4924	−0.934315
$805$	−2.42388	−0.0854306
$806$	−4.53969	−0.159904
$807$	−57.8562	−2.03663
$808$	5.85686	0.206044
$809$	−22.9517	−0.806939	−0.403469	−	0.914993i	$-0.632196\pi$
$809$	−22.9517	−0.806939	−0.403469	+	0.914993i	$0.632196\pi$
$810$	−29.4165	−1.03359
$811$	−25.3841	−0.891356	−0.445678	−	0.895193i	$-0.647037\pi$
$811$	−25.3841	−0.891356	−0.445678	+	0.895193i	$0.647037\pi$
$812$	−8.23533	−0.289003
$813$	90.1176	3.16056
$814$	0	0
$815$	7.31437	0.256211
$816$	−3.20408	−0.112165
$817$	3.19865	0.111907
$818$	9.24769	0.323338
$819$	8.55519	0.298943
$820$	8.53772	0.298150
$821$	−0.156645	−0.00546695	−0.00273348	−	0.999996i	$-0.500870\pi$
$821$	−0.156645	−0.00546695	−0.00273348	+	0.999996i	$0.500870\pi$
$822$	55.8845	1.94920
$823$	20.2569	0.706112	0.353056	−	0.935602i	$-0.385143\pi$
$823$	20.2569	0.706112	0.353056	+	0.935602i	$0.385143\pi$
$824$	−11.1086	−0.386986
$825$	0	0
$826$	11.8882	0.413644
$827$	−5.20676	−0.181057	−0.0905284	−	0.995894i	$-0.528856\pi$
$827$	−5.20676	−0.181057	−0.0905284	+	0.995894i	$0.528856\pi$
$828$	19.0930	0.663527
$829$	38.9470	1.35268	0.676342	−	0.736587i	$-0.263564\pi$
$829$	38.9470	1.35268	0.676342	+	0.736587i	$0.263564\pi$
$830$	0.382041	0.0132608
$831$	14.1703	0.491563
$832$	1.08609	0.0376535
$833$	0.971513	0.0336609
$834$	32.3603	1.12055
$835$	12.6498	0.437764
$836$	0	0
$837$	67.2310	2.32384
$838$	2.02744	0.0700367
$839$	9.50578	0.328176	0.164088	−	0.986446i	$-0.447532\pi$
$839$	9.50578	0.328176	0.164088	+	0.986446i	$0.447532\pi$
$840$	3.29803	0.113793
$841$	38.8206	1.33864
$842$	9.29834	0.320442
$843$	85.3144	2.93839
$844$	12.6514	0.435477
$845$	11.8204	0.406634
$846$	−97.6284	−3.35653
$847$	0	0
$848$	−0.323543	−0.0111105
$849$	−89.5245	−3.07247
$850$	0.971513	0.0333226
$851$	14.7448	0.505444
$852$	−13.7913	−0.472481
$853$	−1.34852	−0.0461725	−0.0230863	−	0.999733i	$-0.507349\pi$
$853$	−1.34852	−0.0461725	−0.0230863	+	0.999733i	$0.507349\pi$
$854$	13.1507	0.450006
$855$	8.23066	0.281482
$856$	7.35576	0.251415
$857$	24.4121	0.833900	0.416950	−	0.908929i	$-0.363099\pi$
$857$	24.4121	0.833900	0.416950	+	0.908929i	$0.363099\pi$
$858$	0	0
$859$	4.39769	0.150047	0.0750236	−	0.997182i	$-0.476097\pi$
$859$	4.39769	0.150047	0.0750236	+	0.997182i	$0.476097\pi$
$860$	3.06122	0.104387
$861$	28.1577	0.959612
$862$	−18.1249	−0.617338
$863$	−20.6638	−0.703405	−0.351703	−	0.936112i	$-0.614397\pi$
$863$	−20.6638	−0.703405	−0.351703	+	0.936112i	$0.614397\pi$
$864$	−16.0846	−0.547210
$865$	−1.01451	−0.0344943
$866$	−33.4904	−1.13805
$867$	52.9538	1.79840
$868$	−4.17984	−0.141873
$869$	0	0
$870$	−27.1604	−0.920823
$871$	8.72435	0.295613
$872$	−1.17544	−0.0398053
$873$	117.031	3.96090
$874$	−2.53270	−0.0856698
$875$	−1.00000	−0.0338062
$876$	32.7866	1.10776
$877$	17.7328	0.598794	0.299397	−	0.954129i	$-0.403215\pi$
$877$	17.7328	0.598794	0.299397	+	0.954129i	$0.403215\pi$
$878$	−39.7487	−1.34145
$879$	94.8758	3.20008
$880$	0	0
$881$	52.1966	1.75855	0.879274	−	0.476317i	$-0.158029\pi$
$881$	52.1966	1.75855	0.879274	+	0.476317i	$0.158029\pi$
$882$	7.87703	0.265233
$883$	3.26731	0.109954	0.0549768	−	0.998488i	$-0.482492\pi$
$883$	3.26731	0.109954	0.0549768	+	0.998488i	$0.482492\pi$
$884$	1.05515	0.0354887
$885$	39.2078	1.31795
$886$	36.0159	1.20998
$887$	−43.5164	−1.46114	−0.730569	−	0.682839i	$-0.760745\pi$
$887$	−43.5164	−1.46114	−0.730569	+	0.682839i	$0.760745\pi$
$888$	−20.0623	−0.673248
$889$	6.94515	0.232933
$890$	11.2206	0.376116
$891$	0	0
$892$	−19.2003	−0.642873
$893$	12.9505	0.433371
$894$	56.9150	1.90352
$895$	17.1959	0.574796
$896$	1.00000	0.0334077
$897$	−8.68228	−0.289893
$898$	5.64047	0.188225
$899$	34.4223	1.14805
$900$	7.87703	0.262568
$901$	−0.314327	−0.0104717
$902$	0	0
$903$	10.0960	0.335975
$904$	11.3045	0.375983
$905$	−20.3704	−0.677134
$906$	−51.6659	−1.71648
$907$	19.0450	0.632377	0.316189	−	0.948696i	$-0.397597\pi$
$907$	19.0450	0.632377	0.316189	+	0.948696i	$0.397597\pi$
$908$	2.24667	0.0745582
$909$	46.1346	1.53019
$910$	−1.08609	−0.0360036
$911$	13.1363	0.435226	0.217613	−	0.976035i	$-0.430173\pi$
$911$	13.1363	0.435226	0.217613	+	0.976035i	$0.430173\pi$
$912$	3.44609	0.114112
$913$	0	0
$914$	−21.2353	−0.702401
$915$	43.3713	1.43381
$916$	−4.78822	−0.158207
$917$	−4.83817	−0.159770
$918$	−15.6264	−0.515748
$919$	−20.2209	−0.667024	−0.333512	−	0.942746i	$-0.608234\pi$
$919$	−20.2209	−0.667024	−0.333512	+	0.942746i	$0.608234\pi$
$920$	−2.42388	−0.0799130
$921$	74.8523	2.46647
$922$	−36.7740	−1.21109
$923$	4.54167	0.149491
$924$	0	0
$925$	6.08312	0.200012
$926$	21.8388	0.717669
$927$	−87.5026	−2.87396
$928$	−8.23533	−0.270338
$929$	−26.7617	−0.878022	−0.439011	−	0.898482i	$-0.644671\pi$
$929$	−26.7617	−0.878022	−0.439011	+	0.898482i	$0.644671\pi$
$930$	−13.7852	−0.452036
$931$	−1.04489	−0.0342450
$932$	12.7428	0.417404
$933$	−2.50335	−0.0819560
$934$	34.4719	1.12795
$935$	0	0
$936$	8.55519	0.279635
$937$	38.9586	1.27272	0.636361	−	0.771391i	$-0.280439\pi$
$937$	38.9586	1.27272	0.636361	+	0.771391i	$0.280439\pi$
$938$	8.03278	0.262280
$939$	−71.3256	−2.32762
$940$	12.3941	0.404250
$941$	17.2136	0.561149	0.280574	−	0.959832i	$-0.409475\pi$
$941$	17.2136	0.561149	0.280574	+	0.959832i	$0.409475\pi$
$942$	−30.5329	−0.994817
$943$	−20.6944	−0.673903
$944$	11.8882	0.386929
$945$	16.0846	0.523232
$946$	0	0
$947$	−9.19053	−0.298652	−0.149326	−	0.988788i	$-0.547710\pi$
$947$	−9.19053	−0.298652	−0.149326	+	0.988788i	$0.547710\pi$
$948$	37.7302	1.22542
$949$	−10.7971	−0.350489
$950$	−1.04489	−0.0339008
$951$	−0.282931	−0.00917465
$952$	0.971513	0.0314869
$953$	−15.1329	−0.490204	−0.245102	−	0.969497i	$-0.578822\pi$
$953$	−15.1329	−0.490204	−0.245102	+	0.969497i	$0.578822\pi$
$954$	−2.54856	−0.0825127
$955$	6.42615	0.207945
$956$	−2.25974	−0.0730851
$957$	0	0
$958$	−5.73461	−0.185277
$959$	−16.9448	−0.547176
$960$	3.29803	0.106444
$961$	−13.5290	−0.436419
$962$	6.60683	0.213013
$963$	57.9416	1.86714
$964$	1.94631	0.0626865
$965$	−14.0142	−0.451133
$966$	−7.99404	−0.257204
$967$	−34.7020	−1.11594	−0.557970	−	0.829861i	$-0.688420\pi$
$967$	−34.7020	−1.11594	−0.557970	+	0.829861i	$0.688420\pi$
$968$	0	0
$969$	3.34793	0.107551
$970$	−14.8572	−0.477037
$971$	−8.12170	−0.260638	−0.130319	−	0.991472i	$-0.541600\pi$
$971$	−8.12170	−0.260638	−0.130319	+	0.991472i	$0.541600\pi$
$972$	−48.7628	−1.56407
$973$	−9.81201	−0.314559
$974$	6.98339	0.223762
$975$	−3.58197	−0.114715
$976$	13.1507	0.420942
$977$	23.7897	0.761101	0.380550	−	0.924760i	$-0.375735\pi$
$977$	23.7897	0.761101	0.380550	+	0.924760i	$0.375735\pi$
$978$	24.1230	0.771369
$979$	0	0
$980$	−1.00000	−0.0319438
$981$	−9.25896	−0.295616
$982$	−42.0589	−1.34215
$983$	−23.2293	−0.740901	−0.370451	−	0.928852i	$-0.620797\pi$
$983$	−23.2293	−0.740901	−0.370451	+	0.928852i	$0.620797\pi$
$984$	28.1577	0.897635
$985$	−21.3383	−0.679896
$986$	−8.00073	−0.254795
$987$	40.8760	1.30110
$988$	−1.13485	−0.0361044
$989$	−7.42005	−0.235944
$990$	0	0
$991$	19.2128	0.610315	0.305157	−	0.952302i	$-0.401291\pi$
$991$	19.2128	0.610315	0.305157	+	0.952302i	$0.401291\pi$
$992$	−4.17984	−0.132710
$993$	74.5443	2.36559
$994$	4.18166	0.132634
$995$	26.4689	0.839121
$996$	1.25998	0.0399241
$997$	12.0455	0.381486	0.190743	−	0.981640i	$-0.438910\pi$
$997$	12.0455	0.381486	0.190743	+	0.981640i	$0.438910\pi$
$998$	−19.9215	−0.630603
$999$	−97.8445	−3.09566

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.da.1.1		6
11.3	even	5		770.2.n.h.141.3	yes	12
11.4	even	5		770.2.n.h.71.3	✓	12
11.10	odd	2		8470.2.a.cu.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.h.71.3	✓	12	11.4	even	5
770.2.n.h.141.3	yes	12	11.3	even	5
8470.2.a.cu.1.1		6	11.10	odd	2
8470.2.a.da.1.1		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.29803 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.29803 q^{6} +1.00000 q^{7} +1.00000 q^{8} +7.87703 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.29803 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.29803 q^{6} +1.00000 q^{7} +1.00000 q^{8} +7.87703 q^{9} -1.00000 q^{10} -3.29803 q^{12} +1.08609 q^{13} +1.00000 q^{14} +3.29803 q^{15} +1.00000 q^{16} +0.971513 q^{17} +7.87703 q^{18} -1.04489 q^{19} -1.00000 q^{20} -3.29803 q^{21} +2.42388 q^{23} -3.29803 q^{24} +1.00000 q^{25} +1.08609 q^{26} -16.0846 q^{27} +1.00000 q^{28} -8.23533 q^{29} +3.29803 q^{30} -4.17984 q^{31} +1.00000 q^{32} +0.971513 q^{34} -1.00000 q^{35} +7.87703 q^{36} +6.08312 q^{37} -1.04489 q^{38} -3.58197 q^{39} -1.00000 q^{40} -8.53772 q^{41} -3.29803 q^{42} -3.06122 q^{43} -7.87703 q^{45} +2.42388 q^{46} -12.3941 q^{47} -3.29803 q^{48} +1.00000 q^{49} +1.00000 q^{50} -3.20408 q^{51} +1.08609 q^{52} -0.323543 q^{53} -16.0846 q^{54} +1.00000 q^{56} +3.44609 q^{57} -8.23533 q^{58} +11.8882 q^{59} +3.29803 q^{60} +13.1507 q^{61} -4.17984 q^{62} +7.87703 q^{63} +1.00000 q^{64} -1.08609 q^{65} +8.03278 q^{67} +0.971513 q^{68} -7.99404 q^{69} -1.00000 q^{70} +4.18166 q^{71} +7.87703 q^{72} -9.94125 q^{73} +6.08312 q^{74} -3.29803 q^{75} -1.04489 q^{76} -3.58197 q^{78} -11.4402 q^{79} -1.00000 q^{80} +29.4165 q^{81} -8.53772 q^{82} -0.382041 q^{83} -3.29803 q^{84} -0.971513 q^{85} -3.06122 q^{86} +27.1604 q^{87} -11.2206 q^{89} -7.87703 q^{90} +1.08609 q^{91} +2.42388 q^{92} +13.7852 q^{93} -12.3941 q^{94} +1.04489 q^{95} -3.29803 q^{96} +14.8572 q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 5 q^{3} + 6 q^{4} - 6 q^{5} - 5 q^{6} + 6 q^{7} + 6 q^{8} + 11 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 - 5 * q^3 + 6 * q^4 - 6 * q^5 - 5 * q^6 + 6 * q^7 + 6 * q^8 + 11 * q^9	\( 6 q + 6 q^{2} - 5 q^{3} + 6 q^{4} - 6 q^{5} - 5 q^{6} + 6 q^{7} + 6 q^{8} + 11 q^{9} - 6 q^{10} - 5 q^{12} + 6 q^{14} + 5 q^{15} + 6 q^{16} - 15 q^{17} + 11 q^{18} - 13 q^{19} - 6 q^{20} - 5 q^{21} - 2 q^{23} - 5 q^{24} + 6 q^{25} - 26 q^{27} + 6 q^{28} - 4 q^{29} + 5 q^{30} - 2 q^{31} + 6 q^{32} - 15 q^{34} - 6 q^{35} + 11 q^{36} - 13 q^{38} - 30 q^{39} - 6 q^{40} - 17 q^{41} - 5 q^{42} + 15 q^{43} - 11 q^{45} - 2 q^{46} - 18 q^{47} - 5 q^{48} + 6 q^{49} + 6 q^{50} + 6 q^{51} + 22 q^{53} - 26 q^{54} + 6 q^{56} - 2 q^{57} - 4 q^{58} - 7 q^{59} + 5 q^{60} - 20 q^{61} - 2 q^{62} + 11 q^{63} + 6 q^{64} - 29 q^{67} - 15 q^{68} + 12 q^{69} - 6 q^{70} - 2 q^{71} + 11 q^{72} + q^{73} - 5 q^{75} - 13 q^{76} - 30 q^{78} - 12 q^{79} - 6 q^{80} + 22 q^{81} - 17 q^{82} - 35 q^{83} - 5 q^{84} + 15 q^{85} + 15 q^{86} - 29 q^{89} - 11 q^{90} - 2 q^{92} + 8 q^{93} - 18 q^{94} + 13 q^{95} - 5 q^{96} - 19 q^{97} + 6 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 - 5 * q^3 + 6 * q^4 - 6 * q^5 - 5 * q^6 + 6 * q^7 + 6 * q^8 + 11 * q^9 - 6 * q^10 - 5 * q^12 + 6 * q^14 + 5 * q^15 + 6 * q^16 - 15 * q^17 + 11 * q^18 - 13 * q^19 - 6 * q^20 - 5 * q^21 - 2 * q^23 - 5 * q^24 + 6 * q^25 - 26 * q^27 + 6 * q^28 - 4 * q^29 + 5 * q^30 - 2 * q^31 + 6 * q^32 - 15 * q^34 - 6 * q^35 + 11 * q^36 - 13 * q^38 - 30 * q^39 - 6 * q^40 - 17 * q^41 - 5 * q^42 + 15 * q^43 - 11 * q^45 - 2 * q^46 - 18 * q^47 - 5 * q^48 + 6 * q^49 + 6 * q^50 + 6 * q^51 + 22 * q^53 - 26 * q^54 + 6 * q^56 - 2 * q^57 - 4 * q^58 - 7 * q^59 + 5 * q^60 - 20 * q^61 - 2 * q^62 + 11 * q^63 + 6 * q^64 - 29 * q^67 - 15 * q^68 + 12 * q^69 - 6 * q^70 - 2 * q^71 + 11 * q^72 + q^73 - 5 * q^75 - 13 * q^76 - 30 * q^78 - 12 * q^79 - 6 * q^80 + 22 * q^81 - 17 * q^82 - 35 * q^83 - 5 * q^84 + 15 * q^85 + 15 * q^86 - 29 * q^89 - 11 * q^90 - 2 * q^92 + 8 * q^93 - 18 * q^94 + 13 * q^95 - 5 * q^96 - 19 * q^97 + 6 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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