LMFDB - Embedded newform 8670.2.a.cc.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8670,2,Mod(1,8670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8670, 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("8670.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8670 = 2 \cdot 3 \cdot 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8670.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:	$69.2302985525$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.46609344.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 15x^{4} + 72x^{2} - 111 $ x^6 - 15x^4 + 72x^2 - 111
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.62286$ of defining polynomial
Character	$\chi$	$=$	8670.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -0.910909 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -0.910909 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +6.06586 q^{11} -1.00000 q^{12} -4.27666 q^{13} +0.910909 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{18} -4.59942 q^{19} +1.00000 q^{20} +0.910909 q^{21} -6.06586 q^{22} -6.68210 q^{23} +1.00000 q^{24} +1.00000 q^{25} +4.27666 q^{26} -1.00000 q^{27} -0.910909 q^{28} +7.90445 q^{29} +1.00000 q^{30} +0.108126 q^{31} -1.00000 q^{32} -6.06586 q^{33} -0.910909 q^{35} +1.00000 q^{36} -7.67461 q^{37} +4.59942 q^{38} +4.27666 q^{39} -1.00000 q^{40} +11.4501 q^{41} -0.910909 q^{42} +2.36407 q^{43} +6.06586 q^{44} +1.00000 q^{45} +6.68210 q^{46} +10.2234 q^{47} -1.00000 q^{48} -6.17024 q^{49} -1.00000 q^{50} -4.27666 q^{52} -3.35203 q^{53} +1.00000 q^{54} +6.06586 q^{55} +0.910909 q^{56} +4.59942 q^{57} -7.90445 q^{58} +6.48746 q^{59} -1.00000 q^{60} +7.03317 q^{61} -0.108126 q^{62} -0.910909 q^{63} +1.00000 q^{64} -4.27666 q^{65} +6.06586 q^{66} -1.82448 q^{67} +6.68210 q^{69} +0.910909 q^{70} -14.2110 q^{71} -1.00000 q^{72} -16.9470 q^{73} +7.67461 q^{74} -1.00000 q^{75} -4.59942 q^{76} -5.52544 q^{77} -4.27666 q^{78} +0.277340 q^{79} +1.00000 q^{80} +1.00000 q^{81} -11.4501 q^{82} -9.64155 q^{83} +0.910909 q^{84} -2.36407 q^{86} -7.90445 q^{87} -6.06586 q^{88} -16.0457 q^{89} -1.00000 q^{90} +3.89565 q^{91} -6.68210 q^{92} -0.108126 q^{93} -10.2234 q^{94} -4.59942 q^{95} +1.00000 q^{96} +1.63668 q^{97} +6.17024 q^{98} +6.06586 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} + 6 q^{5} + 6 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 + 6 * q^5 + 6 * q^6 - 6 * q^8 + 6 * q^9	$ 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} + 6 q^{5} + 6 q^{6} - 6 q^{8} + 6 q^{9} - 6 q^{10} + 6 q^{11} - 6 q^{12} + 6 q^{13} - 6 q^{15} + 6 q^{16} - 6 q^{18} + 6 q^{19} + 6 q^{20} - 6 q^{22} - 12 q^{23} + 6 q^{24} + 6 q^{25} - 6 q^{26} - 6 q^{27} - 6 q^{29} + 6 q^{30} - 12 q^{31} - 6 q^{32} - 6 q^{33} + 6 q^{36} - 12 q^{37} - 6 q^{38} - 6 q^{39} - 6 q^{40} - 12 q^{41} + 6 q^{44} + 6 q^{45} + 12 q^{46} - 6 q^{47} - 6 q^{48} + 6 q^{49} - 6 q^{50} + 6 q^{52} - 30 q^{53} + 6 q^{54} + 6 q^{55} - 6 q^{57} + 6 q^{58} + 6 q^{59} - 6 q^{60} - 6 q^{61} + 12 q^{62} + 6 q^{64} + 6 q^{65} + 6 q^{66} - 24 q^{67} + 12 q^{69} - 6 q^{71} - 6 q^{72} - 36 q^{73} + 12 q^{74} - 6 q^{75} + 6 q^{76} - 54 q^{77} + 6 q^{78} - 12 q^{79} + 6 q^{80} + 6 q^{81} + 12 q^{82} + 12 q^{83} + 6 q^{87} - 6 q^{88} - 18 q^{89} - 6 q^{90} + 24 q^{91} - 12 q^{92} + 12 q^{93} + 6 q^{94} + 6 q^{95} + 6 q^{96} - 30 q^{97} - 6 q^{98} + 6 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 + 6 * q^5 + 6 * q^6 - 6 * q^8 + 6 * q^9 - 6 * q^10 + 6 * q^11 - 6 * q^12 + 6 * q^13 - 6 * q^15 + 6 * q^16 - 6 * q^18 + 6 * q^19 + 6 * q^20 - 6 * q^22 - 12 * q^23 + 6 * q^24 + 6 * q^25 - 6 * q^26 - 6 * q^27 - 6 * q^29 + 6 * q^30 - 12 * q^31 - 6 * q^32 - 6 * q^33 + 6 * q^36 - 12 * q^37 - 6 * q^38 - 6 * q^39 - 6 * q^40 - 12 * q^41 + 6 * q^44 + 6 * q^45 + 12 * q^46 - 6 * q^47 - 6 * q^48 + 6 * q^49 - 6 * q^50 + 6 * q^52 - 30 * q^53 + 6 * q^54 + 6 * q^55 - 6 * q^57 + 6 * q^58 + 6 * q^59 - 6 * q^60 - 6 * q^61 + 12 * q^62 + 6 * q^64 + 6 * q^65 + 6 * q^66 - 24 * q^67 + 12 * q^69 - 6 * q^71 - 6 * q^72 - 36 * q^73 + 12 * q^74 - 6 * q^75 + 6 * q^76 - 54 * q^77 + 6 * q^78 - 12 * q^79 + 6 * q^80 + 6 * q^81 + 12 * q^82 + 12 * q^83 + 6 * q^87 - 6 * q^88 - 18 * q^89 - 6 * q^90 + 24 * q^91 - 12 * q^92 + 12 * q^93 + 6 * q^94 + 6 * q^95 + 6 * q^96 - 30 * q^97 - 6 * q^98 + 6 * q^99

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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.00000	0.408248
$7$	−0.910909	−0.344291	−0.172146	−	0.985072i	$-0.555070\pi$
$7$	−0.910909	−0.344291	−0.172146	+	0.985072i	$0.555070\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	6.06586	1.82892	0.914462	−	0.404671i	$-0.132614\pi$
$11$	6.06586	1.82892	0.914462	+	0.404671i	$0.132614\pi$
$12$	−1.00000	−0.288675
$13$	−4.27666	−1.18613	−0.593066	−	0.805154i	$-0.702083\pi$
$13$	−4.27666	−1.18613	−0.593066	+	0.805154i	$0.702083\pi$
$14$	0.910909	0.243451
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	0	0
$17$	0	0
$18$	−1.00000	−0.235702
$19$	−4.59942	−1.05518	−0.527590	−	0.849499i	$-0.676904\pi$
$19$	−4.59942	−1.05518	−0.527590	+	0.849499i	$0.676904\pi$
$20$	1.00000	0.223607
$21$	0.910909	0.198777
$22$	−6.06586	−1.29324
$23$	−6.68210	−1.39331	−0.696657	−	0.717404i	$-0.745330\pi$
$23$	−6.68210	−1.39331	−0.696657	+	0.717404i	$0.745330\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	4.27666	0.838722
$27$	−1.00000	−0.192450
$28$	−0.910909	−0.172146
$29$	7.90445	1.46782	0.733910	−	0.679247i	$-0.237694\pi$
$29$	7.90445	1.46782	0.733910	+	0.679247i	$0.237694\pi$
$30$	1.00000	0.182574
$31$	0.108126	0.0194200	0.00970998	−	0.999953i	$-0.496909\pi$
$31$	0.108126	0.0194200	0.00970998	+	0.999953i	$0.496909\pi$
$32$	−1.00000	−0.176777
$33$	−6.06586	−1.05593
$34$	0	0
$35$	−0.910909	−0.153972
$36$	1.00000	0.166667
$37$	−7.67461	−1.26170	−0.630849	−	0.775905i	$-0.717293\pi$
$37$	−7.67461	−1.26170	−0.630849	+	0.775905i	$0.717293\pi$
$38$	4.59942	0.746125
$39$	4.27666	0.684813
$40$	−1.00000	−0.158114
$41$	11.4501	1.78820	0.894099	−	0.447869i	$-0.147817\pi$
$41$	11.4501	1.78820	0.894099	+	0.447869i	$0.147817\pi$
$42$	−0.910909	−0.140556
$43$	2.36407	0.360517	0.180259	−	0.983619i	$-0.442307\pi$
$43$	2.36407	0.360517	0.180259	+	0.983619i	$0.442307\pi$
$44$	6.06586	0.914462
$45$	1.00000	0.149071
$46$	6.68210	0.985222
$47$	10.2234	1.49123	0.745616	−	0.666376i	$-0.232155\pi$
$47$	10.2234	1.49123	0.745616	+	0.666376i	$0.232155\pi$
$48$	−1.00000	−0.144338
$49$	−6.17024	−0.881464
$50$	−1.00000	−0.141421
$51$	0	0
$52$	−4.27666	−0.593066
$53$	−3.35203	−0.460436	−0.230218	−	0.973139i	$-0.573944\pi$
$53$	−3.35203	−0.460436	−0.230218	+	0.973139i	$0.573944\pi$
$54$	1.00000	0.136083
$55$	6.06586	0.817920
$56$	0.910909	0.121725
$57$	4.59942	0.609208
$58$	−7.90445	−1.03790
$59$	6.48746	0.844595	0.422298	−	0.906457i	$-0.361224\pi$
$59$	6.48746	0.844595	0.422298	+	0.906457i	$0.361224\pi$
$60$	−1.00000	−0.129099
$61$	7.03317	0.900505	0.450252	−	0.892901i	$-0.351334\pi$
$61$	7.03317	0.900505	0.450252	+	0.892901i	$0.351334\pi$
$62$	−0.108126	−0.0137320
$63$	−0.910909	−0.114764
$64$	1.00000	0.125000
$65$	−4.27666	−0.530454
$66$	6.06586	0.746655
$67$	−1.82448	−0.222895	−0.111448	−	0.993770i	$-0.535549\pi$
$67$	−1.82448	−0.222895	−0.111448	+	0.993770i	$0.535549\pi$
$68$	0	0
$69$	6.68210	0.804431
$70$	0.910909	0.108874
$71$	−14.2110	−1.68653	−0.843267	−	0.537495i	$-0.819371\pi$
$71$	−14.2110	−1.68653	−0.843267	+	0.537495i	$0.819371\pi$
$72$	−1.00000	−0.117851
$73$	−16.9470	−1.98349	−0.991745	−	0.128222i	$-0.959073\pi$
$73$	−16.9470	−1.98349	−0.991745	+	0.128222i	$0.959073\pi$
$74$	7.67461	0.892156
$75$	−1.00000	−0.115470
$76$	−4.59942	−0.527590
$77$	−5.52544	−0.629683
$78$	−4.27666	−0.484236
$79$	0.277340	0.0312032	0.0156016	−	0.999878i	$-0.495034\pi$
$79$	0.277340	0.0312032	0.0156016	+	0.999878i	$0.495034\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−11.4501	−1.26445
$83$	−9.64155	−1.05830	−0.529149	−	0.848529i	$-0.677489\pi$
$83$	−9.64155	−1.05830	−0.529149	+	0.848529i	$0.677489\pi$
$84$	0.910909	0.0993883
$85$	0	0
$86$	−2.36407	−0.254924
$87$	−7.90445	−0.847446
$88$	−6.06586	−0.646622
$89$	−16.0457	−1.70084	−0.850420	−	0.526104i	$-0.823652\pi$
$89$	−16.0457	−1.70084	−0.850420	+	0.526104i	$0.823652\pi$
$90$	−1.00000	−0.105409
$91$	3.89565	0.408375
$92$	−6.68210	−0.696657
$93$	−0.108126	−0.0112121
$94$	−10.2234	−1.05446
$95$	−4.59942	−0.471891
$96$	1.00000	0.102062
$97$	1.63668	0.166180	0.0830898	−	0.996542i	$-0.473521\pi$
$97$	1.63668	0.166180	0.0830898	+	0.996542i	$0.473521\pi$
$98$	6.17024	0.623289
$99$	6.06586	0.609641
$100$	1.00000	0.100000
$101$	−11.2284	−1.11727	−0.558634	−	0.829415i	$-0.688674\pi$
$101$	−11.2284	−1.11727	−0.558634	+	0.829415i	$0.688674\pi$
$102$	0	0
$103$	6.98603	0.688354	0.344177	−	0.938905i	$-0.388158\pi$
$103$	6.98603	0.688354	0.344177	+	0.938905i	$0.388158\pi$
$104$	4.27666	0.419361
$105$	0.910909	0.0888956
$106$	3.35203	0.325578
$107$	2.07828	0.200915	0.100457	−	0.994941i	$-0.467969\pi$
$107$	2.07828	0.200915	0.100457	+	0.994941i	$0.467969\pi$
$108$	−1.00000	−0.0962250
$109$	−9.83804	−0.942314	−0.471157	−	0.882049i	$-0.656163\pi$
$109$	−9.83804	−0.942314	−0.471157	+	0.882049i	$0.656163\pi$
$110$	−6.06586	−0.578357
$111$	7.67461	0.728442
$112$	−0.910909	−0.0860728
$113$	10.5921	0.996419	0.498210	−	0.867057i	$-0.333991\pi$
$113$	10.5921	0.996419	0.498210	+	0.867057i	$0.333991\pi$
$114$	−4.59942	−0.430775
$115$	−6.68210	−0.623109
$116$	7.90445	0.733910
$117$	−4.27666	−0.395377
$118$	−6.48746	−0.597219
$119$	0	0
$120$	1.00000	0.0912871
$121$	25.7946	2.34496
$122$	−7.03317	−0.636753
$123$	−11.4501	−1.03242
$124$	0.108126	0.00970998
$125$	1.00000	0.0894427
$126$	0.910909	0.0811502
$127$	2.16309	0.191943	0.0959715	−	0.995384i	$-0.469404\pi$
$127$	2.16309	0.191943	0.0959715	+	0.995384i	$0.469404\pi$
$128$	−1.00000	−0.0883883
$129$	−2.36407	−0.208145
$130$	4.27666	0.375088
$131$	−16.3338	−1.42709	−0.713545	−	0.700609i	$-0.752912\pi$
$131$	−16.3338	−1.42709	−0.713545	+	0.700609i	$0.752912\pi$
$132$	−6.06586	−0.527965
$133$	4.18965	0.363289
$134$	1.82448	0.157611
$135$	−1.00000	−0.0860663
$136$	0	0
$137$	−3.29410	−0.281434	−0.140717	−	0.990050i	$-0.544941\pi$
$137$	−3.29410	−0.281434	−0.140717	+	0.990050i	$0.544941\pi$
$138$	−6.68210	−0.568818
$139$	−7.68214	−0.651590	−0.325795	−	0.945440i	$-0.605632\pi$
$139$	−7.68214	−0.651590	−0.325795	+	0.945440i	$0.605632\pi$
$140$	−0.910909	−0.0769859
$141$	−10.2234	−0.860963
$142$	14.2110	1.19256
$143$	−25.9416	−2.16934
$144$	1.00000	0.0833333
$145$	7.90445	0.656429
$146$	16.9470	1.40254
$147$	6.17024	0.508913
$148$	−7.67461	−0.630849
$149$	3.22904	0.264533	0.132267	−	0.991214i	$-0.457774\pi$
$149$	3.22904	0.264533	0.132267	+	0.991214i	$0.457774\pi$
$150$	1.00000	0.0816497
$151$	14.9816	1.21919	0.609593	−	0.792715i	$-0.291333\pi$
$151$	14.9816	1.21919	0.609593	+	0.792715i	$0.291333\pi$
$152$	4.59942	0.373062
$153$	0	0
$154$	5.52544	0.445253
$155$	0.108126	0.00868487
$156$	4.27666	0.342407
$157$	16.9235	1.35064	0.675320	−	0.737524i	$-0.264005\pi$
$157$	16.9235	1.35064	0.675320	+	0.737524i	$0.264005\pi$
$158$	−0.277340	−0.0220640
$159$	3.35203	0.265833
$160$	−1.00000	−0.0790569
$161$	6.08679	0.479706
$162$	−1.00000	−0.0785674
$163$	6.71534	0.525986	0.262993	−	0.964798i	$-0.415290\pi$
$163$	6.71534	0.525986	0.262993	+	0.964798i	$0.415290\pi$
$164$	11.4501	0.894099
$165$	−6.06586	−0.472226
$166$	9.64155	0.748329
$167$	−2.31745	−0.179330	−0.0896649	−	0.995972i	$-0.528580\pi$
$167$	−2.31745	−0.179330	−0.0896649	+	0.995972i	$0.528580\pi$
$168$	−0.910909	−0.0702782
$169$	5.28980	0.406908
$170$	0	0
$171$	−4.59942	−0.351727
$172$	2.36407	0.180259
$173$	−2.31752	−0.176197	−0.0880987	−	0.996112i	$-0.528079\pi$
$173$	−2.31752	−0.176197	−0.0880987	+	0.996112i	$0.528079\pi$
$174$	7.90445	0.599235
$175$	−0.910909	−0.0688583
$176$	6.06586	0.457231
$177$	−6.48746	−0.487627
$178$	16.0457	1.20268
$179$	15.2927	1.14303	0.571514	−	0.820592i	$-0.306356\pi$
$179$	15.2927	1.14303	0.571514	+	0.820592i	$0.306356\pi$
$180$	1.00000	0.0745356
$181$	−20.5393	−1.52668	−0.763339	−	0.645998i	$-0.776441\pi$
$181$	−20.5393	−1.52668	−0.763339	+	0.645998i	$0.776441\pi$
$182$	−3.89565	−0.288765
$183$	−7.03317	−0.519907
$184$	6.68210	0.492611
$185$	−7.67461	−0.564249
$186$	0.108126	0.00792816
$187$	0	0
$188$	10.2234	0.745616
$189$	0.910909	0.0662589
$190$	4.59942	0.333677
$191$	24.2575	1.75521	0.877606	−	0.479383i	$-0.159140\pi$
$191$	24.2575	1.75521	0.877606	+	0.479383i	$0.159140\pi$
$192$	−1.00000	−0.0721688
$193$	−14.5971	−1.05072	−0.525362	−	0.850879i	$-0.676070\pi$
$193$	−14.5971	−1.05072	−0.525362	+	0.850879i	$0.676070\pi$
$194$	−1.63668	−0.117507
$195$	4.27666	0.306258
$196$	−6.17024	−0.440732
$197$	23.3001	1.66007	0.830033	−	0.557714i	$-0.188321\pi$
$197$	23.3001	1.66007	0.830033	+	0.557714i	$0.188321\pi$
$198$	−6.06586	−0.431082
$199$	−5.37447	−0.380986	−0.190493	−	0.981689i	$-0.561009\pi$
$199$	−5.37447	−0.380986	−0.190493	+	0.981689i	$0.561009\pi$
$200$	−1.00000	−0.0707107
$201$	1.82448	0.128689
$202$	11.2284	0.790027
$203$	−7.20023	−0.505357
$204$	0	0
$205$	11.4501	0.799707
$206$	−6.98603	−0.486740
$207$	−6.68210	−0.464438
$208$	−4.27666	−0.296533
$209$	−27.8994	−1.92984
$210$	−0.910909	−0.0628587
$211$	−1.82509	−0.125645	−0.0628223	−	0.998025i	$-0.520010\pi$
$211$	−1.82509	−0.125645	−0.0628223	+	0.998025i	$0.520010\pi$
$212$	−3.35203	−0.230218
$213$	14.2110	0.973721
$214$	−2.07828	−0.142068
$215$	2.36407	0.161228
$216$	1.00000	0.0680414
$217$	−0.0984927	−0.00668612
$218$	9.83804	0.666316
$219$	16.9470	1.14517
$220$	6.06586	0.408960
$221$	0	0
$222$	−7.67461	−0.515086
$223$	−3.85650	−0.258250	−0.129125	−	0.991628i	$-0.541217\pi$
$223$	−3.85650	−0.258250	−0.129125	+	0.991628i	$0.541217\pi$
$224$	0.910909	0.0608627
$225$	1.00000	0.0666667
$226$	−10.5921	−0.704575
$227$	3.77275	0.250406	0.125203	−	0.992131i	$-0.460042\pi$
$227$	3.77275	0.250406	0.125203	+	0.992131i	$0.460042\pi$
$228$	4.59942	0.304604
$229$	−4.88240	−0.322638	−0.161319	−	0.986902i	$-0.551575\pi$
$229$	−4.88240	−0.322638	−0.161319	+	0.986902i	$0.551575\pi$
$230$	6.68210	0.440605
$231$	5.52544	0.363547
$232$	−7.90445	−0.518952
$233$	−19.6670	−1.28843	−0.644215	−	0.764844i	$-0.722816\pi$
$233$	−19.6670	−1.28843	−0.644215	+	0.764844i	$0.722816\pi$
$234$	4.27666	0.279574
$235$	10.2234	0.666899
$236$	6.48746	0.422298
$237$	−0.277340	−0.0180152
$238$	0	0
$239$	−19.2547	−1.24548	−0.622741	−	0.782428i	$-0.713981\pi$
$239$	−19.2547	−1.24548	−0.622741	+	0.782428i	$0.713981\pi$
$240$	−1.00000	−0.0645497
$241$	−4.77219	−0.307404	−0.153702	−	0.988117i	$-0.549120\pi$
$241$	−4.77219	−0.307404	−0.153702	+	0.988117i	$0.549120\pi$
$242$	−25.7946	−1.65814
$243$	−1.00000	−0.0641500
$244$	7.03317	0.450252
$245$	−6.17024	−0.394202
$246$	11.4501	0.730029
$247$	19.6701	1.25158
$248$	−0.108126	−0.00686599
$249$	9.64155	0.611008
$250$	−1.00000	−0.0632456
$251$	−20.3194	−1.28255	−0.641275	−	0.767311i	$-0.721594\pi$
$251$	−20.3194	−1.28255	−0.641275	+	0.767311i	$0.721594\pi$
$252$	−0.910909	−0.0573819
$253$	−40.5327	−2.54827
$254$	−2.16309	−0.135724
$255$	0	0
$256$	1.00000	0.0625000
$257$	−5.24186	−0.326978	−0.163489	−	0.986545i	$-0.552275\pi$
$257$	−5.24186	−0.326978	−0.163489	+	0.986545i	$0.552275\pi$
$258$	2.36407	0.147181
$259$	6.99087	0.434392
$260$	−4.27666	−0.265227
$261$	7.90445	0.489273
$262$	16.3338	1.00910
$263$	4.51951	0.278685	0.139342	−	0.990244i	$-0.455501\pi$
$263$	4.51951	0.278685	0.139342	+	0.990244i	$0.455501\pi$
$264$	6.06586	0.373328
$265$	−3.35203	−0.205913
$266$	−4.18965	−0.256884
$267$	16.0457	0.981981
$268$	−1.82448	−0.111448
$269$	−26.8528	−1.63725	−0.818623	−	0.574331i	$-0.805262\pi$
$269$	−26.8528	−1.63725	−0.818623	+	0.574331i	$0.805262\pi$
$270$	1.00000	0.0608581
$271$	−3.49535	−0.212327	−0.106164	−	0.994349i	$-0.533857\pi$
$271$	−3.49535	−0.212327	−0.106164	+	0.994349i	$0.533857\pi$
$272$	0	0
$273$	−3.89565	−0.235775
$274$	3.29410	0.199004
$275$	6.06586	0.365785
$276$	6.68210	0.402215
$277$	−15.4247	−0.926779	−0.463390	−	0.886155i	$-0.653367\pi$
$277$	−15.4247	−0.926779	−0.463390	+	0.886155i	$0.653367\pi$
$278$	7.68214	0.460744
$279$	0.108126	0.00647332
$280$	0.910909	0.0544372
$281$	−21.1614	−1.26238	−0.631190	−	0.775628i	$-0.717433\pi$
$281$	−21.1614	−1.26238	−0.631190	+	0.775628i	$0.717433\pi$
$282$	10.2234	0.608793
$283$	5.11480	0.304044	0.152022	−	0.988377i	$-0.451422\pi$
$283$	5.11480	0.304044	0.152022	+	0.988377i	$0.451422\pi$
$284$	−14.2110	−0.843267
$285$	4.59942	0.272446
$286$	25.9416	1.53396
$287$	−10.4300	−0.615661
$288$	−1.00000	−0.0589256
$289$	0	0
$290$	−7.90445	−0.464165
$291$	−1.63668	−0.0959439
$292$	−16.9470	−0.991745
$293$	27.0948	1.58289	0.791447	−	0.611237i	$-0.209328\pi$
$293$	27.0948	1.58289	0.791447	+	0.611237i	$0.209328\pi$
$294$	−6.17024	−0.359856
$295$	6.48746	0.377714
$296$	7.67461	0.446078
$297$	−6.06586	−0.351977
$298$	−3.22904	−0.187053
$299$	28.5771	1.65265
$300$	−1.00000	−0.0577350
$301$	−2.15345	−0.124123
$302$	−14.9816	−0.862094
$303$	11.2284	0.645054
$304$	−4.59942	−0.263795
$305$	7.03317	0.402718
$306$	0	0
$307$	−0.0460189	−0.00262644	−0.00131322	−	0.999999i	$-0.500418\pi$
$307$	−0.0460189	−0.00262644	−0.00131322	+	0.999999i	$0.500418\pi$
$308$	−5.52544	−0.314841
$309$	−6.98603	−0.397422
$310$	−0.108126	−0.00614113
$311$	10.4669	0.593524	0.296762	−	0.954951i	$-0.404093\pi$
$311$	10.4669	0.593524	0.296762	+	0.954951i	$0.404093\pi$
$312$	−4.27666	−0.242118
$313$	8.62404	0.487459	0.243730	−	0.969843i	$-0.421629\pi$
$313$	8.62404	0.487459	0.243730	+	0.969843i	$0.421629\pi$
$314$	−16.9235	−0.955047
$315$	−0.910909	−0.0513239
$316$	0.277340	0.0156016
$317$	25.8237	1.45041	0.725203	−	0.688535i	$-0.241746\pi$
$317$	25.8237	1.45041	0.725203	+	0.688535i	$0.241746\pi$
$318$	−3.35203	−0.187972
$319$	47.9472	2.68453
$320$	1.00000	0.0559017
$321$	−2.07828	−0.115998
$322$	−6.08679	−0.339203
$323$	0	0
$324$	1.00000	0.0555556
$325$	−4.27666	−0.237226
$326$	−6.71534	−0.371928
$327$	9.83804	0.544045
$328$	−11.4501	−0.632224
$329$	−9.31257	−0.513418
$330$	6.06586	0.333914
$331$	−3.11196	−0.171049	−0.0855244	−	0.996336i	$-0.527257\pi$
$331$	−3.11196	−0.171049	−0.0855244	+	0.996336i	$0.527257\pi$
$332$	−9.64155	−0.529149
$333$	−7.67461	−0.420566
$334$	2.31745	0.126805
$335$	−1.82448	−0.0996818
$336$	0.910909	0.0496942
$337$	11.4716	0.624896	0.312448	−	0.949935i	$-0.398851\pi$
$337$	11.4716	0.624896	0.312448	+	0.949935i	$0.398851\pi$
$338$	−5.28980	−0.287727
$339$	−10.5921	−0.575283
$340$	0	0
$341$	0.655875	0.0355176
$342$	4.59942	0.248708
$343$	11.9969	0.647771
$344$	−2.36407	−0.127462
$345$	6.68210	0.359752
$346$	2.31752	0.124590
$347$	−18.8550	−1.01219	−0.506094	−	0.862478i	$-0.668911\pi$
$347$	−18.8550	−1.01219	−0.506094	+	0.862478i	$0.668911\pi$
$348$	−7.90445	−0.423723
$349$	33.5335	1.79501	0.897504	−	0.441006i	$-0.145378\pi$
$349$	33.5335	1.79501	0.897504	+	0.441006i	$0.145378\pi$
$350$	0.910909	0.0486901
$351$	4.27666	0.228271
$352$	−6.06586	−0.323311
$353$	32.1735	1.71242	0.856211	−	0.516626i	$-0.172812\pi$
$353$	32.1735	1.71242	0.856211	+	0.516626i	$0.172812\pi$
$354$	6.48746	0.344805
$355$	−14.2110	−0.754241
$356$	−16.0457	−0.850420
$357$	0	0
$358$	−15.2927	−0.808243
$359$	−6.10557	−0.322240	−0.161120	−	0.986935i	$-0.551511\pi$
$359$	−6.10557	−0.322240	−0.161120	+	0.986935i	$0.551511\pi$
$360$	−1.00000	−0.0527046
$361$	2.15467	0.113404
$362$	20.5393	1.07952
$363$	−25.7946	−1.35387
$364$	3.89565	0.204187
$365$	−16.9470	−0.887044
$366$	7.03317	0.367630
$367$	−9.98246	−0.521080	−0.260540	−	0.965463i	$-0.583901\pi$
$367$	−9.98246	−0.521080	−0.260540	+	0.965463i	$0.583901\pi$
$368$	−6.68210	−0.348329
$369$	11.4501	0.596066
$370$	7.67461	0.398984
$371$	3.05339	0.158524
$372$	−0.108126	−0.00560606
$373$	6.26244	0.324257	0.162128	−	0.986770i	$-0.448164\pi$
$373$	6.26244	0.324257	0.162128	+	0.986770i	$0.448164\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	−10.2234	−0.527230
$377$	−33.8046	−1.74103
$378$	−0.910909	−0.0468521
$379$	−16.2348	−0.833926	−0.416963	−	0.908923i	$-0.636906\pi$
$379$	−16.2348	−0.833926	−0.416963	+	0.908923i	$0.636906\pi$
$380$	−4.59942	−0.235945
$381$	−2.16309	−0.110818
$382$	−24.2575	−1.24112
$383$	−14.0220	−0.716492	−0.358246	−	0.933627i	$-0.616625\pi$
$383$	−14.0220	−0.716492	−0.358246	+	0.933627i	$0.616625\pi$
$384$	1.00000	0.0510310
$385$	−5.52544	−0.281603
$386$	14.5971	0.742974
$387$	2.36407	0.120172
$388$	1.63668	0.0830898
$389$	−7.90249	−0.400672	−0.200336	−	0.979727i	$-0.564203\pi$
$389$	−7.90249	−0.400672	−0.200336	+	0.979727i	$0.564203\pi$
$390$	−4.27666	−0.216557
$391$	0	0
$392$	6.17024	0.311644
$393$	16.3338	0.823931
$394$	−23.3001	−1.17384
$395$	0.277340	0.0139545
$396$	6.06586	0.304821
$397$	−31.6615	−1.58904	−0.794522	−	0.607235i	$-0.792279\pi$
$397$	−31.6615	−1.58904	−0.794522	+	0.607235i	$0.792279\pi$
$398$	5.37447	0.269398
$399$	−4.18965	−0.209745
$400$	1.00000	0.0500000
$401$	−7.29931	−0.364510	−0.182255	−	0.983251i	$-0.558340\pi$
$401$	−7.29931	−0.364510	−0.182255	+	0.983251i	$0.558340\pi$
$402$	−1.82448	−0.0909966
$403$	−0.462417	−0.0230346
$404$	−11.2284	−0.558634
$405$	1.00000	0.0496904
$406$	7.20023	0.357342
$407$	−46.5531	−2.30755
$408$	0	0
$409$	6.40228	0.316572	0.158286	−	0.987393i	$-0.449403\pi$
$409$	6.40228	0.316572	0.158286	+	0.987393i	$0.449403\pi$
$410$	−11.4501	−0.565478
$411$	3.29410	0.162486
$412$	6.98603	0.344177
$413$	−5.90949	−0.290787
$414$	6.68210	0.328407
$415$	−9.64155	−0.473285
$416$	4.27666	0.209680
$417$	7.68214	0.376196
$418$	27.8994	1.36461
$419$	−29.9090	−1.46115	−0.730576	−	0.682831i	$-0.760748\pi$
$419$	−29.9090	−1.46115	−0.730576	+	0.682831i	$0.760748\pi$
$420$	0.910909	0.0444478
$421$	−7.96871	−0.388371	−0.194186	−	0.980965i	$-0.562206\pi$
$421$	−7.96871	−0.388371	−0.194186	+	0.980965i	$0.562206\pi$
$422$	1.82509	0.0888441
$423$	10.2234	0.497077
$424$	3.35203	0.162789
$425$	0	0
$426$	−14.2110	−0.688524
$427$	−6.40658	−0.310036
$428$	2.07828	0.100457
$429$	25.9416	1.25247
$430$	−2.36407	−0.114006
$431$	18.7864	0.904911	0.452455	−	0.891787i	$-0.350548\pi$
$431$	18.7864	0.904911	0.452455	+	0.891787i	$0.350548\pi$
$432$	−1.00000	−0.0481125
$433$	−9.72054	−0.467140	−0.233570	−	0.972340i	$-0.575041\pi$
$433$	−9.72054	−0.467140	−0.233570	+	0.972340i	$0.575041\pi$
$434$	0.0984927	0.00472780
$435$	−7.90445	−0.378989
$436$	−9.83804	−0.471157
$437$	30.7338	1.47020
$438$	−16.9470	−0.809757
$439$	−29.1989	−1.39359	−0.696793	−	0.717272i	$-0.745390\pi$
$439$	−29.1989	−1.39359	−0.696793	+	0.717272i	$0.745390\pi$
$440$	−6.06586	−0.289178
$441$	−6.17024	−0.293821
$442$	0	0
$443$	−2.86239	−0.135996	−0.0679982	−	0.997685i	$-0.521661\pi$
$443$	−2.86239	−0.135996	−0.0679982	+	0.997685i	$0.521661\pi$
$444$	7.67461	0.364221
$445$	−16.0457	−0.760639
$446$	3.85650	0.182610
$447$	−3.22904	−0.152728
$448$	−0.910909	−0.0430364
$449$	−23.4776	−1.10797	−0.553987	−	0.832525i	$-0.686894\pi$
$449$	−23.4776	−1.10797	−0.553987	+	0.832525i	$0.686894\pi$
$450$	−1.00000	−0.0471405
$451$	69.4544	3.27048
$452$	10.5921	0.498210
$453$	−14.9816	−0.703897
$454$	−3.77275	−0.177064
$455$	3.89565	0.182631
$456$	−4.59942	−0.215388
$457$	6.54347	0.306091	0.153045	−	0.988219i	$-0.451092\pi$
$457$	6.54347	0.306091	0.153045	+	0.988219i	$0.451092\pi$
$458$	4.88240	0.228139
$459$	0	0
$460$	−6.68210	−0.311555
$461$	−26.0322	−1.21244	−0.606220	−	0.795297i	$-0.707315\pi$
$461$	−26.0322	−1.21244	−0.606220	+	0.795297i	$0.707315\pi$
$462$	−5.52544	−0.257067
$463$	−27.1179	−1.26027	−0.630137	−	0.776484i	$-0.717001\pi$
$463$	−27.1179	−1.26027	−0.630137	+	0.776484i	$0.717001\pi$
$464$	7.90445	0.366955
$465$	−0.108126	−0.00501421
$466$	19.6670	0.911058
$467$	−7.71126	−0.356834	−0.178417	−	0.983955i	$-0.557098\pi$
$467$	−7.71126	−0.356834	−0.178417	+	0.983955i	$0.557098\pi$
$468$	−4.27666	−0.197689
$469$	1.66193	0.0767409
$470$	−10.2234	−0.471569
$471$	−16.9235	−0.779793
$472$	−6.48746	−0.298609
$473$	14.3401	0.659359
$474$	0.277340	0.0127386
$475$	−4.59942	−0.211036
$476$	0	0
$477$	−3.35203	−0.153479
$478$	19.2547	0.880689
$479$	38.0806	1.73995	0.869973	−	0.493100i	$-0.164136\pi$
$479$	38.0806	1.73995	0.869973	+	0.493100i	$0.164136\pi$
$480$	1.00000	0.0456435
$481$	32.8217	1.49654
$482$	4.77219	0.217367
$483$	−6.08679	−0.276958
$484$	25.7946	1.17248
$485$	1.63668	0.0743178
$486$	1.00000	0.0453609
$487$	9.35905	0.424099	0.212049	−	0.977259i	$-0.431986\pi$
$487$	9.35905	0.424099	0.212049	+	0.977259i	$0.431986\pi$
$488$	−7.03317	−0.318376
$489$	−6.71534	−0.303678
$490$	6.17024	0.278743
$491$	−38.5620	−1.74028	−0.870138	−	0.492808i	$-0.835971\pi$
$491$	−38.5620	−1.74028	−0.870138	+	0.492808i	$0.835971\pi$
$492$	−11.4501	−0.516208
$493$	0	0
$494$	−19.6701	−0.885002
$495$	6.06586	0.272640
$496$	0.108126	0.00485499
$497$	12.9449	0.580659
$498$	−9.64155	−0.432048
$499$	29.0164	1.29895	0.649475	−	0.760383i	$-0.274989\pi$
$499$	29.0164	1.29895	0.649475	+	0.760383i	$0.274989\pi$
$500$	1.00000	0.0447214
$501$	2.31745	0.103536
$502$	20.3194	0.906900
$503$	−19.5916	−0.873547	−0.436773	−	0.899572i	$-0.643879\pi$
$503$	−19.5916	−0.873547	−0.436773	+	0.899572i	$0.643879\pi$
$504$	0.910909	0.0405751
$505$	−11.2284	−0.499657
$506$	40.5327	1.80190
$507$	−5.28980	−0.234928
$508$	2.16309	0.0959715
$509$	−3.47795	−0.154157	−0.0770786	−	0.997025i	$-0.524559\pi$
$509$	−3.47795	−0.154157	−0.0770786	+	0.997025i	$0.524559\pi$
$510$	0	0
$511$	15.4371	0.682899
$512$	−1.00000	−0.0441942
$513$	4.59942	0.203069
$514$	5.24186	0.231208
$515$	6.98603	0.307841
$516$	−2.36407	−0.104072
$517$	62.0135	2.72735
$518$	−6.99087	−0.307161
$519$	2.31752	0.101728
$520$	4.27666	0.187544
$521$	−27.6918	−1.21320	−0.606599	−	0.795008i	$-0.707467\pi$
$521$	−27.6918	−1.21320	−0.606599	+	0.795008i	$0.707467\pi$
$522$	−7.90445	−0.345968
$523$	−40.0408	−1.75086	−0.875432	−	0.483342i	$-0.839423\pi$
$523$	−40.0408	−1.75086	−0.875432	+	0.483342i	$0.839423\pi$
$524$	−16.3338	−0.713545
$525$	0.910909	0.0397553
$526$	−4.51951	−0.197060
$527$	0	0
$528$	−6.06586	−0.263983
$529$	21.6505	0.941327
$530$	3.35203	0.145603
$531$	6.48746	0.281532
$532$	4.18965	0.181645
$533$	−48.9680	−2.12104
$534$	−16.0457	−0.694365
$535$	2.07828	0.0898519
$536$	1.82448	0.0788054
$537$	−15.2927	−0.659928
$538$	26.8528	1.15771
$539$	−37.4278	−1.61213
$540$	−1.00000	−0.0430331
$541$	−26.9229	−1.15751	−0.578754	−	0.815502i	$-0.696461\pi$
$541$	−26.9229	−1.15751	−0.578754	+	0.815502i	$0.696461\pi$
$542$	3.49535	0.150138
$543$	20.5393	0.881428
$544$	0	0
$545$	−9.83804	−0.421415
$546$	3.89565	0.166718
$547$	15.5656	0.665535	0.332768	−	0.943009i	$-0.392018\pi$
$547$	15.5656	0.665535	0.332768	+	0.943009i	$0.392018\pi$
$548$	−3.29410	−0.140717
$549$	7.03317	0.300168
$550$	−6.06586	−0.258649
$551$	−36.3559	−1.54881
$552$	−6.68210	−0.284409
$553$	−0.252631	−0.0107430
$554$	15.4247	0.655332
$555$	7.67461	0.325769
$556$	−7.68214	−0.325795
$557$	−11.2322	−0.475925	−0.237962	−	0.971274i	$-0.576479\pi$
$557$	−11.2322	−0.475925	−0.237962	+	0.971274i	$0.576479\pi$
$558$	−0.108126	−0.00457733
$559$	−10.1103	−0.427621
$560$	−0.910909	−0.0384929
$561$	0	0
$562$	21.1614	0.892638
$563$	−2.05570	−0.0866373	−0.0433186	−	0.999061i	$-0.513793\pi$
$563$	−2.05570	−0.0866373	−0.0433186	+	0.999061i	$0.513793\pi$
$564$	−10.2234	−0.430482
$565$	10.5921	0.445612
$566$	−5.11480	−0.214991
$567$	−0.910909	−0.0382546
$568$	14.2110	0.596280
$569$	−40.5417	−1.69960	−0.849798	−	0.527109i	$-0.823276\pi$
$569$	−40.5417	−1.69960	−0.849798	+	0.527109i	$0.823276\pi$
$570$	−4.59942	−0.192649
$571$	17.6246	0.737565	0.368782	−	0.929516i	$-0.379775\pi$
$571$	17.6246	0.737565	0.368782	+	0.929516i	$0.379775\pi$
$572$	−25.9416	−1.08467
$573$	−24.2575	−1.01337
$574$	10.4300	0.435338
$575$	−6.68210	−0.278663
$576$	1.00000	0.0416667
$577$	1.82358	0.0759165	0.0379583	−	0.999279i	$-0.487915\pi$
$577$	1.82358	0.0759165	0.0379583	+	0.999279i	$0.487915\pi$
$578$	0	0
$579$	14.5971	0.606636
$580$	7.90445	0.328214
$581$	8.78257	0.364363
$582$	1.63668	0.0678426
$583$	−20.3329	−0.842103
$584$	16.9470	0.701270
$585$	−4.27666	−0.176818
$586$	−27.0948	−1.11928
$587$	21.0875	0.870373	0.435186	−	0.900340i	$-0.356682\pi$
$587$	21.0875	0.870373	0.435186	+	0.900340i	$0.356682\pi$
$588$	6.17024	0.254457
$589$	−0.497316	−0.0204915
$590$	−6.48746	−0.267084
$591$	−23.3001	−0.958440
$592$	−7.67461	−0.315425
$593$	4.37898	0.179823	0.0899115	−	0.995950i	$-0.471342\pi$
$593$	4.37898	0.179823	0.0899115	+	0.995950i	$0.471342\pi$
$594$	6.06586	0.248885
$595$	0	0
$596$	3.22904	0.132267
$597$	5.37447	0.219962
$598$	−28.5771	−1.16860
$599$	13.5838	0.555019	0.277510	−	0.960723i	$-0.410491\pi$
$599$	13.5838	0.555019	0.277510	+	0.960723i	$0.410491\pi$
$600$	1.00000	0.0408248
$601$	−23.9422	−0.976623	−0.488311	−	0.872669i	$-0.662387\pi$
$601$	−23.9422	−0.976623	−0.488311	+	0.872669i	$0.662387\pi$
$602$	2.15345	0.0877682
$603$	−1.82448	−0.0742985
$604$	14.9816	0.609593
$605$	25.7946	1.04870
$606$	−11.2284	−0.456122
$607$	−29.2869	−1.18872	−0.594359	−	0.804200i	$-0.702594\pi$
$607$	−29.2869	−1.18872	−0.594359	+	0.804200i	$0.702594\pi$
$608$	4.59942	0.186531
$609$	7.20023	0.291768
$610$	−7.03317	−0.284765
$611$	−43.7219	−1.76880
$612$	0	0
$613$	−10.2330	−0.413306	−0.206653	−	0.978414i	$-0.566257\pi$
$613$	−10.2330	−0.413306	−0.206653	+	0.978414i	$0.566257\pi$
$614$	0.0460189	0.00185717
$615$	−11.4501	−0.461711
$616$	5.52544	0.222626
$617$	−34.5734	−1.39187	−0.695936	−	0.718104i	$-0.745010\pi$
$617$	−34.5734	−1.39187	−0.695936	+	0.718104i	$0.745010\pi$
$618$	6.98603	0.281020
$619$	−9.32841	−0.374940	−0.187470	−	0.982270i	$-0.560029\pi$
$619$	−9.32841	−0.374940	−0.187470	+	0.982270i	$0.560029\pi$
$620$	0.108126	0.00434243
$621$	6.68210	0.268144
$622$	−10.4669	−0.419685
$623$	14.6162	0.585584
$624$	4.27666	0.171203
$625$	1.00000	0.0400000
$626$	−8.62404	−0.344686
$627$	27.8994	1.11420
$628$	16.9235	0.675320
$629$	0	0
$630$	0.910909	0.0362915
$631$	21.2047	0.844146	0.422073	−	0.906562i	$-0.361303\pi$
$631$	21.2047	0.844146	0.422073	+	0.906562i	$0.361303\pi$
$632$	−0.277340	−0.0110320
$633$	1.82509	0.0725409
$634$	−25.8237	−1.02559
$635$	2.16309	0.0858395
$636$	3.35203	0.132916
$637$	26.3880	1.04553
$638$	−47.9472	−1.89825
$639$	−14.2110	−0.562178
$640$	−1.00000	−0.0395285
$641$	8.01291	0.316491	0.158245	−	0.987400i	$-0.449416\pi$
$641$	8.01291	0.316491	0.158245	+	0.987400i	$0.449416\pi$
$642$	2.07828	0.0820232
$643$	36.6870	1.44679	0.723397	−	0.690432i	$-0.242580\pi$
$643$	36.6870	1.44679	0.723397	+	0.690432i	$0.242580\pi$
$644$	6.08679	0.239853
$645$	−2.36407	−0.0930852
$646$	0	0
$647$	38.7364	1.52289	0.761443	−	0.648231i	$-0.224491\pi$
$647$	38.7364	1.52289	0.761443	+	0.648231i	$0.224491\pi$
$648$	−1.00000	−0.0392837
$649$	39.3520	1.54470
$650$	4.27666	0.167744
$651$	0.0984927	0.00386023
$652$	6.71534	0.262993
$653$	−37.0470	−1.44976	−0.724880	−	0.688875i	$-0.758105\pi$
$653$	−37.0470	−1.44976	−0.724880	+	0.688875i	$0.758105\pi$
$654$	−9.83804	−0.384698
$655$	−16.3338	−0.638214
$656$	11.4501	0.447050
$657$	−16.9470	−0.661164
$658$	9.31257	0.363042
$659$	26.0396	1.01436	0.507179	−	0.861841i	$-0.330688\pi$
$659$	26.0396	1.01436	0.507179	+	0.861841i	$0.330688\pi$
$660$	−6.06586	−0.236113
$661$	−21.1146	−0.821262	−0.410631	−	0.911802i	$-0.634692\pi$
$661$	−21.1146	−0.821262	−0.410631	+	0.911802i	$0.634692\pi$
$662$	3.11196	0.120950
$663$	0	0
$664$	9.64155	0.374165
$665$	4.18965	0.162468
$666$	7.67461	0.297385
$667$	−52.8183	−2.04513
$668$	−2.31745	−0.0896649
$669$	3.85650	0.149101
$670$	1.82448	0.0704857
$671$	42.6622	1.64696
$672$	−0.910909	−0.0351391
$673$	39.3374	1.51634	0.758172	−	0.652054i	$-0.226093\pi$
$673$	39.3374	1.51634	0.758172	+	0.652054i	$0.226093\pi$
$674$	−11.4716	−0.441868
$675$	−1.00000	−0.0384900
$676$	5.28980	0.203454
$677$	−11.4959	−0.441824	−0.220912	−	0.975294i	$-0.570903\pi$
$677$	−11.4959	−0.441824	−0.220912	+	0.975294i	$0.570903\pi$
$678$	10.5921	0.406787
$679$	−1.49087	−0.0572142
$680$	0	0
$681$	−3.77275	−0.144572
$682$	−0.655875	−0.0251148
$683$	−44.3706	−1.69780	−0.848898	−	0.528557i	$-0.822733\pi$
$683$	−44.3706	−1.69780	−0.848898	+	0.528557i	$0.822733\pi$
$684$	−4.59942	−0.175863
$685$	−3.29410	−0.125861
$686$	−11.9969	−0.458044
$687$	4.88240	0.186275
$688$	2.36407	0.0901293
$689$	14.3355	0.546138
$690$	−6.68210	−0.254383
$691$	−40.3754	−1.53595	−0.767976	−	0.640478i	$-0.778736\pi$
$691$	−40.3754	−1.53595	−0.767976	+	0.640478i	$0.778736\pi$
$692$	−2.31752	−0.0880987
$693$	−5.52544	−0.209894
$694$	18.8550	0.715725
$695$	−7.68214	−0.291400
$696$	7.90445	0.299617
$697$	0	0
$698$	−33.5335	−1.26926
$699$	19.6670	0.743876
$700$	−0.910909	−0.0344291
$701$	−25.9190	−0.978948	−0.489474	−	0.872018i	$-0.662811\pi$
$701$	−25.9190	−0.978948	−0.489474	+	0.872018i	$0.662811\pi$
$702$	−4.27666	−0.161412
$703$	35.2988	1.33132
$704$	6.06586	0.228616
$705$	−10.2234	−0.385035
$706$	−32.1735	−1.21087
$707$	10.2280	0.384665
$708$	−6.48746	−0.243814
$709$	12.8818	0.483785	0.241892	−	0.970303i	$-0.422232\pi$
$709$	12.8818	0.483785	0.241892	+	0.970303i	$0.422232\pi$
$710$	14.2110	0.533329
$711$	0.277340	0.0104011
$712$	16.0457	0.601338
$713$	−0.722507	−0.0270581
$714$	0	0
$715$	−25.9416	−0.970160
$716$	15.2927	0.571514
$717$	19.2547	0.719080
$718$	6.10557	0.227858
$719$	17.3966	0.648784	0.324392	−	0.945923i	$-0.394840\pi$
$719$	17.3966	0.648784	0.324392	+	0.945923i	$0.394840\pi$
$720$	1.00000	0.0372678
$721$	−6.36364	−0.236994
$722$	−2.15467	−0.0801887
$723$	4.77219	0.177480
$724$	−20.5393	−0.763339
$725$	7.90445	0.293564
$726$	25.7946	0.957328
$727$	25.2264	0.935595	0.467797	−	0.883836i	$-0.345048\pi$
$727$	25.2264	0.935595	0.467797	+	0.883836i	$0.345048\pi$
$728$	−3.89565	−0.144382
$729$	1.00000	0.0370370
$730$	16.9470	0.627235
$731$	0	0
$732$	−7.03317	−0.259953
$733$	10.2703	0.379344	0.189672	−	0.981848i	$-0.439258\pi$
$733$	10.2703	0.379344	0.189672	+	0.981848i	$0.439258\pi$
$734$	9.98246	0.368459
$735$	6.17024	0.227593
$736$	6.68210	0.246306
$737$	−11.0670	−0.407659
$738$	−11.4501	−0.421482
$739$	2.56354	0.0943013	0.0471507	−	0.998888i	$-0.484986\pi$
$739$	2.56354	0.0943013	0.0471507	+	0.998888i	$0.484986\pi$
$740$	−7.67461	−0.282124
$741$	−19.6701	−0.722601
$742$	−3.05339	−0.112094
$743$	−19.8811	−0.729367	−0.364684	−	0.931132i	$-0.618823\pi$
$743$	−19.8811	−0.729367	−0.364684	+	0.931132i	$0.618823\pi$
$744$	0.108126	0.00396408
$745$	3.22904	0.118303
$746$	−6.26244	−0.229284
$747$	−9.64155	−0.352766
$748$	0	0
$749$	−1.89312	−0.0691733
$750$	1.00000	0.0365148
$751$	−3.05370	−0.111431	−0.0557156	−	0.998447i	$-0.517744\pi$
$751$	−3.05370	−0.111431	−0.0557156	+	0.998447i	$0.517744\pi$
$752$	10.2234	0.372808
$753$	20.3194	0.740481
$754$	33.8046	1.23109
$755$	14.9816	0.545236
$756$	0.910909	0.0331294
$757$	22.3024	0.810593	0.405296	−	0.914185i	$-0.367168\pi$
$757$	22.3024	0.810593	0.405296	+	0.914185i	$0.367168\pi$
$758$	16.2348	0.589675
$759$	40.5327	1.47124
$760$	4.59942	0.166839
$761$	19.7983	0.717689	0.358844	−	0.933397i	$-0.383171\pi$
$761$	19.7983	0.717689	0.358844	+	0.933397i	$0.383171\pi$
$762$	2.16309	0.0783604
$763$	8.96156	0.324430
$764$	24.2575	0.877606
$765$	0	0
$766$	14.0220	0.506637
$767$	−27.7446	−1.00180
$768$	−1.00000	−0.0360844
$769$	−30.7474	−1.10878	−0.554390	−	0.832257i	$-0.687049\pi$
$769$	−30.7474	−1.10878	−0.554390	+	0.832257i	$0.687049\pi$
$770$	5.52544	0.199123
$771$	5.24186	0.188781
$772$	−14.5971	−0.525362
$773$	−7.04597	−0.253426	−0.126713	−	0.991939i	$-0.540443\pi$
$773$	−7.04597	−0.253426	−0.126713	+	0.991939i	$0.540443\pi$
$774$	−2.36407	−0.0849747
$775$	0.108126	0.00388399
$776$	−1.63668	−0.0587534
$777$	−6.99087	−0.250796
$778$	7.90249	0.283318
$779$	−52.6636	−1.88687
$780$	4.27666	0.153129
$781$	−86.2018	−3.08454
$782$	0	0
$783$	−7.90445	−0.282482
$784$	−6.17024	−0.220366
$785$	16.9235	0.604025
$786$	−16.3338	−0.582607
$787$	−47.4912	−1.69288	−0.846440	−	0.532484i	$-0.821259\pi$
$787$	−47.4912	−1.69288	−0.846440	+	0.532484i	$0.821259\pi$
$788$	23.3001	0.830033
$789$	−4.51951	−0.160899
$790$	−0.277340	−0.00986731
$791$	−9.64843	−0.343059
$792$	−6.06586	−0.215541
$793$	−30.0784	−1.06812
$794$	31.6615	1.12362
$795$	3.35203	0.118884
$796$	−5.37447	−0.190493
$797$	−6.72550	−0.238229	−0.119115	−	0.992881i	$-0.538006\pi$
$797$	−6.72550	−0.238229	−0.119115	+	0.992881i	$0.538006\pi$
$798$	4.18965	0.148312
$799$	0	0
$800$	−1.00000	−0.0353553
$801$	−16.0457	−0.566947
$802$	7.29931	0.257748
$803$	−102.798	−3.62766
$804$	1.82448	0.0643443
$805$	6.08679	0.214531
$806$	0.462417	0.0162879
$807$	26.8528	0.945264
$808$	11.2284	0.395014
$809$	6.09489	0.214285	0.107142	−	0.994244i	$-0.465830\pi$
$809$	6.09489	0.214285	0.107142	+	0.994244i	$0.465830\pi$
$810$	−1.00000	−0.0351364
$811$	32.8568	1.15376	0.576879	−	0.816829i	$-0.304270\pi$
$811$	32.8568	1.15376	0.576879	+	0.816829i	$0.304270\pi$
$812$	−7.20023	−0.252679
$813$	3.49535	0.122587
$814$	46.5531	1.63169
$815$	6.71534	0.235228
$816$	0	0
$817$	−10.8734	−0.380410
$818$	−6.40228	−0.223850
$819$	3.89565	0.136125
$820$	11.4501	0.399853
$821$	30.8289	1.07594	0.537968	−	0.842965i	$-0.319192\pi$
$821$	30.8289	1.07594	0.537968	+	0.842965i	$0.319192\pi$
$822$	−3.29410	−0.114895
$823$	31.9249	1.11283	0.556416	−	0.830904i	$-0.312176\pi$
$823$	31.9249	1.11283	0.556416	+	0.830904i	$0.312176\pi$
$824$	−6.98603	−0.243370
$825$	−6.06586	−0.211186
$826$	5.90949	0.205617
$827$	−34.5144	−1.20018	−0.600092	−	0.799931i	$-0.704869\pi$
$827$	−34.5144	−1.20018	−0.600092	+	0.799931i	$0.704869\pi$
$828$	−6.68210	−0.232219
$829$	−2.56748	−0.0891722	−0.0445861	−	0.999006i	$-0.514197\pi$
$829$	−2.56748	−0.0891722	−0.0445861	+	0.999006i	$0.514197\pi$
$830$	9.64155	0.334663
$831$	15.4247	0.535076
$832$	−4.27666	−0.148266
$833$	0	0
$834$	−7.68214	−0.266011
$835$	−2.31745	−0.0801987
$836$	−27.8994	−0.964922
$837$	−0.108126	−0.00373737
$838$	29.9090	1.03319
$839$	−24.2306	−0.836532	−0.418266	−	0.908325i	$-0.637362\pi$
$839$	−24.2306	−0.836532	−0.418266	+	0.908325i	$0.637362\pi$
$840$	−0.910909	−0.0314293
$841$	33.4803	1.15449
$842$	7.96871	0.274620
$843$	21.1614	0.728836
$844$	−1.82509	−0.0628223
$845$	5.28980	0.181975
$846$	−10.2234	−0.351487
$847$	−23.4965	−0.807351
$848$	−3.35203	−0.115109
$849$	−5.11480	−0.175540
$850$	0	0
$851$	51.2826	1.75794
$852$	14.2110	0.486860
$853$	28.9231	0.990308	0.495154	−	0.868805i	$-0.335112\pi$
$853$	28.9231	0.990308	0.495154	+	0.868805i	$0.335112\pi$
$854$	6.40658	0.219228
$855$	−4.59942	−0.157297
$856$	−2.07828	−0.0710342
$857$	−44.7778	−1.52958	−0.764791	−	0.644279i	$-0.777158\pi$
$857$	−44.7778	−1.52958	−0.764791	+	0.644279i	$0.777158\pi$
$858$	−25.9416	−0.885631
$859$	3.38972	0.115656	0.0578279	−	0.998327i	$-0.481583\pi$
$859$	3.38972	0.115656	0.0578279	+	0.998327i	$0.481583\pi$
$860$	2.36407	0.0806141
$861$	10.4300	0.355452
$862$	−18.7864	−0.639869
$863$	32.1447	1.09422	0.547110	−	0.837061i	$-0.315728\pi$
$863$	32.1447	1.09422	0.547110	+	0.837061i	$0.315728\pi$
$864$	1.00000	0.0340207
$865$	−2.31752	−0.0787979
$866$	9.72054	0.330318
$867$	0	0
$868$	−0.0984927	−0.00334306
$869$	1.68230	0.0570682
$870$	7.90445	0.267986
$871$	7.80266	0.264383
$872$	9.83804	0.333158
$873$	1.63668	0.0553932
$874$	−30.7338	−1.03959
$875$	−0.910909	−0.0307943
$876$	16.9470	0.572585
$877$	−14.5590	−0.491623	−0.245812	−	0.969318i	$-0.579054\pi$
$877$	−14.5590	−0.491623	−0.245812	+	0.969318i	$0.579054\pi$
$878$	29.1989	0.985414
$879$	−27.0948	−0.913885
$880$	6.06586	0.204480
$881$	−52.7078	−1.77577	−0.887885	−	0.460065i	$-0.847826\pi$
$881$	−52.7078	−1.77577	−0.887885	+	0.460065i	$0.847826\pi$
$882$	6.17024	0.207763
$883$	−36.7471	−1.23664	−0.618319	−	0.785927i	$-0.712186\pi$
$883$	−36.7471	−1.23664	−0.618319	+	0.785927i	$0.712186\pi$
$884$	0	0
$885$	−6.48746	−0.218074
$886$	2.86239	0.0961639
$887$	−25.9439	−0.871111	−0.435555	−	0.900162i	$-0.643448\pi$
$887$	−25.9439	−0.871111	−0.435555	+	0.900162i	$0.643448\pi$
$888$	−7.67461	−0.257543
$889$	−1.97038	−0.0660843
$890$	16.0457	0.537853
$891$	6.06586	0.203214
$892$	−3.85650	−0.129125
$893$	−47.0216	−1.57352
$894$	3.22904	0.107995
$895$	15.2927	0.511178
$896$	0.910909	0.0304313
$897$	−28.5771	−0.954161
$898$	23.4776	0.783456
$899$	0.854674	0.0285050
$900$	1.00000	0.0333333
$901$	0	0
$902$	−69.4544	−2.31258
$903$	2.15345	0.0716624
$904$	−10.5921	−0.352287
$905$	−20.5393	−0.682751
$906$	14.9816	0.497730
$907$	−41.8856	−1.39079	−0.695395	−	0.718628i	$-0.744771\pi$
$907$	−41.8856	−1.39079	−0.695395	+	0.718628i	$0.744771\pi$
$908$	3.77275	0.125203
$909$	−11.2284	−0.372422
$910$	−3.89565	−0.129139
$911$	0.581823	0.0192767	0.00963833	−	0.999954i	$-0.496932\pi$
$911$	0.581823	0.0192767	0.00963833	+	0.999954i	$0.496932\pi$
$912$	4.59942	0.152302
$913$	−58.4842	−1.93555
$914$	−6.54347	−0.216439
$915$	−7.03317	−0.232509
$916$	−4.88240	−0.161319
$917$	14.8786	0.491335
$918$	0	0
$919$	18.3963	0.606837	0.303418	−	0.952857i	$-0.401872\pi$
$919$	18.3963	0.606837	0.303418	+	0.952857i	$0.401872\pi$
$920$	6.68210	0.220302
$921$	0.0460189	0.00151637
$922$	26.0322	0.857324
$923$	60.7755	2.00045
$924$	5.52544	0.181774
$925$	−7.67461	−0.252340
$926$	27.1179	0.891148
$927$	6.98603	0.229451
$928$	−7.90445	−0.259476
$929$	−28.9000	−0.948180	−0.474090	−	0.880476i	$-0.657223\pi$
$929$	−28.9000	−0.948180	−0.474090	+	0.880476i	$0.657223\pi$
$930$	0.108126	0.00354558
$931$	28.3796	0.930102
$932$	−19.6670	−0.644215
$933$	−10.4669	−0.342671
$934$	7.71126	0.252320
$935$	0	0
$936$	4.27666	0.139787
$937$	−28.2139	−0.921709	−0.460855	−	0.887476i	$-0.652457\pi$
$937$	−28.2139	−0.921709	−0.460855	+	0.887476i	$0.652457\pi$
$938$	−1.66193	−0.0542640
$939$	−8.62404	−0.281435
$940$	10.2234	0.333450
$941$	15.4324	0.503082	0.251541	−	0.967847i	$-0.419063\pi$
$941$	15.4324	0.503082	0.251541	+	0.967847i	$0.419063\pi$
$942$	16.9235	0.551397
$943$	−76.5105	−2.49152
$944$	6.48746	0.211149
$945$	0.910909	0.0296319
$946$	−14.3401	−0.466237
$947$	43.5410	1.41489	0.707447	−	0.706767i	$-0.249847\pi$
$947$	43.5410	1.41489	0.707447	+	0.706767i	$0.249847\pi$
$948$	−0.277340	−0.00900758
$949$	72.4763	2.35268
$950$	4.59942	0.149225
$951$	−25.8237	−0.837392
$952$	0	0
$953$	−18.3996	−0.596022	−0.298011	−	0.954562i	$-0.596323\pi$
$953$	−18.3996	−0.596022	−0.298011	+	0.954562i	$0.596323\pi$
$954$	3.35203	0.108526
$955$	24.2575	0.784954
$956$	−19.2547	−0.622741
$957$	−47.9472	−1.54991
$958$	−38.0806	−1.23033
$959$	3.00063	0.0968953
$960$	−1.00000	−0.0322749
$961$	−30.9883	−0.999623
$962$	−32.8217	−1.05821
$963$	2.07828	0.0669716
$964$	−4.77219	−0.153702
$965$	−14.5971	−0.469898
$966$	6.08679	0.195839
$967$	−32.4421	−1.04327	−0.521634	−	0.853169i	$-0.674677\pi$
$967$	−32.4421	−1.04327	−0.521634	+	0.853169i	$0.674677\pi$
$968$	−25.7946	−0.829070
$969$	0	0
$970$	−1.63668	−0.0525506
$971$	5.33136	0.171092	0.0855458	−	0.996334i	$-0.472737\pi$
$971$	5.33136	0.171092	0.0855458	+	0.996334i	$0.472737\pi$
$972$	−1.00000	−0.0320750
$973$	6.99773	0.224337
$974$	−9.35905	−0.299883
$975$	4.27666	0.136963
$976$	7.03317	0.225126
$977$	−17.7390	−0.567520	−0.283760	−	0.958895i	$-0.591582\pi$
$977$	−17.7390	−0.567520	−0.283760	+	0.958895i	$0.591582\pi$
$978$	6.71534	0.214733
$979$	−97.3309	−3.11071
$980$	−6.17024	−0.197101
$981$	−9.83804	−0.314105
$982$	38.5620	1.23056
$983$	59.1282	1.88590	0.942948	−	0.332939i	$-0.108040\pi$
$983$	59.1282	1.88590	0.942948	+	0.332939i	$0.108040\pi$
$984$	11.4501	0.365014
$985$	23.3001	0.742404
$986$	0	0
$987$	9.31257	0.296422
$988$	19.6701	0.625791
$989$	−15.7970	−0.502314
$990$	−6.06586	−0.192786
$991$	−38.1746	−1.21266	−0.606328	−	0.795215i	$-0.707358\pi$
$991$	−38.1746	−1.21266	−0.606328	+	0.795215i	$0.707358\pi$
$992$	−0.108126	−0.00343300
$993$	3.11196	0.0987551
$994$	−12.9449	−0.410588
$995$	−5.37447	−0.170382
$996$	9.64155	0.305504
$997$	−14.9945	−0.474881	−0.237441	−	0.971402i	$-0.576308\pi$
$997$	−14.9945	−0.474881	−0.237441	+	0.971402i	$0.576308\pi$
$998$	−29.0164	−0.918497
$999$	7.67461	0.242814

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8670.2.a.cc.1.3	✓	6
17.16	even	2		8670.2.a.cd.1.4	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8670.2.a.cc.1.3	✓	6	1.1	even	1	trivial
8670.2.a.cd.1.4	yes	6	17.16	even	2

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:	\( N \)	\(=\)	\( 8670 = 2 \cdot 3 \cdot 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8670.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -0.910909 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -0.910909 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +6.06586 q^{11} -1.00000 q^{12} -4.27666 q^{13} +0.910909 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{18} -4.59942 q^{19} +1.00000 q^{20} +0.910909 q^{21} -6.06586 q^{22} -6.68210 q^{23} +1.00000 q^{24} +1.00000 q^{25} +4.27666 q^{26} -1.00000 q^{27} -0.910909 q^{28} +7.90445 q^{29} +1.00000 q^{30} +0.108126 q^{31} -1.00000 q^{32} -6.06586 q^{33} -0.910909 q^{35} +1.00000 q^{36} -7.67461 q^{37} +4.59942 q^{38} +4.27666 q^{39} -1.00000 q^{40} +11.4501 q^{41} -0.910909 q^{42} +2.36407 q^{43} +6.06586 q^{44} +1.00000 q^{45} +6.68210 q^{46} +10.2234 q^{47} -1.00000 q^{48} -6.17024 q^{49} -1.00000 q^{50} -4.27666 q^{52} -3.35203 q^{53} +1.00000 q^{54} +6.06586 q^{55} +0.910909 q^{56} +4.59942 q^{57} -7.90445 q^{58} +6.48746 q^{59} -1.00000 q^{60} +7.03317 q^{61} -0.108126 q^{62} -0.910909 q^{63} +1.00000 q^{64} -4.27666 q^{65} +6.06586 q^{66} -1.82448 q^{67} +6.68210 q^{69} +0.910909 q^{70} -14.2110 q^{71} -1.00000 q^{72} -16.9470 q^{73} +7.67461 q^{74} -1.00000 q^{75} -4.59942 q^{76} -5.52544 q^{77} -4.27666 q^{78} +0.277340 q^{79} +1.00000 q^{80} +1.00000 q^{81} -11.4501 q^{82} -9.64155 q^{83} +0.910909 q^{84} -2.36407 q^{86} -7.90445 q^{87} -6.06586 q^{88} -16.0457 q^{89} -1.00000 q^{90} +3.89565 q^{91} -6.68210 q^{92} -0.108126 q^{93} -10.2234 q^{94} -4.59942 q^{95} +1.00000 q^{96} +1.63668 q^{97} +6.17024 q^{98} +6.06586 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} + 6 q^{5} + 6 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 + 6 * q^5 + 6 * q^6 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} + 6 q^{5} + 6 q^{6} - 6 q^{8} + 6 q^{9} - 6 q^{10} + 6 q^{11} - 6 q^{12} + 6 q^{13} - 6 q^{15} + 6 q^{16} - 6 q^{18} + 6 q^{19} + 6 q^{20} - 6 q^{22} - 12 q^{23} + 6 q^{24} + 6 q^{25} - 6 q^{26} - 6 q^{27} - 6 q^{29} + 6 q^{30} - 12 q^{31} - 6 q^{32} - 6 q^{33} + 6 q^{36} - 12 q^{37} - 6 q^{38} - 6 q^{39} - 6 q^{40} - 12 q^{41} + 6 q^{44} + 6 q^{45} + 12 q^{46} - 6 q^{47} - 6 q^{48} + 6 q^{49} - 6 q^{50} + 6 q^{52} - 30 q^{53} + 6 q^{54} + 6 q^{55} - 6 q^{57} + 6 q^{58} + 6 q^{59} - 6 q^{60} - 6 q^{61} + 12 q^{62} + 6 q^{64} + 6 q^{65} + 6 q^{66} - 24 q^{67} + 12 q^{69} - 6 q^{71} - 6 q^{72} - 36 q^{73} + 12 q^{74} - 6 q^{75} + 6 q^{76} - 54 q^{77} + 6 q^{78} - 12 q^{79} + 6 q^{80} + 6 q^{81} + 12 q^{82} + 12 q^{83} + 6 q^{87} - 6 q^{88} - 18 q^{89} - 6 q^{90} + 24 q^{91} - 12 q^{92} + 12 q^{93} + 6 q^{94} + 6 q^{95} + 6 q^{96} - 30 q^{97} - 6 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 + 6 * q^5 + 6 * q^6 - 6 * q^8 + 6 * q^9 - 6 * q^10 + 6 * q^11 - 6 * q^12 + 6 * q^13 - 6 * q^15 + 6 * q^16 - 6 * q^18 + 6 * q^19 + 6 * q^20 - 6 * q^22 - 12 * q^23 + 6 * q^24 + 6 * q^25 - 6 * q^26 - 6 * q^27 - 6 * q^29 + 6 * q^30 - 12 * q^31 - 6 * q^32 - 6 * q^33 + 6 * q^36 - 12 * q^37 - 6 * q^38 - 6 * q^39 - 6 * q^40 - 12 * q^41 + 6 * q^44 + 6 * q^45 + 12 * q^46 - 6 * q^47 - 6 * q^48 + 6 * q^49 - 6 * q^50 + 6 * q^52 - 30 * q^53 + 6 * q^54 + 6 * q^55 - 6 * q^57 + 6 * q^58 + 6 * q^59 - 6 * q^60 - 6 * q^61 + 12 * q^62 + 6 * q^64 + 6 * q^65 + 6 * q^66 - 24 * q^67 + 12 * q^69 - 6 * q^71 - 6 * q^72 - 36 * q^73 + 12 * q^74 - 6 * q^75 + 6 * q^76 - 54 * q^77 + 6 * q^78 - 12 * q^79 + 6 * q^80 + 6 * q^81 + 12 * q^82 + 12 * q^83 + 6 * q^87 - 6 * q^88 - 18 * q^89 - 6 * q^90 + 24 * q^91 - 12 * q^92 + 12 * q^93 + 6 * q^94 + 6 * q^95 + 6 * q^96 - 30 * q^97 - 6 * q^98 + 6 * q^99

Introduction

L-functions

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Database

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