LMFDB - Embedded newform 8670.2.a.ce.1.6

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:	$0$
Dimension:	$6$
Coefficient field:	6.6.204493248.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 24x^{4} + 189x^{2} - 487 $ x^6 - 24x^4 + 189x^2 - 487
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$3.08741$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +3.08741 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +3.08741 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +3.95163 q^{11} +1.00000 q^{12} +3.50350 q^{13} -3.08741 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{18} +3.27034 q^{19} +1.00000 q^{20} +3.08741 q^{21} -3.95163 q^{22} -1.55532 q^{23} -1.00000 q^{24} +1.00000 q^{25} -3.50350 q^{26} +1.00000 q^{27} +3.08741 q^{28} +5.75341 q^{29} -1.00000 q^{30} -2.55075 q^{31} -1.00000 q^{32} +3.95163 q^{33} +3.08741 q^{35} +1.00000 q^{36} +5.91312 q^{37} -3.27034 q^{38} +3.50350 q^{39} -1.00000 q^{40} +3.64464 q^{41} -3.08741 q^{42} +5.39105 q^{43} +3.95163 q^{44} +1.00000 q^{45} +1.55532 q^{46} +2.90974 q^{47} +1.00000 q^{48} +2.53209 q^{49} -1.00000 q^{50} +3.50350 q^{52} -7.75247 q^{53} -1.00000 q^{54} +3.95163 q^{55} -3.08741 q^{56} +3.27034 q^{57} -5.75341 q^{58} -12.3478 q^{59} +1.00000 q^{60} -2.93297 q^{61} +2.55075 q^{62} +3.08741 q^{63} +1.00000 q^{64} +3.50350 q^{65} -3.95163 q^{66} +3.87415 q^{67} -1.55532 q^{69} -3.08741 q^{70} -12.0566 q^{71} -1.00000 q^{72} -10.1941 q^{73} -5.91312 q^{74} +1.00000 q^{75} +3.27034 q^{76} +12.2003 q^{77} -3.50350 q^{78} +12.8514 q^{79} +1.00000 q^{80} +1.00000 q^{81} -3.64464 q^{82} +11.9051 q^{83} +3.08741 q^{84} -5.39105 q^{86} +5.75341 q^{87} -3.95163 q^{88} +1.87654 q^{89} -1.00000 q^{90} +10.8167 q^{91} -1.55532 q^{92} -2.55075 q^{93} -2.90974 q^{94} +3.27034 q^{95} -1.00000 q^{96} -11.2343 q^{97} -2.53209 q^{98} +3.95163 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 6 q^{24} + 6 q^{25} - 6 q^{26} + 6 q^{27} + 6 q^{29} - 6 q^{30} - 6 q^{32} + 6 q^{33} + 6 q^{36} + 6 q^{38} + 6 q^{39} - 6 q^{40} + 12 q^{41} + 24 q^{43} + 6 q^{44} + 6 q^{45} + 6 q^{47} + 6 q^{48} + 6 q^{49} - 6 q^{50} + 6 q^{52} - 6 q^{53} - 6 q^{54} + 6 q^{55} - 6 q^{57} - 6 q^{58} - 18 q^{59} + 6 q^{60} - 6 q^{61} + 6 q^{64} + 6 q^{65} - 6 q^{66} + 36 q^{67} + 30 q^{71} - 6 q^{72} + 12 q^{73} + 6 q^{75} - 6 q^{76} - 6 q^{77} - 6 q^{78} + 12 q^{79} + 6 q^{80} + 6 q^{81} - 12 q^{82} + 36 q^{83} - 24 q^{86} + 6 q^{87} - 6 q^{88} - 30 q^{89} - 6 q^{90} + 12 q^{91} - 6 q^{94} - 6 q^{95} - 6 q^{96} + 18 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 - 6 * q^24 + 6 * q^25 - 6 * q^26 + 6 * q^27 + 6 * q^29 - 6 * q^30 - 6 * q^32 + 6 * q^33 + 6 * q^36 + 6 * q^38 + 6 * q^39 - 6 * q^40 + 12 * q^41 + 24 * q^43 + 6 * q^44 + 6 * q^45 + 6 * q^47 + 6 * q^48 + 6 * q^49 - 6 * q^50 + 6 * q^52 - 6 * q^53 - 6 * q^54 + 6 * q^55 - 6 * q^57 - 6 * q^58 - 18 * q^59 + 6 * q^60 - 6 * q^61 + 6 * q^64 + 6 * q^65 - 6 * q^66 + 36 * q^67 + 30 * q^71 - 6 * q^72 + 12 * q^73 + 6 * q^75 - 6 * q^76 - 6 * q^77 - 6 * q^78 + 12 * q^79 + 6 * q^80 + 6 * q^81 - 12 * q^82 + 36 * q^83 - 24 * q^86 + 6 * q^87 - 6 * q^88 - 30 * q^89 - 6 * q^90 + 12 * q^91 - 6 * q^94 - 6 * q^95 - 6 * q^96 + 18 * 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
$7$	3.08741	1.16693	0.583465	−	0.812138i	$-0.301696\pi$
$7$	3.08741	1.16693	0.583465	+	0.812138i	$0.301696\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	3.95163	1.19146	0.595731	−	0.803184i	$-0.296863\pi$
$11$	3.95163	1.19146	0.595731	+	0.803184i	$0.296863\pi$
$12$	1.00000	0.288675
$13$	3.50350	0.971697	0.485848	−	0.874043i	$-0.338511\pi$
$13$	3.50350	0.971697	0.485848	+	0.874043i	$0.338511\pi$
$14$	−3.08741	−0.825145
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	0	0
$17$	0	0
$18$	−1.00000	−0.235702
$19$	3.27034	0.750268	0.375134	−	0.926971i	$-0.377597\pi$
$19$	3.27034	0.750268	0.375134	+	0.926971i	$0.377597\pi$
$20$	1.00000	0.223607
$21$	3.08741	0.673728
$22$	−3.95163	−0.842491
$23$	−1.55532	−0.324306	−0.162153	−	0.986766i	$-0.551844\pi$
$23$	−1.55532	−0.324306	−0.162153	+	0.986766i	$0.551844\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−3.50350	−0.687093
$27$	1.00000	0.192450
$28$	3.08741	0.583465
$29$	5.75341	1.06838	0.534191	−	0.845364i	$-0.320616\pi$
$29$	5.75341	1.06838	0.534191	+	0.845364i	$0.320616\pi$
$30$	−1.00000	−0.182574
$31$	−2.55075	−0.458128	−0.229064	−	0.973411i	$-0.573566\pi$
$31$	−2.55075	−0.458128	−0.229064	+	0.973411i	$0.573566\pi$
$32$	−1.00000	−0.176777
$33$	3.95163	0.687891
$34$	0	0
$35$	3.08741	0.521867
$36$	1.00000	0.166667
$37$	5.91312	0.972110	0.486055	−	0.873928i	$-0.338435\pi$
$37$	5.91312	0.972110	0.486055	+	0.873928i	$0.338435\pi$
$38$	−3.27034	−0.530519
$39$	3.50350	0.561009
$40$	−1.00000	−0.158114
$41$	3.64464	0.569196	0.284598	−	0.958647i	$-0.408140\pi$
$41$	3.64464	0.569196	0.284598	+	0.958647i	$0.408140\pi$
$42$	−3.08741	−0.476397
$43$	5.39105	0.822127	0.411063	−	0.911607i	$-0.365157\pi$
$43$	5.39105	0.822127	0.411063	+	0.911607i	$0.365157\pi$
$44$	3.95163	0.595731
$45$	1.00000	0.149071
$46$	1.55532	0.229319
$47$	2.90974	0.424429	0.212215	−	0.977223i	$-0.431932\pi$
$47$	2.90974	0.424429	0.212215	+	0.977223i	$0.431932\pi$
$48$	1.00000	0.144338
$49$	2.53209	0.361727
$50$	−1.00000	−0.141421
$51$	0	0
$52$	3.50350	0.485848
$53$	−7.75247	−1.06488	−0.532442	−	0.846466i	$-0.678726\pi$
$53$	−7.75247	−1.06488	−0.532442	+	0.846466i	$0.678726\pi$
$54$	−1.00000	−0.136083
$55$	3.95163	0.532838
$56$	−3.08741	−0.412572
$57$	3.27034	0.433167
$58$	−5.75341	−0.755460
$59$	−12.3478	−1.60755	−0.803775	−	0.594934i	$-0.797178\pi$
$59$	−12.3478	−1.60755	−0.803775	+	0.594934i	$0.797178\pi$
$60$	1.00000	0.129099
$61$	−2.93297	−0.375529	−0.187764	−	0.982214i	$-0.560124\pi$
$61$	−2.93297	−0.375529	−0.187764	+	0.982214i	$0.560124\pi$
$62$	2.55075	0.323945
$63$	3.08741	0.388977
$64$	1.00000	0.125000
$65$	3.50350	0.434556
$66$	−3.95163	−0.486412
$67$	3.87415	0.473303	0.236651	−	0.971595i	$-0.423950\pi$
$67$	3.87415	0.473303	0.236651	+	0.971595i	$0.423950\pi$
$68$	0	0
$69$	−1.55532	−0.187238
$70$	−3.08741	−0.369016
$71$	−12.0566	−1.43085	−0.715427	−	0.698688i	$-0.753768\pi$
$71$	−12.0566	−1.43085	−0.715427	+	0.698688i	$0.753768\pi$
$72$	−1.00000	−0.117851
$73$	−10.1941	−1.19313	−0.596567	−	0.802563i	$-0.703469\pi$
$73$	−10.1941	−1.19313	−0.596567	+	0.802563i	$0.703469\pi$
$74$	−5.91312	−0.687386
$75$	1.00000	0.115470
$76$	3.27034	0.375134
$77$	12.2003	1.39035
$78$	−3.50350	−0.396693
$79$	12.8514	1.44590	0.722948	−	0.690902i	$-0.242786\pi$
$79$	12.8514	1.44590	0.722948	+	0.690902i	$0.242786\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−3.64464	−0.402483
$83$	11.9051	1.30676	0.653378	−	0.757031i	$-0.273351\pi$
$83$	11.9051	1.30676	0.653378	+	0.757031i	$0.273351\pi$
$84$	3.08741	0.336864
$85$	0	0
$86$	−5.39105	−0.581331
$87$	5.75341	0.616831
$88$	−3.95163	−0.421245
$89$	1.87654	0.198912	0.0994562	−	0.995042i	$-0.468290\pi$
$89$	1.87654	0.198912	0.0994562	+	0.995042i	$0.468290\pi$
$90$	−1.00000	−0.105409
$91$	10.8167	1.13390
$92$	−1.55532	−0.162153
$93$	−2.55075	−0.264500
$94$	−2.90974	−0.300117
$95$	3.27034	0.335530
$96$	−1.00000	−0.102062
$97$	−11.2343	−1.14067	−0.570334	−	0.821413i	$-0.693186\pi$
$97$	−11.2343	−1.14067	−0.570334	+	0.821413i	$0.693186\pi$
$98$	−2.53209	−0.255780
$99$	3.95163	0.397154
$100$	1.00000	0.100000
$101$	14.3854	1.43140	0.715701	−	0.698407i	$-0.246107\pi$
$101$	14.3854	1.43140	0.715701	+	0.698407i	$0.246107\pi$
$102$	0	0
$103$	7.22663	0.712061	0.356031	−	0.934474i	$-0.384130\pi$
$103$	7.22663	0.712061	0.356031	+	0.934474i	$0.384130\pi$
$104$	−3.50350	−0.343547
$105$	3.08741	0.301300
$106$	7.75247	0.752987
$107$	−18.5081	−1.78924	−0.894622	−	0.446823i	$-0.852555\pi$
$107$	−18.5081	−1.78924	−0.894622	+	0.446823i	$0.852555\pi$
$108$	1.00000	0.0962250
$109$	−6.17645	−0.591597	−0.295798	−	0.955250i	$-0.595586\pi$
$109$	−6.17645	−0.591597	−0.295798	+	0.955250i	$0.595586\pi$
$110$	−3.95163	−0.376773
$111$	5.91312	0.561248
$112$	3.08741	0.291733
$113$	13.3898	1.25961	0.629805	−	0.776754i	$-0.283135\pi$
$113$	13.3898	1.25961	0.629805	+	0.776754i	$0.283135\pi$
$114$	−3.27034	−0.306295
$115$	−1.55532	−0.145034
$116$	5.75341	0.534191
$117$	3.50350	0.323899
$118$	12.3478	1.13671
$119$	0	0
$120$	−1.00000	−0.0912871
$121$	4.61539	0.419581
$122$	2.93297	0.265539
$123$	3.64464	0.328626
$124$	−2.55075	−0.229064
$125$	1.00000	0.0894427
$126$	−3.08741	−0.275048
$127$	8.77327	0.778502	0.389251	−	0.921132i	$-0.372734\pi$
$127$	8.77327	0.778502	0.389251	+	0.921132i	$0.372734\pi$
$128$	−1.00000	−0.0883883
$129$	5.39105	0.474655
$130$	−3.50350	−0.307277
$131$	−13.9041	−1.21480	−0.607402	−	0.794395i	$-0.707788\pi$
$131$	−13.9041	−1.21480	−0.607402	+	0.794395i	$0.707788\pi$
$132$	3.95163	0.343945
$133$	10.0969	0.875510
$134$	−3.87415	−0.334676
$135$	1.00000	0.0860663
$136$	0	0
$137$	−14.3376	−1.22495	−0.612474	−	0.790491i	$-0.709825\pi$
$137$	−14.3376	−1.22495	−0.612474	+	0.790491i	$0.709825\pi$
$138$	1.55532	0.132398
$139$	6.01511	0.510195	0.255098	−	0.966915i	$-0.417892\pi$
$139$	6.01511	0.510195	0.255098	+	0.966915i	$0.417892\pi$
$140$	3.08741	0.260934
$141$	2.90974	0.245044
$142$	12.0566	1.01177
$143$	13.8445	1.15774
$144$	1.00000	0.0833333
$145$	5.75341	0.477795
$146$	10.1941	0.843673
$147$	2.53209	0.208843
$148$	5.91312	0.486055
$149$	−8.22202	−0.673574	−0.336787	−	0.941581i	$-0.609340\pi$
$149$	−8.22202	−0.673574	−0.336787	+	0.941581i	$0.609340\pi$
$150$	−1.00000	−0.0816497
$151$	−14.2549	−1.16004	−0.580022	−	0.814601i	$-0.696956\pi$
$151$	−14.2549	−1.16004	−0.580022	+	0.814601i	$0.696956\pi$
$152$	−3.27034	−0.265260
$153$	0	0
$154$	−12.2003	−0.983128
$155$	−2.55075	−0.204881
$156$	3.50350	0.280505
$157$	8.92906	0.712617	0.356308	−	0.934368i	$-0.384035\pi$
$157$	8.92906	0.712617	0.356308	+	0.934368i	$0.384035\pi$
$158$	−12.8514	−1.02240
$159$	−7.75247	−0.614811
$160$	−1.00000	−0.0790569
$161$	−4.80191	−0.378443
$162$	−1.00000	−0.0785674
$163$	−20.4926	−1.60510	−0.802552	−	0.596583i	$-0.796525\pi$
$163$	−20.4926	−1.60510	−0.802552	+	0.596583i	$0.796525\pi$
$164$	3.64464	0.284598
$165$	3.95163	0.307634
$166$	−11.9051	−0.924017
$167$	−17.1341	−1.32588	−0.662938	−	0.748674i	$-0.730691\pi$
$167$	−17.1341	−1.32588	−0.662938	+	0.748674i	$0.730691\pi$
$168$	−3.08741	−0.238199
$169$	−0.725473	−0.0558056
$170$	0	0
$171$	3.27034	0.250089
$172$	5.39105	0.411063
$173$	−1.31134	−0.0996990	−0.0498495	−	0.998757i	$-0.515874\pi$
$173$	−1.31134	−0.0996990	−0.0498495	+	0.998757i	$0.515874\pi$
$174$	−5.75341	−0.436165
$175$	3.08741	0.233386
$176$	3.95163	0.297865
$177$	−12.3478	−0.928119
$178$	−1.87654	−0.140652
$179$	−0.231557	−0.0173074	−0.00865370	−	0.999963i	$-0.502755\pi$
$179$	−0.231557	−0.0173074	−0.00865370	+	0.999963i	$0.502755\pi$
$180$	1.00000	0.0745356
$181$	−10.2011	−0.758240	−0.379120	−	0.925347i	$-0.623773\pi$
$181$	−10.2011	−0.758240	−0.379120	+	0.925347i	$0.623773\pi$
$182$	−10.8167	−0.801790
$183$	−2.93297	−0.216812
$184$	1.55532	0.114660
$185$	5.91312	0.434741
$186$	2.55075	0.187030
$187$	0	0
$188$	2.90974	0.212215
$189$	3.08741	0.224576
$190$	−3.27034	−0.237255
$191$	0.217533	0.0157402	0.00787008	−	0.999969i	$-0.497495\pi$
$191$	0.217533	0.0157402	0.00787008	+	0.999969i	$0.497495\pi$
$192$	1.00000	0.0721688
$193$	26.8426	1.93218	0.966088	−	0.258214i	$-0.0831340\pi$
$193$	26.8426	1.93218	0.966088	+	0.258214i	$0.0831340\pi$
$194$	11.2343	0.806575
$195$	3.50350	0.250891
$196$	2.53209	0.180863
$197$	−7.28615	−0.519117	−0.259558	−	0.965727i	$-0.583577\pi$
$197$	−7.28615	−0.519117	−0.259558	+	0.965727i	$0.583577\pi$
$198$	−3.95163	−0.280830
$199$	−15.6273	−1.10779	−0.553893	−	0.832588i	$-0.686858\pi$
$199$	−15.6273	−1.10779	−0.553893	+	0.832588i	$0.686858\pi$
$200$	−1.00000	−0.0707107
$201$	3.87415	0.273262
$202$	−14.3854	−1.01215
$203$	17.7631	1.24673
$204$	0	0
$205$	3.64464	0.254552
$206$	−7.22663	−0.503503
$207$	−1.55532	−0.108102
$208$	3.50350	0.242924
$209$	12.9232	0.893915
$210$	−3.08741	−0.213051
$211$	19.3853	1.33454	0.667270	−	0.744816i	$-0.267463\pi$
$211$	19.3853	1.33454	0.667270	+	0.744816i	$0.267463\pi$
$212$	−7.75247	−0.532442
$213$	−12.0566	−0.826104
$214$	18.5081	1.26519
$215$	5.39105	0.367666
$216$	−1.00000	−0.0680414
$217$	−7.87520	−0.534603
$218$	6.17645	0.418322
$219$	−10.1941	−0.688856
$220$	3.95163	0.266419
$221$	0	0
$222$	−5.91312	−0.396862
$223$	−14.7267	−0.986172	−0.493086	−	0.869981i	$-0.664131\pi$
$223$	−14.7267	−0.986172	−0.493086	+	0.869981i	$0.664131\pi$
$224$	−3.08741	−0.206286
$225$	1.00000	0.0666667
$226$	−13.3898	−0.890678
$227$	0.262411	0.0174169	0.00870843	−	0.999962i	$-0.497228\pi$
$227$	0.262411	0.0174169	0.00870843	+	0.999962i	$0.497228\pi$
$228$	3.27034	0.216584
$229$	−8.17383	−0.540142	−0.270071	−	0.962840i	$-0.587047\pi$
$229$	−8.17383	−0.540142	−0.270071	+	0.962840i	$0.587047\pi$
$230$	1.55532	0.102555
$231$	12.2003	0.802721
$232$	−5.75341	−0.377730
$233$	−10.6788	−0.699590	−0.349795	−	0.936826i	$-0.613749\pi$
$233$	−10.6788	−0.699590	−0.349795	+	0.936826i	$0.613749\pi$
$234$	−3.50350	−0.229031
$235$	2.90974	0.189811
$236$	−12.3478	−0.803775
$237$	12.8514	0.834789
$238$	0	0
$239$	−28.5760	−1.84843	−0.924214	−	0.381874i	$-0.875279\pi$
$239$	−28.5760	−1.84843	−0.924214	+	0.381874i	$0.875279\pi$
$240$	1.00000	0.0645497
$241$	−7.57174	−0.487739	−0.243869	−	0.969808i	$-0.578417\pi$
$241$	−7.57174	−0.487739	−0.243869	+	0.969808i	$0.578417\pi$
$242$	−4.61539	−0.296688
$243$	1.00000	0.0641500
$244$	−2.93297	−0.187764
$245$	2.53209	0.161769
$246$	−3.64464	−0.232373
$247$	11.4576	0.729032
$248$	2.55075	0.161973
$249$	11.9051	0.754456
$250$	−1.00000	−0.0632456
$251$	−17.7780	−1.12214	−0.561070	−	0.827768i	$-0.689610\pi$
$251$	−17.7780	−1.12214	−0.561070	+	0.827768i	$0.689610\pi$
$252$	3.08741	0.194488
$253$	−6.14605	−0.386399
$254$	−8.77327	−0.550484
$255$	0	0
$256$	1.00000	0.0625000
$257$	−20.9004	−1.30373	−0.651865	−	0.758335i	$-0.726013\pi$
$257$	−20.9004	−1.30373	−0.651865	+	0.758335i	$0.726013\pi$
$258$	−5.39105	−0.335632
$259$	18.2562	1.13439
$260$	3.50350	0.217278
$261$	5.75341	0.356127
$262$	13.9041	0.858996
$263$	8.23360	0.507705	0.253853	−	0.967243i	$-0.418302\pi$
$263$	8.23360	0.507705	0.253853	+	0.967243i	$0.418302\pi$
$264$	−3.95163	−0.243206
$265$	−7.75247	−0.476231
$266$	−10.0969	−0.619079
$267$	1.87654	0.114842
$268$	3.87415	0.236651
$269$	21.3825	1.30372	0.651858	−	0.758341i	$-0.273990\pi$
$269$	21.3825	1.30372	0.651858	+	0.758341i	$0.273990\pi$
$270$	−1.00000	−0.0608581
$271$	28.5163	1.73224	0.866122	−	0.499832i	$-0.166605\pi$
$271$	28.5163	1.73224	0.866122	+	0.499832i	$0.166605\pi$
$272$	0	0
$273$	10.8167	0.654659
$274$	14.3376	0.866168
$275$	3.95163	0.238292
$276$	−1.55532	−0.0936192
$277$	15.1457	0.910016	0.455008	−	0.890487i	$-0.349636\pi$
$277$	15.1457	0.910016	0.455008	+	0.890487i	$0.349636\pi$
$278$	−6.01511	−0.360763
$279$	−2.55075	−0.152709
$280$	−3.08741	−0.184508
$281$	−10.9195	−0.651400	−0.325700	−	0.945473i	$-0.605600\pi$
$281$	−10.9195	−0.651400	−0.325700	+	0.945473i	$0.605600\pi$
$282$	−2.90974	−0.173273
$283$	21.2893	1.26552	0.632759	−	0.774349i	$-0.281922\pi$
$283$	21.2893	1.26552	0.632759	+	0.774349i	$0.281922\pi$
$284$	−12.0566	−0.715427
$285$	3.27034	0.193718
$286$	−13.8445	−0.818645
$287$	11.2525	0.664213
$288$	−1.00000	−0.0589256
$289$	0	0
$290$	−5.75341	−0.337852
$291$	−11.2343	−0.658565
$292$	−10.1941	−0.596567
$293$	−12.9203	−0.754811	−0.377406	−	0.926048i	$-0.623184\pi$
$293$	−12.9203	−0.754811	−0.377406	+	0.926048i	$0.623184\pi$
$294$	−2.53209	−0.147674
$295$	−12.3478	−0.718918
$296$	−5.91312	−0.343693
$297$	3.95163	0.229297
$298$	8.22202	0.476289
$299$	−5.44906	−0.315128
$300$	1.00000	0.0577350
$301$	16.6444	0.959365
$302$	14.2549	0.820274
$303$	14.3854	0.826420
$304$	3.27034	0.187567
$305$	−2.93297	−0.167941
$306$	0	0
$307$	−14.8343	−0.846638	−0.423319	−	0.905981i	$-0.639135\pi$
$307$	−14.8343	−0.846638	−0.423319	+	0.905981i	$0.639135\pi$
$308$	12.2003	0.695176
$309$	7.22663	0.411109
$310$	2.55075	0.144873
$311$	8.45812	0.479616	0.239808	−	0.970820i	$-0.422916\pi$
$311$	8.45812	0.479616	0.239808	+	0.970820i	$0.422916\pi$
$312$	−3.50350	−0.198347
$313$	−14.3937	−0.813580	−0.406790	−	0.913522i	$-0.633352\pi$
$313$	−14.3937	−0.813580	−0.406790	+	0.913522i	$0.633352\pi$
$314$	−8.92906	−0.503896
$315$	3.08741	0.173956
$316$	12.8514	0.722948
$317$	10.3456	0.581068	0.290534	−	0.956865i	$-0.406167\pi$
$317$	10.3456	0.581068	0.290534	+	0.956865i	$0.406167\pi$
$318$	7.75247	0.434737
$319$	22.7354	1.27294
$320$	1.00000	0.0559017
$321$	−18.5081	−1.03302
$322$	4.80191	0.267600
$323$	0	0
$324$	1.00000	0.0555556
$325$	3.50350	0.194339
$326$	20.4926	1.13498
$327$	−6.17645	−0.341559
$328$	−3.64464	−0.201241
$329$	8.98356	0.495280
$330$	−3.95163	−0.217530
$331$	20.3745	1.11988	0.559942	−	0.828532i	$-0.310823\pi$
$331$	20.3745	1.11988	0.559942	+	0.828532i	$0.310823\pi$
$332$	11.9051	0.653378
$333$	5.91312	0.324037
$334$	17.1341	0.937536
$335$	3.87415	0.211667
$336$	3.08741	0.168432
$337$	35.4566	1.93145	0.965723	−	0.259574i	$-0.0835823\pi$
$337$	35.4566	1.93145	0.965723	+	0.259574i	$0.0835823\pi$
$338$	0.725473	0.0394605
$339$	13.3898	0.727236
$340$	0	0
$341$	−10.0796	−0.545842
$342$	−3.27034	−0.176840
$343$	−13.7943	−0.744820
$344$	−5.39105	−0.290666
$345$	−1.55532	−0.0837356
$346$	1.31134	0.0704979
$347$	19.5321	1.04854	0.524268	−	0.851553i	$-0.324339\pi$
$347$	19.5321	1.04854	0.524268	+	0.851553i	$0.324339\pi$
$348$	5.75341	0.308415
$349$	22.2987	1.19362	0.596811	−	0.802382i	$-0.296434\pi$
$349$	22.2987	1.19362	0.596811	+	0.802382i	$0.296434\pi$
$350$	−3.08741	−0.165029
$351$	3.50350	0.187003
$352$	−3.95163	−0.210623
$353$	18.4251	0.980667	0.490333	−	0.871535i	$-0.336875\pi$
$353$	18.4251	0.980667	0.490333	+	0.871535i	$0.336875\pi$
$354$	12.3478	0.656279
$355$	−12.0566	−0.639897
$356$	1.87654	0.0994562
$357$	0	0
$358$	0.231557	0.0122382
$359$	−32.8440	−1.73344	−0.866721	−	0.498793i	$-0.833777\pi$
$359$	−32.8440	−1.73344	−0.866721	+	0.498793i	$0.833777\pi$
$360$	−1.00000	−0.0527046
$361$	−8.30487	−0.437099
$362$	10.2011	0.536157
$363$	4.61539	0.242245
$364$	10.8167	0.566951
$365$	−10.1941	−0.533586
$366$	2.93297	0.153309
$367$	−29.0408	−1.51592	−0.757958	−	0.652303i	$-0.773803\pi$
$367$	−29.0408	−1.51592	−0.757958	+	0.652303i	$0.773803\pi$
$368$	−1.55532	−0.0810766
$369$	3.64464	0.189732
$370$	−5.91312	−0.307408
$371$	−23.9350	−1.24265
$372$	−2.55075	−0.132250
$373$	−28.1333	−1.45669	−0.728343	−	0.685213i	$-0.759709\pi$
$373$	−28.1333	−1.45669	−0.728343	+	0.685213i	$0.759709\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	−2.90974	−0.150058
$377$	20.1571	1.03814
$378$	−3.08741	−0.158799
$379$	−5.62844	−0.289113	−0.144557	−	0.989497i	$-0.546176\pi$
$379$	−5.62844	−0.289113	−0.144557	+	0.989497i	$0.546176\pi$
$380$	3.27034	0.167765
$381$	8.77327	0.449468
$382$	−0.217533	−0.0111300
$383$	−4.56950	−0.233490	−0.116745	−	0.993162i	$-0.537246\pi$
$383$	−4.56950	−0.233490	−0.116745	+	0.993162i	$0.537246\pi$
$384$	−1.00000	−0.0510310
$385$	12.2003	0.621785
$386$	−26.8426	−1.36625
$387$	5.39105	0.274042
$388$	−11.2343	−0.570334
$389$	−22.4871	−1.14014	−0.570070	−	0.821596i	$-0.693084\pi$
$389$	−22.4871	−1.14014	−0.570070	+	0.821596i	$0.693084\pi$
$390$	−3.50350	−0.177407
$391$	0	0
$392$	−2.53209	−0.127890
$393$	−13.9041	−0.701367
$394$	7.28615	0.367071
$395$	12.8514	0.646625
$396$	3.95163	0.198577
$397$	−29.9951	−1.50541	−0.752706	−	0.658356i	$-0.771252\pi$
$397$	−29.9951	−1.50541	−0.752706	+	0.658356i	$0.771252\pi$
$398$	15.6273	0.783323
$399$	10.0969	0.505476
$400$	1.00000	0.0500000
$401$	−13.2656	−0.662455	−0.331227	−	0.943551i	$-0.607463\pi$
$401$	−13.2656	−0.662455	−0.331227	+	0.943551i	$0.607463\pi$
$402$	−3.87415	−0.193225
$403$	−8.93655	−0.445161
$404$	14.3854	0.715701
$405$	1.00000	0.0496904
$406$	−17.7631	−0.881570
$407$	23.3665	1.15823
$408$	0	0
$409$	−25.4791	−1.25986	−0.629931	−	0.776651i	$-0.716917\pi$
$409$	−25.4791	−1.25986	−0.629931	+	0.776651i	$0.716917\pi$
$410$	−3.64464	−0.179996
$411$	−14.3376	−0.707224
$412$	7.22663	0.356031
$413$	−38.1228	−1.87590
$414$	1.55532	0.0764398
$415$	11.9051	0.584399
$416$	−3.50350	−0.171773
$417$	6.01511	0.294561
$418$	−12.9232	−0.632093
$419$	6.58335	0.321618	0.160809	−	0.986986i	$-0.448590\pi$
$419$	6.58335	0.321618	0.160809	+	0.986986i	$0.448590\pi$
$420$	3.08741	0.150650
$421$	8.57800	0.418066	0.209033	−	0.977909i	$-0.432968\pi$
$421$	8.57800	0.418066	0.209033	+	0.977909i	$0.432968\pi$
$422$	−19.3853	−0.943663
$423$	2.90974	0.141476
$424$	7.75247	0.376493
$425$	0	0
$426$	12.0566	0.584143
$427$	−9.05528	−0.438216
$428$	−18.5081	−0.894622
$429$	13.8445	0.668421
$430$	−5.39105	−0.259979
$431$	27.4300	1.32126	0.660629	−	0.750712i	$-0.270290\pi$
$431$	27.4300	1.32126	0.660629	+	0.750712i	$0.270290\pi$
$432$	1.00000	0.0481125
$433$	−24.3323	−1.16933	−0.584667	−	0.811273i	$-0.698775\pi$
$433$	−24.3323	−1.16933	−0.584667	+	0.811273i	$0.698775\pi$
$434$	7.87520	0.378022
$435$	5.75341	0.275855
$436$	−6.17645	−0.295798
$437$	−5.08642	−0.243317
$438$	10.1941	0.487095
$439$	35.4417	1.69154	0.845770	−	0.533548i	$-0.179142\pi$
$439$	35.4417	1.69154	0.845770	+	0.533548i	$0.179142\pi$
$440$	−3.95163	−0.188387
$441$	2.53209	0.120576
$442$	0	0
$443$	27.5568	1.30926	0.654632	−	0.755948i	$-0.272824\pi$
$443$	27.5568	1.30926	0.654632	+	0.755948i	$0.272824\pi$
$444$	5.91312	0.280624
$445$	1.87654	0.0889563
$446$	14.7267	0.697329
$447$	−8.22202	−0.388888
$448$	3.08741	0.145866
$449$	−14.6209	−0.690004	−0.345002	−	0.938602i	$-0.612122\pi$
$449$	−14.6209	−0.690004	−0.345002	+	0.938602i	$0.612122\pi$
$450$	−1.00000	−0.0471405
$451$	14.4023	0.678176
$452$	13.3898	0.629805
$453$	−14.2549	−0.669751
$454$	−0.262411	−0.0123156
$455$	10.8167	0.507097
$456$	−3.27034	−0.153148
$457$	−22.8777	−1.07017	−0.535087	−	0.844797i	$-0.679721\pi$
$457$	−22.8777	−1.07017	−0.535087	+	0.844797i	$0.679721\pi$
$458$	8.17383	0.381938
$459$	0	0
$460$	−1.55532	−0.0725171
$461$	−16.0162	−0.745951	−0.372975	−	0.927841i	$-0.621662\pi$
$461$	−16.0162	−0.745951	−0.372975	+	0.927841i	$0.621662\pi$
$462$	−12.2003	−0.567609
$463$	14.7389	0.684975	0.342488	−	0.939522i	$-0.388731\pi$
$463$	14.7389	0.684975	0.342488	+	0.939522i	$0.388731\pi$
$464$	5.75341	0.267096
$465$	−2.55075	−0.118288
$466$	10.6788	0.494685
$467$	18.4636	0.854393	0.427196	−	0.904159i	$-0.359501\pi$
$467$	18.4636	0.854393	0.427196	+	0.904159i	$0.359501\pi$
$468$	3.50350	0.161949
$469$	11.9611	0.552312
$470$	−2.90974	−0.134216
$471$	8.92906	0.411430
$472$	12.3478	0.568355
$473$	21.3034	0.979532
$474$	−12.8514	−0.590285
$475$	3.27034	0.150054
$476$	0	0
$477$	−7.75247	−0.354961
$478$	28.5760	1.30704
$479$	4.73139	0.216183	0.108091	−	0.994141i	$-0.465526\pi$
$479$	4.73139	0.216183	0.108091	+	0.994141i	$0.465526\pi$
$480$	−1.00000	−0.0456435
$481$	20.7166	0.944596
$482$	7.57174	0.344883
$483$	−4.80191	−0.218494
$484$	4.61539	0.209790
$485$	−11.2343	−0.510123
$486$	−1.00000	−0.0453609
$487$	−19.0649	−0.863913	−0.431957	−	0.901894i	$-0.642177\pi$
$487$	−19.0649	−0.863913	−0.431957	+	0.901894i	$0.642177\pi$
$488$	2.93297	0.132769
$489$	−20.4926	−0.926707
$490$	−2.53209	−0.114388
$491$	22.5745	1.01877	0.509387	−	0.860537i	$-0.329872\pi$
$491$	22.5745	1.01877	0.509387	+	0.860537i	$0.329872\pi$
$492$	3.64464	0.164313
$493$	0	0
$494$	−11.4576	−0.515504
$495$	3.95163	0.177613
$496$	−2.55075	−0.114532
$497$	−37.2236	−1.66971
$498$	−11.9051	−0.533481
$499$	−21.9553	−0.982853	−0.491427	−	0.870919i	$-0.663524\pi$
$499$	−21.9553	−0.982853	−0.491427	+	0.870919i	$0.663524\pi$
$500$	1.00000	0.0447214
$501$	−17.1341	−0.765495
$502$	17.7780	0.793473
$503$	−26.4725	−1.18035	−0.590175	−	0.807275i	$-0.700941\pi$
$503$	−26.4725	−1.18035	−0.590175	+	0.807275i	$0.700941\pi$
$504$	−3.08741	−0.137524
$505$	14.3854	0.640142
$506$	6.14605	0.273225
$507$	−0.725473	−0.0322194
$508$	8.77327	0.389251
$509$	−0.693947	−0.0307586	−0.0153793	−	0.999882i	$-0.504896\pi$
$509$	−0.693947	−0.0307586	−0.0153793	+	0.999882i	$0.504896\pi$
$510$	0	0
$511$	−31.4735	−1.39230
$512$	−1.00000	−0.0441942
$513$	3.27034	0.144389
$514$	20.9004	0.921876
$515$	7.22663	0.318444
$516$	5.39105	0.237328
$517$	11.4982	0.505691
$518$	−18.2562	−0.802131
$519$	−1.31134	−0.0575613
$520$	−3.50350	−0.153639
$521$	10.9589	0.480119	0.240059	−	0.970758i	$-0.422833\pi$
$521$	10.9589	0.480119	0.240059	+	0.970758i	$0.422833\pi$
$522$	−5.75341	−0.251820
$523$	2.66514	0.116538	0.0582692	−	0.998301i	$-0.481442\pi$
$523$	2.66514	0.116538	0.0582692	+	0.998301i	$0.481442\pi$
$524$	−13.9041	−0.607402
$525$	3.08741	0.134746
$526$	−8.23360	−0.359002
$527$	0	0
$528$	3.95163	0.171973
$529$	−20.5810	−0.894825
$530$	7.75247	0.336746
$531$	−12.3478	−0.535850
$532$	10.0969	0.437755
$533$	12.7690	0.553086
$534$	−1.87654	−0.0812056
$535$	−18.5081	−0.800174
$536$	−3.87415	−0.167338
$537$	−0.231557	−0.00999243
$538$	−21.3825	−0.921866
$539$	10.0059	0.430984
$540$	1.00000	0.0430331
$541$	27.4741	1.18120	0.590602	−	0.806963i	$-0.298890\pi$
$541$	27.4741	1.18120	0.590602	+	0.806963i	$0.298890\pi$
$542$	−28.5163	−1.22488
$543$	−10.2011	−0.437770
$544$	0	0
$545$	−6.17645	−0.264570
$546$	−10.8167	−0.462914
$547$	26.1153	1.11661	0.558306	−	0.829635i	$-0.311452\pi$
$547$	26.1153	1.11661	0.558306	+	0.829635i	$0.311452\pi$
$548$	−14.3376	−0.612474
$549$	−2.93297	−0.125176
$550$	−3.95163	−0.168498
$551$	18.8156	0.801572
$552$	1.55532	0.0661988
$553$	39.6776	1.68726
$554$	−15.1457	−0.643478
$555$	5.91312	0.250998
$556$	6.01511	0.255098
$557$	21.0451	0.891709	0.445854	−	0.895105i	$-0.352900\pi$
$557$	21.0451	0.891709	0.445854	+	0.895105i	$0.352900\pi$
$558$	2.55075	0.107982
$559$	18.8875	0.798858
$560$	3.08741	0.130467
$561$	0	0
$562$	10.9195	0.460610
$563$	26.6775	1.12432	0.562161	−	0.827028i	$-0.309970\pi$
$563$	26.6775	1.12432	0.562161	+	0.827028i	$0.309970\pi$
$564$	2.90974	0.122522
$565$	13.3898	0.563314
$566$	−21.2893	−0.894856
$567$	3.08741	0.129659
$568$	12.0566	0.505883
$569$	−45.0684	−1.88936	−0.944682	−	0.327987i	$-0.893630\pi$
$569$	−45.0684	−1.88936	−0.944682	+	0.327987i	$0.893630\pi$
$570$	−3.27034	−0.136979
$571$	−39.1197	−1.63711	−0.818554	−	0.574430i	$-0.805224\pi$
$571$	−39.1197	−1.63711	−0.818554	+	0.574430i	$0.805224\pi$
$572$	13.8445	0.578870
$573$	0.217533	0.00908759
$574$	−11.2525	−0.469669
$575$	−1.55532	−0.0648613
$576$	1.00000	0.0416667
$577$	−8.45037	−0.351794	−0.175897	−	0.984409i	$-0.556283\pi$
$577$	−8.45037	−0.351794	−0.175897	+	0.984409i	$0.556283\pi$
$578$	0	0
$579$	26.8426	1.11554
$580$	5.75341	0.238898
$581$	36.7560	1.52489
$582$	11.2343	0.465676
$583$	−30.6349	−1.26877
$584$	10.1941	0.421836
$585$	3.50350	0.144852
$586$	12.9203	0.533732
$587$	−17.4970	−0.722178	−0.361089	−	0.932531i	$-0.617595\pi$
$587$	−17.4970	−0.722178	−0.361089	+	0.932531i	$0.617595\pi$
$588$	2.53209	0.104422
$589$	−8.34181	−0.343718
$590$	12.3478	0.508352
$591$	−7.28615	−0.299712
$592$	5.91312	0.243028
$593$	22.3148	0.916357	0.458179	−	0.888860i	$-0.348502\pi$
$593$	22.3148	0.916357	0.458179	+	0.888860i	$0.348502\pi$
$594$	−3.95163	−0.162137
$595$	0	0
$596$	−8.22202	−0.336787
$597$	−15.6273	−0.639581
$598$	5.44906	0.222829
$599$	−31.0120	−1.26712	−0.633559	−	0.773695i	$-0.718407\pi$
$599$	−31.0120	−1.26712	−0.633559	+	0.773695i	$0.718407\pi$
$600$	−1.00000	−0.0408248
$601$	47.0186	1.91793	0.958963	−	0.283530i	$-0.0915055\pi$
$601$	47.0186	1.91793	0.958963	+	0.283530i	$0.0915055\pi$
$602$	−16.6444	−0.678373
$603$	3.87415	0.157768
$604$	−14.2549	−0.580022
$605$	4.61539	0.187642
$606$	−14.3854	−0.584367
$607$	19.8981	0.807638	0.403819	−	0.914839i	$-0.367683\pi$
$607$	19.8981	0.807638	0.403819	+	0.914839i	$0.367683\pi$
$608$	−3.27034	−0.132630
$609$	17.7631	0.719799
$610$	2.93297	0.118753
$611$	10.1943	0.412417
$612$	0	0
$613$	28.8966	1.16712	0.583562	−	0.812069i	$-0.301659\pi$
$613$	28.8966	1.16712	0.583562	+	0.812069i	$0.301659\pi$
$614$	14.8343	0.598663
$615$	3.64464	0.146966
$616$	−12.2003	−0.491564
$617$	−20.4069	−0.821552	−0.410776	−	0.911736i	$-0.634742\pi$
$617$	−20.4069	−0.821552	−0.410776	+	0.911736i	$0.634742\pi$
$618$	−7.22663	−0.290698
$619$	3.23960	0.130210	0.0651052	−	0.997878i	$-0.479262\pi$
$619$	3.23960	0.130210	0.0651052	+	0.997878i	$0.479262\pi$
$620$	−2.55075	−0.102440
$621$	−1.55532	−0.0624128
$622$	−8.45812	−0.339140
$623$	5.79363	0.232117
$624$	3.50350	0.140252
$625$	1.00000	0.0400000
$626$	14.3937	0.575288
$627$	12.9232	0.516102
$628$	8.92906	0.356308
$629$	0	0
$630$	−3.08741	−0.123005
$631$	2.06579	0.0822379	0.0411189	−	0.999154i	$-0.486908\pi$
$631$	2.06579	0.0822379	0.0411189	+	0.999154i	$0.486908\pi$
$632$	−12.8514	−0.511202
$633$	19.3853	0.770497
$634$	−10.3456	−0.410877
$635$	8.77327	0.348157
$636$	−7.75247	−0.307406
$637$	8.87118	0.351489
$638$	−22.7354	−0.900102
$639$	−12.0566	−0.476951
$640$	−1.00000	−0.0395285
$641$	−10.6498	−0.420640	−0.210320	−	0.977633i	$-0.567451\pi$
$641$	−10.6498	−0.420640	−0.210320	+	0.977633i	$0.567451\pi$
$642$	18.5081	0.730456
$643$	38.7273	1.52726	0.763629	−	0.645656i	$-0.223416\pi$
$643$	38.7273	1.52726	0.763629	+	0.645656i	$0.223416\pi$
$644$	−4.80191	−0.189222
$645$	5.39105	0.212272
$646$	0	0
$647$	−12.7626	−0.501751	−0.250875	−	0.968019i	$-0.580718\pi$
$647$	−12.7626	−0.501751	−0.250875	+	0.968019i	$0.580718\pi$
$648$	−1.00000	−0.0392837
$649$	−48.7940	−1.91533
$650$	−3.50350	−0.137419
$651$	−7.87520	−0.308653
$652$	−20.4926	−0.802552
$653$	−10.0338	−0.392652	−0.196326	−	0.980539i	$-0.562901\pi$
$653$	−10.0338	−0.392652	−0.196326	+	0.980539i	$0.562901\pi$
$654$	6.17645	0.241518
$655$	−13.9041	−0.543277
$656$	3.64464	0.142299
$657$	−10.1941	−0.397711
$658$	−8.98356	−0.350216
$659$	−21.0452	−0.819804	−0.409902	−	0.912129i	$-0.634437\pi$
$659$	−21.0452	−0.819804	−0.409902	+	0.912129i	$0.634437\pi$
$660$	3.95163	0.153817
$661$	42.0721	1.63642	0.818208	−	0.574923i	$-0.194968\pi$
$661$	42.0721	1.63642	0.818208	+	0.574923i	$0.194968\pi$
$662$	−20.3745	−0.791877
$663$	0	0
$664$	−11.9051	−0.462008
$665$	10.0969	0.391540
$666$	−5.91312	−0.229129
$667$	−8.94840	−0.346483
$668$	−17.1341	−0.662938
$669$	−14.7267	−0.569367
$670$	−3.87415	−0.149672
$671$	−11.5900	−0.447428
$672$	−3.08741	−0.119099
$673$	47.4908	1.83063	0.915317	−	0.402734i	$-0.131940\pi$
$673$	47.4908	1.83063	0.915317	+	0.402734i	$0.131940\pi$
$674$	−35.4566	−1.36574
$675$	1.00000	0.0384900
$676$	−0.725473	−0.0279028
$677$	42.0236	1.61510	0.807549	−	0.589800i	$-0.200793\pi$
$677$	42.0236	1.61510	0.807549	+	0.589800i	$0.200793\pi$
$678$	−13.3898	−0.514233
$679$	−34.6848	−1.33108
$680$	0	0
$681$	0.262411	0.0100556
$682$	10.0796	0.385968
$683$	49.8783	1.90854	0.954271	−	0.298943i	$-0.0966341\pi$
$683$	49.8783	1.90854	0.954271	+	0.298943i	$0.0966341\pi$
$684$	3.27034	0.125045
$685$	−14.3376	−0.547813
$686$	13.7943	0.526667
$687$	−8.17383	−0.311851
$688$	5.39105	0.205532
$689$	−27.1608	−1.03474
$690$	1.55532	0.0592100
$691$	16.1311	0.613656	0.306828	−	0.951765i	$-0.400732\pi$
$691$	16.1311	0.613656	0.306828	+	0.951765i	$0.400732\pi$
$692$	−1.31134	−0.0498495
$693$	12.2003	0.463451
$694$	−19.5321	−0.741427
$695$	6.01511	0.228166
$696$	−5.75341	−0.218083
$697$	0	0
$698$	−22.2987	−0.844019
$699$	−10.6788	−0.403909
$700$	3.08741	0.116693
$701$	−25.0357	−0.945584	−0.472792	−	0.881174i	$-0.656754\pi$
$701$	−25.0357	−0.945584	−0.472792	+	0.881174i	$0.656754\pi$
$702$	−3.50350	−0.132231
$703$	19.3379	0.729343
$704$	3.95163	0.148933
$705$	2.90974	0.109587
$706$	−18.4251	−0.693436
$707$	44.4136	1.67035
$708$	−12.3478	−0.464060
$709$	11.6513	0.437572	0.218786	−	0.975773i	$-0.429790\pi$
$709$	11.6513	0.437572	0.218786	+	0.975773i	$0.429790\pi$
$710$	12.0566	0.452476
$711$	12.8514	0.481966
$712$	−1.87654	−0.0703261
$713$	3.96723	0.148574
$714$	0	0
$715$	13.8445	0.517757
$716$	−0.231557	−0.00865370
$717$	−28.5760	−1.06719
$718$	32.8440	1.22573
$719$	−28.4338	−1.06040	−0.530201	−	0.847872i	$-0.677883\pi$
$719$	−28.4338	−1.06040	−0.530201	+	0.847872i	$0.677883\pi$
$720$	1.00000	0.0372678
$721$	22.3116	0.830926
$722$	8.30487	0.309075
$723$	−7.57174	−0.281596
$724$	−10.2011	−0.379120
$725$	5.75341	0.213676
$726$	−4.61539	−0.171293
$727$	18.3641	0.681088	0.340544	−	0.940229i	$-0.389389\pi$
$727$	18.3641	0.681088	0.340544	+	0.940229i	$0.389389\pi$
$728$	−10.8167	−0.400895
$729$	1.00000	0.0370370
$730$	10.1941	0.377302
$731$	0	0
$732$	−2.93297	−0.108406
$733$	40.6463	1.50130	0.750652	−	0.660698i	$-0.229740\pi$
$733$	40.6463	1.50130	0.750652	+	0.660698i	$0.229740\pi$
$734$	29.0408	1.07191
$735$	2.53209	0.0933975
$736$	1.55532	0.0573298
$737$	15.3092	0.563922
$738$	−3.64464	−0.134161
$739$	39.5081	1.45333	0.726664	−	0.686993i	$-0.241070\pi$
$739$	39.5081	1.45333	0.726664	+	0.686993i	$0.241070\pi$
$740$	5.91312	0.217370
$741$	11.4576	0.420907
$742$	23.9350	0.878683
$743$	16.9955	0.623506	0.311753	−	0.950163i	$-0.399084\pi$
$743$	16.9955	0.623506	0.311753	+	0.950163i	$0.399084\pi$
$744$	2.55075	0.0935149
$745$	−8.22202	−0.301231
$746$	28.1333	1.03003
$747$	11.9051	0.435586
$748$	0	0
$749$	−57.1420	−2.08792
$750$	−1.00000	−0.0365148
$751$	−34.4645	−1.25763	−0.628814	−	0.777556i	$-0.716459\pi$
$751$	−34.4645	−1.25763	−0.628814	+	0.777556i	$0.716459\pi$
$752$	2.90974	0.106107
$753$	−17.7780	−0.647868
$754$	−20.1571	−0.734078
$755$	−14.2549	−0.518787
$756$	3.08741	0.112288
$757$	−4.78051	−0.173751	−0.0868753	−	0.996219i	$-0.527688\pi$
$757$	−4.78051	−0.173751	−0.0868753	+	0.996219i	$0.527688\pi$
$758$	5.62844	0.204434
$759$	−6.14605	−0.223087
$760$	−3.27034	−0.118628
$761$	−46.7603	−1.69506	−0.847529	−	0.530749i	$-0.821911\pi$
$761$	−46.7603	−1.69506	−0.847529	+	0.530749i	$0.821911\pi$
$762$	−8.77327	−0.317822
$763$	−19.0692	−0.690352
$764$	0.217533	0.00787008
$765$	0	0
$766$	4.56950	0.165103
$767$	−43.2606	−1.56205
$768$	1.00000	0.0360844
$769$	47.7918	1.72342	0.861709	−	0.507404i	$-0.169395\pi$
$769$	47.7918	1.72342	0.861709	+	0.507404i	$0.169395\pi$
$770$	−12.2003	−0.439668
$771$	−20.9004	−0.752709
$772$	26.8426	0.966088
$773$	−34.5300	−1.24196	−0.620979	−	0.783828i	$-0.713265\pi$
$773$	−34.5300	−1.24196	−0.620979	+	0.783828i	$0.713265\pi$
$774$	−5.39105	−0.193777
$775$	−2.55075	−0.0916256
$776$	11.2343	0.403287
$777$	18.2562	0.654938
$778$	22.4871	0.806201
$779$	11.9192	0.427050
$780$	3.50350	0.125445
$781$	−47.6432	−1.70481
$782$	0	0
$783$	5.75341	0.205610
$784$	2.53209	0.0904317
$785$	8.92906	0.318692
$786$	13.9041	0.495941
$787$	49.2202	1.75451	0.877255	−	0.480025i	$-0.159373\pi$
$787$	49.2202	1.75451	0.877255	+	0.480025i	$0.159373\pi$
$788$	−7.28615	−0.259558
$789$	8.23360	0.293124
$790$	−12.8514	−0.457233
$791$	41.3399	1.46988
$792$	−3.95163	−0.140415
$793$	−10.2757	−0.364900
$794$	29.9951	1.06449
$795$	−7.75247	−0.274952
$796$	−15.6273	−0.553893
$797$	3.47089	0.122945	0.0614727	−	0.998109i	$-0.480420\pi$
$797$	3.47089	0.122945	0.0614727	+	0.998109i	$0.480420\pi$
$798$	−10.0969	−0.357426
$799$	0	0
$800$	−1.00000	−0.0353553
$801$	1.87654	0.0663041
$802$	13.2656	0.468426
$803$	−40.2835	−1.42157
$804$	3.87415	0.136631
$805$	−4.80191	−0.169245
$806$	8.93655	0.314777
$807$	21.3825	0.752701
$808$	−14.3854	−0.506077
$809$	−48.0270	−1.68854	−0.844270	−	0.535918i	$-0.819966\pi$
$809$	−48.0270	−1.68854	−0.844270	+	0.535918i	$0.819966\pi$
$810$	−1.00000	−0.0351364
$811$	−1.53556	−0.0539209	−0.0269604	−	0.999637i	$-0.508583\pi$
$811$	−1.53556	−0.0539209	−0.0269604	+	0.999637i	$0.508583\pi$
$812$	17.7631	0.623364
$813$	28.5163	1.00011
$814$	−23.3665	−0.818994
$815$	−20.4926	−0.717824
$816$	0	0
$817$	17.6306	0.616815
$818$	25.4791	0.890856
$819$	10.8167	0.377968
$820$	3.64464	0.127276
$821$	37.6974	1.31565	0.657825	−	0.753171i	$-0.271477\pi$
$821$	37.6974	1.31565	0.657825	+	0.753171i	$0.271477\pi$
$822$	14.3376	0.500083
$823$	−33.5340	−1.16892	−0.584460	−	0.811422i	$-0.698694\pi$
$823$	−33.5340	−1.16892	−0.584460	+	0.811422i	$0.698694\pi$
$824$	−7.22663	−0.251752
$825$	3.95163	0.137578
$826$	38.1228	1.32646
$827$	16.4470	0.571919	0.285959	−	0.958242i	$-0.407688\pi$
$827$	16.4470	0.571919	0.285959	+	0.958242i	$0.407688\pi$
$828$	−1.55532	−0.0540511
$829$	10.2211	0.354992	0.177496	−	0.984122i	$-0.443200\pi$
$829$	10.2211	0.354992	0.177496	+	0.984122i	$0.443200\pi$
$830$	−11.9051	−0.413233
$831$	15.1457	0.525398
$832$	3.50350	0.121462
$833$	0	0
$834$	−6.01511	−0.208286
$835$	−17.1341	−0.592950
$836$	12.9232	0.446957
$837$	−2.55075	−0.0881667
$838$	−6.58335	−0.227418
$839$	32.5067	1.12226	0.561128	−	0.827729i	$-0.310367\pi$
$839$	32.5067	1.12226	0.561128	+	0.827729i	$0.310367\pi$
$840$	−3.08741	−0.106526
$841$	4.10177	0.141440
$842$	−8.57800	−0.295617
$843$	−10.9195	−0.376086
$844$	19.3853	0.667270
$845$	−0.725473	−0.0249570
$846$	−2.90974	−0.100039
$847$	14.2496	0.489621
$848$	−7.75247	−0.266221
$849$	21.2893	0.730647
$850$	0	0
$851$	−9.19678	−0.315262
$852$	−12.0566	−0.413052
$853$	5.09362	0.174402	0.0872012	−	0.996191i	$-0.472208\pi$
$853$	5.09362	0.174402	0.0872012	+	0.996191i	$0.472208\pi$
$854$	9.05528	0.309865
$855$	3.27034	0.111843
$856$	18.5081	0.632593
$857$	−2.24541	−0.0767019	−0.0383510	−	0.999264i	$-0.512210\pi$
$857$	−2.24541	−0.0767019	−0.0383510	+	0.999264i	$0.512210\pi$
$858$	−13.8445	−0.472645
$859$	−20.4035	−0.696158	−0.348079	−	0.937465i	$-0.613166\pi$
$859$	−20.4035	−0.696158	−0.348079	+	0.937465i	$0.613166\pi$
$860$	5.39105	0.183833
$861$	11.2525	0.383483
$862$	−27.4300	−0.934271
$863$	11.9224	0.405843	0.202922	−	0.979195i	$-0.434956\pi$
$863$	11.9224	0.405843	0.202922	+	0.979195i	$0.434956\pi$
$864$	−1.00000	−0.0340207
$865$	−1.31134	−0.0445868
$866$	24.3323	0.826844
$867$	0	0
$868$	−7.87520	−0.267302
$869$	50.7840	1.72273
$870$	−5.75341	−0.195059
$871$	13.5731	0.459907
$872$	6.17645	0.209161
$873$	−11.2343	−0.380223
$874$	5.08642	0.172051
$875$	3.08741	0.104373
$876$	−10.1941	−0.344428
$877$	−15.9979	−0.540211	−0.270106	−	0.962831i	$-0.587059\pi$
$877$	−15.9979	−0.540211	−0.270106	+	0.962831i	$0.587059\pi$
$878$	−35.4417	−1.19610
$879$	−12.9203	−0.435790
$880$	3.95163	0.133209
$881$	−31.9487	−1.07638	−0.538190	−	0.842824i	$-0.680892\pi$
$881$	−31.9487	−1.07638	−0.538190	+	0.842824i	$0.680892\pi$
$882$	−2.53209	−0.0852599
$883$	13.0828	0.440271	0.220135	−	0.975469i	$-0.429350\pi$
$883$	13.0828	0.440271	0.220135	+	0.975469i	$0.429350\pi$
$884$	0	0
$885$	−12.3478	−0.415067
$886$	−27.5568	−0.925789
$887$	16.5288	0.554984	0.277492	−	0.960728i	$-0.410497\pi$
$887$	16.5288	0.554984	0.277492	+	0.960728i	$0.410497\pi$
$888$	−5.91312	−0.198431
$889$	27.0867	0.908458
$890$	−1.87654	−0.0629016
$891$	3.95163	0.132385
$892$	−14.7267	−0.493086
$893$	9.51585	0.318436
$894$	8.22202	0.274985
$895$	−0.231557	−0.00774011
$896$	−3.08741	−0.103143
$897$	−5.44906	−0.181939
$898$	14.6209	0.487906
$899$	−14.6755	−0.489456
$900$	1.00000	0.0333333
$901$	0	0
$902$	−14.4023	−0.479543
$903$	16.6444	0.553890
$904$	−13.3898	−0.445339
$905$	−10.2011	−0.339095
$906$	14.2549	0.473586
$907$	23.7247	0.787766	0.393883	−	0.919160i	$-0.371131\pi$
$907$	23.7247	0.787766	0.393883	+	0.919160i	$0.371131\pi$
$908$	0.262411	0.00870843
$909$	14.3854	0.477134
$910$	−10.8167	−0.358571
$911$	18.1109	0.600040	0.300020	−	0.953933i	$-0.403007\pi$
$911$	18.1109	0.600040	0.300020	+	0.953933i	$0.403007\pi$
$912$	3.27034	0.108292
$913$	47.0446	1.55695
$914$	22.8777	0.756727
$915$	−2.93297	−0.0969611
$916$	−8.17383	−0.270071
$917$	−42.9275	−1.41759
$918$	0	0
$919$	−27.4321	−0.904902	−0.452451	−	0.891789i	$-0.649450\pi$
$919$	−27.4321	−0.904902	−0.452451	+	0.891789i	$0.649450\pi$
$920$	1.55532	0.0512774
$921$	−14.8343	−0.488806
$922$	16.0162	0.527467
$923$	−42.2403	−1.39036
$924$	12.2003	0.401360
$925$	5.91312	0.194422
$926$	−14.7389	−0.484351
$927$	7.22663	0.237354
$928$	−5.75341	−0.188865
$929$	37.2296	1.22146	0.610731	−	0.791838i	$-0.290876\pi$
$929$	37.2296	1.22146	0.610731	+	0.791838i	$0.290876\pi$
$930$	2.55075	0.0836423
$931$	8.28079	0.271392
$932$	−10.6788	−0.349795
$933$	8.45812	0.276906
$934$	−18.4636	−0.604147
$935$	0	0
$936$	−3.50350	−0.114516
$937$	15.6858	0.512433	0.256217	−	0.966619i	$-0.417524\pi$
$937$	15.6858	0.512433	0.256217	+	0.966619i	$0.417524\pi$
$938$	−11.9611	−0.390543
$939$	−14.3937	−0.469721
$940$	2.90974	0.0949053
$941$	15.4088	0.502312	0.251156	−	0.967947i	$-0.419189\pi$
$941$	15.4088	0.502312	0.251156	+	0.967947i	$0.419189\pi$
$942$	−8.92906	−0.290925
$943$	−5.66857	−0.184594
$944$	−12.3478	−0.401887
$945$	3.08741	0.100433
$946$	−21.3034	−0.692634
$947$	−13.3896	−0.435103	−0.217552	−	0.976049i	$-0.569807\pi$
$947$	−13.3896	−0.435103	−0.217552	+	0.976049i	$0.569807\pi$
$948$	12.8514	0.417394
$949$	−35.7152	−1.15936
$950$	−3.27034	−0.106104
$951$	10.3456	0.335480
$952$	0	0
$953$	21.5109	0.696805	0.348403	−	0.937345i	$-0.386724\pi$
$953$	21.5109	0.696805	0.348403	+	0.937345i	$0.386724\pi$
$954$	7.75247	0.250996
$955$	0.217533	0.00703921
$956$	−28.5760	−0.924214
$957$	22.7354	0.734930
$958$	−4.73139	−0.152864
$959$	−44.2661	−1.42943
$960$	1.00000	0.0322749
$961$	−24.4937	−0.790119
$962$	−20.7166	−0.667930
$963$	−18.5081	−0.596415
$964$	−7.57174	−0.243869
$965$	26.8426	0.864095
$966$	4.80191	0.154499
$967$	−14.9927	−0.482133	−0.241066	−	0.970509i	$-0.577497\pi$
$967$	−14.9927	−0.482133	−0.241066	+	0.970509i	$0.577497\pi$
$968$	−4.61539	−0.148344
$969$	0	0
$970$	11.2343	0.360711
$971$	−18.3150	−0.587757	−0.293879	−	0.955843i	$-0.594946\pi$
$971$	−18.3150	−0.587757	−0.293879	+	0.955843i	$0.594946\pi$
$972$	1.00000	0.0320750
$973$	18.5711	0.595363
$974$	19.0649	0.610879
$975$	3.50350	0.112202
$976$	−2.93297	−0.0938821
$977$	10.1011	0.323163	0.161582	−	0.986859i	$-0.448340\pi$
$977$	10.1011	0.323163	0.161582	+	0.986859i	$0.448340\pi$
$978$	20.4926	0.655281
$979$	7.41537	0.236996
$980$	2.53209	0.0808846
$981$	−6.17645	−0.197199
$982$	−22.5745	−0.720383
$983$	−38.0667	−1.21414	−0.607069	−	0.794649i	$-0.707655\pi$
$983$	−38.0667	−1.21414	−0.607069	+	0.794649i	$0.707655\pi$
$984$	−3.64464	−0.116187
$985$	−7.28615	−0.232156
$986$	0	0
$987$	8.98356	0.285950
$988$	11.4576	0.364516
$989$	−8.38480	−0.266621
$990$	−3.95163	−0.125591
$991$	33.7097	1.07082	0.535412	−	0.844591i	$-0.320156\pi$
$991$	33.7097	1.07082	0.535412	+	0.844591i	$0.320156\pi$
$992$	2.55075	0.0809863
$993$	20.3745	0.646565
$994$	37.2236	1.18066
$995$	−15.6273	−0.495417
$996$	11.9051	0.377228
$997$	−37.3937	−1.18427	−0.592135	−	0.805839i	$-0.701715\pi$
$997$	−37.3937	−1.18427	−0.592135	+	0.805839i	$0.701715\pi$
$998$	21.9553	0.694982
$999$	5.91312	0.187083

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8670.2.a.ce.1.6	yes	6
17.16	even	2		8670.2.a.cb.1.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8670.2.a.cb.1.1	✓	6	17.16	even	2
8670.2.a.ce.1.6	yes	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +3.08741 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +3.08741 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +3.95163 q^{11} +1.00000 q^{12} +3.50350 q^{13} -3.08741 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{18} +3.27034 q^{19} +1.00000 q^{20} +3.08741 q^{21} -3.95163 q^{22} -1.55532 q^{23} -1.00000 q^{24} +1.00000 q^{25} -3.50350 q^{26} +1.00000 q^{27} +3.08741 q^{28} +5.75341 q^{29} -1.00000 q^{30} -2.55075 q^{31} -1.00000 q^{32} +3.95163 q^{33} +3.08741 q^{35} +1.00000 q^{36} +5.91312 q^{37} -3.27034 q^{38} +3.50350 q^{39} -1.00000 q^{40} +3.64464 q^{41} -3.08741 q^{42} +5.39105 q^{43} +3.95163 q^{44} +1.00000 q^{45} +1.55532 q^{46} +2.90974 q^{47} +1.00000 q^{48} +2.53209 q^{49} -1.00000 q^{50} +3.50350 q^{52} -7.75247 q^{53} -1.00000 q^{54} +3.95163 q^{55} -3.08741 q^{56} +3.27034 q^{57} -5.75341 q^{58} -12.3478 q^{59} +1.00000 q^{60} -2.93297 q^{61} +2.55075 q^{62} +3.08741 q^{63} +1.00000 q^{64} +3.50350 q^{65} -3.95163 q^{66} +3.87415 q^{67} -1.55532 q^{69} -3.08741 q^{70} -12.0566 q^{71} -1.00000 q^{72} -10.1941 q^{73} -5.91312 q^{74} +1.00000 q^{75} +3.27034 q^{76} +12.2003 q^{77} -3.50350 q^{78} +12.8514 q^{79} +1.00000 q^{80} +1.00000 q^{81} -3.64464 q^{82} +11.9051 q^{83} +3.08741 q^{84} -5.39105 q^{86} +5.75341 q^{87} -3.95163 q^{88} +1.87654 q^{89} -1.00000 q^{90} +10.8167 q^{91} -1.55532 q^{92} -2.55075 q^{93} -2.90974 q^{94} +3.27034 q^{95} -1.00000 q^{96} -11.2343 q^{97} -2.53209 q^{98} +3.95163 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} + 6 q^{5} - 6 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 + 6 * q^5 - 6 * q^6 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} + 6 q^{5} - 6 q^{6} - 6 q^{8} + 6 q^{9} - 6 q^{10} + 6 q^{11} + 6 q^{12} + 6 q^{13} + 6 q^{15} + 6 q^{16} - 6 q^{18} - 6 q^{19} + 6 q^{20} - 6 q^{22} - 6 q^{24} + 6 q^{25} - 6 q^{26} + 6 q^{27} + 6 q^{29} - 6 q^{30} - 6 q^{32} + 6 q^{33} + 6 q^{36} + 6 q^{38} + 6 q^{39} - 6 q^{40} + 12 q^{41} + 24 q^{43} + 6 q^{44} + 6 q^{45} + 6 q^{47} + 6 q^{48} + 6 q^{49} - 6 q^{50} + 6 q^{52} - 6 q^{53} - 6 q^{54} + 6 q^{55} - 6 q^{57} - 6 q^{58} - 18 q^{59} + 6 q^{60} - 6 q^{61} + 6 q^{64} + 6 q^{65} - 6 q^{66} + 36 q^{67} + 30 q^{71} - 6 q^{72} + 12 q^{73} + 6 q^{75} - 6 q^{76} - 6 q^{77} - 6 q^{78} + 12 q^{79} + 6 q^{80} + 6 q^{81} - 12 q^{82} + 36 q^{83} - 24 q^{86} + 6 q^{87} - 6 q^{88} - 30 q^{89} - 6 q^{90} + 12 q^{91} - 6 q^{94} - 6 q^{95} - 6 q^{96} + 18 q^{97} - 6 q^{98} + 6 q^{99}+O(q^{100}) \) 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 - 6 * q^24 + 6 * q^25 - 6 * q^26 + 6 * q^27 + 6 * q^29 - 6 * q^30 - 6 * q^32 + 6 * q^33 + 6 * q^36 + 6 * q^38 + 6 * q^39 - 6 * q^40 + 12 * q^41 + 24 * q^43 + 6 * q^44 + 6 * q^45 + 6 * q^47 + 6 * q^48 + 6 * q^49 - 6 * q^50 + 6 * q^52 - 6 * q^53 - 6 * q^54 + 6 * q^55 - 6 * q^57 - 6 * q^58 - 18 * q^59 + 6 * q^60 - 6 * q^61 + 6 * q^64 + 6 * q^65 - 6 * q^66 + 36 * q^67 + 30 * q^71 - 6 * q^72 + 12 * q^73 + 6 * q^75 - 6 * q^76 - 6 * q^77 - 6 * q^78 + 12 * q^79 + 6 * q^80 + 6 * q^81 - 12 * q^82 + 36 * q^83 - 24 * q^86 + 6 * q^87 - 6 * q^88 - 30 * q^89 - 6 * q^90 + 12 * q^91 - 6 * q^94 - 6 * q^95 - 6 * q^96 + 18 * q^97 - 6 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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