LMFDB - Embedded newform 8670.2.a.bs.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [8670,2,Mod(1,8670)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [3,3,3,3,3,3,-6,3,3,3,-12,3,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$69.2302985525$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
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			1.1
Root			$-1.53209$ 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)

$f(q)$	$=$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -3.53209 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -4.34730 q^{11} +1.00000 q^{12} +2.57398 q^{13} -3.53209 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{18} -0.389185 q^{19} +1.00000 q^{20} -3.53209 q^{21} -4.34730 q^{22} +2.94356 q^{23} +1.00000 q^{24} +1.00000 q^{25} +2.57398 q^{26} +1.00000 q^{27} -3.53209 q^{28} -5.06418 q^{29} +1.00000 q^{30} -6.69459 q^{31} +1.00000 q^{32} -4.34730 q^{33} -3.53209 q^{35} +1.00000 q^{36} +0.758770 q^{37} -0.389185 q^{38} +2.57398 q^{39} +1.00000 q^{40} -5.69459 q^{41} -3.53209 q^{42} -1.30541 q^{43} -4.34730 q^{44} +1.00000 q^{45} +2.94356 q^{46} -1.07873 q^{47} +1.00000 q^{48} +5.47565 q^{49} +1.00000 q^{50} +2.57398 q^{52} +0.716881 q^{53} +1.00000 q^{54} -4.34730 q^{55} -3.53209 q^{56} -0.389185 q^{57} -5.06418 q^{58} +5.78106 q^{59} +1.00000 q^{60} +0.128356 q^{61} -6.69459 q^{62} -3.53209 q^{63} +1.00000 q^{64} +2.57398 q^{65} -4.34730 q^{66} -12.3696 q^{67} +2.94356 q^{69} -3.53209 q^{70} -14.2567 q^{71} +1.00000 q^{72} -7.19253 q^{73} +0.758770 q^{74} +1.00000 q^{75} -0.389185 q^{76} +15.3550 q^{77} +2.57398 q^{78} -4.82295 q^{79} +1.00000 q^{80} +1.00000 q^{81} -5.69459 q^{82} +15.5175 q^{83} -3.53209 q^{84} -1.30541 q^{86} -5.06418 q^{87} -4.34730 q^{88} -17.6313 q^{89} +1.00000 q^{90} -9.09152 q^{91} +2.94356 q^{92} -6.69459 q^{93} -1.07873 q^{94} -0.389185 q^{95} +1.00000 q^{96} +11.1925 q^{97} +5.47565 q^{98} -4.34730 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} - 6 q^{7} + 3 q^{8} + 3 q^{9} + 3 q^{10} - 12 q^{11} + 3 q^{12} - 6 q^{14} + 3 q^{15} + 3 q^{16} + 3 q^{18} + 3 q^{19} + 3 q^{20} - 6 q^{21} - 12 q^{22}+ \cdots - 12 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 - 6 * q^7 + 3 * q^8 + 3 * q^9 + 3 * q^10 - 12 * q^11 + 3 * q^12 - 6 * q^14 + 3 * q^15 + 3 * q^16 + 3 * q^18 + 3 * q^19 + 3 * q^20 - 6 * q^21 - 12 * q^22 - 6 * q^23 + 3 * q^24 + 3 * q^25 + 3 * q^27 - 6 * q^28 - 6 * q^29 + 3 * q^30 - 18 * q^31 + 3 * q^32 - 12 * q^33 - 6 * q^35 + 3 * q^36 - 9 * q^37 + 3 * q^38 + 3 * q^40 - 15 * q^41 - 6 * q^42 - 6 * q^43 - 12 * q^44 + 3 * q^45 - 6 * q^46 - 12 * q^47 + 3 * q^48 - 3 * q^49 + 3 * q^50 - 6 * q^53 + 3 * q^54 - 12 * q^55 - 6 * q^56 + 3 * q^57 - 6 * q^58 + 3 * q^60 - 18 * q^61 - 18 * q^62 - 6 * q^63 + 3 * q^64 - 12 * q^66 - 30 * q^67 - 6 * q^69 - 6 * q^70 - 6 * q^71 + 3 * q^72 + 6 * q^73 - 9 * q^74 + 3 * q^75 + 3 * q^76 + 21 * q^77 + 6 * q^79 + 3 * q^80 + 3 * q^81 - 15 * q^82 + 24 * q^83 - 6 * q^84 - 6 * q^86 - 6 * q^87 - 12 * q^88 + 6 * q^89 + 3 * q^90 + 3 * q^91 - 6 * q^92 - 18 * q^93 - 12 * q^94 + 3 * q^95 + 3 * q^96 + 6 * q^97 - 3 * q^98 - 12 * q^99

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
$7$	−3.53209	−1.33500	−0.667502	−	0.744608i	$-0.732636\pi$
$7$	−3.53209	−1.33500	−0.667502	+	0.744608i	$0.732636\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	−4.34730	−1.31076	−0.655380	−	0.755300i	$-0.727491\pi$
$11$	−4.34730	−1.31076	−0.655380	+	0.755300i	$0.727491\pi$
$12$	1.00000	0.288675
$13$	2.57398	0.713893	0.356947	−	0.934125i	$-0.383818\pi$
$13$	2.57398	0.713893	0.356947	+	0.934125i	$0.383818\pi$
$14$	−3.53209	−0.943990
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	0	0
$17$	0	0
$18$	1.00000	0.235702
$19$	−0.389185	−0.0892853	−0.0446426	−	0.999003i	$-0.514215\pi$
$19$	−0.389185	−0.0892853	−0.0446426	+	0.999003i	$0.514215\pi$
$20$	1.00000	0.223607
$21$	−3.53209	−0.770765
$22$	−4.34730	−0.926847
$23$	2.94356	0.613775	0.306888	−	0.951746i	$-0.400712\pi$
$23$	2.94356	0.613775	0.306888	+	0.951746i	$0.400712\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	2.57398	0.504799
$27$	1.00000	0.192450
$28$	−3.53209	−0.667502
$29$	−5.06418	−0.940394	−0.470197	−	0.882561i	$-0.655817\pi$
$29$	−5.06418	−0.940394	−0.470197	+	0.882561i	$0.655817\pi$
$30$	1.00000	0.182574
$31$	−6.69459	−1.20238	−0.601192	−	0.799104i	$-0.705307\pi$
$31$	−6.69459	−1.20238	−0.601192	+	0.799104i	$0.705307\pi$
$32$	1.00000	0.176777
$33$	−4.34730	−0.756767
$34$	0	0
$35$	−3.53209	−0.597032
$36$	1.00000	0.166667
$37$	0.758770	0.124741	0.0623705	−	0.998053i	$-0.480134\pi$
$37$	0.758770	0.124741	0.0623705	+	0.998053i	$0.480134\pi$
$38$	−0.389185	−0.0631342
$39$	2.57398	0.412166
$40$	1.00000	0.158114
$41$	−5.69459	−0.889346	−0.444673	−	0.895693i	$-0.646680\pi$
$41$	−5.69459	−0.889346	−0.444673	+	0.895693i	$0.646680\pi$
$42$	−3.53209	−0.545013
$43$	−1.30541	−0.199073	−0.0995364	−	0.995034i	$-0.531736\pi$
$43$	−1.30541	−0.199073	−0.0995364	+	0.995034i	$0.531736\pi$
$44$	−4.34730	−0.655380
$45$	1.00000	0.149071
$46$	2.94356	0.434005
$47$	−1.07873	−0.157348	−0.0786742	−	0.996900i	$-0.525069\pi$
$47$	−1.07873	−0.157348	−0.0786742	+	0.996900i	$0.525069\pi$
$48$	1.00000	0.144338
$49$	5.47565	0.782236
$50$	1.00000	0.141421
$51$	0	0
$52$	2.57398	0.356947
$53$	0.716881	0.0984712	0.0492356	−	0.998787i	$-0.484321\pi$
$53$	0.716881	0.0984712	0.0492356	+	0.998787i	$0.484321\pi$
$54$	1.00000	0.136083
$55$	−4.34730	−0.586189
$56$	−3.53209	−0.471995
$57$	−0.389185	−0.0515489
$58$	−5.06418	−0.664959
$59$	5.78106	0.752630	0.376315	−	0.926492i	$-0.377191\pi$
$59$	5.78106	0.752630	0.376315	+	0.926492i	$0.377191\pi$
$60$	1.00000	0.129099
$61$	0.128356	0.0164342	0.00821712	−	0.999966i	$-0.497384\pi$
$61$	0.128356	0.0164342	0.00821712	+	0.999966i	$0.497384\pi$
$62$	−6.69459	−0.850214
$63$	−3.53209	−0.445001
$64$	1.00000	0.125000
$65$	2.57398	0.319263
$66$	−4.34730	−0.535115
$67$	−12.3696	−1.51119	−0.755593	−	0.655042i	$-0.772651\pi$
$67$	−12.3696	−1.51119	−0.755593	+	0.655042i	$0.772651\pi$
$68$	0	0
$69$	2.94356	0.354363
$70$	−3.53209	−0.422165
$71$	−14.2567	−1.69196	−0.845980	−	0.533214i	$-0.820984\pi$
$71$	−14.2567	−1.69196	−0.845980	+	0.533214i	$0.820984\pi$
$72$	1.00000	0.117851
$73$	−7.19253	−0.841822	−0.420911	−	0.907102i	$-0.638290\pi$
$73$	−7.19253	−0.841822	−0.420911	+	0.907102i	$0.638290\pi$
$74$	0.758770	0.0882053
$75$	1.00000	0.115470
$76$	−0.389185	−0.0446426
$77$	15.3550	1.74987
$78$	2.57398	0.291446
$79$	−4.82295	−0.542624	−0.271312	−	0.962491i	$-0.587458\pi$
$79$	−4.82295	−0.542624	−0.271312	+	0.962491i	$0.587458\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−5.69459	−0.628863
$83$	15.5175	1.70327	0.851636	−	0.524134i	$-0.175611\pi$
$83$	15.5175	1.70327	0.851636	+	0.524134i	$0.175611\pi$
$84$	−3.53209	−0.385382
$85$	0	0
$86$	−1.30541	−0.140766
$87$	−5.06418	−0.542937
$88$	−4.34730	−0.463423
$89$	−17.6313	−1.86892	−0.934460	−	0.356069i	$-0.884117\pi$
$89$	−17.6313	−1.86892	−0.934460	+	0.356069i	$0.884117\pi$
$90$	1.00000	0.105409
$91$	−9.09152	−0.953050
$92$	2.94356	0.306888
$93$	−6.69459	−0.694197
$94$	−1.07873	−0.111262
$95$	−0.389185	−0.0399296
$96$	1.00000	0.102062
$97$	11.1925	1.13643	0.568215	−	0.822880i	$-0.307634\pi$
$97$	11.1925	1.13643	0.568215	+	0.822880i	$0.307634\pi$
$98$	5.47565	0.553124
$99$	−4.34730	−0.436920
$100$	1.00000	0.100000
$101$	−8.90673	−0.886252	−0.443126	−	0.896459i	$-0.646131\pi$
$101$	−8.90673	−0.886252	−0.443126	+	0.896459i	$0.646131\pi$
$102$	0	0
$103$	−19.9222	−1.96299	−0.981497	−	0.191479i	$-0.938672\pi$
$103$	−19.9222	−1.96299	−0.981497	+	0.191479i	$0.938672\pi$
$104$	2.57398	0.252399
$105$	−3.53209	−0.344697
$106$	0.716881	0.0696297
$107$	7.75877	0.750069	0.375034	−	0.927011i	$-0.377631\pi$
$107$	7.75877	0.750069	0.375034	+	0.927011i	$0.377631\pi$
$108$	1.00000	0.0962250
$109$	15.6459	1.49861	0.749303	−	0.662228i	$-0.230389\pi$
$109$	15.6459	1.49861	0.749303	+	0.662228i	$0.230389\pi$
$110$	−4.34730	−0.414498
$111$	0.758770	0.0720193
$112$	−3.53209	−0.333751
$113$	−6.49794	−0.611275	−0.305637	−	0.952148i	$-0.598870\pi$
$113$	−6.49794	−0.611275	−0.305637	+	0.952148i	$0.598870\pi$
$114$	−0.389185	−0.0364506
$115$	2.94356	0.274489
$116$	−5.06418	−0.470197
$117$	2.57398	0.237964
$118$	5.78106	0.532190
$119$	0	0
$120$	1.00000	0.0912871
$121$	7.89899	0.718090
$122$	0.128356	0.0116208
$123$	−5.69459	−0.513464
$124$	−6.69459	−0.601192
$125$	1.00000	0.0894427
$126$	−3.53209	−0.314663
$127$	−15.3696	−1.36383	−0.681915	−	0.731431i	$-0.738853\pi$
$127$	−15.3696	−1.36383	−0.681915	+	0.731431i	$0.738853\pi$
$128$	1.00000	0.0883883
$129$	−1.30541	−0.114935
$130$	2.57398	0.225753
$131$	3.15570	0.275715	0.137857	−	0.990452i	$-0.455978\pi$
$131$	3.15570	0.275715	0.137857	+	0.990452i	$0.455978\pi$
$132$	−4.34730	−0.378384
$133$	1.37464	0.119196
$134$	−12.3696	−1.06857
$135$	1.00000	0.0860663
$136$	0	0
$137$	−2.04458	−0.174680	−0.0873400	−	0.996179i	$-0.527837\pi$
$137$	−2.04458	−0.174680	−0.0873400	+	0.996179i	$0.527837\pi$
$138$	2.94356	0.250573
$139$	3.12836	0.265344	0.132672	−	0.991160i	$-0.457644\pi$
$139$	3.12836	0.265344	0.132672	+	0.991160i	$0.457644\pi$
$140$	−3.53209	−0.298516
$141$	−1.07873	−0.0908451
$142$	−14.2567	−1.19640
$143$	−11.1898	−0.935742
$144$	1.00000	0.0833333
$145$	−5.06418	−0.420557
$146$	−7.19253	−0.595258
$147$	5.47565	0.451624
$148$	0.758770	0.0623705
$149$	2.69459	0.220750	0.110375	−	0.993890i	$-0.464795\pi$
$149$	2.69459	0.220750	0.110375	+	0.993890i	$0.464795\pi$
$150$	1.00000	0.0816497
$151$	−5.14796	−0.418935	−0.209467	−	0.977816i	$-0.567173\pi$
$151$	−5.14796	−0.418935	−0.209467	+	0.977816i	$0.567173\pi$
$152$	−0.389185	−0.0315671
$153$	0	0
$154$	15.3550	1.23734
$155$	−6.69459	−0.537723
$156$	2.57398	0.206083
$157$	13.4192	1.07097	0.535485	−	0.844545i	$-0.320129\pi$
$157$	13.4192	1.07097	0.535485	+	0.844545i	$0.320129\pi$
$158$	−4.82295	−0.383693
$159$	0.716881	0.0568524
$160$	1.00000	0.0790569
$161$	−10.3969	−0.819393
$162$	1.00000	0.0785674
$163$	20.9222	1.63875	0.819377	−	0.573255i	$-0.194320\pi$
$163$	20.9222	1.63875	0.819377	+	0.573255i	$0.194320\pi$
$164$	−5.69459	−0.444673
$165$	−4.34730	−0.338437
$166$	15.5175	1.20439
$167$	12.6432	0.978361	0.489180	−	0.872183i	$-0.337296\pi$
$167$	12.6432	0.978361	0.489180	+	0.872183i	$0.337296\pi$
$168$	−3.53209	−0.272507
$169$	−6.37464	−0.490357
$170$	0	0
$171$	−0.389185	−0.0297618
$172$	−1.30541	−0.0995364
$173$	−18.1753	−1.38184	−0.690921	−	0.722930i	$-0.742795\pi$
$173$	−18.1753	−1.38184	−0.690921	+	0.722930i	$0.742795\pi$
$174$	−5.06418	−0.383914
$175$	−3.53209	−0.267001
$176$	−4.34730	−0.327690
$177$	5.78106	0.434531
$178$	−17.6313	−1.32153
$179$	25.2841	1.88982	0.944909	−	0.327332i	$-0.106150\pi$
$179$	25.2841	1.88982	0.944909	+	0.327332i	$0.106150\pi$
$180$	1.00000	0.0745356
$181$	−7.30541	−0.543007	−0.271503	−	0.962438i	$-0.587521\pi$
$181$	−7.30541	−0.543007	−0.271503	+	0.962438i	$0.587521\pi$
$182$	−9.09152	−0.673908
$183$	0.128356	0.00948831
$184$	2.94356	0.217002
$185$	0.758770	0.0557859
$186$	−6.69459	−0.490871
$187$	0	0
$188$	−1.07873	−0.0786742
$189$	−3.53209	−0.256922
$190$	−0.389185	−0.0282345
$191$	−1.54664	−0.111911	−0.0559554	−	0.998433i	$-0.517820\pi$
$191$	−1.54664	−0.111911	−0.0559554	+	0.998433i	$0.517820\pi$
$192$	1.00000	0.0721688
$193$	−9.34998	−0.673027	−0.336513	−	0.941679i	$-0.609248\pi$
$193$	−9.34998	−0.673027	−0.336513	+	0.941679i	$0.609248\pi$
$194$	11.1925	0.803577
$195$	2.57398	0.184326
$196$	5.47565	0.391118
$197$	−1.93851	−0.138113	−0.0690566	−	0.997613i	$-0.521999\pi$
$197$	−1.93851	−0.138113	−0.0690566	+	0.997613i	$0.521999\pi$
$198$	−4.34730	−0.308949
$199$	−27.3756	−1.94060	−0.970301	−	0.241899i	$-0.922230\pi$
$199$	−27.3756	−1.94060	−0.970301	+	0.241899i	$0.922230\pi$
$200$	1.00000	0.0707107
$201$	−12.3696	−0.872483
$202$	−8.90673	−0.626675
$203$	17.8871	1.25543
$204$	0	0
$205$	−5.69459	−0.397728
$206$	−19.9222	−1.38805
$207$	2.94356	0.204592
$208$	2.57398	0.178473
$209$	1.69190	0.117031
$210$	−3.53209	−0.243737
$211$	−9.45842	−0.651144	−0.325572	−	0.945517i	$-0.605557\pi$
$211$	−9.45842	−0.651144	−0.325572	+	0.945517i	$0.605557\pi$
$212$	0.716881	0.0492356
$213$	−14.2567	−0.976854
$214$	7.75877	0.530379
$215$	−1.30541	−0.0890280
$216$	1.00000	0.0680414
$217$	23.6459	1.60519
$218$	15.6459	1.05967
$219$	−7.19253	−0.486026
$220$	−4.34730	−0.293095
$221$	0	0
$222$	0.758770	0.0509253
$223$	23.1165	1.54800	0.773998	−	0.633189i	$-0.218254\pi$
$223$	23.1165	1.54800	0.773998	+	0.633189i	$0.218254\pi$
$224$	−3.53209	−0.235998
$225$	1.00000	0.0666667
$226$	−6.49794	−0.432237
$227$	−12.4243	−0.824628	−0.412314	−	0.911042i	$-0.635279\pi$
$227$	−12.4243	−0.824628	−0.412314	+	0.911042i	$0.635279\pi$
$228$	−0.389185	−0.0257744
$229$	−11.1088	−0.734087	−0.367044	−	0.930204i	$-0.619630\pi$
$229$	−11.1088	−0.734087	−0.367044	+	0.930204i	$0.619630\pi$
$230$	2.94356	0.194093
$231$	15.3550	1.01029
$232$	−5.06418	−0.332480
$233$	−18.4979	−1.21184	−0.605920	−	0.795525i	$-0.707195\pi$
$233$	−18.4979	−1.21184	−0.605920	+	0.795525i	$0.707195\pi$
$234$	2.57398	0.168266
$235$	−1.07873	−0.0703683
$236$	5.78106	0.376315
$237$	−4.82295	−0.313284
$238$	0	0
$239$	−26.4688	−1.71213	−0.856064	−	0.516870i	$-0.827097\pi$
$239$	−26.4688	−1.71213	−0.856064	+	0.516870i	$0.827097\pi$
$240$	1.00000	0.0645497
$241$	−3.85710	−0.248457	−0.124229	−	0.992254i	$-0.539646\pi$
$241$	−3.85710	−0.248457	−0.124229	+	0.992254i	$0.539646\pi$
$242$	7.89899	0.507766
$243$	1.00000	0.0641500
$244$	0.128356	0.00821712
$245$	5.47565	0.349827
$246$	−5.69459	−0.363074
$247$	−1.00175	−0.0637401
$248$	−6.69459	−0.425107
$249$	15.5175	0.983384
$250$	1.00000	0.0632456
$251$	−14.4757	−0.913695	−0.456848	−	0.889545i	$-0.651022\pi$
$251$	−14.4757	−0.913695	−0.456848	+	0.889545i	$0.651022\pi$
$252$	−3.53209	−0.222501
$253$	−12.7965	−0.804512
$254$	−15.3696	−0.964374
$255$	0	0
$256$	1.00000	0.0625000
$257$	6.72369	0.419412	0.209706	−	0.977764i	$-0.432749\pi$
$257$	6.72369	0.419412	0.209706	+	0.977764i	$0.432749\pi$
$258$	−1.30541	−0.0812711
$259$	−2.68004	−0.166530
$260$	2.57398	0.159631
$261$	−5.06418	−0.313465
$262$	3.15570	0.194960
$263$	−26.7915	−1.65203	−0.826017	−	0.563645i	$-0.809399\pi$
$263$	−26.7915	−1.65203	−0.826017	+	0.563645i	$0.809399\pi$
$264$	−4.34730	−0.267558
$265$	0.716881	0.0440377
$266$	1.37464	0.0842844
$267$	−17.6313	−1.07902
$268$	−12.3696	−0.755593
$269$	13.2472	0.807697	0.403848	−	0.914826i	$-0.367672\pi$
$269$	13.2472	0.807697	0.403848	+	0.914826i	$0.367672\pi$
$270$	1.00000	0.0608581
$271$	−6.08378	−0.369563	−0.184782	−	0.982780i	$-0.559158\pi$
$271$	−6.08378	−0.369563	−0.184782	+	0.982780i	$0.559158\pi$
$272$	0	0
$273$	−9.09152	−0.550244
$274$	−2.04458	−0.123517
$275$	−4.34730	−0.262152
$276$	2.94356	0.177182
$277$	3.29767	0.198138	0.0990688	−	0.995081i	$-0.468414\pi$
$277$	3.29767	0.198138	0.0990688	+	0.995081i	$0.468414\pi$
$278$	3.12836	0.187626
$279$	−6.69459	−0.400795
$280$	−3.53209	−0.211083
$281$	8.80066	0.525003	0.262502	−	0.964932i	$-0.415452\pi$
$281$	8.80066	0.525003	0.262502	+	0.964932i	$0.415452\pi$
$282$	−1.07873	−0.0642372
$283$	−20.2412	−1.20322	−0.601608	−	0.798791i	$-0.705473\pi$
$283$	−20.2412	−1.20322	−0.601608	+	0.798791i	$0.705473\pi$
$284$	−14.2567	−0.845980
$285$	−0.389185	−0.0230534
$286$	−11.1898	−0.661669
$287$	20.1138	1.18728
$288$	1.00000	0.0589256
$289$	0	0
$290$	−5.06418	−0.297379
$291$	11.1925	0.656118
$292$	−7.19253	−0.420911
$293$	31.9641	1.86736	0.933681	−	0.358105i	$-0.116577\pi$
$293$	31.9641	1.86736	0.933681	+	0.358105i	$0.116577\pi$
$294$	5.47565	0.319347
$295$	5.78106	0.336586
$296$	0.758770	0.0441026
$297$	−4.34730	−0.252256
$298$	2.69459	0.156094
$299$	7.57667	0.438170
$300$	1.00000	0.0577350
$301$	4.61081	0.265763
$302$	−5.14796	−0.296232
$303$	−8.90673	−0.511678
$304$	−0.389185	−0.0223213
$305$	0.128356	0.00734962
$306$	0	0
$307$	−28.9222	−1.65068	−0.825339	−	0.564638i	$-0.809016\pi$
$307$	−28.9222	−1.65068	−0.825339	+	0.564638i	$0.809016\pi$
$308$	15.3550	0.874934
$309$	−19.9222	−1.13333
$310$	−6.69459	−0.380227
$311$	−22.4534	−1.27321	−0.636607	−	0.771189i	$-0.719663\pi$
$311$	−22.4534	−1.27321	−0.636607	+	0.771189i	$0.719663\pi$
$312$	2.57398	0.145723
$313$	−4.49794	−0.254239	−0.127119	−	0.991887i	$-0.540573\pi$
$313$	−4.49794	−0.254239	−0.127119	+	0.991887i	$0.540573\pi$
$314$	13.4192	0.757290
$315$	−3.53209	−0.199011
$316$	−4.82295	−0.271312
$317$	6.84255	0.384316	0.192158	−	0.981364i	$-0.438451\pi$
$317$	6.84255	0.384316	0.192158	+	0.981364i	$0.438451\pi$
$318$	0.716881	0.0402007
$319$	22.0155	1.23263
$320$	1.00000	0.0559017
$321$	7.75877	0.433052
$322$	−10.3969	−0.579398
$323$	0	0
$324$	1.00000	0.0555556
$325$	2.57398	0.142779
$326$	20.9222	1.15877
$327$	15.6459	0.865220
$328$	−5.69459	−0.314431
$329$	3.81016	0.210061
$330$	−4.34730	−0.239311
$331$	−14.8476	−0.816098	−0.408049	−	0.912960i	$-0.633791\pi$
$331$	−14.8476	−0.816098	−0.408049	+	0.912960i	$0.633791\pi$
$332$	15.5175	0.851636
$333$	0.758770	0.0415804
$334$	12.6432	0.691806
$335$	−12.3696	−0.675823
$336$	−3.53209	−0.192691
$337$	3.10876	0.169345	0.0846723	−	0.996409i	$-0.473016\pi$
$337$	3.10876	0.169345	0.0846723	+	0.996409i	$0.473016\pi$
$338$	−6.37464	−0.346735
$339$	−6.49794	−0.352920
$340$	0	0
$341$	29.1034	1.57604
$342$	−0.389185	−0.0210447
$343$	5.38413	0.290716
$344$	−1.30541	−0.0703828
$345$	2.94356	0.158476
$346$	−18.1753	−0.977110
$347$	−9.55674	−0.513033	−0.256516	−	0.966540i	$-0.582575\pi$
$347$	−9.55674	−0.513033	−0.256516	+	0.966540i	$0.582575\pi$
$348$	−5.06418	−0.271468
$349$	14.0000	0.749403	0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000	0.749403	0.374701	+	0.927146i	$0.377745\pi$
$350$	−3.53209	−0.188798
$351$	2.57398	0.137389
$352$	−4.34730	−0.231712
$353$	27.6905	1.47382	0.736908	−	0.675993i	$-0.236285\pi$
$353$	27.6905	1.47382	0.736908	+	0.675993i	$0.236285\pi$
$354$	5.78106	0.307260
$355$	−14.2567	−0.756668
$356$	−17.6313	−0.934460
$357$	0	0
$358$	25.2841	1.33630
$359$	18.9959	1.00256	0.501282	−	0.865284i	$-0.332862\pi$
$359$	18.9959	1.00256	0.501282	+	0.865284i	$0.332862\pi$
$360$	1.00000	0.0527046
$361$	−18.8485	−0.992028
$362$	−7.30541	−0.383964
$363$	7.89899	0.414589
$364$	−9.09152	−0.476525
$365$	−7.19253	−0.376474
$366$	0.128356	0.00670925
$367$	7.49525	0.391249	0.195624	−	0.980679i	$-0.437327\pi$
$367$	7.49525	0.391249	0.195624	+	0.980679i	$0.437327\pi$
$368$	2.94356	0.153444
$369$	−5.69459	−0.296449
$370$	0.758770	0.0394466
$371$	−2.53209	−0.131460
$372$	−6.69459	−0.347098
$373$	35.9718	1.86255	0.931276	−	0.364316i	$-0.118697\pi$
$373$	35.9718	1.86255	0.931276	+	0.364316i	$0.118697\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	−1.07873	−0.0556310
$377$	−13.0351	−0.671341
$378$	−3.53209	−0.181671
$379$	5.13247	0.263637	0.131819	−	0.991274i	$-0.457918\pi$
$379$	5.13247	0.263637	0.131819	+	0.991274i	$0.457918\pi$
$380$	−0.389185	−0.0199648
$381$	−15.3696	−0.787408
$382$	−1.54664	−0.0791328
$383$	−25.8384	−1.32028	−0.660141	−	0.751142i	$-0.729504\pi$
$383$	−25.8384	−1.32028	−0.660141	+	0.751142i	$0.729504\pi$
$384$	1.00000	0.0510310
$385$	15.3550	0.782565
$386$	−9.34998	−0.475902
$387$	−1.30541	−0.0663576
$388$	11.1925	0.568215
$389$	20.0446	1.01630	0.508150	−	0.861268i	$-0.330329\pi$
$389$	20.0446	1.01630	0.508150	+	0.861268i	$0.330329\pi$
$390$	2.57398	0.130338
$391$	0	0
$392$	5.47565	0.276562
$393$	3.15570	0.159184
$394$	−1.93851	−0.0976608
$395$	−4.82295	−0.242669
$396$	−4.34730	−0.218460
$397$	29.3678	1.47393	0.736965	−	0.675931i	$-0.236258\pi$
$397$	29.3678	1.47393	0.736965	+	0.675931i	$0.236258\pi$
$398$	−27.3756	−1.37221
$399$	1.37464	0.0688180
$400$	1.00000	0.0500000
$401$	−8.58853	−0.428891	−0.214445	−	0.976736i	$-0.568794\pi$
$401$	−8.58853	−0.428891	−0.214445	+	0.976736i	$0.568794\pi$
$402$	−12.3696	−0.616939
$403$	−17.2317	−0.858374
$404$	−8.90673	−0.443126
$405$	1.00000	0.0496904
$406$	17.8871	0.887723
$407$	−3.29860	−0.163506
$408$	0	0
$409$	35.6928	1.76490	0.882449	−	0.470409i	$-0.155894\pi$
$409$	35.6928	1.76490	0.882449	+	0.470409i	$0.155894\pi$
$410$	−5.69459	−0.281236
$411$	−2.04458	−0.100852
$412$	−19.9222	−0.981497
$413$	−20.4192	−1.00476
$414$	2.94356	0.144668
$415$	15.5175	0.761726
$416$	2.57398	0.126200
$417$	3.12836	0.153196
$418$	1.69190	0.0827537
$419$	−34.4165	−1.68136	−0.840679	−	0.541534i	$-0.817844\pi$
$419$	−34.4165	−1.68136	−0.840679	+	0.541534i	$0.817844\pi$
$420$	−3.53209	−0.172348
$421$	36.7648	1.79180	0.895902	−	0.444251i	$-0.146530\pi$
$421$	36.7648	1.79180	0.895902	+	0.444251i	$0.146530\pi$
$422$	−9.45842	−0.460428
$423$	−1.07873	−0.0524494
$424$	0.716881	0.0348148
$425$	0	0
$426$	−14.2567	−0.690740
$427$	−0.453363	−0.0219398
$428$	7.75877	0.375034
$429$	−11.1898	−0.540251
$430$	−1.30541	−0.0629523
$431$	27.2918	1.31460	0.657300	−	0.753629i	$-0.271699\pi$
$431$	27.2918	1.31460	0.657300	+	0.753629i	$0.271699\pi$
$432$	1.00000	0.0481125
$433$	14.0993	0.677567	0.338784	−	0.940864i	$-0.389985\pi$
$433$	14.0993	0.677567	0.338784	+	0.940864i	$0.389985\pi$
$434$	23.6459	1.13504
$435$	−5.06418	−0.242809
$436$	15.6459	0.749303
$437$	−1.14559	−0.0548011
$438$	−7.19253	−0.343673
$439$	36.0019	1.71828	0.859138	−	0.511744i	$-0.171001\pi$
$439$	36.0019	1.71828	0.859138	+	0.511744i	$0.171001\pi$
$440$	−4.34730	−0.207249
$441$	5.47565	0.260745
$442$	0	0
$443$	−24.8093	−1.17873	−0.589364	−	0.807868i	$-0.700621\pi$
$443$	−24.8093	−1.17873	−0.589364	+	0.807868i	$0.700621\pi$
$444$	0.758770	0.0360097
$445$	−17.6313	−0.835806
$446$	23.1165	1.09460
$447$	2.69459	0.127450
$448$	−3.53209	−0.166876
$449$	10.0892	0.476137	0.238068	−	0.971248i	$-0.423486\pi$
$449$	10.0892	0.476137	0.238068	+	0.971248i	$0.423486\pi$
$450$	1.00000	0.0471405
$451$	24.7561	1.16572
$452$	−6.49794	−0.305637
$453$	−5.14796	−0.241872
$454$	−12.4243	−0.583100
$455$	−9.09152	−0.426217
$456$	−0.389185	−0.0182253
$457$	−27.6614	−1.29394	−0.646972	−	0.762513i	$-0.723965\pi$
$457$	−27.6614	−1.29394	−0.646972	+	0.762513i	$0.723965\pi$
$458$	−11.1088	−0.519078
$459$	0	0
$460$	2.94356	0.137244
$461$	31.9709	1.48903	0.744517	−	0.667604i	$-0.232680\pi$
$461$	31.9709	1.48903	0.744517	+	0.667604i	$0.232680\pi$
$462$	15.3550	0.714381
$463$	10.1138	0.470029	0.235014	−	0.971992i	$-0.424486\pi$
$463$	10.1138	0.470029	0.235014	+	0.971992i	$0.424486\pi$
$464$	−5.06418	−0.235099
$465$	−6.69459	−0.310454
$466$	−18.4979	−0.856901
$467$	0.437882	0.0202627	0.0101314	−	0.999949i	$-0.496775\pi$
$467$	0.437882	0.0202627	0.0101314	+	0.999949i	$0.496775\pi$
$468$	2.57398	0.118982
$469$	43.6905	2.01744
$470$	−1.07873	−0.0497579
$471$	13.4192	0.618325
$472$	5.78106	0.266095
$473$	5.67499	0.260936
$474$	−4.82295	−0.221525
$475$	−0.389185	−0.0178571
$476$	0	0
$477$	0.716881	0.0328237
$478$	−26.4688	−1.21066
$479$	19.4201	0.887329	0.443665	−	0.896193i	$-0.353678\pi$
$479$	19.4201	0.887329	0.443665	+	0.896193i	$0.353678\pi$
$480$	1.00000	0.0456435
$481$	1.95306	0.0890518
$482$	−3.85710	−0.175686
$483$	−10.3969	−0.473077
$484$	7.89899	0.359045
$485$	11.1925	0.508227
$486$	1.00000	0.0453609
$487$	−31.0856	−1.40863	−0.704313	−	0.709890i	$-0.748745\pi$
$487$	−31.0856	−1.40863	−0.704313	+	0.709890i	$0.748745\pi$
$488$	0.128356	0.00581038
$489$	20.9222	0.946135
$490$	5.47565	0.247365
$491$	34.8084	1.57088	0.785441	−	0.618937i	$-0.212436\pi$
$491$	34.8084	1.57088	0.785441	+	0.618937i	$0.212436\pi$
$492$	−5.69459	−0.256732
$493$	0	0
$494$	−1.00175	−0.0450711
$495$	−4.34730	−0.195396
$496$	−6.69459	−0.300596
$497$	50.3560	2.25877
$498$	15.5175	0.695358
$499$	−16.3550	−0.732152	−0.366076	−	0.930585i	$-0.619299\pi$
$499$	−16.3550	−0.732152	−0.366076	+	0.930585i	$0.619299\pi$
$500$	1.00000	0.0447214
$501$	12.6432	0.564857
$502$	−14.4757	−0.646080
$503$	−31.4570	−1.40260	−0.701299	−	0.712867i	$-0.747396\pi$
$503$	−31.4570	−1.40260	−0.701299	+	0.712867i	$0.747396\pi$
$504$	−3.53209	−0.157332
$505$	−8.90673	−0.396344
$506$	−12.7965	−0.568876
$507$	−6.37464	−0.283108
$508$	−15.3696	−0.681915
$509$	−34.4789	−1.52825	−0.764126	−	0.645067i	$-0.776830\pi$
$509$	−34.4789	−1.52825	−0.764126	+	0.645067i	$0.776830\pi$
$510$	0	0
$511$	25.4047	1.12384
$512$	1.00000	0.0441942
$513$	−0.389185	−0.0171830
$514$	6.72369	0.296569
$515$	−19.9222	−0.877877
$516$	−1.30541	−0.0574674
$517$	4.68954	0.206246
$518$	−2.68004	−0.117754
$519$	−18.1753	−0.797807
$520$	2.57398	0.112876
$521$	−13.9905	−0.612935	−0.306468	−	0.951881i	$-0.599147\pi$
$521$	−13.9905	−0.612935	−0.306468	+	0.951881i	$0.599147\pi$
$522$	−5.06418	−0.221653
$523$	21.6459	0.946509	0.473254	−	0.880926i	$-0.343079\pi$
$523$	21.6459	0.946509	0.473254	+	0.880926i	$0.343079\pi$
$524$	3.15570	0.137857
$525$	−3.53209	−0.154153
$526$	−26.7915	−1.16816
$527$	0	0
$528$	−4.34730	−0.189192
$529$	−14.3354	−0.623280
$530$	0.716881	0.0311393
$531$	5.78106	0.250877
$532$	1.37464	0.0595981
$533$	−14.6578	−0.634898
$534$	−17.6313	−0.762983
$535$	7.75877	0.335441
$536$	−12.3696	−0.534285
$537$	25.2841	1.09109
$538$	13.2472	0.571128
$539$	−23.8043	−1.02532
$540$	1.00000	0.0430331
$541$	−5.39456	−0.231930	−0.115965	−	0.993253i	$-0.536996\pi$
$541$	−5.39456	−0.231930	−0.115965	+	0.993253i	$0.536996\pi$
$542$	−6.08378	−0.261321
$543$	−7.30541	−0.313505
$544$	0	0
$545$	15.6459	0.670197
$546$	−9.09152	−0.389081
$547$	−22.2121	−0.949722	−0.474861	−	0.880061i	$-0.657502\pi$
$547$	−22.2121	−0.949722	−0.474861	+	0.880061i	$0.657502\pi$
$548$	−2.04458	−0.0873400
$549$	0.128356	0.00547808
$550$	−4.34730	−0.185369
$551$	1.97090	0.0839633
$552$	2.94356	0.125286
$553$	17.0351	0.724405
$554$	3.29767	0.140104
$555$	0.758770	0.0322080
$556$	3.12836	0.132672
$557$	−21.6260	−0.916322	−0.458161	−	0.888869i	$-0.651492\pi$
$557$	−21.6260	−0.916322	−0.458161	+	0.888869i	$0.651492\pi$
$558$	−6.69459	−0.283405
$559$	−3.36009	−0.142117
$560$	−3.53209	−0.149258
$561$	0	0
$562$	8.80066	0.371233
$563$	4.45336	0.187687	0.0938434	−	0.995587i	$-0.470085\pi$
$563$	4.45336	0.187687	0.0938434	+	0.995587i	$0.470085\pi$
$564$	−1.07873	−0.0454225
$565$	−6.49794	−0.273370
$566$	−20.2412	−0.850802
$567$	−3.53209	−0.148334
$568$	−14.2567	−0.598198
$569$	10.8580	0.455192	0.227596	−	0.973756i	$-0.426913\pi$
$569$	10.8580	0.455192	0.227596	+	0.973756i	$0.426913\pi$
$570$	−0.389185	−0.0163012
$571$	33.3833	1.39705	0.698524	−	0.715587i	$-0.253841\pi$
$571$	33.3833	1.39705	0.698524	+	0.715587i	$0.253841\pi$
$572$	−11.1898	−0.467871
$573$	−1.54664	−0.0646117
$574$	20.1138	0.839534
$575$	2.94356	0.122755
$576$	1.00000	0.0416667
$577$	−23.3993	−0.974125	−0.487063	−	0.873367i	$-0.661932\pi$
$577$	−23.3993	−0.974125	−0.487063	+	0.873367i	$0.661932\pi$
$578$	0	0
$579$	−9.34998	−0.388572
$580$	−5.06418	−0.210279
$581$	−54.8093	−2.27387
$582$	11.1925	0.463945
$583$	−3.11650	−0.129072
$584$	−7.19253	−0.297629
$585$	2.57398	0.106421
$586$	31.9641	1.32042
$587$	21.9763	0.907058	0.453529	−	0.891241i	$-0.350165\pi$
$587$	21.9763	0.907058	0.453529	+	0.891241i	$0.350165\pi$
$588$	5.47565	0.225812
$589$	2.60544	0.107355
$590$	5.78106	0.238002
$591$	−1.93851	−0.0797397
$592$	0.758770	0.0311853
$593$	−5.81345	−0.238730	−0.119365	−	0.992850i	$-0.538086\pi$
$593$	−5.81345	−0.238730	−0.119365	+	0.992850i	$0.538086\pi$
$594$	−4.34730	−0.178372
$595$	0	0
$596$	2.69459	0.110375
$597$	−27.3756	−1.12041
$598$	7.57667	0.309833
$599$	−8.04458	−0.328693	−0.164346	−	0.986403i	$-0.552551\pi$
$599$	−8.04458	−0.328693	−0.164346	+	0.986403i	$0.552551\pi$
$600$	1.00000	0.0408248
$601$	38.7769	1.58174	0.790872	−	0.611981i	$-0.209627\pi$
$601$	38.7769	1.58174	0.790872	+	0.611981i	$0.209627\pi$
$602$	4.61081	0.187923
$603$	−12.3696	−0.503728
$604$	−5.14796	−0.209467
$605$	7.89899	0.321139
$606$	−8.90673	−0.361811
$607$	34.4712	1.39914	0.699572	−	0.714563i	$-0.253374\pi$
$607$	34.4712	1.39914	0.699572	+	0.714563i	$0.253374\pi$
$608$	−0.389185	−0.0157836
$609$	17.8871	0.724823
$610$	0.128356	0.00519696
$611$	−2.77662	−0.112330
$612$	0	0
$613$	−34.0692	−1.37604	−0.688022	−	0.725690i	$-0.741521\pi$
$613$	−34.0692	−1.37604	−0.688022	+	0.725690i	$0.741521\pi$
$614$	−28.9222	−1.16721
$615$	−5.69459	−0.229628
$616$	15.3550	0.618672
$617$	41.4492	1.66868	0.834342	−	0.551247i	$-0.185848\pi$
$617$	41.4492	1.66868	0.834342	+	0.551247i	$0.185848\pi$
$618$	−19.9222	−0.801389
$619$	36.1584	1.45333	0.726664	−	0.686993i	$-0.241070\pi$
$619$	36.1584	1.45333	0.726664	+	0.686993i	$0.241070\pi$
$620$	−6.69459	−0.268861
$621$	2.94356	0.118121
$622$	−22.4534	−0.900298
$623$	62.2755	2.49501
$624$	2.57398	0.103042
$625$	1.00000	0.0400000
$626$	−4.49794	−0.179774
$627$	1.69190	0.0675682
$628$	13.4192	0.535485
$629$	0	0
$630$	−3.53209	−0.140722
$631$	−12.6554	−0.503803	−0.251902	−	0.967753i	$-0.581056\pi$
$631$	−12.6554	−0.503803	−0.251902	+	0.967753i	$0.581056\pi$
$632$	−4.82295	−0.191847
$633$	−9.45842	−0.375938
$634$	6.84255	0.271752
$635$	−15.3696	−0.609923
$636$	0.716881	0.0284262
$637$	14.0942	0.558433
$638$	22.0155	0.871601
$639$	−14.2567	−0.563987
$640$	1.00000	0.0395285
$641$	27.9855	1.10536	0.552679	−	0.833394i	$-0.313605\pi$
$641$	27.9855	1.10536	0.552679	+	0.833394i	$0.313605\pi$
$642$	7.75877	0.306214
$643$	8.31139	0.327769	0.163885	−	0.986480i	$-0.447598\pi$
$643$	8.31139	0.327769	0.163885	+	0.986480i	$0.447598\pi$
$644$	−10.3969	−0.409696
$645$	−1.30541	−0.0514004
$646$	0	0
$647$	28.1607	1.10711	0.553557	−	0.832812i	$-0.313270\pi$
$647$	28.1607	1.10711	0.553557	+	0.832812i	$0.313270\pi$
$648$	1.00000	0.0392837
$649$	−25.1320	−0.986516
$650$	2.57398	0.100960
$651$	23.6459	0.926756
$652$	20.9222	0.819377
$653$	21.9118	0.857474	0.428737	−	0.903429i	$-0.358959\pi$
$653$	21.9118	0.857474	0.428737	+	0.903429i	$0.358959\pi$
$654$	15.6459	0.611803
$655$	3.15570	0.123303
$656$	−5.69459	−0.222336
$657$	−7.19253	−0.280607
$658$	3.81016	0.148535
$659$	−15.1729	−0.591054	−0.295527	−	0.955334i	$-0.595495\pi$
$659$	−15.1729	−0.591054	−0.295527	+	0.955334i	$0.595495\pi$
$660$	−4.34730	−0.169218
$661$	21.3993	0.832336	0.416168	−	0.909288i	$-0.363373\pi$
$661$	21.3993	0.832336	0.416168	+	0.909288i	$0.363373\pi$
$662$	−14.8476	−0.577068
$663$	0	0
$664$	15.5175	0.602197
$665$	1.37464	0.0533062
$666$	0.758770	0.0294018
$667$	−14.9067	−0.577191
$668$	12.6432	0.489180
$669$	23.1165	0.893735
$670$	−12.3696	−0.477879
$671$	−0.558000	−0.0215413
$672$	−3.53209	−0.136253
$673$	10.9067	0.420423	0.210212	−	0.977656i	$-0.432585\pi$
$673$	10.9067	0.420423	0.210212	+	0.977656i	$0.432585\pi$
$674$	3.10876	0.119745
$675$	1.00000	0.0384900
$676$	−6.37464	−0.245178
$677$	35.1334	1.35029	0.675143	−	0.737687i	$-0.264082\pi$
$677$	35.1334	1.35029	0.675143	+	0.737687i	$0.264082\pi$
$678$	−6.49794	−0.249552
$679$	−39.5330	−1.51714
$680$	0	0
$681$	−12.4243	−0.476099
$682$	29.1034	1.11443
$683$	5.88713	0.225265	0.112632	−	0.993637i	$-0.464072\pi$
$683$	5.88713	0.225265	0.112632	+	0.993637i	$0.464072\pi$
$684$	−0.389185	−0.0148809
$685$	−2.04458	−0.0781193
$686$	5.38413	0.205567
$687$	−11.1088	−0.423825
$688$	−1.30541	−0.0497682
$689$	1.84524	0.0702979
$690$	2.94356	0.112060
$691$	−45.3988	−1.72705	−0.863526	−	0.504305i	$-0.831749\pi$
$691$	−45.3988	−1.72705	−0.863526	+	0.504305i	$0.831749\pi$
$692$	−18.1753	−0.690921
$693$	15.3550	0.583290
$694$	−9.55674	−0.362769
$695$	3.12836	0.118665
$696$	−5.06418	−0.191957
$697$	0	0
$698$	14.0000	0.529908
$699$	−18.4979	−0.699656
$700$	−3.53209	−0.133500
$701$	28.2412	1.06666	0.533328	−	0.845908i	$-0.320941\pi$
$701$	28.2412	1.06666	0.533328	+	0.845908i	$0.320941\pi$
$702$	2.57398	0.0971485
$703$	−0.295302	−0.0111375
$704$	−4.34730	−0.163845
$705$	−1.07873	−0.0406272
$706$	27.6905	1.04214
$707$	31.4593	1.18315
$708$	5.78106	0.217266
$709$	37.4492	1.40644	0.703218	−	0.710974i	$-0.251746\pi$
$709$	37.4492	1.40644	0.703218	+	0.710974i	$0.251746\pi$
$710$	−14.2567	−0.535045
$711$	−4.82295	−0.180875
$712$	−17.6313	−0.660763
$713$	−19.7060	−0.737994
$714$	0	0
$715$	−11.1898	−0.418476
$716$	25.2841	0.944909
$717$	−26.4688	−0.988497
$718$	18.9959	0.708920
$719$	−26.6946	−0.995540	−0.497770	−	0.867309i	$-0.665848\pi$
$719$	−26.6946	−0.995540	−0.497770	+	0.867309i	$0.665848\pi$
$720$	1.00000	0.0372678
$721$	70.3670	2.62060
$722$	−18.8485	−0.701470
$723$	−3.85710	−0.143447
$724$	−7.30541	−0.271503
$725$	−5.06418	−0.188079
$726$	7.89899	0.293159
$727$	−4.47472	−0.165958	−0.0829791	−	0.996551i	$-0.526443\pi$
$727$	−4.47472	−0.165958	−0.0829791	+	0.996551i	$0.526443\pi$
$728$	−9.09152	−0.336954
$729$	1.00000	0.0370370
$730$	−7.19253	−0.266208
$731$	0	0
$732$	0.128356	0.00474416
$733$	−42.0506	−1.55317	−0.776587	−	0.630011i	$-0.783051\pi$
$733$	−42.0506	−1.55317	−0.776587	+	0.630011i	$0.783051\pi$
$734$	7.49525	0.276655
$735$	5.47565	0.201972
$736$	2.94356	0.108501
$737$	53.7743	1.98080
$738$	−5.69459	−0.209621
$739$	20.7425	0.763024	0.381512	−	0.924364i	$-0.375403\pi$
$739$	20.7425	0.763024	0.381512	+	0.924364i	$0.375403\pi$
$740$	0.758770	0.0278930
$741$	−1.00175	−0.0368004
$742$	−2.53209	−0.0929559
$743$	8.46204	0.310442	0.155221	−	0.987880i	$-0.450391\pi$
$743$	8.46204	0.310442	0.155221	+	0.987880i	$0.450391\pi$
$744$	−6.69459	−0.245436
$745$	2.69459	0.0987222
$746$	35.9718	1.31702
$747$	15.5175	0.567757
$748$	0	0
$749$	−27.4047	−1.00134
$750$	1.00000	0.0365148
$751$	−22.9959	−0.839132	−0.419566	−	0.907725i	$-0.637818\pi$
$751$	−22.9959	−0.839132	−0.419566	+	0.907725i	$0.637818\pi$
$752$	−1.07873	−0.0393371
$753$	−14.4757	−0.527522
$754$	−13.0351	−0.474710
$755$	−5.14796	−0.187353
$756$	−3.53209	−0.128461
$757$	−26.5594	−0.965319	−0.482659	−	0.875808i	$-0.660329\pi$
$757$	−26.5594	−0.965319	−0.482659	+	0.875808i	$0.660329\pi$
$758$	5.13247	0.186420
$759$	−12.7965	−0.464485
$760$	−0.389185	−0.0141172
$761$	10.6563	0.386292	0.193146	−	0.981170i	$-0.438131\pi$
$761$	10.6563	0.386292	0.193146	+	0.981170i	$0.438131\pi$
$762$	−15.3696	−0.556781
$763$	−55.2627	−2.00064
$764$	−1.54664	−0.0559554
$765$	0	0
$766$	−25.8384	−0.933580
$767$	14.8803	0.537297
$768$	1.00000	0.0360844
$769$	13.9564	0.503279	0.251640	−	0.967821i	$-0.419030\pi$
$769$	13.9564	0.503279	0.251640	+	0.967821i	$0.419030\pi$
$770$	15.3550	0.553357
$771$	6.72369	0.242148
$772$	−9.34998	−0.336513
$773$	−3.71007	−0.133442	−0.0667210	−	0.997772i	$-0.521254\pi$
$773$	−3.71007	−0.133442	−0.0667210	+	0.997772i	$0.521254\pi$
$774$	−1.30541	−0.0469219
$775$	−6.69459	−0.240477
$776$	11.1925	0.401789
$777$	−2.68004	−0.0961461
$778$	20.0446	0.718633
$779$	2.21625	0.0794055
$780$	2.57398	0.0921632
$781$	61.9781	2.21775
$782$	0	0
$783$	−5.06418	−0.180979
$784$	5.47565	0.195559
$785$	13.4192	0.478952
$786$	3.15570	0.112560
$787$	−46.9614	−1.67399	−0.836997	−	0.547208i	$-0.815691\pi$
$787$	−46.9614	−1.67399	−0.836997	+	0.547208i	$0.815691\pi$
$788$	−1.93851	−0.0690566
$789$	−26.7915	−0.953802
$790$	−4.82295	−0.171593
$791$	22.9513	0.816054
$792$	−4.34730	−0.154474
$793$	0.330384	0.0117323
$794$	29.3678	1.04223
$795$	0.716881	0.0254252
$796$	−27.3756	−0.970301
$797$	−9.26176	−0.328068	−0.164034	−	0.986455i	$-0.552451\pi$
$797$	−9.26176	−0.328068	−0.164034	+	0.986455i	$0.552451\pi$
$798$	1.37464	0.0486616
$799$	0	0
$800$	1.00000	0.0353553
$801$	−17.6313	−0.622973
$802$	−8.58853	−0.303271
$803$	31.2681	1.10343
$804$	−12.3696	−0.436242
$805$	−10.3969	−0.366443
$806$	−17.2317	−0.606962
$807$	13.2472	0.466324
$808$	−8.90673	−0.313338
$809$	−15.0256	−0.528271	−0.264136	−	0.964486i	$-0.585087\pi$
$809$	−15.0256	−0.528271	−0.264136	+	0.964486i	$0.585087\pi$
$810$	1.00000	0.0351364
$811$	3.04425	0.106898	0.0534491	−	0.998571i	$-0.482979\pi$
$811$	3.04425	0.106898	0.0534491	+	0.998571i	$0.482979\pi$
$812$	17.8871	0.627715
$813$	−6.08378	−0.213367
$814$	−3.29860	−0.115616
$815$	20.9222	0.732873
$816$	0	0
$817$	0.508045	0.0177743
$818$	35.6928	1.24797
$819$	−9.09152	−0.317683
$820$	−5.69459	−0.198864
$821$	−26.2431	−0.915890	−0.457945	−	0.888980i	$-0.651414\pi$
$821$	−26.2431	−0.915890	−0.457945	+	0.888980i	$0.651414\pi$
$822$	−2.04458	−0.0713128
$823$	−48.4552	−1.68904	−0.844522	−	0.535522i	$-0.820115\pi$
$823$	−48.4552	−1.68904	−0.844522	+	0.535522i	$0.820115\pi$
$824$	−19.9222	−0.694023
$825$	−4.34730	−0.151353
$826$	−20.4192	−0.710475
$827$	23.1634	0.805472	0.402736	−	0.915316i	$-0.368059\pi$
$827$	23.1634	0.805472	0.402736	+	0.915316i	$0.368059\pi$
$828$	2.94356	0.102296
$829$	−30.5817	−1.06215	−0.531073	−	0.847326i	$-0.678211\pi$
$829$	−30.5817	−1.06215	−0.531073	+	0.847326i	$0.678211\pi$
$830$	15.5175	0.538622
$831$	3.29767	0.114395
$832$	2.57398	0.0892366
$833$	0	0
$834$	3.12836	0.108326
$835$	12.6432	0.437536
$836$	1.69190	0.0585157
$837$	−6.69459	−0.231399
$838$	−34.4165	−1.18890
$839$	−14.9203	−0.515107	−0.257554	−	0.966264i	$-0.582916\pi$
$839$	−14.9203	−0.515107	−0.257554	+	0.966264i	$0.582916\pi$
$840$	−3.53209	−0.121869
$841$	−3.35410	−0.115659
$842$	36.7648	1.26700
$843$	8.80066	0.303111
$844$	−9.45842	−0.325572
$845$	−6.37464	−0.219294
$846$	−1.07873	−0.0370874
$847$	−27.8999	−0.958653
$848$	0.716881	0.0246178
$849$	−20.2412	−0.694677
$850$	0	0
$851$	2.23349	0.0765630
$852$	−14.2567	−0.488427
$853$	17.0473	0.583687	0.291844	−	0.956466i	$-0.405731\pi$
$853$	17.0473	0.583687	0.291844	+	0.956466i	$0.405731\pi$
$854$	−0.453363	−0.0155138
$855$	−0.389185	−0.0133099
$856$	7.75877	0.265189
$857$	38.9804	1.33155	0.665773	−	0.746155i	$-0.268102\pi$
$857$	38.9804	1.33155	0.665773	+	0.746155i	$0.268102\pi$
$858$	−11.1898	−0.382015
$859$	−43.4243	−1.48162	−0.740808	−	0.671716i	$-0.765557\pi$
$859$	−43.4243	−1.48162	−0.740808	+	0.671716i	$0.765557\pi$
$860$	−1.30541	−0.0445140
$861$	20.1138	0.685477
$862$	27.2918	0.929562
$863$	2.22432	0.0757166	0.0378583	−	0.999283i	$-0.487946\pi$
$863$	2.22432	0.0757166	0.0378583	+	0.999283i	$0.487946\pi$
$864$	1.00000	0.0340207
$865$	−18.1753	−0.617979
$866$	14.0993	0.479112
$867$	0	0
$868$	23.6459	0.802594
$869$	20.9668	0.711249
$870$	−5.06418	−0.171692
$871$	−31.8390	−1.07882
$872$	15.6459	0.529837
$873$	11.1925	0.378810
$874$	−1.14559	−0.0387502
$875$	−3.53209	−0.119406
$876$	−7.19253	−0.243013
$877$	−16.3942	−0.553594	−0.276797	−	0.960928i	$-0.589273\pi$
$877$	−16.3942	−0.553594	−0.276797	+	0.960928i	$0.589273\pi$
$878$	36.0019	1.21500
$879$	31.9641	1.07812
$880$	−4.34730	−0.146547
$881$	2.67137	0.0900008	0.0450004	−	0.998987i	$-0.485671\pi$
$881$	2.67137	0.0900008	0.0450004	+	0.998987i	$0.485671\pi$
$882$	5.47565	0.184375
$883$	18.1147	0.609610	0.304805	−	0.952415i	$-0.401409\pi$
$883$	18.1147	0.609610	0.304805	+	0.952415i	$0.401409\pi$
$884$	0	0
$885$	5.78106	0.194328
$886$	−24.8093	−0.833486
$887$	−38.8735	−1.30524	−0.652622	−	0.757683i	$-0.726331\pi$
$887$	−38.8735	−1.30524	−0.652622	+	0.757683i	$0.726331\pi$
$888$	0.758770	0.0254627
$889$	54.2867	1.82072
$890$	−17.6313	−0.591004
$891$	−4.34730	−0.145640
$892$	23.1165	0.773998
$893$	0.419824	0.0140489
$894$	2.69459	0.0901207
$895$	25.2841	0.845153
$896$	−3.53209	−0.117999
$897$	7.57667	0.252978
$898$	10.0892	0.336679
$899$	33.9026	1.13072
$900$	1.00000	0.0333333
$901$	0	0
$902$	24.7561	0.824287
$903$	4.61081	0.153438
$904$	−6.49794	−0.216118
$905$	−7.30541	−0.242840
$906$	−5.14796	−0.171029
$907$	20.3250	0.674881	0.337440	−	0.941347i	$-0.390439\pi$
$907$	20.3250	0.674881	0.337440	+	0.941347i	$0.390439\pi$
$908$	−12.4243	−0.412314
$909$	−8.90673	−0.295417
$910$	−9.09152	−0.301381
$911$	11.9216	0.394980	0.197490	−	0.980305i	$-0.436721\pi$
$911$	11.9216	0.394980	0.197490	+	0.980305i	$0.436721\pi$
$912$	−0.389185	−0.0128872
$913$	−67.4593	−2.23258
$914$	−27.6614	−0.914957
$915$	0.128356	0.00424330
$916$	−11.1088	−0.367044
$917$	−11.1462	−0.368080
$918$	0	0
$919$	−20.4189	−0.673557	−0.336779	−	0.941584i	$-0.609337\pi$
$919$	−20.4189	−0.673557	−0.336779	+	0.941584i	$0.609337\pi$
$920$	2.94356	0.0970464
$921$	−28.9222	−0.953019
$922$	31.9709	1.05291
$923$	−36.6965	−1.20788
$924$	15.3550	0.505144
$925$	0.758770	0.0249482
$926$	10.1138	0.332360
$927$	−19.9222	−0.654331
$928$	−5.06418	−0.166240
$929$	53.2026	1.74552	0.872761	−	0.488148i	$-0.162327\pi$
$929$	53.2026	1.74552	0.872761	+	0.488148i	$0.162327\pi$
$930$	−6.69459	−0.219524
$931$	−2.13104	−0.0698421
$932$	−18.4979	−0.605920
$933$	−22.4534	−0.735090
$934$	0.437882	0.0143279
$935$	0	0
$936$	2.57398	0.0841331
$937$	0.552623	0.0180534	0.00902670	−	0.999959i	$-0.497127\pi$
$937$	0.552623	0.0180534	0.00902670	+	0.999959i	$0.497127\pi$
$938$	43.6905	1.42654
$939$	−4.49794	−0.146785
$940$	−1.07873	−0.0351842
$941$	40.5871	1.32310	0.661551	−	0.749900i	$-0.269899\pi$
$941$	40.5871	1.32310	0.661551	+	0.749900i	$0.269899\pi$
$942$	13.4192	0.437222
$943$	−16.7624	−0.545859
$944$	5.78106	0.188157
$945$	−3.53209	−0.114899
$946$	5.67499	0.184510
$947$	24.9614	0.811137	0.405568	−	0.914065i	$-0.367074\pi$
$947$	24.9614	0.811137	0.405568	+	0.914065i	$0.367074\pi$
$948$	−4.82295	−0.156642
$949$	−18.5134	−0.600971
$950$	−0.389185	−0.0126268
$951$	6.84255	0.221885
$952$	0	0
$953$	−12.5763	−0.407388	−0.203694	−	0.979035i	$-0.565295\pi$
$953$	−12.5763	−0.407388	−0.203694	+	0.979035i	$0.565295\pi$
$954$	0.716881	0.0232099
$955$	−1.54664	−0.0500480
$956$	−26.4688	−0.856064
$957$	22.0155	0.711659
$958$	19.4201	0.627437
$959$	7.22163	0.233199
$960$	1.00000	0.0322749
$961$	13.8176	0.445728
$962$	1.95306	0.0629691
$963$	7.75877	0.250023
$964$	−3.85710	−0.124229
$965$	−9.34998	−0.300987
$966$	−10.3969	−0.334516
$967$	4.46286	0.143516	0.0717579	−	0.997422i	$-0.477139\pi$
$967$	4.46286	0.143516	0.0717579	+	0.997422i	$0.477139\pi$
$968$	7.89899	0.253883
$969$	0	0
$970$	11.1925	0.359371
$971$	18.9554	0.608308	0.304154	−	0.952623i	$-0.401626\pi$
$971$	18.9554	0.608308	0.304154	+	0.952623i	$0.401626\pi$
$972$	1.00000	0.0320750
$973$	−11.0496	−0.354235
$974$	−31.0856	−0.996048
$975$	2.57398	0.0824333
$976$	0.128356	0.00410856
$977$	−29.4629	−0.942600	−0.471300	−	0.881973i	$-0.656215\pi$
$977$	−29.4629	−0.942600	−0.471300	+	0.881973i	$0.656215\pi$
$978$	20.9222	0.669018
$979$	76.6487	2.44970
$980$	5.47565	0.174913
$981$	15.6459	0.499535
$982$	34.8084	1.11078
$983$	24.5716	0.783713	0.391856	−	0.920026i	$-0.371833\pi$
$983$	24.5716	0.783713	0.391856	+	0.920026i	$0.371833\pi$
$984$	−5.69459	−0.181537
$985$	−1.93851	−0.0617661
$986$	0	0
$987$	3.81016	0.121279
$988$	−1.00175	−0.0318701
$989$	−3.84255	−0.122186
$990$	−4.34730	−0.138166
$991$	−38.2668	−1.21559	−0.607793	−	0.794096i	$-0.707945\pi$
$991$	−38.2668	−1.21559	−0.607793	+	0.794096i	$0.707945\pi$
$992$	−6.69459	−0.212554
$993$	−14.8476	−0.471174
$994$	50.3560	1.59719
$995$	−27.3756	−0.867864
$996$	15.5175	0.491692
$997$	−20.8108	−0.659084	−0.329542	−	0.944141i	$-0.606894\pi$
$997$	−20.8108	−0.659084	−0.329542	+	0.944141i	$0.606894\pi$
$998$	−16.3550	−0.517710
$999$	0.758770	0.0240064

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8670.2.a.bs.1.1	yes	3
17.16	even	2		8670.2.a.bp.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8670.2.a.bp.1.3	✓	3	17.16	even	2
8670.2.a.bs.1.1	yes	3	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -3.53209 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -4.34730 q^{11} +1.00000 q^{12} +2.57398 q^{13} -3.53209 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{18} -0.389185 q^{19} +1.00000 q^{20} -3.53209 q^{21} -4.34730 q^{22} +2.94356 q^{23} +1.00000 q^{24} +1.00000 q^{25} +2.57398 q^{26} +1.00000 q^{27} -3.53209 q^{28} -5.06418 q^{29} +1.00000 q^{30} -6.69459 q^{31} +1.00000 q^{32} -4.34730 q^{33} -3.53209 q^{35} +1.00000 q^{36} +0.758770 q^{37} -0.389185 q^{38} +2.57398 q^{39} +1.00000 q^{40} -5.69459 q^{41} -3.53209 q^{42} -1.30541 q^{43} -4.34730 q^{44} +1.00000 q^{45} +2.94356 q^{46} -1.07873 q^{47} +1.00000 q^{48} +5.47565 q^{49} +1.00000 q^{50} +2.57398 q^{52} +0.716881 q^{53} +1.00000 q^{54} -4.34730 q^{55} -3.53209 q^{56} -0.389185 q^{57} -5.06418 q^{58} +5.78106 q^{59} +1.00000 q^{60} +0.128356 q^{61} -6.69459 q^{62} -3.53209 q^{63} +1.00000 q^{64} +2.57398 q^{65} -4.34730 q^{66} -12.3696 q^{67} +2.94356 q^{69} -3.53209 q^{70} -14.2567 q^{71} +1.00000 q^{72} -7.19253 q^{73} +0.758770 q^{74} +1.00000 q^{75} -0.389185 q^{76} +15.3550 q^{77} +2.57398 q^{78} -4.82295 q^{79} +1.00000 q^{80} +1.00000 q^{81} -5.69459 q^{82} +15.5175 q^{83} -3.53209 q^{84} -1.30541 q^{86} -5.06418 q^{87} -4.34730 q^{88} -17.6313 q^{89} +1.00000 q^{90} -9.09152 q^{91} +2.94356 q^{92} -6.69459 q^{93} -1.07873 q^{94} -0.389185 q^{95} +1.00000 q^{96} +11.1925 q^{97} +5.47565 q^{98} -4.34730 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} - 6 q^{7} + 3 q^{8} + 3 q^{9} + 3 q^{10} - 12 q^{11} + 3 q^{12} - 6 q^{14} + 3 q^{15} + 3 q^{16} + 3 q^{18} + 3 q^{19} + 3 q^{20} - 6 q^{21} - 12 q^{22}+ \cdots - 12 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 - 6 * q^7 + 3 * q^8 + 3 * q^9 + 3 * q^10 - 12 * q^11 + 3 * q^12 - 6 * q^14 + 3 * q^15 + 3 * q^16 + 3 * q^18 + 3 * q^19 + 3 * q^20 - 6 * q^21 - 12 * q^22 - 6 * q^23 + 3 * q^24 + 3 * q^25 + 3 * q^27 - 6 * q^28 - 6 * q^29 + 3 * q^30 - 18 * q^31 + 3 * q^32 - 12 * q^33 - 6 * q^35 + 3 * q^36 - 9 * q^37 + 3 * q^38 + 3 * q^40 - 15 * q^41 - 6 * q^42 - 6 * q^43 - 12 * q^44 + 3 * q^45 - 6 * q^46 - 12 * q^47 + 3 * q^48 - 3 * q^49 + 3 * q^50 - 6 * q^53 + 3 * q^54 - 12 * q^55 - 6 * q^56 + 3 * q^57 - 6 * q^58 + 3 * q^60 - 18 * q^61 - 18 * q^62 - 6 * q^63 + 3 * q^64 - 12 * q^66 - 30 * q^67 - 6 * q^69 - 6 * q^70 - 6 * q^71 + 3 * q^72 + 6 * q^73 - 9 * q^74 + 3 * q^75 + 3 * q^76 + 21 * q^77 + 6 * q^79 + 3 * q^80 + 3 * q^81 - 15 * q^82 + 24 * q^83 - 6 * q^84 - 6 * q^86 - 6 * q^87 - 12 * q^88 + 6 * q^89 + 3 * q^90 + 3 * q^91 - 6 * q^92 - 18 * q^93 - 12 * q^94 + 3 * q^95 + 3 * q^96 + 6 * q^97 - 3 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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