LMFDB - Embedded newform 6069.2.a.be.1.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [6069,2,Mod(1,6069)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6069, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("6069.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 6069 = 3 \cdot 7 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6069.a (trivial)

Newform invariants

comment:select newform

sage:traces = [10,4,10,12,-6,4,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$48.4612089867$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 8x^{8} + 44x^{7} + 5x^{6} - 144x^{5} + 48x^{4} + 160x^{3} - 44x^{2} - 64x - 2 $ x^10 - 4x^9 - 8x^8 + 44x^7 + 5x^6 - 144x^5 + 48x^4 + 160x^3 - 44x^2 - 64*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 357)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$1.71520$ of defining polynomial
Character	$\chi$	$=$	6069.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.71520 q^{2} +1.00000 q^{3} +0.941909 q^{4} +3.54799 q^{5} +1.71520 q^{6} -1.00000 q^{7} -1.81484 q^{8} +1.00000 q^{9} +6.08552 q^{10} -2.56590 q^{11} +0.941909 q^{12} -3.70620 q^{13} -1.71520 q^{14} +3.54799 q^{15} -4.99663 q^{16} +1.71520 q^{18} +6.90985 q^{19} +3.34189 q^{20} -1.00000 q^{21} -4.40103 q^{22} +7.63588 q^{23} -1.81484 q^{24} +7.58826 q^{25} -6.35687 q^{26} +1.00000 q^{27} -0.941909 q^{28} +9.71633 q^{29} +6.08552 q^{30} +1.15815 q^{31} -4.94054 q^{32} -2.56590 q^{33} -3.54799 q^{35} +0.941909 q^{36} +9.09331 q^{37} +11.8518 q^{38} -3.70620 q^{39} -6.43903 q^{40} -8.53056 q^{41} -1.71520 q^{42} -1.71992 q^{43} -2.41685 q^{44} +3.54799 q^{45} +13.0971 q^{46} +0.699863 q^{47} -4.99663 q^{48} +1.00000 q^{49} +13.0154 q^{50} -3.49090 q^{52} +3.38235 q^{53} +1.71520 q^{54} -9.10380 q^{55} +1.81484 q^{56} +6.90985 q^{57} +16.6654 q^{58} +10.9220 q^{59} +3.34189 q^{60} +5.12696 q^{61} +1.98646 q^{62} -1.00000 q^{63} +1.51925 q^{64} -13.1496 q^{65} -4.40103 q^{66} -2.86834 q^{67} +7.63588 q^{69} -6.08552 q^{70} -12.9174 q^{71} -1.81484 q^{72} +1.42420 q^{73} +15.5968 q^{74} +7.58826 q^{75} +6.50846 q^{76} +2.56590 q^{77} -6.35687 q^{78} +11.0332 q^{79} -17.7280 q^{80} +1.00000 q^{81} -14.6316 q^{82} +8.11587 q^{83} -0.941909 q^{84} -2.95001 q^{86} +9.71633 q^{87} +4.65669 q^{88} +11.1085 q^{89} +6.08552 q^{90} +3.70620 q^{91} +7.19230 q^{92} +1.15815 q^{93} +1.20040 q^{94} +24.5161 q^{95} -4.94054 q^{96} +1.77067 q^{97} +1.71520 q^{98} -2.56590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + 10 q^{3} + 12 q^{4} - 6 q^{5} + 4 q^{6} - 10 q^{7} + 12 q^{8} + 10 q^{9} - 2 q^{11} + 12 q^{12} + 6 q^{13} - 4 q^{14} - 6 q^{15} + 20 q^{16} + 4 q^{18} + 6 q^{19} - 16 q^{20} - 10 q^{21}+ \cdots - 2 q^{99}+O(q^{100}) $ 10 * q + 4 * q^2 + 10 * q^3 + 12 * q^4 - 6 * q^5 + 4 * q^6 - 10 * q^7 + 12 * q^8 + 10 * q^9 - 2 * q^11 + 12 * q^12 + 6 * q^13 - 4 * q^14 - 6 * q^15 + 20 * q^16 + 4 * q^18 + 6 * q^19 - 16 * q^20 - 10 * q^21 + 24 * q^22 + 18 * q^23 + 12 * q^24 + 4 * q^25 + 12 * q^26 + 10 * q^27 - 12 * q^28 - 12 * q^29 - 8 * q^31 + 28 * q^32 - 2 * q^33 + 6 * q^35 + 12 * q^36 + 24 * q^37 + 32 * q^38 + 6 * q^39 - 36 * q^40 - 2 * q^41 - 4 * q^42 + 6 * q^43 + 28 * q^44 - 6 * q^45 - 28 * q^46 + 16 * q^47 + 20 * q^48 + 10 * q^49 + 52 * q^50 + 24 * q^52 - 12 * q^53 + 4 * q^54 + 18 * q^55 - 12 * q^56 + 6 * q^57 + 20 * q^58 + 20 * q^59 - 16 * q^60 - 4 * q^61 - 24 * q^62 - 10 * q^63 + 56 * q^64 - 38 * q^65 + 24 * q^66 + 20 * q^67 + 18 * q^69 - 20 * q^71 + 12 * q^72 + 20 * q^73 + 36 * q^74 + 4 * q^75 - 8 * q^76 + 2 * q^77 + 12 * q^78 + 20 * q^79 - 92 * q^80 + 10 * q^81 + 8 * q^82 + 36 * q^83 - 12 * q^84 - 12 * q^87 + 92 * q^88 + 32 * q^89 - 6 * q^91 + 40 * q^92 - 8 * q^93 + 60 * q^94 - 14 * q^95 + 28 * q^96 + 36 * q^97 + 4 * q^98 - 2 * 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 $

$2$	1.71520	1.21283	0.606415	−	0.795149i	$-0.292607\pi$
$2$	1.71520	1.21283	0.606415	+	0.795149i	$0.292607\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.941909	0.470955
$5$	3.54799	1.58671	0.793356	−	0.608758i	$-0.208332\pi$
$5$	3.54799	1.58671	0.793356	+	0.608758i	$0.208332\pi$
$6$	1.71520	0.700227
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.81484	−0.641642
$9$	1.00000	0.333333
$10$	6.08552	1.92441
$11$	−2.56590	−0.773648	−0.386824	−	0.922153i	$-0.626428\pi$
$11$	−2.56590	−0.773648	−0.386824	+	0.922153i	$0.626428\pi$
$12$	0.941909	0.271906
$13$	−3.70620	−1.02791	−0.513957	−	0.857816i	$-0.671821\pi$
$13$	−3.70620	−1.02791	−0.513957	+	0.857816i	$0.671821\pi$
$14$	−1.71520	−0.458406
$15$	3.54799	0.916088
$16$	−4.99663	−1.24916
$17$	0	0
$17$	0	0
$18$	1.71520	0.404276
$19$	6.90985	1.58523	0.792615	−	0.609723i	$-0.208719\pi$
$19$	6.90985	1.58523	0.792615	+	0.609723i	$0.208719\pi$
$20$	3.34189	0.747269
$21$	−1.00000	−0.218218
$22$	−4.40103	−0.938303
$23$	7.63588	1.59219	0.796095	−	0.605171i	$-0.206895\pi$
$23$	7.63588	1.59219	0.796095	+	0.605171i	$0.206895\pi$
$24$	−1.81484	−0.370452
$25$	7.58826	1.51765
$26$	−6.35687	−1.24668
$27$	1.00000	0.192450
$28$	−0.941909	−0.178004
$29$	9.71633	1.80428	0.902139	−	0.431446i	$-0.141997\pi$
$29$	9.71633	1.80428	0.902139	+	0.431446i	$0.141997\pi$
$30$	6.08552	1.11106
$31$	1.15815	0.208010	0.104005	−	0.994577i	$-0.466834\pi$
$31$	1.15815	0.208010	0.104005	+	0.994577i	$0.466834\pi$
$32$	−4.94054	−0.873372
$33$	−2.56590	−0.446666
$34$	0	0
$35$	−3.54799	−0.599721
$36$	0.941909	0.156985
$37$	9.09331	1.49493	0.747466	−	0.664300i	$-0.231270\pi$
$37$	9.09331	1.49493	0.747466	+	0.664300i	$0.231270\pi$
$38$	11.8518	1.92261
$39$	−3.70620	−0.593466
$40$	−6.43903	−1.01810
$41$	−8.53056	−1.33225	−0.666125	−	0.745841i	$-0.732048\pi$
$41$	−8.53056	−1.33225	−0.666125	+	0.745841i	$0.732048\pi$
$42$	−1.71520	−0.264661
$43$	−1.71992	−0.262286	−0.131143	−	0.991363i	$-0.541865\pi$
$43$	−1.71992	−0.262286	−0.131143	+	0.991363i	$0.541865\pi$
$44$	−2.41685	−0.364353
$45$	3.54799	0.528904
$46$	13.0971	1.93106
$47$	0.699863	0.102086	0.0510428	−	0.998696i	$-0.483746\pi$
$47$	0.699863	0.102086	0.0510428	+	0.998696i	$0.483746\pi$
$48$	−4.99663	−0.721201
$49$	1.00000	0.142857
$50$	13.0154	1.84065
$51$	0	0
$52$	−3.49090	−0.484101
$53$	3.38235	0.464602	0.232301	−	0.972644i	$-0.425375\pi$
$53$	3.38235	0.464602	0.232301	+	0.972644i	$0.425375\pi$
$54$	1.71520	0.233409
$55$	−9.10380	−1.22756
$56$	1.81484	0.242518
$57$	6.90985	0.915233
$58$	16.6654	2.18828
$59$	10.9220	1.42193	0.710965	−	0.703228i	$-0.248259\pi$
$59$	10.9220	1.42193	0.710965	+	0.703228i	$0.248259\pi$
$60$	3.34189	0.431436
$61$	5.12696	0.656440	0.328220	−	0.944601i	$-0.393551\pi$
$61$	5.12696	0.656440	0.328220	+	0.944601i	$0.393551\pi$
$62$	1.98646	0.252281
$63$	−1.00000	−0.125988
$64$	1.51925	0.189906
$65$	−13.1496	−1.63100
$66$	−4.40103	−0.541730
$67$	−2.86834	−0.350423	−0.175212	−	0.984531i	$-0.556061\pi$
$67$	−2.86834	−0.350423	−0.175212	+	0.984531i	$0.556061\pi$
$68$	0	0
$69$	7.63588	0.919252
$70$	−6.08552	−0.727359
$71$	−12.9174	−1.53302	−0.766509	−	0.642233i	$-0.778008\pi$
$71$	−12.9174	−1.53302	−0.766509	+	0.642233i	$0.778008\pi$
$72$	−1.81484	−0.213881
$73$	1.42420	0.166690	0.0833448	−	0.996521i	$-0.473440\pi$
$73$	1.42420	0.166690	0.0833448	+	0.996521i	$0.473440\pi$
$74$	15.5968	1.81310
$75$	7.58826	0.876217
$76$	6.50846	0.746571
$77$	2.56590	0.292412
$78$	−6.35687	−0.719773
$79$	11.0332	1.24133	0.620664	−	0.784077i	$-0.286863\pi$
$79$	11.0332	1.24133	0.620664	+	0.784077i	$0.286863\pi$
$80$	−17.7280	−1.98205
$81$	1.00000	0.111111
$82$	−14.6316	−1.61579
$83$	8.11587	0.890832	0.445416	−	0.895324i	$-0.353056\pi$
$83$	8.11587	0.890832	0.445416	+	0.895324i	$0.353056\pi$
$84$	−0.941909	−0.102771
$85$	0	0
$86$	−2.95001	−0.318108
$87$	9.71633	1.04170
$88$	4.65669	0.496405
$89$	11.1085	1.17750	0.588752	−	0.808314i	$-0.299619\pi$
$89$	11.1085	1.17750	0.588752	+	0.808314i	$0.299619\pi$
$90$	6.08552	0.641470
$91$	3.70620	0.388515
$92$	7.19230	0.749849
$93$	1.15815	0.120095
$94$	1.20040	0.123812
$95$	24.5161	2.51530
$96$	−4.94054	−0.504241
$97$	1.77067	0.179785	0.0898923	−	0.995951i	$-0.471348\pi$
$97$	1.77067	0.179785	0.0898923	+	0.995951i	$0.471348\pi$
$98$	1.71520	0.173261
$99$	−2.56590	−0.257883
$100$	7.14746	0.714746
$101$	9.90253	0.985339	0.492669	−	0.870217i	$-0.336021\pi$
$101$	9.90253	0.985339	0.492669	+	0.870217i	$0.336021\pi$
$102$	0	0
$103$	−5.57897	−0.549712	−0.274856	−	0.961485i	$-0.588630\pi$
$103$	−5.57897	−0.549712	−0.274856	+	0.961485i	$0.588630\pi$
$104$	6.72614	0.659552
$105$	−3.54799	−0.346249
$106$	5.80141	0.563483
$107$	−5.62786	−0.544066	−0.272033	−	0.962288i	$-0.587696\pi$
$107$	−5.62786	−0.544066	−0.272033	+	0.962288i	$0.587696\pi$
$108$	0.941909	0.0906353
$109$	−16.2122	−1.55285	−0.776425	−	0.630209i	$-0.782969\pi$
$109$	−16.2122	−1.55285	−0.776425	+	0.630209i	$0.782969\pi$
$110$	−15.6148	−1.48882
$111$	9.09331	0.863099
$112$	4.99663	0.472137
$113$	−9.68119	−0.910729	−0.455365	−	0.890305i	$-0.650491\pi$
$113$	−9.68119	−0.910729	−0.455365	+	0.890305i	$0.650491\pi$
$114$	11.8518	1.11002
$115$	27.0920	2.52635
$116$	9.15190	0.849733
$117$	−3.70620	−0.342638
$118$	18.7335	1.72456
$119$	0	0
$120$	−6.43903	−0.587800
$121$	−4.41615	−0.401468
$122$	8.79376	0.796150
$123$	−8.53056	−0.769174
$124$	1.09087	0.0979634
$125$	9.18315	0.821366
$126$	−1.71520	−0.152802
$127$	−1.97182	−0.174971	−0.0874855	−	0.996166i	$-0.527883\pi$
$127$	−1.97182	−0.174971	−0.0874855	+	0.996166i	$0.527883\pi$
$128$	12.4869	1.10369
$129$	−1.71992	−0.151431
$130$	−22.5541	−1.97813
$131$	−8.55799	−0.747715	−0.373857	−	0.927486i	$-0.621965\pi$
$131$	−8.55799	−0.747715	−0.373857	+	0.927486i	$0.621965\pi$
$132$	−2.41685	−0.210360
$133$	−6.90985	−0.599160
$134$	−4.91977	−0.425004
$135$	3.54799	0.305363
$136$	0	0
$137$	−18.7573	−1.60254	−0.801270	−	0.598303i	$-0.795842\pi$
$137$	−18.7573	−1.60254	−0.801270	+	0.598303i	$0.795842\pi$
$138$	13.0971	1.11490
$139$	6.45433	0.547450	0.273725	−	0.961808i	$-0.411744\pi$
$139$	6.45433	0.547450	0.273725	+	0.961808i	$0.411744\pi$
$140$	−3.34189	−0.282441
$141$	0.699863	0.0589391
$142$	−22.1560	−1.85929
$143$	9.50973	0.795244
$144$	−4.99663	−0.416385
$145$	34.4735	2.86287
$146$	2.44278	0.202166
$147$	1.00000	0.0824786
$148$	8.56508	0.704045
$149$	15.4004	1.26165	0.630824	−	0.775926i	$-0.282717\pi$
$149$	15.4004	1.26165	0.630824	+	0.775926i	$0.282717\pi$
$150$	13.0154	1.06270
$151$	−10.0010	−0.813872	−0.406936	−	0.913457i	$-0.633403\pi$
$151$	−10.0010	−0.813872	−0.406936	+	0.913457i	$0.633403\pi$
$152$	−12.5403	−1.01715
$153$	0	0
$154$	4.40103	0.354645
$155$	4.10912	0.330052
$156$	−3.49090	−0.279496
$157$	7.69824	0.614387	0.307193	−	0.951647i	$-0.400610\pi$
$157$	7.69824	0.614387	0.307193	+	0.951647i	$0.400610\pi$
$158$	18.9241	1.50552
$159$	3.38235	0.268238
$160$	−17.5290	−1.38579
$161$	−7.63588	−0.601791
$162$	1.71520	0.134759
$163$	5.90357	0.462404	0.231202	−	0.972906i	$-0.425734\pi$
$163$	5.90357	0.462404	0.231202	+	0.972906i	$0.425734\pi$
$164$	−8.03501	−0.627429
$165$	−9.10380	−0.708730
$166$	13.9203	1.08043
$167$	3.22712	0.249722	0.124861	−	0.992174i	$-0.460152\pi$
$167$	3.22712	0.249722	0.124861	+	0.992174i	$0.460152\pi$
$168$	1.81484	0.140018
$169$	0.735888	0.0566068
$170$	0	0
$171$	6.90985	0.528410
$172$	−1.62001	−0.123525
$173$	−22.3933	−1.70253	−0.851265	−	0.524736i	$-0.824164\pi$
$173$	−22.3933	−1.70253	−0.851265	+	0.524736i	$0.824164\pi$
$174$	16.6654	1.26340
$175$	−7.58826	−0.573619
$176$	12.8208	0.966408
$177$	10.9220	0.820951
$178$	19.0534	1.42811
$179$	14.0892	1.05308	0.526538	−	0.850152i	$-0.323490\pi$
$179$	14.0892	1.05308	0.526538	+	0.850152i	$0.323490\pi$
$180$	3.34189	0.249090
$181$	−20.8864	−1.55247	−0.776235	−	0.630443i	$-0.782873\pi$
$181$	−20.8864	−1.55247	−0.776235	+	0.630443i	$0.782873\pi$
$182$	6.35687	0.471202
$183$	5.12696	0.378996
$184$	−13.8579	−1.02162
$185$	32.2630	2.37202
$186$	1.98646	0.145654
$187$	0	0
$188$	0.659207	0.0480776
$189$	−1.00000	−0.0727393
$190$	42.0500	3.05063
$191$	−4.70406	−0.340373	−0.170187	−	0.985412i	$-0.554437\pi$
$191$	−4.70406	−0.340373	−0.170187	+	0.985412i	$0.554437\pi$
$192$	1.51925	0.109642
$193$	−5.10354	−0.367361	−0.183680	−	0.982986i	$-0.558801\pi$
$193$	−5.10354	−0.367361	−0.183680	+	0.982986i	$0.558801\pi$
$194$	3.03706	0.218048
$195$	−13.1496	−0.941660
$196$	0.941909	0.0672792
$197$	−13.4842	−0.960708	−0.480354	−	0.877075i	$-0.659492\pi$
$197$	−13.4842	−0.960708	−0.480354	+	0.877075i	$0.659492\pi$
$198$	−4.40103	−0.312768
$199$	−4.19363	−0.297279	−0.148639	−	0.988891i	$-0.547489\pi$
$199$	−4.19363	−0.297279	−0.148639	+	0.988891i	$0.547489\pi$
$200$	−13.7715	−0.973789
$201$	−2.86834	−0.202317
$202$	16.9848	1.19505
$203$	−9.71633	−0.681953
$204$	0	0
$205$	−30.2664	−2.11389
$206$	−9.56904	−0.666707
$207$	7.63588	0.530730
$208$	18.5185	1.28403
$209$	−17.7300	−1.22641
$210$	−6.08552	−0.419941
$211$	−17.8725	−1.23040	−0.615198	−	0.788372i	$-0.710924\pi$
$211$	−17.8725	−1.23040	−0.615198	+	0.788372i	$0.710924\pi$
$212$	3.18587	0.218807
$213$	−12.9174	−0.885089
$214$	−9.65291	−0.659859
$215$	−6.10228	−0.416172
$216$	−1.81484	−0.123484
$217$	−1.15815	−0.0786205
$218$	−27.8072	−1.88334
$219$	1.42420	0.0962382
$220$	−8.57496	−0.578124
$221$	0	0
$222$	15.5968	1.04679
$223$	1.60272	0.107326	0.0536632	−	0.998559i	$-0.482910\pi$
$223$	1.60272	0.107326	0.0536632	+	0.998559i	$0.482910\pi$
$224$	4.94054	0.330103
$225$	7.58826	0.505884
$226$	−16.6052	−1.10456
$227$	−11.7490	−0.779807	−0.389904	−	0.920856i	$-0.627492\pi$
$227$	−11.7490	−0.779807	−0.389904	+	0.920856i	$0.627492\pi$
$228$	6.50846	0.431033
$229$	−1.47791	−0.0976633	−0.0488317	−	0.998807i	$-0.515550\pi$
$229$	−1.47791	−0.0976633	−0.0488317	+	0.998807i	$0.515550\pi$
$230$	46.4683	3.06403
$231$	2.56590	0.168824
$232$	−17.6336	−1.15770
$233$	−13.7652	−0.901788	−0.450894	−	0.892578i	$-0.648895\pi$
$233$	−13.7652	−0.901788	−0.450894	+	0.892578i	$0.648895\pi$
$234$	−6.35687	−0.415561
$235$	2.48311	0.161980
$236$	10.2876	0.669664
$237$	11.0332	0.716681
$238$	0	0
$239$	13.6486	0.882852	0.441426	−	0.897298i	$-0.354473\pi$
$239$	13.6486	0.882852	0.441426	+	0.897298i	$0.354473\pi$
$240$	−17.7280	−1.14434
$241$	−17.3323	−1.11647	−0.558236	−	0.829682i	$-0.688522\pi$
$241$	−17.3323	−1.11647	−0.558236	+	0.829682i	$0.688522\pi$
$242$	−7.57458	−0.486912
$243$	1.00000	0.0641500
$244$	4.82913	0.309153
$245$	3.54799	0.226673
$246$	−14.6316	−0.932877
$247$	−25.6093	−1.62948
$248$	−2.10186	−0.133468
$249$	8.11587	0.514322
$250$	15.7509	0.996176
$251$	−16.8092	−1.06099	−0.530493	−	0.847690i	$-0.677993\pi$
$251$	−16.8092	−1.06099	−0.530493	+	0.847690i	$0.677993\pi$
$252$	−0.941909	−0.0593347
$253$	−19.5929	−1.23180
$254$	−3.38207	−0.212210
$255$	0	0
$256$	18.3790	1.14869
$257$	−6.87575	−0.428897	−0.214449	−	0.976735i	$-0.568795\pi$
$257$	−6.87575	−0.428897	−0.214449	+	0.976735i	$0.568795\pi$
$258$	−2.95001	−0.183660
$259$	−9.09331	−0.565031
$260$	−12.3857	−0.768128
$261$	9.71633	0.601426
$262$	−14.6787	−0.906850
$263$	0.998666	0.0615804	0.0307902	−	0.999526i	$-0.490198\pi$
$263$	0.998666	0.0615804	0.0307902	+	0.999526i	$0.490198\pi$
$264$	4.65669	0.286600
$265$	12.0006	0.737189
$266$	−11.8518	−0.726679
$267$	11.1085	0.679832
$268$	−2.70172	−0.165034
$269$	2.43642	0.148551	0.0742755	−	0.997238i	$-0.476336\pi$
$269$	2.43642	0.148551	0.0742755	+	0.997238i	$0.476336\pi$
$270$	6.08552	0.370353
$271$	11.8042	0.717056	0.358528	−	0.933519i	$-0.383279\pi$
$271$	11.8042	0.717056	0.358528	+	0.933519i	$0.383279\pi$
$272$	0	0
$273$	3.70620	0.224309
$274$	−32.1724	−1.94361
$275$	−19.4707	−1.17413
$276$	7.19230	0.432926
$277$	−12.8645	−0.772953	−0.386476	−	0.922299i	$-0.626308\pi$
$277$	−12.8645	−0.772953	−0.386476	+	0.922299i	$0.626308\pi$
$278$	11.0705	0.663963
$279$	1.15815	0.0693368
$280$	6.43903	0.384806
$281$	−17.9398	−1.07020	−0.535098	−	0.844790i	$-0.679725\pi$
$281$	−17.9398	−1.07020	−0.535098	+	0.844790i	$0.679725\pi$
$282$	1.20040	0.0714831
$283$	−19.0719	−1.13371	−0.566853	−	0.823819i	$-0.691839\pi$
$283$	−19.0719	−1.13371	−0.566853	+	0.823819i	$0.691839\pi$
$284$	−12.1671	−0.721982
$285$	24.5161	1.45221
$286$	16.3111	0.964495
$287$	8.53056	0.503543
$288$	−4.94054	−0.291124
$289$	0	0
$290$	59.1289	3.47217
$291$	1.77067	0.103799
$292$	1.34146	0.0785032
$293$	−16.9285	−0.988974	−0.494487	−	0.869185i	$-0.664644\pi$
$293$	−16.9285	−0.988974	−0.494487	+	0.869185i	$0.664644\pi$
$294$	1.71520	0.100032
$295$	38.7514	2.25619
$296$	−16.5029	−0.959210
$297$	−2.56590	−0.148889
$298$	26.4147	1.53016
$299$	−28.3001	−1.63663
$300$	7.14746	0.412659
$301$	1.71992	0.0991348
$302$	−17.1537	−0.987087
$303$	9.90253	0.568886
$304$	−34.5260	−1.98020
$305$	18.1904	1.04158
$306$	0	0
$307$	−21.9034	−1.25010	−0.625048	−	0.780587i	$-0.714921\pi$
$307$	−21.9034	−1.25010	−0.625048	+	0.780587i	$0.714921\pi$
$308$	2.41685	0.137713
$309$	−5.57897	−0.317376
$310$	7.04796	0.400297
$311$	27.2225	1.54365	0.771823	−	0.635837i	$-0.219345\pi$
$311$	27.2225	1.54365	0.771823	+	0.635837i	$0.219345\pi$
$312$	6.72614	0.380793
$313$	7.20038	0.406990	0.203495	−	0.979076i	$-0.434770\pi$
$313$	7.20038	0.406990	0.203495	+	0.979076i	$0.434770\pi$
$314$	13.2040	0.745146
$315$	−3.54799	−0.199907
$316$	10.3922	0.584609
$317$	18.5681	1.04289	0.521445	−	0.853285i	$-0.325393\pi$
$317$	18.5681	1.04289	0.521445	+	0.853285i	$0.325393\pi$
$318$	5.80141	0.325327
$319$	−24.9311	−1.39588
$320$	5.39027	0.301326
$321$	−5.62786	−0.314117
$322$	−13.0971	−0.729870
$323$	0	0
$324$	0.941909	0.0523283
$325$	−28.1236	−1.56002
$326$	10.1258	0.560816
$327$	−16.2122	−0.896539
$328$	15.4816	0.854826
$329$	−0.699863	−0.0385847
$330$	−15.6148	−0.859569
$331$	−8.06322	−0.443194	−0.221597	−	0.975138i	$-0.571127\pi$
$331$	−8.06322	−0.443194	−0.221597	+	0.975138i	$0.571127\pi$
$332$	7.64441	0.419542
$333$	9.09331	0.498310
$334$	5.53515	0.302870
$335$	−10.1769	−0.556021
$336$	4.99663	0.272588
$337$	26.5965	1.44881	0.724403	−	0.689377i	$-0.242116\pi$
$337$	26.5965	1.44881	0.724403	+	0.689377i	$0.242116\pi$
$338$	1.26220	0.0686544
$339$	−9.68119	−0.525810
$340$	0	0
$341$	−2.97171	−0.160927
$342$	11.8518	0.640871
$343$	−1.00000	−0.0539949
$344$	3.12138	0.168294
$345$	27.0920	1.45859
$346$	−38.4090	−2.06488
$347$	19.8429	1.06522	0.532611	−	0.846360i	$-0.321211\pi$
$347$	19.8429	1.06522	0.532611	+	0.846360i	$0.321211\pi$
$348$	9.15190	0.490593
$349$	−10.8244	−0.579418	−0.289709	−	0.957115i	$-0.593559\pi$
$349$	−10.8244	−0.579418	−0.289709	+	0.957115i	$0.593559\pi$
$350$	−13.0154	−0.695702
$351$	−3.70620	−0.197822
$352$	12.6769	0.675683
$353$	25.1471	1.33845	0.669224	−	0.743061i	$-0.266627\pi$
$353$	25.1471	1.33845	0.669224	+	0.743061i	$0.266627\pi$
$354$	18.7335	0.995674
$355$	−45.8310	−2.43246
$356$	10.4632	0.554551
$357$	0	0
$358$	24.1658	1.27720
$359$	20.1240	1.06210	0.531051	−	0.847340i	$-0.321797\pi$
$359$	20.1240	1.06210	0.531051	+	0.847340i	$0.321797\pi$
$360$	−6.43903	−0.339367
$361$	28.7461	1.51295
$362$	−35.8243	−1.88288
$363$	−4.41615	−0.231788
$364$	3.49090	0.182973
$365$	5.05304	0.264488
$366$	8.79376	0.459657
$367$	27.4219	1.43141	0.715706	−	0.698402i	$-0.246105\pi$
$367$	27.4219	1.43141	0.715706	+	0.698402i	$0.246105\pi$
$368$	−38.1536	−1.98889
$369$	−8.53056	−0.444083
$370$	55.3375	2.87686
$371$	−3.38235	−0.175603
$372$	1.09087	0.0565592
$373$	9.01770	0.466919	0.233460	−	0.972367i	$-0.424995\pi$
$373$	9.01770	0.466919	0.233460	+	0.972367i	$0.424995\pi$
$374$	0	0
$375$	9.18315	0.474216
$376$	−1.27014	−0.0655023
$377$	−36.0106	−1.85464
$378$	−1.71520	−0.0882203
$379$	−4.01505	−0.206239	−0.103120	−	0.994669i	$-0.532882\pi$
$379$	−4.01505	−0.206239	−0.103120	+	0.994669i	$0.532882\pi$
$380$	23.0920	1.18459
$381$	−1.97182	−0.101020
$382$	−8.06839	−0.412815
$383$	7.39041	0.377632	0.188816	−	0.982012i	$-0.439535\pi$
$383$	7.39041	0.377632	0.188816	+	0.982012i	$0.439535\pi$
$384$	12.4869	0.637219
$385$	9.10380	0.463973
$386$	−8.75358	−0.445546
$387$	−1.71992	−0.0874287
$388$	1.66781	0.0846704
$389$	16.1413	0.818397	0.409199	−	0.912445i	$-0.365808\pi$
$389$	16.1413	0.818397	0.409199	+	0.912445i	$0.365808\pi$
$390$	−22.5541	−1.14207
$391$	0	0
$392$	−1.81484	−0.0916631
$393$	−8.55799	−0.431693
$394$	−23.1281	−1.16517
$395$	39.1456	1.96963
$396$	−2.41685	−0.121451
$397$	−6.71255	−0.336893	−0.168447	−	0.985711i	$-0.553875\pi$
$397$	−6.71255	−0.336893	−0.168447	+	0.985711i	$0.553875\pi$
$398$	−7.19291	−0.360548
$399$	−6.90985	−0.345925
$400$	−37.9157	−1.89579
$401$	1.98200	0.0989763	0.0494882	−	0.998775i	$-0.484241\pi$
$401$	1.98200	0.0989763	0.0494882	+	0.998775i	$0.484241\pi$
$402$	−4.91977	−0.245376
$403$	−4.29234	−0.213817
$404$	9.32729	0.464050
$405$	3.54799	0.176301
$406$	−16.6654	−0.827092
$407$	−23.3325	−1.15655
$408$	0	0
$409$	−15.3390	−0.758464	−0.379232	−	0.925302i	$-0.623812\pi$
$409$	−15.3390	−0.758464	−0.379232	+	0.925302i	$0.623812\pi$
$410$	−51.9129	−2.56379
$411$	−18.7573	−0.925227
$412$	−5.25488	−0.258889
$413$	−10.9220	−0.537439
$414$	13.0971	0.643685
$415$	28.7951	1.41349
$416$	18.3106	0.897751
$417$	6.45433	0.316070
$418$	−30.4105	−1.48743
$419$	0.267102	0.0130488	0.00652440	−	0.999979i	$-0.497923\pi$
$419$	0.267102	0.0130488	0.00652440	+	0.999979i	$0.497923\pi$
$420$	−3.34189	−0.163067
$421$	−16.4415	−0.801309	−0.400655	−	0.916229i	$-0.631217\pi$
$421$	−16.4415	−0.801309	−0.400655	+	0.916229i	$0.631217\pi$
$422$	−30.6550	−1.49226
$423$	0.699863	0.0340285
$424$	−6.13842	−0.298108
$425$	0	0
$426$	−22.1560	−1.07346
$427$	−5.12696	−0.248111
$428$	−5.30094	−0.256231
$429$	9.50973	0.459134
$430$	−10.4666	−0.504746
$431$	2.16358	0.104216	0.0521079	−	0.998641i	$-0.483406\pi$
$431$	2.16358	0.104216	0.0521079	+	0.998641i	$0.483406\pi$
$432$	−4.99663	−0.240400
$433$	−5.65283	−0.271658	−0.135829	−	0.990732i	$-0.543370\pi$
$433$	−5.65283	−0.271658	−0.135829	+	0.990732i	$0.543370\pi$
$434$	−1.98646	−0.0953532
$435$	34.4735	1.65288
$436$	−15.2705	−0.731322
$437$	52.7628	2.52399
$438$	2.44278	0.116721
$439$	−1.91768	−0.0915257	−0.0457628	−	0.998952i	$-0.514572\pi$
$439$	−1.91768	−0.0915257	−0.0457628	+	0.998952i	$0.514572\pi$
$440$	16.5219	0.787652
$441$	1.00000	0.0476190
$442$	0	0
$443$	28.4710	1.35270	0.676348	−	0.736582i	$-0.263562\pi$
$443$	28.4710	1.35270	0.676348	+	0.736582i	$0.263562\pi$
$444$	8.56508	0.406480
$445$	39.4131	1.86836
$446$	2.74899	0.130169
$447$	15.4004	0.728413
$448$	−1.51925	−0.0717776
$449$	13.0555	0.616128	0.308064	−	0.951366i	$-0.400319\pi$
$449$	13.0555	0.616128	0.308064	+	0.951366i	$0.400319\pi$
$450$	13.0154	0.613551
$451$	21.8886	1.03069
$452$	−9.11880	−0.428912
$453$	−10.0010	−0.469889
$454$	−20.1518	−0.945773
$455$	13.1496	0.616461
$456$	−12.5403	−0.587251
$457$	−8.80710	−0.411979	−0.205989	−	0.978554i	$-0.566041\pi$
$457$	−8.80710	−0.411979	−0.205989	+	0.978554i	$0.566041\pi$
$458$	−2.53492	−0.118449
$459$	0	0
$460$	25.5183	1.18979
$461$	8.14899	0.379536	0.189768	−	0.981829i	$-0.439226\pi$
$461$	8.14899	0.379536	0.189768	+	0.981829i	$0.439226\pi$
$462$	4.40103	0.204755
$463$	−0.328011	−0.0152440	−0.00762199	−	0.999971i	$-0.502426\pi$
$463$	−0.328011	−0.0152440	−0.00762199	+	0.999971i	$0.502426\pi$
$464$	−48.5489	−2.25382
$465$	4.10912	0.190556
$466$	−23.6101	−1.09371
$467$	−23.0220	−1.06533	−0.532666	−	0.846326i	$-0.678810\pi$
$467$	−23.0220	−1.06533	−0.532666	+	0.846326i	$0.678810\pi$
$468$	−3.49090	−0.161367
$469$	2.86834	0.132448
$470$	4.25903	0.196454
$471$	7.69824	0.354716
$472$	−19.8217	−0.912369
$473$	4.41316	0.202917
$474$	18.9241	0.869211
$475$	52.4338	2.40583
$476$	0	0
$477$	3.38235	0.154867
$478$	23.4100	1.07075
$479$	27.6393	1.26287	0.631437	−	0.775427i	$-0.282466\pi$
$479$	27.6393	1.26287	0.631437	+	0.775427i	$0.282466\pi$
$480$	−17.5290	−0.800085
$481$	−33.7016	−1.53666
$482$	−29.7284	−1.35409
$483$	−7.63588	−0.347444
$484$	−4.15961	−0.189073
$485$	6.28234	0.285266
$486$	1.71520	0.0778030
$487$	2.19186	0.0993229	0.0496614	−	0.998766i	$-0.484186\pi$
$487$	2.19186	0.0993229	0.0496614	+	0.998766i	$0.484186\pi$
$488$	−9.30459	−0.421199
$489$	5.90357	0.266969
$490$	6.08552	0.274916
$491$	−8.04025	−0.362851	−0.181426	−	0.983405i	$-0.558071\pi$
$491$	−8.04025	−0.362851	−0.181426	+	0.983405i	$0.558071\pi$
$492$	−8.03501	−0.362246
$493$	0	0
$494$	−43.9250	−1.97628
$495$	−9.10380	−0.409186
$496$	−5.78685	−0.259837
$497$	12.9174	0.579427
$498$	13.9203	0.623785
$499$	−11.4393	−0.512094	−0.256047	−	0.966664i	$-0.582420\pi$
$499$	−11.4393	−0.512094	−0.256047	+	0.966664i	$0.582420\pi$
$500$	8.64969	0.386826
$501$	3.22712	0.144177
$502$	−28.8311	−1.28679
$503$	7.94657	0.354320	0.177160	−	0.984182i	$-0.443309\pi$
$503$	7.94657	0.354320	0.177160	+	0.984182i	$0.443309\pi$
$504$	1.81484	0.0808392
$505$	35.1341	1.56345
$506$	−33.6057	−1.49396
$507$	0.735888	0.0326819
$508$	−1.85728	−0.0824034
$509$	23.7079	1.05083	0.525417	−	0.850845i	$-0.323909\pi$
$509$	23.7079	1.05083	0.525417	+	0.850845i	$0.323909\pi$
$510$	0	0
$511$	−1.42420	−0.0630027
$512$	6.54989	0.289467
$513$	6.90985	0.305078
$514$	−11.7933	−0.520179
$515$	−19.7941	−0.872234
$516$	−1.62001	−0.0713171
$517$	−1.79578	−0.0789783
$518$	−15.5968	−0.685286
$519$	−22.3933	−0.982956
$520$	23.8643	1.04652
$521$	7.85281	0.344038	0.172019	−	0.985094i	$-0.444971\pi$
$521$	7.85281	0.344038	0.172019	+	0.985094i	$0.444971\pi$
$522$	16.6654	0.729427
$523$	7.79018	0.340641	0.170320	−	0.985389i	$-0.445520\pi$
$523$	7.79018	0.340641	0.170320	+	0.985389i	$0.445520\pi$
$524$	−8.06085	−0.352140
$525$	−7.58826	−0.331179
$526$	1.71291	0.0746865
$527$	0	0
$528$	12.8208	0.557956
$529$	35.3066	1.53507
$530$	20.5834	0.894085
$531$	10.9220	0.473977
$532$	−6.50846	−0.282177
$533$	31.6159	1.36944
$534$	19.0534	0.824520
$535$	−19.9676	−0.863276
$536$	5.20557	0.224846
$537$	14.0892	0.607994
$538$	4.17894	0.180167
$539$	−2.56590	−0.110521
$540$	3.34189	0.143812
$541$	−13.7305	−0.590321	−0.295160	−	0.955448i	$-0.595373\pi$
$541$	−13.7305	−0.590321	−0.295160	+	0.955448i	$0.595373\pi$
$542$	20.2466	0.869666
$543$	−20.8864	−0.896319
$544$	0	0
$545$	−57.5209	−2.46393
$546$	6.35687	0.272049
$547$	−21.0362	−0.899443	−0.449722	−	0.893169i	$-0.648477\pi$
$547$	−21.0362	−0.899443	−0.449722	+	0.893169i	$0.648477\pi$
$548$	−17.6676	−0.754724
$549$	5.12696	0.218813
$550$	−33.3962	−1.42402
$551$	67.1384	2.86019
$552$	−13.8579	−0.589830
$553$	−11.0332	−0.469178
$554$	−22.0652	−0.937460
$555$	32.2630	1.36949
$556$	6.07940	0.257824
$557$	18.9903	0.804645	0.402323	−	0.915498i	$-0.368203\pi$
$557$	18.9903	0.804645	0.402323	+	0.915498i	$0.368203\pi$
$558$	1.98646	0.0840937
$559$	6.37438	0.269607
$560$	17.7280	0.749145
$561$	0	0
$562$	−30.7703	−1.29797
$563$	−17.8871	−0.753851	−0.376925	−	0.926244i	$-0.623019\pi$
$563$	−17.8871	−0.753851	−0.376925	+	0.926244i	$0.623019\pi$
$564$	0.659207	0.0277576
$565$	−34.3488	−1.44506
$566$	−32.7121	−1.37499
$567$	−1.00000	−0.0419961
$568$	23.4431	0.983649
$569$	17.6081	0.738170	0.369085	−	0.929396i	$-0.379671\pi$
$569$	17.6081	0.738170	0.369085	+	0.929396i	$0.379671\pi$
$570$	42.0500	1.76128
$571$	−16.2996	−0.682115	−0.341058	−	0.940042i	$-0.610785\pi$
$571$	−16.2996	−0.682115	−0.341058	+	0.940042i	$0.610785\pi$
$572$	8.95731	0.374524
$573$	−4.70406	−0.196515
$574$	14.6316	0.610711
$575$	57.9431	2.41639
$576$	1.51925	0.0633019
$577$	18.0748	0.752464	0.376232	−	0.926526i	$-0.377220\pi$
$577$	18.0748	0.752464	0.376232	+	0.926526i	$0.377220\pi$
$578$	0	0
$579$	−5.10354	−0.212096
$580$	32.4709	1.34828
$581$	−8.11587	−0.336703
$582$	3.03706	0.125890
$583$	−8.67879	−0.359439
$584$	−2.58468	−0.106955
$585$	−13.1496	−0.543667
$586$	−29.0358	−1.19946
$587$	−5.40978	−0.223286	−0.111643	−	0.993748i	$-0.535611\pi$
$587$	−5.40978	−0.223286	−0.111643	+	0.993748i	$0.535611\pi$
$588$	0.941909	0.0388437
$589$	8.00266	0.329744
$590$	66.4663	2.73638
$591$	−13.4842	−0.554665
$592$	−45.4359	−1.86740
$593$	8.20619	0.336988	0.168494	−	0.985703i	$-0.446110\pi$
$593$	8.20619	0.336988	0.168494	+	0.985703i	$0.446110\pi$
$594$	−4.40103	−0.180577
$595$	0	0
$596$	14.5058	0.594179
$597$	−4.19363	−0.171634
$598$	−48.5402	−1.98496
$599$	16.5369	0.675681	0.337840	−	0.941203i	$-0.390304\pi$
$599$	16.5369	0.675681	0.337840	+	0.941203i	$0.390304\pi$
$600$	−13.7715	−0.562217
$601$	−30.9489	−1.26243	−0.631215	−	0.775608i	$-0.717444\pi$
$601$	−30.9489	−1.26243	−0.631215	+	0.775608i	$0.717444\pi$
$602$	2.95001	0.120234
$603$	−2.86834	−0.116808
$604$	−9.42006	−0.383297
$605$	−15.6685	−0.637014
$606$	16.9848	0.689961
$607$	−9.74513	−0.395542	−0.197771	−	0.980248i	$-0.563370\pi$
$607$	−9.74513	−0.395542	−0.197771	+	0.980248i	$0.563370\pi$
$608$	−34.1384	−1.38449
$609$	−9.71633	−0.393726
$610$	31.2002	1.26326
$611$	−2.59383	−0.104935
$612$	0	0
$613$	41.7672	1.68696	0.843480	−	0.537160i	$-0.180503\pi$
$613$	41.7672	1.68696	0.843480	+	0.537160i	$0.180503\pi$
$614$	−37.5688	−1.51615
$615$	−30.2664	−1.22046
$616$	−4.65669	−0.187623
$617$	38.7721	1.56091	0.780453	−	0.625215i	$-0.214989\pi$
$617$	38.7721	1.56091	0.780453	+	0.625215i	$0.214989\pi$
$618$	−9.56904	−0.384923
$619$	−44.5425	−1.79031	−0.895156	−	0.445752i	$-0.852936\pi$
$619$	−44.5425	−1.79031	−0.895156	+	0.445752i	$0.852936\pi$
$620$	3.87042	0.155440
$621$	7.63588	0.306417
$622$	46.6920	1.87218
$623$	−11.1085	−0.445055
$624$	18.5185	0.741332
$625$	−5.35957	−0.214383
$626$	12.3501	0.493609
$627$	−17.7300	−0.708068
$628$	7.25105	0.289348
$629$	0	0
$630$	−6.08552	−0.242453
$631$	7.99744	0.318373	0.159186	−	0.987249i	$-0.449113\pi$
$631$	7.99744	0.318373	0.159186	+	0.987249i	$0.449113\pi$
$632$	−20.0234	−0.796487
$633$	−17.8725	−0.710370
$634$	31.8481	1.26485
$635$	−6.99602	−0.277628
$636$	3.18587	0.126328
$637$	−3.70620	−0.146845
$638$	−42.7619	−1.69296
$639$	−12.9174	−0.511006
$640$	44.3034	1.75125
$641$	−39.0209	−1.54123	−0.770616	−	0.637299i	$-0.780051\pi$
$641$	−39.0209	−1.54123	−0.770616	+	0.637299i	$0.780051\pi$
$642$	−9.65291	−0.380970
$643$	5.89337	0.232412	0.116206	−	0.993225i	$-0.462927\pi$
$643$	5.89337	0.232412	0.116206	+	0.993225i	$0.462927\pi$
$644$	−7.19230	−0.283416
$645$	−6.10228	−0.240277
$646$	0	0
$647$	−27.4242	−1.07816	−0.539079	−	0.842255i	$-0.681228\pi$
$647$	−27.4242	−1.07816	−0.539079	+	0.842255i	$0.681228\pi$
$648$	−1.81484	−0.0712935
$649$	−28.0249	−1.10007
$650$	−48.2376	−1.89203
$651$	−1.15815	−0.0453916
$652$	5.56063	0.217771
$653$	−21.4263	−0.838474	−0.419237	−	0.907877i	$-0.637702\pi$
$653$	−21.4263	−0.838474	−0.419237	+	0.907877i	$0.637702\pi$
$654$	−27.8072	−1.08735
$655$	−30.3637	−1.18641
$656$	42.6240	1.66419
$657$	1.42420	0.0555632
$658$	−1.20040	−0.0467966
$659$	−10.2775	−0.400356	−0.200178	−	0.979760i	$-0.564152\pi$
$659$	−10.2775	−0.400356	−0.200178	+	0.979760i	$0.564152\pi$
$660$	−8.57496	−0.333780
$661$	5.90247	0.229580	0.114790	−	0.993390i	$-0.463381\pi$
$661$	5.90247	0.229580	0.114790	+	0.993390i	$0.463381\pi$
$662$	−13.8300	−0.537519
$663$	0	0
$664$	−14.7290	−0.571595
$665$	−24.5161	−0.950695
$666$	15.5968	0.604365
$667$	74.1927	2.87275
$668$	3.03965	0.117608
$669$	1.60272	0.0619649
$670$	−17.4553	−0.674358
$671$	−13.1553	−0.507854
$672$	4.94054	0.190585
$673$	3.75945	0.144916	0.0724580	−	0.997371i	$-0.476916\pi$
$673$	3.75945	0.144916	0.0724580	+	0.997371i	$0.476916\pi$
$674$	45.6184	1.75715
$675$	7.58826	0.292072
$676$	0.693140	0.0266592
$677$	−19.0565	−0.732401	−0.366200	−	0.930536i	$-0.619341\pi$
$677$	−19.0565	−0.732401	−0.366200	+	0.930536i	$0.619341\pi$
$678$	−16.6052	−0.637718
$679$	−1.77067	−0.0679522
$680$	0	0
$681$	−11.7490	−0.450222
$682$	−5.09707	−0.195177
$683$	−38.9918	−1.49198	−0.745989	−	0.665958i	$-0.768023\pi$
$683$	−38.9918	−1.49198	−0.745989	+	0.665958i	$0.768023\pi$
$684$	6.50846	0.248857
$685$	−66.5506	−2.54277
$686$	−1.71520	−0.0654866
$687$	−1.47791	−0.0563860
$688$	8.59382	0.327636
$689$	−12.5357	−0.477571
$690$	46.4683	1.76902
$691$	15.1384	0.575894	0.287947	−	0.957646i	$-0.407027\pi$
$691$	15.1384	0.575894	0.287947	+	0.957646i	$0.407027\pi$
$692$	−21.0924	−0.801815
$693$	2.56590	0.0974705
$694$	34.0345	1.29193
$695$	22.8999	0.868644
$696$	−17.6336	−0.668398
$697$	0	0
$698$	−18.5660	−0.702735
$699$	−13.7652	−0.520647
$700$	−7.14746	−0.270148
$701$	4.53361	0.171232	0.0856160	−	0.996328i	$-0.472714\pi$
$701$	4.53361	0.171232	0.0856160	+	0.996328i	$0.472714\pi$
$702$	−6.35687	−0.239924
$703$	62.8335	2.36981
$704$	−3.89823	−0.146920
$705$	2.48311	0.0935193
$706$	43.1324	1.62331
$707$	−9.90253	−0.372423
$708$	10.2876	0.386631
$709$	40.4319	1.51845	0.759226	−	0.650827i	$-0.225578\pi$
$709$	40.4319	1.51845	0.759226	+	0.650827i	$0.225578\pi$
$710$	−78.6093	−2.95016
$711$	11.0332	0.413776
$712$	−20.1602	−0.755535
$713$	8.84351	0.331192
$714$	0	0
$715$	33.7405	1.26182
$716$	13.2707	0.495951
$717$	13.6486	0.509715
$718$	34.5166	1.28815
$719$	47.5309	1.77260	0.886302	−	0.463107i	$-0.153265\pi$
$719$	47.5309	1.77260	0.886302	+	0.463107i	$0.153265\pi$
$720$	−17.7280	−0.660684
$721$	5.57897	0.207772
$722$	49.3053	1.83495
$723$	−17.3323	−0.644596
$724$	−19.6731	−0.731143
$725$	73.7301	2.73827
$726$	−7.57458	−0.281119
$727$	12.1751	0.451549	0.225774	−	0.974180i	$-0.427509\pi$
$727$	12.1751	0.451549	0.225774	+	0.974180i	$0.427509\pi$
$728$	−6.72614	−0.249287
$729$	1.00000	0.0370370
$730$	8.66697	0.320779
$731$	0	0
$732$	4.82913	0.178490
$733$	16.4228	0.606589	0.303294	−	0.952897i	$-0.401913\pi$
$733$	16.4228	0.606589	0.303294	+	0.952897i	$0.401913\pi$
$734$	47.0340	1.73606
$735$	3.54799	0.130870
$736$	−37.7253	−1.39057
$737$	7.35988	0.271105
$738$	−14.6316	−0.538597
$739$	−14.0884	−0.518249	−0.259125	−	0.965844i	$-0.583434\pi$
$739$	−14.0884	−0.518249	−0.259125	+	0.965844i	$0.583434\pi$
$740$	30.3888	1.11712
$741$	−25.6093	−0.940780
$742$	−5.80141	−0.212977
$743$	−52.3998	−1.92236	−0.961180	−	0.275921i	$-0.911017\pi$
$743$	−52.3998	−1.92236	−0.961180	+	0.275921i	$0.911017\pi$
$744$	−2.10186	−0.0770578
$745$	54.6405	2.00187
$746$	15.4672	0.566293
$747$	8.11587	0.296944
$748$	0	0
$749$	5.62786	0.205638
$750$	15.7509	0.575143
$751$	19.2295	0.701696	0.350848	−	0.936432i	$-0.385893\pi$
$751$	19.2295	0.701696	0.350848	+	0.936432i	$0.385893\pi$
$752$	−3.49695	−0.127521
$753$	−16.8092	−0.612560
$754$	−61.7654	−2.24936
$755$	−35.4836	−1.29138
$756$	−0.941909	−0.0342569
$757$	−28.7663	−1.04553	−0.522764	−	0.852477i	$-0.675099\pi$
$757$	−28.7663	−1.04553	−0.522764	+	0.852477i	$0.675099\pi$
$758$	−6.88661	−0.250133
$759$	−19.5929	−0.711178
$760$	−44.4928	−1.61392
$761$	−39.8043	−1.44291	−0.721453	−	0.692463i	$-0.756525\pi$
$761$	−39.8043	−1.44291	−0.721453	+	0.692463i	$0.756525\pi$
$762$	−3.38207	−0.122519
$763$	16.2122	0.586922
$764$	−4.43079	−0.160300
$765$	0	0
$766$	12.6760	0.458004
$767$	−40.4793	−1.46162
$768$	18.3790	0.663195
$769$	1.97929	0.0713750	0.0356875	−	0.999363i	$-0.488638\pi$
$769$	1.97929	0.0713750	0.0356875	+	0.999363i	$0.488638\pi$
$770$	15.6148	0.562720
$771$	−6.87575	−0.247624
$772$	−4.80707	−0.173010
$773$	−30.2810	−1.08913	−0.544565	−	0.838718i	$-0.683305\pi$
$773$	−30.2810	−1.08913	−0.544565	+	0.838718i	$0.683305\pi$
$774$	−2.95001	−0.106036
$775$	8.78837	0.315687
$776$	−3.21348	−0.115357
$777$	−9.09331	−0.326221
$778$	27.6856	0.992576
$779$	−58.9449	−2.11192
$780$	−12.3857	−0.443479
$781$	33.1449	1.18602
$782$	0	0
$783$	9.71633	0.347233
$784$	−4.99663	−0.178451
$785$	27.3133	0.974854
$786$	−14.6787	−0.523570
$787$	53.2070	1.89663	0.948313	−	0.317337i	$-0.102789\pi$
$787$	53.2070	1.89663	0.948313	+	0.317337i	$0.102789\pi$
$788$	−12.7009	−0.452450
$789$	0.998666	0.0355534
$790$	67.1425	2.38882
$791$	9.68119	0.344223
$792$	4.65669	0.165468
$793$	−19.0015	−0.674764
$794$	−11.5134	−0.408594
$795$	12.0006	0.425616
$796$	−3.95002	−0.140005
$797$	−39.2847	−1.39154	−0.695768	−	0.718266i	$-0.744936\pi$
$797$	−39.2847	−1.39154	−0.695768	+	0.718266i	$0.744936\pi$
$798$	−11.8518	−0.419548
$799$	0	0
$800$	−37.4901	−1.32547
$801$	11.1085	0.392501
$802$	3.39952	0.120041
$803$	−3.65435	−0.128959
$804$	−2.70172	−0.0952822
$805$	−27.0920	−0.954869
$806$	−7.36222	−0.259323
$807$	2.43642	0.0857660
$808$	−17.9715	−0.632234
$809$	46.3440	1.62937	0.814684	−	0.579905i	$-0.196910\pi$
$809$	46.3440	1.62937	0.814684	+	0.579905i	$0.196910\pi$
$810$	6.08552	0.213823
$811$	45.9210	1.61250	0.806252	−	0.591572i	$-0.201492\pi$
$811$	45.9210	1.61250	0.806252	+	0.591572i	$0.201492\pi$
$812$	−9.15190	−0.321169
$813$	11.8042	0.413992
$814$	−40.0200	−1.40270
$815$	20.9458	0.733701
$816$	0	0
$817$	−11.8844	−0.415784
$818$	−26.3094	−0.919887
$819$	3.70620	0.129505
$820$	−28.5082	−0.995549
$821$	−35.4875	−1.23852	−0.619262	−	0.785185i	$-0.712568\pi$
$821$	−35.4875	−1.23852	−0.619262	+	0.785185i	$0.712568\pi$
$822$	−32.1724	−1.12214
$823$	−10.5388	−0.367359	−0.183680	−	0.982986i	$-0.558801\pi$
$823$	−10.5388	−0.367359	−0.183680	+	0.982986i	$0.558801\pi$
$824$	10.1249	0.352718
$825$	−19.4707	−0.677884
$826$	−18.7335	−0.651822
$827$	55.2114	1.91989	0.959944	−	0.280194i	$-0.0903986\pi$
$827$	55.2114	1.91989	0.959944	+	0.280194i	$0.0903986\pi$
$828$	7.19230	0.249950
$829$	−37.2823	−1.29487	−0.647435	−	0.762121i	$-0.724158\pi$
$829$	−37.2823	−1.29487	−0.647435	+	0.762121i	$0.724158\pi$
$830$	49.3893	1.71433
$831$	−12.8645	−0.446264
$832$	−5.63062	−0.195207
$833$	0	0
$834$	11.0705	0.383339
$835$	11.4498	0.396237
$836$	−16.7001	−0.577584
$837$	1.15815	0.0400316
$838$	0.458134	0.0158260
$839$	−23.2421	−0.802407	−0.401203	−	0.915989i	$-0.631408\pi$
$839$	−23.2421	−0.802407	−0.401203	+	0.915989i	$0.631408\pi$
$840$	6.43903	0.222168
$841$	65.4071	2.25542
$842$	−28.2004	−0.971851
$843$	−17.9398	−0.617878
$844$	−16.8343	−0.579461
$845$	2.61093	0.0898186
$846$	1.20040	0.0412708
$847$	4.41615	0.151741
$848$	−16.9004	−0.580361
$849$	−19.0719	−0.654546
$850$	0	0
$851$	69.4354	2.38022
$852$	−12.1671	−0.416837
$853$	14.1046	0.482932	0.241466	−	0.970409i	$-0.422372\pi$
$853$	14.1046	0.482932	0.241466	+	0.970409i	$0.422372\pi$
$854$	−8.79376	−0.300916
$855$	24.5161	0.838434
$856$	10.2137	0.349096
$857$	−36.2404	−1.23795	−0.618975	−	0.785411i	$-0.712452\pi$
$857$	−36.2404	−1.23795	−0.618975	+	0.785411i	$0.712452\pi$
$858$	16.3111	0.556851
$859$	35.1436	1.19908	0.599542	−	0.800343i	$-0.295349\pi$
$859$	35.1436	1.19908	0.599542	+	0.800343i	$0.295349\pi$
$860$	−5.74780	−0.195998
$861$	8.53056	0.290721
$862$	3.71096	0.126396
$863$	−18.5693	−0.632106	−0.316053	−	0.948742i	$-0.602358\pi$
$863$	−18.5693	−0.632106	−0.316053	+	0.948742i	$0.602358\pi$
$864$	−4.94054	−0.168080
$865$	−79.4513	−2.70142
$866$	−9.69573	−0.329474
$867$	0	0
$868$	−1.09087	−0.0370267
$869$	−28.3100	−0.960351
$870$	59.1289	2.00466
$871$	10.6306	0.360205
$872$	29.4226	0.996374
$873$	1.77067	0.0599282
$874$	90.4987	3.06117
$875$	−9.18315	−0.310447
$876$	1.34146	0.0453239
$877$	−17.9724	−0.606886	−0.303443	−	0.952850i	$-0.598136\pi$
$877$	−17.9724	−0.606886	−0.303443	+	0.952850i	$0.598136\pi$
$878$	−3.28920	−0.111005
$879$	−16.9285	−0.570984
$880$	45.4883	1.53341
$881$	−34.5997	−1.16569	−0.582846	−	0.812583i	$-0.698061\pi$
$881$	−34.5997	−1.16569	−0.582846	+	0.812583i	$0.698061\pi$
$882$	1.71520	0.0577538
$883$	20.3212	0.683863	0.341931	−	0.939725i	$-0.388919\pi$
$883$	20.3212	0.683863	0.341931	+	0.939725i	$0.388919\pi$
$884$	0	0
$885$	38.7514	1.30261
$886$	48.8334	1.64059
$887$	−19.1066	−0.641536	−0.320768	−	0.947158i	$-0.603941\pi$
$887$	−19.1066	−0.641536	−0.320768	+	0.947158i	$0.603941\pi$
$888$	−16.5029	−0.553800
$889$	1.97182	0.0661328
$890$	67.6013	2.26600
$891$	−2.56590	−0.0859609
$892$	1.50962	0.0505459
$893$	4.83595	0.161829
$894$	26.4147	0.883440
$895$	49.9884	1.67093
$896$	−12.4869	−0.417157
$897$	−28.3001	−0.944911
$898$	22.3928	0.747259
$899$	11.2530	0.375308
$900$	7.14746	0.238249
$901$	0	0
$902$	37.5433	1.25005
$903$	1.71992	0.0572355
$904$	17.5698	0.584362
$905$	−74.1047	−2.46332
$906$	−17.1537	−0.569895
$907$	58.2318	1.93356	0.966778	−	0.255617i	$-0.0822785\pi$
$907$	58.2318	1.93356	0.966778	+	0.255617i	$0.0822785\pi$
$908$	−11.0665	−0.367254
$909$	9.90253	0.328446
$910$	22.5541	0.747662
$911$	2.34627	0.0777355	0.0388678	−	0.999244i	$-0.487625\pi$
$911$	2.34627	0.0777355	0.0388678	+	0.999244i	$0.487625\pi$
$912$	−34.5260	−1.14327
$913$	−20.8245	−0.689191
$914$	−15.1059	−0.499660
$915$	18.1904	0.601357
$916$	−1.39206	−0.0459950
$917$	8.55799	0.282610
$918$	0	0
$919$	−0.903634	−0.0298081	−0.0149041	−	0.999889i	$-0.504744\pi$
$919$	−0.903634	−0.0298081	−0.0149041	+	0.999889i	$0.504744\pi$
$920$	−49.1676	−1.62101
$921$	−21.9034	−0.721743
$922$	13.9771	0.460313
$923$	47.8746	1.57581
$924$	2.41685	0.0795084
$925$	69.0025	2.26879
$926$	−0.562605	−0.0184883
$927$	−5.57897	−0.183237
$928$	−48.0039	−1.57580
$929$	−27.9197	−0.916016	−0.458008	−	0.888948i	$-0.651437\pi$
$929$	−27.9197	−0.916016	−0.458008	+	0.888948i	$0.651437\pi$
$930$	7.04796	0.231112
$931$	6.90985	0.226461
$932$	−12.9656	−0.424701
$933$	27.2225	0.891225
$934$	−39.4873	−1.29206
$935$	0	0
$936$	6.72614	0.219851
$937$	36.6825	1.19836	0.599182	−	0.800613i	$-0.295493\pi$
$937$	36.6825	1.19836	0.599182	+	0.800613i	$0.295493\pi$
$938$	4.91977	0.160636
$939$	7.20038	0.234976
$940$	2.33886	0.0762853
$941$	33.3450	1.08702	0.543508	−	0.839404i	$-0.317096\pi$
$941$	33.3450	1.08702	0.543508	+	0.839404i	$0.317096\pi$
$942$	13.2040	0.430210
$943$	−65.1383	−2.12119
$944$	−54.5734	−1.77621
$945$	−3.54799	−0.115416
$946$	7.56945	0.246104
$947$	−19.7611	−0.642149	−0.321074	−	0.947054i	$-0.604044\pi$
$947$	−19.7611	−0.642149	−0.321074	+	0.947054i	$0.604044\pi$
$948$	10.3922	0.337524
$949$	−5.27835	−0.171342
$950$	89.9344	2.91786
$951$	18.5681	0.602113
$952$	0	0
$953$	36.5884	1.18521	0.592607	−	0.805491i	$-0.298099\pi$
$953$	36.5884	1.18521	0.592607	+	0.805491i	$0.298099\pi$
$954$	5.80141	0.187828
$955$	−16.6900	−0.540074
$956$	12.8557	0.415783
$957$	−24.9311	−0.805910
$958$	47.4070	1.53165
$959$	18.7573	0.605703
$960$	5.39027	0.173970
$961$	−29.6587	−0.956732
$962$	−57.8050	−1.86371
$963$	−5.62786	−0.181355
$964$	−16.3255	−0.525808
$965$	−18.1073	−0.582895
$966$	−13.0971	−0.421391
$967$	−29.3184	−0.942815	−0.471408	−	0.881915i	$-0.656254\pi$
$967$	−29.3184	−0.942815	−0.471408	+	0.881915i	$0.656254\pi$
$968$	8.01459	0.257599
$969$	0	0
$970$	10.7755	0.345979
$971$	30.8608	0.990370	0.495185	−	0.868788i	$-0.335100\pi$
$971$	30.8608	0.990370	0.495185	+	0.868788i	$0.335100\pi$
$972$	0.941909	0.0302118
$973$	−6.45433	−0.206916
$974$	3.75948	0.120462
$975$	−28.1236	−0.900676
$976$	−25.6175	−0.819996
$977$	−54.9490	−1.75797	−0.878987	−	0.476847i	$-0.841780\pi$
$977$	−54.9490	−1.75797	−0.878987	+	0.476847i	$0.841780\pi$
$978$	10.1258	0.323788
$979$	−28.5034	−0.910974
$980$	3.34189	0.106753
$981$	−16.2122	−0.517617
$982$	−13.7906	−0.440077
$983$	12.6067	0.402091	0.201046	−	0.979582i	$-0.435566\pi$
$983$	12.6067	0.402091	0.201046	+	0.979582i	$0.435566\pi$
$984$	15.4816	0.493534
$985$	−47.8418	−1.52437
$986$	0	0
$987$	−0.699863	−0.0222769
$988$	−24.1216	−0.767411
$989$	−13.1331	−0.417609
$990$	−15.6148	−0.496272
$991$	9.52255	0.302494	0.151247	−	0.988496i	$-0.451671\pi$
$991$	9.52255	0.302494	0.151247	+	0.988496i	$0.451671\pi$
$992$	−5.72189	−0.181670
$993$	−8.06322	−0.255878
$994$	22.1560	0.702746
$995$	−14.8790	−0.471695
$996$	7.64441	0.242223
$997$	−56.5013	−1.78941	−0.894707	−	0.446654i	$-0.852615\pi$
$997$	−56.5013	−1.78941	−0.894707	+	0.446654i	$0.852615\pi$
$998$	−19.6207	−0.621082
$999$	9.09331	0.287700

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6069.2.a.be.1.8		10
17.8	even	8		357.2.k.b.64.3	✓	20
17.15	even	8		357.2.k.b.106.8	yes	20
17.16	even	2		6069.2.a.bd.1.8		10
51.8	odd	8		1071.2.n.b.64.8		20
51.32	odd	8		1071.2.n.b.820.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.k.b.64.3	✓	20	17.8	even	8
357.2.k.b.106.8	yes	20	17.15	even	8
1071.2.n.b.64.8		20	51.8	odd	8
1071.2.n.b.820.3		20	51.32	odd	8
6069.2.a.bd.1.8		10	17.16	even	2
6069.2.a.be.1.8		10	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:	\( N \)	\(=\)	\( 6069 = 3 \cdot 7 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6069.a (trivial)

\(f(q)\)	\(=\)	\(q+1.71520 q^{2} +1.00000 q^{3} +0.941909 q^{4} +3.54799 q^{5} +1.71520 q^{6} -1.00000 q^{7} -1.81484 q^{8} +1.00000 q^{9} +6.08552 q^{10} -2.56590 q^{11} +0.941909 q^{12} -3.70620 q^{13} -1.71520 q^{14} +3.54799 q^{15} -4.99663 q^{16} +1.71520 q^{18} +6.90985 q^{19} +3.34189 q^{20} -1.00000 q^{21} -4.40103 q^{22} +7.63588 q^{23} -1.81484 q^{24} +7.58826 q^{25} -6.35687 q^{26} +1.00000 q^{27} -0.941909 q^{28} +9.71633 q^{29} +6.08552 q^{30} +1.15815 q^{31} -4.94054 q^{32} -2.56590 q^{33} -3.54799 q^{35} +0.941909 q^{36} +9.09331 q^{37} +11.8518 q^{38} -3.70620 q^{39} -6.43903 q^{40} -8.53056 q^{41} -1.71520 q^{42} -1.71992 q^{43} -2.41685 q^{44} +3.54799 q^{45} +13.0971 q^{46} +0.699863 q^{47} -4.99663 q^{48} +1.00000 q^{49} +13.0154 q^{50} -3.49090 q^{52} +3.38235 q^{53} +1.71520 q^{54} -9.10380 q^{55} +1.81484 q^{56} +6.90985 q^{57} +16.6654 q^{58} +10.9220 q^{59} +3.34189 q^{60} +5.12696 q^{61} +1.98646 q^{62} -1.00000 q^{63} +1.51925 q^{64} -13.1496 q^{65} -4.40103 q^{66} -2.86834 q^{67} +7.63588 q^{69} -6.08552 q^{70} -12.9174 q^{71} -1.81484 q^{72} +1.42420 q^{73} +15.5968 q^{74} +7.58826 q^{75} +6.50846 q^{76} +2.56590 q^{77} -6.35687 q^{78} +11.0332 q^{79} -17.7280 q^{80} +1.00000 q^{81} -14.6316 q^{82} +8.11587 q^{83} -0.941909 q^{84} -2.95001 q^{86} +9.71633 q^{87} +4.65669 q^{88} +11.1085 q^{89} +6.08552 q^{90} +3.70620 q^{91} +7.19230 q^{92} +1.15815 q^{93} +1.20040 q^{94} +24.5161 q^{95} -4.94054 q^{96} +1.77067 q^{97} +1.71520 q^{98} -2.56590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 10 q^{3} + 12 q^{4} - 6 q^{5} + 4 q^{6} - 10 q^{7} + 12 q^{8} + 10 q^{9} - 2 q^{11} + 12 q^{12} + 6 q^{13} - 4 q^{14} - 6 q^{15} + 20 q^{16} + 4 q^{18} + 6 q^{19} - 16 q^{20} - 10 q^{21}+ \cdots - 2 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 + 10 * q^3 + 12 * q^4 - 6 * q^5 + 4 * q^6 - 10 * q^7 + 12 * q^8 + 10 * q^9 - 2 * q^11 + 12 * q^12 + 6 * q^13 - 4 * q^14 - 6 * q^15 + 20 * q^16 + 4 * q^18 + 6 * q^19 - 16 * q^20 - 10 * q^21 + 24 * q^22 + 18 * q^23 + 12 * q^24 + 4 * q^25 + 12 * q^26 + 10 * q^27 - 12 * q^28 - 12 * q^29 - 8 * q^31 + 28 * q^32 - 2 * q^33 + 6 * q^35 + 12 * q^36 + 24 * q^37 + 32 * q^38 + 6 * q^39 - 36 * q^40 - 2 * q^41 - 4 * q^42 + 6 * q^43 + 28 * q^44 - 6 * q^45 - 28 * q^46 + 16 * q^47 + 20 * q^48 + 10 * q^49 + 52 * q^50 + 24 * q^52 - 12 * q^53 + 4 * q^54 + 18 * q^55 - 12 * q^56 + 6 * q^57 + 20 * q^58 + 20 * q^59 - 16 * q^60 - 4 * q^61 - 24 * q^62 - 10 * q^63 + 56 * q^64 - 38 * q^65 + 24 * q^66 + 20 * q^67 + 18 * q^69 - 20 * q^71 + 12 * q^72 + 20 * q^73 + 36 * q^74 + 4 * q^75 - 8 * q^76 + 2 * q^77 + 12 * q^78 + 20 * q^79 - 92 * q^80 + 10 * q^81 + 8 * q^82 + 36 * q^83 - 12 * q^84 - 12 * q^87 + 92 * q^88 + 32 * q^89 - 6 * q^91 + 40 * q^92 - 8 * q^93 + 60 * q^94 - 14 * q^95 + 28 * q^96 + 36 * q^97 + 4 * q^98 - 2 * q^99

Introduction

L-functions

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Groups

Database

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