LMFDB - Embedded newform 2667.2.a.q.1.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2667,2,Mod(1,2667)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2667, 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("2667.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2667 = 3 \cdot 7 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2667.a (trivial)

Newform invariants

comment:select newform

sage:traces = [19,4,19,22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	yes
Analytic conductor:	$21.2961022191$
Analytic rank:	$0$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 4 x^{18} - 22 x^{17} + 101 x^{16} + 178 x^{15} - 1035 x^{14} - 583 x^{13} + 5572 x^{12} + \cdots + 210 $ x^19 - 4x^18 - 22x^17 + 101x^16 + 178x^15 - 1035x^14 - 583x^13 + 5572x^12 + 21x^11 - 17032x^10 + 4985x^9 + 29792x^8 - 13249x^7 - 28600x^6 + 14000x^5 + 13725x^4 - 5723x^3 - 2913x^2 + 608x + 210
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-0.407951$ of defining polynomial
Character	$\chi$	$=$	2667.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.407951 q^{2} +1.00000 q^{3} -1.83358 q^{4} -1.08992 q^{5} -0.407951 q^{6} +1.00000 q^{7} +1.56391 q^{8} +1.00000 q^{9} +0.444635 q^{10} +2.30086 q^{11} -1.83358 q^{12} -1.28207 q^{13} -0.407951 q^{14} -1.08992 q^{15} +3.02915 q^{16} +3.85945 q^{17} -0.407951 q^{18} -5.48075 q^{19} +1.99845 q^{20} +1.00000 q^{21} -0.938637 q^{22} +5.15478 q^{23} +1.56391 q^{24} -3.81207 q^{25} +0.523023 q^{26} +1.00000 q^{27} -1.83358 q^{28} -3.35002 q^{29} +0.444635 q^{30} -0.261843 q^{31} -4.36357 q^{32} +2.30086 q^{33} -1.57447 q^{34} -1.08992 q^{35} -1.83358 q^{36} +4.76674 q^{37} +2.23588 q^{38} -1.28207 q^{39} -1.70454 q^{40} +4.53932 q^{41} -0.407951 q^{42} +3.17008 q^{43} -4.21880 q^{44} -1.08992 q^{45} -2.10290 q^{46} +0.491884 q^{47} +3.02915 q^{48} +1.00000 q^{49} +1.55514 q^{50} +3.85945 q^{51} +2.35078 q^{52} -11.3199 q^{53} -0.407951 q^{54} -2.50775 q^{55} +1.56391 q^{56} -5.48075 q^{57} +1.36664 q^{58} +1.96040 q^{59} +1.99845 q^{60} +0.0291708 q^{61} +0.106819 q^{62} +1.00000 q^{63} -4.27818 q^{64} +1.39736 q^{65} -0.938637 q^{66} +13.7705 q^{67} -7.07659 q^{68} +5.15478 q^{69} +0.444635 q^{70} +1.95435 q^{71} +1.56391 q^{72} +10.9732 q^{73} -1.94460 q^{74} -3.81207 q^{75} +10.0494 q^{76} +2.30086 q^{77} +0.523023 q^{78} +1.31077 q^{79} -3.30154 q^{80} +1.00000 q^{81} -1.85182 q^{82} -9.68361 q^{83} -1.83358 q^{84} -4.20649 q^{85} -1.29324 q^{86} -3.35002 q^{87} +3.59834 q^{88} +13.3023 q^{89} +0.444635 q^{90} -1.28207 q^{91} -9.45169 q^{92} -0.261843 q^{93} -0.200664 q^{94} +5.97359 q^{95} -4.36357 q^{96} -2.44284 q^{97} -0.407951 q^{98} +2.30086 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 4 q^{2} + 19 q^{3} + 22 q^{4} + 5 q^{5} + 4 q^{6} + 19 q^{7} + 9 q^{8} + 19 q^{9} - 9 q^{11} + 22 q^{12} + 24 q^{13} + 4 q^{14} + 5 q^{15} + 20 q^{16} + 17 q^{17} + 4 q^{18} + 23 q^{19} + 5 q^{20}+ \cdots - 9 q^{99}+O(q^{100}) $ 19 * q + 4 * q^2 + 19 * q^3 + 22 * q^4 + 5 * q^5 + 4 * q^6 + 19 * q^7 + 9 * q^8 + 19 * q^9 - 9 * q^11 + 22 * q^12 + 24 * q^13 + 4 * q^14 + 5 * q^15 + 20 * q^16 + 17 * q^17 + 4 * q^18 + 23 * q^19 + 5 * q^20 + 19 * q^21 - 3 * q^22 - 17 * q^23 + 9 * q^24 + 38 * q^25 + 28 * q^26 + 19 * q^27 + 22 * q^28 + 2 * q^29 + 16 * q^31 + 17 * q^32 - 9 * q^33 + 29 * q^34 + 5 * q^35 + 22 * q^36 + 56 * q^37 + 2 * q^38 + 24 * q^39 - 13 * q^40 - 7 * q^41 + 4 * q^42 + 19 * q^43 - 29 * q^44 + 5 * q^45 + 10 * q^46 + 25 * q^47 + 20 * q^48 + 19 * q^49 - 9 * q^50 + 17 * q^51 + 16 * q^52 + 18 * q^53 + 4 * q^54 + 10 * q^55 + 9 * q^56 + 23 * q^57 + 31 * q^58 + 11 * q^59 + 5 * q^60 + 26 * q^61 + 26 * q^62 + 19 * q^63 + 45 * q^64 + 27 * q^65 - 3 * q^66 + 24 * q^67 + 14 * q^68 - 17 * q^69 - 32 * q^71 + 9 * q^72 + 51 * q^73 + 38 * q^75 + 12 * q^76 - 9 * q^77 + 28 * q^78 + 30 * q^79 - 30 * q^80 + 19 * q^81 - 52 * q^82 + q^83 + 22 * q^84 + 44 * q^85 - 24 * q^86 + 2 * q^87 - 30 * q^88 + 5 * q^89 + 24 * q^91 - 88 * q^92 + 16 * q^93 + 7 * q^94 - 24 * q^95 + 17 * q^96 + 5 * q^97 + 4 * q^98 - 9 * 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 $

$2$	−0.407951	−0.288465	−0.144232	−	0.989544i	$-0.546071\pi$
$2$	−0.407951	−0.288465	−0.144232	+	0.989544i	$0.546071\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.83358	−0.916788
$5$	−1.08992	−0.487428	−0.243714	−	0.969847i	$-0.578366\pi$
$5$	−1.08992	−0.487428	−0.243714	+	0.969847i	$0.578366\pi$
$6$	−0.407951	−0.166545
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.56391	0.552926
$9$	1.00000	0.333333
$10$	0.444635	0.140606
$11$	2.30086	0.693734	0.346867	−	0.937914i	$-0.387245\pi$
$11$	2.30086	0.693734	0.346867	+	0.937914i	$0.387245\pi$
$12$	−1.83358	−0.529308
$13$	−1.28207	−0.355583	−0.177791	−	0.984068i	$-0.556895\pi$
$13$	−1.28207	−0.355583	−0.177791	+	0.984068i	$0.556895\pi$
$14$	−0.407951	−0.109030
$15$	−1.08992	−0.281417
$16$	3.02915	0.757288
$17$	3.85945	0.936053	0.468027	−	0.883714i	$-0.344965\pi$
$17$	3.85945	0.936053	0.468027	+	0.883714i	$0.344965\pi$
$18$	−0.407951	−0.0961550
$19$	−5.48075	−1.25737	−0.628685	−	0.777660i	$-0.716406\pi$
$19$	−5.48075	−1.25737	−0.628685	+	0.777660i	$0.716406\pi$
$20$	1.99845	0.446868
$21$	1.00000	0.218218
$22$	−0.938637	−0.200118
$23$	5.15478	1.07485	0.537423	−	0.843313i	$-0.319398\pi$
$23$	5.15478	1.07485	0.537423	+	0.843313i	$0.319398\pi$
$24$	1.56391	0.319232
$25$	−3.81207	−0.762414
$26$	0.523023	0.102573
$27$	1.00000	0.192450
$28$	−1.83358	−0.346513
$29$	−3.35002	−0.622082	−0.311041	−	0.950396i	$-0.600678\pi$
$29$	−3.35002	−0.622082	−0.311041	+	0.950396i	$0.600678\pi$
$30$	0.444635	0.0811788
$31$	−0.261843	−0.0470284	−0.0235142	−	0.999724i	$-0.507485\pi$
$31$	−0.261843	−0.0470284	−0.0235142	+	0.999724i	$0.507485\pi$
$32$	−4.36357	−0.771377
$33$	2.30086	0.400528
$34$	−1.57447	−0.270019
$35$	−1.08992	−0.184230
$36$	−1.83358	−0.305596
$37$	4.76674	0.783648	0.391824	−	0.920040i	$-0.371844\pi$
$37$	4.76674	0.783648	0.391824	+	0.920040i	$0.371844\pi$
$38$	2.23588	0.362707
$39$	−1.28207	−0.205296
$40$	−1.70454	−0.269512
$41$	4.53932	0.708923	0.354461	−	0.935071i	$-0.384664\pi$
$41$	4.53932	0.708923	0.354461	+	0.935071i	$0.384664\pi$
$42$	−0.407951	−0.0629482
$43$	3.17008	0.483433	0.241716	−	0.970347i	$-0.422290\pi$
$43$	3.17008	0.483433	0.241716	+	0.970347i	$0.422290\pi$
$44$	−4.21880	−0.636007
$45$	−1.08992	−0.162476
$46$	−2.10290	−0.310056
$47$	0.491884	0.0717486	0.0358743	−	0.999356i	$-0.488578\pi$
$47$	0.491884	0.0717486	0.0358743	+	0.999356i	$0.488578\pi$
$48$	3.02915	0.437221
$49$	1.00000	0.142857
$50$	1.55514	0.219930
$51$	3.85945	0.540431
$52$	2.35078	0.325994
$53$	−11.3199	−1.55490	−0.777452	−	0.628943i	$-0.783488\pi$
$53$	−11.3199	−1.55490	−0.777452	+	0.628943i	$0.783488\pi$
$54$	−0.407951	−0.0555151
$55$	−2.50775	−0.338145
$56$	1.56391	0.208986
$57$	−5.48075	−0.725943
$58$	1.36664	0.179449
$59$	1.96040	0.255222	0.127611	−	0.991824i	$-0.459269\pi$
$59$	1.96040	0.255222	0.127611	+	0.991824i	$0.459269\pi$
$60$	1.99845	0.257999
$61$	0.0291708	0.00373494	0.00186747	−	0.999998i	$-0.499406\pi$
$61$	0.0291708	0.00373494	0.00186747	+	0.999998i	$0.499406\pi$
$62$	0.106819	0.0135660
$63$	1.00000	0.125988
$64$	−4.27818	−0.534773
$65$	1.39736	0.173321
$66$	−0.938637	−0.115538
$67$	13.7705	1.68234	0.841169	−	0.540772i	$-0.181868\pi$
$67$	13.7705	1.68234	0.841169	+	0.540772i	$0.181868\pi$
$68$	−7.07659	−0.858162
$69$	5.15478	0.620563
$70$	0.444635	0.0531440
$71$	1.95435	0.231938	0.115969	−	0.993253i	$-0.463003\pi$
$71$	1.95435	0.231938	0.115969	+	0.993253i	$0.463003\pi$
$72$	1.56391	0.184309
$73$	10.9732	1.28431	0.642155	−	0.766575i	$-0.278040\pi$
$73$	10.9732	1.28431	0.642155	+	0.766575i	$0.278040\pi$
$74$	−1.94460	−0.226055
$75$	−3.81207	−0.440180
$76$	10.0494	1.15274
$77$	2.30086	0.262207
$78$	0.523023	0.0592207
$79$	1.31077	0.147473	0.0737364	−	0.997278i	$-0.476508\pi$
$79$	1.31077	0.147473	0.0737364	+	0.997278i	$0.476508\pi$
$80$	−3.30154	−0.369123
$81$	1.00000	0.111111
$82$	−1.85182	−0.204499
$83$	−9.68361	−1.06291	−0.531457	−	0.847085i	$-0.678355\pi$
$83$	−9.68361	−1.06291	−0.531457	+	0.847085i	$0.678355\pi$
$84$	−1.83358	−0.200060
$85$	−4.20649	−0.456258
$86$	−1.29324	−0.139453
$87$	−3.35002	−0.359159
$88$	3.59834	0.383584
$89$	13.3023	1.41004	0.705022	−	0.709186i	$-0.250937\pi$
$89$	13.3023	1.41004	0.705022	+	0.709186i	$0.250937\pi$
$90$	0.444635	0.0468686
$91$	−1.28207	−0.134398
$92$	−9.45169	−0.985406
$93$	−0.261843	−0.0271518
$94$	−0.200664	−0.0206970
$95$	5.97359	0.612877
$96$	−4.36357	−0.445355
$97$	−2.44284	−0.248033	−0.124016	−	0.992280i	$-0.539578\pi$
$97$	−2.44284	−0.248033	−0.124016	+	0.992280i	$0.539578\pi$
$98$	−0.407951	−0.0412093
$99$	2.30086	0.231245
$100$	6.98972	0.698972
$101$	16.2404	1.61598	0.807991	−	0.589195i	$-0.200555\pi$
$101$	16.2404	1.61598	0.807991	+	0.589195i	$0.200555\pi$
$102$	−1.57447	−0.155895
$103$	16.7605	1.65146	0.825730	−	0.564066i	$-0.190764\pi$
$103$	16.7605	1.65146	0.825730	+	0.564066i	$0.190764\pi$
$104$	−2.00505	−0.196611
$105$	−1.08992	−0.106365
$106$	4.61795	0.448535
$107$	−7.03427	−0.680028	−0.340014	−	0.940420i	$-0.610432\pi$
$107$	−7.03427	−0.680028	−0.340014	+	0.940420i	$0.610432\pi$
$108$	−1.83358	−0.176436
$109$	8.64818	0.828345	0.414173	−	0.910198i	$-0.364071\pi$
$109$	8.64818	0.828345	0.414173	+	0.910198i	$0.364071\pi$
$110$	1.02304	0.0975431
$111$	4.76674	0.452439
$112$	3.02915	0.286228
$113$	−9.06671	−0.852924	−0.426462	−	0.904505i	$-0.640240\pi$
$113$	−9.06671	−0.852924	−0.426462	+	0.904505i	$0.640240\pi$
$114$	2.23588	0.209409
$115$	−5.61831	−0.523910
$116$	6.14251	0.570318
$117$	−1.28207	−0.118528
$118$	−0.799745	−0.0736225
$119$	3.85945	0.353795
$120$	−1.70454	−0.155603
$121$	−5.70606	−0.518733
$122$	−0.0119003	−0.00107740
$123$	4.53932	0.409297
$124$	0.480109	0.0431150
$125$	9.60447	0.859050
$126$	−0.407951	−0.0363432
$127$	1.00000	0.0887357
$127$	1.00000	0.0887357
$128$	10.4724	0.925640
$129$	3.17008	0.279110
$130$	−0.570054	−0.0499970
$131$	13.6779	1.19504	0.597521	−	0.801853i	$-0.296153\pi$
$131$	13.6779	1.19504	0.597521	+	0.801853i	$0.296153\pi$
$132$	−4.21880	−0.367199
$133$	−5.48075	−0.475241
$134$	−5.61770	−0.485296
$135$	−1.08992	−0.0938055
$136$	6.03583	0.517568
$137$	−21.0777	−1.80079	−0.900394	−	0.435076i	$-0.856722\pi$
$137$	−21.0777	−1.80079	−0.900394	+	0.435076i	$0.856722\pi$
$138$	−2.10290	−0.179011
$139$	10.4381	0.885348	0.442674	−	0.896683i	$-0.354030\pi$
$139$	10.4381	0.885348	0.442674	+	0.896683i	$0.354030\pi$
$140$	1.99845	0.168900
$141$	0.491884	0.0414241
$142$	−0.797278	−0.0669061
$143$	−2.94986	−0.246680
$144$	3.02915	0.252429
$145$	3.65125	0.303220
$146$	−4.47651	−0.370479
$147$	1.00000	0.0824786
$148$	−8.74019	−0.718439
$149$	0.369201	0.0302461	0.0151231	−	0.999886i	$-0.495186\pi$
$149$	0.369201	0.0302461	0.0151231	+	0.999886i	$0.495186\pi$
$150$	1.55514	0.126977
$151$	10.3324	0.840841	0.420420	−	0.907329i	$-0.361883\pi$
$151$	10.3324	0.840841	0.420420	+	0.907329i	$0.361883\pi$
$152$	−8.57140	−0.695233
$153$	3.85945	0.312018
$154$	−0.938637	−0.0756375
$155$	0.285388	0.0229229
$156$	2.35078	0.188213
$157$	19.4698	1.55386	0.776929	−	0.629589i	$-0.216777\pi$
$157$	19.4698	1.55386	0.776929	+	0.629589i	$0.216777\pi$
$158$	−0.534729	−0.0425407
$159$	−11.3199	−0.897724
$160$	4.75595	0.375991
$161$	5.15478	0.406254
$162$	−0.407951	−0.0320517
$163$	13.8845	1.08752	0.543760	−	0.839241i	$-0.317000\pi$
$163$	13.8845	1.08752	0.543760	+	0.839241i	$0.317000\pi$
$164$	−8.32319	−0.649932
$165$	−2.50775	−0.195228
$166$	3.95044	0.306614
$167$	−8.27086	−0.640018	−0.320009	−	0.947414i	$-0.603686\pi$
$167$	−8.27086	−0.640018	−0.320009	+	0.947414i	$0.603686\pi$
$168$	1.56391	0.120658
$169$	−11.3563	−0.873561
$170$	1.71604	0.131615
$171$	−5.48075	−0.419123
$172$	−5.81258	−0.443205
$173$	17.6707	1.34348	0.671738	−	0.740789i	$-0.265548\pi$
$173$	17.6707	1.34348	0.671738	+	0.740789i	$0.265548\pi$
$174$	1.36664	0.103605
$175$	−3.81207	−0.288165
$176$	6.96965	0.525357
$177$	1.96040	0.147352
$178$	−5.42670	−0.406748
$179$	17.8016	1.33056	0.665279	−	0.746595i	$-0.268313\pi$
$179$	17.8016	1.33056	0.665279	+	0.746595i	$0.268313\pi$
$180$	1.99845	0.148956
$181$	24.5660	1.82598	0.912989	−	0.407984i	$-0.133768\pi$
$181$	24.5660	1.82598	0.912989	+	0.407984i	$0.133768\pi$
$182$	0.523023	0.0387690
$183$	0.0291708	0.00215637
$184$	8.06162	0.594311
$185$	−5.19538	−0.381972
$186$	0.106819	0.00783235
$187$	8.88003	0.649372
$188$	−0.901906	−0.0657783
$189$	1.00000	0.0727393
$190$	−2.43693	−0.176794
$191$	23.1438	1.67463	0.837314	−	0.546723i	$-0.184125\pi$
$191$	23.1438	1.67463	0.837314	+	0.546723i	$0.184125\pi$
$192$	−4.27818	−0.308751
$193$	4.89303	0.352208	0.176104	−	0.984372i	$-0.443651\pi$
$193$	4.89303	0.352208	0.176104	+	0.984372i	$0.443651\pi$
$194$	0.996560	0.0715488
$195$	1.39736	0.100067
$196$	−1.83358	−0.130970
$197$	23.9211	1.70431	0.852155	−	0.523289i	$-0.175295\pi$
$197$	23.9211	1.70431	0.852155	+	0.523289i	$0.175295\pi$
$198$	−0.938637	−0.0667060
$199$	−12.8048	−0.907707	−0.453853	−	0.891076i	$-0.649951\pi$
$199$	−12.8048	−0.907707	−0.453853	+	0.891076i	$0.649951\pi$
$200$	−5.96174	−0.421559
$201$	13.7705	0.971298
$202$	−6.62530	−0.466154
$203$	−3.35002	−0.235125
$204$	−7.07659	−0.495460
$205$	−4.94751	−0.345549
$206$	−6.83746	−0.476388
$207$	5.15478	0.358282
$208$	−3.88359	−0.269279
$209$	−12.6104	−0.872281
$210$	0.444635	0.0306827
$211$	−3.97912	−0.273934	−0.136967	−	0.990576i	$-0.543735\pi$
$211$	−3.97912	−0.273934	−0.136967	+	0.990576i	$0.543735\pi$
$212$	20.7558	1.42552
$213$	1.95435	0.133910
$214$	2.86964	0.196164
$215$	−3.45514	−0.235639
$216$	1.56391	0.106411
$217$	−0.261843	−0.0177751
$218$	−3.52803	−0.238949
$219$	10.9732	0.741497
$220$	4.59816	0.310008
$221$	−4.94809	−0.332844
$222$	−1.94460	−0.130513
$223$	1.15283	0.0771992	0.0385996	−	0.999255i	$-0.487710\pi$
$223$	1.15283	0.0771992	0.0385996	+	0.999255i	$0.487710\pi$
$224$	−4.36357	−0.291553
$225$	−3.81207	−0.254138
$226$	3.69877	0.246039
$227$	−16.2210	−1.07663	−0.538314	−	0.842744i	$-0.680939\pi$
$227$	−16.2210	−1.07663	−0.538314	+	0.842744i	$0.680939\pi$
$228$	10.0494	0.665536
$229$	−16.9029	−1.11698	−0.558488	−	0.829512i	$-0.688618\pi$
$229$	−16.9029	−1.11698	−0.558488	+	0.829512i	$0.688618\pi$
$230$	2.29200	0.151130
$231$	2.30086	0.151385
$232$	−5.23913	−0.343966
$233$	−6.97836	−0.457168	−0.228584	−	0.973524i	$-0.573409\pi$
$233$	−6.97836	−0.457168	−0.228584	+	0.973524i	$0.573409\pi$
$234$	0.523023	0.0341911
$235$	−0.536115	−0.0349723
$236$	−3.59453	−0.233984
$237$	1.31077	0.0851434
$238$	−1.57447	−0.102057
$239$	−27.3643	−1.77005	−0.885025	−	0.465544i	$-0.845859\pi$
$239$	−27.3643	−1.77005	−0.885025	+	0.465544i	$0.845859\pi$
$240$	−3.30154	−0.213113
$241$	−25.1019	−1.61695	−0.808477	−	0.588528i	$-0.799708\pi$
$241$	−25.1019	−1.61695	−0.808477	+	0.588528i	$0.799708\pi$
$242$	2.32779	0.149636
$243$	1.00000	0.0641500
$244$	−0.0534869	−0.00342415
$245$	−1.08992	−0.0696325
$246$	−1.85182	−0.118068
$247$	7.02671	0.447099
$248$	−0.409499	−0.0260032
$249$	−9.68361	−0.613674
$250$	−3.91815	−0.247806
$251$	7.05092	0.445050	0.222525	−	0.974927i	$-0.428570\pi$
$251$	7.05092	0.445050	0.222525	+	0.974927i	$0.428570\pi$
$252$	−1.83358	−0.115504
$253$	11.8604	0.745658
$254$	−0.407951	−0.0255971
$255$	−4.20649	−0.263421
$256$	4.28413	0.267758
$257$	0.0574366	0.00358280	0.00179140	−	0.999998i	$-0.499430\pi$
$257$	0.0574366	0.00358280	0.00179140	+	0.999998i	$0.499430\pi$
$258$	−1.29324	−0.0805135
$259$	4.76674	0.296191
$260$	−2.56216	−0.158899
$261$	−3.35002	−0.207361
$262$	−5.57990	−0.344728
$263$	−14.6910	−0.905885	−0.452943	−	0.891540i	$-0.649626\pi$
$263$	−14.6910	−0.905885	−0.452943	+	0.891540i	$0.649626\pi$
$264$	3.59834	0.221462
$265$	12.3378	0.757903
$266$	2.23588	0.137090
$267$	13.3023	0.814089
$268$	−25.2493	−1.54235
$269$	−9.26332	−0.564795	−0.282397	−	0.959298i	$-0.591130\pi$
$269$	−9.26332	−0.564795	−0.282397	+	0.959298i	$0.591130\pi$
$270$	0.444635	0.0270596
$271$	13.1700	0.800024	0.400012	−	0.916510i	$-0.369006\pi$
$271$	13.1700	0.800024	0.400012	+	0.916510i	$0.369006\pi$
$272$	11.6909	0.708862
$273$	−1.28207	−0.0775945
$274$	8.59866	0.519464
$275$	−8.77103	−0.528913
$276$	−9.45169	−0.568925
$277$	16.3591	0.982922	0.491461	−	0.870900i	$-0.336463\pi$
$277$	16.3591	0.982922	0.491461	+	0.870900i	$0.336463\pi$
$278$	−4.25823	−0.255392
$279$	−0.261843	−0.0156761
$280$	−1.70454	−0.101866
$281$	−7.16275	−0.427294	−0.213647	−	0.976911i	$-0.568534\pi$
$281$	−7.16275	−0.427294	−0.213647	+	0.976911i	$0.568534\pi$
$282$	−0.200664	−0.0119494
$283$	−2.99945	−0.178299	−0.0891494	−	0.996018i	$-0.528415\pi$
$283$	−2.99945	−0.178299	−0.0891494	+	0.996018i	$0.528415\pi$
$284$	−3.58345	−0.212638
$285$	5.97359	0.353845
$286$	1.20340	0.0711585
$287$	4.53932	0.267948
$288$	−4.36357	−0.257126
$289$	−2.10467	−0.123804
$290$	−1.48953	−0.0874684
$291$	−2.44284	−0.143202
$292$	−20.1201	−1.17744
$293$	−7.96629	−0.465396	−0.232698	−	0.972549i	$-0.574755\pi$
$293$	−7.96629	−0.465396	−0.232698	+	0.972549i	$0.574755\pi$
$294$	−0.407951	−0.0237922
$295$	−2.13668	−0.124402
$296$	7.45476	0.433299
$297$	2.30086	0.133509
$298$	−0.150616	−0.00872495
$299$	−6.60880	−0.382197
$300$	6.98972	0.403552
$301$	3.17008	0.182720
$302$	−4.21512	−0.242553
$303$	16.2404	0.932988
$304$	−16.6020	−0.952191
$305$	−0.0317939	−0.00182051
$306$	−1.57447	−0.0900062
$307$	9.84980	0.562158	0.281079	−	0.959685i	$-0.409308\pi$
$307$	9.84980	0.562158	0.281079	+	0.959685i	$0.409308\pi$
$308$	−4.21880	−0.240388
$309$	16.7605	0.953471
$310$	−0.116424	−0.00661246
$311$	−31.7455	−1.80012	−0.900062	−	0.435762i	$-0.856479\pi$
$311$	−31.7455	−1.80012	−0.900062	+	0.435762i	$0.856479\pi$
$312$	−2.00505	−0.113513
$313$	−12.9459	−0.731748	−0.365874	−	0.930664i	$-0.619230\pi$
$313$	−12.9459	−0.731748	−0.365874	+	0.930664i	$0.619230\pi$
$314$	−7.94272	−0.448233
$315$	−1.08992	−0.0614101
$316$	−2.40339	−0.135201
$317$	−4.65835	−0.261639	−0.130819	−	0.991406i	$-0.541761\pi$
$317$	−4.65835	−0.261639	−0.130819	+	0.991406i	$0.541761\pi$
$318$	4.61795	0.258962
$319$	−7.70791	−0.431560
$320$	4.66288	0.260663
$321$	−7.03427	−0.392615
$322$	−2.10290	−0.117190
$323$	−21.1527	−1.17697
$324$	−1.83358	−0.101865
$325$	4.88735	0.271101
$326$	−5.66421	−0.313712
$327$	8.64818	0.478245
$328$	7.09910	0.391982
$329$	0.491884	0.0271184
$330$	1.02304	0.0563165
$331$	14.0354	0.771458	0.385729	−	0.922612i	$-0.373950\pi$
$331$	14.0354	0.771458	0.385729	+	0.922612i	$0.373950\pi$
$332$	17.7556	0.974467
$333$	4.76674	0.261216
$334$	3.37410	0.184623
$335$	−15.0088	−0.820018
$336$	3.02915	0.165254
$337$	−19.7961	−1.07836	−0.539182	−	0.842190i	$-0.681266\pi$
$337$	−19.7961	−1.07836	−0.539182	+	0.842190i	$0.681266\pi$
$338$	4.63281	0.251992
$339$	−9.06671	−0.492436
$340$	7.71293	0.418292
$341$	−0.602463	−0.0326252
$342$	2.23588	0.120902
$343$	1.00000	0.0539949
$344$	4.95772	0.267303
$345$	−5.61831	−0.302480
$346$	−7.20877	−0.387546
$347$	−21.2045	−1.13832	−0.569158	−	0.822228i	$-0.692731\pi$
$347$	−21.2045	−1.13832	−0.569158	+	0.822228i	$0.692731\pi$
$348$	6.14251	0.329273
$349$	−3.55610	−0.190354	−0.0951769	−	0.995460i	$-0.530342\pi$
$349$	−3.55610	−0.190354	−0.0951769	+	0.995460i	$0.530342\pi$
$350$	1.55514	0.0831256
$351$	−1.28207	−0.0684319
$352$	−10.0399	−0.535131
$353$	−15.4845	−0.824156	−0.412078	−	0.911149i	$-0.635197\pi$
$353$	−15.4845	−0.824156	−0.412078	+	0.911149i	$0.635197\pi$
$354$	−0.799745	−0.0425060
$355$	−2.13009	−0.113053
$356$	−24.3908	−1.29271
$357$	3.85945	0.204264
$358$	−7.26220	−0.383819
$359$	14.4272	0.761436	0.380718	−	0.924691i	$-0.375677\pi$
$359$	14.4272	0.761436	0.380718	+	0.924691i	$0.375677\pi$
$360$	−1.70454	−0.0898372
$361$	11.0386	0.580979
$362$	−10.0217	−0.526731
$363$	−5.70606	−0.299490
$364$	2.35078	0.123214
$365$	−11.9599	−0.626009
$366$	−0.0119003	−0.000622037 0
$367$	37.0573	1.93438	0.967188	−	0.254063i	$-0.0817671\pi$
$367$	37.0573	1.93438	0.967188	+	0.254063i	$0.0817671\pi$
$368$	15.6146	0.813969
$369$	4.53932	0.236308
$370$	2.11946	0.110185
$371$	−11.3199	−0.587698
$372$	0.480109	0.0248925
$373$	29.5070	1.52782	0.763908	−	0.645325i	$-0.223278\pi$
$373$	29.5070	1.52782	0.763908	+	0.645325i	$0.223278\pi$
$374$	−3.62262	−0.187321
$375$	9.60447	0.495973
$376$	0.769262	0.0396717
$377$	4.29496	0.221202
$378$	−0.407951	−0.0209827
$379$	20.2256	1.03892	0.519460	−	0.854495i	$-0.326133\pi$
$379$	20.2256	1.03892	0.519460	+	0.854495i	$0.326133\pi$
$380$	−10.9530	−0.561878
$381$	1.00000	0.0512316
$382$	−9.44154	−0.483071
$383$	−1.33594	−0.0682635	−0.0341317	−	0.999417i	$-0.510867\pi$
$383$	−1.33594	−0.0682635	−0.0341317	+	0.999417i	$0.510867\pi$
$384$	10.4724	0.534419
$385$	−2.50775	−0.127807
$386$	−1.99612	−0.101600
$387$	3.17008	0.161144
$388$	4.47914	0.227394
$389$	−31.0104	−1.57229	−0.786144	−	0.618044i	$-0.787925\pi$
$389$	−31.0104	−1.57229	−0.786144	+	0.618044i	$0.787925\pi$
$390$	−0.570054	−0.0288658
$391$	19.8946	1.00611
$392$	1.56391	0.0789894
$393$	13.6779	0.689957
$394$	−9.75865	−0.491634
$395$	−1.42863	−0.0718823
$396$	−4.21880	−0.212002
$397$	−1.70559	−0.0856012	−0.0428006	−	0.999084i	$-0.513628\pi$
$397$	−1.70559	−0.0856012	−0.0428006	+	0.999084i	$0.513628\pi$
$398$	5.22372	0.261842
$399$	−5.48075	−0.274381
$400$	−11.5473	−0.577367
$401$	31.1528	1.55570	0.777849	−	0.628451i	$-0.216311\pi$
$401$	31.1528	1.55570	0.777849	+	0.628451i	$0.216311\pi$
$402$	−5.61770	−0.280186
$403$	0.335701	0.0167225
$404$	−29.7780	−1.48151
$405$	−1.08992	−0.0541586
$406$	1.36664	0.0678253
$407$	10.9676	0.543643
$408$	6.03583	0.298818
$409$	28.7531	1.42175	0.710875	−	0.703318i	$-0.248299\pi$
$409$	28.7531	1.42175	0.710875	+	0.703318i	$0.248299\pi$
$410$	2.01834	0.0996787
$411$	−21.0777	−1.03969
$412$	−30.7316	−1.51404
$413$	1.96040	0.0964647
$414$	−2.10290	−0.103352
$415$	10.5544	0.518094
$416$	5.59441	0.274288
$417$	10.4381	0.511156
$418$	5.14443	0.251622
$419$	−10.0450	−0.490730	−0.245365	−	0.969431i	$-0.578908\pi$
$419$	−10.0450	−0.490730	−0.245365	+	0.969431i	$0.578908\pi$
$420$	1.99845	0.0975146
$421$	−24.2888	−1.18376	−0.591882	−	0.806025i	$-0.701615\pi$
$421$	−24.2888	−1.18376	−0.591882	+	0.806025i	$0.701615\pi$
$422$	1.62329	0.0790203
$423$	0.491884	0.0239162
$424$	−17.7033	−0.859747
$425$	−14.7125	−0.713660
$426$	−0.797278	−0.0386283
$427$	0.0291708	0.00141167
$428$	12.8979	0.623442
$429$	−2.94986	−0.142421
$430$	1.40953	0.0679735
$431$	8.94786	0.431003	0.215502	−	0.976503i	$-0.430861\pi$
$431$	8.94786	0.431003	0.215502	+	0.976503i	$0.430861\pi$
$432$	3.02915	0.145740
$433$	−12.7200	−0.611282	−0.305641	−	0.952147i	$-0.598871\pi$
$433$	−12.7200	−0.611282	−0.305641	+	0.952147i	$0.598871\pi$
$434$	0.106819	0.00512748
$435$	3.65125	0.175064
$436$	−15.8571	−0.759417
$437$	−28.2521	−1.35148
$438$	−4.47651	−0.213896
$439$	20.2200	0.965048	0.482524	−	0.875883i	$-0.339720\pi$
$439$	20.2200	0.965048	0.482524	+	0.875883i	$0.339720\pi$
$440$	−3.92190	−0.186969
$441$	1.00000	0.0476190
$442$	2.01858	0.0960140
$443$	−8.70900	−0.413777	−0.206889	−	0.978364i	$-0.566334\pi$
$443$	−8.70900	−0.413777	−0.206889	+	0.978364i	$0.566334\pi$
$444$	−8.74019	−0.414791
$445$	−14.4985	−0.687295
$446$	−0.470298	−0.0222693
$447$	0.369201	0.0174626
$448$	−4.27818	−0.202125
$449$	−2.31692	−0.109342	−0.0546711	−	0.998504i	$-0.517411\pi$
$449$	−2.31692	−0.109342	−0.0546711	+	0.998504i	$0.517411\pi$
$450$	1.55514	0.0733099
$451$	10.4443	0.491804
$452$	16.6245	0.781951
$453$	10.3324	0.485460
$454$	6.61739	0.310570
$455$	1.39736	0.0655092
$456$	−8.57140	−0.401393
$457$	−2.94767	−0.137886	−0.0689430	−	0.997621i	$-0.521963\pi$
$457$	−2.94767	−0.137886	−0.0689430	+	0.997621i	$0.521963\pi$
$458$	6.89557	0.322209
$459$	3.85945	0.180144
$460$	10.3016	0.480314
$461$	14.1185	0.657564	0.328782	−	0.944406i	$-0.393362\pi$
$461$	14.1185	0.657564	0.328782	+	0.944406i	$0.393362\pi$
$462$	−0.938637	−0.0436693
$463$	−37.5227	−1.74383	−0.871913	−	0.489661i	$-0.837121\pi$
$463$	−37.5227	−1.74383	−0.871913	+	0.489661i	$0.837121\pi$
$464$	−10.1477	−0.471096
$465$	0.285388	0.0132346
$466$	2.84683	0.131877
$467$	30.4306	1.40816	0.704081	−	0.710120i	$-0.251359\pi$
$467$	30.4306	1.40816	0.704081	+	0.710120i	$0.251359\pi$
$468$	2.35078	0.108665
$469$	13.7705	0.635864
$470$	0.218709	0.0100883
$471$	19.4698	0.897120
$472$	3.06588	0.141119
$473$	7.29390	0.335374
$474$	−0.534729	−0.0245609
$475$	20.8930	0.958637
$476$	−7.07659	−0.324355
$477$	−11.3199	−0.518301
$478$	11.1633	0.510597
$479$	25.2836	1.15524	0.577619	−	0.816306i	$-0.303982\pi$
$479$	25.2836	1.15524	0.577619	+	0.816306i	$0.303982\pi$
$480$	4.75595	0.217078
$481$	−6.11131	−0.278652
$482$	10.2403	0.466434
$483$	5.15478	0.234551
$484$	10.4625	0.475568
$485$	2.66251	0.120898
$486$	−0.407951	−0.0185050
$487$	−23.6931	−1.07364	−0.536819	−	0.843697i	$-0.680374\pi$
$487$	−23.6931	−1.07364	−0.536819	+	0.843697i	$0.680374\pi$
$488$	0.0456206	0.00206515
$489$	13.8845	0.627880
$490$	0.444635	0.0200865
$491$	29.3480	1.32445	0.662227	−	0.749303i	$-0.269611\pi$
$491$	29.3480	1.32445	0.662227	+	0.749303i	$0.269611\pi$
$492$	−8.32319	−0.375238
$493$	−12.9292	−0.582302
$494$	−2.86656	−0.128972
$495$	−2.50775	−0.112715
$496$	−0.793162	−0.0356140
$497$	1.95435	0.0876645
$498$	3.95044	0.177023
$499$	23.3986	1.04746	0.523732	−	0.851883i	$-0.324539\pi$
$499$	23.3986	1.04746	0.523732	+	0.851883i	$0.324539\pi$
$500$	−17.6105	−0.787566
$501$	−8.27086	−0.369515
$502$	−2.87643	−0.128381
$503$	−15.4011	−0.686701	−0.343351	−	0.939207i	$-0.611562\pi$
$503$	−15.4011	−0.686701	−0.343351	+	0.939207i	$0.611562\pi$
$504$	1.56391	0.0696621
$505$	−17.7008	−0.787675
$506$	−4.83847	−0.215096
$507$	−11.3563	−0.504351
$508$	−1.83358	−0.0813518
$509$	−9.83148	−0.435773	−0.217886	−	0.975974i	$-0.569916\pi$
$509$	−9.83148	−0.435773	−0.217886	+	0.975974i	$0.569916\pi$
$510$	1.71604	0.0759877
$511$	10.9732	0.485424
$512$	−22.6926	−1.00288
$513$	−5.48075	−0.241981
$514$	−0.0234313	−0.00103351
$515$	−18.2676	−0.804967
$516$	−5.81258	−0.255885
$517$	1.13175	0.0497745
$518$	−1.94460	−0.0854407
$519$	17.6707	0.775657
$520$	2.18534	0.0958337
$521$	−0.581283	−0.0254665	−0.0127332	−	0.999919i	$-0.504053\pi$
$521$	−0.581283	−0.0254665	−0.0127332	+	0.999919i	$0.504053\pi$
$522$	1.36664	0.0598163
$523$	9.39466	0.410800	0.205400	−	0.978678i	$-0.434150\pi$
$523$	9.39466	0.410800	0.205400	+	0.978678i	$0.434150\pi$
$524$	−25.0794	−1.09560
$525$	−3.81207	−0.166372
$526$	5.99320	0.261316
$527$	−1.01057	−0.0440211
$528$	6.96965	0.303315
$529$	3.57179	0.155295
$530$	−5.03321	−0.218628
$531$	1.96040	0.0850739
$532$	10.0494	0.435695
$533$	−5.81974	−0.252081
$534$	−5.42670	−0.234836
$535$	7.66680	0.331465
$536$	21.5359	0.930209
$537$	17.8016	0.768198
$538$	3.77898	0.162923
$539$	2.30086	0.0991049
$540$	1.99845	0.0859998
$541$	16.0235	0.688905	0.344452	−	0.938804i	$-0.388065\pi$
$541$	16.0235	0.688905	0.344452	+	0.938804i	$0.388065\pi$
$542$	−5.37274	−0.230779
$543$	24.5660	1.05423
$544$	−16.8410	−0.722050
$545$	−9.42584	−0.403758
$546$	0.523023	0.0223833
$547$	−21.8696	−0.935077	−0.467538	−	0.883973i	$-0.654859\pi$
$547$	−21.8696	−0.935077	−0.467538	+	0.883973i	$0.654859\pi$
$548$	38.6475	1.65094
$549$	0.0291708	0.00124498
$550$	3.57815	0.152573
$551$	18.3606	0.782188
$552$	8.06162	0.343125
$553$	1.31077	0.0557395
$554$	−6.67370	−0.283539
$555$	−5.19538	−0.220531
$556$	−19.1390	−0.811676
$557$	9.18821	0.389317	0.194658	−	0.980871i	$-0.437640\pi$
$557$	9.18821	0.389317	0.194658	+	0.980871i	$0.437640\pi$
$558$	0.106819	0.00452201
$559$	−4.06427	−0.171900
$560$	−3.30154	−0.139515
$561$	8.88003	0.374915
$562$	2.92205	0.123259
$563$	−26.1377	−1.10157	−0.550786	−	0.834647i	$-0.685672\pi$
$563$	−26.1377	−1.10157	−0.550786	+	0.834647i	$0.685672\pi$
$564$	−0.901906	−0.0379771
$565$	9.88200	0.415739
$566$	1.22363	0.0514330
$567$	1.00000	0.0419961
$568$	3.05643	0.128245
$569$	−17.4717	−0.732451	−0.366225	−	0.930526i	$-0.619350\pi$
$569$	−17.4717	−0.732451	−0.366225	+	0.930526i	$0.619350\pi$
$570$	−2.43693	−0.102072
$571$	23.0247	0.963553	0.481776	−	0.876294i	$-0.339992\pi$
$571$	23.0247	0.963553	0.481776	+	0.876294i	$0.339992\pi$
$572$	5.40880	0.226153
$573$	23.1438	0.966847
$574$	−1.85182	−0.0772935
$575$	−19.6504	−0.819478
$576$	−4.27818	−0.178258
$577$	4.55690	0.189706	0.0948531	−	0.995491i	$-0.469762\pi$
$577$	4.55690	0.189706	0.0948531	+	0.995491i	$0.469762\pi$
$578$	0.858603	0.0357132
$579$	4.89303	0.203347
$580$	−6.69485	−0.277989
$581$	−9.68361	−0.401744
$582$	0.996560	0.0413087
$583$	−26.0454	−1.07869
$584$	17.1610	0.710129
$585$	1.39736	0.0577736
$586$	3.24986	0.134250
$587$	−3.20341	−0.132219	−0.0661094	−	0.997812i	$-0.521059\pi$
$587$	−3.20341	−0.132219	−0.0661094	+	0.997812i	$0.521059\pi$
$588$	−1.83358	−0.0756154
$589$	1.43509	0.0591321
$590$	0.871660	0.0358857
$591$	23.9211	0.983984
$592$	14.4392	0.593447
$593$	−36.9825	−1.51869	−0.759344	−	0.650689i	$-0.774480\pi$
$593$	−36.9825	−1.51869	−0.759344	+	0.650689i	$0.774480\pi$
$594$	−0.938637	−0.0385127
$595$	−4.20649	−0.172449
$596$	−0.676958	−0.0277293
$597$	−12.8048	−0.524065
$598$	2.69607	0.110250
$599$	−38.3476	−1.56684	−0.783421	−	0.621491i	$-0.786527\pi$
$599$	−38.3476	−1.56684	−0.783421	+	0.621491i	$0.786527\pi$
$600$	−5.96174	−0.243387
$601$	−33.1185	−1.35093	−0.675467	−	0.737391i	$-0.736058\pi$
$601$	−33.1185	−1.35093	−0.675467	+	0.737391i	$0.736058\pi$
$602$	−1.29324	−0.0527084
$603$	13.7705	0.560779
$604$	−18.9453	−0.770873
$605$	6.21916	0.252845
$606$	−6.62530	−0.269134
$607$	−1.37747	−0.0559096	−0.0279548	−	0.999609i	$-0.508899\pi$
$607$	−1.37747	−0.0559096	−0.0279548	+	0.999609i	$0.508899\pi$
$608$	23.9156	0.969907
$609$	−3.35002	−0.135749
$610$	0.0129704	0.000525154 0
$611$	−0.630630	−0.0255126
$612$	−7.07659	−0.286054
$613$	6.71060	0.271039	0.135519	−	0.990775i	$-0.456730\pi$
$613$	6.71060	0.271039	0.135519	+	0.990775i	$0.456730\pi$
$614$	−4.01824	−0.162163
$615$	−4.94751	−0.199503
$616$	3.59834	0.144981
$617$	−20.8740	−0.840356	−0.420178	−	0.907442i	$-0.638032\pi$
$617$	−20.8740	−0.840356	−0.420178	+	0.907442i	$0.638032\pi$
$618$	−6.83746	−0.275043
$619$	10.0657	0.404576	0.202288	−	0.979326i	$-0.435162\pi$
$619$	10.0657	0.404576	0.202288	+	0.979326i	$0.435162\pi$
$620$	−0.523281	−0.0210155
$621$	5.15478	0.206854
$622$	12.9506	0.519273
$623$	13.3023	0.532946
$624$	−3.88359	−0.155468
$625$	8.59224	0.343689
$626$	5.28131	0.211084
$627$	−12.6104	−0.503612
$628$	−35.6993	−1.42456
$629$	18.3970	0.733536
$630$	0.444635	0.0177147
$631$	−45.6084	−1.81564	−0.907821	−	0.419359i	$-0.862255\pi$
$631$	−45.6084	−1.81564	−0.907821	+	0.419359i	$0.862255\pi$
$632$	2.04992	0.0815416
$633$	−3.97912	−0.158156
$634$	1.90038	0.0754736
$635$	−1.08992	−0.0432522
$636$	20.7558	0.823022
$637$	−1.28207	−0.0507975
$638$	3.14445	0.124490
$639$	1.95435	0.0773128
$640$	−11.4141	−0.451183
$641$	−36.7175	−1.45025	−0.725126	−	0.688616i	$-0.758219\pi$
$641$	−36.7175	−1.45025	−0.725126	+	0.688616i	$0.758219\pi$
$642$	2.86964	0.113256
$643$	−45.1998	−1.78250	−0.891252	−	0.453508i	$-0.850172\pi$
$643$	−45.1998	−1.78250	−0.891252	+	0.453508i	$0.850172\pi$
$644$	−9.45169	−0.372449
$645$	−3.45514	−0.136046
$646$	8.62925	0.339513
$647$	4.64930	0.182783	0.0913915	−	0.995815i	$-0.470869\pi$
$647$	4.64930	0.182783	0.0913915	+	0.995815i	$0.470869\pi$
$648$	1.56391	0.0614362
$649$	4.51059	0.177056
$650$	−1.99380	−0.0782032
$651$	−0.261843	−0.0102624
$652$	−25.4584	−0.997026
$653$	38.9603	1.52463	0.762317	−	0.647204i	$-0.224062\pi$
$653$	38.9603	1.52463	0.762317	+	0.647204i	$0.224062\pi$
$654$	−3.52803	−0.137957
$655$	−14.9078	−0.582496
$656$	13.7503	0.536859
$657$	10.9732	0.428103
$658$	−0.200664	−0.00782271
$659$	−19.9316	−0.776425	−0.388212	−	0.921570i	$-0.626907\pi$
$659$	−19.9316	−0.776425	−0.388212	+	0.921570i	$0.626907\pi$
$660$	4.59816	0.178983
$661$	−36.2288	−1.40914	−0.704569	−	0.709635i	$-0.748860\pi$
$661$	−36.2288	−1.40914	−0.704569	+	0.709635i	$0.748860\pi$
$662$	−5.72578	−0.222539
$663$	−4.94809	−0.192168
$664$	−15.1443	−0.587713
$665$	5.97359	0.231646
$666$	−1.94460	−0.0753516
$667$	−17.2686	−0.668643
$668$	15.1652	0.586761
$669$	1.15283	0.0445710
$670$	6.12286	0.236547
$671$	0.0671179	0.00259106
$672$	−4.36357	−0.168328
$673$	10.0220	0.386320	0.193160	−	0.981167i	$-0.438126\pi$
$673$	10.0220	0.386320	0.193160	+	0.981167i	$0.438126\pi$
$674$	8.07585	0.311070
$675$	−3.81207	−0.146727
$676$	20.8226	0.800870
$677$	2.27813	0.0875555	0.0437778	−	0.999041i	$-0.486061\pi$
$677$	2.27813	0.0875555	0.0437778	+	0.999041i	$0.486061\pi$
$678$	3.69877	0.142051
$679$	−2.44284	−0.0937477
$680$	−6.57858	−0.252277
$681$	−16.2210	−0.621592
$682$	0.245775	0.00941123
$683$	−34.7013	−1.32781	−0.663904	−	0.747817i	$-0.731102\pi$
$683$	−34.7013	−1.32781	−0.663904	+	0.747817i	$0.731102\pi$
$684$	10.0494	0.384247
$685$	22.9730	0.877754
$686$	−0.407951	−0.0155756
$687$	−16.9029	−0.644887
$688$	9.60266	0.366098
$689$	14.5129	0.552897
$690$	2.29200	0.0872548
$691$	25.5923	0.973576	0.486788	−	0.873520i	$-0.338168\pi$
$691$	25.5923	0.973576	0.486788	+	0.873520i	$0.338168\pi$
$692$	−32.4005	−1.23168
$693$	2.30086	0.0874023
$694$	8.65038	0.328364
$695$	−11.3767	−0.431543
$696$	−5.23913	−0.198589
$697$	17.5193	0.663590
$698$	1.45072	0.0549104
$699$	−6.97836	−0.263946
$700$	6.98972	0.264187
$701$	−34.4738	−1.30206	−0.651028	−	0.759054i	$-0.725662\pi$
$701$	−34.4738	−1.30206	−0.651028	+	0.759054i	$0.725662\pi$
$702$	0.523023	0.0197402
$703$	−26.1253	−0.985335
$704$	−9.84349	−0.370990
$705$	−0.536115	−0.0201912
$706$	6.31691	0.237740
$707$	16.2404	0.610784
$708$	−3.59453	−0.135091
$709$	−5.12099	−0.192323	−0.0961614	−	0.995366i	$-0.530656\pi$
$709$	−5.12099	−0.192323	−0.0961614	+	0.995366i	$0.530656\pi$
$710$	0.868971	0.0326119
$711$	1.31077	0.0491576
$712$	20.8037	0.779650
$713$	−1.34974	−0.0505483
$714$	−1.57447	−0.0589229
$715$	3.21512	0.120239
$716$	−32.6407	−1.21984
$717$	−27.3643	−1.02194
$718$	−5.88557	−0.219648
$719$	−9.38376	−0.349955	−0.174978	−	0.984572i	$-0.555985\pi$
$719$	−9.38376	−0.349955	−0.174978	+	0.984572i	$0.555985\pi$
$720$	−3.30154	−0.123041
$721$	16.7605	0.624193
$722$	−4.50321	−0.167592
$723$	−25.1019	−0.933548
$724$	−45.0437	−1.67404
$725$	12.7705	0.474284
$726$	2.32779	0.0863925
$727$	−17.8615	−0.662445	−0.331222	−	0.943553i	$-0.607461\pi$
$727$	−17.8615	−0.662445	−0.331222	+	0.943553i	$0.607461\pi$
$728$	−2.00505	−0.0743120
$729$	1.00000	0.0370370
$730$	4.87904	0.180582
$731$	12.2348	0.452519
$732$	−0.0534869	−0.00197693
$733$	20.4202	0.754238	0.377119	−	0.926165i	$-0.376915\pi$
$733$	20.4202	0.754238	0.377119	+	0.926165i	$0.376915\pi$
$734$	−15.1176	−0.557999
$735$	−1.08992	−0.0402024
$736$	−22.4932	−0.829112
$737$	31.6840	1.16710
$738$	−1.85182	−0.0681665
$739$	51.1576	1.88186	0.940931	−	0.338597i	$-0.109952\pi$
$739$	51.1576	1.88186	0.940931	+	0.338597i	$0.109952\pi$
$740$	9.52612	0.350187
$741$	7.02671	0.258133
$742$	4.61795	0.169530
$743$	32.3657	1.18738	0.593691	−	0.804693i	$-0.297670\pi$
$743$	32.3657	1.18738	0.593691	+	0.804693i	$0.297670\pi$
$744$	−0.409499	−0.0150130
$745$	−0.402400	−0.0147428
$746$	−12.0374	−0.440722
$747$	−9.68361	−0.354305
$748$	−16.2822	−0.595337
$749$	−7.03427	−0.257027
$750$	−3.91815	−0.143071
$751$	−50.9969	−1.86090	−0.930452	−	0.366414i	$-0.880585\pi$
$751$	−50.9969	−1.86090	−0.930452	+	0.366414i	$0.880585\pi$
$752$	1.48999	0.0543344
$753$	7.05092	0.256950
$754$	−1.75213	−0.0638090
$755$	−11.2615	−0.409849
$756$	−1.83358	−0.0666865
$757$	37.7384	1.37162	0.685812	−	0.727779i	$-0.259447\pi$
$757$	37.7384	1.37162	0.685812	+	0.727779i	$0.259447\pi$
$758$	−8.25106	−0.299692
$759$	11.8604	0.430506
$760$	9.34216	0.338876
$761$	43.9468	1.59307	0.796535	−	0.604593i	$-0.206664\pi$
$761$	43.9468	1.59307	0.796535	+	0.604593i	$0.206664\pi$
$762$	−0.407951	−0.0147785
$763$	8.64818	0.313085
$764$	−42.4359	−1.53528
$765$	−4.20649	−0.152086
$766$	0.544999	0.0196916
$767$	−2.51337	−0.0907525
$768$	4.28413	0.154590
$769$	42.1961	1.52163	0.760816	−	0.648968i	$-0.224799\pi$
$769$	42.1961	1.52163	0.760816	+	0.648968i	$0.224799\pi$
$770$	1.02304	0.0368678
$771$	0.0574366	0.00206853
$772$	−8.97174	−0.322900
$773$	−40.4493	−1.45486	−0.727430	−	0.686182i	$-0.759285\pi$
$773$	−40.4493	−1.45486	−0.727430	+	0.686182i	$0.759285\pi$
$774$	−1.29324	−0.0464845
$775$	0.998164	0.0358551
$776$	−3.82039	−0.137144
$777$	4.76674	0.171006
$778$	12.6507	0.453550
$779$	−24.8789	−0.891378
$780$	−2.56216	−0.0917401
$781$	4.49667	0.160904
$782$	−8.11603	−0.290229
$783$	−3.35002	−0.119720
$784$	3.02915	0.108184
$785$	−21.2205	−0.757393
$786$	−5.57990	−0.199029
$787$	17.1152	0.610090	0.305045	−	0.952338i	$-0.401329\pi$
$787$	17.1152	0.610090	0.305045	+	0.952338i	$0.401329\pi$
$788$	−43.8612	−1.56249
$789$	−14.6910	−0.523013
$790$	0.582812	0.0207355
$791$	−9.06671	−0.322375
$792$	3.59834	0.127861
$793$	−0.0373991	−0.00132808
$794$	0.695798	0.0246929
$795$	12.3378	0.437576
$796$	23.4785	0.832175
$797$	6.60740	0.234046	0.117023	−	0.993129i	$-0.462665\pi$
$797$	6.60740	0.234046	0.117023	+	0.993129i	$0.462665\pi$
$798$	2.23588	0.0791492
$799$	1.89840	0.0671605
$800$	16.6342	0.588109
$801$	13.3023	0.470015
$802$	−12.7088	−0.448764
$803$	25.2477	0.890970
$804$	−25.2493	−0.890475
$805$	−5.61831	−0.198019
$806$	−0.136950	−0.00482385
$807$	−9.26332	−0.326084
$808$	25.3986	0.893519
$809$	−8.40122	−0.295371	−0.147686	−	0.989034i	$-0.547182\pi$
$809$	−8.40122	−0.295371	−0.147686	+	0.989034i	$0.547182\pi$
$810$	0.444635	0.0156229
$811$	40.8644	1.43494	0.717472	−	0.696588i	$-0.245299\pi$
$811$	40.8644	1.43494	0.717472	+	0.696588i	$0.245299\pi$
$812$	6.14251	0.215560
$813$	13.1700	0.461894
$814$	−4.47424	−0.156822
$815$	−15.1331	−0.530088
$816$	11.6909	0.409262
$817$	−17.3744	−0.607854
$818$	−11.7299	−0.410125
$819$	−1.28207	−0.0447992
$820$	9.07163	0.316795
$821$	5.24790	0.183153	0.0915764	−	0.995798i	$-0.470809\pi$
$821$	5.24790	0.183153	0.0915764	+	0.995798i	$0.470809\pi$
$822$	8.59866	0.299913
$823$	−13.5425	−0.472060	−0.236030	−	0.971746i	$-0.575846\pi$
$823$	−13.5425	−0.472060	−0.236030	+	0.971746i	$0.575846\pi$
$824$	26.2119	0.913135
$825$	−8.77103	−0.305368
$826$	−0.799745	−0.0278267
$827$	−21.6919	−0.754301	−0.377150	−	0.926152i	$-0.623096\pi$
$827$	−21.6919	−0.754301	−0.377150	+	0.926152i	$0.623096\pi$
$828$	−9.45169	−0.328469
$829$	51.7300	1.79666	0.898328	−	0.439325i	$-0.144782\pi$
$829$	51.7300	1.79666	0.898328	+	0.439325i	$0.144782\pi$
$830$	−4.30567	−0.149452
$831$	16.3591	0.567490
$832$	5.48494	0.190156
$833$	3.85945	0.133722
$834$	−4.25823	−0.147450
$835$	9.01459	0.311963
$836$	23.1222	0.799697
$837$	−0.261843	−0.00905061
$838$	4.09787	0.141558
$839$	−21.3671	−0.737673	−0.368836	−	0.929494i	$-0.620244\pi$
$839$	−21.3671	−0.737673	−0.368836	+	0.929494i	$0.620244\pi$
$840$	−1.70454	−0.0588122
$841$	−17.7774	−0.613014
$842$	9.90865	0.341474
$843$	−7.16275	−0.246698
$844$	7.29601	0.251139
$845$	12.3775	0.425798
$846$	−0.200664	−0.00689899
$847$	−5.70606	−0.196062
$848$	−34.2896	−1.17751
$849$	−2.99945	−0.102941
$850$	6.00197	0.205866
$851$	24.5715	0.842301
$852$	−3.58345	−0.122767
$853$	−33.7067	−1.15410	−0.577048	−	0.816710i	$-0.695796\pi$
$853$	−33.7067	−1.15410	−0.577048	+	0.816710i	$0.695796\pi$
$854$	−0.0119003	−0.000407219 0
$855$	5.97359	0.204292
$856$	−11.0010	−0.376005
$857$	18.6766	0.637982	0.318991	−	0.947758i	$-0.396656\pi$
$857$	18.6766	0.637982	0.318991	+	0.947758i	$0.396656\pi$
$858$	1.20340	0.0410834
$859$	−37.7733	−1.28881	−0.644405	−	0.764684i	$-0.722895\pi$
$859$	−37.7733	−1.28881	−0.644405	+	0.764684i	$0.722895\pi$
$860$	6.33526	0.216031
$861$	4.53932	0.154700
$862$	−3.65029	−0.124329
$863$	−19.9811	−0.680166	−0.340083	−	0.940395i	$-0.610455\pi$
$863$	−19.9811	−0.680166	−0.340083	+	0.940395i	$0.610455\pi$
$864$	−4.36357	−0.148452
$865$	−19.2597	−0.654848
$866$	5.18912	0.176334
$867$	−2.10467	−0.0714784
$868$	0.480109	0.0162960
$869$	3.01589	0.102307
$870$	−1.48953	−0.0504999
$871$	−17.6548	−0.598211
$872$	13.5250	0.458014
$873$	−2.44284	−0.0826777
$874$	11.5255	0.389855
$875$	9.60447	0.324690
$876$	−20.1201	−0.679795
$877$	−20.6716	−0.698030	−0.349015	−	0.937117i	$-0.613484\pi$
$877$	−20.6716	−0.698030	−0.349015	+	0.937117i	$0.613484\pi$
$878$	−8.24877	−0.278382
$879$	−7.96629	−0.268696
$880$	−7.59637	−0.256074
$881$	−5.74429	−0.193530	−0.0967651	−	0.995307i	$-0.530850\pi$
$881$	−5.74429	−0.193530	−0.0967651	+	0.995307i	$0.530850\pi$
$882$	−0.407951	−0.0137364
$883$	0.269530	0.00907042	0.00453521	−	0.999990i	$-0.498556\pi$
$883$	0.269530	0.00907042	0.00453521	+	0.999990i	$0.498556\pi$
$884$	9.07270	0.305148
$885$	−2.13668	−0.0718236
$886$	3.55285	0.119360
$887$	7.13439	0.239550	0.119775	−	0.992801i	$-0.461783\pi$
$887$	7.13439	0.239550	0.119775	+	0.992801i	$0.461783\pi$
$888$	7.45476	0.250166
$889$	1.00000	0.0335389
$890$	5.91468	0.198260
$891$	2.30086	0.0770816
$892$	−2.11380	−0.0707753
$893$	−2.69589	−0.0902145
$894$	−0.150616	−0.00503735
$895$	−19.4024	−0.648551
$896$	10.4724	0.349859
$897$	−6.60880	−0.220662
$898$	0.945190	0.0315414
$899$	0.877178	0.0292555
$900$	6.98972	0.232991
$901$	−43.6884	−1.45547
$902$	−4.26077	−0.141868
$903$	3.17008	0.105494
$904$	−14.1795	−0.471604
$905$	−26.7750	−0.890033
$906$	−4.21512	−0.140038
$907$	18.4478	0.612549	0.306275	−	0.951943i	$-0.400917\pi$
$907$	18.4478	0.612549	0.306275	+	0.951943i	$0.400917\pi$
$908$	29.7425	0.987040
$909$	16.2404	0.538661
$910$	−0.570054	−0.0188971
$911$	48.1253	1.59446	0.797231	−	0.603675i	$-0.206297\pi$
$911$	48.1253	1.59446	0.797231	+	0.603675i	$0.206297\pi$
$912$	−16.6020	−0.549748
$913$	−22.2806	−0.737380
$914$	1.20250	0.0397753
$915$	−0.0317939	−0.00105107
$916$	30.9928	1.02403
$917$	13.6779	0.451683
$918$	−1.57447	−0.0519651
$919$	−44.9642	−1.48323	−0.741615	−	0.670825i	$-0.765940\pi$
$919$	−44.9642	−1.48323	−0.741615	+	0.670825i	$0.765940\pi$
$920$	−8.78654	−0.289684
$921$	9.84980	0.324562
$922$	−5.75966	−0.189684
$923$	−2.50561	−0.0824733
$924$	−4.21880	−0.138788
$925$	−18.1712	−0.597464
$926$	15.3074	0.503033
$927$	16.7605	0.550487
$928$	14.6180	0.479860
$929$	12.6354	0.414553	0.207276	−	0.978282i	$-0.433540\pi$
$929$	12.6354	0.414553	0.207276	+	0.978282i	$0.433540\pi$
$930$	−0.116424	−0.00381771
$931$	−5.48075	−0.179624
$932$	12.7954	0.419126
$933$	−31.7455	−1.03930
$934$	−12.4142	−0.406205
$935$	−9.67854	−0.316522
$936$	−2.00505	−0.0655370
$937$	46.3648	1.51467	0.757335	−	0.653026i	$-0.226501\pi$
$937$	46.3648	1.51467	0.757335	+	0.653026i	$0.226501\pi$
$938$	−5.61770	−0.183424
$939$	−12.9459	−0.422475
$940$	0.983007	0.0320622
$941$	2.85670	0.0931259	0.0465629	−	0.998915i	$-0.485173\pi$
$941$	2.85670	0.0931259	0.0465629	+	0.998915i	$0.485173\pi$
$942$	−7.94272	−0.258788
$943$	23.3992	0.761983
$944$	5.93834	0.193276
$945$	−1.08992	−0.0354552
$946$	−2.97555	−0.0967436
$947$	10.6467	0.345971	0.172985	−	0.984924i	$-0.444659\pi$
$947$	10.6467	0.345971	0.172985	+	0.984924i	$0.444659\pi$
$948$	−2.40339	−0.0780585
$949$	−14.0684	−0.456679
$950$	−8.52332	−0.276533
$951$	−4.65835	−0.151057
$952$	6.03583	0.195622
$953$	−26.1036	−0.845577	−0.422789	−	0.906228i	$-0.638949\pi$
$953$	−26.1036	−0.845577	−0.422789	+	0.906228i	$0.638949\pi$
$954$	4.61795	0.149512
$955$	−25.2249	−0.816260
$956$	50.1745	1.62276
$957$	−7.70791	−0.249161
$958$	−10.3145	−0.333246
$959$	−21.0777	−0.680634
$960$	4.66288	0.150494
$961$	−30.9314	−0.997788
$962$	2.49311	0.0803812
$963$	−7.03427	−0.226676
$964$	46.0262	1.48240
$965$	−5.33302	−0.171676
$966$	−2.10290	−0.0676597
$967$	−13.5836	−0.436818	−0.218409	−	0.975857i	$-0.570087\pi$
$967$	−13.5836	−0.436818	−0.218409	+	0.975857i	$0.570087\pi$
$968$	−8.92377	−0.286821
$969$	−21.1527	−0.679521
$970$	−1.08617	−0.0348749
$971$	−39.0472	−1.25308	−0.626542	−	0.779388i	$-0.715530\pi$
$971$	−39.0472	−1.25308	−0.626542	+	0.779388i	$0.715530\pi$
$972$	−1.83358	−0.0588120
$973$	10.4381	0.334630
$974$	9.66564	0.309707
$975$	4.88735	0.156520
$976$	0.0883629	0.00282843
$977$	13.9595	0.446604	0.223302	−	0.974749i	$-0.428316\pi$
$977$	13.9595	0.446604	0.223302	+	0.974749i	$0.428316\pi$
$978$	−5.66421	−0.181121
$979$	30.6067	0.978196
$980$	1.99845	0.0638383
$981$	8.64818	0.276115
$982$	−11.9725	−0.382059
$983$	11.1853	0.356755	0.178378	−	0.983962i	$-0.442915\pi$
$983$	11.1853	0.356755	0.178378	+	0.983962i	$0.442915\pi$
$984$	7.09910	0.226311
$985$	−26.0722	−0.830728
$986$	5.27448	0.167974
$987$	0.491884	0.0156568
$988$	−12.8840	−0.409895
$989$	16.3411	0.519616
$990$	1.02304	0.0325144
$991$	36.4779	1.15876	0.579379	−	0.815059i	$-0.303295\pi$
$991$	36.4779	1.15876	0.579379	+	0.815059i	$0.303295\pi$
$992$	1.14257	0.0362766
$993$	14.0354	0.445401
$994$	−0.797278	−0.0252881
$995$	13.9562	0.442442
$996$	17.7556	0.562609
$997$	−34.7863	−1.10169	−0.550846	−	0.834607i	$-0.685695\pi$
$997$	−34.7863	−1.10169	−0.550846	+	0.834607i	$0.685695\pi$
$998$	−9.54548	−0.302157
$999$	4.76674	0.150813

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.q.1.8	✓	19
3.2	odd	2		8001.2.a.v.1.12		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.q.1.8	✓	19	1.1	even	1	trivial
8001.2.a.v.1.12		19	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2667 = 3 \cdot 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2667.a (trivial)

\(f(q)\)	\(=\)	\(q-0.407951 q^{2} +1.00000 q^{3} -1.83358 q^{4} -1.08992 q^{5} -0.407951 q^{6} +1.00000 q^{7} +1.56391 q^{8} +1.00000 q^{9} +0.444635 q^{10} +2.30086 q^{11} -1.83358 q^{12} -1.28207 q^{13} -0.407951 q^{14} -1.08992 q^{15} +3.02915 q^{16} +3.85945 q^{17} -0.407951 q^{18} -5.48075 q^{19} +1.99845 q^{20} +1.00000 q^{21} -0.938637 q^{22} +5.15478 q^{23} +1.56391 q^{24} -3.81207 q^{25} +0.523023 q^{26} +1.00000 q^{27} -1.83358 q^{28} -3.35002 q^{29} +0.444635 q^{30} -0.261843 q^{31} -4.36357 q^{32} +2.30086 q^{33} -1.57447 q^{34} -1.08992 q^{35} -1.83358 q^{36} +4.76674 q^{37} +2.23588 q^{38} -1.28207 q^{39} -1.70454 q^{40} +4.53932 q^{41} -0.407951 q^{42} +3.17008 q^{43} -4.21880 q^{44} -1.08992 q^{45} -2.10290 q^{46} +0.491884 q^{47} +3.02915 q^{48} +1.00000 q^{49} +1.55514 q^{50} +3.85945 q^{51} +2.35078 q^{52} -11.3199 q^{53} -0.407951 q^{54} -2.50775 q^{55} +1.56391 q^{56} -5.48075 q^{57} +1.36664 q^{58} +1.96040 q^{59} +1.99845 q^{60} +0.0291708 q^{61} +0.106819 q^{62} +1.00000 q^{63} -4.27818 q^{64} +1.39736 q^{65} -0.938637 q^{66} +13.7705 q^{67} -7.07659 q^{68} +5.15478 q^{69} +0.444635 q^{70} +1.95435 q^{71} +1.56391 q^{72} +10.9732 q^{73} -1.94460 q^{74} -3.81207 q^{75} +10.0494 q^{76} +2.30086 q^{77} +0.523023 q^{78} +1.31077 q^{79} -3.30154 q^{80} +1.00000 q^{81} -1.85182 q^{82} -9.68361 q^{83} -1.83358 q^{84} -4.20649 q^{85} -1.29324 q^{86} -3.35002 q^{87} +3.59834 q^{88} +13.3023 q^{89} +0.444635 q^{90} -1.28207 q^{91} -9.45169 q^{92} -0.261843 q^{93} -0.200664 q^{94} +5.97359 q^{95} -4.36357 q^{96} -2.44284 q^{97} -0.407951 q^{98} +2.30086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 4 q^{2} + 19 q^{3} + 22 q^{4} + 5 q^{5} + 4 q^{6} + 19 q^{7} + 9 q^{8} + 19 q^{9} - 9 q^{11} + 22 q^{12} + 24 q^{13} + 4 q^{14} + 5 q^{15} + 20 q^{16} + 17 q^{17} + 4 q^{18} + 23 q^{19} + 5 q^{20}+ \cdots - 9 q^{99}+O(q^{100}) \) 19 * q + 4 * q^2 + 19 * q^3 + 22 * q^4 + 5 * q^5 + 4 * q^6 + 19 * q^7 + 9 * q^8 + 19 * q^9 - 9 * q^11 + 22 * q^12 + 24 * q^13 + 4 * q^14 + 5 * q^15 + 20 * q^16 + 17 * q^17 + 4 * q^18 + 23 * q^19 + 5 * q^20 + 19 * q^21 - 3 * q^22 - 17 * q^23 + 9 * q^24 + 38 * q^25 + 28 * q^26 + 19 * q^27 + 22 * q^28 + 2 * q^29 + 16 * q^31 + 17 * q^32 - 9 * q^33 + 29 * q^34 + 5 * q^35 + 22 * q^36 + 56 * q^37 + 2 * q^38 + 24 * q^39 - 13 * q^40 - 7 * q^41 + 4 * q^42 + 19 * q^43 - 29 * q^44 + 5 * q^45 + 10 * q^46 + 25 * q^47 + 20 * q^48 + 19 * q^49 - 9 * q^50 + 17 * q^51 + 16 * q^52 + 18 * q^53 + 4 * q^54 + 10 * q^55 + 9 * q^56 + 23 * q^57 + 31 * q^58 + 11 * q^59 + 5 * q^60 + 26 * q^61 + 26 * q^62 + 19 * q^63 + 45 * q^64 + 27 * q^65 - 3 * q^66 + 24 * q^67 + 14 * q^68 - 17 * q^69 - 32 * q^71 + 9 * q^72 + 51 * q^73 + 38 * q^75 + 12 * q^76 - 9 * q^77 + 28 * q^78 + 30 * q^79 - 30 * q^80 + 19 * q^81 - 52 * q^82 + q^83 + 22 * q^84 + 44 * q^85 - 24 * q^86 + 2 * q^87 - 30 * q^88 + 5 * q^89 + 24 * q^91 - 88 * q^92 + 16 * q^93 + 7 * q^94 - 24 * q^95 + 17 * q^96 + 5 * q^97 + 4 * q^98 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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