LMFDB - Embedded newform 2667.2.a.o.1.14

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 = [16,5,-16,19] 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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} - 13 x^{14} + 98 x^{13} + 9 x^{12} - 712 x^{11} + 565 x^{10} + 2282 x^{9} - 3082 x^{8} + \cdots + 4 $ x^16 - 5x^15 - 13x^14 + 98x^13 + 9x^12 - 712x^11 + 565x^10 + 2282x^9 - 3082x^8 - 2747x^7 + 5821x^6 - 158x^5 - 3341x^4 + 1002x^3 + 416x^2 - 148*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$2.41798$ 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)

$f(q)$	$=$	\(q+2.41798 q^{2} -1.00000 q^{3} +3.84663 q^{4} +2.86533 q^{5} -2.41798 q^{6} -1.00000 q^{7} +4.46511 q^{8} +1.00000 q^{9} +6.92831 q^{10} -5.94265 q^{11} -3.84663 q^{12} +5.81109 q^{13} -2.41798 q^{14} -2.86533 q^{15} +3.10329 q^{16} -2.46675 q^{17} +2.41798 q^{18} +4.96080 q^{19} +11.0219 q^{20} +1.00000 q^{21} -14.3692 q^{22} +5.91940 q^{23} -4.46511 q^{24} +3.21012 q^{25} +14.0511 q^{26} -1.00000 q^{27} -3.84663 q^{28} +9.12150 q^{29} -6.92831 q^{30} +1.52132 q^{31} -1.42653 q^{32} +5.94265 q^{33} -5.96456 q^{34} -2.86533 q^{35} +3.84663 q^{36} +10.9350 q^{37} +11.9951 q^{38} -5.81109 q^{39} +12.7940 q^{40} +7.45599 q^{41} +2.41798 q^{42} -6.37361 q^{43} -22.8592 q^{44} +2.86533 q^{45} +14.3130 q^{46} -3.77187 q^{47} -3.10329 q^{48} +1.00000 q^{49} +7.76200 q^{50} +2.46675 q^{51} +22.3531 q^{52} +13.0229 q^{53} -2.41798 q^{54} -17.0277 q^{55} -4.46511 q^{56} -4.96080 q^{57} +22.0556 q^{58} -12.1352 q^{59} -11.0219 q^{60} -13.1708 q^{61} +3.67852 q^{62} -1.00000 q^{63} -9.65590 q^{64} +16.6507 q^{65} +14.3692 q^{66} -2.34916 q^{67} -9.48868 q^{68} -5.91940 q^{69} -6.92831 q^{70} +10.9342 q^{71} +4.46511 q^{72} -9.61640 q^{73} +26.4406 q^{74} -3.21012 q^{75} +19.0824 q^{76} +5.94265 q^{77} -14.0511 q^{78} -12.9373 q^{79} +8.89194 q^{80} +1.00000 q^{81} +18.0284 q^{82} -2.71284 q^{83} +3.84663 q^{84} -7.06806 q^{85} -15.4113 q^{86} -9.12150 q^{87} -26.5346 q^{88} -1.78782 q^{89} +6.92831 q^{90} -5.81109 q^{91} +22.7697 q^{92} -1.52132 q^{93} -9.12031 q^{94} +14.2143 q^{95} +1.42653 q^{96} -5.89963 q^{97} +2.41798 q^{98} -5.94265 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 5 q^{2} - 16 q^{3} + 19 q^{4} - q^{5} - 5 q^{6} - 16 q^{7} + 6 q^{8} + 16 q^{9} - 12 q^{10} + 11 q^{11} - 19 q^{12} + 18 q^{13} - 5 q^{14} + q^{15} + 25 q^{16} - 5 q^{17} + 5 q^{18} - 11 q^{19}+ \cdots + 11 q^{99}+O(q^{100}) $ 16 * q + 5 * q^2 - 16 * q^3 + 19 * q^4 - q^5 - 5 * q^6 - 16 * q^7 + 6 * q^8 + 16 * q^9 - 12 * q^10 + 11 * q^11 - 19 * q^12 + 18 * q^13 - 5 * q^14 + q^15 + 25 * q^16 - 5 * q^17 + 5 * q^18 - 11 * q^19 - q^20 + 16 * q^21 + q^22 + 13 * q^23 - 6 * q^24 + 33 * q^25 + 8 * q^26 - 16 * q^27 - 19 * q^28 + 24 * q^29 + 12 * q^30 - 42 * q^31 + 42 * q^32 - 11 * q^33 + 9 * q^34 + q^35 + 19 * q^36 + 40 * q^37 + 38 * q^38 - 18 * q^39 - 61 * q^40 + 9 * q^41 + 5 * q^42 + 7 * q^43 + 3 * q^44 - q^45 + 24 * q^46 + 31 * q^47 - 25 * q^48 + 16 * q^49 + 6 * q^50 + 5 * q^51 + 52 * q^52 + 66 * q^53 - 5 * q^54 - 36 * q^55 - 6 * q^56 + 11 * q^57 + 19 * q^58 - 7 * q^59 + q^60 + 6 * q^61 + 52 * q^62 - 16 * q^63 + 10 * q^64 + 51 * q^65 - q^66 + 16 * q^67 + 14 * q^68 - 13 * q^69 + 12 * q^70 + 46 * q^71 + 6 * q^72 + 39 * q^73 + 72 * q^74 - 33 * q^75 + 24 * q^76 - 11 * q^77 - 8 * q^78 + 4 * q^79 - 2 * q^80 + 16 * q^81 - 18 * q^82 + 15 * q^83 + 19 * q^84 - 4 * q^85 + 14 * q^86 - 24 * q^87 + 58 * q^88 - q^89 - 12 * q^90 - 18 * q^91 + 26 * q^92 + 42 * q^93 + 5 * q^94 + 44 * q^95 - 42 * q^96 + 41 * q^97 + 5 * q^98 + 11 * 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 $

$2$	2.41798	1.70977	0.854885	−	0.518817i	$-0.173628\pi$
$2$	2.41798	1.70977	0.854885	+	0.518817i	$0.173628\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.84663	1.92331
$5$	2.86533	1.28141	0.640707	−	0.767785i	$-0.278641\pi$
$5$	2.86533	1.28141	0.640707	+	0.767785i	$0.278641\pi$
$6$	−2.41798	−0.987136
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	4.46511	1.57865
$9$	1.00000	0.333333
$10$	6.92831	2.19092
$11$	−5.94265	−1.79178	−0.895889	−	0.444278i	$-0.853460\pi$
$11$	−5.94265	−1.79178	−0.895889	+	0.444278i	$0.853460\pi$
$12$	−3.84663	−1.11043
$13$	5.81109	1.61171	0.805854	−	0.592115i	$-0.201707\pi$
$13$	5.81109	1.61171	0.805854	+	0.592115i	$0.201707\pi$
$14$	−2.41798	−0.646232
$15$	−2.86533	−0.739825
$16$	3.10329	0.775822
$17$	−2.46675	−0.598276	−0.299138	−	0.954210i	$-0.596699\pi$
$17$	−2.46675	−0.598276	−0.299138	+	0.954210i	$0.596699\pi$
$18$	2.41798	0.569923
$19$	4.96080	1.13809	0.569043	−	0.822308i	$-0.307314\pi$
$19$	4.96080	1.13809	0.569043	+	0.822308i	$0.307314\pi$
$20$	11.0219	2.46456
$21$	1.00000	0.218218
$22$	−14.3692	−3.06353
$23$	5.91940	1.23428	0.617140	−	0.786853i	$-0.288291\pi$
$23$	5.91940	1.23428	0.617140	+	0.786853i	$0.288291\pi$
$24$	−4.46511	−0.911436
$25$	3.21012	0.642024
$26$	14.0511	2.75565
$27$	−1.00000	−0.192450
$28$	−3.84663	−0.726944
$29$	9.12150	1.69382	0.846910	−	0.531737i	$-0.178460\pi$
$29$	9.12150	1.69382	0.846910	+	0.531737i	$0.178460\pi$
$30$	−6.92831	−1.26493
$31$	1.52132	0.273237	0.136619	−	0.990624i	$-0.456377\pi$
$31$	1.52132	0.273237	0.136619	+	0.990624i	$0.456377\pi$
$32$	−1.42653	−0.252177
$33$	5.94265	1.03448
$34$	−5.96456	−1.02291
$35$	−2.86533	−0.484329
$36$	3.84663	0.641105
$37$	10.9350	1.79770	0.898850	−	0.438256i	$-0.144404\pi$
$37$	10.9350	1.79770	0.898850	+	0.438256i	$0.144404\pi$
$38$	11.9951	1.94587
$39$	−5.81109	−0.930520
$40$	12.7940	2.02291
$41$	7.45599	1.16443	0.582215	−	0.813035i	$-0.302186\pi$
$41$	7.45599	1.16443	0.582215	+	0.813035i	$0.302186\pi$
$42$	2.41798	0.373102
$43$	−6.37361	−0.971967	−0.485983	−	0.873968i	$-0.661538\pi$
$43$	−6.37361	−0.971967	−0.485983	+	0.873968i	$0.661538\pi$
$44$	−22.8592	−3.44615
$45$	2.86533	0.427138
$46$	14.3130	2.11034
$47$	−3.77187	−0.550184	−0.275092	−	0.961418i	$-0.588708\pi$
$47$	−3.77187	−0.550184	−0.275092	+	0.961418i	$0.588708\pi$
$48$	−3.10329	−0.447921
$49$	1.00000	0.142857
$50$	7.76200	1.09771
$51$	2.46675	0.345415
$52$	22.3531	3.09982
$53$	13.0229	1.78883	0.894414	−	0.447240i	$-0.147593\pi$
$53$	13.0229	1.78883	0.894414	+	0.447240i	$0.147593\pi$
$54$	−2.41798	−0.329045
$55$	−17.0277	−2.29601
$56$	−4.46511	−0.596675
$57$	−4.96080	−0.657074
$58$	22.0556	2.89604
$59$	−12.1352	−1.57986	−0.789931	−	0.613195i	$-0.789884\pi$
$59$	−12.1352	−1.57986	−0.789931	+	0.613195i	$0.789884\pi$
$60$	−11.0219	−1.42292
$61$	−13.1708	−1.68635	−0.843175	−	0.537639i	$-0.819316\pi$
$61$	−13.1708	−1.68635	−0.843175	+	0.537639i	$0.819316\pi$
$62$	3.67852	0.467173
$63$	−1.00000	−0.125988
$64$	−9.65590	−1.20699
$65$	16.6507	2.06527
$66$	14.3692	1.76873
$67$	−2.34916	−0.286995	−0.143498	−	0.989651i	$-0.545835\pi$
$67$	−2.34916	−0.286995	−0.143498	+	0.989651i	$0.545835\pi$
$68$	−9.48868	−1.15067
$69$	−5.91940	−0.712612
$70$	−6.92831	−0.828092
$71$	10.9342	1.29765	0.648826	−	0.760937i	$-0.275260\pi$
$71$	10.9342	1.29765	0.648826	+	0.760937i	$0.275260\pi$
$72$	4.46511	0.526218
$73$	−9.61640	−1.12551	−0.562757	−	0.826622i	$-0.690259\pi$
$73$	−9.61640	−1.12551	−0.562757	+	0.826622i	$0.690259\pi$
$74$	26.4406	3.07366
$75$	−3.21012	−0.370673
$76$	19.0824	2.18890
$77$	5.94265	0.677228
$78$	−14.0511	−1.59097
$79$	−12.9373	−1.45556	−0.727778	−	0.685813i	$-0.759447\pi$
$79$	−12.9373	−1.45556	−0.727778	+	0.685813i	$0.759447\pi$
$80$	8.89194	0.994149
$81$	1.00000	0.111111
$82$	18.0284	1.99091
$83$	−2.71284	−0.297772	−0.148886	−	0.988854i	$-0.547569\pi$
$83$	−2.71284	−0.297772	−0.148886	+	0.988854i	$0.547569\pi$
$84$	3.84663	0.419701
$85$	−7.06806	−0.766639
$86$	−15.4113	−1.66184
$87$	−9.12150	−0.977927
$88$	−26.5346	−2.82860
$89$	−1.78782	−0.189509	−0.0947543	−	0.995501i	$-0.530207\pi$
$89$	−1.78782	−0.189509	−0.0947543	+	0.995501i	$0.530207\pi$
$90$	6.92831	0.730308
$91$	−5.81109	−0.609168
$92$	22.7697	2.37391
$93$	−1.52132	−0.157754
$94$	−9.12031	−0.940688
$95$	14.2143	1.45836
$96$	1.42653	0.145595
$97$	−5.89963	−0.599017	−0.299508	−	0.954094i	$-0.596823\pi$
$97$	−5.89963	−0.599017	−0.299508	+	0.954094i	$0.596823\pi$
$98$	2.41798	0.244253
$99$	−5.94265	−0.597259
$100$	12.3481	1.23481
$101$	−0.292411	−0.0290960	−0.0145480	−	0.999894i	$-0.504631\pi$
$101$	−0.292411	−0.0290960	−0.0145480	+	0.999894i	$0.504631\pi$
$102$	5.96456	0.590579
$103$	−0.384246	−0.0378608	−0.0189304	−	0.999821i	$-0.506026\pi$
$103$	−0.384246	−0.0378608	−0.0189304	+	0.999821i	$0.506026\pi$
$104$	25.9472	2.54433
$105$	2.86533	0.279628
$106$	31.4890	3.05848
$107$	−6.48261	−0.626697	−0.313349	−	0.949638i	$-0.601451\pi$
$107$	−6.48261	−0.626697	−0.313349	+	0.949638i	$0.601451\pi$
$108$	−3.84663	−0.370142
$109$	−7.32894	−0.701985	−0.350993	−	0.936378i	$-0.614156\pi$
$109$	−7.32894	−0.701985	−0.350993	+	0.936378i	$0.614156\pi$
$110$	−41.1726	−3.92565
$111$	−10.9350	−1.03790
$112$	−3.10329	−0.293233
$113$	−8.75155	−0.823277	−0.411638	−	0.911347i	$-0.635043\pi$
$113$	−8.75155	−0.823277	−0.411638	+	0.911347i	$0.635043\pi$
$114$	−11.9951	−1.12345
$115$	16.9610	1.58162
$116$	35.0870	3.25775
$117$	5.81109	0.537236
$118$	−29.3426	−2.70120
$119$	2.46675	0.226127
$120$	−12.7940	−1.16793
$121$	24.3151	2.21047
$122$	−31.8468	−2.88327
$123$	−7.45599	−0.672284
$124$	5.85195	0.525521
$125$	−5.12860	−0.458716
$126$	−2.41798	−0.215411
$127$	1.00000	0.0887357
$127$	1.00000	0.0887357
$128$	−20.4947	−1.81149
$129$	6.37361	0.561165
$130$	40.2611	3.53113
$131$	6.98949	0.610675	0.305337	−	0.952244i	$-0.401231\pi$
$131$	6.98949	0.610675	0.305337	+	0.952244i	$0.401231\pi$
$132$	22.8592	1.98964
$133$	−4.96080	−0.430156
$134$	−5.68022	−0.490696
$135$	−2.86533	−0.246608
$136$	−11.0143	−0.944470
$137$	−13.3983	−1.14470	−0.572349	−	0.820010i	$-0.693968\pi$
$137$	−13.3983	−1.14470	−0.572349	+	0.820010i	$0.693968\pi$
$138$	−14.3130	−1.21840
$139$	−4.56630	−0.387308	−0.193654	−	0.981070i	$-0.562034\pi$
$139$	−4.56630	−0.387308	−0.193654	+	0.981070i	$0.562034\pi$
$140$	−11.0219	−0.931517
$141$	3.77187	0.317649
$142$	26.4387	2.21869
$143$	−34.5333	−2.88782
$144$	3.10329	0.258607
$145$	26.1361	2.17049
$146$	−23.2523	−1.92437
$147$	−1.00000	−0.0824786
$148$	42.0628	3.45754
$149$	−4.52922	−0.371048	−0.185524	−	0.982640i	$-0.559398\pi$
$149$	−4.52922	−0.371048	−0.185524	+	0.982640i	$0.559398\pi$
$150$	−7.76200	−0.633765
$151$	8.08303	0.657788	0.328894	−	0.944367i	$-0.393324\pi$
$151$	8.08303	0.657788	0.328894	+	0.944367i	$0.393324\pi$
$152$	22.1505	1.79664
$153$	−2.46675	−0.199425
$154$	14.3692	1.15790
$155$	4.35908	0.350130
$156$	−22.3531	−1.78968
$157$	−22.0319	−1.75834	−0.879168	−	0.476512i	$-0.841901\pi$
$157$	−22.0319	−1.75834	−0.879168	+	0.476512i	$0.841901\pi$
$158$	−31.2821	−2.48867
$159$	−13.0229	−1.03278
$160$	−4.08748	−0.323144
$161$	−5.91940	−0.466514
$162$	2.41798	0.189974
$163$	8.72198	0.683158	0.341579	−	0.939853i	$-0.389038\pi$
$163$	8.72198	0.683158	0.341579	+	0.939853i	$0.389038\pi$
$164$	28.6804	2.23957
$165$	17.0277	1.32560
$166$	−6.55958	−0.509122
$167$	2.92573	0.226400	0.113200	−	0.993572i	$-0.463890\pi$
$167$	2.92573	0.226400	0.113200	+	0.993572i	$0.463890\pi$
$168$	4.46511	0.344491
$169$	20.7688	1.59760
$170$	−17.0904	−1.31078
$171$	4.96080	0.379362
$172$	−24.5169	−1.86940
$173$	18.6048	1.41450	0.707248	−	0.706966i	$-0.249936\pi$
$173$	18.6048	1.41450	0.707248	+	0.706966i	$0.249936\pi$
$174$	−22.0556	−1.67203
$175$	−3.21012	−0.242662
$176$	−18.4418	−1.39010
$177$	12.1352	0.912134
$178$	−4.32292	−0.324016
$179$	4.73174	0.353667	0.176833	−	0.984241i	$-0.443415\pi$
$179$	4.73174	0.353667	0.176833	+	0.984241i	$0.443415\pi$
$180$	11.0219	0.821521
$181$	−10.1816	−0.756790	−0.378395	−	0.925644i	$-0.623524\pi$
$181$	−10.1816	−0.756790	−0.378395	+	0.925644i	$0.623524\pi$
$182$	−14.0511	−1.04154
$183$	13.1708	0.973615
$184$	26.4308	1.94850
$185$	31.3324	2.30360
$186$	−3.67852	−0.269722
$187$	14.6591	1.07198
$188$	−14.5090	−1.05818
$189$	1.00000	0.0727393
$190$	34.3700	2.49346
$191$	19.9897	1.44641	0.723203	−	0.690635i	$-0.242669\pi$
$191$	19.9897	1.44641	0.723203	+	0.690635i	$0.242669\pi$
$192$	9.65590	0.696854
$193$	−17.4744	−1.25783	−0.628916	−	0.777473i	$-0.716501\pi$
$193$	−17.4744	−1.25783	−0.628916	+	0.777473i	$0.716501\pi$
$194$	−14.2652	−1.02418
$195$	−16.6507	−1.19238
$196$	3.84663	0.274759
$197$	−0.0269163	−0.00191771	−0.000958855	−	1.00000i	$-0.500305\pi$
$197$	−0.0269163	−0.00191771	−0.000958855		1.00000i	$0.500305\pi$
$198$	−14.3692	−1.02118
$199$	−11.1642	−0.791411	−0.395706	−	0.918377i	$-0.629500\pi$
$199$	−11.1642	−0.791411	−0.395706	+	0.918377i	$0.629500\pi$
$200$	14.3335	1.01353
$201$	2.34916	0.165697
$202$	−0.707043	−0.0497474
$203$	−9.12150	−0.640204
$204$	9.48868	0.664341
$205$	21.3639	1.49212
$206$	−0.929098	−0.0647333
$207$	5.91940	0.411427
$208$	18.0335	1.25040
$209$	−29.4803	−2.03920
$210$	6.92831	0.478099
$211$	7.93667	0.546383	0.273191	−	0.961960i	$-0.411921\pi$
$211$	7.93667	0.546383	0.273191	+	0.961960i	$0.411921\pi$
$212$	50.0941	3.44048
$213$	−10.9342	−0.749199
$214$	−15.6748	−1.07151
$215$	−18.2625	−1.24549
$216$	−4.46511	−0.303812
$217$	−1.52132	−0.103274
$218$	−17.7212	−1.20023
$219$	9.61640	0.649816
$220$	−65.4991	−4.41595
$221$	−14.3345	−0.964245
$222$	−26.4406	−1.77458
$223$	16.2035	1.08507	0.542534	−	0.840034i	$-0.317465\pi$
$223$	16.2035	1.08507	0.542534	+	0.840034i	$0.317465\pi$
$224$	1.42653	0.0953141
$225$	3.21012	0.214008
$226$	−21.1611	−1.40761
$227$	1.13795	0.0755283	0.0377641	−	0.999287i	$-0.487976\pi$
$227$	1.13795	0.0755283	0.0377641	+	0.999287i	$0.487976\pi$
$228$	−19.0824	−1.26376
$229$	−16.1025	−1.06409	−0.532043	−	0.846717i	$-0.678576\pi$
$229$	−16.1025	−1.06409	−0.532043	+	0.846717i	$0.678576\pi$
$230$	41.0114	2.70421
$231$	−5.94265	−0.390998
$232$	40.7285	2.67396
$233$	−11.7016	−0.766599	−0.383300	−	0.923624i	$-0.625212\pi$
$233$	−11.7016	−0.766599	−0.383300	+	0.923624i	$0.625212\pi$
$234$	14.0511	0.918550
$235$	−10.8077	−0.705014
$236$	−46.6794	−3.03857
$237$	12.9373	0.840366
$238$	5.96456	0.386625
$239$	21.5712	1.39532	0.697661	−	0.716428i	$-0.254224\pi$
$239$	21.5712	1.39532	0.697661	+	0.716428i	$0.254224\pi$
$240$	−8.89194	−0.573972
$241$	1.24666	0.0803044	0.0401522	−	0.999194i	$-0.487216\pi$
$241$	1.24666	0.0803044	0.0401522	+	0.999194i	$0.487216\pi$
$242$	58.7935	3.77939
$243$	−1.00000	−0.0641500
$244$	−50.6632	−3.24338
$245$	2.86533	0.183059
$246$	−18.0284	−1.14945
$247$	28.8277	1.83426
$248$	6.79286	0.431347
$249$	2.71284	0.171919
$250$	−12.4009	−0.784299
$251$	−17.4247	−1.09983	−0.549917	−	0.835219i	$-0.685341\pi$
$251$	−17.4247	−1.09983	−0.549917	+	0.835219i	$0.685341\pi$
$252$	−3.84663	−0.242315
$253$	−35.1769	−2.21156
$254$	2.41798	0.151718
$255$	7.06806	0.442619
$256$	−30.2440	−1.89025
$257$	7.74905	0.483372	0.241686	−	0.970354i	$-0.422300\pi$
$257$	7.74905	0.483372	0.241686	+	0.970354i	$0.422300\pi$
$258$	15.4113	0.959463
$259$	−10.9350	−0.679467
$260$	64.0490	3.97215
$261$	9.12150	0.564607
$262$	16.9004	1.04411
$263$	−23.7131	−1.46221	−0.731107	−	0.682262i	$-0.760996\pi$
$263$	−23.7131	−1.46221	−0.731107	+	0.682262i	$0.760996\pi$
$264$	26.5346	1.63309
$265$	37.3148	2.29223
$266$	−11.9951	−0.735468
$267$	1.78782	0.109413
$268$	−9.03634	−0.551982
$269$	−3.63039	−0.221349	−0.110674	−	0.993857i	$-0.535301\pi$
$269$	−3.63039	−0.221349	−0.110674	+	0.993857i	$0.535301\pi$
$270$	−6.92831	−0.421644
$271$	13.2306	0.803699	0.401850	−	0.915706i	$-0.368367\pi$
$271$	13.2306	0.803699	0.401850	+	0.915706i	$0.368367\pi$
$272$	−7.65504	−0.464155
$273$	5.81109	0.351703
$274$	−32.3969	−1.95717
$275$	−19.0766	−1.15036
$276$	−22.7697	−1.37058
$277$	5.09376	0.306055	0.153027	−	0.988222i	$-0.451098\pi$
$277$	5.09376	0.306055	0.153027	+	0.988222i	$0.451098\pi$
$278$	−11.0412	−0.662208
$279$	1.52132	0.0910790
$280$	−12.7940	−0.764588
$281$	9.47263	0.565090	0.282545	−	0.959254i	$-0.408821\pi$
$281$	9.47263	0.565090	0.282545	+	0.959254i	$0.408821\pi$
$282$	9.12031	0.543106
$283$	29.4196	1.74881	0.874406	−	0.485195i	$-0.161252\pi$
$283$	29.4196	1.74881	0.874406	+	0.485195i	$0.161252\pi$
$284$	42.0598	2.49579
$285$	−14.2143	−0.841985
$286$	−83.5009	−4.93751
$287$	−7.45599	−0.440113
$288$	−1.42653	−0.0840591
$289$	−10.9151	−0.642066
$290$	63.1966	3.71103
$291$	5.89963	0.345843
$292$	−36.9907	−2.16472
$293$	−12.0828	−0.705885	−0.352943	−	0.935645i	$-0.614819\pi$
$293$	−12.0828	−0.705885	−0.352943	+	0.935645i	$0.614819\pi$
$294$	−2.41798	−0.141019
$295$	−34.7712	−2.02446
$296$	48.8259	2.83795
$297$	5.94265	0.344828
$298$	−10.9516	−0.634406
$299$	34.3982	1.98930
$300$	−12.3481	−0.712920
$301$	6.37361	0.367369
$302$	19.5446	1.12467
$303$	0.292411	0.0167986
$304$	15.3948	0.882952
$305$	−37.7387	−2.16091
$306$	−5.96456	−0.340971
$307$	−14.4483	−0.824607	−0.412304	−	0.911046i	$-0.635276\pi$
$307$	−14.4483	−0.824607	−0.412304	+	0.911046i	$0.635276\pi$
$308$	22.8592	1.30252
$309$	0.384246	0.0218590
$310$	10.5402	0.598642
$311$	−8.00701	−0.454036	−0.227018	−	0.973891i	$-0.572898\pi$
$311$	−8.00701	−0.454036	−0.227018	+	0.973891i	$0.572898\pi$
$312$	−25.9472	−1.46897
$313$	15.2196	0.860263	0.430131	−	0.902766i	$-0.358467\pi$
$313$	15.2196	0.860263	0.430131	+	0.902766i	$0.358467\pi$
$314$	−53.2726	−3.00635
$315$	−2.86533	−0.161443
$316$	−49.7648	−2.79949
$317$	−19.1583	−1.07604	−0.538019	−	0.842933i	$-0.680827\pi$
$317$	−19.1583	−1.07604	−0.538019	+	0.842933i	$0.680827\pi$
$318$	−31.4890	−1.76582
$319$	−54.2059	−3.03495
$320$	−27.6673	−1.54665
$321$	6.48261	0.361824
$322$	−14.3130	−0.797632
$323$	−12.2371	−0.680889
$324$	3.84663	0.213702
$325$	18.6543	1.03475
$326$	21.0896	1.16804
$327$	7.32894	0.405292
$328$	33.2918	1.83823
$329$	3.77187	0.207950
$330$	41.1726	2.26648
$331$	−34.7472	−1.90988	−0.954940	−	0.296799i	$-0.904081\pi$
$331$	−34.7472	−1.90988	−0.954940	+	0.296799i	$0.904081\pi$
$332$	−10.4353	−0.572710
$333$	10.9350	0.599234
$334$	7.07437	0.387092
$335$	−6.73112	−0.367760
$336$	3.10329	0.169298
$337$	−15.1407	−0.824765	−0.412382	−	0.911011i	$-0.635303\pi$
$337$	−15.1407	−0.824765	−0.412382	+	0.911011i	$0.635303\pi$
$338$	50.2186	2.73153
$339$	8.75155	0.475319
$340$	−27.1882	−1.47449
$341$	−9.04068	−0.489580
$342$	11.9951	0.648622
$343$	−1.00000	−0.0539949
$344$	−28.4589	−1.53440
$345$	−16.9610	−0.913151
$346$	44.9860	2.41846
$347$	9.52937	0.511564	0.255782	−	0.966735i	$-0.417667\pi$
$347$	9.52937	0.511564	0.255782	+	0.966735i	$0.417667\pi$
$348$	−35.0870	−1.88086
$349$	−17.8724	−0.956689	−0.478345	−	0.878172i	$-0.658763\pi$
$349$	−17.8724	−0.956689	−0.478345	+	0.878172i	$0.658763\pi$
$350$	−7.76200	−0.414897
$351$	−5.81109	−0.310173
$352$	8.47738	0.451846
$353$	29.9672	1.59499	0.797495	−	0.603325i	$-0.206158\pi$
$353$	29.9672	1.59499	0.797495	+	0.603325i	$0.206158\pi$
$354$	29.3426	1.55954
$355$	31.3301	1.66283
$356$	−6.87708	−0.364485
$357$	−2.46675	−0.130554
$358$	11.4412	0.604689
$359$	16.0299	0.846027	0.423013	−	0.906123i	$-0.360972\pi$
$359$	16.0299	0.846027	0.423013	+	0.906123i	$0.360972\pi$
$360$	12.7940	0.674304
$361$	5.60956	0.295240
$362$	−24.6188	−1.29394
$363$	−24.3151	−1.27621
$364$	−22.3531	−1.17162
$365$	−27.5542	−1.44225
$366$	31.8468	1.66466
$367$	−30.8788	−1.61186	−0.805929	−	0.592012i	$-0.798334\pi$
$367$	−30.8788	−1.61186	−0.805929	+	0.592012i	$0.798334\pi$
$368$	18.3696	0.957581
$369$	7.45599	0.388144
$370$	75.7610	3.93863
$371$	−13.0229	−0.676113
$372$	−5.85195	−0.303410
$373$	5.78052	0.299304	0.149652	−	0.988739i	$-0.452185\pi$
$373$	5.78052	0.299304	0.149652	+	0.988739i	$0.452185\pi$
$374$	35.4453	1.83283
$375$	5.12860	0.264840
$376$	−16.8418	−0.868550
$377$	53.0059	2.72994
$378$	2.41798	0.124367
$379$	13.7475	0.706159	0.353080	−	0.935593i	$-0.385134\pi$
$379$	13.7475	0.706159	0.353080	+	0.935593i	$0.385134\pi$
$380$	54.6773	2.80488
$381$	−1.00000	−0.0512316
$382$	48.3348	2.47302
$383$	0.702358	0.0358888	0.0179444	−	0.999839i	$-0.494288\pi$
$383$	0.702358	0.0358888	0.0179444	+	0.999839i	$0.494288\pi$
$384$	20.4947	1.04587
$385$	17.0277	0.867810
$386$	−42.2527	−2.15060
$387$	−6.37361	−0.323989
$388$	−22.6937	−1.15210
$389$	34.6654	1.75761	0.878803	−	0.477184i	$-0.158342\pi$
$389$	34.6654	1.75761	0.878803	+	0.477184i	$0.158342\pi$
$390$	−40.2611	−2.03870
$391$	−14.6017	−0.738440
$392$	4.46511	0.225522
$393$	−6.98949	−0.352573
$394$	−0.0650832	−0.00327884
$395$	−37.0695	−1.86517
$396$	−22.8592	−1.14872
$397$	−16.7668	−0.841501	−0.420751	−	0.907176i	$-0.638233\pi$
$397$	−16.7668	−0.841501	−0.420751	+	0.907176i	$0.638233\pi$
$398$	−26.9949	−1.35313
$399$	4.96080	0.248351
$400$	9.96192	0.498096
$401$	−4.08639	−0.204065	−0.102032	−	0.994781i	$-0.532535\pi$
$401$	−4.08639	−0.204065	−0.102032	+	0.994781i	$0.532535\pi$
$402$	5.68022	0.283304
$403$	8.84053	0.440378
$404$	−1.12480	−0.0559607
$405$	2.86533	0.142379
$406$	−22.0556	−1.09460
$407$	−64.9829	−3.22108
$408$	11.0143	0.545290
$409$	28.8726	1.42766	0.713830	−	0.700319i	$-0.246959\pi$
$409$	28.8726	1.42766	0.713830	+	0.700319i	$0.246959\pi$
$410$	51.6575	2.55118
$411$	13.3983	0.660892
$412$	−1.47805	−0.0728183
$413$	12.1352	0.597132
$414$	14.3130	0.703445
$415$	−7.77317	−0.381570
$416$	−8.28970	−0.406436
$417$	4.56630	0.223613
$418$	−71.2829	−3.48656
$419$	−12.8305	−0.626811	−0.313406	−	0.949619i	$-0.601470\pi$
$419$	−12.8305	−0.626811	−0.313406	+	0.949619i	$0.601470\pi$
$420$	11.0219	0.537812
$421$	−4.40335	−0.214606	−0.107303	−	0.994226i	$-0.534222\pi$
$421$	−4.40335	−0.214606	−0.107303	+	0.994226i	$0.534222\pi$
$422$	19.1907	0.934189
$423$	−3.77187	−0.183395
$424$	58.1485	2.82394
$425$	−7.91857	−0.384107
$426$	−26.4387	−1.28096
$427$	13.1708	0.637380
$428$	−24.9362	−1.20534
$429$	34.5333	1.66728
$430$	−44.1584	−2.12951
$431$	12.8114	0.617103	0.308552	−	0.951208i	$-0.400156\pi$
$431$	12.8114	0.617103	0.308552	+	0.951208i	$0.400156\pi$
$432$	−3.10329	−0.149307
$433$	−10.6612	−0.512344	−0.256172	−	0.966631i	$-0.582461\pi$
$433$	−10.6612	−0.512344	−0.256172	+	0.966631i	$0.582461\pi$
$434$	−3.67852	−0.176575
$435$	−26.1361	−1.25313
$436$	−28.1917	−1.35014
$437$	29.3650	1.40472
$438$	23.2523	1.11104
$439$	7.15197	0.341345	0.170672	−	0.985328i	$-0.445406\pi$
$439$	7.15197	0.341345	0.170672	+	0.985328i	$0.445406\pi$
$440$	−76.0304	−3.62461
$441$	1.00000	0.0476190
$442$	−34.6606	−1.64864
$443$	39.4432	1.87400	0.937000	−	0.349329i	$-0.113590\pi$
$443$	39.4432	1.87400	0.937000	+	0.349329i	$0.113590\pi$
$444$	−42.0628	−1.99621
$445$	−5.12270	−0.242839
$446$	39.1798	1.85522
$447$	4.52922	0.214225
$448$	9.65590	0.456198
$449$	−21.2990	−1.00516	−0.502582	−	0.864530i	$-0.667616\pi$
$449$	−21.2990	−1.00516	−0.502582	+	0.864530i	$0.667616\pi$
$450$	7.76200	0.365904
$451$	−44.3084	−2.08640
$452$	−33.6640	−1.58342
$453$	−8.08303	−0.379774
$454$	2.75154	0.129136
$455$	−16.6507	−0.780597
$456$	−22.1505	−1.03729
$457$	28.1983	1.31906	0.659530	−	0.751678i	$-0.270755\pi$
$457$	28.1983	1.31906	0.659530	+	0.751678i	$0.270755\pi$
$458$	−38.9356	−1.81934
$459$	2.46675	0.115138
$460$	65.2428	3.04196
$461$	33.2624	1.54919	0.774593	−	0.632461i	$-0.217955\pi$
$461$	33.2624	1.54919	0.774593	+	0.632461i	$0.217955\pi$
$462$	−14.3692	−0.668517
$463$	24.3142	1.12998	0.564988	−	0.825099i	$-0.308881\pi$
$463$	24.3142	1.12998	0.564988	+	0.825099i	$0.308881\pi$
$464$	28.3066	1.31410
$465$	−4.35908	−0.202148
$466$	−28.2943	−1.31071
$467$	−4.18602	−0.193706	−0.0968529	−	0.995299i	$-0.530878\pi$
$467$	−4.18602	−0.193706	−0.0968529	+	0.995299i	$0.530878\pi$
$468$	22.3531	1.03327
$469$	2.34916	0.108474
$470$	−26.1327	−1.20541
$471$	22.0319	1.01518
$472$	−54.1848	−2.49406
$473$	37.8762	1.74155
$474$	31.2821	1.43683
$475$	15.9248	0.730678
$476$	9.48868	0.434913
$477$	13.0229	0.596276
$478$	52.1586	2.38568
$479$	−24.6994	−1.12854	−0.564271	−	0.825589i	$-0.690843\pi$
$479$	−24.6994	−1.12854	−0.564271	+	0.825589i	$0.690843\pi$
$480$	4.08748	0.186567
$481$	63.5442	2.89737
$482$	3.01440	0.137302
$483$	5.91940	0.269342
$484$	93.5313	4.25142
$485$	−16.9044	−0.767589
$486$	−2.41798	−0.109682
$487$	−3.19849	−0.144937	−0.0724686	−	0.997371i	$-0.523088\pi$
$487$	−3.19849	−0.144937	−0.0724686	+	0.997371i	$0.523088\pi$
$488$	−58.8091	−2.66216
$489$	−8.72198	−0.394422
$490$	6.92831	0.312989
$491$	14.4712	0.653075	0.326538	−	0.945184i	$-0.394118\pi$
$491$	14.4712	0.653075	0.326538	+	0.945184i	$0.394118\pi$
$492$	−28.6804	−1.29301
$493$	−22.5005	−1.01337
$494$	69.7048	3.13617
$495$	−17.0277	−0.765337
$496$	4.72109	0.211983
$497$	−10.9342	−0.490466
$498$	6.55958	0.293942
$499$	9.59004	0.429309	0.214655	−	0.976690i	$-0.431137\pi$
$499$	9.59004	0.429309	0.214655	+	0.976690i	$0.431137\pi$
$500$	−19.7278	−0.882255
$501$	−2.92573	−0.130712
$502$	−42.1325	−1.88046
$503$	−3.29941	−0.147114	−0.0735568	−	0.997291i	$-0.523435\pi$
$503$	−3.29941	−0.147114	−0.0735568	+	0.997291i	$0.523435\pi$
$504$	−4.46511	−0.198892
$505$	−0.837854	−0.0372840
$506$	−85.0571	−3.78125
$507$	−20.7688	−0.922375
$508$	3.84663	0.170666
$509$	−25.4914	−1.12988	−0.564942	−	0.825131i	$-0.691102\pi$
$509$	−25.4914	−1.12988	−0.564942	+	0.825131i	$0.691102\pi$
$510$	17.0904	0.756777
$511$	9.61640	0.425404
$512$	−32.1400	−1.42040
$513$	−4.96080	−0.219025
$514$	18.7370	0.826455
$515$	−1.10099	−0.0485154
$516$	24.5169	1.07930
$517$	22.4149	0.985807
$518$	−26.4406	−1.16173
$519$	−18.6048	−0.816660
$520$	74.3472	3.26034
$521$	14.4182	0.631672	0.315836	−	0.948814i	$-0.397715\pi$
$521$	14.4182	0.631672	0.315836	+	0.948814i	$0.397715\pi$
$522$	22.0556	0.965347
$523$	−15.8407	−0.692667	−0.346333	−	0.938112i	$-0.612573\pi$
$523$	−15.8407	−0.692667	−0.346333	+	0.938112i	$0.612573\pi$
$524$	26.8860	1.17452
$525$	3.21012	0.140101
$526$	−57.3379	−2.50005
$527$	−3.75272	−0.163471
$528$	18.4418	0.802575
$529$	12.0393	0.523447
$530$	90.2264	3.91919
$531$	−12.1352	−0.526621
$532$	−19.0824	−0.827325
$533$	43.3275	1.87672
$534$	4.32292	0.187071
$535$	−18.5748	−0.803059
$536$	−10.4892	−0.453066
$537$	−4.73174	−0.204190
$538$	−8.77820	−0.378455
$539$	−5.94265	−0.255968
$540$	−11.0219	−0.474305
$541$	−29.1139	−1.25170	−0.625851	−	0.779943i	$-0.715248\pi$
$541$	−29.1139	−1.25170	−0.625851	+	0.779943i	$0.715248\pi$
$542$	31.9912	1.37414
$543$	10.1816	0.436933
$544$	3.51890	0.150872
$545$	−20.9998	−0.899535
$546$	14.0511	0.601332
$547$	−33.0139	−1.41157	−0.705786	−	0.708425i	$-0.749406\pi$
$547$	−33.0139	−1.41157	−0.705786	+	0.708425i	$0.749406\pi$
$548$	−51.5384	−2.20161
$549$	−13.1708	−0.562117
$550$	−46.1269	−1.96686
$551$	45.2500	1.92771
$552$	−26.4308	−1.12497
$553$	12.9373	0.550149
$554$	12.3166	0.523283
$555$	−31.3324	−1.32998
$556$	−17.5649	−0.744916
$557$	−21.0505	−0.891940	−0.445970	−	0.895048i	$-0.647141\pi$
$557$	−21.0505	−0.891940	−0.445970	+	0.895048i	$0.647141\pi$
$558$	3.67852	0.155724
$559$	−37.0376	−1.56653
$560$	−8.89194	−0.375753
$561$	−14.6591	−0.618906
$562$	22.9046	0.966174
$563$	−18.6899	−0.787686	−0.393843	−	0.919178i	$-0.628855\pi$
$563$	−18.6899	−0.787686	−0.393843	+	0.919178i	$0.628855\pi$
$564$	14.5090	0.610938
$565$	−25.0761	−1.05496
$566$	71.1359	2.99007
$567$	−1.00000	−0.0419961
$568$	48.8224	2.04854
$569$	−15.5497	−0.651877	−0.325938	−	0.945391i	$-0.605680\pi$
$569$	−15.5497	−0.651877	−0.325938	+	0.945391i	$0.605680\pi$
$570$	−34.3700	−1.43960
$571$	10.8384	0.453571	0.226786	−	0.973945i	$-0.427178\pi$
$571$	10.8384	0.453571	0.226786	+	0.973945i	$0.427178\pi$
$572$	−132.837	−5.55419
$573$	−19.9897	−0.835083
$574$	−18.0284	−0.752493
$575$	19.0020	0.792437
$576$	−9.65590	−0.402329
$577$	26.5432	1.10501	0.552505	−	0.833510i	$-0.313672\pi$
$577$	26.5432	1.10501	0.552505	+	0.833510i	$0.313672\pi$
$578$	−26.3926	−1.09779
$579$	17.4744	0.726210
$580$	100.536	4.17452
$581$	2.71284	0.112547
$582$	14.2652	0.591311
$583$	−77.3904	−3.20518
$584$	−42.9383	−1.77680
$585$	16.6507	0.688422
$586$	−29.2160	−1.20690
$587$	22.6806	0.936128	0.468064	−	0.883695i	$-0.344952\pi$
$587$	22.6806	0.936128	0.468064	+	0.883695i	$0.344952\pi$
$588$	−3.84663	−0.158632
$589$	7.54697	0.310967
$590$	−84.0762	−3.46136
$591$	0.0269163	0.00110719
$592$	33.9344	1.39470
$593$	−31.6754	−1.30075	−0.650376	−	0.759612i	$-0.725389\pi$
$593$	−31.6754	−1.30075	−0.650376	+	0.759612i	$0.725389\pi$
$594$	14.3692	0.589576
$595$	7.06806	0.289762
$596$	−17.4222	−0.713641
$597$	11.1642	0.456922
$598$	83.1741	3.40124
$599$	−13.2647	−0.541980	−0.270990	−	0.962582i	$-0.587351\pi$
$599$	−13.2647	−0.541980	−0.270990	+	0.962582i	$0.587351\pi$
$600$	−14.3335	−0.585164
$601$	−28.7624	−1.17324	−0.586622	−	0.809861i	$-0.699542\pi$
$601$	−28.7624	−1.17324	−0.586622	+	0.809861i	$0.699542\pi$
$602$	15.4113	0.628116
$603$	−2.34916	−0.0956651
$604$	31.0924	1.26513
$605$	69.6709	2.83253
$606$	0.707043	0.0287217
$607$	13.7938	0.559873	0.279937	−	0.960018i	$-0.409687\pi$
$607$	13.7938	0.559873	0.279937	+	0.960018i	$0.409687\pi$
$608$	−7.07673	−0.286999
$609$	9.12150	0.369622
$610$	−91.2515	−3.69467
$611$	−21.9187	−0.886735
$612$	−9.48868	−0.383557
$613$	−2.67053	−0.107862	−0.0539308	−	0.998545i	$-0.517175\pi$
$613$	−2.67053	−0.107862	−0.0539308	+	0.998545i	$0.517175\pi$
$614$	−34.9357	−1.40989
$615$	−21.3639	−0.861475
$616$	26.5346	1.06911
$617$	3.24977	0.130831	0.0654155	−	0.997858i	$-0.479163\pi$
$617$	3.24977	0.130831	0.0654155	+	0.997858i	$0.479163\pi$
$618$	0.929098	0.0373738
$619$	−39.3418	−1.58128	−0.790640	−	0.612282i	$-0.790252\pi$
$619$	−39.3418	−1.58128	−0.790640	+	0.612282i	$0.790252\pi$
$620$	16.7678	0.673410
$621$	−5.91940	−0.237537
$622$	−19.3608	−0.776297
$623$	1.78782	0.0716275
$624$	−18.0335	−0.721917
$625$	−30.7457	−1.22983
$626$	36.8007	1.47085
$627$	29.4803	1.17733
$628$	−84.7484	−3.38183
$629$	−26.9739	−1.07552
$630$	−6.92831	−0.276031
$631$	11.7580	0.468077	0.234039	−	0.972227i	$-0.424806\pi$
$631$	11.7580	0.468077	0.234039	+	0.972227i	$0.424806\pi$
$632$	−57.7663	−2.29782
$633$	−7.93667	−0.315454
$634$	−46.3244	−1.83978
$635$	2.86533	0.113707
$636$	−50.0941	−1.98636
$637$	5.81109	0.230244
$638$	−131.069	−5.18906
$639$	10.9342	0.432551
$640$	−58.7241	−2.32127
$641$	−26.1532	−1.03299	−0.516494	−	0.856291i	$-0.672763\pi$
$641$	−26.1532	−1.03299	−0.516494	+	0.856291i	$0.672763\pi$
$642$	15.6748	0.618636
$643$	−42.2728	−1.66708	−0.833539	−	0.552461i	$-0.813689\pi$
$643$	−42.2728	−1.66708	−0.833539	+	0.552461i	$0.813689\pi$
$644$	−22.7697	−0.897253
$645$	18.2625	0.719085
$646$	−29.5890	−1.16416
$647$	−18.8312	−0.740331	−0.370165	−	0.928966i	$-0.620699\pi$
$647$	−18.8312	−0.740331	−0.370165	+	0.928966i	$0.620699\pi$
$648$	4.46511	0.175406
$649$	72.1150	2.83076
$650$	45.1057	1.76919
$651$	1.52132	0.0596252
$652$	33.5502	1.31393
$653$	−42.9175	−1.67949	−0.839746	−	0.542979i	$-0.817296\pi$
$653$	−42.9175	−1.67949	−0.839746	+	0.542979i	$0.817296\pi$
$654$	17.7212	0.692955
$655$	20.0272	0.782527
$656$	23.1381	0.903391
$657$	−9.61640	−0.375171
$658$	9.12031	0.355547
$659$	36.1838	1.40952	0.704760	−	0.709446i	$-0.251055\pi$
$659$	36.1838	1.40952	0.704760	+	0.709446i	$0.251055\pi$
$660$	65.4991	2.54955
$661$	−10.4284	−0.405620	−0.202810	−	0.979218i	$-0.565007\pi$
$661$	−10.4284	−0.405620	−0.202810	+	0.979218i	$0.565007\pi$
$662$	−84.0181	−3.26546
$663$	14.3345	0.556707
$664$	−12.1131	−0.470080
$665$	−14.2143	−0.551208
$666$	26.4406	1.02455
$667$	53.9938	2.09065
$668$	11.2542	0.435439
$669$	−16.2035	−0.626464
$670$	−16.2757	−0.628785
$671$	78.2696	3.02156
$672$	−1.42653	−0.0550296
$673$	1.54766	0.0596579	0.0298290	−	0.999555i	$-0.490504\pi$
$673$	1.54766	0.0596579	0.0298290	+	0.999555i	$0.490504\pi$
$674$	−36.6098	−1.41016
$675$	−3.21012	−0.123558
$676$	79.8899	3.07269
$677$	−13.1548	−0.505580	−0.252790	−	0.967521i	$-0.581348\pi$
$677$	−13.1548	−0.505580	−0.252790	+	0.967521i	$0.581348\pi$
$678$	21.1611	0.812686
$679$	5.89963	0.226407
$680$	−31.5597	−1.21026
$681$	−1.13795	−0.0436063
$682$	−21.8602	−0.837070
$683$	6.32001	0.241828	0.120914	−	0.992663i	$-0.461417\pi$
$683$	6.32001	0.241828	0.120914	+	0.992663i	$0.461417\pi$
$684$	19.0824	0.729632
$685$	−38.3907	−1.46683
$686$	−2.41798	−0.0923189
$687$	16.1025	0.614350
$688$	−19.7791	−0.754073
$689$	75.6771	2.88307
$690$	−41.0114	−1.56128
$691$	−12.5225	−0.476379	−0.238190	−	0.971219i	$-0.576554\pi$
$691$	−12.5225	−0.476379	−0.238190	+	0.971219i	$0.576554\pi$
$692$	71.5657	2.72052
$693$	5.94265	0.225743
$694$	23.0418	0.874656
$695$	−13.0840	−0.496303
$696$	−40.7285	−1.54381
$697$	−18.3921	−0.696650
$698$	−43.2152	−1.63572
$699$	11.7016	0.442596
$700$	−12.3481	−0.466715
$701$	32.2849	1.21939	0.609693	−	0.792638i	$-0.291293\pi$
$701$	32.2849	1.21939	0.609693	+	0.792638i	$0.291293\pi$
$702$	−14.0511	−0.530325
$703$	54.2463	2.04594
$704$	57.3816	2.16265
$705$	10.8077	0.407040
$706$	72.4600	2.72707
$707$	0.292411	0.0109972
$708$	46.6794	1.75432
$709$	24.5194	0.920846	0.460423	−	0.887700i	$-0.347698\pi$
$709$	24.5194	0.920846	0.460423	+	0.887700i	$0.347698\pi$
$710$	75.7556	2.84306
$711$	−12.9373	−0.485185
$712$	−7.98281	−0.299169
$713$	9.00530	0.337251
$714$	−5.96456	−0.223218
$715$	−98.9494	−3.70050
$716$	18.2012	0.680212
$717$	−21.5712	−0.805590
$718$	38.7600	1.44651
$719$	−4.97860	−0.185670	−0.0928352	−	0.995681i	$-0.529593\pi$
$719$	−4.97860	−0.185670	−0.0928352	+	0.995681i	$0.529593\pi$
$720$	8.89194	0.331383
$721$	0.384246	0.0143101
$722$	13.5638	0.504793
$723$	−1.24666	−0.0463638
$724$	−39.1647	−1.45554
$725$	29.2811	1.08747
$726$	−58.7935	−2.18203
$727$	−5.39878	−0.200230	−0.100115	−	0.994976i	$-0.531921\pi$
$727$	−5.39878	−0.200230	−0.100115	+	0.994976i	$0.531921\pi$
$728$	−25.9472	−0.961666
$729$	1.00000	0.0370370
$730$	−66.6254	−2.46592
$731$	15.7221	0.581504
$732$	50.6632	1.87257
$733$	46.1590	1.70492	0.852460	−	0.522792i	$-0.175110\pi$
$733$	46.1590	1.70492	0.852460	+	0.522792i	$0.175110\pi$
$734$	−74.6642	−2.75591
$735$	−2.86533	−0.105689
$736$	−8.44420	−0.311257
$737$	13.9602	0.514232
$738$	18.0284	0.663636
$739$	−7.62697	−0.280563	−0.140281	−	0.990112i	$-0.544801\pi$
$739$	−7.62697	−0.280563	−0.140281	+	0.990112i	$0.544801\pi$
$740$	120.524	4.43055
$741$	−28.8277	−1.05901
$742$	−31.4890	−1.15600
$743$	29.1648	1.06995	0.534977	−	0.844867i	$-0.320320\pi$
$743$	29.1648	1.06995	0.534977	+	0.844867i	$0.320320\pi$
$744$	−6.79286	−0.249038
$745$	−12.9777	−0.475466
$746$	13.9772	0.511741
$747$	−2.71284	−0.0992575
$748$	56.3880	2.06175
$749$	6.48261	0.236869
$750$	12.4009	0.452815
$751$	−16.1853	−0.590609	−0.295304	−	0.955403i	$-0.595421\pi$
$751$	−16.1853	−0.590609	−0.295304	+	0.955403i	$0.595421\pi$
$752$	−11.7052	−0.426844
$753$	17.4247	0.634990
$754$	128.167	4.66757
$755$	23.1606	0.842899
$756$	3.84663	0.139900
$757$	29.7380	1.08085	0.540424	−	0.841393i	$-0.318264\pi$
$757$	29.7380	1.08085	0.540424	+	0.841393i	$0.318264\pi$
$758$	33.2411	1.20737
$759$	35.1769	1.27684
$760$	63.4686	2.30225
$761$	30.9215	1.12090	0.560451	−	0.828188i	$-0.310628\pi$
$761$	30.9215	1.12090	0.560451	+	0.828188i	$0.310628\pi$
$762$	−2.41798	−0.0875942
$763$	7.32894	0.265326
$764$	76.8931	2.78189
$765$	−7.06806	−0.255546
$766$	1.69829	0.0613617
$767$	−70.5185	−2.54628
$768$	30.2440	1.09134
$769$	8.67272	0.312746	0.156373	−	0.987698i	$-0.450020\pi$
$769$	8.67272	0.312746	0.156373	+	0.987698i	$0.450020\pi$
$770$	41.1726	1.48376
$771$	−7.74905	−0.279075
$772$	−67.2174	−2.41921
$773$	46.3828	1.66827	0.834137	−	0.551557i	$-0.185966\pi$
$773$	46.3828	1.66827	0.834137	+	0.551557i	$0.185966\pi$
$774$	−15.4113	−0.553946
$775$	4.88362	0.175425
$776$	−26.3425	−0.945641
$777$	10.9350	0.392290
$778$	83.8203	3.00510
$779$	36.9877	1.32522
$780$	−64.0490	−2.29332
$781$	−64.9782	−2.32510
$782$	−35.3066	−1.26256
$783$	−9.12150	−0.325976
$784$	3.10329	0.110832
$785$	−63.1286	−2.25316
$786$	−16.9004	−0.602819
$787$	3.41934	0.121886	0.0609431	−	0.998141i	$-0.480589\pi$
$787$	3.41934	0.121886	0.0609431	+	0.998141i	$0.480589\pi$
$788$	−0.103537	−0.00368836
$789$	23.7131	0.844210
$790$	−89.6334	−3.18901
$791$	8.75155	0.311169
$792$	−26.5346	−0.942866
$793$	−76.5368	−2.71790
$794$	−40.5418	−1.43877
$795$	−37.3148	−1.32342
$796$	−42.9446	−1.52213
$797$	25.0547	0.887482	0.443741	−	0.896155i	$-0.353651\pi$
$797$	25.0547	0.887482	0.443741	+	0.896155i	$0.353651\pi$
$798$	11.9951	0.424623
$799$	9.30427	0.329161
$800$	−4.57933	−0.161904
$801$	−1.78782	−0.0631696
$802$	−9.88081	−0.348904
$803$	57.1469	2.01667
$804$	9.03634	0.318687
$805$	−16.9610	−0.597798
$806$	21.3762	0.752946
$807$	3.63039	0.127796
$808$	−1.30565	−0.0459325
$809$	31.7389	1.11588	0.557941	−	0.829881i	$-0.311592\pi$
$809$	31.7389	1.11588	0.557941	+	0.829881i	$0.311592\pi$
$810$	6.92831	0.243436
$811$	11.1326	0.390920	0.195460	−	0.980712i	$-0.437380\pi$
$811$	11.1326	0.390920	0.195460	+	0.980712i	$0.437380\pi$
$812$	−35.0870	−1.23131
$813$	−13.2306	−0.464016
$814$	−157.127	−5.50731
$815$	24.9914	0.875409
$816$	7.65504	0.267980
$817$	−31.6182	−1.10618
$818$	69.8135	2.44097
$819$	−5.81109	−0.203056
$820$	82.1789	2.86981
$821$	30.4868	1.06400	0.531998	−	0.846746i	$-0.321441\pi$
$821$	30.4868	1.06400	0.531998	+	0.846746i	$0.321441\pi$
$822$	32.3969	1.12997
$823$	51.0907	1.78091	0.890454	−	0.455073i	$-0.150387\pi$
$823$	51.0907	1.78091	0.890454	+	0.455073i	$0.150387\pi$
$824$	−1.71570	−0.0597692
$825$	19.0766	0.664163
$826$	29.3426	1.02096
$827$	−33.8562	−1.17730	−0.588648	−	0.808389i	$-0.700340\pi$
$827$	−33.8562	−1.17730	−0.588648	+	0.808389i	$0.700340\pi$
$828$	22.7697	0.791303
$829$	−31.5681	−1.09640	−0.548202	−	0.836346i	$-0.684687\pi$
$829$	−31.5681	−1.09640	−0.548202	+	0.836346i	$0.684687\pi$
$830$	−18.7954	−0.652397
$831$	−5.09376	−0.176701
$832$	−56.1113	−1.94531
$833$	−2.46675	−0.0854679
$834$	11.0412	0.382326
$835$	8.38320	0.290113
$836$	−113.400	−3.92202
$837$	−1.52132	−0.0525845
$838$	−31.0239	−1.07170
$839$	−38.0449	−1.31346	−0.656728	−	0.754128i	$-0.728060\pi$
$839$	−38.0449	−1.31346	−0.656728	+	0.754128i	$0.728060\pi$
$840$	12.7940	0.441435
$841$	54.2017	1.86902
$842$	−10.6472	−0.366927
$843$	−9.47263	−0.326255
$844$	30.5294	1.05087
$845$	59.5095	2.04719
$846$	−9.12031	−0.313563
$847$	−24.3151	−0.835478
$848$	40.4137	1.38781
$849$	−29.4196	−1.00968
$850$	−19.1469	−0.656735
$851$	64.7286	2.21887
$852$	−42.0598	−1.44095
$853$	−49.6692	−1.70064	−0.850320	−	0.526266i	$-0.823592\pi$
$853$	−49.6692	−1.70064	−0.850320	+	0.526266i	$0.823592\pi$
$854$	31.8468	1.08977
$855$	14.2143	0.486120
$856$	−28.9455	−0.989338
$857$	−51.1798	−1.74827	−0.874135	−	0.485683i	$-0.838571\pi$
$857$	−51.1798	−1.74827	−0.874135	+	0.485683i	$0.838571\pi$
$858$	83.5009	2.85067
$859$	22.3730	0.763357	0.381678	−	0.924295i	$-0.375346\pi$
$859$	22.3730	0.763357	0.381678	+	0.924295i	$0.375346\pi$
$860$	−70.2490	−2.39547
$861$	7.45599	0.254100
$862$	30.9777	1.05510
$863$	−36.7882	−1.25229	−0.626143	−	0.779708i	$-0.715367\pi$
$863$	−36.7882	−1.25229	−0.626143	+	0.779708i	$0.715367\pi$
$864$	1.42653	0.0485315
$865$	53.3089	1.81256
$866$	−25.7786	−0.875991
$867$	10.9151	0.370697
$868$	−5.85195	−0.198628
$869$	76.8817	2.60803
$870$	−63.1966	−2.14256
$871$	−13.6512	−0.462553
$872$	−32.7245	−1.10819
$873$	−5.89963	−0.199672
$874$	71.0039	2.40174
$875$	5.12860	0.173378
$876$	36.9907	1.24980
$877$	8.02579	0.271012	0.135506	−	0.990777i	$-0.456734\pi$
$877$	8.02579	0.271012	0.135506	+	0.990777i	$0.456734\pi$
$878$	17.2933	0.583621
$879$	12.0828	0.407543
$880$	−52.8417	−1.78129
$881$	42.4618	1.43058	0.715288	−	0.698830i	$-0.246296\pi$
$881$	42.4618	1.43058	0.715288	+	0.698830i	$0.246296\pi$
$882$	2.41798	0.0814176
$883$	54.1159	1.82114	0.910572	−	0.413350i	$-0.135641\pi$
$883$	54.1159	1.82114	0.910572	+	0.413350i	$0.135641\pi$
$884$	−55.1396	−1.85455
$885$	34.7712	1.16882
$886$	95.3727	3.20411
$887$	8.66097	0.290807	0.145403	−	0.989372i	$-0.453552\pi$
$887$	8.66097	0.290807	0.145403	+	0.989372i	$0.453552\pi$
$888$	−48.8259	−1.63849
$889$	−1.00000	−0.0335389
$890$	−12.3866	−0.415199
$891$	−5.94265	−0.199086
$892$	62.3289	2.08693
$893$	−18.7115	−0.626157
$894$	10.9516	0.366275
$895$	13.5580	0.453194
$896$	20.4947	0.684680
$897$	−34.3982	−1.14852
$898$	−51.5007	−1.71860
$899$	13.8767	0.462814
$900$	12.3481	0.411604
$901$	−32.1242	−1.07021
$902$	−107.137	−3.56727
$903$	−6.37361	−0.212100
$904$	−39.0766	−1.29967
$905$	−29.1736	−0.969762
$906$	−19.5446	−0.649326
$907$	25.1110	0.833798	0.416899	−	0.908953i	$-0.363117\pi$
$907$	25.1110	0.833798	0.416899	+	0.908953i	$0.363117\pi$
$908$	4.37726	0.145265
$909$	−0.292411	−0.00969865
$910$	−40.2611	−1.33464
$911$	10.3906	0.344255	0.172128	−	0.985075i	$-0.444936\pi$
$911$	10.3906	0.344255	0.172128	+	0.985075i	$0.444936\pi$
$912$	−15.3948	−0.509773
$913$	16.1214	0.533542
$914$	68.1829	2.25529
$915$	37.7387	1.24760
$916$	−61.9405	−2.04657
$917$	−6.98949	−0.230813
$918$	5.96456	0.196860
$919$	35.9077	1.18448	0.592242	−	0.805760i	$-0.298243\pi$
$919$	35.9077	1.18448	0.592242	+	0.805760i	$0.298243\pi$
$920$	75.7328	2.49684
$921$	14.4483	0.476087
$922$	80.4279	2.64875
$923$	63.5397	2.09143
$924$	−22.8592	−0.752012
$925$	35.1026	1.15417
$926$	58.7912	1.93200
$927$	−0.384246	−0.0126203
$928$	−13.0121	−0.427143
$929$	13.2349	0.434222	0.217111	−	0.976147i	$-0.430337\pi$
$929$	13.2349	0.434222	0.217111	+	0.976147i	$0.430337\pi$
$930$	−10.5402	−0.345626
$931$	4.96080	0.162584
$932$	−45.0118	−1.47441
$933$	8.00701	0.262138
$934$	−10.1217	−0.331192
$935$	42.0031	1.37365
$936$	25.9472	0.848109
$937$	−58.2756	−1.90378	−0.951890	−	0.306441i	$-0.900862\pi$
$937$	−58.2756	−1.90378	−0.951890	+	0.306441i	$0.900862\pi$
$938$	5.68022	0.185466
$939$	−15.2196	−0.496673
$940$	−41.5730	−1.35596
$941$	1.11789	0.0364421	0.0182210	−	0.999834i	$-0.494200\pi$
$941$	1.11789	0.0364421	0.0182210	+	0.999834i	$0.494200\pi$
$942$	53.2726	1.73572
$943$	44.1350	1.43723
$944$	−37.6589	−1.22569
$945$	2.86533	0.0932092
$946$	91.5838	2.97765
$947$	14.8068	0.481157	0.240579	−	0.970630i	$-0.422663\pi$
$947$	14.8068	0.481157	0.240579	+	0.970630i	$0.422663\pi$
$948$	49.7648	1.61629
$949$	−55.8818	−1.81400
$950$	38.5058	1.24929
$951$	19.1583	0.621251
$952$	11.0143	0.356976
$953$	43.8606	1.42079	0.710393	−	0.703806i	$-0.248517\pi$
$953$	43.8606	1.42079	0.710393	+	0.703806i	$0.248517\pi$
$954$	31.4890	1.01949
$955$	57.2772	1.85345
$956$	82.9762	2.68364
$957$	54.2059	1.75223
$958$	−59.7226	−1.92955
$959$	13.3983	0.432655
$960$	27.6673	0.892959
$961$	−28.6856	−0.925341
$962$	153.649	4.95383
$963$	−6.48261	−0.208899
$964$	4.79544	0.154451
$965$	−50.0698	−1.61181
$966$	14.3130	0.460513
$967$	24.8577	0.799371	0.399686	−	0.916652i	$-0.369119\pi$
$967$	24.8577	0.799371	0.399686	+	0.916652i	$0.369119\pi$
$968$	108.570	3.48956
$969$	12.2371	0.393112
$970$	−40.8745	−1.31240
$971$	−10.5828	−0.339617	−0.169808	−	0.985477i	$-0.554315\pi$
$971$	−10.5828	−0.339617	−0.169808	+	0.985477i	$0.554315\pi$
$972$	−3.84663	−0.123381
$973$	4.56630	0.146389
$974$	−7.73388	−0.247809
$975$	−18.6543	−0.597416
$976$	−40.8728	−1.30831
$977$	27.6129	0.883416	0.441708	−	0.897159i	$-0.354373\pi$
$977$	27.6129	0.883416	0.441708	+	0.897159i	$0.354373\pi$
$978$	−21.0896	−0.674370
$979$	10.6244	0.339557
$980$	11.0219	0.352080
$981$	−7.32894	−0.233995
$982$	34.9910	1.11661
$983$	−3.15604	−0.100662	−0.0503310	−	0.998733i	$-0.516028\pi$
$983$	−3.15604	−0.100662	−0.0503310	+	0.998733i	$0.516028\pi$
$984$	−33.2918	−1.06130
$985$	−0.0771242	−0.00245738
$986$	−54.4057	−1.73263
$987$	−3.77187	−0.120060
$988$	110.889	3.52786
$989$	−37.7279	−1.19968
$990$	−41.1726	−1.30855
$991$	−24.4911	−0.777987	−0.388993	−	0.921241i	$-0.627177\pi$
$991$	−24.4911	−0.777987	−0.388993	+	0.921241i	$0.627177\pi$
$992$	−2.17021	−0.0689042
$993$	34.7472	1.10267
$994$	−26.4387	−0.838584
$995$	−31.9892	−1.01413
$996$	10.4353	0.330654
$997$	5.17107	0.163769	0.0818847	−	0.996642i	$-0.473906\pi$
$997$	5.17107	0.163769	0.0818847	+	0.996642i	$0.473906\pi$
$998$	23.1885	0.734020
$999$	−10.9350	−0.345968

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.o.1.14	✓	16
3.2	odd	2		8001.2.a.r.1.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.o.1.14	✓	16	1.1	even	1	trivial
8001.2.a.r.1.3		16	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)

\(f(q)\)	\(=\)	\(q+2.41798 q^{2} -1.00000 q^{3} +3.84663 q^{4} +2.86533 q^{5} -2.41798 q^{6} -1.00000 q^{7} +4.46511 q^{8} +1.00000 q^{9} +6.92831 q^{10} -5.94265 q^{11} -3.84663 q^{12} +5.81109 q^{13} -2.41798 q^{14} -2.86533 q^{15} +3.10329 q^{16} -2.46675 q^{17} +2.41798 q^{18} +4.96080 q^{19} +11.0219 q^{20} +1.00000 q^{21} -14.3692 q^{22} +5.91940 q^{23} -4.46511 q^{24} +3.21012 q^{25} +14.0511 q^{26} -1.00000 q^{27} -3.84663 q^{28} +9.12150 q^{29} -6.92831 q^{30} +1.52132 q^{31} -1.42653 q^{32} +5.94265 q^{33} -5.96456 q^{34} -2.86533 q^{35} +3.84663 q^{36} +10.9350 q^{37} +11.9951 q^{38} -5.81109 q^{39} +12.7940 q^{40} +7.45599 q^{41} +2.41798 q^{42} -6.37361 q^{43} -22.8592 q^{44} +2.86533 q^{45} +14.3130 q^{46} -3.77187 q^{47} -3.10329 q^{48} +1.00000 q^{49} +7.76200 q^{50} +2.46675 q^{51} +22.3531 q^{52} +13.0229 q^{53} -2.41798 q^{54} -17.0277 q^{55} -4.46511 q^{56} -4.96080 q^{57} +22.0556 q^{58} -12.1352 q^{59} -11.0219 q^{60} -13.1708 q^{61} +3.67852 q^{62} -1.00000 q^{63} -9.65590 q^{64} +16.6507 q^{65} +14.3692 q^{66} -2.34916 q^{67} -9.48868 q^{68} -5.91940 q^{69} -6.92831 q^{70} +10.9342 q^{71} +4.46511 q^{72} -9.61640 q^{73} +26.4406 q^{74} -3.21012 q^{75} +19.0824 q^{76} +5.94265 q^{77} -14.0511 q^{78} -12.9373 q^{79} +8.89194 q^{80} +1.00000 q^{81} +18.0284 q^{82} -2.71284 q^{83} +3.84663 q^{84} -7.06806 q^{85} -15.4113 q^{86} -9.12150 q^{87} -26.5346 q^{88} -1.78782 q^{89} +6.92831 q^{90} -5.81109 q^{91} +22.7697 q^{92} -1.52132 q^{93} -9.12031 q^{94} +14.2143 q^{95} +1.42653 q^{96} -5.89963 q^{97} +2.41798 q^{98} -5.94265 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 5 q^{2} - 16 q^{3} + 19 q^{4} - q^{5} - 5 q^{6} - 16 q^{7} + 6 q^{8} + 16 q^{9} - 12 q^{10} + 11 q^{11} - 19 q^{12} + 18 q^{13} - 5 q^{14} + q^{15} + 25 q^{16} - 5 q^{17} + 5 q^{18} - 11 q^{19}+ \cdots + 11 q^{99}+O(q^{100}) \) 16 * q + 5 * q^2 - 16 * q^3 + 19 * q^4 - q^5 - 5 * q^6 - 16 * q^7 + 6 * q^8 + 16 * q^9 - 12 * q^10 + 11 * q^11 - 19 * q^12 + 18 * q^13 - 5 * q^14 + q^15 + 25 * q^16 - 5 * q^17 + 5 * q^18 - 11 * q^19 - q^20 + 16 * q^21 + q^22 + 13 * q^23 - 6 * q^24 + 33 * q^25 + 8 * q^26 - 16 * q^27 - 19 * q^28 + 24 * q^29 + 12 * q^30 - 42 * q^31 + 42 * q^32 - 11 * q^33 + 9 * q^34 + q^35 + 19 * q^36 + 40 * q^37 + 38 * q^38 - 18 * q^39 - 61 * q^40 + 9 * q^41 + 5 * q^42 + 7 * q^43 + 3 * q^44 - q^45 + 24 * q^46 + 31 * q^47 - 25 * q^48 + 16 * q^49 + 6 * q^50 + 5 * q^51 + 52 * q^52 + 66 * q^53 - 5 * q^54 - 36 * q^55 - 6 * q^56 + 11 * q^57 + 19 * q^58 - 7 * q^59 + q^60 + 6 * q^61 + 52 * q^62 - 16 * q^63 + 10 * q^64 + 51 * q^65 - q^66 + 16 * q^67 + 14 * q^68 - 13 * q^69 + 12 * q^70 + 46 * q^71 + 6 * q^72 + 39 * q^73 + 72 * q^74 - 33 * q^75 + 24 * q^76 - 11 * q^77 - 8 * q^78 + 4 * q^79 - 2 * q^80 + 16 * q^81 - 18 * q^82 + 15 * q^83 + 19 * q^84 - 4 * q^85 + 14 * q^86 - 24 * q^87 + 58 * q^88 - q^89 - 12 * q^90 - 18 * q^91 + 26 * q^92 + 42 * q^93 + 5 * q^94 + 44 * q^95 - 42 * q^96 + 41 * q^97 + 5 * q^98 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more