LMFDB - Embedded newform 889.2.a.c.1.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [889,2,Mod(1,889)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(889, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([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("889.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 889 = 7 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	889.a (trivial)

Newform invariants

comment:select newform

sage:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$7.09870073969$
Analytic rank:	$1$
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} - 2 x^{15} - 20 x^{14} + 38 x^{13} + 155 x^{12} - 275 x^{11} - 593 x^{10} + 957 x^{9} + 1177 x^{8} + \cdots + 1 $ x^16 - 2x^15 - 20x^14 + 38x^13 + 155x^12 - 275x^11 - 593x^10 + 957x^9 + 1177x^8 - 1655x^7 - 1150x^6 + 1279x^5 + 474x^4 - 280x^3 - 83x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-0.532475$ of defining polynomial
Character	$\chi$	$=$	889.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.532475 q^{2} +1.70041 q^{3} -1.71647 q^{4} -0.118172 q^{5} +0.905424 q^{6} -1.00000 q^{7} -1.97893 q^{8} -0.108620 q^{9} -0.0629236 q^{10} -5.22568 q^{11} -2.91870 q^{12} -2.19166 q^{13} -0.532475 q^{14} -0.200940 q^{15} +2.37921 q^{16} -1.28158 q^{17} -0.0578377 q^{18} +8.34525 q^{19} +0.202839 q^{20} -1.70041 q^{21} -2.78254 q^{22} -9.05966 q^{23} -3.36498 q^{24} -4.98604 q^{25} -1.16700 q^{26} -5.28592 q^{27} +1.71647 q^{28} -9.26366 q^{29} -0.106996 q^{30} +6.76707 q^{31} +5.22473 q^{32} -8.88577 q^{33} -0.682411 q^{34} +0.118172 q^{35} +0.186444 q^{36} +6.01829 q^{37} +4.44364 q^{38} -3.72670 q^{39} +0.233854 q^{40} -4.32714 q^{41} -0.905424 q^{42} +2.14731 q^{43} +8.96972 q^{44} +0.0128359 q^{45} -4.82404 q^{46} +1.79425 q^{47} +4.04562 q^{48} +1.00000 q^{49} -2.65494 q^{50} -2.17921 q^{51} +3.76191 q^{52} +4.27074 q^{53} -2.81462 q^{54} +0.617528 q^{55} +1.97893 q^{56} +14.1903 q^{57} -4.93267 q^{58} +11.1673 q^{59} +0.344908 q^{60} -10.4330 q^{61} +3.60330 q^{62} +0.108620 q^{63} -1.97638 q^{64} +0.258992 q^{65} -4.73145 q^{66} -14.4350 q^{67} +2.19980 q^{68} -15.4051 q^{69} +0.0629236 q^{70} -4.12479 q^{71} +0.214952 q^{72} +16.5937 q^{73} +3.20459 q^{74} -8.47828 q^{75} -14.3244 q^{76} +5.22568 q^{77} -1.98438 q^{78} -11.3780 q^{79} -0.281156 q^{80} -8.66234 q^{81} -2.30410 q^{82} +6.41125 q^{83} +2.91870 q^{84} +0.151447 q^{85} +1.14339 q^{86} -15.7520 q^{87} +10.3412 q^{88} -3.69932 q^{89} +0.00683479 q^{90} +2.19166 q^{91} +15.5506 q^{92} +11.5068 q^{93} +0.955391 q^{94} -0.986174 q^{95} +8.88415 q^{96} +6.10975 q^{97} +0.532475 q^{98} +0.567615 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 4 q^{3} + 12 q^{4} - 9 q^{5} - 12 q^{6} - 16 q^{7} - 6 q^{8} + 14 q^{9} - 2 q^{10} - 22 q^{11} - 10 q^{12} - 4 q^{13} + 2 q^{14} - 14 q^{15} + 12 q^{16} - 18 q^{17} - 5 q^{18} - 15 q^{19}+ \cdots - 73 q^{99}+O(q^{100}) $ 16 * q - 2 * q^2 - 4 * q^3 + 12 * q^4 - 9 * q^5 - 12 * q^6 - 16 * q^7 - 6 * q^8 + 14 * q^9 - 2 * q^10 - 22 * q^11 - 10 * q^12 - 4 * q^13 + 2 * q^14 - 14 * q^15 + 12 * q^16 - 18 * q^17 - 5 * q^18 - 15 * q^19 - 40 * q^20 + 4 * q^21 - 11 * q^22 - 5 * q^23 - 26 * q^24 + 15 * q^25 - 24 * q^26 - 10 * q^27 - 12 * q^28 - 12 * q^29 + 3 * q^30 - 32 * q^31 - 9 * q^32 - 10 * q^33 - 14 * q^34 + 9 * q^35 + 10 * q^36 - 2 * q^37 + 3 * q^38 - 41 * q^39 - 14 * q^40 - 45 * q^41 + 12 * q^42 - 3 * q^43 - 54 * q^44 - 22 * q^45 - 49 * q^47 + 10 * q^48 + 16 * q^49 - 6 * q^50 - 12 * q^51 + 38 * q^52 + 16 * q^53 - 67 * q^54 + 7 * q^55 + 6 * q^56 + 8 * q^57 + 16 * q^58 - 35 * q^59 + 56 * q^60 - 11 * q^61 + 17 * q^62 - 14 * q^63 - 2 * q^64 + 14 * q^65 + 86 * q^66 + 17 * q^67 - 71 * q^68 - 17 * q^69 + 2 * q^70 - 81 * q^71 + 13 * q^72 - 15 * q^73 + 13 * q^74 - 48 * q^75 + 14 * q^76 + 22 * q^77 - 10 * q^78 - 34 * q^79 - 33 * q^80 + 40 * q^81 - 14 * q^82 - 39 * q^83 + 10 * q^84 - 17 * q^85 + 36 * q^86 + 7 * q^87 + 61 * q^88 - 32 * q^89 + 79 * q^90 + 4 * q^91 + 37 * q^92 + 27 * q^93 + 13 * q^94 - 33 * q^95 - 55 * q^96 - 4 * q^97 - 2 * q^98 - 73 * 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 $

$2$	0.532475	0.376517	0.188258	−	0.982120i	$-0.439716\pi$
$2$	0.532475	0.376517	0.188258	+	0.982120i	$0.439716\pi$
$3$	1.70041	0.981730	0.490865	−	0.871236i	$-0.336681\pi$
$3$	1.70041	0.981730	0.490865	+	0.871236i	$0.336681\pi$
$4$	−1.71647	−0.858235
$5$	−0.118172	−0.0528481	−0.0264241	−	0.999651i	$-0.508412\pi$
$5$	−0.118172	−0.0528481	−0.0264241	+	0.999651i	$0.508412\pi$
$6$	0.905424	0.369638
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.97893	−0.699657
$9$	−0.108620	−0.0362068
$10$	−0.0629236	−0.0198982
$11$	−5.22568	−1.57560	−0.787800	−	0.615931i	$-0.788780\pi$
$11$	−5.22568	−1.57560	−0.787800	+	0.615931i	$0.788780\pi$
$12$	−2.91870	−0.842555
$13$	−2.19166	−0.607856	−0.303928	−	0.952695i	$-0.598298\pi$
$13$	−2.19166	−0.607856	−0.303928	+	0.952695i	$0.598298\pi$
$14$	−0.532475	−0.142310
$15$	−0.200940	−0.0518826
$16$	2.37921	0.594803
$17$	−1.28158	−0.310829	−0.155415	−	0.987849i	$-0.549671\pi$
$17$	−1.28158	−0.310829	−0.155415	+	0.987849i	$0.549671\pi$
$18$	−0.0578377	−0.0136325
$19$	8.34525	1.91453	0.957266	−	0.289210i	$-0.0933925\pi$
$19$	8.34525	1.91453	0.957266	+	0.289210i	$0.0933925\pi$
$20$	0.202839	0.0453561
$21$	−1.70041	−0.371059
$22$	−2.78254	−0.593240
$23$	−9.05966	−1.88907	−0.944535	−	0.328412i	$-0.893487\pi$
$23$	−9.05966	−1.88907	−0.944535	+	0.328412i	$0.893487\pi$
$24$	−3.36498	−0.686874
$25$	−4.98604	−0.997207
$26$	−1.16700	−0.228868
$27$	−5.28592	−1.01727
$28$	1.71647	0.324382
$29$	−9.26366	−1.72022	−0.860109	−	0.510111i	$-0.829604\pi$
$29$	−9.26366	−1.72022	−0.860109	+	0.510111i	$0.829604\pi$
$30$	−0.106996	−0.0195346
$31$	6.76707	1.21540	0.607701	−	0.794166i	$-0.292092\pi$
$31$	6.76707	1.21540	0.607701	+	0.794166i	$0.292092\pi$
$32$	5.22473	0.923610
$33$	−8.88577	−1.54681
$34$	−0.682411	−0.117033
$35$	0.118172	0.0199747
$36$	0.186444	0.0310740
$37$	6.01829	0.989401	0.494700	−	0.869064i	$-0.335278\pi$
$37$	6.01829	0.989401	0.494700	+	0.869064i	$0.335278\pi$
$38$	4.44364	0.720853
$39$	−3.72670	−0.596750
$40$	0.233854	0.0369755
$41$	−4.32714	−0.675786	−0.337893	−	0.941184i	$-0.609714\pi$
$41$	−4.32714	−0.675786	−0.337893	+	0.941184i	$0.609714\pi$
$42$	−0.905424	−0.139710
$43$	2.14731	0.327461	0.163730	−	0.986505i	$-0.447647\pi$
$43$	2.14731	0.327461	0.163730	+	0.986505i	$0.447647\pi$
$44$	8.96972	1.35224
$45$	0.0128359	0.00191346
$46$	−4.82404	−0.711266
$47$	1.79425	0.261718	0.130859	−	0.991401i	$-0.458227\pi$
$47$	1.79425	0.261718	0.130859	+	0.991401i	$0.458227\pi$
$48$	4.04562	0.583935
$49$	1.00000	0.142857
$50$	−2.65494	−0.375465
$51$	−2.17921	−0.305151
$52$	3.76191	0.521683
$53$	4.27074	0.586631	0.293315	−	0.956016i	$-0.405241\pi$
$53$	4.27074	0.586631	0.293315	+	0.956016i	$0.405241\pi$
$54$	−2.81462	−0.383021
$55$	0.617528	0.0832675
$56$	1.97893	0.264445
$57$	14.1903	1.87955
$58$	−4.93267	−0.647691
$59$	11.1673	1.45386	0.726931	−	0.686710i	$-0.240946\pi$
$59$	11.1673	1.45386	0.726931	+	0.686710i	$0.240946\pi$
$60$	0.344908	0.0445274
$61$	−10.4330	−1.33581	−0.667907	−	0.744245i	$-0.732810\pi$
$61$	−10.4330	−1.33581	−0.667907	+	0.744245i	$0.732810\pi$
$62$	3.60330	0.457619
$63$	0.108620	0.0136849
$64$	−1.97638	−0.247048
$65$	0.258992	0.0321240
$66$	−4.73145	−0.582401
$67$	−14.4350	−1.76352	−0.881760	−	0.471699i	$-0.843641\pi$
$67$	−14.4350	−1.76352	−0.881760	+	0.471699i	$0.843641\pi$
$68$	2.19980	0.266765
$69$	−15.4051	−1.85456
$70$	0.0629236	0.00752081
$71$	−4.12479	−0.489523	−0.244761	−	0.969583i	$-0.578710\pi$
$71$	−4.12479	−0.489523	−0.244761	+	0.969583i	$0.578710\pi$
$72$	0.214952	0.0253323
$73$	16.5937	1.94215	0.971075	−	0.238774i	$-0.0767454\pi$
$73$	16.5937	1.94215	0.971075	+	0.238774i	$0.0767454\pi$
$74$	3.20459	0.372526
$75$	−8.47828	−0.978988
$76$	−14.3244	−1.64312
$77$	5.22568	0.595521
$78$	−1.98438	−0.224686
$79$	−11.3780	−1.28012	−0.640060	−	0.768325i	$-0.721091\pi$
$79$	−11.3780	−1.28012	−0.640060	+	0.768325i	$0.721091\pi$
$80$	−0.281156	−0.0314342
$81$	−8.66234	−0.962482
$82$	−2.30410	−0.254445
$83$	6.41125	0.703727	0.351863	−	0.936051i	$-0.385548\pi$
$83$	6.41125	0.703727	0.351863	+	0.936051i	$0.385548\pi$
$84$	2.91870	0.318456
$85$	0.151447	0.0164267
$86$	1.14339	0.123295
$87$	−15.7520	−1.68879
$88$	10.3412	1.10238
$89$	−3.69932	−0.392127	−0.196064	−	0.980591i	$-0.562816\pi$
$89$	−3.69932	−0.392127	−0.196064	+	0.980591i	$0.562816\pi$
$90$	0.00683479	0.000720450 0
$91$	2.19166	0.229748
$92$	15.5506	1.62127
$93$	11.5068	1.19320
$94$	0.955391	0.0985410
$95$	−0.986174	−0.101179
$96$	8.88415	0.906735
$97$	6.10975	0.620351	0.310176	−	0.950679i	$-0.399612\pi$
$97$	6.10975	0.620351	0.310176	+	0.950679i	$0.399612\pi$
$98$	0.532475	0.0537881
$99$	0.567615	0.0570475
$100$	8.55838	0.855838
$101$	0.593672	0.0590726	0.0295363	−	0.999564i	$-0.490597\pi$
$101$	0.593672	0.0590726	0.0295363	+	0.999564i	$0.490597\pi$
$102$	−1.16038	−0.114894
$103$	7.82074	0.770600	0.385300	−	0.922791i	$-0.374098\pi$
$103$	7.82074	0.770600	0.385300	+	0.922791i	$0.374098\pi$
$104$	4.33713	0.425290
$105$	0.200940	0.0196098
$106$	2.27406	0.220876
$107$	−11.0220	−1.06553	−0.532767	−	0.846262i	$-0.678848\pi$
$107$	−11.0220	−1.06553	−0.532767	+	0.846262i	$0.678848\pi$
$108$	9.07312	0.873061
$109$	−0.329550	−0.0315652	−0.0157826	−	0.999875i	$-0.505024\pi$
$109$	−0.329550	−0.0315652	−0.0157826	+	0.999875i	$0.505024\pi$
$110$	0.328818	0.0313516
$111$	10.2335	0.971324
$112$	−2.37921	−0.224814
$113$	−1.82578	−0.171755	−0.0858777	−	0.996306i	$-0.527369\pi$
$113$	−1.82578	−0.171755	−0.0858777	+	0.996306i	$0.527369\pi$
$114$	7.55599	0.707683
$115$	1.07060	0.0998337
$116$	15.9008	1.47635
$117$	0.238059	0.0220085
$118$	5.94632	0.547404
$119$	1.28158	0.117482
$120$	0.397646	0.0363000
$121$	16.3077	1.48252
$122$	−5.55533	−0.502956
$123$	−7.35790	−0.663440
$124$	−11.6155	−1.04310
$125$	1.18007	0.105549
$126$	0.0578377	0.00515259
$127$	−1.00000	−0.0887357
$127$	−1.00000	−0.0887357
$128$	−11.5018	−1.01663
$129$	3.65129	0.321478
$130$	0.137907	0.0120952
$131$	−8.23408	−0.719415	−0.359707	−	0.933065i	$-0.617123\pi$
$131$	−8.23408	−0.719415	−0.359707	+	0.933065i	$0.617123\pi$
$132$	15.2522	1.32753
$133$	−8.34525	−0.723625
$134$	−7.68629	−0.663994
$135$	0.624647	0.0537611
$136$	2.53616	0.217474
$137$	−3.79688	−0.324390	−0.162195	−	0.986759i	$-0.551857\pi$
$137$	−3.79688	−0.324390	−0.162195	+	0.986759i	$0.551857\pi$
$138$	−8.20283	−0.698271
$139$	−4.53910	−0.385001	−0.192501	−	0.981297i	$-0.561660\pi$
$139$	−4.53910	−0.385001	−0.192501	+	0.981297i	$0.561660\pi$
$140$	−0.202839	−0.0171430
$141$	3.05094	0.256936
$142$	−2.19635	−0.184314
$143$	11.4529	0.957738
$144$	−0.258431	−0.0215359
$145$	1.09470	0.0909102
$146$	8.83575	0.731252
$147$	1.70041	0.140247
$148$	−10.3302	−0.849138
$149$	−4.89325	−0.400871	−0.200435	−	0.979707i	$-0.564236\pi$
$149$	−4.89325	−0.400871	−0.200435	+	0.979707i	$0.564236\pi$
$150$	−4.51447	−0.368605
$151$	11.1366	0.906286	0.453143	−	0.891438i	$-0.350303\pi$
$151$	11.1366	0.906286	0.453143	+	0.891438i	$0.350303\pi$
$152$	−16.5146	−1.33951
$153$	0.139206	0.0112541
$154$	2.78254	0.224224
$155$	−0.799678	−0.0642317
$156$	6.39678	0.512152
$157$	−15.9627	−1.27397	−0.636983	−	0.770878i	$-0.719818\pi$
$157$	−15.9627	−1.27397	−0.636983	+	0.770878i	$0.719818\pi$
$158$	−6.05848	−0.481987
$159$	7.26198	0.575913
$160$	−0.617416	−0.0488110
$161$	9.05966	0.714001
$162$	−4.61248	−0.362391
$163$	−11.4892	−0.899906	−0.449953	−	0.893052i	$-0.648559\pi$
$163$	−11.4892	−0.899906	−0.449953	+	0.893052i	$0.648559\pi$
$164$	7.42741	0.579984
$165$	1.05005	0.0817462
$166$	3.41383	0.264965
$167$	−14.2726	−1.10445	−0.552223	−	0.833697i	$-0.686220\pi$
$167$	−14.2726	−1.10445	−0.552223	+	0.833697i	$0.686220\pi$
$168$	3.36498	0.259614
$169$	−8.19665	−0.630511
$170$	0.0806418	0.00618495
$171$	−0.906465	−0.0693191
$172$	−3.68579	−0.281039
$173$	3.15204	0.239645	0.119823	−	0.992795i	$-0.461767\pi$
$173$	3.15204	0.239645	0.119823	+	0.992795i	$0.461767\pi$
$174$	−8.38753	−0.635857
$175$	4.98604	0.376909
$176$	−12.4330	−0.937171
$177$	18.9890	1.42730
$178$	−1.96980	−0.147642
$179$	22.0690	1.64951	0.824757	−	0.565488i	$-0.191312\pi$
$179$	22.0690	1.64951	0.824757	+	0.565488i	$0.191312\pi$
$180$	−0.0220324	−0.00164220
$181$	17.7881	1.32218	0.661089	−	0.750307i	$-0.270094\pi$
$181$	17.7881	1.32218	0.661089	+	0.750307i	$0.270094\pi$
$182$	1.16700	0.0865039
$183$	−17.7404	−1.31141
$184$	17.9284	1.32170
$185$	−0.711193	−0.0522879
$186$	6.12706	0.449258
$187$	6.69713	0.489743
$188$	−3.07977	−0.224615
$189$	5.28592	0.384494
$190$	−0.525113	−0.0380957
$191$	9.64651	0.697997	0.348999	−	0.937123i	$-0.386522\pi$
$191$	9.64651	0.697997	0.348999	+	0.937123i	$0.386522\pi$
$192$	−3.36066	−0.242534
$193$	12.1823	0.876901	0.438451	−	0.898755i	$-0.355527\pi$
$193$	12.1823	0.876901	0.438451	+	0.898755i	$0.355527\pi$
$194$	3.25329	0.233573
$195$	0.440392	0.0315371
$196$	−1.71647	−0.122605
$197$	5.07522	0.361595	0.180797	−	0.983520i	$-0.442132\pi$
$197$	5.07522	0.361595	0.180797	+	0.983520i	$0.442132\pi$
$198$	0.302241	0.0214793
$199$	3.43881	0.243771	0.121885	−	0.992544i	$-0.461106\pi$
$199$	3.43881	0.243771	0.121885	+	0.992544i	$0.461106\pi$
$200$	9.86700	0.697703
$201$	−24.5454	−1.73130
$202$	0.316116	0.0222418
$203$	9.26366	0.650181
$204$	3.74055	0.261891
$205$	0.511347	0.0357140
$206$	4.16435	0.290144
$207$	0.984064	0.0683972
$208$	−5.21441	−0.361554
$209$	−43.6096	−3.01654
$210$	0.106996	0.00738340
$211$	−13.3818	−0.921243	−0.460621	−	0.887597i	$-0.652373\pi$
$211$	−13.3818	−0.921243	−0.460621	+	0.887597i	$0.652373\pi$
$212$	−7.33059	−0.503467
$213$	−7.01382	−0.480579
$214$	−5.86892	−0.401191
$215$	−0.253751	−0.0173057
$216$	10.4604	0.711743
$217$	−6.76707	−0.459379
$218$	−0.175477	−0.0118848
$219$	28.2161	1.90667
$220$	−1.05997	−0.0714631
$221$	2.80879	0.188940
$222$	5.44910	0.365720
$223$	−3.72789	−0.249638	−0.124819	−	0.992180i	$-0.539835\pi$
$223$	−3.72789	−0.249638	−0.124819	+	0.992180i	$0.539835\pi$
$224$	−5.22473	−0.349092
$225$	0.541585	0.0361057
$226$	−0.972184	−0.0646687
$227$	7.52598	0.499517	0.249759	−	0.968308i	$-0.419649\pi$
$227$	7.52598	0.499517	0.249759	+	0.968308i	$0.419649\pi$
$228$	−24.3572	−1.61310
$229$	−0.811157	−0.0536027	−0.0268014	−	0.999641i	$-0.508532\pi$
$229$	−0.811157	−0.0536027	−0.0268014	+	0.999641i	$0.508532\pi$
$230$	0.570066	0.0375891
$231$	8.88577	0.584641
$232$	18.3321	1.20356
$233$	21.7672	1.42602	0.713008	−	0.701156i	$-0.247332\pi$
$233$	21.7672	1.42602	0.713008	+	0.701156i	$0.247332\pi$
$234$	0.126760	0.00828658
$235$	−0.212029	−0.0138313
$236$	−19.1684	−1.24776
$237$	−19.3472	−1.25673
$238$	0.682411	0.0442341
$239$	10.2516	0.663119	0.331559	−	0.943434i	$-0.392425\pi$
$239$	10.2516	0.663119	0.331559	+	0.943434i	$0.392425\pi$
$240$	−0.478079	−0.0308599
$241$	12.4960	0.804938	0.402469	−	0.915434i	$-0.368152\pi$
$241$	12.4960	0.804938	0.402469	+	0.915434i	$0.368152\pi$
$242$	8.68343	0.558192
$243$	1.12826	0.0723776
$244$	17.9080	1.14644
$245$	−0.118172	−0.00754973
$246$	−3.91790	−0.249796
$247$	−18.2899	−1.16376
$248$	−13.3915	−0.850364
$249$	10.9017	0.690869
$250$	0.628358	0.0397408
$251$	−21.5708	−1.36154	−0.680769	−	0.732498i	$-0.738354\pi$
$251$	−21.5708	−1.36154	−0.680769	+	0.732498i	$0.738354\pi$
$252$	−0.186444	−0.0117449
$253$	47.3428	2.97642
$254$	−0.532475	−0.0334105
$255$	0.257522	0.0161266
$256$	−2.17167	−0.135729
$257$	−19.5843	−1.22163	−0.610817	−	0.791772i	$-0.709159\pi$
$257$	−19.5843	−1.22163	−0.610817	+	0.791772i	$0.709159\pi$
$258$	1.94422	0.121042
$259$	−6.01829	−0.373958
$260$	−0.444552	−0.0275700
$261$	1.00622	0.0622836
$262$	−4.38444	−0.270872
$263$	−7.21804	−0.445083	−0.222542	−	0.974923i	$-0.571435\pi$
$263$	−7.21804	−0.445083	−0.222542	+	0.974923i	$0.571435\pi$
$264$	17.5843	1.08224
$265$	−0.504681	−0.0310023
$266$	−4.44364	−0.272457
$267$	−6.29034	−0.384963
$268$	24.7773	1.51351
$269$	−14.4911	−0.883538	−0.441769	−	0.897129i	$-0.645649\pi$
$269$	−14.4911	−0.883538	−0.441769	+	0.897129i	$0.645649\pi$
$270$	0.332609	0.0202419
$271$	−17.3584	−1.05445	−0.527224	−	0.849726i	$-0.676767\pi$
$271$	−17.3584	−1.05445	−0.527224	+	0.849726i	$0.676767\pi$
$272$	−3.04916	−0.184882
$273$	3.72670	0.225550
$274$	−2.02175	−0.122138
$275$	26.0554	1.57120
$276$	26.4424	1.59164
$277$	−25.4371	−1.52836	−0.764182	−	0.645000i	$-0.776857\pi$
$277$	−25.4371	−1.52836	−0.764182	+	0.645000i	$0.776857\pi$
$278$	−2.41696	−0.144959
$279$	−0.735042	−0.0440058
$280$	−0.233854	−0.0139754
$281$	10.7927	0.643837	0.321918	−	0.946767i	$-0.395672\pi$
$281$	10.7927	0.643837	0.321918	+	0.946767i	$0.395672\pi$
$282$	1.62455	0.0967407
$283$	1.47440	0.0876441	0.0438220	−	0.999039i	$-0.486047\pi$
$283$	1.47440	0.0876441	0.0438220	+	0.999039i	$0.486047\pi$
$284$	7.08009	0.420126
$285$	−1.67690	−0.0993308
$286$	6.09837	0.360604
$287$	4.32714	0.255423
$288$	−0.567512	−0.0334410
$289$	−15.3575	−0.903385
$290$	0.582903	0.0342292
$291$	10.3891	0.609017
$292$	−28.4827	−1.66682
$293$	12.6888	0.741290	0.370645	−	0.928775i	$-0.379137\pi$
$293$	12.6888	0.741290	0.370645	+	0.928775i	$0.379137\pi$
$294$	0.905424	0.0528054
$295$	−1.31966	−0.0768339
$296$	−11.9098	−0.692241
$297$	27.6225	1.60282
$298$	−2.60553	−0.150934
$299$	19.8557	1.14828
$300$	14.5527	0.840202
$301$	−2.14731	−0.123769
$302$	5.92998	0.341232
$303$	1.00948	0.0579933
$304$	19.8551	1.13877
$305$	1.23289	0.0705952
$306$	0.0741238	0.00423737
$307$	−7.60261	−0.433904	−0.216952	−	0.976182i	$-0.569612\pi$
$307$	−7.60261	−0.433904	−0.216952	+	0.976182i	$0.569612\pi$
$308$	−8.96972	−0.511097
$309$	13.2984	0.756521
$310$	−0.425808	−0.0241843
$311$	−34.6469	−1.96465	−0.982324	−	0.187190i	$-0.940062\pi$
$311$	−34.6469	−1.96465	−0.982324	+	0.187190i	$0.940062\pi$
$312$	7.37488	0.417520
$313$	−13.4142	−0.758216	−0.379108	−	0.925352i	$-0.623769\pi$
$313$	−13.4142	−0.758216	−0.379108	+	0.925352i	$0.623769\pi$
$314$	−8.49977	−0.479670
$315$	−0.0128359	−0.000723221 0
$316$	19.5299	1.09864
$317$	−25.3786	−1.42540	−0.712702	−	0.701467i	$-0.752529\pi$
$317$	−25.3786	−1.42540	−0.712702	+	0.701467i	$0.752529\pi$
$318$	3.86683	0.216841
$319$	48.4089	2.71038
$320$	0.233553	0.0130560
$321$	−18.7418	−1.04607
$322$	4.82404	0.268833
$323$	−10.6951	−0.595093
$324$	14.8686	0.826036
$325$	10.9277	0.606158
$326$	−6.11773	−0.338830
$327$	−0.560369	−0.0309885
$328$	8.56311	0.472818
$329$	−1.79425	−0.0989199
$330$	0.559125	0.0307788
$331$	4.32910	0.237949	0.118974	−	0.992897i	$-0.462039\pi$
$331$	4.32910	0.237949	0.118974	+	0.992897i	$0.462039\pi$
$332$	−11.0047	−0.603963
$333$	−0.653709	−0.0358230
$334$	−7.59979	−0.415842
$335$	1.70582	0.0931986
$336$	−4.04562	−0.220707
$337$	−30.9193	−1.68428	−0.842141	−	0.539257i	$-0.818705\pi$
$337$	−30.9193	−1.68428	−0.842141	+	0.539257i	$0.818705\pi$
$338$	−4.36451	−0.237398
$339$	−3.10457	−0.168617
$340$	−0.259954	−0.0140980
$341$	−35.3625	−1.91499
$342$	−0.482670	−0.0260998
$343$	−1.00000	−0.0539949
$344$	−4.24936	−0.229110
$345$	1.82045	0.0980097
$346$	1.67838	0.0902304
$347$	11.4166	0.612873	0.306436	−	0.951891i	$-0.400863\pi$
$347$	11.4166	0.612873	0.306436	+	0.951891i	$0.400863\pi$
$348$	27.0378	1.44938
$349$	−25.1259	−1.34496	−0.672479	−	0.740116i	$-0.734771\pi$
$349$	−25.1259	−1.34496	−0.672479	+	0.740116i	$0.734771\pi$
$350$	2.65494	0.141912
$351$	11.5849	0.618357
$352$	−27.3027	−1.45524
$353$	16.4066	0.873234	0.436617	−	0.899647i	$-0.356176\pi$
$353$	16.4066	0.873234	0.436617	+	0.899647i	$0.356176\pi$
$354$	10.1112	0.537402
$355$	0.487435	0.0258704
$356$	6.34977	0.336537
$357$	2.17921	0.115336
$358$	11.7512	0.621069
$359$	−17.7879	−0.938809	−0.469404	−	0.882983i	$-0.655531\pi$
$359$	−17.7879	−0.938809	−0.469404	+	0.882983i	$0.655531\pi$
$360$	−0.0254013	−0.00133877
$361$	50.6432	2.66543
$362$	9.47172	0.497822
$363$	27.7297	1.45543
$364$	−3.76191	−0.197178
$365$	−1.96091	−0.102639
$366$	−9.44632	−0.493767
$367$	−23.9393	−1.24962	−0.624812	−	0.780776i	$-0.714824\pi$
$367$	−23.9393	−1.24962	−0.624812	+	0.780776i	$0.714824\pi$
$368$	−21.5548	−1.12362
$369$	0.470016	0.0244681
$370$	−0.378693	−0.0196873
$371$	−4.27074	−0.221726
$372$	−19.7510	−1.02404
$373$	24.1062	1.24817	0.624085	−	0.781356i	$-0.285472\pi$
$373$	24.1062	1.24817	0.624085	+	0.781356i	$0.285472\pi$
$374$	3.56606	0.184396
$375$	2.00660	0.103620
$376$	−3.55068	−0.183112
$377$	20.3027	1.04564
$378$	2.81462	0.144768
$379$	−9.74899	−0.500772	−0.250386	−	0.968146i	$-0.580558\pi$
$379$	−9.74899	−0.500772	−0.250386	+	0.968146i	$0.580558\pi$
$380$	1.69274	0.0868357
$381$	−1.70041	−0.0871144
$382$	5.13653	0.262808
$383$	21.0940	1.07785	0.538925	−	0.842354i	$-0.318831\pi$
$383$	21.0940	1.07785	0.538925	+	0.842354i	$0.318831\pi$
$384$	−19.5578	−0.998053
$385$	−0.617528	−0.0314722
$386$	6.48677	0.330168
$387$	−0.233241	−0.0118563
$388$	−10.4872	−0.532407
$389$	11.4795	0.582032	0.291016	−	0.956718i	$-0.406007\pi$
$389$	11.4795	0.582032	0.291016	+	0.956718i	$0.406007\pi$
$390$	0.234498	0.0118743
$391$	11.6107	0.587178
$392$	−1.97893	−0.0999510
$393$	−14.0013	−0.706271
$394$	2.70243	0.136146
$395$	1.34456	0.0676520
$396$	−0.974295	−0.0489601
$397$	33.4207	1.67734	0.838668	−	0.544643i	$-0.183335\pi$
$397$	33.4207	1.67734	0.838668	+	0.544643i	$0.183335\pi$
$398$	1.83108	0.0917838
$399$	−14.1903	−0.710404
$400$	−11.8628	−0.593141
$401$	0.506322	0.0252845	0.0126423	−	0.999920i	$-0.495976\pi$
$401$	0.506322	0.0252845	0.0126423	+	0.999920i	$0.495976\pi$
$402$	−13.0698	−0.651863
$403$	−14.8311	−0.738789
$404$	−1.01902	−0.0506982
$405$	1.02365	0.0508654
$406$	4.93267	0.244804
$407$	−31.4496	−1.55890
$408$	4.31250	0.213501
$409$	27.6889	1.36913	0.684563	−	0.728953i	$-0.259993\pi$
$409$	27.6889	1.36913	0.684563	+	0.728953i	$0.259993\pi$
$410$	0.272280	0.0134469
$411$	−6.45624	−0.318463
$412$	−13.4241	−0.661356
$413$	−11.1673	−0.549508
$414$	0.523990	0.0257527
$415$	−0.757631	−0.0371906
$416$	−11.4508	−0.561422
$417$	−7.71830	−0.377967
$418$	−23.2210	−1.13578
$419$	5.22108	0.255067	0.127533	−	0.991834i	$-0.459294\pi$
$419$	5.22108	0.255067	0.127533	+	0.991834i	$0.459294\pi$
$420$	−0.344908	−0.0168298
$421$	−30.2687	−1.47521	−0.737603	−	0.675235i	$-0.764042\pi$
$421$	−30.2687	−1.47521	−0.737603	+	0.675235i	$0.764042\pi$
$422$	−7.12549	−0.346863
$423$	−0.194892	−0.00947596
$424$	−8.45148	−0.410440
$425$	6.39002	0.309961
$426$	−3.73469	−0.180946
$427$	10.4330	0.504890
$428$	18.9189	0.914479
$429$	19.4745	0.940240
$430$	−0.135116	−0.00651588
$431$	−12.4316	−0.598807	−0.299403	−	0.954127i	$-0.596788\pi$
$431$	−12.4316	−0.598807	−0.299403	+	0.954127i	$0.596788\pi$
$432$	−12.5763	−0.605078
$433$	27.6679	1.32964	0.664818	−	0.747006i	$-0.268509\pi$
$433$	27.6679	1.32964	0.664818	+	0.747006i	$0.268509\pi$
$434$	−3.60330	−0.172964
$435$	1.86144	0.0892493
$436$	0.565664	0.0270904
$437$	−75.6051	−3.61668
$438$	15.0244	0.717892
$439$	5.41016	0.258213	0.129106	−	0.991631i	$-0.458789\pi$
$439$	5.41016	0.258213	0.129106	+	0.991631i	$0.458789\pi$
$440$	−1.22204	−0.0582587
$441$	−0.108620	−0.00517240
$442$	1.49561	0.0711389
$443$	−11.5485	−0.548686	−0.274343	−	0.961632i	$-0.588460\pi$
$443$	−11.5485	−0.548686	−0.274343	+	0.961632i	$0.588460\pi$
$444$	−17.5656	−0.833624
$445$	0.437156	0.0207232
$446$	−1.98501	−0.0939930
$447$	−8.32051	−0.393547
$448$	1.97638	0.0933754
$449$	−37.7469	−1.78138	−0.890692	−	0.454607i	$-0.849780\pi$
$449$	−37.7469	−1.78138	−0.890692	+	0.454607i	$0.849780\pi$
$450$	0.288381	0.0135944
$451$	22.6123	1.06477
$452$	3.13390	0.147406
$453$	18.9368	0.889728
$454$	4.00740	0.188077
$455$	−0.258992	−0.0121417
$456$	−28.0816	−1.31504
$457$	−4.86171	−0.227421	−0.113711	−	0.993514i	$-0.536274\pi$
$457$	−4.86171	−0.227421	−0.113711	+	0.993514i	$0.536274\pi$
$458$	−0.431921	−0.0201823
$459$	6.77434	0.316199
$460$	−1.83765	−0.0856808
$461$	−22.2371	−1.03569	−0.517843	−	0.855475i	$-0.673265\pi$
$461$	−22.2371	−1.03569	−0.517843	+	0.855475i	$0.673265\pi$
$462$	4.73145	0.220127
$463$	−34.0919	−1.58439	−0.792193	−	0.610271i	$-0.791061\pi$
$463$	−34.0919	−1.58439	−0.792193	+	0.610271i	$0.791061\pi$
$464$	−22.0402	−1.02319
$465$	−1.35978	−0.0630581
$466$	11.5905	0.536919
$467$	−18.0906	−0.837131	−0.418566	−	0.908187i	$-0.637467\pi$
$467$	−18.0906	−0.837131	−0.418566	+	0.908187i	$0.637467\pi$
$468$	−0.408621	−0.0188885
$469$	14.4350	0.666548
$470$	−0.112900	−0.00520771
$471$	−27.1431	−1.25069
$472$	−22.0993	−1.01720
$473$	−11.2211	−0.515948
$474$	−10.3019	−0.473181
$475$	−41.6097	−1.90918
$476$	−2.19980	−0.100828
$477$	−0.463889	−0.0212400
$478$	5.45871	0.249675
$479$	13.8985	0.635037	0.317519	−	0.948252i	$-0.397150\pi$
$479$	13.8985	0.635037	0.317519	+	0.948252i	$0.397150\pi$
$480$	−1.04986	−0.0479192
$481$	−13.1900	−0.601413
$482$	6.65380	0.303072
$483$	15.4051	0.700956
$484$	−27.9916	−1.27235
$485$	−0.722001	−0.0327844
$486$	0.600768	0.0272514
$487$	−1.46671	−0.0664628	−0.0332314	−	0.999448i	$-0.510580\pi$
$487$	−1.46671	−0.0664628	−0.0332314	+	0.999448i	$0.510580\pi$
$488$	20.6462	0.934611
$489$	−19.5363	−0.883464
$490$	−0.0629236	−0.00284260
$491$	13.3834	0.603983	0.301992	−	0.953311i	$-0.402349\pi$
$491$	13.3834	0.603983	0.301992	+	0.953311i	$0.402349\pi$
$492$	12.6296	0.569387
$493$	11.8721	0.534694
$494$	−9.73892	−0.438175
$495$	−0.0670762	−0.00301485
$496$	16.1003	0.722924
$497$	4.12479	0.185022
$498$	5.80490	0.260124
$499$	21.8737	0.979201	0.489601	−	0.871947i	$-0.337143\pi$
$499$	21.8737	0.979201	0.489601	+	0.871947i	$0.337143\pi$
$500$	−2.02555	−0.0905855
$501$	−24.2692	−1.08427
$502$	−11.4859	−0.512642
$503$	−41.4018	−1.84601	−0.923007	−	0.384784i	$-0.874276\pi$
$503$	−41.4018	−1.84601	−0.923007	+	0.384784i	$0.874276\pi$
$504$	−0.214952	−0.00957473
$505$	−0.0701554	−0.00312187
$506$	25.2089	1.12067
$507$	−13.9376	−0.618992
$508$	1.71647	0.0761561
$509$	12.5384	0.555757	0.277878	−	0.960616i	$-0.410369\pi$
$509$	12.5384	0.555757	0.277878	+	0.960616i	$0.410369\pi$
$510$	0.137124	0.00607194
$511$	−16.5937	−0.734064
$512$	21.8473	0.965523
$513$	−44.1123	−1.94761
$514$	−10.4281	−0.459965
$515$	−0.924192	−0.0407248
$516$	−6.26733	−0.275904
$517$	−9.37614	−0.412362
$518$	−3.20459	−0.140802
$519$	5.35975	0.235267
$520$	−0.512527	−0.0224758
$521$	−25.5657	−1.12006	−0.560028	−	0.828474i	$-0.689210\pi$
$521$	−25.5657	−1.12006	−0.560028	+	0.828474i	$0.689210\pi$
$522$	0.535788	0.0234508
$523$	−0.965570	−0.0422214	−0.0211107	−	0.999777i	$-0.506720\pi$
$523$	−0.965570	−0.0422214	−0.0211107	+	0.999777i	$0.506720\pi$
$524$	14.1335	0.617427
$525$	8.47828	0.370023
$526$	−3.84343	−0.167581
$527$	−8.67256	−0.377783
$528$	−21.1411	−0.920049
$529$	59.0774	2.56858
$530$	−0.268730	−0.0116729
$531$	−1.21300	−0.0526397
$532$	14.3244	0.621040
$533$	9.48361	0.410781
$534$	−3.34945	−0.144945
$535$	1.30249	0.0563115
$536$	28.5659	1.23386
$537$	37.5262	1.61938
$538$	−7.71615	−0.332667
$539$	−5.22568	−0.225086
$540$	−1.07219	−0.0461396
$541$	−1.43271	−0.0615970	−0.0307985	−	0.999526i	$-0.509805\pi$
$541$	−1.43271	−0.0615970	−0.0307985	+	0.999526i	$0.509805\pi$
$542$	−9.24292	−0.397017
$543$	30.2470	1.29802
$544$	−6.69592	−0.287085
$545$	0.0389436	0.00166816
$546$	1.98438	0.0849235
$547$	−13.4988	−0.577167	−0.288584	−	0.957455i	$-0.593184\pi$
$547$	−13.4988	−0.577167	−0.288584	+	0.957455i	$0.593184\pi$
$548$	6.51724	0.278403
$549$	1.13324	0.0483656
$550$	13.8739	0.591583
$551$	−77.3075	−3.29341
$552$	30.4856	1.29755
$553$	11.3780	0.483840
$554$	−13.5446	−0.575455
$555$	−1.20932	−0.0513326
$556$	7.79122	0.330421
$557$	29.6076	1.25451	0.627257	−	0.778812i	$-0.284178\pi$
$557$	29.6076	1.25451	0.627257	+	0.778812i	$0.284178\pi$
$558$	−0.391392	−0.0165689
$559$	−4.70615	−0.199049
$560$	0.281156	0.0118810
$561$	11.3878	0.480795
$562$	5.74683	0.242415
$563$	18.3169	0.771963	0.385982	−	0.922506i	$-0.373863\pi$
$563$	18.3169	0.771963	0.385982	+	0.922506i	$0.373863\pi$
$564$	−5.23686	−0.220511
$565$	0.215756	0.00907694
$566$	0.785082	0.0329995
$567$	8.66234	0.363784
$568$	8.16267	0.342498
$569$	−35.3075	−1.48017	−0.740083	−	0.672516i	$-0.765214\pi$
$569$	−35.3075	−1.48017	−0.740083	+	0.672516i	$0.765214\pi$
$570$	−0.892906	−0.0373997
$571$	3.93893	0.164839	0.0824196	−	0.996598i	$-0.473735\pi$
$571$	3.93893	0.164839	0.0824196	+	0.996598i	$0.473735\pi$
$572$	−19.6585	−0.821964
$573$	16.4030	0.685245
$574$	2.30410	0.0961711
$575$	45.1718	1.88379
$576$	0.214676	0.00894483
$577$	33.2150	1.38276	0.691380	−	0.722492i	$-0.257003\pi$
$577$	33.2150	1.38276	0.691380	+	0.722492i	$0.257003\pi$
$578$	−8.17751	−0.340140
$579$	20.7149	0.860880
$580$	−1.87903	−0.0780224
$581$	−6.41125	−0.265984
$582$	5.53191	0.229305
$583$	−22.3175	−0.924296
$584$	−32.8378	−1.35884
$585$	−0.0281319	−0.00116311
$586$	6.75649	0.279108
$587$	24.6822	1.01874	0.509372	−	0.860546i	$-0.329878\pi$
$587$	24.6822	1.01874	0.509372	+	0.860546i	$0.329878\pi$
$588$	−2.91870	−0.120365
$589$	56.4729	2.32692
$590$	−0.702689	−0.0289292
$591$	8.62994	0.354988
$592$	14.3188	0.588498
$593$	6.61375	0.271594	0.135797	−	0.990737i	$-0.456640\pi$
$593$	6.61375	0.271594	0.135797	+	0.990737i	$0.456640\pi$
$594$	14.7083	0.603488
$595$	−0.151447	−0.00620873
$596$	8.39912	0.344041
$597$	5.84737	0.239317
$598$	10.5726	0.432347
$599$	−25.3672	−1.03648	−0.518239	−	0.855236i	$-0.673412\pi$
$599$	−25.3672	−1.03648	−0.518239	+	0.855236i	$0.673412\pi$
$600$	16.7779	0.684955
$601$	−10.2704	−0.418940	−0.209470	−	0.977815i	$-0.567174\pi$
$601$	−10.2704	−0.418940	−0.209470	+	0.977815i	$0.567174\pi$
$602$	−1.14339	−0.0466010
$603$	1.56794	0.0638514
$604$	−19.1157	−0.777807
$605$	−1.92711	−0.0783482
$606$	0.537525	0.0218355
$607$	−0.280009	−0.0113652	−0.00568261	−	0.999984i	$-0.501809\pi$
$607$	−0.280009	−0.0113652	−0.00568261	+	0.999984i	$0.501809\pi$
$608$	43.6016	1.76828
$609$	15.7520	0.638302
$610$	0.656485	0.0265803
$611$	−3.93237	−0.159087
$612$	−0.238943	−0.00965870
$613$	−34.3249	−1.38637	−0.693185	−	0.720760i	$-0.743793\pi$
$613$	−34.3249	−1.38637	−0.693185	+	0.720760i	$0.743793\pi$
$614$	−4.04820	−0.163372
$615$	0.869498	0.0350615
$616$	−10.3412	−0.416660
$617$	−7.14920	−0.287816	−0.143908	−	0.989591i	$-0.545967\pi$
$617$	−7.14920	−0.287816	−0.143908	+	0.989591i	$0.545967\pi$
$618$	7.08108	0.284843
$619$	10.8686	0.436846	0.218423	−	0.975854i	$-0.429909\pi$
$619$	10.8686	0.436846	0.218423	+	0.975854i	$0.429909\pi$
$620$	1.37262	0.0551259
$621$	47.8886	1.92170
$622$	−18.4486	−0.739723
$623$	3.69932	0.148210
$624$	−8.86661	−0.354949
$625$	24.7907	0.991629
$626$	−7.14273	−0.285481
$627$	−74.1539	−2.96142
$628$	27.3996	1.09336
$629$	−7.71293	−0.307535
$630$	−0.00683479	−0.000272305 0
$631$	−46.4839	−1.85050	−0.925248	−	0.379362i	$-0.876143\pi$
$631$	−46.4839	−1.85050	−0.925248	+	0.379362i	$0.876143\pi$
$632$	22.5162	0.895645
$633$	−22.7545	−0.904411
$634$	−13.5135	−0.536689
$635$	0.118172	0.00468951
$636$	−12.4650	−0.494269
$637$	−2.19166	−0.0868366
$638$	25.7765	1.02050
$639$	0.448037	0.0177241
$640$	1.35919	0.0537268
$641$	13.4471	0.531127	0.265563	−	0.964093i	$-0.414442\pi$
$641$	13.4471	0.531127	0.265563	+	0.964093i	$0.414442\pi$
$642$	−9.97955	−0.393862
$643$	−40.9464	−1.61477	−0.807383	−	0.590027i	$-0.799117\pi$
$643$	−40.9464	−1.61477	−0.807383	+	0.590027i	$0.799117\pi$
$644$	−15.5506	−0.612781
$645$	−0.431480	−0.0169895
$646$	−5.69489	−0.224062
$647$	−9.04141	−0.355454	−0.177727	−	0.984080i	$-0.556874\pi$
$647$	−9.04141	−0.355454	−0.177727	+	0.984080i	$0.556874\pi$
$648$	17.1421	0.673407
$649$	−58.3568	−2.29071
$650$	5.81871	0.228229
$651$	−11.5068	−0.450986
$652$	19.7209	0.772331
$653$	−9.65099	−0.377672	−0.188836	−	0.982009i	$-0.560472\pi$
$653$	−9.65099	−0.377672	−0.188836	+	0.982009i	$0.560472\pi$
$654$	−0.298383	−0.0116677
$655$	0.973037	0.0380197
$656$	−10.2952	−0.401960
$657$	−1.80242	−0.0703191
$658$	−0.955391	−0.0372450
$659$	−25.6398	−0.998786	−0.499393	−	0.866376i	$-0.666444\pi$
$659$	−25.6398	−0.998786	−0.499393	+	0.866376i	$0.666444\pi$
$660$	−1.80238	−0.0701574
$661$	5.36192	0.208555	0.104277	−	0.994548i	$-0.466747\pi$
$661$	5.36192	0.208555	0.104277	+	0.994548i	$0.466747\pi$
$662$	2.30514	0.0895918
$663$	4.77608	0.185488
$664$	−12.6874	−0.492367
$665$	0.986174	0.0382422
$666$	−0.348084	−0.0134880
$667$	83.9256	3.24961
$668$	24.4985	0.947874
$669$	−6.33893	−0.245077
$670$	0.908304	0.0350908
$671$	54.5197	2.10471
$672$	−8.88415	−0.342714
$673$	10.4649	0.403392	0.201696	−	0.979448i	$-0.435355\pi$
$673$	10.4649	0.403392	0.201696	+	0.979448i	$0.435355\pi$
$674$	−16.4638	−0.634161
$675$	26.3558	1.01443
$676$	14.0693	0.541127
$677$	9.28929	0.357017	0.178508	−	0.983938i	$-0.442873\pi$
$677$	9.28929	0.357017	0.178508	+	0.983938i	$0.442873\pi$
$678$	−1.65311	−0.0634872
$679$	−6.10975	−0.234471
$680$	−0.299703	−0.0114931
$681$	12.7972	0.490391
$682$	−18.8297	−0.721025
$683$	−16.7140	−0.639544	−0.319772	−	0.947494i	$-0.603606\pi$
$683$	−16.7140	−0.639544	−0.319772	+	0.947494i	$0.603606\pi$
$684$	1.55592	0.0594921
$685$	0.448685	0.0171434
$686$	−0.532475	−0.0203300
$687$	−1.37930	−0.0526234
$688$	5.10889	0.194775
$689$	−9.35998	−0.356587
$690$	0.969344	0.0369023
$691$	32.0986	1.22109	0.610544	−	0.791982i	$-0.290951\pi$
$691$	32.0986	1.22109	0.610544	+	0.791982i	$0.290951\pi$
$692$	−5.41038	−0.205672
$693$	−0.567615	−0.0215619
$694$	6.07903	0.230757
$695$	0.536394	0.0203466
$696$	31.1720	1.18157
$697$	5.54559	0.210054
$698$	−13.3789	−0.506399
$699$	37.0131	1.39996
$700$	−8.55838	−0.323476
$701$	8.24121	0.311266	0.155633	−	0.987815i	$-0.450258\pi$
$701$	8.24121	0.311266	0.155633	+	0.987815i	$0.450258\pi$
$702$	6.16867	0.232822
$703$	50.2241	1.89424
$704$	10.3279	0.389249
$705$	−0.360536	−0.0135786
$706$	8.73610	0.328787
$707$	−0.593672	−0.0223273
$708$	−32.5940	−1.22496
$709$	18.5251	0.695723	0.347862	−	0.937546i	$-0.386908\pi$
$709$	18.5251	0.695723	0.347862	+	0.937546i	$0.386908\pi$
$710$	0.259547	0.00974062
$711$	1.23588	0.0463491
$712$	7.32069	0.274354
$713$	−61.3073	−2.29598
$714$	1.16038	0.0434260
$715$	−1.35341	−0.0506146
$716$	−37.8807	−1.41567
$717$	17.4318	0.651004
$718$	−9.47161	−0.353477
$719$	−29.8462	−1.11308	−0.556538	−	0.830822i	$-0.687871\pi$
$719$	−29.8462	−1.11308	−0.556538	+	0.830822i	$0.687871\pi$
$720$	0.0305393	0.00113813
$721$	−7.82074	−0.291260
$722$	26.9662	1.00358
$723$	21.2483	0.790231
$724$	−30.5327	−1.13474
$725$	46.1889	1.71541
$726$	14.7654	0.547994
$727$	−42.7041	−1.58381	−0.791904	−	0.610645i	$-0.790910\pi$
$727$	−42.7041	−1.58381	−0.791904	+	0.610645i	$0.790910\pi$
$728$	−4.33713	−0.160745
$729$	27.9055	1.03354
$730$	−1.04414	−0.0386453
$731$	−2.75195	−0.101785
$732$	30.4509	1.12550
$733$	13.0748	0.482930	0.241465	−	0.970409i	$-0.422372\pi$
$733$	13.0748	0.482930	0.241465	+	0.970409i	$0.422372\pi$
$734$	−12.7471	−0.470504
$735$	−0.200940	−0.00741179
$736$	−47.3342	−1.74476
$737$	75.4328	2.77860
$738$	0.250272	0.00921264
$739$	−11.8892	−0.437351	−0.218676	−	0.975798i	$-0.570174\pi$
$739$	−11.8892	−0.437351	−0.218676	+	0.975798i	$0.570174\pi$
$740$	1.22074	0.0448753
$741$	−31.1003	−1.14250
$742$	−2.27406	−0.0834834
$743$	24.3686	0.893998	0.446999	−	0.894534i	$-0.352493\pi$
$743$	24.3686	0.893998	0.446999	+	0.894534i	$0.352493\pi$
$744$	−22.7711	−0.834827
$745$	0.578245	0.0211853
$746$	12.8359	0.469957
$747$	−0.696393	−0.0254797
$748$	−11.4954	−0.420315
$749$	11.0220	0.402734
$750$	1.06846	0.0390147
$751$	14.6876	0.535957	0.267978	−	0.963425i	$-0.413644\pi$
$751$	14.6876	0.535957	0.267978	+	0.963425i	$0.413644\pi$
$752$	4.26889	0.155670
$753$	−36.6791	−1.33666
$754$	10.8107	0.393703
$755$	−1.31604	−0.0478955
$756$	−9.07312	−0.329986
$757$	−2.79722	−0.101667	−0.0508334	−	0.998707i	$-0.516188\pi$
$757$	−2.79722	−0.101667	−0.0508334	+	0.998707i	$0.516188\pi$
$758$	−5.19110	−0.188549
$759$	80.5020	2.92204
$760$	1.95157	0.0707908
$761$	36.1872	1.31179	0.655893	−	0.754854i	$-0.272292\pi$
$761$	36.1872	1.31179	0.655893	+	0.754854i	$0.272292\pi$
$762$	−0.905424	−0.0328000
$763$	0.329550	0.0119305
$764$	−16.5580	−0.599046
$765$	−0.0164503	−0.000594760 0
$766$	11.2320	0.405829
$767$	−24.4749	−0.883739
$768$	−3.69272	−0.133249
$769$	−9.22886	−0.332801	−0.166401	−	0.986058i	$-0.553214\pi$
$769$	−9.22886	−0.332801	−0.166401	+	0.986058i	$0.553214\pi$
$770$	−0.328818	−0.0118498
$771$	−33.3012	−1.19931
$772$	−20.9106	−0.752588
$773$	−4.09236	−0.147192	−0.0735959	−	0.997288i	$-0.523448\pi$
$773$	−4.09236	−0.147192	−0.0735959	+	0.997288i	$0.523448\pi$
$774$	−0.124195	−0.00446410
$775$	−33.7408	−1.21201
$776$	−12.0908	−0.434033
$777$	−10.2335	−0.367126
$778$	6.11253	0.219145
$779$	−36.1111	−1.29381
$780$	−0.755920	−0.0270663
$781$	21.5548	0.771293
$782$	6.18241	0.221083
$783$	48.9669	1.74993
$784$	2.37921	0.0849718
$785$	1.88635	0.0673267
$786$	−7.45533	−0.265923
$787$	−10.3020	−0.367225	−0.183613	−	0.982999i	$-0.558779\pi$
$787$	−10.3020	−0.367225	−0.183613	+	0.982999i	$0.558779\pi$
$788$	−8.71147	−0.310333
$789$	−12.2736	−0.436952
$790$	0.715943	0.0254721
$791$	1.82578	0.0649174
$792$	−1.12327	−0.0399136
$793$	22.8656	0.811982
$794$	17.7957	0.631545
$795$	−0.858163	−0.0304359
$796$	−5.90262	−0.209213
$797$	40.9311	1.44986	0.724928	−	0.688825i	$-0.241873\pi$
$797$	40.9311	1.44986	0.724928	+	0.688825i	$0.241873\pi$
$798$	−7.55599	−0.267479
$799$	−2.29947	−0.0813495
$800$	−26.0507	−0.921030
$801$	0.401822	0.0141977
$802$	0.269604	0.00952004
$803$	−86.7135	−3.06005
$804$	42.1314	1.48586
$805$	−1.07060	−0.0377336
$806$	−7.89718	−0.278166
$807$	−24.6408	−0.867396
$808$	−1.17483	−0.0413305
$809$	9.34786	0.328653	0.164327	−	0.986406i	$-0.447455\pi$
$809$	9.34786	0.328653	0.164327	+	0.986406i	$0.447455\pi$
$810$	0.545066	0.0191517
$811$	−10.7341	−0.376925	−0.188463	−	0.982080i	$-0.560350\pi$
$811$	−10.7341	−0.376925	−0.188463	+	0.982080i	$0.560350\pi$
$812$	−15.9008	−0.558008
$813$	−29.5163	−1.03518
$814$	−16.7461	−0.586952
$815$	1.35770	0.0475583
$816$	−5.18480	−0.181504
$817$	17.9198	0.626934
$818$	14.7436	0.515499
$819$	−0.238059	−0.00831844
$820$	−0.877712	−0.0306510
$821$	13.9500	0.486859	0.243430	−	0.969919i	$-0.421728\pi$
$821$	13.9500	0.486859	0.243430	+	0.969919i	$0.421728\pi$
$822$	−3.43779	−0.119907
$823$	−7.62995	−0.265963	−0.132982	−	0.991119i	$-0.542455\pi$
$823$	−7.62995	−0.265963	−0.132982	+	0.991119i	$0.542455\pi$
$824$	−15.4767	−0.539156
$825$	44.3048	1.54249
$826$	−5.94632	−0.206899
$827$	−50.6423	−1.76101	−0.880503	−	0.474040i	$-0.842795\pi$
$827$	−50.6423	−1.76101	−0.880503	+	0.474040i	$0.842795\pi$
$828$	−1.68912	−0.0587009
$829$	27.1635	0.943428	0.471714	−	0.881752i	$-0.343635\pi$
$829$	27.1635	0.943428	0.471714	+	0.881752i	$0.343635\pi$
$830$	−0.403419	−0.0140029
$831$	−43.2533	−1.50044
$832$	4.33155	0.150170
$833$	−1.28158	−0.0444042
$834$	−4.10980	−0.142311
$835$	1.68662	0.0583678
$836$	74.8545	2.58890
$837$	−35.7702	−1.23640
$838$	2.78010	0.0960368
$839$	18.7378	0.646900	0.323450	−	0.946245i	$-0.395157\pi$
$839$	18.7378	0.646900	0.323450	+	0.946245i	$0.395157\pi$
$840$	−0.397646	−0.0137201
$841$	56.8153	1.95915
$842$	−16.1173	−0.555440
$843$	18.3519	0.632074
$844$	22.9695	0.790643
$845$	0.968614	0.0333213
$846$	−0.103775	−0.00356786
$847$	−16.3077	−0.560339
$848$	10.1610	0.348930
$849$	2.50708	0.0860428
$850$	3.40252	0.116706
$851$	−54.5236	−1.86905
$852$	12.0390	0.412450
$853$	49.8498	1.70682	0.853412	−	0.521238i	$-0.174530\pi$
$853$	49.8498	1.70682	0.853412	+	0.521238i	$0.174530\pi$
$854$	5.55533	0.190100
$855$	0.107119	0.00366338
$856$	21.8117	0.745508
$857$	39.2898	1.34211	0.671057	−	0.741406i	$-0.265841\pi$
$857$	39.2898	1.34211	0.671057	+	0.741406i	$0.265841\pi$
$858$	10.3697	0.354016
$859$	37.3922	1.27581	0.637903	−	0.770117i	$-0.279802\pi$
$859$	37.3922	1.27581	0.637903	+	0.770117i	$0.279802\pi$
$860$	0.435556	0.0148524
$861$	7.35790	0.250757
$862$	−6.61949	−0.225461
$863$	41.1465	1.40064	0.700322	−	0.713827i	$-0.253040\pi$
$863$	41.1465	1.40064	0.700322	+	0.713827i	$0.253040\pi$
$864$	−27.6175	−0.939565
$865$	−0.372483	−0.0126648
$866$	14.7325	0.500630
$867$	−26.1141	−0.886880
$868$	11.6155	0.394255
$869$	59.4575	2.01696
$870$	0.991171	0.0336039
$871$	31.6366	1.07197
$872$	0.652157	0.0220848
$873$	−0.663644	−0.0224609
$874$	−40.2578	−1.36174
$875$	−1.18007	−0.0398936
$876$	−48.4321	−1.63637
$877$	−40.2479	−1.35907	−0.679537	−	0.733641i	$-0.737819\pi$
$877$	−40.2479	−1.35907	−0.679537	+	0.733641i	$0.737819\pi$
$878$	2.88077	0.0972214
$879$	21.5762	0.727746
$880$	1.46923	0.0495277
$881$	45.5773	1.53554	0.767769	−	0.640727i	$-0.221367\pi$
$881$	45.5773	1.53554	0.767769	+	0.640727i	$0.221367\pi$
$882$	−0.0578377	−0.00194750
$883$	11.2401	0.378259	0.189130	−	0.981952i	$-0.439433\pi$
$883$	11.2401	0.378259	0.189130	+	0.981952i	$0.439433\pi$
$884$	−4.82120	−0.162155
$885$	−2.24397	−0.0754301
$886$	−6.14929	−0.206589
$887$	18.7760	0.630437	0.315219	−	0.949019i	$-0.397922\pi$
$887$	18.7760	0.630437	0.315219	+	0.949019i	$0.397922\pi$
$888$	−20.2514	−0.679593
$889$	1.00000	0.0335389
$890$	0.232775	0.00780262
$891$	45.2666	1.51649
$892$	6.39882	0.214248
$893$	14.9734	0.501066
$894$	−4.43046	−0.148177
$895$	−2.60793	−0.0871736
$896$	11.5018	0.384249
$897$	33.7627	1.12730
$898$	−20.0993	−0.670721
$899$	−62.6878	−2.09076
$900$	−0.929615	−0.0309872
$901$	−5.47330	−0.182342
$902$	12.0405	0.400903
$903$	−3.65129	−0.121507
$904$	3.61309	0.120170
$905$	−2.10205	−0.0698746
$906$	10.0834	0.334998
$907$	−28.0916	−0.932767	−0.466383	−	0.884583i	$-0.654443\pi$
$907$	−28.0916	−0.932767	−0.466383	+	0.884583i	$0.654443\pi$
$908$	−12.9181	−0.428703
$909$	−0.0644849	−0.00213883
$910$	−0.137907	−0.00457157
$911$	−11.5012	−0.381053	−0.190526	−	0.981682i	$-0.561019\pi$
$911$	−11.5012	−0.381053	−0.190526	+	0.981682i	$0.561019\pi$
$912$	33.7617	1.11796
$913$	−33.5031	−1.10879
$914$	−2.58874	−0.0856279
$915$	2.09642	0.0693054
$916$	1.39233	0.0460038
$917$	8.23408	0.271913
$918$	3.60717	0.119054
$919$	−21.4575	−0.707818	−0.353909	−	0.935280i	$-0.615148\pi$
$919$	−21.4575	−0.707818	−0.353909	+	0.935280i	$0.615148\pi$
$920$	−2.11864	−0.0698493
$921$	−12.9275	−0.425976
$922$	−11.8407	−0.389953
$923$	9.04013	0.297559
$924$	−15.2522	−0.501759
$925$	−30.0074	−0.986637
$926$	−18.1531	−0.596548
$927$	−0.849492	−0.0279010
$928$	−48.4001	−1.58881
$929$	58.5953	1.92245	0.961225	−	0.275766i	$-0.0889316\pi$
$929$	58.5953	1.92245	0.961225	+	0.275766i	$0.0889316\pi$
$930$	−0.724047	−0.0237424
$931$	8.34525	0.273504
$932$	−37.3628	−1.22386
$933$	−58.9138	−1.92875
$934$	−9.63277	−0.315194
$935$	−0.791413	−0.0258820
$936$	−0.471101	−0.0153984
$937$	−37.4295	−1.22277	−0.611384	−	0.791334i	$-0.709387\pi$
$937$	−37.4295	−1.22277	−0.611384	+	0.791334i	$0.709387\pi$
$938$	7.68629	0.250966
$939$	−22.8096	−0.744363
$940$	0.363942	0.0118705
$941$	−44.8032	−1.46054	−0.730272	−	0.683157i	$-0.760607\pi$
$941$	−44.8032	−1.46054	−0.730272	+	0.683157i	$0.760607\pi$
$942$	−14.4530	−0.470906
$943$	39.2024	1.27661
$944$	26.5694	0.864761
$945$	−0.624647	−0.0203198
$946$	−5.97497	−0.194263
$947$	30.9990	1.00733	0.503666	−	0.863898i	$-0.331984\pi$
$947$	30.9990	1.00733	0.503666	+	0.863898i	$0.331984\pi$
$948$	33.2088	1.07857
$949$	−36.3678	−1.18055
$950$	−22.1561	−0.718840
$951$	−43.1539	−1.39936
$952$	−2.53616	−0.0821974
$953$	45.1029	1.46103	0.730513	−	0.682899i	$-0.239281\pi$
$953$	45.1029	1.46103	0.730513	+	0.682899i	$0.239281\pi$
$954$	−0.247010	−0.00799723
$955$	−1.13995	−0.0368878
$956$	−17.5965	−0.569112
$957$	82.3147	2.66086
$958$	7.40059	0.239102
$959$	3.79688	0.122608
$960$	0.397135	0.0128175
$961$	14.7932	0.477201
$962$	−7.02335	−0.226442
$963$	1.19721	0.0385796
$964$	−21.4490	−0.690826
$965$	−1.43961	−0.0463426
$966$	8.20283	0.263922
$967$	57.9650	1.86403	0.932015	−	0.362420i	$-0.118049\pi$
$967$	57.9650	1.86403	0.932015	+	0.362420i	$0.118049\pi$
$968$	−32.2717	−1.03725
$969$	−18.1861	−0.584220
$970$	−0.384448	−0.0123439
$971$	48.9510	1.57091	0.785457	−	0.618916i	$-0.212428\pi$
$971$	48.9510	1.57091	0.785457	+	0.618916i	$0.212428\pi$
$972$	−1.93662	−0.0621170
$973$	4.53910	0.145517
$974$	−0.780984	−0.0250243
$975$	18.5815	0.595084
$976$	−24.8224	−0.794546
$977$	38.2915	1.22505	0.612526	−	0.790450i	$-0.290153\pi$
$977$	38.2915	1.22505	0.612526	+	0.790450i	$0.290153\pi$
$978$	−10.4026	−0.332639
$979$	19.3314	0.617836
$980$	0.202839	0.00647944
$981$	0.0357959	0.00114288
$982$	7.12632	0.227410
$983$	−4.26394	−0.135999	−0.0679993	−	0.997685i	$-0.521662\pi$
$983$	−4.26394	−0.135999	−0.0679993	+	0.997685i	$0.521662\pi$
$984$	14.5608	0.464180
$985$	−0.599749	−0.0191096
$986$	6.32162	0.201321
$987$	−3.05094	−0.0971126
$988$	31.3941	0.998779
$989$	−19.4539	−0.618596
$990$	−0.0357164	−0.00113514
$991$	8.67251	0.275491	0.137746	−	0.990468i	$-0.456014\pi$
$991$	8.67251	0.275491	0.137746	+	0.990468i	$0.456014\pi$
$992$	35.3561	1.12256
$993$	7.36123	0.233602
$994$	2.19635	0.0696640
$995$	−0.406371	−0.0128828
$996$	−18.7125	−0.592928
$997$	31.2119	0.988492	0.494246	−	0.869322i	$-0.335444\pi$
$997$	31.2119	0.988492	0.494246	+	0.869322i	$0.335444\pi$
$998$	11.6472	0.368686
$999$	−31.8122	−1.00649

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	889.2.a.c.1.11	✓	16
3.2	odd	2		8001.2.a.t.1.6		16
7.6	odd	2		6223.2.a.k.1.11		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
889.2.a.c.1.11	✓	16	1.1	even	1	trivial
6223.2.a.k.1.11		16	7.6	odd	2
8001.2.a.t.1.6		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:	\( N \)	\(=\)	\( 889 = 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	889.a (trivial)

\(f(q)\)	\(=\)	\(q+0.532475 q^{2} +1.70041 q^{3} -1.71647 q^{4} -0.118172 q^{5} +0.905424 q^{6} -1.00000 q^{7} -1.97893 q^{8} -0.108620 q^{9} -0.0629236 q^{10} -5.22568 q^{11} -2.91870 q^{12} -2.19166 q^{13} -0.532475 q^{14} -0.200940 q^{15} +2.37921 q^{16} -1.28158 q^{17} -0.0578377 q^{18} +8.34525 q^{19} +0.202839 q^{20} -1.70041 q^{21} -2.78254 q^{22} -9.05966 q^{23} -3.36498 q^{24} -4.98604 q^{25} -1.16700 q^{26} -5.28592 q^{27} +1.71647 q^{28} -9.26366 q^{29} -0.106996 q^{30} +6.76707 q^{31} +5.22473 q^{32} -8.88577 q^{33} -0.682411 q^{34} +0.118172 q^{35} +0.186444 q^{36} +6.01829 q^{37} +4.44364 q^{38} -3.72670 q^{39} +0.233854 q^{40} -4.32714 q^{41} -0.905424 q^{42} +2.14731 q^{43} +8.96972 q^{44} +0.0128359 q^{45} -4.82404 q^{46} +1.79425 q^{47} +4.04562 q^{48} +1.00000 q^{49} -2.65494 q^{50} -2.17921 q^{51} +3.76191 q^{52} +4.27074 q^{53} -2.81462 q^{54} +0.617528 q^{55} +1.97893 q^{56} +14.1903 q^{57} -4.93267 q^{58} +11.1673 q^{59} +0.344908 q^{60} -10.4330 q^{61} +3.60330 q^{62} +0.108620 q^{63} -1.97638 q^{64} +0.258992 q^{65} -4.73145 q^{66} -14.4350 q^{67} +2.19980 q^{68} -15.4051 q^{69} +0.0629236 q^{70} -4.12479 q^{71} +0.214952 q^{72} +16.5937 q^{73} +3.20459 q^{74} -8.47828 q^{75} -14.3244 q^{76} +5.22568 q^{77} -1.98438 q^{78} -11.3780 q^{79} -0.281156 q^{80} -8.66234 q^{81} -2.30410 q^{82} +6.41125 q^{83} +2.91870 q^{84} +0.151447 q^{85} +1.14339 q^{86} -15.7520 q^{87} +10.3412 q^{88} -3.69932 q^{89} +0.00683479 q^{90} +2.19166 q^{91} +15.5506 q^{92} +11.5068 q^{93} +0.955391 q^{94} -0.986174 q^{95} +8.88415 q^{96} +6.10975 q^{97} +0.532475 q^{98} +0.567615 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 4 q^{3} + 12 q^{4} - 9 q^{5} - 12 q^{6} - 16 q^{7} - 6 q^{8} + 14 q^{9} - 2 q^{10} - 22 q^{11} - 10 q^{12} - 4 q^{13} + 2 q^{14} - 14 q^{15} + 12 q^{16} - 18 q^{17} - 5 q^{18} - 15 q^{19}+ \cdots - 73 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 - 4 * q^3 + 12 * q^4 - 9 * q^5 - 12 * q^6 - 16 * q^7 - 6 * q^8 + 14 * q^9 - 2 * q^10 - 22 * q^11 - 10 * q^12 - 4 * q^13 + 2 * q^14 - 14 * q^15 + 12 * q^16 - 18 * q^17 - 5 * q^18 - 15 * q^19 - 40 * q^20 + 4 * q^21 - 11 * q^22 - 5 * q^23 - 26 * q^24 + 15 * q^25 - 24 * q^26 - 10 * q^27 - 12 * q^28 - 12 * q^29 + 3 * q^30 - 32 * q^31 - 9 * q^32 - 10 * q^33 - 14 * q^34 + 9 * q^35 + 10 * q^36 - 2 * q^37 + 3 * q^38 - 41 * q^39 - 14 * q^40 - 45 * q^41 + 12 * q^42 - 3 * q^43 - 54 * q^44 - 22 * q^45 - 49 * q^47 + 10 * q^48 + 16 * q^49 - 6 * q^50 - 12 * q^51 + 38 * q^52 + 16 * q^53 - 67 * q^54 + 7 * q^55 + 6 * q^56 + 8 * q^57 + 16 * q^58 - 35 * q^59 + 56 * q^60 - 11 * q^61 + 17 * q^62 - 14 * q^63 - 2 * q^64 + 14 * q^65 + 86 * q^66 + 17 * q^67 - 71 * q^68 - 17 * q^69 + 2 * q^70 - 81 * q^71 + 13 * q^72 - 15 * q^73 + 13 * q^74 - 48 * q^75 + 14 * q^76 + 22 * q^77 - 10 * q^78 - 34 * q^79 - 33 * q^80 + 40 * q^81 - 14 * q^82 - 39 * q^83 + 10 * q^84 - 17 * q^85 + 36 * q^86 + 7 * q^87 + 61 * q^88 - 32 * q^89 + 79 * q^90 + 4 * q^91 + 37 * q^92 + 27 * q^93 + 13 * q^94 - 33 * q^95 - 55 * q^96 - 4 * q^97 - 2 * q^98 - 73 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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