LMFDB - Embedded newform 8015.2.a.m.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$67$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.76232 q^{2} -3.28691 q^{3} +1.10578 q^{4} +1.00000 q^{5} +5.79259 q^{6} -1.00000 q^{7} +1.57590 q^{8} +7.80377 q^{9} +O(q^{10})$	\(q-1.76232 q^{2} -3.28691 q^{3} +1.10578 q^{4} +1.00000 q^{5} +5.79259 q^{6} -1.00000 q^{7} +1.57590 q^{8} +7.80377 q^{9} -1.76232 q^{10} +4.40636 q^{11} -3.63460 q^{12} +5.43044 q^{13} +1.76232 q^{14} -3.28691 q^{15} -4.98881 q^{16} -1.03103 q^{17} -13.7528 q^{18} -5.58530 q^{19} +1.10578 q^{20} +3.28691 q^{21} -7.76543 q^{22} -5.83481 q^{23} -5.17984 q^{24} +1.00000 q^{25} -9.57019 q^{26} -15.7895 q^{27} -1.10578 q^{28} -2.55617 q^{29} +5.79259 q^{30} +6.32288 q^{31} +5.64009 q^{32} -14.4833 q^{33} +1.81701 q^{34} -1.00000 q^{35} +8.62926 q^{36} +3.64651 q^{37} +9.84310 q^{38} -17.8494 q^{39} +1.57590 q^{40} +5.95517 q^{41} -5.79259 q^{42} -9.29106 q^{43} +4.87248 q^{44} +7.80377 q^{45} +10.2828 q^{46} -1.03700 q^{47} +16.3978 q^{48} +1.00000 q^{49} -1.76232 q^{50} +3.38890 q^{51} +6.00488 q^{52} +2.25858 q^{53} +27.8263 q^{54} +4.40636 q^{55} -1.57590 q^{56} +18.3584 q^{57} +4.50480 q^{58} -3.22683 q^{59} -3.63460 q^{60} +11.7743 q^{61} -11.1430 q^{62} -7.80377 q^{63} +0.0379570 q^{64} +5.43044 q^{65} +25.5243 q^{66} +2.58147 q^{67} -1.14009 q^{68} +19.1785 q^{69} +1.76232 q^{70} +7.64634 q^{71} +12.2980 q^{72} +11.6989 q^{73} -6.42632 q^{74} -3.28691 q^{75} -6.17612 q^{76} -4.40636 q^{77} +31.4563 q^{78} -1.20217 q^{79} -4.98881 q^{80} +28.4875 q^{81} -10.4949 q^{82} +1.63094 q^{83} +3.63460 q^{84} -1.03103 q^{85} +16.3738 q^{86} +8.40189 q^{87} +6.94399 q^{88} +3.55742 q^{89} -13.7528 q^{90} -5.43044 q^{91} -6.45203 q^{92} -20.7827 q^{93} +1.82754 q^{94} -5.58530 q^{95} -18.5385 q^{96} -15.7490 q^{97} -1.76232 q^{98} +34.3862 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9}+O(q^{10}) $ 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9} + 3 q^{10} + 11 q^{11} + 9 q^{12} + 19 q^{13} - 3 q^{14} + 93 q^{16} + 7 q^{17} + 9 q^{18} + 36 q^{19} + 73 q^{20} - 8 q^{22} - 2 q^{23} + 37 q^{24} + 67 q^{25} + 39 q^{26} + 6 q^{27} - 73 q^{28} + 56 q^{29} + 17 q^{30} + 63 q^{31} + 27 q^{32} + 51 q^{33} + 55 q^{34} - 67 q^{35} + 148 q^{36} + 28 q^{37} + 10 q^{38} + 7 q^{39} + 12 q^{40} + 84 q^{41} - 17 q^{42} - 11 q^{43} + 41 q^{44} + 97 q^{45} + 17 q^{46} - 10 q^{47} + 10 q^{48} + 67 q^{49} + 3 q^{50} - q^{51} + 49 q^{52} + 3 q^{53} + 20 q^{54} + 11 q^{55} - 12 q^{56} + 45 q^{57} + 22 q^{58} + 80 q^{59} + 9 q^{60} + 64 q^{61} - 37 q^{62} - 97 q^{63} + 110 q^{64} + 19 q^{65} + 75 q^{66} + 22 q^{67} + 7 q^{68} + 107 q^{69} - 3 q^{70} + 24 q^{71} + 72 q^{72} + 83 q^{73} + 52 q^{74} + 115 q^{76} - 11 q^{77} - 70 q^{78} - 32 q^{79} + 93 q^{80} + 183 q^{81} + 56 q^{82} - 58 q^{83} - 9 q^{84} + 7 q^{85} + 51 q^{86} + 20 q^{87} - 5 q^{88} + 129 q^{89} + 9 q^{90} - 19 q^{91} - 37 q^{92} + 33 q^{93} + 89 q^{94} + 36 q^{95} + 129 q^{96} + 126 q^{97} + 3 q^{98} - 27 q^{99}+O(q^{100}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9 + 3 * q^10 + 11 * q^11 + 9 * q^12 + 19 * q^13 - 3 * q^14 + 93 * q^16 + 7 * q^17 + 9 * q^18 + 36 * q^19 + 73 * q^20 - 8 * q^22 - 2 * q^23 + 37 * q^24 + 67 * q^25 + 39 * q^26 + 6 * q^27 - 73 * q^28 + 56 * q^29 + 17 * q^30 + 63 * q^31 + 27 * q^32 + 51 * q^33 + 55 * q^34 - 67 * q^35 + 148 * q^36 + 28 * q^37 + 10 * q^38 + 7 * q^39 + 12 * q^40 + 84 * q^41 - 17 * q^42 - 11 * q^43 + 41 * q^44 + 97 * q^45 + 17 * q^46 - 10 * q^47 + 10 * q^48 + 67 * q^49 + 3 * q^50 - q^51 + 49 * q^52 + 3 * q^53 + 20 * q^54 + 11 * q^55 - 12 * q^56 + 45 * q^57 + 22 * q^58 + 80 * q^59 + 9 * q^60 + 64 * q^61 - 37 * q^62 - 97 * q^63 + 110 * q^64 + 19 * q^65 + 75 * q^66 + 22 * q^67 + 7 * q^68 + 107 * q^69 - 3 * q^70 + 24 * q^71 + 72 * q^72 + 83 * q^73 + 52 * q^74 + 115 * q^76 - 11 * q^77 - 70 * q^78 - 32 * q^79 + 93 * q^80 + 183 * q^81 + 56 * q^82 - 58 * q^83 - 9 * q^84 + 7 * q^85 + 51 * q^86 + 20 * q^87 - 5 * q^88 + 129 * q^89 + 9 * q^90 - 19 * q^91 - 37 * q^92 + 33 * q^93 + 89 * q^94 + 36 * q^95 + 129 * q^96 + 126 * q^97 + 3 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.76232	−1.24615	−0.623075	−	0.782162i	$-0.714117\pi$
$2$	−1.76232	−1.24615	−0.623075	+	0.782162i	$0.714117\pi$
$3$	−3.28691	−1.89770	−0.948849	−	0.315731i	$-0.897750\pi$
$3$	−3.28691	−1.89770	−0.948849	+	0.315731i	$0.897750\pi$
$4$	1.10578	0.552891
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	5.79259	2.36482
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.57590	0.557165
$9$	7.80377	2.60126
$10$	−1.76232	−0.557295
$11$	4.40636	1.32857	0.664284	−	0.747480i	$-0.268736\pi$
$11$	4.40636	1.32857	0.664284	+	0.747480i	$0.268736\pi$
$12$	−3.63460	−1.04922
$13$	5.43044	1.50613	0.753066	−	0.657944i	$-0.228574\pi$
$13$	5.43044	1.50613	0.753066	+	0.657944i	$0.228574\pi$
$14$	1.76232	0.471001
$15$	−3.28691	−0.848676
$16$	−4.98881	−1.24720
$17$	−1.03103	−0.250061	−0.125031	−	0.992153i	$-0.539903\pi$
$17$	−1.03103	−0.250061	−0.125031	+	0.992153i	$0.539903\pi$
$18$	−13.7528	−3.24156
$19$	−5.58530	−1.28136	−0.640678	−	0.767810i	$-0.721347\pi$
$19$	−5.58530	−1.28136	−0.640678	+	0.767810i	$0.721347\pi$
$20$	1.10578	0.247260
$21$	3.28691	0.717262
$22$	−7.76543	−1.65560
$23$	−5.83481	−1.21664	−0.608321	−	0.793691i	$-0.708157\pi$
$23$	−5.83481	−1.21664	−0.608321	+	0.793691i	$0.708157\pi$
$24$	−5.17984	−1.05733
$25$	1.00000	0.200000
$26$	−9.57019	−1.87687
$27$	−15.7895	−3.03870
$28$	−1.10578	−0.208973
$29$	−2.55617	−0.474669	−0.237334	−	0.971428i	$-0.576274\pi$
$29$	−2.55617	−0.474669	−0.237334	+	0.971428i	$0.576274\pi$
$30$	5.79259	1.05758
$31$	6.32288	1.13562	0.567811	−	0.823159i	$-0.307790\pi$
$31$	6.32288	1.13562	0.567811	+	0.823159i	$0.307790\pi$
$32$	5.64009	0.997037
$33$	−14.4833	−2.52122
$34$	1.81701	0.311614
$35$	−1.00000	−0.169031
$36$	8.62926	1.43821
$37$	3.64651	0.599482	0.299741	−	0.954021i	$-0.403100\pi$
$37$	3.64651	0.599482	0.299741	+	0.954021i	$0.403100\pi$
$38$	9.84310	1.59676
$39$	−17.8494	−2.85818
$40$	1.57590	0.249172
$41$	5.95517	0.930041	0.465021	−	0.885300i	$-0.346047\pi$
$41$	5.95517	0.930041	0.465021	+	0.885300i	$0.346047\pi$
$42$	−5.79259	−0.893817
$43$	−9.29106	−1.41687	−0.708436	−	0.705775i	$-0.750599\pi$
$43$	−9.29106	−1.41687	−0.708436	+	0.705775i	$0.750599\pi$
$44$	4.87248	0.734553
$45$	7.80377	1.16332
$46$	10.2828	1.51612
$47$	−1.03700	−0.151263	−0.0756314	−	0.997136i	$-0.524097\pi$
$47$	−1.03700	−0.151263	−0.0756314	+	0.997136i	$0.524097\pi$
$48$	16.3978	2.36681
$49$	1.00000	0.142857
$50$	−1.76232	−0.249230
$51$	3.38890	0.474541
$52$	6.00488	0.832727
$53$	2.25858	0.310240	0.155120	−	0.987896i	$-0.450424\pi$
$53$	2.25858	0.310240	0.155120	+	0.987896i	$0.450424\pi$
$54$	27.8263	3.78667
$55$	4.40636	0.594154
$56$	−1.57590	−0.210589
$57$	18.3584	2.43163
$58$	4.50480	0.591509
$59$	−3.22683	−0.420097	−0.210049	−	0.977691i	$-0.567362\pi$
$59$	−3.22683	−0.420097	−0.210049	+	0.977691i	$0.567362\pi$
$60$	−3.63460	−0.469225
$61$	11.7743	1.50754	0.753772	−	0.657136i	$-0.228232\pi$
$61$	11.7743	1.50754	0.753772	+	0.657136i	$0.228232\pi$
$62$	−11.1430	−1.41516
$63$	−7.80377	−0.983182
$64$	0.0379570	0.00474462
$65$	5.43044	0.673563
$66$	25.5243	3.14182
$67$	2.58147	0.315377	0.157689	−	0.987489i	$-0.449596\pi$
$67$	2.58147	0.315377	0.157689	+	0.987489i	$0.449596\pi$
$68$	−1.14009	−0.138257
$69$	19.1785	2.30882
$70$	1.76232	0.210638
$71$	7.64634	0.907454	0.453727	−	0.891141i	$-0.350094\pi$
$71$	7.64634	0.907454	0.453727	+	0.891141i	$0.350094\pi$
$72$	12.2980	1.44933
$73$	11.6989	1.36925	0.684624	−	0.728897i	$-0.259967\pi$
$73$	11.6989	1.36925	0.684624	+	0.728897i	$0.259967\pi$
$74$	−6.42632	−0.747045
$75$	−3.28691	−0.379539
$76$	−6.17612	−0.708450
$77$	−4.40636	−0.502152
$78$	31.4563	3.56173
$79$	−1.20217	−0.135255	−0.0676276	−	0.997711i	$-0.521543\pi$
$79$	−1.20217	−0.135255	−0.0676276	+	0.997711i	$0.521543\pi$
$80$	−4.98881	−0.557766
$81$	28.4875	3.16527
$82$	−10.4949	−1.15897
$83$	1.63094	0.179019	0.0895093	−	0.995986i	$-0.471470\pi$
$83$	1.63094	0.179019	0.0895093	+	0.995986i	$0.471470\pi$
$84$	3.63460	0.396568
$85$	−1.03103	−0.111831
$86$	16.3738	1.76564
$87$	8.40189	0.900778
$88$	6.94399	0.740232
$89$	3.55742	0.377085	0.188543	−	0.982065i	$-0.439624\pi$
$89$	3.55742	0.377085	0.188543	+	0.982065i	$0.439624\pi$
$90$	−13.7528	−1.44967
$91$	−5.43044	−0.569265
$92$	−6.45203	−0.672670
$93$	−20.7827	−2.15507
$94$	1.82754	0.188496
$95$	−5.58530	−0.573040
$96$	−18.5385	−1.89207
$97$	−15.7490	−1.59907	−0.799535	−	0.600620i	$-0.794921\pi$
$97$	−15.7490	−1.59907	−0.799535	+	0.600620i	$0.794921\pi$
$98$	−1.76232	−0.178021
$99$	34.3862	3.45595
$100$	1.10578	0.110578
$101$	16.7386	1.66555	0.832775	−	0.553611i	$-0.186751\pi$
$101$	16.7386	1.66555	0.832775	+	0.553611i	$0.186751\pi$
$102$	−5.97233	−0.591349
$103$	−12.0463	−1.18696	−0.593480	−	0.804849i	$-0.702246\pi$
$103$	−12.0463	−1.18696	−0.593480	+	0.804849i	$0.702246\pi$
$104$	8.55783	0.839165
$105$	3.28691	0.320769
$106$	−3.98035	−0.386606
$107$	−5.65632	−0.546817	−0.273408	−	0.961898i	$-0.588151\pi$
$107$	−5.65632	−0.546817	−0.273408	+	0.961898i	$0.588151\pi$
$108$	−17.4598	−1.68007
$109$	−10.1238	−0.969683	−0.484842	−	0.874602i	$-0.661123\pi$
$109$	−10.1238	−0.969683	−0.484842	+	0.874602i	$0.661123\pi$
$110$	−7.76543	−0.740405
$111$	−11.9857	−1.13764
$112$	4.98881	0.471398
$113$	−10.9738	−1.03233	−0.516163	−	0.856491i	$-0.672640\pi$
$113$	−10.9738	−1.03233	−0.516163	+	0.856491i	$0.672640\pi$
$114$	−32.3534	−3.03017
$115$	−5.83481	−0.544099
$116$	−2.82657	−0.262440
$117$	42.3779	3.91784
$118$	5.68672	0.523505
$119$	1.03103	0.0945143
$120$	−5.17984	−0.472853
$121$	8.41603	0.765094
$122$	−20.7501	−1.87863
$123$	−19.5741	−1.76494
$124$	6.99172	0.627875
$125$	1.00000	0.0894427
$126$	13.7528	1.22519
$127$	17.3350	1.53823	0.769117	−	0.639108i	$-0.220696\pi$
$127$	17.3350	1.53823	0.769117	+	0.639108i	$0.220696\pi$
$128$	−11.3471	−1.00295
$129$	30.5389	2.68880
$130$	−9.57019	−0.839361
$131$	−10.1945	−0.890697	−0.445348	−	0.895357i	$-0.646920\pi$
$131$	−10.1945	−0.890697	−0.445348	+	0.895357i	$0.646920\pi$
$132$	−16.0154	−1.39396
$133$	5.58530	0.484307
$134$	−4.54939	−0.393008
$135$	−15.7895	−1.35895
$136$	−1.62480	−0.139325
$137$	3.18481	0.272096	0.136048	−	0.990702i	$-0.456560\pi$
$137$	3.18481	0.272096	0.136048	+	0.990702i	$0.456560\pi$
$138$	−33.7987	−2.87714
$139$	−12.3160	−1.04463	−0.522316	−	0.852752i	$-0.674932\pi$
$139$	−12.3160	−1.04463	−0.522316	+	0.852752i	$0.674932\pi$
$140$	−1.10578	−0.0934556
$141$	3.40854	0.287051
$142$	−13.4753	−1.13082
$143$	23.9285	2.00100
$144$	−38.9315	−3.24429
$145$	−2.55617	−0.212278
$146$	−20.6172	−1.70629
$147$	−3.28691	−0.271100
$148$	4.03224	0.331448
$149$	21.9670	1.79961	0.899805	−	0.436293i	$-0.143709\pi$
$149$	21.9670	1.79961	0.899805	+	0.436293i	$0.143709\pi$
$150$	5.79259	0.472963
$151$	−9.44146	−0.768335	−0.384168	−	0.923263i	$-0.625511\pi$
$151$	−9.44146	−0.768335	−0.384168	+	0.923263i	$0.625511\pi$
$152$	−8.80188	−0.713927
$153$	−8.04591	−0.650473
$154$	7.76543	0.625756
$155$	6.32288	0.507866
$156$	−19.7375	−1.58026
$157$	−17.4523	−1.39285	−0.696424	−	0.717630i	$-0.745227\pi$
$157$	−17.4523	−1.39285	−0.696424	+	0.717630i	$0.745227\pi$
$158$	2.11862	0.168548
$159$	−7.42375	−0.588742
$160$	5.64009	0.445888
$161$	5.83481	0.459848
$162$	−50.2041	−3.94441
$163$	−0.502139	−0.0393306	−0.0196653	−	0.999807i	$-0.506260\pi$
$163$	−0.502139	−0.0393306	−0.0196653	+	0.999807i	$0.506260\pi$
$164$	6.58512	0.514211
$165$	−14.4833	−1.12752
$166$	−2.87424	−0.223084
$167$	12.9429	1.00155	0.500776	−	0.865577i	$-0.333048\pi$
$167$	12.9429	1.00155	0.500776	+	0.865577i	$0.333048\pi$
$168$	5.17984	0.399633
$169$	16.4897	1.26844
$170$	1.81701	0.139358
$171$	−43.5864	−3.33313
$172$	−10.2739	−0.783376
$173$	4.06779	0.309268	0.154634	−	0.987972i	$-0.450580\pi$
$173$	4.06779	0.309268	0.154634	+	0.987972i	$0.450580\pi$
$174$	−14.8068	−1.12250
$175$	−1.00000	−0.0755929
$176$	−21.9825	−1.65699
$177$	10.6063	0.797218
$178$	−6.26932	−0.469905
$179$	12.7406	0.952275	0.476137	−	0.879371i	$-0.342037\pi$
$179$	12.7406	0.952275	0.476137	+	0.879371i	$0.342037\pi$
$180$	8.62926	0.643187
$181$	−6.87661	−0.511134	−0.255567	−	0.966791i	$-0.582262\pi$
$181$	−6.87661	−0.511134	−0.255567	+	0.966791i	$0.582262\pi$
$182$	9.57019	0.709389
$183$	−38.7010	−2.86086
$184$	−9.19509	−0.677871
$185$	3.64651	0.268097
$186$	36.6259	2.68554
$187$	−4.54309	−0.332224
$188$	−1.14670	−0.0836318
$189$	15.7895	1.14852
$190$	9.84310	0.714094
$191$	8.29513	0.600214	0.300107	−	0.953905i	$-0.402978\pi$
$191$	8.29513	0.600214	0.300107	+	0.953905i	$0.402978\pi$
$192$	−0.124761	−0.00900385
$193$	5.73607	0.412891	0.206446	−	0.978458i	$-0.433810\pi$
$193$	5.73607	0.412891	0.206446	+	0.978458i	$0.433810\pi$
$194$	27.7548	1.99268
$195$	−17.8494	−1.27822
$196$	1.10578	0.0789844
$197$	0.400857	0.0285599	0.0142800	−	0.999898i	$-0.495454\pi$
$197$	0.400857	0.0285599	0.0142800	+	0.999898i	$0.495454\pi$
$198$	−60.5996	−4.30663
$199$	25.2282	1.78838	0.894191	−	0.447686i	$-0.147752\pi$
$199$	25.2282	1.78838	0.894191	+	0.447686i	$0.147752\pi$
$200$	1.57590	0.111433
$201$	−8.48507	−0.598491
$202$	−29.4988	−2.07553
$203$	2.55617	0.179408
$204$	3.74738	0.262369
$205$	5.95517	0.415927
$206$	21.2295	1.47913
$207$	−45.5335	−3.16480
$208$	−27.0914	−1.87845
$209$	−24.6109	−1.70237
$210$	−5.79259	−0.399727
$211$	−2.40582	−0.165623	−0.0828116	−	0.996565i	$-0.526390\pi$
$211$	−2.40582	−0.165623	−0.0828116	+	0.996565i	$0.526390\pi$
$212$	2.49750	0.171529
$213$	−25.1328	−1.72207
$214$	9.96826	0.681416
$215$	−9.29106	−0.633645
$216$	−24.8827	−1.69306
$217$	−6.32288	−0.429225
$218$	17.8414	1.20837
$219$	−38.4531	−2.59842
$220$	4.87248	0.328502
$221$	−5.59894	−0.376626
$222$	21.1227	1.41767
$223$	19.8283	1.32780	0.663900	−	0.747821i	$-0.268900\pi$
$223$	19.8283	1.32780	0.663900	+	0.747821i	$0.268900\pi$
$224$	−5.64009	−0.376845
$225$	7.80377	0.520251
$226$	19.3393	1.28643
$227$	23.7096	1.57366	0.786831	−	0.617169i	$-0.211720\pi$
$227$	23.7096	1.57366	0.786831	+	0.617169i	$0.211720\pi$
$228$	20.3004	1.34442
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	10.2828	0.678029
$231$	14.4833	0.952932
$232$	−4.02827	−0.264469
$233$	−18.0360	−1.18158	−0.590789	−	0.806826i	$-0.701183\pi$
$233$	−18.0360	−1.18158	−0.590789	+	0.806826i	$0.701183\pi$
$234$	−74.6835	−4.88221
$235$	−1.03700	−0.0676467
$236$	−3.56817	−0.232268
$237$	3.95144	0.256673
$238$	−1.81701	−0.117779
$239$	16.3556	1.05795	0.528977	−	0.848636i	$-0.322576\pi$
$239$	16.3556	1.05795	0.528977	+	0.848636i	$0.322576\pi$
$240$	16.3978	1.05847
$241$	13.6237	0.877577	0.438788	−	0.898590i	$-0.355408\pi$
$241$	13.6237	0.877577	0.438788	+	0.898590i	$0.355408\pi$
$242$	−14.8318	−0.953422
$243$	−46.2671	−2.96803
$244$	13.0198	0.833508
$245$	1.00000	0.0638877
$246$	34.4959	2.19938
$247$	−30.3306	−1.92989
$248$	9.96423	0.632729
$249$	−5.36074	−0.339723
$250$	−1.76232	−0.111459
$251$	−0.876001	−0.0552927	−0.0276463	−	0.999618i	$-0.508801\pi$
$251$	−0.876001	−0.0552927	−0.0276463	+	0.999618i	$0.508801\pi$
$252$	−8.62926	−0.543592
$253$	−25.7103	−1.61639
$254$	−30.5499	−1.91687
$255$	3.38890	0.212221
$256$	19.9213	1.24508
$257$	−14.1919	−0.885265	−0.442633	−	0.896703i	$-0.645955\pi$
$257$	−14.1919	−0.885265	−0.442633	+	0.896703i	$0.645955\pi$
$258$	−53.8193	−3.35064
$259$	−3.64651	−0.226583
$260$	6.00488	0.372407
$261$	−19.9477	−1.23473
$262$	17.9660	1.10994
$263$	−4.28934	−0.264492	−0.132246	−	0.991217i	$-0.542219\pi$
$263$	−4.28934	−0.264492	−0.132246	+	0.991217i	$0.542219\pi$
$264$	−22.8243	−1.40474
$265$	2.25858	0.138744
$266$	−9.84310	−0.603519
$267$	−11.6929	−0.715594
$268$	2.85455	0.174369
$269$	13.6871	0.834519	0.417259	−	0.908787i	$-0.362991\pi$
$269$	13.6871	0.834519	0.417259	+	0.908787i	$0.362991\pi$
$270$	27.8263	1.69345
$271$	9.10500	0.553089	0.276545	−	0.961001i	$-0.410811\pi$
$271$	9.10500	0.553089	0.276545	+	0.961001i	$0.410811\pi$
$272$	5.14361	0.311877
$273$	17.8494	1.08029
$274$	−5.61266	−0.339073
$275$	4.40636	0.265714
$276$	21.2072	1.27653
$277$	−8.09876	−0.486607	−0.243304	−	0.969950i	$-0.578231\pi$
$277$	−8.09876	−0.486607	−0.243304	+	0.969950i	$0.578231\pi$
$278$	21.7048	1.30177
$279$	49.3423	2.95404
$280$	−1.57590	−0.0941781
$281$	−28.4769	−1.69879	−0.849394	−	0.527759i	$-0.823032\pi$
$281$	−28.4769	−1.69879	−0.849394	+	0.527759i	$0.823032\pi$
$282$	−6.00695	−0.357709
$283$	24.8978	1.48002	0.740011	−	0.672595i	$-0.234820\pi$
$283$	24.8978	1.48002	0.740011	+	0.672595i	$0.234820\pi$
$284$	8.45519	0.501723
$285$	18.3584	1.08746
$286$	−42.1697	−2.49355
$287$	−5.95517	−0.351523
$288$	44.0140	2.59355
$289$	−15.9370	−0.937469
$290$	4.50480	0.264531
$291$	51.7656	3.03455
$292$	12.9364	0.757045
$293$	15.6565	0.914660	0.457330	−	0.889297i	$-0.348806\pi$
$293$	15.6565	0.914660	0.457330	+	0.889297i	$0.348806\pi$
$294$	5.79259	0.337831
$295$	−3.22683	−0.187873
$296$	5.74653	0.334011
$297$	−69.5744	−4.03712
$298$	−38.7130	−2.24258
$299$	−31.6856	−1.83242
$300$	−3.63460	−0.209844
$301$	9.29106	0.535528
$302$	16.6389	0.957461
$303$	−55.0182	−3.16071
$304$	27.8640	1.59811
$305$	11.7743	0.674194
$306$	14.1795	0.810588
$307$	9.28328	0.529825	0.264912	−	0.964272i	$-0.414657\pi$
$307$	9.28328	0.529825	0.264912	+	0.964272i	$0.414657\pi$
$308$	−4.87248	−0.277635
$309$	39.5952	2.25249
$310$	−11.1430	−0.632877
$311$	12.1809	0.690715	0.345358	−	0.938471i	$-0.387758\pi$
$311$	12.1809	0.690715	0.345358	+	0.938471i	$0.387758\pi$
$312$	−28.1288	−1.59248
$313$	−14.0380	−0.793477	−0.396738	−	0.917932i	$-0.629858\pi$
$313$	−14.0380	−0.793477	−0.396738	+	0.917932i	$0.629858\pi$
$314$	30.7567	1.73570
$315$	−7.80377	−0.439692
$316$	−1.32934	−0.0747813
$317$	−23.1156	−1.29830	−0.649151	−	0.760659i	$-0.724876\pi$
$317$	−23.1156	−1.29830	−0.649151	+	0.760659i	$0.724876\pi$
$318$	13.0830	0.733661
$319$	−11.2634	−0.630630
$320$	0.0379570	0.00212186
$321$	18.5918	1.03769
$322$	−10.2828	−0.573039
$323$	5.75861	0.320417
$324$	31.5009	1.75005
$325$	5.43044	0.301227
$326$	0.884932	0.0490118
$327$	33.2760	1.84017
$328$	9.38476	0.518187
$329$	1.03700	0.0571719
$330$	25.5243	1.40506
$331$	1.82351	0.100229	0.0501146	−	0.998743i	$-0.484041\pi$
$331$	1.82351	0.100229	0.0501146	+	0.998743i	$0.484041\pi$
$332$	1.80346	0.0989778
$333$	28.4565	1.55941
$334$	−22.8096	−1.24808
$335$	2.58147	0.141041
$336$	−16.3978	−0.894571
$337$	24.7765	1.34966	0.674831	−	0.737972i	$-0.264217\pi$
$337$	24.7765	1.34966	0.674831	+	0.737972i	$0.264217\pi$
$338$	−29.0601	−1.58066
$339$	36.0698	1.95904
$340$	−1.14009	−0.0618302
$341$	27.8609	1.50875
$342$	76.8133	4.15359
$343$	−1.00000	−0.0539949
$344$	−14.6418	−0.789432
$345$	19.1785	1.03254
$346$	−7.16876	−0.385395
$347$	27.9134	1.49847	0.749235	−	0.662305i	$-0.230422\pi$
$347$	27.9134	1.49847	0.749235	+	0.662305i	$0.230422\pi$
$348$	9.29066	0.498032
$349$	19.7461	1.05698	0.528491	−	0.848939i	$-0.322758\pi$
$349$	19.7461	1.05698	0.528491	+	0.848939i	$0.322758\pi$
$350$	1.76232	0.0942001
$351$	−85.7441	−4.57668
$352$	24.8523	1.32463
$353$	−9.08110	−0.483338	−0.241669	−	0.970359i	$-0.577695\pi$
$353$	−9.08110	−0.483338	−0.241669	+	0.970359i	$0.577695\pi$
$354$	−18.6917	−0.993453
$355$	7.64634	0.405826
$356$	3.93373	0.208487
$357$	−3.38890	−0.179360
$358$	−22.4530	−1.18668
$359$	−24.7752	−1.30758	−0.653792	−	0.756674i	$-0.726823\pi$
$359$	−24.7752	−1.30758	−0.653792	+	0.756674i	$0.726823\pi$
$360$	12.2980	0.648160
$361$	12.1956	0.641872
$362$	12.1188	0.636950
$363$	−27.6627	−1.45192
$364$	−6.00488	−0.314741
$365$	11.6989	0.612346
$366$	68.2037	3.56507
$367$	20.6897	1.08000	0.539998	−	0.841666i	$-0.318425\pi$
$367$	20.6897	1.08000	0.539998	+	0.841666i	$0.318425\pi$
$368$	29.1088	1.51740
$369$	46.4727	2.41927
$370$	−6.42632	−0.334089
$371$	−2.25858	−0.117260
$372$	−22.9812	−1.19152
$373$	−29.4653	−1.52565	−0.762827	−	0.646602i	$-0.776189\pi$
$373$	−29.4653	−1.52565	−0.762827	+	0.646602i	$0.776189\pi$
$374$	8.00639	0.414000
$375$	−3.28691	−0.169735
$376$	−1.63422	−0.0842783
$377$	−13.8811	−0.714914
$378$	−27.8263	−1.43123
$379$	−34.1260	−1.75294	−0.876468	−	0.481461i	$-0.840106\pi$
$379$	−34.1260	−1.75294	−0.876468	+	0.481461i	$0.840106\pi$
$380$	−6.17612	−0.316828
$381$	−56.9786	−2.91910
$382$	−14.6187	−0.747958
$383$	−14.3001	−0.730703	−0.365352	−	0.930870i	$-0.619051\pi$
$383$	−14.3001	−0.730703	−0.365352	+	0.930870i	$0.619051\pi$
$384$	37.2968	1.90329
$385$	−4.40636	−0.224569
$386$	−10.1088	−0.514524
$387$	−72.5052	−3.68565
$388$	−17.4150	−0.884111
$389$	−0.477694	−0.0242200	−0.0121100	−	0.999927i	$-0.503855\pi$
$389$	−0.477694	−0.0242200	−0.0121100	+	0.999927i	$0.503855\pi$
$390$	31.4563	1.59285
$391$	6.01586	0.304235
$392$	1.57590	0.0795950
$393$	33.5084	1.69027
$394$	−0.706440	−0.0355899
$395$	−1.20217	−0.0604879
$396$	38.0237	1.91076
$397$	−27.5143	−1.38090	−0.690450	−	0.723380i	$-0.742588\pi$
$397$	−27.5143	−1.38090	−0.690450	+	0.723380i	$0.742588\pi$
$398$	−44.4603	−2.22859
$399$	−18.3584	−0.919068
$400$	−4.98881	−0.249441
$401$	1.78056	0.0889167	0.0444584	−	0.999011i	$-0.485844\pi$
$401$	1.78056	0.0889167	0.0444584	+	0.999011i	$0.485844\pi$
$402$	14.9534	0.745810
$403$	34.3360	1.71040
$404$	18.5092	0.920868
$405$	28.4875	1.41555
$406$	−4.50480	−0.223569
$407$	16.0678	0.796453
$408$	5.34057	0.264398
$409$	21.2748	1.05197	0.525987	−	0.850493i	$-0.323696\pi$
$409$	21.2748	1.05197	0.525987	+	0.850493i	$0.323696\pi$
$410$	−10.4949	−0.518308
$411$	−10.4682	−0.516356
$412$	−13.3206	−0.656259
$413$	3.22683	0.158782
$414$	80.2447	3.94381
$415$	1.63094	0.0800596
$416$	30.6282	1.50167
$417$	40.4817	1.98240
$418$	43.3723	2.12141
$419$	−36.6104	−1.78853	−0.894266	−	0.447535i	$-0.852302\pi$
$419$	−36.6104	−1.78853	−0.894266	+	0.447535i	$0.852302\pi$
$420$	3.63460	0.177350
$421$	20.5594	1.00200	0.501002	−	0.865446i	$-0.332965\pi$
$421$	20.5594	1.00200	0.501002	+	0.865446i	$0.332965\pi$
$422$	4.23983	0.206391
$423$	−8.09254	−0.393473
$424$	3.55930	0.172855
$425$	−1.03103	−0.0500123
$426$	44.2922	2.14596
$427$	−11.7743	−0.569798
$428$	−6.25465	−0.302330
$429$	−78.6507	−3.79729
$430$	16.3738	0.789617
$431$	−32.6963	−1.57493	−0.787464	−	0.616361i	$-0.788606\pi$
$431$	−32.6963	−1.57493	−0.787464	+	0.616361i	$0.788606\pi$
$432$	78.7710	3.78987
$433$	−18.0489	−0.867376	−0.433688	−	0.901063i	$-0.642788\pi$
$433$	−18.0489	−0.867376	−0.433688	+	0.901063i	$0.642788\pi$
$434$	11.1430	0.534879
$435$	8.40189	0.402840
$436$	−11.1947	−0.536129
$437$	32.5892	1.55895
$438$	67.7667	3.23802
$439$	5.09009	0.242937	0.121468	−	0.992595i	$-0.461240\pi$
$439$	5.09009	0.242937	0.121468	+	0.992595i	$0.461240\pi$
$440$	6.94399	0.331042
$441$	7.80377	0.371608
$442$	9.86714	0.469332
$443$	7.97576	0.378940	0.189470	−	0.981887i	$-0.439323\pi$
$443$	7.97576	0.378940	0.189470	+	0.981887i	$0.439323\pi$
$444$	−13.2536	−0.628988
$445$	3.55742	0.168638
$446$	−34.9438	−1.65464
$447$	−72.2036	−3.41511
$448$	−0.0379570	−0.00179330
$449$	−33.1302	−1.56351	−0.781756	−	0.623584i	$-0.785676\pi$
$449$	−33.1302	−1.56351	−0.781756	+	0.623584i	$0.785676\pi$
$450$	−13.7528	−0.648311
$451$	26.2406	1.23562
$452$	−12.1346	−0.570763
$453$	31.0332	1.45807
$454$	−41.7840	−1.96102
$455$	−5.43044	−0.254583
$456$	28.9310	1.35482
$457$	9.21874	0.431234	0.215617	−	0.976478i	$-0.430824\pi$
$457$	9.21874	0.431234	0.215617	+	0.976478i	$0.430824\pi$
$458$	1.76232	0.0823479
$459$	16.2795	0.759861
$460$	−6.45203	−0.300827
$461$	19.1824	0.893413	0.446706	−	0.894681i	$-0.352597\pi$
$461$	19.1824	0.893413	0.446706	+	0.894681i	$0.352597\pi$
$462$	−25.5243	−1.18750
$463$	33.2009	1.54298	0.771489	−	0.636243i	$-0.219512\pi$
$463$	33.2009	1.54298	0.771489	+	0.636243i	$0.219512\pi$
$464$	12.7522	0.592008
$465$	−20.7827	−0.963776
$466$	31.7853	1.47242
$467$	2.69104	0.124527	0.0622633	−	0.998060i	$-0.480168\pi$
$467$	2.69104	0.124527	0.0622633	+	0.998060i	$0.480168\pi$
$468$	46.8607	2.16614
$469$	−2.58147	−0.119201
$470$	1.82754	0.0842980
$471$	57.3643	2.64321
$472$	−5.08516	−0.234064
$473$	−40.9398	−1.88241
$474$	−6.96370	−0.319854
$475$	−5.58530	−0.256271
$476$	1.14009	0.0522561
$477$	17.6254	0.807013
$478$	−28.8238	−1.31837
$479$	−29.0584	−1.32771	−0.663857	−	0.747860i	$-0.731082\pi$
$479$	−29.0584	−1.32771	−0.663857	+	0.747860i	$0.731082\pi$
$480$	−18.5385	−0.846161
$481$	19.8021	0.902900
$482$	−24.0093	−1.09359
$483$	−19.1785	−0.872652
$484$	9.30630	0.423013
$485$	−15.7490	−0.715126
$486$	81.5375	3.69862
$487$	18.7216	0.848356	0.424178	−	0.905579i	$-0.360563\pi$
$487$	18.7216	0.848356	0.424178	+	0.905579i	$0.360563\pi$
$488$	18.5551	0.839951
$489$	1.65049	0.0746376
$490$	−1.76232	−0.0796136
$491$	5.02410	0.226735	0.113367	−	0.993553i	$-0.463836\pi$
$491$	5.02410	0.226735	0.113367	+	0.993553i	$0.463836\pi$
$492$	−21.6447	−0.975817
$493$	2.63548	0.118696
$494$	53.4524	2.40494
$495$	34.3862	1.54555
$496$	−31.5436	−1.41635
$497$	−7.64634	−0.342985
$498$	9.44736	0.423346
$499$	38.1903	1.70963	0.854816	−	0.518931i	$-0.173670\pi$
$499$	38.1903	1.70963	0.854816	+	0.518931i	$0.173670\pi$
$500$	1.10578	0.0494521
$501$	−42.5421	−1.90064
$502$	1.54380	0.0689030
$503$	24.6208	1.09779	0.548894	−	0.835892i	$-0.315049\pi$
$503$	24.6208	1.09779	0.548894	+	0.835892i	$0.315049\pi$
$504$	−12.2980	−0.547795
$505$	16.7386	0.744857
$506$	45.3098	2.01427
$507$	−54.2000	−2.40711
$508$	19.1688	0.850476
$509$	7.48466	0.331752	0.165876	−	0.986147i	$-0.446955\pi$
$509$	7.48466	0.331752	0.165876	+	0.986147i	$0.446955\pi$
$510$	−5.97233	−0.264459
$511$	−11.6989	−0.517527
$512$	−12.4136	−0.548609
$513$	88.1893	3.89365
$514$	25.0107	1.10317
$515$	−12.0463	−0.530825
$516$	33.7693	1.48661
$517$	−4.56942	−0.200963
$518$	6.42632	0.282356
$519$	−13.3705	−0.586898
$520$	8.55783	0.375286
$521$	−8.08744	−0.354317	−0.177159	−	0.984182i	$-0.556691\pi$
$521$	−8.08744	−0.354317	−0.177159	+	0.984182i	$0.556691\pi$
$522$	35.1544	1.53866
$523$	−12.8726	−0.562881	−0.281441	−	0.959579i	$-0.590812\pi$
$523$	−12.8726	−0.562881	−0.281441	+	0.959579i	$0.590812\pi$
$524$	−11.2729	−0.492458
$525$	3.28691	0.143452
$526$	7.55920	0.329597
$527$	−6.51907	−0.283975
$528$	72.2545	3.14447
$529$	11.0450	0.480218
$530$	−3.98035	−0.172895
$531$	−25.1814	−1.09278
$532$	6.17612	0.267769
$533$	32.3392	1.40077
$534$	20.6067	0.891738
$535$	−5.65632	−0.244544
$536$	4.06815	0.175717
$537$	−41.8771	−1.80713
$538$	−24.1211	−1.03994
$539$	4.40636	0.189795
$540$	−17.4598	−0.751350
$541$	−37.0626	−1.59345	−0.796723	−	0.604344i	$-0.793435\pi$
$541$	−37.0626	−1.59345	−0.796723	+	0.604344i	$0.793435\pi$
$542$	−16.0459	−0.689232
$543$	22.6028	0.969978
$544$	−5.81510	−0.249320
$545$	−10.1238	−0.433656
$546$	−31.4563	−1.34621
$547$	−22.2088	−0.949579	−0.474789	−	0.880099i	$-0.657476\pi$
$547$	−22.2088	−0.949579	−0.474789	+	0.880099i	$0.657476\pi$
$548$	3.52170	0.150440
$549$	91.8839	3.92151
$550$	−7.76543	−0.331119
$551$	14.2770	0.608219
$552$	30.2234	1.28639
$553$	1.20217	0.0511216
$554$	14.2726	0.606386
$555$	−11.9857	−0.508766
$556$	−13.6188	−0.577568
$557$	−21.1021	−0.894127	−0.447063	−	0.894502i	$-0.647530\pi$
$557$	−21.1021	−0.894127	−0.447063	+	0.894502i	$0.647530\pi$
$558$	−86.9570	−3.68118
$559$	−50.4545	−2.13400
$560$	4.98881	0.210816
$561$	14.9327	0.630460
$562$	50.1855	2.11695
$563$	−46.8024	−1.97248	−0.986242	−	0.165308i	$-0.947138\pi$
$563$	−46.8024	−1.97248	−0.986242	+	0.165308i	$0.947138\pi$
$564$	3.76910	0.158708
$565$	−10.9738	−0.461670
$566$	−43.8780	−1.84433
$567$	−28.4875	−1.19636
$568$	12.0499	0.505602
$569$	−26.3851	−1.10612	−0.553061	−	0.833141i	$-0.686540\pi$
$569$	−26.3851	−1.10612	−0.553061	+	0.833141i	$0.686540\pi$
$570$	−32.3534	−1.35513
$571$	−2.86020	−0.119696	−0.0598479	−	0.998208i	$-0.519062\pi$
$571$	−2.86020	−0.119696	−0.0598479	+	0.998208i	$0.519062\pi$
$572$	26.4597	1.10634
$573$	−27.2653	−1.13903
$574$	10.4949	0.438050
$575$	−5.83481	−0.243328
$576$	0.296207	0.0123420
$577$	2.32932	0.0969707	0.0484853	−	0.998824i	$-0.484561\pi$
$577$	2.32932	0.0969707	0.0484853	+	0.998824i	$0.484561\pi$
$578$	28.0861	1.16823
$579$	−18.8539	−0.783542
$580$	−2.82657	−0.117367
$581$	−1.63094	−0.0676627
$582$	−91.2276	−3.78151
$583$	9.95213	0.412175
$584$	18.4362	0.762897
$585$	42.3779	1.75211
$586$	−27.5917	−1.13980
$587$	29.6281	1.22288	0.611441	−	0.791290i	$-0.290590\pi$
$587$	29.6281	1.22288	0.611441	+	0.791290i	$0.290590\pi$
$588$	−3.63460	−0.149889
$589$	−35.3152	−1.45514
$590$	5.68672	0.234118
$591$	−1.31758	−0.0541981
$592$	−18.1917	−0.747676
$593$	23.3009	0.956852	0.478426	−	0.878128i	$-0.341207\pi$
$593$	23.3009	0.956852	0.478426	+	0.878128i	$0.341207\pi$
$594$	122.613	5.03086
$595$	1.03103	0.0422681
$596$	24.2907	0.994988
$597$	−82.9229	−3.39381
$598$	55.8402	2.28348
$599$	−43.9232	−1.79465	−0.897326	−	0.441369i	$-0.854493\pi$
$599$	−43.9232	−1.79465	−0.897326	+	0.441369i	$0.854493\pi$
$600$	−5.17984	−0.211466
$601$	41.8269	1.70615	0.853077	−	0.521785i	$-0.174734\pi$
$601$	41.8269	1.70615	0.853077	+	0.521785i	$0.174734\pi$
$602$	−16.3738	−0.667348
$603$	20.1452	0.820377
$604$	−10.4402	−0.424806
$605$	8.41603	0.342160
$606$	96.9598	3.93872
$607$	−0.263730	−0.0107045	−0.00535223	−	0.999986i	$-0.501704\pi$
$607$	−0.263730	−0.0107045	−0.00535223	+	0.999986i	$0.501704\pi$
$608$	−31.5016	−1.27756
$609$	−8.40189	−0.340462
$610$	−20.7501	−0.840147
$611$	−5.63139	−0.227822
$612$	−8.89702	−0.359641
$613$	35.6994	1.44189	0.720943	−	0.692994i	$-0.243709\pi$
$613$	35.6994	1.44189	0.720943	+	0.692994i	$0.243709\pi$
$614$	−16.3601	−0.660241
$615$	−19.5741	−0.789304
$616$	−6.94399	−0.279781
$617$	−41.8226	−1.68371	−0.841857	−	0.539700i	$-0.818538\pi$
$617$	−41.8226	−1.68371	−0.841857	+	0.539700i	$0.818538\pi$
$618$	−69.7795	−2.80694
$619$	−31.7655	−1.27676	−0.638381	−	0.769720i	$-0.720396\pi$
$619$	−31.7655	−1.27676	−0.638381	+	0.769720i	$0.720396\pi$
$620$	6.99172	0.280794
$621$	92.1290	3.69701
$622$	−21.4667	−0.860735
$623$	−3.55742	−0.142525
$624$	89.0470	3.56473
$625$	1.00000	0.0400000
$626$	24.7396	0.988792
$627$	80.8936	3.23058
$628$	−19.2985	−0.770093
$629$	−3.75965	−0.149907
$630$	13.7528	0.547923
$631$	8.63712	0.343838	0.171919	−	0.985111i	$-0.445003\pi$
$631$	8.63712	0.343838	0.171919	+	0.985111i	$0.445003\pi$
$632$	−1.89451	−0.0753594
$633$	7.90770	0.314303
$634$	40.7372	1.61788
$635$	17.3350	0.687919
$636$	−8.20905	−0.325510
$637$	5.43044	0.215162
$638$	19.8498	0.785860
$639$	59.6703	2.36052
$640$	−11.3471	−0.448533
$641$	−19.3749	−0.765261	−0.382631	−	0.923901i	$-0.624982\pi$
$641$	−19.3749	−0.765261	−0.382631	+	0.923901i	$0.624982\pi$
$642$	−32.7647	−1.29312
$643$	−9.35555	−0.368947	−0.184473	−	0.982838i	$-0.559058\pi$
$643$	−9.35555	−0.368947	−0.184473	+	0.982838i	$0.559058\pi$
$644$	6.45203	0.254246
$645$	30.5389	1.20247
$646$	−10.1485	−0.399288
$647$	−5.42711	−0.213362	−0.106681	−	0.994293i	$-0.534022\pi$
$647$	−5.42711	−0.213362	−0.106681	+	0.994293i	$0.534022\pi$
$648$	44.8934	1.76358
$649$	−14.2186	−0.558128
$650$	−9.57019	−0.375374
$651$	20.7827	0.814539
$652$	−0.555257	−0.0217455
$653$	−39.5272	−1.54682	−0.773410	−	0.633906i	$-0.781451\pi$
$653$	−39.5272	−1.54682	−0.773410	+	0.633906i	$0.781451\pi$
$654$	−58.6430	−2.29312
$655$	−10.1945	−0.398332
$656$	−29.7092	−1.15995
$657$	91.2951	3.56176
$658$	−1.82754	−0.0712448
$659$	37.8741	1.47537	0.737683	−	0.675147i	$-0.235920\pi$
$659$	37.8741	1.47537	0.737683	+	0.675147i	$0.235920\pi$
$660$	−16.0154	−0.623398
$661$	29.4787	1.14659	0.573295	−	0.819349i	$-0.305665\pi$
$661$	29.4787	1.14659	0.573295	+	0.819349i	$0.305665\pi$
$662$	−3.21361	−0.124901
$663$	18.4032	0.714721
$664$	2.57020	0.0997430
$665$	5.58530	0.216589
$666$	−50.1495	−1.94325
$667$	14.9148	0.577502
$668$	14.3120	0.553749
$669$	−65.1737	−2.51976
$670$	−4.54939	−0.175758
$671$	51.8818	2.00288
$672$	18.5385	0.715137
$673$	14.0686	0.542304	0.271152	−	0.962537i	$-0.412595\pi$
$673$	14.0686	0.542304	0.271152	+	0.962537i	$0.412595\pi$
$674$	−43.6642	−1.68188
$675$	−15.7895	−0.607740
$676$	18.2340	0.701307
$677$	43.1973	1.66021	0.830103	−	0.557611i	$-0.188282\pi$
$677$	43.1973	1.66021	0.830103	+	0.557611i	$0.188282\pi$
$678$	−63.5666	−2.44126
$679$	15.7490	0.604392
$680$	−1.62480	−0.0623082
$681$	−77.9313	−2.98633
$682$	−49.0999	−1.88013
$683$	11.5041	0.440190	0.220095	−	0.975478i	$-0.429363\pi$
$683$	11.5041	0.440190	0.220095	+	0.975478i	$0.429363\pi$
$684$	−48.1970	−1.84286
$685$	3.18481	0.121685
$686$	1.76232	0.0672858
$687$	3.28691	0.125403
$688$	46.3513	1.76713
$689$	12.2651	0.467263
$690$	−33.7987	−1.28669
$691$	29.7992	1.13361	0.566807	−	0.823850i	$-0.308178\pi$
$691$	29.7992	1.13361	0.566807	+	0.823850i	$0.308178\pi$
$692$	4.49809	0.170992
$693$	−34.3862	−1.30622
$694$	−49.1924	−1.86732
$695$	−12.3160	−0.467174
$696$	13.2406	0.501882
$697$	−6.13995	−0.232567
$698$	−34.7989	−1.31716
$699$	59.2827	2.24228
$700$	−1.10578	−0.0417946
$701$	1.63907	0.0619069	0.0309535	−	0.999521i	$-0.490146\pi$
$701$	1.63907	0.0619069	0.0309535	+	0.999521i	$0.490146\pi$
$702$	151.109	5.70324
$703$	−20.3668	−0.768150
$704$	0.167252	0.00630355
$705$	3.40854	0.128373
$706$	16.0038	0.602312
$707$	−16.7386	−0.629519
$708$	11.7282	0.440774
$709$	35.2610	1.32426	0.662128	−	0.749391i	$-0.269654\pi$
$709$	35.2610	1.32426	0.662128	+	0.749391i	$0.269654\pi$
$710$	−13.4753	−0.505720
$711$	−9.38148	−0.351833
$712$	5.60614	0.210099
$713$	−36.8928	−1.38165
$714$	5.97233	0.223509
$715$	23.9285	0.894875
$716$	14.0883	0.526504
$717$	−53.7593	−2.00768
$718$	43.6619	1.62945
$719$	20.4135	0.761295	0.380648	−	0.924720i	$-0.375701\pi$
$719$	20.4135	0.761295	0.380648	+	0.924720i	$0.375701\pi$
$720$	−38.9315	−1.45089
$721$	12.0463	0.448629
$722$	−21.4925	−0.799869
$723$	−44.7797	−1.66537
$724$	−7.60403	−0.282601
$725$	−2.55617	−0.0949337
$726$	48.7507	1.80931
$727$	13.4566	0.499078	0.249539	−	0.968365i	$-0.419721\pi$
$727$	13.4566	0.499078	0.249539	+	0.968365i	$0.419721\pi$
$728$	−8.55783	−0.317174
$729$	66.6132	2.46716
$730$	−20.6172	−0.763075
$731$	9.57935	0.354305
$732$	−42.7949	−1.58175
$733$	16.4925	0.609166	0.304583	−	0.952486i	$-0.401483\pi$
$733$	16.4925	0.609166	0.304583	+	0.952486i	$0.401483\pi$
$734$	−36.4620	−1.34584
$735$	−3.28691	−0.121239
$736$	−32.9089	−1.21304
$737$	11.3749	0.419000
$738$	−81.9000	−3.01478
$739$	−23.1080	−0.850040	−0.425020	−	0.905184i	$-0.639733\pi$
$739$	−23.1080	−0.850040	−0.425020	+	0.905184i	$0.639733\pi$
$740$	4.03224	0.148228
$741$	99.6940	3.66235
$742$	3.98035	0.146123
$743$	18.9617	0.695636	0.347818	−	0.937562i	$-0.386923\pi$
$743$	18.9617	0.695636	0.347818	+	0.937562i	$0.386923\pi$
$744$	−32.7515	−1.20073
$745$	21.9670	0.804810
$746$	51.9273	1.90120
$747$	12.7275	0.465673
$748$	−5.02366	−0.183683
$749$	5.65632	0.206677
$750$	5.79259	0.211516
$751$	4.51863	0.164887	0.0824436	−	0.996596i	$-0.473728\pi$
$751$	4.51863	0.164887	0.0824436	+	0.996596i	$0.473728\pi$
$752$	5.17342	0.188655
$753$	2.87934	0.104929
$754$	24.4630	0.890891
$755$	−9.44146	−0.343610
$756$	17.4598	0.635006
$757$	40.2363	1.46241	0.731207	−	0.682156i	$-0.238958\pi$
$757$	40.2363	1.46241	0.731207	+	0.682156i	$0.238958\pi$
$758$	60.1410	2.18442
$759$	84.5074	3.06742
$760$	−8.80188	−0.319278
$761$	−19.4041	−0.703397	−0.351699	−	0.936113i	$-0.614396\pi$
$761$	−19.4041	−0.703397	−0.351699	+	0.936113i	$0.614396\pi$
$762$	100.415	3.63764
$763$	10.1238	0.366506
$764$	9.17260	0.331853
$765$	−8.04591	−0.290900
$766$	25.2015	0.910566
$767$	−17.5231	−0.632722
$768$	−65.4795	−2.36279
$769$	−43.3047	−1.56161	−0.780803	−	0.624777i	$-0.785190\pi$
$769$	−43.3047	−1.56161	−0.780803	+	0.624777i	$0.785190\pi$
$770$	7.76543	0.279847
$771$	46.6474	1.67997
$772$	6.34284	0.228284
$773$	12.7836	0.459795	0.229897	−	0.973215i	$-0.426161\pi$
$773$	12.7836	0.459795	0.229897	+	0.973215i	$0.426161\pi$
$774$	127.778	4.59287
$775$	6.32288	0.227124
$776$	−24.8189	−0.890946
$777$	11.9857	0.429986
$778$	0.841851	0.0301818
$779$	−33.2614	−1.19171
$780$	−19.7375	−0.706716
$781$	33.6926	1.20561
$782$	−10.6019	−0.379123
$783$	40.3607	1.44237
$784$	−4.98881	−0.178172
$785$	−17.4523	−0.622901
$786$	−59.0526	−2.10633
$787$	−21.6351	−0.771207	−0.385604	−	0.922664i	$-0.626007\pi$
$787$	−21.6351	−0.771207	−0.385604	+	0.922664i	$0.626007\pi$
$788$	0.443261	0.0157905
$789$	14.0987	0.501926
$790$	2.11862	0.0753771
$791$	10.9738	0.390182
$792$	54.1893	1.92553
$793$	63.9396	2.27056
$794$	48.4890	1.72081
$795$	−7.42375	−0.263293
$796$	27.8969	0.988780
$797$	−10.8565	−0.384558	−0.192279	−	0.981340i	$-0.561588\pi$
$797$	−10.8565	−0.384558	−0.192279	+	0.981340i	$0.561588\pi$
$798$	32.3534	1.14530
$799$	1.06918	0.0378249
$800$	5.64009	0.199407
$801$	27.7612	0.980895
$802$	−3.13792	−0.110804
$803$	51.5494	1.81914
$804$	−9.38264	−0.330900
$805$	5.83481	0.205650
$806$	−60.5111	−2.13141
$807$	−44.9883	−1.58366
$808$	26.3783	0.927987
$809$	−30.5519	−1.07415	−0.537074	−	0.843535i	$-0.680470\pi$
$809$	−30.5519	−1.07415	−0.537074	+	0.843535i	$0.680470\pi$
$810$	−50.2041	−1.76399
$811$	20.9648	0.736175	0.368088	−	0.929791i	$-0.380013\pi$
$811$	20.9648	0.736175	0.368088	+	0.929791i	$0.380013\pi$
$812$	2.82657	0.0991930
$813$	−29.9273	−1.04960
$814$	−28.3167	−0.992500
$815$	−0.502139	−0.0175892
$816$	−16.9066	−0.591848
$817$	51.8933	1.81552
$818$	−37.4931	−1.31092
$819$	−42.3779	−1.48080
$820$	6.58512	0.229962
$821$	3.52819	0.123135	0.0615674	−	0.998103i	$-0.480390\pi$
$821$	3.52819	0.123135	0.0615674	+	0.998103i	$0.480390\pi$
$822$	18.4483	0.643458
$823$	4.95964	0.172882	0.0864410	−	0.996257i	$-0.472451\pi$
$823$	4.95964	0.172882	0.0864410	+	0.996257i	$0.472451\pi$
$824$	−18.9838	−0.661333
$825$	−14.4833	−0.504244
$826$	−5.68672	−0.197866
$827$	−24.3741	−0.847571	−0.423785	−	0.905763i	$-0.639299\pi$
$827$	−24.3741	−0.847571	−0.423785	+	0.905763i	$0.639299\pi$
$828$	−50.3501	−1.74979
$829$	44.3078	1.53887	0.769437	−	0.638723i	$-0.220537\pi$
$829$	44.3078	1.53887	0.769437	+	0.638723i	$0.220537\pi$
$830$	−2.87424	−0.0997663
$831$	26.6199	0.923433
$832$	0.206123	0.00714603
$833$	−1.03103	−0.0357230
$834$	−71.3418	−2.47036
$835$	12.9429	0.447907
$836$	−27.2142	−0.941224
$837$	−99.8353	−3.45081
$838$	64.5193	2.22878
$839$	−6.06520	−0.209394	−0.104697	−	0.994504i	$-0.533387\pi$
$839$	−6.06520	−0.209394	−0.104697	+	0.994504i	$0.533387\pi$
$840$	5.17984	0.178722
$841$	−22.4660	−0.774690
$842$	−36.2323	−1.24865
$843$	93.6009	3.22379
$844$	−2.66031	−0.0915716
$845$	16.4897	0.567262
$846$	14.2617	0.490326
$847$	−8.41603	−0.289178
$848$	−11.2676	−0.386932
$849$	−81.8368	−2.80863
$850$	1.81701	0.0623228
$851$	−21.2767	−0.729355
$852$	−27.7914	−0.952119
$853$	16.4050	0.561696	0.280848	−	0.959752i	$-0.409384\pi$
$853$	16.4050	0.561696	0.280848	+	0.959752i	$0.409384\pi$
$854$	20.7501	0.710054
$855$	−43.5864	−1.49062
$856$	−8.91379	−0.304667
$857$	−26.5654	−0.907456	−0.453728	−	0.891140i	$-0.649906\pi$
$857$	−26.5654	−0.907456	−0.453728	+	0.891140i	$0.649906\pi$
$858$	138.608	4.73200
$859$	−34.1507	−1.16521	−0.582603	−	0.812757i	$-0.697966\pi$
$859$	−34.1507	−1.16521	−0.582603	+	0.812757i	$0.697966\pi$
$860$	−10.2739	−0.350337
$861$	19.5741	0.667083
$862$	57.6215	1.96260
$863$	39.4616	1.34329	0.671644	−	0.740874i	$-0.265589\pi$
$863$	39.4616	1.34329	0.671644	+	0.740874i	$0.265589\pi$
$864$	−89.0545	−3.02969
$865$	4.06779	0.138309
$866$	31.8080	1.08088
$867$	52.3834	1.77903
$868$	−6.99172	−0.237315
$869$	−5.29721	−0.179696
$870$	−14.8068	−0.501999
$871$	14.0185	0.475000
$872$	−15.9541	−0.540274
$873$	−122.902	−4.15959
$874$	−57.4326	−1.94269
$875$	−1.00000	−0.0338062
$876$	−42.5207	−1.43664
$877$	31.0030	1.04690	0.523448	−	0.852058i	$-0.324645\pi$
$877$	31.0030	1.04690	0.523448	+	0.852058i	$0.324645\pi$
$878$	−8.97038	−0.302736
$879$	−51.4614	−1.73575
$880$	−21.9825	−0.741030
$881$	−12.7521	−0.429628	−0.214814	−	0.976655i	$-0.568914\pi$
$881$	−12.7521	−0.429628	−0.214814	+	0.976655i	$0.568914\pi$
$882$	−13.7528	−0.463079
$883$	−35.9565	−1.21003	−0.605016	−	0.796213i	$-0.706833\pi$
$883$	−35.9565	−1.21003	−0.605016	+	0.796213i	$0.706833\pi$
$884$	−6.19121	−0.208233
$885$	10.6063	0.356527
$886$	−14.0559	−0.472216
$887$	−10.6441	−0.357392	−0.178696	−	0.983904i	$-0.557188\pi$
$887$	−10.6441	−0.357392	−0.178696	+	0.983904i	$0.557188\pi$
$888$	−18.8883	−0.633851
$889$	−17.3350	−0.581398
$890$	−6.26932	−0.210148
$891$	125.526	4.20528
$892$	21.9258	0.734129
$893$	5.79198	0.193821
$894$	127.246	4.25575
$895$	12.7406	0.425870
$896$	11.3471	0.379079
$897$	104.148	3.47739
$898$	58.3862	1.94837
$899$	−16.1623	−0.539044
$900$	8.62926	0.287642
$901$	−2.32866	−0.0775790
$902$	−46.2445	−1.53977
$903$	−30.5389	−1.01627
$904$	−17.2936	−0.575176
$905$	−6.87661	−0.228586
$906$	−54.6905	−1.81697
$907$	37.7018	1.25187	0.625934	−	0.779876i	$-0.284718\pi$
$907$	37.7018	1.25187	0.625934	+	0.779876i	$0.284718\pi$
$908$	26.2176	0.870063
$909$	130.624	4.33252
$910$	9.57019	0.317249
$911$	3.78226	0.125312	0.0626559	−	0.998035i	$-0.480043\pi$
$911$	3.78226	0.125312	0.0626559	+	0.998035i	$0.480043\pi$
$912$	−91.5864	−3.03273
$913$	7.18650	0.237839
$914$	−16.2464	−0.537383
$915$	−38.7010	−1.27942
$916$	−1.10578	−0.0365361
$917$	10.1945	0.336652
$918$	−28.6897	−0.946901
$919$	−25.0239	−0.825463	−0.412731	−	0.910853i	$-0.635425\pi$
$919$	−25.0239	−0.825463	−0.412731	+	0.910853i	$0.635425\pi$
$920$	−9.19509	−0.303153
$921$	−30.5133	−1.00545
$922$	−33.8055	−1.11333
$923$	41.5230	1.36675
$924$	16.0154	0.526867
$925$	3.64651	0.119896
$926$	−58.5107	−1.92278
$927$	−94.0067	−3.08759
$928$	−14.4170	−0.473262
$929$	29.7903	0.977388	0.488694	−	0.872455i	$-0.337474\pi$
$929$	29.7903	0.977388	0.488694	+	0.872455i	$0.337474\pi$
$930$	36.6259	1.20101
$931$	−5.58530	−0.183051
$932$	−19.9439	−0.653284
$933$	−40.0375	−1.31077
$934$	−4.74249	−0.155179
$935$	−4.54309	−0.148575
$936$	66.7833	2.18288
$937$	11.6512	0.380628	0.190314	−	0.981723i	$-0.439049\pi$
$937$	11.6512	0.380628	0.190314	+	0.981723i	$0.439049\pi$
$938$	4.54939	0.148543
$939$	46.1417	1.50578
$940$	−1.14670	−0.0374013
$941$	4.46755	0.145638	0.0728190	−	0.997345i	$-0.476800\pi$
$941$	4.46755	0.145638	0.0728190	+	0.997345i	$0.476800\pi$
$942$	−101.094	−3.29383
$943$	−34.7473	−1.13153
$944$	16.0980	0.523947
$945$	15.7895	0.513634
$946$	72.1491	2.34577
$947$	−43.7087	−1.42034	−0.710172	−	0.704029i	$-0.751383\pi$
$947$	−43.7087	−1.42034	−0.710172	+	0.704029i	$0.751383\pi$
$948$	4.36943	0.141912
$949$	63.5299	2.06227
$950$	9.84310	0.319352
$951$	75.9789	2.46379
$952$	1.62480	0.0526601
$953$	55.8288	1.80847	0.904236	−	0.427032i	$-0.140441\pi$
$953$	55.8288	1.80847	0.904236	+	0.427032i	$0.140441\pi$
$954$	−31.0617	−1.00566
$955$	8.29513	0.268424
$956$	18.0857	0.584934
$957$	37.0218	1.19674
$958$	51.2103	1.65453
$959$	−3.18481	−0.102843
$960$	−0.124761	−0.00402665
$961$	8.97878	0.289638
$962$	−34.8978	−1.12515
$963$	−44.1406	−1.42241
$964$	15.0648	0.485204
$965$	5.73607	0.184650
$966$	33.7987	1.08746
$967$	−22.4190	−0.720947	−0.360474	−	0.932769i	$-0.617385\pi$
$967$	−22.4190	−0.720947	−0.360474	+	0.932769i	$0.617385\pi$
$968$	13.2628	0.426284
$969$	−18.9280	−0.608055
$970$	27.7548	0.891154
$971$	28.2722	0.907297	0.453648	−	0.891181i	$-0.350122\pi$
$971$	28.2722	0.907297	0.453648	+	0.891181i	$0.350122\pi$
$972$	−51.1613	−1.64100
$973$	12.3160	0.394834
$974$	−32.9935	−1.05718
$975$	−17.8494	−0.571637
$976$	−58.7397	−1.88021
$977$	22.6727	0.725363	0.362681	−	0.931913i	$-0.381861\pi$
$977$	22.6727	0.725363	0.362681	+	0.931913i	$0.381861\pi$
$978$	−2.90869	−0.0930096
$979$	15.6753	0.500984
$980$	1.10578	0.0353229
$981$	−79.0037	−2.52239
$982$	−8.85409	−0.282545
$983$	26.0855	0.831998	0.415999	−	0.909365i	$-0.363432\pi$
$983$	26.0855	0.831998	0.415999	+	0.909365i	$0.363432\pi$
$984$	−30.8468	−0.983361
$985$	0.400857	0.0127724
$986$	−4.64458	−0.147913
$987$	−3.40854	−0.108495
$988$	−33.5391	−1.06702
$989$	54.2116	1.72383
$990$	−60.5996	−1.92598
$991$	50.8117	1.61409	0.807043	−	0.590492i	$-0.201066\pi$
$991$	50.8117	1.61409	0.807043	+	0.590492i	$0.201066\pi$
$992$	35.6616	1.13226
$993$	−5.99371	−0.190205
$994$	13.4753	0.427411
$995$	25.2282	0.799788
$996$	−5.92781	−0.187830
$997$	−23.6891	−0.750243	−0.375121	−	0.926976i	$-0.622399\pi$
$997$	−23.6891	−0.750243	−0.375121	+	0.926976i	$0.622399\pi$
$998$	−67.3036	−2.13046
$999$	−57.5767	−1.82164

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.m.1.16	✓	67

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.m.1.16	✓	67	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.76232 q^{2} -3.28691 q^{3} +1.10578 q^{4} +1.00000 q^{5} +5.79259 q^{6} -1.00000 q^{7} +1.57590 q^{8} +7.80377 q^{9} +O(q^{10})\)	\(q-1.76232 q^{2} -3.28691 q^{3} +1.10578 q^{4} +1.00000 q^{5} +5.79259 q^{6} -1.00000 q^{7} +1.57590 q^{8} +7.80377 q^{9} -1.76232 q^{10} +4.40636 q^{11} -3.63460 q^{12} +5.43044 q^{13} +1.76232 q^{14} -3.28691 q^{15} -4.98881 q^{16} -1.03103 q^{17} -13.7528 q^{18} -5.58530 q^{19} +1.10578 q^{20} +3.28691 q^{21} -7.76543 q^{22} -5.83481 q^{23} -5.17984 q^{24} +1.00000 q^{25} -9.57019 q^{26} -15.7895 q^{27} -1.10578 q^{28} -2.55617 q^{29} +5.79259 q^{30} +6.32288 q^{31} +5.64009 q^{32} -14.4833 q^{33} +1.81701 q^{34} -1.00000 q^{35} +8.62926 q^{36} +3.64651 q^{37} +9.84310 q^{38} -17.8494 q^{39} +1.57590 q^{40} +5.95517 q^{41} -5.79259 q^{42} -9.29106 q^{43} +4.87248 q^{44} +7.80377 q^{45} +10.2828 q^{46} -1.03700 q^{47} +16.3978 q^{48} +1.00000 q^{49} -1.76232 q^{50} +3.38890 q^{51} +6.00488 q^{52} +2.25858 q^{53} +27.8263 q^{54} +4.40636 q^{55} -1.57590 q^{56} +18.3584 q^{57} +4.50480 q^{58} -3.22683 q^{59} -3.63460 q^{60} +11.7743 q^{61} -11.1430 q^{62} -7.80377 q^{63} +0.0379570 q^{64} +5.43044 q^{65} +25.5243 q^{66} +2.58147 q^{67} -1.14009 q^{68} +19.1785 q^{69} +1.76232 q^{70} +7.64634 q^{71} +12.2980 q^{72} +11.6989 q^{73} -6.42632 q^{74} -3.28691 q^{75} -6.17612 q^{76} -4.40636 q^{77} +31.4563 q^{78} -1.20217 q^{79} -4.98881 q^{80} +28.4875 q^{81} -10.4949 q^{82} +1.63094 q^{83} +3.63460 q^{84} -1.03103 q^{85} +16.3738 q^{86} +8.40189 q^{87} +6.94399 q^{88} +3.55742 q^{89} -13.7528 q^{90} -5.43044 q^{91} -6.45203 q^{92} -20.7827 q^{93} +1.82754 q^{94} -5.58530 q^{95} -18.5385 q^{96} -15.7490 q^{97} -1.76232 q^{98} +34.3862 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9}+O(q^{10}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9} + 3 q^{10} + 11 q^{11} + 9 q^{12} + 19 q^{13} - 3 q^{14} + 93 q^{16} + 7 q^{17} + 9 q^{18} + 36 q^{19} + 73 q^{20} - 8 q^{22} - 2 q^{23} + 37 q^{24} + 67 q^{25} + 39 q^{26} + 6 q^{27} - 73 q^{28} + 56 q^{29} + 17 q^{30} + 63 q^{31} + 27 q^{32} + 51 q^{33} + 55 q^{34} - 67 q^{35} + 148 q^{36} + 28 q^{37} + 10 q^{38} + 7 q^{39} + 12 q^{40} + 84 q^{41} - 17 q^{42} - 11 q^{43} + 41 q^{44} + 97 q^{45} + 17 q^{46} - 10 q^{47} + 10 q^{48} + 67 q^{49} + 3 q^{50} - q^{51} + 49 q^{52} + 3 q^{53} + 20 q^{54} + 11 q^{55} - 12 q^{56} + 45 q^{57} + 22 q^{58} + 80 q^{59} + 9 q^{60} + 64 q^{61} - 37 q^{62} - 97 q^{63} + 110 q^{64} + 19 q^{65} + 75 q^{66} + 22 q^{67} + 7 q^{68} + 107 q^{69} - 3 q^{70} + 24 q^{71} + 72 q^{72} + 83 q^{73} + 52 q^{74} + 115 q^{76} - 11 q^{77} - 70 q^{78} - 32 q^{79} + 93 q^{80} + 183 q^{81} + 56 q^{82} - 58 q^{83} - 9 q^{84} + 7 q^{85} + 51 q^{86} + 20 q^{87} - 5 q^{88} + 129 q^{89} + 9 q^{90} - 19 q^{91} - 37 q^{92} + 33 q^{93} + 89 q^{94} + 36 q^{95} + 129 q^{96} + 126 q^{97} + 3 q^{98} - 27 q^{99}+O(q^{100}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9 + 3 * q^10 + 11 * q^11 + 9 * q^12 + 19 * q^13 - 3 * q^14 + 93 * q^16 + 7 * q^17 + 9 * q^18 + 36 * q^19 + 73 * q^20 - 8 * q^22 - 2 * q^23 + 37 * q^24 + 67 * q^25 + 39 * q^26 + 6 * q^27 - 73 * q^28 + 56 * q^29 + 17 * q^30 + 63 * q^31 + 27 * q^32 + 51 * q^33 + 55 * q^34 - 67 * q^35 + 148 * q^36 + 28 * q^37 + 10 * q^38 + 7 * q^39 + 12 * q^40 + 84 * q^41 - 17 * q^42 - 11 * q^43 + 41 * q^44 + 97 * q^45 + 17 * q^46 - 10 * q^47 + 10 * q^48 + 67 * q^49 + 3 * q^50 - q^51 + 49 * q^52 + 3 * q^53 + 20 * q^54 + 11 * q^55 - 12 * q^56 + 45 * q^57 + 22 * q^58 + 80 * q^59 + 9 * q^60 + 64 * q^61 - 37 * q^62 - 97 * q^63 + 110 * q^64 + 19 * q^65 + 75 * q^66 + 22 * q^67 + 7 * q^68 + 107 * q^69 - 3 * q^70 + 24 * q^71 + 72 * q^72 + 83 * q^73 + 52 * q^74 + 115 * q^76 - 11 * q^77 - 70 * q^78 - 32 * q^79 + 93 * q^80 + 183 * q^81 + 56 * q^82 - 58 * q^83 - 9 * q^84 + 7 * q^85 + 51 * q^86 + 20 * q^87 - 5 * q^88 + 129 * q^89 + 9 * q^90 - 19 * q^91 - 37 * q^92 + 33 * q^93 + 89 * q^94 + 36 * q^95 + 129 * q^96 + 126 * q^97 + 3 * q^98 - 27 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more