LMFDB - Embedded newform 6014.2.a.j.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.05301 q^{3} +1.00000 q^{4} -2.11820 q^{5} +2.05301 q^{6} -1.54348 q^{7} -1.00000 q^{8} +1.21485 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.05301 q^{3} +1.00000 q^{4} -2.11820 q^{5} +2.05301 q^{6} -1.54348 q^{7} -1.00000 q^{8} +1.21485 q^{9} +2.11820 q^{10} +1.93945 q^{11} -2.05301 q^{12} -0.601755 q^{13} +1.54348 q^{14} +4.34869 q^{15} +1.00000 q^{16} +2.46330 q^{17} -1.21485 q^{18} +8.02174 q^{19} -2.11820 q^{20} +3.16877 q^{21} -1.93945 q^{22} +6.61579 q^{23} +2.05301 q^{24} -0.513221 q^{25} +0.601755 q^{26} +3.66494 q^{27} -1.54348 q^{28} +10.4398 q^{29} -4.34869 q^{30} -1.00000 q^{31} -1.00000 q^{32} -3.98170 q^{33} -2.46330 q^{34} +3.26939 q^{35} +1.21485 q^{36} +2.60265 q^{37} -8.02174 q^{38} +1.23541 q^{39} +2.11820 q^{40} -6.32192 q^{41} -3.16877 q^{42} +1.64447 q^{43} +1.93945 q^{44} -2.57329 q^{45} -6.61579 q^{46} -8.52235 q^{47} -2.05301 q^{48} -4.61768 q^{49} +0.513221 q^{50} -5.05718 q^{51} -0.601755 q^{52} -12.0453 q^{53} -3.66494 q^{54} -4.10814 q^{55} +1.54348 q^{56} -16.4687 q^{57} -10.4398 q^{58} +9.73602 q^{59} +4.34869 q^{60} -2.23597 q^{61} +1.00000 q^{62} -1.87508 q^{63} +1.00000 q^{64} +1.27464 q^{65} +3.98170 q^{66} -7.05005 q^{67} +2.46330 q^{68} -13.5823 q^{69} -3.26939 q^{70} +10.0895 q^{71} -1.21485 q^{72} +11.2894 q^{73} -2.60265 q^{74} +1.05365 q^{75} +8.02174 q^{76} -2.99349 q^{77} -1.23541 q^{78} -2.93306 q^{79} -2.11820 q^{80} -11.1687 q^{81} +6.32192 q^{82} -13.1425 q^{83} +3.16877 q^{84} -5.21777 q^{85} -1.64447 q^{86} -21.4330 q^{87} -1.93945 q^{88} +1.08863 q^{89} +2.57329 q^{90} +0.928794 q^{91} +6.61579 q^{92} +2.05301 q^{93} +8.52235 q^{94} -16.9917 q^{95} +2.05301 q^{96} +1.00000 q^{97} +4.61768 q^{98} +2.35613 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9}+O(q^{10}) $ 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 5 q^{14} - q^{15} + 32 q^{16} + 14 q^{17} - 30 q^{18} + 33 q^{19} + 4 q^{22} - 2 q^{23} + 2 q^{24} + 46 q^{25} - 10 q^{26} - 5 q^{27} + 5 q^{28} - q^{29} + q^{30} - 32 q^{31} - 32 q^{32} + 32 q^{33} - 14 q^{34} + 8 q^{35} + 30 q^{36} + 31 q^{37} - 33 q^{38} + 4 q^{39} + 31 q^{41} + 15 q^{43} - 4 q^{44} + q^{45} + 2 q^{46} - 14 q^{47} - 2 q^{48} + 75 q^{49} - 46 q^{50} + 27 q^{51} + 10 q^{52} - 31 q^{53} + 5 q^{54} + 14 q^{55} - 5 q^{56} + 51 q^{57} + q^{58} - 8 q^{59} - q^{60} + 24 q^{61} + 32 q^{62} + 23 q^{63} + 32 q^{64} + 20 q^{65} - 32 q^{66} + 17 q^{67} + 14 q^{68} - 31 q^{69} - 8 q^{70} - 31 q^{71} - 30 q^{72} + 19 q^{73} - 31 q^{74} - 40 q^{75} + 33 q^{76} + 8 q^{77} - 4 q^{78} + 39 q^{79} + 116 q^{81} - 31 q^{82} - 6 q^{83} + 56 q^{85} - 15 q^{86} - 17 q^{87} + 4 q^{88} + 8 q^{89} - q^{90} + 34 q^{91} - 2 q^{92} + 2 q^{93} + 14 q^{94} - 22 q^{95} + 2 q^{96} + 32 q^{97} - 75 q^{98} - 27 q^{99}+O(q^{100}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 5 * q^14 - q^15 + 32 * q^16 + 14 * q^17 - 30 * q^18 + 33 * q^19 + 4 * q^22 - 2 * q^23 + 2 * q^24 + 46 * q^25 - 10 * q^26 - 5 * q^27 + 5 * q^28 - q^29 + q^30 - 32 * q^31 - 32 * q^32 + 32 * q^33 - 14 * q^34 + 8 * q^35 + 30 * q^36 + 31 * q^37 - 33 * q^38 + 4 * q^39 + 31 * q^41 + 15 * q^43 - 4 * q^44 + q^45 + 2 * q^46 - 14 * q^47 - 2 * q^48 + 75 * q^49 - 46 * q^50 + 27 * q^51 + 10 * q^52 - 31 * q^53 + 5 * q^54 + 14 * q^55 - 5 * q^56 + 51 * q^57 + q^58 - 8 * q^59 - q^60 + 24 * q^61 + 32 * q^62 + 23 * q^63 + 32 * q^64 + 20 * q^65 - 32 * q^66 + 17 * q^67 + 14 * q^68 - 31 * q^69 - 8 * q^70 - 31 * q^71 - 30 * q^72 + 19 * q^73 - 31 * q^74 - 40 * q^75 + 33 * q^76 + 8 * q^77 - 4 * q^78 + 39 * q^79 + 116 * q^81 - 31 * q^82 - 6 * q^83 + 56 * q^85 - 15 * q^86 - 17 * q^87 + 4 * q^88 + 8 * q^89 - q^90 + 34 * q^91 - 2 * q^92 + 2 * q^93 + 14 * q^94 - 22 * q^95 + 2 * q^96 + 32 * q^97 - 75 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.05301	−1.18531	−0.592653	−	0.805458i	$-0.701919\pi$
$3$	−2.05301	−1.18531	−0.592653	+	0.805458i	$0.701919\pi$
$4$	1.00000	0.500000
$5$	−2.11820	−0.947289	−0.473644	−	0.880716i	$-0.657062\pi$
$5$	−2.11820	−0.947289	−0.473644	+	0.880716i	$0.657062\pi$
$6$	2.05301	0.838137
$7$	−1.54348	−0.583379	−0.291689	−	0.956513i	$-0.594217\pi$
$7$	−1.54348	−0.583379	−0.291689	+	0.956513i	$0.594217\pi$
$8$	−1.00000	−0.353553
$9$	1.21485	0.404949
$10$	2.11820	0.669834
$11$	1.93945	0.584765	0.292383	−	0.956301i	$-0.405552\pi$
$11$	1.93945	0.584765	0.292383	+	0.956301i	$0.405552\pi$
$12$	−2.05301	−0.592653
$13$	−0.601755	−0.166897	−0.0834484	−	0.996512i	$-0.526593\pi$
$13$	−0.601755	−0.166897	−0.0834484	+	0.996512i	$0.526593\pi$
$14$	1.54348	0.412511
$15$	4.34869	1.12283
$16$	1.00000	0.250000
$17$	2.46330	0.597438	0.298719	−	0.954341i	$-0.403441\pi$
$17$	2.46330	0.597438	0.298719	+	0.954341i	$0.403441\pi$
$18$	−1.21485	−0.286342
$19$	8.02174	1.84031	0.920156	−	0.391551i	$-0.128061\pi$
$19$	8.02174	1.84031	0.920156	+	0.391551i	$0.128061\pi$
$20$	−2.11820	−0.473644
$21$	3.16877	0.691482
$22$	−1.93945	−0.413491
$23$	6.61579	1.37949	0.689744	−	0.724054i	$-0.257723\pi$
$23$	6.61579	1.37949	0.689744	+	0.724054i	$0.257723\pi$
$24$	2.05301	0.419069
$25$	−0.513221	−0.102644
$26$	0.601755	0.118014
$27$	3.66494	0.705317
$28$	−1.54348	−0.291689
$29$	10.4398	1.93862	0.969312	−	0.245834i	$-0.0790619\pi$
$29$	10.4398	1.93862	0.969312	+	0.245834i	$0.0790619\pi$
$30$	−4.34869	−0.793958
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	−3.98170	−0.693125
$34$	−2.46330	−0.422452
$35$	3.26939	0.552628
$36$	1.21485	0.202474
$37$	2.60265	0.427873	0.213936	−	0.976848i	$-0.431372\pi$
$37$	2.60265	0.427873	0.213936	+	0.976848i	$0.431372\pi$
$38$	−8.02174	−1.30130
$39$	1.23541	0.197824
$40$	2.11820	0.334917
$41$	−6.32192	−0.987318	−0.493659	−	0.869656i	$-0.664341\pi$
$41$	−6.32192	−0.987318	−0.493659	+	0.869656i	$0.664341\pi$
$42$	−3.16877	−0.488952
$43$	1.64447	0.250779	0.125390	−	0.992108i	$-0.459982\pi$
$43$	1.64447	0.250779	0.125390	+	0.992108i	$0.459982\pi$
$44$	1.93945	0.292383
$45$	−2.57329	−0.383603
$46$	−6.61579	−0.975445
$47$	−8.52235	−1.24311	−0.621556	−	0.783369i	$-0.713499\pi$
$47$	−8.52235	−1.24311	−0.621556	+	0.783369i	$0.713499\pi$
$48$	−2.05301	−0.296326
$49$	−4.61768	−0.659669
$50$	0.513221	0.0725805
$51$	−5.05718	−0.708146
$52$	−0.601755	−0.0834484
$53$	−12.0453	−1.65455	−0.827273	−	0.561800i	$-0.810109\pi$
$53$	−12.0453	−1.65455	−0.827273	+	0.561800i	$0.810109\pi$
$54$	−3.66494	−0.498735
$55$	−4.10814	−0.553941
$56$	1.54348	0.206256
$57$	−16.4687	−2.18133
$58$	−10.4398	−1.37081
$59$	9.73602	1.26752	0.633761	−	0.773529i	$-0.281510\pi$
$59$	9.73602	1.26752	0.633761	+	0.773529i	$0.281510\pi$
$60$	4.34869	0.561413
$61$	−2.23597	−0.286287	−0.143143	−	0.989702i	$-0.545721\pi$
$61$	−2.23597	−0.286287	−0.143143	+	0.989702i	$0.545721\pi$
$62$	1.00000	0.127000
$63$	−1.87508	−0.236238
$64$	1.00000	0.125000
$65$	1.27464	0.158099
$66$	3.98170	0.490113
$67$	−7.05005	−0.861301	−0.430650	−	0.902519i	$-0.641716\pi$
$67$	−7.05005	−0.861301	−0.430650	+	0.902519i	$0.641716\pi$
$68$	2.46330	0.298719
$69$	−13.5823	−1.63511
$70$	−3.26939	−0.390767
$71$	10.0895	1.19741	0.598704	−	0.800970i	$-0.295682\pi$
$71$	10.0895	1.19741	0.598704	+	0.800970i	$0.295682\pi$
$72$	−1.21485	−0.143171
$73$	11.2894	1.32132	0.660662	−	0.750683i	$-0.270276\pi$
$73$	11.2894	1.32132	0.660662	+	0.750683i	$0.270276\pi$
$74$	−2.60265	−0.302552
$75$	1.05365	0.121665
$76$	8.02174	0.920156
$77$	−2.99349	−0.341140
$78$	−1.23541	−0.139882
$79$	−2.93306	−0.329995	−0.164997	−	0.986294i	$-0.552762\pi$
$79$	−2.93306	−0.329995	−0.164997	+	0.986294i	$0.552762\pi$
$80$	−2.11820	−0.236822
$81$	−11.1687	−1.24097
$82$	6.32192	0.698139
$83$	−13.1425	−1.44258	−0.721289	−	0.692634i	$-0.756450\pi$
$83$	−13.1425	−1.44258	−0.721289	+	0.692634i	$0.756450\pi$
$84$	3.16877	0.345741
$85$	−5.21777	−0.565946
$86$	−1.64447	−0.177328
$87$	−21.4330	−2.29786
$88$	−1.93945	−0.206746
$89$	1.08863	0.115395	0.0576975	−	0.998334i	$-0.481624\pi$
$89$	1.08863	0.115395	0.0576975	+	0.998334i	$0.481624\pi$
$90$	2.57329	0.271248
$91$	0.928794	0.0973641
$92$	6.61579	0.689744
$93$	2.05301	0.212887
$94$	8.52235	0.879014
$95$	−16.9917	−1.74331
$96$	2.05301	0.209534
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	4.61768	0.466457
$99$	2.35613	0.236800
$100$	−0.513221	−0.0513221
$101$	−6.83026	−0.679636	−0.339818	−	0.940491i	$-0.610366\pi$
$101$	−6.83026	−0.679636	−0.339818	+	0.940491i	$0.610366\pi$
$102$	5.05718	0.500735
$103$	8.39080	0.826770	0.413385	−	0.910556i	$-0.364346\pi$
$103$	8.39080	0.826770	0.413385	+	0.910556i	$0.364346\pi$
$104$	0.601755	0.0590069
$105$	−6.71209	−0.655033
$106$	12.0453	1.16994
$107$	−9.93424	−0.960379	−0.480190	−	0.877165i	$-0.659432\pi$
$107$	−9.93424	−0.960379	−0.480190	+	0.877165i	$0.659432\pi$
$108$	3.66494	0.352659
$109$	13.1293	1.25756	0.628779	−	0.777584i	$-0.283555\pi$
$109$	13.1293	1.25756	0.628779	+	0.777584i	$0.283555\pi$
$110$	4.10814	0.391696
$111$	−5.34326	−0.507160
$112$	−1.54348	−0.145845
$113$	19.7717	1.85996	0.929982	−	0.367604i	$-0.119822\pi$
$113$	19.7717	1.85996	0.929982	+	0.367604i	$0.119822\pi$
$114$	16.4687	1.54244
$115$	−14.0136	−1.30677
$116$	10.4398	0.969312
$117$	−0.731040	−0.0675847
$118$	−9.73602	−0.896273
$119$	−3.80204	−0.348533
$120$	−4.34869	−0.396979
$121$	−7.23855	−0.658050
$122$	2.23597	0.202435
$123$	12.9790	1.17027
$124$	−1.00000	−0.0898027
$125$	11.6781	1.04452
$126$	1.87508	0.167046
$127$	5.12231	0.454531	0.227266	−	0.973833i	$-0.427021\pi$
$127$	5.12231	0.454531	0.227266	+	0.973833i	$0.427021\pi$
$128$	−1.00000	−0.0883883
$129$	−3.37611	−0.297250
$130$	−1.27464	−0.111793
$131$	15.4731	1.35189	0.675945	−	0.736952i	$-0.263736\pi$
$131$	15.4731	1.35189	0.675945	+	0.736952i	$0.263736\pi$
$132$	−3.98170	−0.346563
$133$	−12.3814	−1.07360
$134$	7.05005	0.609032
$135$	−7.76308	−0.668139
$136$	−2.46330	−0.211226
$137$	−20.9560	−1.79039	−0.895196	−	0.445673i	$-0.852964\pi$
$137$	−20.9560	−1.79039	−0.895196	+	0.445673i	$0.852964\pi$
$138$	13.5823	1.15620
$139$	18.1723	1.54135	0.770677	−	0.637226i	$-0.219918\pi$
$139$	18.1723	1.54135	0.770677	+	0.637226i	$0.219918\pi$
$140$	3.26939	0.276314
$141$	17.4965	1.47347
$142$	−10.0895	−0.846696
$143$	−1.16707	−0.0975954
$144$	1.21485	0.101237
$145$	−22.1136	−1.83644
$146$	−11.2894	−0.934318
$147$	9.48015	0.781909
$148$	2.60265	0.213936
$149$	6.82406	0.559049	0.279525	−	0.960139i	$-0.409823\pi$
$149$	6.82406	0.559049	0.279525	+	0.960139i	$0.409823\pi$
$150$	−1.05365	−0.0860300
$151$	1.05760	0.0860663	0.0430332	−	0.999074i	$-0.486298\pi$
$151$	1.05760	0.0860663	0.0430332	+	0.999074i	$0.486298\pi$
$152$	−8.02174	−0.650649
$153$	2.99253	0.241932
$154$	2.99349	0.241222
$155$	2.11820	0.170138
$156$	1.23541	0.0989118
$157$	11.1685	0.891341	0.445671	−	0.895197i	$-0.352965\pi$
$157$	11.1685	0.891341	0.445671	+	0.895197i	$0.352965\pi$
$158$	2.93306	0.233341
$159$	24.7291	1.96114
$160$	2.11820	0.167459
$161$	−10.2113	−0.804764
$162$	11.1687	0.877495
$163$	−9.64552	−0.755495	−0.377748	−	0.925909i	$-0.623301\pi$
$163$	−9.64552	−0.755495	−0.377748	+	0.925909i	$0.623301\pi$
$164$	−6.32192	−0.493659
$165$	8.43405	0.656590
$166$	13.1425	1.02006
$167$	−7.88903	−0.610471	−0.305236	−	0.952277i	$-0.598735\pi$
$167$	−7.88903	−0.610471	−0.305236	+	0.952277i	$0.598735\pi$
$168$	−3.16877	−0.244476
$169$	−12.6379	−0.972145
$170$	5.21777	0.400184
$171$	9.74518	0.745232
$172$	1.64447	0.125390
$173$	−12.8893	−0.979953	−0.489977	−	0.871736i	$-0.662995\pi$
$173$	−12.8893	−0.979953	−0.489977	+	0.871736i	$0.662995\pi$
$174$	21.4330	1.62483
$175$	0.792145	0.0598805
$176$	1.93945	0.146191
$177$	−19.9881	−1.50240
$178$	−1.08863	−0.0815966
$179$	−13.3274	−0.996138	−0.498069	−	0.867137i	$-0.665957\pi$
$179$	−13.3274	−0.996138	−0.498069	+	0.867137i	$0.665957\pi$
$180$	−2.57329	−0.191802
$181$	1.75830	0.130694	0.0653468	−	0.997863i	$-0.479185\pi$
$181$	1.75830	0.130694	0.0653468	+	0.997863i	$0.479185\pi$
$182$	−0.928794	−0.0688468
$183$	4.59047	0.339337
$184$	−6.61579	−0.487723
$185$	−5.51293	−0.405319
$186$	−2.05301	−0.150534
$187$	4.77744	0.349361
$188$	−8.52235	−0.621556
$189$	−5.65674	−0.411467
$190$	16.9917	1.23270
$191$	4.75769	0.344254	0.172127	−	0.985075i	$-0.444936\pi$
$191$	4.75769	0.344254	0.172127	+	0.985075i	$0.444936\pi$
$192$	−2.05301	−0.148163
$193$	20.0256	1.44148	0.720738	−	0.693208i	$-0.243803\pi$
$193$	20.0256	1.44148	0.720738	+	0.693208i	$0.243803\pi$
$194$	−1.00000	−0.0717958
$195$	−2.61684	−0.187396
$196$	−4.61768	−0.329835
$197$	−5.90473	−0.420695	−0.210347	−	0.977627i	$-0.567459\pi$
$197$	−5.90473	−0.420695	−0.210347	+	0.977627i	$0.567459\pi$
$198$	−2.35613	−0.167443
$199$	−15.9333	−1.12948	−0.564741	−	0.825269i	$-0.691024\pi$
$199$	−15.9333	−1.12948	−0.564741	+	0.825269i	$0.691024\pi$
$200$	0.513221	0.0362902
$201$	14.4738	1.02090
$202$	6.83026	0.480575
$203$	−16.1136	−1.13095
$204$	−5.05718	−0.354073
$205$	13.3911	0.935275
$206$	−8.39080	−0.584615
$207$	8.03717	0.558622
$208$	−0.601755	−0.0417242
$209$	15.5577	1.07615
$210$	6.71209	0.463178
$211$	3.01136	0.207310	0.103655	−	0.994613i	$-0.466946\pi$
$211$	3.01136	0.207310	0.103655	+	0.994613i	$0.466946\pi$
$212$	−12.0453	−0.827273
$213$	−20.7139	−1.41930
$214$	9.93424	0.679091
$215$	−3.48332	−0.237560
$216$	−3.66494	−0.249367
$217$	1.54348	0.104778
$218$	−13.1293	−0.889228
$219$	−23.1772	−1.56617
$220$	−4.10814	−0.276971
$221$	−1.48230	−0.0997105
$222$	5.34326	0.358616
$223$	−14.3040	−0.957868	−0.478934	−	0.877851i	$-0.658977\pi$
$223$	−14.3040	−0.957868	−0.478934	+	0.877851i	$0.658977\pi$
$224$	1.54348	0.103128
$225$	−0.623485	−0.0415657
$226$	−19.7717	−1.31519
$227$	14.3245	0.950748	0.475374	−	0.879784i	$-0.342313\pi$
$227$	14.3245	0.950748	0.475374	+	0.879784i	$0.342313\pi$
$228$	−16.4687	−1.09067
$229$	10.3916	0.686699	0.343350	−	0.939208i	$-0.388438\pi$
$229$	10.3916	0.686699	0.343350	+	0.939208i	$0.388438\pi$
$230$	14.0136	0.924028
$231$	6.14566	0.404355
$232$	−10.4398	−0.685407
$233$	11.7599	0.770419	0.385210	−	0.922829i	$-0.374129\pi$
$233$	11.7599	0.770419	0.385210	+	0.922829i	$0.374129\pi$
$234$	0.731040	0.0477896
$235$	18.0521	1.17759
$236$	9.73602	0.633761
$237$	6.02159	0.391144
$238$	3.80204	0.246450
$239$	−6.64600	−0.429894	−0.214947	−	0.976626i	$-0.568958\pi$
$239$	−6.64600	−0.429894	−0.214947	+	0.976626i	$0.568958\pi$
$240$	4.34869	0.280707
$241$	27.5614	1.77538	0.887692	−	0.460437i	$-0.152307\pi$
$241$	27.5614	1.77538	0.887692	+	0.460437i	$0.152307\pi$
$242$	7.23855	0.465311
$243$	11.9346	0.765605
$244$	−2.23597	−0.143143
$245$	9.78119	0.624897
$246$	−12.9790	−0.827508
$247$	−4.82712	−0.307142
$248$	1.00000	0.0635001
$249$	26.9817	1.70990
$250$	−11.6781	−0.738589
$251$	−10.8998	−0.687992	−0.343996	−	0.938971i	$-0.611781\pi$
$251$	−10.8998	−0.687992	−0.343996	+	0.938971i	$0.611781\pi$
$252$	−1.87508	−0.118119
$253$	12.8310	0.806676
$254$	−5.12231	−0.321402
$255$	10.7121	0.670819
$256$	1.00000	0.0625000
$257$	24.1542	1.50670	0.753348	−	0.657622i	$-0.228438\pi$
$257$	24.1542	1.50670	0.753348	+	0.657622i	$0.228438\pi$
$258$	3.37611	0.210188
$259$	−4.01712	−0.249612
$260$	1.27464	0.0790497
$261$	12.6828	0.785043
$262$	−15.4731	−0.955931
$263$	−11.1610	−0.688214	−0.344107	−	0.938930i	$-0.611818\pi$
$263$	−11.1610	−0.688214	−0.344107	+	0.938930i	$0.611818\pi$
$264$	3.98170	0.245057
$265$	25.5143	1.56733
$266$	12.3814	0.759150
$267$	−2.23498	−0.136778
$268$	−7.05005	−0.430650
$269$	−2.93660	−0.179048	−0.0895238	−	0.995985i	$-0.528535\pi$
$269$	−2.93660	−0.179048	−0.0895238	+	0.995985i	$0.528535\pi$
$270$	7.76308	0.472446
$271$	10.5018	0.637941	0.318970	−	0.947765i	$-0.396663\pi$
$271$	10.5018	0.637941	0.318970	+	0.947765i	$0.396663\pi$
$272$	2.46330	0.149359
$273$	−1.90682	−0.115406
$274$	20.9560	1.26600
$275$	−0.995365	−0.0600228
$276$	−13.5823	−0.817557
$277$	−15.5091	−0.931854	−0.465927	−	0.884823i	$-0.654279\pi$
$277$	−15.5091	−0.931854	−0.465927	+	0.884823i	$0.654279\pi$
$278$	−18.1723	−1.08990
$279$	−1.21485	−0.0727309
$280$	−3.26939	−0.195384
$281$	−10.6483	−0.635226	−0.317613	−	0.948220i	$-0.602881\pi$
$281$	−10.6483	−0.635226	−0.317613	+	0.948220i	$0.602881\pi$
$282$	−17.4965	−1.04190
$283$	22.2249	1.32113	0.660566	−	0.750768i	$-0.270316\pi$
$283$	22.2249	1.32113	0.660566	+	0.750768i	$0.270316\pi$
$284$	10.0895	0.598704
$285$	34.8840	2.06635
$286$	1.16707	0.0690104
$287$	9.75772	0.575980
$288$	−1.21485	−0.0715855
$289$	−10.9322	−0.643068
$290$	22.1136	1.29856
$291$	−2.05301	−0.120350
$292$	11.2894	0.660662
$293$	19.4865	1.13841	0.569206	−	0.822195i	$-0.307251\pi$
$293$	19.4865	1.13841	0.569206	+	0.822195i	$0.307251\pi$
$294$	−9.48015	−0.552893
$295$	−20.6228	−1.20071
$296$	−2.60265	−0.151276
$297$	7.10795	0.412445
$298$	−6.82406	−0.395307
$299$	−3.98109	−0.230232
$300$	1.05365	0.0608324
$301$	−2.53820	−0.146299
$302$	−1.05760	−0.0608581
$303$	14.0226	0.805576
$304$	8.02174	0.460078
$305$	4.73624	0.271196
$306$	−2.99253	−0.171072
$307$	−10.5068	−0.599657	−0.299829	−	0.953993i	$-0.596929\pi$
$307$	−10.5068	−0.599657	−0.299829	+	0.953993i	$0.596929\pi$
$308$	−2.99349	−0.170570
$309$	−17.2264	−0.979975
$310$	−2.11820	−0.120306
$311$	−10.1817	−0.577352	−0.288676	−	0.957427i	$-0.593215\pi$
$311$	−10.1817	−0.577352	−0.288676	+	0.957427i	$0.593215\pi$
$312$	−1.23541	−0.0699412
$313$	18.0774	1.02179	0.510897	−	0.859642i	$-0.329313\pi$
$313$	18.0774	1.02179	0.510897	+	0.859642i	$0.329313\pi$
$314$	−11.1685	−0.630274
$315$	3.97181	0.223786
$316$	−2.93306	−0.164997
$317$	−18.2855	−1.02701	−0.513507	−	0.858085i	$-0.671654\pi$
$317$	−18.2855	−1.02701	−0.513507	+	0.858085i	$0.671654\pi$
$318$	−24.7291	−1.38674
$319$	20.2474	1.13364
$320$	−2.11820	−0.118411
$321$	20.3951	1.13834
$322$	10.2113	0.569054
$323$	19.7599	1.09947
$324$	−11.1687	−0.620483
$325$	0.308834	0.0171310
$326$	9.64552	0.534216
$327$	−26.9546	−1.49059
$328$	6.32192	0.349070
$329$	13.1540	0.725206
$330$	−8.43405	−0.464279
$331$	−8.32572	−0.457623	−0.228812	−	0.973471i	$-0.573484\pi$
$331$	−8.32572	−0.457623	−0.228812	+	0.973471i	$0.573484\pi$
$332$	−13.1425	−0.721289
$333$	3.16182	0.173266
$334$	7.88903	0.431668
$335$	14.9334	0.815900
$336$	3.16877	0.172870
$337$	−22.2276	−1.21082	−0.605408	−	0.795915i	$-0.706990\pi$
$337$	−22.2276	−1.21082	−0.605408	+	0.795915i	$0.706990\pi$
$338$	12.6379	0.687411
$339$	−40.5915	−2.20463
$340$	−5.21777	−0.282973
$341$	−1.93945	−0.105027
$342$	−9.74518	−0.526959
$343$	17.9316	0.968216
$344$	−1.64447	−0.0886639
$345$	28.7700	1.54892
$346$	12.8893	0.692932
$347$	−32.7446	−1.75782	−0.878911	−	0.476986i	$-0.841729\pi$
$347$	−32.7446	−1.75782	−0.878911	+	0.476986i	$0.841729\pi$
$348$	−21.4330	−1.14893
$349$	3.30066	0.176680	0.0883400	−	0.996090i	$-0.471844\pi$
$349$	3.30066	0.176680	0.0883400	+	0.996090i	$0.471844\pi$
$350$	−0.792145	−0.0423419
$351$	−2.20539	−0.117715
$352$	−1.93945	−0.103373
$353$	−13.3296	−0.709464	−0.354732	−	0.934968i	$-0.615428\pi$
$353$	−13.3296	−0.709464	−0.354732	+	0.934968i	$0.615428\pi$
$354$	19.9881	1.06236
$355$	−21.3717	−1.13429
$356$	1.08863	0.0576975
$357$	7.80563	0.413118
$358$	13.3274	0.704376
$359$	−30.9591	−1.63396	−0.816981	−	0.576665i	$-0.804354\pi$
$359$	−30.9591	−1.63396	−0.816981	+	0.576665i	$0.804354\pi$
$360$	2.57329	0.135624
$361$	45.3483	2.38675
$362$	−1.75830	−0.0924143
$363$	14.8608	0.779990
$364$	0.928794	0.0486820
$365$	−23.9132	−1.25168
$366$	−4.59047	−0.239948
$367$	30.9888	1.61760	0.808801	−	0.588083i	$-0.200117\pi$
$367$	30.9888	1.61760	0.808801	+	0.588083i	$0.200117\pi$
$368$	6.61579	0.344872
$369$	−7.68016	−0.399813
$370$	5.51293	0.286604
$371$	18.5916	0.965227
$372$	2.05301	0.106444
$373$	0.755417	0.0391140	0.0195570	−	0.999809i	$-0.493774\pi$
$373$	0.755417	0.0391140	0.0195570	+	0.999809i	$0.493774\pi$
$374$	−4.77744	−0.247035
$375$	−23.9753	−1.23808
$376$	8.52235	0.439507
$377$	−6.28221	−0.323550
$378$	5.65674	0.290951
$379$	15.2483	0.783251	0.391625	−	0.920125i	$-0.371913\pi$
$379$	15.2483	0.783251	0.391625	+	0.920125i	$0.371913\pi$
$380$	−16.9917	−0.871654
$381$	−10.5161	−0.538758
$382$	−4.75769	−0.243424
$383$	14.6150	0.746792	0.373396	−	0.927672i	$-0.378193\pi$
$383$	14.6150	0.746792	0.373396	+	0.927672i	$0.378193\pi$
$384$	2.05301	0.104767
$385$	6.34081	0.323158
$386$	−20.0256	−1.01928
$387$	1.99778	0.101553
$388$	1.00000	0.0507673
$389$	13.6379	0.691467	0.345733	−	0.938333i	$-0.387630\pi$
$389$	13.6379	0.691467	0.345733	+	0.938333i	$0.387630\pi$
$390$	2.61684	0.132509
$391$	16.2967	0.824158
$392$	4.61768	0.233228
$393$	−31.7664	−1.60240
$394$	5.90473	0.297476
$395$	6.21280	0.312600
$396$	2.35613	0.118400
$397$	−7.68029	−0.385463	−0.192731	−	0.981252i	$-0.561735\pi$
$397$	−7.68029	−0.385463	−0.192731	+	0.981252i	$0.561735\pi$
$398$	15.9333	0.798664
$399$	25.4190	1.27254
$400$	−0.513221	−0.0256611
$401$	6.85216	0.342181	0.171090	−	0.985255i	$-0.445271\pi$
$401$	6.85216	0.342181	0.171090	+	0.985255i	$0.445271\pi$
$402$	−14.4738	−0.721888
$403$	0.601755	0.0299756
$404$	−6.83026	−0.339818
$405$	23.6575	1.17555
$406$	16.1136	0.799704
$407$	5.04769	0.250205
$408$	5.05718	0.250368
$409$	6.92162	0.342252	0.171126	−	0.985249i	$-0.445259\pi$
$409$	6.92162	0.342252	0.171126	+	0.985249i	$0.445259\pi$
$410$	−13.3911	−0.661339
$411$	43.0228	2.12216
$412$	8.39080	0.413385
$413$	−15.0273	−0.739445
$414$	−8.03717	−0.395005
$415$	27.8385	1.36654
$416$	0.601755	0.0295035
$417$	−37.3079	−1.82697
$418$	−15.5577	−0.760953
$419$	13.5032	0.659677	0.329838	−	0.944037i	$-0.393006\pi$
$419$	13.5032	0.659677	0.329838	+	0.944037i	$0.393006\pi$
$420$	−6.71209	−0.327517
$421$	19.1340	0.932535	0.466267	−	0.884644i	$-0.345599\pi$
$421$	19.1340	0.932535	0.466267	+	0.884644i	$0.345599\pi$
$422$	−3.01136	−0.146591
$423$	−10.3533	−0.503397
$424$	12.0453	0.584970
$425$	−1.26422	−0.0613236
$426$	20.7139	1.00359
$427$	3.45117	0.167014
$428$	−9.93424	−0.480190
$429$	2.39601	0.115680
$430$	3.48332	0.167981
$431$	0.995703	0.0479613	0.0239807	−	0.999712i	$-0.492366\pi$
$431$	0.995703	0.0479613	0.0239807	+	0.999712i	$0.492366\pi$
$432$	3.66494	0.176329
$433$	−21.1281	−1.01535	−0.507675	−	0.861548i	$-0.669495\pi$
$433$	−21.1281	−1.01535	−0.507675	+	0.861548i	$0.669495\pi$
$434$	−1.54348	−0.0740892
$435$	45.3995	2.17674
$436$	13.1293	0.628779
$437$	53.0701	2.53869
$438$	23.1772	1.10745
$439$	5.02745	0.239947	0.119974	−	0.992777i	$-0.461719\pi$
$439$	5.02745	0.239947	0.119974	+	0.992777i	$0.461719\pi$
$440$	4.10814	0.195848
$441$	−5.60978	−0.267132
$442$	1.48230	0.0705060
$443$	−3.95203	−0.187767	−0.0938833	−	0.995583i	$-0.529928\pi$
$443$	−3.95203	−0.187767	−0.0938833	+	0.995583i	$0.529928\pi$
$444$	−5.34326	−0.253580
$445$	−2.30595	−0.109312
$446$	14.3040	0.677315
$447$	−14.0099	−0.662644
$448$	−1.54348	−0.0729223
$449$	−3.87029	−0.182650	−0.0913252	−	0.995821i	$-0.529110\pi$
$449$	−3.87029	−0.182650	−0.0913252	+	0.995821i	$0.529110\pi$
$450$	0.623485	0.0293914
$451$	−12.2610	−0.577349
$452$	19.7717	0.929982
$453$	−2.17126	−0.102015
$454$	−14.3245	−0.672280
$455$	−1.96737	−0.0922319
$456$	16.4687	0.771218
$457$	35.9929	1.68367	0.841837	−	0.539731i	$-0.181474\pi$
$457$	35.9929	1.68367	0.841837	+	0.539731i	$0.181474\pi$
$458$	−10.3916	−0.485570
$459$	9.02784	0.421383
$460$	−14.0136	−0.653386
$461$	2.26777	0.105621	0.0528103	−	0.998605i	$-0.483182\pi$
$461$	2.26777	0.105621	0.0528103	+	0.998605i	$0.483182\pi$
$462$	−6.14566	−0.285922
$463$	37.2182	1.72968	0.864838	−	0.502051i	$-0.167421\pi$
$463$	37.2182	1.72968	0.864838	+	0.502051i	$0.167421\pi$
$464$	10.4398	0.484656
$465$	−4.34869	−0.201666
$466$	−11.7599	−0.544769
$467$	−19.1444	−0.885895	−0.442947	−	0.896548i	$-0.646067\pi$
$467$	−19.1444	−0.885895	−0.442947	+	0.896548i	$0.646067\pi$
$468$	−0.731040	−0.0337923
$469$	10.8816	0.502465
$470$	−18.0521	−0.832680
$471$	−22.9290	−1.05651
$472$	−9.73602	−0.448136
$473$	3.18936	0.146647
$474$	−6.02159	−0.276581
$475$	−4.11693	−0.188898
$476$	−3.80204	−0.174266
$477$	−14.6332	−0.670006
$478$	6.64600	0.303981
$479$	18.6810	0.853557	0.426779	−	0.904356i	$-0.359648\pi$
$479$	18.6810	0.853557	0.426779	+	0.904356i	$0.359648\pi$
$480$	−4.34869	−0.198490
$481$	−1.56616	−0.0714106
$482$	−27.5614	−1.25539
$483$	20.9639	0.953891
$484$	−7.23855	−0.329025
$485$	−2.11820	−0.0961826
$486$	−11.9346	−0.541365
$487$	−6.06670	−0.274908	−0.137454	−	0.990508i	$-0.543892\pi$
$487$	−6.06670	−0.274908	−0.137454	+	0.990508i	$0.543892\pi$
$488$	2.23597	0.101218
$489$	19.8023	0.895492
$490$	−9.78119	−0.441869
$491$	−7.92591	−0.357691	−0.178846	−	0.983877i	$-0.557236\pi$
$491$	−7.92591	−0.357691	−0.178846	+	0.983877i	$0.557236\pi$
$492$	12.9790	0.585137
$493$	25.7164	1.15821
$494$	4.82712	0.217182
$495$	−4.99076	−0.224318
$496$	−1.00000	−0.0449013
$497$	−15.5730	−0.698543
$498$	−26.9817	−1.20908
$499$	9.98904	0.447171	0.223585	−	0.974684i	$-0.428224\pi$
$499$	9.98904	0.447171	0.223585	+	0.974684i	$0.428224\pi$
$500$	11.6781	0.522261
$501$	16.1962	0.723595
$502$	10.8998	0.486484
$503$	−38.0010	−1.69438	−0.847191	−	0.531288i	$-0.821708\pi$
$503$	−38.0010	−1.69438	−0.847191	+	0.531288i	$0.821708\pi$
$504$	1.87508	0.0835229
$505$	14.4679	0.643812
$506$	−12.8310	−0.570406
$507$	25.9457	1.15229
$508$	5.12231	0.227266
$509$	−27.7094	−1.22820	−0.614099	−	0.789229i	$-0.710480\pi$
$509$	−27.7094	−1.22820	−0.614099	+	0.789229i	$0.710480\pi$
$510$	−10.7121	−0.474341
$511$	−17.4249	−0.770833
$512$	−1.00000	−0.0441942
$513$	29.3992	1.29800
$514$	−24.1542	−1.06539
$515$	−17.7734	−0.783190
$516$	−3.37611	−0.148625
$517$	−16.5286	−0.726929
$518$	4.01712	0.176502
$519$	26.4618	1.16154
$520$	−1.27464	−0.0558966
$521$	−0.630427	−0.0276195	−0.0138097	−	0.999905i	$-0.504396\pi$
$521$	−0.630427	−0.0276195	−0.0138097	+	0.999905i	$0.504396\pi$
$522$	−12.6828	−0.555109
$523$	0.522879	0.0228639	0.0114319	−	0.999935i	$-0.496361\pi$
$523$	0.522879	0.0228639	0.0114319	+	0.999935i	$0.496361\pi$
$524$	15.4731	0.675945
$525$	−1.62628	−0.0709767
$526$	11.1610	0.486641
$527$	−2.46330	−0.107303
$528$	−3.98170	−0.173281
$529$	20.7687	0.902986
$530$	−25.5143	−1.10827
$531$	11.8278	0.513281
$532$	−12.3814	−0.536800
$533$	3.80425	0.164780
$534$	2.23498	0.0967169
$535$	21.0427	0.909756
$536$	7.05005	0.304516
$537$	27.3613	1.18073
$538$	2.93660	0.126606
$539$	−8.95575	−0.385752
$540$	−7.76308	−0.334070
$541$	9.48138	0.407636	0.203818	−	0.979009i	$-0.434665\pi$
$541$	9.48138	0.407636	0.203818	+	0.979009i	$0.434665\pi$
$542$	−10.5018	−0.451092
$543$	−3.60981	−0.154912
$544$	−2.46330	−0.105613
$545$	−27.8105	−1.19127
$546$	1.90682	0.0816045
$547$	13.6079	0.581833	0.290916	−	0.956748i	$-0.406040\pi$
$547$	13.6079	0.581833	0.290916	+	0.956748i	$0.406040\pi$
$548$	−20.9560	−0.895196
$549$	−2.71636	−0.115931
$550$	0.995365	0.0424425
$551$	83.7454	3.56767
$552$	13.5823	0.578100
$553$	4.52710	0.192512
$554$	15.5091	0.658920
$555$	11.3181	0.480427
$556$	18.1723	0.770677
$557$	−3.87354	−0.164127	−0.0820636	−	0.996627i	$-0.526151\pi$
$557$	−3.87354	−0.164127	−0.0820636	+	0.996627i	$0.526151\pi$
$558$	1.21485	0.0514285
$559$	−0.989568	−0.0418543
$560$	3.26939	0.138157
$561$	−9.80812	−0.414099
$562$	10.6483	0.449172
$563$	−46.1751	−1.94605	−0.973024	−	0.230704i	$-0.925897\pi$
$563$	−46.1751	−1.94605	−0.973024	+	0.230704i	$0.925897\pi$
$564$	17.4965	0.736734
$565$	−41.8804	−1.76192
$566$	−22.2249	−0.934182
$567$	17.2386	0.723953
$568$	−10.0895	−0.423348
$569$	30.7707	1.28997	0.644987	−	0.764194i	$-0.276863\pi$
$569$	30.7707	1.28997	0.644987	+	0.764194i	$0.276863\pi$
$570$	−34.8840	−1.46113
$571$	−18.1554	−0.759779	−0.379889	−	0.925032i	$-0.624038\pi$
$571$	−18.1554	−0.759779	−0.379889	+	0.925032i	$0.624038\pi$
$572$	−1.16707	−0.0487977
$573$	−9.76758	−0.408046
$574$	−9.75772	−0.407280
$575$	−3.39537	−0.141597
$576$	1.21485	0.0506186
$577$	−4.50626	−0.187598	−0.0937991	−	0.995591i	$-0.529901\pi$
$577$	−4.50626	−0.187598	−0.0937991	+	0.995591i	$0.529901\pi$
$578$	10.9322	0.454718
$579$	−41.1128	−1.70859
$580$	−22.1136	−0.918218
$581$	20.2851	0.841570
$582$	2.05301	0.0851000
$583$	−23.3612	−0.967521
$584$	−11.2894	−0.467159
$585$	1.54849	0.0640222
$586$	−19.4865	−0.804979
$587$	5.52200	0.227917	0.113959	−	0.993485i	$-0.463647\pi$
$587$	5.52200	0.227917	0.113959	+	0.993485i	$0.463647\pi$
$588$	9.48015	0.390955
$589$	−8.02174	−0.330530
$590$	20.6228	0.849029
$591$	12.1225	0.498652
$592$	2.60265	0.106968
$593$	23.4917	0.964689	0.482344	−	0.875982i	$-0.339785\pi$
$593$	23.4917	0.964689	0.482344	+	0.875982i	$0.339785\pi$
$594$	−7.10795	−0.291643
$595$	8.05349	0.330161
$596$	6.82406	0.279525
$597$	32.7112	1.33878
$598$	3.98109	0.162799
$599$	7.09914	0.290063	0.145031	−	0.989427i	$-0.453672\pi$
$599$	7.09914	0.290063	0.145031	+	0.989427i	$0.453672\pi$
$600$	−1.05365	−0.0430150
$601$	14.5649	0.594113	0.297057	−	0.954860i	$-0.403995\pi$
$601$	14.5649	0.594113	0.297057	+	0.954860i	$0.403995\pi$
$602$	2.53820	0.103449
$603$	−8.56473	−0.348783
$604$	1.05760	0.0430332
$605$	15.3327	0.623363
$606$	−14.0226	−0.569629
$607$	−6.54089	−0.265487	−0.132743	−	0.991150i	$-0.542379\pi$
$607$	−6.54089	−0.265487	−0.132743	+	0.991150i	$0.542379\pi$
$608$	−8.02174	−0.325324
$609$	33.0813	1.34052
$610$	−4.73624	−0.191765
$611$	5.12837	0.207472
$612$	2.99253	0.120966
$613$	−25.7630	−1.04056	−0.520279	−	0.853996i	$-0.674172\pi$
$613$	−25.7630	−1.04056	−0.520279	+	0.853996i	$0.674172\pi$
$614$	10.5068	0.424022
$615$	−27.4920	−1.10859
$616$	2.99349	0.120611
$617$	−19.5624	−0.787554	−0.393777	−	0.919206i	$-0.628832\pi$
$617$	−19.5624	−0.787554	−0.393777	+	0.919206i	$0.628832\pi$
$618$	17.2264	0.692947
$619$	19.1769	0.770786	0.385393	−	0.922753i	$-0.374066\pi$
$619$	19.1769	0.770786	0.385393	+	0.922753i	$0.374066\pi$
$620$	2.11820	0.0850690
$621$	24.2465	0.972977
$622$	10.1817	0.408250
$623$	−1.68028	−0.0673190
$624$	1.23541	0.0494559
$625$	−22.1705	−0.886820
$626$	−18.0774	−0.722517
$627$	−31.9402	−1.27557
$628$	11.1685	0.445671
$629$	6.41110	0.255627
$630$	−3.97181	−0.158241
$631$	−36.8312	−1.46623	−0.733114	−	0.680106i	$-0.761934\pi$
$631$	−36.8312	−1.46623	−0.733114	+	0.680106i	$0.761934\pi$
$632$	2.93306	0.116671
$633$	−6.18234	−0.245726
$634$	18.2855	0.726209
$635$	−10.8501	−0.430572
$636$	24.7291	0.980571
$637$	2.77871	0.110097
$638$	−20.2474	−0.801604
$639$	12.2572	0.484889
$640$	2.11820	0.0837293
$641$	11.8478	0.467962	0.233981	−	0.972241i	$-0.424825\pi$
$641$	11.8478	0.467962	0.233981	+	0.972241i	$0.424825\pi$
$642$	−20.3951	−0.804930
$643$	−31.1610	−1.22887	−0.614436	−	0.788967i	$-0.710616\pi$
$643$	−31.1610	−1.22887	−0.614436	+	0.788967i	$0.710616\pi$
$644$	−10.2113	−0.402382
$645$	7.15129	0.281582
$646$	−19.7599	−0.777445
$647$	−11.2694	−0.443045	−0.221522	−	0.975155i	$-0.571103\pi$
$647$	−11.2694	−0.443045	−0.221522	+	0.975155i	$0.571103\pi$
$648$	11.1687	0.438747
$649$	18.8825	0.741202
$650$	−0.308834	−0.0121135
$651$	−3.16877	−0.124194
$652$	−9.64552	−0.377748
$653$	30.2247	1.18278	0.591392	−	0.806384i	$-0.298579\pi$
$653$	30.2247	1.18278	0.591392	+	0.806384i	$0.298579\pi$
$654$	26.9546	1.05401
$655$	−32.7751	−1.28063
$656$	−6.32192	−0.246829
$657$	13.7149	0.535069
$658$	−13.1540	−0.512798
$659$	46.7355	1.82056	0.910279	−	0.413995i	$-0.135867\pi$
$659$	46.7355	1.82056	0.910279	+	0.413995i	$0.135867\pi$
$660$	8.43405	0.328295
$661$	9.36780	0.364365	0.182183	−	0.983265i	$-0.441684\pi$
$661$	9.36780	0.364365	0.182183	+	0.983265i	$0.441684\pi$
$662$	8.32572	0.323588
$663$	3.04318	0.118187
$664$	13.1425	0.510028
$665$	26.2262	1.01701
$666$	−3.16182	−0.122518
$667$	69.0676	2.67431
$668$	−7.88903	−0.305236
$669$	29.3663	1.13537
$670$	−14.9334	−0.576929
$671$	−4.33655	−0.167410
$672$	−3.16877	−0.122238
$673$	−7.53716	−0.290536	−0.145268	−	0.989392i	$-0.546404\pi$
$673$	−7.53716	−0.290536	−0.145268	+	0.989392i	$0.546404\pi$
$674$	22.2276	0.856176
$675$	−1.88092	−0.0723968
$676$	−12.6379	−0.486073
$677$	46.4471	1.78511	0.892554	−	0.450940i	$-0.148911\pi$
$677$	46.4471	1.78511	0.892554	+	0.450940i	$0.148911\pi$
$678$	40.5915	1.55891
$679$	−1.54348	−0.0592331
$680$	5.21777	0.200092
$681$	−29.4082	−1.12693
$682$	1.93945	0.0742652
$683$	−35.0513	−1.34120	−0.670600	−	0.741819i	$-0.733963\pi$
$683$	−35.0513	−1.34120	−0.670600	+	0.741819i	$0.733963\pi$
$684$	9.74518	0.372616
$685$	44.3890	1.69602
$686$	−17.9316	−0.684632
$687$	−21.3341	−0.813948
$688$	1.64447	0.0626949
$689$	7.24831	0.276139
$690$	−28.7700	−1.09526
$691$	−15.9205	−0.605645	−0.302822	−	0.953047i	$-0.597929\pi$
$691$	−15.9205	−0.605645	−0.302822	+	0.953047i	$0.597929\pi$
$692$	−12.8893	−0.489977
$693$	−3.63663	−0.138144
$694$	32.7446	1.24297
$695$	−38.4926	−1.46011
$696$	21.4330	0.812417
$697$	−15.5728	−0.589861
$698$	−3.30066	−0.124932
$699$	−24.1433	−0.913182
$700$	0.792145	0.0299403
$701$	23.7127	0.895615	0.447808	−	0.894130i	$-0.352205\pi$
$701$	23.7127	0.895615	0.447808	+	0.894130i	$0.352205\pi$
$702$	2.20539	0.0832372
$703$	20.8778	0.787419
$704$	1.93945	0.0730956
$705$	−37.0610	−1.39580
$706$	13.3296	0.501667
$707$	10.5423	0.396485
$708$	−19.9881	−0.751200
$709$	37.4570	1.40673	0.703364	−	0.710830i	$-0.251681\pi$
$709$	37.4570	1.40673	0.703364	+	0.710830i	$0.251681\pi$
$710$	21.3717	0.802065
$711$	−3.56321	−0.133631
$712$	−1.08863	−0.0407983
$713$	−6.61579	−0.247763
$714$	−7.80563	−0.292118
$715$	2.47209	0.0924510
$716$	−13.3274	−0.498069
$717$	13.6443	0.509556
$718$	30.9591	1.15539
$719$	−26.9599	−1.00543	−0.502717	−	0.864451i	$-0.667666\pi$
$719$	−26.9599	−1.00543	−0.502717	+	0.864451i	$0.667666\pi$
$720$	−2.57329	−0.0959008
$721$	−12.9510	−0.482320
$722$	−45.3483	−1.68769
$723$	−56.5838	−2.10437
$724$	1.75830	0.0653468
$725$	−5.35793	−0.198989
$726$	−14.8608	−0.551536
$727$	7.49515	0.277980	0.138990	−	0.990294i	$-0.455614\pi$
$727$	7.49515	0.277980	0.138990	+	0.990294i	$0.455614\pi$
$728$	−0.928794	−0.0344234
$729$	9.00421	0.333489
$730$	23.9132	0.885068
$731$	4.05082	0.149825
$732$	4.59047	0.169669
$733$	0.458920	0.0169506	0.00847529	−	0.999964i	$-0.497302\pi$
$733$	0.458920	0.0169506	0.00847529	+	0.999964i	$0.497302\pi$
$734$	−30.9888	−1.14382
$735$	−20.0809	−0.740694
$736$	−6.61579	−0.243861
$737$	−13.6732	−0.503659
$738$	7.68016	0.282711
$739$	28.7325	1.05694	0.528471	−	0.848951i	$-0.322765\pi$
$739$	28.7325	1.05694	0.528471	+	0.848951i	$0.322765\pi$
$740$	−5.51293	−0.202659
$741$	9.91012	0.364058
$742$	−18.5916	−0.682519
$743$	3.62552	0.133008	0.0665038	−	0.997786i	$-0.478816\pi$
$743$	3.62552	0.133008	0.0665038	+	0.997786i	$0.478816\pi$
$744$	−2.05301	−0.0752670
$745$	−14.4547	−0.529581
$746$	−0.755417	−0.0276578
$747$	−15.9661	−0.584170
$748$	4.77744	0.174680
$749$	15.3332	0.560265
$750$	23.9753	0.875453
$751$	−20.5984	−0.751646	−0.375823	−	0.926691i	$-0.622640\pi$
$751$	−20.5984	−0.751646	−0.375823	+	0.926691i	$0.622640\pi$
$752$	−8.52235	−0.310778
$753$	22.3775	0.815480
$754$	6.28221	0.228785
$755$	−2.24021	−0.0815296
$756$	−5.65674	−0.205734
$757$	6.66727	0.242326	0.121163	−	0.992633i	$-0.461338\pi$
$757$	6.66727	0.242326	0.121163	+	0.992633i	$0.461338\pi$
$758$	−15.2483	−0.553842
$759$	−26.3421	−0.956158
$760$	16.9917	0.616352
$761$	34.7532	1.25980	0.629901	−	0.776676i	$-0.283096\pi$
$761$	34.7532	1.25980	0.629901	+	0.776676i	$0.283096\pi$
$762$	10.5161	0.380960
$763$	−20.2647	−0.733633
$764$	4.75769	0.172127
$765$	−6.33878	−0.229179
$766$	−14.6150	−0.528061
$767$	−5.85870	−0.211545
$768$	−2.05301	−0.0740816
$769$	22.7614	0.820797	0.410399	−	0.911906i	$-0.365390\pi$
$769$	22.7614	0.820797	0.410399	+	0.911906i	$0.365390\pi$
$770$	−6.34081	−0.228507
$771$	−49.5887	−1.78589
$772$	20.0256	0.720738
$773$	−16.2348	−0.583925	−0.291962	−	0.956430i	$-0.594308\pi$
$773$	−16.2348	−0.583925	−0.291962	+	0.956430i	$0.594308\pi$
$774$	−1.99778	−0.0718087
$775$	0.513221	0.0184355
$776$	−1.00000	−0.0358979
$777$	8.24719	0.295866
$778$	−13.6379	−0.488941
$779$	−50.7128	−1.81697
$780$	−2.61684	−0.0936981
$781$	19.5681	0.700203
$782$	−16.2967	−0.582768
$783$	38.2612	1.36735
$784$	−4.61768	−0.164917
$785$	−23.6571	−0.844358
$786$	31.7664	1.13307
$787$	39.8444	1.42030	0.710149	−	0.704052i	$-0.248628\pi$
$787$	39.8444	1.42030	0.710149	+	0.704052i	$0.248628\pi$
$788$	−5.90473	−0.210347
$789$	22.9135	0.815743
$790$	−6.21280	−0.221042
$791$	−30.5171	−1.08506
$792$	−2.35613	−0.0837214
$793$	1.34551	0.0477803
$794$	7.68029	0.272563
$795$	−52.3811	−1.85777
$796$	−15.9333	−0.564741
$797$	24.9708	0.884512	0.442256	−	0.896889i	$-0.354178\pi$
$797$	24.9708	0.884512	0.442256	+	0.896889i	$0.354178\pi$
$798$	−25.4190	−0.899824
$799$	−20.9931	−0.742683
$800$	0.513221	0.0181451
$801$	1.32252	0.0467291
$802$	−6.85216	−0.241958
$803$	21.8952	0.772664
$804$	14.4738	0.510452
$805$	21.6296	0.762344
$806$	−0.601755	−0.0211959
$807$	6.02886	0.212226
$808$	6.83026	0.240288
$809$	−8.08324	−0.284192	−0.142096	−	0.989853i	$-0.545384\pi$
$809$	−8.08324	−0.284192	−0.142096	+	0.989853i	$0.545384\pi$
$810$	−23.6575	−0.831241
$811$	37.4565	1.31528	0.657638	−	0.753334i	$-0.271556\pi$
$811$	37.4565	1.31528	0.657638	+	0.753334i	$0.271556\pi$
$812$	−16.1136	−0.565476
$813$	−21.5603	−0.756154
$814$	−5.04769	−0.176922
$815$	20.4312	0.715672
$816$	−5.05718	−0.177037
$817$	13.1915	0.461513
$818$	−6.92162	−0.242009
$819$	1.12834	0.0394275
$820$	13.3911	0.467637
$821$	−26.9540	−0.940700	−0.470350	−	0.882480i	$-0.655872\pi$
$821$	−26.9540	−0.940700	−0.470350	+	0.882480i	$0.655872\pi$
$822$	−43.0228	−1.50059
$823$	40.9796	1.42846	0.714230	−	0.699911i	$-0.246777\pi$
$823$	40.9796	1.42846	0.714230	+	0.699911i	$0.246777\pi$
$824$	−8.39080	−0.292307
$825$	2.04349	0.0711453
$826$	15.0273	0.522867
$827$	24.7755	0.861530	0.430765	−	0.902464i	$-0.358244\pi$
$827$	24.7755	0.861530	0.430765	+	0.902464i	$0.358244\pi$
$828$	8.03717	0.279311
$829$	8.08017	0.280636	0.140318	−	0.990106i	$-0.455188\pi$
$829$	8.08017	0.280636	0.140318	+	0.990106i	$0.455188\pi$
$830$	−27.8385	−0.966288
$831$	31.8404	1.10453
$832$	−0.601755	−0.0208621
$833$	−11.3747	−0.394111
$834$	37.3079	1.29187
$835$	16.7106	0.578293
$836$	15.5577	0.538075
$837$	−3.66494	−0.126679
$838$	−13.5032	−0.466462
$839$	−30.1389	−1.04051	−0.520255	−	0.854011i	$-0.674163\pi$
$839$	−30.1389	−1.04051	−0.520255	+	0.854011i	$0.674163\pi$
$840$	6.71209	0.231589
$841$	79.9896	2.75826
$842$	−19.1340	−0.659401
$843$	21.8611	0.752936
$844$	3.01136	0.103655
$845$	26.7696	0.920902
$846$	10.3533	0.355955
$847$	11.1725	0.383892
$848$	−12.0453	−0.413637
$849$	−45.6279	−1.56595
$850$	1.26422	0.0433623
$851$	17.2186	0.590245
$852$	−20.7139	−0.709648
$853$	−19.8602	−0.680001	−0.340000	−	0.940425i	$-0.610427\pi$
$853$	−19.8602	−0.680001	−0.340000	+	0.940425i	$0.610427\pi$
$854$	−3.45117	−0.118096
$855$	−20.6423	−0.705950
$856$	9.93424	0.339545
$857$	24.5889	0.839940	0.419970	−	0.907538i	$-0.362041\pi$
$857$	24.5889	0.839940	0.419970	+	0.907538i	$0.362041\pi$
$858$	−2.39601	−0.0817984
$859$	11.3559	0.387459	0.193730	−	0.981055i	$-0.437942\pi$
$859$	11.3559	0.387459	0.193730	+	0.981055i	$0.437942\pi$
$860$	−3.48332	−0.118780
$861$	−20.0327	−0.682712
$862$	−0.995703	−0.0339138
$863$	6.53755	0.222541	0.111270	−	0.993790i	$-0.464508\pi$
$863$	6.53755	0.222541	0.111270	+	0.993790i	$0.464508\pi$
$864$	−3.66494	−0.124684
$865$	27.3021	0.928299
$866$	21.1281	0.717961
$867$	22.4438	0.762232
$868$	1.54348	0.0523890
$869$	−5.68850	−0.192969
$870$	−45.3995	−1.53919
$871$	4.24240	0.143748
$872$	−13.1293	−0.444614
$873$	1.21485	0.0411163
$874$	−53.0701	−1.79512
$875$	−18.0249	−0.609352
$876$	−23.1772	−0.783087
$877$	−25.5474	−0.862674	−0.431337	−	0.902191i	$-0.641958\pi$
$877$	−25.5474	−0.862674	−0.431337	+	0.902191i	$0.641958\pi$
$878$	−5.02745	−0.169668
$879$	−40.0059	−1.34937
$880$	−4.10814	−0.138485
$881$	−43.0944	−1.45189	−0.725944	−	0.687754i	$-0.758597\pi$
$881$	−43.0944	−1.45189	−0.725944	+	0.687754i	$0.758597\pi$
$882$	5.60978	0.188891
$883$	−15.2294	−0.512510	−0.256255	−	0.966609i	$-0.582489\pi$
$883$	−15.2294	−0.512510	−0.256255	+	0.966609i	$0.582489\pi$
$884$	−1.48230	−0.0498552
$885$	42.3389	1.42321
$886$	3.95203	0.132771
$887$	57.8228	1.94150	0.970749	−	0.240095i	$-0.0771787\pi$
$887$	57.8228	1.94150	0.970749	+	0.240095i	$0.0771787\pi$
$888$	5.34326	0.179308
$889$	−7.90616	−0.265164
$890$	2.30595	0.0772955
$891$	−21.6611	−0.725673
$892$	−14.3040	−0.478934
$893$	−68.3641	−2.28772
$894$	14.0099	0.468560
$895$	28.2302	0.943631
$896$	1.54348	0.0515639
$897$	8.17320	0.272895
$898$	3.87029	0.129153
$899$	−10.4398	−0.348187
$900$	−0.623485	−0.0207828
$901$	−29.6711	−0.988489
$902$	12.2610	0.408247
$903$	5.21095	0.173409
$904$	−19.7717	−0.657597
$905$	−3.72444	−0.123805
$906$	2.17126	0.0721354
$907$	−5.61263	−0.186364	−0.0931822	−	0.995649i	$-0.529704\pi$
$907$	−5.61263	−0.186364	−0.0931822	+	0.995649i	$0.529704\pi$
$908$	14.3245	0.475374
$909$	−8.29771	−0.275218
$910$	1.96737	0.0652178
$911$	−20.0661	−0.664820	−0.332410	−	0.943135i	$-0.607862\pi$
$911$	−20.0661	−0.664820	−0.332410	+	0.943135i	$0.607862\pi$
$912$	−16.4687	−0.545333
$913$	−25.4892	−0.843569
$914$	−35.9929	−1.19054
$915$	−9.72354	−0.321450
$916$	10.3916	0.343350
$917$	−23.8823	−0.788664
$918$	−9.02784	−0.297963
$919$	−0.235064	−0.00775404	−0.00387702	−	0.999992i	$-0.501234\pi$
$919$	−0.235064	−0.00775404	−0.00387702	+	0.999992i	$0.501234\pi$
$920$	14.0136	0.462014
$921$	21.5706	0.710777
$922$	−2.26777	−0.0746851
$923$	−6.07144	−0.199844
$924$	6.14566	0.202177
$925$	−1.33573	−0.0439187
$926$	−37.2182	−1.22307
$927$	10.1935	0.334800
$928$	−10.4398	−0.342703
$929$	55.6669	1.82637	0.913185	−	0.407544i	$-0.133615\pi$
$929$	55.6669	1.82637	0.913185	+	0.407544i	$0.133615\pi$
$930$	4.34869	0.142599
$931$	−37.0419	−1.21400
$932$	11.7599	0.385210
$933$	20.9032	0.684339
$934$	19.1444	0.626422
$935$	−10.1196	−0.330946
$936$	0.731040	0.0238948
$937$	43.0392	1.40603	0.703015	−	0.711175i	$-0.251836\pi$
$937$	43.0392	1.40603	0.703015	+	0.711175i	$0.251836\pi$
$938$	−10.8816	−0.355296
$939$	−37.1130	−1.21114
$940$	18.0521	0.588793
$941$	7.51547	0.244997	0.122499	−	0.992469i	$-0.460909\pi$
$941$	7.51547	0.244997	0.122499	+	0.992469i	$0.460909\pi$
$942$	22.9290	0.747067
$943$	−41.8245	−1.36199
$944$	9.73602	0.316880
$945$	11.9821	0.389778
$946$	−3.18936	−0.103695
$947$	−13.9986	−0.454894	−0.227447	−	0.973790i	$-0.573038\pi$
$947$	−13.9986	−0.454894	−0.227447	+	0.973790i	$0.573038\pi$
$948$	6.02159	0.195572
$949$	−6.79346	−0.220525
$950$	4.11693	0.133571
$951$	37.5402	1.21733
$952$	3.80204	0.123225
$953$	13.1232	0.425102	0.212551	−	0.977150i	$-0.431823\pi$
$953$	13.1232	0.425102	0.212551	+	0.977150i	$0.431823\pi$
$954$	14.6332	0.473766
$955$	−10.0777	−0.326108
$956$	−6.64600	−0.214947
$957$	−41.5682	−1.34371
$958$	−18.6810	−0.603556
$959$	32.3451	1.04448
$960$	4.34869	0.140353
$961$	1.00000	0.0322581
$962$	1.56616	0.0504949
$963$	−12.0686	−0.388904
$964$	27.5614	0.887692
$965$	−42.4183	−1.36549
$966$	−20.9639	−0.674503
$967$	46.4369	1.49331	0.746655	−	0.665212i	$-0.231659\pi$
$967$	46.4369	1.49331	0.746655	+	0.665212i	$0.231659\pi$
$968$	7.23855	0.232656
$969$	−40.5673	−1.30321
$970$	2.11820	0.0680114
$971$	36.6209	1.17522	0.587611	−	0.809144i	$-0.300069\pi$
$971$	36.6209	1.17522	0.587611	+	0.809144i	$0.300069\pi$
$972$	11.9346	0.382803
$973$	−28.0485	−0.899193
$974$	6.06670	0.194389
$975$	−0.634038	−0.0203055
$976$	−2.23597	−0.0715717
$977$	−16.4850	−0.527403	−0.263702	−	0.964604i	$-0.584943\pi$
$977$	−16.4850	−0.527403	−0.263702	+	0.964604i	$0.584943\pi$
$978$	−19.8023	−0.633209
$979$	2.11135	0.0674790
$980$	9.78119	0.312449
$981$	15.9501	0.509247
$982$	7.92591	0.252926
$983$	−37.2105	−1.18683	−0.593415	−	0.804897i	$-0.702221\pi$
$983$	−37.2105	−1.18683	−0.593415	+	0.804897i	$0.702221\pi$
$984$	−12.9790	−0.413754
$985$	12.5074	0.398519
$986$	−25.7164	−0.818976
$987$	−27.0054	−0.859590
$988$	−4.82712	−0.153571
$989$	10.8795	0.345947
$990$	4.99076	0.158617
$991$	−35.1136	−1.11542	−0.557710	−	0.830036i	$-0.688320\pi$
$991$	−35.1136	−1.11542	−0.557710	+	0.830036i	$0.688320\pi$
$992$	1.00000	0.0317500
$993$	17.0928	0.542423
$994$	15.5730	0.493944
$995$	33.7499	1.06994
$996$	26.9817	0.854948
$997$	−38.5227	−1.22003	−0.610014	−	0.792391i	$-0.708836\pi$
$997$	−38.5227	−1.22003	−0.610014	+	0.792391i	$0.708836\pi$
$998$	−9.98904	−0.316198
$999$	9.53854	0.301786

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.j.1.7	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.j.1.7	✓	32	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.05301 q^{3} +1.00000 q^{4} -2.11820 q^{5} +2.05301 q^{6} -1.54348 q^{7} -1.00000 q^{8} +1.21485 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.05301 q^{3} +1.00000 q^{4} -2.11820 q^{5} +2.05301 q^{6} -1.54348 q^{7} -1.00000 q^{8} +1.21485 q^{9} +2.11820 q^{10} +1.93945 q^{11} -2.05301 q^{12} -0.601755 q^{13} +1.54348 q^{14} +4.34869 q^{15} +1.00000 q^{16} +2.46330 q^{17} -1.21485 q^{18} +8.02174 q^{19} -2.11820 q^{20} +3.16877 q^{21} -1.93945 q^{22} +6.61579 q^{23} +2.05301 q^{24} -0.513221 q^{25} +0.601755 q^{26} +3.66494 q^{27} -1.54348 q^{28} +10.4398 q^{29} -4.34869 q^{30} -1.00000 q^{31} -1.00000 q^{32} -3.98170 q^{33} -2.46330 q^{34} +3.26939 q^{35} +1.21485 q^{36} +2.60265 q^{37} -8.02174 q^{38} +1.23541 q^{39} +2.11820 q^{40} -6.32192 q^{41} -3.16877 q^{42} +1.64447 q^{43} +1.93945 q^{44} -2.57329 q^{45} -6.61579 q^{46} -8.52235 q^{47} -2.05301 q^{48} -4.61768 q^{49} +0.513221 q^{50} -5.05718 q^{51} -0.601755 q^{52} -12.0453 q^{53} -3.66494 q^{54} -4.10814 q^{55} +1.54348 q^{56} -16.4687 q^{57} -10.4398 q^{58} +9.73602 q^{59} +4.34869 q^{60} -2.23597 q^{61} +1.00000 q^{62} -1.87508 q^{63} +1.00000 q^{64} +1.27464 q^{65} +3.98170 q^{66} -7.05005 q^{67} +2.46330 q^{68} -13.5823 q^{69} -3.26939 q^{70} +10.0895 q^{71} -1.21485 q^{72} +11.2894 q^{73} -2.60265 q^{74} +1.05365 q^{75} +8.02174 q^{76} -2.99349 q^{77} -1.23541 q^{78} -2.93306 q^{79} -2.11820 q^{80} -11.1687 q^{81} +6.32192 q^{82} -13.1425 q^{83} +3.16877 q^{84} -5.21777 q^{85} -1.64447 q^{86} -21.4330 q^{87} -1.93945 q^{88} +1.08863 q^{89} +2.57329 q^{90} +0.928794 q^{91} +6.61579 q^{92} +2.05301 q^{93} +8.52235 q^{94} -16.9917 q^{95} +2.05301 q^{96} +1.00000 q^{97} +4.61768 q^{98} +2.35613 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9}+O(q^{10}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 5 q^{14} - q^{15} + 32 q^{16} + 14 q^{17} - 30 q^{18} + 33 q^{19} + 4 q^{22} - 2 q^{23} + 2 q^{24} + 46 q^{25} - 10 q^{26} - 5 q^{27} + 5 q^{28} - q^{29} + q^{30} - 32 q^{31} - 32 q^{32} + 32 q^{33} - 14 q^{34} + 8 q^{35} + 30 q^{36} + 31 q^{37} - 33 q^{38} + 4 q^{39} + 31 q^{41} + 15 q^{43} - 4 q^{44} + q^{45} + 2 q^{46} - 14 q^{47} - 2 q^{48} + 75 q^{49} - 46 q^{50} + 27 q^{51} + 10 q^{52} - 31 q^{53} + 5 q^{54} + 14 q^{55} - 5 q^{56} + 51 q^{57} + q^{58} - 8 q^{59} - q^{60} + 24 q^{61} + 32 q^{62} + 23 q^{63} + 32 q^{64} + 20 q^{65} - 32 q^{66} + 17 q^{67} + 14 q^{68} - 31 q^{69} - 8 q^{70} - 31 q^{71} - 30 q^{72} + 19 q^{73} - 31 q^{74} - 40 q^{75} + 33 q^{76} + 8 q^{77} - 4 q^{78} + 39 q^{79} + 116 q^{81} - 31 q^{82} - 6 q^{83} + 56 q^{85} - 15 q^{86} - 17 q^{87} + 4 q^{88} + 8 q^{89} - q^{90} + 34 q^{91} - 2 q^{92} + 2 q^{93} + 14 q^{94} - 22 q^{95} + 2 q^{96} + 32 q^{97} - 75 q^{98} - 27 q^{99}+O(q^{100}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 5 * q^14 - q^15 + 32 * q^16 + 14 * q^17 - 30 * q^18 + 33 * q^19 + 4 * q^22 - 2 * q^23 + 2 * q^24 + 46 * q^25 - 10 * q^26 - 5 * q^27 + 5 * q^28 - q^29 + q^30 - 32 * q^31 - 32 * q^32 + 32 * q^33 - 14 * q^34 + 8 * q^35 + 30 * q^36 + 31 * q^37 - 33 * q^38 + 4 * q^39 + 31 * q^41 + 15 * q^43 - 4 * q^44 + q^45 + 2 * q^46 - 14 * q^47 - 2 * q^48 + 75 * q^49 - 46 * q^50 + 27 * q^51 + 10 * q^52 - 31 * q^53 + 5 * q^54 + 14 * q^55 - 5 * q^56 + 51 * q^57 + q^58 - 8 * q^59 - q^60 + 24 * q^61 + 32 * q^62 + 23 * q^63 + 32 * q^64 + 20 * q^65 - 32 * q^66 + 17 * q^67 + 14 * q^68 - 31 * q^69 - 8 * q^70 - 31 * q^71 - 30 * q^72 + 19 * q^73 - 31 * q^74 - 40 * q^75 + 33 * q^76 + 8 * q^77 - 4 * q^78 + 39 * q^79 + 116 * q^81 - 31 * q^82 - 6 * q^83 + 56 * q^85 - 15 * q^86 - 17 * q^87 + 4 * q^88 + 8 * q^89 - q^90 + 34 * q^91 - 2 * q^92 + 2 * q^93 + 14 * q^94 - 22 * q^95 + 2 * q^96 + 32 * q^97 - 75 * q^98 - 27 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more