LMFDB - Embedded newform 6010.2.a.c.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, 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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 9 x^{14} + 75 x^{13} - 178 x^{12} - 232 x^{11} + 872 x^{10} + 228 x^{9} - 1986 x^{8} + \cdots - 10 $ x^16 - 8x^15 + 9x^14 + 75x^13 - 178x^12 - 232x^11 + 872x^10 + 228x^9 - 1986x^8 + 164x^7 + 2332x^6 - 440x^5 - 1344x^4 + 244x^3 + 295x^2 - 41*x - 10
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$0.630852$ of defining polynomial
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.369148 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.369148 q^{6} +4.16284 q^{7} +1.00000 q^{8} -2.86373 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.369148 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.369148 q^{6} +4.16284 q^{7} +1.00000 q^{8} -2.86373 q^{9} +1.00000 q^{10} -5.82166 q^{11} -0.369148 q^{12} -5.41212 q^{13} +4.16284 q^{14} -0.369148 q^{15} +1.00000 q^{16} -3.34718 q^{17} -2.86373 q^{18} +1.75502 q^{19} +1.00000 q^{20} -1.53670 q^{21} -5.82166 q^{22} +1.42765 q^{23} -0.369148 q^{24} +1.00000 q^{25} -5.41212 q^{26} +2.16459 q^{27} +4.16284 q^{28} +3.08933 q^{29} -0.369148 q^{30} +0.619086 q^{31} +1.00000 q^{32} +2.14906 q^{33} -3.34718 q^{34} +4.16284 q^{35} -2.86373 q^{36} +7.58549 q^{37} +1.75502 q^{38} +1.99788 q^{39} +1.00000 q^{40} -4.82786 q^{41} -1.53670 q^{42} -0.960138 q^{43} -5.82166 q^{44} -2.86373 q^{45} +1.42765 q^{46} -6.56789 q^{47} -0.369148 q^{48} +10.3292 q^{49} +1.00000 q^{50} +1.23561 q^{51} -5.41212 q^{52} -2.02653 q^{53} +2.16459 q^{54} -5.82166 q^{55} +4.16284 q^{56} -0.647864 q^{57} +3.08933 q^{58} -11.0567 q^{59} -0.369148 q^{60} -9.76047 q^{61} +0.619086 q^{62} -11.9212 q^{63} +1.00000 q^{64} -5.41212 q^{65} +2.14906 q^{66} +7.72164 q^{67} -3.34718 q^{68} -0.527016 q^{69} +4.16284 q^{70} -7.24797 q^{71} -2.86373 q^{72} -7.65437 q^{73} +7.58549 q^{74} -0.369148 q^{75} +1.75502 q^{76} -24.2346 q^{77} +1.99788 q^{78} -13.0618 q^{79} +1.00000 q^{80} +7.79214 q^{81} -4.82786 q^{82} -9.11232 q^{83} -1.53670 q^{84} -3.34718 q^{85} -0.960138 q^{86} -1.14042 q^{87} -5.82166 q^{88} +14.0986 q^{89} -2.86373 q^{90} -22.5298 q^{91} +1.42765 q^{92} -0.228534 q^{93} -6.56789 q^{94} +1.75502 q^{95} -0.369148 q^{96} -16.8622 q^{97} +10.3292 q^{98} +16.6717 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9} + 16 q^{10} - 14 q^{11} - 8 q^{12} - 20 q^{13} - 10 q^{14} - 8 q^{15} + 16 q^{16} - 27 q^{17} - 2 q^{18} - 17 q^{19} + 16 q^{20} - 12 q^{21} - 14 q^{22} - 9 q^{23} - 8 q^{24} + 16 q^{25} - 20 q^{26} - 11 q^{27} - 10 q^{28} - 23 q^{29} - 8 q^{30} - 21 q^{31} + 16 q^{32} - 9 q^{33} - 27 q^{34} - 10 q^{35} - 2 q^{36} - 16 q^{37} - 17 q^{38} - 6 q^{39} + 16 q^{40} - 35 q^{41} - 12 q^{42} + 3 q^{43} - 14 q^{44} - 2 q^{45} - 9 q^{46} - 25 q^{47} - 8 q^{48} - 24 q^{49} + 16 q^{50} - q^{51} - 20 q^{52} - 39 q^{53} - 11 q^{54} - 14 q^{55} - 10 q^{56} - 6 q^{57} - 23 q^{58} - 32 q^{59} - 8 q^{60} - 38 q^{61} - 21 q^{62} + q^{63} + 16 q^{64} - 20 q^{65} - 9 q^{66} + 5 q^{67} - 27 q^{68} - 25 q^{69} - 10 q^{70} - 16 q^{71} - 2 q^{72} - 17 q^{73} - 16 q^{74} - 8 q^{75} - 17 q^{76} - 34 q^{77} - 6 q^{78} - 40 q^{79} + 16 q^{80} - 28 q^{81} - 35 q^{82} - 22 q^{83} - 12 q^{84} - 27 q^{85} + 3 q^{86} + 10 q^{87} - 14 q^{88} - 46 q^{89} - 2 q^{90} - q^{91} - 9 q^{92} + 14 q^{93} - 25 q^{94} - 17 q^{95} - 8 q^{96} - 21 q^{97} - 24 q^{98} + 15 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9 + 16 * q^10 - 14 * q^11 - 8 * q^12 - 20 * q^13 - 10 * q^14 - 8 * q^15 + 16 * q^16 - 27 * q^17 - 2 * q^18 - 17 * q^19 + 16 * q^20 - 12 * q^21 - 14 * q^22 - 9 * q^23 - 8 * q^24 + 16 * q^25 - 20 * q^26 - 11 * q^27 - 10 * q^28 - 23 * q^29 - 8 * q^30 - 21 * q^31 + 16 * q^32 - 9 * q^33 - 27 * q^34 - 10 * q^35 - 2 * q^36 - 16 * q^37 - 17 * q^38 - 6 * q^39 + 16 * q^40 - 35 * q^41 - 12 * q^42 + 3 * q^43 - 14 * q^44 - 2 * q^45 - 9 * q^46 - 25 * q^47 - 8 * q^48 - 24 * q^49 + 16 * q^50 - q^51 - 20 * q^52 - 39 * q^53 - 11 * q^54 - 14 * q^55 - 10 * q^56 - 6 * q^57 - 23 * q^58 - 32 * q^59 - 8 * q^60 - 38 * q^61 - 21 * q^62 + q^63 + 16 * q^64 - 20 * q^65 - 9 * q^66 + 5 * q^67 - 27 * q^68 - 25 * q^69 - 10 * q^70 - 16 * q^71 - 2 * q^72 - 17 * q^73 - 16 * q^74 - 8 * q^75 - 17 * q^76 - 34 * q^77 - 6 * q^78 - 40 * q^79 + 16 * q^80 - 28 * q^81 - 35 * q^82 - 22 * q^83 - 12 * q^84 - 27 * q^85 + 3 * q^86 + 10 * q^87 - 14 * q^88 - 46 * q^89 - 2 * q^90 - q^91 - 9 * q^92 + 14 * q^93 - 25 * q^94 - 17 * q^95 - 8 * q^96 - 21 * q^97 - 24 * q^98 + 15 * 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
$3$	−0.369148	−0.213128	−0.106564	−	0.994306i	$-0.533985\pi$
$3$	−0.369148	−0.213128	−0.106564	+	0.994306i	$0.533985\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.369148	−0.150704
$7$	4.16284	1.57340	0.786702	−	0.617333i	$-0.211787\pi$
$7$	4.16284	1.57340	0.786702	+	0.617333i	$0.211787\pi$
$8$	1.00000	0.353553
$9$	−2.86373	−0.954577
$10$	1.00000	0.316228
$11$	−5.82166	−1.75530	−0.877648	−	0.479305i	$-0.840889\pi$
$11$	−5.82166	−1.75530	−0.877648	+	0.479305i	$0.840889\pi$
$12$	−0.369148	−0.106564
$13$	−5.41212	−1.50105	−0.750526	−	0.660840i	$-0.770200\pi$
$13$	−5.41212	−1.50105	−0.750526	+	0.660840i	$0.770200\pi$
$14$	4.16284	1.11256
$15$	−0.369148	−0.0953137
$16$	1.00000	0.250000
$17$	−3.34718	−0.811811	−0.405906	−	0.913915i	$-0.633044\pi$
$17$	−3.34718	−0.811811	−0.405906	+	0.913915i	$0.633044\pi$
$18$	−2.86373	−0.674988
$19$	1.75502	0.402630	0.201315	−	0.979527i	$-0.435478\pi$
$19$	1.75502	0.402630	0.201315	+	0.979527i	$0.435478\pi$
$20$	1.00000	0.223607
$21$	−1.53670	−0.335336
$22$	−5.82166	−1.24118
$23$	1.42765	0.297686	0.148843	−	0.988861i	$-0.452445\pi$
$23$	1.42765	0.297686	0.148843	+	0.988861i	$0.452445\pi$
$24$	−0.369148	−0.0753521
$25$	1.00000	0.200000
$26$	−5.41212	−1.06140
$27$	2.16459	0.416575
$28$	4.16284	0.786702
$29$	3.08933	0.573674	0.286837	−	0.957979i	$-0.407396\pi$
$29$	3.08933	0.573674	0.286837	+	0.957979i	$0.407396\pi$
$30$	−0.369148	−0.0673970
$31$	0.619086	0.111191	0.0555955	−	0.998453i	$-0.482294\pi$
$31$	0.619086	0.111191	0.0555955	+	0.998453i	$0.482294\pi$
$32$	1.00000	0.176777
$33$	2.14906	0.374103
$34$	−3.34718	−0.574037
$35$	4.16284	0.703648
$36$	−2.86373	−0.477288
$37$	7.58549	1.24705	0.623524	−	0.781805i	$-0.285701\pi$
$37$	7.58549	1.24705	0.623524	+	0.781805i	$0.285701\pi$
$38$	1.75502	0.284703
$39$	1.99788	0.319916
$40$	1.00000	0.158114
$41$	−4.82786	−0.753985	−0.376992	−	0.926216i	$-0.623042\pi$
$41$	−4.82786	−0.753985	−0.376992	+	0.926216i	$0.623042\pi$
$42$	−1.53670	−0.237119
$43$	−0.960138	−0.146420	−0.0732099	−	0.997317i	$-0.523324\pi$
$43$	−0.960138	−0.146420	−0.0732099	+	0.997317i	$0.523324\pi$
$44$	−5.82166	−0.877648
$45$	−2.86373	−0.426900
$46$	1.42765	0.210496
$47$	−6.56789	−0.958025	−0.479012	−	0.877808i	$-0.659005\pi$
$47$	−6.56789	−0.958025	−0.479012	+	0.877808i	$0.659005\pi$
$48$	−0.369148	−0.0532820
$49$	10.3292	1.47560
$50$	1.00000	0.141421
$51$	1.23561	0.173020
$52$	−5.41212	−0.750526
$53$	−2.02653	−0.278365	−0.139183	−	0.990267i	$-0.544448\pi$
$53$	−2.02653	−0.278365	−0.139183	+	0.990267i	$0.544448\pi$
$54$	2.16459	0.294563
$55$	−5.82166	−0.784993
$56$	4.16284	0.556282
$57$	−0.647864	−0.0858117
$58$	3.08933	0.405649
$59$	−11.0567	−1.43945	−0.719727	−	0.694257i	$-0.755733\pi$
$59$	−11.0567	−1.43945	−0.719727	+	0.694257i	$0.755733\pi$
$60$	−0.369148	−0.0476568
$61$	−9.76047	−1.24970	−0.624850	−	0.780745i	$-0.714840\pi$
$61$	−9.76047	−1.24970	−0.624850	+	0.780745i	$0.714840\pi$
$62$	0.619086	0.0786240
$63$	−11.9212	−1.50193
$64$	1.00000	0.125000
$65$	−5.41212	−0.671291
$66$	2.14906	0.264531
$67$	7.72164	0.943349	0.471674	−	0.881773i	$-0.343650\pi$
$67$	7.72164	0.943349	0.471674	+	0.881773i	$0.343650\pi$
$68$	−3.34718	−0.405906
$69$	−0.527016	−0.0634452
$70$	4.16284	0.497554
$71$	−7.24797	−0.860176	−0.430088	−	0.902787i	$-0.641518\pi$
$71$	−7.24797	−0.860176	−0.430088	+	0.902787i	$0.641518\pi$
$72$	−2.86373	−0.337494
$73$	−7.65437	−0.895877	−0.447938	−	0.894064i	$-0.647842\pi$
$73$	−7.65437	−0.895877	−0.447938	+	0.894064i	$0.647842\pi$
$74$	7.58549	0.881796
$75$	−0.369148	−0.0426256
$76$	1.75502	0.201315
$77$	−24.2346	−2.76179
$78$	1.99788	0.226215
$79$	−13.0618	−1.46957	−0.734783	−	0.678302i	$-0.762716\pi$
$79$	−13.0618	−1.46957	−0.734783	+	0.678302i	$0.762716\pi$
$80$	1.00000	0.111803
$81$	7.79214	0.865793
$82$	−4.82786	−0.533148
$83$	−9.11232	−1.00021	−0.500103	−	0.865966i	$-0.666705\pi$
$83$	−9.11232	−1.00021	−0.500103	+	0.865966i	$0.666705\pi$
$84$	−1.53670	−0.167668
$85$	−3.34718	−0.363053
$86$	−0.960138	−0.103534
$87$	−1.14042	−0.122266
$88$	−5.82166	−0.620591
$89$	14.0986	1.49445	0.747227	−	0.664569i	$-0.231385\pi$
$89$	14.0986	1.49445	0.747227	+	0.664569i	$0.231385\pi$
$90$	−2.86373	−0.301864
$91$	−22.5298	−2.36176
$92$	1.42765	0.148843
$93$	−0.228534	−0.0236979
$94$	−6.56789	−0.677426
$95$	1.75502	0.180062
$96$	−0.369148	−0.0376760
$97$	−16.8622	−1.71210	−0.856050	−	0.516894i	$-0.827088\pi$
$97$	−16.8622	−1.71210	−0.856050	+	0.516894i	$0.827088\pi$
$98$	10.3292	1.04341
$99$	16.6717	1.67557
$100$	1.00000	0.100000
$101$	−1.07213	−0.106681	−0.0533404	−	0.998576i	$-0.516987\pi$
$101$	−1.07213	−0.106681	−0.0533404	+	0.998576i	$0.516987\pi$
$102$	1.23561	0.122343
$103$	−11.5651	−1.13954	−0.569772	−	0.821802i	$-0.692969\pi$
$103$	−11.5651	−1.13954	−0.569772	+	0.821802i	$0.692969\pi$
$104$	−5.41212	−0.530702
$105$	−1.53670	−0.149967
$106$	−2.02653	−0.196834
$107$	−2.17984	−0.210733	−0.105366	−	0.994433i	$-0.533602\pi$
$107$	−2.17984	−0.210733	−0.105366	+	0.994433i	$0.533602\pi$
$108$	2.16459	0.208287
$109$	6.57445	0.629718	0.314859	−	0.949138i	$-0.398043\pi$
$109$	6.57445	0.629718	0.314859	+	0.949138i	$0.398043\pi$
$110$	−5.82166	−0.555074
$111$	−2.80017	−0.265781
$112$	4.16284	0.393351
$113$	−13.2143	−1.24309	−0.621547	−	0.783377i	$-0.713496\pi$
$113$	−13.2143	−1.24309	−0.621547	+	0.783377i	$0.713496\pi$
$114$	−0.647864	−0.0606781
$115$	1.42765	0.133129
$116$	3.08933	0.286837
$117$	15.4989	1.43287
$118$	−11.0567	−1.01785
$119$	−13.9338	−1.27731
$120$	−0.369148	−0.0336985
$121$	22.8917	2.08107
$122$	−9.76047	−0.883671
$123$	1.78220	0.160695
$124$	0.619086	0.0555955
$125$	1.00000	0.0894427
$126$	−11.9212	−1.06203
$127$	8.65471	0.767981	0.383990	−	0.923337i	$-0.374550\pi$
$127$	8.65471	0.767981	0.383990	+	0.923337i	$0.374550\pi$
$128$	1.00000	0.0883883
$129$	0.354433	0.0312061
$130$	−5.41212	−0.474675
$131$	−17.1560	−1.49892	−0.749462	−	0.662047i	$-0.769688\pi$
$131$	−17.1560	−1.49892	−0.749462	+	0.662047i	$0.769688\pi$
$132$	2.14906	0.187051
$133$	7.30588	0.633500
$134$	7.72164	0.667048
$135$	2.16459	0.186298
$136$	−3.34718	−0.287019
$137$	−18.9259	−1.61695	−0.808474	−	0.588532i	$-0.799706\pi$
$137$	−18.9259	−1.61695	−0.808474	+	0.588532i	$0.799706\pi$
$138$	−0.527016	−0.0448625
$139$	12.5656	1.06580	0.532902	−	0.846177i	$-0.321101\pi$
$139$	12.5656	1.06580	0.532902	+	0.846177i	$0.321101\pi$
$140$	4.16284	0.351824
$141$	2.42452	0.204182
$142$	−7.24797	−0.608236
$143$	31.5075	2.63479
$144$	−2.86373	−0.238644
$145$	3.08933	0.256555
$146$	−7.65437	−0.633480
$147$	−3.81301	−0.314492
$148$	7.58549	0.623524
$149$	−0.878117	−0.0719382	−0.0359691	−	0.999353i	$-0.511452\pi$
$149$	−0.878117	−0.0719382	−0.0359691	+	0.999353i	$0.511452\pi$
$150$	−0.369148	−0.0301408
$151$	−7.86702	−0.640209	−0.320104	−	0.947382i	$-0.603718\pi$
$151$	−7.86702	−0.640209	−0.320104	+	0.947382i	$0.603718\pi$
$152$	1.75502	0.142351
$153$	9.58543	0.774936
$154$	−24.2346	−1.95288
$155$	0.619086	0.0497262
$156$	1.99788	0.159958
$157$	−9.05288	−0.722499	−0.361249	−	0.932469i	$-0.617650\pi$
$157$	−9.05288	−0.722499	−0.361249	+	0.932469i	$0.617650\pi$
$158$	−13.0618	−1.03914
$159$	0.748091	0.0593274
$160$	1.00000	0.0790569
$161$	5.94308	0.468381
$162$	7.79214	0.612208
$163$	3.41660	0.267609	0.133804	−	0.991008i	$-0.457281\pi$
$163$	3.41660	0.267609	0.133804	+	0.991008i	$0.457281\pi$
$164$	−4.82786	−0.376992
$165$	2.14906	0.167304
$166$	−9.11232	−0.707253
$167$	−7.87126	−0.609097	−0.304548	−	0.952497i	$-0.598506\pi$
$167$	−7.87126	−0.609097	−0.304548	+	0.952497i	$0.598506\pi$
$168$	−1.53670	−0.118559
$169$	16.2911	1.25316
$170$	−3.34718	−0.256717
$171$	−5.02592	−0.384341
$172$	−0.960138	−0.0732099
$173$	−0.552131	−0.0419777	−0.0209889	−	0.999780i	$-0.506681\pi$
$173$	−0.552131	−0.0419777	−0.0209889	+	0.999780i	$0.506681\pi$
$174$	−1.14042	−0.0864550
$175$	4.16284	0.314681
$176$	−5.82166	−0.438824
$177$	4.08155	0.306788
$178$	14.0986	1.05674
$179$	−0.182267	−0.0136233	−0.00681165	−	0.999977i	$-0.502168\pi$
$179$	−0.182267	−0.0136233	−0.00681165	+	0.999977i	$0.502168\pi$
$180$	−2.86373	−0.213450
$181$	11.9718	0.889855	0.444928	−	0.895567i	$-0.353229\pi$
$181$	11.9718	0.889855	0.444928	+	0.895567i	$0.353229\pi$
$182$	−22.5298	−1.67002
$183$	3.60306	0.266346
$184$	1.42765	0.105248
$185$	7.58549	0.557696
$186$	−0.228534	−0.0167570
$187$	19.4862	1.42497
$188$	−6.56789	−0.479012
$189$	9.01082	0.655440
$190$	1.75502	0.127323
$191$	−7.68594	−0.556135	−0.278067	−	0.960562i	$-0.589694\pi$
$191$	−7.68594	−0.556135	−0.278067	+	0.960562i	$0.589694\pi$
$192$	−0.369148	−0.0266410
$193$	8.39566	0.604333	0.302166	−	0.953255i	$-0.402290\pi$
$193$	8.39566	0.604333	0.302166	+	0.953255i	$0.402290\pi$
$194$	−16.8622	−1.21064
$195$	1.99788	0.143071
$196$	10.3292	0.737800
$197$	22.5343	1.60550	0.802751	−	0.596314i	$-0.203369\pi$
$197$	22.5343	1.60550	0.802751	+	0.596314i	$0.203369\pi$
$198$	16.6717	1.18480
$199$	13.9385	0.988071	0.494036	−	0.869442i	$-0.335521\pi$
$199$	13.9385	0.988071	0.494036	+	0.869442i	$0.335521\pi$
$200$	1.00000	0.0707107
$201$	−2.85043	−0.201054
$202$	−1.07213	−0.0754347
$203$	12.8604	0.902621
$204$	1.23561	0.0865098
$205$	−4.82786	−0.337192
$206$	−11.5651	−0.805780
$207$	−4.08841	−0.284164
$208$	−5.41212	−0.375263
$209$	−10.2172	−0.706736
$210$	−1.53670	−0.106043
$211$	−9.00652	−0.620034	−0.310017	−	0.950731i	$-0.600335\pi$
$211$	−9.00652	−0.620034	−0.310017	+	0.950731i	$0.600335\pi$
$212$	−2.02653	−0.139183
$213$	2.67558	0.183328
$214$	−2.17984	−0.149011
$215$	−0.960138	−0.0654809
$216$	2.16459	0.147281
$217$	2.57715	0.174949
$218$	6.57445	0.445278
$219$	2.82560	0.190936
$220$	−5.82166	−0.392496
$221$	18.1154	1.21857
$222$	−2.80017	−0.187935
$223$	−0.780941	−0.0522957	−0.0261478	−	0.999658i	$-0.508324\pi$
$223$	−0.780941	−0.0522957	−0.0261478	+	0.999658i	$0.508324\pi$
$224$	4.16284	0.278141
$225$	−2.86373	−0.190915
$226$	−13.2143	−0.879001
$227$	−20.8939	−1.38678	−0.693390	−	0.720562i	$-0.743884\pi$
$227$	−20.8939	−1.38678	−0.693390	+	0.720562i	$0.743884\pi$
$228$	−0.647864	−0.0429059
$229$	−22.0570	−1.45757	−0.728783	−	0.684745i	$-0.759914\pi$
$229$	−22.0570	−1.45757	−0.728783	+	0.684745i	$0.759914\pi$
$230$	1.42765	0.0941366
$231$	8.94617	0.588615
$232$	3.08933	0.202824
$233$	6.54871	0.429020	0.214510	−	0.976722i	$-0.431184\pi$
$233$	6.54871	0.429020	0.214510	+	0.976722i	$0.431184\pi$
$234$	15.4989	1.01319
$235$	−6.56789	−0.428442
$236$	−11.0567	−0.719727
$237$	4.82174	0.313206
$238$	−13.9338	−0.903193
$239$	−0.382128	−0.0247178	−0.0123589	−	0.999924i	$-0.503934\pi$
$239$	−0.382128	−0.0247178	−0.0123589	+	0.999924i	$0.503934\pi$
$240$	−0.369148	−0.0238284
$241$	−6.04288	−0.389256	−0.194628	−	0.980877i	$-0.562350\pi$
$241$	−6.04288	−0.389256	−0.194628	+	0.980877i	$0.562350\pi$
$242$	22.8917	1.47154
$243$	−9.37021	−0.601099
$244$	−9.76047	−0.624850
$245$	10.3292	0.659909
$246$	1.78220	0.113629
$247$	−9.49841	−0.604369
$248$	0.619086	0.0393120
$249$	3.36380	0.213172
$250$	1.00000	0.0632456
$251$	21.8330	1.37809	0.689043	−	0.724720i	$-0.258031\pi$
$251$	21.8330	1.37809	0.689043	+	0.724720i	$0.258031\pi$
$252$	−11.9212	−0.750967
$253$	−8.31131	−0.522528
$254$	8.65471	0.543045
$255$	1.23561	0.0773767
$256$	1.00000	0.0625000
$257$	−27.0645	−1.68823	−0.844117	−	0.536159i	$-0.819875\pi$
$257$	−27.0645	−1.68823	−0.844117	+	0.536159i	$0.819875\pi$
$258$	0.354433	0.0220661
$259$	31.5772	1.96211
$260$	−5.41212	−0.335646
$261$	−8.84700	−0.547615
$262$	−17.1560	−1.05990
$263$	13.6417	0.841181	0.420590	−	0.907251i	$-0.361823\pi$
$263$	13.6417	0.841181	0.420590	+	0.907251i	$0.361823\pi$
$264$	2.14906	0.132265
$265$	−2.02653	−0.124489
$266$	7.30588	0.447952
$267$	−5.20449	−0.318510
$268$	7.72164	0.471674
$269$	27.1335	1.65436	0.827179	−	0.561938i	$-0.189944\pi$
$269$	27.1335	1.65436	0.827179	+	0.561938i	$0.189944\pi$
$270$	2.16459	0.131733
$271$	−3.30015	−0.200470	−0.100235	−	0.994964i	$-0.531959\pi$
$271$	−3.30015	−0.200470	−0.100235	+	0.994964i	$0.531959\pi$
$272$	−3.34718	−0.202953
$273$	8.31683	0.503358
$274$	−18.9259	−1.14335
$275$	−5.82166	−0.351059
$276$	−0.527016	−0.0317226
$277$	−10.6013	−0.636968	−0.318484	−	0.947928i	$-0.603174\pi$
$277$	−10.6013	−0.636968	−0.318484	+	0.947928i	$0.603174\pi$
$278$	12.5656	0.753637
$279$	−1.77289	−0.106140
$280$	4.16284	0.248777
$281$	18.0958	1.07951	0.539754	−	0.841823i	$-0.318517\pi$
$281$	18.0958	1.07951	0.539754	+	0.841823i	$0.318517\pi$
$282$	2.42452	0.144378
$283$	−0.607994	−0.0361415	−0.0180708	−	0.999837i	$-0.505752\pi$
$283$	−0.607994	−0.0361415	−0.0180708	+	0.999837i	$0.505752\pi$
$284$	−7.24797	−0.430088
$285$	−0.647864	−0.0383762
$286$	31.5075	1.86308
$287$	−20.0976	−1.18632
$288$	−2.86373	−0.168747
$289$	−5.79636	−0.340962
$290$	3.08933	0.181412
$291$	6.22466	0.364896
$292$	−7.65437	−0.447938
$293$	−7.68527	−0.448978	−0.224489	−	0.974477i	$-0.572071\pi$
$293$	−7.68527	−0.448978	−0.224489	+	0.974477i	$0.572071\pi$
$294$	−3.81301	−0.222379
$295$	−11.0567	−0.643743
$296$	7.58549	0.440898
$297$	−12.6015	−0.731212
$298$	−0.878117	−0.0508680
$299$	−7.72663	−0.446843
$300$	−0.369148	−0.0213128
$301$	−3.99690	−0.230377
$302$	−7.86702	−0.452696
$303$	0.395774	0.0227366
$304$	1.75502	0.100658
$305$	−9.76047	−0.558883
$306$	9.58543	0.547963
$307$	5.77300	0.329482	0.164741	−	0.986337i	$-0.447321\pi$
$307$	5.77300	0.329482	0.164741	+	0.986337i	$0.447321\pi$
$308$	−24.2346	−1.38090
$309$	4.26924	0.242869
$310$	0.619086	0.0351617
$311$	8.81259	0.499716	0.249858	−	0.968282i	$-0.419616\pi$
$311$	8.81259	0.499716	0.249858	+	0.968282i	$0.419616\pi$
$312$	1.99788	0.113107
$313$	21.9247	1.23926	0.619628	−	0.784895i	$-0.287283\pi$
$313$	21.9247	1.23926	0.619628	+	0.784895i	$0.287283\pi$
$314$	−9.05288	−0.510884
$315$	−11.9212	−0.671686
$316$	−13.0618	−0.734783
$317$	18.5721	1.04311	0.521556	−	0.853217i	$-0.325352\pi$
$317$	18.5721	1.04311	0.521556	+	0.853217i	$0.325352\pi$
$318$	0.748091	0.0419508
$319$	−17.9850	−1.00697
$320$	1.00000	0.0559017
$321$	0.804684	0.0449131
$322$	5.94308	0.331195
$323$	−5.87439	−0.326860
$324$	7.79214	0.432896
$325$	−5.41212	−0.300211
$326$	3.41660	0.189228
$327$	−2.42695	−0.134210
$328$	−4.82786	−0.266574
$329$	−27.3410	−1.50736
$330$	2.14906	0.118302
$331$	3.57680	0.196599	0.0982994	−	0.995157i	$-0.468660\pi$
$331$	3.57680	0.196599	0.0982994	+	0.995157i	$0.468660\pi$
$332$	−9.11232	−0.500103
$333$	−21.7228	−1.19040
$334$	−7.87126	−0.430696
$335$	7.72164	0.421878
$336$	−1.53670	−0.0838341
$337$	31.0316	1.69040	0.845199	−	0.534451i	$-0.179482\pi$
$337$	31.0316	1.69040	0.845199	+	0.534451i	$0.179482\pi$
$338$	16.2911	0.886118
$339$	4.87803	0.264938
$340$	−3.34718	−0.181527
$341$	−3.60411	−0.195173
$342$	−5.02592	−0.271770
$343$	13.8589	0.748312
$344$	−0.960138	−0.0517672
$345$	−0.527016	−0.0283736
$346$	−0.552131	−0.0296828
$347$	5.56644	0.298822	0.149411	−	0.988775i	$-0.452262\pi$
$347$	5.56644	0.298822	0.149411	+	0.988775i	$0.452262\pi$
$348$	−1.14042	−0.0611329
$349$	0.543281	0.0290812	0.0145406	−	0.999894i	$-0.495371\pi$
$349$	0.543281	0.0290812	0.0145406	+	0.999894i	$0.495371\pi$
$350$	4.16284	0.222513
$351$	−11.7150	−0.625301
$352$	−5.82166	−0.310296
$353$	12.3199	0.655722	0.327861	−	0.944726i	$-0.393672\pi$
$353$	12.3199	0.655722	0.327861	+	0.944726i	$0.393672\pi$
$354$	4.08155	0.216932
$355$	−7.24797	−0.384682
$356$	14.0986	0.747227
$357$	5.14363	0.272230
$358$	−0.182267	−0.00963313
$359$	−6.87528	−0.362863	−0.181432	−	0.983404i	$-0.558073\pi$
$359$	−6.87528	−0.362863	−0.181432	+	0.983404i	$0.558073\pi$
$360$	−2.86373	−0.150932
$361$	−15.9199	−0.837889
$362$	11.9718	0.629223
$363$	−8.45044	−0.443533
$364$	−22.5298	−1.18088
$365$	−7.65437	−0.400648
$366$	3.60306	0.188335
$367$	13.3616	0.697470	0.348735	−	0.937221i	$-0.386611\pi$
$367$	13.3616	0.697470	0.348735	+	0.937221i	$0.386611\pi$
$368$	1.42765	0.0744215
$369$	13.8257	0.719736
$370$	7.58549	0.394351
$371$	−8.43612	−0.437981
$372$	−0.228534	−0.0118490
$373$	−10.2148	−0.528902	−0.264451	−	0.964399i	$-0.585191\pi$
$373$	−10.2148	−0.528902	−0.264451	+	0.964399i	$0.585191\pi$
$374$	19.4862	1.00761
$375$	−0.369148	−0.0190627
$376$	−6.56789	−0.338713
$377$	−16.7198	−0.861115
$378$	9.01082	0.463466
$379$	33.6867	1.73037	0.865184	−	0.501455i	$-0.167202\pi$
$379$	33.6867	1.73037	0.865184	+	0.501455i	$0.167202\pi$
$380$	1.75502	0.0900309
$381$	−3.19487	−0.163678
$382$	−7.68594	−0.393247
$383$	37.2300	1.90236	0.951181	−	0.308634i	$-0.0998719\pi$
$383$	37.2300	1.90236	0.951181	+	0.308634i	$0.0998719\pi$
$384$	−0.369148	−0.0188380
$385$	−24.2346	−1.23511
$386$	8.39566	0.427328
$387$	2.74958	0.139769
$388$	−16.8622	−0.856050
$389$	18.0289	0.914102	0.457051	−	0.889441i	$-0.348906\pi$
$389$	18.0289	0.914102	0.457051	+	0.889441i	$0.348906\pi$
$390$	1.99788	0.101166
$391$	−4.77862	−0.241665
$392$	10.3292	0.521704
$393$	6.33310	0.319463
$394$	22.5343	1.13526
$395$	−13.0618	−0.657210
$396$	16.6717	0.837783
$397$	−25.0886	−1.25916	−0.629580	−	0.776935i	$-0.716773\pi$
$397$	−25.0886	−1.25916	−0.629580	+	0.776935i	$0.716773\pi$
$398$	13.9385	0.698672
$399$	−2.69695	−0.135017
$400$	1.00000	0.0500000
$401$	−6.82379	−0.340764	−0.170382	−	0.985378i	$-0.554500\pi$
$401$	−6.82379	−0.340764	−0.170382	+	0.985378i	$0.554500\pi$
$402$	−2.85043	−0.142167
$403$	−3.35057	−0.166904
$404$	−1.07213	−0.0533404
$405$	7.79214	0.387194
$406$	12.8604	0.638249
$407$	−44.1602	−2.18894
$408$	1.23561	0.0611717
$409$	5.08364	0.251370	0.125685	−	0.992070i	$-0.459887\pi$
$409$	5.08364	0.251370	0.125685	+	0.992070i	$0.459887\pi$
$410$	−4.82786	−0.238431
$411$	6.98646	0.344617
$412$	−11.5651	−0.569772
$413$	−46.0270	−2.26484
$414$	−4.08841	−0.200934
$415$	−9.11232	−0.447306
$416$	−5.41212	−0.265351
$417$	−4.63859	−0.227153
$418$	−10.2172	−0.499738
$419$	4.98760	0.243660	0.121830	−	0.992551i	$-0.461124\pi$
$419$	4.98760	0.243660	0.121830	+	0.992551i	$0.461124\pi$
$420$	−1.53670	−0.0749835
$421$	29.1556	1.42096	0.710478	−	0.703719i	$-0.248479\pi$
$421$	29.1556	1.42096	0.710478	+	0.703719i	$0.248479\pi$
$422$	−9.00652	−0.438430
$423$	18.8086	0.914508
$424$	−2.02653	−0.0984171
$425$	−3.34718	−0.162362
$426$	2.67558	0.129632
$427$	−40.6312	−1.96628
$428$	−2.17984	−0.105366
$429$	−11.6310	−0.561548
$430$	−0.960138	−0.0463020
$431$	19.1082	0.920408	0.460204	−	0.887813i	$-0.347776\pi$
$431$	19.1082	0.920408	0.460204	+	0.887813i	$0.347776\pi$
$432$	2.16459	0.104144
$433$	30.5975	1.47042	0.735212	−	0.677837i	$-0.237083\pi$
$433$	30.5975	1.47042	0.735212	+	0.677837i	$0.237083\pi$
$434$	2.57715	0.123707
$435$	−1.14042	−0.0546790
$436$	6.57445	0.314859
$437$	2.50557	0.119857
$438$	2.82560	0.135012
$439$	−3.20036	−0.152745	−0.0763724	−	0.997079i	$-0.524334\pi$
$439$	−3.20036	−0.152745	−0.0763724	+	0.997079i	$0.524334\pi$
$440$	−5.82166	−0.277537
$441$	−29.5800	−1.40857
$442$	18.1154	0.861660
$443$	−21.8417	−1.03773	−0.518866	−	0.854856i	$-0.673646\pi$
$443$	−21.8417	−1.03773	−0.518866	+	0.854856i	$0.673646\pi$
$444$	−2.80017	−0.132890
$445$	14.0986	0.668340
$446$	−0.780941	−0.0369786
$447$	0.324155	0.0153320
$448$	4.16284	0.196676
$449$	−26.0499	−1.22937	−0.614686	−	0.788772i	$-0.710717\pi$
$449$	−26.0499	−1.22937	−0.614686	+	0.788772i	$0.710717\pi$
$450$	−2.86373	−0.134998
$451$	28.1061	1.32347
$452$	−13.2143	−0.621547
$453$	2.90410	0.136446
$454$	−20.8939	−0.980602
$455$	−22.5298	−1.05621
$456$	−0.647864	−0.0303390
$457$	−31.2787	−1.46315	−0.731577	−	0.681759i	$-0.761215\pi$
$457$	−31.2787	−1.46315	−0.731577	+	0.681759i	$0.761215\pi$
$458$	−22.0570	−1.03065
$459$	−7.24527	−0.338180
$460$	1.42765	0.0665646
$461$	6.43891	0.299890	0.149945	−	0.988694i	$-0.452090\pi$
$461$	6.43891	0.299890	0.149945	+	0.988694i	$0.452090\pi$
$462$	8.94617	0.416213
$463$	−7.66434	−0.356192	−0.178096	−	0.984013i	$-0.556994\pi$
$463$	−7.66434	−0.356192	−0.178096	+	0.984013i	$0.556994\pi$
$464$	3.08933	0.143418
$465$	−0.228534	−0.0105980
$466$	6.54871	0.303363
$467$	4.35278	0.201423	0.100711	−	0.994916i	$-0.467888\pi$
$467$	4.35278	0.201423	0.100711	+	0.994916i	$0.467888\pi$
$468$	15.4989	0.716435
$469$	32.1439	1.48427
$470$	−6.56789	−0.302954
$471$	3.34186	0.153985
$472$	−11.0567	−0.508924
$473$	5.58960	0.257010
$474$	4.82174	0.221470
$475$	1.75502	0.0805261
$476$	−13.9338	−0.638654
$477$	5.80344	0.265721
$478$	−0.382128	−0.0174781
$479$	34.4459	1.57387	0.786936	−	0.617034i	$-0.211666\pi$
$479$	34.4459	1.57387	0.786936	+	0.617034i	$0.211666\pi$
$480$	−0.369148	−0.0168492
$481$	−41.0536	−1.87188
$482$	−6.04288	−0.275246
$483$	−2.19388	−0.0998250
$484$	22.8917	1.04053
$485$	−16.8622	−0.765674
$486$	−9.37021	−0.425041
$487$	40.0127	1.81315	0.906574	−	0.422047i	$-0.138688\pi$
$487$	40.0127	1.81315	0.906574	+	0.422047i	$0.138688\pi$
$488$	−9.76047	−0.441836
$489$	−1.26123	−0.0570349
$490$	10.3292	0.466626
$491$	10.2272	0.461548	0.230774	−	0.973007i	$-0.425874\pi$
$491$	10.2272	0.461548	0.230774	+	0.973007i	$0.425874\pi$
$492$	1.78220	0.0803476
$493$	−10.3405	−0.465715
$494$	−9.49841	−0.427354
$495$	16.6717	0.749335
$496$	0.619086	0.0277978
$497$	−30.1721	−1.35340
$498$	3.36380	0.150735
$499$	1.46831	0.0657304	0.0328652	−	0.999460i	$-0.489537\pi$
$499$	1.46831	0.0657304	0.0328652	+	0.999460i	$0.489537\pi$
$500$	1.00000	0.0447214
$501$	2.90566	0.129815
$502$	21.8330	0.974454
$503$	−36.6027	−1.63203	−0.816016	−	0.578029i	$-0.803822\pi$
$503$	−36.6027	−1.63203	−0.816016	+	0.578029i	$0.803822\pi$
$504$	−11.9212	−0.531014
$505$	−1.07213	−0.0477091
$506$	−8.31131	−0.369483
$507$	−6.01382	−0.267083
$508$	8.65471	0.383990
$509$	−31.8240	−1.41058	−0.705288	−	0.708921i	$-0.749182\pi$
$509$	−31.8240	−1.41058	−0.705288	+	0.708921i	$0.749182\pi$
$510$	1.23561	0.0547136
$511$	−31.8639	−1.40958
$512$	1.00000	0.0441942
$513$	3.79890	0.167726
$514$	−27.0645	−1.19376
$515$	−11.5651	−0.509620
$516$	0.354433	0.0156031
$517$	38.2360	1.68162
$518$	31.5772	1.38742
$519$	0.203818	0.00894663
$520$	−5.41212	−0.237337
$521$	−29.6770	−1.30017	−0.650087	−	0.759859i	$-0.725268\pi$
$521$	−29.6770	−1.30017	−0.650087	+	0.759859i	$0.725268\pi$
$522$	−8.84700	−0.387223
$523$	0.604889	0.0264499	0.0132250	−	0.999913i	$-0.495790\pi$
$523$	0.604889	0.0264499	0.0132250	+	0.999913i	$0.495790\pi$
$524$	−17.1560	−0.749462
$525$	−1.53670	−0.0670673
$526$	13.6417	0.594805
$527$	−2.07219	−0.0902662
$528$	2.14906	0.0935257
$529$	−20.9618	−0.911383
$530$	−2.02653	−0.0880269
$531$	31.6633	1.37407
$532$	7.30588	0.316750
$533$	26.1290	1.13177
$534$	−5.20449	−0.225220
$535$	−2.17984	−0.0942426
$536$	7.72164	0.333524
$537$	0.0672837	0.00290351
$538$	27.1335	1.16981
$539$	−60.1331	−2.59012
$540$	2.16459	0.0931489
$541$	40.5285	1.74246	0.871228	−	0.490878i	$-0.163324\pi$
$541$	40.5285	1.74246	0.871228	+	0.490878i	$0.163324\pi$
$542$	−3.30015	−0.141753
$543$	−4.41936	−0.189653
$544$	−3.34718	−0.143509
$545$	6.57445	0.281618
$546$	8.31683	0.355928
$547$	4.00737	0.171343	0.0856714	−	0.996323i	$-0.472696\pi$
$547$	4.00737	0.171343	0.0856714	+	0.996323i	$0.472696\pi$
$548$	−18.9259	−0.808474
$549$	27.9513	1.19293
$550$	−5.82166	−0.248236
$551$	5.42185	0.230978
$552$	−0.527016	−0.0224313
$553$	−54.3741	−2.31222
$554$	−10.6013	−0.450404
$555$	−2.80017	−0.118861
$556$	12.5656	0.532902
$557$	−15.3152	−0.648924	−0.324462	−	0.945899i	$-0.605183\pi$
$557$	−15.3152	−0.648924	−0.324462	+	0.945899i	$0.605183\pi$
$558$	−1.77289	−0.0750526
$559$	5.19639	0.219784
$560$	4.16284	0.175912
$561$	−7.19329	−0.303701
$562$	18.0958	0.763327
$563$	−35.0521	−1.47727	−0.738635	−	0.674105i	$-0.764529\pi$
$563$	−35.0521	−1.47727	−0.738635	+	0.674105i	$0.764529\pi$
$564$	2.42452	0.102091
$565$	−13.2143	−0.555929
$566$	−0.607994	−0.0255559
$567$	32.4374	1.36224
$568$	−7.24797	−0.304118
$569$	−19.9201	−0.835095	−0.417548	−	0.908655i	$-0.637110\pi$
$569$	−19.9201	−0.835095	−0.417548	+	0.908655i	$0.637110\pi$
$570$	−0.647864	−0.0271361
$571$	−12.4459	−0.520843	−0.260422	−	0.965495i	$-0.583862\pi$
$571$	−12.4459	−0.520843	−0.260422	+	0.965495i	$0.583862\pi$
$572$	31.5075	1.31740
$573$	2.83725	0.118528
$574$	−20.0976	−0.838857
$575$	1.42765	0.0595372
$576$	−2.86373	−0.119322
$577$	−2.36528	−0.0984679	−0.0492340	−	0.998787i	$-0.515678\pi$
$577$	−2.36528	−0.0984679	−0.0492340	+	0.998787i	$0.515678\pi$
$578$	−5.79636	−0.241097
$579$	−3.09924	−0.128800
$580$	3.08933	0.128277
$581$	−37.9331	−1.57373
$582$	6.22466	0.258021
$583$	11.7978	0.488614
$584$	−7.65437	−0.316740
$585$	15.4989	0.640799
$586$	−7.68527	−0.317476
$587$	−30.6950	−1.26692	−0.633459	−	0.773776i	$-0.718365\pi$
$587$	−30.6950	−1.26692	−0.633459	+	0.773776i	$0.718365\pi$
$588$	−3.81301	−0.157246
$589$	1.08651	0.0447689
$590$	−11.0567	−0.455195
$591$	−8.31850	−0.342177
$592$	7.58549	0.311762
$593$	−24.7436	−1.01610	−0.508049	−	0.861328i	$-0.669633\pi$
$593$	−24.7436	−1.01610	−0.508049	+	0.861328i	$0.669633\pi$
$594$	−12.6015	−0.517045
$595$	−13.9338	−0.571229
$596$	−0.878117	−0.0359691
$597$	−5.14536	−0.210586
$598$	−7.72663	−0.315965
$599$	−3.51303	−0.143538	−0.0717692	−	0.997421i	$-0.522864\pi$
$599$	−3.51303	−0.143538	−0.0717692	+	0.997421i	$0.522864\pi$
$600$	−0.369148	−0.0150704
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	−3.99690	−0.162901
$603$	−22.1127	−0.900498
$604$	−7.86702	−0.320104
$605$	22.8917	0.930681
$606$	0.395774	0.0160772
$607$	28.1302	1.14177	0.570884	−	0.821031i	$-0.306601\pi$
$607$	28.1302	1.14177	0.570884	+	0.821031i	$0.306601\pi$
$608$	1.75502	0.0711757
$609$	−4.74738	−0.192374
$610$	−9.76047	−0.395190
$611$	35.5462	1.43805
$612$	9.58543	0.387468
$613$	26.7512	1.08047	0.540235	−	0.841514i	$-0.318335\pi$
$613$	26.7512	1.08047	0.540235	+	0.841514i	$0.318335\pi$
$614$	5.77300	0.232979
$615$	1.78220	0.0718650
$616$	−24.2346	−0.976441
$617$	3.04683	0.122661	0.0613304	−	0.998118i	$-0.480466\pi$
$617$	3.04683	0.122661	0.0613304	+	0.998118i	$0.480466\pi$
$618$	4.26924	0.171734
$619$	9.80886	0.394251	0.197126	−	0.980378i	$-0.436839\pi$
$619$	9.80886	0.394251	0.197126	+	0.980378i	$0.436839\pi$
$620$	0.619086	0.0248631
$621$	3.09028	0.124009
$622$	8.81259	0.353353
$623$	58.6903	2.35138
$624$	1.99788	0.0799791
$625$	1.00000	0.0400000
$626$	21.9247	0.876287
$627$	3.77165	0.150625
$628$	−9.05288	−0.361249
$629$	−25.3900	−1.01237
$630$	−11.9212	−0.474953
$631$	−15.1280	−0.602236	−0.301118	−	0.953587i	$-0.597360\pi$
$631$	−15.1280	−0.602236	−0.301118	+	0.953587i	$0.597360\pi$
$632$	−13.0618	−0.519570
$633$	3.32474	0.132147
$634$	18.5721	0.737591
$635$	8.65471	0.343452
$636$	0.748091	0.0296637
$637$	−55.9029	−2.21495
$638$	−17.9850	−0.712034
$639$	20.7562	0.821104
$640$	1.00000	0.0395285
$641$	−40.6938	−1.60731	−0.803655	−	0.595096i	$-0.797114\pi$
$641$	−40.6938	−1.60731	−0.803655	+	0.595096i	$0.797114\pi$
$642$	0.804684	0.0317583
$643$	32.0074	1.26225	0.631125	−	0.775681i	$-0.282594\pi$
$643$	32.0074	1.26225	0.631125	+	0.775681i	$0.282594\pi$
$644$	5.94308	0.234190
$645$	0.354433	0.0139558
$646$	−5.87439	−0.231125
$647$	−12.4024	−0.487589	−0.243794	−	0.969827i	$-0.578392\pi$
$647$	−12.4024	−0.487589	−0.243794	+	0.969827i	$0.578392\pi$
$648$	7.79214	0.306104
$649$	64.3681	2.52667
$650$	−5.41212	−0.212281
$651$	−0.951352	−0.0372864
$652$	3.41660	0.133804
$653$	13.5657	0.530866	0.265433	−	0.964129i	$-0.414485\pi$
$653$	13.5657	0.530866	0.265433	+	0.964129i	$0.414485\pi$
$654$	−2.42695	−0.0949011
$655$	−17.1560	−0.670340
$656$	−4.82786	−0.188496
$657$	21.9201	0.855183
$658$	−27.3410	−1.06586
$659$	11.9465	0.465369	0.232685	−	0.972552i	$-0.425249\pi$
$659$	11.9465	0.465369	0.232685	+	0.972552i	$0.425249\pi$
$660$	2.14906	0.0836519
$661$	−12.3930	−0.482032	−0.241016	−	0.970521i	$-0.577481\pi$
$661$	−12.3930	−0.482032	−0.241016	+	0.970521i	$0.577481\pi$
$662$	3.57680	0.139016
$663$	−6.68726	−0.259712
$664$	−9.11232	−0.353626
$665$	7.30588	0.283310
$666$	−21.7228	−0.841741
$667$	4.41049	0.170775
$668$	−7.87126	−0.304548
$669$	0.288283	0.0111457
$670$	7.72164	0.298313
$671$	56.8221	2.19359
$672$	−1.53670	−0.0592796
$673$	−20.0884	−0.774350	−0.387175	−	0.922006i	$-0.626549\pi$
$673$	−20.0884	−0.774350	−0.387175	+	0.922006i	$0.626549\pi$
$674$	31.0316	1.19529
$675$	2.16459	0.0833150
$676$	16.2911	0.626580
$677$	−2.72011	−0.104542	−0.0522711	−	0.998633i	$-0.516646\pi$
$677$	−2.72011	−0.104542	−0.0522711	+	0.998633i	$0.516646\pi$
$678$	4.87803	0.187340
$679$	−70.1947	−2.69382
$680$	−3.34718	−0.128359
$681$	7.71297	0.295562
$682$	−3.60411	−0.138008
$683$	6.69570	0.256204	0.128102	−	0.991761i	$-0.459112\pi$
$683$	6.69570	0.256204	0.128102	+	0.991761i	$0.459112\pi$
$684$	−5.02592	−0.192171
$685$	−18.9259	−0.723121
$686$	13.8589	0.529137
$687$	8.14229	0.310648
$688$	−0.960138	−0.0366049
$689$	10.9678	0.417841
$690$	−0.527016	−0.0200631
$691$	30.6613	1.16641	0.583205	−	0.812325i	$-0.301799\pi$
$691$	30.6613	1.16641	0.583205	+	0.812325i	$0.301799\pi$
$692$	−0.552131	−0.0209889
$693$	69.4014	2.63634
$694$	5.56644	0.211299
$695$	12.5656	0.476642
$696$	−1.14042	−0.0432275
$697$	16.1597	0.612093
$698$	0.543281	0.0205635
$699$	−2.41745	−0.0914362
$700$	4.16284	0.157340
$701$	33.1265	1.25117	0.625585	−	0.780156i	$-0.284861\pi$
$701$	33.1265	1.25117	0.625585	+	0.780156i	$0.284861\pi$
$702$	−11.7150	−0.442154
$703$	13.3127	0.502099
$704$	−5.82166	−0.219412
$705$	2.42452	0.0913129
$706$	12.3199	0.463665
$707$	−4.46310	−0.167852
$708$	4.08155	0.153394
$709$	−40.8442	−1.53394	−0.766968	−	0.641685i	$-0.778236\pi$
$709$	−40.8442	−1.53394	−0.766968	+	0.641685i	$0.778236\pi$
$710$	−7.24797	−0.272012
$711$	37.4055	1.40281
$712$	14.0986	0.528369
$713$	0.883839	0.0331000
$714$	5.14363	0.192496
$715$	31.5075	1.17832
$716$	−0.182267	−0.00681165
$717$	0.141062	0.00526805
$718$	−6.87528	−0.256583
$719$	−0.157445	−0.00587170	−0.00293585	−	0.999996i	$-0.500935\pi$
$719$	−0.157445	−0.00587170	−0.00293585	+	0.999996i	$0.500935\pi$
$720$	−2.86373	−0.106725
$721$	−48.1437	−1.79296
$722$	−15.9199	−0.592477
$723$	2.23072	0.0829613
$724$	11.9718	0.444928
$725$	3.08933	0.114735
$726$	−8.45044	−0.313625
$727$	51.4199	1.90706	0.953529	−	0.301301i	$-0.0974210\pi$
$727$	51.4199	1.90706	0.953529	+	0.301301i	$0.0974210\pi$
$728$	−22.5298	−0.835009
$729$	−19.9174	−0.737682
$730$	−7.65437	−0.283301
$731$	3.21376	0.118865
$732$	3.60306	0.133173
$733$	47.4024	1.75085	0.875425	−	0.483355i	$-0.160582\pi$
$733$	47.4024	1.75085	0.875425	+	0.483355i	$0.160582\pi$
$734$	13.3616	0.493185
$735$	−3.81301	−0.140645
$736$	1.42765	0.0526240
$737$	−44.9528	−1.65586
$738$	13.8257	0.508930
$739$	−29.1051	−1.07065	−0.535323	−	0.844647i	$-0.679810\pi$
$739$	−29.1051	−1.07065	−0.535323	+	0.844647i	$0.679810\pi$
$740$	7.58549	0.278848
$741$	3.50632	0.128808
$742$	−8.43612	−0.309700
$743$	25.8972	0.950075	0.475037	−	0.879966i	$-0.342435\pi$
$743$	25.8972	0.950075	0.475037	+	0.879966i	$0.342435\pi$
$744$	−0.228534	−0.00837848
$745$	−0.878117	−0.0321717
$746$	−10.2148	−0.373990
$747$	26.0952	0.954774
$748$	19.4862	0.712485
$749$	−9.07431	−0.331568
$750$	−0.369148	−0.0134794
$751$	−16.5748	−0.604824	−0.302412	−	0.953177i	$-0.597792\pi$
$751$	−16.5748	−0.604824	−0.302412	+	0.953177i	$0.597792\pi$
$752$	−6.56789	−0.239506
$753$	−8.05962	−0.293709
$754$	−16.7198	−0.608900
$755$	−7.86702	−0.286310
$756$	9.01082	0.327720
$757$	6.60003	0.239882	0.119941	−	0.992781i	$-0.461729\pi$
$757$	6.60003	0.239882	0.119941	+	0.992781i	$0.461729\pi$
$758$	33.6867	1.22355
$759$	3.06811	0.111365
$760$	1.75502	0.0636614
$761$	39.5336	1.43309	0.716545	−	0.697541i	$-0.245722\pi$
$761$	39.5336	1.43309	0.716545	+	0.697541i	$0.245722\pi$
$762$	−3.19487	−0.115738
$763$	27.3684	0.990801
$764$	−7.68594	−0.278067
$765$	9.58543	0.346562
$766$	37.2300	1.34517
$767$	59.8400	2.16070
$768$	−0.369148	−0.0133205
$769$	−15.7661	−0.568541	−0.284271	−	0.958744i	$-0.591751\pi$
$769$	−15.7661	−0.568541	−0.284271	+	0.958744i	$0.591751\pi$
$770$	−24.2346	−0.873355
$771$	9.99080	0.359810
$772$	8.39566	0.302166
$773$	28.4704	1.02401	0.512005	−	0.858983i	$-0.328903\pi$
$773$	28.4704	1.02401	0.512005	+	0.858983i	$0.328903\pi$
$774$	2.74958	0.0988315
$775$	0.619086	0.0222382
$776$	−16.8622	−0.605319
$777$	−11.6567	−0.418180
$778$	18.0289	0.646367
$779$	−8.47301	−0.303577
$780$	1.99788	0.0715354
$781$	42.1952	1.50986
$782$	−4.77862	−0.170883
$783$	6.68711	0.238978
$784$	10.3292	0.368900
$785$	−9.05288	−0.323111
$786$	6.33310	0.225894
$787$	19.6431	0.700200	0.350100	−	0.936712i	$-0.386148\pi$
$787$	19.6431	0.700200	0.350100	+	0.936712i	$0.386148\pi$
$788$	22.5343	0.802751
$789$	−5.03580	−0.179279
$790$	−13.0618	−0.464718
$791$	−55.0089	−1.95589
$792$	16.6717	0.592402
$793$	52.8249	1.87587
$794$	−25.0886	−0.890361
$795$	0.748091	0.0265320
$796$	13.9385	0.494036
$797$	27.2835	0.966432	0.483216	−	0.875501i	$-0.339469\pi$
$797$	27.2835	0.966432	0.483216	+	0.875501i	$0.339469\pi$
$798$	−2.69695	−0.0954711
$799$	21.9839	0.777735
$800$	1.00000	0.0353553
$801$	−40.3747	−1.42657
$802$	−6.82379	−0.240957
$803$	44.5612	1.57253
$804$	−2.85043	−0.100527
$805$	5.94308	0.209466
$806$	−3.35057	−0.118019
$807$	−10.0163	−0.352590
$808$	−1.07213	−0.0377173
$809$	−1.58977	−0.0558934	−0.0279467	−	0.999609i	$-0.508897\pi$
$809$	−1.58977	−0.0558934	−0.0279467	+	0.999609i	$0.508897\pi$
$810$	7.79214	0.273788
$811$	−24.1140	−0.846757	−0.423378	−	0.905953i	$-0.639156\pi$
$811$	−24.1140	−0.846757	−0.423378	+	0.905953i	$0.639156\pi$
$812$	12.8604	0.451310
$813$	1.21824	0.0427257
$814$	−44.1602	−1.54781
$815$	3.41660	0.119678
$816$	1.23561	0.0432549
$817$	−1.68507	−0.0589530
$818$	5.08364	0.177745
$819$	64.5192	2.25448
$820$	−4.82786	−0.168596
$821$	−12.8203	−0.447431	−0.223715	−	0.974655i	$-0.571819\pi$
$821$	−12.8203	−0.447431	−0.223715	+	0.974655i	$0.571819\pi$
$822$	6.98646	0.243681
$823$	−18.5144	−0.645373	−0.322686	−	0.946506i	$-0.604586\pi$
$823$	−18.5144	−0.645373	−0.322686	+	0.946506i	$0.604586\pi$
$824$	−11.5651	−0.402890
$825$	2.14906	0.0748205
$826$	−46.0270	−1.60149
$827$	36.9928	1.28637	0.643183	−	0.765712i	$-0.277613\pi$
$827$	36.9928	1.28637	0.643183	+	0.765712i	$0.277613\pi$
$828$	−4.08841	−0.142082
$829$	32.8939	1.14245	0.571226	−	0.820793i	$-0.306468\pi$
$829$	32.8939	1.14245	0.571226	+	0.820793i	$0.306468\pi$
$830$	−9.11232	−0.316293
$831$	3.91344	0.135756
$832$	−5.41212	−0.187632
$833$	−34.5738	−1.19791
$834$	−4.63859	−0.160621
$835$	−7.87126	−0.272396
$836$	−10.2172	−0.353368
$837$	1.34006	0.0463194
$838$	4.98760	0.172294
$839$	−30.5336	−1.05414	−0.527068	−	0.849823i	$-0.676709\pi$
$839$	−30.5336	−1.05414	−0.527068	+	0.849823i	$0.676709\pi$
$840$	−1.53670	−0.0530213
$841$	−19.4561	−0.670899
$842$	29.1556	1.00477
$843$	−6.68005	−0.230073
$844$	−9.00652	−0.310017
$845$	16.2911	0.560430
$846$	18.8086	0.646655
$847$	95.2945	3.27436
$848$	−2.02653	−0.0695914
$849$	0.224440	0.00770277
$850$	−3.34718	−0.114807
$851$	10.8294	0.371229
$852$	2.67558	0.0916638
$853$	−31.6568	−1.08391	−0.541953	−	0.840409i	$-0.682315\pi$
$853$	−31.6568	−1.08391	−0.541953	+	0.840409i	$0.682315\pi$
$854$	−40.6312	−1.39037
$855$	−5.02592	−0.171883
$856$	−2.17984	−0.0745053
$857$	−39.6206	−1.35342	−0.676708	−	0.736252i	$-0.736594\pi$
$857$	−39.6206	−1.35342	−0.676708	+	0.736252i	$0.736594\pi$
$858$	−11.6310	−0.397074
$859$	−9.29871	−0.317268	−0.158634	−	0.987337i	$-0.550709\pi$
$859$	−9.29871	−0.317268	−0.158634	+	0.987337i	$0.550709\pi$
$860$	−0.960138	−0.0327404
$861$	7.41899	0.252838
$862$	19.1082	0.650827
$863$	12.8588	0.437720	0.218860	−	0.975756i	$-0.429766\pi$
$863$	12.8588	0.437720	0.218860	+	0.975756i	$0.429766\pi$
$864$	2.16459	0.0736407
$865$	−0.552131	−0.0187730
$866$	30.5975	1.03975
$867$	2.13972	0.0726685
$868$	2.57715	0.0874743
$869$	76.0413	2.57953
$870$	−1.14042	−0.0386639
$871$	−41.7905	−1.41602
$872$	6.57445	0.222639
$873$	48.2888	1.63433
$874$	2.50557	0.0847520
$875$	4.16284	0.140730
$876$	2.82560	0.0954681
$877$	32.8369	1.10882	0.554412	−	0.832242i	$-0.312943\pi$
$877$	32.8369	1.10882	0.554412	+	0.832242i	$0.312943\pi$
$878$	−3.20036	−0.108007
$879$	2.83701	0.0956898
$880$	−5.82166	−0.196248
$881$	−3.10232	−0.104520	−0.0522599	−	0.998634i	$-0.516642\pi$
$881$	−3.10232	−0.104520	−0.0522599	+	0.998634i	$0.516642\pi$
$882$	−29.5800	−0.996012
$883$	−0.794855	−0.0267490	−0.0133745	−	0.999911i	$-0.504257\pi$
$883$	−0.794855	−0.0267490	−0.0133745	+	0.999911i	$0.504257\pi$
$884$	18.1154	0.609286
$885$	4.08155	0.137200
$886$	−21.8417	−0.733787
$887$	1.49267	0.0501191	0.0250595	−	0.999686i	$-0.492022\pi$
$887$	1.49267	0.0501191	0.0250595	+	0.999686i	$0.492022\pi$
$888$	−2.80017	−0.0939676
$889$	36.0281	1.20834
$890$	14.0986	0.472588
$891$	−45.3632	−1.51972
$892$	−0.780941	−0.0261478
$893$	−11.5268	−0.385730
$894$	0.324155	0.0108414
$895$	−0.182267	−0.00609253
$896$	4.16284	0.139071
$897$	2.85227	0.0952346
$898$	−26.0499	−0.869298
$899$	1.91256	0.0637874
$900$	−2.86373	−0.0954577
$901$	6.78317	0.225980
$902$	28.1061	0.935832
$903$	1.47545	0.0490998
$904$	−13.2143	−0.439500
$905$	11.9718	0.397955
$906$	2.90410	0.0964821
$907$	3.96265	0.131578	0.0657888	−	0.997834i	$-0.479044\pi$
$907$	3.96265	0.131578	0.0657888	+	0.997834i	$0.479044\pi$
$908$	−20.8939	−0.693390
$909$	3.07029	0.101835
$910$	−22.5298	−0.746855
$911$	51.2229	1.69709	0.848545	−	0.529123i	$-0.177479\pi$
$911$	51.2229	1.69709	0.848545	+	0.529123i	$0.177479\pi$
$912$	−0.647864	−0.0214529
$913$	53.0488	1.75566
$914$	−31.2787	−1.03461
$915$	3.60306	0.119114
$916$	−22.0570	−0.728783
$917$	−71.4175	−2.35841
$918$	−7.24527	−0.239129
$919$	−34.2406	−1.12949	−0.564747	−	0.825264i	$-0.691026\pi$
$919$	−34.2406	−1.12949	−0.564747	+	0.825264i	$0.691026\pi$
$920$	1.42765	0.0470683
$921$	−2.13109	−0.0702219
$922$	6.43891	0.212054
$923$	39.2269	1.29117
$924$	8.94617	0.294307
$925$	7.58549	0.249409
$926$	−7.66434	−0.251866
$927$	33.1194	1.08778
$928$	3.08933	0.101412
$929$	−50.2409	−1.64835	−0.824175	−	0.566335i	$-0.808361\pi$
$929$	−50.2409	−1.64835	−0.824175	+	0.566335i	$0.808361\pi$
$930$	−0.228534	−0.00749394
$931$	18.1280	0.594122
$932$	6.54871	0.214510
$933$	−3.25315	−0.106503
$934$	4.35278	0.142427
$935$	19.4862	0.637266
$936$	15.4989	0.506596
$937$	−5.67679	−0.185453	−0.0927263	−	0.995692i	$-0.529558\pi$
$937$	−5.67679	−0.185453	−0.0927263	+	0.995692i	$0.529558\pi$
$938$	32.1439	1.04954
$939$	−8.09346	−0.264120
$940$	−6.56789	−0.214221
$941$	−57.6442	−1.87915	−0.939574	−	0.342345i	$-0.888779\pi$
$941$	−57.6442	−1.87915	−0.939574	+	0.342345i	$0.888779\pi$
$942$	3.34186	0.108884
$943$	−6.89250	−0.224451
$944$	−11.0567	−0.359863
$945$	9.01082	0.293122
$946$	5.58960	0.181734
$947$	44.0431	1.43121	0.715604	−	0.698507i	$-0.246152\pi$
$947$	44.0431	1.43121	0.715604	+	0.698507i	$0.246152\pi$
$948$	4.82174	0.156603
$949$	41.4264	1.34476
$950$	1.75502	0.0569405
$951$	−6.85585	−0.222316
$952$	−13.9338	−0.451596
$953$	5.87978	0.190465	0.0952325	−	0.995455i	$-0.469641\pi$
$953$	5.87978	0.190465	0.0952325	+	0.995455i	$0.469641\pi$
$954$	5.80344	0.187893
$955$	−7.68594	−0.248711
$956$	−0.382128	−0.0123589
$957$	6.63914	0.214613
$958$	34.4459	1.11290
$959$	−78.7853	−2.54411
$960$	−0.369148	−0.0119142
$961$	−30.6167	−0.987637
$962$	−41.0536	−1.32362
$963$	6.24247	0.201161
$964$	−6.04288	−0.194628
$965$	8.39566	0.270266
$966$	−2.19388	−0.0705869
$967$	16.6669	0.535971	0.267986	−	0.963423i	$-0.413642\pi$
$967$	16.6669	0.535971	0.267986	+	0.963423i	$0.413642\pi$
$968$	22.8917	0.735768
$969$	2.16852	0.0696630
$970$	−16.8622	−0.541413
$971$	57.0624	1.83122	0.915609	−	0.402069i	$-0.131709\pi$
$971$	57.0624	1.83122	0.915609	+	0.402069i	$0.131709\pi$
$972$	−9.37021	−0.300550
$973$	52.3087	1.67694
$974$	40.0127	1.28209
$975$	1.99788	0.0639832
$976$	−9.76047	−0.312425
$977$	−12.8129	−0.409922	−0.204961	−	0.978770i	$-0.565707\pi$
$977$	−12.8129	−0.409922	−0.204961	+	0.978770i	$0.565707\pi$
$978$	−1.26123	−0.0403297
$979$	−82.0775	−2.62321
$980$	10.3292	0.329954
$981$	−18.8274	−0.601114
$982$	10.2272	0.326363
$983$	−19.9684	−0.636893	−0.318446	−	0.947941i	$-0.603161\pi$
$983$	−19.9684	−0.636893	−0.318446	+	0.947941i	$0.603161\pi$
$984$	1.78220	0.0568143
$985$	22.5343	0.718003
$986$	−10.3405	−0.329310
$987$	10.0929	0.321260
$988$	−9.49841	−0.302185
$989$	−1.37074	−0.0435871
$990$	16.6717	0.529860
$991$	−27.8951	−0.886116	−0.443058	−	0.896493i	$-0.646106\pi$
$991$	−27.8951	−0.886116	−0.443058	+	0.896493i	$0.646106\pi$
$992$	0.619086	0.0196560
$993$	−1.32037	−0.0419007
$994$	−30.1721	−0.957002
$995$	13.9385	0.441879
$996$	3.36380	0.106586
$997$	43.5865	1.38040	0.690199	−	0.723620i	$-0.257523\pi$
$997$	43.5865	1.38040	0.690199	+	0.723620i	$0.257523\pi$
$998$	1.46831	0.0464784
$999$	16.4194	0.519488

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.c.1.9	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.c.1.9	✓	16	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.369148 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.369148 q^{6} +4.16284 q^{7} +1.00000 q^{8} -2.86373 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.369148 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.369148 q^{6} +4.16284 q^{7} +1.00000 q^{8} -2.86373 q^{9} +1.00000 q^{10} -5.82166 q^{11} -0.369148 q^{12} -5.41212 q^{13} +4.16284 q^{14} -0.369148 q^{15} +1.00000 q^{16} -3.34718 q^{17} -2.86373 q^{18} +1.75502 q^{19} +1.00000 q^{20} -1.53670 q^{21} -5.82166 q^{22} +1.42765 q^{23} -0.369148 q^{24} +1.00000 q^{25} -5.41212 q^{26} +2.16459 q^{27} +4.16284 q^{28} +3.08933 q^{29} -0.369148 q^{30} +0.619086 q^{31} +1.00000 q^{32} +2.14906 q^{33} -3.34718 q^{34} +4.16284 q^{35} -2.86373 q^{36} +7.58549 q^{37} +1.75502 q^{38} +1.99788 q^{39} +1.00000 q^{40} -4.82786 q^{41} -1.53670 q^{42} -0.960138 q^{43} -5.82166 q^{44} -2.86373 q^{45} +1.42765 q^{46} -6.56789 q^{47} -0.369148 q^{48} +10.3292 q^{49} +1.00000 q^{50} +1.23561 q^{51} -5.41212 q^{52} -2.02653 q^{53} +2.16459 q^{54} -5.82166 q^{55} +4.16284 q^{56} -0.647864 q^{57} +3.08933 q^{58} -11.0567 q^{59} -0.369148 q^{60} -9.76047 q^{61} +0.619086 q^{62} -11.9212 q^{63} +1.00000 q^{64} -5.41212 q^{65} +2.14906 q^{66} +7.72164 q^{67} -3.34718 q^{68} -0.527016 q^{69} +4.16284 q^{70} -7.24797 q^{71} -2.86373 q^{72} -7.65437 q^{73} +7.58549 q^{74} -0.369148 q^{75} +1.75502 q^{76} -24.2346 q^{77} +1.99788 q^{78} -13.0618 q^{79} +1.00000 q^{80} +7.79214 q^{81} -4.82786 q^{82} -9.11232 q^{83} -1.53670 q^{84} -3.34718 q^{85} -0.960138 q^{86} -1.14042 q^{87} -5.82166 q^{88} +14.0986 q^{89} -2.86373 q^{90} -22.5298 q^{91} +1.42765 q^{92} -0.228534 q^{93} -6.56789 q^{94} +1.75502 q^{95} -0.369148 q^{96} -16.8622 q^{97} +10.3292 q^{98} +16.6717 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9} + 16 q^{10} - 14 q^{11} - 8 q^{12} - 20 q^{13} - 10 q^{14} - 8 q^{15} + 16 q^{16} - 27 q^{17} - 2 q^{18} - 17 q^{19} + 16 q^{20} - 12 q^{21} - 14 q^{22} - 9 q^{23} - 8 q^{24} + 16 q^{25} - 20 q^{26} - 11 q^{27} - 10 q^{28} - 23 q^{29} - 8 q^{30} - 21 q^{31} + 16 q^{32} - 9 q^{33} - 27 q^{34} - 10 q^{35} - 2 q^{36} - 16 q^{37} - 17 q^{38} - 6 q^{39} + 16 q^{40} - 35 q^{41} - 12 q^{42} + 3 q^{43} - 14 q^{44} - 2 q^{45} - 9 q^{46} - 25 q^{47} - 8 q^{48} - 24 q^{49} + 16 q^{50} - q^{51} - 20 q^{52} - 39 q^{53} - 11 q^{54} - 14 q^{55} - 10 q^{56} - 6 q^{57} - 23 q^{58} - 32 q^{59} - 8 q^{60} - 38 q^{61} - 21 q^{62} + q^{63} + 16 q^{64} - 20 q^{65} - 9 q^{66} + 5 q^{67} - 27 q^{68} - 25 q^{69} - 10 q^{70} - 16 q^{71} - 2 q^{72} - 17 q^{73} - 16 q^{74} - 8 q^{75} - 17 q^{76} - 34 q^{77} - 6 q^{78} - 40 q^{79} + 16 q^{80} - 28 q^{81} - 35 q^{82} - 22 q^{83} - 12 q^{84} - 27 q^{85} + 3 q^{86} + 10 q^{87} - 14 q^{88} - 46 q^{89} - 2 q^{90} - q^{91} - 9 q^{92} + 14 q^{93} - 25 q^{94} - 17 q^{95} - 8 q^{96} - 21 q^{97} - 24 q^{98} + 15 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9 + 16 * q^10 - 14 * q^11 - 8 * q^12 - 20 * q^13 - 10 * q^14 - 8 * q^15 + 16 * q^16 - 27 * q^17 - 2 * q^18 - 17 * q^19 + 16 * q^20 - 12 * q^21 - 14 * q^22 - 9 * q^23 - 8 * q^24 + 16 * q^25 - 20 * q^26 - 11 * q^27 - 10 * q^28 - 23 * q^29 - 8 * q^30 - 21 * q^31 + 16 * q^32 - 9 * q^33 - 27 * q^34 - 10 * q^35 - 2 * q^36 - 16 * q^37 - 17 * q^38 - 6 * q^39 + 16 * q^40 - 35 * q^41 - 12 * q^42 + 3 * q^43 - 14 * q^44 - 2 * q^45 - 9 * q^46 - 25 * q^47 - 8 * q^48 - 24 * q^49 + 16 * q^50 - q^51 - 20 * q^52 - 39 * q^53 - 11 * q^54 - 14 * q^55 - 10 * q^56 - 6 * q^57 - 23 * q^58 - 32 * q^59 - 8 * q^60 - 38 * q^61 - 21 * q^62 + q^63 + 16 * q^64 - 20 * q^65 - 9 * q^66 + 5 * q^67 - 27 * q^68 - 25 * q^69 - 10 * q^70 - 16 * q^71 - 2 * q^72 - 17 * q^73 - 16 * q^74 - 8 * q^75 - 17 * q^76 - 34 * q^77 - 6 * q^78 - 40 * q^79 + 16 * q^80 - 28 * q^81 - 35 * q^82 - 22 * q^83 - 12 * q^84 - 27 * q^85 + 3 * q^86 + 10 * q^87 - 14 * q^88 - 46 * q^89 - 2 * q^90 - q^91 - 9 * q^92 + 14 * q^93 - 25 * q^94 - 17 * q^95 - 8 * q^96 - 21 * q^97 - 24 * q^98 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more