LMFDB - Embedded newform 6018.2.a.z.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.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:	$48.0539719364$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 4 x^{10} - 27 x^{9} + 117 x^{8} + 200 x^{7} - 1023 x^{6} - 484 x^{5} + 3403 x^{4} + 562 x^{3} + \cdots + 1200 $ x^11 - 4x^10 - 27x^9 + 117x^8 + 200x^7 - 1023x^6 - 484x^5 + 3403x^4 + 562x^3 - 4372x^2 - 692x + 1200
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			1.6
Root			$0.504544$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.504544 q^{5} -1.00000 q^{6} +2.39214 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.504544 q^{5} -1.00000 q^{6} +2.39214 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.504544 q^{10} +1.10857 q^{11} -1.00000 q^{12} +2.49075 q^{13} +2.39214 q^{14} -0.504544 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +8.61570 q^{19} +0.504544 q^{20} -2.39214 q^{21} +1.10857 q^{22} -0.297149 q^{23} -1.00000 q^{24} -4.74544 q^{25} +2.49075 q^{26} -1.00000 q^{27} +2.39214 q^{28} +7.46215 q^{29} -0.504544 q^{30} +5.69421 q^{31} +1.00000 q^{32} -1.10857 q^{33} -1.00000 q^{34} +1.20694 q^{35} +1.00000 q^{36} -11.5598 q^{37} +8.61570 q^{38} -2.49075 q^{39} +0.504544 q^{40} -4.27848 q^{41} -2.39214 q^{42} +0.580112 q^{43} +1.10857 q^{44} +0.504544 q^{45} -0.297149 q^{46} +10.6814 q^{47} -1.00000 q^{48} -1.27766 q^{49} -4.74544 q^{50} +1.00000 q^{51} +2.49075 q^{52} +1.44391 q^{53} -1.00000 q^{54} +0.559322 q^{55} +2.39214 q^{56} -8.61570 q^{57} +7.46215 q^{58} -1.00000 q^{59} -0.504544 q^{60} +2.02440 q^{61} +5.69421 q^{62} +2.39214 q^{63} +1.00000 q^{64} +1.25670 q^{65} -1.10857 q^{66} -6.76235 q^{67} -1.00000 q^{68} +0.297149 q^{69} +1.20694 q^{70} -3.30733 q^{71} +1.00000 q^{72} +16.7045 q^{73} -11.5598 q^{74} +4.74544 q^{75} +8.61570 q^{76} +2.65185 q^{77} -2.49075 q^{78} +5.03441 q^{79} +0.504544 q^{80} +1.00000 q^{81} -4.27848 q^{82} -11.1379 q^{83} -2.39214 q^{84} -0.504544 q^{85} +0.580112 q^{86} -7.46215 q^{87} +1.10857 q^{88} -10.9550 q^{89} +0.504544 q^{90} +5.95823 q^{91} -0.297149 q^{92} -5.69421 q^{93} +10.6814 q^{94} +4.34700 q^{95} -1.00000 q^{96} -7.46768 q^{97} -1.27766 q^{98} +1.10857 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 3 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 3 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 3 q^{7} + 11 q^{8} + 11 q^{9} + 4 q^{10} + 9 q^{11} - 11 q^{12} + 6 q^{13} + 3 q^{14} - 4 q^{15} + 11 q^{16} - 11 q^{17} + 11 q^{18} - q^{19} + 4 q^{20} - 3 q^{21} + 9 q^{22} + 10 q^{23} - 11 q^{24} + 15 q^{25} + 6 q^{26} - 11 q^{27} + 3 q^{28} + 14 q^{29} - 4 q^{30} + 17 q^{31} + 11 q^{32} - 9 q^{33} - 11 q^{34} + 8 q^{35} + 11 q^{36} + 30 q^{37} - q^{38} - 6 q^{39} + 4 q^{40} + 10 q^{41} - 3 q^{42} + 11 q^{43} + 9 q^{44} + 4 q^{45} + 10 q^{46} - 6 q^{47} - 11 q^{48} + 18 q^{49} + 15 q^{50} + 11 q^{51} + 6 q^{52} + 10 q^{53} - 11 q^{54} - 11 q^{55} + 3 q^{56} + q^{57} + 14 q^{58} - 11 q^{59} - 4 q^{60} + 13 q^{61} + 17 q^{62} + 3 q^{63} + 11 q^{64} + 32 q^{65} - 9 q^{66} + 26 q^{67} - 11 q^{68} - 10 q^{69} + 8 q^{70} + 14 q^{71} + 11 q^{72} + 20 q^{73} + 30 q^{74} - 15 q^{75} - q^{76} + 26 q^{77} - 6 q^{78} + 15 q^{79} + 4 q^{80} + 11 q^{81} + 10 q^{82} + 2 q^{83} - 3 q^{84} - 4 q^{85} + 11 q^{86} - 14 q^{87} + 9 q^{88} + q^{89} + 4 q^{90} + 17 q^{91} + 10 q^{92} - 17 q^{93} - 6 q^{94} + 3 q^{95} - 11 q^{96} + 33 q^{97} + 18 q^{98} + 9 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 3 * q^7 + 11 * q^8 + 11 * q^9 + 4 * q^10 + 9 * q^11 - 11 * q^12 + 6 * q^13 + 3 * q^14 - 4 * q^15 + 11 * q^16 - 11 * q^17 + 11 * q^18 - q^19 + 4 * q^20 - 3 * q^21 + 9 * q^22 + 10 * q^23 - 11 * q^24 + 15 * q^25 + 6 * q^26 - 11 * q^27 + 3 * q^28 + 14 * q^29 - 4 * q^30 + 17 * q^31 + 11 * q^32 - 9 * q^33 - 11 * q^34 + 8 * q^35 + 11 * q^36 + 30 * q^37 - q^38 - 6 * q^39 + 4 * q^40 + 10 * q^41 - 3 * q^42 + 11 * q^43 + 9 * q^44 + 4 * q^45 + 10 * q^46 - 6 * q^47 - 11 * q^48 + 18 * q^49 + 15 * q^50 + 11 * q^51 + 6 * q^52 + 10 * q^53 - 11 * q^54 - 11 * q^55 + 3 * q^56 + q^57 + 14 * q^58 - 11 * q^59 - 4 * q^60 + 13 * q^61 + 17 * q^62 + 3 * q^63 + 11 * q^64 + 32 * q^65 - 9 * q^66 + 26 * q^67 - 11 * q^68 - 10 * q^69 + 8 * q^70 + 14 * q^71 + 11 * q^72 + 20 * q^73 + 30 * q^74 - 15 * q^75 - q^76 + 26 * q^77 - 6 * q^78 + 15 * q^79 + 4 * q^80 + 11 * q^81 + 10 * q^82 + 2 * q^83 - 3 * q^84 - 4 * q^85 + 11 * q^86 - 14 * q^87 + 9 * q^88 + q^89 + 4 * q^90 + 17 * q^91 + 10 * q^92 - 17 * q^93 - 6 * q^94 + 3 * q^95 - 11 * q^96 + 33 * q^97 + 18 * q^98 + 9 * 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	0.504544	0.225639	0.112820	−	0.993615i	$-0.464012\pi$
$5$	0.504544	0.225639	0.112820	+	0.993615i	$0.464012\pi$
$6$	−1.00000	−0.408248
$7$	2.39214	0.904144	0.452072	−	0.891981i	$-0.350685\pi$
$7$	2.39214	0.904144	0.452072	+	0.891981i	$0.350685\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.504544	0.159551
$11$	1.10857	0.334246	0.167123	−	0.985936i	$-0.446552\pi$
$11$	1.10857	0.334246	0.167123	+	0.985936i	$0.446552\pi$
$12$	−1.00000	−0.288675
$13$	2.49075	0.690811	0.345405	−	0.938454i	$-0.387741\pi$
$13$	2.49075	0.690811	0.345405	+	0.938454i	$0.387741\pi$
$14$	2.39214	0.639327
$15$	−0.504544	−0.130273
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	8.61570	1.97658	0.988288	−	0.152599i	$-0.0487641\pi$
$19$	8.61570	1.97658	0.988288	+	0.152599i	$0.0487641\pi$
$20$	0.504544	0.112820
$21$	−2.39214	−0.522008
$22$	1.10857	0.236348
$23$	−0.297149	−0.0619599	−0.0309800	−	0.999520i	$-0.509863\pi$
$23$	−0.297149	−0.0619599	−0.0309800	+	0.999520i	$0.509863\pi$
$24$	−1.00000	−0.204124
$25$	−4.74544	−0.949087
$26$	2.49075	0.488477
$27$	−1.00000	−0.192450
$28$	2.39214	0.452072
$29$	7.46215	1.38569	0.692844	−	0.721088i	$-0.256358\pi$
$29$	7.46215	1.38569	0.692844	+	0.721088i	$0.256358\pi$
$30$	−0.504544	−0.0921168
$31$	5.69421	1.02271	0.511355	−	0.859369i	$-0.329144\pi$
$31$	5.69421	1.02271	0.511355	+	0.859369i	$0.329144\pi$
$32$	1.00000	0.176777
$33$	−1.10857	−0.192977
$34$	−1.00000	−0.171499
$35$	1.20694	0.204010
$36$	1.00000	0.166667
$37$	−11.5598	−1.90042	−0.950212	−	0.311603i	$-0.899134\pi$
$37$	−11.5598	−1.90042	−0.950212	+	0.311603i	$0.899134\pi$
$38$	8.61570	1.39765
$39$	−2.49075	−0.398840
$40$	0.504544	0.0797755
$41$	−4.27848	−0.668187	−0.334093	−	0.942540i	$-0.608430\pi$
$41$	−4.27848	−0.668187	−0.334093	+	0.942540i	$0.608430\pi$
$42$	−2.39214	−0.369115
$43$	0.580112	0.0884662	0.0442331	−	0.999021i	$-0.485916\pi$
$43$	0.580112	0.0884662	0.0442331	+	0.999021i	$0.485916\pi$
$44$	1.10857	0.167123
$45$	0.504544	0.0752130
$46$	−0.297149	−0.0438123
$47$	10.6814	1.55805	0.779023	−	0.626996i	$-0.215716\pi$
$47$	10.6814	1.55805	0.779023	+	0.626996i	$0.215716\pi$
$48$	−1.00000	−0.144338
$49$	−1.27766	−0.182523
$50$	−4.74544	−0.671106
$51$	1.00000	0.140028
$52$	2.49075	0.345405
$53$	1.44391	0.198336	0.0991680	−	0.995071i	$-0.468382\pi$
$53$	1.44391	0.198336	0.0991680	+	0.995071i	$0.468382\pi$
$54$	−1.00000	−0.136083
$55$	0.559322	0.0754190
$56$	2.39214	0.319663
$57$	−8.61570	−1.14118
$58$	7.46215	0.979829
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−0.504544	−0.0651364
$61$	2.02440	0.259198	0.129599	−	0.991567i	$-0.458631\pi$
$61$	2.02440	0.259198	0.129599	+	0.991567i	$0.458631\pi$
$62$	5.69421	0.723166
$63$	2.39214	0.301381
$64$	1.00000	0.125000
$65$	1.25670	0.155874
$66$	−1.10857	−0.136455
$67$	−6.76235	−0.826153	−0.413076	−	0.910696i	$-0.635546\pi$
$67$	−6.76235	−0.826153	−0.413076	+	0.910696i	$0.635546\pi$
$68$	−1.00000	−0.121268
$69$	0.297149	0.0357726
$70$	1.20694	0.144257
$71$	−3.30733	−0.392507	−0.196254	−	0.980553i	$-0.562878\pi$
$71$	−3.30733	−0.392507	−0.196254	+	0.980553i	$0.562878\pi$
$72$	1.00000	0.117851
$73$	16.7045	1.95511	0.977557	−	0.210672i	$-0.0675651\pi$
$73$	16.7045	1.95511	0.977557	+	0.210672i	$0.0675651\pi$
$74$	−11.5598	−1.34380
$75$	4.74544	0.547956
$76$	8.61570	0.988288
$77$	2.65185	0.302207
$78$	−2.49075	−0.282022
$79$	5.03441	0.566415	0.283208	−	0.959059i	$-0.408601\pi$
$79$	5.03441	0.566415	0.283208	+	0.959059i	$0.408601\pi$
$80$	0.504544	0.0564098
$81$	1.00000	0.111111
$82$	−4.27848	−0.472479
$83$	−11.1379	−1.22254	−0.611271	−	0.791421i	$-0.709342\pi$
$83$	−11.1379	−1.22254	−0.611271	+	0.791421i	$0.709342\pi$
$84$	−2.39214	−0.261004
$85$	−0.504544	−0.0547255
$86$	0.580112	0.0625551
$87$	−7.46215	−0.800027
$88$	1.10857	0.118174
$89$	−10.9550	−1.16123	−0.580615	−	0.814178i	$-0.697188\pi$
$89$	−10.9550	−1.16123	−0.580615	+	0.814178i	$0.697188\pi$
$90$	0.504544	0.0531836
$91$	5.95823	0.624592
$92$	−0.297149	−0.0309800
$93$	−5.69421	−0.590462
$94$	10.6814	1.10170
$95$	4.34700	0.445993
$96$	−1.00000	−0.102062
$97$	−7.46768	−0.758228	−0.379114	−	0.925350i	$-0.623771\pi$
$97$	−7.46768	−0.758228	−0.379114	+	0.925350i	$0.623771\pi$
$98$	−1.27766	−0.129063
$99$	1.10857	0.111415
$100$	−4.74544	−0.474544
$101$	−11.0160	−1.09613	−0.548066	−	0.836435i	$-0.684636\pi$
$101$	−11.0160	−1.09613	−0.548066	+	0.836435i	$0.684636\pi$
$102$	1.00000	0.0990148
$103$	0.756325	0.0745229	0.0372615	−	0.999306i	$-0.488137\pi$
$103$	0.756325	0.0745229	0.0372615	+	0.999306i	$0.488137\pi$
$104$	2.49075	0.244238
$105$	−1.20694	−0.117785
$106$	1.44391	0.140245
$107$	−11.2590	−1.08845	−0.544225	−	0.838939i	$-0.683176\pi$
$107$	−11.2590	−1.08845	−0.544225	+	0.838939i	$0.683176\pi$
$108$	−1.00000	−0.0962250
$109$	16.4184	1.57259	0.786297	−	0.617848i	$-0.211995\pi$
$109$	16.4184	1.57259	0.786297	+	0.617848i	$0.211995\pi$
$110$	0.559322	0.0533293
$111$	11.5598	1.09721
$112$	2.39214	0.226036
$113$	3.44593	0.324166	0.162083	−	0.986777i	$-0.448179\pi$
$113$	3.44593	0.324166	0.162083	+	0.986777i	$0.448179\pi$
$114$	−8.61570	−0.806934
$115$	−0.149925	−0.0139806
$116$	7.46215	0.692844
$117$	2.49075	0.230270
$118$	−1.00000	−0.0920575
$119$	−2.39214	−0.219287
$120$	−0.504544	−0.0460584
$121$	−9.77107	−0.888279
$122$	2.02440	0.183280
$123$	4.27848	0.385778
$124$	5.69421	0.511355
$125$	−4.91700	−0.439790
$126$	2.39214	0.213109
$127$	12.7425	1.13071	0.565357	−	0.824847i	$-0.308739\pi$
$127$	12.7425	1.13071	0.565357	+	0.824847i	$0.308739\pi$
$128$	1.00000	0.0883883
$129$	−0.580112	−0.0510760
$130$	1.25670	0.110219
$131$	−6.32230	−0.552382	−0.276191	−	0.961103i	$-0.589072\pi$
$131$	−6.32230	−0.552382	−0.276191	+	0.961103i	$0.589072\pi$
$132$	−1.10857	−0.0964886
$133$	20.6100	1.78711
$134$	−6.76235	−0.584178
$135$	−0.504544	−0.0434243
$136$	−1.00000	−0.0857493
$137$	2.01041	0.171761	0.0858805	−	0.996305i	$-0.472630\pi$
$137$	2.01041	0.171761	0.0858805	+	0.996305i	$0.472630\pi$
$138$	0.297149	0.0252950
$139$	16.0190	1.35872	0.679358	−	0.733807i	$-0.262259\pi$
$139$	16.0190	1.35872	0.679358	+	0.733807i	$0.262259\pi$
$140$	1.20694	0.102005
$141$	−10.6814	−0.899538
$142$	−3.30733	−0.277545
$143$	2.76117	0.230901
$144$	1.00000	0.0833333
$145$	3.76499	0.312665
$146$	16.7045	1.38247
$147$	1.27766	0.105380
$148$	−11.5598	−0.950212
$149$	4.02796	0.329983	0.164992	−	0.986295i	$-0.447240\pi$
$149$	4.02796	0.329983	0.164992	+	0.986295i	$0.447240\pi$
$150$	4.74544	0.387463
$151$	−3.76173	−0.306125	−0.153063	−	0.988216i	$-0.548914\pi$
$151$	−3.76173	−0.306125	−0.153063	+	0.988216i	$0.548914\pi$
$152$	8.61570	0.698825
$153$	−1.00000	−0.0808452
$154$	2.65185	0.213693
$155$	2.87298	0.230763
$156$	−2.49075	−0.199420
$157$	0.703406	0.0561379	0.0280690	−	0.999606i	$-0.491064\pi$
$157$	0.703406	0.0561379	0.0280690	+	0.999606i	$0.491064\pi$
$158$	5.03441	0.400516
$159$	−1.44391	−0.114509
$160$	0.504544	0.0398877
$161$	−0.710823	−0.0560207
$162$	1.00000	0.0785674
$163$	7.07001	0.553766	0.276883	−	0.960904i	$-0.410699\pi$
$163$	7.07001	0.553766	0.276883	+	0.960904i	$0.410699\pi$
$164$	−4.27848	−0.334093
$165$	−0.559322	−0.0435432
$166$	−11.1379	−0.864468
$167$	14.6374	1.13268	0.566339	−	0.824172i	$-0.308359\pi$
$167$	14.6374	1.13268	0.566339	+	0.824172i	$0.308359\pi$
$168$	−2.39214	−0.184558
$169$	−6.79615	−0.522781
$170$	−0.504544	−0.0386968
$171$	8.61570	0.658859
$172$	0.580112	0.0442331
$173$	14.1671	1.07711	0.538554	−	0.842591i	$-0.318971\pi$
$173$	14.1671	1.07711	0.538554	+	0.842591i	$0.318971\pi$
$174$	−7.46215	−0.565704
$175$	−11.3518	−0.858112
$176$	1.10857	0.0835616
$177$	1.00000	0.0751646
$178$	−10.9550	−0.821113
$179$	−13.8282	−1.03357	−0.516786	−	0.856115i	$-0.672872\pi$
$179$	−13.8282	−1.03357	−0.516786	+	0.856115i	$0.672872\pi$
$180$	0.504544	0.0376065
$181$	−17.2329	−1.28091	−0.640456	−	0.767995i	$-0.721254\pi$
$181$	−17.2329	−1.28091	−0.640456	+	0.767995i	$0.721254\pi$
$182$	5.95823	0.441654
$183$	−2.02440	−0.149648
$184$	−0.297149	−0.0219061
$185$	−5.83245	−0.428810
$186$	−5.69421	−0.417520
$187$	−1.10857	−0.0810666
$188$	10.6814	0.779023
$189$	−2.39214	−0.174003
$190$	4.34700	0.315365
$191$	−15.1512	−1.09630	−0.548151	−	0.836379i	$-0.684668\pi$
$191$	−15.1512	−1.09630	−0.548151	+	0.836379i	$0.684668\pi$
$192$	−1.00000	−0.0721688
$193$	19.2590	1.38630	0.693148	−	0.720795i	$-0.256223\pi$
$193$	19.2590	1.38630	0.693148	+	0.720795i	$0.256223\pi$
$194$	−7.46768	−0.536148
$195$	−1.25670	−0.0899938
$196$	−1.27766	−0.0912615
$197$	20.0314	1.42718	0.713589	−	0.700565i	$-0.247069\pi$
$197$	20.0314	1.42718	0.713589	+	0.700565i	$0.247069\pi$
$198$	1.10857	0.0787826
$199$	16.4279	1.16454	0.582270	−	0.812996i	$-0.302165\pi$
$199$	16.4279	1.16454	0.582270	+	0.812996i	$0.302165\pi$
$200$	−4.74544	−0.335553
$201$	6.76235	0.476980
$202$	−11.0160	−0.775082
$203$	17.8505	1.25286
$204$	1.00000	0.0700140
$205$	−2.15868	−0.150769
$206$	0.756325	0.0526957
$207$	−0.297149	−0.0206533
$208$	2.49075	0.172703
$209$	9.55110	0.660663
$210$	−1.20694	−0.0832869
$211$	−18.4141	−1.26768	−0.633839	−	0.773465i	$-0.718522\pi$
$211$	−18.4141	−1.26768	−0.633839	+	0.773465i	$0.718522\pi$
$212$	1.44391	0.0991680
$213$	3.30733	0.226614
$214$	−11.2590	−0.769651
$215$	0.292692	0.0199614
$216$	−1.00000	−0.0680414
$217$	13.6214	0.924678
$218$	16.4184	1.11199
$219$	−16.7045	−1.12879
$220$	0.559322	0.0377095
$221$	−2.49075	−0.167546
$222$	11.5598	0.775845
$223$	18.3528	1.22899	0.614497	−	0.788919i	$-0.289359\pi$
$223$	18.3528	1.22899	0.614497	+	0.788919i	$0.289359\pi$
$224$	2.39214	0.159832
$225$	−4.74544	−0.316362
$226$	3.44593	0.229220
$227$	−10.3618	−0.687735	−0.343867	−	0.939018i	$-0.611737\pi$
$227$	−10.3618	−0.687735	−0.343867	+	0.939018i	$0.611737\pi$
$228$	−8.61570	−0.570588
$229$	14.7633	0.975586	0.487793	−	0.872959i	$-0.337802\pi$
$229$	14.7633	0.975586	0.487793	+	0.872959i	$0.337802\pi$
$230$	−0.149925	−0.00988576
$231$	−2.65185	−0.174479
$232$	7.46215	0.489914
$233$	9.14378	0.599029	0.299514	−	0.954092i	$-0.403175\pi$
$233$	9.14378	0.599029	0.299514	+	0.954092i	$0.403175\pi$
$234$	2.49075	0.162826
$235$	5.38925	0.351556
$236$	−1.00000	−0.0650945
$237$	−5.03441	−0.327020
$238$	−2.39214	−0.155059
$239$	−18.7515	−1.21293	−0.606466	−	0.795109i	$-0.707413\pi$
$239$	−18.7515	−1.21293	−0.606466	+	0.795109i	$0.707413\pi$
$240$	−0.504544	−0.0325682
$241$	−26.0481	−1.67791	−0.838954	−	0.544203i	$-0.816832\pi$
$241$	−26.0481	−1.67791	−0.838954	+	0.544203i	$0.816832\pi$
$242$	−9.77107	−0.628108
$243$	−1.00000	−0.0641500
$244$	2.02440	0.129599
$245$	−0.644637	−0.0411843
$246$	4.27848	0.272786
$247$	21.4596	1.36544
$248$	5.69421	0.361583
$249$	11.1379	0.705835
$250$	−4.91700	−0.310979
$251$	13.1829	0.832098	0.416049	−	0.909342i	$-0.363415\pi$
$251$	13.1829	0.832098	0.416049	+	0.909342i	$0.363415\pi$
$252$	2.39214	0.150691
$253$	−0.329411	−0.0207099
$254$	12.7425	0.799535
$255$	0.504544	0.0315958
$256$	1.00000	0.0625000
$257$	7.11818	0.444020	0.222010	−	0.975044i	$-0.428738\pi$
$257$	7.11818	0.444020	0.222010	+	0.975044i	$0.428738\pi$
$258$	−0.580112	−0.0361162
$259$	−27.6527	−1.71826
$260$	1.25670	0.0779369
$261$	7.46215	0.461896
$262$	−6.32230	−0.390593
$263$	−1.95363	−0.120466	−0.0602329	−	0.998184i	$-0.519184\pi$
$263$	−1.95363	−0.120466	−0.0602329	+	0.998184i	$0.519184\pi$
$264$	−1.10857	−0.0682277
$265$	0.728516	0.0447524
$266$	20.6100	1.26368
$267$	10.9550	0.670436
$268$	−6.76235	−0.413076
$269$	−16.9311	−1.03231	−0.516155	−	0.856495i	$-0.672637\pi$
$269$	−16.9311	−1.03231	−0.516155	+	0.856495i	$0.672637\pi$
$270$	−0.504544	−0.0307056
$271$	3.34033	0.202911	0.101455	−	0.994840i	$-0.467650\pi$
$271$	3.34033	0.202911	0.101455	+	0.994840i	$0.467650\pi$
$272$	−1.00000	−0.0606339
$273$	−5.95823	−0.360609
$274$	2.01041	0.121453
$275$	−5.26064	−0.317229
$276$	0.297149	0.0178863
$277$	5.13891	0.308767	0.154384	−	0.988011i	$-0.450661\pi$
$277$	5.13891	0.308767	0.154384	+	0.988011i	$0.450661\pi$
$278$	16.0190	0.960757
$279$	5.69421	0.340904
$280$	1.20694	0.0721285
$281$	22.1434	1.32096	0.660481	−	0.750843i	$-0.270352\pi$
$281$	22.1434	1.32096	0.660481	+	0.750843i	$0.270352\pi$
$282$	−10.6814	−0.636069
$283$	−0.0742288	−0.00441245	−0.00220622	−	0.999998i	$-0.500702\pi$
$283$	−0.0742288	−0.00441245	−0.00220622	+	0.999998i	$0.500702\pi$
$284$	−3.30733	−0.196254
$285$	−4.34700	−0.257494
$286$	2.76117	0.163272
$287$	−10.2347	−0.604137
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	3.76499	0.221088
$291$	7.46768	0.437763
$292$	16.7045	0.977557
$293$	20.8035	1.21535	0.607676	−	0.794185i	$-0.292102\pi$
$293$	20.8035	1.21535	0.607676	+	0.794185i	$0.292102\pi$
$294$	1.27766	0.0745147
$295$	−0.504544	−0.0293757
$296$	−11.5598	−0.671902
$297$	−1.10857	−0.0643257
$298$	4.02796	0.233333
$299$	−0.740126	−0.0428026
$300$	4.74544	0.273978
$301$	1.38771	0.0799862
$302$	−3.76173	−0.216463
$303$	11.0160	0.632852
$304$	8.61570	0.494144
$305$	1.02140	0.0584851
$306$	−1.00000	−0.0571662
$307$	−1.86618	−0.106509	−0.0532543	−	0.998581i	$-0.516959\pi$
$307$	−1.86618	−0.106509	−0.0532543	+	0.998581i	$0.516959\pi$
$308$	2.65185	0.151103
$309$	−0.756325	−0.0430258
$310$	2.87298	0.163174
$311$	7.60542	0.431264	0.215632	−	0.976475i	$-0.430819\pi$
$311$	7.60542	0.431264	0.215632	+	0.976475i	$0.430819\pi$
$312$	−2.49075	−0.141011
$313$	−13.4270	−0.758938	−0.379469	−	0.925204i	$-0.623893\pi$
$313$	−13.4270	−0.758938	−0.379469	+	0.925204i	$0.623893\pi$
$314$	0.703406	0.0396955
$315$	1.20694	0.0680034
$316$	5.03441	0.283208
$317$	−5.58422	−0.313641	−0.156821	−	0.987627i	$-0.550124\pi$
$317$	−5.58422	−0.313641	−0.156821	+	0.987627i	$0.550124\pi$
$318$	−1.44391	−0.0809703
$319$	8.27232	0.463161
$320$	0.504544	0.0282049
$321$	11.2590	0.628417
$322$	−0.710823	−0.0396126
$323$	−8.61570	−0.479390
$324$	1.00000	0.0555556
$325$	−11.8197	−0.655639
$326$	7.07001	0.391572
$327$	−16.4184	−0.907938
$328$	−4.27848	−0.236240
$329$	25.5515	1.40870
$330$	−0.559322	−0.0307897
$331$	−8.47838	−0.466014	−0.233007	−	0.972475i	$-0.574856\pi$
$331$	−8.47838	−0.466014	−0.233007	+	0.972475i	$0.574856\pi$
$332$	−11.1379	−0.611271
$333$	−11.5598	−0.633475
$334$	14.6374	0.800924
$335$	−3.41191	−0.186412
$336$	−2.39214	−0.130502
$337$	−14.0945	−0.767779	−0.383889	−	0.923379i	$-0.625416\pi$
$337$	−14.0945	−0.767779	−0.383889	+	0.923379i	$0.625416\pi$
$338$	−6.79615	−0.369662
$339$	−3.44593	−0.187157
$340$	−0.504544	−0.0273628
$341$	6.31243	0.341837
$342$	8.61570	0.465884
$343$	−19.8013	−1.06917
$344$	0.580112	0.0312775
$345$	0.149925	0.00807169
$346$	14.1671	0.761630
$347$	1.41517	0.0759702	0.0379851	−	0.999278i	$-0.487906\pi$
$347$	1.41517	0.0759702	0.0379851	+	0.999278i	$0.487906\pi$
$348$	−7.46215	−0.400013
$349$	28.2991	1.51482	0.757408	−	0.652942i	$-0.226466\pi$
$349$	28.2991	1.51482	0.757408	+	0.652942i	$0.226466\pi$
$350$	−11.3518	−0.606777
$351$	−2.49075	−0.132947
$352$	1.10857	0.0590870
$353$	25.1682	1.33957	0.669783	−	0.742557i	$-0.266387\pi$
$353$	25.1682	1.33957	0.669783	+	0.742557i	$0.266387\pi$
$354$	1.00000	0.0531494
$355$	−1.66869	−0.0885650
$356$	−10.9550	−0.580615
$357$	2.39214	0.126606
$358$	−13.8282	−0.730845
$359$	−25.8153	−1.36248	−0.681239	−	0.732061i	$-0.738559\pi$
$359$	−25.8153	−1.36248	−0.681239	+	0.732061i	$0.738559\pi$
$360$	0.504544	0.0265918
$361$	55.2302	2.90685
$362$	−17.2329	−0.905741
$363$	9.77107	0.512848
$364$	5.95823	0.312296
$365$	8.42816	0.441150
$366$	−2.02440	−0.105817
$367$	−19.5427	−1.02012	−0.510060	−	0.860139i	$-0.670377\pi$
$367$	−19.5427	−1.02012	−0.510060	+	0.860139i	$0.670377\pi$
$368$	−0.297149	−0.0154900
$369$	−4.27848	−0.222729
$370$	−5.83245	−0.303214
$371$	3.45403	0.179324
$372$	−5.69421	−0.295231
$373$	−15.6479	−0.810218	−0.405109	−	0.914268i	$-0.632767\pi$
$373$	−15.6479	−0.810218	−0.405109	+	0.914268i	$0.632767\pi$
$374$	−1.10857	−0.0573228
$375$	4.91700	0.253913
$376$	10.6814	0.550852
$377$	18.5864	0.957247
$378$	−2.39214	−0.123038
$379$	19.6388	1.00878	0.504389	−	0.863477i	$-0.331718\pi$
$379$	19.6388	1.00878	0.504389	+	0.863477i	$0.331718\pi$
$380$	4.34700	0.222996
$381$	−12.7425	−0.652817
$382$	−15.1512	−0.775203
$383$	−27.4639	−1.40334	−0.701669	−	0.712503i	$-0.747562\pi$
$383$	−27.4639	−1.40334	−0.701669	+	0.712503i	$0.747562\pi$
$384$	−1.00000	−0.0510310
$385$	1.33798	0.0681897
$386$	19.2590	0.980259
$387$	0.580112	0.0294887
$388$	−7.46768	−0.379114
$389$	0.794891	0.0403026	0.0201513	−	0.999797i	$-0.493585\pi$
$389$	0.794891	0.0403026	0.0201513	+	0.999797i	$0.493585\pi$
$390$	−1.25670	−0.0636352
$391$	0.297149	0.0150275
$392$	−1.27766	−0.0645316
$393$	6.32230	0.318918
$394$	20.0314	1.00917
$395$	2.54008	0.127805
$396$	1.10857	0.0557077
$397$	34.5396	1.73349	0.866746	−	0.498749i	$-0.166207\pi$
$397$	34.5396	1.73349	0.866746	+	0.498749i	$0.166207\pi$
$398$	16.4279	0.823454
$399$	−20.6100	−1.03179
$400$	−4.74544	−0.237272
$401$	14.5890	0.728540	0.364270	−	0.931293i	$-0.381319\pi$
$401$	14.5890	0.728540	0.364270	+	0.931293i	$0.381319\pi$
$402$	6.76235	0.337276
$403$	14.1829	0.706499
$404$	−11.0160	−0.548066
$405$	0.504544	0.0250710
$406$	17.8505	0.885907
$407$	−12.8149	−0.635210
$408$	1.00000	0.0495074
$409$	−15.2900	−0.756041	−0.378020	−	0.925797i	$-0.623395\pi$
$409$	−15.2900	−0.756041	−0.378020	+	0.925797i	$0.623395\pi$
$410$	−2.15868	−0.106610
$411$	−2.01041	−0.0991663
$412$	0.756325	0.0372615
$413$	−2.39214	−0.117710
$414$	−0.297149	−0.0146041
$415$	−5.61956	−0.275853
$416$	2.49075	0.122119
$417$	−16.0190	−0.784455
$418$	9.55110	0.467160
$419$	−17.9073	−0.874830	−0.437415	−	0.899260i	$-0.644106\pi$
$419$	−17.9073	−0.874830	−0.437415	+	0.899260i	$0.644106\pi$
$420$	−1.20694	−0.0588927
$421$	32.9581	1.60628	0.803139	−	0.595791i	$-0.203161\pi$
$421$	32.9581	1.60628	0.803139	+	0.595791i	$0.203161\pi$
$422$	−18.4141	−0.896384
$423$	10.6814	0.519349
$424$	1.44391	0.0701224
$425$	4.74544	0.230187
$426$	3.30733	0.160240
$427$	4.84265	0.234352
$428$	−11.2590	−0.544225
$429$	−2.76117	−0.133311
$430$	0.292692	0.0141149
$431$	−23.3410	−1.12430	−0.562148	−	0.827037i	$-0.690025\pi$
$431$	−23.3410	−1.12430	−0.562148	+	0.827037i	$0.690025\pi$
$432$	−1.00000	−0.0481125
$433$	0.989051	0.0475308	0.0237654	−	0.999718i	$-0.492435\pi$
$433$	0.989051	0.0475308	0.0237654	+	0.999718i	$0.492435\pi$
$434$	13.6214	0.653846
$435$	−3.76499	−0.180517
$436$	16.4184	0.786297
$437$	−2.56015	−0.122469
$438$	−16.7045	−0.798172
$439$	12.8751	0.614493	0.307247	−	0.951630i	$-0.400592\pi$
$439$	12.8751	0.614493	0.307247	+	0.951630i	$0.400592\pi$
$440$	0.559322	0.0266647
$441$	−1.27766	−0.0608410
$442$	−2.49075	−0.118473
$443$	5.89332	0.280000	0.140000	−	0.990151i	$-0.455290\pi$
$443$	5.89332	0.280000	0.140000	+	0.990151i	$0.455290\pi$
$444$	11.5598	0.548605
$445$	−5.52729	−0.262019
$446$	18.3528	0.869031
$447$	−4.02796	−0.190516
$448$	2.39214	0.113018
$449$	−38.4053	−1.81246	−0.906229	−	0.422786i	$-0.861052\pi$
$449$	−38.4053	−1.81246	−0.906229	+	0.422786i	$0.861052\pi$
$450$	−4.74544	−0.223702
$451$	−4.74300	−0.223339
$452$	3.44593	0.162083
$453$	3.76173	0.176742
$454$	−10.3618	−0.486302
$455$	3.00619	0.140932
$456$	−8.61570	−0.403467
$457$	17.1916	0.804188	0.402094	−	0.915598i	$-0.368282\pi$
$457$	17.1916	0.804188	0.402094	+	0.915598i	$0.368282\pi$
$458$	14.7633	0.689843
$459$	1.00000	0.0466760
$460$	−0.149925	−0.00699029
$461$	−6.69144	−0.311651	−0.155826	−	0.987785i	$-0.549804\pi$
$461$	−6.69144	−0.311651	−0.155826	+	0.987785i	$0.549804\pi$
$462$	−2.65185	−0.123375
$463$	15.1088	0.702167	0.351083	−	0.936344i	$-0.385813\pi$
$463$	15.1088	0.702167	0.351083	+	0.936344i	$0.385813\pi$
$464$	7.46215	0.346422
$465$	−2.87298	−0.133231
$466$	9.14378	0.423577
$467$	12.6074	0.583400	0.291700	−	0.956510i	$-0.405779\pi$
$467$	12.6074	0.583400	0.291700	+	0.956510i	$0.405779\pi$
$468$	2.49075	0.115135
$469$	−16.1765	−0.746962
$470$	5.38925	0.248588
$471$	−0.703406	−0.0324113
$472$	−1.00000	−0.0460287
$473$	0.643094	0.0295695
$474$	−5.03441	−0.231238
$475$	−40.8852	−1.87594
$476$	−2.39214	−0.109644
$477$	1.44391	0.0661120
$478$	−18.7515	−0.857672
$479$	−25.2284	−1.15272	−0.576358	−	0.817198i	$-0.695526\pi$
$479$	−25.2284	−1.15272	−0.576358	+	0.817198i	$0.695526\pi$
$480$	−0.504544	−0.0230292
$481$	−28.7927	−1.31283
$482$	−26.0481	−1.18646
$483$	0.710823	0.0323436
$484$	−9.77107	−0.444140
$485$	−3.76778	−0.171086
$486$	−1.00000	−0.0453609
$487$	28.3456	1.28446	0.642231	−	0.766511i	$-0.278009\pi$
$487$	28.3456	1.28446	0.642231	+	0.766511i	$0.278009\pi$
$488$	2.02440	0.0916402
$489$	−7.07001	−0.319717
$490$	−0.644637	−0.0291217
$491$	11.1301	0.502293	0.251147	−	0.967949i	$-0.419192\pi$
$491$	11.1301	0.502293	0.251147	+	0.967949i	$0.419192\pi$
$492$	4.27848	0.192889
$493$	−7.46215	−0.336078
$494$	21.4596	0.965512
$495$	0.559322	0.0251397
$496$	5.69421	0.255678
$497$	−7.91159	−0.354883
$498$	11.1379	0.499101
$499$	2.70729	0.121195	0.0605975	−	0.998162i	$-0.480699\pi$
$499$	2.70729	0.121195	0.0605975	+	0.998162i	$0.480699\pi$
$500$	−4.91700	−0.219895
$501$	−14.6374	−0.653952
$502$	13.1829	0.588382
$503$	30.5328	1.36139	0.680695	−	0.732567i	$-0.261678\pi$
$503$	30.5328	1.36139	0.680695	+	0.732567i	$0.261678\pi$
$504$	2.39214	0.106554
$505$	−5.55806	−0.247330
$506$	−0.329411	−0.0146441
$507$	6.79615	0.301828
$508$	12.7425	0.565357
$509$	5.62596	0.249366	0.124683	−	0.992197i	$-0.460209\pi$
$509$	5.62596	0.249366	0.124683	+	0.992197i	$0.460209\pi$
$510$	0.504544	0.0223416
$511$	39.9595	1.76771
$512$	1.00000	0.0441942
$513$	−8.61570	−0.380392
$514$	7.11818	0.313969
$515$	0.381600	0.0168153
$516$	−0.580112	−0.0255380
$517$	11.8411	0.520771
$518$	−27.6527	−1.21499
$519$	−14.1671	−0.621869
$520$	1.25670	0.0551097
$521$	1.66052	0.0727486	0.0363743	−	0.999338i	$-0.488419\pi$
$521$	1.66052	0.0727486	0.0363743	+	0.999338i	$0.488419\pi$
$522$	7.46215	0.326610
$523$	−20.2227	−0.884279	−0.442139	−	0.896946i	$-0.645780\pi$
$523$	−20.2227	−0.884279	−0.442139	+	0.896946i	$0.645780\pi$
$524$	−6.32230	−0.276191
$525$	11.3518	0.495431
$526$	−1.95363	−0.0851822
$527$	−5.69421	−0.248044
$528$	−1.10857	−0.0482443
$529$	−22.9117	−0.996161
$530$	0.728516	0.0316447
$531$	−1.00000	−0.0433963
$532$	20.6100	0.893555
$533$	−10.6566	−0.461591
$534$	10.9550	0.474070
$535$	−5.68068	−0.245597
$536$	−6.76235	−0.292089
$537$	13.8282	0.596733
$538$	−16.9311	−0.729953
$539$	−1.41638	−0.0610076
$540$	−0.504544	−0.0217121
$541$	−8.72783	−0.375239	−0.187619	−	0.982242i	$-0.560077\pi$
$541$	−8.72783	−0.375239	−0.187619	+	0.982242i	$0.560077\pi$
$542$	3.34033	0.143479
$543$	17.2329	0.739534
$544$	−1.00000	−0.0428746
$545$	8.28380	0.354839
$546$	−5.95823	−0.254989
$547$	−25.2236	−1.07848	−0.539241	−	0.842152i	$-0.681289\pi$
$547$	−25.2236	−1.07848	−0.539241	+	0.842152i	$0.681289\pi$
$548$	2.01041	0.0858805
$549$	2.02440	0.0863992
$550$	−5.26064	−0.224315
$551$	64.2917	2.73892
$552$	0.297149	0.0126475
$553$	12.0430	0.512121
$554$	5.13891	0.218331
$555$	5.83245	0.247574
$556$	16.0190	0.679358
$557$	33.2320	1.40809	0.704043	−	0.710158i	$-0.251376\pi$
$557$	33.2320	1.40809	0.704043	+	0.710158i	$0.251376\pi$
$558$	5.69421	0.241055
$559$	1.44492	0.0611134
$560$	1.20694	0.0510026
$561$	1.10857	0.0468038
$562$	22.1434	0.934062
$563$	−23.5533	−0.992652	−0.496326	−	0.868136i	$-0.665318\pi$
$563$	−23.5533	−0.992652	−0.496326	+	0.868136i	$0.665318\pi$
$564$	−10.6814	−0.449769
$565$	1.73862	0.0731445
$566$	−0.0742288	−0.00312007
$567$	2.39214	0.100460
$568$	−3.30733	−0.138772
$569$	10.5300	0.441440	0.220720	−	0.975337i	$-0.429159\pi$
$569$	10.5300	0.441440	0.220720	+	0.975337i	$0.429159\pi$
$570$	−4.34700	−0.182076
$571$	2.09884	0.0878339	0.0439169	−	0.999035i	$-0.486016\pi$
$571$	2.09884	0.0878339	0.0439169	+	0.999035i	$0.486016\pi$
$572$	2.76117	0.115450
$573$	15.1512	0.632950
$574$	−10.2347	−0.427190
$575$	1.41010	0.0588054
$576$	1.00000	0.0416667
$577$	−10.9289	−0.454974	−0.227487	−	0.973781i	$-0.573051\pi$
$577$	−10.9289	−0.454974	−0.227487	+	0.973781i	$0.573051\pi$
$578$	1.00000	0.0415945
$579$	−19.2590	−0.800378
$580$	3.76499	0.156333
$581$	−26.6434	−1.10535
$582$	7.46768	0.309545
$583$	1.60067	0.0662931
$584$	16.7045	0.691237
$585$	1.25670	0.0519579
$586$	20.8035	0.859384
$587$	−39.4414	−1.62792	−0.813961	−	0.580920i	$-0.802693\pi$
$587$	−39.4414	−1.62792	−0.813961	+	0.580920i	$0.802693\pi$
$588$	1.27766	0.0526899
$589$	49.0596	2.02147
$590$	−0.504544	−0.0207718
$591$	−20.0314	−0.823981
$592$	−11.5598	−0.475106
$593$	−12.9734	−0.532753	−0.266376	−	0.963869i	$-0.585826\pi$
$593$	−12.9734	−0.532753	−0.266376	+	0.963869i	$0.585826\pi$
$594$	−1.10857	−0.0454852
$595$	−1.20694	−0.0494798
$596$	4.02796	0.164992
$597$	−16.4279	−0.672347
$598$	−0.740126	−0.0302660
$599$	−20.4463	−0.835412	−0.417706	−	0.908582i	$-0.637166\pi$
$599$	−20.4463	−0.835412	−0.417706	+	0.908582i	$0.637166\pi$
$600$	4.74544	0.193732
$601$	−23.0064	−0.938451	−0.469225	−	0.883078i	$-0.655467\pi$
$601$	−23.0064	−0.938451	−0.469225	+	0.883078i	$0.655467\pi$
$602$	1.38771	0.0565588
$603$	−6.76235	−0.275384
$604$	−3.76173	−0.153063
$605$	−4.92994	−0.200431
$606$	11.0160	0.447494
$607$	30.4276	1.23502	0.617508	−	0.786564i	$-0.288142\pi$
$607$	30.4276	1.23502	0.617508	+	0.786564i	$0.288142\pi$
$608$	8.61570	0.349413
$609$	−17.8505	−0.723340
$610$	1.02140	0.0413552
$611$	26.6048	1.07631
$612$	−1.00000	−0.0404226
$613$	1.10836	0.0447663	0.0223831	−	0.999749i	$-0.492875\pi$
$613$	1.10836	0.0447663	0.0223831	+	0.999749i	$0.492875\pi$
$614$	−1.86618	−0.0753129
$615$	2.15868	0.0870466
$616$	2.65185	0.106846
$617$	9.67515	0.389507	0.194753	−	0.980852i	$-0.437609\pi$
$617$	9.67515	0.389507	0.194753	+	0.980852i	$0.437609\pi$
$618$	−0.756325	−0.0304239
$619$	−3.57748	−0.143791	−0.0718956	−	0.997412i	$-0.522905\pi$
$619$	−3.57748	−0.143791	−0.0718956	+	0.997412i	$0.522905\pi$
$620$	2.87298	0.115382
$621$	0.297149	0.0119242
$622$	7.60542	0.304950
$623$	−26.2060	−1.04992
$624$	−2.49075	−0.0997099
$625$	21.2463	0.849853
$626$	−13.4270	−0.536650
$627$	−9.55110	−0.381434
$628$	0.703406	0.0280690
$629$	11.5598	0.460921
$630$	1.20694	0.0480857
$631$	−5.60227	−0.223023	−0.111511	−	0.993763i	$-0.535569\pi$
$631$	−5.60227	−0.223023	−0.111511	+	0.993763i	$0.535569\pi$
$632$	5.03441	0.200258
$633$	18.4141	0.731894
$634$	−5.58422	−0.221778
$635$	6.42915	0.255133
$636$	−1.44391	−0.0572547
$637$	−3.18234	−0.126089
$638$	8.27232	0.327504
$639$	−3.30733	−0.130836
$640$	0.504544	0.0199439
$641$	−21.3042	−0.841464	−0.420732	−	0.907185i	$-0.638227\pi$
$641$	−21.3042	−0.841464	−0.420732	+	0.907185i	$0.638227\pi$
$642$	11.2590	0.444358
$643$	31.4256	1.23930	0.619652	−	0.784877i	$-0.287274\pi$
$643$	31.4256	1.23930	0.619652	+	0.784877i	$0.287274\pi$
$644$	−0.710823	−0.0280104
$645$	−0.292692	−0.0115247
$646$	−8.61570	−0.338980
$647$	13.6932	0.538336	0.269168	−	0.963093i	$-0.413251\pi$
$647$	13.6932	0.538336	0.269168	+	0.963093i	$0.413251\pi$
$648$	1.00000	0.0392837
$649$	−1.10857	−0.0435152
$650$	−11.8197	−0.463607
$651$	−13.6214	−0.533863
$652$	7.07001	0.276883
$653$	3.21180	0.125687	0.0628437	−	0.998023i	$-0.479983\pi$
$653$	3.21180	0.125687	0.0628437	+	0.998023i	$0.479983\pi$
$654$	−16.4184	−0.642009
$655$	−3.18988	−0.124639
$656$	−4.27848	−0.167047
$657$	16.7045	0.651705
$658$	25.5515	0.996100
$659$	−30.5900	−1.19162	−0.595809	−	0.803126i	$-0.703168\pi$
$659$	−30.5900	−1.19162	−0.595809	+	0.803126i	$0.703168\pi$
$660$	−0.559322	−0.0217716
$661$	−35.0348	−1.36270	−0.681348	−	0.731959i	$-0.738606\pi$
$661$	−35.0348	−1.36270	−0.681348	+	0.731959i	$0.738606\pi$
$662$	−8.47838	−0.329522
$663$	2.49075	0.0967328
$664$	−11.1379	−0.432234
$665$	10.3986	0.403242
$666$	−11.5598	−0.447934
$667$	−2.21737	−0.0858571
$668$	14.6374	0.566339
$669$	−18.3528	−0.709561
$670$	−3.41191	−0.131813
$671$	2.24419	0.0866358
$672$	−2.39214	−0.0922788
$673$	38.1022	1.46873	0.734365	−	0.678755i	$-0.237480\pi$
$673$	38.1022	1.46873	0.734365	+	0.678755i	$0.237480\pi$
$674$	−14.0945	−0.542902
$675$	4.74544	0.182652
$676$	−6.79615	−0.261390
$677$	−12.6958	−0.487938	−0.243969	−	0.969783i	$-0.578449\pi$
$677$	−12.6958	−0.487938	−0.243969	+	0.969783i	$0.578449\pi$
$678$	−3.44593	−0.132340
$679$	−17.8638	−0.685548
$680$	−0.504544	−0.0193484
$681$	10.3618	0.397064
$682$	6.31243	0.241715
$683$	10.2184	0.390994	0.195497	−	0.980704i	$-0.437368\pi$
$683$	10.2184	0.390994	0.195497	+	0.980704i	$0.437368\pi$
$684$	8.61570	0.329429
$685$	1.01434	0.0387560
$686$	−19.8013	−0.756018
$687$	−14.7633	−0.563255
$688$	0.580112	0.0221166
$689$	3.59642	0.137013
$690$	0.149925	0.00570755
$691$	25.0757	0.953923	0.476962	−	0.878924i	$-0.341738\pi$
$691$	25.0757	0.953923	0.476962	+	0.878924i	$0.341738\pi$
$692$	14.1671	0.538554
$693$	2.65185	0.100736
$694$	1.41517	0.0537190
$695$	8.08230	0.306579
$696$	−7.46215	−0.282852
$697$	4.27848	0.162059
$698$	28.2991	1.07114
$699$	−9.14378	−0.345849
$700$	−11.3518	−0.429056
$701$	−38.8909	−1.46889	−0.734445	−	0.678668i	$-0.762557\pi$
$701$	−38.8909	−1.46889	−0.734445	+	0.678668i	$0.762557\pi$
$702$	−2.49075	−0.0940074
$703$	−99.5960	−3.75633
$704$	1.10857	0.0417808
$705$	−5.38925	−0.202971
$706$	25.1682	0.947216
$707$	−26.3518	−0.991062
$708$	1.00000	0.0375823
$709$	−10.1284	−0.380381	−0.190190	−	0.981747i	$-0.560911\pi$
$709$	−10.1284	−0.380381	−0.190190	+	0.981747i	$0.560911\pi$
$710$	−1.66869	−0.0626249
$711$	5.03441	0.188805
$712$	−10.9550	−0.410557
$713$	−1.69203	−0.0633671
$714$	2.39214	0.0895236
$715$	1.39313	0.0521003
$716$	−13.8282	−0.516786
$717$	18.7515	0.700287
$718$	−25.8153	−0.963418
$719$	−11.7671	−0.438839	−0.219420	−	0.975631i	$-0.570416\pi$
$719$	−11.7671	−0.438839	−0.219420	+	0.975631i	$0.570416\pi$
$720$	0.504544	0.0188033
$721$	1.80924	0.0673795
$722$	55.2302	2.05546
$723$	26.0481	0.968740
$724$	−17.2329	−0.640456
$725$	−35.4112	−1.31514
$726$	9.77107	0.362639
$727$	13.9324	0.516723	0.258362	−	0.966048i	$-0.416817\pi$
$727$	13.9324	0.516723	0.258362	+	0.966048i	$0.416817\pi$
$728$	5.95823	0.220827
$729$	1.00000	0.0370370
$730$	8.42816	0.311940
$731$	−0.580112	−0.0214562
$732$	−2.02440	−0.0748239
$733$	−16.1110	−0.595072	−0.297536	−	0.954711i	$-0.596165\pi$
$733$	−16.1110	−0.595072	−0.297536	+	0.954711i	$0.596165\pi$
$734$	−19.5427	−0.721333
$735$	0.644637	0.0237778
$736$	−0.297149	−0.0109531
$737$	−7.49654	−0.276139
$738$	−4.27848	−0.157493
$739$	−42.0875	−1.54822	−0.774108	−	0.633054i	$-0.781801\pi$
$739$	−42.0875	−1.54822	−0.774108	+	0.633054i	$0.781801\pi$
$740$	−5.83245	−0.214405
$741$	−21.4596	−0.788337
$742$	3.45403	0.126801
$743$	−24.5756	−0.901592	−0.450796	−	0.892627i	$-0.648860\pi$
$743$	−24.5756	−0.901592	−0.450796	+	0.892627i	$0.648860\pi$
$744$	−5.69421	−0.208760
$745$	2.03228	0.0744571
$746$	−15.6479	−0.572911
$747$	−11.1379	−0.407514
$748$	−1.10857	−0.0405333
$749$	−26.9332	−0.984117
$750$	4.91700	0.179544
$751$	0.617599	0.0225365	0.0112683	−	0.999937i	$-0.496413\pi$
$751$	0.617599	0.0225365	0.0112683	+	0.999937i	$0.496413\pi$
$752$	10.6814	0.389511
$753$	−13.1829	−0.480412
$754$	18.5864	0.676876
$755$	−1.89796	−0.0690738
$756$	−2.39214	−0.0870013
$757$	−14.9892	−0.544791	−0.272396	−	0.962185i	$-0.587816\pi$
$757$	−14.9892	−0.544791	−0.272396	+	0.962185i	$0.587816\pi$
$758$	19.6388	0.713314
$759$	0.329411	0.0119569
$760$	4.34700	0.157682
$761$	1.22757	0.0444993	0.0222496	−	0.999752i	$-0.492917\pi$
$761$	1.22757	0.0444993	0.0222496	+	0.999752i	$0.492917\pi$
$762$	−12.7425	−0.461612
$763$	39.2751	1.42185
$764$	−15.1512	−0.548151
$765$	−0.504544	−0.0182418
$766$	−27.4639	−0.992310
$767$	−2.49075	−0.0899359
$768$	−1.00000	−0.0360844
$769$	−33.5426	−1.20958	−0.604789	−	0.796386i	$-0.706743\pi$
$769$	−33.5426	−1.20958	−0.604789	+	0.796386i	$0.706743\pi$
$770$	1.33798	0.0482174
$771$	−7.11818	−0.256355
$772$	19.2590	0.693148
$773$	−14.5190	−0.522211	−0.261105	−	0.965310i	$-0.584087\pi$
$773$	−14.5190	−0.522211	−0.261105	+	0.965310i	$0.584087\pi$
$774$	0.580112	0.0208517
$775$	−27.0215	−0.970641
$776$	−7.46768	−0.268074
$777$	27.6527	0.992037
$778$	0.794891	0.0284982
$779$	−36.8621	−1.32072
$780$	−1.25670	−0.0449969
$781$	−3.66640	−0.131194
$782$	0.297149	0.0106260
$783$	−7.46215	−0.266676
$784$	−1.27766	−0.0456308
$785$	0.354900	0.0126669
$786$	6.32230	0.225509
$787$	−35.0506	−1.24942	−0.624709	−	0.780857i	$-0.714783\pi$
$787$	−35.0506	−1.24942	−0.624709	+	0.780857i	$0.714783\pi$
$788$	20.0314	0.713589
$789$	1.95363	0.0695510
$790$	2.54008	0.0903720
$791$	8.24315	0.293093
$792$	1.10857	0.0393913
$793$	5.04227	0.179056
$794$	34.5396	1.22576
$795$	−0.728516	−0.0258378
$796$	16.4279	0.582270
$797$	−12.7732	−0.452449	−0.226224	−	0.974075i	$-0.572638\pi$
$797$	−12.7732	−0.452449	−0.226224	+	0.974075i	$0.572638\pi$
$798$	−20.6100	−0.729585
$799$	−10.6814	−0.377882
$800$	−4.74544	−0.167776
$801$	−10.9550	−0.387077
$802$	14.5890	0.515155
$803$	18.5181	0.653490
$804$	6.76235	0.238490
$805$	−0.358642	−0.0126405
$806$	14.1829	0.499570
$807$	16.9311	0.596004
$808$	−11.0160	−0.387541
$809$	28.0387	0.985789	0.492894	−	0.870089i	$-0.335939\pi$
$809$	28.0387	0.985789	0.492894	+	0.870089i	$0.335939\pi$
$810$	0.504544	0.0177279
$811$	20.2701	0.711780	0.355890	−	0.934528i	$-0.384178\pi$
$811$	20.2701	0.711780	0.355890	+	0.934528i	$0.384178\pi$
$812$	17.8505	0.626431
$813$	−3.34033	−0.117150
$814$	−12.8149	−0.449161
$815$	3.56713	0.124951
$816$	1.00000	0.0350070
$817$	4.99807	0.174860
$818$	−15.2900	−0.534602
$819$	5.95823	0.208197
$820$	−2.15868	−0.0753845
$821$	−41.4149	−1.44539	−0.722694	−	0.691168i	$-0.757097\pi$
$821$	−41.4149	−1.44539	−0.722694	+	0.691168i	$0.757097\pi$
$822$	−2.01041	−0.0701212
$823$	3.06872	0.106969	0.0534844	−	0.998569i	$-0.482967\pi$
$823$	3.06872	0.106969	0.0534844	+	0.998569i	$0.482967\pi$
$824$	0.756325	0.0263478
$825$	5.26064	0.183152
$826$	−2.39214	−0.0832332
$827$	−23.2288	−0.807746	−0.403873	−	0.914815i	$-0.632336\pi$
$827$	−23.2288	−0.807746	−0.403873	+	0.914815i	$0.632336\pi$
$828$	−0.297149	−0.0103267
$829$	−34.8779	−1.21136	−0.605680	−	0.795709i	$-0.707099\pi$
$829$	−34.8779	−1.21136	−0.605680	+	0.795709i	$0.707099\pi$
$830$	−5.61956	−0.195058
$831$	−5.13891	−0.178267
$832$	2.49075	0.0863513
$833$	1.27766	0.0442683
$834$	−16.0190	−0.554693
$835$	7.38523	0.255576
$836$	9.55110	0.330332
$837$	−5.69421	−0.196821
$838$	−17.9073	−0.618598
$839$	10.4365	0.360309	0.180155	−	0.983638i	$-0.442340\pi$
$839$	10.4365	0.360309	0.180155	+	0.983638i	$0.442340\pi$
$840$	−1.20694	−0.0416434
$841$	26.6837	0.920129
$842$	32.9581	1.13581
$843$	−22.1434	−0.762658
$844$	−18.4141	−0.633839
$845$	−3.42896	−0.117960
$846$	10.6814	0.367235
$847$	−23.3738	−0.803133
$848$	1.44391	0.0495840
$849$	0.0742288	0.00254753
$850$	4.74544	0.162767
$851$	3.43500	0.117750
$852$	3.30733	0.113307
$853$	−21.1065	−0.722673	−0.361337	−	0.932435i	$-0.617679\pi$
$853$	−21.1065	−0.722673	−0.361337	+	0.932435i	$0.617679\pi$
$854$	4.84265	0.165712
$855$	4.34700	0.148664
$856$	−11.2590	−0.384825
$857$	−5.23109	−0.178690	−0.0893452	−	0.996001i	$-0.528477\pi$
$857$	−5.23109	−0.178690	−0.0893452	+	0.996001i	$0.528477\pi$
$858$	−2.76117	−0.0942649
$859$	15.2586	0.520617	0.260309	−	0.965525i	$-0.416176\pi$
$859$	15.2586	0.520617	0.260309	+	0.965525i	$0.416176\pi$
$860$	0.292692	0.00998072
$861$	10.2347	0.348799
$862$	−23.3410	−0.794997
$863$	−49.1199	−1.67206	−0.836030	−	0.548684i	$-0.815129\pi$
$863$	−49.1199	−1.67206	−0.836030	+	0.548684i	$0.815129\pi$
$864$	−1.00000	−0.0340207
$865$	7.14795	0.243038
$866$	0.989051	0.0336093
$867$	−1.00000	−0.0339618
$868$	13.6214	0.462339
$869$	5.58099	0.189322
$870$	−3.76499	−0.127645
$871$	−16.8434	−0.570715
$872$	16.4184	0.555996
$873$	−7.46768	−0.252743
$874$	−2.56015	−0.0865983
$875$	−11.7622	−0.397634
$876$	−16.7045	−0.564393
$877$	30.5044	1.03006	0.515030	−	0.857172i	$-0.327781\pi$
$877$	30.5044	1.03006	0.515030	+	0.857172i	$0.327781\pi$
$878$	12.8751	0.434512
$879$	−20.8035	−0.701684
$880$	0.559322	0.0188548
$881$	−56.2584	−1.89539	−0.947697	−	0.319170i	$-0.896596\pi$
$881$	−56.2584	−1.89539	−0.947697	+	0.319170i	$0.896596\pi$
$882$	−1.27766	−0.0430211
$883$	−33.7703	−1.13646	−0.568230	−	0.822870i	$-0.692372\pi$
$883$	−33.7703	−1.13646	−0.568230	+	0.822870i	$0.692372\pi$
$884$	−2.49075	−0.0837731
$885$	0.504544	0.0169601
$886$	5.89332	0.197990
$887$	37.2395	1.25038	0.625191	−	0.780472i	$-0.285021\pi$
$887$	37.2395	1.25038	0.625191	+	0.780472i	$0.285021\pi$
$888$	11.5598	0.387923
$889$	30.4818	1.02233
$890$	−5.52729	−0.185275
$891$	1.10857	0.0371385
$892$	18.3528	0.614497
$893$	92.0279	3.07960
$894$	−4.02796	−0.134715
$895$	−6.97696	−0.233214
$896$	2.39214	0.0799158
$897$	0.740126	0.0247121
$898$	−38.4053	−1.28160
$899$	42.4911	1.41716
$900$	−4.74544	−0.158181
$901$	−1.44391	−0.0481036
$902$	−4.74300	−0.157925
$903$	−1.38771	−0.0461801
$904$	3.44593	0.114610
$905$	−8.69476	−0.289024
$906$	3.76173	0.124975
$907$	16.4577	0.546470	0.273235	−	0.961947i	$-0.411906\pi$
$907$	16.4577	0.546470	0.273235	+	0.961947i	$0.411906\pi$
$908$	−10.3618	−0.343867
$909$	−11.0160	−0.365377
$910$	3.00619	0.0996543
$911$	13.8845	0.460014	0.230007	−	0.973189i	$-0.426125\pi$
$911$	13.8845	0.460014	0.230007	+	0.973189i	$0.426125\pi$
$912$	−8.61570	−0.285294
$913$	−12.3471	−0.408630
$914$	17.1916	0.568647
$915$	−1.02140	−0.0337664
$916$	14.7633	0.487793
$917$	−15.1238	−0.499433
$918$	1.00000	0.0330049
$919$	−35.6337	−1.17545	−0.587724	−	0.809062i	$-0.699976\pi$
$919$	−35.6337	−1.17545	−0.587724	+	0.809062i	$0.699976\pi$
$920$	−0.149925	−0.00494288
$921$	1.86618	0.0614928
$922$	−6.69144	−0.220371
$923$	−8.23773	−0.271148
$924$	−2.65185	−0.0872396
$925$	54.8564	1.80367
$926$	15.1088	0.496507
$927$	0.756325	0.0248410
$928$	7.46215	0.244957
$929$	35.2337	1.15598	0.577990	−	0.816044i	$-0.303837\pi$
$929$	35.2337	1.15598	0.577990	+	0.816044i	$0.303837\pi$
$930$	−2.87298	−0.0942088
$931$	−11.0079	−0.360771
$932$	9.14378	0.299514
$933$	−7.60542	−0.248990
$934$	12.6074	0.412526
$935$	−0.559322	−0.0182918
$936$	2.49075	0.0814128
$937$	−44.2551	−1.44575	−0.722875	−	0.690979i	$-0.757180\pi$
$937$	−44.2551	−1.44575	−0.722875	+	0.690979i	$0.757180\pi$
$938$	−16.1765	−0.528182
$939$	13.4270	0.438173
$940$	5.38925	0.175778
$941$	1.66900	0.0544078	0.0272039	−	0.999630i	$-0.491340\pi$
$941$	1.66900	0.0544078	0.0272039	+	0.999630i	$0.491340\pi$
$942$	−0.703406	−0.0229182
$943$	1.27135	0.0414008
$944$	−1.00000	−0.0325472
$945$	−1.20694	−0.0392618
$946$	0.643094	0.0209088
$947$	8.85192	0.287649	0.143824	−	0.989603i	$-0.454060\pi$
$947$	8.85192	0.287649	0.143824	+	0.989603i	$0.454060\pi$
$948$	−5.03441	−0.163510
$949$	41.6068	1.35061
$950$	−40.8852	−1.32649
$951$	5.58422	0.181081
$952$	−2.39214	−0.0775297
$953$	8.56063	0.277306	0.138653	−	0.990341i	$-0.455723\pi$
$953$	8.56063	0.277306	0.138653	+	0.990341i	$0.455723\pi$
$954$	1.44391	0.0467483
$955$	−7.64445	−0.247369
$956$	−18.7515	−0.606466
$957$	−8.27232	−0.267406
$958$	−25.2284	−0.815093
$959$	4.80919	0.155297
$960$	−0.504544	−0.0162841
$961$	1.42405	0.0459372
$962$	−28.7927	−0.928313
$963$	−11.2590	−0.362817
$964$	−26.0481	−0.838954
$965$	9.71704	0.312802
$966$	0.710823	0.0228704
$967$	−3.10825	−0.0999544	−0.0499772	−	0.998750i	$-0.515915\pi$
$967$	−3.10825	−0.0999544	−0.0499772	+	0.998750i	$0.515915\pi$
$968$	−9.77107	−0.314054
$969$	8.61570	0.276776
$970$	−3.76778	−0.120976
$971$	−15.1937	−0.487589	−0.243794	−	0.969827i	$-0.578392\pi$
$971$	−15.1937	−0.487589	−0.243794	+	0.969827i	$0.578392\pi$
$972$	−1.00000	−0.0320750
$973$	38.3197	1.22847
$974$	28.3456	0.908252
$975$	11.8197	0.378534
$976$	2.02440	0.0647994
$977$	−51.2713	−1.64031	−0.820157	−	0.572138i	$-0.806114\pi$
$977$	−51.2713	−1.64031	−0.820157	+	0.572138i	$0.806114\pi$
$978$	−7.07001	−0.226074
$979$	−12.1444	−0.388137
$980$	−0.644637	−0.0205922
$981$	16.4184	0.524198
$982$	11.1301	0.355175
$983$	−51.6796	−1.64832	−0.824161	−	0.566356i	$-0.808353\pi$
$983$	−51.6796	−1.64832	−0.824161	+	0.566356i	$0.808353\pi$
$984$	4.27848	0.136393
$985$	10.1067	0.322027
$986$	−7.46215	−0.237643
$987$	−25.5515	−0.813312
$988$	21.4596	0.682720
$989$	−0.172380	−0.00548136
$990$	0.559322	0.0177764
$991$	31.3000	0.994278	0.497139	−	0.867671i	$-0.334384\pi$
$991$	31.3000	0.994278	0.497139	+	0.867671i	$0.334384\pi$
$992$	5.69421	0.180791
$993$	8.47838	0.269053
$994$	−7.91159	−0.250940
$995$	8.28858	0.262766
$996$	11.1379	0.352918
$997$	35.0239	1.10922	0.554609	−	0.832111i	$-0.312868\pi$
$997$	35.0239	1.10922	0.554609	+	0.832111i	$0.312868\pi$
$998$	2.70729	0.0856978
$999$	11.5598	0.365737

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.z.1.6	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.z.1.6	✓	11	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:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.504544 q^{5} -1.00000 q^{6} +2.39214 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.504544 q^{5} -1.00000 q^{6} +2.39214 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.504544 q^{10} +1.10857 q^{11} -1.00000 q^{12} +2.49075 q^{13} +2.39214 q^{14} -0.504544 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +8.61570 q^{19} +0.504544 q^{20} -2.39214 q^{21} +1.10857 q^{22} -0.297149 q^{23} -1.00000 q^{24} -4.74544 q^{25} +2.49075 q^{26} -1.00000 q^{27} +2.39214 q^{28} +7.46215 q^{29} -0.504544 q^{30} +5.69421 q^{31} +1.00000 q^{32} -1.10857 q^{33} -1.00000 q^{34} +1.20694 q^{35} +1.00000 q^{36} -11.5598 q^{37} +8.61570 q^{38} -2.49075 q^{39} +0.504544 q^{40} -4.27848 q^{41} -2.39214 q^{42} +0.580112 q^{43} +1.10857 q^{44} +0.504544 q^{45} -0.297149 q^{46} +10.6814 q^{47} -1.00000 q^{48} -1.27766 q^{49} -4.74544 q^{50} +1.00000 q^{51} +2.49075 q^{52} +1.44391 q^{53} -1.00000 q^{54} +0.559322 q^{55} +2.39214 q^{56} -8.61570 q^{57} +7.46215 q^{58} -1.00000 q^{59} -0.504544 q^{60} +2.02440 q^{61} +5.69421 q^{62} +2.39214 q^{63} +1.00000 q^{64} +1.25670 q^{65} -1.10857 q^{66} -6.76235 q^{67} -1.00000 q^{68} +0.297149 q^{69} +1.20694 q^{70} -3.30733 q^{71} +1.00000 q^{72} +16.7045 q^{73} -11.5598 q^{74} +4.74544 q^{75} +8.61570 q^{76} +2.65185 q^{77} -2.49075 q^{78} +5.03441 q^{79} +0.504544 q^{80} +1.00000 q^{81} -4.27848 q^{82} -11.1379 q^{83} -2.39214 q^{84} -0.504544 q^{85} +0.580112 q^{86} -7.46215 q^{87} +1.10857 q^{88} -10.9550 q^{89} +0.504544 q^{90} +5.95823 q^{91} -0.297149 q^{92} -5.69421 q^{93} +10.6814 q^{94} +4.34700 q^{95} -1.00000 q^{96} -7.46768 q^{97} -1.27766 q^{98} +1.10857 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 3 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 3 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 3 q^{7} + 11 q^{8} + 11 q^{9} + 4 q^{10} + 9 q^{11} - 11 q^{12} + 6 q^{13} + 3 q^{14} - 4 q^{15} + 11 q^{16} - 11 q^{17} + 11 q^{18} - q^{19} + 4 q^{20} - 3 q^{21} + 9 q^{22} + 10 q^{23} - 11 q^{24} + 15 q^{25} + 6 q^{26} - 11 q^{27} + 3 q^{28} + 14 q^{29} - 4 q^{30} + 17 q^{31} + 11 q^{32} - 9 q^{33} - 11 q^{34} + 8 q^{35} + 11 q^{36} + 30 q^{37} - q^{38} - 6 q^{39} + 4 q^{40} + 10 q^{41} - 3 q^{42} + 11 q^{43} + 9 q^{44} + 4 q^{45} + 10 q^{46} - 6 q^{47} - 11 q^{48} + 18 q^{49} + 15 q^{50} + 11 q^{51} + 6 q^{52} + 10 q^{53} - 11 q^{54} - 11 q^{55} + 3 q^{56} + q^{57} + 14 q^{58} - 11 q^{59} - 4 q^{60} + 13 q^{61} + 17 q^{62} + 3 q^{63} + 11 q^{64} + 32 q^{65} - 9 q^{66} + 26 q^{67} - 11 q^{68} - 10 q^{69} + 8 q^{70} + 14 q^{71} + 11 q^{72} + 20 q^{73} + 30 q^{74} - 15 q^{75} - q^{76} + 26 q^{77} - 6 q^{78} + 15 q^{79} + 4 q^{80} + 11 q^{81} + 10 q^{82} + 2 q^{83} - 3 q^{84} - 4 q^{85} + 11 q^{86} - 14 q^{87} + 9 q^{88} + q^{89} + 4 q^{90} + 17 q^{91} + 10 q^{92} - 17 q^{93} - 6 q^{94} + 3 q^{95} - 11 q^{96} + 33 q^{97} + 18 q^{98} + 9 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 3 * q^7 + 11 * q^8 + 11 * q^9 + 4 * q^10 + 9 * q^11 - 11 * q^12 + 6 * q^13 + 3 * q^14 - 4 * q^15 + 11 * q^16 - 11 * q^17 + 11 * q^18 - q^19 + 4 * q^20 - 3 * q^21 + 9 * q^22 + 10 * q^23 - 11 * q^24 + 15 * q^25 + 6 * q^26 - 11 * q^27 + 3 * q^28 + 14 * q^29 - 4 * q^30 + 17 * q^31 + 11 * q^32 - 9 * q^33 - 11 * q^34 + 8 * q^35 + 11 * q^36 + 30 * q^37 - q^38 - 6 * q^39 + 4 * q^40 + 10 * q^41 - 3 * q^42 + 11 * q^43 + 9 * q^44 + 4 * q^45 + 10 * q^46 - 6 * q^47 - 11 * q^48 + 18 * q^49 + 15 * q^50 + 11 * q^51 + 6 * q^52 + 10 * q^53 - 11 * q^54 - 11 * q^55 + 3 * q^56 + q^57 + 14 * q^58 - 11 * q^59 - 4 * q^60 + 13 * q^61 + 17 * q^62 + 3 * q^63 + 11 * q^64 + 32 * q^65 - 9 * q^66 + 26 * q^67 - 11 * q^68 - 10 * q^69 + 8 * q^70 + 14 * q^71 + 11 * q^72 + 20 * q^73 + 30 * q^74 - 15 * q^75 - q^76 + 26 * q^77 - 6 * q^78 + 15 * q^79 + 4 * q^80 + 11 * q^81 + 10 * q^82 + 2 * q^83 - 3 * q^84 - 4 * q^85 + 11 * q^86 - 14 * q^87 + 9 * q^88 + q^89 + 4 * q^90 + 17 * q^91 + 10 * q^92 - 17 * q^93 - 6 * q^94 + 3 * q^95 - 11 * q^96 + 33 * q^97 + 18 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more