LMFDB - Embedded newform 6018.2.a.bb.1.3

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:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 4 x^{12} - 41 x^{11} + 179 x^{10} + 540 x^{9} - 2773 x^{8} - 2260 x^{7} + 17621 x^{6} + \cdots + 128 $ x^13 - 4x^12 - 41x^11 + 179x^10 + 540x^9 - 2773x^8 - 2260x^7 + 17621x^6 - 838x^5 - 44478x^4 + 16472x^3 + 29944x^2 - 6856x + 128
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.41505$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.41505 q^{5} +1.00000 q^{6} +1.11075 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.41505 q^{5} +1.00000 q^{6} +1.11075 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.41505 q^{10} +0.225397 q^{11} +1.00000 q^{12} +4.24122 q^{13} +1.11075 q^{14} -2.41505 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -2.00507 q^{19} -2.41505 q^{20} +1.11075 q^{21} +0.225397 q^{22} +4.30418 q^{23} +1.00000 q^{24} +0.832456 q^{25} +4.24122 q^{26} +1.00000 q^{27} +1.11075 q^{28} -0.556101 q^{29} -2.41505 q^{30} +8.00416 q^{31} +1.00000 q^{32} +0.225397 q^{33} +1.00000 q^{34} -2.68251 q^{35} +1.00000 q^{36} -4.67961 q^{37} -2.00507 q^{38} +4.24122 q^{39} -2.41505 q^{40} -2.49503 q^{41} +1.11075 q^{42} -4.44605 q^{43} +0.225397 q^{44} -2.41505 q^{45} +4.30418 q^{46} +9.35165 q^{47} +1.00000 q^{48} -5.76624 q^{49} +0.832456 q^{50} +1.00000 q^{51} +4.24122 q^{52} +7.05794 q^{53} +1.00000 q^{54} -0.544346 q^{55} +1.11075 q^{56} -2.00507 q^{57} -0.556101 q^{58} -1.00000 q^{59} -2.41505 q^{60} -11.8192 q^{61} +8.00416 q^{62} +1.11075 q^{63} +1.00000 q^{64} -10.2427 q^{65} +0.225397 q^{66} +8.08996 q^{67} +1.00000 q^{68} +4.30418 q^{69} -2.68251 q^{70} +10.9700 q^{71} +1.00000 q^{72} +0.775824 q^{73} -4.67961 q^{74} +0.832456 q^{75} -2.00507 q^{76} +0.250360 q^{77} +4.24122 q^{78} -4.12926 q^{79} -2.41505 q^{80} +1.00000 q^{81} -2.49503 q^{82} +7.37225 q^{83} +1.11075 q^{84} -2.41505 q^{85} -4.44605 q^{86} -0.556101 q^{87} +0.225397 q^{88} +5.90124 q^{89} -2.41505 q^{90} +4.71093 q^{91} +4.30418 q^{92} +8.00416 q^{93} +9.35165 q^{94} +4.84235 q^{95} +1.00000 q^{96} -4.80376 q^{97} -5.76624 q^{98} +0.225397 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 4 * q^5 + 13 * q^6 + 11 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9} + 4 q^{10} + 7 q^{11} + 13 q^{12} + 6 q^{13} + 11 q^{14} + 4 q^{15} + 13 q^{16} + 13 q^{17} + 13 q^{18} + 9 q^{19} + 4 q^{20} + 11 q^{21} + 7 q^{22} + 2 q^{23} + 13 q^{24} + 33 q^{25} + 6 q^{26} + 13 q^{27} + 11 q^{28} + 14 q^{29} + 4 q^{30} - 5 q^{31} + 13 q^{32} + 7 q^{33} + 13 q^{34} + 24 q^{35} + 13 q^{36} + 4 q^{37} + 9 q^{38} + 6 q^{39} + 4 q^{40} + 28 q^{41} + 11 q^{42} + q^{43} + 7 q^{44} + 4 q^{45} + 2 q^{46} + 12 q^{47} + 13 q^{48} + 32 q^{49} + 33 q^{50} + 13 q^{51} + 6 q^{52} + 22 q^{53} + 13 q^{54} - 7 q^{55} + 11 q^{56} + 9 q^{57} + 14 q^{58} - 13 q^{59} + 4 q^{60} - 9 q^{61} - 5 q^{62} + 11 q^{63} + 13 q^{64} + 34 q^{65} + 7 q^{66} + 26 q^{67} + 13 q^{68} + 2 q^{69} + 24 q^{70} + 8 q^{71} + 13 q^{72} + 4 q^{73} + 4 q^{74} + 33 q^{75} + 9 q^{76} + 38 q^{77} + 6 q^{78} - 17 q^{79} + 4 q^{80} + 13 q^{81} + 28 q^{82} + 14 q^{83} + 11 q^{84} + 4 q^{85} + q^{86} + 14 q^{87} + 7 q^{88} + 19 q^{89} + 4 q^{90} - 5 q^{91} + 2 q^{92} - 5 q^{93} + 12 q^{94} + 25 q^{95} + 13 q^{96} - 5 q^{97} + 32 q^{98} + 7 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 4 * q^5 + 13 * q^6 + 11 * q^7 + 13 * q^8 + 13 * q^9 + 4 * q^10 + 7 * q^11 + 13 * q^12 + 6 * q^13 + 11 * q^14 + 4 * q^15 + 13 * q^16 + 13 * q^17 + 13 * q^18 + 9 * q^19 + 4 * q^20 + 11 * q^21 + 7 * q^22 + 2 * q^23 + 13 * q^24 + 33 * q^25 + 6 * q^26 + 13 * q^27 + 11 * q^28 + 14 * q^29 + 4 * q^30 - 5 * q^31 + 13 * q^32 + 7 * q^33 + 13 * q^34 + 24 * q^35 + 13 * q^36 + 4 * q^37 + 9 * q^38 + 6 * q^39 + 4 * q^40 + 28 * q^41 + 11 * q^42 + q^43 + 7 * q^44 + 4 * q^45 + 2 * q^46 + 12 * q^47 + 13 * q^48 + 32 * q^49 + 33 * q^50 + 13 * q^51 + 6 * q^52 + 22 * q^53 + 13 * q^54 - 7 * q^55 + 11 * q^56 + 9 * q^57 + 14 * q^58 - 13 * q^59 + 4 * q^60 - 9 * q^61 - 5 * q^62 + 11 * q^63 + 13 * q^64 + 34 * q^65 + 7 * q^66 + 26 * q^67 + 13 * q^68 + 2 * q^69 + 24 * q^70 + 8 * q^71 + 13 * q^72 + 4 * q^73 + 4 * q^74 + 33 * q^75 + 9 * q^76 + 38 * q^77 + 6 * q^78 - 17 * q^79 + 4 * q^80 + 13 * q^81 + 28 * q^82 + 14 * q^83 + 11 * q^84 + 4 * q^85 + q^86 + 14 * q^87 + 7 * q^88 + 19 * q^89 + 4 * q^90 - 5 * q^91 + 2 * q^92 - 5 * q^93 + 12 * q^94 + 25 * q^95 + 13 * q^96 - 5 * q^97 + 32 * q^98 + 7 * 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
$5$	−2.41505	−1.08004	−0.540021	−	0.841651i	$-0.681584\pi$
$5$	−2.41505	−1.08004	−0.540021	+	0.841651i	$0.681584\pi$
$6$	1.00000	0.408248
$7$	1.11075	0.419823	0.209912	−	0.977720i	$-0.432682\pi$
$7$	1.11075	0.419823	0.209912	+	0.977720i	$0.432682\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.41505	−0.763705
$11$	0.225397	0.0679599	0.0339799	−	0.999423i	$-0.489182\pi$
$11$	0.225397	0.0679599	0.0339799	+	0.999423i	$0.489182\pi$
$12$	1.00000	0.288675
$13$	4.24122	1.17630	0.588151	−	0.808751i	$-0.299856\pi$
$13$	4.24122	1.17630	0.588151	+	0.808751i	$0.299856\pi$
$14$	1.11075	0.296860
$15$	−2.41505	−0.623563
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	−2.00507	−0.459995	−0.229998	−	0.973191i	$-0.573872\pi$
$19$	−2.00507	−0.459995	−0.229998	+	0.973191i	$0.573872\pi$
$20$	−2.41505	−0.540021
$21$	1.11075	0.242385
$22$	0.225397	0.0480549
$23$	4.30418	0.897483	0.448741	−	0.893662i	$-0.351872\pi$
$23$	4.30418	0.897483	0.448741	+	0.893662i	$0.351872\pi$
$24$	1.00000	0.204124
$25$	0.832456	0.166491
$26$	4.24122	0.831771
$27$	1.00000	0.192450
$28$	1.11075	0.209912
$29$	−0.556101	−0.103265	−0.0516327	−	0.998666i	$-0.516443\pi$
$29$	−0.556101	−0.103265	−0.0516327	+	0.998666i	$0.516443\pi$
$30$	−2.41505	−0.440925
$31$	8.00416	1.43759	0.718794	−	0.695223i	$-0.244694\pi$
$31$	8.00416	1.43759	0.718794	+	0.695223i	$0.244694\pi$
$32$	1.00000	0.176777
$33$	0.225397	0.0392367
$34$	1.00000	0.171499
$35$	−2.68251	−0.453427
$36$	1.00000	0.166667
$37$	−4.67961	−0.769323	−0.384662	−	0.923058i	$-0.625682\pi$
$37$	−4.67961	−0.769323	−0.384662	+	0.923058i	$0.625682\pi$
$38$	−2.00507	−0.325266
$39$	4.24122	0.679139
$40$	−2.41505	−0.381853
$41$	−2.49503	−0.389659	−0.194829	−	0.980837i	$-0.562415\pi$
$41$	−2.49503	−0.389659	−0.194829	+	0.980837i	$0.562415\pi$
$42$	1.11075	0.171392
$43$	−4.44605	−0.678017	−0.339008	−	0.940783i	$-0.610091\pi$
$43$	−4.44605	−0.678017	−0.339008	+	0.940783i	$0.610091\pi$
$44$	0.225397	0.0339799
$45$	−2.41505	−0.360014
$46$	4.30418	0.634616
$47$	9.35165	1.36408	0.682039	−	0.731316i	$-0.261093\pi$
$47$	9.35165	1.36408	0.682039	+	0.731316i	$0.261093\pi$
$48$	1.00000	0.144338
$49$	−5.76624	−0.823748
$50$	0.832456	0.117727
$51$	1.00000	0.140028
$52$	4.24122	0.588151
$53$	7.05794	0.969483	0.484742	−	0.874657i	$-0.338914\pi$
$53$	7.05794	0.969483	0.484742	+	0.874657i	$0.338914\pi$
$54$	1.00000	0.136083
$55$	−0.544346	−0.0733995
$56$	1.11075	0.148430
$57$	−2.00507	−0.265578
$58$	−0.556101	−0.0730197
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−2.41505	−0.311781
$61$	−11.8192	−1.51329	−0.756646	−	0.653825i	$-0.773163\pi$
$61$	−11.8192	−1.51329	−0.756646	+	0.653825i	$0.773163\pi$
$62$	8.00416	1.01653
$63$	1.11075	0.139941
$64$	1.00000	0.125000
$65$	−10.2427	−1.27046
$66$	0.225397	0.0277445
$67$	8.08996	0.988346	0.494173	−	0.869364i	$-0.335471\pi$
$67$	8.08996	0.988346	0.494173	+	0.869364i	$0.335471\pi$
$68$	1.00000	0.121268
$69$	4.30418	0.518162
$70$	−2.68251	−0.320621
$71$	10.9700	1.30190	0.650949	−	0.759121i	$-0.274371\pi$
$71$	10.9700	1.30190	0.650949	+	0.759121i	$0.274371\pi$
$72$	1.00000	0.117851
$73$	0.775824	0.0908033	0.0454017	−	0.998969i	$-0.485543\pi$
$73$	0.775824	0.0908033	0.0454017	+	0.998969i	$0.485543\pi$
$74$	−4.67961	−0.543994
$75$	0.832456	0.0961237
$76$	−2.00507	−0.229998
$77$	0.250360	0.0285312
$78$	4.24122	0.480223
$79$	−4.12926	−0.464578	−0.232289	−	0.972647i	$-0.574621\pi$
$79$	−4.12926	−0.464578	−0.232289	+	0.972647i	$0.574621\pi$
$80$	−2.41505	−0.270011
$81$	1.00000	0.111111
$82$	−2.49503	−0.275530
$83$	7.37225	0.809209	0.404605	−	0.914492i	$-0.367409\pi$
$83$	7.37225	0.809209	0.404605	+	0.914492i	$0.367409\pi$
$84$	1.11075	0.121193
$85$	−2.41505	−0.261949
$86$	−4.44605	−0.479430
$87$	−0.556101	−0.0596203
$88$	0.225397	0.0240274
$89$	5.90124	0.625530	0.312765	−	0.949830i	$-0.398745\pi$
$89$	5.90124	0.625530	0.312765	+	0.949830i	$0.398745\pi$
$90$	−2.41505	−0.254568
$91$	4.71093	0.493839
$92$	4.30418	0.448741
$93$	8.00416	0.829992
$94$	9.35165	0.964549
$95$	4.84235	0.496814
$96$	1.00000	0.102062
$97$	−4.80376	−0.487748	−0.243874	−	0.969807i	$-0.578418\pi$
$97$	−4.80376	−0.487748	−0.243874	+	0.969807i	$0.578418\pi$
$98$	−5.76624	−0.582478
$99$	0.225397	0.0226533
$100$	0.832456	0.0832456
$101$	4.53643	0.451392	0.225696	−	0.974198i	$-0.427534\pi$
$101$	4.53643	0.451392	0.225696	+	0.974198i	$0.427534\pi$
$102$	1.00000	0.0990148
$103$	−3.62963	−0.357638	−0.178819	−	0.983882i	$-0.557228\pi$
$103$	−3.62963	−0.357638	−0.178819	+	0.983882i	$0.557228\pi$
$104$	4.24122	0.415886
$105$	−2.68251	−0.261786
$106$	7.05794	0.685528
$107$	−4.14289	−0.400508	−0.200254	−	0.979744i	$-0.564177\pi$
$107$	−4.14289	−0.400508	−0.200254	+	0.979744i	$0.564177\pi$
$108$	1.00000	0.0962250
$109$	16.4415	1.57481	0.787407	−	0.616433i	$-0.211423\pi$
$109$	16.4415	1.57481	0.787407	+	0.616433i	$0.211423\pi$
$110$	−0.544346	−0.0519013
$111$	−4.67961	−0.444169
$112$	1.11075	0.104956
$113$	9.12148	0.858076	0.429038	−	0.903286i	$-0.358853\pi$
$113$	9.12148	0.858076	0.429038	+	0.903286i	$0.358853\pi$
$114$	−2.00507	−0.187792
$115$	−10.3948	−0.969319
$116$	−0.556101	−0.0516327
$117$	4.24122	0.392101
$118$	−1.00000	−0.0920575
$119$	1.11075	0.101822
$120$	−2.41505	−0.220463
$121$	−10.9492	−0.995381
$122$	−11.8192	−1.07006
$123$	−2.49503	−0.224969
$124$	8.00416	0.718794
$125$	10.0648	0.900225
$126$	1.11075	0.0989533
$127$	7.38457	0.655274	0.327637	−	0.944804i	$-0.393748\pi$
$127$	7.38457	0.655274	0.327637	+	0.944804i	$0.393748\pi$
$128$	1.00000	0.0883883
$129$	−4.44605	−0.391453
$130$	−10.2427	−0.898348
$131$	12.5482	1.09634	0.548169	−	0.836368i	$-0.315325\pi$
$131$	12.5482	1.09634	0.548169	+	0.836368i	$0.315325\pi$
$132$	0.225397	0.0196183
$133$	−2.22713	−0.193117
$134$	8.08996	0.698866
$135$	−2.41505	−0.207854
$136$	1.00000	0.0857493
$137$	6.82797	0.583353	0.291676	−	0.956517i	$-0.405787\pi$
$137$	6.82797	0.583353	0.291676	+	0.956517i	$0.405787\pi$
$138$	4.30418	0.366396
$139$	15.4132	1.30733	0.653665	−	0.756784i	$-0.273231\pi$
$139$	15.4132	1.30733	0.653665	+	0.756784i	$0.273231\pi$
$140$	−2.68251	−0.226714
$141$	9.35165	0.787551
$142$	10.9700	0.920582
$143$	0.955960	0.0799414
$144$	1.00000	0.0833333
$145$	1.34301	0.111531
$146$	0.775824	0.0642076
$147$	−5.76624	−0.475591
$148$	−4.67961	−0.384662
$149$	15.2076	1.24585	0.622926	−	0.782281i	$-0.285944\pi$
$149$	15.2076	1.24585	0.622926	+	0.782281i	$0.285944\pi$
$150$	0.832456	0.0679697
$151$	−7.35113	−0.598227	−0.299113	−	0.954218i	$-0.596691\pi$
$151$	−7.35113	−0.598227	−0.299113	+	0.954218i	$0.596691\pi$
$152$	−2.00507	−0.162633
$153$	1.00000	0.0808452
$154$	0.250360	0.0201746
$155$	−19.3304	−1.55266
$156$	4.24122	0.339569
$157$	22.2380	1.77479	0.887393	−	0.461013i	$-0.152514\pi$
$157$	22.2380	1.77479	0.887393	+	0.461013i	$0.152514\pi$
$158$	−4.12926	−0.328506
$159$	7.05794	0.559731
$160$	−2.41505	−0.190926
$161$	4.78086	0.376784
$162$	1.00000	0.0785674
$163$	−12.5439	−0.982511	−0.491255	−	0.871016i	$-0.663462\pi$
$163$	−12.5439	−0.982511	−0.491255	+	0.871016i	$0.663462\pi$
$164$	−2.49503	−0.194829
$165$	−0.544346	−0.0423772
$166$	7.37225	0.572197
$167$	−13.9794	−1.08176	−0.540878	−	0.841101i	$-0.681908\pi$
$167$	−13.9794	−1.08176	−0.540878	+	0.841101i	$0.681908\pi$
$168$	1.11075	0.0856961
$169$	4.98794	0.383687
$170$	−2.41505	−0.185226
$171$	−2.00507	−0.153332
$172$	−4.44605	−0.339008
$173$	1.46904	0.111689	0.0558445	−	0.998439i	$-0.482215\pi$
$173$	1.46904	0.111689	0.0558445	+	0.998439i	$0.482215\pi$
$174$	−0.556101	−0.0421579
$175$	0.924649	0.0698969
$176$	0.225397	0.0169900
$177$	−1.00000	−0.0751646
$178$	5.90124	0.442317
$179$	9.55821	0.714414	0.357207	−	0.934025i	$-0.383729\pi$
$179$	9.55821	0.714414	0.357207	+	0.934025i	$0.383729\pi$
$180$	−2.41505	−0.180007
$181$	−22.2532	−1.65407	−0.827034	−	0.562151i	$-0.809974\pi$
$181$	−22.2532	−1.65407	−0.827034	+	0.562151i	$0.809974\pi$
$182$	4.71093	0.349197
$183$	−11.8192	−0.873700
$184$	4.30418	0.317308
$185$	11.3015	0.830901
$186$	8.00416	0.586893
$187$	0.225397	0.0164827
$188$	9.35165	0.682039
$189$	1.11075	0.0807951
$190$	4.84235	0.351301
$191$	8.16738	0.590971	0.295486	−	0.955347i	$-0.404519\pi$
$191$	8.16738	0.590971	0.295486	+	0.955347i	$0.404519\pi$
$192$	1.00000	0.0721688
$193$	−6.91620	−0.497839	−0.248920	−	0.968524i	$-0.580075\pi$
$193$	−6.91620	−0.497839	−0.248920	+	0.968524i	$0.580075\pi$
$194$	−4.80376	−0.344890
$195$	−10.2427	−0.733498
$196$	−5.76624	−0.411874
$197$	−0.0735786	−0.00524226	−0.00262113	−	0.999997i	$-0.500834\pi$
$197$	−0.0735786	−0.00524226	−0.00262113	+	0.999997i	$0.500834\pi$
$198$	0.225397	0.0160183
$199$	6.06695	0.430075	0.215037	−	0.976606i	$-0.431013\pi$
$199$	6.06695	0.430075	0.215037	+	0.976606i	$0.431013\pi$
$200$	0.832456	0.0588635
$201$	8.08996	0.570622
$202$	4.53643	0.319182
$203$	−0.617689	−0.0433533
$204$	1.00000	0.0700140
$205$	6.02562	0.420848
$206$	−3.62963	−0.252888
$207$	4.30418	0.299161
$208$	4.24122	0.294076
$209$	−0.451938	−0.0312612
$210$	−2.68251	−0.185111
$211$	6.11037	0.420655	0.210328	−	0.977631i	$-0.432547\pi$
$211$	6.11037	0.420655	0.210328	+	0.977631i	$0.432547\pi$
$212$	7.05794	0.484742
$213$	10.9700	0.751652
$214$	−4.14289	−0.283202
$215$	10.7374	0.732287
$216$	1.00000	0.0680414
$217$	8.89060	0.603534
$218$	16.4415	1.11356
$219$	0.775824	0.0524253
$220$	−0.544346	−0.0366998
$221$	4.24122	0.285295
$222$	−4.67961	−0.314075
$223$	−15.5405	−1.04067	−0.520334	−	0.853963i	$-0.674193\pi$
$223$	−15.5405	−1.04067	−0.520334	+	0.853963i	$0.674193\pi$
$224$	1.11075	0.0742150
$225$	0.832456	0.0554970
$226$	9.12148	0.606752
$227$	4.92743	0.327045	0.163522	−	0.986540i	$-0.447714\pi$
$227$	4.92743	0.327045	0.163522	+	0.986540i	$0.447714\pi$
$228$	−2.00507	−0.132789
$229$	9.33763	0.617048	0.308524	−	0.951217i	$-0.400165\pi$
$229$	9.33763	0.617048	0.308524	+	0.951217i	$0.400165\pi$
$230$	−10.3948	−0.685412
$231$	0.250360	0.0164725
$232$	−0.556101	−0.0365098
$233$	−8.21264	−0.538028	−0.269014	−	0.963136i	$-0.586698\pi$
$233$	−8.21264	−0.538028	−0.269014	+	0.963136i	$0.586698\pi$
$234$	4.24122	0.277257
$235$	−22.5847	−1.47326
$236$	−1.00000	−0.0650945
$237$	−4.12926	−0.268224
$238$	1.11075	0.0719991
$239$	−8.80662	−0.569653	−0.284827	−	0.958579i	$-0.591936\pi$
$239$	−8.80662	−0.569653	−0.284827	+	0.958579i	$0.591936\pi$
$240$	−2.41505	−0.155891
$241$	−6.03805	−0.388945	−0.194472	−	0.980908i	$-0.562299\pi$
$241$	−6.03805	−0.388945	−0.194472	+	0.980908i	$0.562299\pi$
$242$	−10.9492	−0.703841
$243$	1.00000	0.0641500
$244$	−11.8192	−0.756646
$245$	13.9257	0.889683
$246$	−2.49503	−0.159077
$247$	−8.50395	−0.541093
$248$	8.00416	0.508264
$249$	7.37225	0.467197
$250$	10.0648	0.636555
$251$	−0.788494	−0.0497693	−0.0248847	−	0.999690i	$-0.507922\pi$
$251$	−0.788494	−0.0497693	−0.0248847	+	0.999690i	$0.507922\pi$
$252$	1.11075	0.0699706
$253$	0.970150	0.0609928
$254$	7.38457	0.463349
$255$	−2.41505	−0.151236
$256$	1.00000	0.0625000
$257$	−23.6446	−1.47491	−0.737456	−	0.675396i	$-0.763973\pi$
$257$	−23.6446	−1.47491	−0.737456	+	0.675396i	$0.763973\pi$
$258$	−4.44605	−0.276799
$259$	−5.19787	−0.322980
$260$	−10.2427	−0.635228
$261$	−0.556101	−0.0344218
$262$	12.5482	0.775228
$263$	−2.16601	−0.133562	−0.0667809	−	0.997768i	$-0.521273\pi$
$263$	−2.16601	−0.133562	−0.0667809	+	0.997768i	$0.521273\pi$
$264$	0.225397	0.0138723
$265$	−17.0453	−1.04708
$266$	−2.22713	−0.136554
$267$	5.90124	0.361150
$268$	8.08996	0.494173
$269$	9.21723	0.561985	0.280992	−	0.959710i	$-0.409336\pi$
$269$	9.21723	0.561985	0.280992	+	0.959710i	$0.409336\pi$
$270$	−2.41505	−0.146975
$271$	−11.7982	−0.716688	−0.358344	−	0.933590i	$-0.616659\pi$
$271$	−11.7982	−0.716688	−0.358344	+	0.933590i	$0.616659\pi$
$272$	1.00000	0.0606339
$273$	4.71093	0.285118
$274$	6.82797	0.412493
$275$	0.187633	0.0113147
$276$	4.30418	0.259081
$277$	−16.8531	−1.01260	−0.506302	−	0.862356i	$-0.668988\pi$
$277$	−16.8531	−1.01260	−0.506302	+	0.862356i	$0.668988\pi$
$278$	15.4132	0.924422
$279$	8.00416	0.479196
$280$	−2.68251	−0.160311
$281$	3.22572	0.192430	0.0962151	−	0.995361i	$-0.469326\pi$
$281$	3.22572	0.192430	0.0962151	+	0.995361i	$0.469326\pi$
$282$	9.35165	0.556882
$283$	23.4674	1.39499	0.697495	−	0.716590i	$-0.254298\pi$
$283$	23.4674	1.39499	0.697495	+	0.716590i	$0.254298\pi$
$284$	10.9700	0.650949
$285$	4.84235	0.286836
$286$	0.955960	0.0565271
$287$	−2.77135	−0.163588
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	1.34301	0.0788644
$291$	−4.80376	−0.281602
$292$	0.775824	0.0454017
$293$	−21.2104	−1.23913	−0.619564	−	0.784946i	$-0.712690\pi$
$293$	−21.2104	−1.23913	−0.619564	+	0.784946i	$0.712690\pi$
$294$	−5.76624	−0.336294
$295$	2.41505	0.140610
$296$	−4.67961	−0.271997
$297$	0.225397	0.0130789
$298$	15.2076	0.880950
$299$	18.2550	1.05571
$300$	0.832456	0.0480618
$301$	−4.93845	−0.284647
$302$	−7.35113	−0.423010
$303$	4.53643	0.260611
$304$	−2.00507	−0.114999
$305$	28.5439	1.63442
$306$	1.00000	0.0571662
$307$	24.7950	1.41513	0.707564	−	0.706649i	$-0.249794\pi$
$307$	24.7950	1.41513	0.707564	+	0.706649i	$0.249794\pi$
$308$	0.250360	0.0142656
$309$	−3.62963	−0.206482
$310$	−19.3304	−1.09789
$311$	20.5465	1.16508	0.582542	−	0.812801i	$-0.302058\pi$
$311$	20.5465	1.16508	0.582542	+	0.812801i	$0.302058\pi$
$312$	4.24122	0.240112
$313$	−26.4973	−1.49771	−0.748857	−	0.662732i	$-0.769397\pi$
$313$	−26.4973	−1.49771	−0.748857	+	0.662732i	$0.769397\pi$
$314$	22.2380	1.25496
$315$	−2.68251	−0.151142
$316$	−4.12926	−0.232289
$317$	21.2366	1.19277	0.596384	−	0.802699i	$-0.296604\pi$
$317$	21.2366	1.19277	0.596384	+	0.802699i	$0.296604\pi$
$318$	7.05794	0.395790
$319$	−0.125344	−0.00701791
$320$	−2.41505	−0.135005
$321$	−4.14289	−0.231233
$322$	4.78086	0.266427
$323$	−2.00507	−0.111565
$324$	1.00000	0.0555556
$325$	3.53063	0.195844
$326$	−12.5439	−0.694740
$327$	16.4415	0.909219
$328$	−2.49503	−0.137765
$329$	10.3873	0.572672
$330$	−0.544346	−0.0299652
$331$	28.3974	1.56086	0.780432	−	0.625241i	$-0.214999\pi$
$331$	28.3974	1.56086	0.780432	+	0.625241i	$0.214999\pi$
$332$	7.37225	0.404605
$333$	−4.67961	−0.256441
$334$	−13.9794	−0.764917
$335$	−19.5376	−1.06746
$336$	1.11075	0.0605963
$337$	14.0447	0.765066	0.382533	−	0.923942i	$-0.375052\pi$
$337$	14.0447	0.765066	0.382533	+	0.923942i	$0.375052\pi$
$338$	4.98794	0.271308
$339$	9.12148	0.495411
$340$	−2.41505	−0.130974
$341$	1.80412	0.0976984
$342$	−2.00507	−0.108422
$343$	−14.1801	−0.765652
$344$	−4.44605	−0.239715
$345$	−10.3948	−0.559637
$346$	1.46904	0.0789760
$347$	9.90148	0.531539	0.265770	−	0.964037i	$-0.414374\pi$
$347$	9.90148	0.531539	0.265770	+	0.964037i	$0.414374\pi$
$348$	−0.556101	−0.0298102
$349$	9.21538	0.493288	0.246644	−	0.969106i	$-0.420672\pi$
$349$	9.21538	0.493288	0.246644	+	0.969106i	$0.420672\pi$
$350$	0.924649	0.0494245
$351$	4.24122	0.226380
$352$	0.225397	0.0120137
$353$	22.0286	1.17247	0.586233	−	0.810143i	$-0.300611\pi$
$353$	22.0286	1.17247	0.586233	+	0.810143i	$0.300611\pi$
$354$	−1.00000	−0.0531494
$355$	−26.4931	−1.40611
$356$	5.90124	0.312765
$357$	1.11075	0.0587870
$358$	9.55821	0.505167
$359$	−1.36375	−0.0719761	−0.0359881	−	0.999352i	$-0.511458\pi$
$359$	−1.36375	−0.0719761	−0.0359881	+	0.999352i	$0.511458\pi$
$360$	−2.41505	−0.127284
$361$	−14.9797	−0.788404
$362$	−22.2532	−1.16960
$363$	−10.9492	−0.574684
$364$	4.71093	0.246920
$365$	−1.87365	−0.0980714
$366$	−11.8192	−0.617799
$367$	−23.2324	−1.21272	−0.606361	−	0.795190i	$-0.707371\pi$
$367$	−23.2324	−1.21272	−0.606361	+	0.795190i	$0.707371\pi$
$368$	4.30418	0.224371
$369$	−2.49503	−0.129886
$370$	11.3015	0.587536
$371$	7.83960	0.407012
$372$	8.00416	0.414996
$373$	−2.02259	−0.104726	−0.0523630	−	0.998628i	$-0.516675\pi$
$373$	−2.02259	−0.104726	−0.0523630	+	0.998628i	$0.516675\pi$
$374$	0.225397	0.0116550
$375$	10.0648	0.519745
$376$	9.35165	0.482274
$377$	−2.35855	−0.121471
$378$	1.11075	0.0571307
$379$	17.8084	0.914758	0.457379	−	0.889272i	$-0.348788\pi$
$379$	17.8084	0.914758	0.457379	+	0.889272i	$0.348788\pi$
$380$	4.84235	0.248407
$381$	7.38457	0.378323
$382$	8.16738	0.417880
$383$	−30.7587	−1.57170	−0.785848	−	0.618420i	$-0.787773\pi$
$383$	−30.7587	−1.57170	−0.785848	+	0.618420i	$0.787773\pi$
$384$	1.00000	0.0510310
$385$	−0.604631	−0.0308148
$386$	−6.91620	−0.352025
$387$	−4.44605	−0.226006
$388$	−4.80376	−0.243874
$389$	20.5705	1.04297	0.521483	−	0.853262i	$-0.325379\pi$
$389$	20.5705	1.04297	0.521483	+	0.853262i	$0.325379\pi$
$390$	−10.2427	−0.518662
$391$	4.30418	0.217672
$392$	−5.76624	−0.291239
$393$	12.5482	0.632971
$394$	−0.0735786	−0.00370684
$395$	9.97235	0.501764
$396$	0.225397	0.0113266
$397$	−37.1682	−1.86542	−0.932708	−	0.360632i	$-0.882561\pi$
$397$	−37.1682	−1.86542	−0.932708	+	0.360632i	$0.882561\pi$
$398$	6.06695	0.304109
$399$	−2.22713	−0.111496
$400$	0.832456	0.0416228
$401$	−33.3032	−1.66308	−0.831541	−	0.555464i	$-0.812541\pi$
$401$	−33.3032	−1.66308	−0.831541	+	0.555464i	$0.812541\pi$
$402$	8.08996	0.403491
$403$	33.9474	1.69104
$404$	4.53643	0.225696
$405$	−2.41505	−0.120005
$406$	−0.617689	−0.0306554
$407$	−1.05477	−0.0522831
$408$	1.00000	0.0495074
$409$	−18.5656	−0.918011	−0.459006	−	0.888433i	$-0.651794\pi$
$409$	−18.5656	−0.918011	−0.459006	+	0.888433i	$0.651794\pi$
$410$	6.02562	0.297584
$411$	6.82797	0.336799
$412$	−3.62963	−0.178819
$413$	−1.11075	−0.0546564
$414$	4.30418	0.211539
$415$	−17.8043	−0.873980
$416$	4.24122	0.207943
$417$	15.4132	0.754787
$418$	−0.451938	−0.0221050
$419$	−18.2543	−0.891782	−0.445891	−	0.895087i	$-0.647113\pi$
$419$	−18.2543	−0.891782	−0.445891	+	0.895087i	$0.647113\pi$
$420$	−2.68251	−0.130893
$421$	−14.2267	−0.693368	−0.346684	−	0.937982i	$-0.612692\pi$
$421$	−14.2267	−0.693368	−0.346684	+	0.937982i	$0.612692\pi$
$422$	6.11037	0.297448
$423$	9.35165	0.454693
$424$	7.05794	0.342764
$425$	0.832456	0.0403800
$426$	10.9700	0.531498
$427$	−13.1281	−0.635315
$428$	−4.14289	−0.200254
$429$	0.955960	0.0461542
$430$	10.7374	0.517805
$431$	−16.4991	−0.794732	−0.397366	−	0.917660i	$-0.630076\pi$
$431$	−16.4991	−0.794732	−0.397366	+	0.917660i	$0.630076\pi$
$432$	1.00000	0.0481125
$433$	9.08498	0.436596	0.218298	−	0.975882i	$-0.429949\pi$
$433$	9.08498	0.436596	0.218298	+	0.975882i	$0.429949\pi$
$434$	8.89060	0.426763
$435$	1.34301	0.0643925
$436$	16.4415	0.787407
$437$	−8.63019	−0.412838
$438$	0.775824	0.0370703
$439$	8.86600	0.423151	0.211576	−	0.977362i	$-0.432141\pi$
$439$	8.86600	0.423151	0.211576	+	0.977362i	$0.432141\pi$
$440$	−0.544346	−0.0259507
$441$	−5.76624	−0.274583
$442$	4.24122	0.201734
$443$	−38.0293	−1.80683	−0.903414	−	0.428770i	$-0.858947\pi$
$443$	−38.0293	−1.80683	−0.903414	+	0.428770i	$0.858947\pi$
$444$	−4.67961	−0.222084
$445$	−14.2518	−0.675599
$446$	−15.5405	−0.735864
$447$	15.2076	0.719293
$448$	1.11075	0.0524779
$449$	−21.5380	−1.01644	−0.508221	−	0.861227i	$-0.669697\pi$
$449$	−21.5380	−1.01644	−0.508221	+	0.861227i	$0.669697\pi$
$450$	0.832456	0.0392423
$451$	−0.562374	−0.0264812
$452$	9.12148	0.429038
$453$	−7.35113	−0.345386
$454$	4.92743	0.231256
$455$	−11.3771	−0.533367
$456$	−2.00507	−0.0938961
$457$	−15.2458	−0.713170	−0.356585	−	0.934263i	$-0.616059\pi$
$457$	−15.2458	−0.713170	−0.356585	+	0.934263i	$0.616059\pi$
$458$	9.33763	0.436319
$459$	1.00000	0.0466760
$460$	−10.3948	−0.484660
$461$	−19.4984	−0.908133	−0.454067	−	0.890968i	$-0.650027\pi$
$461$	−19.4984	−0.908133	−0.454067	+	0.890968i	$0.650027\pi$
$462$	0.250360	0.0116478
$463$	22.0758	1.02595	0.512976	−	0.858403i	$-0.328543\pi$
$463$	22.0758	1.02595	0.512976	+	0.858403i	$0.328543\pi$
$464$	−0.556101	−0.0258164
$465$	−19.3304	−0.896427
$466$	−8.21264	−0.380443
$467$	23.7377	1.09845	0.549226	−	0.835674i	$-0.314923\pi$
$467$	23.7377	1.09845	0.549226	+	0.835674i	$0.314923\pi$
$468$	4.24122	0.196050
$469$	8.98591	0.414931
$470$	−22.5847	−1.04175
$471$	22.2380	1.02467
$472$	−1.00000	−0.0460287
$473$	−1.00213	−0.0460779
$474$	−4.12926	−0.189663
$475$	−1.66913	−0.0765851
$476$	1.11075	0.0509111
$477$	7.05794	0.323161
$478$	−8.80662	−0.402806
$479$	17.1622	0.784160	0.392080	−	0.919931i	$-0.371756\pi$
$479$	17.1622	0.784160	0.392080	+	0.919931i	$0.371756\pi$
$480$	−2.41505	−0.110231
$481$	−19.8472	−0.904957
$482$	−6.03805	−0.275026
$483$	4.78086	0.217537
$484$	−10.9492	−0.497691
$485$	11.6013	0.526789
$486$	1.00000	0.0453609
$487$	−22.6072	−1.02443	−0.512215	−	0.858857i	$-0.671175\pi$
$487$	−22.6072	−1.02443	−0.512215	+	0.858857i	$0.671175\pi$
$488$	−11.8192	−0.535030
$489$	−12.5439	−0.567253
$490$	13.9257	0.629101
$491$	0.199856	0.00901939	0.00450970	−	0.999990i	$-0.498565\pi$
$491$	0.199856	0.00901939	0.00450970	+	0.999990i	$0.498565\pi$
$492$	−2.49503	−0.112485
$493$	−0.556101	−0.0250455
$494$	−8.50395	−0.382611
$495$	−0.544346	−0.0244665
$496$	8.00416	0.359397
$497$	12.1849	0.546568
$498$	7.37225	0.330358
$499$	−25.2118	−1.12864	−0.564318	−	0.825558i	$-0.690861\pi$
$499$	−25.2118	−1.12864	−0.564318	+	0.825558i	$0.690861\pi$
$500$	10.0648	0.450112
$501$	−13.9794	−0.624552
$502$	−0.788494	−0.0351922
$503$	−19.3725	−0.863775	−0.431888	−	0.901927i	$-0.642152\pi$
$503$	−19.3725	−0.863775	−0.431888	+	0.901927i	$0.642152\pi$
$504$	1.11075	0.0494767
$505$	−10.9557	−0.487522
$506$	0.970150	0.0431284
$507$	4.98794	0.221522
$508$	7.38457	0.327637
$509$	−5.61499	−0.248880	−0.124440	−	0.992227i	$-0.539713\pi$
$509$	−5.61499	−0.248880	−0.124440	+	0.992227i	$0.539713\pi$
$510$	−2.41505	−0.106940
$511$	0.861745	0.0381214
$512$	1.00000	0.0441942
$513$	−2.00507	−0.0885261
$514$	−23.6446	−1.04292
$515$	8.76572	0.386264
$516$	−4.44605	−0.195727
$517$	2.10784	0.0927026
$518$	−5.19787	−0.228381
$519$	1.46904	0.0644836
$520$	−10.2427	−0.449174
$521$	−38.9655	−1.70711	−0.853555	−	0.521003i	$-0.825558\pi$
$521$	−38.9655	−1.70711	−0.853555	+	0.521003i	$0.825558\pi$
$522$	−0.556101	−0.0243399
$523$	18.4761	0.807904	0.403952	−	0.914780i	$-0.367636\pi$
$523$	18.4761	0.807904	0.403952	+	0.914780i	$0.367636\pi$
$524$	12.5482	0.548169
$525$	0.924649	0.0403550
$526$	−2.16601	−0.0944425
$527$	8.00416	0.348667
$528$	0.225397	0.00980916
$529$	−4.47407	−0.194525
$530$	−17.0453	−0.740399
$531$	−1.00000	−0.0433963
$532$	−2.22713	−0.0965584
$533$	−10.5820	−0.458356
$534$	5.90124	0.255372
$535$	10.0053	0.432565
$536$	8.08996	0.349433
$537$	9.55821	0.412467
$538$	9.21723	0.397383
$539$	−1.29970	−0.0559818
$540$	−2.41505	−0.103927
$541$	25.6559	1.10303	0.551517	−	0.834164i	$-0.314049\pi$
$541$	25.6559	1.10303	0.551517	+	0.834164i	$0.314049\pi$
$542$	−11.7982	−0.506775
$543$	−22.2532	−0.954977
$544$	1.00000	0.0428746
$545$	−39.7071	−1.70087
$546$	4.71093	0.201609
$547$	−23.0955	−0.987492	−0.493746	−	0.869606i	$-0.664373\pi$
$547$	−23.0955	−0.987492	−0.493746	+	0.869606i	$0.664373\pi$
$548$	6.82797	0.291676
$549$	−11.8192	−0.504431
$550$	0.187633	0.00800071
$551$	1.11502	0.0475016
$552$	4.30418	0.183198
$553$	−4.58657	−0.195041
$554$	−16.8531	−0.716019
$555$	11.3015	0.479721
$556$	15.4132	0.653665
$557$	0.937959	0.0397426	0.0198713	−	0.999803i	$-0.493674\pi$
$557$	0.937959	0.0397426	0.0198713	+	0.999803i	$0.493674\pi$
$558$	8.00416	0.338843
$559$	−18.8567	−0.797553
$560$	−2.68251	−0.113357
$561$	0.225397	0.00951629
$562$	3.22572	0.136069
$563$	−23.9074	−1.00758	−0.503789	−	0.863827i	$-0.668061\pi$
$563$	−23.9074	−1.00758	−0.503789	+	0.863827i	$0.668061\pi$
$564$	9.35165	0.393775
$565$	−22.0288	−0.926759
$566$	23.4674	0.986407
$567$	1.11075	0.0466470
$568$	10.9700	0.460291
$569$	16.4396	0.689185	0.344592	−	0.938752i	$-0.388017\pi$
$569$	16.4396	0.689185	0.344592	+	0.938752i	$0.388017\pi$
$570$	4.84235	0.202824
$571$	−20.4930	−0.857607	−0.428803	−	0.903398i	$-0.641065\pi$
$571$	−20.4930	−0.857607	−0.428803	+	0.903398i	$0.641065\pi$
$572$	0.955960	0.0399707
$573$	8.16738	0.341197
$574$	−2.77135	−0.115674
$575$	3.58304	0.149423
$576$	1.00000	0.0416667
$577$	21.9670	0.914497	0.457248	−	0.889339i	$-0.348835\pi$
$577$	21.9670	0.914497	0.457248	+	0.889339i	$0.348835\pi$
$578$	1.00000	0.0415945
$579$	−6.91620	−0.287427
$580$	1.34301	0.0557655
$581$	8.18871	0.339725
$582$	−4.80376	−0.199122
$583$	1.59084	0.0658860
$584$	0.775824	0.0321038
$585$	−10.2427	−0.423485
$586$	−21.2104	−0.876195
$587$	40.3251	1.66440	0.832199	−	0.554478i	$-0.187082\pi$
$587$	40.3251	1.66440	0.832199	+	0.554478i	$0.187082\pi$
$588$	−5.76624	−0.237796
$589$	−16.0489	−0.661284
$590$	2.41505	0.0994259
$591$	−0.0735786	−0.00302662
$592$	−4.67961	−0.192331
$593$	6.35143	0.260822	0.130411	−	0.991460i	$-0.458370\pi$
$593$	6.35143	0.260822	0.130411	+	0.991460i	$0.458370\pi$
$594$	0.225397	0.00924817
$595$	−2.68251	−0.109972
$596$	15.2076	0.622926
$597$	6.06695	0.248304
$598$	18.2550	0.746500
$599$	−2.94239	−0.120223	−0.0601114	−	0.998192i	$-0.519146\pi$
$599$	−2.94239	−0.120223	−0.0601114	+	0.998192i	$0.519146\pi$
$600$	0.832456	0.0339849
$601$	23.7151	0.967361	0.483681	−	0.875245i	$-0.339300\pi$
$601$	23.7151	0.967361	0.483681	+	0.875245i	$0.339300\pi$
$602$	−4.93845	−0.201276
$603$	8.08996	0.329449
$604$	−7.35113	−0.299113
$605$	26.4428	1.07505
$606$	4.53643	0.184280
$607$	−10.6353	−0.431672	−0.215836	−	0.976430i	$-0.569248\pi$
$607$	−10.6353	−0.431672	−0.215836	+	0.976430i	$0.569248\pi$
$608$	−2.00507	−0.0813164
$609$	−0.617689	−0.0250300
$610$	28.5439	1.15571
$611$	39.6624	1.60457
$612$	1.00000	0.0404226
$613$	19.7618	0.798172	0.399086	−	0.916914i	$-0.369328\pi$
$613$	19.7618	0.798172	0.399086	+	0.916914i	$0.369328\pi$
$614$	24.7950	1.00065
$615$	6.02562	0.242977
$616$	0.250360	0.0100873
$617$	−31.8793	−1.28341	−0.641706	−	0.766951i	$-0.721773\pi$
$617$	−31.8793	−1.28341	−0.641706	+	0.766951i	$0.721773\pi$
$618$	−3.62963	−0.146005
$619$	−18.9628	−0.762181	−0.381090	−	0.924538i	$-0.624451\pi$
$619$	−18.9628	−0.762181	−0.381090	+	0.924538i	$0.624451\pi$
$620$	−19.3304	−0.776328
$621$	4.30418	0.172721
$622$	20.5465	0.823838
$623$	6.55479	0.262612
$624$	4.24122	0.169785
$625$	−28.4693	−1.13877
$626$	−26.4973	−1.05904
$627$	−0.451938	−0.0180487
$628$	22.2380	0.887393
$629$	−4.67961	−0.186588
$630$	−2.68251	−0.106874
$631$	14.5861	0.580665	0.290332	−	0.956926i	$-0.406234\pi$
$631$	14.5861	0.580665	0.290332	+	0.956926i	$0.406234\pi$
$632$	−4.12926	−0.164253
$633$	6.11037	0.242865
$634$	21.2366	0.843414
$635$	−17.8341	−0.707724
$636$	7.05794	0.279866
$637$	−24.4559	−0.968977
$638$	−0.125344	−0.00496241
$639$	10.9700	0.433966
$640$	−2.41505	−0.0954631
$641$	−2.43070	−0.0960068	−0.0480034	−	0.998847i	$-0.515286\pi$
$641$	−2.43070	−0.0960068	−0.0480034	+	0.998847i	$0.515286\pi$
$642$	−4.14289	−0.163507
$643$	43.4772	1.71457	0.857286	−	0.514840i	$-0.172149\pi$
$643$	43.4772	1.71457	0.857286	+	0.514840i	$0.172149\pi$
$644$	4.78086	0.188392
$645$	10.7374	0.422786
$646$	−2.00507	−0.0788885
$647$	−29.3760	−1.15489	−0.577445	−	0.816430i	$-0.695950\pi$
$647$	−29.3760	−1.15489	−0.577445	+	0.816430i	$0.695950\pi$
$648$	1.00000	0.0392837
$649$	−0.225397	−0.00884762
$650$	3.53063	0.138483
$651$	8.89060	0.348450
$652$	−12.5439	−0.491255
$653$	−1.22517	−0.0479444	−0.0239722	−	0.999713i	$-0.507631\pi$
$653$	−1.22517	−0.0479444	−0.0239722	+	0.999713i	$0.507631\pi$
$654$	16.4415	0.642915
$655$	−30.3044	−1.18409
$656$	−2.49503	−0.0974146
$657$	0.775824	0.0302678
$658$	10.3873	0.404940
$659$	−12.5401	−0.488495	−0.244247	−	0.969713i	$-0.578541\pi$
$659$	−12.5401	−0.488495	−0.244247	+	0.969713i	$0.578541\pi$
$660$	−0.544346	−0.0211886
$661$	−14.8137	−0.576187	−0.288094	−	0.957602i	$-0.593021\pi$
$661$	−14.8137	−0.576187	−0.288094	+	0.957602i	$0.593021\pi$
$662$	28.3974	1.10370
$663$	4.24122	0.164715
$664$	7.37225	0.286099
$665$	5.37863	0.208574
$666$	−4.67961	−0.181331
$667$	−2.39356	−0.0926790
$668$	−13.9794	−0.540878
$669$	−15.5405	−0.600830
$670$	−19.5376	−0.754805
$671$	−2.66402	−0.102843
$672$	1.11075	0.0428480
$673$	16.3332	0.629600	0.314800	−	0.949158i	$-0.398063\pi$
$673$	16.3332	0.629600	0.314800	+	0.949158i	$0.398063\pi$
$674$	14.0447	0.540983
$675$	0.832456	0.0320412
$676$	4.98794	0.191844
$677$	−11.6817	−0.448964	−0.224482	−	0.974478i	$-0.572069\pi$
$677$	−11.6817	−0.448964	−0.224482	+	0.974478i	$0.572069\pi$
$678$	9.12148	0.350308
$679$	−5.33577	−0.204768
$680$	−2.41505	−0.0926129
$681$	4.92743	0.188819
$682$	1.80412	0.0690832
$683$	−34.1194	−1.30554	−0.652771	−	0.757556i	$-0.726393\pi$
$683$	−34.1194	−1.30554	−0.652771	+	0.757556i	$0.726393\pi$
$684$	−2.00507	−0.0766659
$685$	−16.4899	−0.630045
$686$	−14.1801	−0.541398
$687$	9.33763	0.356253
$688$	−4.44605	−0.169504
$689$	29.9343	1.14041
$690$	−10.3948	−0.395723
$691$	−18.1449	−0.690265	−0.345132	−	0.938554i	$-0.612166\pi$
$691$	−18.1449	−0.690265	−0.345132	+	0.938554i	$0.612166\pi$
$692$	1.46904	0.0558445
$693$	0.250360	0.00951038
$694$	9.90148	0.375855
$695$	−37.2236	−1.41197
$696$	−0.556101	−0.0210790
$697$	−2.49503	−0.0945061
$698$	9.21538	0.348807
$699$	−8.21264	−0.310631
$700$	0.924649	0.0349484
$701$	4.52043	0.170734	0.0853671	−	0.996350i	$-0.472794\pi$
$701$	4.52043	0.170734	0.0853671	+	0.996350i	$0.472794\pi$
$702$	4.24122	0.160074
$703$	9.38296	0.353885
$704$	0.225397	0.00849499
$705$	−22.5847	−0.850588
$706$	22.0286	0.829058
$707$	5.03883	0.189505
$708$	−1.00000	−0.0375823
$709$	−23.3125	−0.875519	−0.437759	−	0.899092i	$-0.644228\pi$
$709$	−23.3125	−0.875519	−0.437759	+	0.899092i	$0.644228\pi$
$710$	−26.4931	−0.994267
$711$	−4.12926	−0.154859
$712$	5.90124	0.221158
$713$	34.4513	1.29021
$714$	1.11075	0.0415687
$715$	−2.30869	−0.0863401
$716$	9.55821	0.357207
$717$	−8.80662	−0.328889
$718$	−1.36375	−0.0508948
$719$	−11.5365	−0.430239	−0.215120	−	0.976588i	$-0.569014\pi$
$719$	−11.5365	−0.430239	−0.215120	+	0.976588i	$0.569014\pi$
$720$	−2.41505	−0.0900035
$721$	−4.03160	−0.150145
$722$	−14.9797	−0.557486
$723$	−6.03805	−0.224557
$724$	−22.2532	−0.827034
$725$	−0.462930	−0.0171928
$726$	−10.9492	−0.406363
$727$	5.01365	0.185946	0.0929730	−	0.995669i	$-0.470363\pi$
$727$	5.01365	0.185946	0.0929730	+	0.995669i	$0.470363\pi$
$728$	4.71093	0.174599
$729$	1.00000	0.0370370
$730$	−1.87365	−0.0693470
$731$	−4.44605	−0.164443
$732$	−11.8192	−0.436850
$733$	−14.9880	−0.553593	−0.276796	−	0.960929i	$-0.589273\pi$
$733$	−14.9880	−0.553593	−0.276796	+	0.960929i	$0.589273\pi$
$734$	−23.2324	−0.857524
$735$	13.9257	0.513659
$736$	4.30418	0.158654
$737$	1.82346	0.0671679
$738$	−2.49503	−0.0918434
$739$	4.91529	0.180812	0.0904059	−	0.995905i	$-0.471184\pi$
$739$	4.91529	0.180812	0.0904059	+	0.995905i	$0.471184\pi$
$740$	11.3015	0.415451
$741$	−8.50395	−0.312400
$742$	7.83960	0.287801
$743$	17.1161	0.627928	0.313964	−	0.949435i	$-0.398343\pi$
$743$	17.1161	0.627928	0.313964	+	0.949435i	$0.398343\pi$
$744$	8.00416	0.293447
$745$	−36.7270	−1.34557
$746$	−2.02259	−0.0740524
$747$	7.37225	0.269736
$748$	0.225397	0.00824135
$749$	−4.60170	−0.168143
$750$	10.0648	0.367515
$751$	−10.4789	−0.382380	−0.191190	−	0.981553i	$-0.561235\pi$
$751$	−10.4789	−0.382380	−0.191190	+	0.981553i	$0.561235\pi$
$752$	9.35165	0.341019
$753$	−0.788494	−0.0287343
$754$	−2.35855	−0.0858932
$755$	17.7533	0.646110
$756$	1.11075	0.0403975
$757$	−14.3258	−0.520681	−0.260340	−	0.965517i	$-0.583835\pi$
$757$	−14.3258	−0.520681	−0.260340	+	0.965517i	$0.583835\pi$
$758$	17.8084	0.646832
$759$	0.970150	0.0352142
$760$	4.84235	0.175650
$761$	13.0162	0.471836	0.235918	−	0.971773i	$-0.424190\pi$
$761$	13.0162	0.471836	0.235918	+	0.971773i	$0.424190\pi$
$762$	7.38457	0.267515
$763$	18.2624	0.661144
$764$	8.16738	0.295486
$765$	−2.41505	−0.0873162
$766$	−30.7587	−1.11136
$767$	−4.24122	−0.153142
$768$	1.00000	0.0360844
$769$	19.4511	0.701423	0.350712	−	0.936483i	$-0.385940\pi$
$769$	19.4511	0.701423	0.350712	+	0.936483i	$0.385940\pi$
$770$	−0.604631	−0.0217894
$771$	−23.6446	−0.851540
$772$	−6.91620	−0.248920
$773$	−34.1432	−1.22805	−0.614023	−	0.789288i	$-0.710450\pi$
$773$	−34.1432	−1.22805	−0.614023	+	0.789288i	$0.710450\pi$
$774$	−4.44605	−0.159810
$775$	6.66310	0.239346
$776$	−4.80376	−0.172445
$777$	−5.19787	−0.186473
$778$	20.5705	0.737488
$779$	5.00272	0.179241
$780$	−10.2427	−0.366749
$781$	2.47261	0.0884769
$782$	4.30418	0.153917
$783$	−0.556101	−0.0198734
$784$	−5.76624	−0.205937
$785$	−53.7059	−1.91684
$786$	12.5482	0.447578
$787$	12.0949	0.431137	0.215568	−	0.976489i	$-0.430840\pi$
$787$	12.0949	0.431137	0.215568	+	0.976489i	$0.430840\pi$
$788$	−0.0735786	−0.00262113
$789$	−2.16601	−0.0771120
$790$	9.97235	0.354800
$791$	10.1317	0.360241
$792$	0.225397	0.00800915
$793$	−50.1278	−1.78009
$794$	−37.1682	−1.31905
$795$	−17.0453	−0.604534
$796$	6.06695	0.215037
$797$	10.3127	0.365293	0.182647	−	0.983179i	$-0.441534\pi$
$797$	10.3127	0.365293	0.182647	+	0.983179i	$0.441534\pi$
$798$	−2.22713	−0.0788396
$799$	9.35165	0.330838
$800$	0.832456	0.0294317
$801$	5.90124	0.208510
$802$	−33.3032	−1.17598
$803$	0.174869	0.00617098
$804$	8.08996	0.285311
$805$	−11.5460	−0.406943
$806$	33.9474	1.19575
$807$	9.21723	0.324462
$808$	4.53643	0.159591
$809$	34.3088	1.20623	0.603116	−	0.797654i	$-0.293926\pi$
$809$	34.3088	1.20623	0.603116	+	0.797654i	$0.293926\pi$
$810$	−2.41505	−0.0848561
$811$	−31.5472	−1.10777	−0.553887	−	0.832592i	$-0.686856\pi$
$811$	−31.5472	−1.10777	−0.553887	+	0.832592i	$0.686856\pi$
$812$	−0.617689	−0.0216766
$813$	−11.7982	−0.413780
$814$	−1.05477	−0.0369697
$815$	30.2940	1.06115
$816$	1.00000	0.0350070
$817$	8.91466	0.311884
$818$	−18.5656	−0.649132
$819$	4.71093	0.164613
$820$	6.02562	0.210424
$821$	22.2564	0.776753	0.388377	−	0.921501i	$-0.373036\pi$
$821$	22.2564	0.776753	0.388377	+	0.921501i	$0.373036\pi$
$822$	6.82797	0.238153
$823$	−24.6764	−0.860165	−0.430082	−	0.902790i	$-0.641515\pi$
$823$	−24.6764	−0.860165	−0.430082	+	0.902790i	$0.641515\pi$
$824$	−3.62963	−0.126444
$825$	0.187633	0.00653255
$826$	−1.11075	−0.0386479
$827$	−30.7133	−1.06801	−0.534003	−	0.845483i	$-0.679313\pi$
$827$	−30.7133	−1.06801	−0.534003	+	0.845483i	$0.679313\pi$
$828$	4.30418	0.149580
$829$	2.17608	0.0755783	0.0377892	−	0.999286i	$-0.487968\pi$
$829$	2.17608	0.0755783	0.0377892	+	0.999286i	$0.487968\pi$
$830$	−17.8043	−0.617997
$831$	−16.8531	−0.584627
$832$	4.24122	0.147038
$833$	−5.76624	−0.199788
$834$	15.4132	0.533715
$835$	33.7609	1.16834
$836$	−0.451938	−0.0156306
$837$	8.00416	0.276664
$838$	−18.2543	−0.630585
$839$	−18.5194	−0.639360	−0.319680	−	0.947526i	$-0.603575\pi$
$839$	−18.5194	−0.639360	−0.319680	+	0.947526i	$0.603575\pi$
$840$	−2.68251	−0.0925554
$841$	−28.6908	−0.989336
$842$	−14.2267	−0.490285
$843$	3.22572	0.111100
$844$	6.11037	0.210328
$845$	−12.0461	−0.414399
$846$	9.35165	0.321516
$847$	−12.1618	−0.417884
$848$	7.05794	0.242371
$849$	23.4674	0.805398
$850$	0.832456	0.0285530
$851$	−20.1419	−0.690454
$852$	10.9700	0.375826
$853$	−36.1008	−1.23607	−0.618035	−	0.786151i	$-0.712071\pi$
$853$	−36.1008	−1.23607	−0.618035	+	0.786151i	$0.712071\pi$
$854$	−13.1281	−0.449236
$855$	4.84235	0.165605
$856$	−4.14289	−0.141601
$857$	1.35508	0.0462885	0.0231443	−	0.999732i	$-0.492632\pi$
$857$	1.35508	0.0462885	0.0231443	+	0.999732i	$0.492632\pi$
$858$	0.955960	0.0326359
$859$	46.2200	1.57701	0.788503	−	0.615031i	$-0.210856\pi$
$859$	46.2200	1.57701	0.788503	+	0.615031i	$0.210856\pi$
$860$	10.7374	0.366143
$861$	−2.77135	−0.0944475
$862$	−16.4991	−0.561960
$863$	40.5831	1.38147	0.690733	−	0.723110i	$-0.257288\pi$
$863$	40.5831	1.38147	0.690733	+	0.723110i	$0.257288\pi$
$864$	1.00000	0.0340207
$865$	−3.54780	−0.120629
$866$	9.08498	0.308720
$867$	1.00000	0.0339618
$868$	8.89060	0.301767
$869$	−0.930724	−0.0315727
$870$	1.34301	0.0455324
$871$	34.3113	1.16259
$872$	16.4415	0.556781
$873$	−4.80376	−0.162583
$874$	−8.63019	−0.291920
$875$	11.1795	0.377935
$876$	0.775824	0.0262127
$877$	−32.0706	−1.08295	−0.541473	−	0.840718i	$-0.682133\pi$
$877$	−32.0706	−1.08295	−0.541473	+	0.840718i	$0.682133\pi$
$878$	8.86600	0.299213
$879$	−21.2104	−0.715411
$880$	−0.544346	−0.0183499
$881$	3.82596	0.128900	0.0644499	−	0.997921i	$-0.479471\pi$
$881$	3.82596	0.128900	0.0644499	+	0.997921i	$0.479471\pi$
$882$	−5.76624	−0.194159
$883$	13.5605	0.456349	0.228174	−	0.973620i	$-0.426724\pi$
$883$	13.5605	0.456349	0.228174	+	0.973620i	$0.426724\pi$
$884$	4.24122	0.142648
$885$	2.41505	0.0811809
$886$	−38.0293	−1.27762
$887$	−46.2828	−1.55403	−0.777013	−	0.629485i	$-0.783266\pi$
$887$	−46.2828	−1.55403	−0.777013	+	0.629485i	$0.783266\pi$
$888$	−4.67961	−0.157037
$889$	8.20239	0.275099
$890$	−14.2518	−0.477721
$891$	0.225397	0.00755110
$892$	−15.5405	−0.520334
$893$	−18.7507	−0.627469
$894$	15.2076	0.508617
$895$	−23.0835	−0.771598
$896$	1.11075	0.0371075
$897$	18.2550	0.609515
$898$	−21.5380	−0.718733
$899$	−4.45112	−0.148453
$900$	0.832456	0.0277485
$901$	7.05794	0.235134
$902$	−0.562374	−0.0187250
$903$	−4.93845	−0.164341
$904$	9.12148	0.303376
$905$	53.7426	1.78646
$906$	−7.35113	−0.244225
$907$	−1.23267	−0.0409303	−0.0204651	−	0.999791i	$-0.506515\pi$
$907$	−1.23267	−0.0409303	−0.0204651	+	0.999791i	$0.506515\pi$
$908$	4.92743	0.163522
$909$	4.53643	0.150464
$910$	−11.3771	−0.377148
$911$	−5.89615	−0.195348	−0.0976740	−	0.995218i	$-0.531140\pi$
$911$	−5.89615	−0.195348	−0.0976740	+	0.995218i	$0.531140\pi$
$912$	−2.00507	−0.0663946
$913$	1.66169	0.0549938
$914$	−15.2458	−0.504287
$915$	28.5439	0.943632
$916$	9.33763	0.308524
$917$	13.9378	0.460268
$918$	1.00000	0.0330049
$919$	−25.4585	−0.839799	−0.419899	−	0.907571i	$-0.637935\pi$
$919$	−25.4585	−0.839799	−0.419899	+	0.907571i	$0.637935\pi$
$920$	−10.3948	−0.342706
$921$	24.7950	0.817025
$922$	−19.4984	−0.642147
$923$	46.5262	1.53143
$924$	0.250360	0.00823623
$925$	−3.89557	−0.128085
$926$	22.0758	0.725457
$927$	−3.62963	−0.119213
$928$	−0.556101	−0.0182549
$929$	39.2799	1.28873	0.644367	−	0.764717i	$-0.277121\pi$
$929$	39.2799	1.28873	0.644367	+	0.764717i	$0.277121\pi$
$930$	−19.3304	−0.633869
$931$	11.5617	0.378920
$932$	−8.21264	−0.269014
$933$	20.5465	0.672661
$934$	23.7377	0.776722
$935$	−0.544346	−0.0178020
$936$	4.24122	0.138629
$937$	−16.5652	−0.541160	−0.270580	−	0.962697i	$-0.587215\pi$
$937$	−16.5652	−0.541160	−0.270580	+	0.962697i	$0.587215\pi$
$938$	8.98591	0.293400
$939$	−26.4973	−0.864706
$940$	−22.5847	−0.736631
$941$	−21.8708	−0.712968	−0.356484	−	0.934301i	$-0.616025\pi$
$941$	−21.8708	−0.712968	−0.356484	+	0.934301i	$0.616025\pi$
$942$	22.2380	0.724554
$943$	−10.7391	−0.349712
$944$	−1.00000	−0.0325472
$945$	−2.68251	−0.0872621
$946$	−1.00213	−0.0325820
$947$	−19.8091	−0.643710	−0.321855	−	0.946789i	$-0.604306\pi$
$947$	−19.8091	−0.643710	−0.321855	+	0.946789i	$0.604306\pi$
$948$	−4.12926	−0.134112
$949$	3.29044	0.106812
$950$	−1.66913	−0.0541539
$951$	21.2366	0.688645
$952$	1.11075	0.0359996
$953$	0.955962	0.0309666	0.0154833	−	0.999880i	$-0.495071\pi$
$953$	0.955962	0.0309666	0.0154833	+	0.999880i	$0.495071\pi$
$954$	7.05794	0.228509
$955$	−19.7246	−0.638274
$956$	−8.80662	−0.284827
$957$	−0.125344	−0.00405179
$958$	17.1622	0.554485
$959$	7.58415	0.244905
$960$	−2.41505	−0.0779453
$961$	33.0665	1.06666
$962$	−19.8472	−0.639901
$963$	−4.14289	−0.133503
$964$	−6.03805	−0.194472
$965$	16.7030	0.537687
$966$	4.78086	0.153822
$967$	38.4569	1.23669	0.618346	−	0.785906i	$-0.287803\pi$
$967$	38.4569	1.23669	0.618346	+	0.785906i	$0.287803\pi$
$968$	−10.9492	−0.351920
$969$	−2.00507	−0.0644122
$970$	11.6013	0.372496
$971$	−35.5090	−1.13954	−0.569768	−	0.821805i	$-0.692967\pi$
$971$	−35.5090	−1.13954	−0.569768	+	0.821805i	$0.692967\pi$
$972$	1.00000	0.0320750
$973$	17.1202	0.548848
$974$	−22.6072	−0.724382
$975$	3.53063	0.113071
$976$	−11.8192	−0.378323
$977$	−4.26805	−0.136547	−0.0682734	−	0.997667i	$-0.521749\pi$
$977$	−4.26805	−0.136547	−0.0682734	+	0.997667i	$0.521749\pi$
$978$	−12.5439	−0.401108
$979$	1.33012	0.0425110
$980$	13.9257	0.444841
$981$	16.4415	0.524938
$982$	0.199856	0.00637767
$983$	−48.9600	−1.56158	−0.780791	−	0.624792i	$-0.785184\pi$
$983$	−48.9600	−1.56158	−0.780791	+	0.624792i	$0.785184\pi$
$984$	−2.49503	−0.0795387
$985$	0.177696	0.00566186
$986$	−0.556101	−0.0177099
$987$	10.3873	0.330632
$988$	−8.50395	−0.270547
$989$	−19.1366	−0.608508
$990$	−0.544346	−0.0173004
$991$	44.2192	1.40467	0.702334	−	0.711847i	$-0.252141\pi$
$991$	44.2192	1.40467	0.702334	+	0.711847i	$0.252141\pi$
$992$	8.00416	0.254132
$993$	28.3974	0.901165
$994$	12.1849	0.386482
$995$	−14.6520	−0.464499
$996$	7.37225	0.233599
$997$	−38.4325	−1.21717	−0.608584	−	0.793489i	$-0.708262\pi$
$997$	−38.4325	−1.21717	−0.608584	+	0.793489i	$0.708262\pi$
$998$	−25.2118	−0.798066
$999$	−4.67961	−0.148056

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.bb.1.3	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.bb.1.3	✓	13	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.41505 q^{5} +1.00000 q^{6} +1.11075 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.41505 q^{5} +1.00000 q^{6} +1.11075 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.41505 q^{10} +0.225397 q^{11} +1.00000 q^{12} +4.24122 q^{13} +1.11075 q^{14} -2.41505 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -2.00507 q^{19} -2.41505 q^{20} +1.11075 q^{21} +0.225397 q^{22} +4.30418 q^{23} +1.00000 q^{24} +0.832456 q^{25} +4.24122 q^{26} +1.00000 q^{27} +1.11075 q^{28} -0.556101 q^{29} -2.41505 q^{30} +8.00416 q^{31} +1.00000 q^{32} +0.225397 q^{33} +1.00000 q^{34} -2.68251 q^{35} +1.00000 q^{36} -4.67961 q^{37} -2.00507 q^{38} +4.24122 q^{39} -2.41505 q^{40} -2.49503 q^{41} +1.11075 q^{42} -4.44605 q^{43} +0.225397 q^{44} -2.41505 q^{45} +4.30418 q^{46} +9.35165 q^{47} +1.00000 q^{48} -5.76624 q^{49} +0.832456 q^{50} +1.00000 q^{51} +4.24122 q^{52} +7.05794 q^{53} +1.00000 q^{54} -0.544346 q^{55} +1.11075 q^{56} -2.00507 q^{57} -0.556101 q^{58} -1.00000 q^{59} -2.41505 q^{60} -11.8192 q^{61} +8.00416 q^{62} +1.11075 q^{63} +1.00000 q^{64} -10.2427 q^{65} +0.225397 q^{66} +8.08996 q^{67} +1.00000 q^{68} +4.30418 q^{69} -2.68251 q^{70} +10.9700 q^{71} +1.00000 q^{72} +0.775824 q^{73} -4.67961 q^{74} +0.832456 q^{75} -2.00507 q^{76} +0.250360 q^{77} +4.24122 q^{78} -4.12926 q^{79} -2.41505 q^{80} +1.00000 q^{81} -2.49503 q^{82} +7.37225 q^{83} +1.11075 q^{84} -2.41505 q^{85} -4.44605 q^{86} -0.556101 q^{87} +0.225397 q^{88} +5.90124 q^{89} -2.41505 q^{90} +4.71093 q^{91} +4.30418 q^{92} +8.00416 q^{93} +9.35165 q^{94} +4.84235 q^{95} +1.00000 q^{96} -4.80376 q^{97} -5.76624 q^{98} +0.225397 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 4 * q^5 + 13 * q^6 + 11 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9} + 4 q^{10} + 7 q^{11} + 13 q^{12} + 6 q^{13} + 11 q^{14} + 4 q^{15} + 13 q^{16} + 13 q^{17} + 13 q^{18} + 9 q^{19} + 4 q^{20} + 11 q^{21} + 7 q^{22} + 2 q^{23} + 13 q^{24} + 33 q^{25} + 6 q^{26} + 13 q^{27} + 11 q^{28} + 14 q^{29} + 4 q^{30} - 5 q^{31} + 13 q^{32} + 7 q^{33} + 13 q^{34} + 24 q^{35} + 13 q^{36} + 4 q^{37} + 9 q^{38} + 6 q^{39} + 4 q^{40} + 28 q^{41} + 11 q^{42} + q^{43} + 7 q^{44} + 4 q^{45} + 2 q^{46} + 12 q^{47} + 13 q^{48} + 32 q^{49} + 33 q^{50} + 13 q^{51} + 6 q^{52} + 22 q^{53} + 13 q^{54} - 7 q^{55} + 11 q^{56} + 9 q^{57} + 14 q^{58} - 13 q^{59} + 4 q^{60} - 9 q^{61} - 5 q^{62} + 11 q^{63} + 13 q^{64} + 34 q^{65} + 7 q^{66} + 26 q^{67} + 13 q^{68} + 2 q^{69} + 24 q^{70} + 8 q^{71} + 13 q^{72} + 4 q^{73} + 4 q^{74} + 33 q^{75} + 9 q^{76} + 38 q^{77} + 6 q^{78} - 17 q^{79} + 4 q^{80} + 13 q^{81} + 28 q^{82} + 14 q^{83} + 11 q^{84} + 4 q^{85} + q^{86} + 14 q^{87} + 7 q^{88} + 19 q^{89} + 4 q^{90} - 5 q^{91} + 2 q^{92} - 5 q^{93} + 12 q^{94} + 25 q^{95} + 13 q^{96} - 5 q^{97} + 32 q^{98} + 7 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 4 * q^5 + 13 * q^6 + 11 * q^7 + 13 * q^8 + 13 * q^9 + 4 * q^10 + 7 * q^11 + 13 * q^12 + 6 * q^13 + 11 * q^14 + 4 * q^15 + 13 * q^16 + 13 * q^17 + 13 * q^18 + 9 * q^19 + 4 * q^20 + 11 * q^21 + 7 * q^22 + 2 * q^23 + 13 * q^24 + 33 * q^25 + 6 * q^26 + 13 * q^27 + 11 * q^28 + 14 * q^29 + 4 * q^30 - 5 * q^31 + 13 * q^32 + 7 * q^33 + 13 * q^34 + 24 * q^35 + 13 * q^36 + 4 * q^37 + 9 * q^38 + 6 * q^39 + 4 * q^40 + 28 * q^41 + 11 * q^42 + q^43 + 7 * q^44 + 4 * q^45 + 2 * q^46 + 12 * q^47 + 13 * q^48 + 32 * q^49 + 33 * q^50 + 13 * q^51 + 6 * q^52 + 22 * q^53 + 13 * q^54 - 7 * q^55 + 11 * q^56 + 9 * q^57 + 14 * q^58 - 13 * q^59 + 4 * q^60 - 9 * q^61 - 5 * q^62 + 11 * q^63 + 13 * q^64 + 34 * q^65 + 7 * q^66 + 26 * q^67 + 13 * q^68 + 2 * q^69 + 24 * q^70 + 8 * q^71 + 13 * q^72 + 4 * q^73 + 4 * q^74 + 33 * q^75 + 9 * q^76 + 38 * q^77 + 6 * q^78 - 17 * q^79 + 4 * q^80 + 13 * q^81 + 28 * q^82 + 14 * q^83 + 11 * q^84 + 4 * q^85 + q^86 + 14 * q^87 + 7 * q^88 + 19 * q^89 + 4 * q^90 - 5 * q^91 + 2 * q^92 - 5 * q^93 + 12 * q^94 + 25 * q^95 + 13 * q^96 - 5 * q^97 + 32 * q^98 + 7 * q^99

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