LMFDB - Embedded newform 6018.2.a.bb.1.10

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			1.10
Root			$2.71857$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.71857 q^{5} +1.00000 q^{6} +1.56988 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.71857 q^{5} +1.00000 q^{6} +1.56988 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.71857 q^{10} +3.34838 q^{11} +1.00000 q^{12} -0.269621 q^{13} +1.56988 q^{14} +2.71857 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +4.26085 q^{19} +2.71857 q^{20} +1.56988 q^{21} +3.34838 q^{22} +8.99608 q^{23} +1.00000 q^{24} +2.39064 q^{25} -0.269621 q^{26} +1.00000 q^{27} +1.56988 q^{28} -8.55316 q^{29} +2.71857 q^{30} +5.67885 q^{31} +1.00000 q^{32} +3.34838 q^{33} +1.00000 q^{34} +4.26784 q^{35} +1.00000 q^{36} -2.61490 q^{37} +4.26085 q^{38} -0.269621 q^{39} +2.71857 q^{40} -2.42101 q^{41} +1.56988 q^{42} -11.3475 q^{43} +3.34838 q^{44} +2.71857 q^{45} +8.99608 q^{46} -8.87826 q^{47} +1.00000 q^{48} -4.53547 q^{49} +2.39064 q^{50} +1.00000 q^{51} -0.269621 q^{52} -6.64902 q^{53} +1.00000 q^{54} +9.10282 q^{55} +1.56988 q^{56} +4.26085 q^{57} -8.55316 q^{58} -1.00000 q^{59} +2.71857 q^{60} -6.19807 q^{61} +5.67885 q^{62} +1.56988 q^{63} +1.00000 q^{64} -0.732986 q^{65} +3.34838 q^{66} -14.2823 q^{67} +1.00000 q^{68} +8.99608 q^{69} +4.26784 q^{70} -12.7654 q^{71} +1.00000 q^{72} +6.38818 q^{73} -2.61490 q^{74} +2.39064 q^{75} +4.26085 q^{76} +5.25656 q^{77} -0.269621 q^{78} +1.50524 q^{79} +2.71857 q^{80} +1.00000 q^{81} -2.42101 q^{82} -6.12503 q^{83} +1.56988 q^{84} +2.71857 q^{85} -11.3475 q^{86} -8.55316 q^{87} +3.34838 q^{88} +7.05823 q^{89} +2.71857 q^{90} -0.423274 q^{91} +8.99608 q^{92} +5.67885 q^{93} -8.87826 q^{94} +11.5834 q^{95} +1.00000 q^{96} +4.17573 q^{97} -4.53547 q^{98} +3.34838 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	2.71857	1.21578	0.607892	−	0.794020i	$-0.292016\pi$
$5$	2.71857	1.21578	0.607892	+	0.794020i	$0.292016\pi$
$6$	1.00000	0.408248
$7$	1.56988	0.593359	0.296680	−	0.954977i	$-0.404121\pi$
$7$	1.56988	0.593359	0.296680	+	0.954977i	$0.404121\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.71857	0.859689
$11$	3.34838	1.00957	0.504787	−	0.863244i	$-0.331571\pi$
$11$	3.34838	1.00957	0.504787	+	0.863244i	$0.331571\pi$
$12$	1.00000	0.288675
$13$	−0.269621	−0.0747795	−0.0373898	−	0.999301i	$-0.511904\pi$
$13$	−0.269621	−0.0747795	−0.0373898	+	0.999301i	$0.511904\pi$
$14$	1.56988	0.419568
$15$	2.71857	0.701933
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	4.26085	0.977505	0.488753	−	0.872422i	$-0.337452\pi$
$19$	4.26085	0.977505	0.488753	+	0.872422i	$0.337452\pi$
$20$	2.71857	0.607892
$21$	1.56988	0.342576
$22$	3.34838	0.713877
$23$	8.99608	1.87581	0.937906	−	0.346890i	$-0.112762\pi$
$23$	8.99608	1.87581	0.937906	+	0.346890i	$0.112762\pi$
$24$	1.00000	0.204124
$25$	2.39064	0.478129
$26$	−0.269621	−0.0528771
$27$	1.00000	0.192450
$28$	1.56988	0.296680
$29$	−8.55316	−1.58828	−0.794141	−	0.607734i	$-0.792079\pi$
$29$	−8.55316	−1.58828	−0.794141	+	0.607734i	$0.792079\pi$
$30$	2.71857	0.496341
$31$	5.67885	1.01995	0.509976	−	0.860189i	$-0.329654\pi$
$31$	5.67885	1.01995	0.509976	+	0.860189i	$0.329654\pi$
$32$	1.00000	0.176777
$33$	3.34838	0.582878
$34$	1.00000	0.171499
$35$	4.26784	0.721396
$36$	1.00000	0.166667
$37$	−2.61490	−0.429887	−0.214943	−	0.976626i	$-0.568957\pi$
$37$	−2.61490	−0.429887	−0.214943	+	0.976626i	$0.568957\pi$
$38$	4.26085	0.691201
$39$	−0.269621	−0.0431740
$40$	2.71857	0.429844
$41$	−2.42101	−0.378098	−0.189049	−	0.981968i	$-0.560540\pi$
$41$	−2.42101	−0.378098	−0.189049	+	0.981968i	$0.560540\pi$
$42$	1.56988	0.242238
$43$	−11.3475	−1.73048	−0.865238	−	0.501361i	$-0.832833\pi$
$43$	−11.3475	−1.73048	−0.865238	+	0.501361i	$0.832833\pi$
$44$	3.34838	0.504787
$45$	2.71857	0.405261
$46$	8.99608	1.32640
$47$	−8.87826	−1.29503	−0.647513	−	0.762054i	$-0.724191\pi$
$47$	−8.87826	−1.29503	−0.647513	+	0.762054i	$0.724191\pi$
$48$	1.00000	0.144338
$49$	−4.53547	−0.647925
$50$	2.39064	0.338088
$51$	1.00000	0.140028
$52$	−0.269621	−0.0373898
$53$	−6.64902	−0.913313	−0.456656	−	0.889643i	$-0.650953\pi$
$53$	−6.64902	−0.913313	−0.456656	+	0.889643i	$0.650953\pi$
$54$	1.00000	0.136083
$55$	9.10282	1.22742
$56$	1.56988	0.209784
$57$	4.26085	0.564363
$58$	−8.55316	−1.12308
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	2.71857	0.350966
$61$	−6.19807	−0.793582	−0.396791	−	0.917909i	$-0.629876\pi$
$61$	−6.19807	−0.793582	−0.396791	+	0.917909i	$0.629876\pi$
$62$	5.67885	0.721215
$63$	1.56988	0.197786
$64$	1.00000	0.125000
$65$	−0.732986	−0.0909157
$66$	3.34838	0.412157
$67$	−14.2823	−1.74486	−0.872430	−	0.488740i	$-0.837457\pi$
$67$	−14.2823	−1.74486	−0.872430	+	0.488740i	$0.837457\pi$
$68$	1.00000	0.121268
$69$	8.99608	1.08300
$70$	4.26784	0.510104
$71$	−12.7654	−1.51498	−0.757489	−	0.652848i	$-0.773574\pi$
$71$	−12.7654	−1.51498	−0.757489	+	0.652848i	$0.773574\pi$
$72$	1.00000	0.117851
$73$	6.38818	0.747679	0.373840	−	0.927493i	$-0.378041\pi$
$73$	6.38818	0.747679	0.373840	+	0.927493i	$0.378041\pi$
$74$	−2.61490	−0.303976
$75$	2.39064	0.276048
$76$	4.26085	0.488753
$77$	5.25656	0.599040
$78$	−0.269621	−0.0305286
$79$	1.50524	0.169353	0.0846766	−	0.996408i	$-0.473014\pi$
$79$	1.50524	0.169353	0.0846766	+	0.996408i	$0.473014\pi$
$80$	2.71857	0.303946
$81$	1.00000	0.111111
$82$	−2.42101	−0.267355
$83$	−6.12503	−0.672309	−0.336155	−	0.941807i	$-0.609126\pi$
$83$	−6.12503	−0.672309	−0.336155	+	0.941807i	$0.609126\pi$
$84$	1.56988	0.171288
$85$	2.71857	0.294871
$86$	−11.3475	−1.22363
$87$	−8.55316	−0.916995
$88$	3.34838	0.356938
$89$	7.05823	0.748171	0.374086	−	0.927394i	$-0.377957\pi$
$89$	7.05823	0.748171	0.374086	+	0.927394i	$0.377957\pi$
$90$	2.71857	0.286563
$91$	−0.423274	−0.0443711
$92$	8.99608	0.937906
$93$	5.67885	0.588870
$94$	−8.87826	−0.915722
$95$	11.5834	1.18843
$96$	1.00000	0.102062
$97$	4.17573	0.423981	0.211990	−	0.977272i	$-0.432005\pi$
$97$	4.17573	0.423981	0.211990	+	0.977272i	$0.432005\pi$
$98$	−4.53547	−0.458152
$99$	3.34838	0.336525
$100$	2.39064	0.239064
$101$	−5.48724	−0.546001	−0.273000	−	0.962014i	$-0.588016\pi$
$101$	−5.48724	−0.546001	−0.273000	+	0.962014i	$0.588016\pi$
$102$	1.00000	0.0990148
$103$	8.46777	0.834355	0.417177	−	0.908825i	$-0.363019\pi$
$103$	8.46777	0.834355	0.417177	+	0.908825i	$0.363019\pi$
$104$	−0.269621	−0.0264386
$105$	4.26784	0.416498
$106$	−6.64902	−0.645809
$107$	14.7517	1.42610	0.713049	−	0.701114i	$-0.247314\pi$
$107$	14.7517	1.42610	0.713049	+	0.701114i	$0.247314\pi$
$108$	1.00000	0.0962250
$109$	−12.0900	−1.15801	−0.579005	−	0.815324i	$-0.696559\pi$
$109$	−12.0900	−1.15801	−0.579005	+	0.815324i	$0.696559\pi$
$110$	9.10282	0.867920
$111$	−2.61490	−0.248195
$112$	1.56988	0.148340
$113$	−5.85092	−0.550408	−0.275204	−	0.961386i	$-0.588745\pi$
$113$	−5.85092	−0.550408	−0.275204	+	0.961386i	$0.588745\pi$
$114$	4.26085	0.399065
$115$	24.4565	2.28058
$116$	−8.55316	−0.794141
$117$	−0.269621	−0.0249265
$118$	−1.00000	−0.0920575
$119$	1.56988	0.143911
$120$	2.71857	0.248171
$121$	0.211644	0.0192404
$122$	−6.19807	−0.561147
$123$	−2.42101	−0.218295
$124$	5.67885	0.509976
$125$	−7.09373	−0.634482
$126$	1.56988	0.139856
$127$	10.2727	0.911553	0.455777	−	0.890094i	$-0.349362\pi$
$127$	10.2727	0.911553	0.455777	+	0.890094i	$0.349362\pi$
$128$	1.00000	0.0883883
$129$	−11.3475	−0.999091
$130$	−0.732986	−0.0642871
$131$	14.4070	1.25875	0.629374	−	0.777103i	$-0.283312\pi$
$131$	14.4070	1.25875	0.629374	+	0.777103i	$0.283312\pi$
$132$	3.34838	0.291439
$133$	6.68902	0.580012
$134$	−14.2823	−1.23380
$135$	2.71857	0.233978
$136$	1.00000	0.0857493
$137$	−20.6923	−1.76786	−0.883931	−	0.467617i	$-0.845113\pi$
$137$	−20.6923	−1.76786	−0.883931	+	0.467617i	$0.845113\pi$
$138$	8.99608	0.765797
$139$	17.0175	1.44340	0.721701	−	0.692205i	$-0.243361\pi$
$139$	17.0175	1.44340	0.721701	+	0.692205i	$0.243361\pi$
$140$	4.26784	0.360698
$141$	−8.87826	−0.747684
$142$	−12.7654	−1.07125
$143$	−0.902795	−0.0754955
$144$	1.00000	0.0833333
$145$	−23.2524	−1.93101
$146$	6.38818	0.528689
$147$	−4.53547	−0.374080
$148$	−2.61490	−0.214943
$149$	9.18601	0.752547	0.376274	−	0.926509i	$-0.377205\pi$
$149$	9.18601	0.752547	0.376274	+	0.926509i	$0.377205\pi$
$150$	2.39064	0.195195
$151$	−6.00736	−0.488872	−0.244436	−	0.969665i	$-0.578603\pi$
$151$	−6.00736	−0.488872	−0.244436	+	0.969665i	$0.578603\pi$
$152$	4.26085	0.345600
$153$	1.00000	0.0808452
$154$	5.25656	0.423585
$155$	15.4384	1.24004
$156$	−0.269621	−0.0215870
$157$	11.8143	0.942884	0.471442	−	0.881897i	$-0.343734\pi$
$157$	11.8143	0.942884	0.471442	+	0.881897i	$0.343734\pi$
$158$	1.50524	0.119751
$159$	−6.64902	−0.527301
$160$	2.71857	0.214922
$161$	14.1228	1.11303
$162$	1.00000	0.0785674
$163$	11.2176	0.878630	0.439315	−	0.898333i	$-0.355221\pi$
$163$	11.2176	0.878630	0.439315	+	0.898333i	$0.355221\pi$
$164$	−2.42101	−0.189049
$165$	9.10282	0.708653
$166$	−6.12503	−0.475394
$167$	1.03582	0.0801540	0.0400770	−	0.999197i	$-0.487240\pi$
$167$	1.03582	0.0801540	0.0400770	+	0.999197i	$0.487240\pi$
$168$	1.56988	0.121119
$169$	−12.9273	−0.994408
$170$	2.71857	0.208505
$171$	4.26085	0.325835
$172$	−11.3475	−0.865238
$173$	0.766047	0.0582415	0.0291207	−	0.999576i	$-0.490729\pi$
$173$	0.766047	0.0582415	0.0291207	+	0.999576i	$0.490729\pi$
$174$	−8.55316	−0.648413
$175$	3.75303	0.283702
$176$	3.34838	0.252394
$177$	−1.00000	−0.0751646
$178$	7.05823	0.529037
$179$	6.84072	0.511299	0.255650	−	0.966770i	$-0.417711\pi$
$179$	6.84072	0.511299	0.255650	+	0.966770i	$0.417711\pi$
$180$	2.71857	0.202631
$181$	14.1995	1.05544	0.527720	−	0.849419i	$-0.323047\pi$
$181$	14.1995	1.05544	0.527720	+	0.849419i	$0.323047\pi$
$182$	−0.423274	−0.0313751
$183$	−6.19807	−0.458175
$184$	8.99608	0.663200
$185$	−7.10880	−0.522649
$186$	5.67885	0.416394
$187$	3.34838	0.244858
$188$	−8.87826	−0.647513
$189$	1.56988	0.114192
$190$	11.5834	0.840350
$191$	−24.3882	−1.76467	−0.882335	−	0.470622i	$-0.844030\pi$
$191$	−24.3882	−1.76467	−0.882335	+	0.470622i	$0.844030\pi$
$192$	1.00000	0.0721688
$193$	−18.3416	−1.32026	−0.660128	−	0.751153i	$-0.729498\pi$
$193$	−18.3416	−1.32026	−0.660128	+	0.751153i	$0.729498\pi$
$194$	4.17573	0.299800
$195$	−0.732986	−0.0524902
$196$	−4.53547	−0.323962
$197$	3.64879	0.259966	0.129983	−	0.991516i	$-0.458508\pi$
$197$	3.64879	0.259966	0.129983	+	0.991516i	$0.458508\pi$
$198$	3.34838	0.237959
$199$	14.0668	0.997167	0.498584	−	0.866842i	$-0.333854\pi$
$199$	14.0668	0.997167	0.498584	+	0.866842i	$0.333854\pi$
$200$	2.39064	0.169044
$201$	−14.2823	−1.00739
$202$	−5.48724	−0.386081
$203$	−13.4274	−0.942422
$204$	1.00000	0.0700140
$205$	−6.58168	−0.459685
$206$	8.46777	0.589978
$207$	8.99608	0.625271
$208$	−0.269621	−0.0186949
$209$	14.2669	0.986864
$210$	4.26784	0.294509
$211$	−0.186574	−0.0128443	−0.00642214	−	0.999979i	$-0.502044\pi$
$211$	−0.186574	−0.0128443	−0.00642214	+	0.999979i	$0.502044\pi$
$212$	−6.64902	−0.456656
$213$	−12.7654	−0.874673
$214$	14.7517	1.00840
$215$	−30.8490	−2.10388
$216$	1.00000	0.0680414
$217$	8.91513	0.605198
$218$	−12.0900	−0.818837
$219$	6.38818	0.431673
$220$	9.10282	0.613712
$221$	−0.269621	−0.0181367
$222$	−2.61490	−0.175501
$223$	1.27089	0.0851049	0.0425524	−	0.999094i	$-0.486451\pi$
$223$	1.27089	0.0851049	0.0425524	+	0.999094i	$0.486451\pi$
$224$	1.56988	0.104892
$225$	2.39064	0.159376
$226$	−5.85092	−0.389197
$227$	−9.20637	−0.611048	−0.305524	−	0.952184i	$-0.598832\pi$
$227$	−9.20637	−0.611048	−0.305524	+	0.952184i	$0.598832\pi$
$228$	4.26085	0.282182
$229$	−10.1171	−0.668559	−0.334279	−	0.942474i	$-0.608493\pi$
$229$	−10.1171	−0.668559	−0.334279	+	0.942474i	$0.608493\pi$
$230$	24.4565	1.61261
$231$	5.25656	0.345856
$232$	−8.55316	−0.561542
$233$	−3.78205	−0.247770	−0.123885	−	0.992297i	$-0.539535\pi$
$233$	−3.78205	−0.247770	−0.123885	+	0.992297i	$0.539535\pi$
$234$	−0.269621	−0.0176257
$235$	−24.1362	−1.57447
$236$	−1.00000	−0.0650945
$237$	1.50524	0.0977761
$238$	1.56988	0.101760
$239$	18.2535	1.18072	0.590360	−	0.807140i	$-0.298986\pi$
$239$	18.2535	1.18072	0.590360	+	0.807140i	$0.298986\pi$
$240$	2.71857	0.175483
$241$	−21.4055	−1.37885	−0.689423	−	0.724359i	$-0.742136\pi$
$241$	−21.4055	−1.37885	−0.689423	+	0.724359i	$0.742136\pi$
$242$	0.211644	0.0136050
$243$	1.00000	0.0641500
$244$	−6.19807	−0.396791
$245$	−12.3300	−0.787736
$246$	−2.42101	−0.154358
$247$	−1.14882	−0.0730974
$248$	5.67885	0.360608
$249$	−6.12503	−0.388158
$250$	−7.09373	−0.448647
$251$	5.79161	0.365563	0.182782	−	0.983154i	$-0.441490\pi$
$251$	5.79161	0.365563	0.182782	+	0.983154i	$0.441490\pi$
$252$	1.56988	0.0988932
$253$	30.1223	1.89377
$254$	10.2727	0.644565
$255$	2.71857	0.170244
$256$	1.00000	0.0625000
$257$	19.4842	1.21539	0.607694	−	0.794171i	$-0.292095\pi$
$257$	19.4842	1.21539	0.607694	+	0.794171i	$0.292095\pi$
$258$	−11.3475	−0.706464
$259$	−4.10508	−0.255077
$260$	−0.732986	−0.0454579
$261$	−8.55316	−0.529427
$262$	14.4070	0.890069
$263$	−8.75623	−0.539932	−0.269966	−	0.962870i	$-0.587013\pi$
$263$	−8.75623	−0.539932	−0.269966	+	0.962870i	$0.587013\pi$
$264$	3.34838	0.206079
$265$	−18.0758	−1.11039
$266$	6.68902	0.410130
$267$	7.05823	0.431957
$268$	−14.2823	−0.872430
$269$	19.4918	1.18844	0.594218	−	0.804304i	$-0.297461\pi$
$269$	19.4918	1.18844	0.594218	+	0.804304i	$0.297461\pi$
$270$	2.71857	0.165447
$271$	−15.8731	−0.964221	−0.482110	−	0.876110i	$-0.660130\pi$
$271$	−15.8731	−0.964221	−0.482110	+	0.876110i	$0.660130\pi$
$272$	1.00000	0.0606339
$273$	−0.423274	−0.0256177
$274$	−20.6923	−1.25007
$275$	8.00478	0.482707
$276$	8.99608	0.541500
$277$	9.44691	0.567610	0.283805	−	0.958882i	$-0.408403\pi$
$277$	9.44691	0.567610	0.283805	+	0.958882i	$0.408403\pi$
$278$	17.0175	1.02064
$279$	5.67885	0.339984
$280$	4.26784	0.255052
$281$	3.14736	0.187756	0.0938778	−	0.995584i	$-0.470074\pi$
$281$	3.14736	0.187756	0.0938778	+	0.995584i	$0.470074\pi$
$282$	−8.87826	−0.528692
$283$	14.8579	0.883212	0.441606	−	0.897209i	$-0.354409\pi$
$283$	14.8579	0.883212	0.441606	+	0.897209i	$0.354409\pi$
$284$	−12.7654	−0.757489
$285$	11.5834	0.686143
$286$	−0.902795	−0.0533834
$287$	−3.80069	−0.224348
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−23.2524	−1.36543
$291$	4.17573	0.244786
$292$	6.38818	0.373840
$293$	−7.06184	−0.412557	−0.206279	−	0.978493i	$-0.566135\pi$
$293$	−7.06184	−0.412557	−0.206279	+	0.978493i	$0.566135\pi$
$294$	−4.53547	−0.264514
$295$	−2.71857	−0.158281
$296$	−2.61490	−0.151988
$297$	3.34838	0.194293
$298$	9.18601	0.532131
$299$	−2.42554	−0.140272
$300$	2.39064	0.138024
$301$	−17.8142	−1.02679
$302$	−6.00736	−0.345684
$303$	−5.48724	−0.315234
$304$	4.26085	0.244376
$305$	−16.8499	−0.964823
$306$	1.00000	0.0571662
$307$	2.94827	0.168267	0.0841333	−	0.996455i	$-0.473188\pi$
$307$	2.94827	0.168267	0.0841333	+	0.996455i	$0.473188\pi$
$308$	5.25656	0.299520
$309$	8.46777	0.481715
$310$	15.4384	0.876841
$311$	8.82485	0.500411	0.250206	−	0.968193i	$-0.419502\pi$
$311$	8.82485	0.500411	0.250206	+	0.968193i	$0.419502\pi$
$312$	−0.269621	−0.0152643
$313$	6.50132	0.367477	0.183738	−	0.982975i	$-0.441180\pi$
$313$	6.50132	0.367477	0.183738	+	0.982975i	$0.441180\pi$
$314$	11.8143	0.666720
$315$	4.26784	0.240465
$316$	1.50524	0.0846766
$317$	−10.0410	−0.563956	−0.281978	−	0.959421i	$-0.590991\pi$
$317$	−10.0410	−0.563956	−0.281978	+	0.959421i	$0.590991\pi$
$318$	−6.64902	−0.372858
$319$	−28.6392	−1.60349
$320$	2.71857	0.151973
$321$	14.7517	0.823358
$322$	14.1228	0.787031
$323$	4.26085	0.237080
$324$	1.00000	0.0555556
$325$	−0.644569	−0.0357543
$326$	11.2176	0.621285
$327$	−12.0900	−0.668578
$328$	−2.42101	−0.133678
$329$	−13.9378	−0.768416
$330$	9.10282	0.501094
$331$	−27.7264	−1.52398	−0.761990	−	0.647589i	$-0.775778\pi$
$331$	−27.7264	−1.52398	−0.761990	+	0.647589i	$0.775778\pi$
$332$	−6.12503	−0.336155
$333$	−2.61490	−0.143296
$334$	1.03582	0.0566774
$335$	−38.8275	−2.12137
$336$	1.56988	0.0856440
$337$	31.7224	1.72803	0.864015	−	0.503466i	$-0.167942\pi$
$337$	31.7224	1.72803	0.864015	+	0.503466i	$0.167942\pi$
$338$	−12.9273	−0.703153
$339$	−5.85092	−0.317778
$340$	2.71857	0.147435
$341$	19.0150	1.02972
$342$	4.26085	0.230400
$343$	−18.1093	−0.977811
$344$	−11.3475	−0.611816
$345$	24.4565	1.31669
$346$	0.766047	0.0411829
$347$	2.38350	0.127953	0.0639766	−	0.997951i	$-0.479622\pi$
$347$	2.38350	0.127953	0.0639766	+	0.997951i	$0.479622\pi$
$348$	−8.55316	−0.458497
$349$	2.05189	0.109835	0.0549176	−	0.998491i	$-0.482510\pi$
$349$	2.05189	0.109835	0.0549176	+	0.998491i	$0.482510\pi$
$350$	3.75303	0.200608
$351$	−0.269621	−0.0143913
$352$	3.34838	0.178469
$353$	5.14587	0.273887	0.136944	−	0.990579i	$-0.456272\pi$
$353$	5.14587	0.273887	0.136944	+	0.990579i	$0.456272\pi$
$354$	−1.00000	−0.0531494
$355$	−34.7038	−1.84188
$356$	7.05823	0.374086
$357$	1.56988	0.0830869
$358$	6.84072	0.361543
$359$	−4.01306	−0.211801	−0.105901	−	0.994377i	$-0.533773\pi$
$359$	−4.01306	−0.211801	−0.105901	+	0.994377i	$0.533773\pi$
$360$	2.71857	0.143281
$361$	−0.845178	−0.0444831
$362$	14.1995	0.746308
$363$	0.211644	0.0111085
$364$	−0.423274	−0.0221856
$365$	17.3667	0.909016
$366$	−6.19807	−0.323978
$367$	0.404510	0.0211152	0.0105576	−	0.999944i	$-0.496639\pi$
$367$	0.404510	0.0211152	0.0105576	+	0.999944i	$0.496639\pi$
$368$	8.99608	0.468953
$369$	−2.42101	−0.126033
$370$	−7.10880	−0.369569
$371$	−10.4382	−0.541922
$372$	5.67885	0.294435
$373$	35.2554	1.82545	0.912727	−	0.408571i	$-0.133973\pi$
$373$	35.2554	1.82545	0.912727	+	0.408571i	$0.133973\pi$
$374$	3.34838	0.173141
$375$	−7.09373	−0.366318
$376$	−8.87826	−0.457861
$377$	2.30611	0.118771
$378$	1.56988	0.0807460
$379$	12.8294	0.659000	0.329500	−	0.944156i	$-0.393120\pi$
$379$	12.8294	0.659000	0.329500	+	0.944156i	$0.393120\pi$
$380$	11.5834	0.594217
$381$	10.2727	0.526285
$382$	−24.3882	−1.24781
$383$	−30.3394	−1.55027	−0.775135	−	0.631796i	$-0.782318\pi$
$383$	−30.3394	−1.55027	−0.775135	+	0.631796i	$0.782318\pi$
$384$	1.00000	0.0510310
$385$	14.2903	0.728303
$386$	−18.3416	−0.933562
$387$	−11.3475	−0.576826
$388$	4.17573	0.211990
$389$	13.0630	0.662319	0.331160	−	0.943575i	$-0.392560\pi$
$389$	13.0630	0.662319	0.331160	+	0.943575i	$0.392560\pi$
$390$	−0.732986	−0.0371162
$391$	8.99608	0.454951
$392$	−4.53547	−0.229076
$393$	14.4070	0.726738
$394$	3.64879	0.183823
$395$	4.09212	0.205897
$396$	3.34838	0.168262
$397$	22.7077	1.13967	0.569833	−	0.821761i	$-0.307008\pi$
$397$	22.7077	1.13967	0.569833	+	0.821761i	$0.307008\pi$
$398$	14.0668	0.705104
$399$	6.68902	0.334870
$400$	2.39064	0.119532
$401$	30.5990	1.52804	0.764020	−	0.645192i	$-0.223223\pi$
$401$	30.5990	1.52804	0.764020	+	0.645192i	$0.223223\pi$
$402$	−14.2823	−0.712336
$403$	−1.53114	−0.0762716
$404$	−5.48724	−0.273000
$405$	2.71857	0.135087
$406$	−13.4274	−0.666393
$407$	−8.75568	−0.434003
$408$	1.00000	0.0495074
$409$	−23.2770	−1.15098	−0.575488	−	0.817811i	$-0.695188\pi$
$409$	−23.2770	−1.15098	−0.575488	+	0.817811i	$0.695188\pi$
$410$	−6.58168	−0.325046
$411$	−20.6923	−1.02068
$412$	8.46777	0.417177
$413$	−1.56988	−0.0772488
$414$	8.99608	0.442133
$415$	−16.6513	−0.817382
$416$	−0.269621	−0.0132193
$417$	17.0175	0.833348
$418$	14.2669	0.697819
$419$	9.59399	0.468697	0.234349	−	0.972153i	$-0.424704\pi$
$419$	9.59399	0.468697	0.234349	+	0.972153i	$0.424704\pi$
$420$	4.26784	0.208249
$421$	−14.3221	−0.698015	−0.349007	−	0.937120i	$-0.613481\pi$
$421$	−14.3221	−0.698015	−0.349007	+	0.937120i	$0.613481\pi$
$422$	−0.186574	−0.00908227
$423$	−8.87826	−0.431676
$424$	−6.64902	−0.322905
$425$	2.39064	0.115963
$426$	−12.7654	−0.618487
$427$	−9.73023	−0.470879
$428$	14.7517	0.713049
$429$	−0.902795	−0.0435873
$430$	−30.8490	−1.48767
$431$	16.6079	0.799974	0.399987	−	0.916521i	$-0.369015\pi$
$431$	16.6079	0.799974	0.399987	+	0.916521i	$0.369015\pi$
$432$	1.00000	0.0481125
$433$	12.5920	0.605132	0.302566	−	0.953128i	$-0.402157\pi$
$433$	12.5920	0.605132	0.302566	+	0.953128i	$0.402157\pi$
$434$	8.91513	0.427940
$435$	−23.2524	−1.11487
$436$	−12.0900	−0.579005
$437$	38.3309	1.83362
$438$	6.38818	0.305239
$439$	10.7711	0.514078	0.257039	−	0.966401i	$-0.417253\pi$
$439$	10.7711	0.514078	0.257039	+	0.966401i	$0.417253\pi$
$440$	9.10282	0.433960
$441$	−4.53547	−0.215975
$442$	−0.269621	−0.0128246
$443$	17.9690	0.853735	0.426867	−	0.904314i	$-0.359617\pi$
$443$	17.9690	0.853735	0.426867	+	0.904314i	$0.359617\pi$
$444$	−2.61490	−0.124098
$445$	19.1883	0.909614
$446$	1.27089	0.0601782
$447$	9.18601	0.434483
$448$	1.56988	0.0741699
$449$	21.6463	1.02155	0.510776	−	0.859714i	$-0.329358\pi$
$449$	21.6463	1.02155	0.510776	+	0.859714i	$0.329358\pi$
$450$	2.39064	0.112696
$451$	−8.10645	−0.381718
$452$	−5.85092	−0.275204
$453$	−6.00736	−0.282250
$454$	−9.20637	−0.432076
$455$	−1.15070	−0.0539457
$456$	4.26085	0.199532
$457$	−31.2299	−1.46087	−0.730437	−	0.682980i	$-0.760683\pi$
$457$	−31.2299	−1.46087	−0.730437	+	0.682980i	$0.760683\pi$
$458$	−10.1171	−0.472742
$459$	1.00000	0.0466760
$460$	24.4565	1.14029
$461$	4.77612	0.222446	0.111223	−	0.993795i	$-0.464523\pi$
$461$	4.77612	0.222446	0.111223	+	0.993795i	$0.464523\pi$
$462$	5.25656	0.244557
$463$	−25.8612	−1.20187	−0.600936	−	0.799297i	$-0.705205\pi$
$463$	−25.8612	−1.20187	−0.600936	+	0.799297i	$0.705205\pi$
$464$	−8.55316	−0.397070
$465$	15.4384	0.715938
$466$	−3.78205	−0.175200
$467$	−1.62038	−0.0749824	−0.0374912	−	0.999297i	$-0.511937\pi$
$467$	−1.62038	−0.0749824	−0.0374912	+	0.999297i	$0.511937\pi$
$468$	−0.269621	−0.0124633
$469$	−22.4215	−1.03533
$470$	−24.1362	−1.11332
$471$	11.8143	0.544374
$472$	−1.00000	−0.0460287
$473$	−37.9957	−1.74705
$474$	1.50524	0.0691382
$475$	10.1862	0.467374
$476$	1.56988	0.0719554
$477$	−6.64902	−0.304438
$478$	18.2535	0.834896
$479$	12.2484	0.559646	0.279823	−	0.960052i	$-0.409724\pi$
$479$	12.2484	0.559646	0.279823	+	0.960052i	$0.409724\pi$
$480$	2.71857	0.124085
$481$	0.705033	0.0321467
$482$	−21.4055	−0.974992
$483$	14.1228	0.642608
$484$	0.211644	0.00962020
$485$	11.3520	0.515469
$486$	1.00000	0.0453609
$487$	17.3394	0.785722	0.392861	−	0.919598i	$-0.371485\pi$
$487$	17.3394	0.785722	0.392861	+	0.919598i	$0.371485\pi$
$488$	−6.19807	−0.280573
$489$	11.2176	0.507277
$490$	−12.3300	−0.557013
$491$	19.6231	0.885579	0.442790	−	0.896626i	$-0.353989\pi$
$491$	19.6231	0.885579	0.442790	+	0.896626i	$0.353989\pi$
$492$	−2.42101	−0.109147
$493$	−8.55316	−0.385215
$494$	−1.14882	−0.0516877
$495$	9.10282	0.409141
$496$	5.67885	0.254988
$497$	−20.0402	−0.898926
$498$	−6.12503	−0.274469
$499$	6.15297	0.275445	0.137722	−	0.990471i	$-0.456022\pi$
$499$	6.15297	0.275445	0.137722	+	0.990471i	$0.456022\pi$
$500$	−7.09373	−0.317241
$501$	1.03582	0.0462769
$502$	5.79161	0.258492
$503$	26.0023	1.15939	0.579693	−	0.814835i	$-0.303173\pi$
$503$	26.0023	1.15939	0.579693	+	0.814835i	$0.303173\pi$
$504$	1.56988	0.0699281
$505$	−14.9175	−0.663819
$506$	30.1223	1.33910
$507$	−12.9273	−0.574122
$508$	10.2727	0.455777
$509$	−9.81933	−0.435234	−0.217617	−	0.976034i	$-0.569828\pi$
$509$	−9.81933	−0.435234	−0.217617	+	0.976034i	$0.569828\pi$
$510$	2.71857	0.120380
$511$	10.0287	0.443643
$512$	1.00000	0.0441942
$513$	4.26085	0.188121
$514$	19.4842	0.859410
$515$	23.0203	1.01439
$516$	−11.3475	−0.499546
$517$	−29.7278	−1.30743
$518$	−4.10508	−0.180367
$519$	0.766047	0.0336257
$520$	−0.732986	−0.0321436
$521$	−30.3305	−1.32880	−0.664402	−	0.747376i	$-0.731313\pi$
$521$	−30.3305	−1.32880	−0.664402	+	0.747376i	$0.731313\pi$
$522$	−8.55316	−0.374362
$523$	−12.2715	−0.536596	−0.268298	−	0.963336i	$-0.586461\pi$
$523$	−12.2715	−0.536596	−0.268298	+	0.963336i	$0.586461\pi$
$524$	14.4070	0.629374
$525$	3.75303	0.163796
$526$	−8.75623	−0.381790
$527$	5.67885	0.247375
$528$	3.34838	0.145720
$529$	57.9294	2.51867
$530$	−18.0758	−0.785164
$531$	−1.00000	−0.0433963
$532$	6.68902	0.290006
$533$	0.652755	0.0282740
$534$	7.05823	0.305440
$535$	40.1035	1.73383
$536$	−14.2823	−0.616901
$537$	6.84072	0.295199
$538$	19.4918	0.840352
$539$	−15.1865	−0.654128
$540$	2.71857	0.116989
$541$	−31.2044	−1.34158	−0.670791	−	0.741647i	$-0.734045\pi$
$541$	−31.2044	−1.34158	−0.670791	+	0.741647i	$0.734045\pi$
$542$	−15.8731	−0.681807
$543$	14.1995	0.609358
$544$	1.00000	0.0428746
$545$	−32.8675	−1.40789
$546$	−0.423274	−0.0181144
$547$	7.53452	0.322153	0.161076	−	0.986942i	$-0.448503\pi$
$547$	7.53452	0.322153	0.161076	+	0.986942i	$0.448503\pi$
$548$	−20.6923	−0.883931
$549$	−6.19807	−0.264527
$550$	8.00478	0.341325
$551$	−36.4437	−1.55255
$552$	8.99608	0.382899
$553$	2.36305	0.100487
$554$	9.44691	0.401361
$555$	−7.10880	−0.301752
$556$	17.0175	0.721701
$557$	22.4496	0.951222	0.475611	−	0.879656i	$-0.342227\pi$
$557$	22.4496	0.951222	0.475611	+	0.879656i	$0.342227\pi$
$558$	5.67885	0.240405
$559$	3.05953	0.129404
$560$	4.26784	0.180349
$561$	3.34838	0.141369
$562$	3.14736	0.132763
$563$	−28.3044	−1.19289	−0.596444	−	0.802654i	$-0.703420\pi$
$563$	−28.3044	−1.19289	−0.596444	+	0.802654i	$0.703420\pi$
$564$	−8.87826	−0.373842
$565$	−15.9062	−0.669177
$566$	14.8579	0.624525
$567$	1.56988	0.0659288
$568$	−12.7654	−0.535626
$569$	−44.8573	−1.88052	−0.940258	−	0.340462i	$-0.889417\pi$
$569$	−44.8573	−1.88052	−0.940258	+	0.340462i	$0.889417\pi$
$570$	11.5834	0.485176
$571$	−20.9226	−0.875582	−0.437791	−	0.899077i	$-0.644239\pi$
$571$	−20.9226	−0.875582	−0.437791	+	0.899077i	$0.644239\pi$
$572$	−0.902795	−0.0377478
$573$	−24.3882	−1.01883
$574$	−3.80069	−0.158638
$575$	21.5064	0.896880
$576$	1.00000	0.0416667
$577$	33.6040	1.39895	0.699476	−	0.714656i	$-0.253417\pi$
$577$	33.6040	1.39895	0.699476	+	0.714656i	$0.253417\pi$
$578$	1.00000	0.0415945
$579$	−18.3416	−0.762251
$580$	−23.2524	−0.965503
$581$	−9.61556	−0.398921
$582$	4.17573	0.173089
$583$	−22.2634	−0.922057
$584$	6.38818	0.264345
$585$	−0.732986	−0.0303052
$586$	−7.06184	−0.291722
$587$	−21.4396	−0.884908	−0.442454	−	0.896791i	$-0.645892\pi$
$587$	−21.4396	−0.884908	−0.442454	+	0.896791i	$0.645892\pi$
$588$	−4.53547	−0.187040
$589$	24.1967	0.997009
$590$	−2.71857	−0.111922
$591$	3.64879	0.150091
$592$	−2.61490	−0.107472
$593$	31.4410	1.29113	0.645564	−	0.763706i	$-0.276622\pi$
$593$	31.4410	1.29113	0.645564	+	0.763706i	$0.276622\pi$
$594$	3.34838	0.137386
$595$	4.26784	0.174964
$596$	9.18601	0.376274
$597$	14.0668	0.575715
$598$	−2.42554	−0.0991875
$599$	−3.23541	−0.132195	−0.0660977	−	0.997813i	$-0.521055\pi$
$599$	−3.23541	−0.132195	−0.0660977	+	0.997813i	$0.521055\pi$
$600$	2.39064	0.0975976
$601$	17.3650	0.708332	0.354166	−	0.935183i	$-0.384765\pi$
$601$	17.3650	0.708332	0.354166	+	0.935183i	$0.384765\pi$
$602$	−17.8142	−0.726053
$603$	−14.2823	−0.581620
$604$	−6.00736	−0.244436
$605$	0.575371	0.0233922
$606$	−5.48724	−0.222904
$607$	−14.3997	−0.584468	−0.292234	−	0.956347i	$-0.594399\pi$
$607$	−14.3997	−0.584468	−0.292234	+	0.956347i	$0.594399\pi$
$608$	4.26085	0.172800
$609$	−13.4274	−0.544107
$610$	−16.8499	−0.682233
$611$	2.39377	0.0968415
$612$	1.00000	0.0404226
$613$	−22.2758	−0.899711	−0.449855	−	0.893101i	$-0.648524\pi$
$613$	−22.2758	−0.899711	−0.449855	+	0.893101i	$0.648524\pi$
$614$	2.94827	0.118983
$615$	−6.58168	−0.265399
$616$	5.25656	0.211793
$617$	−13.3294	−0.536623	−0.268311	−	0.963332i	$-0.586466\pi$
$617$	−13.3294	−0.536623	−0.268311	+	0.963332i	$0.586466\pi$
$618$	8.46777	0.340624
$619$	−11.5926	−0.465946	−0.232973	−	0.972483i	$-0.574845\pi$
$619$	−11.5926	−0.465946	−0.232973	+	0.972483i	$0.574845\pi$
$620$	15.4384	0.620020
$621$	8.99608	0.361000
$622$	8.82485	0.353844
$623$	11.0806	0.443934
$624$	−0.269621	−0.0107935
$625$	−31.2380	−1.24952
$626$	6.50132	0.259845
$627$	14.2669	0.569766
$628$	11.8143	0.471442
$629$	−2.61490	−0.104263
$630$	4.26784	0.170035
$631$	4.04488	0.161024	0.0805120	−	0.996754i	$-0.474344\pi$
$631$	4.04488	0.161024	0.0805120	+	0.996754i	$0.474344\pi$
$632$	1.50524	0.0598754
$633$	−0.186574	−0.00741564
$634$	−10.0410	−0.398777
$635$	27.9270	1.10825
$636$	−6.64902	−0.263651
$637$	1.22286	0.0484515
$638$	−28.6392	−1.13384
$639$	−12.7654	−0.504993
$640$	2.71857	0.107461
$641$	23.4264	0.925288	0.462644	−	0.886544i	$-0.346901\pi$
$641$	23.4264	0.925288	0.462644	+	0.886544i	$0.346901\pi$
$642$	14.7517	0.582202
$643$	18.1668	0.716428	0.358214	−	0.933640i	$-0.383386\pi$
$643$	18.1668	0.716428	0.358214	+	0.933640i	$0.383386\pi$
$644$	14.1228	0.556515
$645$	−30.8490	−1.21468
$646$	4.26085	0.167641
$647$	−34.3070	−1.34875	−0.674373	−	0.738391i	$-0.735586\pi$
$647$	−34.3070	−1.34875	−0.674373	+	0.738391i	$0.735586\pi$
$648$	1.00000	0.0392837
$649$	−3.34838	−0.131435
$650$	−0.644569	−0.0252821
$651$	8.91513	0.349411
$652$	11.2176	0.439315
$653$	7.07873	0.277012	0.138506	−	0.990362i	$-0.455770\pi$
$653$	7.07873	0.277012	0.138506	+	0.990362i	$0.455770\pi$
$654$	−12.0900	−0.472756
$655$	39.1666	1.53036
$656$	−2.42101	−0.0945244
$657$	6.38818	0.249226
$658$	−13.9378	−0.543352
$659$	31.2101	1.21577	0.607887	−	0.794024i	$-0.292017\pi$
$659$	31.2101	1.21577	0.607887	+	0.794024i	$0.292017\pi$
$660$	9.10282	0.354327
$661$	−10.6162	−0.412923	−0.206461	−	0.978455i	$-0.566195\pi$
$661$	−10.6162	−0.412923	−0.206461	+	0.978455i	$0.566195\pi$
$662$	−27.7264	−1.07762
$663$	−0.269621	−0.0104712
$664$	−6.12503	−0.237697
$665$	18.1846	0.705169
$666$	−2.61490	−0.101325
$667$	−76.9449	−2.97932
$668$	1.03582	0.0400770
$669$	1.27089	0.0491353
$670$	−38.8275	−1.50004
$671$	−20.7535	−0.801180
$672$	1.56988	0.0605595
$673$	−13.0762	−0.504049	−0.252025	−	0.967721i	$-0.581096\pi$
$673$	−13.0762	−0.504049	−0.252025	+	0.967721i	$0.581096\pi$
$674$	31.7224	1.22190
$675$	2.39064	0.0920159
$676$	−12.9273	−0.497204
$677$	1.09679	0.0421532	0.0210766	−	0.999778i	$-0.493291\pi$
$677$	1.09679	0.0421532	0.0210766	+	0.999778i	$0.493291\pi$
$678$	−5.85092	−0.224703
$679$	6.55540	0.251573
$680$	2.71857	0.104253
$681$	−9.20637	−0.352789
$682$	19.0150	0.728120
$683$	0.390123	0.0149277	0.00746383	−	0.999972i	$-0.497624\pi$
$683$	0.390123	0.0149277	0.00746383	+	0.999972i	$0.497624\pi$
$684$	4.26085	0.162918
$685$	−56.2535	−2.14934
$686$	−18.1093	−0.691417
$687$	−10.1171	−0.385993
$688$	−11.3475	−0.432619
$689$	1.79272	0.0682971
$690$	24.4565	0.931043
$691$	2.14618	0.0816447	0.0408223	−	0.999166i	$-0.487002\pi$
$691$	2.14618	0.0816447	0.0408223	+	0.999166i	$0.487002\pi$
$692$	0.766047	0.0291207
$693$	5.25656	0.199680
$694$	2.38350	0.0904766
$695$	46.2632	1.75486
$696$	−8.55316	−0.324207
$697$	−2.42101	−0.0917021
$698$	2.05189	0.0776653
$699$	−3.78205	−0.143050
$700$	3.75303	0.141851
$701$	38.3095	1.44693	0.723465	−	0.690362i	$-0.242549\pi$
$701$	38.3095	1.44693	0.723465	+	0.690362i	$0.242549\pi$
$702$	−0.269621	−0.0101762
$703$	−11.1417	−0.420217
$704$	3.34838	0.126197
$705$	−24.1362	−0.909022
$706$	5.14587	0.193667
$707$	−8.61431	−0.323975
$708$	−1.00000	−0.0375823
$709$	−2.81636	−0.105771	−0.0528853	−	0.998601i	$-0.516842\pi$
$709$	−2.81636	−0.105771	−0.0528853	+	0.998601i	$0.516842\pi$
$710$	−34.7038	−1.30241
$711$	1.50524	0.0564511
$712$	7.05823	0.264518
$713$	51.0874	1.91324
$714$	1.56988	0.0587513
$715$	−2.45431	−0.0917862
$716$	6.84072	0.255650
$717$	18.2535	0.681689
$718$	−4.01306	−0.149766
$719$	−13.4298	−0.500848	−0.250424	−	0.968136i	$-0.580570\pi$
$719$	−13.4298	−0.500848	−0.250424	+	0.968136i	$0.580570\pi$
$720$	2.71857	0.101315
$721$	13.2934	0.495072
$722$	−0.845178	−0.0314543
$723$	−21.4055	−0.796077
$724$	14.1995	0.527720
$725$	−20.4476	−0.759403
$726$	0.211644	0.00785486
$727$	26.8213	0.994748	0.497374	−	0.867536i	$-0.334298\pi$
$727$	26.8213	0.994748	0.497374	+	0.867536i	$0.334298\pi$
$728$	−0.423274	−0.0156876
$729$	1.00000	0.0370370
$730$	17.3667	0.642771
$731$	−11.3475	−0.419702
$732$	−6.19807	−0.229087
$733$	−32.4462	−1.19843	−0.599214	−	0.800589i	$-0.704520\pi$
$733$	−32.4462	−1.19843	−0.599214	+	0.800589i	$0.704520\pi$
$734$	0.404510	0.0149307
$735$	−12.3300	−0.454800
$736$	8.99608	0.331600
$737$	−47.8225	−1.76156
$738$	−2.42101	−0.0891185
$739$	22.2208	0.817407	0.408704	−	0.912667i	$-0.365981\pi$
$739$	22.2208	0.817407	0.408704	+	0.912667i	$0.365981\pi$
$740$	−7.10880	−0.261325
$741$	−1.14882	−0.0422028
$742$	−10.4382	−0.383197
$743$	−26.0417	−0.955379	−0.477690	−	0.878529i	$-0.658526\pi$
$743$	−26.0417	−0.955379	−0.477690	+	0.878529i	$0.658526\pi$
$744$	5.67885	0.208197
$745$	24.9729	0.914934
$746$	35.2554	1.29079
$747$	−6.12503	−0.224103
$748$	3.34838	0.122429
$749$	23.1584	0.846189
$750$	−7.09373	−0.259026
$751$	−34.3481	−1.25338	−0.626690	−	0.779269i	$-0.715591\pi$
$751$	−34.3481	−1.25338	−0.626690	+	0.779269i	$0.715591\pi$
$752$	−8.87826	−0.323757
$753$	5.79161	0.211058
$754$	2.30611	0.0839837
$755$	−16.3314	−0.594362
$756$	1.56988	0.0570960
$757$	16.8522	0.612505	0.306252	−	0.951950i	$-0.400925\pi$
$757$	16.8522	0.612505	0.306252	+	0.951950i	$0.400925\pi$
$758$	12.8294	0.465984
$759$	30.1223	1.09337
$760$	11.5834	0.420175
$761$	10.6897	0.387501	0.193750	−	0.981051i	$-0.437935\pi$
$761$	10.6897	0.387501	0.193750	+	0.981051i	$0.437935\pi$
$762$	10.2727	0.372140
$763$	−18.9798	−0.687116
$764$	−24.3882	−0.882335
$765$	2.71857	0.0982902
$766$	−30.3394	−1.09621
$767$	0.269621	0.00973547
$768$	1.00000	0.0360844
$769$	30.1109	1.08583	0.542914	−	0.839789i	$-0.317321\pi$
$769$	30.1109	1.08583	0.542914	+	0.839789i	$0.317321\pi$
$770$	14.2903	0.514988
$771$	19.4842	0.701705
$772$	−18.3416	−0.660128
$773$	−31.5679	−1.13542	−0.567709	−	0.823229i	$-0.692170\pi$
$773$	−31.5679	−1.13542	−0.567709	+	0.823229i	$0.692170\pi$
$774$	−11.3475	−0.407877
$775$	13.5761	0.487669
$776$	4.17573	0.149900
$777$	−4.10508	−0.147269
$778$	13.0630	0.468331
$779$	−10.3155	−0.369593
$780$	−0.732986	−0.0262451
$781$	−42.7435	−1.52948
$782$	8.99608	0.321699
$783$	−8.55316	−0.305665
$784$	−4.53547	−0.161981
$785$	32.1181	1.14634
$786$	14.4070	0.513881
$787$	−15.3469	−0.547057	−0.273528	−	0.961864i	$-0.588191\pi$
$787$	−15.3469	−0.547057	−0.273528	+	0.961864i	$0.588191\pi$
$788$	3.64879	0.129983
$789$	−8.75623	−0.311730
$790$	4.09212	0.145591
$791$	−9.18524	−0.326590
$792$	3.34838	0.118979
$793$	1.67113	0.0593437
$794$	22.7077	0.805865
$795$	−18.0758	−0.641084
$796$	14.0668	0.498584
$797$	−16.3457	−0.578993	−0.289497	−	0.957179i	$-0.593488\pi$
$797$	−16.3457	−0.578993	−0.289497	+	0.957179i	$0.593488\pi$
$798$	6.68902	0.236789
$799$	−8.87826	−0.314090
$800$	2.39064	0.0845220
$801$	7.05823	0.249390
$802$	30.5990	1.08049
$803$	21.3900	0.754838
$804$	−14.2823	−0.503697
$805$	38.3938	1.35320
$806$	−1.53114	−0.0539321
$807$	19.4918	0.686144
$808$	−5.48724	−0.193040
$809$	32.1534	1.13045	0.565227	−	0.824936i	$-0.308789\pi$
$809$	32.1534	1.13045	0.565227	+	0.824936i	$0.308789\pi$
$810$	2.71857	0.0955210
$811$	47.8723	1.68103	0.840513	−	0.541792i	$-0.182254\pi$
$811$	47.8723	1.68103	0.840513	+	0.541792i	$0.182254\pi$
$812$	−13.4274	−0.471211
$813$	−15.8731	−0.556693
$814$	−8.75568	−0.306886
$815$	30.4959	1.06822
$816$	1.00000	0.0350070
$817$	−48.3499	−1.69155
$818$	−23.2770	−0.813862
$819$	−0.423274	−0.0147904
$820$	−6.58168	−0.229842
$821$	43.3620	1.51335	0.756673	−	0.653794i	$-0.226824\pi$
$821$	43.3620	1.51335	0.756673	+	0.653794i	$0.226824\pi$
$822$	−20.6923	−0.721727
$823$	−39.4982	−1.37682	−0.688411	−	0.725321i	$-0.741691\pi$
$823$	−39.4982	−1.37682	−0.688411	+	0.725321i	$0.741691\pi$
$824$	8.46777	0.294989
$825$	8.00478	0.278691
$826$	−1.56988	−0.0546232
$827$	54.0412	1.87920	0.939598	−	0.342280i	$-0.111199\pi$
$827$	54.0412	1.87920	0.939598	+	0.342280i	$0.111199\pi$
$828$	8.99608	0.312635
$829$	−4.38606	−0.152334	−0.0761670	−	0.997095i	$-0.524268\pi$
$829$	−4.38606	−0.152334	−0.0761670	+	0.997095i	$0.524268\pi$
$830$	−16.6513	−0.577976
$831$	9.44691	0.327710
$832$	−0.269621	−0.00934744
$833$	−4.53547	−0.157145
$834$	17.0175	0.589266
$835$	2.81595	0.0974499
$836$	14.2669	0.493432
$837$	5.67885	0.196290
$838$	9.59399	0.331419
$839$	−30.7991	−1.06330	−0.531652	−	0.846963i	$-0.678429\pi$
$839$	−30.7991	−1.06330	−0.531652	+	0.846963i	$0.678429\pi$
$840$	4.26784	0.147254
$841$	44.1565	1.52264
$842$	−14.3221	−0.493571
$843$	3.14736	0.108401
$844$	−0.186574	−0.00642214
$845$	−35.1438	−1.20898
$846$	−8.87826	−0.305241
$847$	0.332257	0.0114165
$848$	−6.64902	−0.228328
$849$	14.8579	0.509923
$850$	2.39064	0.0819984
$851$	−23.5238	−0.806387
$852$	−12.7654	−0.437336
$853$	44.0750	1.50910	0.754550	−	0.656242i	$-0.227855\pi$
$853$	44.0750	1.50910	0.754550	+	0.656242i	$0.227855\pi$
$854$	−9.73023	−0.332962
$855$	11.5834	0.396145
$856$	14.7517	0.504202
$857$	49.9199	1.70523	0.852615	−	0.522540i	$-0.175015\pi$
$857$	49.9199	1.70523	0.852615	+	0.522540i	$0.175015\pi$
$858$	−0.902795	−0.0308209
$859$	−57.2471	−1.95324	−0.976622	−	0.214962i	$-0.931037\pi$
$859$	−57.2471	−1.95324	−0.976622	+	0.214962i	$0.931037\pi$
$860$	−30.8490	−1.05194
$861$	−3.80069	−0.129527
$862$	16.6079	0.565667
$863$	18.8980	0.643296	0.321648	−	0.946859i	$-0.395763\pi$
$863$	18.8980	0.643296	0.321648	+	0.946859i	$0.395763\pi$
$864$	1.00000	0.0340207
$865$	2.08256	0.0708090
$866$	12.5920	0.427893
$867$	1.00000	0.0339618
$868$	8.91513	0.302599
$869$	5.04013	0.170975
$870$	−23.2524	−0.788330
$871$	3.85081	0.130480
$872$	−12.0900	−0.409418
$873$	4.17573	0.141327
$874$	38.3309	1.29656
$875$	−11.1363	−0.376476
$876$	6.38818	0.215836
$877$	13.9254	0.470227	0.235114	−	0.971968i	$-0.424454\pi$
$877$	13.9254	0.470227	0.235114	+	0.971968i	$0.424454\pi$
$878$	10.7711	0.363508
$879$	−7.06184	−0.238190
$880$	9.10282	0.306856
$881$	20.0508	0.675530	0.337765	−	0.941230i	$-0.390329\pi$
$881$	20.0508	0.675530	0.337765	+	0.941230i	$0.390329\pi$
$882$	−4.53547	−0.152717
$883$	−28.0660	−0.944496	−0.472248	−	0.881466i	$-0.656557\pi$
$883$	−28.0660	−0.944496	−0.472248	+	0.881466i	$0.656557\pi$
$884$	−0.269621	−0.00906835
$885$	−2.71857	−0.0913839
$886$	17.9690	0.603682
$887$	37.7183	1.26646	0.633228	−	0.773965i	$-0.281729\pi$
$887$	37.7183	1.26646	0.633228	+	0.773965i	$0.281729\pi$
$888$	−2.61490	−0.0877503
$889$	16.1269	0.540879
$890$	19.1883	0.643194
$891$	3.34838	0.112175
$892$	1.27089	0.0425524
$893$	−37.8289	−1.26590
$894$	9.18601	0.307226
$895$	18.5970	0.621629
$896$	1.56988	0.0524460
$897$	−2.42554	−0.0809863
$898$	21.6463	0.722346
$899$	−48.5721	−1.61997
$900$	2.39064	0.0796881
$901$	−6.64902	−0.221511
$902$	−8.10645	−0.269915
$903$	−17.8142	−0.592820
$904$	−5.85092	−0.194599
$905$	38.6023	1.28319
$906$	−6.00736	−0.199581
$907$	2.51074	0.0833677	0.0416838	−	0.999131i	$-0.486728\pi$
$907$	2.51074	0.0833677	0.0416838	+	0.999131i	$0.486728\pi$
$908$	−9.20637	−0.305524
$909$	−5.48724	−0.182000
$910$	−1.15070	−0.0381454
$911$	14.8565	0.492219	0.246109	−	0.969242i	$-0.420848\pi$
$911$	14.8565	0.492219	0.246109	+	0.969242i	$0.420848\pi$
$912$	4.26085	0.141091
$913$	−20.5089	−0.678746
$914$	−31.2299	−1.03299
$915$	−16.8499	−0.557041
$916$	−10.1171	−0.334279
$917$	22.6173	0.746889
$918$	1.00000	0.0330049
$919$	−35.0569	−1.15642	−0.578211	−	0.815888i	$-0.696249\pi$
$919$	−35.0569	−1.15642	−0.578211	+	0.815888i	$0.696249\pi$
$920$	24.4565	0.806307
$921$	2.94827	0.0971488
$922$	4.77612	0.157293
$923$	3.44183	0.113289
$924$	5.25656	0.172928
$925$	−6.25130	−0.205541
$926$	−25.8612	−0.849852
$927$	8.46777	0.278118
$928$	−8.55316	−0.280771
$929$	−37.1332	−1.21830	−0.609150	−	0.793055i	$-0.708489\pi$
$929$	−37.1332	−1.21830	−0.609150	+	0.793055i	$0.708489\pi$
$930$	15.4384	0.506245
$931$	−19.3250	−0.633350
$932$	−3.78205	−0.123885
$933$	8.82485	0.288913
$934$	−1.62038	−0.0530206
$935$	9.10282	0.297694
$936$	−0.269621	−0.00881285
$937$	32.5621	1.06376	0.531878	−	0.846821i	$-0.321486\pi$
$937$	32.5621	1.06376	0.531878	+	0.846821i	$0.321486\pi$
$938$	−22.4215	−0.732088
$939$	6.50132	0.212163
$940$	−24.1362	−0.787236
$941$	36.9438	1.20433	0.602166	−	0.798371i	$-0.294304\pi$
$941$	36.9438	1.20433	0.602166	+	0.798371i	$0.294304\pi$
$942$	11.8143	0.384931
$943$	−21.7796	−0.709240
$944$	−1.00000	−0.0325472
$945$	4.26784	0.138833
$946$	−37.9957	−1.23535
$947$	0.717076	0.0233018	0.0116509	−	0.999932i	$-0.496291\pi$
$947$	0.717076	0.0233018	0.0116509	+	0.999932i	$0.496291\pi$
$948$	1.50524	0.0488881
$949$	−1.72239	−0.0559111
$950$	10.1862	0.330483
$951$	−10.0410	−0.325600
$952$	1.56988	0.0508801
$953$	25.4824	0.825457	0.412729	−	0.910854i	$-0.364576\pi$
$953$	25.4824	0.825457	0.412729	+	0.910854i	$0.364576\pi$
$954$	−6.64902	−0.215270
$955$	−66.3012	−2.14546
$956$	18.2535	0.590360
$957$	−28.6392	−0.925774
$958$	12.2484	0.395729
$959$	−32.4844	−1.04898
$960$	2.71857	0.0877416
$961$	1.24938	0.0403027
$962$	0.705033	0.0227312
$963$	14.7517	0.475366
$964$	−21.4055	−0.689423
$965$	−49.8630	−1.60515
$966$	14.1228	0.454393
$967$	−53.2179	−1.71137	−0.855686	−	0.517495i	$-0.826865\pi$
$967$	−53.2179	−1.71137	−0.855686	+	0.517495i	$0.826865\pi$
$968$	0.211644	0.00680251
$969$	4.26085	0.136878
$970$	11.3520	0.364492
$971$	−8.30670	−0.266575	−0.133287	−	0.991077i	$-0.542553\pi$
$971$	−8.30670	−0.266575	−0.133287	+	0.991077i	$0.542553\pi$
$972$	1.00000	0.0320750
$973$	26.7154	0.856456
$974$	17.3394	0.555590
$975$	−0.644569	−0.0206427
$976$	−6.19807	−0.198395
$977$	4.40553	0.140945	0.0704727	−	0.997514i	$-0.477549\pi$
$977$	4.40553	0.140945	0.0704727	+	0.997514i	$0.477549\pi$
$978$	11.2176	0.358699
$979$	23.6336	0.755335
$980$	−12.3300	−0.393868
$981$	−12.0900	−0.386003
$982$	19.6231	0.626199
$983$	−17.6659	−0.563455	−0.281728	−	0.959494i	$-0.590907\pi$
$983$	−17.6659	−0.563455	−0.281728	+	0.959494i	$0.590907\pi$
$984$	−2.42101	−0.0771789
$985$	9.91951	0.316062
$986$	−8.55316	−0.272388
$987$	−13.9378	−0.443645
$988$	−1.14882	−0.0365487
$989$	−102.083	−3.24605
$990$	9.10282	0.289307
$991$	−12.1469	−0.385858	−0.192929	−	0.981213i	$-0.561799\pi$
$991$	−12.1469	−0.385858	−0.192929	+	0.981213i	$0.561799\pi$
$992$	5.67885	0.180304
$993$	−27.7264	−0.879870
$994$	−20.0402	−0.635637
$995$	38.2416	1.21234
$996$	−6.12503	−0.194079
$997$	−17.2943	−0.547714	−0.273857	−	0.961770i	$-0.588300\pi$
$997$	−17.2943	−0.547714	−0.273857	+	0.961770i	$0.588300\pi$
$998$	6.15297	0.194769
$999$	−2.61490	−0.0827318

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.bb.1.10	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.bb.1.10	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.71857 q^{5} +1.00000 q^{6} +1.56988 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.71857 q^{5} +1.00000 q^{6} +1.56988 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.71857 q^{10} +3.34838 q^{11} +1.00000 q^{12} -0.269621 q^{13} +1.56988 q^{14} +2.71857 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +4.26085 q^{19} +2.71857 q^{20} +1.56988 q^{21} +3.34838 q^{22} +8.99608 q^{23} +1.00000 q^{24} +2.39064 q^{25} -0.269621 q^{26} +1.00000 q^{27} +1.56988 q^{28} -8.55316 q^{29} +2.71857 q^{30} +5.67885 q^{31} +1.00000 q^{32} +3.34838 q^{33} +1.00000 q^{34} +4.26784 q^{35} +1.00000 q^{36} -2.61490 q^{37} +4.26085 q^{38} -0.269621 q^{39} +2.71857 q^{40} -2.42101 q^{41} +1.56988 q^{42} -11.3475 q^{43} +3.34838 q^{44} +2.71857 q^{45} +8.99608 q^{46} -8.87826 q^{47} +1.00000 q^{48} -4.53547 q^{49} +2.39064 q^{50} +1.00000 q^{51} -0.269621 q^{52} -6.64902 q^{53} +1.00000 q^{54} +9.10282 q^{55} +1.56988 q^{56} +4.26085 q^{57} -8.55316 q^{58} -1.00000 q^{59} +2.71857 q^{60} -6.19807 q^{61} +5.67885 q^{62} +1.56988 q^{63} +1.00000 q^{64} -0.732986 q^{65} +3.34838 q^{66} -14.2823 q^{67} +1.00000 q^{68} +8.99608 q^{69} +4.26784 q^{70} -12.7654 q^{71} +1.00000 q^{72} +6.38818 q^{73} -2.61490 q^{74} +2.39064 q^{75} +4.26085 q^{76} +5.25656 q^{77} -0.269621 q^{78} +1.50524 q^{79} +2.71857 q^{80} +1.00000 q^{81} -2.42101 q^{82} -6.12503 q^{83} +1.56988 q^{84} +2.71857 q^{85} -11.3475 q^{86} -8.55316 q^{87} +3.34838 q^{88} +7.05823 q^{89} +2.71857 q^{90} -0.423274 q^{91} +8.99608 q^{92} +5.67885 q^{93} -8.87826 q^{94} +11.5834 q^{95} +1.00000 q^{96} +4.17573 q^{97} -4.53547 q^{98} +3.34838 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) \) 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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