LMFDB - Embedded newform 6018.2.a.bb.1.12

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			1.12
Root			$3.59366$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.59366 q^{5} +1.00000 q^{6} +2.37015 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.59366 q^{5} +1.00000 q^{6} +2.37015 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.59366 q^{10} -1.96393 q^{11} +1.00000 q^{12} +0.610996 q^{13} +2.37015 q^{14} +3.59366 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +3.35546 q^{19} +3.59366 q^{20} +2.37015 q^{21} -1.96393 q^{22} -8.11010 q^{23} +1.00000 q^{24} +7.91440 q^{25} +0.610996 q^{26} +1.00000 q^{27} +2.37015 q^{28} +7.78398 q^{29} +3.59366 q^{30} +2.58625 q^{31} +1.00000 q^{32} -1.96393 q^{33} +1.00000 q^{34} +8.51751 q^{35} +1.00000 q^{36} -2.69086 q^{37} +3.35546 q^{38} +0.610996 q^{39} +3.59366 q^{40} +1.03487 q^{41} +2.37015 q^{42} -11.7466 q^{43} -1.96393 q^{44} +3.59366 q^{45} -8.11010 q^{46} -5.48284 q^{47} +1.00000 q^{48} -1.38239 q^{49} +7.91440 q^{50} +1.00000 q^{51} +0.610996 q^{52} +6.28345 q^{53} +1.00000 q^{54} -7.05770 q^{55} +2.37015 q^{56} +3.35546 q^{57} +7.78398 q^{58} -1.00000 q^{59} +3.59366 q^{60} +7.14741 q^{61} +2.58625 q^{62} +2.37015 q^{63} +1.00000 q^{64} +2.19571 q^{65} -1.96393 q^{66} +0.765914 q^{67} +1.00000 q^{68} -8.11010 q^{69} +8.51751 q^{70} -2.00707 q^{71} +1.00000 q^{72} -3.25099 q^{73} -2.69086 q^{74} +7.91440 q^{75} +3.35546 q^{76} -4.65481 q^{77} +0.610996 q^{78} -11.0065 q^{79} +3.59366 q^{80} +1.00000 q^{81} +1.03487 q^{82} +2.20728 q^{83} +2.37015 q^{84} +3.59366 q^{85} -11.7466 q^{86} +7.78398 q^{87} -1.96393 q^{88} +11.2950 q^{89} +3.59366 q^{90} +1.44815 q^{91} -8.11010 q^{92} +2.58625 q^{93} -5.48284 q^{94} +12.0584 q^{95} +1.00000 q^{96} -10.3247 q^{97} -1.38239 q^{98} -1.96393 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	3.59366	1.60713	0.803567	−	0.595214i	$-0.202933\pi$
$5$	3.59366	1.60713	0.803567	+	0.595214i	$0.202933\pi$
$6$	1.00000	0.408248
$7$	2.37015	0.895832	0.447916	−	0.894076i	$-0.352166\pi$
$7$	2.37015	0.895832	0.447916	+	0.894076i	$0.352166\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.59366	1.13642
$11$	−1.96393	−0.592148	−0.296074	−	0.955165i	$-0.595677\pi$
$11$	−1.96393	−0.592148	−0.296074	+	0.955165i	$0.595677\pi$
$12$	1.00000	0.288675
$13$	0.610996	0.169460	0.0847299	−	0.996404i	$-0.472997\pi$
$13$	0.610996	0.169460	0.0847299	+	0.996404i	$0.472997\pi$
$14$	2.37015	0.633449
$15$	3.59366	0.927879
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	3.35546	0.769795	0.384897	−	0.922959i	$-0.374237\pi$
$19$	3.35546	0.769795	0.384897	+	0.922959i	$0.374237\pi$
$20$	3.59366	0.803567
$21$	2.37015	0.517209
$22$	−1.96393	−0.418712
$23$	−8.11010	−1.69107	−0.845537	−	0.533917i	$-0.820719\pi$
$23$	−8.11010	−1.69107	−0.845537	+	0.533917i	$0.820719\pi$
$24$	1.00000	0.204124
$25$	7.91440	1.58288
$26$	0.610996	0.119826
$27$	1.00000	0.192450
$28$	2.37015	0.447916
$29$	7.78398	1.44545	0.722724	−	0.691137i	$-0.242890\pi$
$29$	7.78398	1.44545	0.722724	+	0.691137i	$0.242890\pi$
$30$	3.59366	0.656110
$31$	2.58625	0.464504	0.232252	−	0.972656i	$-0.425391\pi$
$31$	2.58625	0.464504	0.232252	+	0.972656i	$0.425391\pi$
$32$	1.00000	0.176777
$33$	−1.96393	−0.341877
$34$	1.00000	0.171499
$35$	8.51751	1.43972
$36$	1.00000	0.166667
$37$	−2.69086	−0.442374	−0.221187	−	0.975231i	$-0.570993\pi$
$37$	−2.69086	−0.442374	−0.221187	+	0.975231i	$0.570993\pi$
$38$	3.35546	0.544327
$39$	0.610996	0.0978377
$40$	3.59366	0.568208
$41$	1.03487	0.161619	0.0808097	−	0.996730i	$-0.474249\pi$
$41$	1.03487	0.161619	0.0808097	+	0.996730i	$0.474249\pi$
$42$	2.37015	0.365722
$43$	−11.7466	−1.79135	−0.895673	−	0.444714i	$-0.853305\pi$
$43$	−11.7466	−1.79135	−0.895673	+	0.444714i	$0.853305\pi$
$44$	−1.96393	−0.296074
$45$	3.59366	0.535711
$46$	−8.11010	−1.19577
$47$	−5.48284	−0.799755	−0.399877	−	0.916569i	$-0.630947\pi$
$47$	−5.48284	−0.799755	−0.399877	+	0.916569i	$0.630947\pi$
$48$	1.00000	0.144338
$49$	−1.38239	−0.197484
$50$	7.91440	1.11926
$51$	1.00000	0.140028
$52$	0.610996	0.0847299
$53$	6.28345	0.863098	0.431549	−	0.902089i	$-0.357967\pi$
$53$	6.28345	0.863098	0.431549	+	0.902089i	$0.357967\pi$
$54$	1.00000	0.136083
$55$	−7.05770	−0.951661
$56$	2.37015	0.316725
$57$	3.35546	0.444441
$58$	7.78398	1.02209
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	3.59366	0.463940
$61$	7.14741	0.915133	0.457566	−	0.889176i	$-0.348721\pi$
$61$	7.14741	0.915133	0.457566	+	0.889176i	$0.348721\pi$
$62$	2.58625	0.328454
$63$	2.37015	0.298611
$64$	1.00000	0.125000
$65$	2.19571	0.272345
$66$	−1.96393	−0.241743
$67$	0.765914	0.0935713	0.0467857	−	0.998905i	$-0.485102\pi$
$67$	0.765914	0.0935713	0.0467857	+	0.998905i	$0.485102\pi$
$68$	1.00000	0.121268
$69$	−8.11010	−0.976342
$70$	8.51751	1.01804
$71$	−2.00707	−0.238195	−0.119098	−	0.992883i	$-0.538000\pi$
$71$	−2.00707	−0.238195	−0.119098	+	0.992883i	$0.538000\pi$
$72$	1.00000	0.117851
$73$	−3.25099	−0.380499	−0.190250	−	0.981736i	$-0.560930\pi$
$73$	−3.25099	−0.380499	−0.190250	+	0.981736i	$0.560930\pi$
$74$	−2.69086	−0.312806
$75$	7.91440	0.913876
$76$	3.35546	0.384897
$77$	−4.65481	−0.530465
$78$	0.610996	0.0691817
$79$	−11.0065	−1.23833	−0.619163	−	0.785263i	$-0.712528\pi$
$79$	−11.0065	−1.23833	−0.619163	+	0.785263i	$0.712528\pi$
$80$	3.59366	0.401783
$81$	1.00000	0.111111
$82$	1.03487	0.114282
$83$	2.20728	0.242280	0.121140	−	0.992635i	$-0.461345\pi$
$83$	2.20728	0.242280	0.121140	+	0.992635i	$0.461345\pi$
$84$	2.37015	0.258605
$85$	3.59366	0.389787
$86$	−11.7466	−1.26667
$87$	7.78398	0.834530
$88$	−1.96393	−0.209356
$89$	11.2950	1.19726	0.598632	−	0.801024i	$-0.295711\pi$
$89$	11.2950	1.19726	0.598632	+	0.801024i	$0.295711\pi$
$90$	3.59366	0.378805
$91$	1.44815	0.151808
$92$	−8.11010	−0.845537
$93$	2.58625	0.268181
$94$	−5.48284	−0.565512
$95$	12.0584	1.23716
$96$	1.00000	0.102062
$97$	−10.3247	−1.04832	−0.524159	−	0.851620i	$-0.675620\pi$
$97$	−10.3247	−1.04832	−0.524159	+	0.851620i	$0.675620\pi$
$98$	−1.38239	−0.139642
$99$	−1.96393	−0.197383
$100$	7.91440	0.791440
$101$	4.91627	0.489187	0.244594	−	0.969626i	$-0.421345\pi$
$101$	4.91627	0.489187	0.244594	+	0.969626i	$0.421345\pi$
$102$	1.00000	0.0990148
$103$	11.8739	1.16997	0.584987	−	0.811043i	$-0.301100\pi$
$103$	11.8739	1.16997	0.584987	+	0.811043i	$0.301100\pi$
$104$	0.610996	0.0599131
$105$	8.51751	0.831224
$106$	6.28345	0.610303
$107$	−1.69618	−0.163976	−0.0819880	−	0.996633i	$-0.526127\pi$
$107$	−1.69618	−0.163976	−0.0819880	+	0.996633i	$0.526127\pi$
$108$	1.00000	0.0962250
$109$	6.66344	0.638242	0.319121	−	0.947714i	$-0.396612\pi$
$109$	6.66344	0.638242	0.319121	+	0.947714i	$0.396612\pi$
$110$	−7.05770	−0.672926
$111$	−2.69086	−0.255405
$112$	2.37015	0.223958
$113$	6.24549	0.587526	0.293763	−	0.955878i	$-0.405092\pi$
$113$	6.24549	0.587526	0.293763	+	0.955878i	$0.405092\pi$
$114$	3.35546	0.314267
$115$	−29.1450	−2.71778
$116$	7.78398	0.722724
$117$	0.610996	0.0564866
$118$	−1.00000	−0.0920575
$119$	2.37015	0.217271
$120$	3.59366	0.328055
$121$	−7.14297	−0.649361
$122$	7.14741	0.647096
$123$	1.03487	0.0933110
$124$	2.58625	0.232252
$125$	10.4734	0.936765
$126$	2.37015	0.211150
$127$	−6.79769	−0.603197	−0.301599	−	0.953435i	$-0.597520\pi$
$127$	−6.79769	−0.603197	−0.301599	+	0.953435i	$0.597520\pi$
$128$	1.00000	0.0883883
$129$	−11.7466	−1.03423
$130$	2.19571	0.192577
$131$	−3.06329	−0.267641	−0.133820	−	0.991006i	$-0.542724\pi$
$131$	−3.06329	−0.267641	−0.133820	+	0.991006i	$0.542724\pi$
$132$	−1.96393	−0.170938
$133$	7.95293	0.689607
$134$	0.765914	0.0661649
$135$	3.59366	0.309293
$136$	1.00000	0.0857493
$137$	13.3543	1.14093	0.570467	−	0.821320i	$-0.306762\pi$
$137$	13.3543	1.14093	0.570467	+	0.821320i	$0.306762\pi$
$138$	−8.11010	−0.690378
$139$	−3.74908	−0.317992	−0.158996	−	0.987279i	$-0.550826\pi$
$139$	−3.74908	−0.317992	−0.158996	+	0.987279i	$0.550826\pi$
$140$	8.51751	0.719861
$141$	−5.48284	−0.461739
$142$	−2.00707	−0.168430
$143$	−1.19995	−0.100345
$144$	1.00000	0.0833333
$145$	27.9730	2.32303
$146$	−3.25099	−0.269054
$147$	−1.38239	−0.114018
$148$	−2.69086	−0.221187
$149$	−13.7627	−1.12749	−0.563743	−	0.825950i	$-0.690639\pi$
$149$	−13.7627	−1.12749	−0.563743	+	0.825950i	$0.690639\pi$
$150$	7.91440	0.646208
$151$	13.6939	1.11440	0.557198	−	0.830379i	$-0.311876\pi$
$151$	13.6939	1.11440	0.557198	+	0.830379i	$0.311876\pi$
$152$	3.35546	0.272163
$153$	1.00000	0.0808452
$154$	−4.65481	−0.375096
$155$	9.29410	0.746520
$156$	0.610996	0.0489188
$157$	2.25476	0.179950	0.0899748	−	0.995944i	$-0.471321\pi$
$157$	2.25476	0.179950	0.0899748	+	0.995944i	$0.471321\pi$
$158$	−11.0065	−0.875628
$159$	6.28345	0.498310
$160$	3.59366	0.284104
$161$	−19.2222	−1.51492
$162$	1.00000	0.0785674
$163$	−8.28105	−0.648622	−0.324311	−	0.945951i	$-0.605132\pi$
$163$	−8.28105	−0.648622	−0.324311	+	0.945951i	$0.605132\pi$
$164$	1.03487	0.0808097
$165$	−7.05770	−0.549442
$166$	2.20728	0.171318
$167$	9.94469	0.769543	0.384772	−	0.923012i	$-0.374280\pi$
$167$	9.94469	0.769543	0.384772	+	0.923012i	$0.374280\pi$
$168$	2.37015	0.182861
$169$	−12.6267	−0.971283
$170$	3.59366	0.275621
$171$	3.35546	0.256598
$172$	−11.7466	−0.895673
$173$	−24.7572	−1.88225	−0.941127	−	0.338052i	$-0.890232\pi$
$173$	−24.7572	−1.88225	−0.941127	+	0.338052i	$0.890232\pi$
$174$	7.78398	0.590102
$175$	18.7583	1.41799
$176$	−1.96393	−0.148037
$177$	−1.00000	−0.0751646
$178$	11.2950	0.846594
$179$	−9.42285	−0.704297	−0.352148	−	0.935944i	$-0.614549\pi$
$179$	−9.42285	−0.704297	−0.352148	+	0.935944i	$0.614549\pi$
$180$	3.59366	0.267856
$181$	−11.7975	−0.876903	−0.438452	−	0.898755i	$-0.644473\pi$
$181$	−11.7975	−0.876903	−0.438452	+	0.898755i	$0.644473\pi$
$182$	1.44815	0.107344
$183$	7.14741	0.528352
$184$	−8.11010	−0.597885
$185$	−9.67003	−0.710955
$186$	2.58625	0.189633
$187$	−1.96393	−0.143617
$188$	−5.48284	−0.399877
$189$	2.37015	0.172403
$190$	12.0584	0.874806
$191$	−18.4058	−1.33180	−0.665899	−	0.746041i	$-0.731952\pi$
$191$	−18.4058	−1.33180	−0.665899	+	0.746041i	$0.731952\pi$
$192$	1.00000	0.0721688
$193$	11.0355	0.794351	0.397176	−	0.917743i	$-0.369990\pi$
$193$	11.0355	0.794351	0.397176	+	0.917743i	$0.369990\pi$
$194$	−10.3247	−0.741273
$195$	2.19571	0.157238
$196$	−1.38239	−0.0987421
$197$	7.59915	0.541417	0.270709	−	0.962661i	$-0.412742\pi$
$197$	7.59915	0.541417	0.270709	+	0.962661i	$0.412742\pi$
$198$	−1.96393	−0.139571
$199$	−20.3686	−1.44389	−0.721947	−	0.691948i	$-0.756753\pi$
$199$	−20.3686	−1.44389	−0.721947	+	0.691948i	$0.756753\pi$
$200$	7.91440	0.559632
$201$	0.765914	0.0540234
$202$	4.91627	0.345908
$203$	18.4492	1.29488
$204$	1.00000	0.0700140
$205$	3.71897	0.259744
$206$	11.8739	0.827297
$207$	−8.11010	−0.563691
$208$	0.610996	0.0423650
$209$	−6.58989	−0.455832
$210$	8.51751	0.587764
$211$	−18.1124	−1.24691	−0.623454	−	0.781860i	$-0.714271\pi$
$211$	−18.1124	−1.24691	−0.623454	+	0.781860i	$0.714271\pi$
$212$	6.28345	0.431549
$213$	−2.00707	−0.137522
$214$	−1.69618	−0.115949
$215$	−42.2134	−2.87893
$216$	1.00000	0.0680414
$217$	6.12979	0.416118
$218$	6.66344	0.451305
$219$	−3.25099	−0.219681
$220$	−7.05770	−0.475830
$221$	0.610996	0.0411000
$222$	−2.69086	−0.180599
$223$	7.12982	0.477448	0.238724	−	0.971087i	$-0.423271\pi$
$223$	7.12982	0.477448	0.238724	+	0.971087i	$0.423271\pi$
$224$	2.37015	0.158362
$225$	7.91440	0.527626
$226$	6.24549	0.415444
$227$	14.2133	0.943367	0.471683	−	0.881768i	$-0.343647\pi$
$227$	14.2133	0.943367	0.471683	+	0.881768i	$0.343647\pi$
$228$	3.35546	0.222221
$229$	3.51168	0.232058	0.116029	−	0.993246i	$-0.462983\pi$
$229$	3.51168	0.232058	0.116029	+	0.993246i	$0.462983\pi$
$230$	−29.1450	−1.92176
$231$	−4.65481	−0.306264
$232$	7.78398	0.511043
$233$	−29.3922	−1.92555	−0.962773	−	0.270310i	$-0.912874\pi$
$233$	−29.3922	−1.92555	−0.962773	+	0.270310i	$0.912874\pi$
$234$	0.610996	0.0399421
$235$	−19.7035	−1.28531
$236$	−1.00000	−0.0650945
$237$	−11.0065	−0.714947
$238$	2.37015	0.153634
$239$	2.89766	0.187434	0.0937170	−	0.995599i	$-0.470125\pi$
$239$	2.89766	0.187434	0.0937170	+	0.995599i	$0.470125\pi$
$240$	3.59366	0.231970
$241$	11.1534	0.718457	0.359228	−	0.933250i	$-0.383040\pi$
$241$	11.1534	0.718457	0.359228	+	0.933250i	$0.383040\pi$
$242$	−7.14297	−0.459168
$243$	1.00000	0.0641500
$244$	7.14741	0.457566
$245$	−4.96784	−0.317384
$246$	1.03487	0.0659809
$247$	2.05017	0.130449
$248$	2.58625	0.164227
$249$	2.20728	0.139881
$250$	10.4734	0.662393
$251$	10.8557	0.685204	0.342602	−	0.939481i	$-0.388692\pi$
$251$	10.8557	0.685204	0.342602	+	0.939481i	$0.388692\pi$
$252$	2.37015	0.149305
$253$	15.9277	1.00137
$254$	−6.79769	−0.426525
$255$	3.59366	0.225044
$256$	1.00000	0.0625000
$257$	−10.0932	−0.629595	−0.314798	−	0.949159i	$-0.601937\pi$
$257$	−10.0932	−0.629595	−0.314798	+	0.949159i	$0.601937\pi$
$258$	−11.7466	−0.731314
$259$	−6.37774	−0.396293
$260$	2.19571	0.136172
$261$	7.78398	0.481816
$262$	−3.06329	−0.189250
$263$	−6.50745	−0.401267	−0.200633	−	0.979666i	$-0.564300\pi$
$263$	−6.50745	−0.401267	−0.200633	+	0.979666i	$0.564300\pi$
$264$	−1.96393	−0.120872
$265$	22.5806	1.38711
$266$	7.95293	0.487626
$267$	11.2950	0.691241
$268$	0.765914	0.0467857
$269$	−13.4452	−0.819769	−0.409884	−	0.912137i	$-0.634431\pi$
$269$	−13.4452	−0.819769	−0.409884	+	0.912137i	$0.634431\pi$
$270$	3.59366	0.218703
$271$	8.64147	0.524932	0.262466	−	0.964941i	$-0.415464\pi$
$271$	8.64147	0.524932	0.262466	+	0.964941i	$0.415464\pi$
$272$	1.00000	0.0606339
$273$	1.44815	0.0876461
$274$	13.3543	0.806763
$275$	−15.5433	−0.937298
$276$	−8.11010	−0.488171
$277$	−17.2300	−1.03525	−0.517626	−	0.855607i	$-0.673184\pi$
$277$	−17.2300	−1.03525	−0.517626	+	0.855607i	$0.673184\pi$
$278$	−3.74908	−0.224855
$279$	2.58625	0.154835
$280$	8.51751	0.509019
$281$	9.56706	0.570723	0.285362	−	0.958420i	$-0.407886\pi$
$281$	9.56706	0.570723	0.285362	+	0.958420i	$0.407886\pi$
$282$	−5.48284	−0.326499
$283$	15.6878	0.932546	0.466273	−	0.884641i	$-0.345596\pi$
$283$	15.6878	0.932546	0.466273	+	0.884641i	$0.345596\pi$
$284$	−2.00707	−0.119098
$285$	12.0584	0.714276
$286$	−1.19995	−0.0709548
$287$	2.45280	0.144784
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	27.9730	1.64263
$291$	−10.3247	−0.605247
$292$	−3.25099	−0.190250
$293$	−4.02337	−0.235048	−0.117524	−	0.993070i	$-0.537496\pi$
$293$	−4.02337	−0.235048	−0.117524	+	0.993070i	$0.537496\pi$
$294$	−1.38239	−0.0806226
$295$	−3.59366	−0.209231
$296$	−2.69086	−0.156403
$297$	−1.96393	−0.113959
$298$	−13.7627	−0.797253
$299$	−4.95524	−0.286569
$300$	7.91440	0.456938
$301$	−27.8413	−1.60474
$302$	13.6939	0.787998
$303$	4.91627	0.282432
$304$	3.35546	0.192449
$305$	25.6854	1.47074
$306$	1.00000	0.0571662
$307$	−0.372573	−0.0212639	−0.0106319	−	0.999943i	$-0.503384\pi$
$307$	−0.372573	−0.0212639	−0.0106319	+	0.999943i	$0.503384\pi$
$308$	−4.65481	−0.265233
$309$	11.8739	0.675485
$310$	9.29410	0.527869
$311$	28.1096	1.59395	0.796974	−	0.604014i	$-0.206433\pi$
$311$	28.1096	1.59395	0.796974	+	0.604014i	$0.206433\pi$
$312$	0.610996	0.0345908
$313$	30.2827	1.71168	0.855839	−	0.517242i	$-0.173041\pi$
$313$	30.2827	1.71168	0.855839	+	0.517242i	$0.173041\pi$
$314$	2.25476	0.127244
$315$	8.51751	0.479908
$316$	−11.0065	−0.619163
$317$	32.0851	1.80208	0.901040	−	0.433737i	$-0.142805\pi$
$317$	32.0851	1.80208	0.901040	+	0.433737i	$0.142805\pi$
$318$	6.28345	0.352358
$319$	−15.2872	−0.855919
$320$	3.59366	0.200892
$321$	−1.69618	−0.0946716
$322$	−19.2222	−1.07121
$323$	3.35546	0.186703
$324$	1.00000	0.0555556
$325$	4.83566	0.268234
$326$	−8.28105	−0.458645
$327$	6.66344	0.368489
$328$	1.03487	0.0571411
$329$	−12.9952	−0.716446
$330$	−7.05770	−0.388514
$331$	10.8136	0.594370	0.297185	−	0.954820i	$-0.403952\pi$
$331$	10.8136	0.594370	0.297185	+	0.954820i	$0.403952\pi$
$332$	2.20728	0.121140
$333$	−2.69086	−0.147458
$334$	9.94469	0.544149
$335$	2.75244	0.150382
$336$	2.37015	0.129302
$337$	−0.00809265	−0.000440835 0	−0.000220417	−	1.00000i	$-0.500070\pi$
$337$	−0.00809265	−0.000440835 0	−0.000220417		1.00000i	$0.500070\pi$
$338$	−12.6267	−0.686801
$339$	6.24549	0.339208
$340$	3.59366	0.194894
$341$	−5.07921	−0.275055
$342$	3.35546	0.181442
$343$	−19.8675	−1.07275
$344$	−11.7466	−0.633336
$345$	−29.1450	−1.56911
$346$	−24.7572	−1.33096
$347$	−4.40404	−0.236421	−0.118211	−	0.992989i	$-0.537716\pi$
$347$	−4.40404	−0.236421	−0.118211	+	0.992989i	$0.537716\pi$
$348$	7.78398	0.417265
$349$	−10.1812	−0.544985	−0.272493	−	0.962158i	$-0.587848\pi$
$349$	−10.1812	−0.544985	−0.272493	+	0.962158i	$0.587848\pi$
$350$	18.7583	1.00267
$351$	0.610996	0.0326126
$352$	−1.96393	−0.104678
$353$	10.2428	0.545171	0.272586	−	0.962132i	$-0.412121\pi$
$353$	10.2428	0.545171	0.272586	+	0.962132i	$0.412121\pi$
$354$	−1.00000	−0.0531494
$355$	−7.21273	−0.382812
$356$	11.2950	0.598632
$357$	2.37015	0.125442
$358$	−9.42285	−0.498013
$359$	−21.9832	−1.16023	−0.580116	−	0.814534i	$-0.696993\pi$
$359$	−21.9832	−1.16023	−0.580116	+	0.814534i	$0.696993\pi$
$360$	3.59366	0.189403
$361$	−7.74091	−0.407416
$362$	−11.7975	−0.620064
$363$	−7.14297	−0.374909
$364$	1.44815	0.0759038
$365$	−11.6829	−0.611513
$366$	7.14741	0.373601
$367$	27.9583	1.45941	0.729706	−	0.683761i	$-0.239657\pi$
$367$	27.9583	1.45941	0.729706	+	0.683761i	$0.239657\pi$
$368$	−8.11010	−0.422768
$369$	1.03487	0.0538732
$370$	−9.67003	−0.502721
$371$	14.8927	0.773191
$372$	2.58625	0.134091
$373$	−24.1962	−1.25283	−0.626415	−	0.779490i	$-0.715479\pi$
$373$	−24.1962	−1.25283	−0.626415	+	0.779490i	$0.715479\pi$
$374$	−1.96393	−0.101553
$375$	10.4734	0.540841
$376$	−5.48284	−0.282756
$377$	4.75598	0.244945
$378$	2.37015	0.121907
$379$	−37.4433	−1.92333	−0.961667	−	0.274221i	$-0.911580\pi$
$379$	−37.4433	−1.92333	−0.961667	+	0.274221i	$0.911580\pi$
$380$	12.0584	0.618581
$381$	−6.79769	−0.348256
$382$	−18.4058	−0.941724
$383$	11.9970	0.613018	0.306509	−	0.951868i	$-0.400839\pi$
$383$	11.9970	0.613018	0.306509	+	0.951868i	$0.400839\pi$
$384$	1.00000	0.0510310
$385$	−16.7278	−0.852529
$386$	11.0355	0.561691
$387$	−11.7466	−0.597115
$388$	−10.3247	−0.524159
$389$	−22.5843	−1.14507	−0.572535	−	0.819881i	$-0.694040\pi$
$389$	−22.5843	−1.14507	−0.572535	+	0.819881i	$0.694040\pi$
$390$	2.19571	0.111184
$391$	−8.11010	−0.410146
$392$	−1.38239	−0.0698212
$393$	−3.06329	−0.154522
$394$	7.59915	0.382840
$395$	−39.5535	−1.99015
$396$	−1.96393	−0.0986913
$397$	−1.25592	−0.0630327	−0.0315163	−	0.999503i	$-0.510034\pi$
$397$	−1.25592	−0.0630327	−0.0315163	+	0.999503i	$0.510034\pi$
$398$	−20.3686	−1.02099
$399$	7.95293	0.398145
$400$	7.91440	0.395720
$401$	21.6809	1.08269	0.541346	−	0.840800i	$-0.317915\pi$
$401$	21.6809	1.08269	0.541346	+	0.840800i	$0.317915\pi$
$402$	0.765914	0.0382003
$403$	1.58019	0.0787147
$404$	4.91627	0.244594
$405$	3.59366	0.178570
$406$	18.4492	0.915618
$407$	5.28466	0.261951
$408$	1.00000	0.0495074
$409$	−35.0088	−1.73107	−0.865537	−	0.500845i	$-0.833023\pi$
$409$	−35.0088	−1.73107	−0.865537	+	0.500845i	$0.833023\pi$
$410$	3.71897	0.183667
$411$	13.3543	0.658719
$412$	11.8739	0.584987
$413$	−2.37015	−0.116627
$414$	−8.11010	−0.398590
$415$	7.93221	0.389377
$416$	0.610996	0.0299565
$417$	−3.74908	−0.183593
$418$	−6.58989	−0.322322
$419$	7.67994	0.375190	0.187595	−	0.982246i	$-0.439931\pi$
$419$	7.67994	0.375190	0.187595	+	0.982246i	$0.439931\pi$
$420$	8.51751	0.415612
$421$	−9.27765	−0.452165	−0.226082	−	0.974108i	$-0.572592\pi$
$421$	−9.27765	−0.452165	−0.226082	+	0.974108i	$0.572592\pi$
$422$	−18.1124	−0.881697
$423$	−5.48284	−0.266585
$424$	6.28345	0.305151
$425$	7.91440	0.383905
$426$	−2.00707	−0.0972429
$427$	16.9404	0.819805
$428$	−1.69618	−0.0819880
$429$	−1.19995	−0.0579344
$430$	−42.2134	−2.03571
$431$	7.93390	0.382162	0.191081	−	0.981574i	$-0.438801\pi$
$431$	7.93390	0.382162	0.191081	+	0.981574i	$0.438801\pi$
$432$	1.00000	0.0481125
$433$	23.4097	1.12500	0.562498	−	0.826798i	$-0.309840\pi$
$433$	23.4097	1.12500	0.562498	+	0.826798i	$0.309840\pi$
$434$	6.12979	0.294240
$435$	27.9730	1.34120
$436$	6.66344	0.319121
$437$	−27.2131	−1.30178
$438$	−3.25099	−0.155338
$439$	13.6790	0.652861	0.326431	−	0.945221i	$-0.394154\pi$
$439$	13.6790	0.652861	0.326431	+	0.945221i	$0.394154\pi$
$440$	−7.05770	−0.336463
$441$	−1.38239	−0.0658281
$442$	0.610996	0.0290621
$443$	6.51834	0.309696	0.154848	−	0.987938i	$-0.450511\pi$
$443$	6.51834	0.309696	0.154848	+	0.987938i	$0.450511\pi$
$444$	−2.69086	−0.127702
$445$	40.5903	1.92417
$446$	7.12982	0.337607
$447$	−13.7627	−0.650954
$448$	2.37015	0.111979
$449$	−6.72108	−0.317187	−0.158594	−	0.987344i	$-0.550696\pi$
$449$	−6.72108	−0.317187	−0.158594	+	0.987344i	$0.550696\pi$
$450$	7.91440	0.373088
$451$	−2.03241	−0.0957026
$452$	6.24549	0.293763
$453$	13.6939	0.643397
$454$	14.2133	0.667061
$455$	5.20417	0.243975
$456$	3.35546	0.157134
$457$	20.7022	0.968409	0.484205	−	0.874955i	$-0.339109\pi$
$457$	20.7022	0.968409	0.484205	+	0.874955i	$0.339109\pi$
$458$	3.51168	0.164090
$459$	1.00000	0.0466760
$460$	−29.1450	−1.35889
$461$	−4.26458	−0.198621	−0.0993106	−	0.995056i	$-0.531664\pi$
$461$	−4.26458	−0.198621	−0.0993106	+	0.995056i	$0.531664\pi$
$462$	−4.65481	−0.216561
$463$	−27.2176	−1.26491	−0.632455	−	0.774597i	$-0.717953\pi$
$463$	−27.2176	−1.26491	−0.632455	+	0.774597i	$0.717953\pi$
$464$	7.78398	0.361362
$465$	9.29410	0.431003
$466$	−29.3922	−1.36157
$467$	−8.33413	−0.385657	−0.192829	−	0.981232i	$-0.561766\pi$
$467$	−8.33413	−0.385657	−0.192829	+	0.981232i	$0.561766\pi$
$468$	0.610996	0.0282433
$469$	1.81533	0.0838242
$470$	−19.7035	−0.908854
$471$	2.25476	0.103894
$472$	−1.00000	−0.0460287
$473$	23.0696	1.06074
$474$	−11.0065	−0.505544
$475$	26.5564	1.21849
$476$	2.37015	0.108636
$477$	6.28345	0.287699
$478$	2.89766	0.132536
$479$	−11.3014	−0.516373	−0.258187	−	0.966095i	$-0.583125\pi$
$479$	−11.3014	−0.516373	−0.258187	+	0.966095i	$0.583125\pi$
$480$	3.59366	0.164027
$481$	−1.64410	−0.0749647
$482$	11.1534	0.508026
$483$	−19.2222	−0.874639
$484$	−7.14297	−0.324681
$485$	−37.1036	−1.68479
$486$	1.00000	0.0453609
$487$	39.3643	1.78377	0.891884	−	0.452265i	$-0.149384\pi$
$487$	39.3643	1.78377	0.891884	+	0.452265i	$0.149384\pi$
$488$	7.14741	0.323548
$489$	−8.28105	−0.374482
$490$	−4.96784	−0.224424
$491$	−15.2726	−0.689242	−0.344621	−	0.938742i	$-0.611993\pi$
$491$	−15.2726	−0.689242	−0.344621	+	0.938742i	$0.611993\pi$
$492$	1.03487	0.0466555
$493$	7.78398	0.350573
$494$	2.05017	0.0922415
$495$	−7.05770	−0.317220
$496$	2.58625	0.116126
$497$	−4.75706	−0.213383
$498$	2.20728	0.0989105
$499$	−2.03144	−0.0909396	−0.0454698	−	0.998966i	$-0.514478\pi$
$499$	−2.03144	−0.0909396	−0.0454698	+	0.998966i	$0.514478\pi$
$500$	10.4734	0.468382
$501$	9.94469	0.444296
$502$	10.8557	0.484512
$503$	22.6582	1.01028	0.505139	−	0.863038i	$-0.331441\pi$
$503$	22.6582	1.01028	0.505139	+	0.863038i	$0.331441\pi$
$504$	2.37015	0.105575
$505$	17.6674	0.786189
$506$	15.9277	0.708072
$507$	−12.6267	−0.560771
$508$	−6.79769	−0.301599
$509$	22.5817	1.00092	0.500458	−	0.865761i	$-0.333165\pi$
$509$	22.5817	1.00092	0.500458	+	0.865761i	$0.333165\pi$
$510$	3.59366	0.159130
$511$	−7.70532	−0.340863
$512$	1.00000	0.0441942
$513$	3.35546	0.148147
$514$	−10.0932	−0.445191
$515$	42.6709	1.88031
$516$	−11.7466	−0.517117
$517$	10.7679	0.473573
$518$	−6.37774	−0.280222
$519$	−24.7572	−1.08672
$520$	2.19571	0.0962884
$521$	11.4656	0.502316	0.251158	−	0.967946i	$-0.419189\pi$
$521$	11.4656	0.502316	0.251158	+	0.967946i	$0.419189\pi$
$522$	7.78398	0.340695
$523$	−7.91390	−0.346051	−0.173025	−	0.984917i	$-0.555354\pi$
$523$	−7.91390	−0.346051	−0.173025	+	0.984917i	$0.555354\pi$
$524$	−3.06329	−0.133820
$525$	18.7583	0.818680
$526$	−6.50745	−0.283738
$527$	2.58625	0.112659
$528$	−1.96393	−0.0854692
$529$	42.7738	1.85973
$530$	22.5806	0.980838
$531$	−1.00000	−0.0433963
$532$	7.95293	0.344803
$533$	0.632301	0.0273880
$534$	11.2950	0.488781
$535$	−6.09550	−0.263531
$536$	0.765914	0.0330825
$537$	−9.42285	−0.406626
$538$	−13.4452	−0.579664
$539$	2.71492	0.116940
$540$	3.59366	0.154647
$541$	14.9487	0.642694	0.321347	−	0.946962i	$-0.395864\pi$
$541$	14.9487	0.642694	0.321347	+	0.946962i	$0.395864\pi$
$542$	8.64147	0.371183
$543$	−11.7975	−0.506280
$544$	1.00000	0.0428746
$545$	23.9461	1.02574
$546$	1.44815	0.0619752
$547$	−14.7791	−0.631909	−0.315954	−	0.948774i	$-0.602325\pi$
$547$	−14.7791	−0.631909	−0.315954	+	0.948774i	$0.602325\pi$
$548$	13.3543	0.570467
$549$	7.14741	0.305044
$550$	−15.5433	−0.662770
$551$	26.1188	1.11270
$552$	−8.11010	−0.345189
$553$	−26.0870	−1.10933
$554$	−17.2300	−0.732033
$555$	−9.67003	−0.410470
$556$	−3.74908	−0.158996
$557$	36.5308	1.54786	0.773930	−	0.633271i	$-0.218288\pi$
$557$	36.5308	1.54786	0.773930	+	0.633271i	$0.218288\pi$
$558$	2.58625	0.109485
$559$	−7.17715	−0.303561
$560$	8.51751	0.359931
$561$	−1.96393	−0.0829173
$562$	9.56706	0.403562
$563$	46.1435	1.94472	0.972358	−	0.233497i	$-0.0750168\pi$
$563$	46.1435	1.94472	0.972358	+	0.233497i	$0.0750168\pi$
$564$	−5.48284	−0.230869
$565$	22.4442	0.944233
$566$	15.6878	0.659409
$567$	2.37015	0.0995369
$568$	−2.00707	−0.0842148
$569$	−28.2533	−1.18444	−0.592220	−	0.805776i	$-0.701748\pi$
$569$	−28.2533	−1.18444	−0.592220	+	0.805776i	$0.701748\pi$
$570$	12.0584	0.505070
$571$	−5.63282	−0.235726	−0.117863	−	0.993030i	$-0.537604\pi$
$571$	−5.63282	−0.235726	−0.117863	+	0.993030i	$0.537604\pi$
$572$	−1.19995	−0.0501726
$573$	−18.4058	−0.768914
$574$	2.45280	0.102378
$575$	−64.1866	−2.67677
$576$	1.00000	0.0416667
$577$	12.6604	0.527059	0.263530	−	0.964651i	$-0.415113\pi$
$577$	12.6604	0.527059	0.263530	+	0.964651i	$0.415113\pi$
$578$	1.00000	0.0415945
$579$	11.0355	0.458619
$580$	27.9730	1.16151
$581$	5.23158	0.217042
$582$	−10.3247	−0.427974
$583$	−12.3403	−0.511082
$584$	−3.25099	−0.134527
$585$	2.19571	0.0907815
$586$	−4.02337	−0.166204
$587$	−2.22050	−0.0916497	−0.0458249	−	0.998949i	$-0.514592\pi$
$587$	−2.22050	−0.0916497	−0.0458249	+	0.998949i	$0.514592\pi$
$588$	−1.38239	−0.0570088
$589$	8.67804	0.357572
$590$	−3.59366	−0.147949
$591$	7.59915	0.312587
$592$	−2.69086	−0.110594
$593$	−23.7020	−0.973327	−0.486663	−	0.873590i	$-0.661786\pi$
$593$	−23.7020	−0.973327	−0.486663	+	0.873590i	$0.661786\pi$
$594$	−1.96393	−0.0805811
$595$	8.51751	0.349184
$596$	−13.7627	−0.563743
$597$	−20.3686	−0.833633
$598$	−4.95524	−0.202635
$599$	18.1628	0.742111	0.371056	−	0.928611i	$-0.378996\pi$
$599$	18.1628	0.742111	0.371056	+	0.928611i	$0.378996\pi$
$600$	7.91440	0.323104
$601$	18.6947	0.762571	0.381286	−	0.924457i	$-0.375481\pi$
$601$	18.6947	0.762571	0.381286	+	0.924457i	$0.375481\pi$
$602$	−27.8413	−1.13473
$603$	0.765914	0.0311904
$604$	13.6939	0.557198
$605$	−25.6694	−1.04361
$606$	4.91627	0.199710
$607$	−28.4540	−1.15491	−0.577456	−	0.816422i	$-0.695954\pi$
$607$	−28.4540	−1.15491	−0.577456	+	0.816422i	$0.695954\pi$
$608$	3.35546	0.136082
$609$	18.4492	0.747599
$610$	25.6854	1.03997
$611$	−3.35000	−0.135526
$612$	1.00000	0.0404226
$613$	10.7538	0.434341	0.217170	−	0.976134i	$-0.430317\pi$
$613$	10.7538	0.434341	0.217170	+	0.976134i	$0.430317\pi$
$614$	−0.372573	−0.0150358
$615$	3.71897	0.149963
$616$	−4.65481	−0.187548
$617$	15.0260	0.604925	0.302462	−	0.953161i	$-0.402191\pi$
$617$	15.0260	0.604925	0.302462	+	0.953161i	$0.402191\pi$
$618$	11.8739	0.477640
$619$	−16.5693	−0.665976	−0.332988	−	0.942931i	$-0.608057\pi$
$619$	−16.5693	−0.665976	−0.332988	+	0.942931i	$0.608057\pi$
$620$	9.29410	0.373260
$621$	−8.11010	−0.325447
$622$	28.1096	1.12709
$623$	26.7708	1.07255
$624$	0.610996	0.0244594
$625$	−1.93431	−0.0773726
$626$	30.2827	1.21034
$627$	−6.58989	−0.263175
$628$	2.25476	0.0899748
$629$	−2.69086	−0.107292
$630$	8.51751	0.339346
$631$	7.00142	0.278722	0.139361	−	0.990242i	$-0.455495\pi$
$631$	7.00142	0.278722	0.139361	+	0.990242i	$0.455495\pi$
$632$	−11.0065	−0.437814
$633$	−18.1124	−0.719903
$634$	32.0851	1.27426
$635$	−24.4286	−0.969419
$636$	6.28345	0.249155
$637$	−0.844635	−0.0334656
$638$	−15.2872	−0.605226
$639$	−2.00707	−0.0793985
$640$	3.59366	0.142052
$641$	−45.1606	−1.78374	−0.891868	−	0.452296i	$-0.850605\pi$
$641$	−45.1606	−1.78374	−0.891868	+	0.452296i	$0.850605\pi$
$642$	−1.69618	−0.0669429
$643$	−2.38344	−0.0939936	−0.0469968	−	0.998895i	$-0.514965\pi$
$643$	−2.38344	−0.0939936	−0.0469968	+	0.998895i	$0.514965\pi$
$644$	−19.2222	−0.757459
$645$	−42.2134	−1.66215
$646$	3.35546	0.132019
$647$	12.4708	0.490279	0.245139	−	0.969488i	$-0.421166\pi$
$647$	12.4708	0.490279	0.245139	+	0.969488i	$0.421166\pi$
$648$	1.00000	0.0392837
$649$	1.96393	0.0770911
$650$	4.83566	0.189670
$651$	6.12979	0.240246
$652$	−8.28105	−0.324311
$653$	11.3034	0.442335	0.221168	−	0.975236i	$-0.429013\pi$
$653$	11.3034	0.442335	0.221168	+	0.975236i	$0.429013\pi$
$654$	6.66344	0.260561
$655$	−11.0084	−0.430134
$656$	1.03487	0.0404049
$657$	−3.25099	−0.126833
$658$	−12.9952	−0.506604
$659$	−37.4197	−1.45766	−0.728832	−	0.684692i	$-0.759937\pi$
$659$	−37.4197	−1.45766	−0.728832	+	0.684692i	$0.759937\pi$
$660$	−7.05770	−0.274721
$661$	30.1161	1.17138	0.585691	−	0.810534i	$-0.300823\pi$
$661$	30.1161	1.17138	0.585691	+	0.810534i	$0.300823\pi$
$662$	10.8136	0.420283
$663$	0.610996	0.0237291
$664$	2.20728	0.0856590
$665$	28.5801	1.10829
$666$	−2.69086	−0.104269
$667$	−63.1289	−2.44436
$668$	9.94469	0.384772
$669$	7.12982	0.275655
$670$	2.75244	0.106336
$671$	−14.0370	−0.541894
$672$	2.37015	0.0914305
$673$	−6.00385	−0.231431	−0.115716	−	0.993282i	$-0.536916\pi$
$673$	−6.00385	−0.231431	−0.115716	+	0.993282i	$0.536916\pi$
$674$	−0.00809265	−0.000311717 0
$675$	7.91440	0.304625
$676$	−12.6267	−0.485642
$677$	45.4242	1.74579	0.872897	−	0.487905i	$-0.162239\pi$
$677$	45.4242	1.74579	0.872897	+	0.487905i	$0.162239\pi$
$678$	6.24549	0.239856
$679$	−24.4712	−0.939118
$680$	3.59366	0.137811
$681$	14.2133	0.544653
$682$	−5.07921	−0.194493
$683$	−14.7016	−0.562541	−0.281271	−	0.959628i	$-0.590756\pi$
$683$	−14.7016	−0.562541	−0.281271	+	0.959628i	$0.590756\pi$
$684$	3.35546	0.128299
$685$	47.9908	1.83364
$686$	−19.8675	−0.758545
$687$	3.51168	0.133979
$688$	−11.7466	−0.447836
$689$	3.83916	0.146260
$690$	−29.1450	−1.10953
$691$	−15.2647	−0.580697	−0.290349	−	0.956921i	$-0.593771\pi$
$691$	−15.2647	−0.580697	−0.290349	+	0.956921i	$0.593771\pi$
$692$	−24.7572	−0.941127
$693$	−4.65481	−0.176822
$694$	−4.40404	−0.167175
$695$	−13.4729	−0.511056
$696$	7.78398	0.295051
$697$	1.03487	0.0391985
$698$	−10.1812	−0.385363
$699$	−29.3922	−1.11171
$700$	18.7583	0.708997
$701$	−16.3724	−0.618377	−0.309189	−	0.951001i	$-0.600057\pi$
$701$	−16.3724	−0.618377	−0.309189	+	0.951001i	$0.600057\pi$
$702$	0.610996	0.0230606
$703$	−9.02906	−0.340537
$704$	−1.96393	−0.0740185
$705$	−19.7035	−0.742076
$706$	10.2428	0.385494
$707$	11.6523	0.438230
$708$	−1.00000	−0.0375823
$709$	−25.0166	−0.939518	−0.469759	−	0.882795i	$-0.655659\pi$
$709$	−25.0166	−0.939518	−0.469759	+	0.882795i	$0.655659\pi$
$710$	−7.21273	−0.270689
$711$	−11.0065	−0.412775
$712$	11.2950	0.423297
$713$	−20.9747	−0.785510
$714$	2.37015	0.0887006
$715$	−4.31223	−0.161268
$716$	−9.42285	−0.352148
$717$	2.89766	0.108215
$718$	−21.9832	−0.820407
$719$	9.06283	0.337986	0.168993	−	0.985617i	$-0.445948\pi$
$719$	9.06283	0.337986	0.168993	+	0.985617i	$0.445948\pi$
$720$	3.59366	0.133928
$721$	28.1430	1.04810
$722$	−7.74091	−0.288087
$723$	11.1534	0.414801
$724$	−11.7975	−0.438452
$725$	61.6055	2.28797
$726$	−7.14297	−0.265101
$727$	−12.2731	−0.455183	−0.227592	−	0.973757i	$-0.573085\pi$
$727$	−12.2731	−0.455183	−0.227592	+	0.973757i	$0.573085\pi$
$728$	1.44815	0.0536721
$729$	1.00000	0.0370370
$730$	−11.6829	−0.432405
$731$	−11.7466	−0.434465
$732$	7.14741	0.264176
$733$	22.9255	0.846774	0.423387	−	0.905949i	$-0.360841\pi$
$733$	22.9255	0.846774	0.423387	+	0.905949i	$0.360841\pi$
$734$	27.9583	1.03196
$735$	−4.96784	−0.183242
$736$	−8.11010	−0.298942
$737$	−1.50420	−0.0554080
$738$	1.03487	0.0380941
$739$	20.4834	0.753493	0.376746	−	0.926316i	$-0.377043\pi$
$739$	20.4834	0.753493	0.376746	+	0.926316i	$0.377043\pi$
$740$	−9.67003	−0.355477
$741$	2.05017	0.0753149
$742$	14.8927	0.546729
$743$	30.5603	1.12115	0.560575	−	0.828104i	$-0.310580\pi$
$743$	30.5603	1.12115	0.560575	+	0.828104i	$0.310580\pi$
$744$	2.58625	0.0948164
$745$	−49.4585	−1.81202
$746$	−24.1962	−0.885885
$747$	2.20728	0.0807601
$748$	−1.96393	−0.0718085
$749$	−4.02020	−0.146895
$750$	10.4734	0.382433
$751$	6.68813	0.244053	0.122027	−	0.992527i	$-0.461061\pi$
$751$	6.68813	0.244053	0.122027	+	0.992527i	$0.461061\pi$
$752$	−5.48284	−0.199939
$753$	10.8557	0.395603
$754$	4.75598	0.173203
$755$	49.2114	1.79098
$756$	2.37015	0.0862015
$757$	−38.3302	−1.39314	−0.696568	−	0.717491i	$-0.745291\pi$
$757$	−38.3302	−1.39314	−0.696568	+	0.717491i	$0.745291\pi$
$758$	−37.4433	−1.36000
$759$	15.9277	0.578139
$760$	12.0584	0.437403
$761$	−17.8032	−0.645366	−0.322683	−	0.946507i	$-0.604585\pi$
$761$	−17.8032	−0.645366	−0.322683	+	0.946507i	$0.604585\pi$
$762$	−6.79769	−0.246254
$763$	15.7934	0.571758
$764$	−18.4058	−0.665899
$765$	3.59366	0.129929
$766$	11.9970	0.433469
$767$	−0.610996	−0.0220618
$768$	1.00000	0.0360844
$769$	−52.5188	−1.89387	−0.946937	−	0.321418i	$-0.895840\pi$
$769$	−52.5188	−1.89387	−0.946937	+	0.321418i	$0.895840\pi$
$770$	−16.7278	−0.602829
$771$	−10.0932	−0.363497
$772$	11.0355	0.397176
$773$	32.6181	1.17319	0.586595	−	0.809880i	$-0.300468\pi$
$773$	32.6181	1.17319	0.586595	+	0.809880i	$0.300468\pi$
$774$	−11.7466	−0.422224
$775$	20.4686	0.735253
$776$	−10.3247	−0.370637
$777$	−6.37774	−0.228800
$778$	−22.5843	−0.809686
$779$	3.47246	0.124414
$780$	2.19571	0.0786191
$781$	3.94175	0.141047
$782$	−8.11010	−0.290017
$783$	7.78398	0.278177
$784$	−1.38239	−0.0493711
$785$	8.10285	0.289203
$786$	−3.06329	−0.109264
$787$	15.3511	0.547207	0.273604	−	0.961843i	$-0.411784\pi$
$787$	15.3511	0.547207	0.273604	+	0.961843i	$0.411784\pi$
$788$	7.59915	0.270709
$789$	−6.50745	−0.231671
$790$	−39.5535	−1.40725
$791$	14.8027	0.526325
$792$	−1.96393	−0.0697853
$793$	4.36704	0.155078
$794$	−1.25592	−0.0445708
$795$	22.5806	0.800851
$796$	−20.3686	−0.721947
$797$	37.2868	1.32077	0.660383	−	0.750929i	$-0.270394\pi$
$797$	37.2868	1.32077	0.660383	+	0.750929i	$0.270394\pi$
$798$	7.95293	0.281531
$799$	−5.48284	−0.193969
$800$	7.91440	0.279816
$801$	11.2950	0.399088
$802$	21.6809	0.765579
$803$	6.38472	0.225312
$804$	0.765914	0.0270117
$805$	−69.0779	−2.43468
$806$	1.58019	0.0556597
$807$	−13.4452	−0.473294
$808$	4.91627	0.172954
$809$	−1.09126	−0.0383665	−0.0191833	−	0.999816i	$-0.506107\pi$
$809$	−1.09126	−0.0383665	−0.0191833	+	0.999816i	$0.506107\pi$
$810$	3.59366	0.126268
$811$	−54.8799	−1.92709	−0.963547	−	0.267537i	$-0.913790\pi$
$811$	−54.8799	−1.92709	−0.963547	+	0.267537i	$0.913790\pi$
$812$	18.4492	0.647440
$813$	8.64147	0.303070
$814$	5.28466	0.185227
$815$	−29.7593	−1.04242
$816$	1.00000	0.0350070
$817$	−39.4153	−1.37897
$818$	−35.0088	−1.22405
$819$	1.44815	0.0506025
$820$	3.71897	0.129872
$821$	9.02861	0.315101	0.157550	−	0.987511i	$-0.449640\pi$
$821$	9.02861	0.315101	0.157550	+	0.987511i	$0.449640\pi$
$822$	13.3543	0.465785
$823$	−0.724790	−0.0252646	−0.0126323	−	0.999920i	$-0.504021\pi$
$823$	−0.724790	−0.0252646	−0.0126323	+	0.999920i	$0.504021\pi$
$824$	11.8739	0.413648
$825$	−15.5433	−0.541149
$826$	−2.37015	−0.0824681
$827$	−23.4949	−0.816997	−0.408498	−	0.912759i	$-0.633947\pi$
$827$	−23.4949	−0.816997	−0.408498	+	0.912759i	$0.633947\pi$
$828$	−8.11010	−0.281846
$829$	45.1554	1.56831	0.784155	−	0.620565i	$-0.213097\pi$
$829$	45.1554	1.56831	0.784155	+	0.620565i	$0.213097\pi$
$830$	7.93221	0.275331
$831$	−17.2300	−0.597703
$832$	0.610996	0.0211825
$833$	−1.38239	−0.0478970
$834$	−3.74908	−0.129820
$835$	35.7378	1.23676
$836$	−6.58989	−0.227916
$837$	2.58625	0.0893938
$838$	7.67994	0.265299
$839$	18.8600	0.651119	0.325559	−	0.945522i	$-0.394447\pi$
$839$	18.8600	0.651119	0.325559	+	0.945522i	$0.394447\pi$
$840$	8.51751	0.293882
$841$	31.5903	1.08932
$842$	−9.27765	−0.319729
$843$	9.56706	0.329507
$844$	−18.1124	−0.623454
$845$	−45.3760	−1.56098
$846$	−5.48284	−0.188504
$847$	−16.9299	−0.581719
$848$	6.28345	0.215775
$849$	15.6878	0.538406
$850$	7.91440	0.271462
$851$	21.8231	0.748088
$852$	−2.00707	−0.0687611
$853$	0.656674	0.0224841	0.0112420	−	0.999937i	$-0.496421\pi$
$853$	0.656674	0.0224841	0.0112420	+	0.999937i	$0.496421\pi$
$854$	16.9404	0.579690
$855$	12.0584	0.412388
$856$	−1.69618	−0.0579743
$857$	−52.1391	−1.78104	−0.890519	−	0.454947i	$-0.849658\pi$
$857$	−52.1391	−1.78104	−0.890519	+	0.454947i	$0.849658\pi$
$858$	−1.19995	−0.0409658
$859$	−35.2109	−1.20138	−0.600690	−	0.799482i	$-0.705107\pi$
$859$	−35.2109	−1.20138	−0.600690	+	0.799482i	$0.705107\pi$
$860$	−42.2134	−1.43947
$861$	2.45280	0.0835911
$862$	7.93390	0.270230
$863$	39.0856	1.33049	0.665245	−	0.746626i	$-0.268327\pi$
$863$	39.0856	1.33049	0.665245	+	0.746626i	$0.268327\pi$
$864$	1.00000	0.0340207
$865$	−88.9690	−3.02504
$866$	23.4097	0.795493
$867$	1.00000	0.0339618
$868$	6.12979	0.208059
$869$	21.6160	0.733272
$870$	27.9730	0.948373
$871$	0.467970	0.0158566
$872$	6.66344	0.225653
$873$	−10.3247	−0.349440
$874$	−27.2131	−0.920497
$875$	24.8234	0.839184
$876$	−3.25099	−0.109841
$877$	−25.0228	−0.844960	−0.422480	−	0.906372i	$-0.638840\pi$
$877$	−25.0228	−0.844960	−0.422480	+	0.906372i	$0.638840\pi$
$878$	13.6790	0.461643
$879$	−4.02337	−0.135705
$880$	−7.05770	−0.237915
$881$	−15.3385	−0.516766	−0.258383	−	0.966043i	$-0.583190\pi$
$881$	−15.3385	−0.516766	−0.258383	+	0.966043i	$0.583190\pi$
$882$	−1.38239	−0.0465475
$883$	9.87208	0.332222	0.166111	−	0.986107i	$-0.446879\pi$
$883$	9.87208	0.332222	0.166111	+	0.986107i	$0.446879\pi$
$884$	0.610996	0.0205500
$885$	−3.59366	−0.120800
$886$	6.51834	0.218988
$887$	18.0525	0.606145	0.303073	−	0.952967i	$-0.401988\pi$
$887$	18.0525	0.606145	0.303073	+	0.952967i	$0.401988\pi$
$888$	−2.69086	−0.0902993
$889$	−16.1115	−0.540364
$890$	40.5903	1.36059
$891$	−1.96393	−0.0657942
$892$	7.12982	0.238724
$893$	−18.3974	−0.615647
$894$	−13.7627	−0.460294
$895$	−33.8625	−1.13190
$896$	2.37015	0.0791811
$897$	−4.95524	−0.165451
$898$	−6.72108	−0.224285
$899$	20.1313	0.671416
$900$	7.91440	0.263813
$901$	6.28345	0.209332
$902$	−2.03241	−0.0676720
$903$	−27.8413	−0.926500
$904$	6.24549	0.207722
$905$	−42.3963	−1.40930
$906$	13.6939	0.454951
$907$	−2.34965	−0.0780188	−0.0390094	−	0.999239i	$-0.512420\pi$
$907$	−2.34965	−0.0780188	−0.0390094	+	0.999239i	$0.512420\pi$
$908$	14.2133	0.471683
$909$	4.91627	0.163062
$910$	5.20417	0.172516
$911$	−25.3742	−0.840685	−0.420343	−	0.907365i	$-0.638090\pi$
$911$	−25.3742	−0.840685	−0.420343	+	0.907365i	$0.638090\pi$
$912$	3.35546	0.111110
$913$	−4.33494	−0.143466
$914$	20.7022	0.684769
$915$	25.6854	0.849132
$916$	3.51168	0.116029
$917$	−7.26045	−0.239761
$918$	1.00000	0.0330049
$919$	−0.234585	−0.00773826	−0.00386913	−	0.999993i	$-0.501232\pi$
$919$	−0.234585	−0.00773826	−0.00386913	+	0.999993i	$0.501232\pi$
$920$	−29.1450	−0.960881
$921$	−0.372573	−0.0122767
$922$	−4.26458	−0.140446
$923$	−1.22631	−0.0403646
$924$	−4.65481	−0.153132
$925$	−21.2965	−0.700225
$926$	−27.2176	−0.894427
$927$	11.8739	0.389991
$928$	7.78398	0.255522
$929$	−39.4679	−1.29490	−0.647450	−	0.762108i	$-0.724164\pi$
$929$	−39.4679	−1.29490	−0.647450	+	0.762108i	$0.724164\pi$
$930$	9.29410	0.304765
$931$	−4.63855	−0.152022
$932$	−29.3922	−0.962773
$933$	28.1096	0.920266
$934$	−8.33413	−0.272701
$935$	−7.05770	−0.230812
$936$	0.610996	0.0199710
$937$	−0.655598	−0.0214175	−0.0107087	−	0.999943i	$-0.503409\pi$
$937$	−0.655598	−0.0214175	−0.0107087	+	0.999943i	$0.503409\pi$
$938$	1.81533	0.0592727
$939$	30.2827	0.988238
$940$	−19.7035	−0.642657
$941$	41.6093	1.35642	0.678212	−	0.734867i	$-0.262755\pi$
$941$	41.6093	1.35642	0.678212	+	0.734867i	$0.262755\pi$
$942$	2.25476	0.0734641
$943$	−8.39290	−0.273310
$944$	−1.00000	−0.0325472
$945$	8.51751	0.277075
$946$	23.0696	0.750057
$947$	4.99087	0.162181	0.0810907	−	0.996707i	$-0.474160\pi$
$947$	4.99087	0.162181	0.0810907	+	0.996707i	$0.474160\pi$
$948$	−11.0065	−0.357474
$949$	−1.98634	−0.0644793
$950$	26.5564	0.861604
$951$	32.0851	1.04043
$952$	2.37015	0.0768170
$953$	−39.3675	−1.27524	−0.637619	−	0.770352i	$-0.720081\pi$
$953$	−39.3675	−1.27524	−0.637619	+	0.770352i	$0.720081\pi$
$954$	6.28345	0.203434
$955$	−66.1443	−2.14038
$956$	2.89766	0.0937170
$957$	−15.2872	−0.494165
$958$	−11.3014	−0.365131
$959$	31.6517	1.02209
$960$	3.59366	0.115985
$961$	−24.3113	−0.784236
$962$	−1.64410	−0.0530080
$963$	−1.69618	−0.0546587
$964$	11.1534	0.359228
$965$	39.6578	1.27663
$966$	−19.2222	−0.618463
$967$	−55.5777	−1.78726	−0.893629	−	0.448806i	$-0.851849\pi$
$967$	−55.5777	−1.78726	−0.893629	+	0.448806i	$0.851849\pi$
$968$	−7.14297	−0.229584
$969$	3.35546	0.107793
$970$	−37.1036	−1.19133
$971$	40.8063	1.30954	0.654768	−	0.755830i	$-0.272766\pi$
$971$	40.8063	1.30954	0.654768	+	0.755830i	$0.272766\pi$
$972$	1.00000	0.0320750
$973$	−8.88587	−0.284868
$974$	39.3643	1.26131
$975$	4.83566	0.154865
$976$	7.14741	0.228783
$977$	−4.19464	−0.134198	−0.0670992	−	0.997746i	$-0.521374\pi$
$977$	−4.19464	−0.134198	−0.0670992	+	0.997746i	$0.521374\pi$
$978$	−8.28105	−0.264799
$979$	−22.1826	−0.708958
$980$	−4.96784	−0.158692
$981$	6.66344	0.212747
$982$	−15.2726	−0.487368
$983$	−33.5663	−1.07060	−0.535299	−	0.844663i	$-0.679801\pi$
$983$	−33.5663	−1.07060	−0.535299	+	0.844663i	$0.679801\pi$
$984$	1.03487	0.0329904
$985$	27.3088	0.870130
$986$	7.78398	0.247892
$987$	−12.9952	−0.413641
$988$	2.05017	0.0652246
$989$	95.2664	3.02930
$990$	−7.05770	−0.224309
$991$	−34.3695	−1.09178	−0.545891	−	0.837856i	$-0.683809\pi$
$991$	−34.3695	−1.09178	−0.545891	+	0.837856i	$0.683809\pi$
$992$	2.58625	0.0821134
$993$	10.8136	0.343160
$994$	−4.75706	−0.150885
$995$	−73.1980	−2.32053
$996$	2.20728	0.0699403
$997$	−42.3738	−1.34199	−0.670996	−	0.741461i	$-0.734133\pi$
$997$	−42.3738	−1.34199	−0.670996	+	0.741461i	$0.734133\pi$
$998$	−2.03144	−0.0643040
$999$	−2.69086	−0.0851350

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.bb.1.12	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.bb.1.12	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.59366 q^{5} +1.00000 q^{6} +2.37015 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.59366 q^{5} +1.00000 q^{6} +2.37015 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.59366 q^{10} -1.96393 q^{11} +1.00000 q^{12} +0.610996 q^{13} +2.37015 q^{14} +3.59366 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +3.35546 q^{19} +3.59366 q^{20} +2.37015 q^{21} -1.96393 q^{22} -8.11010 q^{23} +1.00000 q^{24} +7.91440 q^{25} +0.610996 q^{26} +1.00000 q^{27} +2.37015 q^{28} +7.78398 q^{29} +3.59366 q^{30} +2.58625 q^{31} +1.00000 q^{32} -1.96393 q^{33} +1.00000 q^{34} +8.51751 q^{35} +1.00000 q^{36} -2.69086 q^{37} +3.35546 q^{38} +0.610996 q^{39} +3.59366 q^{40} +1.03487 q^{41} +2.37015 q^{42} -11.7466 q^{43} -1.96393 q^{44} +3.59366 q^{45} -8.11010 q^{46} -5.48284 q^{47} +1.00000 q^{48} -1.38239 q^{49} +7.91440 q^{50} +1.00000 q^{51} +0.610996 q^{52} +6.28345 q^{53} +1.00000 q^{54} -7.05770 q^{55} +2.37015 q^{56} +3.35546 q^{57} +7.78398 q^{58} -1.00000 q^{59} +3.59366 q^{60} +7.14741 q^{61} +2.58625 q^{62} +2.37015 q^{63} +1.00000 q^{64} +2.19571 q^{65} -1.96393 q^{66} +0.765914 q^{67} +1.00000 q^{68} -8.11010 q^{69} +8.51751 q^{70} -2.00707 q^{71} +1.00000 q^{72} -3.25099 q^{73} -2.69086 q^{74} +7.91440 q^{75} +3.35546 q^{76} -4.65481 q^{77} +0.610996 q^{78} -11.0065 q^{79} +3.59366 q^{80} +1.00000 q^{81} +1.03487 q^{82} +2.20728 q^{83} +2.37015 q^{84} +3.59366 q^{85} -11.7466 q^{86} +7.78398 q^{87} -1.96393 q^{88} +11.2950 q^{89} +3.59366 q^{90} +1.44815 q^{91} -8.11010 q^{92} +2.58625 q^{93} -5.48284 q^{94} +12.0584 q^{95} +1.00000 q^{96} -10.3247 q^{97} -1.38239 q^{98} -1.96393 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) \) 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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