LMFDB - Embedded newform 6018.2.a.bb.1.4

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			1.4
Root			$-2.08866$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.08866 q^{5} +1.00000 q^{6} +3.96496 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.08866 q^{5} +1.00000 q^{6} +3.96496 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.08866 q^{10} +6.58247 q^{11} +1.00000 q^{12} +3.63743 q^{13} +3.96496 q^{14} -2.08866 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -2.36767 q^{19} -2.08866 q^{20} +3.96496 q^{21} +6.58247 q^{22} -3.85694 q^{23} +1.00000 q^{24} -0.637500 q^{25} +3.63743 q^{26} +1.00000 q^{27} +3.96496 q^{28} +8.69548 q^{29} -2.08866 q^{30} -2.28675 q^{31} +1.00000 q^{32} +6.58247 q^{33} +1.00000 q^{34} -8.28145 q^{35} +1.00000 q^{36} +9.90184 q^{37} -2.36767 q^{38} +3.63743 q^{39} -2.08866 q^{40} +5.04037 q^{41} +3.96496 q^{42} -9.71028 q^{43} +6.58247 q^{44} -2.08866 q^{45} -3.85694 q^{46} -11.7270 q^{47} +1.00000 q^{48} +8.72089 q^{49} -0.637500 q^{50} +1.00000 q^{51} +3.63743 q^{52} +6.23654 q^{53} +1.00000 q^{54} -13.7485 q^{55} +3.96496 q^{56} -2.36767 q^{57} +8.69548 q^{58} -1.00000 q^{59} -2.08866 q^{60} -9.54334 q^{61} -2.28675 q^{62} +3.96496 q^{63} +1.00000 q^{64} -7.59735 q^{65} +6.58247 q^{66} -14.5150 q^{67} +1.00000 q^{68} -3.85694 q^{69} -8.28145 q^{70} +1.74136 q^{71} +1.00000 q^{72} +2.18844 q^{73} +9.90184 q^{74} -0.637500 q^{75} -2.36767 q^{76} +26.0992 q^{77} +3.63743 q^{78} +1.65549 q^{79} -2.08866 q^{80} +1.00000 q^{81} +5.04037 q^{82} -11.2547 q^{83} +3.96496 q^{84} -2.08866 q^{85} -9.71028 q^{86} +8.69548 q^{87} +6.58247 q^{88} +2.37136 q^{89} -2.08866 q^{90} +14.4222 q^{91} -3.85694 q^{92} -2.28675 q^{93} -11.7270 q^{94} +4.94525 q^{95} +1.00000 q^{96} +7.54044 q^{97} +8.72089 q^{98} +6.58247 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−2.08866	−0.934077	−0.467039	−	0.884237i	$-0.654679\pi$
$5$	−2.08866	−0.934077	−0.467039	+	0.884237i	$0.654679\pi$
$6$	1.00000	0.408248
$7$	3.96496	1.49861	0.749306	−	0.662223i	$-0.230387\pi$
$7$	3.96496	1.49861	0.749306	+	0.662223i	$0.230387\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.08866	−0.660492
$11$	6.58247	1.98469	0.992344	−	0.123501i	$-0.0394123\pi$
$11$	6.58247	1.98469	0.992344	+	0.123501i	$0.0394123\pi$
$12$	1.00000	0.288675
$13$	3.63743	1.00884	0.504421	−	0.863458i	$-0.331706\pi$
$13$	3.63743	1.00884	0.504421	+	0.863458i	$0.331706\pi$
$14$	3.96496	1.05968
$15$	−2.08866	−0.539290
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	−2.36767	−0.543180	−0.271590	−	0.962413i	$-0.587550\pi$
$19$	−2.36767	−0.543180	−0.271590	+	0.962413i	$0.587550\pi$
$20$	−2.08866	−0.467039
$21$	3.96496	0.865225
$22$	6.58247	1.40339
$23$	−3.85694	−0.804228	−0.402114	−	0.915590i	$-0.631724\pi$
$23$	−3.85694	−0.804228	−0.402114	+	0.915590i	$0.631724\pi$
$24$	1.00000	0.204124
$25$	−0.637500	−0.127500
$26$	3.63743	0.713358
$27$	1.00000	0.192450
$28$	3.96496	0.749306
$29$	8.69548	1.61471	0.807355	−	0.590067i	$-0.200899\pi$
$29$	8.69548	1.61471	0.807355	+	0.590067i	$0.200899\pi$
$30$	−2.08866	−0.381335
$31$	−2.28675	−0.410713	−0.205356	−	0.978687i	$-0.565835\pi$
$31$	−2.28675	−0.410713	−0.205356	+	0.978687i	$0.565835\pi$
$32$	1.00000	0.176777
$33$	6.58247	1.14586
$34$	1.00000	0.171499
$35$	−8.28145	−1.39982
$36$	1.00000	0.166667
$37$	9.90184	1.62785	0.813926	−	0.580968i	$-0.197326\pi$
$37$	9.90184	1.62785	0.813926	+	0.580968i	$0.197326\pi$
$38$	−2.36767	−0.384087
$39$	3.63743	0.582455
$40$	−2.08866	−0.330246
$41$	5.04037	0.787173	0.393586	−	0.919288i	$-0.371234\pi$
$41$	5.04037	0.787173	0.393586	+	0.919288i	$0.371234\pi$
$42$	3.96496	0.611806
$43$	−9.71028	−1.48080	−0.740402	−	0.672164i	$-0.765365\pi$
$43$	−9.71028	−1.48080	−0.740402	+	0.672164i	$0.765365\pi$
$44$	6.58247	0.992344
$45$	−2.08866	−0.311359
$46$	−3.85694	−0.568675
$47$	−11.7270	−1.71056	−0.855279	−	0.518168i	$-0.826614\pi$
$47$	−11.7270	−1.71056	−0.855279	+	0.518168i	$0.826614\pi$
$48$	1.00000	0.144338
$49$	8.72089	1.24584
$50$	−0.637500	−0.0901561
$51$	1.00000	0.140028
$52$	3.63743	0.504421
$53$	6.23654	0.856655	0.428328	−	0.903624i	$-0.359103\pi$
$53$	6.23654	0.856655	0.428328	+	0.903624i	$0.359103\pi$
$54$	1.00000	0.136083
$55$	−13.7485	−1.85385
$56$	3.96496	0.529840
$57$	−2.36767	−0.313605
$58$	8.69548	1.14177
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−2.08866	−0.269645
$61$	−9.54334	−1.22190	−0.610950	−	0.791669i	$-0.709212\pi$
$61$	−9.54334	−1.22190	−0.610950	+	0.791669i	$0.709212\pi$
$62$	−2.28675	−0.290418
$63$	3.96496	0.499538
$64$	1.00000	0.125000
$65$	−7.59735	−0.942335
$66$	6.58247	0.810246
$67$	−14.5150	−1.77329	−0.886647	−	0.462448i	$-0.846971\pi$
$67$	−14.5150	−1.77329	−0.886647	+	0.462448i	$0.846971\pi$
$68$	1.00000	0.121268
$69$	−3.85694	−0.464321
$70$	−8.28145	−0.989822
$71$	1.74136	0.206661	0.103331	−	0.994647i	$-0.467050\pi$
$71$	1.74136	0.206661	0.103331	+	0.994647i	$0.467050\pi$
$72$	1.00000	0.117851
$73$	2.18844	0.256137	0.128069	−	0.991765i	$-0.459122\pi$
$73$	2.18844	0.256137	0.128069	+	0.991765i	$0.459122\pi$
$74$	9.90184	1.15107
$75$	−0.637500	−0.0736122
$76$	−2.36767	−0.271590
$77$	26.0992	2.97428
$78$	3.63743	0.411858
$79$	1.65549	0.186257	0.0931286	−	0.995654i	$-0.470313\pi$
$79$	1.65549	0.186257	0.0931286	+	0.995654i	$0.470313\pi$
$80$	−2.08866	−0.233519
$81$	1.00000	0.111111
$82$	5.04037	0.556615
$83$	−11.2547	−1.23537	−0.617685	−	0.786426i	$-0.711929\pi$
$83$	−11.2547	−1.23537	−0.617685	+	0.786426i	$0.711929\pi$
$84$	3.96496	0.432612
$85$	−2.08866	−0.226547
$86$	−9.71028	−1.04709
$87$	8.69548	0.932253
$88$	6.58247	0.701693
$89$	2.37136	0.251364	0.125682	−	0.992071i	$-0.459888\pi$
$89$	2.37136	0.251364	0.125682	+	0.992071i	$0.459888\pi$
$90$	−2.08866	−0.220164
$91$	14.4222	1.51186
$92$	−3.85694	−0.402114
$93$	−2.28675	−0.237125
$94$	−11.7270	−1.20955
$95$	4.94525	0.507372
$96$	1.00000	0.102062
$97$	7.54044	0.765616	0.382808	−	0.923828i	$-0.374957\pi$
$97$	7.54044	0.765616	0.382808	+	0.923828i	$0.374957\pi$
$98$	8.72089	0.880943
$99$	6.58247	0.661563
$100$	−0.637500	−0.0637500
$101$	10.7445	1.06912	0.534561	−	0.845130i	$-0.320477\pi$
$101$	10.7445	1.06912	0.534561	+	0.845130i	$0.320477\pi$
$102$	1.00000	0.0990148
$103$	−10.0499	−0.990249	−0.495124	−	0.868822i	$-0.664877\pi$
$103$	−10.0499	−0.990249	−0.495124	+	0.868822i	$0.664877\pi$
$104$	3.63743	0.356679
$105$	−8.28145	−0.808186
$106$	6.23654	0.605747
$107$	−7.47882	−0.723005	−0.361502	−	0.932371i	$-0.617736\pi$
$107$	−7.47882	−0.723005	−0.361502	+	0.932371i	$0.617736\pi$
$108$	1.00000	0.0962250
$109$	−13.7953	−1.32135	−0.660677	−	0.750671i	$-0.729731\pi$
$109$	−13.7953	−1.32135	−0.660677	+	0.750671i	$0.729731\pi$
$110$	−13.7485	−1.31087
$111$	9.90184	0.939841
$112$	3.96496	0.374653
$113$	−8.30037	−0.780833	−0.390417	−	0.920638i	$-0.627669\pi$
$113$	−8.30037	−0.780833	−0.390417	+	0.920638i	$0.627669\pi$
$114$	−2.36767	−0.221752
$115$	8.05583	0.751210
$116$	8.69548	0.807355
$117$	3.63743	0.336280
$118$	−1.00000	−0.0920575
$119$	3.96496	0.363467
$120$	−2.08866	−0.190668
$121$	32.3289	2.93899
$122$	−9.54334	−0.864013
$123$	5.04037	0.454474
$124$	−2.28675	−0.205356
$125$	11.7748	1.05317
$126$	3.96496	0.353226
$127$	5.42968	0.481806	0.240903	−	0.970549i	$-0.422556\pi$
$127$	5.42968	0.481806	0.240903	+	0.970549i	$0.422556\pi$
$128$	1.00000	0.0883883
$129$	−9.71028	−0.854943
$130$	−7.59735	−0.666332
$131$	−13.6410	−1.19182	−0.595911	−	0.803050i	$-0.703209\pi$
$131$	−13.6410	−1.19182	−0.595911	+	0.803050i	$0.703209\pi$
$132$	6.58247	0.572930
$133$	−9.38771	−0.814017
$134$	−14.5150	−1.25391
$135$	−2.08866	−0.179763
$136$	1.00000	0.0857493
$137$	−1.65034	−0.140998	−0.0704991	−	0.997512i	$-0.522459\pi$
$137$	−1.65034	−0.140998	−0.0704991	+	0.997512i	$0.522459\pi$
$138$	−3.85694	−0.328325
$139$	−5.89000	−0.499583	−0.249792	−	0.968300i	$-0.580362\pi$
$139$	−5.89000	−0.499583	−0.249792	+	0.968300i	$0.580362\pi$
$140$	−8.28145	−0.699910
$141$	−11.7270	−0.987591
$142$	1.74136	0.146132
$143$	23.9433	2.00224
$144$	1.00000	0.0833333
$145$	−18.1619	−1.50826
$146$	2.18844	0.181116
$147$	8.72089	0.719287
$148$	9.90184	0.813926
$149$	−20.7561	−1.70041	−0.850203	−	0.526454i	$-0.823521\pi$
$149$	−20.7561	−1.70041	−0.850203	+	0.526454i	$0.823521\pi$
$150$	−0.637500	−0.0520517
$151$	−11.7153	−0.953378	−0.476689	−	0.879072i	$-0.658163\pi$
$151$	−11.7153	−0.953378	−0.476689	+	0.879072i	$0.658163\pi$
$152$	−2.36767	−0.192043
$153$	1.00000	0.0808452
$154$	26.0992	2.10313
$155$	4.77625	0.383637
$156$	3.63743	0.291227
$157$	−3.51497	−0.280525	−0.140263	−	0.990114i	$-0.544795\pi$
$157$	−3.51497	−0.280525	−0.140263	+	0.990114i	$0.544795\pi$
$158$	1.65549	0.131704
$159$	6.23654	0.494590
$160$	−2.08866	−0.165123
$161$	−15.2926	−1.20523
$162$	1.00000	0.0785674
$163$	8.73156	0.683908	0.341954	−	0.939717i	$-0.388911\pi$
$163$	8.73156	0.683908	0.341954	+	0.939717i	$0.388911\pi$
$164$	5.04037	0.393586
$165$	−13.7485	−1.07032
$166$	−11.2547	−0.873538
$167$	18.1979	1.40820	0.704098	−	0.710102i	$-0.251351\pi$
$167$	18.1979	1.40820	0.704098	+	0.710102i	$0.251351\pi$
$168$	3.96496	0.305903
$169$	0.230886	0.0177604
$170$	−2.08866	−0.160193
$171$	−2.36767	−0.181060
$172$	−9.71028	−0.740402
$173$	16.5164	1.25572	0.627861	−	0.778325i	$-0.283931\pi$
$173$	16.5164	1.25572	0.627861	+	0.778325i	$0.283931\pi$
$174$	8.69548	0.659202
$175$	−2.52766	−0.191073
$176$	6.58247	0.496172
$177$	−1.00000	−0.0751646
$178$	2.37136	0.177741
$179$	1.70980	0.127797	0.0638984	−	0.997956i	$-0.479647\pi$
$179$	1.70980	0.127797	0.0638984	+	0.997956i	$0.479647\pi$
$180$	−2.08866	−0.155680
$181$	−17.6980	−1.31548	−0.657741	−	0.753244i	$-0.728488\pi$
$181$	−17.6980	−1.31548	−0.657741	+	0.753244i	$0.728488\pi$
$182$	14.4222	1.06905
$183$	−9.54334	−0.705464
$184$	−3.85694	−0.284337
$185$	−20.6816	−1.52054
$186$	−2.28675	−0.167673
$187$	6.58247	0.481358
$188$	−11.7270	−0.855279
$189$	3.96496	0.288408
$190$	4.94525	0.358766
$191$	−2.63395	−0.190586	−0.0952929	−	0.995449i	$-0.530379\pi$
$191$	−2.63395	−0.190586	−0.0952929	+	0.995449i	$0.530379\pi$
$192$	1.00000	0.0721688
$193$	20.9023	1.50458	0.752291	−	0.658831i	$-0.228949\pi$
$193$	20.9023	1.50458	0.752291	+	0.658831i	$0.228949\pi$
$194$	7.54044	0.541372
$195$	−7.59735	−0.544058
$196$	8.72089	0.622920
$197$	14.6153	1.04130	0.520650	−	0.853770i	$-0.325690\pi$
$197$	14.6153	1.04130	0.520650	+	0.853770i	$0.325690\pi$
$198$	6.58247	0.467796
$199$	13.5116	0.957812	0.478906	−	0.877866i	$-0.341033\pi$
$199$	13.5116	0.957812	0.478906	+	0.877866i	$0.341033\pi$
$200$	−0.637500	−0.0450781
$201$	−14.5150	−1.02381
$202$	10.7445	0.755983
$203$	34.4772	2.41982
$204$	1.00000	0.0700140
$205$	−10.5276	−0.735280
$206$	−10.0499	−0.700211
$207$	−3.85694	−0.268076
$208$	3.63743	0.252210
$209$	−15.5851	−1.07804
$210$	−8.28145	−0.571474
$211$	−11.0332	−0.759557	−0.379778	−	0.925077i	$-0.624000\pi$
$211$	−11.0332	−0.759557	−0.379778	+	0.925077i	$0.624000\pi$
$212$	6.23654	0.428328
$213$	1.74136	0.119316
$214$	−7.47882	−0.511242
$215$	20.2815	1.38319
$216$	1.00000	0.0680414
$217$	−9.06687	−0.615499
$218$	−13.7953	−0.934338
$219$	2.18844	0.147881
$220$	−13.7485	−0.926926
$221$	3.63743	0.244680
$222$	9.90184	0.664568
$223$	−20.8730	−1.39776	−0.698880	−	0.715239i	$-0.746318\pi$
$223$	−20.8730	−1.39776	−0.698880	+	0.715239i	$0.746318\pi$
$224$	3.96496	0.264920
$225$	−0.637500	−0.0425000
$226$	−8.30037	−0.552132
$227$	10.1609	0.674404	0.337202	−	0.941432i	$-0.390519\pi$
$227$	10.1609	0.674404	0.337202	+	0.941432i	$0.390519\pi$
$228$	−2.36767	−0.156803
$229$	−4.35727	−0.287937	−0.143968	−	0.989582i	$-0.545986\pi$
$229$	−4.35727	−0.287937	−0.143968	+	0.989582i	$0.545986\pi$
$230$	8.05583	0.531186
$231$	26.0992	1.71720
$232$	8.69548	0.570886
$233$	23.4601	1.53693	0.768463	−	0.639895i	$-0.221022\pi$
$233$	23.4601	1.53693	0.768463	+	0.639895i	$0.221022\pi$
$234$	3.63743	0.237786
$235$	24.4937	1.59779
$236$	−1.00000	−0.0650945
$237$	1.65549	0.107536
$238$	3.96496	0.257010
$239$	−1.84306	−0.119218	−0.0596090	−	0.998222i	$-0.518985\pi$
$239$	−1.84306	−0.119218	−0.0596090	+	0.998222i	$0.518985\pi$
$240$	−2.08866	−0.134822
$241$	8.18866	0.527478	0.263739	−	0.964594i	$-0.415044\pi$
$241$	8.18866	0.527478	0.263739	+	0.964594i	$0.415044\pi$
$242$	32.3289	2.07818
$243$	1.00000	0.0641500
$244$	−9.54334	−0.610950
$245$	−18.2150	−1.16371
$246$	5.04037	0.321362
$247$	−8.61223	−0.547983
$248$	−2.28675	−0.145209
$249$	−11.2547	−0.713241
$250$	11.7748	0.744705
$251$	11.8802	0.749870	0.374935	−	0.927051i	$-0.377665\pi$
$251$	11.8802	0.749870	0.374935	+	0.927051i	$0.377665\pi$
$252$	3.96496	0.249769
$253$	−25.3882	−1.59614
$254$	5.42968	0.340688
$255$	−2.08866	−0.130797
$256$	1.00000	0.0625000
$257$	1.26624	0.0789858	0.0394929	−	0.999220i	$-0.487426\pi$
$257$	1.26624	0.0789858	0.0394929	+	0.999220i	$0.487426\pi$
$258$	−9.71028	−0.604536
$259$	39.2604	2.43952
$260$	−7.59735	−0.471168
$261$	8.69548	0.538236
$262$	−13.6410	−0.842746
$263$	7.77336	0.479326	0.239663	−	0.970856i	$-0.422963\pi$
$263$	7.77336	0.479326	0.239663	+	0.970856i	$0.422963\pi$
$264$	6.58247	0.405123
$265$	−13.0260	−0.800182
$266$	−9.38771	−0.575597
$267$	2.37136	0.145125
$268$	−14.5150	−0.886647
$269$	−0.662713	−0.0404063	−0.0202032	−	0.999796i	$-0.506431\pi$
$269$	−0.662713	−0.0404063	−0.0202032	+	0.999796i	$0.506431\pi$
$270$	−2.08866	−0.127112
$271$	20.9492	1.27257	0.636285	−	0.771454i	$-0.280470\pi$
$271$	20.9492	1.27257	0.636285	+	0.771454i	$0.280470\pi$
$272$	1.00000	0.0606339
$273$	14.4222	0.872874
$274$	−1.65034	−0.0997008
$275$	−4.19632	−0.253048
$276$	−3.85694	−0.232160
$277$	14.6998	0.883227	0.441614	−	0.897205i	$-0.354406\pi$
$277$	14.6998	0.883227	0.441614	+	0.897205i	$0.354406\pi$
$278$	−5.89000	−0.353259
$279$	−2.28675	−0.136904
$280$	−8.28145	−0.494911
$281$	31.3314	1.86907	0.934536	−	0.355867i	$-0.115815\pi$
$281$	31.3314	1.86907	0.934536	+	0.355867i	$0.115815\pi$
$282$	−11.7270	−0.698332
$283$	−25.0529	−1.48924	−0.744619	−	0.667490i	$-0.767369\pi$
$283$	−25.0529	−1.48924	−0.744619	+	0.667490i	$0.767369\pi$
$284$	1.74136	0.103331
$285$	4.94525	0.292932
$286$	23.9433	1.41579
$287$	19.9848	1.17967
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−18.1619	−1.06650
$291$	7.54044	0.442029
$292$	2.18844	0.128069
$293$	28.7940	1.68216	0.841081	−	0.540909i	$-0.181920\pi$
$293$	28.7940	1.68216	0.841081	+	0.540909i	$0.181920\pi$
$294$	8.72089	0.508612
$295$	2.08866	0.121606
$296$	9.90184	0.575533
$297$	6.58247	0.381954
$298$	−20.7561	−1.20237
$299$	−14.0293	−0.811338
$300$	−0.637500	−0.0368061
$301$	−38.5009	−2.21915
$302$	−11.7153	−0.674140
$303$	10.7445	0.617258
$304$	−2.36767	−0.135795
$305$	19.9328	1.14135
$306$	1.00000	0.0571662
$307$	−33.6415	−1.92002	−0.960011	−	0.279961i	$-0.909679\pi$
$307$	−33.6415	−1.92002	−0.960011	+	0.279961i	$0.909679\pi$
$308$	26.0992	1.48714
$309$	−10.0499	−0.571720
$310$	4.77625	0.271272
$311$	−4.26050	−0.241591	−0.120795	−	0.992677i	$-0.538544\pi$
$311$	−4.26050	−0.241591	−0.120795	+	0.992677i	$0.538544\pi$
$312$	3.63743	0.205929
$313$	−13.3243	−0.753137	−0.376568	−	0.926389i	$-0.622896\pi$
$313$	−13.3243	−0.753137	−0.376568	+	0.926389i	$0.622896\pi$
$314$	−3.51497	−0.198361
$315$	−8.28145	−0.466607
$316$	1.65549	0.0931286
$317$	13.0836	0.734847	0.367424	−	0.930054i	$-0.380240\pi$
$317$	13.0836	0.734847	0.367424	+	0.930054i	$0.380240\pi$
$318$	6.23654	0.349728
$319$	57.2377	3.20470
$320$	−2.08866	−0.116760
$321$	−7.47882	−0.417427
$322$	−15.2926	−0.852223
$323$	−2.36767	−0.131741
$324$	1.00000	0.0555556
$325$	−2.31886	−0.128627
$326$	8.73156	0.483596
$327$	−13.7953	−0.762884
$328$	5.04037	0.278308
$329$	−46.4970	−2.56346
$330$	−13.7485	−0.756832
$331$	27.6529	1.51994	0.759971	−	0.649957i	$-0.225213\pi$
$331$	27.6529	1.51994	0.759971	+	0.649957i	$0.225213\pi$
$332$	−11.2547	−0.617685
$333$	9.90184	0.542618
$334$	18.1979	0.995746
$335$	30.3170	1.65639
$336$	3.96496	0.216306
$337$	15.5189	0.845368	0.422684	−	0.906277i	$-0.361088\pi$
$337$	15.5189	0.845368	0.422684	+	0.906277i	$0.361088\pi$
$338$	0.230886	0.0125585
$339$	−8.30037	−0.450814
$340$	−2.08866	−0.113273
$341$	−15.0525	−0.815137
$342$	−2.36767	−0.128029
$343$	6.82324	0.368420
$344$	−9.71028	−0.523543
$345$	8.05583	0.433712
$346$	16.5164	0.887930
$347$	23.2549	1.24839	0.624194	−	0.781270i	$-0.285428\pi$
$347$	23.2549	1.24839	0.624194	+	0.781270i	$0.285428\pi$
$348$	8.69548	0.466126
$349$	2.50256	0.133959	0.0669795	−	0.997754i	$-0.478664\pi$
$349$	2.50256	0.133959	0.0669795	+	0.997754i	$0.478664\pi$
$350$	−2.52766	−0.135109
$351$	3.63743	0.194152
$352$	6.58247	0.350847
$353$	8.11418	0.431874	0.215937	−	0.976407i	$-0.430719\pi$
$353$	8.11418	0.431874	0.215937	+	0.976407i	$0.430719\pi$
$354$	−1.00000	−0.0531494
$355$	−3.63711	−0.193038
$356$	2.37136	0.125682
$357$	3.96496	0.209848
$358$	1.70980	0.0903660
$359$	−25.9815	−1.37125	−0.685626	−	0.727954i	$-0.740472\pi$
$359$	−25.9815	−1.37125	−0.685626	+	0.727954i	$0.740472\pi$
$360$	−2.08866	−0.110082
$361$	−13.3941	−0.704955
$362$	−17.6980	−0.930186
$363$	32.3289	1.69683
$364$	14.4222	0.755931
$365$	−4.57090	−0.239252
$366$	−9.54334	−0.498838
$367$	8.05528	0.420482	0.210241	−	0.977650i	$-0.432575\pi$
$367$	8.05528	0.420482	0.210241	+	0.977650i	$0.432575\pi$
$368$	−3.85694	−0.201057
$369$	5.04037	0.262391
$370$	−20.6816	−1.07518
$371$	24.7276	1.28379
$372$	−2.28675	−0.118563
$373$	14.5314	0.752410	0.376205	−	0.926537i	$-0.377229\pi$
$373$	14.5314	0.752410	0.376205	+	0.926537i	$0.377229\pi$
$374$	6.58247	0.340371
$375$	11.7748	0.608049
$376$	−11.7270	−0.604774
$377$	31.6292	1.62899
$378$	3.96496	0.203935
$379$	18.1085	0.930174	0.465087	−	0.885265i	$-0.346023\pi$
$379$	18.1085	0.930174	0.465087	+	0.885265i	$0.346023\pi$
$380$	4.94525	0.253686
$381$	5.42968	0.278171
$382$	−2.63395	−0.134764
$383$	−14.6743	−0.749820	−0.374910	−	0.927061i	$-0.622326\pi$
$383$	−14.6743	−0.749820	−0.374910	+	0.927061i	$0.622326\pi$
$384$	1.00000	0.0510310
$385$	−54.5124	−2.77821
$386$	20.9023	1.06390
$387$	−9.71028	−0.493601
$388$	7.54044	0.382808
$389$	−23.0893	−1.17068	−0.585338	−	0.810790i	$-0.699038\pi$
$389$	−23.0893	−1.17068	−0.585338	+	0.810790i	$0.699038\pi$
$390$	−7.59735	−0.384707
$391$	−3.85694	−0.195054
$392$	8.72089	0.440471
$393$	−13.6410	−0.688099
$394$	14.6153	0.736310
$395$	−3.45776	−0.173979
$396$	6.58247	0.330781
$397$	−34.6863	−1.74086	−0.870428	−	0.492295i	$-0.836158\pi$
$397$	−34.6863	−1.74086	−0.870428	+	0.492295i	$0.836158\pi$
$398$	13.5116	0.677275
$399$	−9.38771	−0.469973
$400$	−0.637500	−0.0318750
$401$	−1.04303	−0.0520864	−0.0260432	−	0.999661i	$-0.508291\pi$
$401$	−1.04303	−0.0520864	−0.0260432	+	0.999661i	$0.508291\pi$
$402$	−14.5150	−0.723944
$403$	−8.31789	−0.414344
$404$	10.7445	0.534561
$405$	−2.08866	−0.103786
$406$	34.4772	1.71107
$407$	65.1786	3.23078
$408$	1.00000	0.0495074
$409$	3.49622	0.172877	0.0864385	−	0.996257i	$-0.472451\pi$
$409$	3.49622	0.172877	0.0864385	+	0.996257i	$0.472451\pi$
$410$	−10.5276	−0.519922
$411$	−1.65034	−0.0814054
$412$	−10.0499	−0.495124
$413$	−3.96496	−0.195103
$414$	−3.85694	−0.189558
$415$	23.5073	1.15393
$416$	3.63743	0.178340
$417$	−5.89000	−0.288434
$418$	−15.5851	−0.762292
$419$	−4.72428	−0.230796	−0.115398	−	0.993319i	$-0.536814\pi$
$419$	−4.72428	−0.230796	−0.115398	+	0.993319i	$0.536814\pi$
$420$	−8.28145	−0.404093
$421$	−24.0205	−1.17069	−0.585343	−	0.810786i	$-0.699040\pi$
$421$	−24.0205	−1.17069	−0.585343	+	0.810786i	$0.699040\pi$
$422$	−11.0332	−0.537088
$423$	−11.7270	−0.570186
$424$	6.23654	0.302873
$425$	−0.637500	−0.0309233
$426$	1.74136	0.0843691
$427$	−37.8389	−1.83115
$428$	−7.47882	−0.361502
$429$	23.9433	1.15599
$430$	20.2815	0.978060
$431$	−3.31095	−0.159483	−0.0797414	−	0.996816i	$-0.525409\pi$
$431$	−3.31095	−0.159483	−0.0797414	+	0.996816i	$0.525409\pi$
$432$	1.00000	0.0481125
$433$	−29.1923	−1.40289	−0.701446	−	0.712722i	$-0.747462\pi$
$433$	−29.1923	−1.40289	−0.701446	+	0.712722i	$0.747462\pi$
$434$	−9.06687	−0.435224
$435$	−18.1619	−0.870796
$436$	−13.7953	−0.660677
$437$	9.13196	0.436841
$438$	2.18844	0.104568
$439$	−39.7496	−1.89715	−0.948573	−	0.316558i	$-0.897473\pi$
$439$	−39.7496	−1.89715	−0.948573	+	0.316558i	$0.897473\pi$
$440$	−13.7485	−0.655436
$441$	8.72089	0.415280
$442$	3.63743	0.173015
$443$	−16.3089	−0.774860	−0.387430	−	0.921899i	$-0.626637\pi$
$443$	−16.3089	−0.774860	−0.387430	+	0.921899i	$0.626637\pi$
$444$	9.90184	0.469921
$445$	−4.95296	−0.234793
$446$	−20.8730	−0.988365
$447$	−20.7561	−0.981730
$448$	3.96496	0.187327
$449$	1.17772	0.0555802	0.0277901	−	0.999614i	$-0.491153\pi$
$449$	1.17772	0.0555802	0.0277901	+	0.999614i	$0.491153\pi$
$450$	−0.637500	−0.0300520
$451$	33.1780	1.56229
$452$	−8.30037	−0.390417
$453$	−11.7153	−0.550433
$454$	10.1609	0.476876
$455$	−30.1232	−1.41220
$456$	−2.36767	−0.110876
$457$	29.3480	1.37284	0.686422	−	0.727204i	$-0.259180\pi$
$457$	29.3480	1.37284	0.686422	+	0.727204i	$0.259180\pi$
$458$	−4.35727	−0.203602
$459$	1.00000	0.0466760
$460$	8.05583	0.375605
$461$	−19.2748	−0.897718	−0.448859	−	0.893603i	$-0.648169\pi$
$461$	−19.2748	−0.897718	−0.448859	+	0.893603i	$0.648169\pi$
$462$	26.0992	1.21424
$463$	5.41608	0.251707	0.125853	−	0.992049i	$-0.459833\pi$
$463$	5.41608	0.251707	0.125853	+	0.992049i	$0.459833\pi$
$464$	8.69548	0.403677
$465$	4.77625	0.221493
$466$	23.4601	1.08677
$467$	1.34293	0.0621434	0.0310717	−	0.999517i	$-0.490108\pi$
$467$	1.34293	0.0621434	0.0310717	+	0.999517i	$0.490108\pi$
$468$	3.63743	0.168140
$469$	−57.5515	−2.65748
$470$	24.4937	1.12981
$471$	−3.51497	−0.161961
$472$	−1.00000	−0.0460287
$473$	−63.9176	−2.93894
$474$	1.65549	0.0760392
$475$	1.50939	0.0692555
$476$	3.96496	0.181734
$477$	6.23654	0.285552
$478$	−1.84306	−0.0842998
$479$	−33.3654	−1.52450	−0.762251	−	0.647282i	$-0.775906\pi$
$479$	−33.3654	−1.52450	−0.762251	+	0.647282i	$0.775906\pi$
$480$	−2.08866	−0.0953338
$481$	36.0172	1.64224
$482$	8.18866	0.372983
$483$	−15.2926	−0.695837
$484$	32.3289	1.46949
$485$	−15.7494	−0.715144
$486$	1.00000	0.0453609
$487$	−38.8593	−1.76088	−0.880441	−	0.474156i	$-0.842753\pi$
$487$	−38.8593	−1.76088	−0.880441	+	0.474156i	$0.842753\pi$
$488$	−9.54334	−0.432007
$489$	8.73156	0.394855
$490$	−18.2150	−0.822868
$491$	6.25710	0.282379	0.141189	−	0.989983i	$-0.454907\pi$
$491$	6.25710	0.282379	0.141189	+	0.989983i	$0.454907\pi$
$492$	5.04037	0.227237
$493$	8.69548	0.391625
$494$	−8.61223	−0.387482
$495$	−13.7485	−0.617951
$496$	−2.28675	−0.102678
$497$	6.90441	0.309705
$498$	−11.2547	−0.504337
$499$	4.09475	0.183306	0.0916531	−	0.995791i	$-0.470785\pi$
$499$	4.09475	0.183306	0.0916531	+	0.995791i	$0.470785\pi$
$500$	11.7748	0.526586
$501$	18.1979	0.813023
$502$	11.8802	0.530238
$503$	−18.7293	−0.835097	−0.417549	−	0.908655i	$-0.637111\pi$
$503$	−18.7293	−0.835097	−0.417549	+	0.908655i	$0.637111\pi$
$504$	3.96496	0.176613
$505$	−22.4417	−0.998642
$506$	−25.3882	−1.12864
$507$	0.230886	0.0102540
$508$	5.42968	0.240903
$509$	41.2808	1.82974	0.914871	−	0.403747i	$-0.132292\pi$
$509$	41.2808	1.82974	0.914871	+	0.403747i	$0.132292\pi$
$510$	−2.08866	−0.0924874
$511$	8.67706	0.383851
$512$	1.00000	0.0441942
$513$	−2.36767	−0.104535
$514$	1.26624	0.0558514
$515$	20.9909	0.924969
$516$	−9.71028	−0.427471
$517$	−77.1926	−3.39493
$518$	39.2604	1.72500
$519$	16.5164	0.724992
$520$	−7.59735	−0.333166
$521$	2.74452	0.120239	0.0601197	−	0.998191i	$-0.480852\pi$
$521$	2.74452	0.120239	0.0601197	+	0.998191i	$0.480852\pi$
$522$	8.69548	0.380591
$523$	−2.87633	−0.125773	−0.0628866	−	0.998021i	$-0.520031\pi$
$523$	−2.87633	−0.125773	−0.0628866	+	0.998021i	$0.520031\pi$
$524$	−13.6410	−0.595911
$525$	−2.52766	−0.110316
$526$	7.77336	0.338935
$527$	−2.28675	−0.0996124
$528$	6.58247	0.286465
$529$	−8.12402	−0.353218
$530$	−13.0260	−0.565814
$531$	−1.00000	−0.0433963
$532$	−9.38771	−0.407009
$533$	18.3340	0.794132
$534$	2.37136	0.102619
$535$	15.6207	0.675342
$536$	−14.5150	−0.626954
$537$	1.70980	0.0737835
$538$	−0.662713	−0.0285716
$539$	57.4050	2.47261
$540$	−2.08866	−0.0898816
$541$	−29.3326	−1.26111	−0.630554	−	0.776145i	$-0.717172\pi$
$541$	−29.3326	−1.26111	−0.630554	+	0.776145i	$0.717172\pi$
$542$	20.9492	0.899843
$543$	−17.6980	−0.759494
$544$	1.00000	0.0428746
$545$	28.8138	1.23425
$546$	14.4222	0.617215
$547$	14.7753	0.631746	0.315873	−	0.948801i	$-0.397703\pi$
$547$	14.7753	0.631746	0.315873	+	0.948801i	$0.397703\pi$
$548$	−1.65034	−0.0704991
$549$	−9.54334	−0.407300
$550$	−4.19632	−0.178932
$551$	−20.5880	−0.877079
$552$	−3.85694	−0.164162
$553$	6.56395	0.279128
$554$	14.6998	0.624536
$555$	−20.6816	−0.877884
$556$	−5.89000	−0.249792
$557$	30.4274	1.28925	0.644625	−	0.764499i	$-0.277014\pi$
$557$	30.4274	1.28925	0.644625	+	0.764499i	$0.277014\pi$
$558$	−2.28675	−0.0968059
$559$	−35.3205	−1.49390
$560$	−8.28145	−0.349955
$561$	6.58247	0.277912
$562$	31.3314	1.32163
$563$	−38.5899	−1.62637	−0.813186	−	0.582004i	$-0.802269\pi$
$563$	−38.5899	−1.62637	−0.813186	+	0.582004i	$0.802269\pi$
$564$	−11.7270	−0.493796
$565$	17.3367	0.729358
$566$	−25.0529	−1.05305
$567$	3.96496	0.166513
$568$	1.74136	0.0730658
$569$	45.0616	1.88908	0.944541	−	0.328393i	$-0.106507\pi$
$569$	45.0616	1.88908	0.944541	+	0.328393i	$0.106507\pi$
$570$	4.94525	0.207134
$571$	−29.7124	−1.24343	−0.621713	−	0.783245i	$-0.713563\pi$
$571$	−29.7124	−1.24343	−0.621713	+	0.783245i	$0.713563\pi$
$572$	23.9433	1.00112
$573$	−2.63395	−0.110035
$574$	19.9848	0.834151
$575$	2.45880	0.102539
$576$	1.00000	0.0416667
$577$	13.3868	0.557298	0.278649	−	0.960393i	$-0.410113\pi$
$577$	13.3868	0.557298	0.278649	+	0.960393i	$0.410113\pi$
$578$	1.00000	0.0415945
$579$	20.9023	0.868671
$580$	−18.1619	−0.754131
$581$	−44.6246	−1.85134
$582$	7.54044	0.312561
$583$	41.0519	1.70019
$584$	2.18844	0.0905582
$585$	−7.59735	−0.314112
$586$	28.7940	1.18947
$587$	−28.5858	−1.17986	−0.589930	−	0.807454i	$-0.700845\pi$
$587$	−28.5858	−1.17986	−0.589930	+	0.807454i	$0.700845\pi$
$588$	8.72089	0.359643
$589$	5.41427	0.223091
$590$	2.08866	0.0859888
$591$	14.6153	0.601194
$592$	9.90184	0.406963
$593$	9.51578	0.390766	0.195383	−	0.980727i	$-0.437405\pi$
$593$	9.51578	0.390766	0.195383	+	0.980727i	$0.437405\pi$
$594$	6.58247	0.270082
$595$	−8.28145	−0.339506
$596$	−20.7561	−0.850203
$597$	13.5116	0.552993
$598$	−14.0293	−0.573702
$599$	−1.07210	−0.0438049	−0.0219025	−	0.999760i	$-0.506972\pi$
$599$	−1.07210	−0.0438049	−0.0219025	+	0.999760i	$0.506972\pi$
$600$	−0.637500	−0.0260258
$601$	−28.2469	−1.15222	−0.576108	−	0.817374i	$-0.695429\pi$
$601$	−28.2469	−1.15222	−0.576108	+	0.817374i	$0.695429\pi$
$602$	−38.5009	−1.56918
$603$	−14.5150	−0.591098
$604$	−11.7153	−0.476689
$605$	−67.5240	−2.74524
$606$	10.7445	0.436467
$607$	32.0193	1.29962	0.649811	−	0.760096i	$-0.274848\pi$
$607$	32.0193	1.29962	0.649811	+	0.760096i	$0.274848\pi$
$608$	−2.36767	−0.0960216
$609$	34.4772	1.39709
$610$	19.9328	0.807055
$611$	−42.6561	−1.72568
$612$	1.00000	0.0404226
$613$	−35.6564	−1.44015	−0.720075	−	0.693897i	$-0.755892\pi$
$613$	−35.6564	−1.44015	−0.720075	+	0.693897i	$0.755892\pi$
$614$	−33.6415	−1.35766
$615$	−10.5276	−0.424514
$616$	26.0992	1.05157
$617$	−31.9579	−1.28658	−0.643289	−	0.765624i	$-0.722430\pi$
$617$	−31.9579	−1.28658	−0.643289	+	0.765624i	$0.722430\pi$
$618$	−10.0499	−0.404267
$619$	24.1175	0.969366	0.484683	−	0.874690i	$-0.338935\pi$
$619$	24.1175	0.969366	0.484683	+	0.874690i	$0.338935\pi$
$620$	4.77625	0.191819
$621$	−3.85694	−0.154774
$622$	−4.26050	−0.170830
$623$	9.40234	0.376697
$624$	3.63743	0.145614
$625$	−21.4061	−0.856244
$626$	−13.3243	−0.532548
$627$	−15.5851	−0.622409
$628$	−3.51497	−0.140263
$629$	9.90184	0.394812
$630$	−8.28145	−0.329941
$631$	−30.1270	−1.19934	−0.599669	−	0.800248i	$-0.704701\pi$
$631$	−30.1270	−1.19934	−0.599669	+	0.800248i	$0.704701\pi$
$632$	1.65549	0.0658519
$633$	−11.0332	−0.438530
$634$	13.0836	0.519615
$635$	−11.3408	−0.450044
$636$	6.23654	0.247295
$637$	31.7216	1.25686
$638$	57.2377	2.26606
$639$	1.74136	0.0688871
$640$	−2.08866	−0.0825615
$641$	−11.7771	−0.465169	−0.232585	−	0.972576i	$-0.574718\pi$
$641$	−11.7771	−0.465169	−0.232585	+	0.972576i	$0.574718\pi$
$642$	−7.47882	−0.295166
$643$	−20.4943	−0.808217	−0.404109	−	0.914711i	$-0.632418\pi$
$643$	−20.4943	−0.808217	−0.404109	+	0.914711i	$0.632418\pi$
$644$	−15.2926	−0.602613
$645$	20.2815	0.798583
$646$	−2.36767	−0.0931547
$647$	−11.9806	−0.471005	−0.235502	−	0.971874i	$-0.575674\pi$
$647$	−11.9806	−0.471005	−0.235502	+	0.971874i	$0.575674\pi$
$648$	1.00000	0.0392837
$649$	−6.58247	−0.258384
$650$	−2.31886	−0.0909532
$651$	−9.06687	−0.355359
$652$	8.73156	0.341954
$653$	−23.3654	−0.914359	−0.457179	−	0.889375i	$-0.651140\pi$
$653$	−23.3654	−0.914359	−0.457179	+	0.889375i	$0.651140\pi$
$654$	−13.7953	−0.539440
$655$	28.4915	1.11325
$656$	5.04037	0.196793
$657$	2.18844	0.0853791
$658$	−46.4970	−1.81264
$659$	40.3093	1.57023	0.785114	−	0.619352i	$-0.212604\pi$
$659$	40.3093	1.57023	0.785114	+	0.619352i	$0.212604\pi$
$660$	−13.7485	−0.535161
$661$	20.3420	0.791213	0.395606	−	0.918420i	$-0.370534\pi$
$661$	20.3420	0.791213	0.395606	+	0.918420i	$0.370534\pi$
$662$	27.6529	1.07476
$663$	3.63743	0.141266
$664$	−11.2547	−0.436769
$665$	19.6077	0.760355
$666$	9.90184	0.383689
$667$	−33.5379	−1.29859
$668$	18.1979	0.704098
$669$	−20.8730	−0.806997
$670$	30.3170	1.17125
$671$	−62.8187	−2.42509
$672$	3.96496	0.152952
$673$	18.0742	0.696709	0.348355	−	0.937363i	$-0.386741\pi$
$673$	18.0742	0.696709	0.348355	+	0.937363i	$0.386741\pi$
$674$	15.5189	0.597766
$675$	−0.637500	−0.0245374
$676$	0.230886	0.00888021
$677$	6.82375	0.262258	0.131129	−	0.991365i	$-0.458140\pi$
$677$	6.82375	0.262258	0.131129	+	0.991365i	$0.458140\pi$
$678$	−8.30037	−0.318774
$679$	29.8975	1.14736
$680$	−2.08866	−0.0800964
$681$	10.1609	0.389367
$682$	−15.0525	−0.576389
$683$	22.0979	0.845551	0.422776	−	0.906234i	$-0.361056\pi$
$683$	22.0979	0.845551	0.422776	+	0.906234i	$0.361056\pi$
$684$	−2.36767	−0.0905301
$685$	3.44700	0.131703
$686$	6.82324	0.260512
$687$	−4.35727	−0.166240
$688$	−9.71028	−0.370201
$689$	22.6850	0.864229
$690$	8.05583	0.306680
$691$	−15.7171	−0.597908	−0.298954	−	0.954268i	$-0.596638\pi$
$691$	−15.7171	−0.597908	−0.298954	+	0.954268i	$0.596638\pi$
$692$	16.5164	0.627861
$693$	26.0992	0.991427
$694$	23.2549	0.882743
$695$	12.3022	0.466649
$696$	8.69548	0.329601
$697$	5.04037	0.190917
$698$	2.50256	0.0947234
$699$	23.4601	0.887344
$700$	−2.52766	−0.0955366
$701$	−27.9182	−1.05446	−0.527228	−	0.849724i	$-0.676769\pi$
$701$	−27.9182	−1.05446	−0.527228	+	0.849724i	$0.676769\pi$
$702$	3.63743	0.137286
$703$	−23.4443	−0.884218
$704$	6.58247	0.248086
$705$	24.4937	0.922486
$706$	8.11418	0.305381
$707$	42.6016	1.60220
$708$	−1.00000	−0.0375823
$709$	21.3650	0.802381	0.401190	−	0.915995i	$-0.368597\pi$
$709$	21.3650	0.802381	0.401190	+	0.915995i	$0.368597\pi$
$710$	−3.63711	−0.136498
$711$	1.65549	0.0620857
$712$	2.37136	0.0888705
$713$	8.81986	0.330306
$714$	3.96496	0.148385
$715$	−50.0093	−1.87024
$716$	1.70980	0.0638984
$717$	−1.84306	−0.0688305
$718$	−25.9815	−0.969622
$719$	−36.3051	−1.35395	−0.676976	−	0.736005i	$-0.736710\pi$
$719$	−36.3051	−1.35395	−0.676976	+	0.736005i	$0.736710\pi$
$720$	−2.08866	−0.0778398
$721$	−39.8475	−1.48400
$722$	−13.3941	−0.498478
$723$	8.18866	0.304539
$724$	−17.6980	−0.657741
$725$	−5.54337	−0.205875
$726$	32.3289	1.19984
$727$	12.5269	0.464599	0.232299	−	0.972644i	$-0.425375\pi$
$727$	12.5269	0.464599	0.232299	+	0.972644i	$0.425375\pi$
$728$	14.4222	0.534524
$729$	1.00000	0.0370370
$730$	−4.57090	−0.169177
$731$	−9.71028	−0.359148
$732$	−9.54334	−0.352732
$733$	−23.9782	−0.885653	−0.442827	−	0.896607i	$-0.646024\pi$
$733$	−23.9782	−0.885653	−0.442827	+	0.896607i	$0.646024\pi$
$734$	8.05528	0.297326
$735$	−18.2150	−0.671869
$736$	−3.85694	−0.142169
$737$	−95.5447	−3.51944
$738$	5.04037	0.185538
$739$	−39.8933	−1.46750	−0.733750	−	0.679420i	$-0.762231\pi$
$739$	−39.8933	−1.46750	−0.733750	+	0.679420i	$0.762231\pi$
$740$	−20.6816	−0.760270
$741$	−8.61223	−0.316378
$742$	24.7276	0.907780
$743$	−17.9617	−0.658952	−0.329476	−	0.944164i	$-0.606872\pi$
$743$	−17.9617	−0.658952	−0.329476	+	0.944164i	$0.606872\pi$
$744$	−2.28675	−0.0838364
$745$	43.3525	1.58831
$746$	14.5314	0.532034
$747$	−11.2547	−0.411790
$748$	6.58247	0.240679
$749$	−29.6532	−1.08350
$750$	11.7748	0.429956
$751$	−3.02823	−0.110502	−0.0552509	−	0.998473i	$-0.517596\pi$
$751$	−3.02823	−0.110502	−0.0552509	+	0.998473i	$0.517596\pi$
$752$	−11.7270	−0.427639
$753$	11.8802	0.432938
$754$	31.6292	1.15187
$755$	24.4693	0.890528
$756$	3.96496	0.144204
$757$	42.3282	1.53845	0.769223	−	0.638981i	$-0.220644\pi$
$757$	42.3282	1.53845	0.769223	+	0.638981i	$0.220644\pi$
$758$	18.1085	0.657732
$759$	−25.3882	−0.921533
$760$	4.94525	0.179383
$761$	−10.5044	−0.380786	−0.190393	−	0.981708i	$-0.560976\pi$
$761$	−10.5044	−0.380786	−0.190393	+	0.981708i	$0.560976\pi$
$762$	5.42968	0.196696
$763$	−54.6979	−1.98020
$764$	−2.63395	−0.0952929
$765$	−2.08866	−0.0755157
$766$	−14.6743	−0.530203
$767$	−3.63743	−0.131340
$768$	1.00000	0.0360844
$769$	5.86325	0.211434	0.105717	−	0.994396i	$-0.466286\pi$
$769$	5.86325	0.211434	0.105717	+	0.994396i	$0.466286\pi$
$770$	−54.5124	−1.96449
$771$	1.26624	0.0456025
$772$	20.9023	0.752291
$773$	−28.2984	−1.01782	−0.508912	−	0.860819i	$-0.669952\pi$
$773$	−28.2984	−1.01782	−0.508912	+	0.860819i	$0.669952\pi$
$774$	−9.71028	−0.349029
$775$	1.45780	0.0523659
$776$	7.54044	0.270686
$777$	39.2604	1.40846
$778$	−23.0893	−0.827793
$779$	−11.9339	−0.427577
$780$	−7.59735	−0.272029
$781$	11.4624	0.410158
$782$	−3.85694	−0.137924
$783$	8.69548	0.310751
$784$	8.72089	0.311460
$785$	7.34158	0.262032
$786$	−13.6410	−0.486559
$787$	31.5616	1.12505	0.562525	−	0.826780i	$-0.309830\pi$
$787$	31.5616	1.12505	0.562525	+	0.826780i	$0.309830\pi$
$788$	14.6153	0.520650
$789$	7.77336	0.276739
$790$	−3.45776	−0.123021
$791$	−32.9106	−1.17017
$792$	6.58247	0.233898
$793$	−34.7132	−1.23270
$794$	−34.6863	−1.23097
$795$	−13.0260	−0.461985
$796$	13.5116	0.478906
$797$	−31.3547	−1.11064	−0.555320	−	0.831637i	$-0.687404\pi$
$797$	−31.3547	−1.11064	−0.555320	+	0.831637i	$0.687404\pi$
$798$	−9.38771	−0.332321
$799$	−11.7270	−0.414871
$800$	−0.637500	−0.0225390
$801$	2.37136	0.0837879
$802$	−1.04303	−0.0368306
$803$	14.4053	0.508353
$804$	−14.5150	−0.511906
$805$	31.9410	1.12577
$806$	−8.31789	−0.292985
$807$	−0.662713	−0.0233286
$808$	10.7445	0.377992
$809$	7.80154	0.274287	0.137144	−	0.990551i	$-0.456208\pi$
$809$	7.80154	0.274287	0.137144	+	0.990551i	$0.456208\pi$
$810$	−2.08866	−0.0733880
$811$	5.69925	0.200128	0.100064	−	0.994981i	$-0.468095\pi$
$811$	5.69925	0.200128	0.100064	+	0.994981i	$0.468095\pi$
$812$	34.4772	1.20991
$813$	20.9492	0.734719
$814$	65.1786	2.28451
$815$	−18.2373	−0.638823
$816$	1.00000	0.0350070
$817$	22.9907	0.804344
$818$	3.49622	0.122243
$819$	14.4222	0.503954
$820$	−10.5276	−0.367640
$821$	57.2136	1.99677	0.998385	−	0.0568162i	$-0.0180949\pi$
$821$	57.2136	1.99677	0.998385	+	0.0568162i	$0.0180949\pi$
$822$	−1.65034	−0.0575623
$823$	−24.7599	−0.863074	−0.431537	−	0.902095i	$-0.642029\pi$
$823$	−24.7599	−0.863074	−0.431537	+	0.902095i	$0.642029\pi$
$824$	−10.0499	−0.350106
$825$	−4.19632	−0.146097
$826$	−3.96496	−0.137959
$827$	−35.6530	−1.23978	−0.619889	−	0.784690i	$-0.712822\pi$
$827$	−35.6530	−1.23978	−0.619889	+	0.784690i	$0.712822\pi$
$828$	−3.85694	−0.134038
$829$	28.7868	0.999808	0.499904	−	0.866081i	$-0.333369\pi$
$829$	28.7868	0.999808	0.499904	+	0.866081i	$0.333369\pi$
$830$	23.5073	0.815952
$831$	14.6998	0.509931
$832$	3.63743	0.126105
$833$	8.72089	0.302161
$834$	−5.89000	−0.203954
$835$	−38.0093	−1.31536
$836$	−15.5851	−0.539022
$837$	−2.28675	−0.0790417
$838$	−4.72428	−0.163197
$839$	18.4934	0.638464	0.319232	−	0.947677i	$-0.396575\pi$
$839$	18.4934	0.638464	0.319232	+	0.947677i	$0.396575\pi$
$840$	−8.28145	−0.285737
$841$	46.6113	1.60729
$842$	−24.0205	−0.827800
$843$	31.3314	1.07911
$844$	−11.0332	−0.379778
$845$	−0.482241	−0.0165896
$846$	−11.7270	−0.403182
$847$	128.183	4.40441
$848$	6.23654	0.214164
$849$	−25.0529	−0.859812
$850$	−0.637500	−0.0218661
$851$	−38.1908	−1.30916
$852$	1.74136	0.0596580
$853$	2.21073	0.0756941	0.0378470	−	0.999284i	$-0.487950\pi$
$853$	2.21073	0.0756941	0.0378470	+	0.999284i	$0.487950\pi$
$854$	−37.8389	−1.29482
$855$	4.94525	0.169124
$856$	−7.47882	−0.255621
$857$	47.9865	1.63919	0.819593	−	0.572946i	$-0.194199\pi$
$857$	47.9865	1.63919	0.819593	+	0.572946i	$0.194199\pi$
$858$	23.9433	0.817409
$859$	24.9698	0.851960	0.425980	−	0.904733i	$-0.359929\pi$
$859$	24.9698	0.851960	0.425980	+	0.904733i	$0.359929\pi$
$860$	20.2815	0.691593
$861$	19.9848	0.681081
$862$	−3.31095	−0.112771
$863$	−35.8655	−1.22087	−0.610437	−	0.792065i	$-0.709006\pi$
$863$	−35.8655	−1.22087	−0.610437	+	0.792065i	$0.709006\pi$
$864$	1.00000	0.0340207
$865$	−34.4972	−1.17294
$866$	−29.1923	−0.991995
$867$	1.00000	0.0339618
$868$	−9.06687	−0.307750
$869$	10.8972	0.369663
$870$	−18.1619	−0.615746
$871$	−52.7974	−1.78897
$872$	−13.7953	−0.467169
$873$	7.54044	0.255205
$874$	9.13196	0.308893
$875$	46.6867	1.57830
$876$	2.18844	0.0739405
$877$	34.9337	1.17963	0.589814	−	0.807539i	$-0.299201\pi$
$877$	34.9337	1.17963	0.589814	+	0.807539i	$0.299201\pi$
$878$	−39.7496	−1.34149
$879$	28.7940	0.971197
$880$	−13.7485	−0.463463
$881$	−34.4492	−1.16062	−0.580311	−	0.814395i	$-0.697069\pi$
$881$	−34.4492	−1.16062	−0.580311	+	0.814395i	$0.697069\pi$
$882$	8.72089	0.293648
$883$	48.5951	1.63536	0.817678	−	0.575676i	$-0.195261\pi$
$883$	48.5951	1.63536	0.817678	+	0.575676i	$0.195261\pi$
$884$	3.63743	0.122340
$885$	2.08866	0.0702095
$886$	−16.3089	−0.547908
$887$	−26.0490	−0.874640	−0.437320	−	0.899306i	$-0.644072\pi$
$887$	−26.0490	−0.874640	−0.437320	+	0.899306i	$0.644072\pi$
$888$	9.90184	0.332284
$889$	21.5284	0.722041
$890$	−4.95296	−0.166024
$891$	6.58247	0.220521
$892$	−20.8730	−0.698880
$893$	27.7656	0.929142
$894$	−20.7561	−0.694188
$895$	−3.57120	−0.119372
$896$	3.96496	0.132460
$897$	−14.0293	−0.468426
$898$	1.17772	0.0393012
$899$	−19.8844	−0.663181
$900$	−0.637500	−0.0212500
$901$	6.23654	0.207769
$902$	33.1780	1.10471
$903$	−38.5009	−1.28123
$904$	−8.30037	−0.276066
$905$	36.9651	1.22876
$906$	−11.7153	−0.389215
$907$	42.7184	1.41844	0.709221	−	0.704987i	$-0.249047\pi$
$907$	42.7184	1.41844	0.709221	+	0.704987i	$0.249047\pi$
$908$	10.1609	0.337202
$909$	10.7445	0.356374
$910$	−30.1232	−0.998573
$911$	−12.6456	−0.418968	−0.209484	−	0.977812i	$-0.567178\pi$
$911$	−12.6456	−0.418968	−0.209484	+	0.977812i	$0.567178\pi$
$912$	−2.36767	−0.0784013
$913$	−74.0840	−2.45182
$914$	29.3480	0.970747
$915$	19.9328	0.658958
$916$	−4.35727	−0.143968
$917$	−54.0861	−1.78608
$918$	1.00000	0.0330049
$919$	−36.2844	−1.19691	−0.598456	−	0.801156i	$-0.704219\pi$
$919$	−36.2844	−1.19691	−0.598456	+	0.801156i	$0.704219\pi$
$920$	8.05583	0.265593
$921$	−33.6415	−1.10853
$922$	−19.2748	−0.634782
$923$	6.33407	0.208488
$924$	26.0992	0.858601
$925$	−6.31242	−0.207551
$926$	5.41608	0.177984
$927$	−10.0499	−0.330083
$928$	8.69548	0.285443
$929$	−49.3921	−1.62050	−0.810250	−	0.586084i	$-0.800669\pi$
$929$	−49.3921	−1.62050	−0.810250	+	0.586084i	$0.800669\pi$
$930$	4.77625	0.156619
$931$	−20.6482	−0.676716
$932$	23.4601	0.768463
$933$	−4.26050	−0.139482
$934$	1.34293	0.0439420
$935$	−13.7485	−0.449625
$936$	3.63743	0.118893
$937$	−25.7962	−0.842725	−0.421363	−	0.906892i	$-0.638448\pi$
$937$	−25.7962	−0.842725	−0.421363	+	0.906892i	$0.638448\pi$
$938$	−57.5515	−1.87912
$939$	−13.3243	−0.434824
$940$	24.4937	0.798896
$941$	−25.2327	−0.822563	−0.411282	−	0.911508i	$-0.634919\pi$
$941$	−25.2327	−0.822563	−0.411282	+	0.911508i	$0.634919\pi$
$942$	−3.51497	−0.114524
$943$	−19.4404	−0.633066
$944$	−1.00000	−0.0325472
$945$	−8.28145	−0.269395
$946$	−63.9176	−2.07814
$947$	−13.7504	−0.446828	−0.223414	−	0.974724i	$-0.571720\pi$
$947$	−13.7504	−0.446828	−0.223414	+	0.974724i	$0.571720\pi$
$948$	1.65549	0.0537678
$949$	7.96029	0.258402
$950$	1.50939	0.0489710
$951$	13.0836	0.424264
$952$	3.96496	0.128505
$953$	−55.9165	−1.81131	−0.905656	−	0.424013i	$-0.860621\pi$
$953$	−55.9165	−1.81131	−0.905656	+	0.424013i	$0.860621\pi$
$954$	6.23654	0.201916
$955$	5.50142	0.178022
$956$	−1.84306	−0.0596090
$957$	57.2377	1.85023
$958$	−33.3654	−1.07799
$959$	−6.54354	−0.211302
$960$	−2.08866	−0.0674112
$961$	−25.7708	−0.831315
$962$	36.0172	1.16124
$963$	−7.47882	−0.241002
$964$	8.18866	0.263739
$965$	−43.6579	−1.40540
$966$	−15.2926	−0.492031
$967$	−10.4878	−0.337266	−0.168633	−	0.985679i	$-0.553935\pi$
$967$	−10.4878	−0.337266	−0.168633	+	0.985679i	$0.553935\pi$
$968$	32.3289	1.03909
$969$	−2.36767	−0.0760605
$970$	−15.7494	−0.505683
$971$	47.6212	1.52824	0.764118	−	0.645076i	$-0.223174\pi$
$971$	47.6212	1.52824	0.764118	+	0.645076i	$0.223174\pi$
$972$	1.00000	0.0320750
$973$	−23.3536	−0.748682
$974$	−38.8593	−1.24513
$975$	−2.31886	−0.0742630
$976$	−9.54334	−0.305475
$977$	20.1183	0.643642	0.321821	−	0.946801i	$-0.395705\pi$
$977$	20.1183	0.643642	0.321821	+	0.946801i	$0.395705\pi$
$978$	8.73156	0.279204
$979$	15.6094	0.498879
$980$	−18.2150	−0.581856
$981$	−13.7953	−0.440451
$982$	6.25710	0.199672
$983$	61.4068	1.95857	0.979286	−	0.202480i	$-0.0649001\pi$
$983$	61.4068	1.95857	0.979286	+	0.202480i	$0.0649001\pi$
$984$	5.04037	0.160681
$985$	−30.5265	−0.972654
$986$	8.69548	0.276920
$987$	−46.4970	−1.48002
$988$	−8.61223	−0.273991
$989$	37.4520	1.19090
$990$	−13.7485	−0.436957
$991$	24.3457	0.773367	0.386684	−	0.922212i	$-0.373621\pi$
$991$	24.3457	0.773367	0.386684	+	0.922212i	$0.373621\pi$
$992$	−2.28675	−0.0726044
$993$	27.6529	0.877539
$994$	6.90441	0.218995
$995$	−28.2211	−0.894670
$996$	−11.2547	−0.356620
$997$	27.6722	0.876388	0.438194	−	0.898880i	$-0.355618\pi$
$997$	27.6722	0.876388	0.438194	+	0.898880i	$0.355618\pi$
$998$	4.09475	0.129617
$999$	9.90184	0.313280

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.bb.1.4	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.bb.1.4	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.08866 q^{5} +1.00000 q^{6} +3.96496 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.08866 q^{5} +1.00000 q^{6} +3.96496 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.08866 q^{10} +6.58247 q^{11} +1.00000 q^{12} +3.63743 q^{13} +3.96496 q^{14} -2.08866 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -2.36767 q^{19} -2.08866 q^{20} +3.96496 q^{21} +6.58247 q^{22} -3.85694 q^{23} +1.00000 q^{24} -0.637500 q^{25} +3.63743 q^{26} +1.00000 q^{27} +3.96496 q^{28} +8.69548 q^{29} -2.08866 q^{30} -2.28675 q^{31} +1.00000 q^{32} +6.58247 q^{33} +1.00000 q^{34} -8.28145 q^{35} +1.00000 q^{36} +9.90184 q^{37} -2.36767 q^{38} +3.63743 q^{39} -2.08866 q^{40} +5.04037 q^{41} +3.96496 q^{42} -9.71028 q^{43} +6.58247 q^{44} -2.08866 q^{45} -3.85694 q^{46} -11.7270 q^{47} +1.00000 q^{48} +8.72089 q^{49} -0.637500 q^{50} +1.00000 q^{51} +3.63743 q^{52} +6.23654 q^{53} +1.00000 q^{54} -13.7485 q^{55} +3.96496 q^{56} -2.36767 q^{57} +8.69548 q^{58} -1.00000 q^{59} -2.08866 q^{60} -9.54334 q^{61} -2.28675 q^{62} +3.96496 q^{63} +1.00000 q^{64} -7.59735 q^{65} +6.58247 q^{66} -14.5150 q^{67} +1.00000 q^{68} -3.85694 q^{69} -8.28145 q^{70} +1.74136 q^{71} +1.00000 q^{72} +2.18844 q^{73} +9.90184 q^{74} -0.637500 q^{75} -2.36767 q^{76} +26.0992 q^{77} +3.63743 q^{78} +1.65549 q^{79} -2.08866 q^{80} +1.00000 q^{81} +5.04037 q^{82} -11.2547 q^{83} +3.96496 q^{84} -2.08866 q^{85} -9.71028 q^{86} +8.69548 q^{87} +6.58247 q^{88} +2.37136 q^{89} -2.08866 q^{90} +14.4222 q^{91} -3.85694 q^{92} -2.28675 q^{93} -11.7270 q^{94} +4.94525 q^{95} +1.00000 q^{96} +7.54044 q^{97} +8.72089 q^{98} +6.58247 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) \) 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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