LMFDB - Embedded newform 6026.2.a.m.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$41$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.148340 q^{3} +1.00000 q^{4} -1.78404 q^{5} -0.148340 q^{6} -0.469198 q^{7} +1.00000 q^{8} -2.97800 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.148340 q^{3} +1.00000 q^{4} -1.78404 q^{5} -0.148340 q^{6} -0.469198 q^{7} +1.00000 q^{8} -2.97800 q^{9} -1.78404 q^{10} -5.56177 q^{11} -0.148340 q^{12} -6.07992 q^{13} -0.469198 q^{14} +0.264644 q^{15} +1.00000 q^{16} +6.38110 q^{17} -2.97800 q^{18} -0.00859418 q^{19} -1.78404 q^{20} +0.0696005 q^{21} -5.56177 q^{22} +1.00000 q^{23} -0.148340 q^{24} -1.81720 q^{25} -6.07992 q^{26} +0.886773 q^{27} -0.469198 q^{28} +5.46570 q^{29} +0.264644 q^{30} +7.21292 q^{31} +1.00000 q^{32} +0.825030 q^{33} +6.38110 q^{34} +0.837067 q^{35} -2.97800 q^{36} -10.0784 q^{37} -0.00859418 q^{38} +0.901893 q^{39} -1.78404 q^{40} +7.76967 q^{41} +0.0696005 q^{42} +0.302031 q^{43} -5.56177 q^{44} +5.31286 q^{45} +1.00000 q^{46} -2.07372 q^{47} -0.148340 q^{48} -6.77985 q^{49} -1.81720 q^{50} -0.946570 q^{51} -6.07992 q^{52} -14.1624 q^{53} +0.886773 q^{54} +9.92241 q^{55} -0.469198 q^{56} +0.00127486 q^{57} +5.46570 q^{58} +7.20376 q^{59} +0.264644 q^{60} +4.23674 q^{61} +7.21292 q^{62} +1.39727 q^{63} +1.00000 q^{64} +10.8468 q^{65} +0.825030 q^{66} -12.8229 q^{67} +6.38110 q^{68} -0.148340 q^{69} +0.837067 q^{70} +14.5559 q^{71} -2.97800 q^{72} -5.13547 q^{73} -10.0784 q^{74} +0.269563 q^{75} -0.00859418 q^{76} +2.60957 q^{77} +0.901893 q^{78} +11.8844 q^{79} -1.78404 q^{80} +8.80244 q^{81} +7.76967 q^{82} +5.49578 q^{83} +0.0696005 q^{84} -11.3841 q^{85} +0.302031 q^{86} -0.810779 q^{87} -5.56177 q^{88} +13.7665 q^{89} +5.31286 q^{90} +2.85268 q^{91} +1.00000 q^{92} -1.06996 q^{93} -2.07372 q^{94} +0.0153324 q^{95} -0.148340 q^{96} +7.46944 q^{97} -6.77985 q^{98} +16.5629 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9}+O(q^{10}) $ 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9} + 9 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 12 q^{14} + 10 q^{15} + 41 q^{16} + 10 q^{17} + 63 q^{18} + 16 q^{19} + 9 q^{20} + 16 q^{21} + 4 q^{22} + 41 q^{23} + 4 q^{24} + 76 q^{25} + 16 q^{26} + 7 q^{27} + 12 q^{28} + 28 q^{29} + 10 q^{30} + 25 q^{31} + 41 q^{32} + 5 q^{33} + 10 q^{34} + 4 q^{35} + 63 q^{36} + 26 q^{37} + 16 q^{38} + 50 q^{39} + 9 q^{40} + 27 q^{41} + 16 q^{42} + 12 q^{43} + 4 q^{44} + 44 q^{45} + 41 q^{46} + 18 q^{47} + 4 q^{48} + 87 q^{49} + 76 q^{50} + 24 q^{51} + 16 q^{52} + 63 q^{53} + 7 q^{54} + 18 q^{55} + 12 q^{56} - 12 q^{57} + 28 q^{58} + 33 q^{59} + 10 q^{60} + 24 q^{61} + 25 q^{62} + 48 q^{63} + 41 q^{64} + 21 q^{65} + 5 q^{66} - 9 q^{67} + 10 q^{68} + 4 q^{69} + 4 q^{70} + 36 q^{71} + 63 q^{72} + 36 q^{73} + 26 q^{74} + 6 q^{75} + 16 q^{76} + 48 q^{77} + 50 q^{78} + 51 q^{79} + 9 q^{80} + 149 q^{81} + 27 q^{82} - 27 q^{83} + 16 q^{84} + 52 q^{85} + 12 q^{86} - 3 q^{87} + 4 q^{88} + 68 q^{89} + 44 q^{90} + 22 q^{91} + 41 q^{92} + 45 q^{93} + 18 q^{94} + 46 q^{95} + 4 q^{96} + 16 q^{97} + 87 q^{98} - 10 q^{99}+O(q^{100}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9 + 9 * q^10 + 4 * q^11 + 4 * q^12 + 16 * q^13 + 12 * q^14 + 10 * q^15 + 41 * q^16 + 10 * q^17 + 63 * q^18 + 16 * q^19 + 9 * q^20 + 16 * q^21 + 4 * q^22 + 41 * q^23 + 4 * q^24 + 76 * q^25 + 16 * q^26 + 7 * q^27 + 12 * q^28 + 28 * q^29 + 10 * q^30 + 25 * q^31 + 41 * q^32 + 5 * q^33 + 10 * q^34 + 4 * q^35 + 63 * q^36 + 26 * q^37 + 16 * q^38 + 50 * q^39 + 9 * q^40 + 27 * q^41 + 16 * q^42 + 12 * q^43 + 4 * q^44 + 44 * q^45 + 41 * q^46 + 18 * q^47 + 4 * q^48 + 87 * q^49 + 76 * q^50 + 24 * q^51 + 16 * q^52 + 63 * q^53 + 7 * q^54 + 18 * q^55 + 12 * q^56 - 12 * q^57 + 28 * q^58 + 33 * q^59 + 10 * q^60 + 24 * q^61 + 25 * q^62 + 48 * q^63 + 41 * q^64 + 21 * q^65 + 5 * q^66 - 9 * q^67 + 10 * q^68 + 4 * q^69 + 4 * q^70 + 36 * q^71 + 63 * q^72 + 36 * q^73 + 26 * q^74 + 6 * q^75 + 16 * q^76 + 48 * q^77 + 50 * q^78 + 51 * q^79 + 9 * q^80 + 149 * q^81 + 27 * q^82 - 27 * q^83 + 16 * q^84 + 52 * q^85 + 12 * q^86 - 3 * q^87 + 4 * q^88 + 68 * q^89 + 44 * q^90 + 22 * q^91 + 41 * q^92 + 45 * q^93 + 18 * q^94 + 46 * q^95 + 4 * q^96 + 16 * q^97 + 87 * q^98 - 10 * 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
$3$	−0.148340	−0.0856439	−0.0428219	−	0.999083i	$-0.513635\pi$
$3$	−0.148340	−0.0856439	−0.0428219	+	0.999083i	$0.513635\pi$
$4$	1.00000	0.500000
$5$	−1.78404	−0.797847	−0.398923	−	0.916984i	$-0.630616\pi$
$5$	−1.78404	−0.797847	−0.398923	+	0.916984i	$0.630616\pi$
$6$	−0.148340	−0.0605594
$7$	−0.469198	−0.177340	−0.0886700	−	0.996061i	$-0.528262\pi$
$7$	−0.469198	−0.177340	−0.0886700	+	0.996061i	$0.528262\pi$
$8$	1.00000	0.353553
$9$	−2.97800	−0.992665
$10$	−1.78404	−0.564163
$11$	−5.56177	−1.67694	−0.838468	−	0.544951i	$-0.816548\pi$
$11$	−5.56177	−1.67694	−0.838468	+	0.544951i	$0.816548\pi$
$12$	−0.148340	−0.0428219
$13$	−6.07992	−1.68627	−0.843133	−	0.537705i	$-0.819292\pi$
$13$	−6.07992	−1.68627	−0.843133	+	0.537705i	$0.819292\pi$
$14$	−0.469198	−0.125398
$15$	0.264644	0.0683307
$16$	1.00000	0.250000
$17$	6.38110	1.54765	0.773823	−	0.633402i	$-0.218342\pi$
$17$	6.38110	1.54765	0.773823	+	0.633402i	$0.218342\pi$
$18$	−2.97800	−0.701920
$19$	−0.00859418	−0.00197164	−0.000985820	−	1.00000i	$-0.500314\pi$
$19$	−0.00859418	−0.00197164	−0.000985820		1.00000i	$0.500314\pi$
$20$	−1.78404	−0.398923
$21$	0.0696005	0.0151881
$22$	−5.56177	−1.18577
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−0.148340	−0.0302797
$25$	−1.81720	−0.363441
$26$	−6.07992	−1.19237
$27$	0.886773	0.170660
$28$	−0.469198	−0.0886700
$29$	5.46570	1.01495	0.507477	−	0.861665i	$-0.330578\pi$
$29$	5.46570	1.01495	0.507477	+	0.861665i	$0.330578\pi$
$30$	0.264644	0.0483171
$31$	7.21292	1.29548	0.647739	−	0.761862i	$-0.275715\pi$
$31$	7.21292	1.29548	0.647739	+	0.761862i	$0.275715\pi$
$32$	1.00000	0.176777
$33$	0.825030	0.143619
$34$	6.38110	1.09435
$35$	0.837067	0.141490
$36$	−2.97800	−0.496333
$37$	−10.0784	−1.65688	−0.828441	−	0.560076i	$-0.810772\pi$
$37$	−10.0784	−1.65688	−0.828441	+	0.560076i	$0.810772\pi$
$38$	−0.00859418	−0.00139416
$39$	0.901893	0.144418
$40$	−1.78404	−0.282081
$41$	7.76967	1.21342	0.606710	−	0.794924i	$-0.292489\pi$
$41$	7.76967	1.21342	0.606710	+	0.794924i	$0.292489\pi$
$42$	0.0696005	0.0107396
$43$	0.302031	0.0460594	0.0230297	−	0.999735i	$-0.492669\pi$
$43$	0.302031	0.0460594	0.0230297	+	0.999735i	$0.492669\pi$
$44$	−5.56177	−0.838468
$45$	5.31286	0.791994
$46$	1.00000	0.147442
$47$	−2.07372	−0.302483	−0.151241	−	0.988497i	$-0.548327\pi$
$47$	−2.07372	−0.302483	−0.151241	+	0.988497i	$0.548327\pi$
$48$	−0.148340	−0.0214110
$49$	−6.77985	−0.968551
$50$	−1.81720	−0.256991
$51$	−0.946570	−0.132546
$52$	−6.07992	−0.843133
$53$	−14.1624	−1.94536	−0.972681	−	0.232146i	$-0.925425\pi$
$53$	−14.1624	−1.94536	−0.972681	+	0.232146i	$0.925425\pi$
$54$	0.886773	0.120675
$55$	9.92241	1.33794
$56$	−0.469198	−0.0626992
$57$	0.00127486	0.000168859 0
$58$	5.46570	0.717681
$59$	7.20376	0.937849	0.468925	−	0.883238i	$-0.344642\pi$
$59$	7.20376	0.937849	0.468925	+	0.883238i	$0.344642\pi$
$60$	0.264644	0.0341653
$61$	4.23674	0.542458	0.271229	−	0.962515i	$-0.412570\pi$
$61$	4.23674	0.542458	0.271229	+	0.962515i	$0.412570\pi$
$62$	7.21292	0.916042
$63$	1.39727	0.176039
$64$	1.00000	0.125000
$65$	10.8468	1.34538
$66$	0.825030	0.101554
$67$	−12.8229	−1.56657	−0.783285	−	0.621663i	$-0.786457\pi$
$67$	−12.8229	−1.56657	−0.783285	+	0.621663i	$0.786457\pi$
$68$	6.38110	0.773823
$69$	−0.148340	−0.0178580
$70$	0.837067	0.100049
$71$	14.5559	1.72747	0.863734	−	0.503948i	$-0.168120\pi$
$71$	14.5559	1.72747	0.863734	+	0.503948i	$0.168120\pi$
$72$	−2.97800	−0.350960
$73$	−5.13547	−0.601061	−0.300531	−	0.953772i	$-0.597164\pi$
$73$	−5.13547	−0.601061	−0.300531	+	0.953772i	$0.597164\pi$
$74$	−10.0784	−1.17159
$75$	0.269563	0.0311265
$76$	−0.00859418	−0.000985820 0
$77$	2.60957	0.297388
$78$	0.901893	0.102119
$79$	11.8844	1.33709	0.668547	−	0.743670i	$-0.266916\pi$
$79$	11.8844	1.33709	0.668547	+	0.743670i	$0.266916\pi$
$80$	−1.78404	−0.199462
$81$	8.80244	0.978049
$82$	7.76967	0.858017
$83$	5.49578	0.603240	0.301620	−	0.953428i	$-0.402473\pi$
$83$	5.49578	0.603240	0.301620	+	0.953428i	$0.402473\pi$
$84$	0.0696005	0.00759404
$85$	−11.3841	−1.23478
$86$	0.302031	0.0325689
$87$	−0.810779	−0.0869246
$88$	−5.56177	−0.592886
$89$	13.7665	1.45924	0.729620	−	0.683852i	$-0.239697\pi$
$89$	13.7665	1.45924	0.729620	+	0.683852i	$0.239697\pi$
$90$	5.31286	0.560025
$91$	2.85268	0.299043
$92$	1.00000	0.104257
$93$	−1.06996	−0.110950
$94$	−2.07372	−0.213888
$95$	0.0153324	0.00157307
$96$	−0.148340	−0.0151398
$97$	7.46944	0.758407	0.379203	−	0.925313i	$-0.376198\pi$
$97$	7.46944	0.758407	0.379203	+	0.925313i	$0.376198\pi$
$98$	−6.77985	−0.684869
$99$	16.5629	1.66464
$100$	−1.81720	−0.181720
$101$	−1.94348	−0.193383	−0.0966917	−	0.995314i	$-0.530826\pi$
$101$	−1.94348	−0.193383	−0.0966917	+	0.995314i	$0.530826\pi$
$102$	−0.946570	−0.0937244
$103$	1.77422	0.174819	0.0874096	−	0.996172i	$-0.472141\pi$
$103$	1.77422	0.174819	0.0874096	+	0.996172i	$0.472141\pi$
$104$	−6.07992	−0.596185
$105$	−0.124170	−0.0121178
$106$	−14.1624	−1.37558
$107$	−3.11586	−0.301221	−0.150611	−	0.988593i	$-0.548124\pi$
$107$	−3.11586	−0.301221	−0.150611	+	0.988593i	$0.548124\pi$
$108$	0.886773	0.0853298
$109$	11.2482	1.07738	0.538690	−	0.842504i	$-0.318919\pi$
$109$	11.2482	1.07738	0.538690	+	0.842504i	$0.318919\pi$
$110$	9.92241	0.946065
$111$	1.49503	0.141902
$112$	−0.469198	−0.0443350
$113$	13.8601	1.30385	0.651923	−	0.758285i	$-0.273962\pi$
$113$	13.8601	1.30385	0.651923	+	0.758285i	$0.273962\pi$
$114$	0.00127486	0.000119401 0
$115$	−1.78404	−0.166363
$116$	5.46570	0.507477
$117$	18.1060	1.67390
$118$	7.20376	0.663160
$119$	−2.99400	−0.274459
$120$	0.264644	0.0241585
$121$	19.9333	1.81212
$122$	4.23674	0.383576
$123$	−1.15255	−0.103922
$124$	7.21292	0.647739
$125$	12.1622	1.08782
$126$	1.39727	0.124479
$127$	−2.85528	−0.253365	−0.126682	−	0.991943i	$-0.540433\pi$
$127$	−2.85528	−0.253365	−0.126682	+	0.991943i	$0.540433\pi$
$128$	1.00000	0.0883883
$129$	−0.0448032	−0.00394470
$130$	10.8468	0.951329
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	0.825030	0.0718096
$133$	0.00403237	0.000349651 0
$134$	−12.8229	−1.10773
$135$	−1.58204	−0.136160
$136$	6.38110	0.547175
$137$	−15.8133	−1.35102	−0.675511	−	0.737350i	$-0.736077\pi$
$137$	−15.8133	−1.35102	−0.675511	+	0.737350i	$0.736077\pi$
$138$	−0.148340	−0.0126275
$139$	7.94742	0.674092	0.337046	−	0.941488i	$-0.390572\pi$
$139$	7.94742	0.674092	0.337046	+	0.941488i	$0.390572\pi$
$140$	0.837067	0.0707451
$141$	0.307614	0.0259058
$142$	14.5559	1.22150
$143$	33.8151	2.82776
$144$	−2.97800	−0.248166
$145$	−9.75102	−0.809778
$146$	−5.13547	−0.425014
$147$	1.00572	0.0829504
$148$	−10.0784	−0.828441
$149$	−7.38278	−0.604821	−0.302410	−	0.953178i	$-0.597791\pi$
$149$	−7.38278	−0.604821	−0.302410	+	0.953178i	$0.597791\pi$
$150$	0.269563	0.0220097
$151$	0.832857	0.0677769	0.0338885	−	0.999426i	$-0.489211\pi$
$151$	0.832857	0.0677769	0.0338885	+	0.999426i	$0.489211\pi$
$152$	−0.00859418	−0.000697080 0
$153$	−19.0029	−1.53629
$154$	2.60957	0.210285
$155$	−12.8681	−1.03359
$156$	0.901893	0.0722092
$157$	6.21340	0.495884	0.247942	−	0.968775i	$-0.420246\pi$
$157$	6.21340	0.495884	0.247942	+	0.968775i	$0.420246\pi$
$158$	11.8844	0.945469
$159$	2.10085	0.166608
$160$	−1.78404	−0.141041
$161$	−0.469198	−0.0369779
$162$	8.80244	0.691585
$163$	−0.130408	−0.0102144	−0.00510719	−	0.999987i	$-0.501626\pi$
$163$	−0.130408	−0.0102144	−0.00510719	+	0.999987i	$0.501626\pi$
$164$	7.76967	0.606710
$165$	−1.47189	−0.114586
$166$	5.49578	0.426555
$167$	11.8239	0.914961	0.457480	−	0.889220i	$-0.348752\pi$
$167$	11.8239	0.914961	0.457480	+	0.889220i	$0.348752\pi$
$168$	0.0696005	0.00536980
$169$	23.9654	1.84350
$170$	−11.3841	−0.873124
$171$	0.0255934	0.00195718
$172$	0.302031	0.0230297
$173$	−5.06316	−0.384945	−0.192472	−	0.981302i	$-0.561651\pi$
$173$	−5.06316	−0.384945	−0.192472	+	0.981302i	$0.561651\pi$
$174$	−0.810779	−0.0614650
$175$	0.852628	0.0644526
$176$	−5.56177	−0.419234
$177$	−1.06860	−0.0803210
$178$	13.7665	1.03184
$179$	−11.0554	−0.826322	−0.413161	−	0.910658i	$-0.635575\pi$
$179$	−11.0554	−0.826322	−0.413161	+	0.910658i	$0.635575\pi$
$180$	5.31286	0.395997
$181$	19.4391	1.44490	0.722450	−	0.691423i	$-0.243016\pi$
$181$	19.4391	1.44490	0.722450	+	0.691423i	$0.243016\pi$
$182$	2.85268	0.211455
$183$	−0.628475	−0.0464582
$184$	1.00000	0.0737210
$185$	17.9803	1.32194
$186$	−1.06996	−0.0784534
$187$	−35.4902	−2.59530
$188$	−2.07372	−0.151241
$189$	−0.416072	−0.0302648
$190$	0.0153324	0.00111233
$191$	−24.2837	−1.75711	−0.878553	−	0.477645i	$-0.841491\pi$
$191$	−24.2837	−1.75711	−0.878553	+	0.477645i	$0.841491\pi$
$192$	−0.148340	−0.0107055
$193$	−12.5283	−0.901804	−0.450902	−	0.892573i	$-0.648898\pi$
$193$	−12.5283	−0.901804	−0.450902	+	0.892573i	$0.648898\pi$
$194$	7.46944	0.536275
$195$	−1.60901	−0.115224
$196$	−6.77985	−0.484275
$197$	10.5595	0.752333	0.376166	−	0.926552i	$-0.377242\pi$
$197$	10.5595	0.752333	0.376166	+	0.926552i	$0.377242\pi$
$198$	16.5629	1.17708
$199$	3.47750	0.246513	0.123257	−	0.992375i	$-0.460666\pi$
$199$	3.47750	0.246513	0.123257	+	0.992375i	$0.460666\pi$
$200$	−1.81720	−0.128496
$201$	1.90215	0.134167
$202$	−1.94348	−0.136743
$203$	−2.56449	−0.179992
$204$	−0.946570	−0.0662731
$205$	−13.8614	−0.968122
$206$	1.77422	0.123616
$207$	−2.97800	−0.206985
$208$	−6.07992	−0.421567
$209$	0.0477989	0.00330632
$210$	−0.124170	−0.00856855
$211$	1.40838	0.0969567	0.0484783	−	0.998824i	$-0.484563\pi$
$211$	1.40838	0.0969567	0.0484783	+	0.998824i	$0.484563\pi$
$212$	−14.1624	−0.972681
$213$	−2.15922	−0.147947
$214$	−3.11586	−0.212995
$215$	−0.538836	−0.0367483
$216$	0.886773	0.0603373
$217$	−3.38428	−0.229740
$218$	11.2482	0.761822
$219$	0.761793	0.0514772
$220$	9.92241	0.668969
$221$	−38.7966	−2.60974
$222$	1.49503	0.100340
$223$	−23.9442	−1.60342	−0.801710	−	0.597713i	$-0.796076\pi$
$223$	−23.9442	−1.60342	−0.801710	+	0.597713i	$0.796076\pi$
$224$	−0.469198	−0.0313496
$225$	5.41163	0.360775
$226$	13.8601	0.921959
$227$	−6.94462	−0.460930	−0.230465	−	0.973081i	$-0.574025\pi$
$227$	−6.94462	−0.460930	−0.230465	+	0.973081i	$0.574025\pi$
$228$	0.00127486	8.44295e−5 0
$229$	1.83722	0.121407	0.0607035	−	0.998156i	$-0.480666\pi$
$229$	1.83722	0.121407	0.0607035	+	0.998156i	$0.480666\pi$
$230$	−1.78404	−0.117636
$231$	−0.387102	−0.0254694
$232$	5.46570	0.358841
$233$	1.75040	0.114672	0.0573362	−	0.998355i	$-0.481739\pi$
$233$	1.75040	0.114672	0.0573362	+	0.998355i	$0.481739\pi$
$234$	18.1060	1.18362
$235$	3.69959	0.241335
$236$	7.20376	0.468925
$237$	−1.76292	−0.114514
$238$	−2.99400	−0.194072
$239$	26.1495	1.69147	0.845736	−	0.533601i	$-0.179162\pi$
$239$	26.1495	1.69147	0.845736	+	0.533601i	$0.179162\pi$
$240$	0.264644	0.0170827
$241$	13.8413	0.891597	0.445799	−	0.895133i	$-0.352920\pi$
$241$	13.8413	0.891597	0.445799	+	0.895133i	$0.352920\pi$
$242$	19.9333	1.28136
$243$	−3.96607	−0.254423
$244$	4.23674	0.271229
$245$	12.0955	0.772755
$246$	−1.15255	−0.0734839
$247$	0.0522520	0.00332471
$248$	7.21292	0.458021
$249$	−0.815241	−0.0516638
$250$	12.1622	0.769203
$251$	17.0142	1.07393	0.536964	−	0.843605i	$-0.319571\pi$
$251$	17.0142	1.07393	0.536964	+	0.843605i	$0.319571\pi$
$252$	1.39727	0.0880196
$253$	−5.56177	−0.349665
$254$	−2.85528	−0.179156
$255$	1.68872	0.105752
$256$	1.00000	0.0625000
$257$	−0.990171	−0.0617652	−0.0308826	−	0.999523i	$-0.509832\pi$
$257$	−0.990171	−0.0617652	−0.0308826	+	0.999523i	$0.509832\pi$
$258$	−0.0448032	−0.00278933
$259$	4.72877	0.293832
$260$	10.8468	0.672691
$261$	−16.2768	−1.00751
$262$	1.00000	0.0617802
$263$	7.50313	0.462663	0.231332	−	0.972875i	$-0.425692\pi$
$263$	7.50313	0.462663	0.231332	+	0.972875i	$0.425692\pi$
$264$	0.825030	0.0507771
$265$	25.2664	1.55210
$266$	0.00403237	0.000247240 0
$267$	−2.04211	−0.124975
$268$	−12.8229	−0.783285
$269$	−17.6096	−1.07367	−0.536837	−	0.843686i	$-0.680381\pi$
$269$	−17.6096	−1.07367	−0.536837	+	0.843686i	$0.680381\pi$
$270$	−1.58204	−0.0962797
$271$	26.4597	1.60731	0.803655	−	0.595095i	$-0.202886\pi$
$271$	26.4597	1.60731	0.803655	+	0.595095i	$0.202886\pi$
$272$	6.38110	0.386911
$273$	−0.423166	−0.0256112
$274$	−15.8133	−0.955317
$275$	10.1069	0.609467
$276$	−0.148340	−0.00892899
$277$	16.8931	1.01501	0.507504	−	0.861650i	$-0.330568\pi$
$277$	16.8931	1.01501	0.507504	+	0.861650i	$0.330568\pi$
$278$	7.94742	0.476655
$279$	−21.4800	−1.28598
$280$	0.837067	0.0500243
$281$	−16.7680	−1.00030	−0.500149	−	0.865939i	$-0.666721\pi$
$281$	−16.7680	−1.00030	−0.500149	+	0.865939i	$0.666721\pi$
$282$	0.307614	0.0183182
$283$	−28.0588	−1.66792	−0.833961	−	0.551823i	$-0.813932\pi$
$283$	−28.0588	−1.66792	−0.833961	+	0.551823i	$0.813932\pi$
$284$	14.5559	0.863734
$285$	−0.00227439	−0.000134724 0
$286$	33.8151	1.99953
$287$	−3.64551	−0.215188
$288$	−2.97800	−0.175480
$289$	23.7185	1.39521
$290$	−9.75102	−0.572600
$291$	−1.10801	−0.0649529
$292$	−5.13547	−0.300531
$293$	−27.6841	−1.61732	−0.808660	−	0.588276i	$-0.799807\pi$
$293$	−27.6841	−1.61732	−0.808660	+	0.588276i	$0.799807\pi$
$294$	1.00572	0.0586548
$295$	−12.8518	−0.748260
$296$	−10.0784	−0.585797
$297$	−4.93203	−0.286185
$298$	−7.38278	−0.427673
$299$	−6.07992	−0.351611
$300$	0.269563	0.0155632
$301$	−0.141712	−0.00816817
$302$	0.832857	0.0479255
$303$	0.288295	0.0165621
$304$	−0.00859418	−0.000492910 0
$305$	−7.55850	−0.432799
$306$	−19.0029	−1.08632
$307$	−6.77321	−0.386567	−0.193284	−	0.981143i	$-0.561914\pi$
$307$	−6.77321	−0.386567	−0.193284	+	0.981143i	$0.561914\pi$
$308$	2.60957	0.148694
$309$	−0.263187	−0.0149722
$310$	−12.8681	−0.730861
$311$	−7.25401	−0.411337	−0.205669	−	0.978622i	$-0.565937\pi$
$311$	−7.25401	−0.411337	−0.205669	+	0.978622i	$0.565937\pi$
$312$	0.901893	0.0510596
$313$	−10.5494	−0.596290	−0.298145	−	0.954521i	$-0.596368\pi$
$313$	−10.5494	−0.596290	−0.298145	+	0.954521i	$0.596368\pi$
$314$	6.21340	0.350643
$315$	−2.49278	−0.140452
$316$	11.8844	0.668547
$317$	−2.74965	−0.154436	−0.0772178	−	0.997014i	$-0.524604\pi$
$317$	−2.74965	−0.154436	−0.0772178	+	0.997014i	$0.524604\pi$
$318$	2.10085	0.117810
$319$	−30.3990	−1.70201
$320$	−1.78404	−0.0997308
$321$	0.462204	0.0257977
$322$	−0.469198	−0.0261474
$323$	−0.0548404	−0.00305140
$324$	8.80244	0.489025
$325$	11.0485	0.612858
$326$	−0.130408	−0.00722266
$327$	−1.66855	−0.0922710
$328$	7.76967	0.429008
$329$	0.972983	0.0536423
$330$	−1.47189	−0.0810247
$331$	−3.66342	−0.201360	−0.100680	−	0.994919i	$-0.532102\pi$
$331$	−3.66342	−0.201360	−0.100680	+	0.994919i	$0.532102\pi$
$332$	5.49578	0.301620
$333$	30.0135	1.64473
$334$	11.8239	0.646975
$335$	22.8766	1.24988
$336$	0.0696005	0.00379702
$337$	21.2475	1.15742	0.578712	−	0.815532i	$-0.303556\pi$
$337$	21.2475	1.15742	0.578712	+	0.815532i	$0.303556\pi$
$338$	23.9654	1.30355
$339$	−2.05600	−0.111666
$340$	−11.3841	−0.617392
$341$	−40.1166	−2.17244
$342$	0.0255934	0.00138393
$343$	6.46547	0.349103
$344$	0.302031	0.0162844
$345$	0.264644	0.0142479
$346$	−5.06316	−0.272197
$347$	−0.994706	−0.0533986	−0.0266993	−	0.999644i	$-0.508500\pi$
$347$	−0.994706	−0.0533986	−0.0266993	+	0.999644i	$0.508500\pi$
$348$	−0.810779	−0.0434623
$349$	−2.47302	−0.132378	−0.0661890	−	0.997807i	$-0.521084\pi$
$349$	−2.47302	−0.132378	−0.0661890	+	0.997807i	$0.521084\pi$
$350$	0.852628	0.0455749
$351$	−5.39151	−0.287777
$352$	−5.56177	−0.296443
$353$	0.873625	0.0464984	0.0232492	−	0.999730i	$-0.492599\pi$
$353$	0.873625	0.0464984	0.0232492	+	0.999730i	$0.492599\pi$
$354$	−1.06860	−0.0567955
$355$	−25.9683	−1.37825
$356$	13.7665	0.729620
$357$	0.444128	0.0235058
$358$	−11.0554	−0.584298
$359$	−14.6789	−0.774724	−0.387362	−	0.921928i	$-0.626614\pi$
$359$	−14.6789	−0.774724	−0.387362	+	0.921928i	$0.626614\pi$
$360$	5.31286	0.280012
$361$	−18.9999	−0.999996
$362$	19.4391	1.02170
$363$	−2.95689	−0.155197
$364$	2.85268	0.149521
$365$	9.16188	0.479555
$366$	−0.628475	−0.0328509
$367$	3.49969	0.182682	0.0913411	−	0.995820i	$-0.470885\pi$
$367$	3.49969	0.182682	0.0913411	+	0.995820i	$0.470885\pi$
$368$	1.00000	0.0521286
$369$	−23.1381	−1.20452
$370$	17.9803	0.934752
$371$	6.64499	0.344991
$372$	−1.06996	−0.0554749
$373$	−16.8226	−0.871043	−0.435521	−	0.900178i	$-0.643436\pi$
$373$	−16.8226	−0.871043	−0.435521	+	0.900178i	$0.643436\pi$
$374$	−35.4902	−1.83516
$375$	−1.80413	−0.0931648
$376$	−2.07372	−0.106944
$377$	−33.2310	−1.71148
$378$	−0.416072	−0.0214004
$379$	21.6089	1.10997	0.554986	−	0.831860i	$-0.312724\pi$
$379$	21.6089	1.10997	0.554986	+	0.831860i	$0.312724\pi$
$380$	0.0153324	0.000786533 0
$381$	0.423551	0.0216992
$382$	−24.2837	−1.24246
$383$	17.9231	0.915830	0.457915	−	0.888996i	$-0.348596\pi$
$383$	17.9231	0.915830	0.457915	+	0.888996i	$0.348596\pi$
$384$	−0.148340	−0.00756992
$385$	−4.65557	−0.237270
$386$	−12.5283	−0.637672
$387$	−0.899448	−0.0457215
$388$	7.46944	0.379203
$389$	20.3594	1.03226	0.516130	−	0.856510i	$-0.327372\pi$
$389$	20.3594	1.03226	0.516130	+	0.856510i	$0.327372\pi$
$390$	−1.60901	−0.0814755
$391$	6.38110	0.322706
$392$	−6.77985	−0.342434
$393$	−0.148340	−0.00748274
$394$	10.5595	0.531979
$395$	−21.2022	−1.06680
$396$	16.5629	0.832318
$397$	13.2416	0.664579	0.332289	−	0.943177i	$-0.392179\pi$
$397$	13.2416	0.664579	0.332289	+	0.943177i	$0.392179\pi$
$398$	3.47750	0.174311
$399$	−0.000598160 0	−2.99454e−5 0
$400$	−1.81720	−0.0908602
$401$	14.7355	0.735854	0.367927	−	0.929855i	$-0.380068\pi$
$401$	14.7355	0.735854	0.367927	+	0.929855i	$0.380068\pi$
$402$	1.90215	0.0948705
$403$	−43.8540	−2.18452
$404$	−1.94348	−0.0966917
$405$	−15.7039	−0.780333
$406$	−2.56449	−0.127274
$407$	56.0539	2.77849
$408$	−0.946570	−0.0468622
$409$	−3.92326	−0.193993	−0.0969963	−	0.995285i	$-0.530924\pi$
$409$	−3.92326	−0.193993	−0.0969963	+	0.995285i	$0.530924\pi$
$410$	−13.8614	−0.684566
$411$	2.34574	0.115707
$412$	1.77422	0.0874096
$413$	−3.37998	−0.166318
$414$	−2.97800	−0.146360
$415$	−9.80469	−0.481293
$416$	−6.07992	−0.298093
$417$	−1.17892	−0.0577318
$418$	0.0477989	0.00233792
$419$	27.5155	1.34422	0.672110	−	0.740451i	$-0.265388\pi$
$419$	27.5155	1.34422	0.672110	+	0.740451i	$0.265388\pi$
$420$	−0.124170	−0.00605888
$421$	−6.57783	−0.320584	−0.160292	−	0.987070i	$-0.551244\pi$
$421$	−6.57783	−0.320584	−0.160292	+	0.987070i	$0.551244\pi$
$422$	1.40838	0.0685587
$423$	6.17552	0.300264
$424$	−14.1624	−0.687789
$425$	−11.5958	−0.562477
$426$	−2.15922	−0.104614
$427$	−1.98787	−0.0961996
$428$	−3.11586	−0.150611
$429$	−5.01612	−0.242180
$430$	−0.538836	−0.0259850
$431$	21.6326	1.04201	0.521004	−	0.853554i	$-0.325558\pi$
$431$	21.6326	1.04201	0.521004	+	0.853554i	$0.325558\pi$
$432$	0.886773	0.0426649
$433$	−26.4662	−1.27188	−0.635942	−	0.771737i	$-0.719388\pi$
$433$	−26.4662	−1.27188	−0.635942	+	0.771737i	$0.719388\pi$
$434$	−3.38428	−0.162451
$435$	1.44646	0.0693525
$436$	11.2482	0.538690
$437$	−0.00859418	−0.000411116 0
$438$	0.761793	0.0363999
$439$	29.8726	1.42574	0.712870	−	0.701296i	$-0.247395\pi$
$439$	29.8726	1.42574	0.712870	+	0.701296i	$0.247395\pi$
$440$	9.92241	0.473032
$441$	20.1904	0.961446
$442$	−38.7966	−1.84537
$443$	−12.0747	−0.573688	−0.286844	−	0.957977i	$-0.592606\pi$
$443$	−12.0747	−0.573688	−0.286844	+	0.957977i	$0.592606\pi$
$444$	1.49503	0.0709509
$445$	−24.5599	−1.16425
$446$	−23.9442	−1.13379
$447$	1.09516	0.0517992
$448$	−0.469198	−0.0221675
$449$	−41.2702	−1.94766	−0.973831	−	0.227273i	$-0.927019\pi$
$449$	−41.2702	−1.94766	−0.973831	+	0.227273i	$0.927019\pi$
$450$	5.41163	0.255106
$451$	−43.2131	−2.03483
$452$	13.8601	0.651923
$453$	−0.123546	−0.00580468
$454$	−6.94462	−0.325927
$455$	−5.08930	−0.238590
$456$	0.00127486	5.97006e−5 0
$457$	37.0077	1.73115	0.865573	−	0.500783i	$-0.166955\pi$
$457$	37.0077	1.73115	0.865573	+	0.500783i	$0.166955\pi$
$458$	1.83722	0.0858477
$459$	5.65859	0.264120
$460$	−1.78404	−0.0831813
$461$	−0.156874	−0.00730634	−0.00365317	−	0.999993i	$-0.501163\pi$
$461$	−0.156874	−0.00730634	−0.00365317	+	0.999993i	$0.501163\pi$
$462$	−0.387102	−0.0180096
$463$	40.5625	1.88510	0.942550	−	0.334066i	$-0.108421\pi$
$463$	40.5625	1.88510	0.942550	+	0.334066i	$0.108421\pi$
$464$	5.46570	0.253739
$465$	1.90885	0.0885209
$466$	1.75040	0.0810857
$467$	17.4843	0.809076	0.404538	−	0.914521i	$-0.367432\pi$
$467$	17.4843	0.809076	0.404538	+	0.914521i	$0.367432\pi$
$468$	18.1060	0.836949
$469$	6.01649	0.277816
$470$	3.69959	0.170650
$471$	−0.921693	−0.0424694
$472$	7.20376	0.331580
$473$	−1.67983	−0.0772386
$474$	−1.76292	−0.0809736
$475$	0.0156174	0.000716575 0
$476$	−2.99400	−0.137230
$477$	42.1757	1.93109
$478$	26.1495	1.19605
$479$	−32.2922	−1.47547	−0.737734	−	0.675091i	$-0.764104\pi$
$479$	−32.2922	−1.47547	−0.737734	+	0.675091i	$0.764104\pi$
$480$	0.264644	0.0120793
$481$	61.2760	2.79395
$482$	13.8413	0.630455
$483$	0.0696005	0.00316693
$484$	19.9333	0.906058
$485$	−13.3258	−0.605092
$486$	−3.96607	−0.179905
$487$	−2.43705	−0.110433	−0.0552167	−	0.998474i	$-0.517585\pi$
$487$	−2.43705	−0.110433	−0.0552167	+	0.998474i	$0.517585\pi$
$488$	4.23674	0.191788
$489$	0.0193447	0.000874799 0
$490$	12.0955	0.546420
$491$	−28.5275	−1.28743	−0.643713	−	0.765267i	$-0.722607\pi$
$491$	−28.5275	−1.28743	−0.643713	+	0.765267i	$0.722607\pi$
$492$	−1.15255	−0.0519609
$493$	34.8772	1.57079
$494$	0.0522520	0.00235093
$495$	−29.5489	−1.32812
$496$	7.21292	0.323870
$497$	−6.82959	−0.306349
$498$	−0.815241	−0.0365318
$499$	40.8138	1.82708	0.913538	−	0.406752i	$-0.133339\pi$
$499$	40.8138	1.82708	0.913538	+	0.406752i	$0.133339\pi$
$500$	12.1622	0.543908
$501$	−1.75395	−0.0783608
$502$	17.0142	0.759382
$503$	−37.1206	−1.65513	−0.827563	−	0.561373i	$-0.810273\pi$
$503$	−37.1206	−1.65513	−0.827563	+	0.561373i	$0.810273\pi$
$504$	1.39727	0.0622393
$505$	3.46724	0.154290
$506$	−5.56177	−0.247251
$507$	−3.55502	−0.157884
$508$	−2.85528	−0.126682
$509$	41.4166	1.83576	0.917880	−	0.396858i	$-0.129900\pi$
$509$	41.4166	1.83576	0.917880	+	0.396858i	$0.129900\pi$
$510$	1.68872	0.0747777
$511$	2.40955	0.106592
$512$	1.00000	0.0441942
$513$	−0.00762109	−0.000336479 0
$514$	−0.990171	−0.0436746
$515$	−3.16528	−0.139479
$516$	−0.0448032	−0.00197235
$517$	11.5335	0.507244
$518$	4.72877	0.207770
$519$	0.751066	0.0329682
$520$	10.8468	0.475664
$521$	31.6124	1.38496	0.692482	−	0.721435i	$-0.256517\pi$
$521$	31.6124	1.38496	0.692482	+	0.721435i	$0.256517\pi$
$522$	−16.2768	−0.712417
$523$	13.6392	0.596399	0.298200	−	0.954504i	$-0.403614\pi$
$523$	13.6392	0.596399	0.298200	+	0.954504i	$0.403614\pi$
$524$	1.00000	0.0436852
$525$	−0.126478	−0.00551997
$526$	7.50313	0.327152
$527$	46.0264	2.00494
$528$	0.825030	0.0359048
$529$	1.00000	0.0434783
$530$	25.2664	1.09750
$531$	−21.4528	−0.930970
$532$	0.00403237	0.000174825 0
$533$	−47.2390	−2.04615
$534$	−2.04211	−0.0883707
$535$	5.55881	0.240328
$536$	−12.8229	−0.553866
$537$	1.63996	0.0707694
$538$	−17.6096	−0.759202
$539$	37.7080	1.62420
$540$	−1.58204	−0.0680801
$541$	−20.9372	−0.900162	−0.450081	−	0.892988i	$-0.648605\pi$
$541$	−20.9372	−0.900162	−0.450081	+	0.892988i	$0.648605\pi$
$542$	26.4597	1.13654
$543$	−2.88359	−0.123747
$544$	6.38110	0.273588
$545$	−20.0672	−0.859584
$546$	−0.423166	−0.0181098
$547$	20.3171	0.868696	0.434348	−	0.900745i	$-0.356979\pi$
$547$	20.3171	0.868696	0.434348	+	0.900745i	$0.356979\pi$
$548$	−15.8133	−0.675511
$549$	−12.6170	−0.538480
$550$	10.1069	0.430958
$551$	−0.0469732	−0.00200113
$552$	−0.148340	−0.00631375
$553$	−5.57611	−0.237120
$554$	16.8931	0.717719
$555$	−2.66719	−0.113216
$556$	7.94742	0.337046
$557$	18.0624	0.765327	0.382664	−	0.923888i	$-0.375007\pi$
$557$	18.0624	0.765327	0.382664	+	0.923888i	$0.375007\pi$
$558$	−21.4800	−0.909323
$559$	−1.83633	−0.0776684
$560$	0.837067	0.0353725
$561$	5.26460	0.222272
$562$	−16.7680	−0.707317
$563$	18.3020	0.771337	0.385668	−	0.922638i	$-0.373971\pi$
$563$	18.3020	0.771337	0.385668	+	0.922638i	$0.373971\pi$
$564$	0.307614	0.0129529
$565$	−24.7269	−1.04027
$566$	−28.0588	−1.17940
$567$	−4.13008	−0.173447
$568$	14.5559	0.610752
$569$	−23.0707	−0.967173	−0.483586	−	0.875297i	$-0.660666\pi$
$569$	−23.0707	−0.967173	−0.483586	+	0.875297i	$0.660666\pi$
$570$	−0.00227439	−9.52639e−5 0
$571$	−12.2119	−0.511052	−0.255526	−	0.966802i	$-0.582249\pi$
$571$	−12.2119	−0.511052	−0.255526	+	0.966802i	$0.582249\pi$
$572$	33.8151	1.41388
$573$	3.60223	0.150485
$574$	−3.64551	−0.152161
$575$	−1.81720	−0.0757826
$576$	−2.97800	−0.124083
$577$	29.0278	1.20844	0.604221	−	0.796816i	$-0.293484\pi$
$577$	29.0278	1.20844	0.604221	+	0.796816i	$0.293484\pi$
$578$	23.7185	0.986559
$579$	1.85844	0.0772340
$580$	−9.75102	−0.404889
$581$	−2.57861	−0.106979
$582$	−1.10801	−0.0459286
$583$	78.7683	3.26225
$584$	−5.13547	−0.212507
$585$	−32.3018	−1.33551
$586$	−27.6841	−1.14362
$587$	1.20102	0.0495715	0.0247857	−	0.999693i	$-0.492110\pi$
$587$	1.20102	0.0495715	0.0247857	+	0.999693i	$0.492110\pi$
$588$	1.00572	0.0414752
$589$	−0.0619892	−0.00255422
$590$	−12.8518	−0.529100
$591$	−1.56639	−0.0644327
$592$	−10.0784	−0.414221
$593$	−13.4522	−0.552414	−0.276207	−	0.961098i	$-0.589078\pi$
$593$	−13.4522	−0.552414	−0.276207	+	0.961098i	$0.589078\pi$
$594$	−4.93203	−0.202363
$595$	5.34141	0.218976
$596$	−7.38278	−0.302410
$597$	−0.515851	−0.0211124
$598$	−6.07992	−0.248626
$599$	−21.3224	−0.871209	−0.435604	−	0.900138i	$-0.643465\pi$
$599$	−21.3224	−0.871209	−0.435604	+	0.900138i	$0.643465\pi$
$600$	0.269563	0.0110049
$601$	35.4698	1.44684	0.723422	−	0.690406i	$-0.242568\pi$
$601$	35.4698	1.44684	0.723422	+	0.690406i	$0.242568\pi$
$602$	−0.141712	−0.00577577
$603$	38.1866	1.55508
$604$	0.832857	0.0338885
$605$	−35.5617	−1.44579
$606$	0.288295	0.0117112
$607$	−5.70564	−0.231585	−0.115792	−	0.993273i	$-0.536941\pi$
$607$	−5.70564	−0.231585	−0.115792	+	0.993273i	$0.536941\pi$
$608$	−0.00859418	−0.000348540 0
$609$	0.380416	0.0154152
$610$	−7.55850	−0.306035
$611$	12.6080	0.510067
$612$	−19.0029	−0.768147
$613$	3.81564	0.154112	0.0770560	−	0.997027i	$-0.475448\pi$
$613$	3.81564	0.154112	0.0770560	+	0.997027i	$0.475448\pi$
$614$	−6.77321	−0.273344
$615$	2.05619	0.0829137
$616$	2.60957	0.105143
$617$	−35.3615	−1.42360	−0.711799	−	0.702383i	$-0.752119\pi$
$617$	−35.3615	−1.42360	−0.711799	+	0.702383i	$0.752119\pi$
$618$	−0.263187	−0.0105869
$619$	41.1195	1.65273	0.826366	−	0.563133i	$-0.190404\pi$
$619$	41.1195	1.65273	0.826366	+	0.563133i	$0.190404\pi$
$620$	−12.8681	−0.516797
$621$	0.886773	0.0355850
$622$	−7.25401	−0.290859
$623$	−6.45919	−0.258782
$624$	0.901893	0.0361046
$625$	−12.6117	−0.504470
$626$	−10.5494	−0.421641
$627$	−0.00709046	−0.000283166 0
$628$	6.21340	0.247942
$629$	−64.3115	−2.56427
$630$	−2.49278	−0.0993148
$631$	−27.8034	−1.10683	−0.553417	−	0.832904i	$-0.686676\pi$
$631$	−27.8034	−1.10683	−0.553417	+	0.832904i	$0.686676\pi$
$632$	11.8844	0.472734
$633$	−0.208918	−0.00830374
$634$	−2.74965	−0.109202
$635$	5.09393	0.202146
$636$	2.10085	0.0833041
$637$	41.2210	1.63323
$638$	−30.3990	−1.20351
$639$	−43.3474	−1.71480
$640$	−1.78404	−0.0705203
$641$	1.27696	0.0504369	0.0252184	−	0.999682i	$-0.491972\pi$
$641$	1.27696	0.0504369	0.0252184	+	0.999682i	$0.491972\pi$
$642$	0.462204	0.0182418
$643$	−23.0032	−0.907158	−0.453579	−	0.891216i	$-0.649853\pi$
$643$	−23.0032	−0.907158	−0.453579	+	0.891216i	$0.649853\pi$
$644$	−0.469198	−0.0184890
$645$	0.0799307	0.00314727
$646$	−0.0548404	−0.00215767
$647$	−13.0470	−0.512930	−0.256465	−	0.966554i	$-0.582558\pi$
$647$	−13.0470	−0.512930	−0.256465	+	0.966554i	$0.582558\pi$
$648$	8.80244	0.345793
$649$	−40.0656	−1.57271
$650$	11.0485	0.433356
$651$	0.502023	0.0196758
$652$	−0.130408	−0.00510719
$653$	37.2130	1.45626	0.728129	−	0.685440i	$-0.240390\pi$
$653$	37.2130	1.45626	0.728129	+	0.685440i	$0.240390\pi$
$654$	−1.66855	−0.0652454
$655$	−1.78404	−0.0697082
$656$	7.76967	0.303355
$657$	15.2934	0.596652
$658$	0.972983	0.0379308
$659$	−21.8076	−0.849504	−0.424752	−	0.905310i	$-0.639639\pi$
$659$	−21.8076	−0.849504	−0.424752	+	0.905310i	$0.639639\pi$
$660$	−1.47189	−0.0572931
$661$	−5.17629	−0.201334	−0.100667	−	0.994920i	$-0.532098\pi$
$661$	−5.17629	−0.201334	−0.100667	+	0.994920i	$0.532098\pi$
$662$	−3.66342	−0.142383
$663$	5.75507	0.223508
$664$	5.49578	0.213278
$665$	−0.00719391	−0.000278968 0
$666$	30.0135	1.16300
$667$	5.46570	0.211633
$668$	11.8239	0.457480
$669$	3.55187	0.137323
$670$	22.8766	0.883800
$671$	−23.5637	−0.909668
$672$	0.0696005	0.00268490
$673$	33.5936	1.29494	0.647469	−	0.762092i	$-0.275828\pi$
$673$	33.5936	1.29494	0.647469	+	0.762092i	$0.275828\pi$
$674$	21.2475	0.818422
$675$	−1.61145	−0.0620246
$676$	23.9654	0.921748
$677$	−41.9825	−1.61352	−0.806760	−	0.590879i	$-0.798781\pi$
$677$	−41.9825	−1.61352	−0.806760	+	0.590879i	$0.798781\pi$
$678$	−2.05600	−0.0789601
$679$	−3.50464	−0.134496
$680$	−11.3841	−0.436562
$681$	1.03016	0.0394759
$682$	−40.1166	−1.53614
$683$	−5.96433	−0.228219	−0.114109	−	0.993468i	$-0.536401\pi$
$683$	−5.96433	−0.228219	−0.114109	+	0.993468i	$0.536401\pi$
$684$	0.0255934	0.000978590 0
$685$	28.2116	1.07791
$686$	6.46547	0.246853
$687$	−0.272533	−0.0103978
$688$	0.302031	0.0115148
$689$	86.1066	3.28040
$690$	0.264644	0.0100748
$691$	−37.9711	−1.44449	−0.722244	−	0.691638i	$-0.756889\pi$
$691$	−37.9711	−1.44449	−0.722244	+	0.691638i	$0.756889\pi$
$692$	−5.06316	−0.192472
$693$	−7.77128	−0.295207
$694$	−0.994706	−0.0377585
$695$	−14.1785	−0.537822
$696$	−0.810779	−0.0307325
$697$	49.5791	1.87794
$698$	−2.47302	−0.0936053
$699$	−0.259653	−0.00982100
$700$	0.852628	0.0322263
$701$	−8.15659	−0.308070	−0.154035	−	0.988065i	$-0.549227\pi$
$701$	−8.15659	−0.308070	−0.154035	+	0.988065i	$0.549227\pi$
$702$	−5.39151	−0.203489
$703$	0.0866158	0.00326678
$704$	−5.56177	−0.209617
$705$	−0.548796	−0.0206689
$706$	0.873625	0.0328793
$707$	0.911876	0.0342946
$708$	−1.06860	−0.0401605
$709$	28.6597	1.07634	0.538169	−	0.842837i	$-0.319116\pi$
$709$	28.6597	1.07634	0.538169	+	0.842837i	$0.319116\pi$
$710$	−25.9683	−0.974573
$711$	−35.3916	−1.32729
$712$	13.7665	0.515920
$713$	7.21292	0.270126
$714$	0.444128	0.0166211
$715$	−60.3275	−2.25612
$716$	−11.0554	−0.413161
$717$	−3.87901	−0.144864
$718$	−14.6789	−0.547812
$719$	14.5549	0.542807	0.271404	−	0.962466i	$-0.412512\pi$
$719$	14.5549	0.542807	0.271404	+	0.962466i	$0.412512\pi$
$720$	5.31286	0.197999
$721$	−0.832460	−0.0310024
$722$	−18.9999	−0.707104
$723$	−2.05321	−0.0763598
$724$	19.4391	0.722450
$725$	−9.93229	−0.368876
$726$	−2.95689	−0.109741
$727$	−46.0031	−1.70616	−0.853081	−	0.521778i	$-0.825269\pi$
$727$	−46.0031	−1.70616	−0.853081	+	0.521778i	$0.825269\pi$
$728$	2.85268	0.105728
$729$	−25.8190	−0.956259
$730$	9.16188	0.339096
$731$	1.92729	0.0712835
$732$	−0.628475	−0.0232291
$733$	−6.09097	−0.224975	−0.112488	−	0.993653i	$-0.535882\pi$
$733$	−6.09097	−0.224975	−0.112488	+	0.993653i	$0.535882\pi$
$734$	3.49969	0.129176
$735$	−1.79424	−0.0661817
$736$	1.00000	0.0368605
$737$	71.3181	2.62704
$738$	−23.1381	−0.851723
$739$	−41.3579	−1.52137	−0.760687	−	0.649119i	$-0.775138\pi$
$739$	−41.3579	−1.52137	−0.760687	+	0.649119i	$0.775138\pi$
$740$	17.9803	0.660969
$741$	−0.00775103	−0.000284741 0
$742$	6.64499	0.243945
$743$	−5.42144	−0.198893	−0.0994467	−	0.995043i	$-0.531707\pi$
$743$	−5.42144	−0.198893	−0.0994467	+	0.995043i	$0.531707\pi$
$744$	−1.06996	−0.0392267
$745$	13.1712	0.482554
$746$	−16.8226	−0.615920
$747$	−16.3664	−0.598815
$748$	−35.4902	−1.29765
$749$	1.46195	0.0534186
$750$	−1.80413	−0.0658775
$751$	7.97790	0.291118	0.145559	−	0.989350i	$-0.453502\pi$
$751$	7.97790	0.291118	0.145559	+	0.989350i	$0.453502\pi$
$752$	−2.07372	−0.0756207
$753$	−2.52388	−0.0919753
$754$	−33.2310	−1.21020
$755$	−1.48585	−0.0540756
$756$	−0.416072	−0.0151324
$757$	−6.15317	−0.223641	−0.111820	−	0.993728i	$-0.535668\pi$
$757$	−6.15317	−0.223641	−0.111820	+	0.993728i	$0.535668\pi$
$758$	21.6089	0.784869
$759$	0.825030	0.0299467
$760$	0.0153324	0.000556163 0
$761$	−22.2439	−0.806341	−0.403170	−	0.915125i	$-0.632092\pi$
$761$	−22.2439	−0.806341	−0.403170	+	0.915125i	$0.632092\pi$
$762$	0.423551	0.0153436
$763$	−5.27762	−0.191063
$764$	−24.2837	−0.878553
$765$	33.9019	1.22573
$766$	17.9231	0.647589
$767$	−43.7983	−1.58146
$768$	−0.148340	−0.00535274
$769$	−3.43291	−0.123794	−0.0618969	−	0.998083i	$-0.519715\pi$
$769$	−3.43291	−0.123794	−0.0618969	+	0.998083i	$0.519715\pi$
$770$	−4.65557	−0.167775
$771$	0.146881	0.00528981
$772$	−12.5283	−0.450902
$773$	−35.9613	−1.29344	−0.646719	−	0.762729i	$-0.723859\pi$
$773$	−35.9613	−1.29344	−0.646719	+	0.762729i	$0.723859\pi$
$774$	−0.899448	−0.0323300
$775$	−13.1073	−0.470830
$776$	7.46944	0.268137
$777$	−0.701464	−0.0251649
$778$	20.3594	0.729918
$779$	−0.0667740	−0.00239243
$780$	−1.60901	−0.0576119
$781$	−80.9566	−2.89685
$782$	6.38110	0.228188
$783$	4.84683	0.173212
$784$	−6.77985	−0.242138
$785$	−11.0850	−0.395639
$786$	−0.148340	−0.00529110
$787$	10.7593	0.383529	0.191765	−	0.981441i	$-0.438579\pi$
$787$	10.7593	0.383529	0.191765	+	0.981441i	$0.438579\pi$
$788$	10.5595	0.376166
$789$	−1.11301	−0.0396242
$790$	−21.2022	−0.754339
$791$	−6.50312	−0.231224
$792$	16.5629	0.588538
$793$	−25.7590	−0.914730
$794$	13.2416	0.469928
$795$	−3.74800	−0.132928
$796$	3.47750	0.123257
$797$	48.6502	1.72328	0.861640	−	0.507520i	$-0.169438\pi$
$797$	48.6502	1.72328	0.861640	+	0.507520i	$0.169438\pi$
$798$	−0.000598160 0	−2.11746e−5 0
$799$	−13.2326	−0.468136
$800$	−1.81720	−0.0642479
$801$	−40.9964	−1.44854
$802$	14.7355	0.520328
$803$	28.5623	1.00794
$804$	1.90215	0.0670835
$805$	0.837067	0.0295027
$806$	−43.8540	−1.54469
$807$	2.61219	0.0919536
$808$	−1.94348	−0.0683714
$809$	−16.9026	−0.594265	−0.297133	−	0.954836i	$-0.596030\pi$
$809$	−16.9026	−0.594265	−0.297133	+	0.954836i	$0.596030\pi$
$810$	−15.7039	−0.551779
$811$	15.8162	0.555384	0.277692	−	0.960670i	$-0.410431\pi$
$811$	15.8162	0.555384	0.277692	+	0.960670i	$0.410431\pi$
$812$	−2.56449	−0.0899960
$813$	−3.92501	−0.137656
$814$	56.0539	1.96469
$815$	0.232654	0.00814951
$816$	−0.946570	−0.0331366
$817$	−0.00259571	−9.08125e−5 0
$818$	−3.92326	−0.137174
$819$	−8.49528	−0.296849
$820$	−13.8614	−0.484061
$821$	23.5606	0.822272	0.411136	−	0.911574i	$-0.365132\pi$
$821$	23.5606	0.822272	0.411136	+	0.911574i	$0.365132\pi$
$822$	2.34574	0.0818170
$823$	−55.9907	−1.95171	−0.975857	−	0.218409i	$-0.929913\pi$
$823$	−55.9907	−1.95171	−0.975857	+	0.218409i	$0.929913\pi$
$824$	1.77422	0.0618079
$825$	−1.49925	−0.0521971
$826$	−3.37998	−0.117605
$827$	−40.7601	−1.41737	−0.708684	−	0.705526i	$-0.750711\pi$
$827$	−40.7601	−1.41737	−0.708684	+	0.705526i	$0.750711\pi$
$828$	−2.97800	−0.103492
$829$	13.4187	0.466050	0.233025	−	0.972471i	$-0.425138\pi$
$829$	13.4187	0.466050	0.233025	+	0.972471i	$0.425138\pi$
$830$	−9.80469	−0.340326
$831$	−2.50591	−0.0869292
$832$	−6.07992	−0.210783
$833$	−43.2630	−1.49897
$834$	−1.17892	−0.0408226
$835$	−21.0943	−0.729998
$836$	0.0477989	0.00165316
$837$	6.39622	0.221086
$838$	27.5155	0.950507
$839$	−43.1487	−1.48966	−0.744830	−	0.667255i	$-0.767469\pi$
$839$	−43.1487	−1.48966	−0.744830	+	0.667255i	$0.767469\pi$
$840$	−0.124170	−0.00428428
$841$	0.873864	0.0301332
$842$	−6.57783	−0.226687
$843$	2.48736	0.0856694
$844$	1.40838	0.0484783
$845$	−42.7553	−1.47083
$846$	6.17552	0.212319
$847$	−9.35264	−0.321361
$848$	−14.1624	−0.486340
$849$	4.16223	0.142847
$850$	−11.5958	−0.397732
$851$	−10.0784	−0.345484
$852$	−2.15922	−0.0739735
$853$	−12.8872	−0.441251	−0.220625	−	0.975359i	$-0.570810\pi$
$853$	−12.8872	−0.441251	−0.220625	+	0.975359i	$0.570810\pi$
$854$	−1.98787	−0.0680234
$855$	−0.0456597	−0.00156153
$856$	−3.11586	−0.106498
$857$	−36.4317	−1.24448	−0.622241	−	0.782825i	$-0.713778\pi$
$857$	−36.4317	−1.24448	−0.622241	+	0.782825i	$0.713778\pi$
$858$	−5.01612	−0.171247
$859$	44.3248	1.51234	0.756171	−	0.654374i	$-0.227068\pi$
$859$	44.3248	1.51234	0.756171	+	0.654374i	$0.227068\pi$
$860$	−0.538836	−0.0183742
$861$	0.540773	0.0184295
$862$	21.6326	0.736811
$863$	20.7949	0.707867	0.353934	−	0.935271i	$-0.384844\pi$
$863$	20.7949	0.707867	0.353934	+	0.935271i	$0.384844\pi$
$864$	0.886773	0.0301686
$865$	9.03287	0.307127
$866$	−26.4662	−0.899358
$867$	−3.51839	−0.119491
$868$	−3.38428	−0.114870
$869$	−66.0980	−2.24222
$870$	1.44646	0.0490396
$871$	77.9624	2.64165
$872$	11.2482	0.380911
$873$	−22.2440	−0.752844
$874$	−0.00859418	−0.000290703 0
$875$	−5.70646	−0.192913
$876$	0.761793	0.0257386
$877$	48.0132	1.62129	0.810646	−	0.585537i	$-0.199116\pi$
$877$	48.0132	1.62129	0.810646	+	0.585537i	$0.199116\pi$
$878$	29.8726	1.00815
$879$	4.10664	0.138514
$880$	9.92241	0.334484
$881$	−49.4764	−1.66690	−0.833451	−	0.552594i	$-0.813638\pi$
$881$	−49.4764	−1.66690	−0.833451	+	0.552594i	$0.813638\pi$
$882$	20.1904	0.679845
$883$	7.70200	0.259193	0.129596	−	0.991567i	$-0.458632\pi$
$883$	7.70200	0.259193	0.129596	+	0.991567i	$0.458632\pi$
$884$	−38.7966	−1.30487
$885$	1.90643	0.0640839
$886$	−12.0747	−0.405659
$887$	11.2613	0.378116	0.189058	−	0.981966i	$-0.439457\pi$
$887$	11.2613	0.378116	0.189058	+	0.981966i	$0.439457\pi$
$888$	1.49503	0.0501699
$889$	1.33969	0.0449318
$890$	−24.5599	−0.823249
$891$	−48.9571	−1.64013
$892$	−23.9442	−0.801710
$893$	0.0178219	0.000596387 0
$894$	1.09516	0.0366275
$895$	19.7233	0.659278
$896$	−0.469198	−0.0156748
$897$	0.901893	0.0301133
$898$	−41.2702	−1.37720
$899$	39.4236	1.31485
$900$	5.41163	0.180388
$901$	−90.3721	−3.01073
$902$	−43.2131	−1.43884
$903$	0.0210216	0.000699553 0
$904$	13.8601	0.460979
$905$	−34.6802	−1.15281
$906$	−0.123546	−0.00410453
$907$	−7.79615	−0.258867	−0.129434	−	0.991588i	$-0.541316\pi$
$907$	−7.79615	−0.258867	−0.129434	+	0.991588i	$0.541316\pi$
$908$	−6.94462	−0.230465
$909$	5.78767	0.191965
$910$	−5.08930	−0.168709
$911$	−31.6806	−1.04962	−0.524812	−	0.851218i	$-0.675864\pi$
$911$	−31.6806	−1.04962	−0.524812	+	0.851218i	$0.675864\pi$
$912$	0.00127486	4.22147e−5 0
$913$	−30.5663	−1.01160
$914$	37.0077	1.22410
$915$	1.12122	0.0370665
$916$	1.83722	0.0607035
$917$	−0.469198	−0.0154943
$918$	5.65859	0.186761
$919$	41.2027	1.35915	0.679576	−	0.733605i	$-0.262164\pi$
$919$	41.2027	1.35915	0.679576	+	0.733605i	$0.262164\pi$
$920$	−1.78404	−0.0588180
$921$	1.00473	0.0331071
$922$	−0.156874	−0.00516637
$923$	−88.4987	−2.91297
$924$	−0.387102	−0.0127347
$925$	18.3146	0.602179
$926$	40.5625	1.33297
$927$	−5.28362	−0.173537
$928$	5.46570	0.179420
$929$	20.9460	0.687215	0.343608	−	0.939113i	$-0.388351\pi$
$929$	20.9460	0.687215	0.343608	+	0.939113i	$0.388351\pi$
$930$	1.90885	0.0625937
$931$	0.0582673	0.00190963
$932$	1.75040	0.0573362
$933$	1.07606	0.0352285
$934$	17.4843	0.572103
$935$	63.3159	2.07065
$936$	18.1060	0.591812
$937$	−18.7396	−0.612196	−0.306098	−	0.952000i	$-0.599023\pi$
$937$	−18.7396	−0.612196	−0.306098	+	0.952000i	$0.599023\pi$
$938$	6.01649	0.196445
$939$	1.56490	0.0510686
$940$	3.69959	0.120667
$941$	31.6761	1.03261	0.516306	−	0.856404i	$-0.327307\pi$
$941$	31.6761	1.03261	0.516306	+	0.856404i	$0.327307\pi$
$942$	−0.921693	−0.0300304
$943$	7.76967	0.253015
$944$	7.20376	0.234462
$945$	0.742288	0.0241466
$946$	−1.67983	−0.0546159
$947$	34.9492	1.13569	0.567847	−	0.823134i	$-0.307776\pi$
$947$	34.9492	1.13569	0.567847	+	0.823134i	$0.307776\pi$
$948$	−1.76292	−0.0572570
$949$	31.2232	1.01355
$950$	0.0156174	0.000506695 0
$951$	0.407881	0.0132265
$952$	−2.99400	−0.0970361
$953$	33.5699	1.08744	0.543718	−	0.839268i	$-0.317016\pi$
$953$	33.5699	1.08744	0.543718	+	0.839268i	$0.317016\pi$
$954$	42.1757	1.36549
$955$	43.3230	1.40190
$956$	26.1495	0.845736
$957$	4.50937	0.145767
$958$	−32.2922	−1.04331
$959$	7.41956	0.239590
$960$	0.264644	0.00854133
$961$	21.0262	0.678265
$962$	61.2760	1.97562
$963$	9.27900	0.299012
$964$	13.8413	0.445799
$965$	22.3509	0.719501
$966$	0.0696005	0.00223936
$967$	−0.0989303	−0.00318138	−0.00159069	−	0.999999i	$-0.500506\pi$
$967$	−0.0989303	−0.00318138	−0.00159069	+	0.999999i	$0.500506\pi$
$968$	19.9333	0.640679
$969$	0.00813499	0.000261334 0
$970$	−13.3258	−0.427865
$971$	27.9271	0.896223	0.448112	−	0.893978i	$-0.352097\pi$
$971$	27.9271	0.896223	0.448112	+	0.893978i	$0.352097\pi$
$972$	−3.96607	−0.127212
$973$	−3.72891	−0.119543
$974$	−2.43705	−0.0780881
$975$	−1.63892	−0.0524875
$976$	4.23674	0.135615
$977$	28.9948	0.927626	0.463813	−	0.885933i	$-0.346481\pi$
$977$	28.9948	0.927626	0.463813	+	0.885933i	$0.346481\pi$
$978$	0.0193447	0.000618576 0
$979$	−76.5658	−2.44705
$980$	12.0955	0.386377
$981$	−33.4970	−1.06948
$982$	−28.5275	−0.910348
$983$	−18.9102	−0.603141	−0.301571	−	0.953444i	$-0.597511\pi$
$983$	−18.9102	−0.603141	−0.301571	+	0.953444i	$0.597511\pi$
$984$	−1.15255	−0.0367419
$985$	−18.8385	−0.600246
$986$	34.8772	1.11072
$987$	−0.144332	−0.00459413
$988$	0.0522520	0.00166236
$989$	0.302031	0.00960404
$990$	−29.5489	−0.939126
$991$	38.5970	1.22607	0.613036	−	0.790055i	$-0.289948\pi$
$991$	38.5970	1.22607	0.613036	+	0.790055i	$0.289948\pi$
$992$	7.21292	0.229010
$993$	0.543430	0.0172452
$994$	−6.82959	−0.216622
$995$	−6.20400	−0.196680
$996$	−0.815241	−0.0258319
$997$	50.0352	1.58463	0.792315	−	0.610112i	$-0.208875\pi$
$997$	50.0352	1.58463	0.792315	+	0.610112i	$0.208875\pi$
$998$	40.8138	1.29194
$999$	−8.93727	−0.282763

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.m.1.20	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.m.1.20	✓	41	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.148340 q^{3} +1.00000 q^{4} -1.78404 q^{5} -0.148340 q^{6} -0.469198 q^{7} +1.00000 q^{8} -2.97800 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.148340 q^{3} +1.00000 q^{4} -1.78404 q^{5} -0.148340 q^{6} -0.469198 q^{7} +1.00000 q^{8} -2.97800 q^{9} -1.78404 q^{10} -5.56177 q^{11} -0.148340 q^{12} -6.07992 q^{13} -0.469198 q^{14} +0.264644 q^{15} +1.00000 q^{16} +6.38110 q^{17} -2.97800 q^{18} -0.00859418 q^{19} -1.78404 q^{20} +0.0696005 q^{21} -5.56177 q^{22} +1.00000 q^{23} -0.148340 q^{24} -1.81720 q^{25} -6.07992 q^{26} +0.886773 q^{27} -0.469198 q^{28} +5.46570 q^{29} +0.264644 q^{30} +7.21292 q^{31} +1.00000 q^{32} +0.825030 q^{33} +6.38110 q^{34} +0.837067 q^{35} -2.97800 q^{36} -10.0784 q^{37} -0.00859418 q^{38} +0.901893 q^{39} -1.78404 q^{40} +7.76967 q^{41} +0.0696005 q^{42} +0.302031 q^{43} -5.56177 q^{44} +5.31286 q^{45} +1.00000 q^{46} -2.07372 q^{47} -0.148340 q^{48} -6.77985 q^{49} -1.81720 q^{50} -0.946570 q^{51} -6.07992 q^{52} -14.1624 q^{53} +0.886773 q^{54} +9.92241 q^{55} -0.469198 q^{56} +0.00127486 q^{57} +5.46570 q^{58} +7.20376 q^{59} +0.264644 q^{60} +4.23674 q^{61} +7.21292 q^{62} +1.39727 q^{63} +1.00000 q^{64} +10.8468 q^{65} +0.825030 q^{66} -12.8229 q^{67} +6.38110 q^{68} -0.148340 q^{69} +0.837067 q^{70} +14.5559 q^{71} -2.97800 q^{72} -5.13547 q^{73} -10.0784 q^{74} +0.269563 q^{75} -0.00859418 q^{76} +2.60957 q^{77} +0.901893 q^{78} +11.8844 q^{79} -1.78404 q^{80} +8.80244 q^{81} +7.76967 q^{82} +5.49578 q^{83} +0.0696005 q^{84} -11.3841 q^{85} +0.302031 q^{86} -0.810779 q^{87} -5.56177 q^{88} +13.7665 q^{89} +5.31286 q^{90} +2.85268 q^{91} +1.00000 q^{92} -1.06996 q^{93} -2.07372 q^{94} +0.0153324 q^{95} -0.148340 q^{96} +7.46944 q^{97} -6.77985 q^{98} +16.5629 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9}+O(q^{10}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9} + 9 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 12 q^{14} + 10 q^{15} + 41 q^{16} + 10 q^{17} + 63 q^{18} + 16 q^{19} + 9 q^{20} + 16 q^{21} + 4 q^{22} + 41 q^{23} + 4 q^{24} + 76 q^{25} + 16 q^{26} + 7 q^{27} + 12 q^{28} + 28 q^{29} + 10 q^{30} + 25 q^{31} + 41 q^{32} + 5 q^{33} + 10 q^{34} + 4 q^{35} + 63 q^{36} + 26 q^{37} + 16 q^{38} + 50 q^{39} + 9 q^{40} + 27 q^{41} + 16 q^{42} + 12 q^{43} + 4 q^{44} + 44 q^{45} + 41 q^{46} + 18 q^{47} + 4 q^{48} + 87 q^{49} + 76 q^{50} + 24 q^{51} + 16 q^{52} + 63 q^{53} + 7 q^{54} + 18 q^{55} + 12 q^{56} - 12 q^{57} + 28 q^{58} + 33 q^{59} + 10 q^{60} + 24 q^{61} + 25 q^{62} + 48 q^{63} + 41 q^{64} + 21 q^{65} + 5 q^{66} - 9 q^{67} + 10 q^{68} + 4 q^{69} + 4 q^{70} + 36 q^{71} + 63 q^{72} + 36 q^{73} + 26 q^{74} + 6 q^{75} + 16 q^{76} + 48 q^{77} + 50 q^{78} + 51 q^{79} + 9 q^{80} + 149 q^{81} + 27 q^{82} - 27 q^{83} + 16 q^{84} + 52 q^{85} + 12 q^{86} - 3 q^{87} + 4 q^{88} + 68 q^{89} + 44 q^{90} + 22 q^{91} + 41 q^{92} + 45 q^{93} + 18 q^{94} + 46 q^{95} + 4 q^{96} + 16 q^{97} + 87 q^{98} - 10 q^{99}+O(q^{100}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9 + 9 * q^10 + 4 * q^11 + 4 * q^12 + 16 * q^13 + 12 * q^14 + 10 * q^15 + 41 * q^16 + 10 * q^17 + 63 * q^18 + 16 * q^19 + 9 * q^20 + 16 * q^21 + 4 * q^22 + 41 * q^23 + 4 * q^24 + 76 * q^25 + 16 * q^26 + 7 * q^27 + 12 * q^28 + 28 * q^29 + 10 * q^30 + 25 * q^31 + 41 * q^32 + 5 * q^33 + 10 * q^34 + 4 * q^35 + 63 * q^36 + 26 * q^37 + 16 * q^38 + 50 * q^39 + 9 * q^40 + 27 * q^41 + 16 * q^42 + 12 * q^43 + 4 * q^44 + 44 * q^45 + 41 * q^46 + 18 * q^47 + 4 * q^48 + 87 * q^49 + 76 * q^50 + 24 * q^51 + 16 * q^52 + 63 * q^53 + 7 * q^54 + 18 * q^55 + 12 * q^56 - 12 * q^57 + 28 * q^58 + 33 * q^59 + 10 * q^60 + 24 * q^61 + 25 * q^62 + 48 * q^63 + 41 * q^64 + 21 * q^65 + 5 * q^66 - 9 * q^67 + 10 * q^68 + 4 * q^69 + 4 * q^70 + 36 * q^71 + 63 * q^72 + 36 * q^73 + 26 * q^74 + 6 * q^75 + 16 * q^76 + 48 * q^77 + 50 * q^78 + 51 * q^79 + 9 * q^80 + 149 * q^81 + 27 * q^82 - 27 * q^83 + 16 * q^84 + 52 * q^85 + 12 * q^86 - 3 * q^87 + 4 * q^88 + 68 * q^89 + 44 * q^90 + 22 * q^91 + 41 * q^92 + 45 * q^93 + 18 * q^94 + 46 * q^95 + 4 * q^96 + 16 * q^97 + 87 * q^98 - 10 * q^99

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