LMFDB - Embedded newform 6026.2.a.g.1.12

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:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.775060 q^{3} +1.00000 q^{4} +0.913280 q^{5} +0.775060 q^{6} -1.54834 q^{7} +1.00000 q^{8} -2.39928 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.775060 q^{3} +1.00000 q^{4} +0.913280 q^{5} +0.775060 q^{6} -1.54834 q^{7} +1.00000 q^{8} -2.39928 q^{9} +0.913280 q^{10} -0.0230193 q^{11} +0.775060 q^{12} -0.791216 q^{13} -1.54834 q^{14} +0.707846 q^{15} +1.00000 q^{16} +1.96957 q^{17} -2.39928 q^{18} -6.85395 q^{19} +0.913280 q^{20} -1.20006 q^{21} -0.0230193 q^{22} -1.00000 q^{23} +0.775060 q^{24} -4.16592 q^{25} -0.791216 q^{26} -4.18477 q^{27} -1.54834 q^{28} -0.310696 q^{29} +0.707846 q^{30} +6.80832 q^{31} +1.00000 q^{32} -0.0178413 q^{33} +1.96957 q^{34} -1.41407 q^{35} -2.39928 q^{36} +7.76351 q^{37} -6.85395 q^{38} -0.613239 q^{39} +0.913280 q^{40} -5.60947 q^{41} -1.20006 q^{42} -7.38357 q^{43} -0.0230193 q^{44} -2.19122 q^{45} -1.00000 q^{46} +6.94631 q^{47} +0.775060 q^{48} -4.60264 q^{49} -4.16592 q^{50} +1.52653 q^{51} -0.791216 q^{52} -11.3719 q^{53} -4.18477 q^{54} -0.0210231 q^{55} -1.54834 q^{56} -5.31222 q^{57} -0.310696 q^{58} -2.96974 q^{59} +0.707846 q^{60} +1.46375 q^{61} +6.80832 q^{62} +3.71490 q^{63} +1.00000 q^{64} -0.722602 q^{65} -0.0178413 q^{66} -2.84855 q^{67} +1.96957 q^{68} -0.775060 q^{69} -1.41407 q^{70} +3.85538 q^{71} -2.39928 q^{72} -5.74271 q^{73} +7.76351 q^{74} -3.22884 q^{75} -6.85395 q^{76} +0.0356417 q^{77} -0.613239 q^{78} -16.9635 q^{79} +0.913280 q^{80} +3.95441 q^{81} -5.60947 q^{82} -7.56884 q^{83} -1.20006 q^{84} +1.79877 q^{85} -7.38357 q^{86} -0.240808 q^{87} -0.0230193 q^{88} -14.2610 q^{89} -2.19122 q^{90} +1.22507 q^{91} -1.00000 q^{92} +5.27685 q^{93} +6.94631 q^{94} -6.25958 q^{95} +0.775060 q^{96} +0.312256 q^{97} -4.60264 q^{98} +0.0552298 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) $ 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9} - 13 q^{10} - 4 q^{11} - 4 q^{13} - 18 q^{14} - 16 q^{15} + 21 q^{16} - 12 q^{17} + 7 q^{18} - 18 q^{19} - 13 q^{20} - 24 q^{21} - 4 q^{22} - 21 q^{23} + 2 q^{25} - 4 q^{26} - 9 q^{27} - 18 q^{28} - 16 q^{29} - 16 q^{30} - 7 q^{31} + 21 q^{32} - 15 q^{33} - 12 q^{34} + 7 q^{36} - 44 q^{37} - 18 q^{38} - 14 q^{39} - 13 q^{40} - 23 q^{41} - 24 q^{42} - 18 q^{43} - 4 q^{44} - 36 q^{45} - 21 q^{46} + 2 q^{47} - 13 q^{49} + 2 q^{50} - 26 q^{51} - 4 q^{52} - 39 q^{53} - 9 q^{54} - 32 q^{55} - 18 q^{56} - 22 q^{57} - 16 q^{58} - 27 q^{59} - 16 q^{60} - 34 q^{61} - 7 q^{62} - 28 q^{63} + 21 q^{64} - 25 q^{65} - 15 q^{66} - 19 q^{67} - 12 q^{68} - 24 q^{71} + 7 q^{72} - 8 q^{73} - 44 q^{74} + 50 q^{75} - 18 q^{76} - 16 q^{77} - 14 q^{78} - 27 q^{79} - 13 q^{80} + 33 q^{81} - 23 q^{82} + 7 q^{83} - 24 q^{84} - 22 q^{85} - 18 q^{86} - 15 q^{87} - 4 q^{88} - 12 q^{89} - 36 q^{90} - 20 q^{91} - 21 q^{92} - 43 q^{93} + 2 q^{94} - 14 q^{95} - 52 q^{97} - 13 q^{98} - 30 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9 - 13 * q^10 - 4 * q^11 - 4 * q^13 - 18 * q^14 - 16 * q^15 + 21 * q^16 - 12 * q^17 + 7 * q^18 - 18 * q^19 - 13 * q^20 - 24 * q^21 - 4 * q^22 - 21 * q^23 + 2 * q^25 - 4 * q^26 - 9 * q^27 - 18 * q^28 - 16 * q^29 - 16 * q^30 - 7 * q^31 + 21 * q^32 - 15 * q^33 - 12 * q^34 + 7 * q^36 - 44 * q^37 - 18 * q^38 - 14 * q^39 - 13 * q^40 - 23 * q^41 - 24 * q^42 - 18 * q^43 - 4 * q^44 - 36 * q^45 - 21 * q^46 + 2 * q^47 - 13 * q^49 + 2 * q^50 - 26 * q^51 - 4 * q^52 - 39 * q^53 - 9 * q^54 - 32 * q^55 - 18 * q^56 - 22 * q^57 - 16 * q^58 - 27 * q^59 - 16 * q^60 - 34 * q^61 - 7 * q^62 - 28 * q^63 + 21 * q^64 - 25 * q^65 - 15 * q^66 - 19 * q^67 - 12 * q^68 - 24 * q^71 + 7 * q^72 - 8 * q^73 - 44 * q^74 + 50 * q^75 - 18 * q^76 - 16 * q^77 - 14 * q^78 - 27 * q^79 - 13 * q^80 + 33 * q^81 - 23 * q^82 + 7 * q^83 - 24 * q^84 - 22 * q^85 - 18 * q^86 - 15 * q^87 - 4 * q^88 - 12 * q^89 - 36 * q^90 - 20 * q^91 - 21 * q^92 - 43 * q^93 + 2 * q^94 - 14 * q^95 - 52 * q^97 - 13 * q^98 - 30 * 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
$3$	0.775060	0.447481	0.223740	−	0.974649i	$-0.428173\pi$
$3$	0.775060	0.447481	0.223740	+	0.974649i	$0.428173\pi$
$4$	1.00000	0.500000
$5$	0.913280	0.408431	0.204216	−	0.978926i	$-0.434536\pi$
$5$	0.913280	0.408431	0.204216	+	0.978926i	$0.434536\pi$
$6$	0.775060	0.316417
$7$	−1.54834	−0.585217	−0.292609	−	0.956232i	$-0.594523\pi$
$7$	−1.54834	−0.585217	−0.292609	+	0.956232i	$0.594523\pi$
$8$	1.00000	0.353553
$9$	−2.39928	−0.799761
$10$	0.913280	0.288804
$11$	−0.0230193	−0.00694058	−0.00347029	−	0.999994i	$-0.501105\pi$
$11$	−0.0230193	−0.00694058	−0.00347029	+	0.999994i	$0.501105\pi$
$12$	0.775060	0.223740
$13$	−0.791216	−0.219444	−0.109722	−	0.993962i	$-0.534996\pi$
$13$	−0.791216	−0.219444	−0.109722	+	0.993962i	$0.534996\pi$
$14$	−1.54834	−0.413811
$15$	0.707846	0.182765
$16$	1.00000	0.250000
$17$	1.96957	0.477690	0.238845	−	0.971058i	$-0.423231\pi$
$17$	1.96957	0.477690	0.238845	+	0.971058i	$0.423231\pi$
$18$	−2.39928	−0.565516
$19$	−6.85395	−1.57240	−0.786202	−	0.617969i	$-0.787956\pi$
$19$	−6.85395	−1.57240	−0.786202	+	0.617969i	$0.787956\pi$
$20$	0.913280	0.204216
$21$	−1.20006	−0.261874
$22$	−0.0230193	−0.00490773
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0.775060	0.158208
$25$	−4.16592	−0.833184
$26$	−0.791216	−0.155170
$27$	−4.18477	−0.805359
$28$	−1.54834	−0.292609
$29$	−0.310696	−0.0576947	−0.0288474	−	0.999584i	$-0.509184\pi$
$29$	−0.310696	−0.0576947	−0.0288474	+	0.999584i	$0.509184\pi$
$30$	0.707846	0.129234
$31$	6.80832	1.22281	0.611405	−	0.791318i	$-0.290605\pi$
$31$	6.80832	1.22281	0.611405	+	0.791318i	$0.290605\pi$
$32$	1.00000	0.176777
$33$	−0.0178413	−0.00310578
$34$	1.96957	0.337778
$35$	−1.41407	−0.239021
$36$	−2.39928	−0.399880
$37$	7.76351	1.27631	0.638157	−	0.769907i	$-0.279697\pi$
$37$	7.76351	1.27631	0.638157	+	0.769907i	$0.279697\pi$
$38$	−6.85395	−1.11186
$39$	−0.613239	−0.0981969
$40$	0.913280	0.144402
$41$	−5.60947	−0.876053	−0.438026	−	0.898962i	$-0.644322\pi$
$41$	−5.60947	−0.876053	−0.438026	+	0.898962i	$0.644322\pi$
$42$	−1.20006	−0.185173
$43$	−7.38357	−1.12598	−0.562992	−	0.826462i	$-0.690350\pi$
$43$	−7.38357	−1.12598	−0.562992	+	0.826462i	$0.690350\pi$
$44$	−0.0230193	−0.00347029
$45$	−2.19122	−0.326647
$46$	−1.00000	−0.147442
$47$	6.94631	1.01322	0.506612	−	0.862174i	$-0.330898\pi$
$47$	6.94631	1.01322	0.506612	+	0.862174i	$0.330898\pi$
$48$	0.775060	0.111870
$49$	−4.60264	−0.657521
$50$	−4.16592	−0.589150
$51$	1.52653	0.213757
$52$	−0.791216	−0.109722
$53$	−11.3719	−1.56206	−0.781028	−	0.624496i	$-0.785305\pi$
$53$	−11.3719	−1.56206	−0.781028	+	0.624496i	$0.785305\pi$
$54$	−4.18477	−0.569474
$55$	−0.0210231	−0.00283475
$56$	−1.54834	−0.206906
$57$	−5.31222	−0.703621
$58$	−0.310696	−0.0407963
$59$	−2.96974	−0.386627	−0.193313	−	0.981137i	$-0.561923\pi$
$59$	−2.96974	−0.386627	−0.193313	+	0.981137i	$0.561923\pi$
$60$	0.707846	0.0913826
$61$	1.46375	0.187414	0.0937071	−	0.995600i	$-0.470128\pi$
$61$	1.46375	0.187414	0.0937071	+	0.995600i	$0.470128\pi$
$62$	6.80832	0.864657
$63$	3.71490	0.468034
$64$	1.00000	0.125000
$65$	−0.722602	−0.0896277
$66$	−0.0178413	−0.00219611
$67$	−2.84855	−0.348006	−0.174003	−	0.984745i	$-0.555670\pi$
$67$	−2.84855	−0.348006	−0.174003	+	0.984745i	$0.555670\pi$
$68$	1.96957	0.238845
$69$	−0.775060	−0.0933062
$70$	−1.41407	−0.169013
$71$	3.85538	0.457550	0.228775	−	0.973479i	$-0.426528\pi$
$71$	3.85538	0.457550	0.228775	+	0.973479i	$0.426528\pi$
$72$	−2.39928	−0.282758
$73$	−5.74271	−0.672133	−0.336067	−	0.941838i	$-0.609097\pi$
$73$	−5.74271	−0.672133	−0.336067	+	0.941838i	$0.609097\pi$
$74$	7.76351	0.902490
$75$	−3.22884	−0.372834
$76$	−6.85395	−0.786202
$77$	0.0356417	0.00406175
$78$	−0.613239	−0.0694357
$79$	−16.9635	−1.90854	−0.954271	−	0.298943i	$-0.903366\pi$
$79$	−16.9635	−1.90854	−0.954271	+	0.298943i	$0.903366\pi$
$80$	0.913280	0.102108
$81$	3.95441	0.439378
$82$	−5.60947	−0.619463
$83$	−7.56884	−0.830789	−0.415394	−	0.909641i	$-0.636356\pi$
$83$	−7.56884	−0.830789	−0.415394	+	0.909641i	$0.636356\pi$
$84$	−1.20006	−0.130937
$85$	1.79877	0.195103
$86$	−7.38357	−0.796191
$87$	−0.240808	−0.0258173
$88$	−0.0230193	−0.00245386
$89$	−14.2610	−1.51166	−0.755832	−	0.654765i	$-0.772767\pi$
$89$	−14.2610	−1.51166	−0.755832	+	0.654765i	$0.772767\pi$
$90$	−2.19122	−0.230975
$91$	1.22507	0.128422
$92$	−1.00000	−0.104257
$93$	5.27685	0.547184
$94$	6.94631	0.716457
$95$	−6.25958	−0.642219
$96$	0.775060	0.0791042
$97$	0.312256	0.0317048	0.0158524	−	0.999874i	$-0.494954\pi$
$97$	0.312256	0.0317048	0.0158524	+	0.999874i	$0.494954\pi$
$98$	−4.60264	−0.464937
$99$	0.0552298	0.00555080
$100$	−4.16592	−0.416592
$101$	−5.29903	−0.527273	−0.263637	−	0.964622i	$-0.584922\pi$
$101$	−5.29903	−0.527273	−0.263637	+	0.964622i	$0.584922\pi$
$102$	1.52653	0.151149
$103$	10.3529	1.02010	0.510050	−	0.860145i	$-0.329627\pi$
$103$	10.3529	1.02010	0.510050	+	0.860145i	$0.329627\pi$
$104$	−0.791216	−0.0775851
$105$	−1.09599	−0.106957
$106$	−11.3719	−1.10454
$107$	−5.27682	−0.510129	−0.255065	−	0.966924i	$-0.582097\pi$
$107$	−5.27682	−0.510129	−0.255065	+	0.966924i	$0.582097\pi$
$108$	−4.18477	−0.402679
$109$	17.0584	1.63390	0.816951	−	0.576707i	$-0.195663\pi$
$109$	17.0584	1.63390	0.816951	+	0.576707i	$0.195663\pi$
$110$	−0.0210231	−0.00200447
$111$	6.01718	0.571126
$112$	−1.54834	−0.146304
$113$	11.0623	1.04066	0.520329	−	0.853966i	$-0.325809\pi$
$113$	11.0623	1.04066	0.520329	+	0.853966i	$0.325809\pi$
$114$	−5.31222	−0.497535
$115$	−0.913280	−0.0851638
$116$	−0.310696	−0.0288474
$117$	1.89835	0.175503
$118$	−2.96974	−0.273386
$119$	−3.04956	−0.279553
$120$	0.707846	0.0646172
$121$	−10.9995	−0.999952
$122$	1.46375	0.132522
$123$	−4.34768	−0.392017
$124$	6.80832	0.611405
$125$	−8.37105	−0.748729
$126$	3.71490	0.330950
$127$	−20.2094	−1.79329	−0.896645	−	0.442750i	$-0.854003\pi$
$127$	−20.2094	−1.79329	−0.896645	+	0.442750i	$0.854003\pi$
$128$	1.00000	0.0883883
$129$	−5.72271	−0.503856
$130$	−0.722602	−0.0633763
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−0.0178413	−0.00155289
$133$	10.6122	0.920199
$134$	−2.84855	−0.246077
$135$	−3.82186	−0.328934
$136$	1.96957	0.168889
$137$	−6.67887	−0.570614	−0.285307	−	0.958436i	$-0.592096\pi$
$137$	−6.67887	−0.570614	−0.285307	+	0.958436i	$0.592096\pi$
$138$	−0.775060	−0.0659775
$139$	−6.36928	−0.540235	−0.270118	−	0.962827i	$-0.587063\pi$
$139$	−6.36928	−0.540235	−0.270118	+	0.962827i	$0.587063\pi$
$140$	−1.41407	−0.119511
$141$	5.38380	0.453398
$142$	3.85538	0.323537
$143$	0.0182132	0.00152307
$144$	−2.39928	−0.199940
$145$	−0.283752	−0.0235643
$146$	−5.74271	−0.475270
$147$	−3.56732	−0.294228
$148$	7.76351	0.638157
$149$	5.22066	0.427693	0.213847	−	0.976867i	$-0.431401\pi$
$149$	5.22066	0.427693	0.213847	+	0.976867i	$0.431401\pi$
$150$	−3.22884	−0.263633
$151$	18.1974	1.48088	0.740440	−	0.672123i	$-0.234617\pi$
$151$	18.1974	1.48088	0.740440	+	0.672123i	$0.234617\pi$
$152$	−6.85395	−0.555929
$153$	−4.72555	−0.382038
$154$	0.0356417	0.00287209
$155$	6.21790	0.499434
$156$	−0.613239	−0.0490985
$157$	−12.4549	−0.994012	−0.497006	−	0.867747i	$-0.665567\pi$
$157$	−12.4549	−0.994012	−0.497006	+	0.867747i	$0.665567\pi$
$158$	−16.9635	−1.34954
$159$	−8.81393	−0.698990
$160$	0.913280	0.0722011
$161$	1.54834	0.122026
$162$	3.95441	0.310687
$163$	12.0727	0.945609	0.472805	−	0.881167i	$-0.343242\pi$
$163$	12.0727	0.945609	0.472805	+	0.881167i	$0.343242\pi$
$164$	−5.60947	−0.438026
$165$	−0.0162941	−0.00126850
$166$	−7.56884	−0.587456
$167$	15.2347	1.17890	0.589450	−	0.807805i	$-0.299345\pi$
$167$	15.2347	1.17890	0.589450	+	0.807805i	$0.299345\pi$
$168$	−1.20006	−0.0925863
$169$	−12.3740	−0.951844
$170$	1.79877	0.137959
$171$	16.4446	1.25755
$172$	−7.38357	−0.562992
$173$	−17.9825	−1.36718	−0.683591	−	0.729865i	$-0.739583\pi$
$173$	−17.9825	−1.36718	−0.683591	+	0.729865i	$0.739583\pi$
$174$	−0.240808	−0.0182556
$175$	6.45026	0.487594
$176$	−0.0230193	−0.00173514
$177$	−2.30172	−0.173008
$178$	−14.2610	−1.06891
$179$	−5.28481	−0.395005	−0.197502	−	0.980302i	$-0.563283\pi$
$179$	−5.28481	−0.395005	−0.197502	+	0.980302i	$0.563283\pi$
$180$	−2.19122	−0.163324
$181$	15.6855	1.16589	0.582946	−	0.812511i	$-0.301900\pi$
$181$	15.6855	1.16589	0.582946	+	0.812511i	$0.301900\pi$
$182$	1.22507	0.0908083
$183$	1.13449	0.0838642
$184$	−1.00000	−0.0737210
$185$	7.09026	0.521286
$186$	5.27685	0.386918
$187$	−0.0453380	−0.00331544
$188$	6.94631	0.506612
$189$	6.47944	0.471310
$190$	−6.25958	−0.454118
$191$	19.0585	1.37903	0.689514	−	0.724273i	$-0.257824\pi$
$191$	19.0585	1.37903	0.689514	+	0.724273i	$0.257824\pi$
$192$	0.775060	0.0559351
$193$	4.41122	0.317527	0.158763	−	0.987317i	$-0.449249\pi$
$193$	4.41122	0.317527	0.158763	+	0.987317i	$0.449249\pi$
$194$	0.312256	0.0224187
$195$	−0.560059	−0.0401067
$196$	−4.60264	−0.328760
$197$	4.27431	0.304532	0.152266	−	0.988340i	$-0.451343\pi$
$197$	4.27431	0.304532	0.152266	+	0.988340i	$0.451343\pi$
$198$	0.0552298	0.00392501
$199$	−12.6493	−0.896683	−0.448341	−	0.893862i	$-0.647985\pi$
$199$	−12.6493	−0.896683	−0.448341	+	0.893862i	$0.647985\pi$
$200$	−4.16592	−0.294575
$201$	−2.20780	−0.155726
$202$	−5.29903	−0.372838
$203$	0.481062	0.0337640
$204$	1.52653	0.106879
$205$	−5.12302	−0.357807
$206$	10.3529	0.721320
$207$	2.39928	0.166762
$208$	−0.791216	−0.0548610
$209$	0.157773	0.0109134
$210$	−1.09599	−0.0756303
$211$	15.2235	1.04803	0.524015	−	0.851709i	$-0.324434\pi$
$211$	15.2235	1.04803	0.524015	+	0.851709i	$0.324434\pi$
$212$	−11.3719	−0.781028
$213$	2.98815	0.204745
$214$	−5.27682	−0.360716
$215$	−6.74327	−0.459887
$216$	−4.18477	−0.284737
$217$	−10.5416	−0.715610
$218$	17.0584	1.15534
$219$	−4.45094	−0.300767
$220$	−0.0210231	−0.00141737
$221$	−1.55835	−0.104826
$222$	6.01718	0.403847
$223$	15.1547	1.01483	0.507416	−	0.861701i	$-0.330601\pi$
$223$	15.1547	1.01483	0.507416	+	0.861701i	$0.330601\pi$
$224$	−1.54834	−0.103453
$225$	9.99522	0.666348
$226$	11.0623	0.735856
$227$	−23.6392	−1.56899	−0.784495	−	0.620135i	$-0.787078\pi$
$227$	−23.6392	−1.56899	−0.784495	+	0.620135i	$0.787078\pi$
$228$	−5.31222	−0.351811
$229$	1.62497	0.107381	0.0536907	−	0.998558i	$-0.482902\pi$
$229$	1.62497	0.107381	0.0536907	+	0.998558i	$0.482902\pi$
$230$	−0.913280	−0.0602199
$231$	0.0276244	0.00181755
$232$	−0.310696	−0.0203982
$233$	−26.6810	−1.74793	−0.873964	−	0.485991i	$-0.838459\pi$
$233$	−26.6810	−1.74793	−0.873964	+	0.485991i	$0.838459\pi$
$234$	1.89835	0.124099
$235$	6.34392	0.413832
$236$	−2.96974	−0.193313
$237$	−13.1477	−0.854036
$238$	−3.04956	−0.197673
$239$	6.35612	0.411144	0.205572	−	0.978642i	$-0.434095\pi$
$239$	6.35612	0.411144	0.205572	+	0.978642i	$0.434095\pi$
$240$	0.707846	0.0456913
$241$	−2.63836	−0.169952	−0.0849759	−	0.996383i	$-0.527081\pi$
$241$	−2.63836	−0.169952	−0.0849759	+	0.996383i	$0.527081\pi$
$242$	−10.9995	−0.707073
$243$	15.6192	1.00197
$244$	1.46375	0.0937071
$245$	−4.20350	−0.268552
$246$	−4.34768	−0.277198
$247$	5.42296	0.345054
$248$	6.80832	0.432329
$249$	−5.86631	−0.371762
$250$	−8.37105	−0.529432
$251$	8.89454	0.561418	0.280709	−	0.959793i	$-0.409430\pi$
$251$	8.89454	0.561418	0.280709	+	0.959793i	$0.409430\pi$
$252$	3.71490	0.234017
$253$	0.0230193	0.00144721
$254$	−20.2094	−1.26805
$255$	1.39415	0.0873051
$256$	1.00000	0.0625000
$257$	8.82070	0.550220	0.275110	−	0.961413i	$-0.411286\pi$
$257$	8.82070	0.550220	0.275110	+	0.961413i	$0.411286\pi$
$258$	−5.72271	−0.356280
$259$	−12.0206	−0.746921
$260$	−0.722602	−0.0448138
$261$	0.745447	0.0461420
$262$	1.00000	0.0617802
$263$	−3.46050	−0.213384	−0.106692	−	0.994292i	$-0.534026\pi$
$263$	−3.46050	−0.213384	−0.106692	+	0.994292i	$0.534026\pi$
$264$	−0.0178413	−0.00109806
$265$	−10.3858	−0.637993
$266$	10.6122	0.650679
$267$	−11.0531	−0.676441
$268$	−2.84855	−0.174003
$269$	−8.29803	−0.505940	−0.252970	−	0.967474i	$-0.581407\pi$
$269$	−8.29803	−0.505940	−0.252970	+	0.967474i	$0.581407\pi$
$270$	−3.82186	−0.232591
$271$	−9.15821	−0.556322	−0.278161	−	0.960535i	$-0.589725\pi$
$271$	−9.15821	−0.556322	−0.278161	+	0.960535i	$0.589725\pi$
$272$	1.96957	0.119422
$273$	0.949503	0.0574665
$274$	−6.67887	−0.403485
$275$	0.0958965	0.00578278
$276$	−0.775060	−0.0466531
$277$	4.66727	0.280429	0.140215	−	0.990121i	$-0.455221\pi$
$277$	4.66727	0.280429	0.140215	+	0.990121i	$0.455221\pi$
$278$	−6.36928	−0.382004
$279$	−16.3351	−0.977956
$280$	−1.41407	−0.0845067
$281$	−31.5897	−1.88448	−0.942242	−	0.334933i	$-0.891286\pi$
$281$	−31.5897	−1.88448	−0.942242	+	0.334933i	$0.891286\pi$
$282$	5.38380	0.320601
$283$	−12.9879	−0.772049	−0.386025	−	0.922488i	$-0.626152\pi$
$283$	−12.9879	−0.772049	−0.386025	+	0.922488i	$0.626152\pi$
$284$	3.85538	0.228775
$285$	−4.85155	−0.287381
$286$	0.0182132	0.00107697
$287$	8.68537	0.512681
$288$	−2.39928	−0.141379
$289$	−13.1208	−0.771812
$290$	−0.283752	−0.0166625
$291$	0.242017	0.0141873
$292$	−5.74271	−0.336067
$293$	18.0143	1.05241	0.526204	−	0.850358i	$-0.323615\pi$
$293$	18.0143	1.05241	0.526204	+	0.850358i	$0.323615\pi$
$294$	−3.56732	−0.208051
$295$	−2.71220	−0.157910
$296$	7.76351	0.451245
$297$	0.0963303	0.00558965
$298$	5.22066	0.302425
$299$	0.791216	0.0457572
$300$	−3.22884	−0.186417
$301$	11.4323	0.658945
$302$	18.1974	1.04714
$303$	−4.10706	−0.235945
$304$	−6.85395	−0.393101
$305$	1.33681	0.0765458
$306$	−4.72555	−0.270141
$307$	8.00563	0.456906	0.228453	−	0.973555i	$-0.426633\pi$
$307$	8.00563	0.456906	0.228453	+	0.973555i	$0.426633\pi$
$308$	0.0356417	0.00203087
$309$	8.02410	0.456475
$310$	6.21790	0.353153
$311$	−0.00408541	−0.000231662 0	−0.000115831	−	1.00000i	$-0.500037\pi$
$311$	−0.00408541	−0.000231662 0	−0.000115831		1.00000i	$0.500037\pi$
$312$	−0.613239	−0.0347178
$313$	10.3872	0.587120	0.293560	−	0.955941i	$-0.405160\pi$
$313$	10.3872	0.587120	0.293560	+	0.955941i	$0.405160\pi$
$314$	−12.4549	−0.702873
$315$	3.39275	0.191160
$316$	−16.9635	−0.954271
$317$	−6.84905	−0.384681	−0.192340	−	0.981328i	$-0.561608\pi$
$317$	−6.84905	−0.384681	−0.192340	+	0.981328i	$0.561608\pi$
$318$	−8.81393	−0.494261
$319$	0.00715199	0.000400435 0
$320$	0.913280	0.0510539
$321$	−4.08985	−0.228273
$322$	1.54834	0.0862856
$323$	−13.4993	−0.751122
$324$	3.95441	0.219689
$325$	3.29614	0.182837
$326$	12.0727	0.668647
$327$	13.2213	0.731140
$328$	−5.60947	−0.309731
$329$	−10.7552	−0.592956
$330$	−0.0162941	−0.000896962 0
$331$	27.9271	1.53501	0.767505	−	0.641043i	$-0.221498\pi$
$331$	27.9271	1.53501	0.767505	+	0.641043i	$0.221498\pi$
$332$	−7.56884	−0.415394
$333$	−18.6269	−1.02075
$334$	15.2347	0.833608
$335$	−2.60152	−0.142136
$336$	−1.20006	−0.0654684
$337$	18.4443	1.00472	0.502362	−	0.864658i	$-0.332465\pi$
$337$	18.4443	1.00472	0.502362	+	0.864658i	$0.332465\pi$
$338$	−12.3740	−0.673056
$339$	8.57397	0.465674
$340$	1.79877	0.0975517
$341$	−0.156723	−0.00848701
$342$	16.4446	0.889221
$343$	17.9648	0.970010
$344$	−7.38357	−0.398095
$345$	−0.707846	−0.0381092
$346$	−17.9825	−0.966744
$347$	−0.769524	−0.0413102	−0.0206551	−	0.999787i	$-0.506575\pi$
$347$	−0.769524	−0.0413102	−0.0206551	+	0.999787i	$0.506575\pi$
$348$	−0.240808	−0.0129086
$349$	30.4350	1.62915	0.814574	−	0.580060i	$-0.196971\pi$
$349$	30.4350	1.62915	0.814574	+	0.580060i	$0.196971\pi$
$350$	6.45026	0.344781
$351$	3.31105	0.176731
$352$	−0.0230193	−0.00122693
$353$	10.4434	0.555848	0.277924	−	0.960603i	$-0.410354\pi$
$353$	10.4434	0.555848	0.277924	+	0.960603i	$0.410354\pi$
$354$	−2.30172	−0.122335
$355$	3.52104	0.186878
$356$	−14.2610	−0.755832
$357$	−2.36359	−0.125094
$358$	−5.28481	−0.279311
$359$	22.4756	1.18622	0.593110	−	0.805122i	$-0.297900\pi$
$359$	22.4756	1.18622	0.593110	+	0.805122i	$0.297900\pi$
$360$	−2.19122	−0.115487
$361$	27.9767	1.47246
$362$	15.6855	0.824410
$363$	−8.52524	−0.447459
$364$	1.22507	0.0642112
$365$	−5.24470	−0.274520
$366$	1.13449	0.0593010
$367$	−4.89033	−0.255273	−0.127637	−	0.991821i	$-0.540739\pi$
$367$	−4.89033	−0.255273	−0.127637	+	0.991821i	$0.540739\pi$
$368$	−1.00000	−0.0521286
$369$	13.4587	0.700633
$370$	7.09026	0.368605
$371$	17.6076	0.914143
$372$	5.27685	0.273592
$373$	−5.98809	−0.310052	−0.155026	−	0.987910i	$-0.549546\pi$
$373$	−5.98809	−0.310052	−0.155026	+	0.987910i	$0.549546\pi$
$374$	−0.0453380	−0.00234437
$375$	−6.48806	−0.335042
$376$	6.94631	0.358228
$377$	0.245827	0.0126608
$378$	6.47944	0.333266
$379$	−7.52975	−0.386778	−0.193389	−	0.981122i	$-0.561948\pi$
$379$	−7.52975	−0.386778	−0.193389	+	0.981122i	$0.561948\pi$
$380$	−6.25958	−0.321110
$381$	−15.6635	−0.802463
$382$	19.0585	0.975120
$383$	−0.452650	−0.0231293	−0.0115647	−	0.999933i	$-0.503681\pi$
$383$	−0.452650	−0.0231293	−0.0115647	+	0.999933i	$0.503681\pi$
$384$	0.775060	0.0395521
$385$	0.0325508	0.00165894
$386$	4.41122	0.224525
$387$	17.7153	0.900518
$388$	0.312256	0.0158524
$389$	31.0214	1.57285	0.786425	−	0.617686i	$-0.211930\pi$
$389$	31.0214	1.57285	0.786425	+	0.617686i	$0.211930\pi$
$390$	−0.560059	−0.0283597
$391$	−1.96957	−0.0996052
$392$	−4.60264	−0.232469
$393$	0.775060	0.0390966
$394$	4.27431	0.215337
$395$	−15.4924	−0.779508
$396$	0.0552298	0.00277540
$397$	26.6904	1.33955	0.669777	−	0.742563i	$-0.266390\pi$
$397$	26.6904	1.33955	0.669777	+	0.742563i	$0.266390\pi$
$398$	−12.6493	−0.634050
$399$	8.22513	0.411771
$400$	−4.16592	−0.208296
$401$	−9.57909	−0.478357	−0.239178	−	0.970976i	$-0.576878\pi$
$401$	−9.57909	−0.478357	−0.239178	+	0.970976i	$0.576878\pi$
$402$	−2.20780	−0.110115
$403$	−5.38685	−0.268338
$404$	−5.29903	−0.263637
$405$	3.61148	0.179456
$406$	0.481062	0.0238747
$407$	−0.178710	−0.00885835
$408$	1.52653	0.0755746
$409$	13.6762	0.676243	0.338122	−	0.941102i	$-0.390208\pi$
$409$	13.6762	0.676243	0.338122	+	0.941102i	$0.390208\pi$
$410$	−5.12302	−0.253008
$411$	−5.17652	−0.255339
$412$	10.3529	0.510050
$413$	4.59816	0.226261
$414$	2.39928	0.117918
$415$	−6.91247	−0.339320
$416$	−0.791216	−0.0387926
$417$	−4.93657	−0.241745
$418$	0.157773	0.00771694
$419$	4.26612	0.208413	0.104207	−	0.994556i	$-0.466770\pi$
$419$	4.26612	0.208413	0.104207	+	0.994556i	$0.466770\pi$
$420$	−1.09599	−0.0534787
$421$	30.1533	1.46958	0.734790	−	0.678294i	$-0.237281\pi$
$421$	30.1533	1.46958	0.734790	+	0.678294i	$0.237281\pi$
$422$	15.2235	0.741069
$423$	−16.6662	−0.810336
$424$	−11.3719	−0.552270
$425$	−8.20506	−0.398004
$426$	2.98815	0.144776
$427$	−2.26638	−0.109678
$428$	−5.27682	−0.255065
$429$	0.0141163	0.000681543 0
$430$	−6.74327	−0.325189
$431$	−19.5365	−0.941042	−0.470521	−	0.882389i	$-0.655934\pi$
$431$	−19.5365	−0.941042	−0.470521	+	0.882389i	$0.655934\pi$
$432$	−4.18477	−0.201340
$433$	−36.8020	−1.76859	−0.884295	−	0.466929i	$-0.845360\pi$
$433$	−36.8020	−1.76859	−0.884295	+	0.466929i	$0.845360\pi$
$434$	−10.5416	−0.506013
$435$	−0.219925	−0.0105446
$436$	17.0584	0.816951
$437$	6.85395	0.327869
$438$	−4.45094	−0.212674
$439$	−27.7562	−1.32473	−0.662365	−	0.749181i	$-0.730447\pi$
$439$	−27.7562	−1.32473	−0.662365	+	0.749181i	$0.730447\pi$
$440$	−0.0210231	−0.00100223
$441$	11.0430	0.525859
$442$	−1.55835	−0.0741233
$443$	4.01350	0.190687	0.0953436	−	0.995444i	$-0.469605\pi$
$443$	4.01350	0.190687	0.0953436	+	0.995444i	$0.469605\pi$
$444$	6.01718	0.285563
$445$	−13.0243	−0.617411
$446$	15.1547	0.717594
$447$	4.04632	0.191385
$448$	−1.54834	−0.0731522
$449$	2.27622	0.107422	0.0537108	−	0.998557i	$-0.482895\pi$
$449$	2.27622	0.107422	0.0537108	+	0.998557i	$0.482895\pi$
$450$	9.99522	0.471179
$451$	0.129126	0.00608031
$452$	11.0623	0.520329
$453$	14.1040	0.662665
$454$	−23.6392	−1.10944
$455$	1.11883	0.0524517
$456$	−5.31222	−0.248768
$457$	18.6029	0.870208	0.435104	−	0.900380i	$-0.356712\pi$
$457$	18.6029	0.870208	0.435104	+	0.900380i	$0.356712\pi$
$458$	1.62497	0.0759301
$459$	−8.24217	−0.384712
$460$	−0.913280	−0.0425819
$461$	−20.7969	−0.968607	−0.484303	−	0.874900i	$-0.660927\pi$
$461$	−20.7969	−0.968607	−0.484303	+	0.874900i	$0.660927\pi$
$462$	0.0276244	0.00128520
$463$	−16.9028	−0.785542	−0.392771	−	0.919636i	$-0.628483\pi$
$463$	−16.9028	−0.785542	−0.392771	+	0.919636i	$0.628483\pi$
$464$	−0.310696	−0.0144237
$465$	4.81924	0.223487
$466$	−26.6810	−1.23597
$467$	−12.0335	−0.556846	−0.278423	−	0.960459i	$-0.589812\pi$
$467$	−12.0335	−0.556846	−0.278423	+	0.960459i	$0.589812\pi$
$468$	1.89835	0.0877513
$469$	4.41053	0.203659
$470$	6.34392	0.292623
$471$	−9.65332	−0.444802
$472$	−2.96974	−0.136693
$473$	0.169965	0.00781498
$474$	−13.1477	−0.603895
$475$	28.5530	1.31010
$476$	−3.04956	−0.139776
$477$	27.2845	1.24927
$478$	6.35612	0.290722
$479$	10.7276	0.490158	0.245079	−	0.969503i	$-0.421186\pi$
$479$	10.7276	0.490158	0.245079	+	0.969503i	$0.421186\pi$
$480$	0.707846	0.0323086
$481$	−6.14261	−0.280079
$482$	−2.63836	−0.120174
$483$	1.20006	0.0546044
$484$	−10.9995	−0.499976
$485$	0.285177	0.0129492
$486$	15.6192	0.708501
$487$	21.3200	0.966101	0.483050	−	0.875593i	$-0.339529\pi$
$487$	21.3200	0.966101	0.483050	+	0.875593i	$0.339529\pi$
$488$	1.46375	0.0662609
$489$	9.35709	0.423142
$490$	−4.20350	−0.189895
$491$	0.758231	0.0342185	0.0171092	−	0.999854i	$-0.494554\pi$
$491$	0.758231	0.0342185	0.0171092	+	0.999854i	$0.494554\pi$
$492$	−4.34768	−0.196008
$493$	−0.611936	−0.0275602
$494$	5.42296	0.243990
$495$	0.0504402	0.00226712
$496$	6.80832	0.305703
$497$	−5.96944	−0.267766
$498$	−5.86631	−0.262875
$499$	−14.8283	−0.663806	−0.331903	−	0.943314i	$-0.607691\pi$
$499$	−14.8283	−0.663806	−0.331903	+	0.943314i	$0.607691\pi$
$500$	−8.37105	−0.374365
$501$	11.8078	0.527535
$502$	8.89454	0.396983
$503$	9.26811	0.413245	0.206622	−	0.978421i	$-0.433753\pi$
$503$	9.26811	0.413245	0.206622	+	0.978421i	$0.433753\pi$
$504$	3.71490	0.165475
$505$	−4.83950	−0.215355
$506$	0.0230193	0.00102333
$507$	−9.59057	−0.425932
$508$	−20.2094	−0.896645
$509$	12.5426	0.555941	0.277970	−	0.960590i	$-0.410338\pi$
$509$	12.5426	0.555941	0.277970	+	0.960590i	$0.410338\pi$
$510$	1.39415	0.0617340
$511$	8.89167	0.393344
$512$	1.00000	0.0441942
$513$	28.6822	1.26635
$514$	8.82070	0.389064
$515$	9.45508	0.416641
$516$	−5.72271	−0.251928
$517$	−0.159899	−0.00703235
$518$	−12.0206	−0.528153
$519$	−13.9375	−0.611788
$520$	−0.722602	−0.0316882
$521$	−19.9292	−0.873112	−0.436556	−	0.899677i	$-0.643802\pi$
$521$	−19.9292	−0.873112	−0.436556	+	0.899677i	$0.643802\pi$
$522$	0.745447	0.0326273
$523$	31.5626	1.38014	0.690068	−	0.723745i	$-0.257581\pi$
$523$	31.5626	1.38014	0.690068	+	0.723745i	$0.257581\pi$
$524$	1.00000	0.0436852
$525$	4.99934	0.218189
$526$	−3.46050	−0.150885
$527$	13.4094	0.584124
$528$	−0.0178413	−0.000776444 0
$529$	1.00000	0.0434783
$530$	−10.3858	−0.451129
$531$	7.12524	0.309209
$532$	10.6122	0.460099
$533$	4.43831	0.192244
$534$	−11.0531	−0.478316
$535$	−4.81921	−0.208353
$536$	−2.84855	−0.123039
$537$	−4.09604	−0.176757
$538$	−8.29803	−0.357753
$539$	0.105950	0.00456357
$540$	−3.82186	−0.164467
$541$	−36.2763	−1.55964	−0.779821	−	0.626003i	$-0.784690\pi$
$541$	−36.2763	−1.55964	−0.779821	+	0.626003i	$0.784690\pi$
$542$	−9.15821	−0.393379
$543$	12.1572	0.521714
$544$	1.96957	0.0844445
$545$	15.5791	0.667336
$546$	0.949503	0.0406350
$547$	−9.41198	−0.402427	−0.201214	−	0.979547i	$-0.564489\pi$
$547$	−9.41198	−0.402427	−0.201214	+	0.979547i	$0.564489\pi$
$548$	−6.67887	−0.285307
$549$	−3.51195	−0.149886
$550$	0.0958965	0.00408904
$551$	2.12949	0.0907195
$552$	−0.775060	−0.0329887
$553$	26.2653	1.11691
$554$	4.66727	0.198293
$555$	5.49537	0.233266
$556$	−6.36928	−0.270118
$557$	−21.2963	−0.902352	−0.451176	−	0.892435i	$-0.648995\pi$
$557$	−21.2963	−0.902352	−0.451176	+	0.892435i	$0.648995\pi$
$558$	−16.3351	−0.691519
$559$	5.84200	0.247090
$560$	−1.41407	−0.0597553
$561$	−0.0351397	−0.00148360
$562$	−31.5897	−1.33253
$563$	−22.5545	−0.950558	−0.475279	−	0.879835i	$-0.657653\pi$
$563$	−22.5545	−0.950558	−0.475279	+	0.879835i	$0.657653\pi$
$564$	5.38380	0.226699
$565$	10.1030	0.425037
$566$	−12.9879	−0.545921
$567$	−6.12276	−0.257132
$568$	3.85538	0.161768
$569$	5.79248	0.242833	0.121417	−	0.992602i	$-0.461256\pi$
$569$	5.79248	0.242833	0.121417	+	0.992602i	$0.461256\pi$
$570$	−4.85155	−0.203209
$571$	13.4411	0.562494	0.281247	−	0.959635i	$-0.409252\pi$
$571$	13.4411	0.562494	0.281247	+	0.959635i	$0.409252\pi$
$572$	0.0182132	0.000761533 0
$573$	14.7715	0.617088
$574$	8.68537	0.362520
$575$	4.16592	0.173731
$576$	−2.39928	−0.0999701
$577$	−13.5444	−0.563861	−0.281931	−	0.959435i	$-0.590975\pi$
$577$	−13.5444	−0.563861	−0.281931	+	0.959435i	$0.590975\pi$
$578$	−13.1208	−0.545754
$579$	3.41896	0.142087
$580$	−0.283752	−0.0117822
$581$	11.7191	0.486192
$582$	0.242017	0.0100319
$583$	0.261774	0.0108416
$584$	−5.74271	−0.237635
$585$	1.73373	0.0716807
$586$	18.0143	0.744165
$587$	21.2870	0.878610	0.439305	−	0.898338i	$-0.355225\pi$
$587$	21.2870	0.878610	0.439305	+	0.898338i	$0.355225\pi$
$588$	−3.56732	−0.147114
$589$	−46.6639	−1.92275
$590$	−2.71220	−0.111660
$591$	3.31284	0.136272
$592$	7.76351	0.319078
$593$	−11.3655	−0.466725	−0.233362	−	0.972390i	$-0.574973\pi$
$593$	−11.3655	−0.466725	−0.233362	+	0.972390i	$0.574973\pi$
$594$	0.0963303	0.00395248
$595$	−2.78510	−0.114178
$596$	5.22066	0.213847
$597$	−9.80393	−0.401248
$598$	0.791216	0.0323552
$599$	26.5036	1.08291	0.541454	−	0.840731i	$-0.317874\pi$
$599$	26.5036	1.08291	0.541454	+	0.840731i	$0.317874\pi$
$600$	−3.22884	−0.131817
$601$	−11.0850	−0.452165	−0.226082	−	0.974108i	$-0.572592\pi$
$601$	−11.0850	−0.452165	−0.226082	+	0.974108i	$0.572592\pi$
$602$	11.4323	0.465945
$603$	6.83448	0.278322
$604$	18.1974	0.740440
$605$	−10.0456	−0.408412
$606$	−4.10706	−0.166838
$607$	−37.7098	−1.53059	−0.765296	−	0.643678i	$-0.777408\pi$
$607$	−37.7098	−1.53059	−0.765296	+	0.643678i	$0.777408\pi$
$608$	−6.85395	−0.277965
$609$	0.372852	0.0151087
$610$	1.33681	0.0541260
$611$	−5.49603	−0.222346
$612$	−4.72555	−0.191019
$613$	17.5319	0.708107	0.354054	−	0.935225i	$-0.384803\pi$
$613$	17.5319	0.708107	0.354054	+	0.935225i	$0.384803\pi$
$614$	8.00563	0.323081
$615$	−3.97065	−0.160112
$616$	0.0356417	0.00143604
$617$	−6.49364	−0.261424	−0.130712	−	0.991420i	$-0.541726\pi$
$617$	−6.49364	−0.261424	−0.130712	+	0.991420i	$0.541726\pi$
$618$	8.02410	0.322777
$619$	−17.4644	−0.701953	−0.350976	−	0.936384i	$-0.614150\pi$
$619$	−17.4644	−0.701953	−0.350976	+	0.936384i	$0.614150\pi$
$620$	6.21790	0.249717
$621$	4.18477	0.167929
$622$	−0.00408541	−0.000163810 0
$623$	22.0809	0.884652
$624$	−0.613239	−0.0245492
$625$	13.1845	0.527380
$626$	10.3872	0.415156
$627$	0.122284	0.00488354
$628$	−12.4549	−0.497006
$629$	15.2907	0.609682
$630$	3.39275	0.135170
$631$	6.21083	0.247249	0.123625	−	0.992329i	$-0.460548\pi$
$631$	6.21083	0.247249	0.123625	+	0.992329i	$0.460548\pi$
$632$	−16.9635	−0.674772
$633$	11.7991	0.468973
$634$	−6.84905	−0.272010
$635$	−18.4568	−0.732436
$636$	−8.81393	−0.349495
$637$	3.64168	0.144289
$638$	0.00715199	0.000283150 0
$639$	−9.25016	−0.365931
$640$	0.913280	0.0361006
$641$	−1.54079	−0.0608575	−0.0304288	−	0.999537i	$-0.509687\pi$
$641$	−1.54079	−0.0608575	−0.0304288	+	0.999537i	$0.509687\pi$
$642$	−4.08985	−0.161413
$643$	−20.6614	−0.814806	−0.407403	−	0.913249i	$-0.633566\pi$
$643$	−20.6614	−0.814806	−0.407403	+	0.913249i	$0.633566\pi$
$644$	1.54834	0.0610131
$645$	−5.22643	−0.205791
$646$	−13.4993	−0.531123
$647$	20.9442	0.823401	0.411700	−	0.911319i	$-0.364935\pi$
$647$	20.9442	0.823401	0.411700	+	0.911319i	$0.364935\pi$
$648$	3.95441	0.155344
$649$	0.0683612	0.00268341
$650$	3.29614	0.129285
$651$	−8.17036	−0.320222
$652$	12.0727	0.472805
$653$	−22.1584	−0.867123	−0.433562	−	0.901124i	$-0.642743\pi$
$653$	−22.1584	−0.867123	−0.433562	+	0.901124i	$0.642743\pi$
$654$	13.2213	0.516994
$655$	0.913280	0.0356848
$656$	−5.60947	−0.219013
$657$	13.7784	0.537546
$658$	−10.7552	−0.419283
$659$	−4.23585	−0.165005	−0.0825026	−	0.996591i	$-0.526291\pi$
$659$	−4.23585	−0.165005	−0.0825026	+	0.996591i	$0.526291\pi$
$660$	−0.0162941	−0.000634248 0
$661$	−16.6901	−0.649171	−0.324586	−	0.945856i	$-0.605225\pi$
$661$	−16.6901	−0.649171	−0.324586	+	0.945856i	$0.605225\pi$
$662$	27.9271	1.08542
$663$	−1.20782	−0.0469077
$664$	−7.56884	−0.293728
$665$	9.69195	0.375838
$666$	−18.6269	−0.721776
$667$	0.310696	0.0120302
$668$	15.2347	0.589450
$669$	11.7458	0.454118
$670$	−2.60152	−0.100506
$671$	−0.0336945	−0.00130076
$672$	−1.20006	−0.0462931
$673$	−21.9146	−0.844747	−0.422374	−	0.906422i	$-0.638803\pi$
$673$	−21.9146	−0.844747	−0.422374	+	0.906422i	$0.638803\pi$
$674$	18.4443	0.710447
$675$	17.4334	0.671012
$676$	−12.3740	−0.475922
$677$	−26.5567	−1.02066	−0.510328	−	0.859980i	$-0.670476\pi$
$677$	−26.5567	−1.02066	−0.510328	+	0.859980i	$0.670476\pi$
$678$	8.57397	0.329281
$679$	−0.483479	−0.0185542
$680$	1.79877	0.0689795
$681$	−18.3218	−0.702093
$682$	−0.156723	−0.00600122
$683$	−3.56420	−0.136380	−0.0681901	−	0.997672i	$-0.521722\pi$
$683$	−3.56420	−0.136380	−0.0681901	+	0.997672i	$0.521722\pi$
$684$	16.4446	0.628774
$685$	−6.09968	−0.233057
$686$	17.9648	0.685901
$687$	1.25945	0.0480511
$688$	−7.38357	−0.281496
$689$	8.99766	0.342784
$690$	−0.707846	−0.0269472
$691$	27.8215	1.05838	0.529189	−	0.848504i	$-0.322496\pi$
$691$	27.8215	1.05838	0.529189	+	0.848504i	$0.322496\pi$
$692$	−17.9825	−0.683591
$693$	−0.0855145	−0.00324843
$694$	−0.769524	−0.0292107
$695$	−5.81694	−0.220649
$696$	−0.240808	−0.00912779
$697$	−11.0482	−0.418482
$698$	30.4350	1.15198
$699$	−20.6793	−0.782164
$700$	6.45026	0.243797
$701$	8.00186	0.302226	0.151113	−	0.988516i	$-0.451714\pi$
$701$	8.00186	0.302226	0.151113	+	0.988516i	$0.451714\pi$
$702$	3.31105	0.124968
$703$	−53.2107	−2.00688
$704$	−0.0230193	−0.000867572 0
$705$	4.91692	0.185182
$706$	10.4434	0.393044
$707$	8.20470	0.308569
$708$	−2.30172	−0.0865040
$709$	−29.0985	−1.09282	−0.546409	−	0.837518i	$-0.684006\pi$
$709$	−29.0985	−1.09282	−0.546409	+	0.837518i	$0.684006\pi$
$710$	3.52104	0.132142
$711$	40.7002	1.52638
$712$	−14.2610	−0.534454
$713$	−6.80832	−0.254974
$714$	−2.36359	−0.0884551
$715$	0.0166338	0.000622068 0
$716$	−5.28481	−0.197502
$717$	4.92638	0.183979
$718$	22.4756	0.838784
$719$	15.4471	0.576078	0.288039	−	0.957619i	$-0.406997\pi$
$719$	15.4471	0.576078	0.288039	+	0.957619i	$0.406997\pi$
$720$	−2.19122	−0.0816618
$721$	−16.0298	−0.596980
$722$	27.9767	1.04118
$723$	−2.04489	−0.0760501
$724$	15.6855	0.582946
$725$	1.29433	0.0480703
$726$	−8.52524	−0.316401
$727$	−0.471505	−0.0174871	−0.00874357	−	0.999962i	$-0.502783\pi$
$727$	−0.471505	−0.0174871	−0.00874357	+	0.999962i	$0.502783\pi$
$728$	1.22507	0.0454042
$729$	0.242592	0.00898488
$730$	−5.24470	−0.194115
$731$	−14.5424	−0.537871
$732$	1.13449	0.0419321
$733$	−18.9860	−0.701265	−0.350633	−	0.936513i	$-0.614033\pi$
$733$	−18.9860	−0.701265	−0.350633	+	0.936513i	$0.614033\pi$
$734$	−4.89033	−0.180506
$735$	−3.25796	−0.120172
$736$	−1.00000	−0.0368605
$737$	0.0655716	0.00241536
$738$	13.4587	0.495422
$739$	27.8820	1.02565	0.512827	−	0.858492i	$-0.328598\pi$
$739$	27.8820	1.02565	0.512827	+	0.858492i	$0.328598\pi$
$740$	7.09026	0.260643
$741$	4.20311	0.154405
$742$	17.6076	0.646396
$743$	−9.97160	−0.365822	−0.182911	−	0.983129i	$-0.558552\pi$
$743$	−9.97160	−0.365822	−0.182911	+	0.983129i	$0.558552\pi$
$744$	5.27685	0.193459
$745$	4.76792	0.174683
$746$	−5.98809	−0.219240
$747$	18.1598	0.664432
$748$	−0.0453380	−0.00165772
$749$	8.17031	0.298537
$750$	−6.48806	−0.236911
$751$	−26.8392	−0.979376	−0.489688	−	0.871898i	$-0.662889\pi$
$751$	−26.8392	−0.979376	−0.489688	+	0.871898i	$0.662889\pi$
$752$	6.94631	0.253306
$753$	6.89379	0.251224
$754$	0.245827	0.00895250
$755$	16.6193	0.604837
$756$	6.47944	0.235655
$757$	−30.1811	−1.09695	−0.548475	−	0.836167i	$-0.684791\pi$
$757$	−30.1811	−1.09695	−0.548475	+	0.836167i	$0.684791\pi$
$758$	−7.52975	−0.273493
$759$	0.0178413	0.000647599 0
$760$	−6.25958	−0.227059
$761$	21.0235	0.762101	0.381050	−	0.924554i	$-0.375562\pi$
$761$	21.0235	0.762101	0.381050	+	0.924554i	$0.375562\pi$
$762$	−15.6635	−0.567427
$763$	−26.4122	−0.956188
$764$	19.0585	0.689514
$765$	−4.31575	−0.156036
$766$	−0.452650	−0.0163549
$767$	2.34970	0.0848428
$768$	0.775060	0.0279676
$769$	−11.3270	−0.408460	−0.204230	−	0.978923i	$-0.565469\pi$
$769$	−11.3270	−0.408460	−0.204230	+	0.978923i	$0.565469\pi$
$770$	0.0325508	0.00117305
$771$	6.83657	0.246213
$772$	4.41122	0.158763
$773$	−16.6214	−0.597829	−0.298914	−	0.954280i	$-0.596625\pi$
$773$	−16.6214	−0.597829	−0.298914	+	0.954280i	$0.596625\pi$
$774$	17.7153	0.636762
$775$	−28.3629	−1.01883
$776$	0.312256	0.0112094
$777$	−9.31664	−0.334233
$778$	31.0214	1.11217
$779$	38.4471	1.37751
$780$	−0.560059	−0.0200533
$781$	−0.0887482	−0.00317566
$782$	−1.96957	−0.0704315
$783$	1.30019	0.0464649
$784$	−4.60264	−0.164380
$785$	−11.3748	−0.405986
$786$	0.775060	0.0276455
$787$	−19.0176	−0.677904	−0.338952	−	0.940804i	$-0.610072\pi$
$787$	−19.0176	−0.677904	−0.338952	+	0.940804i	$0.610072\pi$
$788$	4.27431	0.152266
$789$	−2.68210	−0.0954851
$790$	−15.4924	−0.551195
$791$	−17.1283	−0.609011
$792$	0.0552298	0.00196250
$793$	−1.15814	−0.0411269
$794$	26.6904	0.947207
$795$	−8.04959	−0.285489
$796$	−12.6493	−0.448341
$797$	17.3233	0.613624	0.306812	−	0.951770i	$-0.400738\pi$
$797$	17.3233	0.613624	0.306812	+	0.951770i	$0.400738\pi$
$798$	8.22513	0.291166
$799$	13.6812	0.484007
$800$	−4.16592	−0.147288
$801$	34.2162	1.20897
$802$	−9.57909	−0.338249
$803$	0.132193	0.00466499
$804$	−2.20780	−0.0778630
$805$	1.41407	0.0498393
$806$	−5.38685	−0.189744
$807$	−6.43146	−0.226398
$808$	−5.29903	−0.186419
$809$	13.7539	0.483562	0.241781	−	0.970331i	$-0.422268\pi$
$809$	13.7539	0.483562	0.241781	+	0.970331i	$0.422268\pi$
$810$	3.61148	0.126894
$811$	17.2543	0.605880	0.302940	−	0.953010i	$-0.402032\pi$
$811$	17.2543	0.605880	0.302940	+	0.953010i	$0.402032\pi$
$812$	0.481062	0.0168820
$813$	−7.09816	−0.248943
$814$	−0.178710	−0.00626380
$815$	11.0258	0.386216
$816$	1.52653	0.0534393
$817$	50.6066	1.77050
$818$	13.6762	0.478176
$819$	−2.93929	−0.102707
$820$	−5.12302	−0.178904
$821$	−5.31965	−0.185657	−0.0928285	−	0.995682i	$-0.529591\pi$
$821$	−5.31965	−0.185657	−0.0928285	+	0.995682i	$0.529591\pi$
$822$	−5.17652	−0.180552
$823$	40.1944	1.40109	0.700545	−	0.713608i	$-0.252940\pi$
$823$	40.1944	1.40109	0.700545	+	0.713608i	$0.252940\pi$
$824$	10.3529	0.360660
$825$	0.0743255	0.00258768
$826$	4.59816	0.159990
$827$	27.9964	0.973529	0.486764	−	0.873533i	$-0.338177\pi$
$827$	27.9964	0.973529	0.486764	+	0.873533i	$0.338177\pi$
$828$	2.39928	0.0833808
$829$	3.75802	0.130521	0.0652607	−	0.997868i	$-0.479212\pi$
$829$	3.75802	0.130521	0.0652607	+	0.997868i	$0.479212\pi$
$830$	−6.91247	−0.239935
$831$	3.61741	0.125487
$832$	−0.791216	−0.0274305
$833$	−9.06521	−0.314091
$834$	−4.93657	−0.170940
$835$	13.9136	0.481499
$836$	0.157773	0.00545670
$837$	−28.4912	−0.984801
$838$	4.26612	0.147371
$839$	51.1714	1.76663	0.883317	−	0.468776i	$-0.155305\pi$
$839$	51.1714	1.76663	0.883317	+	0.468776i	$0.155305\pi$
$840$	−1.09599	−0.0378151
$841$	−28.9035	−0.996671
$842$	30.1533	1.03915
$843$	−24.4839	−0.843270
$844$	15.2235	0.524015
$845$	−11.3009	−0.388763
$846$	−16.6662	−0.572994
$847$	17.0309	0.585189
$848$	−11.3719	−0.390514
$849$	−10.0664	−0.345477
$850$	−8.20506	−0.281431
$851$	−7.76351	−0.266130
$852$	2.98815	0.102372
$853$	19.2618	0.659510	0.329755	−	0.944066i	$-0.393034\pi$
$853$	19.2618	0.659510	0.329755	+	0.944066i	$0.393034\pi$
$854$	−2.26638	−0.0775541
$855$	15.0185	0.513622
$856$	−5.27682	−0.180358
$857$	15.1226	0.516577	0.258288	−	0.966068i	$-0.416841\pi$
$857$	15.1226	0.516577	0.258288	+	0.966068i	$0.416841\pi$
$858$	0.0141163	0.000481924 0
$859$	29.4824	1.00593	0.502963	−	0.864308i	$-0.332243\pi$
$859$	29.4824	1.00593	0.502963	+	0.864308i	$0.332243\pi$
$860$	−6.74327	−0.229943
$861$	6.73168	0.229415
$862$	−19.5365	−0.665417
$863$	7.50768	0.255564	0.127782	−	0.991802i	$-0.459214\pi$
$863$	7.50768	0.255564	0.127782	+	0.991802i	$0.459214\pi$
$864$	−4.18477	−0.142369
$865$	−16.4230	−0.558400
$866$	−36.8020	−1.25058
$867$	−10.1694	−0.345371
$868$	−10.5416	−0.357805
$869$	0.390488	0.0132464
$870$	−0.219925	−0.00745615
$871$	2.25382	0.0763678
$872$	17.0584	0.577671
$873$	−0.749191	−0.0253563
$874$	6.85395	0.231838
$875$	12.9612	0.438170
$876$	−4.45094	−0.150383
$877$	7.60940	0.256951	0.128476	−	0.991713i	$-0.458992\pi$
$877$	7.60940	0.256951	0.128476	+	0.991713i	$0.458992\pi$
$878$	−27.7562	−0.936726
$879$	13.9622	0.470933
$880$	−0.0210231	−0.000708687 0
$881$	−16.7951	−0.565840	−0.282920	−	0.959144i	$-0.591303\pi$
$881$	−16.7951	−0.565840	−0.282920	+	0.959144i	$0.591303\pi$
$882$	11.0430	0.371839
$883$	−21.0859	−0.709597	−0.354798	−	0.934943i	$-0.615451\pi$
$883$	−21.0859	−0.709597	−0.354798	+	0.934943i	$0.615451\pi$
$884$	−1.55835	−0.0524131
$885$	−2.10212	−0.0706619
$886$	4.01350	0.134836
$887$	−5.41679	−0.181878	−0.0909389	−	0.995856i	$-0.528987\pi$
$887$	−5.41679	−0.181878	−0.0909389	+	0.995856i	$0.528987\pi$
$888$	6.01718	0.201923
$889$	31.2910	1.04946
$890$	−13.0243	−0.436575
$891$	−0.0910276	−0.00304954
$892$	15.1547	0.507416
$893$	−47.6097	−1.59320
$894$	4.04632	0.135329
$895$	−4.82651	−0.161332
$896$	−1.54834	−0.0517264
$897$	0.613239	0.0204755
$898$	2.27622	0.0759586
$899$	−2.11531	−0.0705497
$900$	9.99522	0.333174
$901$	−22.3978	−0.746179
$902$	0.129126	0.00429943
$903$	8.86069	0.294865
$904$	11.0623	0.367928
$905$	14.3252	0.476187
$906$	14.1040	0.468575
$907$	−38.0219	−1.26250	−0.631248	−	0.775581i	$-0.717457\pi$
$907$	−38.0219	−1.26250	−0.631248	+	0.775581i	$0.717457\pi$
$908$	−23.6392	−0.784495
$909$	12.7139	0.421692
$910$	1.11883	0.0370889
$911$	−0.0917014	−0.00303820	−0.00151910	−	0.999999i	$-0.500484\pi$
$911$	−0.0917014	−0.00303820	−0.00151910	+	0.999999i	$0.500484\pi$
$912$	−5.31222	−0.175905
$913$	0.174229	0.00576615
$914$	18.6029	0.615330
$915$	1.03611	0.0342528
$916$	1.62497	0.0536907
$917$	−1.54834	−0.0511307
$918$	−8.24217	−0.272032
$919$	−51.9738	−1.71446	−0.857229	−	0.514935i	$-0.827816\pi$
$919$	−51.9738	−1.71446	−0.857229	+	0.514935i	$0.827816\pi$
$920$	−0.913280	−0.0301099
$921$	6.20484	0.204457
$922$	−20.7969	−0.684908
$923$	−3.05044	−0.100407
$924$	0.0276244	0.000908777 0
$925$	−32.3422	−1.06340
$926$	−16.9028	−0.555462
$927$	−24.8395	−0.815836
$928$	−0.310696	−0.0101991
$929$	−33.3385	−1.09380	−0.546901	−	0.837197i	$-0.684193\pi$
$929$	−33.3385	−1.09380	−0.546901	+	0.837197i	$0.684193\pi$
$930$	4.81924	0.158029
$931$	31.5463	1.03389
$932$	−26.6810	−0.873964
$933$	−0.00316644	−0.000103664 0
$934$	−12.0335	−0.393750
$935$	−0.0414063	−0.00135413
$936$	1.89835	0.0620495
$937$	11.2759	0.368367	0.184184	−	0.982892i	$-0.441036\pi$
$937$	11.2759	0.368367	0.184184	+	0.982892i	$0.441036\pi$
$938$	4.41053	0.144009
$939$	8.05071	0.262725
$940$	6.34392	0.206916
$941$	19.2290	0.626847	0.313423	−	0.949613i	$-0.398524\pi$
$941$	19.2290	0.626847	0.313423	+	0.949613i	$0.398524\pi$
$942$	−9.65332	−0.314522
$943$	5.60947	0.182670
$944$	−2.96974	−0.0966567
$945$	5.91754	0.192498
$946$	0.169965	0.00552602
$947$	−51.9644	−1.68862	−0.844308	−	0.535859i	$-0.819988\pi$
$947$	−51.9644	−1.68862	−0.844308	+	0.535859i	$0.819988\pi$
$948$	−13.1477	−0.427018
$949$	4.54372	0.147495
$950$	28.5530	0.926382
$951$	−5.30842	−0.172137
$952$	−3.04956	−0.0988367
$953$	−21.8861	−0.708961	−0.354481	−	0.935063i	$-0.615342\pi$
$953$	−21.8861	−0.708961	−0.354481	+	0.935063i	$0.615342\pi$
$954$	27.2845	0.883368
$955$	17.4058	0.563238
$956$	6.35612	0.205572
$957$	0.00554322	0.000179187 0
$958$	10.7276	0.346594
$959$	10.3412	0.333934
$960$	0.707846	0.0228456
$961$	15.3532	0.495265
$962$	−6.14261	−0.198046
$963$	12.6606	0.407982
$964$	−2.63836	−0.0849759
$965$	4.02868	0.129688
$966$	1.20006	0.0386112
$967$	14.0096	0.450519	0.225260	−	0.974299i	$-0.427677\pi$
$967$	14.0096	0.450519	0.225260	+	0.974299i	$0.427677\pi$
$968$	−10.9995	−0.353536
$969$	−10.4628	−0.336113
$970$	0.285177	0.00915650
$971$	18.8327	0.604370	0.302185	−	0.953249i	$-0.402284\pi$
$971$	18.8327	0.604370	0.302185	+	0.953249i	$0.402284\pi$
$972$	15.6192	0.500986
$973$	9.86181	0.316155
$974$	21.3200	0.683136
$975$	2.55471	0.0818161
$976$	1.46375	0.0468535
$977$	56.3236	1.80195	0.900977	−	0.433868i	$-0.142851\pi$
$977$	56.3236	1.80195	0.900977	+	0.433868i	$0.142851\pi$
$978$	9.35709	0.299207
$979$	0.328278	0.0104918
$980$	−4.20350	−0.134276
$981$	−40.9280	−1.30673
$982$	0.758231	0.0241961
$983$	−41.5654	−1.32573	−0.662866	−	0.748738i	$-0.730660\pi$
$983$	−41.5654	−1.32573	−0.662866	+	0.748738i	$0.730660\pi$
$984$	−4.34768	−0.138599
$985$	3.90364	0.124380
$986$	−0.611936	−0.0194880
$987$	−8.33596	−0.265336
$988$	5.42296	0.172527
$989$	7.38357	0.234784
$990$	0.0504402	0.00160310
$991$	27.0628	0.859679	0.429840	−	0.902905i	$-0.358570\pi$
$991$	27.0628	0.859679	0.429840	+	0.902905i	$0.358570\pi$
$992$	6.80832	0.216164
$993$	21.6451	0.686888
$994$	−5.96944	−0.189339
$995$	−11.5523	−0.366233
$996$	−5.86631	−0.185881
$997$	−12.0137	−0.380479	−0.190240	−	0.981738i	$-0.560926\pi$
$997$	−12.0137	−0.380479	−0.190240	+	0.981738i	$0.560926\pi$
$998$	−14.8283	−0.469382
$999$	−32.4885	−1.02789

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.g.1.12	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.g.1.12	✓	21	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.775060 q^{3} +1.00000 q^{4} +0.913280 q^{5} +0.775060 q^{6} -1.54834 q^{7} +1.00000 q^{8} -2.39928 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.775060 q^{3} +1.00000 q^{4} +0.913280 q^{5} +0.775060 q^{6} -1.54834 q^{7} +1.00000 q^{8} -2.39928 q^{9} +0.913280 q^{10} -0.0230193 q^{11} +0.775060 q^{12} -0.791216 q^{13} -1.54834 q^{14} +0.707846 q^{15} +1.00000 q^{16} +1.96957 q^{17} -2.39928 q^{18} -6.85395 q^{19} +0.913280 q^{20} -1.20006 q^{21} -0.0230193 q^{22} -1.00000 q^{23} +0.775060 q^{24} -4.16592 q^{25} -0.791216 q^{26} -4.18477 q^{27} -1.54834 q^{28} -0.310696 q^{29} +0.707846 q^{30} +6.80832 q^{31} +1.00000 q^{32} -0.0178413 q^{33} +1.96957 q^{34} -1.41407 q^{35} -2.39928 q^{36} +7.76351 q^{37} -6.85395 q^{38} -0.613239 q^{39} +0.913280 q^{40} -5.60947 q^{41} -1.20006 q^{42} -7.38357 q^{43} -0.0230193 q^{44} -2.19122 q^{45} -1.00000 q^{46} +6.94631 q^{47} +0.775060 q^{48} -4.60264 q^{49} -4.16592 q^{50} +1.52653 q^{51} -0.791216 q^{52} -11.3719 q^{53} -4.18477 q^{54} -0.0210231 q^{55} -1.54834 q^{56} -5.31222 q^{57} -0.310696 q^{58} -2.96974 q^{59} +0.707846 q^{60} +1.46375 q^{61} +6.80832 q^{62} +3.71490 q^{63} +1.00000 q^{64} -0.722602 q^{65} -0.0178413 q^{66} -2.84855 q^{67} +1.96957 q^{68} -0.775060 q^{69} -1.41407 q^{70} +3.85538 q^{71} -2.39928 q^{72} -5.74271 q^{73} +7.76351 q^{74} -3.22884 q^{75} -6.85395 q^{76} +0.0356417 q^{77} -0.613239 q^{78} -16.9635 q^{79} +0.913280 q^{80} +3.95441 q^{81} -5.60947 q^{82} -7.56884 q^{83} -1.20006 q^{84} +1.79877 q^{85} -7.38357 q^{86} -0.240808 q^{87} -0.0230193 q^{88} -14.2610 q^{89} -2.19122 q^{90} +1.22507 q^{91} -1.00000 q^{92} +5.27685 q^{93} +6.94631 q^{94} -6.25958 q^{95} +0.775060 q^{96} +0.312256 q^{97} -4.60264 q^{98} +0.0552298 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) \) 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9} - 13 q^{10} - 4 q^{11} - 4 q^{13} - 18 q^{14} - 16 q^{15} + 21 q^{16} - 12 q^{17} + 7 q^{18} - 18 q^{19} - 13 q^{20} - 24 q^{21} - 4 q^{22} - 21 q^{23} + 2 q^{25} - 4 q^{26} - 9 q^{27} - 18 q^{28} - 16 q^{29} - 16 q^{30} - 7 q^{31} + 21 q^{32} - 15 q^{33} - 12 q^{34} + 7 q^{36} - 44 q^{37} - 18 q^{38} - 14 q^{39} - 13 q^{40} - 23 q^{41} - 24 q^{42} - 18 q^{43} - 4 q^{44} - 36 q^{45} - 21 q^{46} + 2 q^{47} - 13 q^{49} + 2 q^{50} - 26 q^{51} - 4 q^{52} - 39 q^{53} - 9 q^{54} - 32 q^{55} - 18 q^{56} - 22 q^{57} - 16 q^{58} - 27 q^{59} - 16 q^{60} - 34 q^{61} - 7 q^{62} - 28 q^{63} + 21 q^{64} - 25 q^{65} - 15 q^{66} - 19 q^{67} - 12 q^{68} - 24 q^{71} + 7 q^{72} - 8 q^{73} - 44 q^{74} + 50 q^{75} - 18 q^{76} - 16 q^{77} - 14 q^{78} - 27 q^{79} - 13 q^{80} + 33 q^{81} - 23 q^{82} + 7 q^{83} - 24 q^{84} - 22 q^{85} - 18 q^{86} - 15 q^{87} - 4 q^{88} - 12 q^{89} - 36 q^{90} - 20 q^{91} - 21 q^{92} - 43 q^{93} + 2 q^{94} - 14 q^{95} - 52 q^{97} - 13 q^{98} - 30 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9 - 13 * q^10 - 4 * q^11 - 4 * q^13 - 18 * q^14 - 16 * q^15 + 21 * q^16 - 12 * q^17 + 7 * q^18 - 18 * q^19 - 13 * q^20 - 24 * q^21 - 4 * q^22 - 21 * q^23 + 2 * q^25 - 4 * q^26 - 9 * q^27 - 18 * q^28 - 16 * q^29 - 16 * q^30 - 7 * q^31 + 21 * q^32 - 15 * q^33 - 12 * q^34 + 7 * q^36 - 44 * q^37 - 18 * q^38 - 14 * q^39 - 13 * q^40 - 23 * q^41 - 24 * q^42 - 18 * q^43 - 4 * q^44 - 36 * q^45 - 21 * q^46 + 2 * q^47 - 13 * q^49 + 2 * q^50 - 26 * q^51 - 4 * q^52 - 39 * q^53 - 9 * q^54 - 32 * q^55 - 18 * q^56 - 22 * q^57 - 16 * q^58 - 27 * q^59 - 16 * q^60 - 34 * q^61 - 7 * q^62 - 28 * q^63 + 21 * q^64 - 25 * q^65 - 15 * q^66 - 19 * q^67 - 12 * q^68 - 24 * q^71 + 7 * q^72 - 8 * q^73 - 44 * q^74 + 50 * q^75 - 18 * q^76 - 16 * q^77 - 14 * q^78 - 27 * q^79 - 13 * q^80 + 33 * q^81 - 23 * q^82 + 7 * q^83 - 24 * q^84 - 22 * q^85 - 18 * q^86 - 15 * q^87 - 4 * q^88 - 12 * q^89 - 36 * q^90 - 20 * q^91 - 21 * q^92 - 43 * q^93 + 2 * q^94 - 14 * q^95 - 52 * q^97 - 13 * q^98 - 30 * q^99

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