LMFDB - Embedded newform 4029.2.a.h.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.38168 q^{2} +1.00000 q^{3} +3.67240 q^{4} +4.36966 q^{5} -2.38168 q^{6} -4.18483 q^{7} -3.98313 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.38168 q^{2} +1.00000 q^{3} +3.67240 q^{4} +4.36966 q^{5} -2.38168 q^{6} -4.18483 q^{7} -3.98313 q^{8} +1.00000 q^{9} -10.4071 q^{10} +1.39544 q^{11} +3.67240 q^{12} -0.773626 q^{13} +9.96693 q^{14} +4.36966 q^{15} +2.14173 q^{16} -1.00000 q^{17} -2.38168 q^{18} -7.43227 q^{19} +16.0471 q^{20} -4.18483 q^{21} -3.32349 q^{22} -3.06376 q^{23} -3.98313 q^{24} +14.0939 q^{25} +1.84253 q^{26} +1.00000 q^{27} -15.3684 q^{28} +1.78243 q^{29} -10.4071 q^{30} -10.4199 q^{31} +2.86533 q^{32} +1.39544 q^{33} +2.38168 q^{34} -18.2863 q^{35} +3.67240 q^{36} -3.14548 q^{37} +17.7013 q^{38} -0.773626 q^{39} -17.4049 q^{40} -2.80032 q^{41} +9.96693 q^{42} +5.21573 q^{43} +5.12461 q^{44} +4.36966 q^{45} +7.29690 q^{46} +0.527410 q^{47} +2.14173 q^{48} +10.5128 q^{49} -33.5672 q^{50} -1.00000 q^{51} -2.84107 q^{52} +2.73509 q^{53} -2.38168 q^{54} +6.09759 q^{55} +16.6687 q^{56} -7.43227 q^{57} -4.24517 q^{58} +4.55162 q^{59} +16.0471 q^{60} -11.1342 q^{61} +24.8168 q^{62} -4.18483 q^{63} -11.1078 q^{64} -3.38048 q^{65} -3.32349 q^{66} +9.39127 q^{67} -3.67240 q^{68} -3.06376 q^{69} +43.5521 q^{70} -1.25137 q^{71} -3.98313 q^{72} -9.12122 q^{73} +7.49152 q^{74} +14.0939 q^{75} -27.2943 q^{76} -5.83967 q^{77} +1.84253 q^{78} +1.00000 q^{79} +9.35865 q^{80} +1.00000 q^{81} +6.66947 q^{82} -0.320604 q^{83} -15.3684 q^{84} -4.36966 q^{85} -12.4222 q^{86} +1.78243 q^{87} -5.55820 q^{88} -14.4702 q^{89} -10.4071 q^{90} +3.23749 q^{91} -11.2514 q^{92} -10.4199 q^{93} -1.25612 q^{94} -32.4765 q^{95} +2.86533 q^{96} +7.35640 q^{97} -25.0381 q^{98} +1.39544 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9	\( 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9} - 9 q^{10} - 19 q^{11} + 21 q^{12} - 12 q^{13} - 15 q^{14} - 12 q^{15} + q^{16} - 25 q^{17} - 7 q^{18} - 35 q^{19} - 11 q^{20} - 4 q^{21} - 2 q^{22} - 16 q^{23} - 21 q^{24} + 19 q^{25} - 5 q^{26} + 25 q^{27} + 3 q^{28} - 37 q^{29} - 9 q^{30} - 28 q^{31} - 19 q^{32} - 19 q^{33} + 7 q^{34} - 42 q^{35} + 21 q^{36} + 8 q^{37} - 35 q^{38} - 12 q^{39} - 9 q^{40} - 34 q^{41} - 15 q^{42} - 19 q^{43} - 56 q^{44} - 12 q^{45} + q^{46} - 25 q^{47} + q^{48} + 25 q^{49} - 7 q^{50} - 25 q^{51} - 37 q^{52} - 44 q^{53} - 7 q^{54} - 11 q^{55} - 18 q^{56} - 35 q^{57} - 3 q^{58} - 47 q^{59} - 11 q^{60} - 28 q^{61} + 11 q^{62} - 4 q^{63} - 9 q^{64} - 63 q^{65} - 2 q^{66} - 28 q^{67} - 21 q^{68} - 16 q^{69} + 5 q^{70} - 27 q^{71} - 21 q^{72} - 21 q^{73} - 18 q^{74} + 19 q^{75} - 50 q^{76} - 58 q^{77} - 5 q^{78} + 25 q^{79} - 56 q^{80} + 25 q^{81} - 5 q^{82} - 61 q^{83} + 3 q^{84} + 12 q^{85} - 28 q^{86} - 37 q^{87} + 15 q^{88} - 34 q^{89} - 9 q^{90} - 30 q^{91} - 31 q^{92} - 28 q^{93} + q^{94} - 32 q^{95} - 19 q^{96} - 11 q^{97} - 66 q^{98} - 19 q^{99}+O(q^{100}) \) 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9 - 9 * q^10 - 19 * q^11 + 21 * q^12 - 12 * q^13 - 15 * q^14 - 12 * q^15 + q^16 - 25 * q^17 - 7 * q^18 - 35 * q^19 - 11 * q^20 - 4 * q^21 - 2 * q^22 - 16 * q^23 - 21 * q^24 + 19 * q^25 - 5 * q^26 + 25 * q^27 + 3 * q^28 - 37 * q^29 - 9 * q^30 - 28 * q^31 - 19 * q^32 - 19 * q^33 + 7 * q^34 - 42 * q^35 + 21 * q^36 + 8 * q^37 - 35 * q^38 - 12 * q^39 - 9 * q^40 - 34 * q^41 - 15 * q^42 - 19 * q^43 - 56 * q^44 - 12 * q^45 + q^46 - 25 * q^47 + q^48 + 25 * q^49 - 7 * q^50 - 25 * q^51 - 37 * q^52 - 44 * q^53 - 7 * q^54 - 11 * q^55 - 18 * q^56 - 35 * q^57 - 3 * q^58 - 47 * q^59 - 11 * q^60 - 28 * q^61 + 11 * q^62 - 4 * q^63 - 9 * q^64 - 63 * q^65 - 2 * q^66 - 28 * q^67 - 21 * q^68 - 16 * q^69 + 5 * q^70 - 27 * q^71 - 21 * q^72 - 21 * q^73 - 18 * q^74 + 19 * q^75 - 50 * q^76 - 58 * q^77 - 5 * q^78 + 25 * q^79 - 56 * q^80 + 25 * q^81 - 5 * q^82 - 61 * q^83 + 3 * q^84 + 12 * q^85 - 28 * q^86 - 37 * q^87 + 15 * q^88 - 34 * q^89 - 9 * q^90 - 30 * q^91 - 31 * q^92 - 28 * q^93 + q^94 - 32 * q^95 - 19 * q^96 - 11 * q^97 - 66 * q^98 - 19 * 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 $

$2$	−2.38168	−1.68410	−0.842051	−	0.539398i	$-0.818652\pi$
$2$	−2.38168	−1.68410	−0.842051	+	0.539398i	$0.818652\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.67240	1.83620
$5$	4.36966	1.95417	0.977086	−	0.212846i	$-0.0682734\pi$
$5$	4.36966	1.95417	0.977086	+	0.212846i	$0.0682734\pi$
$6$	−2.38168	−0.972317
$7$	−4.18483	−1.58172	−0.790858	−	0.611999i	$-0.790366\pi$
$7$	−4.18483	−1.58172	−0.790858	+	0.611999i	$0.790366\pi$
$8$	−3.98313	−1.40825
$9$	1.00000	0.333333
$10$	−10.4071	−3.29102
$11$	1.39544	0.420740	0.210370	−	0.977622i	$-0.432533\pi$
$11$	1.39544	0.420740	0.210370	+	0.977622i	$0.432533\pi$
$12$	3.67240	1.06013
$13$	−0.773626	−0.214565	−0.107283	−	0.994229i	$-0.534215\pi$
$13$	−0.773626	−0.214565	−0.107283	+	0.994229i	$0.534215\pi$
$14$	9.96693	2.66377
$15$	4.36966	1.12824
$16$	2.14173	0.535433
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.38168	−0.561367
$19$	−7.43227	−1.70508	−0.852540	−	0.522662i	$-0.824939\pi$
$19$	−7.43227	−1.70508	−0.852540	+	0.522662i	$0.824939\pi$
$20$	16.0471	3.58825
$21$	−4.18483	−0.913205
$22$	−3.32349	−0.708570
$23$	−3.06376	−0.638839	−0.319419	−	0.947613i	$-0.603488\pi$
$23$	−3.06376	−0.638839	−0.319419	+	0.947613i	$0.603488\pi$
$24$	−3.98313	−0.813053
$25$	14.0939	2.81879
$26$	1.84253	0.361350
$27$	1.00000	0.192450
$28$	−15.3684	−2.90435
$29$	1.78243	0.330988	0.165494	−	0.986211i	$-0.447078\pi$
$29$	1.78243	0.330988	0.165494	+	0.986211i	$0.447078\pi$
$30$	−10.4071	−1.90007
$31$	−10.4199	−1.87147	−0.935733	−	0.352708i	$-0.885261\pi$
$31$	−10.4199	−1.87147	−0.935733	+	0.352708i	$0.885261\pi$
$32$	2.86533	0.506524
$33$	1.39544	0.242914
$34$	2.38168	0.408455
$35$	−18.2863	−3.09095
$36$	3.67240	0.612067
$37$	−3.14548	−0.517113	−0.258557	−	0.965996i	$-0.583247\pi$
$37$	−3.14548	−0.517113	−0.258557	+	0.965996i	$0.583247\pi$
$38$	17.7013	2.87153
$39$	−0.773626	−0.123879
$40$	−17.4049	−2.75196
$41$	−2.80032	−0.437337	−0.218668	−	0.975799i	$-0.570171\pi$
$41$	−2.80032	−0.437337	−0.218668	+	0.975799i	$0.570171\pi$
$42$	9.96693	1.53793
$43$	5.21573	0.795392	0.397696	−	0.917517i	$-0.369810\pi$
$43$	5.21573	0.795392	0.397696	+	0.917517i	$0.369810\pi$
$44$	5.12461	0.772564
$45$	4.36966	0.651390
$46$	7.29690	1.07587
$47$	0.527410	0.0769307	0.0384653	−	0.999260i	$-0.487753\pi$
$47$	0.527410	0.0769307	0.0384653	+	0.999260i	$0.487753\pi$
$48$	2.14173	0.309133
$49$	10.5128	1.50183
$50$	−33.5672	−4.74712
$51$	−1.00000	−0.140028
$52$	−2.84107	−0.393985
$53$	2.73509	0.375693	0.187847	−	0.982198i	$-0.439849\pi$
$53$	2.73509	0.375693	0.187847	+	0.982198i	$0.439849\pi$
$54$	−2.38168	−0.324106
$55$	6.09759	0.822198
$56$	16.6687	2.22745
$57$	−7.43227	−0.984428
$58$	−4.24517	−0.557418
$59$	4.55162	0.592571	0.296285	−	0.955099i	$-0.404252\pi$
$59$	4.55162	0.592571	0.296285	+	0.955099i	$0.404252\pi$
$60$	16.0471	2.07168
$61$	−11.1342	−1.42558	−0.712792	−	0.701375i	$-0.752570\pi$
$61$	−11.1342	−1.42558	−0.712792	+	0.701375i	$0.752570\pi$
$62$	24.8168	3.15174
$63$	−4.18483	−0.527239
$64$	−11.1078	−1.38847
$65$	−3.38048	−0.419297
$66$	−3.32349	−0.409093
$67$	9.39127	1.14733	0.573663	−	0.819091i	$-0.305522\pi$
$67$	9.39127	1.14733	0.573663	+	0.819091i	$0.305522\pi$
$68$	−3.67240	−0.445344
$69$	−3.06376	−0.368834
$70$	43.5521	5.20547
$71$	−1.25137	−0.148510	−0.0742552	−	0.997239i	$-0.523658\pi$
$71$	−1.25137	−0.148510	−0.0742552	+	0.997239i	$0.523658\pi$
$72$	−3.98313	−0.469416
$73$	−9.12122	−1.06756	−0.533779	−	0.845624i	$-0.679229\pi$
$73$	−9.12122	−1.06756	−0.533779	+	0.845624i	$0.679229\pi$
$74$	7.49152	0.870871
$75$	14.0939	1.62743
$76$	−27.2943	−3.13087
$77$	−5.83967	−0.665492
$78$	1.84253	0.208625
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	9.35865	1.04633
$81$	1.00000	0.111111
$82$	6.66947	0.736520
$83$	−0.320604	−0.0351908	−0.0175954	−	0.999845i	$-0.505601\pi$
$83$	−0.320604	−0.0351908	−0.0175954	+	0.999845i	$0.505601\pi$
$84$	−15.3684	−1.67683
$85$	−4.36966	−0.473956
$86$	−12.4222	−1.33952
$87$	1.78243	0.191096
$88$	−5.55820	−0.592507
$89$	−14.4702	−1.53384	−0.766921	−	0.641742i	$-0.778212\pi$
$89$	−14.4702	−1.53384	−0.766921	+	0.641742i	$0.778212\pi$
$90$	−10.4071	−1.09701
$91$	3.23749	0.339382
$92$	−11.2514	−1.17304
$93$	−10.4199	−1.08049
$94$	−1.25612	−0.129559
$95$	−32.4765	−3.33202
$96$	2.86533	0.292442
$97$	7.35640	0.746929	0.373464	−	0.927644i	$-0.378170\pi$
$97$	7.35640	0.746929	0.373464	+	0.927644i	$0.378170\pi$
$98$	−25.0381	−2.52923
$99$	1.39544	0.140247
$100$	51.7586	5.17586
$101$	−10.9485	−1.08942	−0.544709	−	0.838625i	$-0.683360\pi$
$101$	−10.9485	−1.08942	−0.544709	+	0.838625i	$0.683360\pi$
$102$	2.38168	0.235822
$103$	−10.2657	−1.01151	−0.505756	−	0.862677i	$-0.668786\pi$
$103$	−10.2657	−1.01151	−0.505756	+	0.862677i	$0.668786\pi$
$104$	3.08145	0.302161
$105$	−18.2863	−1.78456
$106$	−6.51411	−0.632706
$107$	−11.0209	−1.06543	−0.532717	−	0.846293i	$-0.678829\pi$
$107$	−11.0209	−1.06543	−0.532717	+	0.846293i	$0.678829\pi$
$108$	3.67240	0.353377
$109$	12.2846	1.17665	0.588327	−	0.808623i	$-0.299787\pi$
$109$	12.2846	1.17665	0.588327	+	0.808623i	$0.299787\pi$
$110$	−14.5225	−1.38467
$111$	−3.14548	−0.298555
$112$	−8.96279	−0.846904
$113$	−8.50246	−0.799844	−0.399922	−	0.916549i	$-0.630963\pi$
$113$	−8.50246	−0.799844	−0.399922	+	0.916549i	$0.630963\pi$
$114$	17.7013	1.65788
$115$	−13.3876	−1.24840
$116$	6.54578	0.607761
$117$	−0.773626	−0.0715218
$118$	−10.8405	−0.997950
$119$	4.18483	0.383623
$120$	−17.4049	−1.58884
$121$	−9.05275	−0.822978
$122$	26.5180	2.40083
$123$	−2.80032	−0.252496
$124$	−38.2660	−3.43639
$125$	39.7374	3.55422
$126$	9.96693	0.887924
$127$	−18.7310	−1.66211	−0.831054	−	0.556192i	$-0.812262\pi$
$127$	−18.7310	−1.66211	−0.831054	+	0.556192i	$0.812262\pi$
$128$	20.7245	1.83180
$129$	5.21573	0.459220
$130$	8.05123	0.706140
$131$	−11.9064	−1.04026	−0.520132	−	0.854086i	$-0.674117\pi$
$131$	−11.9064	−1.04026	−0.520132	+	0.854086i	$0.674117\pi$
$132$	5.12461	0.446040
$133$	31.1028	2.69695
$134$	−22.3670	−1.93221
$135$	4.36966	0.376080
$136$	3.98313	0.341550
$137$	−6.92224	−0.591407	−0.295704	−	0.955280i	$-0.595554\pi$
$137$	−6.92224	−0.591407	−0.295704	+	0.955280i	$0.595554\pi$
$138$	7.29690	0.621154
$139$	−9.71670	−0.824160	−0.412080	−	0.911148i	$-0.635198\pi$
$139$	−9.71670	−0.824160	−0.412080	+	0.911148i	$0.635198\pi$
$140$	−67.1546	−5.67560
$141$	0.527410	0.0444159
$142$	2.98037	0.250107
$143$	−1.07955	−0.0902762
$144$	2.14173	0.178478
$145$	7.78859	0.646807
$146$	21.7238	1.79788
$147$	10.5128	0.867081
$148$	−11.5515	−0.949523
$149$	−14.5529	−1.19222	−0.596112	−	0.802901i	$-0.703289\pi$
$149$	−14.5529	−1.19222	−0.596112	+	0.802901i	$0.703289\pi$
$150$	−33.5672	−2.74075
$151$	12.8639	1.04685	0.523425	−	0.852072i	$-0.324654\pi$
$151$	12.8639	1.04685	0.523425	+	0.852072i	$0.324654\pi$
$152$	29.6037	2.40118
$153$	−1.00000	−0.0808452
$154$	13.9082	1.12076
$155$	−45.5314	−3.65717
$156$	−2.84107	−0.227467
$157$	17.2050	1.37311	0.686553	−	0.727079i	$-0.259123\pi$
$157$	17.2050	1.37311	0.686553	+	0.727079i	$0.259123\pi$
$158$	−2.38168	−0.189476
$159$	2.73509	0.216907
$160$	12.5205	0.989834
$161$	12.8213	1.01046
$162$	−2.38168	−0.187122
$163$	2.23585	0.175125	0.0875626	−	0.996159i	$-0.472092\pi$
$163$	2.23585	0.175125	0.0875626	+	0.996159i	$0.472092\pi$
$164$	−10.2839	−0.803038
$165$	6.09759	0.474696
$166$	0.763575	0.0592649
$167$	−9.73250	−0.753123	−0.376562	−	0.926392i	$-0.622894\pi$
$167$	−9.73250	−0.753123	−0.376562	+	0.926392i	$0.622894\pi$
$168$	16.6687	1.28602
$169$	−12.4015	−0.953962
$170$	10.4071	0.798191
$171$	−7.43227	−0.568360
$172$	19.1543	1.46050
$173$	6.79212	0.516395	0.258198	−	0.966092i	$-0.416871\pi$
$173$	6.79212	0.516395	0.258198	+	0.966092i	$0.416871\pi$
$174$	−4.24517	−0.321825
$175$	−58.9807	−4.45852
$176$	2.98865	0.225278
$177$	4.55162	0.342121
$178$	34.4635	2.58315
$179$	−9.57249	−0.715482	−0.357741	−	0.933821i	$-0.616453\pi$
$179$	−9.57249	−0.715482	−0.357741	+	0.933821i	$0.616453\pi$
$180$	16.0471	1.19608
$181$	−4.72090	−0.350902	−0.175451	−	0.984488i	$-0.556138\pi$
$181$	−4.72090	−0.350902	−0.175451	+	0.984488i	$0.556138\pi$
$182$	−7.71067	−0.571553
$183$	−11.1342	−0.823062
$184$	12.2034	0.899643
$185$	−13.7447	−1.01053
$186$	24.8168	1.81966
$187$	−1.39544	−0.102044
$188$	1.93686	0.141260
$189$	−4.18483	−0.304402
$190$	77.3486	5.61146
$191$	−16.5087	−1.19453	−0.597264	−	0.802044i	$-0.703746\pi$
$191$	−16.5087	−1.19453	−0.597264	+	0.802044i	$0.703746\pi$
$192$	−11.1078	−0.801634
$193$	4.77961	0.344044	0.172022	−	0.985093i	$-0.444970\pi$
$193$	4.77961	0.344044	0.172022	+	0.985093i	$0.444970\pi$
$194$	−17.5206	−1.25790
$195$	−3.38048	−0.242081
$196$	38.6072	2.75766
$197$	18.7655	1.33698	0.668492	−	0.743719i	$-0.266940\pi$
$197$	18.7655	1.33698	0.668492	+	0.743719i	$0.266940\pi$
$198$	−3.32349	−0.236190
$199$	21.6132	1.53212	0.766061	−	0.642768i	$-0.222214\pi$
$199$	21.6132	1.53212	0.766061	+	0.642768i	$0.222214\pi$
$200$	−56.1379	−3.96955
$201$	9.39127	0.662409
$202$	26.0758	1.83469
$203$	−7.45915	−0.523529
$204$	−3.67240	−0.257120
$205$	−12.2365	−0.854631
$206$	24.4497	1.70349
$207$	−3.06376	−0.212946
$208$	−1.65690	−0.114885
$209$	−10.3713	−0.717396
$210$	43.5521	3.00538
$211$	0.916825	0.0631168	0.0315584	−	0.999502i	$-0.489953\pi$
$211$	0.916825	0.0631168	0.0315584	+	0.999502i	$0.489953\pi$
$212$	10.0443	0.689849
$213$	−1.25137	−0.0857425
$214$	26.2483	1.79430
$215$	22.7910	1.55433
$216$	−3.98313	−0.271018
$217$	43.6054	2.96013
$218$	−29.2580	−1.98160
$219$	−9.12122	−0.616355
$220$	22.3928	1.50972
$221$	0.773626	0.0520397
$222$	7.49152	0.502798
$223$	9.75878	0.653496	0.326748	−	0.945111i	$-0.394047\pi$
$223$	9.75878	0.653496	0.326748	+	0.945111i	$0.394047\pi$
$224$	−11.9909	−0.801177
$225$	14.0939	0.939595
$226$	20.2501	1.34702
$227$	6.16481	0.409173	0.204586	−	0.978848i	$-0.434415\pi$
$227$	6.16481	0.409173	0.204586	+	0.978848i	$0.434415\pi$
$228$	−27.2943	−1.80761
$229$	20.4272	1.34987	0.674934	−	0.737878i	$-0.264172\pi$
$229$	20.4272	1.34987	0.674934	+	0.737878i	$0.264172\pi$
$230$	31.8850	2.10243
$231$	−5.83967	−0.384222
$232$	−7.09963	−0.466113
$233$	8.02201	0.525540	0.262770	−	0.964859i	$-0.415364\pi$
$233$	8.02201	0.525540	0.262770	+	0.964859i	$0.415364\pi$
$234$	1.84253	0.120450
$235$	2.30460	0.150336
$236$	16.7154	1.08808
$237$	1.00000	0.0649570
$238$	−9.96693	−0.646060
$239$	16.6581	1.07752	0.538760	−	0.842459i	$-0.318893\pi$
$239$	16.6581	1.07752	0.538760	+	0.842459i	$0.318893\pi$
$240$	9.35865	0.604098
$241$	8.21979	0.529483	0.264742	−	0.964319i	$-0.414713\pi$
$241$	8.21979	0.529483	0.264742	+	0.964319i	$0.414713\pi$
$242$	21.5608	1.38598
$243$	1.00000	0.0641500
$244$	−40.8892	−2.61766
$245$	45.9373	2.93483
$246$	6.66947	0.425230
$247$	5.74980	0.365851
$248$	41.5037	2.63549
$249$	−0.320604	−0.0203174
$250$	−94.6417	−5.98567
$251$	−25.8731	−1.63310	−0.816549	−	0.577276i	$-0.804116\pi$
$251$	−25.8731	−1.63310	−0.816549	+	0.577276i	$0.804116\pi$
$252$	−15.3684	−0.968117
$253$	−4.27529	−0.268785
$254$	44.6112	2.79916
$255$	−4.36966	−0.273639
$256$	−27.1436	−1.69647
$257$	−13.0658	−0.815024	−0.407512	−	0.913200i	$-0.633603\pi$
$257$	−13.0658	−0.815024	−0.407512	+	0.913200i	$0.633603\pi$
$258$	−12.4222	−0.773373
$259$	13.1633	0.817926
$260$	−12.4145	−0.769914
$261$	1.78243	0.110329
$262$	28.3572	1.75191
$263$	20.5041	1.26434	0.632169	−	0.774831i	$-0.282165\pi$
$263$	20.5041	1.26434	0.632169	+	0.774831i	$0.282165\pi$
$264$	−5.55820	−0.342084
$265$	11.9514	0.734169
$266$	−74.0769	−4.54195
$267$	−14.4702	−0.885564
$268$	34.4885	2.10672
$269$	15.3655	0.936851	0.468425	−	0.883503i	$-0.344821\pi$
$269$	15.3655	0.936851	0.468425	+	0.883503i	$0.344821\pi$
$270$	−10.4071	−0.633358
$271$	−20.0413	−1.21742	−0.608710	−	0.793393i	$-0.708313\pi$
$271$	−20.0413	−1.21742	−0.608710	+	0.793393i	$0.708313\pi$
$272$	−2.14173	−0.129862
$273$	3.23749	0.195942
$274$	16.4866	0.995990
$275$	19.6672	1.18598
$276$	−11.2514	−0.677253
$277$	−1.85320	−0.111348	−0.0556739	−	0.998449i	$-0.517731\pi$
$277$	−1.85320	−0.111348	−0.0556739	+	0.998449i	$0.517731\pi$
$278$	23.1421	1.38797
$279$	−10.4199	−0.623822
$280$	72.8366	4.35282
$281$	4.39121	0.261958	0.130979	−	0.991385i	$-0.458188\pi$
$281$	4.39121	0.261958	0.130979	+	0.991385i	$0.458188\pi$
$282$	−1.25612	−0.0748010
$283$	−20.7764	−1.23503	−0.617514	−	0.786560i	$-0.711860\pi$
$283$	−20.7764	−1.23503	−0.617514	+	0.786560i	$0.711860\pi$
$284$	−4.59554	−0.272695
$285$	−32.4765	−1.92374
$286$	2.57114	0.152034
$287$	11.7189	0.691743
$288$	2.86533	0.168841
$289$	1.00000	0.0588235
$290$	−18.5499	−1.08929
$291$	7.35640	0.431240
$292$	−33.4968	−1.96025
$293$	11.4282	0.667642	0.333821	−	0.942636i	$-0.391662\pi$
$293$	11.4282	0.667642	0.333821	+	0.942636i	$0.391662\pi$
$294$	−25.0381	−1.46025
$295$	19.8890	1.15798
$296$	12.5288	0.728224
$297$	1.39544	0.0809715
$298$	34.6605	2.00783
$299$	2.37021	0.137073
$300$	51.7586	2.98828
$301$	−21.8270	−1.25808
$302$	−30.6377	−1.76300
$303$	−10.9485	−0.628975
$304$	−15.9179	−0.912957
$305$	−48.6526	−2.78584
$306$	2.38168	0.136152
$307$	−15.3049	−0.873498	−0.436749	−	0.899583i	$-0.643870\pi$
$307$	−15.3049	−0.873498	−0.436749	+	0.899583i	$0.643870\pi$
$308$	−21.4456	−1.22198
$309$	−10.2657	−0.583996
$310$	108.441	6.15904
$311$	−10.7547	−0.609845	−0.304922	−	0.952377i	$-0.598631\pi$
$311$	−10.7547	−0.609845	−0.304922	+	0.952377i	$0.598631\pi$
$312$	3.08145	0.174453
$313$	−10.6217	−0.600375	−0.300187	−	0.953880i	$-0.597049\pi$
$313$	−10.6217	−0.600375	−0.300187	+	0.953880i	$0.597049\pi$
$314$	−40.9768	−2.31245
$315$	−18.2863	−1.03032
$316$	3.67240	0.206589
$317$	30.1109	1.69120	0.845599	−	0.533818i	$-0.179243\pi$
$317$	30.1109	1.69120	0.845599	+	0.533818i	$0.179243\pi$
$318$	−6.51411	−0.365293
$319$	2.48726	0.139260
$320$	−48.5372	−2.71331
$321$	−11.0209	−0.615129
$322$	−30.5363	−1.70172
$323$	7.43227	0.413543
$324$	3.67240	0.204022
$325$	−10.9034	−0.604814
$326$	−5.32508	−0.294929
$327$	12.2846	0.679341
$328$	11.1540	0.615879
$329$	−2.20712	−0.121682
$330$	−14.5225	−0.799437
$331$	−11.7763	−0.647283	−0.323641	−	0.946180i	$-0.604907\pi$
$331$	−11.7763	−0.647283	−0.323641	+	0.946180i	$0.604907\pi$
$332$	−1.17739	−0.0646174
$333$	−3.14548	−0.172371
$334$	23.1797	1.26834
$335$	41.0366	2.24207
$336$	−8.96279	−0.488960
$337$	14.4015	0.784499	0.392249	−	0.919859i	$-0.371697\pi$
$337$	14.4015	0.784499	0.392249	+	0.919859i	$0.371697\pi$
$338$	29.5364	1.60657
$339$	−8.50246	−0.461790
$340$	−16.0471	−0.870279
$341$	−14.5403	−0.787401
$342$	17.7013	0.957176
$343$	−14.7004	−0.793749
$344$	−20.7749	−1.12011
$345$	−13.3876	−0.720764
$346$	−16.1767	−0.869663
$347$	−19.3137	−1.03681	−0.518406	−	0.855135i	$-0.673474\pi$
$347$	−19.3137	−1.03681	−0.518406	+	0.855135i	$0.673474\pi$
$348$	6.54578	0.350891
$349$	−13.8334	−0.740485	−0.370243	−	0.928935i	$-0.620725\pi$
$349$	−13.8334	−0.740485	−0.370243	+	0.928935i	$0.620725\pi$
$350$	140.473	7.50860
$351$	−0.773626	−0.0412931
$352$	3.99839	0.213115
$353$	7.48537	0.398406	0.199203	−	0.979958i	$-0.436165\pi$
$353$	7.48537	0.398406	0.199203	+	0.979958i	$0.436165\pi$
$354$	−10.8405	−0.576167
$355$	−5.46807	−0.290215
$356$	−53.1405	−2.81644
$357$	4.18483	0.221485
$358$	22.7986	1.20494
$359$	4.10020	0.216400	0.108200	−	0.994129i	$-0.465491\pi$
$359$	4.10020	0.216400	0.108200	+	0.994129i	$0.465491\pi$
$360$	−17.4049	−0.917319
$361$	36.2387	1.90730
$362$	11.2437	0.590955
$363$	−9.05275	−0.475146
$364$	11.8894	0.623173
$365$	−39.8566	−2.08619
$366$	26.5180	1.38612
$367$	−37.4127	−1.95293	−0.976464	−	0.215681i	$-0.930803\pi$
$367$	−37.4127	−1.95293	−0.976464	+	0.215681i	$0.930803\pi$
$368$	−6.56176	−0.342055
$369$	−2.80032	−0.145779
$370$	32.7354	1.70183
$371$	−11.4459	−0.594241
$372$	−38.2660	−1.98400
$373$	−10.0470	−0.520214	−0.260107	−	0.965580i	$-0.583758\pi$
$373$	−10.0470	−0.520214	−0.260107	+	0.965580i	$0.583758\pi$
$374$	3.32349	0.171853
$375$	39.7374	2.05203
$376$	−2.10074	−0.108337
$377$	−1.37893	−0.0710186
$378$	9.96693	0.512643
$379$	−19.4067	−0.996854	−0.498427	−	0.866932i	$-0.666089\pi$
$379$	−19.4067	−0.996854	−0.498427	+	0.866932i	$0.666089\pi$
$380$	−119.267	−6.11826
$381$	−18.7310	−0.959618
$382$	39.3185	2.01171
$383$	12.1341	0.620025	0.310012	−	0.950733i	$-0.399667\pi$
$383$	12.1341	0.620025	0.310012	+	0.950733i	$0.399667\pi$
$384$	20.7245	1.05759
$385$	−25.5174	−1.30048
$386$	−11.3835	−0.579405
$387$	5.21573	0.265131
$388$	27.0156	1.37151
$389$	−22.5082	−1.14121	−0.570604	−	0.821225i	$-0.693291\pi$
$389$	−22.5082	−1.14121	−0.570604	+	0.821225i	$0.693291\pi$
$390$	8.05123	0.407690
$391$	3.06376	0.154941
$392$	−41.8738	−2.11495
$393$	−11.9064	−0.600597
$394$	−44.6934	−2.25162
$395$	4.36966	0.219861
$396$	5.12461	0.257521
$397$	19.8683	0.997161	0.498581	−	0.866843i	$-0.333855\pi$
$397$	19.8683	0.997161	0.498581	+	0.866843i	$0.333855\pi$
$398$	−51.4758	−2.58025
$399$	31.1028	1.55709
$400$	30.1854	1.50927
$401$	15.7912	0.788575	0.394288	−	0.918987i	$-0.370991\pi$
$401$	15.7912	0.788575	0.394288	+	0.918987i	$0.370991\pi$
$402$	−22.3670	−1.11556
$403$	8.06110	0.401552
$404$	−40.2073	−2.00039
$405$	4.36966	0.217130
$406$	17.7653	0.881677
$407$	−4.38931	−0.217570
$408$	3.98313	0.197194
$409$	−23.7707	−1.17539	−0.587694	−	0.809084i	$-0.699964\pi$
$409$	−23.7707	−1.17539	−0.587694	+	0.809084i	$0.699964\pi$
$410$	29.1433	1.43929
$411$	−6.92224	−0.341449
$412$	−37.6998	−1.85734
$413$	−19.0478	−0.937279
$414$	7.29690	0.358623
$415$	−1.40093	−0.0687689
$416$	−2.21670	−0.108682
$417$	−9.71670	−0.475829
$418$	24.7010	1.20817
$419$	34.8892	1.70445	0.852226	−	0.523174i	$-0.175252\pi$
$419$	34.8892	1.70445	0.852226	+	0.523174i	$0.175252\pi$
$420$	−67.1546	−3.27681
$421$	−18.1811	−0.886095	−0.443047	−	0.896498i	$-0.646103\pi$
$421$	−18.1811	−0.886095	−0.443047	+	0.896498i	$0.646103\pi$
$422$	−2.18358	−0.106295
$423$	0.527410	0.0256436
$424$	−10.8942	−0.529070
$425$	−14.0939	−0.683656
$426$	2.98037	0.144399
$427$	46.5946	2.25487
$428$	−40.4733	−1.95635
$429$	−1.07955	−0.0521210
$430$	−54.2808	−2.61765
$431$	−23.6037	−1.13695	−0.568474	−	0.822701i	$-0.692466\pi$
$431$	−23.6037	−1.13695	−0.568474	+	0.822701i	$0.692466\pi$
$432$	2.14173	0.103044
$433$	0.383522	0.0184309	0.00921544	−	0.999958i	$-0.497067\pi$
$433$	0.383522	0.0184309	0.00921544	+	0.999958i	$0.497067\pi$
$434$	−103.854	−4.98516
$435$	7.78859	0.373434
$436$	45.1141	2.16057
$437$	22.7707	1.08927
$438$	21.7238	1.03800
$439$	2.01804	0.0963158	0.0481579	−	0.998840i	$-0.484665\pi$
$439$	2.01804	0.0963158	0.0481579	+	0.998840i	$0.484665\pi$
$440$	−24.2875	−1.15786
$441$	10.5128	0.500609
$442$	−1.84253	−0.0876402
$443$	−36.0659	−1.71354	−0.856772	−	0.515695i	$-0.827534\pi$
$443$	−36.0659	−1.71354	−0.856772	+	0.515695i	$0.827534\pi$
$444$	−11.5515	−0.548208
$445$	−63.2300	−2.99739
$446$	−23.2423	−1.10056
$447$	−14.5529	−0.688331
$448$	46.4841	2.19617
$449$	−2.36817	−0.111761	−0.0558805	−	0.998437i	$-0.517797\pi$
$449$	−2.36817	−0.111761	−0.0558805	+	0.998437i	$0.517797\pi$
$450$	−33.5672	−1.58237
$451$	−3.90767	−0.184005
$452$	−31.2244	−1.46867
$453$	12.8639	0.604399
$454$	−14.6826	−0.689089
$455$	14.1467	0.663210
$456$	29.6037	1.38632
$457$	6.04928	0.282973	0.141487	−	0.989940i	$-0.454812\pi$
$457$	6.04928	0.282973	0.141487	+	0.989940i	$0.454812\pi$
$458$	−48.6511	−2.27332
$459$	−1.00000	−0.0466760
$460$	−49.1646	−2.29231
$461$	−10.0505	−0.468096	−0.234048	−	0.972225i	$-0.575197\pi$
$461$	−10.0505	−0.468096	−0.234048	+	0.972225i	$0.575197\pi$
$462$	13.9082	0.647069
$463$	21.6029	1.00397	0.501985	−	0.864876i	$-0.332603\pi$
$463$	21.6029	1.00397	0.501985	+	0.864876i	$0.332603\pi$
$464$	3.81748	0.177222
$465$	−45.5314	−2.11147
$466$	−19.1059	−0.885063
$467$	29.3736	1.35925	0.679623	−	0.733561i	$-0.262143\pi$
$467$	29.3736	1.35925	0.679623	+	0.733561i	$0.262143\pi$
$468$	−2.84107	−0.131328
$469$	−39.3008	−1.81474
$470$	−5.48883	−0.253181
$471$	17.2050	0.792764
$472$	−18.1297	−0.834487
$473$	7.27823	0.334653
$474$	−2.38168	−0.109394
$475$	−104.750	−4.80625
$476$	15.3684	0.704408
$477$	2.73509	0.125231
$478$	−39.6742	−1.81465
$479$	27.3378	1.24909	0.624547	−	0.780987i	$-0.285284\pi$
$479$	27.3378	1.24909	0.624547	+	0.780987i	$0.285284\pi$
$480$	12.5205	0.571481
$481$	2.43342	0.110955
$482$	−19.5769	−0.891704
$483$	12.8213	0.583390
$484$	−33.2454	−1.51115
$485$	32.1450	1.45963
$486$	−2.38168	−0.108035
$487$	−28.8820	−1.30877	−0.654385	−	0.756161i	$-0.727073\pi$
$487$	−28.8820	−1.30877	−0.654385	+	0.756161i	$0.727073\pi$
$488$	44.3488	2.00758
$489$	2.23585	0.101109
$490$	−109.408	−4.94255
$491$	31.9188	1.44048	0.720238	−	0.693728i	$-0.244033\pi$
$491$	31.9188	1.44048	0.720238	+	0.693728i	$0.244033\pi$
$492$	−10.2839	−0.463634
$493$	−1.78243	−0.0802764
$494$	−13.6942	−0.616131
$495$	6.09759	0.274066
$496$	−22.3166	−1.00205
$497$	5.23677	0.234901
$498$	0.763575	0.0342166
$499$	−29.0549	−1.30068	−0.650338	−	0.759645i	$-0.725373\pi$
$499$	−29.0549	−1.30068	−0.650338	+	0.759645i	$0.725373\pi$
$500$	145.932	6.52626
$501$	−9.73250	−0.434816
$502$	61.6216	2.75031
$503$	4.25884	0.189892	0.0949461	−	0.995482i	$-0.469732\pi$
$503$	4.25884	0.189892	0.0949461	+	0.995482i	$0.469732\pi$
$504$	16.6687	0.742483
$505$	−47.8413	−2.12891
$506$	10.1824	0.452662
$507$	−12.4015	−0.550770
$508$	−68.7877	−3.05196
$509$	−31.5951	−1.40043	−0.700214	−	0.713933i	$-0.746912\pi$
$509$	−31.5951	−1.40043	−0.700214	+	0.713933i	$0.746912\pi$
$510$	10.4071	0.460836
$511$	38.1707	1.68857
$512$	23.1984	1.02523
$513$	−7.43227	−0.328143
$514$	31.1186	1.37258
$515$	−44.8577	−1.97667
$516$	19.1543	0.843220
$517$	0.735968	0.0323678
$518$	−31.3507	−1.37747
$519$	6.79212	0.298141
$520$	13.4649	0.590475
$521$	−16.6380	−0.728924	−0.364462	−	0.931218i	$-0.618747\pi$
$521$	−16.6380	−0.728924	−0.364462	+	0.931218i	$0.618747\pi$
$522$	−4.24517	−0.185806
$523$	−26.2084	−1.14601	−0.573007	−	0.819550i	$-0.694223\pi$
$523$	−26.2084	−1.14601	−0.573007	+	0.819550i	$0.694223\pi$
$524$	−43.7250	−1.91013
$525$	−58.9807	−2.57413
$526$	−48.8342	−2.12927
$527$	10.4199	0.453897
$528$	2.98865	0.130064
$529$	−13.6134	−0.591885
$530$	−28.4644	−1.23642
$531$	4.55162	0.197524
$532$	114.222	4.95215
$533$	2.16640	0.0938373
$534$	34.4635	1.49138
$535$	−48.1577	−2.08204
$536$	−37.4066	−1.61572
$537$	−9.57249	−0.413083
$538$	−36.5957	−1.57775
$539$	14.6699	0.631879
$540$	16.0471	0.690559
$541$	45.6783	1.96386	0.981932	−	0.189233i	$-0.0606002\pi$
$541$	45.6783	1.96386	0.981932	+	0.189233i	$0.0606002\pi$
$542$	47.7319	2.05026
$543$	−4.72090	−0.202593
$544$	−2.86533	−0.122850
$545$	53.6796	2.29938
$546$	−7.71067	−0.329986
$547$	7.50451	0.320869	0.160435	−	0.987046i	$-0.448710\pi$
$547$	7.50451	0.320869	0.160435	+	0.987046i	$0.448710\pi$
$548$	−25.4213	−1.08594
$549$	−11.1342	−0.475195
$550$	−46.8410	−1.99731
$551$	−13.2475	−0.564361
$552$	12.2034	0.519409
$553$	−4.18483	−0.177957
$554$	4.41373	0.187521
$555$	−13.7447	−0.583428
$556$	−35.6836	−1.51332
$557$	21.2392	0.899934	0.449967	−	0.893045i	$-0.351436\pi$
$557$	21.2392	0.899934	0.449967	+	0.893045i	$0.351436\pi$
$558$	24.8168	1.05058
$559$	−4.03503	−0.170663
$560$	−39.1643	−1.65500
$561$	−1.39544	−0.0589154
$562$	−10.4585	−0.441163
$563$	−32.2285	−1.35827	−0.679135	−	0.734014i	$-0.737645\pi$
$563$	−32.2285	−1.35827	−0.679135	+	0.734014i	$0.737645\pi$
$564$	1.93686	0.0815566
$565$	−37.1528	−1.56303
$566$	49.4827	2.07991
$567$	−4.18483	−0.175746
$568$	4.98437	0.209140
$569$	−28.5619	−1.19738	−0.598688	−	0.800983i	$-0.704311\pi$
$569$	−28.5619	−1.19738	−0.598688	+	0.800983i	$0.704311\pi$
$570$	77.3486	3.23978
$571$	20.7350	0.867733	0.433867	−	0.900977i	$-0.357149\pi$
$571$	20.7350	0.867733	0.433867	+	0.900977i	$0.357149\pi$
$572$	−3.96453	−0.165765
$573$	−16.5087	−0.689661
$574$	−27.9106	−1.16497
$575$	−43.1804	−1.80075
$576$	−11.1078	−0.462824
$577$	21.9278	0.912866	0.456433	−	0.889758i	$-0.349127\pi$
$577$	21.9278	0.912866	0.456433	+	0.889758i	$0.349127\pi$
$578$	−2.38168	−0.0990648
$579$	4.77961	0.198634
$580$	28.6028	1.18767
$581$	1.34167	0.0556619
$582$	−17.5206	−0.726252
$583$	3.81665	0.158069
$584$	36.3310	1.50339
$585$	−3.38048	−0.139766
$586$	−27.2183	−1.12438
$587$	45.9764	1.89765	0.948825	−	0.315803i	$-0.102274\pi$
$587$	45.9764	1.89765	0.948825	+	0.315803i	$0.102274\pi$
$588$	38.6072	1.59213
$589$	77.4434	3.19100
$590$	−47.3693	−1.95016
$591$	18.7655	0.771908
$592$	−6.73677	−0.276880
$593$	−15.1197	−0.620894	−0.310447	−	0.950591i	$-0.600479\pi$
$593$	−15.1197	−0.620894	−0.310447	+	0.950591i	$0.600479\pi$
$594$	−3.32349	−0.136364
$595$	18.2863	0.749664
$596$	−53.4443	−2.18916
$597$	21.6132	0.884571
$598$	−5.64508	−0.230844
$599$	29.6196	1.21022	0.605112	−	0.796140i	$-0.293128\pi$
$599$	29.6196	1.21022	0.605112	+	0.796140i	$0.293128\pi$
$600$	−56.1379	−2.29182
$601$	−17.0586	−0.695835	−0.347917	−	0.937525i	$-0.613111\pi$
$601$	−17.0586	−0.695835	−0.347917	+	0.937525i	$0.613111\pi$
$602$	51.9848	2.11874
$603$	9.39127	0.382442
$604$	47.2415	1.92223
$605$	−39.5575	−1.60824
$606$	26.0758	1.05926
$607$	43.7924	1.77748	0.888740	−	0.458412i	$-0.151581\pi$
$607$	43.7924	1.77748	0.888740	+	0.458412i	$0.151581\pi$
$608$	−21.2959	−0.863663
$609$	−7.45915	−0.302260
$610$	115.875	4.69164
$611$	−0.408018	−0.0165066
$612$	−3.67240	−0.148448
$613$	44.2569	1.78752	0.893760	−	0.448545i	$-0.148058\pi$
$613$	44.2569	1.78752	0.893760	+	0.448545i	$0.148058\pi$
$614$	36.4514	1.47106
$615$	−12.2365	−0.493421
$616$	23.2601	0.937178
$617$	−10.5778	−0.425847	−0.212924	−	0.977069i	$-0.568299\pi$
$617$	−10.5778	−0.425847	−0.212924	+	0.977069i	$0.568299\pi$
$618$	24.4497	0.983509
$619$	−24.4425	−0.982428	−0.491214	−	0.871039i	$-0.663447\pi$
$619$	−24.4425	−0.982428	−0.491214	+	0.871039i	$0.663447\pi$
$620$	−167.209	−6.71529
$621$	−3.06376	−0.122945
$622$	25.6143	1.02704
$623$	60.5554	2.42610
$624$	−1.65690	−0.0663291
$625$	103.169	4.12677
$626$	25.2975	1.01109
$627$	−10.3713	−0.414189
$628$	63.1836	2.52130
$629$	3.14548	0.125418
$630$	43.5521	1.73516
$631$	22.9805	0.914840	0.457420	−	0.889251i	$-0.348774\pi$
$631$	22.9805	0.914840	0.457420	+	0.889251i	$0.348774\pi$
$632$	−3.98313	−0.158440
$633$	0.916825	0.0364405
$634$	−71.7146	−2.84815
$635$	−81.8481	−3.24804
$636$	10.0443	0.398284
$637$	−8.13297	−0.322240
$638$	−5.92387	−0.234528
$639$	−1.25137	−0.0495035
$640$	90.5590	3.57966
$641$	−14.2268	−0.561926	−0.280963	−	0.959719i	$-0.590654\pi$
$641$	−14.2268	−0.561926	−0.280963	+	0.959719i	$0.590654\pi$
$642$	26.2483	1.03594
$643$	47.2199	1.86217	0.931086	−	0.364800i	$-0.118863\pi$
$643$	47.2199	1.86217	0.931086	+	0.364800i	$0.118863\pi$
$644$	47.0850	1.85541
$645$	22.7910	0.897394
$646$	−17.7013	−0.696448
$647$	48.9920	1.92607	0.963036	−	0.269371i	$-0.0868159\pi$
$647$	48.9920	1.92607	0.963036	+	0.269371i	$0.0868159\pi$
$648$	−3.98313	−0.156472
$649$	6.35150	0.249318
$650$	25.9685	1.01857
$651$	43.6054	1.70903
$652$	8.21093	0.321565
$653$	−1.20538	−0.0471701	−0.0235851	−	0.999722i	$-0.507508\pi$
$653$	−1.20538	−0.0471701	−0.0235851	+	0.999722i	$0.507508\pi$
$654$	−29.2580	−1.14408
$655$	−52.0268	−2.03286
$656$	−5.99754	−0.234165
$657$	−9.12122	−0.355853
$658$	5.25666	0.204926
$659$	−24.7491	−0.964087	−0.482044	−	0.876147i	$-0.660105\pi$
$659$	−24.7491	−0.964087	−0.482044	+	0.876147i	$0.660105\pi$
$660$	22.3928	0.871638
$661$	−1.74488	−0.0678679	−0.0339340	−	0.999424i	$-0.510804\pi$
$661$	−1.74488	−0.0678679	−0.0339340	+	0.999424i	$0.510804\pi$
$662$	28.0473	1.09009
$663$	0.773626	0.0300452
$664$	1.27700	0.0495574
$665$	135.909	5.27031
$666$	7.49152	0.290290
$667$	−5.46093	−0.211448
$668$	−35.7416	−1.38289
$669$	9.75878	0.377296
$670$	−97.7362	−3.77588
$671$	−15.5370	−0.599801
$672$	−11.9909	−0.462560
$673$	5.31153	0.204744	0.102372	−	0.994746i	$-0.467357\pi$
$673$	5.31153	0.204744	0.102372	+	0.994746i	$0.467357\pi$
$674$	−34.2997	−1.32118
$675$	14.0939	0.542476
$676$	−45.5433	−1.75167
$677$	−15.1537	−0.582406	−0.291203	−	0.956661i	$-0.594055\pi$
$677$	−15.1537	−0.582406	−0.291203	+	0.956661i	$0.594055\pi$
$678$	20.2501	0.777702
$679$	−30.7853	−1.18143
$680$	17.4049	0.667448
$681$	6.16481	0.236236
$682$	34.6303	1.32606
$683$	22.2520	0.851449	0.425724	−	0.904853i	$-0.360019\pi$
$683$	22.2520	0.851449	0.425724	+	0.904853i	$0.360019\pi$
$684$	−27.2943	−1.04362
$685$	−30.2479	−1.15571
$686$	35.0117	1.33675
$687$	20.4272	0.779347
$688$	11.1707	0.425879
$689$	−2.11594	−0.0806108
$690$	31.8850	1.21384
$691$	−38.6200	−1.46917	−0.734587	−	0.678514i	$-0.762624\pi$
$691$	−38.6200	−1.46917	−0.734587	+	0.678514i	$0.762624\pi$
$692$	24.9434	0.948206
$693$	−5.83967	−0.221831
$694$	45.9990	1.74610
$695$	−42.4587	−1.61055
$696$	−7.09963	−0.269111
$697$	2.80032	0.106070
$698$	32.9467	1.24705
$699$	8.02201	0.303420
$700$	−216.601	−8.18674
$701$	11.6674	0.440672	0.220336	−	0.975424i	$-0.429285\pi$
$701$	11.6674	0.440672	0.220336	+	0.975424i	$0.429285\pi$
$702$	1.84253	0.0695418
$703$	23.3780	0.881719
$704$	−15.5002	−0.584186
$705$	2.30460	0.0867963
$706$	−17.8278	−0.670956
$707$	45.8176	1.72315
$708$	16.7154	0.628203
$709$	8.53863	0.320675	0.160337	−	0.987062i	$-0.448742\pi$
$709$	8.53863	0.320675	0.160337	+	0.987062i	$0.448742\pi$
$710$	13.0232	0.488751
$711$	1.00000	0.0375029
$712$	57.6368	2.16003
$713$	31.9240	1.19557
$714$	−9.96693	−0.373003
$715$	−4.71725	−0.176415
$716$	−35.1540	−1.31377
$717$	16.6581	0.622106
$718$	−9.76537	−0.364440
$719$	−40.9587	−1.52750	−0.763751	−	0.645511i	$-0.776645\pi$
$719$	−40.9587	−1.52750	−0.763751	+	0.645511i	$0.776645\pi$
$720$	9.35865	0.348776
$721$	42.9603	1.59992
$722$	−86.3089	−3.21208
$723$	8.21979	0.305697
$724$	−17.3371	−0.644327
$725$	25.1214	0.932985
$726$	21.5608	0.800195
$727$	−52.1225	−1.93312	−0.966558	−	0.256448i	$-0.917448\pi$
$727$	−52.1225	−1.93312	−0.966558	+	0.256448i	$0.917448\pi$
$728$	−12.8953	−0.477933
$729$	1.00000	0.0370370
$730$	94.9257	3.51336
$731$	−5.21573	−0.192911
$732$	−40.8892	−1.51131
$733$	36.5693	1.35072	0.675359	−	0.737489i	$-0.263989\pi$
$733$	36.5693	1.35072	0.675359	+	0.737489i	$0.263989\pi$
$734$	89.1051	3.28893
$735$	45.9373	1.69442
$736$	−8.77869	−0.323587
$737$	13.1049	0.482726
$738$	6.66947	0.245507
$739$	−15.0789	−0.554686	−0.277343	−	0.960771i	$-0.589454\pi$
$739$	−15.0789	−0.554686	−0.277343	+	0.960771i	$0.589454\pi$
$740$	−50.4759	−1.85553
$741$	5.74980	0.211224
$742$	27.2604	1.00076
$743$	−32.2005	−1.18132	−0.590661	−	0.806920i	$-0.701133\pi$
$743$	−32.2005	−1.18132	−0.590661	+	0.806920i	$0.701133\pi$
$744$	41.5037	1.52160
$745$	−63.5914	−2.32981
$746$	23.9287	0.876093
$747$	−0.320604	−0.0117303
$748$	−5.12461	−0.187374
$749$	46.1207	1.68521
$750$	−94.6417	−3.45583
$751$	31.9302	1.16515	0.582574	−	0.812778i	$-0.302046\pi$
$751$	31.9302	1.16515	0.582574	+	0.812778i	$0.302046\pi$
$752$	1.12957	0.0411912
$753$	−25.8731	−0.942870
$754$	3.28417	0.119603
$755$	56.2109	2.04572
$756$	−15.3684	−0.558942
$757$	−29.8532	−1.08503	−0.542517	−	0.840045i	$-0.682529\pi$
$757$	−29.8532	−1.08503	−0.542517	+	0.840045i	$0.682529\pi$
$758$	46.2205	1.67880
$759$	−4.27529	−0.155183
$760$	129.358	4.69231
$761$	−10.1544	−0.368098	−0.184049	−	0.982917i	$-0.558920\pi$
$761$	−10.1544	−0.368098	−0.184049	+	0.982917i	$0.558920\pi$
$762$	44.6112	1.61610
$763$	−51.4090	−1.86113
$764$	−60.6266	−2.19339
$765$	−4.36966	−0.157985
$766$	−28.8996	−1.04419
$767$	−3.52125	−0.127145
$768$	−27.1436	−0.979460
$769$	53.6112	1.93327	0.966635	−	0.256159i	$-0.0824572\pi$
$769$	53.6112	1.93327	0.966635	+	0.256159i	$0.0824572\pi$
$770$	60.7742	2.19015
$771$	−13.0658	−0.470554
$772$	17.5526	0.631733
$773$	4.09209	0.147182	0.0735912	−	0.997288i	$-0.476554\pi$
$773$	4.09209	0.147182	0.0735912	+	0.997288i	$0.476554\pi$
$774$	−12.4222	−0.446507
$775$	−146.857	−5.27526
$776$	−29.3015	−1.05186
$777$	13.1633	0.472230
$778$	53.6072	1.92191
$779$	20.8127	0.745694
$780$	−12.4145	−0.444510
$781$	−1.74621	−0.0624843
$782$	−7.29690	−0.260937
$783$	1.78243	0.0636987
$784$	22.5156	0.804128
$785$	75.1799	2.68329
$786$	28.3572	1.01147
$787$	31.7275	1.13097	0.565483	−	0.824760i	$-0.308690\pi$
$787$	31.7275	1.13097	0.565483	+	0.824760i	$0.308690\pi$
$788$	68.9144	2.45497
$789$	20.5041	0.729965
$790$	−10.4071	−0.370269
$791$	35.5813	1.26513
$792$	−5.55820	−0.197502
$793$	8.61369	0.305881
$794$	−47.3199	−1.67932
$795$	11.9514	0.423873
$796$	79.3725	2.81328
$797$	−16.5300	−0.585523	−0.292761	−	0.956186i	$-0.594574\pi$
$797$	−16.5300	−0.585523	−0.292761	+	0.956186i	$0.594574\pi$
$798$	−74.0769	−2.62229
$799$	−0.527410	−0.0186584
$800$	40.3838	1.42778
$801$	−14.4702	−0.511281
$802$	−37.6096	−1.32804
$803$	−12.7281	−0.449164
$804$	34.4885	1.21632
$805$	56.0248	1.97462
$806$	−19.1990	−0.676254
$807$	15.3655	0.540891
$808$	43.6093	1.53417
$809$	1.04398	0.0367045	0.0183523	−	0.999832i	$-0.494158\pi$
$809$	1.04398	0.0367045	0.0183523	+	0.999832i	$0.494158\pi$
$810$	−10.4071	−0.365669
$811$	35.9876	1.26370	0.631849	−	0.775092i	$-0.282296\pi$
$811$	35.9876	1.26370	0.631849	+	0.775092i	$0.282296\pi$
$812$	−27.3930	−0.961305
$813$	−20.0413	−0.702878
$814$	10.4539	0.366411
$815$	9.76990	0.342225
$816$	−2.14173	−0.0749757
$817$	−38.7647	−1.35621
$818$	56.6143	1.97947
$819$	3.23749	0.113127
$820$	−44.9372	−1.56927
$821$	45.0704	1.57297	0.786484	−	0.617611i	$-0.211899\pi$
$821$	45.0704	1.57297	0.786484	+	0.617611i	$0.211899\pi$
$822$	16.4866	0.575035
$823$	−25.7940	−0.899124	−0.449562	−	0.893249i	$-0.648420\pi$
$823$	−25.7940	−0.899124	−0.449562	+	0.893249i	$0.648420\pi$
$824$	40.8897	1.42446
$825$	19.6672	0.684724
$826$	45.3657	1.57847
$827$	32.2585	1.12174	0.560869	−	0.827904i	$-0.310467\pi$
$827$	32.2585	1.12174	0.560869	+	0.827904i	$0.310467\pi$
$828$	−11.2514	−0.391012
$829$	−25.2376	−0.876537	−0.438269	−	0.898844i	$-0.644408\pi$
$829$	−25.2376	−0.876537	−0.438269	+	0.898844i	$0.644408\pi$
$830$	3.33656	0.115814
$831$	−1.85320	−0.0642867
$832$	8.59326	0.297918
$833$	−10.5128	−0.364247
$834$	23.1421	0.801345
$835$	−42.5277	−1.47173
$836$	−38.0875	−1.31728
$837$	−10.4199	−0.360164
$838$	−83.0950	−2.87047
$839$	−47.5193	−1.64055	−0.820274	−	0.571971i	$-0.806179\pi$
$839$	−47.5193	−1.64055	−0.820274	+	0.571971i	$0.806179\pi$
$840$	72.8366	2.51310
$841$	−25.8230	−0.890447
$842$	43.3017	1.49227
$843$	4.39121	0.151241
$844$	3.36695	0.115895
$845$	−54.1903	−1.86420
$846$	−1.25612	−0.0431864
$847$	37.8842	1.30172
$848$	5.85783	0.201159
$849$	−20.7764	−0.713043
$850$	33.5672	1.15135
$851$	9.63699	0.330352
$852$	−4.59554	−0.157441
$853$	−0.896368	−0.0306911	−0.0153455	−	0.999882i	$-0.504885\pi$
$853$	−0.896368	−0.0306911	−0.0153455	+	0.999882i	$0.504885\pi$
$854$	−110.973	−3.79743
$855$	−32.4765	−1.11067
$856$	43.8978	1.50040
$857$	−49.3631	−1.68621	−0.843105	−	0.537749i	$-0.819275\pi$
$857$	−49.3631	−1.68621	−0.843105	+	0.537749i	$0.819275\pi$
$858$	2.57114	0.0877771
$859$	−30.2407	−1.03180	−0.515899	−	0.856649i	$-0.672542\pi$
$859$	−30.2407	−1.03180	−0.515899	+	0.856649i	$0.672542\pi$
$860$	83.6976	2.85407
$861$	11.7189	0.399378
$862$	56.2164	1.91474
$863$	−41.8897	−1.42594	−0.712971	−	0.701193i	$-0.752651\pi$
$863$	−41.8897	−1.42594	−0.712971	+	0.701193i	$0.752651\pi$
$864$	2.86533	0.0974805
$865$	29.6793	1.00913
$866$	−0.913427	−0.0310395
$867$	1.00000	0.0339618
$868$	160.137	5.43539
$869$	1.39544	0.0473370
$870$	−18.5499	−0.628902
$871$	−7.26533	−0.246176
$872$	−48.9312	−1.65702
$873$	7.35640	0.248976
$874$	−54.2326	−1.83444
$875$	−166.294	−5.62177
$876$	−33.4968	−1.13175
$877$	−52.0397	−1.75726	−0.878629	−	0.477506i	$-0.841541\pi$
$877$	−52.0397	−1.75726	−0.878629	+	0.477506i	$0.841541\pi$
$878$	−4.80633	−0.162206
$879$	11.4282	0.385463
$880$	13.0594	0.440232
$881$	10.3555	0.348886	0.174443	−	0.984667i	$-0.444188\pi$
$881$	10.3555	0.348886	0.174443	+	0.984667i	$0.444188\pi$
$882$	−25.0381	−0.843077
$883$	−5.38776	−0.181313	−0.0906563	−	0.995882i	$-0.528896\pi$
$883$	−5.38776	−0.181313	−0.0906563	+	0.995882i	$0.528896\pi$
$884$	2.84107	0.0955554
$885$	19.8890	0.668563
$886$	85.8976	2.88578
$887$	−37.2220	−1.24979	−0.624896	−	0.780708i	$-0.714859\pi$
$887$	−37.2220	−1.24979	−0.624896	+	0.780708i	$0.714859\pi$
$888$	12.5288	0.420440
$889$	78.3860	2.62898
$890$	150.594	5.04791
$891$	1.39544	0.0467489
$892$	35.8382	1.19995
$893$	−3.91985	−0.131173
$894$	34.6605	1.15922
$895$	−41.8285	−1.39817
$896$	−86.7285	−2.89739
$897$	2.37021	0.0791389
$898$	5.64023	0.188217
$899$	−18.5727	−0.619433
$900$	51.7586	1.72529
$901$	−2.73509	−0.0911190
$902$	9.30683	0.309883
$903$	−21.8270	−0.726355
$904$	33.8664	1.12638
$905$	−20.6287	−0.685723
$906$	−30.6377	−1.01787
$907$	35.1470	1.16704	0.583519	−	0.812100i	$-0.301675\pi$
$907$	35.1470	1.16704	0.583519	+	0.812100i	$0.301675\pi$
$908$	22.6397	0.751324
$909$	−10.9485	−0.363139
$910$	−33.6930	−1.11691
$911$	34.9805	1.15895	0.579477	−	0.814988i	$-0.303257\pi$
$911$	34.9805	1.15895	0.579477	+	0.814988i	$0.303257\pi$
$912$	−15.9179	−0.527096
$913$	−0.447382	−0.0148062
$914$	−14.4074	−0.476556
$915$	−48.6526	−1.60840
$916$	75.0169	2.47863
$917$	49.8261	1.64540
$918$	2.38168	0.0786072
$919$	−30.2422	−0.997598	−0.498799	−	0.866718i	$-0.666225\pi$
$919$	−30.2422	−0.997598	−0.498799	+	0.866718i	$0.666225\pi$
$920$	53.3245	1.75806
$921$	−15.3049	−0.504314
$922$	23.9370	0.788322
$923$	0.968093	0.0318652
$924$	−21.4456	−0.705509
$925$	−44.3321	−1.45763
$926$	−51.4512	−1.69079
$927$	−10.2657	−0.337170
$928$	5.10724	0.167653
$929$	7.50660	0.246284	0.123142	−	0.992389i	$-0.460703\pi$
$929$	7.50660	0.246284	0.123142	+	0.992389i	$0.460703\pi$
$930$	108.441	3.55593
$931$	−78.1339	−2.56074
$932$	29.4601	0.964996
$933$	−10.7547	−0.352094
$934$	−69.9585	−2.28911
$935$	−6.09759	−0.199412
$936$	3.08145	0.100720
$937$	23.3573	0.763051	0.381525	−	0.924358i	$-0.375399\pi$
$937$	23.3573	0.763051	0.381525	+	0.924358i	$0.375399\pi$
$938$	93.6021	3.05622
$939$	−10.6217	−0.346627
$940$	8.46343	0.276047
$941$	−31.0606	−1.01255	−0.506273	−	0.862374i	$-0.668977\pi$
$941$	−31.0606	−1.01255	−0.506273	+	0.862374i	$0.668977\pi$
$942$	−40.9768	−1.33510
$943$	8.57952	0.279388
$944$	9.74836	0.317282
$945$	−18.2863	−0.594853
$946$	−17.3344	−0.563590
$947$	16.0750	0.522368	0.261184	−	0.965289i	$-0.415887\pi$
$947$	16.0750	0.522368	0.261184	+	0.965289i	$0.415887\pi$
$948$	3.67240	0.119274
$949$	7.05641	0.229061
$950$	249.481	8.09423
$951$	30.1109	0.976414
$952$	−16.6687	−0.540236
$953$	−54.2710	−1.75801	−0.879006	−	0.476811i	$-0.841792\pi$
$953$	−54.2710	−1.75801	−0.879006	+	0.476811i	$0.841792\pi$
$954$	−6.51411	−0.210902
$955$	−72.1375	−2.33431
$956$	61.1751	1.97854
$957$	2.48726	0.0804018
$958$	−65.1098	−2.10360
$959$	28.9684	0.935439
$960$	−48.5372	−1.56653
$961$	77.5740	2.50239
$962$	−5.79564	−0.186859
$963$	−11.0209	−0.355145
$964$	30.1864	0.972238
$965$	20.8853	0.672320
$966$	−30.5363	−0.982489
$967$	−0.374080	−0.0120296	−0.00601481	−	0.999982i	$-0.501915\pi$
$967$	−0.374080	−0.0120296	−0.00601481	+	0.999982i	$0.501915\pi$
$968$	36.0583	1.15896
$969$	7.43227	0.238759
$970$	−76.5590	−2.45816
$971$	−47.1611	−1.51347	−0.756736	−	0.653720i	$-0.773207\pi$
$971$	−47.1611	−1.51347	−0.756736	+	0.653720i	$0.773207\pi$
$972$	3.67240	0.117792
$973$	40.6627	1.30359
$974$	68.7878	2.20410
$975$	−10.9034	−0.349189
$976$	−23.8464	−0.763306
$977$	−21.6427	−0.692412	−0.346206	−	0.938158i	$-0.612530\pi$
$977$	−21.6427	−0.692412	−0.346206	+	0.938158i	$0.612530\pi$
$978$	−5.32508	−0.170277
$979$	−20.1923	−0.645349
$980$	168.700	5.38894
$981$	12.2846	0.392218
$982$	−76.0204	−2.42591
$983$	−35.2946	−1.12572	−0.562861	−	0.826552i	$-0.690299\pi$
$983$	−35.2946	−1.12572	−0.562861	+	0.826552i	$0.690299\pi$
$984$	11.1540	0.355578
$985$	81.9987	2.61270
$986$	4.24517	0.135194
$987$	−2.20712	−0.0702534
$988$	21.1156	0.671776
$989$	−15.9798	−0.508127
$990$	−14.5225	−0.461555
$991$	6.68347	0.212308	0.106154	−	0.994350i	$-0.466146\pi$
$991$	6.68347	0.212308	0.106154	+	0.994350i	$0.466146\pi$
$992$	−29.8564	−0.947942
$993$	−11.7763	−0.373709
$994$	−12.4723	−0.395598
$995$	94.4425	2.99403
$996$	−1.17739	−0.0373069
$997$	19.2016	0.608120	0.304060	−	0.952653i	$-0.401658\pi$
$997$	19.2016	0.608120	0.304060	+	0.952653i	$0.401658\pi$
$998$	69.1995	2.19047
$999$	−3.14548	−0.0995184

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.h.1.3	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.h.1.3	✓	25	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.38168 q^{2} +1.00000 q^{3} +3.67240 q^{4} +4.36966 q^{5} -2.38168 q^{6} -4.18483 q^{7} -3.98313 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.38168 q^{2} +1.00000 q^{3} +3.67240 q^{4} +4.36966 q^{5} -2.38168 q^{6} -4.18483 q^{7} -3.98313 q^{8} +1.00000 q^{9} -10.4071 q^{10} +1.39544 q^{11} +3.67240 q^{12} -0.773626 q^{13} +9.96693 q^{14} +4.36966 q^{15} +2.14173 q^{16} -1.00000 q^{17} -2.38168 q^{18} -7.43227 q^{19} +16.0471 q^{20} -4.18483 q^{21} -3.32349 q^{22} -3.06376 q^{23} -3.98313 q^{24} +14.0939 q^{25} +1.84253 q^{26} +1.00000 q^{27} -15.3684 q^{28} +1.78243 q^{29} -10.4071 q^{30} -10.4199 q^{31} +2.86533 q^{32} +1.39544 q^{33} +2.38168 q^{34} -18.2863 q^{35} +3.67240 q^{36} -3.14548 q^{37} +17.7013 q^{38} -0.773626 q^{39} -17.4049 q^{40} -2.80032 q^{41} +9.96693 q^{42} +5.21573 q^{43} +5.12461 q^{44} +4.36966 q^{45} +7.29690 q^{46} +0.527410 q^{47} +2.14173 q^{48} +10.5128 q^{49} -33.5672 q^{50} -1.00000 q^{51} -2.84107 q^{52} +2.73509 q^{53} -2.38168 q^{54} +6.09759 q^{55} +16.6687 q^{56} -7.43227 q^{57} -4.24517 q^{58} +4.55162 q^{59} +16.0471 q^{60} -11.1342 q^{61} +24.8168 q^{62} -4.18483 q^{63} -11.1078 q^{64} -3.38048 q^{65} -3.32349 q^{66} +9.39127 q^{67} -3.67240 q^{68} -3.06376 q^{69} +43.5521 q^{70} -1.25137 q^{71} -3.98313 q^{72} -9.12122 q^{73} +7.49152 q^{74} +14.0939 q^{75} -27.2943 q^{76} -5.83967 q^{77} +1.84253 q^{78} +1.00000 q^{79} +9.35865 q^{80} +1.00000 q^{81} +6.66947 q^{82} -0.320604 q^{83} -15.3684 q^{84} -4.36966 q^{85} -12.4222 q^{86} +1.78243 q^{87} -5.55820 q^{88} -14.4702 q^{89} -10.4071 q^{90} +3.23749 q^{91} -11.2514 q^{92} -10.4199 q^{93} -1.25612 q^{94} -32.4765 q^{95} +2.86533 q^{96} +7.35640 q^{97} -25.0381 q^{98} +1.39544 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9	\( 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9} - 9 q^{10} - 19 q^{11} + 21 q^{12} - 12 q^{13} - 15 q^{14} - 12 q^{15} + q^{16} - 25 q^{17} - 7 q^{18} - 35 q^{19} - 11 q^{20} - 4 q^{21} - 2 q^{22} - 16 q^{23} - 21 q^{24} + 19 q^{25} - 5 q^{26} + 25 q^{27} + 3 q^{28} - 37 q^{29} - 9 q^{30} - 28 q^{31} - 19 q^{32} - 19 q^{33} + 7 q^{34} - 42 q^{35} + 21 q^{36} + 8 q^{37} - 35 q^{38} - 12 q^{39} - 9 q^{40} - 34 q^{41} - 15 q^{42} - 19 q^{43} - 56 q^{44} - 12 q^{45} + q^{46} - 25 q^{47} + q^{48} + 25 q^{49} - 7 q^{50} - 25 q^{51} - 37 q^{52} - 44 q^{53} - 7 q^{54} - 11 q^{55} - 18 q^{56} - 35 q^{57} - 3 q^{58} - 47 q^{59} - 11 q^{60} - 28 q^{61} + 11 q^{62} - 4 q^{63} - 9 q^{64} - 63 q^{65} - 2 q^{66} - 28 q^{67} - 21 q^{68} - 16 q^{69} + 5 q^{70} - 27 q^{71} - 21 q^{72} - 21 q^{73} - 18 q^{74} + 19 q^{75} - 50 q^{76} - 58 q^{77} - 5 q^{78} + 25 q^{79} - 56 q^{80} + 25 q^{81} - 5 q^{82} - 61 q^{83} + 3 q^{84} + 12 q^{85} - 28 q^{86} - 37 q^{87} + 15 q^{88} - 34 q^{89} - 9 q^{90} - 30 q^{91} - 31 q^{92} - 28 q^{93} + q^{94} - 32 q^{95} - 19 q^{96} - 11 q^{97} - 66 q^{98} - 19 q^{99}+O(q^{100}) \) 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9 - 9 * q^10 - 19 * q^11 + 21 * q^12 - 12 * q^13 - 15 * q^14 - 12 * q^15 + q^16 - 25 * q^17 - 7 * q^18 - 35 * q^19 - 11 * q^20 - 4 * q^21 - 2 * q^22 - 16 * q^23 - 21 * q^24 + 19 * q^25 - 5 * q^26 + 25 * q^27 + 3 * q^28 - 37 * q^29 - 9 * q^30 - 28 * q^31 - 19 * q^32 - 19 * q^33 + 7 * q^34 - 42 * q^35 + 21 * q^36 + 8 * q^37 - 35 * q^38 - 12 * q^39 - 9 * q^40 - 34 * q^41 - 15 * q^42 - 19 * q^43 - 56 * q^44 - 12 * q^45 + q^46 - 25 * q^47 + q^48 + 25 * q^49 - 7 * q^50 - 25 * q^51 - 37 * q^52 - 44 * q^53 - 7 * q^54 - 11 * q^55 - 18 * q^56 - 35 * q^57 - 3 * q^58 - 47 * q^59 - 11 * q^60 - 28 * q^61 + 11 * q^62 - 4 * q^63 - 9 * q^64 - 63 * q^65 - 2 * q^66 - 28 * q^67 - 21 * q^68 - 16 * q^69 + 5 * q^70 - 27 * q^71 - 21 * q^72 - 21 * q^73 - 18 * q^74 + 19 * q^75 - 50 * q^76 - 58 * q^77 - 5 * q^78 + 25 * q^79 - 56 * q^80 + 25 * q^81 - 5 * q^82 - 61 * q^83 + 3 * q^84 + 12 * q^85 - 28 * q^86 - 37 * q^87 + 15 * q^88 - 34 * q^89 - 9 * q^90 - 30 * q^91 - 31 * q^92 - 28 * q^93 + q^94 - 32 * q^95 - 19 * q^96 - 11 * q^97 - 66 * q^98 - 19 * q^99

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