LMFDB - Embedded newform 4015.2.a.g.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$1$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.55668 q^{2} +0.570205 q^{3} +4.53663 q^{4} -1.00000 q^{5} -1.45783 q^{6} -4.65776 q^{7} -6.48536 q^{8} -2.67487 q^{9} +O(q^{10})$	\(q-2.55668 q^{2} +0.570205 q^{3} +4.53663 q^{4} -1.00000 q^{5} -1.45783 q^{6} -4.65776 q^{7} -6.48536 q^{8} -2.67487 q^{9} +2.55668 q^{10} -1.00000 q^{11} +2.58681 q^{12} +6.22385 q^{13} +11.9084 q^{14} -0.570205 q^{15} +7.50776 q^{16} -6.53308 q^{17} +6.83879 q^{18} +8.14474 q^{19} -4.53663 q^{20} -2.65588 q^{21} +2.55668 q^{22} +0.223755 q^{23} -3.69799 q^{24} +1.00000 q^{25} -15.9124 q^{26} -3.23584 q^{27} -21.1305 q^{28} +3.99086 q^{29} +1.45783 q^{30} +0.206630 q^{31} -6.22424 q^{32} -0.570205 q^{33} +16.7030 q^{34} +4.65776 q^{35} -12.1349 q^{36} -6.91365 q^{37} -20.8235 q^{38} +3.54887 q^{39} +6.48536 q^{40} -1.37339 q^{41} +6.79024 q^{42} -1.23631 q^{43} -4.53663 q^{44} +2.67487 q^{45} -0.572071 q^{46} +3.77842 q^{47} +4.28096 q^{48} +14.6947 q^{49} -2.55668 q^{50} -3.72520 q^{51} +28.2353 q^{52} +0.653648 q^{53} +8.27301 q^{54} +1.00000 q^{55} +30.2073 q^{56} +4.64417 q^{57} -10.2034 q^{58} +0.0138942 q^{59} -2.58681 q^{60} +13.5085 q^{61} -0.528288 q^{62} +12.4589 q^{63} +0.897889 q^{64} -6.22385 q^{65} +1.45783 q^{66} +11.5944 q^{67} -29.6382 q^{68} +0.127586 q^{69} -11.9084 q^{70} -14.2670 q^{71} +17.3475 q^{72} -1.00000 q^{73} +17.6760 q^{74} +0.570205 q^{75} +36.9497 q^{76} +4.65776 q^{77} -9.07333 q^{78} +3.96863 q^{79} -7.50776 q^{80} +6.17951 q^{81} +3.51132 q^{82} +14.9648 q^{83} -12.0487 q^{84} +6.53308 q^{85} +3.16085 q^{86} +2.27561 q^{87} +6.48536 q^{88} -8.92964 q^{89} -6.83879 q^{90} -28.9892 q^{91} +1.01509 q^{92} +0.117822 q^{93} -9.66022 q^{94} -8.14474 q^{95} -3.54909 q^{96} -13.9889 q^{97} -37.5698 q^{98} +2.67487 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9}+O(q^{10}) $ 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9} + 5 q^{10} - 32 q^{11} - 24 q^{12} - q^{13} - 5 q^{14} + 7 q^{15} + 47 q^{16} - 30 q^{17} - 11 q^{18} + 16 q^{19} - 37 q^{20} + q^{21} + 5 q^{22} - 26 q^{23} - 21 q^{24} + 32 q^{25} - q^{26} - 31 q^{27} - 24 q^{28} - 10 q^{29} + 3 q^{30} - 2 q^{31} - 31 q^{32} + 7 q^{33} - 14 q^{34} + 38 q^{36} - 28 q^{37} - 63 q^{38} - 2 q^{39} + 18 q^{40} - 62 q^{41} - 9 q^{42} + 8 q^{43} - 37 q^{44} - 29 q^{45} + 19 q^{46} - 21 q^{47} - 79 q^{48} + 34 q^{49} - 5 q^{50} + 17 q^{51} + 15 q^{52} - 32 q^{53} + 5 q^{54} + 32 q^{55} - 52 q^{56} - 57 q^{57} + 4 q^{58} - 37 q^{59} + 24 q^{60} + 15 q^{61} - 22 q^{62} + 5 q^{63} + 70 q^{64} + q^{65} + 3 q^{66} - 42 q^{67} - 81 q^{68} - 8 q^{69} + 5 q^{70} - 40 q^{71} - 27 q^{72} - 32 q^{73} - 17 q^{74} - 7 q^{75} + 21 q^{76} - 105 q^{78} + 18 q^{79} - 47 q^{80} + 12 q^{81} - 70 q^{82} - 26 q^{83} + 22 q^{84} + 30 q^{85} - 45 q^{86} - 18 q^{87} + 18 q^{88} - 83 q^{89} + 11 q^{90} - 18 q^{91} - 73 q^{92} - 68 q^{93} + 56 q^{94} - 16 q^{95} - 35 q^{96} - 99 q^{97} - 61 q^{98} - 29 q^{99}+O(q^{100}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9 + 5 * q^10 - 32 * q^11 - 24 * q^12 - q^13 - 5 * q^14 + 7 * q^15 + 47 * q^16 - 30 * q^17 - 11 * q^18 + 16 * q^19 - 37 * q^20 + q^21 + 5 * q^22 - 26 * q^23 - 21 * q^24 + 32 * q^25 - q^26 - 31 * q^27 - 24 * q^28 - 10 * q^29 + 3 * q^30 - 2 * q^31 - 31 * q^32 + 7 * q^33 - 14 * q^34 + 38 * q^36 - 28 * q^37 - 63 * q^38 - 2 * q^39 + 18 * q^40 - 62 * q^41 - 9 * q^42 + 8 * q^43 - 37 * q^44 - 29 * q^45 + 19 * q^46 - 21 * q^47 - 79 * q^48 + 34 * q^49 - 5 * q^50 + 17 * q^51 + 15 * q^52 - 32 * q^53 + 5 * q^54 + 32 * q^55 - 52 * q^56 - 57 * q^57 + 4 * q^58 - 37 * q^59 + 24 * q^60 + 15 * q^61 - 22 * q^62 + 5 * q^63 + 70 * q^64 + q^65 + 3 * q^66 - 42 * q^67 - 81 * q^68 - 8 * q^69 + 5 * q^70 - 40 * q^71 - 27 * q^72 - 32 * q^73 - 17 * q^74 - 7 * q^75 + 21 * q^76 - 105 * q^78 + 18 * q^79 - 47 * q^80 + 12 * q^81 - 70 * q^82 - 26 * q^83 + 22 * q^84 + 30 * q^85 - 45 * q^86 - 18 * q^87 + 18 * q^88 - 83 * q^89 + 11 * q^90 - 18 * q^91 - 73 * q^92 - 68 * q^93 + 56 * q^94 - 16 * q^95 - 35 * q^96 - 99 * q^97 - 61 * q^98 - 29 * 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 $

$2$	−2.55668	−1.80785	−0.903924	−	0.427693i	$-0.859327\pi$
$2$	−2.55668	−1.80785	−0.903924	+	0.427693i	$0.859327\pi$
$3$	0.570205	0.329208	0.164604	−	0.986360i	$-0.447365\pi$
$3$	0.570205	0.329208	0.164604	+	0.986360i	$0.447365\pi$
$4$	4.53663	2.26832
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.45783	−0.595158
$7$	−4.65776	−1.76047	−0.880234	−	0.474540i	$-0.842614\pi$
$7$	−4.65776	−1.76047	−0.880234	+	0.474540i	$0.842614\pi$
$8$	−6.48536	−2.29292
$9$	−2.67487	−0.891622
$10$	2.55668	0.808494
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	2.58681	0.746748
$13$	6.22385	1.72618	0.863092	−	0.505046i	$-0.168525\pi$
$13$	6.22385	1.72618	0.863092	+	0.505046i	$0.168525\pi$
$14$	11.9084	3.18266
$15$	−0.570205	−0.147226
$16$	7.50776	1.87694
$17$	−6.53308	−1.58451	−0.792253	−	0.610193i	$-0.791092\pi$
$17$	−6.53308	−1.58451	−0.792253	+	0.610193i	$0.791092\pi$
$18$	6.83879	1.61192
$19$	8.14474	1.86853	0.934266	−	0.356577i	$-0.116056\pi$
$19$	8.14474	1.86853	0.934266	+	0.356577i	$0.116056\pi$
$20$	−4.53663	−1.01442
$21$	−2.65588	−0.579560
$22$	2.55668	0.545087
$23$	0.223755	0.0466562	0.0233281	−	0.999728i	$-0.492574\pi$
$23$	0.223755	0.0466562	0.0233281	+	0.999728i	$0.492574\pi$
$24$	−3.69799	−0.754848
$25$	1.00000	0.200000
$26$	−15.9124	−3.12068
$27$	−3.23584	−0.622737
$28$	−21.1305	−3.99330
$29$	3.99086	0.741083	0.370542	−	0.928816i	$-0.379172\pi$
$29$	3.99086	0.741083	0.370542	+	0.928816i	$0.379172\pi$
$30$	1.45783	0.266163
$31$	0.206630	0.0371119	0.0185560	−	0.999828i	$-0.494093\pi$
$31$	0.206630	0.0371119	0.0185560	+	0.999828i	$0.494093\pi$
$32$	−6.22424	−1.10030
$33$	−0.570205	−0.0992599
$34$	16.7030	2.86454
$35$	4.65776	0.787305
$36$	−12.1349	−2.02248
$37$	−6.91365	−1.13660	−0.568298	−	0.822823i	$-0.692398\pi$
$37$	−6.91365	−1.13660	−0.568298	+	0.822823i	$0.692398\pi$
$38$	−20.8235	−3.37802
$39$	3.54887	0.568274
$40$	6.48536	1.02543
$41$	−1.37339	−0.214487	−0.107244	−	0.994233i	$-0.534202\pi$
$41$	−1.37339	−0.214487	−0.107244	+	0.994233i	$0.534202\pi$
$42$	6.79024	1.04776
$43$	−1.23631	−0.188535	−0.0942677	−	0.995547i	$-0.530051\pi$
$43$	−1.23631	−0.188535	−0.0942677	+	0.995547i	$0.530051\pi$
$44$	−4.53663	−0.683923
$45$	2.67487	0.398746
$46$	−0.572071	−0.0843472
$47$	3.77842	0.551139	0.275570	−	0.961281i	$-0.411134\pi$
$47$	3.77842	0.551139	0.275570	+	0.961281i	$0.411134\pi$
$48$	4.28096	0.617903
$49$	14.6947	2.09925
$50$	−2.55668	−0.361570
$51$	−3.72520	−0.521632
$52$	28.2353	3.91553
$53$	0.653648	0.0897854	0.0448927	−	0.998992i	$-0.485705\pi$
$53$	0.653648	0.0897854	0.0448927	+	0.998992i	$0.485705\pi$
$54$	8.27301	1.12581
$55$	1.00000	0.134840
$56$	30.2073	4.03661
$57$	4.64417	0.615136
$58$	−10.2034	−1.33977
$59$	0.0138942	0.00180888	0.000904438	−	1.00000i	$-0.499712\pi$
$59$	0.0138942	0.00180888	0.000904438		1.00000i	$0.499712\pi$
$60$	−2.58681	−0.333956
$61$	13.5085	1.72959	0.864795	−	0.502126i	$-0.167449\pi$
$61$	13.5085	1.72959	0.864795	+	0.502126i	$0.167449\pi$
$62$	−0.528288	−0.0670927
$63$	12.4589	1.56967
$64$	0.897889	0.112236
$65$	−6.22385	−0.771973
$66$	1.45783	0.179447
$67$	11.5944	1.41649	0.708243	−	0.705968i	$-0.249488\pi$
$67$	11.5944	1.41649	0.708243	+	0.705968i	$0.249488\pi$
$68$	−29.6382	−3.59416
$69$	0.127586	0.0153596
$70$	−11.9084	−1.42333
$71$	−14.2670	−1.69319	−0.846593	−	0.532241i	$-0.821350\pi$
$71$	−14.2670	−1.69319	−0.846593	+	0.532241i	$0.821350\pi$
$72$	17.3475	2.04442
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	17.6760	2.05479
$75$	0.570205	0.0658416
$76$	36.9497	4.23842
$77$	4.65776	0.530801
$78$	−9.07333	−1.02735
$79$	3.96863	0.446506	0.223253	−	0.974761i	$-0.428332\pi$
$79$	3.96863	0.446506	0.223253	+	0.974761i	$0.428332\pi$
$80$	−7.50776	−0.839393
$81$	6.17951	0.686612
$82$	3.51132	0.387761
$83$	14.9648	1.64260	0.821298	−	0.570499i	$-0.193250\pi$
$83$	14.9648	1.64260	0.821298	+	0.570499i	$0.193250\pi$
$84$	−12.0487	−1.31462
$85$	6.53308	0.708612
$86$	3.16085	0.340843
$87$	2.27561	0.243971
$88$	6.48536	0.691342
$89$	−8.92964	−0.946540	−0.473270	−	0.880917i	$-0.656927\pi$
$89$	−8.92964	−0.946540	−0.473270	+	0.880917i	$0.656927\pi$
$90$	−6.83879	−0.720871
$91$	−28.9892	−3.03889
$92$	1.01509	0.105831
$93$	0.117822	0.0122175
$94$	−9.66022	−0.996376
$95$	−8.14474	−0.835633
$96$	−3.54909	−0.362228
$97$	−13.9889	−1.42035	−0.710176	−	0.704024i	$-0.751385\pi$
$97$	−13.9889	−1.42035	−0.710176	+	0.704024i	$0.751385\pi$
$98$	−37.5698	−3.79512
$99$	2.67487	0.268834
$100$	4.53663	0.453663
$101$	15.7872	1.57089	0.785443	−	0.618935i	$-0.212435\pi$
$101$	15.7872	1.57089	0.785443	+	0.618935i	$0.212435\pi$
$102$	9.52415	0.943031
$103$	−2.44986	−0.241392	−0.120696	−	0.992690i	$-0.538513\pi$
$103$	−2.44986	−0.241392	−0.120696	+	0.992690i	$0.538513\pi$
$104$	−40.3639	−3.95801
$105$	2.65588	0.259187
$106$	−1.67117	−0.162318
$107$	8.28420	0.800864	0.400432	−	0.916327i	$-0.368860\pi$
$107$	8.28420	0.800864	0.400432	+	0.916327i	$0.368860\pi$
$108$	−14.6798	−1.41256
$109$	4.12349	0.394958	0.197479	−	0.980307i	$-0.436725\pi$
$109$	4.12349	0.394958	0.197479	+	0.980307i	$0.436725\pi$
$110$	−2.55668	−0.243770
$111$	−3.94220	−0.374177
$112$	−34.9693	−3.30429
$113$	−5.01718	−0.471976	−0.235988	−	0.971756i	$-0.575833\pi$
$113$	−5.01718	−0.471976	−0.235988	+	0.971756i	$0.575833\pi$
$114$	−11.8737	−1.11207
$115$	−0.223755	−0.0208653
$116$	18.1050	1.68101
$117$	−16.6480	−1.53910
$118$	−0.0355232	−0.00327017
$119$	30.4295	2.78947
$120$	3.69799	0.337578
$121$	1.00000	0.0909091
$122$	−34.5370	−3.12683
$123$	−0.783113	−0.0706109
$124$	0.937406	0.0841815
$125$	−1.00000	−0.0894427
$126$	−31.8534	−2.83773
$127$	−20.7562	−1.84182	−0.920909	−	0.389777i	$-0.872552\pi$
$127$	−20.7562	−1.84182	−0.920909	+	0.389777i	$0.872552\pi$
$128$	10.1529	0.897394
$129$	−0.704950	−0.0620673
$130$	15.9124	1.39561
$131$	−21.7242	−1.89805	−0.949024	−	0.315204i	$-0.897927\pi$
$131$	−21.7242	−1.89805	−0.949024	+	0.315204i	$0.897927\pi$
$132$	−2.58681	−0.225153
$133$	−37.9363	−3.28949
$134$	−29.6433	−2.56079
$135$	3.23584	0.278496
$136$	42.3694	3.63315
$137$	5.64092	0.481937	0.240968	−	0.970533i	$-0.422535\pi$
$137$	5.64092	0.481937	0.240968	+	0.970533i	$0.422535\pi$
$138$	−0.326198	−0.0277678
$139$	−2.72790	−0.231378	−0.115689	−	0.993286i	$-0.536908\pi$
$139$	−2.72790	−0.231378	−0.115689	+	0.993286i	$0.536908\pi$
$140$	21.1305	1.78586
$141$	2.15447	0.181439
$142$	36.4763	3.06102
$143$	−6.22385	−0.520464
$144$	−20.0823	−1.67352
$145$	−3.99086	−0.331422
$146$	2.55668	0.211593
$147$	8.37900	0.691089
$148$	−31.3647	−2.57816
$149$	−14.6327	−1.19876	−0.599378	−	0.800466i	$-0.704585\pi$
$149$	−14.6327	−1.19876	−0.599378	+	0.800466i	$0.704585\pi$
$150$	−1.45783	−0.119032
$151$	−11.0838	−0.901988	−0.450994	−	0.892527i	$-0.648930\pi$
$151$	−11.0838	−0.901988	−0.450994	+	0.892527i	$0.648930\pi$
$152$	−52.8216	−4.28440
$153$	17.4751	1.41278
$154$	−11.9084	−0.959608
$155$	−0.206630	−0.0165969
$156$	16.0999	1.28902
$157$	−10.0647	−0.803249	−0.401625	−	0.915804i	$-0.631554\pi$
$157$	−10.0647	−0.803249	−0.401625	+	0.915804i	$0.631554\pi$
$158$	−10.1465	−0.807215
$159$	0.372713	0.0295581
$160$	6.22424	0.492069
$161$	−1.04220	−0.0821366
$162$	−15.7990	−1.24129
$163$	−5.02882	−0.393888	−0.196944	−	0.980415i	$-0.563102\pi$
$163$	−5.02882	−0.393888	−0.196944	+	0.980415i	$0.563102\pi$
$164$	−6.23056	−0.486525
$165$	0.570205	0.0443904
$166$	−38.2602	−2.96957
$167$	−1.12336	−0.0869283	−0.0434642	−	0.999055i	$-0.513839\pi$
$167$	−1.12336	−0.0869283	−0.0434642	+	0.999055i	$0.513839\pi$
$168$	17.2243	1.32889
$169$	25.7363	1.97971
$170$	−16.7030	−1.28106
$171$	−21.7861	−1.66602
$172$	−5.60868	−0.427658
$173$	6.91547	0.525774	0.262887	−	0.964827i	$-0.415325\pi$
$173$	6.91547	0.525774	0.262887	+	0.964827i	$0.415325\pi$
$174$	−5.81800	−0.441062
$175$	−4.65776	−0.352094
$176$	−7.50776	−0.565919
$177$	0.00792257	0.000595497 0
$178$	22.8303	1.71120
$179$	5.99284	0.447926	0.223963	−	0.974598i	$-0.428101\pi$
$179$	5.99284	0.447926	0.223963	+	0.974598i	$0.428101\pi$
$180$	12.1349	0.904481
$181$	15.2960	1.13695	0.568473	−	0.822702i	$-0.307535\pi$
$181$	15.2960	1.13695	0.568473	+	0.822702i	$0.307535\pi$
$182$	74.1162	5.49386
$183$	7.70263	0.569395
$184$	−1.45113	−0.106979
$185$	6.91365	0.508301
$186$	−0.301233	−0.0220874
$187$	6.53308	0.477746
$188$	17.1413	1.25016
$189$	15.0717	1.09631
$190$	20.8235	1.51070
$191$	5.13102	0.371268	0.185634	−	0.982619i	$-0.440566\pi$
$191$	5.13102	0.371268	0.185634	+	0.982619i	$0.440566\pi$
$192$	0.511980	0.0369490
$193$	17.1737	1.23619	0.618096	−	0.786103i	$-0.287904\pi$
$193$	17.1737	1.23619	0.618096	+	0.786103i	$0.287904\pi$
$194$	35.7651	2.56778
$195$	−3.54887	−0.254140
$196$	66.6645	4.76175
$197$	−12.2411	−0.872144	−0.436072	−	0.899912i	$-0.643631\pi$
$197$	−12.2411	−0.872144	−0.436072	+	0.899912i	$0.643631\pi$
$198$	−6.83879	−0.486011
$199$	−10.9775	−0.778172	−0.389086	−	0.921201i	$-0.627209\pi$
$199$	−10.9775	−0.778172	−0.389086	+	0.921201i	$0.627209\pi$
$200$	−6.48536	−0.458584
$201$	6.61121	0.466319
$202$	−40.3629	−2.83992
$203$	−18.5884	−1.30465
$204$	−16.8998	−1.18323
$205$	1.37339	0.0959217
$206$	6.26351	0.436399
$207$	−0.598515	−0.0415997
$208$	46.7271	3.23994
$209$	−8.14474	−0.563384
$210$	−6.79024	−0.468571
$211$	19.6958	1.35592	0.677958	−	0.735101i	$-0.262865\pi$
$211$	19.6958	1.35592	0.677958	+	0.735101i	$0.262865\pi$
$212$	2.96536	0.203662
$213$	−8.13514	−0.557410
$214$	−21.1801	−1.44784
$215$	1.23631	0.0843156
$216$	20.9856	1.42789
$217$	−0.962434	−0.0653343
$218$	−10.5425	−0.714025
$219$	−0.570205	−0.0385309
$220$	4.53663	0.305860
$221$	−40.6609	−2.73515
$222$	10.0789	0.676455
$223$	−24.5897	−1.64665	−0.823324	−	0.567572i	$-0.807883\pi$
$223$	−24.5897	−1.64665	−0.823324	+	0.567572i	$0.807883\pi$
$224$	28.9910	1.93704
$225$	−2.67487	−0.178324
$226$	12.8273	0.853261
$227$	−24.3001	−1.61286	−0.806428	−	0.591332i	$-0.798602\pi$
$227$	−24.3001	−1.61286	−0.806428	+	0.591332i	$0.798602\pi$
$228$	21.0689	1.39532
$229$	−6.15585	−0.406790	−0.203395	−	0.979097i	$-0.565198\pi$
$229$	−6.15585	−0.406790	−0.203395	+	0.979097i	$0.565198\pi$
$230$	0.572071	0.0377212
$231$	2.65588	0.174744
$232$	−25.8821	−1.69925
$233$	−22.7707	−1.49176	−0.745880	−	0.666080i	$-0.767971\pi$
$233$	−22.7707	−1.49176	−0.745880	+	0.666080i	$0.767971\pi$
$234$	42.5636	2.78247
$235$	−3.77842	−0.246477
$236$	0.0630331	0.00410310
$237$	2.26293	0.146993
$238$	−77.7987	−5.04294
$239$	20.0929	1.29970	0.649851	−	0.760062i	$-0.274831\pi$
$239$	20.0929	1.29970	0.649851	+	0.760062i	$0.274831\pi$
$240$	−4.28096	−0.276335
$241$	5.49176	0.353756	0.176878	−	0.984233i	$-0.443400\pi$
$241$	5.49176	0.353756	0.176878	+	0.984233i	$0.443400\pi$
$242$	−2.55668	−0.164350
$243$	13.2311	0.848775
$244$	61.2832	3.92325
$245$	−14.6947	−0.938811
$246$	2.00217	0.127654
$247$	50.6916	3.22543
$248$	−1.34007	−0.0850947
$249$	8.53299	0.540756
$250$	2.55668	0.161699
$251$	−0.805663	−0.0508530	−0.0254265	−	0.999677i	$-0.508094\pi$
$251$	−0.805663	−0.0508530	−0.0254265	+	0.999677i	$0.508094\pi$
$252$	56.5214	3.56051
$253$	−0.223755	−0.0140674
$254$	53.0671	3.32973
$255$	3.72520	0.233281
$256$	−27.7534	−1.73459
$257$	−13.8952	−0.866756	−0.433378	−	0.901212i	$-0.642678\pi$
$257$	−13.8952	−0.866756	−0.433378	+	0.901212i	$0.642678\pi$
$258$	1.80233	0.112208
$259$	32.2021	2.00094
$260$	−28.2353	−1.75108
$261$	−10.6750	−0.660766
$262$	55.5418	3.43138
$263$	7.91551	0.488091	0.244046	−	0.969764i	$-0.421525\pi$
$263$	7.91551	0.488091	0.244046	+	0.969764i	$0.421525\pi$
$264$	3.69799	0.227595
$265$	−0.653648	−0.0401533
$266$	96.9910	5.94690
$267$	−5.09173	−0.311609
$268$	52.5997	3.21304
$269$	−4.12523	−0.251520	−0.125760	−	0.992061i	$-0.540137\pi$
$269$	−4.12523	−0.251520	−0.125760	+	0.992061i	$0.540137\pi$
$270$	−8.27301	−0.503479
$271$	−6.41157	−0.389475	−0.194738	−	0.980855i	$-0.562386\pi$
$271$	−6.41157	−0.389475	−0.194738	+	0.980855i	$0.562386\pi$
$272$	−49.0488	−2.97402
$273$	−16.5298	−1.00043
$274$	−14.4221	−0.871268
$275$	−1.00000	−0.0603023
$276$	0.578812	0.0348404
$277$	−5.72025	−0.343696	−0.171848	−	0.985123i	$-0.554974\pi$
$277$	−5.72025	−0.343696	−0.171848	+	0.985123i	$0.554974\pi$
$278$	6.97438	0.418296
$279$	−0.552708	−0.0330898
$280$	−30.2073	−1.80523
$281$	1.31750	0.0785952	0.0392976	−	0.999228i	$-0.487488\pi$
$281$	1.31750	0.0785952	0.0392976	+	0.999228i	$0.487488\pi$
$282$	−5.50831	−0.328015
$283$	−15.2450	−0.906222	−0.453111	−	0.891454i	$-0.649686\pi$
$283$	−15.2450	−0.906222	−0.453111	+	0.891454i	$0.649686\pi$
$284$	−64.7243	−3.84068
$285$	−4.64417	−0.275097
$286$	15.9124	0.940920
$287$	6.39692	0.377598
$288$	16.6490	0.981052
$289$	25.6812	1.51066
$290$	10.2034	0.599162
$291$	−7.97651	−0.467591
$292$	−4.53663	−0.265486
$293$	4.16164	0.243125	0.121563	−	0.992584i	$-0.461209\pi$
$293$	4.16164	0.243125	0.121563	+	0.992584i	$0.461209\pi$
$294$	−21.4225	−1.24938
$295$	−0.0138942	−0.000808954 0
$296$	44.8375	2.60613
$297$	3.23584	0.187762
$298$	37.4111	2.16717
$299$	1.39262	0.0805371
$300$	2.58681	0.149350
$301$	5.75843	0.331910
$302$	28.3378	1.63066
$303$	9.00194	0.517148
$304$	61.1488	3.50712
$305$	−13.5085	−0.773496
$306$	−44.6784	−2.55409
$307$	9.27486	0.529344	0.264672	−	0.964338i	$-0.414736\pi$
$307$	9.27486	0.529344	0.264672	+	0.964338i	$0.414736\pi$
$308$	21.1305	1.20402
$309$	−1.39692	−0.0794681
$310$	0.528288	0.0300048
$311$	11.3519	0.643706	0.321853	−	0.946790i	$-0.395694\pi$
$311$	11.3519	0.643706	0.321853	+	0.946790i	$0.395694\pi$
$312$	−23.0157	−1.30301
$313$	−6.11542	−0.345664	−0.172832	−	0.984951i	$-0.555292\pi$
$313$	−6.11542	−0.345664	−0.172832	+	0.984951i	$0.555292\pi$
$314$	25.7322	1.45215
$315$	−12.4589	−0.701979
$316$	18.0042	1.01282
$317$	−31.0607	−1.74454	−0.872272	−	0.489020i	$-0.837354\pi$
$317$	−31.0607	−1.74454	−0.872272	+	0.489020i	$0.837354\pi$
$318$	−0.952910	−0.0534365
$319$	−3.99086	−0.223445
$320$	−0.897889	−0.0501935
$321$	4.72369	0.263651
$322$	2.66457	0.148491
$323$	−53.2103	−2.96070
$324$	28.0342	1.55745
$325$	6.22385	0.345237
$326$	12.8571	0.712089
$327$	2.35123	0.130023
$328$	8.90693	0.491803
$329$	−17.5990	−0.970262
$330$	−1.45783	−0.0802511
$331$	−19.8494	−1.09102	−0.545511	−	0.838103i	$-0.683665\pi$
$331$	−19.8494	−1.09102	−0.545511	+	0.838103i	$0.683665\pi$
$332$	67.8896	3.72593
$333$	18.4931	1.01341
$334$	2.87208	0.157153
$335$	−11.5944	−0.633472
$336$	−19.9397	−1.08780
$337$	−9.59068	−0.522438	−0.261219	−	0.965280i	$-0.584124\pi$
$337$	−9.59068	−0.522438	−0.261219	+	0.965280i	$0.584124\pi$
$338$	−65.7995	−3.57902
$339$	−2.86082	−0.155378
$340$	29.6382	1.60736
$341$	−0.206630	−0.0111897
$342$	55.7002	3.01192
$343$	−35.8402	−1.93519
$344$	8.01791	0.432297
$345$	−0.127586	−0.00686901
$346$	−17.6807	−0.950519
$347$	−15.0365	−0.807202	−0.403601	−	0.914935i	$-0.632242\pi$
$347$	−15.0365	−0.807202	−0.403601	+	0.914935i	$0.632242\pi$
$348$	10.3236	0.553402
$349$	0.908518	0.0486318	0.0243159	−	0.999704i	$-0.492259\pi$
$349$	0.908518	0.0486318	0.0243159	+	0.999704i	$0.492259\pi$
$350$	11.9084	0.636532
$351$	−20.1394	−1.07496
$352$	6.22424	0.331753
$353$	−11.9213	−0.634507	−0.317253	−	0.948341i	$-0.602761\pi$
$353$	−11.9213	−0.634507	−0.317253	+	0.948341i	$0.602761\pi$
$354$	−0.0202555	−0.00107657
$355$	14.2670	0.757216
$356$	−40.5105	−2.14705
$357$	17.3511	0.918316
$358$	−15.3218	−0.809782
$359$	−32.2099	−1.69997	−0.849987	−	0.526804i	$-0.823390\pi$
$359$	−32.2099	−1.69997	−0.849987	+	0.526804i	$0.823390\pi$
$360$	−17.3475	−0.914292
$361$	47.3368	2.49141
$362$	−39.1071	−2.05542
$363$	0.570205	0.0299280
$364$	−131.513	−6.89317
$365$	1.00000	0.0523424
$366$	−19.6932	−1.02938
$367$	−1.31100	−0.0684338	−0.0342169	−	0.999414i	$-0.510894\pi$
$367$	−1.31100	−0.0684338	−0.0342169	+	0.999414i	$0.510894\pi$
$368$	1.67990	0.0875708
$369$	3.67363	0.191242
$370$	−17.6760	−0.918932
$371$	−3.04453	−0.158064
$372$	0.534513	0.0277132
$373$	−29.6559	−1.53553	−0.767763	−	0.640734i	$-0.778630\pi$
$373$	−29.6559	−1.53553	−0.767763	+	0.640734i	$0.778630\pi$
$374$	−16.7030	−0.863693
$375$	−0.570205	−0.0294453
$376$	−24.5044	−1.26372
$377$	24.8385	1.27925
$378$	−38.5337	−1.98196
$379$	10.1466	0.521197	0.260599	−	0.965447i	$-0.416080\pi$
$379$	10.1466	0.521197	0.260599	+	0.965447i	$0.416080\pi$
$380$	−36.9497	−1.89548
$381$	−11.8353	−0.606341
$382$	−13.1184	−0.671195
$383$	10.3183	0.527241	0.263620	−	0.964626i	$-0.415083\pi$
$383$	10.3183	0.527241	0.263620	+	0.964626i	$0.415083\pi$
$384$	5.78921	0.295429
$385$	−4.65776	−0.237381
$386$	−43.9078	−2.23485
$387$	3.30696	0.168102
$388$	−63.4623	−3.22181
$389$	−25.0742	−1.27131	−0.635657	−	0.771972i	$-0.719271\pi$
$389$	−25.0742	−1.27131	−0.635657	+	0.771972i	$0.719271\pi$
$390$	9.07333	0.459446
$391$	−1.46181	−0.0739269
$392$	−95.3006	−4.81341
$393$	−12.3872	−0.624852
$394$	31.2967	1.57670
$395$	−3.96863	−0.199683
$396$	12.1349	0.609801
$397$	−4.15110	−0.208338	−0.104169	−	0.994560i	$-0.533218\pi$
$397$	−4.15110	−0.208338	−0.104169	+	0.994560i	$0.533218\pi$
$398$	28.0659	1.40682
$399$	−21.6314	−1.08293
$400$	7.50776	0.375388
$401$	−26.1418	−1.30546	−0.652730	−	0.757590i	$-0.726376\pi$
$401$	−26.1418	−1.30546	−0.652730	+	0.757590i	$0.726376\pi$
$402$	−16.9028	−0.843033
$403$	1.28604	0.0640620
$404$	71.6207	3.56326
$405$	−6.17951	−0.307062
$406$	47.5248	2.35861
$407$	6.91365	0.342697
$408$	24.1592	1.19606
$409$	34.4510	1.70349	0.851745	−	0.523956i	$-0.175545\pi$
$409$	34.4510	1.70349	0.851745	+	0.523956i	$0.175545\pi$
$410$	−3.51132	−0.173412
$411$	3.21648	0.158657
$412$	−11.1141	−0.547552
$413$	−0.0647161	−0.00318447
$414$	1.53021	0.0752059
$415$	−14.9648	−0.734592
$416$	−38.7387	−1.89932
$417$	−1.55546	−0.0761714
$418$	20.8235	1.01851
$419$	2.27763	0.111269	0.0556347	−	0.998451i	$-0.482282\pi$
$419$	2.27763	0.111269	0.0556347	+	0.998451i	$0.482282\pi$
$420$	12.0487	0.587918
$421$	−38.0236	−1.85316	−0.926578	−	0.376102i	$-0.877264\pi$
$421$	−38.0236	−1.85316	−0.926578	+	0.376102i	$0.877264\pi$
$422$	−50.3560	−2.45129
$423$	−10.1068	−0.491408
$424$	−4.23914	−0.205871
$425$	−6.53308	−0.316901
$426$	20.7990	1.00771
$427$	−62.9195	−3.04489
$428$	37.5823	1.81661
$429$	−3.54887	−0.171341
$430$	−3.16085	−0.152430
$431$	12.3339	0.594102	0.297051	−	0.954862i	$-0.403997\pi$
$431$	12.3339	0.594102	0.297051	+	0.954862i	$0.403997\pi$
$432$	−24.2939	−1.16884
$433$	26.1424	1.25633	0.628163	−	0.778082i	$-0.283807\pi$
$433$	26.1424	1.25633	0.628163	+	0.778082i	$0.283807\pi$
$434$	2.46064	0.118115
$435$	−2.27561	−0.109107
$436$	18.7067	0.895890
$437$	1.82243	0.0871785
$438$	1.45783	0.0696580
$439$	−6.51350	−0.310872	−0.155436	−	0.987846i	$-0.549678\pi$
$439$	−6.51350	−0.310872	−0.155436	+	0.987846i	$0.549678\pi$
$440$	−6.48536	−0.309178
$441$	−39.3064	−1.87173
$442$	103.957	4.94473
$443$	−22.9251	−1.08921	−0.544603	−	0.838694i	$-0.683320\pi$
$443$	−22.9251	−1.08921	−0.544603	+	0.838694i	$0.683320\pi$
$444$	−17.8843	−0.848751
$445$	8.92964	0.423306
$446$	62.8681	2.97689
$447$	−8.34362	−0.394640
$448$	−4.18215	−0.197588
$449$	−29.0393	−1.37045	−0.685224	−	0.728332i	$-0.740296\pi$
$449$	−29.0393	−1.37045	−0.685224	+	0.728332i	$0.740296\pi$
$450$	6.83879	0.322384
$451$	1.37339	0.0646704
$452$	−22.7611	−1.07059
$453$	−6.32005	−0.296942
$454$	62.1277	2.91580
$455$	28.9892	1.35903
$456$	−30.1191	−1.41046
$457$	−35.3264	−1.65250	−0.826249	−	0.563306i	$-0.809529\pi$
$457$	−35.3264	−1.65250	−0.826249	+	0.563306i	$0.809529\pi$
$458$	15.7386	0.735415
$459$	21.1400	0.986730
$460$	−1.01509	−0.0473290
$461$	21.6438	1.00805	0.504027	−	0.863688i	$-0.331851\pi$
$461$	21.6438	1.00805	0.504027	+	0.863688i	$0.331851\pi$
$462$	−6.79024	−0.315910
$463$	28.7904	1.33800	0.669001	−	0.743261i	$-0.266722\pi$
$463$	28.7904	1.33800	0.669001	+	0.743261i	$0.266722\pi$
$464$	29.9624	1.39097
$465$	−0.117822	−0.00546385
$466$	58.2176	2.69688
$467$	−17.3157	−0.801275	−0.400638	−	0.916237i	$-0.631211\pi$
$467$	−17.3157	−0.801275	−0.400638	+	0.916237i	$0.631211\pi$
$468$	−75.5257	−3.49117
$469$	−54.0041	−2.49368
$470$	9.66022	0.445593
$471$	−5.73893	−0.264436
$472$	−0.0901092	−0.00414761
$473$	1.23631	0.0568456
$474$	−5.78560	−0.265742
$475$	8.14474	0.373706
$476$	138.048	6.32740
$477$	−1.74842	−0.0800547
$478$	−51.3712	−2.34966
$479$	−16.2918	−0.744391	−0.372196	−	0.928154i	$-0.621395\pi$
$479$	−16.2918	−0.744391	−0.372196	+	0.928154i	$0.621395\pi$
$480$	3.54909	0.161993
$481$	−43.0295	−1.96198
$482$	−14.0407	−0.639537
$483$	−0.594266	−0.0270400
$484$	4.53663	0.206210
$485$	13.9889	0.635201
$486$	−33.8277	−1.53446
$487$	33.8669	1.53466	0.767328	−	0.641255i	$-0.221586\pi$
$487$	33.8669	1.53466	0.767328	+	0.641255i	$0.221586\pi$
$488$	−87.6077	−3.96581
$489$	−2.86746	−0.129671
$490$	37.5698	1.69723
$491$	13.0860	0.590562	0.295281	−	0.955410i	$-0.404587\pi$
$491$	13.0860	0.590562	0.295281	+	0.955410i	$0.404587\pi$
$492$	−3.55270	−0.160168
$493$	−26.0726	−1.17425
$494$	−129.602	−5.83109
$495$	−2.67487	−0.120226
$496$	1.55133	0.0696568
$497$	66.4525	2.98080
$498$	−21.8161	−0.977605
$499$	0.895329	0.0400804	0.0200402	−	0.999799i	$-0.493621\pi$
$499$	0.895329	0.0400804	0.0200402	+	0.999799i	$0.493621\pi$
$500$	−4.53663	−0.202884
$501$	−0.640546	−0.0286175
$502$	2.05982	0.0919345
$503$	36.1987	1.61402	0.807010	−	0.590538i	$-0.201085\pi$
$503$	36.1987	1.61402	0.807010	+	0.590538i	$0.201085\pi$
$504$	−80.8004	−3.59914
$505$	−15.7872	−0.702521
$506$	0.572071	0.0254317
$507$	14.6750	0.651738
$508$	−94.1634	−4.17783
$509$	−16.7119	−0.740740	−0.370370	−	0.928884i	$-0.620769\pi$
$509$	−16.7119	−0.740740	−0.370370	+	0.928884i	$0.620769\pi$
$510$	−9.52415	−0.421736
$511$	4.65776	0.206047
$512$	50.6510	2.23848
$513$	−26.3551	−1.16360
$514$	35.5255	1.56696
$515$	2.44986	0.107954
$516$	−3.19810	−0.140788
$517$	−3.77842	−0.166175
$518$	−82.3306	−3.61740
$519$	3.94324	0.173089
$520$	40.3639	1.77007
$521$	−1.23174	−0.0539634	−0.0269817	−	0.999636i	$-0.508590\pi$
$521$	−1.23174	−0.0539634	−0.0269817	+	0.999636i	$0.508590\pi$
$522$	27.2926	1.19457
$523$	25.6983	1.12371	0.561855	−	0.827236i	$-0.310088\pi$
$523$	25.6983	1.12371	0.561855	+	0.827236i	$0.310088\pi$
$524$	−98.5545	−4.30537
$525$	−2.65588	−0.115912
$526$	−20.2374	−0.882395
$527$	−1.34993	−0.0588040
$528$	−4.28096	−0.186305
$529$	−22.9499	−0.997823
$530$	1.67117	0.0725910
$531$	−0.0371653	−0.00161283
$532$	−172.103	−7.46160
$533$	−8.54776	−0.370245
$534$	13.0179	0.563341
$535$	−8.28420	−0.358157
$536$	−75.1942	−3.24789
$537$	3.41715	0.147461
$538$	10.5469	0.454710
$539$	−14.6947	−0.632947
$540$	14.6798	0.631718
$541$	−7.12603	−0.306372	−0.153186	−	0.988197i	$-0.548953\pi$
$541$	−7.12603	−0.306372	−0.153186	+	0.988197i	$0.548953\pi$
$542$	16.3924	0.704112
$543$	8.72187	0.374291
$544$	40.6634	1.74343
$545$	−4.12349	−0.176631
$546$	42.2614	1.80862
$547$	19.2110	0.821403	0.410701	−	0.911770i	$-0.365284\pi$
$547$	19.2110	0.821403	0.410701	+	0.911770i	$0.365284\pi$
$548$	25.5908	1.09318
$549$	−36.1335	−1.54214
$550$	2.55668	0.109017
$551$	32.5045	1.38474
$552$	−0.827443	−0.0352183
$553$	−18.4849	−0.786059
$554$	14.6249	0.621351
$555$	3.94220	0.167337
$556$	−12.3755	−0.524837
$557$	8.76268	0.371287	0.185643	−	0.982617i	$-0.440563\pi$
$557$	8.76268	0.371287	0.185643	+	0.982617i	$0.440563\pi$
$558$	1.41310	0.0598213
$559$	−7.69460	−0.325447
$560$	34.9693	1.47772
$561$	3.72520	0.157278
$562$	−3.36842	−0.142088
$563$	46.1775	1.94615	0.973075	−	0.230488i	$-0.0740323\pi$
$563$	46.1775	1.94615	0.973075	+	0.230488i	$0.0740323\pi$
$564$	9.77405	0.411562
$565$	5.01718	0.211074
$566$	38.9767	1.63831
$567$	−28.7827	−1.20876
$568$	92.5269	3.88234
$569$	−39.7334	−1.66571	−0.832856	−	0.553489i	$-0.813296\pi$
$569$	−39.7334	−1.66571	−0.832856	+	0.553489i	$0.813296\pi$
$570$	11.8737	0.497334
$571$	17.8278	0.746071	0.373036	−	0.927817i	$-0.378317\pi$
$571$	17.8278	0.746071	0.373036	+	0.927817i	$0.378317\pi$
$572$	−28.2353	−1.18058
$573$	2.92573	0.122224
$574$	−16.3549	−0.682640
$575$	0.223755	0.00933123
$576$	−2.40173	−0.100072
$577$	8.74599	0.364100	0.182050	−	0.983289i	$-0.441727\pi$
$577$	8.74599	0.364100	0.182050	+	0.983289i	$0.441727\pi$
$578$	−65.6586	−2.73104
$579$	9.79254	0.406964
$580$	−18.1050	−0.751771
$581$	−69.7023	−2.89174
$582$	20.3934	0.845334
$583$	−0.653648	−0.0270713
$584$	6.48536	0.268366
$585$	16.6480	0.688308
$586$	−10.6400	−0.439534
$587$	31.7947	1.31231	0.656154	−	0.754627i	$-0.272182\pi$
$587$	31.7947	1.31231	0.656154	+	0.754627i	$0.272182\pi$
$588$	38.0124	1.56761
$589$	1.68295	0.0693448
$590$	0.0355232	0.00146247
$591$	−6.97995	−0.287117
$592$	−51.9060	−2.13332
$593$	4.26697	0.175223	0.0876116	−	0.996155i	$-0.472077\pi$
$593$	4.26697	0.175223	0.0876116	+	0.996155i	$0.472077\pi$
$594$	−8.27301	−0.339446
$595$	−30.4295	−1.24749
$596$	−66.3830	−2.71916
$597$	−6.25941	−0.256180
$598$	−3.56048	−0.145599
$599$	−39.0933	−1.59731	−0.798654	−	0.601790i	$-0.794454\pi$
$599$	−39.0933	−1.59731	−0.798654	+	0.601790i	$0.794454\pi$
$600$	−3.69799	−0.150970
$601$	0.458974	0.0187219	0.00936096	−	0.999956i	$-0.497020\pi$
$601$	0.458974	0.0187219	0.00936096	+	0.999956i	$0.497020\pi$
$602$	−14.7225	−0.600044
$603$	−31.0136	−1.26297
$604$	−50.2832	−2.04599
$605$	−1.00000	−0.0406558
$606$	−23.0151	−0.934925
$607$	24.2577	0.984589	0.492294	−	0.870429i	$-0.336158\pi$
$607$	24.2577	0.984589	0.492294	+	0.870429i	$0.336158\pi$
$608$	−50.6948	−2.05595
$609$	−10.5992	−0.429502
$610$	34.5370	1.39836
$611$	23.5163	0.951368
$612$	79.2782	3.20463
$613$	−6.77520	−0.273648	−0.136824	−	0.990595i	$-0.543689\pi$
$613$	−6.77520	−0.273648	−0.136824	+	0.990595i	$0.543689\pi$
$614$	−23.7129	−0.956974
$615$	0.783113	0.0315782
$616$	−30.2073	−1.21709
$617$	2.71802	0.109423	0.0547116	−	0.998502i	$-0.482576\pi$
$617$	2.71802	0.109423	0.0547116	+	0.998502i	$0.482576\pi$
$618$	3.57148	0.143666
$619$	−14.8477	−0.596779	−0.298390	−	0.954444i	$-0.596449\pi$
$619$	−14.8477	−0.596779	−0.298390	+	0.954444i	$0.596449\pi$
$620$	−0.937406	−0.0376471
$621$	−0.724035	−0.0290545
$622$	−29.0232	−1.16372
$623$	41.5921	1.66635
$624$	26.6440	1.06662
$625$	1.00000	0.0400000
$626$	15.6352	0.624908
$627$	−4.64417	−0.185470
$628$	−45.6598	−1.82202
$629$	45.1674	1.80094
$630$	31.8534	1.26907
$631$	−30.1956	−1.20207	−0.601035	−	0.799223i	$-0.705245\pi$
$631$	−30.1956	−1.20207	−0.601035	+	0.799223i	$0.705245\pi$
$632$	−25.7380	−1.02380
$633$	11.2306	0.446378
$634$	79.4125	3.15387
$635$	20.7562	0.823686
$636$	1.69086	0.0670471
$637$	91.4577	3.62369
$638$	10.2034	0.403955
$639$	38.1624	1.50968
$640$	−10.1529	−0.401327
$641$	−14.4392	−0.570316	−0.285158	−	0.958481i	$-0.592046\pi$
$641$	−14.4392	−0.570316	−0.285158	+	0.958481i	$0.592046\pi$
$642$	−12.0770	−0.476640
$643$	13.5335	0.533711	0.266855	−	0.963737i	$-0.414015\pi$
$643$	13.5335	0.533711	0.266855	+	0.963737i	$0.414015\pi$
$644$	−4.72806	−0.186312
$645$	0.704950	0.0277574
$646$	136.042	5.35249
$647$	13.9487	0.548381	0.274190	−	0.961675i	$-0.411590\pi$
$647$	13.9487	0.548381	0.274190	+	0.961675i	$0.411590\pi$
$648$	−40.0764	−1.57435
$649$	−0.0138942	−0.000545397 0
$650$	−15.9124	−0.624136
$651$	−0.548785	−0.0215086
$652$	−22.8139	−0.893462
$653$	36.7124	1.43667	0.718334	−	0.695699i	$-0.244905\pi$
$653$	36.7124	1.43667	0.718334	+	0.695699i	$0.244905\pi$
$654$	−6.01136	−0.235063
$655$	21.7242	0.848833
$656$	−10.3111	−0.402580
$657$	2.67487	0.104356
$658$	44.9950	1.75409
$659$	−9.60178	−0.374032	−0.187016	−	0.982357i	$-0.559882\pi$
$659$	−9.60178	−0.374032	−0.187016	+	0.982357i	$0.559882\pi$
$660$	2.58681	0.100691
$661$	−15.7388	−0.612168	−0.306084	−	0.952005i	$-0.599019\pi$
$661$	−15.7388	−0.612168	−0.306084	+	0.952005i	$0.599019\pi$
$662$	50.7487	1.97240
$663$	−23.1850	−0.900433
$664$	−97.0520	−3.76635
$665$	37.9363	1.47110
$666$	−47.2810	−1.83210
$667$	0.892974	0.0345761
$668$	−5.09628	−0.197181
$669$	−14.0212	−0.542089
$670$	29.6433	1.14522
$671$	−13.5085	−0.521491
$672$	16.5308	0.637690
$673$	−38.1368	−1.47006	−0.735032	−	0.678032i	$-0.762833\pi$
$673$	−38.1368	−1.47006	−0.735032	+	0.678032i	$0.762833\pi$
$674$	24.5203	0.944488
$675$	−3.23584	−0.124547
$676$	116.756	4.49062
$677$	−10.4310	−0.400898	−0.200449	−	0.979704i	$-0.564240\pi$
$677$	−10.4310	−0.400898	−0.200449	+	0.979704i	$0.564240\pi$
$678$	7.31421	0.280900
$679$	65.1567	2.50049
$680$	−42.3694	−1.62479
$681$	−13.8561	−0.530965
$682$	0.528288	0.0202292
$683$	−26.1635	−1.00112	−0.500560	−	0.865702i	$-0.666872\pi$
$683$	−26.1635	−1.00112	−0.500560	+	0.865702i	$0.666872\pi$
$684$	−98.8355	−3.77907
$685$	−5.64092	−0.215529
$686$	91.6320	3.49853
$687$	−3.51010	−0.133919
$688$	−9.28191	−0.353870
$689$	4.06821	0.154986
$690$	0.326198	0.0124181
$691$	14.3516	0.545962	0.272981	−	0.962019i	$-0.411990\pi$
$691$	14.3516	0.545962	0.272981	+	0.962019i	$0.411990\pi$
$692$	31.3730	1.19262
$693$	−12.4589	−0.473274
$694$	38.4436	1.45930
$695$	2.72790	0.103475
$696$	−14.7581	−0.559405
$697$	8.97246	0.339856
$698$	−2.32279	−0.0879190
$699$	−12.9840	−0.491100
$700$	−21.1305	−0.798659
$701$	−2.30122	−0.0869158	−0.0434579	−	0.999055i	$-0.513837\pi$
$701$	−2.30122	−0.0869158	−0.0434579	+	0.999055i	$0.513837\pi$
$702$	51.4900	1.94336
$703$	−56.3099	−2.12377
$704$	−0.897889	−0.0338404
$705$	−2.15447	−0.0811422
$706$	30.4790	1.14709
$707$	−73.5330	−2.76549
$708$	0.0359418	0.00135077
$709$	−8.25409	−0.309989	−0.154994	−	0.987915i	$-0.549536\pi$
$709$	−8.25409	−0.309989	−0.154994	+	0.987915i	$0.549536\pi$
$710$	−36.4763	−1.36893
$711$	−10.6156	−0.398114
$712$	57.9120	2.17034
$713$	0.0462346	0.00173150
$714$	−44.3612	−1.66018
$715$	6.22385	0.232759
$716$	27.1873	1.01604
$717$	11.4571	0.427872
$718$	82.3505	3.07329
$719$	5.82486	0.217231	0.108615	−	0.994084i	$-0.465358\pi$
$719$	5.82486	0.217231	0.108615	+	0.994084i	$0.465358\pi$
$720$	20.0823	0.748421
$721$	11.4108	0.424962
$722$	−121.025	−4.50410
$723$	3.13143	0.116459
$724$	69.3925	2.57895
$725$	3.99086	0.148217
$726$	−1.45783	−0.0541053
$727$	20.3420	0.754444	0.377222	−	0.926123i	$-0.376879\pi$
$727$	20.3420	0.754444	0.377222	+	0.926123i	$0.376879\pi$
$728$	188.005	6.96794
$729$	−10.9941	−0.407189
$730$	−2.55668	−0.0946271
$731$	8.07691	0.298735
$732$	34.9440	1.29157
$733$	−32.6096	−1.20446	−0.602232	−	0.798321i	$-0.705722\pi$
$733$	−32.6096	−1.20446	−0.602232	+	0.798321i	$0.705722\pi$
$734$	3.35182	0.123718
$735$	−8.37900	−0.309064
$736$	−1.39270	−0.0513358
$737$	−11.5944	−0.427087
$738$	−9.39232	−0.345736
$739$	−40.6282	−1.49453	−0.747267	−	0.664524i	$-0.768634\pi$
$739$	−40.6282	−1.49453	−0.747267	+	0.664524i	$0.768634\pi$
$740$	31.3647	1.15299
$741$	28.9046	1.06184
$742$	7.78391	0.285756
$743$	−8.61652	−0.316109	−0.158055	−	0.987430i	$-0.550522\pi$
$743$	−8.61652	−0.316109	−0.158055	+	0.987430i	$0.550522\pi$
$744$	−0.764116	−0.0280139
$745$	14.6327	0.536100
$746$	75.8208	2.77600
$747$	−40.0288	−1.46458
$748$	29.6382	1.08368
$749$	−38.5858	−1.40989
$750$	1.45783	0.0532326
$751$	24.4910	0.893690	0.446845	−	0.894611i	$-0.352548\pi$
$751$	24.4910	0.893690	0.446845	+	0.894611i	$0.352548\pi$
$752$	28.3675	1.03445
$753$	−0.459393	−0.0167412
$754$	−63.5041	−2.31268
$755$	11.0838	0.403381
$756$	68.3750	2.48677
$757$	44.6779	1.62385	0.811924	−	0.583764i	$-0.198421\pi$
$757$	44.6779	1.62385	0.811924	+	0.583764i	$0.198421\pi$
$758$	−25.9417	−0.942246
$759$	−0.127586	−0.00463109
$760$	52.8216	1.91604
$761$	−47.3675	−1.71707	−0.858535	−	0.512755i	$-0.828625\pi$
$761$	−47.3675	−1.71707	−0.858535	+	0.512755i	$0.828625\pi$
$762$	30.2591	1.09617
$763$	−19.2062	−0.695311
$764$	23.2775	0.842152
$765$	−17.4751	−0.631814
$766$	−26.3806	−0.953172
$767$	0.0864757	0.00312246
$768$	−15.8251	−0.571040
$769$	−39.8256	−1.43615	−0.718074	−	0.695967i	$-0.754976\pi$
$769$	−39.8256	−1.43615	−0.718074	+	0.695967i	$0.754976\pi$
$770$	11.9084	0.429150
$771$	−7.92308	−0.285343
$772$	77.9109	2.80407
$773$	31.7306	1.14127	0.570634	−	0.821204i	$-0.306697\pi$
$773$	31.7306	1.14127	0.570634	+	0.821204i	$0.306697\pi$
$774$	−8.45485	−0.303903
$775$	0.206630	0.00742238
$776$	90.7228	3.25676
$777$	18.3618	0.658726
$778$	64.1068	2.29834
$779$	−11.1859	−0.400776
$780$	−16.0999	−0.576469
$781$	14.2670	0.510515
$782$	3.73739	0.133649
$783$	−12.9138	−0.461500
$784$	110.324	3.94016
$785$	10.0647	0.359224
$786$	31.6702	1.12964
$787$	−28.7557	−1.02503	−0.512515	−	0.858678i	$-0.671286\pi$
$787$	−28.7557	−1.02503	−0.512515	+	0.858678i	$0.671286\pi$
$788$	−55.5335	−1.97830
$789$	4.51346	0.160683
$790$	10.1465	0.360997
$791$	23.3688	0.830899
$792$	−17.3475	−0.616416
$793$	84.0750	2.98559
$794$	10.6130	0.376643
$795$	−0.372713	−0.0132188
$796$	−49.8007	−1.76514
$797$	−12.5408	−0.444220	−0.222110	−	0.975022i	$-0.571294\pi$
$797$	−12.5408	−0.444220	−0.222110	+	0.975022i	$0.571294\pi$
$798$	55.3047	1.95777
$799$	−24.6847	−0.873283
$800$	−6.22424	−0.220060
$801$	23.8856	0.843956
$802$	66.8364	2.36007
$803$	1.00000	0.0352892
$804$	29.9926	1.05776
$805$	1.04220	0.0367326
$806$	−3.28799	−0.115814
$807$	−2.35223	−0.0828024
$808$	−102.386	−3.60192
$809$	26.9058	0.945957	0.472978	−	0.881074i	$-0.343179\pi$
$809$	26.9058	0.945957	0.472978	+	0.881074i	$0.343179\pi$
$810$	15.7990	0.555122
$811$	−48.8023	−1.71368	−0.856839	−	0.515583i	$-0.827575\pi$
$811$	−48.8023	−1.71368	−0.856839	+	0.515583i	$0.827575\pi$
$812$	−84.3289	−2.95936
$813$	−3.65591	−0.128218
$814$	−17.6760	−0.619544
$815$	5.02882	0.176152
$816$	−27.9679	−0.979071
$817$	−10.0694	−0.352284
$818$	−88.0802	−3.07965
$819$	77.5422	2.70954
$820$	6.23056	0.217581
$821$	42.2701	1.47524	0.737618	−	0.675219i	$-0.235951\pi$
$821$	42.2701	1.47524	0.737618	+	0.675219i	$0.235951\pi$
$822$	−8.22353	−0.286828
$823$	27.8878	0.972107	0.486054	−	0.873929i	$-0.338436\pi$
$823$	27.8878	0.972107	0.486054	+	0.873929i	$0.338436\pi$
$824$	15.8882	0.553492
$825$	−0.570205	−0.0198520
$826$	0.165458	0.00575704
$827$	−15.6897	−0.545583	−0.272791	−	0.962073i	$-0.587947\pi$
$827$	−15.6897	−0.545583	−0.272791	+	0.962073i	$0.587947\pi$
$828$	−2.71524	−0.0943611
$829$	47.7196	1.65737	0.828685	−	0.559715i	$-0.189089\pi$
$829$	47.7196	1.65737	0.828685	+	0.559715i	$0.189089\pi$
$830$	38.2602	1.32803
$831$	−3.26171	−0.113148
$832$	5.58832	0.193740
$833$	−96.0018	−3.32627
$834$	3.97683	0.137706
$835$	1.12336	0.0388755
$836$	−36.9497	−1.27793
$837$	−0.668622	−0.0231110
$838$	−5.82318	−0.201158
$839$	13.6210	0.470250	0.235125	−	0.971965i	$-0.424450\pi$
$839$	13.6210	0.470250	0.235125	+	0.971965i	$0.424450\pi$
$840$	−17.2243	−0.594296
$841$	−13.0731	−0.450796
$842$	97.2143	3.35023
$843$	0.751243	0.0258742
$844$	89.3526	3.07564
$845$	−25.7363	−0.885355
$846$	25.8398	0.888391
$847$	−4.65776	−0.160043
$848$	4.90743	0.168522
$849$	−8.69278	−0.298335
$850$	16.7030	0.572909
$851$	−1.54696	−0.0530292
$852$	−36.9061	−1.26438
$853$	−10.3991	−0.356057	−0.178029	−	0.984025i	$-0.556972\pi$
$853$	−10.3991	−0.356057	−0.178029	+	0.984025i	$0.556972\pi$
$854$	160.865	5.50469
$855$	21.7861	0.745069
$856$	−53.7260	−1.83632
$857$	40.4551	1.38192	0.690960	−	0.722893i	$-0.257188\pi$
$857$	40.4551	1.38192	0.690960	+	0.722893i	$0.257188\pi$
$858$	9.07333	0.309759
$859$	14.8481	0.506610	0.253305	−	0.967386i	$-0.418482\pi$
$859$	14.8481	0.506610	0.253305	+	0.967386i	$0.418482\pi$
$860$	5.60868	0.191254
$861$	3.64755	0.124308
$862$	−31.5338	−1.07405
$863$	15.8622	0.539955	0.269977	−	0.962867i	$-0.412984\pi$
$863$	15.8622	0.539955	0.269977	+	0.962867i	$0.412984\pi$
$864$	20.1406	0.685198
$865$	−6.91547	−0.235133
$866$	−66.8380	−2.27125
$867$	14.6435	0.497320
$868$	−4.36621	−0.148199
$869$	−3.96863	−0.134627
$870$	5.81800	0.197249
$871$	72.1620	2.44512
$872$	−26.7423	−0.905609
$873$	37.4183	1.26642
$874$	−4.65937	−0.157606
$875$	4.65776	0.157461
$876$	−2.58681	−0.0874002
$877$	−30.8827	−1.04284	−0.521418	−	0.853301i	$-0.674597\pi$
$877$	−30.8827	−1.04284	−0.521418	+	0.853301i	$0.674597\pi$
$878$	16.6530	0.562010
$879$	2.37299	0.0800388
$880$	7.50776	0.253086
$881$	−7.76906	−0.261746	−0.130873	−	0.991399i	$-0.541778\pi$
$881$	−7.76906	−0.261746	−0.130873	+	0.991399i	$0.541778\pi$
$882$	100.494	3.38381
$883$	−2.90971	−0.0979196	−0.0489598	−	0.998801i	$-0.515591\pi$
$883$	−2.90971	−0.0979196	−0.0489598	+	0.998801i	$0.515591\pi$
$884$	−184.464	−6.20418
$885$	−0.00792257	−0.000266314 0
$886$	58.6123	1.96912
$887$	1.38602	0.0465378	0.0232689	−	0.999729i	$-0.492593\pi$
$887$	1.38602	0.0465378	0.0232689	+	0.999729i	$0.492593\pi$
$888$	25.5666	0.857958
$889$	96.6776	3.24246
$890$	−22.8303	−0.765272
$891$	−6.17951	−0.207021
$892$	−111.554	−3.73512
$893$	30.7742	1.02982
$894$	21.3320	0.713449
$895$	−5.99284	−0.200319
$896$	−47.2896	−1.57983
$897$	0.794077	0.0265135
$898$	74.2443	2.47756
$899$	0.824632	0.0275030
$900$	−12.1349	−0.404496
$901$	−4.27034	−0.142265
$902$	−3.51132	−0.116914
$903$	3.28349	0.109268
$904$	32.5382	1.08220
$905$	−15.2960	−0.508457
$906$	16.1584	0.536826
$907$	−31.2964	−1.03918	−0.519591	−	0.854415i	$-0.673916\pi$
$907$	−31.2964	−1.03918	−0.519591	+	0.854415i	$0.673916\pi$
$908$	−110.241	−3.65847
$909$	−42.2287	−1.40064
$910$	−74.1162	−2.45693
$911$	36.1287	1.19700	0.598499	−	0.801124i	$-0.295764\pi$
$911$	36.1287	1.19700	0.598499	+	0.801124i	$0.295764\pi$
$912$	34.8673	1.15457
$913$	−14.9648	−0.495262
$914$	90.3183	2.98746
$915$	−7.70263	−0.254641
$916$	−27.9268	−0.922728
$917$	101.186	3.34145
$918$	−54.0483	−1.78386
$919$	−47.5906	−1.56987	−0.784934	−	0.619580i	$-0.787303\pi$
$919$	−47.5906	−1.56987	−0.784934	+	0.619580i	$0.787303\pi$
$920$	1.45113	0.0478424
$921$	5.28857	0.174264
$922$	−55.3364	−1.82241
$923$	−88.7959	−2.92275
$924$	12.0487	0.396374
$925$	−6.91365	−0.227319
$926$	−73.6079	−2.41891
$927$	6.55304	0.215230
$928$	−24.8400	−0.815414
$929$	−32.3653	−1.06187	−0.530936	−	0.847412i	$-0.678159\pi$
$929$	−32.3653	−1.06187	−0.530936	+	0.847412i	$0.678159\pi$
$930$	0.301233	0.00987781
$931$	119.685	3.92251
$932$	−103.302	−3.38378
$933$	6.47290	0.211913
$934$	44.2708	1.44858
$935$	−6.53308	−0.213655
$936$	107.968	3.52905
$937$	−39.1058	−1.27753	−0.638765	−	0.769402i	$-0.720555\pi$
$937$	−39.1058	−1.27753	−0.638765	+	0.769402i	$0.720555\pi$
$938$	138.071	4.50819
$939$	−3.48704	−0.113795
$940$	−17.1413	−0.559087
$941$	−60.7734	−1.98116	−0.990579	−	0.136944i	$-0.956272\pi$
$941$	−60.7734	−1.98116	−0.990579	+	0.136944i	$0.956272\pi$
$942$	14.6726	0.478060
$943$	−0.307303	−0.0100072
$944$	0.104315	0.00339515
$945$	−15.0717	−0.490284
$946$	−3.16085	−0.102768
$947$	−29.5250	−0.959434	−0.479717	−	0.877423i	$-0.659261\pi$
$947$	−29.5250	−0.959434	−0.479717	+	0.877423i	$0.659261\pi$
$948$	10.2661	0.333427
$949$	−6.22385	−0.202035
$950$	−20.8235	−0.675605
$951$	−17.7110	−0.574318
$952$	−197.346	−6.39604
$953$	−38.0748	−1.23336	−0.616682	−	0.787212i	$-0.711524\pi$
$953$	−38.0748	−1.23336	−0.616682	+	0.787212i	$0.711524\pi$
$954$	4.47016	0.144727
$955$	−5.13102	−0.166036
$956$	91.1540	2.94813
$957$	−2.27561	−0.0735599
$958$	41.6530	1.34575
$959$	−26.2741	−0.848434
$960$	−0.511980	−0.0165241
$961$	−30.9573	−0.998623
$962$	110.013	3.54695
$963$	−22.1591	−0.714068
$964$	24.9141	0.802429
$965$	−17.1737	−0.552842
$966$	1.51935	0.0488843
$967$	18.9439	0.609196	0.304598	−	0.952481i	$-0.401478\pi$
$967$	18.9439	0.609196	0.304598	+	0.952481i	$0.401478\pi$
$968$	−6.48536	−0.208447
$969$	−30.3408	−0.974686
$970$	−35.7651	−1.14835
$971$	41.7510	1.33985	0.669927	−	0.742427i	$-0.266325\pi$
$971$	41.7510	1.33985	0.669927	+	0.742427i	$0.266325\pi$
$972$	60.0246	1.92529
$973$	12.7059	0.407333
$974$	−86.5869	−2.77442
$975$	3.54887	0.113655
$976$	101.419	3.24633
$977$	−5.22054	−0.167020	−0.0835099	−	0.996507i	$-0.526613\pi$
$977$	−5.22054	−0.167020	−0.0835099	+	0.996507i	$0.526613\pi$
$978$	7.33118	0.234425
$979$	8.92964	0.285393
$980$	−66.6645	−2.12952
$981$	−11.0298	−0.352154
$982$	−33.4567	−1.06765
$983$	−19.0415	−0.607328	−0.303664	−	0.952779i	$-0.598210\pi$
$983$	−19.0415	−0.607328	−0.303664	+	0.952779i	$0.598210\pi$
$984$	5.07877	0.161905
$985$	12.2411	0.390035
$986$	66.6593	2.12287
$987$	−10.0350	−0.319418
$988$	229.969	7.31630
$989$	−0.276630	−0.00879634
$990$	6.83879	0.217351
$991$	7.47983	0.237605	0.118802	−	0.992918i	$-0.462095\pi$
$991$	7.47983	0.237605	0.118802	+	0.992918i	$0.462095\pi$
$992$	−1.28612	−0.0408342
$993$	−11.3182	−0.359173
$994$	−169.898	−5.38883
$995$	10.9775	0.348009
$996$	38.7110	1.22661
$997$	−13.3426	−0.422563	−0.211282	−	0.977425i	$-0.567764\pi$
$997$	−13.3426	−0.422563	−0.211282	+	0.977425i	$0.567764\pi$
$998$	−2.28907	−0.0724593
$999$	22.3714	0.707801

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.g.1.4	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.g.1.4	✓	32	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.55668 q^{2} +0.570205 q^{3} +4.53663 q^{4} -1.00000 q^{5} -1.45783 q^{6} -4.65776 q^{7} -6.48536 q^{8} -2.67487 q^{9} +O(q^{10})\)	\(q-2.55668 q^{2} +0.570205 q^{3} +4.53663 q^{4} -1.00000 q^{5} -1.45783 q^{6} -4.65776 q^{7} -6.48536 q^{8} -2.67487 q^{9} +2.55668 q^{10} -1.00000 q^{11} +2.58681 q^{12} +6.22385 q^{13} +11.9084 q^{14} -0.570205 q^{15} +7.50776 q^{16} -6.53308 q^{17} +6.83879 q^{18} +8.14474 q^{19} -4.53663 q^{20} -2.65588 q^{21} +2.55668 q^{22} +0.223755 q^{23} -3.69799 q^{24} +1.00000 q^{25} -15.9124 q^{26} -3.23584 q^{27} -21.1305 q^{28} +3.99086 q^{29} +1.45783 q^{30} +0.206630 q^{31} -6.22424 q^{32} -0.570205 q^{33} +16.7030 q^{34} +4.65776 q^{35} -12.1349 q^{36} -6.91365 q^{37} -20.8235 q^{38} +3.54887 q^{39} +6.48536 q^{40} -1.37339 q^{41} +6.79024 q^{42} -1.23631 q^{43} -4.53663 q^{44} +2.67487 q^{45} -0.572071 q^{46} +3.77842 q^{47} +4.28096 q^{48} +14.6947 q^{49} -2.55668 q^{50} -3.72520 q^{51} +28.2353 q^{52} +0.653648 q^{53} +8.27301 q^{54} +1.00000 q^{55} +30.2073 q^{56} +4.64417 q^{57} -10.2034 q^{58} +0.0138942 q^{59} -2.58681 q^{60} +13.5085 q^{61} -0.528288 q^{62} +12.4589 q^{63} +0.897889 q^{64} -6.22385 q^{65} +1.45783 q^{66} +11.5944 q^{67} -29.6382 q^{68} +0.127586 q^{69} -11.9084 q^{70} -14.2670 q^{71} +17.3475 q^{72} -1.00000 q^{73} +17.6760 q^{74} +0.570205 q^{75} +36.9497 q^{76} +4.65776 q^{77} -9.07333 q^{78} +3.96863 q^{79} -7.50776 q^{80} +6.17951 q^{81} +3.51132 q^{82} +14.9648 q^{83} -12.0487 q^{84} +6.53308 q^{85} +3.16085 q^{86} +2.27561 q^{87} +6.48536 q^{88} -8.92964 q^{89} -6.83879 q^{90} -28.9892 q^{91} +1.01509 q^{92} +0.117822 q^{93} -9.66022 q^{94} -8.14474 q^{95} -3.54909 q^{96} -13.9889 q^{97} -37.5698 q^{98} +2.67487 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9}+O(q^{10}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9} + 5 q^{10} - 32 q^{11} - 24 q^{12} - q^{13} - 5 q^{14} + 7 q^{15} + 47 q^{16} - 30 q^{17} - 11 q^{18} + 16 q^{19} - 37 q^{20} + q^{21} + 5 q^{22} - 26 q^{23} - 21 q^{24} + 32 q^{25} - q^{26} - 31 q^{27} - 24 q^{28} - 10 q^{29} + 3 q^{30} - 2 q^{31} - 31 q^{32} + 7 q^{33} - 14 q^{34} + 38 q^{36} - 28 q^{37} - 63 q^{38} - 2 q^{39} + 18 q^{40} - 62 q^{41} - 9 q^{42} + 8 q^{43} - 37 q^{44} - 29 q^{45} + 19 q^{46} - 21 q^{47} - 79 q^{48} + 34 q^{49} - 5 q^{50} + 17 q^{51} + 15 q^{52} - 32 q^{53} + 5 q^{54} + 32 q^{55} - 52 q^{56} - 57 q^{57} + 4 q^{58} - 37 q^{59} + 24 q^{60} + 15 q^{61} - 22 q^{62} + 5 q^{63} + 70 q^{64} + q^{65} + 3 q^{66} - 42 q^{67} - 81 q^{68} - 8 q^{69} + 5 q^{70} - 40 q^{71} - 27 q^{72} - 32 q^{73} - 17 q^{74} - 7 q^{75} + 21 q^{76} - 105 q^{78} + 18 q^{79} - 47 q^{80} + 12 q^{81} - 70 q^{82} - 26 q^{83} + 22 q^{84} + 30 q^{85} - 45 q^{86} - 18 q^{87} + 18 q^{88} - 83 q^{89} + 11 q^{90} - 18 q^{91} - 73 q^{92} - 68 q^{93} + 56 q^{94} - 16 q^{95} - 35 q^{96} - 99 q^{97} - 61 q^{98} - 29 q^{99}+O(q^{100}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9 + 5 * q^10 - 32 * q^11 - 24 * q^12 - q^13 - 5 * q^14 + 7 * q^15 + 47 * q^16 - 30 * q^17 - 11 * q^18 + 16 * q^19 - 37 * q^20 + q^21 + 5 * q^22 - 26 * q^23 - 21 * q^24 + 32 * q^25 - q^26 - 31 * q^27 - 24 * q^28 - 10 * q^29 + 3 * q^30 - 2 * q^31 - 31 * q^32 + 7 * q^33 - 14 * q^34 + 38 * q^36 - 28 * q^37 - 63 * q^38 - 2 * q^39 + 18 * q^40 - 62 * q^41 - 9 * q^42 + 8 * q^43 - 37 * q^44 - 29 * q^45 + 19 * q^46 - 21 * q^47 - 79 * q^48 + 34 * q^49 - 5 * q^50 + 17 * q^51 + 15 * q^52 - 32 * q^53 + 5 * q^54 + 32 * q^55 - 52 * q^56 - 57 * q^57 + 4 * q^58 - 37 * q^59 + 24 * q^60 + 15 * q^61 - 22 * q^62 + 5 * q^63 + 70 * q^64 + q^65 + 3 * q^66 - 42 * q^67 - 81 * q^68 - 8 * q^69 + 5 * q^70 - 40 * q^71 - 27 * q^72 - 32 * q^73 - 17 * q^74 - 7 * q^75 + 21 * q^76 - 105 * q^78 + 18 * q^79 - 47 * q^80 + 12 * q^81 - 70 * q^82 - 26 * q^83 + 22 * q^84 + 30 * q^85 - 45 * q^86 - 18 * q^87 + 18 * q^88 - 83 * q^89 + 11 * q^90 - 18 * q^91 - 73 * q^92 - 68 * q^93 + 56 * q^94 - 16 * q^95 - 35 * q^96 - 99 * q^97 - 61 * q^98 - 29 * q^99

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