LMFDB - Embedded newform 4029.2.a.j.1.20

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:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
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)

$f(q)$	$=$	$q+2.09012 q^{2} +1.00000 q^{3} +2.36860 q^{4} +3.44470 q^{5} +2.09012 q^{6} +0.589185 q^{7} +0.770426 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.09012 q^{2} +1.00000 q^{3} +2.36860 q^{4} +3.44470 q^{5} +2.09012 q^{6} +0.589185 q^{7} +0.770426 q^{8} +1.00000 q^{9} +7.19983 q^{10} +2.31278 q^{11} +2.36860 q^{12} +3.11616 q^{13} +1.23147 q^{14} +3.44470 q^{15} -3.12692 q^{16} -1.00000 q^{17} +2.09012 q^{18} +8.17464 q^{19} +8.15912 q^{20} +0.589185 q^{21} +4.83398 q^{22} -8.79647 q^{23} +0.770426 q^{24} +6.86593 q^{25} +6.51315 q^{26} +1.00000 q^{27} +1.39555 q^{28} +1.82972 q^{29} +7.19983 q^{30} -7.98881 q^{31} -8.07650 q^{32} +2.31278 q^{33} -2.09012 q^{34} +2.02956 q^{35} +2.36860 q^{36} -1.76961 q^{37} +17.0860 q^{38} +3.11616 q^{39} +2.65388 q^{40} -7.42723 q^{41} +1.23147 q^{42} -6.21964 q^{43} +5.47805 q^{44} +3.44470 q^{45} -18.3857 q^{46} -0.237857 q^{47} -3.12692 q^{48} -6.65286 q^{49} +14.3506 q^{50} -1.00000 q^{51} +7.38094 q^{52} +10.6795 q^{53} +2.09012 q^{54} +7.96682 q^{55} +0.453923 q^{56} +8.17464 q^{57} +3.82433 q^{58} +9.49886 q^{59} +8.15912 q^{60} -8.69691 q^{61} -16.6976 q^{62} +0.589185 q^{63} -10.6270 q^{64} +10.7342 q^{65} +4.83398 q^{66} -1.10324 q^{67} -2.36860 q^{68} -8.79647 q^{69} +4.24203 q^{70} -4.94510 q^{71} +0.770426 q^{72} -13.4107 q^{73} -3.69870 q^{74} +6.86593 q^{75} +19.3625 q^{76} +1.36265 q^{77} +6.51315 q^{78} -1.00000 q^{79} -10.7713 q^{80} +1.00000 q^{81} -15.5238 q^{82} +3.34631 q^{83} +1.39555 q^{84} -3.44470 q^{85} -12.9998 q^{86} +1.82972 q^{87} +1.78182 q^{88} +3.08022 q^{89} +7.19983 q^{90} +1.83599 q^{91} -20.8353 q^{92} -7.98881 q^{93} -0.497151 q^{94} +28.1592 q^{95} -8.07650 q^{96} +7.76786 q^{97} -13.9053 q^{98} +2.31278 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9} + 13 q^{10} + 19 q^{11} + 26 q^{12} + 17 q^{14} + 6 q^{15} + 16 q^{16} - 25 q^{17} + 6 q^{18} + 25 q^{19} + 32 q^{20} + 4 q^{21} - 7 q^{22} + 8 q^{23} + 18 q^{24} + 15 q^{25} + 20 q^{26} + 25 q^{27} + 9 q^{28} + 21 q^{29} + 13 q^{30} + 4 q^{31} + 27 q^{32} + 19 q^{33} - 6 q^{34} + 50 q^{35} + 26 q^{36} - 8 q^{37} + 31 q^{38} + 52 q^{40} + 40 q^{41} + 17 q^{42} + 21 q^{43} + 34 q^{44} + 6 q^{45} + 29 q^{46} + 43 q^{47} + 16 q^{48} + 21 q^{49} + 13 q^{50} - 25 q^{51} + 3 q^{52} + 44 q^{53} + 6 q^{54} + 13 q^{55} + 38 q^{56} + 25 q^{57} - 5 q^{58} + 45 q^{59} + 32 q^{60} + 22 q^{61} + 4 q^{62} + 4 q^{63} + 26 q^{64} + 43 q^{65} - 7 q^{66} + 8 q^{67} - 26 q^{68} + 8 q^{69} + 29 q^{70} + 9 q^{71} + 18 q^{72} - 7 q^{73} + 18 q^{74} + 15 q^{75} + 33 q^{76} + 20 q^{77} + 20 q^{78} - 25 q^{79} + 42 q^{80} + 25 q^{81} - 43 q^{82} + 41 q^{83} + 9 q^{84} - 6 q^{85} - 12 q^{86} + 21 q^{87} - 43 q^{88} + 68 q^{89} + 13 q^{90} + 10 q^{91} + 2 q^{92} + 4 q^{93} - 17 q^{94} + 8 q^{95} + 27 q^{96} + 15 q^{97} + 11 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9 + 13 * q^10 + 19 * q^11 + 26 * q^12 + 17 * q^14 + 6 * q^15 + 16 * q^16 - 25 * q^17 + 6 * q^18 + 25 * q^19 + 32 * q^20 + 4 * q^21 - 7 * q^22 + 8 * q^23 + 18 * q^24 + 15 * q^25 + 20 * q^26 + 25 * q^27 + 9 * q^28 + 21 * q^29 + 13 * q^30 + 4 * q^31 + 27 * q^32 + 19 * q^33 - 6 * q^34 + 50 * q^35 + 26 * q^36 - 8 * q^37 + 31 * q^38 + 52 * q^40 + 40 * q^41 + 17 * q^42 + 21 * q^43 + 34 * q^44 + 6 * q^45 + 29 * q^46 + 43 * q^47 + 16 * q^48 + 21 * q^49 + 13 * q^50 - 25 * q^51 + 3 * q^52 + 44 * q^53 + 6 * q^54 + 13 * q^55 + 38 * q^56 + 25 * q^57 - 5 * q^58 + 45 * q^59 + 32 * q^60 + 22 * q^61 + 4 * q^62 + 4 * q^63 + 26 * q^64 + 43 * q^65 - 7 * q^66 + 8 * q^67 - 26 * q^68 + 8 * q^69 + 29 * q^70 + 9 * q^71 + 18 * q^72 - 7 * q^73 + 18 * q^74 + 15 * q^75 + 33 * q^76 + 20 * q^77 + 20 * q^78 - 25 * q^79 + 42 * q^80 + 25 * q^81 - 43 * q^82 + 41 * q^83 + 9 * q^84 - 6 * q^85 - 12 * q^86 + 21 * q^87 - 43 * q^88 + 68 * q^89 + 13 * q^90 + 10 * q^91 + 2 * q^92 + 4 * q^93 - 17 * q^94 + 8 * q^95 + 27 * q^96 + 15 * q^97 + 11 * 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 $

$2$	2.09012	1.47794	0.738969	−	0.673739i	$-0.235313\pi$
$2$	2.09012	1.47794	0.738969	+	0.673739i	$0.235313\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.36860	1.18430
$5$	3.44470	1.54052	0.770258	−	0.637733i	$-0.220128\pi$
$5$	3.44470	1.54052	0.770258	+	0.637733i	$0.220128\pi$
$6$	2.09012	0.853288
$7$	0.589185	0.222691	0.111345	−	0.993782i	$-0.464484\pi$
$7$	0.589185	0.222691	0.111345	+	0.993782i	$0.464484\pi$
$8$	0.770426	0.272387
$9$	1.00000	0.333333
$10$	7.19983	2.27679
$11$	2.31278	0.697329	0.348664	−	0.937248i	$-0.386635\pi$
$11$	2.31278	0.697329	0.348664	+	0.937248i	$0.386635\pi$
$12$	2.36860	0.683757
$13$	3.11616	0.864267	0.432133	−	0.901810i	$-0.357761\pi$
$13$	3.11616	0.864267	0.432133	+	0.901810i	$0.357761\pi$
$14$	1.23147	0.329123
$15$	3.44470	0.889417
$16$	−3.12692	−0.781731
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	2.09012	0.492646
$19$	8.17464	1.87539	0.937695	−	0.347458i	$-0.112955\pi$
$19$	8.17464	1.87539	0.937695	+	0.347458i	$0.112955\pi$
$20$	8.15912	1.82443
$21$	0.589185	0.128571
$22$	4.83398	1.03061
$23$	−8.79647	−1.83419	−0.917095	−	0.398668i	$-0.869472\pi$
$23$	−8.79647	−1.83419	−0.917095	+	0.398668i	$0.869472\pi$
$24$	0.770426	0.157263
$25$	6.86593	1.37319
$26$	6.51315	1.27733
$27$	1.00000	0.192450
$28$	1.39555	0.263733
$29$	1.82972	0.339770	0.169885	−	0.985464i	$-0.445660\pi$
$29$	1.82972	0.339770	0.169885	+	0.985464i	$0.445660\pi$
$30$	7.19983	1.31450
$31$	−7.98881	−1.43483	−0.717416	−	0.696645i	$-0.754675\pi$
$31$	−7.98881	−1.43483	−0.717416	+	0.696645i	$0.754675\pi$
$32$	−8.07650	−1.42774
$33$	2.31278	0.402603
$34$	−2.09012	−0.358453
$35$	2.02956	0.343059
$36$	2.36860	0.394767
$37$	−1.76961	−0.290922	−0.145461	−	0.989364i	$-0.546467\pi$
$37$	−1.76961	−0.290922	−0.145461	+	0.989364i	$0.546467\pi$
$38$	17.0860	2.77171
$39$	3.11616	0.498985
$40$	2.65388	0.419616
$41$	−7.42723	−1.15994	−0.579969	−	0.814638i	$-0.696935\pi$
$41$	−7.42723	−1.15994	−0.579969	+	0.814638i	$0.696935\pi$
$42$	1.23147	0.190020
$43$	−6.21964	−0.948486	−0.474243	−	0.880394i	$-0.657278\pi$
$43$	−6.21964	−0.948486	−0.474243	+	0.880394i	$0.657278\pi$
$44$	5.47805	0.825848
$45$	3.44470	0.513505
$46$	−18.3857	−2.71082
$47$	−0.237857	−0.0346951	−0.0173475	−	0.999850i	$-0.505522\pi$
$47$	−0.237857	−0.0346951	−0.0173475	+	0.999850i	$0.505522\pi$
$48$	−3.12692	−0.451333
$49$	−6.65286	−0.950409
$50$	14.3506	2.02949
$51$	−1.00000	−0.140028
$52$	7.38094	1.02355
$53$	10.6795	1.46694	0.733471	−	0.679720i	$-0.237899\pi$
$53$	10.6795	1.46694	0.733471	+	0.679720i	$0.237899\pi$
$54$	2.09012	0.284429
$55$	7.96682	1.07425
$56$	0.453923	0.0606581
$57$	8.17464	1.08276
$58$	3.82433	0.502159
$59$	9.49886	1.23665	0.618323	−	0.785924i	$-0.287812\pi$
$59$	9.49886	1.23665	0.618323	+	0.785924i	$0.287812\pi$
$60$	8.15912	1.05334
$61$	−8.69691	−1.11353	−0.556763	−	0.830672i	$-0.687957\pi$
$61$	−8.69691	−1.11353	−0.556763	+	0.830672i	$0.687957\pi$
$62$	−16.6976	−2.12059
$63$	0.589185	0.0742303
$64$	−10.6270	−1.32838
$65$	10.7342	1.33142
$66$	4.83398	0.595022
$67$	−1.10324	−0.134782	−0.0673910	−	0.997727i	$-0.521467\pi$
$67$	−1.10324	−0.134782	−0.0673910	+	0.997727i	$0.521467\pi$
$68$	−2.36860	−0.287235
$69$	−8.79647	−1.05897
$70$	4.24203	0.507020
$71$	−4.94510	−0.586875	−0.293438	−	0.955978i	$-0.594799\pi$
$71$	−4.94510	−0.586875	−0.293438	+	0.955978i	$0.594799\pi$
$72$	0.770426	0.0907956
$73$	−13.4107	−1.56961	−0.784803	−	0.619745i	$-0.787236\pi$
$73$	−13.4107	−1.56961	−0.784803	+	0.619745i	$0.787236\pi$
$74$	−3.69870	−0.429965
$75$	6.86593	0.792810
$76$	19.3625	2.22103
$77$	1.36265	0.155289
$78$	6.51315	0.737469
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	−10.7713	−1.20427
$81$	1.00000	0.111111
$82$	−15.5238	−1.71432
$83$	3.34631	0.367306	0.183653	−	0.982991i	$-0.441208\pi$
$83$	3.34631	0.367306	0.183653	+	0.982991i	$0.441208\pi$
$84$	1.39555	0.152266
$85$	−3.44470	−0.373630
$86$	−12.9998	−1.40180
$87$	1.82972	0.196166
$88$	1.78182	0.189943
$89$	3.08022	0.326502	0.163251	−	0.986585i	$-0.447802\pi$
$89$	3.08022	0.326502	0.163251	+	0.986585i	$0.447802\pi$
$90$	7.19983	0.758929
$91$	1.83599	0.192464
$92$	−20.8353	−2.17224
$93$	−7.98881	−0.828401
$94$	−0.497151	−0.0512772
$95$	28.1592	2.88907
$96$	−8.07650	−0.824304
$97$	7.76786	0.788707	0.394353	−	0.918959i	$-0.370969\pi$
$97$	7.76786	0.788707	0.394353	+	0.918959i	$0.370969\pi$
$98$	−13.9053	−1.40465
$99$	2.31278	0.232443
$100$	16.2627	1.62627
$101$	1.14745	0.114175	0.0570876	−	0.998369i	$-0.481819\pi$
$101$	1.14745	0.114175	0.0570876	+	0.998369i	$0.481819\pi$
$102$	−2.09012	−0.206953
$103$	18.7631	1.84878	0.924392	−	0.381444i	$-0.124573\pi$
$103$	18.7631	1.84878	0.924392	+	0.381444i	$0.124573\pi$
$104$	2.40077	0.235415
$105$	2.02956	0.198065
$106$	22.3215	2.16805
$107$	7.43070	0.718353	0.359176	−	0.933270i	$-0.383058\pi$
$107$	7.43070	0.718353	0.359176	+	0.933270i	$0.383058\pi$
$108$	2.36860	0.227919
$109$	16.6756	1.59723	0.798616	−	0.601840i	$-0.205566\pi$
$109$	16.6756	1.59723	0.798616	+	0.601840i	$0.205566\pi$
$110$	16.6516	1.58767
$111$	−1.76961	−0.167964
$112$	−1.84234	−0.174084
$113$	−6.10692	−0.574491	−0.287245	−	0.957857i	$-0.592740\pi$
$113$	−6.10692	−0.574491	−0.287245	+	0.957857i	$0.592740\pi$
$114$	17.0860	1.60025
$115$	−30.3012	−2.82560
$116$	4.33387	0.402390
$117$	3.11616	0.288089
$118$	19.8538	1.82769
$119$	−0.589185	−0.0540105
$120$	2.65388	0.242265
$121$	−5.65106	−0.513733
$122$	−18.1776	−1.64572
$123$	−7.42723	−0.669691
$124$	−18.9223	−1.69927
$125$	6.42757	0.574899
$126$	1.23147	0.109708
$127$	−0.438436	−0.0389049	−0.0194525	−	0.999811i	$-0.506192\pi$
$127$	−0.438436	−0.0389049	−0.0194525	+	0.999811i	$0.506192\pi$
$128$	−6.05873	−0.535521
$129$	−6.21964	−0.547609
$130$	22.4358	1.96775
$131$	−2.81184	−0.245671	−0.122836	−	0.992427i	$-0.539199\pi$
$131$	−2.81184	−0.245671	−0.122836	+	0.992427i	$0.539199\pi$
$132$	5.47805	0.476803
$133$	4.81637	0.417633
$134$	−2.30590	−0.199200
$135$	3.44470	0.296472
$136$	−0.770426	−0.0660635
$137$	−12.6152	−1.07779	−0.538897	−	0.842372i	$-0.681159\pi$
$137$	−12.6152	−1.07779	−0.538897	+	0.842372i	$0.681159\pi$
$138$	−18.3857	−1.56509
$139$	13.5319	1.14776	0.573880	−	0.818939i	$-0.305437\pi$
$139$	13.5319	1.14776	0.573880	+	0.818939i	$0.305437\pi$
$140$	4.80723	0.406285
$141$	−0.237857	−0.0200312
$142$	−10.3359	−0.867365
$143$	7.20698	0.602678
$144$	−3.12692	−0.260577
$145$	6.30282	0.523420
$146$	−28.0300	−2.31978
$147$	−6.65286	−0.548719
$148$	−4.19151	−0.344540
$149$	−7.47921	−0.612720	−0.306360	−	0.951916i	$-0.599111\pi$
$149$	−7.47921	−0.612720	−0.306360	+	0.951916i	$0.599111\pi$
$150$	14.3506	1.17172
$151$	−17.8562	−1.45312	−0.726559	−	0.687105i	$-0.758881\pi$
$151$	−17.8562	−1.45312	−0.726559	+	0.687105i	$0.758881\pi$
$152$	6.29796	0.510832
$153$	−1.00000	−0.0808452
$154$	2.84811	0.229507
$155$	−27.5190	−2.21038
$156$	7.38094	0.590948
$157$	21.6798	1.73024	0.865118	−	0.501569i	$-0.167244\pi$
$157$	21.6798	1.73024	0.865118	+	0.501569i	$0.167244\pi$
$158$	−2.09012	−0.166281
$159$	10.6795	0.846940
$160$	−27.8211	−2.19945
$161$	−5.18275	−0.408458
$162$	2.09012	0.164215
$163$	23.4156	1.83405	0.917025	−	0.398830i	$-0.130584\pi$
$163$	23.4156	1.83405	0.917025	+	0.398830i	$0.130584\pi$
$164$	−17.5922	−1.37372
$165$	7.96682	0.620216
$166$	6.99420	0.542855
$167$	17.0341	1.31814	0.659069	−	0.752083i	$-0.270951\pi$
$167$	17.0341	1.31814	0.659069	+	0.752083i	$0.270951\pi$
$168$	0.453923	0.0350209
$169$	−3.28956	−0.253043
$170$	−7.19983	−0.552202
$171$	8.17464	0.625130
$172$	−14.7319	−1.12329
$173$	−14.9554	−1.13704	−0.568518	−	0.822671i	$-0.692483\pi$
$173$	−14.9554	−1.13704	−0.568518	+	0.822671i	$0.692483\pi$
$174$	3.82433	0.289922
$175$	4.04530	0.305796
$176$	−7.23188	−0.545123
$177$	9.49886	0.713978
$178$	6.43803	0.482550
$179$	0.984683	0.0735987	0.0367993	−	0.999323i	$-0.488284\pi$
$179$	0.984683	0.0735987	0.0367993	+	0.999323i	$0.488284\pi$
$180$	8.15912	0.608145
$181$	−13.3643	−0.993359	−0.496679	−	0.867934i	$-0.665447\pi$
$181$	−13.3643	−0.993359	−0.496679	+	0.867934i	$0.665447\pi$
$182$	3.83745	0.284450
$183$	−8.69691	−0.642894
$184$	−6.77703	−0.499609
$185$	−6.09577	−0.448170
$186$	−16.6976	−1.22433
$187$	−2.31278	−0.169127
$188$	−0.563390	−0.0410894
$189$	0.589185	0.0428569
$190$	58.8560	4.26986
$191$	9.18551	0.664640	0.332320	−	0.943167i	$-0.392169\pi$
$191$	9.18551	0.664640	0.332320	+	0.943167i	$0.392169\pi$
$192$	−10.6270	−0.766938
$193$	2.61050	0.187908	0.0939539	−	0.995577i	$-0.470049\pi$
$193$	2.61050	0.187908	0.0939539	+	0.995577i	$0.470049\pi$
$194$	16.2358	1.16566
$195$	10.7342	0.768693
$196$	−15.7580	−1.12557
$197$	−6.88440	−0.490493	−0.245246	−	0.969461i	$-0.578869\pi$
$197$	−6.88440	−0.490493	−0.245246	+	0.969461i	$0.578869\pi$
$198$	4.83398	0.343536
$199$	−12.3551	−0.875828	−0.437914	−	0.899017i	$-0.644283\pi$
$199$	−12.3551	−0.875828	−0.437914	+	0.899017i	$0.644283\pi$
$200$	5.28969	0.374038
$201$	−1.10324	−0.0778164
$202$	2.39830	0.168744
$203$	1.07804	0.0756637
$204$	−2.36860	−0.165835
$205$	−25.5846	−1.78690
$206$	39.2172	2.73239
$207$	−8.79647	−0.611397
$208$	−9.74399	−0.675624
$209$	18.9061	1.30776
$210$	4.24203	0.292728
$211$	15.9945	1.10111	0.550553	−	0.834800i	$-0.314417\pi$
$211$	15.9945	1.10111	0.550553	+	0.834800i	$0.314417\pi$
$212$	25.2955	1.73730
$213$	−4.94510	−0.338833
$214$	15.5311	1.06168
$215$	−21.4248	−1.46116
$216$	0.770426	0.0524209
$217$	−4.70688	−0.319524
$218$	34.8540	2.36061
$219$	−13.4107	−0.906213
$220$	18.8702	1.27223
$221$	−3.11616	−0.209615
$222$	−3.69870	−0.248241
$223$	−19.4170	−1.30026	−0.650128	−	0.759824i	$-0.725285\pi$
$223$	−19.4170	−1.30026	−0.650128	+	0.759824i	$0.725285\pi$
$224$	−4.75855	−0.317944
$225$	6.86593	0.457729
$226$	−12.7642	−0.849062
$227$	−11.9325	−0.791985	−0.395993	−	0.918254i	$-0.629599\pi$
$227$	−11.9325	−0.791985	−0.395993	+	0.918254i	$0.629599\pi$
$228$	19.3625	1.28231
$229$	−26.3900	−1.74390	−0.871949	−	0.489596i	$-0.837144\pi$
$229$	−26.3900	−1.74390	−0.871949	+	0.489596i	$0.837144\pi$
$230$	−63.3331	−4.17606
$231$	1.36265	0.0896560
$232$	1.40966	0.0925488
$233$	17.3003	1.13338	0.566690	−	0.823931i	$-0.308224\pi$
$233$	17.3003	1.13338	0.566690	+	0.823931i	$0.308224\pi$
$234$	6.51315	0.425778
$235$	−0.819346	−0.0534483
$236$	22.4990	1.46456
$237$	−1.00000	−0.0649570
$238$	−1.23147	−0.0798242
$239$	13.3499	0.863532	0.431766	−	0.901986i	$-0.357891\pi$
$239$	13.3499	0.863532	0.431766	+	0.901986i	$0.357891\pi$
$240$	−10.7713	−0.695285
$241$	−24.9770	−1.60891	−0.804456	−	0.594012i	$-0.797543\pi$
$241$	−24.9770	−1.60891	−0.804456	+	0.594012i	$0.797543\pi$
$242$	−11.8114	−0.759265
$243$	1.00000	0.0641500
$244$	−20.5995	−1.31875
$245$	−22.9171	−1.46412
$246$	−15.5238	−0.989762
$247$	25.4735	1.62084
$248$	−6.15479	−0.390829
$249$	3.34631	0.212064
$250$	13.4344	0.849666
$251$	6.32087	0.398969	0.199485	−	0.979901i	$-0.436073\pi$
$251$	6.32087	0.398969	0.199485	+	0.979901i	$0.436073\pi$
$252$	1.39555	0.0879111
$253$	−20.3443	−1.27903
$254$	−0.916385	−0.0574991
$255$	−3.44470	−0.215715
$256$	8.59054	0.536909
$257$	−1.46060	−0.0911095	−0.0455548	−	0.998962i	$-0.514506\pi$
$257$	−1.46060	−0.0911095	−0.0455548	+	0.998962i	$0.514506\pi$
$258$	−12.9998	−0.809332
$259$	−1.04263	−0.0647858
$260$	25.4251	1.57680
$261$	1.82972	0.113257
$262$	−5.87708	−0.363087
$263$	13.3891	0.825607	0.412804	−	0.910820i	$-0.364550\pi$
$263$	13.3891	0.825607	0.412804	+	0.910820i	$0.364550\pi$
$264$	1.78182	0.109664
$265$	36.7877	2.25985
$266$	10.0668	0.617235
$267$	3.08022	0.188506
$268$	−2.61313	−0.159623
$269$	−15.1258	−0.922239	−0.461119	−	0.887338i	$-0.652552\pi$
$269$	−15.1258	−0.922239	−0.461119	+	0.887338i	$0.652552\pi$
$270$	7.19983	0.438168
$271$	15.9348	0.967969	0.483985	−	0.875077i	$-0.339189\pi$
$271$	15.9348	0.967969	0.483985	+	0.875077i	$0.339189\pi$
$272$	3.12692	0.189598
$273$	1.83599	0.111119
$274$	−26.3674	−1.59291
$275$	15.8794	0.957562
$276$	−20.8353	−1.25414
$277$	4.83990	0.290801	0.145401	−	0.989373i	$-0.453553\pi$
$277$	4.83990	0.290801	0.145401	+	0.989373i	$0.453553\pi$
$278$	28.2833	1.69632
$279$	−7.98881	−0.478277
$280$	1.56363	0.0934447
$281$	−5.24259	−0.312747	−0.156373	−	0.987698i	$-0.549980\pi$
$281$	−5.24259	−0.312747	−0.156373	+	0.987698i	$0.549980\pi$
$282$	−0.497151	−0.0296049
$283$	5.37362	0.319429	0.159714	−	0.987163i	$-0.448943\pi$
$283$	5.37362	0.319429	0.159714	+	0.987163i	$0.448943\pi$
$284$	−11.7130	−0.695037
$285$	28.1592	1.66800
$286$	15.0635	0.890721
$287$	−4.37601	−0.258308
$288$	−8.07650	−0.475912
$289$	1.00000	0.0588235
$290$	13.1736	0.773583
$291$	7.76786	0.455360
$292$	−31.7647	−1.85889
$293$	−11.4239	−0.667388	−0.333694	−	0.942681i	$-0.608295\pi$
$293$	−11.4239	−0.667388	−0.333694	+	0.942681i	$0.608295\pi$
$294$	−13.9053	−0.810972
$295$	32.7207	1.90507
$296$	−1.36335	−0.0792434
$297$	2.31278	0.134201
$298$	−15.6324	−0.905563
$299$	−27.4112	−1.58523
$300$	16.2627	0.938926
$301$	−3.66452	−0.211219
$302$	−37.3216	−2.14762
$303$	1.14745	0.0659191
$304$	−25.5615	−1.46605
$305$	−29.9582	−1.71540
$306$	−2.09012	−0.119484
$307$	−2.77735	−0.158512	−0.0792559	−	0.996854i	$-0.525254\pi$
$307$	−2.77735	−0.158512	−0.0792559	+	0.996854i	$0.525254\pi$
$308$	3.22759	0.183909
$309$	18.7631	1.06740
$310$	−57.5181	−3.26681
$311$	−21.8333	−1.23805	−0.619027	−	0.785369i	$-0.712473\pi$
$311$	−21.8333	−1.23805	−0.619027	+	0.785369i	$0.712473\pi$
$312$	2.40077	0.135917
$313$	13.4049	0.757688	0.378844	−	0.925461i	$-0.376322\pi$
$313$	13.4049	0.757688	0.378844	+	0.925461i	$0.376322\pi$
$314$	45.3134	2.55718
$315$	2.02956	0.114353
$316$	−2.36860	−0.133244
$317$	−13.3058	−0.747329	−0.373665	−	0.927564i	$-0.621899\pi$
$317$	−13.3058	−0.747329	−0.373665	+	0.927564i	$0.621899\pi$
$318$	22.3215	1.25173
$319$	4.23173	0.236931
$320$	−36.6068	−2.04638
$321$	7.43070	0.414741
$322$	−10.8326	−0.603675
$323$	−8.17464	−0.454849
$324$	2.36860	0.131589
$325$	21.3953	1.18680
$326$	48.9414	2.71061
$327$	16.6756	0.922163
$328$	−5.72213	−0.315952
$329$	−0.140142	−0.00772628
$330$	16.6516	0.916641
$331$	−6.40269	−0.351924	−0.175962	−	0.984397i	$-0.556304\pi$
$331$	−6.40269	−0.351924	−0.175962	+	0.984397i	$0.556304\pi$
$332$	7.92609	0.435001
$333$	−1.76961	−0.0969741
$334$	35.6033	1.94813
$335$	−3.80032	−0.207634
$336$	−1.84234	−0.100508
$337$	−0.151427	−0.00824877	−0.00412439	−	0.999991i	$-0.501313\pi$
$337$	−0.151427	−0.00824877	−0.00412439	+	0.999991i	$0.501313\pi$
$338$	−6.87557	−0.373982
$339$	−6.10692	−0.331682
$340$	−8.15912	−0.442490
$341$	−18.4763	−1.00055
$342$	17.0860	0.923904
$343$	−8.04406	−0.434338
$344$	−4.79177	−0.258355
$345$	−30.3012	−1.63136
$346$	−31.2586	−1.68047
$347$	−1.19009	−0.0638871	−0.0319436	−	0.999490i	$-0.510170\pi$
$347$	−1.19009	−0.0638871	−0.0319436	+	0.999490i	$0.510170\pi$
$348$	4.33387	0.232320
$349$	20.3617	1.08994	0.544969	−	0.838456i	$-0.316541\pi$
$349$	20.3617	1.08994	0.544969	+	0.838456i	$0.316541\pi$
$350$	8.45517	0.451948
$351$	3.11616	0.166328
$352$	−18.6791	−0.995602
$353$	12.9646	0.690038	0.345019	−	0.938596i	$-0.387872\pi$
$353$	12.9646	0.690038	0.345019	+	0.938596i	$0.387872\pi$
$354$	19.8538	1.05522
$355$	−17.0344	−0.904090
$356$	7.29581	0.386677
$357$	−0.589185	−0.0311830
$358$	2.05811	0.108774
$359$	−1.62655	−0.0858461	−0.0429230	−	0.999078i	$-0.513667\pi$
$359$	−1.62655	−0.0858461	−0.0429230	+	0.999078i	$0.513667\pi$
$360$	2.65388	0.139872
$361$	47.8247	2.51709
$362$	−27.9329	−1.46812
$363$	−5.65106	−0.296604
$364$	4.34874	0.227936
$365$	−46.1959	−2.41800
$366$	−18.1776	−0.950158
$367$	−31.9674	−1.66869	−0.834343	−	0.551246i	$-0.814153\pi$
$367$	−31.9674	−1.66869	−0.834343	+	0.551246i	$0.814153\pi$
$368$	27.5059	1.43384
$369$	−7.42723	−0.386646
$370$	−12.7409	−0.662368
$371$	6.29220	0.326675
$372$	−18.9223	−0.981077
$373$	−10.7368	−0.555932	−0.277966	−	0.960591i	$-0.589660\pi$
$373$	−10.7368	−0.555932	−0.277966	+	0.960591i	$0.589660\pi$
$374$	−4.83398	−0.249959
$375$	6.42757	0.331918
$376$	−0.183252	−0.00945047
$377$	5.70169	0.293652
$378$	1.23147	0.0633398
$379$	−25.3801	−1.30369	−0.651844	−	0.758353i	$-0.726004\pi$
$379$	−25.3801	−1.30369	−0.651844	+	0.758353i	$0.726004\pi$
$380$	66.6979	3.42153
$381$	−0.438436	−0.0224618
$382$	19.1988	0.982297
$383$	−32.9754	−1.68496	−0.842481	−	0.538726i	$-0.818906\pi$
$383$	−32.9754	−1.68496	−0.842481	+	0.538726i	$0.818906\pi$
$384$	−6.05873	−0.309183
$385$	4.69393	0.239225
$386$	5.45626	0.277716
$387$	−6.21964	−0.316162
$388$	18.3990	0.934067
$389$	24.7065	1.25267	0.626334	−	0.779555i	$-0.284555\pi$
$389$	24.7065	1.25267	0.626334	+	0.779555i	$0.284555\pi$
$390$	22.4358	1.13608
$391$	8.79647	0.444857
$392$	−5.12554	−0.258879
$393$	−2.81184	−0.141838
$394$	−14.3892	−0.724918
$395$	−3.44470	−0.173321
$396$	5.47805	0.275283
$397$	18.3056	0.918731	0.459366	−	0.888247i	$-0.348077\pi$
$397$	18.3056	0.918731	0.459366	+	0.888247i	$0.348077\pi$
$398$	−25.8236	−1.29442
$399$	4.81637	0.241120
$400$	−21.4692	−1.07346
$401$	32.9567	1.64578	0.822889	−	0.568203i	$-0.192361\pi$
$401$	32.9567	1.64578	0.822889	+	0.568203i	$0.192361\pi$
$402$	−2.30590	−0.115008
$403$	−24.8944	−1.24008
$404$	2.71785	0.135218
$405$	3.44470	0.171168
$406$	2.25324	0.111826
$407$	−4.09272	−0.202868
$408$	−0.770426	−0.0381418
$409$	−6.49072	−0.320945	−0.160473	−	0.987040i	$-0.551302\pi$
$409$	−6.49072	−0.320945	−0.160473	+	0.987040i	$0.551302\pi$
$410$	−53.4748	−2.64093
$411$	−12.6152	−0.622264
$412$	44.4424	2.18952
$413$	5.59658	0.275390
$414$	−18.3857	−0.903607
$415$	11.5270	0.565840
$416$	−25.1677	−1.23395
$417$	13.5319	0.662660
$418$	39.5161	1.93279
$419$	11.4457	0.559161	0.279580	−	0.960122i	$-0.409805\pi$
$419$	11.4457	0.559161	0.279580	+	0.960122i	$0.409805\pi$
$420$	4.80723	0.234569
$421$	−1.41702	−0.0690612	−0.0345306	−	0.999404i	$-0.510994\pi$
$421$	−1.41702	−0.0690612	−0.0345306	+	0.999404i	$0.510994\pi$
$422$	33.4304	1.62737
$423$	−0.237857	−0.0115650
$424$	8.22777	0.399576
$425$	−6.86593	−0.333047
$426$	−10.3359	−0.500774
$427$	−5.12409	−0.247972
$428$	17.6004	0.850747
$429$	7.20698	0.347956
$430$	−44.7803	−2.15950
$431$	−12.7732	−0.615262	−0.307631	−	0.951506i	$-0.599536\pi$
$431$	−12.7732	−0.615262	−0.307631	+	0.951506i	$0.599536\pi$
$432$	−3.12692	−0.150444
$433$	−22.4275	−1.07780	−0.538898	−	0.842371i	$-0.681159\pi$
$433$	−22.4275	−1.07780	−0.538898	+	0.842371i	$0.681159\pi$
$434$	−9.83796	−0.472237
$435$	6.30282	0.302197
$436$	39.4979	1.89161
$437$	−71.9080	−3.43982
$438$	−28.0300	−1.33933
$439$	−19.8144	−0.945690	−0.472845	−	0.881146i	$-0.656773\pi$
$439$	−19.8144	−0.945690	−0.472845	+	0.881146i	$0.656773\pi$
$440$	6.13784	0.292610
$441$	−6.65286	−0.316803
$442$	−6.51315	−0.309799
$443$	26.1734	1.24354	0.621768	−	0.783201i	$-0.286415\pi$
$443$	26.1734	1.24354	0.621768	+	0.783201i	$0.286415\pi$
$444$	−4.19151	−0.198920
$445$	10.6104	0.502982
$446$	−40.5838	−1.92170
$447$	−7.47921	−0.353754
$448$	−6.26127	−0.295817
$449$	32.1908	1.51918	0.759590	−	0.650403i	$-0.225400\pi$
$449$	32.1908	1.51918	0.759590	+	0.650403i	$0.225400\pi$
$450$	14.3506	0.676495
$451$	−17.1775	−0.808858
$452$	−14.4649	−0.680370
$453$	−17.8562	−0.838958
$454$	−24.9403	−1.17051
$455$	6.32444	0.296494
$456$	6.29796	0.294929
$457$	4.25011	0.198812	0.0994058	−	0.995047i	$-0.468306\pi$
$457$	4.25011	0.198812	0.0994058	+	0.995047i	$0.468306\pi$
$458$	−55.1582	−2.57738
$459$	−1.00000	−0.0466760
$460$	−71.7714	−3.34636
$461$	21.5439	1.00340	0.501700	−	0.865042i	$-0.332708\pi$
$461$	21.5439	1.00340	0.501700	+	0.865042i	$0.332708\pi$
$462$	2.84811	0.132506
$463$	19.9000	0.924833	0.462416	−	0.886663i	$-0.346983\pi$
$463$	19.9000	0.924833	0.462416	+	0.886663i	$0.346983\pi$
$464$	−5.72138	−0.265609
$465$	−27.5190	−1.27616
$466$	36.1597	1.67507
$467$	10.2868	0.476016	0.238008	−	0.971263i	$-0.423506\pi$
$467$	10.2868	0.476016	0.238008	+	0.971263i	$0.423506\pi$
$468$	7.38094	0.341184
$469$	−0.650011	−0.0300147
$470$	−1.71253	−0.0789932
$471$	21.6798	0.998952
$472$	7.31817	0.336846
$473$	−14.3846	−0.661406
$474$	−2.09012	−0.0960024
$475$	56.1265	2.57526
$476$	−1.39555	−0.0639647
$477$	10.6795	0.488981
$478$	27.9029	1.27625
$479$	4.99140	0.228063	0.114031	−	0.993477i	$-0.463624\pi$
$479$	4.99140	0.228063	0.114031	+	0.993477i	$0.463624\pi$
$480$	−27.8211	−1.26985
$481$	−5.51439	−0.251434
$482$	−52.2050	−2.37787
$483$	−5.18275	−0.235823
$484$	−13.3851	−0.608415
$485$	26.7579	1.21501
$486$	2.09012	0.0948098
$487$	−15.2648	−0.691716	−0.345858	−	0.938287i	$-0.612412\pi$
$487$	−15.2648	−0.691716	−0.345858	+	0.938287i	$0.612412\pi$
$488$	−6.70033	−0.303310
$489$	23.4156	1.05889
$490$	−47.8995	−2.16388
$491$	−11.3301	−0.511320	−0.255660	−	0.966767i	$-0.582293\pi$
$491$	−11.3301	−0.511320	−0.255660	+	0.966767i	$0.582293\pi$
$492$	−17.5922	−0.793116
$493$	−1.82972	−0.0824063
$494$	53.2426	2.39550
$495$	7.96682	0.358082
$496$	24.9804	1.12165
$497$	−2.91358	−0.130692
$498$	6.99420	0.313418
$499$	−2.95177	−0.132139	−0.0660697	−	0.997815i	$-0.521046\pi$
$499$	−2.95177	−0.132139	−0.0660697	+	0.997815i	$0.521046\pi$
$500$	15.2244	0.680854
$501$	17.0341	0.761027
$502$	13.2114	0.589652
$503$	0.268390	0.0119669	0.00598345	−	0.999982i	$-0.498095\pi$
$503$	0.268390	0.0119669	0.00598345	+	0.999982i	$0.498095\pi$
$504$	0.453923	0.0202194
$505$	3.95261	0.175889
$506$	−42.5220	−1.89033
$507$	−3.28956	−0.146094
$508$	−1.03848	−0.0460752
$509$	17.5333	0.777152	0.388576	−	0.921417i	$-0.372967\pi$
$509$	17.5333	0.777152	0.388576	+	0.921417i	$0.372967\pi$
$510$	−7.19983	−0.318814
$511$	−7.90139	−0.349537
$512$	30.0727	1.32904
$513$	8.17464	0.360919
$514$	−3.05282	−0.134654
$515$	64.6332	2.84808
$516$	−14.7319	−0.648534
$517$	−0.550111	−0.0241939
$518$	−2.17922	−0.0957494
$519$	−14.9554	−0.656468
$520$	8.26992	0.362660
$521$	36.0140	1.57780	0.788900	−	0.614521i	$-0.210651\pi$
$521$	36.0140	1.57780	0.788900	+	0.614521i	$0.210651\pi$
$522$	3.82433	0.167386
$523$	−12.8175	−0.560468	−0.280234	−	0.959932i	$-0.590412\pi$
$523$	−12.8175	−0.560468	−0.280234	+	0.959932i	$0.590412\pi$
$524$	−6.66013	−0.290949
$525$	4.04530	0.176552
$526$	27.9848	1.22020
$527$	7.98881	0.347998
$528$	−7.23188	−0.314727
$529$	54.3779	2.36425
$530$	76.8906	3.33992
$531$	9.49886	0.412215
$532$	11.4081	0.494603
$533$	−23.1444	−1.00250
$534$	6.43803	0.278601
$535$	25.5965	1.10663
$536$	−0.849964	−0.0367128
$537$	0.984683	0.0424922
$538$	−31.6148	−1.36301
$539$	−15.3866	−0.662747
$540$	8.15912	0.351113
$541$	−5.65116	−0.242962	−0.121481	−	0.992594i	$-0.538764\pi$
$541$	−5.65116	−0.242962	−0.121481	+	0.992594i	$0.538764\pi$
$542$	33.3056	1.43060
$543$	−13.3643	−0.573516
$544$	8.07650	0.346277
$545$	57.4424	2.46056
$546$	3.83745	0.164228
$547$	18.1125	0.774433	0.387216	−	0.921989i	$-0.373437\pi$
$547$	18.1125	0.774433	0.387216	+	0.921989i	$0.373437\pi$
$548$	−29.8805	−1.27643
$549$	−8.69691	−0.371175
$550$	33.1898	1.41522
$551$	14.9573	0.637201
$552$	−6.77703	−0.288449
$553$	−0.589185	−0.0250547
$554$	10.1160	0.429786
$555$	−6.09577	−0.258751
$556$	32.0517	1.35930
$557$	18.7589	0.794840	0.397420	−	0.917637i	$-0.369906\pi$
$557$	18.7589	0.794840	0.397420	+	0.917637i	$0.369906\pi$
$558$	−16.6976	−0.706865
$559$	−19.3814	−0.819745
$560$	−6.34629	−0.268180
$561$	−2.31278	−0.0976455
$562$	−10.9577	−0.462221
$563$	18.3229	0.772220	0.386110	−	0.922453i	$-0.373819\pi$
$563$	18.3229	0.772220	0.386110	+	0.922453i	$0.373819\pi$
$564$	−0.563390	−0.0237230
$565$	−21.0365	−0.885012
$566$	11.2315	0.472096
$567$	0.589185	0.0247434
$568$	−3.80983	−0.159857
$569$	−20.5677	−0.862242	−0.431121	−	0.902294i	$-0.641882\pi$
$569$	−20.5677	−0.862242	−0.431121	+	0.902294i	$0.641882\pi$
$570$	58.8560	2.46521
$571$	32.3069	1.35200	0.676001	−	0.736901i	$-0.263712\pi$
$571$	32.3069	1.35200	0.676001	+	0.736901i	$0.263712\pi$
$572$	17.0705	0.713753
$573$	9.18551	0.383730
$574$	−9.14639	−0.381763
$575$	−60.3960	−2.51869
$576$	−10.6270	−0.442792
$577$	−13.6017	−0.566247	−0.283124	−	0.959083i	$-0.591371\pi$
$577$	−13.6017	−0.566247	−0.283124	+	0.959083i	$0.591371\pi$
$578$	2.09012	0.0869376
$579$	2.61050	0.108489
$580$	14.9289	0.619888
$581$	1.97160	0.0817957
$582$	16.2358	0.672994
$583$	24.6993	1.02294
$584$	−10.3320	−0.427540
$585$	10.7342	0.443805
$586$	−23.8772	−0.986359
$587$	7.17718	0.296234	0.148117	−	0.988970i	$-0.452679\pi$
$587$	7.17718	0.296234	0.148117	+	0.988970i	$0.452679\pi$
$588$	−15.7580	−0.649849
$589$	−65.3056	−2.69087
$590$	68.3902	2.81558
$591$	−6.88440	−0.283186
$592$	5.53344	0.227423
$593$	−29.1288	−1.19618	−0.598089	−	0.801430i	$-0.704073\pi$
$593$	−29.1288	−1.19618	−0.598089	+	0.801430i	$0.704073\pi$
$594$	4.83398	0.198341
$595$	−2.02956	−0.0832040
$596$	−17.7153	−0.725646
$597$	−12.3551	−0.505659
$598$	−57.2927	−2.34287
$599$	40.3804	1.64990	0.824949	−	0.565208i	$-0.191204\pi$
$599$	40.3804	1.64990	0.824949	+	0.565208i	$0.191204\pi$
$600$	5.28969	0.215951
$601$	33.8287	1.37990	0.689951	−	0.723856i	$-0.257632\pi$
$601$	33.8287	1.37990	0.689951	+	0.723856i	$0.257632\pi$
$602$	−7.65928	−0.312169
$603$	−1.10324	−0.0449273
$604$	−42.2943	−1.72093
$605$	−19.4662	−0.791413
$606$	2.39830	0.0974244
$607$	8.77089	0.355999	0.178000	−	0.984031i	$-0.443037\pi$
$607$	8.77089	0.355999	0.178000	+	0.984031i	$0.443037\pi$
$608$	−66.0225	−2.67757
$609$	1.07804	0.0436844
$610$	−62.6163	−2.53526
$611$	−0.741201	−0.0299858
$612$	−2.36860	−0.0957451
$613$	−28.1223	−1.13585	−0.567925	−	0.823080i	$-0.692254\pi$
$613$	−28.1223	−1.13585	−0.567925	+	0.823080i	$0.692254\pi$
$614$	−5.80500	−0.234271
$615$	−25.5846	−1.03167
$616$	1.04982	0.0422986
$617$	0.555735	0.0223730	0.0111865	−	0.999937i	$-0.496439\pi$
$617$	0.555735	0.0223730	0.0111865	+	0.999937i	$0.496439\pi$
$618$	39.2172	1.57755
$619$	−0.379118	−0.0152380	−0.00761902	−	0.999971i	$-0.502425\pi$
$619$	−0.379118	−0.0152380	−0.00761902	+	0.999971i	$0.502425\pi$
$620$	−65.1816	−2.61776
$621$	−8.79647	−0.352990
$622$	−45.6343	−1.82977
$623$	1.81482	0.0727091
$624$	−9.74399	−0.390072
$625$	−12.1886	−0.487545
$626$	28.0178	1.11982
$627$	18.9061	0.755038
$628$	51.3508	2.04912
$629$	1.76961	0.0705590
$630$	4.24203	0.169007
$631$	−18.2471	−0.726407	−0.363203	−	0.931710i	$-0.618317\pi$
$631$	−18.2471	−0.726407	−0.363203	+	0.931710i	$0.618317\pi$
$632$	−0.770426	−0.0306459
$633$	15.9945	0.635724
$634$	−27.8108	−1.10451
$635$	−1.51028	−0.0599337
$636$	25.2955	1.00303
$637$	−20.7314	−0.821407
$638$	8.84482	0.350170
$639$	−4.94510	−0.195625
$640$	−20.8705	−0.824979
$641$	−47.2875	−1.86774	−0.933871	−	0.357609i	$-0.883592\pi$
$641$	−47.2875	−1.86774	−0.933871	+	0.357609i	$0.883592\pi$
$642$	15.5311	0.612962
$643$	−39.1944	−1.54568	−0.772838	−	0.634603i	$-0.781164\pi$
$643$	−39.1944	−1.54568	−0.772838	+	0.634603i	$0.781164\pi$
$644$	−12.2759	−0.483737
$645$	−21.4248	−0.843599
$646$	−17.0860	−0.672239
$647$	2.94335	0.115715	0.0578576	−	0.998325i	$-0.481573\pi$
$647$	2.94335	0.115715	0.0578576	+	0.998325i	$0.481573\pi$
$648$	0.770426	0.0302652
$649$	21.9687	0.862349
$650$	44.7188	1.75402
$651$	−4.70688	−0.184477
$652$	55.4622	2.17207
$653$	−22.2263	−0.869781	−0.434890	−	0.900483i	$-0.643213\pi$
$653$	−22.2263	−0.869781	−0.434890	+	0.900483i	$0.643213\pi$
$654$	34.8540	1.36290
$655$	−9.68593	−0.378461
$656$	23.2244	0.906760
$657$	−13.4107	−0.523202
$658$	−0.292914	−0.0114190
$659$	−20.0713	−0.781867	−0.390933	−	0.920419i	$-0.627848\pi$
$659$	−20.0713	−0.781867	−0.390933	+	0.920419i	$0.627848\pi$
$660$	18.8702	0.734523
$661$	36.8945	1.43503	0.717515	−	0.696544i	$-0.245280\pi$
$661$	36.8945	1.43503	0.717515	+	0.696544i	$0.245280\pi$
$662$	−13.3824	−0.520121
$663$	−3.11616	−0.121022
$664$	2.57809	0.100049
$665$	16.5909	0.643369
$666$	−3.69870	−0.143322
$667$	−16.0950	−0.623203
$668$	40.3470	1.56107
$669$	−19.4170	−0.750704
$670$	−7.94313	−0.306870
$671$	−20.1140	−0.776493
$672$	−4.75855	−0.183565
$673$	−36.5742	−1.40983	−0.704916	−	0.709291i	$-0.749015\pi$
$673$	−36.5742	−1.40983	−0.704916	+	0.709291i	$0.749015\pi$
$674$	−0.316501	−0.0121912
$675$	6.86593	0.264270
$676$	−7.79166	−0.299679
$677$	−45.8763	−1.76317	−0.881585	−	0.472025i	$-0.843523\pi$
$677$	−45.8763	−1.76317	−0.881585	+	0.472025i	$0.843523\pi$
$678$	−12.7642	−0.490206
$679$	4.57670	0.175638
$680$	−2.65388	−0.101772
$681$	−11.9325	−0.457253
$682$	−38.6178	−1.47875
$683$	−11.0296	−0.422037	−0.211018	−	0.977482i	$-0.567678\pi$
$683$	−11.0296	−0.422037	−0.211018	+	0.977482i	$0.567678\pi$
$684$	19.3625	0.740343
$685$	−43.4557	−1.66036
$686$	−16.8131	−0.641925
$687$	−26.3900	−1.00684
$688$	19.4483	0.741461
$689$	33.2790	1.26783
$690$	−63.3331	−2.41105
$691$	−8.95703	−0.340741	−0.170371	−	0.985380i	$-0.554497\pi$
$691$	−8.95703	−0.340741	−0.170371	+	0.985380i	$0.554497\pi$
$692$	−35.4234	−1.34659
$693$	1.36265	0.0517629
$694$	−2.48742	−0.0944213
$695$	46.6133	1.76814
$696$	1.40966	0.0534331
$697$	7.42723	0.281326
$698$	42.5585	1.61086
$699$	17.3003	0.654358
$700$	9.58172	0.362155
$701$	−7.88335	−0.297750	−0.148875	−	0.988856i	$-0.547565\pi$
$701$	−7.88335	−0.297750	−0.148875	+	0.988856i	$0.547565\pi$
$702$	6.51315	0.245823
$703$	−14.4659	−0.545593
$704$	−24.5779	−0.926315
$705$	−0.819346	−0.0308584
$706$	27.0976	1.01983
$707$	0.676058	0.0254258
$708$	22.4990	0.845565
$709$	−7.58028	−0.284683	−0.142342	−	0.989818i	$-0.545463\pi$
$709$	−7.58028	−0.284683	−0.142342	+	0.989818i	$0.545463\pi$
$710$	−35.6039	−1.33619
$711$	−1.00000	−0.0375029
$712$	2.37308	0.0889349
$713$	70.2733	2.63176
$714$	−1.23147	−0.0460865
$715$	24.8259	0.928434
$716$	2.33232	0.0871630
$717$	13.3499	0.498560
$718$	−3.39969	−0.126875
$719$	30.1662	1.12501	0.562505	−	0.826794i	$-0.309838\pi$
$719$	30.1662	1.12501	0.562505	+	0.826794i	$0.309838\pi$
$720$	−10.7713	−0.401423
$721$	11.0549	0.411707
$722$	99.9595	3.72011
$723$	−24.9770	−0.928906
$724$	−31.6547	−1.17644
$725$	12.5627	0.466567
$726$	−11.8114	−0.438362
$727$	18.0855	0.670754	0.335377	−	0.942084i	$-0.391136\pi$
$727$	18.0855	0.670754	0.335377	+	0.942084i	$0.391136\pi$
$728$	1.41450	0.0524247
$729$	1.00000	0.0370370
$730$	−96.5549	−3.57366
$731$	6.21964	0.230042
$732$	−20.5995	−0.761381
$733$	−13.9812	−0.516406	−0.258203	−	0.966091i	$-0.583130\pi$
$733$	−13.9812	−0.516406	−0.258203	+	0.966091i	$0.583130\pi$
$734$	−66.8158	−2.46622
$735$	−22.9171	−0.845309
$736$	71.0447	2.61874
$737$	−2.55154	−0.0939874
$738$	−15.5238	−0.571439
$739$	24.6404	0.906410	0.453205	−	0.891406i	$-0.350281\pi$
$739$	24.6404	0.906410	0.453205	+	0.891406i	$0.350281\pi$
$740$	−14.4385	−0.530769
$741$	25.4735	0.935791
$742$	13.1515	0.482805
$743$	42.3225	1.55266	0.776330	−	0.630326i	$-0.217079\pi$
$743$	42.3225	1.55266	0.776330	+	0.630326i	$0.217079\pi$
$744$	−6.15479	−0.225645
$745$	−25.7636	−0.943905
$746$	−22.4413	−0.821633
$747$	3.34631	0.122435
$748$	−5.47805	−0.200297
$749$	4.37806	0.159971
$750$	13.4344	0.490555
$751$	39.1149	1.42732	0.713661	−	0.700491i	$-0.247036\pi$
$751$	39.1149	1.42732	0.713661	+	0.700491i	$0.247036\pi$
$752$	0.743762	0.0271222
$753$	6.32087	0.230345
$754$	11.9172	0.433999
$755$	−61.5092	−2.23855
$756$	1.39555	0.0507555
$757$	37.5944	1.36639	0.683197	−	0.730234i	$-0.260589\pi$
$757$	37.5944	1.36639	0.683197	+	0.730234i	$0.260589\pi$
$758$	−53.0474	−1.92677
$759$	−20.3443	−0.738450
$760$	21.6945	0.786944
$761$	−13.3815	−0.485079	−0.242539	−	0.970142i	$-0.577980\pi$
$761$	−13.3815	−0.485079	−0.242539	+	0.970142i	$0.577980\pi$
$762$	−0.916385	−0.0331971
$763$	9.82501	0.355689
$764$	21.7568	0.787134
$765$	−3.44470	−0.124543
$766$	−68.9225	−2.49027
$767$	29.5999	1.06879
$768$	8.59054	0.309984
$769$	−51.9196	−1.87227	−0.936135	−	0.351641i	$-0.885624\pi$
$769$	−51.9196	−1.87227	−0.936135	+	0.351641i	$0.885624\pi$
$770$	9.81087	0.353559
$771$	−1.46060	−0.0526021
$772$	6.18324	0.222540
$773$	−48.5071	−1.74468	−0.872339	−	0.488901i	$-0.837398\pi$
$773$	−48.5071	−1.74468	−0.872339	+	0.488901i	$0.837398\pi$
$774$	−12.9998	−0.467268
$775$	−54.8506	−1.97029
$776$	5.98456	0.214833
$777$	−1.04263	−0.0374041
$778$	51.6395	1.85137
$779$	−60.7149	−2.17534
$780$	25.4251	0.910365
$781$	−11.4369	−0.409245
$782$	18.3857	0.657471
$783$	1.82972	0.0653887
$784$	20.8030	0.742964
$785$	74.6803	2.66545
$786$	−5.87708	−0.209629
$787$	37.5684	1.33917	0.669584	−	0.742736i	$-0.266472\pi$
$787$	37.5684	1.33917	0.669584	+	0.742736i	$0.266472\pi$
$788$	−16.3064	−0.580892
$789$	13.3891	0.476664
$790$	−7.19983	−0.256158
$791$	−3.59810	−0.127934
$792$	1.78182	0.0633144
$793$	−27.1010	−0.962383
$794$	38.2609	1.35783
$795$	36.7877	1.30472
$796$	−29.2643	−1.03724
$797$	30.9358	1.09580	0.547902	−	0.836543i	$-0.315427\pi$
$797$	30.9358	1.09580	0.547902	+	0.836543i	$0.315427\pi$
$798$	10.0668	0.356361
$799$	0.237857	0.00841479
$800$	−55.4527	−1.96055
$801$	3.08022	0.108834
$802$	68.8834	2.43236
$803$	−31.0160	−1.09453
$804$	−2.61313	−0.0921581
$805$	−17.8530	−0.629235
$806$	−52.0323	−1.83276
$807$	−15.1258	−0.532455
$808$	0.884023	0.0310998
$809$	5.80023	0.203925	0.101963	−	0.994788i	$-0.467488\pi$
$809$	5.80023	0.203925	0.101963	+	0.994788i	$0.467488\pi$
$810$	7.19983	0.252976
$811$	18.9258	0.664575	0.332288	−	0.943178i	$-0.392180\pi$
$811$	18.9258	0.664575	0.332288	+	0.943178i	$0.392180\pi$
$812$	2.55345	0.0896086
$813$	15.9348	0.558857
$814$	−8.55427	−0.299827
$815$	80.6596	2.82538
$816$	3.12692	0.109464
$817$	−50.8433	−1.77878
$818$	−13.5664	−0.474338
$819$	1.83599	0.0641548
$820$	−60.5997	−2.11623
$821$	−47.1055	−1.64399	−0.821996	−	0.569493i	$-0.807140\pi$
$821$	−47.1055	−1.64399	−0.821996	+	0.569493i	$0.807140\pi$
$822$	−26.3674	−0.919668
$823$	−5.39741	−0.188142	−0.0940710	−	0.995565i	$-0.529988\pi$
$823$	−5.39741	−0.188142	−0.0940710	+	0.995565i	$0.529988\pi$
$824$	14.4556	0.503584
$825$	15.8794	0.552849
$826$	11.6975	0.407009
$827$	−6.61750	−0.230113	−0.115057	−	0.993359i	$-0.536705\pi$
$827$	−6.61750	−0.230113	−0.115057	+	0.993359i	$0.536705\pi$
$828$	−20.8353	−0.724078
$829$	−40.8225	−1.41782	−0.708912	−	0.705297i	$-0.750814\pi$
$829$	−40.8225	−1.41782	−0.708912	+	0.705297i	$0.750814\pi$
$830$	24.0929	0.836277
$831$	4.83990	0.167894
$832$	−33.1154	−1.14807
$833$	6.65286	0.230508
$834$	28.2833	0.979371
$835$	58.6773	2.03061
$836$	44.7811	1.54879
$837$	−7.98881	−0.276134
$838$	23.9230	0.826405
$839$	26.0845	0.900537	0.450269	−	0.892893i	$-0.351328\pi$
$839$	26.0845	0.900537	0.450269	+	0.892893i	$0.351328\pi$
$840$	1.56363	0.0539503
$841$	−25.6521	−0.884556
$842$	−2.96174	−0.102068
$843$	−5.24259	−0.180564
$844$	37.8846	1.30404
$845$	−11.3315	−0.389817
$846$	−0.497151	−0.0170924
$847$	−3.32952	−0.114404
$848$	−33.3940	−1.14675
$849$	5.37362	0.184422
$850$	−14.3506	−0.492222
$851$	15.5663	0.533607
$852$	−11.7130	−0.401280
$853$	23.5593	0.806655	0.403328	−	0.915056i	$-0.367853\pi$
$853$	23.5593	0.806655	0.403328	+	0.915056i	$0.367853\pi$
$854$	−10.7100	−0.366487
$855$	28.1592	0.963023
$856$	5.72481	0.195670
$857$	−17.1218	−0.584871	−0.292435	−	0.956285i	$-0.594466\pi$
$857$	−17.1218	−0.584871	−0.292435	+	0.956285i	$0.594466\pi$
$858$	15.0635	0.514258
$859$	15.4431	0.526911	0.263455	−	0.964672i	$-0.415138\pi$
$859$	15.4431	0.526911	0.263455	+	0.964672i	$0.415138\pi$
$860$	−50.7468	−1.73045
$861$	−4.37601	−0.149134
$862$	−26.6975	−0.909320
$863$	−44.0731	−1.50027	−0.750134	−	0.661286i	$-0.770011\pi$
$863$	−44.0731	−1.50027	−0.750134	+	0.661286i	$0.770011\pi$
$864$	−8.07650	−0.274768
$865$	−51.5168	−1.75162
$866$	−46.8761	−1.59292
$867$	1.00000	0.0339618
$868$	−11.1487	−0.378413
$869$	−2.31278	−0.0784556
$870$	13.1736	0.446628
$871$	−3.43787	−0.116488
$872$	12.8473	0.435065
$873$	7.76786	0.262902
$874$	−150.296	−5.08385
$875$	3.78703	0.128025
$876$	−31.7647	−1.07323
$877$	−41.6588	−1.40672	−0.703358	−	0.710835i	$-0.748317\pi$
$877$	−41.6588	−1.40672	−0.703358	+	0.710835i	$0.748317\pi$
$878$	−41.4145	−1.39767
$879$	−11.4239	−0.385317
$880$	−24.9116	−0.839771
$881$	48.1837	1.62335	0.811675	−	0.584109i	$-0.198556\pi$
$881$	48.1837	1.62335	0.811675	+	0.584109i	$0.198556\pi$
$882$	−13.9053	−0.468215
$883$	32.9755	1.10972	0.554858	−	0.831945i	$-0.312773\pi$
$883$	32.9755	1.10972	0.554858	+	0.831945i	$0.312773\pi$
$884$	−7.38094	−0.248248
$885$	32.7207	1.09989
$886$	54.7056	1.83787
$887$	9.79079	0.328742	0.164371	−	0.986399i	$-0.447441\pi$
$887$	9.79079	0.328742	0.164371	+	0.986399i	$0.447441\pi$
$888$	−1.36335	−0.0457512
$889$	−0.258320	−0.00866378
$890$	22.1770	0.743376
$891$	2.31278	0.0774810
$892$	−45.9911	−1.53990
$893$	−1.94440	−0.0650668
$894$	−15.6324	−0.522827
$895$	3.39193	0.113380
$896$	−3.56971	−0.119256
$897$	−27.4112	−0.915233
$898$	67.2827	2.24525
$899$	−14.6173	−0.487513
$900$	16.2627	0.542089
$901$	−10.6795	−0.355786
$902$	−35.9031	−1.19544
$903$	−3.66452	−0.121947
$904$	−4.70493	−0.156484
$905$	−46.0359	−1.53028
$906$	−37.3216	−1.23993
$907$	−46.6101	−1.54766	−0.773831	−	0.633392i	$-0.781662\pi$
$907$	−46.6101	−1.54766	−0.773831	+	0.633392i	$0.781662\pi$
$908$	−28.2633	−0.937950
$909$	1.14745	0.0380584
$910$	13.2188	0.438200
$911$	53.8787	1.78508	0.892540	−	0.450969i	$-0.148921\pi$
$911$	53.8787	1.78508	0.892540	+	0.450969i	$0.148921\pi$
$912$	−25.5615	−0.846425
$913$	7.73928	0.256133
$914$	8.88324	0.293831
$915$	−29.9582	−0.990388
$916$	−62.5074	−2.06530
$917$	−1.65669	−0.0547088
$918$	−2.09012	−0.0689843
$919$	2.18032	0.0719222	0.0359611	−	0.999353i	$-0.488551\pi$
$919$	2.18032	0.0719222	0.0359611	+	0.999353i	$0.488551\pi$
$920$	−23.3448	−0.769655
$921$	−2.77735	−0.0915169
$922$	45.0294	1.48296
$923$	−15.4097	−0.507217
$924$	3.22759	0.106180
$925$	−12.1500	−0.399491
$926$	41.5935	1.36685
$927$	18.7631	0.616261
$928$	−14.7777	−0.485102
$929$	−4.92781	−0.161676	−0.0808382	−	0.996727i	$-0.525760\pi$
$929$	−4.92781	−0.161676	−0.0808382	+	0.996727i	$0.525760\pi$
$930$	−57.5181	−1.88609
$931$	−54.3847	−1.78239
$932$	40.9776	1.34227
$933$	−21.8333	−0.714791
$934$	21.5006	0.703523
$935$	−7.96682	−0.260543
$936$	2.40077	0.0784716
$937$	−50.8851	−1.66234	−0.831172	−	0.556015i	$-0.812330\pi$
$937$	−50.8851	−1.66234	−0.831172	+	0.556015i	$0.812330\pi$
$938$	−1.35860	−0.0443599
$939$	13.4049	0.437451
$940$	−1.94071	−0.0632989
$941$	−49.1097	−1.60093	−0.800465	−	0.599379i	$-0.795414\pi$
$941$	−49.1097	−1.60093	−0.800465	+	0.599379i	$0.795414\pi$
$942$	45.3134	1.47639
$943$	65.3334	2.12755
$944$	−29.7022	−0.966725
$945$	2.02956	0.0660217
$946$	−30.0656	−0.977518
$947$	−8.98379	−0.291934	−0.145967	−	0.989289i	$-0.546629\pi$
$947$	−8.98379	−0.291934	−0.145967	+	0.989289i	$0.546629\pi$
$948$	−2.36860	−0.0769287
$949$	−41.7899	−1.35656
$950$	117.311	3.80608
$951$	−13.3058	−0.431471
$952$	−0.453923	−0.0147117
$953$	46.7267	1.51363	0.756813	−	0.653632i	$-0.226755\pi$
$953$	46.7267	1.51363	0.756813	+	0.653632i	$0.226755\pi$
$954$	22.3215	0.722684
$955$	31.6413	1.02389
$956$	31.6206	1.02268
$957$	4.23173	0.136792
$958$	10.4326	0.337063
$959$	−7.43271	−0.240015
$960$	−36.6068	−1.18148
$961$	32.8211	1.05874
$962$	−11.5257	−0.371605
$963$	7.43070	0.239451
$964$	−59.1607	−1.90544
$965$	8.99238	0.289475
$966$	−10.8326	−0.348532
$967$	−5.53209	−0.177900	−0.0889501	−	0.996036i	$-0.528351\pi$
$967$	−5.53209	−0.177900	−0.0889501	+	0.996036i	$0.528351\pi$
$968$	−4.35372	−0.139934
$969$	−8.17464	−0.262607
$970$	55.9273	1.79572
$971$	15.8531	0.508749	0.254374	−	0.967106i	$-0.418130\pi$
$971$	15.8531	0.508749	0.254374	+	0.967106i	$0.418130\pi$
$972$	2.36860	0.0759730
$973$	7.97279	0.255596
$974$	−31.9054	−1.02231
$975$	21.3953	0.685199
$976$	27.1946	0.870477
$977$	21.7182	0.694827	0.347414	−	0.937712i	$-0.387060\pi$
$977$	21.7182	0.694827	0.347414	+	0.937712i	$0.387060\pi$
$978$	48.9414	1.56497
$979$	7.12386	0.227679
$980$	−54.2815	−1.73396
$981$	16.6756	0.532411
$982$	−23.6812	−0.755699
$983$	5.91043	0.188513	0.0942567	−	0.995548i	$-0.469953\pi$
$983$	5.91043	0.188513	0.0942567	+	0.995548i	$0.469953\pi$
$984$	−5.72213	−0.182415
$985$	−23.7147	−0.755612
$986$	−3.82433	−0.121791
$987$	−0.140142	−0.00446077
$988$	60.3366	1.91956
$989$	54.7108	1.73970
$990$	16.6516	0.529223
$991$	21.3063	0.676817	0.338408	−	0.940999i	$-0.390111\pi$
$991$	21.3063	0.676817	0.338408	+	0.940999i	$0.390111\pi$
$992$	64.5216	2.04856
$993$	−6.40269	−0.203183
$994$	−6.08973	−0.193154
$995$	−42.5595	−1.34923
$996$	7.92609	0.251148
$997$	−0.476831	−0.0151014	−0.00755069	−	0.999971i	$-0.502403\pi$
$997$	−0.476831	−0.0151014	−0.00755069	+	0.999971i	$0.502403\pi$
$998$	−6.16955	−0.195294
$999$	−1.76961	−0.0559880

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.j.1.20	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.j.1.20	✓	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)

\(f(q)\)	\(=\)	\(q+2.09012 q^{2} +1.00000 q^{3} +2.36860 q^{4} +3.44470 q^{5} +2.09012 q^{6} +0.589185 q^{7} +0.770426 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.09012 q^{2} +1.00000 q^{3} +2.36860 q^{4} +3.44470 q^{5} +2.09012 q^{6} +0.589185 q^{7} +0.770426 q^{8} +1.00000 q^{9} +7.19983 q^{10} +2.31278 q^{11} +2.36860 q^{12} +3.11616 q^{13} +1.23147 q^{14} +3.44470 q^{15} -3.12692 q^{16} -1.00000 q^{17} +2.09012 q^{18} +8.17464 q^{19} +8.15912 q^{20} +0.589185 q^{21} +4.83398 q^{22} -8.79647 q^{23} +0.770426 q^{24} +6.86593 q^{25} +6.51315 q^{26} +1.00000 q^{27} +1.39555 q^{28} +1.82972 q^{29} +7.19983 q^{30} -7.98881 q^{31} -8.07650 q^{32} +2.31278 q^{33} -2.09012 q^{34} +2.02956 q^{35} +2.36860 q^{36} -1.76961 q^{37} +17.0860 q^{38} +3.11616 q^{39} +2.65388 q^{40} -7.42723 q^{41} +1.23147 q^{42} -6.21964 q^{43} +5.47805 q^{44} +3.44470 q^{45} -18.3857 q^{46} -0.237857 q^{47} -3.12692 q^{48} -6.65286 q^{49} +14.3506 q^{50} -1.00000 q^{51} +7.38094 q^{52} +10.6795 q^{53} +2.09012 q^{54} +7.96682 q^{55} +0.453923 q^{56} +8.17464 q^{57} +3.82433 q^{58} +9.49886 q^{59} +8.15912 q^{60} -8.69691 q^{61} -16.6976 q^{62} +0.589185 q^{63} -10.6270 q^{64} +10.7342 q^{65} +4.83398 q^{66} -1.10324 q^{67} -2.36860 q^{68} -8.79647 q^{69} +4.24203 q^{70} -4.94510 q^{71} +0.770426 q^{72} -13.4107 q^{73} -3.69870 q^{74} +6.86593 q^{75} +19.3625 q^{76} +1.36265 q^{77} +6.51315 q^{78} -1.00000 q^{79} -10.7713 q^{80} +1.00000 q^{81} -15.5238 q^{82} +3.34631 q^{83} +1.39555 q^{84} -3.44470 q^{85} -12.9998 q^{86} +1.82972 q^{87} +1.78182 q^{88} +3.08022 q^{89} +7.19983 q^{90} +1.83599 q^{91} -20.8353 q^{92} -7.98881 q^{93} -0.497151 q^{94} +28.1592 q^{95} -8.07650 q^{96} +7.76786 q^{97} -13.9053 q^{98} +2.31278 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9} + 13 q^{10} + 19 q^{11} + 26 q^{12} + 17 q^{14} + 6 q^{15} + 16 q^{16} - 25 q^{17} + 6 q^{18} + 25 q^{19} + 32 q^{20} + 4 q^{21} - 7 q^{22} + 8 q^{23} + 18 q^{24} + 15 q^{25} + 20 q^{26} + 25 q^{27} + 9 q^{28} + 21 q^{29} + 13 q^{30} + 4 q^{31} + 27 q^{32} + 19 q^{33} - 6 q^{34} + 50 q^{35} + 26 q^{36} - 8 q^{37} + 31 q^{38} + 52 q^{40} + 40 q^{41} + 17 q^{42} + 21 q^{43} + 34 q^{44} + 6 q^{45} + 29 q^{46} + 43 q^{47} + 16 q^{48} + 21 q^{49} + 13 q^{50} - 25 q^{51} + 3 q^{52} + 44 q^{53} + 6 q^{54} + 13 q^{55} + 38 q^{56} + 25 q^{57} - 5 q^{58} + 45 q^{59} + 32 q^{60} + 22 q^{61} + 4 q^{62} + 4 q^{63} + 26 q^{64} + 43 q^{65} - 7 q^{66} + 8 q^{67} - 26 q^{68} + 8 q^{69} + 29 q^{70} + 9 q^{71} + 18 q^{72} - 7 q^{73} + 18 q^{74} + 15 q^{75} + 33 q^{76} + 20 q^{77} + 20 q^{78} - 25 q^{79} + 42 q^{80} + 25 q^{81} - 43 q^{82} + 41 q^{83} + 9 q^{84} - 6 q^{85} - 12 q^{86} + 21 q^{87} - 43 q^{88} + 68 q^{89} + 13 q^{90} + 10 q^{91} + 2 q^{92} + 4 q^{93} - 17 q^{94} + 8 q^{95} + 27 q^{96} + 15 q^{97} + 11 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9 + 13 * q^10 + 19 * q^11 + 26 * q^12 + 17 * q^14 + 6 * q^15 + 16 * q^16 - 25 * q^17 + 6 * q^18 + 25 * q^19 + 32 * q^20 + 4 * q^21 - 7 * q^22 + 8 * q^23 + 18 * q^24 + 15 * q^25 + 20 * q^26 + 25 * q^27 + 9 * q^28 + 21 * q^29 + 13 * q^30 + 4 * q^31 + 27 * q^32 + 19 * q^33 - 6 * q^34 + 50 * q^35 + 26 * q^36 - 8 * q^37 + 31 * q^38 + 52 * q^40 + 40 * q^41 + 17 * q^42 + 21 * q^43 + 34 * q^44 + 6 * q^45 + 29 * q^46 + 43 * q^47 + 16 * q^48 + 21 * q^49 + 13 * q^50 - 25 * q^51 + 3 * q^52 + 44 * q^53 + 6 * q^54 + 13 * q^55 + 38 * q^56 + 25 * q^57 - 5 * q^58 + 45 * q^59 + 32 * q^60 + 22 * q^61 + 4 * q^62 + 4 * q^63 + 26 * q^64 + 43 * q^65 - 7 * q^66 + 8 * q^67 - 26 * q^68 + 8 * q^69 + 29 * q^70 + 9 * q^71 + 18 * q^72 - 7 * q^73 + 18 * q^74 + 15 * q^75 + 33 * q^76 + 20 * q^77 + 20 * q^78 - 25 * q^79 + 42 * q^80 + 25 * q^81 - 43 * q^82 + 41 * q^83 + 9 * q^84 - 6 * q^85 - 12 * q^86 + 21 * q^87 - 43 * q^88 + 68 * q^89 + 13 * q^90 + 10 * q^91 + 2 * q^92 + 4 * q^93 - 17 * q^94 + 8 * q^95 + 27 * q^96 + 15 * q^97 + 11 * q^98 + 19 * q^99

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