LMFDB - Embedded newform 4019.2.a.a.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4019,2,Mod(1,4019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4019, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4019.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:	$32.0918765724$
Analytic rank:	$1$
Dimension:	$149$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	4019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.45807 q^{2} -2.34751 q^{3} +4.04212 q^{4} -0.597755 q^{5} +5.77034 q^{6} -0.214441 q^{7} -5.01969 q^{8} +2.51079 q^{9} +O(q^{10})$	\(q-2.45807 q^{2} -2.34751 q^{3} +4.04212 q^{4} -0.597755 q^{5} +5.77034 q^{6} -0.214441 q^{7} -5.01969 q^{8} +2.51079 q^{9} +1.46933 q^{10} +3.16141 q^{11} -9.48891 q^{12} +3.93889 q^{13} +0.527112 q^{14} +1.40324 q^{15} +4.25451 q^{16} +1.98247 q^{17} -6.17171 q^{18} +1.46690 q^{19} -2.41620 q^{20} +0.503402 q^{21} -7.77099 q^{22} -0.740239 q^{23} +11.7838 q^{24} -4.64269 q^{25} -9.68209 q^{26} +1.14842 q^{27} -0.866797 q^{28} -1.43106 q^{29} -3.44925 q^{30} -10.2923 q^{31} -0.418526 q^{32} -7.42144 q^{33} -4.87306 q^{34} +0.128183 q^{35} +10.1489 q^{36} +5.27791 q^{37} -3.60574 q^{38} -9.24658 q^{39} +3.00055 q^{40} +1.13319 q^{41} -1.23740 q^{42} -1.58731 q^{43} +12.7788 q^{44} -1.50084 q^{45} +1.81956 q^{46} +7.90491 q^{47} -9.98750 q^{48} -6.95402 q^{49} +11.4121 q^{50} -4.65387 q^{51} +15.9215 q^{52} -10.3185 q^{53} -2.82290 q^{54} -1.88975 q^{55} +1.07643 q^{56} -3.44355 q^{57} +3.51764 q^{58} +6.02301 q^{59} +5.67205 q^{60} -14.1710 q^{61} +25.2993 q^{62} -0.538417 q^{63} -7.48026 q^{64} -2.35449 q^{65} +18.2424 q^{66} +0.784066 q^{67} +8.01340 q^{68} +1.73772 q^{69} -0.315084 q^{70} -15.9060 q^{71} -12.6034 q^{72} +5.78835 q^{73} -12.9735 q^{74} +10.8987 q^{75} +5.92937 q^{76} -0.677937 q^{77} +22.7288 q^{78} +3.57990 q^{79} -2.54316 q^{80} -10.2283 q^{81} -2.78547 q^{82} +10.3207 q^{83} +2.03481 q^{84} -1.18503 q^{85} +3.90173 q^{86} +3.35942 q^{87} -15.8693 q^{88} +12.7893 q^{89} +3.68917 q^{90} -0.844660 q^{91} -2.99214 q^{92} +24.1613 q^{93} -19.4309 q^{94} -0.876845 q^{95} +0.982494 q^{96} -13.5170 q^{97} +17.0935 q^{98} +7.93765 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9}+O(q^{10}) $ 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9	\( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9} - 58 q^{10} - 33 q^{11} - 33 q^{12} - 107 q^{13} - 28 q^{14} - 24 q^{15} + 74 q^{16} - 39 q^{17} - 33 q^{18} - 93 q^{19} - 63 q^{20} - 113 q^{21} - 38 q^{22} - 11 q^{23} - 130 q^{24} + 85 q^{25} - 33 q^{26} - 30 q^{27} - 94 q^{28} - 85 q^{29} - 16 q^{30} - 129 q^{31} - 35 q^{32} - 64 q^{33} - 78 q^{34} - 27 q^{35} + 79 q^{36} - 135 q^{37} - 11 q^{38} - 73 q^{39} - 146 q^{40} - 101 q^{41} + 4 q^{42} - 55 q^{43} - 82 q^{44} - 168 q^{45} - 113 q^{46} - 40 q^{47} - 65 q^{48} + 27 q^{49} - 5 q^{50} - 49 q^{51} - 177 q^{52} - 32 q^{53} - 155 q^{54} - 128 q^{55} - 44 q^{56} - 47 q^{57} - 46 q^{58} - 53 q^{59} - 11 q^{60} - 347 q^{61} - 11 q^{62} - 73 q^{63} + q^{64} - 31 q^{65} - 37 q^{66} - 40 q^{67} - 80 q^{68} - 175 q^{69} - 61 q^{70} - 31 q^{71} - 68 q^{72} - 193 q^{73} - 33 q^{74} - 56 q^{75} - 248 q^{76} - 84 q^{77} + 40 q^{78} - 111 q^{79} - 54 q^{80} + 49 q^{81} - 74 q^{82} - 24 q^{83} - 159 q^{84} - 258 q^{85} - q^{86} - 66 q^{87} - 97 q^{88} - 76 q^{89} - 75 q^{90} - 134 q^{91} + 31 q^{92} - 97 q^{93} - 111 q^{94} - 14 q^{95} - 216 q^{96} - 140 q^{97} - 13 q^{98} - 116 q^{99}+O(q^{100}) \) 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9 - 58 * q^10 - 33 * q^11 - 33 * q^12 - 107 * q^13 - 28 * q^14 - 24 * q^15 + 74 * q^16 - 39 * q^17 - 33 * q^18 - 93 * q^19 - 63 * q^20 - 113 * q^21 - 38 * q^22 - 11 * q^23 - 130 * q^24 + 85 * q^25 - 33 * q^26 - 30 * q^27 - 94 * q^28 - 85 * q^29 - 16 * q^30 - 129 * q^31 - 35 * q^32 - 64 * q^33 - 78 * q^34 - 27 * q^35 + 79 * q^36 - 135 * q^37 - 11 * q^38 - 73 * q^39 - 146 * q^40 - 101 * q^41 + 4 * q^42 - 55 * q^43 - 82 * q^44 - 168 * q^45 - 113 * q^46 - 40 * q^47 - 65 * q^48 + 27 * q^49 - 5 * q^50 - 49 * q^51 - 177 * q^52 - 32 * q^53 - 155 * q^54 - 128 * q^55 - 44 * q^56 - 47 * q^57 - 46 * q^58 - 53 * q^59 - 11 * q^60 - 347 * q^61 - 11 * q^62 - 73 * q^63 + q^64 - 31 * q^65 - 37 * q^66 - 40 * q^67 - 80 * q^68 - 175 * q^69 - 61 * q^70 - 31 * q^71 - 68 * q^72 - 193 * q^73 - 33 * q^74 - 56 * q^75 - 248 * q^76 - 84 * q^77 + 40 * q^78 - 111 * q^79 - 54 * q^80 + 49 * q^81 - 74 * q^82 - 24 * q^83 - 159 * q^84 - 258 * q^85 - q^86 - 66 * q^87 - 97 * q^88 - 76 * q^89 - 75 * q^90 - 134 * q^91 + 31 * q^92 - 97 * q^93 - 111 * q^94 - 14 * q^95 - 216 * q^96 - 140 * q^97 - 13 * q^98 - 116 * 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 $

$2$	−2.45807	−1.73812	−0.869060	−	0.494707i	$-0.835276\pi$
$2$	−2.45807	−1.73812	−0.869060	+	0.494707i	$0.835276\pi$
$3$	−2.34751	−1.35533	−0.677667	−	0.735369i	$-0.737009\pi$
$3$	−2.34751	−1.35533	−0.677667	+	0.735369i	$0.737009\pi$
$4$	4.04212	2.02106
$5$	−0.597755	−0.267324	−0.133662	−	0.991027i	$-0.542674\pi$
$5$	−0.597755	−0.267324	−0.133662	+	0.991027i	$0.542674\pi$
$6$	5.77034	2.35573
$7$	−0.214441	−0.0810511	−0.0405256	−	0.999179i	$-0.512903\pi$
$7$	−0.214441	−0.0810511	−0.0405256	+	0.999179i	$0.512903\pi$
$8$	−5.01969	−1.77473
$9$	2.51079	0.836930
$10$	1.46933	0.464642
$11$	3.16141	0.953202	0.476601	−	0.879120i	$-0.341869\pi$
$11$	3.16141	0.953202	0.476601	+	0.879120i	$0.341869\pi$
$12$	−9.48891	−2.73921
$13$	3.93889	1.09245	0.546226	−	0.837638i	$-0.316064\pi$
$13$	3.93889	1.09245	0.546226	+	0.837638i	$0.316064\pi$
$14$	0.527112	0.140877
$15$	1.40324	0.362314
$16$	4.25451	1.06363
$17$	1.98247	0.480820	0.240410	−	0.970671i	$-0.422718\pi$
$17$	1.98247	0.480820	0.240410	+	0.970671i	$0.422718\pi$
$18$	−6.17171	−1.45469
$19$	1.46690	0.336529	0.168265	−	0.985742i	$-0.446184\pi$
$19$	1.46690	0.336529	0.168265	+	0.985742i	$0.446184\pi$
$20$	−2.41620	−0.540279
$21$	0.503402	0.109851
$22$	−7.77099	−1.65678
$23$	−0.740239	−0.154350	−0.0771752	−	0.997018i	$-0.524590\pi$
$23$	−0.740239	−0.154350	−0.0771752	+	0.997018i	$0.524590\pi$
$24$	11.7838	2.40535
$25$	−4.64269	−0.928538
$26$	−9.68209	−1.89881
$27$	1.14842	0.221014
$28$	−0.866797	−0.163809
$29$	−1.43106	−0.265741	−0.132870	−	0.991133i	$-0.542419\pi$
$29$	−1.43106	−0.265741	−0.132870	+	0.991133i	$0.542419\pi$
$30$	−3.44925	−0.629745
$31$	−10.2923	−1.84855	−0.924277	−	0.381722i	$-0.875331\pi$
$31$	−10.2923	−1.84855	−0.924277	+	0.381722i	$0.875331\pi$
$32$	−0.418526	−0.0739857
$33$	−7.42144	−1.29191
$34$	−4.87306	−0.835723
$35$	0.128183	0.0216669
$36$	10.1489	1.69149
$37$	5.27791	0.867683	0.433842	−	0.900989i	$-0.357158\pi$
$37$	5.27791	0.867683	0.433842	+	0.900989i	$0.357158\pi$
$38$	−3.60574	−0.584928
$39$	−9.24658	−1.48064
$40$	3.00055	0.474428
$41$	1.13319	0.176975	0.0884875	−	0.996077i	$-0.471797\pi$
$41$	1.13319	0.176975	0.0884875	+	0.996077i	$0.471797\pi$
$42$	−1.23740	−0.190935
$43$	−1.58731	−0.242063	−0.121031	−	0.992649i	$-0.538620\pi$
$43$	−1.58731	−0.242063	−0.121031	+	0.992649i	$0.538620\pi$
$44$	12.7788	1.92648
$45$	−1.50084	−0.223732
$46$	1.81956	0.268280
$47$	7.90491	1.15305	0.576525	−	0.817079i	$-0.304408\pi$
$47$	7.90491	1.15305	0.576525	+	0.817079i	$0.304408\pi$
$48$	−9.98750	−1.44157
$49$	−6.95402	−0.993431
$50$	11.4121	1.61391
$51$	−4.65387	−0.651672
$52$	15.9215	2.20791
$53$	−10.3185	−1.41736	−0.708680	−	0.705530i	$-0.750709\pi$
$53$	−10.3185	−1.41736	−0.708680	+	0.705530i	$0.750709\pi$
$54$	−2.82290	−0.384149
$55$	−1.88975	−0.254814
$56$	1.07643	0.143844
$57$	−3.44355	−0.456109
$58$	3.51764	0.461889
$59$	6.02301	0.784130	0.392065	−	0.919938i	$-0.371761\pi$
$59$	6.02301	0.784130	0.392065	+	0.919938i	$0.371761\pi$
$60$	5.67205	0.732258
$61$	−14.1710	−1.81441	−0.907205	−	0.420690i	$-0.861788\pi$
$61$	−14.1710	−1.81441	−0.907205	+	0.420690i	$0.861788\pi$
$62$	25.2993	3.21301
$63$	−0.538417	−0.0678341
$64$	−7.48026	−0.935032
$65$	−2.35449	−0.292039
$66$	18.2424	2.24549
$67$	0.784066	0.0957889	0.0478945	−	0.998852i	$-0.484749\pi$
$67$	0.784066	0.0957889	0.0478945	+	0.998852i	$0.484749\pi$
$68$	8.01340	0.971767
$69$	1.73772	0.209196
$70$	−0.315084	−0.0376597
$71$	−15.9060	−1.88770	−0.943849	−	0.330377i	$-0.892824\pi$
$71$	−15.9060	−1.88770	−0.943849	+	0.330377i	$0.892824\pi$
$72$	−12.6034	−1.48532
$73$	5.78835	0.677476	0.338738	−	0.940881i	$-0.390000\pi$
$73$	5.78835	0.677476	0.338738	+	0.940881i	$0.390000\pi$
$74$	−12.9735	−1.50814
$75$	10.8987	1.25848
$76$	5.92937	0.680146
$77$	−0.677937	−0.0772581
$78$	22.7288	2.57353
$79$	3.57990	0.402770	0.201385	−	0.979512i	$-0.435456\pi$
$79$	3.57990	0.402770	0.201385	+	0.979512i	$0.435456\pi$
$80$	−2.54316	−0.284334
$81$	−10.2283	−1.13648
$82$	−2.78547	−0.307604
$83$	10.3207	1.13285	0.566423	−	0.824115i	$-0.308327\pi$
$83$	10.3207	1.13285	0.566423	+	0.824115i	$0.308327\pi$
$84$	2.03481	0.222016
$85$	−1.18503	−0.128535
$86$	3.90173	0.420734
$87$	3.35942	0.360167
$88$	−15.8693	−1.69167
$89$	12.7893	1.35566	0.677832	−	0.735217i	$-0.262920\pi$
$89$	12.7893	1.35566	0.677832	+	0.735217i	$0.262920\pi$
$90$	3.68917	0.388873
$91$	−0.844660	−0.0885445
$92$	−2.99214	−0.311952
$93$	24.1613	2.50541
$94$	−19.4309	−2.00414
$95$	−0.876845	−0.0899624
$96$	0.982494	0.100275
$97$	−13.5170	−1.37245	−0.686224	−	0.727391i	$-0.740733\pi$
$97$	−13.5170	−1.37245	−0.686224	+	0.727391i	$0.740733\pi$
$98$	17.0935	1.72670
$99$	7.93765	0.797764
$100$	−18.7663	−1.87663
$101$	13.2083	1.31428	0.657139	−	0.753769i	$-0.271766\pi$
$101$	13.2083	1.31428	0.657139	+	0.753769i	$0.271766\pi$
$102$	11.4396	1.13268
$103$	4.73427	0.466481	0.233241	−	0.972419i	$-0.425067\pi$
$103$	4.73427	0.466481	0.233241	+	0.972419i	$0.425067\pi$
$104$	−19.7720	−1.93880
$105$	−0.300911	−0.0293659
$106$	25.3637	2.46354
$107$	−12.1846	−1.17793	−0.588963	−	0.808160i	$-0.700464\pi$
$107$	−12.1846	−1.17793	−0.588963	+	0.808160i	$0.700464\pi$
$108$	4.64206	0.446683
$109$	2.70558	0.259148	0.129574	−	0.991570i	$-0.458639\pi$
$109$	2.70558	0.259148	0.129574	+	0.991570i	$0.458639\pi$
$110$	4.64515	0.442898
$111$	−12.3899	−1.17600
$112$	−0.912342	−0.0862082
$113$	−13.4765	−1.26776	−0.633882	−	0.773430i	$-0.718539\pi$
$113$	−13.4765	−1.26776	−0.633882	+	0.773430i	$0.718539\pi$
$114$	8.46450	0.792773
$115$	0.442482	0.0412616
$116$	−5.78451	−0.537078
$117$	9.88974	0.914306
$118$	−14.8050	−1.36291
$119$	−0.425124	−0.0389710
$120$	−7.04380	−0.643008
$121$	−1.00546	−0.0914055
$122$	34.8333	3.15366
$123$	−2.66018	−0.239860
$124$	−41.6028	−3.73604
$125$	5.76397	0.515545
$126$	1.32347	0.117904
$127$	0.447158	0.0396789	0.0198394	−	0.999803i	$-0.493684\pi$
$127$	0.447158	0.0396789	0.0198394	+	0.999803i	$0.493684\pi$
$128$	19.2241	1.69918
$129$	3.72622	0.328076
$130$	5.78752	0.507599
$131$	−20.4938	−1.79055	−0.895275	−	0.445514i	$-0.853021\pi$
$131$	−20.4938	−1.79055	−0.895275	+	0.445514i	$0.853021\pi$
$132$	−29.9984	−2.61102
$133$	−0.314563	−0.0272761
$134$	−1.92729	−0.166493
$135$	−0.686475	−0.0590824
$136$	−9.95139	−0.853325
$137$	12.5308	1.07058	0.535290	−	0.844668i	$-0.320202\pi$
$137$	12.5308	1.07058	0.535290	+	0.844668i	$0.320202\pi$
$138$	−4.27143	−0.363609
$139$	−5.10316	−0.432844	−0.216422	−	0.976300i	$-0.569439\pi$
$139$	−5.10316	−0.432844	−0.216422	+	0.976300i	$0.569439\pi$
$140$	0.518133	0.0437902
$141$	−18.5568	−1.56277
$142$	39.0982	3.28105
$143$	12.4525	1.04133
$144$	10.6822	0.890182
$145$	0.855422	0.0710389
$146$	−14.2282	−1.17753
$147$	16.3246	1.34643
$148$	21.3340	1.75364
$149$	7.57246	0.620360	0.310180	−	0.950678i	$-0.399611\pi$
$149$	7.57246	0.620360	0.310180	+	0.950678i	$0.399611\pi$
$150$	−26.7899	−2.18739
$151$	−3.41049	−0.277542	−0.138771	−	0.990325i	$-0.544315\pi$
$151$	−3.41049	−0.277542	−0.138771	+	0.990325i	$0.544315\pi$
$152$	−7.36336	−0.597247
$153$	4.97757	0.402413
$154$	1.66642	0.134284
$155$	6.15229	0.494164
$156$	−37.3758	−2.99246
$157$	3.85175	0.307403	0.153701	−	0.988117i	$-0.450881\pi$
$157$	3.85175	0.307403	0.153701	+	0.988117i	$0.450881\pi$
$158$	−8.79965	−0.700063
$159$	24.2228	1.92100
$160$	0.250176	0.0197782
$161$	0.158738	0.0125103
$162$	25.1419	1.97534
$163$	3.52750	0.276295	0.138147	−	0.990412i	$-0.455885\pi$
$163$	3.52750	0.276295	0.138147	+	0.990412i	$0.455885\pi$
$164$	4.58050	0.357677
$165$	4.43621	0.345358
$166$	−25.3691	−1.96902
$167$	23.0884	1.78663	0.893316	−	0.449429i	$-0.148372\pi$
$167$	23.0884	1.78663	0.893316	+	0.449429i	$0.148372\pi$
$168$	−2.52692	−0.194956
$169$	2.51487	0.193452
$170$	2.91290	0.223409
$171$	3.68307	0.281651
$172$	−6.41610	−0.489223
$173$	13.2093	1.00429	0.502144	−	0.864784i	$-0.332545\pi$
$173$	13.2093	1.00429	0.502144	+	0.864784i	$0.332545\pi$
$174$	−8.25769	−0.626014
$175$	0.995583	0.0752590
$176$	13.4503	1.01385
$177$	−14.1391	−1.06276
$178$	−31.4370	−2.35631
$179$	19.9795	1.49334	0.746669	−	0.665196i	$-0.231652\pi$
$179$	19.9795	1.49334	0.746669	+	0.665196i	$0.231652\pi$
$180$	−6.06658	−0.452176
$181$	−6.89170	−0.512256	−0.256128	−	0.966643i	$-0.582447\pi$
$181$	−6.89170	−0.512256	−0.256128	+	0.966643i	$0.582447\pi$
$182$	2.07624	0.153901
$183$	33.2665	2.45913
$184$	3.71577	0.273930
$185$	−3.15490	−0.231953
$186$	−59.3902	−4.35470
$187$	6.26742	0.458319
$188$	31.9526	2.33039
$189$	−0.246269	−0.0179134
$190$	2.15535	0.156365
$191$	−11.5826	−0.838086	−0.419043	−	0.907966i	$-0.637634\pi$
$191$	−11.5826	−0.838086	−0.419043	+	0.907966i	$0.637634\pi$
$192$	17.5600	1.26728
$193$	13.4770	0.970094	0.485047	−	0.874488i	$-0.338802\pi$
$193$	13.4770	0.970094	0.485047	+	0.874488i	$0.338802\pi$
$194$	33.2259	2.38548
$195$	5.52719	0.395811
$196$	−28.1090	−2.00778
$197$	15.7135	1.11954	0.559770	−	0.828648i	$-0.310890\pi$
$197$	15.7135	1.11954	0.559770	+	0.828648i	$0.310890\pi$
$198$	−19.5113	−1.38661
$199$	−5.05467	−0.358316	−0.179158	−	0.983820i	$-0.557337\pi$
$199$	−5.05467	−0.358316	−0.179158	+	0.983820i	$0.557337\pi$
$200$	23.3048	1.64790
$201$	−1.84060	−0.129826
$202$	−32.4671	−2.28437
$203$	0.306877	0.0215386
$204$	−18.8115	−1.31707
$205$	−0.677372	−0.0473097
$206$	−11.6372	−0.810800
$207$	−1.85858	−0.129181
$208$	16.7581	1.16196
$209$	4.63747	0.320780
$210$	0.739662	0.0510415
$211$	23.6286	1.62666	0.813329	−	0.581803i	$-0.197653\pi$
$211$	23.6286	1.62666	0.813329	+	0.581803i	$0.197653\pi$
$212$	−41.7088	−2.86457
$213$	37.3395	2.55846
$214$	29.9506	2.04738
$215$	0.948824	0.0647092
$216$	−5.76472	−0.392239
$217$	2.20710	0.149827
$218$	−6.65052	−0.450430
$219$	−13.5882	−0.918206
$220$	−7.63861	−0.514995
$221$	7.80875	0.525273
$222$	30.4554	2.04403
$223$	−12.3243	−0.825298	−0.412649	−	0.910890i	$-0.635396\pi$
$223$	−12.3243	−0.825298	−0.412649	+	0.910890i	$0.635396\pi$
$224$	0.0897493	0.00599663
$225$	−11.6568	−0.777121
$226$	33.1262	2.20353
$227$	3.37795	0.224202	0.112101	−	0.993697i	$-0.464242\pi$
$227$	3.37795	0.224202	0.112101	+	0.993697i	$0.464242\pi$
$228$	−13.9192	−0.921825
$229$	−23.4011	−1.54639	−0.773193	−	0.634170i	$-0.781342\pi$
$229$	−23.4011	−1.54639	−0.773193	+	0.634170i	$0.781342\pi$
$230$	−1.08765	−0.0717177
$231$	1.59146	0.104711
$232$	7.18346	0.471617
$233$	−16.9882	−1.11294	−0.556468	−	0.830869i	$-0.687844\pi$
$233$	−16.9882	−1.11294	−0.556468	+	0.830869i	$0.687844\pi$
$234$	−24.3097	−1.58917
$235$	−4.72521	−0.308238
$236$	24.3458	1.58477
$237$	−8.40384	−0.545888
$238$	1.04498	0.0677363
$239$	4.52881	0.292945	0.146472	−	0.989215i	$-0.453208\pi$
$239$	4.52881	0.292945	0.146472	+	0.989215i	$0.453208\pi$
$240$	5.97008	0.385367
$241$	13.4721	0.867815	0.433908	−	0.900957i	$-0.357134\pi$
$241$	13.4721	0.867815	0.433908	+	0.900957i	$0.357134\pi$
$242$	2.47150	0.158874
$243$	20.5657	1.31929
$244$	−57.2809	−3.66703
$245$	4.15680	0.265568
$246$	6.53891	0.416906
$247$	5.77795	0.367642
$248$	51.6642	3.28068
$249$	−24.2280	−1.53539
$250$	−14.1683	−0.896079
$251$	18.3507	1.15828	0.579142	−	0.815227i	$-0.303388\pi$
$251$	18.3507	1.15828	0.579142	+	0.815227i	$0.303388\pi$
$252$	−2.17635	−0.137097
$253$	−2.34020	−0.147127
$254$	−1.09915	−0.0689667
$255$	2.78188	0.174208
$256$	−32.2936	−2.01835
$257$	−21.2055	−1.32276	−0.661381	−	0.750050i	$-0.730029\pi$
$257$	−21.2055	−1.32276	−0.661381	+	0.750050i	$0.730029\pi$
$258$	−9.15933	−0.570235
$259$	−1.13180	−0.0703267
$260$	−9.51716	−0.590229
$261$	−3.59308	−0.222406
$262$	50.3752	3.11219
$263$	4.37092	0.269522	0.134761	−	0.990878i	$-0.456973\pi$
$263$	4.37092	0.269522	0.134761	+	0.990878i	$0.456973\pi$
$264$	37.2533	2.29278
$265$	6.16796	0.378895
$266$	0.773218	0.0474091
$267$	−30.0230	−1.83738
$268$	3.16929	0.193595
$269$	−25.1699	−1.53463	−0.767317	−	0.641267i	$-0.778409\pi$
$269$	−25.1699	−1.53463	−0.767317	+	0.641267i	$0.778409\pi$
$270$	1.68741	0.102692
$271$	−26.1757	−1.59006	−0.795030	−	0.606570i	$-0.792545\pi$
$271$	−26.1757	−1.59006	−0.795030	+	0.606570i	$0.792545\pi$
$272$	8.43445	0.511414
$273$	1.98285	0.120007
$274$	−30.8017	−1.86080
$275$	−14.6775	−0.885084
$276$	7.02406	0.422799
$277$	−25.4229	−1.52752	−0.763758	−	0.645502i	$-0.776648\pi$
$277$	−25.4229	−1.52752	−0.763758	+	0.645502i	$0.776648\pi$
$278$	12.5439	0.752335
$279$	−25.8419	−1.54711
$280$	−0.643440	−0.0384529
$281$	4.46160	0.266157	0.133078	−	0.991106i	$-0.457514\pi$
$281$	4.46160	0.266157	0.133078	+	0.991106i	$0.457514\pi$
$282$	45.6141	2.71628
$283$	9.23069	0.548708	0.274354	−	0.961629i	$-0.411536\pi$
$283$	9.23069	0.548708	0.274354	+	0.961629i	$0.411536\pi$
$284$	−64.2941	−3.81515
$285$	2.05840	0.121929
$286$	−30.6091	−1.80995
$287$	−0.243003	−0.0143440
$288$	−1.05083	−0.0619209
$289$	−13.0698	−0.768812
$290$	−2.10269	−0.123474
$291$	31.7314	1.86012
$292$	23.3972	1.36922
$293$	−13.1664	−0.769187	−0.384594	−	0.923086i	$-0.625658\pi$
$293$	−13.1664	−0.769187	−0.384594	+	0.923086i	$0.625658\pi$
$294$	−40.1271	−2.34026
$295$	−3.60029	−0.209617
$296$	−26.4935	−1.53990
$297$	3.63064	0.210671
$298$	−18.6137	−1.07826
$299$	−2.91572	−0.168621
$300$	44.0541	2.54346
$301$	0.340385	0.0196194
$302$	8.38324	0.482401
$303$	−31.0067	−1.78129
$304$	6.24093	0.357942
$305$	8.47079	0.485036
$306$	−12.2352	−0.699442
$307$	14.2503	0.813306	0.406653	−	0.913583i	$-0.366696\pi$
$307$	14.2503	0.813306	0.406653	+	0.913583i	$0.366696\pi$
$308$	−2.74031	−0.156143
$309$	−11.1137	−0.632238
$310$	−15.1228	−0.858916
$311$	29.8160	1.69071	0.845355	−	0.534205i	$-0.179389\pi$
$311$	29.8160	1.69071	0.845355	+	0.534205i	$0.179389\pi$
$312$	46.4149	2.62773
$313$	−21.4889	−1.21463	−0.607313	−	0.794463i	$-0.707752\pi$
$313$	−21.4889	−1.21463	−0.607313	+	0.794463i	$0.707752\pi$
$314$	−9.46788	−0.534303
$315$	0.321842	0.0181337
$316$	14.4704	0.814023
$317$	−31.2550	−1.75546	−0.877729	−	0.479158i	$-0.840942\pi$
$317$	−31.2550	−1.75546	−0.877729	+	0.479158i	$0.840942\pi$
$318$	−59.5415	−3.33892
$319$	−4.52416	−0.253305
$320$	4.47136	0.249957
$321$	28.6034	1.59648
$322$	−0.390189	−0.0217444
$323$	2.90808	0.161810
$324$	−41.3441	−2.29689
$325$	−18.2871	−1.01438
$326$	−8.67085	−0.480234
$327$	−6.35137	−0.351232
$328$	−5.68827	−0.314082
$329$	−1.69514	−0.0934560
$330$	−10.9045	−0.600274
$331$	31.3329	1.72221	0.861107	−	0.508425i	$-0.169772\pi$
$331$	31.3329	1.72221	0.861107	+	0.508425i	$0.169772\pi$
$332$	41.7176	2.28955
$333$	13.2517	0.726190
$334$	−56.7529	−3.10538
$335$	−0.468680	−0.0256067
$336$	2.14173	0.116841
$337$	−9.01088	−0.490854	−0.245427	−	0.969415i	$-0.578928\pi$
$337$	−9.01088	−0.490854	−0.245427	+	0.969415i	$0.578928\pi$
$338$	−6.18175	−0.336243
$339$	31.6362	1.71824
$340$	−4.79005	−0.259777
$341$	−32.5383	−1.76205
$342$	−9.05325	−0.489544
$343$	2.99231	0.161570
$344$	7.96780	0.429595
$345$	−1.03873	−0.0559233
$346$	−32.4695	−1.74557
$347$	−19.9947	−1.07337	−0.536686	−	0.843782i	$-0.680324\pi$
$347$	−19.9947	−1.07337	−0.536686	+	0.843782i	$0.680324\pi$
$348$	13.5792	0.727920
$349$	−1.64714	−0.0881695	−0.0440848	−	0.999028i	$-0.514037\pi$
$349$	−1.64714	−0.0881695	−0.0440848	+	0.999028i	$0.514037\pi$
$350$	−2.44722	−0.130809
$351$	4.52351	0.241447
$352$	−1.32314	−0.0705234
$353$	−6.43786	−0.342653	−0.171326	−	0.985214i	$-0.554805\pi$
$353$	−6.43786	−0.342653	−0.171326	+	0.985214i	$0.554805\pi$
$354$	34.7549	1.84720
$355$	9.50792	0.504628
$356$	51.6959	2.73988
$357$	0.997981	0.0528187
$358$	−49.1111	−2.59560
$359$	−28.7563	−1.51770	−0.758851	−	0.651264i	$-0.774239\pi$
$359$	−28.7563	−1.51770	−0.758851	+	0.651264i	$0.774239\pi$
$360$	7.53374	0.397063
$361$	−16.8482	−0.886748
$362$	16.9403	0.890363
$363$	2.36033	0.123885
$364$	−3.41422	−0.178954
$365$	−3.46002	−0.181106
$366$	−81.7715	−4.27426
$367$	−14.2452	−0.743594	−0.371797	−	0.928314i	$-0.621258\pi$
$367$	−14.2452	−0.743594	−0.371797	+	0.928314i	$0.621258\pi$
$368$	−3.14935	−0.164171
$369$	2.84521	0.148116
$370$	7.75497	0.403162
$371$	2.21272	0.114879
$372$	97.6629	5.06358
$373$	33.4950	1.73431	0.867153	−	0.498042i	$-0.165947\pi$
$373$	33.4950	1.73431	0.867153	+	0.498042i	$0.165947\pi$
$374$	−15.4058	−0.796613
$375$	−13.5310	−0.698736
$376$	−39.6802	−2.04635
$377$	−5.63678	−0.290309
$378$	0.605347	0.0311357
$379$	−22.2303	−1.14190	−0.570948	−	0.820986i	$-0.693424\pi$
$379$	−22.2303	−1.14190	−0.570948	+	0.820986i	$0.693424\pi$
$380$	−3.54432	−0.181820
$381$	−1.04971	−0.0537782
$382$	28.4708	1.45669
$383$	23.8874	1.22059	0.610296	−	0.792174i	$-0.291051\pi$
$383$	23.8874	1.22059	0.610296	+	0.792174i	$0.291051\pi$
$384$	−45.1286	−2.30296
$385$	0.405241	0.0206530
$386$	−33.1274	−1.68614
$387$	−3.98541	−0.202590
$388$	−54.6375	−2.77380
$389$	−36.3981	−1.84546	−0.922728	−	0.385453i	$-0.874045\pi$
$389$	−36.3981	−1.84546	−0.922728	+	0.385453i	$0.874045\pi$
$390$	−13.5862	−0.687966
$391$	−1.46750	−0.0742148
$392$	34.9070	1.76307
$393$	48.1093	2.42679
$394$	−38.6249	−1.94589
$395$	−2.13990	−0.107670
$396$	32.0850	1.61233
$397$	−19.2904	−0.968156	−0.484078	−	0.875025i	$-0.660845\pi$
$397$	−19.2904	−0.968156	−0.484078	+	0.875025i	$0.660845\pi$
$398$	12.4248	0.622797
$399$	0.738439	0.0369682
$400$	−19.7524	−0.987619
$401$	−15.7451	−0.786273	−0.393137	−	0.919480i	$-0.628610\pi$
$401$	−15.7451	−0.786273	−0.393137	+	0.919480i	$0.628610\pi$
$402$	4.52433	0.225653
$403$	−40.5403	−2.01946
$404$	53.3897	2.65624
$405$	6.11402	0.303808
$406$	−0.754327	−0.0374366
$407$	16.6857	0.827078
$408$	23.3610	1.15654
$409$	36.8991	1.82454	0.912271	−	0.409586i	$-0.134327\pi$
$409$	36.8991	1.82454	0.912271	+	0.409586i	$0.134327\pi$
$410$	1.66503	0.0822300
$411$	−29.4162	−1.45099
$412$	19.1365	0.942787
$413$	−1.29158	−0.0635546
$414$	4.56854	0.224531
$415$	−6.16927	−0.302837
$416$	−1.64853	−0.0808259
$417$	11.9797	0.586648
$418$	−11.3992	−0.557555
$419$	22.6718	1.10759	0.553795	−	0.832653i	$-0.313179\pi$
$419$	22.6718	1.10759	0.553795	+	0.832653i	$0.313179\pi$
$420$	−1.21632	−0.0593504
$421$	29.7601	1.45042	0.725210	−	0.688528i	$-0.241743\pi$
$421$	29.7601	1.45042	0.725210	+	0.688528i	$0.241743\pi$
$422$	−58.0808	−2.82733
$423$	19.8476	0.965023
$424$	51.7958	2.51543
$425$	−9.20400	−0.446460
$426$	−91.7833	−4.44691
$427$	3.03884	0.147060
$428$	−49.2515	−2.38066
$429$	−29.2323	−1.41135
$430$	−2.33228	−0.112472
$431$	−27.2666	−1.31339	−0.656693	−	0.754158i	$-0.728045\pi$
$431$	−27.2666	−1.31339	−0.656693	+	0.754158i	$0.728045\pi$
$432$	4.88597	0.235077
$433$	−39.1366	−1.88078	−0.940392	−	0.340092i	$-0.889542\pi$
$433$	−39.1366	−1.88078	−0.940392	+	0.340092i	$0.889542\pi$
$434$	−5.42520	−0.260418
$435$	−2.00811	−0.0962815
$436$	10.9363	0.523754
$437$	−1.08585	−0.0519434
$438$	33.4008	1.59595
$439$	−7.55430	−0.360547	−0.180274	−	0.983617i	$-0.557698\pi$
$439$	−7.55430	−0.360547	−0.180274	+	0.983617i	$0.557698\pi$
$440$	9.48597	0.452226
$441$	−17.4601	−0.831432
$442$	−19.1945	−0.912988
$443$	18.8508	0.895626	0.447813	−	0.894127i	$-0.352203\pi$
$443$	18.8508	0.895626	0.447813	+	0.894127i	$0.352203\pi$
$444$	−50.0816	−2.37677
$445$	−7.64487	−0.362402
$446$	30.2941	1.43447
$447$	−17.7764	−0.840795
$448$	1.60407	0.0757854
$449$	19.2308	0.907560	0.453780	−	0.891114i	$-0.350075\pi$
$449$	19.2308	0.907560	0.453780	+	0.891114i	$0.350075\pi$
$450$	28.6533	1.35073
$451$	3.58249	0.168693
$452$	−54.4737	−2.56223
$453$	8.00616	0.376162
$454$	−8.30324	−0.389690
$455$	0.504900	0.0236701
$456$	17.2855	0.809470
$457$	−39.4634	−1.84602	−0.923010	−	0.384776i	$-0.874279\pi$
$457$	−39.4634	−1.84602	−0.923010	+	0.384776i	$0.874279\pi$
$458$	57.5216	2.68781
$459$	2.27672	0.106268
$460$	1.78857	0.0833923
$461$	2.45811	0.114486	0.0572429	−	0.998360i	$-0.481769\pi$
$461$	2.45811	0.114486	0.0572429	+	0.998360i	$0.481769\pi$
$462$	−3.91193	−0.181999
$463$	−27.1080	−1.25982	−0.629908	−	0.776670i	$-0.716907\pi$
$463$	−27.1080	−1.25982	−0.629908	+	0.776670i	$0.716907\pi$
$464$	−6.08845	−0.282649
$465$	−14.4425	−0.669757
$466$	41.7583	1.93442
$467$	−23.6135	−1.09270	−0.546352	−	0.837555i	$-0.683984\pi$
$467$	−23.6135	−1.09270	−0.546352	+	0.837555i	$0.683984\pi$
$468$	39.9755	1.84787
$469$	−0.168136	−0.00776380
$470$	11.6149	0.535755
$471$	−9.04201	−0.416634
$472$	−30.2336	−1.39162
$473$	−5.01815	−0.230735
$474$	20.6572	0.948819
$475$	−6.81034	−0.312480
$476$	−1.71840	−0.0787628
$477$	−25.9077	−1.18623
$478$	−11.1322	−0.509173
$479$	−0.422380	−0.0192990	−0.00964951	−	0.999953i	$-0.503072\pi$
$479$	−0.422380	−0.0192990	−0.00964951	+	0.999953i	$0.503072\pi$
$480$	−0.587291	−0.0268060
$481$	20.7891	0.947902
$482$	−33.1154	−1.50837
$483$	−0.372638	−0.0169556
$484$	−4.06419	−0.184736
$485$	8.07988	0.366889
$486$	−50.5521	−2.29309
$487$	−10.0619	−0.455950	−0.227975	−	0.973667i	$-0.573210\pi$
$487$	−10.0619	−0.455950	−0.227975	+	0.973667i	$0.573210\pi$
$488$	71.1339	3.22008
$489$	−8.28083	−0.374472
$490$	−10.2177	−0.461589
$491$	−8.53990	−0.385400	−0.192700	−	0.981258i	$-0.561724\pi$
$491$	−8.53990	−0.385400	−0.192700	+	0.981258i	$0.561724\pi$
$492$	−10.7528	−0.484772
$493$	−2.83703	−0.127773
$494$	−14.2026	−0.639006
$495$	−4.74477	−0.213262
$496$	−43.7888	−1.96617
$497$	3.41091	0.153000
$498$	59.5541	2.66868
$499$	7.51029	0.336207	0.168103	−	0.985769i	$-0.446236\pi$
$499$	7.51029	0.336207	0.168103	+	0.985769i	$0.446236\pi$
$500$	23.2987	1.04195
$501$	−54.2001	−2.42148
$502$	−45.1073	−2.01324
$503$	3.27329	0.145949	0.0729743	−	0.997334i	$-0.476751\pi$
$503$	3.27329	0.145949	0.0729743	+	0.997334i	$0.476751\pi$
$504$	2.70268	0.120387
$505$	−7.89535	−0.351339
$506$	5.75239	0.255725
$507$	−5.90369	−0.262192
$508$	1.80747	0.0801935
$509$	−43.1416	−1.91222	−0.956108	−	0.293014i	$-0.905342\pi$
$509$	−43.1416	−1.91222	−0.956108	+	0.293014i	$0.905342\pi$
$510$	−6.83805	−0.302794
$511$	−1.24126	−0.0549102
$512$	40.9320	1.80896
$513$	1.68462	0.0743776
$514$	52.1246	2.29912
$515$	−2.82993	−0.124702
$516$	15.0619	0.663061
$517$	24.9907	1.09909
$518$	2.78205	0.122236
$519$	−31.0090	−1.36115
$520$	11.8188	0.518290
$521$	−35.9078	−1.57315	−0.786574	−	0.617496i	$-0.788147\pi$
$521$	−35.9078	−1.57315	−0.786574	+	0.617496i	$0.788147\pi$
$522$	8.83206	0.386569
$523$	5.48498	0.239841	0.119921	−	0.992783i	$-0.461736\pi$
$523$	5.48498	0.239841	0.119921	+	0.992783i	$0.461736\pi$
$524$	−82.8384	−3.61881
$525$	−2.33714	−0.102001
$526$	−10.7440	−0.468462
$527$	−20.4042	−0.888822
$528$	−31.5746	−1.37411
$529$	−22.4520	−0.976176
$530$	−15.1613	−0.658565
$531$	15.1225	0.656262
$532$	−1.27150	−0.0551266
$533$	4.46352	0.193337
$534$	73.7987	3.19358
$535$	7.28339	0.314888
$536$	−3.93577	−0.169999
$537$	−46.9020	−2.02397
$538$	61.8694	2.66738
$539$	−21.9845	−0.946940
$540$	−2.77482	−0.119409
$541$	−5.72503	−0.246138	−0.123069	−	0.992398i	$-0.539274\pi$
$541$	−5.72503	−0.246138	−0.123069	+	0.992398i	$0.539274\pi$
$542$	64.3418	2.76372
$543$	16.1783	0.694278
$544$	−0.829717	−0.0355738
$545$	−1.61728	−0.0692765
$546$	−4.87398	−0.208587
$547$	12.6489	0.540829	0.270415	−	0.962744i	$-0.412839\pi$
$547$	12.6489	0.540829	0.270415	+	0.962744i	$0.412839\pi$
$548$	50.6511	2.16371
$549$	−35.5804	−1.51853
$550$	36.0783	1.53838
$551$	−2.09921	−0.0894294
$552$	−8.72279	−0.371267
$553$	−0.767677	−0.0326450
$554$	62.4915	2.65501
$555$	7.40615	0.314374
$556$	−20.6276	−0.874804
$557$	27.1468	1.15025	0.575123	−	0.818067i	$-0.304954\pi$
$557$	27.1468	1.15025	0.575123	+	0.818067i	$0.304954\pi$
$558$	63.5212	2.68907
$559$	−6.25225	−0.264442
$560$	0.545358	0.0230456
$561$	−14.7128	−0.621175
$562$	−10.9669	−0.462612
$563$	−29.2236	−1.23163	−0.615815	−	0.787891i	$-0.711173\pi$
$563$	−29.2236	−1.23163	−0.615815	+	0.787891i	$0.711173\pi$
$564$	−75.0090	−3.15845
$565$	8.05566	0.338904
$566$	−22.6897	−0.953720
$567$	2.19337	0.0921128
$568$	79.8433	3.35015
$569$	41.0577	1.72123	0.860615	−	0.509256i	$-0.170079\pi$
$569$	41.0577	1.72123	0.860615	+	0.509256i	$0.170079\pi$
$570$	−5.05970	−0.211927
$571$	8.70211	0.364172	0.182086	−	0.983283i	$-0.441715\pi$
$571$	8.70211	0.364172	0.182086	+	0.983283i	$0.441715\pi$
$572$	50.3344	2.10459
$573$	27.1902	1.13589
$574$	0.597319	0.0249316
$575$	3.43670	0.143320
$576$	−18.7814	−0.782557
$577$	18.9137	0.787388	0.393694	−	0.919242i	$-0.371197\pi$
$577$	18.9137	0.787388	0.393694	+	0.919242i	$0.371197\pi$
$578$	32.1265	1.33629
$579$	−31.6373	−1.31480
$580$	3.45772	0.143574
$581$	−2.21319	−0.0918185
$582$	−77.9980	−3.23312
$583$	−32.6212	−1.35103
$584$	−29.0557	−1.20233
$585$	−5.91164	−0.244416
$586$	32.3639	1.33694
$587$	−26.1559	−1.07957	−0.539784	−	0.841803i	$-0.681494\pi$
$587$	−26.1559	−1.07957	−0.539784	+	0.841803i	$0.681494\pi$
$588$	65.9860	2.72122
$589$	−15.0978	−0.622092
$590$	8.84977	0.364339
$591$	−36.8875	−1.51735
$592$	22.4549	0.922892
$593$	40.9756	1.68267	0.841333	−	0.540517i	$-0.181771\pi$
$593$	40.9756	1.68267	0.841333	+	0.540517i	$0.181771\pi$
$594$	−8.92437	−0.366171
$595$	0.254120	0.0104179
$596$	30.6088	1.25379
$597$	11.8659	0.485638
$598$	7.16706	0.293083
$599$	−0.774229	−0.0316341	−0.0158171	−	0.999875i	$-0.505035\pi$
$599$	−0.774229	−0.0316341	−0.0158171	+	0.999875i	$0.505035\pi$
$600$	−54.7083	−2.23346
$601$	−10.7986	−0.440482	−0.220241	−	0.975445i	$-0.570684\pi$
$601$	−10.7986	−0.440482	−0.220241	+	0.975445i	$0.570684\pi$
$602$	−0.836690	−0.0341010
$603$	1.96863	0.0801686
$604$	−13.7856	−0.560929
$605$	0.601019	0.0244349
$606$	76.2166	3.09609
$607$	−11.1441	−0.452327	−0.226163	−	0.974089i	$-0.572618\pi$
$607$	−11.1441	−0.452327	−0.226163	+	0.974089i	$0.572618\pi$
$608$	−0.613935	−0.0248983
$609$	−0.720397	−0.0291920
$610$	−20.8218	−0.843051
$611$	31.1366	1.25965
$612$	20.1200	0.813301
$613$	36.5139	1.47478	0.737392	−	0.675465i	$-0.236057\pi$
$613$	36.5139	1.47478	0.737392	+	0.675465i	$0.236057\pi$
$614$	−35.0282	−1.41362
$615$	1.59014	0.0641205
$616$	3.40303	0.137112
$617$	32.1836	1.29566	0.647832	−	0.761783i	$-0.275676\pi$
$617$	32.1836	1.29566	0.647832	+	0.761783i	$0.275676\pi$
$618$	27.3183	1.09891
$619$	−38.2353	−1.53681	−0.768403	−	0.639966i	$-0.778948\pi$
$619$	−38.2353	−1.53681	−0.768403	+	0.639966i	$0.778948\pi$
$620$	24.8683	0.998735
$621$	−0.850106	−0.0341136
$622$	−73.2899	−2.93866
$623$	−2.74255	−0.109878
$624$	−39.3397	−1.57485
$625$	19.7680	0.790720
$626$	52.8213	2.11116
$627$	−10.8865	−0.434764
$628$	15.5692	0.621280
$629$	10.4633	0.417200
$630$	−0.791110	−0.0315186
$631$	50.0320	1.99174	0.995871	−	0.0907842i	$-0.0289374\pi$
$631$	50.0320	1.99174	0.995871	+	0.0907842i	$0.0289374\pi$
$632$	−17.9700	−0.714807
$633$	−55.4683	−2.20467
$634$	76.8272	3.05120
$635$	−0.267291	−0.0106071
$636$	97.9117	3.88245
$637$	−27.3911	−1.08528
$638$	11.1207	0.440274
$639$	−39.9367	−1.57987
$640$	−11.4913	−0.454233
$641$	30.1528	1.19096	0.595482	−	0.803369i	$-0.296961\pi$
$641$	30.1528	1.19096	0.595482	+	0.803369i	$0.296961\pi$
$642$	−70.3092	−2.77488
$643$	31.6371	1.24764	0.623822	−	0.781566i	$-0.285579\pi$
$643$	31.6371	1.24764	0.623822	+	0.781566i	$0.285579\pi$
$644$	0.641637	0.0252840
$645$	−2.22737	−0.0877026
$646$	−7.14828	−0.281245
$647$	−6.84109	−0.268951	−0.134475	−	0.990917i	$-0.542935\pi$
$647$	−6.84109	−0.268951	−0.134475	+	0.990917i	$0.542935\pi$
$648$	51.3429	2.01694
$649$	19.0412	0.747434
$650$	44.9509	1.76312
$651$	−5.18117	−0.203066
$652$	14.2586	0.558409
$653$	6.26116	0.245018	0.122509	−	0.992467i	$-0.460906\pi$
$653$	6.26116	0.245018	0.122509	+	0.992467i	$0.460906\pi$
$654$	15.6121	0.610483
$655$	12.2503	0.478658
$656$	4.82118	0.188236
$657$	14.5333	0.567000
$658$	4.16677	0.162438
$659$	−13.7398	−0.535229	−0.267614	−	0.963526i	$-0.586235\pi$
$659$	−13.7398	−0.535229	−0.267614	+	0.963526i	$0.586235\pi$
$660$	17.9317	0.697990
$661$	−33.0297	−1.28471	−0.642354	−	0.766408i	$-0.722042\pi$
$661$	−33.0297	−1.28471	−0.642354	+	0.766408i	$0.722042\pi$
$662$	−77.0186	−2.99341
$663$	−18.3311	−0.711921
$664$	−51.8068	−2.01049
$665$	0.188032	0.00729155
$666$	−32.5737	−1.26221
$667$	1.05932	0.0410172
$668$	93.3261	3.61089
$669$	28.9314	1.11855
$670$	1.15205	0.0445075
$671$	−44.8004	−1.72950
$672$	−0.210687	−0.00812743
$673$	−0.972372	−0.0374822	−0.0187411	−	0.999824i	$-0.505966\pi$
$673$	−0.972372	−0.0374822	−0.0187411	+	0.999824i	$0.505966\pi$
$674$	22.1494	0.853163
$675$	−5.33177	−0.205220
$676$	10.1654	0.390978
$677$	−5.54860	−0.213250	−0.106625	−	0.994299i	$-0.534004\pi$
$677$	−5.54860	−0.213250	−0.106625	+	0.994299i	$0.534004\pi$
$678$	−77.7641	−2.98651
$679$	2.89861	0.111238
$680$	5.94850	0.228115
$681$	−7.92976	−0.303869
$682$	79.9814	3.06265
$683$	−24.5280	−0.938536	−0.469268	−	0.883056i	$-0.655482\pi$
$683$	−24.5280	−0.938536	−0.469268	+	0.883056i	$0.655482\pi$
$684$	14.8874	0.569235
$685$	−7.49037	−0.286192
$686$	−7.35533	−0.280828
$687$	54.9342	2.09587
$688$	−6.75323	−0.257465
$689$	−40.6436	−1.54840
$690$	2.55327	0.0972014
$691$	−40.7951	−1.55192	−0.775960	−	0.630782i	$-0.782734\pi$
$691$	−40.7951	−1.55192	−0.775960	+	0.630782i	$0.782734\pi$
$692$	53.3938	2.02973
$693$	−1.70216	−0.0646597
$694$	49.1485	1.86565
$695$	3.05044	0.115710
$696$	−16.8632	−0.639199
$697$	2.24652	0.0850931
$698$	4.04880	0.153249
$699$	39.8800	1.50840
$700$	4.02427	0.152103
$701$	45.1305	1.70455	0.852277	−	0.523091i	$-0.175221\pi$
$701$	45.1305	1.70455	0.852277	+	0.523091i	$0.175221\pi$
$702$	−11.1191	−0.419664
$703$	7.74215	0.292001
$704$	−23.6482	−0.891275
$705$	11.0925	0.417766
$706$	15.8247	0.595572
$707$	−2.83241	−0.106524
$708$	−57.1519	−2.14790
$709$	−48.0351	−1.80399	−0.901997	−	0.431741i	$-0.857899\pi$
$709$	−48.0351	−1.80399	−0.901997	+	0.431741i	$0.857899\pi$
$710$	−23.3711	−0.877104
$711$	8.98838	0.337090
$712$	−64.1983	−2.40593
$713$	7.61877	0.285325
$714$	−2.45311	−0.0918053
$715$	−7.44353	−0.278372
$716$	80.7596	3.01813
$717$	−10.6314	−0.397038
$718$	70.6852	2.63795
$719$	43.6802	1.62900	0.814498	−	0.580166i	$-0.197013\pi$
$719$	43.6802	1.62900	0.814498	+	0.580166i	$0.197013\pi$
$720$	−6.38534	−0.237967
$721$	−1.01522	−0.0378088
$722$	41.4141	1.54127
$723$	−31.6259	−1.17618
$724$	−27.8571	−1.03530
$725$	6.64395	0.246750
$726$	−5.80185	−0.215327
$727$	36.3971	1.34989	0.674946	−	0.737867i	$-0.264167\pi$
$727$	36.3971	1.34989	0.674946	+	0.737867i	$0.264167\pi$
$728$	4.23993	0.157142
$729$	−17.5933	−0.651605
$730$	8.50498	0.314784
$731$	−3.14680	−0.116389
$732$	134.467	4.97005
$733$	−15.8550	−0.585617	−0.292808	−	0.956171i	$-0.594590\pi$
$733$	−15.8550	−0.585617	−0.292808	+	0.956171i	$0.594590\pi$
$734$	35.0158	1.29246
$735$	−9.75812	−0.359934
$736$	0.309809	0.0114197
$737$	2.47876	0.0913062
$738$	−6.99373	−0.257443
$739$	12.8125	0.471317	0.235659	−	0.971836i	$-0.424275\pi$
$739$	12.8125	0.471317	0.235659	+	0.971836i	$0.424275\pi$
$740$	−12.7525	−0.468791
$741$	−13.5638	−0.498278
$742$	−5.43902	−0.199673
$743$	28.9592	1.06241	0.531204	−	0.847244i	$-0.321740\pi$
$743$	28.9592	1.06241	0.531204	+	0.847244i	$0.321740\pi$
$744$	−121.282	−4.44642
$745$	−4.52648	−0.165837
$746$	−82.3332	−3.01443
$747$	25.9132	0.948113
$748$	25.3337	0.926291
$749$	2.61287	0.0954723
$750$	33.2601	1.21449
$751$	−25.1550	−0.917920	−0.458960	−	0.888457i	$-0.651778\pi$
$751$	−25.1550	−0.917920	−0.458960	+	0.888457i	$0.651778\pi$
$752$	33.6316	1.22642
$753$	−43.0783	−1.56986
$754$	13.8556	0.504592
$755$	2.03864	0.0741937
$756$	−0.995449	−0.0362041
$757$	−11.5749	−0.420698	−0.210349	−	0.977626i	$-0.567460\pi$
$757$	−11.5749	−0.420698	−0.210349	+	0.977626i	$0.567460\pi$
$758$	54.6438	1.98475
$759$	5.49364	0.199407
$760$	4.40149	0.159659
$761$	−48.1812	−1.74657	−0.873284	−	0.487212i	$-0.838014\pi$
$761$	−48.1812	−1.74657	−0.873284	+	0.487212i	$0.838014\pi$
$762$	2.58026	0.0934729
$763$	−0.580188	−0.0210042
$764$	−46.8182	−1.69382
$765$	−2.97537	−0.107575
$766$	−58.7171	−2.12153
$767$	23.7240	0.856624
$768$	75.8096	2.73554
$769$	−19.3904	−0.699236	−0.349618	−	0.936892i	$-0.613689\pi$
$769$	−19.3904	−0.699236	−0.349618	+	0.936892i	$0.613689\pi$
$770$	−0.996111	−0.0358974
$771$	49.7800	1.79278
$772$	54.4756	1.96062
$773$	19.7893	0.711772	0.355886	−	0.934529i	$-0.384179\pi$
$773$	19.7893	0.711772	0.355886	+	0.934529i	$0.384179\pi$
$774$	9.79642	0.352125
$775$	47.7840	1.71645
$776$	67.8513	2.43572
$777$	2.65691	0.0953162
$778$	89.4691	3.20762
$779$	1.66228	0.0595572
$780$	22.3416	0.799957
$781$	−50.2855	−1.79936
$782$	3.60723	0.128994
$783$	−1.64346	−0.0587324
$784$	−29.5859	−1.05664
$785$	−2.30240	−0.0821763
$786$	−118.256	−4.21806
$787$	−2.72822	−0.0972505	−0.0486253	−	0.998817i	$-0.515484\pi$
$787$	−2.72822	−0.0972505	−0.0486253	+	0.998817i	$0.515484\pi$
$788$	63.5159	2.26266
$789$	−10.2608	−0.365293
$790$	5.26004	0.187144
$791$	2.88992	0.102754
$792$	−39.8445	−1.41581
$793$	−55.8180	−1.98216
$794$	47.4171	1.68277
$795$	−14.4793	−0.513529
$796$	−20.4316	−0.724179
$797$	−19.5032	−0.690838	−0.345419	−	0.938449i	$-0.612263\pi$
$797$	−19.5032	−0.690838	−0.345419	+	0.938449i	$0.612263\pi$
$798$	−1.81514	−0.0642551
$799$	15.6713	0.554410
$800$	1.94309	0.0686985
$801$	32.1113	1.13460
$802$	38.7026	1.36664
$803$	18.2994	0.645771
$804$	−7.43993	−0.262386
$805$	−0.0948863	−0.00334430
$806$	99.6511	3.51006
$807$	59.0865	2.07994
$808$	−66.3017	−2.33249
$809$	8.81818	0.310031	0.155015	−	0.987912i	$-0.450457\pi$
$809$	8.81818	0.310031	0.155015	+	0.987912i	$0.450457\pi$
$810$	−15.0287	−0.528055
$811$	45.8992	1.61174	0.805870	−	0.592093i	$-0.201698\pi$
$811$	45.8992	1.61174	0.805870	+	0.592093i	$0.201698\pi$
$812$	1.24044	0.0435308
$813$	61.4477	2.15506
$814$	−41.0146	−1.43756
$815$	−2.10858	−0.0738604
$816$	−19.7999	−0.693137
$817$	−2.32842	−0.0814611
$818$	−90.7007	−3.17127
$819$	−2.12077	−0.0741056
$820$	−2.73802	−0.0956159
$821$	6.92463	0.241671	0.120836	−	0.992673i	$-0.461443\pi$
$821$	6.92463	0.241671	0.120836	+	0.992673i	$0.461443\pi$
$822$	72.3071	2.52200
$823$	13.4758	0.469738	0.234869	−	0.972027i	$-0.424534\pi$
$823$	13.4758	0.469738	0.234869	+	0.972027i	$0.424534\pi$
$824$	−23.7645	−0.827877
$825$	34.4554	1.19958
$826$	3.17480	0.110465
$827$	27.0372	0.940175	0.470088	−	0.882620i	$-0.344222\pi$
$827$	27.0372	0.940175	0.470088	+	0.882620i	$0.344222\pi$
$828$	−7.51263	−0.261082
$829$	−24.1657	−0.839311	−0.419655	−	0.907683i	$-0.637849\pi$
$829$	−24.1657	−0.839311	−0.419655	+	0.907683i	$0.637849\pi$
$830$	15.1645	0.526368
$831$	59.6806	2.07030
$832$	−29.4639	−1.02148
$833$	−13.7861	−0.477662
$834$	−29.4470	−1.01967
$835$	−13.8012	−0.477610
$836$	18.7452	0.648317
$837$	−11.8199	−0.408556
$838$	−55.7290	−1.92513
$839$	−45.5490	−1.57253	−0.786263	−	0.617892i	$-0.787987\pi$
$839$	−45.5490	−1.57253	−0.786263	+	0.617892i	$0.787987\pi$
$840$	1.51048	0.0521165
$841$	−26.9521	−0.929382
$842$	−73.1526	−2.52100
$843$	−10.4736	−0.360731
$844$	95.5097	3.28758
$845$	−1.50328	−0.0517144
$846$	−48.7868	−1.67733
$847$	0.215612	0.00740852
$848$	−43.9003	−1.50754
$849$	−21.6691	−0.743682
$850$	22.6241	0.776001
$851$	−3.90691	−0.133927
$852$	150.931	5.17081
$853$	−25.4615	−0.871786	−0.435893	−	0.899998i	$-0.643567\pi$
$853$	−25.4615	−0.871786	−0.435893	+	0.899998i	$0.643567\pi$
$854$	−7.46970	−0.255608
$855$	−2.20157	−0.0752923
$856$	61.1627	2.09050
$857$	−44.7593	−1.52895	−0.764474	−	0.644655i	$-0.777001\pi$
$857$	−44.7593	−1.52895	−0.764474	+	0.644655i	$0.777001\pi$
$858$	71.8550	2.45309
$859$	−20.2182	−0.689836	−0.344918	−	0.938633i	$-0.612093\pi$
$859$	−20.2182	−0.689836	−0.344918	+	0.938633i	$0.612093\pi$
$860$	3.83526	0.130781
$861$	0.570452	0.0194409
$862$	67.0233	2.28282
$863$	−55.4911	−1.88894	−0.944470	−	0.328599i	$-0.893424\pi$
$863$	−55.4911	−1.88894	−0.944470	+	0.328599i	$0.893424\pi$
$864$	−0.480645	−0.0163519
$865$	−7.89596	−0.268471
$866$	96.2006	3.26903
$867$	30.6815	1.04200
$868$	8.92135	0.302810
$869$	11.3175	0.383921
$870$	4.93608	0.167349
$871$	3.08835	0.104645
$872$	−13.5812	−0.459917
$873$	−33.9385	−1.14864
$874$	2.66911	0.0902839
$875$	−1.23603	−0.0417855
$876$	−54.9252	−1.85575
$877$	29.9125	1.01007	0.505037	−	0.863098i	$-0.331479\pi$
$877$	29.9125	1.01007	0.505037	+	0.863098i	$0.331479\pi$
$878$	18.5690	0.626674
$879$	30.9081	1.04251
$880$	−8.03997	−0.271027
$881$	7.18051	0.241918	0.120959	−	0.992658i	$-0.461403\pi$
$881$	7.18051	0.241918	0.120959	+	0.992658i	$0.461403\pi$
$882$	42.9181	1.44513
$883$	−10.5541	−0.355175	−0.177587	−	0.984105i	$-0.556829\pi$
$883$	−10.5541	−0.355175	−0.177587	+	0.984105i	$0.556829\pi$
$884$	31.5639	1.06161
$885$	8.45171	0.284101
$886$	−46.3365	−1.55671
$887$	−33.4783	−1.12409	−0.562045	−	0.827107i	$-0.689985\pi$
$887$	−33.4783	−1.12409	−0.562045	+	0.827107i	$0.689985\pi$
$888$	62.1936	2.08708
$889$	−0.0958891	−0.00321602
$890$	18.7917	0.629898
$891$	−32.3359	−1.08329
$892$	−49.8164	−1.66798
$893$	11.5957	0.388035
$894$	43.6957	1.46140
$895$	−11.9429	−0.399205
$896$	−4.12243	−0.137721
$897$	6.84468	0.228537
$898$	−47.2708	−1.57745
$899$	14.7289	0.491236
$900$	−47.1183	−1.57061
$901$	−20.4562	−0.681495
$902$	−8.80603	−0.293209
$903$	−0.799055	−0.0265909
$904$	67.6479	2.24993
$905$	4.11955	0.136939
$906$	−19.6797	−0.653815
$907$	−8.29936	−0.275576	−0.137788	−	0.990462i	$-0.543999\pi$
$907$	−8.29936	−0.275576	−0.137788	+	0.990462i	$0.543999\pi$
$908$	13.6541	0.453126
$909$	33.1634	1.09996
$910$	−1.24108	−0.0411415
$911$	56.0414	1.85673	0.928367	−	0.371665i	$-0.121213\pi$
$911$	56.0414	1.85673	0.928367	+	0.371665i	$0.121213\pi$
$912$	−14.6506	−0.485131
$913$	32.6281	1.07983
$914$	97.0039	3.20860
$915$	−19.8852	−0.657386
$916$	−94.5900	−3.12534
$917$	4.39471	0.145126
$918$	−5.59633	−0.184706
$919$	−9.70724	−0.320212	−0.160106	−	0.987100i	$-0.551184\pi$
$919$	−9.70724	−0.320212	−0.160106	+	0.987100i	$0.551184\pi$
$920$	−2.22112	−0.0732282
$921$	−33.4526	−1.10230
$922$	−6.04222	−0.198990
$923$	−62.6521	−2.06222
$924$	6.43289	0.211626
$925$	−24.5037	−0.805676
$926$	66.6334	2.18971
$927$	11.8868	0.390412
$928$	0.598935	0.0196610
$929$	−7.10545	−0.233122	−0.116561	−	0.993184i	$-0.537187\pi$
$929$	−7.10545	−0.233122	−0.116561	+	0.993184i	$0.537187\pi$
$930$	35.5008	1.16412
$931$	−10.2008	−0.334318
$932$	−68.6685	−2.24931
$933$	−69.9933	−2.29148
$934$	58.0438	1.89925
$935$	−3.74638	−0.122520
$936$	−49.6434	−1.62264
$937$	−4.73888	−0.154812	−0.0774062	−	0.997000i	$-0.524664\pi$
$937$	−4.73888	−0.154812	−0.0774062	+	0.997000i	$0.524664\pi$
$938$	0.413291	0.0134944
$939$	50.4454	1.64622
$940$	−19.0999	−0.622969
$941$	−5.71778	−0.186394	−0.0931972	−	0.995648i	$-0.529709\pi$
$941$	−5.71778	−0.186394	−0.0931972	+	0.995648i	$0.529709\pi$
$942$	22.2259	0.724159
$943$	−0.838833	−0.0273162
$944$	25.6250	0.834022
$945$	0.147209	0.00478869
$946$	12.3350	0.401044
$947$	−37.8612	−1.23032	−0.615162	−	0.788401i	$-0.710909\pi$
$947$	−37.8612	−1.23032	−0.615162	+	0.788401i	$0.710909\pi$
$948$	−33.9693	−1.10327
$949$	22.7997	0.740110
$950$	16.7403	0.543128
$951$	73.3714	2.37923
$952$	2.13399	0.0691629
$953$	32.1270	1.04069	0.520347	−	0.853955i	$-0.325803\pi$
$953$	32.1270	1.04069	0.520347	+	0.853955i	$0.325803\pi$
$954$	63.6830	2.06181
$955$	6.92355	0.224041
$956$	18.3060	0.592059
$957$	10.6205	0.343312
$958$	1.03824	0.0335440
$959$	−2.68712	−0.0867717
$960$	−10.4966	−0.338775
$961$	74.9318	2.41715
$962$	−51.1012	−1.64757
$963$	−30.5929	−0.985842
$964$	54.4559	1.75391
$965$	−8.05594	−0.259330
$966$	0.915971	0.0294709
$967$	38.0417	1.22334	0.611670	−	0.791113i	$-0.290498\pi$
$967$	38.0417	1.22334	0.611670	+	0.791113i	$0.290498\pi$
$968$	5.04710	0.162220
$969$	−6.82674	−0.219307
$970$	−19.8609	−0.637697
$971$	−15.2091	−0.488083	−0.244042	−	0.969765i	$-0.578473\pi$
$971$	−15.2091	−0.488083	−0.244042	+	0.969765i	$0.578473\pi$
$972$	83.1293	2.66637
$973$	1.09433	0.0350825
$974$	24.7330	0.792496
$975$	42.9290	1.37483
$976$	−60.2906	−1.92986
$977$	45.7713	1.46435	0.732177	−	0.681115i	$-0.238505\pi$
$977$	45.7713	1.46435	0.732177	+	0.681115i	$0.238505\pi$
$978$	20.3549	0.650877
$979$	40.4323	1.29222
$980$	16.8023	0.536730
$981$	6.79315	0.216889
$982$	20.9917	0.669872
$983$	23.7223	0.756624	0.378312	−	0.925678i	$-0.376505\pi$
$983$	23.7223	0.756624	0.378312	+	0.925678i	$0.376505\pi$
$984$	13.3533	0.425686
$985$	−9.39282	−0.299280
$986$	6.97363	0.222086
$987$	3.97935	0.126664
$988$	23.3552	0.743027
$989$	1.17499	0.0373625
$990$	11.6630	0.370674
$991$	30.4711	0.967947	0.483974	−	0.875083i	$-0.339193\pi$
$991$	30.4711	0.967947	0.483974	+	0.875083i	$0.339193\pi$
$992$	4.30761	0.136767
$993$	−73.5543	−2.33417
$994$	−8.38426	−0.265932
$995$	3.02146	0.0957867
$996$	−97.9324	−3.10311
$997$	−11.8465	−0.375182	−0.187591	−	0.982247i	$-0.560068\pi$
$997$	−11.8465	−0.375182	−0.187591	+	0.982247i	$0.560068\pi$
$998$	−18.4608	−0.584367
$999$	6.06127	0.191770

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4019.2.a.a.1.12	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4019.2.a.a.1.12	✓	149	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:	\( N \)	\(=\)	\( 4019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.45807 q^{2} -2.34751 q^{3} +4.04212 q^{4} -0.597755 q^{5} +5.77034 q^{6} -0.214441 q^{7} -5.01969 q^{8} +2.51079 q^{9} +O(q^{10})\)	\(q-2.45807 q^{2} -2.34751 q^{3} +4.04212 q^{4} -0.597755 q^{5} +5.77034 q^{6} -0.214441 q^{7} -5.01969 q^{8} +2.51079 q^{9} +1.46933 q^{10} +3.16141 q^{11} -9.48891 q^{12} +3.93889 q^{13} +0.527112 q^{14} +1.40324 q^{15} +4.25451 q^{16} +1.98247 q^{17} -6.17171 q^{18} +1.46690 q^{19} -2.41620 q^{20} +0.503402 q^{21} -7.77099 q^{22} -0.740239 q^{23} +11.7838 q^{24} -4.64269 q^{25} -9.68209 q^{26} +1.14842 q^{27} -0.866797 q^{28} -1.43106 q^{29} -3.44925 q^{30} -10.2923 q^{31} -0.418526 q^{32} -7.42144 q^{33} -4.87306 q^{34} +0.128183 q^{35} +10.1489 q^{36} +5.27791 q^{37} -3.60574 q^{38} -9.24658 q^{39} +3.00055 q^{40} +1.13319 q^{41} -1.23740 q^{42} -1.58731 q^{43} +12.7788 q^{44} -1.50084 q^{45} +1.81956 q^{46} +7.90491 q^{47} -9.98750 q^{48} -6.95402 q^{49} +11.4121 q^{50} -4.65387 q^{51} +15.9215 q^{52} -10.3185 q^{53} -2.82290 q^{54} -1.88975 q^{55} +1.07643 q^{56} -3.44355 q^{57} +3.51764 q^{58} +6.02301 q^{59} +5.67205 q^{60} -14.1710 q^{61} +25.2993 q^{62} -0.538417 q^{63} -7.48026 q^{64} -2.35449 q^{65} +18.2424 q^{66} +0.784066 q^{67} +8.01340 q^{68} +1.73772 q^{69} -0.315084 q^{70} -15.9060 q^{71} -12.6034 q^{72} +5.78835 q^{73} -12.9735 q^{74} +10.8987 q^{75} +5.92937 q^{76} -0.677937 q^{77} +22.7288 q^{78} +3.57990 q^{79} -2.54316 q^{80} -10.2283 q^{81} -2.78547 q^{82} +10.3207 q^{83} +2.03481 q^{84} -1.18503 q^{85} +3.90173 q^{86} +3.35942 q^{87} -15.8693 q^{88} +12.7893 q^{89} +3.68917 q^{90} -0.844660 q^{91} -2.99214 q^{92} +24.1613 q^{93} -19.4309 q^{94} -0.876845 q^{95} +0.982494 q^{96} -13.5170 q^{97} +17.0935 q^{98} +7.93765 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9}+O(q^{10}) \) 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9	\( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9} - 58 q^{10} - 33 q^{11} - 33 q^{12} - 107 q^{13} - 28 q^{14} - 24 q^{15} + 74 q^{16} - 39 q^{17} - 33 q^{18} - 93 q^{19} - 63 q^{20} - 113 q^{21} - 38 q^{22} - 11 q^{23} - 130 q^{24} + 85 q^{25} - 33 q^{26} - 30 q^{27} - 94 q^{28} - 85 q^{29} - 16 q^{30} - 129 q^{31} - 35 q^{32} - 64 q^{33} - 78 q^{34} - 27 q^{35} + 79 q^{36} - 135 q^{37} - 11 q^{38} - 73 q^{39} - 146 q^{40} - 101 q^{41} + 4 q^{42} - 55 q^{43} - 82 q^{44} - 168 q^{45} - 113 q^{46} - 40 q^{47} - 65 q^{48} + 27 q^{49} - 5 q^{50} - 49 q^{51} - 177 q^{52} - 32 q^{53} - 155 q^{54} - 128 q^{55} - 44 q^{56} - 47 q^{57} - 46 q^{58} - 53 q^{59} - 11 q^{60} - 347 q^{61} - 11 q^{62} - 73 q^{63} + q^{64} - 31 q^{65} - 37 q^{66} - 40 q^{67} - 80 q^{68} - 175 q^{69} - 61 q^{70} - 31 q^{71} - 68 q^{72} - 193 q^{73} - 33 q^{74} - 56 q^{75} - 248 q^{76} - 84 q^{77} + 40 q^{78} - 111 q^{79} - 54 q^{80} + 49 q^{81} - 74 q^{82} - 24 q^{83} - 159 q^{84} - 258 q^{85} - q^{86} - 66 q^{87} - 97 q^{88} - 76 q^{89} - 75 q^{90} - 134 q^{91} + 31 q^{92} - 97 q^{93} - 111 q^{94} - 14 q^{95} - 216 q^{96} - 140 q^{97} - 13 q^{98} - 116 q^{99}+O(q^{100}) \) 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9 - 58 * q^10 - 33 * q^11 - 33 * q^12 - 107 * q^13 - 28 * q^14 - 24 * q^15 + 74 * q^16 - 39 * q^17 - 33 * q^18 - 93 * q^19 - 63 * q^20 - 113 * q^21 - 38 * q^22 - 11 * q^23 - 130 * q^24 + 85 * q^25 - 33 * q^26 - 30 * q^27 - 94 * q^28 - 85 * q^29 - 16 * q^30 - 129 * q^31 - 35 * q^32 - 64 * q^33 - 78 * q^34 - 27 * q^35 + 79 * q^36 - 135 * q^37 - 11 * q^38 - 73 * q^39 - 146 * q^40 - 101 * q^41 + 4 * q^42 - 55 * q^43 - 82 * q^44 - 168 * q^45 - 113 * q^46 - 40 * q^47 - 65 * q^48 + 27 * q^49 - 5 * q^50 - 49 * q^51 - 177 * q^52 - 32 * q^53 - 155 * q^54 - 128 * q^55 - 44 * q^56 - 47 * q^57 - 46 * q^58 - 53 * q^59 - 11 * q^60 - 347 * q^61 - 11 * q^62 - 73 * q^63 + q^64 - 31 * q^65 - 37 * q^66 - 40 * q^67 - 80 * q^68 - 175 * q^69 - 61 * q^70 - 31 * q^71 - 68 * q^72 - 193 * q^73 - 33 * q^74 - 56 * q^75 - 248 * q^76 - 84 * q^77 + 40 * q^78 - 111 * q^79 - 54 * q^80 + 49 * q^81 - 74 * q^82 - 24 * q^83 - 159 * q^84 - 258 * q^85 - q^86 - 66 * q^87 - 97 * q^88 - 76 * q^89 - 75 * q^90 - 134 * q^91 + 31 * q^92 - 97 * q^93 - 111 * q^94 - 14 * q^95 - 216 * q^96 - 140 * q^97 - 13 * q^98 - 116 * q^99

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