LMFDB - Embedded newform 4013.2.a.b.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4013,2,Mod(1,4013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4013, 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("4013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4013.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:	$32.0439663311$
Analytic rank:	$1$
Dimension:	$157$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	4013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51870 q^{2} -2.55292 q^{3} +4.34385 q^{4} +0.976255 q^{5} +6.43005 q^{6} +1.70978 q^{7} -5.90347 q^{8} +3.51742 q^{9} +O(q^{10})$	\(q-2.51870 q^{2} -2.55292 q^{3} +4.34385 q^{4} +0.976255 q^{5} +6.43005 q^{6} +1.70978 q^{7} -5.90347 q^{8} +3.51742 q^{9} -2.45890 q^{10} +4.17377 q^{11} -11.0895 q^{12} -1.21071 q^{13} -4.30641 q^{14} -2.49230 q^{15} +6.18136 q^{16} -0.279831 q^{17} -8.85932 q^{18} +6.13525 q^{19} +4.24071 q^{20} -4.36493 q^{21} -10.5125 q^{22} +2.44051 q^{23} +15.0711 q^{24} -4.04693 q^{25} +3.04942 q^{26} -1.32092 q^{27} +7.42702 q^{28} +3.74203 q^{29} +6.27737 q^{30} -2.71974 q^{31} -3.76207 q^{32} -10.6553 q^{33} +0.704812 q^{34} +1.66918 q^{35} +15.2791 q^{36} -6.09875 q^{37} -15.4529 q^{38} +3.09085 q^{39} -5.76329 q^{40} -6.40081 q^{41} +10.9939 q^{42} +6.04242 q^{43} +18.1303 q^{44} +3.43390 q^{45} -6.14690 q^{46} -11.7029 q^{47} -15.7805 q^{48} -4.07667 q^{49} +10.1930 q^{50} +0.714388 q^{51} -5.25915 q^{52} +3.51186 q^{53} +3.32701 q^{54} +4.07467 q^{55} -10.0936 q^{56} -15.6628 q^{57} -9.42505 q^{58} -10.0019 q^{59} -10.8262 q^{60} -7.38514 q^{61} +6.85020 q^{62} +6.01399 q^{63} -2.88720 q^{64} -1.18196 q^{65} +26.8375 q^{66} -9.43644 q^{67} -1.21555 q^{68} -6.23042 q^{69} -4.20416 q^{70} +1.52496 q^{71} -20.7650 q^{72} -7.27110 q^{73} +15.3609 q^{74} +10.3315 q^{75} +26.6507 q^{76} +7.13621 q^{77} -7.78493 q^{78} -7.03448 q^{79} +6.03459 q^{80} -7.18004 q^{81} +16.1217 q^{82} -11.2907 q^{83} -18.9606 q^{84} -0.273187 q^{85} -15.2190 q^{86} -9.55311 q^{87} -24.6397 q^{88} +13.8931 q^{89} -8.64896 q^{90} -2.07004 q^{91} +10.6012 q^{92} +6.94328 q^{93} +29.4762 q^{94} +5.98957 q^{95} +9.60427 q^{96} +5.32653 q^{97} +10.2679 q^{98} +14.6809 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 157 q - 15 q^{2} - 51 q^{3} + 137 q^{4} - 13 q^{5} - 15 q^{6} - 49 q^{7} - 42 q^{8} + 144 q^{9}+O(q^{10}) $ 157 * q - 15 * q^2 - 51 * q^3 + 137 * q^4 - 13 * q^5 - 15 * q^6 - 49 * q^7 - 42 * q^8 + 144 * q^9	\( 157 q - 15 q^{2} - 51 q^{3} + 137 q^{4} - 13 q^{5} - 15 q^{6} - 49 q^{7} - 42 q^{8} + 144 q^{9} - 61 q^{10} - 27 q^{11} - 93 q^{12} - 97 q^{13} - 12 q^{14} - 36 q^{15} + 105 q^{16} - 45 q^{17} - 68 q^{18} - 128 q^{19} - 30 q^{20} - 26 q^{21} - 68 q^{22} - 41 q^{23} - 40 q^{24} + 102 q^{25} - 5 q^{26} - 189 q^{27} - 115 q^{28} - 26 q^{29} - 12 q^{30} - 88 q^{31} - 89 q^{32} - 52 q^{33} - 61 q^{34} - 87 q^{35} + 110 q^{36} - 62 q^{37} - 37 q^{38} - 20 q^{39} - 161 q^{40} - 34 q^{41} - 53 q^{42} - 254 q^{43} - 19 q^{44} - 46 q^{45} - 52 q^{46} - 76 q^{47} - 162 q^{48} + 96 q^{49} - 54 q^{50} - 76 q^{51} - 259 q^{52} - 48 q^{53} - 12 q^{54} - 194 q^{55} - 10 q^{56} - 30 q^{57} - 52 q^{58} - 64 q^{59} - 31 q^{60} - 107 q^{61} - 51 q^{62} - 106 q^{63} + 54 q^{64} - 17 q^{65} - 13 q^{66} - 193 q^{67} - 118 q^{68} - 55 q^{69} - 86 q^{70} - 11 q^{71} - 172 q^{72} - 173 q^{73} - 11 q^{74} - 209 q^{75} - 213 q^{76} - 84 q^{77} - 30 q^{78} - 111 q^{79} - 6 q^{80} + 157 q^{81} - 117 q^{82} - 154 q^{83} - 6 q^{84} - 91 q^{85} + 28 q^{86} - 165 q^{87} - 165 q^{88} - 32 q^{89} - 103 q^{90} - 200 q^{91} - 86 q^{92} - 39 q^{93} - 118 q^{94} - 22 q^{95} - 28 q^{96} - 151 q^{97} - 38 q^{98} - 91 q^{99}+O(q^{100}) \) 157 * q - 15 * q^2 - 51 * q^3 + 137 * q^4 - 13 * q^5 - 15 * q^6 - 49 * q^7 - 42 * q^8 + 144 * q^9 - 61 * q^10 - 27 * q^11 - 93 * q^12 - 97 * q^13 - 12 * q^14 - 36 * q^15 + 105 * q^16 - 45 * q^17 - 68 * q^18 - 128 * q^19 - 30 * q^20 - 26 * q^21 - 68 * q^22 - 41 * q^23 - 40 * q^24 + 102 * q^25 - 5 * q^26 - 189 * q^27 - 115 * q^28 - 26 * q^29 - 12 * q^30 - 88 * q^31 - 89 * q^32 - 52 * q^33 - 61 * q^34 - 87 * q^35 + 110 * q^36 - 62 * q^37 - 37 * q^38 - 20 * q^39 - 161 * q^40 - 34 * q^41 - 53 * q^42 - 254 * q^43 - 19 * q^44 - 46 * q^45 - 52 * q^46 - 76 * q^47 - 162 * q^48 + 96 * q^49 - 54 * q^50 - 76 * q^51 - 259 * q^52 - 48 * q^53 - 12 * q^54 - 194 * q^55 - 10 * q^56 - 30 * q^57 - 52 * q^58 - 64 * q^59 - 31 * q^60 - 107 * q^61 - 51 * q^62 - 106 * q^63 + 54 * q^64 - 17 * q^65 - 13 * q^66 - 193 * q^67 - 118 * q^68 - 55 * q^69 - 86 * q^70 - 11 * q^71 - 172 * q^72 - 173 * q^73 - 11 * q^74 - 209 * q^75 - 213 * q^76 - 84 * q^77 - 30 * q^78 - 111 * q^79 - 6 * q^80 + 157 * q^81 - 117 * q^82 - 154 * q^83 - 6 * q^84 - 91 * q^85 + 28 * q^86 - 165 * q^87 - 165 * q^88 - 32 * q^89 - 103 * q^90 - 200 * q^91 - 86 * q^92 - 39 * q^93 - 118 * q^94 - 22 * q^95 - 28 * q^96 - 151 * q^97 - 38 * q^98 - 91 * 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 $

$2$	−2.51870	−1.78099	−0.890495	−	0.454992i	$-0.849642\pi$
$2$	−2.51870	−1.78099	−0.890495	+	0.454992i	$0.849642\pi$
$3$	−2.55292	−1.47393	−0.736965	−	0.675931i	$-0.763742\pi$
$3$	−2.55292	−1.47393	−0.736965	+	0.675931i	$0.763742\pi$
$4$	4.34385	2.17193
$5$	0.976255	0.436595	0.218297	−	0.975882i	$-0.429950\pi$
$5$	0.976255	0.436595	0.218297	+	0.975882i	$0.429950\pi$
$6$	6.43005	2.62506
$7$	1.70978	0.646235	0.323117	−	0.946359i	$-0.395269\pi$
$7$	1.70978	0.646235	0.323117	+	0.946359i	$0.395269\pi$
$8$	−5.90347	−2.08719
$9$	3.51742	1.17247
$10$	−2.45890	−0.777571
$11$	4.17377	1.25844	0.629220	−	0.777228i	$-0.283375\pi$
$11$	4.17377	1.25844	0.629220	+	0.777228i	$0.283375\pi$
$12$	−11.0895	−3.20127
$13$	−1.21071	−0.335791	−0.167895	−	0.985805i	$-0.553697\pi$
$13$	−1.21071	−0.335791	−0.167895	+	0.985805i	$0.553697\pi$
$14$	−4.30641	−1.15094
$15$	−2.49230	−0.643510
$16$	6.18136	1.54534
$17$	−0.279831	−0.0678691	−0.0339345	−	0.999424i	$-0.510804\pi$
$17$	−0.279831	−0.0678691	−0.0339345	+	0.999424i	$0.510804\pi$
$18$	−8.85932	−2.08816
$19$	6.13525	1.40752	0.703762	−	0.710436i	$-0.251502\pi$
$19$	6.13525	1.40752	0.703762	+	0.710436i	$0.251502\pi$
$20$	4.24071	0.948252
$21$	−4.36493	−0.952505
$22$	−10.5125	−2.24127
$23$	2.44051	0.508881	0.254440	−	0.967088i	$-0.418109\pi$
$23$	2.44051	0.508881	0.254440	+	0.967088i	$0.418109\pi$
$24$	15.0711	3.07638
$25$	−4.04693	−0.809385
$26$	3.04942	0.598040
$27$	−1.32092	−0.254211
$28$	7.42702	1.40357
$29$	3.74203	0.694877	0.347439	−	0.937703i	$-0.387051\pi$
$29$	3.74203	0.694877	0.347439	+	0.937703i	$0.387051\pi$
$30$	6.27737	1.14609
$31$	−2.71974	−0.488479	−0.244240	−	0.969715i	$-0.578538\pi$
$31$	−2.71974	−0.488479	−0.244240	+	0.969715i	$0.578538\pi$
$32$	−3.76207	−0.665046
$33$	−10.6553	−1.85485
$34$	0.704812	0.120874
$35$	1.66918	0.282143
$36$	15.2791	2.54652
$37$	−6.09875	−1.00263	−0.501314	−	0.865265i	$-0.667150\pi$
$37$	−6.09875	−1.00263	−0.501314	+	0.865265i	$0.667150\pi$
$38$	−15.4529	−2.50679
$39$	3.09085	0.494932
$40$	−5.76329	−0.911257
$41$	−6.40081	−0.999639	−0.499819	−	0.866130i	$-0.666600\pi$
$41$	−6.40081	−0.999639	−0.499819	+	0.866130i	$0.666600\pi$
$42$	10.9939	1.69640
$43$	6.04242	0.921460	0.460730	−	0.887540i	$-0.347588\pi$
$43$	6.04242	0.921460	0.460730	+	0.887540i	$0.347588\pi$
$44$	18.1303	2.73324
$45$	3.43390	0.511895
$46$	−6.14690	−0.906311
$47$	−11.7029	−1.70705	−0.853525	−	0.521052i	$-0.825540\pi$
$47$	−11.7029	−1.70705	−0.853525	+	0.521052i	$0.825540\pi$
$48$	−15.7805	−2.27773
$49$	−4.07667	−0.582381
$50$	10.1930	1.44151
$51$	0.714388	0.100034
$52$	−5.25915	−0.729313
$53$	3.51186	0.482392	0.241196	−	0.970476i	$-0.422460\pi$
$53$	3.51186	0.482392	0.241196	+	0.970476i	$0.422460\pi$
$54$	3.32701	0.452748
$55$	4.07467	0.549428
$56$	−10.0936	−1.34882
$57$	−15.6628	−2.07459
$58$	−9.42505	−1.23757
$59$	−10.0019	−1.30213	−0.651066	−	0.759021i	$-0.725678\pi$
$59$	−10.0019	−1.30213	−0.651066	+	0.759021i	$0.725678\pi$
$60$	−10.8262	−1.39766
$61$	−7.38514	−0.945570	−0.472785	−	0.881178i	$-0.656751\pi$
$61$	−7.38514	−0.945570	−0.472785	+	0.881178i	$0.656751\pi$
$62$	6.85020	0.869977
$63$	6.01399	0.757692
$64$	−2.88720	−0.360900
$65$	−1.18196	−0.146604
$66$	26.8375	3.30347
$67$	−9.43644	−1.15285	−0.576423	−	0.817152i	$-0.695552\pi$
$67$	−9.43644	−1.15285	−0.576423	+	0.817152i	$0.695552\pi$
$68$	−1.21555	−0.147407
$69$	−6.23042	−0.750055
$70$	−4.20416	−0.502493
$71$	1.52496	0.180980	0.0904899	−	0.995897i	$-0.471157\pi$
$71$	1.52496	0.180980	0.0904899	+	0.995897i	$0.471157\pi$
$72$	−20.7650	−2.44717
$73$	−7.27110	−0.851018	−0.425509	−	0.904954i	$-0.639905\pi$
$73$	−7.27110	−0.851018	−0.425509	+	0.904954i	$0.639905\pi$
$74$	15.3609	1.78567
$75$	10.3315	1.19298
$76$	26.6507	3.05704
$77$	7.13621	0.813247
$78$	−7.78493	−0.881470
$79$	−7.03448	−0.791441	−0.395720	−	0.918371i	$-0.629505\pi$
$79$	−7.03448	−0.791441	−0.395720	+	0.918371i	$0.629505\pi$
$80$	6.03459	0.674688
$81$	−7.18004	−0.797782
$82$	16.1217	1.78035
$83$	−11.2907	−1.23932	−0.619660	−	0.784870i	$-0.712730\pi$
$83$	−11.2907	−1.23932	−0.619660	+	0.784870i	$0.712730\pi$
$84$	−18.9606	−2.06877
$85$	−0.273187	−0.0296313
$86$	−15.2190	−1.64111
$87$	−9.55311	−1.02420
$88$	−24.6397	−2.62660
$89$	13.8931	1.47266	0.736332	−	0.676620i	$-0.236556\pi$
$89$	13.8931	1.47266	0.736332	+	0.676620i	$0.236556\pi$
$90$	−8.64896	−0.911680
$91$	−2.07004	−0.217000
$92$	10.6012	1.10525
$93$	6.94328	0.719984
$94$	29.4762	3.04024
$95$	5.98957	0.614517
$96$	9.60427	0.980232
$97$	5.32653	0.540827	0.270414	−	0.962744i	$-0.412840\pi$
$97$	5.32653	0.540827	0.270414	+	0.962744i	$0.412840\pi$
$98$	10.2679	1.03721
$99$	14.6809	1.47548
$100$	−17.5793	−1.75793
$101$	−0.652201	−0.0648964	−0.0324482	−	0.999473i	$-0.510330\pi$
$101$	−0.652201	−0.0648964	−0.0324482	+	0.999473i	$0.510330\pi$
$102$	−1.79933	−0.178160
$103$	−18.0137	−1.77494	−0.887471	−	0.460864i	$-0.847539\pi$
$103$	−18.0137	−1.77494	−0.887471	+	0.460864i	$0.847539\pi$
$104$	7.14739	0.700860
$105$	−4.26128	−0.415859
$106$	−8.84534	−0.859135
$107$	−12.3239	−1.19140	−0.595700	−	0.803207i	$-0.703125\pi$
$107$	−12.3239	−1.19140	−0.595700	+	0.803207i	$0.703125\pi$
$108$	−5.73789	−0.552129
$109$	6.67066	0.638934	0.319467	−	0.947597i	$-0.396496\pi$
$109$	6.67066	0.638934	0.319467	+	0.947597i	$0.396496\pi$
$110$	−10.2629	−0.978526
$111$	15.5696	1.47781
$112$	10.5687	0.998653
$113$	−14.3371	−1.34872	−0.674361	−	0.738402i	$-0.735581\pi$
$113$	−14.3371	−1.34872	−0.674361	+	0.738402i	$0.735581\pi$
$114$	39.4500	3.69483
$115$	2.38256	0.222175
$116$	16.2548	1.50922
$117$	−4.25857	−0.393705
$118$	25.1917	2.31909
$119$	−0.478449	−0.0438594
$120$	14.7132	1.34313
$121$	6.42036	0.583669
$122$	18.6010	1.68405
$123$	16.3408	1.47340
$124$	−11.8141	−1.06094
$125$	−8.83211	−0.789968
$126$	−15.1474	−1.34944
$127$	−10.6880	−0.948407	−0.474203	−	0.880415i	$-0.657264\pi$
$127$	−10.6880	−0.948407	−0.474203	+	0.880415i	$0.657264\pi$
$128$	14.7961	1.30781
$129$	−15.4258	−1.35817
$130$	2.97701	0.261101
$131$	14.8696	1.29916	0.649580	−	0.760293i	$-0.274945\pi$
$131$	14.8696	1.29916	0.649580	+	0.760293i	$0.274945\pi$
$132$	−46.2851	−4.02860
$133$	10.4899	0.909591
$134$	23.7676	2.05321
$135$	−1.28956	−0.110987
$136$	1.65198	0.141656
$137$	5.83326	0.498369	0.249184	−	0.968456i	$-0.419838\pi$
$137$	5.83326	0.498369	0.249184	+	0.968456i	$0.419838\pi$
$138$	15.6926	1.33584
$139$	18.0239	1.52876	0.764382	−	0.644763i	$-0.223044\pi$
$139$	18.0239	1.52876	0.764382	+	0.644763i	$0.223044\pi$
$140$	7.25067	0.612793
$141$	29.8767	2.51607
$142$	−3.84093	−0.322323
$143$	−5.05323	−0.422572
$144$	21.7424	1.81187
$145$	3.65318	0.303380
$146$	18.3137	1.51566
$147$	10.4074	0.858389
$148$	−26.4921	−2.17764
$149$	20.8920	1.71154	0.855771	−	0.517355i	$-0.173083\pi$
$149$	20.8920	1.71154	0.855771	+	0.517355i	$0.173083\pi$
$150$	−26.0219	−2.12468
$151$	−6.25912	−0.509360	−0.254680	−	0.967025i	$-0.581970\pi$
$151$	−6.25912	−0.509360	−0.254680	+	0.967025i	$0.581970\pi$
$152$	−36.2193	−2.93777
$153$	−0.984283	−0.0795746
$154$	−17.9740	−1.44839
$155$	−2.65516	−0.213267
$156$	13.4262	1.07496
$157$	−9.76999	−0.779730	−0.389865	−	0.920872i	$-0.627478\pi$
$157$	−9.76999	−0.779730	−0.389865	+	0.920872i	$0.627478\pi$
$158$	17.7177	1.40955
$159$	−8.96552	−0.711012
$160$	−3.67274	−0.290356
$161$	4.17272	0.328856
$162$	18.0844	1.42084
$163$	−0.736362	−0.0576763	−0.0288381	−	0.999584i	$-0.509181\pi$
$163$	−0.736362	−0.0576763	−0.0288381	+	0.999584i	$0.509181\pi$
$164$	−27.8042	−2.17114
$165$	−10.4023	−0.809818
$166$	28.4380	2.20722
$167$	15.6615	1.21192	0.605961	−	0.795494i	$-0.292789\pi$
$167$	15.6615	1.21192	0.605961	+	0.795494i	$0.292789\pi$
$168$	25.7682	1.98806
$169$	−11.5342	−0.887245
$170$	0.688076	0.0527730
$171$	21.5802	1.65028
$172$	26.2474	2.00134
$173$	−18.8153	−1.43050	−0.715249	−	0.698870i	$-0.753687\pi$
$173$	−18.8153	−1.43050	−0.715249	+	0.698870i	$0.753687\pi$
$174$	24.0614	1.82409
$175$	−6.91934	−0.523053
$176$	25.7996	1.94472
$177$	25.5340	1.91925
$178$	−34.9925	−2.62280
$179$	11.6867	0.873505	0.436753	−	0.899582i	$-0.356129\pi$
$179$	11.6867	0.873505	0.436753	+	0.899582i	$0.356129\pi$
$180$	14.9163	1.11180
$181$	−18.4778	−1.37345	−0.686723	−	0.726919i	$-0.740951\pi$
$181$	−18.4778	−1.37345	−0.686723	+	0.726919i	$0.740951\pi$
$182$	5.21382	0.386474
$183$	18.8537	1.39371
$184$	−14.4074	−1.06213
$185$	−5.95394	−0.437742
$186$	−17.4880	−1.28229
$187$	−1.16795	−0.0854091
$188$	−50.8359	−3.70759
$189$	−2.25848	−0.164280
$190$	−15.0859	−1.09445
$191$	18.0667	1.30726	0.653631	−	0.756814i	$-0.273245\pi$
$191$	18.0667	1.30726	0.653631	+	0.756814i	$0.273245\pi$
$192$	7.37080	0.531941
$193$	−10.2747	−0.739591	−0.369796	−	0.929113i	$-0.620572\pi$
$193$	−10.2747	−0.739591	−0.369796	+	0.929113i	$0.620572\pi$
$194$	−13.4159	−0.963208
$195$	3.01746	0.216085
$196$	−17.7084	−1.26489
$197$	13.8174	0.984445	0.492223	−	0.870469i	$-0.336185\pi$
$197$	13.8174	0.984445	0.492223	+	0.870469i	$0.336185\pi$
$198$	−36.9768	−2.62782
$199$	16.0122	1.13507	0.567536	−	0.823349i	$-0.307897\pi$
$199$	16.0122	1.13507	0.567536	+	0.823349i	$0.307897\pi$
$200$	23.8909	1.68934
$201$	24.0905	1.69921
$202$	1.64270	0.115580
$203$	6.39803	0.449054
$204$	3.10320	0.217267
$205$	−6.24882	−0.436437
$206$	45.3711	3.16115
$207$	8.58427	0.596648
$208$	−7.48384	−0.518911
$209$	25.6071	1.77128
$210$	10.7329	0.740640
$211$	−15.9583	−1.09862	−0.549308	−	0.835620i	$-0.685108\pi$
$211$	−15.9583	−1.09862	−0.549308	+	0.835620i	$0.685108\pi$
$212$	15.2550	1.04772
$213$	−3.89311	−0.266752
$214$	31.0403	2.12187
$215$	5.89894	0.402305
$216$	7.79802	0.530588
$217$	−4.65014	−0.315672
$218$	−16.8014	−1.13794
$219$	18.5626	1.25434
$220$	17.6998	1.19332
$221$	0.338795	0.0227898
$222$	−39.2153	−2.63196
$223$	−6.62629	−0.443729	−0.221864	−	0.975078i	$-0.571214\pi$
$223$	−6.62629	−0.443729	−0.221864	+	0.975078i	$0.571214\pi$
$224$	−6.43230	−0.429776
$225$	−14.2347	−0.948981
$226$	36.1109	2.40206
$227$	−10.3331	−0.685835	−0.342917	−	0.939366i	$-0.611415\pi$
$227$	−10.3331	−0.685835	−0.342917	+	0.939366i	$0.611415\pi$
$228$	−68.0371	−4.50586
$229$	−0.785016	−0.0518753	−0.0259376	−	0.999664i	$-0.508257\pi$
$229$	−0.785016	−0.0518753	−0.0259376	+	0.999664i	$0.508257\pi$
$230$	−6.00095	−0.395691
$231$	−18.2182	−1.19867
$232$	−22.0910	−1.45034
$233$	19.3574	1.26814	0.634072	−	0.773274i	$-0.281382\pi$
$233$	19.3574	1.26814	0.634072	+	0.773274i	$0.281382\pi$
$234$	10.7261	0.701185
$235$	−11.4251	−0.745289
$236$	−43.4467	−2.82814
$237$	17.9585	1.16653
$238$	1.20507	0.0781131
$239$	−8.76454	−0.566931	−0.283466	−	0.958982i	$-0.591484\pi$
$239$	−8.76454	−0.566931	−0.283466	+	0.958982i	$0.591484\pi$
$240$	−15.4058	−0.994443
$241$	−14.9234	−0.961304	−0.480652	−	0.876911i	$-0.659600\pi$
$241$	−14.9234	−0.961304	−0.480652	+	0.876911i	$0.659600\pi$
$242$	−16.1710	−1.03951
$243$	22.2928	1.43009
$244$	−32.0800	−2.05371
$245$	−3.97987	−0.254264
$246$	−41.1575	−2.62411
$247$	−7.42802	−0.472633
$248$	16.0559	1.01955
$249$	28.8244	1.82667
$250$	22.2454	1.40693
$251$	−9.29744	−0.586849	−0.293424	−	0.955982i	$-0.594795\pi$
$251$	−9.29744	−0.586849	−0.293424	+	0.955982i	$0.594795\pi$
$252$	26.1239	1.64565
$253$	10.1861	0.640395
$254$	26.9199	1.68910
$255$	0.697425	0.0436745
$256$	−31.4926	−1.96829
$257$	−1.54505	−0.0963777	−0.0481889	−	0.998838i	$-0.515345\pi$
$257$	−1.54505	−0.0963777	−0.0481889	+	0.998838i	$0.515345\pi$
$258$	38.8531	2.41889
$259$	−10.4275	−0.647934
$260$	−5.13427	−0.318414
$261$	13.1623	0.814724
$262$	−37.4520	−2.31379
$263$	4.65951	0.287318	0.143659	−	0.989627i	$-0.454113\pi$
$263$	4.65951	0.287318	0.143659	+	0.989627i	$0.454113\pi$
$264$	62.9033	3.87143
$265$	3.42848	0.210610
$266$	−26.4209	−1.61997
$267$	−35.4680	−2.17061
$268$	−40.9905	−2.50390
$269$	−10.1262	−0.617403	−0.308701	−	0.951159i	$-0.599894\pi$
$269$	−10.1262	−0.617403	−0.308701	+	0.951159i	$0.599894\pi$
$270$	3.24801	0.197667
$271$	−1.82245	−0.110706	−0.0553529	−	0.998467i	$-0.517628\pi$
$271$	−1.82245	−0.110706	−0.0553529	+	0.998467i	$0.517628\pi$
$272$	−1.72974	−0.104881
$273$	5.28466	0.319842
$274$	−14.6922	−0.887590
$275$	−16.8909	−1.01856
$276$	−27.0640	−1.62906
$277$	0.423590	0.0254511	0.0127255	−	0.999919i	$-0.495949\pi$
$277$	0.423590	0.0254511	0.0127255	+	0.999919i	$0.495949\pi$
$278$	−45.3967	−2.72272
$279$	−9.56644	−0.572728
$280$	−9.85394	−0.588886
$281$	11.0799	0.660972	0.330486	−	0.943811i	$-0.392787\pi$
$281$	11.0799	0.660972	0.330486	+	0.943811i	$0.392787\pi$
$282$	−75.2505	−4.48110
$283$	21.4721	1.27638	0.638192	−	0.769878i	$-0.279683\pi$
$283$	21.4721	1.27638	0.638192	+	0.769878i	$0.279683\pi$
$284$	6.62422	0.393075
$285$	−15.2909	−0.905756
$286$	12.7276	0.752597
$287$	−10.9440	−0.646001
$288$	−13.2328	−0.779748
$289$	−16.9217	−0.995394
$290$	−9.20126	−0.540316
$291$	−13.5982	−0.797142
$292$	−31.5846	−1.84835
$293$	3.52390	0.205869	0.102934	−	0.994688i	$-0.467177\pi$
$293$	3.52390	0.205869	0.102934	+	0.994688i	$0.467177\pi$
$294$	−26.2132	−1.52878
$295$	−9.76438	−0.568504
$296$	36.0038	2.09268
$297$	−5.51322	−0.319910
$298$	−52.6208	−3.04824
$299$	−2.95475	−0.170877
$300$	44.8785	2.59106
$301$	10.3312	0.595480
$302$	15.7648	0.907165
$303$	1.66502	0.0956528
$304$	37.9242	2.17510
$305$	−7.20978	−0.412831
$306$	2.47912	0.141722
$307$	13.7615	0.785410	0.392705	−	0.919664i	$-0.371539\pi$
$307$	13.7615	0.785410	0.392705	+	0.919664i	$0.371539\pi$
$308$	30.9987	1.76631
$309$	45.9876	2.61614
$310$	6.68755	0.379827
$311$	−10.9347	−0.620050	−0.310025	−	0.950728i	$-0.600337\pi$
$311$	−10.9347	−0.620050	−0.310025	+	0.950728i	$0.600337\pi$
$312$	−18.2467	−1.03302
$313$	−21.7170	−1.22752	−0.613758	−	0.789494i	$-0.710343\pi$
$313$	−21.7170	−1.22752	−0.613758	+	0.789494i	$0.710343\pi$
$314$	24.6077	1.38869
$315$	5.87119	0.330804
$316$	−30.5567	−1.71895
$317$	−12.4820	−0.701058	−0.350529	−	0.936552i	$-0.613998\pi$
$317$	−12.4820	−0.701058	−0.350529	+	0.936552i	$0.613998\pi$
$318$	22.5815	1.26631
$319$	15.6184	0.874461
$320$	−2.81864	−0.157567
$321$	31.4621	1.75604
$322$	−10.5098	−0.585690
$323$	−1.71684	−0.0955274
$324$	−31.1890	−1.73272
$325$	4.89966	0.271784
$326$	1.85467	0.102721
$327$	−17.0297	−0.941744
$328$	37.7870	2.08644
$329$	−20.0094	−1.10315
$330$	26.2003	1.44228
$331$	−22.2289	−1.22181	−0.610904	−	0.791704i	$-0.709194\pi$
$331$	−22.2289	−1.22181	−0.610904	+	0.791704i	$0.709194\pi$
$332$	−49.0454	−2.69171
$333$	−21.4519	−1.17555
$334$	−39.4466	−2.15842
$335$	−9.21238	−0.503326
$336$	−26.9812	−1.47195
$337$	3.88116	0.211420	0.105710	−	0.994397i	$-0.466288\pi$
$337$	3.88116	0.211420	0.105710	+	0.994397i	$0.466288\pi$
$338$	29.0512	1.58017
$339$	36.6015	1.98792
$340$	−1.18668	−0.0643570
$341$	−11.3516	−0.614721
$342$	−54.3542	−2.93914
$343$	−18.9386	−1.02259
$344$	−35.6712	−1.92326
$345$	−6.08248	−0.327470
$346$	47.3900	2.54770
$347$	−13.1607	−0.706505	−0.353253	−	0.935528i	$-0.614924\pi$
$347$	−13.1607	−0.706505	−0.353253	+	0.935528i	$0.614924\pi$
$348$	−41.4973	−2.22449
$349$	7.05730	0.377768	0.188884	−	0.981999i	$-0.439513\pi$
$349$	7.05730	0.377768	0.188884	+	0.981999i	$0.439513\pi$
$350$	17.4277	0.931552
$351$	1.59925	0.0853618
$352$	−15.7020	−0.836920
$353$	29.9439	1.59376	0.796878	−	0.604141i	$-0.206484\pi$
$353$	29.9439	1.59376	0.796878	+	0.604141i	$0.206484\pi$
$354$	−64.3125	−3.41817
$355$	1.48875	0.0790148
$356$	60.3496	3.19852
$357$	1.22144	0.0646457
$358$	−29.4353	−1.55570
$359$	−33.2601	−1.75540	−0.877700	−	0.479211i	$-0.840923\pi$
$359$	−33.2601	−1.75540	−0.877700	+	0.479211i	$0.840923\pi$
$360$	−20.2719	−1.06842
$361$	18.6413	0.981123
$362$	46.5401	2.44609
$363$	−16.3907	−0.860288
$364$	−8.99197	−0.471307
$365$	−7.09845	−0.371550
$366$	−47.4868	−2.48218
$367$	−5.16226	−0.269468	−0.134734	−	0.990882i	$-0.543018\pi$
$367$	−5.16226	−0.269468	−0.134734	+	0.990882i	$0.543018\pi$
$368$	15.0857	0.786394
$369$	−22.5143	−1.17205
$370$	14.9962	0.779615
$371$	6.00450	0.311738
$372$	30.1606	1.56375
$373$	26.1863	1.35587	0.677937	−	0.735120i	$-0.262874\pi$
$373$	26.1863	1.35587	0.677937	+	0.735120i	$0.262874\pi$
$374$	2.94172	0.152113
$375$	22.5477	1.16436
$376$	69.0880	3.56294
$377$	−4.53051	−0.233333
$378$	5.68844	0.292582
$379$	3.33316	0.171213	0.0856064	−	0.996329i	$-0.472717\pi$
$379$	3.33316	0.171213	0.0856064	+	0.996329i	$0.472717\pi$
$380$	26.0178	1.33469
$381$	27.2856	1.39789
$382$	−45.5046	−2.32822
$383$	−17.9774	−0.918600	−0.459300	−	0.888281i	$-0.651900\pi$
$383$	−17.9774	−0.918600	−0.459300	+	0.888281i	$0.651900\pi$
$384$	−37.7734	−1.92761
$385$	6.96677	0.355059
$386$	25.8790	1.31721
$387$	21.2537	1.08039
$388$	23.1377	1.17464
$389$	23.0793	1.17017	0.585083	−	0.810973i	$-0.301062\pi$
$389$	23.0793	1.17017	0.585083	+	0.810973i	$0.301062\pi$
$390$	−7.60008	−0.384845
$391$	−0.682930	−0.0345373
$392$	24.0665	1.21554
$393$	−37.9609	−1.91487
$394$	−34.8018	−1.75329
$395$	−6.86745	−0.345539
$396$	63.7716	3.20464
$397$	18.0210	0.904449	0.452224	−	0.891904i	$-0.350631\pi$
$397$	18.0210	0.904449	0.452224	+	0.891904i	$0.350631\pi$
$398$	−40.3298	−2.02155
$399$	−26.7799	−1.34067
$400$	−25.0155	−1.25078
$401$	29.4307	1.46970	0.734848	−	0.678231i	$-0.237253\pi$
$401$	29.4307	1.46970	0.734848	+	0.678231i	$0.237253\pi$
$402$	−60.6768	−3.02628
$403$	3.29281	0.164027
$404$	−2.83306	−0.140950
$405$	−7.00955	−0.348307
$406$	−16.1147	−0.799761
$407$	−25.4548	−1.26175
$408$	−4.21737	−0.208791
$409$	6.01634	0.297489	0.148744	−	0.988876i	$-0.452477\pi$
$409$	6.01634	0.297489	0.148744	+	0.988876i	$0.452477\pi$
$410$	15.7389	0.777290
$411$	−14.8919	−0.734561
$412$	−78.2488	−3.85504
$413$	−17.1010	−0.841483
$414$	−21.6212	−1.06262
$415$	−11.0227	−0.541081
$416$	4.55478	0.223316
$417$	−46.0136	−2.25329
$418$	−64.4967	−3.15464
$419$	−22.7558	−1.11169	−0.555847	−	0.831285i	$-0.687606\pi$
$419$	−22.7558	−1.11169	−0.555847	+	0.831285i	$0.687606\pi$
$420$	−18.5104	−0.903215
$421$	−23.5312	−1.14684	−0.573421	−	0.819261i	$-0.694384\pi$
$421$	−23.5312	−1.14684	−0.573421	+	0.819261i	$0.694384\pi$
$422$	40.1942	1.95662
$423$	−41.1641	−2.00147
$424$	−20.7322	−1.00684
$425$	1.13246	0.0549322
$426$	9.80559	0.475082
$427$	−12.6269	−0.611060
$428$	−53.5334	−2.58763
$429$	12.9005	0.622842
$430$	−14.8577	−0.716501
$431$	17.1113	0.824222	0.412111	−	0.911134i	$-0.364792\pi$
$431$	17.1113	0.824222	0.412111	+	0.911134i	$0.364792\pi$
$432$	−8.16510	−0.392843
$433$	−6.20289	−0.298092	−0.149046	−	0.988830i	$-0.547620\pi$
$433$	−6.20289	−0.298092	−0.149046	+	0.988830i	$0.547620\pi$
$434$	11.7123	0.562209
$435$	−9.32628	−0.447161
$436$	28.9764	1.38772
$437$	14.9731	0.716261
$438$	−46.7536	−2.23397
$439$	−27.6279	−1.31861	−0.659303	−	0.751877i	$-0.729149\pi$
$439$	−27.6279	−1.31861	−0.659303	+	0.751877i	$0.729149\pi$
$440$	−24.0547	−1.14676
$441$	−14.3393	−0.682825
$442$	−0.853323	−0.0405884
$443$	−19.8160	−0.941487	−0.470744	−	0.882270i	$-0.656014\pi$
$443$	−19.8160	−0.941487	−0.470744	+	0.882270i	$0.656014\pi$
$444$	67.6323	3.20969
$445$	13.5632	0.642958
$446$	16.6896	0.790277
$447$	−53.3358	−2.52269
$448$	−4.93646	−0.233226
$449$	−14.6224	−0.690075	−0.345037	−	0.938589i	$-0.612134\pi$
$449$	−14.6224	−0.690075	−0.345037	+	0.938589i	$0.612134\pi$
$450$	35.8530	1.69013
$451$	−26.7155	−1.25798
$452$	−62.2783	−2.92933
$453$	15.9790	0.750761
$454$	26.0261	1.22147
$455$	−2.02089	−0.0947409
$456$	92.4650	4.33007
$457$	7.28335	0.340701	0.170350	−	0.985384i	$-0.445510\pi$
$457$	7.28335	0.340701	0.170350	+	0.985384i	$0.445510\pi$
$458$	1.97722	0.0923894
$459$	0.369635	0.0172531
$460$	10.3495	0.482547
$461$	2.30732	0.107463	0.0537313	−	0.998555i	$-0.482889\pi$
$461$	2.30732	0.107463	0.0537313	+	0.998555i	$0.482889\pi$
$462$	45.8862	2.13482
$463$	18.6412	0.866331	0.433166	−	0.901314i	$-0.357397\pi$
$463$	18.6412	0.866331	0.433166	+	0.901314i	$0.357397\pi$
$464$	23.1308	1.07382
$465$	6.77841	0.314341
$466$	−48.7554	−2.25855
$467$	−10.6130	−0.491112	−0.245556	−	0.969382i	$-0.578971\pi$
$467$	−10.6130	−0.491112	−0.245556	+	0.969382i	$0.578971\pi$
$468$	−18.4986	−0.855099
$469$	−16.1342	−0.745008
$470$	28.7763	1.32735
$471$	24.9420	1.14927
$472$	59.0457	2.71780
$473$	25.2197	1.15960
$474$	−45.2320	−2.07758
$475$	−24.8289	−1.13923
$476$	−2.07831	−0.0952593
$477$	12.3527	0.565591
$478$	22.0753	1.00970
$479$	−30.5907	−1.39772	−0.698861	−	0.715257i	$-0.746310\pi$
$479$	−30.5907	−1.39772	−0.698861	+	0.715257i	$0.746310\pi$
$480$	9.37622	0.427964
$481$	7.38383	0.336674
$482$	37.5877	1.71207
$483$	−10.6526	−0.484711
$484$	27.8891	1.26769
$485$	5.20005	0.236122
$486$	−56.1490	−2.54697
$487$	−8.66128	−0.392480	−0.196240	−	0.980556i	$-0.562873\pi$
$487$	−8.66128	−0.392480	−0.196240	+	0.980556i	$0.562873\pi$
$488$	43.5979	1.97359
$489$	1.87987	0.0850109
$490$	10.0241	0.452842
$491$	5.06921	0.228770	0.114385	−	0.993436i	$-0.463510\pi$
$491$	5.06921	0.228770	0.114385	+	0.993436i	$0.463510\pi$
$492$	70.9819	3.20011
$493$	−1.04714	−0.0471607
$494$	18.7090	0.841756
$495$	14.3323	0.644189
$496$	−16.8117	−0.754867
$497$	2.60735	0.116955
$498$	−72.6001	−3.25329
$499$	23.8025	1.06554	0.532772	−	0.846259i	$-0.321150\pi$
$499$	23.8025	1.06554	0.532772	+	0.846259i	$0.321150\pi$
$500$	−38.3654	−1.71575
$501$	−39.9826	−1.78629
$502$	23.4175	1.04517
$503$	4.87344	0.217296	0.108648	−	0.994080i	$-0.465348\pi$
$503$	4.87344	0.217296	0.108648	+	0.994080i	$0.465348\pi$
$504$	−35.5034	−1.58145
$505$	−0.636714	−0.0283334
$506$	−25.6558	−1.14054
$507$	29.4459	1.30774
$508$	−46.4271	−2.05987
$509$	−38.5669	−1.70945	−0.854724	−	0.519083i	$-0.826273\pi$
$509$	−38.5669	−1.70945	−0.854724	+	0.519083i	$0.826273\pi$
$510$	−1.75661	−0.0777838
$511$	−12.4320	−0.549958
$512$	49.7283	2.19770
$513$	−8.10419	−0.357809
$514$	3.89153	0.171648
$515$	−17.5860	−0.774930
$516$	−67.0076	−2.94984
$517$	−48.8454	−2.14822
$518$	26.2638	1.15396
$519$	48.0339	2.10845
$520$	6.97768	0.305992
$521$	33.6265	1.47321	0.736603	−	0.676325i	$-0.236429\pi$
$521$	33.6265	1.47321	0.736603	+	0.676325i	$0.236429\pi$
$522$	−33.1518	−1.45102
$523$	−27.3723	−1.19691	−0.598453	−	0.801158i	$-0.704218\pi$
$523$	−27.3723	−1.19691	−0.598453	+	0.801158i	$0.704218\pi$
$524$	64.5913	2.82168
$525$	17.6645	0.770943
$526$	−11.7359	−0.511710
$527$	0.761068	0.0331526
$528$	−65.8644	−2.86638
$529$	−17.0439	−0.741041
$530$	−8.63531	−0.375094
$531$	−35.1807	−1.52671
$532$	45.5666	1.97556
$533$	7.74953	0.335669
$534$	89.3333	3.86583
$535$	−12.0313	−0.520159
$536$	55.7078	2.40621
$537$	−29.8352	−1.28749
$538$	25.5048	1.09959
$539$	−17.0151	−0.732891
$540$	−5.60165	−0.241056
$541$	−12.0840	−0.519530	−0.259765	−	0.965672i	$-0.583645\pi$
$541$	−12.0840	−0.519530	−0.259765	+	0.965672i	$0.583645\pi$
$542$	4.59020	0.197166
$543$	47.1725	2.02436
$544$	1.05275	0.0451361
$545$	6.51227	0.278955
$546$	−13.3105	−0.569636
$547$	−21.9258	−0.937481	−0.468741	−	0.883336i	$-0.655292\pi$
$547$	−21.9258	−0.937481	−0.468741	+	0.883336i	$0.655292\pi$
$548$	25.3388	1.08242
$549$	−25.9766	−1.10865
$550$	42.5432	1.81405
$551$	22.9583	0.978056
$552$	36.7811	1.56551
$553$	−12.0274	−0.511456
$554$	−1.06690	−0.0453281
$555$	15.2000	0.645202
$556$	78.2931	3.32037
$557$	11.1586	0.472806	0.236403	−	0.971655i	$-0.424032\pi$
$557$	11.1586	0.472806	0.236403	+	0.971655i	$0.424032\pi$
$558$	24.0950	1.02002
$559$	−7.31562	−0.309418
$560$	10.3178	0.436006
$561$	2.98169	0.125887
$562$	−27.9070	−1.17718
$563$	−18.5865	−0.783330	−0.391665	−	0.920108i	$-0.628101\pi$
$563$	−18.5865	−0.783330	−0.391665	+	0.920108i	$0.628101\pi$
$564$	129.780	5.46473
$565$	−13.9967	−0.588845
$566$	−54.0818	−2.27323
$567$	−12.2763	−0.515554
$568$	−9.00258	−0.377740
$569$	32.0351	1.34298	0.671490	−	0.741013i	$-0.265655\pi$
$569$	32.0351	1.34298	0.671490	+	0.741013i	$0.265655\pi$
$570$	38.5133	1.61314
$571$	−24.3165	−1.01761	−0.508807	−	0.860881i	$-0.669913\pi$
$571$	−24.3165	−1.01761	−0.508807	+	0.860881i	$0.669913\pi$
$572$	−21.9505	−0.917796
$573$	−46.1229	−1.92681
$574$	27.5645	1.15052
$575$	−9.87654	−0.411880
$576$	−10.1555	−0.423145
$577$	6.44589	0.268346	0.134173	−	0.990958i	$-0.457162\pi$
$577$	6.44589	0.268346	0.134173	+	0.990958i	$0.457162\pi$
$578$	42.6207	1.77279
$579$	26.2306	1.09011
$580$	15.8689	0.658919
$581$	−19.3046	−0.800892
$582$	34.2499	1.41970
$583$	14.6577	0.607060
$584$	42.9247	1.77624
$585$	−4.15745	−0.171890
$586$	−8.87565	−0.366650
$587$	−1.84073	−0.0759752	−0.0379876	−	0.999278i	$-0.512095\pi$
$587$	−1.84073	−0.0759752	−0.0379876	+	0.999278i	$0.512095\pi$
$588$	45.2083	1.86436
$589$	−16.6863	−0.687546
$590$	24.5935	1.01250
$591$	−35.2746	−1.45100
$592$	−37.6986	−1.54940
$593$	−11.1782	−0.459034	−0.229517	−	0.973305i	$-0.573715\pi$
$593$	−11.1782	−0.459034	−0.229517	+	0.973305i	$0.573715\pi$
$594$	13.8862	0.569756
$595$	−0.467088	−0.0191488
$596$	90.7520	3.71735
$597$	−40.8778	−1.67302
$598$	7.44212	0.304331
$599$	−19.5645	−0.799383	−0.399691	−	0.916650i	$-0.630883\pi$
$599$	−19.5645	−0.799383	−0.399691	+	0.916650i	$0.630883\pi$
$600$	−60.9916	−2.48997
$601$	39.0613	1.59334	0.796671	−	0.604413i	$-0.206592\pi$
$601$	39.0613	1.59334	0.796671	+	0.604413i	$0.206592\pi$
$602$	−26.0212	−1.06054
$603$	−33.1919	−1.35168
$604$	−27.1887	−1.10629
$605$	6.26791	0.254827
$606$	−4.19368	−0.170357
$607$	35.5059	1.44114	0.720571	−	0.693381i	$-0.243880\pi$
$607$	35.5059	1.44114	0.720571	+	0.693381i	$0.243880\pi$
$608$	−23.0813	−0.936068
$609$	−16.3337	−0.661874
$610$	18.1593	0.735248
$611$	14.1689	0.573211
$612$	−4.27558	−0.172830
$613$	18.6224	0.752152	0.376076	−	0.926589i	$-0.377273\pi$
$613$	18.6224	0.752152	0.376076	+	0.926589i	$0.377273\pi$
$614$	−34.6611	−1.39881
$615$	15.9528	0.643278
$616$	−42.1284	−1.69740
$617$	−38.8603	−1.56446	−0.782229	−	0.622991i	$-0.785917\pi$
$617$	−38.8603	−1.56446	−0.782229	+	0.622991i	$0.785917\pi$
$618$	−115.829	−4.65932
$619$	−45.1865	−1.81620	−0.908100	−	0.418753i	$-0.862467\pi$
$619$	−45.1865	−1.81620	−0.908100	+	0.418753i	$0.862467\pi$
$620$	−11.5336	−0.463201
$621$	−3.22372	−0.129363
$622$	27.5412	1.10430
$623$	23.7541	0.951687
$624$	19.1057	0.764839
$625$	11.6122	0.464489
$626$	54.6986	2.18619
$627$	−65.3731	−2.61075
$628$	−42.4394	−1.69352
$629$	1.70662	0.0680475
$630$	−14.7878	−0.589159
$631$	19.3404	0.769928	0.384964	−	0.922932i	$-0.374214\pi$
$631$	19.3404	0.769928	0.384964	+	0.922932i	$0.374214\pi$
$632$	41.5278	1.65189
$633$	40.7403	1.61928
$634$	31.4384	1.24858
$635$	−10.4342	−0.414069
$636$	−38.9449	−1.54427
$637$	4.93566	0.195558
$638$	−39.3380	−1.55741
$639$	5.36393	0.212194
$640$	14.4448	0.570981
$641$	20.9738	0.828414	0.414207	−	0.910183i	$-0.364059\pi$
$641$	20.9738	0.828414	0.414207	+	0.910183i	$0.364059\pi$
$642$	−79.2435	−3.12749
$643$	28.2448	1.11387	0.556933	−	0.830557i	$-0.311978\pi$
$643$	28.2448	1.11387	0.556933	+	0.830557i	$0.311978\pi$
$644$	18.1257	0.714252
$645$	−15.0595	−0.592969
$646$	4.32420	0.170133
$647$	−19.2848	−0.758164	−0.379082	−	0.925363i	$-0.623760\pi$
$647$	−19.2848	−0.758164	−0.379082	+	0.925363i	$0.623760\pi$
$648$	42.3871	1.66512
$649$	−41.7455	−1.63865
$650$	−12.3408	−0.484045
$651$	11.8715	0.465279
$652$	−3.19865	−0.125269
$653$	21.0938	0.825465	0.412732	−	0.910852i	$-0.364574\pi$
$653$	21.0938	0.825465	0.412732	+	0.910852i	$0.364574\pi$
$654$	42.8927	1.67724
$655$	14.5165	0.567206
$656$	−39.5657	−1.54478
$657$	−25.5755	−0.997795
$658$	50.3977	1.96471
$659$	26.2056	1.02082	0.510412	−	0.859930i	$-0.329493\pi$
$659$	26.2056	1.02082	0.510412	+	0.859930i	$0.329493\pi$
$660$	−45.1861	−1.75887
$661$	33.0047	1.28373	0.641867	−	0.766816i	$-0.278160\pi$
$661$	33.0047	1.28373	0.641867	+	0.766816i	$0.278160\pi$
$662$	55.9879	2.17603
$663$	−0.864917	−0.0335906
$664$	66.6546	2.58670
$665$	10.2408	0.397122
$666$	54.0308	2.09365
$667$	9.13244	0.353610
$668$	68.0312	2.63221
$669$	16.9164	0.654026
$670$	23.2032	0.896419
$671$	−30.8239	−1.18994
$672$	16.4212	0.633460
$673$	10.3076	0.397328	0.198664	−	0.980068i	$-0.436340\pi$
$673$	10.3076	0.397328	0.198664	+	0.980068i	$0.436340\pi$
$674$	−9.77549	−0.376538
$675$	5.34567	0.205755
$676$	−50.1028	−1.92703
$677$	43.8215	1.68420	0.842098	−	0.539325i	$-0.181320\pi$
$677$	43.8215	1.68420	0.842098	+	0.539325i	$0.181320\pi$
$678$	−92.1883	−3.54047
$679$	9.10718	0.349501
$680$	1.61275	0.0618462
$681$	26.3797	1.01087
$682$	28.5912	1.09481
$683$	1.49346	0.0571457	0.0285729	−	0.999592i	$-0.490904\pi$
$683$	1.49346	0.0571457	0.0285729	+	0.999592i	$0.490904\pi$
$684$	93.7414	3.58429
$685$	5.69475	0.217585
$686$	47.7007	1.82122
$687$	2.00408	0.0764606
$688$	37.3504	1.42397
$689$	−4.25185	−0.161983
$690$	15.3200	0.583221
$691$	−21.6368	−0.823103	−0.411551	−	0.911387i	$-0.635013\pi$
$691$	−21.6368	−0.823103	−0.411551	+	0.911387i	$0.635013\pi$
$692$	−81.7308	−3.10694
$693$	25.1010	0.953509
$694$	33.1480	1.25828
$695$	17.5959	0.667451
$696$	56.3965	2.13770
$697$	1.79115	0.0678446
$698$	−17.7752	−0.672802
$699$	−49.4179	−1.86915
$700$	−30.0566	−1.13603
$701$	39.4637	1.49052	0.745262	−	0.666772i	$-0.232325\pi$
$701$	39.4637	1.49052	0.745262	+	0.666772i	$0.232325\pi$
$702$	−4.02804	−0.152029
$703$	−37.4174	−1.41122
$704$	−12.0505	−0.454170
$705$	29.1673	1.09850
$706$	−75.4198	−2.83846
$707$	−1.11512	−0.0419383
$708$	110.916	4.16848
$709$	27.1583	1.01995	0.509975	−	0.860189i	$-0.329655\pi$
$709$	27.1583	1.01995	0.509975	+	0.860189i	$0.329655\pi$
$710$	−3.74973	−0.140725
$711$	−24.7432	−0.927942
$712$	−82.0174	−3.07373
$713$	−6.63753	−0.248578
$714$	−3.07645	−0.115133
$715$	−4.93324	−0.184493
$716$	50.7653	1.89719
$717$	22.3752	0.835617
$718$	83.7722	3.12635
$719$	−15.7274	−0.586532	−0.293266	−	0.956031i	$-0.594742\pi$
$719$	−15.7274	−0.586532	−0.293266	+	0.956031i	$0.594742\pi$
$720$	21.2262	0.791052
$721$	−30.7994	−1.14703
$722$	−46.9520	−1.74737
$723$	38.0984	1.41690
$724$	−80.2650	−2.98302
$725$	−15.1437	−0.562423
$726$	41.2832	1.53216
$727$	26.6803	0.989519	0.494759	−	0.869030i	$-0.335256\pi$
$727$	26.6803	0.989519	0.494759	+	0.869030i	$0.335256\pi$
$728$	12.2204	0.452920
$729$	−35.3718	−1.31007
$730$	17.8789	0.661727
$731$	−1.69086	−0.0625387
$732$	81.8977	3.02703
$733$	−39.8165	−1.47066	−0.735328	−	0.677711i	$-0.762972\pi$
$733$	−39.8165	−1.47066	−0.735328	+	0.677711i	$0.762972\pi$
$734$	13.0022	0.479919
$735$	10.1603	0.374768
$736$	−9.18135	−0.338429
$737$	−39.3856	−1.45079
$738$	56.7068	2.08741
$739$	−32.1444	−1.18245	−0.591226	−	0.806506i	$-0.701356\pi$
$739$	−32.1444	−1.18245	−0.591226	+	0.806506i	$0.701356\pi$
$740$	−25.8631	−0.950745
$741$	18.9632	0.696629
$742$	−15.1235	−0.555203
$743$	44.7205	1.64064	0.820319	−	0.571907i	$-0.193796\pi$
$743$	44.7205	1.64064	0.820319	+	0.571907i	$0.193796\pi$
$744$	−40.9894	−1.50275
$745$	20.3960	0.747250
$746$	−65.9554	−2.41480
$747$	−39.7142	−1.45307
$748$	−5.07341	−0.185502
$749$	−21.0712	−0.769924
$750$	−56.7909	−2.07371
$751$	2.21974	0.0809995	0.0404998	−	0.999180i	$-0.487105\pi$
$751$	2.21974	0.0809995	0.0404998	+	0.999180i	$0.487105\pi$
$752$	−72.3402	−2.63797
$753$	23.7356	0.864975
$754$	11.4110	0.415565
$755$	−6.11049	−0.222384
$756$	−9.81051	−0.356805
$757$	−0.203274	−0.00738811	−0.00369406	−	0.999993i	$-0.501176\pi$
$757$	−0.203274	−0.00738811	−0.00369406	+	0.999993i	$0.501176\pi$
$758$	−8.39522	−0.304928
$759$	−26.0043	−0.943898
$760$	−35.3593	−1.28262
$761$	46.5798	1.68852	0.844259	−	0.535936i	$-0.180041\pi$
$761$	46.5798	1.68852	0.844259	+	0.535936i	$0.180041\pi$
$762$	−68.7244	−2.48962
$763$	11.4053	0.412901
$764$	78.4792	2.83928
$765$	−0.960912	−0.0347418
$766$	45.2796	1.63602
$767$	12.1094	0.437244
$768$	80.3983	2.90112
$769$	−51.7065	−1.86458	−0.932291	−	0.361708i	$-0.882194\pi$
$769$	−51.7065	−1.86458	−0.932291	+	0.361708i	$0.882194\pi$
$770$	−17.5472	−0.632357
$771$	3.94440	0.142054
$772$	−44.6319	−1.60634
$773$	−18.9385	−0.681171	−0.340586	−	0.940213i	$-0.610625\pi$
$773$	−18.9385	−0.681171	−0.340586	+	0.940213i	$0.610625\pi$
$774$	−53.5317	−1.92416
$775$	11.0066	0.395368
$776$	−31.4450	−1.12881
$777$	26.6206	0.955009
$778$	−58.1298	−2.08406
$779$	−39.2706	−1.40701
$780$	13.1074	0.469320
$781$	6.36485	0.227752
$782$	1.72010	0.0615105
$783$	−4.94293	−0.176646
$784$	−25.1994	−0.899977
$785$	−9.53801	−0.340426
$786$	95.6121	3.41037
$787$	−49.9533	−1.78064	−0.890322	−	0.455332i	$-0.849521\pi$
$787$	−49.9533	−1.78064	−0.890322	+	0.455332i	$0.849521\pi$
$788$	60.0206	2.13814
$789$	−11.8954	−0.423487
$790$	17.2970	0.615401
$791$	−24.5132	−0.871591
$792$	−86.6681	−3.07962
$793$	8.94127	0.317514
$794$	−45.3896	−1.61081
$795$	−8.75263	−0.310424
$796$	69.5545	2.46529
$797$	−1.86555	−0.0660811	−0.0330405	−	0.999454i	$-0.510519\pi$
$797$	−1.86555	−0.0660811	−0.0330405	+	0.999454i	$0.510519\pi$
$798$	67.4506	2.38773
$799$	3.27485	0.115856
$800$	15.2248	0.538279
$801$	48.8678	1.72666
$802$	−74.1270	−2.61752
$803$	−30.3479	−1.07095
$804$	104.646	3.69057
$805$	4.07364	0.143577
$806$	−8.29361	−0.292130
$807$	25.8513	0.910009
$808$	3.85025	0.135451
$809$	1.92498	0.0676786	0.0338393	−	0.999427i	$-0.489227\pi$
$809$	1.92498	0.0676786	0.0338393	+	0.999427i	$0.489227\pi$
$810$	17.6550	0.620332
$811$	12.0173	0.421984	0.210992	−	0.977488i	$-0.432331\pi$
$811$	12.0173	0.421984	0.210992	+	0.977488i	$0.432331\pi$
$812$	27.7921	0.975312
$813$	4.65257	0.163173
$814$	64.1130	2.24716
$815$	−0.718877	−0.0251812
$816$	4.41589	0.154587
$817$	37.0718	1.29698
$818$	−15.1534	−0.529825
$819$	−7.28120	−0.254426
$820$	−27.1440	−0.947909
$821$	43.7978	1.52855	0.764276	−	0.644889i	$-0.223096\pi$
$821$	43.7978	1.52855	0.764276	+	0.644889i	$0.223096\pi$
$822$	37.5081	1.30825
$823$	−6.62175	−0.230820	−0.115410	−	0.993318i	$-0.536818\pi$
$823$	−6.62175	−0.230820	−0.115410	+	0.993318i	$0.536818\pi$
$824$	106.343	3.70464
$825$	43.1213	1.50129
$826$	43.0722	1.49867
$827$	−54.8145	−1.90609	−0.953043	−	0.302836i	$-0.902066\pi$
$827$	−54.8145	−1.90609	−0.953043	+	0.302836i	$0.902066\pi$
$828$	37.2888	1.29588
$829$	8.66582	0.300976	0.150488	−	0.988612i	$-0.451915\pi$
$829$	8.66582	0.300976	0.150488	+	0.988612i	$0.451915\pi$
$830$	27.7628	0.963659
$831$	−1.08139	−0.0375131
$832$	3.49556	0.121187
$833$	1.14078	0.0395257
$834$	115.894	4.01309
$835$	15.2896	0.529119
$836$	111.234	3.84710
$837$	3.59256	0.124177
$838$	57.3151	1.97992
$839$	−22.4667	−0.775638	−0.387819	−	0.921736i	$-0.626771\pi$
$839$	−22.4667	−0.775638	−0.387819	+	0.921736i	$0.626771\pi$
$840$	25.1564	0.867977
$841$	−14.9972	−0.517145
$842$	59.2681	2.04251
$843$	−28.2862	−0.974227
$844$	−69.3206	−2.38611
$845$	−11.2603	−0.387366
$846$	103.680	3.56460
$847$	10.9774	0.377187
$848$	21.7081	0.745460
$849$	−54.8166	−1.88130
$850$	−2.85232	−0.0978338
$851$	−14.8840	−0.510218
$852$	−16.9111	−0.579366
$853$	20.4107	0.698848	0.349424	−	0.936965i	$-0.386377\pi$
$853$	20.4107	0.698848	0.349424	+	0.936965i	$0.386377\pi$
$854$	31.8035	1.08829
$855$	21.0678	0.720504
$856$	72.7540	2.48668
$857$	44.8013	1.53038	0.765192	−	0.643802i	$-0.222644\pi$
$857$	44.8013	1.53038	0.765192	+	0.643802i	$0.222644\pi$
$858$	−32.4925	−1.10928
$859$	−7.23373	−0.246812	−0.123406	−	0.992356i	$-0.539382\pi$
$859$	−7.23373	−0.246812	−0.123406	+	0.992356i	$0.539382\pi$
$860$	25.6242	0.873776
$861$	27.9391	0.952161
$862$	−43.0982	−1.46793
$863$	34.6798	1.18051	0.590257	−	0.807215i	$-0.299026\pi$
$863$	34.6798	1.18051	0.590257	+	0.807215i	$0.299026\pi$
$864$	4.96940	0.169062
$865$	−18.3685	−0.624548
$866$	15.6232	0.530899
$867$	43.1998	1.46714
$868$	−20.1995	−0.685617
$869$	−29.3603	−0.995980
$870$	23.4901	0.796389
$871$	11.4248	0.387115
$872$	−39.3801	−1.33358
$873$	18.7356	0.634105
$874$	−37.7128	−1.27565
$875$	−15.1009	−0.510505
$876$	80.6331	2.72434
$877$	2.02177	0.0682702	0.0341351	−	0.999417i	$-0.489132\pi$
$877$	2.02177	0.0682702	0.0341351	+	0.999417i	$0.489132\pi$
$878$	69.5864	2.34843
$879$	−8.99625	−0.303436
$880$	25.1870	0.849053
$881$	−51.1992	−1.72494	−0.862472	−	0.506105i	$-0.831085\pi$
$881$	−51.1992	−1.72494	−0.862472	+	0.506105i	$0.831085\pi$
$882$	36.1165	1.21610
$883$	39.6191	1.33329	0.666645	−	0.745375i	$-0.267730\pi$
$883$	39.6191	1.33329	0.666645	+	0.745375i	$0.267730\pi$
$884$	1.47168	0.0494978
$885$	24.9277	0.837936
$886$	49.9106	1.67678
$887$	−59.1273	−1.98530	−0.992651	−	0.121016i	$-0.961385\pi$
$887$	−59.1273	−1.98530	−0.992651	+	0.121016i	$0.961385\pi$
$888$	−91.9149	−3.08446
$889$	−18.2741	−0.612893
$890$	−34.1617	−1.14510
$891$	−29.9678	−1.00396
$892$	−28.7836	−0.963747
$893$	−71.8005	−2.40271
$894$	134.337	4.49290
$895$	11.4092	0.381368
$896$	25.2981	0.845149
$897$	7.54324	0.251861
$898$	36.8295	1.22902
$899$	−10.1773	−0.339433
$900$	−61.8335	−2.06112
$901$	−0.982730	−0.0327395
$902$	67.2884	2.24046
$903$	−26.3747	−0.877696
$904$	84.6387	2.81504
$905$	−18.0391	−0.599639
$906$	−40.2464	−1.33710
$907$	51.0329	1.69452	0.847259	−	0.531180i	$-0.178251\pi$
$907$	51.0329	1.69452	0.847259	+	0.531180i	$0.178251\pi$
$908$	−44.8857	−1.48958
$909$	−2.29406	−0.0760892
$910$	5.09002	0.168733
$911$	−5.02620	−0.166525	−0.0832627	−	0.996528i	$-0.526534\pi$
$911$	−5.02620	−0.166525	−0.0832627	+	0.996528i	$0.526534\pi$
$912$	−96.8177	−3.20595
$913$	−47.1250	−1.55961
$914$	−18.3446	−0.606785
$915$	18.4060	0.608484
$916$	−3.40999	−0.112669
$917$	25.4236	0.839562
$918$	−0.931001	−0.0307276
$919$	23.6453	0.779987	0.389994	−	0.920818i	$-0.372477\pi$
$919$	23.6453	0.779987	0.389994	+	0.920818i	$0.372477\pi$
$920$	−14.0653	−0.463721
$921$	−35.1320	−1.15764
$922$	−5.81145	−0.191390
$923$	−1.84629	−0.0607714
$924$	−79.1372	−2.60342
$925$	24.6812	0.811513
$926$	−46.9517	−1.54293
$927$	−63.3616	−2.08107
$928$	−14.0778	−0.462126
$929$	−40.4994	−1.32874	−0.664372	−	0.747402i	$-0.731301\pi$
$929$	−40.4994	−1.32874	−0.664372	+	0.747402i	$0.731301\pi$
$930$	−17.0728	−0.559839
$931$	−25.0114	−0.819715
$932$	84.0856	2.75431
$933$	27.9154	0.913910
$934$	26.7310	0.874666
$935$	−1.14022	−0.0372892
$936$	25.1403	0.821738
$937$	14.1534	0.462373	0.231187	−	0.972909i	$-0.425739\pi$
$937$	14.1534	0.462373	0.231187	+	0.972909i	$0.425739\pi$
$938$	40.6372	1.32685
$939$	55.4418	1.80927
$940$	−49.6288	−1.61871
$941$	−9.87614	−0.321953	−0.160976	−	0.986958i	$-0.551464\pi$
$941$	−9.87614	−0.321953	−0.160976	+	0.986958i	$0.551464\pi$
$942$	−62.8215	−2.04684
$943$	−15.6212	−0.508697
$944$	−61.8252	−2.01224
$945$	−2.20485	−0.0717239
$946$	−63.5208	−2.06524
$947$	7.85653	0.255303	0.127652	−	0.991819i	$-0.459256\pi$
$947$	7.85653	0.255303	0.127652	+	0.991819i	$0.459256\pi$
$948$	78.0090	2.53362
$949$	8.80320	0.285764
$950$	62.5366	2.02896
$951$	31.8655	1.03331
$952$	2.82451	0.0915429
$953$	49.2263	1.59460	0.797299	−	0.603585i	$-0.206262\pi$
$953$	49.2263	1.59460	0.797299	+	0.603585i	$0.206262\pi$
$954$	−31.1127	−1.00731
$955$	17.6377	0.570743
$956$	−38.0719	−1.23133
$957$	−39.8725	−1.28889
$958$	77.0487	2.48933
$959$	9.97356	0.322063
$960$	7.19578	0.232243
$961$	−23.6030	−0.761388
$962$	−18.5977	−0.599612
$963$	−43.3484	−1.39688
$964$	−64.8253	−2.08788
$965$	−10.0308	−0.322902
$966$	26.8308	0.863266
$967$	20.3902	0.655706	0.327853	−	0.944729i	$-0.393675\pi$
$967$	20.3902	0.655706	0.327853	+	0.944729i	$0.393675\pi$
$968$	−37.9024	−1.21823
$969$	4.38295	0.140801
$970$	−13.0974	−0.420532
$971$	−19.6085	−0.629266	−0.314633	−	0.949213i	$-0.601881\pi$
$971$	−19.6085	−0.629266	−0.314633	+	0.949213i	$0.601881\pi$
$972$	96.8369	3.10604
$973$	30.8168	0.987941
$974$	21.8152	0.699004
$975$	−12.5084	−0.400591
$976$	−45.6502	−1.46123
$977$	−39.0408	−1.24903	−0.624513	−	0.781015i	$-0.714702\pi$
$977$	−39.0408	−1.24903	−0.624513	+	0.781015i	$0.714702\pi$
$978$	−4.73484	−0.151404
$979$	57.9866	1.85326
$980$	−17.2880	−0.552244
$981$	23.4635	0.749132
$982$	−12.7678	−0.407438
$983$	−2.07574	−0.0662059	−0.0331029	−	0.999452i	$-0.510539\pi$
$983$	−2.07574	−0.0662059	−0.0331029	+	0.999452i	$0.510539\pi$
$984$	−96.4673	−3.07526
$985$	13.4893	0.429804
$986$	2.63743	0.0839928
$987$	51.0825	1.62597
$988$	−32.2662	−1.02653
$989$	14.7466	0.468913
$990$	−36.0988	−1.14729
$991$	37.5684	1.19340	0.596700	−	0.802465i	$-0.296478\pi$
$991$	37.5684	1.19340	0.596700	+	0.802465i	$0.296478\pi$
$992$	10.2318	0.324861
$993$	56.7486	1.80086
$994$	−6.56713	−0.208297
$995$	15.6320	0.495566
$996$	125.209	3.96740
$997$	8.93943	0.283114	0.141557	−	0.989930i	$-0.454789\pi$
$997$	8.93943	0.283114	0.141557	+	0.989930i	$0.454789\pi$
$998$	−59.9513	−1.89773
$999$	8.05597	0.254880

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4013.2.a.b.1.12	✓	157

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4013.2.a.b.1.12	✓	157	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:	\( N \)	\(=\)	\( 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.51870 q^{2} -2.55292 q^{3} +4.34385 q^{4} +0.976255 q^{5} +6.43005 q^{6} +1.70978 q^{7} -5.90347 q^{8} +3.51742 q^{9} +O(q^{10})\)	\(q-2.51870 q^{2} -2.55292 q^{3} +4.34385 q^{4} +0.976255 q^{5} +6.43005 q^{6} +1.70978 q^{7} -5.90347 q^{8} +3.51742 q^{9} -2.45890 q^{10} +4.17377 q^{11} -11.0895 q^{12} -1.21071 q^{13} -4.30641 q^{14} -2.49230 q^{15} +6.18136 q^{16} -0.279831 q^{17} -8.85932 q^{18} +6.13525 q^{19} +4.24071 q^{20} -4.36493 q^{21} -10.5125 q^{22} +2.44051 q^{23} +15.0711 q^{24} -4.04693 q^{25} +3.04942 q^{26} -1.32092 q^{27} +7.42702 q^{28} +3.74203 q^{29} +6.27737 q^{30} -2.71974 q^{31} -3.76207 q^{32} -10.6553 q^{33} +0.704812 q^{34} +1.66918 q^{35} +15.2791 q^{36} -6.09875 q^{37} -15.4529 q^{38} +3.09085 q^{39} -5.76329 q^{40} -6.40081 q^{41} +10.9939 q^{42} +6.04242 q^{43} +18.1303 q^{44} +3.43390 q^{45} -6.14690 q^{46} -11.7029 q^{47} -15.7805 q^{48} -4.07667 q^{49} +10.1930 q^{50} +0.714388 q^{51} -5.25915 q^{52} +3.51186 q^{53} +3.32701 q^{54} +4.07467 q^{55} -10.0936 q^{56} -15.6628 q^{57} -9.42505 q^{58} -10.0019 q^{59} -10.8262 q^{60} -7.38514 q^{61} +6.85020 q^{62} +6.01399 q^{63} -2.88720 q^{64} -1.18196 q^{65} +26.8375 q^{66} -9.43644 q^{67} -1.21555 q^{68} -6.23042 q^{69} -4.20416 q^{70} +1.52496 q^{71} -20.7650 q^{72} -7.27110 q^{73} +15.3609 q^{74} +10.3315 q^{75} +26.6507 q^{76} +7.13621 q^{77} -7.78493 q^{78} -7.03448 q^{79} +6.03459 q^{80} -7.18004 q^{81} +16.1217 q^{82} -11.2907 q^{83} -18.9606 q^{84} -0.273187 q^{85} -15.2190 q^{86} -9.55311 q^{87} -24.6397 q^{88} +13.8931 q^{89} -8.64896 q^{90} -2.07004 q^{91} +10.6012 q^{92} +6.94328 q^{93} +29.4762 q^{94} +5.98957 q^{95} +9.60427 q^{96} +5.32653 q^{97} +10.2679 q^{98} +14.6809 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 157 q - 15 q^{2} - 51 q^{3} + 137 q^{4} - 13 q^{5} - 15 q^{6} - 49 q^{7} - 42 q^{8} + 144 q^{9}+O(q^{10}) \) 157 * q - 15 * q^2 - 51 * q^3 + 137 * q^4 - 13 * q^5 - 15 * q^6 - 49 * q^7 - 42 * q^8 + 144 * q^9	\( 157 q - 15 q^{2} - 51 q^{3} + 137 q^{4} - 13 q^{5} - 15 q^{6} - 49 q^{7} - 42 q^{8} + 144 q^{9} - 61 q^{10} - 27 q^{11} - 93 q^{12} - 97 q^{13} - 12 q^{14} - 36 q^{15} + 105 q^{16} - 45 q^{17} - 68 q^{18} - 128 q^{19} - 30 q^{20} - 26 q^{21} - 68 q^{22} - 41 q^{23} - 40 q^{24} + 102 q^{25} - 5 q^{26} - 189 q^{27} - 115 q^{28} - 26 q^{29} - 12 q^{30} - 88 q^{31} - 89 q^{32} - 52 q^{33} - 61 q^{34} - 87 q^{35} + 110 q^{36} - 62 q^{37} - 37 q^{38} - 20 q^{39} - 161 q^{40} - 34 q^{41} - 53 q^{42} - 254 q^{43} - 19 q^{44} - 46 q^{45} - 52 q^{46} - 76 q^{47} - 162 q^{48} + 96 q^{49} - 54 q^{50} - 76 q^{51} - 259 q^{52} - 48 q^{53} - 12 q^{54} - 194 q^{55} - 10 q^{56} - 30 q^{57} - 52 q^{58} - 64 q^{59} - 31 q^{60} - 107 q^{61} - 51 q^{62} - 106 q^{63} + 54 q^{64} - 17 q^{65} - 13 q^{66} - 193 q^{67} - 118 q^{68} - 55 q^{69} - 86 q^{70} - 11 q^{71} - 172 q^{72} - 173 q^{73} - 11 q^{74} - 209 q^{75} - 213 q^{76} - 84 q^{77} - 30 q^{78} - 111 q^{79} - 6 q^{80} + 157 q^{81} - 117 q^{82} - 154 q^{83} - 6 q^{84} - 91 q^{85} + 28 q^{86} - 165 q^{87} - 165 q^{88} - 32 q^{89} - 103 q^{90} - 200 q^{91} - 86 q^{92} - 39 q^{93} - 118 q^{94} - 22 q^{95} - 28 q^{96} - 151 q^{97} - 38 q^{98} - 91 q^{99}+O(q^{100}) \) 157 * q - 15 * q^2 - 51 * q^3 + 137 * q^4 - 13 * q^5 - 15 * q^6 - 49 * q^7 - 42 * q^8 + 144 * q^9 - 61 * q^10 - 27 * q^11 - 93 * q^12 - 97 * q^13 - 12 * q^14 - 36 * q^15 + 105 * q^16 - 45 * q^17 - 68 * q^18 - 128 * q^19 - 30 * q^20 - 26 * q^21 - 68 * q^22 - 41 * q^23 - 40 * q^24 + 102 * q^25 - 5 * q^26 - 189 * q^27 - 115 * q^28 - 26 * q^29 - 12 * q^30 - 88 * q^31 - 89 * q^32 - 52 * q^33 - 61 * q^34 - 87 * q^35 + 110 * q^36 - 62 * q^37 - 37 * q^38 - 20 * q^39 - 161 * q^40 - 34 * q^41 - 53 * q^42 - 254 * q^43 - 19 * q^44 - 46 * q^45 - 52 * q^46 - 76 * q^47 - 162 * q^48 + 96 * q^49 - 54 * q^50 - 76 * q^51 - 259 * q^52 - 48 * q^53 - 12 * q^54 - 194 * q^55 - 10 * q^56 - 30 * q^57 - 52 * q^58 - 64 * q^59 - 31 * q^60 - 107 * q^61 - 51 * q^62 - 106 * q^63 + 54 * q^64 - 17 * q^65 - 13 * q^66 - 193 * q^67 - 118 * q^68 - 55 * q^69 - 86 * q^70 - 11 * q^71 - 172 * q^72 - 173 * q^73 - 11 * q^74 - 209 * q^75 - 213 * q^76 - 84 * q^77 - 30 * q^78 - 111 * q^79 - 6 * q^80 + 157 * q^81 - 117 * q^82 - 154 * q^83 - 6 * q^84 - 91 * q^85 + 28 * q^86 - 165 * q^87 - 165 * q^88 - 32 * q^89 - 103 * q^90 - 200 * q^91 - 86 * q^92 - 39 * q^93 - 118 * q^94 - 22 * q^95 - 28 * q^96 - 151 * q^97 - 38 * q^98 - 91 * q^99

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