LMFDB - Embedded newform 4011.2.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.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:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.77095 q^{2} -1.00000 q^{3} +5.67816 q^{4} +3.12132 q^{5} +2.77095 q^{6} +1.00000 q^{7} -10.1920 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.77095 q^{2} -1.00000 q^{3} +5.67816 q^{4} +3.12132 q^{5} +2.77095 q^{6} +1.00000 q^{7} -10.1920 q^{8} +1.00000 q^{9} -8.64902 q^{10} +6.28403 q^{11} -5.67816 q^{12} -4.18867 q^{13} -2.77095 q^{14} -3.12132 q^{15} +16.8852 q^{16} -2.52915 q^{17} -2.77095 q^{18} +7.47189 q^{19} +17.7234 q^{20} -1.00000 q^{21} -17.4127 q^{22} +2.45749 q^{23} +10.1920 q^{24} +4.74265 q^{25} +11.6066 q^{26} -1.00000 q^{27} +5.67816 q^{28} -10.0275 q^{29} +8.64902 q^{30} -0.646166 q^{31} -26.4040 q^{32} -6.28403 q^{33} +7.00814 q^{34} +3.12132 q^{35} +5.67816 q^{36} +6.32439 q^{37} -20.7042 q^{38} +4.18867 q^{39} -31.8125 q^{40} -8.93290 q^{41} +2.77095 q^{42} -1.68259 q^{43} +35.6817 q^{44} +3.12132 q^{45} -6.80958 q^{46} +3.24892 q^{47} -16.8852 q^{48} +1.00000 q^{49} -13.1416 q^{50} +2.52915 q^{51} -23.7839 q^{52} +0.780543 q^{53} +2.77095 q^{54} +19.6145 q^{55} -10.1920 q^{56} -7.47189 q^{57} +27.7856 q^{58} +7.64211 q^{59} -17.7234 q^{60} +0.562450 q^{61} +1.79049 q^{62} +1.00000 q^{63} +39.3938 q^{64} -13.0742 q^{65} +17.4127 q^{66} +9.19848 q^{67} -14.3609 q^{68} -2.45749 q^{69} -8.64902 q^{70} -3.14925 q^{71} -10.1920 q^{72} -1.05983 q^{73} -17.5246 q^{74} -4.74265 q^{75} +42.4266 q^{76} +6.28403 q^{77} -11.6066 q^{78} +4.70214 q^{79} +52.7041 q^{80} +1.00000 q^{81} +24.7526 q^{82} +4.81026 q^{83} -5.67816 q^{84} -7.89428 q^{85} +4.66238 q^{86} +10.0275 q^{87} -64.0468 q^{88} +9.27522 q^{89} -8.64902 q^{90} -4.18867 q^{91} +13.9540 q^{92} +0.646166 q^{93} -9.00258 q^{94} +23.3222 q^{95} +26.4040 q^{96} +9.03905 q^{97} -2.77095 q^{98} +6.28403 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9}+O(q^{10}) $ 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9	\( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9} + 4 q^{10} - 8 q^{11} - 34 q^{12} + 26 q^{13} - 6 q^{14} - 8 q^{15} + 62 q^{16} + 9 q^{17} - 6 q^{18} + 25 q^{19} + 20 q^{20} - 28 q^{21} + 3 q^{22} - 30 q^{23} + 15 q^{24} + 42 q^{25} + 25 q^{26} - 28 q^{27} + 34 q^{28} - 5 q^{29} - 4 q^{30} + 18 q^{31} - 26 q^{32} + 8 q^{33} + 30 q^{34} + 8 q^{35} + 34 q^{36} + 36 q^{37} - 2 q^{38} - 26 q^{39} + 28 q^{40} + 21 q^{41} + 6 q^{42} + 8 q^{43} - 20 q^{44} + 8 q^{45} + 24 q^{46} + 6 q^{47} - 62 q^{48} + 28 q^{49} - 48 q^{50} - 9 q^{51} + 54 q^{52} - 12 q^{53} + 6 q^{54} + 15 q^{55} - 15 q^{56} - 25 q^{57} + 19 q^{58} + 33 q^{59} - 20 q^{60} + 48 q^{61} + 28 q^{63} + 75 q^{64} + 21 q^{65} - 3 q^{66} + 27 q^{67} + 19 q^{68} + 30 q^{69} + 4 q^{70} - 45 q^{71} - 15 q^{72} + 61 q^{73} - 31 q^{74} - 42 q^{75} + 63 q^{76} - 8 q^{77} - 25 q^{78} + 35 q^{79} + 84 q^{80} + 28 q^{81} + 11 q^{82} + 43 q^{83} - 34 q^{84} + 43 q^{85} - q^{86} + 5 q^{87} - 27 q^{88} + 25 q^{89} + 4 q^{90} + 26 q^{91} - 102 q^{92} - 18 q^{93} + 55 q^{94} - 43 q^{95} + 26 q^{96} + 40 q^{97} - 6 q^{98} - 8 q^{99}+O(q^{100}) \) 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9 + 4 * q^10 - 8 * q^11 - 34 * q^12 + 26 * q^13 - 6 * q^14 - 8 * q^15 + 62 * q^16 + 9 * q^17 - 6 * q^18 + 25 * q^19 + 20 * q^20 - 28 * q^21 + 3 * q^22 - 30 * q^23 + 15 * q^24 + 42 * q^25 + 25 * q^26 - 28 * q^27 + 34 * q^28 - 5 * q^29 - 4 * q^30 + 18 * q^31 - 26 * q^32 + 8 * q^33 + 30 * q^34 + 8 * q^35 + 34 * q^36 + 36 * q^37 - 2 * q^38 - 26 * q^39 + 28 * q^40 + 21 * q^41 + 6 * q^42 + 8 * q^43 - 20 * q^44 + 8 * q^45 + 24 * q^46 + 6 * q^47 - 62 * q^48 + 28 * q^49 - 48 * q^50 - 9 * q^51 + 54 * q^52 - 12 * q^53 + 6 * q^54 + 15 * q^55 - 15 * q^56 - 25 * q^57 + 19 * q^58 + 33 * q^59 - 20 * q^60 + 48 * q^61 + 28 * q^63 + 75 * q^64 + 21 * q^65 - 3 * q^66 + 27 * q^67 + 19 * q^68 + 30 * q^69 + 4 * q^70 - 45 * q^71 - 15 * q^72 + 61 * q^73 - 31 * q^74 - 42 * q^75 + 63 * q^76 - 8 * q^77 - 25 * q^78 + 35 * q^79 + 84 * q^80 + 28 * q^81 + 11 * q^82 + 43 * q^83 - 34 * q^84 + 43 * q^85 - q^86 + 5 * q^87 - 27 * q^88 + 25 * q^89 + 4 * q^90 + 26 * q^91 - 102 * q^92 - 18 * q^93 + 55 * q^94 - 43 * q^95 + 26 * q^96 + 40 * q^97 - 6 * q^98 - 8 * 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 $

$2$	−2.77095	−1.95936	−0.979679	−	0.200574i	$-0.935719\pi$
$2$	−2.77095	−1.95936	−0.979679	+	0.200574i	$0.935719\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.67816	2.83908
$5$	3.12132	1.39590	0.697949	−	0.716148i	$-0.254096\pi$
$5$	3.12132	1.39590	0.697949	+	0.716148i	$0.254096\pi$
$6$	2.77095	1.13124
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−10.1920	−3.60341
$9$	1.00000	0.333333
$10$	−8.64902	−2.73506
$11$	6.28403	1.89471	0.947353	−	0.320190i	$-0.103747\pi$
$11$	6.28403	1.89471	0.947353	+	0.320190i	$0.103747\pi$
$12$	−5.67816	−1.63914
$13$	−4.18867	−1.16173	−0.580864	−	0.814001i	$-0.697285\pi$
$13$	−4.18867	−1.16173	−0.580864	+	0.814001i	$0.697285\pi$
$14$	−2.77095	−0.740567
$15$	−3.12132	−0.805922
$16$	16.8852	4.22130
$17$	−2.52915	−0.613408	−0.306704	−	0.951805i	$-0.599226\pi$
$17$	−2.52915	−0.613408	−0.306704	+	0.951805i	$0.599226\pi$
$18$	−2.77095	−0.653119
$19$	7.47189	1.71417	0.857085	−	0.515175i	$-0.172273\pi$
$19$	7.47189	1.71417	0.857085	+	0.515175i	$0.172273\pi$
$20$	17.7234	3.96306
$21$	−1.00000	−0.218218
$22$	−17.4127	−3.71241
$23$	2.45749	0.512422	0.256211	−	0.966621i	$-0.417526\pi$
$23$	2.45749	0.512422	0.256211	+	0.966621i	$0.417526\pi$
$24$	10.1920	2.08043
$25$	4.74265	0.948529
$26$	11.6066	2.27624
$27$	−1.00000	−0.192450
$28$	5.67816	1.07307
$29$	−10.0275	−1.86205	−0.931026	−	0.364952i	$-0.881085\pi$
$29$	−10.0275	−1.86205	−0.931026	+	0.364952i	$0.881085\pi$
$30$	8.64902	1.57909
$31$	−0.646166	−0.116055	−0.0580274	−	0.998315i	$-0.518481\pi$
$31$	−0.646166	−0.116055	−0.0580274	+	0.998315i	$0.518481\pi$
$32$	−26.4040	−4.66761
$33$	−6.28403	−1.09391
$34$	7.00814	1.20189
$35$	3.12132	0.527600
$36$	5.67816	0.946360
$37$	6.32439	1.03972	0.519861	−	0.854251i	$-0.325984\pi$
$37$	6.32439	1.03972	0.519861	+	0.854251i	$0.325984\pi$
$38$	−20.7042	−3.35867
$39$	4.18867	0.670724
$40$	−31.8125	−5.03000
$41$	−8.93290	−1.39508	−0.697542	−	0.716544i	$-0.745723\pi$
$41$	−8.93290	−1.39508	−0.697542	+	0.716544i	$0.745723\pi$
$42$	2.77095	0.427567
$43$	−1.68259	−0.256593	−0.128297	−	0.991736i	$-0.540951\pi$
$43$	−1.68259	−0.256593	−0.128297	+	0.991736i	$0.540951\pi$
$44$	35.6817	5.37922
$45$	3.12132	0.465299
$46$	−6.80958	−1.00402
$47$	3.24892	0.473903	0.236952	−	0.971521i	$-0.423852\pi$
$47$	3.24892	0.473903	0.236952	+	0.971521i	$0.423852\pi$
$48$	−16.8852	−2.43717
$49$	1.00000	0.142857
$50$	−13.1416	−1.85851
$51$	2.52915	0.354151
$52$	−23.7839	−3.29824
$53$	0.780543	0.107216	0.0536079	−	0.998562i	$-0.482928\pi$
$53$	0.780543	0.107216	0.0536079	+	0.998562i	$0.482928\pi$
$54$	2.77095	0.377078
$55$	19.6145	2.64482
$56$	−10.1920	−1.36196
$57$	−7.47189	−0.989677
$58$	27.7856	3.64843
$59$	7.64211	0.994918	0.497459	−	0.867488i	$-0.334267\pi$
$59$	7.64211	0.994918	0.497459	+	0.867488i	$0.334267\pi$
$60$	−17.7234	−2.28808
$61$	0.562450	0.0720143	0.0360072	−	0.999352i	$-0.488536\pi$
$61$	0.562450	0.0720143	0.0360072	+	0.999352i	$0.488536\pi$
$62$	1.79049	0.227393
$63$	1.00000	0.125988
$64$	39.3938	4.92422
$65$	−13.0742	−1.62165
$66$	17.4127	2.14336
$67$	9.19848	1.12377	0.561887	−	0.827214i	$-0.310076\pi$
$67$	9.19848	1.12377	0.561887	+	0.827214i	$0.310076\pi$
$68$	−14.3609	−1.74152
$69$	−2.45749	−0.295847
$70$	−8.64902	−1.03376
$71$	−3.14925	−0.373747	−0.186873	−	0.982384i	$-0.559835\pi$
$71$	−3.14925	−0.373747	−0.186873	+	0.982384i	$0.559835\pi$
$72$	−10.1920	−1.20114
$73$	−1.05983	−0.124043	−0.0620216	−	0.998075i	$-0.519755\pi$
$73$	−1.05983	−0.124043	−0.0620216	+	0.998075i	$0.519755\pi$
$74$	−17.5246	−2.03719
$75$	−4.74265	−0.547634
$76$	42.4266	4.86667
$77$	6.28403	0.716132
$78$	−11.6066	−1.31419
$79$	4.70214	0.529032	0.264516	−	0.964381i	$-0.414788\pi$
$79$	4.70214	0.529032	0.264516	+	0.964381i	$0.414788\pi$
$80$	52.7041	5.89250
$81$	1.00000	0.111111
$82$	24.7526	2.73347
$83$	4.81026	0.527995	0.263997	−	0.964523i	$-0.414959\pi$
$83$	4.81026	0.527995	0.263997	+	0.964523i	$0.414959\pi$
$84$	−5.67816	−0.619538
$85$	−7.89428	−0.856255
$86$	4.66238	0.502758
$87$	10.0275	1.07506
$88$	−64.0468	−6.82741
$89$	9.27522	0.983171	0.491586	−	0.870829i	$-0.336418\pi$
$89$	9.27522	0.983171	0.491586	+	0.870829i	$0.336418\pi$
$90$	−8.64902	−0.911687
$91$	−4.18867	−0.439092
$92$	13.9540	1.45481
$93$	0.646166	0.0670043
$94$	−9.00258	−0.928546
$95$	23.3222	2.39281
$96$	26.4040	2.69485
$97$	9.03905	0.917776	0.458888	−	0.888494i	$-0.348248\pi$
$97$	9.03905	0.917776	0.458888	+	0.888494i	$0.348248\pi$
$98$	−2.77095	−0.279908
$99$	6.28403	0.631569
$100$	26.9295	2.69295
$101$	14.0962	1.40263	0.701313	−	0.712854i	$-0.252598\pi$
$101$	14.0962	1.40263	0.701313	+	0.712854i	$0.252598\pi$
$102$	−7.00814	−0.693909
$103$	2.82334	0.278192	0.139096	−	0.990279i	$-0.455580\pi$
$103$	2.82334	0.278192	0.139096	+	0.990279i	$0.455580\pi$
$104$	42.6909	4.18619
$105$	−3.12132	−0.304610
$106$	−2.16284	−0.210074
$107$	−8.31043	−0.803399	−0.401700	−	0.915772i	$-0.631580\pi$
$107$	−8.31043	−0.803399	−0.401700	+	0.915772i	$0.631580\pi$
$108$	−5.67816	−0.546381
$109$	8.87269	0.849849	0.424925	−	0.905229i	$-0.360301\pi$
$109$	8.87269	0.849849	0.424925	+	0.905229i	$0.360301\pi$
$110$	−54.3507	−5.18214
$111$	−6.32439	−0.600284
$112$	16.8852	1.59550
$113$	3.10645	0.292230	0.146115	−	0.989268i	$-0.453323\pi$
$113$	3.10645	0.292230	0.146115	+	0.989268i	$0.453323\pi$
$114$	20.7042	1.93913
$115$	7.67062	0.715289
$116$	−56.9375	−5.28652
$117$	−4.18867	−0.387242
$118$	−21.1759	−1.94940
$119$	−2.52915	−0.231847
$120$	31.8125	2.90407
$121$	28.4890	2.58991
$122$	−1.55852	−0.141102
$123$	8.93290	0.805452
$124$	−3.66903	−0.329489
$125$	−0.803282	−0.0718477
$126$	−2.77095	−0.246856
$127$	12.0322	1.06769	0.533843	−	0.845583i	$-0.320747\pi$
$127$	12.0322	1.06769	0.533843	+	0.845583i	$0.320747\pi$
$128$	−56.3501	−4.98070
$129$	1.68259	0.148144
$130$	36.2279	3.17740
$131$	−3.12647	−0.273161	−0.136581	−	0.990629i	$-0.543611\pi$
$131$	−3.12647	−0.273161	−0.136581	+	0.990629i	$0.543611\pi$
$132$	−35.6817	−3.10570
$133$	7.47189	0.647895
$134$	−25.4885	−2.20187
$135$	−3.12132	−0.268641
$136$	25.7771	2.21036
$137$	−18.4357	−1.57507	−0.787533	−	0.616273i	$-0.788642\pi$
$137$	−18.4357	−1.57507	−0.787533	+	0.616273i	$0.788642\pi$
$138$	6.80958	0.579670
$139$	10.5629	0.895935	0.447968	−	0.894050i	$-0.352148\pi$
$139$	10.5629	0.895935	0.447968	+	0.894050i	$0.352148\pi$
$140$	17.7234	1.49790
$141$	−3.24892	−0.273608
$142$	8.72640	0.732303
$143$	−26.3217	−2.20113
$144$	16.8852	1.40710
$145$	−31.2989	−2.59923
$146$	2.93672	0.243045
$147$	−1.00000	−0.0824786
$148$	35.9109	2.95186
$149$	−11.3777	−0.932097	−0.466049	−	0.884759i	$-0.654323\pi$
$149$	−11.3777	−0.932097	−0.466049	+	0.884759i	$0.654323\pi$
$150$	13.1416	1.07301
$151$	6.39766	0.520634	0.260317	−	0.965523i	$-0.416173\pi$
$151$	6.39766	0.520634	0.260317	+	0.965523i	$0.416173\pi$
$152$	−76.1535	−6.17687
$153$	−2.52915	−0.204469
$154$	−17.4127	−1.40316
$155$	−2.01689	−0.162001
$156$	23.7839	1.90424
$157$	−14.2298	−1.13566	−0.567832	−	0.823145i	$-0.692218\pi$
$157$	−14.2298	−1.13566	−0.567832	+	0.823145i	$0.692218\pi$
$158$	−13.0294	−1.03656
$159$	−0.780543	−0.0619011
$160$	−82.4154	−6.51551
$161$	2.45749	0.193677
$162$	−2.77095	−0.217706
$163$	−4.98369	−0.390352	−0.195176	−	0.980768i	$-0.562528\pi$
$163$	−4.98369	−0.390352	−0.195176	+	0.980768i	$0.562528\pi$
$164$	−50.7224	−3.96075
$165$	−19.6145	−1.52699
$166$	−13.3290	−1.03453
$167$	−17.5637	−1.35912	−0.679561	−	0.733619i	$-0.737830\pi$
$167$	−17.5637	−1.35912	−0.679561	+	0.733619i	$0.737830\pi$
$168$	10.1920	0.786330
$169$	4.54494	0.349611
$170$	21.8746	1.67771
$171$	7.47189	0.571390
$172$	−9.55404	−0.728489
$173$	23.7435	1.80519	0.902593	−	0.430494i	$-0.141661\pi$
$173$	23.7435	1.80519	0.902593	+	0.430494i	$0.141661\pi$
$174$	−27.7856	−2.10642
$175$	4.74265	0.358510
$176$	106.107	7.99812
$177$	−7.64211	−0.574416
$178$	−25.7012	−1.92638
$179$	−15.7072	−1.17401	−0.587005	−	0.809583i	$-0.699693\pi$
$179$	−15.7072	−1.17401	−0.587005	+	0.809583i	$0.699693\pi$
$180$	17.7234	1.32102
$181$	22.5661	1.67733	0.838664	−	0.544649i	$-0.183337\pi$
$181$	22.5661	1.67733	0.838664	+	0.544649i	$0.183337\pi$
$182$	11.6066	0.860337
$183$	−0.562450	−0.0415775
$184$	−25.0467	−1.84647
$185$	19.7404	1.45135
$186$	−1.79049	−0.131285
$187$	−15.8932	−1.16223
$188$	18.4479	1.34545
$189$	−1.00000	−0.0727393
$190$	−64.6246	−4.68836
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	−39.3938	−2.84300
$193$	19.8086	1.42585	0.712927	−	0.701239i	$-0.247369\pi$
$193$	19.8086	1.42585	0.712927	+	0.701239i	$0.247369\pi$
$194$	−25.0467	−1.79825
$195$	13.0742	0.936261
$196$	5.67816	0.405583
$197$	−25.9345	−1.84775	−0.923877	−	0.382690i	$-0.874998\pi$
$197$	−25.9345	−1.84775	−0.923877	+	0.382690i	$0.874998\pi$
$198$	−17.4127	−1.23747
$199$	23.9062	1.69466	0.847332	−	0.531063i	$-0.178207\pi$
$199$	23.9062	1.69466	0.847332	+	0.531063i	$0.178207\pi$
$200$	−48.3370	−3.41794
$201$	−9.19848	−0.648811
$202$	−39.0599	−2.74824
$203$	−10.0275	−0.703790
$204$	14.3609	1.00546
$205$	−27.8824	−1.94739
$206$	−7.82334	−0.545078
$207$	2.45749	0.170807
$208$	−70.7264	−4.90400
$209$	46.9536	3.24785
$210$	8.64902	0.596839
$211$	−18.2027	−1.25313	−0.626563	−	0.779371i	$-0.715539\pi$
$211$	−18.2027	−1.25313	−0.626563	+	0.779371i	$0.715539\pi$
$212$	4.43205	0.304394
$213$	3.14925	0.215783
$214$	23.0278	1.57415
$215$	−5.25192	−0.358178
$216$	10.1920	0.693477
$217$	−0.646166	−0.0438646
$218$	−24.5858	−1.66516
$219$	1.05983	0.0716164
$220$	111.374	7.50884
$221$	10.5938	0.712613
$222$	17.5246	1.17617
$223$	−8.92944	−0.597960	−0.298980	−	0.954259i	$-0.596646\pi$
$223$	−8.92944	−0.597960	−0.298980	+	0.954259i	$0.596646\pi$
$224$	−26.4040	−1.76419
$225$	4.74265	0.316176
$226$	−8.60781	−0.572583
$227$	21.3965	1.42013	0.710067	−	0.704134i	$-0.248665\pi$
$227$	21.3965	1.42013	0.710067	+	0.704134i	$0.248665\pi$
$228$	−42.4266	−2.80977
$229$	−13.2826	−0.877741	−0.438870	−	0.898550i	$-0.644621\pi$
$229$	−13.2826	−0.877741	−0.438870	+	0.898550i	$0.644621\pi$
$230$	−21.2549	−1.40151
$231$	−6.28403	−0.413459
$232$	102.200	6.70975
$233$	24.5926	1.61112	0.805558	−	0.592517i	$-0.201866\pi$
$233$	24.5926	1.61112	0.805558	+	0.592517i	$0.201866\pi$
$234$	11.6066	0.758746
$235$	10.1409	0.661520
$236$	43.3931	2.82465
$237$	−4.70214	−0.305437
$238$	7.00814	0.454270
$239$	−3.18917	−0.206290	−0.103145	−	0.994666i	$-0.532891\pi$
$239$	−3.18917	−0.206290	−0.103145	+	0.994666i	$0.532891\pi$
$240$	−52.7041	−3.40203
$241$	−19.8971	−1.28168	−0.640841	−	0.767673i	$-0.721414\pi$
$241$	−19.8971	−1.28168	−0.640841	+	0.767673i	$0.721414\pi$
$242$	−78.9417	−5.07456
$243$	−1.00000	−0.0641500
$244$	3.19368	0.204454
$245$	3.12132	0.199414
$246$	−24.7526	−1.57817
$247$	−31.2973	−1.99140
$248$	6.58572	0.418194
$249$	−4.81026	−0.304838
$250$	2.22585	0.140775
$251$	−14.6897	−0.927208	−0.463604	−	0.886042i	$-0.653444\pi$
$251$	−14.6897	−0.927208	−0.463604	+	0.886042i	$0.653444\pi$
$252$	5.67816	0.357690
$253$	15.4429	0.970890
$254$	−33.3407	−2.09198
$255$	7.89428	0.494359
$256$	77.3559	4.83474
$257$	21.0752	1.31463	0.657317	−	0.753614i	$-0.271691\pi$
$257$	21.0752	1.31463	0.657317	+	0.753614i	$0.271691\pi$
$258$	−4.66238	−0.290267
$259$	6.32439	0.392978
$260$	−74.2373	−4.60400
$261$	−10.0275	−0.620684
$262$	8.66330	0.535220
$263$	−13.5216	−0.833779	−0.416890	−	0.908957i	$-0.636880\pi$
$263$	−13.5216	−0.833779	−0.416890	+	0.908957i	$0.636880\pi$
$264$	64.0468	3.94181
$265$	2.43633	0.149662
$266$	−20.7042	−1.26946
$267$	−9.27522	−0.567634
$268$	52.2304	3.19048
$269$	−3.24595	−0.197909	−0.0989546	−	0.995092i	$-0.531550\pi$
$269$	−3.24595	−0.197909	−0.0989546	+	0.995092i	$0.531550\pi$
$270$	8.64902	0.526363
$271$	−11.9017	−0.722976	−0.361488	−	0.932377i	$-0.617731\pi$
$271$	−11.9017	−0.722976	−0.361488	+	0.932377i	$0.617731\pi$
$272$	−42.7051	−2.58938
$273$	4.18867	0.253510
$274$	51.0843	3.08612
$275$	29.8029	1.79718
$276$	−13.9540	−0.839934
$277$	−32.4703	−1.95095	−0.975475	−	0.220108i	$-0.929359\pi$
$277$	−32.4703	−1.95095	−0.975475	+	0.220108i	$0.929359\pi$
$278$	−29.2693	−1.75546
$279$	−0.646166	−0.0386850
$280$	−31.8125	−1.90116
$281$	12.4448	0.742395	0.371197	−	0.928554i	$-0.378947\pi$
$281$	12.4448	0.742395	0.371197	+	0.928554i	$0.378947\pi$
$282$	9.00258	0.536096
$283$	25.9746	1.54403	0.772015	−	0.635605i	$-0.219249\pi$
$283$	25.9746	1.54403	0.772015	+	0.635605i	$0.219249\pi$
$284$	−17.8819	−1.06110
$285$	−23.3222	−1.38149
$286$	72.9361	4.31280
$287$	−8.93290	−0.527292
$288$	−26.4040	−1.55587
$289$	−10.6034	−0.623730
$290$	86.7277	5.09283
$291$	−9.03905	−0.529878
$292$	−6.01786	−0.352169
$293$	25.8471	1.51001	0.755003	−	0.655722i	$-0.227636\pi$
$293$	25.8471	1.51001	0.755003	+	0.655722i	$0.227636\pi$
$294$	2.77095	0.161605
$295$	23.8535	1.38880
$296$	−64.4581	−3.74655
$297$	−6.28403	−0.364636
$298$	31.5270	1.82631
$299$	−10.2936	−0.595295
$300$	−26.9295	−1.55478
$301$	−1.68259	−0.0969831
$302$	−17.7276	−1.02011
$303$	−14.0962	−0.809806
$304$	126.164	7.23602
$305$	1.75559	0.100525
$306$	7.00814	0.400629
$307$	−7.06752	−0.403365	−0.201682	−	0.979451i	$-0.564641\pi$
$307$	−7.06752	−0.403365	−0.201682	+	0.979451i	$0.564641\pi$
$308$	35.6817	2.03316
$309$	−2.82334	−0.160614
$310$	5.58871	0.317417
$311$	−0.183809	−0.0104228	−0.00521141	−	0.999986i	$-0.501659\pi$
$311$	−0.183809	−0.0104228	−0.00521141	+	0.999986i	$0.501659\pi$
$312$	−42.6909	−2.41690
$313$	17.5154	0.990027	0.495013	−	0.868885i	$-0.335163\pi$
$313$	17.5154	0.990027	0.495013	+	0.868885i	$0.335163\pi$
$314$	39.4301	2.22517
$315$	3.12132	0.175867
$316$	26.6995	1.50196
$317$	−0.396811	−0.0222871	−0.0111436	−	0.999938i	$-0.503547\pi$
$317$	−0.396811	−0.0222871	−0.0111436	+	0.999938i	$0.503547\pi$
$318$	2.16284	0.121286
$319$	−63.0129	−3.52804
$320$	122.961	6.87371
$321$	8.31043	0.463843
$322$	−6.80958	−0.379483
$323$	−18.8975	−1.05149
$324$	5.67816	0.315453
$325$	−19.8654	−1.10193
$326$	13.8095	0.764840
$327$	−8.87269	−0.490661
$328$	91.0440	5.02707
$329$	3.24892	0.179119
$330$	54.3507	2.99191
$331$	−4.85520	−0.266866	−0.133433	−	0.991058i	$-0.542600\pi$
$331$	−4.85520	−0.266866	−0.133433	+	0.991058i	$0.542600\pi$
$332$	27.3134	1.49902
$333$	6.32439	0.346574
$334$	48.6682	2.66301
$335$	28.7114	1.56867
$336$	−16.8852	−0.921162
$337$	−20.0135	−1.09020	−0.545101	−	0.838370i	$-0.683509\pi$
$337$	−20.0135	−1.09020	−0.545101	+	0.838370i	$0.683509\pi$
$338$	−12.5938	−0.685012
$339$	−3.10645	−0.168719
$340$	−44.8250	−2.43098
$341$	−4.06053	−0.219890
$342$	−20.7042	−1.11956
$343$	1.00000	0.0539949
$344$	17.1490	0.924612
$345$	−7.67062	−0.412972
$346$	−65.7921	−3.53701
$347$	−14.6130	−0.784467	−0.392233	−	0.919866i	$-0.628297\pi$
$347$	−14.6130	−0.784467	−0.392233	+	0.919866i	$0.628297\pi$
$348$	56.9375	3.05217
$349$	−12.2712	−0.656861	−0.328431	−	0.944528i	$-0.606520\pi$
$349$	−12.2712	−0.656861	−0.328431	+	0.944528i	$0.606520\pi$
$350$	−13.1416	−0.702450
$351$	4.18867	0.223575
$352$	−165.924	−8.84375
$353$	−12.6400	−0.672761	−0.336381	−	0.941726i	$-0.609203\pi$
$353$	−12.6400	−0.672761	−0.336381	+	0.941726i	$0.609203\pi$
$354$	21.1759	1.12549
$355$	−9.82981	−0.521712
$356$	52.6662	2.79130
$357$	2.52915	0.133857
$358$	43.5238	2.30030
$359$	20.8439	1.10010	0.550049	−	0.835132i	$-0.314609\pi$
$359$	20.8439	1.10010	0.550049	+	0.835132i	$0.314609\pi$
$360$	−31.8125	−1.67667
$361$	36.8292	1.93838
$362$	−62.5296	−3.28648
$363$	−28.4890	−1.49529
$364$	−23.7839	−1.24662
$365$	−3.30806	−0.173152
$366$	1.55852	0.0814651
$367$	8.02339	0.418818	0.209409	−	0.977828i	$-0.432846\pi$
$367$	8.02339	0.418818	0.209409	+	0.977828i	$0.432846\pi$
$368$	41.4952	2.16309
$369$	−8.93290	−0.465028
$370$	−54.6998	−2.84371
$371$	0.780543	0.0405238
$372$	3.66903	0.190231
$373$	−0.0307904	−0.00159427	−0.000797134	−	1.00000i	$-0.500254\pi$
$373$	−0.0307904	−0.00159427	−0.000797134		1.00000i	$0.500254\pi$
$374$	44.0393	2.27722
$375$	0.803282	0.0414813
$376$	−33.1129	−1.70767
$377$	42.0017	2.16320
$378$	2.77095	0.142522
$379$	−36.0067	−1.84954	−0.924769	−	0.380528i	$-0.875742\pi$
$379$	−36.0067	−1.84954	−0.924769	+	0.380528i	$0.875742\pi$
$380$	132.427	6.79337
$381$	−12.0322	−0.616429
$382$	2.77095	0.141774
$383$	10.2197	0.522205	0.261102	−	0.965311i	$-0.415914\pi$
$383$	10.2197	0.522205	0.261102	+	0.965311i	$0.415914\pi$
$384$	56.3501	2.87561
$385$	19.6145	0.999646
$386$	−54.8886	−2.79376
$387$	−1.68259	−0.0855311
$388$	51.3252	2.60564
$389$	33.4957	1.69830	0.849149	−	0.528153i	$-0.177115\pi$
$389$	33.4957	1.69830	0.849149	+	0.528153i	$0.177115\pi$
$390$	−36.2279	−1.83447
$391$	−6.21535	−0.314324
$392$	−10.1920	−0.514774
$393$	3.12647	0.157710
$394$	71.8631	3.62041
$395$	14.6769	0.738474
$396$	35.6817	1.79307
$397$	0.601160	0.0301713	0.0150857	−	0.999886i	$-0.495198\pi$
$397$	0.601160	0.0301713	0.0150857	+	0.999886i	$0.495198\pi$
$398$	−66.2428	−3.32045
$399$	−7.47189	−0.374063
$400$	80.0805	4.00402
$401$	1.41896	0.0708596	0.0354298	−	0.999372i	$-0.488720\pi$
$401$	1.41896	0.0708596	0.0354298	+	0.999372i	$0.488720\pi$
$402$	25.4885	1.27125
$403$	2.70658	0.134824
$404$	80.0406	3.98217
$405$	3.12132	0.155100
$406$	27.7856	1.37898
$407$	39.7426	1.96997
$408$	−25.7771	−1.27615
$409$	−13.4833	−0.666707	−0.333353	−	0.942802i	$-0.608180\pi$
$409$	−13.4833	−0.666707	−0.333353	+	0.942802i	$0.608180\pi$
$410$	77.2608	3.81564
$411$	18.4357	0.909365
$412$	16.0314	0.789810
$413$	7.64211	0.376044
$414$	−6.80958	−0.334673
$415$	15.0144	0.737027
$416$	110.598	5.42249
$417$	−10.5629	−0.517268
$418$	−130.106	−6.36370
$419$	−19.7643	−0.965548	−0.482774	−	0.875745i	$-0.660371\pi$
$419$	−19.7643	−0.965548	−0.482774	+	0.875745i	$0.660371\pi$
$420$	−17.7234	−0.864812
$421$	38.7865	1.89034	0.945170	−	0.326579i	$-0.105896\pi$
$421$	38.7865	1.89034	0.945170	+	0.326579i	$0.105896\pi$
$422$	50.4388	2.45532
$423$	3.24892	0.157968
$424$	−7.95529	−0.386343
$425$	−11.9949	−0.581836
$426$	−8.72640	−0.422795
$427$	0.562450	0.0272189
$428$	−47.1879	−2.28091
$429$	26.3217	1.27082
$430$	14.5528	0.701798
$431$	13.6177	0.655939	0.327970	−	0.944688i	$-0.393636\pi$
$431$	13.6177	0.655939	0.327970	+	0.944688i	$0.393636\pi$
$432$	−16.8852	−0.812389
$433$	15.5880	0.749110	0.374555	−	0.927205i	$-0.377796\pi$
$433$	15.5880	0.749110	0.374555	+	0.927205i	$0.377796\pi$
$434$	1.79049	0.0859464
$435$	31.2989	1.50067
$436$	50.3805	2.41279
$437$	18.3621	0.878379
$438$	−2.93672	−0.140322
$439$	30.2955	1.44592	0.722962	−	0.690887i	$-0.242780\pi$
$439$	30.2955	1.44592	0.722962	+	0.690887i	$0.242780\pi$
$440$	−199.911	−9.53037
$441$	1.00000	0.0476190
$442$	−29.3548	−1.39626
$443$	−18.7402	−0.890371	−0.445186	−	0.895438i	$-0.646862\pi$
$443$	−18.7402	−0.890371	−0.445186	+	0.895438i	$0.646862\pi$
$444$	−35.9109	−1.70426
$445$	28.9509	1.37241
$446$	24.7430	1.17162
$447$	11.3777	0.538147
$448$	39.3938	1.86118
$449$	−28.5754	−1.34855	−0.674277	−	0.738478i	$-0.735545\pi$
$449$	−28.5754	−1.34855	−0.674277	+	0.738478i	$0.735545\pi$
$450$	−13.1416	−0.619503
$451$	−56.1346	−2.64327
$452$	17.6389	0.829665
$453$	−6.39766	−0.300588
$454$	−59.2886	−2.78255
$455$	−13.0742	−0.612927
$456$	76.1535	3.56621
$457$	−4.50402	−0.210689	−0.105345	−	0.994436i	$-0.533595\pi$
$457$	−4.50402	−0.210689	−0.105345	+	0.994436i	$0.533595\pi$
$458$	36.8055	1.71981
$459$	2.52915	0.118050
$460$	43.5550	2.03076
$461$	39.9024	1.85844	0.929219	−	0.369529i	$-0.120481\pi$
$461$	39.9024	1.85844	0.929219	+	0.369529i	$0.120481\pi$
$462$	17.4127	0.810113
$463$	7.54424	0.350611	0.175305	−	0.984514i	$-0.443909\pi$
$463$	7.54424	0.350611	0.175305	+	0.984514i	$0.443909\pi$
$464$	−169.316	−7.86028
$465$	2.01689	0.0935311
$466$	−68.1449	−3.15675
$467$	37.5637	1.73824	0.869120	−	0.494601i	$-0.164686\pi$
$467$	37.5637	1.73824	0.869120	+	0.494601i	$0.164686\pi$
$468$	−23.7839	−1.09941
$469$	9.19848	0.424746
$470$	−28.1000	−1.29615
$471$	14.2298	0.655676
$472$	−77.8883	−3.58510
$473$	−10.5735	−0.486169
$474$	13.0294	0.598460
$475$	35.4366	1.62594
$476$	−14.3609	−0.658231
$477$	0.780543	0.0357386
$478$	8.83704	0.404197
$479$	16.6389	0.760251	0.380126	−	0.924935i	$-0.375881\pi$
$479$	16.6389	0.760251	0.380126	+	0.924935i	$0.375881\pi$
$480$	82.4154	3.76173
$481$	−26.4908	−1.20787
$482$	55.1338	2.51127
$483$	−2.45749	−0.111820
$484$	161.765	7.35297
$485$	28.2138	1.28112
$486$	2.77095	0.125693
$487$	21.7702	0.986504	0.493252	−	0.869886i	$-0.335808\pi$
$487$	21.7702	0.986504	0.493252	+	0.869886i	$0.335808\pi$
$488$	−5.73249	−0.259497
$489$	4.98369	0.225370
$490$	−8.64902	−0.390723
$491$	39.0490	1.76226	0.881128	−	0.472877i	$-0.156785\pi$
$491$	39.0490	1.76226	0.881128	+	0.472877i	$0.156785\pi$
$492$	50.7224	2.28674
$493$	25.3609	1.14220
$494$	86.7232	3.90186
$495$	19.6145	0.881605
$496$	−10.9106	−0.489902
$497$	−3.14925	−0.141263
$498$	13.3290	0.597287
$499$	−14.8130	−0.663120	−0.331560	−	0.943434i	$-0.607575\pi$
$499$	−14.8130	−0.663120	−0.331560	+	0.943434i	$0.607575\pi$
$500$	−4.56116	−0.203981
$501$	17.5637	0.784690
$502$	40.7045	1.81673
$503$	−17.9496	−0.800335	−0.400167	−	0.916442i	$-0.631048\pi$
$503$	−17.9496	−0.800335	−0.400167	+	0.916442i	$0.631048\pi$
$504$	−10.1920	−0.453988
$505$	43.9988	1.95792
$506$	−42.7916	−1.90232
$507$	−4.54494	−0.201848
$508$	68.3209	3.03125
$509$	−38.7245	−1.71644	−0.858218	−	0.513286i	$-0.828428\pi$
$509$	−38.7245	−1.71644	−0.858218	+	0.513286i	$0.828428\pi$
$510$	−21.8746	−0.968626
$511$	−1.05983	−0.0468839
$512$	−101.649	−4.49229
$513$	−7.47189	−0.329892
$514$	−58.3983	−2.57584
$515$	8.81256	0.388328
$516$	9.55404	0.420593
$517$	20.4163	0.897908
$518$	−17.5246	−0.769985
$519$	−23.7435	−1.04223
$520$	133.252	5.84349
$521$	−23.5216	−1.03050	−0.515250	−	0.857040i	$-0.672301\pi$
$521$	−23.5216	−1.03050	−0.515250	+	0.857040i	$0.672301\pi$
$522$	27.7856	1.21614
$523$	−19.8943	−0.869918	−0.434959	−	0.900450i	$-0.643237\pi$
$523$	−19.8943	−0.869918	−0.434959	+	0.900450i	$0.643237\pi$
$524$	−17.7526	−0.775526
$525$	−4.74265	−0.206986
$526$	37.4677	1.63367
$527$	1.63425	0.0711890
$528$	−106.107	−4.61771
$529$	−16.9607	−0.737423
$530$	−6.75093	−0.293242
$531$	7.64211	0.331639
$532$	42.4266	1.83943
$533$	37.4169	1.62071
$534$	25.7012	1.11220
$535$	−25.9395	−1.12146
$536$	−93.7509	−4.04942
$537$	15.7072	0.677815
$538$	8.99436	0.387775
$539$	6.28403	0.270672
$540$	−17.7234	−0.762692
$541$	−28.1072	−1.20842	−0.604211	−	0.796825i	$-0.706511\pi$
$541$	−28.1072	−1.20842	−0.604211	+	0.796825i	$0.706511\pi$
$542$	32.9790	1.41657
$543$	−22.5661	−0.968406
$544$	66.7796	2.86315
$545$	27.6945	1.18630
$546$	−11.6066	−0.496716
$547$	−25.7852	−1.10249	−0.551247	−	0.834342i	$-0.685848\pi$
$547$	−25.7852	−1.10249	−0.551247	+	0.834342i	$0.685848\pi$
$548$	−104.681	−4.47174
$549$	0.562450	0.0240048
$550$	−82.5824	−3.52133
$551$	−74.9241	−3.19188
$552$	25.0467	1.06606
$553$	4.70214	0.199955
$554$	89.9735	3.82261
$555$	−19.7404	−0.837935
$556$	59.9780	2.54363
$557$	23.3192	0.988066	0.494033	−	0.869443i	$-0.335522\pi$
$557$	23.3192	0.988066	0.494033	+	0.869443i	$0.335522\pi$
$558$	1.79049	0.0757976
$559$	7.04783	0.298091
$560$	52.7041	2.22715
$561$	15.8932	0.671013
$562$	−34.4839	−1.45462
$563$	8.31894	0.350602	0.175301	−	0.984515i	$-0.443910\pi$
$563$	8.31894	0.350602	0.175301	+	0.984515i	$0.443910\pi$
$564$	−18.4479	−0.776796
$565$	9.69622	0.407923
$566$	−71.9743	−3.02530
$567$	1.00000	0.0419961
$568$	32.0971	1.34676
$569$	−39.6174	−1.66085	−0.830424	−	0.557132i	$-0.811902\pi$
$569$	−39.6174	−1.66085	−0.830424	+	0.557132i	$0.811902\pi$
$570$	64.6246	2.70683
$571$	−6.34564	−0.265557	−0.132778	−	0.991146i	$-0.542390\pi$
$571$	−6.34564	−0.265557	−0.132778	+	0.991146i	$0.542390\pi$
$572$	−149.459	−6.24919
$573$	1.00000	0.0417756
$574$	24.7526	1.03315
$575$	11.6550	0.486048
$576$	39.3938	1.64141
$577$	−20.9118	−0.870570	−0.435285	−	0.900293i	$-0.643352\pi$
$577$	−20.9118	−0.870570	−0.435285	+	0.900293i	$0.643352\pi$
$578$	29.3815	1.22211
$579$	−19.8086	−0.823217
$580$	−177.720	−7.37944
$581$	4.81026	0.199563
$582$	25.0467	1.03822
$583$	4.90496	0.203142
$584$	10.8017	0.446979
$585$	−13.0742	−0.540551
$586$	−71.6211	−2.95864
$587$	2.85454	0.117819	0.0589097	−	0.998263i	$-0.481238\pi$
$587$	2.85454	0.117819	0.0589097	+	0.998263i	$0.481238\pi$
$588$	−5.67816	−0.234163
$589$	−4.82808	−0.198938
$590$	−66.0968	−2.72116
$591$	25.9345	1.06680
$592$	106.788	4.38898
$593$	−31.7185	−1.30252	−0.651262	−	0.758853i	$-0.725760\pi$
$593$	−31.7185	−1.30252	−0.651262	+	0.758853i	$0.725760\pi$
$594$	17.4127	0.714453
$595$	−7.89428	−0.323634
$596$	−64.6044	−2.64630
$597$	−23.9062	−0.978415
$598$	28.5231	1.16640
$599$	45.3864	1.85444	0.927219	−	0.374520i	$-0.122192\pi$
$599$	45.3864	1.85444	0.927219	+	0.374520i	$0.122192\pi$
$600$	48.3370	1.97335
$601$	−22.6636	−0.924469	−0.462234	−	0.886758i	$-0.652952\pi$
$601$	−22.6636	−0.924469	−0.462234	+	0.886758i	$0.652952\pi$
$602$	4.66238	0.190025
$603$	9.19848	0.374591
$604$	36.3269	1.47812
$605$	88.9234	3.61525
$606$	39.0599	1.58670
$607$	42.2788	1.71604	0.858022	−	0.513613i	$-0.171693\pi$
$607$	42.2788	1.71604	0.858022	+	0.513613i	$0.171693\pi$
$608$	−197.288	−8.00108
$609$	10.0275	0.406333
$610$	−4.86464	−0.196964
$611$	−13.6086	−0.550546
$612$	−14.3609	−0.580505
$613$	3.37584	0.136349	0.0681745	−	0.997673i	$-0.478283\pi$
$613$	3.37584	0.136349	0.0681745	+	0.997673i	$0.478283\pi$
$614$	19.5837	0.790335
$615$	27.8824	1.12433
$616$	−64.0468	−2.58052
$617$	11.2173	0.451593	0.225796	−	0.974175i	$-0.427502\pi$
$617$	11.2173	0.451593	0.225796	+	0.974175i	$0.427502\pi$
$618$	7.82334	0.314701
$619$	−3.52849	−0.141822	−0.0709111	−	0.997483i	$-0.522591\pi$
$619$	−3.52849	−0.141822	−0.0709111	+	0.997483i	$0.522591\pi$
$620$	−11.4522	−0.459933
$621$	−2.45749	−0.0986157
$622$	0.509324	0.0204220
$623$	9.27522	0.371604
$624$	70.7264	2.83132
$625$	−26.2205	−1.04882
$626$	−48.5342	−1.93982
$627$	−46.9536	−1.87515
$628$	−80.7992	−3.22424
$629$	−15.9953	−0.637775
$630$	−8.64902	−0.344585
$631$	14.9987	0.597089	0.298545	−	0.954396i	$-0.403499\pi$
$631$	14.9987	0.597089	0.298545	+	0.954396i	$0.403499\pi$
$632$	−47.9242	−1.90632
$633$	18.2027	0.723493
$634$	1.09954	0.0436684
$635$	37.5564	1.49038
$636$	−4.43205	−0.175742
$637$	−4.18867	−0.165961
$638$	174.605	6.91270
$639$	−3.14925	−0.124582
$640$	−175.887	−6.95254
$641$	10.3042	0.406992	0.203496	−	0.979076i	$-0.434770\pi$
$641$	10.3042	0.406992	0.203496	+	0.979076i	$0.434770\pi$
$642$	−23.0278	−0.908834
$643$	27.3567	1.07884	0.539422	−	0.842036i	$-0.318643\pi$
$643$	27.3567	1.07884	0.539422	+	0.842036i	$0.318643\pi$
$644$	13.9540	0.549866
$645$	5.25192	0.206794
$646$	52.3641	2.06024
$647$	−5.60051	−0.220179	−0.110089	−	0.993922i	$-0.535114\pi$
$647$	−5.60051	−0.220179	−0.110089	+	0.993922i	$0.535114\pi$
$648$	−10.1920	−0.400379
$649$	48.0232	1.88508
$650$	55.0459	2.15908
$651$	0.646166	0.0253252
$652$	−28.2982	−1.10824
$653$	20.1826	0.789806	0.394903	−	0.918723i	$-0.370778\pi$
$653$	20.1826	0.789806	0.394903	+	0.918723i	$0.370778\pi$
$654$	24.5858	0.961379
$655$	−9.75873	−0.381305
$656$	−150.834	−5.88906
$657$	−1.05983	−0.0413477
$658$	−9.00258	−0.350957
$659$	12.1601	0.473692	0.236846	−	0.971547i	$-0.423886\pi$
$659$	12.1601	0.473692	0.236846	+	0.971547i	$0.423886\pi$
$660$	−111.374	−4.33523
$661$	−5.97958	−0.232579	−0.116289	−	0.993215i	$-0.537100\pi$
$661$	−5.97958	−0.232579	−0.116289	+	0.993215i	$0.537100\pi$
$662$	13.4535	0.522886
$663$	−10.5938	−0.411427
$664$	−49.0262	−1.90258
$665$	23.3222	0.904395
$666$	−17.5246	−0.679063
$667$	−24.6424	−0.954157
$668$	−99.7297	−3.85866
$669$	8.92944	0.345232
$670$	−79.5579	−3.07359
$671$	3.53445	0.136446
$672$	26.4040	1.01856
$673$	2.35548	0.0907970	0.0453985	−	0.998969i	$-0.485544\pi$
$673$	2.35548	0.0907970	0.0453985	+	0.998969i	$0.485544\pi$
$674$	55.4563	2.13610
$675$	−4.74265	−0.182545
$676$	25.8069	0.992573
$677$	4.20383	0.161566	0.0807831	−	0.996732i	$-0.474258\pi$
$677$	4.20383	0.161566	0.0807831	+	0.996732i	$0.474258\pi$
$678$	8.60781	0.330581
$679$	9.03905	0.346887
$680$	80.4585	3.08544
$681$	−21.3965	−0.819915
$682$	11.2515	0.430843
$683$	1.58480	0.0606407	0.0303203	−	0.999540i	$-0.490347\pi$
$683$	1.58480	0.0606407	0.0303203	+	0.999540i	$0.490347\pi$
$684$	42.4266	1.62222
$685$	−57.5437	−2.19863
$686$	−2.77095	−0.105795
$687$	13.2826	0.506764
$688$	−28.4109	−1.08316
$689$	−3.26943	−0.124556
$690$	21.2549	0.809160
$691$	−12.0353	−0.457843	−0.228922	−	0.973445i	$-0.573520\pi$
$691$	−12.0353	−0.457843	−0.228922	+	0.973445i	$0.573520\pi$
$692$	134.820	5.12507
$693$	6.28403	0.238711
$694$	40.4919	1.53705
$695$	32.9703	1.25063
$696$	−102.200	−3.87388
$697$	22.5926	0.855756
$698$	34.0028	1.28703
$699$	−24.5926	−0.930178
$700$	26.9295	1.01784
$701$	8.10005	0.305935	0.152967	−	0.988231i	$-0.451117\pi$
$701$	8.10005	0.305935	0.152967	+	0.988231i	$0.451117\pi$
$702$	−11.6066	−0.438062
$703$	47.2552	1.78226
$704$	247.552	9.32995
$705$	−10.1409	−0.381929
$706$	35.0249	1.31818
$707$	14.0962	0.530143
$708$	−43.3931	−1.63081
$709$	2.99551	0.112499	0.0562494	−	0.998417i	$-0.482086\pi$
$709$	2.99551	0.112499	0.0562494	+	0.998417i	$0.482086\pi$
$710$	27.2379	1.02222
$711$	4.70214	0.176344
$712$	−94.5330	−3.54277
$713$	−1.58795	−0.0594691
$714$	−7.00814	−0.262273
$715$	−82.1585	−3.07256
$716$	−89.1879	−3.33311
$717$	3.18917	0.119102
$718$	−57.7574	−2.15549
$719$	−10.1687	−0.379229	−0.189615	−	0.981859i	$-0.560724\pi$
$719$	−10.1687	−0.379229	−0.189615	+	0.981859i	$0.560724\pi$
$720$	52.7041	1.96417
$721$	2.82334	0.105147
$722$	−102.052	−3.79798
$723$	19.8971	0.739980
$724$	128.134	4.76207
$725$	−47.5567	−1.76621
$726$	78.9417	2.92980
$727$	37.2391	1.38112	0.690561	−	0.723274i	$-0.257364\pi$
$727$	37.2391	1.38112	0.690561	+	0.723274i	$0.257364\pi$
$728$	42.6909	1.58223
$729$	1.00000	0.0370370
$730$	9.16646	0.339266
$731$	4.25553	0.157396
$732$	−3.19368	−0.118042
$733$	38.7345	1.43069	0.715345	−	0.698771i	$-0.246269\pi$
$733$	38.7345	1.43069	0.715345	+	0.698771i	$0.246269\pi$
$734$	−22.2324	−0.820613
$735$	−3.12132	−0.115132
$736$	−64.8876	−2.39179
$737$	57.8035	2.12922
$738$	24.7526	0.911156
$739$	−6.01367	−0.221217	−0.110608	−	0.993864i	$-0.535280\pi$
$739$	−6.01367	−0.221217	−0.110608	+	0.993864i	$0.535280\pi$
$740$	112.089	4.12049
$741$	31.2973	1.14973
$742$	−2.16284	−0.0794005
$743$	−6.87020	−0.252043	−0.126022	−	0.992028i	$-0.540221\pi$
$743$	−6.87020	−0.252043	−0.126022	+	0.992028i	$0.540221\pi$
$744$	−6.58572	−0.241444
$745$	−35.5134	−1.30111
$746$	0.0853187	0.00312374
$747$	4.81026	0.175998
$748$	−90.2443	−3.29966
$749$	−8.31043	−0.303656
$750$	−2.22585	−0.0812766
$751$	−39.9437	−1.45757	−0.728783	−	0.684744i	$-0.759914\pi$
$751$	−39.9437	−1.45757	−0.728783	+	0.684744i	$0.759914\pi$
$752$	54.8586	2.00049
$753$	14.6897	0.535324
$754$	−116.385	−4.23848
$755$	19.9691	0.726752
$756$	−5.67816	−0.206513
$757$	12.7390	0.463005	0.231503	−	0.972834i	$-0.425636\pi$
$757$	12.7390	0.463005	0.231503	+	0.972834i	$0.425636\pi$
$758$	99.7727	3.62391
$759$	−15.4429	−0.560543
$760$	−237.700	−8.62227
$761$	13.7756	0.499364	0.249682	−	0.968328i	$-0.419674\pi$
$761$	13.7756	0.499364	0.249682	+	0.968328i	$0.419674\pi$
$762$	33.3407	1.20780
$763$	8.87269	0.321213
$764$	−5.67816	−0.205429
$765$	−7.89428	−0.285418
$766$	−28.3184	−1.02319
$767$	−32.0103	−1.15582
$768$	−77.3559	−2.79134
$769$	4.39596	0.158522	0.0792611	−	0.996854i	$-0.474744\pi$
$769$	4.39596	0.158522	0.0792611	+	0.996854i	$0.474744\pi$
$770$	−54.3507	−1.95866
$771$	−21.0752	−0.759004
$772$	112.476	4.04811
$773$	−19.9349	−0.717008	−0.358504	−	0.933528i	$-0.616713\pi$
$773$	−19.9349	−0.717008	−0.358504	+	0.933528i	$0.616713\pi$
$774$	4.66238	0.167586
$775$	−3.06454	−0.110081
$776$	−92.1259	−3.30713
$777$	−6.32439	−0.226886
$778$	−92.8149	−3.32757
$779$	−66.7456	−2.39141
$780$	74.2373	2.65812
$781$	−19.7900	−0.708140
$782$	17.2224	0.615873
$783$	10.0275	0.358352
$784$	16.8852	0.603042
$785$	−44.4158	−1.58527
$786$	−8.66330	−0.309010
$787$	7.70489	0.274650	0.137325	−	0.990526i	$-0.456150\pi$
$787$	7.70489	0.274650	0.137325	+	0.990526i	$0.456150\pi$
$788$	−147.260	−5.24592
$789$	13.5216	0.481383
$790$	−40.6689	−1.44694
$791$	3.10645	0.110453
$792$	−64.0468	−2.27580
$793$	−2.35592	−0.0836610
$794$	−1.66578	−0.0591164
$795$	−2.43633	−0.0864075
$796$	135.743	4.81129
$797$	−32.2287	−1.14160	−0.570799	−	0.821090i	$-0.693366\pi$
$797$	−32.2287	−1.14160	−0.570799	+	0.821090i	$0.693366\pi$
$798$	20.7042	0.732922
$799$	−8.21699	−0.290696
$800$	−125.225	−4.42737
$801$	9.27522	0.327724
$802$	−3.93187	−0.138839
$803$	−6.65998	−0.235025
$804$	−52.2304	−1.84203
$805$	7.67062	0.270354
$806$	−7.49978	−0.264169
$807$	3.24595	0.114263
$808$	−143.669	−5.05424
$809$	−2.02505	−0.0711971	−0.0355986	−	0.999366i	$-0.511334\pi$
$809$	−2.02505	−0.0711971	−0.0355986	+	0.999366i	$0.511334\pi$
$810$	−8.64902	−0.303896
$811$	−19.2173	−0.674812	−0.337406	−	0.941359i	$-0.609550\pi$
$811$	−19.2173	−0.674812	−0.337406	+	0.941359i	$0.609550\pi$
$812$	−56.9375	−1.99812
$813$	11.9017	0.417411
$814$	−110.125	−3.85987
$815$	−15.5557	−0.544892
$816$	42.7051	1.49498
$817$	−12.5722	−0.439845
$818$	37.3616	1.30632
$819$	−4.18867	−0.146364
$820$	−158.321	−5.52881
$821$	36.6066	1.27758	0.638790	−	0.769381i	$-0.279435\pi$
$821$	36.6066	1.27758	0.638790	+	0.769381i	$0.279435\pi$
$822$	−51.0843	−1.78177
$823$	0.928218	0.0323557	0.0161778	−	0.999869i	$-0.494850\pi$
$823$	0.928218	0.0323557	0.0161778	+	0.999869i	$0.494850\pi$
$824$	−28.7755	−1.00244
$825$	−29.8029	−1.03761
$826$	−21.1759	−0.736804
$827$	−49.7236	−1.72906	−0.864529	−	0.502583i	$-0.832383\pi$
$827$	−49.7236	−1.72906	−0.864529	+	0.502583i	$0.832383\pi$
$828$	13.9540	0.484936
$829$	−16.7810	−0.582828	−0.291414	−	0.956597i	$-0.594126\pi$
$829$	−16.7810	−0.582828	−0.291414	+	0.956597i	$0.594126\pi$
$830$	−41.6041	−1.44410
$831$	32.4703	1.12638
$832$	−165.007	−5.72060
$833$	−2.52915	−0.0876297
$834$	29.2693	1.01351
$835$	−54.8221	−1.89720
$836$	266.610	9.22090
$837$	0.646166	0.0223348
$838$	54.7658	1.89185
$839$	−29.0370	−1.00247	−0.501234	−	0.865312i	$-0.667121\pi$
$839$	−29.0370	−1.00247	−0.501234	+	0.865312i	$0.667121\pi$
$840$	31.8125	1.09764
$841$	71.5500	2.46724
$842$	−107.476	−3.70385
$843$	−12.4448	−0.428622
$844$	−103.358	−3.55772
$845$	14.1862	0.488021
$846$	−9.00258	−0.309515
$847$	28.4890	0.978895
$848$	13.1796	0.452590
$849$	−25.9746	−0.891446
$850$	33.2371	1.14002
$851$	15.5421	0.532777
$852$	17.8819	0.612624
$853$	−3.07111	−0.105153	−0.0525765	−	0.998617i	$-0.516743\pi$
$853$	−3.07111	−0.105153	−0.0525765	+	0.998617i	$0.516743\pi$
$854$	−1.55852	−0.0533314
$855$	23.3222	0.797602
$856$	84.6998	2.89498
$857$	33.1704	1.13308	0.566540	−	0.824034i	$-0.308281\pi$
$857$	33.1704	1.13308	0.566540	+	0.824034i	$0.308281\pi$
$858$	−72.9361	−2.49000
$859$	−19.0705	−0.650677	−0.325339	−	0.945598i	$-0.605478\pi$
$859$	−19.0705	−0.650677	−0.325339	+	0.945598i	$0.605478\pi$
$860$	−29.8212	−1.01690
$861$	8.93290	0.304432
$862$	−37.7338	−1.28522
$863$	36.6286	1.24685	0.623426	−	0.781883i	$-0.285740\pi$
$863$	36.6286	1.24685	0.623426	+	0.781883i	$0.285740\pi$
$864$	26.4040	0.898282
$865$	74.1112	2.51986
$866$	−43.1934	−1.46777
$867$	10.6034	0.360111
$868$	−3.66903	−0.124535
$869$	29.5484	1.00236
$870$	−86.7277	−2.94035
$871$	−38.5294	−1.30552
$872$	−90.4304	−3.06236
$873$	9.03905	0.305925
$874$	−50.8805	−1.72106
$875$	−0.803282	−0.0271559
$876$	6.01786	0.203325
$877$	11.5987	0.391661	0.195831	−	0.980638i	$-0.437260\pi$
$877$	11.5987	0.391661	0.195831	+	0.980638i	$0.437260\pi$
$878$	−83.9473	−2.83308
$879$	−25.8471	−0.871802
$880$	331.194	11.1645
$881$	−5.27022	−0.177558	−0.0887790	−	0.996051i	$-0.528297\pi$
$881$	−5.27022	−0.177558	−0.0887790	+	0.996051i	$0.528297\pi$
$882$	−2.77095	−0.0933027
$883$	−13.8075	−0.464660	−0.232330	−	0.972637i	$-0.574635\pi$
$883$	−13.8075	−0.464660	−0.232330	+	0.972637i	$0.574635\pi$
$884$	60.1530	2.02317
$885$	−23.8535	−0.801826
$886$	51.9280	1.74456
$887$	−11.5753	−0.388660	−0.194330	−	0.980936i	$-0.562253\pi$
$887$	−11.5753	−0.388660	−0.194330	+	0.980936i	$0.562253\pi$
$888$	64.4581	2.16307
$889$	12.0322	0.403548
$890$	−80.2216	−2.68903
$891$	6.28403	0.210523
$892$	−50.7028	−1.69766
$893$	24.2756	0.812351
$894$	−31.5270	−1.05442
$895$	−49.0272	−1.63880
$896$	−56.3501	−1.88253
$897$	10.2936	0.343694
$898$	79.1809	2.64230
$899$	6.47941	0.216100
$900$	26.9295	0.897650
$901$	−1.97411	−0.0657671
$902$	155.546	5.17912
$903$	1.68259	0.0559932
$904$	−31.6609	−1.05303
$905$	70.4362	2.34138
$906$	17.7276	0.588960
$907$	−4.15249	−0.137881	−0.0689405	−	0.997621i	$-0.521962\pi$
$907$	−4.15249	−0.137881	−0.0689405	+	0.997621i	$0.521962\pi$
$908$	121.493	4.03187
$909$	14.0962	0.467542
$910$	36.2279	1.20094
$911$	−7.38233	−0.244588	−0.122294	−	0.992494i	$-0.539025\pi$
$911$	−7.38233	−0.244588	−0.122294	+	0.992494i	$0.539025\pi$
$912$	−126.164	−4.17772
$913$	30.2278	1.00040
$914$	12.4804	0.412816
$915$	−1.75559	−0.0580379
$916$	−75.4209	−2.49198
$917$	−3.12647	−0.103245
$918$	−7.00814	−0.231303
$919$	46.6371	1.53841	0.769207	−	0.638999i	$-0.220651\pi$
$919$	46.6371	1.53841	0.769207	+	0.638999i	$0.220651\pi$
$920$	−78.1789	−2.57748
$921$	7.06752	0.232883
$922$	−110.567	−3.64134
$923$	13.1911	0.434192
$924$	−35.6817	−1.17384
$925$	29.9943	0.986208
$926$	−20.9047	−0.686971
$927$	2.82334	0.0927307
$928$	264.765	8.69134
$929$	12.4393	0.408119	0.204059	−	0.978959i	$-0.434586\pi$
$929$	12.4393	0.408119	0.204059	+	0.978959i	$0.434586\pi$
$930$	−5.58871	−0.183261
$931$	7.47189	0.244881
$932$	139.641	4.57409
$933$	0.183809	0.00601762
$934$	−104.087	−3.40583
$935$	−49.6079	−1.62235
$936$	42.6909	1.39540
$937$	2.75370	0.0899594	0.0449797	−	0.998988i	$-0.485678\pi$
$937$	2.75370	0.0899594	0.0449797	+	0.998988i	$0.485678\pi$
$938$	−25.4885	−0.832230
$939$	−17.5154	−0.571592
$940$	57.5817	1.87811
$941$	−1.01943	−0.0332325	−0.0166162	−	0.999862i	$-0.505289\pi$
$941$	−1.01943	−0.0332325	−0.0166162	+	0.999862i	$0.505289\pi$
$942$	−39.4301	−1.28470
$943$	−21.9525	−0.714872
$944$	129.038	4.19984
$945$	−3.12132	−0.101537
$946$	29.2986	0.952579
$947$	−20.0523	−0.651611	−0.325806	−	0.945437i	$-0.605636\pi$
$947$	−20.0523	−0.651611	−0.325806	+	0.945437i	$0.605636\pi$
$948$	−26.6995	−0.867160
$949$	4.43926	0.144104
$950$	−98.1929	−3.18580
$951$	0.396811	0.0128675
$952$	25.7771	0.835439
$953$	−19.8395	−0.642663	−0.321332	−	0.946967i	$-0.604130\pi$
$953$	−19.8395	−0.642663	−0.321332	+	0.946967i	$0.604130\pi$
$954$	−2.16284	−0.0700247
$955$	−3.12132	−0.101004
$956$	−18.1086	−0.585675
$957$	63.0129	2.03692
$958$	−46.1056	−1.48960
$959$	−18.4357	−0.595319
$960$	−122.961	−3.96854
$961$	−30.5825	−0.986531
$962$	73.4045	2.36666
$963$	−8.31043	−0.267800
$964$	−112.979	−3.63880
$965$	61.8290	1.99034
$966$	6.80958	0.219095
$967$	−45.5916	−1.46613	−0.733064	−	0.680159i	$-0.761911\pi$
$967$	−45.5916	−1.46613	−0.733064	+	0.680159i	$0.761911\pi$
$968$	−290.360	−9.33253
$969$	18.8975	0.607076
$970$	−78.1789	−2.51017
$971$	−10.0997	−0.324114	−0.162057	−	0.986781i	$-0.551813\pi$
$971$	−10.0997	−0.324114	−0.162057	+	0.986781i	$0.551813\pi$
$972$	−5.67816	−0.182127
$973$	10.5629	0.338632
$974$	−60.3242	−1.93291
$975$	19.8654	0.636201
$976$	9.49707	0.303994
$977$	52.0880	1.66644	0.833221	−	0.552940i	$-0.186494\pi$
$977$	52.0880	1.66644	0.833221	+	0.552940i	$0.186494\pi$
$978$	−13.8095	−0.441580
$979$	58.2857	1.86282
$980$	17.7234	0.566152
$981$	8.87269	0.283283
$982$	−108.203	−3.45289
$983$	−12.7020	−0.405130	−0.202565	−	0.979269i	$-0.564928\pi$
$983$	−12.7020	−0.405130	−0.202565	+	0.979269i	$0.564928\pi$
$984$	−91.0440	−2.90238
$985$	−80.9498	−2.57927
$986$	−70.2738	−2.23797
$987$	−3.24892	−0.103414
$988$	−177.711	−5.65374
$989$	−4.13496	−0.131484
$990$	−54.3507	−1.72738
$991$	7.83029	0.248737	0.124369	−	0.992236i	$-0.460309\pi$
$991$	7.83029	0.248737	0.124369	+	0.992236i	$0.460309\pi$
$992$	17.0614	0.541699
$993$	4.85520	0.154075
$994$	8.72640	0.276785
$995$	74.6189	2.36558
$996$	−27.3134	−0.865460
$997$	−36.4300	−1.15375	−0.576875	−	0.816832i	$-0.695728\pi$
$997$	−36.4300	−1.15375	−0.576875	+	0.816832i	$0.695728\pi$
$998$	41.0460	1.29929
$999$	−6.32439	−0.200095

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.l.1.1	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.l.1.1	✓	28	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.77095 q^{2} -1.00000 q^{3} +5.67816 q^{4} +3.12132 q^{5} +2.77095 q^{6} +1.00000 q^{7} -10.1920 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.77095 q^{2} -1.00000 q^{3} +5.67816 q^{4} +3.12132 q^{5} +2.77095 q^{6} +1.00000 q^{7} -10.1920 q^{8} +1.00000 q^{9} -8.64902 q^{10} +6.28403 q^{11} -5.67816 q^{12} -4.18867 q^{13} -2.77095 q^{14} -3.12132 q^{15} +16.8852 q^{16} -2.52915 q^{17} -2.77095 q^{18} +7.47189 q^{19} +17.7234 q^{20} -1.00000 q^{21} -17.4127 q^{22} +2.45749 q^{23} +10.1920 q^{24} +4.74265 q^{25} +11.6066 q^{26} -1.00000 q^{27} +5.67816 q^{28} -10.0275 q^{29} +8.64902 q^{30} -0.646166 q^{31} -26.4040 q^{32} -6.28403 q^{33} +7.00814 q^{34} +3.12132 q^{35} +5.67816 q^{36} +6.32439 q^{37} -20.7042 q^{38} +4.18867 q^{39} -31.8125 q^{40} -8.93290 q^{41} +2.77095 q^{42} -1.68259 q^{43} +35.6817 q^{44} +3.12132 q^{45} -6.80958 q^{46} +3.24892 q^{47} -16.8852 q^{48} +1.00000 q^{49} -13.1416 q^{50} +2.52915 q^{51} -23.7839 q^{52} +0.780543 q^{53} +2.77095 q^{54} +19.6145 q^{55} -10.1920 q^{56} -7.47189 q^{57} +27.7856 q^{58} +7.64211 q^{59} -17.7234 q^{60} +0.562450 q^{61} +1.79049 q^{62} +1.00000 q^{63} +39.3938 q^{64} -13.0742 q^{65} +17.4127 q^{66} +9.19848 q^{67} -14.3609 q^{68} -2.45749 q^{69} -8.64902 q^{70} -3.14925 q^{71} -10.1920 q^{72} -1.05983 q^{73} -17.5246 q^{74} -4.74265 q^{75} +42.4266 q^{76} +6.28403 q^{77} -11.6066 q^{78} +4.70214 q^{79} +52.7041 q^{80} +1.00000 q^{81} +24.7526 q^{82} +4.81026 q^{83} -5.67816 q^{84} -7.89428 q^{85} +4.66238 q^{86} +10.0275 q^{87} -64.0468 q^{88} +9.27522 q^{89} -8.64902 q^{90} -4.18867 q^{91} +13.9540 q^{92} +0.646166 q^{93} -9.00258 q^{94} +23.3222 q^{95} +26.4040 q^{96} +9.03905 q^{97} -2.77095 q^{98} +6.28403 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9}+O(q^{10}) \) 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9	\( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9} + 4 q^{10} - 8 q^{11} - 34 q^{12} + 26 q^{13} - 6 q^{14} - 8 q^{15} + 62 q^{16} + 9 q^{17} - 6 q^{18} + 25 q^{19} + 20 q^{20} - 28 q^{21} + 3 q^{22} - 30 q^{23} + 15 q^{24} + 42 q^{25} + 25 q^{26} - 28 q^{27} + 34 q^{28} - 5 q^{29} - 4 q^{30} + 18 q^{31} - 26 q^{32} + 8 q^{33} + 30 q^{34} + 8 q^{35} + 34 q^{36} + 36 q^{37} - 2 q^{38} - 26 q^{39} + 28 q^{40} + 21 q^{41} + 6 q^{42} + 8 q^{43} - 20 q^{44} + 8 q^{45} + 24 q^{46} + 6 q^{47} - 62 q^{48} + 28 q^{49} - 48 q^{50} - 9 q^{51} + 54 q^{52} - 12 q^{53} + 6 q^{54} + 15 q^{55} - 15 q^{56} - 25 q^{57} + 19 q^{58} + 33 q^{59} - 20 q^{60} + 48 q^{61} + 28 q^{63} + 75 q^{64} + 21 q^{65} - 3 q^{66} + 27 q^{67} + 19 q^{68} + 30 q^{69} + 4 q^{70} - 45 q^{71} - 15 q^{72} + 61 q^{73} - 31 q^{74} - 42 q^{75} + 63 q^{76} - 8 q^{77} - 25 q^{78} + 35 q^{79} + 84 q^{80} + 28 q^{81} + 11 q^{82} + 43 q^{83} - 34 q^{84} + 43 q^{85} - q^{86} + 5 q^{87} - 27 q^{88} + 25 q^{89} + 4 q^{90} + 26 q^{91} - 102 q^{92} - 18 q^{93} + 55 q^{94} - 43 q^{95} + 26 q^{96} + 40 q^{97} - 6 q^{98} - 8 q^{99}+O(q^{100}) \) 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9 + 4 * q^10 - 8 * q^11 - 34 * q^12 + 26 * q^13 - 6 * q^14 - 8 * q^15 + 62 * q^16 + 9 * q^17 - 6 * q^18 + 25 * q^19 + 20 * q^20 - 28 * q^21 + 3 * q^22 - 30 * q^23 + 15 * q^24 + 42 * q^25 + 25 * q^26 - 28 * q^27 + 34 * q^28 - 5 * q^29 - 4 * q^30 + 18 * q^31 - 26 * q^32 + 8 * q^33 + 30 * q^34 + 8 * q^35 + 34 * q^36 + 36 * q^37 - 2 * q^38 - 26 * q^39 + 28 * q^40 + 21 * q^41 + 6 * q^42 + 8 * q^43 - 20 * q^44 + 8 * q^45 + 24 * q^46 + 6 * q^47 - 62 * q^48 + 28 * q^49 - 48 * q^50 - 9 * q^51 + 54 * q^52 - 12 * q^53 + 6 * q^54 + 15 * q^55 - 15 * q^56 - 25 * q^57 + 19 * q^58 + 33 * q^59 - 20 * q^60 + 48 * q^61 + 28 * q^63 + 75 * q^64 + 21 * q^65 - 3 * q^66 + 27 * q^67 + 19 * q^68 + 30 * q^69 + 4 * q^70 - 45 * q^71 - 15 * q^72 + 61 * q^73 - 31 * q^74 - 42 * q^75 + 63 * q^76 - 8 * q^77 - 25 * q^78 + 35 * q^79 + 84 * q^80 + 28 * q^81 + 11 * q^82 + 43 * q^83 - 34 * q^84 + 43 * q^85 - q^86 + 5 * q^87 - 27 * q^88 + 25 * q^89 + 4 * q^90 + 26 * q^91 - 102 * q^92 - 18 * q^93 + 55 * q^94 - 43 * q^95 + 26 * q^96 + 40 * q^97 - 6 * q^98 - 8 * q^99

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