LMFDB - Embedded newform 6023.2.a.c.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$0$
Dimension:	$138$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.56824 q^{2} -3.23259 q^{3} +4.59584 q^{4} -2.23172 q^{5} +8.30205 q^{6} +3.00174 q^{7} -6.66674 q^{8} +7.44963 q^{9} +O(q^{10})$	\(q-2.56824 q^{2} -3.23259 q^{3} +4.59584 q^{4} -2.23172 q^{5} +8.30205 q^{6} +3.00174 q^{7} -6.66674 q^{8} +7.44963 q^{9} +5.73158 q^{10} -4.24801 q^{11} -14.8565 q^{12} +4.02229 q^{13} -7.70919 q^{14} +7.21423 q^{15} +7.93008 q^{16} -1.85331 q^{17} -19.1324 q^{18} +1.00000 q^{19} -10.2566 q^{20} -9.70340 q^{21} +10.9099 q^{22} -2.49674 q^{23} +21.5508 q^{24} -0.0194305 q^{25} -10.3302 q^{26} -14.3838 q^{27} +13.7955 q^{28} +1.40698 q^{29} -18.5278 q^{30} -5.52317 q^{31} -7.03286 q^{32} +13.7321 q^{33} +4.75974 q^{34} -6.69905 q^{35} +34.2373 q^{36} +5.39577 q^{37} -2.56824 q^{38} -13.0024 q^{39} +14.8783 q^{40} +3.23794 q^{41} +24.9206 q^{42} -10.9769 q^{43} -19.5232 q^{44} -16.6255 q^{45} +6.41222 q^{46} -1.63152 q^{47} -25.6347 q^{48} +2.01046 q^{49} +0.0499020 q^{50} +5.99099 q^{51} +18.4858 q^{52} +8.47194 q^{53} +36.9410 q^{54} +9.48037 q^{55} -20.0118 q^{56} -3.23259 q^{57} -3.61347 q^{58} +0.541291 q^{59} +33.1555 q^{60} -7.23708 q^{61} +14.1848 q^{62} +22.3619 q^{63} +2.20188 q^{64} -8.97662 q^{65} -35.2672 q^{66} +0.903608 q^{67} -8.51753 q^{68} +8.07093 q^{69} +17.2047 q^{70} +11.1530 q^{71} -49.6647 q^{72} +16.7656 q^{73} -13.8576 q^{74} +0.0628107 q^{75} +4.59584 q^{76} -12.7514 q^{77} +33.3933 q^{78} -1.43325 q^{79} -17.6977 q^{80} +24.1480 q^{81} -8.31580 q^{82} +9.95222 q^{83} -44.5953 q^{84} +4.13607 q^{85} +28.1913 q^{86} -4.54820 q^{87} +28.3204 q^{88} -14.9092 q^{89} +42.6982 q^{90} +12.0739 q^{91} -11.4746 q^{92} +17.8541 q^{93} +4.19014 q^{94} -2.23172 q^{95} +22.7343 q^{96} +4.35895 q^{97} -5.16333 q^{98} -31.6461 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) $ 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * 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 $

$2$	−2.56824	−1.81602	−0.908009	−	0.418951i	$-0.862398\pi$
$2$	−2.56824	−1.81602	−0.908009	+	0.418951i	$0.862398\pi$
$3$	−3.23259	−1.86634	−0.933168	−	0.359441i	$-0.882967\pi$
$3$	−3.23259	−1.86634	−0.933168	+	0.359441i	$0.882967\pi$
$4$	4.59584	2.29792
$5$	−2.23172	−0.998055	−0.499028	−	0.866586i	$-0.666309\pi$
$5$	−2.23172	−0.998055	−0.499028	+	0.866586i	$0.666309\pi$
$6$	8.30205	3.38930
$7$	3.00174	1.13455	0.567276	−	0.823528i	$-0.307997\pi$
$7$	3.00174	1.13455	0.567276	+	0.823528i	$0.307997\pi$
$8$	−6.66674	−2.35705
$9$	7.44963	2.48321
$10$	5.73158	1.81249
$11$	−4.24801	−1.28082	−0.640412	−	0.768032i	$-0.721236\pi$
$11$	−4.24801	−1.28082	−0.640412	+	0.768032i	$0.721236\pi$
$12$	−14.8565	−4.28869
$13$	4.02229	1.11558	0.557791	−	0.829981i	$-0.311649\pi$
$13$	4.02229	1.11558	0.557791	+	0.829981i	$0.311649\pi$
$14$	−7.70919	−2.06037
$15$	7.21423	1.86271
$16$	7.93008	1.98252
$17$	−1.85331	−0.449494	−0.224747	−	0.974417i	$-0.572156\pi$
$17$	−1.85331	−0.449494	−0.224747	+	0.974417i	$0.572156\pi$
$18$	−19.1324	−4.50955
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−10.2566	−2.29345
$21$	−9.70340	−2.11745
$22$	10.9099	2.32600
$23$	−2.49674	−0.520606	−0.260303	−	0.965527i	$-0.583822\pi$
$23$	−2.49674	−0.520606	−0.260303	+	0.965527i	$0.583822\pi$
$24$	21.5508	4.39904
$25$	−0.0194305	−0.00388609
$26$	−10.3302	−2.02592
$27$	−14.3838	−2.76816
$28$	13.7955	2.60711
$29$	1.40698	0.261270	0.130635	−	0.991431i	$-0.458298\pi$
$29$	1.40698	0.261270	0.130635	+	0.991431i	$0.458298\pi$
$30$	−18.5278	−3.38271
$31$	−5.52317	−0.991990	−0.495995	−	0.868325i	$-0.665197\pi$
$31$	−5.52317	−0.991990	−0.495995	+	0.868325i	$0.665197\pi$
$32$	−7.03286	−1.24325
$33$	13.7321	2.39045
$34$	4.75974	0.816289
$35$	−6.69905	−1.13235
$36$	34.2373	5.70622
$37$	5.39577	0.887059	0.443530	−	0.896260i	$-0.353726\pi$
$37$	5.39577	0.887059	0.443530	+	0.896260i	$0.353726\pi$
$38$	−2.56824	−0.416623
$39$	−13.0024	−2.08205
$40$	14.8783	2.35246
$41$	3.23794	0.505681	0.252841	−	0.967508i	$-0.418635\pi$
$41$	3.23794	0.505681	0.252841	+	0.967508i	$0.418635\pi$
$42$	24.9206	3.84534
$43$	−10.9769	−1.67396	−0.836980	−	0.547234i	$-0.815681\pi$
$43$	−10.9769	−1.67396	−0.836980	+	0.547234i	$0.815681\pi$
$44$	−19.5232	−2.94323
$45$	−16.6255	−2.47838
$46$	6.41222	0.945430
$47$	−1.63152	−0.237982	−0.118991	−	0.992895i	$-0.537966\pi$
$47$	−1.63152	−0.237982	−0.118991	+	0.992895i	$0.537966\pi$
$48$	−25.6347	−3.70005
$49$	2.01046	0.287208
$50$	0.0499020	0.00705721
$51$	5.99099	0.838907
$52$	18.4858	2.56352
$53$	8.47194	1.16371	0.581855	−	0.813293i	$-0.302327\pi$
$53$	8.47194	1.16371	0.581855	+	0.813293i	$0.302327\pi$
$54$	36.9410	5.02704
$55$	9.48037	1.27833
$56$	−20.0118	−2.67419
$57$	−3.23259	−0.428167
$58$	−3.61347	−0.474472
$59$	0.541291	0.0704701	0.0352351	−	0.999379i	$-0.488782\pi$
$59$	0.541291	0.0704701	0.0352351	+	0.999379i	$0.488782\pi$
$60$	33.1555	4.28035
$61$	−7.23708	−0.926613	−0.463307	−	0.886198i	$-0.653337\pi$
$61$	−7.23708	−0.926613	−0.463307	+	0.886198i	$0.653337\pi$
$62$	14.1848	1.80147
$63$	22.3619	2.81733
$64$	2.20188	0.275235
$65$	−8.97662	−1.11341
$66$	−35.2672	−4.34110
$67$	0.903608	0.110393	0.0551966	−	0.998476i	$-0.482421\pi$
$67$	0.903608	0.110393	0.0551966	+	0.998476i	$0.482421\pi$
$68$	−8.51753	−1.03290
$69$	8.07093	0.971625
$70$	17.2047	2.05636
$71$	11.1530	1.32362	0.661810	−	0.749672i	$-0.269789\pi$
$71$	11.1530	1.32362	0.661810	+	0.749672i	$0.269789\pi$
$72$	−49.6647	−5.85304
$73$	16.7656	1.96227	0.981135	−	0.193323i	$-0.0619267\pi$
$73$	16.7656	1.96227	0.981135	+	0.193323i	$0.0619267\pi$
$74$	−13.8576	−1.61092
$75$	0.0628107	0.00725275
$76$	4.59584	0.527179
$77$	−12.7514	−1.45316
$78$	33.3933	3.78104
$79$	−1.43325	−0.161253	−0.0806266	−	0.996744i	$-0.525692\pi$
$79$	−1.43325	−0.161253	−0.0806266	+	0.996744i	$0.525692\pi$
$80$	−17.6977	−1.97866
$81$	24.1480	2.68312
$82$	−8.31580	−0.918326
$83$	9.95222	1.09240	0.546199	−	0.837655i	$-0.316074\pi$
$83$	9.95222	1.09240	0.546199	+	0.837655i	$0.316074\pi$
$84$	−44.5953	−4.86574
$85$	4.13607	0.448620
$86$	28.1913	3.03994
$87$	−4.54820	−0.487618
$88$	28.3204	3.01896
$89$	−14.9092	−1.58038	−0.790188	−	0.612865i	$-0.790017\pi$
$89$	−14.9092	−1.58038	−0.790188	+	0.612865i	$0.790017\pi$
$90$	42.6982	4.50078
$91$	12.0739	1.26569
$92$	−11.4746	−1.19631
$93$	17.8541	1.85139
$94$	4.19014	0.432180
$95$	−2.23172	−0.228970
$96$	22.7343	2.32031
$97$	4.35895	0.442584	0.221292	−	0.975208i	$-0.428973\pi$
$97$	4.35895	0.442584	0.221292	+	0.975208i	$0.428973\pi$
$98$	−5.16333	−0.521575
$99$	−31.6461	−3.18055
$100$	−0.0892993	−0.00892993
$101$	−13.2706	−1.32048	−0.660239	−	0.751055i	$-0.729545\pi$
$101$	−13.2706	−1.32048	−0.660239	+	0.751055i	$0.729545\pi$
$102$	−15.3863	−1.52347
$103$	3.96316	0.390502	0.195251	−	0.980753i	$-0.437448\pi$
$103$	3.96316	0.390502	0.195251	+	0.980753i	$0.437448\pi$
$104$	−26.8156	−2.62948
$105$	21.6553	2.11334
$106$	−21.7579	−2.11332
$107$	−3.27286	−0.316400	−0.158200	−	0.987407i	$-0.550569\pi$
$107$	−3.27286	−0.316400	−0.158200	+	0.987407i	$0.550569\pi$
$108$	−66.1057	−6.36102
$109$	9.78406	0.937143	0.468571	−	0.883426i	$-0.344769\pi$
$109$	9.78406	0.937143	0.468571	+	0.883426i	$0.344769\pi$
$110$	−24.3478	−2.32148
$111$	−17.4423	−1.65555
$112$	23.8041	2.24927
$113$	8.36200	0.786631	0.393316	−	0.919404i	$-0.371328\pi$
$113$	8.36200	0.786631	0.393316	+	0.919404i	$0.371328\pi$
$114$	8.30205	0.777558
$115$	5.57202	0.519593
$116$	6.46628	0.600379
$117$	29.9646	2.77022
$118$	−1.39016	−0.127975
$119$	−5.56316	−0.509974
$120$	−48.0954	−4.39049
$121$	7.04561	0.640510
$122$	18.5865	1.68275
$123$	−10.4669	−0.943771
$124$	−25.3836	−2.27952
$125$	11.2020	1.00193
$126$	−57.4306	−5.11632
$127$	4.24295	0.376501	0.188251	−	0.982121i	$-0.439718\pi$
$127$	4.24295	0.376501	0.188251	+	0.982121i	$0.439718\pi$
$128$	8.41077	0.743414
$129$	35.4838	3.12417
$130$	23.0541	2.02198
$131$	−11.5535	−1.00943	−0.504716	−	0.863286i	$-0.668403\pi$
$131$	−11.5535	−1.00943	−0.504716	+	0.863286i	$0.668403\pi$
$132$	63.1105	5.49306
$133$	3.00174	0.260284
$134$	−2.32068	−0.200476
$135$	32.1006	2.76278
$136$	12.3555	1.05948
$137$	9.18569	0.784786	0.392393	−	0.919798i	$-0.371647\pi$
$137$	9.18569	0.784786	0.392393	+	0.919798i	$0.371647\pi$
$138$	−20.7281	−1.76449
$139$	−8.48062	−0.719317	−0.359658	−	0.933084i	$-0.617107\pi$
$139$	−8.48062	−0.719317	−0.359658	+	0.933084i	$0.617107\pi$
$140$	−30.7878	−2.60204
$141$	5.27405	0.444155
$142$	−28.6436	−2.40372
$143$	−17.0867	−1.42887
$144$	59.0761	4.92301
$145$	−3.13999	−0.260762
$146$	−43.0582	−3.56352
$147$	−6.49898	−0.536027
$148$	24.7981	2.03839
$149$	−11.0091	−0.901902	−0.450951	−	0.892549i	$-0.648915\pi$
$149$	−11.0091	−0.901902	−0.450951	+	0.892549i	$0.648915\pi$
$150$	−0.161313	−0.0131711
$151$	−14.6228	−1.18999	−0.594994	−	0.803730i	$-0.702846\pi$
$151$	−14.6228	−1.18999	−0.594994	+	0.803730i	$0.702846\pi$
$152$	−6.66674	−0.540744
$153$	−13.8065	−1.11619
$154$	32.7487	2.63897
$155$	12.3262	0.990061
$156$	−59.7570	−4.78439
$157$	15.6781	1.25125	0.625625	−	0.780124i	$-0.284844\pi$
$157$	15.6781	1.25125	0.625625	+	0.780124i	$0.284844\pi$
$158$	3.68092	0.292839
$159$	−27.3863	−2.17187
$160$	15.6954	1.24083
$161$	−7.49456	−0.590654
$162$	−62.0179	−4.87259
$163$	−11.7516	−0.920454	−0.460227	−	0.887801i	$-0.652232\pi$
$163$	−11.7516	−0.920454	−0.460227	+	0.887801i	$0.652232\pi$
$164$	14.8811	1.16202
$165$	−30.6461	−2.38580
$166$	−25.5597	−1.98381
$167$	2.91757	0.225769	0.112884	−	0.993608i	$-0.463991\pi$
$167$	2.91757	0.225769	0.112884	+	0.993608i	$0.463991\pi$
$168$	64.6900	4.99094
$169$	3.17883	0.244525
$170$	−10.6224	−0.814702
$171$	7.44963	0.569687
$172$	−50.4480	−3.84663
$173$	−24.4635	−1.85993	−0.929964	−	0.367650i	$-0.880162\pi$
$173$	−24.4635	−1.85993	−0.929964	+	0.367650i	$0.880162\pi$
$174$	11.6809	0.885523
$175$	−0.0583252	−0.00440897
$176$	−33.6871	−2.53926
$177$	−1.74977	−0.131521
$178$	38.2904	2.86999
$179$	1.59588	0.119282	0.0596408	−	0.998220i	$-0.481004\pi$
$179$	1.59588	0.119282	0.0596408	+	0.998220i	$0.481004\pi$
$180$	−76.4080	−5.69512
$181$	20.2541	1.50548	0.752738	−	0.658320i	$-0.228733\pi$
$181$	20.2541	1.50548	0.752738	+	0.658320i	$0.228733\pi$
$182$	−31.0086	−2.29851
$183$	23.3945	1.72937
$184$	16.6451	1.22709
$185$	−12.0418	−0.885334
$186$	−45.8536	−3.36215
$187$	7.87289	0.575723
$188$	−7.49823	−0.546865
$189$	−43.1765	−3.14063
$190$	5.73158	0.415813
$191$	1.81528	0.131349	0.0656746	−	0.997841i	$-0.479080\pi$
$191$	1.81528	0.131349	0.0656746	+	0.997841i	$0.479080\pi$
$192$	−7.11776	−0.513680
$193$	−15.9055	−1.14491	−0.572453	−	0.819937i	$-0.694008\pi$
$193$	−15.9055	−1.14491	−0.572453	+	0.819937i	$0.694008\pi$
$194$	−11.1948	−0.803741
$195$	29.0177	2.07800
$196$	9.23975	0.659982
$197$	−11.9391	−0.850623	−0.425311	−	0.905047i	$-0.639835\pi$
$197$	−11.9391	−0.850623	−0.425311	+	0.905047i	$0.639835\pi$
$198$	81.2747	5.77594
$199$	8.93005	0.633035	0.316517	−	0.948587i	$-0.397486\pi$
$199$	8.93005	0.633035	0.316517	+	0.948587i	$0.397486\pi$
$200$	0.129538	0.00915971
$201$	−2.92099	−0.206031
$202$	34.0822	2.39801
$203$	4.22340	0.296425
$204$	27.5337	1.92774
$205$	−7.22617	−0.504698
$206$	−10.1783	−0.709159
$207$	−18.5998	−1.29277
$208$	31.8971	2.21167
$209$	−4.24801	−0.293841
$210$	−55.6158	−3.83786
$211$	−1.14778	−0.0790162	−0.0395081	−	0.999219i	$-0.512579\pi$
$211$	−1.14778	−0.0790162	−0.0395081	+	0.999219i	$0.512579\pi$
$212$	38.9357	2.67411
$213$	−36.0531	−2.47032
$214$	8.40549	0.574588
$215$	24.4973	1.67070
$216$	95.8931	6.52470
$217$	−16.5791	−1.12546
$218$	−25.1278	−1.70187
$219$	−54.1964	−3.66225
$220$	43.5703	2.93751
$221$	−7.45456	−0.501448
$222$	44.7960	3.00651
$223$	−25.9766	−1.73952	−0.869760	−	0.493476i	$-0.835726\pi$
$223$	−25.9766	−1.73952	−0.869760	+	0.493476i	$0.835726\pi$
$224$	−21.1108	−1.41053
$225$	−0.144750	−0.00964998
$226$	−21.4756	−1.42854
$227$	−20.0543	−1.33105	−0.665526	−	0.746375i	$-0.731793\pi$
$227$	−20.0543	−1.33105	−0.665526	+	0.746375i	$0.731793\pi$
$228$	−14.8565	−0.983893
$229$	3.12931	0.206791	0.103395	−	0.994640i	$-0.467029\pi$
$229$	3.12931	0.206791	0.103395	+	0.994640i	$0.467029\pi$
$230$	−14.3103	−0.943591
$231$	41.2202	2.71209
$232$	−9.38000	−0.615827
$233$	−2.20954	−0.144752	−0.0723759	−	0.997377i	$-0.523058\pi$
$233$	−2.20954	−0.144752	−0.0723759	+	0.997377i	$0.523058\pi$
$234$	−76.9561	−5.03078
$235$	3.64110	0.237519
$236$	2.48769	0.161935
$237$	4.63310	0.300952
$238$	14.2875	0.926123
$239$	4.27961	0.276825	0.138412	−	0.990375i	$-0.455800\pi$
$239$	4.27961	0.276825	0.138412	+	0.990375i	$0.455800\pi$
$240$	57.2094	3.69285
$241$	21.4362	1.38083	0.690414	−	0.723415i	$-0.257428\pi$
$241$	21.4362	1.38083	0.690414	+	0.723415i	$0.257428\pi$
$242$	−18.0948	−1.16318
$243$	−34.9093	−2.23943
$244$	−33.2605	−2.12928
$245$	−4.48678	−0.286650
$246$	26.8816	1.71391
$247$	4.02229	0.255932
$248$	36.8215	2.33817
$249$	−32.1714	−2.03878
$250$	−28.7693	−1.81953
$251$	−21.4805	−1.35583	−0.677917	−	0.735138i	$-0.737117\pi$
$251$	−21.4805	−1.35583	−0.677917	+	0.735138i	$0.737117\pi$
$252$	102.772	6.47400
$253$	10.6062	0.666804
$254$	−10.8969	−0.683733
$255$	−13.3702	−0.837275
$256$	−26.0046	−1.62529
$257$	8.53993	0.532706	0.266353	−	0.963876i	$-0.414181\pi$
$257$	8.53993	0.532706	0.266353	+	0.963876i	$0.414181\pi$
$258$	−91.1307	−5.67355
$259$	16.1967	1.00642
$260$	−41.2551	−2.55854
$261$	10.4815	0.648789
$262$	29.6721	1.83315
$263$	23.2558	1.43401	0.717007	−	0.697066i	$-0.245512\pi$
$263$	23.2558	1.43401	0.717007	+	0.697066i	$0.245512\pi$
$264$	−91.5482	−5.63440
$265$	−18.9070	−1.16145
$266$	−7.70919	−0.472681
$267$	48.1954	2.94951
$268$	4.15284	0.253675
$269$	−8.65712	−0.527834	−0.263917	−	0.964545i	$-0.585015\pi$
$269$	−8.65712	−0.527834	−0.263917	+	0.964545i	$0.585015\pi$
$270$	−82.4420	−5.01726
$271$	7.69715	0.467568	0.233784	−	0.972289i	$-0.424889\pi$
$271$	7.69715	0.467568	0.233784	+	0.972289i	$0.424889\pi$
$272$	−14.6969	−0.891131
$273$	−39.0299	−2.36220
$274$	−23.5910	−1.42519
$275$	0.0825408	0.00497740
$276$	37.0927	2.23272
$277$	−30.1574	−1.81198	−0.905991	−	0.423297i	$-0.860873\pi$
$277$	−30.1574	−1.81198	−0.905991	+	0.423297i	$0.860873\pi$
$278$	21.7802	1.30629
$279$	−41.1455	−2.46332
$280$	44.6608	2.66899
$281$	29.3844	1.75293	0.876463	−	0.481470i	$-0.159897\pi$
$281$	29.3844	1.75293	0.876463	+	0.481470i	$0.159897\pi$
$282$	−13.5450	−0.806593
$283$	2.83166	0.168325	0.0841623	−	0.996452i	$-0.473179\pi$
$283$	2.83166	0.168325	0.0841623	+	0.996452i	$0.473179\pi$
$284$	51.2575	3.04157
$285$	7.21423	0.427334
$286$	43.8828	2.59485
$287$	9.71946	0.573722
$288$	−52.3921	−3.08724
$289$	−13.5652	−0.797955
$290$	8.06425	0.473549
$291$	−14.0907	−0.826011
$292$	77.0523	4.50914
$293$	−14.3372	−0.837586	−0.418793	−	0.908082i	$-0.637547\pi$
$293$	−14.3372	−0.837586	−0.418793	+	0.908082i	$0.637547\pi$
$294$	16.6909	0.973435
$295$	−1.20801	−0.0703331
$296$	−35.9722	−2.09084
$297$	61.1026	3.54553
$298$	28.2740	1.63787
$299$	−10.0426	−0.580779
$300$	0.288668	0.0166663
$301$	−32.9498	−1.89919
$302$	37.5549	2.16104
$303$	42.8985	2.46446
$304$	7.93008	0.454821
$305$	16.1511	0.924811
$306$	35.4583	2.02702
$307$	9.82658	0.560832	0.280416	−	0.959879i	$-0.409528\pi$
$307$	9.82658	0.560832	0.280416	+	0.959879i	$0.409528\pi$
$308$	−58.6036	−3.33925
$309$	−12.8113	−0.728808
$310$	−31.6565	−1.79797
$311$	−6.99319	−0.396547	−0.198274	−	0.980147i	$-0.563533\pi$
$311$	−6.99319	−0.396547	−0.198274	+	0.980147i	$0.563533\pi$
$312$	86.6837	4.90750
$313$	−17.4668	−0.987280	−0.493640	−	0.869666i	$-0.664334\pi$
$313$	−17.4668	−0.987280	−0.493640	+	0.869666i	$0.664334\pi$
$314$	−40.2651	−2.27229
$315$	−49.9054	−2.81185
$316$	−6.58699	−0.370547
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	70.3345	3.94416
$319$	−5.97689	−0.334641
$320$	−4.91397	−0.274699
$321$	10.5798	0.590508
$322$	19.2478	1.07264
$323$	−1.85331	−0.103121
$324$	110.981	6.16559
$325$	−0.0781550	−0.00433526
$326$	30.1808	1.67156
$327$	−31.6278	−1.74902
$328$	−21.5865	−1.19192
$329$	−4.89742	−0.270003
$330$	78.7065	4.33265
$331$	−32.4277	−1.78239	−0.891194	−	0.453623i	$-0.850131\pi$
$331$	−32.4277	−1.78239	−0.891194	+	0.453623i	$0.850131\pi$
$332$	45.7388	2.51025
$333$	40.1965	2.20275
$334$	−7.49302	−0.410000
$335$	−2.01660	−0.110179
$336$	−76.9487	−4.19790
$337$	32.7241	1.78260	0.891298	−	0.453419i	$-0.149796\pi$
$337$	32.7241	1.78260	0.891298	+	0.453419i	$0.149796\pi$
$338$	−8.16398	−0.444062
$339$	−27.0309	−1.46812
$340$	19.0087	1.03089
$341$	23.4625	1.27056
$342$	−19.1324	−1.03456
$343$	−14.9773	−0.808699
$344$	73.1800	3.94560
$345$	−18.0120	−0.969735
$346$	62.8282	3.37766
$347$	13.6106	0.730658	0.365329	−	0.930879i	$-0.380957\pi$
$347$	13.6106	0.730658	0.365329	+	0.930879i	$0.380957\pi$
$348$	−20.9028	−1.12051
$349$	−14.6385	−0.783582	−0.391791	−	0.920054i	$-0.628144\pi$
$349$	−14.6385	−0.783582	−0.391791	+	0.920054i	$0.628144\pi$
$350$	0.149793	0.00800677
$351$	−57.8559	−3.08812
$352$	29.8757	1.59238
$353$	10.4798	0.557785	0.278892	−	0.960322i	$-0.410033\pi$
$353$	10.4798	0.557785	0.278892	+	0.960322i	$0.410033\pi$
$354$	4.49383	0.238844
$355$	−24.8904	−1.32105
$356$	−68.5205	−3.63158
$357$	17.9834	0.951783
$358$	−4.09860	−0.216617
$359$	−5.29659	−0.279544	−0.139772	−	0.990184i	$-0.544637\pi$
$359$	−5.29659	−0.279544	−0.139772	+	0.990184i	$0.544637\pi$
$360$	110.838	5.84166
$361$	1.00000	0.0526316
$362$	−52.0174	−2.73397
$363$	−22.7756	−1.19541
$364$	55.4897	2.90845
$365$	−37.4162	−1.95845
$366$	−60.0826	−3.14057
$367$	6.96235	0.363432	0.181716	−	0.983351i	$-0.441835\pi$
$367$	6.96235	0.363432	0.181716	+	0.983351i	$0.441835\pi$
$368$	−19.7993	−1.03211
$369$	24.1214	1.25571
$370$	30.9263	1.60778
$371$	25.4306	1.32029
$372$	82.0547	4.25434
$373$	3.66538	0.189786	0.0948930	−	0.995487i	$-0.469749\pi$
$373$	3.66538	0.189786	0.0948930	+	0.995487i	$0.469749\pi$
$374$	−20.2195	−1.04552
$375$	−36.2113	−1.86994
$376$	10.8770	0.560936
$377$	5.65930	0.291469
$378$	110.887	5.70343
$379$	11.2865	0.579746	0.289873	−	0.957065i	$-0.406387\pi$
$379$	11.2865	0.579746	0.289873	+	0.957065i	$0.406387\pi$
$380$	−10.2566	−0.526154
$381$	−13.7157	−0.702677
$382$	−4.66208	−0.238533
$383$	19.5126	0.997048	0.498524	−	0.866876i	$-0.333876\pi$
$383$	19.5126	0.997048	0.498524	+	0.866876i	$0.333876\pi$
$384$	−27.1886	−1.38746
$385$	28.4576	1.45034
$386$	40.8492	2.07917
$387$	−81.7737	−4.15679
$388$	20.0330	1.01702
$389$	−14.2225	−0.721107	−0.360554	−	0.932739i	$-0.617412\pi$
$389$	−14.2225	−0.721107	−0.360554	+	0.932739i	$0.617412\pi$
$390$	−74.5244	−3.77369
$391$	4.62723	0.234009
$392$	−13.4032	−0.676964
$393$	37.3476	1.88394
$394$	30.6623	1.54475
$395$	3.19861	0.160939
$396$	−145.441	−7.30866
$397$	11.7949	0.591971	0.295986	−	0.955192i	$-0.404352\pi$
$397$	11.7949	0.591971	0.295986	+	0.955192i	$0.404352\pi$
$398$	−22.9345	−1.14960
$399$	−9.70340	−0.485777
$400$	−0.154085	−0.00770426
$401$	−7.15020	−0.357064	−0.178532	−	0.983934i	$-0.557135\pi$
$401$	−7.15020	−0.357064	−0.178532	+	0.983934i	$0.557135\pi$
$402$	7.50180	0.374156
$403$	−22.2158	−1.10665
$404$	−60.9898	−3.03436
$405$	−53.8916	−2.67790
$406$	−10.8467	−0.538313
$407$	−22.9213	−1.13617
$408$	−39.9404	−1.97734
$409$	−30.0659	−1.48666	−0.743332	−	0.668923i	$-0.766756\pi$
$409$	−30.0659	−1.48666	−0.743332	+	0.668923i	$0.766756\pi$
$410$	18.5585	0.916540
$411$	−29.6936	−1.46467
$412$	18.2141	0.897343
$413$	1.62482	0.0799520
$414$	47.7686	2.34770
$415$	−22.2106	−1.09027
$416$	−28.2882	−1.38694
$417$	27.4144	1.34249
$418$	10.9099	0.533621
$419$	12.6569	0.618330	0.309165	−	0.951008i	$-0.399950\pi$
$419$	12.6569	0.618330	0.309165	+	0.951008i	$0.399950\pi$
$420$	99.5241	4.85628
$421$	18.2210	0.888039	0.444019	−	0.896017i	$-0.353552\pi$
$421$	18.2210	0.888039	0.444019	+	0.896017i	$0.353552\pi$
$422$	2.94776	0.143495
$423$	−12.1542	−0.590960
$424$	−56.4802	−2.74292
$425$	0.0360107	0.00174678
$426$	92.5929	4.48614
$427$	−21.7238	−1.05129
$428$	−15.0416	−0.727062
$429$	55.2344	2.66674
$430$	−62.9149	−3.03403
$431$	22.6436	1.09070	0.545351	−	0.838208i	$-0.316396\pi$
$431$	22.6436	1.09070	0.545351	+	0.838208i	$0.316396\pi$
$432$	−114.065	−5.48794
$433$	−25.3244	−1.21701	−0.608506	−	0.793549i	$-0.708231\pi$
$433$	−25.3244	−1.21701	−0.608506	+	0.793549i	$0.708231\pi$
$434$	42.5791	2.04386
$435$	10.1503	0.486670
$436$	44.9660	2.15348
$437$	−2.49674	−0.119435
$438$	139.189	6.65072
$439$	−29.1622	−1.39184	−0.695918	−	0.718121i	$-0.745002\pi$
$439$	−29.1622	−1.39184	−0.695918	+	0.718121i	$0.745002\pi$
$440$	−63.2032	−3.01309
$441$	14.9772	0.713198
$442$	19.1451	0.910638
$443$	36.6330	1.74049	0.870243	−	0.492623i	$-0.163962\pi$
$443$	36.6330	1.74049	0.870243	+	0.492623i	$0.163962\pi$
$444$	−80.1621	−3.80433
$445$	33.2732	1.57730
$446$	66.7140	3.15900
$447$	35.5879	1.68325
$448$	6.60947	0.312268
$449$	4.07075	0.192111	0.0960554	−	0.995376i	$-0.469377\pi$
$449$	4.07075	0.192111	0.0960554	+	0.995376i	$0.469377\pi$
$450$	0.371751	0.0175245
$451$	−13.7548	−0.647689
$452$	38.4304	1.80762
$453$	47.2695	2.22092
$454$	51.5042	2.41721
$455$	−26.9455	−1.26323
$456$	21.5508	1.00921
$457$	3.68138	0.172208	0.0861038	−	0.996286i	$-0.472558\pi$
$457$	3.68138	0.172208	0.0861038	+	0.996286i	$0.472558\pi$
$458$	−8.03682	−0.375536
$459$	26.6577	1.24427
$460$	25.6081	1.19398
$461$	16.5678	0.771639	0.385819	−	0.922574i	$-0.373919\pi$
$461$	16.5678	0.771639	0.385819	+	0.922574i	$0.373919\pi$
$462$	−105.863	−4.92520
$463$	27.3252	1.26991	0.634954	−	0.772550i	$-0.281019\pi$
$463$	27.3252	1.26991	0.634954	+	0.772550i	$0.281019\pi$
$464$	11.1575	0.517974
$465$	−39.8454	−1.84779
$466$	5.67463	0.262872
$467$	−31.6245	−1.46341	−0.731705	−	0.681622i	$-0.761275\pi$
$467$	−31.6245	−1.46341	−0.731705	+	0.681622i	$0.761275\pi$
$468$	137.712	6.36576
$469$	2.71240	0.125247
$470$	−9.35122	−0.431340
$471$	−50.6809	−2.33525
$472$	−3.60865	−0.166102
$473$	46.6300	2.14405
$474$	−11.8989	−0.546535
$475$	−0.0194305	−0.000891531 0
$476$	−25.5674	−1.17188
$477$	63.1128	2.88973
$478$	−10.9911	−0.502719
$479$	24.8284	1.13444	0.567220	−	0.823566i	$-0.308019\pi$
$479$	24.8284	1.13444	0.567220	+	0.823566i	$0.308019\pi$
$480$	−50.7366	−2.31580
$481$	21.7034	0.989588
$482$	−55.0533	−2.50761
$483$	24.2268	1.10236
$484$	32.3805	1.47184
$485$	−9.72795	−0.441723
$486$	89.6552	4.06684
$487$	29.3149	1.32839	0.664193	−	0.747562i	$-0.268776\pi$
$487$	29.3149	1.32839	0.664193	+	0.747562i	$0.268776\pi$
$488$	48.2477	2.18407
$489$	37.9880	1.71788
$490$	11.5231	0.520561
$491$	−37.5548	−1.69482	−0.847412	−	0.530936i	$-0.821841\pi$
$491$	−37.5548	−1.69482	−0.847412	+	0.530936i	$0.821841\pi$
$492$	−48.1043	−2.16871
$493$	−2.60758	−0.117439
$494$	−10.3302	−0.464778
$495$	70.6252	3.17437
$496$	−43.7992	−1.96664
$497$	33.4785	1.50172
$498$	82.6239	3.70246
$499$	−23.1236	−1.03515	−0.517577	−	0.855637i	$-0.673166\pi$
$499$	−23.1236	−1.03515	−0.517577	+	0.855637i	$0.673166\pi$
$500$	51.4824	2.30236
$501$	−9.43132	−0.421360
$502$	55.1669	2.46222
$503$	43.8348	1.95450	0.977248	−	0.212102i	$-0.0680309\pi$
$503$	43.8348	1.95450	0.977248	+	0.212102i	$0.0680309\pi$
$504$	−149.081	−6.64058
$505$	29.6164	1.31791
$506$	−27.2392	−1.21093
$507$	−10.2758	−0.456366
$508$	19.4999	0.865170
$509$	−27.3684	−1.21308	−0.606542	−	0.795051i	$-0.707444\pi$
$509$	−27.3684	−1.21308	−0.606542	+	0.795051i	$0.707444\pi$
$510$	34.3379	1.52051
$511$	50.3261	2.22630
$512$	49.9645	2.20814
$513$	−14.3838	−0.635061
$514$	−21.9326	−0.967404
$515$	−8.84466	−0.389743
$516$	163.078	7.17910
$517$	6.93074	0.304814
$518$	−41.5970	−1.82767
$519$	79.0805	3.47125
$520$	59.8448	2.62437
$521$	19.0741	0.835653	0.417827	−	0.908527i	$-0.362792\pi$
$521$	19.0741	0.835653	0.417827	+	0.908527i	$0.362792\pi$
$522$	−26.9190	−1.17821
$523$	31.7602	1.38878	0.694388	−	0.719601i	$-0.255675\pi$
$523$	31.7602	1.38878	0.694388	+	0.719601i	$0.255675\pi$
$524$	−53.0979	−2.31959
$525$	0.188541	0.00822862
$526$	−59.7264	−2.60420
$527$	10.2361	0.445894
$528$	108.896	4.73911
$529$	−16.7663	−0.728970
$530$	48.5576	2.10921
$531$	4.03242	0.174992
$532$	13.7955	0.598112
$533$	13.0239	0.564129
$534$	−123.777	−5.35636
$535$	7.30411	0.315784
$536$	−6.02412	−0.260202
$537$	−5.15882	−0.222619
$538$	22.2335	0.958556
$539$	−8.54045	−0.367863
$540$	147.529	6.34865
$541$	28.9188	1.24332	0.621658	−	0.783289i	$-0.286459\pi$
$541$	28.9188	1.24332	0.621658	+	0.783289i	$0.286459\pi$
$542$	−19.7681	−0.849113
$543$	−65.4732	−2.80972
$544$	13.0341	0.558831
$545$	−21.8353	−0.935320
$546$	100.238	4.28979
$547$	−7.77752	−0.332543	−0.166271	−	0.986080i	$-0.553173\pi$
$547$	−7.77752	−0.332543	−0.166271	+	0.986080i	$0.553173\pi$
$548$	42.2160	1.80338
$549$	−53.9135	−2.30097
$550$	−0.211984	−0.00903905
$551$	1.40698	0.0599395
$552$	−53.8068	−2.29017
$553$	−4.30224	−0.182950
$554$	77.4513	3.29059
$555$	38.9263	1.65233
$556$	−38.9756	−1.65293
$557$	11.4326	0.484414	0.242207	−	0.970225i	$-0.422129\pi$
$557$	11.4326	0.484414	0.242207	+	0.970225i	$0.422129\pi$
$558$	105.671	4.47343
$559$	−44.1522	−1.86744
$560$	−53.1240	−2.24490
$561$	−25.4498	−1.07449
$562$	−75.4661	−3.18334
$563$	−8.97078	−0.378073	−0.189037	−	0.981970i	$-0.560537\pi$
$563$	−8.97078	−0.378073	−0.189037	+	0.981970i	$0.560537\pi$
$564$	24.2387	1.02063
$565$	−18.6616	−0.785101
$566$	−7.27237	−0.305681
$567$	72.4862	3.04413
$568$	−74.3543	−3.11984
$569$	−36.5467	−1.53212	−0.766058	−	0.642771i	$-0.777785\pi$
$569$	−36.5467	−1.53212	−0.766058	+	0.642771i	$0.777785\pi$
$570$	−18.5278	−0.776046
$571$	−37.8307	−1.58317	−0.791583	−	0.611062i	$-0.790743\pi$
$571$	−37.8307	−1.58317	−0.791583	+	0.611062i	$0.790743\pi$
$572$	−78.5280	−3.28342
$573$	−5.86806	−0.245142
$574$	−24.9619	−1.04189
$575$	0.0485128	0.00202312
$576$	16.4032	0.683465
$577$	33.5391	1.39625	0.698126	−	0.715975i	$-0.254017\pi$
$577$	33.5391	1.39625	0.698126	+	0.715975i	$0.254017\pi$
$578$	34.8387	1.44910
$579$	51.4161	2.13678
$580$	−14.4309	−0.599211
$581$	29.8740	1.23938
$582$	36.1882	1.50005
$583$	−35.9889	−1.49051
$584$	−111.772	−4.62517
$585$	−66.8725	−2.76484
$586$	36.8212	1.52107
$587$	39.2782	1.62118	0.810592	−	0.585611i	$-0.199145\pi$
$587$	39.2782	1.62118	0.810592	+	0.585611i	$0.199145\pi$
$588$	−29.8683	−1.23175
$589$	−5.52317	−0.227578
$590$	3.10246	0.127726
$591$	38.5941	1.58755
$592$	42.7889	1.75861
$593$	−0.238142	−0.00977933	−0.00488967	−	0.999988i	$-0.501556\pi$
$593$	−0.238142	−0.00977933	−0.00488967	+	0.999988i	$0.501556\pi$
$594$	−156.926	−6.43875
$595$	12.4154	0.508983
$596$	−50.5962	−2.07250
$597$	−28.8672	−1.18146
$598$	25.7918	1.05471
$599$	3.96353	0.161945	0.0809727	−	0.996716i	$-0.474197\pi$
$599$	3.96353	0.161945	0.0809727	+	0.996716i	$0.474197\pi$
$600$	−0.418742	−0.0170951
$601$	−22.4271	−0.914822	−0.457411	−	0.889255i	$-0.651223\pi$
$601$	−22.4271	−0.914822	−0.457411	+	0.889255i	$0.651223\pi$
$602$	84.6229	3.44897
$603$	6.73154	0.274129
$604$	−67.2042	−2.73450
$605$	−15.7238	−0.639264
$606$	−110.174	−4.47550
$607$	15.9460	0.647228	0.323614	−	0.946189i	$-0.395102\pi$
$607$	15.9460	0.647228	0.323614	+	0.946189i	$0.395102\pi$
$608$	−7.03286	−0.285220
$609$	−13.6525	−0.553228
$610$	−41.4799	−1.67947
$611$	−6.56247	−0.265489
$612$	−63.4524	−2.56491
$613$	−34.1654	−1.37993	−0.689963	−	0.723844i	$-0.742373\pi$
$613$	−34.1654	−1.37993	−0.689963	+	0.723844i	$0.742373\pi$
$614$	−25.2370	−1.01848
$615$	23.3592	0.941935
$616$	85.0105	3.42517
$617$	−22.3032	−0.897892	−0.448946	−	0.893559i	$-0.648201\pi$
$617$	−22.3032	−0.897892	−0.448946	+	0.893559i	$0.648201\pi$
$618$	32.9024	1.32353
$619$	−12.3956	−0.498219	−0.249110	−	0.968475i	$-0.580138\pi$
$619$	−12.3956	−0.498219	−0.249110	+	0.968475i	$0.580138\pi$
$620$	56.6491	2.27508
$621$	35.9126	1.44112
$622$	17.9602	0.720137
$623$	−44.7537	−1.79302
$624$	−103.110	−4.12771
$625$	−24.9025	−0.996099
$626$	44.8588	1.79292
$627$	13.7321	0.548406
$628$	72.0541	2.87527
$629$	−10.0000	−0.398728
$630$	128.169	5.10637
$631$	20.2859	0.807567	0.403784	−	0.914855i	$-0.367695\pi$
$631$	20.2859	0.807567	0.403784	+	0.914855i	$0.367695\pi$
$632$	9.55510	0.380081
$633$	3.71029	0.147471
$634$	2.56824	0.101998
$635$	−9.46907	−0.375769
$636$	−125.863	−4.99079
$637$	8.08665	0.320405
$638$	15.3501	0.607715
$639$	83.0858	3.28682
$640$	−18.7705	−0.741968
$641$	43.8908	1.73358	0.866792	−	0.498670i	$-0.166178\pi$
$641$	43.8908	1.73358	0.866792	+	0.498670i	$0.166178\pi$
$642$	−27.1715	−1.07237
$643$	−26.5373	−1.04653	−0.523264	−	0.852170i	$-0.675286\pi$
$643$	−26.5373	−1.04653	−0.523264	+	0.852170i	$0.675286\pi$
$644$	−34.4438	−1.35728
$645$	−79.1898	−3.11809
$646$	4.75974	0.187270
$647$	−10.7509	−0.422662	−0.211331	−	0.977415i	$-0.567780\pi$
$647$	−10.7509	−0.422662	−0.211331	+	0.977415i	$0.567780\pi$
$648$	−160.989	−6.32423
$649$	−2.29941	−0.0902598
$650$	0.200720	0.00787291
$651$	53.5935	2.10049
$652$	−54.0084	−2.11513
$653$	20.0833	0.785920	0.392960	−	0.919556i	$-0.371451\pi$
$653$	20.0833	0.785920	0.392960	+	0.919556i	$0.371451\pi$
$654$	81.2277	3.17626
$655$	25.7841	1.00747
$656$	25.6771	1.00252
$657$	124.898	4.87273
$658$	12.5777	0.490331
$659$	34.1951	1.33205	0.666025	−	0.745929i	$-0.267994\pi$
$659$	34.1951	1.33205	0.666025	+	0.745929i	$0.267994\pi$
$660$	−140.845	−5.48238
$661$	−28.7156	−1.11691	−0.558453	−	0.829536i	$-0.688605\pi$
$661$	−28.7156	−1.11691	−0.558453	+	0.829536i	$0.688605\pi$
$662$	83.2820	3.23685
$663$	24.0975	0.935870
$664$	−66.3489	−2.57484
$665$	−6.69905	−0.259778
$666$	−103.234	−4.00024
$667$	−3.51287	−0.136019
$668$	13.4087	0.518799
$669$	83.9715	3.24653
$670$	5.17910	0.200086
$671$	30.7432	1.18683
$672$	68.2426	2.63252
$673$	33.9539	1.30883	0.654414	−	0.756136i	$-0.272915\pi$
$673$	33.9539	1.30883	0.654414	+	0.756136i	$0.272915\pi$
$674$	−84.0432	−3.23722
$675$	0.279484	0.0107573
$676$	14.6094	0.561900
$677$	20.9937	0.806854	0.403427	−	0.915012i	$-0.367819\pi$
$677$	20.9937	0.806854	0.403427	+	0.915012i	$0.367819\pi$
$678$	69.4218	2.66613
$679$	13.0844	0.502135
$680$	−27.5741	−1.05742
$681$	64.8273	2.48419
$682$	−60.2572	−2.30737
$683$	−23.7814	−0.909970	−0.454985	−	0.890499i	$-0.650355\pi$
$683$	−23.7814	−0.909970	−0.454985	+	0.890499i	$0.650355\pi$
$684$	34.2373	1.30910
$685$	−20.4999	−0.783260
$686$	38.4653	1.46861
$687$	−10.1158	−0.385941
$688$	−87.0476	−3.31866
$689$	34.0766	1.29822
$690$	46.2592	1.76106
$691$	17.3046	0.658298	0.329149	−	0.944278i	$-0.393238\pi$
$691$	17.3046	0.658298	0.329149	+	0.944278i	$0.393238\pi$
$692$	−112.431	−4.27397
$693$	−94.9934	−3.60850
$694$	−34.9554	−1.32689
$695$	18.9264	0.717918
$696$	30.3217	1.14934
$697$	−6.00091	−0.227301
$698$	37.5952	1.42300
$699$	7.14254	0.270156
$700$	−0.268054	−0.0101315
$701$	7.14185	0.269744	0.134872	−	0.990863i	$-0.456938\pi$
$701$	7.14185	0.269744	0.134872	+	0.990863i	$0.456938\pi$
$702$	148.588	5.60808
$703$	5.39577	0.203505
$704$	−9.35360	−0.352527
$705$	−11.7702	−0.443291
$706$	−26.9147	−1.01295
$707$	−39.8351	−1.49815
$708$	−8.04168	−0.302225
$709$	21.3774	0.802845	0.401423	−	0.915893i	$-0.368516\pi$
$709$	21.3774	0.802845	0.401423	+	0.915893i	$0.368516\pi$
$710$	63.9245	2.39904
$711$	−10.6772	−0.400425
$712$	99.3960	3.72502
$713$	13.7899	0.516436
$714$	−46.1857	−1.72846
$715$	38.1328	1.42609
$716$	7.33441	0.274100
$717$	−13.8342	−0.516648
$718$	13.6029	0.507656
$719$	39.5923	1.47654	0.738272	−	0.674503i	$-0.235642\pi$
$719$	39.5923	1.47654	0.738272	+	0.674503i	$0.235642\pi$
$720$	−131.841	−4.91344
$721$	11.8964	0.443045
$722$	−2.56824	−0.0955799
$723$	−69.2944	−2.57709
$724$	93.0847	3.45947
$725$	−0.0273383	−0.00101532
$726$	58.4930	2.17088
$727$	−29.7223	−1.10234	−0.551170	−	0.834393i	$-0.685819\pi$
$727$	−29.7223	−1.10234	−0.551170	+	0.834393i	$0.685819\pi$
$728$	−80.4934	−2.98329
$729$	40.4031	1.49641
$730$	96.0937	3.55659
$731$	20.3436	0.752435
$732$	107.517	3.97396
$733$	−48.3131	−1.78448	−0.892242	−	0.451557i	$-0.850869\pi$
$733$	−48.3131	−1.78448	−0.892242	+	0.451557i	$0.850869\pi$
$734$	−17.8810	−0.659998
$735$	14.5039	0.534984
$736$	17.5592	0.647241
$737$	−3.83854	−0.141394
$738$	−61.9496	−2.28040
$739$	−13.1360	−0.483215	−0.241607	−	0.970374i	$-0.577675\pi$
$739$	−13.1360	−0.483215	−0.241607	+	0.970374i	$0.577675\pi$
$740$	−55.3424	−2.03443
$741$	−13.0024	−0.477655
$742$	−65.3117	−2.39767
$743$	−18.9361	−0.694699	−0.347350	−	0.937736i	$-0.612918\pi$
$743$	−18.9361	−0.694699	−0.347350	+	0.937736i	$0.612918\pi$
$744$	−119.029	−4.36381
$745$	24.5693	0.900148
$746$	−9.41356	−0.344655
$747$	74.1403	2.71265
$748$	36.1826	1.32297
$749$	−9.82430	−0.358972
$750$	92.9992	3.39585
$751$	22.0439	0.804394	0.402197	−	0.915553i	$-0.368247\pi$
$751$	22.0439	0.804394	0.402197	+	0.915553i	$0.368247\pi$
$752$	−12.9381	−0.471805
$753$	69.4375	2.53044
$754$	−14.5344	−0.529312
$755$	32.6340	1.18767
$756$	−198.432	−7.21691
$757$	52.4799	1.90742	0.953708	−	0.300735i	$-0.0972318\pi$
$757$	52.4799	1.90742	0.953708	+	0.300735i	$0.0972318\pi$
$758$	−28.9863	−1.05283
$759$	−34.2854	−1.24448
$760$	14.8783	0.539692
$761$	7.52787	0.272885	0.136442	−	0.990648i	$-0.456433\pi$
$761$	7.52787	0.272885	0.136442	+	0.990648i	$0.456433\pi$
$762$	35.2252	1.27607
$763$	29.3692	1.06324
$764$	8.34275	0.301830
$765$	30.8122	1.11402
$766$	−50.1130	−1.81066
$767$	2.17723	0.0786153
$768$	84.0622	3.03333
$769$	18.3645	0.662239	0.331120	−	0.943589i	$-0.392574\pi$
$769$	18.3645	0.662239	0.331120	+	0.943589i	$0.392574\pi$
$770$	−73.0859	−2.63383
$771$	−27.6061	−0.994209
$772$	−73.0994	−2.63090
$773$	−43.6934	−1.57154	−0.785771	−	0.618517i	$-0.787734\pi$
$773$	−43.6934	−1.57154	−0.785771	+	0.618517i	$0.787734\pi$
$774$	210.014	7.54881
$775$	0.107318	0.00385496
$776$	−29.0600	−1.04319
$777$	−52.3573	−1.87831
$778$	36.5266	1.30954
$779$	3.23794	0.116011
$780$	133.361	4.77509
$781$	−47.3782	−1.69532
$782$	−11.8838	−0.424965
$783$	−20.2378	−0.723239
$784$	15.9431	0.569396
$785$	−34.9891	−1.24882
$786$	−95.9176	−3.42127
$787$	49.5989	1.76801	0.884005	−	0.467478i	$-0.154837\pi$
$787$	49.5989	1.76801	0.884005	+	0.467478i	$0.154837\pi$
$788$	−54.8701	−1.95466
$789$	−75.1764	−2.67635
$790$	−8.21479	−0.292269
$791$	25.1006	0.892474
$792$	210.976	7.49672
$793$	−29.1096	−1.03371
$794$	−30.2922	−1.07503
$795$	61.1185	2.16765
$796$	41.0411	1.45466
$797$	−42.0355	−1.48897	−0.744487	−	0.667637i	$-0.767306\pi$
$797$	−42.0355	−1.48897	−0.744487	+	0.667637i	$0.767306\pi$
$798$	24.9206	0.882181
$799$	3.02372	0.106972
$800$	0.136652	0.00483136
$801$	−111.068	−3.92440
$802$	18.3634	0.648435
$803$	−71.2207	−2.51332
$804$	−13.4244	−0.473443
$805$	16.7258	0.589506
$806$	57.0554	2.00969
$807$	27.9849	0.985116
$808$	88.4719	3.11243
$809$	21.6030	0.759522	0.379761	−	0.925085i	$-0.376006\pi$
$809$	21.6030	0.759522	0.379761	+	0.925085i	$0.376006\pi$
$810$	138.407	4.86311
$811$	−19.2018	−0.674266	−0.337133	−	0.941457i	$-0.609457\pi$
$811$	−19.2018	−0.674266	−0.337133	+	0.941457i	$0.609457\pi$
$812$	19.4101	0.681161
$813$	−24.8817	−0.872640
$814$	58.8674	2.06330
$815$	26.2262	0.918664
$816$	47.5091	1.66315
$817$	−10.9769	−0.384033
$818$	77.2164	2.69981
$819$	89.9459	3.14296
$820$	−33.2104	−1.15976
$821$	−53.4228	−1.86447	−0.932234	−	0.361856i	$-0.882143\pi$
$821$	−53.4228	−1.86447	−0.932234	+	0.361856i	$0.882143\pi$
$822$	76.2601	2.65988
$823$	−26.5198	−0.924421	−0.462211	−	0.886770i	$-0.652944\pi$
$823$	−26.5198	−0.924421	−0.462211	+	0.886770i	$0.652944\pi$
$824$	−26.4214	−0.920432
$825$	−0.266821	−0.00928950
$826$	−4.17292	−0.145194
$827$	36.1797	1.25809	0.629046	−	0.777368i	$-0.283446\pi$
$827$	36.1797	1.25809	0.629046	+	0.777368i	$0.283446\pi$
$828$	−85.4816	−2.97069
$829$	34.4696	1.19718	0.598589	−	0.801056i	$-0.295728\pi$
$829$	34.4696	1.19718	0.598589	+	0.801056i	$0.295728\pi$
$830$	57.0420	1.97996
$831$	97.4864	3.38177
$832$	8.85659	0.307047
$833$	−3.72600	−0.129098
$834$	−70.4066	−2.43798
$835$	−6.51121	−0.225330
$836$	−19.5232	−0.675224
$837$	79.4442	2.74599
$838$	−32.5059	−1.12290
$839$	28.4248	0.981335	0.490667	−	0.871347i	$-0.336753\pi$
$839$	28.4248	0.981335	0.490667	+	0.871347i	$0.336753\pi$
$840$	−144.370	−4.98124
$841$	−27.0204	−0.931738
$842$	−46.7959	−1.61269
$843$	−94.9876	−3.27155
$844$	−5.27500	−0.181573
$845$	−7.09425	−0.244050
$846$	31.2150	1.07319
$847$	21.1491	0.726692
$848$	67.1832	2.30708
$849$	−9.15359	−0.314150
$850$	−0.0924840	−0.00317218
$851$	−13.4718	−0.461808
$852$	−165.694	−5.67660
$853$	−17.8191	−0.610114	−0.305057	−	0.952334i	$-0.598676\pi$
$853$	−17.8191	−0.610114	−0.305057	+	0.952334i	$0.598676\pi$
$854$	55.7920	1.90916
$855$	−16.6255	−0.568579
$856$	21.8193	0.745769
$857$	19.7636	0.675113	0.337557	−	0.941305i	$-0.390400\pi$
$857$	19.7636	0.675113	0.337557	+	0.941305i	$0.390400\pi$
$858$	−141.855	−4.84285
$859$	−20.9556	−0.714995	−0.357497	−	0.933914i	$-0.616370\pi$
$859$	−20.9556	−0.714995	−0.357497	+	0.933914i	$0.616370\pi$
$860$	112.586	3.83915
$861$	−31.4190	−1.07076
$862$	−58.1541	−1.98074
$863$	−38.1795	−1.29964	−0.649822	−	0.760086i	$-0.725157\pi$
$863$	−38.1795	−1.29964	−0.649822	+	0.760086i	$0.725157\pi$
$864$	101.159	3.44151
$865$	54.5957	1.85631
$866$	65.0390	2.21012
$867$	43.8508	1.48925
$868$	−76.1951	−2.58623
$869$	6.08846	0.206537
$870$	−26.0684	−0.883801
$871$	3.63457	0.123153
$872$	−65.2278	−2.20889
$873$	32.4725	1.09903
$874$	6.41222	0.216896
$875$	33.6254	1.13675
$876$	−249.078	−8.41557
$877$	0.963782	0.0325446	0.0162723	−	0.999868i	$-0.494820\pi$
$877$	0.963782	0.0325446	0.0162723	+	0.999868i	$0.494820\pi$
$878$	74.8955	2.52760
$879$	46.3461	1.56322
$880$	75.1801	2.53432
$881$	−24.9957	−0.842125	−0.421063	−	0.907032i	$-0.638343\pi$
$881$	−24.9957	−0.842125	−0.421063	+	0.907032i	$0.638343\pi$
$882$	−38.4649	−1.29518
$883$	0.0752341	0.00253183	0.00126591	−	0.999999i	$-0.499597\pi$
$883$	0.0752341	0.00253183	0.00126591	+	0.999999i	$0.499597\pi$
$884$	−34.2600	−1.15229
$885$	3.90500	0.131265
$886$	−94.0822	−3.16075
$887$	2.66511	0.0894855	0.0447427	−	0.998999i	$-0.485753\pi$
$887$	2.66511	0.0894855	0.0447427	+	0.998999i	$0.485753\pi$
$888$	116.283	3.90221
$889$	12.7362	0.427160
$890$	−85.4535	−2.86441
$891$	−102.581	−3.43660
$892$	−119.384	−3.99728
$893$	−1.63152	−0.0545969
$894$	−91.3983	−3.05682
$895$	−3.56155	−0.119050
$896$	25.2470	0.843442
$897$	32.4636	1.08393
$898$	−10.4547	−0.348877
$899$	−7.77101	−0.259178
$900$	−0.665247	−0.0221749
$901$	−15.7011	−0.523081
$902$	35.3256	1.17621
$903$	106.513	3.54453
$904$	−55.7473	−1.85413
$905$	−45.2015	−1.50255
$906$	−121.399	−4.03322
$907$	−10.3427	−0.343425	−0.171713	−	0.985147i	$-0.554930\pi$
$907$	−10.3427	−0.343425	−0.171713	+	0.985147i	$0.554930\pi$
$908$	−92.1664	−3.05865
$909$	−98.8613	−3.27902
$910$	69.2025	2.29404
$911$	−6.04477	−0.200272	−0.100136	−	0.994974i	$-0.531928\pi$
$911$	−6.04477	−0.200272	−0.100136	+	0.994974i	$0.531928\pi$
$912$	−25.6347	−0.848849
$913$	−42.2772	−1.39917
$914$	−9.45466	−0.312732
$915$	−52.2099	−1.72601
$916$	14.3818	0.475189
$917$	−34.6806	−1.14525
$918$	−68.4632	−2.25962
$919$	42.2158	1.39257	0.696286	−	0.717765i	$-0.254835\pi$
$919$	42.2158	1.39257	0.696286	+	0.717765i	$0.254835\pi$
$920$	−37.1472	−1.22471
$921$	−31.7653	−1.04670
$922$	−42.5500	−1.40131
$923$	44.8607	1.47661
$924$	189.441	6.23216
$925$	−0.104842	−0.00344719
$926$	−70.1775	−2.30618
$927$	29.5241	0.969698
$928$	−9.89512	−0.324823
$929$	25.1024	0.823584	0.411792	−	0.911278i	$-0.364903\pi$
$929$	25.1024	0.823584	0.411792	+	0.911278i	$0.364903\pi$
$930$	102.332	3.35561
$931$	2.01046	0.0658901
$932$	−10.1547	−0.332628
$933$	22.6061	0.740091
$934$	81.2193	2.65758
$935$	−17.5701	−0.574603
$936$	−199.766	−6.52955
$937$	34.0451	1.11220	0.556102	−	0.831114i	$-0.312296\pi$
$937$	34.0451	1.11220	0.556102	+	0.831114i	$0.312296\pi$
$938$	−6.96608	−0.227451
$939$	56.4629	1.84260
$940$	16.7339	0.545801
$941$	50.2900	1.63941	0.819704	−	0.572788i	$-0.194138\pi$
$941$	50.2900	1.63941	0.819704	+	0.572788i	$0.194138\pi$
$942$	130.161	4.24086
$943$	−8.08429	−0.263261
$944$	4.29249	0.139709
$945$	96.3578	3.13452
$946$	−119.757	−3.89363
$947$	36.6367	1.19053	0.595266	−	0.803529i	$-0.297047\pi$
$947$	36.6367	1.19053	0.595266	+	0.803529i	$0.297047\pi$
$948$	21.2930	0.691565
$949$	67.4363	2.18908
$950$	0.0499020	0.00161904
$951$	3.23259	0.104824
$952$	37.0882	1.20203
$953$	10.1355	0.328322	0.164161	−	0.986434i	$-0.447508\pi$
$953$	10.1355	0.328322	0.164161	+	0.986434i	$0.447508\pi$
$954$	−162.089	−5.24781
$955$	−4.05120	−0.131094
$956$	19.6684	0.636122
$957$	19.3208	0.624553
$958$	−63.7653	−2.06016
$959$	27.5731	0.890381
$960$	15.8848	0.512681
$961$	−0.494624	−0.0159556
$962$	−55.7394	−1.79711
$963$	−24.3816	−0.785686
$964$	98.5175	3.17303
$965$	35.4967	1.14268
$966$	−62.2203	−2.00190
$967$	31.0730	0.999239	0.499619	−	0.866245i	$-0.333473\pi$
$967$	31.0730	0.999239	0.499619	+	0.866245i	$0.333473\pi$
$968$	−46.9713	−1.50971
$969$	5.99099	0.192458
$970$	24.9837	0.802178
$971$	−51.6502	−1.65753	−0.828767	−	0.559594i	$-0.810957\pi$
$971$	−51.6502	−1.65753	−0.828767	+	0.559594i	$0.810957\pi$
$972$	−160.437	−5.14603
$973$	−25.4566	−0.816102
$974$	−75.2876	−2.41237
$975$	0.252643	0.00809105
$976$	−57.3906	−1.83703
$977$	−43.2909	−1.38500	−0.692500	−	0.721418i	$-0.743491\pi$
$977$	−43.2909	−1.38500	−0.692500	+	0.721418i	$0.743491\pi$
$978$	−97.5622	−3.11969
$979$	63.3346	2.02418
$980$	−20.6205	−0.658698
$981$	72.8875	2.32712
$982$	96.4496	3.07783
$983$	−44.5931	−1.42230	−0.711150	−	0.703041i	$-0.751825\pi$
$983$	−44.5931	−1.42230	−0.711150	+	0.703041i	$0.751825\pi$
$984$	69.7803	2.22451
$985$	26.6446	0.848969
$986$	6.69688	0.213272
$987$	15.8313	0.503917
$988$	18.4858	0.588112
$989$	27.4064	0.871473
$990$	−181.382	−5.76471
$991$	4.32129	0.137270	0.0686351	−	0.997642i	$-0.478136\pi$
$991$	4.32129	0.137270	0.0686351	+	0.997642i	$0.478136\pi$
$992$	38.8436	1.23329
$993$	104.825	3.32653
$994$	−85.9807	−2.72714
$995$	−19.9294	−0.631804
$996$	−147.855	−4.68496
$997$	−33.5447	−1.06237	−0.531185	−	0.847256i	$-0.678253\pi$
$997$	−33.5447	−1.06237	−0.531185	+	0.847256i	$0.678253\pi$
$998$	59.3869	1.87986
$999$	−77.6117	−2.45553

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.c.1.9	✓	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.c.1.9	✓	138	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.56824 q^{2} -3.23259 q^{3} +4.59584 q^{4} -2.23172 q^{5} +8.30205 q^{6} +3.00174 q^{7} -6.66674 q^{8} +7.44963 q^{9} +O(q^{10})\)	\(q-2.56824 q^{2} -3.23259 q^{3} +4.59584 q^{4} -2.23172 q^{5} +8.30205 q^{6} +3.00174 q^{7} -6.66674 q^{8} +7.44963 q^{9} +5.73158 q^{10} -4.24801 q^{11} -14.8565 q^{12} +4.02229 q^{13} -7.70919 q^{14} +7.21423 q^{15} +7.93008 q^{16} -1.85331 q^{17} -19.1324 q^{18} +1.00000 q^{19} -10.2566 q^{20} -9.70340 q^{21} +10.9099 q^{22} -2.49674 q^{23} +21.5508 q^{24} -0.0194305 q^{25} -10.3302 q^{26} -14.3838 q^{27} +13.7955 q^{28} +1.40698 q^{29} -18.5278 q^{30} -5.52317 q^{31} -7.03286 q^{32} +13.7321 q^{33} +4.75974 q^{34} -6.69905 q^{35} +34.2373 q^{36} +5.39577 q^{37} -2.56824 q^{38} -13.0024 q^{39} +14.8783 q^{40} +3.23794 q^{41} +24.9206 q^{42} -10.9769 q^{43} -19.5232 q^{44} -16.6255 q^{45} +6.41222 q^{46} -1.63152 q^{47} -25.6347 q^{48} +2.01046 q^{49} +0.0499020 q^{50} +5.99099 q^{51} +18.4858 q^{52} +8.47194 q^{53} +36.9410 q^{54} +9.48037 q^{55} -20.0118 q^{56} -3.23259 q^{57} -3.61347 q^{58} +0.541291 q^{59} +33.1555 q^{60} -7.23708 q^{61} +14.1848 q^{62} +22.3619 q^{63} +2.20188 q^{64} -8.97662 q^{65} -35.2672 q^{66} +0.903608 q^{67} -8.51753 q^{68} +8.07093 q^{69} +17.2047 q^{70} +11.1530 q^{71} -49.6647 q^{72} +16.7656 q^{73} -13.8576 q^{74} +0.0628107 q^{75} +4.59584 q^{76} -12.7514 q^{77} +33.3933 q^{78} -1.43325 q^{79} -17.6977 q^{80} +24.1480 q^{81} -8.31580 q^{82} +9.95222 q^{83} -44.5953 q^{84} +4.13607 q^{85} +28.1913 q^{86} -4.54820 q^{87} +28.3204 q^{88} -14.9092 q^{89} +42.6982 q^{90} +12.0739 q^{91} -11.4746 q^{92} +17.8541 q^{93} +4.19014 q^{94} -2.23172 q^{95} +22.7343 q^{96} +4.35895 q^{97} -5.16333 q^{98} -31.6461 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * q^99

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