LMFDB - Embedded newform 667.4.a.b.1.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [667,4,Mod(1,667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(667, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("667.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	667.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:	$39.3542739738$
Analytic rank:	$1$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.28
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.89475 q^{2} +2.46279 q^{3} +0.379604 q^{4} +10.1446 q^{5} +7.12917 q^{6} -9.06087 q^{7} -22.0592 q^{8} -20.9347 q^{9} +O(q^{10})$	\(q+2.89475 q^{2} +2.46279 q^{3} +0.379604 q^{4} +10.1446 q^{5} +7.12917 q^{6} -9.06087 q^{7} -22.0592 q^{8} -20.9347 q^{9} +29.3661 q^{10} -12.4279 q^{11} +0.934885 q^{12} +4.52500 q^{13} -26.2290 q^{14} +24.9840 q^{15} -66.8927 q^{16} +56.0824 q^{17} -60.6007 q^{18} -115.118 q^{19} +3.85093 q^{20} -22.3150 q^{21} -35.9756 q^{22} -23.0000 q^{23} -54.3271 q^{24} -22.0871 q^{25} +13.0988 q^{26} -118.053 q^{27} -3.43955 q^{28} +29.0000 q^{29} +72.3226 q^{30} -163.787 q^{31} -17.1646 q^{32} -30.6072 q^{33} +162.345 q^{34} -91.9190 q^{35} -7.94689 q^{36} -118.015 q^{37} -333.238 q^{38} +11.1441 q^{39} -223.782 q^{40} -177.223 q^{41} -64.5965 q^{42} +335.635 q^{43} -4.71767 q^{44} -212.374 q^{45} -66.5794 q^{46} -529.852 q^{47} -164.743 q^{48} -260.901 q^{49} -63.9366 q^{50} +138.119 q^{51} +1.71771 q^{52} +436.327 q^{53} -341.734 q^{54} -126.076 q^{55} +199.875 q^{56} -283.511 q^{57} +83.9479 q^{58} +760.464 q^{59} +9.48404 q^{60} -705.723 q^{61} -474.122 q^{62} +189.686 q^{63} +485.454 q^{64} +45.9044 q^{65} -88.6004 q^{66} +176.246 q^{67} +21.2891 q^{68} -56.6441 q^{69} -266.083 q^{70} +829.225 q^{71} +461.802 q^{72} -986.129 q^{73} -341.625 q^{74} -54.3957 q^{75} -43.6992 q^{76} +112.607 q^{77} +32.2595 q^{78} -83.3779 q^{79} -678.600 q^{80} +274.497 q^{81} -513.018 q^{82} +570.593 q^{83} -8.47088 q^{84} +568.933 q^{85} +971.580 q^{86} +71.4209 q^{87} +274.149 q^{88} -409.496 q^{89} -614.770 q^{90} -41.0005 q^{91} -8.73090 q^{92} -403.372 q^{93} -1533.79 q^{94} -1167.82 q^{95} -42.2729 q^{96} +1175.91 q^{97} -755.243 q^{98} +260.173 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 8 q^{2} - 16 q^{3} + 152 q^{4} - 80 q^{5} - 16 q^{6} - 38 q^{7} - 138 q^{8} + 312 q^{9}+O(q^{10}) $ 38 * q - 8 * q^2 - 16 * q^3 + 152 * q^4 - 80 * q^5 - 16 * q^6 - 38 * q^7 - 138 * q^8 + 312 * q^9	\( 38 q - 8 q^{2} - 16 q^{3} + 152 q^{4} - 80 q^{5} - 16 q^{6} - 38 q^{7} - 138 q^{8} + 312 q^{9} + 30 q^{10} - 100 q^{11} - 173 q^{12} - 160 q^{13} - 304 q^{14} - 208 q^{15} + 552 q^{16} - 666 q^{17} - 315 q^{18} - 252 q^{19} - 747 q^{20} - 470 q^{21} - 323 q^{22} - 874 q^{23} - 114 q^{24} + 910 q^{25} - 119 q^{26} - 526 q^{27} - 619 q^{28} + 1102 q^{29} - 533 q^{30} + 358 q^{31} - 1272 q^{32} - 604 q^{33} - 553 q^{34} + 16 q^{35} + 1230 q^{36} - 1206 q^{37} - 2010 q^{38} - 240 q^{39} - 418 q^{40} - 1094 q^{41} - 1184 q^{42} - 936 q^{43} - 2153 q^{44} - 3654 q^{45} + 184 q^{46} - 1702 q^{47} - 1319 q^{48} + 1920 q^{49} - 1255 q^{50} - 270 q^{51} - 2202 q^{52} - 4640 q^{53} - 1529 q^{54} - 318 q^{55} - 2435 q^{56} - 1980 q^{57} - 232 q^{58} + 318 q^{59} - 3279 q^{60} - 2212 q^{61} - 541 q^{62} - 1044 q^{63} + 1186 q^{64} - 2438 q^{65} - 3503 q^{66} - 496 q^{67} - 6099 q^{68} + 368 q^{69} + 4068 q^{70} + 870 q^{71} - 3869 q^{72} - 2810 q^{73} - 2793 q^{74} - 3638 q^{75} + 1548 q^{76} - 6072 q^{77} + 2170 q^{78} - 3084 q^{79} - 6702 q^{80} + 362 q^{81} - 1183 q^{82} - 5566 q^{83} - 6518 q^{84} - 120 q^{85} - 2095 q^{86} - 464 q^{87} - 1220 q^{88} - 6506 q^{89} + 165 q^{90} + 44 q^{91} - 3496 q^{92} - 5928 q^{93} + 135 q^{94} - 2024 q^{95} - 3164 q^{96} - 7472 q^{97} - 6422 q^{98} - 944 q^{99}+O(q^{100}) \) 38 * q - 8 * q^2 - 16 * q^3 + 152 * q^4 - 80 * q^5 - 16 * q^6 - 38 * q^7 - 138 * q^8 + 312 * q^9 + 30 * q^10 - 100 * q^11 - 173 * q^12 - 160 * q^13 - 304 * q^14 - 208 * q^15 + 552 * q^16 - 666 * q^17 - 315 * q^18 - 252 * q^19 - 747 * q^20 - 470 * q^21 - 323 * q^22 - 874 * q^23 - 114 * q^24 + 910 * q^25 - 119 * q^26 - 526 * q^27 - 619 * q^28 + 1102 * q^29 - 533 * q^30 + 358 * q^31 - 1272 * q^32 - 604 * q^33 - 553 * q^34 + 16 * q^35 + 1230 * q^36 - 1206 * q^37 - 2010 * q^38 - 240 * q^39 - 418 * q^40 - 1094 * q^41 - 1184 * q^42 - 936 * q^43 - 2153 * q^44 - 3654 * q^45 + 184 * q^46 - 1702 * q^47 - 1319 * q^48 + 1920 * q^49 - 1255 * q^50 - 270 * q^51 - 2202 * q^52 - 4640 * q^53 - 1529 * q^54 - 318 * q^55 - 2435 * q^56 - 1980 * q^57 - 232 * q^58 + 318 * q^59 - 3279 * q^60 - 2212 * q^61 - 541 * q^62 - 1044 * q^63 + 1186 * q^64 - 2438 * q^65 - 3503 * q^66 - 496 * q^67 - 6099 * q^68 + 368 * q^69 + 4068 * q^70 + 870 * q^71 - 3869 * q^72 - 2810 * q^73 - 2793 * q^74 - 3638 * q^75 + 1548 * q^76 - 6072 * q^77 + 2170 * q^78 - 3084 * q^79 - 6702 * q^80 + 362 * q^81 - 1183 * q^82 - 5566 * q^83 - 6518 * q^84 - 120 * q^85 - 2095 * q^86 - 464 * q^87 - 1220 * q^88 - 6506 * q^89 + 165 * q^90 + 44 * q^91 - 3496 * q^92 - 5928 * q^93 + 135 * q^94 - 2024 * q^95 - 3164 * q^96 - 7472 * q^97 - 6422 * q^98 - 944 * 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 $

$2$	2.89475	1.02345	0.511725	−	0.859149i	$-0.329007\pi$
$2$	2.89475	1.02345	0.511725	+	0.859149i	$0.329007\pi$
$3$	2.46279	0.473964	0.236982	−	0.971514i	$-0.423842\pi$
$3$	2.46279	0.473964	0.236982	+	0.971514i	$0.423842\pi$
$4$	0.379604	0.0474505
$5$	10.1446	0.907361	0.453680	−	0.891164i	$-0.350111\pi$
$5$	10.1446	0.907361	0.453680	+	0.891164i	$0.350111\pi$
$6$	7.12917	0.485078
$7$	−9.06087	−0.489241	−0.244621	−	0.969619i	$-0.578663\pi$
$7$	−9.06087	−0.489241	−0.244621	+	0.969619i	$0.578663\pi$
$8$	−22.0592	−0.974887
$9$	−20.9347	−0.775358
$10$	29.3661	0.928639
$11$	−12.4279	−0.340649	−0.170325	−	0.985388i	$-0.554482\pi$
$11$	−12.4279	−0.340649	−0.170325	+	0.985388i	$0.554482\pi$
$12$	0.934885	0.0224898
$13$	4.52500	0.0965393	0.0482696	−	0.998834i	$-0.484629\pi$
$13$	4.52500	0.0965393	0.0482696	+	0.998834i	$0.484629\pi$
$14$	−26.2290	−0.500714
$15$	24.9840	0.430056
$16$	−66.8927	−1.04520
$17$	56.0824	0.800116	0.400058	−	0.916490i	$-0.368990\pi$
$17$	56.0824	0.800116	0.400058	+	0.916490i	$0.368990\pi$
$18$	−60.6007	−0.793541
$19$	−115.118	−1.38999	−0.694996	−	0.719014i	$-0.744594\pi$
$19$	−115.118	−1.38999	−0.694996	+	0.719014i	$0.744594\pi$
$20$	3.85093	0.0430548
$21$	−22.3150	−0.231883
$22$	−35.9756	−0.348638
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−54.3271	−0.462061
$25$	−22.0871	−0.176696
$26$	13.0988	0.0988031
$27$	−118.053	−0.841456
$28$	−3.43955	−0.0232148
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	72.3226	0.440141
$31$	−163.787	−0.948933	−0.474467	−	0.880273i	$-0.657359\pi$
$31$	−163.787	−0.948933	−0.474467	+	0.880273i	$0.657359\pi$
$32$	−17.1646	−0.0948222
$33$	−30.6072	−0.161456
$34$	162.345	0.818879
$35$	−91.9190	−0.443918
$36$	−7.94689	−0.0367912
$37$	−118.015	−0.524367	−0.262184	−	0.965018i	$-0.584443\pi$
$37$	−118.015	−0.524367	−0.262184	+	0.965018i	$0.584443\pi$
$38$	−333.238	−1.42259
$39$	11.1441	0.0457561
$40$	−223.782	−0.884574
$41$	−177.223	−0.675064	−0.337532	−	0.941314i	$-0.609592\pi$
$41$	−177.223	−0.675064	−0.337532	+	0.941314i	$0.609592\pi$
$42$	−64.5965	−0.237320
$43$	335.635	1.19032	0.595160	−	0.803607i	$-0.297089\pi$
$43$	335.635	1.19032	0.595160	+	0.803607i	$0.297089\pi$
$44$	−4.71767	−0.0161640
$45$	−212.374	−0.703530
$46$	−66.5794	−0.213404
$47$	−529.852	−1.64440	−0.822201	−	0.569198i	$-0.807254\pi$
$47$	−529.852	−1.64440	−0.822201	+	0.569198i	$0.807254\pi$
$48$	−164.743	−0.495386
$49$	−260.901	−0.760643
$50$	−63.9366	−0.180840
$51$	138.119	0.379226
$52$	1.71771	0.00458084
$53$	436.327	1.13083	0.565417	−	0.824805i	$-0.308715\pi$
$53$	436.327	1.13083	0.565417	+	0.824805i	$0.308715\pi$
$54$	−341.734	−0.861188
$55$	−126.076	−0.309092
$56$	199.875	0.476955
$57$	−283.511	−0.658805
$58$	83.9479	0.190050
$59$	760.464	1.67803	0.839017	−	0.544105i	$-0.183131\pi$
$59$	760.464	1.67803	0.839017	+	0.544105i	$0.183131\pi$
$60$	9.48404	0.0204064
$61$	−705.723	−1.48129	−0.740645	−	0.671897i	$-0.765480\pi$
$61$	−705.723	−1.48129	−0.740645	+	0.671897i	$0.765480\pi$
$62$	−474.122	−0.971186
$63$	189.686	0.379337
$64$	485.454	0.948153
$65$	45.9044	0.0875959
$66$	−88.6004	−0.165242
$67$	176.246	0.321371	0.160686	−	0.987006i	$-0.448629\pi$
$67$	176.246	0.321371	0.160686	+	0.987006i	$0.448629\pi$
$68$	21.2891	0.0379659
$69$	−56.6441	−0.0988283
$70$	−266.083	−0.454328
$71$	829.225	1.38607	0.693034	−	0.720904i	$-0.256273\pi$
$71$	829.225	1.38607	0.693034	+	0.720904i	$0.256273\pi$
$72$	461.802	0.755887
$73$	−986.129	−1.58106	−0.790532	−	0.612421i	$-0.790196\pi$
$73$	−986.129	−1.58106	−0.790532	+	0.612421i	$0.790196\pi$
$74$	−341.625	−0.536664
$75$	−54.3957	−0.0837477
$76$	−43.6992	−0.0659558
$77$	112.607	0.166660
$78$	32.2595	0.0468291
$79$	−83.3779	−0.118744	−0.0593718	−	0.998236i	$-0.518910\pi$
$79$	−83.3779	−0.118744	−0.0593718	+	0.998236i	$0.518910\pi$
$80$	−678.600	−0.948373
$81$	274.497	0.376539
$82$	−513.018	−0.690894
$83$	570.593	0.754587	0.377293	−	0.926094i	$-0.376855\pi$
$83$	570.593	0.754587	0.377293	+	0.926094i	$0.376855\pi$
$84$	−8.47088	−0.0110030
$85$	568.933	0.725994
$86$	971.580	1.21823
$87$	71.4209	0.0880129
$88$	274.149	0.332095
$89$	−409.496	−0.487713	−0.243857	−	0.969811i	$-0.578413\pi$
$89$	−409.496	−0.487713	−0.243857	+	0.969811i	$0.578413\pi$
$90$	−614.770	−0.720028
$91$	−41.0005	−0.0472310
$92$	−8.73090	−0.00989412
$93$	−403.372	−0.449760
$94$	−1533.79	−1.68296
$95$	−1167.82	−1.26122
$96$	−42.2729	−0.0449423
$97$	1175.91	1.23088	0.615441	−	0.788183i	$-0.288978\pi$
$97$	1175.91	1.23088	0.615441	+	0.788183i	$0.288978\pi$
$98$	−755.243	−0.778480
$99$	260.173	0.264125
$100$	−8.38434	−0.00838434
$101$	−1236.61	−1.21829	−0.609143	−	0.793060i	$-0.708486\pi$
$101$	−1236.61	−1.21829	−0.609143	+	0.793060i	$0.708486\pi$
$102$	399.821	0.388119
$103$	−289.326	−0.276778	−0.138389	−	0.990378i	$-0.544192\pi$
$103$	−289.326	−0.276778	−0.138389	+	0.990378i	$0.544192\pi$
$104$	−99.8179	−0.0941149
$105$	−226.377	−0.210401
$106$	1263.06	1.15735
$107$	900.047	0.813186	0.406593	−	0.913609i	$-0.366717\pi$
$107$	900.047	0.813186	0.406593	+	0.913609i	$0.366717\pi$
$108$	−44.8134	−0.0399275
$109$	−1086.59	−0.954829	−0.477414	−	0.878678i	$-0.658426\pi$
$109$	−1086.59	−0.954829	−0.477414	+	0.878678i	$0.658426\pi$
$110$	−364.958	−0.316340
$111$	−290.647	−0.248531
$112$	606.107	0.511354
$113$	−864.776	−0.719922	−0.359961	−	0.932967i	$-0.617210\pi$
$113$	−864.776	−0.719922	−0.359961	+	0.932967i	$0.617210\pi$
$114$	−820.694	−0.674255
$115$	−233.326	−0.189198
$116$	11.0085	0.00881134
$117$	−94.7295	−0.0748525
$118$	2201.36	1.71738
$119$	−508.155	−0.391450
$120$	−551.127	−0.419256
$121$	−1176.55	−0.883958
$122$	−2042.90	−1.51603
$123$	−436.463	−0.319956
$124$	−62.1741	−0.0450274
$125$	−1492.14	−1.06769
$126$	549.096	0.388233
$127$	−813.830	−0.568628	−0.284314	−	0.958731i	$-0.591766\pi$
$127$	−813.830	−0.568628	−0.284314	+	0.958731i	$0.591766\pi$
$128$	1542.59	1.06521
$129$	826.597	0.564169
$130$	132.882	0.0896501
$131$	−601.065	−0.400880	−0.200440	−	0.979706i	$-0.564237\pi$
$131$	−601.065	−0.400880	−0.200440	+	0.979706i	$0.564237\pi$
$132$	−11.6186	−0.00766115
$133$	1043.07	0.680041
$134$	510.189	0.328908
$135$	−1197.60	−0.763504
$136$	−1237.13	−0.780023
$137$	1156.03	0.720920	0.360460	−	0.932775i	$-0.382620\pi$
$137$	1156.03	0.720920	0.360460	+	0.932775i	$0.382620\pi$
$138$	−163.971	−0.101146
$139$	1496.76	0.913333	0.456667	−	0.889638i	$-0.349043\pi$
$139$	1496.76	0.913333	0.456667	+	0.889638i	$0.349043\pi$
$140$	−34.8928	−0.0210642
$141$	−1304.91	−0.779387
$142$	2400.40	1.41857
$143$	−56.2362	−0.0328860
$144$	1400.38	0.810404
$145$	294.193	0.168493
$146$	−2854.60	−1.61814
$147$	−642.543	−0.360517
$148$	−44.7991	−0.0248815
$149$	−124.431	−0.0684146	−0.0342073	−	0.999415i	$-0.510891\pi$
$149$	−124.431	−0.0684146	−0.0342073	+	0.999415i	$0.510891\pi$
$150$	−157.462	−0.0857116
$151$	−250.216	−0.134849	−0.0674247	−	0.997724i	$-0.521478\pi$
$151$	−250.216	−0.134849	−0.0674247	+	0.997724i	$0.521478\pi$
$152$	2539.40	1.35508
$153$	−1174.07	−0.620377
$154$	325.971	0.170568
$155$	−1661.55	−0.861025
$156$	4.23036	0.00217115
$157$	3189.34	1.62126	0.810628	−	0.585562i	$-0.199126\pi$
$157$	3189.34	1.62126	0.810628	+	0.585562i	$0.199126\pi$
$158$	−241.358	−0.121528
$159$	1074.58	0.535974
$160$	−174.129	−0.0860379
$161$	208.400	0.102014
$162$	794.601	0.385369
$163$	−2884.25	−1.38596	−0.692980	−	0.720956i	$-0.743703\pi$
$163$	−2884.25	−1.38596	−0.692980	+	0.720956i	$0.743703\pi$
$164$	−67.2747	−0.0320321
$165$	−310.498	−0.146498
$166$	1651.73	0.772282
$167$	3126.61	1.44877	0.724383	−	0.689397i	$-0.242125\pi$
$167$	3126.61	1.44877	0.724383	+	0.689397i	$0.242125\pi$
$168$	492.251	0.226059
$169$	−2176.52	−0.990680
$170$	1646.92	0.743019
$171$	2409.95	1.07774
$172$	127.408	0.0564814
$173$	1860.63	0.817695	0.408847	−	0.912603i	$-0.365931\pi$
$173$	1860.63	0.817695	0.408847	+	0.912603i	$0.365931\pi$
$174$	206.746	0.0900768
$175$	200.128	0.0864472
$176$	831.334	0.356046
$177$	1872.86	0.795327
$178$	−1185.39	−0.499150
$179$	−909.693	−0.379853	−0.189926	−	0.981798i	$-0.560825\pi$
$179$	−909.693	−0.379853	−0.189926	+	0.981798i	$0.560825\pi$
$180$	−80.6181	−0.0333829
$181$	3086.70	1.26758	0.633792	−	0.773503i	$-0.281497\pi$
$181$	3086.70	1.26758	0.633792	+	0.773503i	$0.281497\pi$
$182$	−118.686	−0.0483386
$183$	−1738.05	−0.702077
$184$	507.361	0.203278
$185$	−1197.22	−0.475790
$186$	−1167.66	−0.460307
$187$	−696.985	−0.272559
$188$	−201.134	−0.0780277
$189$	1069.66	0.411675
$190$	−3380.56	−1.29080
$191$	−2124.76	−0.804934	−0.402467	−	0.915435i	$-0.631847\pi$
$191$	−2124.76	−0.804934	−0.402467	+	0.915435i	$0.631847\pi$
$192$	1195.57	0.449390
$193$	−4091.27	−1.52589	−0.762943	−	0.646466i	$-0.776246\pi$
$193$	−4091.27	−1.52589	−0.762943	+	0.646466i	$0.776246\pi$
$194$	3403.97	1.25975
$195$	113.053	0.0415173
$196$	−99.0390	−0.0360929
$197$	5220.87	1.88818	0.944091	−	0.329685i	$-0.106942\pi$
$197$	5220.87	1.88818	0.944091	+	0.329685i	$0.106942\pi$
$198$	753.138	0.270319
$199$	3383.67	1.20534	0.602668	−	0.797992i	$-0.294104\pi$
$199$	3383.67	1.20534	0.602668	+	0.797992i	$0.294104\pi$
$200$	487.222	0.172259
$201$	434.057	0.152318
$202$	−3579.67	−1.24685
$203$	−262.765	−0.0908498
$204$	52.4306	0.0179945
$205$	−1797.86	−0.612526
$206$	−837.527	−0.283268
$207$	481.498	0.161673
$208$	−302.690	−0.100903
$209$	1430.67	0.473500
$210$	−655.306	−0.215335
$211$	3668.14	1.19680	0.598400	−	0.801197i	$-0.295803\pi$
$211$	3668.14	1.19680	0.598400	+	0.801197i	$0.295803\pi$
$212$	165.632	0.0536587
$213$	2042.21	0.656946
$214$	2605.42	0.832255
$215$	3404.88	1.08005
$216$	2604.15	0.820324
$217$	1484.05	0.464257
$218$	−3145.41	−0.977220
$219$	−2428.63	−0.749367
$220$	−47.8589	−0.0146666
$221$	253.773	0.0772426
$222$	−841.351	−0.254359
$223$	−700.570	−0.210375	−0.105188	−	0.994452i	$-0.533544\pi$
$223$	−700.570	−0.210375	−0.105188	+	0.994452i	$0.533544\pi$
$224$	155.527	0.0463909
$225$	462.385	0.137003
$226$	−2503.31	−0.736805
$227$	3589.13	1.04942	0.524711	−	0.851280i	$-0.324173\pi$
$227$	3589.13	1.04942	0.524711	+	0.851280i	$0.324173\pi$
$228$	−107.622	−0.0312607
$229$	−5064.83	−1.46154	−0.730772	−	0.682622i	$-0.760840\pi$
$229$	−5064.83	−1.46154	−0.730772	+	0.682622i	$0.760840\pi$
$230$	−675.421	−0.193635
$231$	277.328	0.0789907
$232$	−639.716	−0.181032
$233$	3359.45	0.944570	0.472285	−	0.881446i	$-0.343429\pi$
$233$	3359.45	0.944570	0.472285	+	0.881446i	$0.343429\pi$
$234$	−274.219	−0.0766078
$235$	−5375.14	−1.49207
$236$	288.675	0.0796236
$237$	−205.342	−0.0562802
$238$	−1470.99	−0.400629
$239$	−3005.83	−0.813518	−0.406759	−	0.913535i	$-0.633341\pi$
$239$	−3005.83	−0.813518	−0.406759	+	0.913535i	$0.633341\pi$
$240$	−1671.25	−0.449494
$241$	−5641.00	−1.50775	−0.753877	−	0.657016i	$-0.771819\pi$
$241$	−5641.00	−1.50775	−0.753877	+	0.657016i	$0.771819\pi$
$242$	−3405.82	−0.904687
$243$	3863.46	1.01992
$244$	−267.896	−0.0702880
$245$	−2646.73	−0.690178
$246$	−1263.45	−0.327459
$247$	−520.908	−0.134189
$248$	3613.00	0.925103
$249$	1405.25	0.357647
$250$	−4319.38	−1.09273
$251$	−1765.35	−0.443935	−0.221968	−	0.975054i	$-0.571248\pi$
$251$	−1765.35	−0.443935	−0.221968	+	0.975054i	$0.571248\pi$
$252$	72.0058	0.0179998
$253$	285.841	0.0710303
$254$	−2355.84	−0.581962
$255$	1401.16	0.344095
$256$	581.780	0.142036
$257$	5.45561	0.00132417	0.000662085	−	1.00000i	$-0.499789\pi$
$257$	5.45561	0.00132417	0.000662085		1.00000i	$0.499789\pi$
$258$	2392.79	0.577399
$259$	1069.32	0.256542
$260$	17.4255	0.00415647
$261$	−607.106	−0.143980
$262$	−1739.94	−0.410281
$263$	4605.24	1.07974	0.539869	−	0.841749i	$-0.318474\pi$
$263$	4605.24	1.07974	0.539869	+	0.841749i	$0.318474\pi$
$264$	675.170	0.157401
$265$	4426.37	1.02607
$266$	3019.43	0.695988
$267$	−1008.50	−0.231158
$268$	66.9038	0.0152492
$269$	−5346.84	−1.21191	−0.605953	−	0.795500i	$-0.707208\pi$
$269$	−5346.84	−1.21191	−0.605953	+	0.795500i	$0.707208\pi$
$270$	−3466.76	−0.781408
$271$	−3064.25	−0.686864	−0.343432	−	0.939178i	$-0.611589\pi$
$271$	−3064.25	−0.686864	−0.343432	+	0.939178i	$0.611589\pi$
$272$	−3751.50	−0.836281
$273$	−100.976	−0.0223858
$274$	3346.41	0.737826
$275$	274.495	0.0601916
$276$	−21.5024	−0.00468946
$277$	−865.400	−0.187714	−0.0938571	−	0.995586i	$-0.529920\pi$
$277$	−865.400	−0.187714	−0.0938571	+	0.995586i	$0.529920\pi$
$278$	4332.75	0.934751
$279$	3428.82	0.735763
$280$	2027.66	0.432770
$281$	2735.41	0.580714	0.290357	−	0.956918i	$-0.406226\pi$
$281$	2735.41	0.580714	0.290357	+	0.956918i	$0.406226\pi$
$282$	−3777.40	−0.797663
$283$	−5109.70	−1.07329	−0.536643	−	0.843809i	$-0.680308\pi$
$283$	−5109.70	−1.07329	−0.536643	+	0.843809i	$0.680308\pi$
$284$	314.777	0.0657697
$285$	−2876.10	−0.597774
$286$	−162.790	−0.0336572
$287$	1605.80	0.330269
$288$	359.336	0.0735212
$289$	−1767.77	−0.359814
$290$	851.618	0.172444
$291$	2896.02	0.583393
$292$	−374.339	−0.0750224
$293$	9294.18	1.85315	0.926573	−	0.376115i	$-0.122740\pi$
$293$	9294.18	1.85315	0.926573	+	0.376115i	$0.122740\pi$
$294$	−1860.00	−0.368971
$295$	7714.61	1.52258
$296$	2603.32	0.511199
$297$	1467.15	0.286641
$298$	−360.197	−0.0700189
$299$	−104.075	−0.0201298
$300$	−20.6489	−0.00397387
$301$	−3041.14	−0.582354
$302$	−724.313	−0.138012
$303$	−3045.50	−0.577423
$304$	7700.54	1.45282
$305$	−7159.28	−1.34406
$306$	−3398.63	−0.634925
$307$	−4722.17	−0.877879	−0.438939	−	0.898517i	$-0.644646\pi$
$307$	−4722.17	−0.877879	−0.438939	+	0.898517i	$0.644646\pi$
$308$	42.7462	0.00790810
$309$	−712.548	−0.131183
$310$	−4809.78	−0.881216
$311$	5982.56	1.09080	0.545402	−	0.838175i	$-0.316377\pi$
$311$	5982.56	1.09080	0.545402	+	0.838175i	$0.316377\pi$
$312$	−245.830	−0.0446070
$313$	−5322.39	−0.961148	−0.480574	−	0.876954i	$-0.659572\pi$
$313$	−5322.39	−0.961148	−0.480574	+	0.876954i	$0.659572\pi$
$314$	9232.36	1.65927
$315$	1924.29	0.344196
$316$	−31.6506	−0.00563445
$317$	7008.34	1.24173	0.620864	−	0.783919i	$-0.286782\pi$
$317$	7008.34	1.24173	0.620864	+	0.783919i	$0.286782\pi$
$318$	3110.65	0.548543
$319$	−360.408	−0.0632570
$320$	4924.74	0.860317
$321$	2216.63	0.385421
$322$	603.267	0.104406
$323$	−6456.08	−1.11215
$324$	104.200	0.0178670
$325$	−99.9440	−0.0170581
$326$	−8349.18	−1.41846
$327$	−2676.04	−0.452554
$328$	3909.40	0.658111
$329$	4800.92	0.804509
$330$	−898.815	−0.149934
$331$	−285.936	−0.0474817	−0.0237408	−	0.999718i	$-0.507558\pi$
$331$	−285.936	−0.0474817	−0.0237408	+	0.999718i	$0.507558\pi$
$332$	216.599	0.0358055
$333$	2470.61	0.406573
$334$	9050.76	1.48274
$335$	1787.95	0.291600
$336$	1492.71	0.242363
$337$	7550.82	1.22053	0.610267	−	0.792196i	$-0.291062\pi$
$337$	7550.82	1.22053	0.610267	+	0.792196i	$0.291062\pi$
$338$	−6300.50	−1.01391
$339$	−2129.76	−0.341217
$340$	215.970	0.0344488
$341$	2035.52	0.323254
$342$	6976.22	1.10301
$343$	5471.87	0.861379
$344$	−7403.82	−1.16043
$345$	−574.632	−0.0896729
$346$	5386.07	0.836870
$347$	6561.59	1.01511	0.507557	−	0.861618i	$-0.330549\pi$
$347$	6561.59	1.01511	0.507557	+	0.861618i	$0.330549\pi$
$348$	27.1117	0.00417626
$349$	−8949.00	−1.37258	−0.686288	−	0.727330i	$-0.740761\pi$
$349$	−8949.00	−1.37258	−0.686288	+	0.727330i	$0.740761\pi$
$350$	579.322	0.0884744
$351$	−534.190	−0.0812335
$352$	213.320	0.0323011
$353$	−1716.55	−0.258818	−0.129409	−	0.991591i	$-0.541308\pi$
$353$	−1716.55	−0.258818	−0.129409	+	0.991591i	$0.541308\pi$
$354$	5421.48	0.813978
$355$	8412.16	1.25766
$356$	−155.446	−0.0231423
$357$	−1251.48	−0.185533
$358$	−2633.34	−0.388760
$359$	5581.14	0.820505	0.410252	−	0.911972i	$-0.365441\pi$
$359$	5581.14	0.820505	0.410252	+	0.911972i	$0.365441\pi$
$360$	4684.79	0.685862
$361$	6393.10	0.932075
$362$	8935.25	1.29731
$363$	−2897.59	−0.418964
$364$	−15.5640	−0.00224114
$365$	−10003.9	−1.43460
$366$	−5031.22	−0.718541
$367$	−10825.0	−1.53967	−0.769836	−	0.638241i	$-0.779662\pi$
$367$	−10825.0	−1.53967	−0.769836	+	0.638241i	$0.779662\pi$
$368$	1538.53	0.217939
$369$	3710.11	0.523416
$370$	−3465.65	−0.486948
$371$	−3953.51	−0.553250
$372$	−153.122	−0.0213414
$373$	−11466.7	−1.59176	−0.795878	−	0.605456i	$-0.792991\pi$
$373$	−11466.7	−1.59176	−0.795878	+	0.605456i	$0.792991\pi$
$374$	−2017.60	−0.278951
$375$	−3674.82	−0.506046
$376$	11688.1	1.60311
$377$	131.225	0.0179269
$378$	3096.41	0.421329
$379$	−2792.68	−0.378497	−0.189249	−	0.981929i	$-0.560605\pi$
$379$	−2792.68	−0.378497	−0.189249	+	0.981929i	$0.560605\pi$
$380$	−443.311	−0.0598457
$381$	−2004.29	−0.269509
$382$	−6150.66	−0.823810
$383$	−4710.94	−0.628506	−0.314253	−	0.949339i	$-0.601754\pi$
$383$	−4710.94	−0.628506	−0.314253	+	0.949339i	$0.601754\pi$
$384$	3799.07	0.504871
$385$	1142.36	0.151221
$386$	−11843.2	−1.56167
$387$	−7026.40	−0.922925
$388$	446.380	0.0584060
$389$	8006.36	1.04354	0.521772	−	0.853085i	$-0.325271\pi$
$389$	8006.36	1.04354	0.521772	+	0.853085i	$0.325271\pi$
$390$	327.260	0.0424909
$391$	−1289.89	−0.166836
$392$	5755.25	0.741541
$393$	−1480.30	−0.190003
$394$	15113.1	1.93246
$395$	−845.835	−0.107743
$396$	98.7630	0.0125329
$397$	−9446.73	−1.19425	−0.597126	−	0.802148i	$-0.703691\pi$
$397$	−9446.73	−1.19425	−0.597126	+	0.802148i	$0.703691\pi$
$398$	9794.89	1.23360
$399$	2568.85	0.322315
$400$	1477.46	0.184683
$401$	2798.05	0.348448	0.174224	−	0.984706i	$-0.444258\pi$
$401$	2798.05	0.348448	0.174224	+	0.984706i	$0.444258\pi$
$402$	1256.49	0.155890
$403$	−741.135	−0.0916093
$404$	−469.421	−0.0578083
$405$	2784.66	0.341657
$406$	−760.641	−0.0929803
$407$	1466.68	0.178625
$408$	−3046.79	−0.369703
$409$	−13981.9	−1.69037	−0.845183	−	0.534478i	$-0.820508\pi$
$409$	−13981.9	−1.69037	−0.845183	+	0.534478i	$0.820508\pi$
$410$	−5204.36	−0.626890
$411$	2847.05	0.341690
$412$	−109.829	−0.0131333
$413$	−6890.47	−0.820963
$414$	1393.82	0.165465
$415$	5788.44	0.684682
$416$	−77.6701	−0.00915406
$417$	3686.20	0.432887
$418$	4141.44	0.484603
$419$	252.827	0.0294783	0.0147391	−	0.999891i	$-0.495308\pi$
$419$	252.827	0.0294783	0.0147391	+	0.999891i	$0.495308\pi$
$420$	−85.9337	−0.00998365
$421$	−4901.00	−0.567364	−0.283682	−	0.958918i	$-0.591556\pi$
$421$	−4901.00	−0.567364	−0.283682	+	0.958918i	$0.591556\pi$
$422$	10618.4	1.22487
$423$	11092.3	1.27500
$424$	−9625.02	−1.10243
$425$	−1238.70	−0.141378
$426$	5911.68	0.672352
$427$	6394.47	0.724708
$428$	341.662	0.0385861
$429$	−138.498	−0.0155868
$430$	9856.29	1.10538
$431$	−7566.75	−0.845655	−0.422828	−	0.906210i	$-0.638962\pi$
$431$	−7566.75	−0.845655	−0.422828	+	0.906210i	$0.638962\pi$
$432$	7896.88	0.879488
$433$	−4334.14	−0.481029	−0.240514	−	0.970646i	$-0.577316\pi$
$433$	−4334.14	−0.481029	−0.240514	+	0.970646i	$0.577316\pi$
$434$	4295.96	0.475144
$435$	724.536	0.0798594
$436$	−412.474	−0.0453071
$437$	2647.71	0.289833
$438$	−7030.28	−0.766940
$439$	−916.747	−0.0996673	−0.0498336	−	0.998758i	$-0.515869\pi$
$439$	−916.747	−0.0996673	−0.0498336	+	0.998758i	$0.515869\pi$
$440$	2781.13	0.301330
$441$	5461.87	0.589771
$442$	734.611	0.0790540
$443$	−7013.41	−0.752183	−0.376092	−	0.926582i	$-0.622732\pi$
$443$	−7013.41	−0.752183	−0.376092	+	0.926582i	$0.622732\pi$
$444$	−110.331	−0.0117929
$445$	−4154.17	−0.442532
$446$	−2027.98	−0.215309
$447$	−306.447	−0.0324260
$448$	−4398.64	−0.463876
$449$	−14829.9	−1.55872	−0.779361	−	0.626575i	$-0.784456\pi$
$449$	−14829.9	−1.55872	−0.779361	+	0.626575i	$0.784456\pi$
$450$	1338.49	0.140216
$451$	2202.51	0.229960
$452$	−328.273	−0.0341607
$453$	−616.228	−0.0639137
$454$	10389.7	1.07403
$455$	−415.934	−0.0428555
$456$	6254.01	0.642261
$457$	−859.688	−0.0879967	−0.0439984	−	0.999032i	$-0.514010\pi$
$457$	−859.688	−0.0879967	−0.0439984	+	0.999032i	$0.514010\pi$
$458$	−14661.4	−1.49582
$459$	−6620.69	−0.673262
$460$	−88.5715	−0.00897754
$461$	4177.91	0.422093	0.211046	−	0.977476i	$-0.432313\pi$
$461$	4177.91	0.422093	0.211046	+	0.977476i	$0.432313\pi$
$462$	802.797	0.0808430
$463$	9320.09	0.935511	0.467755	−	0.883858i	$-0.345063\pi$
$463$	9320.09	0.935511	0.467755	+	0.883858i	$0.345063\pi$
$464$	−1939.89	−0.194089
$465$	−4092.04	−0.408095
$466$	9724.78	0.966720
$467$	−3319.05	−0.328880	−0.164440	−	0.986387i	$-0.552582\pi$
$467$	−3319.05	−0.328880	−0.164440	+	0.986387i	$0.552582\pi$
$468$	−35.9597	−0.00355179
$469$	−1596.94	−0.157228
$470$	−15559.7	−1.52705
$471$	7854.67	0.768416
$472$	−16775.2	−1.63589
$473$	−4171.22	−0.405482
$474$	−594.415	−0.0575999
$475$	2542.61	0.245607
$476$	−192.898	−0.0185745
$477$	−9134.37	−0.876801
$478$	−8701.13	−0.832595
$479$	6718.26	0.640846	0.320423	−	0.947275i	$-0.396175\pi$
$479$	6718.26	0.640846	0.320423	+	0.947275i	$0.396175\pi$
$480$	−428.842	−0.0407789
$481$	−534.020	−0.0506220
$482$	−16329.3	−1.54311
$483$	513.245	0.0483509
$484$	−446.623	−0.0419443
$485$	11929.1	1.11685
$486$	11183.8	1.04384
$487$	6317.75	0.587853	0.293927	−	0.955828i	$-0.405038\pi$
$487$	6317.75	0.587853	0.293927	+	0.955828i	$0.405038\pi$
$488$	15567.7	1.44409
$489$	−7103.29	−0.656895
$490$	−7661.64	−0.706362
$491$	−5618.96	−0.516456	−0.258228	−	0.966084i	$-0.583139\pi$
$491$	−5618.96	−0.516456	−0.258228	+	0.966084i	$0.583139\pi$
$492$	−165.683	−0.0151821
$493$	1626.39	0.148578
$494$	−1507.90	−0.137335
$495$	2639.36	0.239657
$496$	10956.1	0.991824
$497$	−7513.50	−0.678122
$498$	4067.85	0.366034
$499$	15283.5	1.37111	0.685556	−	0.728020i	$-0.259559\pi$
$499$	15283.5	1.37111	0.685556	+	0.728020i	$0.259559\pi$
$500$	−566.423	−0.0506624
$501$	7700.17	0.686663
$502$	−5110.25	−0.454345
$503$	−10000.9	−0.886518	−0.443259	−	0.896393i	$-0.646178\pi$
$503$	−10000.9	−0.886518	−0.443259	+	0.896393i	$0.646178\pi$
$504$	−4184.33	−0.369811
$505$	−12544.9	−1.10542
$506$	827.440	0.0726960
$507$	−5360.32	−0.469547
$508$	−308.933	−0.0269817
$509$	14259.7	1.24175	0.620875	−	0.783910i	$-0.286777\pi$
$509$	14259.7	1.24175	0.620875	+	0.783910i	$0.286777\pi$
$510$	4056.02	0.352164
$511$	8935.19	0.773522
$512$	−10656.6	−0.919843
$513$	13590.0	1.16962
$514$	15.7926	0.00135522
$515$	−2935.09	−0.251137
$516$	313.780	0.0267701
$517$	6584.93	0.560164
$518$	3095.42	0.262558
$519$	4582.34	0.387558
$520$	−1012.61	−0.0853961
$521$	−23616.6	−1.98592	−0.992958	−	0.118469i	$-0.962202\pi$
$521$	−23616.6	−1.98592	−0.992958	+	0.118469i	$0.962202\pi$
$522$	−1757.42	−0.147357
$523$	15563.3	1.30121	0.650607	−	0.759415i	$-0.274515\pi$
$523$	15563.3	1.30121	0.650607	+	0.759415i	$0.274515\pi$
$524$	−228.167	−0.0190220
$525$	492.873	0.0409728
$526$	13331.0	1.10506
$527$	−9185.54	−0.759257
$528$	2047.40	0.168753
$529$	529.000	0.0434783
$530$	12813.2	1.05014
$531$	−15920.1	−1.30108
$532$	395.953	0.0322683
$533$	−801.936	−0.0651701
$534$	−2919.36	−0.236579
$535$	9130.62	0.737853
$536$	−3887.84	−0.313301
$537$	−2240.38	−0.180036
$538$	−15477.8	−1.24033
$539$	3242.44	0.259113
$540$	−454.614	−0.0362287
$541$	15235.3	1.21075	0.605377	−	0.795939i	$-0.293023\pi$
$541$	15235.3	1.21075	0.605377	+	0.795939i	$0.293023\pi$
$542$	−8870.26	−0.702971
$543$	7601.89	0.600789
$544$	−962.634	−0.0758688
$545$	−11023.0	−0.866374
$546$	−292.299	−0.0229107
$547$	−15976.8	−1.24884	−0.624422	−	0.781087i	$-0.714665\pi$
$547$	−15976.8	−1.24884	−0.624422	+	0.781087i	$0.714665\pi$
$548$	438.833	0.0342081
$549$	14774.1	1.14853
$550$	794.596	0.0616031
$551$	−3338.42	−0.258115
$552$	1249.52	0.0963464
$553$	755.476	0.0580943
$554$	−2505.12	−0.192116
$555$	−2948.49	−0.225507
$556$	568.176	0.0433382
$557$	−12040.2	−0.915902	−0.457951	−	0.888977i	$-0.651417\pi$
$557$	−12040.2	−0.915902	−0.457951	+	0.888977i	$0.651417\pi$
$558$	9925.59	0.753017
$559$	1518.75	0.114913
$560$	6148.71	0.463983
$561$	−1716.53	−0.129183
$562$	7918.33	0.594332
$563$	−26045.1	−1.94968	−0.974840	−	0.222907i	$-0.928446\pi$
$563$	−26045.1	−1.94968	−0.974840	+	0.222907i	$0.928446\pi$
$564$	−495.351	−0.0369823
$565$	−8772.80	−0.653229
$566$	−14791.3	−1.09846
$567$	−2487.18	−0.184218
$568$	−18292.0	−1.35126
$569$	−20339.2	−1.49853	−0.749264	−	0.662272i	$-0.769593\pi$
$569$	−20339.2	−1.49853	−0.749264	+	0.662272i	$0.769593\pi$
$570$	−8325.61	−0.611792
$571$	−23188.4	−1.69948	−0.849742	−	0.527199i	$-0.823242\pi$
$571$	−23188.4	−1.69948	−0.849742	+	0.527199i	$0.823242\pi$
$572$	−21.3475	−0.00156046
$573$	−5232.84	−0.381509
$574$	4648.39	0.338014
$575$	508.002	0.0368438
$576$	−10162.8	−0.735158
$577$	25555.3	1.84382	0.921908	−	0.387409i	$-0.126630\pi$
$577$	25555.3	1.84382	0.921908	+	0.387409i	$0.126630\pi$
$578$	−5117.25	−0.368252
$579$	−10075.9	−0.723214
$580$	111.677	0.00799507
$581$	−5170.07	−0.369175
$582$	8383.25	0.597074
$583$	−5422.62	−0.385218
$584$	21753.2	1.54136
$585$	−960.993	−0.0679182
$586$	26904.4	1.89660
$587$	26111.0	1.83597	0.917986	−	0.396613i	$-0.129815\pi$
$587$	26111.0	1.83597	0.917986	+	0.396613i	$0.129815\pi$
$588$	−243.912	−0.0171067
$589$	18854.7	1.31901
$590$	22331.9	1.55829
$591$	12857.9	0.894930
$592$	7894.37	0.548068
$593$	2158.59	0.149482	0.0747409	−	0.997203i	$-0.476187\pi$
$593$	2158.59	0.149482	0.0747409	+	0.997203i	$0.476187\pi$
$594$	4247.03	0.293363
$595$	−5155.03	−0.355186
$596$	−47.2345	−0.00324631
$597$	8333.26	0.571286
$598$	−301.272	−0.0206019
$599$	−15843.8	−1.08074	−0.540368	−	0.841429i	$-0.681715\pi$
$599$	−15843.8	−1.08074	−0.540368	+	0.841429i	$0.681715\pi$
$600$	1199.93	0.0816446
$601$	−10911.3	−0.740567	−0.370283	−	0.928919i	$-0.620739\pi$
$601$	−10911.3	−0.740567	−0.370283	+	0.928919i	$0.620739\pi$
$602$	−8803.36	−0.596010
$603$	−3689.65	−0.249178
$604$	−94.9829	−0.00639868
$605$	−11935.6	−0.802069
$606$	−8815.97	−0.590964
$607$	−24172.3	−1.61635	−0.808176	−	0.588942i	$-0.799545\pi$
$607$	−24172.3	−1.61635	−0.808176	+	0.588942i	$0.799545\pi$
$608$	1975.96	0.131802
$609$	−647.135	−0.0430595
$610$	−20724.4	−1.37558
$611$	−2397.58	−0.158749
$612$	−445.681	−0.0294372
$613$	−4389.42	−0.289212	−0.144606	−	0.989489i	$-0.546191\pi$
$613$	−4389.42	−0.289212	−0.144606	+	0.989489i	$0.546191\pi$
$614$	−13669.5	−0.898465
$615$	−4427.74	−0.290315
$616$	−2484.03	−0.162474
$617$	9579.04	0.625021	0.312510	−	0.949914i	$-0.398830\pi$
$617$	9579.04	0.625021	0.312510	+	0.949914i	$0.398830\pi$
$618$	−2062.65	−0.134259
$619$	−21646.7	−1.40558	−0.702789	−	0.711398i	$-0.748062\pi$
$619$	−21646.7	−1.40558	−0.702789	+	0.711398i	$0.748062\pi$
$620$	−630.731	−0.0408561
$621$	2715.22	0.175456
$622$	17318.1	1.11638
$623$	3710.39	0.238609
$624$	−745.461	−0.0478242
$625$	−12376.3	−0.792082
$626$	−15407.0	−0.983687
$627$	3523.43	0.224422
$628$	1210.69	0.0769294
$629$	−6618.58	−0.419555
$630$	5570.36	0.352267
$631$	−21519.8	−1.35767	−0.678833	−	0.734292i	$-0.737514\pi$
$631$	−21519.8	−1.35767	−0.678833	+	0.734292i	$0.737514\pi$
$632$	1839.25	0.115762
$633$	9033.84	0.567240
$634$	20287.4	1.27085
$635$	−8255.98	−0.515950
$636$	407.916	0.0254323
$637$	−1180.58	−0.0734319
$638$	−1043.29	−0.0647404
$639$	−17359.6	−1.07470
$640$	15648.9	0.966530
$641$	−20272.6	−1.24917	−0.624587	−	0.780955i	$-0.714733\pi$
$641$	−20272.6	−1.24917	−0.624587	+	0.780955i	$0.714733\pi$
$642$	6416.59	0.394459
$643$	29769.7	1.82582	0.912910	−	0.408162i	$-0.133830\pi$
$643$	29769.7	1.82582	0.912910	+	0.408162i	$0.133830\pi$
$644$	79.1096	0.00484061
$645$	8385.49	0.511905
$646$	−18688.8	−1.13823
$647$	−5212.25	−0.316715	−0.158357	−	0.987382i	$-0.550620\pi$
$647$	−5212.25	−0.316715	−0.158357	+	0.987382i	$0.550620\pi$
$648$	−6055.17	−0.367083
$649$	−9450.95	−0.571621
$650$	−289.313	−0.0174582
$651$	3654.90	0.220041
$652$	−1094.87	−0.0657646
$653$	−16725.1	−1.00230	−0.501150	−	0.865360i	$-0.667090\pi$
$653$	−16725.1	−1.00230	−0.501150	+	0.865360i	$0.667090\pi$
$654$	−7746.47	−0.463167
$655$	−6097.57	−0.363743
$656$	11854.9	0.705576
$657$	20644.3	1.22589
$658$	13897.5	0.823375
$659$	9820.20	0.580487	0.290243	−	0.956953i	$-0.406264\pi$
$659$	9820.20	0.580487	0.290243	+	0.956953i	$0.406264\pi$
$660$	−117.866	−0.00695143
$661$	−23819.8	−1.40164	−0.700821	−	0.713338i	$-0.747183\pi$
$661$	−23819.8	−1.40164	−0.700821	+	0.713338i	$0.747183\pi$
$662$	−827.713	−0.0485952
$663$	624.989	0.0366102
$664$	−12586.8	−0.735637
$665$	10581.5	0.617042
$666$	7151.81	0.416107
$667$	−667.000	−0.0387202
$668$	1186.87	0.0687448
$669$	−1725.36	−0.0997102
$670$	5175.67	0.298438
$671$	8770.64	0.504600
$672$	383.029	0.0219876
$673$	−7612.68	−0.436029	−0.218014	−	0.975946i	$-0.569958\pi$
$673$	−7612.68	−0.436029	−0.218014	+	0.975946i	$0.569958\pi$
$674$	21857.8	1.24915
$675$	2607.44	0.148682
$676$	−826.218	−0.0470083
$677$	−27082.6	−1.53747	−0.768736	−	0.639566i	$-0.779114\pi$
$677$	−27082.6	−1.53747	−0.768736	+	0.639566i	$0.779114\pi$
$678$	−6165.13	−0.349219
$679$	−10654.8	−0.602198
$680$	−12550.2	−0.707762
$681$	8839.27	0.497388
$682$	5892.33	0.330834
$683$	7164.94	0.401404	0.200702	−	0.979652i	$-0.435678\pi$
$683$	7164.94	0.401404	0.200702	+	0.979652i	$0.435678\pi$
$684$	914.829	0.0511394
$685$	11727.4	0.654135
$686$	15839.7	0.881579
$687$	−12473.6	−0.692718
$688$	−22451.5	−1.24412
$689$	1974.38	0.109170
$690$	−1663.42	−0.0917758
$691$	−5931.72	−0.326561	−0.163280	−	0.986580i	$-0.552208\pi$
$691$	−5931.72	−0.326561	−0.163280	+	0.986580i	$0.552208\pi$
$692$	706.304	0.0388000
$693$	−2357.40	−0.129221
$694$	18994.2	1.03892
$695$	15184.0	0.828723
$696$	−1575.49	−0.0858026
$697$	−9939.10	−0.540129
$698$	−25905.2	−1.40476
$699$	8273.61	0.447692
$700$	75.9695	0.00410197
$701$	8126.77	0.437866	0.218933	−	0.975740i	$-0.429742\pi$
$701$	8126.77	0.437866	0.218933	+	0.975740i	$0.429742\pi$
$702$	−1546.35	−0.0831384
$703$	13585.7	0.728866
$704$	−6033.17	−0.322988
$705$	−13237.8	−0.707185
$706$	−4969.00	−0.264888
$707$	11204.7	0.596036
$708$	710.946	0.0377387
$709$	−9805.82	−0.519415	−0.259707	−	0.965687i	$-0.583626\pi$
$709$	−9805.82	−0.519415	−0.259707	+	0.965687i	$0.583626\pi$
$710$	24351.1	1.28716
$711$	1745.49	0.0920688
$712$	9033.14	0.475465
$713$	3767.09	0.197866
$714$	−3622.73	−0.189884
$715$	−570.493	−0.0298395
$716$	−345.323	−0.0180242
$717$	−7402.72	−0.385578
$718$	16156.0	0.839746
$719$	15402.2	0.798895	0.399447	−	0.916756i	$-0.369202\pi$
$719$	15402.2	0.798895	0.399447	+	0.916756i	$0.369202\pi$
$720$	14206.3	0.735329
$721$	2621.54	0.135411
$722$	18506.5	0.953933
$723$	−13892.6	−0.714621
$724$	1171.73	0.0601476
$725$	−640.525	−0.0328117
$726$	−8387.81	−0.428789
$727$	−21553.8	−1.09957	−0.549785	−	0.835306i	$-0.685290\pi$
$727$	−21553.8	−1.09957	−0.549785	+	0.835306i	$0.685290\pi$
$728$	904.437	0.0460449
$729$	2103.46	0.106867
$730$	−28958.8	−1.46824
$731$	18823.2	0.952395
$732$	−659.770	−0.0333139
$733$	−2962.92	−0.149301	−0.0746506	−	0.997210i	$-0.523784\pi$
$733$	−2962.92	−0.149301	−0.0746506	+	0.997210i	$0.523784\pi$
$734$	−31335.7	−1.57578
$735$	−6518.34	−0.327119
$736$	394.787	0.0197718
$737$	−2190.36	−0.109475
$738$	10739.9	0.535691
$739$	35012.2	1.74282	0.871411	−	0.490553i	$-0.163205\pi$
$739$	35012.2	1.74282	0.871411	+	0.490553i	$0.163205\pi$
$740$	−454.469	−0.0225765
$741$	−1282.89	−0.0636006
$742$	−11444.4	−0.566224
$743$	−15411.9	−0.760978	−0.380489	−	0.924786i	$-0.624244\pi$
$743$	−15411.9	−0.760978	−0.380489	+	0.924786i	$0.624244\pi$
$744$	8898.04	0.438465
$745$	−1262.30	−0.0620767
$746$	−33193.4	−1.62908
$747$	−11945.2	−0.585075
$748$	−264.578	−0.0129331
$749$	−8155.22	−0.397844
$750$	−10637.7	−0.517912
$751$	−32598.1	−1.58392	−0.791960	−	0.610573i	$-0.790939\pi$
$751$	−32598.1	−1.58392	−0.791960	+	0.610573i	$0.790939\pi$
$752$	35443.2	1.71873
$753$	−4347.67	−0.210409
$754$	379.865	0.0183473
$755$	−2538.34	−0.122357
$756$	406.049	0.0195342
$757$	22288.0	1.07011	0.535053	−	0.844818i	$-0.320292\pi$
$757$	22288.0	1.07011	0.535053	+	0.844818i	$0.320292\pi$
$758$	−8084.13	−0.387373
$759$	703.966	0.0336658
$760$	25761.2	1.22955
$761$	−8230.74	−0.392069	−0.196034	−	0.980597i	$-0.562806\pi$
$761$	−8230.74	−0.392069	−0.196034	+	0.980597i	$0.562806\pi$
$762$	−5801.93	−0.275829
$763$	9845.45	0.467142
$764$	−806.569	−0.0381945
$765$	−11910.4	−0.562906
$766$	−13637.0	−0.643244
$767$	3441.10	0.161996
$768$	1432.80	0.0673200
$769$	−31586.6	−1.48120	−0.740600	−	0.671946i	$-0.765459\pi$
$769$	−31586.6	−1.48120	−0.740600	+	0.671946i	$0.765459\pi$
$770$	3306.84	0.154767
$771$	13.4360	0.000627608 0
$772$	−1553.06	−0.0724041
$773$	26007.5	1.21012	0.605061	−	0.796179i	$-0.293149\pi$
$773$	26007.5	1.21012	0.605061	+	0.796179i	$0.293149\pi$
$774$	−20339.7	−0.944568
$775$	3617.56	0.167673
$776$	−25939.6	−1.19997
$777$	2633.51	0.121592
$778$	23176.5	1.06802
$779$	20401.5	0.938333
$780$	42.9153	0.00197002
$781$	−10305.5	−0.472164
$782$	−3733.93	−0.170748
$783$	−3423.54	−0.156254
$784$	17452.4	0.795023
$785$	32354.6	1.47106
$786$	−4285.09	−0.194458
$787$	4700.30	0.212894	0.106447	−	0.994318i	$-0.466053\pi$
$787$	4700.30	0.212894	0.106447	+	0.994318i	$0.466053\pi$
$788$	1981.87	0.0895953
$789$	11341.7	0.511756
$790$	−2448.49	−0.110270
$791$	7835.62	0.352216
$792$	−5739.21	−0.257492
$793$	−3193.40	−0.143003
$794$	−27346.0	−1.22226
$795$	10901.2	0.486322
$796$	1284.46	0.0571939
$797$	−21559.9	−0.958208	−0.479104	−	0.877758i	$-0.659038\pi$
$797$	−21559.9	−0.958208	−0.479104	+	0.877758i	$0.659038\pi$
$798$	7436.20	0.329873
$799$	−29715.4	−1.31571
$800$	379.117	0.0167547
$801$	8572.66	0.378152
$802$	8099.66	0.356620
$803$	12255.5	0.538589
$804$	164.770	0.00722759
$805$	2114.14	0.0925634
$806$	−2145.40	−0.0937576
$807$	−13168.1	−0.574400
$808$	27278.5	1.18769
$809$	−33009.3	−1.43454	−0.717272	−	0.696794i	$-0.754609\pi$
$809$	−33009.3	−1.43454	−0.717272	+	0.696794i	$0.754609\pi$
$810$	8060.91	0.349669
$811$	−31073.9	−1.34544	−0.672719	−	0.739898i	$-0.734874\pi$
$811$	−31073.9	−1.34544	−0.672719	+	0.739898i	$0.734874\pi$
$812$	−99.7469	−0.00431087
$813$	−7546.60	−0.325548
$814$	4245.67	0.182814
$815$	−29259.5	−1.25757
$816$	−9239.16	−0.396367
$817$	−38637.5	−1.65454
$818$	−40474.1	−1.73000
$819$	858.332	0.0366209
$820$	−682.475	−0.0290647
$821$	−5489.45	−0.233353	−0.116677	−	0.993170i	$-0.537224\pi$
$821$	−5489.45	−0.233353	−0.116677	+	0.993170i	$0.537224\pi$
$822$	8241.51	0.349703
$823$	−4310.67	−0.182576	−0.0912882	−	0.995825i	$-0.529098\pi$
$823$	−4310.67	−0.182576	−0.0912882	+	0.995825i	$0.529098\pi$
$824$	6382.29	0.269827
$825$	676.023	0.0285286
$826$	−19946.2	−0.840215
$827$	15034.5	0.632164	0.316082	−	0.948732i	$-0.397633\pi$
$827$	15034.5	0.632164	0.316082	+	0.948732i	$0.397633\pi$
$828$	182.779	0.00767149
$829$	40575.6	1.69994	0.849970	−	0.526831i	$-0.176620\pi$
$829$	40575.6	1.69994	0.849970	+	0.526831i	$0.176620\pi$
$830$	16756.1	0.700738
$831$	−2131.30	−0.0889697
$832$	2196.68	0.0915340
$833$	−14631.9	−0.608603
$834$	10670.6	0.443038
$835$	31718.2	1.31455
$836$	543.088	0.0224678
$837$	19335.5	0.798485
$838$	731.871	0.0301695
$839$	−32062.1	−1.31932	−0.659658	−	0.751566i	$-0.729299\pi$
$839$	−32062.1	−1.31932	−0.659658	+	0.751566i	$0.729299\pi$
$840$	4993.69	0.205117
$841$	841.000	0.0344828
$842$	−14187.2	−0.580669
$843$	6736.73	0.275238
$844$	1392.44	0.0567888
$845$	−22080.0	−0.898904
$846$	32109.4	1.30490
$847$	10660.6	0.432469
$848$	−29187.1	−1.18195
$849$	−12584.1	−0.508699
$850$	−3585.72	−0.144693
$851$	2714.35	0.109338
$852$	775.230	0.0311725
$853$	12539.4	0.503329	0.251665	−	0.967815i	$-0.419022\pi$
$853$	12539.4	0.503329	0.251665	+	0.967815i	$0.419022\pi$
$854$	18510.4	0.741702
$855$	24448.0	0.977900
$856$	−19854.3	−0.792764
$857$	30571.8	1.21857	0.609283	−	0.792952i	$-0.291457\pi$
$857$	30571.8	1.21857	0.609283	+	0.792952i	$0.291457\pi$
$858$	−400.917	−0.0159523
$859$	42782.8	1.69934	0.849668	−	0.527319i	$-0.176803\pi$
$859$	42782.8	1.69934	0.849668	+	0.527319i	$0.176803\pi$
$860$	1292.51	0.0512490
$861$	3954.74	0.156536
$862$	−21903.9	−0.865486
$863$	−11818.6	−0.466176	−0.233088	−	0.972456i	$-0.574883\pi$
$863$	−11818.6	−0.466176	−0.233088	+	0.972456i	$0.574883\pi$
$864$	2026.34	0.0797887
$865$	18875.4	0.741944
$866$	−12546.3	−0.492309
$867$	−4353.63	−0.170539
$868$	563.352	0.0220293
$869$	1036.21	0.0404499
$870$	2097.35	0.0817321
$871$	797.514	0.0310250
$872$	23969.3	0.930850
$873$	−24617.3	−0.954374
$874$	7664.47	0.296630
$875$	13520.1	0.522357
$876$	−921.917	−0.0355579
$877$	25660.4	0.988017	0.494008	−	0.869457i	$-0.335531\pi$
$877$	25660.4	0.988017	0.494008	+	0.869457i	$0.335531\pi$
$878$	−2653.76	−0.102005
$879$	22889.6	0.878324
$880$	8433.55	0.323063
$881$	42972.0	1.64332	0.821658	−	0.569980i	$-0.193049\pi$
$881$	42972.0	1.64332	0.821658	+	0.569980i	$0.193049\pi$
$882$	15810.8	0.603601
$883$	957.486	0.0364915	0.0182457	−	0.999834i	$-0.494192\pi$
$883$	957.486	0.0364915	0.0182457	+	0.999834i	$0.494192\pi$
$884$	96.3333	0.00366520
$885$	18999.4	0.721649
$886$	−20302.1	−0.769822
$887$	47845.6	1.81116	0.905580	−	0.424176i	$-0.139436\pi$
$887$	47845.6	1.81116	0.905580	+	0.424176i	$0.139436\pi$
$888$	6411.42	0.242290
$889$	7374.01	0.278196
$890$	−12025.3	−0.452909
$891$	−3411.41	−0.128268
$892$	−265.940	−0.00998241
$893$	60995.4	2.28570
$894$	−887.088	−0.0331864
$895$	−9228.47	−0.344663
$896$	−13977.2	−0.521145
$897$	−256.315	−0.00954081
$898$	−42928.9	−1.59527
$899$	−4749.81	−0.176213
$900$	175.524	0.00650087
$901$	24470.3	0.904798
$902$	6375.72	0.235353
$903$	−7489.69	−0.276015
$904$	19076.2	0.701843
$905$	31313.4	1.15016
$906$	−1783.83	−0.0654125
$907$	−15843.1	−0.580001	−0.290001	−	0.957026i	$-0.593656\pi$
$907$	−15843.1	−0.580001	−0.290001	+	0.957026i	$0.593656\pi$
$908$	1362.45	0.0497957
$909$	25887.9	0.944608
$910$	−1204.03	−0.0438605
$911$	24805.3	0.902127	0.451064	−	0.892492i	$-0.351045\pi$
$911$	24805.3	0.902127	0.451064	+	0.892492i	$0.351045\pi$
$912$	18964.8	0.688583
$913$	−7091.25	−0.257050
$914$	−2488.59	−0.0900603
$915$	−17631.8	−0.637037
$916$	−1922.63	−0.0693510
$917$	5446.18	0.196127
$918$	−19165.3	−0.689050
$919$	−22846.8	−0.820072	−0.410036	−	0.912069i	$-0.634484\pi$
$919$	−22846.8	−0.820072	−0.410036	+	0.912069i	$0.634484\pi$
$920$	5146.98	0.184446
$921$	−11629.7	−0.416083
$922$	12094.0	0.431991
$923$	3752.25	0.133810
$924$	105.275	0.00374815
$925$	2606.61	0.0926539
$926$	26979.4	0.957449
$927$	6056.94	0.214602
$928$	−497.775	−0.0176080
$929$	−52232.1	−1.84465	−0.922324	−	0.386417i	$-0.873712\pi$
$929$	−52232.1	−1.84465	−0.922324	+	0.386417i	$0.873712\pi$
$930$	−11845.5	−0.417665
$931$	30034.3	1.05729
$932$	1275.26	0.0448203
$933$	14733.8	0.517002
$934$	−9607.82	−0.336593
$935$	−7070.63	−0.247309
$936$	2089.65	0.0729727
$937$	35859.7	1.25025	0.625126	−	0.780524i	$-0.285047\pi$
$937$	35859.7	1.25025	0.625126	+	0.780524i	$0.285047\pi$
$938$	−4622.76	−0.160915
$939$	−13107.9	−0.455549
$940$	−2040.43	−0.0707993
$941$	6652.82	0.230474	0.115237	−	0.993338i	$-0.463237\pi$
$941$	6652.82	0.230474	0.115237	+	0.993338i	$0.463237\pi$
$942$	22737.3	0.786436
$943$	4076.13	0.140761
$944$	−50869.5	−1.75388
$945$	10851.3	0.373538
$946$	−12074.7	−0.414991
$947$	41832.7	1.43546	0.717729	−	0.696322i	$-0.245181\pi$
$947$	41832.7	1.43546	0.717729	+	0.696322i	$0.245181\pi$
$948$	−77.9487	−0.00267052
$949$	−4462.24	−0.152635
$950$	7360.24	0.251366
$951$	17260.1	0.588534
$952$	11209.5	0.381619
$953$	−8616.07	−0.292867	−0.146433	−	0.989221i	$-0.546779\pi$
$953$	−8616.07	−0.292867	−0.146433	+	0.989221i	$0.546779\pi$
$954$	−26441.8	−0.897362
$955$	−21554.9	−0.730365
$956$	−1141.03	−0.0386019
$957$	−887.609	−0.0299815
$958$	19447.7	0.655874
$959$	−10474.6	−0.352704
$960$	12128.6	0.407759
$961$	−2964.96	−0.0995254
$962$	−1545.86	−0.0518091
$963$	−18842.2	−0.630510
$964$	−2141.35	−0.0715437
$965$	−41504.3	−1.38453
$966$	1485.72	0.0494847
$967$	32988.2	1.09703	0.548516	−	0.836140i	$-0.315193\pi$
$967$	32988.2	1.09703	0.548516	+	0.836140i	$0.315193\pi$
$968$	25953.7	0.861759
$969$	−15900.0	−0.527121
$970$	34531.9	1.14304
$971$	−6124.85	−0.202426	−0.101213	−	0.994865i	$-0.532272\pi$
$971$	−6124.85	−0.202426	−0.101213	+	0.994865i	$0.532272\pi$
$972$	1466.58	0.0483958
$973$	−13561.9	−0.446840
$974$	18288.3	0.601638
$975$	−246.141	−0.00808494
$976$	47207.8	1.54824
$977$	2580.08	0.0844872	0.0422436	−	0.999107i	$-0.486549\pi$
$977$	2580.08	0.0844872	0.0422436	+	0.999107i	$0.486549\pi$
$978$	−20562.3	−0.672300
$979$	5089.16	0.166139
$980$	−1004.71	−0.0327493
$981$	22747.4	0.740335
$982$	−16265.5	−0.528567
$983$	−31182.3	−1.01176	−0.505880	−	0.862604i	$-0.668832\pi$
$983$	−31182.3	−1.01176	−0.505880	+	0.862604i	$0.668832\pi$
$984$	9628.02	0.311921
$985$	52963.7	1.71326
$986$	4708.00	0.152062
$987$	11823.7	0.381308
$988$	−197.739	−0.00636733
$989$	−7719.59	−0.248199
$990$	7640.29	0.245277
$991$	9775.09	0.313336	0.156668	−	0.987651i	$-0.449925\pi$
$991$	9775.09	0.313336	0.156668	+	0.987651i	$0.449925\pi$
$992$	2811.34	0.0899799
$993$	−704.199	−0.0225046
$994$	−21749.7	−0.694024
$995$	34326.0	1.09367
$996$	533.439	0.0169705
$997$	61639.3	1.95801	0.979005	−	0.203835i	$-0.0653407\pi$
$997$	61639.3	1.95801	0.979005	+	0.203835i	$0.0653407\pi$
$998$	44242.1	1.40327
$999$	13932.1	0.441232

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.4.a.b.1.28	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.4.a.b.1.28	✓	38	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:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	667.a (trivial)

\(f(q)\)	\(=\)	\(q+2.89475 q^{2} +2.46279 q^{3} +0.379604 q^{4} +10.1446 q^{5} +7.12917 q^{6} -9.06087 q^{7} -22.0592 q^{8} -20.9347 q^{9} +O(q^{10})\)	\(q+2.89475 q^{2} +2.46279 q^{3} +0.379604 q^{4} +10.1446 q^{5} +7.12917 q^{6} -9.06087 q^{7} -22.0592 q^{8} -20.9347 q^{9} +29.3661 q^{10} -12.4279 q^{11} +0.934885 q^{12} +4.52500 q^{13} -26.2290 q^{14} +24.9840 q^{15} -66.8927 q^{16} +56.0824 q^{17} -60.6007 q^{18} -115.118 q^{19} +3.85093 q^{20} -22.3150 q^{21} -35.9756 q^{22} -23.0000 q^{23} -54.3271 q^{24} -22.0871 q^{25} +13.0988 q^{26} -118.053 q^{27} -3.43955 q^{28} +29.0000 q^{29} +72.3226 q^{30} -163.787 q^{31} -17.1646 q^{32} -30.6072 q^{33} +162.345 q^{34} -91.9190 q^{35} -7.94689 q^{36} -118.015 q^{37} -333.238 q^{38} +11.1441 q^{39} -223.782 q^{40} -177.223 q^{41} -64.5965 q^{42} +335.635 q^{43} -4.71767 q^{44} -212.374 q^{45} -66.5794 q^{46} -529.852 q^{47} -164.743 q^{48} -260.901 q^{49} -63.9366 q^{50} +138.119 q^{51} +1.71771 q^{52} +436.327 q^{53} -341.734 q^{54} -126.076 q^{55} +199.875 q^{56} -283.511 q^{57} +83.9479 q^{58} +760.464 q^{59} +9.48404 q^{60} -705.723 q^{61} -474.122 q^{62} +189.686 q^{63} +485.454 q^{64} +45.9044 q^{65} -88.6004 q^{66} +176.246 q^{67} +21.2891 q^{68} -56.6441 q^{69} -266.083 q^{70} +829.225 q^{71} +461.802 q^{72} -986.129 q^{73} -341.625 q^{74} -54.3957 q^{75} -43.6992 q^{76} +112.607 q^{77} +32.2595 q^{78} -83.3779 q^{79} -678.600 q^{80} +274.497 q^{81} -513.018 q^{82} +570.593 q^{83} -8.47088 q^{84} +568.933 q^{85} +971.580 q^{86} +71.4209 q^{87} +274.149 q^{88} -409.496 q^{89} -614.770 q^{90} -41.0005 q^{91} -8.73090 q^{92} -403.372 q^{93} -1533.79 q^{94} -1167.82 q^{95} -42.2729 q^{96} +1175.91 q^{97} -755.243 q^{98} +260.173 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 8 q^{2} - 16 q^{3} + 152 q^{4} - 80 q^{5} - 16 q^{6} - 38 q^{7} - 138 q^{8} + 312 q^{9}+O(q^{10}) \) 38 * q - 8 * q^2 - 16 * q^3 + 152 * q^4 - 80 * q^5 - 16 * q^6 - 38 * q^7 - 138 * q^8 + 312 * q^9	\( 38 q - 8 q^{2} - 16 q^{3} + 152 q^{4} - 80 q^{5} - 16 q^{6} - 38 q^{7} - 138 q^{8} + 312 q^{9} + 30 q^{10} - 100 q^{11} - 173 q^{12} - 160 q^{13} - 304 q^{14} - 208 q^{15} + 552 q^{16} - 666 q^{17} - 315 q^{18} - 252 q^{19} - 747 q^{20} - 470 q^{21} - 323 q^{22} - 874 q^{23} - 114 q^{24} + 910 q^{25} - 119 q^{26} - 526 q^{27} - 619 q^{28} + 1102 q^{29} - 533 q^{30} + 358 q^{31} - 1272 q^{32} - 604 q^{33} - 553 q^{34} + 16 q^{35} + 1230 q^{36} - 1206 q^{37} - 2010 q^{38} - 240 q^{39} - 418 q^{40} - 1094 q^{41} - 1184 q^{42} - 936 q^{43} - 2153 q^{44} - 3654 q^{45} + 184 q^{46} - 1702 q^{47} - 1319 q^{48} + 1920 q^{49} - 1255 q^{50} - 270 q^{51} - 2202 q^{52} - 4640 q^{53} - 1529 q^{54} - 318 q^{55} - 2435 q^{56} - 1980 q^{57} - 232 q^{58} + 318 q^{59} - 3279 q^{60} - 2212 q^{61} - 541 q^{62} - 1044 q^{63} + 1186 q^{64} - 2438 q^{65} - 3503 q^{66} - 496 q^{67} - 6099 q^{68} + 368 q^{69} + 4068 q^{70} + 870 q^{71} - 3869 q^{72} - 2810 q^{73} - 2793 q^{74} - 3638 q^{75} + 1548 q^{76} - 6072 q^{77} + 2170 q^{78} - 3084 q^{79} - 6702 q^{80} + 362 q^{81} - 1183 q^{82} - 5566 q^{83} - 6518 q^{84} - 120 q^{85} - 2095 q^{86} - 464 q^{87} - 1220 q^{88} - 6506 q^{89} + 165 q^{90} + 44 q^{91} - 3496 q^{92} - 5928 q^{93} + 135 q^{94} - 2024 q^{95} - 3164 q^{96} - 7472 q^{97} - 6422 q^{98} - 944 q^{99}+O(q^{100}) \) 38 * q - 8 * q^2 - 16 * q^3 + 152 * q^4 - 80 * q^5 - 16 * q^6 - 38 * q^7 - 138 * q^8 + 312 * q^9 + 30 * q^10 - 100 * q^11 - 173 * q^12 - 160 * q^13 - 304 * q^14 - 208 * q^15 + 552 * q^16 - 666 * q^17 - 315 * q^18 - 252 * q^19 - 747 * q^20 - 470 * q^21 - 323 * q^22 - 874 * q^23 - 114 * q^24 + 910 * q^25 - 119 * q^26 - 526 * q^27 - 619 * q^28 + 1102 * q^29 - 533 * q^30 + 358 * q^31 - 1272 * q^32 - 604 * q^33 - 553 * q^34 + 16 * q^35 + 1230 * q^36 - 1206 * q^37 - 2010 * q^38 - 240 * q^39 - 418 * q^40 - 1094 * q^41 - 1184 * q^42 - 936 * q^43 - 2153 * q^44 - 3654 * q^45 + 184 * q^46 - 1702 * q^47 - 1319 * q^48 + 1920 * q^49 - 1255 * q^50 - 270 * q^51 - 2202 * q^52 - 4640 * q^53 - 1529 * q^54 - 318 * q^55 - 2435 * q^56 - 1980 * q^57 - 232 * q^58 + 318 * q^59 - 3279 * q^60 - 2212 * q^61 - 541 * q^62 - 1044 * q^63 + 1186 * q^64 - 2438 * q^65 - 3503 * q^66 - 496 * q^67 - 6099 * q^68 + 368 * q^69 + 4068 * q^70 + 870 * q^71 - 3869 * q^72 - 2810 * q^73 - 2793 * q^74 - 3638 * q^75 + 1548 * q^76 - 6072 * q^77 + 2170 * q^78 - 3084 * q^79 - 6702 * q^80 + 362 * q^81 - 1183 * q^82 - 5566 * q^83 - 6518 * q^84 - 120 * q^85 - 2095 * q^86 - 464 * q^87 - 1220 * q^88 - 6506 * q^89 + 165 * q^90 + 44 * q^91 - 3496 * q^92 - 5928 * q^93 + 135 * q^94 - 2024 * q^95 - 3164 * q^96 - 7472 * q^97 - 6422 * q^98 - 944 * q^99

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