LMFDB - Embedded newform 6023.2.a.d.1.11

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:	$140$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-2.54565 q^{2} +1.89511 q^{3} +4.48036 q^{4} +0.316502 q^{5} -4.82430 q^{6} +4.66425 q^{7} -6.31414 q^{8} +0.591450 q^{9} +O(q^{10})$	\(q-2.54565 q^{2} +1.89511 q^{3} +4.48036 q^{4} +0.316502 q^{5} -4.82430 q^{6} +4.66425 q^{7} -6.31414 q^{8} +0.591450 q^{9} -0.805706 q^{10} -5.53509 q^{11} +8.49078 q^{12} +3.33573 q^{13} -11.8736 q^{14} +0.599808 q^{15} +7.11290 q^{16} +4.94232 q^{17} -1.50563 q^{18} -1.00000 q^{19} +1.41804 q^{20} +8.83927 q^{21} +14.0904 q^{22} -4.57605 q^{23} -11.9660 q^{24} -4.89983 q^{25} -8.49161 q^{26} -4.56447 q^{27} +20.8975 q^{28} -7.40314 q^{29} -1.52690 q^{30} +9.17278 q^{31} -5.47871 q^{32} -10.4896 q^{33} -12.5814 q^{34} +1.47625 q^{35} +2.64991 q^{36} -1.44497 q^{37} +2.54565 q^{38} +6.32158 q^{39} -1.99844 q^{40} +2.63740 q^{41} -22.5017 q^{42} +7.90393 q^{43} -24.7992 q^{44} +0.187195 q^{45} +11.6490 q^{46} +7.76536 q^{47} +13.4797 q^{48} +14.7552 q^{49} +12.4733 q^{50} +9.36625 q^{51} +14.9453 q^{52} -0.605101 q^{53} +11.6196 q^{54} -1.75187 q^{55} -29.4507 q^{56} -1.89511 q^{57} +18.8458 q^{58} +3.69609 q^{59} +2.68735 q^{60} -6.99411 q^{61} -23.3507 q^{62} +2.75867 q^{63} -0.278896 q^{64} +1.05577 q^{65} +26.7029 q^{66} -8.29778 q^{67} +22.1434 q^{68} -8.67212 q^{69} -3.75801 q^{70} +9.96718 q^{71} -3.73450 q^{72} +0.947379 q^{73} +3.67839 q^{74} -9.28572 q^{75} -4.48036 q^{76} -25.8170 q^{77} -16.0925 q^{78} +11.6227 q^{79} +2.25125 q^{80} -10.4245 q^{81} -6.71392 q^{82} +11.7301 q^{83} +39.6031 q^{84} +1.56426 q^{85} -20.1207 q^{86} -14.0298 q^{87} +34.9493 q^{88} -9.66359 q^{89} -0.476535 q^{90} +15.5587 q^{91} -20.5023 q^{92} +17.3834 q^{93} -19.7679 q^{94} -0.316502 q^{95} -10.3828 q^{96} -1.85979 q^{97} -37.5616 q^{98} -3.27373 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9}+O(q^{10}) $ 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9} + 8 q^{10} + 19 q^{11} + 17 q^{12} + 28 q^{13} + 5 q^{14} + 14 q^{15} + 202 q^{16} + 38 q^{17} + 26 q^{18} - 140 q^{19} + 36 q^{20} + 4 q^{21} + 53 q^{22} + 58 q^{23} + 47 q^{24} + 279 q^{25} + 29 q^{26} + 21 q^{27} + 69 q^{28} + 18 q^{29} + 50 q^{30} + 20 q^{31} + 13 q^{32} + 47 q^{33} + 6 q^{34} + 35 q^{35} + 230 q^{36} + 88 q^{37} - 4 q^{38} + 32 q^{39} + 32 q^{40} + 24 q^{41} + 75 q^{42} + 100 q^{43} + 63 q^{44} + 87 q^{45} + 23 q^{46} + 35 q^{47} + 46 q^{48} + 255 q^{49} + 11 q^{50} - 6 q^{51} + 47 q^{52} + 77 q^{53} + 16 q^{54} + 63 q^{55} + 21 q^{56} - 3 q^{57} + 165 q^{58} + 18 q^{59} + 28 q^{60} + 99 q^{61} + 34 q^{62} + 89 q^{63} + 298 q^{64} + 78 q^{65} - 3 q^{66} + 28 q^{67} + 93 q^{68} + 19 q^{69} + 16 q^{70} + q^{71} + 43 q^{72} + 201 q^{73} + 32 q^{74} + 22 q^{75} - 162 q^{76} + 86 q^{77} + 122 q^{78} + 58 q^{79} + 92 q^{80} + 288 q^{81} + 143 q^{82} + 57 q^{83} + q^{84} + 136 q^{85} - 6 q^{86} + 43 q^{87} + 198 q^{88} + 46 q^{89} + 30 q^{90} + 26 q^{91} + 129 q^{92} + 111 q^{93} + 44 q^{94} - 13 q^{95} + 32 q^{96} + 110 q^{97} - 34 q^{98} + 62 q^{99}+O(q^{100}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9 + 8 * q^10 + 19 * q^11 + 17 * q^12 + 28 * q^13 + 5 * q^14 + 14 * q^15 + 202 * q^16 + 38 * q^17 + 26 * q^18 - 140 * q^19 + 36 * q^20 + 4 * q^21 + 53 * q^22 + 58 * q^23 + 47 * q^24 + 279 * q^25 + 29 * q^26 + 21 * q^27 + 69 * q^28 + 18 * q^29 + 50 * q^30 + 20 * q^31 + 13 * q^32 + 47 * q^33 + 6 * q^34 + 35 * q^35 + 230 * q^36 + 88 * q^37 - 4 * q^38 + 32 * q^39 + 32 * q^40 + 24 * q^41 + 75 * q^42 + 100 * q^43 + 63 * q^44 + 87 * q^45 + 23 * q^46 + 35 * q^47 + 46 * q^48 + 255 * q^49 + 11 * q^50 - 6 * q^51 + 47 * q^52 + 77 * q^53 + 16 * q^54 + 63 * q^55 + 21 * q^56 - 3 * q^57 + 165 * q^58 + 18 * q^59 + 28 * q^60 + 99 * q^61 + 34 * q^62 + 89 * q^63 + 298 * q^64 + 78 * q^65 - 3 * q^66 + 28 * q^67 + 93 * q^68 + 19 * q^69 + 16 * q^70 + q^71 + 43 * q^72 + 201 * q^73 + 32 * q^74 + 22 * q^75 - 162 * q^76 + 86 * q^77 + 122 * q^78 + 58 * q^79 + 92 * q^80 + 288 * q^81 + 143 * q^82 + 57 * q^83 + q^84 + 136 * q^85 - 6 * q^86 + 43 * q^87 + 198 * q^88 + 46 * q^89 + 30 * q^90 + 26 * q^91 + 129 * q^92 + 111 * q^93 + 44 * q^94 - 13 * q^95 + 32 * q^96 + 110 * q^97 - 34 * q^98 + 62 * 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 $

$2$	−2.54565	−1.80005	−0.900025	−	0.435838i	$-0.856452\pi$
$2$	−2.54565	−1.80005	−0.900025	+	0.435838i	$0.856452\pi$
$3$	1.89511	1.09414	0.547072	−	0.837086i	$-0.315742\pi$
$3$	1.89511	1.09414	0.547072	+	0.837086i	$0.315742\pi$
$4$	4.48036	2.24018
$5$	0.316502	0.141544	0.0707721	−	0.997493i	$-0.477454\pi$
$5$	0.316502	0.141544	0.0707721	+	0.997493i	$0.477454\pi$
$6$	−4.82430	−1.96951
$7$	4.66425	1.76292	0.881460	−	0.472259i	$-0.156561\pi$
$7$	4.66425	1.76292	0.881460	+	0.472259i	$0.156561\pi$
$8$	−6.31414	−2.23238
$9$	0.591450	0.197150
$10$	−0.805706	−0.254787
$11$	−5.53509	−1.66889	−0.834446	−	0.551090i	$-0.814212\pi$
$11$	−5.53509	−1.66889	−0.834446	+	0.551090i	$0.814212\pi$
$12$	8.49078	2.45108
$13$	3.33573	0.925164	0.462582	−	0.886576i	$-0.346923\pi$
$13$	3.33573	0.925164	0.462582	+	0.886576i	$0.346923\pi$
$14$	−11.8736	−3.17334
$15$	0.599808	0.154870
$16$	7.11290	1.77822
$17$	4.94232	1.19869	0.599345	−	0.800491i	$-0.295428\pi$
$17$	4.94232	1.19869	0.599345	+	0.800491i	$0.295428\pi$
$18$	−1.50563	−0.354880
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	1.41804	0.317084
$21$	8.83927	1.92889
$22$	14.0904	3.00409
$23$	−4.57605	−0.954172	−0.477086	−	0.878857i	$-0.658307\pi$
$23$	−4.57605	−0.954172	−0.477086	+	0.878857i	$0.658307\pi$
$24$	−11.9660	−2.44255
$25$	−4.89983	−0.979965
$26$	−8.49161	−1.66534
$27$	−4.56447	−0.878433
$28$	20.8975	3.94926
$29$	−7.40314	−1.37473	−0.687364	−	0.726313i	$-0.741232\pi$
$29$	−7.40314	−1.37473	−0.687364	+	0.726313i	$0.741232\pi$
$30$	−1.52690	−0.278773
$31$	9.17278	1.64748	0.823740	−	0.566968i	$-0.191884\pi$
$31$	9.17278	1.64748	0.823740	+	0.566968i	$0.191884\pi$
$32$	−5.47871	−0.968508
$33$	−10.4896	−1.82601
$34$	−12.5814	−2.15770
$35$	1.47625	0.249531
$36$	2.64991	0.441651
$37$	−1.44497	−0.237551	−0.118776	−	0.992921i	$-0.537897\pi$
$37$	−1.44497	−0.237551	−0.118776	+	0.992921i	$0.537897\pi$
$38$	2.54565	0.412960
$39$	6.32158	1.01226
$40$	−1.99844	−0.315981
$41$	2.63740	0.411893	0.205947	−	0.978563i	$-0.433973\pi$
$41$	2.63740	0.411893	0.205947	+	0.978563i	$0.433973\pi$
$42$	−22.5017	−3.47209
$43$	7.90393	1.20534	0.602669	−	0.797991i	$-0.294104\pi$
$43$	7.90393	1.20534	0.602669	+	0.797991i	$0.294104\pi$
$44$	−24.7992	−3.73862
$45$	0.187195	0.0279054
$46$	11.6490	1.71756
$47$	7.76536	1.13269	0.566347	−	0.824167i	$-0.308356\pi$
$47$	7.76536	1.13269	0.566347	+	0.824167i	$0.308356\pi$
$48$	13.4797	1.94563
$49$	14.7552	2.10789
$50$	12.4733	1.76399
$51$	9.36625	1.31154
$52$	14.9453	2.07253
$53$	−0.605101	−0.0831170	−0.0415585	−	0.999136i	$-0.513232\pi$
$53$	−0.605101	−0.0831170	−0.0415585	+	0.999136i	$0.513232\pi$
$54$	11.6196	1.58122
$55$	−1.75187	−0.236222
$56$	−29.4507	−3.93551
$57$	−1.89511	−0.251014
$58$	18.8458	2.47458
$59$	3.69609	0.481190	0.240595	−	0.970626i	$-0.422657\pi$
$59$	3.69609	0.481190	0.240595	+	0.970626i	$0.422657\pi$
$60$	2.68735	0.346936
$61$	−6.99411	−0.895504	−0.447752	−	0.894158i	$-0.647775\pi$
$61$	−6.99411	−0.895504	−0.447752	+	0.894158i	$0.647775\pi$
$62$	−23.3507	−2.96555
$63$	2.75867	0.347560
$64$	−0.278896	−0.0348620
$65$	1.05577	0.130952
$66$	26.7029	3.28690
$67$	−8.29778	−1.01374	−0.506868	−	0.862024i	$-0.669197\pi$
$67$	−8.29778	−1.01374	−0.506868	+	0.862024i	$0.669197\pi$
$68$	22.1434	2.68528
$69$	−8.67212	−1.04400
$70$	−3.75801	−0.449168
$71$	9.96718	1.18289	0.591443	−	0.806347i	$-0.298558\pi$
$71$	9.96718	1.18289	0.591443	+	0.806347i	$0.298558\pi$
$72$	−3.73450	−0.440115
$73$	0.947379	0.110882	0.0554412	−	0.998462i	$-0.482343\pi$
$73$	0.947379	0.110882	0.0554412	+	0.998462i	$0.482343\pi$
$74$	3.67839	0.427604
$75$	−9.28572	−1.07222
$76$	−4.48036	−0.513932
$77$	−25.8170	−2.94212
$78$	−16.0925	−1.82212
$79$	11.6227	1.30766	0.653828	−	0.756643i	$-0.273162\pi$
$79$	11.6227	1.30766	0.653828	+	0.756643i	$0.273162\pi$
$80$	2.25125	0.251697
$81$	−10.4245	−1.15828
$82$	−6.71392	−0.741429
$83$	11.7301	1.28754	0.643770	−	0.765219i	$-0.277369\pi$
$83$	11.7301	1.28754	0.643770	+	0.765219i	$0.277369\pi$
$84$	39.6031	4.32105
$85$	1.56426	0.169667
$86$	−20.1207	−2.16967
$87$	−14.0298	−1.50415
$88$	34.9493	3.72561
$89$	−9.66359	−1.02434	−0.512169	−	0.858884i	$-0.671158\pi$
$89$	−9.66359	−1.02434	−0.512169	+	0.858884i	$0.671158\pi$
$90$	−0.476535	−0.0502312
$91$	15.5587	1.63099
$92$	−20.5023	−2.13752
$93$	17.3834	1.80258
$94$	−19.7679	−2.03891
$95$	−0.316502	−0.0324725
$96$	−10.3828	−1.05969
$97$	−1.85979	−0.188833	−0.0944166	−	0.995533i	$-0.530099\pi$
$97$	−1.85979	−0.188833	−0.0944166	+	0.995533i	$0.530099\pi$
$98$	−37.5616	−3.79430
$99$	−3.27373	−0.329022
$100$	−21.9530	−2.19530
$101$	5.45710	0.543002	0.271501	−	0.962438i	$-0.412480\pi$
$101$	5.45710	0.543002	0.271501	+	0.962438i	$0.412480\pi$
$102$	−23.8433	−2.36083
$103$	13.0148	1.28238	0.641192	−	0.767380i	$-0.278440\pi$
$103$	13.0148	1.28238	0.641192	+	0.767380i	$0.278440\pi$
$104$	−21.0622	−2.06532
$105$	2.79765	0.273023
$106$	1.54038	0.149615
$107$	1.91919	0.185535	0.0927675	−	0.995688i	$-0.470429\pi$
$107$	1.91919	0.185535	0.0927675	+	0.995688i	$0.470429\pi$
$108$	−20.4505	−1.96785
$109$	14.1159	1.35206	0.676029	−	0.736875i	$-0.263700\pi$
$109$	14.1159	1.35206	0.676029	+	0.736875i	$0.263700\pi$
$110$	4.45965	0.425211
$111$	−2.73838	−0.259915
$112$	33.1763	3.13487
$113$	−16.5722	−1.55898	−0.779488	−	0.626417i	$-0.784521\pi$
$113$	−16.5722	−1.55898	−0.779488	+	0.626417i	$0.784521\pi$
$114$	4.82430	0.451837
$115$	−1.44833	−0.135057
$116$	−33.1687	−3.07964
$117$	1.97292	0.182396
$118$	−9.40898	−0.866167
$119$	23.0522	2.11319
$120$	−3.78727	−0.345729
$121$	19.6372	1.78520
$122$	17.8046	1.61195
$123$	4.99818	0.450670
$124$	41.0973	3.69065
$125$	−3.13332	−0.280253
$126$	−7.02262	−0.625625
$127$	19.1078	1.69554	0.847771	−	0.530362i	$-0.177944\pi$
$127$	19.1078	1.69554	0.847771	+	0.530362i	$0.177944\pi$
$128$	11.6674	1.03126
$129$	14.9788	1.31881
$130$	−2.68761	−0.235719
$131$	18.4194	1.60931	0.804654	−	0.593744i	$-0.202351\pi$
$131$	18.4194	1.60931	0.804654	+	0.593744i	$0.202351\pi$
$132$	−46.9972	−4.09058
$133$	−4.66425	−0.404441
$134$	21.1233	1.82477
$135$	−1.44467	−0.124337
$136$	−31.2065	−2.67594
$137$	22.9348	1.95945	0.979725	−	0.200345i	$-0.0642062\pi$
$137$	22.9348	1.95945	0.979725	+	0.200345i	$0.0642062\pi$
$138$	22.0762	1.87925
$139$	−2.12317	−0.180085	−0.0900426	−	0.995938i	$-0.528700\pi$
$139$	−2.12317	−0.180085	−0.0900426	+	0.995938i	$0.528700\pi$
$140$	6.61411	0.558994
$141$	14.7162	1.23933
$142$	−25.3730	−2.12925
$143$	−18.4635	−1.54400
$144$	4.20692	0.350577
$145$	−2.34311	−0.194585
$146$	−2.41170	−0.199594
$147$	27.9628	2.30633
$148$	−6.47397	−0.532157
$149$	24.4012	1.99903	0.999513	−	0.0311948i	$-0.00993122\pi$
$149$	24.4012	1.99903	0.999513	+	0.0311948i	$0.00993122\pi$
$150$	23.6382	1.93005
$151$	−4.75068	−0.386605	−0.193302	−	0.981139i	$-0.561920\pi$
$151$	−4.75068	−0.386605	−0.193302	+	0.981139i	$0.561920\pi$
$152$	6.31414	0.512144
$153$	2.92314	0.236322
$154$	65.7212	5.29597
$155$	2.90321	0.233191
$156$	28.3229	2.26765
$157$	−16.1839	−1.29161	−0.645807	−	0.763501i	$-0.723479\pi$
$157$	−16.1839	−1.29161	−0.645807	+	0.763501i	$0.723479\pi$
$158$	−29.5874	−2.35385
$159$	−1.14673	−0.0909419
$160$	−1.73402	−0.137087
$161$	−21.3438	−1.68213
$162$	26.5373	2.08497
$163$	23.6260	1.85053	0.925266	−	0.379318i	$-0.123841\pi$
$163$	23.6260	1.85053	0.925266	+	0.379318i	$0.123841\pi$
$164$	11.8165	0.922715
$165$	−3.31999	−0.258461
$166$	−29.8607	−2.31764
$167$	−16.2965	−1.26106	−0.630531	−	0.776164i	$-0.717163\pi$
$167$	−16.2965	−1.26106	−0.630531	+	0.776164i	$0.717163\pi$
$168$	−55.8124	−4.30602
$169$	−1.87293	−0.144072
$170$	−3.98206	−0.305410
$171$	−0.591450	−0.0452293
$172$	35.4124	2.70017
$173$	17.1955	1.30735	0.653676	−	0.756775i	$-0.273226\pi$
$173$	17.1955	1.30735	0.653676	+	0.756775i	$0.273226\pi$
$174$	35.7150	2.70755
$175$	−22.8540	−1.72760
$176$	−39.3705	−2.96766
$177$	7.00451	0.526491
$178$	24.6002	1.84386
$179$	16.2993	1.21827	0.609135	−	0.793066i	$-0.291517\pi$
$179$	16.2993	1.21827	0.609135	+	0.793066i	$0.291517\pi$
$180$	0.838702	0.0625132
$181$	13.7710	1.02359	0.511796	−	0.859107i	$-0.328981\pi$
$181$	13.7710	1.02359	0.511796	+	0.859107i	$0.328981\pi$
$182$	−39.6070	−2.93586
$183$	−13.2546	−0.979810
$184$	28.8938	2.13008
$185$	−0.457336	−0.0336240
$186$	−44.2523	−3.24473
$187$	−27.3562	−2.00048
$188$	34.7916	2.53744
$189$	−21.2898	−1.54861
$190$	0.805706	0.0584520
$191$	−10.5101	−0.760487	−0.380244	−	0.924886i	$-0.624160\pi$
$191$	−10.5101	−0.760487	−0.380244	+	0.924886i	$0.624160\pi$
$192$	−0.528540	−0.0381441
$193$	−17.1093	−1.23155	−0.615776	−	0.787921i	$-0.711157\pi$
$193$	−17.1093	−1.23155	−0.615776	+	0.787921i	$0.711157\pi$
$194$	4.73439	0.339909
$195$	2.00079	0.143280
$196$	66.1086	4.72204
$197$	14.6514	1.04387	0.521934	−	0.852986i	$-0.325211\pi$
$197$	14.6514	1.04387	0.521934	+	0.852986i	$0.325211\pi$
$198$	8.33378	0.592256
$199$	14.4925	1.02734	0.513672	−	0.857987i	$-0.328285\pi$
$199$	14.4925	1.02734	0.513672	+	0.857987i	$0.328285\pi$
$200$	30.9382	2.18766
$201$	−15.7252	−1.10917
$202$	−13.8919	−0.977430
$203$	−34.5301	−2.42354
$204$	41.9642	2.93808
$205$	0.834745	0.0583011
$206$	−33.1311	−2.30836
$207$	−2.70650	−0.188115
$208$	23.7267	1.64515
$209$	5.53509	0.382870
$210$	−7.12185	−0.491455
$211$	3.62012	0.249219	0.124610	−	0.992206i	$-0.460232\pi$
$211$	3.62012	0.249219	0.124610	+	0.992206i	$0.460232\pi$
$212$	−2.71107	−0.186197
$213$	18.8889	1.29425
$214$	−4.88559	−0.333972
$215$	2.50161	0.170609
$216$	28.8207	1.96100
$217$	42.7841	2.90437
$218$	−35.9342	−2.43377
$219$	1.79539	0.121321
$220$	−7.84900	−0.529180
$221$	16.4862	1.10898
$222$	6.97096	0.467860
$223$	−6.09079	−0.407869	−0.203935	−	0.978985i	$-0.565373\pi$
$223$	−6.09079	−0.407869	−0.203935	+	0.978985i	$0.565373\pi$
$224$	−25.5540	−1.70740
$225$	−2.89800	−0.193200
$226$	42.1870	2.80624
$227$	−1.66290	−0.110370	−0.0551852	−	0.998476i	$-0.517575\pi$
$227$	−1.66290	−0.110370	−0.0551852	+	0.998476i	$0.517575\pi$
$228$	−8.49078	−0.562316
$229$	−14.3276	−0.946794	−0.473397	−	0.880849i	$-0.656972\pi$
$229$	−14.3276	−0.946794	−0.473397	+	0.880849i	$0.656972\pi$
$230$	3.68695	0.243110
$231$	−48.9261	−3.21910
$232$	46.7444	3.06892
$233$	−3.40222	−0.222887	−0.111443	−	0.993771i	$-0.535547\pi$
$233$	−3.40222	−0.222887	−0.111443	+	0.993771i	$0.535547\pi$
$234$	−5.02236	−0.328322
$235$	2.45776	0.160326
$236$	16.5598	1.07795
$237$	22.0263	1.43076
$238$	−58.6830	−3.80385
$239$	25.5476	1.65254	0.826269	−	0.563275i	$-0.190459\pi$
$239$	25.5476	1.65254	0.826269	+	0.563275i	$0.190459\pi$
$240$	4.26637	0.275393
$241$	10.5789	0.681449	0.340725	−	0.940163i	$-0.389328\pi$
$241$	10.5789	0.681449	0.340725	+	0.940163i	$0.389328\pi$
$242$	−49.9895	−3.21345
$243$	−6.06225	−0.388894
$244$	−31.3361	−2.00609
$245$	4.67006	0.298359
$246$	−12.7236	−0.811229
$247$	−3.33573	−0.212247
$248$	−57.9182	−3.67781
$249$	22.2298	1.40875
$250$	7.97635	0.504469
$251$	−15.0680	−0.951084	−0.475542	−	0.879693i	$-0.657748\pi$
$251$	−15.0680	−0.951084	−0.475542	+	0.879693i	$0.657748\pi$
$252$	12.3598	0.778596
$253$	25.3288	1.59241
$254$	−48.6418	−3.05206
$255$	2.96444	0.185641
$256$	−29.1434	−1.82146
$257$	−18.1833	−1.13424	−0.567122	−	0.823634i	$-0.691943\pi$
$257$	−18.1833	−1.13424	−0.567122	+	0.823634i	$0.691943\pi$
$258$	−38.1309	−2.37393
$259$	−6.73969	−0.418784
$260$	4.73021	0.293355
$261$	−4.37859	−0.271028
$262$	−46.8894	−2.89683
$263$	−5.88636	−0.362968	−0.181484	−	0.983394i	$-0.558090\pi$
$263$	−5.88636	−0.362968	−0.181484	+	0.983394i	$0.558090\pi$
$264$	66.2329	4.07635
$265$	−0.191516	−0.0117647
$266$	11.8736	0.728015
$267$	−18.3136	−1.12077
$268$	−37.1770	−2.27095
$269$	9.28943	0.566387	0.283193	−	0.959063i	$-0.408606\pi$
$269$	9.28943	0.566387	0.283193	+	0.959063i	$0.408606\pi$
$270$	3.67762	0.223813
$271$	4.10786	0.249535	0.124767	−	0.992186i	$-0.460182\pi$
$271$	4.10786	0.249535	0.124767	+	0.992186i	$0.460182\pi$
$272$	35.1542	2.13154
$273$	29.4854	1.78454
$274$	−58.3840	−3.52711
$275$	27.1210	1.63546
$276$	−38.8542	−2.33875
$277$	−16.9305	−1.01725	−0.508627	−	0.860987i	$-0.669847\pi$
$277$	−16.9305	−1.01725	−0.508627	+	0.860987i	$0.669847\pi$
$278$	5.40486	0.324162
$279$	5.42524	0.324801
$280$	−9.32122	−0.557049
$281$	7.66355	0.457169	0.228585	−	0.973524i	$-0.426590\pi$
$281$	7.66355	0.457169	0.228585	+	0.973524i	$0.426590\pi$
$282$	−37.4624	−2.23086
$283$	0.896363	0.0532832	0.0266416	−	0.999645i	$-0.491519\pi$
$283$	0.896363	0.0532832	0.0266416	+	0.999645i	$0.491519\pi$
$284$	44.6565	2.64988
$285$	−0.599808	−0.0355295
$286$	47.0018	2.77927
$287$	12.3015	0.726135
$288$	−3.24038	−0.190941
$289$	7.42655	0.436856
$290$	5.96475	0.350262
$291$	−3.52451	−0.206611
$292$	4.24460	0.248396
$293$	−30.2868	−1.76937	−0.884687	−	0.466186i	$-0.845628\pi$
$293$	−30.2868	−1.76937	−0.884687	+	0.466186i	$0.845628\pi$
$294$	−71.1835	−4.15151
$295$	1.16982	0.0681097
$296$	9.12373	0.530306
$297$	25.2648	1.46601
$298$	−62.1171	−3.59835
$299$	−15.2644	−0.882765
$300$	−41.6034	−2.40197
$301$	36.8659	2.12491
$302$	12.0936	0.695908
$303$	10.3418	0.594122
$304$	−7.11290	−0.407953
$305$	−2.21365	−0.126753
$306$	−7.44130	−0.425391
$307$	−24.5666	−1.40209	−0.701045	−	0.713117i	$-0.747283\pi$
$307$	−24.5666	−1.40209	−0.701045	+	0.713117i	$0.747283\pi$
$308$	−115.670	−6.59088
$309$	24.6645	1.40311
$310$	−7.39056	−0.419756
$311$	15.4303	0.874975	0.437487	−	0.899225i	$-0.355868\pi$
$311$	15.4303	0.874975	0.437487	+	0.899225i	$0.355868\pi$
$312$	−39.9153	−2.25976
$313$	13.4409	0.759726	0.379863	−	0.925043i	$-0.375971\pi$
$313$	13.4409	0.759726	0.379863	+	0.925043i	$0.375971\pi$
$314$	41.1985	2.32497
$315$	0.873125	0.0491950
$316$	52.0739	2.92939
$317$	1.00000	0.0561656
$317$	1.00000	0.0561656
$318$	2.91919	0.163700
$319$	40.9770	2.29427
$320$	−0.0882713	−0.00493452
$321$	3.63708	0.203002
$322$	54.3340	3.02791
$323$	−4.94232	−0.274998
$324$	−46.7057	−2.59476
$325$	−16.3445	−0.906629
$326$	−60.1437	−3.33105
$327$	26.7512	1.47934
$328$	−16.6529	−0.919505
$329$	36.2196	1.99685
$330$	8.45154	0.465242
$331$	−31.5538	−1.73436	−0.867178	−	0.497998i	$-0.834069\pi$
$331$	−31.5538	−1.73436	−0.867178	+	0.497998i	$0.834069\pi$
$332$	52.5549	2.88432
$333$	−0.854626	−0.0468332
$334$	41.4853	2.26997
$335$	−2.62627	−0.143488
$336$	62.8728	3.42999
$337$	6.16200	0.335665	0.167833	−	0.985815i	$-0.446323\pi$
$337$	6.16200	0.335665	0.167833	+	0.985815i	$0.446323\pi$
$338$	4.76783	0.259336
$339$	−31.4061	−1.70574
$340$	7.00843	0.380086
$341$	−50.7722	−2.74947
$342$	1.50563	0.0814150
$343$	36.1722	1.95311
$344$	−49.9065	−2.69078
$345$	−2.74475	−0.147772
$346$	−43.7739	−2.35330
$347$	−3.58728	−0.192575	−0.0962875	−	0.995354i	$-0.530697\pi$
$347$	−3.58728	−0.192575	−0.0962875	+	0.995354i	$0.530697\pi$
$348$	−62.8584	−3.36957
$349$	−12.7690	−0.683511	−0.341756	−	0.939789i	$-0.611022\pi$
$349$	−12.7690	−0.683511	−0.341756	+	0.939789i	$0.611022\pi$
$350$	58.1784	3.10977
$351$	−15.2258	−0.812695
$352$	30.3251	1.61633
$353$	−17.7649	−0.945530	−0.472765	−	0.881189i	$-0.656744\pi$
$353$	−17.7649	−0.945530	−0.472765	+	0.881189i	$0.656744\pi$
$354$	−17.8311	−0.947711
$355$	3.15463	0.167431
$356$	−43.2964	−2.29470
$357$	43.6865	2.31214
$358$	−41.4925	−2.19295
$359$	−17.9441	−0.947052	−0.473526	−	0.880780i	$-0.657019\pi$
$359$	−17.9441	−0.947052	−0.473526	+	0.880780i	$0.657019\pi$
$360$	−1.18198	−0.0622957
$361$	1.00000	0.0526316
$362$	−35.0562	−1.84252
$363$	37.2147	1.95327
$364$	69.7083	3.65371
$365$	0.299848	0.0156947
$366$	33.7417	1.76371
$367$	1.52729	0.0797241	0.0398621	−	0.999205i	$-0.487308\pi$
$367$	1.52729	0.0797241	0.0398621	+	0.999205i	$0.487308\pi$
$368$	−32.5489	−1.69673
$369$	1.55989	0.0812048
$370$	1.16422	0.0605249
$371$	−2.82234	−0.146529
$372$	77.8841	4.03810
$373$	−7.61685	−0.394385	−0.197193	−	0.980365i	$-0.563182\pi$
$373$	−7.61685	−0.394385	−0.197193	+	0.980365i	$0.563182\pi$
$374$	69.6394	3.60097
$375$	−5.93799	−0.306637
$376$	−49.0316	−2.52861
$377$	−24.6948	−1.27185
$378$	54.1965	2.78757
$379$	3.63609	0.186773	0.0933866	−	0.995630i	$-0.470231\pi$
$379$	3.63609	0.186773	0.0933866	+	0.995630i	$0.470231\pi$
$380$	−1.41804	−0.0727441
$381$	36.2114	1.85517
$382$	26.7552	1.36891
$383$	5.26058	0.268803	0.134402	−	0.990927i	$-0.457089\pi$
$383$	5.26058	0.268803	0.134402	+	0.990927i	$0.457089\pi$
$384$	22.1110	1.12835
$385$	−8.17115	−0.416440
$386$	43.5543	2.21686
$387$	4.67478	0.237632
$388$	−8.33253	−0.423020
$389$	4.14762	0.210293	0.105146	−	0.994457i	$-0.466469\pi$
$389$	4.14762	0.210293	0.105146	+	0.994457i	$0.466469\pi$
$390$	−5.09333	−0.257911
$391$	−22.6163	−1.14376
$392$	−93.1664	−4.70561
$393$	34.9068	1.76081
$394$	−37.2973	−1.87901
$395$	3.67861	0.185091
$396$	−14.6675	−0.737068
$397$	−6.47950	−0.325197	−0.162598	−	0.986692i	$-0.551987\pi$
$397$	−6.47950	−0.325197	−0.162598	+	0.986692i	$0.551987\pi$
$398$	−36.8928	−1.84927
$399$	−8.83927	−0.442517
$400$	−34.8520	−1.74260
$401$	−35.9748	−1.79650	−0.898249	−	0.439488i	$-0.855160\pi$
$401$	−35.9748	−1.79650	−0.898249	+	0.439488i	$0.855160\pi$
$402$	40.0310	1.99657
$403$	30.5979	1.52419
$404$	24.4498	1.21642
$405$	−3.29939	−0.163948
$406$	87.9016	4.36248
$407$	7.99802	0.396447
$408$	−59.1398	−2.92786
$409$	0.173147	0.00856155	0.00428077	−	0.999991i	$-0.498637\pi$
$409$	0.173147	0.00856155	0.00428077	+	0.999991i	$0.498637\pi$
$410$	−2.12497	−0.104945
$411$	43.4640	2.14392
$412$	58.3109	2.87277
$413$	17.2395	0.848300
$414$	6.88982	0.338616
$415$	3.71259	0.182244
$416$	−18.2755	−0.896029
$417$	−4.02365	−0.197039
$418$	−14.0904	−0.689185
$419$	−29.8459	−1.45807	−0.729033	−	0.684479i	$-0.760030\pi$
$419$	−29.8459	−1.45807	−0.729033	+	0.684479i	$0.760030\pi$
$420$	12.5345	0.611620
$421$	21.2863	1.03743	0.518716	−	0.854946i	$-0.326410\pi$
$421$	21.2863	1.03743	0.518716	+	0.854946i	$0.326410\pi$
$422$	−9.21558	−0.448607
$423$	4.59282	0.223311
$424$	3.82069	0.185549
$425$	−24.2165	−1.17467
$426$	−48.0847	−2.32971
$427$	−32.6223	−1.57870
$428$	8.59865	0.415632
$429$	−34.9905	−1.68936
$430$	−6.36824	−0.307104
$431$	−2.30301	−0.110932	−0.0554660	−	0.998461i	$-0.517664\pi$
$431$	−2.30301	−0.110932	−0.0554660	+	0.998461i	$0.517664\pi$
$432$	−32.4666	−1.56205
$433$	11.5598	0.555530	0.277765	−	0.960649i	$-0.410406\pi$
$433$	11.5598	0.555530	0.277765	+	0.960649i	$0.410406\pi$
$434$	−108.914	−5.22802
$435$	−4.44046	−0.212904
$436$	63.2443	3.02885
$437$	4.57605	0.218902
$438$	−4.57044	−0.218384
$439$	−20.3669	−0.972058	−0.486029	−	0.873943i	$-0.661555\pi$
$439$	−20.3669	−0.972058	−0.486029	+	0.873943i	$0.661555\pi$
$440$	11.0615	0.527338
$441$	8.72696	0.415570
$442$	−41.9683	−1.99623
$443$	−4.23451	−0.201188	−0.100594	−	0.994928i	$-0.532074\pi$
$443$	−4.23451	−0.201188	−0.100594	+	0.994928i	$0.532074\pi$
$444$	−12.2689	−0.582257
$445$	−3.05855	−0.144989
$446$	15.5050	0.734185
$447$	46.2431	2.18722
$448$	−1.30084	−0.0614590
$449$	−20.8798	−0.985380	−0.492690	−	0.870205i	$-0.663986\pi$
$449$	−20.8798	−0.985380	−0.492690	+	0.870205i	$0.663986\pi$
$450$	7.37731	0.347770
$451$	−14.5983	−0.687406
$452$	−74.2492	−3.49239
$453$	−9.00307	−0.423001
$454$	4.23316	0.198672
$455$	4.92435	0.230857
$456$	11.9660	0.560359
$457$	−14.7038	−0.687816	−0.343908	−	0.939003i	$-0.611751\pi$
$457$	−14.7038	−0.687816	−0.343908	+	0.939003i	$0.611751\pi$
$458$	36.4731	1.70428
$459$	−22.5591	−1.05297
$460$	−6.48904	−0.302553
$461$	3.93563	0.183300	0.0916502	−	0.995791i	$-0.470786\pi$
$461$	3.93563	0.183300	0.0916502	+	0.995791i	$0.470786\pi$
$462$	124.549	5.79455
$463$	−12.1457	−0.564458	−0.282229	−	0.959347i	$-0.591074\pi$
$463$	−12.1457	−0.564458	−0.282229	+	0.959347i	$0.591074\pi$
$464$	−52.6578	−2.44458
$465$	5.50190	0.255145
$466$	8.66088	0.401207
$467$	−2.48781	−0.115122	−0.0575610	−	0.998342i	$-0.518332\pi$
$467$	−2.48781	−0.115122	−0.0575610	+	0.998342i	$0.518332\pi$
$468$	8.83937	0.408600
$469$	−38.7029	−1.78713
$470$	−6.25660	−0.288595
$471$	−30.6702	−1.41321
$472$	−23.3376	−1.07420
$473$	−43.7489	−2.01158
$474$	−56.0714	−2.57545
$475$	4.89983	0.224819
$476$	103.282	4.73393
$477$	−0.357887	−0.0163865
$478$	−65.0355	−2.97465
$479$	4.28565	0.195816	0.0979082	−	0.995195i	$-0.468785\pi$
$479$	4.28565	0.195816	0.0979082	+	0.995195i	$0.468785\pi$
$480$	−3.28617	−0.149992
$481$	−4.82002	−0.219774
$482$	−26.9303	−1.22664
$483$	−40.4489	−1.84049
$484$	87.9817	3.99917
$485$	−0.588628	−0.0267282
$486$	15.4324	0.700028
$487$	−4.93276	−0.223525	−0.111762	−	0.993735i	$-0.535650\pi$
$487$	−4.93276	−0.223525	−0.111762	+	0.993735i	$0.535650\pi$
$488$	44.1618	1.99911
$489$	44.7740	2.02475
$490$	−11.8884	−0.537061
$491$	−1.80599	−0.0815031	−0.0407515	−	0.999169i	$-0.512975\pi$
$491$	−1.80599	−0.0815031	−0.0407515	+	0.999169i	$0.512975\pi$
$492$	22.3936	1.00958
$493$	−36.5887	−1.64787
$494$	8.49161	0.382056
$495$	−1.03614	−0.0465712
$496$	65.2451	2.92959
$497$	46.4894	2.08533
$498$	−56.5893	−2.53583
$499$	−36.8886	−1.65136	−0.825680	−	0.564139i	$-0.809208\pi$
$499$	−36.8886	−1.65136	−0.825680	+	0.564139i	$0.809208\pi$
$500$	−14.0384	−0.627816
$501$	−30.8837	−1.37978
$502$	38.3579	1.71200
$503$	18.1362	0.808653	0.404327	−	0.914615i	$-0.367506\pi$
$503$	18.1362	0.808653	0.404327	+	0.914615i	$0.367506\pi$
$504$	−17.4186	−0.775887
$505$	1.72719	0.0768587
$506$	−64.4784	−2.86642
$507$	−3.54941	−0.157635
$508$	85.6097	3.79832
$509$	32.5396	1.44229	0.721146	−	0.692783i	$-0.243616\pi$
$509$	32.5396	1.44229	0.721146	+	0.692783i	$0.243616\pi$
$510$	−7.54645	−0.334162
$511$	4.41881	0.195477
$512$	50.8541	2.24746
$513$	4.56447	0.201526
$514$	46.2884	2.04169
$515$	4.11921	0.181514
$516$	67.1105	2.95438
$517$	−42.9820	−1.89034
$518$	17.1569	0.753832
$519$	32.5874	1.43043
$520$	−6.66625	−0.292334
$521$	29.8223	1.30654	0.653270	−	0.757125i	$-0.273397\pi$
$521$	29.8223	1.30654	0.653270	+	0.757125i	$0.273397\pi$
$522$	11.1464	0.487863
$523$	−28.5264	−1.24737	−0.623687	−	0.781674i	$-0.714366\pi$
$523$	−28.5264	−1.24737	−0.623687	+	0.781674i	$0.714366\pi$
$524$	82.5254	3.60514
$525$	−43.3109	−1.89024
$526$	14.9846	0.653361
$527$	45.3348	1.97482
$528$	−74.6115	−3.24705
$529$	−2.05981	−0.0895567
$530$	0.487533	0.0211771
$531$	2.18605	0.0948667
$532$	−20.8975	−0.906022
$533$	8.79766	0.381069
$534$	46.6201	2.01745
$535$	0.607428	0.0262614
$536$	52.3933	2.26305
$537$	30.8891	1.33296
$538$	−23.6477	−1.01952
$539$	−81.6713	−3.51783
$540$	−6.47262	−0.278537
$541$	37.8510	1.62734	0.813670	−	0.581327i	$-0.197466\pi$
$541$	37.8510	1.62734	0.813670	+	0.581327i	$0.197466\pi$
$542$	−10.4572	−0.449175
$543$	26.0976	1.11996
$544$	−27.0775	−1.16094
$545$	4.46771	0.191376
$546$	−75.0596	−3.21226
$547$	−10.8761	−0.465028	−0.232514	−	0.972593i	$-0.574695\pi$
$547$	−10.8761	−0.465028	−0.232514	+	0.972593i	$0.574695\pi$
$548$	102.756	4.38952
$549$	−4.13667	−0.176549
$550$	−69.0406	−2.94390
$551$	7.40314	0.315384
$552$	54.7570	2.33061
$553$	54.2112	2.30529
$554$	43.0991	1.83111
$555$	−0.866703	−0.0367895
$556$	−9.51257	−0.403423
$557$	12.3233	0.522153	0.261077	−	0.965318i	$-0.415922\pi$
$557$	12.3233	0.522153	0.261077	+	0.965318i	$0.415922\pi$
$558$	−13.8108	−0.584657
$559$	26.3653	1.11514
$560$	10.5004	0.443722
$561$	−51.8430	−2.18882
$562$	−19.5088	−0.822927
$563$	−27.3809	−1.15397	−0.576983	−	0.816756i	$-0.695770\pi$
$563$	−27.3809	−1.15397	−0.576983	+	0.816756i	$0.695770\pi$
$564$	65.9340	2.77632
$565$	−5.24513	−0.220664
$566$	−2.28183	−0.0959125
$567$	−48.6226	−2.04196
$568$	−62.9341	−2.64066
$569$	33.0975	1.38752	0.693760	−	0.720206i	$-0.255953\pi$
$569$	33.0975	1.38752	0.693760	+	0.720206i	$0.255953\pi$
$570$	1.52690	0.0639549
$571$	15.8545	0.663489	0.331745	−	0.943369i	$-0.392363\pi$
$571$	15.8545	0.663489	0.331745	+	0.943369i	$0.392363\pi$
$572$	−82.7233	−3.45883
$573$	−19.9179	−0.832082
$574$	−31.3154	−1.30708
$575$	22.4218	0.935055
$576$	−0.164953	−0.00687305
$577$	−3.96527	−0.165076	−0.0825381	−	0.996588i	$-0.526303\pi$
$577$	−3.96527	−0.165076	−0.0825381	+	0.996588i	$0.526303\pi$
$578$	−18.9054	−0.786362
$579$	−32.4240	−1.34749
$580$	−10.4980	−0.435905
$581$	54.7119	2.26983
$582$	8.97219	0.371909
$583$	3.34929	0.138713
$584$	−5.98188	−0.247532
$585$	0.624432	0.0258171
$586$	77.0998	3.18496
$587$	12.9203	0.533279	0.266640	−	0.963796i	$-0.414087\pi$
$587$	12.9203	0.533279	0.266640	+	0.963796i	$0.414087\pi$
$588$	125.283	5.16659
$589$	−9.17278	−0.377958
$590$	−2.97796	−0.122601
$591$	27.7660	1.14214
$592$	−10.2779	−0.422419
$593$	32.6578	1.34109	0.670547	−	0.741867i	$-0.266059\pi$
$593$	32.6578	1.34109	0.670547	+	0.741867i	$0.266059\pi$
$594$	−64.3154	−2.63889
$595$	7.29608	0.299110
$596$	109.326	4.47818
$597$	27.4649	1.12406
$598$	38.8580	1.58902
$599$	−44.6873	−1.82587	−0.912937	−	0.408101i	$-0.866191\pi$
$599$	−44.6873	−1.82587	−0.912937	+	0.408101i	$0.866191\pi$
$600$	58.6313	2.39361
$601$	−32.2859	−1.31697	−0.658484	−	0.752595i	$-0.728802\pi$
$601$	−32.2859	−1.31697	−0.658484	+	0.752595i	$0.728802\pi$
$602$	−93.8478	−3.82495
$603$	−4.90772	−0.199858
$604$	−21.2847	−0.866064
$605$	6.21522	0.252685
$606$	−26.3267	−1.06945
$607$	−29.4296	−1.19451	−0.597255	−	0.802052i	$-0.703742\pi$
$607$	−29.4296	−1.19451	−0.597255	+	0.802052i	$0.703742\pi$
$608$	5.47871	0.222191
$609$	−65.4383	−2.65170
$610$	5.63520	0.228163
$611$	25.9031	1.04793
$612$	13.0967	0.529403
$613$	4.49454	0.181533	0.0907664	−	0.995872i	$-0.471068\pi$
$613$	4.49454	0.181533	0.0907664	+	0.995872i	$0.471068\pi$
$614$	62.5381	2.52383
$615$	1.58194	0.0637898
$616$	163.012	6.56795
$617$	−21.6954	−0.873422	−0.436711	−	0.899602i	$-0.643857\pi$
$617$	−21.6954	−0.873422	−0.436711	+	0.899602i	$0.643857\pi$
$618$	−62.7872	−2.52567
$619$	2.03464	0.0817791	0.0408895	−	0.999164i	$-0.486981\pi$
$619$	2.03464	0.0817791	0.0408895	+	0.999164i	$0.486981\pi$
$620$	13.0074	0.522390
$621$	20.8872	0.838176
$622$	−39.2803	−1.57500
$623$	−45.0734	−1.80583
$624$	44.9647	1.80003
$625$	23.5074	0.940297
$626$	−34.2160	−1.36754
$627$	10.4896	0.418915
$628$	−72.5095	−2.89345
$629$	−7.14150	−0.284750
$630$	−2.22268	−0.0885535
$631$	12.4420	0.495308	0.247654	−	0.968849i	$-0.420340\pi$
$631$	12.4420	0.495308	0.247654	+	0.968849i	$0.420340\pi$
$632$	−73.3874	−2.91919
$633$	6.86053	0.272682
$634$	−2.54565	−0.101101
$635$	6.04766	0.239994
$636$	−5.13778	−0.203726
$637$	49.2193	1.95014
$638$	−104.313	−4.12981
$639$	5.89509	0.233206
$640$	3.69276	0.145969
$641$	−18.5946	−0.734444	−0.367222	−	0.930133i	$-0.619691\pi$
$641$	−18.5946	−0.734444	−0.367222	+	0.930133i	$0.619691\pi$
$642$	−9.25874	−0.365413
$643$	−21.5171	−0.848552	−0.424276	−	0.905533i	$-0.639471\pi$
$643$	−21.5171	−0.848552	−0.424276	+	0.905533i	$0.639471\pi$
$644$	−95.6279	−3.76827
$645$	4.74084	0.186670
$646$	12.5814	0.495010
$647$	44.0666	1.73243	0.866217	−	0.499667i	$-0.166544\pi$
$647$	44.0666	1.73243	0.866217	+	0.499667i	$0.166544\pi$
$648$	65.8220	2.58573
$649$	−20.4582	−0.803055
$650$	41.6074	1.63198
$651$	81.0807	3.17780
$652$	105.853	4.14553
$653$	43.0317	1.68396	0.841981	−	0.539507i	$-0.181389\pi$
$653$	43.0317	1.68396	0.841981	+	0.539507i	$0.181389\pi$
$654$	−68.0993	−2.66289
$655$	5.82977	0.227788
$656$	18.7596	0.732439
$657$	0.560327	0.0218604
$658$	−92.2025	−3.59443
$659$	−33.2290	−1.29442	−0.647209	−	0.762313i	$-0.724064\pi$
$659$	−33.2290	−1.29442	−0.647209	+	0.762313i	$0.724064\pi$
$660$	−14.8747	−0.578998
$661$	−35.5010	−1.38083	−0.690415	−	0.723413i	$-0.742572\pi$
$661$	−35.5010	−1.38083	−0.690415	+	0.723413i	$0.742572\pi$
$662$	80.3252	3.12193
$663$	31.2433	1.21339
$664$	−74.0652	−2.87429
$665$	−1.47625	−0.0572463
$666$	2.17558	0.0843021
$667$	33.8771	1.31173
$668$	−73.0142	−2.82501
$669$	−11.5427	−0.446268
$670$	6.68557	0.258286
$671$	38.7130	1.49450
$672$	−48.4278	−1.86814
$673$	−15.6112	−0.601769	−0.300885	−	0.953661i	$-0.597282\pi$
$673$	−15.6112	−0.601769	−0.300885	+	0.953661i	$0.597282\pi$
$674$	−15.6863	−0.604214
$675$	22.3651	0.860834
$676$	−8.39140	−0.322746
$677$	2.01484	0.0774365	0.0387183	−	0.999250i	$-0.487673\pi$
$677$	2.01484	0.0774365	0.0387183	+	0.999250i	$0.487673\pi$
$678$	79.9491	3.07042
$679$	−8.67453	−0.332898
$680$	−9.87693	−0.378763
$681$	−3.15138	−0.120761
$682$	129.248	4.94918
$683$	−20.7050	−0.792254	−0.396127	−	0.918196i	$-0.629646\pi$
$683$	−20.7050	−0.792254	−0.396127	+	0.918196i	$0.629646\pi$
$684$	−2.64991	−0.101322
$685$	7.25891	0.277349
$686$	−92.0818	−3.51570
$687$	−27.1524	−1.03593
$688$	56.2198	2.14336
$689$	−2.01845	−0.0768968
$690$	6.98718	0.265997
$691$	−38.1194	−1.45013	−0.725066	−	0.688680i	$-0.758191\pi$
$691$	−38.1194	−1.45013	−0.725066	+	0.688680i	$0.758191\pi$
$692$	77.0421	2.92870
$693$	−15.2695	−0.580039
$694$	9.13197	0.346645
$695$	−0.671989	−0.0254900
$696$	88.5859	3.35784
$697$	13.0349	0.493732
$698$	32.5056	1.23035
$699$	−6.44759	−0.243870
$700$	−102.394	−3.87013
$701$	−25.3004	−0.955583	−0.477792	−	0.878473i	$-0.658563\pi$
$701$	−25.3004	−0.955583	−0.477792	+	0.878473i	$0.658563\pi$
$702$	38.7597	1.46289
$703$	1.44497	0.0544980
$704$	1.54372	0.0581810
$705$	4.65772	0.175420
$706$	45.2233	1.70200
$707$	25.4533	0.957268
$708$	31.3827	1.17943
$709$	0.917146	0.0344441	0.0172221	−	0.999852i	$-0.494518\pi$
$709$	0.917146	0.0344441	0.0172221	+	0.999852i	$0.494518\pi$
$710$	−8.03061	−0.301383
$711$	6.87425	0.257804
$712$	61.0173	2.28672
$713$	−41.9751	−1.57198
$714$	−111.211	−4.16196
$715$	−5.84375	−0.218544
$716$	73.0269	2.72914
$717$	48.4156	1.80811
$718$	45.6794	1.70474
$719$	44.0937	1.64442	0.822208	−	0.569186i	$-0.192742\pi$
$719$	44.0937	1.64442	0.822208	+	0.569186i	$0.192742\pi$
$720$	1.33150	0.0496221
$721$	60.7041	2.26074
$722$	−2.54565	−0.0947395
$723$	20.0483	0.745603
$724$	61.6991	2.29303
$725$	36.2741	1.34719
$726$	−94.7358	−3.51597
$727$	47.8820	1.77585	0.887923	−	0.459992i	$-0.152148\pi$
$727$	47.8820	1.77585	0.887923	+	0.459992i	$0.152148\pi$
$728$	−98.2395	−3.64100
$729$	19.7850	0.732777
$730$	−0.763309	−0.0282513
$731$	39.0638	1.44483
$732$	−59.3855	−2.19495
$733$	11.0573	0.408409	0.204205	−	0.978928i	$-0.434539\pi$
$733$	11.0573	0.408409	0.204205	+	0.978928i	$0.434539\pi$
$734$	−3.88796	−0.143507
$735$	8.85028	0.326447
$736$	25.0708	0.924123
$737$	45.9290	1.69182
$738$	−3.97095	−0.146173
$739$	16.8623	0.620291	0.310145	−	0.950689i	$-0.399622\pi$
$739$	16.8623	0.620291	0.310145	+	0.950689i	$0.399622\pi$
$740$	−2.04903	−0.0753238
$741$	−6.32158	−0.232229
$742$	7.18470	0.263759
$743$	−22.7239	−0.833660	−0.416830	−	0.908984i	$-0.636859\pi$
$743$	−22.7239	−0.833660	−0.416830	+	0.908984i	$0.636859\pi$
$744$	−109.761	−4.02405
$745$	7.72305	0.282951
$746$	19.3899	0.709914
$747$	6.93774	0.253839
$748$	−122.566	−4.48144
$749$	8.95157	0.327083
$750$	15.1161	0.551961
$751$	31.6105	1.15348	0.576741	−	0.816927i	$-0.304324\pi$
$751$	31.6105	1.15348	0.576741	+	0.816927i	$0.304324\pi$
$752$	55.2342	2.01418
$753$	−28.5556	−1.04062
$754$	62.8646	2.28939
$755$	−1.50360	−0.0547216
$756$	−95.3861	−3.46916
$757$	−36.2439	−1.31731	−0.658654	−	0.752446i	$-0.728874\pi$
$757$	−36.2439	−1.31731	−0.658654	+	0.752446i	$0.728874\pi$
$758$	−9.25622	−0.336201
$759$	48.0009	1.74232
$760$	1.99844	0.0724910
$761$	−29.6810	−1.07594	−0.537969	−	0.842965i	$-0.680808\pi$
$761$	−29.6810	−1.07594	−0.537969	+	0.842965i	$0.680808\pi$
$762$	−92.1817	−3.33939
$763$	65.8400	2.38357
$764$	−47.0892	−1.70363
$765$	0.925180	0.0334499
$766$	−13.3916	−0.483859
$767$	12.3292	0.445180
$768$	−55.2299	−1.99294
$769$	14.3250	0.516575	0.258287	−	0.966068i	$-0.416842\pi$
$769$	14.3250	0.516575	0.258287	+	0.966068i	$0.416842\pi$
$770$	20.8009	0.749613
$771$	−34.4594	−1.24102
$772$	−76.6557	−2.75890
$773$	−48.7533	−1.75353	−0.876767	−	0.480916i	$-0.840304\pi$
$773$	−48.7533	−1.75353	−0.876767	+	0.480916i	$0.840304\pi$
$774$	−11.9004	−0.427750
$775$	−44.9450	−1.61447
$776$	11.7430	0.421548
$777$	−12.7725	−0.458210
$778$	−10.5584	−0.378537
$779$	−2.63740	−0.0944948
$780$	8.96427	0.320973
$781$	−55.1692	−1.97411
$782$	57.5733	2.05882
$783$	33.7914	1.20761
$784$	104.952	3.74829
$785$	−5.12223	−0.182820
$786$	−88.8606	−3.16955
$787$	−20.1129	−0.716948	−0.358474	−	0.933540i	$-0.616703\pi$
$787$	−20.1129	−0.716948	−0.358474	+	0.933540i	$0.616703\pi$
$788$	65.6434	2.33845
$789$	−11.1553	−0.397139
$790$	−9.36448	−0.333173
$791$	−77.2966	−2.74835
$792$	20.6708	0.734504
$793$	−23.3304	−0.828488
$794$	16.4946	0.585370
$795$	−0.362944	−0.0128723
$796$	64.9315	2.30143
$797$	31.4974	1.11569	0.557847	−	0.829944i	$-0.311628\pi$
$797$	31.4974	1.11569	0.557847	+	0.829944i	$0.311628\pi$
$798$	22.5017	0.796553
$799$	38.3789	1.35775
$800$	26.8447	0.949104
$801$	−5.71553	−0.201948
$802$	91.5795	3.23378
$803$	−5.24383	−0.185051
$804$	−70.4547	−2.48474
$805$	−6.75537	−0.238095
$806$	−77.8917	−2.74362
$807$	17.6045	0.619708
$808$	−34.4569	−1.21219
$809$	19.9961	0.703026	0.351513	−	0.936183i	$-0.385667\pi$
$809$	19.9961	0.703026	0.351513	+	0.936183i	$0.385667\pi$
$810$	8.39911	0.295115
$811$	15.4908	0.543956	0.271978	−	0.962303i	$-0.412322\pi$
$811$	15.4908	0.543956	0.271978	+	0.962303i	$0.412322\pi$
$812$	−154.707	−5.42915
$813$	7.78486	0.273027
$814$	−20.3602	−0.713625
$815$	7.47769	0.261932
$816$	66.6212	2.33221
$817$	−7.90393	−0.276524
$818$	−0.440771	−0.0154112
$819$	9.20216	0.321550
$820$	3.73996	0.130605
$821$	27.6540	0.965132	0.482566	−	0.875860i	$-0.339705\pi$
$821$	27.6540	0.965132	0.482566	+	0.875860i	$0.339705\pi$
$822$	−110.644	−3.85916
$823$	43.0063	1.49911	0.749553	−	0.661944i	$-0.230268\pi$
$823$	43.0063	1.49911	0.749553	+	0.661944i	$0.230268\pi$
$824$	−82.1771	−2.86278
$825$	51.3973	1.78942
$826$	−43.8858	−1.52698
$827$	−44.5986	−1.55085	−0.775423	−	0.631442i	$-0.782463\pi$
$827$	−44.5986	−1.55085	−0.775423	+	0.631442i	$0.782463\pi$
$828$	−12.1261	−0.421411
$829$	51.1885	1.77785	0.888925	−	0.458052i	$-0.151453\pi$
$829$	51.1885	1.77785	0.888925	+	0.458052i	$0.151453\pi$
$830$	−9.45097	−0.328048
$831$	−32.0851	−1.11302
$832$	−0.930321	−0.0322531
$833$	72.9249	2.52670
$834$	10.2428	0.354680
$835$	−5.15789	−0.178496
$836$	24.7992	0.857698
$837$	−41.8689	−1.44720
$838$	75.9773	2.62459
$839$	37.7700	1.30396	0.651982	−	0.758234i	$-0.273938\pi$
$839$	37.7700	1.30396	0.651982	+	0.758234i	$0.273938\pi$
$840$	−17.6648	−0.609492
$841$	25.8065	0.889878
$842$	−54.1877	−1.86743
$843$	14.5233	0.500209
$844$	16.2194	0.558296
$845$	−0.592787	−0.0203925
$846$	−11.6917	−0.401970
$847$	91.5928	3.14716
$848$	−4.30402	−0.147801
$849$	1.69871	0.0582995
$850$	61.6469	2.11447
$851$	6.61224	0.226665
$852$	84.6291	2.89935
$853$	16.1477	0.552888	0.276444	−	0.961030i	$-0.410844\pi$
$853$	16.1477	0.552888	0.276444	+	0.961030i	$0.410844\pi$
$854$	83.0450	2.84174
$855$	−0.187195	−0.00640195
$856$	−12.1180	−0.414185
$857$	29.1814	0.996819	0.498409	−	0.866942i	$-0.333918\pi$
$857$	29.1814	0.996819	0.498409	+	0.866942i	$0.333918\pi$
$858$	89.0737	3.04093
$859$	2.05743	0.0701984	0.0350992	−	0.999384i	$-0.488825\pi$
$859$	2.05743	0.0701984	0.0350992	+	0.999384i	$0.488825\pi$
$860$	11.2081	0.382194
$861$	23.3127	0.794496
$862$	5.86267	0.199683
$863$	−3.07626	−0.104717	−0.0523586	−	0.998628i	$-0.516674\pi$
$863$	−3.07626	−0.104717	−0.0523586	+	0.998628i	$0.516674\pi$
$864$	25.0074	0.850769
$865$	5.44242	0.185048
$866$	−29.4273	−0.999981
$867$	14.0741	0.477983
$868$	191.688	6.50632
$869$	−64.3327	−2.18234
$870$	11.3039	0.383237
$871$	−27.6791	−0.937872
$872$	−89.1297	−3.01831
$873$	−1.09997	−0.0372285
$874$	−11.6490	−0.394034
$875$	−14.6146	−0.494063
$876$	8.04399	0.271781
$877$	16.4822	0.556565	0.278282	−	0.960499i	$-0.410235\pi$
$877$	16.4822	0.556565	0.278282	+	0.960499i	$0.410235\pi$
$878$	51.8470	1.74975
$879$	−57.3969	−1.93595
$880$	−12.4609	−0.420056
$881$	50.2810	1.69401	0.847005	−	0.531585i	$-0.178403\pi$
$881$	50.2810	1.69401	0.847005	+	0.531585i	$0.178403\pi$
$882$	−22.2158	−0.748046
$883$	−20.3725	−0.685588	−0.342794	−	0.939411i	$-0.611373\pi$
$883$	−20.3725	−0.685588	−0.342794	+	0.939411i	$0.611373\pi$
$884$	73.8642	2.48432
$885$	2.21694	0.0745218
$886$	10.7796	0.362148
$887$	−3.89311	−0.130718	−0.0653590	−	0.997862i	$-0.520819\pi$
$887$	−3.89311	−0.130718	−0.0653590	+	0.997862i	$0.520819\pi$
$888$	17.2905	0.580231
$889$	89.1234	2.98910
$890$	7.78601	0.260988
$891$	57.7007	1.93305
$892$	−27.2889	−0.913700
$893$	−7.76536	−0.259858
$894$	−117.719	−3.93711
$895$	5.15878	0.172439
$896$	54.4196	1.81803
$897$	−28.9278	−0.965872
$898$	53.1528	1.77373
$899$	−67.9074	−2.26484
$900$	−12.9841	−0.432803
$901$	−2.99060	−0.0996314
$902$	37.1622	1.23736
$903$	69.8650	2.32496
$904$	104.639	3.48024
$905$	4.35856	0.144883
$906$	22.9187	0.761423
$907$	−14.2907	−0.474515	−0.237258	−	0.971447i	$-0.576249\pi$
$907$	−14.2907	−0.474515	−0.237258	+	0.971447i	$0.576249\pi$
$908$	−7.45038	−0.247249
$909$	3.22760	0.107053
$910$	−12.5357	−0.415554
$911$	−48.5421	−1.60827	−0.804135	−	0.594447i	$-0.797371\pi$
$911$	−48.5421	−1.60827	−0.804135	+	0.594447i	$0.797371\pi$
$912$	−13.4797	−0.446359
$913$	−64.9269	−2.14877
$914$	37.4309	1.23810
$915$	−4.19512	−0.138686
$916$	−64.1928	−2.12099
$917$	85.9125	2.83708
$918$	57.4277	1.89540
$919$	32.7326	1.07975	0.539874	−	0.841746i	$-0.318472\pi$
$919$	32.7326	1.07975	0.539874	+	0.841746i	$0.318472\pi$
$920$	9.14495	0.301500
$921$	−46.5565	−1.53409
$922$	−10.0187	−0.329950
$923$	33.2478	1.09436
$924$	−219.207	−7.21137
$925$	7.08009	0.232792
$926$	30.9187	1.01605
$927$	7.69759	0.252822
$928$	40.5596	1.33144
$929$	−36.6497	−1.20244	−0.601219	−	0.799085i	$-0.705318\pi$
$929$	−36.6497	−1.20244	−0.601219	+	0.799085i	$0.705318\pi$
$930$	−14.0059	−0.459273
$931$	−14.7552	−0.483582
$932$	−15.2432	−0.499306
$933$	29.2422	0.957348
$934$	6.33309	0.207225
$935$	−8.65830	−0.283157
$936$	−12.4573	−0.407178
$937$	−49.4702	−1.61612	−0.808061	−	0.589099i	$-0.799483\pi$
$937$	−49.4702	−1.61612	−0.808061	+	0.589099i	$0.799483\pi$
$938$	98.5243	3.21693
$939$	25.4721	0.831249
$940$	11.0116	0.359160
$941$	−27.0221	−0.880894	−0.440447	−	0.897779i	$-0.645180\pi$
$941$	−27.0221	−0.880894	−0.440447	+	0.897779i	$0.645180\pi$
$942$	78.0759	2.54385
$943$	−12.0689	−0.393017
$944$	26.2899	0.855664
$945$	−6.73828	−0.219196
$946$	111.370	3.62094
$947$	8.37251	0.272070	0.136035	−	0.990704i	$-0.456564\pi$
$947$	8.37251	0.272070	0.136035	+	0.990704i	$0.456564\pi$
$948$	98.6859	3.20517
$949$	3.16020	0.102584
$950$	−12.4733	−0.404686
$951$	1.89511	0.0614532
$952$	−145.555	−4.71746
$953$	−22.7311	−0.736333	−0.368167	−	0.929760i	$-0.620014\pi$
$953$	−22.7311	−0.736333	−0.368167	+	0.929760i	$0.620014\pi$
$954$	0.911056	0.0294965
$955$	−3.32648	−0.107643
$956$	114.463	3.70198
$957$	77.6561	2.51026
$958$	−10.9098	−0.352479
$959$	106.973	3.45435
$960$	−0.167284	−0.00539907
$961$	53.1399	1.71419
$962$	12.2701	0.395604
$963$	1.13510	0.0365782
$964$	47.3974	1.52657
$965$	−5.41513	−0.174319
$966$	102.969	3.31297
$967$	47.9446	1.54180	0.770898	−	0.636959i	$-0.219808\pi$
$967$	47.9446	1.54180	0.770898	+	0.636959i	$0.219808\pi$
$968$	−123.992	−3.98525
$969$	−9.36625	−0.300887
$970$	1.49844	0.0481122
$971$	59.7327	1.91691	0.958456	−	0.285240i	$-0.0920734\pi$
$971$	59.7327	1.91691	0.958456	+	0.285240i	$0.0920734\pi$
$972$	−27.1611	−0.871191
$973$	−9.90300	−0.317476
$974$	12.5571	0.402356
$975$	−30.9746	−0.991982
$976$	−49.7484	−1.59241
$977$	−38.8945	−1.24435	−0.622173	−	0.782880i	$-0.713750\pi$
$977$	−38.8945	−1.24435	−0.622173	+	0.782880i	$0.713750\pi$
$978$	−113.979	−3.64465
$979$	53.4888	1.70951
$980$	20.9235	0.668378
$981$	8.34884	0.266558
$982$	4.59742	0.146710
$983$	23.0924	0.736532	0.368266	−	0.929720i	$-0.379952\pi$
$983$	23.0924	0.736532	0.368266	+	0.929720i	$0.379952\pi$
$984$	−31.5592	−1.00607
$985$	4.63720	0.147753
$986$	93.1422	2.96625
$987$	68.6401	2.18484
$988$	−14.9453	−0.475472
$989$	−36.1687	−1.15010
$990$	2.63766	0.0838304
$991$	−15.3479	−0.487544	−0.243772	−	0.969833i	$-0.578385\pi$
$991$	−15.3479	−0.487544	−0.243772	+	0.969833i	$0.578385\pi$
$992$	−50.2550	−1.59560
$993$	−59.7981	−1.89763
$994$	−118.346	−3.75370
$995$	4.58690	0.145415
$996$	99.5973	3.15586
$997$	−8.20030	−0.259706	−0.129853	−	0.991533i	$-0.541451\pi$
$997$	−8.20030	−0.259706	−0.129853	+	0.991533i	$0.541451\pi$
$998$	93.9056	2.97253
$999$	6.59552	0.208673

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.d.1.11	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.d.1.11	✓	140	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)

\(f(q)\)	\(=\)	\(q-2.54565 q^{2} +1.89511 q^{3} +4.48036 q^{4} +0.316502 q^{5} -4.82430 q^{6} +4.66425 q^{7} -6.31414 q^{8} +0.591450 q^{9} +O(q^{10})\)	\(q-2.54565 q^{2} +1.89511 q^{3} +4.48036 q^{4} +0.316502 q^{5} -4.82430 q^{6} +4.66425 q^{7} -6.31414 q^{8} +0.591450 q^{9} -0.805706 q^{10} -5.53509 q^{11} +8.49078 q^{12} +3.33573 q^{13} -11.8736 q^{14} +0.599808 q^{15} +7.11290 q^{16} +4.94232 q^{17} -1.50563 q^{18} -1.00000 q^{19} +1.41804 q^{20} +8.83927 q^{21} +14.0904 q^{22} -4.57605 q^{23} -11.9660 q^{24} -4.89983 q^{25} -8.49161 q^{26} -4.56447 q^{27} +20.8975 q^{28} -7.40314 q^{29} -1.52690 q^{30} +9.17278 q^{31} -5.47871 q^{32} -10.4896 q^{33} -12.5814 q^{34} +1.47625 q^{35} +2.64991 q^{36} -1.44497 q^{37} +2.54565 q^{38} +6.32158 q^{39} -1.99844 q^{40} +2.63740 q^{41} -22.5017 q^{42} +7.90393 q^{43} -24.7992 q^{44} +0.187195 q^{45} +11.6490 q^{46} +7.76536 q^{47} +13.4797 q^{48} +14.7552 q^{49} +12.4733 q^{50} +9.36625 q^{51} +14.9453 q^{52} -0.605101 q^{53} +11.6196 q^{54} -1.75187 q^{55} -29.4507 q^{56} -1.89511 q^{57} +18.8458 q^{58} +3.69609 q^{59} +2.68735 q^{60} -6.99411 q^{61} -23.3507 q^{62} +2.75867 q^{63} -0.278896 q^{64} +1.05577 q^{65} +26.7029 q^{66} -8.29778 q^{67} +22.1434 q^{68} -8.67212 q^{69} -3.75801 q^{70} +9.96718 q^{71} -3.73450 q^{72} +0.947379 q^{73} +3.67839 q^{74} -9.28572 q^{75} -4.48036 q^{76} -25.8170 q^{77} -16.0925 q^{78} +11.6227 q^{79} +2.25125 q^{80} -10.4245 q^{81} -6.71392 q^{82} +11.7301 q^{83} +39.6031 q^{84} +1.56426 q^{85} -20.1207 q^{86} -14.0298 q^{87} +34.9493 q^{88} -9.66359 q^{89} -0.476535 q^{90} +15.5587 q^{91} -20.5023 q^{92} +17.3834 q^{93} -19.7679 q^{94} -0.316502 q^{95} -10.3828 q^{96} -1.85979 q^{97} -37.5616 q^{98} -3.27373 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9}+O(q^{10}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9} + 8 q^{10} + 19 q^{11} + 17 q^{12} + 28 q^{13} + 5 q^{14} + 14 q^{15} + 202 q^{16} + 38 q^{17} + 26 q^{18} - 140 q^{19} + 36 q^{20} + 4 q^{21} + 53 q^{22} + 58 q^{23} + 47 q^{24} + 279 q^{25} + 29 q^{26} + 21 q^{27} + 69 q^{28} + 18 q^{29} + 50 q^{30} + 20 q^{31} + 13 q^{32} + 47 q^{33} + 6 q^{34} + 35 q^{35} + 230 q^{36} + 88 q^{37} - 4 q^{38} + 32 q^{39} + 32 q^{40} + 24 q^{41} + 75 q^{42} + 100 q^{43} + 63 q^{44} + 87 q^{45} + 23 q^{46} + 35 q^{47} + 46 q^{48} + 255 q^{49} + 11 q^{50} - 6 q^{51} + 47 q^{52} + 77 q^{53} + 16 q^{54} + 63 q^{55} + 21 q^{56} - 3 q^{57} + 165 q^{58} + 18 q^{59} + 28 q^{60} + 99 q^{61} + 34 q^{62} + 89 q^{63} + 298 q^{64} + 78 q^{65} - 3 q^{66} + 28 q^{67} + 93 q^{68} + 19 q^{69} + 16 q^{70} + q^{71} + 43 q^{72} + 201 q^{73} + 32 q^{74} + 22 q^{75} - 162 q^{76} + 86 q^{77} + 122 q^{78} + 58 q^{79} + 92 q^{80} + 288 q^{81} + 143 q^{82} + 57 q^{83} + q^{84} + 136 q^{85} - 6 q^{86} + 43 q^{87} + 198 q^{88} + 46 q^{89} + 30 q^{90} + 26 q^{91} + 129 q^{92} + 111 q^{93} + 44 q^{94} - 13 q^{95} + 32 q^{96} + 110 q^{97} - 34 q^{98} + 62 q^{99}+O(q^{100}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9 + 8 * q^10 + 19 * q^11 + 17 * q^12 + 28 * q^13 + 5 * q^14 + 14 * q^15 + 202 * q^16 + 38 * q^17 + 26 * q^18 - 140 * q^19 + 36 * q^20 + 4 * q^21 + 53 * q^22 + 58 * q^23 + 47 * q^24 + 279 * q^25 + 29 * q^26 + 21 * q^27 + 69 * q^28 + 18 * q^29 + 50 * q^30 + 20 * q^31 + 13 * q^32 + 47 * q^33 + 6 * q^34 + 35 * q^35 + 230 * q^36 + 88 * q^37 - 4 * q^38 + 32 * q^39 + 32 * q^40 + 24 * q^41 + 75 * q^42 + 100 * q^43 + 63 * q^44 + 87 * q^45 + 23 * q^46 + 35 * q^47 + 46 * q^48 + 255 * q^49 + 11 * q^50 - 6 * q^51 + 47 * q^52 + 77 * q^53 + 16 * q^54 + 63 * q^55 + 21 * q^56 - 3 * q^57 + 165 * q^58 + 18 * q^59 + 28 * q^60 + 99 * q^61 + 34 * q^62 + 89 * q^63 + 298 * q^64 + 78 * q^65 - 3 * q^66 + 28 * q^67 + 93 * q^68 + 19 * q^69 + 16 * q^70 + q^71 + 43 * q^72 + 201 * q^73 + 32 * q^74 + 22 * q^75 - 162 * q^76 + 86 * q^77 + 122 * q^78 + 58 * q^79 + 92 * q^80 + 288 * q^81 + 143 * q^82 + 57 * q^83 + q^84 + 136 * q^85 - 6 * q^86 + 43 * q^87 + 198 * q^88 + 46 * q^89 + 30 * q^90 + 26 * q^91 + 129 * q^92 + 111 * q^93 + 44 * q^94 - 13 * q^95 + 32 * q^96 + 110 * q^97 - 34 * q^98 + 62 * q^99

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