LMFDB - Embedded newform 6023.2.a.d.1.1

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			1.1
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)

$f(q)$	$=$	$q-2.81146 q^{2} +3.38830 q^{3} +5.90432 q^{4} +1.31579 q^{5} -9.52607 q^{6} +1.88433 q^{7} -10.9768 q^{8} +8.48057 q^{9} +O(q^{10})$	\(q-2.81146 q^{2} +3.38830 q^{3} +5.90432 q^{4} +1.31579 q^{5} -9.52607 q^{6} +1.88433 q^{7} -10.9768 q^{8} +8.48057 q^{9} -3.69930 q^{10} +0.400278 q^{11} +20.0056 q^{12} -5.35705 q^{13} -5.29773 q^{14} +4.45830 q^{15} +19.0523 q^{16} +2.10954 q^{17} -23.8428 q^{18} -1.00000 q^{19} +7.76885 q^{20} +6.38468 q^{21} -1.12537 q^{22} +3.51121 q^{23} -37.1928 q^{24} -3.26869 q^{25} +15.0611 q^{26} +18.5698 q^{27} +11.1257 q^{28} -3.94230 q^{29} -12.5343 q^{30} +3.72300 q^{31} -31.6112 q^{32} +1.35626 q^{33} -5.93090 q^{34} +2.47939 q^{35} +50.0720 q^{36} +7.99304 q^{37} +2.81146 q^{38} -18.1513 q^{39} -14.4432 q^{40} -2.66869 q^{41} -17.9503 q^{42} +8.32013 q^{43} +2.36337 q^{44} +11.1587 q^{45} -9.87163 q^{46} +6.10548 q^{47} +64.5550 q^{48} -3.44929 q^{49} +9.18980 q^{50} +7.14776 q^{51} -31.6297 q^{52} -2.04955 q^{53} -52.2083 q^{54} +0.526682 q^{55} -20.6840 q^{56} -3.38830 q^{57} +11.0836 q^{58} +6.58746 q^{59} +26.3232 q^{60} +12.7730 q^{61} -10.4671 q^{62} +15.9802 q^{63} +50.7691 q^{64} -7.04876 q^{65} -3.81307 q^{66} -5.15589 q^{67} +12.4554 q^{68} +11.8970 q^{69} -6.97071 q^{70} -13.1268 q^{71} -93.0898 q^{72} +3.50516 q^{73} -22.4721 q^{74} -11.0753 q^{75} -5.90432 q^{76} +0.754256 q^{77} +51.0316 q^{78} +9.99320 q^{79} +25.0689 q^{80} +37.4783 q^{81} +7.50292 q^{82} -5.88994 q^{83} +37.6972 q^{84} +2.77572 q^{85} -23.3917 q^{86} -13.3577 q^{87} -4.39378 q^{88} +5.49575 q^{89} -31.3722 q^{90} -10.0945 q^{91} +20.7313 q^{92} +12.6146 q^{93} -17.1653 q^{94} -1.31579 q^{95} -107.108 q^{96} +2.06789 q^{97} +9.69755 q^{98} +3.39458 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.81146	−1.98800	−0.994002	−	0.109363i	$-0.965119\pi$
$2$	−2.81146	−1.98800	−0.994002	+	0.109363i	$0.965119\pi$
$3$	3.38830	1.95624	0.978118	−	0.208053i	$-0.0667126\pi$
$3$	3.38830	1.95624	0.978118	+	0.208053i	$0.0667126\pi$
$4$	5.90432	2.95216
$5$	1.31579	0.588440	0.294220	−	0.955738i	$-0.404940\pi$
$5$	1.31579	0.588440	0.294220	+	0.955738i	$0.404940\pi$
$6$	−9.52607	−3.88900
$7$	1.88433	0.712211	0.356105	−	0.934446i	$-0.384104\pi$
$7$	1.88433	0.712211	0.356105	+	0.934446i	$0.384104\pi$
$8$	−10.9768	−3.88090
$9$	8.48057	2.82686
$10$	−3.69930	−1.16982
$11$	0.400278	0.120688	0.0603441	−	0.998178i	$-0.480780\pi$
$11$	0.400278	0.120688	0.0603441	+	0.998178i	$0.480780\pi$
$12$	20.0056	5.77512
$13$	−5.35705	−1.48578	−0.742889	−	0.669415i	$-0.766545\pi$
$13$	−5.35705	−1.48578	−0.742889	+	0.669415i	$0.766545\pi$
$14$	−5.29773	−1.41588
$15$	4.45830	1.15113
$16$	19.0523	4.76308
$17$	2.10954	0.511639	0.255820	−	0.966725i	$-0.417655\pi$
$17$	2.10954	0.511639	0.255820	+	0.966725i	$0.417655\pi$
$18$	−23.8428	−5.61980
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	7.76885	1.73717
$21$	6.38468	1.39325
$22$	−1.12537	−0.239929
$23$	3.51121	0.732138	0.366069	−	0.930588i	$-0.380703\pi$
$23$	3.51121	0.732138	0.366069	+	0.930588i	$0.380703\pi$
$24$	−37.1928	−7.59195
$25$	−3.26869	−0.653738
$26$	15.0611	2.95373
$27$	18.5698	3.57376
$28$	11.1257	2.10256
$29$	−3.94230	−0.732067	−0.366034	−	0.930602i	$-0.619284\pi$
$29$	−3.94230	−0.732067	−0.366034	+	0.930602i	$0.619284\pi$
$30$	−12.5343	−2.28845
$31$	3.72300	0.668670	0.334335	−	0.942454i	$-0.391488\pi$
$31$	3.72300	0.668670	0.334335	+	0.942454i	$0.391488\pi$
$32$	−31.6112	−5.58813
$33$	1.35626	0.236095
$34$	−5.93090	−1.01714
$35$	2.47939	0.419093
$36$	50.0720	8.34533
$37$	7.99304	1.31405	0.657024	−	0.753870i	$-0.271815\pi$
$37$	7.99304	1.31405	0.657024	+	0.753870i	$0.271815\pi$
$38$	2.81146	0.456079
$39$	−18.1513	−2.90653
$40$	−14.4432	−2.28368
$41$	−2.66869	−0.416779	−0.208390	−	0.978046i	$-0.566822\pi$
$41$	−2.66869	−0.416779	−0.208390	+	0.978046i	$0.566822\pi$
$42$	−17.9503	−2.76979
$43$	8.32013	1.26881	0.634404	−	0.773002i	$-0.281246\pi$
$43$	8.32013	1.26881	0.634404	+	0.773002i	$0.281246\pi$
$44$	2.36337	0.356291
$45$	11.1587	1.66344
$46$	−9.87163	−1.45549
$47$	6.10548	0.890576	0.445288	−	0.895387i	$-0.353101\pi$
$47$	6.10548	0.890576	0.445288	+	0.895387i	$0.353101\pi$
$48$	64.5550	9.31771
$49$	−3.44929	−0.492756
$50$	9.18980	1.29963
$51$	7.14776	1.00089
$52$	−31.6297	−4.38625
$53$	−2.04955	−0.281528	−0.140764	−	0.990043i	$-0.544956\pi$
$53$	−2.04955	−0.281528	−0.140764	+	0.990043i	$0.544956\pi$
$54$	−52.2083	−7.10465
$55$	0.526682	0.0710178
$56$	−20.6840	−2.76402
$57$	−3.38830	−0.448791
$58$	11.0836	1.45535
$59$	6.58746	0.857614	0.428807	−	0.903396i	$-0.358934\pi$
$59$	6.58746	0.857614	0.428807	+	0.903396i	$0.358934\pi$
$60$	26.3232	3.39831
$61$	12.7730	1.63541	0.817707	−	0.575635i	$-0.195245\pi$
$61$	12.7730	1.63541	0.817707	+	0.575635i	$0.195245\pi$
$62$	−10.4671	−1.32932
$63$	15.9802	2.01332
$64$	50.7691	6.34613
$65$	−7.04876	−0.874291
$66$	−3.81307	−0.469357
$67$	−5.15589	−0.629893	−0.314946	−	0.949109i	$-0.601987\pi$
$67$	−5.15589	−0.629893	−0.314946	+	0.949109i	$0.601987\pi$
$68$	12.4554	1.51044
$69$	11.8970	1.43223
$70$	−6.97071	−0.833159
$71$	−13.1268	−1.55786	−0.778932	−	0.627109i	$-0.784238\pi$
$71$	−13.1268	−1.55786	−0.778932	+	0.627109i	$0.784238\pi$
$72$	−93.0898	−10.9707
$73$	3.50516	0.410247	0.205124	−	0.978736i	$-0.434240\pi$
$73$	3.50516	0.410247	0.205124	+	0.978736i	$0.434240\pi$
$74$	−22.4721	−2.61233
$75$	−11.0753	−1.27887
$76$	−5.90432	−0.677272
$77$	0.754256	0.0859555
$78$	51.0316	5.77819
$79$	9.99320	1.12432	0.562161	−	0.827028i	$-0.309970\pi$
$79$	9.99320	1.12432	0.562161	+	0.827028i	$0.309970\pi$
$80$	25.0689	2.80279
$81$	37.4783	4.16426
$82$	7.50292	0.828559
$83$	−5.88994	−0.646505	−0.323253	−	0.946313i	$-0.604776\pi$
$83$	−5.88994	−0.646505	−0.323253	+	0.946313i	$0.604776\pi$
$84$	37.6972	4.11310
$85$	2.77572	0.301069
$86$	−23.3917	−2.52239
$87$	−13.3577	−1.43210
$88$	−4.39378	−0.468379
$89$	5.49575	0.582549	0.291274	−	0.956640i	$-0.405921\pi$
$89$	5.49575	0.582549	0.291274	+	0.956640i	$0.405921\pi$
$90$	−31.3722	−3.30692
$91$	−10.0945	−1.05819
$92$	20.7313	2.16139
$93$	12.6146	1.30808
$94$	−17.1653	−1.77047
$95$	−1.31579	−0.134997
$96$	−107.108	−10.9317
$97$	2.06789	0.209963	0.104981	−	0.994474i	$-0.466522\pi$
$97$	2.06789	0.209963	0.104981	+	0.994474i	$0.466522\pi$
$98$	9.69755	0.979601
$99$	3.39458	0.341168
$100$	−19.2994	−1.92994
$101$	−14.6773	−1.46045	−0.730223	−	0.683209i	$-0.760584\pi$
$101$	−14.6773	−1.46045	−0.730223	+	0.683209i	$0.760584\pi$
$102$	−20.0957	−1.98977
$103$	−5.94785	−0.586059	−0.293030	−	0.956103i	$-0.594663\pi$
$103$	−5.94785	−0.586059	−0.293030	+	0.956103i	$0.594663\pi$
$104$	58.8035	5.76615
$105$	8.40091	0.819845
$106$	5.76224	0.559678
$107$	0.477834	0.0461939	0.0230970	−	0.999733i	$-0.492647\pi$
$107$	0.477834	0.0461939	0.0230970	+	0.999733i	$0.492647\pi$
$108$	109.642	10.5503
$109$	0.384158	0.0367957	0.0183979	−	0.999831i	$-0.494143\pi$
$109$	0.384158	0.0367957	0.0183979	+	0.999831i	$0.494143\pi$
$110$	−1.48075	−0.141184
$111$	27.0828	2.57059
$112$	35.9009	3.39232
$113$	8.06644	0.758827	0.379414	−	0.925227i	$-0.376126\pi$
$113$	8.06644	0.758827	0.379414	+	0.925227i	$0.376126\pi$
$114$	9.52607	0.892198
$115$	4.62002	0.430819
$116$	−23.2766	−2.16118
$117$	−45.4308	−4.20008
$118$	−18.5204	−1.70494
$119$	3.97508	0.364395
$120$	−48.9380	−4.46741
$121$	−10.8398	−0.985434
$122$	−35.9108	−3.25121
$123$	−9.04232	−0.815318
$124$	21.9818	1.97402
$125$	−10.8799	−0.973126
$126$	−44.9277	−4.00248
$127$	−4.96790	−0.440830	−0.220415	−	0.975406i	$-0.570741\pi$
$127$	−4.96790	−0.440830	−0.220415	+	0.975406i	$0.570741\pi$
$128$	−79.5129	−7.02801
$129$	28.1911	2.48209
$130$	19.8173	1.73809
$131$	20.7595	1.81376	0.906882	−	0.421384i	$-0.138456\pi$
$131$	20.7595	1.81376	0.906882	+	0.421384i	$0.138456\pi$
$132$	8.00779	0.696989
$133$	−1.88433	−0.163392
$134$	14.4956	1.25223
$135$	24.4340	2.10294
$136$	−23.1561	−1.98562
$137$	−23.0789	−1.97176	−0.985881	−	0.167450i	$-0.946447\pi$
$137$	−23.0789	−1.97176	−0.985881	+	0.167450i	$0.946447\pi$
$138$	−33.4480	−2.84729
$139$	−2.66982	−0.226451	−0.113226	−	0.993569i	$-0.536118\pi$
$139$	−2.66982	−0.226451	−0.113226	+	0.993569i	$0.536118\pi$
$140$	14.6391	1.23723
$141$	20.6872	1.74218
$142$	36.9055	3.09704
$143$	−2.14431	−0.179316
$144$	161.575	13.4645
$145$	−5.18725	−0.430778
$146$	−9.85461	−0.815573
$147$	−11.6872	−0.963947
$148$	47.1934	3.87928
$149$	−23.8812	−1.95642	−0.978211	−	0.207612i	$-0.933431\pi$
$149$	−23.8812	−1.95642	−0.978211	+	0.207612i	$0.933431\pi$
$150$	31.1378	2.54239
$151$	11.8828	0.967008	0.483504	−	0.875342i	$-0.339364\pi$
$151$	11.8828	0.967008	0.483504	+	0.875342i	$0.339364\pi$
$152$	10.9768	0.890339
$153$	17.8901	1.44633
$154$	−2.12056	−0.170880
$155$	4.89869	0.393472
$156$	−107.171	−8.58054
$157$	22.4863	1.79460	0.897301	−	0.441418i	$-0.145525\pi$
$157$	22.4863	1.79460	0.897301	+	0.441418i	$0.145525\pi$
$158$	−28.0955	−2.23516
$159$	−6.94450	−0.550734
$160$	−41.5938	−3.28828
$161$	6.61629	0.521436
$162$	−105.369	−8.27856
$163$	4.15658	0.325569	0.162784	−	0.986662i	$-0.447953\pi$
$163$	4.15658	0.325569	0.162784	+	0.986662i	$0.447953\pi$
$164$	−15.7568	−1.23040
$165$	1.78456	0.138928
$166$	16.5593	1.28525
$167$	6.22125	0.481415	0.240708	−	0.970598i	$-0.422621\pi$
$167$	6.22125	0.481415	0.240708	+	0.970598i	$0.422621\pi$
$168$	−70.0836	−5.40707
$169$	15.6980	1.20754
$170$	−7.80383	−0.598527
$171$	−8.48057	−0.648525
$172$	49.1247	3.74572
$173$	−1.11410	−0.0847037	−0.0423518	−	0.999103i	$-0.513485\pi$
$173$	−1.11410	−0.0847037	−0.0423518	+	0.999103i	$0.513485\pi$
$174$	37.5546	2.84701
$175$	−6.15930	−0.465599
$176$	7.62622	0.574848
$177$	22.3203	1.67770
$178$	−15.4511	−1.15811
$179$	14.2964	1.06857	0.534283	−	0.845305i	$-0.320582\pi$
$179$	14.2964	1.06857	0.534283	+	0.845305i	$0.320582\pi$
$180$	65.8843	4.91072
$181$	−24.2420	−1.80189	−0.900946	−	0.433932i	$-0.857126\pi$
$181$	−24.2420	−1.80189	−0.900946	+	0.433932i	$0.857126\pi$
$182$	28.3802	2.10368
$183$	43.2787	3.19925
$184$	−38.5420	−2.84135
$185$	10.5172	0.773238
$186$	−35.4655	−2.60046
$187$	0.844403	0.0617489
$188$	36.0487	2.62912
$189$	34.9917	2.54527
$190$	3.69930	0.268375
$191$	−13.3016	−0.962473	−0.481237	−	0.876591i	$-0.659812\pi$
$191$	−13.3016	−0.962473	−0.481237	+	0.876591i	$0.659812\pi$
$192$	172.021	12.4145
$193$	23.5712	1.69669	0.848347	−	0.529441i	$-0.177598\pi$
$193$	23.5712	1.69669	0.848347	+	0.529441i	$0.177598\pi$
$194$	−5.81380	−0.417407
$195$	−23.8833	−1.71032
$196$	−20.3657	−1.45469
$197$	8.65217	0.616442	0.308221	−	0.951315i	$-0.400266\pi$
$197$	8.65217	0.616442	0.308221	+	0.951315i	$0.400266\pi$
$198$	−9.54374	−0.678244
$199$	14.0719	0.997532	0.498766	−	0.866737i	$-0.333787\pi$
$199$	14.0719	0.997532	0.498766	+	0.866737i	$0.333787\pi$
$200$	35.8799	2.53709
$201$	−17.4697	−1.23222
$202$	41.2647	2.90337
$203$	−7.42861	−0.521386
$204$	42.2027	2.95478
$205$	−3.51144	−0.245250
$206$	16.7222	1.16509
$207$	29.7771	2.06965
$208$	−102.064	−7.07688
$209$	−0.400278	−0.0276878
$210$	−23.6188	−1.62985
$211$	12.9877	0.894107	0.447054	−	0.894507i	$-0.352473\pi$
$211$	12.9877	0.894107	0.447054	+	0.894507i	$0.352473\pi$
$212$	−12.1012	−0.831115
$213$	−44.4775	−3.04755
$214$	−1.34341	−0.0918337
$215$	10.9476	0.746617
$216$	−203.838	−13.8694
$217$	7.01536	0.476234
$218$	−1.08005	−0.0731500
$219$	11.8765	0.802540
$220$	3.10970	0.209656
$221$	−11.3009	−0.760182
$222$	−76.1423	−5.11033
$223$	10.1632	0.680577	0.340289	−	0.940321i	$-0.389475\pi$
$223$	10.1632	0.680577	0.340289	+	0.940321i	$0.389475\pi$
$224$	−59.5660	−3.97992
$225$	−27.7204	−1.84802
$226$	−22.6785	−1.50855
$227$	2.34043	0.155340	0.0776700	−	0.996979i	$-0.475252\pi$
$227$	2.34043	0.155340	0.0776700	+	0.996979i	$0.475252\pi$
$228$	−20.0056	−1.32490
$229$	22.4782	1.48540	0.742702	−	0.669622i	$-0.233544\pi$
$229$	22.4782	1.48540	0.742702	+	0.669622i	$0.233544\pi$
$230$	−12.9890	−0.856470
$231$	2.55565	0.168149
$232$	43.2740	2.84108
$233$	11.7575	0.770261	0.385130	−	0.922862i	$-0.374156\pi$
$233$	11.7575	0.770261	0.385130	+	0.922862i	$0.374156\pi$
$234$	127.727	8.34977
$235$	8.03354	0.524051
$236$	38.8945	2.53181
$237$	33.8599	2.19944
$238$	−11.1758	−0.724419
$239$	10.6751	0.690516	0.345258	−	0.938508i	$-0.387791\pi$
$239$	10.6751	0.690516	0.345258	+	0.938508i	$0.387791\pi$
$240$	84.9409	5.48291
$241$	3.01363	0.194125	0.0970624	−	0.995278i	$-0.469055\pi$
$241$	3.01363	0.194125	0.0970624	+	0.995278i	$0.469055\pi$
$242$	30.4756	1.95905
$243$	71.2784	4.57251
$244$	75.4158	4.82800
$245$	−4.53855	−0.289957
$246$	25.4221	1.62086
$247$	5.35705	0.340861
$248$	−40.8667	−2.59504
$249$	−19.9569	−1.26472
$250$	30.5884	1.93458
$251$	1.29768	0.0819086	0.0409543	−	0.999161i	$-0.486960\pi$
$251$	1.29768	0.0819086	0.0409543	+	0.999161i	$0.486960\pi$
$252$	94.3522	5.94363
$253$	1.40546	0.0883605
$254$	13.9671	0.876371
$255$	9.40497	0.588962
$256$	122.009	7.62558
$257$	−26.9733	−1.68255	−0.841273	−	0.540610i	$-0.818193\pi$
$257$	−26.9733	−1.68255	−0.841273	+	0.540610i	$0.818193\pi$
$258$	−79.2582	−4.93440
$259$	15.0615	0.935879
$260$	−41.6181	−2.58105
$261$	−33.4330	−2.06945
$262$	−58.3645	−3.60577
$263$	22.1100	1.36336	0.681680	−	0.731650i	$-0.261250\pi$
$263$	22.1100	1.36336	0.681680	+	0.731650i	$0.261250\pi$
$264$	−14.8875	−0.916260
$265$	−2.69679	−0.165662
$266$	5.29773	0.324825
$267$	18.6213	1.13960
$268$	−30.4420	−1.85954
$269$	−16.8452	−1.02707	−0.513534	−	0.858069i	$-0.671664\pi$
$269$	−16.8452	−1.02707	−0.513534	+	0.858069i	$0.671664\pi$
$270$	−68.6952	−4.18066
$271$	−20.1733	−1.22544	−0.612720	−	0.790300i	$-0.709925\pi$
$271$	−20.1733	−1.22544	−0.612720	+	0.790300i	$0.709925\pi$
$272$	40.1917	2.43698
$273$	−34.2030	−2.07006
$274$	64.8854	3.91987
$275$	−1.30838	−0.0788986
$276$	70.2438	4.22818
$277$	−10.1192	−0.608003	−0.304001	−	0.952672i	$-0.598323\pi$
$277$	−10.1192	−0.608003	−0.304001	+	0.952672i	$0.598323\pi$
$278$	7.50609	0.450186
$279$	31.5731	1.89023
$280$	−27.2159	−1.62646
$281$	−5.33155	−0.318054	−0.159027	−	0.987274i	$-0.550836\pi$
$281$	−5.33155	−0.318054	−0.159027	+	0.987274i	$0.550836\pi$
$282$	−58.1612	−3.46345
$283$	10.7573	0.639454	0.319727	−	0.947510i	$-0.396409\pi$
$283$	10.7573	0.639454	0.319727	+	0.947510i	$0.396409\pi$
$284$	−77.5048	−4.59906
$285$	−4.45830	−0.264087
$286$	6.02864	0.356481
$287$	−5.02870	−0.296835
$288$	−268.081	−15.7968
$289$	−12.5498	−0.738225
$290$	14.5838	0.856387
$291$	7.00664	0.410736
$292$	20.6955	1.21112
$293$	−8.93832	−0.522182	−0.261091	−	0.965314i	$-0.584082\pi$
$293$	−8.93832	−0.522182	−0.261091	+	0.965314i	$0.584082\pi$
$294$	32.8582	1.91633
$295$	8.66773	0.504655
$296$	−87.7383	−5.09969
$297$	7.43308	0.431311
$298$	67.1410	3.88937
$299$	−18.8097	−1.08779
$300$	−65.3921	−3.77541
$301$	15.6779	0.903658
$302$	−33.4080	−1.92242
$303$	−49.7311	−2.85698
$304$	−19.0523	−1.09273
$305$	16.8066	0.962343
$306$	−50.2974	−2.87531
$307$	−10.6611	−0.608460	−0.304230	−	0.952599i	$-0.598399\pi$
$307$	−10.6611	−0.608460	−0.304230	+	0.952599i	$0.598399\pi$
$308$	4.45337	0.253754
$309$	−20.1531	−1.14647
$310$	−13.7725	−0.782224
$311$	26.1097	1.48055	0.740273	−	0.672307i	$-0.234696\pi$
$311$	26.1097	1.48055	0.740273	+	0.672307i	$0.234696\pi$
$312$	199.244	11.2800
$313$	−7.49080	−0.423405	−0.211702	−	0.977334i	$-0.567901\pi$
$313$	−7.49080	−0.423405	−0.211702	+	0.977334i	$0.567901\pi$
$314$	−63.2194	−3.56768
$315$	21.0266	1.18472
$316$	59.0030	3.31918
$317$	1.00000	0.0561656
$317$	1.00000	0.0561656
$318$	19.5242	1.09486
$319$	−1.57802	−0.0883519
$320$	66.8015	3.73432
$321$	1.61904	0.0903662
$322$	−18.6014	−1.03662
$323$	−2.10954	−0.117378
$324$	221.284	12.2936
$325$	17.5105	0.971310
$326$	−11.6861	−0.647231
$327$	1.30164	0.0719811
$328$	29.2938	1.61748
$329$	11.5048	0.634278
$330$	−5.01721	−0.276189
$331$	−25.8059	−1.41842	−0.709210	−	0.704998i	$-0.750948\pi$
$331$	−25.8059	−1.41842	−0.709210	+	0.704998i	$0.750948\pi$
$332$	−34.7761	−1.90859
$333$	67.7855	3.71462
$334$	−17.4908	−0.957055
$335$	−6.78408	−0.370654
$336$	121.643	6.63617
$337$	−5.20627	−0.283604	−0.141802	−	0.989895i	$-0.545290\pi$
$337$	−5.20627	−0.283604	−0.141802	+	0.989895i	$0.545290\pi$
$338$	−44.1342	−2.40058
$339$	27.3315	1.48444
$340$	16.3887	0.888804
$341$	1.49023	0.0807006
$342$	23.8428	1.28927
$343$	−19.6899	−1.06316
$344$	−91.3287	−4.92412
$345$	15.6540	0.842784
$346$	3.13226	0.168391
$347$	−6.20393	−0.333045	−0.166522	−	0.986038i	$-0.553254\pi$
$347$	−6.20393	−0.333045	−0.166522	+	0.986038i	$0.553254\pi$
$348$	−78.8681	−4.22777
$349$	−26.6816	−1.42823	−0.714116	−	0.700028i	$-0.753171\pi$
$349$	−26.6816	−1.42823	−0.714116	+	0.700028i	$0.753171\pi$
$350$	17.3166	0.925613
$351$	−99.4793	−5.30981
$352$	−12.6533	−0.674422
$353$	−6.32145	−0.336457	−0.168228	−	0.985748i	$-0.553805\pi$
$353$	−6.32145	−0.336457	−0.168228	+	0.985748i	$0.553805\pi$
$354$	−62.7526	−3.33526
$355$	−17.2721	−0.916709
$356$	32.4487	1.71978
$357$	13.4688	0.712842
$358$	−40.1939	−2.12431
$359$	−19.1551	−1.01097	−0.505485	−	0.862836i	$-0.668686\pi$
$359$	−19.1551	−1.01097	−0.505485	+	0.862836i	$0.668686\pi$
$360$	−122.487	−6.45562
$361$	1.00000	0.0526316
$362$	68.1554	3.58217
$363$	−36.7284	−1.92774
$364$	−59.6009	−3.12393
$365$	4.61206	0.241406
$366$	−121.676	−6.36013
$367$	28.7470	1.50058	0.750292	−	0.661107i	$-0.229913\pi$
$367$	28.7470	1.50058	0.750292	+	0.661107i	$0.229913\pi$
$368$	66.8967	3.48723
$369$	−22.6320	−1.17818
$370$	−29.5686	−1.53720
$371$	−3.86204	−0.200507
$372$	74.4807	3.86165
$373$	21.6264	1.11977	0.559887	−	0.828569i	$-0.310844\pi$
$373$	21.6264	1.11977	0.559887	+	0.828569i	$0.310844\pi$
$374$	−2.37401	−0.122757
$375$	−36.8643	−1.90366
$376$	−67.0189	−3.45623
$377$	21.1191	1.08769
$378$	−98.3777	−5.06000
$379$	11.6755	0.599728	0.299864	−	0.953982i	$-0.403059\pi$
$379$	11.6755	0.599728	0.299864	+	0.953982i	$0.403059\pi$
$380$	−7.76885	−0.398534
$381$	−16.8327	−0.862367
$382$	37.3971	1.91340
$383$	−28.4465	−1.45355	−0.726775	−	0.686875i	$-0.758982\pi$
$383$	−28.4465	−1.45355	−0.726775	+	0.686875i	$0.758982\pi$
$384$	−269.413	−13.7484
$385$	0.992444	0.0505796
$386$	−66.2696	−3.37303
$387$	70.5594	3.58674
$388$	12.2095	0.619843
$389$	−13.4221	−0.680525	−0.340262	−	0.940330i	$-0.610516\pi$
$389$	−13.4221	−0.680525	−0.340262	+	0.940330i	$0.610516\pi$
$390$	67.1470	3.40012
$391$	7.40705	0.374591
$392$	37.8623	1.91234
$393$	70.3393	3.54815
$394$	−24.3252	−1.22549
$395$	13.1490	0.661597
$396$	20.0427	1.00718
$397$	−17.8726	−0.897000	−0.448500	−	0.893783i	$-0.648042\pi$
$397$	−17.8726	−0.897000	−0.448500	+	0.893783i	$0.648042\pi$
$398$	−39.5627	−1.98310
$399$	−6.38468	−0.319634
$400$	−62.2762	−3.11381
$401$	−17.4307	−0.870450	−0.435225	−	0.900322i	$-0.643331\pi$
$401$	−17.4307	−0.870450	−0.435225	+	0.900322i	$0.643331\pi$
$402$	49.1154	2.44965
$403$	−19.9443	−0.993495
$404$	−86.6594	−4.31147
$405$	49.3137	2.45042
$406$	20.8852	1.03652
$407$	3.19944	0.158590
$408$	−78.4598	−3.88434
$409$	−21.4147	−1.05889	−0.529445	−	0.848344i	$-0.677600\pi$
$409$	−21.4147	−1.05889	−0.529445	+	0.848344i	$0.677600\pi$
$410$	9.87228	0.487557
$411$	−78.1981	−3.85723
$412$	−35.1180	−1.73014
$413$	12.4130	0.610802
$414$	−83.7170	−4.11447
$415$	−7.74994	−0.380429
$416$	169.343	8.30271
$417$	−9.04614	−0.442992
$418$	1.12537	0.0550434
$419$	15.1891	0.742034	0.371017	−	0.928626i	$-0.379009\pi$
$419$	15.1891	0.742034	0.371017	+	0.928626i	$0.379009\pi$
$420$	49.6016	2.42031
$421$	24.2932	1.18398	0.591989	−	0.805946i	$-0.298343\pi$
$421$	24.2932	1.18398	0.591989	+	0.805946i	$0.298343\pi$
$422$	−36.5143	−1.77749
$423$	51.7779	2.51753
$424$	22.4976	1.09258
$425$	−6.89545	−0.334478
$426$	125.047	6.05854
$427$	24.0686	1.16476
$428$	2.82128	0.136372
$429$	−7.26555	−0.350784
$430$	−30.7786	−1.48428
$431$	7.92572	0.381768	0.190884	−	0.981613i	$-0.438865\pi$
$431$	7.92572	0.381768	0.190884	+	0.981613i	$0.438865\pi$
$432$	353.798	17.0221
$433$	13.8872	0.667375	0.333687	−	0.942684i	$-0.391707\pi$
$433$	13.8872	0.667375	0.333687	+	0.942684i	$0.391707\pi$
$434$	−19.7234	−0.946754
$435$	−17.5759	−0.842702
$436$	2.26819	0.108627
$437$	−3.51121	−0.167964
$438$	−33.3904	−1.59545
$439$	−37.1981	−1.77537	−0.887685	−	0.460451i	$-0.847688\pi$
$439$	−37.1981	−1.77537	−0.887685	+	0.460451i	$0.847688\pi$
$440$	−5.78131	−0.275613
$441$	−29.2520	−1.39295
$442$	31.7721	1.51125
$443$	0.337859	0.0160522	0.00802608	−	0.999968i	$-0.497445\pi$
$443$	0.337859	0.0160522	0.00802608	+	0.999968i	$0.497445\pi$
$444$	159.905	7.58878
$445$	7.23127	0.342795
$446$	−28.5734	−1.35299
$447$	−80.9166	−3.82722
$448$	95.6658	4.51978
$449$	−16.9670	−0.800721	−0.400361	−	0.916358i	$-0.631115\pi$
$449$	−16.9670	−0.800721	−0.400361	+	0.916358i	$0.631115\pi$
$450$	77.9347	3.67388
$451$	−1.06822	−0.0503004
$452$	47.6268	2.24018
$453$	40.2625	1.89170
$454$	−6.58004	−0.308817
$455$	−13.2822	−0.622679
$456$	37.1928	1.74171
$457$	23.5024	1.09940	0.549699	−	0.835363i	$-0.314743\pi$
$457$	23.5024	1.09940	0.549699	+	0.835363i	$0.314743\pi$
$458$	−63.1967	−2.95299
$459$	39.1738	1.82848
$460$	27.2781	1.27185
$461$	−20.6060	−0.959719	−0.479859	−	0.877345i	$-0.659312\pi$
$461$	−20.6060	−0.959719	−0.479859	+	0.877345i	$0.659312\pi$
$462$	−7.18510	−0.334281
$463$	−20.7341	−0.963594	−0.481797	−	0.876283i	$-0.660016\pi$
$463$	−20.7341	−0.963594	−0.481797	+	0.876283i	$0.660016\pi$
$464$	−75.1100	−3.48690
$465$	16.5982	0.769724
$466$	−33.0558	−1.53128
$467$	−4.78077	−0.221228	−0.110614	−	0.993863i	$-0.535282\pi$
$467$	−4.78077	−0.221228	−0.110614	+	0.993863i	$0.535282\pi$
$468$	−268.238	−12.3993
$469$	−9.71542	−0.448616
$470$	−22.5860	−1.04181
$471$	76.1903	3.51066
$472$	−72.3095	−3.32831
$473$	3.33036	0.153130
$474$	−95.1959	−4.37249
$475$	3.26869	0.149978
$476$	23.4701	1.07575
$477$	−17.3814	−0.795838
$478$	−30.0127	−1.37275
$479$	6.38649	0.291806	0.145903	−	0.989299i	$-0.453391\pi$
$479$	6.38649	0.291806	0.145903	+	0.989299i	$0.453391\pi$
$480$	−140.932	−6.43264
$481$	−42.8191	−1.95238
$482$	−8.47270	−0.385921
$483$	22.4179	1.02005
$484$	−64.0015	−2.90916
$485$	2.72092	0.123550
$486$	−200.396	−9.09016
$487$	−31.3967	−1.42272	−0.711359	−	0.702829i	$-0.751920\pi$
$487$	−31.3967	−1.42272	−0.711359	+	0.702829i	$0.751920\pi$
$488$	−140.207	−6.34688
$489$	14.0837	0.636889
$490$	12.7600	0.576436
$491$	−5.27909	−0.238242	−0.119121	−	0.992880i	$-0.538008\pi$
$491$	−5.27909	−0.238242	−0.119121	+	0.992880i	$0.538008\pi$
$492$	−53.3887	−2.40695
$493$	−8.31646	−0.374554
$494$	−15.0611	−0.677633
$495$	4.46656	0.200757
$496$	70.9318	3.18493
$497$	−24.7352	−1.10953
$498$	56.1080	2.51426
$499$	18.5435	0.830120	0.415060	−	0.909794i	$-0.363761\pi$
$499$	18.5435	0.830120	0.415060	+	0.909794i	$0.363761\pi$
$500$	−64.2383	−2.87282
$501$	21.0795	0.941761
$502$	−3.64837	−0.162835
$503$	6.84177	0.305059	0.152530	−	0.988299i	$-0.451258\pi$
$503$	6.84177	0.305059	0.152530	+	0.988299i	$0.451258\pi$
$504$	−175.412	−7.81348
$505$	−19.3123	−0.859385
$506$	−3.95140	−0.175661
$507$	53.1894	2.36222
$508$	−29.3321	−1.30140
$509$	−43.7973	−1.94128	−0.970640	−	0.240536i	$-0.922677\pi$
$509$	−43.7973	−1.94128	−0.970640	+	0.240536i	$0.922677\pi$
$510$	−26.4417	−1.17086
$511$	6.60488	0.292183
$512$	−183.999	−8.13167
$513$	−18.5698	−0.819877
$514$	75.8343	3.34491
$515$	−7.82614	−0.344861
$516$	166.449	7.32751
$517$	2.44389	0.107482
$518$	−42.3449	−1.86053
$519$	−3.77491	−0.165700
$520$	77.3731	3.39304
$521$	−26.5309	−1.16234	−0.581170	−	0.813782i	$-0.697405\pi$
$521$	−26.5309	−1.16234	−0.581170	+	0.813782i	$0.697405\pi$
$522$	93.9955	4.11407
$523$	5.55244	0.242791	0.121396	−	0.992604i	$-0.461263\pi$
$523$	5.55244	0.242791	0.121396	+	0.992604i	$0.461263\pi$
$524$	122.571	5.35452
$525$	−20.8695	−0.910822
$526$	−62.1614	−2.71037
$527$	7.85382	0.342118
$528$	25.8399	1.12454
$529$	−10.6714	−0.463974
$530$	7.58191	0.329337
$531$	55.8654	2.42435
$532$	−11.1257	−0.482360
$533$	14.2963	0.619241
$534$	−52.3530	−2.26553
$535$	0.628730	0.0271824
$536$	56.5954	2.44455
$537$	48.4406	2.09037
$538$	47.3596	2.04182
$539$	−1.38068	−0.0594699
$540$	144.266	6.20822
$541$	4.34838	0.186952	0.0934758	−	0.995622i	$-0.470202\pi$
$541$	4.34838	0.186952	0.0934758	+	0.995622i	$0.470202\pi$
$542$	56.7164	2.43618
$543$	−82.1390	−3.52492
$544$	−66.6852	−2.85911
$545$	0.505473	0.0216521
$546$	96.1605	4.11529
$547$	41.3976	1.77003	0.885017	−	0.465558i	$-0.154146\pi$
$547$	41.3976	1.77003	0.885017	+	0.465558i	$0.154146\pi$
$548$	−136.265	−5.82095
$549$	108.322	4.62308
$550$	3.67847	0.156851
$551$	3.94230	0.167948
$552$	−130.592	−5.55835
$553$	18.8305	0.800755
$554$	28.4497	1.20871
$555$	35.6353	1.51264
$556$	−15.7635	−0.668520
$557$	−25.6253	−1.08578	−0.542890	−	0.839804i	$-0.682670\pi$
$557$	−25.6253	−1.08578	−0.542890	+	0.839804i	$0.682670\pi$
$558$	−88.7666	−3.75779
$559$	−44.5713	−1.88517
$560$	47.2381	1.99618
$561$	2.86109	0.120795
$562$	14.9895	0.632292
$563$	3.42802	0.144474	0.0722368	−	0.997388i	$-0.476986\pi$
$563$	3.42802	0.144474	0.0722368	+	0.997388i	$0.476986\pi$
$564$	122.144	5.14318
$565$	10.6138	0.446524
$566$	−30.2437	−1.27124
$567$	70.6216	2.96583
$568$	144.091	6.04591
$569$	10.0917	0.423067	0.211534	−	0.977371i	$-0.432154\pi$
$569$	10.0917	0.423067	0.211534	+	0.977371i	$0.432154\pi$
$570$	12.5343	0.525005
$571$	−10.4200	−0.436064	−0.218032	−	0.975942i	$-0.569964\pi$
$571$	−10.4200	−0.436064	−0.218032	+	0.975942i	$0.569964\pi$
$572$	−12.6607	−0.529369
$573$	−45.0699	−1.88282
$574$	14.1380	0.590108
$575$	−11.4771	−0.478627
$576$	430.551	17.9396
$577$	−31.3208	−1.30390	−0.651951	−	0.758261i	$-0.726049\pi$
$577$	−31.3208	−1.30390	−0.651951	+	0.758261i	$0.726049\pi$
$578$	35.2834	1.46759
$579$	79.8663	3.31913
$580$	−30.6272	−1.27172
$581$	−11.0986	−0.460448
$582$	−19.6989	−0.816545
$583$	−0.820390	−0.0339771
$584$	−38.4755	−1.59213
$585$	−59.7775	−2.47150
$586$	25.1297	1.03810
$587$	−3.78404	−0.156184	−0.0780920	−	0.996946i	$-0.524883\pi$
$587$	−3.78404	−0.156184	−0.0780920	+	0.996946i	$0.524883\pi$
$588$	−69.0051	−2.84572
$589$	−3.72300	−0.153403
$590$	−24.3690	−1.00326
$591$	29.3161	1.20590
$592$	152.286	6.25892
$593$	−14.4136	−0.591896	−0.295948	−	0.955204i	$-0.595635\pi$
$593$	−14.4136	−0.591896	−0.295948	+	0.955204i	$0.595635\pi$
$594$	−20.8978	−0.857448
$595$	5.23038	0.214425
$596$	−141.002	−5.77567
$597$	47.6799	1.95141
$598$	52.8828	2.16254
$599$	−39.4327	−1.61118	−0.805589	−	0.592475i	$-0.798151\pi$
$599$	−39.4327	−1.61118	−0.805589	+	0.592475i	$0.798151\pi$
$600$	121.572	4.96315
$601$	−16.2957	−0.664714	−0.332357	−	0.943154i	$-0.607844\pi$
$601$	−16.2957	−0.664714	−0.332357	+	0.943154i	$0.607844\pi$
$602$	−44.0778	−1.79648
$603$	−43.7249	−1.78062
$604$	70.1598	2.85476
$605$	−14.2629	−0.579869
$606$	139.817	5.67968
$607$	19.7071	0.799888	0.399944	−	0.916540i	$-0.369030\pi$
$607$	19.7071	0.799888	0.399944	+	0.916540i	$0.369030\pi$
$608$	31.6112	1.28200
$609$	−25.1703	−1.01995
$610$	−47.2511	−1.91314
$611$	−32.7073	−1.32320
$612$	105.629	4.26980
$613$	14.0792	0.568652	0.284326	−	0.958728i	$-0.408230\pi$
$613$	14.0792	0.568652	0.284326	+	0.958728i	$0.408230\pi$
$614$	29.9732	1.20962
$615$	−11.8978	−0.479766
$616$	−8.27935	−0.333585
$617$	6.71662	0.270401	0.135201	−	0.990818i	$-0.456832\pi$
$617$	6.71662	0.270401	0.135201	+	0.990818i	$0.456832\pi$
$618$	56.6597	2.27919
$619$	−22.3782	−0.899456	−0.449728	−	0.893166i	$-0.648479\pi$
$619$	−22.3782	−0.899456	−0.449728	+	0.893166i	$0.648479\pi$
$620$	28.9234	1.16159
$621$	65.2025	2.61648
$622$	−73.4064	−2.94333
$623$	10.3558	0.414897
$624$	−345.824	−13.8440
$625$	2.02780	0.0811120
$626$	21.0601	0.841730
$627$	−1.35626	−0.0541638
$628$	132.766	5.29795
$629$	16.8617	0.672319
$630$	−59.1156	−2.35522
$631$	5.35736	0.213273	0.106636	−	0.994298i	$-0.465992\pi$
$631$	5.35736	0.213273	0.106636	+	0.994298i	$0.465992\pi$
$632$	−109.694	−4.36338
$633$	44.0061	1.74908
$634$	−2.81146	−0.111657
$635$	−6.53672	−0.259402
$636$	−41.0025	−1.62586
$637$	18.4780	0.732126
$638$	4.43653	0.175644
$639$	−111.323	−4.40386
$640$	−104.622	−4.13556
$641$	20.5906	0.813280	0.406640	−	0.913588i	$-0.366700\pi$
$641$	20.5906	0.813280	0.406640	+	0.913588i	$0.366700\pi$
$642$	−4.55188	−0.179648
$643$	12.1050	0.477373	0.238687	−	0.971097i	$-0.423283\pi$
$643$	12.1050	0.477373	0.238687	+	0.971097i	$0.423283\pi$
$644$	39.0646	1.53936
$645$	37.0936	1.46056
$646$	5.93090	0.233348
$647$	19.5031	0.766744	0.383372	−	0.923594i	$-0.374763\pi$
$647$	19.5031	0.766744	0.383372	+	0.923594i	$0.374763\pi$
$648$	−411.394	−16.1611
$649$	2.63681	0.103504
$650$	−49.2302	−1.93097
$651$	23.7701	0.931625
$652$	24.5418	0.961130
$653$	15.6172	0.611146	0.305573	−	0.952169i	$-0.401152\pi$
$653$	15.6172	0.611146	0.305573	+	0.952169i	$0.401152\pi$
$654$	−3.65952	−0.143099
$655$	27.3152	1.06729
$656$	−50.8448	−1.98515
$657$	29.7257	1.15971
$658$	−32.3452	−1.26095
$659$	25.4250	0.990418	0.495209	−	0.868774i	$-0.335091\pi$
$659$	25.4250	0.990418	0.495209	+	0.868774i	$0.335091\pi$
$660$	10.5366	0.410136
$661$	−47.3553	−1.84191	−0.920955	−	0.389670i	$-0.872589\pi$
$661$	−47.3553	−1.84191	−0.920955	+	0.389670i	$0.872589\pi$
$662$	72.5522	2.81982
$663$	−38.2909	−1.48710
$664$	64.6529	2.50902
$665$	−2.47939	−0.0961466
$666$	−190.576	−7.38468
$667$	−13.8422	−0.535974
$668$	36.7323	1.42121
$669$	34.4359	1.33137
$670$	19.0732	0.736862
$671$	5.11274	0.197375
$672$	−201.828	−7.78567
$673$	10.7215	0.413283	0.206641	−	0.978417i	$-0.433747\pi$
$673$	10.7215	0.413283	0.206641	+	0.978417i	$0.433747\pi$
$674$	14.6372	0.563805
$675$	−60.6989	−2.33630
$676$	92.6857	3.56484
$677$	32.5145	1.24963	0.624817	−	0.780771i	$-0.285173\pi$
$677$	32.5145	1.24963	0.624817	+	0.780771i	$0.285173\pi$
$678$	−76.8415	−2.95108
$679$	3.89660	0.149538
$680$	−30.4686	−1.16842
$681$	7.93009	0.303882
$682$	−4.18973	−0.160433
$683$	9.53861	0.364985	0.182492	−	0.983207i	$-0.441584\pi$
$683$	9.53861	0.364985	0.182492	+	0.983207i	$0.441584\pi$
$684$	−50.0720	−1.91455
$685$	−30.3670	−1.16026
$686$	55.3575	2.11356
$687$	76.1630	2.90580
$688$	158.518	6.04344
$689$	10.9796	0.418288
$690$	−44.0107	−1.67546
$691$	31.8860	1.21300	0.606500	−	0.795083i	$-0.292573\pi$
$691$	31.8860	1.21300	0.606500	+	0.795083i	$0.292573\pi$
$692$	−6.57802	−0.250059
$693$	6.39652	0.242984
$694$	17.4421	0.662094
$695$	−3.51293	−0.133253
$696$	146.625	5.55782
$697$	−5.62972	−0.213241
$698$	75.0142	2.83933
$699$	39.8380	1.50681
$700$	−36.3665	−1.37452
$701$	−51.7124	−1.95315	−0.976575	−	0.215176i	$-0.930967\pi$
$701$	−51.7124	−1.95315	−0.976575	+	0.215176i	$0.930967\pi$
$702$	279.682	10.5559
$703$	−7.99304	−0.301463
$704$	20.3217	0.765904
$705$	27.2200	1.02517
$706$	17.7725	0.668878
$707$	−27.6569	−1.04014
$708$	131.786	4.95282
$709$	7.17834	0.269588	0.134794	−	0.990874i	$-0.456963\pi$
$709$	7.17834	0.269588	0.134794	+	0.990874i	$0.456963\pi$
$710$	48.5599	1.82242
$711$	84.7480	3.17830
$712$	−60.3260	−2.26081
$713$	13.0722	0.489559
$714$	−37.8669	−1.41713
$715$	−2.82146	−0.105517
$716$	84.4108	3.15458
$717$	36.1705	1.35081
$718$	53.8539	2.00981
$719$	3.73017	0.139112	0.0695559	−	0.997578i	$-0.477842\pi$
$719$	3.73017	0.139112	0.0695559	+	0.997578i	$0.477842\pi$
$720$	212.599	7.92308
$721$	−11.2077	−0.417398
$722$	−2.81146	−0.104632
$723$	10.2111	0.379754
$724$	−143.132	−5.31947
$725$	12.8862	0.478580
$726$	103.261	3.83236
$727$	−13.5776	−0.503564	−0.251782	−	0.967784i	$-0.581017\pi$
$727$	−13.5776	−0.503564	−0.251782	+	0.967784i	$0.581017\pi$
$728$	110.805	4.10672
$729$	129.077	4.78064
$730$	−12.9666	−0.479916
$731$	17.5517	0.649172
$732$	255.531	9.44471
$733$	0.318586	0.0117672	0.00588362	−	0.999983i	$-0.498127\pi$
$733$	0.318586	0.0117672	0.00588362	+	0.999983i	$0.498127\pi$
$734$	−80.8212	−2.98317
$735$	−15.3780	−0.567225
$736$	−110.994	−4.09128
$737$	−2.06379	−0.0760207
$738$	63.6290	2.34222
$739$	−38.6884	−1.42318	−0.711588	−	0.702597i	$-0.752024\pi$
$739$	−38.6884	−1.42318	−0.711588	+	0.702597i	$0.752024\pi$
$740$	62.0968	2.28272
$741$	18.1513	0.666804
$742$	10.8580	0.398609
$743$	11.3321	0.415735	0.207867	−	0.978157i	$-0.433348\pi$
$743$	11.3321	0.415735	0.207867	+	0.978157i	$0.433348\pi$
$744$	−138.469	−5.07651
$745$	−31.4227	−1.15124
$746$	−60.8019	−2.22612
$747$	−49.9500	−1.82758
$748$	4.98563	0.182293
$749$	0.900398	0.0328998
$750$	103.643	3.78449
$751$	−10.6378	−0.388179	−0.194089	−	0.980984i	$-0.562175\pi$
$751$	−10.6378	−0.388179	−0.194089	+	0.980984i	$0.562175\pi$
$752$	116.324	4.24189
$753$	4.39692	0.160233
$754$	−59.3755	−2.16233
$755$	15.6353	0.569026
$756$	206.602	7.51404
$757$	−33.8381	−1.22986	−0.614932	−	0.788580i	$-0.710817\pi$
$757$	−33.8381	−1.22986	−0.614932	+	0.788580i	$0.710817\pi$
$758$	−32.8251	−1.19226
$759$	4.76212	0.172854
$760$	14.4432	0.523911
$761$	14.0550	0.509492	0.254746	−	0.967008i	$-0.418008\pi$
$761$	14.0550	0.509492	0.254746	+	0.967008i	$0.418008\pi$
$762$	47.3246	1.71439
$763$	0.723882	0.0262063
$764$	−78.5371	−2.84137
$765$	23.5397	0.851079
$766$	79.9764	2.88966
$767$	−35.2893	−1.27422
$768$	413.404	14.9174
$769$	47.6949	1.71992	0.859961	−	0.510360i	$-0.170488\pi$
$769$	47.6949	1.71992	0.859961	+	0.510360i	$0.170488\pi$
$770$	−2.79022	−0.100553
$771$	−91.3935	−3.29146
$772$	139.172	5.00891
$773$	25.6417	0.922269	0.461134	−	0.887330i	$-0.347443\pi$
$773$	25.6417	0.922269	0.461134	+	0.887330i	$0.347443\pi$
$774$	−198.375	−7.13045
$775$	−12.1693	−0.437135
$776$	−22.6989	−0.814844
$777$	51.0330	1.83080
$778$	37.7356	1.35289
$779$	2.66869	0.0956157
$780$	−141.015	−5.04913
$781$	−5.25436	−0.188016
$782$	−20.8246	−0.744688
$783$	−73.2077	−2.61623
$784$	−65.7171	−2.34704
$785$	29.5873	1.05602
$786$	−197.756	−7.05374
$787$	0.953378	0.0339843	0.0169921	−	0.999856i	$-0.494591\pi$
$787$	0.953378	0.0339843	0.0169921	+	0.999856i	$0.494591\pi$
$788$	51.0852	1.81983
$789$	74.9153	2.66705
$790$	−36.9678	−1.31526
$791$	15.1999	0.540445
$792$	−37.2618	−1.32404
$793$	−68.4255	−2.42986
$794$	50.2481	1.78324
$795$	−9.13751	−0.324074
$796$	83.0851	2.94487
$797$	−13.5056	−0.478392	−0.239196	−	0.970971i	$-0.576884\pi$
$797$	−13.5056	−0.478392	−0.239196	+	0.970971i	$0.576884\pi$
$798$	17.9503	0.635433
$799$	12.8798	0.455654
$800$	103.327	3.65317
$801$	46.6071	1.64678
$802$	49.0059	1.73046
$803$	1.40304	0.0495121
$804$	−103.147	−3.63770
$805$	8.70566	0.306834
$806$	56.0725	1.97507
$807$	−57.0765	−2.00919
$808$	161.110	5.66784
$809$	6.87340	0.241656	0.120828	−	0.992673i	$-0.461445\pi$
$809$	6.87340	0.241656	0.120828	+	0.992673i	$0.461445\pi$
$810$	−138.644	−4.87144
$811$	9.61705	0.337700	0.168850	−	0.985642i	$-0.445995\pi$
$811$	9.61705	0.337700	0.168850	+	0.985642i	$0.445995\pi$
$812$	−43.8608	−1.53921
$813$	−68.3531	−2.39725
$814$	−8.99509	−0.315278
$815$	5.46920	0.191578
$816$	136.182	4.76731
$817$	−8.32013	−0.291085
$818$	60.2066	2.10508
$819$	−85.6067	−2.99134
$820$	−20.7327	−0.724016
$821$	6.69214	0.233557	0.116779	−	0.993158i	$-0.462743\pi$
$821$	6.69214	0.233557	0.116779	+	0.993158i	$0.462743\pi$
$822$	219.851	7.66818
$823$	−28.8078	−1.00418	−0.502088	−	0.864817i	$-0.667435\pi$
$823$	−28.8078	−1.00418	−0.502088	+	0.864817i	$0.667435\pi$
$824$	65.2886	2.27444
$825$	−4.43320	−0.154344
$826$	−34.8986	−1.21428
$827$	35.1789	1.22329	0.611644	−	0.791133i	$-0.290508\pi$
$827$	35.1789	1.22329	0.611644	+	0.791133i	$0.290508\pi$
$828$	175.813	6.10993
$829$	35.8425	1.24486	0.622430	−	0.782675i	$-0.286145\pi$
$829$	35.8425	1.24486	0.622430	+	0.782675i	$0.286145\pi$
$830$	21.7887	0.756295
$831$	−34.2868	−1.18940
$832$	−271.972	−9.42895
$833$	−7.27643	−0.252113
$834$	25.4329	0.880669
$835$	8.18588	0.283284
$836$	−2.36337	−0.0817388
$837$	69.1353	2.38967
$838$	−42.7034	−1.47517
$839$	39.1973	1.35324	0.676620	−	0.736332i	$-0.263444\pi$
$839$	39.1973	1.35324	0.676620	+	0.736332i	$0.263444\pi$
$840$	−92.2154	−3.18174
$841$	−13.4583	−0.464078
$842$	−68.2994	−2.35375
$843$	−18.0649	−0.622188
$844$	76.6832	2.63955
$845$	20.6553	0.710562
$846$	−145.572	−5.00486
$847$	−20.4257	−0.701837
$848$	−39.0488	−1.34094
$849$	36.4489	1.25092
$850$	19.3863	0.664944
$851$	28.0652	0.962064
$852$	−262.609	−8.99684
$853$	−46.8592	−1.60443	−0.802215	−	0.597035i	$-0.796345\pi$
$853$	−46.8592	−1.60443	−0.802215	+	0.597035i	$0.796345\pi$
$854$	−67.6678	−2.31555
$855$	−11.1587	−0.381618
$856$	−5.24511	−0.179274
$857$	15.2230	0.520006	0.260003	−	0.965608i	$-0.416276\pi$
$857$	15.2230	0.520006	0.260003	+	0.965608i	$0.416276\pi$
$858$	20.4268	0.697360
$859$	−28.5117	−0.972806	−0.486403	−	0.873735i	$-0.661691\pi$
$859$	−28.5117	−0.972806	−0.486403	+	0.873735i	$0.661691\pi$
$860$	64.6379	2.20413
$861$	−17.0387	−0.580678
$862$	−22.2828	−0.758957
$863$	−7.49118	−0.255003	−0.127501	−	0.991838i	$-0.540696\pi$
$863$	−7.49118	−0.255003	−0.127501	+	0.991838i	$0.540696\pi$
$864$	−587.014	−19.9706
$865$	−1.46593	−0.0498430
$866$	−39.0433	−1.32674
$867$	−42.5226	−1.44414
$868$	41.4209	1.40592
$869$	4.00006	0.135693
$870$	49.4141	1.67530
$871$	27.6204	0.935880
$872$	−4.21685	−0.142800
$873$	17.5369	0.593534
$874$	9.87163	0.333913
$875$	−20.5013	−0.693071
$876$	70.1227	2.36923
$877$	−8.46244	−0.285756	−0.142878	−	0.989740i	$-0.545636\pi$
$877$	−8.46244	−0.285756	−0.142878	+	0.989740i	$0.545636\pi$
$878$	104.581	3.52944
$879$	−30.2857	−1.02151
$880$	10.0345	0.338264
$881$	39.2491	1.32234	0.661168	−	0.750238i	$-0.270061\pi$
$881$	39.2491	1.32234	0.661168	+	0.750238i	$0.270061\pi$
$882$	82.2408	2.76919
$883$	15.4480	0.519865	0.259933	−	0.965627i	$-0.416300\pi$
$883$	15.4480	0.519865	0.259933	+	0.965627i	$0.416300\pi$
$884$	−66.7242	−2.24418
$885$	29.3689	0.987223
$886$	−0.949877	−0.0319117
$887$	−50.6371	−1.70023	−0.850114	−	0.526598i	$-0.823467\pi$
$887$	−50.6371	−1.70023	−0.850114	+	0.526598i	$0.823467\pi$
$888$	−297.284	−9.97618
$889$	−9.36117	−0.313964
$890$	−20.3304	−0.681478
$891$	15.0017	0.502577
$892$	60.0067	2.00917
$893$	−6.10548	−0.204312
$894$	227.494	7.60853
$895$	18.8112	0.628787
$896$	−149.829	−5.00542
$897$	−63.7329	−2.12798
$898$	47.7020	1.59184
$899$	−14.6772	−0.489511
$900$	−163.670	−5.45566
$901$	−4.32362	−0.144041
$902$	3.00325	0.0999974
$903$	53.1214	1.76777
$904$	−88.5441	−2.94493
$905$	−31.8974	−1.06031
$906$	−113.196	−3.76070
$907$	−42.2295	−1.40221	−0.701103	−	0.713060i	$-0.747309\pi$
$907$	−42.2295	−1.40221	−0.701103	+	0.713060i	$0.747309\pi$
$908$	13.8187	0.458589
$909$	−124.472	−4.12847
$910$	37.3424	1.23789
$911$	−43.2940	−1.43439	−0.717197	−	0.696870i	$-0.754575\pi$
$911$	−43.2940	−1.43439	−0.717197	+	0.696870i	$0.754575\pi$
$912$	−64.5550	−2.13763
$913$	−2.35761	−0.0780256
$914$	−66.0762	−2.18561
$915$	56.9458	1.88257
$916$	132.719	4.38515
$917$	39.1178	1.29178
$918$	−110.136	−3.63502
$919$	−32.9332	−1.08637	−0.543184	−	0.839614i	$-0.682781\pi$
$919$	−32.9332	−1.08637	−0.543184	+	0.839614i	$0.682781\pi$
$920$	−50.7132	−1.67197
$921$	−36.1229	−1.19029
$922$	57.9331	1.90792
$923$	70.3209	2.31464
$924$	15.0893	0.496403
$925$	−26.1268	−0.859043
$926$	58.2931	1.91563
$927$	−50.4412	−1.65671
$928$	124.621	4.09088
$929$	−22.4705	−0.737232	−0.368616	−	0.929582i	$-0.620168\pi$
$929$	−22.4705	−0.737232	−0.368616	+	0.929582i	$0.620168\pi$
$930$	−46.6653	−1.53021
$931$	3.44929	0.113046
$932$	69.4202	2.27393
$933$	88.4675	2.89630
$934$	13.4410	0.439801
$935$	1.11106	0.0363355
$936$	498.687	16.3001
$937$	−8.49021	−0.277363	−0.138682	−	0.990337i	$-0.544286\pi$
$937$	−8.49021	−0.277363	−0.138682	+	0.990337i	$0.544286\pi$
$938$	27.3145	0.891851
$939$	−25.3811	−0.828280
$940$	47.4326	1.54708
$941$	−22.4006	−0.730239	−0.365120	−	0.930961i	$-0.618972\pi$
$941$	−22.4006	−0.730239	−0.365120	+	0.930961i	$0.618972\pi$
$942$	−214.206	−6.97921
$943$	−9.37033	−0.305140
$944$	125.506	4.08489
$945$	46.0418	1.49774
$946$	−9.36319	−0.304424
$947$	40.5277	1.31697	0.658487	−	0.752592i	$-0.271197\pi$
$947$	40.5277	1.31697	0.658487	+	0.752592i	$0.271197\pi$
$948$	199.920	6.49309
$949$	−18.7773	−0.609536
$950$	−9.18980	−0.298157
$951$	3.38830	0.109873
$952$	−43.6338	−1.41418
$953$	5.23184	0.169476	0.0847380	−	0.996403i	$-0.472995\pi$
$953$	5.23184	0.169476	0.0847380	+	0.996403i	$0.472995\pi$
$954$	48.8671	1.58213
$955$	−17.5022	−0.566358
$956$	63.0293	2.03851
$957$	−5.34679	−0.172837
$958$	−17.9554	−0.580112
$959$	−43.4883	−1.40431
$960$	226.344	7.30521
$961$	−17.1393	−0.552881
$962$	120.384	3.88134
$963$	4.05230	0.130584
$964$	17.7934	0.573087
$965$	31.0148	0.998402
$966$	−63.0272	−2.02787
$967$	−7.53835	−0.242417	−0.121208	−	0.992627i	$-0.538677\pi$
$967$	−7.53835	−0.242417	−0.121208	+	0.992627i	$0.538677\pi$
$968$	118.987	3.82437
$969$	−7.14776	−0.229619
$970$	−7.64975	−0.245619
$971$	−1.11605	−0.0358157	−0.0179079	−	0.999840i	$-0.505701\pi$
$971$	−1.11605	−0.0358157	−0.0179079	+	0.999840i	$0.505701\pi$
$972$	420.850	13.4988
$973$	−5.03083	−0.161281
$974$	88.2705	2.82837
$975$	59.3309	1.90011
$976$	243.355	7.78961
$977$	−48.3853	−1.54798	−0.773992	−	0.633196i	$-0.781743\pi$
$977$	−48.3853	−1.54798	−0.773992	+	0.633196i	$0.781743\pi$
$978$	−39.5959	−1.26614
$979$	2.19983	0.0703068
$980$	−26.7971	−0.856000
$981$	3.25788	0.104016
$982$	14.8420	0.473626
$983$	51.1894	1.63269	0.816344	−	0.577566i	$-0.195997\pi$
$983$	51.1894	1.63269	0.816344	+	0.577566i	$0.195997\pi$
$984$	99.2561	3.16417
$985$	11.3845	0.362739
$986$	23.3814	0.744615
$987$	38.9815	1.24080
$988$	31.6297	1.00628
$989$	29.2137	0.928942
$990$	−12.5576	−0.399106
$991$	3.70324	0.117637	0.0588186	−	0.998269i	$-0.481267\pi$
$991$	3.70324	0.117637	0.0588186	+	0.998269i	$0.481267\pi$
$992$	−117.688	−3.73661
$993$	−87.4380	−2.77476
$994$	69.5422	2.20574
$995$	18.5157	0.586988
$996$	−117.832	−3.73364
$997$	−26.5465	−0.840737	−0.420368	−	0.907353i	$-0.638099\pi$
$997$	−26.5465	−0.840737	−0.420368	+	0.907353i	$0.638099\pi$
$998$	−52.1343	−1.65028
$999$	148.429	4.69609

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.d.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-2.81146 q^{2} +3.38830 q^{3} +5.90432 q^{4} +1.31579 q^{5} -9.52607 q^{6} +1.88433 q^{7} -10.9768 q^{8} +8.48057 q^{9} +O(q^{10})\)	\(q-2.81146 q^{2} +3.38830 q^{3} +5.90432 q^{4} +1.31579 q^{5} -9.52607 q^{6} +1.88433 q^{7} -10.9768 q^{8} +8.48057 q^{9} -3.69930 q^{10} +0.400278 q^{11} +20.0056 q^{12} -5.35705 q^{13} -5.29773 q^{14} +4.45830 q^{15} +19.0523 q^{16} +2.10954 q^{17} -23.8428 q^{18} -1.00000 q^{19} +7.76885 q^{20} +6.38468 q^{21} -1.12537 q^{22} +3.51121 q^{23} -37.1928 q^{24} -3.26869 q^{25} +15.0611 q^{26} +18.5698 q^{27} +11.1257 q^{28} -3.94230 q^{29} -12.5343 q^{30} +3.72300 q^{31} -31.6112 q^{32} +1.35626 q^{33} -5.93090 q^{34} +2.47939 q^{35} +50.0720 q^{36} +7.99304 q^{37} +2.81146 q^{38} -18.1513 q^{39} -14.4432 q^{40} -2.66869 q^{41} -17.9503 q^{42} +8.32013 q^{43} +2.36337 q^{44} +11.1587 q^{45} -9.87163 q^{46} +6.10548 q^{47} +64.5550 q^{48} -3.44929 q^{49} +9.18980 q^{50} +7.14776 q^{51} -31.6297 q^{52} -2.04955 q^{53} -52.2083 q^{54} +0.526682 q^{55} -20.6840 q^{56} -3.38830 q^{57} +11.0836 q^{58} +6.58746 q^{59} +26.3232 q^{60} +12.7730 q^{61} -10.4671 q^{62} +15.9802 q^{63} +50.7691 q^{64} -7.04876 q^{65} -3.81307 q^{66} -5.15589 q^{67} +12.4554 q^{68} +11.8970 q^{69} -6.97071 q^{70} -13.1268 q^{71} -93.0898 q^{72} +3.50516 q^{73} -22.4721 q^{74} -11.0753 q^{75} -5.90432 q^{76} +0.754256 q^{77} +51.0316 q^{78} +9.99320 q^{79} +25.0689 q^{80} +37.4783 q^{81} +7.50292 q^{82} -5.88994 q^{83} +37.6972 q^{84} +2.77572 q^{85} -23.3917 q^{86} -13.3577 q^{87} -4.39378 q^{88} +5.49575 q^{89} -31.3722 q^{90} -10.0945 q^{91} +20.7313 q^{92} +12.6146 q^{93} -17.1653 q^{94} -1.31579 q^{95} -107.108 q^{96} +2.06789 q^{97} +9.69755 q^{98} +3.39458 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9}+O(q^{10}) \) 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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