LMFDB - Embedded newform 2013.4.a.g.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,4,Mod(1,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2013.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:	$118.770844842$
Analytic rank:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.275199 q^{2} -3.00000 q^{3} -7.92427 q^{4} +15.4654 q^{5} +0.825597 q^{6} -21.6439 q^{7} +4.38234 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-0.275199 q^{2} -3.00000 q^{3} -7.92427 q^{4} +15.4654 q^{5} +0.825597 q^{6} -21.6439 q^{7} +4.38234 q^{8} +9.00000 q^{9} -4.25605 q^{10} +11.0000 q^{11} +23.7728 q^{12} +80.4266 q^{13} +5.95639 q^{14} -46.3961 q^{15} +62.1881 q^{16} -115.151 q^{17} -2.47679 q^{18} -0.685333 q^{19} -122.552 q^{20} +64.9318 q^{21} -3.02719 q^{22} +74.6888 q^{23} -13.1470 q^{24} +114.177 q^{25} -22.1333 q^{26} -27.0000 q^{27} +171.512 q^{28} -7.01663 q^{29} +12.7681 q^{30} +160.518 q^{31} -52.1728 q^{32} -33.0000 q^{33} +31.6894 q^{34} -334.731 q^{35} -71.3184 q^{36} +276.927 q^{37} +0.188603 q^{38} -241.280 q^{39} +67.7744 q^{40} -181.961 q^{41} -17.8692 q^{42} +209.932 q^{43} -87.1669 q^{44} +139.188 q^{45} -20.5543 q^{46} -329.527 q^{47} -186.564 q^{48} +125.460 q^{49} -31.4214 q^{50} +345.453 q^{51} -637.322 q^{52} -208.434 q^{53} +7.43037 q^{54} +170.119 q^{55} -94.8512 q^{56} +2.05600 q^{57} +1.93097 q^{58} +580.865 q^{59} +367.655 q^{60} +61.0000 q^{61} -44.1744 q^{62} -194.796 q^{63} -483.147 q^{64} +1243.83 q^{65} +9.08157 q^{66} -370.415 q^{67} +912.487 q^{68} -224.066 q^{69} +92.1177 q^{70} -692.704 q^{71} +39.4411 q^{72} -691.422 q^{73} -76.2100 q^{74} -342.531 q^{75} +5.43076 q^{76} -238.083 q^{77} +66.4000 q^{78} +674.867 q^{79} +961.761 q^{80} +81.0000 q^{81} +50.0755 q^{82} +442.923 q^{83} -514.537 q^{84} -1780.85 q^{85} -57.7731 q^{86} +21.0499 q^{87} +48.2058 q^{88} -1077.25 q^{89} -38.3044 q^{90} -1740.75 q^{91} -591.854 q^{92} -481.554 q^{93} +90.6854 q^{94} -10.5989 q^{95} +156.518 q^{96} +393.379 q^{97} -34.5266 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 4 q^{2} - 117 q^{3} + 182 q^{4} + 5 q^{5} - 12 q^{6} + 77 q^{7} + 27 q^{8} + 351 q^{9}+O(q^{10}) $ 39 * q + 4 * q^2 - 117 * q^3 + 182 * q^4 + 5 * q^5 - 12 * q^6 + 77 * q^7 + 27 * q^8 + 351 * q^9	\( 39 q + 4 q^{2} - 117 q^{3} + 182 q^{4} + 5 q^{5} - 12 q^{6} + 77 q^{7} + 27 q^{8} + 351 q^{9} + 95 q^{10} + 429 q^{11} - 546 q^{12} + 169 q^{13} + 46 q^{14} - 15 q^{15} + 822 q^{16} + 294 q^{17} + 36 q^{18} + 259 q^{19} + 426 q^{20} - 231 q^{21} + 44 q^{22} + 177 q^{23} - 81 q^{24} + 1388 q^{25} + 695 q^{26} - 1053 q^{27} + 1104 q^{28} - 18 q^{29} - 285 q^{30} + 422 q^{31} + 55 q^{32} - 1287 q^{33} + 364 q^{34} + 906 q^{35} + 1638 q^{36} + 424 q^{37} + 9 q^{38} - 507 q^{39} + 1067 q^{40} + 16 q^{41} - 138 q^{42} + 1013 q^{43} + 2002 q^{44} + 45 q^{45} + 9 q^{46} + 1615 q^{47} - 2466 q^{48} + 2024 q^{49} - 1342 q^{50} - 882 q^{51} + 1298 q^{52} - 541 q^{53} - 108 q^{54} + 55 q^{55} - 161 q^{56} - 777 q^{57} + 1061 q^{58} + 1019 q^{59} - 1278 q^{60} + 2379 q^{61} + 879 q^{62} + 693 q^{63} + 1055 q^{64} - 1134 q^{65} - 132 q^{66} + 1917 q^{67} + 3526 q^{68} - 531 q^{69} + 758 q^{70} - 479 q^{71} + 243 q^{72} + 3319 q^{73} - 332 q^{74} - 4164 q^{75} + 692 q^{76} + 847 q^{77} - 2085 q^{78} + 651 q^{79} + 2973 q^{80} + 3159 q^{81} - 826 q^{82} + 4001 q^{83} - 3312 q^{84} + 3595 q^{85} - 6247 q^{86} + 54 q^{87} + 297 q^{88} - 1625 q^{89} + 855 q^{90} + 2048 q^{91} - 507 q^{92} - 1266 q^{93} - 2436 q^{94} + 1400 q^{95} - 165 q^{96} + 2176 q^{97} - 1396 q^{98} + 3861 q^{99}+O(q^{100}) \) 39 * q + 4 * q^2 - 117 * q^3 + 182 * q^4 + 5 * q^5 - 12 * q^6 + 77 * q^7 + 27 * q^8 + 351 * q^9 + 95 * q^10 + 429 * q^11 - 546 * q^12 + 169 * q^13 + 46 * q^14 - 15 * q^15 + 822 * q^16 + 294 * q^17 + 36 * q^18 + 259 * q^19 + 426 * q^20 - 231 * q^21 + 44 * q^22 + 177 * q^23 - 81 * q^24 + 1388 * q^25 + 695 * q^26 - 1053 * q^27 + 1104 * q^28 - 18 * q^29 - 285 * q^30 + 422 * q^31 + 55 * q^32 - 1287 * q^33 + 364 * q^34 + 906 * q^35 + 1638 * q^36 + 424 * q^37 + 9 * q^38 - 507 * q^39 + 1067 * q^40 + 16 * q^41 - 138 * q^42 + 1013 * q^43 + 2002 * q^44 + 45 * q^45 + 9 * q^46 + 1615 * q^47 - 2466 * q^48 + 2024 * q^49 - 1342 * q^50 - 882 * q^51 + 1298 * q^52 - 541 * q^53 - 108 * q^54 + 55 * q^55 - 161 * q^56 - 777 * q^57 + 1061 * q^58 + 1019 * q^59 - 1278 * q^60 + 2379 * q^61 + 879 * q^62 + 693 * q^63 + 1055 * q^64 - 1134 * q^65 - 132 * q^66 + 1917 * q^67 + 3526 * q^68 - 531 * q^69 + 758 * q^70 - 479 * q^71 + 243 * q^72 + 3319 * q^73 - 332 * q^74 - 4164 * q^75 + 692 * q^76 + 847 * q^77 - 2085 * q^78 + 651 * q^79 + 2973 * q^80 + 3159 * q^81 - 826 * q^82 + 4001 * q^83 - 3312 * q^84 + 3595 * q^85 - 6247 * q^86 + 54 * q^87 + 297 * q^88 - 1625 * q^89 + 855 * q^90 + 2048 * q^91 - 507 * q^92 - 1266 * q^93 - 2436 * q^94 + 1400 * q^95 - 165 * q^96 + 2176 * q^97 - 1396 * q^98 + 3861 * 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 $

$2$	−0.275199	−0.0972975	−0.0486488	−	0.998816i	$-0.515491\pi$
$2$	−0.275199	−0.0972975	−0.0486488	+	0.998816i	$0.515491\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−7.92427	−0.990533
$5$	15.4654	1.38326	0.691631	−	0.722251i	$-0.256892\pi$
$5$	15.4654	1.38326	0.691631	+	0.722251i	$0.256892\pi$
$6$	0.825597	0.0561748
$7$	−21.6439	−1.16866	−0.584332	−	0.811515i	$-0.698643\pi$
$7$	−21.6439	−1.16866	−0.584332	+	0.811515i	$0.698643\pi$
$8$	4.38234	0.193674
$9$	9.00000	0.333333
$10$	−4.25605	−0.134588
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	23.7728	0.571885
$13$	80.4266	1.71587	0.857936	−	0.513757i	$-0.171747\pi$
$13$	80.4266	1.71587	0.857936	+	0.513757i	$0.171747\pi$
$14$	5.95639	0.113708
$15$	−46.3961	−0.798627
$16$	62.1881	0.971689
$17$	−115.151	−1.64284	−0.821419	−	0.570326i	$-0.806817\pi$
$17$	−115.151	−1.64284	−0.821419	+	0.570326i	$0.806817\pi$
$18$	−2.47679	−0.0324325
$19$	−0.685333	−0.00827507	−0.00413753	−	0.999991i	$-0.501317\pi$
$19$	−0.685333	−0.00827507	−0.00413753	+	0.999991i	$0.501317\pi$
$20$	−122.552	−1.37017
$21$	64.9318	0.674728
$22$	−3.02719	−0.0293363
$23$	74.6888	0.677117	0.338558	−	0.940945i	$-0.390061\pi$
$23$	74.6888	0.677117	0.338558	+	0.940945i	$0.390061\pi$
$24$	−13.1470	−0.111818
$25$	114.177	0.913416
$26$	−22.1333	−0.166950
$27$	−27.0000	−0.192450
$28$	171.512	1.15760
$29$	−7.01663	−0.0449295	−0.0224648	−	0.999748i	$-0.507151\pi$
$29$	−7.01663	−0.0449295	−0.0224648	+	0.999748i	$0.507151\pi$
$30$	12.7681	0.0777045
$31$	160.518	0.929997	0.464998	−	0.885312i	$-0.346055\pi$
$31$	160.518	0.929997	0.464998	+	0.885312i	$0.346055\pi$
$32$	−52.1728	−0.288217
$33$	−33.0000	−0.174078
$34$	31.6894	0.159844
$35$	−334.731	−1.61657
$36$	−71.3184	−0.330178
$37$	276.927	1.23045	0.615223	−	0.788353i	$-0.289066\pi$
$37$	276.927	1.23045	0.615223	+	0.788353i	$0.289066\pi$
$38$	0.188603	0.000805144 0
$39$	−241.280	−0.990659
$40$	67.7744	0.267902
$41$	−181.961	−0.693111	−0.346556	−	0.938029i	$-0.612649\pi$
$41$	−181.961	−0.693111	−0.346556	+	0.938029i	$0.612649\pi$
$42$	−17.8692	−0.0656494
$43$	209.932	0.744520	0.372260	−	0.928129i	$-0.378583\pi$
$43$	209.932	0.744520	0.372260	+	0.928129i	$0.378583\pi$
$44$	−87.1669	−0.298657
$45$	139.188	0.461088
$46$	−20.5543	−0.0658818
$47$	−329.527	−1.02269	−0.511345	−	0.859376i	$-0.670852\pi$
$47$	−329.527	−1.02269	−0.511345	+	0.859376i	$0.670852\pi$
$48$	−186.564	−0.561005
$49$	125.460	0.365774
$50$	−31.4214	−0.0888732
$51$	345.453	0.948492
$52$	−637.322	−1.69963
$53$	−208.434	−0.540200	−0.270100	−	0.962832i	$-0.587057\pi$
$53$	−208.434	−0.540200	−0.270100	+	0.962832i	$0.587057\pi$
$54$	7.43037	0.0187249
$55$	170.119	0.417069
$56$	−94.8512	−0.226340
$57$	2.05600	0.00477761
$58$	1.93097	0.00437153
$59$	580.865	1.28173	0.640866	−	0.767652i	$-0.278575\pi$
$59$	580.865	1.28173	0.640866	+	0.767652i	$0.278575\pi$
$60$	367.655	0.791067
$61$	61.0000	0.128037
$61$	61.0000	0.128037
$62$	−44.1744	−0.0904864
$63$	−194.796	−0.389554
$64$	−483.147	−0.943646
$65$	1243.83	2.37350
$66$	9.08157	0.0169373
$67$	−370.415	−0.675423	−0.337711	−	0.941250i	$-0.609653\pi$
$67$	−370.415	−0.675423	−0.337711	+	0.941250i	$0.609653\pi$
$68$	912.487	1.62728
$69$	−224.066	−0.390934
$70$	92.1177	0.157288
$71$	−692.704	−1.15787	−0.578936	−	0.815373i	$-0.696532\pi$
$71$	−692.704	−1.15787	−0.578936	+	0.815373i	$0.696532\pi$
$72$	39.4411	0.0645580
$73$	−691.422	−1.10856	−0.554280	−	0.832331i	$-0.687006\pi$
$73$	−691.422	−1.10856	−0.554280	+	0.832331i	$0.687006\pi$
$74$	−76.2100	−0.119719
$75$	−342.531	−0.527361
$76$	5.43076	0.00819673
$77$	−238.083	−0.352365
$78$	66.4000	0.0963886
$79$	674.867	0.961119	0.480560	−	0.876962i	$-0.340434\pi$
$79$	674.867	0.961119	0.480560	+	0.876962i	$0.340434\pi$
$80$	961.761	1.34410
$81$	81.0000	0.111111
$82$	50.0755	0.0674380
$83$	442.923	0.585748	0.292874	−	0.956151i	$-0.405388\pi$
$83$	442.923	0.585748	0.292874	+	0.956151i	$0.405388\pi$
$84$	−514.537	−0.668341
$85$	−1780.85	−2.27248
$86$	−57.7731	−0.0724399
$87$	21.0499	0.0259401
$88$	48.2058	0.0583949
$89$	−1077.25	−1.28302	−0.641509	−	0.767116i	$-0.721691\pi$
$89$	−1077.25	−1.28302	−0.641509	+	0.767116i	$0.721691\pi$
$90$	−38.3044	−0.0448627
$91$	−1740.75	−2.00528
$92$	−591.854	−0.670707
$93$	−481.554	−0.536934
$94$	90.6854	0.0995052
$95$	−10.5989	−0.0114466
$96$	156.518	0.166402
$97$	393.379	0.411769	0.205884	−	0.978576i	$-0.433993\pi$
$97$	393.379	0.411769	0.205884	+	0.978576i	$0.433993\pi$
$98$	−34.5266	−0.0355889
$99$	99.0000	0.100504
$100$	−904.769	−0.904769
$101$	−149.560	−0.147344	−0.0736720	−	0.997283i	$-0.523472\pi$
$101$	−149.560	−0.147344	−0.0736720	+	0.997283i	$0.523472\pi$
$102$	−95.0683	−0.0922860
$103$	302.298	0.289188	0.144594	−	0.989491i	$-0.453812\pi$
$103$	302.298	0.289188	0.144594	+	0.989491i	$0.453812\pi$
$104$	352.457	0.332320
$105$	1004.19	0.933326
$106$	57.3608	0.0525602
$107$	1645.06	1.48630	0.743148	−	0.669127i	$-0.233332\pi$
$107$	1645.06	1.48630	0.743148	+	0.669127i	$0.233332\pi$
$108$	213.955	0.190628
$109$	−1015.62	−0.892468	−0.446234	−	0.894916i	$-0.647235\pi$
$109$	−1015.62	−0.892468	−0.446234	+	0.894916i	$0.647235\pi$
$110$	−46.8165	−0.0405798
$111$	−830.781	−0.710399
$112$	−1346.00	−1.13558
$113$	−524.683	−0.436797	−0.218398	−	0.975860i	$-0.570083\pi$
$113$	−524.683	−0.436797	−0.218398	+	0.975860i	$0.570083\pi$
$114$	−0.565809	−0.000464850 0
$115$	1155.09	0.936631
$116$	55.6016	0.0445042
$117$	723.839	0.571957
$118$	−159.854	−0.124709
$119$	2492.32	1.91992
$120$	−203.323	−0.154673
$121$	121.000	0.0909091
$122$	−16.7871	−0.0124577
$123$	545.884	0.400168
$124$	−1271.99	−0.921192
$125$	−167.381	−0.119768
$126$	53.6075	0.0379027
$127$	1160.43	0.810801	0.405401	−	0.914139i	$-0.367132\pi$
$127$	1160.43	0.810801	0.405401	+	0.914139i	$0.367132\pi$
$128$	550.344	0.380031
$129$	−629.796	−0.429849
$130$	−342.300	−0.230936
$131$	−327.036	−0.218117	−0.109058	−	0.994035i	$-0.534784\pi$
$131$	−327.036	−0.218117	−0.109058	+	0.994035i	$0.534784\pi$
$132$	261.501	0.172430
$133$	14.8333	0.00967077
$134$	101.938	0.0657170
$135$	−417.564	−0.266209
$136$	−504.631	−0.318175
$137$	−2343.55	−1.46148	−0.730740	−	0.682656i	$-0.760825\pi$
$137$	−2343.55	−1.46148	−0.730740	+	0.682656i	$0.760825\pi$
$138$	61.6628	0.0380369
$139$	1295.73	0.790663	0.395332	−	0.918538i	$-0.370630\pi$
$139$	1295.73	0.790663	0.395332	+	0.918538i	$0.370630\pi$
$140$	2652.50	1.60126
$141$	988.580	0.590450
$142$	190.632	0.112658
$143$	884.693	0.517355
$144$	559.693	0.323896
$145$	−108.515	−0.0621493
$146$	190.279	0.107860
$147$	−376.381	−0.211180
$148$	−2194.44	−1.21880
$149$	1280.54	0.704069	0.352035	−	0.935987i	$-0.385490\pi$
$149$	1280.54	0.704069	0.352035	+	0.935987i	$0.385490\pi$
$150$	94.2642	0.0513109
$151$	3114.06	1.67827	0.839135	−	0.543923i	$-0.183062\pi$
$151$	3114.06	1.67827	0.839135	+	0.543923i	$0.183062\pi$
$152$	−3.00337	−0.00160266
$153$	−1036.36	−0.547612
$154$	65.5203	0.0342843
$155$	2482.47	1.28643
$156$	1911.97	0.981280
$157$	95.9613	0.0487805	0.0243903	−	0.999703i	$-0.492236\pi$
$157$	95.9613	0.0487805	0.0243903	+	0.999703i	$0.492236\pi$
$158$	−185.723	−0.0935145
$159$	625.302	0.311885
$160$	−806.871	−0.398680
$161$	−1616.56	−0.791322
$162$	−22.2911	−0.0108108
$163$	2358.80	1.13347	0.566734	−	0.823901i	$-0.308207\pi$
$163$	2358.80	1.13347	0.566734	+	0.823901i	$0.308207\pi$
$164$	1441.91	0.686550
$165$	−510.357	−0.240795
$166$	−121.892	−0.0569918
$167$	−1628.53	−0.754608	−0.377304	−	0.926089i	$-0.623149\pi$
$167$	−1628.53	−0.754608	−0.377304	+	0.926089i	$0.623149\pi$
$168$	284.553	0.130677
$169$	4271.44	1.94421
$170$	490.088	0.221106
$171$	−6.16800	−0.00275836
$172$	−1663.56	−0.737471
$173$	3637.76	1.59869	0.799347	−	0.600870i	$-0.205179\pi$
$173$	3637.76	1.59869	0.799347	+	0.600870i	$0.205179\pi$
$174$	−5.79291	−0.00252390
$175$	−2471.24	−1.06748
$176$	684.069	0.292975
$177$	−1742.60	−0.740009
$178$	296.459	0.124834
$179$	3661.18	1.52877	0.764384	−	0.644762i	$-0.223043\pi$
$179$	3661.18	1.52877	0.764384	+	0.644762i	$0.223043\pi$
$180$	−1102.96	−0.456723
$181$	−4563.56	−1.87407	−0.937035	−	0.349236i	$-0.886441\pi$
$181$	−4563.56	−1.87407	−0.937035	+	0.349236i	$0.886441\pi$
$182$	479.052	0.195108
$183$	−183.000	−0.0739221
$184$	327.312	0.131140
$185$	4282.77	1.70203
$186$	132.523	0.0522423
$187$	−1266.66	−0.495334
$188$	2611.26	1.01301
$189$	584.387	0.224909
$190$	2.91681	0.00111373
$191$	−2287.31	−0.866511	−0.433256	−	0.901271i	$-0.642635\pi$
$191$	−2287.31	−0.866511	−0.433256	+	0.901271i	$0.642635\pi$
$192$	1449.44	0.544815
$193$	−4101.36	−1.52965	−0.764825	−	0.644238i	$-0.777175\pi$
$193$	−4101.36	−1.52965	−0.764825	+	0.644238i	$0.777175\pi$
$194$	−108.257	−0.0400641
$195$	−3731.48	−1.37034
$196$	−994.182	−0.362311
$197$	3575.81	1.29323	0.646614	−	0.762818i	$-0.276185\pi$
$197$	3575.81	1.29323	0.646614	+	0.762818i	$0.276185\pi$
$198$	−27.2447	−0.00977877
$199$	−378.586	−0.134861	−0.0674303	−	0.997724i	$-0.521480\pi$
$199$	−378.586	−0.134861	−0.0674303	+	0.997724i	$0.521480\pi$
$200$	500.363	0.176905
$201$	1111.24	0.389956
$202$	41.1586	0.0143362
$203$	151.868	0.0525075
$204$	−2737.46	−0.939513
$205$	−2814.09	−0.958755
$206$	−83.1922	−0.0281373
$207$	672.199	0.225706
$208$	5001.58	1.66729
$209$	−7.53867	−0.00249503
$210$	−276.353	−0.0908103
$211$	−1723.65	−0.562374	−0.281187	−	0.959653i	$-0.590728\pi$
$211$	−1723.65	−0.562374	−0.281187	+	0.959653i	$0.590728\pi$
$212$	1651.69	0.535086
$213$	2078.11	0.668497
$214$	−452.718	−0.144613
$215$	3246.67	1.02987
$216$	−118.323	−0.0372726
$217$	−3474.24	−1.08685
$218$	279.498	0.0868349
$219$	2074.27	0.640027
$220$	−1348.07	−0.413121
$221$	−9261.21	−2.81890
$222$	228.630	0.0691200
$223$	−2433.18	−0.730662	−0.365331	−	0.930878i	$-0.619044\pi$
$223$	−2433.18	−0.730662	−0.365331	+	0.930878i	$0.619044\pi$
$224$	1129.23	0.336829
$225$	1027.59	0.304472
$226$	144.392	0.0424992
$227$	685.624	0.200469	0.100235	−	0.994964i	$-0.468041\pi$
$227$	685.624	0.200469	0.100235	+	0.994964i	$0.468041\pi$
$228$	−16.2923	−0.00473238
$229$	1232.00	0.355513	0.177757	−	0.984074i	$-0.443116\pi$
$229$	1232.00	0.355513	0.177757	+	0.984074i	$0.443116\pi$
$230$	−317.879	−0.0911319
$231$	714.250	0.203438
$232$	−30.7493	−0.00870167
$233$	4690.18	1.31873	0.659365	−	0.751823i	$-0.270825\pi$
$233$	4690.18	1.31873	0.659365	+	0.751823i	$0.270825\pi$
$234$	−199.200	−0.0556500
$235$	−5096.25	−1.41465
$236$	−4602.93	−1.26960
$237$	−2024.60	−0.554903
$238$	−685.885	−0.186804
$239$	−1591.45	−0.430722	−0.215361	−	0.976535i	$-0.569093\pi$
$239$	−1591.45	−0.430722	−0.215361	+	0.976535i	$0.569093\pi$
$240$	−2885.28	−0.776017
$241$	4398.95	1.17577	0.587886	−	0.808944i	$-0.299960\pi$
$241$	4398.95	1.17577	0.587886	+	0.808944i	$0.299960\pi$
$242$	−33.2991	−0.00884523
$243$	−243.000	−0.0641500
$244$	−483.380	−0.126825
$245$	1940.29	0.505961
$246$	−150.227	−0.0389354
$247$	−55.1190	−0.0141990
$248$	703.445	0.180116
$249$	−1328.77	−0.338182
$250$	46.0630	0.0116531
$251$	5116.21	1.28658	0.643291	−	0.765622i	$-0.277568\pi$
$251$	5116.21	1.28658	0.643291	+	0.765622i	$0.277568\pi$
$252$	1543.61	0.385867
$253$	821.577	0.204158
$254$	−319.350	−0.0788889
$255$	5342.55	1.31201
$256$	3713.72	0.906670
$257$	−1466.23	−0.355879	−0.177940	−	0.984041i	$-0.556943\pi$
$257$	−1466.23	−0.355879	−0.177940	+	0.984041i	$0.556943\pi$
$258$	173.319	0.0418232
$259$	−5993.79	−1.43798
$260$	−9856.40	−2.35103
$261$	−63.1497	−0.0149765
$262$	90.0001	0.0212222
$263$	251.879	0.0590553	0.0295276	−	0.999564i	$-0.490600\pi$
$263$	251.879	0.0590553	0.0295276	+	0.999564i	$0.490600\pi$
$264$	−144.617	−0.0337143
$265$	−3223.51	−0.747239
$266$	−4.08211	−0.000940942 0
$267$	3231.76	0.740750
$268$	2935.26	0.669029
$269$	−342.965	−0.0777359	−0.0388679	−	0.999244i	$-0.512375\pi$
$269$	−342.965	−0.0777359	−0.0388679	+	0.999244i	$0.512375\pi$
$270$	114.913	0.0259015
$271$	4047.74	0.907316	0.453658	−	0.891176i	$-0.350119\pi$
$271$	4047.74	0.907316	0.453658	+	0.891176i	$0.350119\pi$
$272$	−7161.03	−1.59633
$273$	5222.25	1.15775
$274$	644.942	0.142198
$275$	1255.95	0.275405
$276$	1775.56	0.387233
$277$	1077.82	0.233791	0.116896	−	0.993144i	$-0.462706\pi$
$277$	1077.82	0.233791	0.116896	+	0.993144i	$0.462706\pi$
$278$	−356.583	−0.0769296
$279$	1444.66	0.309999
$280$	−1466.91	−0.313087
$281$	1032.61	0.219218	0.109609	−	0.993975i	$-0.465040\pi$
$281$	1032.61	0.219218	0.109609	+	0.993975i	$0.465040\pi$
$282$	−272.056	−0.0574493
$283$	5129.32	1.07741	0.538704	−	0.842495i	$-0.318914\pi$
$283$	5129.32	1.07741	0.538704	+	0.842495i	$0.318914\pi$
$284$	5489.17	1.14691
$285$	31.7968	0.00660869
$286$	−243.466	−0.0503373
$287$	3938.36	0.810014
$288$	−469.555	−0.0960723
$289$	8346.76	1.69891
$290$	29.8631	0.00604697
$291$	−1180.14	−0.237735
$292$	5479.01	1.09806
$293$	3670.23	0.731799	0.365900	−	0.930654i	$-0.380761\pi$
$293$	3670.23	0.731799	0.365900	+	0.930654i	$0.380761\pi$
$294$	103.580	0.0205473
$295$	8983.29	1.77297
$296$	1213.59	0.238305
$297$	−297.000	−0.0580259
$298$	−352.405	−0.0685042
$299$	6006.97	1.16185
$300$	2714.31	0.522369
$301$	−4543.76	−0.870093
$302$	−856.987	−0.163292
$303$	448.679	0.0850691
$304$	−42.6196	−0.00804079
$305$	943.386	0.177109
$306$	285.205	0.0532813
$307$	6383.22	1.18668	0.593338	−	0.804953i	$-0.297810\pi$
$307$	6383.22	1.18668	0.593338	+	0.804953i	$0.297810\pi$
$308$	1886.64	0.349029
$309$	−906.895	−0.166963
$310$	−683.173	−0.125166
$311$	−355.645	−0.0648449	−0.0324224	−	0.999474i	$-0.510322\pi$
$311$	−355.645	−0.0648449	−0.0324224	+	0.999474i	$0.510322\pi$
$312$	−1057.37	−0.191865
$313$	9179.72	1.65773	0.828864	−	0.559451i	$-0.188988\pi$
$313$	9179.72	1.65773	0.828864	+	0.559451i	$0.188988\pi$
$314$	−26.4084	−0.00474622
$315$	−3012.58	−0.538856
$316$	−5347.82	−0.952021
$317$	8480.61	1.50258	0.751291	−	0.659971i	$-0.229431\pi$
$317$	8480.61	1.50258	0.751291	+	0.659971i	$0.229431\pi$
$318$	−172.082	−0.0303456
$319$	−77.1829	−0.0135468
$320$	−7472.04	−1.30531
$321$	−4935.17	−0.858113
$322$	444.876	0.0769936
$323$	78.9169	0.0135946
$324$	−641.866	−0.110059
$325$	9182.87	1.56731
$326$	−649.139	−0.110284
$327$	3046.87	0.515266
$328$	−797.416	−0.134238
$329$	7132.26	1.19518
$330$	140.450	0.0234288
$331$	8348.73	1.38637	0.693184	−	0.720761i	$-0.256207\pi$
$331$	8348.73	1.38637	0.693184	+	0.720761i	$0.256207\pi$
$332$	−3509.84	−0.580203
$333$	2492.34	0.410149
$334$	448.170	0.0734215
$335$	−5728.59	−0.934288
$336$	4037.99	0.655626
$337$	1152.23	0.186249	0.0931243	−	0.995654i	$-0.470315\pi$
$337$	1152.23	0.186249	0.0931243	+	0.995654i	$0.470315\pi$
$338$	−1175.50	−0.189167
$339$	1574.05	0.252185
$340$	14111.9	2.25096
$341$	1765.70	0.280405
$342$	1.69743	0.000268381 0
$343$	4708.42	0.741197
$344$	919.994	0.144194
$345$	−3465.26	−0.540764
$346$	−1001.11	−0.155549
$347$	−4010.13	−0.620390	−0.310195	−	0.950673i	$-0.600394\pi$
$347$	−4010.13	−0.620390	−0.310195	+	0.950673i	$0.600394\pi$
$348$	−166.805	−0.0256945
$349$	1682.92	0.258122	0.129061	−	0.991637i	$-0.458804\pi$
$349$	1682.92	0.258122	0.129061	+	0.991637i	$0.458804\pi$
$350$	680.083	0.103863
$351$	−2171.52	−0.330220
$352$	−573.901	−0.0869007
$353$	−11370.3	−1.71438	−0.857192	−	0.514997i	$-0.827793\pi$
$353$	−11370.3	−1.71438	−0.857192	+	0.514997i	$0.827793\pi$
$354$	479.561	0.0720010
$355$	−10712.9	−1.60164
$356$	8536.43	1.27087
$357$	−7476.97	−1.10847
$358$	−1007.55	−0.148745
$359$	−3524.21	−0.518107	−0.259054	−	0.965863i	$-0.583411\pi$
$359$	−3524.21	−0.518107	−0.259054	+	0.965863i	$0.583411\pi$
$360$	609.970	0.0893007
$361$	−6858.53	−0.999932
$362$	1255.89	0.182342
$363$	−363.000	−0.0524864
$364$	13794.2	1.98629
$365$	−10693.1	−1.53343
$366$	50.3614	0.00719244
$367$	8803.49	1.25215	0.626074	−	0.779763i	$-0.284661\pi$
$367$	8803.49	1.25215	0.626074	+	0.779763i	$0.284661\pi$
$368$	4644.75	0.657947
$369$	−1637.65	−0.231037
$370$	−1178.61	−0.165603
$371$	4511.33	0.631312
$372$	3815.96	0.531851
$373$	7860.04	1.09109	0.545546	−	0.838081i	$-0.316322\pi$
$373$	7860.04	1.09109	0.545546	+	0.838081i	$0.316322\pi$
$374$	348.584	0.0481948
$375$	502.142	0.0691480
$376$	−1444.10	−0.198068
$377$	−564.324	−0.0770932
$378$	−160.823	−0.0218831
$379$	10039.9	1.36073	0.680366	−	0.732873i	$-0.261821\pi$
$379$	10039.9	1.36073	0.680366	+	0.732873i	$0.261821\pi$
$380$	83.9887	0.0113382
$381$	−3481.30	−0.468116
$382$	629.464	0.0843094
$383$	11705.2	1.56163	0.780816	−	0.624761i	$-0.214803\pi$
$383$	11705.2	1.56163	0.780816	+	0.624761i	$0.214803\pi$
$384$	−1651.03	−0.219411
$385$	−3682.04	−0.487414
$386$	1128.69	0.148831
$387$	1889.39	0.248173
$388$	−3117.24	−0.407871
$389$	3714.98	0.484209	0.242104	−	0.970250i	$-0.422162\pi$
$389$	3714.98	0.484209	0.242104	+	0.970250i	$0.422162\pi$
$390$	1026.90	0.133331
$391$	−8600.49	−1.11239
$392$	549.810	0.0708409
$393$	981.109	0.125930
$394$	−984.059	−0.125828
$395$	10437.0	1.32948
$396$	−784.502	−0.0995523
$397$	9047.16	1.14374	0.571869	−	0.820345i	$-0.306218\pi$
$397$	9047.16	1.14374	0.571869	+	0.820345i	$0.306218\pi$
$398$	104.186	0.0131216
$399$	−44.5000	−0.00558342
$400$	7100.46	0.887557
$401$	−1266.47	−0.157716	−0.0788582	−	0.996886i	$-0.525127\pi$
$401$	−1266.47	−0.157716	−0.0788582	+	0.996886i	$0.525127\pi$
$402$	−305.813	−0.0379417
$403$	12909.9	1.59575
$404$	1185.15	0.145949
$405$	1252.69	0.153696
$406$	−41.7938	−0.00510885
$407$	3046.20	0.370994
$408$	1513.89	0.183698
$409$	14985.6	1.81171	0.905855	−	0.423587i	$-0.139229\pi$
$409$	14985.6	1.81171	0.905855	+	0.423587i	$0.139229\pi$
$410$	774.436	0.0932845
$411$	7030.64	0.843786
$412$	−2395.49	−0.286450
$413$	−12572.2	−1.49791
$414$	−184.988	−0.0219606
$415$	6849.96	0.810244
$416$	−4196.08	−0.494543
$417$	−3887.18	−0.456490
$418$	2.07463	0.000242760 0
$419$	5565.27	0.648881	0.324441	−	0.945906i	$-0.394824\pi$
$419$	5565.27	0.648881	0.324441	+	0.945906i	$0.394824\pi$
$420$	−7957.50	−0.924491
$421$	−16190.7	−1.87432	−0.937158	−	0.348905i	$-0.886554\pi$
$421$	−16190.7	−1.87432	−0.937158	+	0.348905i	$0.886554\pi$
$422$	474.346	0.0547176
$423$	−2965.74	−0.340897
$424$	−913.429	−0.104623
$425$	−13147.6	−1.50059
$426$	−571.895	−0.0650431
$427$	−1320.28	−0.149632
$428$	−13035.9	−1.47222
$429$	−2654.08	−0.298695
$430$	−893.481	−0.100203
$431$	−1855.41	−0.207360	−0.103680	−	0.994611i	$-0.533062\pi$
$431$	−1855.41	−0.207360	−0.103680	+	0.994611i	$0.533062\pi$
$432$	−1679.08	−0.187002
$433$	5892.34	0.653967	0.326984	−	0.945030i	$-0.393968\pi$
$433$	5892.34	0.653967	0.326984	+	0.945030i	$0.393968\pi$
$434$	956.108	0.105748
$435$	325.544	0.0358819
$436$	8048.06	0.884019
$437$	−51.1867	−0.00560319
$438$	−570.836	−0.0622730
$439$	6647.56	0.722712	0.361356	−	0.932428i	$-0.382314\pi$
$439$	6647.56	0.722712	0.361356	+	0.932428i	$0.382314\pi$
$440$	745.519	0.0807755
$441$	1129.14	0.121925
$442$	2548.67	0.274272
$443$	−6138.16	−0.658314	−0.329157	−	0.944275i	$-0.606765\pi$
$443$	−6138.16	−0.658314	−0.329157	+	0.944275i	$0.606765\pi$
$444$	6583.33	0.703673
$445$	−16660.1	−1.77475
$446$	669.608	0.0710916
$447$	−3841.63	−0.406494
$448$	10457.2	1.10280
$449$	−6278.12	−0.659873	−0.329936	−	0.944003i	$-0.607027\pi$
$449$	−6278.12	−0.659873	−0.329936	+	0.944003i	$0.607027\pi$
$450$	−282.793	−0.0296244
$451$	−2001.57	−0.208981
$452$	4157.73	0.432662
$453$	−9342.19	−0.968950
$454$	−188.683	−0.0195051
$455$	−26921.3	−2.77382
$456$	9.01010	0.000925299 0
$457$	168.672	0.0172651	0.00863255	−	0.999963i	$-0.497252\pi$
$457$	168.672	0.0172651	0.00863255	+	0.999963i	$0.497252\pi$
$458$	−339.044	−0.0345906
$459$	3109.08	0.316164
$460$	−9153.23	−0.927764
$461$	12667.6	1.27980	0.639900	−	0.768458i	$-0.278976\pi$
$461$	12667.6	1.27980	0.639900	+	0.768458i	$0.278976\pi$
$462$	−196.561	−0.0197940
$463$	−9898.40	−0.993559	−0.496780	−	0.867877i	$-0.665484\pi$
$463$	−9898.40	−0.993559	−0.496780	+	0.867877i	$0.665484\pi$
$464$	−436.351	−0.0436575
$465$	−7447.40	−0.742721
$466$	−1290.73	−0.128309
$467$	−18040.9	−1.78765	−0.893826	−	0.448413i	$-0.851989\pi$
$467$	−18040.9	−1.78765	−0.893826	+	0.448413i	$0.851989\pi$
$468$	−5735.90	−0.566542
$469$	8017.23	0.789342
$470$	1402.48	0.137642
$471$	−287.884	−0.0281635
$472$	2545.55	0.248238
$473$	2309.25	0.224481
$474$	557.168	0.0539906
$475$	−78.2494	−0.00755858
$476$	−19749.8	−1.90175
$477$	−1875.91	−0.180067
$478$	437.966	0.0419081
$479$	12886.5	1.22923	0.614614	−	0.788828i	$-0.289312\pi$
$479$	12886.5	1.22923	0.614614	+	0.788828i	$0.289312\pi$
$480$	2420.61	0.230178
$481$	22272.3	2.11129
$482$	−1210.59	−0.114400
$483$	4849.68	0.456870
$484$	−958.836	−0.0900485
$485$	6083.74	0.569584
$486$	66.8733	0.00624164
$487$	−2418.37	−0.225024	−0.112512	−	0.993650i	$-0.535890\pi$
$487$	−2418.37	−0.225024	−0.112512	+	0.993650i	$0.535890\pi$
$488$	267.323	0.0247974
$489$	−7076.40	−0.654409
$490$	−533.966	−0.0492288
$491$	689.445	0.0633691	0.0316845	−	0.999498i	$-0.489913\pi$
$491$	689.445	0.0633691	0.0316845	+	0.999498i	$0.489913\pi$
$492$	−4325.73	−0.396380
$493$	807.972	0.0738119
$494$	15.1687	0.00138152
$495$	1531.07	0.139023
$496$	9982.31	0.903668
$497$	14992.9	1.35316
$498$	365.676	0.0329043
$499$	−21605.1	−1.93823	−0.969115	−	0.246611i	$-0.920683\pi$
$499$	−21605.1	−1.93823	−0.969115	+	0.246611i	$0.920683\pi$
$500$	1326.37	0.118634
$501$	4885.60	0.435673
$502$	−1407.98	−0.125181
$503$	20771.1	1.84122	0.920612	−	0.390477i	$-0.127690\pi$
$503$	20771.1	1.84122	0.920612	+	0.390477i	$0.127690\pi$
$504$	−853.660	−0.0754465
$505$	−2312.99	−0.203815
$506$	−226.097	−0.0198641
$507$	−12814.3	−1.12249
$508$	−9195.58	−0.803125
$509$	9212.35	0.802220	0.401110	−	0.916030i	$-0.368624\pi$
$509$	9212.35	0.802220	0.401110	+	0.916030i	$0.368624\pi$
$510$	−1470.27	−0.127656
$511$	14965.1	1.29553
$512$	−5424.77	−0.468248
$513$	18.5040	0.00159254
$514$	403.505	0.0346262
$515$	4675.15	0.400023
$516$	4990.67	0.425779
$517$	−3624.79	−0.308353
$518$	1649.49	0.139912
$519$	−10913.3	−0.923006
$520$	5450.87	0.459685
$521$	−20217.8	−1.70011	−0.850056	−	0.526693i	$-0.823432\pi$
$521$	−20217.8	−1.70011	−0.850056	+	0.526693i	$0.823432\pi$
$522$	17.3787	0.00145718
$523$	−13611.5	−1.13803	−0.569014	−	0.822328i	$-0.692675\pi$
$523$	−13611.5	−1.13803	−0.569014	+	0.822328i	$0.692675\pi$
$524$	2591.52	0.216052
$525$	7413.73	0.616308
$526$	−69.3169	−0.00574593
$527$	−18483.8	−1.52783
$528$	−2052.21	−0.169149
$529$	−6588.59	−0.541513
$530$	887.105	0.0727045
$531$	5227.79	0.427244
$532$	−117.543	−0.00957922
$533$	−14634.5	−1.18929
$534$	−889.376	−0.0720732
$535$	25441.4	2.05594
$536$	−1623.28	−0.130812
$537$	−10983.5	−0.882634
$538$	94.3836	0.00756351
$539$	1380.06	0.110285
$540$	3308.89	0.263689
$541$	9850.91	0.782853	0.391427	−	0.920209i	$-0.371982\pi$
$541$	9850.91	0.782853	0.391427	+	0.920209i	$0.371982\pi$
$542$	−1113.93	−0.0882796
$543$	13690.7	1.08199
$544$	6007.76	0.473493
$545$	−15707.0	−1.23452
$546$	−1437.16	−0.112646
$547$	−18566.5	−1.45127	−0.725635	−	0.688080i	$-0.758454\pi$
$547$	−18566.5	−1.45127	−0.725635	+	0.688080i	$0.758454\pi$
$548$	18570.9	1.44764
$549$	549.000	0.0426790
$550$	−345.635	−0.0267963
$551$	4.80873	0.000371795 0
$552$	−981.935	−0.0757137
$553$	−14606.8	−1.12322
$554$	−296.616	−0.0227473
$555$	−12848.3	−0.982668
$556$	−10267.7	−0.783178
$557$	−15504.0	−1.17940	−0.589700	−	0.807623i	$-0.700754\pi$
$557$	−15504.0	−1.17940	−0.589700	+	0.807623i	$0.700754\pi$
$558$	−397.570	−0.0301621
$559$	16884.1	1.27750
$560$	−20816.3	−1.57080
$561$	3799.98	0.285981
$562$	−284.173	−0.0213294
$563$	16008.5	1.19836	0.599182	−	0.800613i	$-0.295493\pi$
$563$	16008.5	1.19836	0.599182	+	0.800613i	$0.295493\pi$
$564$	−7833.77	−0.584860
$565$	−8114.41	−0.604205
$566$	−1411.58	−0.104829
$567$	−1753.16	−0.129851
$568$	−3035.67	−0.224250
$569$	−13945.6	−1.02747	−0.513735	−	0.857949i	$-0.671738\pi$
$569$	−13945.6	−1.02747	−0.513735	+	0.857949i	$0.671738\pi$
$570$	−8.75044	−0.000643010 0
$571$	−8333.25	−0.610745	−0.305373	−	0.952233i	$-0.598781\pi$
$571$	−8333.25	−0.610745	−0.305373	+	0.952233i	$0.598781\pi$
$572$	−7010.54	−0.512457
$573$	6861.92	0.500280
$574$	−1083.83	−0.0788123
$575$	8527.75	0.618490
$576$	−4348.32	−0.314549
$577$	−5890.33	−0.424987	−0.212494	−	0.977162i	$-0.568158\pi$
$577$	−5890.33	−0.424987	−0.212494	+	0.977162i	$0.568158\pi$
$578$	−2297.02	−0.165300
$579$	12304.1	0.883144
$580$	859.899	0.0615610
$581$	−9586.60	−0.684542
$582$	324.772	0.0231310
$583$	−2292.77	−0.162877
$584$	−3030.05	−0.214699
$585$	11194.4	0.791167
$586$	−1010.04	−0.0712022
$587$	19124.7	1.34474	0.672369	−	0.740216i	$-0.265277\pi$
$587$	19124.7	1.34474	0.672369	+	0.740216i	$0.265277\pi$
$588$	2982.55	0.209180
$589$	−110.008	−0.00769578
$590$	−2472.19	−0.172506
$591$	−10727.4	−0.746645
$592$	17221.6	1.19561
$593$	15427.0	1.06832	0.534158	−	0.845385i	$-0.320629\pi$
$593$	15427.0	1.06832	0.534158	+	0.845385i	$0.320629\pi$
$594$	81.7341	0.00564577
$595$	38544.7	2.65576
$596$	−10147.4	−0.697404
$597$	1135.76	0.0778618
$598$	−1653.11	−0.113045
$599$	21592.8	1.47289	0.736443	−	0.676500i	$-0.236504\pi$
$599$	21592.8	1.47289	0.736443	+	0.676500i	$0.236504\pi$
$600$	−1501.09	−0.102136
$601$	−144.252	−0.00979061	−0.00489531	−	0.999988i	$-0.501558\pi$
$601$	−144.252	−0.00979061	−0.00489531	+	0.999988i	$0.501558\pi$
$602$	1250.44	0.0846579
$603$	−3333.73	−0.225141
$604$	−24676.7	−1.66238
$605$	1871.31	0.125751
$606$	−123.476	−0.00827701
$607$	13509.0	0.903319	0.451660	−	0.892190i	$-0.350832\pi$
$607$	13509.0	0.903319	0.451660	+	0.892190i	$0.350832\pi$
$608$	35.7558	0.00238501
$609$	−455.603	−0.0303152
$610$	−259.619	−0.0172322
$611$	−26502.7	−1.75480
$612$	8212.39	0.542428
$613$	4122.05	0.271595	0.135798	−	0.990737i	$-0.456640\pi$
$613$	4122.05	0.271595	0.135798	+	0.990737i	$0.456640\pi$
$614$	−1756.66	−0.115461
$615$	8442.28	0.553538
$616$	−1043.36	−0.0682440
$617$	4837.09	0.315614	0.157807	−	0.987470i	$-0.449558\pi$
$617$	4837.09	0.315614	0.157807	+	0.987470i	$0.449558\pi$
$618$	249.577	0.0162451
$619$	1815.99	0.117917	0.0589585	−	0.998260i	$-0.481222\pi$
$619$	1815.99	0.117917	0.0589585	+	0.998260i	$0.481222\pi$
$620$	−19671.7	−1.27425
$621$	−2016.60	−0.130311
$622$	97.8730	0.00630925
$623$	23316.0	1.49941
$624$	−15004.7	−0.962612
$625$	−16860.7	−1.07909
$626$	−2526.25	−0.161293
$627$	22.6160	0.00144050
$628$	−760.423	−0.0483187
$629$	−31888.4	−2.02142
$630$	829.059	0.0524294
$631$	−249.448	−0.0157375	−0.00786874	−	0.999969i	$-0.502505\pi$
$631$	−249.448	−0.0157375	−0.00786874	+	0.999969i	$0.502505\pi$
$632$	2957.50	0.186144
$633$	5170.95	0.324687
$634$	−2333.86	−0.146198
$635$	17946.5	1.12155
$636$	−4955.06	−0.308932
$637$	10090.4	0.627621
$638$	21.2407	0.00131807
$639$	−6234.34	−0.385957
$640$	8511.27	0.525683
$641$	−1761.69	−0.108553	−0.0542764	−	0.998526i	$-0.517285\pi$
$641$	−1761.69	−0.108553	−0.0542764	+	0.998526i	$0.517285\pi$
$642$	1358.15	0.0834923
$643$	−25240.6	−1.54804	−0.774022	−	0.633159i	$-0.781758\pi$
$643$	−25240.6	−1.54804	−0.774022	+	0.633159i	$0.781758\pi$
$644$	12810.1	0.783830
$645$	−9740.02	−0.594594
$646$	−21.7178	−0.00132272
$647$	−12677.8	−0.770351	−0.385176	−	0.922843i	$-0.625859\pi$
$647$	−12677.8	−0.770351	−0.385176	+	0.922843i	$0.625859\pi$
$648$	354.970	0.0215193
$649$	6389.52	0.386457
$650$	−2527.12	−0.152495
$651$	10422.7	0.627495
$652$	−18691.8	−1.12274
$653$	−13929.8	−0.834784	−0.417392	−	0.908726i	$-0.637056\pi$
$653$	−13929.8	−0.834784	−0.417392	+	0.908726i	$0.637056\pi$
$654$	−838.495	−0.0501341
$655$	−5057.73	−0.301713
$656$	−11315.8	−0.673489
$657$	−6222.80	−0.369520
$658$	−1962.79	−0.116288
$659$	−2251.64	−0.133098	−0.0665488	−	0.997783i	$-0.521199\pi$
$659$	−2251.64	−0.133098	−0.0665488	+	0.997783i	$0.521199\pi$
$660$	4044.20	0.238516
$661$	−66.9799	−0.00394133	−0.00197066	−	0.999998i	$-0.500627\pi$
$661$	−66.9799	−0.00394133	−0.00197066	+	0.999998i	$0.500627\pi$
$662$	−2297.56	−0.134890
$663$	27783.6	1.62749
$664$	1941.04	0.113444
$665$	229.402	0.0133772
$666$	−685.890	−0.0399065
$667$	−524.064	−0.0304225
$668$	12904.9	0.747465
$669$	7299.54	0.421848
$670$	1576.50	0.0909039
$671$	671.000	0.0386046
$672$	−3387.68	−0.194468
$673$	30230.4	1.73150	0.865748	−	0.500481i	$-0.166843\pi$
$673$	30230.4	1.73150	0.865748	+	0.500481i	$0.166843\pi$
$674$	−317.092	−0.0181215
$675$	−3082.78	−0.175787
$676$	−33848.0	−1.92581
$677$	−33386.2	−1.89532	−0.947662	−	0.319275i	$-0.896561\pi$
$677$	−33386.2	−1.89532	−0.947662	+	0.319275i	$0.896561\pi$
$678$	−433.177	−0.0245370
$679$	−8514.27	−0.481219
$680$	−7804.30	−0.440119
$681$	−2056.87	−0.115741
$682$	−485.918	−0.0272827
$683$	−18804.8	−1.05351	−0.526755	−	0.850017i	$-0.676591\pi$
$683$	−18804.8	−1.05351	−0.526755	+	0.850017i	$0.676591\pi$
$684$	48.8769	0.00273224
$685$	−36243.8	−2.02161
$686$	−1295.75	−0.0721166
$687$	−3695.99	−0.205256
$688$	13055.3	0.723442
$689$	−16763.6	−0.926914
$690$	953.637	0.0526150
$691$	−4546.19	−0.250283	−0.125141	−	0.992139i	$-0.539938\pi$
$691$	−4546.19	−0.250283	−0.125141	+	0.992139i	$0.539938\pi$
$692$	−28826.6	−1.58356
$693$	−2142.75	−0.117455
$694$	1103.58	0.0603624
$695$	20038.9	1.09370
$696$	92.2478	0.00502391
$697$	20953.0	1.13867
$698$	−463.137	−0.0251146
$699$	−14070.5	−0.761369
$700$	19582.8	1.05737
$701$	6042.29	0.325555	0.162778	−	0.986663i	$-0.447955\pi$
$701$	6042.29	0.325555	0.162778	+	0.986663i	$0.447955\pi$
$702$	597.600	0.0321295
$703$	−189.787	−0.0101820
$704$	−5314.62	−0.284520
$705$	15288.7	0.816748
$706$	3129.08	0.166805
$707$	3237.06	0.172195
$708$	13808.8	0.733003
$709$	19128.5	1.01324	0.506619	−	0.862170i	$-0.330895\pi$
$709$	19128.5	1.01324	0.506619	+	0.862170i	$0.330895\pi$
$710$	2948.18	0.155836
$711$	6073.80	0.320373
$712$	−4720.89	−0.248487
$713$	11988.9	0.629716
$714$	2057.65	0.107851
$715$	13682.1	0.715638
$716$	−29012.1	−1.51429
$717$	4774.35	0.248677
$718$	969.858	0.0504105
$719$	−1256.04	−0.0651494	−0.0325747	−	0.999469i	$-0.510371\pi$
$719$	−1256.04	−0.0651494	−0.0325747	+	0.999469i	$0.510371\pi$
$720$	8655.85	0.448034
$721$	−6542.93	−0.337963
$722$	1887.46	0.0972909
$723$	−13196.8	−0.678833
$724$	36162.8	1.85633
$725$	−801.138	−0.0410393
$726$	99.8972	0.00510680
$727$	28026.5	1.42977	0.714887	−	0.699240i	$-0.246478\pi$
$727$	28026.5	1.42977	0.714887	+	0.699240i	$0.246478\pi$
$728$	−7628.56	−0.388370
$729$	729.000	0.0370370
$730$	2942.72	0.149199
$731$	−24173.9	−1.22312
$732$	1450.14	0.0732223
$733$	3097.90	0.156103	0.0780516	−	0.996949i	$-0.475130\pi$
$733$	3097.90	0.156103	0.0780516	+	0.996949i	$0.475130\pi$
$734$	−2422.71	−0.121831
$735$	−5820.87	−0.292117
$736$	−3896.73	−0.195157
$737$	−4074.56	−0.203648
$738$	450.680	0.0224793
$739$	−27538.1	−1.37078	−0.685390	−	0.728176i	$-0.740368\pi$
$739$	−27538.1	−1.37078	−0.685390	+	0.728176i	$0.740368\pi$
$740$	−33937.8	−1.68592
$741$	165.357	0.00819777
$742$	−1241.51	−0.0614251
$743$	4213.88	0.208065	0.104032	−	0.994574i	$-0.466825\pi$
$743$	4213.88	0.208065	0.104032	+	0.994574i	$0.466825\pi$
$744$	−2110.33	−0.103990
$745$	19804.1	0.973913
$746$	−2163.07	−0.106161
$747$	3986.31	0.195249
$748$	10037.4	0.490645
$749$	−35605.5	−1.73698
$750$	−138.189	−0.00672793
$751$	−12333.6	−0.599280	−0.299640	−	0.954052i	$-0.596867\pi$
$751$	−12333.6	−0.599280	−0.299640	+	0.954052i	$0.596867\pi$
$752$	−20492.6	−0.993736
$753$	−15348.6	−0.742809
$754$	155.301	0.00750098
$755$	48160.1	2.32149
$756$	−4630.83	−0.222780
$757$	−791.758	−0.0380144	−0.0190072	−	0.999819i	$-0.506051\pi$
$757$	−791.758	−0.0380144	−0.0190072	+	0.999819i	$0.506051\pi$
$758$	−2762.98	−0.132396
$759$	−2464.73	−0.117871
$760$	−46.4481	−0.00221691
$761$	−12314.7	−0.586604	−0.293302	−	0.956020i	$-0.594754\pi$
$761$	−12314.7	−0.586604	−0.293302	+	0.956020i	$0.594754\pi$
$762$	958.050	0.0455466
$763$	21982.1	1.04299
$764$	18125.2	0.858308
$765$	−16027.7	−0.757492
$766$	−3221.25	−0.151943
$767$	46717.0	2.19929
$768$	−11141.2	−0.523466
$769$	−19970.9	−0.936503	−0.468251	−	0.883595i	$-0.655116\pi$
$769$	−19970.9	−0.936503	−0.468251	+	0.883595i	$0.655116\pi$
$770$	1013.29	0.0474242
$771$	4398.69	0.205467
$772$	32500.3	1.51517
$773$	20745.5	0.965282	0.482641	−	0.875818i	$-0.339678\pi$
$773$	20745.5	0.965282	0.482641	+	0.875818i	$0.339678\pi$
$774$	−519.958	−0.0241466
$775$	18327.5	0.849474
$776$	1723.92	0.0797489
$777$	17981.4	0.830217
$778$	−1022.36	−0.0471123
$779$	124.704	0.00573554
$780$	29569.2	1.35737
$781$	−7619.75	−0.349111
$782$	2366.85	0.108233
$783$	189.449	0.00864669
$784$	7802.15	0.355418
$785$	1484.07	0.0674763
$786$	−270.000	−0.0122527
$787$	−34164.2	−1.54742	−0.773712	−	0.633538i	$-0.781602\pi$
$787$	−34164.2	−1.54742	−0.773712	+	0.633538i	$0.781602\pi$
$788$	−28335.7	−1.28098
$789$	−755.637	−0.0340956
$790$	−2872.26	−0.129355
$791$	11356.2	0.510468
$792$	433.852	0.0194650
$793$	4906.02	0.219695
$794$	−2489.77	−0.111283
$795$	9670.52	0.431419
$796$	3000.02	0.133584
$797$	−9651.82	−0.428965	−0.214482	−	0.976728i	$-0.568806\pi$
$797$	−9651.82	−0.428965	−0.214482	+	0.976728i	$0.568806\pi$
$798$	12.2463	0.000543253 0
$799$	37945.3	1.68011
$800$	−5956.94	−0.263262
$801$	−9695.27	−0.427672
$802$	348.530	0.0153454
$803$	−7605.64	−0.334243
$804$	−8805.79	−0.386264
$805$	−25000.7	−1.09461
$806$	−3552.80	−0.155263
$807$	1028.90	0.0448808
$808$	−655.421	−0.0285367
$809$	−22584.1	−0.981477	−0.490739	−	0.871307i	$-0.663273\pi$
$809$	−22584.1	−0.981477	−0.490739	+	0.871307i	$0.663273\pi$
$810$	−344.740	−0.0149542
$811$	−29392.3	−1.27263	−0.636315	−	0.771429i	$-0.719542\pi$
$811$	−29392.3	−1.27263	−0.636315	+	0.771429i	$0.719542\pi$
$812$	−1203.44	−0.0520104
$813$	−12143.2	−0.523839
$814$	−838.310	−0.0360968
$815$	36479.7	1.56789
$816$	21483.1	0.921640
$817$	−143.874	−0.00616095
$818$	−4124.02	−0.176275
$819$	−15666.7	−0.668425
$820$	22299.6	0.949679
$821$	−8510.66	−0.361783	−0.180892	−	0.983503i	$-0.557898\pi$
$821$	−8510.66	−0.361783	−0.180892	+	0.983503i	$0.557898\pi$
$822$	−1934.83	−0.0820983
$823$	25320.3	1.07243	0.536215	−	0.844081i	$-0.319854\pi$
$823$	25320.3	1.07243	0.536215	+	0.844081i	$0.319854\pi$
$824$	1324.77	0.0560082
$825$	−3767.84	−0.159005
$826$	3459.86	0.145743
$827$	31102.7	1.30780	0.653898	−	0.756583i	$-0.273133\pi$
$827$	31102.7	1.30780	0.653898	+	0.756583i	$0.273133\pi$
$828$	−5326.68	−0.223569
$829$	39532.5	1.65624	0.828118	−	0.560554i	$-0.189412\pi$
$829$	39532.5	1.65624	0.828118	+	0.560554i	$0.189412\pi$
$830$	−1885.10	−0.0788347
$831$	−3233.47	−0.134979
$832$	−38857.9	−1.61918
$833$	−14446.9	−0.600907
$834$	1069.75	0.0444153
$835$	−25185.8	−1.04382
$836$	59.7384	0.00247141
$837$	−4333.99	−0.178978
$838$	−1531.56	−0.0631345
$839$	9297.04	0.382562	0.191281	−	0.981535i	$-0.438736\pi$
$839$	9297.04	0.382562	0.191281	+	0.981535i	$0.438736\pi$
$840$	4400.72	0.180761
$841$	−24339.8	−0.997981
$842$	4455.67	0.182366
$843$	−3097.83	−0.126566
$844$	13658.6	0.557050
$845$	66059.3	2.68936
$846$	816.169	0.0331684
$847$	−2618.92	−0.106242
$848$	−12962.1	−0.524907
$849$	−15388.0	−0.622042
$850$	3618.21	0.146004
$851$	20683.3	0.833156
$852$	−16467.5	−0.662169
$853$	−11289.0	−0.453139	−0.226570	−	0.973995i	$-0.572751\pi$
$853$	−11289.0	−0.453139	−0.226570	+	0.973995i	$0.572751\pi$
$854$	363.340	0.0145588
$855$	−95.3903	−0.00381553
$856$	7209.20	0.287857
$857$	2888.31	0.115126	0.0575629	−	0.998342i	$-0.481667\pi$
$857$	2888.31	0.115126	0.0575629	+	0.998342i	$0.481667\pi$
$858$	730.399	0.0290623
$859$	−28790.8	−1.14357	−0.571787	−	0.820402i	$-0.693750\pi$
$859$	−28790.8	−1.14357	−0.571787	+	0.820402i	$0.693750\pi$
$860$	−25727.5	−1.02012
$861$	−11815.1	−0.467662
$862$	510.607	0.0201756
$863$	36872.1	1.45439	0.727196	−	0.686430i	$-0.240823\pi$
$863$	36872.1	1.45439	0.727196	+	0.686430i	$0.240823\pi$
$864$	1408.67	0.0554674
$865$	56259.3	2.21141
$866$	−1621.57	−0.0636294
$867$	−25040.3	−0.980868
$868$	27530.8	1.07656
$869$	7423.53	0.289788
$870$	−89.5894	−0.00349122
$871$	−29791.2	−1.15894
$872$	−4450.80	−0.172848
$873$	3540.41	0.137256
$874$	14.0865	0.000545176 0
$875$	3622.78	0.139968
$876$	−16437.0	−0.633968
$877$	44292.9	1.70543	0.852716	−	0.522374i	$-0.174954\pi$
$877$	44292.9	1.70543	0.852716	+	0.522374i	$0.174954\pi$
$878$	−1829.40	−0.0703181
$879$	−11010.7	−0.422504
$880$	10579.4	0.405262
$881$	−9548.62	−0.365155	−0.182577	−	0.983192i	$-0.558444\pi$
$881$	−9548.62	−0.365155	−0.182577	+	0.983192i	$0.558444\pi$
$882$	−310.739	−0.0118630
$883$	5303.58	0.202129	0.101064	−	0.994880i	$-0.467775\pi$
$883$	5303.58	0.202129	0.101064	+	0.994880i	$0.467775\pi$
$884$	73388.3	2.79221
$885$	−26949.9	−1.02363
$886$	1689.22	0.0640523
$887$	−12202.9	−0.461932	−0.230966	−	0.972962i	$-0.574189\pi$
$887$	−12202.9	−0.461932	−0.230966	+	0.972962i	$0.574189\pi$
$888$	−3640.77	−0.137586
$889$	−25116.3	−0.947553
$890$	4584.84	0.172679
$891$	891.000	0.0335013
$892$	19281.2	0.723745
$893$	225.836	0.00846282
$894$	1057.21	0.0395509
$895$	56621.4	2.11469
$896$	−11911.6	−0.444129
$897$	−18020.9	−0.670792
$898$	1727.73	0.0642040
$899$	−1126.30	−0.0417843
$900$	−8142.92	−0.301590
$901$	24001.4	0.887461
$902$	550.831	0.0203333
$903$	13631.3	0.502348
$904$	−2299.34	−0.0845962
$905$	−70577.0	−2.59233
$906$	2570.96	0.0942764
$907$	8391.83	0.307217	0.153609	−	0.988132i	$-0.450910\pi$
$907$	8391.83	0.307217	0.153609	+	0.988132i	$0.450910\pi$
$908$	−5433.07	−0.198571
$909$	−1346.04	−0.0491146
$910$	7408.71	0.269886
$911$	49698.0	1.80743	0.903716	−	0.428133i	$-0.140829\pi$
$911$	49698.0	1.80743	0.903716	+	0.428133i	$0.140829\pi$
$912$	127.859	0.00464235
$913$	4872.15	0.176610
$914$	−46.4184	−0.00167985
$915$	−2830.16	−0.102254
$916$	−9762.66	−0.352148
$917$	7078.36	0.254905
$918$	−855.615	−0.0307620
$919$	10193.4	0.365887	0.182944	−	0.983123i	$-0.441437\pi$
$919$	10193.4	0.365887	0.182944	+	0.983123i	$0.441437\pi$
$920$	5061.99	0.181401
$921$	−19149.7	−0.685128
$922$	−3486.10	−0.124521
$923$	−55711.9	−1.98676
$924$	−5659.91	−0.201512
$925$	31618.7	1.12391
$926$	2724.03	0.0966708
$927$	2720.69	0.0963960
$928$	366.077	0.0129494
$929$	−17609.1	−0.621891	−0.310946	−	0.950428i	$-0.600646\pi$
$929$	−17609.1	−0.621891	−0.310946	+	0.950428i	$0.600646\pi$
$930$	2049.52	0.0722649
$931$	−85.9822	−0.00302680
$932$	−37166.3	−1.30625
$933$	1066.93	0.0374382
$934$	4964.84	0.173934
$935$	−19589.4	−0.685177
$936$	3172.11	0.110773
$937$	951.176	0.0331628	0.0165814	−	0.999863i	$-0.494722\pi$
$937$	951.176	0.0331628	0.0165814	+	0.999863i	$0.494722\pi$
$938$	−2206.33	−0.0768010
$939$	−27539.2	−0.957089
$940$	40384.0	1.40126
$941$	14242.7	0.493409	0.246705	−	0.969091i	$-0.420652\pi$
$941$	14242.7	0.493409	0.246705	+	0.969091i	$0.420652\pi$
$942$	79.2253	0.00274023
$943$	−13590.5	−0.469317
$944$	36122.9	1.24545
$945$	9037.74	0.311109
$946$	−635.504	−0.0218415
$947$	503.189	0.0172666	0.00863329	−	0.999963i	$-0.497252\pi$
$947$	503.189	0.0172666	0.00863329	+	0.999963i	$0.497252\pi$
$948$	16043.5	0.549649
$949$	−55608.7	−1.90214
$950$	21.5341	0.000735431 0
$951$	−25441.8	−0.867516
$952$	10922.2	0.371839
$953$	−13285.2	−0.451575	−0.225787	−	0.974177i	$-0.572495\pi$
$953$	−13285.2	−0.451575	−0.225787	+	0.974177i	$0.572495\pi$
$954$	516.247	0.0175201
$955$	−35374.0	−1.19861
$956$	12611.1	0.426644
$957$	231.549	0.00782122
$958$	−3546.36	−0.119601
$959$	50723.6	1.70798
$960$	22416.1	0.753622
$961$	−4024.96	−0.135106
$962$	−6129.31	−0.205423
$963$	14805.5	0.495432
$964$	−34858.4	−1.16464
$965$	−63429.0	−2.11591
$966$	−1334.63	−0.0444523
$967$	41569.0	1.38239	0.691194	−	0.722669i	$-0.257085\pi$
$967$	41569.0	1.38239	0.691194	+	0.722669i	$0.257085\pi$
$968$	530.263	0.0176067
$969$	−236.751	−0.00784884
$970$	−1674.24	−0.0554191
$971$	45835.0	1.51484	0.757422	−	0.652925i	$-0.226458\pi$
$971$	45835.0	1.51484	0.757422	+	0.652925i	$0.226458\pi$
$972$	1925.60	0.0635427
$973$	−28044.7	−0.924019
$974$	665.532	0.0218943
$975$	−27548.6	−0.904884
$976$	3793.47	0.124412
$977$	9991.29	0.327175	0.163587	−	0.986529i	$-0.447693\pi$
$977$	9991.29	0.327175	0.163587	+	0.986529i	$0.447693\pi$
$978$	1947.42	0.0636723
$979$	−11849.8	−0.386844
$980$	−15375.4	−0.501172
$981$	−9140.60	−0.297489
$982$	−189.735	−0.00616565
$983$	−32456.1	−1.05309	−0.526545	−	0.850147i	$-0.676513\pi$
$983$	−32456.1	−1.05309	−0.526545	+	0.850147i	$0.676513\pi$
$984$	2392.25	0.0775021
$985$	55301.1	1.78887
$986$	−222.353	−0.00718171
$987$	−21396.8	−0.690037
$988$	436.778	0.0140645
$989$	15679.6	0.504127
$990$	−421.349	−0.0135266
$991$	−2064.90	−0.0661894	−0.0330947	−	0.999452i	$-0.510536\pi$
$991$	−2064.90	−0.0661894	−0.0330947	+	0.999452i	$0.510536\pi$
$992$	−8374.68	−0.268041
$993$	−25046.2	−0.800420
$994$	−4126.02	−0.131659
$995$	−5854.96	−0.186548
$996$	10529.5	0.334980
$997$	−32530.7	−1.03336	−0.516678	−	0.856180i	$-0.672832\pi$
$997$	−32530.7	−1.03336	−0.516678	+	0.856180i	$0.672832\pi$
$998$	5945.70	0.188585
$999$	−7477.03	−0.236800

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.g.1.19	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.g.1.19	✓	39	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:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q-0.275199 q^{2} -3.00000 q^{3} -7.92427 q^{4} +15.4654 q^{5} +0.825597 q^{6} -21.6439 q^{7} +4.38234 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-0.275199 q^{2} -3.00000 q^{3} -7.92427 q^{4} +15.4654 q^{5} +0.825597 q^{6} -21.6439 q^{7} +4.38234 q^{8} +9.00000 q^{9} -4.25605 q^{10} +11.0000 q^{11} +23.7728 q^{12} +80.4266 q^{13} +5.95639 q^{14} -46.3961 q^{15} +62.1881 q^{16} -115.151 q^{17} -2.47679 q^{18} -0.685333 q^{19} -122.552 q^{20} +64.9318 q^{21} -3.02719 q^{22} +74.6888 q^{23} -13.1470 q^{24} +114.177 q^{25} -22.1333 q^{26} -27.0000 q^{27} +171.512 q^{28} -7.01663 q^{29} +12.7681 q^{30} +160.518 q^{31} -52.1728 q^{32} -33.0000 q^{33} +31.6894 q^{34} -334.731 q^{35} -71.3184 q^{36} +276.927 q^{37} +0.188603 q^{38} -241.280 q^{39} +67.7744 q^{40} -181.961 q^{41} -17.8692 q^{42} +209.932 q^{43} -87.1669 q^{44} +139.188 q^{45} -20.5543 q^{46} -329.527 q^{47} -186.564 q^{48} +125.460 q^{49} -31.4214 q^{50} +345.453 q^{51} -637.322 q^{52} -208.434 q^{53} +7.43037 q^{54} +170.119 q^{55} -94.8512 q^{56} +2.05600 q^{57} +1.93097 q^{58} +580.865 q^{59} +367.655 q^{60} +61.0000 q^{61} -44.1744 q^{62} -194.796 q^{63} -483.147 q^{64} +1243.83 q^{65} +9.08157 q^{66} -370.415 q^{67} +912.487 q^{68} -224.066 q^{69} +92.1177 q^{70} -692.704 q^{71} +39.4411 q^{72} -691.422 q^{73} -76.2100 q^{74} -342.531 q^{75} +5.43076 q^{76} -238.083 q^{77} +66.4000 q^{78} +674.867 q^{79} +961.761 q^{80} +81.0000 q^{81} +50.0755 q^{82} +442.923 q^{83} -514.537 q^{84} -1780.85 q^{85} -57.7731 q^{86} +21.0499 q^{87} +48.2058 q^{88} -1077.25 q^{89} -38.3044 q^{90} -1740.75 q^{91} -591.854 q^{92} -481.554 q^{93} +90.6854 q^{94} -10.5989 q^{95} +156.518 q^{96} +393.379 q^{97} -34.5266 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 4 q^{2} - 117 q^{3} + 182 q^{4} + 5 q^{5} - 12 q^{6} + 77 q^{7} + 27 q^{8} + 351 q^{9}+O(q^{10}) \) 39 * q + 4 * q^2 - 117 * q^3 + 182 * q^4 + 5 * q^5 - 12 * q^6 + 77 * q^7 + 27 * q^8 + 351 * q^9	\( 39 q + 4 q^{2} - 117 q^{3} + 182 q^{4} + 5 q^{5} - 12 q^{6} + 77 q^{7} + 27 q^{8} + 351 q^{9} + 95 q^{10} + 429 q^{11} - 546 q^{12} + 169 q^{13} + 46 q^{14} - 15 q^{15} + 822 q^{16} + 294 q^{17} + 36 q^{18} + 259 q^{19} + 426 q^{20} - 231 q^{21} + 44 q^{22} + 177 q^{23} - 81 q^{24} + 1388 q^{25} + 695 q^{26} - 1053 q^{27} + 1104 q^{28} - 18 q^{29} - 285 q^{30} + 422 q^{31} + 55 q^{32} - 1287 q^{33} + 364 q^{34} + 906 q^{35} + 1638 q^{36} + 424 q^{37} + 9 q^{38} - 507 q^{39} + 1067 q^{40} + 16 q^{41} - 138 q^{42} + 1013 q^{43} + 2002 q^{44} + 45 q^{45} + 9 q^{46} + 1615 q^{47} - 2466 q^{48} + 2024 q^{49} - 1342 q^{50} - 882 q^{51} + 1298 q^{52} - 541 q^{53} - 108 q^{54} + 55 q^{55} - 161 q^{56} - 777 q^{57} + 1061 q^{58} + 1019 q^{59} - 1278 q^{60} + 2379 q^{61} + 879 q^{62} + 693 q^{63} + 1055 q^{64} - 1134 q^{65} - 132 q^{66} + 1917 q^{67} + 3526 q^{68} - 531 q^{69} + 758 q^{70} - 479 q^{71} + 243 q^{72} + 3319 q^{73} - 332 q^{74} - 4164 q^{75} + 692 q^{76} + 847 q^{77} - 2085 q^{78} + 651 q^{79} + 2973 q^{80} + 3159 q^{81} - 826 q^{82} + 4001 q^{83} - 3312 q^{84} + 3595 q^{85} - 6247 q^{86} + 54 q^{87} + 297 q^{88} - 1625 q^{89} + 855 q^{90} + 2048 q^{91} - 507 q^{92} - 1266 q^{93} - 2436 q^{94} + 1400 q^{95} - 165 q^{96} + 2176 q^{97} - 1396 q^{98} + 3861 q^{99}+O(q^{100}) \) 39 * q + 4 * q^2 - 117 * q^3 + 182 * q^4 + 5 * q^5 - 12 * q^6 + 77 * q^7 + 27 * q^8 + 351 * q^9 + 95 * q^10 + 429 * q^11 - 546 * q^12 + 169 * q^13 + 46 * q^14 - 15 * q^15 + 822 * q^16 + 294 * q^17 + 36 * q^18 + 259 * q^19 + 426 * q^20 - 231 * q^21 + 44 * q^22 + 177 * q^23 - 81 * q^24 + 1388 * q^25 + 695 * q^26 - 1053 * q^27 + 1104 * q^28 - 18 * q^29 - 285 * q^30 + 422 * q^31 + 55 * q^32 - 1287 * q^33 + 364 * q^34 + 906 * q^35 + 1638 * q^36 + 424 * q^37 + 9 * q^38 - 507 * q^39 + 1067 * q^40 + 16 * q^41 - 138 * q^42 + 1013 * q^43 + 2002 * q^44 + 45 * q^45 + 9 * q^46 + 1615 * q^47 - 2466 * q^48 + 2024 * q^49 - 1342 * q^50 - 882 * q^51 + 1298 * q^52 - 541 * q^53 - 108 * q^54 + 55 * q^55 - 161 * q^56 - 777 * q^57 + 1061 * q^58 + 1019 * q^59 - 1278 * q^60 + 2379 * q^61 + 879 * q^62 + 693 * q^63 + 1055 * q^64 - 1134 * q^65 - 132 * q^66 + 1917 * q^67 + 3526 * q^68 - 531 * q^69 + 758 * q^70 - 479 * q^71 + 243 * q^72 + 3319 * q^73 - 332 * q^74 - 4164 * q^75 + 692 * q^76 + 847 * q^77 - 2085 * q^78 + 651 * q^79 + 2973 * q^80 + 3159 * q^81 - 826 * q^82 + 4001 * q^83 - 3312 * q^84 + 3595 * q^85 - 6247 * q^86 + 54 * q^87 + 297 * q^88 - 1625 * q^89 + 855 * q^90 + 2048 * q^91 - 507 * q^92 - 1266 * q^93 - 2436 * q^94 + 1400 * q^95 - 165 * q^96 + 2176 * q^97 - 1396 * q^98 + 3861 * q^99

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