LMFDB - Embedded newform 2013.4.a.e.1.17

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:	$38$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q-0.747694 q^{2} -3.00000 q^{3} -7.44095 q^{4} -10.4401 q^{5} +2.24308 q^{6} -14.9879 q^{7} +11.5451 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-0.747694 q^{2} -3.00000 q^{3} -7.44095 q^{4} -10.4401 q^{5} +2.24308 q^{6} -14.9879 q^{7} +11.5451 q^{8} +9.00000 q^{9} +7.80602 q^{10} -11.0000 q^{11} +22.3229 q^{12} +63.4132 q^{13} +11.2063 q^{14} +31.3204 q^{15} +50.8954 q^{16} +19.9950 q^{17} -6.72924 q^{18} +103.712 q^{19} +77.6845 q^{20} +44.9636 q^{21} +8.22463 q^{22} -53.3469 q^{23} -34.6353 q^{24} -16.0038 q^{25} -47.4136 q^{26} -27.0000 q^{27} +111.524 q^{28} -231.753 q^{29} -23.4180 q^{30} +62.1689 q^{31} -130.415 q^{32} +33.0000 q^{33} -14.9501 q^{34} +156.475 q^{35} -66.9686 q^{36} +349.963 q^{37} -77.5448 q^{38} -190.240 q^{39} -120.532 q^{40} -192.396 q^{41} -33.6190 q^{42} -320.843 q^{43} +81.8505 q^{44} -93.9611 q^{45} +39.8871 q^{46} -188.775 q^{47} -152.686 q^{48} -118.364 q^{49} +11.9659 q^{50} -59.9850 q^{51} -471.855 q^{52} -385.451 q^{53} +20.1877 q^{54} +114.841 q^{55} -173.036 q^{56} -311.136 q^{57} +173.281 q^{58} -19.3837 q^{59} -233.054 q^{60} -61.0000 q^{61} -46.4833 q^{62} -134.891 q^{63} -309.653 q^{64} -662.042 q^{65} -24.6739 q^{66} +195.556 q^{67} -148.782 q^{68} +160.041 q^{69} -116.995 q^{70} +491.594 q^{71} +103.906 q^{72} -5.66998 q^{73} -261.665 q^{74} +48.0113 q^{75} -771.716 q^{76} +164.866 q^{77} +142.241 q^{78} -886.887 q^{79} -531.355 q^{80} +81.0000 q^{81} +143.853 q^{82} -794.262 q^{83} -334.572 q^{84} -208.750 q^{85} +239.892 q^{86} +695.260 q^{87} -126.996 q^{88} +90.6122 q^{89} +70.2541 q^{90} -950.427 q^{91} +396.952 q^{92} -186.507 q^{93} +141.146 q^{94} -1082.77 q^{95} +391.245 q^{96} -228.495 q^{97} +88.5002 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 2 q^{2} - 114 q^{3} + 142 q^{4} + 15 q^{5} + 6 q^{6} + 63 q^{7} - 45 q^{8} + 342 q^{9}+O(q^{10}) $ 38 * q - 2 * q^2 - 114 * q^3 + 142 * q^4 + 15 * q^5 + 6 * q^6 + 63 * q^7 - 45 * q^8 + 342 * q^9	\( 38 q - 2 q^{2} - 114 q^{3} + 142 q^{4} + 15 q^{5} + 6 q^{6} + 63 q^{7} - 45 q^{8} + 342 q^{9} + 95 q^{10} - 418 q^{11} - 426 q^{12} + 13 q^{13} + 26 q^{14} - 45 q^{15} + 486 q^{16} - 224 q^{17} - 18 q^{18} + 367 q^{19} + 18 q^{20} - 189 q^{21} + 22 q^{22} + 51 q^{23} + 135 q^{24} + 773 q^{25} - 439 q^{26} - 1026 q^{27} + 22 q^{28} - 462 q^{29} - 285 q^{30} + 234 q^{31} - 597 q^{32} + 1254 q^{33} + 956 q^{34} - 522 q^{35} + 1278 q^{36} + 954 q^{37} + 705 q^{38} - 39 q^{39} + 1495 q^{40} - 740 q^{41} - 78 q^{42} + 1441 q^{43} - 1562 q^{44} + 135 q^{45} + 581 q^{46} + 1003 q^{47} - 1458 q^{48} + 2707 q^{49} + 388 q^{50} + 672 q^{51} + 788 q^{52} + 735 q^{53} + 54 q^{54} - 165 q^{55} + 1059 q^{56} - 1101 q^{57} + 177 q^{58} + 261 q^{59} - 54 q^{60} - 2318 q^{61} + 1251 q^{62} + 567 q^{63} + 5571 q^{64} - 1354 q^{65} - 66 q^{66} + 3495 q^{67} - 1856 q^{68} - 153 q^{69} + 542 q^{70} - 873 q^{71} - 405 q^{72} + 989 q^{73} - 3406 q^{74} - 2319 q^{75} + 1712 q^{76} - 693 q^{77} + 1317 q^{78} + 2313 q^{79} + 1593 q^{80} + 3078 q^{81} + 5170 q^{82} + 569 q^{83} - 66 q^{84} - 1271 q^{85} + 3065 q^{86} + 1386 q^{87} + 495 q^{88} - 2917 q^{89} + 855 q^{90} + 2740 q^{91} + 1083 q^{92} - 702 q^{93} + 3272 q^{94} + 2696 q^{95} + 1791 q^{96} + 4250 q^{97} + 5952 q^{98} - 3762 q^{99}+O(q^{100}) \) 38 * q - 2 * q^2 - 114 * q^3 + 142 * q^4 + 15 * q^5 + 6 * q^6 + 63 * q^7 - 45 * q^8 + 342 * q^9 + 95 * q^10 - 418 * q^11 - 426 * q^12 + 13 * q^13 + 26 * q^14 - 45 * q^15 + 486 * q^16 - 224 * q^17 - 18 * q^18 + 367 * q^19 + 18 * q^20 - 189 * q^21 + 22 * q^22 + 51 * q^23 + 135 * q^24 + 773 * q^25 - 439 * q^26 - 1026 * q^27 + 22 * q^28 - 462 * q^29 - 285 * q^30 + 234 * q^31 - 597 * q^32 + 1254 * q^33 + 956 * q^34 - 522 * q^35 + 1278 * q^36 + 954 * q^37 + 705 * q^38 - 39 * q^39 + 1495 * q^40 - 740 * q^41 - 78 * q^42 + 1441 * q^43 - 1562 * q^44 + 135 * q^45 + 581 * q^46 + 1003 * q^47 - 1458 * q^48 + 2707 * q^49 + 388 * q^50 + 672 * q^51 + 788 * q^52 + 735 * q^53 + 54 * q^54 - 165 * q^55 + 1059 * q^56 - 1101 * q^57 + 177 * q^58 + 261 * q^59 - 54 * q^60 - 2318 * q^61 + 1251 * q^62 + 567 * q^63 + 5571 * q^64 - 1354 * q^65 - 66 * q^66 + 3495 * q^67 - 1856 * q^68 - 153 * q^69 + 542 * q^70 - 873 * q^71 - 405 * q^72 + 989 * q^73 - 3406 * q^74 - 2319 * q^75 + 1712 * q^76 - 693 * q^77 + 1317 * q^78 + 2313 * q^79 + 1593 * q^80 + 3078 * q^81 + 5170 * q^82 + 569 * q^83 - 66 * q^84 - 1271 * q^85 + 3065 * q^86 + 1386 * q^87 + 495 * q^88 - 2917 * q^89 + 855 * q^90 + 2740 * q^91 + 1083 * q^92 - 702 * q^93 + 3272 * q^94 + 2696 * q^95 + 1791 * q^96 + 4250 * q^97 + 5952 * q^98 - 3762 * 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 $

$2$	−0.747694	−0.264350	−0.132175	−	0.991226i	$-0.542196\pi$
$2$	−0.747694	−0.264350	−0.132175	+	0.991226i	$0.542196\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−7.44095	−0.930119
$5$	−10.4401	−0.933793	−0.466897	−	0.884312i	$-0.654628\pi$
$5$	−10.4401	−0.933793	−0.466897	+	0.884312i	$0.654628\pi$
$6$	2.24308	0.152622
$7$	−14.9879	−0.809268	−0.404634	−	0.914479i	$-0.632601\pi$
$7$	−14.9879	−0.809268	−0.404634	+	0.914479i	$0.632601\pi$
$8$	11.5451	0.510226
$9$	9.00000	0.333333
$10$	7.80602	0.246848
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	22.3229	0.537005
$13$	63.4132	1.35290	0.676448	−	0.736490i	$-0.263518\pi$
$13$	63.4132	1.35290	0.676448	+	0.736490i	$0.263518\pi$
$14$	11.2063	0.213930
$15$	31.3204	0.539126
$16$	50.8954	0.795241
$17$	19.9950	0.285265	0.142632	−	0.989776i	$-0.454443\pi$
$17$	19.9950	0.285265	0.142632	+	0.989776i	$0.454443\pi$
$18$	−6.72924	−0.0881165
$19$	103.712	1.25227	0.626136	−	0.779714i	$-0.284636\pi$
$19$	103.712	1.25227	0.626136	+	0.779714i	$0.284636\pi$
$20$	77.6845	0.868539
$21$	44.9636	0.467231
$22$	8.22463	0.0797044
$23$	−53.3469	−0.483634	−0.241817	−	0.970322i	$-0.577743\pi$
$23$	−53.3469	−0.483634	−0.241817	+	0.970322i	$0.577743\pi$
$24$	−34.6353	−0.294579
$25$	−16.0038	−0.128030
$26$	−47.4136	−0.357638
$27$	−27.0000	−0.192450
$28$	111.524	0.752716
$29$	−231.753	−1.48398	−0.741992	−	0.670409i	$-0.766119\pi$
$29$	−231.753	−1.48398	−0.741992	+	0.670409i	$0.766119\pi$
$30$	−23.4180	−0.142518
$31$	62.1689	0.360189	0.180095	−	0.983649i	$-0.442360\pi$
$31$	62.1689	0.360189	0.180095	+	0.983649i	$0.442360\pi$
$32$	−130.415	−0.720448
$33$	33.0000	0.174078
$34$	−14.9501	−0.0754096
$35$	156.475	0.755689
$36$	−66.9686	−0.310040
$37$	349.963	1.55496	0.777481	−	0.628906i	$-0.216497\pi$
$37$	349.963	1.55496	0.777481	+	0.628906i	$0.216497\pi$
$38$	−77.5448	−0.331038
$39$	−190.240	−0.781095
$40$	−120.532	−0.476446
$41$	−192.396	−0.732859	−0.366429	−	0.930446i	$-0.619420\pi$
$41$	−192.396	−0.732859	−0.366429	+	0.930446i	$0.619420\pi$
$42$	−33.6190	−0.123512
$43$	−320.843	−1.13786	−0.568932	−	0.822385i	$-0.692643\pi$
$43$	−320.843	−1.13786	−0.568932	+	0.822385i	$0.692643\pi$
$44$	81.8505	0.280442
$45$	−93.9611	−0.311264
$46$	39.8871	0.127849
$47$	−188.775	−0.585866	−0.292933	−	0.956133i	$-0.594631\pi$
$47$	−188.775	−0.585866	−0.292933	+	0.956133i	$0.594631\pi$
$48$	−152.686	−0.459133
$49$	−118.364	−0.345085
$50$	11.9659	0.0338447
$51$	−59.9850	−0.164698
$52$	−471.855	−1.25835
$53$	−385.451	−0.998977	−0.499489	−	0.866320i	$-0.666479\pi$
$53$	−385.451	−0.998977	−0.499489	+	0.866320i	$0.666479\pi$
$54$	20.1877	0.0508741
$55$	114.841	0.281549
$56$	−173.036	−0.412910
$57$	−311.136	−0.722999
$58$	173.281	0.392290
$59$	−19.3837	−0.0427720	−0.0213860	−	0.999771i	$-0.506808\pi$
$59$	−19.3837	−0.0427720	−0.0213860	+	0.999771i	$0.506808\pi$
$60$	−233.054	−0.501451
$61$	−61.0000	−0.128037
$61$	−61.0000	−0.128037
$62$	−46.4833	−0.0952159
$63$	−134.891	−0.269756
$64$	−309.653	−0.604791
$65$	−662.042	−1.26333
$66$	−24.6739	−0.0460174
$67$	195.556	0.356582	0.178291	−	0.983978i	$-0.442943\pi$
$67$	195.556	0.356582	0.178291	+	0.983978i	$0.442943\pi$
$68$	−148.782	−0.265330
$69$	160.041	0.279226
$70$	−116.995	−0.199766
$71$	491.594	0.821711	0.410855	−	0.911701i	$-0.365230\pi$
$71$	491.594	0.821711	0.410855	+	0.911701i	$0.365230\pi$
$72$	103.906	0.170075
$73$	−5.66998	−0.00909070	−0.00454535	−	0.999990i	$-0.501447\pi$
$73$	−5.66998	−0.00909070	−0.00454535	+	0.999990i	$0.501447\pi$
$74$	−261.665	−0.411054
$75$	48.0113	0.0739182
$76$	−771.716	−1.16476
$77$	164.866	0.244003
$78$	142.241	0.206482
$79$	−886.887	−1.26307	−0.631535	−	0.775347i	$-0.717575\pi$
$79$	−886.887	−1.26307	−0.631535	+	0.775347i	$0.717575\pi$
$80$	−531.355	−0.742591
$81$	81.0000	0.111111
$82$	143.853	0.193731
$83$	−794.262	−1.05038	−0.525190	−	0.850985i	$-0.676006\pi$
$83$	−794.262	−1.05038	−0.525190	+	0.850985i	$0.676006\pi$
$84$	−334.572	−0.434581
$85$	−208.750	−0.266378
$86$	239.892	0.300794
$87$	695.260	0.856778
$88$	−126.996	−0.153839
$89$	90.6122	0.107920	0.0539600	−	0.998543i	$-0.482816\pi$
$89$	90.6122	0.107920	0.0539600	+	0.998543i	$0.482816\pi$
$90$	70.2541	0.0822826
$91$	−950.427	−1.09486
$92$	396.952	0.449838
$93$	−186.507	−0.207955
$94$	141.146	0.154874
$95$	−1082.77	−1.16936
$96$	391.245	0.415951
$97$	−228.495	−0.239177	−0.119588	−	0.992824i	$-0.538157\pi$
$97$	−228.495	−0.239177	−0.119588	+	0.992824i	$0.538157\pi$
$98$	88.5002	0.0912232
$99$	−99.0000	−0.100504
$100$	119.083	0.119083
$101$	649.490	0.639868	0.319934	−	0.947440i	$-0.396339\pi$
$101$	649.490	0.639868	0.319934	+	0.947440i	$0.396339\pi$
$102$	44.8504	0.0435377
$103$	1108.71	1.06062	0.530311	−	0.847803i	$-0.322075\pi$
$103$	1108.71	1.06062	0.530311	+	0.847803i	$0.322075\pi$
$104$	732.112	0.690283
$105$	−469.425	−0.436297
$106$	288.199	0.264079
$107$	1558.88	1.40843	0.704216	−	0.709986i	$-0.251299\pi$
$107$	1558.88	1.40843	0.704216	+	0.709986i	$0.251299\pi$
$108$	200.906	0.179002
$109$	819.059	0.719739	0.359870	−	0.933003i	$-0.382821\pi$
$109$	819.059	0.719739	0.359870	+	0.933003i	$0.382821\pi$
$110$	−85.8662	−0.0744274
$111$	−1049.89	−0.897758
$112$	−762.813	−0.643563
$113$	−706.738	−0.588356	−0.294178	−	0.955751i	$-0.595046\pi$
$113$	−706.738	−0.588356	−0.294178	+	0.955751i	$0.595046\pi$
$114$	232.634	0.191125
$115$	556.948	0.451615
$116$	1724.47	1.38028
$117$	570.719	0.450965
$118$	14.4931	0.0113068
$119$	−299.682	−0.230855
$120$	361.597	0.275076
$121$	121.000	0.0909091
$122$	45.6093	0.0338465
$123$	577.188	0.423116
$124$	−462.596	−0.335019
$125$	1472.10	1.05335
$126$	100.857	0.0713099
$127$	776.943	0.542855	0.271427	−	0.962459i	$-0.412504\pi$
$127$	776.943	0.542855	0.271427	+	0.962459i	$0.412504\pi$
$128$	1274.85	0.880324
$129$	962.529	0.656946
$130$	495.004	0.333960
$131$	−1614.91	−1.07706	−0.538532	−	0.842605i	$-0.681021\pi$
$131$	−1614.91	−1.07706	−0.538532	+	0.842605i	$0.681021\pi$
$132$	−245.551	−0.161913
$133$	−1554.42	−1.01342
$134$	−146.216	−0.0942622
$135$	281.883	0.179709
$136$	230.844	0.145549
$137$	−1662.72	−1.03690	−0.518452	−	0.855107i	$-0.673492\pi$
$137$	−1662.72	−1.03690	−0.518452	+	0.855107i	$0.673492\pi$
$138$	−119.661	−0.0738134
$139$	−521.391	−0.318157	−0.159078	−	0.987266i	$-0.550852\pi$
$139$	−521.391	−0.318157	−0.159078	+	0.987266i	$0.550852\pi$
$140$	−1164.32	−0.702881
$141$	566.326	0.338250
$142$	−367.562	−0.217219
$143$	−697.545	−0.407914
$144$	458.059	0.265080
$145$	2419.53	1.38573
$146$	4.23941	0.00240312
$147$	355.093	0.199235
$148$	−2604.06	−1.44630
$149$	2309.84	1.27000	0.634999	−	0.772513i	$-0.281000\pi$
$149$	2309.84	1.27000	0.634999	+	0.772513i	$0.281000\pi$
$150$	−35.8977	−0.0195402
$151$	−1680.00	−0.905408	−0.452704	−	0.891661i	$-0.649541\pi$
$151$	−1680.00	−0.905408	−0.452704	+	0.891661i	$0.649541\pi$
$152$	1197.37	0.638942
$153$	179.955	0.0950882
$154$	−123.270	−0.0645022
$155$	−649.051	−0.336342
$156$	1415.56	0.726511
$157$	−981.007	−0.498681	−0.249340	−	0.968416i	$-0.580214\pi$
$157$	−981.007	−0.498681	−0.249340	+	0.968416i	$0.580214\pi$
$158$	663.120	0.333892
$159$	1156.35	0.576760
$160$	1361.55	0.672749
$161$	799.555	0.391390
$162$	−60.5632	−0.0293722
$163$	−3149.92	−1.51363	−0.756813	−	0.653632i	$-0.773244\pi$
$163$	−3149.92	−1.51363	−0.756813	+	0.653632i	$0.773244\pi$
$164$	1431.61	0.681646
$165$	−344.524	−0.162553
$166$	593.865	0.277668
$167$	−2607.76	−1.20835	−0.604175	−	0.796852i	$-0.706497\pi$
$167$	−2607.76	−1.20835	−0.604175	+	0.796852i	$0.706497\pi$
$168$	519.109	0.238394
$169$	1824.23	0.830328
$170$	156.081	0.0704169
$171$	933.408	0.417424
$172$	2387.38	1.05835
$173$	−2361.27	−1.03771	−0.518855	−	0.854862i	$-0.673642\pi$
$173$	−2361.27	−1.03771	−0.518855	+	0.854862i	$0.673642\pi$
$174$	−519.842	−0.226489
$175$	239.862	0.103611
$176$	−559.850	−0.239774
$177$	58.1512	0.0246944
$178$	−67.7502	−0.0285286
$179$	1328.25	0.554625	0.277313	−	0.960780i	$-0.410556\pi$
$179$	1328.25	0.554625	0.277313	+	0.960780i	$0.410556\pi$
$180$	699.161	0.289513
$181$	−2943.79	−1.20890	−0.604449	−	0.796644i	$-0.706607\pi$
$181$	−2943.79	−1.20890	−0.604449	+	0.796644i	$0.706607\pi$
$182$	710.628	0.289425
$183$	183.000	0.0739221
$184$	−615.895	−0.246763
$185$	−3653.66	−1.45201
$186$	139.450	0.0549729
$187$	−219.945	−0.0860105
$188$	1404.67	0.544926
$189$	404.672	0.155744
$190$	809.577	0.309121
$191$	2819.02	1.06794	0.533972	−	0.845502i	$-0.320699\pi$
$191$	2819.02	1.06794	0.533972	+	0.845502i	$0.320699\pi$
$192$	928.959	0.349176
$193$	3021.12	1.12676	0.563381	−	0.826197i	$-0.309500\pi$
$193$	3021.12	1.12676	0.563381	+	0.826197i	$0.309500\pi$
$194$	170.844	0.0632263
$195$	1986.12	0.729381
$196$	880.743	0.320971
$197$	−2519.53	−0.911215	−0.455608	−	0.890181i	$-0.650578\pi$
$197$	−2519.53	−0.911215	−0.455608	+	0.890181i	$0.650578\pi$
$198$	74.0217	0.0265681
$199$	4745.78	1.69055	0.845275	−	0.534331i	$-0.179436\pi$
$199$	4745.78	1.69055	0.845275	+	0.534331i	$0.179436\pi$
$200$	−184.765	−0.0653243
$201$	−586.668	−0.205872
$202$	−485.619	−0.169149
$203$	3473.49	1.20094
$204$	446.345	0.153188
$205$	2008.64	0.684339
$206$	−828.972	−0.280375
$207$	−480.122	−0.161211
$208$	3227.44	1.07588
$209$	−1140.83	−0.377574
$210$	350.986	0.115335
$211$	−1480.02	−0.482886	−0.241443	−	0.970415i	$-0.577621\pi$
$211$	−1480.02	−0.482886	−0.241443	+	0.970415i	$0.577621\pi$
$212$	2868.12	0.929168
$213$	−1474.78	−0.474415
$214$	−1165.56	−0.372319
$215$	3349.64	1.06253
$216$	−311.718	−0.0981931
$217$	−931.779	−0.291490
$218$	−612.405	−0.190263
$219$	17.0099	0.00524852
$220$	−854.530	−0.261874
$221$	1267.95	0.385933
$222$	784.996	0.237322
$223$	4643.66	1.39445	0.697226	−	0.716851i	$-0.254417\pi$
$223$	4643.66	1.39445	0.697226	+	0.716851i	$0.254417\pi$
$224$	1954.64	0.583035
$225$	−144.034	−0.0426767
$226$	528.423	0.155532
$227$	−2212.24	−0.646834	−0.323417	−	0.946257i	$-0.604832\pi$
$227$	−2212.24	−0.646834	−0.323417	+	0.946257i	$0.604832\pi$
$228$	2315.15	0.672476
$229$	−5647.18	−1.62959	−0.814795	−	0.579749i	$-0.803151\pi$
$229$	−5647.18	−1.62959	−0.814795	+	0.579749i	$0.803151\pi$
$230$	−416.426	−0.119384
$231$	−494.599	−0.140875
$232$	−2675.62	−0.757167
$233$	1981.25	0.557066	0.278533	−	0.960427i	$-0.410152\pi$
$233$	1981.25	0.557066	0.278533	+	0.960427i	$0.410152\pi$
$234$	−426.723	−0.119213
$235$	1970.84	0.547078
$236$	144.233	0.0397830
$237$	2660.66	0.729234
$238$	224.070	0.0610265
$239$	3541.37	0.958460	0.479230	−	0.877689i	$-0.340916\pi$
$239$	3541.37	0.958460	0.479230	+	0.877689i	$0.340916\pi$
$240$	1594.06	0.428735
$241$	3437.84	0.918883	0.459442	−	0.888208i	$-0.348050\pi$
$241$	3437.84	0.918883	0.459442	+	0.888208i	$0.348050\pi$
$242$	−90.4709	−0.0240318
$243$	−243.000	−0.0641500
$244$	453.898	0.119090
$245$	1235.74	0.322238
$246$	−431.560	−0.111851
$247$	6576.71	1.69419
$248$	717.746	0.183778
$249$	2382.79	0.606438
$250$	−1100.68	−0.278452
$251$	326.850	0.0821937	0.0410968	−	0.999155i	$-0.486915\pi$
$251$	326.850	0.0821937	0.0410968	+	0.999155i	$0.486915\pi$
$252$	1003.72	0.250905
$253$	586.816	0.145821
$254$	−580.915	−0.143503
$255$	626.251	0.153793
$256$	1524.03	0.372078
$257$	−1624.78	−0.394362	−0.197181	−	0.980367i	$-0.563179\pi$
$257$	−1624.78	−0.394362	−0.197181	+	0.980367i	$0.563179\pi$
$258$	−719.677	−0.173663
$259$	−5245.20	−1.25838
$260$	4926.22	1.17504
$261$	−2085.78	−0.494661
$262$	1207.46	0.284721
$263$	−351.106	−0.0823198	−0.0411599	−	0.999153i	$-0.513105\pi$
$263$	−351.106	−0.0823198	−0.0411599	+	0.999153i	$0.513105\pi$
$264$	380.988	0.0888190
$265$	4024.16	0.932838
$266$	1162.23	0.267898
$267$	−271.837	−0.0623076
$268$	−1455.12	−0.331663
$269$	−1694.38	−0.384045	−0.192022	−	0.981391i	$-0.561505\pi$
$269$	−1694.38	−0.384045	−0.192022	+	0.981391i	$0.561505\pi$
$270$	−210.762	−0.0475059
$271$	−7018.72	−1.57327	−0.786637	−	0.617416i	$-0.788179\pi$
$271$	−7018.72	−1.57327	−0.786637	+	0.617416i	$0.788179\pi$
$272$	1017.65	0.226854
$273$	2851.28	0.632115
$274$	1243.21	0.274105
$275$	176.041	0.0386025
$276$	−1190.85	−0.259714
$277$	−3297.17	−0.715191	−0.357595	−	0.933877i	$-0.616403\pi$
$277$	−3297.17	−0.715191	−0.357595	+	0.933877i	$0.616403\pi$
$278$	389.841	0.0841046
$279$	559.520	0.120063
$280$	1806.52	0.385572
$281$	−5709.67	−1.21214	−0.606069	−	0.795412i	$-0.707254\pi$
$281$	−5709.67	−1.21214	−0.606069	+	0.795412i	$0.707254\pi$
$282$	−423.438	−0.0894163
$283$	2207.95	0.463778	0.231889	−	0.972742i	$-0.425509\pi$
$283$	2207.95	0.463778	0.231889	+	0.972742i	$0.425509\pi$
$284$	−3657.93	−0.764289
$285$	3248.30	0.675132
$286$	521.550	0.107832
$287$	2883.60	0.593079
$288$	−1173.74	−0.240149
$289$	−4513.20	−0.918624
$290$	−1809.07	−0.366318
$291$	685.485	0.138089
$292$	42.1901	0.00845544
$293$	870.456	0.173558	0.0867792	−	0.996228i	$-0.472343\pi$
$293$	870.456	0.173558	0.0867792	+	0.996228i	$0.472343\pi$
$294$	−265.501	−0.0526677
$295$	202.369	0.0399402
$296$	4040.36	0.793383
$297$	297.000	0.0580259
$298$	−1727.05	−0.335723
$299$	−3382.89	−0.654307
$300$	−357.250	−0.0687527
$301$	4808.75	0.920836
$302$	1256.13	0.239344
$303$	−1948.47	−0.369428
$304$	5278.47	0.995858
$305$	636.848	0.119560
$306$	−134.551	−0.0251365
$307$	−5481.37	−1.01902	−0.509509	−	0.860466i	$-0.670173\pi$
$307$	−5481.37	−1.01902	−0.509509	+	0.860466i	$0.670173\pi$
$308$	−1226.76	−0.226952
$309$	−3326.12	−0.612350
$310$	485.291	0.0889120
$311$	4876.79	0.889187	0.444594	−	0.895732i	$-0.353348\pi$
$311$	4876.79	0.889187	0.444594	+	0.895732i	$0.353348\pi$
$312$	−2196.33	−0.398535
$313$	2935.79	0.530163	0.265081	−	0.964226i	$-0.414601\pi$
$313$	2935.79	0.530163	0.265081	+	0.964226i	$0.414601\pi$
$314$	733.492	0.131826
$315$	1408.28	0.251896
$316$	6599.29	1.17481
$317$	−1107.80	−0.196279	−0.0981396	−	0.995173i	$-0.531289\pi$
$317$	−1107.80	−0.196279	−0.0981396	+	0.995173i	$0.531289\pi$
$318$	−864.598	−0.152466
$319$	2549.29	0.447438
$320$	3232.82	0.564750
$321$	−4676.63	−0.813159
$322$	−597.822	−0.103464
$323$	2073.72	0.357229
$324$	−602.717	−0.103347
$325$	−1014.85	−0.173211
$326$	2355.18	0.400126
$327$	−2457.18	−0.415542
$328$	−2221.23	−0.373924
$329$	2829.34	0.474123
$330$	257.599	0.0429707
$331$	−9173.14	−1.52327	−0.761633	−	0.648008i	$-0.775602\pi$
$331$	−9173.14	−1.52327	−0.761633	+	0.648008i	$0.775602\pi$
$332$	5910.07	0.976979
$333$	3149.67	0.518321
$334$	1949.80	0.319427
$335$	−2041.63	−0.332973
$336$	2288.44	0.371561
$337$	11037.0	1.78405	0.892026	−	0.451984i	$-0.149284\pi$
$337$	11037.0	1.78405	0.892026	+	0.451984i	$0.149284\pi$
$338$	−1363.97	−0.219497
$339$	2120.21	0.339688
$340$	1553.30	0.247763
$341$	−683.858	−0.108601
$342$	−697.903	−0.110346
$343$	6914.86	1.08853
$344$	−3704.17	−0.580568
$345$	−1670.84	−0.260740
$346$	1765.51	0.274318
$347$	554.162	0.0857320	0.0428660	−	0.999081i	$-0.486351\pi$
$347$	554.162	0.0857320	0.0428660	+	0.999081i	$0.486351\pi$
$348$	−5173.40	−0.796906
$349$	2928.64	0.449188	0.224594	−	0.974452i	$-0.427894\pi$
$349$	2928.64	0.449188	0.224594	+	0.974452i	$0.427894\pi$
$350$	−179.343	−0.0273894
$351$	−1712.16	−0.260365
$352$	1434.57	0.217223
$353$	−971.248	−0.146443	−0.0732214	−	0.997316i	$-0.523328\pi$
$353$	−971.248	−0.146443	−0.0732214	+	0.997316i	$0.523328\pi$
$354$	−43.4793	−0.00652796
$355$	−5132.30	−0.767308
$356$	−674.241	−0.100378
$357$	899.046	0.133284
$358$	−993.122	−0.146615
$359$	−323.603	−0.0475742	−0.0237871	−	0.999717i	$-0.507572\pi$
$359$	−323.603	−0.0475742	−0.0237871	+	0.999717i	$0.507572\pi$
$360$	−1084.79	−0.158815
$361$	3897.18	0.568184
$362$	2201.06	0.319572
$363$	−363.000	−0.0524864
$364$	7072.09	1.01835
$365$	59.1953	0.00848884
$366$	−136.828	−0.0195413
$367$	5729.31	0.814898	0.407449	−	0.913228i	$-0.366418\pi$
$367$	5729.31	0.814898	0.407449	+	0.913228i	$0.366418\pi$
$368$	−2715.11	−0.384606
$369$	−1731.56	−0.244286
$370$	2731.82	0.383839
$371$	5777.09	0.808440
$372$	1387.79	0.193423
$373$	5377.16	0.746431	0.373216	−	0.927745i	$-0.378255\pi$
$373$	5377.16	0.746431	0.373216	+	0.927745i	$0.378255\pi$
$374$	164.451	0.0227368
$375$	−4416.29	−0.608150
$376$	−2179.43	−0.298924
$377$	−14696.2	−2.00768
$378$	−302.571	−0.0411708
$379$	12360.5	1.67524	0.837620	−	0.546254i	$-0.183947\pi$
$379$	12360.5	1.67524	0.837620	+	0.546254i	$0.183947\pi$
$380$	8056.81	1.08765
$381$	−2330.83	−0.313417
$382$	−2107.76	−0.282310
$383$	−6910.42	−0.921948	−0.460974	−	0.887414i	$-0.652500\pi$
$383$	−6910.42	−0.921948	−0.460974	+	0.887414i	$0.652500\pi$
$384$	−3824.54	−0.508255
$385$	−1721.23	−0.227849
$386$	−2258.87	−0.297859
$387$	−2887.59	−0.379288
$388$	1700.22	0.222463
$389$	−5425.87	−0.707205	−0.353602	−	0.935396i	$-0.615043\pi$
$389$	−5425.87	−0.707205	−0.353602	+	0.935396i	$0.615043\pi$
$390$	−1485.01	−0.192812
$391$	−1066.67	−0.137964
$392$	−1366.53	−0.176072
$393$	4844.73	0.621843
$394$	1883.84	0.240879
$395$	9259.21	1.17945
$396$	736.654	0.0934805
$397$	11139.3	1.40822	0.704112	−	0.710089i	$-0.251345\pi$
$397$	11139.3	1.40822	0.704112	+	0.710089i	$0.251345\pi$
$398$	−3548.39	−0.446896
$399$	4663.26	0.585100
$400$	−814.518	−0.101815
$401$	−1916.58	−0.238676	−0.119338	−	0.992854i	$-0.538077\pi$
$401$	−1916.58	−0.238676	−0.119338	+	0.992854i	$0.538077\pi$
$402$	438.648	0.0544223
$403$	3942.33	0.487299
$404$	−4832.82	−0.595153
$405$	−845.650	−0.103755
$406$	−2597.10	−0.317468
$407$	−3849.60	−0.468839
$408$	−692.533	−0.0840330
$409$	7932.75	0.959045	0.479522	−	0.877530i	$-0.340810\pi$
$409$	7932.75	0.959045	0.479522	+	0.877530i	$0.340810\pi$
$410$	−1501.85	−0.180905
$411$	4988.16	0.598657
$412$	−8249.83	−0.986504
$413$	290.520	0.0346140
$414$	358.984	0.0426162
$415$	8292.20	0.980838
$416$	−8270.03	−0.974691
$417$	1564.17	0.183688
$418$	852.993	0.0998116
$419$	−9462.30	−1.10325	−0.551627	−	0.834091i	$-0.685993\pi$
$419$	−9462.30	−1.10325	−0.551627	+	0.834091i	$0.685993\pi$
$420$	3492.97	0.405809
$421$	−1449.52	−0.167804	−0.0839020	−	0.996474i	$-0.526738\pi$
$421$	−1449.52	−0.167804	−0.0839020	+	0.996474i	$0.526738\pi$
$422$	1106.60	0.127651
$423$	−1698.98	−0.195289
$424$	−4450.07	−0.509704
$425$	−319.995	−0.0365224
$426$	1102.68	0.125411
$427$	914.259	0.103616
$428$	−11599.5	−1.31001
$429$	2092.63	0.235509
$430$	−2504.51	−0.280879
$431$	5196.57	0.580766	0.290383	−	0.956911i	$-0.406217\pi$
$431$	5196.57	0.580766	0.290383	+	0.956911i	$0.406217\pi$
$432$	−1374.18	−0.153044
$433$	−7432.32	−0.824883	−0.412442	−	0.910984i	$-0.635324\pi$
$433$	−7432.32	−0.824883	−0.412442	+	0.910984i	$0.635324\pi$
$434$	696.685	0.0770552
$435$	−7258.60	−0.800054
$436$	−6094.58	−0.669443
$437$	−5532.71	−0.605642
$438$	−12.7182	−0.00138744
$439$	12274.4	1.33445	0.667226	−	0.744855i	$-0.267481\pi$
$439$	12274.4	1.33445	0.667226	+	0.744855i	$0.267481\pi$
$440$	1325.86	0.143654
$441$	−1065.28	−0.115028
$442$	−948.035	−0.102021
$443$	9693.19	1.03959	0.519794	−	0.854292i	$-0.326009\pi$
$443$	9693.19	1.03959	0.519794	+	0.854292i	$0.326009\pi$
$444$	7812.18	0.835022
$445$	−946.003	−0.100775
$446$	−3472.04	−0.368623
$447$	−6929.53	−0.733234
$448$	4641.03	0.489438
$449$	−882.307	−0.0927364	−0.0463682	−	0.998924i	$-0.514765\pi$
$449$	−882.307	−0.0927364	−0.0463682	+	0.998924i	$0.514765\pi$
$450$	107.693	0.0112816
$451$	2116.36	0.220965
$452$	5258.80	0.547242
$453$	5040.01	0.522738
$454$	1654.07	0.170990
$455$	9922.58	1.02237
$456$	−3592.10	−0.368893
$457$	−5473.51	−0.560263	−0.280132	−	0.959962i	$-0.590378\pi$
$457$	−5473.51	−0.560263	−0.280132	+	0.959962i	$0.590378\pi$
$458$	4222.36	0.430782
$459$	−539.865	−0.0548992
$460$	−4144.22	−0.420055
$461$	−5117.68	−0.517037	−0.258519	−	0.966006i	$-0.583234\pi$
$461$	−5117.68	−0.517037	−0.258519	+	0.966006i	$0.583234\pi$
$462$	369.809	0.0372404
$463$	6406.30	0.643037	0.321519	−	0.946903i	$-0.395807\pi$
$463$	6406.30	0.643037	0.321519	+	0.946903i	$0.395807\pi$
$464$	−11795.2	−1.18012
$465$	1947.15	0.194187
$466$	−1481.37	−0.147260
$467$	−8612.37	−0.853390	−0.426695	−	0.904396i	$-0.640322\pi$
$467$	−8612.37	−0.853390	−0.426695	+	0.904396i	$0.640322\pi$
$468$	−4246.69	−0.419452
$469$	−2930.96	−0.288570
$470$	−1473.58	−0.144620
$471$	2943.02	0.287913
$472$	−223.787	−0.0218234
$473$	3529.27	0.343079
$474$	−1989.36	−0.192773
$475$	−1659.78	−0.160328
$476$	2229.92	0.214723
$477$	−3469.06	−0.332992
$478$	−2647.86	−0.253369
$479$	17549.5	1.67402	0.837012	−	0.547185i	$-0.184300\pi$
$479$	17549.5	1.67402	0.837012	+	0.547185i	$0.184300\pi$
$480$	−4084.65	−0.388412
$481$	22192.3	2.10370
$482$	−2570.45	−0.242906
$483$	−2398.66	−0.225969
$484$	−900.355	−0.0845563
$485$	2385.52	0.223342
$486$	181.690	0.0169580
$487$	−1191.98	−0.110911	−0.0554554	−	0.998461i	$-0.517661\pi$
$487$	−1191.98	−0.110911	−0.0554554	+	0.998461i	$0.517661\pi$
$488$	−704.251	−0.0653278
$489$	9449.76	0.873892
$490$	−923.953	−0.0851836
$491$	17895.4	1.64483	0.822414	−	0.568890i	$-0.192627\pi$
$491$	17895.4	1.64483	0.822414	+	0.568890i	$0.192627\pi$
$492$	−4294.83	−0.393549
$493$	−4633.91	−0.423328
$494$	−4917.36	−0.447859
$495$	1033.57	0.0938498
$496$	3164.11	0.286437
$497$	−7367.94	−0.664984
$498$	−1781.59	−0.160312
$499$	17560.2	1.57535	0.787677	−	0.616088i	$-0.211284\pi$
$499$	17560.2	1.57535	0.787677	+	0.616088i	$0.211284\pi$
$500$	−10953.8	−0.979738
$501$	7823.27	0.697641
$502$	−244.384	−0.0217279
$503$	−6972.81	−0.618096	−0.309048	−	0.951046i	$-0.600010\pi$
$503$	−6972.81	−0.618096	−0.309048	+	0.951046i	$0.600010\pi$
$504$	−1557.33	−0.137637
$505$	−6780.75	−0.597504
$506$	−438.758	−0.0385478
$507$	−5472.69	−0.479390
$508$	−5781.20	−0.504920
$509$	13590.9	1.18351	0.591755	−	0.806118i	$-0.298435\pi$
$509$	13590.9	1.18351	0.591755	+	0.806118i	$0.298435\pi$
$510$	−468.244	−0.0406552
$511$	84.9809	0.00735681
$512$	−11338.3	−0.978683
$513$	−2800.22	−0.241000
$514$	1214.84	0.104249
$515$	−11575.0	−0.990401
$516$	−7162.14	−0.611038
$517$	2076.53	0.176645
$518$	3921.80	0.332653
$519$	7083.81	0.599123
$520$	−7643.34	−0.644582
$521$	−1002.79	−0.0843242	−0.0421621	−	0.999111i	$-0.513425\pi$
$521$	−1002.79	−0.0843242	−0.0421621	+	0.999111i	$0.513425\pi$
$522$	1559.52	0.130763
$523$	−530.784	−0.0443778	−0.0221889	−	0.999754i	$-0.507064\pi$
$523$	−530.784	−0.0443778	−0.0221889	+	0.999754i	$0.507064\pi$
$524$	12016.5	1.00180
$525$	−719.586	−0.0598196
$526$	262.520	0.0217612
$527$	1243.07	0.102749
$528$	1679.55	0.138434
$529$	−9321.11	−0.766098
$530$	−3008.84	−0.246595
$531$	−174.454	−0.0142573
$532$	11566.4	0.942605
$533$	−12200.4	−0.991482
$534$	203.251	0.0164710
$535$	−16274.9	−1.31518
$536$	2257.71	0.181937
$537$	−3984.74	−0.320213
$538$	1266.88	0.101522
$539$	1302.01	0.104047
$540$	−2097.48	−0.167150
$541$	3032.87	0.241022	0.120511	−	0.992712i	$-0.461547\pi$
$541$	3032.87	0.241022	0.120511	+	0.992712i	$0.461547\pi$
$542$	5247.85	0.415894
$543$	8831.38	0.697957
$544$	−2607.65	−0.205518
$545$	−8551.08	−0.672088
$546$	−2131.88	−0.167099
$547$	18608.3	1.45454	0.727270	−	0.686351i	$-0.240789\pi$
$547$	18608.3	1.45454	0.727270	+	0.686351i	$0.240789\pi$
$548$	12372.2	0.964445
$549$	−549.000	−0.0426790
$550$	−131.625	−0.0102046
$551$	−24035.6	−1.85835
$552$	1847.68	0.142469
$553$	13292.5	1.02216
$554$	2465.27	0.189060
$555$	10961.0	0.838320
$556$	3879.65	0.295924
$557$	179.899	0.0136850	0.00684252	−	0.999977i	$-0.497822\pi$
$557$	179.899	0.0136850	0.00684252	+	0.999977i	$0.497822\pi$
$558$	−418.350	−0.0317386
$559$	−20345.7	−1.53941
$560$	7963.87	0.600955
$561$	659.835	0.0496582
$562$	4269.09	0.320428
$563$	16260.6	1.21723	0.608616	−	0.793465i	$-0.291725\pi$
$563$	16260.6	1.21723	0.608616	+	0.793465i	$0.291725\pi$
$564$	−4214.01	−0.314613
$565$	7378.43	0.549403
$566$	−1650.87	−0.122600
$567$	−1214.02	−0.0899187
$568$	5675.50	0.419258
$569$	2272.24	0.167412	0.0837059	−	0.996491i	$-0.473324\pi$
$569$	2272.24	0.167412	0.0837059	+	0.996491i	$0.473324\pi$
$570$	−2428.73	−0.178471
$571$	−2886.48	−0.211551	−0.105775	−	0.994390i	$-0.533732\pi$
$571$	−2886.48	−0.211551	−0.105775	+	0.994390i	$0.533732\pi$
$572$	5190.40	0.379408
$573$	−8457.06	−0.616577
$574$	−2156.05	−0.156780
$575$	853.750	0.0619197
$576$	−2786.88	−0.201597
$577$	13816.5	0.996861	0.498430	−	0.866930i	$-0.333910\pi$
$577$	13816.5	0.996861	0.498430	+	0.866930i	$0.333910\pi$
$578$	3374.49	0.242838
$579$	−9063.37	−0.650536
$580$	−18003.6	−1.28890
$581$	11904.3	0.850039
$582$	−512.533	−0.0365037
$583$	4239.96	0.301203
$584$	−65.4605	−0.00463832
$585$	−5958.37	−0.421108
$586$	−650.834	−0.0458801
$587$	19487.2	1.37023	0.685114	−	0.728436i	$-0.259753\pi$
$587$	19487.2	1.37023	0.685114	+	0.728436i	$0.259753\pi$
$588$	−2642.23	−0.185312
$589$	6447.66	0.451055
$590$	−151.310	−0.0105582
$591$	7558.60	0.526090
$592$	17811.5	1.23657
$593$	9969.39	0.690378	0.345189	−	0.938533i	$-0.387815\pi$
$593$	9969.39	0.690378	0.345189	+	0.938533i	$0.387815\pi$
$594$	−222.065	−0.0153391
$595$	3128.72	0.215571
$596$	−17187.4	−1.18125
$597$	−14237.3	−0.976040
$598$	2529.37	0.172966
$599$	6793.08	0.463368	0.231684	−	0.972791i	$-0.425576\pi$
$599$	6793.08	0.463368	0.231684	+	0.972791i	$0.425576\pi$
$600$	554.295	0.0377150
$601$	19745.4	1.34015	0.670077	−	0.742291i	$-0.266261\pi$
$601$	19745.4	1.34015	0.670077	+	0.742291i	$0.266261\pi$
$602$	−3595.47	−0.243423
$603$	1760.00	0.118861
$604$	12500.8	0.842137
$605$	−1263.26	−0.0848903
$606$	1456.86	0.0976581
$607$	−21823.8	−1.45931	−0.729656	−	0.683814i	$-0.760320\pi$
$607$	−21823.8	−1.45931	−0.729656	+	0.683814i	$0.760320\pi$
$608$	−13525.6	−0.902197
$609$	−10420.5	−0.693363
$610$	−476.167	−0.0316056
$611$	−11970.8	−0.792616
$612$	−1339.04	−0.0884433
$613$	−15592.5	−1.02737	−0.513683	−	0.857980i	$-0.671719\pi$
$613$	−15592.5	−1.02737	−0.513683	+	0.857980i	$0.671719\pi$
$614$	4098.38	0.269377
$615$	−6025.92	−0.395103
$616$	1903.40	0.124497
$617$	−22719.8	−1.48244	−0.741219	−	0.671263i	$-0.765752\pi$
$617$	−22719.8	−1.48244	−0.741219	+	0.671263i	$0.765752\pi$
$618$	2486.92	0.161874
$619$	−20911.3	−1.35783	−0.678914	−	0.734218i	$-0.737549\pi$
$619$	−20911.3	−1.35783	−0.678914	+	0.734218i	$0.737549\pi$
$620$	4829.56	0.312838
$621$	1440.37	0.0930755
$622$	−3646.34	−0.235056
$623$	−1358.08	−0.0873362
$624$	−9682.32	−0.621159
$625$	−13368.4	−0.855578
$626$	−2195.07	−0.140148
$627$	3422.50	0.217993
$628$	7299.63	0.463832
$629$	6997.51	0.443576
$630$	−1052.96	−0.0665887
$631$	−1975.00	−0.124601	−0.0623007	−	0.998057i	$-0.519844\pi$
$631$	−1975.00	−0.124601	−0.0623007	+	0.998057i	$0.519844\pi$
$632$	−10239.2	−0.644452
$633$	4440.06	0.278794
$634$	828.298	0.0518863
$635$	−8111.38	−0.506914
$636$	−8604.37	−0.536455
$637$	−7505.85	−0.466865
$638$	−1906.09	−0.118280
$639$	4424.35	0.273904
$640$	−13309.5	−0.822041
$641$	18972.7	1.16907	0.584537	−	0.811367i	$-0.301276\pi$
$641$	18972.7	1.16907	0.584537	+	0.811367i	$0.301276\pi$
$642$	3496.69	0.214958
$643$	6932.90	0.425205	0.212602	−	0.977139i	$-0.431806\pi$
$643$	6932.90	0.425205	0.212602	+	0.977139i	$0.431806\pi$
$644$	−5949.45	−0.364039
$645$	−10048.9	−0.613451
$646$	−1550.51	−0.0944333
$647$	−9923.51	−0.602988	−0.301494	−	0.953468i	$-0.597485\pi$
$647$	−9923.51	−0.602988	−0.301494	+	0.953468i	$0.597485\pi$
$648$	935.153	0.0566918
$649$	213.221	0.0128962
$650$	758.796	0.0457883
$651$	2795.34	0.168292
$652$	23438.4	1.40785
$653$	21303.5	1.27668	0.638339	−	0.769755i	$-0.279622\pi$
$653$	21303.5	1.27668	0.638339	+	0.769755i	$0.279622\pi$
$654$	1837.21	0.109848
$655$	16859.9	1.00576
$656$	−9792.08	−0.582799
$657$	−51.0298	−0.00303023
$658$	−2115.48	−0.125334
$659$	26914.5	1.59096	0.795478	−	0.605982i	$-0.207220\pi$
$659$	26914.5	1.59096	0.795478	+	0.605982i	$0.207220\pi$
$660$	2563.59	0.151193
$661$	52.6731	0.00309946	0.00154973	−	0.999999i	$-0.499507\pi$
$661$	52.6731	0.00309946	0.00154973	+	0.999999i	$0.499507\pi$
$662$	6858.70	0.402675
$663$	−3803.84	−0.222819
$664$	−9169.84	−0.535932
$665$	16228.3	0.946328
$666$	−2354.99	−0.137018
$667$	12363.3	0.717705
$668$	19404.2	1.12391
$669$	−13931.0	−0.805087
$670$	1526.51	0.0880214
$671$	671.000	0.0386046
$672$	−5863.92	−0.336616
$673$	10507.4	0.601828	0.300914	−	0.953651i	$-0.402708\pi$
$673$	10507.4	0.601828	0.300914	+	0.953651i	$0.402708\pi$
$674$	−8252.32	−0.471613
$675$	432.101	0.0246394
$676$	−13574.0	−0.772304
$677$	12638.8	0.717504	0.358752	−	0.933433i	$-0.383202\pi$
$677$	12638.8	0.717504	0.358752	+	0.933433i	$0.383202\pi$
$678$	−1585.27	−0.0897963
$679$	3424.65	0.193558
$680$	−2410.04	−0.135913
$681$	6636.71	0.373450
$682$	511.316	0.0287087
$683$	−10126.7	−0.567329	−0.283665	−	0.958924i	$-0.591550\pi$
$683$	−10126.7	−0.567329	−0.283665	+	0.958924i	$0.591550\pi$
$684$	−6945.45	−0.388254
$685$	17359.0	0.968254
$686$	−5170.20	−0.287754
$687$	16941.5	0.940845
$688$	−16329.5	−0.904876
$689$	−24442.7	−1.35151
$690$	1249.28	0.0689265
$691$	−4362.36	−0.240162	−0.120081	−	0.992764i	$-0.538315\pi$
$691$	−4362.36	−0.240162	−0.120081	+	0.992764i	$0.538315\pi$
$692$	17570.1	0.965195
$693$	1483.80	0.0813345
$694$	−414.344	−0.0226632
$695$	5443.39	0.297093
$696$	8026.85	0.437151
$697$	−3846.96	−0.209059
$698$	−2189.73	−0.118743
$699$	−5943.76	−0.321622
$700$	−1784.80	−0.0963702
$701$	−16953.6	−0.913449	−0.456725	−	0.889608i	$-0.650977\pi$
$701$	−16953.6	−0.913449	−0.456725	+	0.889608i	$0.650977\pi$
$702$	1280.17	0.0688274
$703$	36295.4	1.94724
$704$	3406.18	0.182351
$705$	−5912.52	−0.315856
$706$	726.196	0.0387121
$707$	−9734.46	−0.517824
$708$	−432.700	−0.0229687
$709$	25060.0	1.32743	0.663715	−	0.747985i	$-0.268979\pi$
$709$	25060.0	1.32743	0.663715	+	0.747985i	$0.268979\pi$
$710$	3837.39	0.202838
$711$	−7981.98	−0.421024
$712$	1046.13	0.0550636
$713$	−3316.52	−0.174200
$714$	−672.211	−0.0352337
$715$	7282.46	0.380907
$716$	−9883.43	−0.515868
$717$	−10624.1	−0.553367
$718$	241.956	0.0125762
$719$	−24128.3	−1.25151	−0.625753	−	0.780021i	$-0.715208\pi$
$719$	−24128.3	−1.25151	−0.625753	+	0.780021i	$0.715208\pi$
$720$	−4782.19	−0.247530
$721$	−16617.1	−0.858327
$722$	−2913.89	−0.150199
$723$	−10313.5	−0.530518
$724$	21904.6	1.12442
$725$	3708.92	0.189994
$726$	271.413	0.0138748
$727$	−11355.6	−0.579308	−0.289654	−	0.957131i	$-0.593540\pi$
$727$	−11355.6	−0.579308	−0.289654	+	0.957131i	$0.593540\pi$
$728$	−10972.8	−0.558624
$729$	729.000	0.0370370
$730$	−44.2600	−0.00224402
$731$	−6415.25	−0.324592
$732$	−1361.69	−0.0687564
$733$	−28599.2	−1.44111	−0.720557	−	0.693396i	$-0.756114\pi$
$733$	−28599.2	−1.44111	−0.720557	+	0.693396i	$0.756114\pi$
$734$	−4283.77	−0.215418
$735$	−3707.21	−0.186044
$736$	6957.23	0.348433
$737$	−2151.12	−0.107513
$738$	1294.68	0.0645770
$739$	−10437.6	−0.519556	−0.259778	−	0.965668i	$-0.583649\pi$
$739$	−10437.6	−0.519556	−0.259778	+	0.965668i	$0.583649\pi$
$740$	27186.7	1.35055
$741$	−19730.1	−0.978143
$742$	−4319.49	−0.213711
$743$	6451.77	0.318563	0.159282	−	0.987233i	$-0.449082\pi$
$743$	6451.77	0.318563	0.159282	+	0.987233i	$0.449082\pi$
$744$	−2153.24	−0.106104
$745$	−24115.1	−1.18592
$746$	−4020.47	−0.197319
$747$	−7148.36	−0.350127
$748$	1636.60	0.0800000
$749$	−23364.2	−1.13980
$750$	3302.03	0.160764
$751$	21904.6	1.06433	0.532165	−	0.846641i	$-0.321379\pi$
$751$	21904.6	1.06433	0.532165	+	0.846641i	$0.321379\pi$
$752$	−9607.81	−0.465905
$753$	−980.551	−0.0474545
$754$	10988.3	0.530728
$755$	17539.4	0.845464
$756$	−3011.15	−0.144860
$757$	−23362.4	−1.12169	−0.560847	−	0.827919i	$-0.689524\pi$
$757$	−23362.4	−1.12169	−0.560847	+	0.827919i	$0.689524\pi$
$758$	−9241.86	−0.442849
$759$	−1760.45	−0.0841899
$760$	−12500.6	−0.596640
$761$	−22474.4	−1.07056	−0.535280	−	0.844674i	$-0.679794\pi$
$761$	−22474.4	−1.07056	−0.535280	+	0.844674i	$0.679794\pi$
$762$	1742.75	0.0828517
$763$	−12275.9	−0.582462
$764$	−20976.2	−0.993314
$765$	−1878.75	−0.0887927
$766$	5166.88	0.243717
$767$	−1229.18	−0.0578660
$768$	−4572.09	−0.214819
$769$	−8948.09	−0.419605	−0.209803	−	0.977744i	$-0.567282\pi$
$769$	−8948.09	−0.419605	−0.209803	+	0.977744i	$0.567282\pi$
$770$	1286.95	0.0602317
$771$	4874.34	0.227685
$772$	−22480.0	−1.04802
$773$	−24565.2	−1.14301	−0.571506	−	0.820598i	$-0.693640\pi$
$773$	−24565.2	−1.14301	−0.571506	+	0.820598i	$0.693640\pi$
$774$	2159.03	0.100265
$775$	−994.936	−0.0461150
$776$	−2638.00	−0.122034
$777$	15735.6	0.726527
$778$	4056.89	0.186949
$779$	−19953.8	−0.917738
$780$	−14778.7	−0.678412
$781$	−5407.53	−0.247755
$782$	797.542	0.0364707
$783$	6257.34	0.285593
$784$	−6024.20	−0.274426
$785$	10241.8	0.465665
$786$	−3622.37	−0.164384
$787$	18212.0	0.824891	0.412445	−	0.910982i	$-0.364675\pi$
$787$	18212.0	0.824891	0.412445	+	0.910982i	$0.364675\pi$
$788$	18747.7	0.847539
$789$	1053.32	0.0475274
$790$	−6923.05	−0.311786
$791$	10592.5	0.476138
$792$	−1142.97	−0.0512797
$793$	−3868.20	−0.173221
$794$	−8328.77	−0.372263
$795$	−12072.5	−0.538574
$796$	−35313.2	−1.57241
$797$	−40861.6	−1.81605	−0.908024	−	0.418918i	$-0.862410\pi$
$797$	−40861.6	−1.81605	−0.908024	+	0.418918i	$0.862410\pi$
$798$	−3486.69	−0.154671
$799$	−3774.56	−0.167127
$800$	2087.13	0.0922390
$801$	815.510	0.0359733
$802$	1433.01	0.0630940
$803$	62.3698	0.00274095
$804$	4365.37	0.191486
$805$	−8347.45	−0.365477
$806$	−2947.65	−0.128817
$807$	5083.14	0.221728
$808$	7498.42	0.326477
$809$	40822.0	1.77407	0.887037	−	0.461698i	$-0.152760\pi$
$809$	40822.0	1.77407	0.887037	+	0.461698i	$0.152760\pi$
$810$	632.287	0.0274275
$811$	37269.8	1.61371	0.806856	−	0.590747i	$-0.201167\pi$
$811$	37269.8	1.61371	0.806856	+	0.590747i	$0.201167\pi$
$812$	−25846.0	−1.11702
$813$	21056.2	0.908330
$814$	2878.32	0.123937
$815$	32885.6	1.41341
$816$	−3052.96	−0.130974
$817$	−33275.3	−1.42491
$818$	−5931.27	−0.253523
$819$	−8553.85	−0.364952
$820$	−14946.2	−0.636517
$821$	−13411.2	−0.570100	−0.285050	−	0.958513i	$-0.592010\pi$
$821$	−13411.2	−0.570100	−0.285050	+	0.958513i	$0.592010\pi$
$822$	−3729.62	−0.158255
$823$	36600.4	1.55019	0.775096	−	0.631843i	$-0.217701\pi$
$823$	36600.4	1.55019	0.775096	+	0.631843i	$0.217701\pi$
$824$	12800.1	0.541157
$825$	−528.124	−0.0222872
$826$	−217.220	−0.00915019
$827$	27697.0	1.16459	0.582297	−	0.812976i	$-0.302154\pi$
$827$	27697.0	1.16459	0.582297	+	0.812976i	$0.302154\pi$
$828$	3572.56	0.149946
$829$	10062.9	0.421591	0.210795	−	0.977530i	$-0.432395\pi$
$829$	10062.9	0.421591	0.210795	+	0.977530i	$0.432395\pi$
$830$	−6200.02	−0.259284
$831$	9891.51	0.412915
$832$	−19636.1	−0.818220
$833$	−2366.69	−0.0984406
$834$	−1169.52	−0.0485578
$835$	27225.3	1.12835
$836$	8488.88	0.351189
$837$	−1678.56	−0.0693185
$838$	7074.90	0.291645
$839$	−17981.1	−0.739902	−0.369951	−	0.929051i	$-0.620626\pi$
$839$	−17981.1	−0.739902	−0.369951	+	0.929051i	$0.620626\pi$
$840$	−5419.56	−0.222610
$841$	29320.6	1.20221
$842$	1083.80	0.0443589
$843$	17129.0	0.699828
$844$	11012.8	0.449141
$845$	−19045.2	−0.775355
$846$	1270.32	0.0516245
$847$	−1813.53	−0.0735698
$848$	−19617.7	−0.794428
$849$	−6623.86	−0.267762
$850$	239.258	0.00965469
$851$	−18669.4	−0.752033
$852$	10973.8	0.441263
$853$	13409.5	0.538256	0.269128	−	0.963104i	$-0.413264\pi$
$853$	13409.5	0.538256	0.269128	+	0.963104i	$0.413264\pi$
$854$	−683.586	−0.0273909
$855$	−9744.90	−0.389788
$856$	17997.4	0.718619
$857$	35849.2	1.42892	0.714461	−	0.699675i	$-0.246672\pi$
$857$	35849.2	1.42892	0.714461	+	0.699675i	$0.246672\pi$
$858$	−1564.65	−0.0622567
$859$	−4969.97	−0.197408	−0.0987038	−	0.995117i	$-0.531470\pi$
$859$	−4969.97	−0.197408	−0.0987038	+	0.995117i	$0.531470\pi$
$860$	−24924.5	−0.988279
$861$	−8650.81	−0.342414
$862$	−3885.44	−0.153525
$863$	−21655.8	−0.854197	−0.427099	−	0.904205i	$-0.640464\pi$
$863$	−21655.8	−0.854197	−0.427099	+	0.904205i	$0.640464\pi$
$864$	3521.21	0.138650
$865$	24652.0	0.969008
$866$	5557.10	0.218058
$867$	13539.6	0.530368
$868$	6933.32	0.271120
$869$	9755.76	0.380830
$870$	5427.21	0.211494
$871$	12400.8	0.482418
$872$	9456.11	0.367230
$873$	−2056.45	−0.0797256
$874$	4136.77	0.160101
$875$	−22063.6	−0.852440
$876$	−126.570	−0.00488175
$877$	34872.4	1.34271	0.671356	−	0.741135i	$-0.265712\pi$
$877$	34872.4	1.34271	0.671356	+	0.741135i	$0.265712\pi$
$878$	−9177.48	−0.352762
$879$	−2611.37	−0.100204
$880$	5844.90	0.223900
$881$	−281.415	−0.0107617	−0.00538087	−	0.999986i	$-0.501713\pi$
$881$	−281.415	−0.0107617	−0.00538087	+	0.999986i	$0.501713\pi$
$882$	796.502	0.0304077
$883$	39595.0	1.50904	0.754518	−	0.656279i	$-0.227871\pi$
$883$	39595.0	1.50904	0.754518	+	0.656279i	$0.227871\pi$
$884$	−9434.73	−0.358964
$885$	−607.106	−0.0230595
$886$	−7247.53	−0.274814
$887$	−7224.77	−0.273488	−0.136744	−	0.990606i	$-0.543664\pi$
$887$	−7224.77	−0.273488	−0.136744	+	0.990606i	$0.543664\pi$
$888$	−12121.1	−0.458060
$889$	−11644.7	−0.439315
$890$	707.320	0.0266398
$891$	−891.000	−0.0335013
$892$	−34553.3	−1.29701
$893$	−19578.3	−0.733664
$894$	5181.16	0.193830
$895$	−13867.1	−0.517905
$896$	−19107.2	−0.712418
$897$	10148.7	0.377764
$898$	659.695	0.0245148
$899$	−14407.9	−0.534515
$900$	1071.75	0.0396944
$901$	−7707.09	−0.284973
$902$	−1582.39	−0.0584121
$903$	−14426.2	−0.531645
$904$	−8159.36	−0.300195
$905$	30733.6	1.12886
$906$	−3768.38	−0.138185
$907$	21820.4	0.798826	0.399413	−	0.916771i	$-0.369214\pi$
$907$	21820.4	0.798826	0.399413	+	0.916771i	$0.369214\pi$
$908$	16461.1	0.601633
$909$	5845.41	0.213289
$910$	−7419.05	−0.270263
$911$	−35329.6	−1.28488	−0.642438	−	0.766338i	$-0.722077\pi$
$911$	−35329.6	−1.28488	−0.642438	+	0.766338i	$0.722077\pi$
$912$	−15835.4	−0.574959
$913$	8736.88	0.316702
$914$	4092.51	0.148105
$915$	−1910.54	−0.0690280
$916$	42020.4	1.51571
$917$	24204.0	0.871633
$918$	403.653	0.0145126
$919$	39492.5	1.41756	0.708779	−	0.705430i	$-0.249246\pi$
$919$	39492.5	1.41756	0.708779	+	0.705430i	$0.249246\pi$
$920$	6430.02	0.230426
$921$	16444.1	0.588330
$922$	3826.46	0.136679
$923$	31173.5	1.11169
$924$	3680.29	0.131031
$925$	−5600.73	−0.199082
$926$	−4789.95	−0.169987
$927$	9978.35	0.353540
$928$	30224.1	1.06913
$929$	−6520.87	−0.230294	−0.115147	−	0.993348i	$-0.536734\pi$
$929$	−6520.87	−0.230294	−0.115147	+	0.993348i	$0.536734\pi$
$930$	−1455.87	−0.0513333
$931$	−12275.8	−0.432141
$932$	−14742.4	−0.518137
$933$	−14630.4	−0.513372
$934$	6439.42	0.225593
$935$	2296.25	0.0803160
$936$	6589.00	0.230094
$937$	−31996.8	−1.11557	−0.557785	−	0.829985i	$-0.688349\pi$
$937$	−31996.8	−1.11557	−0.557785	+	0.829985i	$0.688349\pi$
$938$	2191.46	0.0762834
$939$	−8807.38	−0.306089
$940$	−14664.9	−0.508848
$941$	−53913.4	−1.86772	−0.933861	−	0.357636i	$-0.883583\pi$
$941$	−53913.4	−1.86772	−0.933861	+	0.357636i	$0.883583\pi$
$942$	−2200.48	−0.0761098
$943$	10263.7	0.354436
$944$	−986.543	−0.0340140
$945$	−4224.83	−0.145432
$946$	−2638.82	−0.0906927
$947$	−26208.9	−0.899339	−0.449670	−	0.893195i	$-0.648458\pi$
$947$	−26208.9	−0.899339	−0.449670	+	0.893195i	$0.648458\pi$
$948$	−19797.9	−0.678275
$949$	−359.552	−0.0122988
$950$	1241.01	0.0423827
$951$	3323.41	0.113322
$952$	−3459.86	−0.117789
$953$	36185.7	1.22998	0.614989	−	0.788535i	$-0.289160\pi$
$953$	36185.7	1.22998	0.614989	+	0.788535i	$0.289160\pi$
$954$	2593.79	0.0880264
$955$	−29430.9	−0.997238
$956$	−26351.2	−0.891483
$957$	−7647.86	−0.258328
$958$	−13121.7	−0.442528
$959$	24920.6	0.839133
$960$	−9698.45	−0.326058
$961$	−25926.0	−0.870264
$962$	−16593.0	−0.556113
$963$	14029.9	0.469478
$964$	−25580.8	−0.854671
$965$	−31540.9	−1.05216
$966$	1793.47	0.0597348
$967$	−21425.3	−0.712505	−0.356252	−	0.934390i	$-0.615946\pi$
$967$	−21425.3	−0.712505	−0.356252	+	0.934390i	$0.615946\pi$
$968$	1396.96	0.0463842
$969$	−6221.16	−0.206246
$970$	−1783.64	−0.0590403
$971$	22700.0	0.750233	0.375116	−	0.926978i	$-0.377603\pi$
$971$	22700.0	0.750233	0.375116	+	0.926978i	$0.377603\pi$
$972$	1808.15	0.0596672
$973$	7814.53	0.257474
$974$	891.233	0.0293192
$975$	3044.55	0.100004
$976$	−3104.62	−0.101820
$977$	1909.53	0.0625293	0.0312647	−	0.999511i	$-0.490047\pi$
$977$	1909.53	0.0625293	0.0312647	+	0.999511i	$0.490047\pi$
$978$	−7065.53	−0.231013
$979$	−996.734	−0.0325391
$980$	−9195.07	−0.299720
$981$	7371.53	0.239913
$982$	−13380.3	−0.434809
$983$	52515.3	1.70395	0.851973	−	0.523586i	$-0.175406\pi$
$983$	52515.3	1.70395	0.851973	+	0.523586i	$0.175406\pi$
$984$	6663.69	0.215885
$985$	26304.3	0.850887
$986$	3464.74	0.111907
$987$	−8488.01	−0.273735
$988$	−48937.0	−1.57580
$989$	17116.0	0.550310
$990$	−772.796	−0.0248091
$991$	−35600.0	−1.14114	−0.570570	−	0.821249i	$-0.693278\pi$
$991$	−35600.0	−1.14114	−0.570570	+	0.821249i	$0.693278\pi$
$992$	−8107.76	−0.259498
$993$	27519.4	0.879458
$994$	5508.96	0.175788
$995$	−49546.6	−1.57863
$996$	−17730.2	−0.564059
$997$	54143.8	1.71991	0.859956	−	0.510368i	$-0.170491\pi$
$997$	54143.8	1.71991	0.859956	+	0.510368i	$0.170491\pi$
$998$	−13129.6	−0.416444
$999$	−9449.01	−0.299253

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.e.1.17	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.e.1.17	✓	38	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q-0.747694 q^{2} -3.00000 q^{3} -7.44095 q^{4} -10.4401 q^{5} +2.24308 q^{6} -14.9879 q^{7} +11.5451 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-0.747694 q^{2} -3.00000 q^{3} -7.44095 q^{4} -10.4401 q^{5} +2.24308 q^{6} -14.9879 q^{7} +11.5451 q^{8} +9.00000 q^{9} +7.80602 q^{10} -11.0000 q^{11} +22.3229 q^{12} +63.4132 q^{13} +11.2063 q^{14} +31.3204 q^{15} +50.8954 q^{16} +19.9950 q^{17} -6.72924 q^{18} +103.712 q^{19} +77.6845 q^{20} +44.9636 q^{21} +8.22463 q^{22} -53.3469 q^{23} -34.6353 q^{24} -16.0038 q^{25} -47.4136 q^{26} -27.0000 q^{27} +111.524 q^{28} -231.753 q^{29} -23.4180 q^{30} +62.1689 q^{31} -130.415 q^{32} +33.0000 q^{33} -14.9501 q^{34} +156.475 q^{35} -66.9686 q^{36} +349.963 q^{37} -77.5448 q^{38} -190.240 q^{39} -120.532 q^{40} -192.396 q^{41} -33.6190 q^{42} -320.843 q^{43} +81.8505 q^{44} -93.9611 q^{45} +39.8871 q^{46} -188.775 q^{47} -152.686 q^{48} -118.364 q^{49} +11.9659 q^{50} -59.9850 q^{51} -471.855 q^{52} -385.451 q^{53} +20.1877 q^{54} +114.841 q^{55} -173.036 q^{56} -311.136 q^{57} +173.281 q^{58} -19.3837 q^{59} -233.054 q^{60} -61.0000 q^{61} -46.4833 q^{62} -134.891 q^{63} -309.653 q^{64} -662.042 q^{65} -24.6739 q^{66} +195.556 q^{67} -148.782 q^{68} +160.041 q^{69} -116.995 q^{70} +491.594 q^{71} +103.906 q^{72} -5.66998 q^{73} -261.665 q^{74} +48.0113 q^{75} -771.716 q^{76} +164.866 q^{77} +142.241 q^{78} -886.887 q^{79} -531.355 q^{80} +81.0000 q^{81} +143.853 q^{82} -794.262 q^{83} -334.572 q^{84} -208.750 q^{85} +239.892 q^{86} +695.260 q^{87} -126.996 q^{88} +90.6122 q^{89} +70.2541 q^{90} -950.427 q^{91} +396.952 q^{92} -186.507 q^{93} +141.146 q^{94} -1082.77 q^{95} +391.245 q^{96} -228.495 q^{97} +88.5002 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 2 q^{2} - 114 q^{3} + 142 q^{4} + 15 q^{5} + 6 q^{6} + 63 q^{7} - 45 q^{8} + 342 q^{9}+O(q^{10}) \) 38 * q - 2 * q^2 - 114 * q^3 + 142 * q^4 + 15 * q^5 + 6 * q^6 + 63 * q^7 - 45 * q^8 + 342 * q^9	\( 38 q - 2 q^{2} - 114 q^{3} + 142 q^{4} + 15 q^{5} + 6 q^{6} + 63 q^{7} - 45 q^{8} + 342 q^{9} + 95 q^{10} - 418 q^{11} - 426 q^{12} + 13 q^{13} + 26 q^{14} - 45 q^{15} + 486 q^{16} - 224 q^{17} - 18 q^{18} + 367 q^{19} + 18 q^{20} - 189 q^{21} + 22 q^{22} + 51 q^{23} + 135 q^{24} + 773 q^{25} - 439 q^{26} - 1026 q^{27} + 22 q^{28} - 462 q^{29} - 285 q^{30} + 234 q^{31} - 597 q^{32} + 1254 q^{33} + 956 q^{34} - 522 q^{35} + 1278 q^{36} + 954 q^{37} + 705 q^{38} - 39 q^{39} + 1495 q^{40} - 740 q^{41} - 78 q^{42} + 1441 q^{43} - 1562 q^{44} + 135 q^{45} + 581 q^{46} + 1003 q^{47} - 1458 q^{48} + 2707 q^{49} + 388 q^{50} + 672 q^{51} + 788 q^{52} + 735 q^{53} + 54 q^{54} - 165 q^{55} + 1059 q^{56} - 1101 q^{57} + 177 q^{58} + 261 q^{59} - 54 q^{60} - 2318 q^{61} + 1251 q^{62} + 567 q^{63} + 5571 q^{64} - 1354 q^{65} - 66 q^{66} + 3495 q^{67} - 1856 q^{68} - 153 q^{69} + 542 q^{70} - 873 q^{71} - 405 q^{72} + 989 q^{73} - 3406 q^{74} - 2319 q^{75} + 1712 q^{76} - 693 q^{77} + 1317 q^{78} + 2313 q^{79} + 1593 q^{80} + 3078 q^{81} + 5170 q^{82} + 569 q^{83} - 66 q^{84} - 1271 q^{85} + 3065 q^{86} + 1386 q^{87} + 495 q^{88} - 2917 q^{89} + 855 q^{90} + 2740 q^{91} + 1083 q^{92} - 702 q^{93} + 3272 q^{94} + 2696 q^{95} + 1791 q^{96} + 4250 q^{97} + 5952 q^{98} - 3762 q^{99}+O(q^{100}) \) 38 * q - 2 * q^2 - 114 * q^3 + 142 * q^4 + 15 * q^5 + 6 * q^6 + 63 * q^7 - 45 * q^8 + 342 * q^9 + 95 * q^10 - 418 * q^11 - 426 * q^12 + 13 * q^13 + 26 * q^14 - 45 * q^15 + 486 * q^16 - 224 * q^17 - 18 * q^18 + 367 * q^19 + 18 * q^20 - 189 * q^21 + 22 * q^22 + 51 * q^23 + 135 * q^24 + 773 * q^25 - 439 * q^26 - 1026 * q^27 + 22 * q^28 - 462 * q^29 - 285 * q^30 + 234 * q^31 - 597 * q^32 + 1254 * q^33 + 956 * q^34 - 522 * q^35 + 1278 * q^36 + 954 * q^37 + 705 * q^38 - 39 * q^39 + 1495 * q^40 - 740 * q^41 - 78 * q^42 + 1441 * q^43 - 1562 * q^44 + 135 * q^45 + 581 * q^46 + 1003 * q^47 - 1458 * q^48 + 2707 * q^49 + 388 * q^50 + 672 * q^51 + 788 * q^52 + 735 * q^53 + 54 * q^54 - 165 * q^55 + 1059 * q^56 - 1101 * q^57 + 177 * q^58 + 261 * q^59 - 54 * q^60 - 2318 * q^61 + 1251 * q^62 + 567 * q^63 + 5571 * q^64 - 1354 * q^65 - 66 * q^66 + 3495 * q^67 - 1856 * q^68 - 153 * q^69 + 542 * q^70 - 873 * q^71 - 405 * q^72 + 989 * q^73 - 3406 * q^74 - 2319 * q^75 + 1712 * q^76 - 693 * q^77 + 1317 * q^78 + 2313 * q^79 + 1593 * q^80 + 3078 * q^81 + 5170 * q^82 + 569 * q^83 - 66 * q^84 - 1271 * q^85 + 3065 * q^86 + 1386 * q^87 + 495 * q^88 - 2917 * q^89 + 855 * q^90 + 2740 * q^91 + 1083 * q^92 - 702 * q^93 + 3272 * q^94 + 2696 * q^95 + 1791 * q^96 + 4250 * q^97 + 5952 * q^98 - 3762 * q^99

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