LMFDB - Embedded newform 2013.4.a.d.1.1

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:	$1$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q-5.57224 q^{2} -3.00000 q^{3} +23.0498 q^{4} -16.5315 q^{5} +16.7167 q^{6} -30.4189 q^{7} -83.8611 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-5.57224 q^{2} -3.00000 q^{3} +23.0498 q^{4} -16.5315 q^{5} +16.7167 q^{6} -30.4189 q^{7} -83.8611 q^{8} +9.00000 q^{9} +92.1176 q^{10} +11.0000 q^{11} -69.1494 q^{12} -61.2329 q^{13} +169.501 q^{14} +49.5946 q^{15} +282.895 q^{16} -7.29442 q^{17} -50.1501 q^{18} -92.9231 q^{19} -381.049 q^{20} +91.2568 q^{21} -61.2946 q^{22} +17.5842 q^{23} +251.583 q^{24} +148.292 q^{25} +341.204 q^{26} -27.0000 q^{27} -701.150 q^{28} -89.4499 q^{29} -276.353 q^{30} -312.734 q^{31} -905.469 q^{32} -33.0000 q^{33} +40.6462 q^{34} +502.871 q^{35} +207.448 q^{36} -383.100 q^{37} +517.789 q^{38} +183.699 q^{39} +1386.35 q^{40} +327.295 q^{41} -508.504 q^{42} -285.821 q^{43} +253.548 q^{44} -148.784 q^{45} -97.9832 q^{46} +367.713 q^{47} -848.685 q^{48} +582.311 q^{49} -826.316 q^{50} +21.8833 q^{51} -1411.41 q^{52} +655.804 q^{53} +150.450 q^{54} -181.847 q^{55} +2550.96 q^{56} +278.769 q^{57} +498.436 q^{58} -279.318 q^{59} +1143.15 q^{60} -61.0000 q^{61} +1742.63 q^{62} -273.770 q^{63} +2782.33 q^{64} +1012.27 q^{65} +183.884 q^{66} -215.525 q^{67} -168.135 q^{68} -52.7526 q^{69} -2802.12 q^{70} +183.709 q^{71} -754.749 q^{72} -592.778 q^{73} +2134.72 q^{74} -444.875 q^{75} -2141.86 q^{76} -334.608 q^{77} -1023.61 q^{78} +1095.86 q^{79} -4676.69 q^{80} +81.0000 q^{81} -1823.76 q^{82} -1257.28 q^{83} +2103.45 q^{84} +120.588 q^{85} +1592.66 q^{86} +268.350 q^{87} -922.472 q^{88} -547.525 q^{89} +829.058 q^{90} +1862.64 q^{91} +405.312 q^{92} +938.203 q^{93} -2048.98 q^{94} +1536.16 q^{95} +2716.41 q^{96} +1495.38 q^{97} -3244.77 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q - 4 q^{2} - 111 q^{3} + 158 q^{4} - 15 q^{5} + 12 q^{6} - 77 q^{7} - 69 q^{8} + 333 q^{9}+O(q^{10}) $ 37 * q - 4 * q^2 - 111 * q^3 + 158 * q^4 - 15 * q^5 + 12 * q^6 - 77 * q^7 - 69 * q^8 + 333 * q^9	\( 37 q - 4 q^{2} - 111 q^{3} + 158 q^{4} - 15 q^{5} + 12 q^{6} - 77 q^{7} - 69 q^{8} + 333 q^{9} - 45 q^{10} + 407 q^{11} - 474 q^{12} - 169 q^{13} + 102 q^{14} + 45 q^{15} + 598 q^{16} - 338 q^{17} - 36 q^{18} - 235 q^{19} - 550 q^{20} + 231 q^{21} - 44 q^{22} - 53 q^{23} + 207 q^{24} + 750 q^{25} - 75 q^{26} - 999 q^{27} - 1378 q^{28} - 30 q^{29} + 135 q^{30} - 506 q^{31} - 841 q^{32} - 1221 q^{33} - 316 q^{34} - 822 q^{35} + 1422 q^{36} - 830 q^{37} - 371 q^{38} + 507 q^{39} - 613 q^{40} + 16 q^{41} - 306 q^{42} - 1137 q^{43} + 1738 q^{44} - 135 q^{45} - 659 q^{46} - 489 q^{47} - 1794 q^{48} + 2214 q^{49} + 1066 q^{50} + 1014 q^{51} - 2342 q^{52} + 731 q^{53} + 108 q^{54} - 165 q^{55} + 3051 q^{56} + 705 q^{57} - 611 q^{58} - 425 q^{59} + 1650 q^{60} - 2257 q^{61} + 453 q^{62} - 693 q^{63} + 4919 q^{64} + 1346 q^{65} + 132 q^{66} - 1907 q^{67} - 3236 q^{68} + 159 q^{69} - 1050 q^{70} - 561 q^{71} - 621 q^{72} - 2397 q^{73} - 1840 q^{74} - 2250 q^{75} - 3868 q^{76} - 847 q^{77} + 225 q^{78} + 393 q^{79} - 4031 q^{80} + 2997 q^{81} - 1946 q^{82} - 4191 q^{83} + 4134 q^{84} - 2667 q^{85} + 2405 q^{86} + 90 q^{87} - 759 q^{88} + 1437 q^{89} - 405 q^{90} - 5192 q^{91} - 737 q^{92} + 1518 q^{93} - 1960 q^{94} + 1356 q^{95} + 2523 q^{96} - 2368 q^{97} - 3014 q^{98} + 3663 q^{99}+O(q^{100}) \) 37 * q - 4 * q^2 - 111 * q^3 + 158 * q^4 - 15 * q^5 + 12 * q^6 - 77 * q^7 - 69 * q^8 + 333 * q^9 - 45 * q^10 + 407 * q^11 - 474 * q^12 - 169 * q^13 + 102 * q^14 + 45 * q^15 + 598 * q^16 - 338 * q^17 - 36 * q^18 - 235 * q^19 - 550 * q^20 + 231 * q^21 - 44 * q^22 - 53 * q^23 + 207 * q^24 + 750 * q^25 - 75 * q^26 - 999 * q^27 - 1378 * q^28 - 30 * q^29 + 135 * q^30 - 506 * q^31 - 841 * q^32 - 1221 * q^33 - 316 * q^34 - 822 * q^35 + 1422 * q^36 - 830 * q^37 - 371 * q^38 + 507 * q^39 - 613 * q^40 + 16 * q^41 - 306 * q^42 - 1137 * q^43 + 1738 * q^44 - 135 * q^45 - 659 * q^46 - 489 * q^47 - 1794 * q^48 + 2214 * q^49 + 1066 * q^50 + 1014 * q^51 - 2342 * q^52 + 731 * q^53 + 108 * q^54 - 165 * q^55 + 3051 * q^56 + 705 * q^57 - 611 * q^58 - 425 * q^59 + 1650 * q^60 - 2257 * q^61 + 453 * q^62 - 693 * q^63 + 4919 * q^64 + 1346 * q^65 + 132 * q^66 - 1907 * q^67 - 3236 * q^68 + 159 * q^69 - 1050 * q^70 - 561 * q^71 - 621 * q^72 - 2397 * q^73 - 1840 * q^74 - 2250 * q^75 - 3868 * q^76 - 847 * q^77 + 225 * q^78 + 393 * q^79 - 4031 * q^80 + 2997 * q^81 - 1946 * q^82 - 4191 * q^83 + 4134 * q^84 - 2667 * q^85 + 2405 * q^86 + 90 * q^87 - 759 * q^88 + 1437 * q^89 - 405 * q^90 - 5192 * q^91 - 737 * q^92 + 1518 * q^93 - 1960 * q^94 + 1356 * q^95 + 2523 * q^96 - 2368 * q^97 - 3014 * q^98 + 3663 * 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 $

$2$	−5.57224	−1.97008	−0.985041	−	0.172318i	$-0.944874\pi$
$2$	−5.57224	−1.97008	−0.985041	+	0.172318i	$0.944874\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	23.0498	2.88123
$5$	−16.5315	−1.47863	−0.739313	−	0.673362i	$-0.764849\pi$
$5$	−16.5315	−1.47863	−0.739313	+	0.673362i	$0.764849\pi$
$6$	16.7167	1.13743
$7$	−30.4189	−1.64247	−0.821234	−	0.570592i	$-0.806714\pi$
$7$	−30.4189	−1.64247	−0.821234	+	0.570592i	$0.806714\pi$
$8$	−83.8611	−3.70617
$9$	9.00000	0.333333
$10$	92.1176	2.91301
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−69.1494	−1.66348
$13$	−61.2329	−1.30638	−0.653191	−	0.757193i	$-0.726570\pi$
$13$	−61.2329	−1.30638	−0.653191	+	0.757193i	$0.726570\pi$
$14$	169.501	3.23580
$15$	49.5946	0.853685
$16$	282.895	4.42024
$17$	−7.29442	−0.104068	−0.0520340	−	0.998645i	$-0.516570\pi$
$17$	−7.29442	−0.104068	−0.0520340	+	0.998645i	$0.516570\pi$
$18$	−50.1501	−0.656694
$19$	−92.9231	−1.12200	−0.561000	−	0.827815i	$-0.689583\pi$
$19$	−92.9231	−1.12200	−0.561000	+	0.827815i	$0.689583\pi$
$20$	−381.049	−4.26025
$21$	91.2568	0.948279
$22$	−61.2946	−0.594002
$23$	17.5842	0.159416	0.0797078	−	0.996818i	$-0.474601\pi$
$23$	17.5842	0.159416	0.0797078	+	0.996818i	$0.474601\pi$
$24$	251.583	2.13976
$25$	148.292	1.18633
$26$	341.204	2.57368
$27$	−27.0000	−0.192450
$28$	−701.150	−4.73232
$29$	−89.4499	−0.572773	−0.286387	−	0.958114i	$-0.592454\pi$
$29$	−89.4499	−0.572773	−0.286387	+	0.958114i	$0.592454\pi$
$30$	−276.353	−1.68183
$31$	−312.734	−1.81190	−0.905948	−	0.423390i	$-0.860840\pi$
$31$	−312.734	−1.81190	−0.905948	+	0.423390i	$0.860840\pi$
$32$	−905.469	−5.00206
$33$	−33.0000	−0.174078
$34$	40.6462	0.205023
$35$	502.871	2.42859
$36$	207.448	0.960409
$37$	−383.100	−1.70219	−0.851097	−	0.525008i	$-0.824062\pi$
$37$	−383.100	−1.70219	−0.851097	+	0.525008i	$0.824062\pi$
$38$	517.789	2.21043
$39$	183.699	0.754240
$40$	1386.35	5.48004
$41$	327.295	1.24670	0.623352	−	0.781942i	$-0.285771\pi$
$41$	327.295	1.24670	0.623352	+	0.781942i	$0.285771\pi$
$42$	−508.504	−1.86819
$43$	−285.821	−1.01366	−0.506829	−	0.862047i	$-0.669182\pi$
$43$	−285.821	−1.01366	−0.506829	+	0.862047i	$0.669182\pi$
$44$	253.548	0.868722
$45$	−148.784	−0.492875
$46$	−97.9832	−0.314062
$47$	367.713	1.14120	0.570600	−	0.821228i	$-0.306711\pi$
$47$	367.713	1.14120	0.570600	+	0.821228i	$0.306711\pi$
$48$	−848.685	−2.55202
$49$	582.311	1.69770
$50$	−826.316	−2.33718
$51$	21.8833	0.0600837
$52$	−1411.41	−3.76398
$53$	655.804	1.69965	0.849826	−	0.527063i	$-0.176707\pi$
$53$	655.804	1.69965	0.849826	+	0.527063i	$0.176707\pi$
$54$	150.450	0.379143
$55$	−181.847	−0.445822
$56$	2550.96	6.08726
$57$	278.769	0.647788
$58$	498.436	1.12841
$59$	−279.318	−0.616340	−0.308170	−	0.951331i	$-0.599717\pi$
$59$	−279.318	−0.616340	−0.308170	+	0.951331i	$0.599717\pi$
$60$	1143.15	2.45966
$61$	−61.0000	−0.128037
$61$	−61.0000	−0.128037
$62$	1742.63	3.56958
$63$	−273.770	−0.547489
$64$	2782.33	5.43423
$65$	1012.27	1.93165
$66$	183.884	0.342947
$67$	−215.525	−0.392994	−0.196497	−	0.980504i	$-0.562957\pi$
$67$	−215.525	−0.392994	−0.196497	+	0.980504i	$0.562957\pi$
$68$	−168.135	−0.299843
$69$	−52.7526	−0.0920386
$70$	−2802.12	−4.78453
$71$	183.709	0.307075	0.153537	−	0.988143i	$-0.450933\pi$
$71$	183.709	0.307075	0.153537	+	0.988143i	$0.450933\pi$
$72$	−754.749	−1.23539
$73$	−592.778	−0.950404	−0.475202	−	0.879877i	$-0.657625\pi$
$73$	−592.778	−0.950404	−0.475202	+	0.879877i	$0.657625\pi$
$74$	2134.72	3.35346
$75$	−444.875	−0.684930
$76$	−2141.86	−3.23274
$77$	−334.608	−0.495223
$78$	−1023.61	−1.48591
$79$	1095.86	1.56068	0.780341	−	0.625354i	$-0.215046\pi$
$79$	1095.86	1.56068	0.780341	+	0.625354i	$0.215046\pi$
$80$	−4676.69	−6.53587
$81$	81.0000	0.111111
$82$	−1823.76	−2.45611
$83$	−1257.28	−1.66271	−0.831353	−	0.555744i	$-0.812433\pi$
$83$	−1257.28	−1.66271	−0.831353	+	0.555744i	$0.812433\pi$
$84$	2103.45	2.73221
$85$	120.588	0.153878
$86$	1592.66	1.99699
$87$	268.350	0.330691
$88$	−922.472	−1.11745
$89$	−547.525	−0.652107	−0.326054	−	0.945351i	$-0.605719\pi$
$89$	−547.525	−0.652107	−0.326054	+	0.945351i	$0.605719\pi$
$90$	829.058	0.971005
$91$	1862.64	2.14569
$92$	405.312	0.459312
$93$	938.203	1.04610
$94$	−2048.98	−2.24826
$95$	1536.16	1.65902
$96$	2716.41	2.88794
$97$	1495.38	1.56529	0.782645	−	0.622468i	$-0.213870\pi$
$97$	1495.38	1.56529	0.782645	+	0.622468i	$0.213870\pi$
$98$	−3244.77	−3.34461
$99$	99.0000	0.100504
$100$	3418.09	3.41809
$101$	482.549	0.475400	0.237700	−	0.971339i	$-0.423606\pi$
$101$	482.549	0.475400	0.237700	+	0.971339i	$0.423606\pi$
$102$	−121.939	−0.118370
$103$	1172.38	1.12153	0.560767	−	0.827974i	$-0.310507\pi$
$103$	1172.38	1.12153	0.560767	+	0.827974i	$0.310507\pi$
$104$	5135.06	4.84167
$105$	−1508.61	−1.40215
$106$	−3654.29	−3.34846
$107$	−1735.99	−1.56845	−0.784225	−	0.620477i	$-0.786939\pi$
$107$	−1735.99	−1.56845	−0.784225	+	0.620477i	$0.786939\pi$
$108$	−622.345	−0.554492
$109$	−171.658	−0.150842	−0.0754211	−	0.997152i	$-0.524030\pi$
$109$	−171.658	−0.150842	−0.0754211	+	0.997152i	$0.524030\pi$
$110$	1013.29	0.878307
$111$	1149.30	0.982763
$112$	−8605.36	−7.26009
$113$	−328.705	−0.273646	−0.136823	−	0.990596i	$-0.543689\pi$
$113$	−328.705	−0.273646	−0.136823	+	0.990596i	$0.543689\pi$
$114$	−1553.37	−1.27620
$115$	−290.694	−0.235716
$116$	−2061.80	−1.65029
$117$	−551.096	−0.435461
$118$	1556.42	1.21424
$119$	221.888	0.170928
$120$	−4159.06	−3.16390
$121$	121.000	0.0909091
$122$	339.906	0.252243
$123$	−981.884	−0.719785
$124$	−7208.47	−5.22048
$125$	−385.048	−0.275518
$126$	1525.51	1.07860
$127$	1959.21	1.36891	0.684456	−	0.729054i	$-0.260040\pi$
$127$	1959.21	1.36891	0.684456	+	0.729054i	$0.260040\pi$
$128$	−8260.03	−5.70383
$129$	857.463	0.585236
$130$	−5640.63	−3.80551
$131$	152.891	0.101970	0.0509852	−	0.998699i	$-0.483764\pi$
$131$	152.891	0.101970	0.0509852	+	0.998699i	$0.483764\pi$
$132$	−760.644	−0.501557
$133$	2826.62	1.84285
$134$	1200.96	0.774231
$135$	446.351	0.284562
$136$	611.718	0.385694
$137$	2563.16	1.59844	0.799219	−	0.601040i	$-0.205247\pi$
$137$	2563.16	1.59844	0.799219	+	0.601040i	$0.205247\pi$
$138$	293.950	0.181324
$139$	−45.3912	−0.0276981	−0.0138490	−	0.999904i	$-0.504408\pi$
$139$	−45.3912	−0.0276981	−0.0138490	+	0.999904i	$0.504408\pi$
$140$	11591.1	6.99733
$141$	−1103.14	−0.658872
$142$	−1023.67	−0.604963
$143$	−673.562	−0.393889
$144$	2546.06	1.47341
$145$	1478.74	0.846917
$146$	3303.10	1.87237
$147$	−1746.93	−0.980167
$148$	−8830.37	−4.90441
$149$	1079.43	0.593490	0.296745	−	0.954957i	$-0.404099\pi$
$149$	1079.43	0.593490	0.296745	+	0.954957i	$0.404099\pi$
$150$	2478.95	1.34937
$151$	357.700	0.192776	0.0963881	−	0.995344i	$-0.469271\pi$
$151$	357.700	0.192776	0.0963881	+	0.995344i	$0.469271\pi$
$152$	7792.63	4.15833
$153$	−65.6498	−0.0346893
$154$	1864.52	0.975629
$155$	5169.98	2.67911
$156$	4234.22	2.17313
$157$	534.342	0.271625	0.135813	−	0.990735i	$-0.456636\pi$
$157$	534.342	0.271625	0.135813	+	0.990735i	$0.456636\pi$
$158$	−6106.39	−3.07467
$159$	−1967.41	−0.981295
$160$	14968.8	7.39617
$161$	−534.892	−0.261835
$162$	−451.351	−0.218898
$163$	−413.402	−0.198651	−0.0993255	−	0.995055i	$-0.531669\pi$
$163$	−413.402	−0.198651	−0.0993255	+	0.995055i	$0.531669\pi$
$164$	7544.08	3.59203
$165$	545.541	0.257396
$166$	7005.87	3.27567
$167$	−930.491	−0.431159	−0.215580	−	0.976486i	$-0.569164\pi$
$167$	−930.491	−0.431159	−0.215580	+	0.976486i	$0.569164\pi$
$168$	−7652.89	−3.51448
$169$	1552.47	0.706633
$170$	−671.945	−0.303152
$171$	−836.308	−0.374000
$172$	−6588.12	−2.92058
$173$	−4083.63	−1.79464	−0.897320	−	0.441380i	$-0.854489\pi$
$173$	−4083.63	−1.79464	−0.897320	+	0.441380i	$0.854489\pi$
$174$	−1495.31	−0.651488
$175$	−4510.87	−1.94851
$176$	3111.85	1.33275
$177$	837.953	0.355844
$178$	3050.94	1.28471
$179$	−354.695	−0.148107	−0.0740536	−	0.997254i	$-0.523594\pi$
$179$	−354.695	−0.148107	−0.0740536	+	0.997254i	$0.523594\pi$
$180$	−3429.44	−1.42008
$181$	1002.91	0.411854	0.205927	−	0.978567i	$-0.433979\pi$
$181$	1002.91	0.411854	0.205927	+	0.978567i	$0.433979\pi$
$182$	−10379.1	−4.22718
$183$	183.000	0.0739221
$184$	−1474.63	−0.590821
$185$	6333.23	2.51691
$186$	−5227.89	−2.06090
$187$	−80.2386	−0.0313777
$188$	8475.71	3.28805
$189$	821.311	0.316093
$190$	−8559.85	−3.26841
$191$	1407.14	0.533073	0.266536	−	0.963825i	$-0.414121\pi$
$191$	1407.14	0.533073	0.266536	+	0.963825i	$0.414121\pi$
$192$	−8346.98	−3.13746
$193$	1153.50	0.430210	0.215105	−	0.976591i	$-0.430991\pi$
$193$	1153.50	0.430210	0.215105	+	0.976591i	$0.430991\pi$
$194$	−8332.63	−3.08375
$195$	−3036.82	−1.11524
$196$	13422.1	4.89145
$197$	4948.55	1.78969	0.894847	−	0.446373i	$-0.147285\pi$
$197$	4948.55	1.78969	0.894847	+	0.446373i	$0.147285\pi$
$198$	−551.651	−0.198001
$199$	−1378.64	−0.491103	−0.245551	−	0.969384i	$-0.578969\pi$
$199$	−1378.64	−0.491103	−0.245551	+	0.969384i	$0.578969\pi$
$200$	−12435.9	−4.39675
$201$	646.576	0.226895
$202$	−2688.88	−0.936578
$203$	2720.97	0.940761
$204$	504.405	0.173115
$205$	−5410.68	−1.84341
$206$	−6532.77	−2.20951
$207$	158.258	0.0531385
$208$	−17322.5	−5.77451
$209$	−1022.15	−0.338296
$210$	8406.35	2.76235
$211$	5247.23	1.71201	0.856005	−	0.516968i	$-0.172939\pi$
$211$	5247.23	1.71201	0.856005	+	0.516968i	$0.172939\pi$
$212$	15116.2	4.89708
$213$	−551.128	−0.177290
$214$	9673.32	3.08997
$215$	4725.06	1.49882
$216$	2264.25	0.713253
$217$	9513.04	2.97598
$218$	956.516	0.297172
$219$	1778.34	0.548716
$220$	−4191.54	−1.28451
$221$	446.659	0.135953
$222$	−6404.17	−1.93612
$223$	3541.55	1.06350	0.531748	−	0.846903i	$-0.321535\pi$
$223$	3541.55	1.06350	0.531748	+	0.846903i	$0.321535\pi$
$224$	27543.4	8.21572
$225$	1334.63	0.395445
$226$	1831.62	0.539105
$227$	−4070.16	−1.19007	−0.595035	−	0.803699i	$-0.702862\pi$
$227$	−4070.16	−1.19007	−0.595035	+	0.803699i	$0.702862\pi$
$228$	6425.58	1.86642
$229$	−2886.13	−0.832843	−0.416422	−	0.909172i	$-0.636716\pi$
$229$	−2886.13	−0.832843	−0.416422	+	0.909172i	$0.636716\pi$
$230$	1619.81	0.464380
$231$	1003.82	0.285917
$232$	7501.36	2.12280
$233$	1722.80	0.484396	0.242198	−	0.970227i	$-0.422132\pi$
$233$	1722.80	0.484396	0.242198	+	0.970227i	$0.422132\pi$
$234$	3070.84	0.857893
$235$	−6078.86	−1.68741
$236$	−6438.21	−1.77581
$237$	−3287.58	−0.901060
$238$	−1236.41	−0.336743
$239$	7104.23	1.92274	0.961369	−	0.275264i	$-0.0887654\pi$
$239$	7104.23	1.92274	0.961369	+	0.275264i	$0.0887654\pi$
$240$	14030.1	3.77349
$241$	−333.645	−0.0891783	−0.0445892	−	0.999005i	$-0.514198\pi$
$241$	−333.645	−0.0891783	−0.0445892	+	0.999005i	$0.514198\pi$
$242$	−674.240	−0.179098
$243$	−243.000	−0.0641500
$244$	−1406.04	−0.368903
$245$	−9626.49	−2.51026
$246$	5471.29	1.41804
$247$	5689.95	1.46576
$248$	26226.2	6.71519
$249$	3771.85	0.959964
$250$	2145.58	0.542792
$251$	2596.98	0.653068	0.326534	−	0.945185i	$-0.394119\pi$
$251$	2596.98	0.653068	0.326534	+	0.945185i	$0.394119\pi$
$252$	−6310.35	−1.57744
$253$	193.426	0.0480656
$254$	−10917.2	−2.69687
$255$	−361.764	−0.0888413
$256$	23768.2	5.80278
$257$	−2478.82	−0.601652	−0.300826	−	0.953679i	$-0.597262\pi$
$257$	−2478.82	−0.601652	−0.300826	+	0.953679i	$0.597262\pi$
$258$	−4777.99	−1.15296
$259$	11653.5	2.79580
$260$	23332.7	5.56552
$261$	−805.049	−0.190924
$262$	−851.943	−0.200890
$263$	5379.76	1.26133	0.630666	−	0.776054i	$-0.282782\pi$
$263$	5379.76	1.26133	0.630666	+	0.776054i	$0.282782\pi$
$264$	2767.41	0.645161
$265$	−10841.4	−2.51315
$266$	−15750.6	−3.63057
$267$	1642.58	0.376494
$268$	−4967.82	−1.13230
$269$	3946.79	0.894573	0.447287	−	0.894391i	$-0.352390\pi$
$269$	3946.79	0.894573	0.447287	+	0.894391i	$0.352390\pi$
$270$	−2487.18	−0.560610
$271$	4675.20	1.04796	0.523981	−	0.851730i	$-0.324446\pi$
$271$	4675.20	1.04796	0.523981	+	0.851730i	$0.324446\pi$
$272$	−2063.56	−0.460005
$273$	−5587.92	−1.23881
$274$	−14282.6	−3.14905
$275$	1631.21	0.357693
$276$	−1215.94	−0.265184
$277$	−1365.24	−0.296135	−0.148068	−	0.988977i	$-0.547305\pi$
$277$	−1365.24	−0.296135	−0.148068	+	0.988977i	$0.547305\pi$
$278$	252.930	0.0545675
$279$	−2814.61	−0.603965
$280$	−42171.3	−9.00078
$281$	−542.185	−0.115103	−0.0575516	−	0.998343i	$-0.518329\pi$
$281$	−542.185	−0.115103	−0.0575516	+	0.998343i	$0.518329\pi$
$282$	6146.94	1.29803
$283$	−4908.20	−1.03096	−0.515481	−	0.856901i	$-0.672387\pi$
$283$	−4908.20	−1.03096	−0.515481	+	0.856901i	$0.672387\pi$
$284$	4234.47	0.884752
$285$	−4608.48	−0.957835
$286$	3753.25	0.775994
$287$	−9955.95	−2.04767
$288$	−8149.22	−1.66735
$289$	−4859.79	−0.989170
$290$	−8239.91	−1.66850
$291$	−4486.15	−0.903721
$292$	−13663.4	−2.73833
$293$	3002.86	0.598733	0.299367	−	0.954138i	$-0.403225\pi$
$293$	3002.86	0.598733	0.299367	+	0.954138i	$0.403225\pi$
$294$	9734.32	1.93101
$295$	4617.55	0.911336
$296$	32127.1	6.30862
$297$	−297.000	−0.0580259
$298$	−6014.82	−1.16922
$299$	−1076.73	−0.208257
$300$	−10254.3	−1.97344
$301$	8694.37	1.66490
$302$	−1993.19	−0.379785
$303$	−1447.65	−0.274473
$304$	−26287.5	−4.95951
$305$	1008.42	0.189319
$306$	365.816	0.0683409
$307$	−5285.98	−0.982693	−0.491347	−	0.870964i	$-0.663495\pi$
$307$	−5285.98	−0.982693	−0.491347	+	0.870964i	$0.663495\pi$
$308$	−7712.65	−1.42685
$309$	−3517.14	−0.647517
$310$	−28808.3	−5.27808
$311$	−7153.44	−1.30429	−0.652146	−	0.758094i	$-0.726131\pi$
$311$	−7153.44	−1.30429	−0.652146	+	0.758094i	$0.726131\pi$
$312$	−15405.2	−2.79534
$313$	−4009.73	−0.724100	−0.362050	−	0.932159i	$-0.617923\pi$
$313$	−4009.73	−0.724100	−0.362050	+	0.932159i	$0.617923\pi$
$314$	−2977.48	−0.535124
$315$	4525.84	0.809531
$316$	25259.4	4.49668
$317$	2952.48	0.523115	0.261558	−	0.965188i	$-0.415764\pi$
$317$	2952.48	0.523115	0.261558	+	0.965188i	$0.415764\pi$
$318$	10962.9	1.93323
$319$	−983.949	−0.172698
$320$	−45996.2	−8.03520
$321$	5207.96	0.905545
$322$	2980.54	0.515836
$323$	677.820	0.116764
$324$	1867.03	0.320136
$325$	−9080.34	−1.54980
$326$	2303.57	0.391359
$327$	514.973	0.0870888
$328$	−27447.3	−4.62049
$329$	−11185.4	−1.87438
$330$	−3039.88	−0.507091
$331$	−3542.70	−0.588292	−0.294146	−	0.955761i	$-0.595035\pi$
$331$	−3542.70	−0.588292	−0.294146	+	0.955761i	$0.595035\pi$
$332$	−28980.1	−4.79063
$333$	−3447.90	−0.567398
$334$	5184.91	0.849419
$335$	3562.96	0.581091
$336$	25816.1	4.19162
$337$	−2334.44	−0.377344	−0.188672	−	0.982040i	$-0.560418\pi$
$337$	−2334.44	−0.377344	−0.188672	+	0.982040i	$0.560418\pi$
$338$	−8650.74	−1.39212
$339$	986.116	0.157990
$340$	2779.53	0.443356
$341$	−3440.08	−0.546307
$342$	4660.10	0.736812
$343$	−7279.57	−1.14595
$344$	23969.3	3.75679
$345$	872.081	0.136091
$346$	22755.0	3.53559
$347$	3994.80	0.618018	0.309009	−	0.951059i	$-0.400003\pi$
$347$	3994.80	0.618018	0.309009	+	0.951059i	$0.400003\pi$
$348$	6185.41	0.952795
$349$	3420.28	0.524594	0.262297	−	0.964987i	$-0.415520\pi$
$349$	3420.28	0.524594	0.262297	+	0.964987i	$0.415520\pi$
$350$	25135.6	3.83873
$351$	1653.29	0.251413
$352$	−9960.16	−1.50818
$353$	−3025.29	−0.456147	−0.228073	−	0.973644i	$-0.573243\pi$
$353$	−3025.29	−0.456147	−0.228073	+	0.973644i	$0.573243\pi$
$354$	−4669.27	−0.701042
$355$	−3037.00	−0.454049
$356$	−12620.4	−1.87887
$357$	−665.665	−0.0986855
$358$	1976.45	0.291783
$359$	−8390.72	−1.23355	−0.616776	−	0.787138i	$-0.711562\pi$
$359$	−8390.72	−1.23355	−0.616776	+	0.787138i	$0.711562\pi$
$360$	12477.2	1.82668
$361$	1775.70	0.258886
$362$	−5588.43	−0.811385
$363$	−363.000	−0.0524864
$364$	42933.5	6.18221
$365$	9799.54	1.40529
$366$	−1019.72	−0.145633
$367$	−10579.5	−1.50475	−0.752376	−	0.658733i	$-0.771093\pi$
$367$	−10579.5	−1.50475	−0.752376	+	0.658733i	$0.771093\pi$
$368$	4974.48	0.704654
$369$	2945.65	0.415568
$370$	−35290.2	−4.95852
$371$	−19948.8	−2.79162
$372$	21625.4	3.01405
$373$	−1406.75	−0.195278	−0.0976391	−	0.995222i	$-0.531129\pi$
$373$	−1406.75	−0.195278	−0.0976391	+	0.995222i	$0.531129\pi$
$374$	447.108	0.0618167
$375$	1155.14	0.159070
$376$	−30836.8	−4.22948
$377$	5477.28	0.748260
$378$	−4576.54	−0.622729
$379$	−8710.58	−1.18056	−0.590281	−	0.807198i	$-0.700983\pi$
$379$	−8710.58	−1.18056	−0.590281	+	0.807198i	$0.700983\pi$
$380$	35408.2	4.78001
$381$	−5877.63	−0.790342
$382$	−7840.90	−1.05020
$383$	4457.45	0.594687	0.297343	−	0.954771i	$-0.403899\pi$
$383$	4457.45	0.594687	0.297343	+	0.954771i	$0.403899\pi$
$384$	24780.1	3.29311
$385$	5531.59	0.732249
$386$	−6427.55	−0.847548
$387$	−2572.39	−0.337886
$388$	34468.3	4.50995
$389$	−8382.75	−1.09260	−0.546301	−	0.837589i	$-0.683965\pi$
$389$	−8382.75	−1.09260	−0.546301	+	0.837589i	$0.683965\pi$
$390$	16921.9	2.19711
$391$	−128.266	−0.0165901
$392$	−48833.2	−6.29196
$393$	−458.672	−0.0588726
$394$	−27574.5	−3.52584
$395$	−18116.2	−2.30766
$396$	2281.93	0.289574
$397$	−1109.49	−0.140261	−0.0701305	−	0.997538i	$-0.522342\pi$
$397$	−1109.49	−0.140261	−0.0701305	+	0.997538i	$0.522342\pi$
$398$	7682.12	0.967513
$399$	−8479.86	−1.06397
$400$	41951.0	5.24387
$401$	2913.78	0.362861	0.181430	−	0.983404i	$-0.441927\pi$
$401$	2913.78	0.362861	0.181430	+	0.983404i	$0.441927\pi$
$402$	−3602.87	−0.447002
$403$	19149.6	2.36703
$404$	11122.7	1.36974
$405$	−1339.05	−0.164292
$406$	−15161.9	−1.85338
$407$	−4214.10	−0.513231
$408$	−1835.15	−0.222680
$409$	−635.051	−0.0767757	−0.0383879	−	0.999263i	$-0.512222\pi$
$409$	−635.051	−0.0767757	−0.0383879	+	0.999263i	$0.512222\pi$
$410$	30149.6	3.63167
$411$	−7689.49	−0.922858
$412$	27023.1	3.23139
$413$	8496.54	1.01232
$414$	−881.849	−0.104687
$415$	20784.8	2.45852
$416$	55444.5	6.53460
$417$	136.174	0.0159915
$418$	5695.68	0.666471
$419$	5556.99	0.647916	0.323958	−	0.946071i	$-0.394986\pi$
$419$	5556.99	0.647916	0.323958	+	0.946071i	$0.394986\pi$
$420$	−34773.3	−4.03991
$421$	−1143.03	−0.132322	−0.0661611	−	0.997809i	$-0.521075\pi$
$421$	−1143.03	−0.132322	−0.0661611	+	0.997809i	$0.521075\pi$
$422$	−29238.8	−3.37280
$423$	3309.41	0.380400
$424$	−54996.4	−6.29920
$425$	−1081.70	−0.123459
$426$	3071.02	0.349275
$427$	1855.55	0.210296
$428$	−40014.1	−4.51906
$429$	2020.69	0.227412
$430$	−26329.1	−2.95280
$431$	5139.65	0.574404	0.287202	−	0.957870i	$-0.407275\pi$
$431$	5139.65	0.574404	0.287202	+	0.957870i	$0.407275\pi$
$432$	−7638.17	−0.850675
$433$	2482.02	0.275469	0.137735	−	0.990469i	$-0.456018\pi$
$433$	2482.02	0.275469	0.137735	+	0.990469i	$0.456018\pi$
$434$	−53008.9	−5.86292
$435$	−4436.23	−0.488968
$436$	−3956.67	−0.434611
$437$	−1633.98	−0.178864
$438$	−9909.30	−1.08102
$439$	15188.3	1.65125	0.825624	−	0.564220i	$-0.190823\pi$
$439$	15188.3	1.65125	0.825624	+	0.564220i	$0.190823\pi$
$440$	15249.9	1.65229
$441$	5240.80	0.565900
$442$	−2488.89	−0.267838
$443$	−14562.9	−1.56186	−0.780929	−	0.624620i	$-0.785254\pi$
$443$	−14562.9	−1.56186	−0.780929	+	0.624620i	$0.785254\pi$
$444$	26491.1	2.83156
$445$	9051.43	0.964223
$446$	−19734.3	−2.09517
$447$	−3238.28	−0.342652
$448$	−84635.4	−8.92555
$449$	17938.1	1.88542	0.942709	−	0.333617i	$-0.108269\pi$
$449$	17938.1	1.88542	0.942709	+	0.333617i	$0.108269\pi$
$450$	−7436.85	−0.779058
$451$	3600.24	0.375895
$452$	−7576.59	−0.788436
$453$	−1073.10	−0.111299
$454$	22679.9	2.34454
$455$	−30792.3	−3.17267
$456$	−23377.9	−2.40081
$457$	−17514.5	−1.79277	−0.896385	−	0.443277i	$-0.853816\pi$
$457$	−17514.5	−1.79277	−0.896385	+	0.443277i	$0.853816\pi$
$458$	16082.2	1.64077
$459$	196.949	0.0200279
$460$	−6700.43	−0.679150
$461$	−11213.7	−1.13292	−0.566460	−	0.824089i	$-0.691687\pi$
$461$	−11213.7	−1.13292	−0.566460	+	0.824089i	$0.691687\pi$
$462$	−5593.55	−0.563280
$463$	9754.47	0.979112	0.489556	−	0.871972i	$-0.337159\pi$
$463$	9754.47	0.979112	0.489556	+	0.871972i	$0.337159\pi$
$464$	−25304.9	−2.53179
$465$	−15509.9	−1.54679
$466$	−9599.85	−0.954301
$467$	4165.30	0.412734	0.206367	−	0.978475i	$-0.433836\pi$
$467$	4165.30	0.412734	0.206367	+	0.978475i	$0.433836\pi$
$468$	−12702.7	−1.25466
$469$	6556.05	0.645480
$470$	33872.8	3.32433
$471$	−1603.03	−0.156823
$472$	23423.9	2.28426
$473$	−3144.03	−0.305629
$474$	18319.2	1.77516
$475$	−13779.7	−1.33107
$476$	5114.48	0.492483
$477$	5902.23	0.566551
$478$	−39586.4	−3.78795
$479$	−17158.1	−1.63669	−0.818346	−	0.574725i	$-0.805109\pi$
$479$	−17158.1	−1.63669	−0.818346	+	0.574725i	$0.805109\pi$
$480$	−44906.4	−4.27018
$481$	23458.3	2.22372
$482$	1859.15	0.175689
$483$	1604.68	0.151170
$484$	2789.03	0.261930
$485$	−24721.0	−2.31448
$486$	1354.05	0.126381
$487$	15367.3	1.42990	0.714948	−	0.699178i	$-0.246450\pi$
$487$	15367.3	1.42990	0.714948	+	0.699178i	$0.246450\pi$
$488$	5115.52	0.474526
$489$	1240.20	0.114691
$490$	53641.1	4.94542
$491$	1490.76	0.137021	0.0685104	−	0.997650i	$-0.478175\pi$
$491$	1490.76	0.137021	0.0685104	+	0.997650i	$0.478175\pi$
$492$	−22632.2	−2.07386
$493$	652.485	0.0596074
$494$	−31705.8	−2.88767
$495$	−1636.62	−0.148607
$496$	−88471.0	−8.00900
$497$	−5588.24	−0.504360
$498$	−21017.6	−1.89121
$499$	−11804.0	−1.05896	−0.529479	−	0.848323i	$-0.677612\pi$
$499$	−11804.0	−1.05896	−0.529479	+	0.848323i	$0.677612\pi$
$500$	−8875.27	−0.793828
$501$	2791.47	0.248930
$502$	−14471.0	−1.28660
$503$	−21781.8	−1.93082	−0.965412	−	0.260730i	$-0.916037\pi$
$503$	−21781.8	−1.93082	−0.965412	+	0.260730i	$0.916037\pi$
$504$	22958.7	2.02909
$505$	−7977.28	−0.702939
$506$	−1077.82	−0.0946932
$507$	−4657.42	−0.407975
$508$	45159.4	3.94414
$509$	18158.8	1.58129	0.790644	−	0.612277i	$-0.209746\pi$
$509$	18158.8	1.58129	0.790644	+	0.612277i	$0.209746\pi$
$510$	2015.83	0.175025
$511$	18031.7	1.56101
$512$	−66361.8	−5.72813
$513$	2508.92	0.215929
$514$	13812.6	1.18530
$515$	−19381.2	−1.65833
$516$	19764.4	1.68620
$517$	4044.84	0.344085
$518$	−64935.9	−5.50796
$519$	12250.9	1.03614
$520$	−84890.4	−7.15902
$521$	−11524.0	−0.969051	−0.484525	−	0.874777i	$-0.661008\pi$
$521$	−11524.0	−0.969051	−0.484525	+	0.874777i	$0.661008\pi$
$522$	4485.92	0.376137
$523$	10205.0	0.853222	0.426611	−	0.904435i	$-0.359707\pi$
$523$	10205.0	0.853222	0.426611	+	0.904435i	$0.359707\pi$
$524$	3524.10	0.293800
$525$	13532.6	1.12498
$526$	−29977.3	−2.48493
$527$	2281.22	0.188560
$528$	−9335.54	−0.769464
$529$	−11857.8	−0.974587
$530$	60411.1	4.95111
$531$	−2513.86	−0.205447
$532$	65153.0	5.30967
$533$	−20041.2	−1.62867
$534$	−9152.82	−0.741725
$535$	28698.5	2.31915
$536$	18074.2	1.45650
$537$	1064.09	0.0855097
$538$	−21992.5	−1.76238
$539$	6405.42	0.511876
$540$	10288.3	0.819886
$541$	−14649.1	−1.16417	−0.582085	−	0.813128i	$-0.697763\pi$
$541$	−14649.1	−1.16417	−0.582085	+	0.813128i	$0.697763\pi$
$542$	−26051.3	−2.06457
$543$	−3008.72	−0.237784
$544$	6604.87	0.520554
$545$	2837.76	0.223039
$546$	31137.2	2.44057
$547$	−2597.11	−0.203006	−0.101503	−	0.994835i	$-0.532365\pi$
$547$	−2597.11	−0.203006	−0.101503	+	0.994835i	$0.532365\pi$
$548$	59080.4	4.60546
$549$	−549.000	−0.0426790
$550$	−9089.48	−0.704685
$551$	8311.96	0.642652
$552$	4423.89	0.341111
$553$	−33334.9	−2.56337
$554$	7607.46	0.583411
$555$	−18999.7	−1.45314
$556$	−1046.26	−0.0798044
$557$	3728.73	0.283647	0.141823	−	0.989892i	$-0.454703\pi$
$557$	3728.73	0.283647	0.141823	+	0.989892i	$0.454703\pi$
$558$	15683.7	1.18986
$559$	17501.7	1.32422
$560$	142260.	10.7350
$561$	240.716	0.0181159
$562$	3021.18	0.226763
$563$	−4669.77	−0.349569	−0.174784	−	0.984607i	$-0.555923\pi$
$563$	−4669.77	−0.349569	−0.174784	+	0.984607i	$0.555923\pi$
$564$	−25427.1	−1.89836
$565$	5434.00	0.404620
$566$	27349.7	2.03108
$567$	−2463.93	−0.182496
$568$	−15406.1	−1.13807
$569$	21276.6	1.56760	0.783798	−	0.621016i	$-0.213280\pi$
$569$	21276.6	1.56760	0.783798	+	0.621016i	$0.213280\pi$
$570$	25679.6	1.88701
$571$	−20772.7	−1.52243	−0.761216	−	0.648498i	$-0.775398\pi$
$571$	−20772.7	−1.52243	−0.761216	+	0.648498i	$0.775398\pi$
$572$	−15525.5	−1.13488
$573$	−4221.41	−0.307770
$574$	55476.9	4.03408
$575$	2607.59	0.189120
$576$	25041.0	1.81141
$577$	671.550	0.0484523	0.0242262	−	0.999707i	$-0.492288\pi$
$577$	671.550	0.0484523	0.0242262	+	0.999707i	$0.492288\pi$
$578$	27079.9	1.94875
$579$	−3460.49	−0.248382
$580$	34084.8	2.44016
$581$	38245.2	2.73094
$582$	24997.9	1.78040
$583$	7213.84	0.512465
$584$	49711.0	3.52236
$585$	9110.47	0.643883
$586$	−16732.6	−1.17955
$587$	6541.53	0.459962	0.229981	−	0.973195i	$-0.426134\pi$
$587$	6541.53	0.459962	0.229981	+	0.973195i	$0.426134\pi$
$588$	−40266.4	−2.82408
$589$	29060.2	2.03295
$590$	−25730.1	−1.79541
$591$	−14845.7	−1.03328
$592$	−108377.	−7.52410
$593$	1638.53	0.113467	0.0567337	−	0.998389i	$-0.481931\pi$
$593$	1638.53	0.113467	0.0567337	+	0.998389i	$0.481931\pi$
$594$	1654.95	0.114316
$595$	−3668.16	−0.252739
$596$	24880.6	1.70998
$597$	4135.93	0.283538
$598$	5999.80	0.410284
$599$	4750.30	0.324026	0.162013	−	0.986789i	$-0.448201\pi$
$599$	4750.30	0.324026	0.162013	+	0.986789i	$0.448201\pi$
$600$	37307.7	2.53847
$601$	−15398.7	−1.04514	−0.522568	−	0.852598i	$-0.675026\pi$
$601$	−15398.7	−1.04514	−0.522568	+	0.852598i	$0.675026\pi$
$602$	−48447.1	−3.27999
$603$	−1939.73	−0.130998
$604$	8244.91	0.555432
$605$	−2000.32	−0.134421
$606$	8066.63	0.540734
$607$	1703.46	0.113906	0.0569532	−	0.998377i	$-0.481861\pi$
$607$	1703.46	0.113906	0.0569532	+	0.998377i	$0.481861\pi$
$608$	84139.0	5.61231
$609$	−8162.91	−0.543149
$610$	−5619.17	−0.372973
$611$	−22516.1	−1.49084
$612$	−1513.21	−0.0999478
$613$	9858.54	0.649564	0.324782	−	0.945789i	$-0.394709\pi$
$613$	9858.54	0.649564	0.324782	+	0.945789i	$0.394709\pi$
$614$	29454.7	1.93599
$615$	16232.1	1.06429
$616$	28060.6	1.83538
$617$	−15670.8	−1.02250	−0.511249	−	0.859432i	$-0.670817\pi$
$617$	−15670.8	−1.02250	−0.511249	+	0.859432i	$0.670817\pi$
$618$	19598.3	1.27566
$619$	7403.63	0.480738	0.240369	−	0.970682i	$-0.422732\pi$
$619$	7403.63	0.480738	0.240369	+	0.970682i	$0.422732\pi$
$620$	119167.	7.71913
$621$	−474.773	−0.0306795
$622$	39860.7	2.56956
$623$	16655.1	1.07107
$624$	51967.5	3.33392
$625$	−12171.0	−0.778946
$626$	22343.2	1.42654
$627$	3066.46	0.195315
$628$	12316.5	0.782613
$629$	2794.49	0.177144
$630$	−25219.1	−1.59484
$631$	−2256.39	−0.142354	−0.0711771	−	0.997464i	$-0.522676\pi$
$631$	−2256.39	−0.142354	−0.0711771	+	0.997464i	$0.522676\pi$
$632$	−91900.0	−5.78415
$633$	−15741.7	−0.988429
$634$	−16451.9	−1.03058
$635$	−32388.8	−2.02411
$636$	−45348.5	−2.82733
$637$	−35656.6	−2.21784
$638$	5482.79	0.340229
$639$	1653.39	0.102358
$640$	136551.	8.43383
$641$	24995.4	1.54019	0.770093	−	0.637931i	$-0.220210\pi$
$641$	24995.4	1.54019	0.770093	+	0.637931i	$0.220210\pi$
$642$	−29020.0	−1.78400
$643$	7283.66	0.446718	0.223359	−	0.974736i	$-0.428298\pi$
$643$	7283.66	0.446718	0.223359	+	0.974736i	$0.428298\pi$
$644$	−12329.2	−0.754405
$645$	−14175.2	−0.865345
$646$	−3776.97	−0.230036
$647$	15239.9	0.926030	0.463015	−	0.886350i	$-0.346768\pi$
$647$	15239.9	0.926030	0.463015	+	0.886350i	$0.346768\pi$
$648$	−6792.75	−0.411797
$649$	−3072.49	−0.185833
$650$	50597.8	3.05324
$651$	−28539.1	−1.71818
$652$	−9528.83	−0.572358
$653$	23304.7	1.39661	0.698303	−	0.715803i	$-0.253939\pi$
$653$	23304.7	1.39661	0.698303	+	0.715803i	$0.253939\pi$
$654$	−2869.55	−0.171572
$655$	−2527.52	−0.150776
$656$	92590.0	5.51072
$657$	−5335.01	−0.316801
$658$	62327.8	3.69269
$659$	−9791.76	−0.578805	−0.289403	−	0.957207i	$-0.593457\pi$
$659$	−9791.76	−0.578805	−0.289403	+	0.957207i	$0.593457\pi$
$660$	12574.6	0.741615
$661$	20130.3	1.18454	0.592269	−	0.805740i	$-0.298232\pi$
$661$	20130.3	1.18454	0.592269	+	0.805740i	$0.298232\pi$
$662$	19740.8	1.15898
$663$	−1339.98	−0.0784922
$664$	105437.	6.16227
$665$	−46728.4	−2.72489
$666$	19212.5	1.11782
$667$	−1572.90	−0.0913089
$668$	−21447.6	−1.24227
$669$	−10624.6	−0.614009
$670$	−19853.7	−1.14480
$671$	−671.000	−0.0386046
$672$	−82630.2	−4.74335
$673$	−13092.8	−0.749912	−0.374956	−	0.927043i	$-0.622342\pi$
$673$	−13092.8	−0.749912	−0.374956	+	0.927043i	$0.622342\pi$
$674$	13008.1	0.743400
$675$	−4003.88	−0.228310
$676$	35784.2	2.03597
$677$	4057.15	0.230324	0.115162	−	0.993347i	$-0.463261\pi$
$677$	4057.15	0.230324	0.115162	+	0.993347i	$0.463261\pi$
$678$	−5494.87	−0.311252
$679$	−45487.9	−2.57094
$680$	−10112.6	−0.570297
$681$	12210.5	0.687088
$682$	19168.9	1.07627
$683$	8932.94	0.500453	0.250226	−	0.968187i	$-0.419495\pi$
$683$	8932.94	0.500453	0.250226	+	0.968187i	$0.419495\pi$
$684$	−19276.7	−1.07758
$685$	−42373.1	−2.36349
$686$	40563.5	2.25761
$687$	8658.40	0.480842
$688$	−80857.4	−4.48061
$689$	−40156.8	−2.22039
$690$	−4859.44	−0.268110
$691$	−11537.2	−0.635163	−0.317581	−	0.948231i	$-0.602871\pi$
$691$	−11537.2	−0.635163	−0.317581	+	0.948231i	$0.602871\pi$
$692$	−94126.9	−5.17076
$693$	−3011.47	−0.165074
$694$	−22260.0	−1.21755
$695$	750.386	0.0409551
$696$	−22504.1	−1.22560
$697$	−2387.42	−0.129742
$698$	−19058.6	−1.03349
$699$	−5168.40	−0.279666
$700$	−103975.	−5.61411
$701$	35112.7	1.89185	0.945925	−	0.324385i	$-0.105157\pi$
$701$	35112.7	1.89185	0.945925	+	0.324385i	$0.105157\pi$
$702$	−9212.52	−0.495305
$703$	35598.8	1.90986
$704$	30605.6	1.63848
$705$	18236.6	0.974225
$706$	16857.6	0.898647
$707$	−14678.6	−0.780830
$708$	19314.6	1.02527
$709$	−10333.4	−0.547361	−0.273680	−	0.961821i	$-0.588241\pi$
$709$	−10333.4	−0.547361	−0.273680	+	0.961821i	$0.588241\pi$
$710$	16922.9	0.894513
$711$	9862.74	0.520227
$712$	45916.0	2.41682
$713$	−5499.18	−0.288844
$714$	3709.24	0.194419
$715$	11135.0	0.582414
$716$	−8175.66	−0.426730
$717$	−21312.7	−1.11009
$718$	46755.1	2.43020
$719$	2463.67	0.127788	0.0638940	−	0.997957i	$-0.479648\pi$
$719$	2463.67	0.127788	0.0638940	+	0.997957i	$0.479648\pi$
$720$	−42090.2	−2.17862
$721$	−35662.5	−1.84208
$722$	−9894.62	−0.510027
$723$	1000.94	0.0514871
$724$	23116.8	1.18664
$725$	−13264.7	−0.679500
$726$	2022.72	0.103403
$727$	−12076.1	−0.616065	−0.308032	−	0.951376i	$-0.599670\pi$
$727$	−12076.1	−0.616065	−0.308032	+	0.951376i	$0.599670\pi$
$728$	−156203.	−7.95229
$729$	729.000	0.0370370
$730$	−54605.3	−2.76854
$731$	2084.90	0.105489
$732$	4218.11	0.212986
$733$	−24722.8	−1.24578	−0.622890	−	0.782310i	$-0.714041\pi$
$733$	−24722.8	−1.24578	−0.622890	+	0.782310i	$0.714041\pi$
$734$	58951.3	2.96449
$735$	28879.5	1.44930
$736$	−15921.9	−0.797406
$737$	−2370.78	−0.118492
$738$	−16413.9	−0.818703
$739$	−17148.8	−0.853626	−0.426813	−	0.904340i	$-0.640364\pi$
$739$	−17148.8	−0.853626	−0.426813	+	0.904340i	$0.640364\pi$
$740$	145980.	7.25178
$741$	−17069.9	−0.846258
$742$	111160.	5.49973
$743$	17168.1	0.847694	0.423847	−	0.905734i	$-0.360679\pi$
$743$	17168.1	0.847694	0.423847	+	0.905734i	$0.360679\pi$
$744$	−78678.7	−3.87702
$745$	−17844.6	−0.877550
$746$	7838.74	0.384714
$747$	−11315.5	−0.554235
$748$	−1849.48	−0.0904062
$749$	52806.8	2.57613
$750$	−6436.73	−0.313381
$751$	−29191.0	−1.41837	−0.709184	−	0.705023i	$-0.750937\pi$
$751$	−29191.0	−1.41837	−0.709184	+	0.705023i	$0.750937\pi$
$752$	104024.	5.04437
$753$	−7790.95	−0.377049
$754$	−30520.7	−1.47413
$755$	−5913.33	−0.285044
$756$	18931.1	0.910735
$757$	−7804.98	−0.374738	−0.187369	−	0.982290i	$-0.559996\pi$
$757$	−7804.98	−0.374738	−0.187369	+	0.982290i	$0.559996\pi$
$758$	48537.4	2.32580
$759$	−580.278	−0.0277507
$760$	−128824.	−6.14861
$761$	−5289.60	−0.251968	−0.125984	−	0.992032i	$-0.540209\pi$
$761$	−5289.60	−0.251968	−0.125984	+	0.992032i	$0.540209\pi$
$762$	32751.6	1.55704
$763$	5221.64	0.247754
$764$	32434.2	1.53590
$765$	1085.29	0.0512926
$766$	−24838.0	−1.17158
$767$	17103.4	0.805175
$768$	−71304.6	−3.35024
$769$	−2479.19	−0.116257	−0.0581287	−	0.998309i	$-0.518513\pi$
$769$	−2479.19	−0.116257	−0.0581287	+	0.998309i	$0.518513\pi$
$770$	−30823.3	−1.44259
$771$	7436.46	0.347364
$772$	26587.9	1.23953
$773$	−35332.0	−1.64399	−0.821994	−	0.569496i	$-0.807138\pi$
$773$	−35332.0	−1.64399	−0.821994	+	0.569496i	$0.807138\pi$
$774$	14334.0	0.665663
$775$	−46375.9	−2.14951
$776$	−125404.	−5.80123
$777$	−34960.4	−1.61416
$778$	46710.6	2.15252
$779$	−30413.2	−1.39880
$780$	−69998.2	−3.21325
$781$	2020.80	0.0925865
$782$	714.731	0.0326838
$783$	2415.15	0.110230
$784$	164733.	7.50423
$785$	−8833.50	−0.401632
$786$	2555.83	0.115984
$787$	27836.5	1.26082	0.630410	−	0.776263i	$-0.282887\pi$
$787$	27836.5	1.26082	0.630410	+	0.776263i	$0.282887\pi$
$788$	114063.	5.15651
$789$	−16139.3	−0.728230
$790$	100948.	4.54629
$791$	9998.86	0.449454
$792$	−8302.24	−0.372484
$793$	3735.21	0.167265
$794$	6182.33	0.276326
$795$	32524.3	1.45097
$796$	−31777.4	−1.41498
$797$	24334.5	1.08152	0.540760	−	0.841177i	$-0.318137\pi$
$797$	24334.5	1.08152	0.540760	+	0.841177i	$0.318137\pi$
$798$	47251.8	2.09611
$799$	−2682.25	−0.118762
$800$	−134274.	−5.93411
$801$	−4927.73	−0.217369
$802$	−16236.3	−0.714866
$803$	−6520.56	−0.286557
$804$	14903.4	0.653736
$805$	8842.59	0.387156
$806$	−106706.	−4.66324
$807$	−11840.4	−0.516482
$808$	−40467.1	−1.76191
$809$	−21874.1	−0.950621	−0.475311	−	0.879818i	$-0.657664\pi$
$809$	−21874.1	−0.950621	−0.475311	+	0.879818i	$0.657664\pi$
$810$	7461.53	0.323668
$811$	31007.3	1.34256	0.671278	−	0.741206i	$-0.265746\pi$
$811$	31007.3	1.34256	0.671278	+	0.741206i	$0.265746\pi$
$812$	62717.8	2.71055
$813$	−14025.6	−0.605042
$814$	23481.9	1.01111
$815$	6834.16	0.293730
$816$	6190.67	0.265584
$817$	26559.4	1.13733
$818$	3538.65	0.151254
$819$	16763.8	0.715230
$820$	−124715.	−5.31127
$821$	−32880.8	−1.39774	−0.698871	−	0.715248i	$-0.746314\pi$
$821$	−32880.8	−1.39774	−0.698871	+	0.715248i	$0.746314\pi$
$822$	42847.7	1.81811
$823$	−7952.64	−0.336830	−0.168415	−	0.985716i	$-0.553865\pi$
$823$	−7952.64	−0.336830	−0.168415	+	0.985716i	$0.553865\pi$
$824$	−98316.9	−4.15659
$825$	−4893.63	−0.206514
$826$	−47344.7	−1.99435
$827$	4042.75	0.169988	0.0849941	−	0.996381i	$-0.472913\pi$
$827$	4042.75	0.169988	0.0849941	+	0.996381i	$0.472913\pi$
$828$	3647.81	0.153104
$829$	20856.7	0.873805	0.436903	−	0.899509i	$-0.356075\pi$
$829$	20856.7	0.873805	0.436903	+	0.899509i	$0.356075\pi$
$830$	−115818.	−4.84349
$831$	4095.73	0.170974
$832$	−170370.	−7.09918
$833$	−4247.62	−0.176676
$834$	−758.791	−0.0315046
$835$	15382.4	0.637523
$836$	−23560.4	−0.974707
$837$	8443.83	0.348699
$838$	−30964.9	−1.27645
$839$	6546.56	0.269383	0.134692	−	0.990888i	$-0.456996\pi$
$839$	6546.56	0.269383	0.134692	+	0.990888i	$0.456996\pi$
$840$	126514.	5.19660
$841$	−16387.7	−0.671931
$842$	6369.21	0.260686
$843$	1626.55	0.0664549
$844$	120948.	4.93269
$845$	−25664.7	−1.04485
$846$	−18440.8	−0.749419
$847$	−3680.69	−0.149315
$848$	185524.	7.51286
$849$	14724.6	0.595226
$850$	6027.50	0.243225
$851$	−6736.50	−0.271356
$852$	−12703.4	−0.510812
$853$	22052.9	0.885201	0.442600	−	0.896719i	$-0.354056\pi$
$853$	22052.9	0.885201	0.442600	+	0.896719i	$0.354056\pi$
$854$	−10339.6	−0.414301
$855$	13825.5	0.553006
$856$	145582.	5.81294
$857$	−22704.3	−0.904975	−0.452487	−	0.891771i	$-0.649463\pi$
$857$	−22704.3	−0.904975	−0.452487	+	0.891771i	$0.649463\pi$
$858$	−11259.7	−0.448020
$859$	21313.3	0.846566	0.423283	−	0.905997i	$-0.360878\pi$
$859$	21313.3	0.846566	0.423283	+	0.905997i	$0.360878\pi$
$860$	108912.	4.31844
$861$	29867.9	1.18222
$862$	−28639.3	−1.13162
$863$	−31177.1	−1.22976	−0.614879	−	0.788622i	$-0.710795\pi$
$863$	−31177.1	−1.22976	−0.614879	+	0.788622i	$0.710795\pi$
$864$	24447.7	0.962647
$865$	67508.7	2.65360
$866$	−13830.4	−0.542697
$867$	14579.4	0.571097
$868$	219274.	8.57447
$869$	12054.5	0.470563
$870$	24719.7	0.963307
$871$	13197.2	0.513400
$872$	14395.4	0.559047
$873$	13458.4	0.521763
$874$	9104.90	0.352378
$875$	11712.7	0.452529
$876$	40990.3	1.58097
$877$	25199.5	0.970271	0.485136	−	0.874439i	$-0.338770\pi$
$877$	25199.5	0.970271	0.485136	+	0.874439i	$0.338770\pi$
$878$	−84632.8	−3.25310
$879$	−9008.57	−0.345679
$880$	−51443.6	−1.97064
$881$	−6876.69	−0.262976	−0.131488	−	0.991318i	$-0.541975\pi$
$881$	−6876.69	−0.262976	−0.131488	+	0.991318i	$0.541975\pi$
$882$	−29203.0	−1.11487
$883$	−27167.1	−1.03539	−0.517694	−	0.855566i	$-0.673209\pi$
$883$	−27167.1	−1.03539	−0.517694	+	0.855566i	$0.673209\pi$
$884$	10295.4	0.391710
$885$	−13852.6	−0.526160
$886$	81147.8	3.07699
$887$	−4877.26	−0.184625	−0.0923126	−	0.995730i	$-0.529426\pi$
$887$	−4877.26	−0.184625	−0.0923126	+	0.995730i	$0.529426\pi$
$888$	−96381.4	−3.64229
$889$	−59597.1	−2.24839
$890$	−50436.7	−1.89960
$891$	891.000	0.0335013
$892$	81632.0	3.06417
$893$	−34169.0	−1.28043
$894$	18044.4	0.675052
$895$	5863.66	0.218995
$896$	251261.	9.36836
$897$	3230.19	0.120238
$898$	−99955.5	−3.71443
$899$	27974.1	1.03781
$900$	30762.9	1.13936
$901$	−4783.71	−0.176880
$902$	−20061.4	−0.740545
$903$	−26083.1	−0.961231
$904$	27565.6	1.01418
$905$	−16579.6	−0.608977
$906$	5979.57	0.219269
$907$	−24937.3	−0.912931	−0.456466	−	0.889741i	$-0.650885\pi$
$907$	−24937.3	−0.912931	−0.456466	+	0.889741i	$0.650885\pi$
$908$	−93816.4	−3.42886
$909$	4342.94	0.158467
$910$	171582.	6.25042
$911$	−37795.8	−1.37457	−0.687283	−	0.726390i	$-0.741197\pi$
$911$	−37795.8	−1.37457	−0.687283	+	0.726390i	$0.741197\pi$
$912$	78862.4	2.86337
$913$	−13830.1	−0.501325
$914$	97595.1	3.53190
$915$	−3025.27	−0.109303
$916$	−66524.8	−2.39961
$917$	−4650.77	−0.167483
$918$	−1097.45	−0.0394566
$919$	−38896.6	−1.39617	−0.698085	−	0.716015i	$-0.745964\pi$
$919$	−38896.6	−1.39617	−0.698085	+	0.716015i	$0.745964\pi$
$920$	24377.9	0.873603
$921$	15857.9	0.567358
$922$	62485.6	2.23195
$923$	−11249.1	−0.401157
$924$	23138.0	0.823791
$925$	−56810.5	−2.01937
$926$	−54354.2	−1.92893
$927$	10551.4	0.373844
$928$	80994.1	2.86505
$929$	22601.7	0.798210	0.399105	−	0.916905i	$-0.369321\pi$
$929$	22601.7	0.798210	0.399105	+	0.916905i	$0.369321\pi$
$930$	86425.0	3.04730
$931$	−54110.1	−1.90482
$932$	39710.2	1.39566
$933$	21460.3	0.753033
$934$	−23210.0	−0.813121
$935$	1326.47	0.0463959
$936$	46215.5	1.61389
$937$	−16692.5	−0.581986	−0.290993	−	0.956725i	$-0.593986\pi$
$937$	−16692.5	−0.581986	−0.290993	+	0.956725i	$0.593986\pi$
$938$	−36531.8	−1.27165
$939$	12029.2	0.418059
$940$	−140116.	−4.86180
$941$	−586.593	−0.0203213	−0.0101607	−	0.999948i	$-0.503234\pi$
$941$	−586.593	−0.0203213	−0.0101607	+	0.999948i	$0.503234\pi$
$942$	8932.44	0.308954
$943$	5755.21	0.198744
$944$	−79017.6	−2.72437
$945$	−13577.5	−0.467383
$946$	17519.3	0.602115
$947$	20421.7	0.700757	0.350378	−	0.936608i	$-0.386053\pi$
$947$	20421.7	0.700757	0.350378	+	0.936608i	$0.386053\pi$
$948$	−75778.1	−2.59616
$949$	36297.6	1.24159
$950$	76783.9	2.62231
$951$	−8857.43	−0.302021
$952$	−18607.8	−0.633490
$953$	1611.05	0.0547608	0.0273804	−	0.999625i	$-0.491283\pi$
$953$	1611.05	0.0547608	0.0273804	+	0.999625i	$0.491283\pi$
$954$	−32888.6	−1.11615
$955$	−23262.1	−0.788215
$956$	163751.	5.53984
$957$	2951.85	0.0997070
$958$	95609.2	3.22442
$959$	−77968.7	−2.62538
$960$	137988.	4.63912
$961$	68011.8	2.28297
$962$	−130715.	−4.38090
$963$	−15623.9	−0.522816
$964$	−7690.46	−0.256943
$965$	−19069.1	−0.636119
$966$	−8941.63	−0.297818
$967$	50216.8	1.66997	0.834986	−	0.550271i	$-0.185476\pi$
$967$	50216.8	1.66997	0.834986	+	0.550271i	$0.185476\pi$
$968$	−10147.2	−0.336925
$969$	−2033.46	−0.0674140
$970$	137751.	4.55971
$971$	4079.62	0.134831	0.0674157	−	0.997725i	$-0.478525\pi$
$971$	4079.62	0.134831	0.0674157	+	0.997725i	$0.478525\pi$
$972$	−5601.10	−0.184831
$973$	1380.75	0.0454932
$974$	−85630.2	−2.81701
$975$	27241.0	0.894780
$976$	−17256.6	−0.565953
$977$	11367.1	0.372226	0.186113	−	0.982528i	$-0.440411\pi$
$977$	11367.1	0.372226	0.186113	+	0.982528i	$0.440411\pi$
$978$	−6910.71	−0.225951
$979$	−6022.78	−0.196618
$980$	−221889.	−7.23263
$981$	−1544.92	−0.0502808
$982$	−8306.89	−0.269942
$983$	−39681.2	−1.28752	−0.643761	−	0.765227i	$-0.722627\pi$
$983$	−39681.2	−1.28752	−0.643761	+	0.765227i	$0.722627\pi$
$984$	82341.8	2.66764
$985$	−81807.2	−2.64629
$986$	−3635.80	−0.117431
$987$	33556.3	1.08218
$988$	131152.	4.22319
$989$	−5025.93	−0.161593
$990$	9119.64	0.292769
$991$	1834.05	0.0587895	0.0293948	−	0.999568i	$-0.490642\pi$
$991$	1834.05	0.0587895	0.0293948	+	0.999568i	$0.490642\pi$
$992$	283171.	9.06321
$993$	10628.1	0.339650
$994$	31139.0	0.993631
$995$	22791.1	0.726157
$996$	86940.3	2.76587
$997$	4719.36	0.149913	0.0749567	−	0.997187i	$-0.476118\pi$
$997$	4719.36	0.149913	0.0749567	+	0.997187i	$0.476118\pi$
$998$	65774.7	2.08623
$999$	10343.7	0.327588

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.d.1.1	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.d.1.1	✓	37	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)

\(f(q)\)	\(=\)	\(q-5.57224 q^{2} -3.00000 q^{3} +23.0498 q^{4} -16.5315 q^{5} +16.7167 q^{6} -30.4189 q^{7} -83.8611 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-5.57224 q^{2} -3.00000 q^{3} +23.0498 q^{4} -16.5315 q^{5} +16.7167 q^{6} -30.4189 q^{7} -83.8611 q^{8} +9.00000 q^{9} +92.1176 q^{10} +11.0000 q^{11} -69.1494 q^{12} -61.2329 q^{13} +169.501 q^{14} +49.5946 q^{15} +282.895 q^{16} -7.29442 q^{17} -50.1501 q^{18} -92.9231 q^{19} -381.049 q^{20} +91.2568 q^{21} -61.2946 q^{22} +17.5842 q^{23} +251.583 q^{24} +148.292 q^{25} +341.204 q^{26} -27.0000 q^{27} -701.150 q^{28} -89.4499 q^{29} -276.353 q^{30} -312.734 q^{31} -905.469 q^{32} -33.0000 q^{33} +40.6462 q^{34} +502.871 q^{35} +207.448 q^{36} -383.100 q^{37} +517.789 q^{38} +183.699 q^{39} +1386.35 q^{40} +327.295 q^{41} -508.504 q^{42} -285.821 q^{43} +253.548 q^{44} -148.784 q^{45} -97.9832 q^{46} +367.713 q^{47} -848.685 q^{48} +582.311 q^{49} -826.316 q^{50} +21.8833 q^{51} -1411.41 q^{52} +655.804 q^{53} +150.450 q^{54} -181.847 q^{55} +2550.96 q^{56} +278.769 q^{57} +498.436 q^{58} -279.318 q^{59} +1143.15 q^{60} -61.0000 q^{61} +1742.63 q^{62} -273.770 q^{63} +2782.33 q^{64} +1012.27 q^{65} +183.884 q^{66} -215.525 q^{67} -168.135 q^{68} -52.7526 q^{69} -2802.12 q^{70} +183.709 q^{71} -754.749 q^{72} -592.778 q^{73} +2134.72 q^{74} -444.875 q^{75} -2141.86 q^{76} -334.608 q^{77} -1023.61 q^{78} +1095.86 q^{79} -4676.69 q^{80} +81.0000 q^{81} -1823.76 q^{82} -1257.28 q^{83} +2103.45 q^{84} +120.588 q^{85} +1592.66 q^{86} +268.350 q^{87} -922.472 q^{88} -547.525 q^{89} +829.058 q^{90} +1862.64 q^{91} +405.312 q^{92} +938.203 q^{93} -2048.98 q^{94} +1536.16 q^{95} +2716.41 q^{96} +1495.38 q^{97} -3244.77 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 4 q^{2} - 111 q^{3} + 158 q^{4} - 15 q^{5} + 12 q^{6} - 77 q^{7} - 69 q^{8} + 333 q^{9}+O(q^{10}) \) 37 * q - 4 * q^2 - 111 * q^3 + 158 * q^4 - 15 * q^5 + 12 * q^6 - 77 * q^7 - 69 * q^8 + 333 * q^9	\( 37 q - 4 q^{2} - 111 q^{3} + 158 q^{4} - 15 q^{5} + 12 q^{6} - 77 q^{7} - 69 q^{8} + 333 q^{9} - 45 q^{10} + 407 q^{11} - 474 q^{12} - 169 q^{13} + 102 q^{14} + 45 q^{15} + 598 q^{16} - 338 q^{17} - 36 q^{18} - 235 q^{19} - 550 q^{20} + 231 q^{21} - 44 q^{22} - 53 q^{23} + 207 q^{24} + 750 q^{25} - 75 q^{26} - 999 q^{27} - 1378 q^{28} - 30 q^{29} + 135 q^{30} - 506 q^{31} - 841 q^{32} - 1221 q^{33} - 316 q^{34} - 822 q^{35} + 1422 q^{36} - 830 q^{37} - 371 q^{38} + 507 q^{39} - 613 q^{40} + 16 q^{41} - 306 q^{42} - 1137 q^{43} + 1738 q^{44} - 135 q^{45} - 659 q^{46} - 489 q^{47} - 1794 q^{48} + 2214 q^{49} + 1066 q^{50} + 1014 q^{51} - 2342 q^{52} + 731 q^{53} + 108 q^{54} - 165 q^{55} + 3051 q^{56} + 705 q^{57} - 611 q^{58} - 425 q^{59} + 1650 q^{60} - 2257 q^{61} + 453 q^{62} - 693 q^{63} + 4919 q^{64} + 1346 q^{65} + 132 q^{66} - 1907 q^{67} - 3236 q^{68} + 159 q^{69} - 1050 q^{70} - 561 q^{71} - 621 q^{72} - 2397 q^{73} - 1840 q^{74} - 2250 q^{75} - 3868 q^{76} - 847 q^{77} + 225 q^{78} + 393 q^{79} - 4031 q^{80} + 2997 q^{81} - 1946 q^{82} - 4191 q^{83} + 4134 q^{84} - 2667 q^{85} + 2405 q^{86} + 90 q^{87} - 759 q^{88} + 1437 q^{89} - 405 q^{90} - 5192 q^{91} - 737 q^{92} + 1518 q^{93} - 1960 q^{94} + 1356 q^{95} + 2523 q^{96} - 2368 q^{97} - 3014 q^{98} + 3663 q^{99}+O(q^{100}) \) 37 * q - 4 * q^2 - 111 * q^3 + 158 * q^4 - 15 * q^5 + 12 * q^6 - 77 * q^7 - 69 * q^8 + 333 * q^9 - 45 * q^10 + 407 * q^11 - 474 * q^12 - 169 * q^13 + 102 * q^14 + 45 * q^15 + 598 * q^16 - 338 * q^17 - 36 * q^18 - 235 * q^19 - 550 * q^20 + 231 * q^21 - 44 * q^22 - 53 * q^23 + 207 * q^24 + 750 * q^25 - 75 * q^26 - 999 * q^27 - 1378 * q^28 - 30 * q^29 + 135 * q^30 - 506 * q^31 - 841 * q^32 - 1221 * q^33 - 316 * q^34 - 822 * q^35 + 1422 * q^36 - 830 * q^37 - 371 * q^38 + 507 * q^39 - 613 * q^40 + 16 * q^41 - 306 * q^42 - 1137 * q^43 + 1738 * q^44 - 135 * q^45 - 659 * q^46 - 489 * q^47 - 1794 * q^48 + 2214 * q^49 + 1066 * q^50 + 1014 * q^51 - 2342 * q^52 + 731 * q^53 + 108 * q^54 - 165 * q^55 + 3051 * q^56 + 705 * q^57 - 611 * q^58 - 425 * q^59 + 1650 * q^60 - 2257 * q^61 + 453 * q^62 - 693 * q^63 + 4919 * q^64 + 1346 * q^65 + 132 * q^66 - 1907 * q^67 - 3236 * q^68 + 159 * q^69 - 1050 * q^70 - 561 * q^71 - 621 * q^72 - 2397 * q^73 - 1840 * q^74 - 2250 * q^75 - 3868 * q^76 - 847 * q^77 + 225 * q^78 + 393 * q^79 - 4031 * q^80 + 2997 * q^81 - 1946 * q^82 - 4191 * q^83 + 4134 * q^84 - 2667 * q^85 + 2405 * q^86 + 90 * q^87 - 759 * q^88 + 1437 * q^89 - 405 * q^90 - 5192 * q^91 - 737 * q^92 + 1518 * q^93 - 1960 * q^94 + 1356 * q^95 + 2523 * q^96 - 2368 * q^97 - 3014 * q^98 + 3663 * q^99

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