LMFDB - Embedded newform 2013.4.a.e.1.10

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			1.10
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)

$f(q)$	$=$	$q-3.08546 q^{2} -3.00000 q^{3} +1.52008 q^{4} +1.21167 q^{5} +9.25639 q^{6} -4.33357 q^{7} +19.9936 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.08546 q^{2} -3.00000 q^{3} +1.52008 q^{4} +1.21167 q^{5} +9.25639 q^{6} -4.33357 q^{7} +19.9936 q^{8} +9.00000 q^{9} -3.73856 q^{10} -11.0000 q^{11} -4.56023 q^{12} -42.4370 q^{13} +13.3711 q^{14} -3.63501 q^{15} -73.8500 q^{16} -94.1872 q^{17} -27.7692 q^{18} -69.8266 q^{19} +1.84183 q^{20} +13.0007 q^{21} +33.9401 q^{22} -145.743 q^{23} -59.9807 q^{24} -123.532 q^{25} +130.938 q^{26} -27.0000 q^{27} -6.58736 q^{28} +48.9115 q^{29} +11.2157 q^{30} +82.5460 q^{31} +67.9128 q^{32} +33.0000 q^{33} +290.611 q^{34} -5.25086 q^{35} +13.6807 q^{36} -117.526 q^{37} +215.447 q^{38} +127.311 q^{39} +24.2256 q^{40} -173.974 q^{41} -40.1132 q^{42} -24.9368 q^{43} -16.7208 q^{44} +10.9050 q^{45} +449.686 q^{46} +205.560 q^{47} +221.550 q^{48} -324.220 q^{49} +381.153 q^{50} +282.562 q^{51} -64.5075 q^{52} +360.018 q^{53} +83.3075 q^{54} -13.3284 q^{55} -86.6436 q^{56} +209.480 q^{57} -150.915 q^{58} +17.2965 q^{59} -5.52549 q^{60} -61.0000 q^{61} -254.692 q^{62} -39.0022 q^{63} +381.257 q^{64} -51.4197 q^{65} -101.820 q^{66} -841.643 q^{67} -143.172 q^{68} +437.230 q^{69} +16.2013 q^{70} -519.298 q^{71} +179.942 q^{72} +364.743 q^{73} +362.622 q^{74} +370.596 q^{75} -106.142 q^{76} +47.6693 q^{77} -392.814 q^{78} -1261.58 q^{79} -89.4818 q^{80} +81.0000 q^{81} +536.789 q^{82} -580.104 q^{83} +19.7621 q^{84} -114.124 q^{85} +76.9416 q^{86} -146.734 q^{87} -219.929 q^{88} -276.461 q^{89} -33.6471 q^{90} +183.904 q^{91} -221.541 q^{92} -247.638 q^{93} -634.246 q^{94} -84.6068 q^{95} -203.739 q^{96} -369.715 q^{97} +1000.37 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.08546	−1.09088	−0.545438	−	0.838151i	$-0.683637\pi$
$2$	−3.08546	−1.09088	−0.545438	+	0.838151i	$0.683637\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	1.52008	0.190010
$5$	1.21167	0.108375	0.0541875	−	0.998531i	$-0.482743\pi$
$5$	1.21167	0.108375	0.0541875	+	0.998531i	$0.482743\pi$
$6$	9.25639	0.629817
$7$	−4.33357	−0.233991	−0.116996	−	0.993132i	$-0.537326\pi$
$7$	−4.33357	−0.233991	−0.116996	+	0.993132i	$0.537326\pi$
$8$	19.9936	0.883599
$9$	9.00000	0.333333
$10$	−3.73856	−0.118224
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−4.56023	−0.109702
$13$	−42.4370	−0.905378	−0.452689	−	0.891668i	$-0.649535\pi$
$13$	−42.4370	−0.905378	−0.452689	+	0.891668i	$0.649535\pi$
$14$	13.3711	0.255255
$15$	−3.63501	−0.0625704
$16$	−73.8500	−1.15391
$17$	−94.1872	−1.34375	−0.671875	−	0.740665i	$-0.734511\pi$
$17$	−94.1872	−1.34375	−0.671875	+	0.740665i	$0.734511\pi$
$18$	−27.7692	−0.363625
$19$	−69.8266	−0.843122	−0.421561	−	0.906800i	$-0.638518\pi$
$19$	−69.8266	−0.843122	−0.421561	+	0.906800i	$0.638518\pi$
$20$	1.84183	0.0205923
$21$	13.0007	0.135095
$22$	33.9401	0.328911
$23$	−145.743	−1.32129	−0.660644	−	0.750700i	$-0.729717\pi$
$23$	−145.743	−1.32129	−0.660644	+	0.750700i	$0.729717\pi$
$24$	−59.9807	−0.510146
$25$	−123.532	−0.988255
$26$	130.938	0.987655
$27$	−27.0000	−0.192450
$28$	−6.58736	−0.0444605
$29$	48.9115	0.313194	0.156597	−	0.987663i	$-0.449948\pi$
$29$	48.9115	0.313194	0.156597	+	0.987663i	$0.449948\pi$
$30$	11.2157	0.0682565
$31$	82.5460	0.478248	0.239124	−	0.970989i	$-0.423140\pi$
$31$	82.5460	0.478248	0.239124	+	0.970989i	$0.423140\pi$
$32$	67.9128	0.375169
$33$	33.0000	0.174078
$34$	290.611	1.46586
$35$	−5.25086	−0.0253588
$36$	13.6807	0.0633365
$37$	−117.526	−0.522194	−0.261097	−	0.965313i	$-0.584084\pi$
$37$	−117.526	−0.522194	−0.261097	+	0.965313i	$0.584084\pi$
$38$	215.447	0.919741
$39$	127.311	0.522720
$40$	24.2256	0.0957601
$41$	−173.974	−0.662686	−0.331343	−	0.943510i	$-0.607502\pi$
$41$	−173.974	−0.662686	−0.331343	+	0.943510i	$0.607502\pi$
$42$	−40.1132	−0.147372
$43$	−24.9368	−0.0884379	−0.0442190	−	0.999022i	$-0.514080\pi$
$43$	−24.9368	−0.0884379	−0.0442190	+	0.999022i	$0.514080\pi$
$44$	−16.7208	−0.0572900
$45$	10.9050	0.0361250
$46$	449.686	1.44136
$47$	205.560	0.637956	0.318978	−	0.947762i	$-0.396660\pi$
$47$	205.560	0.637956	0.318978	+	0.947762i	$0.396660\pi$
$48$	221.550	0.666208
$49$	−324.220	−0.945248
$50$	381.153	1.07806
$51$	282.562	0.775814
$52$	−64.5075	−0.172031
$53$	360.018	0.933061	0.466530	−	0.884505i	$-0.345504\pi$
$53$	360.018	0.933061	0.466530	+	0.884505i	$0.345504\pi$
$54$	83.3075	0.209939
$55$	−13.3284	−0.0326763
$56$	−86.6436	−0.206754
$57$	209.480	0.486777
$58$	−150.915	−0.341656
$59$	17.2965	0.0381663	0.0190832	−	0.999818i	$-0.493925\pi$
$59$	17.2965	0.0381663	0.0190832	+	0.999818i	$0.493925\pi$
$60$	−5.52549	−0.0118890
$61$	−61.0000	−0.128037
$61$	−61.0000	−0.128037
$62$	−254.692	−0.521709
$63$	−39.0022	−0.0779970
$64$	381.257	0.744643
$65$	−51.4197	−0.0981204
$66$	−101.820	−0.189897
$67$	−841.643	−1.53467	−0.767336	−	0.641245i	$-0.778418\pi$
$67$	−841.643	−1.53467	−0.767336	+	0.641245i	$0.778418\pi$
$68$	−143.172	−0.255325
$69$	437.230	0.762846
$70$	16.2013	0.0276633
$71$	−519.298	−0.868019	−0.434010	−	0.900908i	$-0.642902\pi$
$71$	−519.298	−0.868019	−0.434010	+	0.900908i	$0.642902\pi$
$72$	179.942	0.294533
$73$	364.743	0.584793	0.292396	−	0.956297i	$-0.405547\pi$
$73$	364.743	0.584793	0.292396	+	0.956297i	$0.405547\pi$
$74$	362.622	0.569648
$75$	370.596	0.570569
$76$	−106.142	−0.160201
$77$	47.6693	0.0705509
$78$	−392.814	−0.570223
$79$	−1261.58	−1.79669	−0.898345	−	0.439291i	$-0.855230\pi$
$79$	−1261.58	−1.79669	−0.898345	+	0.439291i	$0.855230\pi$
$80$	−89.4818	−0.125055
$81$	81.0000	0.111111
$82$	536.789	0.722908
$83$	−580.104	−0.767165	−0.383582	−	0.923507i	$-0.625310\pi$
$83$	−580.104	−0.767165	−0.383582	+	0.923507i	$0.625310\pi$
$84$	19.7621	0.0256693
$85$	−114.124	−0.145629
$86$	76.9416	0.0964747
$87$	−146.734	−0.180823
$88$	−219.929	−0.266415
$89$	−276.461	−0.329268	−0.164634	−	0.986355i	$-0.552644\pi$
$89$	−276.461	−0.329268	−0.164634	+	0.986355i	$0.552644\pi$
$90$	−33.6471	−0.0394079
$91$	183.904	0.211850
$92$	−221.541	−0.251057
$93$	−247.638	−0.276117
$94$	−634.246	−0.695931
$95$	−84.6068	−0.0913734
$96$	−203.739	−0.216604
$97$	−369.715	−0.386998	−0.193499	−	0.981100i	$-0.561984\pi$
$97$	−369.715	−0.386998	−0.193499	+	0.981100i	$0.561984\pi$
$98$	1000.37	1.03115
$99$	−99.0000	−0.100504
$100$	−187.778	−0.187778
$101$	−1070.97	−1.05510	−0.527551	−	0.849523i	$-0.676890\pi$
$101$	−1070.97	−1.05510	−0.527551	+	0.849523i	$0.676890\pi$
$102$	−871.833	−0.846317
$103$	510.287	0.488156	0.244078	−	0.969756i	$-0.421515\pi$
$103$	510.287	0.488156	0.244078	+	0.969756i	$0.421515\pi$
$104$	−848.467	−0.799991
$105$	15.7526	0.0146409
$106$	−1110.82	−1.01785
$107$	649.548	0.586861	0.293431	−	0.955980i	$-0.405203\pi$
$107$	649.548	0.586861	0.293431	+	0.955980i	$0.405203\pi$
$108$	−41.0421	−0.0365674
$109$	−1722.27	−1.51342	−0.756712	−	0.653748i	$-0.773195\pi$
$109$	−1722.27	−1.51342	−0.756712	+	0.653748i	$0.773195\pi$
$110$	41.1242	0.0356458
$111$	352.578	0.301489
$112$	320.034	0.270004
$113$	148.453	0.123587	0.0617934	−	0.998089i	$-0.480318\pi$
$113$	148.453	0.123587	0.0617934	+	0.998089i	$0.480318\pi$
$114$	−646.342	−0.531013
$115$	−176.593	−0.143195
$116$	74.3492	0.0595099
$117$	−381.933	−0.301793
$118$	−53.3677	−0.0416347
$119$	408.167	0.314425
$120$	−72.6768	−0.0552871
$121$	121.000	0.0909091
$122$	188.213	0.139672
$123$	521.921	0.382602
$124$	125.476	0.0908717
$125$	−301.139	−0.215477
$126$	120.340	0.0850850
$127$	−1086.84	−0.759385	−0.379692	−	0.925113i	$-0.623970\pi$
$127$	−1086.84	−0.759385	−0.379692	+	0.925113i	$0.623970\pi$
$128$	−1719.66	−1.18748
$129$	74.8105	0.0510596
$130$	158.654	0.107037
$131$	−1773.61	−1.18291	−0.591453	−	0.806339i	$-0.701446\pi$
$131$	−1773.61	−1.18291	−0.591453	+	0.806339i	$0.701446\pi$
$132$	50.1625	0.0330764
$133$	302.599	0.197283
$134$	2596.86	1.67414
$135$	−32.7151	−0.0208568
$136$	−1883.14	−1.18734
$137$	−728.744	−0.454459	−0.227229	−	0.973841i	$-0.572967\pi$
$137$	−728.744	−0.454459	−0.227229	+	0.973841i	$0.572967\pi$
$138$	−1349.06	−0.832170
$139$	2271.64	1.38617	0.693085	−	0.720855i	$-0.256251\pi$
$139$	2271.64	1.38617	0.693085	+	0.720855i	$0.256251\pi$
$140$	−7.98171	−0.00481841
$141$	−616.679	−0.368324
$142$	1602.27	0.946901
$143$	466.807	0.272982
$144$	−664.650	−0.384635
$145$	59.2646	0.0339425
$146$	−1125.40	−0.637936
$147$	972.660	0.545739
$148$	−178.649	−0.0992218
$149$	1313.99	0.722459	0.361229	−	0.932477i	$-0.382357\pi$
$149$	1313.99	0.722459	0.361229	+	0.932477i	$0.382357\pi$
$150$	−1143.46	−0.622420
$151$	2609.28	1.40623	0.703113	−	0.711078i	$-0.251793\pi$
$151$	2609.28	1.40623	0.703113	+	0.711078i	$0.251793\pi$
$152$	−1396.08	−0.744982
$153$	−847.685	−0.447917
$154$	−147.082	−0.0769623
$155$	100.018	0.0518302
$156$	193.523	0.0993219
$157$	2851.88	1.44971	0.724857	−	0.688899i	$-0.241906\pi$
$157$	2851.88	1.44971	0.724857	+	0.688899i	$0.241906\pi$
$158$	3892.55	1.95996
$159$	−1080.05	−0.538703
$160$	82.2880	0.0406590
$161$	631.590	0.309169
$162$	−249.922	−0.121208
$163$	−2277.39	−1.09435	−0.547174	−	0.837019i	$-0.684296\pi$
$163$	−2277.39	−1.09435	−0.547174	+	0.837019i	$0.684296\pi$
$164$	−264.453	−0.125917
$165$	39.9851	0.0188657
$166$	1789.89	0.836882
$167$	−2097.60	−0.971960	−0.485980	−	0.873970i	$-0.661537\pi$
$167$	−2097.60	−0.971960	−0.485980	+	0.873970i	$0.661537\pi$
$168$	259.931	0.119370
$169$	−396.098	−0.180290
$170$	352.125	0.158863
$171$	−628.439	−0.281041
$172$	−37.9059	−0.0168040
$173$	−4119.71	−1.81049	−0.905247	−	0.424886i	$-0.860314\pi$
$173$	−4119.71	−1.81049	−0.905247	+	0.424886i	$0.860314\pi$
$174$	452.744	0.197255
$175$	535.334	0.231243
$176$	812.350	0.347916
$177$	−51.8895	−0.0220353
$178$	853.011	0.359190
$179$	−440.497	−0.183934	−0.0919672	−	0.995762i	$-0.529316\pi$
$179$	−440.497	−0.183934	−0.0919672	+	0.995762i	$0.529316\pi$
$180$	16.5765	0.00686410
$181$	−844.487	−0.346797	−0.173399	−	0.984852i	$-0.555475\pi$
$181$	−844.487	−0.346797	−0.173399	+	0.984852i	$0.555475\pi$
$182$	−567.429	−0.231102
$183$	183.000	0.0739221
$184$	−2913.93	−1.16749
$185$	−142.403	−0.0565928
$186$	764.077	0.301209
$187$	1036.06	0.405156
$188$	312.466	0.121218
$189$	117.007	0.0450316
$190$	261.051	0.0996770
$191$	−3205.52	−1.21436	−0.607181	−	0.794563i	$-0.707700\pi$
$191$	−3205.52	−1.21436	−0.607181	+	0.794563i	$0.707700\pi$
$192$	−1143.77	−0.429920
$193$	1786.09	0.666142	0.333071	−	0.942902i	$-0.391915\pi$
$193$	1786.09	0.666142	0.333071	+	0.942902i	$0.391915\pi$
$194$	1140.74	0.422167
$195$	154.259	0.0566499
$196$	−492.839	−0.179606
$197$	2041.62	0.738373	0.369186	−	0.929355i	$-0.379636\pi$
$197$	2041.62	0.738373	0.369186	+	0.929355i	$0.379636\pi$
$198$	305.461	0.109637
$199$	−693.736	−0.247124	−0.123562	−	0.992337i	$-0.539432\pi$
$199$	−693.736	−0.247124	−0.123562	+	0.992337i	$0.539432\pi$
$200$	−2469.84	−0.873221
$201$	2524.93	0.886044
$202$	3304.43	1.15099
$203$	−211.962	−0.0732847
$204$	429.515	0.147412
$205$	−210.799	−0.0718187
$206$	−1574.47	−0.532517
$207$	−1311.69	−0.440429
$208$	3133.97	1.04472
$209$	768.093	0.254211
$210$	−48.6040	−0.0159714
$211$	−3694.31	−1.20534	−0.602670	−	0.797991i	$-0.705896\pi$
$211$	−3694.31	−1.20534	−0.602670	+	0.797991i	$0.705896\pi$
$212$	547.254	0.177290
$213$	1557.89	0.501151
$214$	−2004.15	−0.640192
$215$	−30.2152	−0.00958447
$216$	−539.826	−0.170049
$217$	−357.719	−0.111906
$218$	5313.99	1.65096
$219$	−1094.23	−0.337630
$220$	−20.2601	−0.00620881
$221$	3997.02	1.21660
$222$	−1087.87	−0.328887
$223$	4680.39	1.40548	0.702740	−	0.711447i	$-0.251960\pi$
$223$	4680.39	1.40548	0.702740	+	0.711447i	$0.251960\pi$
$224$	−294.305	−0.0877862
$225$	−1111.79	−0.329418
$226$	−458.047	−0.134818
$227$	−5092.07	−1.48887	−0.744433	−	0.667697i	$-0.767280\pi$
$227$	−5092.07	−1.48887	−0.744433	+	0.667697i	$0.767280\pi$
$228$	318.425	0.0924922
$229$	4649.61	1.34173	0.670863	−	0.741582i	$-0.265924\pi$
$229$	4649.61	1.34173	0.670863	+	0.741582i	$0.265924\pi$
$230$	544.871	0.156208
$231$	−143.008	−0.0407326
$232$	977.915	0.276738
$233$	4037.07	1.13510	0.567548	−	0.823340i	$-0.307892\pi$
$233$	4037.07	1.13510	0.567548	+	0.823340i	$0.307892\pi$
$234$	1178.44	0.329218
$235$	249.070	0.0691386
$236$	26.2920	0.00725197
$237$	3784.73	1.03732
$238$	−1259.38	−0.342999
$239$	−3572.55	−0.966899	−0.483450	−	0.875372i	$-0.660616\pi$
$239$	−3572.55	−0.966899	−0.483450	+	0.875372i	$0.660616\pi$
$240$	268.445	0.0722003
$241$	−5.05740	−0.00135177	−0.000675883	−	1.00000i	$-0.500215\pi$
$241$	−5.05740	−0.00135177	−0.000675883		1.00000i	$0.500215\pi$
$242$	−373.341	−0.0991705
$243$	−243.000	−0.0641500
$244$	−92.7247	−0.0243282
$245$	−392.848	−0.102441
$246$	−1610.37	−0.417371
$247$	2963.23	0.763344
$248$	1650.39	0.422579
$249$	1740.31	0.442923
$250$	929.152	0.235059
$251$	241.805	0.0608072	0.0304036	−	0.999538i	$-0.490321\pi$
$251$	241.805	0.0608072	0.0304036	+	0.999538i	$0.490321\pi$
$252$	−59.2863	−0.0148202
$253$	1603.18	0.398383
$254$	3353.42	0.828394
$255$	342.371	0.0840789
$256$	2255.88	0.550752
$257$	−3696.24	−0.897140	−0.448570	−	0.893748i	$-0.648067\pi$
$257$	−3696.24	−0.897140	−0.448570	+	0.893748i	$0.648067\pi$
$258$	−230.825	−0.0556997
$259$	509.308	0.122189
$260$	−78.1619	−0.0186438
$261$	440.203	0.104398
$262$	5472.40	1.29040
$263$	6549.07	1.53549	0.767743	−	0.640757i	$-0.221380\pi$
$263$	6549.07	1.53549	0.767743	+	0.640757i	$0.221380\pi$
$264$	659.787	0.153815
$265$	436.223	0.101121
$266$	−933.657	−0.215211
$267$	829.384	0.190103
$268$	−1279.36	−0.291603
$269$	−8369.48	−1.89701	−0.948506	−	0.316759i	$-0.897405\pi$
$269$	−8369.48	−1.89701	−0.948506	+	0.316759i	$0.897405\pi$
$270$	100.941	0.0227522
$271$	2261.13	0.506841	0.253421	−	0.967356i	$-0.418444\pi$
$271$	2261.13	0.506841	0.253421	+	0.967356i	$0.418444\pi$
$272$	6955.72	1.55056
$273$	−551.712	−0.122312
$274$	2248.51	0.495758
$275$	1358.85	0.297970
$276$	664.624	0.144948
$277$	−456.347	−0.0989863	−0.0494932	−	0.998774i	$-0.515761\pi$
$277$	−456.347	−0.0989863	−0.0494932	+	0.998774i	$0.515761\pi$
$278$	−7009.05	−1.51214
$279$	742.914	0.159416
$280$	−104.983	−0.0224070
$281$	−615.656	−0.130701	−0.0653505	−	0.997862i	$-0.520817\pi$
$281$	−615.656	−0.130701	−0.0653505	+	0.997862i	$0.520817\pi$
$282$	1902.74	0.401796
$283$	−7892.47	−1.65780	−0.828902	−	0.559394i	$-0.811034\pi$
$283$	−7892.47	−1.65780	−0.828902	+	0.559394i	$0.811034\pi$
$284$	−789.373	−0.164932
$285$	253.820	0.0527545
$286$	−1440.32	−0.297789
$287$	753.928	0.155063
$288$	611.216	0.125056
$289$	3958.22	0.805664
$290$	−182.859	−0.0370270
$291$	1109.14	0.223434
$292$	554.437	0.111116
$293$	−5683.63	−1.13325	−0.566623	−	0.823977i	$-0.691751\pi$
$293$	−5683.63	−1.13325	−0.566623	+	0.823977i	$0.691751\pi$
$294$	−3001.11	−0.595334
$295$	20.9577	0.00413628
$296$	−2349.76	−0.461410
$297$	297.000	0.0580259
$298$	−4054.27	−0.788113
$299$	6184.92	1.19626
$300$	563.334	0.108414
$301$	108.066	0.0206937
$302$	−8050.83	−1.53402
$303$	3212.91	0.609164
$304$	5156.69	0.972884
$305$	−73.9119	−0.0138760
$306$	2615.50	0.488621
$307$	7746.65	1.44015	0.720073	−	0.693898i	$-0.244108\pi$
$307$	7746.65	1.44015	0.720073	+	0.693898i	$0.244108\pi$
$308$	72.4610	0.0134054
$309$	−1530.86	−0.281837
$310$	−308.603	−0.0565403
$311$	−5166.76	−0.942058	−0.471029	−	0.882118i	$-0.656117\pi$
$311$	−5166.76	−0.942058	−0.471029	+	0.882118i	$0.656117\pi$
$312$	2545.40	0.461875
$313$	4972.42	0.897949	0.448974	−	0.893545i	$-0.351789\pi$
$313$	4972.42	0.897949	0.448974	+	0.893545i	$0.351789\pi$
$314$	−8799.38	−1.58146
$315$	−47.2578	−0.00845293
$316$	−1917.69	−0.341388
$317$	434.659	0.0770122	0.0385061	−	0.999258i	$-0.487740\pi$
$317$	434.659	0.0770122	0.0385061	+	0.999258i	$0.487740\pi$
$318$	3332.46	0.587658
$319$	−538.026	−0.0944316
$320$	461.958	0.0807008
$321$	−1948.64	−0.338824
$322$	−1948.75	−0.337265
$323$	6576.77	1.13295
$324$	123.126	0.0211122
$325$	5242.33	0.894744
$326$	7026.79	1.19380
$327$	5166.80	0.873776
$328$	−3478.35	−0.585549
$329$	−890.807	−0.149276
$330$	−123.373	−0.0205801
$331$	1412.42	0.234542	0.117271	−	0.993100i	$-0.462585\pi$
$331$	1412.42	0.234542	0.117271	+	0.993100i	$0.462585\pi$
$332$	−881.803	−0.145769
$333$	−1057.73	−0.174065
$334$	6472.07	1.06029
$335$	−1019.79	−0.166320
$336$	−960.103	−0.155887
$337$	5296.23	0.856095	0.428047	−	0.903756i	$-0.359202\pi$
$337$	5296.23	0.856095	0.428047	+	0.903756i	$0.359202\pi$
$338$	1222.15	0.196674
$339$	−445.360	−0.0713529
$340$	−173.477	−0.0276709
$341$	−908.006	−0.144197
$342$	1939.03	0.306580
$343$	2891.45	0.455171
$344$	−498.576	−0.0781436
$345$	529.779	0.0826735
$346$	12711.2	1.97502
$347$	12283.9	1.90038	0.950192	−	0.311666i	$-0.100887\pi$
$347$	12283.9	1.90038	0.950192	+	0.311666i	$0.100887\pi$
$348$	−223.048	−0.0343581
$349$	−7268.75	−1.11486	−0.557432	−	0.830223i	$-0.688213\pi$
$349$	−7268.75	−1.11486	−0.557432	+	0.830223i	$0.688213\pi$
$350$	−1651.75	−0.252257
$351$	1145.80	0.174240
$352$	−747.041	−0.113118
$353$	3011.67	0.454093	0.227047	−	0.973884i	$-0.427093\pi$
$353$	3011.67	0.454093	0.227047	+	0.973884i	$0.427093\pi$
$354$	160.103	0.0240378
$355$	−629.218	−0.0940716
$356$	−420.243	−0.0625641
$357$	−1224.50	−0.181534
$358$	1359.14	0.200650
$359$	−8065.91	−1.18580	−0.592900	−	0.805276i	$-0.702017\pi$
$359$	−8065.91	−1.18580	−0.592900	+	0.805276i	$0.702017\pi$
$360$	218.030	0.0319200
$361$	−1983.25	−0.289145
$362$	2605.63	0.378312
$363$	−363.000	−0.0524864
$364$	279.548	0.0402536
$365$	441.948	0.0633770
$366$	−564.640	−0.0806398
$367$	7216.32	1.02640	0.513200	−	0.858269i	$-0.328460\pi$
$367$	7216.32	1.02640	0.513200	+	0.858269i	$0.328460\pi$
$368$	10763.1	1.52464
$369$	−1565.76	−0.220895
$370$	439.378	0.0617357
$371$	−1560.16	−0.218328
$372$	−376.429	−0.0524648
$373$	1177.41	0.163442	0.0817209	−	0.996655i	$-0.473958\pi$
$373$	1177.41	0.163442	0.0817209	+	0.996655i	$0.473958\pi$
$374$	−3196.72	−0.441975
$375$	903.416	0.124406
$376$	4109.87	0.563697
$377$	−2075.66	−0.283559
$378$	−361.019	−0.0491239
$379$	12432.4	1.68498	0.842490	−	0.538713i	$-0.181089\pi$
$379$	12432.4	1.68498	0.842490	+	0.538713i	$0.181089\pi$
$380$	−128.609	−0.0173618
$381$	3260.53	0.438431
$382$	9890.51	1.32472
$383$	−1812.12	−0.241762	−0.120881	−	0.992667i	$-0.538572\pi$
$383$	−1812.12	−0.241762	−0.120881	+	0.992667i	$0.538572\pi$
$384$	5158.97	0.685593
$385$	57.7595	0.00764596
$386$	−5510.90	−0.726678
$387$	−224.431	−0.0294793
$388$	−561.995	−0.0735334
$389$	−3272.23	−0.426500	−0.213250	−	0.976998i	$-0.568405\pi$
$389$	−3272.23	−0.426500	−0.213250	+	0.976998i	$0.568405\pi$
$390$	−475.961	−0.0617980
$391$	13727.2	1.77548
$392$	−6482.31	−0.835220
$393$	5320.82	0.682952
$394$	−6299.34	−0.805473
$395$	−1528.61	−0.194716
$396$	−150.488	−0.0190967
$397$	−12009.1	−1.51818	−0.759090	−	0.650986i	$-0.774356\pi$
$397$	−12009.1	−1.51818	−0.759090	+	0.650986i	$0.774356\pi$
$398$	2140.50	0.269582
$399$	−907.796	−0.113901
$400$	9122.82	1.14035
$401$	−6991.91	−0.870722	−0.435361	−	0.900256i	$-0.643379\pi$
$401$	−6991.91	−0.870722	−0.435361	+	0.900256i	$0.643379\pi$
$402$	−7790.57	−0.966563
$403$	−3503.01	−0.432995
$404$	−1627.95	−0.200480
$405$	98.1453	0.0120417
$406$	653.999	0.0799444
$407$	1292.79	0.157447
$408$	5649.41	0.685509
$409$	−6773.94	−0.818948	−0.409474	−	0.912322i	$-0.634288\pi$
$409$	−6773.94	−0.818948	−0.409474	+	0.912322i	$0.634288\pi$
$410$	650.412	0.0783452
$411$	2186.23	0.262382
$412$	775.675	0.0927543
$413$	−74.9557	−0.00893058
$414$	4047.17	0.480453
$415$	−702.895	−0.0831416
$416$	−2882.02	−0.339670
$417$	−6814.91	−0.800306
$418$	−2369.92	−0.277312
$419$	−89.9880	−0.0104921	−0.00524606	−	0.999986i	$-0.501670\pi$
$419$	−89.9880	−0.0104921	−0.00524606	+	0.999986i	$0.501670\pi$
$420$	23.9451	0.00278191
$421$	13719.3	1.58821	0.794106	−	0.607780i	$-0.207940\pi$
$421$	13719.3	1.58821	0.794106	+	0.607780i	$0.207940\pi$
$422$	11398.7	1.31488
$423$	1850.04	0.212652
$424$	7198.03	0.824451
$425$	11635.1	1.32797
$426$	−4806.82	−0.546693
$427$	264.348	0.0299595
$428$	987.362	0.111509
$429$	−1400.42	−0.157606
$430$	93.2279	0.0104555
$431$	16508.7	1.84500	0.922502	−	0.385993i	$-0.126141\pi$
$431$	16508.7	1.84500	0.922502	+	0.385993i	$0.126141\pi$
$432$	1993.95	0.222069
$433$	−7599.32	−0.843419	−0.421709	−	0.906731i	$-0.638570\pi$
$433$	−7599.32	−0.843419	−0.421709	+	0.906731i	$0.638570\pi$
$434$	1103.73	0.122075
$435$	−177.794	−0.0195967
$436$	−2617.98	−0.287565
$437$	10176.8	1.11401
$438$	3376.20	0.368313
$439$	1486.97	0.161661	0.0808304	−	0.996728i	$-0.474243\pi$
$439$	1486.97	0.161661	0.0808304	+	0.996728i	$0.474243\pi$
$440$	−266.482	−0.0288728
$441$	−2917.98	−0.315083
$442$	−12332.7	−1.32716
$443$	−14495.0	−1.55458	−0.777291	−	0.629142i	$-0.783407\pi$
$443$	−14495.0	−1.55458	−0.777291	+	0.629142i	$0.783407\pi$
$444$	535.946	0.0572857
$445$	−334.980	−0.0356845
$446$	−14441.2	−1.53320
$447$	−3941.97	−0.417112
$448$	−1652.21	−0.174240
$449$	5701.67	0.599283	0.299642	−	0.954052i	$-0.403133\pi$
$449$	5701.67	0.599283	0.299642	+	0.954052i	$0.403133\pi$
$450$	3430.38	0.359354
$451$	1913.71	0.199807
$452$	225.660	0.0234827
$453$	−7827.83	−0.811885
$454$	15711.4	1.62417
$455$	222.831	0.0229593
$456$	4188.25	0.430115
$457$	−9608.09	−0.983474	−0.491737	−	0.870744i	$-0.663638\pi$
$457$	−9608.09	−0.983474	−0.491737	+	0.870744i	$0.663638\pi$
$458$	−14346.2	−1.46366
$459$	2543.05	0.258605
$460$	−268.435	−0.0272083
$461$	16249.6	1.64169	0.820847	−	0.571148i	$-0.193502\pi$
$461$	16249.6	1.64169	0.820847	+	0.571148i	$0.193502\pi$
$462$	441.246	0.0444342
$463$	14789.8	1.48453	0.742266	−	0.670105i	$-0.233751\pi$
$463$	14789.8	1.48453	0.742266	+	0.670105i	$0.233751\pi$
$464$	−3612.11	−0.361397
$465$	−300.055	−0.0299242
$466$	−12456.2	−1.23825
$467$	−1173.50	−0.116280	−0.0581402	−	0.998308i	$-0.518517\pi$
$467$	−1173.50	−0.116280	−0.0581402	+	0.998308i	$0.518517\pi$
$468$	−580.568	−0.0573435
$469$	3647.32	0.359100
$470$	−768.497	−0.0754216
$471$	−8555.65	−0.836993
$472$	345.819	0.0337237
$473$	274.305	0.0266650
$474$	−11677.6	−1.13159
$475$	8625.81	0.833219
$476$	620.445	0.0597438
$477$	3240.16	0.311020
$478$	11023.0	1.05477
$479$	6316.23	0.602497	0.301248	−	0.953546i	$-0.402597\pi$
$479$	6316.23	0.602497	0.301248	+	0.953546i	$0.402597\pi$
$480$	−246.864	−0.0234745
$481$	4987.46	0.472783
$482$	15.6044	0.00147461
$483$	−1894.77	−0.178499
$484$	183.929	0.0172736
$485$	−447.972	−0.0419410
$486$	749.767	0.0699797
$487$	10115.1	0.941191	0.470595	−	0.882349i	$-0.344039\pi$
$487$	10115.1	0.941191	0.470595	+	0.882349i	$0.344039\pi$
$488$	−1219.61	−0.113133
$489$	6832.16	0.631822
$490$	1212.12	0.111751
$491$	−16851.6	−1.54889	−0.774443	−	0.632644i	$-0.781970\pi$
$491$	−16851.6	−1.54889	−0.774443	+	0.632644i	$0.781970\pi$
$492$	793.360	0.0726980
$493$	−4606.84	−0.420855
$494$	−9142.95	−0.832714
$495$	−119.955	−0.0108921
$496$	−6096.02	−0.551853
$497$	2250.42	0.203109
$498$	−5369.67	−0.483174
$499$	−12763.1	−1.14500	−0.572498	−	0.819906i	$-0.694026\pi$
$499$	−12763.1	−1.14500	−0.572498	+	0.819906i	$0.694026\pi$
$500$	−457.754	−0.0409427
$501$	6292.80	0.561161
$502$	−746.081	−0.0663331
$503$	16836.6	1.49246	0.746228	−	0.665691i	$-0.231863\pi$
$503$	16836.6	1.49246	0.746228	+	0.665691i	$0.231863\pi$
$504$	−779.792	−0.0689181
$505$	−1297.66	−0.114347
$506$	−4946.54	−0.434586
$507$	1188.29	0.104091
$508$	−1652.09	−0.144290
$509$	15646.4	1.36250	0.681251	−	0.732050i	$-0.261436\pi$
$509$	15646.4	1.36250	0.681251	+	0.732050i	$0.261436\pi$
$510$	−1056.37	−0.0917197
$511$	−1580.64	−0.136836
$512$	6796.83	0.586680
$513$	1885.32	0.162259
$514$	11404.6	0.978668
$515$	618.300	0.0529039
$516$	113.718	0.00970182
$517$	−2261.15	−0.192351
$518$	−1571.45	−0.133293
$519$	12359.1	1.04529
$520$	−1028.06	−0.0866991
$521$	−1937.55	−0.162928	−0.0814640	−	0.996676i	$-0.525960\pi$
$521$	−1937.55	−0.162928	−0.0814640	+	0.996676i	$0.525960\pi$
$522$	−1358.23	−0.113885
$523$	20838.3	1.74224	0.871122	−	0.491066i	$-0.163393\pi$
$523$	20838.3	1.74224	0.871122	+	0.491066i	$0.163393\pi$
$524$	−2696.02	−0.224764
$525$	−1606.00	−0.133508
$526$	−20206.9	−1.67503
$527$	−7774.77	−0.642646
$528$	−2437.05	−0.200869
$529$	9074.15	0.745800
$530$	−1345.95	−0.110310
$531$	155.669	0.0127221
$532$	459.973	0.0374857
$533$	7382.93	0.599981
$534$	−2559.03	−0.207379
$535$	787.038	0.0636011
$536$	−16827.4	−1.35604
$537$	1321.49	0.106195
$538$	25823.7	2.06940
$539$	3566.42	0.285003
$540$	−49.7295	−0.00396299
$541$	18942.8	1.50539	0.752694	−	0.658371i	$-0.228754\pi$
$541$	18942.8	1.50539	0.752694	+	0.658371i	$0.228754\pi$
$542$	−6976.63	−0.552900
$543$	2533.46	0.200223
$544$	−6396.52	−0.504133
$545$	−2086.82	−0.164017
$546$	1702.29	0.133427
$547$	−789.718	−0.0617293	−0.0308646	−	0.999524i	$-0.509826\pi$
$547$	−789.718	−0.0617293	−0.0308646	+	0.999524i	$0.509826\pi$
$548$	−1107.75	−0.0863515
$549$	−549.000	−0.0426790
$550$	−4192.68	−0.325048
$551$	−3415.32	−0.264061
$552$	8741.79	0.674049
$553$	5467.14	0.420409
$554$	1408.04	0.107982
$555$	427.208	0.0326739
$556$	3453.06	0.263386
$557$	−15511.2	−1.17994	−0.589972	−	0.807424i	$-0.700861\pi$
$557$	−15511.2	−1.17994	−0.589972	+	0.807424i	$0.700861\pi$
$558$	−2292.23	−0.173903
$559$	1058.24	0.0800697
$560$	387.776	0.0292617
$561$	−3108.18	−0.233917
$562$	1899.58	0.142578
$563$	−22219.8	−1.66333	−0.831664	−	0.555280i	$-0.812611\pi$
$563$	−22219.8	−1.66333	−0.831664	+	0.555280i	$0.812611\pi$
$564$	−937.399	−0.0699851
$565$	179.876	0.0133937
$566$	24351.9	1.80846
$567$	−351.020	−0.0259990
$568$	−10382.6	−0.766981
$569$	−13536.1	−0.997296	−0.498648	−	0.866805i	$-0.666170\pi$
$569$	−13536.1	−0.997296	−0.498648	+	0.866805i	$0.666170\pi$
$570$	−783.153	−0.0575486
$571$	18464.3	1.35325	0.676627	−	0.736326i	$-0.263441\pi$
$571$	18464.3	1.35325	0.676627	+	0.736326i	$0.263441\pi$
$572$	709.583	0.0518692
$573$	9616.56	0.701112
$574$	−2326.22	−0.169154
$575$	18004.0	1.30577
$576$	3431.32	0.248214
$577$	−2417.72	−0.174438	−0.0872192	−	0.996189i	$-0.527798\pi$
$577$	−2417.72	−0.174438	−0.0872192	+	0.996189i	$0.527798\pi$
$578$	−12213.0	−0.878879
$579$	−5358.26	−0.384597
$580$	90.0867	0.00644939
$581$	2513.92	0.179510
$582$	−3422.22	−0.243738
$583$	−3960.19	−0.281328
$584$	7292.50	0.516722
$585$	−462.777	−0.0327068
$586$	17536.6	1.23623
$587$	−10347.9	−0.727601	−0.363801	−	0.931477i	$-0.618521\pi$
$587$	−10347.9	−0.727601	−0.363801	+	0.931477i	$0.618521\pi$
$588$	1478.52	0.103696
$589$	−5763.90	−0.403222
$590$	−64.6641	−0.00451216
$591$	−6124.86	−0.426300
$592$	8679.29	0.602562
$593$	−22765.8	−1.57653	−0.788263	−	0.615338i	$-0.789020\pi$
$593$	−22765.8	−1.57653	−0.788263	+	0.615338i	$0.789020\pi$
$594$	−916.382	−0.0632990
$595$	494.564	0.0340759
$596$	1997.37	0.137274
$597$	2081.21	0.142677
$598$	−19083.3	−1.30498
$599$	17842.3	1.21706	0.608529	−	0.793531i	$-0.291760\pi$
$599$	17842.3	1.21706	0.608529	+	0.793531i	$0.291760\pi$
$600$	7409.52	0.504154
$601$	−3430.72	−0.232848	−0.116424	−	0.993200i	$-0.537143\pi$
$601$	−3430.72	−0.232848	−0.116424	+	0.993200i	$0.537143\pi$
$602$	−333.432	−0.0225742
$603$	−7574.79	−0.511558
$604$	3966.30	0.267196
$605$	146.612	0.00985228
$606$	−9913.30	−0.664522
$607$	−3626.47	−0.242494	−0.121247	−	0.992622i	$-0.538689\pi$
$607$	−3626.47	−0.242494	−0.121247	+	0.992622i	$0.538689\pi$
$608$	−4742.12	−0.316313
$609$	635.885	0.0423109
$610$	228.052	0.0151370
$611$	−8723.34	−0.577592
$612$	−1288.55	−0.0851084
$613$	4661.97	0.307170	0.153585	−	0.988135i	$-0.450918\pi$
$613$	4661.97	0.307170	0.153585	+	0.988135i	$0.450918\pi$
$614$	−23902.0	−1.57102
$615$	632.396	0.0414645
$616$	953.079	0.0623387
$617$	7870.65	0.513550	0.256775	−	0.966471i	$-0.417340\pi$
$617$	7870.65	0.513550	0.256775	+	0.966471i	$0.417340\pi$
$618$	4723.41	0.307449
$619$	21106.8	1.37052	0.685261	−	0.728297i	$-0.259688\pi$
$619$	21106.8	1.37052	0.685261	+	0.728297i	$0.259688\pi$
$620$	152.036	0.00984823
$621$	3935.07	0.254282
$622$	15941.8	1.02767
$623$	1198.07	0.0770458
$624$	−9401.92	−0.603170
$625$	15076.6	0.964902
$626$	−15342.2	−0.979550
$627$	−2304.28	−0.146769
$628$	4335.08	0.275460
$629$	11069.4	0.701697
$630$	145.812	0.00922110
$631$	45.9788	0.00290077	0.00145039	−	0.999999i	$-0.499538\pi$
$631$	45.9788	0.00290077	0.00145039	+	0.999999i	$0.499538\pi$
$632$	−25223.4	−1.58755
$633$	11082.9	0.695903
$634$	−1341.12	−0.0840107
$635$	−1316.90	−0.0822984
$636$	−1641.76	−0.102359
$637$	13758.9	0.855807
$638$	1660.06	0.103013
$639$	−4673.68	−0.289340
$640$	−2083.66	−0.128693
$641$	−5228.06	−0.322147	−0.161073	−	0.986942i	$-0.551496\pi$
$641$	−5228.06	−0.322147	−0.161073	+	0.986942i	$0.551496\pi$
$642$	6012.46	0.369615
$643$	−25650.7	−1.57320	−0.786599	−	0.617464i	$-0.788160\pi$
$643$	−25650.7	−1.57320	−0.786599	+	0.617464i	$0.788160\pi$
$644$	960.065	0.0587451
$645$	90.6456	0.00553359
$646$	−20292.4	−1.23590
$647$	16442.6	0.999114	0.499557	−	0.866281i	$-0.333496\pi$
$647$	16442.6	0.999114	0.499557	+	0.866281i	$0.333496\pi$
$648$	1619.48	0.0981776
$649$	−190.262	−0.0115076
$650$	−16175.0	−0.976055
$651$	1073.16	0.0646088
$652$	−3461.80	−0.207937
$653$	12947.8	0.775938	0.387969	−	0.921672i	$-0.373177\pi$
$653$	12947.8	0.775938	0.387969	+	0.921672i	$0.373177\pi$
$654$	−15942.0	−0.953181
$655$	−2149.03	−0.128198
$656$	12848.0	0.764677
$657$	3282.68	0.194931
$658$	2748.55	0.162842
$659$	−13668.6	−0.807974	−0.403987	−	0.914765i	$-0.632376\pi$
$659$	−13668.6	−0.807974	−0.403987	+	0.914765i	$0.632376\pi$
$660$	60.7804	0.00358466
$661$	−5697.29	−0.335248	−0.167624	−	0.985851i	$-0.553609\pi$
$661$	−5697.29	−0.335248	−0.167624	+	0.985851i	$0.553609\pi$
$662$	−4357.96	−0.255856
$663$	−11991.1	−0.702405
$664$	−11598.3	−0.677866
$665$	366.650	0.0213806
$666$	3263.60	0.189883
$667$	−7128.53	−0.413820
$668$	−3188.51	−0.184682
$669$	−14041.2	−0.811454
$670$	3146.54	0.181435
$671$	671.000	0.0386046
$672$	882.916	0.0506834
$673$	14438.3	0.826976	0.413488	−	0.910509i	$-0.364310\pi$
$673$	14438.3	0.826976	0.413488	+	0.910509i	$0.364310\pi$
$674$	−16341.3	−0.933893
$675$	3335.36	0.190190
$676$	−602.099	−0.0342569
$677$	17629.1	1.00080	0.500400	−	0.865794i	$-0.333186\pi$
$677$	17629.1	1.00080	0.500400	+	0.865794i	$0.333186\pi$
$678$	1374.14	0.0778371
$679$	1602.19	0.0905541
$680$	−2281.74	−0.128678
$681$	15276.2	0.859598
$682$	2801.62	0.157301
$683$	−8654.57	−0.484858	−0.242429	−	0.970169i	$-0.577944\pi$
$683$	−8654.57	−0.484858	−0.242429	+	0.970169i	$0.577944\pi$
$684$	−955.276	−0.0534004
$685$	−882.998	−0.0492520
$686$	−8921.45	−0.496534
$687$	−13948.8	−0.774646
$688$	1841.58	0.102049
$689$	−15278.1	−0.844773
$690$	−1634.61	−0.0901865
$691$	−7763.77	−0.427421	−0.213710	−	0.976897i	$-0.568555\pi$
$691$	−7763.77	−0.427421	−0.213710	+	0.976897i	$0.568555\pi$
$692$	−6262.27	−0.344011
$693$	429.024	0.0235170
$694$	−37901.4	−2.07308
$695$	2752.48	0.150226
$696$	−2933.74	−0.159775
$697$	16386.1	0.890484
$698$	22427.5	1.21618
$699$	−12111.2	−0.655348
$700$	813.749	0.0439383
$701$	−3094.79	−0.166746	−0.0833728	−	0.996518i	$-0.526569\pi$
$701$	−3094.79	−0.166746	−0.0833728	+	0.996518i	$0.526569\pi$
$702$	−3535.32	−0.190074
$703$	8206.44	0.440273
$704$	−4193.83	−0.224518
$705$	−747.211	−0.0399172
$706$	−9292.39	−0.495359
$707$	4641.12	0.246885
$708$	−78.8760	−0.00418692
$709$	10532.5	0.557910	0.278955	−	0.960304i	$-0.410012\pi$
$709$	10532.5	0.557910	0.278955	+	0.960304i	$0.410012\pi$
$710$	1941.43	0.102620
$711$	−11354.2	−0.598896
$712$	−5527.45	−0.290941
$713$	−12030.5	−0.631903
$714$	3778.15	0.198031
$715$	565.617	0.0295844
$716$	−669.589	−0.0349493
$717$	10717.6	0.558240
$718$	24887.1	1.29356
$719$	−33875.2	−1.75707	−0.878534	−	0.477679i	$-0.841478\pi$
$719$	−33875.2	−1.75707	−0.878534	+	0.477679i	$0.841478\pi$
$720$	−805.336	−0.0416849
$721$	−2211.37	−0.114224
$722$	6119.23	0.315421
$723$	15.1722	0.000780443 0
$724$	−1283.69	−0.0658947
$725$	−6042.13	−0.309516
$726$	1120.02	0.0572561
$727$	−6460.81	−0.329598	−0.164799	−	0.986327i	$-0.552698\pi$
$727$	−6460.81	−0.329598	−0.164799	+	0.986327i	$0.552698\pi$
$728$	3676.90	0.187191
$729$	729.000	0.0370370
$730$	−1363.61	−0.0691364
$731$	2348.73	0.118838
$732$	278.174	0.0140459
$733$	−32565.4	−1.64097	−0.820485	−	0.571668i	$-0.806296\pi$
$733$	−32565.4	−1.64097	−0.820485	+	0.571668i	$0.806296\pi$
$734$	−22265.7	−1.11967
$735$	1178.54	0.0591445
$736$	−9897.85	−0.495706
$737$	9258.07	0.462721
$738$	4831.10	0.240969
$739$	−33801.8	−1.68257	−0.841286	−	0.540590i	$-0.818201\pi$
$739$	−33801.8	−1.68257	−0.841286	+	0.540590i	$0.818201\pi$
$740$	−216.463	−0.0107532
$741$	−8889.70	−0.440717
$742$	4813.82	0.238168
$743$	14396.3	0.710831	0.355415	−	0.934708i	$-0.384339\pi$
$743$	14396.3	0.710831	0.355415	+	0.934708i	$0.384339\pi$
$744$	−4951.16	−0.243976
$745$	1592.12	0.0782965
$746$	−3632.84	−0.178295
$747$	−5220.94	−0.255722
$748$	1574.89	0.0769835
$749$	−2814.86	−0.137320
$750$	−2787.46	−0.135711
$751$	−7571.16	−0.367877	−0.183938	−	0.982938i	$-0.558885\pi$
$751$	−7571.16	−0.367877	−0.183938	+	0.982938i	$0.558885\pi$
$752$	−15180.6	−0.736141
$753$	−725.416	−0.0351071
$754$	6404.37	0.309328
$755$	3161.58	0.152400
$756$	177.859	0.00855643
$757$	−21716.8	−1.04268	−0.521340	−	0.853349i	$-0.674568\pi$
$757$	−21716.8	−1.04268	−0.521340	+	0.853349i	$0.674568\pi$
$758$	−38359.6	−1.83810
$759$	−4809.53	−0.230007
$760$	−1691.59	−0.0807375
$761$	−13235.1	−0.630449	−0.315225	−	0.949017i	$-0.602080\pi$
$761$	−13235.1	−0.630449	−0.315225	+	0.949017i	$0.602080\pi$
$762$	−10060.3	−0.478274
$763$	7463.57	0.354128
$764$	−4872.63	−0.230740
$765$	−1027.11	−0.0485430
$766$	5591.22	0.263732
$767$	−734.012	−0.0345550
$768$	−6767.64	−0.317977
$769$	−21330.5	−1.00026	−0.500129	−	0.865951i	$-0.666714\pi$
$769$	−21330.5	−1.00026	−0.500129	+	0.865951i	$0.666714\pi$
$770$	−178.215	−0.00834080
$771$	11088.7	0.517964
$772$	2714.99	0.126573
$773$	17817.1	0.829026	0.414513	−	0.910043i	$-0.363952\pi$
$773$	17817.1	0.829026	0.414513	+	0.910043i	$0.363952\pi$
$774$	692.475	0.0321582
$775$	−10197.1	−0.472631
$776$	−7391.91	−0.341951
$777$	−1527.92	−0.0705456
$778$	10096.3	0.465258
$779$	12148.0	0.558725
$780$	234.486	0.0107640
$781$	5712.28	0.261718
$782$	−42354.6	−1.93683
$783$	−1320.61	−0.0602743
$784$	23943.7	1.09073
$785$	3455.54	0.157113
$786$	−16417.2	−0.745015
$787$	−7253.72	−0.328548	−0.164274	−	0.986415i	$-0.552528\pi$
$787$	−7253.72	−0.328548	−0.164274	+	0.986415i	$0.552528\pi$
$788$	3103.42	0.140298
$789$	−19647.2	−0.886514
$790$	4716.48	0.212411
$791$	−643.333	−0.0289182
$792$	−1979.36	−0.0888050
$793$	2588.66	0.115922
$794$	37053.5	1.65614
$795$	−1308.67	−0.0583820
$796$	−1054.53	−0.0469559
$797$	−12120.4	−0.538679	−0.269339	−	0.963045i	$-0.586805\pi$
$797$	−12120.4	−0.538679	−0.269339	+	0.963045i	$0.586805\pi$
$798$	2800.97	0.124252
$799$	−19361.1	−0.857253
$800$	−8389.40	−0.370763
$801$	−2488.15	−0.109756
$802$	21573.3	0.949849
$803$	−4012.17	−0.176322
$804$	3838.09	0.168357
$805$	765.279	0.0335063
$806$	10808.4	0.472344
$807$	25108.4	1.09524
$808$	−21412.5	−0.932288
$809$	15399.0	0.669221	0.334611	−	0.942356i	$-0.391395\pi$
$809$	15399.0	0.669221	0.334611	+	0.942356i	$0.391395\pi$
$810$	−302.824	−0.0131360
$811$	39307.9	1.70196	0.850978	−	0.525201i	$-0.176010\pi$
$811$	39307.9	1.70196	0.850978	+	0.525201i	$0.176010\pi$
$812$	−322.198	−0.0139248
$813$	−6783.39	−0.292625
$814$	−3988.84	−0.171755
$815$	−2759.44	−0.118600
$816$	−20867.2	−0.895217
$817$	1741.25	0.0745639
$818$	20900.7	0.893370
$819$	1655.14	0.0706168
$820$	−320.430	−0.0136462
$821$	−33635.2	−1.42981	−0.714907	−	0.699219i	$-0.753531\pi$
$821$	−33635.2	−1.42981	−0.714907	+	0.699219i	$0.753531\pi$
$822$	−6745.54	−0.286226
$823$	44638.2	1.89063	0.945315	−	0.326158i	$-0.105754\pi$
$823$	44638.2	1.89063	0.945315	+	0.326158i	$0.105754\pi$
$824$	10202.5	0.431334
$825$	−4076.55	−0.172033
$826$	231.273	0.00974215
$827$	21825.1	0.917694	0.458847	−	0.888515i	$-0.348263\pi$
$827$	21825.1	0.917694	0.458847	+	0.888515i	$0.348263\pi$
$828$	−1993.87	−0.0836857
$829$	18510.4	0.775504	0.387752	−	0.921764i	$-0.373252\pi$
$829$	18510.4	0.775504	0.387752	+	0.921764i	$0.373252\pi$
$830$	2168.76	0.0906971
$831$	1369.04	0.0571498
$832$	−16179.4	−0.674184
$833$	30537.4	1.27018
$834$	21027.2	0.873034
$835$	−2541.60	−0.105336
$836$	1167.56	0.0483025
$837$	−2228.74	−0.0920389
$838$	277.655	0.0114456
$839$	−1234.81	−0.0508109	−0.0254055	−	0.999677i	$-0.508088\pi$
$839$	−1234.81	−0.0508109	−0.0254055	+	0.999677i	$0.508088\pi$
$840$	314.950	0.0129367
$841$	−21996.7	−0.901909
$842$	−42330.3	−1.73254
$843$	1846.97	0.0754602
$844$	−5615.63	−0.229026
$845$	−479.940	−0.0195390
$846$	−5708.22	−0.231977
$847$	−524.362	−0.0212719
$848$	−26587.3	−1.07666
$849$	23677.4	0.957133
$850$	−35899.7	−1.44865
$851$	17128.6	0.689968
$852$	2368.12	0.0952235
$853$	17274.1	0.693383	0.346691	−	0.937979i	$-0.387305\pi$
$853$	17274.1	0.693383	0.346691	+	0.937979i	$0.387305\pi$
$854$	−815.636	−0.0326821
$855$	−761.461	−0.0304578
$856$	12986.8	0.518550
$857$	12937.5	0.515678	0.257839	−	0.966188i	$-0.416990\pi$
$857$	12937.5	0.515678	0.257839	+	0.966188i	$0.416990\pi$
$858$	4320.95	0.171929
$859$	39112.3	1.55354	0.776771	−	0.629783i	$-0.216856\pi$
$859$	39112.3	1.55354	0.776771	+	0.629783i	$0.216856\pi$
$860$	−45.9294	−0.00182114
$861$	−2261.78	−0.0895254
$862$	−50937.0	−2.01267
$863$	3480.81	0.137298	0.0686489	−	0.997641i	$-0.478131\pi$
$863$	3480.81	0.137298	0.0686489	+	0.997641i	$0.478131\pi$
$864$	−1833.65	−0.0722013
$865$	−4991.73	−0.196212
$866$	23447.4	0.920065
$867$	−11874.7	−0.465150
$868$	−543.760	−0.0212632
$869$	13877.3	0.541722
$870$	548.576	0.0213776
$871$	35716.8	1.38946
$872$	−34434.2	−1.33726
$873$	−3327.43	−0.128999
$874$	−31400.0	−1.21524
$875$	1305.01	0.0504197
$876$	−1663.31	−0.0641530
$877$	−27044.4	−1.04131	−0.520653	−	0.853768i	$-0.674312\pi$
$877$	−27044.4	−1.04131	−0.520653	+	0.853768i	$0.674312\pi$
$878$	−4587.98	−0.176352
$879$	17050.9	0.654280
$880$	984.300	0.0377054
$881$	−36814.3	−1.40784	−0.703919	−	0.710280i	$-0.748568\pi$
$881$	−36814.3	−1.40784	−0.703919	+	0.710280i	$0.748568\pi$
$882$	9003.32	0.343716
$883$	22417.6	0.854372	0.427186	−	0.904164i	$-0.359505\pi$
$883$	22417.6	0.854372	0.427186	+	0.904164i	$0.359505\pi$
$884$	6075.78	0.231166
$885$	−62.8730	−0.00238808
$886$	44723.9	1.69585
$887$	−11193.3	−0.423713	−0.211856	−	0.977301i	$-0.567951\pi$
$887$	−11193.3	−0.423713	−0.211856	+	0.977301i	$0.567951\pi$
$888$	7049.29	0.266395
$889$	4709.92	0.177689
$890$	1033.57	0.0389273
$891$	−891.000	−0.0335013
$892$	7114.55	0.267055
$893$	−14353.5	−0.537875
$894$	12162.8	0.455017
$895$	−533.737	−0.0199339
$896$	7452.26	0.277860
$897$	−18554.8	−0.690664
$898$	−17592.3	−0.653744
$899$	4037.45	0.149785
$900$	−1690.00	−0.0625926
$901$	−33909.0	−1.25380
$902$	−5904.68	−0.217965
$903$	−324.197	−0.0119475
$904$	2968.11	0.109201
$905$	−1023.24	−0.0375842
$906$	24152.5	0.885665
$907$	−25953.9	−0.950150	−0.475075	−	0.879945i	$-0.657579\pi$
$907$	−25953.9	−0.950150	−0.475075	+	0.879945i	$0.657579\pi$
$908$	−7740.34	−0.282899
$909$	−9638.72	−0.351701
$910$	−687.537	−0.0250457
$911$	31039.1	1.12884	0.564420	−	0.825488i	$-0.309100\pi$
$911$	31039.1	1.12884	0.564420	+	0.825488i	$0.309100\pi$
$912$	−15470.1	−0.561695
$913$	6381.14	0.231309
$914$	29645.4	1.07285
$915$	221.736	0.00801132
$916$	7067.77	0.254941
$917$	7686.06	0.276790
$918$	−7846.50	−0.282106
$919$	12929.9	0.464113	0.232056	−	0.972702i	$-0.425455\pi$
$919$	12929.9	0.464113	0.232056	+	0.972702i	$0.425455\pi$
$920$	−3530.72	−0.126527
$921$	−23240.0	−0.831469
$922$	−50137.6	−1.79088
$923$	22037.5	0.785885
$924$	−217.383	−0.00773958
$925$	14518.2	0.516060
$926$	−45633.3	−1.61944
$927$	4592.58	0.162719
$928$	3321.72	0.117501
$929$	−4284.28	−0.151305	−0.0756526	−	0.997134i	$-0.524104\pi$
$929$	−4284.28	−0.151305	−0.0756526	+	0.997134i	$0.524104\pi$
$930$	925.810	0.0326435
$931$	22639.2	0.796960
$932$	6136.66	0.215679
$933$	15500.3	0.543897
$934$	3620.78	0.126847
$935$	1255.36	0.0439088
$936$	−7636.21	−0.266664
$937$	−26307.5	−0.917213	−0.458607	−	0.888639i	$-0.651651\pi$
$937$	−26307.5	−0.917213	−0.458607	+	0.888639i	$0.651651\pi$
$938$	−11253.7	−0.391733
$939$	−14917.3	−0.518431
$940$	378.606	0.0131370
$941$	−12223.8	−0.423470	−0.211735	−	0.977327i	$-0.567911\pi$
$941$	−12223.8	−0.423470	−0.211735	+	0.977327i	$0.567911\pi$
$942$	26398.1	0.913055
$943$	25355.5	0.875599
$944$	−1277.35	−0.0440403
$945$	141.773	0.00488030
$946$	−846.358	−0.0290882
$947$	25003.1	0.857963	0.428981	−	0.903313i	$-0.358873\pi$
$947$	25003.1	0.857963	0.428981	+	0.903313i	$0.358873\pi$
$948$	5753.08	0.197101
$949$	−15478.6	−0.529459
$950$	−26614.6	−0.908939
$951$	−1303.98	−0.0444630
$952$	8160.71	0.277826
$953$	1814.21	0.0616664	0.0308332	−	0.999525i	$-0.490184\pi$
$953$	1814.21	0.0616664	0.0308332	+	0.999525i	$0.490184\pi$
$954$	−9997.38	−0.339284
$955$	−3884.03	−0.131607
$956$	−5430.55	−0.183720
$957$	1614.08	0.0545201
$958$	−19488.5	−0.657249
$959$	3158.07	0.106339
$960$	−1385.87	−0.0465926
$961$	−22977.2	−0.771279
$962$	−15388.6	−0.515747
$963$	5845.93	0.195620
$964$	−7.68763	−0.000256849 0
$965$	2164.15	0.0721932
$966$	5846.24	0.194720
$967$	−43881.0	−1.45927	−0.729636	−	0.683835i	$-0.760311\pi$
$967$	−43881.0	−1.45927	−0.729636	+	0.683835i	$0.760311\pi$
$968$	2419.22	0.0803272
$969$	−19730.3	−0.654106
$970$	1382.20	0.0457524
$971$	39937.8	1.31994	0.659972	−	0.751290i	$-0.270568\pi$
$971$	39937.8	1.31994	0.659972	+	0.751290i	$0.270568\pi$
$972$	−369.379	−0.0121891
$973$	−9844.31	−0.324352
$974$	−31209.8	−1.02672
$975$	−15727.0	−0.516581
$976$	4504.85	0.147743
$977$	−21076.4	−0.690168	−0.345084	−	0.938572i	$-0.612150\pi$
$977$	−21076.4	−0.690168	−0.345084	+	0.938572i	$0.612150\pi$
$978$	−21080.4	−0.689239
$979$	3041.08	0.0992780
$980$	−597.159	−0.0194648
$981$	−15500.4	−0.504475
$982$	51995.0	1.68964
$983$	−42185.5	−1.36878	−0.684389	−	0.729117i	$-0.739931\pi$
$983$	−42185.5	−1.36878	−0.684389	+	0.729117i	$0.739931\pi$
$984$	10435.1	0.338067
$985$	2473.77	0.0800212
$986$	14214.2	0.459100
$987$	2672.42	0.0861845
$988$	4504.34	0.145043
$989$	3634.38	0.116852
$990$	370.118	0.0118819
$991$	35151.7	1.12677	0.563387	−	0.826193i	$-0.309498\pi$
$991$	35151.7	1.12677	0.563387	+	0.826193i	$0.309498\pi$
$992$	5605.93	0.179424
$993$	−4237.25	−0.135413
$994$	−6943.58	−0.221566
$995$	−840.580	−0.0267821
$996$	2645.41	0.0841596
$997$	−3993.85	−0.126867	−0.0634336	−	0.997986i	$-0.520205\pi$
$997$	−3993.85	−0.126867	−0.0634336	+	0.997986i	$0.520205\pi$
$998$	39379.9	1.24905
$999$	3173.20	0.100496

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.e.1.10	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.e.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-3.08546 q^{2} -3.00000 q^{3} +1.52008 q^{4} +1.21167 q^{5} +9.25639 q^{6} -4.33357 q^{7} +19.9936 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.08546 q^{2} -3.00000 q^{3} +1.52008 q^{4} +1.21167 q^{5} +9.25639 q^{6} -4.33357 q^{7} +19.9936 q^{8} +9.00000 q^{9} -3.73856 q^{10} -11.0000 q^{11} -4.56023 q^{12} -42.4370 q^{13} +13.3711 q^{14} -3.63501 q^{15} -73.8500 q^{16} -94.1872 q^{17} -27.7692 q^{18} -69.8266 q^{19} +1.84183 q^{20} +13.0007 q^{21} +33.9401 q^{22} -145.743 q^{23} -59.9807 q^{24} -123.532 q^{25} +130.938 q^{26} -27.0000 q^{27} -6.58736 q^{28} +48.9115 q^{29} +11.2157 q^{30} +82.5460 q^{31} +67.9128 q^{32} +33.0000 q^{33} +290.611 q^{34} -5.25086 q^{35} +13.6807 q^{36} -117.526 q^{37} +215.447 q^{38} +127.311 q^{39} +24.2256 q^{40} -173.974 q^{41} -40.1132 q^{42} -24.9368 q^{43} -16.7208 q^{44} +10.9050 q^{45} +449.686 q^{46} +205.560 q^{47} +221.550 q^{48} -324.220 q^{49} +381.153 q^{50} +282.562 q^{51} -64.5075 q^{52} +360.018 q^{53} +83.3075 q^{54} -13.3284 q^{55} -86.6436 q^{56} +209.480 q^{57} -150.915 q^{58} +17.2965 q^{59} -5.52549 q^{60} -61.0000 q^{61} -254.692 q^{62} -39.0022 q^{63} +381.257 q^{64} -51.4197 q^{65} -101.820 q^{66} -841.643 q^{67} -143.172 q^{68} +437.230 q^{69} +16.2013 q^{70} -519.298 q^{71} +179.942 q^{72} +364.743 q^{73} +362.622 q^{74} +370.596 q^{75} -106.142 q^{76} +47.6693 q^{77} -392.814 q^{78} -1261.58 q^{79} -89.4818 q^{80} +81.0000 q^{81} +536.789 q^{82} -580.104 q^{83} +19.7621 q^{84} -114.124 q^{85} +76.9416 q^{86} -146.734 q^{87} -219.929 q^{88} -276.461 q^{89} -33.6471 q^{90} +183.904 q^{91} -221.541 q^{92} -247.638 q^{93} -634.246 q^{94} -84.6068 q^{95} -203.739 q^{96} -369.715 q^{97} +1000.37 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 2 q^{2} - 114 q^{3} + 142 q^{4} + 15 q^{5} + 6 q^{6} + 63 q^{7} - 45 q^{8} + 342 q^{9}+O(q^{10}) \) 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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