LMFDB - Embedded newform 2013.4.a.h.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$118.770844842$
Analytic rank:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.382791 q^{2} +3.00000 q^{3} -7.85347 q^{4} +10.1790 q^{5} -1.14837 q^{6} +17.4416 q^{7} +6.06857 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-0.382791 q^{2} +3.00000 q^{3} -7.85347 q^{4} +10.1790 q^{5} -1.14837 q^{6} +17.4416 q^{7} +6.06857 q^{8} +9.00000 q^{9} -3.89641 q^{10} -11.0000 q^{11} -23.5604 q^{12} +66.5345 q^{13} -6.67648 q^{14} +30.5369 q^{15} +60.5048 q^{16} +1.07760 q^{17} -3.44512 q^{18} +75.1961 q^{19} -79.9401 q^{20} +52.3247 q^{21} +4.21070 q^{22} +113.645 q^{23} +18.2057 q^{24} -21.3889 q^{25} -25.4688 q^{26} +27.0000 q^{27} -136.977 q^{28} +82.8805 q^{29} -11.6892 q^{30} +141.008 q^{31} -71.7092 q^{32} -33.0000 q^{33} -0.412494 q^{34} +177.537 q^{35} -70.6812 q^{36} -368.745 q^{37} -28.7844 q^{38} +199.604 q^{39} +61.7717 q^{40} +498.834 q^{41} -20.0294 q^{42} +200.179 q^{43} +86.3882 q^{44} +91.6106 q^{45} -43.5025 q^{46} -522.059 q^{47} +181.514 q^{48} -38.7914 q^{49} +8.18747 q^{50} +3.23279 q^{51} -522.527 q^{52} +51.8378 q^{53} -10.3354 q^{54} -111.968 q^{55} +105.845 q^{56} +225.588 q^{57} -31.7259 q^{58} +424.207 q^{59} -239.820 q^{60} +61.0000 q^{61} -53.9765 q^{62} +156.974 q^{63} -456.589 q^{64} +677.252 q^{65} +12.6321 q^{66} -723.040 q^{67} -8.46287 q^{68} +340.936 q^{69} -67.9596 q^{70} -908.264 q^{71} +54.6171 q^{72} +894.249 q^{73} +141.152 q^{74} -64.1667 q^{75} -590.551 q^{76} -191.857 q^{77} -76.4065 q^{78} +302.411 q^{79} +615.875 q^{80} +81.0000 q^{81} -190.949 q^{82} +635.884 q^{83} -410.931 q^{84} +10.9688 q^{85} -76.6266 q^{86} +248.641 q^{87} -66.7542 q^{88} -4.02365 q^{89} -35.0677 q^{90} +1160.47 q^{91} -892.511 q^{92} +423.023 q^{93} +199.839 q^{94} +765.418 q^{95} -215.128 q^{96} -1791.56 q^{97} +14.8490 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9}+O(q^{10}) $ 39 * q + 8 * q^2 + 117 * q^3 + 154 * q^4 + 65 * q^5 + 24 * q^6 + 35 * q^7 + 75 * q^8 + 351 * q^9	\( 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9} - 21 q^{10} - 429 q^{11} + 462 q^{12} - 27 q^{13} + 164 q^{14} + 195 q^{15} + 686 q^{16} + 170 q^{17} + 72 q^{18} + 139 q^{19} + 1056 q^{20} + 105 q^{21} - 88 q^{22} + 291 q^{23} + 225 q^{24} + 1236 q^{25} + 583 q^{26} + 1053 q^{27} + 976 q^{28} + 374 q^{29} - 63 q^{30} + 232 q^{31} + 933 q^{32} - 1287 q^{33} + 332 q^{34} + 626 q^{35} + 1386 q^{36} + 232 q^{37} + 989 q^{38} - 81 q^{39} - 263 q^{40} + 1014 q^{41} + 492 q^{42} + 515 q^{43} - 1694 q^{44} + 585 q^{45} - 371 q^{46} + 2005 q^{47} + 2058 q^{48} + 2064 q^{49} + 4582 q^{50} + 510 q^{51} + 216 q^{52} + 1485 q^{53} + 216 q^{54} - 715 q^{55} + 2307 q^{56} + 417 q^{57} + 573 q^{58} + 2749 q^{59} + 3168 q^{60} + 2379 q^{61} + 1837 q^{62} + 315 q^{63} + 7295 q^{64} + 3630 q^{65} - 264 q^{66} + 3575 q^{67} + 2630 q^{68} + 873 q^{69} + 4218 q^{70} + 4723 q^{71} + 675 q^{72} + 859 q^{73} + 4232 q^{74} + 3708 q^{75} + 2466 q^{76} - 385 q^{77} + 1749 q^{78} - 1887 q^{79} + 8933 q^{80} + 3159 q^{81} + 6806 q^{82} + 5609 q^{83} + 2928 q^{84} - 565 q^{85} + 5185 q^{86} + 1122 q^{87} - 825 q^{88} + 6725 q^{89} - 189 q^{90} + 2808 q^{91} + 3257 q^{92} + 696 q^{93} + 3184 q^{94} + 3216 q^{95} + 2799 q^{96} + 3512 q^{97} + 4464 q^{98} - 3861 q^{99}+O(q^{100}) \) 39 * q + 8 * q^2 + 117 * q^3 + 154 * q^4 + 65 * q^5 + 24 * q^6 + 35 * q^7 + 75 * q^8 + 351 * q^9 - 21 * q^10 - 429 * q^11 + 462 * q^12 - 27 * q^13 + 164 * q^14 + 195 * q^15 + 686 * q^16 + 170 * q^17 + 72 * q^18 + 139 * q^19 + 1056 * q^20 + 105 * q^21 - 88 * q^22 + 291 * q^23 + 225 * q^24 + 1236 * q^25 + 583 * q^26 + 1053 * q^27 + 976 * q^28 + 374 * q^29 - 63 * q^30 + 232 * q^31 + 933 * q^32 - 1287 * q^33 + 332 * q^34 + 626 * q^35 + 1386 * q^36 + 232 * q^37 + 989 * q^38 - 81 * q^39 - 263 * q^40 + 1014 * q^41 + 492 * q^42 + 515 * q^43 - 1694 * q^44 + 585 * q^45 - 371 * q^46 + 2005 * q^47 + 2058 * q^48 + 2064 * q^49 + 4582 * q^50 + 510 * q^51 + 216 * q^52 + 1485 * q^53 + 216 * q^54 - 715 * q^55 + 2307 * q^56 + 417 * q^57 + 573 * q^58 + 2749 * q^59 + 3168 * q^60 + 2379 * q^61 + 1837 * q^62 + 315 * q^63 + 7295 * q^64 + 3630 * q^65 - 264 * q^66 + 3575 * q^67 + 2630 * q^68 + 873 * q^69 + 4218 * q^70 + 4723 * q^71 + 675 * q^72 + 859 * q^73 + 4232 * q^74 + 3708 * q^75 + 2466 * q^76 - 385 * q^77 + 1749 * q^78 - 1887 * q^79 + 8933 * q^80 + 3159 * q^81 + 6806 * q^82 + 5609 * q^83 + 2928 * q^84 - 565 * q^85 + 5185 * q^86 + 1122 * q^87 - 825 * q^88 + 6725 * q^89 - 189 * q^90 + 2808 * q^91 + 3257 * q^92 + 696 * q^93 + 3184 * q^94 + 3216 * q^95 + 2799 * q^96 + 3512 * q^97 + 4464 * q^98 - 3861 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.382791	−0.135337	−0.0676685	−	0.997708i	$-0.521556\pi$
$2$	−0.382791	−0.135337	−0.0676685	+	0.997708i	$0.521556\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−7.85347	−0.981684
$5$	10.1790	0.910433	0.455217	−	0.890381i	$-0.349562\pi$
$5$	10.1790	0.910433	0.455217	+	0.890381i	$0.349562\pi$
$6$	−1.14837	−0.0781369
$7$	17.4416	0.941757	0.470878	−	0.882198i	$-0.343937\pi$
$7$	17.4416	0.941757	0.470878	+	0.882198i	$0.343937\pi$
$8$	6.06857	0.268195
$9$	9.00000	0.333333
$10$	−3.89641	−0.123215
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−23.5604	−0.566775
$13$	66.5345	1.41949	0.709745	−	0.704459i	$-0.248810\pi$
$13$	66.5345	1.41949	0.709745	+	0.704459i	$0.248810\pi$
$14$	−6.67648	−0.127455
$15$	30.5369	0.525639
$16$	60.5048	0.945387
$17$	1.07760	0.0153739	0.00768693	−	0.999970i	$-0.497553\pi$
$17$	1.07760	0.0153739	0.00768693	+	0.999970i	$0.497553\pi$
$18$	−3.44512	−0.0451124
$19$	75.1961	0.907957	0.453978	−	0.891013i	$-0.350004\pi$
$19$	75.1961	0.907957	0.453978	+	0.891013i	$0.350004\pi$
$20$	−79.9401	−0.893758
$21$	52.3247	0.543723
$22$	4.21070	0.0408057
$23$	113.645	1.03029	0.515146	−	0.857102i	$-0.327738\pi$
$23$	113.645	1.03029	0.515146	+	0.857102i	$0.327738\pi$
$24$	18.2057	0.154843
$25$	−21.3889	−0.171111
$26$	−25.4688	−0.192110
$27$	27.0000	0.192450
$28$	−136.977	−0.924507
$29$	82.8805	0.530707	0.265354	−	0.964151i	$-0.414511\pi$
$29$	82.8805	0.530707	0.265354	+	0.964151i	$0.414511\pi$
$30$	−11.6892	−0.0711384
$31$	141.008	0.816959	0.408480	−	0.912767i	$-0.366059\pi$
$31$	141.008	0.816959	0.408480	+	0.912767i	$0.366059\pi$
$32$	−71.7092	−0.396141
$33$	−33.0000	−0.174078
$34$	−0.412494	−0.00208065
$35$	177.537	0.857407
$36$	−70.6812	−0.327228
$37$	−368.745	−1.63841	−0.819206	−	0.573499i	$-0.805586\pi$
$37$	−368.745	−1.63841	−0.819206	+	0.573499i	$0.805586\pi$
$38$	−28.7844	−0.122880
$39$	199.604	0.819542
$40$	61.7717	0.244174
$41$	498.834	1.90011	0.950057	−	0.312075i	$-0.101024\pi$
$41$	498.834	1.90011	0.950057	+	0.312075i	$0.101024\pi$
$42$	−20.0294	−0.0735859
$43$	200.179	0.709929	0.354965	−	0.934880i	$-0.384493\pi$
$43$	200.179	0.709929	0.354965	+	0.934880i	$0.384493\pi$
$44$	86.3882	0.295989
$45$	91.6106	0.303478
$46$	−43.5025	−0.139437
$47$	−522.059	−1.62021	−0.810107	−	0.586282i	$-0.800591\pi$
$47$	−522.059	−1.62021	−0.810107	+	0.586282i	$0.800591\pi$
$48$	181.514	0.545820
$49$	−38.7914	−0.113095
$50$	8.18747	0.0231577
$51$	3.23279	0.00887610
$52$	−522.527	−1.39349
$53$	51.8378	0.134348	0.0671742	−	0.997741i	$-0.478602\pi$
$53$	51.8378	0.134348	0.0671742	+	0.997741i	$0.478602\pi$
$54$	−10.3354	−0.0260456
$55$	−111.968	−0.274506
$56$	105.845	0.252575
$57$	225.588	0.524209
$58$	−31.7259	−0.0718244
$59$	424.207	0.936053	0.468026	−	0.883714i	$-0.344965\pi$
$59$	424.207	0.936053	0.468026	+	0.883714i	$0.344965\pi$
$60$	−239.820	−0.516011
$61$	61.0000	0.128037
$61$	61.0000	0.128037
$62$	−53.9765	−0.110565
$63$	156.974	0.313919
$64$	−456.589	−0.891775
$65$	677.252	1.29235
$66$	12.6321	0.0235592
$67$	−723.040	−1.31841	−0.659204	−	0.751964i	$-0.729107\pi$
$67$	−723.040	−1.31841	−0.659204	+	0.751964i	$0.729107\pi$
$68$	−8.46287	−0.0150923
$69$	340.936	0.594839
$70$	−67.9596	−0.116039
$71$	−908.264	−1.51819	−0.759093	−	0.650983i	$-0.774357\pi$
$71$	−908.264	−1.51819	−0.759093	+	0.650983i	$0.774357\pi$
$72$	54.6171	0.0893984
$73$	894.249	1.43375	0.716876	−	0.697201i	$-0.245571\pi$
$73$	894.249	1.43375	0.716876	+	0.697201i	$0.245571\pi$
$74$	141.152	0.221738
$75$	−64.1667	−0.0987910
$76$	−590.551	−0.891326
$77$	−191.857	−0.283950
$78$	−76.4065	−0.110914
$79$	302.411	0.430682	0.215341	−	0.976539i	$-0.430914\pi$
$79$	302.411	0.430682	0.215341	+	0.976539i	$0.430914\pi$
$80$	615.875	0.860712
$81$	81.0000	0.111111
$82$	−190.949	−0.257156
$83$	635.884	0.840932	0.420466	−	0.907308i	$-0.361867\pi$
$83$	635.884	0.840932	0.420466	+	0.907308i	$0.361867\pi$
$84$	−410.931	−0.533765
$85$	10.9688	0.0139969
$86$	−76.6266	−0.0960797
$87$	248.641	0.306404
$88$	−66.7542	−0.0808639
$89$	−4.02365	−0.00479220	−0.00239610	−	0.999997i	$-0.500763\pi$
$89$	−4.02365	−0.00479220	−0.00239610	+	0.999997i	$0.500763\pi$
$90$	−35.0677	−0.0410718
$91$	1160.47	1.33681
$92$	−892.511	−1.01142
$93$	423.023	0.471672
$94$	199.839	0.219275
$95$	765.418	0.826634
$96$	−215.128	−0.228712
$97$	−1791.56	−1.87531	−0.937656	−	0.347565i	$-0.887009\pi$
$97$	−1791.56	−1.87531	−0.937656	+	0.347565i	$0.887009\pi$
$98$	14.8490	0.0153059
$99$	−99.0000	−0.100504
$100$	167.977	0.167977
$101$	−332.062	−0.327143	−0.163571	−	0.986531i	$-0.552301\pi$
$101$	−332.062	−0.327143	−0.163571	+	0.986531i	$0.552301\pi$
$102$	−1.23748	−0.00120127
$103$	1637.71	1.56668	0.783341	−	0.621592i	$-0.213514\pi$
$103$	1637.71	1.56668	0.783341	+	0.621592i	$0.213514\pi$
$104$	403.769	0.380700
$105$	532.611	0.495024
$106$	−19.8430	−0.0181823
$107$	990.544	0.894949	0.447474	−	0.894297i	$-0.352324\pi$
$107$	990.544	0.894949	0.447474	+	0.894297i	$0.352324\pi$
$108$	−212.044	−0.188925
$109$	−736.511	−0.647202	−0.323601	−	0.946194i	$-0.604893\pi$
$109$	−736.511	−0.647202	−0.323601	+	0.946194i	$0.604893\pi$
$110$	42.8605	0.0371508
$111$	−1106.23	−0.945938
$112$	1055.30	0.890325
$113$	493.021	0.410438	0.205219	−	0.978716i	$-0.434209\pi$
$113$	493.021	0.410438	0.205219	+	0.978716i	$0.434209\pi$
$114$	−86.3532	−0.0709449
$115$	1156.79	0.938012
$116$	−650.899	−0.520987
$117$	598.811	0.473163
$118$	−162.383	−0.126683
$119$	18.7950	0.0144784
$120$	185.315	0.140974
$121$	121.000	0.0909091
$122$	−23.3503	−0.0173281
$123$	1496.50	1.09703
$124$	−1107.40	−0.801996
$125$	−1490.09	−1.06622
$126$	−60.0883	−0.0424849
$127$	−1122.39	−0.784219	−0.392109	−	0.919919i	$-0.628255\pi$
$127$	−1122.39	−0.784219	−0.392109	+	0.919919i	$0.628255\pi$
$128$	748.452	0.516831
$129$	600.536	0.409878
$130$	−259.246	−0.174903
$131$	−2245.07	−1.49735	−0.748674	−	0.662938i	$-0.769309\pi$
$131$	−2245.07	−1.49735	−0.748674	+	0.662938i	$0.769309\pi$
$132$	259.165	0.170889
$133$	1311.54	0.855074
$134$	276.773	0.178430
$135$	274.832	0.175213
$136$	6.53947	0.00412320
$137$	−207.112	−0.129159	−0.0645795	−	0.997913i	$-0.520571\pi$
$137$	−207.112	−0.129159	−0.0645795	+	0.997913i	$0.520571\pi$
$138$	−130.507	−0.0805038
$139$	−298.364	−0.182064	−0.0910320	−	0.995848i	$-0.529017\pi$
$139$	−298.364	−0.182064	−0.0910320	+	0.995848i	$0.529017\pi$
$140$	−1394.28	−0.841702
$141$	−1566.18	−0.935431
$142$	347.675	0.205467
$143$	−731.880	−0.427992
$144$	544.543	0.315129
$145$	843.636	0.483174
$146$	−342.310	−0.194040
$147$	−116.374	−0.0652952
$148$	2895.93	1.60840
$149$	−1082.29	−0.595064	−0.297532	−	0.954712i	$-0.596163\pi$
$149$	−1082.29	−0.595064	−0.297532	+	0.954712i	$0.596163\pi$
$150$	24.5624	0.0133701
$151$	−2993.51	−1.61330	−0.806649	−	0.591030i	$-0.798721\pi$
$151$	−2993.51	−1.61330	−0.806649	+	0.591030i	$0.798721\pi$
$152$	456.333	0.243510
$153$	9.69837	0.00512462
$154$	73.4413	0.0384290
$155$	1435.31	0.743787
$156$	−1567.58	−0.804532
$157$	2172.81	1.10452	0.552258	−	0.833673i	$-0.313766\pi$
$157$	2172.81	1.10452	0.552258	+	0.833673i	$0.313766\pi$
$158$	−115.760	−0.0582873
$159$	155.513	0.0775661
$160$	−729.925	−0.360660
$161$	1982.16	0.970284
$162$	−31.0061	−0.0150375
$163$	1090.32	0.523929	0.261964	−	0.965078i	$-0.415630\pi$
$163$	1090.32	0.523929	0.261964	+	0.965078i	$0.415630\pi$
$164$	−3917.57	−1.86531
$165$	−335.905	−0.158486
$166$	−243.411	−0.113809
$167$	2253.03	1.04398	0.521990	−	0.852952i	$-0.325190\pi$
$167$	2253.03	1.04398	0.521990	+	0.852952i	$0.325190\pi$
$168$	317.536	0.145824
$169$	2229.84	1.01495
$170$	−4.19876	−0.00189430
$171$	676.765	0.302652
$172$	−1572.10	−0.696926
$173$	−1205.56	−0.529808	−0.264904	−	0.964275i	$-0.585340\pi$
$173$	−1205.56	−0.529808	−0.264904	+	0.964275i	$0.585340\pi$
$174$	−95.1777	−0.0414678
$175$	−373.056	−0.161145
$176$	−665.553	−0.285045
$177$	1272.62	0.540430
$178$	1.54022	0.000648562 0
$179$	−1227.47	−0.512543	−0.256271	−	0.966605i	$-0.582494\pi$
$179$	−1227.47	−0.512543	−0.256271	+	0.966605i	$0.582494\pi$
$180$	−719.461	−0.297919
$181$	1326.47	0.544730	0.272365	−	0.962194i	$-0.412194\pi$
$181$	1326.47	0.544730	0.272365	+	0.962194i	$0.412194\pi$
$182$	−444.216	−0.180920
$183$	183.000	0.0739221
$184$	689.665	0.276319
$185$	−3753.44	−1.49167
$186$	−161.930	−0.0638347
$187$	−11.8536	−0.00463539
$188$	4099.97	1.59054
$189$	470.923	0.181241
$190$	−292.995	−0.111874
$191$	−1537.34	−0.582399	−0.291199	−	0.956662i	$-0.594054\pi$
$191$	−1537.34	−0.582399	−0.291199	+	0.956662i	$0.594054\pi$
$192$	−1369.77	−0.514866
$193$	5149.24	1.92047	0.960234	−	0.279197i	$-0.0900684\pi$
$193$	5149.24	1.92047	0.960234	+	0.279197i	$0.0900684\pi$
$194$	685.793	0.253799
$195$	2031.76	0.746139
$196$	304.647	0.111023
$197$	534.331	0.193246	0.0966231	−	0.995321i	$-0.469196\pi$
$197$	534.331	0.193246	0.0966231	+	0.995321i	$0.469196\pi$
$198$	37.8963	0.0136019
$199$	304.651	0.108523	0.0542616	−	0.998527i	$-0.482720\pi$
$199$	304.651	0.108523	0.0542616	+	0.998527i	$0.482720\pi$
$200$	−129.800	−0.0458912
$201$	−2169.12	−0.761184
$202$	127.110	0.0442746
$203$	1445.57	0.499797
$204$	−25.3886	−0.00871352
$205$	5077.60	1.72993
$206$	−626.901	−0.212030
$207$	1022.81	0.343431
$208$	4025.66	1.34197
$209$	−827.157	−0.273759
$210$	−203.879	−0.0669951
$211$	−202.872	−0.0661909	−0.0330955	−	0.999452i	$-0.510537\pi$
$211$	−202.872	−0.0661909	−0.0330955	+	0.999452i	$0.510537\pi$
$212$	−407.106	−0.131888
$213$	−2724.79	−0.876525
$214$	−379.171	−0.121120
$215$	2037.61	0.646343
$216$	163.851	0.0516142
$217$	2459.40	0.769377
$218$	281.930	0.0875904
$219$	2682.75	0.827777
$220$	879.341	0.269478
$221$	71.6974	0.0218230
$222$	423.457	0.128020
$223$	−4276.74	−1.28427	−0.642134	−	0.766592i	$-0.721951\pi$
$223$	−4276.74	−1.28427	−0.642134	+	0.766592i	$0.721951\pi$
$224$	−1250.72	−0.373069
$225$	−192.500	−0.0570370
$226$	−188.724	−0.0555475
$227$	−57.4333	−0.0167929	−0.00839644	−	0.999965i	$-0.502673\pi$
$227$	−57.4333	−0.0167929	−0.00839644	+	0.999965i	$0.502673\pi$
$228$	−1771.65	−0.514608
$229$	354.570	0.102317	0.0511587	−	0.998691i	$-0.483709\pi$
$229$	354.570	0.102317	0.0511587	+	0.998691i	$0.483709\pi$
$230$	−442.810	−0.126948
$231$	−575.572	−0.163939
$232$	502.966	0.142333
$233$	1847.97	0.519589	0.259795	−	0.965664i	$-0.416345\pi$
$233$	1847.97	0.519589	0.259795	+	0.965664i	$0.416345\pi$
$234$	−229.219	−0.0640365
$235$	−5314.01	−1.47510
$236$	−3331.50	−0.918908
$237$	907.233	0.248655
$238$	−7.19455	−0.00195947
$239$	2527.93	0.684176	0.342088	−	0.939668i	$-0.388866\pi$
$239$	2527.93	0.684176	0.342088	+	0.939668i	$0.388866\pi$
$240$	1847.63	0.496932
$241$	5814.79	1.55421	0.777103	−	0.629373i	$-0.216688\pi$
$241$	5814.79	1.55421	0.777103	+	0.629373i	$0.216688\pi$
$242$	−46.3177	−0.0123034
$243$	243.000	0.0641500
$244$	−479.062	−0.125692
$245$	−394.856	−0.102965
$246$	−572.847	−0.148469
$247$	5003.14	1.28883
$248$	855.715	0.219105
$249$	1907.65	0.485512
$250$	570.391	0.144299
$251$	2957.94	0.743839	0.371919	−	0.928265i	$-0.378700\pi$
$251$	2957.94	0.743839	0.371919	+	0.928265i	$0.378700\pi$
$252$	−1232.79	−0.308169
$253$	−1250.10	−0.310645
$254$	429.640	0.106134
$255$	32.9064	0.00808110
$256$	3366.21	0.821828
$257$	2243.65	0.544571	0.272286	−	0.962216i	$-0.412220\pi$
$257$	2243.65	0.544571	0.272286	+	0.962216i	$0.412220\pi$
$258$	−229.880	−0.0554717
$259$	−6431.49	−1.54299
$260$	−5318.78	−1.26868
$261$	745.924	0.176902
$262$	859.393	0.202647
$263$	−4744.93	−1.11249	−0.556245	−	0.831018i	$-0.687758\pi$
$263$	−4744.93	−1.11249	−0.556245	+	0.831018i	$0.687758\pi$
$264$	−200.263	−0.0466868
$265$	527.654	0.122315
$266$	−502.045	−0.115723
$267$	−12.0709	−0.00276678
$268$	5678.37	1.29426
$269$	7231.86	1.63916	0.819581	−	0.572964i	$-0.194206\pi$
$269$	7231.86	1.63916	0.819581	+	0.572964i	$0.194206\pi$
$270$	−105.203	−0.0237128
$271$	−4994.93	−1.11963	−0.559817	−	0.828617i	$-0.689128\pi$
$271$	−4994.93	−1.11963	−0.559817	+	0.828617i	$0.689128\pi$
$272$	65.1997	0.0145342
$273$	3481.40	0.771810
$274$	79.2806	0.0174800
$275$	235.278	0.0515919
$276$	−2677.53	−0.583944
$277$	1523.50	0.330464	0.165232	−	0.986255i	$-0.447163\pi$
$277$	1523.50	0.330464	0.165232	+	0.986255i	$0.447163\pi$
$278$	114.211	0.0246400
$279$	1269.07	0.272320
$280$	1077.40	0.229952
$281$	8055.24	1.71009	0.855045	−	0.518554i	$-0.173530\pi$
$281$	8055.24	1.71009	0.855045	+	0.518554i	$0.173530\pi$
$282$	599.518	0.126599
$283$	6080.07	1.27711	0.638555	−	0.769576i	$-0.279532\pi$
$283$	6080.07	1.27711	0.638555	+	0.769576i	$0.279532\pi$
$284$	7133.03	1.49038
$285$	2296.25	0.477257
$286$	280.157	0.0579232
$287$	8700.44	1.78945
$288$	−645.383	−0.132047
$289$	−4911.84	−0.999764
$290$	−322.936	−0.0653913
$291$	−5374.68	−1.08271
$292$	−7022.96	−1.40749
$293$	3854.37	0.768515	0.384258	−	0.923226i	$-0.374457\pi$
$293$	3854.37	0.768515	0.384258	+	0.923226i	$0.374457\pi$
$294$	44.5470	0.00883686
$295$	4317.99	0.852214
$296$	−2237.75	−0.439415
$297$	−297.000	−0.0580259
$298$	414.290	0.0805342
$299$	7561.35	1.46249
$300$	503.931	0.0969816
$301$	3491.43	0.668580
$302$	1145.89	0.218339
$303$	−996.187	−0.188876
$304$	4549.72	0.858370
$305$	620.916	0.116569
$306$	−3.71245	−0.000693551 0
$307$	−551.279	−0.102486	−0.0512429	−	0.998686i	$-0.516318\pi$
$307$	−551.279	−0.102486	−0.0512429	+	0.998686i	$0.516318\pi$
$308$	1506.75	0.278749
$309$	4913.13	0.904525
$310$	−549.424	−0.100662
$311$	5753.68	1.04907	0.524535	−	0.851389i	$-0.324239\pi$
$311$	5753.68	1.04907	0.524535	+	0.851389i	$0.324239\pi$
$312$	1211.31	0.219797
$313$	−665.592	−0.120196	−0.0600982	−	0.998192i	$-0.519141\pi$
$313$	−665.592	−0.120196	−0.0600982	+	0.998192i	$0.519141\pi$
$314$	−831.731	−0.149482
$315$	1597.83	0.285802
$316$	−2374.98	−0.422794
$317$	−5846.43	−1.03586	−0.517931	−	0.855423i	$-0.673297\pi$
$317$	−5846.43	−1.03586	−0.517931	+	0.855423i	$0.673297\pi$
$318$	−59.5291	−0.0104976
$319$	−911.685	−0.160014
$320$	−4647.59	−0.811901
$321$	2971.63	0.516699
$322$	−758.752	−0.131315
$323$	81.0311	0.0139588
$324$	−636.131	−0.109076
$325$	−1423.10	−0.242890
$326$	−417.364	−0.0709070
$327$	−2209.53	−0.373662
$328$	3027.20	0.509602
$329$	−9105.53	−1.52585
$330$	128.582	0.0214490
$331$	6430.45	1.06782	0.533912	−	0.845540i	$-0.320721\pi$
$331$	6430.45	1.06782	0.533912	+	0.845540i	$0.320721\pi$
$332$	−4993.90	−0.825530
$333$	−3318.70	−0.546138
$334$	−862.440	−0.141289
$335$	−7359.79	−1.20032
$336$	3165.90	0.514029
$337$	8001.28	1.29335	0.646673	−	0.762768i	$-0.276160\pi$
$337$	8001.28	1.29335	0.646673	+	0.762768i	$0.276160\pi$
$338$	−853.564	−0.137360
$339$	1479.06	0.236967
$340$	−86.1432	−0.0137405
$341$	−1551.09	−0.246323
$342$	−259.060	−0.0409601
$343$	−6659.04	−1.04826
$344$	1214.80	0.190400
$345$	3470.38	0.541562
$346$	461.476	0.0717027
$347$	9224.65	1.42710	0.713552	−	0.700602i	$-0.247085\pi$
$347$	9224.65	1.42710	0.713552	+	0.700602i	$0.247085\pi$
$348$	−1952.70	−0.300792
$349$	−4933.88	−0.756747	−0.378374	−	0.925653i	$-0.623517\pi$
$349$	−4933.88	−0.756747	−0.378374	+	0.925653i	$0.623517\pi$
$350$	142.802	0.0218089
$351$	1796.43	0.273181
$352$	788.801	0.119441
$353$	−3677.73	−0.554521	−0.277260	−	0.960795i	$-0.589426\pi$
$353$	−3677.73	−0.554521	−0.277260	+	0.960795i	$0.589426\pi$
$354$	−487.148	−0.0731403
$355$	−9245.18	−1.38221
$356$	31.5996	0.00470442
$357$	56.3849	0.00835913
$358$	469.863	0.0693660
$359$	985.141	0.144829	0.0724147	−	0.997375i	$-0.476929\pi$
$359$	985.141	0.144829	0.0724147	+	0.997375i	$0.476929\pi$
$360$	555.945	0.0813913
$361$	−1204.54	−0.175615
$362$	−507.763	−0.0737221
$363$	363.000	0.0524864
$364$	−9113.70	−1.31233
$365$	9102.52	1.30534
$366$	−70.0508	−0.0100044
$367$	−10710.3	−1.52335	−0.761677	−	0.647957i	$-0.775623\pi$
$367$	−10710.3	−1.52335	−0.761677	+	0.647957i	$0.775623\pi$
$368$	6876.09	0.974025
$369$	4489.50	0.633372
$370$	1436.78	0.201878
$371$	904.132	0.126523
$372$	−3322.20	−0.463033
$373$	−8786.25	−1.21966	−0.609832	−	0.792531i	$-0.708763\pi$
$373$	−8786.25	−1.21966	−0.609832	+	0.792531i	$0.708763\pi$
$374$	4.53744	0.000627340 0
$375$	−4470.26	−0.615582
$376$	−3168.15	−0.434534
$377$	5514.41	0.753333
$378$	−180.265	−0.0245286
$379$	10796.6	1.46328	0.731639	−	0.681692i	$-0.238756\pi$
$379$	10796.6	1.46328	0.731639	+	0.681692i	$0.238756\pi$
$380$	−6011.19	−0.811493
$381$	−3367.16	−0.452769
$382$	588.481	0.0788201
$383$	1528.03	0.203860	0.101930	−	0.994792i	$-0.467498\pi$
$383$	1528.03	0.203860	0.101930	+	0.994792i	$0.467498\pi$
$384$	2245.36	0.298393
$385$	−1952.91	−0.258518
$386$	−1971.08	−0.259910
$387$	1801.61	0.236643
$388$	14070.0	1.84096
$389$	−10384.1	−1.35346	−0.676729	−	0.736232i	$-0.736603\pi$
$389$	−10384.1	−1.35346	−0.676729	+	0.736232i	$0.736603\pi$
$390$	−777.738	−0.100980
$391$	122.464	0.0158396
$392$	−235.408	−0.0303314
$393$	−6735.21	−0.864495
$394$	−204.537	−0.0261534
$395$	3078.23	0.392107
$396$	777.494	0.0986629
$397$	−3395.88	−0.429305	−0.214653	−	0.976690i	$-0.568862\pi$
$397$	−3395.88	−0.429305	−0.214653	+	0.976690i	$0.568862\pi$
$398$	−116.618	−0.0146872
$399$	3934.62	0.493677
$400$	−1294.13	−0.161766
$401$	−2878.84	−0.358510	−0.179255	−	0.983803i	$-0.557369\pi$
$401$	−2878.84	−0.358510	−0.179255	+	0.983803i	$0.557369\pi$
$402$	830.320	0.103016
$403$	9381.89	1.15967
$404$	2607.84	0.321151
$405$	824.495	0.101159
$406$	−553.350	−0.0676411
$407$	4056.19	0.494000
$408$	19.6184	0.00238053
$409$	12338.5	1.49169	0.745844	−	0.666121i	$-0.232047\pi$
$409$	12338.5	1.49169	0.745844	+	0.666121i	$0.232047\pi$
$410$	−1943.66	−0.234123
$411$	−621.336	−0.0745700
$412$	−12861.7	−1.53799
$413$	7398.85	0.881534
$414$	−391.522	−0.0464789
$415$	6472.64	0.765613
$416$	−4771.14	−0.562318
$417$	−895.092	−0.105115
$418$	316.628	0.0370498
$419$	−1604.92	−0.187126	−0.0935629	−	0.995613i	$-0.529826\pi$
$419$	−1604.92	−0.187126	−0.0935629	+	0.995613i	$0.529826\pi$
$420$	−4182.85	−0.485957
$421$	−5570.97	−0.644922	−0.322461	−	0.946583i	$-0.604510\pi$
$421$	−5570.97	−0.644922	−0.322461	+	0.946583i	$0.604510\pi$
$422$	77.6576	0.00895809
$423$	−4698.53	−0.540072
$424$	314.581	0.0360316
$425$	−23.0486	−0.00263064
$426$	1043.03	0.118626
$427$	1063.94	0.120580
$428$	−7779.21	−0.878557
$429$	−2195.64	−0.247101
$430$	−779.978	−0.0874742
$431$	14547.8	1.62585	0.812925	−	0.582368i	$-0.197874\pi$
$431$	14547.8	1.62585	0.812925	+	0.582368i	$0.197874\pi$
$432$	1633.63	0.181940
$433$	−13922.0	−1.54515	−0.772576	−	0.634922i	$-0.781032\pi$
$433$	−13922.0	−1.54515	−0.772576	+	0.634922i	$0.781032\pi$
$434$	−941.435	−0.104125
$435$	2530.91	0.278960
$436$	5784.17	0.635347
$437$	8545.70	0.935461
$438$	−1026.93	−0.112029
$439$	8898.11	0.967388	0.483694	−	0.875237i	$-0.339295\pi$
$439$	8898.11	0.967388	0.483694	+	0.875237i	$0.339295\pi$
$440$	−679.488	−0.0736212
$441$	−349.123	−0.0376982
$442$	−27.4451	−0.00295346
$443$	−7638.35	−0.819207	−0.409604	−	0.912264i	$-0.634333\pi$
$443$	−7638.35	−0.819207	−0.409604	+	0.912264i	$0.634333\pi$
$444$	8687.78	0.928612
$445$	−40.9565	−0.00436298
$446$	1637.10	0.173809
$447$	−3246.86	−0.343560
$448$	−7963.62	−0.839835
$449$	−12089.1	−1.27065	−0.635323	−	0.772246i	$-0.719133\pi$
$449$	−12089.1	−1.27065	−0.635323	+	0.772246i	$0.719133\pi$
$450$	73.6873	0.00771922
$451$	−5487.17	−0.572906
$452$	−3871.92	−0.402920
$453$	−8980.52	−0.931439
$454$	21.9850	0.00227270
$455$	11812.3	1.21708
$456$	1369.00	0.140590
$457$	−2571.30	−0.263195	−0.131598	−	0.991303i	$-0.542011\pi$
$457$	−2571.30	−0.263195	−0.131598	+	0.991303i	$0.542011\pi$
$458$	−135.726	−0.0138473
$459$	29.0951	0.00295870
$460$	−9084.83	−0.920832
$461$	10780.8	1.08918	0.544589	−	0.838703i	$-0.316686\pi$
$461$	10780.8	1.08918	0.544589	+	0.838703i	$0.316686\pi$
$462$	220.324	0.0221870
$463$	5588.54	0.560954	0.280477	−	0.959861i	$-0.409507\pi$
$463$	5588.54	0.560954	0.280477	+	0.959861i	$0.409507\pi$
$464$	5014.66	0.501724
$465$	4305.93	0.429426
$466$	−707.385	−0.0703197
$467$	20028.5	1.98461	0.992303	−	0.123837i	$-0.0395200\pi$
$467$	20028.5	1.98461	0.992303	+	0.123837i	$0.0395200\pi$
$468$	−4702.74	−0.464497
$469$	−12611.0	−1.24162
$470$	2034.16	0.199635
$471$	6518.42	0.637692
$472$	2574.33	0.251045
$473$	−2201.96	−0.214052
$474$	−347.281	−0.0336522
$475$	−1608.36	−0.155361
$476$	−147.606	−0.0142132
$477$	466.540	0.0447828
$478$	−967.668	−0.0925944
$479$	650.416	0.0620423	0.0310212	−	0.999519i	$-0.490124\pi$
$479$	650.416	0.0620423	0.0310212	+	0.999519i	$0.490124\pi$
$480$	−2189.77	−0.208227
$481$	−24534.3	−2.32571
$482$	−2225.85	−0.210342
$483$	5946.47	0.560194
$484$	−950.270	−0.0892440
$485$	−18236.2	−1.70735
$486$	−93.0182	−0.00868188
$487$	−886.863	−0.0825207	−0.0412603	−	0.999148i	$-0.513137\pi$
$487$	−886.863	−0.0825207	−0.0412603	+	0.999148i	$0.513137\pi$
$488$	370.183	0.0343389
$489$	3270.96	0.302490
$490$	151.147	0.0139350
$491$	4511.96	0.414708	0.207354	−	0.978266i	$-0.433515\pi$
$491$	4511.96	0.414708	0.207354	+	0.978266i	$0.433515\pi$
$492$	−11752.7	−1.07694
$493$	89.3117	0.00815902
$494$	−1915.16	−0.174427
$495$	−1007.72	−0.0915020
$496$	8531.64	0.772343
$497$	−15841.6	−1.42976
$498$	−730.232	−0.0657078
$499$	−12367.2	−1.10948	−0.554740	−	0.832024i	$-0.687182\pi$
$499$	−12367.2	−1.10948	−0.554740	+	0.832024i	$0.687182\pi$
$500$	11702.3	1.04669
$501$	6759.09	0.602742
$502$	−1132.27	−0.100669
$503$	−1345.69	−0.119287	−0.0596435	−	0.998220i	$-0.518996\pi$
$503$	−1345.69	−0.119287	−0.0596435	+	0.998220i	$0.518996\pi$
$504$	952.608	0.0841916
$505$	−3380.05	−0.297842
$506$	478.527	0.0420418
$507$	6689.53	0.585981
$508$	8814.64	0.769855
$509$	−4078.12	−0.355127	−0.177563	−	0.984109i	$-0.556821\pi$
$509$	−4078.12	−0.355127	−0.177563	+	0.984109i	$0.556821\pi$
$510$	−12.5963	−0.00109367
$511$	15597.1	1.35025
$512$	−7276.17	−0.628055
$513$	2030.30	0.174736
$514$	−858.848	−0.0737007
$515$	16670.2	1.42636
$516$	−4716.29	−0.402370
$517$	5742.65	0.488513
$518$	2461.92	0.208823
$519$	−3616.67	−0.305885
$520$	4109.95	0.346602
$521$	−3485.59	−0.293102	−0.146551	−	0.989203i	$-0.546817\pi$
$521$	−3485.59	−0.293102	−0.146551	+	0.989203i	$0.546817\pi$
$522$	−285.533	−0.0239415
$523$	4871.54	0.407299	0.203650	−	0.979044i	$-0.434720\pi$
$523$	4871.54	0.407299	0.203650	+	0.979044i	$0.434720\pi$
$524$	17631.6	1.46992
$525$	−1119.17	−0.0930371
$526$	1816.32	0.150561
$527$	151.949	0.0125598
$528$	−1996.66	−0.164571
$529$	748.293	0.0615018
$530$	−201.981	−0.0165538
$531$	3817.87	0.312018
$532$	−10300.1	−0.839412
$533$	33189.7	2.69719
$534$	4.62065	0.000374448 0
$535$	10082.7	0.814791
$536$	−4387.82	−0.353591
$537$	−3682.40	−0.295917
$538$	−2768.29	−0.221839
$539$	426.706	0.0340993
$540$	−2158.38	−0.172004
$541$	−18725.9	−1.48815	−0.744073	−	0.668098i	$-0.767109\pi$
$541$	−18725.9	−1.48815	−0.744073	+	0.668098i	$0.767109\pi$
$542$	1912.02	0.151528
$543$	3979.42	0.314500
$544$	−77.2736	−0.00609022
$545$	−7496.91	−0.589234
$546$	−1332.65	−0.104454
$547$	−1315.93	−0.102861	−0.0514306	−	0.998677i	$-0.516378\pi$
$547$	−1315.93	−0.102861	−0.0514306	+	0.998677i	$0.516378\pi$
$548$	1626.55	0.126793
$549$	549.000	0.0426790
$550$	−90.0622	−0.00698230
$551$	6232.29	0.481859
$552$	2069.00	0.159533
$553$	5274.52	0.405598
$554$	−583.184	−0.0447240
$555$	−11260.3	−0.861213
$556$	2343.19	0.178729
$557$	10119.3	0.769780	0.384890	−	0.922962i	$-0.374239\pi$
$557$	10119.3	0.769780	0.384890	+	0.922962i	$0.374239\pi$
$558$	−485.789	−0.0368550
$559$	13318.8	1.00774
$560$	10741.8	0.810581
$561$	−35.5607	−0.00267624
$562$	−3083.47	−0.231438
$563$	−11865.0	−0.888192	−0.444096	−	0.895979i	$-0.646475\pi$
$563$	−11865.0	−0.888192	−0.444096	+	0.895979i	$0.646475\pi$
$564$	12299.9	0.918298
$565$	5018.44	0.373676
$566$	−2327.39	−0.172840
$567$	1412.77	0.104640
$568$	−5511.86	−0.407170
$569$	4347.61	0.320319	0.160159	−	0.987091i	$-0.448799\pi$
$569$	4347.61	0.320319	0.160159	+	0.987091i	$0.448799\pi$
$570$	−878.985	−0.0645906
$571$	13671.1	1.00196	0.500980	−	0.865459i	$-0.332973\pi$
$571$	13671.1	1.00196	0.500980	+	0.865459i	$0.332973\pi$
$572$	5747.80	0.420153
$573$	−4612.02	−0.336248
$574$	−3330.45	−0.242178
$575$	−2430.75	−0.176294
$576$	−4109.30	−0.297258
$577$	11990.0	0.865079	0.432540	−	0.901615i	$-0.357618\pi$
$577$	11990.0	0.865079	0.432540	+	0.901615i	$0.357618\pi$
$578$	1880.21	0.135305
$579$	15447.7	1.10878
$580$	−6625.47	−0.474324
$581$	11090.8	0.791953
$582$	2057.38	0.146531
$583$	−570.215	−0.0405076
$584$	5426.81	0.384526
$585$	6095.27	0.430783
$586$	−1475.42	−0.104009
$587$	−363.872	−0.0255854	−0.0127927	−	0.999918i	$-0.504072\pi$
$587$	−363.872	−0.0255854	−0.0127927	+	0.999918i	$0.504072\pi$
$588$	913.942	0.0640992
$589$	10603.2	0.741764
$590$	−1652.89	−0.115336
$591$	1602.99	0.111571
$592$	−22310.8	−1.54893
$593$	447.792	0.0310095	0.0155047	−	0.999880i	$-0.495064\pi$
$593$	447.792	0.0310095	0.0155047	+	0.999880i	$0.495064\pi$
$594$	113.689	0.00785305
$595$	191.313	0.0131816
$596$	8499.72	0.584164
$597$	913.952	0.0626559
$598$	−2894.42	−0.197929
$599$	2588.71	0.176580	0.0882902	−	0.996095i	$-0.471860\pi$
$599$	2588.71	0.176580	0.0882902	+	0.996095i	$0.471860\pi$
$600$	−389.400	−0.0264953
$601$	19419.5	1.31803	0.659016	−	0.752129i	$-0.270973\pi$
$601$	19419.5	1.31803	0.659016	+	0.752129i	$0.270973\pi$
$602$	−1336.49	−0.0904837
$603$	−6507.36	−0.439470
$604$	23509.4	1.58375
$605$	1231.65	0.0827667
$606$	381.331	0.0255619
$607$	−20368.9	−1.36202	−0.681011	−	0.732274i	$-0.738459\pi$
$607$	−20368.9	−1.36202	−0.681011	+	0.732274i	$0.738459\pi$
$608$	−5392.26	−0.359679
$609$	4336.70	0.288558
$610$	−237.681	−0.0157761
$611$	−34734.9	−2.29988
$612$	−76.1659	−0.00503076
$613$	4893.31	0.322413	0.161206	−	0.986921i	$-0.448462\pi$
$613$	4893.31	0.322413	0.161206	+	0.986921i	$0.448462\pi$
$614$	211.025	0.0138701
$615$	15232.8	0.998774
$616$	−1164.30	−0.0761541
$617$	−26803.1	−1.74887	−0.874434	−	0.485145i	$-0.838767\pi$
$617$	−26803.1	−1.74887	−0.874434	+	0.485145i	$0.838767\pi$
$618$	−1880.70	−0.122416
$619$	−5223.60	−0.339183	−0.169591	−	0.985514i	$-0.554245\pi$
$619$	−5223.60	−0.339183	−0.169591	+	0.985514i	$0.554245\pi$
$620$	−11272.2	−0.730164
$621$	3068.43	0.198280
$622$	−2202.46	−0.141978
$623$	−70.1787	−0.00451308
$624$	12077.0	0.774785
$625$	−12493.9	−0.799610
$626$	254.783	0.0162670
$627$	−2481.47	−0.158055
$628$	−17064.1	−1.08429
$629$	−397.358	−0.0251887
$630$	−611.636	−0.0386796
$631$	−25291.7	−1.59564	−0.797818	−	0.602899i	$-0.794012\pi$
$631$	−25291.7	−1.59564	−0.797818	+	0.602899i	$0.794012\pi$
$632$	1835.20	0.115507
$633$	−608.616	−0.0382154
$634$	2237.96	0.140190
$635$	−11424.7	−0.713979
$636$	−1221.32	−0.0761454
$637$	−2580.97	−0.160536
$638$	348.985	0.0216559
$639$	−8174.38	−0.506062
$640$	7618.46	0.470541
$641$	19611.6	1.20844	0.604222	−	0.796816i	$-0.293484\pi$
$641$	19611.6	1.20844	0.604222	+	0.796816i	$0.293484\pi$
$642$	−1137.51	−0.0699285
$643$	−9226.76	−0.565891	−0.282945	−	0.959136i	$-0.591312\pi$
$643$	−9226.76	−0.565891	−0.282945	+	0.959136i	$0.591312\pi$
$644$	−15566.8	−0.952513
$645$	6112.83	0.373166
$646$	−31.0180	−0.00188914
$647$	7075.55	0.429936	0.214968	−	0.976621i	$-0.431035\pi$
$647$	7075.55	0.429936	0.214968	+	0.976621i	$0.431035\pi$
$648$	491.554	0.0297995
$649$	−4666.28	−0.282231
$650$	544.750	0.0328721
$651$	7378.19	0.444200
$652$	−8562.79	−0.514332
$653$	669.946	0.0401486	0.0200743	−	0.999798i	$-0.493610\pi$
$653$	669.946	0.0401486	0.0200743	+	0.999798i	$0.493610\pi$
$654$	845.790	0.0505703
$655$	−22852.5	−1.36324
$656$	30181.8	1.79634
$657$	8048.24	0.477917
$658$	3485.51	0.206504
$659$	8735.57	0.516373	0.258186	−	0.966095i	$-0.416875\pi$
$659$	8735.57	0.516373	0.258186	+	0.966095i	$0.416875\pi$
$660$	2638.02	0.155583
$661$	1660.50	0.0977092	0.0488546	−	0.998806i	$-0.484443\pi$
$661$	1660.50	0.0977092	0.0488546	+	0.998806i	$0.484443\pi$
$662$	−2461.52	−0.144516
$663$	215.092	0.0125995
$664$	3858.91	0.225534
$665$	13350.1	0.778488
$666$	1270.37	0.0739126
$667$	9418.99	0.546784
$668$	−17694.1	−1.02486
$669$	−12830.2	−0.741473
$670$	2817.26	0.162448
$671$	−671.000	−0.0386046
$672$	−3752.17	−0.215391
$673$	−19131.7	−1.09580	−0.547900	−	0.836544i	$-0.684573\pi$
$673$	−19131.7	−1.09580	−0.547900	+	0.836544i	$0.684573\pi$
$674$	−3062.82	−0.175038
$675$	−577.500	−0.0329303
$676$	−17512.0	−0.996360
$677$	−28245.7	−1.60350	−0.801749	−	0.597660i	$-0.796097\pi$
$677$	−28245.7	−1.60350	−0.801749	+	0.597660i	$0.796097\pi$
$678$	−566.172	−0.0320704
$679$	−31247.6	−1.76609
$680$	66.5649	0.00375390
$681$	−172.300	−0.00969538
$682$	593.742	0.0333366
$683$	30268.2	1.69573	0.847864	−	0.530214i	$-0.177889\pi$
$683$	30268.2	1.69573	0.847864	+	0.530214i	$0.177889\pi$
$684$	−5314.96	−0.297109
$685$	−2108.18	−0.117591
$686$	2549.02	0.141869
$687$	1063.71	0.0590729
$688$	12111.8	0.671158
$689$	3449.00	0.190706
$690$	−1328.43	−0.0732934
$691$	−16050.7	−0.883646	−0.441823	−	0.897102i	$-0.645668\pi$
$691$	−16050.7	−0.883646	−0.441823	+	0.897102i	$0.645668\pi$
$692$	9467.81	0.520104
$693$	−1726.72	−0.0946501
$694$	−3531.11	−0.193140
$695$	−3037.03	−0.165757
$696$	1508.90	0.0821761
$697$	537.541	0.0292121
$698$	1888.65	0.102416
$699$	5543.90	0.299985
$700$	2929.78	0.158193
$701$	−10935.4	−0.589194	−0.294597	−	0.955622i	$-0.595185\pi$
$701$	−10935.4	−0.589194	−0.294597	+	0.955622i	$0.595185\pi$
$702$	−687.658	−0.0369715
$703$	−27728.2	−1.48761
$704$	5022.47	0.268880
$705$	−15942.0	−0.851648
$706$	1407.80	0.0750472
$707$	−5791.69	−0.308089
$708$	−9994.50	−0.530532
$709$	13025.1	0.689939	0.344970	−	0.938614i	$-0.387889\pi$
$709$	13025.1	0.689939	0.344970	+	0.938614i	$0.387889\pi$
$710$	3538.97	0.187064
$711$	2721.70	0.143561
$712$	−24.4178	−0.00128525
$713$	16024.9	0.841707
$714$	−21.5837	−0.00113130
$715$	−7449.77	−0.389658
$716$	9639.87	0.503155
$717$	7583.78	0.395009
$718$	−377.103	−0.0196008
$719$	5723.56	0.296875	0.148437	−	0.988922i	$-0.452576\pi$
$719$	5723.56	0.296875	0.148437	+	0.988922i	$0.452576\pi$
$720$	5542.88	0.286904
$721$	28564.2	1.47543
$722$	461.088	0.0237672
$723$	17444.4	0.897321
$724$	−10417.4	−0.534752
$725$	−1772.72	−0.0908099
$726$	−138.953	−0.00710335
$727$	18127.6	0.924780	0.462390	−	0.886677i	$-0.346992\pi$
$727$	18127.6	0.924780	0.462390	+	0.886677i	$0.346992\pi$
$728$	7042.37	0.358527
$729$	729.000	0.0370370
$730$	−3484.36	−0.176660
$731$	215.712	0.0109143
$732$	−1437.19	−0.0725682
$733$	−23209.6	−1.16953	−0.584765	−	0.811203i	$-0.698813\pi$
$733$	−23209.6	−1.16953	−0.584765	+	0.811203i	$0.698813\pi$
$734$	4099.79	0.206166
$735$	−1184.57	−0.0594469
$736$	−8149.43	−0.408141
$737$	7953.44	0.397515
$738$	−1718.54	−0.0857187
$739$	−33954.3	−1.69016	−0.845082	−	0.534637i	$-0.820448\pi$
$739$	−33954.3	−1.69016	−0.845082	+	0.534637i	$0.820448\pi$
$740$	29477.5	1.46434
$741$	15009.4	0.744109
$742$	−346.094	−0.0171233
$743$	−4267.07	−0.210691	−0.105346	−	0.994436i	$-0.533595\pi$
$743$	−4267.07	−0.210691	−0.105346	+	0.994436i	$0.533595\pi$
$744$	2567.14	0.126500
$745$	−11016.6	−0.541766
$746$	3363.30	0.165066
$747$	5722.96	0.280311
$748$	93.0916	0.00455049
$749$	17276.7	0.842824
$750$	1711.17	0.0833110
$751$	−12737.3	−0.618898	−0.309449	−	0.950916i	$-0.600145\pi$
$751$	−12737.3	−0.618898	−0.309449	+	0.950916i	$0.600145\pi$
$752$	−31587.0	−1.53173
$753$	8873.82	0.429455
$754$	−2110.87	−0.101954
$755$	−30470.8	−1.46880
$756$	−3698.38	−0.177922
$757$	−6884.41	−0.330539	−0.165269	−	0.986248i	$-0.552849\pi$
$757$	−6884.41	−0.330539	−0.165269	+	0.986248i	$0.552849\pi$
$758$	−4132.83	−0.198036
$759$	−3750.30	−0.179351
$760$	4644.99	0.221699
$761$	35117.5	1.67281	0.836404	−	0.548113i	$-0.184654\pi$
$761$	35117.5	1.67281	0.836404	+	0.548113i	$0.184654\pi$
$762$	1288.92	0.0612764
$763$	−12845.9	−0.609506
$764$	12073.5	0.571731
$765$	98.7193	0.00466562
$766$	−584.915	−0.0275899
$767$	28224.4	1.32872
$768$	10098.6	0.474483
$769$	5455.13	0.255809	0.127904	−	0.991786i	$-0.459175\pi$
$769$	5455.13	0.255809	0.127904	+	0.991786i	$0.459175\pi$
$770$	747.555	0.0349870
$771$	6730.94	0.314408
$772$	−40439.4	−1.88529
$773$	24375.6	1.13419	0.567094	−	0.823653i	$-0.308068\pi$
$773$	24375.6	1.13419	0.567094	+	0.823653i	$0.308068\pi$
$774$	−689.639	−0.0320266
$775$	−3016.00	−0.139791
$776$	−10872.2	−0.502950
$777$	−19294.5	−0.890843
$778$	3974.94	0.183173
$779$	37510.3	1.72522
$780$	−15956.3	−0.732472
$781$	9990.91	0.457750
$782$	−46.8781	−0.00214368
$783$	2237.77	0.102135
$784$	−2347.07	−0.106918
$785$	22116.9	1.00559
$786$	2578.18	0.116998
$787$	5281.25	0.239207	0.119604	−	0.992822i	$-0.461838\pi$
$787$	5281.25	0.239207	0.119604	+	0.992822i	$0.461838\pi$
$788$	−4196.35	−0.189707
$789$	−14234.8	−0.642297
$790$	−1178.32	−0.0530667
$791$	8599.06	0.386533
$792$	−600.788	−0.0269546
$793$	4058.61	0.181747
$794$	1299.91	0.0581009
$795$	1582.96	0.0706187
$796$	−2392.57	−0.106536
$797$	−30743.0	−1.36634	−0.683169	−	0.730260i	$-0.739399\pi$
$797$	−30743.0	−1.36634	−0.683169	+	0.730260i	$0.739399\pi$
$798$	−1506.14	−0.0668128
$799$	−562.569	−0.0249089
$800$	1533.78	0.0677841
$801$	−36.2128	−0.00159740
$802$	1101.99	0.0485196
$803$	−9836.74	−0.432293
$804$	17035.1	0.747242
$805$	20176.3	0.883379
$806$	−3591.30	−0.156946
$807$	21695.6	0.946370
$808$	−2015.14	−0.0877382
$809$	−23829.4	−1.03559	−0.517797	−	0.855503i	$-0.673248\pi$
$809$	−23829.4	−1.03559	−0.517797	+	0.855503i	$0.673248\pi$
$810$	−315.609	−0.0136906
$811$	14687.8	0.635952	0.317976	−	0.948099i	$-0.396997\pi$
$811$	14687.8	0.635952	0.317976	+	0.948099i	$0.396997\pi$
$812$	−11352.7	−0.490643
$813$	−14984.8	−0.646420
$814$	−1552.67	−0.0668565
$815$	11098.3	0.477002
$816$	195.599	0.00839135
$817$	15052.7	0.644585
$818$	−4723.07	−0.201881
$819$	10444.2	0.445604
$820$	−39876.8	−1.69824
$821$	11781.6	0.500830	0.250415	−	0.968139i	$-0.419433\pi$
$821$	11781.6	0.500830	0.250415	+	0.968139i	$0.419433\pi$
$822$	237.842	0.0100921
$823$	−15684.7	−0.664320	−0.332160	−	0.943223i	$-0.607777\pi$
$823$	−15684.7	−0.664320	−0.332160	+	0.943223i	$0.607777\pi$
$824$	9938.55	0.420177
$825$	705.833	0.0297866
$826$	−2832.21	−0.119304
$827$	−33820.9	−1.42209	−0.711044	−	0.703147i	$-0.751778\pi$
$827$	−33820.9	−1.42209	−0.711044	+	0.703147i	$0.751778\pi$
$828$	−8032.60	−0.337140
$829$	−9127.69	−0.382410	−0.191205	−	0.981550i	$-0.561240\pi$
$829$	−9127.69	−0.382410	−0.191205	+	0.981550i	$0.561240\pi$
$830$	−2477.67	−0.103616
$831$	4570.51	0.190793
$832$	−30378.9	−1.26586
$833$	−41.8015	−0.00173870
$834$	342.633	0.0142259
$835$	22933.5	0.950474
$836$	6496.06	0.268745
$837$	3807.21	0.157224
$838$	614.351	0.0253251
$839$	11609.3	0.477707	0.238854	−	0.971056i	$-0.423228\pi$
$839$	11609.3	0.477707	0.238854	+	0.971056i	$0.423228\pi$
$840$	3232.19	0.132763
$841$	−17519.8	−0.718350
$842$	2132.52	0.0872819
$843$	24165.7	0.987321
$844$	1593.25	0.0649786
$845$	22697.5	0.924044
$846$	1798.55	0.0730917
$847$	2110.43	0.0856142
$848$	3136.43	0.127011
$849$	18240.2	0.737340
$850$	8.82279	0.000356023 0
$851$	−41906.2	−1.68804
$852$	21399.1	0.860470
$853$	−39045.4	−1.56728	−0.783640	−	0.621215i	$-0.786639\pi$
$853$	−39045.4	−1.56728	−0.783640	+	0.621215i	$0.786639\pi$
$854$	−407.265	−0.0163189
$855$	6888.76	0.275545
$856$	6011.18	0.240021
$857$	−26809.7	−1.06861	−0.534306	−	0.845291i	$-0.679427\pi$
$857$	−26809.7	−1.06861	−0.534306	+	0.845291i	$0.679427\pi$
$858$	840.471	0.0334420
$859$	−25093.6	−0.996721	−0.498360	−	0.866970i	$-0.666064\pi$
$859$	−25093.6	−0.996721	−0.498360	+	0.866970i	$0.666064\pi$
$860$	−16002.3	−0.634505
$861$	26101.3	1.03314
$862$	−5568.76	−0.220038
$863$	24034.1	0.948006	0.474003	−	0.880523i	$-0.342808\pi$
$863$	24034.1	0.948006	0.474003	+	0.880523i	$0.342808\pi$
$864$	−1936.15	−0.0762374
$865$	−12271.3	−0.482355
$866$	5329.23	0.209116
$867$	−14735.5	−0.577214
$868$	−19314.8	−0.755285
$869$	−3326.52	−0.129856
$870$	−968.809	−0.0377537
$871$	−48107.1	−1.87147
$872$	−4469.57	−0.173576
$873$	−16124.0	−0.625104
$874$	−3271.22	−0.126602
$875$	−25989.4	−1.00412
$876$	−21068.9	−0.812616
$877$	1862.54	0.0717143	0.0358571	−	0.999357i	$-0.488584\pi$
$877$	1862.54	0.0717143	0.0358571	+	0.999357i	$0.488584\pi$
$878$	−3406.12	−0.130924
$879$	11563.1	0.443702
$880$	−6774.63	−0.259514
$881$	−15106.3	−0.577687	−0.288844	−	0.957376i	$-0.593271\pi$
$881$	−15106.3	−0.577687	−0.288844	+	0.957376i	$0.593271\pi$
$882$	133.641	0.00510196
$883$	596.504	0.0227338	0.0113669	−	0.999935i	$-0.496382\pi$
$883$	596.504	0.0227338	0.0113669	+	0.999935i	$0.496382\pi$
$884$	−563.073	−0.0214233
$885$	12954.0	0.492026
$886$	2923.89	0.110869
$887$	−6156.26	−0.233041	−0.116520	−	0.993188i	$-0.537174\pi$
$887$	−6156.26	−0.233041	−0.116520	+	0.993188i	$0.537174\pi$
$888$	−6713.26	−0.253696
$889$	−19576.2	−0.738543
$890$	15.6778	0.000590473 0
$891$	−891.000	−0.0335013
$892$	33587.3	1.26075
$893$	−39256.8	−1.47108
$894$	1242.87	0.0464964
$895$	−12494.3	−0.466636
$896$	13054.2	0.486729
$897$	22684.0	0.844368
$898$	4627.60	0.171966
$899$	11686.8	0.433566
$900$	1511.79	0.0559923
$901$	55.8602	0.00206545
$902$	2100.44	0.0775354
$903$	10474.3	0.386005
$904$	2991.93	0.110078
$905$	13502.1	0.495940
$906$	3437.66	0.126058
$907$	−14742.9	−0.539723	−0.269862	−	0.962899i	$-0.586978\pi$
$907$	−14742.9	−0.539723	−0.269862	+	0.962899i	$0.586978\pi$
$908$	451.051	0.0164853
$909$	−2988.56	−0.109048
$910$	−4521.66	−0.164716
$911$	−47787.8	−1.73796	−0.868980	−	0.494848i	$-0.835224\pi$
$911$	−47787.8	−1.73796	−0.868980	+	0.494848i	$0.835224\pi$
$912$	13649.2	0.495580
$913$	−6994.73	−0.253551
$914$	984.270	0.0356201
$915$	1862.75	0.0673012
$916$	−2784.61	−0.100443
$917$	−39157.6	−1.41014
$918$	−11.1373	−0.000400422 0
$919$	27543.0	0.988641	0.494320	−	0.869280i	$-0.335417\pi$
$919$	27543.0	0.988641	0.494320	+	0.869280i	$0.335417\pi$
$920$	7020.07	0.251570
$921$	−1653.84	−0.0591702
$922$	−4126.79	−0.147406
$923$	−60430.9	−2.15505
$924$	4520.24	0.160936
$925$	7887.04	0.280351
$926$	−2139.24	−0.0759178
$927$	14739.4	0.522228
$928$	−5943.29	−0.210235
$929$	−8159.81	−0.288175	−0.144088	−	0.989565i	$-0.546025\pi$
$929$	−8159.81	−0.288175	−0.144088	+	0.989565i	$0.546025\pi$
$930$	−1648.27	−0.0581172
$931$	−2916.97	−0.102685
$932$	−14513.0	−0.510073
$933$	17261.0	0.605681
$934$	−7666.75	−0.268591
$935$	−120.657	−0.00422022
$936$	3633.92	0.126900
$937$	−24862.2	−0.866823	−0.433411	−	0.901196i	$-0.642690\pi$
$937$	−24862.2	−0.866823	−0.433411	+	0.901196i	$0.642690\pi$
$938$	4827.36	0.168037
$939$	−1996.78	−0.0693954
$940$	41733.4	1.44808
$941$	−8111.87	−0.281019	−0.140510	−	0.990079i	$-0.544874\pi$
$941$	−8111.87	−0.281019	−0.140510	+	0.990079i	$0.544874\pi$
$942$	−2495.19	−0.0863034
$943$	56690.2	1.95767
$944$	25666.6	0.884932
$945$	4793.50	0.165008
$946$	842.892	0.0289691
$947$	8268.85	0.283740	0.141870	−	0.989885i	$-0.454689\pi$
$947$	8268.85	0.283740	0.141870	+	0.989885i	$0.454689\pi$
$948$	−7124.93	−0.244100
$949$	59498.4	2.03520
$950$	615.666	0.0210262
$951$	−17539.3	−0.598055
$952$	114.059	0.00388305
$953$	−44009.7	−1.49592	−0.747961	−	0.663743i	$-0.768967\pi$
$953$	−44009.7	−1.49592	−0.747961	+	0.663743i	$0.768967\pi$
$954$	−178.587	−0.00606077
$955$	−15648.5	−0.530235
$956$	−19853.0	−0.671645
$957$	−2735.05	−0.0923843
$958$	−248.974	−0.00839663
$959$	−3612.36	−0.121636
$960$	−13942.8	−0.468751
$961$	−9907.81	−0.332577
$962$	9391.49	0.314755
$963$	8914.90	0.298316
$964$	−45666.3	−1.52574
$965$	52413.9	1.74846
$966$	−2276.25	−0.0758150
$967$	32645.7	1.08564	0.542820	−	0.839849i	$-0.317357\pi$
$967$	32645.7	1.08564	0.542820	+	0.839849i	$0.317357\pi$
$968$	734.297	0.0243814
$969$	243.093	0.00805911
$970$	6980.65	0.231067
$971$	17464.0	0.577184	0.288592	−	0.957452i	$-0.406813\pi$
$971$	17464.0	0.577184	0.288592	+	0.957452i	$0.406813\pi$
$972$	−1908.39	−0.0629751
$973$	−5203.94	−0.171460
$974$	339.483	0.0111681
$975$	−4269.30	−0.140233
$976$	3690.79	0.121044
$977$	−18794.2	−0.615435	−0.307718	−	0.951478i	$-0.599565\pi$
$977$	−18794.2	−0.615435	−0.307718	+	0.951478i	$0.599565\pi$
$978$	−1252.09	−0.0409381
$979$	44.2601	0.00144490
$980$	3100.99	0.101079
$981$	−6628.60	−0.215734
$982$	−1727.14	−0.0561254
$983$	34512.3	1.11981	0.559904	−	0.828557i	$-0.310838\pi$
$983$	34512.3	1.11981	0.559904	+	0.828557i	$0.310838\pi$
$984$	9081.61	0.294219
$985$	5438.93	0.175938
$986$	−34.1877	−0.00110422
$987$	−27316.6	−0.880949
$988$	−39292.0	−1.26523
$989$	22749.4	0.731434
$990$	385.745	0.0123836
$991$	−41417.5	−1.32762	−0.663809	−	0.747902i	$-0.731061\pi$
$991$	−41417.5	−1.32762	−0.663809	+	0.747902i	$0.731061\pi$
$992$	−10111.6	−0.323631
$993$	19291.4	0.616508
$994$	6064.01	0.193500
$995$	3101.03	0.0988032
$996$	−14981.7	−0.476620
$997$	−23958.7	−0.761063	−0.380531	−	0.924768i	$-0.624259\pi$
$997$	−23958.7	−0.761063	−0.380531	+	0.924768i	$0.624259\pi$
$998$	4734.04	0.150154
$999$	−9956.11	−0.315313

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.h.1.18	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.h.1.18	✓	39	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.382791 q^{2} +3.00000 q^{3} -7.85347 q^{4} +10.1790 q^{5} -1.14837 q^{6} +17.4416 q^{7} +6.06857 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-0.382791 q^{2} +3.00000 q^{3} -7.85347 q^{4} +10.1790 q^{5} -1.14837 q^{6} +17.4416 q^{7} +6.06857 q^{8} +9.00000 q^{9} -3.89641 q^{10} -11.0000 q^{11} -23.5604 q^{12} +66.5345 q^{13} -6.67648 q^{14} +30.5369 q^{15} +60.5048 q^{16} +1.07760 q^{17} -3.44512 q^{18} +75.1961 q^{19} -79.9401 q^{20} +52.3247 q^{21} +4.21070 q^{22} +113.645 q^{23} +18.2057 q^{24} -21.3889 q^{25} -25.4688 q^{26} +27.0000 q^{27} -136.977 q^{28} +82.8805 q^{29} -11.6892 q^{30} +141.008 q^{31} -71.7092 q^{32} -33.0000 q^{33} -0.412494 q^{34} +177.537 q^{35} -70.6812 q^{36} -368.745 q^{37} -28.7844 q^{38} +199.604 q^{39} +61.7717 q^{40} +498.834 q^{41} -20.0294 q^{42} +200.179 q^{43} +86.3882 q^{44} +91.6106 q^{45} -43.5025 q^{46} -522.059 q^{47} +181.514 q^{48} -38.7914 q^{49} +8.18747 q^{50} +3.23279 q^{51} -522.527 q^{52} +51.8378 q^{53} -10.3354 q^{54} -111.968 q^{55} +105.845 q^{56} +225.588 q^{57} -31.7259 q^{58} +424.207 q^{59} -239.820 q^{60} +61.0000 q^{61} -53.9765 q^{62} +156.974 q^{63} -456.589 q^{64} +677.252 q^{65} +12.6321 q^{66} -723.040 q^{67} -8.46287 q^{68} +340.936 q^{69} -67.9596 q^{70} -908.264 q^{71} +54.6171 q^{72} +894.249 q^{73} +141.152 q^{74} -64.1667 q^{75} -590.551 q^{76} -191.857 q^{77} -76.4065 q^{78} +302.411 q^{79} +615.875 q^{80} +81.0000 q^{81} -190.949 q^{82} +635.884 q^{83} -410.931 q^{84} +10.9688 q^{85} -76.6266 q^{86} +248.641 q^{87} -66.7542 q^{88} -4.02365 q^{89} -35.0677 q^{90} +1160.47 q^{91} -892.511 q^{92} +423.023 q^{93} +199.839 q^{94} +765.418 q^{95} -215.128 q^{96} -1791.56 q^{97} +14.8490 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9}+O(q^{10}) \) 39 * q + 8 * q^2 + 117 * q^3 + 154 * q^4 + 65 * q^5 + 24 * q^6 + 35 * q^7 + 75 * q^8 + 351 * q^9	\( 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9} - 21 q^{10} - 429 q^{11} + 462 q^{12} - 27 q^{13} + 164 q^{14} + 195 q^{15} + 686 q^{16} + 170 q^{17} + 72 q^{18} + 139 q^{19} + 1056 q^{20} + 105 q^{21} - 88 q^{22} + 291 q^{23} + 225 q^{24} + 1236 q^{25} + 583 q^{26} + 1053 q^{27} + 976 q^{28} + 374 q^{29} - 63 q^{30} + 232 q^{31} + 933 q^{32} - 1287 q^{33} + 332 q^{34} + 626 q^{35} + 1386 q^{36} + 232 q^{37} + 989 q^{38} - 81 q^{39} - 263 q^{40} + 1014 q^{41} + 492 q^{42} + 515 q^{43} - 1694 q^{44} + 585 q^{45} - 371 q^{46} + 2005 q^{47} + 2058 q^{48} + 2064 q^{49} + 4582 q^{50} + 510 q^{51} + 216 q^{52} + 1485 q^{53} + 216 q^{54} - 715 q^{55} + 2307 q^{56} + 417 q^{57} + 573 q^{58} + 2749 q^{59} + 3168 q^{60} + 2379 q^{61} + 1837 q^{62} + 315 q^{63} + 7295 q^{64} + 3630 q^{65} - 264 q^{66} + 3575 q^{67} + 2630 q^{68} + 873 q^{69} + 4218 q^{70} + 4723 q^{71} + 675 q^{72} + 859 q^{73} + 4232 q^{74} + 3708 q^{75} + 2466 q^{76} - 385 q^{77} + 1749 q^{78} - 1887 q^{79} + 8933 q^{80} + 3159 q^{81} + 6806 q^{82} + 5609 q^{83} + 2928 q^{84} - 565 q^{85} + 5185 q^{86} + 1122 q^{87} - 825 q^{88} + 6725 q^{89} - 189 q^{90} + 2808 q^{91} + 3257 q^{92} + 696 q^{93} + 3184 q^{94} + 3216 q^{95} + 2799 q^{96} + 3512 q^{97} + 4464 q^{98} - 3861 q^{99}+O(q^{100}) \) 39 * q + 8 * q^2 + 117 * q^3 + 154 * q^4 + 65 * q^5 + 24 * q^6 + 35 * q^7 + 75 * q^8 + 351 * q^9 - 21 * q^10 - 429 * q^11 + 462 * q^12 - 27 * q^13 + 164 * q^14 + 195 * q^15 + 686 * q^16 + 170 * q^17 + 72 * q^18 + 139 * q^19 + 1056 * q^20 + 105 * q^21 - 88 * q^22 + 291 * q^23 + 225 * q^24 + 1236 * q^25 + 583 * q^26 + 1053 * q^27 + 976 * q^28 + 374 * q^29 - 63 * q^30 + 232 * q^31 + 933 * q^32 - 1287 * q^33 + 332 * q^34 + 626 * q^35 + 1386 * q^36 + 232 * q^37 + 989 * q^38 - 81 * q^39 - 263 * q^40 + 1014 * q^41 + 492 * q^42 + 515 * q^43 - 1694 * q^44 + 585 * q^45 - 371 * q^46 + 2005 * q^47 + 2058 * q^48 + 2064 * q^49 + 4582 * q^50 + 510 * q^51 + 216 * q^52 + 1485 * q^53 + 216 * q^54 - 715 * q^55 + 2307 * q^56 + 417 * q^57 + 573 * q^58 + 2749 * q^59 + 3168 * q^60 + 2379 * q^61 + 1837 * q^62 + 315 * q^63 + 7295 * q^64 + 3630 * q^65 - 264 * q^66 + 3575 * q^67 + 2630 * q^68 + 873 * q^69 + 4218 * q^70 + 4723 * q^71 + 675 * q^72 + 859 * q^73 + 4232 * q^74 + 3708 * q^75 + 2466 * q^76 - 385 * q^77 + 1749 * q^78 - 1887 * q^79 + 8933 * q^80 + 3159 * q^81 + 6806 * q^82 + 5609 * q^83 + 2928 * q^84 - 565 * q^85 + 5185 * q^86 + 1122 * q^87 - 825 * q^88 + 6725 * q^89 - 189 * q^90 + 2808 * q^91 + 3257 * q^92 + 696 * q^93 + 3184 * q^94 + 3216 * q^95 + 2799 * q^96 + 3512 * q^97 + 4464 * q^98 - 3861 * q^99

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