LMFDB - Embedded newform 2013.4.a.b.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$118.770844842$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-3.21541 q^{2} -3.00000 q^{3} +2.33885 q^{4} +2.50702 q^{5} +9.64623 q^{6} +5.55272 q^{7} +18.2029 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.21541 q^{2} -3.00000 q^{3} +2.33885 q^{4} +2.50702 q^{5} +9.64623 q^{6} +5.55272 q^{7} +18.2029 q^{8} +9.00000 q^{9} -8.06108 q^{10} -11.0000 q^{11} -7.01656 q^{12} +53.0283 q^{13} -17.8543 q^{14} -7.52105 q^{15} -77.2406 q^{16} -92.3863 q^{17} -28.9387 q^{18} +4.84821 q^{19} +5.86354 q^{20} -16.6582 q^{21} +35.3695 q^{22} +178.313 q^{23} -54.6087 q^{24} -118.715 q^{25} -170.508 q^{26} -27.0000 q^{27} +12.9870 q^{28} +282.414 q^{29} +24.1832 q^{30} +187.826 q^{31} +102.737 q^{32} +33.0000 q^{33} +297.060 q^{34} +13.9208 q^{35} +21.0497 q^{36} -37.5371 q^{37} -15.5890 q^{38} -159.085 q^{39} +45.6350 q^{40} -388.159 q^{41} +53.5628 q^{42} -415.331 q^{43} -25.7274 q^{44} +22.5631 q^{45} -573.348 q^{46} -513.860 q^{47} +231.722 q^{48} -312.167 q^{49} +381.717 q^{50} +277.159 q^{51} +124.025 q^{52} -208.507 q^{53} +86.8160 q^{54} -27.5772 q^{55} +101.076 q^{56} -14.5446 q^{57} -908.078 q^{58} -482.497 q^{59} -17.5906 q^{60} +61.0000 q^{61} -603.937 q^{62} +49.9745 q^{63} +287.584 q^{64} +132.943 q^{65} -106.108 q^{66} +580.625 q^{67} -216.078 q^{68} -534.938 q^{69} -44.7609 q^{70} -44.1804 q^{71} +163.826 q^{72} -287.299 q^{73} +120.697 q^{74} +356.145 q^{75} +11.3393 q^{76} -61.0799 q^{77} +511.523 q^{78} -280.700 q^{79} -193.643 q^{80} +81.0000 q^{81} +1248.09 q^{82} +915.084 q^{83} -38.9610 q^{84} -231.614 q^{85} +1335.46 q^{86} -847.243 q^{87} -200.232 q^{88} +1206.95 q^{89} -72.5497 q^{90} +294.451 q^{91} +417.047 q^{92} -563.477 q^{93} +1652.27 q^{94} +12.1545 q^{95} -308.210 q^{96} -712.705 q^{97} +1003.75 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 2 q^{2} - 108 q^{3} + 118 q^{4} - 5 q^{5} - 6 q^{6} - 63 q^{7} + 3 q^{8} + 324 q^{9}+O(q^{10}) $ 36 * q + 2 * q^2 - 108 * q^3 + 118 * q^4 - 5 * q^5 - 6 * q^6 - 63 * q^7 + 3 * q^8 + 324 * q^9	\( 36 q + 2 q^{2} - 108 q^{3} + 118 q^{4} - 5 q^{5} - 6 q^{6} - 63 q^{7} + 3 q^{8} + 324 q^{9} - 45 q^{10} - 396 q^{11} - 354 q^{12} - 13 q^{13} + 82 q^{14} + 15 q^{15} + 262 q^{16} + 204 q^{17} + 18 q^{18} - 431 q^{19} + 354 q^{20} + 189 q^{21} - 22 q^{22} - 179 q^{23} - 9 q^{24} + 711 q^{25} + 331 q^{26} - 972 q^{27} - 296 q^{28} + 478 q^{29} + 135 q^{30} - 574 q^{31} - 149 q^{32} + 1188 q^{33} + 276 q^{34} - 194 q^{35} + 1062 q^{36} - 12 q^{37} + 325 q^{38} + 39 q^{39} - 185 q^{40} + 900 q^{41} - 246 q^{42} - 1053 q^{43} - 1298 q^{44} - 45 q^{45} - 407 q^{46} - 653 q^{47} - 786 q^{48} + 753 q^{49} - 1520 q^{50} - 612 q^{51} + 60 q^{52} + 735 q^{53} - 54 q^{54} + 55 q^{55} - 809 q^{56} + 1293 q^{57} - 1399 q^{58} - 1127 q^{59} - 1062 q^{60} + 2196 q^{61} - 1795 q^{62} - 567 q^{63} - 2133 q^{64} + 1886 q^{65} + 66 q^{66} - 989 q^{67} + 10 q^{68} + 537 q^{69} - 2130 q^{70} + 61 q^{71} + 27 q^{72} - 1471 q^{73} - 122 q^{74} - 2133 q^{75} - 4064 q^{76} + 693 q^{77} - 993 q^{78} - 1853 q^{79} + 2197 q^{80} + 2916 q^{81} - 2566 q^{82} - 3523 q^{83} + 888 q^{84} - 449 q^{85} - 771 q^{86} - 1434 q^{87} - 33 q^{88} + 2209 q^{89} - 405 q^{90} - 1668 q^{91} - 1999 q^{92} + 1722 q^{93} - 2844 q^{94} + 1220 q^{95} + 447 q^{96} - 3622 q^{97} + 3846 q^{98} - 3564 q^{99}+O(q^{100}) \) 36 * q + 2 * q^2 - 108 * q^3 + 118 * q^4 - 5 * q^5 - 6 * q^6 - 63 * q^7 + 3 * q^8 + 324 * q^9 - 45 * q^10 - 396 * q^11 - 354 * q^12 - 13 * q^13 + 82 * q^14 + 15 * q^15 + 262 * q^16 + 204 * q^17 + 18 * q^18 - 431 * q^19 + 354 * q^20 + 189 * q^21 - 22 * q^22 - 179 * q^23 - 9 * q^24 + 711 * q^25 + 331 * q^26 - 972 * q^27 - 296 * q^28 + 478 * q^29 + 135 * q^30 - 574 * q^31 - 149 * q^32 + 1188 * q^33 + 276 * q^34 - 194 * q^35 + 1062 * q^36 - 12 * q^37 + 325 * q^38 + 39 * q^39 - 185 * q^40 + 900 * q^41 - 246 * q^42 - 1053 * q^43 - 1298 * q^44 - 45 * q^45 - 407 * q^46 - 653 * q^47 - 786 * q^48 + 753 * q^49 - 1520 * q^50 - 612 * q^51 + 60 * q^52 + 735 * q^53 - 54 * q^54 + 55 * q^55 - 809 * q^56 + 1293 * q^57 - 1399 * q^58 - 1127 * q^59 - 1062 * q^60 + 2196 * q^61 - 1795 * q^62 - 567 * q^63 - 2133 * q^64 + 1886 * q^65 + 66 * q^66 - 989 * q^67 + 10 * q^68 + 537 * q^69 - 2130 * q^70 + 61 * q^71 + 27 * q^72 - 1471 * q^73 - 122 * q^74 - 2133 * q^75 - 4064 * q^76 + 693 * q^77 - 993 * q^78 - 1853 * q^79 + 2197 * q^80 + 2916 * q^81 - 2566 * q^82 - 3523 * q^83 + 888 * q^84 - 449 * q^85 - 771 * q^86 - 1434 * q^87 - 33 * q^88 + 2209 * q^89 - 405 * q^90 - 1668 * q^91 - 1999 * q^92 + 1722 * q^93 - 2844 * q^94 + 1220 * q^95 + 447 * q^96 - 3622 * q^97 + 3846 * q^98 - 3564 * 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 $

$2$	−3.21541	−1.13682	−0.568409	−	0.822746i	$-0.692441\pi$
$2$	−3.21541	−1.13682	−0.568409	+	0.822746i	$0.692441\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	2.33885	0.292357
$5$	2.50702	0.224234	0.112117	−	0.993695i	$-0.464237\pi$
$5$	2.50702	0.224234	0.112117	+	0.993695i	$0.464237\pi$
$6$	9.64623	0.656343
$7$	5.55272	0.299819	0.149909	−	0.988700i	$-0.452102\pi$
$7$	5.55272	0.299819	0.149909	+	0.988700i	$0.452102\pi$
$8$	18.2029	0.804462
$9$	9.00000	0.333333
$10$	−8.06108	−0.254914
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−7.01656	−0.168792
$13$	53.0283	1.13134	0.565669	−	0.824632i	$-0.308618\pi$
$13$	53.0283	1.13134	0.565669	+	0.824632i	$0.308618\pi$
$14$	−17.8543	−0.340840
$15$	−7.52105	−0.129462
$16$	−77.2406	−1.20688
$17$	−92.3863	−1.31806	−0.659029	−	0.752118i	$-0.729032\pi$
$17$	−92.3863	−1.31806	−0.659029	+	0.752118i	$0.729032\pi$
$18$	−28.9387	−0.378940
$19$	4.84821	0.0585398	0.0292699	−	0.999572i	$-0.490682\pi$
$19$	4.84821	0.0585398	0.0292699	+	0.999572i	$0.490682\pi$
$20$	5.86354	0.0655564
$21$	−16.6582	−0.173100
$22$	35.3695	0.342764
$23$	178.313	1.61656	0.808278	−	0.588801i	$-0.200400\pi$
$23$	178.313	1.61656	0.808278	+	0.588801i	$0.200400\pi$
$24$	−54.6087	−0.464457
$25$	−118.715	−0.949719
$26$	−170.508	−1.28613
$27$	−27.0000	−0.192450
$28$	12.9870	0.0876540
$29$	282.414	1.80838	0.904190	−	0.427130i	$-0.140475\pi$
$29$	282.414	1.80838	0.904190	+	0.427130i	$0.140475\pi$
$30$	24.1832	0.147174
$31$	187.826	1.08821	0.544105	−	0.839017i	$-0.316869\pi$
$31$	187.826	1.08821	0.544105	+	0.839017i	$0.316869\pi$
$32$	102.737	0.567546
$33$	33.0000	0.174078
$34$	297.060	1.49839
$35$	13.9208	0.0672297
$36$	21.0497	0.0974522
$37$	−37.5371	−0.166785	−0.0833927	−	0.996517i	$-0.526576\pi$
$37$	−37.5371	−0.166785	−0.0833927	+	0.996517i	$0.526576\pi$
$38$	−15.5890	−0.0665492
$39$	−159.085	−0.653179
$40$	45.6350	0.180388
$41$	−388.159	−1.47854	−0.739271	−	0.673408i	$-0.764830\pi$
$41$	−388.159	−1.47854	−0.739271	+	0.673408i	$0.764830\pi$
$42$	53.5628	0.196784
$43$	−415.331	−1.47296	−0.736482	−	0.676457i	$-0.763514\pi$
$43$	−415.331	−1.47296	−0.736482	+	0.676457i	$0.763514\pi$
$44$	−25.7274	−0.0881488
$45$	22.5631	0.0747448
$46$	−573.348	−1.83773
$47$	−513.860	−1.59477	−0.797384	−	0.603472i	$-0.793784\pi$
$47$	−513.860	−1.59477	−0.797384	+	0.603472i	$0.793784\pi$
$48$	231.722	0.696795
$49$	−312.167	−0.910109
$50$	381.717	1.07966
$51$	277.159	0.760981
$52$	124.025	0.330754
$53$	−208.507	−0.540390	−0.270195	−	0.962806i	$-0.587088\pi$
$53$	−208.507	−0.540390	−0.270195	+	0.962806i	$0.587088\pi$
$54$	86.8160	0.218781
$55$	−27.5772	−0.0676092
$56$	101.076	0.241193
$57$	−14.5446	−0.0337980
$58$	−908.078	−2.05580
$59$	−482.497	−1.06467	−0.532337	−	0.846532i	$-0.678686\pi$
$59$	−482.497	−1.06467	−0.532337	+	0.846532i	$0.678686\pi$
$60$	−17.5906	−0.0378490
$61$	61.0000	0.128037
$61$	61.0000	0.128037
$62$	−603.937	−1.23710
$63$	49.9745	0.0999396
$64$	287.584	0.561687
$65$	132.943	0.253685
$66$	−106.108	−0.197895
$67$	580.625	1.05873	0.529363	−	0.848396i	$-0.322431\pi$
$67$	580.625	1.05873	0.529363	+	0.848396i	$0.322431\pi$
$68$	−216.078	−0.385343
$69$	−534.938	−0.933319
$70$	−44.7609	−0.0764279
$71$	−44.1804	−0.0738486	−0.0369243	−	0.999318i	$-0.511756\pi$
$71$	−44.1804	−0.0738486	−0.0369243	+	0.999318i	$0.511756\pi$
$72$	163.826	0.268154
$73$	−287.299	−0.460628	−0.230314	−	0.973116i	$-0.573975\pi$
$73$	−287.299	−0.460628	−0.230314	+	0.973116i	$0.573975\pi$
$74$	120.697	0.189605
$75$	356.145	0.548321
$76$	11.3393	0.0171145
$77$	−61.0799	−0.0903988
$78$	511.523	0.742546
$79$	−280.700	−0.399763	−0.199881	−	0.979820i	$-0.564056\pi$
$79$	−280.700	−0.399763	−0.199881	+	0.979820i	$0.564056\pi$
$80$	−193.643	−0.270625
$81$	81.0000	0.111111
$82$	1248.09	1.68084
$83$	915.084	1.21016	0.605081	−	0.796164i	$-0.293141\pi$
$83$	915.084	1.21016	0.605081	+	0.796164i	$0.293141\pi$
$84$	−38.9610	−0.0506071
$85$	−231.614	−0.295554
$86$	1335.46	1.67449
$87$	−847.243	−1.04407
$88$	−200.232	−0.242554
$89$	1206.95	1.43749	0.718746	−	0.695272i	$-0.244716\pi$
$89$	1206.95	1.43749	0.718746	+	0.695272i	$0.244716\pi$
$90$	−72.5497	−0.0849712
$91$	294.451	0.339197
$92$	417.047	0.472611
$93$	−563.477	−0.628278
$94$	1652.27	1.81296
$95$	12.1545	0.0131266
$96$	−308.210	−0.327673
$97$	−712.705	−0.746023	−0.373012	−	0.927827i	$-0.621675\pi$
$97$	−712.705	−0.746023	−0.373012	+	0.927827i	$0.621675\pi$
$98$	1003.75	1.03463
$99$	−99.0000	−0.100504
$100$	−277.657	−0.277657
$101$	1267.51	1.24873	0.624366	−	0.781132i	$-0.285358\pi$
$101$	1267.51	1.24873	0.624366	+	0.781132i	$0.285358\pi$
$102$	−891.179	−0.865097
$103$	410.774	0.392959	0.196479	−	0.980508i	$-0.437049\pi$
$103$	410.774	0.392959	0.196479	+	0.980508i	$0.437049\pi$
$104$	965.269	0.910119
$105$	−41.7623	−0.0388151
$106$	670.435	0.614325
$107$	839.149	0.758165	0.379082	−	0.925363i	$-0.376240\pi$
$107$	839.149	0.758165	0.379082	+	0.925363i	$0.376240\pi$
$108$	−63.1490	−0.0562640
$109$	−356.375	−0.313160	−0.156580	−	0.987665i	$-0.550047\pi$
$109$	−356.375	−0.313160	−0.156580	+	0.987665i	$0.550047\pi$
$110$	88.6719	0.0768594
$111$	112.611	0.0962936
$112$	−428.896	−0.361847
$113$	−307.295	−0.255822	−0.127911	−	0.991786i	$-0.540827\pi$
$113$	−307.295	−0.255822	−0.127911	+	0.991786i	$0.540827\pi$
$114$	46.7670	0.0384222
$115$	447.033	0.362487
$116$	660.525	0.528692
$117$	477.255	0.377113
$118$	1551.43	1.21034
$119$	−512.996	−0.395178
$120$	−136.905	−0.104147
$121$	121.000	0.0909091
$122$	−196.140	−0.145555
$123$	1164.48	0.853637
$124$	439.297	0.318145
$125$	−610.997	−0.437194
$126$	−160.688	−0.113613
$127$	1966.63	1.37410	0.687048	−	0.726612i	$-0.258906\pi$
$127$	1966.63	1.37410	0.687048	+	0.726612i	$0.258906\pi$
$128$	−1746.59	−1.20608
$129$	1245.99	0.850416
$130$	−427.465	−0.288394
$131$	22.7753	0.0151900	0.00759499	−	0.999971i	$-0.497582\pi$
$131$	22.7753	0.0151900	0.00759499	+	0.999971i	$0.497582\pi$
$132$	77.1821	0.0508927
$133$	26.9208	0.0175513
$134$	−1866.95	−1.20358
$135$	−67.6894	−0.0431539
$136$	−1681.70	−1.06033
$137$	−1409.96	−0.879279	−0.439639	−	0.898174i	$-0.644894\pi$
$137$	−1409.96	−0.879279	−0.439639	+	0.898174i	$0.644894\pi$
$138$	1720.05	1.06101
$139$	−2766.10	−1.68790	−0.843948	−	0.536425i	$-0.819774\pi$
$139$	−2766.10	−1.68790	−0.843948	+	0.536425i	$0.819774\pi$
$140$	32.5586	0.0196550
$141$	1541.58	0.920740
$142$	142.058	0.0839525
$143$	−583.311	−0.341111
$144$	−695.165	−0.402295
$145$	708.017	0.405501
$146$	923.784	0.523650
$147$	936.502	0.525451
$148$	−87.7938	−0.0487608
$149$	−956.239	−0.525760	−0.262880	−	0.964829i	$-0.584672\pi$
$149$	−956.239	−0.525760	−0.262880	+	0.964829i	$0.584672\pi$
$150$	−1145.15	−0.623341
$151$	−3520.49	−1.89731	−0.948654	−	0.316316i	$-0.897554\pi$
$151$	−3520.49	−1.89731	−0.948654	+	0.316316i	$0.897554\pi$
$152$	88.2516	0.0470931
$153$	−831.477	−0.439352
$154$	196.397	0.102767
$155$	470.882	0.244014
$156$	−372.076	−0.190961
$157$	3545.66	1.80239	0.901194	−	0.433417i	$-0.142692\pi$
$157$	3545.66	1.80239	0.901194	+	0.433417i	$0.142692\pi$
$158$	902.567	0.454458
$159$	625.521	0.311994
$160$	257.563	0.127263
$161$	990.121	0.484674
$162$	−260.448	−0.126313
$163$	680.347	0.326926	0.163463	−	0.986550i	$-0.447734\pi$
$163$	680.347	0.326926	0.163463	+	0.986550i	$0.447734\pi$
$164$	−907.847	−0.432262
$165$	82.7315	0.0390342
$166$	−2942.37	−1.37574
$167$	3752.54	1.73881	0.869403	−	0.494104i	$-0.164504\pi$
$167$	3752.54	1.73881	0.869403	+	0.494104i	$0.164504\pi$
$168$	−303.227	−0.139253
$169$	614.999	0.279927
$170$	744.733	0.335991
$171$	43.6339	0.0195133
$172$	−971.399	−0.430631
$173$	−943.842	−0.414792	−0.207396	−	0.978257i	$-0.566499\pi$
$173$	−943.842	−0.414792	−0.207396	+	0.978257i	$0.566499\pi$
$174$	2724.23	1.18692
$175$	−659.191	−0.284744
$176$	849.646	0.363889
$177$	1447.49	0.614690
$178$	−3880.85	−1.63417
$179$	2873.94	1.20005	0.600023	−	0.799982i	$-0.295158\pi$
$179$	2873.94	1.20005	0.600023	+	0.799982i	$0.295158\pi$
$180$	52.7718	0.0218521
$181$	2562.10	1.05215	0.526076	−	0.850437i	$-0.323663\pi$
$181$	2562.10	1.05215	0.526076	+	0.850437i	$0.323663\pi$
$182$	−946.781	−0.385605
$183$	−183.000	−0.0739221
$184$	3245.81	1.30046
$185$	−94.1061	−0.0373990
$186$	1811.81	0.714238
$187$	1016.25	0.397409
$188$	−1201.84	−0.466241
$189$	−149.924	−0.0577002
$190$	−39.0818	−0.0149226
$191$	−1072.95	−0.406470	−0.203235	−	0.979130i	$-0.565145\pi$
$191$	−1072.95	−0.406470	−0.203235	+	0.979130i	$0.565145\pi$
$192$	−862.752	−0.324290
$193$	−2626.90	−0.979734	−0.489867	−	0.871797i	$-0.662955\pi$
$193$	−2626.90	−0.979734	−0.489867	+	0.871797i	$0.662955\pi$
$194$	2291.64	0.848093
$195$	−398.828	−0.146465
$196$	−730.113	−0.266076
$197$	1723.70	0.623394	0.311697	−	0.950182i	$-0.399103\pi$
$197$	1723.70	0.623394	0.311697	+	0.950182i	$0.399103\pi$
$198$	318.325	0.114255
$199$	5012.79	1.78566	0.892832	−	0.450391i	$-0.148715\pi$
$199$	5012.79	1.78566	0.892832	+	0.450391i	$0.148715\pi$
$200$	−2160.96	−0.764013
$201$	−1741.87	−0.611255
$202$	−4075.56	−1.41958
$203$	1568.17	0.542186
$204$	648.234	0.222478
$205$	−973.121	−0.331540
$206$	−1320.81	−0.446723
$207$	1604.81	0.538852
$208$	−4095.94	−1.36539
$209$	−53.3304	−0.0176504
$210$	134.283	0.0441257
$211$	−1399.09	−0.456479	−0.228240	−	0.973605i	$-0.573297\pi$
$211$	−1399.09	−0.456479	−0.228240	+	0.973605i	$0.573297\pi$
$212$	−487.667	−0.157986
$213$	132.541	0.0426365
$214$	−2698.21	−0.861896
$215$	−1041.24	−0.330289
$216$	−491.478	−0.154819
$217$	1042.94	0.326266
$218$	1145.89	0.356007
$219$	861.898	0.265944
$220$	−64.4989	−0.0197660
$221$	−4899.09	−1.49117
$222$	−362.091	−0.109468
$223$	−6507.52	−1.95415	−0.977075	−	0.212894i	$-0.931711\pi$
$223$	−6507.52	−1.95415	−0.977075	+	0.212894i	$0.931711\pi$
$224$	570.469	0.170161
$225$	−1068.43	−0.316573
$226$	988.079	0.290823
$227$	−2729.29	−0.798015	−0.399007	−	0.916948i	$-0.630645\pi$
$227$	−2729.29	−0.798015	−0.399007	+	0.916948i	$0.630645\pi$
$228$	−34.0178	−0.00988106
$229$	4376.96	1.26305	0.631523	−	0.775357i	$-0.282430\pi$
$229$	4376.96	1.26305	0.631523	+	0.775357i	$0.282430\pi$
$230$	−1437.39	−0.412082
$231$	183.240	0.0521918
$232$	5140.76	1.45477
$233$	−1092.17	−0.307083	−0.153542	−	0.988142i	$-0.549068\pi$
$233$	−1092.17	−0.307083	−0.153542	+	0.988142i	$0.549068\pi$
$234$	−1534.57	−0.428709
$235$	−1288.25	−0.357602
$236$	−1128.49	−0.311265
$237$	842.101	0.230803
$238$	1649.49	0.449246
$239$	−4106.53	−1.11142	−0.555711	−	0.831376i	$-0.687554\pi$
$239$	−4106.53	−1.11142	−0.555711	+	0.831376i	$0.687554\pi$
$240$	580.930	0.156245
$241$	−2887.93	−0.771900	−0.385950	−	0.922520i	$-0.626126\pi$
$241$	−2887.93	−0.771900	−0.385950	+	0.922520i	$0.626126\pi$
$242$	−389.064	−0.103347
$243$	−243.000	−0.0641500
$244$	142.670	0.0374324
$245$	−782.608	−0.204078
$246$	−3744.27	−0.970431
$247$	257.092	0.0662284
$248$	3418.97	0.875424
$249$	−2745.25	−0.698688
$250$	1964.60	0.497010
$251$	−6318.80	−1.58900	−0.794500	−	0.607264i	$-0.792267\pi$
$251$	−6318.80	−1.58900	−0.794500	+	0.607264i	$0.792267\pi$
$252$	116.883	0.0292180
$253$	−1961.44	−0.487410
$254$	−6323.52	−1.56210
$255$	694.842	0.170638
$256$	3315.34	0.809410
$257$	−1870.37	−0.453971	−0.226986	−	0.973898i	$-0.572887\pi$
$257$	−1870.37	−0.453971	−0.226986	+	0.973898i	$0.572887\pi$
$258$	−4006.38	−0.966769
$259$	−208.433	−0.0500054
$260$	310.933	0.0741664
$261$	2541.73	0.602793
$262$	−73.2319	−0.0172683
$263$	8044.26	1.88605	0.943024	−	0.332726i	$-0.107968\pi$
$263$	8044.26	1.88605	0.943024	+	0.332726i	$0.107968\pi$
$264$	600.696	0.140039
$265$	−522.730	−0.121174
$266$	−86.5613	−0.0199527
$267$	−3620.86	−0.829937
$268$	1358.00	0.309525
$269$	425.062	0.0963439	0.0481720	−	0.998839i	$-0.484660\pi$
$269$	425.062	0.0963439	0.0481720	+	0.998839i	$0.484660\pi$
$270$	217.649	0.0490582
$271$	−3902.42	−0.874741	−0.437371	−	0.899281i	$-0.644090\pi$
$271$	−3902.42	−0.874741	−0.437371	+	0.899281i	$0.644090\pi$
$272$	7135.97	1.59074
$273$	−883.354	−0.195835
$274$	4533.60	0.999580
$275$	1305.86	0.286351
$276$	−1251.14	−0.272862
$277$	−5124.51	−1.11156	−0.555779	−	0.831330i	$-0.687580\pi$
$277$	−5124.51	−1.11156	−0.555779	+	0.831330i	$0.687580\pi$
$278$	8894.14	1.91883
$279$	1690.43	0.362737
$280$	253.398	0.0540837
$281$	−6703.54	−1.42313	−0.711565	−	0.702620i	$-0.752013\pi$
$281$	−6703.54	−1.42313	−0.711565	+	0.702620i	$0.752013\pi$
$282$	−4956.81	−1.04671
$283$	−3624.70	−0.761364	−0.380682	−	0.924706i	$-0.624311\pi$
$283$	−3624.70	−0.761364	−0.380682	+	0.924706i	$0.624311\pi$
$284$	−103.331	−0.0215901
$285$	−36.4636	−0.00757867
$286$	1875.58	0.387782
$287$	−2155.34	−0.443295
$288$	924.631	0.189182
$289$	3622.23	0.737275
$290$	−2276.56	−0.460981
$291$	2138.12	0.430717
$292$	−671.951	−0.134668
$293$	7268.53	1.44926	0.724628	−	0.689141i	$-0.242012\pi$
$293$	7268.53	1.44926	0.724628	+	0.689141i	$0.242012\pi$
$294$	−3011.24	−0.597343
$295$	−1209.63	−0.238737
$296$	−683.284	−0.134173
$297$	297.000	0.0580259
$298$	3074.70	0.597693
$299$	9455.62	1.82887
$300$	832.970	0.160305
$301$	−2306.22	−0.441622
$302$	11319.8	2.15689
$303$	−3802.53	−0.720955
$304$	−374.479	−0.0706508
$305$	152.928	0.0287103
$306$	2673.54	0.499464
$307$	−3353.70	−0.623472	−0.311736	−	0.950169i	$-0.600910\pi$
$307$	−3353.70	−0.623472	−0.311736	+	0.950169i	$0.600910\pi$
$308$	−142.857	−0.0264287
$309$	−1232.32	−0.226875
$310$	−1514.08	−0.277400
$311$	837.924	0.152779	0.0763896	−	0.997078i	$-0.475661\pi$
$311$	837.924	0.152779	0.0763896	+	0.997078i	$0.475661\pi$
$312$	−2895.81	−0.525457
$313$	−7190.95	−1.29858	−0.649292	−	0.760540i	$-0.724935\pi$
$313$	−7190.95	−1.29858	−0.649292	+	0.760540i	$0.724935\pi$
$314$	−11400.8	−2.04899
$315$	125.287	0.0224099
$316$	−656.517	−0.116873
$317$	6822.10	1.20873	0.604365	−	0.796708i	$-0.293427\pi$
$317$	6822.10	1.20873	0.604365	+	0.796708i	$0.293427\pi$
$318$	−2011.31	−0.354681
$319$	−3106.56	−0.545247
$320$	720.977	0.125950
$321$	−2517.45	−0.437727
$322$	−3183.64	−0.550986
$323$	−447.909	−0.0771588
$324$	189.447	0.0324841
$325$	−6295.25	−1.07445
$326$	−2187.59	−0.371655
$327$	1069.12	0.180803
$328$	−7065.62	−1.18943
$329$	−2853.32	−0.478142
$330$	−266.016	−0.0443748
$331$	−3939.56	−0.654193	−0.327097	−	0.944991i	$-0.606070\pi$
$331$	−3939.56	−0.654193	−0.327097	+	0.944991i	$0.606070\pi$
$332$	2140.25	0.353799
$333$	−337.834	−0.0555952
$334$	−12066.0	−1.97671
$335$	1455.63	0.237402
$336$	1286.69	0.208912
$337$	10582.9	1.71065	0.855326	−	0.518090i	$-0.173357\pi$
$337$	10582.9	1.71065	0.855326	+	0.518090i	$0.173357\pi$
$338$	−1977.47	−0.318226
$339$	921.885	0.147699
$340$	−541.711	−0.0864070
$341$	−2066.08	−0.328108
$342$	−140.301	−0.0221831
$343$	−3637.96	−0.572687
$344$	−7560.24	−1.18494
$345$	−1341.10	−0.209282
$346$	3034.84	0.471543
$347$	5429.68	0.840002	0.420001	−	0.907524i	$-0.362030\pi$
$347$	5429.68	0.840002	0.420001	+	0.907524i	$0.362030\pi$
$348$	−1981.58	−0.305240
$349$	−9787.32	−1.50116	−0.750578	−	0.660782i	$-0.770225\pi$
$349$	−9787.32	−1.50116	−0.750578	+	0.660782i	$0.770225\pi$
$350$	2119.57	0.323702
$351$	−1431.76	−0.217726
$352$	−1130.11	−0.171122
$353$	−8509.98	−1.28312	−0.641559	−	0.767074i	$-0.721712\pi$
$353$	−8509.98	−1.28312	−0.641559	+	0.767074i	$0.721712\pi$
$354$	−4654.28	−0.698791
$355$	−110.761	−0.0165594
$356$	2822.89	0.420260
$357$	1538.99	0.228156
$358$	−9240.89	−1.36424
$359$	6178.24	0.908287	0.454144	−	0.890929i	$-0.349945\pi$
$359$	6178.24	0.908287	0.454144	+	0.890929i	$0.349945\pi$
$360$	410.715	0.0601293
$361$	−6835.49	−0.996573
$362$	−8238.21	−1.19611
$363$	−363.000	−0.0524864
$364$	688.678	0.0991663
$365$	−720.264	−0.103289
$366$	588.420	0.0840360
$367$	−7997.81	−1.13755	−0.568777	−	0.822492i	$-0.692583\pi$
$367$	−7997.81	−1.13755	−0.568777	+	0.822492i	$0.692583\pi$
$368$	−13773.0	−1.95100
$369$	−3493.43	−0.492848
$370$	302.590	0.0425159
$371$	−1157.78	−0.162019
$372$	−1317.89	−0.183681
$373$	−13416.4	−1.86240	−0.931198	−	0.364514i	$-0.881235\pi$
$373$	−13416.4	−1.86240	−0.931198	+	0.364514i	$0.881235\pi$
$374$	−3267.66	−0.451782
$375$	1832.99	0.252414
$376$	−9353.74	−1.28293
$377$	14975.9	2.04589
$378$	482.065	0.0655946
$379$	758.885	0.102853	0.0514265	−	0.998677i	$-0.483623\pi$
$379$	758.885	0.102853	0.0514265	+	0.998677i	$0.483623\pi$
$380$	28.4277	0.00383766
$381$	−5899.89	−0.793334
$382$	3449.96	0.462082
$383$	4608.77	0.614876	0.307438	−	0.951568i	$-0.400528\pi$
$383$	4608.77	0.614876	0.307438	+	0.951568i	$0.400528\pi$
$384$	5239.78	0.696332
$385$	−153.128	−0.0202705
$386$	8446.57	1.11378
$387$	−3737.98	−0.490988
$388$	−1666.91	−0.218105
$389$	4475.47	0.583330	0.291665	−	0.956521i	$-0.405791\pi$
$389$	4475.47	0.583330	0.291665	+	0.956521i	$0.405791\pi$
$390$	1282.40	0.166504
$391$	−16473.7	−2.13071
$392$	−5682.35	−0.732148
$393$	−68.3259	−0.00876994
$394$	−5542.40	−0.708686
$395$	−703.720	−0.0896406
$396$	−231.546	−0.0293829
$397$	5984.30	0.756532	0.378266	−	0.925697i	$-0.376520\pi$
$397$	5984.30	0.756532	0.378266	+	0.925697i	$0.376520\pi$
$398$	−16118.2	−2.02998
$399$	−80.7624	−0.0101333
$400$	9169.61	1.14620
$401$	14991.6	1.86694	0.933470	−	0.358656i	$-0.116765\pi$
$401$	14991.6	1.86694	0.933470	+	0.358656i	$0.116765\pi$
$402$	5600.84	0.694886
$403$	9960.08	1.23113
$404$	2964.52	0.365075
$405$	203.068	0.0249149
$406$	−5042.30	−0.616368
$407$	412.908	0.0502877
$408$	5045.10	0.612180
$409$	−13064.4	−1.57945	−0.789725	−	0.613461i	$-0.789777\pi$
$409$	−13064.4	−1.57945	−0.789725	+	0.613461i	$0.789777\pi$
$410$	3128.98	0.376901
$411$	4229.89	0.507652
$412$	960.739	0.114884
$413$	−2679.17	−0.319210
$414$	−5160.14	−0.612577
$415$	2294.13	0.271360
$416$	5447.96	0.642087
$417$	8298.30	0.974507
$418$	171.479	0.0200653
$419$	−1161.80	−0.135460	−0.0677300	−	0.997704i	$-0.521576\pi$
$419$	−1161.80	−0.135460	−0.0677300	+	0.997704i	$0.521576\pi$
$420$	−97.6758	−0.0113478
$421$	−14306.2	−1.65616	−0.828081	−	0.560609i	$-0.810567\pi$
$421$	−14306.2	−1.65616	−0.828081	+	0.560609i	$0.810567\pi$
$422$	4498.63	0.518934
$423$	−4624.74	−0.531590
$424$	−3795.43	−0.434723
$425$	10967.6	1.25178
$426$	−426.174	−0.0484700
$427$	338.716	0.0383879
$428$	1962.65	0.221654
$429$	1749.93	0.196941
$430$	3348.02	0.375479
$431$	−925.177	−0.103397	−0.0516986	−	0.998663i	$-0.516464\pi$
$431$	−925.177	−0.103397	−0.0516986	+	0.998663i	$0.516464\pi$
$432$	2085.50	0.232265
$433$	3521.47	0.390834	0.195417	−	0.980720i	$-0.437394\pi$
$433$	3521.47	0.390834	0.195417	+	0.980720i	$0.437394\pi$
$434$	−3353.49	−0.370905
$435$	−2124.05	−0.234116
$436$	−833.507	−0.0915545
$437$	864.499	0.0946329
$438$	−2771.35	−0.302330
$439$	−2459.44	−0.267387	−0.133693	−	0.991023i	$-0.542684\pi$
$439$	−2459.44	−0.267387	−0.133693	+	0.991023i	$0.542684\pi$
$440$	−501.985	−0.0543890
$441$	−2809.51	−0.303370
$442$	15752.6	1.69519
$443$	−3227.80	−0.346180	−0.173090	−	0.984906i	$-0.555375\pi$
$443$	−3227.80	−0.346180	−0.173090	+	0.984906i	$0.555375\pi$
$444$	263.381	0.0281521
$445$	3025.85	0.322335
$446$	20924.3	2.22151
$447$	2868.72	0.303547
$448$	1596.87	0.168404
$449$	−5192.17	−0.545732	−0.272866	−	0.962052i	$-0.587972\pi$
$449$	−5192.17	−0.545732	−0.272866	+	0.962052i	$0.587972\pi$
$450$	3435.45	0.359886
$451$	4269.75	0.445797
$452$	−718.718	−0.0747912
$453$	10561.5	1.09541
$454$	8775.78	0.907198
$455$	738.194	0.0760595
$456$	−264.755	−0.0271892
$457$	5641.57	0.577465	0.288732	−	0.957410i	$-0.406766\pi$
$457$	5641.57	0.577465	0.288732	+	0.957410i	$0.406766\pi$
$458$	−14073.7	−1.43585
$459$	2494.43	0.253660
$460$	1045.54	0.105976
$461$	12346.4	1.24735	0.623674	−	0.781684i	$-0.285639\pi$
$461$	12346.4	1.24735	0.623674	+	0.781684i	$0.285639\pi$
$462$	−589.191	−0.0593326
$463$	−13049.0	−1.30980	−0.654899	−	0.755716i	$-0.727289\pi$
$463$	−13049.0	−1.30980	−0.654899	+	0.755716i	$0.727289\pi$
$464$	−21813.9	−2.18251
$465$	−1412.65	−0.140882
$466$	3511.77	0.349098
$467$	−6555.32	−0.649559	−0.324780	−	0.945790i	$-0.605290\pi$
$467$	−6555.32	−0.649559	−0.324780	+	0.945790i	$0.605290\pi$
$468$	1116.23	0.110251
$469$	3224.05	0.317426
$470$	4142.26	0.406528
$471$	−10637.0	−1.04061
$472$	−8782.85	−0.856491
$473$	4568.65	0.444115
$474$	−2707.70	−0.262381
$475$	−575.555	−0.0555964
$476$	−1199.82	−0.115533
$477$	−1876.56	−0.180130
$478$	13204.2	1.26348
$479$	−9427.69	−0.899295	−0.449647	−	0.893206i	$-0.648450\pi$
$479$	−9427.69	−0.899295	−0.449647	+	0.893206i	$0.648450\pi$
$480$	−772.688	−0.0734755
$481$	−1990.53	−0.188691
$482$	9285.88	0.877511
$483$	−2970.36	−0.279827
$484$	283.001	0.0265779
$485$	−1786.76	−0.167284
$486$	781.344	0.0729269
$487$	−17891.8	−1.66480	−0.832398	−	0.554179i	$-0.813032\pi$
$487$	−17891.8	−1.66480	−0.832398	+	0.554179i	$0.813032\pi$
$488$	1110.38	0.103001
$489$	−2041.04	−0.188751
$490$	2516.40	0.231999
$491$	15146.4	1.39215	0.696076	−	0.717968i	$-0.254928\pi$
$491$	15146.4	1.39215	0.696076	+	0.717968i	$0.254928\pi$
$492$	2723.54	0.249566
$493$	−26091.2	−2.38355
$494$	−826.657	−0.0752896
$495$	−248.195	−0.0225364
$496$	−14507.8	−1.31334
$497$	−245.322	−0.0221412
$498$	8827.11	0.794281
$499$	9814.14	0.880444	0.440222	−	0.897889i	$-0.354900\pi$
$499$	9814.14	0.880444	0.440222	+	0.897889i	$0.354900\pi$
$500$	−1429.03	−0.127816
$501$	−11257.6	−1.00390
$502$	20317.5	1.80641
$503$	−11095.2	−0.983519	−0.491760	−	0.870731i	$-0.663646\pi$
$503$	−11095.2	−0.983519	−0.491760	+	0.870731i	$0.663646\pi$
$504$	909.681	0.0803976
$505$	3177.66	0.280008
$506$	6306.83	0.554097
$507$	−1845.00	−0.161616
$508$	4599.66	0.401726
$509$	10279.0	0.895104	0.447552	−	0.894258i	$-0.352296\pi$
$509$	10279.0	0.895104	0.447552	+	0.894258i	$0.352296\pi$
$510$	−2234.20	−0.193984
$511$	−1595.29	−0.138105
$512$	3312.57	0.285930
$513$	−130.902	−0.0112660
$514$	6014.01	0.516083
$515$	1029.82	0.0881148
$516$	2914.20	0.248625
$517$	5652.46	0.480841
$518$	670.198	0.0568471
$519$	2831.53	0.239480
$520$	2419.94	0.204080
$521$	2657.58	0.223475	0.111738	−	0.993738i	$-0.464358\pi$
$521$	2657.58	0.223475	0.111738	+	0.993738i	$0.464358\pi$
$522$	−8172.70	−0.685267
$523$	4584.92	0.383336	0.191668	−	0.981460i	$-0.438610\pi$
$523$	4584.92	0.383336	0.191668	+	0.981460i	$0.438610\pi$
$524$	53.2681	0.00444089
$525$	1977.57	0.164397
$526$	−25865.6	−2.14409
$527$	−17352.5	−1.43432
$528$	−2548.94	−0.210092
$529$	19628.4	1.61325
$530$	1680.79	0.137753
$531$	−4342.48	−0.354892
$532$	62.9638	0.00513125
$533$	−20583.4	−1.67273
$534$	11642.5	0.943488
$535$	2103.76	0.170006
$536$	10569.1	0.851704
$537$	−8621.82	−0.692847
$538$	−1366.75	−0.109526
$539$	3433.84	0.274408
$540$	−158.316	−0.0126163
$541$	2247.81	0.178634	0.0893170	−	0.996003i	$-0.471532\pi$
$541$	2247.81	0.178634	0.0893170	+	0.996003i	$0.471532\pi$
$542$	12547.9	0.994422
$543$	−7686.31	−0.607461
$544$	−9491.48	−0.748058
$545$	−893.436	−0.0702213
$546$	2840.34	0.222629
$547$	−16815.6	−1.31441	−0.657205	−	0.753712i	$-0.728261\pi$
$547$	−16815.6	−1.31441	−0.657205	+	0.753712i	$0.728261\pi$
$548$	−3297.69	−0.257063
$549$	549.000	0.0426790
$550$	−4198.89	−0.325529
$551$	1369.21	0.105862
$552$	−9737.43	−0.750820
$553$	−1558.65	−0.119856
$554$	16477.4	1.26364
$555$	282.318	0.0215923
$556$	−6469.50	−0.493467
$557$	−14190.7	−1.07950	−0.539748	−	0.841827i	$-0.681481\pi$
$557$	−14190.7	−1.07950	−0.539748	+	0.841827i	$0.681481\pi$
$558$	−5435.43	−0.412366
$559$	−22024.3	−1.66642
$560$	−1075.25	−0.0811384
$561$	−3048.75	−0.229444
$562$	21554.6	1.61784
$563$	5369.56	0.401954	0.200977	−	0.979596i	$-0.435588\pi$
$563$	5369.56	0.401954	0.200977	+	0.979596i	$0.435588\pi$
$564$	3605.53	0.269184
$565$	−770.393	−0.0573641
$566$	11654.9	0.865533
$567$	449.771	0.0333132
$568$	−804.212	−0.0594084
$569$	8771.41	0.646251	0.323125	−	0.946356i	$-0.395266\pi$
$569$	8771.41	0.646251	0.323125	+	0.946356i	$0.395266\pi$
$570$	117.246	0.00861557
$571$	9663.04	0.708206	0.354103	−	0.935206i	$-0.384786\pi$
$571$	9663.04	0.708206	0.354103	+	0.935206i	$0.384786\pi$
$572$	−1364.28	−0.0997261
$573$	3218.84	0.234675
$574$	6930.30	0.503946
$575$	−21168.4	−1.53527
$576$	2588.25	0.187229
$577$	−22259.5	−1.60603	−0.803013	−	0.595962i	$-0.796771\pi$
$577$	−22259.5	−1.60603	−0.803013	+	0.595962i	$0.796771\pi$
$578$	−11647.0	−0.838148
$579$	7880.71	0.565649
$580$	1655.95	0.118551
$581$	5081.21	0.362830
$582$	−6874.92	−0.489647
$583$	2293.58	0.162934
$584$	−5229.68	−0.370558
$585$	1196.48	0.0845616
$586$	−23371.3	−1.64754
$587$	−20702.4	−1.45567	−0.727837	−	0.685750i	$-0.759474\pi$
$587$	−20702.4	−1.45567	−0.727837	+	0.685750i	$0.759474\pi$
$588$	2190.34	0.153619
$589$	910.620	0.0637036
$590$	3889.45	0.271400
$591$	−5171.10	−0.359917
$592$	2899.39	0.201291
$593$	903.382	0.0625590	0.0312795	−	0.999511i	$-0.490042\pi$
$593$	903.382	0.0625590	0.0312795	+	0.999511i	$0.490042\pi$
$594$	−954.976	−0.0659649
$595$	−1286.09	−0.0886125
$596$	−2236.50	−0.153709
$597$	−15038.4	−1.03095
$598$	−30403.7	−2.07910
$599$	−18467.6	−1.25971	−0.629854	−	0.776713i	$-0.716885\pi$
$599$	−18467.6	−1.25971	−0.629854	+	0.776713i	$0.716885\pi$
$600$	6482.87	0.441103
$601$	−14472.8	−0.982296	−0.491148	−	0.871076i	$-0.663423\pi$
$601$	−14472.8	−0.982296	−0.491148	+	0.871076i	$0.663423\pi$
$602$	7415.44	0.502045
$603$	5225.62	0.352908
$604$	−8233.91	−0.554690
$605$	303.349	0.0203849
$606$	12226.7	0.819596
$607$	1860.11	0.124381	0.0621906	−	0.998064i	$-0.480191\pi$
$607$	1860.11	0.124381	0.0621906	+	0.998064i	$0.480191\pi$
$608$	498.090	0.0332241
$609$	−4704.51	−0.313032
$610$	−491.726	−0.0326384
$611$	−27249.1	−1.80422
$612$	−1944.70	−0.128448
$613$	−3355.86	−0.221113	−0.110556	−	0.993870i	$-0.535263\pi$
$613$	−3355.86	−0.221113	−0.110556	+	0.993870i	$0.535263\pi$
$614$	10783.5	0.708774
$615$	2919.36	0.191415
$616$	−1111.83	−0.0727224
$617$	5672.47	0.370121	0.185061	−	0.982727i	$-0.440752\pi$
$617$	5672.47	0.370121	0.185061	+	0.982727i	$0.440752\pi$
$618$	3962.42	0.257916
$619$	−25070.9	−1.62792	−0.813962	−	0.580919i	$-0.802693\pi$
$619$	−25070.9	−1.62792	−0.813962	+	0.580919i	$0.802693\pi$
$620$	1101.32	0.0713391
$621$	−4814.44	−0.311106
$622$	−2694.27	−0.173682
$623$	6701.88	0.430987
$624$	12287.8	0.788311
$625$	13307.6	0.851685
$626$	23121.8	1.47625
$627$	159.991	0.0101905
$628$	8292.78	0.526940
$629$	3467.92	0.219833
$630$	−402.848	−0.0254760
$631$	12486.5	0.787764	0.393882	−	0.919161i	$-0.371132\pi$
$631$	12486.5	0.787764	0.393882	+	0.919161i	$0.371132\pi$
$632$	−5109.56	−0.321594
$633$	4197.26	0.263548
$634$	−21935.8	−1.37411
$635$	4930.37	0.308119
$636$	1463.00	0.0912135
$637$	−16553.7	−1.02964
$638$	9988.85	0.619847
$639$	−397.624	−0.0246162
$640$	−4378.74	−0.270445
$641$	2109.83	0.130005	0.0650026	−	0.997885i	$-0.479294\pi$
$641$	2109.83	0.130005	0.0650026	+	0.997885i	$0.479294\pi$
$642$	8094.62	0.497616
$643$	8263.98	0.506843	0.253421	−	0.967356i	$-0.418444\pi$
$643$	8263.98	0.506843	0.253421	+	0.967356i	$0.418444\pi$
$644$	2315.75	0.141698
$645$	3123.73	0.190692
$646$	1440.21	0.0877156
$647$	6755.79	0.410506	0.205253	−	0.978709i	$-0.434198\pi$
$647$	6755.79	0.410506	0.205253	+	0.978709i	$0.434198\pi$
$648$	1474.44	0.0893847
$649$	5307.47	0.321011
$650$	20241.8	1.22146
$651$	−3128.83	−0.188370
$652$	1591.23	0.0955788
$653$	10424.2	0.624703	0.312351	−	0.949967i	$-0.398883\pi$
$653$	10424.2	0.624703	0.312351	+	0.949967i	$0.398883\pi$
$654$	−3437.67	−0.205541
$655$	57.0980	0.00340611
$656$	29981.6	1.78443
$657$	−2585.69	−0.153543
$658$	9174.59	0.543560
$659$	−23889.6	−1.41215	−0.706075	−	0.708137i	$-0.749536\pi$
$659$	−23889.6	−1.41215	−0.706075	+	0.708137i	$0.749536\pi$
$660$	193.497	0.0114119
$661$	−11143.8	−0.655738	−0.327869	−	0.944723i	$-0.606331\pi$
$661$	−11143.8	−0.655738	−0.327869	+	0.944723i	$0.606331\pi$
$662$	12667.3	0.743699
$663$	14697.3	0.860927
$664$	16657.2	0.973530
$665$	67.4908	0.00393561
$666$	1086.27	0.0632016
$667$	50358.1	2.92335
$668$	8776.64	0.508351
$669$	19522.5	1.12823
$670$	−4680.46	−0.269884
$671$	−671.000	−0.0386046
$672$	−1711.41	−0.0982425
$673$	18310.5	1.04876	0.524382	−	0.851483i	$-0.324296\pi$
$673$	18310.5	1.04876	0.524382	+	0.851483i	$0.324296\pi$
$674$	−34028.5	−1.94470
$675$	3205.30	0.182774
$676$	1438.39	0.0818384
$677$	22052.7	1.25193	0.625963	−	0.779853i	$-0.284706\pi$
$677$	22052.7	1.25193	0.625963	+	0.779853i	$0.284706\pi$
$678$	−2964.24	−0.167907
$679$	−3957.46	−0.223672
$680$	−4216.05	−0.237762
$681$	8187.87	0.460734
$682$	6643.30	0.372999
$683$	−8984.78	−0.503357	−0.251679	−	0.967811i	$-0.580983\pi$
$683$	−8984.78	−0.503357	−0.251679	+	0.967811i	$0.580983\pi$
$684$	102.053	0.00570483
$685$	−3534.80	−0.197164
$686$	11697.5	0.651041
$687$	−13130.9	−0.729220
$688$	32080.4	1.77770
$689$	−11056.8	−0.611364
$690$	4312.18	0.237916
$691$	9461.33	0.520877	0.260439	−	0.965490i	$-0.416133\pi$
$691$	9461.33	0.520877	0.260439	+	0.965490i	$0.416133\pi$
$692$	−2207.51	−0.121267
$693$	−549.720	−0.0301329
$694$	−17458.6	−0.954930
$695$	−6934.65	−0.378484
$696$	−15422.3	−0.839914
$697$	35860.6	1.94880
$698$	31470.2	1.70654
$699$	3276.51	0.177294
$700$	−1541.75	−0.0832467
$701$	5704.53	0.307357	0.153678	−	0.988121i	$-0.450888\pi$
$701$	5704.53	0.307357	0.153678	+	0.988121i	$0.450888\pi$
$702$	4603.70	0.247515
$703$	−181.988	−0.00976359
$704$	−3163.42	−0.169355
$705$	3864.76	0.206462
$706$	27363.1	1.45867
$707$	7038.13	0.374393
$708$	3385.47	0.179709
$709$	6682.54	0.353975	0.176987	−	0.984213i	$-0.443365\pi$
$709$	6682.54	0.353975	0.176987	+	0.984213i	$0.443365\pi$
$710$	356.142	0.0188250
$711$	−2526.30	−0.133254
$712$	21970.1	1.15641
$713$	33491.7	1.75915
$714$	−4948.47	−0.259372
$715$	−1462.37	−0.0764889
$716$	6721.72	0.350842
$717$	12319.6	0.641679
$718$	−19865.6	−1.03256
$719$	−5821.40	−0.301950	−0.150975	−	0.988538i	$-0.548241\pi$
$719$	−5821.40	−0.301950	−0.150975	+	0.988538i	$0.548241\pi$
$720$	−1742.79	−0.0902083
$721$	2280.91	0.117816
$722$	21978.9	1.13292
$723$	8663.79	0.445657
$724$	5992.38	0.307604
$725$	−33526.8	−1.71745
$726$	1167.19	0.0596675
$727$	−23813.9	−1.21487	−0.607435	−	0.794370i	$-0.707801\pi$
$727$	−23813.9	−1.21487	−0.607435	+	0.794370i	$0.707801\pi$
$728$	5359.87	0.272871
$729$	729.000	0.0370370
$730$	2315.94	0.117420
$731$	38370.9	1.94145
$732$	−428.010	−0.0216116
$733$	−11269.7	−0.567881	−0.283941	−	0.958842i	$-0.591642\pi$
$733$	−11269.7	−0.567881	−0.283941	+	0.958842i	$0.591642\pi$
$734$	25716.2	1.29319
$735$	2347.82	0.117824
$736$	18319.3	0.917470
$737$	−6386.87	−0.319218
$738$	11232.8	0.560278
$739$	6864.25	0.341685	0.170843	−	0.985298i	$-0.445351\pi$
$739$	6864.25	0.341685	0.170843	+	0.985298i	$0.445351\pi$
$740$	−220.100	−0.0109338
$741$	−771.277	−0.0382370
$742$	3722.74	0.184186
$743$	−31400.1	−1.55042	−0.775208	−	0.631707i	$-0.782355\pi$
$743$	−31400.1	−1.55042	−0.775208	+	0.631707i	$0.782355\pi$
$744$	−10256.9	−0.505426
$745$	−2397.31	−0.117893
$746$	43139.1	2.11721
$747$	8235.76	0.403388
$748$	2376.86	0.116185
$749$	4659.56	0.227312
$750$	−5893.81	−0.286949
$751$	−24386.2	−1.18491	−0.592453	−	0.805605i	$-0.701840\pi$
$751$	−24386.2	−1.18491	−0.592453	+	0.805605i	$0.701840\pi$
$752$	39690.8	1.92470
$753$	18956.4	0.917410
$754$	−48153.8	−2.32581
$755$	−8825.92	−0.425441
$756$	−350.649	−0.0168690
$757$	15058.4	0.722996	0.361498	−	0.932373i	$-0.382265\pi$
$757$	15058.4	0.722996	0.361498	+	0.932373i	$0.382265\pi$
$758$	−2440.12	−0.116925
$759$	5884.32	0.281406
$760$	221.248	0.0105599
$761$	−34968.5	−1.66571	−0.832856	−	0.553490i	$-0.813296\pi$
$761$	−34968.5	−1.66571	−0.832856	+	0.553490i	$0.813296\pi$
$762$	18970.6	0.901877
$763$	−1978.85	−0.0938914
$764$	−2509.46	−0.118834
$765$	−2084.53	−0.0985179
$766$	−14819.1	−0.699002
$767$	−25586.0	−1.20451
$768$	−9946.03	−0.467313
$769$	12128.3	0.568734	0.284367	−	0.958716i	$-0.408217\pi$
$769$	12128.3	0.568734	0.284367	+	0.958716i	$0.408217\pi$
$770$	492.370	0.0230439
$771$	5611.12	0.262100
$772$	−6143.94	−0.286432
$773$	10212.6	0.475189	0.237594	−	0.971364i	$-0.423641\pi$
$773$	10212.6	0.475189	0.237594	+	0.971364i	$0.423641\pi$
$774$	12019.1	0.558164
$775$	−22297.7	−1.03349
$776$	−12973.3	−0.600148
$777$	625.299	0.0288706
$778$	−14390.5	−0.663140
$779$	−1881.88	−0.0865536
$780$	−932.800	−0.0428200
$781$	485.985	0.0222662
$782$	52969.6	2.42223
$783$	−7625.19	−0.348023
$784$	24112.0	1.09840
$785$	8889.03	0.404157
$786$	219.696	0.00996983
$787$	−20091.0	−0.909994	−0.454997	−	0.890493i	$-0.650360\pi$
$787$	−20091.0	−0.909994	−0.454997	+	0.890493i	$0.650360\pi$
$788$	4031.48	0.182253
$789$	−24132.8	−1.08891
$790$	2262.75	0.101905
$791$	−1706.32	−0.0767003
$792$	−1802.09	−0.0808515
$793$	3234.73	0.144853
$794$	−19242.0	−0.860040
$795$	1568.19	0.0699598
$796$	11724.2	0.522050
$797$	−36270.0	−1.61198	−0.805990	−	0.591929i	$-0.798367\pi$
$797$	−36270.0	−1.61198	−0.805990	+	0.591929i	$0.798367\pi$
$798$	259.684	0.0115197
$799$	47473.6	2.10200
$800$	−12196.4	−0.539009
$801$	10862.6	0.479164
$802$	−48204.0	−2.12237
$803$	3160.29	0.138885
$804$	−4073.99	−0.178704
$805$	2482.25	0.108680
$806$	−32025.7	−1.39958
$807$	−1275.19	−0.0556242
$808$	23072.3	1.00456
$809$	26802.5	1.16480	0.582401	−	0.812902i	$-0.302114\pi$
$809$	26802.5	1.16480	0.582401	+	0.812902i	$0.302114\pi$
$810$	−652.947	−0.0283237
$811$	−5585.52	−0.241842	−0.120921	−	0.992662i	$-0.538585\pi$
$811$	−5585.52	−0.241842	−0.120921	+	0.992662i	$0.538585\pi$
$812$	3667.71	0.158512
$813$	11707.2	0.505032
$814$	−1327.67	−0.0571680
$815$	1705.64	0.0733079
$816$	−21407.9	−0.918416
$817$	−2013.62	−0.0862271
$818$	42007.5	1.79555
$819$	2650.06	0.113066
$820$	−2275.99	−0.0969279
$821$	6795.24	0.288862	0.144431	−	0.989515i	$-0.453865\pi$
$821$	6795.24	0.288862	0.144431	+	0.989515i	$0.453865\pi$
$822$	−13600.8	−0.577108
$823$	−39221.8	−1.66122	−0.830611	−	0.556853i	$-0.812009\pi$
$823$	−39221.8	−1.66122	−0.830611	+	0.556853i	$0.812009\pi$
$824$	7477.28	0.316120
$825$	−3917.59	−0.165325
$826$	8614.64	0.362883
$827$	−27616.6	−1.16121	−0.580606	−	0.814184i	$-0.697184\pi$
$827$	−27616.6	−1.16121	−0.580606	+	0.814184i	$0.697184\pi$
$828$	3753.43	0.157537
$829$	−40555.5	−1.69910	−0.849548	−	0.527512i	$-0.823125\pi$
$829$	−40555.5	−1.69910	−0.849548	+	0.527512i	$0.823125\pi$
$830$	−7376.56	−0.308487
$831$	15373.5	0.641759
$832$	15250.1	0.635458
$833$	28840.0	1.19958
$834$	−26682.4	−1.10784
$835$	9407.68	0.389900
$836$	−124.732	−0.00516022
$837$	−5071.30	−0.209426
$838$	3735.67	0.153994
$839$	−741.562	−0.0305144	−0.0152572	−	0.999884i	$-0.504857\pi$
$839$	−741.562	−0.0305144	−0.0152572	+	0.999884i	$0.504857\pi$
$840$	−760.195	−0.0312253
$841$	55368.9	2.27024
$842$	46000.4	1.88275
$843$	20110.6	0.821645
$844$	−3272.26	−0.133455
$845$	1541.81	0.0627691
$846$	14870.4	0.604321
$847$	671.879	0.0272563
$848$	16105.2	0.652188
$849$	10874.1	0.439574
$850$	−35265.4	−1.42305
$851$	−6693.35	−0.269618
$852$	309.994	0.0124651
$853$	45887.9	1.84194	0.920968	−	0.389639i	$-0.127400\pi$
$853$	45887.9	1.84194	0.920968	+	0.389639i	$0.127400\pi$
$854$	−1089.11	−0.0436400
$855$	109.391	0.00437554
$856$	15275.0	0.609915
$857$	30609.6	1.22008	0.610038	−	0.792372i	$-0.291154\pi$
$857$	30609.6	1.22008	0.610038	+	0.792372i	$0.291154\pi$
$858$	−5626.75	−0.223886
$859$	23049.3	0.915519	0.457760	−	0.889076i	$-0.348652\pi$
$859$	23049.3	0.915519	0.457760	+	0.889076i	$0.348652\pi$
$860$	−2435.31	−0.0965621
$861$	6466.02	0.255937
$862$	2974.82	0.117544
$863$	−9823.41	−0.387477	−0.193739	−	0.981053i	$-0.562061\pi$
$863$	−9823.41	−0.387477	−0.193739	+	0.981053i	$0.562061\pi$
$864$	−2773.89	−0.109224
$865$	−2366.23	−0.0930105
$866$	−11323.0	−0.444307
$867$	−10866.7	−0.425666
$868$	2439.29	0.0953860
$869$	3087.71	0.120533
$870$	6829.69	0.266147
$871$	30789.5	1.19778
$872$	−6487.05	−0.251926
$873$	−6414.35	−0.248674
$874$	−2779.72	−0.107580
$875$	−3392.70	−0.131079
$876$	2015.85	0.0777504
$877$	7598.43	0.292567	0.146283	−	0.989243i	$-0.453269\pi$
$877$	7598.43	0.292567	0.146283	+	0.989243i	$0.453269\pi$
$878$	7908.11	0.303970
$879$	−21805.6	−0.836728
$880$	2130.08	0.0815964
$881$	−24407.8	−0.933395	−0.466697	−	0.884417i	$-0.654556\pi$
$881$	−24407.8	−0.933395	−0.466697	+	0.884417i	$0.654556\pi$
$882$	9033.71	0.344876
$883$	−50554.4	−1.92672	−0.963359	−	0.268216i	$-0.913566\pi$
$883$	−50554.4	−1.92672	−0.963359	+	0.268216i	$0.913566\pi$
$884$	−11458.2	−0.435953
$885$	3628.88	0.137835
$886$	10378.7	0.393543
$887$	4536.56	0.171728	0.0858640	−	0.996307i	$-0.472635\pi$
$887$	4536.56	0.171728	0.0858640	+	0.996307i	$0.472635\pi$
$888$	2049.85	0.0774646
$889$	10920.1	0.411980
$890$	−9729.35	−0.366437
$891$	−891.000	−0.0335013
$892$	−15220.1	−0.571309
$893$	−2491.30	−0.0933575
$894$	−9224.10	−0.345078
$895$	7205.01	0.269092
$896$	−9698.35	−0.361606
$897$	−28366.9	−1.05590
$898$	16695.0	0.620399
$899$	53044.7	1.96790
$900$	−2498.91	−0.0925522
$901$	19263.2	0.712265
$902$	−13729.0	−0.506791
$903$	6918.66	0.254971
$904$	−5593.66	−0.205799
$905$	6423.23	0.235929
$906$	−33959.4	−1.24528
$907$	11620.3	0.425409	0.212705	−	0.977117i	$-0.431773\pi$
$907$	11620.3	0.425409	0.212705	+	0.977117i	$0.431773\pi$
$908$	−6383.41	−0.233305
$909$	11407.6	0.416244
$910$	−2373.60	−0.0864658
$911$	6068.76	0.220710	0.110355	−	0.993892i	$-0.464801\pi$
$911$	6068.76	0.220710	0.110355	+	0.993892i	$0.464801\pi$
$912$	1123.44	0.0407903
$913$	−10065.9	−0.364878
$914$	−18139.9	−0.656472
$915$	−458.784	−0.0165759
$916$	10237.1	0.369260
$917$	126.465	0.00455424
$918$	−8020.61	−0.288366
$919$	−52.0372	−0.00186784	−0.000933922	−	1.00000i	$-0.500297\pi$
$919$	−52.0372	−0.00186784	−0.000933922		1.00000i	$0.500297\pi$
$920$	8137.30	0.291607
$921$	10061.1	0.359961
$922$	−39698.6	−1.41801
$923$	−2342.81	−0.0835478
$924$	428.571	0.0152586
$925$	4456.21	0.158399
$926$	41957.7	1.48900
$927$	3696.96	0.130986
$928$	29014.4	1.02634
$929$	−2453.63	−0.0866533	−0.0433267	−	0.999061i	$-0.513796\pi$
$929$	−2453.63	−0.0866533	−0.0433267	+	0.999061i	$0.513796\pi$
$930$	4542.24	0.160157
$931$	−1513.45	−0.0532776
$932$	−2554.42	−0.0897777
$933$	−2513.77	−0.0882071
$934$	21078.0	0.738431
$935$	2547.75	0.0891128
$936$	8687.42	0.303373
$937$	−26996.0	−0.941217	−0.470608	−	0.882342i	$-0.655966\pi$
$937$	−26996.0	−0.941217	−0.470608	+	0.882342i	$0.655966\pi$
$938$	−10366.6	−0.360855
$939$	21572.9	0.749737
$940$	−3013.04	−0.104547
$941$	−27549.4	−0.954393	−0.477197	−	0.878797i	$-0.658347\pi$
$941$	−27549.4	−0.954393	−0.477197	+	0.878797i	$0.658347\pi$
$942$	34202.3	1.18298
$943$	−69213.7	−2.39015
$944$	37268.4	1.28494
$945$	−375.861	−0.0129384
$946$	−14690.1	−0.504879
$947$	14456.9	0.496078	0.248039	−	0.968750i	$-0.420214\pi$
$947$	14456.9	0.496078	0.248039	+	0.968750i	$0.420214\pi$
$948$	1969.55	0.0674768
$949$	−15235.0	−0.521126
$950$	1850.65	0.0632030
$951$	−20466.3	−0.697861
$952$	−9338.01	−0.317906
$953$	23694.7	0.805401	0.402701	−	0.915332i	$-0.368072\pi$
$953$	23694.7	0.805401	0.402701	+	0.915332i	$0.368072\pi$
$954$	6033.92	0.204775
$955$	−2689.89	−0.0911444
$956$	−9604.58	−0.324931
$957$	9319.67	0.314799
$958$	30313.9	1.02233
$959$	−7829.13	−0.263624
$960$	−2162.93	−0.0727170
$961$	5487.53	0.184201
$962$	6400.36	0.214507
$963$	7552.34	0.252722
$964$	−6754.44	−0.225670
$965$	−6585.69	−0.219690
$966$	9550.93	0.318112
$967$	−27232.6	−0.905626	−0.452813	−	0.891605i	$-0.649580\pi$
$967$	−27232.6	−0.905626	−0.452813	+	0.891605i	$0.649580\pi$
$968$	2202.55	0.0731329
$969$	1343.73	0.0445477
$970$	5745.17	0.190172
$971$	37049.9	1.22450	0.612249	−	0.790665i	$-0.290265\pi$
$971$	37049.9	1.22450	0.612249	+	0.790665i	$0.290265\pi$
$972$	−568.341	−0.0187547
$973$	−15359.4	−0.506063
$974$	57529.5	1.89257
$975$	18885.7	0.620336
$976$	−4711.68	−0.154526
$977$	−40737.4	−1.33399	−0.666993	−	0.745064i	$-0.732419\pi$
$977$	−40737.4	−1.33399	−0.666993	+	0.745064i	$0.732419\pi$
$978$	6562.78	0.214575
$979$	−13276.5	−0.433420
$980$	−1830.40	−0.0596634
$981$	−3207.37	−0.104387
$982$	−48701.8	−1.58262
$983$	−35562.7	−1.15389	−0.576946	−	0.816783i	$-0.695756\pi$
$983$	−35562.7	−1.15389	−0.576946	+	0.816783i	$0.695756\pi$
$984$	21196.9	0.686719
$985$	4321.35	0.139786
$986$	83893.9	2.70966
$987$	8559.96	0.276055
$988$	601.301	0.0193623
$989$	−74058.9	−2.38113
$990$	798.047	0.0256198
$991$	14918.5	0.478206	0.239103	−	0.970994i	$-0.423147\pi$
$991$	14918.5	0.478206	0.239103	+	0.970994i	$0.423147\pi$
$992$	19296.6	0.617609
$993$	11818.7	0.377699
$994$	788.809	0.0251705
$995$	12567.1	0.400407
$996$	−6420.74	−0.204266
$997$	24605.5	0.781609	0.390804	−	0.920474i	$-0.372197\pi$
$997$	24605.5	0.781609	0.390804	+	0.920474i	$0.372197\pi$
$998$	−31556.5	−1.00090
$999$	1013.50	0.0320979

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.b.1.9	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.b.1.9	✓	36	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)

\(f(q)\)	\(=\)	\(q-3.21541 q^{2} -3.00000 q^{3} +2.33885 q^{4} +2.50702 q^{5} +9.64623 q^{6} +5.55272 q^{7} +18.2029 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.21541 q^{2} -3.00000 q^{3} +2.33885 q^{4} +2.50702 q^{5} +9.64623 q^{6} +5.55272 q^{7} +18.2029 q^{8} +9.00000 q^{9} -8.06108 q^{10} -11.0000 q^{11} -7.01656 q^{12} +53.0283 q^{13} -17.8543 q^{14} -7.52105 q^{15} -77.2406 q^{16} -92.3863 q^{17} -28.9387 q^{18} +4.84821 q^{19} +5.86354 q^{20} -16.6582 q^{21} +35.3695 q^{22} +178.313 q^{23} -54.6087 q^{24} -118.715 q^{25} -170.508 q^{26} -27.0000 q^{27} +12.9870 q^{28} +282.414 q^{29} +24.1832 q^{30} +187.826 q^{31} +102.737 q^{32} +33.0000 q^{33} +297.060 q^{34} +13.9208 q^{35} +21.0497 q^{36} -37.5371 q^{37} -15.5890 q^{38} -159.085 q^{39} +45.6350 q^{40} -388.159 q^{41} +53.5628 q^{42} -415.331 q^{43} -25.7274 q^{44} +22.5631 q^{45} -573.348 q^{46} -513.860 q^{47} +231.722 q^{48} -312.167 q^{49} +381.717 q^{50} +277.159 q^{51} +124.025 q^{52} -208.507 q^{53} +86.8160 q^{54} -27.5772 q^{55} +101.076 q^{56} -14.5446 q^{57} -908.078 q^{58} -482.497 q^{59} -17.5906 q^{60} +61.0000 q^{61} -603.937 q^{62} +49.9745 q^{63} +287.584 q^{64} +132.943 q^{65} -106.108 q^{66} +580.625 q^{67} -216.078 q^{68} -534.938 q^{69} -44.7609 q^{70} -44.1804 q^{71} +163.826 q^{72} -287.299 q^{73} +120.697 q^{74} +356.145 q^{75} +11.3393 q^{76} -61.0799 q^{77} +511.523 q^{78} -280.700 q^{79} -193.643 q^{80} +81.0000 q^{81} +1248.09 q^{82} +915.084 q^{83} -38.9610 q^{84} -231.614 q^{85} +1335.46 q^{86} -847.243 q^{87} -200.232 q^{88} +1206.95 q^{89} -72.5497 q^{90} +294.451 q^{91} +417.047 q^{92} -563.477 q^{93} +1652.27 q^{94} +12.1545 q^{95} -308.210 q^{96} -712.705 q^{97} +1003.75 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 2 q^{2} - 108 q^{3} + 118 q^{4} - 5 q^{5} - 6 q^{6} - 63 q^{7} + 3 q^{8} + 324 q^{9}+O(q^{10}) \) 36 * q + 2 * q^2 - 108 * q^3 + 118 * q^4 - 5 * q^5 - 6 * q^6 - 63 * q^7 + 3 * q^8 + 324 * q^9	\( 36 q + 2 q^{2} - 108 q^{3} + 118 q^{4} - 5 q^{5} - 6 q^{6} - 63 q^{7} + 3 q^{8} + 324 q^{9} - 45 q^{10} - 396 q^{11} - 354 q^{12} - 13 q^{13} + 82 q^{14} + 15 q^{15} + 262 q^{16} + 204 q^{17} + 18 q^{18} - 431 q^{19} + 354 q^{20} + 189 q^{21} - 22 q^{22} - 179 q^{23} - 9 q^{24} + 711 q^{25} + 331 q^{26} - 972 q^{27} - 296 q^{28} + 478 q^{29} + 135 q^{30} - 574 q^{31} - 149 q^{32} + 1188 q^{33} + 276 q^{34} - 194 q^{35} + 1062 q^{36} - 12 q^{37} + 325 q^{38} + 39 q^{39} - 185 q^{40} + 900 q^{41} - 246 q^{42} - 1053 q^{43} - 1298 q^{44} - 45 q^{45} - 407 q^{46} - 653 q^{47} - 786 q^{48} + 753 q^{49} - 1520 q^{50} - 612 q^{51} + 60 q^{52} + 735 q^{53} - 54 q^{54} + 55 q^{55} - 809 q^{56} + 1293 q^{57} - 1399 q^{58} - 1127 q^{59} - 1062 q^{60} + 2196 q^{61} - 1795 q^{62} - 567 q^{63} - 2133 q^{64} + 1886 q^{65} + 66 q^{66} - 989 q^{67} + 10 q^{68} + 537 q^{69} - 2130 q^{70} + 61 q^{71} + 27 q^{72} - 1471 q^{73} - 122 q^{74} - 2133 q^{75} - 4064 q^{76} + 693 q^{77} - 993 q^{78} - 1853 q^{79} + 2197 q^{80} + 2916 q^{81} - 2566 q^{82} - 3523 q^{83} + 888 q^{84} - 449 q^{85} - 771 q^{86} - 1434 q^{87} - 33 q^{88} + 2209 q^{89} - 405 q^{90} - 1668 q^{91} - 1999 q^{92} + 1722 q^{93} - 2844 q^{94} + 1220 q^{95} + 447 q^{96} - 3622 q^{97} + 3846 q^{98} - 3564 q^{99}+O(q^{100}) \) 36 * q + 2 * q^2 - 108 * q^3 + 118 * q^4 - 5 * q^5 - 6 * q^6 - 63 * q^7 + 3 * q^8 + 324 * q^9 - 45 * q^10 - 396 * q^11 - 354 * q^12 - 13 * q^13 + 82 * q^14 + 15 * q^15 + 262 * q^16 + 204 * q^17 + 18 * q^18 - 431 * q^19 + 354 * q^20 + 189 * q^21 - 22 * q^22 - 179 * q^23 - 9 * q^24 + 711 * q^25 + 331 * q^26 - 972 * q^27 - 296 * q^28 + 478 * q^29 + 135 * q^30 - 574 * q^31 - 149 * q^32 + 1188 * q^33 + 276 * q^34 - 194 * q^35 + 1062 * q^36 - 12 * q^37 + 325 * q^38 + 39 * q^39 - 185 * q^40 + 900 * q^41 - 246 * q^42 - 1053 * q^43 - 1298 * q^44 - 45 * q^45 - 407 * q^46 - 653 * q^47 - 786 * q^48 + 753 * q^49 - 1520 * q^50 - 612 * q^51 + 60 * q^52 + 735 * q^53 - 54 * q^54 + 55 * q^55 - 809 * q^56 + 1293 * q^57 - 1399 * q^58 - 1127 * q^59 - 1062 * q^60 + 2196 * q^61 - 1795 * q^62 - 567 * q^63 - 2133 * q^64 + 1886 * q^65 + 66 * q^66 - 989 * q^67 + 10 * q^68 + 537 * q^69 - 2130 * q^70 + 61 * q^71 + 27 * q^72 - 1471 * q^73 - 122 * q^74 - 2133 * q^75 - 4064 * q^76 + 693 * q^77 - 993 * q^78 - 1853 * q^79 + 2197 * q^80 + 2916 * q^81 - 2566 * q^82 - 3523 * q^83 + 888 * q^84 - 449 * q^85 - 771 * q^86 - 1434 * q^87 - 33 * q^88 + 2209 * q^89 - 405 * q^90 - 1668 * q^91 - 1999 * q^92 + 1722 * q^93 - 2844 * q^94 + 1220 * q^95 + 447 * q^96 - 3622 * q^97 + 3846 * q^98 - 3564 * q^99

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