LMFDB - Embedded newform 2013.4.a.b.1.12

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			1.12
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)

$f(q)$	$=$	$q-2.13143 q^{2} -3.00000 q^{3} -3.45699 q^{4} -8.60507 q^{5} +6.39430 q^{6} +26.5144 q^{7} +24.4198 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.13143 q^{2} -3.00000 q^{3} -3.45699 q^{4} -8.60507 q^{5} +6.39430 q^{6} +26.5144 q^{7} +24.4198 q^{8} +9.00000 q^{9} +18.3411 q^{10} -11.0000 q^{11} +10.3710 q^{12} +1.37835 q^{13} -56.5137 q^{14} +25.8152 q^{15} -24.3933 q^{16} +29.8547 q^{17} -19.1829 q^{18} +55.9134 q^{19} +29.7477 q^{20} -79.5432 q^{21} +23.4458 q^{22} -108.204 q^{23} -73.2594 q^{24} -50.9527 q^{25} -2.93786 q^{26} -27.0000 q^{27} -91.6601 q^{28} +140.192 q^{29} -55.0234 q^{30} -71.2761 q^{31} -143.366 q^{32} +33.0000 q^{33} -63.6333 q^{34} -228.158 q^{35} -31.1129 q^{36} -311.303 q^{37} -119.176 q^{38} -4.13505 q^{39} -210.134 q^{40} +174.038 q^{41} +169.541 q^{42} -166.848 q^{43} +38.0269 q^{44} -77.4457 q^{45} +230.630 q^{46} +490.293 q^{47} +73.1798 q^{48} +360.014 q^{49} +108.602 q^{50} -89.5641 q^{51} -4.76494 q^{52} -451.516 q^{53} +57.5487 q^{54} +94.6558 q^{55} +647.477 q^{56} -167.740 q^{57} -298.810 q^{58} -29.5519 q^{59} -89.2430 q^{60} +61.0000 q^{61} +151.920 q^{62} +238.630 q^{63} +500.721 q^{64} -11.8608 q^{65} -70.3373 q^{66} -1009.73 q^{67} -103.207 q^{68} +324.613 q^{69} +486.305 q^{70} -87.9692 q^{71} +219.778 q^{72} +250.347 q^{73} +663.522 q^{74} +152.858 q^{75} -193.292 q^{76} -291.659 q^{77} +8.81357 q^{78} +160.231 q^{79} +209.906 q^{80} +81.0000 q^{81} -370.951 q^{82} +115.339 q^{83} +274.980 q^{84} -256.902 q^{85} +355.625 q^{86} -420.576 q^{87} -268.618 q^{88} +1492.46 q^{89} +165.070 q^{90} +36.5461 q^{91} +374.062 q^{92} +213.828 q^{93} -1045.03 q^{94} -481.139 q^{95} +430.098 q^{96} -661.549 q^{97} -767.346 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.13143	−0.753575	−0.376788	−	0.926300i	$-0.622971\pi$
$2$	−2.13143	−0.753575	−0.376788	+	0.926300i	$0.622971\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−3.45699	−0.432124
$5$	−8.60507	−0.769661	−0.384831	−	0.922987i	$-0.625740\pi$
$5$	−8.60507	−0.769661	−0.384831	+	0.922987i	$0.625740\pi$
$6$	6.39430	0.435077
$7$	26.5144	1.43164	0.715822	−	0.698283i	$-0.246052\pi$
$7$	26.5144	1.43164	0.715822	+	0.698283i	$0.246052\pi$
$8$	24.4198	1.07921
$9$	9.00000	0.333333
$10$	18.3411	0.579998
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	10.3710	0.249487
$13$	1.37835	0.0294065	0.0147033	−	0.999892i	$-0.495320\pi$
$13$	1.37835	0.0294065	0.0147033	+	0.999892i	$0.495320\pi$
$14$	−56.5137	−1.07885
$15$	25.8152	0.444364
$16$	−24.3933	−0.381145
$17$	29.8547	0.425931	0.212966	−	0.977060i	$-0.431688\pi$
$17$	29.8547	0.425931	0.212966	+	0.977060i	$0.431688\pi$
$18$	−19.1829	−0.251192
$19$	55.9134	0.675127	0.337564	−	0.941303i	$-0.390397\pi$
$19$	55.9134	0.675127	0.337564	+	0.941303i	$0.390397\pi$
$20$	29.7477	0.332589
$21$	−79.5432	−0.826560
$22$	23.4458	0.227212
$23$	−108.204	−0.980964	−0.490482	−	0.871451i	$-0.663179\pi$
$23$	−108.204	−0.980964	−0.490482	+	0.871451i	$0.663179\pi$
$24$	−73.2594	−0.623084
$25$	−50.9527	−0.407621
$26$	−2.93786	−0.0221600
$27$	−27.0000	−0.192450
$28$	−91.6601	−0.618648
$29$	140.192	0.897689	0.448845	−	0.893610i	$-0.351836\pi$
$29$	140.192	0.897689	0.448845	+	0.893610i	$0.351836\pi$
$30$	−55.0234	−0.334862
$31$	−71.2761	−0.412954	−0.206477	−	0.978451i	$-0.566200\pi$
$31$	−71.2761	−0.412954	−0.206477	+	0.978451i	$0.566200\pi$
$32$	−143.366	−0.791992
$33$	33.0000	0.174078
$34$	−63.6333	−0.320971
$35$	−228.158	−1.10188
$36$	−31.1129	−0.144041
$37$	−311.303	−1.38319	−0.691593	−	0.722287i	$-0.743091\pi$
$37$	−311.303	−1.38319	−0.691593	+	0.722287i	$0.743091\pi$
$38$	−119.176	−0.508759
$39$	−4.13505	−0.0169779
$40$	−210.134	−0.830629
$41$	174.038	0.662931	0.331466	−	0.943467i	$-0.392457\pi$
$41$	174.038	0.662931	0.331466	+	0.943467i	$0.392457\pi$
$42$	169.541	0.622875
$43$	−166.848	−0.591723	−0.295861	−	0.955231i	$-0.595607\pi$
$43$	−166.848	−0.591723	−0.295861	+	0.955231i	$0.595607\pi$
$44$	38.0269	0.130290
$45$	−77.4457	−0.256554
$46$	230.630	0.739231
$47$	490.293	1.52163	0.760815	−	0.648969i	$-0.224800\pi$
$47$	490.293	1.52163	0.760815	+	0.648969i	$0.224800\pi$
$48$	73.1798	0.220054
$49$	360.014	1.04960
$50$	108.602	0.307174
$51$	−89.5641	−0.245911
$52$	−4.76494	−0.0127073
$53$	−451.516	−1.17020	−0.585099	−	0.810962i	$-0.698944\pi$
$53$	−451.516	−1.17020	−0.585099	+	0.810962i	$0.698944\pi$
$54$	57.5487	0.145026
$55$	94.6558	0.232062
$56$	647.477	1.54505
$57$	−167.740	−0.389785
$58$	−298.810	−0.676477
$59$	−29.5519	−0.0652089	−0.0326045	−	0.999468i	$-0.510380\pi$
$59$	−29.5519	−0.0652089	−0.0326045	+	0.999468i	$0.510380\pi$
$60$	−89.2430	−0.192020
$61$	61.0000	0.128037
$61$	61.0000	0.128037
$62$	151.920	0.311192
$63$	238.630	0.477215
$64$	500.721	0.977971
$65$	−11.8608	−0.0226331
$66$	−70.3373	−0.131181
$67$	−1009.73	−1.84117	−0.920583	−	0.390546i	$-0.872286\pi$
$67$	−1009.73	−1.84117	−0.920583	+	0.390546i	$0.872286\pi$
$68$	−103.207	−0.184055
$69$	324.613	0.566360
$70$	486.305	0.830350
$71$	−87.9692	−0.147043	−0.0735213	−	0.997294i	$-0.523424\pi$
$71$	−87.9692	−0.147043	−0.0735213	+	0.997294i	$0.523424\pi$
$72$	219.778	0.359738
$73$	250.347	0.401383	0.200691	−	0.979654i	$-0.435681\pi$
$73$	250.347	0.401383	0.200691	+	0.979654i	$0.435681\pi$
$74$	663.522	1.04234
$75$	152.858	0.235340
$76$	−193.292	−0.291739
$77$	−291.659	−0.431657
$78$	8.81357	0.0127941
$79$	160.231	0.228195	0.114097	−	0.993470i	$-0.463602\pi$
$79$	160.231	0.228195	0.114097	+	0.993470i	$0.463602\pi$
$80$	209.906	0.293352
$81$	81.0000	0.111111
$82$	−370.951	−0.499569
$83$	115.339	0.152531	0.0762657	−	0.997088i	$-0.475700\pi$
$83$	115.339	0.152531	0.0762657	+	0.997088i	$0.475700\pi$
$84$	274.980	0.357176
$85$	−256.902	−0.327823
$86$	355.625	0.445908
$87$	−420.576	−0.518281
$88$	−268.618	−0.325395
$89$	1492.46	1.77753	0.888766	−	0.458361i	$-0.151563\pi$
$89$	1492.46	1.77753	0.888766	+	0.458361i	$0.151563\pi$
$90$	165.070	0.193333
$91$	36.5461	0.0420997
$92$	374.062	0.423898
$93$	213.828	0.238419
$94$	−1045.03	−1.14666
$95$	−481.139	−0.519619
$96$	430.098	0.457257
$97$	−661.549	−0.692476	−0.346238	−	0.938147i	$-0.612541\pi$
$97$	−661.549	−0.692476	−0.346238	+	0.938147i	$0.612541\pi$
$98$	−767.346	−0.790955
$99$	−99.0000	−0.100504
$100$	176.143	0.176143
$101$	339.132	0.334108	0.167054	−	0.985948i	$-0.446575\pi$
$101$	339.132	0.334108	0.167054	+	0.985948i	$0.446575\pi$
$102$	190.900	0.185313
$103$	−71.3372	−0.0682433	−0.0341216	−	0.999418i	$-0.510863\pi$
$103$	−71.3372	−0.0682433	−0.0341216	+	0.999418i	$0.510863\pi$
$104$	33.6590	0.0317359
$105$	684.475	0.636171
$106$	962.376	0.881833
$107$	1742.92	1.57472	0.787358	−	0.616496i	$-0.211448\pi$
$107$	1742.92	1.57472	0.787358	+	0.616496i	$0.211448\pi$
$108$	93.3388	0.0831623
$109$	1047.53	0.920505	0.460253	−	0.887788i	$-0.347759\pi$
$109$	1047.53	0.920505	0.460253	+	0.887788i	$0.347759\pi$
$110$	−201.753	−0.174876
$111$	933.909	0.798583
$112$	−646.773	−0.545663
$113$	131.315	0.109319	0.0546597	−	0.998505i	$-0.482593\pi$
$113$	131.315	0.109319	0.0546597	+	0.998505i	$0.482593\pi$
$114$	357.527	0.293732
$115$	931.107	0.755010
$116$	−484.642	−0.387913
$117$	12.4051	0.00980218
$118$	62.9878	0.0491398
$119$	791.580	0.609781
$120$	630.403	0.479564
$121$	121.000	0.0909091
$122$	−130.017	−0.0964854
$123$	−522.114	−0.382744
$124$	246.401	0.178447
$125$	1514.09	1.08339
$126$	−508.623	−0.359617
$127$	577.149	0.403257	0.201629	−	0.979462i	$-0.435377\pi$
$127$	577.149	0.403257	0.201629	+	0.979462i	$0.435377\pi$
$128$	79.6740	0.0550176
$129$	500.544	0.341631
$130$	25.2805	0.0170557
$131$	−372.623	−0.248521	−0.124260	−	0.992250i	$-0.539656\pi$
$131$	−372.623	−0.248521	−0.124260	+	0.992250i	$0.539656\pi$
$132$	−114.081	−0.0752231
$133$	1482.51	0.966541
$134$	2152.17	1.38746
$135$	232.337	0.148121
$136$	729.046	0.459671
$137$	155.972	0.0972672	0.0486336	−	0.998817i	$-0.484513\pi$
$137$	155.972	0.0972672	0.0486336	+	0.998817i	$0.484513\pi$
$138$	−691.891	−0.426795
$139$	1189.30	0.725721	0.362861	−	0.931843i	$-0.381800\pi$
$139$	1189.30	0.725721	0.362861	+	0.931843i	$0.381800\pi$
$140$	788.742	0.476149
$141$	−1470.88	−0.878513
$142$	187.500	0.110808
$143$	−15.1618	−0.00886641
$144$	−219.539	−0.127048
$145$	−1206.36	−0.690917
$146$	−533.599	−0.302472
$147$	−1080.04	−0.605989
$148$	1076.17	0.597708
$149$	−978.250	−0.537862	−0.268931	−	0.963160i	$-0.586670\pi$
$149$	−978.250	−0.537862	−0.268931	+	0.963160i	$0.586670\pi$
$150$	−325.807	−0.177347
$151$	−1456.74	−0.785086	−0.392543	−	0.919734i	$-0.628405\pi$
$151$	−1456.74	−0.785086	−0.392543	+	0.919734i	$0.628405\pi$
$152$	1365.39	0.728606
$153$	268.692	0.141977
$154$	621.651	0.325286
$155$	613.336	0.317835
$156$	14.2948	0.00733655
$157$	−2645.50	−1.34480	−0.672401	−	0.740187i	$-0.734737\pi$
$157$	−2645.50	−1.34480	−0.672401	+	0.740187i	$0.734737\pi$
$158$	−341.522	−0.171962
$159$	1354.55	0.675614
$160$	1233.67	0.609566
$161$	−2868.98	−1.40439
$162$	−172.646	−0.0837306
$163$	771.191	0.370579	0.185289	−	0.982684i	$-0.440678\pi$
$163$	771.191	0.370579	0.185289	+	0.982684i	$0.440678\pi$
$164$	−601.648	−0.286469
$165$	−283.967	−0.133981
$166$	−245.837	−0.114944
$167$	−3094.33	−1.43381	−0.716905	−	0.697171i	$-0.754442\pi$
$167$	−3094.33	−1.43381	−0.716905	+	0.697171i	$0.754442\pi$
$168$	−1942.43	−0.892035
$169$	−2195.10	−0.999135
$170$	547.569	0.247039
$171$	503.221	0.225042
$172$	576.792	0.255698
$173$	1830.25	0.804343	0.402171	−	0.915564i	$-0.368256\pi$
$173$	1830.25	0.804343	0.402171	+	0.915564i	$0.368256\pi$
$174$	896.429	0.390564
$175$	−1350.98	−0.583569
$176$	268.326	0.114919
$177$	88.6556	0.0376484
$178$	−3181.08	−1.33950
$179$	−1570.84	−0.655924	−0.327962	−	0.944691i	$-0.606362\pi$
$179$	−1570.84	−0.655924	−0.327962	+	0.944691i	$0.606362\pi$
$180$	267.729	0.110863
$181$	2732.50	1.12213	0.561063	−	0.827773i	$-0.310392\pi$
$181$	2732.50	1.12213	0.561063	+	0.827773i	$0.310392\pi$
$182$	−77.8956	−0.0317253
$183$	−183.000	−0.0739221
$184$	−2642.33	−1.05867
$185$	2678.79	1.06459
$186$	−455.761	−0.179667
$187$	−328.402	−0.128423
$188$	−1694.94	−0.657533
$189$	−715.889	−0.275520
$190$	1025.52	0.391572
$191$	2285.91	0.865983	0.432991	−	0.901398i	$-0.357458\pi$
$191$	2285.91	0.865983	0.432991	+	0.901398i	$0.357458\pi$
$192$	−1502.16	−0.564632
$193$	175.328	0.0653905	0.0326953	−	0.999465i	$-0.489591\pi$
$193$	175.328	0.0653905	0.0326953	+	0.999465i	$0.489591\pi$
$194$	1410.05	0.521833
$195$	35.5824	0.0130672
$196$	−1244.57	−0.453559
$197$	−4616.51	−1.66961	−0.834803	−	0.550549i	$-0.814419\pi$
$197$	−4616.51	−1.66961	−0.834803	+	0.550549i	$0.814419\pi$
$198$	211.012	0.0757372
$199$	1134.92	0.404281	0.202141	−	0.979356i	$-0.435210\pi$
$199$	1134.92	0.404281	0.202141	+	0.979356i	$0.435210\pi$
$200$	−1244.26	−0.439911
$201$	3029.19	1.06300
$202$	−722.838	−0.251776
$203$	3717.11	1.28517
$204$	309.622	0.106264
$205$	−1497.61	−0.510233
$206$	152.050	0.0514265
$207$	−973.840	−0.326988
$208$	−33.6224	−0.0112081
$209$	−615.047	−0.203558
$210$	−1458.91	−0.479403
$211$	−2121.06	−0.692036	−0.346018	−	0.938228i	$-0.612466\pi$
$211$	−2121.06	−0.692036	−0.346018	+	0.938228i	$0.612466\pi$
$212$	1560.89	0.505671
$213$	263.908	0.0848951
$214$	−3714.92	−1.18667
$215$	1435.74	0.455426
$216$	−659.335	−0.207695
$217$	−1889.84	−0.591203
$218$	−2232.74	−0.693670
$219$	−751.042	−0.231739
$220$	−327.224	−0.100279
$221$	41.1502	0.0125252
$222$	−1990.57	−0.601793
$223$	−628.301	−0.188673	−0.0943366	−	0.995540i	$-0.530073\pi$
$223$	−628.301	−0.188673	−0.0943366	+	0.995540i	$0.530073\pi$
$224$	−3801.26	−1.13385
$225$	−458.574	−0.135874
$226$	−279.890	−0.0823805
$227$	−788.557	−0.230565	−0.115283	−	0.993333i	$-0.536777\pi$
$227$	−788.557	−0.230565	−0.115283	+	0.993333i	$0.536777\pi$
$228$	579.877	0.168435
$229$	−2831.82	−0.817170	−0.408585	−	0.912720i	$-0.633978\pi$
$229$	−2831.82	−0.817170	−0.408585	+	0.912720i	$0.633978\pi$
$230$	−1984.59	−0.568957
$231$	874.976	0.249217
$232$	3423.46	0.968798
$233$	−315.337	−0.0886628	−0.0443314	−	0.999017i	$-0.514116\pi$
$233$	−315.337	−0.0886628	−0.0443314	+	0.999017i	$0.514116\pi$
$234$	−26.4407	−0.00738668
$235$	−4219.01	−1.17114
$236$	102.161	0.0281783
$237$	−480.693	−0.131748
$238$	−1687.20	−0.459516
$239$	1421.81	0.384808	0.192404	−	0.981316i	$-0.438372\pi$
$239$	1421.81	0.384808	0.192404	+	0.981316i	$0.438372\pi$
$240$	−629.718	−0.169367
$241$	−1992.45	−0.532552	−0.266276	−	0.963897i	$-0.585793\pi$
$241$	−1992.45	−0.532552	−0.266276	+	0.963897i	$0.585793\pi$
$242$	−257.903	−0.0685069
$243$	−243.000	−0.0641500
$244$	−210.877	−0.0553278
$245$	−3097.95	−0.807839
$246$	1112.85	0.288426
$247$	77.0681	0.0198532
$248$	−1740.55	−0.445665
$249$	−346.017	−0.0880640
$250$	−3227.17	−0.816417
$251$	−4570.91	−1.14945	−0.574727	−	0.818345i	$-0.694892\pi$
$251$	−4570.91	−1.14945	−0.574727	+	0.818345i	$0.694892\pi$
$252$	−824.941	−0.206216
$253$	1190.25	0.295772
$254$	−1230.15	−0.303885
$255$	770.706	0.189268
$256$	−4175.59	−1.01943
$257$	−3587.52	−0.870752	−0.435376	−	0.900249i	$-0.643385\pi$
$257$	−3587.52	−0.870752	−0.435376	+	0.900249i	$0.643385\pi$
$258$	−1066.88	−0.257445
$259$	−8254.02	−1.98023
$260$	41.0027	0.00978030
$261$	1261.73	0.299230
$262$	794.221	0.187279
$263$	−1999.77	−0.468863	−0.234432	−	0.972133i	$-0.575323\pi$
$263$	−1999.77	−0.468863	−0.234432	+	0.972133i	$0.575323\pi$
$264$	805.854	0.187867
$265$	3885.33	0.900656
$266$	−3159.87	−0.728362
$267$	−4477.38	−1.02626
$268$	3490.63	0.795612
$269$	5383.08	1.22012	0.610060	−	0.792355i	$-0.291145\pi$
$269$	5383.08	1.22012	0.610060	+	0.792355i	$0.291145\pi$
$270$	−495.211	−0.111621
$271$	2040.12	0.457300	0.228650	−	0.973509i	$-0.426569\pi$
$271$	2040.12	0.457300	0.228650	+	0.973509i	$0.426569\pi$
$272$	−728.253	−0.162341
$273$	−109.638	−0.0243063
$274$	−332.444	−0.0732982
$275$	560.480	0.122903
$276$	−1122.19	−0.244738
$277$	−3800.28	−0.824321	−0.412160	−	0.911111i	$-0.635226\pi$
$277$	−3800.28	−0.824321	−0.412160	+	0.911111i	$0.635226\pi$
$278$	−2534.92	−0.546886
$279$	−641.485	−0.137651
$280$	−5571.59	−1.18916
$281$	−4663.10	−0.989954	−0.494977	−	0.868906i	$-0.664824\pi$
$281$	−4663.10	−0.989954	−0.494977	+	0.868906i	$0.664824\pi$
$282$	3135.08	0.662026
$283$	−848.074	−0.178137	−0.0890685	−	0.996026i	$-0.528389\pi$
$283$	−848.074	−0.178137	−0.0890685	+	0.996026i	$0.528389\pi$
$284$	304.109	0.0635406
$285$	1443.42	0.300002
$286$	32.3164	0.00668151
$287$	4614.52	0.949081
$288$	−1290.29	−0.263997
$289$	−4021.70	−0.818583
$290$	2571.28	0.520658
$291$	1984.65	0.399801
$292$	−865.449	−0.173447
$293$	−2966.67	−0.591517	−0.295759	−	0.955263i	$-0.595572\pi$
$293$	−2966.67	−0.591517	−0.295759	+	0.955263i	$0.595572\pi$
$294$	2302.04	0.456658
$295$	254.296	0.0501888
$296$	−7601.96	−1.49275
$297$	297.000	0.0580259
$298$	2085.07	0.405319
$299$	−149.143	−0.0288468
$300$	−528.429	−0.101696
$301$	−4423.87	−0.847136
$302$	3104.95	0.591621
$303$	−1017.40	−0.192897
$304$	−1363.91	−0.257321
$305$	−524.910	−0.0985450
$306$	−572.700	−0.106990
$307$	2370.97	0.440777	0.220389	−	0.975412i	$-0.429267\pi$
$307$	2370.97	0.440777	0.220389	+	0.975412i	$0.429267\pi$
$308$	1008.26	0.186529
$309$	214.011	0.0394003
$310$	−1307.29	−0.239512
$311$	4458.32	0.812889	0.406444	−	0.913676i	$-0.366769\pi$
$311$	4458.32	0.812889	0.406444	+	0.913676i	$0.366769\pi$
$312$	−100.977	−0.0183228
$313$	8265.91	1.49271	0.746353	−	0.665551i	$-0.231803\pi$
$313$	8265.91	1.49271	0.746353	+	0.665551i	$0.231803\pi$
$314$	5638.71	1.01341
$315$	−2053.43	−0.367294
$316$	−553.917	−0.0986085
$317$	7110.01	1.25974	0.629871	−	0.776700i	$-0.283108\pi$
$317$	7110.01	1.25974	0.629871	+	0.776700i	$0.283108\pi$
$318$	−2887.13	−0.509126
$319$	−1542.11	−0.270663
$320$	−4308.74	−0.752706
$321$	−5228.77	−0.909163
$322$	6115.03	1.05831
$323$	1669.28	0.287558
$324$	−280.016	−0.0480138
$325$	−70.2306	−0.0119867
$326$	−1643.74	−0.279259
$327$	−3142.59	−0.531454
$328$	4249.98	0.715444
$329$	12999.8	2.17843
$330$	605.258	0.100965
$331$	1576.86	0.261849	0.130924	−	0.991392i	$-0.458205\pi$
$331$	1576.86	0.261849	0.130924	+	0.991392i	$0.458205\pi$
$332$	−398.726	−0.0659125
$333$	−2801.73	−0.461062
$334$	6595.35	1.08048
$335$	8688.80	1.41707
$336$	1940.32	0.315039
$337$	−875.077	−0.141450	−0.0707248	−	0.997496i	$-0.522531\pi$
$337$	−875.077	−0.141450	−0.0707248	+	0.997496i	$0.522531\pi$
$338$	4678.71	0.752924
$339$	−393.946	−0.0631156
$340$	888.108	0.141660
$341$	784.037	0.124510
$342$	−1072.58	−0.169586
$343$	451.116	0.0710144
$344$	−4074.40	−0.638595
$345$	−2793.32	−0.435905
$346$	−3901.05	−0.606133
$347$	−185.705	−0.0287295	−0.0143648	−	0.999897i	$-0.504573\pi$
$347$	−185.705	−0.0287295	−0.0143648	+	0.999897i	$0.504573\pi$
$348$	1453.93	0.223962
$349$	−5780.18	−0.886551	−0.443275	−	0.896386i	$-0.646184\pi$
$349$	−5780.18	−0.886551	−0.443275	+	0.896386i	$0.646184\pi$
$350$	2879.52	0.439763
$351$	−37.2154	−0.00565929
$352$	1577.02	0.238795
$353$	9895.71	1.49206	0.746028	−	0.665915i	$-0.231959\pi$
$353$	9895.71	1.49206	0.746028	+	0.665915i	$0.231959\pi$
$354$	−188.963	−0.0283709
$355$	756.981	0.113173
$356$	−5159.42	−0.768114
$357$	−2374.74	−0.352057
$358$	3348.15	0.494288
$359$	−752.327	−0.110603	−0.0553013	−	0.998470i	$-0.517612\pi$
$359$	−752.327	−0.110603	−0.0553013	+	0.998470i	$0.517612\pi$
$360$	−1891.21	−0.276876
$361$	−3732.69	−0.544203
$362$	−5824.14	−0.845607
$363$	−363.000	−0.0524864
$364$	−126.340	−0.0181923
$365$	−2154.26	−0.308929
$366$	390.052	0.0557059
$367$	4857.50	0.690898	0.345449	−	0.938438i	$-0.387727\pi$
$367$	4857.50	0.690898	0.345449	+	0.938438i	$0.387727\pi$
$368$	2639.46	0.373889
$369$	1566.34	0.220977
$370$	−5709.65	−0.802245
$371$	−11971.7	−1.67531
$372$	−739.203	−0.103027
$373$	−11996.2	−1.66525	−0.832626	−	0.553835i	$-0.813164\pi$
$373$	−11996.2	−1.66525	−0.832626	+	0.553835i	$0.813164\pi$
$374$	699.966	0.0967765
$375$	−4542.26	−0.625497
$376$	11972.9	1.64216
$377$	193.233	0.0263979
$378$	1525.87	0.207625
$379$	−6442.34	−0.873141	−0.436571	−	0.899670i	$-0.643807\pi$
$379$	−6442.34	−0.873141	−0.436571	+	0.899670i	$0.643807\pi$
$380$	1663.29	0.224540
$381$	−1731.45	−0.232821
$382$	−4872.26	−0.652583
$383$	2336.37	0.311704	0.155852	−	0.987780i	$-0.450188\pi$
$383$	2336.37	0.311704	0.155852	+	0.987780i	$0.450188\pi$
$384$	−239.022	−0.0317644
$385$	2509.74	0.332230
$386$	−373.700	−0.0492767
$387$	−1501.63	−0.197241
$388$	2286.97	0.299235
$389$	−4451.00	−0.580140	−0.290070	−	0.957005i	$-0.593679\pi$
$389$	−4451.00	−0.580140	−0.290070	+	0.957005i	$0.593679\pi$
$390$	−75.8415	−0.00984713
$391$	−3230.41	−0.417823
$392$	8791.47	1.13275
$393$	1117.87	0.143484
$394$	9839.77	1.25817
$395$	−1378.80	−0.175633
$396$	342.242	0.0434301
$397$	−4434.10	−0.560557	−0.280278	−	0.959919i	$-0.590427\pi$
$397$	−4434.10	−0.560557	−0.280278	+	0.959919i	$0.590427\pi$
$398$	−2419.00	−0.304657
$399$	−4447.53	−0.558033
$400$	1242.90	0.155363
$401$	−4195.73	−0.522505	−0.261253	−	0.965270i	$-0.584136\pi$
$401$	−4195.73	−0.522505	−0.261253	+	0.965270i	$0.584136\pi$
$402$	−6456.52	−0.801049
$403$	−98.2433	−0.0121435
$404$	−1172.38	−0.144376
$405$	−697.011	−0.0855179
$406$	−7922.76	−0.968473
$407$	3424.33	0.417047
$408$	−2187.14	−0.265391
$409$	3733.82	0.451408	0.225704	−	0.974196i	$-0.427532\pi$
$409$	3733.82	0.451408	0.225704	+	0.974196i	$0.427532\pi$
$410$	3192.06	0.384499
$411$	−467.917	−0.0561572
$412$	246.612	0.0294896
$413$	−783.550	−0.0933559
$414$	2075.67	0.246410
$415$	−992.501	−0.117397
$416$	−197.608	−0.0232898
$417$	−3567.91	−0.418995
$418$	1310.93	0.153397
$419$	2020.16	0.235540	0.117770	−	0.993041i	$-0.462425\pi$
$419$	2020.16	0.235540	0.117770	+	0.993041i	$0.462425\pi$
$420$	−2366.23	−0.274905
$421$	201.105	0.0232809	0.0116404	−	0.999932i	$-0.496295\pi$
$421$	201.105	0.0232809	0.0116404	+	0.999932i	$0.496295\pi$
$422$	4520.89	0.521501
$423$	4412.64	0.507210
$424$	−11025.9	−1.26289
$425$	−1521.18	−0.173619
$426$	−562.501	−0.0639748
$427$	1617.38	0.183303
$428$	−6025.27	−0.680473
$429$	45.4855	0.00511902
$430$	−3060.18	−0.343198
$431$	3287.37	0.367395	0.183697	−	0.982983i	$-0.441193\pi$
$431$	3287.37	0.367395	0.183697	+	0.982983i	$0.441193\pi$
$432$	658.618	0.0733513
$433$	6378.36	0.707908	0.353954	−	0.935263i	$-0.384837\pi$
$433$	6378.36	0.707908	0.353954	+	0.935263i	$0.384837\pi$
$434$	4028.08	0.445516
$435$	3619.09	0.398901
$436$	−3621.30	−0.397772
$437$	−6050.08	−0.662276
$438$	1600.80	0.174632
$439$	868.295	0.0943997	0.0471998	−	0.998885i	$-0.484970\pi$
$439$	868.295	0.0943997	0.0471998	+	0.998885i	$0.484970\pi$
$440$	2311.48	0.250444
$441$	3240.13	0.349868
$442$	−87.7088	−0.00943865
$443$	−5874.15	−0.629998	−0.314999	−	0.949092i	$-0.602004\pi$
$443$	−5874.15	−0.629998	−0.314999	+	0.949092i	$0.602004\pi$
$444$	−3228.52	−0.345087
$445$	−12842.7	−1.36810
$446$	1339.18	0.142179
$447$	2934.75	0.310534
$448$	13276.3	1.40011
$449$	−10212.6	−1.07341	−0.536707	−	0.843769i	$-0.680332\pi$
$449$	−10212.6	−1.07341	−0.536707	+	0.843769i	$0.680332\pi$
$450$	977.420	0.102391
$451$	−1914.42	−0.199881
$452$	−453.956	−0.0472396
$453$	4370.22	0.453269
$454$	1680.76	0.173748
$455$	−314.482	−0.0324025
$456$	−4096.18	−0.420661
$457$	8431.36	0.863025	0.431513	−	0.902107i	$-0.357980\pi$
$457$	8431.36	0.863025	0.431513	+	0.902107i	$0.357980\pi$
$458$	6035.83	0.615799
$459$	−806.077	−0.0819705
$460$	−3218.83	−0.326258
$461$	−9961.01	−1.00636	−0.503178	−	0.864183i	$-0.667836\pi$
$461$	−9961.01	−1.00636	−0.503178	+	0.864183i	$0.667836\pi$
$462$	−1864.95	−0.187804
$463$	−12339.9	−1.23863	−0.619314	−	0.785144i	$-0.712589\pi$
$463$	−12339.9	−1.23863	−0.619314	+	0.785144i	$0.712589\pi$
$464$	−3419.74	−0.342150
$465$	−1840.01	−0.183502
$466$	672.120	0.0668141
$467$	5604.88	0.555381	0.277690	−	0.960671i	$-0.410431\pi$
$467$	5604.88	0.555381	0.277690	+	0.960671i	$0.410431\pi$
$468$	−42.8845	−0.00423576
$469$	−26772.4	−2.63589
$470$	8992.53	0.882542
$471$	7936.51	0.776422
$472$	−721.651	−0.0703743
$473$	1835.33	0.178411
$474$	1024.56	0.0992823
$475$	−2848.94	−0.275196
$476$	−2736.49	−0.263501
$477$	−4063.64	−0.390066
$478$	−3030.49	−0.289982
$479$	10961.8	1.04563	0.522814	−	0.852446i	$-0.324882\pi$
$479$	10961.8	1.04563	0.522814	+	0.852446i	$0.324882\pi$
$480$	−3701.02	−0.351933
$481$	−429.084	−0.0406747
$482$	4246.78	0.401318
$483$	8606.93	0.810826
$484$	−418.296	−0.0392840
$485$	5692.68	0.532972
$486$	517.938	0.0483419
$487$	−11310.5	−1.05242	−0.526211	−	0.850354i	$-0.676388\pi$
$487$	−11310.5	−1.05242	−0.526211	+	0.850354i	$0.676388\pi$
$488$	1489.61	0.138179
$489$	−2313.57	−0.213954
$490$	6603.07	0.608768
$491$	8629.58	0.793172	0.396586	−	0.917997i	$-0.370195\pi$
$491$	8629.58	0.793172	0.396586	+	0.917997i	$0.370195\pi$
$492$	1804.95	0.165393
$493$	4185.39	0.382354
$494$	−164.266	−0.0149608
$495$	851.902	0.0773539
$496$	1738.66	0.157395
$497$	−2332.45	−0.210513
$498$	737.512	0.0663629
$499$	1977.90	0.177441	0.0887203	−	0.996057i	$-0.471722\pi$
$499$	1977.90	0.177441	0.0887203	+	0.996057i	$0.471722\pi$
$500$	−5234.18	−0.468160
$501$	9282.98	0.827811
$502$	9742.58	0.866201
$503$	1507.85	0.133661	0.0668305	−	0.997764i	$-0.478711\pi$
$503$	1507.85	0.133661	0.0668305	+	0.997764i	$0.478711\pi$
$504$	5827.29	0.515016
$505$	−2918.26	−0.257150
$506$	−2536.94	−0.222886
$507$	6585.30	0.576851
$508$	−1995.20	−0.174257
$509$	−15551.6	−1.35425	−0.677125	−	0.735868i	$-0.736774\pi$
$509$	−15551.6	−1.35425	−0.677125	+	0.735868i	$0.736774\pi$
$510$	−1642.71	−0.142628
$511$	6637.82	0.574637
$512$	8262.59	0.713200
$513$	−1509.66	−0.129928
$514$	7646.56	0.656178
$515$	613.862	0.0525242
$516$	−1730.38	−0.147627
$517$	−5393.22	−0.458788
$518$	17592.9	1.49225
$519$	−5490.75	−0.464388
$520$	−289.638	−0.0244259
$521$	9111.98	0.766225	0.383112	−	0.923702i	$-0.374852\pi$
$521$	9111.98	0.766225	0.383112	+	0.923702i	$0.374852\pi$
$522$	−2689.29	−0.225492
$523$	−16108.0	−1.34676	−0.673378	−	0.739298i	$-0.735157\pi$
$523$	−16108.0	−1.34676	−0.673378	+	0.739298i	$0.735157\pi$
$524$	1288.16	0.107392
$525$	4052.94	0.336924
$526$	4262.37	0.353324
$527$	−2127.93	−0.175890
$528$	−804.978	−0.0663488
$529$	−458.805	−0.0377090
$530$	−8281.32	−0.678712
$531$	−265.967	−0.0217363
$532$	−5125.03	−0.417666
$533$	239.885	0.0194945
$534$	9543.23	0.773363
$535$	−14998.0	−1.21200
$536$	−24657.4	−1.98701
$537$	4712.53	0.378698
$538$	−11473.7	−0.919452
$539$	−3960.15	−0.316467
$540$	−803.187	−0.0640068
$541$	8542.15	0.678846	0.339423	−	0.940634i	$-0.389768\pi$
$541$	8542.15	0.678846	0.339423	+	0.940634i	$0.389768\pi$
$542$	−4348.37	−0.344610
$543$	−8197.49	−0.647860
$544$	−4280.15	−0.337334
$545$	−9014.06	−0.708477
$546$	233.687	0.0183166
$547$	−9919.34	−0.775357	−0.387679	−	0.921795i	$-0.626723\pi$
$547$	−9919.34	−0.775357	−0.387679	+	0.921795i	$0.626723\pi$
$548$	−539.195	−0.0420315
$549$	549.000	0.0426790
$550$	−1194.62	−0.0926163
$551$	7838.61	0.606054
$552$	7926.99	0.611223
$553$	4248.43	0.326694
$554$	8100.05	0.621188
$555$	−8036.36	−0.614639
$556$	−4111.41	−0.313602
$557$	−20036.9	−1.52422	−0.762110	−	0.647448i	$-0.775836\pi$
$557$	−20036.9	−1.52422	−0.762110	+	0.647448i	$0.775836\pi$
$558$	1367.28	0.103731
$559$	−229.975	−0.0174005
$560$	5565.53	0.419976
$561$	985.205	0.0741451
$562$	9939.08	0.746005
$563$	−5906.96	−0.442182	−0.221091	−	0.975253i	$-0.570962\pi$
$563$	−5906.96	−0.442182	−0.221091	+	0.975253i	$0.570962\pi$
$564$	5084.82	0.379627
$565$	−1129.98	−0.0841390
$566$	1807.61	0.134240
$567$	2147.67	0.159072
$568$	−2148.19	−0.158690
$569$	−8488.32	−0.625393	−0.312697	−	0.949853i	$-0.601232\pi$
$569$	−8488.32	−0.625393	−0.312697	+	0.949853i	$0.601232\pi$
$570$	−3076.55	−0.226074
$571$	−18982.7	−1.39125	−0.695624	−	0.718406i	$-0.744872\pi$
$571$	−18982.7	−1.39125	−0.695624	+	0.718406i	$0.744872\pi$
$572$	52.4143	0.00383139
$573$	−6857.73	−0.499975
$574$	−9835.54	−0.715204
$575$	5513.31	0.399862
$576$	4506.49	0.325990
$577$	5814.27	0.419499	0.209750	−	0.977755i	$-0.432735\pi$
$577$	5814.27	0.419499	0.209750	+	0.977755i	$0.432735\pi$
$578$	8571.98	0.616864
$579$	−525.983	−0.0377532
$580$	4170.38	0.298562
$581$	3058.15	0.218371
$582$	−4230.14	−0.301280
$583$	4966.68	0.352828
$584$	6113.44	0.433178
$585$	−106.747	−0.00754436
$586$	6323.25	0.445753
$587$	21561.6	1.51608	0.758041	−	0.652206i	$-0.226156\pi$
$587$	21561.6	1.51608	0.758041	+	0.652206i	$0.226156\pi$
$588$	3733.70	0.261862
$589$	−3985.29	−0.278796
$590$	−542.015	−0.0378210
$591$	13849.5	0.963948
$592$	7593.70	0.527194
$593$	−18179.5	−1.25892	−0.629462	−	0.777031i	$-0.716725\pi$
$593$	−18179.5	−1.25892	−0.629462	+	0.777031i	$0.716725\pi$
$594$	−633.036	−0.0437269
$595$	−6811.60	−0.469325
$596$	3381.80	0.232423
$597$	−3404.75	−0.233412
$598$	317.889	0.0217382
$599$	3571.09	0.243591	0.121795	−	0.992555i	$-0.461135\pi$
$599$	3571.09	0.243591	0.121795	+	0.992555i	$0.461135\pi$
$600$	3732.77	0.253983
$601$	−16636.6	−1.12915	−0.564577	−	0.825381i	$-0.690961\pi$
$601$	−16636.6	−1.12915	−0.564577	+	0.825381i	$0.690961\pi$
$602$	9429.19	0.638381
$603$	−9087.57	−0.613722
$604$	5035.94	0.339254
$605$	−1041.21	−0.0699692
$606$	2168.51	0.145363
$607$	16028.9	1.07182	0.535909	−	0.844276i	$-0.319969\pi$
$607$	16028.9	1.07182	0.535909	+	0.844276i	$0.319969\pi$
$608$	−8016.08	−0.534695
$609$	−11151.3	−0.741994
$610$	1118.81	0.0742611
$611$	675.794	0.0447459
$612$	−928.867	−0.0613517
$613$	2445.06	0.161101	0.0805506	−	0.996751i	$-0.474332\pi$
$613$	2445.06	0.161101	0.0805506	+	0.996751i	$0.474332\pi$
$614$	−5053.57	−0.332159
$615$	4492.83	0.294583
$616$	−7122.25	−0.465850
$617$	−19816.4	−1.29300	−0.646498	−	0.762915i	$-0.723767\pi$
$617$	−19816.4	−1.29300	−0.646498	+	0.762915i	$0.723767\pi$
$618$	−456.151	−0.0296911
$619$	13178.8	0.855739	0.427869	−	0.903841i	$-0.359264\pi$
$619$	13178.8	0.855739	0.427869	+	0.903841i	$0.359264\pi$
$620$	−2120.30	−0.137344
$621$	2921.52	0.188787
$622$	−9502.62	−0.612573
$623$	39571.7	2.54479
$624$	100.867	0.00647103
$625$	−6659.74	−0.426223
$626$	−17618.2	−1.12487
$627$	1845.14	0.117525
$628$	9145.48	0.581122
$629$	−9293.86	−0.589142
$630$	4376.74	0.276783
$631$	−6319.77	−0.398710	−0.199355	−	0.979927i	$-0.563885\pi$
$631$	−6319.77	−0.398710	−0.199355	+	0.979927i	$0.563885\pi$
$632$	3912.81	0.246271
$633$	6363.17	0.399547
$634$	−15154.5	−0.949310
$635$	−4966.41	−0.310372
$636$	−4682.66	−0.291949
$637$	496.225	0.0308652
$638$	3286.91	0.203965
$639$	−791.723	−0.0490142
$640$	−685.601	−0.0423449
$641$	−1981.37	−0.122090	−0.0610448	−	0.998135i	$-0.519443\pi$
$641$	−1981.37	−0.122090	−0.0610448	+	0.998135i	$0.519443\pi$
$642$	11144.8	0.685123
$643$	−9257.56	−0.567780	−0.283890	−	0.958857i	$-0.591625\pi$
$643$	−9257.56	−0.567780	−0.283890	+	0.958857i	$0.591625\pi$
$644$	9918.03	0.606871
$645$	−4307.22	−0.262940
$646$	−3557.95	−0.216696
$647$	−9410.11	−0.571793	−0.285896	−	0.958261i	$-0.592291\pi$
$647$	−9410.11	−0.571793	−0.285896	+	0.958261i	$0.592291\pi$
$648$	1978.00	0.119913
$649$	325.071	0.0196612
$650$	149.692	0.00903291
$651$	5669.53	0.341331
$652$	−2666.00	−0.160136
$653$	9467.66	0.567379	0.283689	−	0.958916i	$-0.408442\pi$
$653$	9467.66	0.567379	0.283689	+	0.958916i	$0.408442\pi$
$654$	6698.21	0.400491
$655$	3206.45	0.191277
$656$	−4245.36	−0.252673
$657$	2253.13	0.133794
$658$	−27708.3	−1.64161
$659$	−10775.7	−0.636968	−0.318484	−	0.947928i	$-0.603174\pi$
$659$	−10775.7	−0.636968	−0.318484	+	0.947928i	$0.603174\pi$
$660$	981.673	0.0578963
$661$	3015.37	0.177435	0.0887173	−	0.996057i	$-0.471723\pi$
$661$	3015.37	0.177435	0.0887173	+	0.996057i	$0.471723\pi$
$662$	−3360.97	−0.197323
$663$	−123.451	−0.00723140
$664$	2816.56	0.164614
$665$	−12757.1	−0.743909
$666$	5971.70	0.347445
$667$	−15169.4	−0.880601
$668$	10697.1	0.619584
$669$	1884.90	0.108931
$670$	−18519.6	−1.06787
$671$	−671.000	−0.0386046
$672$	11403.8	0.654629
$673$	−4797.33	−0.274775	−0.137387	−	0.990517i	$-0.543871\pi$
$673$	−4797.33	−0.274775	−0.137387	+	0.990517i	$0.543871\pi$
$674$	1865.17	0.106593
$675$	1375.72	0.0784468
$676$	7588.44	0.431750
$677$	16614.1	0.943178	0.471589	−	0.881819i	$-0.343681\pi$
$677$	16614.1	0.943178	0.471589	+	0.881819i	$0.343681\pi$
$678$	839.669	0.0475624
$679$	−17540.6	−0.991379
$680$	−6273.50	−0.353791
$681$	2365.67	0.133117
$682$	−1671.12	−0.0938279
$683$	13287.4	0.744403	0.372202	−	0.928152i	$-0.378603\pi$
$683$	13287.4	0.744403	0.372202	+	0.928152i	$0.378603\pi$
$684$	−1739.63	−0.0972462
$685$	−1342.15	−0.0748628
$686$	−961.523	−0.0535147
$687$	8495.46	0.471793
$688$	4069.96	0.225532
$689$	−622.346	−0.0344115
$690$	5953.78	0.328488
$691$	−24415.6	−1.34416	−0.672079	−	0.740480i	$-0.734598\pi$
$691$	−24415.6	−1.34416	−0.672079	+	0.740480i	$0.734598\pi$
$692$	−6327.16	−0.347576
$693$	−2624.93	−0.143886
$694$	395.817	0.0216499
$695$	−10234.0	−0.558560
$696$	−10270.4	−0.559336
$697$	5195.85	0.282363
$698$	12320.1	0.668083
$699$	946.012	0.0511895
$700$	4670.33	0.252174
$701$	7814.74	0.421054	0.210527	−	0.977588i	$-0.432482\pi$
$701$	7814.74	0.421054	0.210527	+	0.977588i	$0.432482\pi$
$702$	79.3222	0.00426470
$703$	−17406.0	−0.933827
$704$	−5507.93	−0.294869
$705$	12657.0	0.676158
$706$	−21092.0	−1.12438
$707$	8991.89	0.478324
$708$	−306.482	−0.0162688
$709$	24892.0	1.31853	0.659266	−	0.751910i	$-0.270867\pi$
$709$	24892.0	1.31853	0.659266	+	0.751910i	$0.270867\pi$
$710$	−1613.46	−0.0852844
$711$	1442.08	0.0760650
$712$	36445.6	1.91834
$713$	7712.39	0.405093
$714$	5061.60	0.265302
$715$	130.469	0.00682413
$716$	5430.39	0.283440
$717$	−4265.42	−0.222169
$718$	1603.54	0.0833474
$719$	35519.6	1.84236	0.921181	−	0.389134i	$-0.127226\pi$
$719$	35519.6	1.84236	0.921181	+	0.389134i	$0.127226\pi$
$720$	1889.15	0.0977841
$721$	−1891.46	−0.0977001
$722$	7955.98	0.410098
$723$	5977.35	0.307469
$724$	−9446.23	−0.484898
$725$	−7143.16	−0.365917
$726$	773.710	0.0395525
$727$	−11031.7	−0.562783	−0.281391	−	0.959593i	$-0.590796\pi$
$727$	−11031.7	−0.562783	−0.281391	+	0.959593i	$0.590796\pi$
$728$	892.449	0.0454346
$729$	729.000	0.0370370
$730$	4591.66	0.232801
$731$	−4981.19	−0.252033
$732$	632.630	0.0319435
$733$	−2581.95	−0.130104	−0.0650521	−	0.997882i	$-0.520721\pi$
$733$	−2581.95	−0.130104	−0.0650521	+	0.997882i	$0.520721\pi$
$734$	−10353.4	−0.520644
$735$	9293.84	0.466406
$736$	15512.8	0.776916
$737$	11107.0	0.555133
$738$	−3338.56	−0.166523
$739$	−6533.58	−0.325226	−0.162613	−	0.986690i	$-0.551992\pi$
$739$	−6533.58	−0.325226	−0.162613	+	0.986690i	$0.551992\pi$
$740$	−9260.54	−0.460033
$741$	−231.204	−0.0114622
$742$	25516.8	1.26247
$743$	7505.93	0.370614	0.185307	−	0.982681i	$-0.440672\pi$
$743$	7505.93	0.370614	0.185307	+	0.982681i	$0.440672\pi$
$744$	5221.65	0.257305
$745$	8417.91	0.413971
$746$	25569.1	1.25489
$747$	1038.05	0.0508438
$748$	1135.28	0.0554947
$749$	46212.6	2.25443
$750$	9681.52	0.471359
$751$	−10460.1	−0.508248	−0.254124	−	0.967172i	$-0.581787\pi$
$751$	−10460.1	−0.508248	−0.254124	+	0.967172i	$0.581787\pi$
$752$	−11959.8	−0.579961
$753$	13712.7	0.663638
$754$	−411.864	−0.0198928
$755$	12535.4	0.604250
$756$	2474.82	0.119059
$757$	−10763.3	−0.516774	−0.258387	−	0.966042i	$-0.583191\pi$
$757$	−10763.3	−0.516774	−0.258387	+	0.966042i	$0.583191\pi$
$758$	13731.4	0.657978
$759$	−3570.75	−0.170764
$760$	−11749.3	−0.560780
$761$	8459.85	0.402982	0.201491	−	0.979490i	$-0.435421\pi$
$761$	8459.85	0.402982	0.201491	+	0.979490i	$0.435421\pi$
$762$	3690.46	0.175448
$763$	27774.6	1.31784
$764$	−7902.37	−0.374212
$765$	−2312.12	−0.109274
$766$	−4979.81	−0.234893
$767$	−40.7328	−0.00191757
$768$	12526.8	0.588568
$769$	−12632.7	−0.592390	−0.296195	−	0.955128i	$-0.595718\pi$
$769$	−12632.7	−0.592390	−0.296195	+	0.955128i	$0.595718\pi$
$770$	−5349.35	−0.250360
$771$	10762.6	0.502729
$772$	−606.107	−0.0282568
$773$	−9051.50	−0.421164	−0.210582	−	0.977576i	$-0.567536\pi$
$773$	−9051.50	−0.421164	−0.210582	+	0.977576i	$0.567536\pi$
$774$	3200.63	0.148636
$775$	3631.71	0.168329
$776$	−16154.9	−0.747329
$777$	24762.1	1.14329
$778$	9487.00	0.437179
$779$	9731.06	0.447563
$780$	−123.008	−0.00564666
$781$	967.661	0.0443350
$782$	6885.40	0.314861
$783$	−3785.18	−0.172760
$784$	−8781.92	−0.400051
$785$	22764.7	1.03504
$786$	−2382.66	−0.108126
$787$	7061.94	0.319861	0.159931	−	0.987128i	$-0.448873\pi$
$787$	7061.94	0.319861	0.159931	+	0.987128i	$0.448873\pi$
$788$	15959.2	0.721477
$789$	5999.31	0.270698
$790$	2938.82	0.132353
$791$	3481.75	0.156507
$792$	−2417.56	−0.108465
$793$	84.0793	0.00376512
$794$	9450.99	0.422422
$795$	−11656.0	−0.519994
$796$	−3923.39	−0.174700
$797$	−19236.3	−0.854939	−0.427469	−	0.904030i	$-0.640595\pi$
$797$	−19236.3	−0.854939	−0.427469	+	0.904030i	$0.640595\pi$
$798$	9479.62	0.420520
$799$	14637.5	0.648109
$800$	7304.88	0.322833
$801$	13432.1	0.592511
$802$	8942.91	0.393747
$803$	−2753.82	−0.121022
$804$	−10471.9	−0.459347
$805$	24687.8	1.08091
$806$	209.399	0.00915108
$807$	−16149.2	−0.704437
$808$	8281.54	0.360574
$809$	−31172.7	−1.35473	−0.677363	−	0.735649i	$-0.736877\pi$
$809$	−31172.7	−1.35473	−0.677363	+	0.735649i	$0.736877\pi$
$810$	1485.63	0.0644442
$811$	−33473.4	−1.44933	−0.724666	−	0.689100i	$-0.758006\pi$
$811$	−33473.4	−1.44933	−0.724666	+	0.689100i	$0.758006\pi$
$812$	−12850.0	−0.555353
$813$	−6120.35	−0.264022
$814$	−7298.74	−0.314276
$815$	−6636.16	−0.285220
$816$	2184.76	0.0937278
$817$	−9329.03	−0.399488
$818$	−7958.40	−0.340170
$819$	328.915	0.0140332
$820$	5177.23	0.220484
$821$	−19936.1	−0.847473	−0.423737	−	0.905785i	$-0.639282\pi$
$821$	−19936.1	−0.847473	−0.423737	+	0.905785i	$0.639282\pi$
$822$	997.333	0.0423187
$823$	−11076.7	−0.469148	−0.234574	−	0.972098i	$-0.575369\pi$
$823$	−11076.7	−0.469148	−0.234574	+	0.972098i	$0.575369\pi$
$824$	−1742.04	−0.0736491
$825$	−1681.44	−0.0709578
$826$	1670.09	0.0703507
$827$	2164.78	0.0910240	0.0455120	−	0.998964i	$-0.485508\pi$
$827$	2164.78	0.0910240	0.0455120	+	0.998964i	$0.485508\pi$
$828$	3366.56	0.141299
$829$	10893.4	0.456384	0.228192	−	0.973616i	$-0.426719\pi$
$829$	10893.4	0.456384	0.228192	+	0.973616i	$0.426719\pi$
$830$	2115.45	0.0884678
$831$	11400.8	0.475922
$832$	690.168	0.0287587
$833$	10748.1	0.447059
$834$	7604.75	0.315745
$835$	26626.9	1.10355
$836$	2126.21	0.0879625
$837$	1924.46	0.0794730
$838$	−4305.83	−0.177497
$839$	7789.61	0.320533	0.160267	−	0.987074i	$-0.448765\pi$
$839$	7789.61	0.320533	0.160267	+	0.987074i	$0.448765\pi$
$840$	16714.8	0.686564
$841$	−4735.22	−0.194154
$842$	−428.641	−0.0175439
$843$	13989.3	0.571550
$844$	7332.48	0.299045
$845$	18889.0	0.768996
$846$	−9405.24	−0.382221
$847$	3208.24	0.130149
$848$	11013.9	0.446015
$849$	2544.22	0.102847
$850$	3242.29	0.130835
$851$	33684.4	1.35686
$852$	−912.326	−0.0366852
$853$	17340.5	0.696046	0.348023	−	0.937486i	$-0.386853\pi$
$853$	17340.5	0.696046	0.348023	+	0.937486i	$0.386853\pi$
$854$	−3447.34	−0.138133
$855$	−4330.25	−0.173206
$856$	42561.8	1.69946
$857$	−17451.0	−0.695584	−0.347792	−	0.937572i	$-0.613069\pi$
$857$	−17451.0	−0.695584	−0.347792	+	0.937572i	$0.613069\pi$
$858$	−96.9493	−0.00385757
$859$	−12793.6	−0.508161	−0.254081	−	0.967183i	$-0.581773\pi$
$859$	−12793.6	−0.508161	−0.254081	+	0.967183i	$0.581773\pi$
$860$	−4963.34	−0.196801
$861$	−13843.6	−0.547952
$862$	−7006.81	−0.276859
$863$	−28255.4	−1.11451	−0.557256	−	0.830341i	$-0.688146\pi$
$863$	−28255.4	−1.11451	−0.557256	+	0.830341i	$0.688146\pi$
$864$	3870.88	0.152419
$865$	−15749.4	−0.619072
$866$	−13595.0	−0.533462
$867$	12065.1	0.472609
$868$	6533.18	0.255473
$869$	−1762.54	−0.0688033
$870$	−7713.84	−0.300602
$871$	−1391.76	−0.0541423
$872$	25580.5	0.993422
$873$	−5953.94	−0.230825
$874$	12895.3	0.499075
$875$	40145.1	1.55103
$876$	2596.35	0.100140
$877$	−307.183	−0.0118276	−0.00591382	−	0.999983i	$-0.501882\pi$
$877$	−307.183	−0.0118276	−0.00591382	+	0.999983i	$0.501882\pi$
$878$	−1850.71	−0.0711373
$879$	8900.00	0.341513
$880$	−2308.96	−0.0884491
$881$	43255.7	1.65417	0.827084	−	0.562078i	$-0.189998\pi$
$881$	43255.7	1.65417	0.827084	+	0.562078i	$0.189998\pi$
$882$	−6906.11	−0.263652
$883$	−6845.51	−0.260894	−0.130447	−	0.991455i	$-0.541641\pi$
$883$	−6845.51	−0.260894	−0.130447	+	0.991455i	$0.541641\pi$
$884$	−142.256	−0.00541242
$885$	−762.888	−0.0289765
$886$	12520.4	0.474751
$887$	5436.48	0.205794	0.102897	−	0.994692i	$-0.467189\pi$
$887$	5436.48	0.205794	0.102897	+	0.994692i	$0.467189\pi$
$888$	22805.9	0.861842
$889$	15302.8	0.577321
$890$	27373.4	1.03096
$891$	−891.000	−0.0335013
$892$	2172.03	0.0815302
$893$	27413.9	1.02729
$894$	−6255.22	−0.234011
$895$	13517.2	0.504839
$896$	2112.51	0.0787656
$897$	447.430	0.0166547
$898$	21767.5	0.808899
$899$	−9992.34	−0.370704
$900$	1585.29	0.0587144
$901$	−13479.9	−0.498424
$902$	4080.46	0.150626
$903$	13271.6	0.489094
$904$	3206.69	0.117979
$905$	−23513.3	−0.863658
$906$	−9314.84	−0.341573
$907$	−20070.5	−0.734765	−0.367382	−	0.930070i	$-0.619746\pi$
$907$	−20070.5	−0.734765	−0.367382	+	0.930070i	$0.619746\pi$
$908$	2726.04	0.0996329
$909$	3052.19	0.111369
$910$	670.297	0.0244177
$911$	2102.74	0.0764731	0.0382366	−	0.999269i	$-0.487826\pi$
$911$	2102.74	0.0764731	0.0382366	+	0.999269i	$0.487826\pi$
$912$	4091.73	0.148564
$913$	−1268.73	−0.0459899
$914$	−17970.9	−0.650355
$915$	1574.73	0.0568950
$916$	9789.58	0.353119
$917$	−9879.88	−0.355793
$918$	1718.10	0.0617709
$919$	−49761.0	−1.78614	−0.893071	−	0.449916i	$-0.851454\pi$
$919$	−49761.0	−1.78614	−0.893071	+	0.449916i	$0.851454\pi$
$920$	22737.5	0.814817
$921$	−7112.92	−0.254483
$922$	21231.2	0.758365
$923$	−121.252	−0.00432401
$924$	−3024.78	−0.107693
$925$	15861.7	0.563817
$926$	26301.7	0.933399
$927$	−642.034	−0.0227478
$928$	−20098.7	−0.710963
$929$	−48248.8	−1.70397	−0.851987	−	0.523563i	$-0.824603\pi$
$929$	−48248.8	−1.70397	−0.851987	+	0.523563i	$0.824603\pi$
$930$	3921.86	0.138283
$931$	20129.6	0.708616
$932$	1090.12	0.0383133
$933$	−13375.0	−0.469321
$934$	−11946.4	−0.418521
$935$	2825.92	0.0988422
$936$	302.931	0.0105786
$937$	−35029.7	−1.22131	−0.610657	−	0.791895i	$-0.709095\pi$
$937$	−35029.7	−1.22131	−0.610657	+	0.791895i	$0.709095\pi$
$938$	57063.6	1.98635
$939$	−24797.7	−0.861814
$940$	14585.1	0.506077
$941$	17646.2	0.611316	0.305658	−	0.952141i	$-0.401124\pi$
$941$	17646.2	0.611316	0.305658	+	0.952141i	$0.401124\pi$
$942$	−16916.1	−0.585093
$943$	−18831.7	−0.650312
$944$	720.866	0.0248540
$945$	6160.28	0.212057
$946$	−3911.88	−0.134446
$947$	−24718.3	−0.848190	−0.424095	−	0.905618i	$-0.639408\pi$
$947$	−24718.3	−0.848190	−0.424095	+	0.905618i	$0.639408\pi$
$948$	1661.75	0.0569316
$949$	345.066	0.0118033
$950$	6072.32	0.207381
$951$	−21330.0	−0.727312
$952$	19330.2	0.658084
$953$	51719.8	1.75800	0.878998	−	0.476826i	$-0.158213\pi$
$953$	51719.8	1.75800	0.878998	+	0.476826i	$0.158213\pi$
$954$	8661.39	0.293944
$955$	−19670.4	−0.666513
$956$	−4915.18	−0.166285
$957$	4626.33	0.156268
$958$	−23364.3	−0.787960
$959$	4135.51	0.139252
$960$	12926.2	0.434575
$961$	−24710.7	−0.829469
$962$	914.564	0.0306515
$963$	15686.3	0.524906
$964$	6887.89	0.230129
$965$	−1508.71	−0.0503286
$966$	−18345.1	−0.611018
$967$	2219.76	0.0738186	0.0369093	−	0.999319i	$-0.488249\pi$
$967$	2219.76	0.0738186	0.0369093	+	0.999319i	$0.488249\pi$
$968$	2954.80	0.0981103
$969$	−5007.83	−0.166021
$970$	−12133.6	−0.401634
$971$	37909.2	1.25290	0.626450	−	0.779462i	$-0.284507\pi$
$971$	37909.2	1.25290	0.626450	+	0.779462i	$0.284507\pi$
$972$	840.049	0.0277208
$973$	31533.6	1.03897
$974$	24107.7	0.793079
$975$	210.692	0.00692055
$976$	−1487.99	−0.0488006
$977$	25268.3	0.827435	0.413717	−	0.910405i	$-0.364230\pi$
$977$	25268.3	0.827435	0.413717	+	0.910405i	$0.364230\pi$
$978$	4931.23	0.161230
$979$	−16417.1	−0.535946
$980$	10709.6	0.349087
$981$	9427.76	0.306835
$982$	−18393.4	−0.597715
$983$	−8268.55	−0.268287	−0.134143	−	0.990962i	$-0.542828\pi$
$983$	−8268.55	−0.268287	−0.134143	+	0.990962i	$0.542828\pi$
$984$	−12749.9	−0.413062
$985$	39725.4	1.28503
$986$	−8920.87	−0.288132
$987$	−38999.5	−1.25772
$988$	−266.424	−0.00857903
$989$	18053.7	0.580459
$990$	−1815.77	−0.0582920
$991$	−7612.14	−0.244004	−0.122002	−	0.992530i	$-0.538931\pi$
$991$	−7612.14	−0.244004	−0.122002	+	0.992530i	$0.538931\pi$
$992$	10218.6	0.327056
$993$	−4730.57	−0.151178
$994$	4971.46	0.158637
$995$	−9766.03	−0.311160
$996$	1196.18	0.0380546
$997$	−1432.00	−0.0454884	−0.0227442	−	0.999741i	$-0.507240\pi$
$997$	−1432.00	−0.0454884	−0.0227442	+	0.999741i	$0.507240\pi$
$998$	−4215.76	−0.133715
$999$	8405.18	0.266194

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.b.1.12	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.b.1.12	✓	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)

\(f(q)\)	\(=\)	\(q-2.13143 q^{2} -3.00000 q^{3} -3.45699 q^{4} -8.60507 q^{5} +6.39430 q^{6} +26.5144 q^{7} +24.4198 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.13143 q^{2} -3.00000 q^{3} -3.45699 q^{4} -8.60507 q^{5} +6.39430 q^{6} +26.5144 q^{7} +24.4198 q^{8} +9.00000 q^{9} +18.3411 q^{10} -11.0000 q^{11} +10.3710 q^{12} +1.37835 q^{13} -56.5137 q^{14} +25.8152 q^{15} -24.3933 q^{16} +29.8547 q^{17} -19.1829 q^{18} +55.9134 q^{19} +29.7477 q^{20} -79.5432 q^{21} +23.4458 q^{22} -108.204 q^{23} -73.2594 q^{24} -50.9527 q^{25} -2.93786 q^{26} -27.0000 q^{27} -91.6601 q^{28} +140.192 q^{29} -55.0234 q^{30} -71.2761 q^{31} -143.366 q^{32} +33.0000 q^{33} -63.6333 q^{34} -228.158 q^{35} -31.1129 q^{36} -311.303 q^{37} -119.176 q^{38} -4.13505 q^{39} -210.134 q^{40} +174.038 q^{41} +169.541 q^{42} -166.848 q^{43} +38.0269 q^{44} -77.4457 q^{45} +230.630 q^{46} +490.293 q^{47} +73.1798 q^{48} +360.014 q^{49} +108.602 q^{50} -89.5641 q^{51} -4.76494 q^{52} -451.516 q^{53} +57.5487 q^{54} +94.6558 q^{55} +647.477 q^{56} -167.740 q^{57} -298.810 q^{58} -29.5519 q^{59} -89.2430 q^{60} +61.0000 q^{61} +151.920 q^{62} +238.630 q^{63} +500.721 q^{64} -11.8608 q^{65} -70.3373 q^{66} -1009.73 q^{67} -103.207 q^{68} +324.613 q^{69} +486.305 q^{70} -87.9692 q^{71} +219.778 q^{72} +250.347 q^{73} +663.522 q^{74} +152.858 q^{75} -193.292 q^{76} -291.659 q^{77} +8.81357 q^{78} +160.231 q^{79} +209.906 q^{80} +81.0000 q^{81} -370.951 q^{82} +115.339 q^{83} +274.980 q^{84} -256.902 q^{85} +355.625 q^{86} -420.576 q^{87} -268.618 q^{88} +1492.46 q^{89} +165.070 q^{90} +36.5461 q^{91} +374.062 q^{92} +213.828 q^{93} -1045.03 q^{94} -481.139 q^{95} +430.098 q^{96} -661.549 q^{97} -767.346 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 2 q^{2} - 108 q^{3} + 118 q^{4} - 5 q^{5} - 6 q^{6} - 63 q^{7} + 3 q^{8} + 324 q^{9}+O(q^{10}) \) 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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