LMFDB - Embedded newform 2013.4.a.g.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.31049 q^{2} -3.00000 q^{3} +20.2013 q^{4} -16.8641 q^{5} +15.9315 q^{6} +32.3654 q^{7} -64.7946 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-5.31049 q^{2} -3.00000 q^{3} +20.2013 q^{4} -16.8641 q^{5} +15.9315 q^{6} +32.3654 q^{7} -64.7946 q^{8} +9.00000 q^{9} +89.5564 q^{10} +11.0000 q^{11} -60.6038 q^{12} +39.9137 q^{13} -171.876 q^{14} +50.5922 q^{15} +182.481 q^{16} -65.1661 q^{17} -47.7944 q^{18} +64.2818 q^{19} -340.675 q^{20} -97.0963 q^{21} -58.4153 q^{22} +138.919 q^{23} +194.384 q^{24} +159.397 q^{25} -211.961 q^{26} -27.0000 q^{27} +653.823 q^{28} +99.5794 q^{29} -268.669 q^{30} -67.7319 q^{31} -450.704 q^{32} -33.0000 q^{33} +346.064 q^{34} -545.813 q^{35} +181.811 q^{36} -66.7639 q^{37} -341.368 q^{38} -119.741 q^{39} +1092.70 q^{40} +365.770 q^{41} +515.629 q^{42} +291.289 q^{43} +222.214 q^{44} -151.777 q^{45} -737.727 q^{46} +455.350 q^{47} -547.442 q^{48} +704.522 q^{49} -846.475 q^{50} +195.498 q^{51} +806.307 q^{52} +17.5539 q^{53} +143.383 q^{54} -185.505 q^{55} -2097.11 q^{56} -192.846 q^{57} -528.815 q^{58} +633.735 q^{59} +1022.03 q^{60} +61.0000 q^{61} +359.689 q^{62} +291.289 q^{63} +933.614 q^{64} -673.108 q^{65} +175.246 q^{66} +622.291 q^{67} -1316.44 q^{68} -416.757 q^{69} +2898.53 q^{70} +123.051 q^{71} -583.151 q^{72} -261.075 q^{73} +354.549 q^{74} -478.191 q^{75} +1298.57 q^{76} +356.020 q^{77} +635.884 q^{78} -333.941 q^{79} -3077.37 q^{80} +81.0000 q^{81} -1942.42 q^{82} +717.762 q^{83} -1961.47 q^{84} +1098.97 q^{85} -1546.89 q^{86} -298.738 q^{87} -712.741 q^{88} -802.150 q^{89} +806.008 q^{90} +1291.83 q^{91} +2806.34 q^{92} +203.196 q^{93} -2418.13 q^{94} -1084.05 q^{95} +1352.11 q^{96} -766.163 q^{97} -3741.35 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 4 q^{2} - 117 q^{3} + 182 q^{4} + 5 q^{5} - 12 q^{6} + 77 q^{7} + 27 q^{8} + 351 q^{9}+O(q^{10}) $ 39 * q + 4 * q^2 - 117 * q^3 + 182 * q^4 + 5 * q^5 - 12 * q^6 + 77 * q^7 + 27 * q^8 + 351 * q^9	\( 39 q + 4 q^{2} - 117 q^{3} + 182 q^{4} + 5 q^{5} - 12 q^{6} + 77 q^{7} + 27 q^{8} + 351 q^{9} + 95 q^{10} + 429 q^{11} - 546 q^{12} + 169 q^{13} + 46 q^{14} - 15 q^{15} + 822 q^{16} + 294 q^{17} + 36 q^{18} + 259 q^{19} + 426 q^{20} - 231 q^{21} + 44 q^{22} + 177 q^{23} - 81 q^{24} + 1388 q^{25} + 695 q^{26} - 1053 q^{27} + 1104 q^{28} - 18 q^{29} - 285 q^{30} + 422 q^{31} + 55 q^{32} - 1287 q^{33} + 364 q^{34} + 906 q^{35} + 1638 q^{36} + 424 q^{37} + 9 q^{38} - 507 q^{39} + 1067 q^{40} + 16 q^{41} - 138 q^{42} + 1013 q^{43} + 2002 q^{44} + 45 q^{45} + 9 q^{46} + 1615 q^{47} - 2466 q^{48} + 2024 q^{49} - 1342 q^{50} - 882 q^{51} + 1298 q^{52} - 541 q^{53} - 108 q^{54} + 55 q^{55} - 161 q^{56} - 777 q^{57} + 1061 q^{58} + 1019 q^{59} - 1278 q^{60} + 2379 q^{61} + 879 q^{62} + 693 q^{63} + 1055 q^{64} - 1134 q^{65} - 132 q^{66} + 1917 q^{67} + 3526 q^{68} - 531 q^{69} + 758 q^{70} - 479 q^{71} + 243 q^{72} + 3319 q^{73} - 332 q^{74} - 4164 q^{75} + 692 q^{76} + 847 q^{77} - 2085 q^{78} + 651 q^{79} + 2973 q^{80} + 3159 q^{81} - 826 q^{82} + 4001 q^{83} - 3312 q^{84} + 3595 q^{85} - 6247 q^{86} + 54 q^{87} + 297 q^{88} - 1625 q^{89} + 855 q^{90} + 2048 q^{91} - 507 q^{92} - 1266 q^{93} - 2436 q^{94} + 1400 q^{95} - 165 q^{96} + 2176 q^{97} - 1396 q^{98} + 3861 q^{99}+O(q^{100}) \) 39 * q + 4 * q^2 - 117 * q^3 + 182 * q^4 + 5 * q^5 - 12 * q^6 + 77 * q^7 + 27 * q^8 + 351 * q^9 + 95 * q^10 + 429 * q^11 - 546 * q^12 + 169 * q^13 + 46 * q^14 - 15 * q^15 + 822 * q^16 + 294 * q^17 + 36 * q^18 + 259 * q^19 + 426 * q^20 - 231 * q^21 + 44 * q^22 + 177 * q^23 - 81 * q^24 + 1388 * q^25 + 695 * q^26 - 1053 * q^27 + 1104 * q^28 - 18 * q^29 - 285 * q^30 + 422 * q^31 + 55 * q^32 - 1287 * q^33 + 364 * q^34 + 906 * q^35 + 1638 * q^36 + 424 * q^37 + 9 * q^38 - 507 * q^39 + 1067 * q^40 + 16 * q^41 - 138 * q^42 + 1013 * q^43 + 2002 * q^44 + 45 * q^45 + 9 * q^46 + 1615 * q^47 - 2466 * q^48 + 2024 * q^49 - 1342 * q^50 - 882 * q^51 + 1298 * q^52 - 541 * q^53 - 108 * q^54 + 55 * q^55 - 161 * q^56 - 777 * q^57 + 1061 * q^58 + 1019 * q^59 - 1278 * q^60 + 2379 * q^61 + 879 * q^62 + 693 * q^63 + 1055 * q^64 - 1134 * q^65 - 132 * q^66 + 1917 * q^67 + 3526 * q^68 - 531 * q^69 + 758 * q^70 - 479 * q^71 + 243 * q^72 + 3319 * q^73 - 332 * q^74 - 4164 * q^75 + 692 * q^76 + 847 * q^77 - 2085 * q^78 + 651 * q^79 + 2973 * q^80 + 3159 * q^81 - 826 * q^82 + 4001 * q^83 - 3312 * q^84 + 3595 * q^85 - 6247 * q^86 + 54 * q^87 + 297 * q^88 - 1625 * q^89 + 855 * q^90 + 2048 * q^91 - 507 * q^92 - 1266 * q^93 - 2436 * q^94 + 1400 * q^95 - 165 * q^96 + 2176 * q^97 - 1396 * q^98 + 3861 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−5.31049	−1.87754	−0.938770	−	0.344544i	$-0.888033\pi$
$2$	−5.31049	−1.87754	−0.938770	+	0.344544i	$0.888033\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	20.2013	2.52516
$5$	−16.8641	−1.50837	−0.754184	−	0.656663i	$-0.771967\pi$
$5$	−16.8641	−1.50837	−0.754184	+	0.656663i	$0.771967\pi$
$6$	15.9315	1.08400
$7$	32.3654	1.74757	0.873785	−	0.486313i	$-0.161658\pi$
$7$	32.3654	1.74757	0.873785	+	0.486313i	$0.161658\pi$
$8$	−64.7946	−2.86354
$9$	9.00000	0.333333
$10$	89.5564	2.83202
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−60.6038	−1.45790
$13$	39.9137	0.851544	0.425772	−	0.904830i	$-0.360003\pi$
$13$	39.9137	0.851544	0.425772	+	0.904830i	$0.360003\pi$
$14$	−171.876	−3.28113
$15$	50.5922	0.870857
$16$	182.481	2.85126
$17$	−65.1661	−0.929712	−0.464856	−	0.885386i	$-0.653894\pi$
$17$	−65.1661	−0.929712	−0.464856	+	0.885386i	$0.653894\pi$
$18$	−47.7944	−0.625847
$19$	64.2818	0.776172	0.388086	−	0.921623i	$-0.373136\pi$
$19$	64.2818	0.776172	0.388086	+	0.921623i	$0.373136\pi$
$20$	−340.675	−3.80887
$21$	−97.0963	−1.00896
$22$	−58.4153	−0.566100
$23$	138.919	1.25942	0.629709	−	0.776831i	$-0.283174\pi$
$23$	138.919	1.25942	0.629709	+	0.776831i	$0.283174\pi$
$24$	194.384	1.65327
$25$	159.397	1.27518
$26$	−211.961	−1.59881
$27$	−27.0000	−0.192450
$28$	653.823	4.41289
$29$	99.5794	0.637635	0.318818	−	0.947816i	$-0.396714\pi$
$29$	99.5794	0.637635	0.318818	+	0.947816i	$0.396714\pi$
$30$	−268.669	−1.63507
$31$	−67.7319	−0.392420	−0.196210	−	0.980562i	$-0.562863\pi$
$31$	−67.7319	−0.392420	−0.196210	+	0.980562i	$0.562863\pi$
$32$	−450.704	−2.48981
$33$	−33.0000	−0.174078
$34$	346.064	1.74557
$35$	−545.813	−2.63598
$36$	181.811	0.841719
$37$	−66.7639	−0.296646	−0.148323	−	0.988939i	$-0.547388\pi$
$37$	−66.7639	−0.296646	−0.148323	+	0.988939i	$0.547388\pi$
$38$	−341.368	−1.45729
$39$	−119.741	−0.491639
$40$	1092.70	4.31928
$41$	365.770	1.39326	0.696631	−	0.717430i	$-0.254682\pi$
$41$	365.770	1.39326	0.696631	+	0.717430i	$0.254682\pi$
$42$	515.629	1.89436
$43$	291.289	1.03305	0.516526	−	0.856272i	$-0.327225\pi$
$43$	291.289	1.03305	0.516526	+	0.856272i	$0.327225\pi$
$44$	222.214	0.761364
$45$	−151.777	−0.502790
$46$	−737.727	−2.36461
$47$	455.350	1.41318	0.706592	−	0.707621i	$-0.250232\pi$
$47$	455.350	1.41318	0.706592	+	0.707621i	$0.250232\pi$
$48$	−547.442	−1.64618
$49$	704.522	2.05400
$50$	−846.475	−2.39419
$51$	195.498	0.536770
$52$	806.307	2.15028
$53$	17.5539	0.0454947	0.0227473	−	0.999741i	$-0.492759\pi$
$53$	17.5539	0.0454947	0.0227473	+	0.999741i	$0.492759\pi$
$54$	143.383	0.361333
$55$	−185.505	−0.454790
$56$	−2097.11	−5.00424
$57$	−192.846	−0.448123
$58$	−528.815	−1.19719
$59$	633.735	1.39839	0.699197	−	0.714929i	$-0.253541\pi$
$59$	633.735	1.39839	0.699197	+	0.714929i	$0.253541\pi$
$60$	1022.03	2.19905
$61$	61.0000	0.128037
$61$	61.0000	0.128037
$62$	359.689	0.736784
$63$	291.289	0.582523
$64$	933.614	1.82346
$65$	−673.108	−1.28444
$66$	175.246	0.326838
$67$	622.291	1.13470	0.567350	−	0.823477i	$-0.307969\pi$
$67$	622.291	1.13470	0.567350	+	0.823477i	$0.307969\pi$
$68$	−1316.44	−2.34767
$69$	−416.757	−0.727125
$70$	2898.53	4.94916
$71$	123.051	0.205683	0.102842	−	0.994698i	$-0.467207\pi$
$71$	123.051	0.205683	0.102842	+	0.994698i	$0.467207\pi$
$72$	−583.151	−0.954515
$73$	−261.075	−0.418582	−0.209291	−	0.977853i	$-0.567116\pi$
$73$	−261.075	−0.418582	−0.209291	+	0.977853i	$0.567116\pi$
$74$	354.549	0.556965
$75$	−478.191	−0.736223
$76$	1298.57	1.95996
$77$	356.020	0.526912
$78$	635.884	0.923072
$79$	−333.941	−0.475586	−0.237793	−	0.971316i	$-0.576424\pi$
$79$	−333.941	−0.475586	−0.237793	+	0.971316i	$0.576424\pi$
$80$	−3077.37	−4.30075
$81$	81.0000	0.111111
$82$	−1942.42	−2.61590
$83$	717.762	0.949212	0.474606	−	0.880198i	$-0.342590\pi$
$83$	717.762	0.949212	0.474606	+	0.880198i	$0.342590\pi$
$84$	−1961.47	−2.54778
$85$	1098.97	1.40235
$86$	−1546.89	−1.93960
$87$	−298.738	−0.368139
$88$	−712.741	−0.863391
$89$	−802.150	−0.955368	−0.477684	−	0.878532i	$-0.658524\pi$
$89$	−802.150	−0.955368	−0.477684	+	0.878532i	$0.658524\pi$
$90$	806.008	0.944008
$91$	1291.83	1.48813
$92$	2806.34	3.18023
$93$	203.196	0.226564
$94$	−2418.13	−2.65331
$95$	−1084.05	−1.17075
$96$	1352.11	1.43749
$97$	−766.163	−0.801980	−0.400990	−	0.916082i	$-0.631334\pi$
$97$	−766.163	−0.801980	−0.400990	+	0.916082i	$0.631334\pi$
$98$	−3741.35	−3.85647
$99$	99.0000	0.100504
$100$	3220.02	3.22002
$101$	192.387	0.189537	0.0947683	−	0.995499i	$-0.469789\pi$
$101$	192.387	0.189537	0.0947683	+	0.995499i	$0.469789\pi$
$102$	−1038.19	−1.00781
$103$	184.936	0.176916	0.0884578	−	0.996080i	$-0.471806\pi$
$103$	184.936	0.176916	0.0884578	+	0.996080i	$0.471806\pi$
$104$	−2586.19	−2.43843
$105$	1637.44	1.52188
$106$	−93.2199	−0.0854181
$107$	106.836	0.0965259	0.0482629	−	0.998835i	$-0.484631\pi$
$107$	106.836	0.0965259	0.0482629	+	0.998835i	$0.484631\pi$
$108$	−545.434	−0.485967
$109$	679.447	0.597057	0.298528	−	0.954401i	$-0.403504\pi$
$109$	679.447	0.597057	0.298528	+	0.954401i	$0.403504\pi$
$110$	985.121	0.853887
$111$	200.292	0.171269
$112$	5906.07	4.98278
$113$	2257.68	1.87951	0.939755	−	0.341849i	$-0.111053\pi$
$113$	2257.68	1.87951	0.939755	+	0.341849i	$0.111053\pi$
$114$	1024.10	0.841369
$115$	−2342.74	−1.89967
$116$	2011.63	1.61013
$117$	359.223	0.283848
$118$	−3365.44	−2.62554
$119$	−2109.13	−1.62474
$120$	−3278.10	−2.49374
$121$	121.000	0.0909091
$122$	−323.940	−0.240394
$123$	−1097.31	−0.804400
$124$	−1368.27	−0.990921
$125$	−580.073	−0.415066
$126$	−1546.89	−1.09371
$127$	−1896.06	−1.32479	−0.662394	−	0.749155i	$-0.730460\pi$
$127$	−1896.06	−1.32479	−0.662394	+	0.749155i	$0.730460\pi$
$128$	−1352.31	−0.933814
$129$	−873.868	−0.596432
$130$	3574.53	2.41159
$131$	2678.76	1.78660	0.893299	−	0.449464i	$-0.148385\pi$
$131$	2678.76	1.78660	0.893299	+	0.449464i	$0.148385\pi$
$132$	−666.641	−0.439573
$133$	2080.51	1.35641
$134$	−3304.67	−2.13045
$135$	455.330	0.290286
$136$	4222.41	2.66227
$137$	606.505	0.378228	0.189114	−	0.981955i	$-0.439438\pi$
$137$	606.505	0.378228	0.189114	+	0.981955i	$0.439438\pi$
$138$	2213.18	1.36521
$139$	−2052.69	−1.25257	−0.626284	−	0.779595i	$-0.715425\pi$
$139$	−2052.69	−1.25257	−0.626284	+	0.779595i	$0.715425\pi$
$140$	−11026.1	−6.65626
$141$	−1366.05	−0.815902
$142$	−653.462	−0.386178
$143$	439.051	0.256750
$144$	1642.33	0.950420
$145$	−1679.31	−0.961789
$146$	1386.43	0.785904
$147$	−2113.57	−1.18588
$148$	−1348.71	−0.749078
$149$	−982.730	−0.540325	−0.270162	−	0.962815i	$-0.587077\pi$
$149$	−982.730	−0.540325	−0.270162	+	0.962815i	$0.587077\pi$
$150$	2539.43	1.38229
$151$	−930.945	−0.501717	−0.250858	−	0.968024i	$-0.580713\pi$
$151$	−930.945	−0.501717	−0.250858	+	0.968024i	$0.580713\pi$
$152$	−4165.12	−2.22260
$153$	−586.495	−0.309904
$154$	−1890.64	−0.989299
$155$	1142.24	0.591913
$156$	−2418.92	−1.24147
$157$	1272.03	0.646617	0.323308	−	0.946294i	$-0.395205\pi$
$157$	1272.03	0.646617	0.323308	+	0.946294i	$0.395205\pi$
$158$	1773.39	0.892932
$159$	−52.6618	−0.0262664
$160$	7600.71	3.75556
$161$	4496.17	2.20092
$162$	−430.149	−0.208616
$163$	1178.09	0.566104	0.283052	−	0.959105i	$-0.408653\pi$
$163$	1178.09	0.566104	0.283052	+	0.959105i	$0.408653\pi$
$164$	7389.02	3.51820
$165$	556.514	0.262573
$166$	−3811.67	−1.78218
$167$	−821.591	−0.380698	−0.190349	−	0.981716i	$-0.560962\pi$
$167$	−821.591	−0.380698	−0.190349	+	0.981716i	$0.560962\pi$
$168$	6291.32	2.88920
$169$	−603.896	−0.274873
$170$	−5836.04	−2.63297
$171$	578.537	0.258724
$172$	5884.41	2.60862
$173$	−4009.91	−1.76224	−0.881121	−	0.472890i	$-0.843211\pi$
$173$	−4009.91	−1.76224	−0.881121	+	0.472890i	$0.843211\pi$
$174$	1586.44	0.691196
$175$	5158.95	2.22846
$176$	2007.29	0.859688
$177$	−1901.20	−0.807363
$178$	4259.81	1.79374
$179$	−1392.50	−0.581455	−0.290728	−	0.956806i	$-0.593897\pi$
$179$	−1392.50	−0.581455	−0.290728	+	0.956806i	$0.593897\pi$
$180$	−3066.08	−1.26962
$181$	2156.23	0.885476	0.442738	−	0.896651i	$-0.354007\pi$
$181$	2156.23	0.885476	0.442738	+	0.896651i	$0.354007\pi$
$182$	−6860.22	−2.79403
$183$	−183.000	−0.0739221
$184$	−9001.20	−3.60640
$185$	1125.91	0.447452
$186$	−1079.07	−0.425382
$187$	−716.827	−0.280319
$188$	9198.65	3.56851
$189$	−873.867	−0.336320
$190$	5756.85	2.19814
$191$	−2659.47	−1.00750	−0.503750	−	0.863850i	$-0.668047\pi$
$191$	−2659.47	−1.00750	−0.503750	+	0.863850i	$0.668047\pi$
$192$	−2800.84	−1.05278
$193$	−3027.29	−1.12906	−0.564531	−	0.825412i	$-0.690943\pi$
$193$	−3027.29	−1.12906	−0.564531	+	0.825412i	$0.690943\pi$
$194$	4068.70	1.50575
$195$	2019.32	0.741573
$196$	14232.2	5.18667
$197$	−5336.36	−1.92995	−0.964975	−	0.262342i	$-0.915505\pi$
$197$	−5336.36	−1.92995	−0.964975	+	0.262342i	$0.915505\pi$
$198$	−525.738	−0.188700
$199$	2923.60	1.04145	0.520725	−	0.853725i	$-0.325662\pi$
$199$	2923.60	1.04145	0.520725	+	0.853725i	$0.325662\pi$
$200$	−10328.1	−3.65152
$201$	−1866.87	−0.655120
$202$	−1021.67	−0.355863
$203$	3222.93	1.11431
$204$	3949.31	1.35543
$205$	−6168.38	−2.10155
$206$	−982.101	−0.332166
$207$	1250.27	0.419806
$208$	7283.48	2.42797
$209$	707.100	0.234025
$210$	−8695.60	−2.85740
$211$	−4916.35	−1.60405	−0.802027	−	0.597288i	$-0.796245\pi$
$211$	−4916.35	−1.60405	−0.802027	+	0.597288i	$0.796245\pi$
$212$	354.612	0.114881
$213$	−369.154	−0.118751
$214$	−567.353	−0.181231
$215$	−4912.32	−1.55822
$216$	1749.45	0.551089
$217$	−2192.17	−0.685781
$218$	−3608.19	−1.12100
$219$	783.224	0.241668
$220$	−3747.43	−1.14842
$221$	−2601.02	−0.791691
$222$	−1063.65	−0.321564
$223$	−5886.15	−1.76756	−0.883780	−	0.467903i	$-0.845010\pi$
$223$	−5886.15	−1.76756	−0.883780	+	0.467903i	$0.845010\pi$
$224$	−14587.3	−4.35112
$225$	1434.57	0.425059
$226$	−11989.4	−3.52885
$227$	−6298.64	−1.84165	−0.920827	−	0.389972i	$-0.872485\pi$
$227$	−6298.64	−1.84165	−0.920827	+	0.389972i	$0.872485\pi$
$228$	−3895.72	−1.13158
$229$	−1663.80	−0.480119	−0.240059	−	0.970758i	$-0.577167\pi$
$229$	−1663.80	−0.480119	−0.240059	+	0.970758i	$0.577167\pi$
$230$	12441.1	3.56670
$231$	−1068.06	−0.304213
$232$	−6452.21	−1.82590
$233$	4191.62	1.17855	0.589275	−	0.807932i	$-0.299413\pi$
$233$	4191.62	1.17855	0.589275	+	0.807932i	$0.299413\pi$
$234$	−1907.65	−0.532936
$235$	−7679.06	−2.13160
$236$	12802.2	3.53117
$237$	1001.82	0.274580
$238$	11200.5	3.05051
$239$	−3783.25	−1.02393	−0.511963	−	0.859008i	$-0.671081\pi$
$239$	−3783.25	−1.02393	−0.511963	+	0.859008i	$0.671081\pi$
$240$	9232.11	2.48304
$241$	−1961.10	−0.524171	−0.262086	−	0.965045i	$-0.584410\pi$
$241$	−1961.10	−0.524171	−0.262086	+	0.965045i	$0.584410\pi$
$242$	−642.569	−0.170685
$243$	−243.000	−0.0641500
$244$	1232.28	0.323313
$245$	−11881.1	−3.09819
$246$	5827.25	1.51029
$247$	2565.73	0.660945
$248$	4388.66	1.12371
$249$	−2153.29	−0.548028
$250$	3080.47	0.779304
$251$	−888.210	−0.223360	−0.111680	−	0.993744i	$-0.535623\pi$
$251$	−888.210	−0.223360	−0.111680	+	0.993744i	$0.535623\pi$
$252$	5884.40	1.47096
$253$	1528.11	0.379729
$254$	10069.0	2.48734
$255$	−3296.90	−0.809646
$256$	−287.504	−0.0701914
$257$	6398.12	1.55293	0.776466	−	0.630159i	$-0.217010\pi$
$257$	6398.12	1.55293	0.776466	+	0.630159i	$0.217010\pi$
$258$	4640.66	1.11983
$259$	−2160.84	−0.518410
$260$	−13597.6	−3.24342
$261$	896.214	0.212545
$262$	−14225.5	−3.35441
$263$	7434.61	1.74311	0.871555	−	0.490298i	$-0.163112\pi$
$263$	7434.61	1.74311	0.871555	+	0.490298i	$0.163112\pi$
$264$	2138.22	0.498479
$265$	−296.031	−0.0686228
$266$	−11048.5	−2.54672
$267$	2406.45	0.551582
$268$	12571.1	2.86530
$269$	−7301.17	−1.65487	−0.827435	−	0.561562i	$-0.810201\pi$
$269$	−7301.17	−1.65487	−0.827435	+	0.561562i	$0.810201\pi$
$270$	−2418.02	−0.545023
$271$	6414.29	1.43779	0.718894	−	0.695120i	$-0.244649\pi$
$271$	6414.29	1.43779	0.718894	+	0.695120i	$0.244649\pi$
$272$	−11891.6	−2.65085
$273$	−3875.48	−0.859174
$274$	−3220.84	−0.710138
$275$	1753.37	0.384480
$276$	−8419.01	−1.83610
$277$	2016.88	0.437482	0.218741	−	0.975783i	$-0.429805\pi$
$277$	2016.88	0.437482	0.218741	+	0.975783i	$0.429805\pi$
$278$	10900.8	2.35175
$279$	−609.587	−0.130807
$280$	35365.7	7.54824
$281$	−2251.52	−0.477987	−0.238993	−	0.971021i	$-0.576817\pi$
$281$	−2251.52	−0.477987	−0.238993	+	0.971021i	$0.576817\pi$
$282$	7254.39	1.53189
$283$	−3723.17	−0.782048	−0.391024	−	0.920380i	$-0.627879\pi$
$283$	−3723.17	−0.782048	−0.391024	+	0.920380i	$0.627879\pi$
$284$	2485.79	0.519382
$285$	3252.16	0.675935
$286$	−2331.57	−0.482059
$287$	11838.3	2.43482
$288$	−4056.34	−0.829938
$289$	−666.376	−0.135635
$290$	8917.97	1.80580
$291$	2298.49	0.463024
$292$	−5274.04	−1.05698
$293$	6032.91	1.20289	0.601444	−	0.798915i	$-0.294592\pi$
$293$	6032.91	1.20289	0.601444	+	0.798915i	$0.294592\pi$
$294$	11224.1	2.22653
$295$	−10687.4	−2.10929
$296$	4325.94	0.849460
$297$	−297.000	−0.0580259
$298$	5218.77	1.01448
$299$	5544.77	1.07245
$300$	−9660.06	−1.85908
$301$	9427.71	1.80533
$302$	4943.77	0.941993
$303$	−577.160	−0.109429
$304$	11730.2	2.21307
$305$	−1028.71	−0.193127
$306$	3114.57	0.581857
$307$	9877.84	1.83635	0.918173	−	0.396180i	$-0.129664\pi$
$307$	9877.84	1.83635	0.918173	+	0.396180i	$0.129664\pi$
$308$	7192.05	1.33054
$309$	−554.809	−0.102142
$310$	−6065.83	−1.11134
$311$	6298.95	1.14849	0.574245	−	0.818683i	$-0.305296\pi$
$311$	6298.95	1.14849	0.574245	+	0.818683i	$0.305296\pi$
$312$	7758.58	1.40783
$313$	4008.08	0.723803	0.361901	−	0.932216i	$-0.382128\pi$
$313$	4008.08	0.723803	0.361901	+	0.932216i	$0.382128\pi$
$314$	−6755.08	−1.21405
$315$	−4912.32	−0.878660
$316$	−6746.03	−1.20093
$317$	1938.27	0.343420	0.171710	−	0.985148i	$-0.445071\pi$
$317$	1938.27	0.343420	0.171710	+	0.985148i	$0.445071\pi$
$318$	279.660	0.0493162
$319$	1095.37	0.192254
$320$	−15744.5	−2.75046
$321$	−320.509	−0.0557293
$322$	−23876.9	−4.13232
$323$	−4189.00	−0.721617
$324$	1636.30	0.280573
$325$	6362.12	1.08587
$326$	−6256.22	−1.06288
$327$	−2038.34	−0.344711
$328$	−23699.9	−3.98966
$329$	14737.6	2.46964
$330$	−2955.36	−0.492992
$331$	−3674.99	−0.610260	−0.305130	−	0.952311i	$-0.598700\pi$
$331$	−3674.99	−0.610260	−0.305130	+	0.952311i	$0.598700\pi$
$332$	14499.7	2.39691
$333$	−600.875	−0.0988821
$334$	4363.05	0.714776
$335$	−10494.4	−1.71155
$336$	−17718.2	−2.87681
$337$	11954.7	1.93238	0.966189	−	0.257835i	$-0.0830090\pi$
$337$	11954.7	1.93238	0.966189	+	0.257835i	$0.0830090\pi$
$338$	3206.98	0.516085
$339$	−6773.04	−1.08514
$340$	22200.5	3.54115
$341$	−745.051	−0.118319
$342$	−3072.31	−0.485765
$343$	11700.8	1.84194
$344$	−18874.0	−2.95819
$345$	7028.22	1.09677
$346$	21294.6	3.30868
$347$	915.832	0.141684	0.0708421	−	0.997488i	$-0.477431\pi$
$347$	915.832	0.141684	0.0708421	+	0.997488i	$0.477431\pi$
$348$	−6034.89	−0.929609
$349$	10018.8	1.53666	0.768332	−	0.640052i	$-0.221087\pi$
$349$	10018.8	1.53666	0.768332	+	0.640052i	$0.221087\pi$
$350$	−27396.5	−4.18402
$351$	−1077.67	−0.163880
$352$	−4957.75	−0.750707
$353$	1304.53	0.196694	0.0983469	−	0.995152i	$-0.468645\pi$
$353$	1304.53	0.196694	0.0983469	+	0.995152i	$0.468645\pi$
$354$	10096.3	1.51586
$355$	−2075.15	−0.310246
$356$	−16204.4	−2.41245
$357$	6327.39	0.938042
$358$	7394.86	1.09171
$359$	−6844.91	−1.00630	−0.503148	−	0.864200i	$-0.667825\pi$
$359$	−6844.91	−1.00630	−0.503148	+	0.864200i	$0.667825\pi$
$360$	9834.31	1.43976
$361$	−2726.84	−0.397557
$362$	−11450.6	−1.66252
$363$	−363.000	−0.0524864
$364$	26096.5	3.75777
$365$	4402.78	0.631376
$366$	971.819	0.138792
$367$	−491.471	−0.0699034	−0.0349517	−	0.999389i	$-0.511128\pi$
$367$	−491.471	−0.0699034	−0.0349517	+	0.999389i	$0.511128\pi$
$368$	25350.0	3.59093
$369$	3291.93	0.464420
$370$	−5979.13	−0.840109
$371$	568.141	0.0795052
$372$	4104.81	0.572109
$373$	1949.58	0.270631	0.135315	−	0.990803i	$-0.456795\pi$
$373$	1949.58	0.270631	0.135315	+	0.990803i	$0.456795\pi$
$374$	3806.70	0.526310
$375$	1740.22	0.239639
$376$	−29504.2	−4.04671
$377$	3974.58	0.542975
$378$	4640.66	0.631454
$379$	−3079.45	−0.417364	−0.208682	−	0.977984i	$-0.566917\pi$
$379$	−3079.45	−0.417364	−0.208682	+	0.977984i	$0.566917\pi$
$380$	−21899.2	−2.95634
$381$	5688.18	0.764867
$382$	14123.1	1.89162
$383$	−6929.70	−0.924520	−0.462260	−	0.886744i	$-0.652961\pi$
$383$	−6929.70	−0.924520	−0.462260	+	0.886744i	$0.652961\pi$
$384$	4056.92	0.539138
$385$	−6003.95	−0.794778
$386$	16076.4	2.11986
$387$	2621.60	0.344350
$388$	−15477.5	−2.02513
$389$	2376.88	0.309801	0.154901	−	0.987930i	$-0.450494\pi$
$389$	2376.88	0.309801	0.154901	+	0.987930i	$0.450494\pi$
$390$	−10723.6	−1.39233
$391$	−9052.81	−1.17090
$392$	−45649.2	−5.88172
$393$	−8036.28	−1.03149
$394$	28338.7	3.62356
$395$	5631.61	0.717359
$396$	1999.92	0.253788
$397$	−1283.81	−0.162299	−0.0811496	−	0.996702i	$-0.525859\pi$
$397$	−1283.81	−0.162299	−0.0811496	+	0.996702i	$0.525859\pi$
$398$	−15525.7	−1.95536
$399$	−6241.53	−0.783126
$400$	29086.9	3.63586
$401$	8519.66	1.06098	0.530488	−	0.847692i	$-0.322009\pi$
$401$	8519.66	1.06098	0.530488	+	0.847692i	$0.322009\pi$
$402$	9914.00	1.23001
$403$	−2703.43	−0.334163
$404$	3886.45	0.478610
$405$	−1365.99	−0.167597
$406$	−17115.3	−2.09217
$407$	−734.403	−0.0894422
$408$	−12667.2	−1.53706
$409$	3836.30	0.463797	0.231899	−	0.972740i	$-0.425506\pi$
$409$	3836.30	0.463797	0.231899	+	0.972740i	$0.425506\pi$
$410$	32757.1	3.94575
$411$	−1819.52	−0.218370
$412$	3735.94	0.446740
$413$	20511.1	2.44379
$414$	−6639.54	−0.788202
$415$	−12104.4	−1.43176
$416$	−17989.3	−2.12019
$417$	6158.07	0.723170
$418$	−3755.05	−0.439391
$419$	−7976.61	−0.930031	−0.465015	−	0.885303i	$-0.653951\pi$
$419$	−7976.61	−0.930031	−0.465015	+	0.885303i	$0.653951\pi$
$420$	33078.3	3.84299
$421$	4083.29	0.472702	0.236351	−	0.971668i	$-0.424049\pi$
$421$	4083.29	0.472702	0.236351	+	0.971668i	$0.424049\pi$
$422$	26108.2	3.01167
$423$	4098.15	0.471061
$424$	−1137.40	−0.130276
$425$	−10387.3	−1.18555
$426$	1960.39	0.222960
$427$	1974.29	0.223753
$428$	2158.23	0.243743
$429$	−1317.15	−0.148235
$430$	26086.8	2.92562
$431$	−6865.00	−0.767229	−0.383614	−	0.923493i	$-0.625321\pi$
$431$	−6865.00	−0.767229	−0.383614	+	0.923493i	$0.625321\pi$
$432$	−4926.98	−0.548726
$433$	−14017.9	−1.55579	−0.777895	−	0.628395i	$-0.783712\pi$
$433$	−14017.9	−1.55579	−0.777895	+	0.628395i	$0.783712\pi$
$434$	11641.5	1.28758
$435$	5037.94	0.555289
$436$	13725.7	1.50766
$437$	8929.97	0.977525
$438$	−4159.30	−0.453742
$439$	13040.4	1.41774	0.708868	−	0.705342i	$-0.249206\pi$
$439$	13040.4	1.41774	0.708868	+	0.705342i	$0.249206\pi$
$440$	12019.7	1.30231
$441$	6340.70	0.684667
$442$	13812.7	1.48643
$443$	1533.30	0.164445	0.0822224	−	0.996614i	$-0.473798\pi$
$443$	1533.30	0.164445	0.0822224	+	0.996614i	$0.473798\pi$
$444$	4046.14	0.432481
$445$	13527.5	1.44105
$446$	31258.3	3.31866
$447$	2948.19	0.311957
$448$	30216.8	3.18663
$449$	11728.2	1.23271	0.616354	−	0.787469i	$-0.288609\pi$
$449$	11728.2	1.23271	0.616354	+	0.787469i	$0.288609\pi$
$450$	−7618.28	−0.798064
$451$	4023.47	0.420084
$452$	45608.0	4.74606
$453$	2792.83	0.289666
$454$	33448.8	3.45778
$455$	−21785.4	−2.24465
$456$	12495.4	1.28322
$457$	14780.4	1.51291	0.756454	−	0.654047i	$-0.226930\pi$
$457$	14780.4	1.51291	0.756454	+	0.654047i	$0.226930\pi$
$458$	8835.60	0.901442
$459$	1759.49	0.178923
$460$	−47326.3	−4.79695
$461$	−6316.17	−0.638120	−0.319060	−	0.947735i	$-0.603367\pi$
$461$	−6316.17	−0.638120	−0.319060	+	0.947735i	$0.603367\pi$
$462$	5671.92	0.571172
$463$	−12822.4	−1.28706	−0.643530	−	0.765421i	$-0.722531\pi$
$463$	−12822.4	−1.28706	−0.643530	+	0.765421i	$0.722531\pi$
$464$	18171.3	1.81807
$465$	−3426.71	−0.341741
$466$	−22259.5	−2.21278
$467$	5014.99	0.496930	0.248465	−	0.968641i	$-0.420074\pi$
$467$	5014.99	0.496930	0.248465	+	0.968641i	$0.420074\pi$
$468$	7256.76	0.716761
$469$	20140.7	1.98297
$470$	40779.5	4.00217
$471$	−3816.08	−0.373324
$472$	−41062.6	−4.00436
$473$	3204.18	0.311477
$474$	−5320.17	−0.515535
$475$	10246.3	0.989756
$476$	−42607.1	−4.10272
$477$	157.985	0.0151649
$478$	20090.9	1.92246
$479$	−3555.86	−0.339188	−0.169594	−	0.985514i	$-0.554246\pi$
$479$	−3555.86	−0.339188	−0.169594	+	0.985514i	$0.554246\pi$
$480$	−22802.1	−2.16827
$481$	−2664.79	−0.252607
$482$	10414.4	0.984152
$483$	−13488.5	−1.27070
$484$	2444.35	0.229560
$485$	12920.6	1.20968
$486$	1290.45	0.120444
$487$	−6264.27	−0.582877	−0.291438	−	0.956590i	$-0.594134\pi$
$487$	−6264.27	−0.582877	−0.291438	+	0.956590i	$0.594134\pi$
$488$	−3952.47	−0.366639
$489$	−3534.26	−0.326840
$490$	63094.5	5.81697
$491$	−3984.94	−0.366269	−0.183134	−	0.983088i	$-0.558624\pi$
$491$	−3984.94	−0.366269	−0.183134	+	0.983088i	$0.558624\pi$
$492$	−22167.1	−2.03124
$493$	−6489.20	−0.592817
$494$	−13625.3	−1.24095
$495$	−1669.54	−0.151597
$496$	−12359.8	−1.11889
$497$	3982.61	0.359446
$498$	11435.0	1.02894
$499$	1044.96	0.0937453	0.0468727	−	0.998901i	$-0.485074\pi$
$499$	1044.96	0.0937453	0.0468727	+	0.998901i	$0.485074\pi$
$500$	−11718.2	−1.04811
$501$	2464.77	0.219796
$502$	4716.83	0.419367
$503$	−10842.3	−0.961101	−0.480550	−	0.876967i	$-0.659563\pi$
$503$	−10842.3	−0.961101	−0.480550	+	0.876967i	$0.659563\pi$
$504$	−18874.0	−1.66808
$505$	−3244.42	−0.285891
$506$	−8115.00	−0.712956
$507$	1811.69	0.158698
$508$	−38302.8	−3.34530
$509$	−4706.37	−0.409835	−0.204918	−	0.978779i	$-0.565693\pi$
$509$	−4706.37	−0.409835	−0.204918	+	0.978779i	$0.565693\pi$
$510$	17508.1	1.52014
$511$	−8449.80	−0.731501
$512$	12345.2	1.06560
$513$	−1735.61	−0.149374
$514$	−33977.1	−2.91569
$515$	−3118.78	−0.266854
$516$	−17653.2	−1.50609
$517$	5008.85	0.426091
$518$	11475.1	0.973336
$519$	12029.7	1.01743
$520$	43613.7	3.67806
$521$	−5818.90	−0.489310	−0.244655	−	0.969610i	$-0.578675\pi$
$521$	−5818.90	−0.489310	−0.244655	+	0.969610i	$0.578675\pi$
$522$	−4759.33	−0.399062
$523$	16130.2	1.34861	0.674305	−	0.738453i	$-0.264443\pi$
$523$	16130.2	1.34861	0.674305	+	0.738453i	$0.264443\pi$
$524$	54114.3	4.51144
$525$	−15476.9	−1.28660
$526$	−39481.4	−3.27276
$527$	4413.83	0.364837
$528$	−6021.86	−0.496341
$529$	7131.47	0.586132
$530$	1572.07	0.128842
$531$	5703.61	0.466131
$532$	42028.9	3.42516
$533$	14599.2	1.18642
$534$	−12779.4	−1.03562
$535$	−1801.70	−0.145597
$536$	−40321.1	−3.24926
$537$	4177.51	0.335703
$538$	38772.7	3.10708
$539$	7749.74	0.619304
$540$	9198.24	0.733017
$541$	23221.3	1.84540	0.922701	−	0.385516i	$-0.125976\pi$
$541$	23221.3	1.84540	0.922701	+	0.385516i	$0.125976\pi$
$542$	−34063.0	−2.69950
$543$	−6468.68	−0.511230
$544$	29370.7	2.31481
$545$	−11458.2	−0.900582
$546$	20580.7	1.61313
$547$	−3089.61	−0.241503	−0.120752	−	0.992683i	$-0.538530\pi$
$547$	−3089.61	−0.241503	−0.120752	+	0.992683i	$0.538530\pi$
$548$	12252.2	0.955085
$549$	549.000	0.0426790
$550$	−9311.23	−0.721877
$551$	6401.15	0.494915
$552$	27003.6	2.08215
$553$	−10808.2	−0.831120
$554$	−10710.6	−0.821391
$555$	−3377.73	−0.258336
$556$	−41466.9	−3.16293
$557$	−19297.5	−1.46798	−0.733989	−	0.679162i	$-0.762343\pi$
$557$	−19297.5	−1.46798	−0.733989	+	0.679162i	$0.762343\pi$
$558$	3237.20	0.245595
$559$	11626.4	0.879689
$560$	−99600.4	−7.51587
$561$	2150.48	0.161842
$562$	11956.7	0.897439
$563$	19940.7	1.49272	0.746358	−	0.665545i	$-0.231801\pi$
$563$	19940.7	1.49272	0.746358	+	0.665545i	$0.231801\pi$
$564$	−27595.9	−2.06028
$565$	−38073.7	−2.83499
$566$	19771.9	1.46833
$567$	2621.60	0.194174
$568$	−7973.06	−0.588983
$569$	1483.64	0.109310	0.0546549	−	0.998505i	$-0.482594\pi$
$569$	1483.64	0.109310	0.0546549	+	0.998505i	$0.482594\pi$
$570$	−17270.6	−1.26909
$571$	−14524.7	−1.06452	−0.532259	−	0.846582i	$-0.678657\pi$
$571$	−14524.7	−1.06452	−0.532259	+	0.846582i	$0.678657\pi$
$572$	8869.38	0.648335
$573$	7978.41	0.581680
$574$	−62867.2	−4.57147
$575$	22143.3	1.60598
$576$	8402.52	0.607822
$577$	356.078	0.0256910	0.0128455	−	0.999917i	$-0.495911\pi$
$577$	356.078	0.0256910	0.0128455	+	0.999917i	$0.495911\pi$
$578$	3538.78	0.254661
$579$	9081.86	0.651864
$580$	−33924.2	−2.42867
$581$	23230.7	1.65881
$582$	−12206.1	−0.869345
$583$	193.093	0.0137172
$584$	16916.2	1.19863
$585$	−6057.97	−0.428147
$586$	−32037.7	−2.25847
$587$	−4403.45	−0.309625	−0.154813	−	0.987944i	$-0.549477\pi$
$587$	−4403.45	−0.309625	−0.154813	+	0.987944i	$0.549477\pi$
$588$	−42696.7	−2.99453
$589$	−4353.93	−0.304585
$590$	56755.0	3.96028
$591$	16009.1	1.11426
$592$	−12183.1	−0.845816
$593$	−8021.21	−0.555467	−0.277733	−	0.960658i	$-0.589583\pi$
$593$	−8021.21	−0.555467	−0.277733	+	0.960658i	$0.589583\pi$
$594$	1577.21	0.108946
$595$	35568.5	2.45070
$596$	−19852.4	−1.36440
$597$	−8770.79	−0.601281
$598$	−29445.4	−2.01357
$599$	−14433.4	−0.984525	−0.492263	−	0.870447i	$-0.663830\pi$
$599$	−14433.4	−0.984525	−0.492263	+	0.870447i	$0.663830\pi$
$600$	30984.2	2.10821
$601$	17973.1	1.21986	0.609931	−	0.792455i	$-0.291197\pi$
$601$	17973.1	1.21986	0.609931	+	0.792455i	$0.291197\pi$
$602$	−50065.7	−3.38958
$603$	5600.62	0.378233
$604$	−18806.3	−1.26691
$605$	−2040.55	−0.137124
$606$	3065.00	0.205457
$607$	19192.3	1.28335	0.641675	−	0.766977i	$-0.278240\pi$
$607$	19192.3	1.28335	0.641675	+	0.766977i	$0.278240\pi$
$608$	−28972.1	−1.93252
$609$	−9668.79	−0.643348
$610$	5462.94	0.362603
$611$	18174.7	1.20339
$612$	−11847.9	−0.782556
$613$	−1344.96	−0.0886174	−0.0443087	−	0.999018i	$-0.514109\pi$
$613$	−1344.96	−0.0886174	−0.0443087	+	0.999018i	$0.514109\pi$
$614$	−52456.1	−3.44781
$615$	18505.1	1.21333
$616$	−23068.2	−1.50884
$617$	14426.1	0.941284	0.470642	−	0.882324i	$-0.344022\pi$
$617$	14426.1	0.941284	0.470642	+	0.882324i	$0.344022\pi$
$618$	2946.30	0.191776
$619$	927.518	0.0602264	0.0301132	−	0.999546i	$-0.490413\pi$
$619$	927.518	0.0602264	0.0301132	+	0.999546i	$0.490413\pi$
$620$	23074.6	1.49467
$621$	−3750.81	−0.242375
$622$	−33450.5	−2.15634
$623$	−25961.9	−1.66957
$624$	−21850.4	−1.40179
$625$	−10142.2	−0.649103
$626$	−21284.9	−1.35897
$627$	−2121.30	−0.135114
$628$	25696.5	1.63281
$629$	4350.74	0.275796
$630$	26086.8	1.64972
$631$	−17050.3	−1.07569	−0.537845	−	0.843044i	$-0.680761\pi$
$631$	−17050.3	−1.07569	−0.537845	+	0.843044i	$0.680761\pi$
$632$	21637.6	1.36186
$633$	14749.0	0.926101
$634$	−10293.2	−0.644785
$635$	31975.3	1.99827
$636$	−1063.83	−0.0663267
$637$	28120.1	1.74907
$638$	−5816.96	−0.360965
$639$	1107.46	0.0685611
$640$	22805.4	1.40854
$641$	−28119.7	−1.73270	−0.866351	−	0.499435i	$-0.833541\pi$
$641$	−28119.7	−1.73270	−0.866351	+	0.499435i	$0.833541\pi$
$642$	1702.06	0.104634
$643$	28425.0	1.74335	0.871674	−	0.490087i	$-0.163035\pi$
$643$	28425.0	1.74335	0.871674	+	0.490087i	$0.163035\pi$
$644$	90828.4	5.55767
$645$	14737.0	0.899640
$646$	22245.6	1.35486
$647$	−28579.1	−1.73657	−0.868285	−	0.496066i	$-0.834778\pi$
$647$	−28579.1	−1.73657	−0.868285	+	0.496066i	$0.834778\pi$
$648$	−5248.36	−0.318172
$649$	6971.08	0.421632
$650$	−33786.0	−2.03876
$651$	6576.52	0.395936
$652$	23798.8	1.42950
$653$	32087.3	1.92293	0.961464	−	0.274931i	$-0.0886551\pi$
$653$	32087.3	1.92293	0.961464	+	0.274931i	$0.0886551\pi$
$654$	10824.6	0.647209
$655$	−45174.8	−2.69485
$656$	66746.0	3.97255
$657$	−2349.67	−0.139527
$658$	−78263.9	−4.63684
$659$	−17102.6	−1.01096	−0.505480	−	0.862838i	$-0.668685\pi$
$659$	−17102.6	−1.01096	−0.505480	+	0.862838i	$0.668685\pi$
$660$	11242.3	0.663039
$661$	22713.8	1.33656	0.668280	−	0.743910i	$-0.267031\pi$
$661$	22713.8	1.33656	0.668280	+	0.743910i	$0.267031\pi$
$662$	19516.0	1.14579
$663$	7803.07	0.457083
$664$	−46507.1	−2.71811
$665$	−35085.9	−2.04597
$666$	3190.94	0.185655
$667$	13833.5	0.803049
$668$	−16597.2	−0.961323
$669$	17658.4	1.02050
$670$	55730.1	3.21350
$671$	671.000	0.0386046
$672$	43761.8	2.51212
$673$	12355.4	0.707674	0.353837	−	0.935307i	$-0.384877\pi$
$673$	12355.4	0.707674	0.353837	+	0.935307i	$0.384877\pi$
$674$	−63485.0	−3.62812
$675$	−4303.72	−0.245408
$676$	−12199.5	−0.694097
$677$	−6860.47	−0.389467	−0.194734	−	0.980856i	$-0.562384\pi$
$677$	−6860.47	−0.389467	−0.194734	+	0.980856i	$0.562384\pi$
$678$	35968.1	2.03739
$679$	−24797.2	−1.40152
$680$	−71207.1	−4.01569
$681$	18895.9	1.06328
$682$	3956.58	0.222149
$683$	−15254.4	−0.854602	−0.427301	−	0.904109i	$-0.640536\pi$
$683$	−15254.4	−0.854602	−0.427301	+	0.904109i	$0.640536\pi$
$684$	11687.2	0.653319
$685$	−10228.1	−0.570507
$686$	−62137.0	−3.45831
$687$	4991.41	0.277197
$688$	53154.7	2.94550
$689$	700.643	0.0387407
$690$	−37323.2	−2.05923
$691$	−33775.4	−1.85944	−0.929721	−	0.368264i	$-0.879952\pi$
$691$	−33775.4	−1.85944	−0.929721	+	0.368264i	$0.879952\pi$
$692$	−81005.3	−4.44994
$693$	3204.18	0.175637
$694$	−4863.51	−0.266018
$695$	34616.7	1.88933
$696$	19356.6	1.05418
$697$	−23835.8	−1.29533
$698$	−53204.9	−2.88515
$699$	−12574.9	−0.680436
$700$	104217.	5.62721
$701$	−16254.6	−0.875788	−0.437894	−	0.899027i	$-0.644275\pi$
$701$	−16254.6	−0.875788	−0.437894	+	0.899027i	$0.644275\pi$
$702$	5722.95	0.307691
$703$	−4291.70	−0.230249
$704$	10269.8	0.549795
$705$	23037.2	1.23068
$706$	−6927.67	−0.369301
$707$	6226.68	0.331228
$708$	−38406.7	−2.03872
$709$	3243.13	0.171789	0.0858945	−	0.996304i	$-0.472625\pi$
$709$	3243.13	0.171789	0.0858945	+	0.996304i	$0.472625\pi$
$710$	11020.0	0.582499
$711$	−3005.47	−0.158529
$712$	51975.0	2.73574
$713$	−9409.24	−0.494220
$714$	−33601.5	−1.76121
$715$	−7404.18	−0.387274
$716$	−28130.3	−1.46827
$717$	11349.8	0.591164
$718$	36349.8	1.88936
$719$	−18184.1	−0.943189	−0.471594	−	0.881816i	$-0.656321\pi$
$719$	−18184.1	−0.943189	−0.471594	+	0.881816i	$0.656321\pi$
$720$	−27696.3	−1.43358
$721$	5985.54	0.309172
$722$	14480.9	0.746429
$723$	5883.29	0.302630
$724$	43558.5	2.23597
$725$	15872.6	0.813097
$726$	1927.71	0.0985453
$727$	19119.5	0.975382	0.487691	−	0.873016i	$-0.337839\pi$
$727$	19119.5	0.975382	0.487691	+	0.873016i	$0.337839\pi$
$728$	−83703.3	−4.26133
$729$	729.000	0.0370370
$730$	−23380.9	−1.18543
$731$	−18982.2	−0.960440
$732$	−3696.83	−0.186665
$733$	7037.26	0.354607	0.177304	−	0.984156i	$-0.443263\pi$
$733$	7037.26	0.354607	0.177304	+	0.984156i	$0.443263\pi$
$734$	2609.95	0.131246
$735$	35643.3	1.78874
$736$	−62611.4	−3.13572
$737$	6845.20	0.342125
$738$	−17481.8	−0.871968
$739$	19243.4	0.957890	0.478945	−	0.877845i	$-0.341019\pi$
$739$	19243.4	0.957890	0.478945	+	0.877845i	$0.341019\pi$
$740$	22744.8	1.12989
$741$	−7697.18	−0.381597
$742$	−3017.10	−0.149274
$743$	40022.6	1.97616	0.988081	−	0.153938i	$-0.0491955\pi$
$743$	40022.6	1.97616	0.988081	+	0.153938i	$0.0491955\pi$
$744$	−13166.0	−0.648775
$745$	16572.8	0.815009
$746$	−10353.2	−0.508120
$747$	6459.86	0.316404
$748$	−14480.8	−0.707849
$749$	3457.81	0.168686
$750$	−9241.40	−0.449931
$751$	18599.0	0.903711	0.451856	−	0.892091i	$-0.350762\pi$
$751$	18599.0	0.903711	0.451856	+	0.892091i	$0.350762\pi$
$752$	83092.6	4.02936
$753$	2664.63	0.128957
$754$	−21107.0	−1.01946
$755$	15699.5	0.756774
$756$	−17653.2	−0.849261
$757$	36818.9	1.76778	0.883888	−	0.467699i	$-0.154917\pi$
$757$	36818.9	1.76778	0.883888	+	0.467699i	$0.154917\pi$
$758$	16353.4	0.783617
$759$	−4584.33	−0.219236
$760$	70240.8	3.35250
$761$	95.7096	0.00455910	0.00227955	−	0.999997i	$-0.499274\pi$
$761$	95.7096	0.00455910	0.00227955	+	0.999997i	$0.499274\pi$
$762$	−30207.0	−1.43607
$763$	21990.6	1.04340
$764$	−53724.6	−2.54409
$765$	9890.70	0.467450
$766$	36800.1	1.73582
$767$	25294.7	1.19079
$768$	862.512	0.0405250
$769$	−38992.3	−1.82847	−0.914237	−	0.405179i	$-0.867209\pi$
$769$	−38992.3	−1.82847	−0.914237	+	0.405179i	$0.867209\pi$
$770$	31883.9	1.49223
$771$	−19194.4	−0.896586
$772$	−61155.0	−2.85106
$773$	42207.6	1.96391	0.981955	−	0.189117i	$-0.0605625\pi$
$773$	42207.6	1.96391	0.981955	+	0.189117i	$0.0605625\pi$
$774$	−13922.0	−0.646532
$775$	−10796.3	−0.500404
$776$	49643.2	2.29651
$777$	6482.53	0.299304
$778$	−12622.4	−0.581664
$779$	23512.4	1.08141
$780$	40792.9	1.87259
$781$	1353.56	0.0620158
$782$	48074.8	2.19840
$783$	−2688.64	−0.122713
$784$	128562.	5.85649
$785$	−21451.6	−0.975336
$786$	42676.5	1.93667
$787$	−9861.84	−0.446679	−0.223340	−	0.974741i	$-0.571696\pi$
$787$	−9861.84	−0.446679	−0.223340	+	0.974741i	$0.571696\pi$
$788$	−107801.	−4.87343
$789$	−22303.8	−1.00638
$790$	−29906.6	−1.34687
$791$	73070.8	3.28457
$792$	−6414.67	−0.287797
$793$	2434.74	0.109029
$794$	6817.67	0.304723
$795$	888.093	0.0396194
$796$	59060.4	2.62982
$797$	−16262.2	−0.722754	−0.361377	−	0.932420i	$-0.617693\pi$
$797$	−16262.2	−0.722754	−0.361377	+	0.932420i	$0.617693\pi$
$798$	33145.6	1.47035
$799$	−29673.4	−1.31385
$800$	−71840.9	−3.17495
$801$	−7219.35	−0.318456
$802$	−45243.5	−1.99203
$803$	−2871.82	−0.126207
$804$	−37713.2	−1.65428
$805$	−75823.8	−3.31980
$806$	14356.5	0.627404
$807$	21903.5	0.955440
$808$	−12465.6	−0.542746
$809$	−23372.9	−1.01576	−0.507879	−	0.861429i	$-0.669570\pi$
$809$	−23372.9	−1.01576	−0.507879	+	0.861429i	$0.669570\pi$
$810$	7254.07	0.314669
$811$	26224.1	1.13545	0.567727	−	0.823217i	$-0.307823\pi$
$811$	26224.1	1.13545	0.567727	+	0.823217i	$0.307823\pi$
$812$	65107.3	2.81381
$813$	−19242.9	−0.830107
$814$	3900.03	0.167931
$815$	−19867.3	−0.853893
$816$	35674.7	1.53047
$817$	18724.6	0.801825
$818$	−20372.6	−0.870798
$819$	11626.4	0.496044
$820$	−124609.	−5.30675
$821$	−37602.8	−1.59847	−0.799236	−	0.601017i	$-0.794763\pi$
$821$	−37602.8	−1.59847	−0.799236	+	0.601017i	$0.794763\pi$
$822$	9662.51	0.409998
$823$	−44986.1	−1.90537	−0.952684	−	0.303962i	$-0.901691\pi$
$823$	−44986.1	−1.90537	−0.952684	+	0.303962i	$0.901691\pi$
$824$	−11982.9	−0.506605
$825$	−5260.10	−0.221980
$826$	−108924.	−4.58832
$827$	−9616.18	−0.404338	−0.202169	−	0.979351i	$-0.564799\pi$
$827$	−9616.18	−0.404338	−0.202169	+	0.979351i	$0.564799\pi$
$828$	25257.0	1.06008
$829$	22726.0	0.952121	0.476060	−	0.879413i	$-0.342064\pi$
$829$	22726.0	0.952121	0.476060	+	0.879413i	$0.342064\pi$
$830$	64280.2	2.68819
$831$	−6050.64	−0.252581
$832$	37264.0	1.55276
$833$	−45911.0	−1.90963
$834$	−32702.3	−1.35778
$835$	13855.4	0.574233
$836$	14284.3	0.590949
$837$	1828.76	0.0755212
$838$	42359.7	1.74617
$839$	16199.8	0.666601	0.333300	−	0.942821i	$-0.391838\pi$
$839$	16199.8	0.666601	0.333300	+	0.942821i	$0.391838\pi$
$840$	−106097.	−4.35798
$841$	−14472.9	−0.593421
$842$	−21684.3	−0.887517
$843$	6754.55	0.275966
$844$	−99316.4	−4.05049
$845$	10184.1	0.414610
$846$	−21763.2	−0.884437
$847$	3916.22	0.158870
$848$	3203.26	0.129717
$849$	11169.5	0.451516
$850$	55161.5	2.22591
$851$	−9274.77	−0.373602
$852$	−7457.37	−0.299866
$853$	12494.0	0.501509	0.250754	−	0.968051i	$-0.419321\pi$
$853$	12494.0	0.501509	0.250754	+	0.968051i	$0.419321\pi$
$854$	−10484.4	−0.420106
$855$	−9756.48	−0.390251
$856$	−6922.43	−0.276406
$857$	9648.55	0.384584	0.192292	−	0.981338i	$-0.438408\pi$
$857$	9648.55	0.384584	0.192292	+	0.981338i	$0.438408\pi$
$858$	6994.72	0.278317
$859$	−14439.4	−0.573534	−0.286767	−	0.958000i	$-0.592581\pi$
$859$	−14439.4	−0.573534	−0.286767	+	0.958000i	$0.592581\pi$
$860$	−99235.1	−3.93476
$861$	−35514.9	−1.40574
$862$	36456.5	1.44050
$863$	−41261.3	−1.62752	−0.813761	−	0.581199i	$-0.802584\pi$
$863$	−41261.3	−1.62752	−0.813761	+	0.581199i	$0.802584\pi$
$864$	12169.0	0.479165
$865$	67623.5	2.65811
$866$	74441.8	2.92106
$867$	1999.13	0.0783091
$868$	−44284.7	−1.73170
$869$	−3673.35	−0.143395
$870$	−26753.9	−1.04258
$871$	24837.9	0.966247
$872$	−44024.5	−1.70970
$873$	−6895.47	−0.267327
$874$	−47422.5	−1.83534
$875$	−18774.3	−0.725357
$876$	15822.1	0.610250
$877$	8497.57	0.327187	0.163593	−	0.986528i	$-0.447692\pi$
$877$	8497.57	0.327187	0.163593	+	0.986528i	$0.447692\pi$
$878$	−69251.0	−2.66185
$879$	−18098.7	−0.694488
$880$	−33851.1	−1.29673
$881$	−23206.7	−0.887460	−0.443730	−	0.896161i	$-0.646345\pi$
$881$	−23206.7	−0.887460	−0.443730	+	0.896161i	$0.646345\pi$
$882$	−33672.2	−1.28549
$883$	−5839.66	−0.222560	−0.111280	−	0.993789i	$-0.535495\pi$
$883$	−5839.66	−0.222560	−0.111280	+	0.993789i	$0.535495\pi$
$884$	−52543.9	−1.99914
$885$	32062.1	1.21780
$886$	−8142.54	−0.308752
$887$	−44173.3	−1.67215	−0.836074	−	0.548616i	$-0.815155\pi$
$887$	−44173.3	−1.67215	−0.836074	+	0.548616i	$0.815155\pi$
$888$	−12977.8	−0.490436
$889$	−61366.8	−2.31516
$890$	−71837.7	−2.70562
$891$	891.000	0.0335013
$892$	−118908.	−4.46337
$893$	29270.8	1.09687
$894$	−15656.3	−0.585711
$895$	23483.3	0.877049
$896$	−43768.0	−1.63190
$897$	−16634.3	−0.619179
$898$	−62282.2	−2.31446
$899$	−6744.70	−0.250221
$900$	28980.2	1.07334
$901$	−1143.92	−0.0422970
$902$	−21366.6	−0.788725
$903$	−28283.1	−1.04231
$904$	−146285.	−5.38206
$905$	−36362.8	−1.33562
$906$	−14831.3	−0.543860
$907$	38981.3	1.42707	0.713535	−	0.700619i	$-0.247093\pi$
$907$	38981.3	1.42707	0.713535	+	0.700619i	$0.247093\pi$
$908$	−127240.	−4.65046
$909$	1731.48	0.0631789
$910$	115691.	4.21442
$911$	−26615.7	−0.967966	−0.483983	−	0.875077i	$-0.660810\pi$
$911$	−26615.7	−0.967966	−0.483983	+	0.875077i	$0.660810\pi$
$912$	−35190.6	−1.27772
$913$	7895.38	0.286198
$914$	−78491.2	−2.84055
$915$	3086.13	0.111502
$916$	−33610.9	−1.21238
$917$	86699.2	3.12220
$918$	−9343.72	−0.335935
$919$	5140.22	0.184505	0.0922526	−	0.995736i	$-0.470593\pi$
$919$	5140.22	0.184505	0.0922526	+	0.995736i	$0.470593\pi$
$920$	151797.	5.43978
$921$	−29633.5	−1.06021
$922$	33541.9	1.19810
$923$	4911.44	0.175148
$924$	−21576.1	−0.768185
$925$	−10642.0	−0.378276
$926$	68093.4	2.41651
$927$	1664.43	0.0589719
$928$	−44880.9	−1.58759
$929$	11927.6	0.421241	0.210620	−	0.977568i	$-0.432452\pi$
$929$	11927.6	0.421241	0.210620	+	0.977568i	$0.432452\pi$
$930$	18197.5	0.641633
$931$	45288.0	1.59426
$932$	84676.0	2.97602
$933$	−18896.8	−0.663081
$934$	−26632.0	−0.933005
$935$	12088.6	0.422824
$936$	−23275.7	−0.812811
$937$	−10397.0	−0.362492	−0.181246	−	0.983438i	$-0.558013\pi$
$937$	−10397.0	−0.362492	−0.181246	+	0.983438i	$0.558013\pi$
$938$	−106957.	−3.72310
$939$	−12024.3	−0.417888
$940$	−155127.	−5.38263
$941$	−41108.1	−1.42411	−0.712053	−	0.702125i	$-0.752235\pi$
$941$	−41108.1	−1.42411	−0.712053	+	0.702125i	$0.752235\pi$
$942$	20265.2	0.700931
$943$	50812.4	1.75470
$944$	115644.	3.98719
$945$	14737.0	0.507294
$946$	−17015.8	−0.584810
$947$	53438.4	1.83370	0.916851	−	0.399230i	$-0.130722\pi$
$947$	53438.4	1.83370	0.916851	+	0.399230i	$0.130722\pi$
$948$	20238.1	0.693357
$949$	−10420.5	−0.356441
$950$	−54413.0	−1.85831
$951$	−5814.81	−0.198274
$952$	136660.	4.65251
$953$	−32416.5	−1.10186	−0.550930	−	0.834552i	$-0.685727\pi$
$953$	−32416.5	−1.10186	−0.550930	+	0.834552i	$0.685727\pi$
$954$	−838.979	−0.0284727
$955$	44849.5	1.51968
$956$	−76426.4	−2.58557
$957$	−3286.12	−0.110998
$958$	18883.3	0.636840
$959$	19629.8	0.660980
$960$	47233.6	1.58798
$961$	−25203.4	−0.846007
$962$	14151.3	0.474280
$963$	961.528	0.0321753
$964$	−39616.6	−1.32361
$965$	51052.4	1.70304
$966$	71630.6	2.38579
$967$	29322.7	0.975135	0.487568	−	0.873085i	$-0.337884\pi$
$967$	29322.7	0.975135	0.487568	+	0.873085i	$0.337884\pi$
$968$	−7840.15	−0.260322
$969$	12567.0	0.416625
$970$	−68614.8	−2.27123
$971$	−36766.4	−1.21513	−0.607564	−	0.794270i	$-0.707853\pi$
$971$	−36766.4	−1.21513	−0.607564	+	0.794270i	$0.707853\pi$
$972$	−4908.91	−0.161989
$973$	−66436.2	−2.18895
$974$	33266.3	1.09437
$975$	−19086.4	−0.626926
$976$	11131.3	0.365067
$977$	−11137.6	−0.364710	−0.182355	−	0.983233i	$-0.558372\pi$
$977$	−11137.6	−0.364710	−0.182355	+	0.983233i	$0.558372\pi$
$978$	18768.6	0.613656
$979$	−8823.65	−0.288054
$980$	−240013.	−7.82341
$981$	6115.02	0.199019
$982$	21162.0	0.687684
$983$	14639.4	0.475001	0.237500	−	0.971387i	$-0.423672\pi$
$983$	14639.4	0.475001	0.237500	+	0.971387i	$0.423672\pi$
$984$	71099.8	2.30343
$985$	89992.8	2.91108
$986$	34460.8	1.11304
$987$	−44212.8	−1.42585
$988$	51830.9	1.66899
$989$	40465.6	1.30104
$990$	8866.09	0.284629
$991$	−26308.3	−0.843301	−0.421650	−	0.906758i	$-0.638549\pi$
$991$	−26308.3	−0.843301	−0.421650	+	0.906758i	$0.638549\pi$
$992$	30527.1	0.977052
$993$	11025.0	0.352334
$994$	−21149.6	−0.674874
$995$	−49303.8	−1.57089
$996$	−43499.1	−1.38386
$997$	38009.9	1.20741	0.603704	−	0.797209i	$-0.293691\pi$
$997$	38009.9	1.20741	0.603704	+	0.797209i	$0.293691\pi$
$998$	−5549.26	−0.176011
$999$	1802.62	0.0570896

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.g.1.2	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.g.1.2	✓	39	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-5.31049 q^{2} -3.00000 q^{3} +20.2013 q^{4} -16.8641 q^{5} +15.9315 q^{6} +32.3654 q^{7} -64.7946 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-5.31049 q^{2} -3.00000 q^{3} +20.2013 q^{4} -16.8641 q^{5} +15.9315 q^{6} +32.3654 q^{7} -64.7946 q^{8} +9.00000 q^{9} +89.5564 q^{10} +11.0000 q^{11} -60.6038 q^{12} +39.9137 q^{13} -171.876 q^{14} +50.5922 q^{15} +182.481 q^{16} -65.1661 q^{17} -47.7944 q^{18} +64.2818 q^{19} -340.675 q^{20} -97.0963 q^{21} -58.4153 q^{22} +138.919 q^{23} +194.384 q^{24} +159.397 q^{25} -211.961 q^{26} -27.0000 q^{27} +653.823 q^{28} +99.5794 q^{29} -268.669 q^{30} -67.7319 q^{31} -450.704 q^{32} -33.0000 q^{33} +346.064 q^{34} -545.813 q^{35} +181.811 q^{36} -66.7639 q^{37} -341.368 q^{38} -119.741 q^{39} +1092.70 q^{40} +365.770 q^{41} +515.629 q^{42} +291.289 q^{43} +222.214 q^{44} -151.777 q^{45} -737.727 q^{46} +455.350 q^{47} -547.442 q^{48} +704.522 q^{49} -846.475 q^{50} +195.498 q^{51} +806.307 q^{52} +17.5539 q^{53} +143.383 q^{54} -185.505 q^{55} -2097.11 q^{56} -192.846 q^{57} -528.815 q^{58} +633.735 q^{59} +1022.03 q^{60} +61.0000 q^{61} +359.689 q^{62} +291.289 q^{63} +933.614 q^{64} -673.108 q^{65} +175.246 q^{66} +622.291 q^{67} -1316.44 q^{68} -416.757 q^{69} +2898.53 q^{70} +123.051 q^{71} -583.151 q^{72} -261.075 q^{73} +354.549 q^{74} -478.191 q^{75} +1298.57 q^{76} +356.020 q^{77} +635.884 q^{78} -333.941 q^{79} -3077.37 q^{80} +81.0000 q^{81} -1942.42 q^{82} +717.762 q^{83} -1961.47 q^{84} +1098.97 q^{85} -1546.89 q^{86} -298.738 q^{87} -712.741 q^{88} -802.150 q^{89} +806.008 q^{90} +1291.83 q^{91} +2806.34 q^{92} +203.196 q^{93} -2418.13 q^{94} -1084.05 q^{95} +1352.11 q^{96} -766.163 q^{97} -3741.35 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 4 q^{2} - 117 q^{3} + 182 q^{4} + 5 q^{5} - 12 q^{6} + 77 q^{7} + 27 q^{8} + 351 q^{9}+O(q^{10}) \) 39 * q + 4 * q^2 - 117 * q^3 + 182 * q^4 + 5 * q^5 - 12 * q^6 + 77 * q^7 + 27 * q^8 + 351 * q^9	\( 39 q + 4 q^{2} - 117 q^{3} + 182 q^{4} + 5 q^{5} - 12 q^{6} + 77 q^{7} + 27 q^{8} + 351 q^{9} + 95 q^{10} + 429 q^{11} - 546 q^{12} + 169 q^{13} + 46 q^{14} - 15 q^{15} + 822 q^{16} + 294 q^{17} + 36 q^{18} + 259 q^{19} + 426 q^{20} - 231 q^{21} + 44 q^{22} + 177 q^{23} - 81 q^{24} + 1388 q^{25} + 695 q^{26} - 1053 q^{27} + 1104 q^{28} - 18 q^{29} - 285 q^{30} + 422 q^{31} + 55 q^{32} - 1287 q^{33} + 364 q^{34} + 906 q^{35} + 1638 q^{36} + 424 q^{37} + 9 q^{38} - 507 q^{39} + 1067 q^{40} + 16 q^{41} - 138 q^{42} + 1013 q^{43} + 2002 q^{44} + 45 q^{45} + 9 q^{46} + 1615 q^{47} - 2466 q^{48} + 2024 q^{49} - 1342 q^{50} - 882 q^{51} + 1298 q^{52} - 541 q^{53} - 108 q^{54} + 55 q^{55} - 161 q^{56} - 777 q^{57} + 1061 q^{58} + 1019 q^{59} - 1278 q^{60} + 2379 q^{61} + 879 q^{62} + 693 q^{63} + 1055 q^{64} - 1134 q^{65} - 132 q^{66} + 1917 q^{67} + 3526 q^{68} - 531 q^{69} + 758 q^{70} - 479 q^{71} + 243 q^{72} + 3319 q^{73} - 332 q^{74} - 4164 q^{75} + 692 q^{76} + 847 q^{77} - 2085 q^{78} + 651 q^{79} + 2973 q^{80} + 3159 q^{81} - 826 q^{82} + 4001 q^{83} - 3312 q^{84} + 3595 q^{85} - 6247 q^{86} + 54 q^{87} + 297 q^{88} - 1625 q^{89} + 855 q^{90} + 2048 q^{91} - 507 q^{92} - 1266 q^{93} - 2436 q^{94} + 1400 q^{95} - 165 q^{96} + 2176 q^{97} - 1396 q^{98} + 3861 q^{99}+O(q^{100}) \) 39 * q + 4 * q^2 - 117 * q^3 + 182 * q^4 + 5 * q^5 - 12 * q^6 + 77 * q^7 + 27 * q^8 + 351 * q^9 + 95 * q^10 + 429 * q^11 - 546 * q^12 + 169 * q^13 + 46 * q^14 - 15 * q^15 + 822 * q^16 + 294 * q^17 + 36 * q^18 + 259 * q^19 + 426 * q^20 - 231 * q^21 + 44 * q^22 + 177 * q^23 - 81 * q^24 + 1388 * q^25 + 695 * q^26 - 1053 * q^27 + 1104 * q^28 - 18 * q^29 - 285 * q^30 + 422 * q^31 + 55 * q^32 - 1287 * q^33 + 364 * q^34 + 906 * q^35 + 1638 * q^36 + 424 * q^37 + 9 * q^38 - 507 * q^39 + 1067 * q^40 + 16 * q^41 - 138 * q^42 + 1013 * q^43 + 2002 * q^44 + 45 * q^45 + 9 * q^46 + 1615 * q^47 - 2466 * q^48 + 2024 * q^49 - 1342 * q^50 - 882 * q^51 + 1298 * q^52 - 541 * q^53 - 108 * q^54 + 55 * q^55 - 161 * q^56 - 777 * q^57 + 1061 * q^58 + 1019 * q^59 - 1278 * q^60 + 2379 * q^61 + 879 * q^62 + 693 * q^63 + 1055 * q^64 - 1134 * q^65 - 132 * q^66 + 1917 * q^67 + 3526 * q^68 - 531 * q^69 + 758 * q^70 - 479 * q^71 + 243 * q^72 + 3319 * q^73 - 332 * q^74 - 4164 * q^75 + 692 * q^76 + 847 * q^77 - 2085 * q^78 + 651 * q^79 + 2973 * q^80 + 3159 * q^81 - 826 * q^82 + 4001 * q^83 - 3312 * q^84 + 3595 * q^85 - 6247 * q^86 + 54 * q^87 + 297 * q^88 - 1625 * q^89 + 855 * q^90 + 2048 * q^91 - 507 * q^92 - 1266 * q^93 - 2436 * q^94 + 1400 * q^95 - 165 * q^96 + 2176 * q^97 - 1396 * q^98 + 3861 * q^99

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