LMFDB - Embedded newform 2013.4.a.h.1.8

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			1.8
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.67115 q^{2} +3.00000 q^{3} +5.47734 q^{4} +14.7390 q^{5} -11.0134 q^{6} -28.2167 q^{7} +9.26107 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.67115 q^{2} +3.00000 q^{3} +5.47734 q^{4} +14.7390 q^{5} -11.0134 q^{6} -28.2167 q^{7} +9.26107 q^{8} +9.00000 q^{9} -54.1090 q^{10} -11.0000 q^{11} +16.4320 q^{12} -27.9083 q^{13} +103.588 q^{14} +44.2169 q^{15} -77.8175 q^{16} -25.0833 q^{17} -33.0403 q^{18} +89.2644 q^{19} +80.7303 q^{20} -84.6501 q^{21} +40.3826 q^{22} -170.510 q^{23} +27.7832 q^{24} +92.2373 q^{25} +102.456 q^{26} +27.0000 q^{27} -154.552 q^{28} +61.6408 q^{29} -162.327 q^{30} +171.523 q^{31} +211.591 q^{32} -33.0000 q^{33} +92.0847 q^{34} -415.885 q^{35} +49.2960 q^{36} -110.137 q^{37} -327.703 q^{38} -83.7249 q^{39} +136.499 q^{40} -438.814 q^{41} +310.763 q^{42} -325.985 q^{43} -60.2507 q^{44} +132.651 q^{45} +625.966 q^{46} +390.251 q^{47} -233.452 q^{48} +453.182 q^{49} -338.617 q^{50} -75.2500 q^{51} -152.863 q^{52} -136.186 q^{53} -99.1210 q^{54} -162.129 q^{55} -261.317 q^{56} +267.793 q^{57} -226.293 q^{58} +552.384 q^{59} +242.191 q^{60} +61.0000 q^{61} -629.685 q^{62} -253.950 q^{63} -154.242 q^{64} -411.340 q^{65} +121.148 q^{66} +802.094 q^{67} -137.390 q^{68} -511.529 q^{69} +1526.78 q^{70} -823.637 q^{71} +83.3496 q^{72} +695.845 q^{73} +404.331 q^{74} +276.712 q^{75} +488.931 q^{76} +310.384 q^{77} +307.367 q^{78} -1208.77 q^{79} -1146.95 q^{80} +81.0000 q^{81} +1610.95 q^{82} -73.7825 q^{83} -463.657 q^{84} -369.703 q^{85} +1196.74 q^{86} +184.923 q^{87} -101.872 q^{88} +996.876 q^{89} -486.981 q^{90} +787.480 q^{91} -933.938 q^{92} +514.568 q^{93} -1432.67 q^{94} +1315.67 q^{95} +634.773 q^{96} +313.136 q^{97} -1663.70 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9}+O(q^{10}) $ 39 * q + 8 * q^2 + 117 * q^3 + 154 * q^4 + 65 * q^5 + 24 * q^6 + 35 * q^7 + 75 * q^8 + 351 * q^9	\( 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9} - 21 q^{10} - 429 q^{11} + 462 q^{12} - 27 q^{13} + 164 q^{14} + 195 q^{15} + 686 q^{16} + 170 q^{17} + 72 q^{18} + 139 q^{19} + 1056 q^{20} + 105 q^{21} - 88 q^{22} + 291 q^{23} + 225 q^{24} + 1236 q^{25} + 583 q^{26} + 1053 q^{27} + 976 q^{28} + 374 q^{29} - 63 q^{30} + 232 q^{31} + 933 q^{32} - 1287 q^{33} + 332 q^{34} + 626 q^{35} + 1386 q^{36} + 232 q^{37} + 989 q^{38} - 81 q^{39} - 263 q^{40} + 1014 q^{41} + 492 q^{42} + 515 q^{43} - 1694 q^{44} + 585 q^{45} - 371 q^{46} + 2005 q^{47} + 2058 q^{48} + 2064 q^{49} + 4582 q^{50} + 510 q^{51} + 216 q^{52} + 1485 q^{53} + 216 q^{54} - 715 q^{55} + 2307 q^{56} + 417 q^{57} + 573 q^{58} + 2749 q^{59} + 3168 q^{60} + 2379 q^{61} + 1837 q^{62} + 315 q^{63} + 7295 q^{64} + 3630 q^{65} - 264 q^{66} + 3575 q^{67} + 2630 q^{68} + 873 q^{69} + 4218 q^{70} + 4723 q^{71} + 675 q^{72} + 859 q^{73} + 4232 q^{74} + 3708 q^{75} + 2466 q^{76} - 385 q^{77} + 1749 q^{78} - 1887 q^{79} + 8933 q^{80} + 3159 q^{81} + 6806 q^{82} + 5609 q^{83} + 2928 q^{84} - 565 q^{85} + 5185 q^{86} + 1122 q^{87} - 825 q^{88} + 6725 q^{89} - 189 q^{90} + 2808 q^{91} + 3257 q^{92} + 696 q^{93} + 3184 q^{94} + 3216 q^{95} + 2799 q^{96} + 3512 q^{97} + 4464 q^{98} - 3861 q^{99}+O(q^{100}) \) 39 * q + 8 * q^2 + 117 * q^3 + 154 * q^4 + 65 * q^5 + 24 * q^6 + 35 * q^7 + 75 * q^8 + 351 * q^9 - 21 * q^10 - 429 * q^11 + 462 * q^12 - 27 * q^13 + 164 * q^14 + 195 * q^15 + 686 * q^16 + 170 * q^17 + 72 * q^18 + 139 * q^19 + 1056 * q^20 + 105 * q^21 - 88 * q^22 + 291 * q^23 + 225 * q^24 + 1236 * q^25 + 583 * q^26 + 1053 * q^27 + 976 * q^28 + 374 * q^29 - 63 * q^30 + 232 * q^31 + 933 * q^32 - 1287 * q^33 + 332 * q^34 + 626 * q^35 + 1386 * q^36 + 232 * q^37 + 989 * q^38 - 81 * q^39 - 263 * q^40 + 1014 * q^41 + 492 * q^42 + 515 * q^43 - 1694 * q^44 + 585 * q^45 - 371 * q^46 + 2005 * q^47 + 2058 * q^48 + 2064 * q^49 + 4582 * q^50 + 510 * q^51 + 216 * q^52 + 1485 * q^53 + 216 * q^54 - 715 * q^55 + 2307 * q^56 + 417 * q^57 + 573 * q^58 + 2749 * q^59 + 3168 * q^60 + 2379 * q^61 + 1837 * q^62 + 315 * q^63 + 7295 * q^64 + 3630 * q^65 - 264 * q^66 + 3575 * q^67 + 2630 * q^68 + 873 * q^69 + 4218 * q^70 + 4723 * q^71 + 675 * q^72 + 859 * q^73 + 4232 * q^74 + 3708 * q^75 + 2466 * q^76 - 385 * q^77 + 1749 * q^78 - 1887 * q^79 + 8933 * q^80 + 3159 * q^81 + 6806 * q^82 + 5609 * q^83 + 2928 * q^84 - 565 * q^85 + 5185 * q^86 + 1122 * q^87 - 825 * q^88 + 6725 * q^89 - 189 * q^90 + 2808 * q^91 + 3257 * q^92 + 696 * q^93 + 3184 * q^94 + 3216 * q^95 + 2799 * q^96 + 3512 * q^97 + 4464 * q^98 - 3861 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−3.67115	−1.29795	−0.648974	−	0.760811i	$-0.724801\pi$
$2$	−3.67115	−1.29795	−0.648974	+	0.760811i	$0.724801\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	5.47734	0.684667
$5$	14.7390	1.31829	0.659147	−	0.752014i	$-0.270918\pi$
$5$	14.7390	1.31829	0.659147	+	0.752014i	$0.270918\pi$
$6$	−11.0134	−0.749370
$7$	−28.2167	−1.52356	−0.761779	−	0.647837i	$-0.775674\pi$
$7$	−28.2167	−1.52356	−0.761779	+	0.647837i	$0.775674\pi$
$8$	9.26107	0.409285
$9$	9.00000	0.333333
$10$	−54.1090	−1.71108
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	16.4320	0.395293
$13$	−27.9083	−0.595413	−0.297707	−	0.954657i	$-0.596222\pi$
$13$	−27.9083	−0.595413	−0.297707	+	0.954657i	$0.596222\pi$
$14$	103.588	1.97750
$15$	44.2169	0.761117
$16$	−77.8175	−1.21590
$17$	−25.0833	−0.357859	−0.178930	−	0.983862i	$-0.557263\pi$
$17$	−25.0833	−0.357859	−0.178930	+	0.983862i	$0.557263\pi$
$18$	−33.0403	−0.432649
$19$	89.2644	1.07782	0.538912	−	0.842362i	$-0.318836\pi$
$19$	89.2644	1.07782	0.538912	+	0.842362i	$0.318836\pi$
$20$	80.7303	0.902593
$21$	−84.6501	−0.879627
$22$	40.3826	0.391346
$23$	−170.510	−1.54581	−0.772906	−	0.634520i	$-0.781198\pi$
$23$	−170.510	−1.54581	−0.772906	+	0.634520i	$0.781198\pi$
$24$	27.7832	0.236301
$25$	92.2373	0.737899
$26$	102.456	0.772815
$27$	27.0000	0.192450
$28$	−154.552	−1.04313
$29$	61.6408	0.394704	0.197352	−	0.980333i	$-0.436766\pi$
$29$	61.6408	0.394704	0.197352	+	0.980333i	$0.436766\pi$
$30$	−162.327	−0.987890
$31$	171.523	0.993754	0.496877	−	0.867821i	$-0.334480\pi$
$31$	171.523	0.993754	0.496877	+	0.867821i	$0.334480\pi$
$32$	211.591	1.16889
$33$	−33.0000	−0.174078
$34$	92.0847	0.464482
$35$	−415.885	−2.00850
$36$	49.2960	0.228222
$37$	−110.137	−0.489364	−0.244682	−	0.969603i	$-0.578684\pi$
$37$	−110.137	−0.489364	−0.244682	+	0.969603i	$0.578684\pi$
$38$	−327.703	−1.39896
$39$	−83.7249	−0.343762
$40$	136.499	0.539558
$41$	−438.814	−1.67149	−0.835746	−	0.549116i	$-0.814964\pi$
$41$	−438.814	−1.67149	−0.835746	+	0.549116i	$0.814964\pi$
$42$	310.763	1.14171
$43$	−325.985	−1.15610	−0.578049	−	0.816002i	$-0.696186\pi$
$43$	−325.985	−1.15610	−0.578049	+	0.816002i	$0.696186\pi$
$44$	−60.2507	−0.206435
$45$	132.651	0.439431
$46$	625.966	2.00638
$47$	390.251	1.21115	0.605574	−	0.795789i	$-0.292944\pi$
$47$	390.251	1.21115	0.605574	+	0.795789i	$0.292944\pi$
$48$	−233.452	−0.701999
$49$	453.182	1.32123
$50$	−338.617	−0.957754
$51$	−75.2500	−0.206610
$52$	−152.863	−0.407660
$53$	−136.186	−0.352955	−0.176478	−	0.984305i	$-0.556470\pi$
$53$	−136.186	−0.352955	−0.176478	+	0.984305i	$0.556470\pi$
$54$	−99.1210	−0.249790
$55$	−162.129	−0.397481
$56$	−261.317	−0.623570
$57$	267.793	0.622282
$58$	−226.293	−0.512305
$59$	552.384	1.21889	0.609443	−	0.792830i	$-0.291393\pi$
$59$	552.384	1.21889	0.609443	+	0.792830i	$0.291393\pi$
$60$	242.191	0.521112
$61$	61.0000	0.128037
$61$	61.0000	0.128037
$62$	−629.685	−1.28984
$63$	−253.950	−0.507853
$64$	−154.242	−0.301255
$65$	−411.340	−0.784930
$66$	121.148	0.225944
$67$	802.094	1.46256	0.731279	−	0.682078i	$-0.238924\pi$
$67$	802.094	1.46256	0.731279	+	0.682078i	$0.238924\pi$
$68$	−137.390	−0.245014
$69$	−511.529	−0.892475
$70$	1526.78	2.60692
$71$	−823.637	−1.37673	−0.688364	−	0.725365i	$-0.741671\pi$
$71$	−823.637	−1.37673	−0.688364	+	0.725365i	$0.741671\pi$
$72$	83.3496	0.136428
$73$	695.845	1.11565	0.557825	−	0.829958i	$-0.311636\pi$
$73$	695.845	1.11565	0.557825	+	0.829958i	$0.311636\pi$
$74$	404.331	0.635169
$75$	276.712	0.426026
$76$	488.931	0.737951
$77$	310.384	0.459370
$78$	307.367	0.446185
$79$	−1208.77	−1.72149	−0.860744	−	0.509038i	$-0.830001\pi$
$79$	−1208.77	−1.72149	−0.860744	+	0.509038i	$0.830001\pi$
$80$	−1146.95	−1.60291
$81$	81.0000	0.111111
$82$	1610.95	2.16951
$83$	−73.7825	−0.0975745	−0.0487872	−	0.998809i	$-0.515536\pi$
$83$	−73.7825	−0.0975745	−0.0487872	+	0.998809i	$0.515536\pi$
$84$	−463.657	−0.602252
$85$	−369.703	−0.471763
$86$	1196.74	1.50055
$87$	184.923	0.227882
$88$	−101.872	−0.123404
$89$	996.876	1.18729	0.593644	−	0.804728i	$-0.297689\pi$
$89$	996.876	1.18729	0.593644	+	0.804728i	$0.297689\pi$
$90$	−486.981	−0.570359
$91$	787.480	0.907146
$92$	−933.938	−1.05837
$93$	514.568	0.573744
$94$	−1432.67	−1.57201
$95$	1315.67	1.42089
$96$	634.773	0.674857
$97$	313.136	0.327775	0.163887	−	0.986479i	$-0.447597\pi$
$97$	313.136	0.327775	0.163887	+	0.986479i	$0.447597\pi$
$98$	−1663.70	−1.71489
$99$	−99.0000	−0.100504
$100$	505.215	0.505215
$101$	−348.504	−0.343341	−0.171670	−	0.985154i	$-0.554916\pi$
$101$	−348.504	−0.343341	−0.171670	+	0.985154i	$0.554916\pi$
$102$	276.254	0.268169
$103$	1988.86	1.90260	0.951302	−	0.308261i	$-0.0997470\pi$
$103$	1988.86	1.90260	0.951302	+	0.308261i	$0.0997470\pi$
$104$	−258.461	−0.243694
$105$	−1247.66	−1.15961
$106$	499.960	0.458117
$107$	1004.89	0.907911	0.453956	−	0.891024i	$-0.350012\pi$
$107$	1004.89	0.907911	0.453956	+	0.891024i	$0.350012\pi$
$108$	147.888	0.131764
$109$	1494.50	1.31328	0.656638	−	0.754206i	$-0.271978\pi$
$109$	1494.50	1.31328	0.656638	+	0.754206i	$0.271978\pi$
$110$	595.199	0.515909
$111$	−330.412	−0.282535
$112$	2195.75	1.85249
$113$	−413.012	−0.343831	−0.171916	−	0.985112i	$-0.554996\pi$
$113$	−413.012	−0.343831	−0.171916	+	0.985112i	$0.554996\pi$
$114$	−983.109	−0.807689
$115$	−2513.14	−2.03784
$116$	337.628	0.270241
$117$	−251.175	−0.198471
$118$	−2027.88	−1.58205
$119$	707.769	0.545219
$120$	409.496	0.311514
$121$	121.000	0.0909091
$122$	−223.940	−0.166185
$123$	−1316.44	−0.965036
$124$	939.488	0.680391
$125$	−482.888	−0.345526
$126$	932.289	0.659166
$127$	1869.34	1.30612	0.653060	−	0.757306i	$-0.273485\pi$
$127$	1869.34	1.30612	0.653060	+	0.757306i	$0.273485\pi$
$128$	−1126.48	−0.777873
$129$	−977.955	−0.667474
$130$	1510.09	1.01880
$131$	2465.62	1.64444	0.822222	−	0.569167i	$-0.192734\pi$
$131$	2465.62	1.64444	0.822222	+	0.569167i	$0.192734\pi$
$132$	−180.752	−0.119185
$133$	−2518.75	−1.64213
$134$	−2944.61	−1.89832
$135$	397.952	0.253706
$136$	−232.299	−0.146466
$137$	1537.85	0.959035	0.479518	−	0.877532i	$-0.340812\pi$
$137$	1537.85	0.959035	0.479518	+	0.877532i	$0.340812\pi$
$138$	1877.90	1.15839
$139$	993.139	0.606021	0.303011	−	0.952987i	$-0.402008\pi$
$139$	993.139	0.606021	0.303011	+	0.952987i	$0.402008\pi$
$140$	−2277.94	−1.37515
$141$	1170.75	0.699257
$142$	3023.69	1.78692
$143$	306.991	0.179524
$144$	−700.357	−0.405299
$145$	908.523	0.520336
$146$	−2554.55	−1.44806
$147$	1359.54	0.762812
$148$	−603.260	−0.335052
$149$	−3046.02	−1.67477	−0.837383	−	0.546617i	$-0.815915\pi$
$149$	−3046.02	−1.67477	−0.837383	+	0.546617i	$0.815915\pi$
$150$	−1015.85	−0.552959
$151$	−3651.78	−1.96806	−0.984032	−	0.177994i	$-0.943039\pi$
$151$	−3651.78	−1.96806	−0.984032	+	0.177994i	$0.943039\pi$
$152$	826.684	0.441137
$153$	−225.750	−0.119286
$154$	−1139.46	−0.596238
$155$	2528.07	1.31006
$156$	−458.590	−0.235363
$157$	−446.109	−0.226773	−0.113387	−	0.993551i	$-0.536170\pi$
$157$	−446.109	−0.226773	−0.113387	+	0.993551i	$0.536170\pi$
$158$	4437.58	2.23440
$159$	−408.559	−0.203779
$160$	3118.63	1.54094
$161$	4811.21	2.35514
$162$	−297.363	−0.144216
$163$	2309.81	1.10993	0.554964	−	0.831874i	$-0.312732\pi$
$163$	2309.81	1.10993	0.554964	+	0.831874i	$0.312732\pi$
$164$	−2403.53	−1.14442
$165$	−486.386	−0.229486
$166$	270.867	0.126647
$167$	−1142.93	−0.529597	−0.264799	−	0.964304i	$-0.585305\pi$
$167$	−1142.93	−0.529597	−0.264799	+	0.964304i	$0.585305\pi$
$168$	−783.950	−0.360018
$169$	−1418.13	−0.645483
$170$	1357.23	0.612324
$171$	803.380	0.359275
$172$	−1785.53	−0.791543
$173$	4293.90	1.88705	0.943524	−	0.331305i	$-0.107489\pi$
$173$	4293.90	1.88705	0.943524	+	0.331305i	$0.107489\pi$
$174$	−678.878	−0.295779
$175$	−2602.63	−1.12423
$176$	855.992	0.366607
$177$	1657.15	0.703724
$178$	−3659.68	−1.54104
$179$	−2432.29	−1.01563	−0.507815	−	0.861466i	$-0.669547\pi$
$179$	−2432.29	−1.01563	−0.507815	+	0.861466i	$0.669547\pi$
$180$	726.573	0.300864
$181$	−2163.11	−0.888302	−0.444151	−	0.895952i	$-0.646495\pi$
$181$	−2163.11	−0.888302	−0.444151	+	0.895952i	$0.646495\pi$
$182$	−2890.96	−1.17743
$183$	183.000	0.0739221
$184$	−1579.10	−0.632678
$185$	−1623.31	−0.645126
$186$	−1889.06	−0.744690
$187$	275.917	0.107899
$188$	2137.54	0.829233
$189$	−761.851	−0.293209
$190$	−4830.00	−1.84424
$191$	−1588.55	−0.601800	−0.300900	−	0.953656i	$-0.597287\pi$
$191$	−1588.55	−0.601800	−0.300900	+	0.953656i	$0.597287\pi$
$192$	−462.727	−0.173930
$193$	−1230.23	−0.458827	−0.229413	−	0.973329i	$-0.573681\pi$
$193$	−1230.23	−0.458827	−0.229413	+	0.973329i	$0.573681\pi$
$194$	−1149.57	−0.425435
$195$	−1234.02	−0.453179
$196$	2482.23	0.904602
$197$	4128.17	1.49299	0.746497	−	0.665389i	$-0.231734\pi$
$197$	4128.17	1.49299	0.746497	+	0.665389i	$0.231734\pi$
$198$	363.444	0.130449
$199$	4202.16	1.49690	0.748450	−	0.663191i	$-0.230798\pi$
$199$	4202.16	1.49690	0.748450	+	0.663191i	$0.230798\pi$
$200$	854.216	0.302011
$201$	2406.28	0.844409
$202$	1279.41	0.445638
$203$	−1739.30	−0.601355
$204$	−412.170	−0.141459
$205$	−6467.66	−2.20352
$206$	−7301.40	−2.46948
$207$	−1534.59	−0.515271
$208$	2171.75	0.723962
$209$	−981.908	−0.324976
$210$	4580.33	1.50511
$211$	−4687.61	−1.52942	−0.764711	−	0.644373i	$-0.777118\pi$
$211$	−4687.61	−1.52942	−0.764711	+	0.644373i	$0.777118\pi$
$212$	−745.938	−0.241657
$213$	−2470.91	−0.794854
$214$	−3689.11	−1.17842
$215$	−4804.68	−1.52408
$216$	250.049	0.0787670
$217$	−4839.80	−1.51404
$218$	−5486.53	−1.70456
$219$	2087.54	0.644121
$220$	−888.034	−0.272142
$221$	700.034	0.213074
$222$	1212.99	0.366715
$223$	−477.612	−0.143423	−0.0717113	−	0.997425i	$-0.522846\pi$
$223$	−477.612	−0.143423	−0.0717113	+	0.997425i	$0.522846\pi$
$224$	−5970.40	−1.78087
$225$	830.136	0.245966
$226$	1516.23	0.446275
$227$	−283.963	−0.0830276	−0.0415138	−	0.999138i	$-0.513218\pi$
$227$	−283.963	−0.0830276	−0.0415138	+	0.999138i	$0.513218\pi$
$228$	1466.79	0.426056
$229$	−1823.46	−0.526191	−0.263095	−	0.964770i	$-0.584743\pi$
$229$	−1823.46	−0.526191	−0.263095	+	0.964770i	$0.584743\pi$
$230$	9226.09	2.64500
$231$	931.151	0.265217
$232$	570.860	0.161547
$233$	6793.93	1.91024	0.955119	−	0.296224i	$-0.0957274\pi$
$233$	6793.93	1.91024	0.955119	+	0.296224i	$0.0957274\pi$
$234$	922.100	0.257605
$235$	5751.90	1.59665
$236$	3025.59	0.834531
$237$	−3626.32	−0.993901
$238$	−2598.33	−0.707666
$239$	−5740.78	−1.55372	−0.776862	−	0.629670i	$-0.783190\pi$
$239$	−5740.78	−1.55372	−0.776862	+	0.629670i	$0.783190\pi$
$240$	−3440.85	−0.925441
$241$	−3453.26	−0.923003	−0.461501	−	0.887139i	$-0.652689\pi$
$241$	−3453.26	−0.923003	−0.461501	+	0.887139i	$0.652689\pi$
$242$	−444.209	−0.117995
$243$	243.000	0.0641500
$244$	334.118	0.0876627
$245$	6679.43	1.74177
$246$	4832.85	1.25257
$247$	−2491.22	−0.641751
$248$	1588.48	0.406729
$249$	−221.347	−0.0563346
$250$	1772.75	0.448475
$251$	4834.75	1.21580	0.607902	−	0.794012i	$-0.292011\pi$
$251$	4834.75	1.21580	0.607902	+	0.794012i	$0.292011\pi$
$252$	−1390.97	−0.347710
$253$	1875.60	0.466080
$254$	−6862.63	−1.69528
$255$	−1109.11	−0.272373
$256$	5369.42	1.31089
$257$	7398.28	1.79569	0.897844	−	0.440313i	$-0.145133\pi$
$257$	7398.28	1.79569	0.897844	+	0.440313i	$0.145133\pi$
$258$	3590.22	0.866346
$259$	3107.71	0.745575
$260$	−2253.05	−0.537416
$261$	554.768	0.131568
$262$	−9051.65	−2.13440
$263$	−3496.25	−0.819725	−0.409863	−	0.912147i	$-0.634423\pi$
$263$	−3496.25	−0.819725	−0.409863	+	0.912147i	$0.634423\pi$
$264$	−305.615	−0.0712474
$265$	−2007.25	−0.465299
$266$	9246.69	2.13139
$267$	2990.63	0.685481
$268$	4393.34	1.00137
$269$	5352.40	1.21317	0.606583	−	0.795020i	$-0.292540\pi$
$269$	5352.40	1.21317	0.606583	+	0.795020i	$0.292540\pi$
$270$	−1460.94	−0.329297
$271$	−5975.74	−1.33948	−0.669742	−	0.742594i	$-0.733595\pi$
$271$	−5975.74	−1.33948	−0.669742	+	0.742594i	$0.733595\pi$
$272$	1951.92	0.435120
$273$	2362.44	0.523741
$274$	−5645.69	−1.24478
$275$	−1014.61	−0.222485
$276$	−2801.81	−0.611049
$277$	2356.76	0.511206	0.255603	−	0.966782i	$-0.417726\pi$
$277$	2356.76	0.511206	0.255603	+	0.966782i	$0.417726\pi$
$278$	−3645.96	−0.786584
$279$	1543.70	0.331251
$280$	−3851.54	−0.822048
$281$	1516.98	0.322048	0.161024	−	0.986950i	$-0.448520\pi$
$281$	1516.98	0.322048	0.161024	+	0.986950i	$0.448520\pi$
$282$	−4298.01	−0.907598
$283$	−4511.79	−0.947696	−0.473848	−	0.880607i	$-0.657135\pi$
$283$	−4511.79	−0.947696	−0.473848	+	0.880607i	$0.657135\pi$
$284$	−4511.34	−0.942601
$285$	3947.00	0.820351
$286$	−1127.01	−0.233012
$287$	12381.9	2.54661
$288$	1904.32	0.389629
$289$	−4283.83	−0.871937
$290$	−3335.32	−0.675369
$291$	939.409	0.189241
$292$	3811.38	0.763850
$293$	−9134.99	−1.82141	−0.910703	−	0.413063i	$-0.864459\pi$
$293$	−9134.99	−1.82141	−0.910703	+	0.413063i	$0.864459\pi$
$294$	−4991.09	−0.990090
$295$	8141.57	1.60685
$296$	−1019.99	−0.200290
$297$	−297.000	−0.0580259
$298$	11182.4	2.17376
$299$	4758.63	0.920397
$300$	1515.65	0.291686
$301$	9198.21	1.76138
$302$	13406.2	2.55444
$303$	−1045.51	−0.198228
$304$	−6946.33	−1.31052
$305$	899.077	0.168790
$306$	828.762	0.154827
$307$	−632.212	−0.117532	−0.0587659	−	0.998272i	$-0.518717\pi$
$307$	−632.212	−0.117532	−0.0587659	+	0.998272i	$0.518717\pi$
$308$	1700.08	0.314516
$309$	5966.58	1.09847
$310$	−9280.92	−1.70039
$311$	9738.91	1.77570	0.887850	−	0.460133i	$-0.152198\pi$
$311$	9738.91	1.77570	0.887850	+	0.460133i	$0.152198\pi$
$312$	−775.382	−0.140697
$313$	−2001.75	−0.361487	−0.180743	−	0.983530i	$-0.557850\pi$
$313$	−2001.75	−0.361487	−0.180743	+	0.983530i	$0.557850\pi$
$314$	1637.73	0.294340
$315$	−3742.97	−0.669499
$316$	−6620.86	−1.17865
$317$	6738.17	1.19386	0.596930	−	0.802294i	$-0.296387\pi$
$317$	6738.17	1.19386	0.596930	+	0.802294i	$0.296387\pi$
$318$	1499.88	0.264494
$319$	−678.049	−0.119008
$320$	−2273.38	−0.397142
$321$	3014.67	0.524183
$322$	−17662.7	−3.05684
$323$	−2239.05	−0.385709
$324$	443.664	0.0760741
$325$	−2574.19	−0.439355
$326$	−8479.66	−1.44063
$327$	4483.50	0.758220
$328$	−4063.88	−0.684117
$329$	−11011.6	−1.84525
$330$	1785.60	0.297860
$331$	8267.52	1.37288	0.686441	−	0.727185i	$-0.259172\pi$
$331$	8267.52	1.37288	0.686441	+	0.727185i	$0.259172\pi$
$332$	−404.132	−0.0668060
$333$	−991.237	−0.163121
$334$	4195.87	0.687389
$335$	11822.0	1.92808
$336$	6587.25	1.06954
$337$	7147.37	1.15532	0.577659	−	0.816278i	$-0.303966\pi$
$337$	7147.37	1.15532	0.577659	+	0.816278i	$0.303966\pi$
$338$	5206.15	0.837803
$339$	−1239.04	−0.198511
$340$	−2024.99	−0.323001
$341$	−1886.75	−0.299628
$342$	−2949.33	−0.466320
$343$	−3108.96	−0.489411
$344$	−3018.97	−0.473174
$345$	−7539.41	−1.17654
$346$	−15763.6	−2.44929
$347$	8205.08	1.26937	0.634685	−	0.772771i	$-0.281130\pi$
$347$	8205.08	1.26937	0.634685	+	0.772771i	$0.281130\pi$
$348$	1012.88	0.156024
$349$	6622.50	1.01574	0.507871	−	0.861433i	$-0.330433\pi$
$349$	6622.50	1.01574	0.507871	+	0.861433i	$0.330433\pi$
$350$	9554.65	1.45919
$351$	−753.524	−0.114587
$352$	−2327.50	−0.352432
$353$	−3903.17	−0.588513	−0.294256	−	0.955727i	$-0.595072\pi$
$353$	−3903.17	−0.588513	−0.294256	+	0.955727i	$0.595072\pi$
$354$	−6083.65	−0.913396
$355$	−12139.6	−1.81493
$356$	5460.22	0.812897
$357$	2123.31	0.314782
$358$	8929.30	1.31823
$359$	13318.0	1.95792	0.978962	−	0.204042i	$-0.0654079\pi$
$359$	13318.0	1.95792	0.978962	+	0.204042i	$0.0654079\pi$
$360$	1228.49	0.179853
$361$	1109.13	0.161705
$362$	7941.10	1.15297
$363$	363.000	0.0524864
$364$	4313.29	0.621094
$365$	10256.0	1.47076
$366$	−671.820	−0.0959470
$367$	7075.63	1.00639	0.503194	−	0.864173i	$-0.332158\pi$
$367$	7075.63	1.00639	0.503194	+	0.864173i	$0.332158\pi$
$368$	13268.6	1.87955
$369$	−3949.32	−0.557164
$370$	5959.42	0.837339
$371$	3842.73	0.537748
$372$	2818.46	0.392824
$373$	8725.34	1.21121	0.605605	−	0.795766i	$-0.292931\pi$
$373$	8725.34	1.21121	0.605605	+	0.795766i	$0.292931\pi$
$374$	−1012.93	−0.140047
$375$	−1448.66	−0.199490
$376$	3614.14	0.495705
$377$	−1720.29	−0.235012
$378$	2796.87	0.380570
$379$	2219.02	0.300748	0.150374	−	0.988629i	$-0.451952\pi$
$379$	2219.02	0.300748	0.150374	+	0.988629i	$0.451952\pi$
$380$	7206.35	0.972836
$381$	5608.03	0.754089
$382$	5831.82	0.781104
$383$	9153.42	1.22120	0.610598	−	0.791941i	$-0.290929\pi$
$383$	9153.42	1.22120	0.610598	+	0.791941i	$0.290929\pi$
$384$	−3379.44	−0.449105
$385$	4574.74	0.605585
$386$	4516.34	0.595533
$387$	−2933.86	−0.385366
$388$	1715.15	0.224417
$389$	−5000.68	−0.651786	−0.325893	−	0.945407i	$-0.605665\pi$
$389$	−5000.68	−0.651786	−0.325893	+	0.945407i	$0.605665\pi$
$390$	4530.27	0.588203
$391$	4276.95	0.553183
$392$	4196.95	0.540760
$393$	7396.85	0.949420
$394$	−15155.1	−1.93783
$395$	−17816.1	−2.26943
$396$	−542.256	−0.0688117
$397$	876.062	0.110751	0.0553757	−	0.998466i	$-0.482364\pi$
$397$	876.062	0.110751	0.0553757	+	0.998466i	$0.482364\pi$
$398$	−15426.8	−1.94290
$399$	−7556.24	−0.948083
$400$	−7177.68	−0.897210
$401$	−8645.05	−1.07659	−0.538296	−	0.842756i	$-0.680932\pi$
$401$	−8645.05	−1.07659	−0.538296	+	0.842756i	$0.680932\pi$
$402$	−8833.83	−1.09600
$403$	−4786.91	−0.591694
$404$	−1908.87	−0.235074
$405$	1193.86	0.146477
$406$	6385.23	0.780527
$407$	1211.51	0.147549
$408$	−696.896	−0.0845624
$409$	6648.05	0.803728	0.401864	−	0.915699i	$-0.368362\pi$
$409$	6648.05	0.803728	0.401864	+	0.915699i	$0.368362\pi$
$410$	23743.7	2.86005
$411$	4613.56	0.553699
$412$	10893.7	1.30265
$413$	−15586.4	−1.85704
$414$	5633.69	0.668794
$415$	−1087.48	−0.128632
$416$	−5905.15	−0.695970
$417$	2979.42	0.349887
$418$	3604.73	0.421802
$419$	−807.155	−0.0941100	−0.0470550	−	0.998892i	$-0.514984\pi$
$419$	−807.155	−0.0941100	−0.0470550	+	0.998892i	$0.514984\pi$
$420$	−6833.83	−0.793945
$421$	7292.10	0.844169	0.422085	−	0.906556i	$-0.361298\pi$
$421$	7292.10	0.844169	0.422085	+	0.906556i	$0.361298\pi$
$422$	17208.9	1.98511
$423$	3512.26	0.403716
$424$	−1261.23	−0.144459
$425$	−2313.62	−0.264064
$426$	9071.08	1.03168
$427$	−1721.22	−0.195072
$428$	5504.13	0.621617
$429$	920.974	0.103648
$430$	17638.7	1.97817
$431$	−6923.69	−0.773788	−0.386894	−	0.922124i	$-0.626452\pi$
$431$	−6923.69	−0.773788	−0.386894	+	0.922124i	$0.626452\pi$
$432$	−2101.07	−0.234000
$433$	10977.3	1.21833	0.609165	−	0.793043i	$-0.291505\pi$
$433$	10977.3	1.21833	0.609165	+	0.793043i	$0.291505\pi$
$434$	17767.6	1.96515
$435$	2725.57	0.300416
$436$	8185.88	0.899157
$437$	−15220.4	−1.66611
$438$	−7663.65	−0.836036
$439$	−11120.0	−1.20895	−0.604477	−	0.796623i	$-0.706618\pi$
$439$	−11120.0	−1.20895	−0.604477	+	0.796623i	$0.706618\pi$
$440$	−1501.49	−0.162683
$441$	4078.63	0.440410
$442$	−2569.93	−0.276559
$443$	4929.82	0.528719	0.264360	−	0.964424i	$-0.414839\pi$
$443$	4929.82	0.528719	0.264360	+	0.964424i	$0.414839\pi$
$444$	−1809.78	−0.193442
$445$	14692.9	1.56519
$446$	1753.38	0.186155
$447$	−9138.07	−0.966926
$448$	4352.21	0.458979
$449$	−9242.95	−0.971496	−0.485748	−	0.874099i	$-0.661453\pi$
$449$	−9242.95	−0.971496	−0.485748	+	0.874099i	$0.661453\pi$
$450$	−3047.55	−0.319251
$451$	4826.95	0.503974
$452$	−2262.21	−0.235410
$453$	−10955.3	−1.13626
$454$	1042.47	0.107766
$455$	11606.6	1.19589
$456$	2480.05	0.254691
$457$	−9482.99	−0.970669	−0.485334	−	0.874329i	$-0.661302\pi$
$457$	−9482.99	−0.970669	−0.485334	+	0.874329i	$0.661302\pi$
$458$	6694.20	0.682968
$459$	−677.250	−0.0688700
$460$	−13765.3	−1.39524
$461$	−6355.47	−0.642090	−0.321045	−	0.947064i	$-0.604034\pi$
$461$	−6355.47	−0.642090	−0.321045	+	0.947064i	$0.604034\pi$
$462$	−3418.39	−0.344238
$463$	12474.0	1.25209	0.626045	−	0.779787i	$-0.284673\pi$
$463$	12474.0	1.25209	0.626045	+	0.779787i	$0.284673\pi$
$464$	−4796.73	−0.479920
$465$	7584.20	0.756363
$466$	−24941.5	−2.47939
$467$	3589.92	0.355721	0.177860	−	0.984056i	$-0.443082\pi$
$467$	3589.92	0.355721	0.177860	+	0.984056i	$0.443082\pi$
$468$	−1375.77	−0.135887
$469$	−22632.4	−2.22829
$470$	−21116.1	−2.07237
$471$	−1338.33	−0.130928
$472$	5115.66	0.498872
$473$	3585.83	0.348577
$474$	13312.8	1.29003
$475$	8233.51	0.795325
$476$	3876.69	0.373294
$477$	−1225.68	−0.117652
$478$	21075.3	2.01665
$479$	4175.19	0.398265	0.199133	−	0.979973i	$-0.436188\pi$
$479$	4175.19	0.398265	0.199133	+	0.979973i	$0.436188\pi$
$480$	9355.90	0.889660
$481$	3073.75	0.291374
$482$	12677.4	1.19801
$483$	14433.6	1.35974
$484$	662.758	0.0622425
$485$	4615.31	0.432104
$486$	−892.089	−0.0832634
$487$	1042.02	0.0969577	0.0484788	−	0.998824i	$-0.484563\pi$
$487$	1042.02	0.0969577	0.0484788	+	0.998824i	$0.484563\pi$
$488$	564.925	0.0524036
$489$	6929.43	0.640818
$490$	−24521.2	−2.26072
$491$	11263.0	1.03522	0.517610	−	0.855617i	$-0.326822\pi$
$491$	11263.0	1.03522	0.517610	+	0.855617i	$0.326822\pi$
$492$	−7210.59	−0.660729
$493$	−1546.16	−0.141248
$494$	9145.63	0.832958
$495$	−1459.16	−0.132494
$496$	−13347.5	−1.20830
$497$	23240.3	2.09753
$498$	812.600	0.0731194
$499$	7775.41	0.697545	0.348773	−	0.937207i	$-0.386599\pi$
$499$	7775.41	0.697545	0.348773	+	0.937207i	$0.386599\pi$
$500$	−2644.94	−0.236571
$501$	−3428.80	−0.305763
$502$	−17749.1	−1.57805
$503$	9038.49	0.801205	0.400603	−	0.916252i	$-0.368801\pi$
$503$	9038.49	0.801205	0.400603	+	0.916252i	$0.368801\pi$
$504$	−2351.85	−0.207857
$505$	−5136.59	−0.452624
$506$	−6885.62	−0.604947
$507$	−4254.38	−0.372670
$508$	10239.0	0.894258
$509$	−196.143	−0.0170804	−0.00854018	−	0.999964i	$-0.502718\pi$
$509$	−196.143	−0.0170804	−0.00854018	+	0.999964i	$0.502718\pi$
$510$	4071.70	0.353525
$511$	−19634.4	−1.69976
$512$	−10700.1	−0.923597
$513$	2410.14	0.207427
$514$	−27160.2	−2.33071
$515$	29313.8	2.50819
$516$	−5356.59	−0.456997
$517$	−4292.76	−0.365175
$518$	−11408.9	−0.967717
$519$	12881.7	1.08949
$520$	−3809.45	−0.321260
$521$	15235.6	1.28116	0.640579	−	0.767892i	$-0.278694\pi$
$521$	15235.6	1.28116	0.640579	+	0.767892i	$0.278694\pi$
$522$	−2036.63	−0.170768
$523$	21538.9	1.80082	0.900410	−	0.435043i	$-0.143267\pi$
$523$	21538.9	1.80082	0.900410	+	0.435043i	$0.143267\pi$
$524$	13505.0	1.12590
$525$	−7807.90	−0.649075
$526$	12835.2	1.06396
$527$	−4302.36	−0.355624
$528$	2567.98	0.211661
$529$	16906.5	1.38954
$530$	7368.90	0.603933
$531$	4971.45	0.406295
$532$	−13796.0	−1.12431
$533$	12246.5	0.995228
$534$	−10979.0	−0.889718
$535$	14811.1	1.19689
$536$	7428.25	0.598604
$537$	−7296.87	−0.586374
$538$	−19649.5	−1.57463
$539$	−4985.00	−0.398366
$540$	2179.72	0.173704
$541$	9848.78	0.782684	0.391342	−	0.920245i	$-0.372011\pi$
$541$	9848.78	0.782684	0.391342	+	0.920245i	$0.372011\pi$
$542$	21937.8	1.73858
$543$	−6489.33	−0.512861
$544$	−5307.41	−0.418297
$545$	22027.4	1.73128
$546$	−8672.87	−0.679789
$547$	−4225.39	−0.330283	−0.165141	−	0.986270i	$-0.552808\pi$
$547$	−4225.39	−0.330283	−0.165141	+	0.986270i	$0.552808\pi$
$548$	8423.35	0.656620
$549$	549.000	0.0426790
$550$	3724.79	0.288774
$551$	5502.33	0.425422
$552$	−4737.30	−0.365277
$553$	34107.6	2.62279
$554$	−8652.02	−0.663518
$555$	−4869.94	−0.372464
$556$	5439.76	0.414923
$557$	11868.0	0.902809	0.451404	−	0.892319i	$-0.350923\pi$
$557$	11868.0	0.902809	0.451404	+	0.892319i	$0.350923\pi$
$558$	−5667.17	−0.429947
$559$	9097.69	0.688356
$560$	32363.1	2.44213
$561$	827.750	0.0622953
$562$	−5569.07	−0.418002
$563$	5675.76	0.424875	0.212437	−	0.977175i	$-0.431860\pi$
$563$	5675.76	0.424875	0.212437	+	0.977175i	$0.431860\pi$
$564$	6412.61	0.478758
$565$	−6087.38	−0.453271
$566$	16563.5	1.23006
$567$	−2285.55	−0.169284
$568$	−7627.76	−0.563475
$569$	17571.3	1.29460	0.647301	−	0.762234i	$-0.275898\pi$
$569$	17571.3	1.29460	0.647301	+	0.762234i	$0.275898\pi$
$570$	−14490.0	−1.06477
$571$	−2012.80	−0.147518	−0.0737592	−	0.997276i	$-0.523500\pi$
$571$	−2012.80	−0.147518	−0.0737592	+	0.997276i	$0.523500\pi$
$572$	1681.50	0.122914
$573$	−4765.66	−0.347449
$574$	−45455.7	−3.30537
$575$	−15727.3	−1.14065
$576$	−1388.18	−0.100418
$577$	−18860.9	−1.36081	−0.680406	−	0.732835i	$-0.738197\pi$
$577$	−18860.9	−1.36081	−0.680406	+	0.732835i	$0.738197\pi$
$578$	15726.6	1.13173
$579$	−3690.68	−0.264904
$580$	4976.29	0.356257
$581$	2081.90	0.148660
$582$	−3448.71	−0.245625
$583$	1498.05	0.106420
$584$	6444.27	0.456619
$585$	−3702.06	−0.261643
$586$	33535.9	2.36409
$587$	−20872.5	−1.46763	−0.733815	−	0.679349i	$-0.762262\pi$
$587$	−20872.5	−1.46763	−0.733815	+	0.679349i	$0.762262\pi$
$588$	7446.69	0.522272
$589$	15310.9	1.07109
$590$	−29888.9	−2.08561
$591$	12384.5	0.861981
$592$	8570.61	0.595017
$593$	−15156.7	−1.04960	−0.524799	−	0.851226i	$-0.675860\pi$
$593$	−15156.7	−1.04960	−0.524799	+	0.851226i	$0.675860\pi$
$594$	1090.33	0.0753145
$595$	10431.8	0.718759
$596$	−16684.1	−1.14666
$597$	12606.5	0.864236
$598$	−17469.6	−1.19463
$599$	6538.11	0.445977	0.222988	−	0.974821i	$-0.428419\pi$
$599$	6538.11	0.445977	0.222988	+	0.974821i	$0.428419\pi$
$600$	2562.65	0.174366
$601$	−986.215	−0.0669360	−0.0334680	−	0.999440i	$-0.510655\pi$
$601$	−986.215	−0.0669360	−0.0334680	+	0.999440i	$0.510655\pi$
$602$	−33768.0	−2.28618
$603$	7218.85	0.487520
$604$	−20002.0	−1.34747
$605$	1783.42	0.119845
$606$	3838.23	0.257289
$607$	−2267.36	−0.151613	−0.0758067	−	0.997123i	$-0.524153\pi$
$607$	−2267.36	−0.151613	−0.0758067	+	0.997123i	$0.524153\pi$
$608$	18887.5	1.25985
$609$	−5217.90	−0.347192
$610$	−3300.65	−0.219081
$611$	−10891.2	−0.721133
$612$	−1236.51	−0.0816715
$613$	10331.9	0.680754	0.340377	−	0.940289i	$-0.389445\pi$
$613$	10331.9	0.680754	0.340377	+	0.940289i	$0.389445\pi$
$614$	2320.94	0.152550
$615$	−19403.0	−1.27220
$616$	2874.48	0.188013
$617$	−24893.9	−1.62430	−0.812148	−	0.583451i	$-0.801702\pi$
$617$	−24893.9	−1.62430	−0.812148	+	0.583451i	$0.801702\pi$
$618$	−21904.2	−1.42575
$619$	16074.2	1.04374	0.521872	−	0.853024i	$-0.325234\pi$
$619$	16074.2	1.04374	0.521872	+	0.853024i	$0.325234\pi$
$620$	13847.1	0.896955
$621$	−4603.76	−0.297492
$622$	−35753.0	−2.30476
$623$	−28128.5	−1.80890
$624$	6515.26	0.417979
$625$	−18646.9	−1.19340
$626$	7348.71	0.469191
$627$	−2945.73	−0.187625
$628$	−2443.49	−0.155264
$629$	2762.61	0.175123
$630$	13741.0	0.868975
$631$	−19464.3	−1.22799	−0.613994	−	0.789310i	$-0.710438\pi$
$631$	−19464.3	−1.22799	−0.613994	+	0.789310i	$0.710438\pi$
$632$	−11194.5	−0.704580
$633$	−14062.8	−0.883013
$634$	−24736.8	−1.54957
$635$	27552.2	1.72185
$636$	−2237.82	−0.139521
$637$	−12647.5	−0.786677
$638$	2489.22	0.154466
$639$	−7412.73	−0.458909
$640$	−16603.2	−1.02547
$641$	11789.6	0.726463	0.363231	−	0.931699i	$-0.381673\pi$
$641$	11789.6	0.726463	0.363231	+	0.931699i	$0.381673\pi$
$642$	−11067.3	−0.680362
$643$	9706.83	0.595335	0.297667	−	0.954670i	$-0.403791\pi$
$643$	9706.83	0.595335	0.297667	+	0.954670i	$0.403791\pi$
$644$	26352.6	1.61248
$645$	−14414.0	−0.879927
$646$	8219.89	0.500630
$647$	−9333.40	−0.567131	−0.283566	−	0.958953i	$-0.591517\pi$
$647$	−9333.40	−0.567131	−0.283566	+	0.958953i	$0.591517\pi$
$648$	750.147	0.0454761
$649$	−6076.22	−0.367508
$650$	9450.23	0.570259
$651$	−14519.4	−0.874133
$652$	12651.6	0.759932
$653$	9048.87	0.542281	0.271141	−	0.962540i	$-0.412599\pi$
$653$	9048.87	0.542281	0.271141	+	0.962540i	$0.412599\pi$
$654$	−16459.6	−0.984130
$655$	36340.7	2.16786
$656$	34147.4	2.03236
$657$	6262.61	0.371884
$658$	40425.2	2.39504
$659$	13808.4	0.816235	0.408118	−	0.912929i	$-0.366185\pi$
$659$	13808.4	0.816235	0.408118	+	0.912929i	$0.366185\pi$
$660$	−2664.10	−0.157121
$661$	−5630.91	−0.331342	−0.165671	−	0.986181i	$-0.552979\pi$
$661$	−5630.91	−0.331342	−0.165671	+	0.986181i	$0.552979\pi$
$662$	−30351.3	−1.78193
$663$	2100.10	0.123018
$664$	−683.305	−0.0399358
$665$	−37123.7	−2.16481
$666$	3638.98	0.211723
$667$	−10510.4	−0.610139
$668$	−6260.23	−0.362598
$669$	−1432.84	−0.0828051
$670$	−43400.5	−2.50255
$671$	−671.000	−0.0386046
$672$	−17911.2	−1.02818
$673$	−3980.95	−0.228015	−0.114008	−	0.993480i	$-0.536369\pi$
$673$	−3980.95	−0.228015	−0.114008	+	0.993480i	$0.536369\pi$
$674$	−26239.1	−1.49954
$675$	2490.41	0.142009
$676$	−7767.56	−0.441941
$677$	−28125.0	−1.59665	−0.798325	−	0.602226i	$-0.794281\pi$
$677$	−28125.0	−1.59665	−0.798325	+	0.602226i	$0.794281\pi$
$678$	4548.69	0.257657
$679$	−8835.67	−0.499384
$680$	−3423.84	−0.193086
$681$	−851.888	−0.0479360
$682$	6926.54	0.388902
$683$	25108.3	1.40665	0.703326	−	0.710868i	$-0.251698\pi$
$683$	25108.3	1.40665	0.703326	+	0.710868i	$0.251698\pi$
$684$	4400.38	0.245984
$685$	22666.4	1.26429
$686$	11413.4	0.635230
$687$	−5470.38	−0.303796
$688$	25367.3	1.40570
$689$	3800.73	0.210154
$690$	27678.3	1.52709
$691$	−19527.7	−1.07506	−0.537532	−	0.843243i	$-0.680643\pi$
$691$	−19527.7	−1.07506	−0.537532	+	0.843243i	$0.680643\pi$
$692$	23519.1	1.29200
$693$	2793.45	0.153123
$694$	−30122.1	−1.64758
$695$	14637.9	0.798914
$696$	1712.58	0.0932689
$697$	11006.9	0.598158
$698$	−24312.2	−1.31838
$699$	20381.8	1.10288
$700$	−14255.5	−0.769725
$701$	−20135.3	−1.08488	−0.542440	−	0.840094i	$-0.682500\pi$
$701$	−20135.3	−1.08488	−0.542440	+	0.840094i	$0.682500\pi$
$702$	2766.30	0.148728
$703$	−9831.35	−0.527449
$704$	1696.67	0.0908318
$705$	17255.7	0.921826
$706$	14329.1	0.763859
$707$	9833.63	0.523100
$708$	9076.78	0.481817
$709$	−30.4492	−0.00161290	−0.000806449	−	1.00000i	$-0.500257\pi$
$709$	−30.4492	−0.00161290	−0.000806449		1.00000i	$0.500257\pi$
$710$	44566.1	2.35569
$711$	−10879.0	−0.573829
$712$	9232.13	0.485939
$713$	−29246.2	−1.53616
$714$	−7794.98	−0.408571
$715$	4524.74	0.236665
$716$	−13322.5	−0.695369
$717$	−17222.3	−0.897043
$718$	−48892.2	−2.54128
$719$	29209.5	1.51506	0.757532	−	0.652798i	$-0.226405\pi$
$719$	29209.5	1.51506	0.757532	+	0.652798i	$0.226405\pi$
$720$	−10322.5	−0.534304
$721$	−56119.0	−2.89873
$722$	−4071.79	−0.209884
$723$	−10359.8	−0.532896
$724$	−11848.1	−0.608191
$725$	5685.59	0.291252
$726$	−1332.63	−0.0681246
$727$	28010.2	1.42894	0.714470	−	0.699666i	$-0.246668\pi$
$727$	28010.2	1.42894	0.714470	+	0.699666i	$0.246668\pi$
$728$	7292.91	0.371282
$729$	729.000	0.0370370
$730$	−37651.5	−1.90896
$731$	8176.79	0.413720
$732$	1002.35	0.0506121
$733$	−6345.68	−0.319759	−0.159879	−	0.987137i	$-0.551111\pi$
$733$	−6345.68	−0.319759	−0.159879	+	0.987137i	$0.551111\pi$
$734$	−25975.7	−1.30624
$735$	20038.3	1.00561
$736$	−36078.3	−1.80688
$737$	−8823.04	−0.440978
$738$	14498.6	0.723169
$739$	30905.8	1.53841	0.769206	−	0.639001i	$-0.220652\pi$
$739$	30905.8	1.53841	0.769206	+	0.639001i	$0.220652\pi$
$740$	−8891.43	−0.441697
$741$	−7473.65	−0.370515
$742$	−14107.2	−0.697968
$743$	10353.7	0.511226	0.255613	−	0.966779i	$-0.417723\pi$
$743$	10353.7	0.511226	0.255613	+	0.966779i	$0.417723\pi$
$744$	4765.45	0.234825
$745$	−44895.3	−2.20783
$746$	−32032.0	−1.57209
$747$	−664.042	−0.0325248
$748$	1511.29	0.0738746
$749$	−28354.7	−1.38326
$750$	5318.26	0.258927
$751$	−2337.88	−0.113596	−0.0567980	−	0.998386i	$-0.518089\pi$
$751$	−2337.88	−0.113596	−0.0567980	+	0.998386i	$0.518089\pi$
$752$	−30368.3	−1.47263
$753$	14504.3	0.701945
$754$	6315.45	0.305033
$755$	−53823.5	−2.59449
$756$	−4172.91	−0.200751
$757$	−4803.43	−0.230626	−0.115313	−	0.993329i	$-0.536787\pi$
$757$	−4803.43	−0.230626	−0.115313	+	0.993329i	$0.536787\pi$
$758$	−8146.35	−0.390355
$759$	5626.81	0.269091
$760$	12184.5	0.581549
$761$	11955.3	0.569487	0.284744	−	0.958604i	$-0.408091\pi$
$761$	11955.3	0.569487	0.284744	+	0.958604i	$0.408091\pi$
$762$	−20587.9	−0.978768
$763$	−42169.8	−2.00085
$764$	−8701.05	−0.412033
$765$	−3327.32	−0.157254
$766$	−33603.6	−1.58505
$767$	−15416.1	−0.725740
$768$	16108.3	0.756845
$769$	−19534.1	−0.916018	−0.458009	−	0.888948i	$-0.651437\pi$
$769$	−19534.1	−0.916018	−0.458009	+	0.888948i	$0.651437\pi$
$770$	−16794.5	−0.786017
$771$	22194.8	1.03674
$772$	−6738.36	−0.314144
$773$	−11411.6	−0.530980	−0.265490	−	0.964114i	$-0.585534\pi$
$773$	−11411.6	−0.530980	−0.265490	+	0.964114i	$0.585534\pi$
$774$	10770.7	0.500185
$775$	15820.8	0.733290
$776$	2899.98	0.134153
$777$	9323.14	0.430458
$778$	18358.3	0.845984
$779$	−39170.4	−1.80157
$780$	−6759.14	−0.310277
$781$	9060.00	0.415099
$782$	−15701.3	−0.718003
$783$	1664.30	0.0759608
$784$	−35265.4	−1.60648
$785$	−6575.19	−0.298954
$786$	−27155.0	−1.23230
$787$	13113.6	0.593964	0.296982	−	0.954883i	$-0.404020\pi$
$787$	13113.6	0.593964	0.296982	+	0.954883i	$0.404020\pi$
$788$	22611.4	1.02220
$789$	−10488.7	−0.473269
$790$	65405.4	2.94560
$791$	11653.8	0.523847
$792$	−916.846	−0.0411347
$793$	−1702.41	−0.0762348
$794$	−3216.15	−0.143749
$795$	−6021.74	−0.268640
$796$	23016.7	1.02488
$797$	−31768.7	−1.41193	−0.705964	−	0.708248i	$-0.749486\pi$
$797$	−31768.7	−1.41193	−0.705964	+	0.708248i	$0.749486\pi$
$798$	27740.1	1.23056
$799$	−9788.80	−0.433420
$800$	19516.6	0.862520
$801$	8971.88	0.395763
$802$	31737.3	1.39736
$803$	−7654.30	−0.336381
$804$	13180.0	0.578139
$805$	70912.4	3.10476
$806$	17573.4	0.767988
$807$	16057.2	0.700422
$808$	−3227.52	−0.140524
$809$	−26555.2	−1.15406	−0.577029	−	0.816724i	$-0.695788\pi$
$809$	−26555.2	−1.15406	−0.577029	+	0.816724i	$0.695788\pi$
$810$	−4382.83	−0.190120
$811$	−2479.82	−0.107371	−0.0536857	−	0.998558i	$-0.517097\pi$
$811$	−2479.82	−0.107371	−0.0536857	+	0.998558i	$0.517097\pi$
$812$	−9526.74	−0.411728
$813$	−17927.2	−0.773352
$814$	−4447.64	−0.191511
$815$	34044.3	1.46321
$816$	5855.77	0.251217
$817$	−29098.8	−1.24607
$818$	−24406.0	−1.04320
$819$	7087.32	0.302382
$820$	−35425.6	−1.50868
$821$	−27046.5	−1.14973	−0.574866	−	0.818248i	$-0.694946\pi$
$821$	−27046.5	−1.14973	−0.574866	+	0.818248i	$0.694946\pi$
$822$	−16937.1	−0.718672
$823$	−1879.22	−0.0795934	−0.0397967	−	0.999208i	$-0.512671\pi$
$823$	−1879.22	−0.0795934	−0.0397967	+	0.999208i	$0.512671\pi$
$824$	18419.0	0.778708
$825$	−3043.83	−0.128452
$826$	57220.1	2.41034
$827$	27219.3	1.14451	0.572254	−	0.820077i	$-0.306069\pi$
$827$	27219.3	1.14451	0.572254	+	0.820077i	$0.306069\pi$
$828$	−8405.44	−0.352789
$829$	7232.45	0.303008	0.151504	−	0.988457i	$-0.451588\pi$
$829$	7232.45	0.303008	0.151504	+	0.988457i	$0.451588\pi$
$830$	3992.29	0.166957
$831$	7070.28	0.295145
$832$	4304.65	0.179371
$833$	−11367.3	−0.472814
$834$	−10937.9	−0.454134
$835$	−16845.6	−0.698165
$836$	−5378.24	−0.222501
$837$	4631.11	0.191248
$838$	2963.19	0.122150
$839$	−36000.2	−1.48136	−0.740682	−	0.671856i	$-0.765498\pi$
$839$	−36000.2	−1.48136	−0.740682	+	0.671856i	$0.765498\pi$
$840$	−11554.6	−0.474610
$841$	−20589.4	−0.844209
$842$	−26770.4	−1.09569
$843$	4550.94	0.185935
$844$	−25675.6	−1.04715
$845$	−20901.7	−0.850937
$846$	−12894.0	−0.524002
$847$	−3414.22	−0.138505
$848$	10597.7	0.429158
$849$	−13535.4	−0.547153
$850$	8493.65	0.342741
$851$	18779.5	0.756465
$852$	−13534.0	−0.544211
$853$	5388.94	0.216312	0.108156	−	0.994134i	$-0.465505\pi$
$853$	5388.94	0.216312	0.108156	+	0.994134i	$0.465505\pi$
$854$	6318.85	0.253193
$855$	11841.0	0.473630
$856$	9306.37	0.371595
$857$	−6680.51	−0.266280	−0.133140	−	0.991097i	$-0.542506\pi$
$857$	−6680.51	−0.266280	−0.133140	+	0.991097i	$0.542506\pi$
$858$	−3381.03	−0.134530
$859$	−10024.4	−0.398172	−0.199086	−	0.979982i	$-0.563797\pi$
$859$	−10024.4	−0.398172	−0.199086	+	0.979982i	$0.563797\pi$
$860$	−26316.9	−1.04349
$861$	37145.6	1.47029
$862$	25417.9	1.00434
$863$	21405.5	0.844323	0.422161	−	0.906521i	$-0.361272\pi$
$863$	21405.5	0.844323	0.422161	+	0.906521i	$0.361272\pi$
$864$	5712.96	0.224952
$865$	63287.7	2.48768
$866$	−40299.4	−1.58133
$867$	−12851.5	−0.503413
$868$	−26509.2	−1.03662
$869$	13296.5	0.519048
$870$	−10006.0	−0.389924
$871$	−22385.1	−0.870827
$872$	13840.7	0.537504
$873$	2818.23	0.109258
$874$	55876.5	2.16253
$875$	13625.5	0.526430
$876$	11434.1	0.441009
$877$	39245.5	1.51109	0.755544	−	0.655097i	$-0.227372\pi$
$877$	39245.5	1.51109	0.755544	+	0.655097i	$0.227372\pi$
$878$	40823.4	1.56916
$879$	−27405.0	−1.05159
$880$	12616.4	0.483296
$881$	40787.7	1.55979	0.779894	−	0.625911i	$-0.215273\pi$
$881$	40787.7	1.55979	0.779894	+	0.625911i	$0.215273\pi$
$882$	−14973.3	−0.571629
$883$	4305.36	0.164085	0.0820424	−	0.996629i	$-0.473856\pi$
$883$	4305.36	0.164085	0.0820424	+	0.996629i	$0.473856\pi$
$884$	3834.32	0.145885
$885$	24424.7	0.927715
$886$	−18098.1	−0.686250
$887$	25428.1	0.962563	0.481282	−	0.876566i	$-0.340171\pi$
$887$	25428.1	0.962563	0.481282	+	0.876566i	$0.340171\pi$
$888$	−3059.97	−0.115637
$889$	−52746.6	−1.98995
$890$	−53939.9	−2.03154
$891$	−891.000	−0.0335013
$892$	−2616.04	−0.0981968
$893$	34835.5	1.30540
$894$	33547.2	1.25502
$895$	−35849.4	−1.33890
$896$	31785.6	1.18514
$897$	14275.9	0.531392
$898$	33932.3	1.26095
$899$	10572.8	0.392239
$900$	4546.94	0.168405
$901$	3416.01	0.126308
$902$	−17720.5	−0.654131
$903$	27594.6	1.01693
$904$	−3824.93	−0.140725
$905$	−31882.0	−1.17104
$906$	40218.7	1.47481
$907$	−3398.99	−0.124434	−0.0622170	−	0.998063i	$-0.519817\pi$
$907$	−3398.99	−0.124434	−0.0622170	+	0.998063i	$0.519817\pi$
$908$	−1555.36	−0.0568463
$909$	−3136.53	−0.114447
$910$	−42609.7	−1.55220
$911$	45351.4	1.64935	0.824675	−	0.565607i	$-0.191358\pi$
$911$	45351.4	1.64935	0.824675	+	0.565607i	$0.191358\pi$
$912$	−20839.0	−0.756631
$913$	811.607	0.0294198
$914$	34813.5	1.25988
$915$	2697.23	0.0974511
$916$	−9987.71	−0.360266
$917$	−69571.6	−2.50540
$918$	2486.29	0.0893896
$919$	24661.2	0.885201	0.442600	−	0.896719i	$-0.354056\pi$
$919$	24661.2	0.885201	0.442600	+	0.896719i	$0.354056\pi$
$920$	−23274.3	−0.834056
$921$	−1896.64	−0.0678570
$922$	23331.9	0.833399
$923$	22986.3	0.819722
$924$	5100.23	0.181586
$925$	−10158.8	−0.361101
$926$	−45794.0	−1.62515
$927$	17899.7	0.634201
$928$	13042.6	0.461364
$929$	−42021.7	−1.48405	−0.742027	−	0.670370i	$-0.766135\pi$
$929$	−42021.7	−1.48405	−0.742027	+	0.670370i	$0.766135\pi$
$930$	−27842.7	−0.981720
$931$	40453.0	1.42405
$932$	37212.7	1.30788
$933$	29216.7	1.02520
$934$	−13179.1	−0.461707
$935$	4066.73	0.142242
$936$	−2326.15	−0.0812313
$937$	−3937.94	−0.137297	−0.0686483	−	0.997641i	$-0.521869\pi$
$937$	−3937.94	−0.137297	−0.0686483	+	0.997641i	$0.521869\pi$
$938$	83087.1	2.89221
$939$	−6005.24	−0.208705
$940$	31505.1	1.09317
$941$	16066.0	0.556573	0.278286	−	0.960498i	$-0.410234\pi$
$941$	16066.0	0.556573	0.278286	+	0.960498i	$0.410234\pi$
$942$	4913.20	0.169937
$943$	74821.9	2.58381
$944$	−42985.1	−1.48204
$945$	−11228.9	−0.386535
$946$	−13164.1	−0.452434
$947$	−21869.5	−0.750437	−0.375219	−	0.926936i	$-0.622432\pi$
$947$	−21869.5	−0.750437	−0.375219	+	0.926936i	$0.622432\pi$
$948$	−19862.6	−0.680492
$949$	−19419.9	−0.664273
$950$	−30226.4	−1.03229
$951$	20214.5	0.689275
$952$	6554.70	0.223150
$953$	−36819.5	−1.25152	−0.625762	−	0.780014i	$-0.715212\pi$
$953$	−36819.5	−1.25152	−0.625762	+	0.780014i	$0.715212\pi$
$954$	4499.64	0.152706
$955$	−23413.7	−0.793349
$956$	−31444.2	−1.06378
$957$	−2034.15	−0.0687092
$958$	−15327.7	−0.516927
$959$	−43393.2	−1.46115
$960$	−6820.13	−0.229290
$961$	−370.979	−0.0124527
$962$	−11284.2	−0.378188
$963$	9044.02	0.302637
$964$	−18914.6	−0.631950
$965$	−18132.3	−0.604868
$966$	−52988.1	−1.76487
$967$	36058.0	1.19912	0.599559	−	0.800331i	$-0.295343\pi$
$967$	36058.0	1.19912	0.599559	+	0.800331i	$0.295343\pi$
$968$	1120.59	0.0372078
$969$	−6717.15	−0.222689
$970$	−16943.5	−0.560848
$971$	12296.9	0.406412	0.203206	−	0.979136i	$-0.434864\pi$
$971$	12296.9	0.406412	0.203206	+	0.979136i	$0.434864\pi$
$972$	1330.99	0.0439214
$973$	−28023.1	−0.923309
$974$	−3825.41	−0.125846
$975$	−7722.56	−0.253662
$976$	−4746.87	−0.155680
$977$	27897.4	0.913528	0.456764	−	0.889588i	$-0.349008\pi$
$977$	27897.4	0.913528	0.456764	+	0.889588i	$0.349008\pi$
$978$	−25439.0	−0.831748
$979$	−10965.6	−0.357981
$980$	36585.5	1.19253
$981$	13450.5	0.437759
$982$	−41348.2	−1.34366
$983$	−4471.97	−0.145101	−0.0725503	−	0.997365i	$-0.523114\pi$
$983$	−4471.97	−0.145101	−0.0725503	+	0.997365i	$0.523114\pi$
$984$	−12191.6	−0.394975
$985$	60845.0	1.96820
$986$	5676.18	0.183333
$987$	−33034.8	−1.06536
$988$	−13645.2	−0.439386
$989$	55583.5	1.78711
$990$	5356.79	0.171970
$991$	−1565.63	−0.0501857	−0.0250928	−	0.999685i	$-0.507988\pi$
$991$	−1565.63	−0.0501857	−0.0250928	+	0.999685i	$0.507988\pi$
$992$	36292.7	1.16159
$993$	24802.6	0.792634
$994$	−85318.6	−2.72248
$995$	61935.5	1.97336
$996$	−1212.39	−0.0385705
$997$	6854.20	0.217728	0.108864	−	0.994057i	$-0.465279\pi$
$997$	6854.20	0.217728	0.108864	+	0.994057i	$0.465279\pi$
$998$	−28544.7	−0.905377
$999$	−2973.71	−0.0941782

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.h.1.8	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.h.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-3.67115 q^{2} +3.00000 q^{3} +5.47734 q^{4} +14.7390 q^{5} -11.0134 q^{6} -28.2167 q^{7} +9.26107 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.67115 q^{2} +3.00000 q^{3} +5.47734 q^{4} +14.7390 q^{5} -11.0134 q^{6} -28.2167 q^{7} +9.26107 q^{8} +9.00000 q^{9} -54.1090 q^{10} -11.0000 q^{11} +16.4320 q^{12} -27.9083 q^{13} +103.588 q^{14} +44.2169 q^{15} -77.8175 q^{16} -25.0833 q^{17} -33.0403 q^{18} +89.2644 q^{19} +80.7303 q^{20} -84.6501 q^{21} +40.3826 q^{22} -170.510 q^{23} +27.7832 q^{24} +92.2373 q^{25} +102.456 q^{26} +27.0000 q^{27} -154.552 q^{28} +61.6408 q^{29} -162.327 q^{30} +171.523 q^{31} +211.591 q^{32} -33.0000 q^{33} +92.0847 q^{34} -415.885 q^{35} +49.2960 q^{36} -110.137 q^{37} -327.703 q^{38} -83.7249 q^{39} +136.499 q^{40} -438.814 q^{41} +310.763 q^{42} -325.985 q^{43} -60.2507 q^{44} +132.651 q^{45} +625.966 q^{46} +390.251 q^{47} -233.452 q^{48} +453.182 q^{49} -338.617 q^{50} -75.2500 q^{51} -152.863 q^{52} -136.186 q^{53} -99.1210 q^{54} -162.129 q^{55} -261.317 q^{56} +267.793 q^{57} -226.293 q^{58} +552.384 q^{59} +242.191 q^{60} +61.0000 q^{61} -629.685 q^{62} -253.950 q^{63} -154.242 q^{64} -411.340 q^{65} +121.148 q^{66} +802.094 q^{67} -137.390 q^{68} -511.529 q^{69} +1526.78 q^{70} -823.637 q^{71} +83.3496 q^{72} +695.845 q^{73} +404.331 q^{74} +276.712 q^{75} +488.931 q^{76} +310.384 q^{77} +307.367 q^{78} -1208.77 q^{79} -1146.95 q^{80} +81.0000 q^{81} +1610.95 q^{82} -73.7825 q^{83} -463.657 q^{84} -369.703 q^{85} +1196.74 q^{86} +184.923 q^{87} -101.872 q^{88} +996.876 q^{89} -486.981 q^{90} +787.480 q^{91} -933.938 q^{92} +514.568 q^{93} -1432.67 q^{94} +1315.67 q^{95} +634.773 q^{96} +313.136 q^{97} -1663.70 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9}+O(q^{10}) \) 39 * q + 8 * q^2 + 117 * q^3 + 154 * q^4 + 65 * q^5 + 24 * q^6 + 35 * q^7 + 75 * q^8 + 351 * q^9	\( 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9} - 21 q^{10} - 429 q^{11} + 462 q^{12} - 27 q^{13} + 164 q^{14} + 195 q^{15} + 686 q^{16} + 170 q^{17} + 72 q^{18} + 139 q^{19} + 1056 q^{20} + 105 q^{21} - 88 q^{22} + 291 q^{23} + 225 q^{24} + 1236 q^{25} + 583 q^{26} + 1053 q^{27} + 976 q^{28} + 374 q^{29} - 63 q^{30} + 232 q^{31} + 933 q^{32} - 1287 q^{33} + 332 q^{34} + 626 q^{35} + 1386 q^{36} + 232 q^{37} + 989 q^{38} - 81 q^{39} - 263 q^{40} + 1014 q^{41} + 492 q^{42} + 515 q^{43} - 1694 q^{44} + 585 q^{45} - 371 q^{46} + 2005 q^{47} + 2058 q^{48} + 2064 q^{49} + 4582 q^{50} + 510 q^{51} + 216 q^{52} + 1485 q^{53} + 216 q^{54} - 715 q^{55} + 2307 q^{56} + 417 q^{57} + 573 q^{58} + 2749 q^{59} + 3168 q^{60} + 2379 q^{61} + 1837 q^{62} + 315 q^{63} + 7295 q^{64} + 3630 q^{65} - 264 q^{66} + 3575 q^{67} + 2630 q^{68} + 873 q^{69} + 4218 q^{70} + 4723 q^{71} + 675 q^{72} + 859 q^{73} + 4232 q^{74} + 3708 q^{75} + 2466 q^{76} - 385 q^{77} + 1749 q^{78} - 1887 q^{79} + 8933 q^{80} + 3159 q^{81} + 6806 q^{82} + 5609 q^{83} + 2928 q^{84} - 565 q^{85} + 5185 q^{86} + 1122 q^{87} - 825 q^{88} + 6725 q^{89} - 189 q^{90} + 2808 q^{91} + 3257 q^{92} + 696 q^{93} + 3184 q^{94} + 3216 q^{95} + 2799 q^{96} + 3512 q^{97} + 4464 q^{98} - 3861 q^{99}+O(q^{100}) \) 39 * q + 8 * q^2 + 117 * q^3 + 154 * q^4 + 65 * q^5 + 24 * q^6 + 35 * q^7 + 75 * q^8 + 351 * q^9 - 21 * q^10 - 429 * q^11 + 462 * q^12 - 27 * q^13 + 164 * q^14 + 195 * q^15 + 686 * q^16 + 170 * q^17 + 72 * q^18 + 139 * q^19 + 1056 * q^20 + 105 * q^21 - 88 * q^22 + 291 * q^23 + 225 * q^24 + 1236 * q^25 + 583 * q^26 + 1053 * q^27 + 976 * q^28 + 374 * q^29 - 63 * q^30 + 232 * q^31 + 933 * q^32 - 1287 * q^33 + 332 * q^34 + 626 * q^35 + 1386 * q^36 + 232 * q^37 + 989 * q^38 - 81 * q^39 - 263 * q^40 + 1014 * q^41 + 492 * q^42 + 515 * q^43 - 1694 * q^44 + 585 * q^45 - 371 * q^46 + 2005 * q^47 + 2058 * q^48 + 2064 * q^49 + 4582 * q^50 + 510 * q^51 + 216 * q^52 + 1485 * q^53 + 216 * q^54 - 715 * q^55 + 2307 * q^56 + 417 * q^57 + 573 * q^58 + 2749 * q^59 + 3168 * q^60 + 2379 * q^61 + 1837 * q^62 + 315 * q^63 + 7295 * q^64 + 3630 * q^65 - 264 * q^66 + 3575 * q^67 + 2630 * q^68 + 873 * q^69 + 4218 * q^70 + 4723 * q^71 + 675 * q^72 + 859 * q^73 + 4232 * q^74 + 3708 * q^75 + 2466 * q^76 - 385 * q^77 + 1749 * q^78 - 1887 * q^79 + 8933 * q^80 + 3159 * q^81 + 6806 * q^82 + 5609 * q^83 + 2928 * q^84 - 565 * q^85 + 5185 * q^86 + 1122 * q^87 - 825 * q^88 + 6725 * q^89 - 189 * q^90 + 2808 * q^91 + 3257 * q^92 + 696 * q^93 + 3184 * q^94 + 3216 * q^95 + 2799 * q^96 + 3512 * q^97 + 4464 * q^98 - 3861 * q^99

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