LMFDB - Embedded newform 2013.4.a.g.1.14

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			1.14
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)

$f(q)$	$=$	$q-1.48743 q^{2} -3.00000 q^{3} -5.78756 q^{4} +8.78636 q^{5} +4.46228 q^{6} -7.23392 q^{7} +20.5080 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-1.48743 q^{2} -3.00000 q^{3} -5.78756 q^{4} +8.78636 q^{5} +4.46228 q^{6} -7.23392 q^{7} +20.5080 q^{8} +9.00000 q^{9} -13.0691 q^{10} +11.0000 q^{11} +17.3627 q^{12} -37.6105 q^{13} +10.7599 q^{14} -26.3591 q^{15} +15.7963 q^{16} -34.9772 q^{17} -13.3869 q^{18} +139.241 q^{19} -50.8515 q^{20} +21.7018 q^{21} -16.3617 q^{22} +163.546 q^{23} -61.5240 q^{24} -47.7999 q^{25} +55.9429 q^{26} -27.0000 q^{27} +41.8667 q^{28} +127.640 q^{29} +39.2072 q^{30} -227.567 q^{31} -187.560 q^{32} -33.0000 q^{33} +52.0261 q^{34} -63.5598 q^{35} -52.0880 q^{36} +356.158 q^{37} -207.111 q^{38} +112.831 q^{39} +180.191 q^{40} +200.071 q^{41} -32.2798 q^{42} -320.374 q^{43} -63.6631 q^{44} +79.0772 q^{45} -243.264 q^{46} -104.192 q^{47} -47.3889 q^{48} -290.670 q^{49} +71.0990 q^{50} +104.932 q^{51} +217.673 q^{52} +206.167 q^{53} +40.1606 q^{54} +96.6499 q^{55} -148.353 q^{56} -417.723 q^{57} -189.855 q^{58} +387.147 q^{59} +152.555 q^{60} +61.0000 q^{61} +338.490 q^{62} -65.1053 q^{63} +152.611 q^{64} -330.459 q^{65} +49.0851 q^{66} -547.928 q^{67} +202.433 q^{68} -490.639 q^{69} +94.5406 q^{70} +865.331 q^{71} +184.572 q^{72} +1029.09 q^{73} -529.760 q^{74} +143.400 q^{75} -805.865 q^{76} -79.5731 q^{77} -167.829 q^{78} -1246.96 q^{79} +138.792 q^{80} +81.0000 q^{81} -297.591 q^{82} +708.460 q^{83} -125.600 q^{84} -307.322 q^{85} +476.533 q^{86} -382.920 q^{87} +225.588 q^{88} +419.595 q^{89} -117.622 q^{90} +272.071 q^{91} -946.535 q^{92} +682.702 q^{93} +154.978 q^{94} +1223.42 q^{95} +562.680 q^{96} -525.892 q^{97} +432.351 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.48743	−0.525885	−0.262943	−	0.964811i	$-0.584693\pi$
$2$	−1.48743	−0.525885	−0.262943	+	0.964811i	$0.584693\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−5.78756	−0.723445
$5$	8.78636	0.785876	0.392938	−	0.919565i	$-0.371459\pi$
$5$	8.78636	0.785876	0.392938	+	0.919565i	$0.371459\pi$
$6$	4.46228	0.303620
$7$	−7.23392	−0.390595	−0.195297	−	0.980744i	$-0.562567\pi$
$7$	−7.23392	−0.390595	−0.195297	+	0.980744i	$0.562567\pi$
$8$	20.5080	0.906334
$9$	9.00000	0.333333
$10$	−13.0691	−0.413280
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	17.3627	0.417681
$13$	−37.6105	−0.802406	−0.401203	−	0.915989i	$-0.631408\pi$
$13$	−37.6105	−0.802406	−0.401203	+	0.915989i	$0.631408\pi$
$14$	10.7599	0.205408
$15$	−26.3591	−0.453725
$16$	15.7963	0.246817
$17$	−34.9772	−0.499013	−0.249507	−	0.968373i	$-0.580268\pi$
$17$	−34.9772	−0.499013	−0.249507	+	0.968373i	$0.580268\pi$
$18$	−13.3869	−0.175295
$19$	139.241	1.68127	0.840633	−	0.541606i	$-0.182183\pi$
$19$	139.241	1.68127	0.840633	+	0.541606i	$0.182183\pi$
$20$	−50.8515	−0.568538
$21$	21.7018	0.225510
$22$	−16.3617	−0.158560
$23$	163.546	1.48269	0.741343	−	0.671126i	$-0.234189\pi$
$23$	163.546	1.48269	0.741343	+	0.671126i	$0.234189\pi$
$24$	−61.5240	−0.523272
$25$	−47.7999	−0.382400
$26$	55.9429	0.421973
$27$	−27.0000	−0.192450
$28$	41.8667	0.282574
$29$	127.640	0.817315	0.408657	−	0.912688i	$-0.365997\pi$
$29$	127.640	0.817315	0.408657	+	0.912688i	$0.365997\pi$
$30$	39.2072	0.238608
$31$	−227.567	−1.31846	−0.659231	−	0.751941i	$-0.729118\pi$
$31$	−227.567	−1.31846	−0.659231	+	0.751941i	$0.729118\pi$
$32$	−187.560	−1.03613
$33$	−33.0000	−0.174078
$34$	52.0261	0.262424
$35$	−63.5598	−0.306959
$36$	−52.0880	−0.241148
$37$	356.158	1.58249	0.791244	−	0.611500i	$-0.209434\pi$
$37$	356.158	1.58249	0.791244	+	0.611500i	$0.209434\pi$
$38$	−207.111	−0.884153
$39$	112.831	0.463269
$40$	180.191	0.712266
$41$	200.071	0.762094	0.381047	−	0.924556i	$-0.375564\pi$
$41$	200.071	0.762094	0.381047	+	0.924556i	$0.375564\pi$
$42$	−32.2798	−0.118592
$43$	−320.374	−1.13620	−0.568099	−	0.822960i	$-0.692321\pi$
$43$	−320.374	−1.13620	−0.568099	+	0.822960i	$0.692321\pi$
$44$	−63.6631	−0.218127
$45$	79.0772	0.261959
$46$	−243.264	−0.779723
$47$	−104.192	−0.323360	−0.161680	−	0.986843i	$-0.551691\pi$
$47$	−104.192	−0.323360	−0.161680	+	0.986843i	$0.551691\pi$
$48$	−47.3889	−0.142500
$49$	−290.670	−0.847436
$50$	71.0990	0.201098
$51$	104.932	0.288105
$52$	217.673	0.580496
$53$	206.167	0.534325	0.267162	−	0.963652i	$-0.413914\pi$
$53$	206.167	0.534325	0.267162	+	0.963652i	$0.413914\pi$
$54$	40.1606	0.101207
$55$	96.6499	0.236950
$56$	−148.353	−0.354010
$57$	−417.723	−0.970679
$58$	−189.855	−0.429814
$59$	387.147	0.854275	0.427138	−	0.904187i	$-0.359522\pi$
$59$	387.147	0.854275	0.427138	+	0.904187i	$0.359522\pi$
$60$	152.555	0.328245
$61$	61.0000	0.128037
$61$	61.0000	0.128037
$62$	338.490	0.693359
$63$	−65.1053	−0.130198
$64$	152.611	0.298069
$65$	−330.459	−0.630591
$66$	49.0851	0.0915449
$67$	−547.928	−0.999106	−0.499553	−	0.866283i	$-0.666502\pi$
$67$	−547.928	−0.999106	−0.499553	+	0.866283i	$0.666502\pi$
$68$	202.433	0.361008
$69$	−490.639	−0.856029
$70$	94.5406	0.161425
$71$	865.331	1.44642	0.723210	−	0.690628i	$-0.242666\pi$
$71$	865.331	1.44642	0.723210	+	0.690628i	$0.242666\pi$
$72$	184.572	0.302111
$73$	1029.09	1.64994	0.824971	−	0.565175i	$-0.191191\pi$
$73$	1029.09	1.64994	0.824971	+	0.565175i	$0.191191\pi$
$74$	−529.760	−0.832207
$75$	143.400	0.220778
$76$	−805.865	−1.21630
$77$	−79.5731	−0.117769
$78$	−167.829	−0.243626
$79$	−1246.96	−1.77588	−0.887938	−	0.459963i	$-0.847863\pi$
$79$	−1246.96	−1.77588	−0.887938	+	0.459963i	$0.847863\pi$
$80$	138.792	0.193968
$81$	81.0000	0.111111
$82$	−297.591	−0.400774
$83$	708.460	0.936911	0.468456	−	0.883487i	$-0.344811\pi$
$83$	708.460	0.936911	0.468456	+	0.883487i	$0.344811\pi$
$84$	−125.600	−0.163144
$85$	−307.322	−0.392162
$86$	476.533	0.597510
$87$	−382.920	−0.471877
$88$	225.588	0.273270
$89$	419.595	0.499741	0.249871	−	0.968279i	$-0.419612\pi$
$89$	419.595	0.499741	0.249871	+	0.968279i	$0.419612\pi$
$90$	−117.622	−0.137760
$91$	272.071	0.313416
$92$	−946.535	−1.07264
$93$	682.702	0.761214
$94$	154.978	0.170050
$95$	1223.42	1.32127
$96$	562.680	0.598211
$97$	−525.892	−0.550476	−0.275238	−	0.961376i	$-0.588757\pi$
$97$	−525.892	−0.550476	−0.275238	+	0.961376i	$0.588757\pi$
$98$	432.351	0.445654
$99$	99.0000	0.100504
$100$	276.645	0.276645
$101$	−1526.49	−1.50388	−0.751939	−	0.659233i	$-0.770881\pi$
$101$	−1526.49	−1.50388	−0.751939	+	0.659233i	$0.770881\pi$
$102$	−156.078	−0.151510
$103$	−1696.31	−1.62274	−0.811372	−	0.584530i	$-0.801279\pi$
$103$	−1696.31	−1.62274	−0.811372	+	0.584530i	$0.801279\pi$
$104$	−771.316	−0.727248
$105$	190.679	0.177223
$106$	−306.659	−0.280994
$107$	345.177	0.311865	0.155932	−	0.987768i	$-0.450162\pi$
$107$	345.177	0.311865	0.155932	+	0.987768i	$0.450162\pi$
$108$	156.264	0.139227
$109$	−963.342	−0.846527	−0.423263	−	0.906007i	$-0.639116\pi$
$109$	−963.342	−0.846527	−0.423263	+	0.906007i	$0.639116\pi$
$110$	−143.760	−0.124609
$111$	−1068.47	−0.913650
$112$	−114.269	−0.0964055
$113$	−475.773	−0.396079	−0.198040	−	0.980194i	$-0.563457\pi$
$113$	−475.773	−0.396079	−0.198040	+	0.980194i	$0.563457\pi$
$114$	621.332	0.510466
$115$	1436.98	1.16521
$116$	−738.723	−0.591282
$117$	−338.494	−0.267469
$118$	−575.853	−0.449251
$119$	253.022	0.194912
$120$	−540.572	−0.411227
$121$	121.000	0.0909091
$122$	−90.7331	−0.0673327
$123$	−600.213	−0.439995
$124$	1317.06	0.953834
$125$	−1518.28	−1.08639
$126$	96.8394	0.0684694
$127$	−965.481	−0.674587	−0.337294	−	0.941399i	$-0.609512\pi$
$127$	−965.481	−0.674587	−0.337294	+	0.941399i	$0.609512\pi$
$128$	1273.48	0.879381
$129$	961.121	0.655984
$130$	491.534	0.331618
$131$	573.727	0.382647	0.191324	−	0.981527i	$-0.438722\pi$
$131$	573.727	0.382647	0.191324	+	0.981527i	$0.438722\pi$
$132$	190.989	0.125936
$133$	−1007.26	−0.656694
$134$	815.004	0.525415
$135$	−237.232	−0.151242
$136$	−717.313	−0.452273
$137$	−603.127	−0.376121	−0.188061	−	0.982157i	$-0.560220\pi$
$137$	−603.127	−0.376121	−0.188061	+	0.982157i	$0.560220\pi$
$138$	729.791	0.450173
$139$	−1138.56	−0.694758	−0.347379	−	0.937725i	$-0.612928\pi$
$139$	−1138.56	−0.694758	−0.347379	+	0.937725i	$0.612928\pi$
$140$	367.856	0.222068
$141$	312.576	0.186692
$142$	−1287.12	−0.760651
$143$	−413.715	−0.241934
$144$	142.167	0.0822724
$145$	1121.49	0.642308
$146$	−1530.70	−0.867680
$147$	872.011	0.489267
$148$	−2061.29	−1.14484
$149$	1063.41	0.584683	0.292341	−	0.956314i	$-0.405566\pi$
$149$	1063.41	0.584683	0.292341	+	0.956314i	$0.405566\pi$
$150$	−213.297	−0.116104
$151$	−2133.22	−1.14966	−0.574832	−	0.818271i	$-0.694933\pi$
$151$	−2133.22	−1.14966	−0.574832	+	0.818271i	$0.694933\pi$
$152$	2855.55	1.52379
$153$	−314.795	−0.166338
$154$	118.359	0.0619329
$155$	−1999.49	−1.03615
$156$	−653.019	−0.335150
$157$	−2093.85	−1.06438	−0.532190	−	0.846625i	$-0.678631\pi$
$157$	−2093.85	−1.06438	−0.532190	+	0.846625i	$0.678631\pi$
$158$	1854.77	0.933907
$159$	−618.501	−0.308493
$160$	−1647.97	−0.814270
$161$	−1183.08	−0.579130
$162$	−120.482	−0.0584317
$163$	3144.90	1.51121	0.755606	−	0.655027i	$-0.227343\pi$
$163$	3144.90	1.51121	0.755606	+	0.655027i	$0.227343\pi$
$164$	−1157.92	−0.551333
$165$	−289.950	−0.136803
$166$	−1053.78	−0.492708
$167$	3076.35	1.42548	0.712740	−	0.701428i	$-0.247454\pi$
$167$	3076.35	1.42548	0.712740	+	0.701428i	$0.247454\pi$
$168$	445.060	0.204388
$169$	−782.451	−0.356145
$170$	457.120	0.206232
$171$	1253.17	0.560422
$172$	1854.18	0.821976
$173$	−2874.46	−1.26324	−0.631621	−	0.775277i	$-0.717610\pi$
$173$	−2874.46	−1.26324	−0.631621	+	0.775277i	$0.717610\pi$
$174$	569.565	0.248153
$175$	345.781	0.149363
$176$	173.759	0.0744181
$177$	−1161.44	−0.493216
$178$	−624.118	−0.262807
$179$	696.170	0.290694	0.145347	−	0.989381i	$-0.453570\pi$
$179$	696.170	0.290694	0.145347	+	0.989381i	$0.453570\pi$
$180$	−457.664	−0.189513
$181$	1400.55	0.575150	0.287575	−	0.957758i	$-0.407151\pi$
$181$	1400.55	0.575150	0.287575	+	0.957758i	$0.407151\pi$
$182$	−404.686	−0.164821
$183$	−183.000	−0.0739221
$184$	3354.01	1.34381
$185$	3129.33	1.24364
$186$	−1015.47	−0.400311
$187$	−384.749	−0.150458
$188$	603.016	0.233933
$189$	195.316	0.0751700
$190$	−1819.75	−0.694834
$191$	4881.34	1.84922	0.924611	−	0.380912i	$-0.124390\pi$
$191$	4881.34	1.84922	0.924611	+	0.380912i	$0.124390\pi$
$192$	−457.834	−0.172090
$193$	4546.06	1.69551	0.847753	−	0.530391i	$-0.177955\pi$
$193$	4546.06	1.69551	0.847753	+	0.530391i	$0.177955\pi$
$194$	782.226	0.289487
$195$	991.378	0.364072
$196$	1682.27	0.613073
$197$	1919.00	0.694027	0.347013	−	0.937860i	$-0.387196\pi$
$197$	1919.00	0.694027	0.347013	+	0.937860i	$0.387196\pi$
$198$	−147.255	−0.0528535
$199$	−2612.10	−0.930487	−0.465243	−	0.885183i	$-0.654033\pi$
$199$	−2612.10	−0.930487	−0.465243	+	0.885183i	$0.654033\pi$
$200$	−980.281	−0.346582
$201$	1643.79	0.576834
$202$	2270.55	0.790867
$203$	−923.337	−0.319239
$204$	−607.298	−0.208428
$205$	1757.90	0.598911
$206$	2523.14	0.853377
$207$	1471.92	0.494229
$208$	−594.106	−0.198047
$209$	1531.65	0.506921
$210$	−283.622	−0.0931989
$211$	143.687	0.0468807	0.0234404	−	0.999725i	$-0.492538\pi$
$211$	143.687	0.0468807	0.0234404	+	0.999725i	$0.492538\pi$
$212$	−1193.20	−0.386554
$213$	−2595.99	−0.835091
$214$	−513.426	−0.164005
$215$	−2814.92	−0.892910
$216$	−553.716	−0.174424
$217$	1646.20	0.514984
$218$	1432.90	0.445176
$219$	−3087.27	−0.952595
$220$	−559.367	−0.171421
$221$	1315.51	0.400411
$222$	1589.28	0.480475
$223$	488.306	0.146634	0.0733170	−	0.997309i	$-0.476642\pi$
$223$	488.306	0.146634	0.0733170	+	0.997309i	$0.476642\pi$
$224$	1356.79	0.404708
$225$	−430.200	−0.127467
$226$	707.678	0.208292
$227$	216.923	0.0634259	0.0317130	−	0.999497i	$-0.489904\pi$
$227$	216.923	0.0634259	0.0317130	+	0.999497i	$0.489904\pi$
$228$	2417.59	0.702233
$229$	−283.234	−0.0817319	−0.0408660	−	0.999165i	$-0.513012\pi$
$229$	−283.234	−0.0817319	−0.0408660	+	0.999165i	$0.513012\pi$
$230$	−2137.40	−0.612765
$231$	238.719	0.0679939
$232$	2617.64	0.740760
$233$	4012.29	1.12813	0.564064	−	0.825731i	$-0.309237\pi$
$233$	4012.29	1.12813	0.564064	+	0.825731i	$0.309237\pi$
$234$	503.486	0.140658
$235$	−915.467	−0.254121
$236$	−2240.64	−0.618021
$237$	3740.89	1.02530
$238$	−376.353	−0.102501
$239$	111.257	0.0301113	0.0150556	−	0.999887i	$-0.495207\pi$
$239$	111.257	0.0301113	0.0150556	+	0.999887i	$0.495207\pi$
$240$	−416.376	−0.111987
$241$	1453.68	0.388547	0.194273	−	0.980947i	$-0.437765\pi$
$241$	1453.68	0.388547	0.194273	+	0.980947i	$0.437765\pi$
$242$	−179.979	−0.0478077
$243$	−243.000	−0.0641500
$244$	−353.041	−0.0926276
$245$	−2553.93	−0.665979
$246$	892.774	0.231387
$247$	−5236.92	−1.34906
$248$	−4666.95	−1.19497
$249$	−2125.38	−0.540926
$250$	2258.33	0.571319
$251$	1495.17	0.375994	0.187997	−	0.982170i	$-0.439800\pi$
$251$	1495.17	0.375994	0.187997	+	0.982170i	$0.439800\pi$
$252$	376.801	0.0941913
$253$	1799.01	0.447047
$254$	1436.08	0.354756
$255$	921.967	0.226415
$256$	−3115.10	−0.760523
$257$	5326.34	1.29279	0.646397	−	0.763001i	$-0.276275\pi$
$257$	5326.34	1.29279	0.646397	+	0.763001i	$0.276275\pi$
$258$	−1429.60	−0.344972
$259$	−2576.42	−0.618112
$260$	1912.55	0.456198
$261$	1148.76	0.272438
$262$	−853.378	−0.201229
$263$	7290.30	1.70928	0.854638	−	0.519225i	$-0.173779\pi$
$263$	7290.30	1.70928	0.854638	+	0.519225i	$0.173779\pi$
$264$	−676.764	−0.157773
$265$	1811.46	0.419913
$266$	1498.22	0.345346
$267$	−1258.79	−0.288526
$268$	3171.17	0.722798
$269$	1495.60	0.338989	0.169495	−	0.985531i	$-0.445786\pi$
$269$	1495.60	0.338989	0.169495	+	0.985531i	$0.445786\pi$
$270$	352.865	0.0795358
$271$	6003.42	1.34569	0.672845	−	0.739784i	$-0.265072\pi$
$271$	6003.42	1.34569	0.672845	+	0.739784i	$0.265072\pi$
$272$	−552.510	−0.123165
$273$	−816.214	−0.180951
$274$	897.107	0.197796
$275$	−525.799	−0.115298
$276$	2839.60	0.619290
$277$	7395.49	1.60416	0.802079	−	0.597218i	$-0.203727\pi$
$277$	7395.49	1.60416	0.802079	+	0.597218i	$0.203727\pi$
$278$	1693.53	0.365363
$279$	−2048.11	−0.439487
$280$	−1303.48	−0.278207
$281$	−6951.04	−1.47567	−0.737836	−	0.674980i	$-0.764152\pi$
$281$	−6951.04	−1.47567	−0.737836	+	0.674980i	$0.764152\pi$
$282$	−464.934	−0.0981787
$283$	5064.99	1.06389	0.531947	−	0.846777i	$-0.321460\pi$
$283$	5064.99	1.06389	0.531947	+	0.846777i	$0.321460\pi$
$284$	−5008.15	−1.04641
$285$	−3670.26	−0.762833
$286$	615.372	0.127230
$287$	−1447.30	−0.297670
$288$	−1688.04	−0.345377
$289$	−3689.59	−0.750986
$290$	−1668.13	−0.337780
$291$	1577.68	0.317818
$292$	−5955.91	−1.19364
$293$	−8237.67	−1.64249	−0.821245	−	0.570575i	$-0.806720\pi$
$293$	−8237.67	−1.64249	−0.821245	+	0.570575i	$0.806720\pi$
$294$	−1297.05	−0.257298
$295$	3401.61	0.671354
$296$	7304.09	1.43426
$297$	−297.000	−0.0580259
$298$	−1581.74	−0.307476
$299$	−6151.06	−1.18972
$300$	−829.935	−0.159721
$301$	2317.56	0.443793
$302$	3173.02	0.604592
$303$	4579.48	0.868265
$304$	2199.49	0.414965
$305$	535.968	0.100621
$306$	468.235	0.0874745
$307$	5975.77	1.11093	0.555464	−	0.831540i	$-0.312540\pi$
$307$	5975.77	1.11093	0.555464	+	0.831540i	$0.312540\pi$
$308$	460.534	0.0851992
$309$	5088.94	0.936892
$310$	2974.09	0.544894
$311$	3429.97	0.625388	0.312694	−	0.949854i	$-0.398769\pi$
$311$	3429.97	0.625388	0.312694	+	0.949854i	$0.398769\pi$
$312$	2313.95	0.419877
$313$	10271.3	1.85485	0.927424	−	0.374010i	$-0.122018\pi$
$313$	10271.3	1.85485	0.927424	+	0.374010i	$0.122018\pi$
$314$	3114.45	0.559741
$315$	−572.038	−0.102320
$316$	7216.87	1.28475
$317$	−518.106	−0.0917973	−0.0458987	−	0.998946i	$-0.514615\pi$
$317$	−518.106	−0.0917973	−0.0458987	+	0.998946i	$0.514615\pi$
$318$	919.976	0.162232
$319$	1404.04	0.246430
$320$	1340.90	0.234245
$321$	−1035.53	−0.180055
$322$	1759.75	0.304556
$323$	−4870.26	−0.838973
$324$	−468.792	−0.0803828
$325$	1797.78	0.306840
$326$	−4677.81	−0.794724
$327$	2890.03	0.488743
$328$	4103.06	0.690712
$329$	753.715	0.126303
$330$	431.279	0.0719429
$331$	−2941.01	−0.488376	−0.244188	−	0.969728i	$-0.578521\pi$
$331$	−2941.01	−0.488376	−0.244188	+	0.969728i	$0.578521\pi$
$332$	−4100.26	−0.677804
$333$	3205.42	0.527496
$334$	−4575.85	−0.749639
$335$	−4814.29	−0.785173
$336$	342.807	0.0556597
$337$	2941.74	0.475509	0.237755	−	0.971325i	$-0.423589\pi$
$337$	2941.74	0.475509	0.237755	+	0.971325i	$0.423589\pi$
$338$	1163.84	0.187291
$339$	1427.32	0.228676
$340$	1778.65	0.283708
$341$	−2503.24	−0.397531
$342$	−1864.00	−0.294718
$343$	4583.92	0.721599
$344$	−6570.22	−1.02977
$345$	−4310.93	−0.672733
$346$	4275.55	0.664320
$347$	2199.32	0.340247	0.170123	−	0.985423i	$-0.445583\pi$
$347$	2199.32	0.340247	0.170123	+	0.985423i	$0.445583\pi$
$348$	2216.17	0.341377
$349$	6150.85	0.943403	0.471701	−	0.881758i	$-0.343640\pi$
$349$	6150.85	0.943403	0.471701	+	0.881758i	$0.343640\pi$
$350$	−514.324	−0.0785480
$351$	1015.48	0.154423
$352$	−2063.16	−0.312405
$353$	8180.15	1.23339	0.616693	−	0.787203i	$-0.288472\pi$
$353$	8180.15	1.23339	0.616693	+	0.787203i	$0.288472\pi$
$354$	1727.56	0.259375
$355$	7603.10	1.13671
$356$	−2428.43	−0.361535
$357$	−759.067	−0.112532
$358$	−1035.50	−0.152872
$359$	−404.730	−0.0595010	−0.0297505	−	0.999557i	$-0.509471\pi$
$359$	−404.730	−0.0595010	−0.0297505	+	0.999557i	$0.509471\pi$
$360$	1621.72	0.237422
$361$	12529.0	1.82665
$362$	−2083.22	−0.302463
$363$	−363.000	−0.0524864
$364$	−1574.63	−0.226739
$365$	9041.95	1.29665
$366$	272.199	0.0388746
$367$	5988.16	0.851715	0.425858	−	0.904790i	$-0.359972\pi$
$367$	5988.16	0.851715	0.425858	+	0.904790i	$0.359972\pi$
$368$	2583.43	0.365952
$369$	1800.64	0.254031
$370$	−4654.66	−0.654011
$371$	−1491.40	−0.208705
$372$	−3951.18	−0.550696
$373$	589.346	0.0818101	0.0409050	−	0.999163i	$-0.486976\pi$
$373$	589.346	0.0818101	0.0409050	+	0.999163i	$0.486976\pi$
$374$	572.287	0.0791237
$375$	4554.85	0.627230
$376$	−2136.77	−0.293073
$377$	−4800.60	−0.655818
$378$	−290.518	−0.0395308
$379$	−12437.7	−1.68571	−0.842853	−	0.538145i	$-0.819125\pi$
$379$	−12437.7	−1.68571	−0.842853	+	0.538145i	$0.819125\pi$
$380$	−7080.61	−0.955863
$381$	2896.44	0.389473
$382$	−7260.65	−0.972479
$383$	231.632	0.0309030	0.0154515	−	0.999881i	$-0.495081\pi$
$383$	231.632	0.0309030	0.0154515	+	0.999881i	$0.495081\pi$
$384$	−3820.44	−0.507711
$385$	−699.158	−0.0925516
$386$	−6761.94	−0.891642
$387$	−2883.36	−0.378733
$388$	3043.63	0.398239
$389$	3612.00	0.470786	0.235393	−	0.971900i	$-0.424362\pi$
$389$	3612.00	0.470786	0.235393	+	0.971900i	$0.424362\pi$
$390$	−1474.60	−0.191460
$391$	−5720.40	−0.739880
$392$	−5961.07	−0.768060
$393$	−1721.18	−0.220922
$394$	−2854.38	−0.364978
$395$	−10956.3	−1.39562
$396$	−572.968	−0.0727089
$397$	1850.81	0.233979	0.116989	−	0.993133i	$-0.462676\pi$
$397$	1850.81	0.233979	0.116989	+	0.993133i	$0.462676\pi$
$398$	3885.31	0.489329
$399$	3021.77	0.379142
$400$	−755.062	−0.0943827
$401$	−1307.19	−0.162788	−0.0813941	−	0.996682i	$-0.525937\pi$
$401$	−1307.19	−0.162788	−0.0813941	+	0.996682i	$0.525937\pi$
$402$	−2445.01	−0.303349
$403$	8558.92	1.05794
$404$	8834.67	1.08797
$405$	711.695	0.0873195
$406$	1373.40	0.167883
$407$	3917.74	0.477138
$408$	2151.94	0.261120
$409$	1716.82	0.207558	0.103779	−	0.994600i	$-0.466907\pi$
$409$	1716.82	0.207558	0.103779	+	0.994600i	$0.466907\pi$
$410$	−2614.74	−0.314958
$411$	1809.38	0.217154
$412$	9817.51	1.17397
$413$	−2800.59	−0.333676
$414$	−2189.37	−0.259908
$415$	6224.79	0.736296
$416$	7054.22	0.831398
$417$	3415.68	0.401119
$418$	−2278.22	−0.266582
$419$	−7947.12	−0.926593	−0.463296	−	0.886203i	$-0.653333\pi$
$419$	−7947.12	−0.926593	−0.463296	+	0.886203i	$0.653333\pi$
$420$	−1103.57	−0.128211
$421$	4178.95	0.483776	0.241888	−	0.970304i	$-0.422233\pi$
$421$	4178.95	0.483776	0.241888	+	0.970304i	$0.422233\pi$
$422$	−213.724	−0.0246539
$423$	−937.727	−0.107787
$424$	4228.07	0.484277
$425$	1671.91	0.190822
$426$	3861.35	0.439162
$427$	−441.269	−0.0500106
$428$	−1997.73	−0.225617
$429$	1241.15	0.139681
$430$	4186.98	0.469568
$431$	4228.82	0.472611	0.236305	−	0.971679i	$-0.424063\pi$
$431$	4228.82	0.472611	0.236305	+	0.971679i	$0.424063\pi$
$432$	−426.500	−0.0475000
$433$	2694.06	0.299003	0.149502	−	0.988761i	$-0.452233\pi$
$433$	2694.06	0.299003	0.149502	+	0.988761i	$0.452233\pi$
$434$	−2448.61	−0.270823
$435$	−3364.47	−0.370837
$436$	5575.40	0.612415
$437$	22772.3	2.49279
$438$	4592.09	0.500955
$439$	−7386.29	−0.803025	−0.401513	−	0.915853i	$-0.631515\pi$
$439$	−7386.29	−0.803025	−0.401513	+	0.915853i	$0.631515\pi$
$440$	1982.10	0.214756
$441$	−2616.03	−0.282479
$442$	−1956.73	−0.210570
$443$	−8405.01	−0.901432	−0.450716	−	0.892667i	$-0.648831\pi$
$443$	−8405.01	−0.901432	−0.450716	+	0.892667i	$0.648831\pi$
$444$	6183.86	0.660975
$445$	3686.71	0.392735
$446$	−726.320	−0.0771127
$447$	−3190.22	−0.337567
$448$	−1103.98	−0.116424
$449$	13138.1	1.38090	0.690450	−	0.723380i	$-0.257413\pi$
$449$	13138.1	1.38090	0.690450	+	0.723380i	$0.257413\pi$
$450$	639.891	0.0670328
$451$	2200.78	0.229780
$452$	2753.56	0.286541
$453$	6399.67	0.663759
$454$	−322.657	−0.0333547
$455$	2390.52	0.246306
$456$	−8566.65	−0.879760
$457$	−9491.36	−0.971526	−0.485763	−	0.874091i	$-0.661458\pi$
$457$	−9491.36	−0.971526	−0.485763	+	0.874091i	$0.661458\pi$
$458$	421.290	0.0429816
$459$	944.385	0.0960351
$460$	−8316.59	−0.842963
$461$	−5614.17	−0.567197	−0.283599	−	0.958943i	$-0.591528\pi$
$461$	−5614.17	−0.567197	−0.283599	+	0.958943i	$0.591528\pi$
$462$	−355.078	−0.0357570
$463$	11002.7	1.10440	0.552201	−	0.833711i	$-0.313788\pi$
$463$	11002.7	1.10440	0.552201	+	0.833711i	$0.313788\pi$
$464$	2016.24	0.201727
$465$	5998.46	0.598219
$466$	−5967.99	−0.593266
$467$	4238.08	0.419946	0.209973	−	0.977707i	$-0.432662\pi$
$467$	4238.08	0.419946	0.209973	+	0.977707i	$0.432662\pi$
$468$	1959.06	0.193499
$469$	3963.67	0.390246
$470$	1361.69	0.133639
$471$	6281.56	0.614520
$472$	7939.61	0.774259
$473$	−3524.11	−0.342577
$474$	−5564.30	−0.539192
$475$	−6655.71	−0.642915
$476$	−1464.38	−0.141008
$477$	1855.50	0.178108
$478$	−165.486	−0.0158351
$479$	8750.13	0.834663	0.417331	−	0.908754i	$-0.362965\pi$
$479$	8750.13	0.834663	0.417331	+	0.908754i	$0.362965\pi$
$480$	4943.90	0.470119
$481$	−13395.3	−1.26980
$482$	−2162.24	−0.204331
$483$	3549.25	0.334361
$484$	−700.295	−0.0657677
$485$	−4620.67	−0.432606
$486$	361.445	0.0337356
$487$	−19395.3	−1.80469	−0.902347	−	0.431011i	$-0.858157\pi$
$487$	−19395.3	−1.80469	−0.902347	+	0.431011i	$0.858157\pi$
$488$	1250.99	0.116044
$489$	−9434.70	−0.872498
$490$	3798.79	0.350228
$491$	6291.13	0.578237	0.289119	−	0.957293i	$-0.406638\pi$
$491$	6291.13	0.578237	0.289119	+	0.957293i	$0.406638\pi$
$492$	3473.77	0.318312
$493$	−4464.49	−0.407851
$494$	7789.54	0.709449
$495$	869.849	0.0789835
$496$	−3594.72	−0.325419
$497$	−6259.73	−0.564965
$498$	3161.35	0.284465
$499$	4206.78	0.377397	0.188699	−	0.982035i	$-0.439573\pi$
$499$	4206.78	0.377397	0.188699	+	0.982035i	$0.439573\pi$
$500$	8787.14	0.785946
$501$	−9229.05	−0.823001
$502$	−2223.96	−0.197730
$503$	−14771.3	−1.30939	−0.654693	−	0.755894i	$-0.727202\pi$
$503$	−14771.3	−1.30939	−0.654693	+	0.755894i	$0.727202\pi$
$504$	−1335.18	−0.118003
$505$	−13412.3	−1.18186
$506$	−2675.90	−0.235095
$507$	2347.35	0.205620
$508$	5587.78	0.488027
$509$	20155.1	1.75513	0.877564	−	0.479460i	$-0.159167\pi$
$509$	20155.1	1.75513	0.877564	+	0.479460i	$0.159167\pi$
$510$	−1371.36	−0.119068
$511$	−7444.35	−0.644459
$512$	−5554.35	−0.479434
$513$	−3759.50	−0.323560
$514$	−7922.55	−0.679861
$515$	−14904.4	−1.27528
$516$	−5562.54	−0.474568
$517$	−1146.11	−0.0974968
$518$	3832.24	0.325056
$519$	8623.37	0.729333
$520$	−6777.06	−0.571526
$521$	−16587.6	−1.39484	−0.697422	−	0.716660i	$-0.745670\pi$
$521$	−16587.6	−1.39484	−0.697422	+	0.716660i	$0.745670\pi$
$522$	−1708.70	−0.143271
$523$	23313.3	1.94918	0.974589	−	0.224001i	$-0.0719119\pi$
$523$	23313.3	1.94918	0.974589	+	0.224001i	$0.0719119\pi$
$524$	−3320.48	−0.276824
$525$	−1037.34	−0.0862350
$526$	−10843.8	−0.898883
$527$	7959.67	0.657929
$528$	−521.278	−0.0429653
$529$	14580.4	1.19836
$530$	−2694.41	−0.220826
$531$	3484.32	0.284758
$532$	5829.56	0.475082
$533$	−7524.77	−0.611508
$534$	1872.35	0.151731
$535$	3032.85	0.245087
$536$	−11236.9	−0.905524
$537$	−2088.51	−0.167832
$538$	−2224.59	−0.178269
$539$	−3197.37	−0.255511
$540$	1372.99	0.109415
$541$	−20078.6	−1.59565	−0.797827	−	0.602887i	$-0.794017\pi$
$541$	−20078.6	−1.59565	−0.797827	+	0.602887i	$0.794017\pi$
$542$	−8929.66	−0.707678
$543$	−4201.65	−0.332063
$544$	6560.32	0.517043
$545$	−8464.27	−0.665265
$546$	1214.06	0.0951592
$547$	−1130.77	−0.0883884	−0.0441942	−	0.999023i	$-0.514072\pi$
$547$	−1130.77	−0.0883884	−0.0441942	+	0.999023i	$0.514072\pi$
$548$	3490.63	0.272103
$549$	549.000	0.0426790
$550$	782.089	0.0606334
$551$	17772.7	1.37412
$552$	−10062.0	−0.775849
$553$	9020.43	0.693648
$554$	−11000.3	−0.843603
$555$	−9388.00	−0.718015
$556$	6589.48	0.502619
$557$	−4082.68	−0.310572	−0.155286	−	0.987870i	$-0.549630\pi$
$557$	−4082.68	−0.310572	−0.155286	+	0.987870i	$0.549630\pi$
$558$	3046.41	0.231120
$559$	12049.4	0.911692
$560$	−1004.01	−0.0757627
$561$	1154.25	0.0868670
$562$	10339.2	0.776034
$563$	−7291.55	−0.545830	−0.272915	−	0.962038i	$-0.587988\pi$
$563$	−7291.55	−0.545830	−0.272915	+	0.962038i	$0.587988\pi$
$564$	−1809.05	−0.135062
$565$	−4180.31	−0.311269
$566$	−7533.80	−0.559487
$567$	−585.948	−0.0433994
$568$	17746.2	1.31094
$569$	8163.69	0.601476	0.300738	−	0.953707i	$-0.402767\pi$
$569$	8163.69	0.601476	0.300738	+	0.953707i	$0.402767\pi$
$570$	5459.25	0.401163
$571$	−4983.38	−0.365233	−0.182616	−	0.983184i	$-0.558457\pi$
$571$	−4983.38	−0.365233	−0.182616	+	0.983184i	$0.558457\pi$
$572$	2394.40	0.175026
$573$	−14644.0	−1.06765
$574$	2152.75	0.156540
$575$	−7817.51	−0.566979
$576$	1373.50	0.0993564
$577$	−14526.5	−1.04809	−0.524043	−	0.851692i	$-0.675577\pi$
$577$	−14526.5	−1.04809	−0.524043	+	0.851692i	$0.675577\pi$
$578$	5488.01	0.394932
$579$	−13638.2	−0.978901
$580$	−6490.68	−0.464674
$581$	−5124.95	−0.365953
$582$	−2346.68	−0.167136
$583$	2267.84	0.161105
$584$	21104.6	1.49540
$585$	−2974.13	−0.210197
$586$	12252.9	0.863762
$587$	−12311.0	−0.865637	−0.432819	−	0.901481i	$-0.642481\pi$
$587$	−12311.0	−0.865637	−0.432819	+	0.901481i	$0.642481\pi$
$588$	−5046.82	−0.353958
$589$	−31686.7	−2.21668
$590$	−5059.65	−0.353055
$591$	−5757.01	−0.400697
$592$	5625.98	0.390585
$593$	15111.1	1.04644	0.523220	−	0.852197i	$-0.324731\pi$
$593$	15111.1	1.04644	0.523220	+	0.852197i	$0.324731\pi$
$594$	441.766	0.0305150
$595$	2223.15	0.153177
$596$	−6154.53	−0.422986
$597$	7836.30	0.537217
$598$	9149.26	0.625654
$599$	18172.5	1.23958	0.619789	−	0.784769i	$-0.287218\pi$
$599$	18172.5	1.23958	0.619789	+	0.784769i	$0.287218\pi$
$600$	2940.84	0.200099
$601$	16021.0	1.08737	0.543686	−	0.839289i	$-0.317028\pi$
$601$	16021.0	1.08737	0.543686	+	0.839289i	$0.317028\pi$
$602$	−3447.20	−0.233384
$603$	−4931.36	−0.333035
$604$	12346.2	0.831719
$605$	1063.15	0.0714432
$606$	−6811.64	−0.456607
$607$	22849.6	1.52790	0.763950	−	0.645276i	$-0.223257\pi$
$607$	22849.6	1.52790	0.763950	+	0.645276i	$0.223257\pi$
$608$	−26116.0	−1.74201
$609$	2770.01	0.184313
$610$	−797.213	−0.0529151
$611$	3918.71	0.259466
$612$	1821.89	0.120336
$613$	18359.4	1.20967	0.604837	−	0.796349i	$-0.293238\pi$
$613$	18359.4	1.20967	0.604837	+	0.796349i	$0.293238\pi$
$614$	−8888.53	−0.584221
$615$	−5273.69	−0.345781
$616$	−1631.89	−0.106738
$617$	−22798.2	−1.48755	−0.743776	−	0.668429i	$-0.766967\pi$
$617$	−22798.2	−1.48755	−0.743776	+	0.668429i	$0.766967\pi$
$618$	−7569.43	−0.492698
$619$	13435.2	0.872387	0.436194	−	0.899853i	$-0.356326\pi$
$619$	13435.2	0.872387	0.436194	+	0.899853i	$0.356326\pi$
$620$	11572.1	0.749595
$621$	−4415.75	−0.285343
$622$	−5101.83	−0.328882
$623$	−3035.32	−0.195197
$624$	1782.32	0.114343
$625$	−7365.17	−0.471371
$626$	−15277.8	−0.975438
$627$	−4594.95	−0.292671
$628$	12118.3	0.770020
$629$	−12457.4	−0.789682
$630$	850.866	0.0538084
$631$	13371.6	0.843602	0.421801	−	0.906688i	$-0.361398\pi$
$631$	13371.6	0.843602	0.421801	+	0.906688i	$0.361398\pi$
$632$	−25572.7	−1.60954
$633$	−431.062	−0.0270666
$634$	770.646	0.0482749
$635$	−8483.06	−0.530142
$636$	3579.61	0.223177
$637$	10932.3	0.679987
$638$	−2088.41	−0.129594
$639$	7787.98	0.482140
$640$	11189.3	0.691084
$641$	15809.5	0.974164	0.487082	−	0.873356i	$-0.338061\pi$
$641$	15809.5	0.974164	0.487082	+	0.873356i	$0.338061\pi$
$642$	1540.28	0.0946884
$643$	4107.51	0.251920	0.125960	−	0.992035i	$-0.459799\pi$
$643$	4107.51	0.251920	0.125960	+	0.992035i	$0.459799\pi$
$644$	6847.16	0.418969
$645$	8444.75	0.515522
$646$	7244.16	0.441204
$647$	19907.8	1.20967	0.604836	−	0.796350i	$-0.293239\pi$
$647$	19907.8	1.20967	0.604836	+	0.796350i	$0.293239\pi$
$648$	1661.15	0.100704
$649$	4258.62	0.257574
$650$	−2674.07	−0.161362
$651$	−4938.61	−0.297326
$652$	−18201.3	−1.09328
$653$	5491.19	0.329077	0.164538	−	0.986371i	$-0.447387\pi$
$653$	5491.19	0.329077	0.164538	+	0.986371i	$0.447387\pi$
$654$	−4298.71	−0.257022
$655$	5040.97	0.300713
$656$	3160.38	0.188098
$657$	9261.80	0.549981
$658$	−1121.10	−0.0664209
$659$	−8224.71	−0.486175	−0.243087	−	0.970004i	$-0.578160\pi$
$659$	−8224.71	−0.486175	−0.243087	+	0.970004i	$0.578160\pi$
$660$	1678.10	0.0989697
$661$	−7672.52	−0.451477	−0.225738	−	0.974188i	$-0.572479\pi$
$661$	−7672.52	−0.451477	−0.225738	+	0.974188i	$0.572479\pi$
$662$	4374.54	0.256830
$663$	−3946.53	−0.231177
$664$	14529.1	0.849155
$665$	−8850.12	−0.516080
$666$	−4767.84	−0.277402
$667$	20875.0	1.21182
$668$	−17804.6	−1.03126
$669$	−1464.92	−0.0846592
$670$	7160.92	0.412911
$671$	671.000	0.0386046
$672$	−4070.38	−0.233658
$673$	−28287.3	−1.62020	−0.810101	−	0.586291i	$-0.800588\pi$
$673$	−28287.3	−1.62020	−0.810101	+	0.586291i	$0.800588\pi$
$674$	−4375.62	−0.250063
$675$	1290.60	0.0735928
$676$	4528.48	0.257651
$677$	742.796	0.0421683	0.0210842	−	0.999778i	$-0.493288\pi$
$677$	742.796	0.0421683	0.0210842	+	0.999778i	$0.493288\pi$
$678$	−2123.03	−0.120258
$679$	3804.26	0.215013
$680$	−6302.57	−0.355430
$681$	−650.769	−0.0366190
$682$	3723.39	0.209056
$683$	−8126.14	−0.455254	−0.227627	−	0.973748i	$-0.573097\pi$
$683$	−8126.14	−0.455254	−0.227627	+	0.973748i	$0.573097\pi$
$684$	−7252.78	−0.405434
$685$	−5299.29	−0.295584
$686$	−6818.25	−0.379478
$687$	849.701	0.0471880
$688$	−5060.71	−0.280433
$689$	−7754.04	−0.428745
$690$	6412.20	0.353780
$691$	1412.17	0.0777447	0.0388724	−	0.999244i	$-0.487623\pi$
$691$	1412.17	0.0777447	0.0388724	+	0.999244i	$0.487623\pi$
$692$	16636.1	0.913886
$693$	−716.158	−0.0392563
$694$	−3271.33	−0.178931
$695$	−10003.8	−0.545993
$696$	−7852.92	−0.427678
$697$	−6997.93	−0.380295
$698$	−9148.95	−0.496122
$699$	−12036.9	−0.651325
$700$	−2001.23	−0.108056
$701$	−35997.6	−1.93953	−0.969764	−	0.244045i	$-0.921525\pi$
$701$	−35997.6	−1.93953	−0.969764	+	0.244045i	$0.921525\pi$
$702$	−1510.46	−0.0812088
$703$	49591.8	2.66058
$704$	1678.73	0.0898712
$705$	2746.40	0.146717
$706$	−12167.4	−0.648620
$707$	11042.5	0.587407
$708$	6721.91	0.356815
$709$	10708.7	0.567242	0.283621	−	0.958936i	$-0.408464\pi$
$709$	10708.7	0.567242	0.283621	+	0.958936i	$0.408464\pi$
$710$	−11309.1	−0.597777
$711$	−11222.7	−0.591959
$712$	8605.06	0.452933
$713$	−37217.8	−1.95486
$714$	1129.06	0.0591792
$715$	−3635.05	−0.190130
$716$	−4029.12	−0.210301
$717$	−333.770	−0.0173847
$718$	602.007	0.0312907
$719$	23168.0	1.20170	0.600850	−	0.799362i	$-0.294829\pi$
$719$	23168.0	1.20170	0.600850	+	0.799362i	$0.294829\pi$
$720$	1249.13	0.0646558
$721$	12271.0	0.633836
$722$	−18636.0	−0.960610
$723$	−4361.04	−0.224327
$724$	−8105.77	−0.416089
$725$	−6101.18	−0.312541
$726$	539.936	0.0276018
$727$	−15550.5	−0.793310	−0.396655	−	0.917968i	$-0.629829\pi$
$727$	−15550.5	−0.793310	−0.396655	+	0.917968i	$0.629829\pi$
$728$	5579.64	0.284059
$729$	729.000	0.0370370
$730$	−13449.2	−0.681889
$731$	11205.8	0.566978
$732$	1059.12	0.0534786
$733$	−7997.57	−0.402997	−0.201499	−	0.979489i	$-0.564581\pi$
$733$	−7997.57	−0.402997	−0.201499	+	0.979489i	$0.564581\pi$
$734$	−8906.96	−0.447905
$735$	7661.80	0.384503
$736$	−30674.7	−1.53626
$737$	−6027.21	−0.301242
$738$	−2678.32	−0.133591
$739$	4764.90	0.237185	0.118592	−	0.992943i	$-0.462162\pi$
$739$	4764.90	0.237185	0.118592	+	0.992943i	$0.462162\pi$
$740$	−18111.2	−0.899704
$741$	15710.8	0.778878
$742$	2218.34	0.109755
$743$	−14836.3	−0.732558	−0.366279	−	0.930505i	$-0.619368\pi$
$743$	−14836.3	−0.732558	−0.366279	+	0.930505i	$0.619368\pi$
$744$	14000.8	0.689914
$745$	9343.48	0.459488
$746$	−876.609	−0.0430227
$747$	6376.14	0.312304
$748$	2226.76	0.108848
$749$	−2496.98	−0.121813
$750$	−6775.00	−0.329851
$751$	−18661.5	−0.906750	−0.453375	−	0.891320i	$-0.649780\pi$
$751$	−18661.5	−0.906750	−0.453375	+	0.891320i	$0.649780\pi$
$752$	−1645.84	−0.0798109
$753$	−4485.52	−0.217080
$754$	7140.54	0.344885
$755$	−18743.3	−0.903493
$756$	−1130.40	−0.0543814
$757$	10601.7	0.509017	0.254509	−	0.967070i	$-0.418086\pi$
$757$	10601.7	0.509017	0.254509	+	0.967070i	$0.418086\pi$
$758$	18500.2	0.886487
$759$	−5397.03	−0.258103
$760$	25089.9	1.19751
$761$	25989.1	1.23798	0.618990	−	0.785399i	$-0.287542\pi$
$761$	25989.1	1.23798	0.618990	+	0.785399i	$0.287542\pi$
$762$	−4308.25	−0.204818
$763$	6968.74	0.330649
$764$	−28251.1	−1.33781
$765$	−2765.90	−0.130721
$766$	−344.536	−0.0162514
$767$	−14560.8	−0.685475
$768$	9345.30	0.439088
$769$	8012.59	0.375736	0.187868	−	0.982194i	$-0.439842\pi$
$769$	8012.59	0.375736	0.187868	+	0.982194i	$0.439842\pi$
$770$	1039.95	0.0486715
$771$	−15979.0	−0.746395
$772$	−26310.6	−1.22661
$773$	1524.14	0.0709178	0.0354589	−	0.999371i	$-0.488711\pi$
$773$	1524.14	0.0709178	0.0354589	+	0.999371i	$0.488711\pi$
$774$	4288.79	0.199170
$775$	10877.7	0.504179
$776$	−10785.0	−0.498916
$777$	7729.26	0.356867
$778$	−5372.59	−0.247579
$779$	27858.1	1.28128
$780$	−5737.66	−0.263386
$781$	9518.64	0.436112
$782$	8508.68	0.389092
$783$	−3446.28	−0.157292
$784$	−4591.51	−0.209162
$785$	−18397.3	−0.836470
$786$	2560.13	0.116179
$787$	12452.6	0.564023	0.282011	−	0.959411i	$-0.408998\pi$
$787$	12452.6	0.564023	0.282011	+	0.959411i	$0.408998\pi$
$788$	−11106.3	−0.502090
$789$	−21870.9	−0.986851
$790$	16296.6	0.733935
$791$	3441.70	0.154707
$792$	2030.29	0.0910900
$793$	−2294.24	−0.102738
$794$	−2752.95	−0.123046
$795$	−5434.37	−0.242437
$796$	15117.7	0.673156
$797$	29234.7	1.29931	0.649653	−	0.760231i	$-0.274914\pi$
$797$	29234.7	1.29931	0.649653	+	0.760231i	$0.274914\pi$
$798$	−4494.67	−0.199385
$799$	3644.34	0.161361
$800$	8965.35	0.396216
$801$	3776.36	0.166580
$802$	1944.35	0.0856079
$803$	11320.0	0.497476
$804$	−9513.50	−0.417308
$805$	−10395.0	−0.455124
$806$	−12730.8	−0.556355
$807$	−4486.79	−0.195716
$808$	−31305.3	−1.36302
$809$	−14443.0	−0.627676	−0.313838	−	0.949477i	$-0.601615\pi$
$809$	−14443.0	−0.627676	−0.313838	+	0.949477i	$0.601615\pi$
$810$	−1058.59	−0.0459200
$811$	34366.2	1.48799	0.743996	−	0.668184i	$-0.232928\pi$
$811$	34366.2	1.48799	0.743996	+	0.668184i	$0.232928\pi$
$812$	5343.86	0.230952
$813$	−18010.3	−0.776934
$814$	−5827.36	−0.250920
$815$	27632.2	1.18762
$816$	1657.53	0.0711093
$817$	−44609.1	−1.91025
$818$	−2553.64	−0.109152
$819$	2448.64	0.104472
$820$	−10173.9	−0.433279
$821$	−7998.99	−0.340033	−0.170016	−	0.985441i	$-0.554382\pi$
$821$	−7998.99	−0.340033	−0.170016	+	0.985441i	$0.554382\pi$
$822$	−2691.32	−0.114198
$823$	38546.3	1.63261	0.816305	−	0.577621i	$-0.196019\pi$
$823$	38546.3	1.63261	0.816305	+	0.577621i	$0.196019\pi$
$824$	−34788.0	−1.47075
$825$	1577.40	0.0665672
$826$	4165.68	0.175475
$827$	44842.0	1.88550	0.942750	−	0.333500i	$-0.108230\pi$
$827$	44842.0	1.88550	0.942750	+	0.333500i	$0.108230\pi$
$828$	−8518.81	−0.357547
$829$	−35039.4	−1.46800	−0.733999	−	0.679151i	$-0.762348\pi$
$829$	−35039.4	−1.46800	−0.733999	+	0.679151i	$0.762348\pi$
$830$	−9258.92	−0.387207
$831$	−22186.5	−0.926161
$832$	−5739.79	−0.239172
$833$	10166.8	0.422881
$834$	−5080.58	−0.210942
$835$	27029.9	1.12025
$836$	−8864.51	−0.366729
$837$	6144.32	0.253738
$838$	11820.8	0.487281
$839$	35590.2	1.46450	0.732248	−	0.681038i	$-0.238471\pi$
$839$	35590.2	1.46450	0.732248	+	0.681038i	$0.238471\pi$
$840$	3910.45	0.160623
$841$	−8097.06	−0.331997
$842$	−6215.89	−0.254411
$843$	20853.1	0.851980
$844$	−831.598	−0.0339156
$845$	−6874.89	−0.279886
$846$	1394.80	0.0566835
$847$	−875.304	−0.0355086
$848$	3256.67	0.131880
$849$	−15195.0	−0.614240
$850$	−2486.84	−0.100351
$851$	58248.4	2.34633
$852$	15024.5	0.604142
$853$	5010.01	0.201102	0.100551	−	0.994932i	$-0.467940\pi$
$853$	5010.01	0.201102	0.100551	+	0.994932i	$0.467940\pi$
$854$	656.356	0.0262998
$855$	11010.8	0.440422
$856$	7078.89	0.282654
$857$	−1570.75	−0.0626088	−0.0313044	−	0.999510i	$-0.509966\pi$
$857$	−1570.75	−0.0626088	−0.0313044	+	0.999510i	$0.509966\pi$
$858$	−1846.12	−0.0734561
$859$	27391.7	1.08800	0.544001	−	0.839085i	$-0.316909\pi$
$859$	27391.7	1.08800	0.544001	+	0.839085i	$0.316909\pi$
$860$	16291.5	0.645971
$861$	4341.89	0.171860
$862$	−6290.07	−0.248539
$863$	17950.5	0.708045	0.354023	−	0.935237i	$-0.384814\pi$
$863$	17950.5	0.708045	0.354023	+	0.935237i	$0.384814\pi$
$864$	5064.12	0.199404
$865$	−25256.0	−0.992751
$866$	−4007.22	−0.157241
$867$	11068.8	0.433582
$868$	−9527.50	−0.372563
$869$	−13716.6	−0.535447
$870$	5004.40	0.195017
$871$	20607.9	0.801688
$872$	−19756.2	−0.767236
$873$	−4733.03	−0.183492
$874$	−33872.2	−1.31092
$875$	10983.1	0.424340
$876$	17867.7	0.689150
$877$	−15378.4	−0.592124	−0.296062	−	0.955169i	$-0.595673\pi$
$877$	−15378.4	−0.592124	−0.296062	+	0.955169i	$0.595673\pi$
$878$	10986.6	0.422299
$879$	24713.0	0.948292
$880$	1526.71	0.0584834
$881$	−49564.4	−1.89542	−0.947711	−	0.319131i	$-0.896609\pi$
$881$	−49564.4	−1.89542	−0.947711	+	0.319131i	$0.896609\pi$
$882$	3891.16	0.148551
$883$	−24025.3	−0.915644	−0.457822	−	0.889044i	$-0.651370\pi$
$883$	−24025.3	−0.915644	−0.457822	+	0.889044i	$0.651370\pi$
$884$	−7613.59	−0.289675
$885$	−10204.8	−0.387606
$886$	12501.9	0.474050
$887$	20022.4	0.757931	0.378966	−	0.925411i	$-0.376280\pi$
$887$	20022.4	0.757931	0.378966	+	0.925411i	$0.376280\pi$
$888$	−21912.3	−0.828072
$889$	6984.21	0.263490
$890$	−5483.72	−0.206533
$891$	891.000	0.0335013
$892$	−2826.10	−0.106082
$893$	−14507.8	−0.543655
$894$	4745.23	0.177521
$895$	6116.80	0.228449
$896$	−9212.25	−0.343482
$897$	18453.2	0.686883
$898$	−19541.9	−0.726195
$899$	−29046.7	−1.07760
$900$	2489.80	0.0922150
$901$	−7211.15	−0.266635
$902$	−3273.50	−0.120838
$903$	−6952.67	−0.256224
$904$	−9757.15	−0.358980
$905$	12305.7	0.451996
$906$	−9519.05	−0.349061
$907$	12672.5	0.463930	0.231965	−	0.972724i	$-0.425485\pi$
$907$	12672.5	0.463930	0.231965	+	0.972724i	$0.425485\pi$
$908$	−1255.45	−0.0458851
$909$	−13738.4	−0.501293
$910$	−3555.72	−0.129529
$911$	14781.4	0.537573	0.268786	−	0.963200i	$-0.413377\pi$
$911$	14781.4	0.537573	0.268786	+	0.963200i	$0.413377\pi$
$912$	−6598.47	−0.239580
$913$	7793.07	0.282489
$914$	14117.7	0.510911
$915$	−1607.90	−0.0580936
$916$	1639.23	0.0591285
$917$	−4150.30	−0.149460
$918$	−1404.70	−0.0505034
$919$	−41013.1	−1.47214	−0.736071	−	0.676905i	$-0.763321\pi$
$919$	−41013.1	−1.47214	−0.736071	+	0.676905i	$0.763321\pi$
$920$	29469.5	1.05607
$921$	−17927.3	−0.641395
$922$	8350.67	0.298281
$923$	−32545.5	−1.16062
$924$	−1381.60	−0.0491898
$925$	−17024.3	−0.605143
$926$	−16365.7	−0.580789
$927$	−15266.8	−0.540915
$928$	−23940.1	−0.846846
$929$	17514.9	0.618564	0.309282	−	0.950970i	$-0.399911\pi$
$929$	17514.9	0.618564	0.309282	+	0.950970i	$0.399911\pi$
$930$	−8922.28	−0.314595
$931$	−40473.2	−1.42476
$932$	−23221.4	−0.816138
$933$	−10289.9	−0.361068
$934$	−6303.83	−0.220843
$935$	−3380.55	−0.118241
$936$	−6941.84	−0.242416
$937$	52969.3	1.84678	0.923389	−	0.383865i	$-0.125407\pi$
$937$	52969.3	1.84678	0.923389	+	0.383865i	$0.125407\pi$
$938$	−5895.67	−0.205225
$939$	−30813.9	−1.07090
$940$	5298.32	0.183843
$941$	−18385.6	−0.636933	−0.318467	−	0.947934i	$-0.603168\pi$
$941$	−18385.6	−0.636933	−0.318467	+	0.947934i	$0.603168\pi$
$942$	−9343.36	−0.323167
$943$	32720.9	1.12995
$944$	6115.49	0.210850
$945$	1716.11	0.0590743
$946$	5241.86	0.180156
$947$	27453.5	0.942046	0.471023	−	0.882121i	$-0.343885\pi$
$947$	27453.5	0.942046	0.471023	+	0.882121i	$0.343885\pi$
$948$	−21650.6	−0.741750
$949$	−38704.6	−1.32392
$950$	9899.88	0.338100
$951$	1554.32	0.0529992
$952$	5188.98	0.176655
$953$	11421.2	0.388215	0.194107	−	0.980980i	$-0.437819\pi$
$953$	11421.2	0.388215	0.194107	+	0.980980i	$0.437819\pi$
$954$	−2759.93	−0.0936645
$955$	42889.2	1.45326
$956$	−643.904	−0.0217838
$957$	−4212.12	−0.142276
$958$	−13015.2	−0.438937
$959$	4362.97	0.146911
$960$	−4022.69	−0.135242
$961$	21995.9	0.738340
$962$	19924.5	0.667768
$963$	3106.59	0.103955
$964$	−8413.25	−0.281092
$965$	39943.3	1.33246
$966$	−5279.25	−0.175835
$967$	4633.73	0.154096	0.0770480	−	0.997027i	$-0.475451\pi$
$967$	4633.73	0.154096	0.0770480	+	0.997027i	$0.475451\pi$
$968$	2481.47	0.0823940
$969$	14610.8	0.484382
$970$	6872.92	0.227501
$971$	−45471.0	−1.50282	−0.751408	−	0.659838i	$-0.770625\pi$
$971$	−45471.0	−1.50282	−0.751408	+	0.659838i	$0.770625\pi$
$972$	1406.38	0.0464090
$973$	8236.25	0.271369
$974$	28849.1	0.949062
$975$	−5393.34	−0.177154
$976$	963.574	0.0316017
$977$	−738.060	−0.0241685	−0.0120843	−	0.999927i	$-0.503847\pi$
$977$	−738.060	−0.0241685	−0.0120843	+	0.999927i	$0.503847\pi$
$978$	14033.4	0.458834
$979$	4615.55	0.150678
$980$	14781.0	0.481799
$981$	−8670.08	−0.282176
$982$	−9357.60	−0.304087
$983$	−10688.5	−0.346807	−0.173404	−	0.984851i	$-0.555476\pi$
$983$	−10688.5	−0.346807	−0.173404	+	0.984851i	$0.555476\pi$
$984$	−12309.2	−0.398783
$985$	16861.0	0.545419
$986$	6640.60	0.214483
$987$	−2261.15	−0.0729211
$988$	30309.0	0.975968
$989$	−52396.0	−1.68463
$990$	−1293.84	−0.0415362
$991$	2263.45	0.0725539	0.0362770	−	0.999342i	$-0.488450\pi$
$991$	2263.45	0.0725539	0.0362770	+	0.999342i	$0.488450\pi$
$992$	42682.5	1.36610
$993$	8823.02	0.281964
$994$	9310.90	0.297106
$995$	−22950.8	−0.731247
$996$	12300.8	0.391330
$997$	−43292.7	−1.37522	−0.687610	−	0.726080i	$-0.741340\pi$
$997$	−43292.7	−1.37522	−0.687610	+	0.726080i	$0.741340\pi$
$998$	−6257.28	−0.198468
$999$	−9616.27	−0.304550

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.g.1.14	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.g.1.14	✓	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)

\(f(q)\)	\(=\)	\(q-1.48743 q^{2} -3.00000 q^{3} -5.78756 q^{4} +8.78636 q^{5} +4.46228 q^{6} -7.23392 q^{7} +20.5080 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-1.48743 q^{2} -3.00000 q^{3} -5.78756 q^{4} +8.78636 q^{5} +4.46228 q^{6} -7.23392 q^{7} +20.5080 q^{8} +9.00000 q^{9} -13.0691 q^{10} +11.0000 q^{11} +17.3627 q^{12} -37.6105 q^{13} +10.7599 q^{14} -26.3591 q^{15} +15.7963 q^{16} -34.9772 q^{17} -13.3869 q^{18} +139.241 q^{19} -50.8515 q^{20} +21.7018 q^{21} -16.3617 q^{22} +163.546 q^{23} -61.5240 q^{24} -47.7999 q^{25} +55.9429 q^{26} -27.0000 q^{27} +41.8667 q^{28} +127.640 q^{29} +39.2072 q^{30} -227.567 q^{31} -187.560 q^{32} -33.0000 q^{33} +52.0261 q^{34} -63.5598 q^{35} -52.0880 q^{36} +356.158 q^{37} -207.111 q^{38} +112.831 q^{39} +180.191 q^{40} +200.071 q^{41} -32.2798 q^{42} -320.374 q^{43} -63.6631 q^{44} +79.0772 q^{45} -243.264 q^{46} -104.192 q^{47} -47.3889 q^{48} -290.670 q^{49} +71.0990 q^{50} +104.932 q^{51} +217.673 q^{52} +206.167 q^{53} +40.1606 q^{54} +96.6499 q^{55} -148.353 q^{56} -417.723 q^{57} -189.855 q^{58} +387.147 q^{59} +152.555 q^{60} +61.0000 q^{61} +338.490 q^{62} -65.1053 q^{63} +152.611 q^{64} -330.459 q^{65} +49.0851 q^{66} -547.928 q^{67} +202.433 q^{68} -490.639 q^{69} +94.5406 q^{70} +865.331 q^{71} +184.572 q^{72} +1029.09 q^{73} -529.760 q^{74} +143.400 q^{75} -805.865 q^{76} -79.5731 q^{77} -167.829 q^{78} -1246.96 q^{79} +138.792 q^{80} +81.0000 q^{81} -297.591 q^{82} +708.460 q^{83} -125.600 q^{84} -307.322 q^{85} +476.533 q^{86} -382.920 q^{87} +225.588 q^{88} +419.595 q^{89} -117.622 q^{90} +272.071 q^{91} -946.535 q^{92} +682.702 q^{93} +154.978 q^{94} +1223.42 q^{95} +562.680 q^{96} -525.892 q^{97} +432.351 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 4 q^{2} - 117 q^{3} + 182 q^{4} + 5 q^{5} - 12 q^{6} + 77 q^{7} + 27 q^{8} + 351 q^{9}+O(q^{10}) \) 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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