LMFDB - Embedded newform 6019.2.a.c.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.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:	$48.0619569766$
Analytic rank:	$1$
Dimension:	$108$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.34425 q^{2} -1.25776 q^{3} +3.49550 q^{4} -1.49624 q^{5} +2.94851 q^{6} +5.17811 q^{7} -3.50582 q^{8} -1.41803 q^{9} +O(q^{10})$	\(q-2.34425 q^{2} -1.25776 q^{3} +3.49550 q^{4} -1.49624 q^{5} +2.94851 q^{6} +5.17811 q^{7} -3.50582 q^{8} -1.41803 q^{9} +3.50756 q^{10} -4.47445 q^{11} -4.39651 q^{12} -1.00000 q^{13} -12.1388 q^{14} +1.88192 q^{15} +1.22752 q^{16} -5.45792 q^{17} +3.32421 q^{18} -3.00133 q^{19} -5.23012 q^{20} -6.51284 q^{21} +10.4892 q^{22} +3.61702 q^{23} +4.40950 q^{24} -2.76126 q^{25} +2.34425 q^{26} +5.55684 q^{27} +18.1001 q^{28} +2.72607 q^{29} -4.41169 q^{30} +7.05094 q^{31} +4.13403 q^{32} +5.62780 q^{33} +12.7947 q^{34} -7.74771 q^{35} -4.95672 q^{36} -1.41371 q^{37} +7.03587 q^{38} +1.25776 q^{39} +5.24556 q^{40} +1.70197 q^{41} +15.2677 q^{42} +4.47900 q^{43} -15.6404 q^{44} +2.12172 q^{45} -8.47919 q^{46} -6.03160 q^{47} -1.54393 q^{48} +19.8128 q^{49} +6.47307 q^{50} +6.86477 q^{51} -3.49550 q^{52} -6.03994 q^{53} -13.0266 q^{54} +6.69486 q^{55} -18.1535 q^{56} +3.77497 q^{57} -6.39059 q^{58} +11.6259 q^{59} +6.57825 q^{60} +12.3219 q^{61} -16.5292 q^{62} -7.34271 q^{63} -12.1462 q^{64} +1.49624 q^{65} -13.1930 q^{66} -5.57653 q^{67} -19.0782 q^{68} -4.54936 q^{69} +18.1626 q^{70} +10.6909 q^{71} +4.97136 q^{72} +6.02805 q^{73} +3.31408 q^{74} +3.47301 q^{75} -10.4912 q^{76} -23.1692 q^{77} -2.94851 q^{78} -12.5624 q^{79} -1.83667 q^{80} -2.73510 q^{81} -3.98985 q^{82} -8.52121 q^{83} -22.7656 q^{84} +8.16637 q^{85} -10.4999 q^{86} -3.42876 q^{87} +15.6866 q^{88} -12.6743 q^{89} -4.97383 q^{90} -5.17811 q^{91} +12.6433 q^{92} -8.86842 q^{93} +14.1396 q^{94} +4.49073 q^{95} -5.19964 q^{96} +9.17600 q^{97} -46.4462 q^{98} +6.34490 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9}+O(q^{10}) $ 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9} - q^{10} - 45 q^{11} - 6 q^{12} - 108 q^{13} - 31 q^{14} - 39 q^{15} + 73 q^{16} + 21 q^{17} - 35 q^{18} - 19 q^{19} - 79 q^{20} - 72 q^{21} - 26 q^{23} - 23 q^{24} + 92 q^{25} + 11 q^{26} + 7 q^{27} - 21 q^{28} - 94 q^{29} - 24 q^{30} - 36 q^{31} - 77 q^{32} - 32 q^{33} - 58 q^{34} - 10 q^{35} + 17 q^{36} - 54 q^{37} - 12 q^{38} - q^{39} - 4 q^{40} - 68 q^{41} - 11 q^{42} - 32 q^{43} - 151 q^{44} - 121 q^{45} - 33 q^{46} - 51 q^{47} - 27 q^{48} + 72 q^{49} - 45 q^{50} - 24 q^{51} - 95 q^{52} - 81 q^{53} - 29 q^{54} + 4 q^{55} - 68 q^{56} - 45 q^{57} - 30 q^{58} - 94 q^{59} - 108 q^{60} - 39 q^{61} - 9 q^{62} - 52 q^{63} + 31 q^{64} + 40 q^{65} - 40 q^{66} - 47 q^{67} + 24 q^{68} - 60 q^{69} - 66 q^{70} - 86 q^{71} - 91 q^{72} - 51 q^{73} - 110 q^{74} - 7 q^{75} - 51 q^{76} - 96 q^{77} + 10 q^{78} - 18 q^{79} - 136 q^{80} - 24 q^{81} - 33 q^{82} - 77 q^{83} - 113 q^{84} - 95 q^{85} - 137 q^{86} + 23 q^{87} + 19 q^{88} - 112 q^{89} - 19 q^{90} + 8 q^{91} - 111 q^{92} - 124 q^{93} - 20 q^{94} - 73 q^{95} - 77 q^{96} - 41 q^{97} - 80 q^{98} - 154 q^{99}+O(q^{100}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9 - q^10 - 45 * q^11 - 6 * q^12 - 108 * q^13 - 31 * q^14 - 39 * q^15 + 73 * q^16 + 21 * q^17 - 35 * q^18 - 19 * q^19 - 79 * q^20 - 72 * q^21 - 26 * q^23 - 23 * q^24 + 92 * q^25 + 11 * q^26 + 7 * q^27 - 21 * q^28 - 94 * q^29 - 24 * q^30 - 36 * q^31 - 77 * q^32 - 32 * q^33 - 58 * q^34 - 10 * q^35 + 17 * q^36 - 54 * q^37 - 12 * q^38 - q^39 - 4 * q^40 - 68 * q^41 - 11 * q^42 - 32 * q^43 - 151 * q^44 - 121 * q^45 - 33 * q^46 - 51 * q^47 - 27 * q^48 + 72 * q^49 - 45 * q^50 - 24 * q^51 - 95 * q^52 - 81 * q^53 - 29 * q^54 + 4 * q^55 - 68 * q^56 - 45 * q^57 - 30 * q^58 - 94 * q^59 - 108 * q^60 - 39 * q^61 - 9 * q^62 - 52 * q^63 + 31 * q^64 + 40 * q^65 - 40 * q^66 - 47 * q^67 + 24 * q^68 - 60 * q^69 - 66 * q^70 - 86 * q^71 - 91 * q^72 - 51 * q^73 - 110 * q^74 - 7 * q^75 - 51 * q^76 - 96 * q^77 + 10 * q^78 - 18 * q^79 - 136 * q^80 - 24 * q^81 - 33 * q^82 - 77 * q^83 - 113 * q^84 - 95 * q^85 - 137 * q^86 + 23 * q^87 + 19 * q^88 - 112 * q^89 - 19 * q^90 + 8 * q^91 - 111 * q^92 - 124 * q^93 - 20 * q^94 - 73 * q^95 - 77 * q^96 - 41 * q^97 - 80 * q^98 - 154 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.34425	−1.65763	−0.828817	−	0.559520i	$-0.810986\pi$
$2$	−2.34425	−1.65763	−0.828817	+	0.559520i	$0.810986\pi$
$3$	−1.25776	−0.726170	−0.363085	−	0.931756i	$-0.618277\pi$
$3$	−1.25776	−0.726170	−0.363085	+	0.931756i	$0.618277\pi$
$4$	3.49550	1.74775
$5$	−1.49624	−0.669140	−0.334570	−	0.942371i	$-0.608591\pi$
$5$	−1.49624	−0.669140	−0.334570	+	0.942371i	$0.608591\pi$
$6$	2.94851	1.20372
$7$	5.17811	1.95714	0.978571	−	0.205911i	$-0.0660158\pi$
$7$	5.17811	1.95714	0.978571	+	0.205911i	$0.0660158\pi$
$8$	−3.50582	−1.23950
$9$	−1.41803	−0.472677
$10$	3.50756	1.10919
$11$	−4.47445	−1.34910	−0.674549	−	0.738231i	$-0.735662\pi$
$11$	−4.47445	−1.34910	−0.674549	+	0.738231i	$0.735662\pi$
$12$	−4.39651	−1.26916
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−12.1388	−3.24422
$15$	1.88192	0.485910
$16$	1.22752	0.306880
$17$	−5.45792	−1.32374	−0.661870	−	0.749619i	$-0.730237\pi$
$17$	−5.45792	−1.32374	−0.661870	+	0.749619i	$0.730237\pi$
$18$	3.32421	0.783525
$19$	−3.00133	−0.688553	−0.344277	−	0.938868i	$-0.611876\pi$
$19$	−3.00133	−0.688553	−0.344277	+	0.938868i	$0.611876\pi$
$20$	−5.23012	−1.16949
$21$	−6.51284	−1.42122
$22$	10.4892	2.23631
$23$	3.61702	0.754201	0.377100	−	0.926172i	$-0.376921\pi$
$23$	3.61702	0.754201	0.377100	+	0.926172i	$0.376921\pi$
$24$	4.40950	0.900085
$25$	−2.76126	−0.552252
$26$	2.34425	0.459745
$27$	5.55684	1.06941
$28$	18.1001	3.42059
$29$	2.72607	0.506219	0.253110	−	0.967438i	$-0.418547\pi$
$29$	2.72607	0.506219	0.253110	+	0.967438i	$0.418547\pi$
$30$	−4.41169	−0.805460
$31$	7.05094	1.26639	0.633193	−	0.773994i	$-0.281744\pi$
$31$	7.05094	1.26639	0.633193	+	0.773994i	$0.281744\pi$
$32$	4.13403	0.730801
$33$	5.62780	0.979674
$34$	12.7947	2.19428
$35$	−7.74771	−1.30960
$36$	−4.95672	−0.826121
$37$	−1.41371	−0.232412	−0.116206	−	0.993225i	$-0.537073\pi$
$37$	−1.41371	−0.232412	−0.116206	+	0.993225i	$0.537073\pi$
$38$	7.03587	1.14137
$39$	1.25776	0.201403
$40$	5.24556	0.829396
$41$	1.70197	0.265803	0.132902	−	0.991129i	$-0.457571\pi$
$41$	1.70197	0.265803	0.132902	+	0.991129i	$0.457571\pi$
$42$	15.2677	2.35586
$43$	4.47900	0.683041	0.341520	−	0.939874i	$-0.389058\pi$
$43$	4.47900	0.683041	0.341520	+	0.939874i	$0.389058\pi$
$44$	−15.6404	−2.35788
$45$	2.12172	0.316287
$46$	−8.47919	−1.25019
$47$	−6.03160	−0.879799	−0.439899	−	0.898047i	$-0.644986\pi$
$47$	−6.03160	−0.879799	−0.439899	+	0.898047i	$0.644986\pi$
$48$	−1.54393	−0.222847
$49$	19.8128	2.83040
$50$	6.47307	0.915431
$51$	6.86477	0.961261
$52$	−3.49550	−0.484739
$53$	−6.03994	−0.829650	−0.414825	−	0.909901i	$-0.636157\pi$
$53$	−6.03994	−0.829650	−0.414825	+	0.909901i	$0.636157\pi$
$54$	−13.0266	−1.77270
$55$	6.69486	0.902735
$56$	−18.1535	−2.42587
$57$	3.77497	0.500007
$58$	−6.39059	−0.839126
$59$	11.6259	1.51356	0.756779	−	0.653671i	$-0.226772\pi$
$59$	11.6259	1.51356	0.756779	+	0.653671i	$0.226772\pi$
$60$	6.57825	0.849249
$61$	12.3219	1.57765	0.788827	−	0.614616i	$-0.210689\pi$
$61$	12.3219	1.57765	0.788827	+	0.614616i	$0.210689\pi$
$62$	−16.5292	−2.09920
$63$	−7.34271	−0.925095
$64$	−12.1462	−1.51828
$65$	1.49624	0.185586
$66$	−13.1930	−1.62394
$67$	−5.57653	−0.681281	−0.340641	−	0.940194i	$-0.610644\pi$
$67$	−5.57653	−0.681281	−0.340641	+	0.940194i	$0.610644\pi$
$68$	−19.0782	−2.31357
$69$	−4.54936	−0.547678
$70$	18.1626	2.17084
$71$	10.6909	1.26878	0.634390	−	0.773013i	$-0.281251\pi$
$71$	10.6909	1.26878	0.634390	+	0.773013i	$0.281251\pi$
$72$	4.97136	0.585881
$73$	6.02805	0.705530	0.352765	−	0.935712i	$-0.385241\pi$
$73$	6.02805	0.705530	0.352765	+	0.935712i	$0.385241\pi$
$74$	3.31408	0.385254
$75$	3.47301	0.401029
$76$	−10.4912	−1.20342
$77$	−23.1692	−2.64037
$78$	−2.94851	−0.333853
$79$	−12.5624	−1.41338	−0.706689	−	0.707525i	$-0.749812\pi$
$79$	−12.5624	−1.41338	−0.706689	+	0.707525i	$0.749812\pi$
$80$	−1.83667	−0.205346
$81$	−2.73510	−0.303900
$82$	−3.98985	−0.440605
$83$	−8.52121	−0.935325	−0.467662	−	0.883907i	$-0.654904\pi$
$83$	−8.52121	−0.935325	−0.467662	+	0.883907i	$0.654904\pi$
$84$	−22.7656	−2.48393
$85$	8.16637	0.885767
$86$	−10.4999	−1.13223
$87$	−3.42876	−0.367601
$88$	15.6866	1.67220
$89$	−12.6743	−1.34347	−0.671735	−	0.740792i	$-0.734451\pi$
$89$	−12.6743	−1.34347	−0.671735	+	0.740792i	$0.734451\pi$
$90$	−4.97383	−0.524288
$91$	−5.17811	−0.542813
$92$	12.6433	1.31815
$93$	−8.86842	−0.919612
$94$	14.1396	1.45838
$95$	4.49073	0.460739
$96$	−5.19964	−0.530686
$97$	9.17600	0.931682	0.465841	−	0.884868i	$-0.345752\pi$
$97$	9.17600	0.931682	0.465841	+	0.884868i	$0.345752\pi$
$98$	−46.4462	−4.69177
$99$	6.34490	0.637687
$100$	−9.65198	−0.965198
$101$	−1.98041	−0.197058	−0.0985291	−	0.995134i	$-0.531414\pi$
$101$	−1.98041	−0.197058	−0.0985291	+	0.995134i	$0.531414\pi$
$102$	−16.0927	−1.59342
$103$	−0.854809	−0.0842269	−0.0421134	−	0.999113i	$-0.513409\pi$
$103$	−0.854809	−0.0842269	−0.0421134	+	0.999113i	$0.513409\pi$
$104$	3.50582	0.343774
$105$	9.74479	0.950994
$106$	14.1591	1.37526
$107$	−2.14887	−0.207739	−0.103870	−	0.994591i	$-0.533122\pi$
$107$	−2.14887	−0.207739	−0.103870	+	0.994591i	$0.533122\pi$
$108$	19.4239	1.86907
$109$	−2.03410	−0.194831	−0.0974156	−	0.995244i	$-0.531058\pi$
$109$	−2.03410	−0.194831	−0.0974156	+	0.995244i	$0.531058\pi$
$110$	−15.6944	−1.49640
$111$	1.77811	0.168771
$112$	6.35624	0.600608
$113$	6.47458	0.609077	0.304538	−	0.952500i	$-0.401498\pi$
$113$	6.47458	0.609077	0.304538	+	0.952500i	$0.401498\pi$
$114$	−8.84947	−0.828829
$115$	−5.41194	−0.504666
$116$	9.52899	0.884744
$117$	1.41803	0.131097
$118$	−27.2539	−2.50892
$119$	−28.2617	−2.59075
$120$	−6.59768	−0.602283
$121$	9.02069	0.820063
$122$	−28.8855	−2.61517
$123$	−2.14068	−0.193019
$124$	24.6466	2.21333
$125$	11.6127	1.03867
$126$	17.2131	1.53347
$127$	−4.75904	−0.422296	−0.211148	−	0.977454i	$-0.567720\pi$
$127$	−4.75904	−0.422296	−0.211148	+	0.977454i	$0.567720\pi$
$128$	20.2057	1.78595
$129$	−5.63352	−0.496004
$130$	−3.50756	−0.307634
$131$	−6.29523	−0.550017	−0.275008	−	0.961442i	$-0.588681\pi$
$131$	−6.29523	−0.550017	−0.275008	+	0.961442i	$0.588681\pi$
$132$	19.6720	1.71223
$133$	−15.5412	−1.34760
$134$	13.0728	1.12932
$135$	−8.31438	−0.715588
$136$	19.1345	1.64077
$137$	11.9633	1.02209	0.511045	−	0.859554i	$-0.329259\pi$
$137$	11.9633	1.02209	0.511045	+	0.859554i	$0.329259\pi$
$138$	10.6648	0.907850
$139$	10.7427	0.911187	0.455593	−	0.890188i	$-0.349427\pi$
$139$	10.7427	0.911187	0.455593	+	0.890188i	$0.349427\pi$
$140$	−27.0821	−2.28886
$141$	7.58633	0.638884
$142$	−25.0622	−2.10317
$143$	4.47445	0.374172
$144$	−1.74066	−0.145055
$145$	−4.07887	−0.338731
$146$	−14.1313	−1.16951
$147$	−24.9198	−2.05535
$148$	−4.94162	−0.406199
$149$	13.1390	1.07639	0.538194	−	0.842821i	$-0.319107\pi$
$149$	13.1390	1.07639	0.538194	+	0.842821i	$0.319107\pi$
$150$	−8.14160	−0.664759
$151$	−7.92367	−0.644819	−0.322409	−	0.946600i	$-0.604493\pi$
$151$	−7.92367	−0.644819	−0.322409	+	0.946600i	$0.604493\pi$
$152$	10.5221	0.853459
$153$	7.73949	0.625701
$154$	54.3143	4.37677
$155$	−10.5499	−0.847390
$156$	4.39651	0.352003
$157$	8.43014	0.672799	0.336399	−	0.941719i	$-0.390791\pi$
$157$	8.43014	0.672799	0.336399	+	0.941719i	$0.390791\pi$
$158$	29.4493	2.34286
$159$	7.59682	0.602467
$160$	−6.18552	−0.489008
$161$	18.7293	1.47608
$162$	6.41176	0.503755
$163$	−10.6079	−0.830877	−0.415438	−	0.909621i	$-0.636372\pi$
$163$	−10.6079	−0.830877	−0.415438	+	0.909621i	$0.636372\pi$
$164$	5.94924	0.464558
$165$	−8.42055	−0.655539
$166$	19.9758	1.55043
$167$	6.80047	0.526236	0.263118	−	0.964764i	$-0.415249\pi$
$167$	6.80047	0.526236	0.263118	+	0.964764i	$0.415249\pi$
$168$	22.8329	1.76159
$169$	1.00000	0.0769231
$170$	−19.1440	−1.46828
$171$	4.25598	0.325463
$172$	15.6563	1.19378
$173$	−18.7285	−1.42390	−0.711952	−	0.702228i	$-0.752189\pi$
$173$	−18.7285	−1.42390	−0.711952	+	0.702228i	$0.752189\pi$
$174$	8.03786	0.609348
$175$	−14.2981	−1.08083
$176$	−5.49248	−0.414011
$177$	−14.6226	−1.09910
$178$	29.7116	2.22698
$179$	−3.77954	−0.282496	−0.141248	−	0.989974i	$-0.545112\pi$
$179$	−3.77954	−0.282496	−0.141248	+	0.989974i	$0.545112\pi$
$180$	7.41646	0.552790
$181$	−13.3727	−0.993985	−0.496993	−	0.867755i	$-0.665562\pi$
$181$	−13.3727	−0.993985	−0.496993	+	0.867755i	$0.665562\pi$
$182$	12.1388	0.899786
$183$	−15.4980	−1.14565
$184$	−12.6806	−0.934828
$185$	2.11525	0.155516
$186$	20.7898	1.52438
$187$	24.4212	1.78585
$188$	−21.0834	−1.53767
$189$	28.7739	2.09299
$190$	−10.5274	−0.763736
$191$	−7.91727	−0.572873	−0.286437	−	0.958099i	$-0.592471\pi$
$191$	−7.91727	−0.572873	−0.286437	+	0.958099i	$0.592471\pi$
$192$	15.2771	1.10253
$193$	22.2458	1.60128	0.800642	−	0.599143i	$-0.204492\pi$
$193$	22.2458	1.60128	0.800642	+	0.599143i	$0.204492\pi$
$194$	−21.5108	−1.54439
$195$	−1.88192	−0.134767
$196$	69.2557	4.94684
$197$	−0.758436	−0.0540364	−0.0270182	−	0.999635i	$-0.508601\pi$
$197$	−0.758436	−0.0540364	−0.0270182	+	0.999635i	$0.508601\pi$
$198$	−14.8740	−1.05705
$199$	−9.48874	−0.672639	−0.336319	−	0.941748i	$-0.609182\pi$
$199$	−9.48874	−0.672639	−0.336319	+	0.941748i	$0.609182\pi$
$200$	9.68048	0.684514
$201$	7.01396	0.494726
$202$	4.64257	0.326650
$203$	14.1159	0.990742
$204$	23.9958	1.68004
$205$	−2.54656	−0.177860
$206$	2.00389	0.139617
$207$	−5.12904	−0.356493
$208$	−1.22752	−0.0851132
$209$	13.4293	0.928925
$210$	−22.8442	−1.57640
$211$	20.6423	1.42107	0.710536	−	0.703661i	$-0.248452\pi$
$211$	20.6423	1.42107	0.710536	+	0.703661i	$0.248452\pi$
$212$	−21.1126	−1.45002
$213$	−13.4467	−0.921351
$214$	5.03749	0.344355
$215$	−6.70167	−0.457050
$216$	−19.4813	−1.32553
$217$	36.5105	2.47850
$218$	4.76843	0.322959
$219$	−7.58187	−0.512335
$220$	23.4019	1.57775
$221$	5.45792	0.367139
$222$	−4.16833	−0.279760
$223$	−6.11156	−0.409260	−0.204630	−	0.978839i	$-0.565599\pi$
$223$	−6.11156	−0.409260	−0.204630	+	0.978839i	$0.565599\pi$
$224$	21.4065	1.43028
$225$	3.91555	0.261036
$226$	−15.1780	−1.00963
$227$	−20.2571	−1.34451	−0.672257	−	0.740318i	$-0.734675\pi$
$227$	−20.2571	−1.34451	−0.672257	+	0.740318i	$0.734675\pi$
$228$	13.1954	0.873887
$229$	−15.5043	−1.02455	−0.512275	−	0.858821i	$-0.671197\pi$
$229$	−15.5043	−1.02455	−0.512275	+	0.858821i	$0.671197\pi$
$230$	12.6869	0.836551
$231$	29.1414	1.91736
$232$	−9.55713	−0.627456
$233$	8.37344	0.548562	0.274281	−	0.961650i	$-0.411560\pi$
$233$	8.37344	0.548562	0.274281	+	0.961650i	$0.411560\pi$
$234$	−3.32421	−0.217311
$235$	9.02473	0.588709
$236$	40.6382	2.64532
$237$	15.8005	1.02635
$238$	66.2525	4.29451
$239$	4.87935	0.315619	0.157810	−	0.987470i	$-0.449557\pi$
$239$	4.87935	0.315619	0.157810	+	0.987470i	$0.449557\pi$
$240$	2.31010	0.149116
$241$	−1.21542	−0.0782918	−0.0391459	−	0.999234i	$-0.512464\pi$
$241$	−1.21542	−0.0782918	−0.0391459	+	0.999234i	$0.512464\pi$
$242$	−21.1467	−1.35936
$243$	−13.2304	−0.848731
$244$	43.0711	2.75734
$245$	−29.6448	−1.89394
$246$	5.01828	0.319954
$247$	3.00133	0.190970
$248$	−24.7193	−1.56968
$249$	10.7177	0.679205
$250$	−27.2231	−1.72174
$251$	−18.0708	−1.14062	−0.570308	−	0.821431i	$-0.693176\pi$
$251$	−18.0708	−1.14062	−0.570308	+	0.821431i	$0.693176\pi$
$252$	−25.6665	−1.61683
$253$	−16.1842	−1.01749
$254$	11.1564	0.700013
$255$	−10.2714	−0.643218
$256$	−23.0748	−1.44217
$257$	−1.37292	−0.0856405	−0.0428203	−	0.999083i	$-0.513634\pi$
$257$	−1.37292	−0.0856405	−0.0428203	+	0.999083i	$0.513634\pi$
$258$	13.2064	0.822193
$259$	−7.32034	−0.454864
$260$	5.23012	0.324358
$261$	−3.86565	−0.239278
$262$	14.7576	0.911727
$263$	7.53096	0.464379	0.232189	−	0.972671i	$-0.425411\pi$
$263$	7.53096	0.464379	0.232189	+	0.972671i	$0.425411\pi$
$264$	−19.7301	−1.21430
$265$	9.03722	0.555152
$266$	36.4325	2.23382
$267$	15.9412	0.975588
$268$	−19.4928	−1.19071
$269$	−15.3063	−0.933244	−0.466622	−	0.884457i	$-0.654529\pi$
$269$	−15.3063	−0.933244	−0.466622	+	0.884457i	$0.654529\pi$
$270$	19.4910	1.18618
$271$	10.0882	0.612817	0.306409	−	0.951900i	$-0.400873\pi$
$271$	10.0882	0.612817	0.306409	+	0.951900i	$0.400873\pi$
$272$	−6.69971	−0.406230
$273$	6.51284	0.394175
$274$	−28.0448	−1.69425
$275$	12.3551	0.745041
$276$	−15.9023	−0.957204
$277$	2.78531	0.167353	0.0836766	−	0.996493i	$-0.473334\pi$
$277$	2.78531	0.167353	0.0836766	+	0.996493i	$0.473334\pi$
$278$	−25.1836	−1.51041
$279$	−9.99844	−0.598591
$280$	27.1621	1.62325
$281$	−23.3741	−1.39438	−0.697191	−	0.716886i	$-0.745567\pi$
$281$	−23.3741	−1.39438	−0.697191	+	0.716886i	$0.745567\pi$
$282$	−17.7842	−1.05904
$283$	−7.64565	−0.454486	−0.227243	−	0.973838i	$-0.572971\pi$
$283$	−7.64565	−0.454486	−0.227243	+	0.973838i	$0.572971\pi$
$284$	37.3702	2.21751
$285$	−5.64827	−0.334575
$286$	−10.4892	−0.620240
$287$	8.81300	0.520215
$288$	−5.86218	−0.345432
$289$	12.7889	0.752287
$290$	9.56188	0.561493
$291$	−11.5412	−0.676560
$292$	21.0711	1.23309
$293$	−16.3217	−0.953526	−0.476763	−	0.879032i	$-0.658190\pi$
$293$	−16.3217	−0.953526	−0.476763	+	0.879032i	$0.658190\pi$
$294$	58.4183	3.40703
$295$	−17.3951	−1.01278
$296$	4.95621	0.288074
$297$	−24.8638	−1.44274
$298$	−30.8010	−1.78426
$299$	−3.61702	−0.209178
$300$	12.1399	0.700898
$301$	23.1927	1.33681
$302$	18.5750	1.06887
$303$	2.49089	0.143098
$304$	−3.68420	−0.211303
$305$	−18.4365	−1.05567
$306$	−18.1433	−1.03718
$307$	−13.0107	−0.742558	−0.371279	−	0.928521i	$-0.621081\pi$
$307$	−13.0107	−0.742558	−0.371279	+	0.928521i	$0.621081\pi$
$308$	−80.9879	−4.61471
$309$	1.07515	0.0611631
$310$	24.7316	1.40466
$311$	30.6153	1.73603	0.868017	−	0.496534i	$-0.165394\pi$
$311$	30.6153	1.73603	0.868017	+	0.496534i	$0.165394\pi$
$312$	−4.40950	−0.249639
$313$	11.6735	0.659825	0.329912	−	0.944012i	$-0.392981\pi$
$313$	11.6735	0.659825	0.329912	+	0.944012i	$0.392981\pi$
$314$	−19.7623	−1.11525
$315$	10.9865	0.619018
$316$	−43.9118	−2.47023
$317$	1.17065	0.0657500	0.0328750	−	0.999459i	$-0.489534\pi$
$317$	1.17065	0.0657500	0.0328750	+	0.999459i	$0.489534\pi$
$318$	−17.8088	−0.998670
$319$	−12.1977	−0.682939
$320$	18.1737	1.01594
$321$	2.70277	0.150854
$322$	−43.9062	−2.44680
$323$	16.3810	0.911466
$324$	−9.56055	−0.531141
$325$	2.76126	0.153167
$326$	24.8676	1.37729
$327$	2.55842	0.141481
$328$	−5.96682	−0.329462
$329$	−31.2323	−1.72189
$330$	19.7399	1.08664
$331$	−10.1935	−0.560286	−0.280143	−	0.959958i	$-0.590382\pi$
$331$	−10.1935	−0.560286	−0.280143	+	0.959958i	$0.590382\pi$
$332$	−29.7859	−1.63471
$333$	2.00468	0.109856
$334$	−15.9420	−0.872307
$335$	8.34384	0.455873
$336$	−7.99464	−0.436144
$337$	13.4903	0.734861	0.367431	−	0.930051i	$-0.380238\pi$
$337$	13.4903	0.734861	0.367431	+	0.930051i	$0.380238\pi$
$338$	−2.34425	−0.127510
$339$	−8.14349	−0.442294
$340$	28.5456	1.54810
$341$	−31.5491	−1.70848
$342$	−9.97708	−0.539499
$343$	66.3462	3.58236
$344$	−15.7026	−0.846626
$345$	6.80694	0.366473
$346$	43.9043	2.36031
$347$	−11.4593	−0.615166	−0.307583	−	0.951521i	$-0.599520\pi$
$347$	−11.4593	−0.615166	−0.307583	+	0.951521i	$0.599520\pi$
$348$	−11.9852	−0.642475
$349$	14.1602	0.757977	0.378989	−	0.925401i	$-0.376272\pi$
$349$	14.1602	0.757977	0.378989	+	0.925401i	$0.376272\pi$
$350$	33.5183	1.79163
$351$	−5.55684	−0.296602
$352$	−18.4975	−0.985921
$353$	−31.4633	−1.67462	−0.837310	−	0.546728i	$-0.815873\pi$
$353$	−31.4633	−1.67462	−0.837310	+	0.546728i	$0.815873\pi$
$354$	34.2790	1.82191
$355$	−15.9962	−0.848992
$356$	−44.3029	−2.34805
$357$	35.5466	1.88132
$358$	8.86018	0.468275
$359$	−1.11037	−0.0586030	−0.0293015	−	0.999571i	$-0.509328\pi$
$359$	−1.11037	−0.0586030	−0.0293015	+	0.999571i	$0.509328\pi$
$360$	−7.43836	−0.392036
$361$	−9.99199	−0.525894
$362$	31.3489	1.64766
$363$	−11.3459	−0.595505
$364$	−18.1001	−0.948702
$365$	−9.01943	−0.472099
$366$	36.3312	1.89906
$367$	−5.93757	−0.309939	−0.154969	−	0.987919i	$-0.549528\pi$
$367$	−5.93757	−0.309939	−0.154969	+	0.987919i	$0.549528\pi$
$368$	4.43997	0.231449
$369$	−2.41345	−0.125639
$370$	−4.95867	−0.257789
$371$	−31.2755	−1.62374
$372$	−30.9996	−1.60725
$373$	11.6189	0.601602	0.300801	−	0.953687i	$-0.402746\pi$
$373$	11.6189	0.601602	0.300801	+	0.953687i	$0.402746\pi$
$374$	−57.2493	−2.96029
$375$	−14.6061	−0.754254
$376$	21.1457	1.09051
$377$	−2.72607	−0.140400
$378$	−67.4532	−3.46942
$379$	−33.9626	−1.74454	−0.872270	−	0.489024i	$-0.837353\pi$
$379$	−33.9626	−1.74454	−0.872270	+	0.489024i	$0.837353\pi$
$380$	15.6973	0.805256
$381$	5.98575	0.306659
$382$	18.5600	0.949614
$383$	−10.1446	−0.518367	−0.259184	−	0.965828i	$-0.583453\pi$
$383$	−10.1446	−0.518367	−0.259184	+	0.965828i	$0.583453\pi$
$384$	−25.4141	−1.29691
$385$	34.6667	1.76678
$386$	−52.1496	−2.65434
$387$	−6.35135	−0.322857
$388$	32.0747	1.62835
$389$	−24.8521	−1.26005	−0.630027	−	0.776573i	$-0.716956\pi$
$389$	−24.8521	−1.26005	−0.630027	+	0.776573i	$0.716956\pi$
$390$	4.41169	0.223394
$391$	−19.7414	−0.998365
$392$	−69.4602	−3.50827
$393$	7.91791	0.399406
$394$	1.77796	0.0895725
$395$	18.7964	0.945747
$396$	22.1786	1.11452
$397$	20.3186	1.01976	0.509882	−	0.860245i	$-0.329689\pi$
$397$	20.3186	1.01976	0.509882	+	0.860245i	$0.329689\pi$
$398$	22.2440	1.11499
$399$	19.5472	0.978585
$400$	−3.38950	−0.169475
$401$	−29.8307	−1.48968	−0.744838	−	0.667245i	$-0.767473\pi$
$401$	−29.8307	−1.48968	−0.744838	+	0.667245i	$0.767473\pi$
$402$	−16.4425	−0.820075
$403$	−7.05094	−0.351232
$404$	−6.92252	−0.344408
$405$	4.09238	0.203352
$406$	−33.0912	−1.64229
$407$	6.32557	0.313547
$408$	−24.0667	−1.19148
$409$	−34.3153	−1.69678	−0.848391	−	0.529370i	$-0.822428\pi$
$409$	−34.3153	−1.69678	−0.848391	+	0.529370i	$0.822428\pi$
$410$	5.96978	0.294826
$411$	−15.0469	−0.742211
$412$	−2.98799	−0.147208
$413$	60.2000	2.96225
$414$	12.0237	0.590935
$415$	12.7498	0.625863
$416$	−4.13403	−0.202688
$417$	−13.5118	−0.661677
$418$	−31.4817	−1.53982
$419$	−8.68179	−0.424133	−0.212067	−	0.977255i	$-0.568019\pi$
$419$	−8.68179	−0.424133	−0.212067	+	0.977255i	$0.568019\pi$
$420$	34.0629	1.66210
$421$	23.1844	1.12994	0.564970	−	0.825111i	$-0.308888\pi$
$421$	23.1844	1.12994	0.564970	+	0.825111i	$0.308888\pi$
$422$	−48.3906	−2.35562
$423$	8.55299	0.415860
$424$	21.1750	1.02835
$425$	15.0707	0.731037
$426$	31.5223	1.52726
$427$	63.8040	3.08769
$428$	−7.51138	−0.363076
$429$	−5.62780	−0.271713
$430$	15.7104	0.757621
$431$	−26.2127	−1.26262	−0.631311	−	0.775530i	$-0.717483\pi$
$431$	−26.2127	−1.26262	−0.631311	+	0.775530i	$0.717483\pi$
$432$	6.82113	0.328182
$433$	25.0046	1.20164	0.600822	−	0.799383i	$-0.294840\pi$
$433$	25.0046	1.20164	0.600822	+	0.799383i	$0.294840\pi$
$434$	−85.5898	−4.10844
$435$	5.13025	0.245977
$436$	−7.11019	−0.340516
$437$	−10.8559	−0.519307
$438$	17.7738	0.849264
$439$	26.3766	1.25888	0.629442	−	0.777047i	$-0.283283\pi$
$439$	26.3766	1.25888	0.629442	+	0.777047i	$0.283283\pi$
$440$	−23.4710	−1.11894
$441$	−28.0952	−1.33787
$442$	−12.7947	−0.608583
$443$	41.8703	1.98932	0.994660	−	0.103208i	$-0.0329107\pi$
$443$	41.8703	1.98932	0.994660	+	0.103208i	$0.0329107\pi$
$444$	6.21539	0.294969
$445$	18.9638	0.898970
$446$	14.3270	0.678404
$447$	−16.5257	−0.781640
$448$	−62.8946	−2.97149
$449$	25.6694	1.21141	0.605707	−	0.795688i	$-0.292890\pi$
$449$	25.6694	1.21141	0.605707	+	0.795688i	$0.292890\pi$
$450$	−9.17901	−0.432703
$451$	−7.61539	−0.358595
$452$	22.6319	1.06451
$453$	9.96610	0.468248
$454$	47.4878	2.22871
$455$	7.74771	0.363218
$456$	−13.2344	−0.619757
$457$	−35.1854	−1.64590	−0.822952	−	0.568111i	$-0.807674\pi$
$457$	−35.1854	−1.64590	−0.822952	+	0.568111i	$0.807674\pi$
$458$	36.3458	1.69833
$459$	−30.3288	−1.41563
$460$	−18.9174	−0.882030
$461$	−4.98291	−0.232077	−0.116039	−	0.993245i	$-0.537020\pi$
$461$	−4.98291	−0.232077	−0.116039	+	0.993245i	$0.537020\pi$
$462$	−68.3146	−3.17828
$463$	−1.00000	−0.0464739
$463$	−1.00000	−0.0464739
$464$	3.34631	0.155349
$465$	13.2693	0.615349
$466$	−19.6294	−0.909316
$467$	−7.17397	−0.331972	−0.165986	−	0.986128i	$-0.553081\pi$
$467$	−7.17397	−0.331972	−0.165986	+	0.986128i	$0.553081\pi$
$468$	4.95672	0.229125
$469$	−28.8759	−1.33336
$470$	−21.1562	−0.975863
$471$	−10.6031	−0.488566
$472$	−40.7582	−1.87605
$473$	−20.0410	−0.921488
$474$	−37.0403	−1.70132
$475$	8.28746	0.380255
$476$	−98.7888	−4.52798
$477$	8.56482	0.392156
$478$	−11.4384	−0.523181
$479$	24.7935	1.13284	0.566421	−	0.824116i	$-0.308327\pi$
$479$	24.7935	1.13284	0.566421	+	0.824116i	$0.308327\pi$
$480$	7.77992	0.355103
$481$	1.41371	0.0644596
$482$	2.84924	0.129779
$483$	−23.5571	−1.07188
$484$	31.5318	1.43326
$485$	−13.7295	−0.623426
$486$	31.0154	1.40688
$487$	−24.6076	−1.11508	−0.557538	−	0.830151i	$-0.688254\pi$
$487$	−24.6076	−1.11508	−0.557538	+	0.830151i	$0.688254\pi$
$488$	−43.1983	−1.95549
$489$	13.3423	0.603358
$490$	69.4947	3.13945
$491$	29.5530	1.33371	0.666855	−	0.745188i	$-0.267640\pi$
$491$	29.5530	1.33371	0.666855	+	0.745188i	$0.267640\pi$
$492$	−7.48275	−0.337348
$493$	−14.8787	−0.670102
$494$	−7.03587	−0.316559
$495$	−9.49351	−0.426702
$496$	8.65517	0.388629
$497$	55.3588	2.48318
$498$	−25.1249	−1.12587
$499$	8.31014	0.372013	0.186006	−	0.982549i	$-0.440445\pi$
$499$	8.31014	0.372013	0.186006	+	0.982549i	$0.440445\pi$
$500$	40.5923	1.81534
$501$	−8.55338	−0.382137
$502$	42.3624	1.89073
$503$	0.291253	0.0129863	0.00649316	−	0.999979i	$-0.497933\pi$
$503$	0.291253	0.0129863	0.00649316	+	0.999979i	$0.497933\pi$
$504$	25.7423	1.14665
$505$	2.96317	0.131859
$506$	37.9397	1.68663
$507$	−1.25776	−0.0558593
$508$	−16.6352	−0.738068
$509$	38.3538	1.70000	0.850001	−	0.526782i	$-0.176601\pi$
$509$	38.3538	1.70000	0.850001	+	0.526782i	$0.176601\pi$
$510$	24.0786	1.06622
$511$	31.2139	1.38082
$512$	13.6816	0.604645
$513$	−16.6779	−0.736349
$514$	3.21847	0.141961
$515$	1.27900	0.0563596
$516$	−19.6920	−0.866891
$517$	26.9881	1.18693
$518$	17.1607	0.753997
$519$	23.5561	1.03400
$520$	−5.24556	−0.230033
$521$	19.0432	0.834299	0.417150	−	0.908838i	$-0.363029\pi$
$521$	19.0432	0.834299	0.417150	+	0.908838i	$0.363029\pi$
$522$	9.06205	0.396635
$523$	−34.1692	−1.49411	−0.747057	−	0.664760i	$-0.768534\pi$
$523$	−34.1692	−1.49411	−0.747057	+	0.664760i	$0.768534\pi$
$524$	−22.0050	−0.961292
$525$	17.9836	0.784870
$526$	−17.6544	−0.769770
$527$	−38.4835	−1.67637
$528$	6.90824	0.300643
$529$	−9.91717	−0.431182
$530$	−21.1855	−0.920238
$531$	−16.4858	−0.715423
$532$	−54.3244	−2.35526
$533$	−1.70197	−0.0737206
$534$	−37.3702	−1.61717
$535$	3.21523	0.139007
$536$	19.5503	0.844445
$537$	4.75377	0.205140
$538$	35.8819	1.54698
$539$	−88.6514	−3.81849
$540$	−29.0629	−1.25067
$541$	−21.0283	−0.904076	−0.452038	−	0.891999i	$-0.649303\pi$
$541$	−21.0283	−0.904076	−0.452038	+	0.891999i	$0.649303\pi$
$542$	−23.6494	−1.01583
$543$	16.8197	0.721803
$544$	−22.5632	−0.967390
$545$	3.04350	0.130369
$546$	−15.2677	−0.653398
$547$	−38.8685	−1.66190	−0.830948	−	0.556350i	$-0.812201\pi$
$547$	−38.8685	−1.66190	−0.830948	+	0.556350i	$0.812201\pi$
$548$	41.8176	1.78636
$549$	−17.4728	−0.745720
$550$	−28.9634	−1.23501
$551$	−8.18186	−0.348559
$552$	15.9492	0.678845
$553$	−65.0493	−2.76618
$554$	−6.52947	−0.277410
$555$	−2.66049	−0.112931
$556$	37.5512	1.59253
$557$	13.6806	0.579665	0.289832	−	0.957077i	$-0.406400\pi$
$557$	13.6806	0.579665	0.289832	+	0.957077i	$0.406400\pi$
$558$	23.4388	0.992245
$559$	−4.47900	−0.189441
$560$	−9.51047	−0.401891
$561$	−30.7161	−1.29683
$562$	54.7947	2.31137
$563$	45.1411	1.90247	0.951236	−	0.308463i	$-0.0998147\pi$
$563$	45.1411	1.90247	0.951236	+	0.308463i	$0.0998147\pi$
$564$	26.5180	1.11661
$565$	−9.68754	−0.407558
$566$	17.9233	0.753372
$567$	−14.1627	−0.594776
$568$	−37.4805	−1.57265
$569$	33.7443	1.41463	0.707317	−	0.706897i	$-0.249906\pi$
$569$	33.7443	1.41463	0.707317	+	0.706897i	$0.249906\pi$
$570$	13.2410	0.554602
$571$	−13.9496	−0.583773	−0.291886	−	0.956453i	$-0.594283\pi$
$571$	−13.9496	−0.583773	−0.291886	+	0.956453i	$0.594283\pi$
$572$	15.6404	0.653959
$573$	9.95805	0.416004
$574$	−20.6599	−0.862326
$575$	−9.98752	−0.416508
$576$	17.2237	0.717656
$577$	26.1031	1.08668	0.543342	−	0.839511i	$-0.317159\pi$
$577$	26.1031	1.08668	0.543342	+	0.839511i	$0.317159\pi$
$578$	−29.9803	−1.24702
$579$	−27.9799	−1.16281
$580$	−14.2577	−0.592018
$581$	−44.1238	−1.83056
$582$	27.0555	1.12149
$583$	27.0254	1.11928
$584$	−21.1333	−0.874502
$585$	−2.12172	−0.0877222
$586$	38.2622	1.58060
$587$	−44.9076	−1.85354	−0.926768	−	0.375635i	$-0.877425\pi$
$587$	−44.9076	−1.85354	−0.926768	+	0.375635i	$0.877425\pi$
$588$	−87.1073	−3.59225
$589$	−21.1622	−0.871974
$590$	40.7784	1.67882
$591$	0.953934	0.0392396
$592$	−1.73536	−0.0713227
$593$	−16.7387	−0.687376	−0.343688	−	0.939084i	$-0.611676\pi$
$593$	−16.7387	−0.687376	−0.343688	+	0.939084i	$0.611676\pi$
$594$	58.2869	2.39154
$595$	42.2864	1.73357
$596$	45.9273	1.88126
$597$	11.9346	0.488450
$598$	8.47919	0.346740
$599$	32.3789	1.32297	0.661483	−	0.749960i	$-0.269927\pi$
$599$	32.3789	1.32297	0.661483	+	0.749960i	$0.269927\pi$
$600$	−12.1758	−0.497073
$601$	−43.5766	−1.77753	−0.888764	−	0.458366i	$-0.848435\pi$
$601$	−43.5766	−1.77753	−0.888764	+	0.458366i	$0.848435\pi$
$602$	−54.3695	−2.21594
$603$	7.90768	0.322026
$604$	−27.6972	−1.12698
$605$	−13.4971	−0.548737
$606$	−5.83926	−0.237204
$607$	−12.8822	−0.522871	−0.261435	−	0.965221i	$-0.584196\pi$
$607$	−12.8822	−0.522871	−0.261435	+	0.965221i	$0.584196\pi$
$608$	−12.4076	−0.503195
$609$	−17.7545	−0.719448
$610$	43.2197	1.74992
$611$	6.03160	0.244012
$612$	27.0534	1.09357
$613$	−2.94338	−0.118882	−0.0594410	−	0.998232i	$-0.518932\pi$
$613$	−2.94338	−0.118882	−0.0594410	+	0.998232i	$0.518932\pi$
$614$	30.5003	1.23089
$615$	3.20298	0.129156
$616$	81.2271	3.27273
$617$	−8.60947	−0.346604	−0.173302	−	0.984869i	$-0.555444\pi$
$617$	−8.60947	−0.346604	−0.173302	+	0.984869i	$0.555444\pi$
$618$	−2.52042	−0.101386
$619$	−38.6566	−1.55374	−0.776870	−	0.629660i	$-0.783194\pi$
$619$	−38.6566	−1.55374	−0.776870	+	0.629660i	$0.783194\pi$
$620$	−36.8772	−1.48103
$621$	20.0992	0.806553
$622$	−71.7699	−2.87771
$623$	−65.6288	−2.62936
$624$	1.54393	0.0618067
$625$	−3.56917	−0.142767
$626$	−27.3656	−1.09375
$627$	−16.8909	−0.674558
$628$	29.4676	1.17588
$629$	7.71591	0.307653
$630$	−25.7550	−1.02611
$631$	−32.3714	−1.28869	−0.644343	−	0.764736i	$-0.722869\pi$
$631$	−32.3714	−1.28869	−0.644343	+	0.764736i	$0.722869\pi$
$632$	44.0415	1.75188
$633$	−25.9631	−1.03194
$634$	−2.74429	−0.108989
$635$	7.12068	0.282575
$636$	26.5547	1.05296
$637$	−19.8128	−0.785012
$638$	28.5944	1.13206
$639$	−15.1601	−0.599723
$640$	−30.2327	−1.19505
$641$	29.8244	1.17799	0.588997	−	0.808135i	$-0.299523\pi$
$641$	29.8244	1.17799	0.588997	+	0.808135i	$0.299523\pi$
$642$	−6.33597	−0.250061
$643$	−17.5453	−0.691919	−0.345959	−	0.938249i	$-0.612447\pi$
$643$	−17.5453	−0.691919	−0.345959	+	0.938249i	$0.612447\pi$
$644$	65.4683	2.57981
$645$	8.42911	0.331896
$646$	−38.4012	−1.51088
$647$	−8.17118	−0.321242	−0.160621	−	0.987016i	$-0.551350\pi$
$647$	−8.17118	−0.321242	−0.160621	+	0.987016i	$0.551350\pi$
$648$	9.58878	0.376683
$649$	−52.0193	−2.04194
$650$	−6.47307	−0.253895
$651$	−45.9216	−1.79981
$652$	−37.0800	−1.45216
$653$	20.1054	0.786786	0.393393	−	0.919370i	$-0.371301\pi$
$653$	20.1054	0.786786	0.393393	+	0.919370i	$0.371301\pi$
$654$	−5.99756	−0.234523
$655$	9.41919	0.368038
$656$	2.08921	0.0815698
$657$	−8.54796	−0.333488
$658$	73.2162	2.85426
$659$	−10.3930	−0.404854	−0.202427	−	0.979297i	$-0.564883\pi$
$659$	−10.3930	−0.404854	−0.202427	+	0.979297i	$0.564883\pi$
$660$	−29.4340	−1.14572
$661$	−8.38998	−0.326332	−0.163166	−	0.986599i	$-0.552171\pi$
$661$	−8.38998	−0.326332	−0.163166	+	0.986599i	$0.552171\pi$
$662$	23.8961	0.928750
$663$	−6.86477	−0.266606
$664$	29.8739	1.15933
$665$	23.2535	0.901731
$666$	−4.69947	−0.182101
$667$	9.86026	0.381791
$668$	23.7710	0.919729
$669$	7.68690	0.297193
$670$	−19.5600	−0.755670
$671$	−55.1336	−2.12841
$672$	−26.9243	−1.03863
$673$	25.5613	0.985317	0.492659	−	0.870223i	$-0.336025\pi$
$673$	25.5613	0.985317	0.492659	+	0.870223i	$0.336025\pi$
$674$	−31.6245	−1.21813
$675$	−15.3439	−0.590586
$676$	3.49550	0.134442
$677$	−34.7542	−1.33571	−0.667856	−	0.744290i	$-0.732788\pi$
$677$	−34.7542	−1.33571	−0.667856	+	0.744290i	$0.732788\pi$
$678$	19.0904	0.733161
$679$	47.5143	1.82343
$680$	−28.6299	−1.09790
$681$	25.4787	0.976346
$682$	73.9588	2.83203
$683$	26.2584	1.00475	0.502376	−	0.864650i	$-0.332459\pi$
$683$	26.2584	1.00475	0.502376	+	0.864650i	$0.332459\pi$
$684$	14.8768	0.568828
$685$	−17.8999	−0.683921
$686$	−155.532	−5.93824
$687$	19.5007	0.743998
$688$	5.49806	0.209612
$689$	6.03994	0.230103
$690$	−15.9572	−0.607479
$691$	−40.4953	−1.54051	−0.770257	−	0.637734i	$-0.779872\pi$
$691$	−40.4953	−1.54051	−0.770257	+	0.637734i	$0.779872\pi$
$692$	−65.4656	−2.48863
$693$	32.8546	1.24804
$694$	26.8634	1.01972
$695$	−16.0737	−0.609711
$696$	12.0206	0.455640
$697$	−9.28923	−0.351855
$698$	−33.1950	−1.25645
$699$	−10.5318	−0.398350
$700$	−49.9790	−1.88903
$701$	−25.0260	−0.945218	−0.472609	−	0.881272i	$-0.656688\pi$
$701$	−25.0260	−0.945218	−0.472609	+	0.881272i	$0.656688\pi$
$702$	13.0266	0.491658
$703$	4.24301	0.160028
$704$	54.3477	2.04831
$705$	−11.3510	−0.427503
$706$	73.7577	2.77591
$707$	−10.2548	−0.385671
$708$	−51.1132	−1.92095
$709$	−34.3255	−1.28912	−0.644561	−	0.764553i	$-0.722960\pi$
$709$	−34.3255	−1.28912	−0.644561	+	0.764553i	$0.722960\pi$
$710$	37.4991	1.40732
$711$	17.8138	0.668070
$712$	44.4338	1.66523
$713$	25.5034	0.955109
$714$	−83.3299	−3.11854
$715$	−6.69486	−0.250374
$716$	−13.2114	−0.493733
$717$	−6.13708	−0.229193
$718$	2.60298	0.0971424
$719$	24.2101	0.902884	0.451442	−	0.892300i	$-0.350910\pi$
$719$	24.2101	0.902884	0.451442	+	0.892300i	$0.350910\pi$
$720$	2.60445	0.0970622
$721$	−4.42630	−0.164844
$722$	23.4237	0.871740
$723$	1.52871	0.0568532
$724$	−46.7443	−1.73724
$725$	−7.52739	−0.279560
$726$	26.5976	0.987130
$727$	17.6219	0.653560	0.326780	−	0.945100i	$-0.394036\pi$
$727$	17.6219	0.653560	0.326780	+	0.945100i	$0.394036\pi$
$728$	18.1535	0.672815
$729$	24.8460	0.920223
$730$	21.1438	0.782567
$731$	−24.4460	−0.904168
$732$	−54.1733	−2.00230
$733$	−8.67013	−0.320238	−0.160119	−	0.987098i	$-0.551188\pi$
$733$	−8.67013	−0.320238	−0.160119	+	0.987098i	$0.551188\pi$
$734$	13.9191	0.513765
$735$	37.2861	1.37532
$736$	14.9529	0.551170
$737$	24.9519	0.919115
$738$	5.65772	0.208264
$739$	14.5765	0.536204	0.268102	−	0.963391i	$-0.413604\pi$
$739$	14.5765	0.536204	0.268102	+	0.963391i	$0.413604\pi$
$740$	7.39386	0.271804
$741$	−3.77497	−0.138677
$742$	73.3175	2.69157
$743$	39.8004	1.46014	0.730068	−	0.683375i	$-0.239488\pi$
$743$	39.8004	1.46014	0.730068	+	0.683375i	$0.239488\pi$
$744$	31.0911	1.13986
$745$	−19.6591	−0.720254
$746$	−27.2375	−0.997236
$747$	12.0833	0.442106
$748$	85.3642	3.12123
$749$	−11.1271	−0.406575
$750$	34.2402	1.25028
$751$	15.8084	0.576856	0.288428	−	0.957502i	$-0.406867\pi$
$751$	15.8084	0.576856	0.288428	+	0.957502i	$0.406867\pi$
$752$	−7.40391	−0.269993
$753$	22.7288	0.828282
$754$	6.39059	0.232732
$755$	11.8557	0.431474
$756$	100.579	3.65803
$757$	−13.0670	−0.474930	−0.237465	−	0.971396i	$-0.576316\pi$
$757$	−13.0670	−0.474930	−0.237465	+	0.971396i	$0.576316\pi$
$758$	79.6167	2.89181
$759$	20.3559	0.738871
$760$	−15.7437	−0.571084
$761$	−38.6858	−1.40236	−0.701179	−	0.712986i	$-0.747342\pi$
$761$	−38.6858	−1.40236	−0.701179	+	0.712986i	$0.747342\pi$
$762$	−14.0321	−0.508328
$763$	−10.5328	−0.381312
$764$	−27.6748	−1.00124
$765$	−11.5802	−0.418682
$766$	23.7816	0.859263
$767$	−11.6259	−0.419785
$768$	29.0226	1.04726
$769$	19.2220	0.693162	0.346581	−	0.938020i	$-0.387343\pi$
$769$	19.2220	0.693162	0.346581	+	0.938020i	$0.387343\pi$
$770$	−81.2674	−2.92867
$771$	1.72681	0.0621896
$772$	77.7601	2.79865
$773$	−16.2179	−0.583319	−0.291659	−	0.956522i	$-0.594207\pi$
$773$	−16.2179	−0.583319	−0.291659	+	0.956522i	$0.594207\pi$
$774$	14.8891	0.535179
$775$	−19.4695	−0.699364
$776$	−32.1694	−1.15482
$777$	9.20726	0.330308
$778$	58.2596	2.08871
$779$	−5.10819	−0.183020
$780$	−6.57825	−0.235539
$781$	−47.8360	−1.71171
$782$	46.2787	1.65492
$783$	15.1483	0.541358
$784$	24.3206	0.868594
$785$	−12.6135	−0.450197
$786$	−18.5616	−0.662069
$787$	−37.8250	−1.34832	−0.674159	−	0.738587i	$-0.735494\pi$
$787$	−37.8250	−1.34832	−0.674159	+	0.738587i	$0.735494\pi$
$788$	−2.65111	−0.0944420
$789$	−9.47216	−0.337218
$790$	−44.0633	−1.56770
$791$	33.5261	1.19205
$792$	−22.2441	−0.790410
$793$	−12.3219	−0.437562
$794$	−47.6319	−1.69039
$795$	−11.3667	−0.403135
$796$	−33.1679	−1.17560
$797$	−27.0933	−0.959692	−0.479846	−	0.877353i	$-0.659308\pi$
$797$	−27.0933	−0.959692	−0.479846	+	0.877353i	$0.659308\pi$
$798$	−45.8235	−1.62213
$799$	32.9200	1.16462
$800$	−11.4151	−0.403586
$801$	17.9725	0.635027
$802$	69.9307	2.46934
$803$	−26.9722	−0.951829
$804$	24.5173	0.864658
$805$	−28.0236	−0.987702
$806$	16.5292	0.582215
$807$	19.2518	0.677694
$808$	6.94297	0.244253
$809$	−0.0911982	−0.00320636	−0.00160318	−	0.999999i	$-0.500510\pi$
$809$	−0.0911982	−0.00320636	−0.00160318	+	0.999999i	$0.500510\pi$
$810$	−9.59354	−0.337083
$811$	−46.4495	−1.63106	−0.815530	−	0.578714i	$-0.803555\pi$
$811$	−46.4495	−1.63106	−0.815530	+	0.578714i	$0.803555\pi$
$812$	49.3422	1.73157
$813$	−12.6886	−0.445010
$814$	−14.8287	−0.519746
$815$	15.8720	0.555973
$816$	8.42665	0.294992
$817$	−13.4430	−0.470310
$818$	80.4436	2.81264
$819$	7.34271	0.256575
$820$	−8.90151	−0.310854
$821$	1.00932	0.0352254	0.0176127	−	0.999845i	$-0.494393\pi$
$821$	1.00932	0.0352254	0.0176127	+	0.999845i	$0.494393\pi$
$822$	35.2738	1.23031
$823$	−45.9688	−1.60237	−0.801187	−	0.598415i	$-0.795798\pi$
$823$	−45.9688	−1.60237	−0.801187	+	0.598415i	$0.795798\pi$
$824$	2.99681	0.104399
$825$	−15.5398	−0.541027
$826$	−141.124	−4.91032
$827$	−22.5703	−0.784845	−0.392423	−	0.919785i	$-0.628363\pi$
$827$	−22.5703	−0.784845	−0.392423	+	0.919785i	$0.628363\pi$
$828$	−17.9286	−0.623061
$829$	−0.880382	−0.0305769	−0.0152885	−	0.999883i	$-0.504867\pi$
$829$	−0.880382	−0.0305769	−0.0152885	+	0.999883i	$0.504867\pi$
$830$	−29.8887	−1.03745
$831$	−3.50327	−0.121527
$832$	12.1462	0.421095
$833$	−108.137	−3.74672
$834$	31.6751	1.09682
$835$	−10.1752	−0.352126
$836$	46.9422	1.62353
$837$	39.1809	1.35429
$838$	20.3523	0.703058
$839$	0.0872672	0.00301280	0.00150640	−	0.999999i	$-0.499520\pi$
$839$	0.0872672	0.00301280	0.00150640	+	0.999999i	$0.499520\pi$
$840$	−34.1635	−1.17875
$841$	−21.5685	−0.743742
$842$	−54.3501	−1.87303
$843$	29.3991	1.01256
$844$	72.1551	2.48368
$845$	−1.49624	−0.0514723
$846$	−20.0503	−0.689344
$847$	46.7101	1.60498
$848$	−7.41415	−0.254603
$849$	9.61642	0.330035
$850$	−35.3295	−1.21179
$851$	−5.11341	−0.175285
$852$	−47.0028	−1.61029
$853$	52.7980	1.80777	0.903885	−	0.427776i	$-0.140703\pi$
$853$	52.7980	1.80777	0.903885	+	0.427776i	$0.140703\pi$
$854$	−149.572	−5.11826
$855$	−6.36798	−0.217780
$856$	7.53356	0.257492
$857$	32.7020	1.11708	0.558539	−	0.829478i	$-0.311362\pi$
$857$	32.7020	1.11708	0.558539	+	0.829478i	$0.311362\pi$
$858$	13.1930	0.450400
$859$	−23.0327	−0.785866	−0.392933	−	0.919567i	$-0.628540\pi$
$859$	−23.0327	−0.785866	−0.392933	+	0.919567i	$0.628540\pi$
$860$	−23.4257	−0.798809
$861$	−11.0847	−0.377765
$862$	61.4491	2.09296
$863$	24.3247	0.828022	0.414011	−	0.910272i	$-0.364128\pi$
$863$	24.3247	0.828022	0.414011	+	0.910272i	$0.364128\pi$
$864$	22.9722	0.781529
$865$	28.0224	0.952791
$866$	−58.6169	−1.99189
$867$	−16.0854	−0.546289
$868$	127.623	4.33179
$869$	56.2097	1.90678
$870$	−12.0266	−0.407739
$871$	5.57653	0.188953
$872$	7.13119	0.241493
$873$	−13.0118	−0.440384
$874$	25.4489	0.860821
$875$	60.1320	2.03283
$876$	−26.5024	−0.895434
$877$	−51.6789	−1.74507	−0.872536	−	0.488550i	$-0.837526\pi$
$877$	−51.6789	−1.74507	−0.872536	+	0.488550i	$0.837526\pi$
$878$	−61.8332	−2.08677
$879$	20.5289	0.692423
$880$	8.21808	0.277031
$881$	−10.5804	−0.356462	−0.178231	−	0.983989i	$-0.557037\pi$
$881$	−10.5804	−0.356462	−0.178231	+	0.983989i	$0.557037\pi$
$882$	65.8621	2.21769
$883$	25.3609	0.853461	0.426731	−	0.904379i	$-0.359665\pi$
$883$	25.3609	0.853461	0.426731	+	0.904379i	$0.359665\pi$
$884$	19.0782	0.641668
$885$	21.8789	0.735452
$886$	−98.1545	−3.29756
$887$	57.0846	1.91671	0.958357	−	0.285573i	$-0.0921838\pi$
$887$	57.0846	1.91671	0.958357	+	0.285573i	$0.0921838\pi$
$888$	−6.23375	−0.209191
$889$	−24.6428	−0.826494
$890$	−44.4558	−1.49016
$891$	12.2381	0.409991
$892$	−21.3630	−0.715285
$893$	18.1028	0.605788
$894$	38.7404	1.29567
$895$	5.65511	0.189029
$896$	104.628	3.49536
$897$	4.54936	0.151899
$898$	−60.1755	−2.00808
$899$	19.2214	0.641069
$900$	13.6868	0.456226
$901$	32.9655	1.09824
$902$	17.8524	0.594419
$903$	−29.1710	−0.970750
$904$	−22.6987	−0.754948
$905$	20.0088	0.665115
$906$	−23.3630	−0.776184
$907$	−15.1131	−0.501823	−0.250912	−	0.968010i	$-0.580730\pi$
$907$	−15.1131	−0.501823	−0.250912	+	0.968010i	$0.580730\pi$
$908$	−70.8088	−2.34987
$909$	2.80828	0.0931448
$910$	−18.1626	−0.602083
$911$	−51.4967	−1.70616	−0.853081	−	0.521778i	$-0.825269\pi$
$911$	−51.4967	−1.70616	−0.853081	+	0.521778i	$0.825269\pi$
$912$	4.63385	0.153442
$913$	38.1277	1.26184
$914$	82.4833	2.72830
$915$	23.1888	0.766597
$916$	−54.1952	−1.79066
$917$	−32.5974	−1.07646
$918$	71.0982	2.34659
$919$	−32.7125	−1.07908	−0.539542	−	0.841958i	$-0.681403\pi$
$919$	−32.7125	−1.07908	−0.539542	+	0.841958i	$0.681403\pi$
$920$	18.9733	0.625531
$921$	16.3644	0.539224
$922$	11.6812	0.384699
$923$	−10.6909	−0.351896
$924$	101.864	3.35107
$925$	3.90361	0.128350
$926$	2.34425	0.0770368
$927$	1.21215	0.0398121
$928$	11.2697	0.369945
$929$	−36.3485	−1.19256	−0.596278	−	0.802778i	$-0.703355\pi$
$929$	−36.3485	−1.19256	−0.596278	+	0.802778i	$0.703355\pi$
$930$	−31.1065	−1.02002
$931$	−59.4649	−1.94888
$932$	29.2694	0.958750
$933$	−38.5068	−1.26066
$934$	16.8176	0.550288
$935$	−36.5400	−1.19499
$936$	−4.97136	−0.162494
$937$	41.9524	1.37052	0.685262	−	0.728297i	$-0.259688\pi$
$937$	41.9524	1.37052	0.685262	+	0.728297i	$0.259688\pi$
$938$	67.6922	2.21023
$939$	−14.6825	−0.479145
$940$	31.5460	1.02892
$941$	8.16376	0.266131	0.133065	−	0.991107i	$-0.457518\pi$
$941$	8.16376	0.266131	0.133065	+	0.991107i	$0.457518\pi$
$942$	24.8564	0.809864
$943$	6.15607	0.200469
$944$	14.2710	0.464481
$945$	−43.0528	−1.40051
$946$	46.9812	1.52749
$947$	33.2129	1.07927	0.539637	−	0.841898i	$-0.318561\pi$
$947$	33.2129	1.07927	0.539637	+	0.841898i	$0.318561\pi$
$948$	55.2306	1.79381
$949$	−6.02805	−0.195679
$950$	−19.4279	−0.630323
$951$	−1.47240	−0.0477457
$952$	99.0805	3.21122
$953$	50.3911	1.63233	0.816164	−	0.577821i	$-0.196097\pi$
$953$	50.3911	1.63233	0.816164	+	0.577821i	$0.196097\pi$
$954$	−20.0781	−0.650051
$955$	11.8462	0.383333
$956$	17.0558	0.551623
$957$	15.3418	0.495930
$958$	−58.1221	−1.87784
$959$	61.9470	2.00037
$960$	−22.8583	−0.737747
$961$	18.7157	0.603734
$962$	−3.31408	−0.106850
$963$	3.04716	0.0981934
$964$	−4.24848	−0.136834
$965$	−33.2851	−1.07148
$966$	55.2236	1.77679
$967$	−30.5047	−0.980965	−0.490483	−	0.871451i	$-0.663179\pi$
$967$	−30.5047	−0.980965	−0.490483	+	0.871451i	$0.663179\pi$
$968$	−31.6249	−1.01646
$969$	−20.6035	−0.661879
$970$	32.1854	1.03341
$971$	−37.9650	−1.21835	−0.609177	−	0.793034i	$-0.708500\pi$
$971$	−37.9650	−1.21835	−0.609177	+	0.793034i	$0.708500\pi$
$972$	−46.2469	−1.48337
$973$	55.6270	1.78332
$974$	57.6863	1.84839
$975$	−3.47301	−0.111225
$976$	15.1253	0.484151
$977$	5.70479	0.182512	0.0912561	−	0.995827i	$-0.470912\pi$
$977$	5.70479	0.182512	0.0912561	+	0.995827i	$0.470912\pi$
$978$	−31.2776	−1.00015
$979$	56.7104	1.81247
$980$	−103.623	−3.31013
$981$	2.88441	0.0920922
$982$	−69.2796	−2.21080
$983$	−14.9043	−0.475375	−0.237687	−	0.971342i	$-0.576389\pi$
$983$	−14.9043	−0.475375	−0.237687	+	0.971342i	$0.576389\pi$
$984$	7.50484	0.239246
$985$	1.13480	0.0361579
$986$	34.8793	1.11078
$987$	39.2828	1.25039
$988$	10.4912	0.333768
$989$	16.2006	0.515150
$990$	22.2552	0.707315
$991$	19.4828	0.618892	0.309446	−	0.950917i	$-0.399856\pi$
$991$	19.4828	0.618892	0.309446	+	0.950917i	$0.399856\pi$
$992$	29.1488	0.925476
$993$	12.8210	0.406863
$994$	−129.775	−4.11621
$995$	14.1975	0.450090
$996$	37.4636	1.18708
$997$	16.8761	0.534473	0.267236	−	0.963631i	$-0.413890\pi$
$997$	16.8761	0.534473	0.267236	+	0.963631i	$0.413890\pi$
$998$	−19.4810	−0.616661
$999$	−7.85575	−0.248545

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.c.1.13	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.c.1.13	✓	108	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.34425 q^{2} -1.25776 q^{3} +3.49550 q^{4} -1.49624 q^{5} +2.94851 q^{6} +5.17811 q^{7} -3.50582 q^{8} -1.41803 q^{9} +O(q^{10})\)	\(q-2.34425 q^{2} -1.25776 q^{3} +3.49550 q^{4} -1.49624 q^{5} +2.94851 q^{6} +5.17811 q^{7} -3.50582 q^{8} -1.41803 q^{9} +3.50756 q^{10} -4.47445 q^{11} -4.39651 q^{12} -1.00000 q^{13} -12.1388 q^{14} +1.88192 q^{15} +1.22752 q^{16} -5.45792 q^{17} +3.32421 q^{18} -3.00133 q^{19} -5.23012 q^{20} -6.51284 q^{21} +10.4892 q^{22} +3.61702 q^{23} +4.40950 q^{24} -2.76126 q^{25} +2.34425 q^{26} +5.55684 q^{27} +18.1001 q^{28} +2.72607 q^{29} -4.41169 q^{30} +7.05094 q^{31} +4.13403 q^{32} +5.62780 q^{33} +12.7947 q^{34} -7.74771 q^{35} -4.95672 q^{36} -1.41371 q^{37} +7.03587 q^{38} +1.25776 q^{39} +5.24556 q^{40} +1.70197 q^{41} +15.2677 q^{42} +4.47900 q^{43} -15.6404 q^{44} +2.12172 q^{45} -8.47919 q^{46} -6.03160 q^{47} -1.54393 q^{48} +19.8128 q^{49} +6.47307 q^{50} +6.86477 q^{51} -3.49550 q^{52} -6.03994 q^{53} -13.0266 q^{54} +6.69486 q^{55} -18.1535 q^{56} +3.77497 q^{57} -6.39059 q^{58} +11.6259 q^{59} +6.57825 q^{60} +12.3219 q^{61} -16.5292 q^{62} -7.34271 q^{63} -12.1462 q^{64} +1.49624 q^{65} -13.1930 q^{66} -5.57653 q^{67} -19.0782 q^{68} -4.54936 q^{69} +18.1626 q^{70} +10.6909 q^{71} +4.97136 q^{72} +6.02805 q^{73} +3.31408 q^{74} +3.47301 q^{75} -10.4912 q^{76} -23.1692 q^{77} -2.94851 q^{78} -12.5624 q^{79} -1.83667 q^{80} -2.73510 q^{81} -3.98985 q^{82} -8.52121 q^{83} -22.7656 q^{84} +8.16637 q^{85} -10.4999 q^{86} -3.42876 q^{87} +15.6866 q^{88} -12.6743 q^{89} -4.97383 q^{90} -5.17811 q^{91} +12.6433 q^{92} -8.86842 q^{93} +14.1396 q^{94} +4.49073 q^{95} -5.19964 q^{96} +9.17600 q^{97} -46.4462 q^{98} +6.34490 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9}+O(q^{10}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9} - q^{10} - 45 q^{11} - 6 q^{12} - 108 q^{13} - 31 q^{14} - 39 q^{15} + 73 q^{16} + 21 q^{17} - 35 q^{18} - 19 q^{19} - 79 q^{20} - 72 q^{21} - 26 q^{23} - 23 q^{24} + 92 q^{25} + 11 q^{26} + 7 q^{27} - 21 q^{28} - 94 q^{29} - 24 q^{30} - 36 q^{31} - 77 q^{32} - 32 q^{33} - 58 q^{34} - 10 q^{35} + 17 q^{36} - 54 q^{37} - 12 q^{38} - q^{39} - 4 q^{40} - 68 q^{41} - 11 q^{42} - 32 q^{43} - 151 q^{44} - 121 q^{45} - 33 q^{46} - 51 q^{47} - 27 q^{48} + 72 q^{49} - 45 q^{50} - 24 q^{51} - 95 q^{52} - 81 q^{53} - 29 q^{54} + 4 q^{55} - 68 q^{56} - 45 q^{57} - 30 q^{58} - 94 q^{59} - 108 q^{60} - 39 q^{61} - 9 q^{62} - 52 q^{63} + 31 q^{64} + 40 q^{65} - 40 q^{66} - 47 q^{67} + 24 q^{68} - 60 q^{69} - 66 q^{70} - 86 q^{71} - 91 q^{72} - 51 q^{73} - 110 q^{74} - 7 q^{75} - 51 q^{76} - 96 q^{77} + 10 q^{78} - 18 q^{79} - 136 q^{80} - 24 q^{81} - 33 q^{82} - 77 q^{83} - 113 q^{84} - 95 q^{85} - 137 q^{86} + 23 q^{87} + 19 q^{88} - 112 q^{89} - 19 q^{90} + 8 q^{91} - 111 q^{92} - 124 q^{93} - 20 q^{94} - 73 q^{95} - 77 q^{96} - 41 q^{97} - 80 q^{98} - 154 q^{99}+O(q^{100}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9 - q^10 - 45 * q^11 - 6 * q^12 - 108 * q^13 - 31 * q^14 - 39 * q^15 + 73 * q^16 + 21 * q^17 - 35 * q^18 - 19 * q^19 - 79 * q^20 - 72 * q^21 - 26 * q^23 - 23 * q^24 + 92 * q^25 + 11 * q^26 + 7 * q^27 - 21 * q^28 - 94 * q^29 - 24 * q^30 - 36 * q^31 - 77 * q^32 - 32 * q^33 - 58 * q^34 - 10 * q^35 + 17 * q^36 - 54 * q^37 - 12 * q^38 - q^39 - 4 * q^40 - 68 * q^41 - 11 * q^42 - 32 * q^43 - 151 * q^44 - 121 * q^45 - 33 * q^46 - 51 * q^47 - 27 * q^48 + 72 * q^49 - 45 * q^50 - 24 * q^51 - 95 * q^52 - 81 * q^53 - 29 * q^54 + 4 * q^55 - 68 * q^56 - 45 * q^57 - 30 * q^58 - 94 * q^59 - 108 * q^60 - 39 * q^61 - 9 * q^62 - 52 * q^63 + 31 * q^64 + 40 * q^65 - 40 * q^66 - 47 * q^67 + 24 * q^68 - 60 * q^69 - 66 * q^70 - 86 * q^71 - 91 * q^72 - 51 * q^73 - 110 * q^74 - 7 * q^75 - 51 * q^76 - 96 * q^77 + 10 * q^78 - 18 * q^79 - 136 * q^80 - 24 * q^81 - 33 * q^82 - 77 * q^83 - 113 * q^84 - 95 * q^85 - 137 * q^86 + 23 * q^87 + 19 * q^88 - 112 * q^89 - 19 * q^90 + 8 * q^91 - 111 * q^92 - 124 * q^93 - 20 * q^94 - 73 * q^95 - 77 * q^96 - 41 * q^97 - 80 * q^98 - 154 * q^99

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