LMFDB - Embedded newform 6013.2.a.e.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6013,2,Mod(1,6013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6013, 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("6013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6013 = 7 \cdot 859 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6013.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:	$48.0140467354$
Analytic rank:	$0$
Dimension:	$109$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.42826 q^{2} +1.22129 q^{3} +3.89645 q^{4} +0.497994 q^{5} -2.96562 q^{6} +1.00000 q^{7} -4.60506 q^{8} -1.50844 q^{9} +O(q^{10})$	\(q-2.42826 q^{2} +1.22129 q^{3} +3.89645 q^{4} +0.497994 q^{5} -2.96562 q^{6} +1.00000 q^{7} -4.60506 q^{8} -1.50844 q^{9} -1.20926 q^{10} +5.72858 q^{11} +4.75871 q^{12} +2.95920 q^{13} -2.42826 q^{14} +0.608198 q^{15} +3.38940 q^{16} +1.50561 q^{17} +3.66288 q^{18} +0.453906 q^{19} +1.94041 q^{20} +1.22129 q^{21} -13.9105 q^{22} -9.08650 q^{23} -5.62414 q^{24} -4.75200 q^{25} -7.18571 q^{26} -5.50613 q^{27} +3.89645 q^{28} -6.84747 q^{29} -1.47686 q^{30} -9.30788 q^{31} +0.979791 q^{32} +6.99629 q^{33} -3.65601 q^{34} +0.497994 q^{35} -5.87755 q^{36} -0.592839 q^{37} -1.10220 q^{38} +3.61406 q^{39} -2.29329 q^{40} +7.11679 q^{41} -2.96562 q^{42} +7.01760 q^{43} +22.3211 q^{44} -0.751194 q^{45} +22.0644 q^{46} +0.677883 q^{47} +4.13945 q^{48} +1.00000 q^{49} +11.5391 q^{50} +1.83879 q^{51} +11.5304 q^{52} +8.46859 q^{53} +13.3703 q^{54} +2.85280 q^{55} -4.60506 q^{56} +0.554353 q^{57} +16.6274 q^{58} +5.81461 q^{59} +2.36981 q^{60} +10.5067 q^{61} +22.6019 q^{62} -1.50844 q^{63} -9.15798 q^{64} +1.47367 q^{65} -16.9888 q^{66} +4.09625 q^{67} +5.86652 q^{68} -11.0973 q^{69} -1.20926 q^{70} +1.08498 q^{71} +6.94645 q^{72} -0.421009 q^{73} +1.43957 q^{74} -5.80360 q^{75} +1.76862 q^{76} +5.72858 q^{77} -8.77587 q^{78} +12.5214 q^{79} +1.68790 q^{80} -2.19930 q^{81} -17.2814 q^{82} +6.18770 q^{83} +4.75871 q^{84} +0.749784 q^{85} -17.0406 q^{86} -8.36278 q^{87} -26.3805 q^{88} +5.14054 q^{89} +1.82409 q^{90} +2.95920 q^{91} -35.4051 q^{92} -11.3677 q^{93} -1.64608 q^{94} +0.226042 q^{95} +1.19661 q^{96} -0.785892 q^{97} -2.42826 q^{98} -8.64122 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 109 q + 19 q^{2} + 38 q^{3} + 111 q^{4} + 43 q^{5} + 14 q^{6} + 109 q^{7} + 48 q^{8} + 119 q^{9}+O(q^{10}) $ 109 * q + 19 * q^2 + 38 * q^3 + 111 * q^4 + 43 * q^5 + 14 * q^6 + 109 * q^7 + 48 * q^8 + 119 * q^9	\( 109 q + 19 q^{2} + 38 q^{3} + 111 q^{4} + 43 q^{5} + 14 q^{6} + 109 q^{7} + 48 q^{8} + 119 q^{9} + 15 q^{10} + 48 q^{11} + 72 q^{12} + 29 q^{13} + 19 q^{14} + 29 q^{15} + 115 q^{16} + 72 q^{17} + 33 q^{18} + 58 q^{19} + 88 q^{20} + 38 q^{21} + 4 q^{22} + 65 q^{23} + 46 q^{24} + 124 q^{25} + 49 q^{26} + 131 q^{27} + 111 q^{28} + 25 q^{29} + 2 q^{30} + 41 q^{31} + 75 q^{32} + 54 q^{33} + 23 q^{34} + 43 q^{35} + 111 q^{36} + 25 q^{37} + 54 q^{38} + 27 q^{39} + 30 q^{40} + 109 q^{41} + 14 q^{42} + 38 q^{43} + 68 q^{44} + 84 q^{45} - 9 q^{46} + 121 q^{47} + 106 q^{48} + 109 q^{49} + 14 q^{50} + 36 q^{51} + 38 q^{52} + 61 q^{53} + 31 q^{54} + 50 q^{55} + 48 q^{56} + 5 q^{57} - 20 q^{58} + 181 q^{59} + 25 q^{60} + 34 q^{61} + 75 q^{62} + 119 q^{63} + 96 q^{64} + 12 q^{65} + 19 q^{66} + 87 q^{67} + 150 q^{68} + 89 q^{69} + 15 q^{70} + 83 q^{71} + 65 q^{72} + 32 q^{73} - 19 q^{74} + 112 q^{75} + 84 q^{76} + 48 q^{77} - 34 q^{78} - 9 q^{79} + 137 q^{80} + 109 q^{81} - 19 q^{82} + 136 q^{83} + 72 q^{84} - 32 q^{85} - 24 q^{86} + 28 q^{87} - 24 q^{88} + 142 q^{89} + 19 q^{90} + 29 q^{91} + 96 q^{92} + 29 q^{93} + 9 q^{94} + 52 q^{95} + 88 q^{96} + 75 q^{97} + 19 q^{98} + 84 q^{99}+O(q^{100}) \) 109 * q + 19 * q^2 + 38 * q^3 + 111 * q^4 + 43 * q^5 + 14 * q^6 + 109 * q^7 + 48 * q^8 + 119 * q^9 + 15 * q^10 + 48 * q^11 + 72 * q^12 + 29 * q^13 + 19 * q^14 + 29 * q^15 + 115 * q^16 + 72 * q^17 + 33 * q^18 + 58 * q^19 + 88 * q^20 + 38 * q^21 + 4 * q^22 + 65 * q^23 + 46 * q^24 + 124 * q^25 + 49 * q^26 + 131 * q^27 + 111 * q^28 + 25 * q^29 + 2 * q^30 + 41 * q^31 + 75 * q^32 + 54 * q^33 + 23 * q^34 + 43 * q^35 + 111 * q^36 + 25 * q^37 + 54 * q^38 + 27 * q^39 + 30 * q^40 + 109 * q^41 + 14 * q^42 + 38 * q^43 + 68 * q^44 + 84 * q^45 - 9 * q^46 + 121 * q^47 + 106 * q^48 + 109 * q^49 + 14 * q^50 + 36 * q^51 + 38 * q^52 + 61 * q^53 + 31 * q^54 + 50 * q^55 + 48 * q^56 + 5 * q^57 - 20 * q^58 + 181 * q^59 + 25 * q^60 + 34 * q^61 + 75 * q^62 + 119 * q^63 + 96 * q^64 + 12 * q^65 + 19 * q^66 + 87 * q^67 + 150 * q^68 + 89 * q^69 + 15 * q^70 + 83 * q^71 + 65 * q^72 + 32 * q^73 - 19 * q^74 + 112 * q^75 + 84 * q^76 + 48 * q^77 - 34 * q^78 - 9 * q^79 + 137 * q^80 + 109 * q^81 - 19 * q^82 + 136 * q^83 + 72 * q^84 - 32 * q^85 - 24 * q^86 + 28 * q^87 - 24 * q^88 + 142 * q^89 + 19 * q^90 + 29 * q^91 + 96 * q^92 + 29 * q^93 + 9 * q^94 + 52 * q^95 + 88 * q^96 + 75 * q^97 + 19 * q^98 + 84 * 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 $

$2$	−2.42826	−1.71704	−0.858519	−	0.512781i	$-0.828615\pi$
$2$	−2.42826	−1.71704	−0.858519	+	0.512781i	$0.828615\pi$
$3$	1.22129	0.705115	0.352557	−	0.935790i	$-0.385312\pi$
$3$	1.22129	0.705115	0.352557	+	0.935790i	$0.385312\pi$
$4$	3.89645	1.94822
$5$	0.497994	0.222710	0.111355	−	0.993781i	$-0.464481\pi$
$5$	0.497994	0.222710	0.111355	+	0.993781i	$0.464481\pi$
$6$	−2.96562	−1.21071
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−4.60506	−1.62814
$9$	−1.50844	−0.502813
$10$	−1.20926	−0.382401
$11$	5.72858	1.72723	0.863617	−	0.504149i	$-0.168194\pi$
$11$	5.72858	1.72723	0.863617	+	0.504149i	$0.168194\pi$
$12$	4.75871	1.37372
$13$	2.95920	0.820735	0.410367	−	0.911920i	$-0.365400\pi$
$13$	2.95920	0.820735	0.410367	+	0.911920i	$0.365400\pi$
$14$	−2.42826	−0.648980
$15$	0.608198	0.157036
$16$	3.38940	0.847349
$17$	1.50561	0.365164	0.182582	−	0.983191i	$-0.441555\pi$
$17$	1.50561	0.365164	0.182582	+	0.983191i	$0.441555\pi$
$18$	3.66288	0.863349
$19$	0.453906	0.104133	0.0520666	−	0.998644i	$-0.483419\pi$
$19$	0.453906	0.104133	0.0520666	+	0.998644i	$0.483419\pi$
$20$	1.94041	0.433888
$21$	1.22129	0.266508
$22$	−13.9105	−2.96573
$23$	−9.08650	−1.89467	−0.947333	−	0.320249i	$-0.896233\pi$
$23$	−9.08650	−1.89467	−0.947333	+	0.320249i	$0.896233\pi$
$24$	−5.62414	−1.14802
$25$	−4.75200	−0.950400
$26$	−7.18571	−1.40923
$27$	−5.50613	−1.05966
$28$	3.89645	0.736359
$29$	−6.84747	−1.27154	−0.635772	−	0.771877i	$-0.719318\pi$
$29$	−6.84747	−1.27154	−0.635772	+	0.771877i	$0.719318\pi$
$30$	−1.47686	−0.269637
$31$	−9.30788	−1.67174	−0.835872	−	0.548924i	$-0.815037\pi$
$31$	−9.30788	−1.67174	−0.835872	+	0.548924i	$0.815037\pi$
$32$	0.979791	0.173204
$33$	6.99629	1.21790
$34$	−3.65601	−0.627000
$35$	0.497994	0.0841764
$36$	−5.87755	−0.979592
$37$	−0.592839	−0.0974621	−0.0487311	−	0.998812i	$-0.515518\pi$
$37$	−0.592839	−0.0974621	−0.0487311	+	0.998812i	$0.515518\pi$
$38$	−1.10220	−0.178801
$39$	3.61406	0.578712
$40$	−2.29329	−0.362602
$41$	7.11679	1.11146	0.555728	−	0.831364i	$-0.312440\pi$
$41$	7.11679	1.11146	0.555728	+	0.831364i	$0.312440\pi$
$42$	−2.96562	−0.457605
$43$	7.01760	1.07017	0.535087	−	0.844797i	$-0.320279\pi$
$43$	7.01760	1.07017	0.535087	+	0.844797i	$0.320279\pi$
$44$	22.3211	3.36504
$45$	−0.751194	−0.111981
$46$	22.0644	3.25322
$47$	0.677883	0.0988794	0.0494397	−	0.998777i	$-0.484256\pi$
$47$	0.677883	0.0988794	0.0494397	+	0.998777i	$0.484256\pi$
$48$	4.13945	0.597478
$49$	1.00000	0.142857
$50$	11.5391	1.63187
$51$	1.83879	0.257482
$52$	11.5304	1.59897
$53$	8.46859	1.16325	0.581625	−	0.813457i	$-0.302417\pi$
$53$	8.46859	1.16325	0.581625	+	0.813457i	$0.302417\pi$
$54$	13.3703	1.81947
$55$	2.85280	0.384672
$56$	−4.60506	−0.615377
$57$	0.554353	0.0734258
$58$	16.6274	2.18329
$59$	5.81461	0.756998	0.378499	−	0.925602i	$-0.376440\pi$
$59$	5.81461	0.756998	0.378499	+	0.925602i	$0.376440\pi$
$60$	2.36981	0.305941
$61$	10.5067	1.34525	0.672623	−	0.739985i	$-0.265168\pi$
$61$	10.5067	1.34525	0.672623	+	0.739985i	$0.265168\pi$
$62$	22.6019	2.87045
$63$	−1.50844	−0.190045
$64$	−9.15798	−1.14475
$65$	1.47367	0.182786
$66$	−16.9888	−2.09118
$67$	4.09625	0.500436	0.250218	−	0.968189i	$-0.419498\pi$
$67$	4.09625	0.500436	0.250218	+	0.968189i	$0.419498\pi$
$68$	5.86652	0.711420
$69$	−11.0973	−1.33596
$70$	−1.20926	−0.144534
$71$	1.08498	0.128764	0.0643818	−	0.997925i	$-0.479492\pi$
$71$	1.08498	0.128764	0.0643818	+	0.997925i	$0.479492\pi$
$72$	6.94645	0.818648
$73$	−0.421009	−0.0492754	−0.0246377	−	0.999696i	$-0.507843\pi$
$73$	−0.421009	−0.0492754	−0.0246377	+	0.999696i	$0.507843\pi$
$74$	1.43957	0.167346
$75$	−5.80360	−0.670141
$76$	1.76862	0.202875
$77$	5.72858	0.652833
$78$	−8.77587	−0.993672
$79$	12.5214	1.40877	0.704384	−	0.709819i	$-0.251223\pi$
$79$	12.5214	1.40877	0.704384	+	0.709819i	$0.251223\pi$
$80$	1.68790	0.188713
$81$	−2.19930	−0.244366
$82$	−17.2814	−1.90841
$83$	6.18770	0.679189	0.339594	−	0.940572i	$-0.389710\pi$
$83$	6.18770	0.679189	0.339594	+	0.940572i	$0.389710\pi$
$84$	4.75871	0.519218
$85$	0.749784	0.0813255
$86$	−17.0406	−1.83753
$87$	−8.36278	−0.896584
$88$	−26.3805	−2.81217
$89$	5.14054	0.544896	0.272448	−	0.962171i	$-0.412167\pi$
$89$	5.14054	0.544896	0.272448	+	0.962171i	$0.412167\pi$
$90$	1.82409	0.192276
$91$	2.95920	0.310209
$92$	−35.4051	−3.69123
$93$	−11.3677	−1.17877
$94$	−1.64608	−0.169780
$95$	0.226042	0.0231915
$96$	1.19661	0.122129
$97$	−0.785892	−0.0797953	−0.0398976	−	0.999204i	$-0.512703\pi$
$97$	−0.785892	−0.0797953	−0.0398976	+	0.999204i	$0.512703\pi$
$98$	−2.42826	−0.245291
$99$	−8.64122	−0.868475
$100$	−18.5159	−1.85159
$101$	5.23248	0.520651	0.260326	−	0.965521i	$-0.416170\pi$
$101$	5.23248	0.520651	0.260326	+	0.965521i	$0.416170\pi$
$102$	−4.46507	−0.442107
$103$	11.0801	1.09176	0.545878	−	0.837865i	$-0.316196\pi$
$103$	11.0801	1.09176	0.545878	+	0.837865i	$0.316196\pi$
$104$	−13.6273	−1.33627
$105$	0.608198	0.0593540
$106$	−20.5639	−1.99735
$107$	8.55909	0.827438	0.413719	−	0.910405i	$-0.364230\pi$
$107$	8.55909	0.827438	0.413719	+	0.910405i	$0.364230\pi$
$108$	−21.4543	−2.06445
$109$	−12.9658	−1.24190	−0.620948	−	0.783852i	$-0.713252\pi$
$109$	−12.9658	−1.24190	−0.620948	+	0.783852i	$0.713252\pi$
$110$	−6.92734	−0.660496
$111$	−0.724031	−0.0687220
$112$	3.38940	0.320268
$113$	2.83237	0.266447	0.133223	−	0.991086i	$-0.457467\pi$
$113$	2.83237	0.266447	0.133223	+	0.991086i	$0.457467\pi$
$114$	−1.34611	−0.126075
$115$	−4.52502	−0.421961
$116$	−26.6808	−2.47725
$117$	−4.46378	−0.412676
$118$	−14.1194	−1.29979
$119$	1.50561	0.138019
$120$	−2.80079	−0.255676
$121$	21.8167	1.98333
$122$	−25.5130	−2.30984
$123$	8.69170	0.783704
$124$	−36.2676	−3.25693
$125$	−4.85644	−0.434373
$126$	3.66288	0.326315
$127$	1.60419	0.142349	0.0711744	−	0.997464i	$-0.477325\pi$
$127$	1.60419	0.142349	0.0711744	+	0.997464i	$0.477325\pi$
$128$	20.2784	1.79237
$129$	8.57056	0.754596
$130$	−3.57844	−0.313850
$131$	19.9904	1.74657	0.873286	−	0.487208i	$-0.161984\pi$
$131$	19.9904	1.74657	0.873286	+	0.487208i	$0.161984\pi$
$132$	27.2607	2.37274
$133$	0.453906	0.0393586
$134$	−9.94675	−0.859269
$135$	−2.74202	−0.235996
$136$	−6.93342	−0.594536
$137$	1.40084	0.119682	0.0598410	−	0.998208i	$-0.480941\pi$
$137$	1.40084	0.119682	0.0598410	+	0.998208i	$0.480941\pi$
$138$	26.9471	2.29389
$139$	6.34754	0.538391	0.269196	−	0.963086i	$-0.413242\pi$
$139$	6.34754	0.538391	0.269196	+	0.963086i	$0.413242\pi$
$140$	1.94041	0.163994
$141$	0.827895	0.0697213
$142$	−2.63462	−0.221092
$143$	16.9520	1.41760
$144$	−5.11270	−0.426058
$145$	−3.41000	−0.283185
$146$	1.02232	0.0846078
$147$	1.22129	0.100731
$148$	−2.30996	−0.189878
$149$	13.8220	1.13234	0.566172	−	0.824287i	$-0.308424\pi$
$149$	13.8220	1.13234	0.566172	+	0.824287i	$0.308424\pi$
$150$	14.0926	1.15066
$151$	18.4438	1.50094	0.750469	−	0.660905i	$-0.229828\pi$
$151$	18.4438	1.50094	0.750469	+	0.660905i	$0.229828\pi$
$152$	−2.09026	−0.169543
$153$	−2.27112	−0.183609
$154$	−13.9105	−1.12094
$155$	−4.63527	−0.372314
$156$	14.0820	1.12746
$157$	−7.01663	−0.559988	−0.279994	−	0.960002i	$-0.590332\pi$
$157$	−7.01663	−0.559988	−0.279994	+	0.960002i	$0.590332\pi$
$158$	−30.4052	−2.41891
$159$	10.3426	0.820225
$160$	0.487930	0.0385742
$161$	−9.08650	−0.716117
$162$	5.34046	0.419586
$163$	−1.75761	−0.137667	−0.0688335	−	0.997628i	$-0.521928\pi$
$163$	−1.75761	−0.137667	−0.0688335	+	0.997628i	$0.521928\pi$
$164$	27.7302	2.16536
$165$	3.48411	0.271238
$166$	−15.0254	−1.16619
$167$	−24.1621	−1.86972	−0.934860	−	0.355016i	$-0.884476\pi$
$167$	−24.1621	−1.86972	−0.934860	+	0.355016i	$0.884476\pi$
$168$	−5.62414	−0.433912
$169$	−4.24312	−0.326394
$170$	−1.82067	−0.139639
$171$	−0.684689	−0.0523595
$172$	27.3437	2.08494
$173$	3.45063	0.262347	0.131173	−	0.991359i	$-0.458126\pi$
$173$	3.45063	0.262347	0.131173	+	0.991359i	$0.458126\pi$
$174$	20.3070	1.53947
$175$	−4.75200	−0.359218
$176$	19.4164	1.46357
$177$	7.10135	0.533770
$178$	−12.4826	−0.935607
$179$	21.3532	1.59601	0.798006	−	0.602649i	$-0.205888\pi$
$179$	21.3532	1.59601	0.798006	+	0.602649i	$0.205888\pi$
$180$	−2.92698	−0.218165
$181$	−15.1260	−1.12431	−0.562153	−	0.827033i	$-0.690027\pi$
$181$	−15.1260	−1.12431	−0.562153	+	0.827033i	$0.690027\pi$
$182$	−7.18571	−0.532640
$183$	12.8318	0.948553
$184$	41.8439	3.08477
$185$	−0.295230	−0.0217058
$186$	27.6036	2.02400
$187$	8.62501	0.630723
$188$	2.64133	0.192639
$189$	−5.50613	−0.400512
$190$	−0.548890	−0.0398207
$191$	−5.02385	−0.363513	−0.181756	−	0.983344i	$-0.558178\pi$
$191$	−5.02385	−0.363513	−0.181756	+	0.983344i	$0.558178\pi$
$192$	−11.1846	−0.807178
$193$	13.3870	0.963617	0.481808	−	0.876277i	$-0.339980\pi$
$193$	13.3870	0.963617	0.481808	+	0.876277i	$0.339980\pi$
$194$	1.90835	0.137012
$195$	1.79978	0.128885
$196$	3.89645	0.278318
$197$	21.6643	1.54352	0.771760	−	0.635914i	$-0.219377\pi$
$197$	21.6643	1.54352	0.771760	+	0.635914i	$0.219377\pi$
$198$	20.9831	1.49121
$199$	1.11340	0.0789265	0.0394633	−	0.999221i	$-0.487435\pi$
$199$	1.11340	0.0789265	0.0394633	+	0.999221i	$0.487435\pi$
$200$	21.8833	1.54738
$201$	5.00273	0.352865
$202$	−12.7058	−0.893979
$203$	−6.84747	−0.480598
$204$	7.16475	0.501633
$205$	3.54412	0.247532
$206$	−26.9054	−1.87459
$207$	13.7064	0.952663
$208$	10.0299	0.695449
$209$	2.60024	0.179862
$210$	−1.47686	−0.101913
$211$	−8.03533	−0.553175	−0.276587	−	0.960989i	$-0.589204\pi$
$211$	−8.03533	−0.553175	−0.276587	+	0.960989i	$0.589204\pi$
$212$	32.9974	2.26627
$213$	1.32508	0.0907931
$214$	−20.7837	−1.42074
$215$	3.49472	0.238338
$216$	25.3561	1.72526
$217$	−9.30788	−0.631860
$218$	31.4843	2.13238
$219$	−0.514176	−0.0347448
$220$	11.1158	0.749426
$221$	4.45540	0.299703
$222$	1.75814	0.117998
$223$	−24.6009	−1.64740	−0.823700	−	0.567026i	$-0.808094\pi$
$223$	−24.6009	−1.64740	−0.823700	+	0.567026i	$0.808094\pi$
$224$	0.979791	0.0654650
$225$	7.16810	0.477874
$226$	−6.87773	−0.457500
$227$	4.00728	0.265973	0.132986	−	0.991118i	$-0.457543\pi$
$227$	4.00728	0.265973	0.132986	+	0.991118i	$0.457543\pi$
$228$	2.16001	0.143050
$229$	−25.8729	−1.70973	−0.854864	−	0.518852i	$-0.826360\pi$
$229$	−25.8729	−1.70973	−0.854864	+	0.518852i	$0.826360\pi$
$230$	10.9879	0.724523
$231$	6.99629	0.460322
$232$	31.5330	2.07025
$233$	11.9375	0.782051	0.391026	−	0.920380i	$-0.372120\pi$
$233$	11.9375	0.782051	0.391026	+	0.920380i	$0.372120\pi$
$234$	10.8392	0.708581
$235$	0.337582	0.0220214
$236$	22.6563	1.47480
$237$	15.2923	0.993344
$238$	−3.65601	−0.236984
$239$	−24.3860	−1.57740	−0.788699	−	0.614779i	$-0.789245\pi$
$239$	−24.3860	−1.57740	−0.788699	+	0.614779i	$0.789245\pi$
$240$	2.06142	0.133064
$241$	−4.25621	−0.274167	−0.137083	−	0.990560i	$-0.543773\pi$
$241$	−4.25621	−0.274167	−0.137083	+	0.990560i	$0.543773\pi$
$242$	−52.9766	−3.40546
$243$	13.8324	0.887350
$244$	40.9388	2.62084
$245$	0.497994	0.0318157
$246$	−21.1057	−1.34565
$247$	1.34320	0.0854657
$248$	42.8634	2.72183
$249$	7.55701	0.478906
$250$	11.7927	0.745836
$251$	11.4512	0.722794	0.361397	−	0.932412i	$-0.382300\pi$
$251$	11.4512	0.722794	0.361397	+	0.932412i	$0.382300\pi$
$252$	−5.87755	−0.370251
$253$	−52.0528	−3.27253
$254$	−3.89539	−0.244418
$255$	0.915708	0.0573438
$256$	−30.9252	−1.93282
$257$	−13.3111	−0.830323	−0.415161	−	0.909748i	$-0.636275\pi$
$257$	−13.3111	−0.830323	−0.415161	+	0.909748i	$0.636275\pi$
$258$	−20.8115	−1.29567
$259$	−0.592839	−0.0368372
$260$	5.74206	0.356107
$261$	10.3290	0.639349
$262$	−48.5420	−2.99893
$263$	12.5084	0.771302	0.385651	−	0.922645i	$-0.373977\pi$
$263$	12.5084	0.771302	0.385651	+	0.922645i	$0.373977\pi$
$264$	−32.2184	−1.98290
$265$	4.21731	0.259067
$266$	−1.10220	−0.0675803
$267$	6.27811	0.384214
$268$	15.9608	0.974961
$269$	16.0722	0.979942	0.489971	−	0.871739i	$-0.337007\pi$
$269$	16.0722	0.979942	0.489971	+	0.871739i	$0.337007\pi$
$270$	6.65834	0.405214
$271$	4.42434	0.268760	0.134380	−	0.990930i	$-0.457096\pi$
$271$	4.42434	0.268760	0.134380	+	0.990930i	$0.457096\pi$
$272$	5.10310	0.309421
$273$	3.61406	0.218733
$274$	−3.40161	−0.205499
$275$	−27.2222	−1.64156
$276$	−43.2400	−2.60274
$277$	14.9616	0.898953	0.449477	−	0.893292i	$-0.351610\pi$
$277$	14.9616	0.898953	0.449477	+	0.893292i	$0.351610\pi$
$278$	−15.4135	−0.924439
$279$	14.0404	0.840575
$280$	−2.29329	−0.137051
$281$	13.3177	0.794469	0.397235	−	0.917717i	$-0.369970\pi$
$281$	13.3177	0.794469	0.397235	+	0.917717i	$0.369970\pi$
$282$	−2.01034	−0.119714
$283$	15.4002	0.915446	0.457723	−	0.889095i	$-0.348665\pi$
$283$	15.4002	0.915446	0.457723	+	0.889095i	$0.348665\pi$
$284$	4.22757	0.250860
$285$	0.276064	0.0163526
$286$	−41.1640	−2.43408
$287$	7.11679	0.420091
$288$	−1.47795	−0.0870893
$289$	−14.7331	−0.866655
$290$	8.28037	0.486240
$291$	−0.959806	−0.0562648
$292$	−1.64044	−0.0959994
$293$	1.99236	0.116395	0.0581974	−	0.998305i	$-0.481465\pi$
$293$	1.99236	0.116395	0.0581974	+	0.998305i	$0.481465\pi$
$294$	−2.96562	−0.172959
$295$	2.89564	0.168591
$296$	2.73006	0.158681
$297$	−31.5424	−1.83027
$298$	−33.5635	−1.94428
$299$	−26.8888	−1.55502
$300$	−22.6134	−1.30558
$301$	7.01760	0.404488
$302$	−44.7864	−2.57717
$303$	6.39040	0.367119
$304$	1.53847	0.0882371
$305$	5.23228	0.299599
$306$	5.51487	0.315264
$307$	−18.9846	−1.08351	−0.541754	−	0.840537i	$-0.682240\pi$
$307$	−18.9846	−1.08351	−0.541754	+	0.840537i	$0.682240\pi$
$308$	22.3211	1.27186
$309$	13.5321	0.769814
$310$	11.2556	0.639277
$311$	−8.81388	−0.499789	−0.249895	−	0.968273i	$-0.580396\pi$
$311$	−8.81388	−0.499789	−0.249895	+	0.968273i	$0.580396\pi$
$312$	−16.6430	−0.942222
$313$	23.4909	1.32779	0.663893	−	0.747828i	$-0.268903\pi$
$313$	23.4909	1.32779	0.663893	+	0.747828i	$0.268903\pi$
$314$	17.0382	0.961521
$315$	−0.751194	−0.0423250
$316$	48.7890	2.74460
$317$	27.8797	1.56588	0.782939	−	0.622099i	$-0.213720\pi$
$317$	27.8797	1.56588	0.782939	+	0.622099i	$0.213720\pi$
$318$	−25.1146	−1.40836
$319$	−39.2263	−2.19625
$320$	−4.56062	−0.254946
$321$	10.4532	0.583439
$322$	22.0644	1.22960
$323$	0.683405	0.0380257
$324$	−8.56943	−0.476080
$325$	−14.0621	−0.780027
$326$	4.26794	0.236379
$327$	−15.8350	−0.875679
$328$	−32.7732	−1.80960
$329$	0.677883	0.0373729
$330$	−8.46033	−0.465726
$331$	16.3479	0.898564	0.449282	−	0.893390i	$-0.351680\pi$
$331$	16.3479	0.898564	0.449282	+	0.893390i	$0.351680\pi$
$332$	24.1100	1.32321
$333$	0.894261	0.0490052
$334$	58.6719	3.21038
$335$	2.03991	0.111452
$336$	4.13945	0.225826
$337$	−9.00955	−0.490781	−0.245391	−	0.969424i	$-0.578916\pi$
$337$	−9.00955	−0.490781	−0.245391	+	0.969424i	$0.578916\pi$
$338$	10.3034	0.560431
$339$	3.45916	0.187876
$340$	2.92149	0.158440
$341$	−53.3210	−2.88749
$342$	1.66260	0.0899033
$343$	1.00000	0.0539949
$344$	−32.3165	−1.74239
$345$	−5.52639	−0.297531
$346$	−8.37903	−0.450459
$347$	12.1487	0.652175	0.326088	−	0.945340i	$-0.394270\pi$
$347$	12.1487	0.652175	0.326088	+	0.945340i	$0.394270\pi$
$348$	−32.5851	−1.74675
$349$	6.44363	0.344920	0.172460	−	0.985017i	$-0.444828\pi$
$349$	6.44363	0.344920	0.172460	+	0.985017i	$0.444828\pi$
$350$	11.5391	0.616791
$351$	−16.2938	−0.869697
$352$	5.61281	0.299164
$353$	17.9270	0.954159	0.477080	−	0.878860i	$-0.341695\pi$
$353$	17.9270	0.954159	0.477080	+	0.878860i	$0.341695\pi$
$354$	−17.2439	−0.916505
$355$	0.540314	0.0286769
$356$	20.0298	1.06158
$357$	1.83879	0.0973192
$358$	−51.8511	−2.74041
$359$	10.0103	0.528324	0.264162	−	0.964478i	$-0.414905\pi$
$359$	10.0103	0.528324	0.264162	+	0.964478i	$0.414905\pi$
$360$	3.45929	0.182321
$361$	−18.7940	−0.989156
$362$	36.7298	1.93048
$363$	26.6446	1.39848
$364$	11.5304	0.604356
$365$	−0.209660	−0.0109741
$366$	−31.1589	−1.62870
$367$	0.955655	0.0498848	0.0249424	−	0.999689i	$-0.492060\pi$
$367$	0.955655	0.0498848	0.0249424	+	0.999689i	$0.492060\pi$
$368$	−30.7978	−1.60544
$369$	−10.7352	−0.558854
$370$	0.716896	0.0372696
$371$	8.46859	0.439667
$372$	−44.2935	−2.29651
$373$	17.1497	0.887976	0.443988	−	0.896033i	$-0.353563\pi$
$373$	17.1497	0.887976	0.443988	+	0.896033i	$0.353563\pi$
$374$	−20.9438	−1.08298
$375$	−5.93114	−0.306283
$376$	−3.12169	−0.160989
$377$	−20.2631	−1.04360
$378$	13.3703	0.687695
$379$	−7.78203	−0.399736	−0.199868	−	0.979823i	$-0.564051\pi$
$379$	−7.78203	−0.399736	−0.199868	+	0.979823i	$0.564051\pi$
$380$	0.880762	0.0451821
$381$	1.95919	0.100372
$382$	12.1992	0.624166
$383$	20.8734	1.06658	0.533291	−	0.845932i	$-0.320955\pi$
$383$	20.8734	1.06658	0.533291	+	0.845932i	$0.320955\pi$
$384$	24.7659	1.26383
$385$	2.85280	0.145392
$386$	−32.5071	−1.65457
$387$	−10.5856	−0.538097
$388$	−3.06219	−0.155459
$389$	−36.0888	−1.82978	−0.914888	−	0.403709i	$-0.867721\pi$
$389$	−36.0888	−1.82978	−0.914888	+	0.403709i	$0.867721\pi$
$390$	−4.37033	−0.221300
$391$	−13.6807	−0.691864
$392$	−4.60506	−0.232591
$393$	24.4142	1.23153
$394$	−52.6066	−2.65028
$395$	6.23559	0.313747
$396$	−33.6700	−1.69198
$397$	0.765571	0.0384229	0.0192115	−	0.999815i	$-0.493884\pi$
$397$	0.765571	0.0384229	0.0192115	+	0.999815i	$0.493884\pi$
$398$	−2.70361	−0.135520
$399$	0.554353	0.0277524
$400$	−16.1064	−0.805321
$401$	21.9290	1.09508	0.547541	−	0.836779i	$-0.315564\pi$
$401$	21.9290	1.09508	0.547541	+	0.836779i	$0.315564\pi$
$402$	−12.1479	−0.605883
$403$	−27.5439	−1.37206
$404$	20.3881	1.01435
$405$	−1.09524	−0.0544227
$406$	16.6274	0.825206
$407$	−3.39613	−0.168340
$408$	−8.46775	−0.419216
$409$	23.3261	1.15340	0.576701	−	0.816955i	$-0.304340\pi$
$409$	23.3261	1.15340	0.576701	+	0.816955i	$0.304340\pi$
$410$	−8.60604	−0.425022
$411$	1.71084	0.0843896
$412$	43.1731	2.12698
$413$	5.81461	0.286118
$414$	−33.2828	−1.63576
$415$	3.08144	0.151262
$416$	2.89940	0.142155
$417$	7.75222	0.379628
$418$	−6.31405	−0.308831
$419$	−27.1176	−1.32478	−0.662391	−	0.749158i	$-0.730458\pi$
$419$	−27.1176	−1.32478	−0.662391	+	0.749158i	$0.730458\pi$
$420$	2.36981	0.115635
$421$	−10.9812	−0.535191	−0.267595	−	0.963531i	$-0.586229\pi$
$421$	−10.9812	−0.535191	−0.267595	+	0.963531i	$0.586229\pi$
$422$	19.5119	0.949823
$423$	−1.02255	−0.0497178
$424$	−38.9984	−1.89393
$425$	−7.15466	−0.347052
$426$	−3.21764	−0.155895
$427$	10.5067	0.508455
$428$	33.3500	1.61203
$429$	20.7034	0.999571
$430$	−8.48610	−0.409236
$431$	−17.9019	−0.862303	−0.431151	−	0.902280i	$-0.641892\pi$
$431$	−17.9019	−0.862303	−0.431151	+	0.902280i	$0.641892\pi$
$432$	−18.6625	−0.897898
$433$	−14.1833	−0.681607	−0.340804	−	0.940134i	$-0.610699\pi$
$433$	−14.1833	−0.681607	−0.340804	+	0.940134i	$0.610699\pi$
$434$	22.6019	1.08493
$435$	−4.16462	−0.199678
$436$	−50.5204	−2.41949
$437$	−4.12442	−0.197298
$438$	1.24855	0.0596582
$439$	−1.11313	−0.0531268	−0.0265634	−	0.999647i	$-0.508456\pi$
$439$	−1.11313	−0.0531268	−0.0265634	+	0.999647i	$0.508456\pi$
$440$	−13.1373	−0.626297
$441$	−1.50844	−0.0718304
$442$	−10.8189	−0.514601
$443$	−21.4015	−1.01682	−0.508408	−	0.861117i	$-0.669766\pi$
$443$	−21.4015	−1.01682	−0.508408	+	0.861117i	$0.669766\pi$
$444$	−2.82115	−0.133886
$445$	2.55996	0.121354
$446$	59.7375	2.82865
$447$	16.8808	0.798433
$448$	−9.15798	−0.432674
$449$	39.2862	1.85403	0.927015	−	0.375023i	$-0.122365\pi$
$449$	39.2862	1.85403	0.927015	+	0.375023i	$0.122365\pi$
$450$	−17.4060	−0.820528
$451$	40.7691	1.91974
$452$	11.0362	0.519098
$453$	22.5254	1.05833
$454$	−9.73072	−0.456686
$455$	1.47367	0.0690865
$456$	−2.55283	−0.119547
$457$	0.0274673	0.00128487	0.000642434	−	1.00000i	$-0.499796\pi$
$457$	0.0274673	0.00128487	0.000642434		1.00000i	$0.499796\pi$
$458$	62.8261	2.93567
$459$	−8.29008	−0.386948
$460$	−17.6315	−0.822073
$461$	38.5321	1.79462	0.897309	−	0.441404i	$-0.145519\pi$
$461$	38.5321	1.79462	0.897309	+	0.441404i	$0.145519\pi$
$462$	−16.9888	−0.790391
$463$	11.6865	0.543118	0.271559	−	0.962422i	$-0.412461\pi$
$463$	11.6865	0.543118	0.271559	+	0.962422i	$0.412461\pi$
$464$	−23.2088	−1.07744
$465$	−5.66103	−0.262524
$466$	−28.9873	−1.34281
$467$	36.3296	1.68113	0.840567	−	0.541708i	$-0.182222\pi$
$467$	36.3296	1.68113	0.840567	+	0.541708i	$0.182222\pi$
$468$	−17.3929	−0.803985
$469$	4.09625	0.189147
$470$	−0.819736	−0.0378116
$471$	−8.56937	−0.394856
$472$	−26.7766	−1.23249
$473$	40.2009	1.84844
$474$	−37.1338	−1.70561
$475$	−2.15696	−0.0989682
$476$	5.86652	0.268892
$477$	−12.7744	−0.584897
$478$	59.2155	2.70846
$479$	−28.1663	−1.28695	−0.643477	−	0.765466i	$-0.722509\pi$
$479$	−28.1663	−1.28695	−0.643477	+	0.765466i	$0.722509\pi$
$480$	0.595906	0.0271993
$481$	−1.75433	−0.0799906
$482$	10.3352	0.470755
$483$	−11.0973	−0.504945
$484$	85.0075	3.86398
$485$	−0.391370	−0.0177712
$486$	−33.5887	−1.52361
$487$	−23.1106	−1.04724	−0.523622	−	0.851951i	$-0.675419\pi$
$487$	−23.1106	−1.04724	−0.523622	+	0.851951i	$0.675419\pi$
$488$	−48.3841	−2.19024
$489$	−2.14656	−0.0970710
$490$	−1.20926	−0.0546288
$491$	−25.9439	−1.17083	−0.585416	−	0.810733i	$-0.699069\pi$
$491$	−25.9439	−1.17083	−0.585416	+	0.810733i	$0.699069\pi$
$492$	33.8667	1.52683
$493$	−10.3096	−0.464322
$494$	−3.26164	−0.146748
$495$	−4.30328	−0.193418
$496$	−31.5481	−1.41655
$497$	1.08498	0.0486681
$498$	−18.3504	−0.822300
$499$	−5.75131	−0.257464	−0.128732	−	0.991679i	$-0.541091\pi$
$499$	−5.75131	−0.257464	−0.128732	+	0.991679i	$0.541091\pi$
$500$	−18.9228	−0.846256
$501$	−29.5091	−1.31837
$502$	−27.8065	−1.24107
$503$	−19.1445	−0.853610	−0.426805	−	0.904344i	$-0.640361\pi$
$503$	−19.1445	−0.853610	−0.426805	+	0.904344i	$0.640361\pi$
$504$	6.94645	0.309420
$505$	2.60575	0.115954
$506$	126.398	5.61906
$507$	−5.18211	−0.230145
$508$	6.25064	0.277327
$509$	−34.0436	−1.50896	−0.754478	−	0.656326i	$-0.772110\pi$
$509$	−34.0436	−1.50896	−0.754478	+	0.656326i	$0.772110\pi$
$510$	−2.22358	−0.0984616
$511$	−0.421009	−0.0186243
$512$	34.5377	1.52636
$513$	−2.49927	−0.110345
$514$	32.3228	1.42570
$515$	5.51783	0.243145
$516$	33.3947	1.47012
$517$	3.88331	0.170788
$518$	1.43957	0.0632509
$519$	4.21424	0.184985
$520$	−6.78632	−0.297600
$521$	−12.6055	−0.552255	−0.276128	−	0.961121i	$-0.589051\pi$
$521$	−12.6055	−0.552255	−0.276128	+	0.961121i	$0.589051\pi$
$522$	−25.0815	−1.09779
$523$	−29.5711	−1.29306	−0.646528	−	0.762890i	$-0.723780\pi$
$523$	−29.5711	−1.29306	−0.646528	+	0.762890i	$0.723780\pi$
$524$	77.8916	3.40271
$525$	−5.80360	−0.253290
$526$	−30.3737	−1.32436
$527$	−14.0140	−0.610460
$528$	23.7132	1.03198
$529$	59.5645	2.58976
$530$	−10.2407	−0.444828
$531$	−8.77099	−0.380628
$532$	1.76862	0.0766794
$533$	21.0600	0.912210
$534$	−15.2449	−0.659711
$535$	4.26237	0.184278
$536$	−18.8635	−0.814778
$537$	26.0785	1.12537
$538$	−39.0276	−1.68260
$539$	5.72858	0.246748
$540$	−10.6841	−0.459772
$541$	−15.3463	−0.659790	−0.329895	−	0.944018i	$-0.607013\pi$
$541$	−15.3463	−0.659790	−0.329895	+	0.944018i	$0.607013\pi$
$542$	−10.7435	−0.461471
$543$	−18.4733	−0.792765
$544$	1.47518	0.0632479
$545$	−6.45688	−0.276582
$546$	−8.77587	−0.375573
$547$	3.68155	0.157412	0.0787059	−	0.996898i	$-0.474921\pi$
$547$	3.68155	0.157412	0.0787059	+	0.996898i	$0.474921\pi$
$548$	5.45831	0.233167
$549$	−15.8487	−0.676407
$550$	66.1027	2.81863
$551$	−3.10811	−0.132410
$552$	51.1037	2.17512
$553$	12.5214	0.532465
$554$	−36.3306	−1.54354
$555$	−0.360563	−0.0153051
$556$	24.7328	1.04891
$557$	3.49800	0.148215	0.0741075	−	0.997250i	$-0.476389\pi$
$557$	3.49800	0.148215	0.0741075	+	0.997250i	$0.476389\pi$
$558$	−34.0937	−1.44330
$559$	20.7665	0.878329
$560$	1.68790	0.0713268
$561$	10.5337	0.444732
$562$	−32.3389	−1.36413
$563$	26.9566	1.13609	0.568044	−	0.822998i	$-0.307701\pi$
$563$	26.9566	1.13609	0.568044	+	0.822998i	$0.307701\pi$
$564$	3.22585	0.135833
$565$	1.41050	0.0593403
$566$	−37.3957	−1.57186
$567$	−2.19930	−0.0923617
$568$	−4.99641	−0.209645
$569$	4.39805	0.184376	0.0921880	−	0.995742i	$-0.470614\pi$
$569$	4.39805	0.184376	0.0921880	+	0.995742i	$0.470614\pi$
$570$	−0.670356	−0.0280781
$571$	−35.6256	−1.49089	−0.745443	−	0.666569i	$-0.767762\pi$
$571$	−35.6256	−1.49089	−0.745443	+	0.666569i	$0.767762\pi$
$572$	66.0527	2.76180
$573$	−6.13560	−0.256318
$574$	−17.2814	−0.721312
$575$	43.1791	1.80069
$576$	13.8142	0.575594
$577$	1.98878	0.0827938	0.0413969	−	0.999143i	$-0.486819\pi$
$577$	1.98878	0.0827938	0.0413969	+	0.999143i	$0.486819\pi$
$578$	35.7759	1.48808
$579$	16.3495	0.679461
$580$	−13.2869	−0.551708
$581$	6.18770	0.256709
$582$	2.33066	0.0966089
$583$	48.5130	2.00921
$584$	1.93877	0.0802270
$585$	−2.22293	−0.0919070
$586$	−4.83796	−0.199854
$587$	40.2505	1.66131	0.830657	−	0.556784i	$-0.187965\pi$
$587$	40.2505	1.66131	0.830657	+	0.556784i	$0.187965\pi$
$588$	4.75871	0.196246
$589$	−4.22490	−0.174084
$590$	−7.03137	−0.289477
$591$	26.4585	1.08836
$592$	−2.00937	−0.0825844
$593$	−17.9658	−0.737768	−0.368884	−	0.929475i	$-0.620260\pi$
$593$	−17.9658	−0.737768	−0.368884	+	0.929475i	$0.620260\pi$
$594$	76.5930	3.14265
$595$	0.749784	0.0307382
$596$	53.8568	2.20606
$597$	1.35978	0.0556523
$598$	65.2930	2.67003
$599$	27.1606	1.10975	0.554875	−	0.831934i	$-0.312766\pi$
$599$	27.1606	1.10975	0.554875	+	0.831934i	$0.312766\pi$
$600$	26.7259	1.09108
$601$	0.749272	0.0305634	0.0152817	−	0.999883i	$-0.495135\pi$
$601$	0.749272	0.0305634	0.0152817	+	0.999883i	$0.495135\pi$
$602$	−17.0406	−0.694521
$603$	−6.17894	−0.251626
$604$	71.8654	2.92416
$605$	10.8646	0.441708
$606$	−15.5176	−0.630358
$607$	40.1622	1.63013	0.815066	−	0.579368i	$-0.196701\pi$
$607$	40.1622	1.63013	0.815066	+	0.579368i	$0.196701\pi$
$608$	0.444733	0.0180363
$609$	−8.36278	−0.338877
$610$	−12.7053	−0.514424
$611$	2.00599	0.0811538
$612$	−8.84929	−0.357711
$613$	24.8473	1.00357	0.501787	−	0.864991i	$-0.332676\pi$
$613$	24.8473	1.00357	0.501787	+	0.864991i	$0.332676\pi$
$614$	46.0996	1.86043
$615$	4.32841	0.174538
$616$	−26.3805	−1.06290
$617$	6.00633	0.241806	0.120903	−	0.992664i	$-0.461421\pi$
$617$	6.00633	0.241806	0.120903	+	0.992664i	$0.461421\pi$
$618$	−32.8594	−1.32180
$619$	−15.0809	−0.606151	−0.303076	−	0.952967i	$-0.598013\pi$
$619$	−15.0809	−0.606151	−0.303076	+	0.952967i	$0.598013\pi$
$620$	−18.0611	−0.725350
$621$	50.0315	2.00769
$622$	21.4024	0.858158
$623$	5.14054	0.205951
$624$	12.2495	0.490371
$625$	21.3415	0.853661
$626$	−57.0421	−2.27986
$627$	3.17566	0.126824
$628$	−27.3399	−1.09098
$629$	−0.892583	−0.0355896
$630$	1.82409	0.0726736
$631$	−39.9445	−1.59017	−0.795083	−	0.606500i	$-0.792573\pi$
$631$	−39.9445	−1.59017	−0.795083	+	0.606500i	$0.792573\pi$
$632$	−57.6619	−2.29367
$633$	−9.81351	−0.390052
$634$	−67.6991	−2.68867
$635$	0.798877	0.0317025
$636$	40.2996	1.59798
$637$	2.95920	0.117248
$638$	95.2517	3.77105
$639$	−1.63663	−0.0647440
$640$	10.0985	0.399179
$641$	−0.957510	−0.0378194	−0.0189097	−	0.999821i	$-0.506019\pi$
$641$	−0.957510	−0.0378194	−0.0189097	+	0.999821i	$0.506019\pi$
$642$	−25.3830	−1.00179
$643$	−39.3825	−1.55309	−0.776546	−	0.630060i	$-0.783030\pi$
$643$	−39.3825	−1.55309	−0.776546	+	0.630060i	$0.783030\pi$
$644$	−35.4051	−1.39515
$645$	4.26809	0.168056
$646$	−1.65948	−0.0652915
$647$	15.0195	0.590476	0.295238	−	0.955424i	$-0.404601\pi$
$647$	15.0195	0.590476	0.295238	+	0.955424i	$0.404601\pi$
$648$	10.1279	0.397861
$649$	33.3095	1.30751
$650$	34.1465	1.33934
$651$	−11.3677	−0.445534
$652$	−6.84844	−0.268206
$653$	−30.7859	−1.20475	−0.602373	−	0.798215i	$-0.705778\pi$
$653$	−30.7859	−1.20475	−0.602373	+	0.798215i	$0.705778\pi$
$654$	38.4516	1.50358
$655$	9.95512	0.388979
$656$	24.1216	0.941791
$657$	0.635067	0.0247763
$658$	−1.64608	−0.0641707
$659$	−27.9225	−1.08771	−0.543854	−	0.839180i	$-0.683035\pi$
$659$	−27.9225	−1.08771	−0.543854	+	0.839180i	$0.683035\pi$
$660$	13.5756	0.528431
$661$	16.7376	0.651018	0.325509	−	0.945539i	$-0.394464\pi$
$661$	16.7376	0.651018	0.325509	+	0.945539i	$0.394464\pi$
$662$	−39.6970	−1.54287
$663$	5.44136	0.211325
$664$	−28.4948	−1.10581
$665$	0.226042	0.00876555
$666$	−2.17150	−0.0841439
$667$	62.2196	2.40915
$668$	−94.1464	−3.64263
$669$	−30.0450	−1.16161
$670$	−4.95342	−0.191367
$671$	60.1886	2.32355
$672$	1.19661	0.0461604
$673$	−49.6510	−1.91391	−0.956953	−	0.290243i	$-0.906264\pi$
$673$	−49.6510	−1.91391	−0.956953	+	0.290243i	$0.906264\pi$
$674$	21.8775	0.842691
$675$	26.1652	1.00710
$676$	−16.5331	−0.635888
$677$	−29.9042	−1.14931	−0.574656	−	0.818395i	$-0.694864\pi$
$677$	−29.9042	−1.14931	−0.574656	+	0.818395i	$0.694864\pi$
$678$	−8.39974	−0.322590
$679$	−0.785892	−0.0301598
$680$	−3.45280	−0.132409
$681$	4.89407	0.187541
$682$	129.477	4.95794
$683$	−34.9281	−1.33649	−0.668244	−	0.743942i	$-0.732954\pi$
$683$	−34.9281	−1.33649	−0.668244	+	0.743942i	$0.732954\pi$
$684$	−2.66785	−0.102008
$685$	0.697611	0.0266544
$686$	−2.42826	−0.0927114
$687$	−31.5984	−1.20556
$688$	23.7854	0.906811
$689$	25.0603	0.954720
$690$	13.4195	0.510872
$691$	−24.4995	−0.932005	−0.466002	−	0.884783i	$-0.654306\pi$
$691$	−24.4995	−0.932005	−0.466002	+	0.884783i	$0.654306\pi$
$692$	13.4452	0.511110
$693$	−8.64122	−0.328253
$694$	−29.5002	−1.11981
$695$	3.16104	0.119905
$696$	38.5111	1.45976
$697$	10.7151	0.405863
$698$	−15.6468	−0.592241
$699$	14.5792	0.551436
$700$	−18.5159	−0.699836
$701$	1.18808	0.0448733	0.0224366	−	0.999748i	$-0.492858\pi$
$701$	1.18808	0.0448733	0.0224366	+	0.999748i	$0.492858\pi$
$702$	39.5655	1.49330
$703$	−0.269093	−0.0101490
$704$	−52.4622	−1.97725
$705$	0.412287	0.0155276
$706$	−43.5315	−1.63833
$707$	5.23248	0.196788
$708$	27.6700	1.03990
$709$	−2.46351	−0.0925189	−0.0462595	−	0.998929i	$-0.514730\pi$
$709$	−2.46351	−0.0925189	−0.0462595	+	0.998929i	$0.514730\pi$
$710$	−1.31202	−0.0492394
$711$	−18.8878	−0.708347
$712$	−23.6725	−0.887164
$713$	84.5760	3.16740
$714$	−4.46507	−0.167101
$715$	8.44201	0.315713
$716$	83.2015	3.10939
$717$	−29.7825	−1.11225
$718$	−24.3076	−0.907153
$719$	5.94222	0.221607	0.110804	−	0.993842i	$-0.464658\pi$
$719$	5.94222	0.221607	0.110804	+	0.993842i	$0.464658\pi$
$720$	−2.54609	−0.0948873
$721$	11.0801	0.412645
$722$	45.6366	1.69842
$723$	−5.19809	−0.193319
$724$	−58.9376	−2.19040
$725$	32.5392	1.20848
$726$	−64.7000	−2.40124
$727$	−38.0012	−1.40939	−0.704693	−	0.709512i	$-0.748915\pi$
$727$	−38.0012	−1.40939	−0.704693	+	0.709512i	$0.748915\pi$
$728$	−13.6273	−0.505062
$729$	23.4913	0.870050
$730$	0.509109	0.0188430
$731$	10.5658	0.390789
$732$	49.9984	1.84799
$733$	−26.9069	−0.993829	−0.496914	−	0.867800i	$-0.665534\pi$
$733$	−26.9069	−0.993829	−0.496914	+	0.867800i	$0.665534\pi$
$734$	−2.32058	−0.0856541
$735$	0.608198	0.0224337
$736$	−8.90287	−0.328164
$737$	23.4657	0.864370
$738$	26.0680	0.959575
$739$	−3.06661	−0.112807	−0.0564036	−	0.998408i	$-0.517963\pi$
$739$	−3.06661	−0.112807	−0.0564036	+	0.998408i	$0.517963\pi$
$740$	−1.15035	−0.0422877
$741$	1.64044	0.0602632
$742$	−20.5639	−0.754926
$743$	−17.5491	−0.643812	−0.321906	−	0.946772i	$-0.604324\pi$
$743$	−17.5491	−0.643812	−0.321906	+	0.946772i	$0.604324\pi$
$744$	52.3488	1.91920
$745$	6.88329	0.252184
$746$	−41.6438	−1.52469
$747$	−9.33377	−0.341505
$748$	33.6069	1.22879
$749$	8.55909	0.312742
$750$	14.4024	0.525900
$751$	−33.9202	−1.23776	−0.618882	−	0.785484i	$-0.712414\pi$
$751$	−33.9202	−1.23776	−0.618882	+	0.785484i	$0.712414\pi$
$752$	2.29761	0.0837854
$753$	13.9853	0.509653
$754$	49.2040	1.79190
$755$	9.18492	0.334274
$756$	−21.4543	−0.780287
$757$	22.5206	0.818526	0.409263	−	0.912417i	$-0.365786\pi$
$757$	22.5206	0.818526	0.409263	+	0.912417i	$0.365786\pi$
$758$	18.8968	0.686363
$759$	−63.5718	−2.30751
$760$	−1.04094	−0.0377588
$761$	18.3034	0.663498	0.331749	−	0.943368i	$-0.392361\pi$
$761$	18.3034	0.663498	0.331749	+	0.943368i	$0.392361\pi$
$762$	−4.75742	−0.172343
$763$	−12.9658	−0.469393
$764$	−19.5751	−0.708204
$765$	−1.13100	−0.0408915
$766$	−50.6861	−1.83136
$767$	17.2066	0.621295
$768$	−37.7688	−1.36286
$769$	−13.3791	−0.482463	−0.241232	−	0.970468i	$-0.577551\pi$
$769$	−13.3791	−0.482463	−0.241232	+	0.970468i	$0.577551\pi$
$770$	−6.92734	−0.249644
$771$	−16.2568	−0.585473
$772$	52.1617	1.87734
$773$	−10.4630	−0.376328	−0.188164	−	0.982138i	$-0.560254\pi$
$773$	−10.4630	−0.376328	−0.188164	+	0.982138i	$0.560254\pi$
$774$	25.7046	0.923934
$775$	44.2310	1.58883
$776$	3.61908	0.129918
$777$	−0.724031	−0.0259745
$778$	87.6330	3.14180
$779$	3.23035	0.115739
$780$	7.01274	0.251096
$781$	6.21541	0.222405
$782$	33.2203	1.18796
$783$	37.7031	1.34740
$784$	3.38940	0.121050
$785$	−3.49424	−0.124715
$786$	−59.2841	−2.11459
$787$	−52.9582	−1.88775	−0.943877	−	0.330296i	$-0.892851\pi$
$787$	−52.9582	−1.88775	−0.943877	+	0.330296i	$0.892851\pi$
$788$	84.4139	3.00712
$789$	15.2765	0.543857
$790$	−15.1416	−0.538715
$791$	2.83237	0.100707
$792$	39.7934	1.41400
$793$	31.0915	1.10409
$794$	−1.85901	−0.0659737
$795$	5.15058	0.182672
$796$	4.33829	0.153766
$797$	−3.04995	−0.108035	−0.0540174	−	0.998540i	$-0.517203\pi$
$797$	−3.04995	−0.108035	−0.0540174	+	0.998540i	$0.517203\pi$
$798$	−1.34611	−0.0476519
$799$	1.02063	0.0361072
$800$	−4.65597	−0.164613
$801$	−7.75418	−0.273981
$802$	−53.2494	−1.88030
$803$	−2.41179	−0.0851101
$804$	19.4928	0.687460
$805$	−4.52502	−0.159486
$806$	66.8837	2.35588
$807$	19.6290	0.690972
$808$	−24.0959	−0.847691
$809$	−49.7930	−1.75063	−0.875314	−	0.483555i	$-0.839345\pi$
$809$	−49.7930	−1.75063	−0.875314	+	0.483555i	$0.839345\pi$
$810$	2.65952	0.0934459
$811$	10.8685	0.381643	0.190822	−	0.981625i	$-0.438885\pi$
$811$	10.8685	0.381643	0.190822	+	0.981625i	$0.438885\pi$
$812$	−26.6808	−0.936313
$813$	5.40343	0.189506
$814$	8.24668	0.289046
$815$	−0.875281	−0.0306598
$816$	6.23240	0.218177
$817$	3.18533	0.111441
$818$	−56.6419	−1.98044
$819$	−4.46378	−0.155977
$820$	13.8095	0.482247
$821$	11.9249	0.416181	0.208091	−	0.978110i	$-0.433275\pi$
$821$	11.9249	0.416181	0.208091	+	0.978110i	$0.433275\pi$
$822$	−4.15437	−0.144900
$823$	18.1062	0.631141	0.315570	−	0.948902i	$-0.397804\pi$
$823$	18.1062	0.631141	0.315570	+	0.948902i	$0.397804\pi$
$824$	−51.0246	−1.77753
$825$	−33.2464	−1.15749
$826$	−14.1194	−0.491276
$827$	2.37024	0.0824215	0.0412107	−	0.999150i	$-0.486878\pi$
$827$	2.37024	0.0824215	0.0412107	+	0.999150i	$0.486878\pi$
$828$	53.4064	1.85600
$829$	−13.1896	−0.458094	−0.229047	−	0.973415i	$-0.573561\pi$
$829$	−13.1896	−0.458094	−0.229047	+	0.973415i	$0.573561\pi$
$830$	−7.48254	−0.259723
$831$	18.2725	0.633865
$832$	−27.1003	−0.939534
$833$	1.50561	0.0521663
$834$	−18.8244	−0.651836
$835$	−12.0326	−0.416405
$836$	10.1317	0.350412
$837$	51.2504	1.77147
$838$	65.8486	2.27470
$839$	−2.71925	−0.0938789	−0.0469394	−	0.998898i	$-0.514947\pi$
$839$	−2.71925	−0.0938789	−0.0469394	+	0.998898i	$0.514947\pi$
$840$	−2.80079	−0.0966364
$841$	17.8879	0.616824
$842$	26.6652	0.918944
$843$	16.2649	0.560192
$844$	−31.3092	−1.07771
$845$	−2.11305	−0.0726911
$846$	2.48300	0.0853675
$847$	21.8167	0.749630
$848$	28.7034	0.985679
$849$	18.8082	0.645495
$850$	17.3734	0.595901
$851$	5.38683	0.184658
$852$	5.16311	0.176885
$853$	2.98747	0.102289	0.0511445	−	0.998691i	$-0.483713\pi$
$853$	2.98747	0.102289	0.0511445	+	0.998691i	$0.483713\pi$
$854$	−25.5130	−0.873038
$855$	−0.340971	−0.0116610
$856$	−39.4151	−1.34718
$857$	−7.87088	−0.268864	−0.134432	−	0.990923i	$-0.542921\pi$
$857$	−7.87088	−0.268864	−0.134432	+	0.990923i	$0.542921\pi$
$858$	−50.2733	−1.71630
$859$	−1.00000	−0.0341196
$859$	−1.00000	−0.0341196
$860$	13.6170	0.464336
$861$	8.69170	0.296212
$862$	43.4704	1.48061
$863$	−19.9621	−0.679518	−0.339759	−	0.940513i	$-0.610345\pi$
$863$	−19.9621	−0.679518	−0.339759	+	0.940513i	$0.610345\pi$
$864$	−5.39486	−0.183537
$865$	1.71839	0.0584271
$866$	34.4408	1.17035
$867$	−17.9935	−0.611092
$868$	−36.2676	−1.23100
$869$	71.7300	2.43327
$870$	10.1128	0.342855
$871$	12.1216	0.410726
$872$	59.7082	2.02197
$873$	1.18547	0.0401221
$874$	10.0152	0.338768
$875$	−4.85644	−0.164178
$876$	−2.00346	−0.0676906
$877$	−2.86759	−0.0968316	−0.0484158	−	0.998827i	$-0.515417\pi$
$877$	−2.86759	−0.0968316	−0.0484158	+	0.998827i	$0.515417\pi$
$878$	2.70297	0.0912208
$879$	2.43326	0.0820717
$880$	9.66927	0.325951
$881$	37.3932	1.25981	0.629904	−	0.776673i	$-0.283094\pi$
$881$	37.3932	1.25981	0.629904	+	0.776673i	$0.283094\pi$
$882$	3.66288	0.123336
$883$	12.1701	0.409558	0.204779	−	0.978808i	$-0.434352\pi$
$883$	12.1701	0.409558	0.204779	+	0.978808i	$0.434352\pi$
$884$	17.3602	0.583888
$885$	3.53643	0.118876
$886$	51.9684	1.74591
$887$	−34.4318	−1.15611	−0.578054	−	0.815999i	$-0.696188\pi$
$887$	−34.4318	−1.15611	−0.578054	+	0.815999i	$0.696188\pi$
$888$	3.33421	0.111889
$889$	1.60419	0.0538028
$890$	−6.21624	−0.208369
$891$	−12.5988	−0.422077
$892$	−95.8562	−3.20950
$893$	0.307695	0.0102966
$894$	−40.9909	−1.37094
$895$	10.6338	0.355447
$896$	20.2784	0.677453
$897$	−32.8391	−1.09647
$898$	−95.3971	−3.18344
$899$	63.7354	2.12570
$900$	27.9301	0.931004
$901$	12.7504	0.424777
$902$	−98.9980	−3.29627
$903$	8.57056	0.285210
$904$	−13.0432	−0.433812
$905$	−7.53265	−0.250394
$906$	−54.6974	−1.81720
$907$	37.4750	1.24434	0.622169	−	0.782883i	$-0.286252\pi$
$907$	37.4750	1.24434	0.622169	+	0.782883i	$0.286252\pi$
$908$	15.6142	0.518174
$909$	−7.89288	−0.261790
$910$	−3.57844	−0.118624
$911$	10.0246	0.332131	0.166065	−	0.986115i	$-0.446894\pi$
$911$	10.0246	0.332131	0.166065	+	0.986115i	$0.446894\pi$
$912$	1.87892	0.0622173
$913$	35.4468	1.17312
$914$	−0.0666979	−0.00220617
$915$	6.39016	0.211252
$916$	−100.812	−3.33093
$917$	19.9904	0.660142
$918$	20.1305	0.664405
$919$	55.4579	1.82939	0.914694	−	0.404147i	$-0.132432\pi$
$919$	55.4579	1.82939	0.914694	+	0.404147i	$0.132432\pi$
$920$	20.8380	0.687009
$921$	−23.1858	−0.763998
$922$	−93.5659	−3.08143
$923$	3.21068	0.105681
$924$	27.2607	0.896810
$925$	2.81717	0.0926280
$926$	−28.3779	−0.932555
$927$	−16.7137	−0.548949
$928$	−6.70909	−0.220237
$929$	−30.5851	−1.00347	−0.501733	−	0.865023i	$-0.667304\pi$
$929$	−30.5851	−1.00347	−0.501733	+	0.865023i	$0.667304\pi$
$930$	13.7464	0.450764
$931$	0.453906	0.0148762
$932$	46.5138	1.52361
$933$	−10.7643	−0.352409
$934$	−88.2177	−2.88657
$935$	4.29520	0.140468
$936$	20.5560	0.671893
$937$	54.7656	1.78911	0.894557	−	0.446953i	$-0.147491\pi$
$937$	54.7656	1.78911	0.894557	+	0.446953i	$0.147491\pi$
$938$	−9.94675	−0.324773
$939$	28.6893	0.936241
$940$	1.31537	0.0429026
$941$	53.1467	1.73253	0.866266	−	0.499583i	$-0.166514\pi$
$941$	53.1467	1.73253	0.866266	+	0.499583i	$0.166514\pi$
$942$	20.8087	0.677983
$943$	−64.6667	−2.10584
$944$	19.7080	0.641441
$945$	−2.74202	−0.0891980
$946$	−97.6183	−3.17384
$947$	−12.5489	−0.407785	−0.203893	−	0.978993i	$-0.565359\pi$
$947$	−12.5489	−0.407785	−0.203893	+	0.978993i	$0.565359\pi$
$948$	59.5857	1.93526
$949$	−1.24585	−0.0404420
$950$	5.23766	0.169932
$951$	34.0493	1.10412
$952$	−6.93342	−0.224714
$953$	18.1104	0.586653	0.293327	−	0.956012i	$-0.405238\pi$
$953$	18.1104	0.586653	0.293327	+	0.956012i	$0.405238\pi$
$954$	31.0194	1.00429
$955$	−2.50185	−0.0809578
$956$	−95.0187	−3.07312
$957$	−47.9069	−1.54861
$958$	68.3952	2.20975
$959$	1.40084	0.0452356
$960$	−5.56986	−0.179766
$961$	55.6366	1.79473
$962$	4.25997	0.137347
$963$	−12.9109	−0.416047
$964$	−16.5841	−0.534138
$965$	6.66664	0.214607
$966$	26.9471	0.867010
$967$	34.0462	1.09485	0.547426	−	0.836854i	$-0.315608\pi$
$967$	34.0462	1.09485	0.547426	+	0.836854i	$0.315608\pi$
$968$	−100.467	−3.22914
$969$	0.834639	0.0268125
$970$	0.950347	0.0305138
$971$	15.8962	0.510134	0.255067	−	0.966923i	$-0.417902\pi$
$971$	15.8962	0.510134	0.255067	+	0.966923i	$0.417902\pi$
$972$	53.8972	1.72875
$973$	6.34754	0.203493
$974$	56.1187	1.79816
$975$	−17.1740	−0.550009
$976$	35.6114	1.13989
$977$	19.0161	0.608379	0.304189	−	0.952612i	$-0.401614\pi$
$977$	19.0161	0.608379	0.304189	+	0.952612i	$0.401614\pi$
$978$	5.21242	0.166675
$979$	29.4480	0.941162
$980$	1.94041	0.0619840
$981$	19.5581	0.624441
$982$	62.9986	2.01037
$983$	33.7935	1.07785	0.538923	−	0.842355i	$-0.318831\pi$
$983$	33.7935	1.07785	0.538923	+	0.842355i	$0.318831\pi$
$984$	−40.0258	−1.27598
$985$	10.7887	0.343757
$986$	25.0344	0.797259
$987$	0.827895	0.0263522
$988$	5.23370	0.166506
$989$	−63.7654	−2.02762
$990$	10.4495	0.332106
$991$	27.8406	0.884384	0.442192	−	0.896920i	$-0.354201\pi$
$991$	27.8406	0.884384	0.442192	+	0.896920i	$0.354201\pi$
$992$	−9.11977	−0.289553
$993$	19.9656	0.633591
$994$	−2.63462	−0.0835650
$995$	0.554464	0.0175777
$996$	29.4455	0.933016
$997$	−22.5919	−0.715492	−0.357746	−	0.933819i	$-0.616455\pi$
$997$	−22.5919	−0.715492	−0.357746	+	0.933819i	$0.616455\pi$
$998$	13.9657	0.442075
$999$	3.26425	0.103276

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.e.1.8	✓	109

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.e.1.8	✓	109	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:	\( N \)	\(=\)	\( 6013 = 7 \cdot 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.42826 q^{2} +1.22129 q^{3} +3.89645 q^{4} +0.497994 q^{5} -2.96562 q^{6} +1.00000 q^{7} -4.60506 q^{8} -1.50844 q^{9} +O(q^{10})\)	\(q-2.42826 q^{2} +1.22129 q^{3} +3.89645 q^{4} +0.497994 q^{5} -2.96562 q^{6} +1.00000 q^{7} -4.60506 q^{8} -1.50844 q^{9} -1.20926 q^{10} +5.72858 q^{11} +4.75871 q^{12} +2.95920 q^{13} -2.42826 q^{14} +0.608198 q^{15} +3.38940 q^{16} +1.50561 q^{17} +3.66288 q^{18} +0.453906 q^{19} +1.94041 q^{20} +1.22129 q^{21} -13.9105 q^{22} -9.08650 q^{23} -5.62414 q^{24} -4.75200 q^{25} -7.18571 q^{26} -5.50613 q^{27} +3.89645 q^{28} -6.84747 q^{29} -1.47686 q^{30} -9.30788 q^{31} +0.979791 q^{32} +6.99629 q^{33} -3.65601 q^{34} +0.497994 q^{35} -5.87755 q^{36} -0.592839 q^{37} -1.10220 q^{38} +3.61406 q^{39} -2.29329 q^{40} +7.11679 q^{41} -2.96562 q^{42} +7.01760 q^{43} +22.3211 q^{44} -0.751194 q^{45} +22.0644 q^{46} +0.677883 q^{47} +4.13945 q^{48} +1.00000 q^{49} +11.5391 q^{50} +1.83879 q^{51} +11.5304 q^{52} +8.46859 q^{53} +13.3703 q^{54} +2.85280 q^{55} -4.60506 q^{56} +0.554353 q^{57} +16.6274 q^{58} +5.81461 q^{59} +2.36981 q^{60} +10.5067 q^{61} +22.6019 q^{62} -1.50844 q^{63} -9.15798 q^{64} +1.47367 q^{65} -16.9888 q^{66} +4.09625 q^{67} +5.86652 q^{68} -11.0973 q^{69} -1.20926 q^{70} +1.08498 q^{71} +6.94645 q^{72} -0.421009 q^{73} +1.43957 q^{74} -5.80360 q^{75} +1.76862 q^{76} +5.72858 q^{77} -8.77587 q^{78} +12.5214 q^{79} +1.68790 q^{80} -2.19930 q^{81} -17.2814 q^{82} +6.18770 q^{83} +4.75871 q^{84} +0.749784 q^{85} -17.0406 q^{86} -8.36278 q^{87} -26.3805 q^{88} +5.14054 q^{89} +1.82409 q^{90} +2.95920 q^{91} -35.4051 q^{92} -11.3677 q^{93} -1.64608 q^{94} +0.226042 q^{95} +1.19661 q^{96} -0.785892 q^{97} -2.42826 q^{98} -8.64122 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 109 q + 19 q^{2} + 38 q^{3} + 111 q^{4} + 43 q^{5} + 14 q^{6} + 109 q^{7} + 48 q^{8} + 119 q^{9}+O(q^{10}) \) 109 * q + 19 * q^2 + 38 * q^3 + 111 * q^4 + 43 * q^5 + 14 * q^6 + 109 * q^7 + 48 * q^8 + 119 * q^9	\( 109 q + 19 q^{2} + 38 q^{3} + 111 q^{4} + 43 q^{5} + 14 q^{6} + 109 q^{7} + 48 q^{8} + 119 q^{9} + 15 q^{10} + 48 q^{11} + 72 q^{12} + 29 q^{13} + 19 q^{14} + 29 q^{15} + 115 q^{16} + 72 q^{17} + 33 q^{18} + 58 q^{19} + 88 q^{20} + 38 q^{21} + 4 q^{22} + 65 q^{23} + 46 q^{24} + 124 q^{25} + 49 q^{26} + 131 q^{27} + 111 q^{28} + 25 q^{29} + 2 q^{30} + 41 q^{31} + 75 q^{32} + 54 q^{33} + 23 q^{34} + 43 q^{35} + 111 q^{36} + 25 q^{37} + 54 q^{38} + 27 q^{39} + 30 q^{40} + 109 q^{41} + 14 q^{42} + 38 q^{43} + 68 q^{44} + 84 q^{45} - 9 q^{46} + 121 q^{47} + 106 q^{48} + 109 q^{49} + 14 q^{50} + 36 q^{51} + 38 q^{52} + 61 q^{53} + 31 q^{54} + 50 q^{55} + 48 q^{56} + 5 q^{57} - 20 q^{58} + 181 q^{59} + 25 q^{60} + 34 q^{61} + 75 q^{62} + 119 q^{63} + 96 q^{64} + 12 q^{65} + 19 q^{66} + 87 q^{67} + 150 q^{68} + 89 q^{69} + 15 q^{70} + 83 q^{71} + 65 q^{72} + 32 q^{73} - 19 q^{74} + 112 q^{75} + 84 q^{76} + 48 q^{77} - 34 q^{78} - 9 q^{79} + 137 q^{80} + 109 q^{81} - 19 q^{82} + 136 q^{83} + 72 q^{84} - 32 q^{85} - 24 q^{86} + 28 q^{87} - 24 q^{88} + 142 q^{89} + 19 q^{90} + 29 q^{91} + 96 q^{92} + 29 q^{93} + 9 q^{94} + 52 q^{95} + 88 q^{96} + 75 q^{97} + 19 q^{98} + 84 q^{99}+O(q^{100}) \) 109 * q + 19 * q^2 + 38 * q^3 + 111 * q^4 + 43 * q^5 + 14 * q^6 + 109 * q^7 + 48 * q^8 + 119 * q^9 + 15 * q^10 + 48 * q^11 + 72 * q^12 + 29 * q^13 + 19 * q^14 + 29 * q^15 + 115 * q^16 + 72 * q^17 + 33 * q^18 + 58 * q^19 + 88 * q^20 + 38 * q^21 + 4 * q^22 + 65 * q^23 + 46 * q^24 + 124 * q^25 + 49 * q^26 + 131 * q^27 + 111 * q^28 + 25 * q^29 + 2 * q^30 + 41 * q^31 + 75 * q^32 + 54 * q^33 + 23 * q^34 + 43 * q^35 + 111 * q^36 + 25 * q^37 + 54 * q^38 + 27 * q^39 + 30 * q^40 + 109 * q^41 + 14 * q^42 + 38 * q^43 + 68 * q^44 + 84 * q^45 - 9 * q^46 + 121 * q^47 + 106 * q^48 + 109 * q^49 + 14 * q^50 + 36 * q^51 + 38 * q^52 + 61 * q^53 + 31 * q^54 + 50 * q^55 + 48 * q^56 + 5 * q^57 - 20 * q^58 + 181 * q^59 + 25 * q^60 + 34 * q^61 + 75 * q^62 + 119 * q^63 + 96 * q^64 + 12 * q^65 + 19 * q^66 + 87 * q^67 + 150 * q^68 + 89 * q^69 + 15 * q^70 + 83 * q^71 + 65 * q^72 + 32 * q^73 - 19 * q^74 + 112 * q^75 + 84 * q^76 + 48 * q^77 - 34 * q^78 - 9 * q^79 + 137 * q^80 + 109 * q^81 - 19 * q^82 + 136 * q^83 + 72 * q^84 - 32 * q^85 - 24 * q^86 + 28 * q^87 - 24 * q^88 + 142 * q^89 + 19 * q^90 + 29 * q^91 + 96 * q^92 + 29 * q^93 + 9 * q^94 + 52 * q^95 + 88 * q^96 + 75 * q^97 + 19 * q^98 + 84 * q^99

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