LMFDB - Embedded newform 6013.2.a.e.1.6

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			1.6
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)

$f(q)$	$=$	$q-2.53104 q^{2} +0.289125 q^{3} +4.40615 q^{4} -2.52674 q^{5} -0.731786 q^{6} +1.00000 q^{7} -6.09005 q^{8} -2.91641 q^{9} +O(q^{10})$	\(q-2.53104 q^{2} +0.289125 q^{3} +4.40615 q^{4} -2.52674 q^{5} -0.731786 q^{6} +1.00000 q^{7} -6.09005 q^{8} -2.91641 q^{9} +6.39527 q^{10} +3.22310 q^{11} +1.27393 q^{12} +0.295446 q^{13} -2.53104 q^{14} -0.730544 q^{15} +6.60184 q^{16} -1.30810 q^{17} +7.38153 q^{18} -5.37595 q^{19} -11.1332 q^{20} +0.289125 q^{21} -8.15777 q^{22} +6.32217 q^{23} -1.76079 q^{24} +1.38441 q^{25} -0.747786 q^{26} -1.71058 q^{27} +4.40615 q^{28} -1.72339 q^{29} +1.84903 q^{30} +5.03594 q^{31} -4.52940 q^{32} +0.931878 q^{33} +3.31085 q^{34} -2.52674 q^{35} -12.8501 q^{36} -10.0376 q^{37} +13.6067 q^{38} +0.0854210 q^{39} +15.3880 q^{40} -6.07216 q^{41} -0.731786 q^{42} -7.48467 q^{43} +14.2014 q^{44} +7.36900 q^{45} -16.0016 q^{46} +10.8622 q^{47} +1.90876 q^{48} +1.00000 q^{49} -3.50399 q^{50} -0.378205 q^{51} +1.30178 q^{52} +3.83827 q^{53} +4.32955 q^{54} -8.14392 q^{55} -6.09005 q^{56} -1.55432 q^{57} +4.36196 q^{58} +1.17293 q^{59} -3.21888 q^{60} +14.4379 q^{61} -12.7461 q^{62} -2.91641 q^{63} -1.73959 q^{64} -0.746516 q^{65} -2.35862 q^{66} -8.85743 q^{67} -5.76369 q^{68} +1.82790 q^{69} +6.39527 q^{70} +11.0535 q^{71} +17.7611 q^{72} -12.7184 q^{73} +25.4055 q^{74} +0.400268 q^{75} -23.6872 q^{76} +3.22310 q^{77} -0.216204 q^{78} -13.1112 q^{79} -16.6811 q^{80} +8.25465 q^{81} +15.3689 q^{82} +1.56809 q^{83} +1.27393 q^{84} +3.30523 q^{85} +18.9440 q^{86} -0.498275 q^{87} -19.6288 q^{88} +0.986945 q^{89} -18.6512 q^{90} +0.295446 q^{91} +27.8564 q^{92} +1.45602 q^{93} -27.4926 q^{94} +13.5836 q^{95} -1.30956 q^{96} -1.18449 q^{97} -2.53104 q^{98} -9.39986 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.53104	−1.78971	−0.894857	−	0.446354i	$-0.852722\pi$
$2$	−2.53104	−1.78971	−0.894857	+	0.446354i	$0.852722\pi$
$3$	0.289125	0.166926	0.0834632	−	0.996511i	$-0.473402\pi$
$3$	0.289125	0.166926	0.0834632	+	0.996511i	$0.473402\pi$
$4$	4.40615	2.20307
$5$	−2.52674	−1.12999	−0.564996	−	0.825094i	$-0.691122\pi$
$5$	−2.52674	−1.12999	−0.564996	+	0.825094i	$0.691122\pi$
$6$	−0.731786	−0.298750
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−6.09005	−2.15316
$9$	−2.91641	−0.972136
$10$	6.39527	2.02236
$11$	3.22310	0.971800	0.485900	−	0.874014i	$-0.338492\pi$
$11$	3.22310	0.971800	0.485900	+	0.874014i	$0.338492\pi$
$12$	1.27393	0.367751
$13$	0.295446	0.0819421	0.0409710	−	0.999160i	$-0.486955\pi$
$13$	0.295446	0.0819421	0.0409710	+	0.999160i	$0.486955\pi$
$14$	−2.53104	−0.676448
$15$	−0.730544	−0.188626
$16$	6.60184	1.65046
$17$	−1.30810	−0.317261	−0.158631	−	0.987338i	$-0.550708\pi$
$17$	−1.30810	−0.317261	−0.158631	+	0.987338i	$0.550708\pi$
$18$	7.38153	1.73984
$19$	−5.37595	−1.23333	−0.616664	−	0.787227i	$-0.711516\pi$
$19$	−5.37595	−1.23333	−0.616664	+	0.787227i	$0.711516\pi$
$20$	−11.1332	−2.48946
$21$	0.289125	0.0630923
$22$	−8.15777	−1.73924
$23$	6.32217	1.31826	0.659131	−	0.752028i	$-0.270924\pi$
$23$	6.32217	1.31826	0.659131	+	0.752028i	$0.270924\pi$
$24$	−1.76079	−0.359419
$25$	1.38441	0.276882
$26$	−0.747786	−0.146653
$27$	−1.71058	−0.329202
$28$	4.40615	0.832684
$29$	−1.72339	−0.320026	−0.160013	−	0.987115i	$-0.551154\pi$
$29$	−1.72339	−0.320026	−0.160013	+	0.987115i	$0.551154\pi$
$30$	1.84903	0.337586
$31$	5.03594	0.904481	0.452241	−	0.891896i	$-0.350625\pi$
$31$	5.03594	0.904481	0.452241	+	0.891896i	$0.350625\pi$
$32$	−4.52940	−0.800693
$33$	0.931878	0.162219
$34$	3.31085	0.567806
$35$	−2.52674	−0.427097
$36$	−12.8501	−2.14169
$37$	−10.0376	−1.65017	−0.825084	−	0.565011i	$-0.808872\pi$
$37$	−10.0376	−1.65017	−0.825084	+	0.565011i	$0.808872\pi$
$38$	13.6067	2.20730
$39$	0.0854210	0.0136783
$40$	15.3880	2.43305
$41$	−6.07216	−0.948312	−0.474156	−	0.880441i	$-0.657247\pi$
$41$	−6.07216	−0.948312	−0.474156	+	0.880441i	$0.657247\pi$
$42$	−0.731786	−0.112917
$43$	−7.48467	−1.14140	−0.570701	−	0.821158i	$-0.693328\pi$
$43$	−7.48467	−1.14140	−0.570701	+	0.821158i	$0.693328\pi$
$44$	14.2014	2.14095
$45$	7.36900	1.09851
$46$	−16.0016	−2.35931
$47$	10.8622	1.58441	0.792206	−	0.610253i	$-0.208932\pi$
$47$	10.8622	1.58441	0.792206	+	0.610253i	$0.208932\pi$
$48$	1.90876	0.275505
$49$	1.00000	0.142857
$50$	−3.50399	−0.495540
$51$	−0.378205	−0.0529593
$52$	1.30178	0.180524
$53$	3.83827	0.527227	0.263613	−	0.964628i	$-0.415086\pi$
$53$	3.83827	0.527227	0.263613	+	0.964628i	$0.415086\pi$
$54$	4.32955	0.589176
$55$	−8.14392	−1.09813
$56$	−6.09005	−0.813817
$57$	−1.55432	−0.205875
$58$	4.36196	0.572754
$59$	1.17293	0.152703	0.0763514	−	0.997081i	$-0.475673\pi$
$59$	1.17293	0.152703	0.0763514	+	0.997081i	$0.475673\pi$
$60$	−3.21888	−0.415556
$61$	14.4379	1.84859	0.924293	−	0.381684i	$-0.124656\pi$
$61$	14.4379	1.84859	0.924293	+	0.381684i	$0.124656\pi$
$62$	−12.7461	−1.61876
$63$	−2.91641	−0.367433
$64$	−1.73959	−0.217449
$65$	−0.746516	−0.0925939
$66$	−2.35862	−0.290326
$67$	−8.85743	−1.08211	−0.541054	−	0.840988i	$-0.681974\pi$
$67$	−8.85743	−1.08211	−0.541054	+	0.840988i	$0.681974\pi$
$68$	−5.76369	−0.698950
$69$	1.82790	0.220053
$70$	6.39527	0.764381
$71$	11.0535	1.31181	0.655907	−	0.754842i	$-0.272286\pi$
$71$	11.0535	1.31181	0.655907	+	0.754842i	$0.272286\pi$
$72$	17.7611	2.09316
$73$	−12.7184	−1.48858	−0.744288	−	0.667859i	$-0.767211\pi$
$73$	−12.7184	−1.48858	−0.744288	+	0.667859i	$0.767211\pi$
$74$	25.4055	2.95333
$75$	0.400268	0.0462189
$76$	−23.6872	−2.71711
$77$	3.22310	0.367306
$78$	−0.216204	−0.0244802
$79$	−13.1112	−1.47513	−0.737564	−	0.675278i	$-0.764024\pi$
$79$	−13.1112	−1.47513	−0.737564	+	0.675278i	$0.764024\pi$
$80$	−16.6811	−1.86501
$81$	8.25465	0.917183
$82$	15.3689	1.69721
$83$	1.56809	0.172121	0.0860603	−	0.996290i	$-0.472572\pi$
$83$	1.56809	0.172121	0.0860603	+	0.996290i	$0.472572\pi$
$84$	1.27393	0.138997
$85$	3.30523	0.358503
$86$	18.9440	2.04278
$87$	−0.498275	−0.0534207
$88$	−19.6288	−2.09244
$89$	0.986945	0.104616	0.0523080	−	0.998631i	$-0.483342\pi$
$89$	0.986945	0.104616	0.0523080	+	0.998631i	$0.483342\pi$
$90$	−18.6512	−1.96601
$91$	0.295446	0.0309712
$92$	27.8564	2.90423
$93$	1.45602	0.150982
$94$	−27.4926	−2.83564
$95$	13.5836	1.39365
$96$	−1.30956	−0.133657
$97$	−1.18449	−0.120266	−0.0601332	−	0.998190i	$-0.519153\pi$
$97$	−1.18449	−0.120266	−0.0601332	+	0.998190i	$0.519153\pi$
$98$	−2.53104	−0.255673
$99$	−9.39986	−0.944721
$100$	6.09992	0.609992
$101$	−6.41675	−0.638490	−0.319245	−	0.947672i	$-0.603429\pi$
$101$	−6.41675	−0.638490	−0.319245	+	0.947672i	$0.603429\pi$
$102$	0.957250	0.0947819
$103$	1.18530	0.116792	0.0583958	−	0.998294i	$-0.481401\pi$
$103$	1.18530	0.116792	0.0583958	+	0.998294i	$0.481401\pi$
$104$	−1.79928	−0.176434
$105$	−0.730544	−0.0712938
$106$	−9.71480	−0.943585
$107$	12.1543	1.17500	0.587501	−	0.809223i	$-0.300112\pi$
$107$	12.1543	1.17500	0.587501	+	0.809223i	$0.300112\pi$
$108$	−7.53707	−0.725255
$109$	−3.19686	−0.306204	−0.153102	−	0.988210i	$-0.548926\pi$
$109$	−3.19686	−0.306204	−0.153102	+	0.988210i	$0.548926\pi$
$110$	20.6126	1.96533
$111$	−2.90211	−0.275457
$112$	6.60184	0.623815
$113$	1.38759	0.130533	0.0652667	−	0.997868i	$-0.479210\pi$
$113$	1.38759	0.130533	0.0652667	+	0.997868i	$0.479210\pi$
$114$	3.93405	0.368457
$115$	−15.9745	−1.48963
$116$	−7.59351	−0.705040
$117$	−0.861642	−0.0796588
$118$	−2.96873	−0.273294
$119$	−1.30810	−0.119913
$120$	4.44905	0.406140
$121$	−0.611653	−0.0556048
$122$	−36.5429	−3.30844
$123$	−1.75561	−0.158298
$124$	22.1891	1.99264
$125$	9.13565	0.817118
$126$	7.38153	0.657599
$127$	−3.11282	−0.276218	−0.138109	−	0.990417i	$-0.544102\pi$
$127$	−3.11282	−0.276218	−0.138109	+	0.990417i	$0.544102\pi$
$128$	13.4618	1.18986
$129$	−2.16401	−0.190530
$130$	1.88946	0.165717
$131$	−21.9862	−1.92094	−0.960471	−	0.278381i	$-0.910202\pi$
$131$	−21.9862	−1.92094	−0.960471	+	0.278381i	$0.910202\pi$
$132$	4.10599	0.357381
$133$	−5.37595	−0.466154
$134$	22.4185	1.93666
$135$	4.32219	0.371995
$136$	7.96640	0.683113
$137$	−6.38763	−0.545732	−0.272866	−	0.962052i	$-0.587972\pi$
$137$	−6.38763	−0.545732	−0.272866	+	0.962052i	$0.587972\pi$
$138$	−4.62647	−0.393832
$139$	−8.41355	−0.713628	−0.356814	−	0.934175i	$-0.616137\pi$
$139$	−8.41355	−0.713628	−0.356814	+	0.934175i	$0.616137\pi$
$140$	−11.1332	−0.940926
$141$	3.14053	0.264480
$142$	−27.9769	−2.34777
$143$	0.952252	0.0796313
$144$	−19.2536	−1.60447
$145$	4.35456	0.361626
$146$	32.1907	2.66412
$147$	0.289125	0.0238466
$148$	−44.2270	−3.63544
$149$	12.1403	0.994573	0.497287	−	0.867586i	$-0.334330\pi$
$149$	12.1403	0.994573	0.497287	+	0.867586i	$0.334330\pi$
$150$	−1.01309	−0.0827187
$151$	2.18738	0.178006	0.0890031	−	0.996031i	$-0.471632\pi$
$151$	2.18738	0.178006	0.0890031	+	0.996031i	$0.471632\pi$
$152$	32.7398	2.65555
$153$	3.81496	0.308421
$154$	−8.15777	−0.657372
$155$	−12.7245	−1.02206
$156$	0.376377	0.0301343
$157$	3.01375	0.240524	0.120262	−	0.992742i	$-0.461627\pi$
$157$	3.01375	0.240524	0.120262	+	0.992742i	$0.461627\pi$
$158$	33.1850	2.64005
$159$	1.10974	0.0880081
$160$	11.4446	0.904776
$161$	6.32217	0.498256
$162$	−20.8928	−1.64149
$163$	21.4132	1.67721	0.838607	−	0.544737i	$-0.183371\pi$
$163$	21.4132	1.67721	0.838607	+	0.544737i	$0.183371\pi$
$164$	−26.7548	−2.08920
$165$	−2.35461	−0.183306
$166$	−3.96890	−0.308047
$167$	−16.1730	−1.25150	−0.625752	−	0.780022i	$-0.715208\pi$
$167$	−16.1730	−1.25150	−0.625752	+	0.780022i	$0.715208\pi$
$168$	−1.76079	−0.135848
$169$	−12.9127	−0.993285
$170$	−8.36566	−0.641617
$171$	15.6785	1.19896
$172$	−32.9785	−2.51459
$173$	2.75549	0.209496	0.104748	−	0.994499i	$-0.466596\pi$
$173$	2.75549	0.209496	0.104748	+	0.994499i	$0.466596\pi$
$174$	1.26115	0.0956078
$175$	1.38441	0.104652
$176$	21.2784	1.60392
$177$	0.339124	0.0254901
$178$	−2.49800	−0.187233
$179$	21.0117	1.57049	0.785244	−	0.619187i	$-0.212538\pi$
$179$	21.0117	1.57049	0.785244	+	0.619187i	$0.212538\pi$
$180$	32.4689	2.42009
$181$	−0.0902325	−0.00670693	−0.00335347	−	0.999994i	$-0.501067\pi$
$181$	−0.0902325	−0.00670693	−0.00335347	+	0.999994i	$0.501067\pi$
$182$	−0.747786	−0.0554296
$183$	4.17436	0.308578
$184$	−38.5023	−2.83843
$185$	25.3623	1.86468
$186$	−3.68523	−0.270214
$187$	−4.21614	−0.308314
$188$	47.8604	3.49058
$189$	−1.71058	−0.124427
$190$	−34.3806	−2.49423
$191$	−22.4058	−1.62123	−0.810613	−	0.585582i	$-0.800866\pi$
$191$	−22.4058	−1.62123	−0.810613	+	0.585582i	$0.800866\pi$
$192$	−0.502960	−0.0362980
$193$	20.6089	1.48346	0.741731	−	0.670698i	$-0.234005\pi$
$193$	20.6089	1.48346	0.741731	+	0.670698i	$0.234005\pi$
$194$	2.99798	0.215242
$195$	−0.215836	−0.0154564
$196$	4.40615	0.314725
$197$	−8.09990	−0.577094	−0.288547	−	0.957466i	$-0.593172\pi$
$197$	−8.09990	−0.577094	−0.288547	+	0.957466i	$0.593172\pi$
$198$	23.7914	1.69078
$199$	13.8692	0.983164	0.491582	−	0.870831i	$-0.336419\pi$
$199$	13.8692	0.983164	0.491582	+	0.870831i	$0.336419\pi$
$200$	−8.43112	−0.596170
$201$	−2.56091	−0.180632
$202$	16.2410	1.14271
$203$	−1.72339	−0.120958
$204$	−1.66643	−0.116673
$205$	15.3428	1.07158
$206$	−3.00005	−0.209023
$207$	−18.4380	−1.28153
$208$	1.95049	0.135242
$209$	−17.3272	−1.19855
$210$	1.84903	0.127595
$211$	−5.08346	−0.349960	−0.174980	−	0.984572i	$-0.555986\pi$
$211$	−5.08346	−0.349960	−0.174980	+	0.984572i	$0.555986\pi$
$212$	16.9120	1.16152
$213$	3.19586	0.218976
$214$	−30.7630	−2.10292
$215$	18.9118	1.28977
$216$	10.4175	0.708823
$217$	5.03594	0.341862
$218$	8.09137	0.548017
$219$	−3.67721	−0.248483
$220$	−35.8833	−2.41925
$221$	−0.386474	−0.0259970
$222$	7.34536	0.492988
$223$	7.85607	0.526082	0.263041	−	0.964785i	$-0.415275\pi$
$223$	7.85607	0.526082	0.263041	+	0.964785i	$0.415275\pi$
$224$	−4.52940	−0.302633
$225$	−4.03750	−0.269167
$226$	−3.51204	−0.233617
$227$	5.19582	0.344859	0.172429	−	0.985022i	$-0.444838\pi$
$227$	5.19582	0.344859	0.172429	+	0.985022i	$0.444838\pi$
$228$	−6.84857	−0.453558
$229$	24.5104	1.61969	0.809847	−	0.586641i	$-0.199550\pi$
$229$	24.5104	1.61969	0.809847	+	0.586641i	$0.199550\pi$
$230$	40.4320	2.66600
$231$	0.931878	0.0613131
$232$	10.4955	0.689065
$233$	4.12455	0.270209	0.135104	−	0.990831i	$-0.456863\pi$
$233$	4.12455	0.270209	0.135104	+	0.990831i	$0.456863\pi$
$234$	2.18085	0.142566
$235$	−27.4459	−1.79037
$236$	5.16811	0.336415
$237$	−3.79078	−0.246238
$238$	3.31085	0.214611
$239$	−6.63821	−0.429390	−0.214695	−	0.976681i	$-0.568876\pi$
$239$	−6.63821	−0.429390	−0.214695	+	0.976681i	$0.568876\pi$
$240$	−4.82293	−0.311319
$241$	20.3477	1.31071	0.655354	−	0.755322i	$-0.272519\pi$
$241$	20.3477	1.31071	0.655354	+	0.755322i	$0.272519\pi$
$242$	1.54812	0.0995167
$243$	7.51837	0.482304
$244$	63.6156	4.07257
$245$	−2.52674	−0.161427
$246$	4.44352	0.283309
$247$	−1.58830	−0.101061
$248$	−30.6691	−1.94749
$249$	0.453375	0.0287315
$250$	−23.1227	−1.46241
$251$	29.0224	1.83188	0.915940	−	0.401314i	$-0.131447\pi$
$251$	29.0224	1.83188	0.915940	+	0.401314i	$0.131447\pi$
$252$	−12.8501	−0.809481
$253$	20.3769	1.28109
$254$	7.87867	0.494352
$255$	0.955625	0.0598436
$256$	−30.5931	−1.91207
$257$	−18.8010	−1.17277	−0.586387	−	0.810031i	$-0.699450\pi$
$257$	−18.8010	−1.17277	−0.586387	+	0.810031i	$0.699450\pi$
$258$	5.47718	0.340994
$259$	−10.0376	−0.623705
$260$	−3.28926	−0.203991
$261$	5.02611	0.311108
$262$	55.6478	3.43793
$263$	−8.14012	−0.501941	−0.250971	−	0.967995i	$-0.580750\pi$
$263$	−8.14012	−0.501941	−0.250971	+	0.967995i	$0.580750\pi$
$264$	−5.67518	−0.349283
$265$	−9.69831	−0.595762
$266$	13.6067	0.834282
$267$	0.285351	0.0174632
$268$	−39.0271	−2.38396
$269$	6.07112	0.370163	0.185081	−	0.982723i	$-0.440745\pi$
$269$	6.07112	0.370163	0.185081	+	0.982723i	$0.440745\pi$
$270$	−10.9396	−0.665765
$271$	−4.17241	−0.253456	−0.126728	−	0.991938i	$-0.540448\pi$
$271$	−4.17241	−0.253456	−0.126728	+	0.991938i	$0.540448\pi$
$272$	−8.63587	−0.523627
$273$	0.0854210	0.00516991
$274$	16.1673	0.976704
$275$	4.46209	0.269074
$276$	8.05398	0.484793
$277$	14.1861	0.852360	0.426180	−	0.904638i	$-0.359859\pi$
$277$	14.1861	0.852360	0.426180	+	0.904638i	$0.359859\pi$
$278$	21.2950	1.27719
$279$	−14.6868	−0.879278
$280$	15.3880	0.919606
$281$	−26.6996	−1.59276	−0.796382	−	0.604794i	$-0.793256\pi$
$281$	−26.6996	−1.59276	−0.796382	+	0.604794i	$0.793256\pi$
$282$	−7.94880	−0.473344
$283$	−8.97698	−0.533626	−0.266813	−	0.963748i	$-0.585971\pi$
$283$	−8.97698	−0.533626	−0.266813	+	0.963748i	$0.585971\pi$
$284$	48.7035	2.89002
$285$	3.92737	0.232637
$286$	−2.41018	−0.142517
$287$	−6.07216	−0.358428
$288$	13.2096	0.778382
$289$	−15.2889	−0.899345
$290$	−11.0215	−0.647207
$291$	−0.342465	−0.0200756
$292$	−56.0391	−3.27944
$293$	21.1130	1.23343	0.616717	−	0.787185i	$-0.288462\pi$
$293$	21.1130	1.23343	0.616717	+	0.787185i	$0.288462\pi$
$294$	−0.731786	−0.0426786
$295$	−2.96369	−0.172553
$296$	61.1293	3.55307
$297$	−5.51337	−0.319918
$298$	−30.7276	−1.78000
$299$	1.86786	0.108021
$300$	1.76364	0.101824
$301$	−7.48467	−0.431409
$302$	−5.53633	−0.318580
$303$	−1.85524	−0.106581
$304$	−35.4911	−2.03556
$305$	−36.4808	−2.08889
$306$	−9.65579	−0.551985
$307$	1.31237	0.0749010	0.0374505	−	0.999298i	$-0.488076\pi$
$307$	1.31237	0.0749010	0.0374505	+	0.999298i	$0.488076\pi$
$308$	14.2014	0.809202
$309$	0.342701	0.0194956
$310$	32.2062	1.82919
$311$	−5.01181	−0.284193	−0.142097	−	0.989853i	$-0.545384\pi$
$311$	−5.01181	−0.284193	−0.142097	+	0.989853i	$0.545384\pi$
$312$	−0.520218	−0.0294515
$313$	11.7713	0.665351	0.332676	−	0.943041i	$-0.392049\pi$
$313$	11.7713	0.665351	0.332676	+	0.943041i	$0.392049\pi$
$314$	−7.62792	−0.430469
$315$	7.36900	0.415196
$316$	−57.7700	−3.24981
$317$	5.71465	0.320967	0.160483	−	0.987039i	$-0.448695\pi$
$317$	5.71465	0.320967	0.160483	+	0.987039i	$0.448695\pi$
$318$	−2.80879	−0.157509
$319$	−5.55465	−0.311001
$320$	4.39550	0.245716
$321$	3.51412	0.196139
$322$	−16.0016	−0.891736
$323$	7.03228	0.391287
$324$	36.3712	2.02062
$325$	0.409019	0.0226883
$326$	−54.1977	−3.00173
$327$	−0.924292	−0.0511135
$328$	36.9797	2.04186
$329$	10.8622	0.598852
$330$	5.95961	0.328066
$331$	−13.3725	−0.735017	−0.367508	−	0.930020i	$-0.619789\pi$
$331$	−13.3725	−0.735017	−0.367508	+	0.930020i	$0.619789\pi$
$332$	6.90925	0.379194
$333$	29.2736	1.60419
$334$	40.9345	2.23983
$335$	22.3804	1.22277
$336$	1.90876	0.104131
$337$	−4.98328	−0.271456	−0.135728	−	0.990746i	$-0.543337\pi$
$337$	−4.98328	−0.271456	−0.135728	+	0.990746i	$0.543337\pi$
$338$	32.6825	1.77770
$339$	0.401187	0.0217895
$340$	14.5633	0.789808
$341$	16.2313	0.878975
$342$	−39.6827	−2.14580
$343$	1.00000	0.0539949
$344$	45.5820	2.45762
$345$	−4.61862	−0.248658
$346$	−6.97424	−0.374938
$347$	−36.0836	−1.93707	−0.968535	−	0.248878i	$-0.919938\pi$
$347$	−36.0836	−1.93707	−0.968535	+	0.248878i	$0.919938\pi$
$348$	−2.19547	−0.117690
$349$	−18.3720	−0.983431	−0.491715	−	0.870756i	$-0.663630\pi$
$349$	−18.3720	−0.983431	−0.491715	+	0.870756i	$0.663630\pi$
$350$	−3.50399	−0.187296
$351$	−0.505385	−0.0269755
$352$	−14.5987	−0.778113
$353$	−26.5619	−1.41375	−0.706873	−	0.707341i	$-0.749895\pi$
$353$	−26.5619	−1.41375	−0.706873	+	0.707341i	$0.749895\pi$
$354$	−0.858336	−0.0456200
$355$	−27.9294	−1.48234
$356$	4.34863	0.230477
$357$	−0.378205	−0.0200167
$358$	−53.1814	−2.81072
$359$	−9.00294	−0.475157	−0.237579	−	0.971368i	$-0.576354\pi$
$359$	−9.00294	−0.475157	−0.237579	+	0.971368i	$0.576354\pi$
$360$	−44.8775	−2.36525
$361$	9.90082	0.521096
$362$	0.228382	0.0120035
$363$	−0.176844	−0.00928192
$364$	1.30178	0.0682318
$365$	32.1361	1.68208
$366$	−10.5655	−0.552266
$367$	13.8384	0.722357	0.361179	−	0.932497i	$-0.382374\pi$
$367$	13.8384	0.722357	0.361179	+	0.932497i	$0.382374\pi$
$368$	41.7379	2.17574
$369$	17.7089	0.921888
$370$	−64.1930	−3.33723
$371$	3.83827	0.199273
$372$	6.41542	0.332624
$373$	34.3713	1.77968	0.889840	−	0.456272i	$-0.150816\pi$
$373$	34.3713	1.77968	0.889840	+	0.456272i	$0.150816\pi$
$374$	10.6712	0.551794
$375$	2.64135	0.136399
$376$	−66.1512	−3.41149
$377$	−0.509169	−0.0262236
$378$	4.32955	0.222688
$379$	−8.74453	−0.449176	−0.224588	−	0.974454i	$-0.572104\pi$
$379$	−8.74453	−0.449176	−0.224588	+	0.974454i	$0.572104\pi$
$380$	59.8514	3.07031
$381$	−0.899996	−0.0461082
$382$	56.7099	2.90153
$383$	15.1599	0.774635	0.387317	−	0.921946i	$-0.373402\pi$
$383$	15.1599	0.774635	0.387317	+	0.921946i	$0.373402\pi$
$384$	3.89214	0.198620
$385$	−8.14392	−0.415053
$386$	−52.1619	−2.65497
$387$	21.8283	1.10960
$388$	−5.21902	−0.264956
$389$	14.8276	0.751788	0.375894	−	0.926663i	$-0.377336\pi$
$389$	14.8276	0.751788	0.375894	+	0.926663i	$0.377336\pi$
$390$	0.546290	0.0276625
$391$	−8.27003	−0.418234
$392$	−6.09005	−0.307594
$393$	−6.35676	−0.320656
$394$	20.5011	1.03283
$395$	33.1286	1.66688
$396$	−41.4172	−2.08129
$397$	16.8209	0.844215	0.422108	−	0.906546i	$-0.361290\pi$
$397$	16.8209	0.844215	0.422108	+	0.906546i	$0.361290\pi$
$398$	−35.1036	−1.75958
$399$	−1.55432	−0.0778134
$400$	9.13965	0.456983
$401$	−18.1018	−0.903958	−0.451979	−	0.892029i	$-0.649282\pi$
$401$	−18.1018	−0.903958	−0.451979	+	0.892029i	$0.649282\pi$
$402$	6.48174	0.323280
$403$	1.48785	0.0741151
$404$	−28.2731	−1.40664
$405$	−20.8573	−1.03641
$406$	4.36196	0.216481
$407$	−32.3521	−1.60363
$408$	2.30329	0.114030
$409$	−1.37063	−0.0677731	−0.0338865	−	0.999426i	$-0.510788\pi$
$409$	−1.37063	−0.0677731	−0.0338865	+	0.999426i	$0.510788\pi$
$410$	−38.8331	−1.91783
$411$	−1.84682	−0.0910971
$412$	5.22263	0.257300
$413$	1.17293	0.0577162
$414$	46.6673	2.29357
$415$	−3.96216	−0.194495
$416$	−1.33820	−0.0656104
$417$	−2.43257	−0.119123
$418$	43.8558	2.14506
$419$	20.8605	1.01910	0.509552	−	0.860440i	$-0.329811\pi$
$419$	20.8605	1.01910	0.509552	+	0.860440i	$0.329811\pi$
$420$	−3.21888	−0.157065
$421$	−11.7759	−0.573921	−0.286960	−	0.957942i	$-0.592645\pi$
$421$	−11.7759	−0.573921	−0.286960	+	0.957942i	$0.592645\pi$
$422$	12.8664	0.626328
$423$	−31.6786	−1.54026
$424$	−23.3752	−1.13520
$425$	−1.81095	−0.0878439
$426$	−8.08883	−0.391905
$427$	14.4379	0.698700
$428$	53.5537	2.58862
$429$	0.275320	0.0132926
$430$	−47.8665	−2.30833
$431$	−7.08570	−0.341306	−0.170653	−	0.985331i	$-0.554588\pi$
$431$	−7.08570	−0.341306	−0.170653	+	0.985331i	$0.554588\pi$
$432$	−11.2930	−0.543334
$433$	6.21534	0.298690	0.149345	−	0.988785i	$-0.452283\pi$
$433$	6.21534	0.298690	0.149345	+	0.988785i	$0.452283\pi$
$434$	−12.7461	−0.611835
$435$	1.25901	0.0603650
$436$	−14.0858	−0.674589
$437$	−33.9876	−1.62585
$438$	9.30715	0.444713
$439$	10.9523	0.522723	0.261362	−	0.965241i	$-0.415828\pi$
$439$	10.9523	0.522723	0.261362	+	0.965241i	$0.415828\pi$
$440$	49.5969	2.36444
$441$	−2.91641	−0.138877
$442$	0.978179	0.0465272
$443$	−5.51650	−0.262097	−0.131048	−	0.991376i	$-0.541834\pi$
$443$	−5.51650	−0.262097	−0.131048	+	0.991376i	$0.541834\pi$
$444$	−12.7871	−0.606851
$445$	−2.49375	−0.118215
$446$	−19.8840	−0.941535
$447$	3.51007	0.166021
$448$	−1.73959	−0.0821881
$449$	22.4565	1.05979	0.529895	−	0.848063i	$-0.322231\pi$
$449$	22.4565	1.05979	0.529895	+	0.848063i	$0.322231\pi$
$450$	10.2191	0.481732
$451$	−19.5711	−0.921569
$452$	6.11392	0.287575
$453$	0.632426	0.0297140
$454$	−13.1508	−0.617199
$455$	−0.746516	−0.0349972
$456$	9.46589	0.443281
$457$	39.0414	1.82628	0.913139	−	0.407648i	$-0.133651\pi$
$457$	39.0414	1.82628	0.913139	+	0.407648i	$0.133651\pi$
$458$	−62.0368	−2.89879
$459$	2.23761	0.104443
$460$	−70.3858	−3.28176
$461$	17.0595	0.794542	0.397271	−	0.917701i	$-0.369957\pi$
$461$	17.0595	0.794542	0.397271	+	0.917701i	$0.369957\pi$
$462$	−2.35862	−0.109733
$463$	30.2558	1.40611	0.703054	−	0.711136i	$-0.251819\pi$
$463$	30.2558	1.40611	0.703054	+	0.711136i	$0.251819\pi$
$464$	−11.3775	−0.528189
$465$	−3.67897	−0.170608
$466$	−10.4394	−0.483596
$467$	6.28049	0.290627	0.145313	−	0.989386i	$-0.453581\pi$
$467$	6.28049	0.290627	0.145313	+	0.989386i	$0.453581\pi$
$468$	−3.79652	−0.175494
$469$	−8.85743	−0.408998
$470$	69.4666	3.20426
$471$	0.871352	0.0401498
$472$	−7.14321	−0.328793
$473$	−24.1238	−1.10921
$474$	9.59461	0.440695
$475$	−7.44252	−0.341486
$476$	−5.76369	−0.264178
$477$	−11.1940	−0.512536
$478$	16.8016	0.768485
$479$	5.01403	0.229097	0.114548	−	0.993418i	$-0.463458\pi$
$479$	5.01403	0.229097	0.114548	+	0.993418i	$0.463458\pi$
$480$	3.30893	0.151031
$481$	−2.96556	−0.135218
$482$	−51.5007	−2.34579
$483$	1.82790	0.0831722
$484$	−2.69503	−0.122502
$485$	2.99289	0.135900
$486$	−19.0293	−0.863185
$487$	−8.45019	−0.382915	−0.191457	−	0.981501i	$-0.561321\pi$
$487$	−8.45019	−0.382915	−0.191457	+	0.981501i	$0.561321\pi$
$488$	−87.9276	−3.98029
$489$	6.19110	0.279971
$490$	6.39527	0.288909
$491$	−14.0934	−0.636026	−0.318013	−	0.948086i	$-0.603016\pi$
$491$	−14.0934	−0.636026	−0.318013	+	0.948086i	$0.603016\pi$
$492$	−7.73549	−0.348743
$493$	2.25437	0.101532
$494$	4.02006	0.180871
$495$	23.7510	1.06753
$496$	33.2465	1.49281
$497$	11.0535	0.495819
$498$	−1.14751	−0.0514211
$499$	−6.62850	−0.296732	−0.148366	−	0.988932i	$-0.547401\pi$
$499$	−6.62850	−0.296732	−0.148366	+	0.988932i	$0.547401\pi$
$500$	40.2530	1.80017
$501$	−4.67602	−0.208909
$502$	−73.4569	−3.27854
$503$	38.1438	1.70075	0.850374	−	0.526179i	$-0.176376\pi$
$503$	38.1438	1.70075	0.850374	+	0.526179i	$0.176376\pi$
$504$	17.7611	0.791140
$505$	16.2135	0.721489
$506$	−51.5748	−2.29278
$507$	−3.73339	−0.165806
$508$	−13.7156	−0.608530
$509$	25.0132	1.10869	0.554346	−	0.832287i	$-0.312969\pi$
$509$	25.0132	1.10869	0.554346	+	0.832287i	$0.312969\pi$
$510$	−2.41872	−0.107103
$511$	−12.7184	−0.562629
$512$	50.5086	2.23219
$513$	9.19600	0.406013
$514$	47.5860	2.09893
$515$	−2.99496	−0.131974
$516$	−9.53493	−0.419752
$517$	35.0099	1.53973
$518$	25.4055	1.11625
$519$	0.796681	0.0349704
$520$	4.54632	0.199369
$521$	−20.8270	−0.912448	−0.456224	−	0.889865i	$-0.650799\pi$
$521$	−20.8270	−0.912448	−0.456224	+	0.889865i	$0.650799\pi$
$522$	−12.7213	−0.556795
$523$	−29.2822	−1.28042	−0.640211	−	0.768199i	$-0.721153\pi$
$523$	−29.2822	−1.28042	−0.640211	+	0.768199i	$0.721153\pi$
$524$	−96.8744	−4.23198
$525$	0.400268	0.0174691
$526$	20.6029	0.898331
$527$	−6.58752	−0.286957
$528$	6.15211	0.267736
$529$	16.9698	0.737817
$530$	24.5468	1.06624
$531$	−3.42075	−0.148448
$532$	−23.6872	−1.02697
$533$	−1.79400	−0.0777066
$534$	−0.722233	−0.0312541
$535$	−30.7108	−1.32774
$536$	53.9422	2.32995
$537$	6.07501	0.262156
$538$	−15.3662	−0.662485
$539$	3.22310	0.138829
$540$	19.0442	0.819533
$541$	23.3158	1.00242	0.501212	−	0.865324i	$-0.332888\pi$
$541$	23.3158	1.00242	0.501212	+	0.865324i	$0.332888\pi$
$542$	10.5605	0.453613
$543$	−0.0260885	−0.00111956
$544$	5.92492	0.254029
$545$	8.07763	0.346008
$546$	−0.216204	−0.00925266
$547$	−24.3738	−1.04215	−0.521073	−	0.853512i	$-0.674468\pi$
$547$	−24.3738	−1.04215	−0.521073	+	0.853512i	$0.674468\pi$
$548$	−28.1448	−1.20229
$549$	−42.1068	−1.79708
$550$	−11.2937	−0.481565
$551$	9.26486	0.394696
$552$	−11.1320	−0.473808
$553$	−13.1112	−0.557546
$554$	−35.9055	−1.52548
$555$	7.33289	0.311264
$556$	−37.0713	−1.57218
$557$	28.2930	1.19881	0.599407	−	0.800445i	$-0.295403\pi$
$557$	28.2930	1.19881	0.599407	+	0.800445i	$0.295403\pi$
$558$	37.1729	1.57366
$559$	−2.21132	−0.0935288
$560$	−16.6811	−0.704906
$561$	−1.21899	−0.0514658
$562$	67.5777	2.85059
$563$	45.8567	1.93263	0.966315	−	0.257364i	$-0.0828538\pi$
$563$	45.8567	1.93263	0.966315	+	0.257364i	$0.0828538\pi$
$564$	13.8376	0.582670
$565$	−3.50607	−0.147502
$566$	22.7211	0.955038
$567$	8.25465	0.346663
$568$	−67.3166	−2.82454
$569$	40.2347	1.68673	0.843363	−	0.537344i	$-0.180572\pi$
$569$	40.2347	1.68673	0.843363	+	0.537344i	$0.180572\pi$
$570$	−9.94031	−0.416354
$571$	31.9257	1.33605	0.668025	−	0.744139i	$-0.267140\pi$
$571$	31.9257	1.33605	0.668025	+	0.744139i	$0.267140\pi$
$572$	4.19576	0.175434
$573$	−6.47808	−0.270626
$574$	15.3689	0.641484
$575$	8.75247	0.365003
$576$	5.07337	0.211390
$577$	5.13806	0.213900	0.106950	−	0.994264i	$-0.465891\pi$
$577$	5.13806	0.213900	0.106950	+	0.994264i	$0.465891\pi$
$578$	38.6967	1.60957
$579$	5.95855	0.247629
$580$	19.1868	0.796689
$581$	1.56809	0.0650555
$582$	0.866790	0.0359296
$583$	12.3711	0.512359
$584$	77.4556	3.20514
$585$	2.17714	0.0900138
$586$	−53.4377	−2.20749
$587$	−17.6558	−0.728734	−0.364367	−	0.931255i	$-0.618715\pi$
$587$	−17.6558	−0.728734	−0.364367	+	0.931255i	$0.618715\pi$
$588$	1.27393	0.0525359
$589$	−27.0730	−1.11552
$590$	7.50122	0.308820
$591$	−2.34188	−0.0963323
$592$	−66.2664	−2.72353
$593$	22.5350	0.925402	0.462701	−	0.886514i	$-0.346880\pi$
$593$	22.5350	0.925402	0.462701	+	0.886514i	$0.346880\pi$
$594$	13.9545	0.572562
$595$	3.30523	0.135501
$596$	53.4920	2.19112
$597$	4.00994	0.164116
$598$	−4.72762	−0.193327
$599$	21.5029	0.878585	0.439293	−	0.898344i	$-0.355229\pi$
$599$	21.5029	0.878585	0.439293	+	0.898344i	$0.355229\pi$
$600$	−2.43765	−0.0995166
$601$	6.88847	0.280986	0.140493	−	0.990082i	$-0.455131\pi$
$601$	6.88847	0.280986	0.140493	+	0.990082i	$0.455131\pi$
$602$	18.9440	0.772099
$603$	25.8319	1.05195
$604$	9.63791	0.392161
$605$	1.54549	0.0628330
$606$	4.69569	0.190749
$607$	−7.80968	−0.316985	−0.158493	−	0.987360i	$-0.550663\pi$
$607$	−7.80968	−0.316985	−0.158493	+	0.987360i	$0.550663\pi$
$608$	24.3498	0.987516
$609$	−0.498275	−0.0201911
$610$	92.3343	3.73851
$611$	3.20919	0.129830
$612$	16.8093	0.679474
$613$	−10.1103	−0.408353	−0.204176	−	0.978934i	$-0.565452\pi$
$613$	−10.1103	−0.408353	−0.204176	+	0.978934i	$0.565452\pi$
$614$	−3.32166	−0.134051
$615$	4.43598	0.178876
$616$	−19.6288	−0.790867
$617$	−30.6342	−1.23329	−0.616643	−	0.787243i	$-0.711508\pi$
$617$	−30.6342	−1.23329	−0.616643	+	0.787243i	$0.711508\pi$
$618$	−0.867390	−0.0348915
$619$	25.4695	1.02370	0.511852	−	0.859074i	$-0.328960\pi$
$619$	25.4695	1.02370	0.511852	+	0.859074i	$0.328960\pi$
$620$	−56.0660	−2.25167
$621$	−10.8146	−0.433974
$622$	12.6851	0.508625
$623$	0.986945	0.0395411
$624$	0.563935	0.0225755
$625$	−30.0055	−1.20022
$626$	−29.7935	−1.19079
$627$	−5.00973	−0.200069
$628$	13.2790	0.529892
$629$	13.1302	0.523534
$630$	−18.6512	−0.743082
$631$	−3.20776	−0.127699	−0.0638495	−	0.997960i	$-0.520338\pi$
$631$	−3.20776	−0.127699	−0.0638495	+	0.997960i	$0.520338\pi$
$632$	79.8479	3.17618
$633$	−1.46976	−0.0584176
$634$	−14.4640	−0.574439
$635$	7.86529	0.312125
$636$	4.88968	0.193888
$637$	0.295446	0.0117060
$638$	14.0590	0.556602
$639$	−32.2366	−1.27526
$640$	−34.0144	−1.34454
$641$	37.3692	1.47599	0.737997	−	0.674804i	$-0.235772\pi$
$641$	37.3692	1.47599	0.737997	+	0.674804i	$0.235772\pi$
$642$	−8.89436	−0.351033
$643$	34.5691	1.36327	0.681636	−	0.731692i	$-0.261269\pi$
$643$	34.5691	1.36327	0.681636	+	0.731692i	$0.261269\pi$
$644$	27.8564	1.09770
$645$	5.46788	0.215297
$646$	−17.7990	−0.700291
$647$	39.5573	1.55516	0.777579	−	0.628785i	$-0.216447\pi$
$647$	39.5573	1.55516	0.777579	+	0.628785i	$0.216447\pi$
$648$	−50.2712	−1.97484
$649$	3.78047	0.148397
$650$	−1.03524	−0.0406055
$651$	1.45602	0.0570658
$652$	94.3499	3.69503
$653$	47.7365	1.86807	0.934036	−	0.357178i	$-0.116261\pi$
$653$	47.7365	1.86807	0.934036	+	0.357178i	$0.116261\pi$
$654$	2.33942	0.0914785
$655$	55.5533	2.17065
$656$	−40.0874	−1.56515
$657$	37.0920	1.44710
$658$	−27.4926	−1.07177
$659$	−49.4866	−1.92772	−0.963862	−	0.266402i	$-0.914165\pi$
$659$	−49.4866	−1.92772	−0.963862	+	0.266402i	$0.914165\pi$
$660$	−10.3748	−0.403837
$661$	44.6284	1.73584	0.867922	−	0.496700i	$-0.165455\pi$
$661$	44.6284	1.73584	0.867922	+	0.496700i	$0.165455\pi$
$662$	33.8462	1.31547
$663$	−0.111739	−0.00433959
$664$	−9.54976	−0.370603
$665$	13.5836	0.526750
$666$	−74.0927	−2.87103
$667$	−10.8956	−0.421878
$668$	−71.2606	−2.75716
$669$	2.27139	0.0878169
$670$	−56.6456	−2.18841
$671$	46.5348	1.79646
$672$	−1.30956	−0.0505175
$673$	35.5597	1.37072	0.685362	−	0.728202i	$-0.259644\pi$
$673$	35.5597	1.37072	0.685362	+	0.728202i	$0.259644\pi$
$674$	12.6129	0.485829
$675$	−2.36815	−0.0911500
$676$	−56.8953	−2.18828
$677$	47.1000	1.81020	0.905101	−	0.425197i	$-0.139795\pi$
$677$	47.1000	1.81020	0.905101	+	0.425197i	$0.139795\pi$
$678$	−1.01542	−0.0389969
$679$	−1.18449	−0.0454564
$680$	−20.1290	−0.771912
$681$	1.50224	0.0575661
$682$	−41.0821	−1.57311
$683$	31.7202	1.21374	0.606870	−	0.794801i	$-0.292425\pi$
$683$	31.7202	1.21374	0.606870	+	0.794801i	$0.292425\pi$
$684$	69.0816	2.64140
$685$	16.1399	0.616673
$686$	−2.53104	−0.0966354
$687$	7.08658	0.270370
$688$	−49.4126	−1.88384
$689$	1.13400	0.0432021
$690$	11.6899	0.445027
$691$	−11.8878	−0.452233	−0.226116	−	0.974100i	$-0.572603\pi$
$691$	−11.8878	−0.452233	−0.226116	+	0.974100i	$0.572603\pi$
$692$	12.1411	0.461535
$693$	−9.39986	−0.357071
$694$	91.3290	3.46680
$695$	21.2589	0.806394
$696$	3.03452	0.115023
$697$	7.94300	0.300862
$698$	46.5002	1.76006
$699$	1.19251	0.0451050
$700$	6.09992	0.230555
$701$	33.1635	1.25257	0.626285	−	0.779594i	$-0.284575\pi$
$701$	33.1635	1.25257	0.626285	+	0.779594i	$0.284575\pi$
$702$	1.27915	0.0482783
$703$	53.9615	2.03520
$704$	−5.60688	−0.211317
$705$	−7.93530	−0.298861
$706$	67.2290	2.53020
$707$	−6.41675	−0.241327
$708$	1.49423	0.0561566
$709$	−8.84896	−0.332330	−0.166165	−	0.986098i	$-0.553138\pi$
$709$	−8.84896	−0.332330	−0.166165	+	0.986098i	$0.553138\pi$
$710$	70.6904	2.65296
$711$	38.2376	1.43402
$712$	−6.01054	−0.225255
$713$	31.8380	1.19234
$714$	0.957250	0.0358242
$715$	−2.40609	−0.0899827
$716$	92.5806	3.45990
$717$	−1.91927	−0.0716766
$718$	22.7868	0.850395
$719$	−48.6385	−1.81391	−0.906956	−	0.421226i	$-0.861600\pi$
$719$	−48.6385	−1.81391	−0.906956	+	0.421226i	$0.861600\pi$
$720$	48.6489	1.81304
$721$	1.18530	0.0441431
$722$	−25.0593	−0.932612
$723$	5.88302	0.218792
$724$	−0.397578	−0.0147759
$725$	−2.38588	−0.0886093
$726$	0.447599	0.0166120
$727$	38.1262	1.41402	0.707012	−	0.707202i	$-0.250043\pi$
$727$	38.1262	1.41402	0.707012	+	0.707202i	$0.250043\pi$
$728$	−1.79928	−0.0666858
$729$	−22.5902	−0.836674
$730$	−81.3376	−3.01044
$731$	9.79070	0.362122
$732$	18.3929	0.679820
$733$	10.4874	0.387360	0.193680	−	0.981065i	$-0.437958\pi$
$733$	10.4874	0.387360	0.193680	+	0.981065i	$0.437958\pi$
$734$	−35.0254	−1.29281
$735$	−0.730544	−0.0269465
$736$	−28.6356	−1.05552
$737$	−28.5483	−1.05159
$738$	−44.8218	−1.64991
$739$	−51.2896	−1.88672	−0.943359	−	0.331773i	$-0.892353\pi$
$739$	−51.2896	−1.88672	−0.943359	+	0.331773i	$0.892353\pi$
$740$	111.750	4.10802
$741$	−0.459219	−0.0168698
$742$	−9.71480	−0.356642
$743$	−6.44101	−0.236298	−0.118149	−	0.992996i	$-0.537696\pi$
$743$	−6.44101	−0.236298	−0.118149	+	0.992996i	$0.537696\pi$
$744$	−8.86721	−0.325088
$745$	−30.6754	−1.12386
$746$	−86.9951	−3.18512
$747$	−4.57320	−0.167325
$748$	−18.5769	−0.679239
$749$	12.1543	0.444109
$750$	−6.68534	−0.244114
$751$	23.0230	0.840120	0.420060	−	0.907496i	$-0.362009\pi$
$751$	23.0230	0.840120	0.420060	+	0.907496i	$0.362009\pi$
$752$	71.7104	2.61501
$753$	8.39112	0.305789
$754$	1.28873	0.0469327
$755$	−5.52693	−0.201146
$756$	−7.53707	−0.274121
$757$	−22.1852	−0.806333	−0.403167	−	0.915127i	$-0.632090\pi$
$757$	−22.1852	−0.806333	−0.403167	+	0.915127i	$0.632090\pi$
$758$	22.1327	0.803897
$759$	5.89149	0.213847
$760$	−82.7249	−3.00075
$761$	−36.3675	−1.31832	−0.659161	−	0.752002i	$-0.729088\pi$
$761$	−36.3675	−1.31832	−0.659161	+	0.752002i	$0.729088\pi$
$762$	2.27792	0.0825204
$763$	−3.19686	−0.115734
$764$	−98.7232	−3.57168
$765$	−9.63940	−0.348513
$766$	−38.3703	−1.38637
$767$	0.346539	0.0125128
$768$	−8.84523	−0.319175
$769$	7.87740	0.284066	0.142033	−	0.989862i	$-0.454636\pi$
$769$	7.87740	0.284066	0.142033	+	0.989862i	$0.454636\pi$
$770$	20.6126	0.742825
$771$	−5.43584	−0.195767
$772$	90.8059	3.26817
$773$	43.2792	1.55665	0.778323	−	0.627864i	$-0.216071\pi$
$773$	43.2792	1.55665	0.778323	+	0.627864i	$0.216071\pi$
$774$	−55.2483	−1.98586
$775$	6.97181	0.250435
$776$	7.21357	0.258952
$777$	−2.90211	−0.104113
$778$	−37.5291	−1.34548
$779$	32.6436	1.16958
$780$	−0.951007	−0.0340515
$781$	35.6266	1.27482
$782$	20.9318	0.748518
$783$	2.94800	0.105353
$784$	6.60184	0.235780
$785$	−7.61497	−0.271790
$786$	16.0892	0.573882
$787$	9.95463	0.354844	0.177422	−	0.984135i	$-0.443224\pi$
$787$	9.95463	0.354844	0.177422	+	0.984135i	$0.443224\pi$
$788$	−35.6894	−1.27138
$789$	−2.35351	−0.0837873
$790$	−83.8498	−2.98324
$791$	1.38759	0.0493370
$792$	57.2456	2.03413
$793$	4.26563	0.151477
$794$	−42.5742	−1.51090
$795$	−2.80402	−0.0994485
$796$	61.1099	2.16598
$797$	10.5031	0.372037	0.186019	−	0.982546i	$-0.440442\pi$
$797$	10.5031	0.372037	0.186019	+	0.982546i	$0.440442\pi$
$798$	3.93405	0.139264
$799$	−14.2088	−0.502673
$800$	−6.27055	−0.221697
$801$	−2.87833	−0.101701
$802$	45.8162	1.61783
$803$	−40.9926	−1.44660
$804$	−11.2837	−0.397946
$805$	−15.9745	−0.563026
$806$	−3.76580	−0.132645
$807$	1.75531	0.0617900
$808$	39.0783	1.37477
$809$	−4.58616	−0.161241	−0.0806204	−	0.996745i	$-0.525690\pi$
$809$	−4.58616	−0.161241	−0.0806204	+	0.996745i	$0.525690\pi$
$810$	52.7907	1.85488
$811$	31.9442	1.12171	0.560856	−	0.827913i	$-0.310472\pi$
$811$	31.9442	1.12171	0.560856	+	0.827913i	$0.310472\pi$
$812$	−7.59351	−0.266480
$813$	−1.20635	−0.0423085
$814$	81.8843	2.87004
$815$	−54.1057	−1.89524
$816$	−2.49685	−0.0874071
$817$	40.2372	1.40772
$818$	3.46910	0.121294
$819$	−0.861642	−0.0301082
$820$	67.6025	2.36078
$821$	−10.6343	−0.371139	−0.185570	−	0.982631i	$-0.559413\pi$
$821$	−10.6343	−0.371139	−0.185570	+	0.982631i	$0.559413\pi$
$822$	4.67438	0.163038
$823$	19.2072	0.669520	0.334760	−	0.942303i	$-0.391345\pi$
$823$	19.2072	0.669520	0.334760	+	0.942303i	$0.391345\pi$
$824$	−7.21856	−0.251470
$825$	1.29010	0.0449156
$826$	−2.96873	−0.103295
$827$	55.5387	1.93127	0.965635	−	0.259902i	$-0.0836902\pi$
$827$	55.5387	1.93127	0.965635	+	0.259902i	$0.0836902\pi$
$828$	−81.2406	−2.82331
$829$	28.2653	0.981693	0.490846	−	0.871246i	$-0.336688\pi$
$829$	28.2653	0.981693	0.490846	+	0.871246i	$0.336688\pi$
$830$	10.0284	0.348090
$831$	4.10156	0.142281
$832$	−0.513957	−0.0178182
$833$	−1.30810	−0.0453230
$834$	6.15692	0.213197
$835$	40.8650	1.41419
$836$	−76.3462	−2.64049
$837$	−8.61439	−0.297757
$838$	−52.7988	−1.82390
$839$	11.8970	0.410730	0.205365	−	0.978685i	$-0.434162\pi$
$839$	11.8970	0.410730	0.205365	+	0.978685i	$0.434162\pi$
$840$	4.44905	0.153507
$841$	−26.0299	−0.897584
$842$	29.8052	1.02715
$843$	−7.71952	−0.265875
$844$	−22.3985	−0.770987
$845$	32.6271	1.12240
$846$	80.1796	2.75663
$847$	−0.611653	−0.0210166
$848$	25.3396	0.870167
$849$	−2.59547	−0.0890763
$850$	4.58358	0.157215
$851$	−63.4592	−2.17535
$852$	14.0814	0.482421
$853$	−18.6623	−0.638986	−0.319493	−	0.947589i	$-0.603513\pi$
$853$	−18.6623	−0.638986	−0.319493	+	0.947589i	$0.603513\pi$
$854$	−36.5429	−1.25047
$855$	−39.6154	−1.35482
$856$	−74.0204	−2.52996
$857$	1.59377	0.0544420	0.0272210	−	0.999629i	$-0.491334\pi$
$857$	1.59377	0.0544420	0.0272210	+	0.999629i	$0.491334\pi$
$858$	−0.696845	−0.0237899
$859$	−1.00000	−0.0341196
$859$	−1.00000	−0.0341196
$860$	83.3282	2.84147
$861$	−1.75561	−0.0598311
$862$	17.9342	0.610840
$863$	12.1094	0.412210	0.206105	−	0.978530i	$-0.433921\pi$
$863$	12.1094	0.412210	0.206105	+	0.978530i	$0.433921\pi$
$864$	7.74791	0.263589
$865$	−6.96240	−0.236729
$866$	−15.7313	−0.534570
$867$	−4.42040	−0.150125
$868$	22.1891	0.753147
$869$	−42.2587	−1.43353
$870$	−3.18661	−0.108036
$871$	−2.61690	−0.0886701
$872$	19.4690	0.659304
$873$	3.45444	0.116915
$874$	86.0240	2.90980
$875$	9.13565	0.308841
$876$	−16.2023	−0.547426
$877$	−14.7202	−0.497065	−0.248532	−	0.968624i	$-0.579948\pi$
$877$	−14.7202	−0.497065	−0.248532	+	0.968624i	$0.579948\pi$
$878$	−27.7206	−0.935525
$879$	6.10429	0.205893
$880$	−53.7649	−1.81241
$881$	−11.7035	−0.394301	−0.197151	−	0.980373i	$-0.563169\pi$
$881$	−11.7035	−0.394301	−0.197151	+	0.980373i	$0.563169\pi$
$882$	7.38153	0.248549
$883$	−8.03627	−0.270442	−0.135221	−	0.990815i	$-0.543174\pi$
$883$	−8.03627	−0.270442	−0.135221	+	0.990815i	$0.543174\pi$
$884$	−1.70286	−0.0572734
$885$	−0.856878	−0.0288036
$886$	13.9625	0.469078
$887$	42.5424	1.42843	0.714217	−	0.699925i	$-0.246783\pi$
$887$	42.5424	1.42843	0.714217	+	0.699925i	$0.246783\pi$
$888$	17.6740	0.593101
$889$	−3.11282	−0.104401
$890$	6.31178	0.211571
$891$	26.6055	0.891319
$892$	34.6150	1.15900
$893$	−58.3946	−1.95410
$894$	−8.88411	−0.297129
$895$	−53.0911	−1.77464
$896$	13.4618	0.449727
$897$	0.540045	0.0180316
$898$	−56.8383	−1.89672
$899$	−8.67889	−0.289457
$900$	−17.7898	−0.592995
$901$	−5.02085	−0.167269
$902$	49.5353	1.64934
$903$	−2.16401	−0.0720136
$904$	−8.45048	−0.281059
$905$	0.227994	0.00757878
$906$	−1.60069	−0.0531795
$907$	5.90337	0.196018	0.0980091	−	0.995186i	$-0.468753\pi$
$907$	5.90337	0.196018	0.0980091	+	0.995186i	$0.468753\pi$
$908$	22.8936	0.759750
$909$	18.7139	0.620699
$910$	1.88946	0.0626350
$911$	−10.0983	−0.334571	−0.167285	−	0.985908i	$-0.553500\pi$
$911$	−10.0983	−0.334571	−0.167285	+	0.985908i	$0.553500\pi$
$912$	−10.2614	−0.339788
$913$	5.05412	0.167267
$914$	−98.8151	−3.26851
$915$	−10.5475	−0.348690
$916$	107.997	3.56831
$917$	−21.9862	−0.726048
$918$	−5.66348	−0.186923
$919$	−51.8165	−1.70927	−0.854634	−	0.519231i	$-0.826218\pi$
$919$	−51.8165	−1.70927	−0.854634	+	0.519231i	$0.826218\pi$
$920$	97.2852	3.20740
$921$	0.379440	0.0125030
$922$	−43.1783	−1.42200
$923$	3.26573	0.107493
$924$	4.10599	0.135077
$925$	−13.8961	−0.456902
$926$	−76.5786	−2.51653
$927$	−3.45683	−0.113537
$928$	7.80593	0.256242
$929$	−45.3911	−1.48923	−0.744616	−	0.667493i	$-0.767367\pi$
$929$	−45.3911	−1.48923	−0.744616	+	0.667493i	$0.767367\pi$
$930$	9.31162	0.305340
$931$	−5.37595	−0.176190
$932$	18.1734	0.595289
$933$	−1.44904	−0.0474394
$934$	−15.8962	−0.520138
$935$	10.6531	0.348393
$936$	5.24744	0.171518
$937$	43.2934	1.41433	0.707167	−	0.707047i	$-0.249973\pi$
$937$	43.2934	1.41433	0.707167	+	0.707047i	$0.249973\pi$
$938$	22.4185	0.731989
$939$	3.40337	0.111065
$940$	−120.931	−3.94433
$941$	33.2694	1.08455	0.542276	−	0.840200i	$-0.317563\pi$
$941$	33.2694	1.08455	0.542276	+	0.840200i	$0.317563\pi$
$942$	−2.20542	−0.0718566
$943$	−38.3892	−1.25012
$944$	7.74351	0.252030
$945$	4.32219	0.140601
$946$	61.0582	1.98517
$947$	58.9688	1.91623	0.958114	−	0.286388i	$-0.0924547\pi$
$947$	58.9688	1.91623	0.958114	+	0.286388i	$0.0924547\pi$
$948$	−16.7027	−0.542480
$949$	−3.75760	−0.121977
$950$	18.8373	0.611162
$951$	1.65225	0.0535778
$952$	7.96640	0.258192
$953$	−18.5706	−0.601560	−0.300780	−	0.953694i	$-0.597247\pi$
$953$	−18.5706	−0.601560	−0.300780	+	0.953694i	$0.597247\pi$
$954$	28.3323	0.917293
$955$	56.6136	1.83197
$956$	−29.2489	−0.945978
$957$	−1.60599	−0.0519143
$958$	−12.6907	−0.410017
$959$	−6.38763	−0.206267
$960$	1.27085	0.0410165
$961$	−5.63932	−0.181913
$962$	7.50595	0.242002
$963$	−35.4469	−1.14226
$964$	89.6548	2.88759
$965$	−52.0733	−1.67630
$966$	−4.62647	−0.148854
$967$	5.30714	0.170666	0.0853330	−	0.996352i	$-0.472805\pi$
$967$	5.30714	0.170666	0.0853330	+	0.996352i	$0.472805\pi$
$968$	3.72500	0.119726
$969$	2.03321	0.0653161
$970$	−7.57511	−0.243222
$971$	−22.3661	−0.717763	−0.358881	−	0.933383i	$-0.616842\pi$
$971$	−22.3661	−0.717763	−0.358881	+	0.933383i	$0.616842\pi$
$972$	33.1270	1.06255
$973$	−8.41355	−0.269726
$974$	21.3877	0.685308
$975$	0.118258	0.00378728
$976$	95.3168	3.05102
$977$	35.4689	1.13475	0.567375	−	0.823459i	$-0.307959\pi$
$977$	35.4689	1.13475	0.567375	+	0.823459i	$0.307959\pi$
$978$	−15.6699	−0.501068
$979$	3.18102	0.101666
$980$	−11.1332	−0.355637
$981$	9.32334	0.297671
$982$	35.6709	1.13830
$983$	−2.38518	−0.0760753	−0.0380377	−	0.999276i	$-0.512111\pi$
$983$	−2.38518	−0.0760753	−0.0380377	+	0.999276i	$0.512111\pi$
$984$	10.6918	0.340841
$985$	20.4663	0.652112
$986$	−5.70589	−0.181713
$987$	3.14053	0.0999642
$988$	−6.99830	−0.222646
$989$	−47.3193	−1.50467
$990$	−60.1146	−1.91057
$991$	−35.2261	−1.11899	−0.559497	−	0.828833i	$-0.689005\pi$
$991$	−35.2261	−1.11899	−0.559497	+	0.828833i	$0.689005\pi$
$992$	−22.8098	−0.724212
$993$	−3.86631	−0.122694
$994$	−27.9769	−0.887374
$995$	−35.0439	−1.11097
$996$	1.99764	0.0632976
$997$	3.91260	0.123913	0.0619567	−	0.998079i	$-0.480266\pi$
$997$	3.91260	0.123913	0.0619567	+	0.998079i	$0.480266\pi$
$998$	16.7770	0.531066
$999$	17.1701	0.543238

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.e.1.6	✓	109

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.e.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-2.53104 q^{2} +0.289125 q^{3} +4.40615 q^{4} -2.52674 q^{5} -0.731786 q^{6} +1.00000 q^{7} -6.09005 q^{8} -2.91641 q^{9} +O(q^{10})\)	\(q-2.53104 q^{2} +0.289125 q^{3} +4.40615 q^{4} -2.52674 q^{5} -0.731786 q^{6} +1.00000 q^{7} -6.09005 q^{8} -2.91641 q^{9} +6.39527 q^{10} +3.22310 q^{11} +1.27393 q^{12} +0.295446 q^{13} -2.53104 q^{14} -0.730544 q^{15} +6.60184 q^{16} -1.30810 q^{17} +7.38153 q^{18} -5.37595 q^{19} -11.1332 q^{20} +0.289125 q^{21} -8.15777 q^{22} +6.32217 q^{23} -1.76079 q^{24} +1.38441 q^{25} -0.747786 q^{26} -1.71058 q^{27} +4.40615 q^{28} -1.72339 q^{29} +1.84903 q^{30} +5.03594 q^{31} -4.52940 q^{32} +0.931878 q^{33} +3.31085 q^{34} -2.52674 q^{35} -12.8501 q^{36} -10.0376 q^{37} +13.6067 q^{38} +0.0854210 q^{39} +15.3880 q^{40} -6.07216 q^{41} -0.731786 q^{42} -7.48467 q^{43} +14.2014 q^{44} +7.36900 q^{45} -16.0016 q^{46} +10.8622 q^{47} +1.90876 q^{48} +1.00000 q^{49} -3.50399 q^{50} -0.378205 q^{51} +1.30178 q^{52} +3.83827 q^{53} +4.32955 q^{54} -8.14392 q^{55} -6.09005 q^{56} -1.55432 q^{57} +4.36196 q^{58} +1.17293 q^{59} -3.21888 q^{60} +14.4379 q^{61} -12.7461 q^{62} -2.91641 q^{63} -1.73959 q^{64} -0.746516 q^{65} -2.35862 q^{66} -8.85743 q^{67} -5.76369 q^{68} +1.82790 q^{69} +6.39527 q^{70} +11.0535 q^{71} +17.7611 q^{72} -12.7184 q^{73} +25.4055 q^{74} +0.400268 q^{75} -23.6872 q^{76} +3.22310 q^{77} -0.216204 q^{78} -13.1112 q^{79} -16.6811 q^{80} +8.25465 q^{81} +15.3689 q^{82} +1.56809 q^{83} +1.27393 q^{84} +3.30523 q^{85} +18.9440 q^{86} -0.498275 q^{87} -19.6288 q^{88} +0.986945 q^{89} -18.6512 q^{90} +0.295446 q^{91} +27.8564 q^{92} +1.45602 q^{93} -27.4926 q^{94} +13.5836 q^{95} -1.30956 q^{96} -1.18449 q^{97} -2.53104 q^{98} -9.39986 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 109 q + 19 q^{2} + 38 q^{3} + 111 q^{4} + 43 q^{5} + 14 q^{6} + 109 q^{7} + 48 q^{8} + 119 q^{9}+O(q^{10}) \) 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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