LMFDB - Embedded newform 6013.2.a.e.1.15

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			1.15
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)

$f(q)$	$=$	$q-2.09226 q^{2} +2.05769 q^{3} +2.37754 q^{4} -3.21058 q^{5} -4.30522 q^{6} +1.00000 q^{7} -0.789909 q^{8} +1.23410 q^{9} +O(q^{10})$	\(q-2.09226 q^{2} +2.05769 q^{3} +2.37754 q^{4} -3.21058 q^{5} -4.30522 q^{6} +1.00000 q^{7} -0.789909 q^{8} +1.23410 q^{9} +6.71736 q^{10} -1.05106 q^{11} +4.89224 q^{12} -6.03586 q^{13} -2.09226 q^{14} -6.60639 q^{15} -3.10239 q^{16} -0.303396 q^{17} -2.58205 q^{18} -7.88878 q^{19} -7.63328 q^{20} +2.05769 q^{21} +2.19908 q^{22} -5.99646 q^{23} -1.62539 q^{24} +5.30784 q^{25} +12.6286 q^{26} -3.63368 q^{27} +2.37754 q^{28} -5.87597 q^{29} +13.8223 q^{30} -3.70314 q^{31} +8.07081 q^{32} -2.16275 q^{33} +0.634781 q^{34} -3.21058 q^{35} +2.93412 q^{36} +0.931951 q^{37} +16.5054 q^{38} -12.4199 q^{39} +2.53607 q^{40} -2.50984 q^{41} -4.30522 q^{42} +3.08098 q^{43} -2.49893 q^{44} -3.96217 q^{45} +12.5461 q^{46} -1.55414 q^{47} -6.38376 q^{48} +1.00000 q^{49} -11.1054 q^{50} -0.624295 q^{51} -14.3505 q^{52} +0.950773 q^{53} +7.60260 q^{54} +3.37451 q^{55} -0.789909 q^{56} -16.2327 q^{57} +12.2940 q^{58} +8.70133 q^{59} -15.7070 q^{60} -1.10085 q^{61} +7.74793 q^{62} +1.23410 q^{63} -10.6814 q^{64} +19.3786 q^{65} +4.52503 q^{66} -6.34168 q^{67} -0.721335 q^{68} -12.3389 q^{69} +6.71736 q^{70} +0.621219 q^{71} -0.974825 q^{72} -2.68798 q^{73} -1.94988 q^{74} +10.9219 q^{75} -18.7559 q^{76} -1.05106 q^{77} +25.9857 q^{78} +13.4934 q^{79} +9.96047 q^{80} -11.1793 q^{81} +5.25123 q^{82} +16.1640 q^{83} +4.89224 q^{84} +0.974076 q^{85} -6.44620 q^{86} -12.0909 q^{87} +0.830239 q^{88} +10.0831 q^{89} +8.28988 q^{90} -6.03586 q^{91} -14.2568 q^{92} -7.61993 q^{93} +3.25165 q^{94} +25.3276 q^{95} +16.6072 q^{96} +11.8556 q^{97} -2.09226 q^{98} -1.29711 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.09226	−1.47945	−0.739725	−	0.672910i	$-0.765044\pi$
$2$	−2.09226	−1.47945	−0.739725	+	0.672910i	$0.765044\pi$
$3$	2.05769	1.18801	0.594005	−	0.804462i	$-0.297546\pi$
$3$	2.05769	1.18801	0.594005	+	0.804462i	$0.297546\pi$
$4$	2.37754	1.18877
$5$	−3.21058	−1.43582	−0.717908	−	0.696138i	$-0.754900\pi$
$5$	−3.21058	−1.43582	−0.717908	+	0.696138i	$0.754900\pi$
$6$	−4.30522	−1.75760
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−0.789909	−0.279275
$9$	1.23410	0.411366
$10$	6.71736	2.12422
$11$	−1.05106	−0.316906	−0.158453	−	0.987367i	$-0.550651\pi$
$11$	−1.05106	−0.316906	−0.158453	+	0.987367i	$0.550651\pi$
$12$	4.89224	1.41227
$13$	−6.03586	−1.67405	−0.837024	−	0.547167i	$-0.815706\pi$
$13$	−6.03586	−1.67405	−0.837024	+	0.547167i	$0.815706\pi$
$14$	−2.09226	−0.559179
$15$	−6.60639	−1.70576
$16$	−3.10239	−0.775597
$17$	−0.303396	−0.0735842	−0.0367921	−	0.999323i	$-0.511714\pi$
$17$	−0.303396	−0.0735842	−0.0367921	+	0.999323i	$0.511714\pi$
$18$	−2.58205	−0.608595
$19$	−7.88878	−1.80981	−0.904905	−	0.425613i	$-0.860059\pi$
$19$	−7.88878	−1.80981	−0.904905	+	0.425613i	$0.860059\pi$
$20$	−7.63328	−1.70685
$21$	2.05769	0.449025
$22$	2.19908	0.468846
$23$	−5.99646	−1.25035	−0.625175	−	0.780485i	$-0.714972\pi$
$23$	−5.99646	−1.25035	−0.625175	+	0.780485i	$0.714972\pi$
$24$	−1.62539	−0.331781
$25$	5.30784	1.06157
$26$	12.6286	2.47667
$27$	−3.63368	−0.699303
$28$	2.37754	0.449313
$29$	−5.87597	−1.09114	−0.545570	−	0.838065i	$-0.683687\pi$
$29$	−5.87597	−1.09114	−0.545570	+	0.838065i	$0.683687\pi$
$30$	13.8223	2.52359
$31$	−3.70314	−0.665104	−0.332552	−	0.943085i	$-0.607910\pi$
$31$	−3.70314	−0.665104	−0.332552	+	0.943085i	$0.607910\pi$
$32$	8.07081	1.42673
$33$	−2.16275	−0.376487
$34$	0.634781	0.108864
$35$	−3.21058	−0.542687
$36$	2.93412	0.489019
$37$	0.931951	0.153212	0.0766059	−	0.997061i	$-0.475592\pi$
$37$	0.931951	0.153212	0.0766059	+	0.997061i	$0.475592\pi$
$38$	16.5054	2.67752
$39$	−12.4199	−1.98878
$40$	2.53607	0.400987
$41$	−2.50984	−0.391971	−0.195985	−	0.980607i	$-0.562791\pi$
$41$	−2.50984	−0.391971	−0.195985	+	0.980607i	$0.562791\pi$
$42$	−4.30522	−0.664310
$43$	3.08098	0.469845	0.234923	−	0.972014i	$-0.424516\pi$
$43$	3.08098	0.469845	0.234923	+	0.972014i	$0.424516\pi$
$44$	−2.49893	−0.376728
$45$	−3.96217	−0.590646
$46$	12.5461	1.84983
$47$	−1.55414	−0.226694	−0.113347	−	0.993555i	$-0.536157\pi$
$47$	−1.55414	−0.226694	−0.113347	+	0.993555i	$0.536157\pi$
$48$	−6.38376	−0.921416
$49$	1.00000	0.142857
$50$	−11.1054	−1.57053
$51$	−0.624295	−0.0874187
$52$	−14.3505	−1.99006
$53$	0.950773	0.130599	0.0652994	−	0.997866i	$-0.479200\pi$
$53$	0.950773	0.130599	0.0652994	+	0.997866i	$0.479200\pi$
$54$	7.60260	1.03458
$55$	3.37451	0.455018
$56$	−0.789909	−0.105556
$57$	−16.2327	−2.15007
$58$	12.2940	1.61429
$59$	8.70133	1.13282	0.566408	−	0.824125i	$-0.308332\pi$
$59$	8.70133	1.13282	0.566408	+	0.824125i	$0.308332\pi$
$60$	−15.7070	−2.02776
$61$	−1.10085	−0.140949	−0.0704745	−	0.997514i	$-0.522451\pi$
$61$	−1.10085	−0.140949	−0.0704745	+	0.997514i	$0.522451\pi$
$62$	7.74793	0.983988
$63$	1.23410	0.155482
$64$	−10.6814	−1.33518
$65$	19.3786	2.40362
$66$	4.52503	0.556993
$67$	−6.34168	−0.774760	−0.387380	−	0.921920i	$-0.626620\pi$
$67$	−6.34168	−0.774760	−0.387380	+	0.921920i	$0.626620\pi$
$68$	−0.721335	−0.0874747
$69$	−12.3389	−1.48543
$70$	6.71736	0.802878
$71$	0.621219	0.0737251	0.0368625	−	0.999320i	$-0.488264\pi$
$71$	0.621219	0.0737251	0.0368625	+	0.999320i	$0.488264\pi$
$72$	−0.974825	−0.114884
$73$	−2.68798	−0.314605	−0.157302	−	0.987550i	$-0.550280\pi$
$73$	−2.68798	−0.314605	−0.157302	+	0.987550i	$0.550280\pi$
$74$	−1.94988	−0.226669
$75$	10.9219	1.26115
$76$	−18.7559	−2.15145
$77$	−1.05106	−0.119779
$78$	25.9857	2.94230
$79$	13.4934	1.51813	0.759063	−	0.651017i	$-0.225657\pi$
$79$	13.4934	1.51813	0.759063	+	0.651017i	$0.225657\pi$
$80$	9.96047	1.11361
$81$	−11.1793	−1.24214
$82$	5.25123	0.579901
$83$	16.1640	1.77423	0.887115	−	0.461549i	$-0.152706\pi$
$83$	16.1640	1.77423	0.887115	+	0.461549i	$0.152706\pi$
$84$	4.89224	0.533788
$85$	0.974076	0.105653
$86$	−6.44620	−0.695112
$87$	−12.0909	−1.29628
$88$	0.830239	0.0885038
$89$	10.0831	1.06881	0.534403	−	0.845230i	$-0.320536\pi$
$89$	10.0831	1.06881	0.534403	+	0.845230i	$0.320536\pi$
$90$	8.28988	0.873830
$91$	−6.03586	−0.632730
$92$	−14.2568	−1.48638
$93$	−7.61993	−0.790150
$94$	3.25165	0.335382
$95$	25.3276	2.59856
$96$	16.6072	1.69497
$97$	11.8556	1.20375	0.601875	−	0.798590i	$-0.294421\pi$
$97$	11.8556	1.20375	0.601875	+	0.798590i	$0.294421\pi$
$98$	−2.09226	−0.211350
$99$	−1.29711	−0.130364
$100$	12.6196	1.26196
$101$	15.1082	1.50332	0.751659	−	0.659552i	$-0.229254\pi$
$101$	15.1082	1.50332	0.751659	+	0.659552i	$0.229254\pi$
$102$	1.30618	0.129332
$103$	−12.9375	−1.27477	−0.637383	−	0.770547i	$-0.719983\pi$
$103$	−12.9375	−1.27477	−0.637383	+	0.770547i	$0.719983\pi$
$104$	4.76778	0.467519
$105$	−6.60639	−0.644718
$106$	−1.98926	−0.193214
$107$	18.0641	1.74632	0.873161	−	0.487431i	$-0.162066\pi$
$107$	18.0641	1.74632	0.873161	+	0.487431i	$0.162066\pi$
$108$	−8.63922	−0.831310
$109$	16.9133	1.62000	0.810001	−	0.586428i	$-0.199466\pi$
$109$	16.9133	1.62000	0.810001	+	0.586428i	$0.199466\pi$
$110$	−7.06033	−0.673176
$111$	1.91767	0.182017
$112$	−3.10239	−0.293148
$113$	3.86760	0.363833	0.181916	−	0.983314i	$-0.441770\pi$
$113$	3.86760	0.363833	0.181916	+	0.983314i	$0.441770\pi$
$114$	33.9630	3.18092
$115$	19.2521	1.79527
$116$	−13.9704	−1.29711
$117$	−7.44885	−0.688646
$118$	−18.2054	−1.67594
$119$	−0.303396	−0.0278122
$120$	5.21844	0.476377
$121$	−9.89528	−0.899571
$122$	2.30325	0.208527
$123$	−5.16448	−0.465665
$124$	−8.80437	−0.790656
$125$	−0.988335	−0.0883994
$126$	−2.58205	−0.230027
$127$	−20.9173	−1.85611	−0.928056	−	0.372442i	$-0.878521\pi$
$127$	−20.9173	−1.85611	−0.928056	+	0.372442i	$0.878521\pi$
$128$	6.20668	0.548598
$129$	6.33971	0.558180
$130$	−40.5451	−3.55604
$131$	7.96847	0.696209	0.348104	−	0.937456i	$-0.386826\pi$
$131$	7.96847	0.696209	0.348104	+	0.937456i	$0.386826\pi$
$132$	−5.14203	−0.447556
$133$	−7.88878	−0.684044
$134$	13.2684	1.14622
$135$	11.6662	1.00407
$136$	0.239655	0.0205502
$137$	−21.3156	−1.82111	−0.910556	−	0.413385i	$-0.864346\pi$
$137$	−21.3156	−1.82111	−0.910556	+	0.413385i	$0.864346\pi$
$138$	25.8161	2.19761
$139$	−23.1319	−1.96202	−0.981010	−	0.193955i	$-0.937868\pi$
$139$	−23.1319	−1.96202	−0.981010	+	0.193955i	$0.937868\pi$
$140$	−7.63328	−0.645130
$141$	−3.19793	−0.269315
$142$	−1.29975	−0.109073
$143$	6.34404	0.530515
$144$	−3.82865	−0.319054
$145$	18.8653	1.56668
$146$	5.62395	0.465442
$147$	2.05769	0.169716
$148$	2.21575	0.182133
$149$	−14.8882	−1.21969	−0.609844	−	0.792521i	$-0.708768\pi$
$149$	−14.8882	−1.21969	−0.609844	+	0.792521i	$0.708768\pi$
$150$	−22.8514	−1.86581
$151$	−15.0300	−1.22312	−0.611562	−	0.791197i	$-0.709459\pi$
$151$	−15.0300	−1.22312	−0.611562	+	0.791197i	$0.709459\pi$
$152$	6.23142	0.505435
$153$	−0.374420	−0.0302700
$154$	2.19908	0.177207
$155$	11.8892	0.954967
$156$	−29.5289	−2.36421
$157$	0.373102	0.0297768	0.0148884	−	0.999889i	$-0.495261\pi$
$157$	0.373102	0.0297768	0.0148884	+	0.999889i	$0.495261\pi$
$158$	−28.2317	−2.24599
$159$	1.95640	0.155152
$160$	−25.9120	−2.04852
$161$	−5.99646	−0.472588
$162$	23.3900	1.83769
$163$	12.0449	0.943426	0.471713	−	0.881752i	$-0.343636\pi$
$163$	12.0449	0.943426	0.471713	+	0.881752i	$0.343636\pi$
$164$	−5.96724	−0.465963
$165$	6.94369	0.540566
$166$	−33.8192	−2.62488
$167$	−0.413096	−0.0319663	−0.0159832	−	0.999872i	$-0.505088\pi$
$167$	−0.413096	−0.0319663	−0.0159832	+	0.999872i	$0.505088\pi$
$168$	−1.62539	−0.125401
$169$	23.4316	1.80243
$170$	−2.03802	−0.156309
$171$	−9.73553	−0.744495
$172$	7.32515	0.558538
$173$	16.6210	1.26367	0.631834	−	0.775104i	$-0.282303\pi$
$173$	16.6210	1.26367	0.631834	+	0.775104i	$0.282303\pi$
$174$	25.2974	1.91779
$175$	5.30784	0.401235
$176$	3.26079	0.245791
$177$	17.9047	1.34580
$178$	−21.0964	−1.58125
$179$	−7.34138	−0.548721	−0.274360	−	0.961627i	$-0.588466\pi$
$179$	−7.34138	−0.548721	−0.274360	+	0.961627i	$0.588466\pi$
$180$	−9.42022	−0.702142
$181$	−6.93257	−0.515294	−0.257647	−	0.966239i	$-0.582947\pi$
$181$	−6.93257	−0.515294	−0.257647	+	0.966239i	$0.582947\pi$
$182$	12.6286	0.936092
$183$	−2.26520	−0.167449
$184$	4.73666	0.349191
$185$	−2.99210	−0.219984
$186$	15.9429	1.16899
$187$	0.318886	0.0233193
$188$	−3.69502	−0.269487
$189$	−3.63368	−0.264312
$190$	−52.9918	−3.84443
$191$	12.2337	0.885196	0.442598	−	0.896720i	$-0.354057\pi$
$191$	12.2337	0.885196	0.442598	+	0.896720i	$0.354057\pi$
$192$	−21.9791	−1.58620
$193$	7.51507	0.540947	0.270473	−	0.962727i	$-0.412820\pi$
$193$	7.51507	0.540947	0.270473	+	0.962727i	$0.412820\pi$
$194$	−24.8049	−1.78089
$195$	39.8753	2.85553
$196$	2.37754	0.169824
$197$	−20.8935	−1.48860	−0.744300	−	0.667846i	$-0.767217\pi$
$197$	−20.8935	−1.48860	−0.744300	+	0.667846i	$0.767217\pi$
$198$	2.71388	0.192867
$199$	22.3430	1.58386	0.791928	−	0.610615i	$-0.209078\pi$
$199$	22.3430	1.58386	0.791928	+	0.610615i	$0.209078\pi$
$200$	−4.19271	−0.296469
$201$	−13.0492	−0.920422
$202$	−31.6102	−2.22408
$203$	−5.87597	−0.412412
$204$	−1.48428	−0.103921
$205$	8.05804	0.562798
$206$	27.0685	1.88595
$207$	−7.40022	−0.514351
$208$	18.7256	1.29839
$209$	8.29156	0.573539
$210$	13.8223	0.953827
$211$	−2.30648	−0.158784	−0.0793922	−	0.996843i	$-0.525298\pi$
$211$	−2.30648	−0.158784	−0.0793922	+	0.996843i	$0.525298\pi$
$212$	2.26050	0.155252
$213$	1.27828	0.0875861
$214$	−37.7947	−2.58360
$215$	−9.89174	−0.674611
$216$	2.87028	0.195298
$217$	−3.70314	−0.251386
$218$	−35.3870	−2.39671
$219$	−5.53104	−0.373753
$220$	8.02302	0.540912
$221$	1.83125	0.123183
$222$	−4.01225	−0.269285
$223$	−2.23474	−0.149649	−0.0748246	−	0.997197i	$-0.523840\pi$
$223$	−2.23474	−0.149649	−0.0748246	+	0.997197i	$0.523840\pi$
$224$	8.07081	0.539253
$225$	6.55039	0.436693
$226$	−8.09200	−0.538272
$227$	18.7056	1.24153	0.620767	−	0.783995i	$-0.286821\pi$
$227$	18.7056	1.24153	0.620767	+	0.783995i	$0.286821\pi$
$228$	−38.5939	−2.55594
$229$	−4.34230	−0.286947	−0.143474	−	0.989654i	$-0.545827\pi$
$229$	−4.34230	−0.286947	−0.143474	+	0.989654i	$0.545827\pi$
$230$	−40.2804	−2.65601
$231$	−2.16275	−0.142299
$232$	4.64148	0.304728
$233$	−5.59457	−0.366512	−0.183256	−	0.983065i	$-0.558664\pi$
$233$	−5.59457	−0.366512	−0.183256	+	0.983065i	$0.558664\pi$
$234$	15.5849	1.01882
$235$	4.98968	0.325491
$236$	20.6878	1.34666
$237$	27.7653	1.80355
$238$	0.634781	0.0411468
$239$	6.59741	0.426751	0.213375	−	0.976970i	$-0.431554\pi$
$239$	6.59741	0.426751	0.213375	+	0.976970i	$0.431554\pi$
$240$	20.4956	1.32298
$241$	−5.67322	−0.365444	−0.182722	−	0.983165i	$-0.558491\pi$
$241$	−5.67322	−0.365444	−0.182722	+	0.983165i	$0.558491\pi$
$242$	20.7035	1.33087
$243$	−12.1025	−0.776376
$244$	−2.61730	−0.167556
$245$	−3.21058	−0.205117
$246$	10.8054	0.688928
$247$	47.6156	3.02971
$248$	2.92515	0.185747
$249$	33.2605	2.10780
$250$	2.06785	0.130782
$251$	−6.54340	−0.413016	−0.206508	−	0.978445i	$-0.566210\pi$
$251$	−6.54340	−0.413016	−0.206508	+	0.978445i	$0.566210\pi$
$252$	2.93412	0.184832
$253$	6.30263	0.396243
$254$	43.7644	2.74602
$255$	2.00435	0.125517
$256$	8.37689	0.523556
$257$	5.99910	0.374213	0.187107	−	0.982340i	$-0.440089\pi$
$257$	5.99910	0.374213	0.187107	+	0.982340i	$0.440089\pi$
$258$	−13.2643	−0.825800
$259$	0.931951	0.0579086
$260$	46.0735	2.85735
$261$	−7.25152	−0.448858
$262$	−16.6721	−1.03001
$263$	−31.3468	−1.93293	−0.966463	−	0.256804i	$-0.917330\pi$
$263$	−31.3468	−1.93293	−0.966463	+	0.256804i	$0.917330\pi$
$264$	1.70838	0.105143
$265$	−3.05253	−0.187516
$266$	16.5054	1.01201
$267$	20.7479	1.26975
$268$	−15.0776	−0.921011
$269$	−0.857537	−0.0522850	−0.0261425	−	0.999658i	$-0.508322\pi$
$269$	−0.857537	−0.0522850	−0.0261425	+	0.999658i	$0.508322\pi$
$270$	−24.4088	−1.48547
$271$	14.0768	0.855102	0.427551	−	0.903991i	$-0.359376\pi$
$271$	14.0768	0.855102	0.427551	+	0.903991i	$0.359376\pi$
$272$	0.941250	0.0570717
$273$	−12.4199	−0.751689
$274$	44.5977	2.69424
$275$	−5.57884	−0.336417
$276$	−29.3362	−1.76583
$277$	−20.6830	−1.24272	−0.621362	−	0.783524i	$-0.713420\pi$
$277$	−20.6830	−1.24272	−0.621362	+	0.783524i	$0.713420\pi$
$278$	48.3978	2.90271
$279$	−4.57004	−0.273601
$280$	2.53607	0.151559
$281$	−17.6810	−1.05476	−0.527379	−	0.849630i	$-0.676825\pi$
$281$	−17.6810	−1.05476	−0.527379	+	0.849630i	$0.676825\pi$
$282$	6.69090	0.398437
$283$	26.8893	1.59841	0.799203	−	0.601062i	$-0.205255\pi$
$283$	26.8893	1.59841	0.799203	+	0.601062i	$0.205255\pi$
$284$	1.47697	0.0876421
$285$	52.1164	3.08711
$286$	−13.2734	−0.784870
$287$	−2.50984	−0.148151
$288$	9.96017	0.586908
$289$	−16.9080	−0.994585
$290$	−39.4710	−2.31782
$291$	24.3951	1.43007
$292$	−6.39079	−0.373993
$293$	−28.7899	−1.68193	−0.840963	−	0.541093i	$-0.818011\pi$
$293$	−28.7899	−1.68193	−0.840963	+	0.541093i	$0.818011\pi$
$294$	−4.30522	−0.251086
$295$	−27.9363	−1.62652
$296$	−0.736156	−0.0427882
$297$	3.81921	0.221613
$298$	31.1499	1.80447
$299$	36.1938	2.09314
$300$	25.9672	1.49922
$301$	3.08098	0.177585
$302$	31.4466	1.80955
$303$	31.0880	1.78596
$304$	24.4741	1.40368
$305$	3.53436	0.202377
$306$	0.783382	0.0447830
$307$	−1.61826	−0.0923587	−0.0461794	−	0.998933i	$-0.514705\pi$
$307$	−1.61826	−0.0923587	−0.0461794	+	0.998933i	$0.514705\pi$
$308$	−2.49893	−0.142390
$309$	−26.6213	−1.51443
$310$	−24.8754	−1.41283
$311$	15.3868	0.872505	0.436252	−	0.899824i	$-0.356306\pi$
$311$	15.3868	0.872505	0.436252	+	0.899824i	$0.356306\pi$
$312$	9.81062	0.555417
$313$	−32.4562	−1.83453	−0.917266	−	0.398275i	$-0.869609\pi$
$313$	−32.4562	−1.83453	−0.917266	+	0.398275i	$0.869609\pi$
$314$	−0.780625	−0.0440532
$315$	−3.96217	−0.223243
$316$	32.0811	1.80470
$317$	4.54123	0.255061	0.127530	−	0.991835i	$-0.459295\pi$
$317$	4.54123	0.255061	0.127530	+	0.991835i	$0.459295\pi$
$318$	−4.09329	−0.229540
$319$	6.17598	0.345789
$320$	34.2936	1.91707
$321$	37.1704	2.07465
$322$	12.5461	0.699169
$323$	2.39342	0.133174
$324$	−26.5792	−1.47662
$325$	−32.0374	−1.77711
$326$	−25.2009	−1.39575
$327$	34.8024	1.92458
$328$	1.98254	0.109468
$329$	−1.55414	−0.0856823
$330$	−14.5280	−0.799740
$331$	8.81519	0.484527	0.242263	−	0.970211i	$-0.422110\pi$
$331$	8.81519	0.484527	0.242263	+	0.970211i	$0.422110\pi$
$332$	38.4305	2.10915
$333$	1.15012	0.0630261
$334$	0.864302	0.0472925
$335$	20.3605	1.11241
$336$	−6.38376	−0.348262
$337$	−11.0261	−0.600628	−0.300314	−	0.953840i	$-0.597091\pi$
$337$	−11.0261	−0.600628	−0.300314	+	0.953840i	$0.597091\pi$
$338$	−49.0250	−2.66661
$339$	7.95832	0.432237
$340$	2.31590	0.125598
$341$	3.89222	0.210775
$342$	20.3692	1.10144
$343$	1.00000	0.0539949
$344$	−2.43369	−0.131216
$345$	39.6150	2.13280
$346$	−34.7753	−1.86953
$347$	13.6991	0.735408	0.367704	−	0.929943i	$-0.380144\pi$
$347$	13.6991	0.735408	0.367704	+	0.929943i	$0.380144\pi$
$348$	−28.7467	−1.54098
$349$	−16.5436	−0.885561	−0.442780	−	0.896630i	$-0.646008\pi$
$349$	−16.5436	−0.885561	−0.442780	+	0.896630i	$0.646008\pi$
$350$	−11.1054	−0.593606
$351$	21.9324	1.17067
$352$	−8.48288	−0.452139
$353$	21.8507	1.16299	0.581497	−	0.813548i	$-0.302467\pi$
$353$	21.8507	1.16299	0.581497	+	0.813548i	$0.302467\pi$
$354$	−37.4612	−1.99104
$355$	−1.99447	−0.105856
$356$	23.9730	1.27057
$357$	−0.624295	−0.0330412
$358$	15.3601	0.811805
$359$	23.4410	1.23717	0.618584	−	0.785719i	$-0.287707\pi$
$359$	23.4410	1.23717	0.618584	+	0.785719i	$0.287707\pi$
$360$	3.12975	0.164953
$361$	43.2329	2.27542
$362$	14.5047	0.762351
$363$	−20.3614	−1.06870
$364$	−14.3505	−0.752171
$365$	8.62999	0.451715
$366$	4.73939	0.247732
$367$	−16.5785	−0.865391	−0.432695	−	0.901540i	$-0.642437\pi$
$367$	−16.5785	−0.865391	−0.432695	+	0.901540i	$0.642437\pi$
$368$	18.6033	0.969766
$369$	−3.09739	−0.161243
$370$	6.26025	0.325455
$371$	0.950773	0.0493617
$372$	−18.1167	−0.939306
$373$	−19.3598	−1.00241	−0.501207	−	0.865327i	$-0.667111\pi$
$373$	−19.3598	−1.00241	−0.501207	+	0.865327i	$0.667111\pi$
$374$	−0.667192	−0.0344997
$375$	−2.03369	−0.105019
$376$	1.22762	0.0633099
$377$	35.4666	1.82662
$378$	7.60260	0.391035
$379$	−27.8640	−1.43128	−0.715638	−	0.698471i	$-0.753864\pi$
$379$	−27.8640	−1.43128	−0.715638	+	0.698471i	$0.753864\pi$
$380$	60.2173	3.08908
$381$	−43.0414	−2.20508
$382$	−25.5960	−1.30960
$383$	−18.0382	−0.921707	−0.460853	−	0.887476i	$-0.652457\pi$
$383$	−18.0382	−0.921707	−0.460853	+	0.887476i	$0.652457\pi$
$384$	12.7714	0.651740
$385$	3.37451	0.171981
$386$	−15.7235	−0.800303
$387$	3.80223	0.193278
$388$	28.1871	1.43098
$389$	−2.27990	−0.115596	−0.0577978	−	0.998328i	$-0.518408\pi$
$389$	−2.27990	−0.115596	−0.0577978	+	0.998328i	$0.518408\pi$
$390$	−83.4293	−4.22461
$391$	1.81930	0.0920060
$392$	−0.789909	−0.0398964
$393$	16.3967	0.827102
$394$	43.7145	2.20231
$395$	−43.3217	−2.17975
$396$	−3.08392	−0.154973
$397$	10.6924	0.536637	0.268319	−	0.963330i	$-0.413532\pi$
$397$	10.6924	0.536637	0.268319	+	0.963330i	$0.413532\pi$
$398$	−46.7474	−2.34323
$399$	−16.2327	−0.812651
$400$	−16.4670	−0.823348
$401$	−18.5628	−0.926984	−0.463492	−	0.886101i	$-0.653404\pi$
$401$	−18.5628	−0.926984	−0.463492	+	0.886101i	$0.653404\pi$
$402$	27.3023	1.36172
$403$	22.3517	1.11342
$404$	35.9203	1.78710
$405$	35.8920	1.78349
$406$	12.2940	0.610143
$407$	−0.979534	−0.0485537
$408$	0.493136	0.0244139
$409$	4.60656	0.227780	0.113890	−	0.993493i	$-0.463669\pi$
$409$	4.60656	0.227780	0.113890	+	0.993493i	$0.463669\pi$
$410$	−16.8595	−0.832631
$411$	−43.8609	−2.16350
$412$	−30.7593	−1.51540
$413$	8.70133	0.428165
$414$	15.4832	0.760956
$415$	−51.8959	−2.54747
$416$	−48.7143	−2.38841
$417$	−47.5983	−2.33090
$418$	−17.3481	−0.848522
$419$	34.0273	1.66234	0.831172	−	0.556016i	$-0.187671\pi$
$419$	34.0273	1.66234	0.831172	+	0.556016i	$0.187671\pi$
$420$	−15.7070	−0.766421
$421$	30.7029	1.49637	0.748185	−	0.663490i	$-0.230926\pi$
$421$	30.7029	1.49637	0.748185	+	0.663490i	$0.230926\pi$
$422$	4.82574	0.234913
$423$	−1.91796	−0.0932542
$424$	−0.751024	−0.0364729
$425$	−1.61037	−0.0781146
$426$	−2.67448	−0.129579
$427$	−1.10085	−0.0532737
$428$	42.9481	2.07598
$429$	13.0541	0.630257
$430$	20.6961	0.998053
$431$	−3.80752	−0.183402	−0.0917008	−	0.995787i	$-0.529230\pi$
$431$	−3.80752	−0.183402	−0.0917008	+	0.995787i	$0.529230\pi$
$432$	11.2731	0.542377
$433$	−14.1584	−0.680407	−0.340203	−	0.940352i	$-0.610496\pi$
$433$	−14.1584	−0.680407	−0.340203	+	0.940352i	$0.610496\pi$
$434$	7.74793	0.371913
$435$	38.8190	1.86123
$436$	40.2121	1.92581
$437$	47.3048	2.26290
$438$	11.5724	0.552949
$439$	−23.6054	−1.12662	−0.563312	−	0.826244i	$-0.690473\pi$
$439$	−23.6054	−1.12662	−0.563312	+	0.826244i	$0.690473\pi$
$440$	−2.66555	−0.127075
$441$	1.23410	0.0587666
$442$	−3.83145	−0.182244
$443$	3.43824	0.163356	0.0816778	−	0.996659i	$-0.473972\pi$
$443$	3.43824	0.163356	0.0816778	+	0.996659i	$0.473972\pi$
$444$	4.55933	0.216376
$445$	−32.3726	−1.53461
$446$	4.67565	0.221398
$447$	−30.6353	−1.44900
$448$	−10.6814	−0.504650
$449$	−18.8171	−0.888036	−0.444018	−	0.896018i	$-0.646447\pi$
$449$	−18.8171	−0.888036	−0.444018	+	0.896018i	$0.646447\pi$
$450$	−13.7051	−0.646065
$451$	2.63798	0.124218
$452$	9.19536	0.432513
$453$	−30.9271	−1.45308
$454$	−39.1369	−1.83678
$455$	19.3786	0.908484
$456$	12.8223	0.600461
$457$	18.9213	0.885100	0.442550	−	0.896744i	$-0.354074\pi$
$457$	18.9213	0.885100	0.442550	+	0.896744i	$0.354074\pi$
$458$	9.08521	0.424524
$459$	1.10244	0.0514576
$460$	45.7727	2.13416
$461$	0.871546	0.0405920	0.0202960	−	0.999794i	$-0.493539\pi$
$461$	0.871546	0.0405920	0.0202960	+	0.999794i	$0.493539\pi$
$462$	4.52503	0.210524
$463$	−3.55195	−0.165073	−0.0825365	−	0.996588i	$-0.526302\pi$
$463$	−3.55195	−0.165073	−0.0825365	+	0.996588i	$0.526302\pi$
$464$	18.2295	0.846285
$465$	24.4644	1.13451
$466$	11.7053	0.542236
$467$	−0.750411	−0.0347249	−0.0173624	−	0.999849i	$-0.505527\pi$
$467$	−0.750411	−0.0347249	−0.0173624	+	0.999849i	$0.505527\pi$
$468$	−17.7099	−0.818641
$469$	−6.34168	−0.292832
$470$	−10.4397	−0.481547
$471$	0.767729	0.0353751
$472$	−6.87326	−0.316367
$473$	−3.23829	−0.148897
$474$	−58.0921	−2.66826
$475$	−41.8724	−1.92124
$476$	−0.721335	−0.0330623
$477$	1.17335	0.0537239
$478$	−13.8035	−0.631356
$479$	−10.5208	−0.480707	−0.240354	−	0.970685i	$-0.577263\pi$
$479$	−10.5208	−0.480707	−0.240354	+	0.970685i	$0.577263\pi$
$480$	−53.3189	−2.43366
$481$	−5.62513	−0.256484
$482$	11.8698	0.540656
$483$	−12.3389	−0.561438
$484$	−23.5264	−1.06938
$485$	−38.0633	−1.72836
$486$	25.3215	1.14861
$487$	−36.4341	−1.65098	−0.825492	−	0.564413i	$-0.809103\pi$
$487$	−36.4341	−1.65098	−0.825492	+	0.564413i	$0.809103\pi$
$488$	0.869568	0.0393635
$489$	24.7846	1.12080
$490$	6.71736	0.303460
$491$	−11.4294	−0.515801	−0.257901	−	0.966171i	$-0.583031\pi$
$491$	−11.4294	−0.515801	−0.257901	+	0.966171i	$0.583031\pi$
$492$	−12.2787	−0.553568
$493$	1.78274	0.0802907
$494$	−99.6241	−4.48230
$495$	4.16447	0.187179
$496$	11.4886	0.515853
$497$	0.621219	0.0278655
$498$	−69.5896	−3.11838
$499$	−36.1046	−1.61626	−0.808131	−	0.589003i	$-0.799521\pi$
$499$	−36.1046	−1.61626	−0.808131	+	0.589003i	$0.799521\pi$
$500$	−2.34981	−0.105087
$501$	−0.850024	−0.0379763
$502$	13.6905	0.611036
$503$	11.3325	0.505289	0.252645	−	0.967559i	$-0.418700\pi$
$503$	11.3325	0.505289	0.252645	+	0.967559i	$0.418700\pi$
$504$	−0.974825	−0.0434221
$505$	−48.5060	−2.15849
$506$	−13.1867	−0.586221
$507$	48.2151	2.14131
$508$	−49.7317	−2.20649
$509$	32.2522	1.42955	0.714777	−	0.699353i	$-0.246528\pi$
$509$	32.2522	1.42955	0.714777	+	0.699353i	$0.246528\pi$
$510$	−4.19361	−0.185696
$511$	−2.68798	−0.118909
$512$	−29.9400	−1.32317
$513$	28.6653	1.26561
$514$	−12.5517	−0.553630
$515$	41.5368	1.83033
$516$	15.0729	0.663548
$517$	1.63349	0.0718406
$518$	−1.94988	−0.0856728
$519$	34.2008	1.50125
$520$	−15.3073	−0.671272
$521$	28.4147	1.24487	0.622436	−	0.782671i	$-0.286143\pi$
$521$	28.4147	1.24487	0.622436	+	0.782671i	$0.286143\pi$
$522$	15.1721	0.664063
$523$	12.2047	0.533672	0.266836	−	0.963742i	$-0.414022\pi$
$523$	12.2047	0.533672	0.266836	+	0.963742i	$0.414022\pi$
$524$	18.9454	0.827632
$525$	10.9219	0.476671
$526$	65.5856	2.85967
$527$	1.12352	0.0489412
$528$	6.70969	0.292002
$529$	12.9576	0.563373
$530$	6.38669	0.277420
$531$	10.7383	0.466002
$532$	−18.7559	−0.813171
$533$	15.1490	0.656178
$534$	−43.4100	−1.87853
$535$	−57.9963	−2.50740
$536$	5.00935	0.216371
$537$	−15.1063	−0.651885
$538$	1.79419	0.0773530
$539$	−1.05106	−0.0452722
$540$	27.7369	1.19361
$541$	−21.1480	−0.909225	−0.454612	−	0.890689i	$-0.650222\pi$
$541$	−21.1480	−0.909225	−0.454612	+	0.890689i	$0.650222\pi$
$542$	−29.4522	−1.26508
$543$	−14.2651	−0.612174
$544$	−2.44865	−0.104985
$545$	−54.3016	−2.32603
$546$	25.9857	1.11209
$547$	−22.0675	−0.943540	−0.471770	−	0.881722i	$-0.656385\pi$
$547$	−22.0675	−0.943540	−0.471770	+	0.881722i	$0.656385\pi$
$548$	−50.6786	−2.16488
$549$	−1.35855	−0.0579816
$550$	11.6724	0.497711
$551$	46.3543	1.97476
$552$	9.74659	0.414842
$553$	13.4934	0.573798
$554$	43.2742	1.83855
$555$	−6.15683	−0.261343
$556$	−54.9970	−2.33239
$557$	8.63053	0.365687	0.182844	−	0.983142i	$-0.441470\pi$
$557$	8.63053	0.365687	0.182844	+	0.983142i	$0.441470\pi$
$558$	9.56170	0.404779
$559$	−18.5964	−0.786543
$560$	9.96047	0.420906
$561$	0.656170	0.0277035
$562$	36.9932	1.56046
$563$	−35.5158	−1.49681	−0.748406	−	0.663241i	$-0.769180\pi$
$563$	−35.5158	−1.49681	−0.748406	+	0.663241i	$0.769180\pi$
$564$	−7.60321	−0.320153
$565$	−12.4172	−0.522397
$566$	−56.2594	−2.36476
$567$	−11.1793	−0.469486
$568$	−0.490706	−0.0205896
$569$	12.4619	0.522429	0.261214	−	0.965281i	$-0.415877\pi$
$569$	12.4619	0.522429	0.261214	+	0.965281i	$0.415877\pi$
$570$	−109.041	−4.56722
$571$	−31.1268	−1.30262	−0.651309	−	0.758813i	$-0.725780\pi$
$571$	−31.1268	−1.30262	−0.651309	+	0.758813i	$0.725780\pi$
$572$	15.0832	0.630660
$573$	25.1731	1.05162
$574$	5.25123	0.219182
$575$	−31.8282	−1.32733
$576$	−13.1819	−0.549247
$577$	20.2224	0.841868	0.420934	−	0.907091i	$-0.361702\pi$
$577$	20.2224	0.841868	0.420934	+	0.907091i	$0.361702\pi$
$578$	35.3758	1.47144
$579$	15.4637	0.642650
$580$	44.8530	1.86242
$581$	16.1640	0.670596
$582$	−51.0408	−2.11571
$583$	−0.999317	−0.0413875
$584$	2.12326	0.0878612
$585$	23.9151	0.988769
$586$	60.2359	2.48832
$587$	26.1542	1.07950	0.539749	−	0.841826i	$-0.318519\pi$
$587$	26.1542	1.07950	0.539749	+	0.841826i	$0.318519\pi$
$588$	4.89224	0.201753
$589$	29.2133	1.20371
$590$	58.4500	2.40635
$591$	−42.9924	−1.76847
$592$	−2.89127	−0.118831
$593$	24.5242	1.00709	0.503543	−	0.863970i	$-0.332029\pi$
$593$	24.5242	1.00709	0.503543	+	0.863970i	$0.332029\pi$
$594$	−7.99077	−0.327865
$595$	0.974076	0.0399332
$596$	−35.3973	−1.44993
$597$	45.9751	1.88164
$598$	−75.7268	−3.09670
$599$	−37.9591	−1.55096	−0.775482	−	0.631369i	$-0.782493\pi$
$599$	−37.9591	−1.55096	−0.775482	+	0.631369i	$0.782493\pi$
$600$	−8.62730	−0.352208
$601$	42.4948	1.73340	0.866699	−	0.498831i	$-0.166237\pi$
$601$	42.4948	1.73340	0.866699	+	0.498831i	$0.166237\pi$
$602$	−6.44620	−0.262728
$603$	−7.82626	−0.318710
$604$	−35.7344	−1.45401
$605$	31.7696	1.29162
$606$	−65.0440	−2.64223
$607$	−23.3747	−0.948749	−0.474375	−	0.880323i	$-0.657326\pi$
$607$	−23.3747	−0.948749	−0.474375	+	0.880323i	$0.657326\pi$
$608$	−63.6688	−2.58211
$609$	−12.0909	−0.489950
$610$	−7.39478	−0.299406
$611$	9.38055	0.379496
$612$	−0.890198	−0.0359841
$613$	36.4687	1.47296	0.736478	−	0.676461i	$-0.236487\pi$
$613$	36.4687	1.47296	0.736478	+	0.676461i	$0.236487\pi$
$614$	3.38581	0.136640
$615$	16.5810	0.668609
$616$	0.830239	0.0334513
$617$	3.98057	0.160252	0.0801258	−	0.996785i	$-0.474468\pi$
$617$	3.98057	0.160252	0.0801258	+	0.996785i	$0.474468\pi$
$618$	55.6986	2.24053
$619$	−20.5223	−0.824863	−0.412431	−	0.910989i	$-0.635320\pi$
$619$	−20.5223	−0.824863	−0.412431	+	0.910989i	$0.635320\pi$
$620$	28.2672	1.13524
$621$	21.7892	0.874372
$622$	−32.1931	−1.29083
$623$	10.0831	0.403971
$624$	38.5315	1.54249
$625$	−23.3661	−0.934642
$626$	67.9067	2.71410
$627$	17.0615	0.681370
$628$	0.887064	0.0353977
$629$	−0.282750	−0.0112740
$630$	8.28988	0.330277
$631$	12.8376	0.511057	0.255528	−	0.966802i	$-0.417751\pi$
$631$	12.8376	0.511057	0.255528	+	0.966802i	$0.417751\pi$
$632$	−10.6586	−0.423975
$633$	−4.74602	−0.188637
$634$	−9.50141	−0.377349
$635$	67.1567	2.66503
$636$	4.65141	0.184441
$637$	−6.03586	−0.239150
$638$	−12.9217	−0.511577
$639$	0.766645	0.0303280
$640$	−19.9271	−0.787686
$641$	−10.9318	−0.431778	−0.215889	−	0.976418i	$-0.569265\pi$
$641$	−10.9318	−0.431778	−0.215889	+	0.976418i	$0.569265\pi$
$642$	−77.7700	−3.06934
$643$	50.0723	1.97466	0.987330	−	0.158683i	$-0.0507249\pi$
$643$	50.0723	1.97466	0.987330	+	0.158683i	$0.0507249\pi$
$644$	−14.2568	−0.561798
$645$	−20.3542	−0.801444
$646$	−5.00765	−0.197023
$647$	−15.4963	−0.609222	−0.304611	−	0.952477i	$-0.598526\pi$
$647$	−15.4963	−0.609222	−0.304611	+	0.952477i	$0.598526\pi$
$648$	8.83062	0.346900
$649$	−9.14560	−0.358996
$650$	67.0304	2.62915
$651$	−7.61993	−0.298649
$652$	28.6371	1.12152
$653$	−40.2282	−1.57425	−0.787126	−	0.616792i	$-0.788432\pi$
$653$	−40.2282	−1.57425	−0.787126	+	0.616792i	$0.788432\pi$
$654$	−72.8156	−2.84732
$655$	−25.5834	−0.999627
$656$	7.78649	0.304011
$657$	−3.31724	−0.129418
$658$	3.25165	0.126763
$659$	−2.38576	−0.0929360	−0.0464680	−	0.998920i	$-0.514797\pi$
$659$	−2.38576	−0.0929360	−0.0464680	+	0.998920i	$0.514797\pi$
$660$	16.5089	0.642608
$661$	2.24446	0.0872993	0.0436497	−	0.999047i	$-0.486101\pi$
$661$	2.24446	0.0872993	0.0436497	+	0.999047i	$0.486101\pi$
$662$	−18.4436	−0.716833
$663$	3.76816	0.146343
$664$	−12.7681	−0.495498
$665$	25.3276	0.982162
$666$	−2.40634	−0.0932439
$667$	35.2350	1.36431
$668$	−0.982151	−0.0380006
$669$	−4.59840	−0.177785
$670$	−42.5994	−1.64576
$671$	1.15705	0.0446675
$672$	16.6072	0.640638
$673$	−0.310404	−0.0119652	−0.00598260	−	0.999982i	$-0.501904\pi$
$673$	−0.310404	−0.0119652	−0.00598260	+	0.999982i	$0.501904\pi$
$674$	23.0693	0.888598
$675$	−19.2870	−0.742357
$676$	55.7096	2.14268
$677$	−8.32076	−0.319793	−0.159896	−	0.987134i	$-0.551116\pi$
$677$	−8.32076	−0.319793	−0.159896	+	0.987134i	$0.551116\pi$
$678$	−16.6509	−0.639472
$679$	11.8556	0.454975
$680$	−0.769431	−0.0295063
$681$	38.4903	1.47495
$682$	−8.14352	−0.311831
$683$	−1.41649	−0.0542005	−0.0271003	−	0.999633i	$-0.508627\pi$
$683$	−1.41649	−0.0542005	−0.0271003	+	0.999633i	$0.508627\pi$
$684$	−23.1466	−0.885033
$685$	68.4354	2.61478
$686$	−2.09226	−0.0798827
$687$	−8.93512	−0.340896
$688$	−9.55839	−0.364410
$689$	−5.73873	−0.218628
$690$	−82.8847	−3.15537
$691$	14.6754	0.558279	0.279139	−	0.960251i	$-0.409951\pi$
$691$	14.6754	0.558279	0.279139	+	0.960251i	$0.409951\pi$
$692$	39.5170	1.50221
$693$	−1.29711	−0.0492730
$694$	−28.6621	−1.08800
$695$	74.2668	2.81710
$696$	9.55074	0.362020
$697$	0.761474	0.0288429
$698$	34.6135	1.31014
$699$	−11.5119	−0.435420
$700$	12.6196	0.476976
$701$	38.0423	1.43684	0.718418	−	0.695612i	$-0.244867\pi$
$701$	38.0423	1.43684	0.718418	+	0.695612i	$0.244867\pi$
$702$	−45.8882	−1.73194
$703$	−7.35196	−0.277284
$704$	11.2268	0.423126
$705$	10.2672	0.386686
$706$	−45.7173	−1.72059
$707$	15.1082	0.568201
$708$	42.5690	1.59984
$709$	−24.6679	−0.926424	−0.463212	−	0.886248i	$-0.653303\pi$
$709$	−24.6679	−0.926424	−0.463212	+	0.886248i	$0.653303\pi$
$710$	4.17295	0.156608
$711$	16.6522	0.624506
$712$	−7.96473	−0.298491
$713$	22.2058	0.831613
$714$	1.30618	0.0488827
$715$	−20.3681	−0.761722
$716$	−17.4544	−0.652303
$717$	13.5754	0.506984
$718$	−49.0446	−1.83033
$719$	−19.3021	−0.719847	−0.359923	−	0.932982i	$-0.617197\pi$
$719$	−19.3021	−0.719847	−0.359923	+	0.932982i	$0.617197\pi$
$720$	12.2922	0.458103
$721$	−12.9375	−0.481816
$722$	−90.4543	−3.36636
$723$	−11.6737	−0.434151
$724$	−16.4825	−0.612566
$725$	−31.1887	−1.15832
$726$	42.6014	1.58108
$727$	22.6204	0.838946	0.419473	−	0.907768i	$-0.362215\pi$
$727$	22.6204	0.838946	0.419473	+	0.907768i	$0.362215\pi$
$728$	4.76778	0.176706
$729$	8.63466	0.319802
$730$	−18.0562	−0.668289
$731$	−0.934756	−0.0345732
$732$	−5.38561	−0.199058
$733$	13.1730	0.486557	0.243279	−	0.969956i	$-0.421777\pi$
$733$	13.1730	0.486557	0.243279	+	0.969956i	$0.421777\pi$
$734$	34.6865	1.28030
$735$	−6.60639	−0.243680
$736$	−48.3963	−1.78391
$737$	6.66547	0.245526
$738$	6.48053	0.238552
$739$	−11.2292	−0.413071	−0.206536	−	0.978439i	$-0.566219\pi$
$739$	−11.2292	−0.413071	−0.206536	+	0.978439i	$0.566219\pi$
$740$	−7.11384	−0.261510
$741$	97.9783	3.59932
$742$	−1.98926	−0.0730281
$743$	37.3398	1.36987	0.684933	−	0.728606i	$-0.259832\pi$
$743$	37.3398	1.36987	0.684933	+	0.728606i	$0.259832\pi$
$744$	6.01905	0.220669
$745$	47.7998	1.75125
$746$	40.5058	1.48302
$747$	19.9480	0.729858
$748$	0.758164	0.0277212
$749$	18.0641	0.660048
$750$	4.25500	0.155371
$751$	−16.2709	−0.593733	−0.296866	−	0.954919i	$-0.595942\pi$
$751$	−16.2709	−0.593733	−0.296866	+	0.954919i	$0.595942\pi$
$752$	4.82153	0.175823
$753$	−13.4643	−0.490666
$754$	−74.2051	−2.70239
$755$	48.2550	1.75618
$756$	−8.63922	−0.314206
$757$	−0.162248	−0.00589701	−0.00294851	−	0.999996i	$-0.500939\pi$
$757$	−0.162248	−0.00589701	−0.00294851	+	0.999996i	$0.500939\pi$
$758$	58.2986	2.11750
$759$	12.9689	0.470740
$760$	−20.0065	−0.725711
$761$	−14.6180	−0.529903	−0.264952	−	0.964262i	$-0.585356\pi$
$761$	−14.6180	−0.529903	−0.264952	+	0.964262i	$0.585356\pi$
$762$	90.0536	3.26230
$763$	16.9133	0.612303
$764$	29.0860	1.05229
$765$	1.20211	0.0434622
$766$	37.7405	1.36362
$767$	−52.5200	−1.89639
$768$	17.2371	0.621989
$769$	52.0790	1.87802	0.939008	−	0.343896i	$-0.111747\pi$
$769$	52.0790	1.87802	0.939008	+	0.343896i	$0.111747\pi$
$770$	−7.06033	−0.254437
$771$	12.3443	0.444569
$772$	17.8674	0.643061
$773$	48.0473	1.72814	0.864070	−	0.503371i	$-0.167907\pi$
$773$	48.0473	1.72814	0.864070	+	0.503371i	$0.167907\pi$
$774$	−7.95525	−0.285945
$775$	−19.6557	−0.706053
$776$	−9.36481	−0.336177
$777$	1.91767	0.0687960
$778$	4.77014	0.171018
$779$	19.7996	0.709393
$780$	94.8050	3.39456
$781$	−0.652936	−0.0233639
$782$	−3.80644	−0.136118
$783$	21.3514	0.763037
$784$	−3.10239	−0.110800
$785$	−1.19787	−0.0427540
$786$	−34.3060	−1.22366
$787$	51.2322	1.82623	0.913116	−	0.407701i	$-0.133669\pi$
$787$	51.2322	1.82623	0.913116	+	0.407701i	$0.133669\pi$
$788$	−49.6751	−1.76960
$789$	−64.5021	−2.29633
$790$	90.6401	3.22483
$791$	3.86760	0.137516
$792$	1.02460	0.0364075
$793$	6.64456	0.235955
$794$	−22.3713	−0.793928
$795$	−6.28118	−0.222770
$796$	53.1214	1.88284
$797$	33.2854	1.17903	0.589515	−	0.807758i	$-0.299319\pi$
$797$	33.2854	1.17903	0.589515	+	0.807758i	$0.299319\pi$
$798$	33.9630	1.20228
$799$	0.471518	0.0166811
$800$	42.8385	1.51457
$801$	12.4435	0.439671
$802$	38.8382	1.37143
$803$	2.82523	0.0997000
$804$	−31.0251	−1.09417
$805$	19.2521	0.678549
$806$	−46.7654	−1.64724
$807$	−1.76455	−0.0621150
$808$	−11.9341	−0.419839
$809$	4.08686	0.143686	0.0718431	−	0.997416i	$-0.477112\pi$
$809$	4.08686	0.143686	0.0718431	+	0.997416i	$0.477112\pi$
$810$	−75.0954	−2.63858
$811$	−20.7905	−0.730053	−0.365027	−	0.930997i	$-0.618940\pi$
$811$	−20.7905	−0.730053	−0.365027	+	0.930997i	$0.618940\pi$
$812$	−13.9704	−0.490263
$813$	28.9656	1.01587
$814$	2.04944	0.0718327
$815$	−38.6710	−1.35459
$816$	1.93680	0.0678017
$817$	−24.3052	−0.850331
$818$	−9.63811	−0.336988
$819$	−7.44885	−0.260284
$820$	19.1583	0.669037
$821$	9.67690	0.337726	0.168863	−	0.985640i	$-0.445990\pi$
$821$	9.67690	0.337726	0.168863	+	0.985640i	$0.445990\pi$
$822$	91.7683	3.20079
$823$	24.1830	0.842966	0.421483	−	0.906836i	$-0.361510\pi$
$823$	24.1830	0.842966	0.421483	+	0.906836i	$0.361510\pi$
$824$	10.2194	0.356010
$825$	−11.4795	−0.399666
$826$	−18.2054	−0.633448
$827$	−22.6651	−0.788143	−0.394071	−	0.919080i	$-0.628934\pi$
$827$	−22.6651	−0.788143	−0.394071	+	0.919080i	$0.628934\pi$
$828$	−17.5943	−0.611445
$829$	−28.7050	−0.996967	−0.498484	−	0.866899i	$-0.666110\pi$
$829$	−28.7050	−0.996967	−0.498484	+	0.866899i	$0.666110\pi$
$830$	108.579	3.76885
$831$	−42.5593	−1.47637
$832$	64.4716	2.23515
$833$	−0.303396	−0.0105120
$834$	99.5879	3.44845
$835$	1.32628	0.0458977
$836$	19.7135	0.681806
$837$	13.4561	0.465109
$838$	−71.1939	−2.45935
$839$	−26.8058	−0.925438	−0.462719	−	0.886505i	$-0.653126\pi$
$839$	−26.8058	−0.925438	−0.462719	+	0.886505i	$0.653126\pi$
$840$	5.21844	0.180053
$841$	5.52704	0.190587
$842$	−64.2384	−2.21380
$843$	−36.3820	−1.25306
$844$	−5.48374	−0.188758
$845$	−75.2292	−2.58796
$846$	4.01286	0.137965
$847$	−9.89528	−0.340006
$848$	−2.94966	−0.101292
$849$	55.3300	1.89892
$850$	3.36932	0.115567
$851$	−5.58841	−0.191568
$852$	3.03915	0.104120
$853$	4.97057	0.170189	0.0850946	−	0.996373i	$-0.472881\pi$
$853$	4.97057	0.170189	0.0850946	+	0.996373i	$0.472881\pi$
$854$	2.30325	0.0788157
$855$	31.2567	1.06896
$856$	−14.2690	−0.487704
$857$	7.34376	0.250858	0.125429	−	0.992103i	$-0.459969\pi$
$857$	7.34376	0.250858	0.125429	+	0.992103i	$0.459969\pi$
$858$	−27.3125	−0.932433
$859$	−1.00000	−0.0341196
$859$	−1.00000	−0.0341196
$860$	−23.5180	−0.801957
$861$	−5.16448	−0.176005
$862$	7.96631	0.271333
$863$	29.9151	1.01832	0.509161	−	0.860671i	$-0.329956\pi$
$863$	29.9151	1.01832	0.509161	+	0.860671i	$0.329956\pi$
$864$	−29.3268	−0.997716
$865$	−53.3629	−1.81439
$866$	29.6229	1.00663
$867$	−34.7914	−1.18158
$868$	−8.80437	−0.298840
$869$	−14.1823	−0.481103
$870$	−81.2192	−2.75359
$871$	38.2775	1.29698
$872$	−13.3600	−0.452426
$873$	14.6309	0.495182
$874$	−98.9738	−3.34784
$875$	−0.988335	−0.0334118
$876$	−13.1503	−0.444307
$877$	42.4956	1.43498	0.717488	−	0.696571i	$-0.245292\pi$
$877$	42.4956	1.43498	0.717488	+	0.696571i	$0.245292\pi$
$878$	49.3886	1.66678
$879$	−59.2408	−1.99814
$880$	−10.4690	−0.352911
$881$	43.1741	1.45457	0.727286	−	0.686334i	$-0.240781\pi$
$881$	43.1741	1.45457	0.727286	+	0.686334i	$0.240781\pi$
$882$	−2.58205	−0.0869421
$883$	−43.4766	−1.46311	−0.731553	−	0.681785i	$-0.761204\pi$
$883$	−43.4766	−1.46311	−0.731553	+	0.681785i	$0.761204\pi$
$884$	4.35388	0.146437
$885$	−57.4844	−1.93232
$886$	−7.19367	−0.241676
$887$	−57.5739	−1.93314	−0.966571	−	0.256398i	$-0.917464\pi$
$887$	−57.5739	−1.93314	−0.966571	+	0.256398i	$0.917464\pi$
$888$	−1.51478	−0.0508328
$889$	−20.9173	−0.701544
$890$	67.7319	2.27038
$891$	11.7501	0.393643
$892$	−5.31318	−0.177898
$893$	12.2602	0.410273
$894$	64.0970	2.14372
$895$	23.5701	0.787862
$896$	6.20668	0.207351
$897$	74.4758	2.48667
$898$	39.3703	1.31380
$899$	21.7596	0.725722
$900$	15.5738	0.519127
$901$	−0.288460	−0.00961000
$902$	−5.51934	−0.183774
$903$	6.33971	0.210972
$904$	−3.05505	−0.101609
$905$	22.2576	0.739867
$906$	64.7075	2.14976
$907$	14.2605	0.473511	0.236756	−	0.971569i	$-0.423916\pi$
$907$	14.2605	0.473511	0.236756	+	0.971569i	$0.423916\pi$
$908$	44.4732	1.47590
$909$	18.6450	0.618414
$910$	−40.5451	−1.34406
$911$	40.6462	1.34667	0.673335	−	0.739338i	$-0.264861\pi$
$911$	40.6462	1.34667	0.673335	+	0.739338i	$0.264861\pi$
$912$	50.3601	1.66759
$913$	−16.9893	−0.562264
$914$	−39.5882	−1.30946
$915$	7.27262	0.240425
$916$	−10.3240	−0.341114
$917$	7.96847	0.263142
$918$	−2.30659	−0.0761290
$919$	−53.0069	−1.74854	−0.874269	−	0.485443i	$-0.838658\pi$
$919$	−53.0069	−1.74854	−0.874269	+	0.485443i	$0.838658\pi$
$920$	−15.2074	−0.501374
$921$	−3.32987	−0.109723
$922$	−1.82350	−0.0600537
$923$	−3.74959	−0.123419
$924$	−5.14203	−0.169160
$925$	4.94664	0.162645
$926$	7.43158	0.244217
$927$	−15.9661	−0.524395
$928$	−47.4238	−1.55676
$929$	53.4740	1.75442	0.877212	−	0.480103i	$-0.159401\pi$
$929$	53.4740	1.75442	0.877212	+	0.480103i	$0.159401\pi$
$930$	−51.1858	−1.67845
$931$	−7.88878	−0.258544
$932$	−13.3013	−0.435699
$933$	31.6613	1.03654
$934$	1.57005	0.0513737
$935$	−1.02381	−0.0334822
$936$	5.88391	0.192322
$937$	−2.90038	−0.0947513	−0.0473756	−	0.998877i	$-0.515086\pi$
$937$	−2.90038	−0.0947513	−0.0473756	+	0.998877i	$0.515086\pi$
$938$	13.2684	0.433230
$939$	−66.7849	−2.17944
$940$	11.8632	0.386934
$941$	−0.709175	−0.0231184	−0.0115592	−	0.999933i	$-0.503679\pi$
$941$	−0.709175	−0.0231184	−0.0115592	+	0.999933i	$0.503679\pi$
$942$	−1.60629	−0.0523356
$943$	15.0502	0.490100
$944$	−26.9949	−0.878609
$945$	11.6662	0.379503
$946$	6.77533	0.220285
$947$	31.4146	1.02084	0.510419	−	0.859926i	$-0.329490\pi$
$947$	31.4146	1.02084	0.510419	+	0.859926i	$0.329490\pi$
$948$	66.0130	2.14400
$949$	16.2243	0.526663
$950$	87.6078	2.84237
$951$	9.34445	0.303014
$952$	0.239655	0.00776726
$953$	7.77814	0.251959	0.125979	−	0.992033i	$-0.459793\pi$
$953$	7.77814	0.251959	0.125979	+	0.992033i	$0.459793\pi$
$954$	−2.45494	−0.0794817
$955$	−39.2772	−1.27098
$956$	15.6856	0.507309
$957$	12.7083	0.410800
$958$	22.0122	0.711182
$959$	−21.3156	−0.688316
$960$	70.5657	2.27750
$961$	−17.2867	−0.557636
$962$	11.7692	0.379455
$963$	22.2929	0.718378
$964$	−13.4883	−0.434429
$965$	−24.1278	−0.776700
$966$	25.8161	0.830619
$967$	−31.9037	−1.02595	−0.512977	−	0.858403i	$-0.671457\pi$
$967$	−31.9037	−1.02595	−0.512977	+	0.858403i	$0.671457\pi$
$968$	7.81637	0.251228
$969$	4.92493	0.158211
$970$	79.6381	2.55703
$971$	−18.3994	−0.590464	−0.295232	−	0.955426i	$-0.595397\pi$
$971$	−18.3994	−0.590464	−0.295232	+	0.955426i	$0.595397\pi$
$972$	−28.7742	−0.922932
$973$	−23.1319	−0.741574
$974$	76.2294	2.44255
$975$	−65.9231	−2.11123
$976$	3.41525	0.109319
$977$	−33.6004	−1.07497	−0.537485	−	0.843273i	$-0.680626\pi$
$977$	−33.6004	−1.07497	−0.537485	+	0.843273i	$0.680626\pi$
$978$	−51.8558	−1.65817
$979$	−10.5979	−0.338711
$980$	−7.63328	−0.243836
$981$	20.8727	0.666414
$982$	23.9132	0.763102
$983$	19.3439	0.616974	0.308487	−	0.951229i	$-0.400177\pi$
$983$	19.3439	0.616974	0.308487	+	0.951229i	$0.400177\pi$
$984$	4.07946	0.130049
$985$	67.0803	2.13735
$986$	−3.72996	−0.118786
$987$	−3.19793	−0.101791
$988$	113.208	3.60163
$989$	−18.4750	−0.587470
$990$	−8.71314	−0.276922
$991$	58.5652	1.86039	0.930193	−	0.367071i	$-0.119639\pi$
$991$	58.5652	1.86039	0.930193	+	0.367071i	$0.119639\pi$
$992$	−29.8874	−0.948925
$993$	18.1390	0.575622
$994$	−1.29975	−0.0412255
$995$	−71.7341	−2.27413
$996$	79.0782	2.50569
$997$	29.5582	0.936117	0.468059	−	0.883697i	$-0.344954\pi$
$997$	29.5582	0.936117	0.468059	+	0.883697i	$0.344954\pi$
$998$	75.5400	2.39118
$999$	−3.38641	−0.107141

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.e.1.15	✓	109

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.e.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-2.09226 q^{2} +2.05769 q^{3} +2.37754 q^{4} -3.21058 q^{5} -4.30522 q^{6} +1.00000 q^{7} -0.789909 q^{8} +1.23410 q^{9} +O(q^{10})\)	\(q-2.09226 q^{2} +2.05769 q^{3} +2.37754 q^{4} -3.21058 q^{5} -4.30522 q^{6} +1.00000 q^{7} -0.789909 q^{8} +1.23410 q^{9} +6.71736 q^{10} -1.05106 q^{11} +4.89224 q^{12} -6.03586 q^{13} -2.09226 q^{14} -6.60639 q^{15} -3.10239 q^{16} -0.303396 q^{17} -2.58205 q^{18} -7.88878 q^{19} -7.63328 q^{20} +2.05769 q^{21} +2.19908 q^{22} -5.99646 q^{23} -1.62539 q^{24} +5.30784 q^{25} +12.6286 q^{26} -3.63368 q^{27} +2.37754 q^{28} -5.87597 q^{29} +13.8223 q^{30} -3.70314 q^{31} +8.07081 q^{32} -2.16275 q^{33} +0.634781 q^{34} -3.21058 q^{35} +2.93412 q^{36} +0.931951 q^{37} +16.5054 q^{38} -12.4199 q^{39} +2.53607 q^{40} -2.50984 q^{41} -4.30522 q^{42} +3.08098 q^{43} -2.49893 q^{44} -3.96217 q^{45} +12.5461 q^{46} -1.55414 q^{47} -6.38376 q^{48} +1.00000 q^{49} -11.1054 q^{50} -0.624295 q^{51} -14.3505 q^{52} +0.950773 q^{53} +7.60260 q^{54} +3.37451 q^{55} -0.789909 q^{56} -16.2327 q^{57} +12.2940 q^{58} +8.70133 q^{59} -15.7070 q^{60} -1.10085 q^{61} +7.74793 q^{62} +1.23410 q^{63} -10.6814 q^{64} +19.3786 q^{65} +4.52503 q^{66} -6.34168 q^{67} -0.721335 q^{68} -12.3389 q^{69} +6.71736 q^{70} +0.621219 q^{71} -0.974825 q^{72} -2.68798 q^{73} -1.94988 q^{74} +10.9219 q^{75} -18.7559 q^{76} -1.05106 q^{77} +25.9857 q^{78} +13.4934 q^{79} +9.96047 q^{80} -11.1793 q^{81} +5.25123 q^{82} +16.1640 q^{83} +4.89224 q^{84} +0.974076 q^{85} -6.44620 q^{86} -12.0909 q^{87} +0.830239 q^{88} +10.0831 q^{89} +8.28988 q^{90} -6.03586 q^{91} -14.2568 q^{92} -7.61993 q^{93} +3.25165 q^{94} +25.3276 q^{95} +16.6072 q^{96} +11.8556 q^{97} -2.09226 q^{98} -1.29711 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 109 q + 19 q^{2} + 38 q^{3} + 111 q^{4} + 43 q^{5} + 14 q^{6} + 109 q^{7} + 48 q^{8} + 119 q^{9}+O(q^{10}) \) 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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