LMFDB - Embedded newform 6013.2.a.f.1.16

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:	$110$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q-2.05159 q^{2} +3.13328 q^{3} +2.20904 q^{4} +2.94582 q^{5} -6.42821 q^{6} -1.00000 q^{7} -0.428856 q^{8} +6.81742 q^{9} +O(q^{10})$	\(q-2.05159 q^{2} +3.13328 q^{3} +2.20904 q^{4} +2.94582 q^{5} -6.42821 q^{6} -1.00000 q^{7} -0.428856 q^{8} +6.81742 q^{9} -6.04363 q^{10} +0.435072 q^{11} +6.92152 q^{12} +6.71615 q^{13} +2.05159 q^{14} +9.23008 q^{15} -3.53823 q^{16} +5.09428 q^{17} -13.9866 q^{18} +2.73947 q^{19} +6.50743 q^{20} -3.13328 q^{21} -0.892590 q^{22} -4.22734 q^{23} -1.34372 q^{24} +3.67787 q^{25} -13.7788 q^{26} +11.9610 q^{27} -2.20904 q^{28} -1.64356 q^{29} -18.9364 q^{30} -1.48768 q^{31} +8.11673 q^{32} +1.36320 q^{33} -10.4514 q^{34} -2.94582 q^{35} +15.0599 q^{36} -7.90599 q^{37} -5.62028 q^{38} +21.0436 q^{39} -1.26333 q^{40} +1.00017 q^{41} +6.42821 q^{42} +7.20934 q^{43} +0.961089 q^{44} +20.0829 q^{45} +8.67278 q^{46} +0.339199 q^{47} -11.0863 q^{48} +1.00000 q^{49} -7.54549 q^{50} +15.9618 q^{51} +14.8362 q^{52} +1.45098 q^{53} -24.5392 q^{54} +1.28164 q^{55} +0.428856 q^{56} +8.58353 q^{57} +3.37191 q^{58} -5.84866 q^{59} +20.3896 q^{60} -12.9324 q^{61} +3.05211 q^{62} -6.81742 q^{63} -9.57576 q^{64} +19.7846 q^{65} -2.79673 q^{66} +3.45375 q^{67} +11.2534 q^{68} -13.2454 q^{69} +6.04363 q^{70} +12.0999 q^{71} -2.92369 q^{72} +0.934048 q^{73} +16.2199 q^{74} +11.5238 q^{75} +6.05159 q^{76} -0.435072 q^{77} -43.1728 q^{78} +11.6266 q^{79} -10.4230 q^{80} +17.0249 q^{81} -2.05194 q^{82} -13.6460 q^{83} -6.92152 q^{84} +15.0068 q^{85} -14.7906 q^{86} -5.14972 q^{87} -0.186583 q^{88} +13.5665 q^{89} -41.2020 q^{90} -6.71615 q^{91} -9.33835 q^{92} -4.66130 q^{93} -0.695899 q^{94} +8.07000 q^{95} +25.4319 q^{96} +0.446008 q^{97} -2.05159 q^{98} +2.96607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9}+O(q^{10}) $ 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9} + 3 q^{10} + 52 q^{11} + 62 q^{12} - 9 q^{13} - 16 q^{14} + 39 q^{15} + 146 q^{16} + 11 q^{17} + 60 q^{18} + 14 q^{19} + 18 q^{20} - 29 q^{21} + 32 q^{22} + 73 q^{23} + 24 q^{24} + 132 q^{25} - 7 q^{26} + 116 q^{27} - 118 q^{28} + 35 q^{29} + 18 q^{30} + 36 q^{31} + 140 q^{32} + 42 q^{33} - 7 q^{34} + 180 q^{36} + 49 q^{37} + 45 q^{39} + 6 q^{40} - 14 q^{41} - 12 q^{42} + 58 q^{43} + 92 q^{44} + 17 q^{45} + 27 q^{46} + 87 q^{47} + 98 q^{48} + 110 q^{49} + 91 q^{50} + 42 q^{51} + 16 q^{52} + 95 q^{53} + 41 q^{54} + 8 q^{55} - 57 q^{56} + 61 q^{57} + 46 q^{58} + 114 q^{59} + 81 q^{60} - 47 q^{61} + 31 q^{62} - 127 q^{63} + 199 q^{64} + 62 q^{65} + 21 q^{66} + 95 q^{67} + 60 q^{68} - 39 q^{69} - 3 q^{70} + 131 q^{71} + 186 q^{72} + 31 q^{73} + 23 q^{74} + 121 q^{75} + 14 q^{76} - 52 q^{77} + 110 q^{78} + 9 q^{79} + 61 q^{80} + 194 q^{81} + 45 q^{82} + 73 q^{83} - 62 q^{84} + 59 q^{85} + 72 q^{86} + 64 q^{87} + 100 q^{88} - 17 q^{89} + 11 q^{90} + 9 q^{91} + 192 q^{92} + 85 q^{93} - 11 q^{94} + 108 q^{95} + 68 q^{96} + 32 q^{97} + 16 q^{98} + 160 q^{99}+O(q^{100}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9 + 3 * q^10 + 52 * q^11 + 62 * q^12 - 9 * q^13 - 16 * q^14 + 39 * q^15 + 146 * q^16 + 11 * q^17 + 60 * q^18 + 14 * q^19 + 18 * q^20 - 29 * q^21 + 32 * q^22 + 73 * q^23 + 24 * q^24 + 132 * q^25 - 7 * q^26 + 116 * q^27 - 118 * q^28 + 35 * q^29 + 18 * q^30 + 36 * q^31 + 140 * q^32 + 42 * q^33 - 7 * q^34 + 180 * q^36 + 49 * q^37 + 45 * q^39 + 6 * q^40 - 14 * q^41 - 12 * q^42 + 58 * q^43 + 92 * q^44 + 17 * q^45 + 27 * q^46 + 87 * q^47 + 98 * q^48 + 110 * q^49 + 91 * q^50 + 42 * q^51 + 16 * q^52 + 95 * q^53 + 41 * q^54 + 8 * q^55 - 57 * q^56 + 61 * q^57 + 46 * q^58 + 114 * q^59 + 81 * q^60 - 47 * q^61 + 31 * q^62 - 127 * q^63 + 199 * q^64 + 62 * q^65 + 21 * q^66 + 95 * q^67 + 60 * q^68 - 39 * q^69 - 3 * q^70 + 131 * q^71 + 186 * q^72 + 31 * q^73 + 23 * q^74 + 121 * q^75 + 14 * q^76 - 52 * q^77 + 110 * q^78 + 9 * q^79 + 61 * q^80 + 194 * q^81 + 45 * q^82 + 73 * q^83 - 62 * q^84 + 59 * q^85 + 72 * q^86 + 64 * q^87 + 100 * q^88 - 17 * q^89 + 11 * q^90 + 9 * q^91 + 192 * q^92 + 85 * q^93 - 11 * q^94 + 108 * q^95 + 68 * q^96 + 32 * q^97 + 16 * q^98 + 160 * 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 $

$2$	−2.05159	−1.45070	−0.725348	−	0.688383i	$-0.758321\pi$
$2$	−2.05159	−1.45070	−0.725348	+	0.688383i	$0.758321\pi$
$3$	3.13328	1.80900	0.904499	−	0.426476i	$-0.140245\pi$
$3$	3.13328	1.80900	0.904499	+	0.426476i	$0.140245\pi$
$4$	2.20904	1.10452
$5$	2.94582	1.31741	0.658706	−	0.752400i	$-0.271104\pi$
$5$	2.94582	1.31741	0.658706	+	0.752400i	$0.271104\pi$
$6$	−6.42821	−2.62431
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.428856	−0.151623
$9$	6.81742	2.27247
$10$	−6.04363	−1.91116
$11$	0.435072	0.131179	0.0655895	−	0.997847i	$-0.479107\pi$
$11$	0.435072	0.131179	0.0655895	+	0.997847i	$0.479107\pi$
$12$	6.92152	1.99807
$13$	6.71615	1.86272	0.931362	−	0.364093i	$-0.118621\pi$
$13$	6.71615	1.86272	0.931362	+	0.364093i	$0.118621\pi$
$14$	2.05159	0.548311
$15$	9.23008	2.38320
$16$	−3.53823	−0.884558
$17$	5.09428	1.23554	0.617772	−	0.786357i	$-0.288035\pi$
$17$	5.09428	1.23554	0.617772	+	0.786357i	$0.288035\pi$
$18$	−13.9866	−3.29667
$19$	2.73947	0.628478	0.314239	−	0.949344i	$-0.398251\pi$
$19$	2.73947	0.628478	0.314239	+	0.949344i	$0.398251\pi$
$20$	6.50743	1.45510
$21$	−3.13328	−0.683737
$22$	−0.892590	−0.190301
$23$	−4.22734	−0.881461	−0.440731	−	0.897639i	$-0.645281\pi$
$23$	−4.22734	−0.881461	−0.440731	+	0.897639i	$0.645281\pi$
$24$	−1.34372	−0.274287
$25$	3.67787	0.735574
$26$	−13.7788	−2.70225
$27$	11.9610	2.30190
$28$	−2.20904	−0.417468
$29$	−1.64356	−0.305201	−0.152600	−	0.988288i	$-0.548765\pi$
$29$	−1.64356	−0.305201	−0.152600	+	0.988288i	$0.548765\pi$
$30$	−18.9364	−3.45729
$31$	−1.48768	−0.267195	−0.133597	−	0.991036i	$-0.542653\pi$
$31$	−1.48768	−0.267195	−0.133597	+	0.991036i	$0.542653\pi$
$32$	8.11673	1.43485
$33$	1.36320	0.237303
$34$	−10.4514	−1.79240
$35$	−2.94582	−0.497935
$36$	15.0599	2.50999
$37$	−7.90599	−1.29974	−0.649868	−	0.760047i	$-0.725176\pi$
$37$	−7.90599	−1.29974	−0.649868	+	0.760047i	$0.725176\pi$
$38$	−5.62028	−0.911731
$39$	21.0436	3.36967
$40$	−1.26333	−0.199751
$41$	1.00017	0.156200	0.0781000	−	0.996946i	$-0.475115\pi$
$41$	1.00017	0.156200	0.0781000	+	0.996946i	$0.475115\pi$
$42$	6.42821	0.991894
$43$	7.20934	1.09941	0.549707	−	0.835357i	$-0.314739\pi$
$43$	7.20934	1.09941	0.549707	+	0.835357i	$0.314739\pi$
$44$	0.961089	0.144890
$45$	20.0829	2.99378
$46$	8.67278	1.27873
$47$	0.339199	0.0494773	0.0247386	−	0.999694i	$-0.492125\pi$
$47$	0.339199	0.0494773	0.0247386	+	0.999694i	$0.492125\pi$
$48$	−11.0863	−1.60016
$49$	1.00000	0.142857
$50$	−7.54549	−1.06709
$51$	15.9618	2.23510
$52$	14.8362	2.05741
$53$	1.45098	0.199308	0.0996539	−	0.995022i	$-0.468226\pi$
$53$	1.45098	0.199308	0.0996539	+	0.995022i	$0.468226\pi$
$54$	−24.5392	−3.33936
$55$	1.28164	0.172817
$56$	0.428856	0.0573083
$57$	8.58353	1.13692
$58$	3.37191	0.442754
$59$	−5.84866	−0.761431	−0.380716	−	0.924692i	$-0.624322\pi$
$59$	−5.84866	−0.761431	−0.380716	+	0.924692i	$0.624322\pi$
$60$	20.3896	2.63228
$61$	−12.9324	−1.65582	−0.827911	−	0.560859i	$-0.810471\pi$
$61$	−12.9324	−1.65582	−0.827911	+	0.560859i	$0.810471\pi$
$62$	3.05211	0.387618
$63$	−6.81742	−0.858914
$64$	−9.57576	−1.19697
$65$	19.7846	2.45398
$66$	−2.79673	−0.344254
$67$	3.45375	0.421943	0.210972	−	0.977492i	$-0.432337\pi$
$67$	3.45375	0.421943	0.210972	+	0.977492i	$0.432337\pi$
$68$	11.2534	1.36468
$69$	−13.2454	−1.59456
$70$	6.04363	0.722352
$71$	12.0999	1.43600	0.717998	−	0.696045i	$-0.245059\pi$
$71$	12.0999	1.43600	0.717998	+	0.696045i	$0.245059\pi$
$72$	−2.92369	−0.344560
$73$	0.934048	0.109322	0.0546610	−	0.998505i	$-0.482592\pi$
$73$	0.934048	0.109322	0.0546610	+	0.998505i	$0.482592\pi$
$74$	16.2199	1.88552
$75$	11.5238	1.33065
$76$	6.05159	0.694165
$77$	−0.435072	−0.0495810
$78$	−43.1728	−4.88836
$79$	11.6266	1.30809	0.654047	−	0.756454i	$-0.273070\pi$
$79$	11.6266	1.30809	0.654047	+	0.756454i	$0.273070\pi$
$80$	−10.4230	−1.16533
$81$	17.0249	1.89166
$82$	−2.05194	−0.226599
$83$	−13.6460	−1.49784	−0.748921	−	0.662659i	$-0.769428\pi$
$83$	−13.6460	−1.49784	−0.748921	+	0.662659i	$0.769428\pi$
$84$	−6.92152	−0.755200
$85$	15.0068	1.62772
$86$	−14.7906	−1.59492
$87$	−5.14972	−0.552108
$88$	−0.186583	−0.0198898
$89$	13.5665	1.43805	0.719025	−	0.694985i	$-0.244589\pi$
$89$	13.5665	1.43805	0.719025	+	0.694985i	$0.244589\pi$
$90$	−41.2020	−4.34307
$91$	−6.71615	−0.704044
$92$	−9.33835	−0.973590
$93$	−4.66130	−0.483355
$94$	−0.695899	−0.0717765
$95$	8.07000	0.827965
$96$	25.4319	2.59564
$97$	0.446008	0.0452853	0.0226426	−	0.999744i	$-0.492792\pi$
$97$	0.446008	0.0452853	0.0226426	+	0.999744i	$0.492792\pi$
$98$	−2.05159	−0.207242
$99$	2.96607	0.298101
$100$	8.12455	0.812455
$101$	−11.4002	−1.13436	−0.567179	−	0.823594i	$-0.691965\pi$
$101$	−11.4002	−1.13436	−0.567179	+	0.823594i	$0.691965\pi$
$102$	−32.7471	−3.24245
$103$	1.88105	0.185345	0.0926726	−	0.995697i	$-0.470459\pi$
$103$	1.88105	0.185345	0.0926726	+	0.995697i	$0.470459\pi$
$104$	−2.88026	−0.282433
$105$	−9.23008	−0.900763
$106$	−2.97683	−0.289135
$107$	−9.56797	−0.924971	−0.462485	−	0.886627i	$-0.653042\pi$
$107$	−9.56797	−0.924971	−0.462485	+	0.886627i	$0.653042\pi$
$108$	26.4223	2.54249
$109$	−19.2740	−1.84612	−0.923058	−	0.384662i	$-0.874318\pi$
$109$	−19.2740	−1.84612	−0.923058	+	0.384662i	$0.874318\pi$
$110$	−2.62941	−0.250705
$111$	−24.7717	−2.35122
$112$	3.53823	0.334332
$113$	−14.6377	−1.37700	−0.688500	−	0.725236i	$-0.741730\pi$
$113$	−14.6377	−1.37700	−0.688500	+	0.725236i	$0.741730\pi$
$114$	−17.6099	−1.64932
$115$	−12.4530	−1.16125
$116$	−3.63068	−0.337100
$117$	45.7868	4.23299
$118$	11.9991	1.10460
$119$	−5.09428	−0.466992
$120$	−3.95837	−0.361348
$121$	−10.8107	−0.982792
$122$	26.5320	2.40209
$123$	3.13380	0.282565
$124$	−3.28633	−0.295121
$125$	−3.89476	−0.348358
$126$	13.9866	1.24602
$127$	−6.38863	−0.566900	−0.283450	−	0.958987i	$-0.591479\pi$
$127$	−6.38863	−0.566900	−0.283450	+	0.958987i	$0.591479\pi$
$128$	3.41211	0.301591
$129$	22.5889	1.98884
$130$	−40.5899	−3.55997
$131$	−0.199527	−0.0174327	−0.00871637	−	0.999962i	$-0.502775\pi$
$131$	−0.199527	−0.0174327	−0.00871637	+	0.999962i	$0.502775\pi$
$132$	3.01136	0.262105
$133$	−2.73947	−0.237542
$134$	−7.08570	−0.612111
$135$	35.2351	3.03255
$136$	−2.18471	−0.187338
$137$	−0.706677	−0.0603755	−0.0301878	−	0.999544i	$-0.509611\pi$
$137$	−0.706677	−0.0603755	−0.0301878	+	0.999544i	$0.509611\pi$
$138$	27.1742	2.31322
$139$	0.172503	0.0146315	0.00731576	−	0.999973i	$-0.497671\pi$
$139$	0.172503	0.0146315	0.00731576	+	0.999973i	$0.497671\pi$
$140$	−6.50743	−0.549978
$141$	1.06280	0.0895043
$142$	−24.8241	−2.08319
$143$	2.92201	0.244350
$144$	−24.1216	−2.01013
$145$	−4.84163	−0.402075
$146$	−1.91629	−0.158593
$147$	3.13328	0.258428
$148$	−17.4646	−1.43558
$149$	−11.0477	−0.905066	−0.452533	−	0.891748i	$-0.649480\pi$
$149$	−11.0477	−0.905066	−0.452533	+	0.891748i	$0.649480\pi$
$150$	−23.6421	−1.93037
$151$	4.24853	0.345740	0.172870	−	0.984945i	$-0.444696\pi$
$151$	4.24853	0.345740	0.172870	+	0.984945i	$0.444696\pi$
$152$	−1.17484	−0.0952921
$153$	34.7299	2.80774
$154$	0.892590	0.0719269
$155$	−4.38243	−0.352005
$156$	46.4860	3.72185
$157$	2.71719	0.216855	0.108428	−	0.994104i	$-0.465418\pi$
$157$	2.71719	0.216855	0.108428	+	0.994104i	$0.465418\pi$
$158$	−23.8530	−1.89765
$159$	4.54633	0.360547
$160$	23.9104	1.89029
$161$	4.22734	0.333161
$162$	−34.9283	−2.74422
$163$	8.66551	0.678735	0.339368	−	0.940654i	$-0.389787\pi$
$163$	8.66551	0.678735	0.339368	+	0.940654i	$0.389787\pi$
$164$	2.20941	0.172526
$165$	4.01574	0.312625
$166$	27.9960	2.17291
$167$	8.43043	0.652366	0.326183	−	0.945307i	$-0.394237\pi$
$167$	8.43043	0.652366	0.326183	+	0.945307i	$0.394237\pi$
$168$	1.34372	0.103671
$169$	32.1067	2.46974
$170$	−30.7880	−2.36133
$171$	18.6761	1.42820
$172$	15.9257	1.21432
$173$	−11.5697	−0.879630	−0.439815	−	0.898088i	$-0.644956\pi$
$173$	−11.5697	−0.879630	−0.439815	+	0.898088i	$0.644956\pi$
$174$	10.5651	0.800940
$175$	−3.67787	−0.278021
$176$	−1.53938	−0.116035
$177$	−18.3255	−1.37743
$178$	−27.8330	−2.08617
$179$	15.4050	1.15143	0.575713	−	0.817652i	$-0.304724\pi$
$179$	15.4050	1.15143	0.575713	+	0.817652i	$0.304724\pi$
$180$	44.3639	3.30669
$181$	17.6748	1.31375	0.656877	−	0.753998i	$-0.271877\pi$
$181$	17.6748	1.31375	0.656877	+	0.753998i	$0.271877\pi$
$182$	13.7788	1.02135
$183$	−40.5207	−2.99538
$184$	1.81292	0.133650
$185$	−23.2896	−1.71229
$186$	9.56310	0.701200
$187$	2.21638	0.162078
$188$	0.749303	0.0546485
$189$	−11.9610	−0.870037
$190$	−16.5564	−1.20112
$191$	−12.1071	−0.876040	−0.438020	−	0.898965i	$-0.644320\pi$
$191$	−12.1071	−0.876040	−0.438020	+	0.898965i	$0.644320\pi$
$192$	−30.0035	−2.16532
$193$	−5.04709	−0.363298	−0.181649	−	0.983363i	$-0.558143\pi$
$193$	−5.04709	−0.363298	−0.181649	+	0.983363i	$0.558143\pi$
$194$	−0.915027	−0.0656951
$195$	61.9906	4.43924
$196$	2.20904	0.157788
$197$	14.1820	1.01042	0.505212	−	0.862995i	$-0.331414\pi$
$197$	14.1820	1.01042	0.505212	+	0.862995i	$0.331414\pi$
$198$	−6.08516	−0.432453
$199$	−23.6390	−1.67572	−0.837862	−	0.545883i	$-0.816194\pi$
$199$	−23.6390	−1.67572	−0.837862	+	0.545883i	$0.816194\pi$
$200$	−1.57728	−0.111530
$201$	10.8216	0.763294
$202$	23.3885	1.64561
$203$	1.64356	0.115355
$204$	35.2602	2.46871
$205$	2.94632	0.205780
$206$	−3.85915	−0.268879
$207$	−28.8196	−2.00310
$208$	−23.7633	−1.64769
$209$	1.19187	0.0824432
$210$	18.9364	1.30673
$211$	10.7123	0.737468	0.368734	−	0.929535i	$-0.379791\pi$
$211$	10.7123	0.737468	0.368734	+	0.929535i	$0.379791\pi$
$212$	3.20527	0.220139
$213$	37.9124	2.59771
$214$	19.6296	1.34185
$215$	21.2374	1.44838
$216$	−5.12956	−0.349022
$217$	1.48768	0.100990
$218$	39.5424	2.67815
$219$	2.92663	0.197763
$220$	2.83120	0.190879
$221$	34.2140	2.30148
$222$	50.8214	3.41091
$223$	−18.5875	−1.24471	−0.622355	−	0.782735i	$-0.713824\pi$
$223$	−18.5875	−1.24471	−0.622355	+	0.782735i	$0.713824\pi$
$224$	−8.11673	−0.542322
$225$	25.0736	1.67157
$226$	30.0306	1.99761
$227$	−26.1768	−1.73742	−0.868709	−	0.495323i	$-0.835050\pi$
$227$	−26.1768	−1.73742	−0.868709	+	0.495323i	$0.835050\pi$
$228$	18.9613	1.25574
$229$	−1.89464	−0.125202	−0.0626008	−	0.998039i	$-0.519939\pi$
$229$	−1.89464	−0.125202	−0.0626008	+	0.998039i	$0.519939\pi$
$230$	25.5485	1.68462
$231$	−1.36320	−0.0896919
$232$	0.704849	0.0462756
$233$	−19.4136	−1.27183	−0.635914	−	0.771760i	$-0.719377\pi$
$233$	−19.4136	−1.27183	−0.635914	+	0.771760i	$0.719377\pi$
$234$	−93.9359	−6.14078
$235$	0.999220	0.0651820
$236$	−12.9199	−0.841014
$237$	36.4293	2.36634
$238$	10.4514	0.677463
$239$	−2.71972	−0.175924	−0.0879620	−	0.996124i	$-0.528035\pi$
$239$	−2.71972	−0.175924	−0.0879620	+	0.996124i	$0.528035\pi$
$240$	−32.6582	−2.10807
$241$	−26.1967	−1.68748	−0.843740	−	0.536752i	$-0.819651\pi$
$241$	−26.1967	−1.68748	−0.843740	+	0.536752i	$0.819651\pi$
$242$	22.1792	1.42573
$243$	17.4608	1.12011
$244$	−28.5681	−1.82889
$245$	2.94582	0.188202
$246$	−6.42929	−0.409916
$247$	18.3987	1.17068
$248$	0.637999	0.0405130
$249$	−42.7566	−2.70959
$250$	7.99046	0.505361
$251$	28.7418	1.81417	0.907083	−	0.420951i	$-0.138304\pi$
$251$	28.7418	1.81417	0.907083	+	0.420951i	$0.138304\pi$
$252$	−15.0599	−0.948686
$253$	−1.83920	−0.115629
$254$	13.1069	0.822399
$255$	47.0206	2.94454
$256$	12.1513	0.759454
$257$	18.9369	1.18125	0.590626	−	0.806946i	$-0.298881\pi$
$257$	18.9369	1.18125	0.590626	+	0.806946i	$0.298881\pi$
$258$	−46.3431	−2.88520
$259$	7.90599	0.491254
$260$	43.7049	2.71046
$261$	−11.2048	−0.693561
$262$	0.409348	0.0252896
$263$	2.77715	0.171247	0.0856233	−	0.996328i	$-0.472712\pi$
$263$	2.77715	0.171247	0.0856233	+	0.996328i	$0.472712\pi$
$264$	−0.584616	−0.0359806
$265$	4.27434	0.262570
$266$	5.62028	0.344602
$267$	42.5077	2.60143
$268$	7.62947	0.466044
$269$	−18.2056	−1.11001	−0.555007	−	0.831846i	$-0.687285\pi$
$269$	−18.2056	−1.11001	−0.555007	+	0.831846i	$0.687285\pi$
$270$	−72.2880	−4.39931
$271$	2.10745	0.128018	0.0640091	−	0.997949i	$-0.479611\pi$
$271$	2.10745	0.128018	0.0640091	+	0.997949i	$0.479611\pi$
$272$	−18.0248	−1.09291
$273$	−21.0436	−1.27361
$274$	1.44981	0.0875865
$275$	1.60014	0.0964919
$276$	−29.2596	−1.76122
$277$	2.77895	0.166971	0.0834856	−	0.996509i	$-0.473395\pi$
$277$	2.77895	0.166971	0.0834856	+	0.996509i	$0.473395\pi$
$278$	−0.353906	−0.0212259
$279$	−10.1421	−0.607193
$280$	1.26333	0.0754986
$281$	14.2811	0.851937	0.425969	−	0.904738i	$-0.359933\pi$
$281$	14.2811	0.851937	0.425969	+	0.904738i	$0.359933\pi$
$282$	−2.18044	−0.129843
$283$	−1.48867	−0.0884923	−0.0442461	−	0.999021i	$-0.514089\pi$
$283$	−1.48867	−0.0884923	−0.0442461	+	0.999021i	$0.514089\pi$
$284$	26.7292	1.58608
$285$	25.2855	1.49779
$286$	−5.99477	−0.354478
$287$	−1.00017	−0.0590380
$288$	55.3351	3.26065
$289$	8.95171	0.526571
$290$	9.93305	0.583289
$291$	1.39747	0.0819209
$292$	2.06334	0.120748
$293$	−1.59938	−0.0934365	−0.0467183	−	0.998908i	$-0.514876\pi$
$293$	−1.59938	−0.0934365	−0.0467183	+	0.998908i	$0.514876\pi$
$294$	−6.42821	−0.374901
$295$	−17.2291	−1.00312
$296$	3.39053	0.197071
$297$	5.20390	0.301961
$298$	22.6655	1.31298
$299$	−28.3915	−1.64192
$300$	25.4564	1.46973
$301$	−7.20934	−0.415540
$302$	−8.71625	−0.501564
$303$	−35.7199	−2.05205
$304$	−9.69289	−0.555926
$305$	−38.0965	−2.18140
$306$	−71.2515	−4.07318
$307$	8.73013	0.498255	0.249127	−	0.968471i	$-0.419856\pi$
$307$	8.73013	0.498255	0.249127	+	0.968471i	$0.419856\pi$
$308$	−0.961089	−0.0547631
$309$	5.89384	0.335289
$310$	8.99097	0.510653
$311$	6.88630	0.390486	0.195243	−	0.980755i	$-0.437450\pi$
$311$	6.88630	0.390486	0.195243	+	0.980755i	$0.437450\pi$
$312$	−9.02465	−0.510920
$313$	−2.12393	−0.120051	−0.0600257	−	0.998197i	$-0.519118\pi$
$313$	−2.12393	−0.120051	−0.0600257	+	0.998197i	$0.519118\pi$
$314$	−5.57456	−0.314591
$315$	−20.0829	−1.13154
$316$	25.6836	1.44481
$317$	−10.8708	−0.610563	−0.305281	−	0.952262i	$-0.598751\pi$
$317$	−10.8708	−0.610563	−0.305281	+	0.952262i	$0.598751\pi$
$318$	−9.32722	−0.523044
$319$	−0.715065	−0.0400359
$320$	−28.2085	−1.57690
$321$	−29.9791	−1.67327
$322$	−8.67278	−0.483315
$323$	13.9556	0.776513
$324$	37.6087	2.08937
$325$	24.7011	1.37017
$326$	−17.7781	−0.984639
$327$	−60.3908	−3.33962
$328$	−0.428928	−0.0236836
$329$	−0.339199	−0.0187007
$330$	−8.23867	−0.453524
$331$	14.3632	0.789472	0.394736	−	0.918795i	$-0.370836\pi$
$331$	14.3632	0.789472	0.394736	+	0.918795i	$0.370836\pi$
$332$	−30.1445	−1.65439
$333$	−53.8985	−2.95362
$334$	−17.2958	−0.946385
$335$	10.1741	0.555873
$336$	11.0863	0.604805
$337$	−11.5905	−0.631374	−0.315687	−	0.948863i	$-0.602235\pi$
$337$	−11.5905	−0.631374	−0.315687	+	0.948863i	$0.602235\pi$
$338$	−65.8698	−3.58285
$339$	−45.8640	−2.49099
$340$	33.1507	1.79785
$341$	−0.647246	−0.0350503
$342$	−38.3158	−2.07188
$343$	−1.00000	−0.0539949
$344$	−3.09177	−0.166697
$345$	−39.0187	−2.10069
$346$	23.7364	1.27608
$347$	24.9358	1.33862	0.669311	−	0.742982i	$-0.266589\pi$
$347$	24.9358	1.33862	0.669311	+	0.742982i	$0.266589\pi$
$348$	−11.3759	−0.609813
$349$	−24.8701	−1.33127	−0.665633	−	0.746279i	$-0.731838\pi$
$349$	−24.8701	−1.33127	−0.665633	+	0.746279i	$0.731838\pi$
$350$	7.54549	0.403324
$351$	80.3320	4.28781
$352$	3.53136	0.188222
$353$	14.2058	0.756097	0.378049	−	0.925786i	$-0.376595\pi$
$353$	14.2058	0.756097	0.378049	+	0.925786i	$0.376595\pi$
$354$	37.5964	1.99823
$355$	35.6442	1.89180
$356$	29.9689	1.58835
$357$	−15.9618	−0.844788
$358$	−31.6049	−1.67037
$359$	−2.54056	−0.134085	−0.0670427	−	0.997750i	$-0.521356\pi$
$359$	−2.54056	−0.134085	−0.0670427	+	0.997750i	$0.521356\pi$
$360$	−8.61267	−0.453928
$361$	−11.4953	−0.605015
$362$	−36.2614	−1.90586
$363$	−33.8729	−1.77787
$364$	−14.8362	−0.777629
$365$	2.75154	0.144022
$366$	83.1321	4.34538
$367$	7.57297	0.395306	0.197653	−	0.980272i	$-0.436668\pi$
$367$	7.57297	0.395306	0.197653	+	0.980272i	$0.436668\pi$
$368$	14.9573	0.779704
$369$	6.81856	0.354960
$370$	47.7809	2.48401
$371$	−1.45098	−0.0753312
$372$	−10.2970	−0.533874
$373$	−32.8497	−1.70089	−0.850446	−	0.526063i	$-0.823668\pi$
$373$	−32.8497	−1.70089	−0.850446	+	0.526063i	$0.823668\pi$
$374$	−4.54710	−0.235125
$375$	−12.2034	−0.630179
$376$	−0.145468	−0.00750192
$377$	−11.0384	−0.568505
$378$	24.5392	1.26216
$379$	12.8555	0.660342	0.330171	−	0.943921i	$-0.392894\pi$
$379$	12.8555	0.660342	0.330171	+	0.943921i	$0.392894\pi$
$380$	17.8269	0.914502
$381$	−20.0174	−1.02552
$382$	24.8389	1.27087
$383$	−27.3967	−1.39991	−0.699953	−	0.714189i	$-0.746796\pi$
$383$	−27.3967	−1.39991	−0.699953	+	0.714189i	$0.746796\pi$
$384$	10.6911	0.545577
$385$	−1.28164	−0.0653186
$386$	10.3546	0.527034
$387$	49.1491	2.49839
$388$	0.985248	0.0500184
$389$	−13.9416	−0.706867	−0.353434	−	0.935460i	$-0.614986\pi$
$389$	−13.9416	−0.706867	−0.353434	+	0.935460i	$0.614986\pi$
$390$	−127.179	−6.43998
$391$	−21.5353	−1.08909
$392$	−0.428856	−0.0216605
$393$	−0.625173	−0.0315358
$394$	−29.0956	−1.46582
$395$	34.2499	1.72330
$396$	6.55214	0.329258
$397$	28.7754	1.44420	0.722099	−	0.691790i	$-0.243177\pi$
$397$	28.7754	1.44420	0.722099	+	0.691790i	$0.243177\pi$
$398$	48.4976	2.43096
$399$	−8.58353	−0.429714
$400$	−13.0132	−0.650658
$401$	34.4580	1.72075	0.860376	−	0.509660i	$-0.170229\pi$
$401$	34.4580	1.72075	0.860376	+	0.509660i	$0.170229\pi$
$402$	−22.2014	−1.10731
$403$	−9.99146	−0.497710
$404$	−25.1834	−1.25292
$405$	50.1525	2.49210
$406$	−3.37191	−0.167345
$407$	−3.43967	−0.170498
$408$	−6.84531	−0.338893
$409$	13.8846	0.686547	0.343274	−	0.939235i	$-0.388464\pi$
$409$	13.8846	0.686547	0.343274	+	0.939235i	$0.388464\pi$
$410$	−6.04464	−0.298524
$411$	−2.21422	−0.109219
$412$	4.15530	0.204717
$413$	5.84866	0.287794
$414$	59.1260	2.90588
$415$	−40.1987	−1.97327
$416$	54.5132	2.67273
$417$	0.540500	0.0264684
$418$	−2.44523	−0.119600
$419$	19.6044	0.957737	0.478868	−	0.877887i	$-0.341047\pi$
$419$	19.6044	0.957737	0.478868	+	0.877887i	$0.341047\pi$
$420$	−20.3896	−0.994909
$421$	0.788107	0.0384100	0.0192050	−	0.999816i	$-0.493886\pi$
$421$	0.788107	0.0384100	0.0192050	+	0.999816i	$0.493886\pi$
$422$	−21.9774	−1.06984
$423$	2.31246	0.112436
$424$	−0.622262	−0.0302197
$425$	18.7361	0.908835
$426$	−77.7808	−3.76849
$427$	12.9324	0.625842
$428$	−21.1360	−1.02165
$429$	9.15545	0.442029
$430$	−43.5706	−2.10116
$431$	22.3223	1.07523	0.537614	−	0.843191i	$-0.319326\pi$
$431$	22.3223	1.07523	0.537614	+	0.843191i	$0.319326\pi$
$432$	−42.3209	−2.03617
$433$	−13.1072	−0.629892	−0.314946	−	0.949110i	$-0.601986\pi$
$433$	−13.1072	−0.629892	−0.314946	+	0.949110i	$0.601986\pi$
$434$	−3.05211	−0.146506
$435$	−15.1702	−0.727353
$436$	−42.5770	−2.03907
$437$	−11.5807	−0.553979
$438$	−6.00425	−0.286894
$439$	38.0950	1.81818	0.909089	−	0.416603i	$-0.136779\pi$
$439$	38.0950	1.81818	0.909089	+	0.416603i	$0.136779\pi$
$440$	−0.549641	−0.0262031
$441$	6.81742	0.324639
$442$	−70.1931	−3.33875
$443$	−8.38013	−0.398152	−0.199076	−	0.979984i	$-0.563794\pi$
$443$	−8.38013	−0.398152	−0.199076	+	0.979984i	$0.563794\pi$
$444$	−54.7215	−2.59697
$445$	39.9646	1.89450
$446$	38.1340	1.80570
$447$	−34.6156	−1.63726
$448$	9.57576	0.452412
$449$	−24.4885	−1.15568	−0.577842	−	0.816149i	$-0.696105\pi$
$449$	−24.4885	−1.15568	−0.577842	+	0.816149i	$0.696105\pi$
$450$	−51.4408	−2.42494
$451$	0.435144	0.0204902
$452$	−32.3352	−1.52092
$453$	13.3118	0.625444
$454$	53.7042	2.52046
$455$	−19.7846	−0.927516
$456$	−3.68110	−0.172383
$457$	−31.1910	−1.45906	−0.729528	−	0.683951i	$-0.760260\pi$
$457$	−31.1910	−1.45906	−0.729528	+	0.683951i	$0.760260\pi$
$458$	3.88704	0.181629
$459$	60.9328	2.84410
$460$	−27.5091	−1.28262
$461$	1.43932	0.0670357	0.0335179	−	0.999438i	$-0.489329\pi$
$461$	1.43932	0.0670357	0.0335179	+	0.999438i	$0.489329\pi$
$462$	2.79673	0.130116
$463$	33.3985	1.55216	0.776080	−	0.630635i	$-0.217205\pi$
$463$	33.3985	1.55216	0.776080	+	0.630635i	$0.217205\pi$
$464$	5.81529	0.269968
$465$	−13.7314	−0.636777
$466$	39.8288	1.84504
$467$	7.05674	0.326547	0.163273	−	0.986581i	$-0.447795\pi$
$467$	7.05674	0.326547	0.163273	+	0.986581i	$0.447795\pi$
$468$	101.145	4.67541
$469$	−3.45375	−0.159480
$470$	−2.04999	−0.0945592
$471$	8.51369	0.392290
$472$	2.50823	0.115451
$473$	3.13658	0.144220
$474$	−74.7382	−3.43284
$475$	10.0754	0.462292
$476$	−11.2534	−0.515801
$477$	9.89195	0.452921
$478$	5.57976	0.255212
$479$	2.26470	0.103477	0.0517385	−	0.998661i	$-0.483524\pi$
$479$	2.26470	0.103477	0.0517385	+	0.998661i	$0.483524\pi$
$480$	74.9180	3.41952
$481$	−53.0978	−2.42105
$482$	53.7450	2.44802
$483$	13.2454	0.602688
$484$	−23.8812	−1.08551
$485$	1.31386	0.0596593
$486$	−35.8224	−1.62494
$487$	−37.7083	−1.70872	−0.854362	−	0.519678i	$-0.826052\pi$
$487$	−37.7083	−1.70872	−0.854362	+	0.519678i	$0.826052\pi$
$488$	5.54613	0.251062
$489$	27.1514	1.22783
$490$	−6.04363	−0.273023
$491$	19.1138	0.862593	0.431296	−	0.902210i	$-0.358056\pi$
$491$	19.1138	0.862593	0.431296	+	0.902210i	$0.358056\pi$
$492$	6.92268	0.312098
$493$	−8.37274	−0.377089
$494$	−37.7467	−1.69830
$495$	8.73750	0.392721
$496$	5.26375	0.236349
$497$	−12.0999	−0.542756
$498$	87.7193	3.93079
$499$	−21.5509	−0.964749	−0.482374	−	0.875965i	$-0.660226\pi$
$499$	−21.5509	−0.964749	−0.482374	+	0.875965i	$0.660226\pi$
$500$	−8.60366	−0.384768
$501$	26.4149	1.18013
$502$	−58.9665	−2.63180
$503$	−0.659382	−0.0294004	−0.0147002	−	0.999892i	$-0.504679\pi$
$503$	−0.659382	−0.0294004	−0.0147002	+	0.999892i	$0.504679\pi$
$504$	2.92369	0.130232
$505$	−33.5829	−1.49442
$506$	3.77328	0.167743
$507$	100.599	4.46776
$508$	−14.1127	−0.626151
$509$	0.418159	0.0185346	0.00926729	−	0.999957i	$-0.497050\pi$
$509$	0.418159	0.0185346	0.00926729	+	0.999957i	$0.497050\pi$
$510$	−96.4672	−4.27164
$511$	−0.934048	−0.0413198
$512$	−31.7537	−1.40333
$513$	32.7669	1.44669
$514$	−38.8508	−1.71364
$515$	5.54123	0.244176
$516$	49.8996	2.19671
$517$	0.147576	0.00649038
$518$	−16.2199	−0.712661
$519$	−36.2511	−1.59125
$520$	−8.48474	−0.372080
$521$	38.9537	1.70659	0.853297	−	0.521425i	$-0.174599\pi$
$521$	38.9537	1.70659	0.853297	+	0.521425i	$0.174599\pi$
$522$	22.9877	1.00615
$523$	4.41705	0.193144	0.0965721	−	0.995326i	$-0.469212\pi$
$523$	4.41705	0.193144	0.0965721	+	0.995326i	$0.469212\pi$
$524$	−0.440762	−0.0192548
$525$	−11.5238	−0.502939
$526$	−5.69759	−0.248427
$527$	−7.57865	−0.330131
$528$	−4.82332	−0.209908
$529$	−5.12959	−0.223026
$530$	−8.76920	−0.380910
$531$	−39.8728	−1.73033
$532$	−6.05159	−0.262370
$533$	6.71728	0.290958
$534$	−87.2085	−3.77388
$535$	−28.1855	−1.21857
$536$	−1.48116	−0.0639765
$537$	48.2682	2.08293
$538$	37.3505	1.61029
$539$	0.435072	0.0187399
$540$	77.8355	3.34951
$541$	−36.1786	−1.55544	−0.777720	−	0.628611i	$-0.783624\pi$
$541$	−36.1786	−1.55544	−0.777720	+	0.628611i	$0.783624\pi$
$542$	−4.32362	−0.185715
$543$	55.3799	2.37658
$544$	41.3489	1.77282
$545$	−56.7778	−2.43209
$546$	43.1728	1.84763
$547$	−24.9709	−1.06768	−0.533839	−	0.845586i	$-0.679251\pi$
$547$	−24.9709	−1.06768	−0.533839	+	0.845586i	$0.679251\pi$
$548$	−1.56108	−0.0666858
$549$	−88.1655	−3.76281
$550$	−3.28283	−0.139980
$551$	−4.50248	−0.191812
$552$	5.68038	0.241773
$553$	−11.6266	−0.494413
$554$	−5.70128	−0.242224
$555$	−72.9729	−3.09753
$556$	0.381065	0.0161608
$557$	26.4042	1.11878	0.559390	−	0.828904i	$-0.311035\pi$
$557$	26.4042	1.11878	0.559390	+	0.828904i	$0.311035\pi$
$558$	20.8075	0.880852
$559$	48.4190	2.04791
$560$	10.4230	0.440452
$561$	6.94452	0.293198
$562$	−29.2989	−1.23590
$563$	−40.6257	−1.71217	−0.856085	−	0.516836i	$-0.827110\pi$
$563$	−40.6257	−1.71217	−0.856085	+	0.516836i	$0.827110\pi$
$564$	2.34777	0.0988591
$565$	−43.1201	−1.81408
$566$	3.05415	0.128375
$567$	−17.0249	−0.714980
$568$	−5.18912	−0.217731
$569$	−27.1151	−1.13672	−0.568362	−	0.822778i	$-0.692423\pi$
$569$	−27.1151	−1.13672	−0.568362	+	0.822778i	$0.692423\pi$
$570$	−51.8757	−2.17283
$571$	−2.83725	−0.118735	−0.0593676	−	0.998236i	$-0.518908\pi$
$571$	−2.83725	−0.118735	−0.0593676	+	0.998236i	$0.518908\pi$
$572$	6.45481	0.269889
$573$	−37.9349	−1.58475
$574$	2.05194	0.0856462
$575$	−15.5476	−0.648380
$576$	−65.2820	−2.72008
$577$	−18.9417	−0.788554	−0.394277	−	0.918992i	$-0.629005\pi$
$577$	−18.9417	−0.788554	−0.394277	+	0.918992i	$0.629005\pi$
$578$	−18.3653	−0.763894
$579$	−15.8139	−0.657205
$580$	−10.6953	−0.444099
$581$	13.6460	0.566131
$582$	−2.86703	−0.118842
$583$	0.631281	0.0261450
$584$	−0.400572	−0.0165758
$585$	134.880	5.57659
$586$	3.28127	0.135548
$587$	−1.61398	−0.0666161	−0.0333080	−	0.999445i	$-0.510604\pi$
$587$	−1.61398	−0.0666161	−0.0333080	+	0.999445i	$0.510604\pi$
$588$	6.92152	0.285439
$589$	−4.07545	−0.167926
$590$	35.3472	1.45522
$591$	44.4360	1.82785
$592$	27.9732	1.14969
$593$	39.1051	1.60585	0.802927	−	0.596078i	$-0.203275\pi$
$593$	39.1051	1.60585	0.802927	+	0.596078i	$0.203275\pi$
$594$	−10.6763	−0.438054
$595$	−15.0068	−0.615221
$596$	−24.4049	−0.999662
$597$	−74.0675	−3.03138
$598$	58.2477	2.38193
$599$	−8.15008	−0.333003	−0.166502	−	0.986041i	$-0.553247\pi$
$599$	−8.15008	−0.333003	−0.166502	+	0.986041i	$0.553247\pi$
$600$	−4.94204	−0.201758
$601$	−30.9086	−1.26079	−0.630394	−	0.776275i	$-0.717107\pi$
$601$	−30.9086	−1.26079	−0.630394	+	0.776275i	$0.717107\pi$
$602$	14.7906	0.602821
$603$	23.5457	0.958854
$604$	9.38515	0.381876
$605$	−31.8464	−1.29474
$606$	73.2826	2.97690
$607$	14.2167	0.577038	0.288519	−	0.957474i	$-0.406837\pi$
$607$	14.2167	0.577038	0.288519	+	0.957474i	$0.406837\pi$
$608$	22.2356	0.901771
$609$	5.14972	0.208677
$610$	78.1586	3.16455
$611$	2.27811	0.0921626
$612$	76.7195	3.10120
$613$	−15.8861	−0.641633	−0.320817	−	0.947141i	$-0.603957\pi$
$613$	−15.8861	−0.641633	−0.320817	+	0.947141i	$0.603957\pi$
$614$	−17.9107	−0.722816
$615$	9.23162	0.372255
$616$	0.186583	0.00751765
$617$	13.8588	0.557934	0.278967	−	0.960301i	$-0.410008\pi$
$617$	13.8588	0.557934	0.278967	+	0.960301i	$0.410008\pi$
$618$	−12.0918	−0.486402
$619$	22.8375	0.917918	0.458959	−	0.888458i	$-0.348223\pi$
$619$	22.8375	0.917918	0.458959	+	0.888458i	$0.348223\pi$
$620$	−9.68095	−0.388796
$621$	−50.5633	−2.02904
$622$	−14.1279	−0.566477
$623$	−13.5665	−0.543531
$624$	−74.4570	−2.98066
$625$	−29.8626	−1.19450
$626$	4.35743	0.174158
$627$	3.73445	0.149139
$628$	6.00236	0.239520
$629$	−40.2753	−1.60588
$630$	41.2020	1.64153
$631$	2.46291	0.0980470	0.0490235	−	0.998798i	$-0.484389\pi$
$631$	2.46291	0.0980470	0.0490235	+	0.998798i	$0.484389\pi$
$632$	−4.98613	−0.198338
$633$	33.5647	1.33408
$634$	22.3024	0.885741
$635$	−18.8198	−0.746840
$636$	10.0430	0.398231
$637$	6.71615	0.266104
$638$	1.46702	0.0580800
$639$	82.4902	3.26326
$640$	10.0515	0.397319
$641$	4.57178	0.180574	0.0902872	−	0.995916i	$-0.471222\pi$
$641$	4.57178	0.180574	0.0902872	+	0.995916i	$0.471222\pi$
$642$	61.5049	2.42740
$643$	27.4982	1.08442	0.542212	−	0.840242i	$-0.317587\pi$
$643$	27.4982	1.08442	0.542212	+	0.840242i	$0.317587\pi$
$644$	9.33835	0.367982
$645$	66.5428	2.62012
$646$	−28.6313	−1.12648
$647$	44.2271	1.73875	0.869374	−	0.494154i	$-0.164522\pi$
$647$	44.2271	1.73875	0.869374	+	0.494154i	$0.164522\pi$
$648$	−7.30125	−0.286820
$649$	−2.54459	−0.0998838
$650$	−50.6767	−1.98770
$651$	4.66130	0.182691
$652$	19.1424	0.749675
$653$	46.0349	1.80148	0.900742	−	0.434355i	$-0.143024\pi$
$653$	46.0349	1.80148	0.900742	+	0.434355i	$0.143024\pi$
$654$	123.897	4.84477
$655$	−0.587771	−0.0229661
$656$	−3.53883	−0.138168
$657$	6.36779	0.248431
$658$	0.695899	0.0271290
$659$	27.5237	1.07217	0.536086	−	0.844163i	$-0.319902\pi$
$659$	27.5237	1.07217	0.536086	+	0.844163i	$0.319902\pi$
$660$	8.87092	0.345300
$661$	−15.3073	−0.595383	−0.297692	−	0.954662i	$-0.596217\pi$
$661$	−15.3073	−0.595383	−0.297692	+	0.954662i	$0.596217\pi$
$662$	−29.4674	−1.14528
$663$	107.202	4.16337
$664$	5.85216	0.227108
$665$	−8.07000	−0.312941
$666$	110.578	4.28480
$667$	6.94787	0.269023
$668$	18.6231	0.720550
$669$	−58.2397	−2.25168
$670$	−20.8732	−0.806402
$671$	−5.62651	−0.217209
$672$	−25.4319	−0.981059
$673$	11.7677	0.453613	0.226806	−	0.973940i	$-0.427172\pi$
$673$	11.7677	0.453613	0.226806	+	0.973940i	$0.427172\pi$
$674$	23.7790	0.915932
$675$	43.9911	1.69322
$676$	70.9248	2.72788
$677$	−27.0006	−1.03772	−0.518859	−	0.854860i	$-0.673643\pi$
$677$	−27.0006	−1.03772	−0.518859	+	0.854860i	$0.673643\pi$
$678$	94.0943	3.61367
$679$	−0.446008	−0.0171162
$680$	−6.43578	−0.246801
$681$	−82.0193	−3.14298
$682$	1.32789	0.0508474
$683$	17.5893	0.673037	0.336518	−	0.941677i	$-0.390751\pi$
$683$	17.5893	0.673037	0.336518	+	0.941677i	$0.390751\pi$
$684$	41.2562	1.57747
$685$	−2.08175	−0.0795394
$686$	2.05159	0.0783302
$687$	−5.93644	−0.226489
$688$	−25.5083	−0.972496
$689$	9.74501	0.371255
$690$	80.0505	3.04747
$691$	−3.29171	−0.125223	−0.0626113	−	0.998038i	$-0.519943\pi$
$691$	−3.29171	−0.125223	−0.0626113	+	0.998038i	$0.519943\pi$
$692$	−25.5579	−0.971567
$693$	−2.96607	−0.112671
$694$	−51.1581	−1.94193
$695$	0.508163	0.0192757
$696$	2.20849	0.0837125
$697$	5.09514	0.192992
$698$	51.0233	1.93126
$699$	−60.8282	−2.30073
$700$	−8.12455	−0.307079
$701$	−13.8910	−0.524655	−0.262327	−	0.964979i	$-0.584490\pi$
$701$	−13.8910	−0.524655	−0.262327	+	0.964979i	$0.584490\pi$
$702$	−164.809	−6.22030
$703$	−21.6582	−0.816856
$704$	−4.16614	−0.157017
$705$	3.13083	0.117914
$706$	−29.1445	−1.09687
$707$	11.4002	0.428747
$708$	−40.4816	−1.52139
$709$	38.9263	1.46191	0.730953	−	0.682428i	$-0.239076\pi$
$709$	38.9263	1.46191	0.730953	+	0.682428i	$0.239076\pi$
$710$	−73.1274	−2.74442
$711$	79.2634	2.97261
$712$	−5.81809	−0.218042
$713$	6.28892	0.235522
$714$	32.7471	1.22553
$715$	8.60771	0.321910
$716$	34.0303	1.27177
$717$	−8.52163	−0.318246
$718$	5.21219	0.194517
$719$	11.2739	0.420444	0.210222	−	0.977654i	$-0.432581\pi$
$719$	11.2739	0.420444	0.210222	+	0.977654i	$0.432581\pi$
$720$	−71.0580	−2.64818
$721$	−1.88105	−0.0700539
$722$	23.5837	0.877693
$723$	−82.0816	−3.05265
$724$	39.0442	1.45106
$725$	−6.04479	−0.224498
$726$	69.4935	2.57915
$727$	31.2629	1.15948	0.579738	−	0.814803i	$-0.303155\pi$
$727$	31.2629	1.15948	0.579738	+	0.814803i	$0.303155\pi$
$728$	2.88026	0.106750
$729$	3.63457	0.134614
$730$	−5.64504	−0.208932
$731$	36.7264	1.35838
$732$	−89.5118	−3.30845
$733$	19.2116	0.709595	0.354798	−	0.934943i	$-0.384550\pi$
$733$	19.2116	0.709595	0.354798	+	0.934943i	$0.384550\pi$
$734$	−15.5367	−0.573469
$735$	9.23008	0.340456
$736$	−34.3122	−1.26476
$737$	1.50263	0.0553501
$738$	−13.9889	−0.514939
$739$	31.4563	1.15714	0.578569	−	0.815633i	$-0.303611\pi$
$739$	31.4563	1.15714	0.578569	+	0.815633i	$0.303611\pi$
$740$	−51.4477	−1.89125
$741$	57.6482	2.11776
$742$	2.97683	0.109283
$743$	−6.21526	−0.228016	−0.114008	−	0.993480i	$-0.536369\pi$
$743$	−6.21526	−0.228016	−0.114008	+	0.993480i	$0.536369\pi$
$744$	1.99903	0.0732879
$745$	−32.5447	−1.19234
$746$	67.3942	2.46748
$747$	−93.0304	−3.40380
$748$	4.89606	0.179018
$749$	9.56797	0.349606
$750$	25.0363	0.914197
$751$	10.2682	0.374693	0.187346	−	0.982294i	$-0.440011\pi$
$751$	10.2682	0.374693	0.187346	+	0.982294i	$0.440011\pi$
$752$	−1.20017	−0.0437655
$753$	90.0560	3.28182
$754$	22.6463	0.824728
$755$	12.5154	0.455483
$756$	−26.4223	−0.960971
$757$	−11.9837	−0.435555	−0.217778	−	0.975998i	$-0.569881\pi$
$757$	−11.9837	−0.435555	−0.217778	+	0.975998i	$0.569881\pi$
$758$	−26.3742	−0.957955
$759$	−5.76271	−0.209173
$760$	−3.46087	−0.125539
$761$	40.6052	1.47194	0.735969	−	0.677015i	$-0.236727\pi$
$761$	40.6052	1.47194	0.735969	+	0.677015i	$0.236727\pi$
$762$	41.0675	1.48772
$763$	19.2740	0.697766
$764$	−26.7450	−0.967602
$765$	102.308	3.69895
$766$	56.2069	2.03084
$767$	−39.2805	−1.41834
$768$	38.0732	1.37385
$769$	16.4854	0.594479	0.297239	−	0.954803i	$-0.403934\pi$
$769$	16.4854	0.594479	0.297239	+	0.954803i	$0.403934\pi$
$770$	2.62941	0.0947574
$771$	59.3345	2.13688
$772$	−11.1492	−0.401269
$773$	33.2031	1.19423	0.597116	−	0.802155i	$-0.296313\pi$
$773$	33.2031	1.19423	0.597116	+	0.802155i	$0.296313\pi$
$774$	−100.834	−3.62440
$775$	−5.47148	−0.196541
$776$	−0.191273	−0.00686631
$777$	24.7717	0.888678
$778$	28.6025	1.02545
$779$	2.73993	0.0981683
$780$	136.939	4.90322
$781$	5.26433	0.188373
$782$	44.1816	1.57993
$783$	−19.6586	−0.702542
$784$	−3.53823	−0.126365
$785$	8.00435	0.285687
$786$	1.28260	0.0457488
$787$	7.78663	0.277563	0.138782	−	0.990323i	$-0.455681\pi$
$787$	7.78663	0.277563	0.138782	+	0.990323i	$0.455681\pi$
$788$	31.3285	1.11603
$789$	8.70159	0.309785
$790$	−70.2668	−2.49998
$791$	14.6377	0.520457
$792$	−1.27201	−0.0451991
$793$	−86.8559	−3.08434
$794$	−59.0355	−2.09509
$795$	13.3927	0.474989
$796$	−52.2194	−1.85087
$797$	10.9511	0.387909	0.193955	−	0.981011i	$-0.437869\pi$
$797$	10.9511	0.387909	0.193955	+	0.981011i	$0.437869\pi$
$798$	17.6099	0.623384
$799$	1.72798	0.0611314
$800$	29.8523	1.05544
$801$	92.4887	3.26793
$802$	−70.6939	−2.49629
$803$	0.406378	0.0143408
$804$	23.9052	0.843072
$805$	12.4530	0.438910
$806$	20.4984	0.722026
$807$	−57.0431	−2.00801
$808$	4.88903	0.171995
$809$	1.50672	0.0529734	0.0264867	−	0.999649i	$-0.491568\pi$
$809$	1.50672	0.0529734	0.0264867	+	0.999649i	$0.491568\pi$
$810$	−102.892	−3.61527
$811$	−1.26462	−0.0444067	−0.0222033	−	0.999753i	$-0.507068\pi$
$811$	−1.26462	−0.0444067	−0.0222033	+	0.999753i	$0.507068\pi$
$812$	3.63068	0.127412
$813$	6.60321	0.231585
$814$	7.05681	0.247341
$815$	25.5271	0.894174
$816$	−56.4765	−1.97707
$817$	19.7498	0.690958
$818$	−28.4855	−0.995971
$819$	−45.7868	−1.59992
$820$	6.50852	0.227287
$821$	50.3258	1.75638	0.878191	−	0.478310i	$-0.158750\pi$
$821$	50.3258	1.75638	0.878191	+	0.478310i	$0.158750\pi$
$822$	4.54267	0.158444
$823$	−36.3216	−1.26609	−0.633046	−	0.774114i	$-0.718196\pi$
$823$	−36.3216	−1.26609	−0.633046	+	0.774114i	$0.718196\pi$
$824$	−0.806699	−0.0281027
$825$	5.01367	0.174554
$826$	−11.9991	−0.417501
$827$	40.2518	1.39969	0.699846	−	0.714294i	$-0.253252\pi$
$827$	40.2518	1.39969	0.699846	+	0.714294i	$0.253252\pi$
$828$	−63.6634	−2.21246
$829$	−34.8023	−1.20874	−0.604368	−	0.796706i	$-0.706574\pi$
$829$	−34.8023	−1.20874	−0.604368	+	0.796706i	$0.706574\pi$
$830$	82.4713	2.86262
$831$	8.70723	0.302050
$832$	−64.3122	−2.22963
$833$	5.09428	0.176506
$834$	−1.10889	−0.0383976
$835$	24.8345	0.859435
$836$	2.63288	0.0910599
$837$	−17.7941	−0.615056
$838$	−40.2202	−1.38938
$839$	−26.1270	−0.902003	−0.451002	−	0.892523i	$-0.648933\pi$
$839$	−26.1270	−0.902003	−0.451002	+	0.892523i	$0.648933\pi$
$840$	3.95837	0.136577
$841$	−26.2987	−0.906852
$842$	−1.61688	−0.0557212
$843$	44.7465	1.54115
$844$	23.6639	0.814547
$845$	94.5805	3.25367
$846$	−4.74423	−0.163110
$847$	10.8107	0.371460
$848$	−5.13391	−0.176299
$849$	−4.66441	−0.160082
$850$	−38.4389	−1.31844
$851$	33.4213	1.14567
$852$	83.7498	2.86922
$853$	−27.5477	−0.943217	−0.471608	−	0.881808i	$-0.656326\pi$
$853$	−27.5477	−0.943217	−0.471608	+	0.881808i	$0.656326\pi$
$854$	−26.5320	−0.907906
$855$	55.0166	1.88153
$856$	4.10328	0.140247
$857$	5.05959	0.172832	0.0864162	−	0.996259i	$-0.472459\pi$
$857$	5.05959	0.172832	0.0864162	+	0.996259i	$0.472459\pi$
$858$	−18.7833	−0.641250
$859$	1.00000	0.0341196
$859$	1.00000	0.0341196
$860$	46.9143	1.59976
$861$	−3.13380	−0.106800
$862$	−45.7964	−1.55983
$863$	40.6529	1.38384	0.691921	−	0.721973i	$-0.256765\pi$
$863$	40.6529	1.38384	0.691921	+	0.721973i	$0.256765\pi$
$864$	97.0844	3.30288
$865$	−34.0824	−1.15883
$866$	26.8907	0.913782
$867$	28.0482	0.952566
$868$	3.28633	0.111545
$869$	5.05840	0.171594
$870$	31.1230	1.05517
$871$	23.1959	0.785964
$872$	8.26577	0.279914
$873$	3.04062	0.102910
$874$	23.7589	0.803655
$875$	3.89476	0.131667
$876$	6.46503	0.218433
$877$	−11.5545	−0.390169	−0.195084	−	0.980786i	$-0.562498\pi$
$877$	−11.5545	−0.390169	−0.195084	+	0.980786i	$0.562498\pi$
$878$	−78.1555	−2.63762
$879$	−5.01129	−0.169026
$880$	−4.53475	−0.152867
$881$	−12.3758	−0.416951	−0.208475	−	0.978028i	$-0.566850\pi$
$881$	−12.3758	−0.416951	−0.208475	+	0.978028i	$0.566850\pi$
$882$	−13.9866	−0.470952
$883$	28.2861	0.951904	0.475952	−	0.879471i	$-0.342104\pi$
$883$	28.2861	0.951904	0.475952	+	0.879471i	$0.342104\pi$
$884$	75.5799	2.54203
$885$	−53.9836	−1.81464
$886$	17.1926	0.577597
$887$	−22.3286	−0.749720	−0.374860	−	0.927081i	$-0.622309\pi$
$887$	−22.3286	−0.749720	−0.374860	+	0.927081i	$0.622309\pi$
$888$	10.6235	0.356500
$889$	6.38863	0.214268
$890$	−81.9911	−2.74835
$891$	7.40707	0.248146
$892$	−41.0604	−1.37480
$893$	0.929227	0.0310954
$894$	71.0172	2.37517
$895$	45.3805	1.51690
$896$	−3.41211	−0.113991
$897$	−88.9583	−2.97023
$898$	50.2404	1.67654
$899$	2.44508	0.0815480
$900$	55.3884	1.84628
$901$	7.39171	0.246254
$902$	−0.892740	−0.0297250
$903$	−22.5889	−0.751710
$904$	6.27747	0.208786
$905$	52.0667	1.73076
$906$	−27.3104	−0.907328
$907$	16.7354	0.555690	0.277845	−	0.960626i	$-0.410380\pi$
$907$	16.7354	0.555690	0.277845	+	0.960626i	$0.410380\pi$
$908$	−57.8256	−1.91901
$909$	−77.7197	−2.57780
$910$	40.5899	1.34554
$911$	52.2607	1.73148	0.865738	−	0.500498i	$-0.166850\pi$
$911$	52.2607	1.73148	0.865738	+	0.500498i	$0.166850\pi$
$912$	−30.3705	−1.00567
$913$	−5.93698	−0.196485
$914$	63.9914	2.11665
$915$	−119.367	−3.94615
$916$	−4.18533	−0.138287
$917$	0.199527	0.00658896
$918$	−125.009	−4.12593
$919$	−27.9183	−0.920940	−0.460470	−	0.887675i	$-0.652319\pi$
$919$	−27.9183	−0.920940	−0.460470	+	0.887675i	$0.652319\pi$
$920$	5.34054	0.176072
$921$	27.3539	0.901342
$922$	−2.95290	−0.0972485
$923$	81.2649	2.67487
$924$	−3.01136	−0.0990663
$925$	−29.0772	−0.956053
$926$	−68.5201	−2.25171
$927$	12.8239	0.421192
$928$	−13.3403	−0.437917
$929$	50.5054	1.65703	0.828514	−	0.559968i	$-0.189187\pi$
$929$	50.5054	1.65703	0.828514	+	0.559968i	$0.189187\pi$
$930$	28.1712	0.923770
$931$	2.73947	0.0897826
$932$	−42.8854	−1.40476
$933$	21.5767	0.706389
$934$	−14.4776	−0.473720
$935$	6.52905	0.213523
$936$	−19.6359	−0.641821
$937$	3.34481	0.109270	0.0546350	−	0.998506i	$-0.482600\pi$
$937$	3.34481	0.109270	0.0546350	+	0.998506i	$0.482600\pi$
$938$	7.08570	0.231356
$939$	−6.65484	−0.217173
$940$	2.20731	0.0719946
$941$	49.0936	1.60040	0.800202	−	0.599730i	$-0.204726\pi$
$941$	49.0936	1.60040	0.800202	+	0.599730i	$0.204726\pi$
$942$	−17.4666	−0.569094
$943$	−4.22805	−0.137684
$944$	20.6939	0.673530
$945$	−35.2351	−1.14620
$946$	−6.43499	−0.209219
$947$	15.0949	0.490517	0.245259	−	0.969458i	$-0.421127\pi$
$947$	15.0949	0.490517	0.245259	+	0.969458i	$0.421127\pi$
$948$	80.4737	2.61366
$949$	6.27320	0.203637
$950$	−20.6707	−0.670645
$951$	−34.0611	−1.10451
$952$	2.18471	0.0708070
$953$	−13.2298	−0.428555	−0.214277	−	0.976773i	$-0.568740\pi$
$953$	−13.2298	−0.428555	−0.214277	+	0.976773i	$0.568740\pi$
$954$	−20.2943	−0.657051
$955$	−35.6654	−1.15411
$956$	−6.00795	−0.194311
$957$	−2.24050	−0.0724249
$958$	−4.64625	−0.150114
$959$	0.706677	0.0228198
$960$	−88.3850	−2.85261
$961$	−28.7868	−0.928607
$962$	108.935	3.51221
$963$	−65.2289	−2.10197
$964$	−57.8695	−1.86385
$965$	−14.8678	−0.478613
$966$	−27.1742	−0.874316
$967$	13.6065	0.437554	0.218777	−	0.975775i	$-0.429793\pi$
$967$	13.6065	0.437554	0.218777	+	0.975775i	$0.429793\pi$
$968$	4.63624	0.149014
$969$	43.7269	1.40471
$970$	−2.69551	−0.0865476
$971$	−51.2735	−1.64544	−0.822722	−	0.568443i	$-0.807546\pi$
$971$	−51.2735	−1.64544	−0.822722	+	0.568443i	$0.807546\pi$
$972$	38.5715	1.23718
$973$	−0.172503	−0.00553020
$974$	77.3620	2.47884
$975$	77.3955	2.47864
$976$	45.7578	1.46467
$977$	11.1732	0.357462	0.178731	−	0.983898i	$-0.442801\pi$
$977$	11.1732	0.357462	0.178731	+	0.983898i	$0.442801\pi$
$978$	−55.7037	−1.78121
$979$	5.90241	0.188642
$980$	6.50743	0.207872
$981$	−131.399	−4.19525
$982$	−39.2137	−1.25136
$983$	51.3369	1.63739	0.818697	−	0.574226i	$-0.194697\pi$
$983$	51.3369	1.63739	0.818697	+	0.574226i	$0.194697\pi$
$984$	−1.34395	−0.0428435
$985$	41.7776	1.33114
$986$	17.1775	0.547042
$987$	−1.06280	−0.0338294
$988$	40.6434	1.29304
$989$	−30.4763	−0.969091
$990$	−17.9258	−0.569719
$991$	−6.36024	−0.202040	−0.101020	−	0.994884i	$-0.532211\pi$
$991$	−6.36024	−0.202040	−0.101020	+	0.994884i	$0.532211\pi$
$992$	−12.0751	−0.383384
$993$	45.0038	1.42815
$994$	24.8241	0.787373
$995$	−69.6363	−2.20762
$996$	−94.4510	−2.99279
$997$	35.0715	1.11072	0.555362	−	0.831609i	$-0.312580\pi$
$997$	35.0715	1.11072	0.555362	+	0.831609i	$0.312580\pi$
$998$	44.2136	1.39956
$999$	−94.5638	−2.99187

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.f.1.16	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.f.1.16	✓	110	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)

\(f(q)\)	\(=\)	\(q-2.05159 q^{2} +3.13328 q^{3} +2.20904 q^{4} +2.94582 q^{5} -6.42821 q^{6} -1.00000 q^{7} -0.428856 q^{8} +6.81742 q^{9} +O(q^{10})\)	\(q-2.05159 q^{2} +3.13328 q^{3} +2.20904 q^{4} +2.94582 q^{5} -6.42821 q^{6} -1.00000 q^{7} -0.428856 q^{8} +6.81742 q^{9} -6.04363 q^{10} +0.435072 q^{11} +6.92152 q^{12} +6.71615 q^{13} +2.05159 q^{14} +9.23008 q^{15} -3.53823 q^{16} +5.09428 q^{17} -13.9866 q^{18} +2.73947 q^{19} +6.50743 q^{20} -3.13328 q^{21} -0.892590 q^{22} -4.22734 q^{23} -1.34372 q^{24} +3.67787 q^{25} -13.7788 q^{26} +11.9610 q^{27} -2.20904 q^{28} -1.64356 q^{29} -18.9364 q^{30} -1.48768 q^{31} +8.11673 q^{32} +1.36320 q^{33} -10.4514 q^{34} -2.94582 q^{35} +15.0599 q^{36} -7.90599 q^{37} -5.62028 q^{38} +21.0436 q^{39} -1.26333 q^{40} +1.00017 q^{41} +6.42821 q^{42} +7.20934 q^{43} +0.961089 q^{44} +20.0829 q^{45} +8.67278 q^{46} +0.339199 q^{47} -11.0863 q^{48} +1.00000 q^{49} -7.54549 q^{50} +15.9618 q^{51} +14.8362 q^{52} +1.45098 q^{53} -24.5392 q^{54} +1.28164 q^{55} +0.428856 q^{56} +8.58353 q^{57} +3.37191 q^{58} -5.84866 q^{59} +20.3896 q^{60} -12.9324 q^{61} +3.05211 q^{62} -6.81742 q^{63} -9.57576 q^{64} +19.7846 q^{65} -2.79673 q^{66} +3.45375 q^{67} +11.2534 q^{68} -13.2454 q^{69} +6.04363 q^{70} +12.0999 q^{71} -2.92369 q^{72} +0.934048 q^{73} +16.2199 q^{74} +11.5238 q^{75} +6.05159 q^{76} -0.435072 q^{77} -43.1728 q^{78} +11.6266 q^{79} -10.4230 q^{80} +17.0249 q^{81} -2.05194 q^{82} -13.6460 q^{83} -6.92152 q^{84} +15.0068 q^{85} -14.7906 q^{86} -5.14972 q^{87} -0.186583 q^{88} +13.5665 q^{89} -41.2020 q^{90} -6.71615 q^{91} -9.33835 q^{92} -4.66130 q^{93} -0.695899 q^{94} +8.07000 q^{95} +25.4319 q^{96} +0.446008 q^{97} -2.05159 q^{98} +2.96607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9}+O(q^{10}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9} + 3 q^{10} + 52 q^{11} + 62 q^{12} - 9 q^{13} - 16 q^{14} + 39 q^{15} + 146 q^{16} + 11 q^{17} + 60 q^{18} + 14 q^{19} + 18 q^{20} - 29 q^{21} + 32 q^{22} + 73 q^{23} + 24 q^{24} + 132 q^{25} - 7 q^{26} + 116 q^{27} - 118 q^{28} + 35 q^{29} + 18 q^{30} + 36 q^{31} + 140 q^{32} + 42 q^{33} - 7 q^{34} + 180 q^{36} + 49 q^{37} + 45 q^{39} + 6 q^{40} - 14 q^{41} - 12 q^{42} + 58 q^{43} + 92 q^{44} + 17 q^{45} + 27 q^{46} + 87 q^{47} + 98 q^{48} + 110 q^{49} + 91 q^{50} + 42 q^{51} + 16 q^{52} + 95 q^{53} + 41 q^{54} + 8 q^{55} - 57 q^{56} + 61 q^{57} + 46 q^{58} + 114 q^{59} + 81 q^{60} - 47 q^{61} + 31 q^{62} - 127 q^{63} + 199 q^{64} + 62 q^{65} + 21 q^{66} + 95 q^{67} + 60 q^{68} - 39 q^{69} - 3 q^{70} + 131 q^{71} + 186 q^{72} + 31 q^{73} + 23 q^{74} + 121 q^{75} + 14 q^{76} - 52 q^{77} + 110 q^{78} + 9 q^{79} + 61 q^{80} + 194 q^{81} + 45 q^{82} + 73 q^{83} - 62 q^{84} + 59 q^{85} + 72 q^{86} + 64 q^{87} + 100 q^{88} - 17 q^{89} + 11 q^{90} + 9 q^{91} + 192 q^{92} + 85 q^{93} - 11 q^{94} + 108 q^{95} + 68 q^{96} + 32 q^{97} + 16 q^{98} + 160 q^{99}+O(q^{100}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9 + 3 * q^10 + 52 * q^11 + 62 * q^12 - 9 * q^13 - 16 * q^14 + 39 * q^15 + 146 * q^16 + 11 * q^17 + 60 * q^18 + 14 * q^19 + 18 * q^20 - 29 * q^21 + 32 * q^22 + 73 * q^23 + 24 * q^24 + 132 * q^25 - 7 * q^26 + 116 * q^27 - 118 * q^28 + 35 * q^29 + 18 * q^30 + 36 * q^31 + 140 * q^32 + 42 * q^33 - 7 * q^34 + 180 * q^36 + 49 * q^37 + 45 * q^39 + 6 * q^40 - 14 * q^41 - 12 * q^42 + 58 * q^43 + 92 * q^44 + 17 * q^45 + 27 * q^46 + 87 * q^47 + 98 * q^48 + 110 * q^49 + 91 * q^50 + 42 * q^51 + 16 * q^52 + 95 * q^53 + 41 * q^54 + 8 * q^55 - 57 * q^56 + 61 * q^57 + 46 * q^58 + 114 * q^59 + 81 * q^60 - 47 * q^61 + 31 * q^62 - 127 * q^63 + 199 * q^64 + 62 * q^65 + 21 * q^66 + 95 * q^67 + 60 * q^68 - 39 * q^69 - 3 * q^70 + 131 * q^71 + 186 * q^72 + 31 * q^73 + 23 * q^74 + 121 * q^75 + 14 * q^76 - 52 * q^77 + 110 * q^78 + 9 * q^79 + 61 * q^80 + 194 * q^81 + 45 * q^82 + 73 * q^83 - 62 * q^84 + 59 * q^85 + 72 * q^86 + 64 * q^87 + 100 * q^88 - 17 * q^89 + 11 * q^90 + 9 * q^91 + 192 * q^92 + 85 * q^93 - 11 * q^94 + 108 * q^95 + 68 * q^96 + 32 * q^97 + 16 * q^98 + 160 * q^99

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