LMFDB - Embedded newform 6014.2.a.k.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, 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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.177510 q^{3} +1.00000 q^{4} -1.23284 q^{5} -0.177510 q^{6} -3.05433 q^{7} +1.00000 q^{8} -2.96849 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.177510 q^{3} +1.00000 q^{4} -1.23284 q^{5} -0.177510 q^{6} -3.05433 q^{7} +1.00000 q^{8} -2.96849 q^{9} -1.23284 q^{10} -5.49033 q^{11} -0.177510 q^{12} +6.80162 q^{13} -3.05433 q^{14} +0.218841 q^{15} +1.00000 q^{16} -7.15489 q^{17} -2.96849 q^{18} +8.08435 q^{19} -1.23284 q^{20} +0.542174 q^{21} -5.49033 q^{22} -8.34433 q^{23} -0.177510 q^{24} -3.48010 q^{25} +6.80162 q^{26} +1.05947 q^{27} -3.05433 q^{28} +5.04538 q^{29} +0.218841 q^{30} +1.00000 q^{31} +1.00000 q^{32} +0.974587 q^{33} -7.15489 q^{34} +3.76551 q^{35} -2.96849 q^{36} -2.85457 q^{37} +8.08435 q^{38} -1.20735 q^{39} -1.23284 q^{40} +6.87641 q^{41} +0.542174 q^{42} +3.45667 q^{43} -5.49033 q^{44} +3.65968 q^{45} -8.34433 q^{46} -1.76971 q^{47} -0.177510 q^{48} +2.32895 q^{49} -3.48010 q^{50} +1.27006 q^{51} +6.80162 q^{52} +2.47883 q^{53} +1.05947 q^{54} +6.76871 q^{55} -3.05433 q^{56} -1.43505 q^{57} +5.04538 q^{58} +2.84240 q^{59} +0.218841 q^{60} -12.4723 q^{61} +1.00000 q^{62} +9.06676 q^{63} +1.00000 q^{64} -8.38533 q^{65} +0.974587 q^{66} +7.21590 q^{67} -7.15489 q^{68} +1.48120 q^{69} +3.76551 q^{70} +13.4257 q^{71} -2.96849 q^{72} -5.02171 q^{73} -2.85457 q^{74} +0.617752 q^{75} +8.08435 q^{76} +16.7693 q^{77} -1.20735 q^{78} +5.34813 q^{79} -1.23284 q^{80} +8.71741 q^{81} +6.87641 q^{82} -11.5119 q^{83} +0.542174 q^{84} +8.82085 q^{85} +3.45667 q^{86} -0.895605 q^{87} -5.49033 q^{88} +6.96947 q^{89} +3.65968 q^{90} -20.7744 q^{91} -8.34433 q^{92} -0.177510 q^{93} -1.76971 q^{94} -9.96673 q^{95} -0.177510 q^{96} +1.00000 q^{97} +2.32895 q^{98} +16.2980 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9}+O(q^{10}) $ 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9} + 9 q^{10} + 5 q^{11} + 9 q^{12} + 16 q^{13} + 19 q^{14} + 22 q^{15} + 37 q^{16} + 3 q^{17} + 52 q^{18} + 36 q^{19} + 9 q^{20} + 6 q^{21} + 5 q^{22} + 11 q^{23} + 9 q^{24} + 58 q^{25} + 16 q^{26} + 24 q^{27} + 19 q^{28} + 5 q^{29} + 22 q^{30} + 37 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 28 q^{35} + 52 q^{36} + 21 q^{37} + 36 q^{38} + 38 q^{39} + 9 q^{40} + 21 q^{41} + 6 q^{42} + 14 q^{43} + 5 q^{44} + 55 q^{45} + 11 q^{46} + 59 q^{47} + 9 q^{48} + 82 q^{49} + 58 q^{50} + 46 q^{51} + 16 q^{52} + 8 q^{53} + 24 q^{54} + 25 q^{55} + 19 q^{56} + 5 q^{58} + 41 q^{59} + 22 q^{60} + 16 q^{61} + 37 q^{62} + 23 q^{63} + 37 q^{64} - 46 q^{65} + q^{66} + 45 q^{67} + 3 q^{68} + 68 q^{69} + 28 q^{70} + 55 q^{71} + 52 q^{72} + 29 q^{73} + 21 q^{74} - 12 q^{75} + 36 q^{76} + 30 q^{77} + 38 q^{78} + 25 q^{79} + 9 q^{80} + 73 q^{81} + 21 q^{82} + 70 q^{83} + 6 q^{84} - 21 q^{85} + 14 q^{86} + 37 q^{87} + 5 q^{88} + 55 q^{90} + 18 q^{91} + 11 q^{92} + 9 q^{93} + 59 q^{94} - 9 q^{95} + 9 q^{96} + 37 q^{97} + 82 q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9 + 9 * q^10 + 5 * q^11 + 9 * q^12 + 16 * q^13 + 19 * q^14 + 22 * q^15 + 37 * q^16 + 3 * q^17 + 52 * q^18 + 36 * q^19 + 9 * q^20 + 6 * q^21 + 5 * q^22 + 11 * q^23 + 9 * q^24 + 58 * q^25 + 16 * q^26 + 24 * q^27 + 19 * q^28 + 5 * q^29 + 22 * q^30 + 37 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 28 * q^35 + 52 * q^36 + 21 * q^37 + 36 * q^38 + 38 * q^39 + 9 * q^40 + 21 * q^41 + 6 * q^42 + 14 * q^43 + 5 * q^44 + 55 * q^45 + 11 * q^46 + 59 * q^47 + 9 * q^48 + 82 * q^49 + 58 * q^50 + 46 * q^51 + 16 * q^52 + 8 * q^53 + 24 * q^54 + 25 * q^55 + 19 * q^56 + 5 * q^58 + 41 * q^59 + 22 * q^60 + 16 * q^61 + 37 * q^62 + 23 * q^63 + 37 * q^64 - 46 * q^65 + q^66 + 45 * q^67 + 3 * q^68 + 68 * q^69 + 28 * q^70 + 55 * q^71 + 52 * q^72 + 29 * q^73 + 21 * q^74 - 12 * q^75 + 36 * q^76 + 30 * q^77 + 38 * q^78 + 25 * q^79 + 9 * q^80 + 73 * q^81 + 21 * q^82 + 70 * q^83 + 6 * q^84 - 21 * q^85 + 14 * q^86 + 37 * q^87 + 5 * q^88 + 55 * q^90 + 18 * q^91 + 11 * q^92 + 9 * q^93 + 59 * q^94 - 9 * q^95 + 9 * q^96 + 37 * q^97 + 82 * q^98 + 33 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.177510	−0.102485	−0.0512427	−	0.998686i	$-0.516318\pi$
$3$	−0.177510	−0.102485	−0.0512427	+	0.998686i	$0.516318\pi$
$4$	1.00000	0.500000
$5$	−1.23284	−0.551344	−0.275672	−	0.961252i	$-0.588900\pi$
$5$	−1.23284	−0.551344	−0.275672	+	0.961252i	$0.588900\pi$
$6$	−0.177510	−0.0724681
$7$	−3.05433	−1.15443	−0.577215	−	0.816592i	$-0.695860\pi$
$7$	−3.05433	−1.15443	−0.577215	+	0.816592i	$0.695860\pi$
$8$	1.00000	0.353553
$9$	−2.96849	−0.989497
$10$	−1.23284	−0.389859
$11$	−5.49033	−1.65540	−0.827699	−	0.561173i	$-0.810350\pi$
$11$	−5.49033	−1.65540	−0.827699	+	0.561173i	$0.810350\pi$
$12$	−0.177510	−0.0512427
$13$	6.80162	1.88643	0.943216	−	0.332181i	$-0.107785\pi$
$13$	6.80162	1.88643	0.943216	+	0.332181i	$0.107785\pi$
$14$	−3.05433	−0.816305
$15$	0.218841	0.0565046
$16$	1.00000	0.250000
$17$	−7.15489	−1.73532	−0.867658	−	0.497162i	$-0.834376\pi$
$17$	−7.15489	−1.73532	−0.867658	+	0.497162i	$0.834376\pi$
$18$	−2.96849	−0.699680
$19$	8.08435	1.85468	0.927339	−	0.374222i	$-0.122090\pi$
$19$	8.08435	1.85468	0.927339	+	0.374222i	$0.122090\pi$
$20$	−1.23284	−0.275672
$21$	0.542174	0.118312
$22$	−5.49033	−1.17054
$23$	−8.34433	−1.73991	−0.869956	−	0.493129i	$-0.835853\pi$
$23$	−8.34433	−1.73991	−0.869956	+	0.493129i	$0.835853\pi$
$24$	−0.177510	−0.0362340
$25$	−3.48010	−0.696020
$26$	6.80162	1.33391
$27$	1.05947	0.203894
$28$	−3.05433	−0.577215
$29$	5.04538	0.936904	0.468452	−	0.883489i	$-0.344812\pi$
$29$	5.04538	0.936904	0.468452	+	0.883489i	$0.344812\pi$
$30$	0.218841	0.0399548
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	0.974587	0.169654
$34$	−7.15489	−1.22705
$35$	3.76551	0.636487
$36$	−2.96849	−0.494748
$37$	−2.85457	−0.469289	−0.234644	−	0.972081i	$-0.575393\pi$
$37$	−2.85457	−0.469289	−0.234644	+	0.972081i	$0.575393\pi$
$38$	8.08435	1.31146
$39$	−1.20735	−0.193331
$40$	−1.23284	−0.194929
$41$	6.87641	1.07392	0.536958	−	0.843609i	$-0.319573\pi$
$41$	6.87641	1.07392	0.536958	+	0.843609i	$0.319573\pi$
$42$	0.542174	0.0836592
$43$	3.45667	0.527137	0.263569	−	0.964641i	$-0.415100\pi$
$43$	3.45667	0.527137	0.263569	+	0.964641i	$0.415100\pi$
$44$	−5.49033	−0.827699
$45$	3.65968	0.545553
$46$	−8.34433	−1.23030
$47$	−1.76971	−0.258138	−0.129069	−	0.991636i	$-0.541199\pi$
$47$	−1.76971	−0.258138	−0.129069	+	0.991636i	$0.541199\pi$
$48$	−0.177510	−0.0256213
$49$	2.32895	0.332707
$50$	−3.48010	−0.492161
$51$	1.27006	0.177844
$52$	6.80162	0.943216
$53$	2.47883	0.340493	0.170247	−	0.985401i	$-0.445544\pi$
$53$	2.47883	0.340493	0.170247	+	0.985401i	$0.445544\pi$
$54$	1.05947	0.144175
$55$	6.76871	0.912693
$56$	−3.05433	−0.408152
$57$	−1.43505	−0.190077
$58$	5.04538	0.662491
$59$	2.84240	0.370049	0.185024	−	0.982734i	$-0.440764\pi$
$59$	2.84240	0.370049	0.185024	+	0.982734i	$0.440764\pi$
$60$	0.218841	0.0282523
$61$	−12.4723	−1.59691	−0.798456	−	0.602054i	$-0.794349\pi$
$61$	−12.4723	−1.59691	−0.798456	+	0.602054i	$0.794349\pi$
$62$	1.00000	0.127000
$63$	9.06676	1.14230
$64$	1.00000	0.125000
$65$	−8.38533	−1.04007
$66$	0.974587	0.119963
$67$	7.21590	0.881562	0.440781	−	0.897615i	$-0.354701\pi$
$67$	7.21590	0.881562	0.440781	+	0.897615i	$0.354701\pi$
$68$	−7.15489	−0.867658
$69$	1.48120	0.178315
$70$	3.76551	0.450065
$71$	13.4257	1.59334	0.796671	−	0.604413i	$-0.206592\pi$
$71$	13.4257	1.59334	0.796671	+	0.604413i	$0.206592\pi$
$72$	−2.96849	−0.349840
$73$	−5.02171	−0.587746	−0.293873	−	0.955844i	$-0.594944\pi$
$73$	−5.02171	−0.587746	−0.293873	+	0.955844i	$0.594944\pi$
$74$	−2.85457	−0.331837
$75$	0.617752	0.0713318
$76$	8.08435	0.927339
$77$	16.7693	1.91104
$78$	−1.20735	−0.136706
$79$	5.34813	0.601712	0.300856	−	0.953670i	$-0.402728\pi$
$79$	5.34813	0.601712	0.300856	+	0.953670i	$0.402728\pi$
$80$	−1.23284	−0.137836
$81$	8.71741	0.968601
$82$	6.87641	0.759373
$83$	−11.5119	−1.26359	−0.631796	−	0.775135i	$-0.717682\pi$
$83$	−11.5119	−1.26359	−0.631796	+	0.775135i	$0.717682\pi$
$84$	0.542174	0.0591560
$85$	8.82085	0.956755
$86$	3.45667	0.372742
$87$	−0.895605	−0.0960189
$88$	−5.49033	−0.585271
$89$	6.96947	0.738763	0.369381	−	0.929278i	$-0.379570\pi$
$89$	6.96947	0.738763	0.369381	+	0.929278i	$0.379570\pi$
$90$	3.65968	0.385764
$91$	−20.7744	−2.17775
$92$	−8.34433	−0.869956
$93$	−0.177510	−0.0184069
$94$	−1.76971	−0.182531
$95$	−9.96673	−1.02257
$96$	−0.177510	−0.0181170
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	2.32895	0.235259
$99$	16.2980	1.63801
$100$	−3.48010	−0.348010
$101$	−3.75055	−0.373194	−0.186597	−	0.982437i	$-0.559746\pi$
$101$	−3.75055	−0.373194	−0.186597	+	0.982437i	$0.559746\pi$
$102$	1.27006	0.125755
$103$	20.1419	1.98464	0.992321	−	0.123692i	$-0.0394735\pi$
$103$	20.1419	1.98464	0.992321	+	0.123692i	$0.0394735\pi$
$104$	6.80162	0.666954
$105$	−0.668415	−0.0652306
$106$	2.47883	0.240765
$107$	−16.9915	−1.64263	−0.821317	−	0.570473i	$-0.806760\pi$
$107$	−16.9915	−1.64263	−0.821317	+	0.570473i	$0.806760\pi$
$108$	1.05947	0.101947
$109$	12.6976	1.21621	0.608104	−	0.793857i	$-0.291930\pi$
$109$	12.6976	1.21621	0.608104	+	0.793857i	$0.291930\pi$
$110$	6.76871	0.645371
$111$	0.506714	0.0480952
$112$	−3.05433	−0.288607
$113$	12.9617	1.21934	0.609669	−	0.792656i	$-0.291303\pi$
$113$	12.9617	1.21934	0.609669	+	0.792656i	$0.291303\pi$
$114$	−1.43505	−0.134405
$115$	10.2872	0.959290
$116$	5.04538	0.468452
$117$	−20.1906	−1.86662
$118$	2.84240	0.261664
$119$	21.8534	2.00330
$120$	0.218841	0.0199774
$121$	19.1437	1.74034
$122$	−12.4723	−1.12919
$123$	−1.22063	−0.110061
$124$	1.00000	0.0898027
$125$	10.4546	0.935090
$126$	9.06676	0.807731
$127$	4.84323	0.429767	0.214884	−	0.976640i	$-0.431063\pi$
$127$	4.84323	0.429767	0.214884	+	0.976640i	$0.431063\pi$
$128$	1.00000	0.0883883
$129$	−0.613593	−0.0540238
$130$	−8.38533	−0.735442
$131$	5.73858	0.501382	0.250691	−	0.968067i	$-0.419342\pi$
$131$	5.73858	0.501382	0.250691	+	0.968067i	$0.419342\pi$
$132$	0.974587	0.0848269
$133$	−24.6923	−2.14109
$134$	7.21590	0.623359
$135$	−1.30615	−0.112416
$136$	−7.15489	−0.613527
$137$	−12.1803	−1.04063	−0.520315	−	0.853975i	$-0.674185\pi$
$137$	−12.1803	−1.04063	−0.520315	+	0.853975i	$0.674185\pi$
$138$	1.48120	0.126088
$139$	18.6053	1.57808	0.789042	−	0.614339i	$-0.210577\pi$
$139$	18.6053	1.57808	0.789042	+	0.614339i	$0.210577\pi$
$140$	3.76551	0.318244
$141$	0.314140	0.0264554
$142$	13.4257	1.12666
$143$	−37.3432	−3.12279
$144$	−2.96849	−0.247374
$145$	−6.22016	−0.516556
$146$	−5.02171	−0.415599
$147$	−0.413411	−0.0340976
$148$	−2.85457	−0.234644
$149$	−4.11816	−0.337373	−0.168686	−	0.985670i	$-0.553953\pi$
$149$	−4.11816	−0.337373	−0.168686	+	0.985670i	$0.553953\pi$
$150$	0.617752	0.0504392
$151$	6.14470	0.500048	0.250024	−	0.968240i	$-0.419561\pi$
$151$	6.14470	0.500048	0.250024	+	0.968240i	$0.419561\pi$
$152$	8.08435	0.655728
$153$	21.2392	1.71709
$154$	16.7693	1.35131
$155$	−1.23284	−0.0990243
$156$	−1.20735	−0.0966657
$157$	8.35139	0.666513	0.333257	−	0.942836i	$-0.391852\pi$
$157$	8.35139	0.666513	0.333257	+	0.942836i	$0.391852\pi$
$158$	5.34813	0.425475
$159$	−0.440016	−0.0348956
$160$	−1.23284	−0.0974647
$161$	25.4863	2.00861
$162$	8.71741	0.684904
$163$	−4.09194	−0.320506	−0.160253	−	0.987076i	$-0.551231\pi$
$163$	−4.09194	−0.320506	−0.160253	+	0.987076i	$0.551231\pi$
$164$	6.87641	0.536958
$165$	−1.20151	−0.0935376
$166$	−11.5119	−0.893494
$167$	−6.65861	−0.515258	−0.257629	−	0.966244i	$-0.582941\pi$
$167$	−6.65861	−0.515258	−0.257629	+	0.966244i	$0.582941\pi$
$168$	0.542174	0.0418296
$169$	33.2621	2.55862
$170$	8.82085	0.676528
$171$	−23.9983	−1.83520
$172$	3.45667	0.263569
$173$	−14.0075	−1.06497	−0.532487	−	0.846438i	$-0.678742\pi$
$173$	−14.0075	−1.06497	−0.532487	+	0.846438i	$0.678742\pi$
$174$	−0.895605	−0.0678956
$175$	10.6294	0.803506
$176$	−5.49033	−0.413849
$177$	−0.504554	−0.0379246
$178$	6.96947	0.522384
$179$	19.1009	1.42767	0.713835	−	0.700314i	$-0.246957\pi$
$179$	19.1009	1.42767	0.713835	+	0.700314i	$0.246957\pi$
$180$	3.65968	0.272776
$181$	−23.0076	−1.71014	−0.855072	−	0.518510i	$-0.826487\pi$
$181$	−23.0076	−1.71014	−0.855072	+	0.518510i	$0.826487\pi$
$182$	−20.7744	−1.53990
$183$	2.21395	0.163660
$184$	−8.34433	−0.615152
$185$	3.51924	0.258739
$186$	−0.177510	−0.0130156
$187$	39.2827	2.87264
$188$	−1.76971	−0.129069
$189$	−3.23596	−0.235381
$190$	−9.96673	−0.723063
$191$	22.4246	1.62259	0.811294	−	0.584639i	$-0.198764\pi$
$191$	22.4246	1.62259	0.811294	+	0.584639i	$0.198764\pi$
$192$	−0.177510	−0.0128107
$193$	−8.99856	−0.647731	−0.323865	−	0.946103i	$-0.604982\pi$
$193$	−8.99856	−0.647731	−0.323865	+	0.946103i	$0.604982\pi$
$194$	1.00000	0.0717958
$195$	1.48848	0.106592
$196$	2.32895	0.166354
$197$	7.73639	0.551195	0.275598	−	0.961273i	$-0.411124\pi$
$197$	7.73639	0.551195	0.275598	+	0.961273i	$0.411124\pi$
$198$	16.2980	1.15825
$199$	−15.4839	−1.09762	−0.548811	−	0.835947i	$-0.684919\pi$
$199$	−15.4839	−1.09762	−0.548811	+	0.835947i	$0.684919\pi$
$200$	−3.48010	−0.246080
$201$	−1.28089	−0.0903472
$202$	−3.75055	−0.263888
$203$	−15.4103	−1.08159
$204$	1.27006	0.0889222
$205$	−8.47753	−0.592096
$206$	20.1419	1.40335
$207$	24.7701	1.72164
$208$	6.80162	0.471608
$209$	−44.3858	−3.07023
$210$	−0.668415	−0.0461250
$211$	26.2495	1.80709	0.903545	−	0.428493i	$-0.140955\pi$
$211$	26.2495	1.80709	0.903545	+	0.428493i	$0.140955\pi$
$212$	2.47883	0.170247
$213$	−2.38320	−0.163294
$214$	−16.9915	−1.16152
$215$	−4.26153	−0.290634
$216$	1.05947	0.0720875
$217$	−3.05433	−0.207342
$218$	12.6976	0.859989
$219$	0.891402	0.0602354
$220$	6.76871	0.456346
$221$	−48.6649	−3.27355
$222$	0.506714	0.0340084
$223$	−16.5506	−1.10831	−0.554155	−	0.832413i	$-0.686959\pi$
$223$	−16.5506	−1.10831	−0.554155	+	0.832413i	$0.686959\pi$
$224$	−3.05433	−0.204076
$225$	10.3306	0.688710
$226$	12.9617	0.862202
$227$	15.7507	1.04541	0.522704	−	0.852514i	$-0.324923\pi$
$227$	15.7507	1.04541	0.522704	+	0.852514i	$0.324923\pi$
$228$	−1.43505	−0.0950386
$229$	−3.90178	−0.257837	−0.128919	−	0.991655i	$-0.541151\pi$
$229$	−3.90178	−0.257837	−0.128919	+	0.991655i	$0.541151\pi$
$230$	10.2872	0.678320
$231$	−2.97671	−0.195853
$232$	5.04538	0.331246
$233$	−7.47060	−0.489416	−0.244708	−	0.969597i	$-0.578692\pi$
$233$	−7.47060	−0.489416	−0.244708	+	0.969597i	$0.578692\pi$
$234$	−20.1906	−1.31990
$235$	2.18177	0.142323
$236$	2.84240	0.185024
$237$	−0.949346	−0.0616666
$238$	21.8534	1.41655
$239$	21.0167	1.35946	0.679728	−	0.733464i	$-0.262098\pi$
$239$	21.0167	1.35946	0.679728	+	0.733464i	$0.262098\pi$
$240$	0.218841	0.0141262
$241$	−3.38666	−0.218154	−0.109077	−	0.994033i	$-0.534790\pi$
$241$	−3.38666	−0.218154	−0.109077	+	0.994033i	$0.534790\pi$
$242$	19.1437	1.23061
$243$	−4.72582	−0.303162
$244$	−12.4723	−0.798456
$245$	−2.87123	−0.183436
$246$	−1.22063	−0.0778246
$247$	54.9867	3.49872
$248$	1.00000	0.0635001
$249$	2.04347	0.129500
$250$	10.4546	0.661209
$251$	10.1784	0.642457	0.321229	−	0.947002i	$-0.395904\pi$
$251$	10.1784	0.642457	0.321229	+	0.947002i	$0.395904\pi$
$252$	9.06676	0.571152
$253$	45.8131	2.88025
$254$	4.84323	0.303891
$255$	−1.56579	−0.0980534
$256$	1.00000	0.0625000
$257$	1.28572	0.0802013	0.0401006	−	0.999196i	$-0.487232\pi$
$257$	1.28572	0.0802013	0.0401006	+	0.999196i	$0.487232\pi$
$258$	−0.613593	−0.0382006
$259$	8.71881	0.541761
$260$	−8.38533	−0.520036
$261$	−14.9772	−0.927064
$262$	5.73858	0.354530
$263$	−6.20922	−0.382877	−0.191438	−	0.981505i	$-0.561315\pi$
$263$	−6.20922	−0.382877	−0.191438	+	0.981505i	$0.561315\pi$
$264$	0.974587	0.0599817
$265$	−3.05600	−0.187729
$266$	−24.6923	−1.51398
$267$	−1.23715	−0.0757123
$268$	7.21590	0.440781
$269$	13.5621	0.826893	0.413447	−	0.910528i	$-0.364325\pi$
$269$	13.5621	0.826893	0.413447	+	0.910528i	$0.364325\pi$
$270$	−1.30615	−0.0794900
$271$	6.62053	0.402169	0.201084	−	0.979574i	$-0.435553\pi$
$271$	6.62053	0.402169	0.201084	+	0.979574i	$0.435553\pi$
$272$	−7.15489	−0.433829
$273$	3.68766	0.223188
$274$	−12.1803	−0.735836
$275$	19.1069	1.15219
$276$	1.48120	0.0891577
$277$	4.91003	0.295015	0.147508	−	0.989061i	$-0.452875\pi$
$277$	4.91003	0.295015	0.147508	+	0.989061i	$0.452875\pi$
$278$	18.6053	1.11587
$279$	−2.96849	−0.177719
$280$	3.76551	0.225032
$281$	−15.4303	−0.920493	−0.460247	−	0.887791i	$-0.652239\pi$
$281$	−15.4303	−0.920493	−0.460247	+	0.887791i	$0.652239\pi$
$282$	0.314140	0.0187068
$283$	−2.80143	−0.166528	−0.0832639	−	0.996528i	$-0.526534\pi$
$283$	−2.80143	−0.166528	−0.0832639	+	0.996528i	$0.526534\pi$
$284$	13.4257	0.796671
$285$	1.76919	0.104798
$286$	−37.3432	−2.20815
$287$	−21.0029	−1.23976
$288$	−2.96849	−0.174920
$289$	34.1925	2.01132
$290$	−6.22016	−0.365261
$291$	−0.177510	−0.0104058
$292$	−5.02171	−0.293873
$293$	−6.97075	−0.407235	−0.203618	−	0.979050i	$-0.565270\pi$
$293$	−6.97075	−0.407235	−0.203618	+	0.979050i	$0.565270\pi$
$294$	−0.413411	−0.0241106
$295$	−3.50423	−0.204024
$296$	−2.85457	−0.165919
$297$	−5.81682	−0.337526
$298$	−4.11816	−0.238559
$299$	−56.7550	−3.28222
$300$	0.617752	0.0356659
$301$	−10.5578	−0.608543
$302$	6.14470	0.353588
$303$	0.665759	0.0382469
$304$	8.08435	0.463670
$305$	15.3763	0.880447
$306$	21.2392	1.21417
$307$	24.3799	1.39144	0.695718	−	0.718315i	$-0.255086\pi$
$307$	24.3799	1.39144	0.695718	+	0.718315i	$0.255086\pi$
$308$	16.7693	0.955520
$309$	−3.57539	−0.203397
$310$	−1.23284	−0.0700207
$311$	−17.3624	−0.984531	−0.492266	−	0.870445i	$-0.663831\pi$
$311$	−17.3624	−0.984531	−0.492266	+	0.870445i	$0.663831\pi$
$312$	−1.20735	−0.0683530
$313$	1.77765	0.100479	0.0502395	−	0.998737i	$-0.484002\pi$
$313$	1.77765	0.100479	0.0502395	+	0.998737i	$0.484002\pi$
$314$	8.35139	0.471296
$315$	−11.1779	−0.629802
$316$	5.34813	0.300856
$317$	−5.38980	−0.302721	−0.151361	−	0.988479i	$-0.548366\pi$
$317$	−5.38980	−0.302721	−0.151361	+	0.988479i	$0.548366\pi$
$318$	−0.440016	−0.0246749
$319$	−27.7008	−1.55095
$320$	−1.23284	−0.0689180
$321$	3.01616	0.168346
$322$	25.4863	1.42030
$323$	−57.8427	−3.21845
$324$	8.71741	0.484300
$325$	−23.6703	−1.31299
$326$	−4.09194	−0.226632
$327$	−2.25395	−0.124643
$328$	6.87641	0.379686
$329$	5.40527	0.298002
$330$	−1.20151	−0.0661411
$331$	−6.58617	−0.362009	−0.181004	−	0.983482i	$-0.557935\pi$
$331$	−6.58617	−0.362009	−0.181004	+	0.983482i	$0.557935\pi$
$332$	−11.5119	−0.631796
$333$	8.47377	0.464360
$334$	−6.65861	−0.364343
$335$	−8.89606	−0.486044
$336$	0.542174	0.0295780
$337$	4.07506	0.221983	0.110991	−	0.993821i	$-0.464597\pi$
$337$	4.07506	0.221983	0.110991	+	0.993821i	$0.464597\pi$
$338$	33.2621	1.80922
$339$	−2.30083	−0.124964
$340$	8.82085	0.478378
$341$	−5.49033	−0.297318
$342$	−23.9983	−1.29768
$343$	14.2669	0.770343
$344$	3.45667	0.186371
$345$	−1.82608	−0.0983131
$346$	−14.0075	−0.753050
$347$	1.12825	0.0605674	0.0302837	−	0.999541i	$-0.490359\pi$
$347$	1.12825	0.0605674	0.0302837	+	0.999541i	$0.490359\pi$
$348$	−0.895605	−0.0480095
$349$	6.73015	0.360257	0.180128	−	0.983643i	$-0.442349\pi$
$349$	6.73015	0.360257	0.180128	+	0.983643i	$0.442349\pi$
$350$	10.6294	0.568165
$351$	7.20608	0.384632
$352$	−5.49033	−0.292636
$353$	2.97597	0.158395	0.0791974	−	0.996859i	$-0.474764\pi$
$353$	2.97597	0.158395	0.0791974	+	0.996859i	$0.474764\pi$
$354$	−0.504554	−0.0268167
$355$	−16.5518	−0.878479
$356$	6.96947	0.369381
$357$	−3.87919	−0.205309
$358$	19.1009	1.00951
$359$	−22.3590	−1.18006	−0.590030	−	0.807381i	$-0.700884\pi$
$359$	−22.3590	−1.18006	−0.590030	+	0.807381i	$0.700884\pi$
$360$	3.65968	0.192882
$361$	46.3568	2.43983
$362$	−23.0076	−1.20925
$363$	−3.39820	−0.178359
$364$	−20.7744	−1.08888
$365$	6.19097	0.324050
$366$	2.21395	0.115725
$367$	−4.94414	−0.258082	−0.129041	−	0.991639i	$-0.541190\pi$
$367$	−4.94414	−0.258082	−0.129041	+	0.991639i	$0.541190\pi$
$368$	−8.34433	−0.434978
$369$	−20.4126	−1.06264
$370$	3.51924	0.182956
$371$	−7.57117	−0.393075
$372$	−0.177510	−0.00920345
$373$	−31.7336	−1.64310	−0.821552	−	0.570133i	$-0.806892\pi$
$373$	−31.7336	−1.64310	−0.821552	+	0.570133i	$0.806892\pi$
$374$	39.2827	2.03126
$375$	−1.85580	−0.0958330
$376$	−1.76971	−0.0912656
$377$	34.3168	1.76741
$378$	−3.23596	−0.166440
$379$	−32.5404	−1.67149	−0.835745	−	0.549118i	$-0.814964\pi$
$379$	−32.5404	−1.67149	−0.835745	+	0.549118i	$0.814964\pi$
$380$	−9.96673	−0.511283
$381$	−0.859721	−0.0440448
$382$	22.4246	1.14734
$383$	23.8919	1.22082	0.610409	−	0.792086i	$-0.291005\pi$
$383$	23.8919	1.22082	0.610409	+	0.792086i	$0.291005\pi$
$384$	−0.177510	−0.00905851
$385$	−20.6739	−1.05364
$386$	−8.99856	−0.458015
$387$	−10.2611	−0.521601
$388$	1.00000	0.0507673
$389$	−21.0100	−1.06525	−0.532624	−	0.846352i	$-0.678794\pi$
$389$	−21.0100	−1.06525	−0.532624	+	0.846352i	$0.678794\pi$
$390$	1.48848	0.0753720
$391$	59.7027	3.01930
$392$	2.32895	0.117630
$393$	−1.01865	−0.0513843
$394$	7.73639	0.389754
$395$	−6.59340	−0.331750
$396$	16.2980	0.819005
$397$	9.90408	0.497072	0.248536	−	0.968623i	$-0.420051\pi$
$397$	9.90408	0.497072	0.248536	+	0.968623i	$0.420051\pi$
$398$	−15.4839	−0.776136
$399$	4.38313	0.219431
$400$	−3.48010	−0.174005
$401$	−18.6627	−0.931973	−0.465986	−	0.884792i	$-0.654300\pi$
$401$	−18.6627	−0.931973	−0.465986	+	0.884792i	$0.654300\pi$
$402$	−1.28089	−0.0638851
$403$	6.80162	0.338813
$404$	−3.75055	−0.186597
$405$	−10.7472	−0.534032
$406$	−15.4103	−0.764800
$407$	15.6725	0.776859
$408$	1.27006	0.0628775
$409$	5.16323	0.255305	0.127653	−	0.991819i	$-0.459256\pi$
$409$	5.16323	0.255305	0.127653	+	0.991819i	$0.459256\pi$
$410$	−8.47753	−0.418675
$411$	2.16211	0.106649
$412$	20.1419	0.992321
$413$	−8.68164	−0.427195
$414$	24.7701	1.21738
$415$	14.1923	0.696673
$416$	6.80162	0.333477
$417$	−3.30263	−0.161730
$418$	−44.3858	−2.17098
$419$	−3.75888	−0.183634	−0.0918168	−	0.995776i	$-0.529267\pi$
$419$	−3.75888	−0.183634	−0.0918168	+	0.995776i	$0.529267\pi$
$420$	−0.668415	−0.0326153
$421$	−19.9998	−0.974729	−0.487364	−	0.873199i	$-0.662042\pi$
$421$	−19.9998	−0.974729	−0.487364	+	0.873199i	$0.662042\pi$
$422$	26.2495	1.27781
$423$	5.25335	0.255427
$424$	2.47883	0.120383
$425$	24.8997	1.20781
$426$	−2.38320	−0.115466
$427$	38.0945	1.84352
$428$	−16.9915	−0.821317
$429$	6.62878	0.320040
$430$	−4.26153	−0.205509
$431$	−15.5972	−0.751291	−0.375646	−	0.926763i	$-0.622579\pi$
$431$	−15.5972	−0.751291	−0.375646	+	0.926763i	$0.622579\pi$
$432$	1.05947	0.0509735
$433$	−22.1763	−1.06573	−0.532863	−	0.846202i	$-0.678884\pi$
$433$	−22.1763	−1.06573	−0.532863	+	0.846202i	$0.678884\pi$
$434$	−3.05433	−0.146613
$435$	1.10414	0.0529394
$436$	12.6976	0.608104
$437$	−67.4585	−3.22698
$438$	0.891402	0.0425928
$439$	26.9905	1.28819	0.644094	−	0.764947i	$-0.277235\pi$
$439$	26.9905	1.28819	0.644094	+	0.764947i	$0.277235\pi$
$440$	6.76871	0.322686
$441$	−6.91346	−0.329213
$442$	−48.6649	−2.31475
$443$	−16.3443	−0.776540	−0.388270	−	0.921546i	$-0.626927\pi$
$443$	−16.3443	−0.776540	−0.388270	+	0.921546i	$0.626927\pi$
$444$	0.506714	0.0240476
$445$	−8.59226	−0.407312
$446$	−16.5506	−0.783694
$447$	0.731014	0.0345758
$448$	−3.05433	−0.144304
$449$	31.7436	1.49807	0.749036	−	0.662529i	$-0.230517\pi$
$449$	31.7436	1.49807	0.749036	+	0.662529i	$0.230517\pi$
$450$	10.3306	0.486991
$451$	−37.7538	−1.77776
$452$	12.9617	0.609669
$453$	−1.09074	−0.0512476
$454$	15.7507	0.739216
$455$	25.6116	1.20069
$456$	−1.43505	−0.0672025
$457$	−1.00412	−0.0469705	−0.0234853	−	0.999724i	$-0.507476\pi$
$457$	−1.00412	−0.0469705	−0.0234853	+	0.999724i	$0.507476\pi$
$458$	−3.90178	−0.182318
$459$	−7.58036	−0.353821
$460$	10.2872	0.479645
$461$	−26.3072	−1.22525	−0.612624	−	0.790374i	$-0.709886\pi$
$461$	−26.3072	−1.22525	−0.612624	+	0.790374i	$0.709886\pi$
$462$	−2.97671	−0.138489
$463$	−10.0184	−0.465597	−0.232798	−	0.972525i	$-0.574788\pi$
$463$	−10.0184	−0.465597	−0.232798	+	0.972525i	$0.574788\pi$
$464$	5.04538	0.234226
$465$	0.218841	0.0101485
$466$	−7.47060	−0.346069
$467$	−39.1990	−1.81391	−0.906956	−	0.421226i	$-0.861600\pi$
$467$	−39.1990	−1.81391	−0.906956	+	0.421226i	$0.861600\pi$
$468$	−20.1906	−0.933309
$469$	−22.0398	−1.01770
$470$	2.18177	0.100637
$471$	−1.48245	−0.0683078
$472$	2.84240	0.130832
$473$	−18.9783	−0.872621
$474$	−0.949346	−0.0436049
$475$	−28.1344	−1.29089
$476$	21.8534	1.00165
$477$	−7.35838	−0.336917
$478$	21.0167	0.961280
$479$	8.30591	0.379507	0.189753	−	0.981832i	$-0.439231\pi$
$479$	8.30591	0.379507	0.189753	+	0.981832i	$0.439231\pi$
$480$	0.218841	0.00998870
$481$	−19.4157	−0.885281
$482$	−3.38666	−0.154258
$483$	−4.52408	−0.205853
$484$	19.1437	0.870170
$485$	−1.23284	−0.0559805
$486$	−4.72582	−0.214368
$487$	−34.8900	−1.58102	−0.790508	−	0.612452i	$-0.790183\pi$
$487$	−34.8900	−1.58102	−0.790508	+	0.612452i	$0.790183\pi$
$488$	−12.4723	−0.564593
$489$	0.726360	0.0328471
$490$	−2.87123	−0.129709
$491$	22.8316	1.03038	0.515188	−	0.857077i	$-0.327722\pi$
$491$	22.8316	1.03038	0.515188	+	0.857077i	$0.327722\pi$
$492$	−1.22063	−0.0550303
$493$	−36.0992	−1.62583
$494$	54.9867	2.47397
$495$	−20.0929	−0.903107
$496$	1.00000	0.0449013
$497$	−41.0067	−1.83940
$498$	2.04347	0.0915700
$499$	9.30953	0.416752	0.208376	−	0.978049i	$-0.433182\pi$
$499$	9.30953	0.416752	0.208376	+	0.978049i	$0.433182\pi$
$500$	10.4546	0.467545
$501$	1.18197	0.0528064
$502$	10.1784	0.454286
$503$	−23.6103	−1.05273	−0.526365	−	0.850259i	$-0.676445\pi$
$503$	−23.6103	−1.05273	−0.526365	+	0.850259i	$0.676445\pi$
$504$	9.06676	0.403865
$505$	4.62383	0.205758
$506$	45.8131	2.03664
$507$	−5.90435	−0.262221
$508$	4.84323	0.214884
$509$	−10.3091	−0.456944	−0.228472	−	0.973551i	$-0.573373\pi$
$509$	−10.3091	−0.456944	−0.228472	+	0.973551i	$0.573373\pi$
$510$	−1.56579	−0.0693342
$511$	15.3380	0.678512
$512$	1.00000	0.0441942
$513$	8.56509	0.378158
$514$	1.28572	0.0567109
$515$	−24.8318	−1.09422
$516$	−0.613593	−0.0270119
$517$	9.71627	0.427321
$518$	8.71881	0.383083
$519$	2.48648	0.109144
$520$	−8.38533	−0.367721
$521$	10.2387	0.448567	0.224283	−	0.974524i	$-0.427996\pi$
$521$	10.2387	0.448567	0.224283	+	0.974524i	$0.427996\pi$
$522$	−14.9772	−0.655533
$523$	40.4480	1.76867	0.884334	−	0.466855i	$-0.154613\pi$
$523$	40.4480	1.76867	0.884334	+	0.466855i	$0.154613\pi$
$524$	5.73858	0.250691
$525$	−1.88682	−0.0823476
$526$	−6.20922	−0.270735
$527$	−7.15489	−0.311672
$528$	0.974587	0.0424135
$529$	46.6278	2.02729
$530$	−3.05600	−0.132744
$531$	−8.43764	−0.366162
$532$	−24.6923	−1.07055
$533$	46.7708	2.02587
$534$	−1.23715	−0.0535367
$535$	20.9479	0.905655
$536$	7.21590	0.311679
$537$	−3.39060	−0.146315
$538$	13.5621	0.584702
$539$	−12.7867	−0.550762
$540$	−1.30615	−0.0562079
$541$	−6.29734	−0.270744	−0.135372	−	0.990795i	$-0.543223\pi$
$541$	−6.29734	−0.270744	−0.135372	+	0.990795i	$0.543223\pi$
$542$	6.62053	0.284376
$543$	4.08408	0.175265
$544$	−7.15489	−0.306763
$545$	−15.6541	−0.670549
$546$	3.68766	0.157817
$547$	19.3199	0.826058	0.413029	−	0.910718i	$-0.364471\pi$
$547$	19.3199	0.826058	0.413029	+	0.910718i	$0.364471\pi$
$548$	−12.1803	−0.520315
$549$	37.0238	1.58014
$550$	19.1069	0.814721
$551$	40.7887	1.73766
$552$	1.48120	0.0630440
$553$	−16.3350	−0.694634
$554$	4.91003	0.208607
$555$	−0.624699	−0.0265170
$556$	18.6053	0.789042
$557$	23.3706	0.990244	0.495122	−	0.868823i	$-0.335123\pi$
$557$	23.3706	0.990244	0.495122	+	0.868823i	$0.335123\pi$
$558$	−2.96849	−0.125666
$559$	23.5110	0.994408
$560$	3.76551	0.159122
$561$	−6.97307	−0.294403
$562$	−15.4303	−0.650887
$563$	40.7905	1.71911	0.859557	−	0.511040i	$-0.170740\pi$
$563$	40.7905	1.71911	0.859557	+	0.511040i	$0.170740\pi$
$564$	0.314140	0.0132277
$565$	−15.9798	−0.672274
$566$	−2.80143	−0.117753
$567$	−26.6259	−1.11818
$568$	13.4257	0.563332
$569$	27.6027	1.15717	0.578583	−	0.815624i	$-0.303606\pi$
$569$	27.6027	1.15717	0.578583	+	0.815624i	$0.303606\pi$
$570$	1.76919	0.0741033
$571$	−13.1427	−0.550006	−0.275003	−	0.961443i	$-0.588679\pi$
$571$	−13.1427	−0.550006	−0.275003	+	0.961443i	$0.588679\pi$
$572$	−37.3432	−1.56140
$573$	−3.98058	−0.166291
$574$	−21.0029	−0.876642
$575$	29.0391	1.21101
$576$	−2.96849	−0.123687
$577$	19.8694	0.827176	0.413588	−	0.910464i	$-0.364275\pi$
$577$	19.8694	0.827176	0.413588	+	0.910464i	$0.364275\pi$
$578$	34.1925	1.42222
$579$	1.59733	0.0663829
$580$	−6.22016	−0.258278
$581$	35.1611	1.45873
$582$	−0.177510	−0.00735802
$583$	−13.6096	−0.563652
$584$	−5.02171	−0.207800
$585$	24.8918	1.02915
$586$	−6.97075	−0.287959
$587$	−39.8974	−1.64674	−0.823370	−	0.567504i	$-0.807909\pi$
$587$	−39.8974	−1.64674	−0.823370	+	0.567504i	$0.807909\pi$
$588$	−0.413411	−0.0170488
$589$	8.08435	0.333110
$590$	−3.50423	−0.144267
$591$	−1.37328	−0.0564894
$592$	−2.85457	−0.117322
$593$	−41.1236	−1.68874	−0.844372	−	0.535757i	$-0.820026\pi$
$593$	−41.1236	−1.68874	−0.844372	+	0.535757i	$0.820026\pi$
$594$	−5.81682	−0.238667
$595$	−26.9418	−1.10451
$596$	−4.11816	−0.168686
$597$	2.74854	0.112490
$598$	−56.7550	−2.32088
$599$	16.3602	0.668458	0.334229	−	0.942492i	$-0.391524\pi$
$599$	16.3602	0.668458	0.334229	+	0.942492i	$0.391524\pi$
$600$	0.617752	0.0252196
$601$	−10.6677	−0.435143	−0.217572	−	0.976044i	$-0.569814\pi$
$601$	−10.6677	−0.435143	−0.217572	+	0.976044i	$0.569814\pi$
$602$	−10.5578	−0.430305
$603$	−21.4203	−0.872303
$604$	6.14470	0.250024
$605$	−23.6012	−0.959525
$606$	0.665759	0.0270446
$607$	14.0869	0.571771	0.285885	−	0.958264i	$-0.407712\pi$
$607$	14.0869	0.571771	0.285885	+	0.958264i	$0.407712\pi$
$608$	8.08435	0.327864
$609$	2.73548	0.110847
$610$	15.3763	0.622570
$611$	−12.0369	−0.486960
$612$	21.2392	0.858545
$613$	26.7342	1.07978	0.539892	−	0.841734i	$-0.318465\pi$
$613$	26.7342	1.07978	0.539892	+	0.841734i	$0.318465\pi$
$614$	24.3799	0.983894
$615$	1.50484	0.0606812
$616$	16.7693	0.675654
$617$	5.04176	0.202974	0.101487	−	0.994837i	$-0.467640\pi$
$617$	5.04176	0.202974	0.101487	+	0.994837i	$0.467640\pi$
$618$	−3.57539	−0.143823
$619$	10.8491	0.436063	0.218031	−	0.975942i	$-0.430036\pi$
$619$	10.8491	0.436063	0.218031	+	0.975942i	$0.430036\pi$
$620$	−1.23284	−0.0495121
$621$	−8.84052	−0.354758
$622$	−17.3624	−0.696169
$623$	−21.2871	−0.852849
$624$	−1.20735	−0.0483329
$625$	4.51160	0.180464
$626$	1.77765	0.0710493
$627$	7.87891	0.314653
$628$	8.35139	0.333257
$629$	20.4241	0.814364
$630$	−11.1779	−0.445337
$631$	28.1437	1.12038	0.560191	−	0.828364i	$-0.310728\pi$
$631$	28.1437	1.12038	0.560191	+	0.828364i	$0.310728\pi$
$632$	5.34813	0.212737
$633$	−4.65954	−0.185200
$634$	−5.38980	−0.214056
$635$	−5.97094	−0.236949
$636$	−0.440016	−0.0174478
$637$	15.8406	0.627629
$638$	−27.7008	−1.09669
$639$	−39.8542	−1.57661
$640$	−1.23284	−0.0487324
$641$	−20.7357	−0.819009	−0.409505	−	0.912308i	$-0.634298\pi$
$641$	−20.7357	−0.819009	−0.409505	+	0.912308i	$0.634298\pi$
$642$	3.01616	0.119038
$643$	−34.5830	−1.36382	−0.681911	−	0.731436i	$-0.738851\pi$
$643$	−34.5830	−1.36382	−0.681911	+	0.731436i	$0.738851\pi$
$644$	25.4863	1.00430
$645$	0.756463	0.0297857
$646$	−57.8427	−2.27579
$647$	15.4812	0.608630	0.304315	−	0.952572i	$-0.401573\pi$
$647$	15.4812	0.608630	0.304315	+	0.952572i	$0.401573\pi$
$648$	8.71741	0.342452
$649$	−15.6057	−0.612578
$650$	−23.6703	−0.928427
$651$	0.542174	0.0212495
$652$	−4.09194	−0.160253
$653$	24.2644	0.949537	0.474769	−	0.880111i	$-0.342532\pi$
$653$	24.2644	0.949537	0.474769	+	0.880111i	$0.342532\pi$
$654$	−2.25395	−0.0881362
$655$	−7.07476	−0.276434
$656$	6.87641	0.268479
$657$	14.9069	0.581573
$658$	5.40527	0.210719
$659$	19.0503	0.742096	0.371048	−	0.928614i	$-0.378999\pi$
$659$	19.0503	0.742096	0.371048	+	0.928614i	$0.378999\pi$
$660$	−1.20151	−0.0467688
$661$	28.3715	1.10352	0.551761	−	0.834002i	$-0.313956\pi$
$661$	28.3715	1.10352	0.551761	+	0.834002i	$0.313956\pi$
$662$	−6.58617	−0.255979
$663$	8.63849	0.335491
$664$	−11.5119	−0.446747
$665$	30.4417	1.18048
$666$	8.47377	0.328352
$667$	−42.1003	−1.63013
$668$	−6.65861	−0.257629
$669$	2.93790	0.113586
$670$	−8.89606	−0.343685
$671$	68.4769	2.64352
$672$	0.542174	0.0209148
$673$	28.4430	1.09640	0.548198	−	0.836349i	$-0.315314\pi$
$673$	28.4430	1.09640	0.548198	+	0.836349i	$0.315314\pi$
$674$	4.07506	0.156965
$675$	−3.68705	−0.141914
$676$	33.2621	1.27931
$677$	18.3675	0.705922	0.352961	−	0.935638i	$-0.385175\pi$
$677$	18.3675	0.705922	0.352961	+	0.935638i	$0.385175\pi$
$678$	−2.30083	−0.0883630
$679$	−3.05433	−0.117215
$680$	8.82085	0.338264
$681$	−2.79590	−0.107139
$682$	−5.49033	−0.210236
$683$	48.4487	1.85384	0.926919	−	0.375262i	$-0.122447\pi$
$683$	48.4487	1.85384	0.926919	+	0.375262i	$0.122447\pi$
$684$	−23.9983	−0.917599
$685$	15.0163	0.573745
$686$	14.2669	0.544714
$687$	0.692604	0.0264245
$688$	3.45667	0.131784
$689$	16.8601	0.642317
$690$	−1.82608	−0.0695179
$691$	1.04627	0.0398020	0.0199010	−	0.999802i	$-0.493665\pi$
$691$	1.04627	0.0398020	0.0199010	+	0.999802i	$0.493665\pi$
$692$	−14.0075	−0.532487
$693$	−49.7795	−1.89097
$694$	1.12825	0.0428276
$695$	−22.9374	−0.870067
$696$	−0.895605	−0.0339478
$697$	−49.2000	−1.86358
$698$	6.73015	0.254740
$699$	1.32611	0.0501579
$700$	10.6294	0.401753
$701$	−33.2736	−1.25673	−0.628364	−	0.777920i	$-0.716275\pi$
$701$	−33.2736	−1.25673	−0.628364	+	0.777920i	$0.716275\pi$
$702$	7.20608	0.271976
$703$	−23.0774	−0.870379
$704$	−5.49033	−0.206925
$705$	−0.387285	−0.0145860
$706$	2.97597	0.112002
$707$	11.4554	0.430826
$708$	−0.504554	−0.0189623
$709$	−31.4709	−1.18191	−0.590957	−	0.806703i	$-0.701250\pi$
$709$	−31.4709	−1.18191	−0.590957	+	0.806703i	$0.701250\pi$
$710$	−16.5518	−0.621179
$711$	−15.8759	−0.595392
$712$	6.96947	0.261192
$713$	−8.34433	−0.312497
$714$	−3.87919	−0.145175
$715$	46.0382	1.72173
$716$	19.1009	0.713835
$717$	−3.73066	−0.139324
$718$	−22.3590	−0.834429
$719$	32.3776	1.20748	0.603741	−	0.797181i	$-0.293676\pi$
$719$	32.3776	1.20748	0.603741	+	0.797181i	$0.293676\pi$
$720$	3.65968	0.136388
$721$	−61.5201	−2.29113
$722$	46.3568	1.72522
$723$	0.601166	0.0223576
$724$	−23.0076	−0.855072
$725$	−17.5584	−0.652104
$726$	−3.39820	−0.126119
$727$	10.1508	0.376472	0.188236	−	0.982124i	$-0.439723\pi$
$727$	10.1508	0.376472	0.188236	+	0.982124i	$0.439723\pi$
$728$	−20.7744	−0.769951
$729$	−25.3133	−0.937531
$730$	6.19097	0.229138
$731$	−24.7321	−0.914749
$732$	2.21395	0.0818300
$733$	19.7764	0.730457	0.365229	−	0.930918i	$-0.380991\pi$
$733$	19.7764	0.730457	0.365229	+	0.930918i	$0.380991\pi$
$734$	−4.94414	−0.182492
$735$	0.509671	0.0187995
$736$	−8.34433	−0.307576
$737$	−39.6177	−1.45934
$738$	−20.4126	−0.751397
$739$	−2.69856	−0.0992680	−0.0496340	−	0.998767i	$-0.515805\pi$
$739$	−2.69856	−0.0992680	−0.0496340	+	0.998767i	$0.515805\pi$
$740$	3.51924	0.129370
$741$	−9.76068	−0.358568
$742$	−7.57117	−0.277946
$743$	15.7419	0.577515	0.288758	−	0.957402i	$-0.406758\pi$
$743$	15.7419	0.577515	0.288758	+	0.957402i	$0.406758\pi$
$744$	−0.177510	−0.00650782
$745$	5.07704	0.186008
$746$	−31.7336	−1.16185
$747$	34.1729	1.25032
$748$	39.2827	1.43632
$749$	51.8978	1.89630
$750$	−1.85580	−0.0677642
$751$	−13.5314	−0.493769	−0.246884	−	0.969045i	$-0.579407\pi$
$751$	−13.5314	−0.493769	−0.246884	+	0.969045i	$0.579407\pi$
$752$	−1.76971	−0.0645345
$753$	−1.80677	−0.0658424
$754$	34.3168	1.24974
$755$	−7.57544	−0.275698
$756$	−3.23596	−0.117691
$757$	34.8928	1.26820	0.634100	−	0.773251i	$-0.281371\pi$
$757$	34.8928	1.26820	0.634100	+	0.773251i	$0.281371\pi$
$758$	−32.5404	−1.18192
$759$	−8.13227	−0.295183
$760$	−9.96673	−0.361531
$761$	−17.0605	−0.618444	−0.309222	−	0.950990i	$-0.600069\pi$
$761$	−17.0605	−0.618444	−0.309222	+	0.950990i	$0.600069\pi$
$762$	−0.859721	−0.0311444
$763$	−38.7827	−1.40403
$764$	22.4246	0.811294
$765$	−26.1846	−0.946706
$766$	23.8919	0.863249
$767$	19.3329	0.698072
$768$	−0.177510	−0.00640533
$769$	2.67847	0.0965883	0.0482941	−	0.998833i	$-0.484622\pi$
$769$	2.67847	0.0965883	0.0482941	+	0.998833i	$0.484622\pi$
$770$	−20.6739	−0.745036
$771$	−0.228229	−0.00821945
$772$	−8.99856	−0.323865
$773$	35.7385	1.28543	0.642713	−	0.766107i	$-0.277809\pi$
$773$	35.7385	1.28543	0.642713	+	0.766107i	$0.277809\pi$
$774$	−10.2611	−0.368827
$775$	−3.48010	−0.125009
$776$	1.00000	0.0358979
$777$	−1.54767	−0.0555225
$778$	−21.0100	−0.753243
$779$	55.5914	1.99177
$780$	1.48848	0.0532960
$781$	−73.7118	−2.63761
$782$	59.7027	2.13497
$783$	5.34541	0.191029
$784$	2.32895	0.0831768
$785$	−10.2959	−0.367478
$786$	−1.01865	−0.0363342
$787$	−22.0799	−0.787065	−0.393533	−	0.919311i	$-0.628747\pi$
$787$	−22.0799	−0.787065	−0.393533	+	0.919311i	$0.628747\pi$
$788$	7.73639	0.275598
$789$	1.10220	0.0392392
$790$	−6.59340	−0.234583
$791$	−39.5894	−1.40764
$792$	16.2980	0.579124
$793$	−84.8317	−3.01246
$794$	9.90408	0.351483
$795$	0.542470	0.0192394
$796$	−15.4839	−0.548811
$797$	51.6534	1.82966	0.914829	−	0.403842i	$-0.132325\pi$
$797$	51.6534	1.82966	0.914829	+	0.403842i	$0.132325\pi$
$798$	4.38313	0.155161
$799$	12.6621	0.447951
$800$	−3.48010	−0.123040
$801$	−20.6888	−0.731003
$802$	−18.6627	−0.659004
$803$	27.5708	0.972954
$804$	−1.28089	−0.0451736
$805$	−31.4206	−1.10743
$806$	6.80162	0.239577
$807$	−2.40740	−0.0847444
$808$	−3.75055	−0.131944
$809$	34.9707	1.22951	0.614753	−	0.788720i	$-0.289256\pi$
$809$	34.9707	1.22951	0.614753	+	0.788720i	$0.289256\pi$
$810$	−10.7472	−0.377618
$811$	54.2787	1.90598	0.952992	−	0.302995i	$-0.0979866\pi$
$811$	54.2787	1.90598	0.952992	+	0.302995i	$0.0979866\pi$
$812$	−15.4103	−0.540795
$813$	−1.17521	−0.0412164
$814$	15.6725	0.549322
$815$	5.04472	0.176709
$816$	1.27006	0.0444611
$817$	27.9449	0.977670
$818$	5.16323	0.180528
$819$	61.6687	2.15488
$820$	−8.47753	−0.296048
$821$	1.29941	0.0453498	0.0226749	−	0.999743i	$-0.492782\pi$
$821$	1.29941	0.0453498	0.0226749	+	0.999743i	$0.492782\pi$
$822$	2.16211	0.0754124
$823$	0.177142	0.00617479	0.00308740	−	0.999995i	$-0.499017\pi$
$823$	0.177142	0.00617479	0.00308740	+	0.999995i	$0.499017\pi$
$824$	20.1419	0.701677
$825$	−3.39166	−0.118083
$826$	−8.68164	−0.302073
$827$	−5.22345	−0.181637	−0.0908185	−	0.995867i	$-0.528948\pi$
$827$	−5.22345	−0.181637	−0.0908185	+	0.995867i	$0.528948\pi$
$828$	24.7701	0.860819
$829$	−9.85023	−0.342113	−0.171056	−	0.985261i	$-0.554718\pi$
$829$	−9.85023	−0.342113	−0.171056	+	0.985261i	$0.554718\pi$
$830$	14.1923	0.492622
$831$	−0.871578	−0.0302347
$832$	6.80162	0.235804
$833$	−16.6634	−0.577352
$834$	−3.30263	−0.114361
$835$	8.20901	0.284085
$836$	−44.3858	−1.53511
$837$	1.05947	0.0366205
$838$	−3.75888	−0.129849
$839$	−5.11438	−0.176568	−0.0882841	−	0.996095i	$-0.528138\pi$
$839$	−5.11438	−0.176568	−0.0882841	+	0.996095i	$0.528138\pi$
$840$	−0.668415	−0.0230625
$841$	−3.54409	−0.122210
$842$	−19.9998	−0.689237
$843$	2.73903	0.0943370
$844$	26.2495	0.903545
$845$	−41.0069	−1.41068
$846$	5.25335	0.180614
$847$	−58.4713	−2.00910
$848$	2.47883	0.0851233
$849$	0.497281	0.0170666
$850$	24.8997	0.854054
$851$	23.8195	0.816521
$852$	−2.38320	−0.0816471
$853$	−56.1514	−1.92259	−0.961294	−	0.275525i	$-0.911148\pi$
$853$	−56.1514	−1.92259	−0.961294	+	0.275525i	$0.911148\pi$
$854$	38.0945	1.30357
$855$	29.5861	1.01182
$856$	−16.9915	−0.580759
$857$	31.1722	1.06482	0.532411	−	0.846486i	$-0.321286\pi$
$857$	31.1722	1.06482	0.532411	+	0.846486i	$0.321286\pi$
$858$	6.62878	0.226303
$859$	−3.56915	−0.121778	−0.0608889	−	0.998145i	$-0.519394\pi$
$859$	−3.56915	−0.121778	−0.0608889	+	0.998145i	$0.519394\pi$
$860$	−4.26153	−0.145317
$861$	3.72821	0.127057
$862$	−15.5972	−0.531243
$863$	45.7529	1.55745	0.778724	−	0.627367i	$-0.215867\pi$
$863$	45.7529	1.55745	0.778724	+	0.627367i	$0.215867\pi$
$864$	1.05947	0.0360437
$865$	17.2691	0.587167
$866$	−22.1763	−0.753582
$867$	−6.06950	−0.206131
$868$	−3.05433	−0.103671
$869$	−29.3630	−0.996073
$870$	1.10414	0.0374338
$871$	49.0798	1.66301
$872$	12.6976	0.429994
$873$	−2.96849	−0.100468
$874$	−67.4585	−2.28182
$875$	−31.9319	−1.07950
$876$	0.891402	0.0301177
$877$	−32.8080	−1.10785	−0.553924	−	0.832567i	$-0.686870\pi$
$877$	−32.8080	−1.10785	−0.553924	+	0.832567i	$0.686870\pi$
$878$	26.9905	0.910886
$879$	1.23738	0.0417356
$880$	6.76871	0.228173
$881$	40.3145	1.35823	0.679115	−	0.734032i	$-0.262364\pi$
$881$	40.3145	1.35823	0.679115	+	0.734032i	$0.262364\pi$
$882$	−6.91346	−0.232788
$883$	−28.7064	−0.966047	−0.483023	−	0.875607i	$-0.660461\pi$
$883$	−28.7064	−0.966047	−0.483023	+	0.875607i	$0.660461\pi$
$884$	−48.6649	−1.63678
$885$	0.622035	0.0209095
$886$	−16.3443	−0.549097
$887$	−27.9662	−0.939014	−0.469507	−	0.882929i	$-0.655568\pi$
$887$	−27.9662	−0.939014	−0.469507	+	0.882929i	$0.655568\pi$
$888$	0.506714	0.0170042
$889$	−14.7928	−0.496136
$890$	−8.59226	−0.288013
$891$	−47.8614	−1.60342
$892$	−16.5506	−0.554155
$893$	−14.3069	−0.478763
$894$	0.731014	0.0244488
$895$	−23.5484	−0.787137
$896$	−3.05433	−0.102038
$897$	10.0746	0.336380
$898$	31.7436	1.05930
$899$	5.04538	0.168273
$900$	10.3306	0.344355
$901$	−17.7357	−0.590863
$902$	−37.7538	−1.25706
$903$	1.87412	0.0623667
$904$	12.9617	0.431101
$905$	28.3648	0.942877
$906$	−1.09074	−0.0362375
$907$	−33.7130	−1.11942	−0.559712	−	0.828688i	$-0.689088\pi$
$907$	−33.7130	−1.11942	−0.559712	+	0.828688i	$0.689088\pi$
$908$	15.7507	0.522704
$909$	11.1335	0.369274
$910$	25.6116	0.849016
$911$	19.4038	0.642878	0.321439	−	0.946930i	$-0.395834\pi$
$911$	19.4038	0.642878	0.321439	+	0.946930i	$0.395834\pi$
$912$	−1.43505	−0.0475193
$913$	63.2039	2.09175
$914$	−1.00412	−0.0332132
$915$	−2.72945	−0.0902329
$916$	−3.90178	−0.128919
$917$	−17.5275	−0.578810
$918$	−7.58036	−0.250189
$919$	−16.3711	−0.540034	−0.270017	−	0.962856i	$-0.587029\pi$
$919$	−16.3711	−0.540034	−0.270017	+	0.962856i	$0.587029\pi$
$920$	10.2872	0.339160
$921$	−4.32767	−0.142602
$922$	−26.3072	−0.866382
$923$	91.3168	3.00573
$924$	−2.97671	−0.0979267
$925$	9.93420	0.326634
$926$	−10.0184	−0.329227
$927$	−59.7911	−1.96380
$928$	5.04538	0.165623
$929$	−44.1941	−1.44996	−0.724981	−	0.688769i	$-0.758152\pi$
$929$	−44.1941	−1.44996	−0.724981	+	0.688769i	$0.758152\pi$
$930$	0.218841	0.00717609
$931$	18.8281	0.617065
$932$	−7.47060	−0.244708
$933$	3.08200	0.100900
$934$	−39.1990	−1.28263
$935$	−48.4294	−1.58381
$936$	−20.1906	−0.659949
$937$	27.5436	0.899810	0.449905	−	0.893077i	$-0.351458\pi$
$937$	27.5436	0.899810	0.449905	+	0.893077i	$0.351458\pi$
$938$	−22.0398	−0.719624
$939$	−0.315551	−0.0102976
$940$	2.18177	0.0711614
$941$	−24.4241	−0.796203	−0.398101	−	0.917341i	$-0.630331\pi$
$941$	−24.4241	−0.796203	−0.398101	+	0.917341i	$0.630331\pi$
$942$	−1.48245	−0.0483009
$943$	−57.3790	−1.86852
$944$	2.84240	0.0925122
$945$	3.98943	0.129776
$946$	−18.9783	−0.617036
$947$	17.9288	0.582607	0.291303	−	0.956631i	$-0.405911\pi$
$947$	17.9288	0.582607	0.291303	+	0.956631i	$0.405911\pi$
$948$	−0.949346	−0.0308333
$949$	−34.1558	−1.10874
$950$	−28.1344	−0.912799
$951$	0.956742	0.0310245
$952$	21.8534	0.708273
$953$	−37.6512	−1.21964	−0.609821	−	0.792539i	$-0.708759\pi$
$953$	−37.6512	−1.21964	−0.609821	+	0.792539i	$0.708759\pi$
$954$	−7.35838	−0.238236
$955$	−27.6460	−0.894603
$956$	21.0167	0.679728
$957$	4.91717	0.158949
$958$	8.30591	0.268352
$959$	37.2026	1.20133
$960$	0.218841	0.00706308
$961$	1.00000	0.0322581
$962$	−19.4157	−0.625988
$963$	50.4392	1.62538
$964$	−3.38666	−0.109077
$965$	11.0938	0.357122
$966$	−4.52408	−0.145560
$967$	27.0080	0.868520	0.434260	−	0.900788i	$-0.357010\pi$
$967$	27.0080	0.868520	0.434260	+	0.900788i	$0.357010\pi$
$968$	19.1437	0.615303
$969$	10.2676	0.329844
$970$	−1.23284	−0.0395842
$971$	−9.23824	−0.296469	−0.148235	−	0.988952i	$-0.547359\pi$
$971$	−9.23824	−0.296469	−0.148235	+	0.988952i	$0.547359\pi$
$972$	−4.72582	−0.151581
$973$	−56.8269	−1.82179
$974$	−34.8900	−1.11795
$975$	4.20172	0.134563
$976$	−12.4723	−0.399228
$977$	−31.2300	−0.999137	−0.499568	−	0.866275i	$-0.666508\pi$
$977$	−31.2300	−0.999137	−0.499568	+	0.866275i	$0.666508\pi$
$978$	0.726360	0.0232264
$979$	−38.2647	−1.22295
$980$	−2.87123	−0.0917180
$981$	−37.6927	−1.20343
$982$	22.8316	0.728586
$983$	11.0822	0.353468	0.176734	−	0.984259i	$-0.443447\pi$
$983$	11.0822	0.353468	0.176734	+	0.984259i	$0.443447\pi$
$984$	−1.22063	−0.0389123
$985$	−9.53775	−0.303898
$986$	−36.0992	−1.14963
$987$	−0.959488	−0.0305408
$988$	54.9867	1.74936
$989$	−28.8436	−0.917172
$990$	−20.0929	−0.638593
$991$	−40.9234	−1.29997	−0.649987	−	0.759945i	$-0.725226\pi$
$991$	−40.9234	−1.29997	−0.649987	+	0.759945i	$0.725226\pi$
$992$	1.00000	0.0317500
$993$	1.16911	0.0371006
$994$	−41.0067	−1.30065
$995$	19.0892	0.605167
$996$	2.04347	0.0647498
$997$	21.8481	0.691936	0.345968	−	0.938246i	$-0.387551\pi$
$997$	21.8481	0.691936	0.345968	+	0.938246i	$0.387551\pi$
$998$	9.30953	0.294688
$999$	−3.02432	−0.0956852

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.k.1.16	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.k.1.16	✓	37	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.177510 q^{3} +1.00000 q^{4} -1.23284 q^{5} -0.177510 q^{6} -3.05433 q^{7} +1.00000 q^{8} -2.96849 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.177510 q^{3} +1.00000 q^{4} -1.23284 q^{5} -0.177510 q^{6} -3.05433 q^{7} +1.00000 q^{8} -2.96849 q^{9} -1.23284 q^{10} -5.49033 q^{11} -0.177510 q^{12} +6.80162 q^{13} -3.05433 q^{14} +0.218841 q^{15} +1.00000 q^{16} -7.15489 q^{17} -2.96849 q^{18} +8.08435 q^{19} -1.23284 q^{20} +0.542174 q^{21} -5.49033 q^{22} -8.34433 q^{23} -0.177510 q^{24} -3.48010 q^{25} +6.80162 q^{26} +1.05947 q^{27} -3.05433 q^{28} +5.04538 q^{29} +0.218841 q^{30} +1.00000 q^{31} +1.00000 q^{32} +0.974587 q^{33} -7.15489 q^{34} +3.76551 q^{35} -2.96849 q^{36} -2.85457 q^{37} +8.08435 q^{38} -1.20735 q^{39} -1.23284 q^{40} +6.87641 q^{41} +0.542174 q^{42} +3.45667 q^{43} -5.49033 q^{44} +3.65968 q^{45} -8.34433 q^{46} -1.76971 q^{47} -0.177510 q^{48} +2.32895 q^{49} -3.48010 q^{50} +1.27006 q^{51} +6.80162 q^{52} +2.47883 q^{53} +1.05947 q^{54} +6.76871 q^{55} -3.05433 q^{56} -1.43505 q^{57} +5.04538 q^{58} +2.84240 q^{59} +0.218841 q^{60} -12.4723 q^{61} +1.00000 q^{62} +9.06676 q^{63} +1.00000 q^{64} -8.38533 q^{65} +0.974587 q^{66} +7.21590 q^{67} -7.15489 q^{68} +1.48120 q^{69} +3.76551 q^{70} +13.4257 q^{71} -2.96849 q^{72} -5.02171 q^{73} -2.85457 q^{74} +0.617752 q^{75} +8.08435 q^{76} +16.7693 q^{77} -1.20735 q^{78} +5.34813 q^{79} -1.23284 q^{80} +8.71741 q^{81} +6.87641 q^{82} -11.5119 q^{83} +0.542174 q^{84} +8.82085 q^{85} +3.45667 q^{86} -0.895605 q^{87} -5.49033 q^{88} +6.96947 q^{89} +3.65968 q^{90} -20.7744 q^{91} -8.34433 q^{92} -0.177510 q^{93} -1.76971 q^{94} -9.96673 q^{95} -0.177510 q^{96} +1.00000 q^{97} +2.32895 q^{98} +16.2980 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9}+O(q^{10}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9} + 9 q^{10} + 5 q^{11} + 9 q^{12} + 16 q^{13} + 19 q^{14} + 22 q^{15} + 37 q^{16} + 3 q^{17} + 52 q^{18} + 36 q^{19} + 9 q^{20} + 6 q^{21} + 5 q^{22} + 11 q^{23} + 9 q^{24} + 58 q^{25} + 16 q^{26} + 24 q^{27} + 19 q^{28} + 5 q^{29} + 22 q^{30} + 37 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 28 q^{35} + 52 q^{36} + 21 q^{37} + 36 q^{38} + 38 q^{39} + 9 q^{40} + 21 q^{41} + 6 q^{42} + 14 q^{43} + 5 q^{44} + 55 q^{45} + 11 q^{46} + 59 q^{47} + 9 q^{48} + 82 q^{49} + 58 q^{50} + 46 q^{51} + 16 q^{52} + 8 q^{53} + 24 q^{54} + 25 q^{55} + 19 q^{56} + 5 q^{58} + 41 q^{59} + 22 q^{60} + 16 q^{61} + 37 q^{62} + 23 q^{63} + 37 q^{64} - 46 q^{65} + q^{66} + 45 q^{67} + 3 q^{68} + 68 q^{69} + 28 q^{70} + 55 q^{71} + 52 q^{72} + 29 q^{73} + 21 q^{74} - 12 q^{75} + 36 q^{76} + 30 q^{77} + 38 q^{78} + 25 q^{79} + 9 q^{80} + 73 q^{81} + 21 q^{82} + 70 q^{83} + 6 q^{84} - 21 q^{85} + 14 q^{86} + 37 q^{87} + 5 q^{88} + 55 q^{90} + 18 q^{91} + 11 q^{92} + 9 q^{93} + 59 q^{94} - 9 q^{95} + 9 q^{96} + 37 q^{97} + 82 q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9 + 9 * q^10 + 5 * q^11 + 9 * q^12 + 16 * q^13 + 19 * q^14 + 22 * q^15 + 37 * q^16 + 3 * q^17 + 52 * q^18 + 36 * q^19 + 9 * q^20 + 6 * q^21 + 5 * q^22 + 11 * q^23 + 9 * q^24 + 58 * q^25 + 16 * q^26 + 24 * q^27 + 19 * q^28 + 5 * q^29 + 22 * q^30 + 37 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 28 * q^35 + 52 * q^36 + 21 * q^37 + 36 * q^38 + 38 * q^39 + 9 * q^40 + 21 * q^41 + 6 * q^42 + 14 * q^43 + 5 * q^44 + 55 * q^45 + 11 * q^46 + 59 * q^47 + 9 * q^48 + 82 * q^49 + 58 * q^50 + 46 * q^51 + 16 * q^52 + 8 * q^53 + 24 * q^54 + 25 * q^55 + 19 * q^56 + 5 * q^58 + 41 * q^59 + 22 * q^60 + 16 * q^61 + 37 * q^62 + 23 * q^63 + 37 * q^64 - 46 * q^65 + q^66 + 45 * q^67 + 3 * q^68 + 68 * q^69 + 28 * q^70 + 55 * q^71 + 52 * q^72 + 29 * q^73 + 21 * q^74 - 12 * q^75 + 36 * q^76 + 30 * q^77 + 38 * q^78 + 25 * q^79 + 9 * q^80 + 73 * q^81 + 21 * q^82 + 70 * q^83 + 6 * q^84 - 21 * q^85 + 14 * q^86 + 37 * q^87 + 5 * q^88 + 55 * q^90 + 18 * q^91 + 11 * q^92 + 9 * q^93 + 59 * q^94 - 9 * q^95 + 9 * q^96 + 37 * q^97 + 82 * q^98 + 33 * q^99

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