LMFDB - Embedded newform 4031.2.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4031,2,Mod(1,4031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4031, 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("4031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4031 = 29 \cdot 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4031.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:	$32.1876970548$
Analytic rank:	$1$
Dimension:	$61$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	4031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49843 q^{2} -0.867725 q^{3} +4.24214 q^{4} +3.27534 q^{5} +2.16795 q^{6} +1.98132 q^{7} -5.60183 q^{8} -2.24705 q^{9} +O(q^{10})$	\(q-2.49843 q^{2} -0.867725 q^{3} +4.24214 q^{4} +3.27534 q^{5} +2.16795 q^{6} +1.98132 q^{7} -5.60183 q^{8} -2.24705 q^{9} -8.18321 q^{10} +2.44571 q^{11} -3.68101 q^{12} -4.07719 q^{13} -4.95018 q^{14} -2.84210 q^{15} +5.51149 q^{16} -3.48151 q^{17} +5.61410 q^{18} +1.20918 q^{19} +13.8945 q^{20} -1.71924 q^{21} -6.11044 q^{22} -5.75094 q^{23} +4.86085 q^{24} +5.72787 q^{25} +10.1866 q^{26} +4.55300 q^{27} +8.40502 q^{28} -1.00000 q^{29} +7.10077 q^{30} -2.86533 q^{31} -2.56639 q^{32} -2.12221 q^{33} +8.69829 q^{34} +6.48949 q^{35} -9.53232 q^{36} +11.8840 q^{37} -3.02104 q^{38} +3.53788 q^{39} -18.3479 q^{40} -0.892481 q^{41} +4.29539 q^{42} -10.8277 q^{43} +10.3751 q^{44} -7.35987 q^{45} +14.3683 q^{46} +12.6747 q^{47} -4.78245 q^{48} -3.07439 q^{49} -14.3107 q^{50} +3.02099 q^{51} -17.2960 q^{52} +4.12783 q^{53} -11.3753 q^{54} +8.01055 q^{55} -11.0990 q^{56} -1.04923 q^{57} +2.49843 q^{58} -14.2386 q^{59} -12.0566 q^{60} -10.5744 q^{61} +7.15883 q^{62} -4.45212 q^{63} -4.61103 q^{64} -13.3542 q^{65} +5.30218 q^{66} +5.16192 q^{67} -14.7690 q^{68} +4.99023 q^{69} -16.2135 q^{70} +1.85405 q^{71} +12.5876 q^{72} +9.25762 q^{73} -29.6913 q^{74} -4.97022 q^{75} +5.12949 q^{76} +4.84573 q^{77} -8.83913 q^{78} -13.4490 q^{79} +18.0520 q^{80} +2.79041 q^{81} +2.22980 q^{82} -14.3099 q^{83} -7.29325 q^{84} -11.4031 q^{85} +27.0522 q^{86} +0.867725 q^{87} -13.7005 q^{88} +5.36321 q^{89} +18.3881 q^{90} -8.07820 q^{91} -24.3963 q^{92} +2.48632 q^{93} -31.6668 q^{94} +3.96046 q^{95} +2.22692 q^{96} +0.827274 q^{97} +7.68113 q^{98} -5.49565 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) $ 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9} - 16 q^{10} - 3 q^{11} - 18 q^{12} - 28 q^{13} - 14 q^{14} - 12 q^{15} + 11 q^{16} - 21 q^{17} - 17 q^{18} - 36 q^{19} - 16 q^{20} - 12 q^{21} - 42 q^{22} - 15 q^{23} - 28 q^{24} - 16 q^{25} - 13 q^{26} - 10 q^{27} - 25 q^{28} - 61 q^{29} - 12 q^{30} - 18 q^{31} - 3 q^{32} - 42 q^{33} - 22 q^{34} - 29 q^{35} - 38 q^{36} - 30 q^{37} - 27 q^{38} - 31 q^{39} - 22 q^{40} - 28 q^{41} - 9 q^{42} - 58 q^{43} - 2 q^{44} - 31 q^{45} - 40 q^{46} - 6 q^{47} - 37 q^{48} - 37 q^{49} - 15 q^{50} - 44 q^{51} - 43 q^{52} - 27 q^{53} - 18 q^{54} - 38 q^{55} - 22 q^{56} - 50 q^{57} + q^{58} - 24 q^{59} + 6 q^{60} - 76 q^{61} - 17 q^{62} - 6 q^{63} - 60 q^{64} - 65 q^{65} - 7 q^{66} - 45 q^{67} - 31 q^{68} - 16 q^{69} - 48 q^{70} - 28 q^{71} - 40 q^{72} - 50 q^{73} - 17 q^{74} - 35 q^{75} - 100 q^{76} + q^{77} - 6 q^{78} - 66 q^{79} - 10 q^{80} - 63 q^{81} - 5 q^{82} - 9 q^{83} - 24 q^{84} - 77 q^{85} + 29 q^{86} + 4 q^{87} - 62 q^{88} - 30 q^{89} + 50 q^{90} - 52 q^{91} - 53 q^{92} - 42 q^{93} - 92 q^{94} - 20 q^{95} - 47 q^{96} - 34 q^{97} + 36 q^{98} - 29 q^{99}+O(q^{100}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9 - 16 * q^10 - 3 * q^11 - 18 * q^12 - 28 * q^13 - 14 * q^14 - 12 * q^15 + 11 * q^16 - 21 * q^17 - 17 * q^18 - 36 * q^19 - 16 * q^20 - 12 * q^21 - 42 * q^22 - 15 * q^23 - 28 * q^24 - 16 * q^25 - 13 * q^26 - 10 * q^27 - 25 * q^28 - 61 * q^29 - 12 * q^30 - 18 * q^31 - 3 * q^32 - 42 * q^33 - 22 * q^34 - 29 * q^35 - 38 * q^36 - 30 * q^37 - 27 * q^38 - 31 * q^39 - 22 * q^40 - 28 * q^41 - 9 * q^42 - 58 * q^43 - 2 * q^44 - 31 * q^45 - 40 * q^46 - 6 * q^47 - 37 * q^48 - 37 * q^49 - 15 * q^50 - 44 * q^51 - 43 * q^52 - 27 * q^53 - 18 * q^54 - 38 * q^55 - 22 * q^56 - 50 * q^57 + q^58 - 24 * q^59 + 6 * q^60 - 76 * q^61 - 17 * q^62 - 6 * q^63 - 60 * q^64 - 65 * q^65 - 7 * q^66 - 45 * q^67 - 31 * q^68 - 16 * q^69 - 48 * q^70 - 28 * q^71 - 40 * q^72 - 50 * q^73 - 17 * q^74 - 35 * q^75 - 100 * q^76 + q^77 - 6 * q^78 - 66 * q^79 - 10 * q^80 - 63 * q^81 - 5 * q^82 - 9 * q^83 - 24 * q^84 - 77 * q^85 + 29 * q^86 + 4 * q^87 - 62 * q^88 - 30 * q^89 + 50 * q^90 - 52 * q^91 - 53 * q^92 - 42 * q^93 - 92 * q^94 - 20 * q^95 - 47 * q^96 - 34 * q^97 + 36 * q^98 - 29 * 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 $

$2$	−2.49843	−1.76666	−0.883328	−	0.468756i	$-0.844702\pi$
$2$	−2.49843	−1.76666	−0.883328	+	0.468756i	$0.844702\pi$
$3$	−0.867725	−0.500981	−0.250491	−	0.968119i	$-0.580592\pi$
$3$	−0.867725	−0.500981	−0.250491	+	0.968119i	$0.580592\pi$
$4$	4.24214	2.12107
$5$	3.27534	1.46478	0.732389	−	0.680886i	$-0.238405\pi$
$5$	3.27534	1.46478	0.732389	+	0.680886i	$0.238405\pi$
$6$	2.16795	0.885061
$7$	1.98132	0.748867	0.374434	−	0.927254i	$-0.377837\pi$
$7$	1.98132	0.748867	0.374434	+	0.927254i	$0.377837\pi$
$8$	−5.60183	−1.98055
$9$	−2.24705	−0.749018
$10$	−8.18321	−2.58776
$11$	2.44571	0.737410	0.368705	−	0.929546i	$-0.379801\pi$
$11$	2.44571	0.737410	0.368705	+	0.929546i	$0.379801\pi$
$12$	−3.68101	−1.06262
$13$	−4.07719	−1.13081	−0.565404	−	0.824814i	$-0.691280\pi$
$13$	−4.07719	−1.13081	−0.565404	+	0.824814i	$0.691280\pi$
$14$	−4.95018	−1.32299
$15$	−2.84210	−0.733826
$16$	5.51149	1.37787
$17$	−3.48151	−0.844389	−0.422195	−	0.906505i	$-0.638740\pi$
$17$	−3.48151	−0.844389	−0.422195	+	0.906505i	$0.638740\pi$
$18$	5.61410	1.32326
$19$	1.20918	0.277404	0.138702	−	0.990334i	$-0.455707\pi$
$19$	1.20918	0.277404	0.138702	+	0.990334i	$0.455707\pi$
$20$	13.8945	3.10690
$21$	−1.71924	−0.375168
$22$	−6.11044	−1.30275
$23$	−5.75094	−1.19915	−0.599577	−	0.800317i	$-0.704664\pi$
$23$	−5.75094	−1.19915	−0.599577	+	0.800317i	$0.704664\pi$
$24$	4.86085	0.992216
$25$	5.72787	1.14557
$26$	10.1866	1.99775
$27$	4.55300	0.876225
$28$	8.40502	1.58840
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	7.10077	1.29642
$31$	−2.86533	−0.514629	−0.257314	−	0.966328i	$-0.582838\pi$
$31$	−2.86533	−0.514629	−0.257314	+	0.966328i	$0.582838\pi$
$32$	−2.56639	−0.453678
$33$	−2.12221	−0.369429
$34$	8.69829	1.49174
$35$	6.48949	1.09692
$36$	−9.53232	−1.58872
$37$	11.8840	1.95372	0.976860	−	0.213881i	$-0.0686106\pi$
$37$	11.8840	1.95372	0.976860	+	0.213881i	$0.0686106\pi$
$38$	−3.02104	−0.490077
$39$	3.53788	0.566514
$40$	−18.3479	−2.90106
$41$	−0.892481	−0.139382	−0.0696910	−	0.997569i	$-0.522201\pi$
$41$	−0.892481	−0.139382	−0.0696910	+	0.997569i	$0.522201\pi$
$42$	4.29539	0.662793
$43$	−10.8277	−1.65121	−0.825603	−	0.564252i	$-0.809165\pi$
$43$	−10.8277	−1.65121	−0.825603	+	0.564252i	$0.809165\pi$
$44$	10.3751	1.56410
$45$	−7.35987	−1.09715
$46$	14.3683	2.11849
$47$	12.6747	1.84879	0.924396	−	0.381434i	$-0.124570\pi$
$47$	12.6747	1.84879	0.924396	+	0.381434i	$0.124570\pi$
$48$	−4.78245	−0.690287
$49$	−3.07439	−0.439198
$50$	−14.3107	−2.02384
$51$	3.02099	0.423023
$52$	−17.2960	−2.39852
$53$	4.12783	0.567001	0.283500	−	0.958972i	$-0.408504\pi$
$53$	4.12783	0.567001	0.283500	+	0.958972i	$0.408504\pi$
$54$	−11.3753	−1.54799
$55$	8.01055	1.08014
$56$	−11.0990	−1.48317
$57$	−1.04923	−0.138974
$58$	2.49843	0.328060
$59$	−14.2386	−1.85371	−0.926853	−	0.375425i	$-0.877497\pi$
$59$	−14.2386	−1.85371	−0.926853	+	0.375425i	$0.877497\pi$
$60$	−12.0566	−1.55650
$61$	−10.5744	−1.35392	−0.676958	−	0.736021i	$-0.736702\pi$
$61$	−10.5744	−1.35392	−0.676958	+	0.736021i	$0.736702\pi$
$62$	7.15883	0.909172
$63$	−4.45212	−0.560915
$64$	−4.61103	−0.576379
$65$	−13.3542	−1.65638
$66$	5.30218	0.652653
$67$	5.16192	0.630629	0.315315	−	0.948987i	$-0.397890\pi$
$67$	5.16192	0.630629	0.315315	+	0.948987i	$0.397890\pi$
$68$	−14.7690	−1.79101
$69$	4.99023	0.600753
$70$	−16.2135	−1.93789
$71$	1.85405	0.220035	0.110018	−	0.993930i	$-0.464909\pi$
$71$	1.85405	0.220035	0.110018	+	0.993930i	$0.464909\pi$
$72$	12.5876	1.48346
$73$	9.25762	1.08352	0.541761	−	0.840532i	$-0.317758\pi$
$73$	9.25762	1.08352	0.541761	+	0.840532i	$0.317758\pi$
$74$	−29.6913	−3.45155
$75$	−4.97022	−0.573911
$76$	5.12949	0.588393
$77$	4.84573	0.552222
$78$	−8.83913	−1.00083
$79$	−13.4490	−1.51313	−0.756565	−	0.653918i	$-0.773124\pi$
$79$	−13.4490	−1.51313	−0.756565	+	0.653918i	$0.773124\pi$
$80$	18.0520	2.01828
$81$	2.79041	0.310046
$82$	2.22980	0.246240
$83$	−14.3099	−1.57071	−0.785356	−	0.619044i	$-0.787520\pi$
$83$	−14.3099	−1.57071	−0.785356	+	0.619044i	$0.787520\pi$
$84$	−7.29325	−0.795758
$85$	−11.4031	−1.23684
$86$	27.0522	2.91711
$87$	0.867725	0.0930299
$88$	−13.7005	−1.46047
$89$	5.36321	0.568499	0.284250	−	0.958750i	$-0.408256\pi$
$89$	5.36321	0.568499	0.284250	+	0.958750i	$0.408256\pi$
$90$	18.3881	1.93828
$91$	−8.07820	−0.846825
$92$	−24.3963	−2.54349
$93$	2.48632	0.257819
$94$	−31.6668	−3.26618
$95$	3.96046	0.406335
$96$	2.22692	0.227284
$97$	0.827274	0.0839970	0.0419985	−	0.999118i	$-0.486628\pi$
$97$	0.827274	0.0839970	0.0419985	+	0.999118i	$0.486628\pi$
$98$	7.68113	0.775912
$99$	−5.49565	−0.552333
$100$	24.2985	2.42985
$101$	−10.3918	−1.03403	−0.517013	−	0.855978i	$-0.672956\pi$
$101$	−10.3918	−1.03403	−0.517013	+	0.855978i	$0.672956\pi$
$102$	−7.54772	−0.747336
$103$	−15.0826	−1.48613	−0.743065	−	0.669219i	$-0.766629\pi$
$103$	−15.0826	−1.48613	−0.743065	+	0.669219i	$0.766629\pi$
$104$	22.8397	2.23962
$105$	−5.63109	−0.549538
$106$	−10.3131	−1.00170
$107$	14.5506	1.40666	0.703328	−	0.710865i	$-0.251696\pi$
$107$	14.5506	1.40666	0.703328	+	0.710865i	$0.251696\pi$
$108$	19.3145	1.85854
$109$	−5.14960	−0.493242	−0.246621	−	0.969112i	$-0.579320\pi$
$109$	−5.14960	−0.493242	−0.246621	+	0.969112i	$0.579320\pi$
$110$	−20.0138	−1.90824
$111$	−10.3120	−0.978776
$112$	10.9200	1.03184
$113$	−3.54863	−0.333827	−0.166913	−	0.985972i	$-0.553380\pi$
$113$	−3.54863	−0.333827	−0.166913	+	0.985972i	$0.553380\pi$
$114$	2.62143	0.245519
$115$	−18.8363	−1.75649
$116$	−4.24214	−0.393873
$117$	9.16166	0.846996
$118$	35.5741	3.27486
$119$	−6.89796	−0.632335
$120$	15.9209	1.45338
$121$	−5.01849	−0.456226
$122$	26.4194	2.39190
$123$	0.774427	0.0698278
$124$	−12.1551	−1.09156
$125$	2.38403	0.213234
$126$	11.1233	0.990943
$127$	1.37783	0.122263	0.0611315	−	0.998130i	$-0.480529\pi$
$127$	1.37783	0.122263	0.0611315	+	0.998130i	$0.480529\pi$
$128$	16.6531	1.47194
$129$	9.39544	0.827223
$130$	33.3645	2.92626
$131$	1.85540	0.162107	0.0810537	−	0.996710i	$-0.474171\pi$
$131$	1.85540	0.162107	0.0810537	+	0.996710i	$0.474171\pi$
$132$	−9.00270	−0.783584
$133$	2.39576	0.207739
$134$	−12.8967	−1.11410
$135$	14.9126	1.28347
$136$	19.5028	1.67235
$137$	−11.5960	−0.990714	−0.495357	−	0.868689i	$-0.664963\pi$
$137$	−11.5960	−0.990714	−0.495357	+	0.868689i	$0.664963\pi$
$138$	−12.4677	−1.06132
$139$	−1.00000	−0.0848189
$139$	−1.00000	−0.0848189
$140$	27.5293	2.32665
$141$	−10.9981	−0.926210
$142$	−4.63221	−0.388727
$143$	−9.97163	−0.833869
$144$	−12.3846	−1.03205
$145$	−3.27534	−0.272002
$146$	−23.1295	−1.91421
$147$	2.66772	0.220030
$148$	50.4137	4.14398
$149$	−5.09836	−0.417674	−0.208837	−	0.977950i	$-0.566968\pi$
$149$	−5.09836	−0.417674	−0.208837	+	0.977950i	$0.566968\pi$
$150$	12.4177	1.01390
$151$	−15.5753	−1.26750	−0.633751	−	0.773537i	$-0.718486\pi$
$151$	−15.5753	−1.26750	−0.633751	+	0.773537i	$0.718486\pi$
$152$	−6.77360	−0.549411
$153$	7.82313	0.632463
$154$	−12.1067	−0.975586
$155$	−9.38495	−0.753817
$156$	15.0082	1.20162
$157$	16.2350	1.29570	0.647848	−	0.761770i	$-0.275669\pi$
$157$	16.2350	1.29570	0.647848	+	0.761770i	$0.275669\pi$
$158$	33.6014	2.67318
$159$	−3.58182	−0.284057
$160$	−8.40580	−0.664537
$161$	−11.3944	−0.898007
$162$	−6.97164	−0.547744
$163$	6.24534	0.489172	0.244586	−	0.969628i	$-0.421348\pi$
$163$	6.24534	0.489172	0.244586	+	0.969628i	$0.421348\pi$
$164$	−3.78603	−0.295639
$165$	−6.95095	−0.541131
$166$	35.7522	2.77491
$167$	−10.6436	−0.823630	−0.411815	−	0.911267i	$-0.635105\pi$
$167$	−10.6436	−0.823630	−0.411815	+	0.911267i	$0.635105\pi$
$168$	9.63087	0.743038
$169$	3.62346	0.278727
$170$	28.4899	2.18507
$171$	−2.71708	−0.207780
$172$	−45.9326	−3.50232
$173$	16.3574	1.24363	0.621814	−	0.783165i	$-0.286396\pi$
$173$	16.3574	1.24363	0.621814	+	0.783165i	$0.286396\pi$
$174$	−2.16795	−0.164352
$175$	11.3487	0.857883
$176$	13.4795	1.01606
$177$	12.3552	0.928671
$178$	−13.3996	−1.00434
$179$	12.7318	0.951619	0.475810	−	0.879548i	$-0.342155\pi$
$179$	12.7318	0.951619	0.475810	+	0.879548i	$0.342155\pi$
$180$	−31.2216	−2.32712
$181$	−9.11335	−0.677390	−0.338695	−	0.940896i	$-0.609986\pi$
$181$	−9.11335	−0.677390	−0.338695	+	0.940896i	$0.609986\pi$
$182$	20.1828	1.49605
$183$	9.17569	0.678287
$184$	32.2158	2.37498
$185$	38.9242	2.86177
$186$	−6.21189	−0.455478
$187$	−8.51476	−0.622661
$188$	53.7678	3.92142
$189$	9.02093	0.656176
$190$	−9.89493	−0.717854
$191$	8.51043	0.615793	0.307897	−	0.951420i	$-0.400375\pi$
$191$	8.51043	0.615793	0.307897	+	0.951420i	$0.400375\pi$
$192$	4.00111	0.288755
$193$	−20.3741	−1.46656	−0.733281	−	0.679926i	$-0.762012\pi$
$193$	−20.3741	−1.46656	−0.733281	+	0.679926i	$0.762012\pi$
$194$	−2.06688	−0.148394
$195$	11.5878	0.829817
$196$	−13.0420	−0.931570
$197$	−5.50200	−0.392001	−0.196001	−	0.980604i	$-0.562795\pi$
$197$	−5.50200	−0.392001	−0.196001	+	0.980604i	$0.562795\pi$
$198$	13.7305	0.975783
$199$	10.0970	0.715759	0.357879	−	0.933768i	$-0.383500\pi$
$199$	10.0970	0.715759	0.357879	+	0.933768i	$0.383500\pi$
$200$	−32.0866	−2.26886
$201$	−4.47913	−0.315933
$202$	25.9632	1.82677
$203$	−1.98132	−0.139061
$204$	12.8155	0.897262
$205$	−2.92318	−0.204164
$206$	37.6827	2.62548
$207$	12.9227	0.898188
$208$	−22.4714	−1.55811
$209$	2.95730	0.204560
$210$	14.0689	0.970845
$211$	4.05894	0.279429	0.139714	−	0.990192i	$-0.455382\pi$
$211$	4.05894	0.279429	0.139714	+	0.990192i	$0.455382\pi$
$212$	17.5108	1.20265
$213$	−1.60881	−0.110234
$214$	−36.3536	−2.48508
$215$	−35.4644	−2.41865
$216$	−25.5051	−1.73540
$217$	−5.67713	−0.385389
$218$	12.8659	0.871388
$219$	−8.03307	−0.542824
$220$	33.9819	2.29106
$221$	14.1948	0.954842
$222$	25.7639	1.72916
$223$	4.19820	0.281132	0.140566	−	0.990071i	$-0.455108\pi$
$223$	4.19820	0.281132	0.140566	+	0.990071i	$0.455108\pi$
$224$	−5.08483	−0.339744
$225$	−12.8708	−0.858056
$226$	8.86599	0.589757
$227$	19.1394	1.27032	0.635162	−	0.772379i	$-0.280933\pi$
$227$	19.1394	1.27032	0.635162	+	0.772379i	$0.280933\pi$
$228$	−4.45099	−0.294774
$229$	−12.6139	−0.833547	−0.416773	−	0.909010i	$-0.636839\pi$
$229$	−12.6139	−0.833547	−0.416773	+	0.909010i	$0.636839\pi$
$230$	47.0611	3.10312
$231$	−4.20476	−0.276653
$232$	5.60183	0.367778
$233$	−4.99031	−0.326926	−0.163463	−	0.986549i	$-0.552266\pi$
$233$	−4.99031	−0.326926	−0.163463	+	0.986549i	$0.552266\pi$
$234$	−22.8897	−1.49635
$235$	41.5139	2.70807
$236$	−60.4021	−3.93184
$237$	11.6700	0.758050
$238$	17.2341	1.11712
$239$	−21.3764	−1.38272	−0.691362	−	0.722509i	$-0.742989\pi$
$239$	−21.3764	−1.38272	−0.691362	+	0.722509i	$0.742989\pi$
$240$	−15.6642	−1.01112
$241$	−2.52755	−0.162814	−0.0814068	−	0.996681i	$-0.525941\pi$
$241$	−2.52755	−0.162814	−0.0814068	+	0.996681i	$0.525941\pi$
$242$	12.5383	0.805995
$243$	−16.0803	−1.03155
$244$	−44.8582	−2.87175
$245$	−10.0697	−0.643328
$246$	−1.93485	−0.123362
$247$	−4.93003	−0.313691
$248$	16.0511	1.01925
$249$	12.4170	0.786897
$250$	−5.95634	−0.376712
$251$	−4.08138	−0.257615	−0.128807	−	0.991670i	$-0.541115\pi$
$251$	−4.08138	−0.257615	−0.128807	+	0.991670i	$0.541115\pi$
$252$	−18.8865	−1.18974
$253$	−14.0651	−0.884268
$254$	−3.44242	−0.215997
$255$	9.89477	0.619635
$256$	−32.3845	−2.02403
$257$	0.260651	0.0162590	0.00812948	−	0.999967i	$-0.497412\pi$
$257$	0.260651	0.0162590	0.00812948	+	0.999967i	$0.497412\pi$
$258$	−23.4738	−1.46142
$259$	23.5460	1.46308
$260$	−56.6504	−3.51331
$261$	2.24705	0.139089
$262$	−4.63559	−0.286388
$263$	−5.47637	−0.337687	−0.168844	−	0.985643i	$-0.554003\pi$
$263$	−5.47637	−0.337687	−0.168844	+	0.985643i	$0.554003\pi$
$264$	11.8882	0.731670
$265$	13.5201	0.830531
$266$	−5.98563	−0.367003
$267$	−4.65379	−0.284807
$268$	21.8976	1.33761
$269$	−7.43193	−0.453133	−0.226566	−	0.973996i	$-0.572750\pi$
$269$	−7.43193	−0.453133	−0.226566	+	0.973996i	$0.572750\pi$
$270$	−37.2581	−2.26746
$271$	26.7980	1.62786	0.813931	−	0.580961i	$-0.197323\pi$
$271$	26.7980	1.62786	0.813931	+	0.580961i	$0.197323\pi$
$272$	−19.1883	−1.16346
$273$	7.00965	0.424243
$274$	28.9718	1.75025
$275$	14.0087	0.844758
$276$	21.1693	1.27424
$277$	−17.4278	−1.04713	−0.523567	−	0.851984i	$-0.675399\pi$
$277$	−17.4278	−1.04713	−0.523567	+	0.851984i	$0.675399\pi$
$278$	2.49843	0.149846
$279$	6.43856	0.385466
$280$	−36.3530	−2.17251
$281$	21.6974	1.29436	0.647180	−	0.762337i	$-0.275948\pi$
$281$	21.6974	1.29436	0.647180	+	0.762337i	$0.275948\pi$
$282$	27.4780	1.63629
$283$	−21.6764	−1.28853	−0.644263	−	0.764804i	$-0.722836\pi$
$283$	−21.6764	−1.28853	−0.644263	+	0.764804i	$0.722836\pi$
$284$	7.86515	0.466711
$285$	−3.43659	−0.203566
$286$	24.9134	1.47316
$287$	−1.76829	−0.104379
$288$	5.76681	0.339813
$289$	−4.87912	−0.287007
$290$	8.18321	0.480535
$291$	−0.717846	−0.0420809
$292$	39.2721	2.29823
$293$	−0.165687	−0.00967954	−0.00483977	−	0.999988i	$-0.501541\pi$
$293$	−0.165687	−0.00967954	−0.00483977	+	0.999988i	$0.501541\pi$
$294$	−6.66511	−0.388717
$295$	−46.6362	−2.71527
$296$	−66.5722	−3.86943
$297$	11.1353	0.646137
$298$	12.7379	0.737886
$299$	23.4477	1.35601
$300$	−21.0844	−1.21731
$301$	−21.4531	−1.23653
$302$	38.9138	2.23924
$303$	9.01724	0.518027
$304$	6.66435	0.382227
$305$	−34.6349	−1.98319
$306$	−19.5455	−1.11734
$307$	−16.0014	−0.913247	−0.456624	−	0.889660i	$-0.650941\pi$
$307$	−16.0014	−0.913247	−0.456624	+	0.889660i	$0.650941\pi$
$308$	20.5563	1.17130
$309$	13.0875	0.744523
$310$	23.4476	1.33173
$311$	−10.2743	−0.582605	−0.291302	−	0.956631i	$-0.594089\pi$
$311$	−10.2743	−0.582605	−0.291302	+	0.956631i	$0.594089\pi$
$312$	−19.8186	−1.12201
$313$	−24.0710	−1.36057	−0.680287	−	0.732946i	$-0.738145\pi$
$313$	−24.0710	−1.36057	−0.680287	+	0.732946i	$0.738145\pi$
$314$	−40.5620	−2.28905
$315$	−14.5822	−0.821616
$316$	−57.0526	−3.20946
$317$	8.02767	0.450879	0.225440	−	0.974257i	$-0.427618\pi$
$317$	8.02767	0.450879	0.225440	+	0.974257i	$0.427618\pi$
$318$	8.94892	0.501830
$319$	−2.44571	−0.136934
$320$	−15.1027	−0.844268
$321$	−12.6259	−0.704709
$322$	28.4682	1.58647
$323$	−4.20975	−0.234237
$324$	11.8373	0.657629
$325$	−23.3536	−1.29543
$326$	−15.6035	−0.864199
$327$	4.46843	0.247105
$328$	4.99952	0.276053
$329$	25.1125	1.38450
$330$	17.3664	0.955992
$331$	0.821892	0.0451753	0.0225876	−	0.999745i	$-0.492810\pi$
$331$	0.821892	0.0451753	0.0225876	+	0.999745i	$0.492810\pi$
$332$	−60.7045	−3.33159
$333$	−26.7040	−1.46337
$334$	26.5924	1.45507
$335$	16.9071	0.923732
$336$	−9.47555	−0.516934
$337$	8.27780	0.450920	0.225460	−	0.974252i	$-0.427611\pi$
$337$	8.27780	0.450920	0.225460	+	0.974252i	$0.427611\pi$
$338$	−9.05295	−0.492415
$339$	3.07923	0.167241
$340$	−48.3737	−2.62343
$341$	−7.00778	−0.379493
$342$	6.78843	0.367076
$343$	−19.9605	−1.07777
$344$	60.6548	3.27029
$345$	16.3447	0.879970
$346$	−40.8677	−2.19706
$347$	13.6307	0.731732	0.365866	−	0.930668i	$-0.380773\pi$
$347$	13.6307	0.731732	0.365866	+	0.930668i	$0.380773\pi$
$348$	3.68101	0.197323
$349$	24.8994	1.33283	0.666417	−	0.745579i	$-0.267827\pi$
$349$	24.8994	1.33283	0.666417	+	0.745579i	$0.267827\pi$
$350$	−28.3540	−1.51558
$351$	−18.5634	−0.990842
$352$	−6.27665	−0.334546
$353$	−8.28003	−0.440702	−0.220351	−	0.975421i	$-0.570720\pi$
$353$	−8.28003	−0.440702	−0.220351	+	0.975421i	$0.570720\pi$
$354$	−30.8685	−1.64064
$355$	6.07265	0.322303
$356$	22.7515	1.20583
$357$	5.98553	0.316788
$358$	−31.8095	−1.68118
$359$	29.7793	1.57169	0.785847	−	0.618422i	$-0.212228\pi$
$359$	29.7793	1.57169	0.785847	+	0.618422i	$0.212228\pi$
$360$	41.2288	2.17295
$361$	−17.5379	−0.923047
$362$	22.7691	1.19671
$363$	4.35467	0.228561
$364$	−34.2689	−1.79618
$365$	30.3219	1.58712
$366$	−22.9248	−1.19830
$367$	28.5998	1.49290	0.746450	−	0.665442i	$-0.231757\pi$
$367$	28.5998	1.49290	0.746450	+	0.665442i	$0.231757\pi$
$368$	−31.6962	−1.65228
$369$	2.00545	0.104400
$370$	−97.2493	−5.05575
$371$	8.17853	0.424608
$372$	10.5473	0.546853
$373$	−30.3035	−1.56905	−0.784527	−	0.620094i	$-0.787094\pi$
$373$	−30.3035	−1.56905	−0.784527	+	0.620094i	$0.787094\pi$
$374$	21.2735	1.10003
$375$	−2.06869	−0.106826
$376$	−71.0014	−3.66162
$377$	4.07719	0.209986
$378$	−22.5381	−1.15924
$379$	−36.9745	−1.89925	−0.949627	−	0.313383i	$-0.898538\pi$
$379$	−36.9745	−1.89925	−0.949627	+	0.313383i	$0.898538\pi$
$380$	16.8009	0.861865
$381$	−1.19558	−0.0612514
$382$	−21.2627	−1.08789
$383$	−5.95864	−0.304472	−0.152236	−	0.988344i	$-0.548647\pi$
$383$	−5.95864	−0.304472	−0.152236	+	0.988344i	$0.548647\pi$
$384$	−14.4503	−0.737415
$385$	15.8714	0.808883
$386$	50.9033	2.59091
$387$	24.3304	1.23678
$388$	3.50941	0.178164
$389$	−3.83762	−0.194575	−0.0972876	−	0.995256i	$-0.531017\pi$
$389$	−3.83762	−0.194575	−0.0972876	+	0.995256i	$0.531017\pi$
$390$	−28.9512	−1.46600
$391$	20.0219	1.01255
$392$	17.2222	0.869852
$393$	−1.60998	−0.0812127
$394$	13.7463	0.692531
$395$	−44.0501	−2.21640
$396$	−23.3133	−1.17154
$397$	−29.3096	−1.47101	−0.735504	−	0.677520i	$-0.763055\pi$
$397$	−29.3096	−1.47101	−0.735504	+	0.677520i	$0.763055\pi$
$398$	−25.2267	−1.26450
$399$	−2.07886	−0.104073
$400$	31.5691	1.57845
$401$	−9.83092	−0.490933	−0.245466	−	0.969405i	$-0.578941\pi$
$401$	−9.83092	−0.490933	−0.245466	+	0.969405i	$0.578941\pi$
$402$	11.1908	0.558145
$403$	11.6825	0.581947
$404$	−44.0836	−2.19324
$405$	9.13956	0.454148
$406$	4.95018	0.245673
$407$	29.0649	1.44069
$408$	−16.9231	−0.837817
$409$	−34.2641	−1.69425	−0.847126	−	0.531392i	$-0.821669\pi$
$409$	−34.2641	−1.69425	−0.847126	+	0.531392i	$0.821669\pi$
$410$	7.30335	0.360687
$411$	10.0621	0.496329
$412$	−63.9824	−3.15219
$413$	−28.2111	−1.38818
$414$	−32.2864	−1.58679
$415$	−46.8697	−2.30075
$416$	10.4636	0.513022
$417$	0.867725	0.0424927
$418$	−7.38859	−0.361388
$419$	−8.21977	−0.401562	−0.200781	−	0.979636i	$-0.564348\pi$
$419$	−8.21977	−0.401562	−0.200781	+	0.979636i	$0.564348\pi$
$420$	−23.8879	−1.16561
$421$	−6.89550	−0.336066	−0.168033	−	0.985781i	$-0.553742\pi$
$421$	−6.89550	−0.336066	−0.168033	+	0.985781i	$0.553742\pi$
$422$	−10.1410	−0.493654
$423$	−28.4807	−1.38478
$424$	−23.1234	−1.12297
$425$	−19.9416	−0.967311
$426$	4.01949	0.194745
$427$	−20.9513	−1.01390
$428$	61.7256	2.98362
$429$	8.65263	0.417753
$430$	88.6052	4.27292
$431$	37.6318	1.81266	0.906330	−	0.422570i	$-0.138872\pi$
$431$	37.6318	1.81266	0.906330	+	0.422570i	$0.138872\pi$
$432$	25.0938	1.20733
$433$	33.4644	1.60820	0.804099	−	0.594496i	$-0.202648\pi$
$433$	33.4644	1.60820	0.804099	+	0.594496i	$0.202648\pi$
$434$	14.1839	0.680849
$435$	2.84210	0.136268
$436$	−21.8453	−1.04620
$437$	−6.95389	−0.332650
$438$	20.0700	0.958983
$439$	−15.7301	−0.750758	−0.375379	−	0.926871i	$-0.622487\pi$
$439$	−15.7301	−0.750758	−0.375379	+	0.926871i	$0.622487\pi$
$440$	−44.8737	−2.13927
$441$	6.90831	0.328967
$442$	−35.4646	−1.68688
$443$	8.57148	0.407243	0.203622	−	0.979050i	$-0.434729\pi$
$443$	8.57148	0.407243	0.203622	+	0.979050i	$0.434729\pi$
$444$	−43.7452	−2.07605
$445$	17.5664	0.832725
$446$	−10.4889	−0.496664
$447$	4.42398	0.209247
$448$	−9.13592	−0.431632
$449$	27.2634	1.28664	0.643321	−	0.765597i	$-0.277556\pi$
$449$	27.2634	1.28664	0.643321	+	0.765597i	$0.277556\pi$
$450$	32.1569	1.51589
$451$	−2.18275	−0.102782
$452$	−15.0538	−0.708070
$453$	13.5151	0.634995
$454$	−47.8183	−2.24423
$455$	−26.4589	−1.24041
$456$	5.87762	0.275245
$457$	−40.6977	−1.90376	−0.951878	−	0.306476i	$-0.900850\pi$
$457$	−40.6977	−1.90376	−0.951878	+	0.306476i	$0.900850\pi$
$458$	31.5148	1.47259
$459$	−15.8513	−0.739875
$460$	−79.9063	−3.72565
$461$	−21.5125	−1.00194	−0.500968	−	0.865466i	$-0.667023\pi$
$461$	−21.5125	−1.00194	−0.500968	+	0.865466i	$0.667023\pi$
$462$	10.5053	0.488750
$463$	0.217725	0.0101185	0.00505927	−	0.999987i	$-0.498390\pi$
$463$	0.217725	0.0101185	0.00505927	+	0.999987i	$0.498390\pi$
$464$	−5.51149	−0.255864
$465$	8.14355	0.377648
$466$	12.4679	0.577565
$467$	−17.7636	−0.822002	−0.411001	−	0.911635i	$-0.634821\pi$
$467$	−17.7636	−0.822002	−0.411001	+	0.911635i	$0.634821\pi$
$468$	38.8651	1.79654
$469$	10.2274	0.472257
$470$	−103.720	−4.78423
$471$	−14.0875	−0.649119
$472$	79.7621	3.67135
$473$	−26.4814	−1.21762
$474$	−29.1567	−1.33921
$475$	6.92600	0.317787
$476$	−29.2621	−1.34123
$477$	−9.27545	−0.424694
$478$	53.4074	2.44280
$479$	26.5875	1.21481	0.607406	−	0.794392i	$-0.292210\pi$
$479$	26.5875	1.21481	0.607406	+	0.794392i	$0.292210\pi$
$480$	7.29392	0.332920
$481$	−48.4533	−2.20928
$482$	6.31490	0.287636
$483$	9.88723	0.449884
$484$	−21.2891	−0.967688
$485$	2.70961	0.123037
$486$	40.1755	1.82240
$487$	8.51282	0.385753	0.192876	−	0.981223i	$-0.438218\pi$
$487$	8.51282	0.385753	0.192876	+	0.981223i	$0.438218\pi$
$488$	59.2362	2.68149
$489$	−5.41923	−0.245066
$490$	25.1583	1.13654
$491$	−34.0259	−1.53557	−0.767783	−	0.640710i	$-0.778640\pi$
$491$	−34.0259	−1.53557	−0.767783	+	0.640710i	$0.778640\pi$
$492$	3.28523	0.148110
$493$	3.48151	0.156799
$494$	12.3173	0.554183
$495$	−18.0001	−0.809046
$496$	−15.7922	−0.709092
$497$	3.67346	0.164777
$498$	−31.0231	−1.39018
$499$	−36.9118	−1.65240	−0.826199	−	0.563379i	$-0.809501\pi$
$499$	−36.9118	−1.65240	−0.826199	+	0.563379i	$0.809501\pi$
$500$	10.1134	0.452285
$501$	9.23575	0.412623
$502$	10.1970	0.455116
$503$	41.0858	1.83193	0.915963	−	0.401263i	$-0.131429\pi$
$503$	41.0858	1.83193	0.915963	+	0.401263i	$0.131429\pi$
$504$	24.9400	1.11092
$505$	−34.0368	−1.51462
$506$	35.1408	1.56220
$507$	−3.14416	−0.139637
$508$	5.84497	0.259328
$509$	21.0276	0.932033	0.466016	−	0.884776i	$-0.345689\pi$
$509$	21.0276	0.932033	0.466016	+	0.884776i	$0.345689\pi$
$510$	−24.7214	−1.09468
$511$	18.3423	0.811414
$512$	47.6042	2.10383
$513$	5.50537	0.243068
$514$	−0.651218	−0.0287240
$515$	−49.4006	−2.17685
$516$	39.8568	1.75460
$517$	30.9986	1.36332
$518$	−58.8279	−2.58475
$519$	−14.1937	−0.623034
$520$	74.8079	3.28054
$521$	0.563519	0.0246882	0.0123441	−	0.999924i	$-0.496071\pi$
$521$	0.563519	0.0246882	0.0123441	+	0.999924i	$0.496071\pi$
$522$	−5.61410	−0.245723
$523$	43.5957	1.90631	0.953154	−	0.302486i	$-0.0978167\pi$
$523$	43.5957	1.90631	0.953154	+	0.302486i	$0.0978167\pi$
$524$	7.87089	0.343841
$525$	−9.84757	−0.429783
$526$	13.6823	0.596577
$527$	9.97567	0.434547
$528$	−11.6965	−0.509025
$529$	10.0733	0.437970
$530$	−33.7789	−1.46726
$531$	31.9949	1.38846
$532$	10.1631	0.440628
$533$	3.63881	0.157614
$534$	11.6272	0.503156
$535$	47.6581	2.06044
$536$	−28.9162	−1.24899
$537$	−11.0477	−0.476743
$538$	18.5682	0.800530
$539$	−7.51907	−0.323869
$540$	63.2615	2.72234
$541$	6.76449	0.290828	0.145414	−	0.989371i	$-0.453549\pi$
$541$	6.76449	0.290828	0.145414	+	0.989371i	$0.453549\pi$
$542$	−66.9529	−2.87587
$543$	7.90788	0.339360
$544$	8.93490	0.383080
$545$	−16.8667	−0.722490
$546$	−17.5131	−0.749492
$547$	6.76551	0.289272	0.144636	−	0.989485i	$-0.453799\pi$
$547$	6.76551	0.289272	0.144636	+	0.989485i	$0.453799\pi$
$548$	−49.1919	−2.10138
$549$	23.7613	1.01411
$550$	−34.9998	−1.49240
$551$	−1.20918	−0.0515126
$552$	−27.9544	−1.18982
$553$	−26.6467	−1.13313
$554$	43.5421	1.84993
$555$	−33.7755	−1.43369
$556$	−4.24214	−0.179907
$557$	32.5722	1.38013	0.690065	−	0.723748i	$-0.257582\pi$
$557$	32.5722	1.38013	0.690065	+	0.723748i	$0.257582\pi$
$558$	−16.0863	−0.680986
$559$	44.1465	1.86720
$560$	35.7667	1.51142
$561$	7.38847	0.311941
$562$	−54.2094	−2.28669
$563$	−8.66575	−0.365218	−0.182609	−	0.983186i	$-0.558454\pi$
$563$	−8.66575	−0.365218	−0.182609	+	0.983186i	$0.558454\pi$
$564$	−46.6556	−1.96456
$565$	−11.6230	−0.488982
$566$	54.1568	2.27638
$567$	5.52869	0.232183
$568$	−10.3861	−0.435790
$569$	23.6259	0.990448	0.495224	−	0.868765i	$-0.335086\pi$
$569$	23.6259	0.990448	0.495224	+	0.868765i	$0.335086\pi$
$570$	8.58608	0.359631
$571$	18.1019	0.757540	0.378770	−	0.925491i	$-0.376347\pi$
$571$	18.1019	0.757540	0.378770	+	0.925491i	$0.376347\pi$
$572$	−42.3011	−1.76870
$573$	−7.38471	−0.308501
$574$	4.41794	0.184401
$575$	−32.9406	−1.37372
$576$	10.3612	0.431718
$577$	−24.3133	−1.01217	−0.506087	−	0.862482i	$-0.668909\pi$
$577$	−24.3133	−1.01217	−0.506087	+	0.862482i	$0.668909\pi$
$578$	12.1901	0.507042
$579$	17.6791	0.734720
$580$	−13.8945	−0.576937
$581$	−28.3524	−1.17626
$582$	1.79349	0.0743424
$583$	10.0955	0.418112
$584$	−51.8596	−2.14597
$585$	30.0076	1.24066
$586$	0.413957	0.0171004
$587$	23.5793	0.973222	0.486611	−	0.873619i	$-0.338233\pi$
$587$	23.5793	0.973222	0.486611	+	0.873619i	$0.338233\pi$
$588$	11.3169	0.466699
$589$	−3.46469	−0.142760
$590$	116.517	4.79694
$591$	4.77422	0.196385
$592$	65.4986	2.69197
$593$	36.4052	1.49498	0.747491	−	0.664272i	$-0.231258\pi$
$593$	36.4052	1.49498	0.747491	+	0.664272i	$0.231258\pi$
$594$	−27.8208	−1.14150
$595$	−22.5932	−0.926231
$596$	−21.6280	−0.885917
$597$	−8.76143	−0.358582
$598$	−58.5823	−2.39561
$599$	−13.3215	−0.544302	−0.272151	−	0.962255i	$-0.587735\pi$
$599$	−13.3215	−0.544302	−0.272151	+	0.962255i	$0.587735\pi$
$600$	27.8423	1.13666
$601$	19.0971	0.778989	0.389494	−	0.921029i	$-0.372650\pi$
$601$	19.0971	0.778989	0.389494	+	0.921029i	$0.372650\pi$
$602$	53.5989	2.18453
$603$	−11.5991	−0.472353
$604$	−66.0728	−2.68846
$605$	−16.4373	−0.668270
$606$	−22.5289	−0.915175
$607$	−19.1580	−0.777600	−0.388800	−	0.921322i	$-0.627110\pi$
$607$	−19.1580	−0.777600	−0.388800	+	0.921322i	$0.627110\pi$
$608$	−3.10321	−0.125852
$609$	1.71924	0.0696670
$610$	86.5328	3.50361
$611$	−51.6770	−2.09063
$612$	33.1868	1.34150
$613$	−48.1804	−1.94599	−0.972994	−	0.230830i	$-0.925856\pi$
$613$	−48.1804	−1.94599	−0.972994	+	0.230830i	$0.925856\pi$
$614$	39.9783	1.61339
$615$	2.53652	0.102282
$616$	−27.1450	−1.09370
$617$	12.0381	0.484636	0.242318	−	0.970197i	$-0.422092\pi$
$617$	12.0381	0.484636	0.242318	+	0.970197i	$0.422092\pi$
$618$	−32.6982	−1.31532
$619$	−11.6613	−0.468707	−0.234353	−	0.972151i	$-0.575297\pi$
$619$	−11.6613	−0.468707	−0.234353	+	0.972151i	$0.575297\pi$
$620$	−39.8123	−1.59890
$621$	−26.1840	−1.05073
$622$	25.6697	1.02926
$623$	10.6262	0.425730
$624$	19.4990	0.780583
$625$	−20.8308	−0.833233
$626$	60.1397	2.40367
$627$	−2.56612	−0.102481
$628$	68.8713	2.74826
$629$	−41.3743	−1.64970
$630$	36.4327	1.45151
$631$	−36.0833	−1.43645	−0.718226	−	0.695810i	$-0.755046\pi$
$631$	−36.0833	−1.43645	−0.718226	+	0.695810i	$0.755046\pi$
$632$	75.3390	2.99683
$633$	−3.52204	−0.139988
$634$	−20.0566	−0.796548
$635$	4.51288	0.179088
$636$	−15.1946	−0.602505
$637$	12.5349	0.496649
$638$	6.11044	0.241915
$639$	−4.16615	−0.164810
$640$	54.5447	2.15607
$641$	30.9032	1.22060	0.610301	−	0.792170i	$-0.291049\pi$
$641$	30.9032	1.22060	0.610301	+	0.792170i	$0.291049\pi$
$642$	31.5449	1.24498
$643$	15.7099	0.619539	0.309770	−	0.950812i	$-0.399748\pi$
$643$	15.7099	0.619539	0.309770	+	0.950812i	$0.399748\pi$
$644$	−48.3368	−1.90474
$645$	30.7733	1.21170
$646$	10.5178	0.413816
$647$	−40.5776	−1.59527	−0.797635	−	0.603140i	$-0.793916\pi$
$647$	−40.5776	−1.59527	−0.797635	+	0.603140i	$0.793916\pi$
$648$	−15.6314	−0.614060
$649$	−34.8235	−1.36694
$650$	58.3473	2.28857
$651$	4.92618	0.193072
$652$	26.4936	1.03757
$653$	−7.13315	−0.279142	−0.139571	−	0.990212i	$-0.544572\pi$
$653$	−7.13315	−0.279142	−0.139571	+	0.990212i	$0.544572\pi$
$654$	−11.1641	−0.436549
$655$	6.07708	0.237451
$656$	−4.91889	−0.192051
$657$	−20.8024	−0.811578
$658$	−62.7419	−2.44593
$659$	−28.8769	−1.12488	−0.562442	−	0.826836i	$-0.690138\pi$
$659$	−28.8769	−1.12488	−0.562442	+	0.826836i	$0.690138\pi$
$660$	−29.4869	−1.14778
$661$	16.5357	0.643164	0.321582	−	0.946882i	$-0.395785\pi$
$661$	16.5357	0.643164	0.321582	+	0.946882i	$0.395785\pi$
$662$	−2.05344	−0.0798091
$663$	−12.3171	−0.478358
$664$	80.1615	3.11087
$665$	7.84693	0.304291
$666$	66.7181	2.58527
$667$	5.75094	0.222677
$668$	−45.1519	−1.74698
$669$	−3.64288	−0.140842
$670$	−42.2411	−1.63192
$671$	−25.8620	−0.998392
$672$	4.41223	0.170205
$673$	33.8059	1.30312	0.651562	−	0.758596i	$-0.274114\pi$
$673$	33.8059	1.30312	0.651562	+	0.758596i	$0.274114\pi$
$674$	−20.6815	−0.796621
$675$	26.0790	1.00378
$676$	15.3712	0.591201
$677$	−31.5729	−1.21344	−0.606722	−	0.794914i	$-0.707516\pi$
$677$	−31.5729	−1.21344	−0.606722	+	0.794914i	$0.707516\pi$
$678$	−7.69323	−0.295457
$679$	1.63909	0.0629026
$680$	63.8784	2.44962
$681$	−16.6077	−0.636409
$682$	17.5084	0.670433
$683$	11.6271	0.444897	0.222449	−	0.974944i	$-0.428595\pi$
$683$	11.6271	0.444897	0.222449	+	0.974944i	$0.428595\pi$
$684$	−11.5262	−0.440717
$685$	−37.9809	−1.45118
$686$	49.8700	1.90404
$687$	10.9454	0.417591
$688$	−59.6766	−2.27515
$689$	−16.8299	−0.641169
$690$	−40.8361	−1.55460
$691$	−12.5778	−0.478483	−0.239242	−	0.970960i	$-0.576899\pi$
$691$	−12.5778	−0.478483	−0.239242	+	0.970960i	$0.576899\pi$
$692$	69.3903	2.63782
$693$	−10.8886	−0.413624
$694$	−34.0552	−1.29272
$695$	−3.27534	−0.124241
$696$	−4.86085	−0.184250
$697$	3.10718	0.117693
$698$	−62.2094	−2.35466
$699$	4.33021	0.163784
$700$	48.1429	1.81963
$701$	−42.5898	−1.60859	−0.804297	−	0.594228i	$-0.797458\pi$
$701$	−42.5898	−1.60859	−0.804297	+	0.594228i	$0.797458\pi$
$702$	46.3794	1.75048
$703$	14.3699	0.541969
$704$	−11.2773	−0.425028
$705$	−36.0227	−1.35669
$706$	20.6871	0.778568
$707$	−20.5895	−0.774347
$708$	52.4124	1.96978
$709$	36.3068	1.36353	0.681765	−	0.731572i	$-0.261213\pi$
$709$	36.3068	1.36353	0.681765	+	0.731572i	$0.261213\pi$
$710$	−15.1721	−0.569398
$711$	30.2206	1.13336
$712$	−30.0438	−1.12594
$713$	16.4784	0.617119
$714$	−14.9544	−0.559655
$715$	−32.6605	−1.22143
$716$	54.0101	2.01845
$717$	18.5488	0.692719
$718$	−74.4015	−2.77664
$719$	20.0066	0.746119	0.373059	−	0.927807i	$-0.378309\pi$
$719$	20.0066	0.746119	0.373059	+	0.927807i	$0.378309\pi$
$720$	−40.5638	−1.51172
$721$	−29.8834	−1.11291
$722$	43.8172	1.63071
$723$	2.19322	0.0815666
$724$	−38.6601	−1.43679
$725$	−5.72787	−0.212728
$726$	−10.8798	−0.403788
$727$	1.88578	0.0699399	0.0349699	−	0.999388i	$-0.488866\pi$
$727$	1.88578	0.0699399	0.0349699	+	0.999388i	$0.488866\pi$
$728$	45.2527	1.67718
$729$	5.58204	0.206742
$730$	−75.7570	−2.80389
$731$	37.6966	1.39426
$732$	38.9246	1.43869
$733$	15.3525	0.567058	0.283529	−	0.958964i	$-0.408495\pi$
$733$	15.3525	0.567058	0.283529	+	0.958964i	$0.408495\pi$
$734$	−71.4546	−2.63744
$735$	8.73770	0.322295
$736$	14.7591	0.544029
$737$	12.6246	0.465032
$738$	−5.01048	−0.184438
$739$	−29.2378	−1.07553	−0.537764	−	0.843095i	$-0.680731\pi$
$739$	−29.2378	−1.07553	−0.537764	+	0.843095i	$0.680731\pi$
$740$	165.122	6.07001
$741$	4.27791	0.157153
$742$	−20.4335	−0.750137
$743$	24.7869	0.909344	0.454672	−	0.890659i	$-0.349756\pi$
$743$	24.7869	0.909344	0.454672	+	0.890659i	$0.349756\pi$
$744$	−13.9279	−0.510623
$745$	−16.6989	−0.611800
$746$	75.7111	2.77198
$747$	32.1551	1.17649
$748$	−36.1208	−1.32071
$749$	28.8293	1.05340
$750$	5.16846	0.188726
$751$	37.8178	1.37999	0.689995	−	0.723814i	$-0.257613\pi$
$751$	37.8178	1.37999	0.689995	+	0.723814i	$0.257613\pi$
$752$	69.8563	2.54740
$753$	3.54152	0.129060
$754$	−10.1866	−0.370973
$755$	−51.0145	−1.85661
$756$	38.2681	1.39180
$757$	46.9918	1.70795	0.853974	−	0.520316i	$-0.174186\pi$
$757$	46.9918	1.70795	0.853974	+	0.520316i	$0.174186\pi$
$758$	92.3782	3.35533
$759$	12.2047	0.443002
$760$	−22.1858	−0.804765
$761$	40.4662	1.46690	0.733450	−	0.679744i	$-0.237909\pi$
$761$	40.4662	1.46690	0.733450	+	0.679744i	$0.237909\pi$
$762$	2.98707	0.108210
$763$	−10.2030	−0.369373
$764$	36.1025	1.30614
$765$	25.6234	0.926417
$766$	14.8872	0.537897
$767$	58.0534	2.09619
$768$	28.1009	1.01400
$769$	5.29017	0.190768	0.0953842	−	0.995441i	$-0.469592\pi$
$769$	5.29017	0.190768	0.0953842	+	0.995441i	$0.469592\pi$
$770$	−39.6536	−1.42902
$771$	−0.226173	−0.00814544
$772$	−86.4300	−3.11068
$773$	−26.9037	−0.967659	−0.483829	−	0.875162i	$-0.660754\pi$
$773$	−26.9037	−0.967659	−0.483829	+	0.875162i	$0.660754\pi$
$774$	−60.7877	−2.18497
$775$	−16.4123	−0.589546
$776$	−4.63425	−0.166360
$777$	−20.4314	−0.732973
$778$	9.58802	0.343747
$779$	−1.07917	−0.0386651
$780$	49.1569	1.76010
$781$	4.53448	0.162256
$782$	−50.0233	−1.78883
$783$	−4.55300	−0.162711
$784$	−16.9444	−0.605158
$785$	53.1753	1.89791
$786$	4.02242	0.143475
$787$	7.21154	0.257064	0.128532	−	0.991705i	$-0.458974\pi$
$787$	7.21154	0.257064	0.128532	+	0.991705i	$0.458974\pi$
$788$	−23.3403	−0.831462
$789$	4.75198	0.169175
$790$	110.056	3.91562
$791$	−7.03095	−0.249992
$792$	30.7857	1.09392
$793$	43.1139	1.53102
$794$	73.2280	2.59876
$795$	−11.7317	−0.416080
$796$	42.8330	1.51818
$797$	−43.9281	−1.55601	−0.778006	−	0.628257i	$-0.783769\pi$
$797$	−43.9281	−1.55601	−0.778006	+	0.628257i	$0.783769\pi$
$798$	5.19388	0.183861
$799$	−44.1270	−1.56110
$800$	−14.6999	−0.519722
$801$	−12.0514	−0.425816
$802$	24.5619	0.867309
$803$	22.6415	0.799000
$804$	−19.0011	−0.670117
$805$	−37.3207	−1.31538
$806$	−29.1879	−1.02810
$807$	6.44887	0.227011
$808$	58.2132	2.04793
$809$	−36.5123	−1.28370	−0.641852	−	0.766829i	$-0.721833\pi$
$809$	−36.5123	−1.28370	−0.641852	+	0.766829i	$0.721833\pi$
$810$	−22.8345	−0.802324
$811$	9.63388	0.338291	0.169146	−	0.985591i	$-0.445899\pi$
$811$	9.63388	0.338291	0.169146	+	0.985591i	$0.445899\pi$
$812$	−8.40502	−0.294959
$813$	−23.2533	−0.815529
$814$	−72.6165	−2.54521
$815$	20.4556	0.716529
$816$	16.6501	0.582871
$817$	−13.0926	−0.458051
$818$	85.6065	2.99316
$819$	18.1521	0.634287
$820$	−12.4005	−0.433046
$821$	−34.5488	−1.20576	−0.602880	−	0.797832i	$-0.705980\pi$
$821$	−34.5488	−1.20576	−0.602880	+	0.797832i	$0.705980\pi$
$822$	−25.1395	−0.876842
$823$	30.1353	1.05045	0.525225	−	0.850963i	$-0.323981\pi$
$823$	30.1353	1.05045	0.525225	+	0.850963i	$0.323981\pi$
$824$	84.4900	2.94335
$825$	−12.1557	−0.423208
$826$	70.4835	2.45243
$827$	3.11633	0.108365	0.0541826	−	0.998531i	$-0.482745\pi$
$827$	3.11633	0.108365	0.0541826	+	0.998531i	$0.482745\pi$
$828$	54.8198	1.90512
$829$	−5.67323	−0.197039	−0.0985197	−	0.995135i	$-0.531411\pi$
$829$	−5.67323	−0.197039	−0.0985197	+	0.995135i	$0.531411\pi$
$830$	117.101	4.06462
$831$	15.1225	0.524594
$832$	18.8001	0.651775
$833$	10.7035	0.370854
$834$	−2.16795	−0.0750699
$835$	−34.8616	−1.20644
$836$	12.5453	0.433887
$837$	−13.0459	−0.450931
$838$	20.5365	0.709421
$839$	−41.1062	−1.41914	−0.709572	−	0.704633i	$-0.751112\pi$
$839$	−41.1062	−1.41914	−0.709572	+	0.704633i	$0.751112\pi$
$840$	31.5444	1.08839
$841$	1.00000	0.0344828
$842$	17.2279	0.593713
$843$	−18.8274	−0.648450
$844$	17.2186	0.592688
$845$	11.8681	0.408274
$846$	71.1569	2.44643
$847$	−9.94321	−0.341653
$848$	22.7505	0.781254
$849$	18.8091	0.645527
$850$	49.8227	1.70890
$851$	−68.3442	−2.34281
$852$	−6.82478	−0.233813
$853$	−36.7805	−1.25934	−0.629670	−	0.776862i	$-0.716810\pi$
$853$	−36.7805	−1.25934	−0.629670	+	0.776862i	$0.716810\pi$
$854$	52.3453	1.79122
$855$	−8.89938	−0.304352
$856$	−81.5098	−2.78595
$857$	49.4753	1.69004	0.845022	−	0.534732i	$-0.179587\pi$
$857$	49.4753	1.69004	0.845022	+	0.534732i	$0.179587\pi$
$858$	−21.6180	−0.738025
$859$	15.4134	0.525897	0.262948	−	0.964810i	$-0.415305\pi$
$859$	15.4134	0.525897	0.262948	+	0.964810i	$0.415305\pi$
$860$	−150.445	−5.13013
$861$	1.53439	0.0522917
$862$	−94.0204	−3.20235
$863$	45.7487	1.55730	0.778652	−	0.627456i	$-0.215904\pi$
$863$	45.7487	1.55730	0.778652	+	0.627456i	$0.215904\pi$
$864$	−11.6848	−0.397524
$865$	53.5760	1.82164
$866$	−83.6084	−2.84113
$867$	4.23373	0.143785
$868$	−24.0832	−0.817437
$869$	−32.8924	−1.11580
$870$	−7.10077	−0.240739
$871$	−21.0461	−0.713121
$872$	28.8472	0.976888
$873$	−1.85893	−0.0629152
$874$	17.3738	0.587678
$875$	4.72352	0.159684
$876$	−34.0774	−1.15137
$877$	−43.9341	−1.48355	−0.741775	−	0.670649i	$-0.766016\pi$
$877$	−43.9341	−1.48355	−0.741775	+	0.670649i	$0.766016\pi$
$878$	39.3006	1.32633
$879$	0.143771	0.00484927
$880$	44.1500	1.48830
$881$	1.90035	0.0640244	0.0320122	−	0.999487i	$-0.489808\pi$
$881$	1.90035	0.0640244	0.0320122	+	0.999487i	$0.489808\pi$
$882$	−17.2599	−0.581172
$883$	28.3227	0.953134	0.476567	−	0.879138i	$-0.341881\pi$
$883$	28.3227	0.953134	0.476567	+	0.879138i	$0.341881\pi$
$884$	60.2162	2.02529
$885$	40.4674	1.36030
$886$	−21.4152	−0.719459
$887$	15.4350	0.518256	0.259128	−	0.965843i	$-0.416565\pi$
$887$	15.4350	0.518256	0.259128	+	0.965843i	$0.416565\pi$
$888$	57.7664	1.93851
$889$	2.72992	0.0915587
$890$	−43.8883	−1.47114
$891$	6.82455	0.228631
$892$	17.8094	0.596301
$893$	15.3259	0.512862
$894$	−11.0530	−0.369667
$895$	41.7010	1.39391
$896$	32.9951	1.10229
$897$	−20.3461	−0.679337
$898$	−68.1158	−2.27305
$899$	2.86533	0.0955642
$900$	−54.5999	−1.82000
$901$	−14.3711	−0.478769
$902$	5.45345	0.181580
$903$	18.6153	0.619480
$904$	19.8788	0.661159
$905$	−29.8494	−0.992226
$906$	−33.7665	−1.12182
$907$	−17.7545	−0.589529	−0.294764	−	0.955570i	$-0.595241\pi$
$907$	−17.7545	−0.589529	−0.294764	+	0.955570i	$0.595241\pi$
$908$	81.1919	2.69445
$909$	23.3510	0.774503
$910$	66.1056	2.19138
$911$	−2.28856	−0.0758234	−0.0379117	−	0.999281i	$-0.512071\pi$
$911$	−2.28856	−0.0758234	−0.0379117	+	0.999281i	$0.512071\pi$
$912$	−5.78282	−0.191488
$913$	−34.9978	−1.15826
$914$	101.680	3.36328
$915$	30.0535	0.993540
$916$	−53.5098	−1.76801
$917$	3.67614	0.121397
$918$	39.6033	1.30710
$919$	−45.8149	−1.51129	−0.755647	−	0.654979i	$-0.772678\pi$
$919$	−45.8149	−1.51129	−0.755647	+	0.654979i	$0.772678\pi$
$920$	105.518	3.47882
$921$	13.8848	0.457520
$922$	53.7474	1.77008
$923$	−7.55931	−0.248818
$924$	−17.8372	−0.586800
$925$	68.0701	2.23813
$926$	−0.543971	−0.0178760
$927$	33.8914	1.11314
$928$	2.56639	0.0842458
$929$	−4.74983	−0.155837	−0.0779184	−	0.996960i	$-0.524827\pi$
$929$	−4.74983	−0.155837	−0.0779184	+	0.996960i	$0.524827\pi$
$930$	−20.3461	−0.667174
$931$	−3.71747	−0.121835
$932$	−21.1696	−0.693433
$933$	8.91530	0.291874
$934$	44.3811	1.45219
$935$	−27.8888	−0.912060
$936$	−51.3221	−1.67751
$937$	−47.8492	−1.56317	−0.781583	−	0.623801i	$-0.785588\pi$
$937$	−47.8492	−1.56317	−0.781583	+	0.623801i	$0.785588\pi$
$938$	−25.5524	−0.834316
$939$	20.8870	0.681622
$940$	176.108	5.74401
$941$	−51.9422	−1.69327	−0.846633	−	0.532177i	$-0.821374\pi$
$941$	−51.9422	−1.69327	−0.846633	+	0.532177i	$0.821374\pi$
$942$	35.1967	1.14677
$943$	5.13260	0.167140
$944$	−78.4757	−2.55417
$945$	29.5466	0.961152
$946$	66.1618	2.15111
$947$	−16.2068	−0.526649	−0.263324	−	0.964707i	$-0.584819\pi$
$947$	−16.2068	−0.526649	−0.263324	+	0.964707i	$0.584819\pi$
$948$	49.5059	1.60788
$949$	−37.7451	−1.22526
$950$	−17.3041	−0.561420
$951$	−6.96581	−0.225882
$952$	38.6412	1.25237
$953$	−4.96897	−0.160961	−0.0804804	−	0.996756i	$-0.525645\pi$
$953$	−4.96897	−0.160961	−0.0804804	+	0.996756i	$0.525645\pi$
$954$	23.1741	0.750288
$955$	27.8746	0.902001
$956$	−90.6817	−2.93286
$957$	2.12221	0.0686012
$958$	−66.4269	−2.14615
$959$	−22.9754	−0.741913
$960$	13.1050	0.422962
$961$	−22.7899	−0.735157
$962$	121.057	3.90304
$963$	−32.6959	−1.05361
$964$	−10.7222	−0.345339
$965$	−66.7323	−2.14819
$966$	−24.7025	−0.794791
$967$	−25.3463	−0.815082	−0.407541	−	0.913187i	$-0.633614\pi$
$967$	−25.3463	−0.815082	−0.407541	+	0.913187i	$0.633614\pi$
$968$	28.1127	0.903577
$969$	3.65290	0.117348
$970$	−6.76976	−0.217364
$971$	48.9887	1.57212	0.786061	−	0.618149i	$-0.212117\pi$
$971$	48.9887	1.57212	0.786061	+	0.618149i	$0.212117\pi$
$972$	−68.2149	−2.18800
$973$	−1.98132	−0.0635181
$974$	−21.2687	−0.681492
$975$	20.2645	0.648984
$976$	−58.2808	−1.86552
$977$	45.2695	1.44830	0.724150	−	0.689642i	$-0.242232\pi$
$977$	45.2695	1.44830	0.724150	+	0.689642i	$0.242232\pi$
$978$	13.5396	0.432947
$979$	13.1169	0.419217
$980$	−42.7170	−1.36454
$981$	11.5714	0.369447
$982$	85.0112	2.71282
$983$	−19.1879	−0.611999	−0.305999	−	0.952032i	$-0.598991\pi$
$983$	−19.1879	−0.611999	−0.305999	+	0.952032i	$0.598991\pi$
$984$	−4.33821	−0.138297
$985$	−18.0209	−0.574195
$986$	−8.69829	−0.277010
$987$	−21.7908	−0.693608
$988$	−20.9139	−0.665360
$989$	62.2693	1.98005
$990$	44.9720	1.42931
$991$	44.4239	1.41117	0.705586	−	0.708625i	$-0.250684\pi$
$991$	44.4239	1.41117	0.705586	+	0.708625i	$0.250684\pi$
$992$	7.35356	0.233476
$993$	−0.713176	−0.0226319
$994$	−9.17788	−0.291105
$995$	33.0712	1.04843
$996$	52.6748	1.66907
$997$	−14.5930	−0.462166	−0.231083	−	0.972934i	$-0.574227\pi$
$997$	−14.5930	−0.462166	−0.231083	+	0.972934i	$0.574227\pi$
$998$	92.2214	2.91922
$999$	54.1079	1.71190

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.c.1.4	✓	61

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.c.1.4	✓	61	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:	\( N \)	\(=\)	\( 4031 = 29 \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.49843 q^{2} -0.867725 q^{3} +4.24214 q^{4} +3.27534 q^{5} +2.16795 q^{6} +1.98132 q^{7} -5.60183 q^{8} -2.24705 q^{9} +O(q^{10})\)	\(q-2.49843 q^{2} -0.867725 q^{3} +4.24214 q^{4} +3.27534 q^{5} +2.16795 q^{6} +1.98132 q^{7} -5.60183 q^{8} -2.24705 q^{9} -8.18321 q^{10} +2.44571 q^{11} -3.68101 q^{12} -4.07719 q^{13} -4.95018 q^{14} -2.84210 q^{15} +5.51149 q^{16} -3.48151 q^{17} +5.61410 q^{18} +1.20918 q^{19} +13.8945 q^{20} -1.71924 q^{21} -6.11044 q^{22} -5.75094 q^{23} +4.86085 q^{24} +5.72787 q^{25} +10.1866 q^{26} +4.55300 q^{27} +8.40502 q^{28} -1.00000 q^{29} +7.10077 q^{30} -2.86533 q^{31} -2.56639 q^{32} -2.12221 q^{33} +8.69829 q^{34} +6.48949 q^{35} -9.53232 q^{36} +11.8840 q^{37} -3.02104 q^{38} +3.53788 q^{39} -18.3479 q^{40} -0.892481 q^{41} +4.29539 q^{42} -10.8277 q^{43} +10.3751 q^{44} -7.35987 q^{45} +14.3683 q^{46} +12.6747 q^{47} -4.78245 q^{48} -3.07439 q^{49} -14.3107 q^{50} +3.02099 q^{51} -17.2960 q^{52} +4.12783 q^{53} -11.3753 q^{54} +8.01055 q^{55} -11.0990 q^{56} -1.04923 q^{57} +2.49843 q^{58} -14.2386 q^{59} -12.0566 q^{60} -10.5744 q^{61} +7.15883 q^{62} -4.45212 q^{63} -4.61103 q^{64} -13.3542 q^{65} +5.30218 q^{66} +5.16192 q^{67} -14.7690 q^{68} +4.99023 q^{69} -16.2135 q^{70} +1.85405 q^{71} +12.5876 q^{72} +9.25762 q^{73} -29.6913 q^{74} -4.97022 q^{75} +5.12949 q^{76} +4.84573 q^{77} -8.83913 q^{78} -13.4490 q^{79} +18.0520 q^{80} +2.79041 q^{81} +2.22980 q^{82} -14.3099 q^{83} -7.29325 q^{84} -11.4031 q^{85} +27.0522 q^{86} +0.867725 q^{87} -13.7005 q^{88} +5.36321 q^{89} +18.3881 q^{90} -8.07820 q^{91} -24.3963 q^{92} +2.48632 q^{93} -31.6668 q^{94} +3.96046 q^{95} +2.22692 q^{96} +0.827274 q^{97} +7.68113 q^{98} -5.49565 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9} - 16 q^{10} - 3 q^{11} - 18 q^{12} - 28 q^{13} - 14 q^{14} - 12 q^{15} + 11 q^{16} - 21 q^{17} - 17 q^{18} - 36 q^{19} - 16 q^{20} - 12 q^{21} - 42 q^{22} - 15 q^{23} - 28 q^{24} - 16 q^{25} - 13 q^{26} - 10 q^{27} - 25 q^{28} - 61 q^{29} - 12 q^{30} - 18 q^{31} - 3 q^{32} - 42 q^{33} - 22 q^{34} - 29 q^{35} - 38 q^{36} - 30 q^{37} - 27 q^{38} - 31 q^{39} - 22 q^{40} - 28 q^{41} - 9 q^{42} - 58 q^{43} - 2 q^{44} - 31 q^{45} - 40 q^{46} - 6 q^{47} - 37 q^{48} - 37 q^{49} - 15 q^{50} - 44 q^{51} - 43 q^{52} - 27 q^{53} - 18 q^{54} - 38 q^{55} - 22 q^{56} - 50 q^{57} + q^{58} - 24 q^{59} + 6 q^{60} - 76 q^{61} - 17 q^{62} - 6 q^{63} - 60 q^{64} - 65 q^{65} - 7 q^{66} - 45 q^{67} - 31 q^{68} - 16 q^{69} - 48 q^{70} - 28 q^{71} - 40 q^{72} - 50 q^{73} - 17 q^{74} - 35 q^{75} - 100 q^{76} + q^{77} - 6 q^{78} - 66 q^{79} - 10 q^{80} - 63 q^{81} - 5 q^{82} - 9 q^{83} - 24 q^{84} - 77 q^{85} + 29 q^{86} + 4 q^{87} - 62 q^{88} - 30 q^{89} + 50 q^{90} - 52 q^{91} - 53 q^{92} - 42 q^{93} - 92 q^{94} - 20 q^{95} - 47 q^{96} - 34 q^{97} + 36 q^{98} - 29 q^{99}+O(q^{100}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9 - 16 * q^10 - 3 * q^11 - 18 * q^12 - 28 * q^13 - 14 * q^14 - 12 * q^15 + 11 * q^16 - 21 * q^17 - 17 * q^18 - 36 * q^19 - 16 * q^20 - 12 * q^21 - 42 * q^22 - 15 * q^23 - 28 * q^24 - 16 * q^25 - 13 * q^26 - 10 * q^27 - 25 * q^28 - 61 * q^29 - 12 * q^30 - 18 * q^31 - 3 * q^32 - 42 * q^33 - 22 * q^34 - 29 * q^35 - 38 * q^36 - 30 * q^37 - 27 * q^38 - 31 * q^39 - 22 * q^40 - 28 * q^41 - 9 * q^42 - 58 * q^43 - 2 * q^44 - 31 * q^45 - 40 * q^46 - 6 * q^47 - 37 * q^48 - 37 * q^49 - 15 * q^50 - 44 * q^51 - 43 * q^52 - 27 * q^53 - 18 * q^54 - 38 * q^55 - 22 * q^56 - 50 * q^57 + q^58 - 24 * q^59 + 6 * q^60 - 76 * q^61 - 17 * q^62 - 6 * q^63 - 60 * q^64 - 65 * q^65 - 7 * q^66 - 45 * q^67 - 31 * q^68 - 16 * q^69 - 48 * q^70 - 28 * q^71 - 40 * q^72 - 50 * q^73 - 17 * q^74 - 35 * q^75 - 100 * q^76 + q^77 - 6 * q^78 - 66 * q^79 - 10 * q^80 - 63 * q^81 - 5 * q^82 - 9 * q^83 - 24 * q^84 - 77 * q^85 + 29 * q^86 + 4 * q^87 - 62 * q^88 - 30 * q^89 + 50 * q^90 - 52 * q^91 - 53 * q^92 - 42 * q^93 - 92 * q^94 - 20 * q^95 - 47 * q^96 - 34 * q^97 + 36 * q^98 - 29 * q^99

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