LMFDB - Embedded newform 6031.2.a.c.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6031,2,Mod(1,6031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, 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("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.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:	$48.1577774590$
Analytic rank:	$1$
Dimension:	$110$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.48517 q^{2} +3.11043 q^{3} +4.17608 q^{4} +3.13519 q^{5} -7.72995 q^{6} -2.09644 q^{7} -5.40793 q^{8} +6.67478 q^{9} +O(q^{10})$	\(q-2.48517 q^{2} +3.11043 q^{3} +4.17608 q^{4} +3.13519 q^{5} -7.72995 q^{6} -2.09644 q^{7} -5.40793 q^{8} +6.67478 q^{9} -7.79149 q^{10} -2.23753 q^{11} +12.9894 q^{12} -1.93981 q^{13} +5.21001 q^{14} +9.75179 q^{15} +5.08748 q^{16} -5.97561 q^{17} -16.5880 q^{18} -3.05916 q^{19} +13.0928 q^{20} -6.52083 q^{21} +5.56064 q^{22} +1.62087 q^{23} -16.8210 q^{24} +4.82942 q^{25} +4.82075 q^{26} +11.4301 q^{27} -8.75489 q^{28} -3.90882 q^{29} -24.2349 q^{30} -9.21307 q^{31} -1.82739 q^{32} -6.95967 q^{33} +14.8504 q^{34} -6.57273 q^{35} +27.8744 q^{36} -1.00000 q^{37} +7.60254 q^{38} -6.03363 q^{39} -16.9549 q^{40} +0.810493 q^{41} +16.2054 q^{42} -6.79506 q^{43} -9.34409 q^{44} +20.9267 q^{45} -4.02815 q^{46} -4.67450 q^{47} +15.8242 q^{48} -2.60495 q^{49} -12.0019 q^{50} -18.5867 q^{51} -8.10078 q^{52} -4.11790 q^{53} -28.4059 q^{54} -7.01507 q^{55} +11.3374 q^{56} -9.51531 q^{57} +9.71410 q^{58} -1.28990 q^{59} +40.7242 q^{60} -4.43220 q^{61} +22.8961 q^{62} -13.9933 q^{63} -5.63356 q^{64} -6.08166 q^{65} +17.2960 q^{66} +10.8719 q^{67} -24.9546 q^{68} +5.04162 q^{69} +16.3344 q^{70} +12.4075 q^{71} -36.0967 q^{72} +3.46105 q^{73} +2.48517 q^{74} +15.0216 q^{75} -12.7753 q^{76} +4.69084 q^{77} +14.9946 q^{78} +0.132456 q^{79} +15.9502 q^{80} +15.5283 q^{81} -2.01421 q^{82} -13.3431 q^{83} -27.2315 q^{84} -18.7347 q^{85} +16.8869 q^{86} -12.1581 q^{87} +12.1004 q^{88} -9.72231 q^{89} -52.0064 q^{90} +4.06668 q^{91} +6.76890 q^{92} -28.6566 q^{93} +11.6169 q^{94} -9.59105 q^{95} -5.68398 q^{96} +10.5892 q^{97} +6.47374 q^{98} -14.9350 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9}+O(q^{10}) $ 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9} - 17 q^{10} - 9 q^{11} - 21 q^{13} - 29 q^{14} - 23 q^{15} + 79 q^{16} - 76 q^{17} - 31 q^{18} - 27 q^{19} - 67 q^{20} - 30 q^{21} - 28 q^{22} - 32 q^{23} - 63 q^{24} + 66 q^{25} - 55 q^{26} - 4 q^{28} - 81 q^{29} - 48 q^{30} - 30 q^{31} - 73 q^{32} - 53 q^{33} - 23 q^{34} - 78 q^{35} + 7 q^{36} - 110 q^{37} - 50 q^{38} - 64 q^{39} - 37 q^{40} - 123 q^{41} - 63 q^{42} - 40 q^{43} - 31 q^{44} - 73 q^{45} + 16 q^{46} - 37 q^{47} - 29 q^{48} + 46 q^{49} - 58 q^{50} - 73 q^{51} - 39 q^{52} - 16 q^{53} - 53 q^{54} - 59 q^{55} - 113 q^{56} - 39 q^{57} + 11 q^{58} - 93 q^{59} - 18 q^{60} - 66 q^{61} - 40 q^{62} - 21 q^{63} + 23 q^{64} - 92 q^{65} - 31 q^{66} + q^{67} - 121 q^{68} - 80 q^{69} - 3 q^{70} - 75 q^{71} - 114 q^{72} - 39 q^{73} + 9 q^{74} - 25 q^{75} - 58 q^{76} - 31 q^{77} + 68 q^{78} - 36 q^{79} - 82 q^{80} - 50 q^{81} - 18 q^{82} - 57 q^{83} - 9 q^{84} - 14 q^{85} - 58 q^{86} - 58 q^{87} - 15 q^{88} - 181 q^{89} + 8 q^{90} - 55 q^{91} - 116 q^{92} - 86 q^{93} - 39 q^{94} - 70 q^{95} - 127 q^{96} - 91 q^{97} - 19 q^{98} - 21 q^{99}+O(q^{100}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9 - 17 * q^10 - 9 * q^11 - 21 * q^13 - 29 * q^14 - 23 * q^15 + 79 * q^16 - 76 * q^17 - 31 * q^18 - 27 * q^19 - 67 * q^20 - 30 * q^21 - 28 * q^22 - 32 * q^23 - 63 * q^24 + 66 * q^25 - 55 * q^26 - 4 * q^28 - 81 * q^29 - 48 * q^30 - 30 * q^31 - 73 * q^32 - 53 * q^33 - 23 * q^34 - 78 * q^35 + 7 * q^36 - 110 * q^37 - 50 * q^38 - 64 * q^39 - 37 * q^40 - 123 * q^41 - 63 * q^42 - 40 * q^43 - 31 * q^44 - 73 * q^45 + 16 * q^46 - 37 * q^47 - 29 * q^48 + 46 * q^49 - 58 * q^50 - 73 * q^51 - 39 * q^52 - 16 * q^53 - 53 * q^54 - 59 * q^55 - 113 * q^56 - 39 * q^57 + 11 * q^58 - 93 * q^59 - 18 * q^60 - 66 * q^61 - 40 * q^62 - 21 * q^63 + 23 * q^64 - 92 * q^65 - 31 * q^66 + q^67 - 121 * q^68 - 80 * q^69 - 3 * q^70 - 75 * q^71 - 114 * q^72 - 39 * q^73 + 9 * q^74 - 25 * q^75 - 58 * q^76 - 31 * q^77 + 68 * q^78 - 36 * q^79 - 82 * q^80 - 50 * q^81 - 18 * q^82 - 57 * q^83 - 9 * q^84 - 14 * q^85 - 58 * q^86 - 58 * q^87 - 15 * q^88 - 181 * q^89 + 8 * q^90 - 55 * q^91 - 116 * q^92 - 86 * q^93 - 39 * q^94 - 70 * q^95 - 127 * q^96 - 91 * q^97 - 19 * q^98 - 21 * 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 $

$2$	−2.48517	−1.75728	−0.878641	−	0.477483i	$-0.841549\pi$
$2$	−2.48517	−1.75728	−0.878641	+	0.477483i	$0.841549\pi$
$3$	3.11043	1.79581	0.897904	−	0.440192i	$-0.145089\pi$
$3$	3.11043	1.79581	0.897904	+	0.440192i	$0.145089\pi$
$4$	4.17608	2.08804
$5$	3.13519	1.40210	0.701050	−	0.713112i	$-0.252715\pi$
$5$	3.13519	1.40210	0.701050	+	0.713112i	$0.252715\pi$
$6$	−7.72995	−3.15574
$7$	−2.09644	−0.792379	−0.396190	−	0.918169i	$-0.629668\pi$
$7$	−2.09644	−0.792379	−0.396190	+	0.918169i	$0.629668\pi$
$8$	−5.40793	−1.91199
$9$	6.67478	2.22493
$10$	−7.79149	−2.46388
$11$	−2.23753	−0.674640	−0.337320	−	0.941390i	$-0.609520\pi$
$11$	−2.23753	−0.674640	−0.337320	+	0.941390i	$0.609520\pi$
$12$	12.9894	3.74972
$13$	−1.93981	−0.538005	−0.269003	−	0.963139i	$-0.586694\pi$
$13$	−1.93981	−0.538005	−0.269003	+	0.963139i	$0.586694\pi$
$14$	5.21001	1.39243
$15$	9.75179	2.51790
$16$	5.08748	1.27187
$17$	−5.97561	−1.44930	−0.724649	−	0.689118i	$-0.757998\pi$
$17$	−5.97561	−1.44930	−0.724649	+	0.689118i	$0.757998\pi$
$18$	−16.5880	−3.90982
$19$	−3.05916	−0.701820	−0.350910	−	0.936409i	$-0.614128\pi$
$19$	−3.05916	−0.701820	−0.350910	+	0.936409i	$0.614128\pi$
$20$	13.0928	2.92764
$21$	−6.52083	−1.42296
$22$	5.56064	1.18553
$23$	1.62087	0.337976	0.168988	−	0.985618i	$-0.445950\pi$
$23$	1.62087	0.337976	0.168988	+	0.985618i	$0.445950\pi$
$24$	−16.8210	−3.43357
$25$	4.82942	0.965884
$26$	4.82075	0.945427
$27$	11.4301	2.19973
$28$	−8.75489	−1.65452
$29$	−3.90882	−0.725850	−0.362925	−	0.931818i	$-0.618222\pi$
$29$	−3.90882	−0.725850	−0.362925	+	0.931818i	$0.618222\pi$
$30$	−24.2349	−4.42466
$31$	−9.21307	−1.65472	−0.827358	−	0.561674i	$-0.810157\pi$
$31$	−9.21307	−1.65472	−0.827358	+	0.561674i	$0.810157\pi$
$32$	−1.82739	−0.323041
$33$	−6.95967	−1.21152
$34$	14.8504	2.54683
$35$	−6.57273	−1.11099
$36$	27.8744	4.64573
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	7.60254	1.23330
$39$	−6.03363	−0.966154
$40$	−16.9549	−2.68080
$41$	0.810493	0.126578	0.0632889	−	0.997995i	$-0.479841\pi$
$41$	0.810493	0.126578	0.0632889	+	0.997995i	$0.479841\pi$
$42$	16.2054	2.50054
$43$	−6.79506	−1.03624	−0.518118	−	0.855309i	$-0.673367\pi$
$43$	−6.79506	−1.03624	−0.518118	+	0.855309i	$0.673367\pi$
$44$	−9.34409	−1.40867
$45$	20.9267	3.11957
$46$	−4.02815	−0.593919
$47$	−4.67450	−0.681846	−0.340923	−	0.940091i	$-0.610740\pi$
$47$	−4.67450	−0.681846	−0.340923	+	0.940091i	$0.610740\pi$
$48$	15.8242	2.28403
$49$	−2.60495	−0.372135
$50$	−12.0019	−1.69733
$51$	−18.5867	−2.60266
$52$	−8.10078	−1.12338
$53$	−4.11790	−0.565637	−0.282818	−	0.959174i	$-0.591269\pi$
$53$	−4.11790	−0.565637	−0.282818	+	0.959174i	$0.591269\pi$
$54$	−28.4059	−3.86555
$55$	−7.01507	−0.945912
$56$	11.3374	1.51502
$57$	−9.51531	−1.26033
$58$	9.71410	1.27552
$59$	−1.28990	−0.167931	−0.0839655	−	0.996469i	$-0.526759\pi$
$59$	−1.28990	−0.167931	−0.0839655	+	0.996469i	$0.526759\pi$
$60$	40.7242	5.25748
$61$	−4.43220	−0.567485	−0.283742	−	0.958901i	$-0.591576\pi$
$61$	−4.43220	−0.567485	−0.283742	+	0.958901i	$0.591576\pi$
$62$	22.8961	2.90780
$63$	−13.9933	−1.76299
$64$	−5.63356	−0.704196
$65$	−6.08166	−0.754337
$66$	17.2960	2.12899
$67$	10.8719	1.32822	0.664109	−	0.747636i	$-0.268811\pi$
$67$	10.8719	1.32822	0.664109	+	0.747636i	$0.268811\pi$
$68$	−24.9546	−3.02619
$69$	5.04162	0.606939
$70$	16.3344	1.95233
$71$	12.4075	1.47250	0.736251	−	0.676709i	$-0.236594\pi$
$71$	12.4075	1.47250	0.736251	+	0.676709i	$0.236594\pi$
$72$	−36.0967	−4.25404
$73$	3.46105	0.405085	0.202542	−	0.979273i	$-0.435080\pi$
$73$	3.46105	0.405085	0.202542	+	0.979273i	$0.435080\pi$
$74$	2.48517	0.288895
$75$	15.0216	1.73454
$76$	−12.7753	−1.46543
$77$	4.69084	0.534571
$78$	14.9946	1.69781
$79$	0.132456	0.0149024	0.00745122	−	0.999972i	$-0.497628\pi$
$79$	0.132456	0.0149024	0.00745122	+	0.999972i	$0.497628\pi$
$80$	15.9502	1.78329
$81$	15.5283	1.72537
$82$	−2.01421	−0.222433
$83$	−13.3431	−1.46460	−0.732299	−	0.680983i	$-0.761553\pi$
$83$	−13.3431	−1.46460	−0.732299	+	0.680983i	$0.761553\pi$
$84$	−27.2315	−2.97120
$85$	−18.7347	−2.03206
$86$	16.8869	1.82096
$87$	−12.1581	−1.30349
$88$	12.1004	1.28991
$89$	−9.72231	−1.03056	−0.515281	−	0.857021i	$-0.672313\pi$
$89$	−9.72231	−1.03056	−0.515281	+	0.857021i	$0.672313\pi$
$90$	−52.0064	−5.48196
$91$	4.06668	0.426304
$92$	6.76890	0.705707
$93$	−28.6566	−2.97155
$94$	11.6169	1.19820
$95$	−9.59105	−0.984021
$96$	−5.68398	−0.580119
$97$	10.5892	1.07517	0.537583	−	0.843211i	$-0.319337\pi$
$97$	10.5892	1.07517	0.537583	+	0.843211i	$0.319337\pi$
$98$	6.47374	0.653946
$99$	−14.9350	−1.50102
$100$	20.1680	2.01680
$101$	−1.06264	−0.105736	−0.0528681	−	0.998602i	$-0.516836\pi$
$101$	−1.06264	−0.105736	−0.0528681	+	0.998602i	$0.516836\pi$
$102$	46.1912	4.57361
$103$	−7.25025	−0.714389	−0.357194	−	0.934030i	$-0.616267\pi$
$103$	−7.25025	−0.714389	−0.357194	+	0.934030i	$0.616267\pi$
$104$	10.4903	1.02866
$105$	−20.4440	−1.99513
$106$	10.2337	0.993983
$107$	−1.79283	−0.173320	−0.0866599	−	0.996238i	$-0.527619\pi$
$107$	−1.79283	−0.173320	−0.0866599	+	0.996238i	$0.527619\pi$
$108$	47.7332	4.59313
$109$	11.0103	1.05460	0.527298	−	0.849681i	$-0.323205\pi$
$109$	11.0103	1.05460	0.527298	+	0.849681i	$0.323205\pi$
$110$	17.4337	1.66223
$111$	−3.11043	−0.295229
$112$	−10.6656	−1.00780
$113$	−0.598251	−0.0562787	−0.0281394	−	0.999604i	$-0.508958\pi$
$113$	−0.598251	−0.0562787	−0.0281394	+	0.999604i	$0.508958\pi$
$114$	23.6472	2.21476
$115$	5.08175	0.473876
$116$	−16.3236	−1.51560
$117$	−12.9478	−1.19702
$118$	3.20563	0.295102
$119$	12.5275	1.14839
$120$	−52.7370	−4.81421
$121$	−5.99347	−0.544861
$122$	11.0148	0.997231
$123$	2.52098	0.227309
$124$	−38.4745	−3.45511
$125$	−0.534806	−0.0478345
$126$	34.7757	3.09806
$127$	3.45645	0.306710	0.153355	−	0.988171i	$-0.450992\pi$
$127$	3.45645	0.306710	0.153355	+	0.988171i	$0.450992\pi$
$128$	17.6552	1.56051
$129$	−21.1355	−1.86088
$130$	15.1140	1.32558
$131$	16.4947	1.44115	0.720575	−	0.693377i	$-0.243878\pi$
$131$	16.4947	1.44115	0.720575	+	0.693377i	$0.243878\pi$
$132$	−29.0641	−2.52971
$133$	6.41334	0.556108
$134$	−27.0186	−2.33405
$135$	35.8357	3.08424
$136$	32.3157	2.77105
$137$	11.1083	0.949045	0.474523	−	0.880243i	$-0.342621\pi$
$137$	11.1083	0.949045	0.474523	+	0.880243i	$0.342621\pi$
$138$	−12.5293	−1.06656
$139$	17.7434	1.50498	0.752489	−	0.658604i	$-0.228853\pi$
$139$	17.7434	1.50498	0.752489	+	0.658604i	$0.228853\pi$
$140$	−27.4483	−2.31980
$141$	−14.5397	−1.22446
$142$	−30.8348	−2.58760
$143$	4.34037	0.362960
$144$	33.9578	2.82981
$145$	−12.2549	−1.01771
$146$	−8.60130	−0.711848
$147$	−8.10250	−0.668283
$148$	−4.17608	−0.343272
$149$	−1.76253	−0.144392	−0.0721960	−	0.997390i	$-0.523001\pi$
$149$	−1.76253	−0.144392	−0.0721960	+	0.997390i	$0.523001\pi$
$150$	−37.3312	−3.04808
$151$	0.233035	0.0189641	0.00948205	−	0.999955i	$-0.496982\pi$
$151$	0.233035	0.0189641	0.00948205	+	0.999955i	$0.496982\pi$
$152$	16.5437	1.34187
$153$	−39.8859	−3.22458
$154$	−11.6575	−0.939391
$155$	−28.8847	−2.32008
$156$	−25.1969	−2.01737
$157$	11.9780	0.955947	0.477974	−	0.878374i	$-0.341371\pi$
$157$	11.9780	0.955947	0.477974	+	0.878374i	$0.341371\pi$
$158$	−0.329175	−0.0261878
$159$	−12.8084	−1.01577
$160$	−5.72923	−0.452935
$161$	−3.39806	−0.267805
$162$	−38.5905	−3.03196
$163$	−1.00000	−0.0783260
$163$	−1.00000	−0.0783260
$164$	3.38468	0.264299
$165$	−21.8199	−1.69868
$166$	33.1599	2.57371
$167$	8.77311	0.678883	0.339442	−	0.940627i	$-0.389762\pi$
$167$	8.77311	0.678883	0.339442	+	0.940627i	$0.389762\pi$
$168$	35.2642	2.72069
$169$	−9.23715	−0.710550
$170$	46.5589	3.57090
$171$	−20.4192	−1.56150
$172$	−28.3767	−2.16370
$173$	−3.49260	−0.265537	−0.132769	−	0.991147i	$-0.542387\pi$
$173$	−3.49260	−0.265537	−0.132769	+	0.991147i	$0.542387\pi$
$174$	30.2150	2.29059
$175$	−10.1246	−0.765346
$176$	−11.3834	−0.858054
$177$	−4.01215	−0.301572
$178$	24.1616	1.81099
$179$	−11.2152	−0.838266	−0.419133	−	0.907925i	$-0.637666\pi$
$179$	−11.2152	−0.838266	−0.419133	+	0.907925i	$0.637666\pi$
$180$	87.3915	6.51378
$181$	−26.3124	−1.95578	−0.977892	−	0.209112i	$-0.932943\pi$
$181$	−26.3124	−1.95578	−0.977892	+	0.209112i	$0.932943\pi$
$182$	−10.1064	−0.749137
$183$	−13.7860	−1.01909
$184$	−8.76558	−0.646207
$185$	−3.13519	−0.230504
$186$	71.2166	5.22186
$187$	13.3706	0.977755
$188$	−19.5211	−1.42372
$189$	−23.9626	−1.74302
$190$	23.8354	1.72920
$191$	11.3048	0.817984	0.408992	−	0.912538i	$-0.365880\pi$
$191$	11.3048	0.817984	0.408992	+	0.912538i	$0.365880\pi$
$192$	−17.5228	−1.26460
$193$	−17.6730	−1.27213	−0.636066	−	0.771634i	$-0.719440\pi$
$193$	−17.6730	−1.27213	−0.636066	+	0.771634i	$0.719440\pi$
$194$	−26.3159	−1.88937
$195$	−18.9166	−1.35464
$196$	−10.8785	−0.777033
$197$	−14.4152	−1.02704	−0.513519	−	0.858078i	$-0.671659\pi$
$197$	−14.4152	−1.02704	−0.513519	+	0.858078i	$0.671659\pi$
$198$	37.1160	2.63772
$199$	−19.4739	−1.38047	−0.690236	−	0.723584i	$-0.742493\pi$
$199$	−19.4739	−1.38047	−0.690236	+	0.723584i	$0.742493\pi$
$200$	−26.1172	−1.84676
$201$	33.8164	2.38522
$202$	2.64083	0.185808
$203$	8.19461	0.575149
$204$	−77.6196	−5.43446
$205$	2.54105	0.177475
$206$	18.0181	1.25538
$207$	10.8190	0.751971
$208$	−9.86872	−0.684273
$209$	6.84496	0.473476
$210$	50.8069	3.50601
$211$	−9.07945	−0.625055	−0.312528	−	0.949909i	$-0.601176\pi$
$211$	−9.07945	−0.625055	−0.312528	+	0.949909i	$0.601176\pi$
$212$	−17.1967	−1.18107
$213$	38.5927	2.64433
$214$	4.45550	0.304572
$215$	−21.3038	−1.45291
$216$	−61.8134	−4.20587
$217$	19.3146	1.31116
$218$	−27.3625	−1.85322
$219$	10.7653	0.727455
$220$	−29.2955	−1.97510
$221$	11.5915	0.779731
$222$	7.72995	0.518801
$223$	−6.87766	−0.460562	−0.230281	−	0.973124i	$-0.573965\pi$
$223$	−6.87766	−0.460562	−0.230281	+	0.973124i	$0.573965\pi$
$224$	3.83102	0.255971
$225$	32.2353	2.14902
$226$	1.48676	0.0988976
$227$	−17.9360	−1.19046	−0.595228	−	0.803557i	$-0.702938\pi$
$227$	−17.9360	−1.19046	−0.595228	+	0.803557i	$0.702938\pi$
$228$	−39.7367	−2.63163
$229$	12.2335	0.808410	0.404205	−	0.914668i	$-0.367548\pi$
$229$	12.2335	0.808410	0.404205	+	0.914668i	$0.367548\pi$
$230$	−12.6290	−0.832733
$231$	14.5905	0.959986
$232$	21.1386	1.38782
$233$	−25.5552	−1.67418	−0.837090	−	0.547065i	$-0.815745\pi$
$233$	−25.5552	−1.67418	−0.837090	+	0.547065i	$0.815745\pi$
$234$	32.1774	2.10351
$235$	−14.6554	−0.956016
$236$	−5.38674	−0.350647
$237$	0.411995	0.0267619
$238$	−31.1330	−2.01805
$239$	17.0473	1.10270	0.551348	−	0.834276i	$-0.314114\pi$
$239$	17.0473	1.10270	0.551348	+	0.834276i	$0.314114\pi$
$240$	49.6120	3.20244
$241$	3.99456	0.257312	0.128656	−	0.991689i	$-0.458934\pi$
$241$	3.99456	0.257312	0.128656	+	0.991689i	$0.458934\pi$
$242$	14.8948	0.957475
$243$	14.0093	0.898699
$244$	−18.5092	−1.18493
$245$	−8.16700	−0.521770
$246$	−6.26507	−0.399446
$247$	5.93418	0.377583
$248$	49.8237	3.16381
$249$	−41.5028	−2.63014
$250$	1.32909	0.0840588
$251$	−18.0535	−1.13953	−0.569763	−	0.821809i	$-0.692965\pi$
$251$	−18.0535	−1.13953	−0.569763	+	0.821809i	$0.692965\pi$
$252$	−58.4370	−3.68118
$253$	−3.62675	−0.228012
$254$	−8.58987	−0.538976
$255$	−58.2729	−3.64919
$256$	−32.6090	−2.03806
$257$	−22.4869	−1.40269	−0.701347	−	0.712820i	$-0.747418\pi$
$257$	−22.4869	−1.40269	−0.701347	+	0.712820i	$0.747418\pi$
$258$	52.5255	3.27009
$259$	2.09644	0.130266
$260$	−25.3975	−1.57509
$261$	−26.0905	−1.61496
$262$	−40.9922	−2.53251
$263$	5.85744	0.361185	0.180593	−	0.983558i	$-0.442198\pi$
$263$	5.85744	0.361185	0.180593	+	0.983558i	$0.442198\pi$
$264$	37.6374	2.31642
$265$	−12.9104	−0.793079
$266$	−15.9383	−0.977238
$267$	−30.2406	−1.85069
$268$	45.4021	2.77337
$269$	1.55912	0.0950609	0.0475305	−	0.998870i	$-0.484865\pi$
$269$	1.55912	0.0950609	0.0475305	+	0.998870i	$0.484865\pi$
$270$	−89.0578	−5.41988
$271$	6.95045	0.422210	0.211105	−	0.977463i	$-0.432294\pi$
$271$	6.95045	0.422210	0.211105	+	0.977463i	$0.432294\pi$
$272$	−30.4008	−1.84332
$273$	12.6491	0.765561
$274$	−27.6060	−1.66774
$275$	−10.8060	−0.651624
$276$	21.0542	1.26731
$277$	7.82522	0.470172	0.235086	−	0.971975i	$-0.424463\pi$
$277$	7.82522	0.470172	0.235086	+	0.971975i	$0.424463\pi$
$278$	−44.0955	−2.64467
$279$	−61.4952	−3.68162
$280$	35.5449	2.12421
$281$	12.5676	0.749719	0.374859	−	0.927082i	$-0.377691\pi$
$281$	12.5676	0.749719	0.374859	+	0.927082i	$0.377691\pi$
$282$	36.1337	2.15173
$283$	19.6184	1.16619	0.583096	−	0.812403i	$-0.301841\pi$
$283$	19.6184	1.16619	0.583096	+	0.812403i	$0.301841\pi$
$284$	51.8148	3.07464
$285$	−29.8323	−1.76711
$286$	−10.7866	−0.637823
$287$	−1.69915	−0.100298
$288$	−12.1975	−0.718742
$289$	18.7079	1.10047
$290$	30.4555	1.78841
$291$	32.9369	1.93079
$292$	14.4536	0.845833
$293$	−1.79605	−0.104926	−0.0524631	−	0.998623i	$-0.516707\pi$
$293$	−1.79605	−0.104926	−0.0524631	+	0.998623i	$0.516707\pi$
$294$	20.1361	1.17436
$295$	−4.04409	−0.235456
$296$	5.40793	0.314330
$297$	−25.5752	−1.48403
$298$	4.38019	0.253738
$299$	−3.14418	−0.181833
$300$	62.7313	3.62179
$301$	14.2454	0.821092
$302$	−0.579131	−0.0333253
$303$	−3.30525	−0.189882
$304$	−15.5634	−0.892623
$305$	−13.8958	−0.795670
$306$	99.1233	5.66650
$307$	10.5065	0.599639	0.299820	−	0.953996i	$-0.403073\pi$
$307$	10.5065	0.599639	0.299820	+	0.953996i	$0.403073\pi$
$308$	19.5893	1.11620
$309$	−22.5514	−1.28290
$310$	71.7835	4.07703
$311$	4.89032	0.277305	0.138652	−	0.990341i	$-0.455723\pi$
$311$	4.89032	0.277305	0.138652	+	0.990341i	$0.455723\pi$
$312$	32.6295	1.84728
$313$	10.0886	0.570239	0.285120	−	0.958492i	$-0.407967\pi$
$313$	10.0886	0.570239	0.285120	+	0.958492i	$0.407967\pi$
$314$	−29.7674	−1.67987
$315$	−43.8715	−2.47188
$316$	0.553146	0.0311169
$317$	16.9234	0.950515	0.475258	−	0.879847i	$-0.342355\pi$
$317$	16.9234	0.950515	0.475258	+	0.879847i	$0.342355\pi$
$318$	31.8311	1.78500
$319$	8.74610	0.489687
$320$	−17.6623	−0.987352
$321$	−5.57648	−0.311249
$322$	8.44477	0.470609
$323$	18.2804	1.01715
$324$	64.8475	3.60264
$325$	−9.36814	−0.519651
$326$	2.48517	0.137641
$327$	34.2468	1.89385
$328$	−4.38309	−0.242016
$329$	9.79980	0.540281
$330$	54.2262	2.98505
$331$	9.16126	0.503548	0.251774	−	0.967786i	$-0.418986\pi$
$331$	9.16126	0.503548	0.251774	+	0.967786i	$0.418986\pi$
$332$	−55.7219	−3.05814
$333$	−6.67478	−0.365776
$334$	−21.8027	−1.19299
$335$	34.0856	1.86229
$336$	−33.1746	−1.80982
$337$	19.9018	1.08412	0.542059	−	0.840340i	$-0.317645\pi$
$337$	19.9018	1.08412	0.542059	+	0.840340i	$0.317645\pi$
$338$	22.9559	1.24864
$339$	−1.86082	−0.101066
$340$	−78.2375	−4.24302
$341$	20.6145	1.11634
$342$	50.7453	2.74399
$343$	20.1362	1.08725
$344$	36.7472	1.98128
$345$	15.8064	0.850990
$346$	8.67971	0.466624
$347$	−20.0768	−1.07778	−0.538890	−	0.842376i	$-0.681156\pi$
$347$	−20.0768	−1.07778	−0.538890	+	0.842376i	$0.681156\pi$
$348$	−50.7733	−2.72173
$349$	0.811601	0.0434440	0.0217220	−	0.999764i	$-0.493085\pi$
$349$	0.811601	0.0434440	0.0217220	+	0.999764i	$0.493085\pi$
$350$	25.1613	1.34493
$351$	−22.1723	−1.18347
$352$	4.08885	0.217936
$353$	25.5483	1.35980	0.679898	−	0.733306i	$-0.262024\pi$
$353$	25.5483	1.35980	0.679898	+	0.733306i	$0.262024\pi$
$354$	9.97089	0.529947
$355$	38.8999	2.06459
$356$	−40.6011	−2.15186
$357$	38.9659	2.06230
$358$	27.8718	1.47307
$359$	25.0067	1.31980	0.659901	−	0.751352i	$-0.270598\pi$
$359$	25.0067	1.31980	0.659901	+	0.751352i	$0.270598\pi$
$360$	−113.170	−5.96459
$361$	−9.64153	−0.507449
$362$	65.3908	3.43686
$363$	−18.6423	−0.978466
$364$	16.9828	0.890140
$365$	10.8510	0.567970
$366$	34.2607	1.79083
$367$	28.4078	1.48287	0.741436	−	0.671023i	$-0.234145\pi$
$367$	28.4078	1.48287	0.741436	+	0.671023i	$0.234145\pi$
$368$	8.24616	0.429861
$369$	5.40986	0.281626
$370$	7.79149	0.405060
$371$	8.63292	0.448199
$372$	−119.672	−6.20472
$373$	23.0386	1.19289	0.596447	−	0.802653i	$-0.296579\pi$
$373$	23.0386	1.19289	0.596447	+	0.802653i	$0.296579\pi$
$374$	−33.2282	−1.71819
$375$	−1.66348	−0.0859016
$376$	25.2794	1.30368
$377$	7.58236	0.390511
$378$	59.5511	3.06298
$379$	9.10734	0.467812	0.233906	−	0.972259i	$-0.424849\pi$
$379$	9.10734	0.467812	0.233906	+	0.972259i	$0.424849\pi$
$380$	−40.0530	−2.05468
$381$	10.7510	0.550793
$382$	−28.0943	−1.43743
$383$	−38.8925	−1.98732	−0.993658	−	0.112447i	$-0.964131\pi$
$383$	−38.8925	−1.98732	−0.993658	+	0.112447i	$0.964131\pi$
$384$	54.9152	2.80238
$385$	14.7067	0.749521
$386$	43.9205	2.23550
$387$	−45.3555	−2.30555
$388$	44.2212	2.24499
$389$	−27.8202	−1.41054	−0.705271	−	0.708937i	$-0.749175\pi$
$389$	−27.8202	−1.41054	−0.705271	+	0.708937i	$0.749175\pi$
$390$	47.0110	2.38049
$391$	−9.68572	−0.489828
$392$	14.0874	0.711519
$393$	51.3057	2.58803
$394$	35.8242	1.80480
$395$	0.415274	0.0208947
$396$	−62.3697	−3.13420
$397$	22.1023	1.10928	0.554640	−	0.832090i	$-0.312856\pi$
$397$	22.1023	1.10928	0.554640	+	0.832090i	$0.312856\pi$
$398$	48.3961	2.42588
$399$	19.9483	0.998662
$400$	24.5696	1.22848
$401$	30.8315	1.53965	0.769825	−	0.638255i	$-0.220343\pi$
$401$	30.8315	1.53965	0.769825	+	0.638255i	$0.220343\pi$
$402$	−84.0396	−4.19151
$403$	17.8716	0.890247
$404$	−4.43765	−0.220781
$405$	48.6842	2.41914
$406$	−20.3650	−1.01070
$407$	2.23753	0.110910
$408$	100.516	4.97627
$409$	13.6545	0.675171	0.337585	−	0.941295i	$-0.390390\pi$
$409$	13.6545	0.675171	0.337585	+	0.941295i	$0.390390\pi$
$410$	−6.31494	−0.311873
$411$	34.5516	1.70430
$412$	−30.2776	−1.49167
$413$	2.70420	0.133065
$414$	−26.8870	−1.32142
$415$	−41.8332	−2.05351
$416$	3.54479	0.173798
$417$	55.1897	2.70265
$418$	−17.0109	−0.832030
$419$	−3.22767	−0.157682	−0.0788410	−	0.996887i	$-0.525122\pi$
$419$	−3.22767	−0.157682	−0.0788410	+	0.996887i	$0.525122\pi$
$420$	−85.3759	−4.16592
$421$	−9.30025	−0.453267	−0.226633	−	0.973980i	$-0.572772\pi$
$421$	−9.30025	−0.453267	−0.226633	+	0.973980i	$0.572772\pi$
$422$	22.5640	1.09840
$423$	−31.2012	−1.51706
$424$	22.2693	1.08149
$425$	−28.8587	−1.39985
$426$	−95.9095	−4.64683
$427$	9.29183	0.449663
$428$	−7.48701	−0.361898
$429$	13.5004	0.651806
$430$	52.9436	2.55317
$431$	−37.3321	−1.79822	−0.899111	−	0.437721i	$-0.855786\pi$
$431$	−37.3321	−1.79822	−0.899111	+	0.437721i	$0.855786\pi$
$432$	58.1506	2.79777
$433$	0.517683	0.0248783	0.0124391	−	0.999923i	$-0.496040\pi$
$433$	0.517683	0.0248783	0.0124391	+	0.999923i	$0.496040\pi$
$434$	−48.0002	−2.30408
$435$	−38.1180	−1.82762
$436$	45.9799	2.20204
$437$	−4.95852	−0.237198
$438$	−26.7537	−1.27834
$439$	8.36784	0.399375	0.199688	−	0.979860i	$-0.436007\pi$
$439$	8.36784	0.399375	0.199688	+	0.979860i	$0.436007\pi$
$440$	37.9370	1.80858
$441$	−17.3874	−0.827973
$442$	−28.8069	−1.37021
$443$	−17.6843	−0.840205	−0.420102	−	0.907477i	$-0.638006\pi$
$443$	−17.6843	−0.840205	−0.420102	+	0.907477i	$0.638006\pi$
$444$	−12.9894	−0.616450
$445$	−30.4813	−1.44495
$446$	17.0922	0.809338
$447$	−5.48223	−0.259300
$448$	11.8104	0.557990
$449$	−18.7509	−0.884910	−0.442455	−	0.896791i	$-0.645892\pi$
$449$	−18.7509	−0.884910	−0.442455	+	0.896791i	$0.645892\pi$
$450$	−80.1102	−3.77643
$451$	−1.81350	−0.0853944
$452$	−2.49834	−0.117512
$453$	0.724838	0.0340559
$454$	44.5741	2.09197
$455$	12.7498	0.597721
$456$	51.4581	2.40975
$457$	20.3124	0.950173	0.475086	−	0.879939i	$-0.342417\pi$
$457$	20.3124	0.950173	0.475086	+	0.879939i	$0.342417\pi$
$458$	−30.4023	−1.42061
$459$	−68.3021	−3.18807
$460$	21.2218	0.989471
$461$	−5.98411	−0.278708	−0.139354	−	0.990243i	$-0.544503\pi$
$461$	−5.98411	−0.278708	−0.139354	+	0.990243i	$0.544503\pi$
$462$	−36.2600	−1.68697
$463$	28.4675	1.32300	0.661500	−	0.749946i	$-0.269920\pi$
$463$	28.4675	1.32300	0.661500	+	0.749946i	$0.269920\pi$
$464$	−19.8860	−0.923186
$465$	−89.8440	−4.16641
$466$	63.5092	2.94201
$467$	5.11733	0.236802	0.118401	−	0.992966i	$-0.462223\pi$
$467$	5.11733	0.236802	0.118401	+	0.992966i	$0.462223\pi$
$468$	−54.0709	−2.49943
$469$	−22.7923	−1.05245
$470$	36.4213	1.67999
$471$	37.2567	1.71670
$472$	6.97570	0.321083
$473$	15.2041	0.699086
$474$	−1.02388	−0.0470282
$475$	−14.7740	−0.677876
$476$	52.3158	2.39789
$477$	−27.4860	−1.25850
$478$	−42.3654	−1.93775
$479$	−13.9949	−0.639443	−0.319722	−	0.947512i	$-0.603589\pi$
$479$	−13.9949	−0.639443	−0.319722	+	0.947512i	$0.603589\pi$
$480$	−17.8204	−0.813385
$481$	1.93981	0.0884476
$482$	−9.92717	−0.452170
$483$	−10.5694	−0.480926
$484$	−25.0292	−1.13769
$485$	33.1990	1.50749
$486$	−34.8156	−1.57927
$487$	6.33170	0.286917	0.143458	−	0.989656i	$-0.454178\pi$
$487$	6.33170	0.286917	0.143458	+	0.989656i	$0.454178\pi$
$488$	23.9690	1.08503
$489$	−3.11043	−0.140659
$490$	20.2964	0.916898
$491$	31.5917	1.42572	0.712858	−	0.701309i	$-0.247401\pi$
$491$	31.5917	1.42572	0.712858	+	0.701309i	$0.247401\pi$
$492$	10.5278	0.474631
$493$	23.3576	1.05197
$494$	−14.7475	−0.663520
$495$	−46.8240	−2.10458
$496$	−46.8713	−2.10458
$497$	−26.0116	−1.16678
$498$	103.142	4.62189
$499$	−30.3206	−1.35734	−0.678669	−	0.734444i	$-0.737443\pi$
$499$	−30.3206	−1.35734	−0.678669	+	0.734444i	$0.737443\pi$
$500$	−2.23339	−0.0998804
$501$	27.2881	1.21914
$502$	44.8660	2.00247
$503$	21.8119	0.972543	0.486271	−	0.873808i	$-0.338357\pi$
$503$	21.8119	0.972543	0.486271	+	0.873808i	$0.338357\pi$
$504$	75.6746	3.37081
$505$	−3.33156	−0.148253
$506$	9.01310	0.400681
$507$	−28.7315	−1.27601
$508$	14.4344	0.640423
$509$	−15.0665	−0.667813	−0.333907	−	0.942606i	$-0.608367\pi$
$509$	−15.0665	−0.667813	−0.333907	+	0.942606i	$0.608367\pi$
$510$	144.818	6.41266
$511$	−7.25587	−0.320981
$512$	45.7286	2.02094
$513$	−34.9666	−1.54381
$514$	55.8838	2.46493
$515$	−22.7309	−1.00164
$516$	−88.2637	−3.88559
$517$	10.4593	0.460000
$518$	−5.21001	−0.228915
$519$	−10.8635	−0.476854
$520$	32.8892	1.44229
$521$	−14.2985	−0.626430	−0.313215	−	0.949682i	$-0.601406\pi$
$521$	−14.2985	−0.626430	−0.313215	+	0.949682i	$0.601406\pi$
$522$	64.8394	2.83794
$523$	9.05890	0.396118	0.198059	−	0.980190i	$-0.436536\pi$
$523$	9.05890	0.396118	0.198059	+	0.980190i	$0.436536\pi$
$524$	68.8833	3.00918
$525$	−31.4918	−1.37441
$526$	−14.5568	−0.634705
$527$	55.0537	2.39818
$528$	−35.4072	−1.54090
$529$	−20.3728	−0.885772
$530$	32.0845	1.39366
$531$	−8.60981	−0.373634
$532$	26.7826	1.16117
$533$	−1.57220	−0.0680995
$534$	75.1530	3.25219
$535$	−5.62087	−0.243012
$536$	−58.7947	−2.53954
$537$	−34.8842	−1.50536
$538$	−3.87467	−0.167049
$539$	5.82864	0.251057
$540$	149.653	6.44002
$541$	−19.4928	−0.838063	−0.419031	−	0.907972i	$-0.637630\pi$
$541$	−19.4928	−0.838063	−0.419031	+	0.907972i	$0.637630\pi$
$542$	−17.2731	−0.741941
$543$	−81.8428	−3.51221
$544$	10.9198	0.468183
$545$	34.5194	1.47865
$546$	−31.4353	−1.34531
$547$	−15.9962	−0.683947	−0.341974	−	0.939710i	$-0.611095\pi$
$547$	−15.9962	−0.683947	−0.341974	+	0.939710i	$0.611095\pi$
$548$	46.3891	1.98164
$549$	−29.5839	−1.26261
$550$	26.8547	1.14509
$551$	11.9577	0.509416
$552$	−27.2647	−1.16046
$553$	−0.277686	−0.0118084
$554$	−19.4470	−0.826224
$555$	−9.75179	−0.413940
$556$	74.0980	3.14246
$557$	−17.3892	−0.736806	−0.368403	−	0.929666i	$-0.620095\pi$
$557$	−17.3892	−0.736806	−0.368403	+	0.929666i	$0.620095\pi$
$558$	152.826	6.46965
$559$	13.1811	0.557501
$560$	−33.4386	−1.41304
$561$	41.5883	1.75586
$562$	−31.2326	−1.31747
$563$	43.2293	1.82190	0.910950	−	0.412517i	$-0.135350\pi$
$563$	43.2293	1.82190	0.910950	+	0.412517i	$0.135350\pi$
$564$	−60.7190	−2.55673
$565$	−1.87563	−0.0789084
$566$	−48.7551	−2.04933
$567$	−32.5542	−1.36715
$568$	−67.0990	−2.81541
$569$	−9.98659	−0.418660	−0.209330	−	0.977845i	$-0.567128\pi$
$569$	−9.98659	−0.418660	−0.209330	+	0.977845i	$0.567128\pi$
$570$	74.1384	3.10532
$571$	−34.2555	−1.43355	−0.716775	−	0.697305i	$-0.754382\pi$
$571$	−34.2555	−1.43355	−0.716775	+	0.697305i	$0.754382\pi$
$572$	18.1257	0.757875
$573$	35.1627	1.46894
$574$	4.22268	0.176251
$575$	7.82788	0.326445
$576$	−37.6028	−1.56678
$577$	11.5068	0.479035	0.239517	−	0.970892i	$-0.423011\pi$
$577$	11.5068	0.479035	0.239517	+	0.970892i	$0.423011\pi$
$578$	−46.4924	−1.93383
$579$	−54.9707	−2.28451
$580$	−51.1774	−2.12503
$581$	27.9730	1.16052
$582$	−81.8537	−3.39295
$583$	9.21390	0.381601
$584$	−18.7171	−0.774519
$585$	−40.5937	−1.67834
$586$	4.46349	0.184385
$587$	−25.2899	−1.04382	−0.521912	−	0.852999i	$-0.674781\pi$
$587$	−25.2899	−1.04382	−0.521912	+	0.852999i	$0.674781\pi$
$588$	−33.8367	−1.39540
$589$	28.1843	1.16131
$590$	10.0503	0.413763
$591$	−44.8374	−1.84436
$592$	−5.08748	−0.209094
$593$	11.9507	0.490755	0.245378	−	0.969428i	$-0.421088\pi$
$593$	11.9507	0.490755	0.245378	+	0.969428i	$0.421088\pi$
$594$	63.5589	2.60785
$595$	39.2761	1.61016
$596$	−7.36046	−0.301496
$597$	−60.5724	−2.47906
$598$	7.81383	0.319531
$599$	−4.20600	−0.171853	−0.0859263	−	0.996301i	$-0.527385\pi$
$599$	−4.20600	−0.171853	−0.0859263	+	0.996301i	$0.527385\pi$
$600$	−81.2356	−3.31643
$601$	−0.495978	−0.0202313	−0.0101157	−	0.999949i	$-0.503220\pi$
$601$	−0.495978	−0.0202313	−0.0101157	+	0.999949i	$0.503220\pi$
$602$	−35.4023	−1.44289
$603$	72.5677	2.95519
$604$	0.973172	0.0395978
$605$	−18.7907	−0.763950
$606$	8.21412	0.333676
$607$	0.366270	0.0148664	0.00743322	−	0.999972i	$-0.497634\pi$
$607$	0.366270	0.0148664	0.00743322	+	0.999972i	$0.497634\pi$
$608$	5.59030	0.226716
$609$	25.4888	1.03286
$610$	34.5334	1.39822
$611$	9.06762	0.366837
$612$	−166.567	−6.73305
$613$	38.0243	1.53579	0.767894	−	0.640577i	$-0.221305\pi$
$613$	38.0243	1.53579	0.767894	+	0.640577i	$0.221305\pi$
$614$	−26.1105	−1.05374
$615$	7.90376	0.318710
$616$	−25.3677	−1.02209
$617$	−39.1842	−1.57750	−0.788749	−	0.614715i	$-0.789271\pi$
$617$	−39.1842	−1.57750	−0.788749	+	0.614715i	$0.789271\pi$
$618$	56.0441	2.25443
$619$	44.8059	1.80090	0.900451	−	0.434957i	$-0.143237\pi$
$619$	44.8059	1.80090	0.900451	+	0.434957i	$0.143237\pi$
$620$	−120.625	−4.84441
$621$	18.5268	0.743456
$622$	−12.1533	−0.487303
$623$	20.3822	0.816597
$624$	−30.6960	−1.22882
$625$	−25.8238	−1.03295
$626$	−25.0718	−1.00207
$627$	21.2908	0.850271
$628$	50.0210	1.99606
$629$	5.97561	0.238263
$630$	109.028	4.34379
$631$	−39.5819	−1.57573	−0.787866	−	0.615847i	$-0.788814\pi$
$631$	−39.5819	−1.57573	−0.787866	+	0.615847i	$0.788814\pi$
$632$	−0.716312	−0.0284934
$633$	−28.2410	−1.12248
$634$	−42.0577	−1.67032
$635$	10.8366	0.430038
$636$	−53.4890	−2.12098
$637$	5.05309	0.200211
$638$	−21.7356	−0.860519
$639$	82.8174	3.27621
$640$	55.3523	2.18799
$641$	13.8666	0.547697	0.273848	−	0.961773i	$-0.411703\pi$
$641$	13.8666	0.547697	0.273848	+	0.961773i	$0.411703\pi$
$642$	13.8585	0.546952
$643$	22.3263	0.880464	0.440232	−	0.897884i	$-0.354896\pi$
$643$	22.3263	0.880464	0.440232	+	0.897884i	$0.354896\pi$
$644$	−14.1906	−0.559187
$645$	−66.2640	−2.60914
$646$	−45.4298	−1.78741
$647$	−37.2087	−1.46283	−0.731413	−	0.681935i	$-0.761139\pi$
$647$	−37.2087	−1.46283	−0.731413	+	0.681935i	$0.761139\pi$
$648$	−83.9760	−3.29889
$649$	2.88619	0.113293
$650$	23.2814	0.913173
$651$	60.0768	2.35460
$652$	−4.17608	−0.163548
$653$	−38.3055	−1.49901	−0.749504	−	0.662000i	$-0.769708\pi$
$653$	−38.3055	−1.49901	−0.749504	+	0.662000i	$0.769708\pi$
$654$	−85.1091	−3.32803
$655$	51.7141	2.02064
$656$	4.12336	0.160990
$657$	23.1017	0.901284
$658$	−24.3542	−0.949425
$659$	−16.7590	−0.652839	−0.326419	−	0.945225i	$-0.605842\pi$
$659$	−16.7590	−0.652839	−0.326419	+	0.945225i	$0.605842\pi$
$660$	−91.1216	−3.54690
$661$	0.232277	0.00903452	0.00451726	−	0.999990i	$-0.498562\pi$
$661$	0.232277	0.00903452	0.00451726	+	0.999990i	$0.498562\pi$
$662$	−22.7673	−0.884876
$663$	36.0546	1.40025
$664$	72.1587	2.80030
$665$	20.1071	0.779718
$666$	16.5880	0.642771
$667$	−6.33571	−0.245320
$668$	36.6372	1.41754
$669$	−21.3925	−0.827081
$670$	−84.7085	−3.27258
$671$	9.91716	0.382848
$672$	11.9161	0.459674
$673$	23.3992	0.901973	0.450986	−	0.892531i	$-0.351072\pi$
$673$	23.3992	0.901973	0.450986	+	0.892531i	$0.351072\pi$
$674$	−49.4593	−1.90510
$675$	55.2009	2.12468
$676$	−38.5751	−1.48366
$677$	−33.4612	−1.28602	−0.643009	−	0.765858i	$-0.722314\pi$
$677$	−33.4612	−1.28602	−0.643009	+	0.765858i	$0.722314\pi$
$678$	4.62445	0.177601
$679$	−22.1995	−0.851940
$680$	101.316	3.88528
$681$	−55.7888	−2.13783
$682$	−51.2306	−1.96172
$683$	41.3240	1.58122	0.790609	−	0.612321i	$-0.209764\pi$
$683$	41.3240	1.58122	0.790609	+	0.612321i	$0.209764\pi$
$684$	−85.2723	−3.26047
$685$	34.8266	1.33066
$686$	−50.0419	−1.91061
$687$	38.0514	1.45175
$688$	−34.5697	−1.31796
$689$	7.98792	0.304316
$690$	−39.2817	−1.49543
$691$	30.8567	1.17385	0.586923	−	0.809643i	$-0.300339\pi$
$691$	30.8567	1.17385	0.586923	+	0.809643i	$0.300339\pi$
$692$	−14.5854	−0.554453
$693$	31.3103	1.18938
$694$	49.8943	1.89396
$695$	55.6291	2.11013
$696$	65.7503	2.49226
$697$	−4.84319	−0.183449
$698$	−2.01697	−0.0763433
$699$	−79.4878	−3.00650
$700$	−42.2810	−1.59807
$701$	−33.5477	−1.26708	−0.633540	−	0.773710i	$-0.718399\pi$
$701$	−33.5477	−1.26708	−0.633540	+	0.773710i	$0.718399\pi$
$702$	55.1019	2.07969
$703$	3.05916	0.115378
$704$	12.6053	0.475078
$705$	−45.5847	−1.71682
$706$	−63.4918	−2.38955
$707$	2.22775	0.0837832
$708$	−16.7551	−0.629694
$709$	20.7908	0.780816	0.390408	−	0.920642i	$-0.372334\pi$
$709$	20.7908	0.780816	0.390408	+	0.920642i	$0.372334\pi$
$710$	−96.6730	−3.62807
$711$	0.884113	0.0331568
$712$	52.5776	1.97043
$713$	−14.9332	−0.559254
$714$	−96.8370	−3.62403
$715$	13.6079	0.508906
$716$	−46.8357	−1.75033
$717$	53.0243	1.98023
$718$	−62.1459	−2.31926
$719$	40.0899	1.49510	0.747551	−	0.664205i	$-0.231230\pi$
$719$	40.0899	1.49510	0.747551	+	0.664205i	$0.231230\pi$
$720$	106.464	3.96768
$721$	15.1997	0.566067
$722$	23.9609	0.891731
$723$	12.4248	0.462083
$724$	−109.883	−4.08375
$725$	−18.8773	−0.701087
$726$	46.3293	1.71944
$727$	37.6663	1.39696	0.698482	−	0.715628i	$-0.253859\pi$
$727$	37.6663	1.39696	0.698482	+	0.715628i	$0.253859\pi$
$728$	−21.9923	−0.815091
$729$	−3.00989	−0.111478
$730$	−26.9667	−0.998083
$731$	40.6046	1.50182
$732$	−57.5716	−2.12791
$733$	−7.17791	−0.265122	−0.132561	−	0.991175i	$-0.542320\pi$
$733$	−7.17791	−0.265122	−0.132561	+	0.991175i	$0.542320\pi$
$734$	−70.5982	−2.60583
$735$	−25.4029	−0.936999
$736$	−2.96198	−0.109180
$737$	−24.3262	−0.896069
$738$	−13.4444	−0.494896
$739$	−11.4080	−0.419649	−0.209824	−	0.977739i	$-0.567289\pi$
$739$	−11.4080	−0.419649	−0.209824	+	0.977739i	$0.567289\pi$
$740$	−13.0928	−0.481301
$741$	18.4579	0.678066
$742$	−21.4543	−0.787611
$743$	−3.46333	−0.127057	−0.0635287	−	0.997980i	$-0.520235\pi$
$743$	−3.46333	−0.127057	−0.0635287	+	0.997980i	$0.520235\pi$
$744$	154.973	5.68159
$745$	−5.52587	−0.202452
$746$	−57.2549	−2.09625
$747$	−89.0624	−3.25862
$748$	55.8367	2.04159
$749$	3.75856	0.137335
$750$	4.13403	0.150953
$751$	−30.4307	−1.11043	−0.555217	−	0.831706i	$-0.687365\pi$
$751$	−30.4307	−1.11043	−0.555217	+	0.831706i	$0.687365\pi$
$752$	−23.7814	−0.867219
$753$	−56.1541	−2.04637
$754$	−18.8435	−0.686238
$755$	0.730608	0.0265896
$756$	−100.070	−3.63950
$757$	−24.4312	−0.887966	−0.443983	−	0.896035i	$-0.646435\pi$
$757$	−24.4312	−0.887966	−0.443983	+	0.896035i	$0.646435\pi$
$758$	−22.6333	−0.822078
$759$	−11.2808	−0.409465
$760$	51.8677	1.88144
$761$	−51.9418	−1.88289	−0.941444	−	0.337170i	$-0.890530\pi$
$761$	−51.9418	−1.88289	−0.941444	+	0.337170i	$0.890530\pi$
$762$	−26.7182	−0.967898
$763$	−23.0824	−0.835640
$764$	47.2096	1.70798
$765$	−125.050	−4.52119
$766$	96.6546	3.49227
$767$	2.50216	0.0903478
$768$	−101.428	−3.65997
$769$	−28.1038	−1.01345	−0.506724	−	0.862108i	$-0.669144\pi$
$769$	−28.1038	−1.01345	−0.506724	+	0.862108i	$0.669144\pi$
$770$	−36.5486	−1.31712
$771$	−69.9440	−2.51897
$772$	−73.8040	−2.65626
$773$	51.3378	1.84649	0.923245	−	0.384211i	$-0.125526\pi$
$773$	51.3378	1.84649	0.923245	+	0.384211i	$0.125526\pi$
$774$	112.716	4.05150
$775$	−44.4938	−1.59826
$776$	−57.2655	−2.05571
$777$	6.52083	0.233933
$778$	69.1381	2.47872
$779$	−2.47943	−0.0888348
$780$	−78.9972	−2.82855
$781$	−27.7622	−0.993408
$782$	24.0707	0.860765
$783$	−44.6784	−1.59668
$784$	−13.2526	−0.473307
$785$	37.5533	1.34033
$786$	−127.503	−4.54790
$787$	0.977791	0.0348545	0.0174272	−	0.999848i	$-0.494452\pi$
$787$	0.977791	0.0348545	0.0174272	+	0.999848i	$0.494452\pi$
$788$	−60.1989	−2.14450
$789$	18.2192	0.648620
$790$	−1.03203	−0.0367179
$791$	1.25420	0.0445941
$792$	80.7674	2.86994
$793$	8.59761	0.305310
$794$	−54.9279	−1.94932
$795$	−40.1569	−1.42422
$796$	−81.3247	−2.88248
$797$	−25.5712	−0.905779	−0.452889	−	0.891567i	$-0.649607\pi$
$797$	−25.5712	−0.905779	−0.452889	+	0.891567i	$0.649607\pi$
$798$	−49.5749	−1.75493
$799$	27.9330	0.988198
$800$	−8.82525	−0.312020
$801$	−64.8943	−2.29293
$802$	−76.6215	−2.70560
$803$	−7.74419	−0.273286
$804$	141.220	4.98044
$805$	−10.6536	−0.375489
$806$	−44.4139	−1.56441
$807$	4.84952	0.170711
$808$	5.74666	0.202167
$809$	−41.8818	−1.47248	−0.736242	−	0.676718i	$-0.763402\pi$
$809$	−41.8818	−1.47248	−0.736242	+	0.676718i	$0.763402\pi$
$810$	−120.989	−4.25111
$811$	−18.4959	−0.649479	−0.324740	−	0.945803i	$-0.605277\pi$
$811$	−18.4959	−0.649479	−0.324740	+	0.945803i	$0.605277\pi$
$812$	34.2213	1.20093
$813$	21.6189	0.758207
$814$	−5.56064	−0.194900
$815$	−3.13519	−0.109821
$816$	−94.5595	−3.31025
$817$	20.7872	0.727251
$818$	−33.9337	−1.18647
$819$	27.1442	0.948496
$820$	10.6116	0.370574
$821$	35.4371	1.23676	0.618382	−	0.785878i	$-0.287789\pi$
$821$	35.4371	1.23676	0.618382	+	0.785878i	$0.287789\pi$
$822$	−85.8666	−2.99494
$823$	−18.0011	−0.627480	−0.313740	−	0.949509i	$-0.601582\pi$
$823$	−18.0011	−0.627480	−0.313740	+	0.949509i	$0.601582\pi$
$824$	39.2089	1.36591
$825$	−33.6112	−1.17019
$826$	−6.72041	−0.233833
$827$	−24.7848	−0.861851	−0.430925	−	0.902388i	$-0.641813\pi$
$827$	−24.7848	−0.861851	−0.430925	+	0.902388i	$0.641813\pi$
$828$	45.1809	1.57014
$829$	−35.0927	−1.21882	−0.609410	−	0.792855i	$-0.708594\pi$
$829$	−35.0927	−1.21882	−0.609410	+	0.792855i	$0.708594\pi$
$830$	103.963	3.60860
$831$	24.3398	0.844338
$832$	10.9280	0.378861
$833$	15.5661	0.539335
$834$	−137.156	−4.74932
$835$	27.5054	0.951862
$836$	28.5851	0.988636
$837$	−105.307	−3.63993
$838$	8.02131	0.277092
$839$	−5.83543	−0.201461	−0.100731	−	0.994914i	$-0.532118\pi$
$839$	−5.83543	−0.201461	−0.100731	+	0.994914i	$0.532118\pi$
$840$	110.560	3.81468
$841$	−13.7211	−0.473142
$842$	23.1127	0.796517
$843$	39.0906	1.34635
$844$	−37.9165	−1.30514
$845$	−28.9602	−0.996262
$846$	77.5405	2.66590
$847$	12.5649	0.431737
$848$	−20.9497	−0.719416
$849$	61.0217	2.09426
$850$	71.7189	2.45994
$851$	−1.62087	−0.0555629
$852$	161.166	5.52146
$853$	24.6901	0.845371	0.422686	−	0.906276i	$-0.361087\pi$
$853$	24.6901	0.845371	0.422686	+	0.906276i	$0.361087\pi$
$854$	−23.0918	−0.790185
$855$	−64.0181	−2.18937
$856$	9.69552	0.331386
$857$	−20.0248	−0.684033	−0.342017	−	0.939694i	$-0.611110\pi$
$857$	−20.0248	−0.684033	−0.342017	+	0.939694i	$0.611110\pi$
$858$	−33.5509	−1.14541
$859$	29.3124	1.00013	0.500064	−	0.865989i	$-0.333310\pi$
$859$	29.3124	1.00013	0.500064	+	0.865989i	$0.333310\pi$
$860$	−88.9663	−3.03373
$861$	−5.28508	−0.180115
$862$	92.7766	3.15998
$863$	26.3146	0.895759	0.447879	−	0.894094i	$-0.352179\pi$
$863$	26.3146	0.895759	0.447879	+	0.894094i	$0.352179\pi$
$864$	−20.8874	−0.710603
$865$	−10.9500	−0.372310
$866$	−1.28653	−0.0437181
$867$	58.1897	1.97623
$868$	80.6595	2.73776
$869$	−0.296374	−0.0100538
$870$	94.7298	3.21164
$871$	−21.0894	−0.714589
$872$	−59.5429	−2.01638
$873$	70.6803	2.39217
$874$	12.3228	0.416824
$875$	1.12119	0.0379031
$876$	44.9569	1.51895
$877$	−47.1631	−1.59258	−0.796292	−	0.604912i	$-0.793208\pi$
$877$	−47.1631	−1.59258	−0.796292	+	0.604912i	$0.793208\pi$
$878$	−20.7955	−0.701815
$879$	−5.58648	−0.188427
$880$	−35.6890	−1.20308
$881$	41.6975	1.40482	0.702412	−	0.711770i	$-0.252106\pi$
$881$	41.6975	1.40482	0.702412	+	0.711770i	$0.252106\pi$
$882$	43.2107	1.45498
$883$	28.2735	0.951478	0.475739	−	0.879587i	$-0.342181\pi$
$883$	28.2735	0.951478	0.475739	+	0.879587i	$0.342181\pi$
$884$	48.4071	1.62811
$885$	−12.5789	−0.422834
$886$	43.9484	1.47648
$887$	15.8651	0.532697	0.266348	−	0.963877i	$-0.414183\pi$
$887$	15.8651	0.532697	0.266348	+	0.963877i	$0.414183\pi$
$888$	16.8210	0.564475
$889$	−7.24623	−0.243031
$890$	75.7512	2.53919
$891$	−34.7450	−1.16400
$892$	−28.7217	−0.961672
$893$	14.3001	0.478533
$894$	13.6243	0.455664
$895$	−35.1619	−1.17533
$896$	−37.0130	−1.23652
$897$	−9.77976	−0.326537
$898$	46.5992	1.55504
$899$	36.0123	1.20108
$900$	134.617	4.48724
$901$	24.6070	0.819776
$902$	4.50686	0.150062
$903$	44.3094	1.47452
$904$	3.23530	0.107604
$905$	−82.4943	−2.74220
$906$	−1.80135	−0.0598458
$907$	−1.97517	−0.0655845	−0.0327922	−	0.999462i	$-0.510440\pi$
$907$	−1.97517	−0.0655845	−0.0327922	+	0.999462i	$0.510440\pi$
$908$	−74.9023	−2.48572
$909$	−7.09285	−0.235255
$910$	−31.6855	−1.05036
$911$	18.0308	0.597387	0.298694	−	0.954349i	$-0.403449\pi$
$911$	18.0308	0.597387	0.298694	+	0.954349i	$0.403449\pi$
$912$	−48.4089	−1.60298
$913$	29.8556	0.988076
$914$	−50.4797	−1.66972
$915$	−43.2219	−1.42887
$916$	51.0879	1.68799
$917$	−34.5802	−1.14194
$918$	169.742	5.60233
$919$	28.5155	0.940638	0.470319	−	0.882496i	$-0.344139\pi$
$919$	28.5155	0.940638	0.470319	+	0.882496i	$0.344139\pi$
$920$	−27.4817	−0.906046
$921$	32.6798	1.07684
$922$	14.8715	0.489768
$923$	−24.0682	−0.792214
$924$	60.9312	2.00449
$925$	−4.82942	−0.158790
$926$	−70.7467	−2.32488
$927$	−48.3938	−1.58946
$928$	7.14296	0.234479
$929$	−55.5021	−1.82097	−0.910483	−	0.413546i	$-0.864290\pi$
$929$	−55.5021	−1.82097	−0.910483	+	0.413546i	$0.864290\pi$
$930$	223.278	7.32156
$931$	7.96895	0.261172
$932$	−106.721	−3.49575
$933$	15.2110	0.497986
$934$	−12.7174	−0.416128
$935$	41.9194	1.37091
$936$	70.0207	2.28870
$937$	18.9440	0.618875	0.309437	−	0.950920i	$-0.399859\pi$
$937$	18.9440	0.618875	0.309437	+	0.950920i	$0.399859\pi$
$938$	56.6429	1.84946
$939$	31.3798	1.02404
$940$	−61.2023	−1.99620
$941$	54.0563	1.76218	0.881092	−	0.472944i	$-0.156809\pi$
$941$	54.0563	1.76218	0.881092	+	0.472944i	$0.156809\pi$
$942$	−92.5893	−3.01672
$943$	1.31371	0.0427802
$944$	−6.56235	−0.213586
$945$	−75.1273	−2.44389
$946$	−37.7849	−1.22849
$947$	2.07394	0.0673941	0.0336971	−	0.999432i	$-0.489272\pi$
$947$	2.07394	0.0673941	0.0336971	+	0.999432i	$0.489272\pi$
$948$	1.72052	0.0558800
$949$	−6.71376	−0.217938
$950$	36.7159	1.19122
$951$	52.6392	1.70694
$952$	−67.7479	−2.19572
$953$	−3.26467	−0.105753	−0.0528766	−	0.998601i	$-0.516839\pi$
$953$	−3.26467	−0.105753	−0.0528766	+	0.998601i	$0.516839\pi$
$954$	68.3075	2.21154
$955$	35.4426	1.14690
$956$	71.1907	2.30247
$957$	27.2041	0.879384
$958$	34.7797	1.12368
$959$	−23.2878	−0.752004
$960$	−54.9373	−1.77310
$961$	53.8807	1.73809
$962$	−4.82075	−0.155427
$963$	−11.9668	−0.385623
$964$	16.6816	0.537278
$965$	−55.4083	−1.78366
$966$	26.2669	0.845123
$967$	−1.67516	−0.0538694	−0.0269347	−	0.999637i	$-0.508575\pi$
$967$	−1.67516	−0.0538694	−0.0269347	+	0.999637i	$0.508575\pi$
$968$	32.4123	1.04177
$969$	56.8598	1.82660
$970$	−82.5053	−2.64909
$971$	−44.4968	−1.42797	−0.713986	−	0.700160i	$-0.753112\pi$
$971$	−44.4968	−1.42797	−0.713986	+	0.700160i	$0.753112\pi$
$972$	58.5041	1.87652
$973$	−37.1980	−1.19251
$974$	−15.7354	−0.504193
$975$	−29.1389	−0.933193
$976$	−22.5487	−0.721767
$977$	−35.1297	−1.12390	−0.561949	−	0.827172i	$-0.689948\pi$
$977$	−35.1297	−1.12390	−0.561949	+	0.827172i	$0.689948\pi$
$978$	7.72995	0.247177
$979$	21.7539	0.695259
$980$	−34.1060	−1.08948
$981$	73.4913	2.34640
$982$	−78.5109	−2.50538
$983$	−4.66517	−0.148796	−0.0743979	−	0.997229i	$-0.523703\pi$
$983$	−4.66517	−0.148796	−0.0743979	+	0.997229i	$0.523703\pi$
$984$	−13.6333	−0.434613
$985$	−45.1943	−1.44001
$986$	−58.0477	−1.84861
$987$	30.4816	0.970240
$988$	24.7816	0.788408
$989$	−11.0139	−0.350223
$990$	116.366	3.69835
$991$	−13.4790	−0.428176	−0.214088	−	0.976814i	$-0.568678\pi$
$991$	−13.4790	−0.428176	−0.214088	+	0.976814i	$0.568678\pi$
$992$	16.8359	0.534541
$993$	28.4955	0.904276
$994$	64.6433	2.05036
$995$	−61.0545	−1.93556
$996$	−173.319	−5.49183
$997$	54.7003	1.73238	0.866188	−	0.499718i	$-0.166563\pi$
$997$	54.7003	1.73238	0.866188	+	0.499718i	$0.166563\pi$
$998$	75.3520	2.38522
$999$	−11.4301	−0.361634

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.c.1.9	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.c.1.9	✓	110	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.48517 q^{2} +3.11043 q^{3} +4.17608 q^{4} +3.13519 q^{5} -7.72995 q^{6} -2.09644 q^{7} -5.40793 q^{8} +6.67478 q^{9} +O(q^{10})\)	\(q-2.48517 q^{2} +3.11043 q^{3} +4.17608 q^{4} +3.13519 q^{5} -7.72995 q^{6} -2.09644 q^{7} -5.40793 q^{8} +6.67478 q^{9} -7.79149 q^{10} -2.23753 q^{11} +12.9894 q^{12} -1.93981 q^{13} +5.21001 q^{14} +9.75179 q^{15} +5.08748 q^{16} -5.97561 q^{17} -16.5880 q^{18} -3.05916 q^{19} +13.0928 q^{20} -6.52083 q^{21} +5.56064 q^{22} +1.62087 q^{23} -16.8210 q^{24} +4.82942 q^{25} +4.82075 q^{26} +11.4301 q^{27} -8.75489 q^{28} -3.90882 q^{29} -24.2349 q^{30} -9.21307 q^{31} -1.82739 q^{32} -6.95967 q^{33} +14.8504 q^{34} -6.57273 q^{35} +27.8744 q^{36} -1.00000 q^{37} +7.60254 q^{38} -6.03363 q^{39} -16.9549 q^{40} +0.810493 q^{41} +16.2054 q^{42} -6.79506 q^{43} -9.34409 q^{44} +20.9267 q^{45} -4.02815 q^{46} -4.67450 q^{47} +15.8242 q^{48} -2.60495 q^{49} -12.0019 q^{50} -18.5867 q^{51} -8.10078 q^{52} -4.11790 q^{53} -28.4059 q^{54} -7.01507 q^{55} +11.3374 q^{56} -9.51531 q^{57} +9.71410 q^{58} -1.28990 q^{59} +40.7242 q^{60} -4.43220 q^{61} +22.8961 q^{62} -13.9933 q^{63} -5.63356 q^{64} -6.08166 q^{65} +17.2960 q^{66} +10.8719 q^{67} -24.9546 q^{68} +5.04162 q^{69} +16.3344 q^{70} +12.4075 q^{71} -36.0967 q^{72} +3.46105 q^{73} +2.48517 q^{74} +15.0216 q^{75} -12.7753 q^{76} +4.69084 q^{77} +14.9946 q^{78} +0.132456 q^{79} +15.9502 q^{80} +15.5283 q^{81} -2.01421 q^{82} -13.3431 q^{83} -27.2315 q^{84} -18.7347 q^{85} +16.8869 q^{86} -12.1581 q^{87} +12.1004 q^{88} -9.72231 q^{89} -52.0064 q^{90} +4.06668 q^{91} +6.76890 q^{92} -28.6566 q^{93} +11.6169 q^{94} -9.59105 q^{95} -5.68398 q^{96} +10.5892 q^{97} +6.47374 q^{98} -14.9350 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9}+O(q^{10}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9} - 17 q^{10} - 9 q^{11} - 21 q^{13} - 29 q^{14} - 23 q^{15} + 79 q^{16} - 76 q^{17} - 31 q^{18} - 27 q^{19} - 67 q^{20} - 30 q^{21} - 28 q^{22} - 32 q^{23} - 63 q^{24} + 66 q^{25} - 55 q^{26} - 4 q^{28} - 81 q^{29} - 48 q^{30} - 30 q^{31} - 73 q^{32} - 53 q^{33} - 23 q^{34} - 78 q^{35} + 7 q^{36} - 110 q^{37} - 50 q^{38} - 64 q^{39} - 37 q^{40} - 123 q^{41} - 63 q^{42} - 40 q^{43} - 31 q^{44} - 73 q^{45} + 16 q^{46} - 37 q^{47} - 29 q^{48} + 46 q^{49} - 58 q^{50} - 73 q^{51} - 39 q^{52} - 16 q^{53} - 53 q^{54} - 59 q^{55} - 113 q^{56} - 39 q^{57} + 11 q^{58} - 93 q^{59} - 18 q^{60} - 66 q^{61} - 40 q^{62} - 21 q^{63} + 23 q^{64} - 92 q^{65} - 31 q^{66} + q^{67} - 121 q^{68} - 80 q^{69} - 3 q^{70} - 75 q^{71} - 114 q^{72} - 39 q^{73} + 9 q^{74} - 25 q^{75} - 58 q^{76} - 31 q^{77} + 68 q^{78} - 36 q^{79} - 82 q^{80} - 50 q^{81} - 18 q^{82} - 57 q^{83} - 9 q^{84} - 14 q^{85} - 58 q^{86} - 58 q^{87} - 15 q^{88} - 181 q^{89} + 8 q^{90} - 55 q^{91} - 116 q^{92} - 86 q^{93} - 39 q^{94} - 70 q^{95} - 127 q^{96} - 91 q^{97} - 19 q^{98} - 21 q^{99}+O(q^{100}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9 - 17 * q^10 - 9 * q^11 - 21 * q^13 - 29 * q^14 - 23 * q^15 + 79 * q^16 - 76 * q^17 - 31 * q^18 - 27 * q^19 - 67 * q^20 - 30 * q^21 - 28 * q^22 - 32 * q^23 - 63 * q^24 + 66 * q^25 - 55 * q^26 - 4 * q^28 - 81 * q^29 - 48 * q^30 - 30 * q^31 - 73 * q^32 - 53 * q^33 - 23 * q^34 - 78 * q^35 + 7 * q^36 - 110 * q^37 - 50 * q^38 - 64 * q^39 - 37 * q^40 - 123 * q^41 - 63 * q^42 - 40 * q^43 - 31 * q^44 - 73 * q^45 + 16 * q^46 - 37 * q^47 - 29 * q^48 + 46 * q^49 - 58 * q^50 - 73 * q^51 - 39 * q^52 - 16 * q^53 - 53 * q^54 - 59 * q^55 - 113 * q^56 - 39 * q^57 + 11 * q^58 - 93 * q^59 - 18 * q^60 - 66 * q^61 - 40 * q^62 - 21 * q^63 + 23 * q^64 - 92 * q^65 - 31 * q^66 + q^67 - 121 * q^68 - 80 * q^69 - 3 * q^70 - 75 * q^71 - 114 * q^72 - 39 * q^73 + 9 * q^74 - 25 * q^75 - 58 * q^76 - 31 * q^77 + 68 * q^78 - 36 * q^79 - 82 * q^80 - 50 * q^81 - 18 * q^82 - 57 * q^83 - 9 * q^84 - 14 * q^85 - 58 * q^86 - 58 * q^87 - 15 * q^88 - 181 * q^89 + 8 * q^90 - 55 * q^91 - 116 * q^92 - 86 * q^93 - 39 * q^94 - 70 * q^95 - 127 * q^96 - 91 * q^97 - 19 * q^98 - 21 * q^99

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