LMFDB - Embedded newform 6031.2.a.c.1.2

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			1.2
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)

$f(q)$	$=$	$q-2.77072 q^{2} +1.69880 q^{3} +5.67692 q^{4} -3.04963 q^{5} -4.70691 q^{6} +3.28914 q^{7} -10.1877 q^{8} -0.114069 q^{9} +O(q^{10})$	\(q-2.77072 q^{2} +1.69880 q^{3} +5.67692 q^{4} -3.04963 q^{5} -4.70691 q^{6} +3.28914 q^{7} -10.1877 q^{8} -0.114069 q^{9} +8.44968 q^{10} -0.672223 q^{11} +9.64396 q^{12} -3.98366 q^{13} -9.11331 q^{14} -5.18071 q^{15} +16.8735 q^{16} +3.10350 q^{17} +0.316055 q^{18} +4.16058 q^{19} -17.3125 q^{20} +5.58760 q^{21} +1.86254 q^{22} -0.955169 q^{23} -17.3069 q^{24} +4.30022 q^{25} +11.0376 q^{26} -5.29019 q^{27} +18.6722 q^{28} -2.24352 q^{29} +14.3543 q^{30} +6.14968 q^{31} -26.3765 q^{32} -1.14197 q^{33} -8.59894 q^{34} -10.0307 q^{35} -0.647562 q^{36} -1.00000 q^{37} -11.5278 q^{38} -6.76746 q^{39} +31.0687 q^{40} -3.24779 q^{41} -15.4817 q^{42} -4.95725 q^{43} -3.81615 q^{44} +0.347869 q^{45} +2.64651 q^{46} +5.02856 q^{47} +28.6648 q^{48} +3.81846 q^{49} -11.9147 q^{50} +5.27223 q^{51} -22.6149 q^{52} +3.72720 q^{53} +14.6577 q^{54} +2.05003 q^{55} -33.5089 q^{56} +7.06801 q^{57} +6.21618 q^{58} -8.16822 q^{59} -29.4105 q^{60} -4.02749 q^{61} -17.0391 q^{62} -0.375190 q^{63} +39.3349 q^{64} +12.1487 q^{65} +3.16410 q^{66} +14.9185 q^{67} +17.6183 q^{68} -1.62264 q^{69} +27.7922 q^{70} -1.56775 q^{71} +1.16211 q^{72} -15.4338 q^{73} +2.77072 q^{74} +7.30523 q^{75} +23.6193 q^{76} -2.21104 q^{77} +18.7508 q^{78} +2.63695 q^{79} -51.4580 q^{80} -8.64478 q^{81} +8.99873 q^{82} +8.61540 q^{83} +31.7204 q^{84} -9.46451 q^{85} +13.7352 q^{86} -3.81130 q^{87} +6.84842 q^{88} -7.89233 q^{89} -0.963848 q^{90} -13.1028 q^{91} -5.42241 q^{92} +10.4471 q^{93} -13.9328 q^{94} -12.6882 q^{95} -44.8085 q^{96} +1.45182 q^{97} -10.5799 q^{98} +0.0766800 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.77072	−1.95920	−0.979599	−	0.200961i	$-0.935593\pi$
$2$	−2.77072	−1.95920	−0.979599	+	0.200961i	$0.935593\pi$
$3$	1.69880	0.980804	0.490402	−	0.871496i	$-0.336850\pi$
$3$	1.69880	0.980804	0.490402	+	0.871496i	$0.336850\pi$
$4$	5.67692	2.83846
$5$	−3.04963	−1.36383	−0.681917	−	0.731429i	$-0.738854\pi$
$5$	−3.04963	−1.36383	−0.681917	+	0.731429i	$0.738854\pi$
$6$	−4.70691	−1.92159
$7$	3.28914	1.24318	0.621590	−	0.783343i	$-0.286487\pi$
$7$	3.28914	1.24318	0.621590	+	0.783343i	$0.286487\pi$
$8$	−10.1877	−3.60190
$9$	−0.114069	−0.0380231
$10$	8.44968	2.67202
$11$	−0.672223	−0.202683	−0.101341	−	0.994852i	$-0.532313\pi$
$11$	−0.672223	−0.202683	−0.101341	+	0.994852i	$0.532313\pi$
$12$	9.64396	2.78397
$13$	−3.98366	−1.10487	−0.552435	−	0.833556i	$-0.686301\pi$
$13$	−3.98366	−1.10487	−0.552435	+	0.833556i	$0.686301\pi$
$14$	−9.11331	−2.43563
$15$	−5.18071	−1.33765
$16$	16.8735	4.21839
$17$	3.10350	0.752709	0.376354	−	0.926476i	$-0.377178\pi$
$17$	3.10350	0.752709	0.376354	+	0.926476i	$0.377178\pi$
$18$	0.316055	0.0744948
$19$	4.16058	0.954504	0.477252	−	0.878767i	$-0.341633\pi$
$19$	4.16058	0.954504	0.477252	+	0.878767i	$0.341633\pi$
$20$	−17.3125	−3.87119
$21$	5.58760	1.21932
$22$	1.86254	0.397096
$23$	−0.955169	−0.199166	−0.0995832	−	0.995029i	$-0.531751\pi$
$23$	−0.955169	−0.199166	−0.0995832	+	0.995029i	$0.531751\pi$
$24$	−17.3069	−3.53276
$25$	4.30022	0.860044
$26$	11.0376	2.16466
$27$	−5.29019	−1.01810
$28$	18.6722	3.52871
$29$	−2.24352	−0.416611	−0.208306	−	0.978064i	$-0.566795\pi$
$29$	−2.24352	−0.416611	−0.208306	+	0.978064i	$0.566795\pi$
$30$	14.3543	2.62073
$31$	6.14968	1.10452	0.552258	−	0.833673i	$-0.313766\pi$
$31$	6.14968	1.10452	0.552258	+	0.833673i	$0.313766\pi$
$32$	−26.3765	−4.66275
$33$	−1.14197	−0.198792
$34$	−8.59894	−1.47471
$35$	−10.0307	−1.69549
$36$	−0.647562	−0.107927
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−11.5278	−1.87006
$39$	−6.76746	−1.08366
$40$	31.0687	4.91240
$41$	−3.24779	−0.507219	−0.253610	−	0.967307i	$-0.581618\pi$
$41$	−3.24779	−0.507219	−0.253610	+	0.967307i	$0.581618\pi$
$42$	−15.4817	−2.38888
$43$	−4.95725	−0.755973	−0.377987	−	0.925811i	$-0.623383\pi$
$43$	−4.95725	−0.755973	−0.377987	+	0.925811i	$0.623383\pi$
$44$	−3.81615	−0.575307
$45$	0.347869	0.0518572
$46$	2.64651	0.390207
$47$	5.02856	0.733491	0.366745	−	0.930321i	$-0.380472\pi$
$47$	5.02856	0.733491	0.366745	+	0.930321i	$0.380472\pi$
$48$	28.6648	4.13741
$49$	3.81846	0.545494
$50$	−11.9147	−1.68500
$51$	5.27223	0.738260
$52$	−22.6149	−3.13612
$53$	3.72720	0.511970	0.255985	−	0.966681i	$-0.417600\pi$
$53$	3.72720	0.511970	0.255985	+	0.966681i	$0.417600\pi$
$54$	14.6577	1.99465
$55$	2.05003	0.276426
$56$	−33.5089	−4.47781
$57$	7.06801	0.936181
$58$	6.21618	0.816224
$59$	−8.16822	−1.06341	−0.531706	−	0.846929i	$-0.678449\pi$
$59$	−8.16822	−1.06341	−0.531706	+	0.846929i	$0.678449\pi$
$60$	−29.4105	−3.79688
$61$	−4.02749	−0.515667	−0.257833	−	0.966189i	$-0.583009\pi$
$61$	−4.02749	−0.515667	−0.257833	+	0.966189i	$0.583009\pi$
$62$	−17.0391	−2.16397
$63$	−0.375190	−0.0472695
$64$	39.3349	4.91687
$65$	12.1487	1.50686
$66$	3.16410	0.389473
$67$	14.9185	1.82258	0.911290	−	0.411766i	$-0.135088\pi$
$67$	14.9185	1.82258	0.911290	+	0.411766i	$0.135088\pi$
$68$	17.6183	2.13653
$69$	−1.62264	−0.195343
$70$	27.7922	3.32180
$71$	−1.56775	−0.186057	−0.0930286	−	0.995663i	$-0.529655\pi$
$71$	−1.56775	−0.186057	−0.0930286	+	0.995663i	$0.529655\pi$
$72$	1.16211	0.136955
$73$	−15.4338	−1.80639	−0.903193	−	0.429234i	$-0.858783\pi$
$73$	−15.4338	−1.80639	−0.903193	+	0.429234i	$0.858783\pi$
$74$	2.77072	0.322090
$75$	7.30523	0.843535
$76$	23.6193	2.70932
$77$	−2.21104	−0.251971
$78$	18.7508	2.12311
$79$	2.63695	0.296680	0.148340	−	0.988936i	$-0.452607\pi$
$79$	2.63695	0.296680	0.148340	+	0.988936i	$0.452607\pi$
$80$	−51.4580	−5.75318
$81$	−8.64478	−0.960531
$82$	8.99873	0.993744
$83$	8.61540	0.945663	0.472831	−	0.881153i	$-0.343232\pi$
$83$	8.61540	0.945663	0.472831	+	0.881153i	$0.343232\pi$
$84$	31.7204	3.46098
$85$	−9.46451	−1.02657
$86$	13.7352	1.48110
$87$	−3.81130	−0.408614
$88$	6.84842	0.730044
$89$	−7.89233	−0.836585	−0.418293	−	0.908312i	$-0.637371\pi$
$89$	−7.89233	−0.836585	−0.418293	+	0.908312i	$0.637371\pi$
$90$	−0.963848	−0.101599
$91$	−13.1028	−1.37355
$92$	−5.42241	−0.565326
$93$	10.4471	1.08331
$94$	−13.9328	−1.43705
$95$	−12.6882	−1.30178
$96$	−44.8085	−4.57325
$97$	1.45182	0.147410	0.0737051	−	0.997280i	$-0.476518\pi$
$97$	1.45182	0.147410	0.0737051	+	0.997280i	$0.476518\pi$
$98$	−10.5799	−1.06873
$99$	0.0766800	0.00770663
$100$	24.4120	2.44120
$101$	−11.3971	−1.13406	−0.567029	−	0.823698i	$-0.691907\pi$
$101$	−11.3971	−1.13406	−0.567029	+	0.823698i	$0.691907\pi$
$102$	−14.6079	−1.44640
$103$	−13.6263	−1.34264	−0.671321	−	0.741167i	$-0.734273\pi$
$103$	−13.6263	−1.34264	−0.671321	+	0.741167i	$0.734273\pi$
$104$	40.5844	3.97963
$105$	−17.0401	−1.66294
$106$	−10.3270	−1.00305
$107$	20.5636	1.98796	0.993980	−	0.109566i	$-0.0349462\pi$
$107$	20.5636	1.98796	0.993980	+	0.109566i	$0.0349462\pi$
$108$	−30.0320	−2.88983
$109$	16.7915	1.60833	0.804167	−	0.594403i	$-0.202612\pi$
$109$	16.7915	1.60833	0.804167	+	0.594403i	$0.202612\pi$
$110$	−5.68007	−0.541573
$111$	−1.69880	−0.161243
$112$	55.4995	5.24421
$113$	6.87500	0.646746	0.323373	−	0.946272i	$-0.395183\pi$
$113$	6.87500	0.646746	0.323373	+	0.946272i	$0.395183\pi$
$114$	−19.5835	−1.83416
$115$	2.91291	0.271630
$116$	−12.7363	−1.18253
$117$	0.454413	0.0420105
$118$	22.6319	2.08343
$119$	10.2078	0.935751
$120$	52.7797	4.81810
$121$	−10.5481	−0.958920
$122$	11.1591	1.01029
$123$	−5.51735	−0.497483
$124$	34.9112	3.13512
$125$	2.13407	0.190877
$126$	1.03955	0.0926103
$127$	6.60912	0.586465	0.293232	−	0.956041i	$-0.405269\pi$
$127$	6.60912	0.586465	0.293232	+	0.956041i	$0.405269\pi$
$128$	−56.2333	−4.97037
$129$	−8.42139	−0.741462
$130$	−33.6607	−2.95223
$131$	−14.9228	−1.30381	−0.651906	−	0.758300i	$-0.726030\pi$
$131$	−14.9228	−1.30381	−0.651906	+	0.758300i	$0.726030\pi$
$132$	−6.48289	−0.564263
$133$	13.6848	1.18662
$134$	−41.3349	−3.57079
$135$	16.1331	1.38852
$136$	−31.6176	−2.71118
$137$	−2.45782	−0.209986	−0.104993	−	0.994473i	$-0.533482\pi$
$137$	−2.45782	−0.209986	−0.104993	+	0.994473i	$0.533482\pi$
$138$	4.49590	0.382716
$139$	1.90228	0.161349	0.0806746	−	0.996740i	$-0.474293\pi$
$139$	1.90228	0.161349	0.0806746	+	0.996740i	$0.474293\pi$
$140$	−56.9432	−4.81258
$141$	8.54253	0.719411
$142$	4.34379	0.364523
$143$	2.67791	0.223938
$144$	−1.92475	−0.160396
$145$	6.84190	0.568189
$146$	42.7627	3.53907
$147$	6.48681	0.535023
$148$	−5.67692	−0.466640
$149$	3.02283	0.247639	0.123820	−	0.992305i	$-0.460486\pi$
$149$	3.02283	0.247639	0.123820	+	0.992305i	$0.460486\pi$
$150$	−20.2408	−1.65265
$151$	−8.59482	−0.699436	−0.349718	−	0.936855i	$-0.613723\pi$
$151$	−8.59482	−0.699436	−0.349718	+	0.936855i	$0.613723\pi$
$152$	−42.3869	−3.43803
$153$	−0.354014	−0.0286203
$154$	6.12618	0.493661
$155$	−18.7542	−1.50638
$156$	−38.4183	−3.07592
$157$	1.98126	0.158121	0.0790607	−	0.996870i	$-0.474808\pi$
$157$	1.98126	0.158121	0.0790607	+	0.996870i	$0.474808\pi$
$158$	−7.30625	−0.581254
$159$	6.33177	0.502142
$160$	80.4385	6.35922
$161$	−3.14169	−0.247600
$162$	23.9523	1.88187
$163$	−1.00000	−0.0783260
$163$	−1.00000	−0.0783260
$164$	−18.4374	−1.43972
$165$	3.48259	0.271120
$166$	−23.8709	−1.85274
$167$	1.33497	0.103303	0.0516516	−	0.998665i	$-0.483551\pi$
$167$	1.33497	0.103303	0.0516516	+	0.998665i	$0.483551\pi$
$168$	−56.9250	−4.39186
$169$	2.86956	0.220736
$170$	26.2235	2.01125
$171$	−0.474595	−0.0362932
$172$	−28.1419	−2.14580
$173$	1.20358	0.0915067	0.0457533	−	0.998953i	$-0.485431\pi$
$173$	1.20358	0.0915067	0.0457533	+	0.998953i	$0.485431\pi$
$174$	10.5601	0.800556
$175$	14.1440	1.06919
$176$	−11.3428	−0.854994
$177$	−13.8762	−1.04300
$178$	21.8675	1.63904
$179$	−4.63223	−0.346229	−0.173115	−	0.984902i	$-0.555383\pi$
$179$	−4.63223	−0.346229	−0.173115	+	0.984902i	$0.555383\pi$
$180$	1.97482	0.147194
$181$	−24.7757	−1.84157	−0.920783	−	0.390075i	$-0.872449\pi$
$181$	−24.7757	−1.84157	−0.920783	+	0.390075i	$0.872449\pi$
$182$	36.3043	2.69106
$183$	−6.84191	−0.505768
$184$	9.73099	0.717378
$185$	3.04963	0.224213
$186$	−28.9460	−2.12243
$187$	−2.08624	−0.152561
$188$	28.5467	2.08198
$189$	−17.4002	−1.26568
$190$	35.1556	2.55045
$191$	−8.69866	−0.629413	−0.314706	−	0.949189i	$-0.601906\pi$
$191$	−8.69866	−0.629413	−0.314706	+	0.949189i	$0.601906\pi$
$192$	66.8223	4.82248
$193$	−19.2559	−1.38607	−0.693035	−	0.720904i	$-0.743727\pi$
$193$	−19.2559	−1.38607	−0.693035	+	0.720904i	$0.743727\pi$
$194$	−4.02260	−0.288806
$195$	20.6382	1.47793
$196$	21.6771	1.54836
$197$	0.440282	0.0313688	0.0156844	−	0.999877i	$-0.495007\pi$
$197$	0.440282	0.0313688	0.0156844	+	0.999877i	$0.495007\pi$
$198$	−0.212459	−0.0150988
$199$	3.42287	0.242641	0.121321	−	0.992613i	$-0.461287\pi$
$199$	3.42287	0.242641	0.121321	+	0.992613i	$0.461287\pi$
$200$	−43.8095	−3.09780
$201$	25.3435	1.78759
$202$	31.5783	2.22184
$203$	−7.37926	−0.517923
$204$	29.9300	2.09552
$205$	9.90454	0.691763
$206$	37.7548	2.63050
$207$	0.108955	0.00757292
$208$	−67.2185	−4.66076
$209$	−2.79684	−0.193461
$210$	47.2134	3.25804
$211$	15.0864	1.03859	0.519296	−	0.854594i	$-0.326194\pi$
$211$	15.0864	1.03859	0.519296	+	0.854594i	$0.326194\pi$
$212$	21.1590	1.45320
$213$	−2.66329	−0.182486
$214$	−56.9761	−3.89481
$215$	15.1178	1.03102
$216$	53.8950	3.66709
$217$	20.2272	1.37311
$218$	−46.5246	−3.15105
$219$	−26.2189	−1.77171
$220$	11.6378	0.784623
$221$	−12.3633	−0.831644
$222$	4.70691	0.315907
$223$	−26.3334	−1.76342	−0.881709	−	0.471794i	$-0.843607\pi$
$223$	−26.3334	−1.76342	−0.881709	+	0.471794i	$0.843607\pi$
$224$	−86.7561	−5.79663
$225$	−0.490523	−0.0327015
$226$	−19.0487	−1.26710
$227$	−24.9511	−1.65606	−0.828030	−	0.560684i	$-0.810538\pi$
$227$	−24.9511	−1.65606	−0.828030	+	0.560684i	$0.810538\pi$
$228$	40.1245	2.65731
$229$	0.264165	0.0174565	0.00872824	−	0.999962i	$-0.497222\pi$
$229$	0.264165	0.0174565	0.00872824	+	0.999962i	$0.497222\pi$
$230$	−8.07086	−0.532177
$231$	−3.75612	−0.247134
$232$	22.8564	1.50059
$233$	11.9232	0.781115	0.390558	−	0.920578i	$-0.372282\pi$
$233$	11.9232	0.781115	0.390558	+	0.920578i	$0.372282\pi$
$234$	−1.25905	−0.0823070
$235$	−15.3352	−1.00036
$236$	−46.3703	−3.01845
$237$	4.47965	0.290985
$238$	−28.2831	−1.83332
$239$	12.3691	0.800091	0.400045	−	0.916495i	$-0.368994\pi$
$239$	12.3691	0.800091	0.400045	+	0.916495i	$0.368994\pi$
$240$	−87.4170	−5.64274
$241$	−27.4260	−1.76667	−0.883333	−	0.468747i	$-0.844706\pi$
$241$	−27.4260	−1.76667	−0.883333	+	0.468747i	$0.844706\pi$
$242$	29.2259	1.87871
$243$	1.18479	0.0760044
$244$	−22.8637	−1.46370
$245$	−11.6449	−0.743963
$246$	15.2871	0.974668
$247$	−16.5744	−1.05460
$248$	−62.6513	−3.97836
$249$	14.6359	0.927510
$250$	−5.91291	−0.373965
$251$	0.194377	0.0122690	0.00613449	−	0.999981i	$-0.498047\pi$
$251$	0.194377	0.0122690	0.00613449	+	0.999981i	$0.498047\pi$
$252$	−2.12992	−0.134172
$253$	0.642086	0.0403676
$254$	−18.3121	−1.14900
$255$	−16.0783	−1.00686
$256$	77.1371	4.82107
$257$	−17.4674	−1.08959	−0.544793	−	0.838571i	$-0.683392\pi$
$257$	−17.4674	−1.08959	−0.544793	+	0.838571i	$0.683392\pi$
$258$	23.3333	1.45267
$259$	−3.28914	−0.204377
$260$	68.9670	4.27715
$261$	0.255917	0.0158409
$262$	41.3470	2.55443
$263$	−11.3281	−0.698523	−0.349261	−	0.937025i	$-0.613567\pi$
$263$	−11.3281	−0.698523	−0.349261	+	0.937025i	$0.613567\pi$
$264$	11.6341	0.716030
$265$	−11.3666	−0.698242
$266$	−37.9167	−2.32482
$267$	−13.4075	−0.820526
$268$	84.6908	5.17332
$269$	5.67713	0.346141	0.173070	−	0.984909i	$-0.444631\pi$
$269$	5.67713	0.346141	0.173070	+	0.984909i	$0.444631\pi$
$270$	−44.7004	−2.72038
$271$	−17.0553	−1.03604	−0.518018	−	0.855370i	$-0.673330\pi$
$271$	−17.0553	−1.03604	−0.518018	+	0.855370i	$0.673330\pi$
$272$	52.3670	3.17522
$273$	−22.2591	−1.34718
$274$	6.80994	0.411403
$275$	−2.89071	−0.174316
$276$	−9.21161	−0.554474
$277$	−32.2872	−1.93995	−0.969975	−	0.243207i	$-0.921801\pi$
$277$	−32.2872	−1.93995	−0.969975	+	0.243207i	$0.921801\pi$
$278$	−5.27069	−0.316115
$279$	−0.701490	−0.0419971
$280$	102.190	6.10699
$281$	3.78962	0.226070	0.113035	−	0.993591i	$-0.463943\pi$
$281$	3.78962	0.226070	0.113035	+	0.993591i	$0.463943\pi$
$282$	−23.6690	−1.40947
$283$	22.7774	1.35398	0.676989	−	0.735993i	$-0.263284\pi$
$283$	22.7774	1.35398	0.676989	+	0.735993i	$0.263284\pi$
$284$	−8.89996	−0.528115
$285$	−21.5548	−1.27680
$286$	−7.41975	−0.438739
$287$	−10.6824	−0.630565
$288$	3.00875	0.177292
$289$	−7.36831	−0.433430
$290$	−18.9570	−1.11319
$291$	2.46636	0.144581
$292$	−87.6162	−5.12735
$293$	−29.6535	−1.73237	−0.866187	−	0.499720i	$-0.833436\pi$
$293$	−29.6535	−1.73237	−0.866187	+	0.499720i	$0.833436\pi$
$294$	−17.9732	−1.04822
$295$	24.9100	1.45032
$296$	10.1877	0.592149
$297$	3.55619	0.206351
$298$	−8.37542	−0.485175
$299$	3.80507	0.220053
$300$	41.4712	2.39434
$301$	−16.3051	−0.939810
$302$	23.8139	1.37033
$303$	−19.3615	−1.11229
$304$	70.2038	4.02646
$305$	12.2823	0.703284
$306$	0.980874	0.0560728
$307$	30.6019	1.74654	0.873271	−	0.487234i	$-0.161994\pi$
$307$	30.6019	1.74654	0.873271	+	0.487234i	$0.161994\pi$
$308$	−12.5519	−0.715209
$309$	−23.1484	−1.31687
$310$	51.9628	2.95129
$311$	16.0534	0.910303	0.455151	−	0.890414i	$-0.349585\pi$
$311$	16.0534	0.910303	0.455151	+	0.890414i	$0.349585\pi$
$312$	68.9450	3.90324
$313$	−12.9961	−0.734583	−0.367291	−	0.930106i	$-0.619715\pi$
$313$	−12.9961	−0.734583	−0.367291	+	0.930106i	$0.619715\pi$
$314$	−5.48952	−0.309791
$315$	1.14419	0.0644678
$316$	14.9697	0.842113
$317$	31.1698	1.75067	0.875336	−	0.483514i	$-0.160640\pi$
$317$	31.1698	1.75067	0.875336	+	0.483514i	$0.160640\pi$
$318$	−17.5436	−0.983796
$319$	1.50815	0.0844400
$320$	−119.957	−6.70579
$321$	34.9335	1.94980
$322$	8.70475	0.485097
$323$	12.9124	0.718463
$324$	−49.0757	−2.72643
$325$	−17.1306	−0.950236
$326$	2.77072	0.153456
$327$	28.5255	1.57746
$328$	33.0876	1.82696
$329$	16.5396	0.911860
$330$	−9.64931	−0.531177
$331$	2.11850	0.116443	0.0582216	−	0.998304i	$-0.481457\pi$
$331$	2.11850	0.116443	0.0582216	+	0.998304i	$0.481457\pi$
$332$	48.9089	2.68422
$333$	0.114069	0.00625096
$334$	−3.69884	−0.202391
$335$	−45.4957	−2.48570
$336$	94.2827	5.14354
$337$	15.2711	0.831870	0.415935	−	0.909394i	$-0.363454\pi$
$337$	15.2711	0.831870	0.415935	+	0.909394i	$0.363454\pi$
$338$	−7.95077	−0.432465
$339$	11.6793	0.634331
$340$	−53.7292	−2.91388
$341$	−4.13396	−0.223866
$342$	1.31497	0.0711055
$343$	−10.4645	−0.565032
$344$	50.5031	2.72294
$345$	4.94845	0.266416
$346$	−3.33480	−0.179280
$347$	−0.491541	−0.0263873	−0.0131937	−	0.999913i	$-0.504200\pi$
$347$	−0.491541	−0.0263873	−0.0131937	+	0.999913i	$0.504200\pi$
$348$	−21.6364	−1.15983
$349$	−16.4918	−0.882787	−0.441393	−	0.897314i	$-0.645516\pi$
$349$	−16.4918	−0.882787	−0.441393	+	0.897314i	$0.645516\pi$
$350$	−39.1892	−2.09475
$351$	21.0743	1.12486
$352$	17.7309	0.945060
$353$	−11.2158	−0.596959	−0.298479	−	0.954416i	$-0.596479\pi$
$353$	−11.2158	−0.596959	−0.298479	+	0.954416i	$0.596479\pi$
$354$	38.4471	2.04344
$355$	4.78104	0.253751
$356$	−44.8041	−2.37461
$357$	17.3411	0.917789
$358$	12.8346	0.678332
$359$	−4.72357	−0.249300	−0.124650	−	0.992201i	$-0.539781\pi$
$359$	−4.72357	−0.249300	−0.124650	+	0.992201i	$0.539781\pi$
$360$	−3.54399	−0.186785
$361$	−1.68954	−0.0889230
$362$	68.6468	3.60799
$363$	−17.9192	−0.940512
$364$	−74.3837	−3.89876
$365$	47.0672	2.46361
$366$	18.9570	0.990900
$367$	−1.00633	−0.0525298	−0.0262649	−	0.999655i	$-0.508361\pi$
$367$	−1.00633	−0.0525298	−0.0262649	+	0.999655i	$0.508361\pi$
$368$	−16.1171	−0.840161
$369$	0.370473	0.0192860
$370$	−8.44968	−0.439278
$371$	12.2593	0.636470
$372$	59.3073	3.07494
$373$	−36.0349	−1.86582	−0.932909	−	0.360113i	$-0.882738\pi$
$373$	−36.0349	−1.86582	−0.932909	+	0.360113i	$0.882738\pi$
$374$	5.78040	0.298897
$375$	3.62536	0.187213
$376$	−51.2296	−2.64196
$377$	8.93743	0.460301
$378$	48.2111	2.47971
$379$	−5.89175	−0.302639	−0.151320	−	0.988485i	$-0.548352\pi$
$379$	−5.89175	−0.302639	−0.151320	+	0.988485i	$0.548352\pi$
$380$	−72.0300	−3.69506
$381$	11.2276	0.575207
$382$	24.1016	1.23314
$383$	−13.1851	−0.673726	−0.336863	−	0.941554i	$-0.609366\pi$
$383$	−13.1851	−0.673726	−0.336863	+	0.941554i	$0.609366\pi$
$384$	−95.5293	−4.87496
$385$	6.74284	0.343647
$386$	53.3528	2.71558
$387$	0.565469	0.0287444
$388$	8.24188	0.418418
$389$	6.48636	0.328871	0.164436	−	0.986388i	$-0.447420\pi$
$389$	6.48636	0.328871	0.164436	+	0.986388i	$0.447420\pi$
$390$	−57.1828	−2.89556
$391$	−2.96436	−0.149914
$392$	−38.9014	−1.96482
$393$	−25.3509	−1.27878
$394$	−1.21990	−0.0614577
$395$	−8.04170	−0.404622
$396$	0.435306	0.0218749
$397$	22.4779	1.12813	0.564066	−	0.825730i	$-0.309236\pi$
$397$	22.4779	1.12813	0.564066	+	0.825730i	$0.309236\pi$
$398$	−9.48384	−0.475382
$399$	23.2477	1.16384
$400$	72.5600	3.62800
$401$	35.2167	1.75864	0.879320	−	0.476232i	$-0.157998\pi$
$401$	35.2167	1.75864	0.879320	+	0.476232i	$0.157998\pi$
$402$	−70.2199	−3.50225
$403$	−24.4983	−1.22035
$404$	−64.7006	−3.21898
$405$	26.3633	1.31001
$406$	20.4459	1.01471
$407$	0.672223	0.0333209
$408$	−53.7120	−2.65914
$409$	−2.97123	−0.146918	−0.0734588	−	0.997298i	$-0.523404\pi$
$409$	−2.97123	−0.146918	−0.0734588	+	0.997298i	$0.523404\pi$
$410$	−27.4428	−1.35530
$411$	−4.17535	−0.205955
$412$	−77.3555	−3.81103
$413$	−26.8664	−1.32201
$414$	−0.301885	−0.0148369
$415$	−26.2737	−1.28973
$416$	105.075	5.15173
$417$	3.23160	0.158252
$418$	7.74927	0.379029
$419$	−27.2517	−1.33133	−0.665667	−	0.746249i	$-0.731853\pi$
$419$	−27.2517	−1.33133	−0.665667	+	0.746249i	$0.731853\pi$
$420$	−96.7352	−4.72020
$421$	23.2305	1.13218	0.566092	−	0.824342i	$-0.308455\pi$
$421$	23.2305	1.13218	0.566092	+	0.824342i	$0.308455\pi$
$422$	−41.8003	−2.03481
$423$	−0.573604	−0.0278896
$424$	−37.9716	−1.84407
$425$	13.3457	0.647363
$426$	7.37924	0.357525
$427$	−13.2470	−0.641066
$428$	116.738	5.64274
$429$	4.54924	0.219639
$430$	−41.8871	−2.01998
$431$	−3.69872	−0.178161	−0.0890806	−	0.996024i	$-0.528393\pi$
$431$	−3.69872	−0.178161	−0.0890806	+	0.996024i	$0.528393\pi$
$432$	−89.2642	−4.29473
$433$	24.7523	1.18952	0.594761	−	0.803903i	$-0.297247\pi$
$433$	24.7523	1.18952	0.594761	+	0.803903i	$0.297247\pi$
$434$	−56.0440	−2.69020
$435$	11.6230	0.557282
$436$	95.3240	4.56519
$437$	−3.97406	−0.190105
$438$	72.6454	3.47113
$439$	3.58957	0.171321	0.0856604	−	0.996324i	$-0.472700\pi$
$439$	3.58957	0.171321	0.0856604	+	0.996324i	$0.472700\pi$
$440$	−20.8851	−0.995659
$441$	−0.435569	−0.0207414
$442$	34.2553	1.62936
$443$	4.42643	0.210306	0.105153	−	0.994456i	$-0.466467\pi$
$443$	4.42643	0.210306	0.105153	+	0.994456i	$0.466467\pi$
$444$	−9.64396	−0.457682
$445$	24.0687	1.14096
$446$	72.9627	3.45489
$447$	5.13518	0.242886
$448$	129.378	6.11255
$449$	4.58696	0.216472	0.108236	−	0.994125i	$-0.465480\pi$
$449$	4.58696	0.216472	0.108236	+	0.994125i	$0.465480\pi$
$450$	1.35910	0.0640688
$451$	2.18324	0.102805
$452$	39.0288	1.83576
$453$	−14.6009	−0.686010
$454$	69.1325	3.24455
$455$	39.9587	1.87329
$456$	−72.0069	−3.37203
$457$	21.2061	0.991980	0.495990	−	0.868328i	$-0.334805\pi$
$457$	21.2061	0.991980	0.495990	+	0.868328i	$0.334805\pi$
$458$	−0.731927	−0.0342007
$459$	−16.4181	−0.766331
$460$	16.5363	0.771010
$461$	24.8229	1.15612	0.578058	−	0.815996i	$-0.303811\pi$
$461$	24.8229	1.15612	0.578058	+	0.815996i	$0.303811\pi$
$462$	10.4072	0.484185
$463$	15.3281	0.712356	0.356178	−	0.934418i	$-0.384080\pi$
$463$	15.3281	0.712356	0.356178	+	0.934418i	$0.384080\pi$
$464$	−37.8562	−1.75743
$465$	−31.8597	−1.47746
$466$	−33.0359	−1.53036
$467$	−26.7658	−1.23857	−0.619286	−	0.785165i	$-0.712578\pi$
$467$	−26.7658	−1.23857	−0.619286	+	0.785165i	$0.712578\pi$
$468$	2.57967	0.119245
$469$	49.0689	2.26579
$470$	42.4897	1.95990
$471$	3.36576	0.155086
$472$	83.2156	3.83031
$473$	3.33238	0.153223
$474$	−12.4119	−0.570097
$475$	17.8914	0.820915
$476$	57.9491	2.65609
$477$	−0.425159	−0.0194667
$478$	−34.2714	−1.56754
$479$	5.84401	0.267020	0.133510	−	0.991047i	$-0.457375\pi$
$479$	5.84401	0.267020	0.133510	+	0.991047i	$0.457375\pi$
$480$	136.649	6.23715
$481$	3.98366	0.181639
$482$	75.9899	3.46125
$483$	−5.33710	−0.242847
$484$	−59.8808	−2.72185
$485$	−4.42752	−0.201043
$486$	−3.28273	−0.148908
$487$	−0.603512	−0.0273477	−0.0136739	−	0.999907i	$-0.504353\pi$
$487$	−0.603512	−0.0273477	−0.0136739	+	0.999907i	$0.504353\pi$
$488$	41.0309	1.85738
$489$	−1.69880	−0.0768225
$490$	32.2647	1.45757
$491$	−35.9744	−1.62350	−0.811752	−	0.584002i	$-0.801486\pi$
$491$	−35.9744	−1.62350	−0.811752	+	0.584002i	$0.801486\pi$
$492$	−31.3216	−1.41208
$493$	−6.96276	−0.313587
$494$	45.9230	2.06617
$495$	−0.233845	−0.0105106
$496$	103.767	4.65927
$497$	−5.15654	−0.231302
$498$	−40.5520	−1.81718
$499$	−5.68569	−0.254526	−0.127263	−	0.991869i	$-0.540619\pi$
$499$	−5.68569	−0.254526	−0.127263	+	0.991869i	$0.540619\pi$
$500$	12.1149	0.541795
$501$	2.26785	0.101320
$502$	−0.538566	−0.0240374
$503$	−9.55310	−0.425952	−0.212976	−	0.977057i	$-0.568316\pi$
$503$	−9.55310	−0.425952	−0.212976	+	0.977057i	$0.568316\pi$
$504$	3.82233	0.170260
$505$	34.7570	1.54667
$506$	−1.77904	−0.0790882
$507$	4.87482	0.216498
$508$	37.5194	1.66466
$509$	12.3634	0.547999	0.274000	−	0.961730i	$-0.411653\pi$
$509$	12.3634	0.547999	0.274000	+	0.961730i	$0.411653\pi$
$510$	44.5486	1.97265
$511$	−50.7639	−2.24566
$512$	−101.259	−4.47506
$513$	−22.0103	−0.971778
$514$	48.3973	2.13471
$515$	41.5552	1.83114
$516$	−47.8075	−2.10461
$517$	−3.38031	−0.148666
$518$	9.11331	0.400416
$519$	2.04465	0.0897501
$520$	−123.767	−5.42756
$521$	−28.1920	−1.23511	−0.617557	−	0.786526i	$-0.711878\pi$
$521$	−28.1920	−1.23511	−0.617557	+	0.786526i	$0.711878\pi$
$522$	−0.709075	−0.0310354
$523$	22.5337	0.985329	0.492665	−	0.870219i	$-0.336023\pi$
$523$	22.5337	0.985329	0.492665	+	0.870219i	$0.336023\pi$
$524$	−84.7155	−3.70081
$525$	24.0279	1.04866
$526$	31.3871	1.36854
$527$	19.0855	0.831378
$528$	−19.2692	−0.838582
$529$	−22.0877	−0.960333
$530$	31.4936	1.36799
$531$	0.931743	0.0404342
$532$	77.6872	3.36817
$533$	12.9381	0.560411
$534$	37.1485	1.60757
$535$	−62.7113	−2.71125
$536$	−151.985	−6.56476
$537$	−7.86925	−0.339583
$538$	−15.7298	−0.678158
$539$	−2.56686	−0.110562
$540$	91.5863	3.94124
$541$	0.353258	0.0151878	0.00759388	−	0.999971i	$-0.497583\pi$
$541$	0.353258	0.0151878	0.00759388	+	0.999971i	$0.497583\pi$
$542$	47.2555	2.02980
$543$	−42.0891	−1.80622
$544$	−81.8594	−3.50969
$545$	−51.2078	−2.19350
$546$	61.6739	2.63940
$547$	−28.8097	−1.23181	−0.615906	−	0.787820i	$-0.711210\pi$
$547$	−28.8097	−1.23181	−0.615906	+	0.787820i	$0.711210\pi$
$548$	−13.9528	−0.596035
$549$	0.459413	0.0196072
$550$	8.00935	0.341520
$551$	−9.33436	−0.397657
$552$	16.5310	0.703608
$553$	8.67329	0.368826
$554$	89.4589	3.80074
$555$	5.18071	0.219909
$556$	10.7991	0.457983
$557$	−3.43860	−0.145698	−0.0728491	−	0.997343i	$-0.523209\pi$
$557$	−3.43860	−0.145698	−0.0728491	+	0.997343i	$0.523209\pi$
$558$	1.94364	0.0822806
$559$	19.7480	0.835251
$560$	−169.253	−7.15223
$561$	−3.54411	−0.149633
$562$	−10.5000	−0.442916
$563$	−39.0678	−1.64651	−0.823255	−	0.567671i	$-0.807844\pi$
$563$	−39.0678	−1.64651	−0.823255	+	0.567671i	$0.807844\pi$
$564$	48.4952	2.04202
$565$	−20.9662	−0.882054
$566$	−63.1100	−2.65271
$567$	−28.4339	−1.19411
$568$	15.9718	0.670160
$569$	−17.8397	−0.747878	−0.373939	−	0.927453i	$-0.621993\pi$
$569$	−17.8397	−0.747878	−0.373939	+	0.927453i	$0.621993\pi$
$570$	59.7224	2.50150
$571$	20.2948	0.849310	0.424655	−	0.905355i	$-0.360395\pi$
$571$	20.2948	0.849310	0.424655	+	0.905355i	$0.360395\pi$
$572$	15.2023	0.635639
$573$	−14.7773	−0.617331
$574$	29.5981	1.23540
$575$	−4.10744	−0.171292
$576$	−4.48691	−0.186954
$577$	2.57084	0.107026	0.0535128	−	0.998567i	$-0.482958\pi$
$577$	2.57084	0.107026	0.0535128	+	0.998567i	$0.482958\pi$
$578$	20.4156	0.849175
$579$	−32.7120	−1.35946
$580$	38.8409	1.61278
$581$	28.3373	1.17563
$582$	−6.83361	−0.283262
$583$	−2.50551	−0.103767
$584$	157.235	6.50643
$585$	−1.38579	−0.0572954
$586$	82.1616	3.39406
$587$	−15.2098	−0.627777	−0.313888	−	0.949460i	$-0.601632\pi$
$587$	−15.2098	−0.627777	−0.313888	+	0.949460i	$0.601632\pi$
$588$	36.8251	1.51864
$589$	25.5863	1.05426
$590$	−69.0188	−2.84146
$591$	0.747952	0.0307666
$592$	−16.8735	−0.693498
$593$	−12.6047	−0.517614	−0.258807	−	0.965929i	$-0.583329\pi$
$593$	−12.6047	−0.517614	−0.258807	+	0.965929i	$0.583329\pi$
$594$	−9.85321	−0.404282
$595$	−31.1301	−1.27621
$596$	17.1603	0.702914
$597$	5.81479	0.237983
$598$	−10.5428	−0.431127
$599$	−18.2298	−0.744849	−0.372424	−	0.928063i	$-0.621473\pi$
$599$	−18.2298	−0.744849	−0.372424	+	0.928063i	$0.621473\pi$
$600$	−74.4236	−3.03833
$601$	−14.3058	−0.583547	−0.291774	−	0.956487i	$-0.594245\pi$
$601$	−14.3058	−0.583547	−0.291774	+	0.956487i	$0.594245\pi$
$602$	45.1769	1.84127
$603$	−1.70174	−0.0693001
$604$	−48.7921	−1.98532
$605$	32.1678	1.30781
$606$	53.6454	2.17919
$607$	−25.2827	−1.02619	−0.513096	−	0.858331i	$-0.671501\pi$
$607$	−25.2827	−1.02619	−0.513096	+	0.858331i	$0.671501\pi$
$608$	−109.742	−4.45061
$609$	−12.5359	−0.507981
$610$	−34.0310	−1.37787
$611$	−20.0321	−0.810411
$612$	−2.00971	−0.0812375
$613$	46.4144	1.87466	0.937330	−	0.348442i	$-0.113289\pi$
$613$	46.4144	1.87466	0.937330	+	0.348442i	$0.113289\pi$
$614$	−84.7895	−3.42182
$615$	16.8259	0.678484
$616$	22.5254	0.907576
$617$	−15.0546	−0.606074	−0.303037	−	0.952979i	$-0.598001\pi$
$617$	−15.0546	−0.606074	−0.303037	+	0.952979i	$0.598001\pi$
$618$	64.1380	2.58001
$619$	−15.5543	−0.625179	−0.312590	−	0.949888i	$-0.601196\pi$
$619$	−15.5543	−0.625179	−0.312590	+	0.949888i	$0.601196\pi$
$620$	−106.466	−4.27579
$621$	5.05302	0.202771
$622$	−44.4795	−1.78346
$623$	−25.9590	−1.04003
$624$	−114.191	−4.57130
$625$	−28.0092	−1.12037
$626$	36.0086	1.43919
$627$	−4.75128	−0.189748
$628$	11.2474	0.448821
$629$	−3.10350	−0.123745
$630$	−3.17023	−0.126305
$631$	−31.8843	−1.26930	−0.634648	−	0.772802i	$-0.718855\pi$
$631$	−31.8843	−1.26930	−0.634648	+	0.772802i	$0.718855\pi$
$632$	−26.8645	−1.06861
$633$	25.6289	1.01866
$634$	−86.3631	−3.42992
$635$	−20.1554	−0.799841
$636$	35.9449	1.42531
$637$	−15.2114	−0.602699
$638$	−4.17866	−0.165435
$639$	0.178832	0.00707447
$640$	171.491	6.77876
$641$	−46.0858	−1.82028	−0.910139	−	0.414302i	$-0.864026\pi$
$641$	−46.0858	−1.82028	−0.910139	+	0.414302i	$0.864026\pi$
$642$	−96.7912	−3.82004
$643$	21.8675	0.862370	0.431185	−	0.902264i	$-0.358096\pi$
$643$	21.8675	0.862370	0.431185	+	0.902264i	$0.358096\pi$
$644$	−17.8351	−0.702801
$645$	25.6821	1.01123
$646$	−35.7766	−1.40761
$647$	−5.25246	−0.206496	−0.103248	−	0.994656i	$-0.532923\pi$
$647$	−5.25246	−0.206496	−0.103248	+	0.994656i	$0.532923\pi$
$648$	88.0706	3.45974
$649$	5.49087	0.215535
$650$	47.4642	1.86170
$651$	34.3620	1.34675
$652$	−5.67692	−0.222325
$653$	38.7446	1.51619	0.758096	−	0.652143i	$-0.226130\pi$
$653$	38.7446	1.51619	0.758096	+	0.652143i	$0.226130\pi$
$654$	−79.0362	−3.09056
$655$	45.5090	1.77818
$656$	−54.8017	−2.13965
$657$	1.76052	0.0686844
$658$	−45.8268	−1.78652
$659$	−17.4145	−0.678374	−0.339187	−	0.940719i	$-0.610152\pi$
$659$	−17.4145	−0.678374	−0.339187	+	0.940719i	$0.610152\pi$
$660$	19.7704	0.769562
$661$	36.0671	1.40285	0.701423	−	0.712745i	$-0.252548\pi$
$661$	36.0671	1.40285	0.701423	+	0.712745i	$0.252548\pi$
$662$	−5.86977	−0.228135
$663$	−21.0028	−0.815680
$664$	−87.7713	−3.40619
$665$	−41.7334	−1.61835
$666$	−0.316055	−0.0122469
$667$	2.14294	0.0829750
$668$	7.57852	0.293222
$669$	−44.7353	−1.72957
$670$	126.056	4.86997
$671$	2.70737	0.104517
$672$	−147.381	−5.68536
$673$	−45.7136	−1.76213	−0.881065	−	0.472995i	$-0.843173\pi$
$673$	−45.7136	−1.76213	−0.881065	+	0.472995i	$0.843173\pi$
$674$	−42.3120	−1.62980
$675$	−22.7490	−0.875609
$676$	16.2903	0.626549
$677$	−41.8282	−1.60759	−0.803793	−	0.594909i	$-0.797188\pi$
$677$	−41.8282	−1.60759	−0.803793	+	0.594909i	$0.797188\pi$
$678$	−32.3600	−1.24278
$679$	4.77525	0.183257
$680$	96.4218	3.69761
$681$	−42.3869	−1.62427
$682$	11.4541	0.438599
$683$	−13.9358	−0.533237	−0.266619	−	0.963802i	$-0.585906\pi$
$683$	−13.9358	−0.533237	−0.266619	+	0.963802i	$0.585906\pi$
$684$	−2.69423	−0.103017
$685$	7.49543	0.286386
$686$	28.9944	1.10701
$687$	0.448763	0.0171214
$688$	−83.6463	−3.18899
$689$	−14.8479	−0.565660
$690$	−13.7108	−0.521962
$691$	−39.9781	−1.52084	−0.760419	−	0.649433i	$-0.775006\pi$
$691$	−39.9781	−1.52084	−0.760419	+	0.649433i	$0.775006\pi$
$692$	6.83264	0.259738
$693$	0.252211	0.00958072
$694$	1.36193	0.0516980
$695$	−5.80124	−0.220054
$696$	38.8285	1.47179
$697$	−10.0795	−0.381788
$698$	45.6943	1.72955
$699$	20.2552	0.766121
$700$	80.2945	3.03485
$701$	23.8673	0.901457	0.450729	−	0.892661i	$-0.351164\pi$
$701$	23.8673	0.901457	0.450729	+	0.892661i	$0.351164\pi$
$702$	−58.3912	−2.20383
$703$	−4.16058	−0.156919
$704$	−26.4418	−0.996565
$705$	−26.0515	−0.981157
$706$	31.0760	1.16956
$707$	−37.4868	−1.40984
$708$	−78.7740	−2.96051
$709$	−4.80545	−0.180472	−0.0902361	−	0.995920i	$-0.528762\pi$
$709$	−4.80545	−0.180472	−0.0902361	+	0.995920i	$0.528762\pi$
$710$	−13.2469	−0.497149
$711$	−0.300794	−0.0112807
$712$	80.4048	3.01330
$713$	−5.87398	−0.219982
$714$	−48.0474	−1.79813
$715$	−8.16662	−0.305414
$716$	−26.2968	−0.982757
$717$	21.0127	0.784732
$718$	13.0877	0.488429
$719$	−23.1402	−0.862983	−0.431492	−	0.902117i	$-0.642013\pi$
$719$	−23.1402	−0.862983	−0.431492	+	0.902117i	$0.642013\pi$
$720$	5.86978	0.218754
$721$	−44.8189	−1.66914
$722$	4.68124	0.174218
$723$	−46.5914	−1.73275
$724$	−140.650	−5.22721
$725$	−9.64764	−0.358304
$726$	49.6491	1.84265
$727$	−35.4677	−1.31542	−0.657712	−	0.753269i	$-0.728476\pi$
$727$	−35.4677	−1.31542	−0.657712	+	0.753269i	$0.728476\pi$
$728$	133.488	4.94740
$729$	27.9471	1.03508
$730$	−130.410	−4.82670
$731$	−15.3848	−0.569027
$732$	−38.8409	−1.43560
$733$	35.8550	1.32434	0.662168	−	0.749355i	$-0.269636\pi$
$733$	35.8550	1.32434	0.662168	+	0.749355i	$0.269636\pi$
$734$	2.78825	0.102916
$735$	−19.7823	−0.729683
$736$	25.1940	0.928663
$737$	−10.0285	−0.369406
$738$	−1.02648	−0.0377852
$739$	−3.04046	−0.111845	−0.0559226	−	0.998435i	$-0.517810\pi$
$739$	−3.04046	−0.111845	−0.0559226	+	0.998435i	$0.517810\pi$
$740$	17.3125	0.636419
$741$	−28.1566	−1.03436
$742$	−33.9671	−1.24697
$743$	−14.9507	−0.548488	−0.274244	−	0.961660i	$-0.588428\pi$
$743$	−14.9507	−0.548488	−0.274244	+	0.961660i	$0.588428\pi$
$744$	−106.432	−3.90199
$745$	−9.21849	−0.337739
$746$	99.8428	3.65551
$747$	−0.982752	−0.0359570
$748$	−11.8434	−0.433038
$749$	67.6366	2.47139
$750$	−10.0449	−0.366787
$751$	−14.1614	−0.516756	−0.258378	−	0.966044i	$-0.583188\pi$
$751$	−14.1614	−0.516756	−0.258378	+	0.966044i	$0.583188\pi$
$752$	84.8496	3.09415
$753$	0.330208	0.0120335
$754$	−24.7632	−0.901821
$755$	26.2110	0.953915
$756$	−98.7794	−3.59257
$757$	−24.0404	−0.873765	−0.436882	−	0.899519i	$-0.643917\pi$
$757$	−24.0404	−0.873765	−0.436882	+	0.899519i	$0.643917\pi$
$758$	16.3244	0.592930
$759$	1.09078	0.0395927
$760$	129.264	4.68890
$761$	−12.5100	−0.453486	−0.226743	−	0.973955i	$-0.572808\pi$
$761$	−12.5100	−0.453486	−0.226743	+	0.973955i	$0.572808\pi$
$762$	−31.1086	−1.12695
$763$	55.2297	1.99945
$764$	−49.3815	−1.78656
$765$	1.07961	0.0390333
$766$	36.5322	1.31996
$767$	32.5394	1.17493
$768$	131.041	4.72852
$769$	1.21034	0.0436461	0.0218231	−	0.999762i	$-0.493053\pi$
$769$	1.21034	0.0436461	0.0218231	+	0.999762i	$0.493053\pi$
$770$	−18.6825	−0.673272
$771$	−29.6736	−1.06867
$772$	−109.314	−3.93430
$773$	25.8171	0.928578	0.464289	−	0.885684i	$-0.346310\pi$
$773$	25.8171	0.928578	0.464289	+	0.885684i	$0.346310\pi$
$774$	−1.56676	−0.0563160
$775$	26.4450	0.949932
$776$	−14.7908	−0.530958
$777$	−5.58760	−0.200454
$778$	−17.9719	−0.644324
$779$	−13.5127	−0.484143
$780$	117.161	4.19505
$781$	1.05387	0.0377106
$782$	8.21343	0.293712
$783$	11.8687	0.424151
$784$	64.4309	2.30110
$785$	−6.04209	−0.215652
$786$	70.2404	2.50539
$787$	−28.3921	−1.01207	−0.506035	−	0.862513i	$-0.668889\pi$
$787$	−28.3921	−1.01207	−0.506035	+	0.862513i	$0.668889\pi$
$788$	2.49944	0.0890390
$789$	−19.2443	−0.685114
$790$	22.2813	0.792734
$791$	22.6129	0.804021
$792$	−0.781194	−0.0277585
$793$	16.0442	0.569745
$794$	−62.2800	−2.21023
$795$	−19.3095	−0.684839
$796$	19.4314	0.688726
$797$	47.1364	1.66966	0.834828	−	0.550511i	$-0.185567\pi$
$797$	47.1364	1.66966	0.834828	+	0.550511i	$0.185567\pi$
$798$	−64.4130	−2.28019
$799$	15.6061	0.552105
$800$	−113.425	−4.01017
$801$	0.900272	0.0318095
$802$	−97.5759	−3.44552
$803$	10.3749	0.366124
$804$	143.873	5.07401
$805$	9.58097	0.337685
$806$	67.8779	2.39090
$807$	9.64432	0.339496
$808$	116.111	4.08477
$809$	5.54443	0.194932	0.0974659	−	0.995239i	$-0.468926\pi$
$809$	5.54443	0.194932	0.0974659	+	0.995239i	$0.468926\pi$
$810$	−73.0456	−2.56656
$811$	0.0993061	0.00348711	0.00174355	−	0.999998i	$-0.499445\pi$
$811$	0.0993061	0.00348711	0.00174355	+	0.999998i	$0.499445\pi$
$812$	−41.8914	−1.47010
$813$	−28.9736	−1.01615
$814$	−1.86254	−0.0652822
$815$	3.04963	0.106824
$816$	88.9612	3.11426
$817$	−20.6250	−0.721579
$818$	8.23245	0.287841
$819$	1.49463	0.0522266
$820$	56.2273	1.96354
$821$	−12.5939	−0.439529	−0.219765	−	0.975553i	$-0.570529\pi$
$821$	−12.5939	−0.439529	−0.219765	+	0.975553i	$0.570529\pi$
$822$	11.5687	0.403506
$823$	−6.53132	−0.227667	−0.113834	−	0.993500i	$-0.536313\pi$
$823$	−6.53132	−0.227667	−0.113834	+	0.993500i	$0.536313\pi$
$824$	138.821	4.83607
$825$	−4.91074	−0.170970
$826$	74.4395	2.59008
$827$	−1.82608	−0.0634991	−0.0317495	−	0.999496i	$-0.510108\pi$
$827$	−1.82608	−0.0634991	−0.0317495	+	0.999496i	$0.510108\pi$
$828$	0.618531	0.0214954
$829$	−27.4185	−0.952283	−0.476142	−	0.879369i	$-0.657965\pi$
$829$	−27.4185	−0.952283	−0.476142	+	0.879369i	$0.657965\pi$
$830$	72.7973	2.52683
$831$	−54.8496	−1.90271
$832$	−156.697	−5.43249
$833$	11.8506	0.410598
$834$	−8.95386	−0.310047
$835$	−4.07116	−0.140888
$836$	−15.8774	−0.549132
$837$	−32.5330	−1.12450
$838$	75.5071	2.60835
$839$	−41.9797	−1.44930	−0.724650	−	0.689117i	$-0.757998\pi$
$839$	−41.9797	−1.44930	−0.724650	+	0.689117i	$0.757998\pi$
$840$	173.600	5.98976
$841$	−23.9666	−0.826435
$842$	−64.3653	−2.21817
$843$	6.43782	0.221730
$844$	85.6443	2.94800
$845$	−8.75110	−0.301047
$846$	1.58930	0.0546412
$847$	−34.6943	−1.19211
$848$	62.8910	2.15969
$849$	38.6944	1.32799
$850$	−36.9773	−1.26831
$851$	0.955169	0.0327428
$852$	−15.1193	−0.517978
$853$	1.88711	0.0646133	0.0323066	−	0.999478i	$-0.489715\pi$
$853$	1.88711	0.0646133	0.0323066	+	0.999478i	$0.489715\pi$
$854$	36.7037	1.25598
$855$	1.44734	0.0494979
$856$	−209.496	−7.16044
$857$	38.7048	1.32213	0.661065	−	0.750329i	$-0.270105\pi$
$857$	38.7048	1.32213	0.661065	+	0.750329i	$0.270105\pi$
$858$	−12.6047	−0.430317
$859$	30.5353	1.04185	0.520925	−	0.853602i	$-0.325587\pi$
$859$	30.5353	1.04185	0.520925	+	0.853602i	$0.325587\pi$
$860$	85.8222	2.92651
$861$	−18.1474	−0.618460
$862$	10.2481	0.349053
$863$	42.2353	1.43771	0.718854	−	0.695161i	$-0.244667\pi$
$863$	42.2353	1.43771	0.718854	+	0.695161i	$0.244667\pi$
$864$	139.537	4.74713
$865$	−3.67048	−0.124800
$866$	−68.5819	−2.33051
$867$	−12.5173	−0.425110
$868$	114.828	3.89752
$869$	−1.77262	−0.0601319
$870$	−32.2042	−1.09183
$871$	−59.4301	−2.01371
$872$	−171.067	−5.79307
$873$	−0.165608	−0.00560499
$874$	11.0110	0.372454
$875$	7.01925	0.237294
$876$	−148.843	−5.02893
$877$	22.8343	0.771058	0.385529	−	0.922696i	$-0.374019\pi$
$877$	22.8343	0.771058	0.385529	+	0.922696i	$0.374019\pi$
$878$	−9.94571	−0.335651
$879$	−50.3754	−1.69912
$880$	34.5913	1.16607
$881$	−15.9792	−0.538352	−0.269176	−	0.963091i	$-0.586751\pi$
$881$	−15.9792	−0.538352	−0.269176	+	0.963091i	$0.586751\pi$
$882$	1.20684	0.0406364
$883$	29.1921	0.982394	0.491197	−	0.871049i	$-0.336560\pi$
$883$	29.1921	0.982394	0.491197	+	0.871049i	$0.336560\pi$
$884$	−70.1853	−2.36059
$885$	42.3172	1.42248
$886$	−12.2644	−0.412032
$887$	−2.15449	−0.0723408	−0.0361704	−	0.999346i	$-0.511516\pi$
$887$	−2.15449	−0.0723408	−0.0361704	+	0.999346i	$0.511516\pi$
$888$	17.3069	0.580783
$889$	21.7383	0.729081
$890$	−66.6876	−2.23537
$891$	5.81122	0.194683
$892$	−149.493	−5.00539
$893$	20.9217	0.700120
$894$	−14.2282	−0.475862
$895$	14.1266	0.472199
$896$	−184.959	−6.17906
$897$	6.46406	0.215829
$898$	−12.7092	−0.424111
$899$	−13.7969	−0.460154
$900$	−2.78466	−0.0928219
$901$	11.5673	0.385364
$902$	−6.04915	−0.201415
$903$	−27.6991	−0.921770
$904$	−70.0406	−2.32952
$905$	75.5568	2.51159
$906$	40.4551	1.34403
$907$	−20.3130	−0.674482	−0.337241	−	0.941418i	$-0.609494\pi$
$907$	−20.3130	−0.674482	−0.337241	+	0.941418i	$0.609494\pi$
$908$	−141.645	−4.70066
$909$	1.30006	0.0431204
$910$	−110.715	−3.67016
$911$	−17.7137	−0.586882	−0.293441	−	0.955977i	$-0.594800\pi$
$911$	−17.7137	−0.586882	−0.293441	+	0.955977i	$0.594800\pi$
$912$	119.262	3.94917
$913$	−5.79147	−0.191670
$914$	−58.7563	−1.94348
$915$	20.8653	0.689784
$916$	1.49964	0.0495495
$917$	−49.0832	−1.62087
$918$	45.4900	1.50139
$919$	−19.5481	−0.644832	−0.322416	−	0.946598i	$-0.604495\pi$
$919$	−19.5481	−0.644832	−0.322416	+	0.946598i	$0.604495\pi$
$920$	−29.6759	−0.978385
$921$	51.9866	1.71302
$922$	−68.7773	−2.26506
$923$	6.24537	0.205569
$924$	−21.3232	−0.701480
$925$	−4.30022	−0.141390
$926$	−42.4699	−1.39565
$927$	1.55435	0.0510514
$928$	59.1762	1.94256
$929$	44.0322	1.44465	0.722325	−	0.691554i	$-0.243074\pi$
$929$	44.0322	1.44465	0.722325	+	0.691554i	$0.243074\pi$
$930$	88.2746	2.89464
$931$	15.8870	0.520676
$932$	67.6871	2.21716
$933$	27.2715	0.892829
$934$	74.1606	2.42661
$935$	6.36226	0.208068
$936$	−4.62944	−0.151318
$937$	1.82734	0.0596965	0.0298482	−	0.999554i	$-0.490498\pi$
$937$	1.82734	0.0596965	0.0298482	+	0.999554i	$0.490498\pi$
$938$	−135.956	−4.43914
$939$	−22.0778	−0.720482
$940$	−87.0568	−2.83948
$941$	−40.2040	−1.31061	−0.655307	−	0.755362i	$-0.727461\pi$
$941$	−40.2040	−1.31061	−0.655307	+	0.755362i	$0.727461\pi$
$942$	−9.32561	−0.303845
$943$	3.10219	0.101021
$944$	−137.827	−4.48588
$945$	53.0641	1.72617
$946$	−9.23310	−0.300194
$947$	−26.9471	−0.875663	−0.437832	−	0.899057i	$-0.644253\pi$
$947$	−26.9471	−0.875663	−0.437832	+	0.899057i	$0.644253\pi$
$948$	25.4306	0.825948
$949$	61.4829	1.99582
$950$	−49.5722	−1.60834
$951$	52.9514	1.71707
$952$	−103.995	−3.37049
$953$	−26.5644	−0.860507	−0.430253	−	0.902708i	$-0.641576\pi$
$953$	−26.5644	−0.860507	−0.430253	+	0.902708i	$0.641576\pi$
$954$	1.17800	0.0381391
$955$	26.5276	0.858414
$956$	70.2184	2.27102
$957$	2.56204	0.0828191
$958$	−16.1922	−0.523145
$959$	−8.08412	−0.261050
$960$	−203.783	−6.57707
$961$	6.81861	0.219955
$962$	−11.0376	−0.355868
$963$	−2.34568	−0.0755883
$964$	−155.695	−5.01460
$965$	58.7233	1.89037
$966$	14.7876	0.475785
$967$	44.5097	1.43134	0.715668	−	0.698440i	$-0.246122\pi$
$967$	44.5097	1.43134	0.715668	+	0.698440i	$0.246122\pi$
$968$	107.461	3.45394
$969$	21.9356	0.704671
$970$	12.2674	0.393883
$971$	−7.46724	−0.239635	−0.119818	−	0.992796i	$-0.538231\pi$
$971$	−7.46724	−0.239635	−0.119818	+	0.992796i	$0.538231\pi$
$972$	6.72596	0.215735
$973$	6.25686	0.200586
$974$	1.67216	0.0535796
$975$	−29.1016	−0.931996
$976$	−67.9580	−2.17528
$977$	44.4840	1.42317	0.711585	−	0.702600i	$-0.247978\pi$
$977$	44.4840	1.42317	0.711585	+	0.702600i	$0.247978\pi$
$978$	4.70691	0.150511
$979$	5.30540	0.169561
$980$	−66.1070	−2.11171
$981$	−1.91539	−0.0611538
$982$	99.6753	3.18077
$983$	20.6321	0.658062	0.329031	−	0.944319i	$-0.393278\pi$
$983$	20.6321	0.658062	0.329031	+	0.944319i	$0.393278\pi$
$984$	56.2093	1.79189
$985$	−1.34270	−0.0427818
$986$	19.2919	0.614379
$987$	28.0976	0.894357
$988$	−94.0913	−2.99344
$989$	4.73501	0.150564
$990$	0.647921	0.0205923
$991$	−52.0005	−1.65185	−0.825925	−	0.563780i	$-0.809347\pi$
$991$	−52.0005	−1.65185	−0.825925	+	0.563780i	$0.809347\pi$
$992$	−162.207	−5.15008
$993$	3.59891	0.114208
$994$	14.2873	0.453167
$995$	−10.4385	−0.330922
$996$	83.0866	2.63270
$997$	−35.6689	−1.12964	−0.564822	−	0.825213i	$-0.691055\pi$
$997$	−35.6689	−1.12964	−0.564822	+	0.825213i	$0.691055\pi$
$998$	15.7535	0.498667
$999$	5.29019	0.167374

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.c.1.2	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.c.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-2.77072 q^{2} +1.69880 q^{3} +5.67692 q^{4} -3.04963 q^{5} -4.70691 q^{6} +3.28914 q^{7} -10.1877 q^{8} -0.114069 q^{9} +O(q^{10})\)	\(q-2.77072 q^{2} +1.69880 q^{3} +5.67692 q^{4} -3.04963 q^{5} -4.70691 q^{6} +3.28914 q^{7} -10.1877 q^{8} -0.114069 q^{9} +8.44968 q^{10} -0.672223 q^{11} +9.64396 q^{12} -3.98366 q^{13} -9.11331 q^{14} -5.18071 q^{15} +16.8735 q^{16} +3.10350 q^{17} +0.316055 q^{18} +4.16058 q^{19} -17.3125 q^{20} +5.58760 q^{21} +1.86254 q^{22} -0.955169 q^{23} -17.3069 q^{24} +4.30022 q^{25} +11.0376 q^{26} -5.29019 q^{27} +18.6722 q^{28} -2.24352 q^{29} +14.3543 q^{30} +6.14968 q^{31} -26.3765 q^{32} -1.14197 q^{33} -8.59894 q^{34} -10.0307 q^{35} -0.647562 q^{36} -1.00000 q^{37} -11.5278 q^{38} -6.76746 q^{39} +31.0687 q^{40} -3.24779 q^{41} -15.4817 q^{42} -4.95725 q^{43} -3.81615 q^{44} +0.347869 q^{45} +2.64651 q^{46} +5.02856 q^{47} +28.6648 q^{48} +3.81846 q^{49} -11.9147 q^{50} +5.27223 q^{51} -22.6149 q^{52} +3.72720 q^{53} +14.6577 q^{54} +2.05003 q^{55} -33.5089 q^{56} +7.06801 q^{57} +6.21618 q^{58} -8.16822 q^{59} -29.4105 q^{60} -4.02749 q^{61} -17.0391 q^{62} -0.375190 q^{63} +39.3349 q^{64} +12.1487 q^{65} +3.16410 q^{66} +14.9185 q^{67} +17.6183 q^{68} -1.62264 q^{69} +27.7922 q^{70} -1.56775 q^{71} +1.16211 q^{72} -15.4338 q^{73} +2.77072 q^{74} +7.30523 q^{75} +23.6193 q^{76} -2.21104 q^{77} +18.7508 q^{78} +2.63695 q^{79} -51.4580 q^{80} -8.64478 q^{81} +8.99873 q^{82} +8.61540 q^{83} +31.7204 q^{84} -9.46451 q^{85} +13.7352 q^{86} -3.81130 q^{87} +6.84842 q^{88} -7.89233 q^{89} -0.963848 q^{90} -13.1028 q^{91} -5.42241 q^{92} +10.4471 q^{93} -13.9328 q^{94} -12.6882 q^{95} -44.8085 q^{96} +1.45182 q^{97} -10.5799 q^{98} +0.0766800 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9}+O(q^{10}) \) 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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