LMFDB - Embedded newform 6031.2.a.d.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:	$0$
Dimension:	$133$
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)

$f(q)$	$=$	$q-2.74334 q^{2} -3.12442 q^{3} +5.52594 q^{4} +0.187024 q^{5} +8.57137 q^{6} +1.31323 q^{7} -9.67287 q^{8} +6.76201 q^{9} +O(q^{10})$	\(q-2.74334 q^{2} -3.12442 q^{3} +5.52594 q^{4} +0.187024 q^{5} +8.57137 q^{6} +1.31323 q^{7} -9.67287 q^{8} +6.76201 q^{9} -0.513072 q^{10} +5.14118 q^{11} -17.2654 q^{12} -4.44283 q^{13} -3.60265 q^{14} -0.584342 q^{15} +15.4841 q^{16} +6.31653 q^{17} -18.5505 q^{18} +1.72032 q^{19} +1.03348 q^{20} -4.10309 q^{21} -14.1040 q^{22} -7.93623 q^{23} +30.2221 q^{24} -4.96502 q^{25} +12.1882 q^{26} -11.7541 q^{27} +7.25685 q^{28} +3.21436 q^{29} +1.60305 q^{30} +1.68529 q^{31} -23.1326 q^{32} -16.0632 q^{33} -17.3284 q^{34} +0.245606 q^{35} +37.3665 q^{36} -1.00000 q^{37} -4.71943 q^{38} +13.8813 q^{39} -1.80906 q^{40} -6.35020 q^{41} +11.2562 q^{42} +10.1632 q^{43} +28.4099 q^{44} +1.26466 q^{45} +21.7718 q^{46} +3.08789 q^{47} -48.3789 q^{48} -5.27542 q^{49} +13.6208 q^{50} -19.7355 q^{51} -24.5508 q^{52} -7.72684 q^{53} +32.2456 q^{54} +0.961526 q^{55} -12.7027 q^{56} -5.37500 q^{57} -8.81810 q^{58} +8.95497 q^{59} -3.22904 q^{60} -1.72140 q^{61} -4.62333 q^{62} +8.88010 q^{63} +32.4923 q^{64} -0.830917 q^{65} +44.0670 q^{66} -0.569089 q^{67} +34.9048 q^{68} +24.7961 q^{69} -0.673783 q^{70} -6.40972 q^{71} -65.4080 q^{72} -5.34288 q^{73} +2.74334 q^{74} +15.5128 q^{75} +9.50638 q^{76} +6.75157 q^{77} -38.0811 q^{78} +3.84400 q^{79} +2.89591 q^{80} +16.4388 q^{81} +17.4208 q^{82} +3.20332 q^{83} -22.6735 q^{84} +1.18134 q^{85} -27.8812 q^{86} -10.0430 q^{87} -49.7300 q^{88} +10.5600 q^{89} -3.46940 q^{90} -5.83447 q^{91} -43.8551 q^{92} -5.26555 q^{93} -8.47116 q^{94} +0.321741 q^{95} +72.2759 q^{96} +13.4093 q^{97} +14.4723 q^{98} +34.7647 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9}+O(q^{10}) $ 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9	\( 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9} + 9 q^{10} + 23 q^{11} + 24 q^{12} + 23 q^{13} + 31 q^{14} + 9 q^{15} + 168 q^{16} + 98 q^{17} + 38 q^{18} + 29 q^{19} + 83 q^{20} + 26 q^{21} + 2 q^{22} + 34 q^{23} + 75 q^{24} + 177 q^{25} + 67 q^{26} + 32 q^{27} + 32 q^{28} + 91 q^{29} + 12 q^{30} + 24 q^{31} + 88 q^{32} + 27 q^{33} + 23 q^{34} + 66 q^{35} + 232 q^{36} - 133 q^{37} + 26 q^{38} + 28 q^{39} + 41 q^{40} + 132 q^{41} + 13 q^{42} + 11 q^{43} + 65 q^{44} + 107 q^{45} + 20 q^{46} + 10 q^{47} + 27 q^{48} + 229 q^{49} + 78 q^{50} + 19 q^{51} + 71 q^{52} + 7 q^{53} + 43 q^{54} + 41 q^{55} + 67 q^{56} + 45 q^{57} + 25 q^{58} + 97 q^{59} - 42 q^{60} + 65 q^{61} + 24 q^{62} + 39 q^{63} + 200 q^{64} + 60 q^{65} + 35 q^{66} + 25 q^{67} + 227 q^{68} + 120 q^{69} + 37 q^{70} + 26 q^{71} + 93 q^{72} + 55 q^{73} - 14 q^{74} + 5 q^{75} + 34 q^{76} + 21 q^{77} - 2 q^{78} + 50 q^{79} + 162 q^{80} + 341 q^{81} + 66 q^{82} + 30 q^{83} - 89 q^{84} + 30 q^{85} - 12 q^{86} + 80 q^{87} - 85 q^{88} + 225 q^{89} - 86 q^{90} + q^{91} + 82 q^{92} + 42 q^{93} - 17 q^{94} + 70 q^{95} + 55 q^{96} + 12 q^{97} + 90 q^{98} + 17 q^{99}+O(q^{100}) \) 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9 + 9 * q^10 + 23 * q^11 + 24 * q^12 + 23 * q^13 + 31 * q^14 + 9 * q^15 + 168 * q^16 + 98 * q^17 + 38 * q^18 + 29 * q^19 + 83 * q^20 + 26 * q^21 + 2 * q^22 + 34 * q^23 + 75 * q^24 + 177 * q^25 + 67 * q^26 + 32 * q^27 + 32 * q^28 + 91 * q^29 + 12 * q^30 + 24 * q^31 + 88 * q^32 + 27 * q^33 + 23 * q^34 + 66 * q^35 + 232 * q^36 - 133 * q^37 + 26 * q^38 + 28 * q^39 + 41 * q^40 + 132 * q^41 + 13 * q^42 + 11 * q^43 + 65 * q^44 + 107 * q^45 + 20 * q^46 + 10 * q^47 + 27 * q^48 + 229 * q^49 + 78 * q^50 + 19 * q^51 + 71 * q^52 + 7 * q^53 + 43 * q^54 + 41 * q^55 + 67 * q^56 + 45 * q^57 + 25 * q^58 + 97 * q^59 - 42 * q^60 + 65 * q^61 + 24 * q^62 + 39 * q^63 + 200 * q^64 + 60 * q^65 + 35 * q^66 + 25 * q^67 + 227 * q^68 + 120 * q^69 + 37 * q^70 + 26 * q^71 + 93 * q^72 + 55 * q^73 - 14 * q^74 + 5 * q^75 + 34 * q^76 + 21 * q^77 - 2 * q^78 + 50 * q^79 + 162 * q^80 + 341 * q^81 + 66 * q^82 + 30 * q^83 - 89 * q^84 + 30 * q^85 - 12 * q^86 + 80 * q^87 - 85 * q^88 + 225 * q^89 - 86 * q^90 + q^91 + 82 * q^92 + 42 * q^93 - 17 * q^94 + 70 * q^95 + 55 * q^96 + 12 * q^97 + 90 * q^98 + 17 * 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 $

$2$	−2.74334	−1.93984	−0.969919	−	0.243429i	$-0.921728\pi$
$2$	−2.74334	−1.93984	−0.969919	+	0.243429i	$0.921728\pi$
$3$	−3.12442	−1.80389	−0.901943	−	0.431855i	$-0.857859\pi$
$3$	−3.12442	−1.80389	−0.901943	+	0.431855i	$0.857859\pi$
$4$	5.52594	2.76297
$5$	0.187024	0.0836398	0.0418199	−	0.999125i	$-0.486684\pi$
$5$	0.187024	0.0836398	0.0418199	+	0.999125i	$0.486684\pi$
$6$	8.57137	3.49925
$7$	1.31323	0.496356	0.248178	−	0.968715i	$-0.420168\pi$
$7$	1.31323	0.496356	0.248178	+	0.968715i	$0.420168\pi$
$8$	−9.67287	−3.41987
$9$	6.76201	2.25400
$10$	−0.513072	−0.162248
$11$	5.14118	1.55013	0.775063	−	0.631885i	$-0.217718\pi$
$11$	5.14118	1.55013	0.775063	+	0.631885i	$0.217718\pi$
$12$	−17.2654	−4.98408
$13$	−4.44283	−1.23222	−0.616110	−	0.787660i	$-0.711292\pi$
$13$	−4.44283	−1.23222	−0.616110	+	0.787660i	$0.711292\pi$
$14$	−3.60265	−0.962849
$15$	−0.584342	−0.150877
$16$	15.4841	3.87103
$17$	6.31653	1.53198	0.765992	−	0.642851i	$-0.222248\pi$
$17$	6.31653	1.53198	0.765992	+	0.642851i	$0.222248\pi$
$18$	−18.5505	−4.37240
$19$	1.72032	0.394668	0.197334	−	0.980336i	$-0.436772\pi$
$19$	1.72032	0.394668	0.197334	+	0.980336i	$0.436772\pi$
$20$	1.03348	0.231094
$21$	−4.10309	−0.895369
$22$	−14.1040	−3.00699
$23$	−7.93623	−1.65482	−0.827410	−	0.561599i	$-0.810186\pi$
$23$	−7.93623	−1.65482	−0.827410	+	0.561599i	$0.810186\pi$
$24$	30.2221	6.16906
$25$	−4.96502	−0.993004
$26$	12.1882	2.39031
$27$	−11.7541	−2.26208
$28$	7.25685	1.37142
$29$	3.21436	0.596892	0.298446	−	0.954427i	$-0.403532\pi$
$29$	3.21436	0.596892	0.298446	+	0.954427i	$0.403532\pi$
$30$	1.60305	0.292676
$31$	1.68529	0.302687	0.151343	−	0.988481i	$-0.451640\pi$
$31$	1.68529	0.302687	0.151343	+	0.988481i	$0.451640\pi$
$32$	−23.1326	−4.08930
$33$	−16.0632	−2.79625
$34$	−17.3284	−2.97180
$35$	0.245606	0.0415151
$36$	37.3665	6.22774
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−4.71943	−0.765592
$39$	13.8813	2.22278
$40$	−1.80906	−0.286037
$41$	−6.35020	−0.991734	−0.495867	−	0.868399i	$-0.665150\pi$
$41$	−6.35020	−0.991734	−0.495867	+	0.868399i	$0.665150\pi$
$42$	11.2562	1.73687
$43$	10.1632	1.54988	0.774938	−	0.632037i	$-0.217781\pi$
$43$	10.1632	1.54988	0.774938	+	0.632037i	$0.217781\pi$
$44$	28.4099	4.28295
$45$	1.26466	0.188524
$46$	21.7718	3.21008
$47$	3.08789	0.450416	0.225208	−	0.974311i	$-0.427694\pi$
$47$	3.08789	0.450416	0.225208	+	0.974311i	$0.427694\pi$
$48$	−48.3789	−6.98290
$49$	−5.27542	−0.753631
$50$	13.6208	1.92627
$51$	−19.7355	−2.76352
$52$	−24.5508	−3.40459
$53$	−7.72684	−1.06136	−0.530681	−	0.847571i	$-0.678064\pi$
$53$	−7.72684	−1.06136	−0.530681	+	0.847571i	$0.678064\pi$
$54$	32.2456	4.38807
$55$	0.961526	0.129652
$56$	−12.7027	−1.69747
$57$	−5.37500	−0.711937
$58$	−8.81810	−1.15787
$59$	8.95497	1.16584	0.582919	−	0.812530i	$-0.301911\pi$
$59$	8.95497	1.16584	0.582919	+	0.812530i	$0.301911\pi$
$60$	−3.22904	−0.416867
$61$	−1.72140	−0.220402	−0.110201	−	0.993909i	$-0.535150\pi$
$61$	−1.72140	−0.220402	−0.110201	+	0.993909i	$0.535150\pi$
$62$	−4.62333	−0.587163
$63$	8.88010	1.11879
$64$	32.4923	4.06154
$65$	−0.830917	−0.103063
$66$	44.0670	5.42427
$67$	−0.569089	−0.0695253	−0.0347626	−	0.999396i	$-0.511068\pi$
$67$	−0.569089	−0.0695253	−0.0347626	+	0.999396i	$0.511068\pi$
$68$	34.9048	4.23282
$69$	24.7961	2.98511
$70$	−0.673783	−0.0805325
$71$	−6.40972	−0.760693	−0.380347	−	0.924844i	$-0.624195\pi$
$71$	−6.40972	−0.760693	−0.380347	+	0.924844i	$0.624195\pi$
$72$	−65.4080	−7.70841
$73$	−5.34288	−0.625337	−0.312669	−	0.949862i	$-0.601223\pi$
$73$	−5.34288	−0.625337	−0.312669	+	0.949862i	$0.601223\pi$
$74$	2.74334	0.318907
$75$	15.5128	1.79127
$76$	9.50638	1.09046
$77$	6.75157	0.769413
$78$	−38.0811	−4.31184
$79$	3.84400	0.432483	0.216242	−	0.976340i	$-0.430620\pi$
$79$	3.84400	0.432483	0.216242	+	0.976340i	$0.430620\pi$
$80$	2.89591	0.323772
$81$	16.4388	1.82653
$82$	17.4208	1.92380
$83$	3.20332	0.351610	0.175805	−	0.984425i	$-0.443747\pi$
$83$	3.20332	0.351610	0.175805	+	0.984425i	$0.443747\pi$
$84$	−22.6735	−2.47388
$85$	1.18134	0.128135
$86$	−27.8812	−3.00651
$87$	−10.0430	−1.07672
$88$	−49.7300	−5.30123
$89$	10.5600	1.11936	0.559681	−	0.828708i	$-0.310924\pi$
$89$	10.5600	1.11936	0.559681	+	0.828708i	$0.310924\pi$
$90$	−3.46940	−0.365707
$91$	−5.83447	−0.611619
$92$	−43.8551	−4.57222
$93$	−5.26555	−0.546012
$94$	−8.47116	−0.873733
$95$	0.321741	0.0330100
$96$	72.2759	7.37663
$97$	13.4093	1.36151	0.680755	−	0.732511i	$-0.261652\pi$
$97$	13.4093	1.36151	0.680755	+	0.732511i	$0.261652\pi$
$98$	14.4723	1.46192
$99$	34.7647	3.49399
$100$	−27.4364	−2.74364
$101$	16.6508	1.65682	0.828410	−	0.560122i	$-0.189246\pi$
$101$	16.6508	1.65682	0.828410	+	0.560122i	$0.189246\pi$
$102$	54.1413	5.36079
$103$	3.45034	0.339972	0.169986	−	0.985446i	$-0.445628\pi$
$103$	3.45034	0.339972	0.169986	+	0.985446i	$0.445628\pi$
$104$	42.9749	4.21404
$105$	−0.767378	−0.0748884
$106$	21.1974	2.05887
$107$	15.5620	1.50444	0.752219	−	0.658914i	$-0.228984\pi$
$107$	15.5620	1.50444	0.752219	+	0.658914i	$0.228984\pi$
$108$	−64.9525	−6.25006
$109$	−9.61585	−0.921031	−0.460515	−	0.887652i	$-0.652335\pi$
$109$	−9.61585	−0.921031	−0.460515	+	0.887652i	$0.652335\pi$
$110$	−2.63780	−0.251504
$111$	3.12442	0.296557
$112$	20.3343	1.92141
$113$	17.0316	1.60220	0.801101	−	0.598530i	$-0.204248\pi$
$113$	17.0316	1.60220	0.801101	+	0.598530i	$0.204248\pi$
$114$	14.7455	1.38104
$115$	−1.48427	−0.138409
$116$	17.7624	1.64919
$117$	−30.0425	−2.77743
$118$	−24.5666	−2.26154
$119$	8.29508	0.760408
$120$	5.65227	0.515979
$121$	15.4318	1.40289
$122$	4.72239	0.427545
$123$	19.8407	1.78897
$124$	9.31280	0.836315
$125$	−1.86370	−0.166694
$126$	−24.3612	−2.17027
$127$	−16.6391	−1.47648	−0.738241	−	0.674537i	$-0.764343\pi$
$127$	−16.6391	−1.47648	−0.738241	+	0.674537i	$0.764343\pi$
$128$	−42.8725	−3.78943
$129$	−31.7542	−2.79580
$130$	2.27949	0.199925
$131$	−11.7476	−1.02639	−0.513195	−	0.858272i	$-0.671538\pi$
$131$	−11.7476	−1.02639	−0.513195	+	0.858272i	$0.671538\pi$
$132$	−88.7644	−7.72595
$133$	2.25918	0.195896
$134$	1.56121	0.134868
$135$	−2.19830	−0.189200
$136$	−61.0989	−5.23919
$137$	17.0461	1.45634	0.728172	−	0.685394i	$-0.240370\pi$
$137$	17.0461	1.45634	0.728172	+	0.685394i	$0.240370\pi$
$138$	−68.0244	−5.79062
$139$	−15.7657	−1.33723	−0.668614	−	0.743610i	$-0.733112\pi$
$139$	−15.7657	−1.33723	−0.668614	+	0.743610i	$0.733112\pi$
$140$	1.35721	0.114705
$141$	−9.64789	−0.812499
$142$	17.5841	1.47562
$143$	−22.8414	−1.91009
$144$	104.704	8.72532
$145$	0.601163	0.0499239
$146$	14.6574	1.21305
$147$	16.4826	1.35946
$148$	−5.52594	−0.454229
$149$	4.61167	0.377803	0.188901	−	0.981996i	$-0.439507\pi$
$149$	4.61167	0.377803	0.188901	+	0.981996i	$0.439507\pi$
$150$	−42.5570	−3.47477
$151$	−0.204830	−0.0166688	−0.00833442	−	0.999965i	$-0.502653\pi$
$151$	−0.204830	−0.0166688	−0.00833442	+	0.999965i	$0.502653\pi$
$152$	−16.6404	−1.34972
$153$	42.7124	3.45310
$154$	−18.5219	−1.49254
$155$	0.315190	0.0253167
$156$	76.7071	6.14148
$157$	4.57964	0.365495	0.182747	−	0.983160i	$-0.441501\pi$
$157$	4.57964	0.365495	0.182747	+	0.983160i	$0.441501\pi$
$158$	−10.5454	−0.838948
$159$	24.1419	1.91458
$160$	−4.32635	−0.342028
$161$	−10.4221	−0.821379
$162$	−45.0972	−3.54317
$163$	1.00000	0.0783260
$163$	1.00000	0.0783260
$164$	−35.0908	−2.74013
$165$	−3.00421	−0.233878
$166$	−8.78780	−0.682065
$167$	2.94714	0.228057	0.114028	−	0.993477i	$-0.463625\pi$
$167$	2.94714	0.228057	0.114028	+	0.993477i	$0.463625\pi$
$168$	39.6887	3.06205
$169$	6.73875	0.518365
$170$	−3.24083	−0.248561
$171$	11.6328	0.889584
$172$	56.1613	4.28226
$173$	4.88559	0.371444	0.185722	−	0.982602i	$-0.440538\pi$
$173$	4.88559	0.371444	0.185722	+	0.982602i	$0.440538\pi$
$174$	27.5515	2.08867
$175$	−6.52023	−0.492883
$176$	79.6067	6.00058
$177$	−27.9791	−2.10304
$178$	−28.9698	−2.17138
$179$	−8.52837	−0.637440	−0.318720	−	0.947849i	$-0.603253\pi$
$179$	−8.52837	−0.637440	−0.318720	+	0.947849i	$0.603253\pi$
$180$	6.98843	0.520887
$181$	7.24762	0.538711	0.269355	−	0.963041i	$-0.413189\pi$
$181$	7.24762	0.538711	0.269355	+	0.963041i	$0.413189\pi$
$182$	16.0060	1.18644
$183$	5.37837	0.397581
$184$	76.7661	5.65927
$185$	−0.187024	−0.0137503
$186$	14.4452	1.05918
$187$	32.4744	2.37477
$188$	17.0635	1.24448
$189$	−15.4359	−1.12280
$190$	−0.882647	−0.0640340
$191$	−1.93718	−0.140169	−0.0700846	−	0.997541i	$-0.522327\pi$
$191$	−1.93718	−0.140169	−0.0700846	+	0.997541i	$0.522327\pi$
$192$	−101.520	−7.32656
$193$	10.2864	0.740431	0.370216	−	0.928946i	$-0.379284\pi$
$193$	10.2864	0.740431	0.370216	+	0.928946i	$0.379284\pi$
$194$	−36.7864	−2.64111
$195$	2.59613	0.185913
$196$	−29.1516	−2.08226
$197$	5.57318	0.397073	0.198536	−	0.980094i	$-0.436381\pi$
$197$	5.57318	0.397073	0.198536	+	0.980094i	$0.436381\pi$
$198$	−95.3717	−6.77777
$199$	−4.37210	−0.309930	−0.154965	−	0.987920i	$-0.549526\pi$
$199$	−4.37210	−0.309930	−0.154965	+	0.987920i	$0.549526\pi$
$200$	48.0260	3.39595
$201$	1.77807	0.125416
$202$	−45.6790	−3.21396
$203$	4.22120	0.296270
$204$	−109.057	−7.63553
$205$	−1.18764	−0.0829484
$206$	−9.46546	−0.659490
$207$	−53.6649	−3.72997
$208$	−68.7934	−4.76996
$209$	8.84448	0.611785
$210$	2.10518	0.145271
$211$	−9.88847	−0.680751	−0.340375	−	0.940290i	$-0.610554\pi$
$211$	−9.88847	−0.680751	−0.340375	+	0.940290i	$0.610554\pi$
$212$	−42.6980	−2.93251
$213$	20.0267	1.37220
$214$	−42.6920	−2.91836
$215$	1.90077	0.129631
$216$	113.696	7.73603
$217$	2.21318	0.150240
$218$	26.3796	1.78665
$219$	16.6934	1.12804
$220$	5.31333	0.358225
$221$	−28.0633	−1.88774
$222$	−8.57137	−0.575272
$223$	−11.3786	−0.761966	−0.380983	−	0.924582i	$-0.624414\pi$
$223$	−11.3786	−0.761966	−0.380983	+	0.924582i	$0.624414\pi$
$224$	−30.3784	−2.02975
$225$	−33.5735	−2.23824
$226$	−46.7236	−3.10801
$227$	15.8865	1.05443	0.527213	−	0.849733i	$-0.323237\pi$
$227$	15.8865	1.05443	0.527213	+	0.849733i	$0.323237\pi$
$228$	−29.7019	−1.96706
$229$	−11.1478	−0.736664	−0.368332	−	0.929694i	$-0.620071\pi$
$229$	−11.1478	−0.736664	−0.368332	+	0.929694i	$0.620071\pi$
$230$	4.07186	0.268490
$231$	−21.0948	−1.38793
$232$	−31.0921	−2.04129
$233$	26.3112	1.72370	0.861851	−	0.507162i	$-0.169306\pi$
$233$	26.3112	1.72370	0.861851	+	0.507162i	$0.169306\pi$
$234$	82.4169	5.38776
$235$	0.577511	0.0376727
$236$	49.4846	3.22117
$237$	−12.0103	−0.780151
$238$	−22.7563	−1.47507
$239$	−22.2031	−1.43620	−0.718098	−	0.695942i	$-0.754987\pi$
$239$	−22.2031	−1.43620	−0.718098	+	0.695942i	$0.754987\pi$
$240$	−9.04803	−0.584048
$241$	−6.37245	−0.410485	−0.205243	−	0.978711i	$-0.565798\pi$
$241$	−6.37245	−0.410485	−0.205243	+	0.978711i	$0.565798\pi$
$242$	−42.3346	−2.72137
$243$	−16.0993	−1.03277
$244$	−9.51234	−0.608965
$245$	−0.986631	−0.0630335
$246$	−54.4298	−3.47032
$247$	−7.64309	−0.486318
$248$	−16.3016	−1.03515
$249$	−10.0085	−0.634263
$250$	5.11277	0.323360
$251$	−19.2573	−1.21551	−0.607754	−	0.794126i	$-0.707929\pi$
$251$	−19.2573	−1.21551	−0.607754	+	0.794126i	$0.707929\pi$
$252$	49.0709	3.09118
$253$	−40.8016	−2.56518
$254$	45.6468	2.86414
$255$	−3.69102	−0.231140
$256$	52.6295	3.28934
$257$	−1.44021	−0.0898376	−0.0449188	−	0.998991i	$-0.514303\pi$
$257$	−1.44021	−0.0898376	−0.0449188	+	0.998991i	$0.514303\pi$
$258$	87.1127	5.42340
$259$	−1.31323	−0.0816003
$260$	−4.59160	−0.284759
$261$	21.7355	1.34540
$262$	32.2276	1.99103
$263$	15.5699	0.960081	0.480041	−	0.877246i	$-0.340622\pi$
$263$	15.5699	0.960081	0.480041	+	0.877246i	$0.340622\pi$
$264$	155.377	9.56282
$265$	−1.44511	−0.0887721
$266$	−6.19771	−0.380006
$267$	−32.9940	−2.01920
$268$	−3.14475	−0.192096
$269$	−1.98561	−0.121065	−0.0605324	−	0.998166i	$-0.519280\pi$
$269$	−1.98561	−0.121065	−0.0605324	+	0.998166i	$0.519280\pi$
$270$	6.03070	0.367017
$271$	−24.7064	−1.50081	−0.750404	−	0.660979i	$-0.770141\pi$
$271$	−24.7064	−1.50081	−0.750404	+	0.660979i	$0.770141\pi$
$272$	97.8059	5.93036
$273$	18.2294	1.10329
$274$	−46.7633	−2.82507
$275$	−25.5261	−1.53928
$276$	137.022	8.24775
$277$	−1.45210	−0.0872484	−0.0436242	−	0.999048i	$-0.513890\pi$
$277$	−1.45210	−0.0872484	−0.0436242	+	0.999048i	$0.513890\pi$
$278$	43.2507	2.59400
$279$	11.3959	0.682257
$280$	−2.37572	−0.141976
$281$	−18.9964	−1.13323	−0.566615	−	0.823983i	$-0.691747\pi$
$281$	−18.9964	−1.13323	−0.566615	+	0.823983i	$0.691747\pi$
$282$	26.4675	1.57612
$283$	−16.6267	−0.988357	−0.494178	−	0.869361i	$-0.664531\pi$
$283$	−16.6267	−0.988357	−0.494178	+	0.869361i	$0.664531\pi$
$284$	−35.4197	−2.10177
$285$	−1.00526	−0.0595462
$286$	62.6619	3.70527
$287$	−8.33929	−0.492253
$288$	−156.423	−9.21729
$289$	22.8985	1.34697
$290$	−1.64920	−0.0968442
$291$	−41.8964	−2.45601
$292$	−29.5244	−1.72779
$293$	−21.5092	−1.25658	−0.628290	−	0.777979i	$-0.716245\pi$
$293$	−21.5092	−1.25658	−0.628290	+	0.777979i	$0.716245\pi$
$294$	−45.2175	−2.63714
$295$	1.67480	0.0975104
$296$	9.67287	0.562224
$297$	−60.4300	−3.50651
$298$	−12.6514	−0.732876
$299$	35.2594	2.03910
$300$	85.7229	4.94921
$301$	13.3467	0.769290
$302$	0.561920	0.0323348
$303$	−52.0242	−2.98871
$304$	26.6376	1.52777
$305$	−0.321943	−0.0184344
$306$	−117.175	−6.69845
$307$	−25.3398	−1.44622	−0.723109	−	0.690734i	$-0.757288\pi$
$307$	−25.3398	−1.44622	−0.723109	+	0.690734i	$0.757288\pi$
$308$	37.3088	2.12587
$309$	−10.7803	−0.613270
$310$	−0.864674	−0.0491102
$311$	27.8545	1.57948	0.789741	−	0.613440i	$-0.210215\pi$
$311$	27.8545	1.57948	0.789741	+	0.613440i	$0.210215\pi$
$312$	−134.272	−7.60164
$313$	22.8221	1.28998	0.644989	−	0.764192i	$-0.276862\pi$
$313$	22.8221	1.28998	0.644989	+	0.764192i	$0.276862\pi$
$314$	−12.5635	−0.709001
$315$	1.66079	0.0935751
$316$	21.2417	1.19494
$317$	6.66917	0.374578	0.187289	−	0.982305i	$-0.440030\pi$
$317$	6.66917	0.374578	0.187289	+	0.982305i	$0.440030\pi$
$318$	−66.2295	−3.71397
$319$	16.5256	0.925257
$320$	6.07685	0.339706
$321$	−48.6223	−2.71383
$322$	28.5915	1.59334
$323$	10.8664	0.604625
$324$	90.8396	5.04665
$325$	22.0588	1.22360
$326$	−2.74334	−0.151940
$327$	30.0440	1.66143
$328$	61.4246	3.39161
$329$	4.05513	0.223566
$330$	8.24159	0.453684
$331$	15.1789	0.834308	0.417154	−	0.908836i	$-0.363028\pi$
$331$	15.1789	0.834308	0.417154	+	0.908836i	$0.363028\pi$
$332$	17.7013	0.971487
$333$	−6.76201	−0.370556
$334$	−8.08503	−0.442393
$335$	−0.106433	−0.00581508
$336$	−63.5328	−3.46600
$337$	−32.2415	−1.75631	−0.878153	−	0.478381i	$-0.841224\pi$
$337$	−32.2415	−1.75631	−0.878153	+	0.478381i	$0.841224\pi$
$338$	−18.4867	−1.00554
$339$	−53.2140	−2.89019
$340$	6.52803	0.354032
$341$	8.66438	0.469202
$342$	−31.9128	−1.72565
$343$	−16.1205	−0.870425
$344$	−98.3075	−5.30038
$345$	4.63748	0.249673
$346$	−13.4029	−0.720542
$347$	−34.7585	−1.86593	−0.932967	−	0.359962i	$-0.882790\pi$
$347$	−34.7585	−1.86593	−0.932967	+	0.359962i	$0.882790\pi$
$348$	−55.4971	−2.97496
$349$	34.3209	1.83716	0.918579	−	0.395238i	$-0.129338\pi$
$349$	34.3209	1.83716	0.918579	+	0.395238i	$0.129338\pi$
$350$	17.8872	0.956113
$351$	52.2215	2.78738
$352$	−118.929	−6.33892
$353$	17.2500	0.918126	0.459063	−	0.888404i	$-0.348185\pi$
$353$	17.2500	0.918126	0.459063	+	0.888404i	$0.348185\pi$
$354$	76.7563	4.07955
$355$	−1.19877	−0.0636242
$356$	58.3542	3.09276
$357$	−25.9173	−1.37169
$358$	23.3963	1.23653
$359$	19.2349	1.01518	0.507589	−	0.861599i	$-0.330537\pi$
$359$	19.2349	1.01518	0.507589	+	0.861599i	$0.330537\pi$
$360$	−12.2329	−0.644730
$361$	−16.0405	−0.844237
$362$	−19.8827	−1.04501
$363$	−48.2153	−2.53065
$364$	−32.2409	−1.68988
$365$	−0.999248	−0.0523030
$366$	−14.7547	−0.771242
$367$	−18.6632	−0.974213	−0.487106	−	0.873343i	$-0.661948\pi$
$367$	−18.6632	−0.974213	−0.487106	+	0.873343i	$0.661948\pi$
$368$	−122.886	−6.40586
$369$	−42.9401	−2.23537
$370$	0.513072	0.0266733
$371$	−10.1471	−0.526813
$372$	−29.0971	−1.50862
$373$	14.8658	0.769724	0.384862	−	0.922974i	$-0.374249\pi$
$373$	14.8658	0.769724	0.384862	+	0.922974i	$0.374249\pi$
$374$	−89.0886	−4.60666
$375$	5.82299	0.300698
$376$	−29.8688	−1.54037
$377$	−14.2809	−0.735502
$378$	42.3460	2.17804
$379$	7.66954	0.393958	0.196979	−	0.980408i	$-0.436887\pi$
$379$	7.66954	0.393958	0.196979	+	0.980408i	$0.436887\pi$
$380$	1.77792	0.0912055
$381$	51.9876	2.66341
$382$	5.31435	0.271906
$383$	19.0146	0.971603	0.485801	−	0.874069i	$-0.338528\pi$
$383$	19.0146	0.971603	0.485801	+	0.874069i	$0.338528\pi$
$384$	133.952	6.83570
$385$	1.26271	0.0643535
$386$	−28.2191	−1.43632
$387$	68.7238	3.49343
$388$	74.0991	3.76181
$389$	−3.60053	−0.182554	−0.0912772	−	0.995826i	$-0.529095\pi$
$389$	−3.60053	−0.182554	−0.0912772	+	0.995826i	$0.529095\pi$
$390$	−7.12209	−0.360641
$391$	−50.1295	−2.53516
$392$	51.0284	2.57732
$393$	36.7044	1.85149
$394$	−15.2892	−0.770257
$395$	0.718920	0.0361728
$396$	192.108	9.65378
$397$	−13.9150	−0.698375	−0.349187	−	0.937053i	$-0.613542\pi$
$397$	−13.9150	−0.698375	−0.349187	+	0.937053i	$0.613542\pi$
$398$	11.9942	0.601214
$399$	−7.05863	−0.353374
$400$	−76.8790	−3.84395
$401$	33.0135	1.64862	0.824308	−	0.566141i	$-0.191564\pi$
$401$	33.0135	1.64862	0.824308	+	0.566141i	$0.191564\pi$
$402$	−4.87787	−0.243286
$403$	−7.48745	−0.372977
$404$	92.0115	4.57774
$405$	3.07445	0.152770
$406$	−11.5802	−0.574717
$407$	−5.14118	−0.254839
$408$	190.899	9.45090
$409$	3.93882	0.194762	0.0973810	−	0.995247i	$-0.468953\pi$
$409$	3.93882	0.194762	0.0973810	+	0.995247i	$0.468953\pi$
$410$	3.25811	0.160906
$411$	−53.2591	−2.62708
$412$	19.0664	0.939332
$413$	11.7600	0.578670
$414$	147.221	7.23553
$415$	0.599097	0.0294085
$416$	102.774	5.03891
$417$	49.2586	2.41221
$418$	−24.2634	−1.18676
$419$	17.3584	0.848013	0.424006	−	0.905659i	$-0.360623\pi$
$419$	17.3584	0.848013	0.424006	+	0.905659i	$0.360623\pi$
$420$	−4.24048	−0.206914
$421$	−20.1700	−0.983024	−0.491512	−	0.870871i	$-0.663556\pi$
$421$	−20.1700	−0.983024	−0.491512	+	0.870871i	$0.663556\pi$
$422$	27.1275	1.32055
$423$	20.8804	1.01524
$424$	74.7407	3.62973
$425$	−31.3617	−1.52127
$426$	−54.9400	−2.66185
$427$	−2.26060	−0.109398
$428$	85.9948	4.15671
$429$	71.3662	3.44559
$430$	−5.21446	−0.251464
$431$	21.8404	1.05201	0.526007	−	0.850480i	$-0.323689\pi$
$431$	21.8404	1.05201	0.526007	+	0.850480i	$0.323689\pi$
$432$	−182.002	−8.75658
$433$	38.1574	1.83373	0.916864	−	0.399200i	$-0.130712\pi$
$433$	38.1574	1.83373	0.916864	+	0.399200i	$0.130712\pi$
$434$	−6.07151	−0.291442
$435$	−1.87829	−0.0900570
$436$	−53.1366	−2.54478
$437$	−13.6529	−0.653105
$438$	−45.7958	−2.18821
$439$	24.9704	1.19177	0.595886	−	0.803069i	$-0.296801\pi$
$439$	24.9704	1.19177	0.595886	+	0.803069i	$0.296801\pi$
$440$	−9.30071	−0.443394
$441$	−35.6724	−1.69869
$442$	76.9872	3.66191
$443$	−12.5392	−0.595756	−0.297878	−	0.954604i	$-0.596279\pi$
$443$	−12.5392	−0.595756	−0.297878	+	0.954604i	$0.596279\pi$
$444$	17.2654	0.819378
$445$	1.97498	0.0936232
$446$	31.2154	1.47809
$447$	−14.4088	−0.681513
$448$	42.6700	2.01597
$449$	−14.7459	−0.695900	−0.347950	−	0.937513i	$-0.613122\pi$
$449$	−14.7459	−0.695900	−0.347950	+	0.937513i	$0.613122\pi$
$450$	92.1038	4.34181
$451$	−32.6475	−1.53731
$452$	94.1158	4.42683
$453$	0.639976	0.0300687
$454$	−43.5822	−2.04541
$455$	−1.09119	−0.0511557
$456$	51.9917	2.43473
$457$	21.3629	0.999316	0.499658	−	0.866223i	$-0.333459\pi$
$457$	21.3629	0.999316	0.499658	+	0.866223i	$0.333459\pi$
$458$	30.5821	1.42901
$459$	−74.2452	−3.46547
$460$	−8.20197	−0.382419
$461$	4.57469	0.213064	0.106532	−	0.994309i	$-0.466025\pi$
$461$	4.57469	0.213064	0.106532	+	0.994309i	$0.466025\pi$
$462$	57.8702	2.69237
$463$	40.2761	1.87179	0.935895	−	0.352279i	$-0.114593\pi$
$463$	40.2761	1.87179	0.935895	+	0.352279i	$0.114593\pi$
$464$	49.7716	2.31059
$465$	−0.984786	−0.0456684
$466$	−72.1806	−3.34370
$467$	21.2444	0.983075	0.491538	−	0.870856i	$-0.336435\pi$
$467$	21.2444	0.983075	0.491538	+	0.870856i	$0.336435\pi$
$468$	−166.013	−7.67395
$469$	−0.747346	−0.0345092
$470$	−1.58431	−0.0730788
$471$	−14.3087	−0.659311
$472$	−86.6202	−3.98702
$473$	52.2510	2.40250
$474$	32.9483	1.51337
$475$	−8.54142	−0.391907
$476$	45.8381	2.10099
$477$	−52.2490	−2.39232
$478$	60.9107	2.78599
$479$	10.7837	0.492720	0.246360	−	0.969178i	$-0.420765\pi$
$479$	10.7837	0.492720	0.246360	+	0.969178i	$0.420765\pi$
$480$	13.5173	0.616979
$481$	4.44283	0.202576
$482$	17.4818	0.796275
$483$	32.5631	1.48167
$484$	85.2750	3.87614
$485$	2.50787	0.113876
$486$	44.1659	2.00341
$487$	20.8011	0.942589	0.471295	−	0.881976i	$-0.343787\pi$
$487$	20.8011	0.942589	0.471295	+	0.881976i	$0.343787\pi$
$488$	16.6508	0.753749
$489$	−3.12442	−0.141291
$490$	2.70667	0.122275
$491$	14.0789	0.635372	0.317686	−	0.948196i	$-0.397094\pi$
$491$	14.0789	0.635372	0.317686	+	0.948196i	$0.397094\pi$
$492$	109.638	4.94288
$493$	20.3036	0.914428
$494$	20.9676	0.943378
$495$	6.50185	0.292236
$496$	26.0952	1.17171
$497$	−8.41745	−0.377574
$498$	27.4568	1.23037
$499$	−27.8045	−1.24470	−0.622349	−	0.782740i	$-0.713822\pi$
$499$	−27.8045	−1.24470	−0.622349	+	0.782740i	$0.713822\pi$
$500$	−10.2987	−0.460572
$501$	−9.20812	−0.411388
$502$	52.8293	2.35789
$503$	6.57923	0.293353	0.146677	−	0.989184i	$-0.453142\pi$
$503$	6.57923	0.293353	0.146677	+	0.989184i	$0.453142\pi$
$504$	−85.8960	−3.82611
$505$	3.11411	0.138576
$506$	111.933	4.97603
$507$	−21.0547	−0.935072
$508$	−91.9467	−4.07948
$509$	−5.95980	−0.264164	−0.132082	−	0.991239i	$-0.542166\pi$
$509$	−5.95980	−0.264164	−0.132082	+	0.991239i	$0.542166\pi$
$510$	10.1257	0.448375
$511$	−7.01645	−0.310390
$512$	−58.6357	−2.59136
$513$	−20.2208	−0.892771
$514$	3.95098	0.174270
$515$	0.645296	0.0284352
$516$	−175.472	−7.72471
$517$	15.8754	0.698201
$518$	3.60265	0.158291
$519$	−15.2646	−0.670043
$520$	8.03735	0.352461
$521$	16.7454	0.733631	0.366816	−	0.930294i	$-0.380448\pi$
$521$	16.7454	0.733631	0.366816	+	0.930294i	$0.380448\pi$
$522$	−59.6281	−2.60985
$523$	−21.3372	−0.933010	−0.466505	−	0.884519i	$-0.654487\pi$
$523$	−21.3372	−0.933010	−0.466505	+	0.884519i	$0.654487\pi$
$524$	−64.9164	−2.83589
$525$	20.3720	0.889105
$526$	−42.7136	−1.86240
$527$	10.6452	0.463711
$528$	−248.725	−10.8244
$529$	39.9838	1.73843
$530$	3.96442	0.172203
$531$	60.5536	2.62780
$532$	12.4841	0.541254
$533$	28.2128	1.22203
$534$	90.5140	3.91692
$535$	2.91047	0.125831
$536$	5.50472	0.237768
$537$	26.6462	1.14987
$538$	5.44721	0.234846
$539$	−27.1219	−1.16822
$540$	−12.1477	−0.522753
$541$	17.5808	0.755858	0.377929	−	0.925835i	$-0.376636\pi$
$541$	17.5808	0.755858	0.377929	+	0.925835i	$0.376636\pi$
$542$	67.7782	2.91132
$543$	−22.6446	−0.971773
$544$	−146.117	−6.26473
$545$	−1.79840	−0.0770348
$546$	−50.0094	−2.14021
$547$	5.02562	0.214880	0.107440	−	0.994212i	$-0.465735\pi$
$547$	5.02562	0.214880	0.107440	+	0.994212i	$0.465735\pi$
$548$	94.1956	4.02384
$549$	−11.6401	−0.496788
$550$	70.0269	2.98596
$551$	5.52973	0.235574
$552$	−239.850	−10.2087
$553$	5.04806	0.214666
$554$	3.98362	0.169248
$555$	0.584342	0.0248040
$556$	−87.1202	−3.69472
$557$	−23.3587	−0.989741	−0.494870	−	0.868967i	$-0.664784\pi$
$557$	−23.3587	−0.989741	−0.494870	+	0.868967i	$0.664784\pi$
$558$	−31.2630	−1.32347
$559$	−45.1535	−1.90979
$560$	3.80300	0.160706
$561$	−101.464	−4.28381
$562$	52.1137	2.19828
$563$	11.2127	0.472557	0.236279	−	0.971685i	$-0.424072\pi$
$563$	11.2127	0.472557	0.236279	+	0.971685i	$0.424072\pi$
$564$	−53.3136	−2.24491
$565$	3.18533	0.134008
$566$	45.6129	1.91725
$567$	21.5879	0.906608
$568$	62.0003	2.60148
$569$	36.9557	1.54926	0.774632	−	0.632413i	$-0.217935\pi$
$569$	36.9557	1.54926	0.774632	+	0.632413i	$0.217935\pi$
$570$	2.75776	0.115510
$571$	−43.9299	−1.83841	−0.919204	−	0.393782i	$-0.871166\pi$
$571$	−43.9299	−1.83841	−0.919204	+	0.393782i	$0.871166\pi$
$572$	−126.220	−5.27753
$573$	6.05256	0.252849
$574$	22.8775	0.954890
$575$	39.4036	1.64324
$576$	219.714	9.15473
$577$	4.10838	0.171034	0.0855170	−	0.996337i	$-0.472746\pi$
$577$	4.10838	0.171034	0.0855170	+	0.996337i	$0.472746\pi$
$578$	−62.8186	−2.61291
$579$	−32.1391	−1.33565
$580$	3.32199	0.137938
$581$	4.20670	0.174523
$582$	114.936	4.76426
$583$	−39.7251	−1.64524
$584$	51.6810	2.13857
$585$	−5.61867	−0.232303
$586$	59.0071	2.43756
$587$	44.7396	1.84660	0.923301	−	0.384077i	$-0.125480\pi$
$587$	44.7396	1.84660	0.923301	+	0.384077i	$0.125480\pi$
$588$	91.0820	3.75616
$589$	2.89923	0.119461
$590$	−4.59454	−0.189154
$591$	−17.4130	−0.716274
$592$	−15.4841	−0.636394
$593$	7.48436	0.307346	0.153673	−	0.988122i	$-0.450890\pi$
$593$	7.48436	0.307346	0.153673	+	0.988122i	$0.450890\pi$
$594$	165.780	6.80205
$595$	1.55138	0.0636004
$596$	25.4838	1.04386
$597$	13.6603	0.559078
$598$	−96.7285	−3.95552
$599$	24.0787	0.983830	0.491915	−	0.870643i	$-0.336297\pi$
$599$	24.0787	0.983830	0.491915	+	0.870643i	$0.336297\pi$
$600$	−150.053	−6.12591
$601$	23.9505	0.976960	0.488480	−	0.872575i	$-0.337552\pi$
$601$	23.9505	0.976960	0.488480	+	0.872575i	$0.337552\pi$
$602$	−36.6145	−1.49230
$603$	−3.84818	−0.156710
$604$	−1.13188	−0.0460555
$605$	2.88611	0.117337
$606$	142.720	5.79762
$607$	−41.9641	−1.70327	−0.851636	−	0.524134i	$-0.824389\pi$
$607$	−41.9641	−1.70327	−0.851636	+	0.524134i	$0.824389\pi$
$608$	−39.7954	−1.61392
$609$	−13.1888	−0.534438
$610$	0.883201	0.0357597
$611$	−13.7190	−0.555011
$612$	236.026	9.54080
$613$	20.0653	0.810432	0.405216	−	0.914221i	$-0.367196\pi$
$613$	20.0653	0.810432	0.405216	+	0.914221i	$0.367196\pi$
$614$	69.5158	2.80543
$615$	3.71069	0.149629
$616$	−65.3071	−2.63130
$617$	2.51295	0.101167	0.0505837	−	0.998720i	$-0.483892\pi$
$617$	2.51295	0.101167	0.0505837	+	0.998720i	$0.483892\pi$
$618$	29.5741	1.18964
$619$	27.5299	1.10652	0.553260	−	0.833009i	$-0.313384\pi$
$619$	27.5299	1.10652	0.553260	+	0.833009i	$0.313384\pi$
$620$	1.74172	0.0699491
$621$	93.2834	3.74333
$622$	−76.4144	−3.06394
$623$	13.8678	0.555602
$624$	214.939	8.60446
$625$	24.4766	0.979062
$626$	−62.6087	−2.50235
$627$	−27.6339	−1.10359
$628$	25.3068	1.00985
$629$	−6.31653	−0.251856
$630$	−4.55613	−0.181520
$631$	17.5074	0.696960	0.348480	−	0.937316i	$-0.386698\pi$
$631$	17.5074	0.696960	0.348480	+	0.937316i	$0.386698\pi$
$632$	−37.1825	−1.47904
$633$	30.8958	1.22800
$634$	−18.2958	−0.726621
$635$	−3.11192	−0.123493
$636$	133.407	5.28992
$637$	23.4378	0.928639
$638$	−45.3355	−1.79485
$639$	−43.3426	−1.71461
$640$	−8.01820	−0.316947
$641$	−36.8236	−1.45444	−0.727222	−	0.686402i	$-0.759189\pi$
$641$	−36.8236	−1.45444	−0.727222	+	0.686402i	$0.759189\pi$
$642$	133.388	5.26440
$643$	−20.4322	−0.805769	−0.402885	−	0.915251i	$-0.631992\pi$
$643$	−20.4322	−0.805769	−0.402885	+	0.915251i	$0.631992\pi$
$644$	−57.5920	−2.26944
$645$	−5.93880	−0.233840
$646$	−29.8104	−1.17287
$647$	−42.9044	−1.68675	−0.843374	−	0.537327i	$-0.819434\pi$
$647$	−42.9044	−1.68675	−0.843374	+	0.537327i	$0.819434\pi$
$648$	−159.010	−6.24650
$649$	46.0391	1.80719
$650$	−60.5148	−2.37358
$651$	−6.91490	−0.271016
$652$	5.52594	0.216412
$653$	16.3001	0.637872	0.318936	−	0.947776i	$-0.396674\pi$
$653$	16.3001	0.637872	0.318936	+	0.947776i	$0.396674\pi$
$654$	−82.4209	−3.22291
$655$	−2.19708	−0.0858470
$656$	−98.3272	−3.83903
$657$	−36.1286	−1.40951
$658$	−11.1246	−0.433682
$659$	−42.4699	−1.65439	−0.827195	−	0.561914i	$-0.810065\pi$
$659$	−42.4699	−1.65439	−0.827195	+	0.561914i	$0.810065\pi$
$660$	−16.6011	−0.646197
$661$	−18.7101	−0.727740	−0.363870	−	0.931450i	$-0.618545\pi$
$661$	−18.7101	−0.727740	−0.363870	+	0.931450i	$0.618545\pi$
$662$	−41.6409	−1.61842
$663$	87.6815	3.40527
$664$	−30.9852	−1.20246
$665$	0.422521	0.0163847
$666$	18.5505	0.718818
$667$	−25.5099	−0.987748
$668$	16.2857	0.630114
$669$	35.5515	1.37450
$670$	0.291983	0.0112803
$671$	−8.85002	−0.341651
$672$	94.9151	3.66143
$673$	−10.4769	−0.403855	−0.201927	−	0.979401i	$-0.564720\pi$
$673$	−10.4769	−0.403855	−0.201927	+	0.979401i	$0.564720\pi$
$674$	88.4495	3.40695
$675$	58.3594	2.24626
$676$	37.2379	1.43223
$677$	−49.4852	−1.90187	−0.950936	−	0.309389i	$-0.899876\pi$
$677$	−49.4852	−1.90187	−0.950936	+	0.309389i	$0.899876\pi$
$678$	145.984	5.60650
$679$	17.6096	0.675793
$680$	−11.4270	−0.438205
$681$	−49.6362	−1.90206
$682$	−23.7694	−0.910177
$683$	−41.7493	−1.59749	−0.798746	−	0.601668i	$-0.794503\pi$
$683$	−41.7493	−1.59749	−0.798746	+	0.601668i	$0.794503\pi$
$684$	64.2822	2.45789
$685$	3.18803	0.121808
$686$	44.2241	1.68848
$687$	34.8303	1.32886
$688$	157.369	5.99962
$689$	34.3290	1.30783
$690$	−12.7222	−0.484326
$691$	−46.2347	−1.75885	−0.879426	−	0.476036i	$-0.842073\pi$
$691$	−46.2347	−1.75885	−0.879426	+	0.476036i	$0.842073\pi$
$692$	26.9975	1.02629
$693$	45.6542	1.73426
$694$	95.3545	3.61961
$695$	−2.94856	−0.111845
$696$	97.1448	3.68226
$697$	−40.1112	−1.51932
$698$	−94.1541	−3.56379
$699$	−82.2072	−3.10936
$700$	−36.0304	−1.36182
$701$	23.4280	0.884862	0.442431	−	0.896803i	$-0.354116\pi$
$701$	23.4280	0.884862	0.442431	+	0.896803i	$0.354116\pi$
$702$	−143.262	−5.40706
$703$	−1.72032	−0.0648831
$704$	167.049	6.29590
$705$	−1.80439	−0.0679572
$706$	−47.3228	−1.78102
$707$	21.8664	0.822372
$708$	−154.611	−5.81063
$709$	−36.1400	−1.35727	−0.678633	−	0.734477i	$-0.737427\pi$
$709$	−36.1400	−1.35727	−0.678633	+	0.734477i	$0.737427\pi$
$710$	3.28864	0.123421
$711$	25.9932	0.974819
$712$	−102.146	−3.82808
$713$	−13.3748	−0.500892
$714$	71.1001	2.66086
$715$	−4.27190	−0.159760
$716$	−47.1273	−1.76123
$717$	69.3717	2.59073
$718$	−52.7679	−1.96928
$719$	3.16546	0.118052	0.0590259	−	0.998256i	$-0.481201\pi$
$719$	3.16546	0.118052	0.0590259	+	0.998256i	$0.481201\pi$
$720$	19.5821	0.729784
$721$	4.53110	0.168747
$722$	44.0046	1.63768
$723$	19.9102	0.740469
$724$	40.0499	1.48844
$725$	−15.9594	−0.592716
$726$	132.271	4.90905
$727$	33.2409	1.23284	0.616419	−	0.787419i	$-0.288583\pi$
$727$	33.2409	1.23284	0.616419	+	0.787419i	$0.288583\pi$
$728$	56.4361	2.09166
$729$	0.984729	0.0364714
$730$	2.74128	0.101459
$731$	64.1963	2.37439
$732$	29.7206	1.09850
$733$	−42.0094	−1.55165	−0.775827	−	0.630946i	$-0.782667\pi$
$733$	−42.0094	−1.55165	−0.775827	+	0.630946i	$0.782667\pi$
$734$	51.1997	1.88981
$735$	3.08265	0.113705
$736$	183.585	6.76705
$737$	−2.92579	−0.107773
$738$	117.799	4.33626
$739$	22.0034	0.809407	0.404703	−	0.914448i	$-0.367375\pi$
$739$	22.0034	0.809407	0.404703	+	0.914448i	$0.367375\pi$
$740$	−1.03348	−0.0379916
$741$	23.8802	0.877262
$742$	27.8371	1.02193
$743$	−15.0463	−0.551994	−0.275997	−	0.961158i	$-0.589008\pi$
$743$	−15.0463	−0.551994	−0.275997	+	0.961158i	$0.589008\pi$
$744$	50.9330	1.86729
$745$	0.862494	0.0315993
$746$	−40.7821	−1.49314
$747$	21.6609	0.792529
$748$	179.452	6.56141
$749$	20.4366	0.746736
$750$	−15.9745	−0.583305
$751$	−3.27470	−0.119495	−0.0597477	−	0.998214i	$-0.519030\pi$
$751$	−3.27470	−0.119495	−0.0597477	+	0.998214i	$0.519030\pi$
$752$	47.8133	1.74357
$753$	60.1678	2.19264
$754$	39.1773	1.42675
$755$	−0.0383082	−0.00139418
$756$	−85.2978	−3.10225
$757$	36.4741	1.32567	0.662837	−	0.748764i	$-0.269352\pi$
$757$	36.4741	1.32567	0.662837	+	0.748764i	$0.269352\pi$
$758$	−21.0402	−0.764214
$759$	127.482	4.62729
$760$	−3.11216	−0.112890
$761$	47.3265	1.71558	0.857792	−	0.513997i	$-0.171836\pi$
$761$	47.3265	1.71558	0.857792	+	0.513997i	$0.171836\pi$
$762$	−142.620	−5.16657
$763$	−12.6278	−0.457159
$764$	−10.7047	−0.387283
$765$	7.98826	0.288816
$766$	−52.1637	−1.88475
$767$	−39.7854	−1.43657
$768$	−164.437	−5.93360
$769$	31.5743	1.13860	0.569299	−	0.822130i	$-0.307215\pi$
$769$	31.5743	1.13860	0.569299	+	0.822130i	$0.307215\pi$
$770$	−3.46404	−0.124835
$771$	4.49981	0.162057
$772$	56.8420	2.04579
$773$	11.0981	0.399170	0.199585	−	0.979881i	$-0.436041\pi$
$773$	11.0981	0.399170	0.199585	+	0.979881i	$0.436041\pi$
$774$	−188.533	−6.77668
$775$	−8.36750	−0.300569
$776$	−129.707	−4.65619
$777$	4.10309	0.147198
$778$	9.87751	0.354126
$779$	−10.9244	−0.391406
$780$	14.3461	0.513672
$781$	−32.9535	−1.17917
$782$	137.522	4.91779
$783$	−37.7819	−1.35022
$784$	−81.6852	−2.91733
$785$	0.856503	0.0305699
$786$	−100.693	−3.59159
$787$	39.0924	1.39350	0.696748	−	0.717316i	$-0.254630\pi$
$787$	39.0924	1.39350	0.696748	+	0.717316i	$0.254630\pi$
$788$	30.7971	1.09710
$789$	−48.6469	−1.73188
$790$	−1.97225	−0.0701694
$791$	22.3665	0.795262
$792$	−336.275	−11.9490
$793$	7.64788	0.271584
$794$	38.1737	1.35473
$795$	4.51512	0.160135
$796$	−24.1600	−0.856327
$797$	−25.9384	−0.918785	−0.459392	−	0.888233i	$-0.651933\pi$
$797$	−25.9384	−0.918785	−0.459392	+	0.888233i	$0.651933\pi$
$798$	19.3643	0.685487
$799$	19.5048	0.690029
$800$	114.854	4.06069
$801$	71.4071	2.52305
$802$	−90.5675	−3.19805
$803$	−27.4687	−0.969351
$804$	9.82552	0.346520
$805$	−1.94919	−0.0686999
$806$	20.5407	0.723514
$807$	6.20388	0.218387
$808$	−161.061	−5.66612
$809$	−9.58725	−0.337070	−0.168535	−	0.985696i	$-0.553904\pi$
$809$	−9.58725	−0.337070	−0.168535	+	0.985696i	$0.553904\pi$
$810$	−8.43427	−0.296350
$811$	27.9615	0.981861	0.490931	−	0.871199i	$-0.336657\pi$
$811$	27.9615	0.981861	0.490931	+	0.871199i	$0.336657\pi$
$812$	23.3261	0.818586
$813$	77.1933	2.70729
$814$	14.1040	0.494346
$815$	0.187024	0.00655117
$816$	−305.587	−10.6977
$817$	17.4840	0.611687
$818$	−10.8055	−0.377807
$819$	−39.4528	−1.37859
$820$	−6.56283	−0.229184
$821$	−13.8673	−0.483971	−0.241985	−	0.970280i	$-0.577799\pi$
$821$	−13.8673	−0.483971	−0.241985	+	0.970280i	$0.577799\pi$
$822$	146.108	5.09611
$823$	22.1165	0.770931	0.385466	−	0.922722i	$-0.374041\pi$
$823$	22.1165	0.770931	0.385466	+	0.922722i	$0.374041\pi$
$824$	−33.3746	−1.16266
$825$	79.7543	2.77669
$826$	−32.2616	−1.12253
$827$	−37.4559	−1.30247	−0.651235	−	0.758876i	$-0.725749\pi$
$827$	−37.4559	−1.30247	−0.651235	+	0.758876i	$0.725749\pi$
$828$	−296.549	−10.3058
$829$	1.03813	0.0360558	0.0180279	−	0.999837i	$-0.494261\pi$
$829$	1.03813	0.0360558	0.0180279	+	0.999837i	$0.494261\pi$
$830$	−1.64353	−0.0570478
$831$	4.53698	0.157386
$832$	−144.358	−5.00471
$833$	−33.3223	−1.15455
$834$	−135.133	−4.67929
$835$	0.551187	0.0190746
$836$	48.8740	1.69034
$837$	−19.8091	−0.684702
$838$	−47.6200	−1.64501
$839$	9.41083	0.324898	0.162449	−	0.986717i	$-0.448061\pi$
$839$	9.41083	0.324898	0.162449	+	0.986717i	$0.448061\pi$
$840$	7.42274	0.256109
$841$	−18.6679	−0.643720
$842$	55.3332	1.90691
$843$	59.3528	2.04422
$844$	−54.6431	−1.88089
$845$	1.26031	0.0433560
$846$	−57.2821	−1.96940
$847$	20.2655	0.696331
$848$	−119.643	−4.10857
$849$	51.9489	1.78288
$850$	86.0360	2.95101
$851$	7.93623	0.272051
$852$	110.666	3.79136
$853$	18.9496	0.648821	0.324411	−	0.945916i	$-0.394834\pi$
$853$	18.9496	0.648821	0.324411	+	0.945916i	$0.394834\pi$
$854$	6.20160	0.212214
$855$	2.17562	0.0744046
$856$	−150.529	−5.14499
$857$	34.4806	1.17783	0.588917	−	0.808193i	$-0.299554\pi$
$857$	34.4806	1.17783	0.588917	+	0.808193i	$0.299554\pi$
$858$	−195.782	−6.68389
$859$	44.4175	1.51551	0.757753	−	0.652542i	$-0.226297\pi$
$859$	44.4175	1.51551	0.757753	+	0.652542i	$0.226297\pi$
$860$	10.5035	0.358167
$861$	26.0555	0.887967
$862$	−59.9157	−2.04074
$863$	−20.7804	−0.707375	−0.353687	−	0.935364i	$-0.615072\pi$
$863$	−20.7804	−0.707375	−0.353687	+	0.935364i	$0.615072\pi$
$864$	271.903	9.25032
$865$	0.913723	0.0310675
$866$	−104.679	−3.55713
$867$	−71.5447	−2.42978
$868$	12.2299	0.415109
$869$	19.7627	0.670403
$870$	5.15279	0.174696
$871$	2.52837	0.0856704
$872$	93.0128	3.14981
$873$	90.6740	3.06885
$874$	37.4545	1.26692
$875$	−2.44747	−0.0827397
$876$	92.2468	3.11673
$877$	52.0400	1.75727	0.878634	−	0.477497i	$-0.158456\pi$
$877$	52.0400	1.75727	0.878634	+	0.477497i	$0.158456\pi$
$878$	−68.5024	−2.31184
$879$	67.2038	2.26673
$880$	14.8884	0.501887
$881$	−47.7665	−1.60930	−0.804648	−	0.593752i	$-0.797646\pi$
$881$	−47.7665	−1.60930	−0.804648	+	0.593752i	$0.797646\pi$
$882$	97.8618	3.29518
$883$	29.4303	0.990410	0.495205	−	0.868776i	$-0.335093\pi$
$883$	29.4303	0.990410	0.495205	+	0.868776i	$0.335093\pi$
$884$	−155.076	−5.21577
$885$	−5.23277	−0.175898
$886$	34.3994	1.15567
$887$	−46.8083	−1.57167	−0.785834	−	0.618438i	$-0.787766\pi$
$887$	−46.8083	−1.57167	−0.785834	+	0.618438i	$0.787766\pi$
$888$	−30.2221	−1.01419
$889$	−21.8510	−0.732860
$890$	−5.41806	−0.181614
$891$	84.5147	2.83135
$892$	−62.8774	−2.10529
$893$	5.31216	0.177765
$894$	39.5283	1.32202
$895$	−1.59501	−0.0533154
$896$	−56.3016	−1.88091
$897$	−110.165	−3.67831
$898$	40.4530	1.34993
$899$	5.41713	0.180671
$900$	−185.525	−6.18418
$901$	−48.8068	−1.62599
$902$	89.5634	2.98213
$903$	−41.7007	−1.38771
$904$	−164.745	−5.47933
$905$	1.35548	0.0450577
$906$	−1.75567	−0.0583284
$907$	−40.9157	−1.35858	−0.679292	−	0.733868i	$-0.737713\pi$
$907$	−40.9157	−1.35858	−0.679292	+	0.733868i	$0.737713\pi$
$908$	87.7879	2.91334
$909$	112.593	3.73448
$910$	2.99350	0.0992337
$911$	8.64911	0.286558	0.143279	−	0.989682i	$-0.454235\pi$
$911$	8.64911	0.286558	0.143279	+	0.989682i	$0.454235\pi$
$912$	−83.2272	−2.75593
$913$	16.4688	0.545039
$914$	−58.6059	−1.93851
$915$	1.00589	0.0332536
$916$	−61.6018	−2.03538
$917$	−15.4273	−0.509455
$918$	203.680	6.72245
$919$	43.0677	1.42067	0.710336	−	0.703863i	$-0.248543\pi$
$919$	43.0677	1.42067	0.710336	+	0.703863i	$0.248543\pi$
$920$	14.3571	0.473340
$921$	79.1722	2.60881
$922$	−12.5499	−0.413310
$923$	28.4773	0.937341
$924$	−116.568	−3.83482
$925$	4.96502	0.163249
$926$	−110.491	−3.63097
$927$	23.3312	0.766298
$928$	−74.3564	−2.44087
$929$	17.7372	0.581939	0.290970	−	0.956732i	$-0.406022\pi$
$929$	17.7372	0.581939	0.290970	+	0.956732i	$0.406022\pi$
$930$	2.70161	0.0885892
$931$	−9.07540	−0.297434
$932$	145.394	4.76253
$933$	−87.0291	−2.84921
$934$	−58.2808	−1.90701
$935$	6.07350	0.198625
$936$	290.597	9.49846
$937$	−3.83399	−0.125251	−0.0626255	−	0.998037i	$-0.519947\pi$
$937$	−3.83399	−0.125251	−0.0626255	+	0.998037i	$0.519947\pi$
$938$	2.05023	0.0669423
$939$	−71.3057	−2.32697
$940$	3.19129	0.104088
$941$	12.8407	0.418594	0.209297	−	0.977852i	$-0.432882\pi$
$941$	12.8407	0.418594	0.209297	+	0.977852i	$0.432882\pi$
$942$	39.2538	1.27896
$943$	50.3966	1.64114
$944$	138.660	4.51300
$945$	−2.88688	−0.0939104
$946$	−143.342	−4.66047
$947$	−46.6298	−1.51526	−0.757632	−	0.652682i	$-0.773644\pi$
$947$	−46.6298	−1.51526	−0.757632	+	0.652682i	$0.773644\pi$
$948$	−66.3680	−2.15553
$949$	23.7375	0.770553
$950$	23.4321	0.760237
$951$	−20.8373	−0.675696
$952$	−80.2372	−2.60050
$953$	0.176399	0.00571412	0.00285706	−	0.999996i	$-0.499091\pi$
$953$	0.176399	0.00571412	0.00285706	+	0.999996i	$0.499091\pi$
$954$	143.337	4.64070
$955$	−0.362299	−0.0117237
$956$	−122.693	−3.96817
$957$	−51.6330	−1.66906
$958$	−29.5834	−0.955796
$959$	22.3855	0.722865
$960$	−18.9866	−0.612791
$961$	−28.1598	−0.908381
$962$	−12.1882	−0.392964
$963$	105.231	3.39101
$964$	−35.2138	−1.13416
$965$	1.92381	0.0619295
$966$	−89.3319	−2.87421
$967$	−6.05215	−0.194624	−0.0973120	−	0.995254i	$-0.531024\pi$
$967$	−6.05215	−0.194624	−0.0973120	+	0.995254i	$0.531024\pi$
$968$	−149.269	−4.79770
$969$	−33.9514	−1.09067
$970$	−6.87994	−0.220902
$971$	55.0415	1.76636	0.883182	−	0.469030i	$-0.155396\pi$
$971$	55.0415	1.76636	0.883182	+	0.469030i	$0.155396\pi$
$972$	−88.9638	−2.85352
$973$	−20.7040	−0.663740
$974$	−57.0647	−1.82847
$975$	−68.9209	−2.20723
$976$	−26.6543	−0.853185
$977$	−9.32039	−0.298186	−0.149093	−	0.988823i	$-0.547635\pi$
$977$	−9.32039	−0.298186	−0.149093	+	0.988823i	$0.547635\pi$
$978$	8.57137	0.274082
$979$	54.2911	1.73515
$980$	−5.45206	−0.174160
$981$	−65.0225	−2.07601
$982$	−38.6233	−1.23252
$983$	−29.1620	−0.930124	−0.465062	−	0.885278i	$-0.653968\pi$
$983$	−29.1620	−0.930124	−0.465062	+	0.885278i	$0.653968\pi$
$984$	−191.916	−6.11807
$985$	1.04232	0.0332111
$986$	−55.6998	−1.77384
$987$	−12.6699	−0.403288
$988$	−42.2352	−1.34368
$989$	−80.6577	−2.56477
$990$	−17.8368	−0.566891
$991$	39.3260	1.24923	0.624616	−	0.780932i	$-0.285255\pi$
$991$	39.3260	1.24923	0.624616	+	0.780932i	$0.285255\pi$
$992$	−38.9850	−1.23778
$993$	−47.4253	−1.50500
$994$	23.0920	0.732433
$995$	−0.817688	−0.0259225
$996$	−55.3064	−1.75245
$997$	14.4940	0.459030	0.229515	−	0.973305i	$-0.426286\pi$
$997$	14.4940	0.459030	0.229515	+	0.973305i	$0.426286\pi$
$998$	76.2772	2.41451
$999$	11.7541	0.371884

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.d.1.2	✓	133

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.d.1.2	✓	133	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)

\(f(q)\)	\(=\)	\(q-2.74334 q^{2} -3.12442 q^{3} +5.52594 q^{4} +0.187024 q^{5} +8.57137 q^{6} +1.31323 q^{7} -9.67287 q^{8} +6.76201 q^{9} +O(q^{10})\)	\(q-2.74334 q^{2} -3.12442 q^{3} +5.52594 q^{4} +0.187024 q^{5} +8.57137 q^{6} +1.31323 q^{7} -9.67287 q^{8} +6.76201 q^{9} -0.513072 q^{10} +5.14118 q^{11} -17.2654 q^{12} -4.44283 q^{13} -3.60265 q^{14} -0.584342 q^{15} +15.4841 q^{16} +6.31653 q^{17} -18.5505 q^{18} +1.72032 q^{19} +1.03348 q^{20} -4.10309 q^{21} -14.1040 q^{22} -7.93623 q^{23} +30.2221 q^{24} -4.96502 q^{25} +12.1882 q^{26} -11.7541 q^{27} +7.25685 q^{28} +3.21436 q^{29} +1.60305 q^{30} +1.68529 q^{31} -23.1326 q^{32} -16.0632 q^{33} -17.3284 q^{34} +0.245606 q^{35} +37.3665 q^{36} -1.00000 q^{37} -4.71943 q^{38} +13.8813 q^{39} -1.80906 q^{40} -6.35020 q^{41} +11.2562 q^{42} +10.1632 q^{43} +28.4099 q^{44} +1.26466 q^{45} +21.7718 q^{46} +3.08789 q^{47} -48.3789 q^{48} -5.27542 q^{49} +13.6208 q^{50} -19.7355 q^{51} -24.5508 q^{52} -7.72684 q^{53} +32.2456 q^{54} +0.961526 q^{55} -12.7027 q^{56} -5.37500 q^{57} -8.81810 q^{58} +8.95497 q^{59} -3.22904 q^{60} -1.72140 q^{61} -4.62333 q^{62} +8.88010 q^{63} +32.4923 q^{64} -0.830917 q^{65} +44.0670 q^{66} -0.569089 q^{67} +34.9048 q^{68} +24.7961 q^{69} -0.673783 q^{70} -6.40972 q^{71} -65.4080 q^{72} -5.34288 q^{73} +2.74334 q^{74} +15.5128 q^{75} +9.50638 q^{76} +6.75157 q^{77} -38.0811 q^{78} +3.84400 q^{79} +2.89591 q^{80} +16.4388 q^{81} +17.4208 q^{82} +3.20332 q^{83} -22.6735 q^{84} +1.18134 q^{85} -27.8812 q^{86} -10.0430 q^{87} -49.7300 q^{88} +10.5600 q^{89} -3.46940 q^{90} -5.83447 q^{91} -43.8551 q^{92} -5.26555 q^{93} -8.47116 q^{94} +0.321741 q^{95} +72.2759 q^{96} +13.4093 q^{97} +14.4723 q^{98} +34.7647 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9}+O(q^{10}) \) 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9	\( 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9} + 9 q^{10} + 23 q^{11} + 24 q^{12} + 23 q^{13} + 31 q^{14} + 9 q^{15} + 168 q^{16} + 98 q^{17} + 38 q^{18} + 29 q^{19} + 83 q^{20} + 26 q^{21} + 2 q^{22} + 34 q^{23} + 75 q^{24} + 177 q^{25} + 67 q^{26} + 32 q^{27} + 32 q^{28} + 91 q^{29} + 12 q^{30} + 24 q^{31} + 88 q^{32} + 27 q^{33} + 23 q^{34} + 66 q^{35} + 232 q^{36} - 133 q^{37} + 26 q^{38} + 28 q^{39} + 41 q^{40} + 132 q^{41} + 13 q^{42} + 11 q^{43} + 65 q^{44} + 107 q^{45} + 20 q^{46} + 10 q^{47} + 27 q^{48} + 229 q^{49} + 78 q^{50} + 19 q^{51} + 71 q^{52} + 7 q^{53} + 43 q^{54} + 41 q^{55} + 67 q^{56} + 45 q^{57} + 25 q^{58} + 97 q^{59} - 42 q^{60} + 65 q^{61} + 24 q^{62} + 39 q^{63} + 200 q^{64} + 60 q^{65} + 35 q^{66} + 25 q^{67} + 227 q^{68} + 120 q^{69} + 37 q^{70} + 26 q^{71} + 93 q^{72} + 55 q^{73} - 14 q^{74} + 5 q^{75} + 34 q^{76} + 21 q^{77} - 2 q^{78} + 50 q^{79} + 162 q^{80} + 341 q^{81} + 66 q^{82} + 30 q^{83} - 89 q^{84} + 30 q^{85} - 12 q^{86} + 80 q^{87} - 85 q^{88} + 225 q^{89} - 86 q^{90} + q^{91} + 82 q^{92} + 42 q^{93} - 17 q^{94} + 70 q^{95} + 55 q^{96} + 12 q^{97} + 90 q^{98} + 17 q^{99}+O(q^{100}) \) 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9 + 9 * q^10 + 23 * q^11 + 24 * q^12 + 23 * q^13 + 31 * q^14 + 9 * q^15 + 168 * q^16 + 98 * q^17 + 38 * q^18 + 29 * q^19 + 83 * q^20 + 26 * q^21 + 2 * q^22 + 34 * q^23 + 75 * q^24 + 177 * q^25 + 67 * q^26 + 32 * q^27 + 32 * q^28 + 91 * q^29 + 12 * q^30 + 24 * q^31 + 88 * q^32 + 27 * q^33 + 23 * q^34 + 66 * q^35 + 232 * q^36 - 133 * q^37 + 26 * q^38 + 28 * q^39 + 41 * q^40 + 132 * q^41 + 13 * q^42 + 11 * q^43 + 65 * q^44 + 107 * q^45 + 20 * q^46 + 10 * q^47 + 27 * q^48 + 229 * q^49 + 78 * q^50 + 19 * q^51 + 71 * q^52 + 7 * q^53 + 43 * q^54 + 41 * q^55 + 67 * q^56 + 45 * q^57 + 25 * q^58 + 97 * q^59 - 42 * q^60 + 65 * q^61 + 24 * q^62 + 39 * q^63 + 200 * q^64 + 60 * q^65 + 35 * q^66 + 25 * q^67 + 227 * q^68 + 120 * q^69 + 37 * q^70 + 26 * q^71 + 93 * q^72 + 55 * q^73 - 14 * q^74 + 5 * q^75 + 34 * q^76 + 21 * q^77 - 2 * q^78 + 50 * q^79 + 162 * q^80 + 341 * q^81 + 66 * q^82 + 30 * q^83 - 89 * q^84 + 30 * q^85 - 12 * q^86 + 80 * q^87 - 85 * q^88 + 225 * q^89 - 86 * q^90 + q^91 + 82 * q^92 + 42 * q^93 - 17 * q^94 + 70 * q^95 + 55 * q^96 + 12 * q^97 + 90 * q^98 + 17 * q^99

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