LMFDB - Embedded newform 6031.2.a.d.1.5

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			1.5
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)

$f(q)$	$=$	$q-2.62634 q^{2} -3.19656 q^{3} +4.89764 q^{4} +4.04178 q^{5} +8.39525 q^{6} -2.68408 q^{7} -7.61017 q^{8} +7.21801 q^{9} +O(q^{10})$	\(q-2.62634 q^{2} -3.19656 q^{3} +4.89764 q^{4} +4.04178 q^{5} +8.39525 q^{6} -2.68408 q^{7} -7.61017 q^{8} +7.21801 q^{9} -10.6151 q^{10} -1.08855 q^{11} -15.6556 q^{12} +1.06200 q^{13} +7.04930 q^{14} -12.9198 q^{15} +10.1916 q^{16} -1.26081 q^{17} -18.9569 q^{18} +1.29250 q^{19} +19.7952 q^{20} +8.57984 q^{21} +2.85890 q^{22} +1.73746 q^{23} +24.3264 q^{24} +11.3360 q^{25} -2.78917 q^{26} -13.4831 q^{27} -13.1457 q^{28} +6.15926 q^{29} +33.9318 q^{30} -5.62423 q^{31} -11.5462 q^{32} +3.47963 q^{33} +3.31131 q^{34} -10.8485 q^{35} +35.3512 q^{36} -1.00000 q^{37} -3.39454 q^{38} -3.39475 q^{39} -30.7587 q^{40} -7.94406 q^{41} -22.5335 q^{42} -9.07705 q^{43} -5.33134 q^{44} +29.1736 q^{45} -4.56315 q^{46} -8.78596 q^{47} -32.5781 q^{48} +0.204296 q^{49} -29.7722 q^{50} +4.03026 q^{51} +5.20129 q^{52} +5.61614 q^{53} +35.4113 q^{54} -4.39969 q^{55} +20.4263 q^{56} -4.13155 q^{57} -16.1763 q^{58} -5.72423 q^{59} -63.2766 q^{60} +14.9917 q^{61} +14.7711 q^{62} -19.3737 q^{63} +9.94101 q^{64} +4.29237 q^{65} -9.13867 q^{66} +13.9602 q^{67} -6.17499 q^{68} -5.55389 q^{69} +28.4917 q^{70} -6.39036 q^{71} -54.9303 q^{72} -2.28824 q^{73} +2.62634 q^{74} -36.2363 q^{75} +6.33019 q^{76} +2.92176 q^{77} +8.91575 q^{78} +12.6707 q^{79} +41.1922 q^{80} +21.4457 q^{81} +20.8638 q^{82} +13.9153 q^{83} +42.0209 q^{84} -5.09592 q^{85} +23.8394 q^{86} -19.6885 q^{87} +8.28407 q^{88} -0.556146 q^{89} -76.6198 q^{90} -2.85050 q^{91} +8.50944 q^{92} +17.9782 q^{93} +23.0749 q^{94} +5.22400 q^{95} +36.9082 q^{96} -7.47582 q^{97} -0.536549 q^{98} -7.85719 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.62634	−1.85710	−0.928550	−	0.371208i	$-0.878944\pi$
$2$	−2.62634	−1.85710	−0.928550	+	0.371208i	$0.878944\pi$
$3$	−3.19656	−1.84554	−0.922768	−	0.385356i	$-0.874079\pi$
$3$	−3.19656	−1.84554	−0.922768	+	0.385356i	$0.874079\pi$
$4$	4.89764	2.44882
$5$	4.04178	1.80754	0.903770	−	0.428018i	$-0.140788\pi$
$5$	4.04178	1.80754	0.903770	+	0.428018i	$0.140788\pi$
$6$	8.39525	3.42735
$7$	−2.68408	−1.01449	−0.507244	−	0.861803i	$-0.669336\pi$
$7$	−2.68408	−1.01449	−0.507244	+	0.861803i	$0.669336\pi$
$8$	−7.61017	−2.69060
$9$	7.21801	2.40600
$10$	−10.6151	−3.35678
$11$	−1.08855	−0.328211	−0.164105	−	0.986443i	$-0.552474\pi$
$11$	−1.08855	−0.328211	−0.164105	+	0.986443i	$0.552474\pi$
$12$	−15.6556	−4.51939
$13$	1.06200	0.294546	0.147273	−	0.989096i	$-0.452950\pi$
$13$	1.06200	0.294546	0.147273	+	0.989096i	$0.452950\pi$
$14$	7.04930	1.88400
$15$	−12.9198	−3.33588
$16$	10.1916	2.54790
$17$	−1.26081	−0.305791	−0.152896	−	0.988242i	$-0.548860\pi$
$17$	−1.26081	−0.305791	−0.152896	+	0.988242i	$0.548860\pi$
$18$	−18.9569	−4.46819
$19$	1.29250	0.296520	0.148260	−	0.988948i	$-0.452633\pi$
$19$	1.29250	0.296520	0.148260	+	0.988948i	$0.452633\pi$
$20$	19.7952	4.42634
$21$	8.57984	1.87227
$22$	2.85890	0.609520
$23$	1.73746	0.362285	0.181142	−	0.983457i	$-0.442020\pi$
$23$	1.73746	0.362285	0.181142	+	0.983457i	$0.442020\pi$
$24$	24.3264	4.96561
$25$	11.3360	2.26720
$26$	−2.78917	−0.547001
$27$	−13.4831	−2.59483
$28$	−13.1457	−2.48430
$29$	6.15926	1.14375	0.571873	−	0.820342i	$-0.306217\pi$
$29$	6.15926	1.14375	0.571873	+	0.820342i	$0.306217\pi$
$30$	33.9318	6.19507
$31$	−5.62423	−1.01014	−0.505071	−	0.863078i	$-0.668534\pi$
$31$	−5.62423	−1.01014	−0.505071	+	0.863078i	$0.668534\pi$
$32$	−11.5462	−2.04110
$33$	3.47963	0.605725
$34$	3.31131	0.567885
$35$	−10.8485	−1.83373
$36$	35.3512	5.89187
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−3.39454	−0.550667
$39$	−3.39475	−0.543595
$40$	−30.7587	−4.86337
$41$	−7.94406	−1.24065	−0.620327	−	0.784343i	$-0.713000\pi$
$41$	−7.94406	−1.24065	−0.620327	+	0.784343i	$0.713000\pi$
$42$	−22.5335	−3.47700
$43$	−9.07705	−1.38424	−0.692119	−	0.721784i	$-0.743323\pi$
$43$	−9.07705	−1.38424	−0.692119	+	0.721784i	$0.743323\pi$
$44$	−5.33134	−0.803729
$45$	29.1736	4.34895
$46$	−4.56315	−0.672799
$47$	−8.78596	−1.28156	−0.640782	−	0.767723i	$-0.721390\pi$
$47$	−8.78596	−1.28156	−0.640782	+	0.767723i	$0.721390\pi$
$48$	−32.5781	−4.70224
$49$	0.204296	0.0291851
$50$	−29.7722	−4.21042
$51$	4.03026	0.564349
$52$	5.20129	0.721290
$53$	5.61614	0.771436	0.385718	−	0.922617i	$-0.373954\pi$
$53$	5.61614	0.771436	0.385718	+	0.922617i	$0.373954\pi$
$54$	35.4113	4.81886
$55$	−4.39969	−0.593254
$56$	20.4263	2.72958
$57$	−4.13155	−0.547238
$58$	−16.1763	−2.12405
$59$	−5.72423	−0.745232	−0.372616	−	0.927986i	$-0.621539\pi$
$59$	−5.72423	−0.745232	−0.372616	+	0.927986i	$0.621539\pi$
$60$	−63.2766	−8.16897
$61$	14.9917	1.91948	0.959742	−	0.280882i	$-0.0906269\pi$
$61$	14.9917	1.91948	0.959742	+	0.280882i	$0.0906269\pi$
$62$	14.7711	1.87593
$63$	−19.3737	−2.44086
$64$	9.94101	1.24263
$65$	4.29237	0.532404
$66$	−9.13867	−1.12489
$67$	13.9602	1.70551	0.852756	−	0.522309i	$-0.174929\pi$
$67$	13.9602	1.70551	0.852756	+	0.522309i	$0.174929\pi$
$68$	−6.17499	−0.748827
$69$	−5.55389	−0.668610
$70$	28.4917	3.40541
$71$	−6.39036	−0.758396	−0.379198	−	0.925315i	$-0.623800\pi$
$71$	−6.39036	−0.758396	−0.379198	+	0.925315i	$0.623800\pi$
$72$	−54.9303	−6.47360
$73$	−2.28824	−0.267818	−0.133909	−	0.990994i	$-0.542753\pi$
$73$	−2.28824	−0.267818	−0.133909	+	0.990994i	$0.542753\pi$
$74$	2.62634	0.305305
$75$	−36.2363	−4.18420
$76$	6.33019	0.726123
$77$	2.92176	0.332966
$78$	8.91575	1.00951
$79$	12.6707	1.42556	0.712780	−	0.701388i	$-0.247436\pi$
$79$	12.6707	1.42556	0.712780	+	0.701388i	$0.247436\pi$
$80$	41.1922	4.60543
$81$	21.4457	2.38285
$82$	20.8638	2.30402
$83$	13.9153	1.52740	0.763702	−	0.645568i	$-0.223380\pi$
$83$	13.9153	1.52740	0.763702	+	0.645568i	$0.223380\pi$
$84$	42.0209	4.58486
$85$	−5.09592	−0.552730
$86$	23.8394	2.57067
$87$	−19.6885	−2.11082
$88$	8.28407	0.883085
$89$	−0.556146	−0.0589514	−0.0294757	−	0.999565i	$-0.509384\pi$
$89$	−0.556146	−0.0589514	−0.0294757	+	0.999565i	$0.509384\pi$
$90$	−76.6198	−8.07644
$91$	−2.85050	−0.298813
$92$	8.50944	0.887170
$93$	17.9782	1.86425
$94$	23.0749	2.37999
$95$	5.22400	0.535971
$96$	36.9082	3.76692
$97$	−7.47582	−0.759054	−0.379527	−	0.925181i	$-0.623913\pi$
$97$	−7.47582	−0.759054	−0.379527	+	0.925181i	$0.623913\pi$
$98$	−0.536549	−0.0541997
$99$	−7.85719	−0.789677
$100$	55.5197	5.55197
$101$	5.64102	0.561302	0.280651	−	0.959810i	$-0.409450\pi$
$101$	5.64102	0.561302	0.280651	+	0.959810i	$0.409450\pi$
$102$	−10.5848	−1.04805
$103$	1.21723	0.119937	0.0599686	−	0.998200i	$-0.480900\pi$
$103$	1.21723	0.119937	0.0599686	+	0.998200i	$0.480900\pi$
$104$	−8.08201	−0.792506
$105$	34.6778	3.38421
$106$	−14.7499	−1.43263
$107$	5.00222	0.483583	0.241792	−	0.970328i	$-0.422265\pi$
$107$	5.00222	0.483583	0.241792	+	0.970328i	$0.422265\pi$
$108$	−66.0356	−6.35428
$109$	0.991268	0.0949463	0.0474731	−	0.998873i	$-0.484883\pi$
$109$	0.991268	0.0949463	0.0474731	+	0.998873i	$0.484883\pi$
$110$	11.5551	1.10173
$111$	3.19656	0.303404
$112$	−27.3551	−2.58481
$113$	−18.0656	−1.69947	−0.849735	−	0.527211i	$-0.823238\pi$
$113$	−18.0656	−1.69947	−0.849735	+	0.527211i	$0.823238\pi$
$114$	10.8508	1.01628
$115$	7.02243	0.654845
$116$	30.1658	2.80083
$117$	7.66553	0.708679
$118$	15.0338	1.38397
$119$	3.38411	0.310221
$120$	98.3220	8.97553
$121$	−9.81505	−0.892278
$122$	−39.3731	−3.56467
$123$	25.3937	2.28967
$124$	−27.5455	−2.47365
$125$	25.6088	2.29052
$126$	50.8819	4.53292
$127$	−9.18952	−0.815438	−0.407719	−	0.913107i	$-0.633676\pi$
$127$	−9.18952	−0.815438	−0.407719	+	0.913107i	$0.633676\pi$
$128$	−3.01603	−0.266582
$129$	29.0154	2.55466
$130$	−11.2732	−0.988727
$131$	17.6138	1.53892	0.769462	−	0.638692i	$-0.220524\pi$
$131$	17.6138	1.53892	0.769462	+	0.638692i	$0.220524\pi$
$132$	17.0420	1.48331
$133$	−3.46917	−0.300815
$134$	−36.6642	−3.16731
$135$	−54.4959	−4.69026
$136$	9.59498	0.822762
$137$	10.6865	0.913012	0.456506	−	0.889720i	$-0.349101\pi$
$137$	10.6865	0.913012	0.456506	+	0.889720i	$0.349101\pi$
$138$	14.5864	1.24168
$139$	8.45562	0.717196	0.358598	−	0.933492i	$-0.383255\pi$
$139$	8.45562	0.717196	0.358598	+	0.933492i	$0.383255\pi$
$140$	−53.1319	−4.49047
$141$	28.0849	2.36517
$142$	16.7832	1.40842
$143$	−1.15604	−0.0966732
$144$	73.5631	6.13026
$145$	24.8944	2.06737
$146$	6.00969	0.497365
$147$	−0.653044	−0.0538622
$148$	−4.89764	−0.402584
$149$	14.9814	1.22732	0.613662	−	0.789569i	$-0.289696\pi$
$149$	14.9814	1.22732	0.613662	+	0.789569i	$0.289696\pi$
$150$	95.1686	7.77049
$151$	8.57599	0.697904	0.348952	−	0.937141i	$-0.386538\pi$
$151$	8.57599	0.697904	0.348952	+	0.937141i	$0.386538\pi$
$152$	−9.83614	−0.797817
$153$	−9.10054	−0.735735
$154$	−7.67353	−0.618351
$155$	−22.7319	−1.82587
$156$	−16.6263	−1.33117
$157$	−16.6450	−1.32841	−0.664207	−	0.747549i	$-0.731231\pi$
$157$	−16.6450	−1.32841	−0.664207	+	0.747549i	$0.731231\pi$
$158$	−33.2774	−2.64741
$159$	−17.9523	−1.42371
$160$	−46.6672	−3.68937
$161$	−4.66348	−0.367534
$162$	−56.3236	−4.42520
$163$	1.00000	0.0783260
$163$	1.00000	0.0783260
$164$	−38.9072	−3.03814
$165$	14.0639	1.09487
$166$	−36.5463	−2.83654
$167$	14.8553	1.14953	0.574767	−	0.818317i	$-0.305093\pi$
$167$	14.8553	1.14953	0.574767	+	0.818317i	$0.305093\pi$
$168$	−65.2941	−5.03755
$169$	−11.8722	−0.913243
$170$	13.3836	1.02647
$171$	9.32928	0.713427
$172$	−44.4561	−3.38975
$173$	−21.6847	−1.64865	−0.824327	−	0.566114i	$-0.808446\pi$
$173$	−21.6847	−1.64865	−0.824327	+	0.566114i	$0.808446\pi$
$174$	51.7085	3.92001
$175$	−30.4268	−2.30005
$176$	−11.0941	−0.836248
$177$	18.2979	1.37535
$178$	1.46063	0.109479
$179$	6.32965	0.473100	0.236550	−	0.971619i	$-0.423983\pi$
$179$	6.32965	0.473100	0.236550	+	0.971619i	$0.423983\pi$
$180$	142.882	10.6498
$181$	13.1625	0.978364	0.489182	−	0.872182i	$-0.337295\pi$
$181$	13.1625	0.978364	0.489182	+	0.872182i	$0.337295\pi$
$182$	7.48636	0.554926
$183$	−47.9218	−3.54248
$184$	−13.2224	−0.974765
$185$	−4.04178	−0.297158
$186$	−47.2168	−3.46210
$187$	1.37246	0.100364
$188$	−43.0305	−3.13832
$189$	36.1899	2.63243
$190$	−13.7200	−0.995352
$191$	−5.81409	−0.420693	−0.210346	−	0.977627i	$-0.567459\pi$
$191$	−5.81409	−0.420693	−0.210346	+	0.977627i	$0.567459\pi$
$192$	−31.7771	−2.29331
$193$	4.56787	0.328802	0.164401	−	0.986394i	$-0.447431\pi$
$193$	4.56787	0.328802	0.164401	+	0.986394i	$0.447431\pi$
$194$	19.6340	1.40964
$195$	−13.7208	−0.982570
$196$	1.00057	0.0714691
$197$	6.42813	0.457985	0.228993	−	0.973428i	$-0.426457\pi$
$197$	6.42813	0.457985	0.228993	+	0.973428i	$0.426457\pi$
$198$	20.6356	1.46651
$199$	12.7344	0.902717	0.451358	−	0.892343i	$-0.350940\pi$
$199$	12.7344	0.902717	0.451358	+	0.892343i	$0.350940\pi$
$200$	−86.2690	−6.10014
$201$	−44.6247	−3.14759
$202$	−14.8152	−1.04239
$203$	−16.5320	−1.16032
$204$	19.7387	1.38199
$205$	−32.1082	−2.24253
$206$	−3.19685	−0.222735
$207$	12.5410	0.871659
$208$	10.8235	0.750473
$209$	−1.40695	−0.0973210
$210$	−91.0756	−6.28482
$211$	−5.27978	−0.363475	−0.181737	−	0.983347i	$-0.558172\pi$
$211$	−5.27978	−0.363475	−0.181737	+	0.983347i	$0.558172\pi$
$212$	27.5058	1.88911
$213$	20.4272	1.39965
$214$	−13.1375	−0.898062
$215$	−36.6875	−2.50207
$216$	102.609	6.98166
$217$	15.0959	1.02478
$218$	−2.60340	−0.176325
$219$	7.31451	0.494269
$220$	−21.5481	−1.45277
$221$	−1.33898	−0.0900695
$222$	−8.39525	−0.563452
$223$	−0.133315	−0.00892746	−0.00446373	−	0.999990i	$-0.501421\pi$
$223$	−0.133315	−0.00892746	−0.00446373	+	0.999990i	$0.501421\pi$
$224$	30.9910	2.07067
$225$	81.8235	5.45490
$226$	47.4464	3.15608
$227$	8.60916	0.571410	0.285705	−	0.958318i	$-0.407772\pi$
$227$	8.60916	0.571410	0.285705	+	0.958318i	$0.407772\pi$
$228$	−20.2349	−1.34009
$229$	8.50431	0.561981	0.280990	−	0.959711i	$-0.409337\pi$
$229$	8.50431	0.561981	0.280990	+	0.959711i	$0.409337\pi$
$230$	−18.4432	−1.21611
$231$	−9.33960	−0.614501
$232$	−46.8730	−3.07736
$233$	3.81123	0.249682	0.124841	−	0.992177i	$-0.460158\pi$
$233$	3.81123	0.249682	0.124841	+	0.992177i	$0.460158\pi$
$234$	−20.1323	−1.31609
$235$	−35.5109	−2.31648
$236$	−28.0352	−1.82494
$237$	−40.5025	−2.63092
$238$	−8.88782	−0.576112
$239$	8.09637	0.523710	0.261855	−	0.965107i	$-0.415666\pi$
$239$	8.09637	0.523710	0.261855	+	0.965107i	$0.415666\pi$
$240$	−131.674	−8.49949
$241$	−27.6879	−1.78353	−0.891767	−	0.452495i	$-0.850534\pi$
$241$	−27.6879	−1.78353	−0.891767	+	0.452495i	$0.850534\pi$
$242$	25.7776	1.65705
$243$	−28.1030	−1.80281
$244$	73.4237	4.70047
$245$	0.825719	0.0527533
$246$	−66.6924	−4.25215
$247$	1.37263	0.0873386
$248$	42.8014	2.71789
$249$	−44.4812	−2.81888
$250$	−67.2573	−4.25372
$251$	13.6292	0.860266	0.430133	−	0.902766i	$-0.358467\pi$
$251$	13.6292	0.860266	0.430133	+	0.902766i	$0.358467\pi$
$252$	−94.8856	−5.97723
$253$	−1.89131	−0.118906
$254$	24.1348	1.51435
$255$	16.2894	1.02008
$256$	−11.9609	−0.747557
$257$	5.91610	0.369036	0.184518	−	0.982829i	$-0.440928\pi$
$257$	5.91610	0.369036	0.184518	+	0.982829i	$0.440928\pi$
$258$	−76.2041	−4.74426
$259$	2.68408	0.166781
$260$	21.0225	1.30376
$261$	44.4576	2.75186
$262$	−46.2597	−2.85794
$263$	−16.9990	−1.04820	−0.524101	−	0.851656i	$-0.675599\pi$
$263$	−16.9990	−1.04820	−0.524101	+	0.851656i	$0.675599\pi$
$264$	−26.4806	−1.62977
$265$	22.6992	1.39440
$266$	9.11121	0.558644
$267$	1.77776	0.108797
$268$	68.3721	4.17649
$269$	−2.78082	−0.169549	−0.0847747	−	0.996400i	$-0.527017\pi$
$269$	−2.78082	−0.169549	−0.0847747	+	0.996400i	$0.527017\pi$
$270$	143.125	8.71029
$271$	14.4458	0.877521	0.438761	−	0.898604i	$-0.355418\pi$
$271$	14.4458	0.877521	0.438761	+	0.898604i	$0.355418\pi$
$272$	−12.8497	−0.779125
$273$	9.11179	0.551470
$274$	−28.0664	−1.69556
$275$	−12.3398	−0.744121
$276$	−27.2010	−1.63731
$277$	14.0885	0.846496	0.423248	−	0.906014i	$-0.360890\pi$
$277$	14.0885	0.846496	0.423248	+	0.906014i	$0.360890\pi$
$278$	−22.2073	−1.33190
$279$	−40.5958	−2.43040
$280$	82.5588	4.93383
$281$	−22.9045	−1.36637	−0.683185	−	0.730245i	$-0.739406\pi$
$281$	−22.9045	−1.36637	−0.683185	+	0.730245i	$0.739406\pi$
$282$	−73.7603	−4.39236
$283$	−16.2520	−0.966080	−0.483040	−	0.875598i	$-0.660467\pi$
$283$	−16.2520	−0.966080	−0.483040	+	0.875598i	$0.660467\pi$
$284$	−31.2977	−1.85718
$285$	−16.6988	−0.989154
$286$	3.03616	0.179532
$287$	21.3225	1.25863
$288$	−83.3406	−4.91089
$289$	−15.4104	−0.906492
$290$	−65.3810	−3.83931
$291$	23.8969	1.40086
$292$	−11.2070	−0.655839
$293$	−6.50887	−0.380252	−0.190126	−	0.981760i	$-0.560890\pi$
$293$	−6.50887	−0.380252	−0.190126	+	0.981760i	$0.560890\pi$
$294$	1.71511	0.100027
$295$	−23.1361	−1.34704
$296$	7.61017	0.442332
$297$	14.6771	0.851652
$298$	−39.3462	−2.27926
$299$	1.84518	0.106710
$300$	−177.472	−10.2464
$301$	24.3636	1.40429
$302$	−22.5234	−1.29608
$303$	−18.0319	−1.03590
$304$	13.1726	0.755502
$305$	60.5930	3.46955
$306$	23.9011	1.36633
$307$	−1.93155	−0.110239	−0.0551196	−	0.998480i	$-0.517554\pi$
$307$	−1.93155	−0.110239	−0.0551196	+	0.998480i	$0.517554\pi$
$308$	14.3097	0.815373
$309$	−3.89095	−0.221348
$310$	59.7016	3.39083
$311$	31.0923	1.76308	0.881540	−	0.472109i	$-0.156507\pi$
$311$	31.0923	1.76308	0.881540	+	0.472109i	$0.156507\pi$
$312$	25.8346	1.46260
$313$	−9.71959	−0.549383	−0.274692	−	0.961532i	$-0.588576\pi$
$313$	−9.71959	−0.549383	−0.274692	+	0.961532i	$0.588576\pi$
$314$	43.7153	2.46700
$315$	−78.3045	−4.41196
$316$	62.0563	3.49094
$317$	−8.92494	−0.501275	−0.250637	−	0.968081i	$-0.580640\pi$
$317$	−8.92494	−0.501275	−0.250637	+	0.968081i	$0.580640\pi$
$318$	47.1489	2.64398
$319$	−6.70467	−0.375390
$320$	40.1794	2.24610
$321$	−15.9899	−0.892470
$322$	12.2479	0.682547
$323$	−1.62959	−0.0906731
$324$	105.033	5.83518
$325$	12.0388	0.667795
$326$	−2.62634	−0.145459
$327$	−3.16865	−0.175227
$328$	60.4557	3.33811
$329$	23.5822	1.30013
$330$	−36.9365	−2.03329
$331$	−30.6490	−1.68462	−0.842312	−	0.538990i	$-0.818806\pi$
$331$	−30.6490	−1.68462	−0.842312	+	0.538990i	$0.818806\pi$
$332$	68.1522	3.74034
$333$	−7.21801	−0.395545
$334$	−39.0149	−2.13480
$335$	56.4242	3.08278
$336$	87.4422	4.77036
$337$	27.0511	1.47356	0.736782	−	0.676130i	$-0.236344\pi$
$337$	27.0511	1.47356	0.736782	+	0.676130i	$0.236344\pi$
$338$	31.1803	1.69598
$339$	57.7478	3.13643
$340$	−24.9580	−1.35354
$341$	6.12227	0.331539
$342$	−24.5018	−1.32491
$343$	18.2402	0.984880
$344$	69.0779	3.72443
$345$	−22.4476	−1.20854
$346$	56.9512	3.06171
$347$	−22.6782	−1.21743	−0.608715	−	0.793389i	$-0.708315\pi$
$347$	−22.6782	−1.21743	−0.608715	+	0.793389i	$0.708315\pi$
$348$	−96.4269	−5.16903
$349$	−1.09895	−0.0588255	−0.0294127	−	0.999567i	$-0.509364\pi$
$349$	−1.09895	−0.0588255	−0.0294127	+	0.999567i	$0.509364\pi$
$350$	79.9110	4.27142
$351$	−14.3191	−0.764297
$352$	12.5686	0.669911
$353$	20.8508	1.10977	0.554887	−	0.831926i	$-0.312761\pi$
$353$	20.8508	1.10977	0.554887	+	0.831926i	$0.312761\pi$
$354$	−48.0564	−2.55417
$355$	−25.8285	−1.37083
$356$	−2.72380	−0.144361
$357$	−10.8175	−0.572525
$358$	−16.6238	−0.878595
$359$	−24.7513	−1.30632	−0.653161	−	0.757219i	$-0.726558\pi$
$359$	−24.7513	−1.30632	−0.653161	+	0.757219i	$0.726558\pi$
$360$	−222.017	−11.7013
$361$	−17.3294	−0.912076
$362$	−34.5693	−1.81692
$363$	31.3744	1.64673
$364$	−13.9607	−0.731739
$365$	−9.24858	−0.484093
$366$	125.859	6.57874
$367$	30.4885	1.59149	0.795744	−	0.605633i	$-0.207080\pi$
$367$	30.4885	1.59149	0.795744	+	0.605633i	$0.207080\pi$
$368$	17.7075	0.923065
$369$	−57.3404	−2.98502
$370$	10.6151	0.551852
$371$	−15.0742	−0.782612
$372$	88.0508	4.56522
$373$	−3.02154	−0.156449	−0.0782247	−	0.996936i	$-0.524925\pi$
$373$	−3.02154	−0.156449	−0.0782247	+	0.996936i	$0.524925\pi$
$374$	−3.60453	−0.186386
$375$	−81.8601	−4.22724
$376$	66.8627	3.44818
$377$	6.54113	0.336885
$378$	−95.0467	−4.88868
$379$	13.3756	0.687060	0.343530	−	0.939142i	$-0.388377\pi$
$379$	13.3756	0.687060	0.343530	+	0.939142i	$0.388377\pi$
$380$	25.5853	1.31250
$381$	29.3749	1.50492
$382$	15.2697	0.781268
$383$	−4.44615	−0.227188	−0.113594	−	0.993527i	$-0.536236\pi$
$383$	−4.44615	−0.227188	−0.113594	+	0.993527i	$0.536236\pi$
$384$	9.64094	0.491987
$385$	11.8091	0.601849
$386$	−11.9967	−0.610618
$387$	−65.5183	−3.33048
$388$	−36.6139	−1.85879
$389$	4.50442	0.228383	0.114192	−	0.993459i	$-0.463572\pi$
$389$	4.50442	0.228383	0.114192	+	0.993459i	$0.463572\pi$
$390$	36.0355	1.82473
$391$	−2.19060	−0.110784
$392$	−1.55473	−0.0785255
$393$	−56.3036	−2.84014
$394$	−16.8824	−0.850524
$395$	51.2120	2.57676
$396$	−38.4817	−1.93378
$397$	24.6979	1.23955	0.619776	−	0.784779i	$-0.287223\pi$
$397$	24.6979	1.23955	0.619776	+	0.784779i	$0.287223\pi$
$398$	−33.4448	−1.67644
$399$	11.0894	0.555166
$400$	115.532	5.77660
$401$	−29.2005	−1.45820	−0.729101	−	0.684406i	$-0.760062\pi$
$401$	−29.2005	−1.45820	−0.729101	+	0.684406i	$0.760062\pi$
$402$	117.200	5.84538
$403$	−5.97293	−0.297533
$404$	27.6277	1.37453
$405$	86.6788	4.30710
$406$	43.4185	2.15482
$407$	1.08855	0.0539575
$408$	−30.6709	−1.51844
$409$	−27.8597	−1.37757	−0.688786	−	0.724964i	$-0.741856\pi$
$409$	−27.8597	−1.37757	−0.688786	+	0.724964i	$0.741856\pi$
$410$	84.3269	4.16461
$411$	−34.1602	−1.68500
$412$	5.96155	0.293705
$413$	15.3643	0.756029
$414$	−32.9369	−1.61876
$415$	56.2427	2.76085
$416$	−12.2621	−0.601197
$417$	−27.0289	−1.32361
$418$	3.69513	0.180735
$419$	38.2742	1.86982	0.934909	−	0.354889i	$-0.115481\pi$
$419$	38.2742	1.86982	0.934909	+	0.354889i	$0.115481\pi$
$420$	169.840	8.28732
$421$	−12.4564	−0.607086	−0.303543	−	0.952818i	$-0.598170\pi$
$421$	−12.4564	−0.607086	−0.303543	+	0.952818i	$0.598170\pi$
$422$	13.8665	0.675009
$423$	−63.4172	−3.08345
$424$	−42.7398	−2.07563
$425$	−14.2925	−0.693290
$426$	−53.6487	−2.59929
$427$	−40.2388	−1.94729
$428$	24.4991	1.18421
$429$	3.69536	0.178414
$430$	96.3536	4.64658
$431$	38.3141	1.84552	0.922762	−	0.385371i	$-0.125927\pi$
$431$	38.3141	1.84552	0.922762	+	0.385371i	$0.125927\pi$
$432$	−137.415	−6.61137
$433$	5.27874	0.253680	0.126840	−	0.991923i	$-0.459517\pi$
$433$	5.27874	0.253680	0.126840	+	0.991923i	$0.459517\pi$
$434$	−39.6469	−1.90311
$435$	−79.5765	−3.81540
$436$	4.85488	0.232506
$437$	2.24566	0.107425
$438$	−19.2104	−0.917906
$439$	−28.4020	−1.35555	−0.677777	−	0.735267i	$-0.737057\pi$
$439$	−28.4020	−1.35555	−0.677777	+	0.735267i	$0.737057\pi$
$440$	33.4824	1.59621
$441$	1.47461	0.0702195
$442$	3.51661	0.167268
$443$	22.7075	1.07887	0.539433	−	0.842028i	$-0.318639\pi$
$443$	22.7075	1.07887	0.539433	+	0.842028i	$0.318639\pi$
$444$	15.6556	0.742982
$445$	−2.24782	−0.106557
$446$	0.350131	0.0165792
$447$	−47.8890	−2.26507
$448$	−26.6825	−1.26063
$449$	−1.06769	−0.0503875	−0.0251937	−	0.999683i	$-0.508020\pi$
$449$	−1.06769	−0.0503875	−0.0251937	+	0.999683i	$0.508020\pi$
$450$	−214.896	−10.1303
$451$	8.64753	0.407196
$452$	−88.4788	−4.16169
$453$	−27.4137	−1.28801
$454$	−22.6105	−1.06117
$455$	−11.5211	−0.540117
$456$	31.4418	1.47240
$457$	−14.1206	−0.660534	−0.330267	−	0.943888i	$-0.607139\pi$
$457$	−14.1206	−0.660534	−0.330267	+	0.943888i	$0.607139\pi$
$458$	−22.3352	−1.04365
$459$	16.9997	0.793477
$460$	34.3933	1.60360
$461$	13.1194	0.611032	0.305516	−	0.952187i	$-0.401171\pi$
$461$	13.1194	0.611032	0.305516	+	0.952187i	$0.401171\pi$
$462$	24.5289	1.14119
$463$	−30.4146	−1.41349	−0.706744	−	0.707470i	$-0.749837\pi$
$463$	−30.4146	−1.41349	−0.706744	+	0.707470i	$0.749837\pi$
$464$	62.7727	2.91415
$465$	72.6640	3.36971
$466$	−10.0096	−0.463684
$467$	26.7658	1.23857	0.619287	−	0.785165i	$-0.287422\pi$
$467$	26.7658	1.23857	0.619287	+	0.785165i	$0.287422\pi$
$468$	37.5430	1.73543
$469$	−37.4704	−1.73022
$470$	93.2637	4.30193
$471$	53.2067	2.45164
$472$	43.5624	2.00512
$473$	9.88085	0.454322
$474$	106.373	4.88589
$475$	14.6518	0.672270
$476$	16.5742	0.759676
$477$	40.5374	1.85608
$478$	−21.2638	−0.972582
$479$	12.2409	0.559299	0.279649	−	0.960102i	$-0.409782\pi$
$479$	12.2409	0.559299	0.279649	+	0.960102i	$0.409782\pi$
$480$	149.175	6.80887
$481$	−1.06200	−0.0484230
$482$	72.7177	3.31220
$483$	14.9071	0.678297
$484$	−48.0706	−2.18503
$485$	−30.2156	−1.37202
$486$	73.8080	3.34800
$487$	−21.7405	−0.985156	−0.492578	−	0.870268i	$-0.663945\pi$
$487$	−21.7405	−0.985156	−0.492578	+	0.870268i	$0.663945\pi$
$488$	−114.089	−5.16457
$489$	−3.19656	−0.144554
$490$	−2.16862	−0.0979681
$491$	−41.9804	−1.89455	−0.947275	−	0.320422i	$-0.896175\pi$
$491$	−41.9804	−1.89455	−0.947275	+	0.320422i	$0.896175\pi$
$492$	124.369	5.60700
$493$	−7.76565	−0.349747
$494$	−3.60500	−0.162197
$495$	−31.7570	−1.42737
$496$	−57.3199	−2.57374
$497$	17.1523	0.769384
$498$	116.823	5.23494
$499$	8.46358	0.378882	0.189441	−	0.981892i	$-0.439332\pi$
$499$	8.46358	0.378882	0.189441	+	0.981892i	$0.439332\pi$
$500$	125.423	5.60907
$501$	−47.4858	−2.12151
$502$	−35.7948	−1.59760
$503$	21.2396	0.947026	0.473513	−	0.880787i	$-0.342986\pi$
$503$	21.2396	0.947026	0.473513	+	0.880787i	$0.342986\pi$
$504$	147.438	6.56739
$505$	22.7998	1.01458
$506$	4.96722	0.220820
$507$	37.9501	1.68542
$508$	−45.0070	−1.99686
$509$	−6.40709	−0.283989	−0.141995	−	0.989867i	$-0.545352\pi$
$509$	−6.40709	−0.283989	−0.141995	+	0.989867i	$0.545352\pi$
$510$	−42.7815	−1.89440
$511$	6.14183	0.271698
$512$	37.4454	1.65487
$513$	−17.4270	−0.769419
$514$	−15.5377	−0.685337
$515$	4.91978	0.216791
$516$	142.107	6.25590
$517$	9.56398	0.420623
$518$	−7.04930	−0.309728
$519$	69.3164	3.04265
$520$	−32.6657	−1.43249
$521$	−14.0002	−0.613360	−0.306680	−	0.951813i	$-0.599218\pi$
$521$	−14.0002	−0.613360	−0.306680	+	0.951813i	$0.599218\pi$
$522$	−116.761	−5.11047
$523$	−29.4829	−1.28920	−0.644598	−	0.764522i	$-0.722975\pi$
$523$	−29.4829	−1.28920	−0.644598	+	0.764522i	$0.722975\pi$
$524$	86.2660	3.76855
$525$	97.2611	4.24482
$526$	44.6450	1.94662
$527$	7.09108	0.308892
$528$	35.4629	1.54333
$529$	−19.9812	−0.868750
$530$	−59.6158	−2.58954
$531$	−41.3176	−1.79303
$532$	−16.9908	−0.736643
$533$	−8.43660	−0.365430
$534$	−4.66898	−0.202047
$535$	20.2179	0.874096
$536$	−106.240	−4.58886
$537$	−20.2331	−0.873124
$538$	7.30336	0.314870
$539$	−0.222387	−0.00957887
$540$	−266.902	−11.4856
$541$	30.4869	1.31073	0.655367	−	0.755310i	$-0.272514\pi$
$541$	30.4869	1.31073	0.655367	+	0.755310i	$0.272514\pi$
$542$	−37.9396	−1.62964
$543$	−42.0749	−1.80561
$544$	14.5576	0.624150
$545$	4.00649	0.171619
$546$	−23.9306	−1.02414
$547$	18.8420	0.805626	0.402813	−	0.915282i	$-0.368032\pi$
$547$	18.8420	0.805626	0.402813	+	0.915282i	$0.368032\pi$
$548$	52.3388	2.23580
$549$	108.210	4.61829
$550$	32.4086	1.38191
$551$	7.96083	0.339143
$552$	42.2661	1.79896
$553$	−34.0091	−1.44621
$554$	−37.0011	−1.57203
$555$	12.9198	0.548416
$556$	41.4126	1.75628
$557$	5.10471	0.216294	0.108147	−	0.994135i	$-0.465508\pi$
$557$	5.10471	0.216294	0.108147	+	0.994135i	$0.465508\pi$
$558$	106.618	4.51350
$559$	−9.63983	−0.407721
$560$	−110.563	−4.67215
$561$	−4.38714	−0.185225
$562$	60.1550	2.53749
$563$	37.6469	1.58663	0.793313	−	0.608814i	$-0.208354\pi$
$563$	37.6469	1.58663	0.793313	+	0.608814i	$0.208354\pi$
$564$	137.550	5.79188
$565$	−73.0173	−3.07186
$566$	42.6831	1.79411
$567$	−57.5620	−2.41737
$568$	48.6318	2.04054
$569$	7.09733	0.297536	0.148768	−	0.988872i	$-0.452469\pi$
$569$	7.09733	0.297536	0.148768	+	0.988872i	$0.452469\pi$
$570$	43.8568	1.83696
$571$	20.4863	0.857326	0.428663	−	0.903464i	$-0.358985\pi$
$571$	20.4863	0.857326	0.428663	+	0.903464i	$0.358985\pi$
$572$	−5.66188	−0.236735
$573$	18.5851	0.776404
$574$	−56.0001	−2.33740
$575$	19.6958	0.821373
$576$	71.7544	2.98976
$577$	−14.4441	−0.601318	−0.300659	−	0.953732i	$-0.597207\pi$
$577$	−14.4441	−0.601318	−0.300659	+	0.953732i	$0.597207\pi$
$578$	40.4728	1.68345
$579$	−14.6015	−0.606816
$580$	121.924	5.06261
$581$	−37.3499	−1.54953
$582$	−62.7613	−2.60154
$583$	−6.11346	−0.253194
$584$	17.4139	0.720593
$585$	30.9824	1.28097
$586$	17.0945	0.706167
$587$	3.48958	0.144030	0.0720151	−	0.997404i	$-0.477057\pi$
$587$	3.48958	0.144030	0.0720151	+	0.997404i	$0.477057\pi$
$588$	−3.19838	−0.131899
$589$	−7.26931	−0.299527
$590$	60.7632	2.50158
$591$	−20.5479	−0.845228
$592$	−10.1916	−0.418872
$593$	41.6611	1.71081	0.855407	−	0.517956i	$-0.173307\pi$
$593$	41.6611	1.71081	0.855407	+	0.517956i	$0.173307\pi$
$594$	−38.5470	−1.58160
$595$	13.6779	0.560738
$596$	73.3735	3.00550
$597$	−40.7063	−1.66600
$598$	−4.84606	−0.198170
$599$	19.0842	0.779761	0.389880	−	0.920865i	$-0.372516\pi$
$599$	19.0842	0.779761	0.389880	+	0.920865i	$0.372516\pi$
$600$	275.764	11.2580
$601$	−30.7075	−1.25259	−0.626293	−	0.779588i	$-0.715429\pi$
$601$	−30.7075	−1.25259	−0.626293	+	0.779588i	$0.715429\pi$
$602$	−63.9869	−2.60791
$603$	100.765	4.10347
$604$	42.0021	1.70904
$605$	−39.6703	−1.61283
$606$	47.3577	1.92378
$607$	41.4517	1.68247	0.841236	−	0.540668i	$-0.181829\pi$
$607$	41.4517	1.68247	0.841236	+	0.540668i	$0.181829\pi$
$608$	−14.9235	−0.605226
$609$	52.8454	2.14140
$610$	−159.138	−6.44329
$611$	−9.33069	−0.377479
$612$	−44.5711	−1.80168
$613$	−0.724884	−0.0292778	−0.0146389	−	0.999893i	$-0.504660\pi$
$613$	−0.724884	−0.0292778	−0.0146389	+	0.999893i	$0.504660\pi$
$614$	5.07289	0.204725
$615$	102.636	4.13868
$616$	−22.2351	−0.895879
$617$	3.11169	0.125272	0.0626360	−	0.998036i	$-0.480049\pi$
$617$	3.11169	0.125272	0.0626360	+	0.998036i	$0.480049\pi$
$618$	10.2189	0.411066
$619$	−16.6213	−0.668066	−0.334033	−	0.942561i	$-0.608410\pi$
$619$	−16.6213	−0.668066	−0.334033	+	0.942561i	$0.608410\pi$
$620$	−111.333	−4.47123
$621$	−23.4264	−0.940069
$622$	−81.6587	−3.27422
$623$	1.49274	0.0598054
$624$	−34.5979	−1.38503
$625$	46.8251	1.87300
$626$	25.5269	1.02026
$627$	4.49741	0.179609
$628$	−81.5211	−3.25305
$629$	1.26081	0.0502717
$630$	205.654	8.19344
$631$	5.37426	0.213946	0.106973	−	0.994262i	$-0.465884\pi$
$631$	5.37426	0.213946	0.106973	+	0.994262i	$0.465884\pi$
$632$	−96.4259	−3.83562
$633$	16.8771	0.670806
$634$	23.4399	0.930917
$635$	−37.1420	−1.47394
$636$	−87.9241	−3.48642
$637$	0.216962	0.00859635
$638$	17.6087	0.697136
$639$	−46.1257	−1.82471
$640$	−12.1901	−0.481858
$641$	48.7369	1.92499	0.962496	−	0.271296i	$-0.0874522\pi$
$641$	48.7369	1.92499	0.962496	+	0.271296i	$0.0874522\pi$
$642$	41.9949	1.65741
$643$	−36.4448	−1.43724	−0.718621	−	0.695402i	$-0.755226\pi$
$643$	−36.4448	−1.43724	−0.718621	+	0.695402i	$0.755226\pi$
$644$	−22.8400	−0.900023
$645$	117.274	4.61765
$646$	4.27986	0.168389
$647$	26.4575	1.04015	0.520075	−	0.854120i	$-0.325904\pi$
$647$	26.4575	1.04015	0.520075	+	0.854120i	$0.325904\pi$
$648$	−163.205	−6.41131
$649$	6.23113	0.244593
$650$	−31.6181	−1.24016
$651$	−48.2550	−1.89126
$652$	4.89764	0.191806
$653$	−24.5554	−0.960929	−0.480464	−	0.877014i	$-0.659532\pi$
$653$	−24.5554	−0.960929	−0.480464	+	0.877014i	$0.659532\pi$
$654$	8.32194	0.325414
$655$	71.1911	2.78167
$656$	−80.9627	−3.16106
$657$	−16.5166	−0.644372
$658$	−61.9349	−2.41447
$659$	7.82707	0.304900	0.152450	−	0.988311i	$-0.451284\pi$
$659$	7.82707	0.304900	0.152450	+	0.988311i	$0.451284\pi$
$660$	68.8799	2.68115
$661$	−29.7491	−1.15711	−0.578553	−	0.815645i	$-0.696382\pi$
$661$	−29.7491	−1.15711	−0.578553	+	0.815645i	$0.696382\pi$
$662$	80.4947	3.12851
$663$	4.28013	0.166227
$664$	−105.898	−4.10964
$665$	−14.0216	−0.543736
$666$	18.9569	0.734566
$667$	10.7014	0.414362
$668$	72.7557	2.81500
$669$	0.426151	0.0164760
$670$	−148.189	−5.72504
$671$	−16.3192	−0.629996
$672$	−99.0645	−3.82150
$673$	−21.8910	−0.843836	−0.421918	−	0.906634i	$-0.638643\pi$
$673$	−21.8910	−0.843836	−0.421918	+	0.906634i	$0.638643\pi$
$674$	−71.0451	−2.73656
$675$	−152.845	−5.88301
$676$	−58.1455	−2.23637
$677$	29.0265	1.11558	0.557789	−	0.829983i	$-0.311650\pi$
$677$	29.0265	1.11558	0.557789	+	0.829983i	$0.311650\pi$
$678$	−151.665	−5.82467
$679$	20.0657	0.770051
$680$	38.7808	1.48718
$681$	−27.5197	−1.05456
$682$	−16.0791	−0.615702
$683$	−43.1241	−1.65010	−0.825049	−	0.565061i	$-0.808853\pi$
$683$	−43.1241	−1.65010	−0.825049	+	0.565061i	$0.808853\pi$
$684$	45.6914	1.74706
$685$	43.1927	1.65031
$686$	−47.9050	−1.82902
$687$	−27.1846	−1.03716
$688$	−92.5096	−3.52690
$689$	5.96434	0.227223
$690$	58.9550	2.24438
$691$	−45.1858	−1.71895	−0.859474	−	0.511180i	$-0.829209\pi$
$691$	−45.1858	−1.71895	−0.859474	+	0.511180i	$0.829209\pi$
$692$	−106.204	−4.03726
$693$	21.0893	0.801117
$694$	59.5606	2.26089
$695$	34.1758	1.29636
$696$	149.833	5.67939
$697$	10.0159	0.379381
$698$	2.88621	0.109245
$699$	−12.1828	−0.460797
$700$	−149.019	−5.63241
$701$	32.5324	1.22873	0.614365	−	0.789022i	$-0.289412\pi$
$701$	32.5324	1.22873	0.614365	+	0.789022i	$0.289412\pi$
$702$	37.6068	1.41938
$703$	−1.29250	−0.0487475
$704$	−10.8213	−0.407844
$705$	113.513	4.27514
$706$	−54.7611	−2.06096
$707$	−15.1410	−0.569434
$708$	89.6164	3.36799
$709$	−19.1532	−0.719312	−0.359656	−	0.933085i	$-0.617106\pi$
$709$	−19.1532	−0.719312	−0.359656	+	0.933085i	$0.617106\pi$
$710$	67.8342	2.54577
$711$	91.4570	3.42990
$712$	4.23237	0.158615
$713$	−9.77186	−0.365959
$714$	28.4105	1.06324
$715$	−4.67247	−0.174741
$716$	31.0004	1.15854
$717$	−25.8805	−0.966527
$718$	65.0052	2.42597
$719$	44.7003	1.66704	0.833521	−	0.552488i	$-0.186322\pi$
$719$	44.7003	1.66704	0.833521	+	0.552488i	$0.186322\pi$
$720$	297.326	11.0807
$721$	−3.26714	−0.121675
$722$	45.5129	1.69382
$723$	88.5061	3.29158
$724$	64.4654	2.39584
$725$	69.8214	2.59310
$726$	−82.3998	−3.05814
$727$	−25.7121	−0.953610	−0.476805	−	0.879009i	$-0.658205\pi$
$727$	−25.7121	−0.953610	−0.476805	+	0.879009i	$0.658205\pi$
$728$	21.6928	0.803987
$729$	25.4960	0.944298
$730$	24.2899	0.899008
$731$	11.4444	0.423287
$732$	−234.704	−8.67489
$733$	42.0337	1.55255	0.776275	−	0.630395i	$-0.217107\pi$
$733$	42.0337	1.55255	0.776275	+	0.630395i	$0.217107\pi$
$734$	−80.0731	−2.95555
$735$	−2.63946	−0.0973581
$736$	−20.0610	−0.739460
$737$	−15.1964	−0.559768
$738$	150.595	5.54348
$739$	32.4106	1.19224	0.596122	−	0.802894i	$-0.296707\pi$
$739$	32.4106	1.19224	0.596122	+	0.802894i	$0.296707\pi$
$740$	−19.7952	−0.727686
$741$	−4.38771	−0.161187
$742$	39.5899	1.45339
$743$	10.3121	0.378313	0.189157	−	0.981947i	$-0.439425\pi$
$743$	10.3121	0.378313	0.189157	+	0.981947i	$0.439425\pi$
$744$	−136.817	−5.01596
$745$	60.5516	2.21844
$746$	7.93558	0.290542
$747$	100.441	3.67494
$748$	6.72180	0.245773
$749$	−13.4264	−0.490589
$750$	214.992	7.85040
$751$	27.3438	0.997788	0.498894	−	0.866663i	$-0.333740\pi$
$751$	27.3438	0.997788	0.498894	+	0.866663i	$0.333740\pi$
$752$	−89.5429	−3.26529
$753$	−43.5665	−1.58765
$754$	−17.1792	−0.625630
$755$	34.6623	1.26149
$756$	177.245	6.44634
$757$	39.5852	1.43875	0.719374	−	0.694623i	$-0.244429\pi$
$757$	39.5852	1.43875	0.719374	+	0.694623i	$0.244429\pi$
$758$	−35.1289	−1.27594
$759$	6.04570	0.219445
$760$	−39.7556	−1.44209
$761$	38.3626	1.39064	0.695321	−	0.718700i	$-0.255262\pi$
$761$	38.3626	1.39064	0.695321	+	0.718700i	$0.255262\pi$
$762$	−77.1483	−2.79479
$763$	−2.66065	−0.0963218
$764$	−28.4753	−1.03020
$765$	−36.7824	−1.32987
$766$	11.6771	0.421910
$767$	−6.07914	−0.219505
$768$	38.2338	1.37964
$769$	32.6877	1.17875	0.589375	−	0.807860i	$-0.299374\pi$
$769$	32.6877	1.17875	0.589375	+	0.807860i	$0.299374\pi$
$770$	−31.0148	−1.11769
$771$	−18.9112	−0.681070
$772$	22.3718	0.805177
$773$	48.2911	1.73691	0.868456	−	0.495767i	$-0.165113\pi$
$773$	48.2911	1.73691	0.868456	+	0.495767i	$0.165113\pi$
$774$	172.073	6.18504
$775$	−63.7563	−2.29020
$776$	56.8923	2.04231
$777$	−8.57984	−0.307800
$778$	−11.8301	−0.424131
$779$	−10.2677	−0.367878
$780$	−67.1998	−2.40614
$781$	6.95624	0.248914
$782$	5.75326	0.205736
$783$	−83.0462	−2.96783
$784$	2.08210	0.0743607
$785$	−67.2754	−2.40116
$786$	147.872	5.27443
$787$	2.33965	0.0833995	0.0416997	−	0.999130i	$-0.486723\pi$
$787$	2.33965	0.0833995	0.0416997	+	0.999130i	$0.486723\pi$
$788$	31.4827	1.12152
$789$	54.3383	1.93450
$790$	−134.500	−4.78530
$791$	48.4896	1.72409
$792$	59.7946	2.12471
$793$	15.9211	0.565376
$794$	−64.8650	−2.30197
$795$	−72.5595	−2.57342
$796$	62.3684	2.21059
$797$	−24.1895	−0.856835	−0.428418	−	0.903581i	$-0.640929\pi$
$797$	−24.1895	−0.856835	−0.428418	+	0.903581i	$0.640929\pi$
$798$	−29.1246	−1.03100
$799$	11.0774	0.391891
$800$	−130.888	−4.62759
$801$	−4.01427	−0.141837
$802$	76.6902	2.70803
$803$	2.49087	0.0879009
$804$	−218.556	−7.70787
$805$	−18.8488	−0.664332
$806$	15.6869	0.552548
$807$	8.88906	0.312910
$808$	−42.9291	−1.51024
$809$	−18.1788	−0.639133	−0.319566	−	0.947564i	$-0.603537\pi$
$809$	−18.1788	−0.639133	−0.319566	+	0.947564i	$0.603537\pi$
$810$	−227.648	−7.99872
$811$	10.1037	0.354790	0.177395	−	0.984140i	$-0.443233\pi$
$811$	10.1037	0.354790	0.177395	+	0.984140i	$0.443233\pi$
$812$	−80.9675	−2.84140
$813$	−46.1770	−1.61950
$814$	−2.85890	−0.100205
$815$	4.04178	0.141577
$816$	41.0747	1.43790
$817$	−11.7321	−0.410454
$818$	73.1689	2.55829
$819$	−20.5749	−0.718946
$820$	−157.254	−5.49156
$821$	29.3409	1.02401	0.512003	−	0.858984i	$-0.328904\pi$
$821$	29.3409	1.02401	0.512003	+	0.858984i	$0.328904\pi$
$822$	89.7161	3.12921
$823$	15.7010	0.547301	0.273650	−	0.961829i	$-0.411769\pi$
$823$	15.7010	0.547301	0.273650	+	0.961829i	$0.411769\pi$
$824$	−9.26333	−0.322703
$825$	39.4451	1.37330
$826$	−40.3519	−1.40402
$827$	−17.3942	−0.604856	−0.302428	−	0.953172i	$-0.597797\pi$
$827$	−17.3942	−0.604856	−0.302428	+	0.953172i	$0.597797\pi$
$828$	61.4213	2.13454
$829$	−14.1793	−0.492469	−0.246234	−	0.969210i	$-0.579193\pi$
$829$	−14.1793	−0.492469	−0.246234	+	0.969210i	$0.579193\pi$
$830$	−147.712	−5.12717
$831$	−45.0348	−1.56224
$832$	10.5574	0.366010
$833$	−0.257578	−0.00892455
$834$	70.9870	2.45808
$835$	60.0417	2.07783
$836$	−6.89075	−0.238322
$837$	75.8323	2.62115
$838$	−100.521	−3.47244
$839$	19.8290	0.684572	0.342286	−	0.939596i	$-0.388799\pi$
$839$	19.8290	0.684572	0.342286	+	0.939596i	$0.388799\pi$
$840$	−263.904	−9.10557
$841$	8.93645	0.308154
$842$	32.7146	1.12742
$843$	73.2158	2.52169
$844$	−25.8584	−0.890084
$845$	−47.9847	−1.65072
$846$	166.555	5.72627
$847$	26.3444	0.905205
$848$	57.2374	1.96554
$849$	51.9505	1.78294
$850$	37.5370	1.28751
$851$	−1.73746	−0.0595593
$852$	100.045	3.42749
$853$	53.1439	1.81961	0.909806	−	0.415033i	$-0.136230\pi$
$853$	53.1439	1.81961	0.909806	+	0.415033i	$0.136230\pi$
$854$	105.681	3.61632
$855$	37.7069	1.28955
$856$	−38.0678	−1.30113
$857$	35.0992	1.19897	0.599483	−	0.800388i	$-0.295373\pi$
$857$	35.0992	1.19897	0.599483	+	0.800388i	$0.295373\pi$
$858$	−9.70526	−0.331332
$859$	26.6349	0.908772	0.454386	−	0.890805i	$-0.349859\pi$
$859$	26.6349	0.908772	0.454386	+	0.890805i	$0.349859\pi$
$860$	−179.682	−6.12711
$861$	−68.1588	−2.32284
$862$	−100.626	−3.42732
$863$	19.5495	0.665472	0.332736	−	0.943020i	$-0.392028\pi$
$863$	19.5495	0.665472	0.332736	+	0.943020i	$0.392028\pi$
$864$	155.679	5.29631
$865$	−87.6447	−2.98001
$866$	−13.8637	−0.471109
$867$	49.2602	1.67296
$868$	73.9342	2.50949
$869$	−13.7927	−0.467884
$870$	208.995	7.08558
$871$	14.8258	0.502352
$872$	−7.54373	−0.255463
$873$	−53.9606	−1.82629
$874$	−5.89786	−0.199498
$875$	−68.7361	−2.32370
$876$	35.8238	1.21037
$877$	−3.94808	−0.133317	−0.0666586	−	0.997776i	$-0.521234\pi$
$877$	−3.94808	−0.133317	−0.0666586	+	0.997776i	$0.521234\pi$
$878$	74.5932	2.51740
$879$	20.8060	0.701770
$880$	−44.8399	−1.51155
$881$	−12.9491	−0.436267	−0.218134	−	0.975919i	$-0.569997\pi$
$881$	−12.9491	−0.436267	−0.218134	+	0.975919i	$0.569997\pi$
$882$	−3.87282	−0.130405
$883$	34.5778	1.16363	0.581817	−	0.813320i	$-0.302342\pi$
$883$	34.5778	1.16363	0.581817	+	0.813320i	$0.302342\pi$
$884$	−6.55784	−0.220564
$885$	73.9560	2.48601
$886$	−59.6376	−2.00356
$887$	3.83226	0.128675	0.0643374	−	0.997928i	$-0.479507\pi$
$887$	3.83226	0.128675	0.0643374	+	0.997928i	$0.479507\pi$
$888$	−24.3264	−0.816341
$889$	24.6654	0.827252
$890$	5.90353	0.197887
$891$	−23.3447	−0.782078
$892$	−0.652931	−0.0218617
$893$	−11.3558	−0.380009
$894$	125.773	4.20646
$895$	25.5831	0.855148
$896$	8.09528	0.270444
$897$	−5.89823	−0.196936
$898$	2.80412	0.0935746
$899$	−34.6411	−1.15534
$900$	400.742	13.3581
$901$	−7.08088	−0.235898
$902$	−22.7113	−0.756204
$903$	−77.8796	−2.59167
$904$	137.482	4.57260
$905$	53.2002	1.76843
$906$	71.9975	2.39196
$907$	54.8504	1.82128	0.910640	−	0.413202i	$-0.135590\pi$
$907$	54.8504	1.82128	0.910640	+	0.413202i	$0.135590\pi$
$908$	42.1646	1.39928
$909$	40.7169	1.35050
$910$	30.2582	1.00305
$911$	−11.1657	−0.369937	−0.184969	−	0.982744i	$-0.559218\pi$
$911$	−11.1657	−0.369937	−0.184969	+	0.982744i	$0.559218\pi$
$912$	−42.1071	−1.39431
$913$	−15.1476	−0.501311
$914$	37.0854	1.22668
$915$	−193.689	−6.40317
$916$	41.6511	1.37619
$917$	−47.2769	−1.56122
$918$	−44.6468	−1.47357
$919$	−52.1567	−1.72049	−0.860246	−	0.509879i	$-0.829690\pi$
$919$	−52.1567	−1.72049	−0.860246	+	0.509879i	$0.829690\pi$
$920$	−53.4419	−1.76193
$921$	6.17431	0.203450
$922$	−34.4560	−1.13475
$923$	−6.78656	−0.223382
$924$	−45.7420	−1.50480
$925$	−11.3360	−0.372726
$926$	79.8790	2.62499
$927$	8.78598	0.288569
$928$	−71.1160	−2.33450
$929$	−7.23105	−0.237243	−0.118622	−	0.992940i	$-0.537848\pi$
$929$	−7.23105	−0.237243	−0.118622	+	0.992940i	$0.537848\pi$
$930$	−190.840	−6.25789
$931$	0.264052	0.00865396
$932$	18.6660	0.611426
$933$	−99.3884	−3.25383
$934$	−70.2960	−2.30016
$935$	5.54717	0.181412
$936$	−58.3360	−1.90677
$937$	37.9182	1.23873	0.619366	−	0.785102i	$-0.287390\pi$
$937$	37.9182	1.23873	0.619366	+	0.785102i	$0.287390\pi$
$938$	98.4098	3.21319
$939$	31.0693	1.01391
$940$	−173.920	−5.67264
$941$	−26.0952	−0.850678	−0.425339	−	0.905034i	$-0.639845\pi$
$941$	−26.0952	−0.850678	−0.425339	+	0.905034i	$0.639845\pi$
$942$	−139.739	−4.55293
$943$	−13.8025	−0.449470
$944$	−58.3391	−1.89878
$945$	146.272	4.75822
$946$	−25.9504	−0.843721
$947$	29.0445	0.943818	0.471909	−	0.881647i	$-0.343565\pi$
$947$	29.0445	0.943818	0.471909	+	0.881647i	$0.343565\pi$
$948$	−198.367	−6.44266
$949$	−2.43011	−0.0788848
$950$	−38.4805	−1.24847
$951$	28.5291	0.925121
$952$	−25.7537	−0.834682
$953$	23.6748	0.766901	0.383451	−	0.923561i	$-0.374736\pi$
$953$	23.6748	0.766901	0.383451	+	0.923561i	$0.374736\pi$
$954$	−106.465	−3.44692
$955$	−23.4993	−0.760419
$956$	39.6531	1.28247
$957$	21.4319	0.692795
$958$	−32.1486	−1.03867
$959$	−28.6835	−0.926240
$960$	−128.436	−4.14525
$961$	0.631960	0.0203858
$962$	2.78917	0.0899264
$963$	36.1061	1.16350
$964$	−135.605	−4.36755
$965$	18.4623	0.594323
$966$	−39.1511	−1.25966
$967$	−45.5431	−1.46457	−0.732284	−	0.680999i	$-0.761546\pi$
$967$	−45.5431	−1.46457	−0.732284	+	0.680999i	$0.761546\pi$
$968$	74.6943	2.40076
$969$	5.20910	0.167340
$970$	79.3564	2.54798
$971$	−25.6709	−0.823820	−0.411910	−	0.911225i	$-0.635138\pi$
$971$	−25.6709	−0.823820	−0.411910	+	0.911225i	$0.635138\pi$
$972$	−137.638	−4.41476
$973$	−22.6956	−0.727587
$974$	57.0978	1.82953
$975$	−38.4829	−1.23244
$976$	152.789	4.89065
$977$	11.8272	0.378385	0.189193	−	0.981940i	$-0.439413\pi$
$977$	11.8272	0.378385	0.189193	+	0.981940i	$0.439413\pi$
$978$	8.39525	0.268450
$979$	0.605394	0.0193485
$980$	4.04407	0.129183
$981$	7.15499	0.228441
$982$	110.255	3.51837
$983$	17.8146	0.568196	0.284098	−	0.958795i	$-0.408306\pi$
$983$	17.8146	0.568196	0.284098	+	0.958795i	$0.408306\pi$
$984$	−193.250	−6.16060
$985$	25.9811	0.827827
$986$	20.3952	0.649515
$987$	−75.3821	−2.39944
$988$	6.72267	0.213877
$989$	−15.7710	−0.501488
$990$	83.4047	2.65077
$991$	−15.6236	−0.496299	−0.248150	−	0.968722i	$-0.579823\pi$
$991$	−15.6236	−0.496299	−0.248150	+	0.968722i	$0.579823\pi$
$992$	64.9385	2.06180
$993$	97.9716	3.10903
$994$	−45.0476	−1.42882
$995$	51.4696	1.63170
$996$	−217.853	−6.90293
$997$	14.6873	0.465152	0.232576	−	0.972578i	$-0.425285\pi$
$997$	14.6873	0.465152	0.232576	+	0.972578i	$0.425285\pi$
$998$	−22.2282	−0.703622
$999$	13.4831	0.426588

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.d.1.5	✓	133

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.d.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-2.62634 q^{2} -3.19656 q^{3} +4.89764 q^{4} +4.04178 q^{5} +8.39525 q^{6} -2.68408 q^{7} -7.61017 q^{8} +7.21801 q^{9} +O(q^{10})\)	\(q-2.62634 q^{2} -3.19656 q^{3} +4.89764 q^{4} +4.04178 q^{5} +8.39525 q^{6} -2.68408 q^{7} -7.61017 q^{8} +7.21801 q^{9} -10.6151 q^{10} -1.08855 q^{11} -15.6556 q^{12} +1.06200 q^{13} +7.04930 q^{14} -12.9198 q^{15} +10.1916 q^{16} -1.26081 q^{17} -18.9569 q^{18} +1.29250 q^{19} +19.7952 q^{20} +8.57984 q^{21} +2.85890 q^{22} +1.73746 q^{23} +24.3264 q^{24} +11.3360 q^{25} -2.78917 q^{26} -13.4831 q^{27} -13.1457 q^{28} +6.15926 q^{29} +33.9318 q^{30} -5.62423 q^{31} -11.5462 q^{32} +3.47963 q^{33} +3.31131 q^{34} -10.8485 q^{35} +35.3512 q^{36} -1.00000 q^{37} -3.39454 q^{38} -3.39475 q^{39} -30.7587 q^{40} -7.94406 q^{41} -22.5335 q^{42} -9.07705 q^{43} -5.33134 q^{44} +29.1736 q^{45} -4.56315 q^{46} -8.78596 q^{47} -32.5781 q^{48} +0.204296 q^{49} -29.7722 q^{50} +4.03026 q^{51} +5.20129 q^{52} +5.61614 q^{53} +35.4113 q^{54} -4.39969 q^{55} +20.4263 q^{56} -4.13155 q^{57} -16.1763 q^{58} -5.72423 q^{59} -63.2766 q^{60} +14.9917 q^{61} +14.7711 q^{62} -19.3737 q^{63} +9.94101 q^{64} +4.29237 q^{65} -9.13867 q^{66} +13.9602 q^{67} -6.17499 q^{68} -5.55389 q^{69} +28.4917 q^{70} -6.39036 q^{71} -54.9303 q^{72} -2.28824 q^{73} +2.62634 q^{74} -36.2363 q^{75} +6.33019 q^{76} +2.92176 q^{77} +8.91575 q^{78} +12.6707 q^{79} +41.1922 q^{80} +21.4457 q^{81} +20.8638 q^{82} +13.9153 q^{83} +42.0209 q^{84} -5.09592 q^{85} +23.8394 q^{86} -19.6885 q^{87} +8.28407 q^{88} -0.556146 q^{89} -76.6198 q^{90} -2.85050 q^{91} +8.50944 q^{92} +17.9782 q^{93} +23.0749 q^{94} +5.22400 q^{95} +36.9082 q^{96} -7.47582 q^{97} -0.536549 q^{98} -7.85719 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9}+O(q^{10}) \) 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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