LMFDB - Embedded newform 6023.2.a.b.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, 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("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$1$
Dimension:	$99$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.56636 q^{2} +2.86321 q^{3} +4.58620 q^{4} -1.49629 q^{5} -7.34803 q^{6} -1.31440 q^{7} -6.63713 q^{8} +5.19797 q^{9} +O(q^{10})$	\(q-2.56636 q^{2} +2.86321 q^{3} +4.58620 q^{4} -1.49629 q^{5} -7.34803 q^{6} -1.31440 q^{7} -6.63713 q^{8} +5.19797 q^{9} +3.84001 q^{10} +5.98208 q^{11} +13.1313 q^{12} +1.85013 q^{13} +3.37322 q^{14} -4.28419 q^{15} +7.86086 q^{16} -3.46147 q^{17} -13.3399 q^{18} -1.00000 q^{19} -6.86228 q^{20} -3.76340 q^{21} -15.3522 q^{22} +0.442595 q^{23} -19.0035 q^{24} -2.76112 q^{25} -4.74811 q^{26} +6.29324 q^{27} -6.02810 q^{28} -2.74531 q^{29} +10.9948 q^{30} +0.0954084 q^{31} -6.89954 q^{32} +17.1279 q^{33} +8.88339 q^{34} +1.96672 q^{35} +23.8389 q^{36} -10.1880 q^{37} +2.56636 q^{38} +5.29732 q^{39} +9.93106 q^{40} -2.51996 q^{41} +9.65824 q^{42} -7.29343 q^{43} +27.4350 q^{44} -7.77765 q^{45} -1.13586 q^{46} -3.12300 q^{47} +22.5073 q^{48} -5.27235 q^{49} +7.08603 q^{50} -9.91092 q^{51} +8.48509 q^{52} -10.9108 q^{53} -16.1507 q^{54} -8.95091 q^{55} +8.72384 q^{56} -2.86321 q^{57} +7.04545 q^{58} -4.29096 q^{59} -19.6481 q^{60} -0.761735 q^{61} -0.244852 q^{62} -6.83220 q^{63} +1.98498 q^{64} -2.76833 q^{65} -43.9565 q^{66} -8.54232 q^{67} -15.8750 q^{68} +1.26724 q^{69} -5.04731 q^{70} +6.58317 q^{71} -34.4996 q^{72} -2.57828 q^{73} +26.1461 q^{74} -7.90567 q^{75} -4.58620 q^{76} -7.86284 q^{77} -13.5948 q^{78} +0.758087 q^{79} -11.7621 q^{80} +2.42495 q^{81} +6.46713 q^{82} -11.7656 q^{83} -17.2597 q^{84} +5.17936 q^{85} +18.7176 q^{86} -7.86040 q^{87} -39.7039 q^{88} +1.41961 q^{89} +19.9603 q^{90} -2.43181 q^{91} +2.02983 q^{92} +0.273174 q^{93} +8.01475 q^{94} +1.49629 q^{95} -19.7548 q^{96} -14.5041 q^{97} +13.5308 q^{98} +31.0946 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9}+O(q^{10}) $ 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9	\( 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9} - 6 q^{10} - 9 q^{11} - 27 q^{12} - 28 q^{13} - 13 q^{14} - 10 q^{15} + 38 q^{16} - 36 q^{17} - 14 q^{18} - 99 q^{19} - 34 q^{20} - 20 q^{21} - 53 q^{22} - 38 q^{23} - 25 q^{24} - 8 q^{25} - 3 q^{26} - 3 q^{27} - 63 q^{28} - 34 q^{29} - 30 q^{30} - 16 q^{31} - 43 q^{32} - 41 q^{33} - 14 q^{34} - 25 q^{35} - 16 q^{36} - 80 q^{37} + 4 q^{38} - 48 q^{39} - 10 q^{40} - 32 q^{41} - 37 q^{42} - 76 q^{43} - 21 q^{44} - 53 q^{45} - 23 q^{46} - 31 q^{47} - 74 q^{48} - 32 q^{49} - 29 q^{50} - 30 q^{51} - 71 q^{52} - 35 q^{53} - 80 q^{54} - 45 q^{55} - 33 q^{56} + 3 q^{57} - 91 q^{58} + 12 q^{59} - 56 q^{60} - 61 q^{61} - 46 q^{62} - 43 q^{63} - 30 q^{64} - 46 q^{65} - 75 q^{66} - 26 q^{67} - 55 q^{68} - 45 q^{69} - 76 q^{70} - 41 q^{71} - 77 q^{72} - 143 q^{73} - 64 q^{74} - 8 q^{75} - 80 q^{76} - 58 q^{77} - 34 q^{78} - 22 q^{79} - 36 q^{80} - 81 q^{81} - 109 q^{82} - 7 q^{83} - 6 q^{84} - 80 q^{85} + 32 q^{86} - 57 q^{87} - 120 q^{88} - 28 q^{89} - 12 q^{90} - 30 q^{91} - 107 q^{92} - 121 q^{93} + 8 q^{94} + 15 q^{95} + 4 q^{96} - 128 q^{97} + 54 q^{98} - 34 q^{99}+O(q^{100}) \) 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9 - 6 * q^10 - 9 * q^11 - 27 * q^12 - 28 * q^13 - 13 * q^14 - 10 * q^15 + 38 * q^16 - 36 * q^17 - 14 * q^18 - 99 * q^19 - 34 * q^20 - 20 * q^21 - 53 * q^22 - 38 * q^23 - 25 * q^24 - 8 * q^25 - 3 * q^26 - 3 * q^27 - 63 * q^28 - 34 * q^29 - 30 * q^30 - 16 * q^31 - 43 * q^32 - 41 * q^33 - 14 * q^34 - 25 * q^35 - 16 * q^36 - 80 * q^37 + 4 * q^38 - 48 * q^39 - 10 * q^40 - 32 * q^41 - 37 * q^42 - 76 * q^43 - 21 * q^44 - 53 * q^45 - 23 * q^46 - 31 * q^47 - 74 * q^48 - 32 * q^49 - 29 * q^50 - 30 * q^51 - 71 * q^52 - 35 * q^53 - 80 * q^54 - 45 * q^55 - 33 * q^56 + 3 * q^57 - 91 * q^58 + 12 * q^59 - 56 * q^60 - 61 * q^61 - 46 * q^62 - 43 * q^63 - 30 * q^64 - 46 * q^65 - 75 * q^66 - 26 * q^67 - 55 * q^68 - 45 * q^69 - 76 * q^70 - 41 * q^71 - 77 * q^72 - 143 * q^73 - 64 * q^74 - 8 * q^75 - 80 * q^76 - 58 * q^77 - 34 * q^78 - 22 * q^79 - 36 * q^80 - 81 * q^81 - 109 * q^82 - 7 * q^83 - 6 * q^84 - 80 * q^85 + 32 * q^86 - 57 * q^87 - 120 * q^88 - 28 * q^89 - 12 * q^90 - 30 * q^91 - 107 * q^92 - 121 * q^93 + 8 * q^94 + 15 * q^95 + 4 * q^96 - 128 * q^97 + 54 * q^98 - 34 * 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 $

$2$	−2.56636	−1.81469	−0.907345	−	0.420386i	$-0.861895\pi$
$2$	−2.56636	−1.81469	−0.907345	+	0.420386i	$0.861895\pi$
$3$	2.86321	1.65307	0.826537	−	0.562882i	$-0.190307\pi$
$3$	2.86321	1.65307	0.826537	+	0.562882i	$0.190307\pi$
$4$	4.58620	2.29310
$5$	−1.49629	−0.669160	−0.334580	−	0.942367i	$-0.608594\pi$
$5$	−1.49629	−0.669160	−0.334580	+	0.942367i	$0.608594\pi$
$6$	−7.34803	−2.99982
$7$	−1.31440	−0.496796	−0.248398	−	0.968658i	$-0.579904\pi$
$7$	−1.31440	−0.496796	−0.248398	+	0.968658i	$0.579904\pi$
$8$	−6.63713	−2.34658
$9$	5.19797	1.73266
$10$	3.84001	1.21432
$11$	5.98208	1.80367	0.901833	−	0.432086i	$-0.142222\pi$
$11$	5.98208	1.80367	0.901833	+	0.432086i	$0.142222\pi$
$12$	13.1313	3.79067
$13$	1.85013	0.513135	0.256567	−	0.966526i	$-0.417408\pi$
$13$	1.85013	0.513135	0.256567	+	0.966526i	$0.417408\pi$
$14$	3.37322	0.901531
$15$	−4.28419	−1.10617
$16$	7.86086	1.96522
$17$	−3.46147	−0.839531	−0.419765	−	0.907633i	$-0.637888\pi$
$17$	−3.46147	−0.839531	−0.419765	+	0.907633i	$0.637888\pi$
$18$	−13.3399	−3.14423
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−6.86228	−1.53445
$21$	−3.76340	−0.821241
$22$	−15.3522	−3.27309
$23$	0.442595	0.0922874	0.0461437	−	0.998935i	$-0.485307\pi$
$23$	0.442595	0.0922874	0.0461437	+	0.998935i	$0.485307\pi$
$24$	−19.0035	−3.87907
$25$	−2.76112	−0.552224
$26$	−4.74811	−0.931181
$27$	6.29324	1.21113
$28$	−6.02810	−1.13920
$29$	−2.74531	−0.509791	−0.254896	−	0.966969i	$-0.582041\pi$
$29$	−2.74531	−0.509791	−0.254896	+	0.966969i	$0.582041\pi$
$30$	10.9948	2.00736
$31$	0.0954084	0.0171359	0.00856793	−	0.999963i	$-0.497273\pi$
$31$	0.0954084	0.0171359	0.00856793	+	0.999963i	$0.497273\pi$
$32$	−6.89954	−1.21968
$33$	17.1279	2.98159
$34$	8.88339	1.52349
$35$	1.96672	0.332436
$36$	23.8389	3.97316
$37$	−10.1880	−1.67490	−0.837450	−	0.546514i	$-0.815955\pi$
$37$	−10.1880	−1.67490	−0.837450	+	0.546514i	$0.815955\pi$
$38$	2.56636	0.416319
$39$	5.29732	0.848250
$40$	9.93106	1.57024
$41$	−2.51996	−0.393552	−0.196776	−	0.980448i	$-0.563047\pi$
$41$	−2.51996	−0.393552	−0.196776	+	0.980448i	$0.563047\pi$
$42$	9.65824	1.49030
$43$	−7.29343	−1.11224	−0.556119	−	0.831103i	$-0.687710\pi$
$43$	−7.29343	−1.11224	−0.556119	+	0.831103i	$0.687710\pi$
$44$	27.4350	4.13599
$45$	−7.77765	−1.15942
$46$	−1.13586	−0.167473
$47$	−3.12300	−0.455537	−0.227768	−	0.973715i	$-0.573143\pi$
$47$	−3.12300	−0.455537	−0.227768	+	0.973715i	$0.573143\pi$
$48$	22.5073	3.24865
$49$	−5.27235	−0.753194
$50$	7.08603	1.00212
$51$	−9.91092	−1.38781
$52$	8.48509	1.17667
$53$	−10.9108	−1.49871	−0.749354	−	0.662170i	$-0.769636\pi$
$53$	−10.9108	−1.49871	−0.749354	+	0.662170i	$0.769636\pi$
$54$	−16.1507	−2.19783
$55$	−8.95091	−1.20694
$56$	8.72384	1.16577
$57$	−2.86321	−0.379241
$58$	7.04545	0.925114
$59$	−4.29096	−0.558636	−0.279318	−	0.960199i	$-0.590108\pi$
$59$	−4.29096	−0.558636	−0.279318	+	0.960199i	$0.590108\pi$
$60$	−19.6481	−2.53657
$61$	−0.761735	−0.0975302	−0.0487651	−	0.998810i	$-0.515529\pi$
$61$	−0.761735	−0.0975302	−0.0487651	+	0.998810i	$0.515529\pi$
$62$	−0.244852	−0.0310963
$63$	−6.83220	−0.860777
$64$	1.98498	0.248122
$65$	−2.76833	−0.343369
$66$	−43.9565	−5.41067
$67$	−8.54232	−1.04361	−0.521805	−	0.853065i	$-0.674741\pi$
$67$	−8.54232	−1.04361	−0.521805	+	0.853065i	$0.674741\pi$
$68$	−15.8750	−1.92513
$69$	1.26724	0.152558
$70$	−5.04731	−0.603269
$71$	6.58317	0.781279	0.390639	−	0.920544i	$-0.372254\pi$
$71$	6.58317	0.781279	0.390639	+	0.920544i	$0.372254\pi$
$72$	−34.4996	−4.06581
$73$	−2.57828	−0.301765	−0.150883	−	0.988552i	$-0.548212\pi$
$73$	−2.57828	−0.301765	−0.150883	+	0.988552i	$0.548212\pi$
$74$	26.1461	3.03943
$75$	−7.90567	−0.912868
$76$	−4.58620	−0.526074
$77$	−7.86284	−0.896054
$78$	−13.5948	−1.53931
$79$	0.758087	0.0852915	0.0426457	−	0.999090i	$-0.486421\pi$
$79$	0.758087	0.0852915	0.0426457	+	0.999090i	$0.486421\pi$
$80$	−11.7621	−1.31504
$81$	2.42495	0.269439
$82$	6.46713	0.714176
$83$	−11.7656	−1.29145	−0.645723	−	0.763571i	$-0.723444\pi$
$83$	−11.7656	−1.29145	−0.645723	+	0.763571i	$0.723444\pi$
$84$	−17.2597	−1.88319
$85$	5.17936	0.561781
$86$	18.7176	2.01837
$87$	−7.86040	−0.842723
$88$	−39.7039	−4.23245
$89$	1.41961	0.150479	0.0752394	−	0.997165i	$-0.476028\pi$
$89$	1.41961	0.150479	0.0752394	+	0.997165i	$0.476028\pi$
$90$	19.9603	2.10400
$91$	−2.43181	−0.254923
$92$	2.02983	0.211624
$93$	0.273174	0.0283268
$94$	8.01475	0.826658
$95$	1.49629	0.153516
$96$	−19.7548	−2.01622
$97$	−14.5041	−1.47267	−0.736335	−	0.676617i	$-0.763445\pi$
$97$	−14.5041	−1.47267	−0.736335	+	0.676617i	$0.763445\pi$
$98$	13.5308	1.36681
$99$	31.0946	3.12513
$100$	−12.6631	−1.26631
$101$	−0.875507	−0.0871162	−0.0435581	−	0.999051i	$-0.513869\pi$
$101$	−0.875507	−0.0871162	−0.0435581	+	0.999051i	$0.513869\pi$
$102$	25.4350	2.51844
$103$	17.3091	1.70551	0.852757	−	0.522308i	$-0.174929\pi$
$103$	17.3091	1.70551	0.852757	+	0.522308i	$0.174929\pi$
$104$	−12.2796	−1.20411
$105$	5.63113	0.549542
$106$	28.0009	2.71969
$107$	3.86462	0.373607	0.186804	−	0.982397i	$-0.440187\pi$
$107$	3.86462	0.373607	0.186804	+	0.982397i	$0.440187\pi$
$108$	28.8621	2.77725
$109$	13.7614	1.31811	0.659053	−	0.752096i	$-0.270957\pi$
$109$	13.7614	1.31811	0.659053	+	0.752096i	$0.270957\pi$
$110$	22.9713	2.19022
$111$	−29.1704	−2.76874
$112$	−10.3323	−0.976312
$113$	−6.56733	−0.617802	−0.308901	−	0.951094i	$-0.599961\pi$
$113$	−6.56733	−0.617802	−0.308901	+	0.951094i	$0.599961\pi$
$114$	7.34803	0.688206
$115$	−0.662249	−0.0617551
$116$	−12.5906	−1.16900
$117$	9.61693	0.889086
$118$	11.0122	1.01375
$119$	4.54976	0.417076
$120$	28.4347	2.59572
$121$	24.7853	2.25321
$122$	1.95489	0.176987
$123$	−7.21518	−0.650571
$124$	0.437562	0.0392943
$125$	11.6129	1.03869
$126$	17.5339	1.56204
$127$	−1.98474	−0.176117	−0.0880584	−	0.996115i	$-0.528066\pi$
$127$	−1.98474	−0.176117	−0.0880584	+	0.996115i	$0.528066\pi$
$128$	8.70491	0.769413
$129$	−20.8826	−1.83861
$130$	7.10454	0.623109
$131$	−4.35732	−0.380701	−0.190350	−	0.981716i	$-0.560962\pi$
$131$	−4.35732	−0.380701	−0.190350	+	0.981716i	$0.560962\pi$
$132$	78.5523	6.83710
$133$	1.31440	0.113973
$134$	21.9227	1.89383
$135$	−9.41649	−0.810443
$136$	22.9743	1.97003
$137$	6.45791	0.551737	0.275868	−	0.961195i	$-0.411035\pi$
$137$	6.45791	0.551737	0.275868	+	0.961195i	$0.411035\pi$
$138$	−3.25220	−0.276846
$139$	−6.89376	−0.584721	−0.292360	−	0.956308i	$-0.594441\pi$
$139$	−6.89376	−0.584721	−0.292360	+	0.956308i	$0.594441\pi$
$140$	9.01978	0.762310
$141$	−8.94181	−0.753036
$142$	−16.8948	−1.41778
$143$	11.0676	0.925523
$144$	40.8605	3.40504
$145$	4.10777	0.341132
$146$	6.61680	0.547610
$147$	−15.0959	−1.24509
$148$	−46.7244	−3.84072
$149$	19.8092	1.62283	0.811416	−	0.584468i	$-0.198697\pi$
$149$	19.8092	1.62283	0.811416	+	0.584468i	$0.198697\pi$
$150$	20.2888	1.65657
$151$	15.8862	1.29280	0.646399	−	0.763000i	$-0.276274\pi$
$151$	15.8862	1.29280	0.646399	+	0.763000i	$0.276274\pi$
$152$	6.63713	0.538342
$153$	−17.9926	−1.45462
$154$	20.1789	1.62606
$155$	−0.142758	−0.0114666
$156$	24.2946	1.94512
$157$	5.68950	0.454072	0.227036	−	0.973886i	$-0.427097\pi$
$157$	5.68950	0.454072	0.227036	+	0.973886i	$0.427097\pi$
$158$	−1.94552	−0.154778
$159$	−31.2398	−2.47748
$160$	10.3237	0.816160
$161$	−0.581746	−0.0458480
$162$	−6.22330	−0.488948
$163$	−12.1043	−0.948084	−0.474042	−	0.880502i	$-0.657206\pi$
$163$	−12.1043	−0.948084	−0.474042	+	0.880502i	$0.657206\pi$
$164$	−11.5571	−0.902455
$165$	−25.6283	−1.99516
$166$	30.1949	2.34358
$167$	3.61094	0.279423	0.139712	−	0.990192i	$-0.455382\pi$
$167$	3.61094	0.279423	0.139712	+	0.990192i	$0.455382\pi$
$168$	24.9782	1.92711
$169$	−9.57701	−0.736693
$170$	−13.2921	−1.01946
$171$	−5.19797	−0.397498
$172$	−33.4491	−2.55047
$173$	21.9374	1.66787	0.833934	−	0.551864i	$-0.186083\pi$
$173$	21.9374	1.66787	0.833934	+	0.551864i	$0.186083\pi$
$174$	20.1726	1.52928
$175$	3.62922	0.274343
$176$	47.0243	3.54459
$177$	−12.2859	−0.923466
$178$	−3.64324	−0.273073
$179$	−3.58063	−0.267629	−0.133814	−	0.991006i	$-0.542723\pi$
$179$	−3.58063	−0.267629	−0.133814	+	0.991006i	$0.542723\pi$
$180$	−35.6699	−2.65868
$181$	−24.7806	−1.84193	−0.920964	−	0.389647i	$-0.872597\pi$
$181$	−24.7806	−1.84193	−0.920964	+	0.389647i	$0.872597\pi$
$182$	6.24091	0.462607
$183$	−2.18101	−0.161225
$184$	−2.93756	−0.216560
$185$	15.2442	1.12078
$186$	−0.701063	−0.0514045
$187$	−20.7068	−1.51423
$188$	−14.3227	−1.04459
$189$	−8.27182	−0.601687
$190$	−3.84001	−0.278584
$191$	−3.32468	−0.240565	−0.120283	−	0.992740i	$-0.538380\pi$
$191$	−3.32468	−0.240565	−0.120283	+	0.992740i	$0.538380\pi$
$192$	5.68340	0.410164
$193$	−16.1728	−1.16414	−0.582071	−	0.813138i	$-0.697757\pi$
$193$	−16.1728	−1.16414	−0.582071	+	0.813138i	$0.697757\pi$
$194$	37.2228	2.67244
$195$	−7.92631	−0.567615
$196$	−24.1801	−1.72715
$197$	18.6870	1.33140	0.665698	−	0.746221i	$-0.268134\pi$
$197$	18.6870	1.33140	0.665698	+	0.746221i	$0.268134\pi$
$198$	−79.8001	−5.67114
$199$	−15.2624	−1.08192	−0.540962	−	0.841047i	$-0.681940\pi$
$199$	−15.2624	−1.08192	−0.540962	+	0.841047i	$0.681940\pi$
$200$	18.3259	1.29584
$201$	−24.4585	−1.72517
$202$	2.24687	0.158089
$203$	3.60843	0.253262
$204$	−45.4535	−3.18238
$205$	3.77059	0.263350
$206$	−44.4213	−3.09498
$207$	2.30059	0.159902
$208$	14.5436	1.00842
$209$	−5.98208	−0.413789
$210$	−14.4515	−0.997249
$211$	3.43041	0.236159	0.118080	−	0.993004i	$-0.462326\pi$
$211$	3.43041	0.236159	0.118080	+	0.993004i	$0.462326\pi$
$212$	−50.0390	−3.43669
$213$	18.8490	1.29151
$214$	−9.91802	−0.677982
$215$	10.9131	0.744265
$216$	−41.7690	−2.84202
$217$	−0.125405	−0.00851303
$218$	−35.3168	−2.39196
$219$	−7.38216	−0.498840
$220$	−41.0507	−2.76764
$221$	−6.40419	−0.430792
$222$	74.8618	5.02440
$223$	−0.693707	−0.0464541	−0.0232270	−	0.999730i	$-0.507394\pi$
$223$	−0.693707	−0.0464541	−0.0232270	+	0.999730i	$0.507394\pi$
$224$	9.06875	0.605931
$225$	−14.3522	−0.956815
$226$	16.8541	1.12112
$227$	9.65783	0.641013	0.320506	−	0.947246i	$-0.396147\pi$
$227$	9.65783	0.641013	0.320506	+	0.947246i	$0.396147\pi$
$228$	−13.1313	−0.869639
$229$	1.06564	0.0704193	0.0352096	−	0.999380i	$-0.488790\pi$
$229$	1.06564	0.0704193	0.0352096	+	0.999380i	$0.488790\pi$
$230$	1.69957	0.112066
$231$	−22.5130	−1.48124
$232$	18.2210	1.19627
$233$	23.5170	1.54065	0.770324	−	0.637653i	$-0.220095\pi$
$233$	23.5170	1.54065	0.770324	+	0.637653i	$0.220095\pi$
$234$	−24.6805	−1.61342
$235$	4.67291	0.304827
$236$	−19.6792	−1.28101
$237$	2.17056	0.140993
$238$	−11.6763	−0.756863
$239$	−11.0307	−0.713516	−0.356758	−	0.934197i	$-0.616118\pi$
$239$	−11.0307	−0.713516	−0.356758	+	0.934197i	$0.616118\pi$
$240$	−33.6774	−2.17387
$241$	−15.0306	−0.968208	−0.484104	−	0.875010i	$-0.660854\pi$
$241$	−15.0306	−0.968208	−0.484104	+	0.875010i	$0.660854\pi$
$242$	−63.6080	−4.08888
$243$	−11.9366	−0.765731
$244$	−3.49347	−0.223647
$245$	7.88896	0.504007
$246$	18.5168	1.18059
$247$	−1.85013	−0.117721
$248$	−0.633238	−0.0402107
$249$	−33.6875	−2.13486
$250$	−29.8028	−1.88490
$251$	28.6078	1.80571	0.902855	−	0.429944i	$-0.141467\pi$
$251$	28.6078	1.80571	0.902855	+	0.429944i	$0.141467\pi$
$252$	−31.3339	−1.97385
$253$	2.64764	0.166456
$254$	5.09355	0.319598
$255$	14.8296	0.928665
$256$	−26.3099	−1.64437
$257$	−13.6738	−0.852949	−0.426474	−	0.904500i	$-0.640245\pi$
$257$	−13.6738	−0.852949	−0.426474	+	0.904500i	$0.640245\pi$
$258$	53.5923	3.33651
$259$	13.3911	0.832084
$260$	−12.6961	−0.787381
$261$	−14.2700	−0.883293
$262$	11.1824	0.690854
$263$	−6.92100	−0.426767	−0.213384	−	0.976969i	$-0.568448\pi$
$263$	−6.92100	−0.426767	−0.213384	+	0.976969i	$0.568448\pi$
$264$	−113.680	−6.99655
$265$	16.3256	1.00288
$266$	−3.37322	−0.206825
$267$	4.06465	0.248753
$268$	−39.1768	−2.39311
$269$	−6.23030	−0.379868	−0.189934	−	0.981797i	$-0.560827\pi$
$269$	−6.23030	−0.379868	−0.189934	+	0.981797i	$0.560827\pi$
$270$	24.1661	1.47070
$271$	−14.1717	−0.860871	−0.430436	−	0.902621i	$-0.641640\pi$
$271$	−14.1717	−0.860871	−0.430436	+	0.902621i	$0.641640\pi$
$272$	−27.2102	−1.64986
$273$	−6.96279	−0.421407
$274$	−16.5733	−1.00123
$275$	−16.5173	−0.996028
$276$	5.81183	0.349831
$277$	−28.0618	−1.68607	−0.843035	−	0.537859i	$-0.819233\pi$
$277$	−28.0618	−1.68607	−0.843035	+	0.537859i	$0.819233\pi$
$278$	17.6919	1.06109
$279$	0.495930	0.0296905
$280$	−13.0534	−0.780088
$281$	25.3189	1.51040	0.755199	−	0.655495i	$-0.227540\pi$
$281$	25.3189	1.51040	0.755199	+	0.655495i	$0.227540\pi$
$282$	22.9479	1.36653
$283$	2.35984	0.140278	0.0701389	−	0.997537i	$-0.477656\pi$
$283$	2.35984	0.140278	0.0701389	+	0.997537i	$0.477656\pi$
$284$	30.1918	1.79155
$285$	4.28419	0.253773
$286$	−28.4036	−1.67954
$287$	3.31224	0.195515
$288$	−35.8636	−2.11328
$289$	−5.01820	−0.295188
$290$	−10.5420	−0.619049
$291$	−41.5283	−2.43443
$292$	−11.8245	−0.691978
$293$	28.0673	1.63971	0.819854	−	0.572572i	$-0.194054\pi$
$293$	28.0673	1.63971	0.819854	+	0.572572i	$0.194054\pi$
$294$	38.7414	2.25944
$295$	6.42051	0.373817
$296$	67.6192	3.93029
$297$	37.6466	2.18448
$298$	−50.8375	−2.94494
$299$	0.818860	0.0473559
$300$	−36.2570	−2.09330
$301$	9.58647	0.552555
$302$	−40.7696	−2.34603
$303$	−2.50676	−0.144010
$304$	−7.86086	−0.450851
$305$	1.13978	0.0652633
$306$	46.1756	2.63968
$307$	−9.12746	−0.520932	−0.260466	−	0.965483i	$-0.583876\pi$
$307$	−9.12746	−0.520932	−0.260466	+	0.965483i	$0.583876\pi$
$308$	−36.0606	−2.05474
$309$	49.5595	2.81934
$310$	0.366370	0.0208084
$311$	15.1187	0.857302	0.428651	−	0.903470i	$-0.358989\pi$
$311$	15.1187	0.857302	0.428651	+	0.903470i	$0.358989\pi$
$312$	−35.1590	−1.99049
$313$	−7.05095	−0.398543	−0.199272	−	0.979944i	$-0.563858\pi$
$313$	−7.05095	−0.398543	−0.199272	+	0.979944i	$0.563858\pi$
$314$	−14.6013	−0.824000
$315$	10.2229	0.575997
$316$	3.47674	0.195582
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	80.1725	4.49585
$319$	−16.4227	−0.919493
$320$	−2.97010	−0.166033
$321$	11.0652	0.617601
$322$	1.49297	0.0832000
$323$	3.46147	0.192602
$324$	11.1213	0.617851
$325$	−5.10845	−0.283366
$326$	31.0641	1.72048
$327$	39.4019	2.17893
$328$	16.7253	0.923502
$329$	4.10487	0.226309
$330$	65.7715	3.62060
$331$	−21.3182	−1.17175	−0.585877	−	0.810400i	$-0.699250\pi$
$331$	−21.3182	−1.17175	−0.585877	+	0.810400i	$0.699250\pi$
$332$	−53.9596	−2.96142
$333$	−52.9570	−2.90203
$334$	−9.26698	−0.507066
$335$	12.7818	0.698343
$336$	−29.5836	−1.61392
$337$	10.7426	0.585187	0.292593	−	0.956237i	$-0.405482\pi$
$337$	10.7426	0.585187	0.292593	+	0.956237i	$0.405482\pi$
$338$	24.5780	1.33687
$339$	−18.8036	−1.02127
$340$	23.7536	1.28822
$341$	0.570741	0.0309073
$342$	13.3399	0.721337
$343$	16.1308	0.870980
$344$	48.4074	2.60995
$345$	−1.89616	−0.102086
$346$	−56.2992	−3.02666
$347$	−30.2575	−1.62431	−0.812153	−	0.583444i	$-0.801705\pi$
$347$	−30.2575	−1.62431	−0.812153	+	0.583444i	$0.801705\pi$
$348$	−36.0494	−1.93245
$349$	4.24882	0.227434	0.113717	−	0.993513i	$-0.463724\pi$
$349$	4.24882	0.227434	0.113717	+	0.993513i	$0.463724\pi$
$350$	−9.31388	−0.497848
$351$	11.6433	0.621475
$352$	−41.2736	−2.19989
$353$	−2.32893	−0.123957	−0.0619783	−	0.998077i	$-0.519741\pi$
$353$	−2.32893	−0.123957	−0.0619783	+	0.998077i	$0.519741\pi$
$354$	31.5301	1.67581
$355$	−9.85032	−0.522801
$356$	6.51064	0.345063
$357$	13.0269	0.689457
$358$	9.18918	0.485663
$359$	−13.3658	−0.705420	−0.352710	−	0.935733i	$-0.614740\pi$
$359$	−13.3658	−0.705420	−0.352710	+	0.935733i	$0.614740\pi$
$360$	51.6213	2.72068
$361$	1.00000	0.0526316
$362$	63.5960	3.34253
$363$	70.9655	3.72472
$364$	−11.1528	−0.584565
$365$	3.85785	0.201929
$366$	5.59725	0.292573
$367$	−25.2979	−1.32054	−0.660271	−	0.751028i	$-0.729559\pi$
$367$	−25.2979	−1.32054	−0.660271	+	0.751028i	$0.729559\pi$
$368$	3.47918	0.181365
$369$	−13.0987	−0.681890
$370$	−39.1221	−2.03386
$371$	14.3411	0.744552
$372$	1.25283	0.0649564
$373$	−11.7457	−0.608167	−0.304084	−	0.952645i	$-0.598350\pi$
$373$	−11.7457	−0.608167	−0.304084	+	0.952645i	$0.598350\pi$
$374$	53.1412	2.74786
$375$	33.2501	1.71703
$376$	20.7278	1.06895
$377$	−5.07919	−0.261592
$378$	21.2285	1.09188
$379$	36.9167	1.89629	0.948143	−	0.317844i	$-0.102959\pi$
$379$	36.9167	1.89629	0.948143	+	0.317844i	$0.102959\pi$
$380$	6.86228	0.352028
$381$	−5.68271	−0.291134
$382$	8.53232	0.436551
$383$	−8.62707	−0.440823	−0.220411	−	0.975407i	$-0.570740\pi$
$383$	−8.62707	−0.440823	−0.220411	+	0.975407i	$0.570740\pi$
$384$	24.9240	1.27190
$385$	11.7651	0.599604
$386$	41.5051	2.11256
$387$	−37.9110	−1.92712
$388$	−66.5189	−3.37698
$389$	−11.8358	−0.600097	−0.300049	−	0.953924i	$-0.597003\pi$
$389$	−11.8358	−0.600097	−0.300049	+	0.953924i	$0.597003\pi$
$390$	20.3418	1.03005
$391$	−1.53203	−0.0774781
$392$	34.9933	1.76743
$393$	−12.4759	−0.629327
$394$	−47.9577	−2.41607
$395$	−1.13432	−0.0570737
$396$	142.606	7.16624
$397$	12.7775	0.641284	0.320642	−	0.947200i	$-0.396101\pi$
$397$	12.7775	0.641284	0.320642	+	0.947200i	$0.396101\pi$
$398$	39.1689	1.96336
$399$	3.76340	0.188406
$400$	−21.7048	−1.08524
$401$	−27.8859	−1.39256	−0.696278	−	0.717772i	$-0.745162\pi$
$401$	−27.8859	−1.39256	−0.696278	+	0.717772i	$0.745162\pi$
$402$	62.7692	3.13064
$403$	0.176518	0.00879300
$404$	−4.01526	−0.199766
$405$	−3.62842	−0.180298
$406$	−9.26054	−0.459593
$407$	−60.9456	−3.02096
$408$	65.7801	3.25660
$409$	27.7163	1.37048	0.685240	−	0.728317i	$-0.259697\pi$
$409$	27.7163	1.37048	0.685240	+	0.728317i	$0.259697\pi$
$410$	−9.67670	−0.477898
$411$	18.4904	0.912062
$412$	79.3829	3.91092
$413$	5.64004	0.277528
$414$	−5.90415	−0.290173
$415$	17.6048	0.864185
$416$	−12.7651	−0.625859
$417$	−19.7383	−0.966587
$418$	15.3522	0.750899
$419$	27.3216	1.33475	0.667374	−	0.744723i	$-0.267418\pi$
$419$	27.3216	1.33475	0.667374	+	0.744723i	$0.267418\pi$
$420$	25.8255	1.26016
$421$	9.11114	0.444050	0.222025	−	0.975041i	$-0.428733\pi$
$421$	9.11114	0.444050	0.222025	+	0.975041i	$0.428733\pi$
$422$	−8.80366	−0.428556
$423$	−16.2333	−0.789288
$424$	72.4162	3.51684
$425$	9.55755	0.463609
$426$	−48.3733	−2.34369
$427$	1.00122	0.0484526
$428$	17.7240	0.856720
$429$	31.6890	1.52996
$430$	−28.0069	−1.35061
$431$	−24.3199	−1.17145	−0.585725	−	0.810510i	$-0.699190\pi$
$431$	−24.3199	−1.17145	−0.585725	+	0.810510i	$0.699190\pi$
$432$	49.4703	2.38014
$433$	−8.86237	−0.425898	−0.212949	−	0.977063i	$-0.568307\pi$
$433$	−8.86237	−0.425898	−0.212949	+	0.977063i	$0.568307\pi$
$434$	0.321834	0.0154485
$435$	11.7614	0.563917
$436$	63.1128	3.02255
$437$	−0.442595	−0.0211722
$438$	18.9453	0.905241
$439$	−0.791614	−0.0377817	−0.0188908	−	0.999822i	$-0.506013\pi$
$439$	−0.791614	−0.0377817	−0.0188908	+	0.999822i	$0.506013\pi$
$440$	59.4084	2.83218
$441$	−27.4055	−1.30502
$442$	16.4355	0.781755
$443$	11.3287	0.538241	0.269121	−	0.963106i	$-0.413267\pi$
$443$	11.3287	0.538241	0.269121	+	0.963106i	$0.413267\pi$
$444$	−133.782	−6.34899
$445$	−2.12415	−0.100694
$446$	1.78030	0.0842998
$447$	56.7179	2.68266
$448$	−2.60905	−0.123266
$449$	9.19039	0.433721	0.216861	−	0.976203i	$-0.430418\pi$
$449$	9.19039	0.433721	0.216861	+	0.976203i	$0.430418\pi$
$450$	36.8330	1.73632
$451$	−15.0746	−0.709836
$452$	−30.1191	−1.41668
$453$	45.4854	2.13709
$454$	−24.7855	−1.16324
$455$	3.63869	0.170585
$456$	19.0035	0.889920
$457$	−26.7160	−1.24972	−0.624860	−	0.780737i	$-0.714844\pi$
$457$	−26.7160	−1.24972	−0.624860	+	0.780737i	$0.714844\pi$
$458$	−2.73481	−0.127789
$459$	−21.7839	−1.01678
$460$	−3.03721	−0.141611
$461$	6.37718	0.297015	0.148507	−	0.988911i	$-0.452553\pi$
$461$	6.37718	0.297015	0.148507	+	0.988911i	$0.452553\pi$
$462$	57.7764	2.68800
$463$	20.0954	0.933910	0.466955	−	0.884281i	$-0.345351\pi$
$463$	20.0954	0.933910	0.466955	+	0.884281i	$0.345351\pi$
$464$	−21.5805	−1.00185
$465$	−0.408747	−0.0189552
$466$	−60.3530	−2.79580
$467$	−31.4372	−1.45474	−0.727369	−	0.686246i	$-0.759257\pi$
$467$	−31.4372	−1.45474	−0.727369	+	0.686246i	$0.759257\pi$
$468$	44.1052	2.03876
$469$	11.2280	0.518462
$470$	−11.9924	−0.553167
$471$	16.2902	0.750615
$472$	28.4797	1.31088
$473$	−43.6299	−2.00610
$474$	−5.57044	−0.255859
$475$	2.76112	0.126689
$476$	20.8661	0.956397
$477$	−56.7138	−2.59674
$478$	28.3087	1.29481
$479$	9.44859	0.431717	0.215858	−	0.976425i	$-0.430745\pi$
$479$	9.44859	0.431717	0.215858	+	0.976425i	$0.430745\pi$
$480$	29.5589	1.34917
$481$	−18.8492	−0.859450
$482$	38.5740	1.75700
$483$	−1.66566	−0.0757902
$484$	113.670	5.16684
$485$	21.7023	0.985453
$486$	30.6335	1.38956
$487$	26.0689	1.18129	0.590647	−	0.806930i	$-0.298872\pi$
$487$	26.0689	1.18129	0.590647	+	0.806930i	$0.298872\pi$
$488$	5.05574	0.228862
$489$	−34.6572	−1.56725
$490$	−20.2459	−0.914617
$491$	−28.8172	−1.30050	−0.650250	−	0.759720i	$-0.725336\pi$
$491$	−28.8172	−1.30050	−0.650250	+	0.759720i	$0.725336\pi$
$492$	−33.0903	−1.49183
$493$	9.50282	0.427986
$494$	4.74811	0.213628
$495$	−46.5265	−2.09121
$496$	0.749992	0.0336756
$497$	−8.65291	−0.388136
$498$	86.4542	3.87411
$499$	29.3483	1.31381	0.656906	−	0.753973i	$-0.271865\pi$
$499$	29.3483	1.31381	0.656906	+	0.753973i	$0.271865\pi$
$500$	53.2590	2.38182
$501$	10.3389	0.461907
$502$	−73.4180	−3.27681
$503$	−9.35889	−0.417292	−0.208646	−	0.977991i	$-0.566906\pi$
$503$	−9.35889	−0.417292	−0.208646	+	0.977991i	$0.566906\pi$
$504$	45.3462	2.01988
$505$	1.31001	0.0582947
$506$	−6.79479	−0.302065
$507$	−27.4210	−1.21781
$508$	−9.10240	−0.403854
$509$	16.5734	0.734603	0.367301	−	0.930102i	$-0.380282\pi$
$509$	16.5734	0.734603	0.367301	+	0.930102i	$0.380282\pi$
$510$	−38.0581	−1.68524
$511$	3.38889	0.149916
$512$	50.1108	2.21461
$513$	−6.29324	−0.277853
$514$	35.0919	1.54784
$515$	−25.8994	−1.14126
$516$	−95.7719	−4.21612
$517$	−18.6821	−0.821636
$518$	−34.3665	−1.50998
$519$	62.8113	2.75711
$520$	18.3738	0.805744
$521$	15.1454	0.663530	0.331765	−	0.943362i	$-0.392356\pi$
$521$	15.1454	0.663530	0.331765	+	0.943362i	$0.392356\pi$
$522$	36.6220	1.60290
$523$	−7.95709	−0.347939	−0.173970	−	0.984751i	$-0.555659\pi$
$523$	−7.95709	−0.347939	−0.173970	+	0.984751i	$0.555659\pi$
$524$	−19.9836	−0.872985
$525$	10.3912	0.453509
$526$	17.7618	0.774450
$527$	−0.330254	−0.0143861
$528$	134.640	5.85947
$529$	−22.8041	−0.991483
$530$	−41.8975	−1.81991
$531$	−22.3043	−0.967923
$532$	6.02810	0.261351
$533$	−4.66227	−0.201945
$534$	−10.4314	−0.451409
$535$	−5.78259	−0.250003
$536$	56.6965	2.44892
$537$	−10.2521	−0.442410
$538$	15.9892	0.689343
$539$	−31.5397	−1.35851
$540$	−43.1860	−1.85843
$541$	26.1488	1.12422	0.562112	−	0.827061i	$-0.309989\pi$
$541$	26.1488	1.12422	0.562112	+	0.827061i	$0.309989\pi$
$542$	36.3698	1.56222
$543$	−70.9521	−3.04484
$544$	23.8826	1.02396
$545$	−20.5911	−0.882025
$546$	17.8690	0.764724
$547$	−16.0755	−0.687338	−0.343669	−	0.939091i	$-0.611670\pi$
$547$	−16.0755	−0.687338	−0.343669	+	0.939091i	$0.611670\pi$
$548$	29.6173	1.26519
$549$	−3.95947	−0.168986
$550$	42.3892	1.80748
$551$	2.74531	0.116954
$552$	−8.41085	−0.357990
$553$	−0.996429	−0.0423725
$554$	72.0167	3.05970
$555$	43.6474	1.85273
$556$	−31.6162	−1.34082
$557$	−17.1493	−0.726641	−0.363320	−	0.931664i	$-0.618357\pi$
$557$	−17.1493	−0.726641	−0.363320	+	0.931664i	$0.618357\pi$
$558$	−1.27273	−0.0538791
$559$	−13.4938	−0.570728
$560$	15.4601	0.653309
$561$	−59.2879	−2.50314
$562$	−64.9774	−2.74091
$563$	18.1791	0.766158	0.383079	−	0.923716i	$-0.374864\pi$
$563$	18.1791	0.766158	0.383079	+	0.923716i	$0.374864\pi$
$564$	−41.0090	−1.72679
$565$	9.82661	0.413409
$566$	−6.05620	−0.254561
$567$	−3.18735	−0.133856
$568$	−43.6934	−1.83333
$569$	−2.43407	−0.102041	−0.0510207	−	0.998698i	$-0.516247\pi$
$569$	−2.43407	−0.102041	−0.0510207	+	0.998698i	$0.516247\pi$
$570$	−10.9948	−0.460520
$571$	11.4311	0.478375	0.239188	−	0.970973i	$-0.423119\pi$
$571$	11.4311	0.478375	0.239188	+	0.970973i	$0.423119\pi$
$572$	50.7585	2.12232
$573$	−9.51925	−0.397672
$574$	−8.50040	−0.354800
$575$	−1.22206	−0.0509634
$576$	10.3178	0.429910
$577$	−24.7817	−1.03167	−0.515837	−	0.856687i	$-0.672519\pi$
$577$	−24.7817	−1.03167	−0.515837	+	0.856687i	$0.672519\pi$
$578$	12.8785	0.535675
$579$	−46.3060	−1.92441
$580$	18.8391	0.782251
$581$	15.4647	0.641586
$582$	106.577	4.41774
$583$	−65.2690	−2.70317
$584$	17.1124	0.708116
$585$	−14.3897	−0.594941
$586$	−72.0308	−2.97556
$587$	−40.7999	−1.68399	−0.841996	−	0.539485i	$-0.818619\pi$
$587$	−40.7999	−1.68399	−0.841996	+	0.539485i	$0.818619\pi$
$588$	−69.2327	−2.85511
$589$	−0.0954084	−0.00393124
$590$	−16.4774	−0.678362
$591$	53.5049	2.20090
$592$	−80.0866	−3.29154
$593$	−6.91800	−0.284088	−0.142044	−	0.989860i	$-0.545368\pi$
$593$	−6.91800	−0.284088	−0.142044	+	0.989860i	$0.545368\pi$
$594$	−96.6148	−3.96415
$595$	−6.80775	−0.279091
$596$	90.8490	3.72132
$597$	−43.6995	−1.78850
$598$	−2.10149	−0.0859363
$599$	−24.8997	−1.01737	−0.508687	−	0.860951i	$-0.669869\pi$
$599$	−24.8997	−1.01737	−0.508687	+	0.860951i	$0.669869\pi$
$600$	52.4710	2.14212
$601$	−22.3530	−0.911796	−0.455898	−	0.890032i	$-0.650682\pi$
$601$	−22.3530	−0.911796	−0.455898	+	0.890032i	$0.650682\pi$
$602$	−24.6023	−1.00272
$603$	−44.4027	−1.80822
$604$	72.8572	2.96452
$605$	−37.0859	−1.50776
$606$	6.43325	0.261333
$607$	14.7877	0.600213	0.300106	−	0.953906i	$-0.402978\pi$
$607$	14.7877	0.600213	0.300106	+	0.953906i	$0.402978\pi$
$608$	6.89954	0.279813
$609$	10.3317	0.418662
$610$	−2.92507	−0.118433
$611$	−5.77797	−0.233752
$612$	−82.5179	−3.33559
$613$	26.6884	1.07793	0.538967	−	0.842327i	$-0.318815\pi$
$613$	26.6884	1.07793	0.538967	+	0.842327i	$0.318815\pi$
$614$	23.4243	0.945330
$615$	10.7960	0.435336
$616$	52.1867	2.10266
$617$	−12.3279	−0.496301	−0.248151	−	0.968721i	$-0.579823\pi$
$617$	−12.3279	−0.496301	−0.248151	+	0.968721i	$0.579823\pi$
$618$	−127.187	−5.11623
$619$	19.4973	0.783664	0.391832	−	0.920037i	$-0.371841\pi$
$619$	19.4973	0.783664	0.391832	+	0.920037i	$0.371841\pi$
$620$	−0.654719	−0.0262942
$621$	2.78535	0.111772
$622$	−38.8000	−1.55574
$623$	−1.86594	−0.0747573
$624$	41.6415	1.66699
$625$	−3.57059	−0.142824
$626$	18.0953	0.723233
$627$	−17.1279	−0.684024
$628$	26.0932	1.04123
$629$	35.2656	1.40613
$630$	−26.2357	−1.04526
$631$	−21.9021	−0.871907	−0.435954	−	0.899969i	$-0.643589\pi$
$631$	−21.9021	−0.871907	−0.435954	+	0.899969i	$0.643589\pi$
$632$	−5.03153	−0.200143
$633$	9.82198	0.390389
$634$	2.56636	0.101923
$635$	2.96974	0.117850
$636$	−143.272	−5.68111
$637$	−9.75456	−0.386490
$638$	42.1465	1.66860
$639$	34.2191	1.35369
$640$	−13.0251	−0.514860
$641$	28.6660	1.13224	0.566120	−	0.824323i	$-0.308444\pi$
$641$	28.6660	1.13224	0.566120	+	0.824323i	$0.308444\pi$
$642$	−28.3974	−1.12075
$643$	13.4375	0.529923	0.264961	−	0.964259i	$-0.414641\pi$
$643$	13.4375	0.529923	0.264961	+	0.964259i	$0.414641\pi$
$644$	−2.66801	−0.105134
$645$	31.2464	1.23033
$646$	−8.88339	−0.349512
$647$	−24.3150	−0.955922	−0.477961	−	0.878381i	$-0.658624\pi$
$647$	−24.3150	−0.955922	−0.477961	+	0.878381i	$0.658624\pi$
$648$	−16.0947	−0.632260
$649$	−25.6689	−1.00759
$650$	13.1101	0.514221
$651$	−0.359060	−0.0140727
$652$	−55.5129	−2.17405
$653$	37.2541	1.45787	0.728933	−	0.684585i	$-0.240016\pi$
$653$	37.2541	1.45787	0.728933	+	0.684585i	$0.240016\pi$
$654$	−101.119	−3.95408
$655$	6.51980	0.254750
$656$	−19.8091	−0.773415
$657$	−13.4018	−0.522855
$658$	−10.5346	−0.410681
$659$	−15.4699	−0.602620	−0.301310	−	0.953526i	$-0.597424\pi$
$659$	−15.4699	−0.602620	−0.301310	+	0.953526i	$0.597424\pi$
$660$	−117.537	−4.57511
$661$	−13.8542	−0.538867	−0.269433	−	0.963019i	$-0.586836\pi$
$661$	−13.8542	−0.538867	−0.269433	+	0.963019i	$0.586836\pi$
$662$	54.7102	2.12637
$663$	−18.3365	−0.712132
$664$	78.0901	3.03048
$665$	−1.96672	−0.0762661
$666$	135.907	5.26628
$667$	−1.21506	−0.0470473
$668$	16.5605	0.640746
$669$	−1.98623	−0.0767920
$670$	−32.8026	−1.26728
$671$	−4.55676	−0.175912
$672$	25.9657	1.00165
$673$	−14.0871	−0.543016	−0.271508	−	0.962436i	$-0.587522\pi$
$673$	−14.0871	−0.543016	−0.271508	+	0.962436i	$0.587522\pi$
$674$	−27.5694	−1.06193
$675$	−17.3764	−0.668818
$676$	−43.9221	−1.68931
$677$	33.5710	1.29024	0.645119	−	0.764082i	$-0.276808\pi$
$677$	33.5710	1.29024	0.645119	+	0.764082i	$0.276808\pi$
$678$	48.2569	1.85329
$679$	19.0642	0.731617
$680$	−34.3761	−1.31826
$681$	27.6524	1.05964
$682$	−1.46473	−0.0560873
$683$	−37.4025	−1.43117	−0.715584	−	0.698526i	$-0.753839\pi$
$683$	−37.4025	−1.43117	−0.715584	+	0.698526i	$0.753839\pi$
$684$	−23.8389	−0.911504
$685$	−9.66290	−0.369200
$686$	−41.3974	−1.58056
$687$	3.05114	0.116408
$688$	−57.3326	−2.18579
$689$	−20.1864	−0.769039
$690$	4.86623	0.185254
$691$	17.4251	0.662884	0.331442	−	0.943476i	$-0.392465\pi$
$691$	17.4251	0.662884	0.331442	+	0.943476i	$0.392465\pi$
$692$	100.609	3.82459
$693$	−40.8708	−1.55255
$694$	77.6516	2.94761
$695$	10.3150	0.391272
$696$	52.1705	1.97752
$697$	8.72279	0.330399
$698$	−10.9040	−0.412722
$699$	67.3340	2.54680
$700$	16.6443	0.629097
$701$	−4.78410	−0.180693	−0.0903465	−	0.995910i	$-0.528797\pi$
$701$	−4.78410	−0.180693	−0.0903465	+	0.995910i	$0.528797\pi$
$702$	−29.8810	−1.12778
$703$	10.1880	0.384249
$704$	11.8743	0.447529
$705$	13.3795	0.503902
$706$	5.97688	0.224943
$707$	1.15077	0.0432790
$708$	−56.3457	−2.11760
$709$	42.3685	1.59118	0.795592	−	0.605833i	$-0.207160\pi$
$709$	42.3685	1.59118	0.795592	+	0.605833i	$0.207160\pi$
$710$	25.2795	0.948721
$711$	3.94051	0.147781
$712$	−9.42217	−0.353111
$713$	0.0422273	0.00158142
$714$	−33.4317	−1.25115
$715$	−16.5604	−0.619323
$716$	−16.4215	−0.613700
$717$	−31.5831	−1.17949
$718$	34.3015	1.28012
$719$	41.0988	1.53273	0.766364	−	0.642407i	$-0.222064\pi$
$719$	41.0988	1.53273	0.766364	+	0.642407i	$0.222064\pi$
$720$	−61.1391	−2.27852
$721$	−22.7510	−0.847293
$722$	−2.56636	−0.0955100
$723$	−43.0358	−1.60052
$724$	−113.649	−4.22373
$725$	7.58014	0.281519
$726$	−182.123	−6.75922
$727$	−3.81832	−0.141614	−0.0708069	−	0.997490i	$-0.522557\pi$
$727$	−3.81832	−0.141614	−0.0708069	+	0.997490i	$0.522557\pi$
$728$	16.1403	0.598198
$729$	−41.4517	−1.53525
$730$	−9.90064	−0.366439
$731$	25.2460	0.933757
$732$	−10.0025	−0.369705
$733$	6.99734	0.258452	0.129226	−	0.991615i	$-0.458751\pi$
$733$	6.99734	0.258452	0.129226	+	0.991615i	$0.458751\pi$
$734$	64.9236	2.39637
$735$	22.5877	0.833161
$736$	−3.05370	−0.112561
$737$	−51.1009	−1.88232
$738$	33.6159	1.23742
$739$	29.1231	1.07131	0.535656	−	0.844436i	$-0.320064\pi$
$739$	29.1231	1.07131	0.535656	+	0.844436i	$0.320064\pi$
$740$	69.9131	2.57006
$741$	−5.29732	−0.194602
$742$	−36.8044	−1.35113
$743$	−0.0682136	−0.00250252	−0.00125126	−	0.999999i	$-0.500398\pi$
$743$	−0.0682136	−0.00250252	−0.00125126	+	0.999999i	$0.500398\pi$
$744$	−1.81309	−0.0664712
$745$	−29.6403	−1.08594
$746$	30.1436	1.10364
$747$	−61.1574	−2.23763
$748$	−94.9657	−3.47229
$749$	−5.07966	−0.185607
$750$	−85.3317	−3.11587
$751$	−18.4564	−0.673485	−0.336743	−	0.941597i	$-0.609325\pi$
$751$	−18.4564	−0.673485	−0.336743	+	0.941597i	$0.609325\pi$
$752$	−24.5495	−0.895228
$753$	81.9102	2.98497
$754$	13.0350	0.474708
$755$	−23.7703	−0.865089
$756$	−37.9363	−1.37973
$757$	39.0394	1.41891	0.709456	−	0.704750i	$-0.248941\pi$
$757$	39.0394	1.41891	0.709456	+	0.704750i	$0.248941\pi$
$758$	−94.7417	−3.44117
$759$	7.58074	0.275163
$760$	−9.93106	−0.360237
$761$	13.8369	0.501586	0.250793	−	0.968041i	$-0.419309\pi$
$761$	13.8369	0.501586	0.250793	+	0.968041i	$0.419309\pi$
$762$	14.5839	0.528319
$763$	−18.0880	−0.654830
$764$	−15.2476	−0.551641
$765$	26.9221	0.973372
$766$	22.1402	0.799957
$767$	−7.93885	−0.286655
$768$	−75.3307	−2.71826
$769$	33.7081	1.21555	0.607773	−	0.794111i	$-0.292063\pi$
$769$	33.7081	1.21555	0.607773	+	0.794111i	$0.292063\pi$
$770$	−30.1934	−1.08810
$771$	−39.1510	−1.40999
$772$	−74.1716	−2.66949
$773$	−9.19751	−0.330812	−0.165406	−	0.986226i	$-0.552893\pi$
$773$	−9.19751	−0.330812	−0.165406	+	0.986226i	$0.552893\pi$
$774$	97.2932	3.49713
$775$	−0.263434	−0.00946284
$776$	96.2658	3.45574
$777$	38.3416	1.37550
$778$	30.3748	1.08899
$779$	2.51996	0.0902871
$780$	−36.3517	−1.30160
$781$	39.3811	1.40917
$782$	3.93174	0.140599
$783$	−17.2769	−0.617425
$784$	−41.4453	−1.48019
$785$	−8.51314	−0.303847
$786$	32.0177	1.14203
$787$	36.2607	1.29255	0.646277	−	0.763103i	$-0.276325\pi$
$787$	36.2607	1.29255	0.646277	+	0.763103i	$0.276325\pi$
$788$	85.7025	3.05303
$789$	−19.8163	−0.705478
$790$	2.91107	0.103571
$791$	8.63209	0.306922
$792$	−206.379	−7.33337
$793$	−1.40931	−0.0500461
$794$	−32.7916	−1.16373
$795$	46.7437	1.65783
$796$	−69.9966	−2.48096
$797$	17.5761	0.622576	0.311288	−	0.950316i	$-0.399240\pi$
$797$	17.5761	0.622576	0.311288	+	0.950316i	$0.399240\pi$
$798$	−9.65824	−0.341898
$799$	10.8102	0.382437
$800$	19.0505	0.673536
$801$	7.37911	0.260728
$802$	71.5653	2.52706
$803$	−15.4235	−0.544283
$804$	−112.171	−3.95598
$805$	0.870460	0.0306797
$806$	−0.453010	−0.0159566
$807$	−17.8387	−0.627950
$808$	5.81086	0.204425
$809$	−9.09040	−0.319601	−0.159801	−	0.987149i	$-0.551085\pi$
$809$	−9.09040	−0.319601	−0.159801	+	0.987149i	$0.551085\pi$
$810$	9.31184	0.327185
$811$	−28.6532	−1.00615	−0.503074	−	0.864243i	$-0.667798\pi$
$811$	−28.6532	−1.00615	−0.503074	+	0.864243i	$0.667798\pi$
$812$	16.5490	0.580757
$813$	−40.5766	−1.42308
$814$	156.408	5.48211
$815$	18.1116	0.634420
$816$	−77.9084	−2.72734
$817$	7.29343	0.255165
$818$	−71.1299	−2.48700
$819$	−12.6405	−0.441694
$820$	17.2927	0.603887
$821$	−16.3321	−0.569993	−0.284997	−	0.958529i	$-0.591992\pi$
$821$	−16.3321	−0.569993	−0.284997	+	0.958529i	$0.591992\pi$
$822$	−47.4529	−1.65511
$823$	29.1737	1.01693	0.508465	−	0.861082i	$-0.330213\pi$
$823$	29.1737	1.01693	0.508465	+	0.861082i	$0.330213\pi$
$824$	−114.883	−4.00212
$825$	−47.2924	−1.64651
$826$	−14.4744	−0.503628
$827$	26.8841	0.934850	0.467425	−	0.884033i	$-0.345182\pi$
$827$	26.8841	0.934850	0.467425	+	0.884033i	$0.345182\pi$
$828$	10.5510	0.366672
$829$	−42.5353	−1.47731	−0.738656	−	0.674083i	$-0.764539\pi$
$829$	−42.5353	−1.47731	−0.738656	+	0.674083i	$0.764539\pi$
$830$	−45.1802	−1.56823
$831$	−80.3468	−2.78720
$832$	3.67247	0.127320
$833$	18.2501	0.632329
$834$	50.6555	1.75406
$835$	−5.40301	−0.186979
$836$	−27.4350	−0.948861
$837$	0.600428	0.0207538
$838$	−70.1171	−2.42215
$839$	0.618499	0.0213530	0.0106765	−	0.999943i	$-0.496602\pi$
$839$	0.618499	0.0213530	0.0106765	+	0.999943i	$0.496602\pi$
$840$	−37.3745	−1.28954
$841$	−21.4633	−0.740113
$842$	−23.3825	−0.805813
$843$	72.4933	2.49680
$844$	15.7326	0.541537
$845$	14.3300	0.492966
$846$	41.6604	1.43231
$847$	−32.5778	−1.11939
$848$	−85.7680	−2.94528
$849$	6.75671	0.231890
$850$	−24.5281	−0.841308
$851$	−4.50917	−0.154572
$852$	86.4453	2.96157
$853$	−8.51838	−0.291664	−0.145832	−	0.989309i	$-0.546586\pi$
$853$	−8.51838	−0.291664	−0.145832	+	0.989309i	$0.546586\pi$
$854$	−2.56950	−0.0879265
$855$	7.77765	0.265990
$856$	−25.6500	−0.876699
$857$	39.6183	1.35334	0.676668	−	0.736288i	$-0.263423\pi$
$857$	39.6183	1.35334	0.676668	+	0.736288i	$0.263423\pi$
$858$	−81.3254	−2.77640
$859$	−31.0116	−1.05810	−0.529052	−	0.848590i	$-0.677452\pi$
$859$	−31.0116	−1.05810	−0.529052	+	0.848590i	$0.677452\pi$
$860$	50.0496	1.70668
$861$	9.48363	0.323201
$862$	62.4137	2.12582
$863$	39.6641	1.35018	0.675091	−	0.737735i	$-0.264104\pi$
$863$	39.6641	1.35018	0.675091	+	0.737735i	$0.264104\pi$
$864$	−43.4204	−1.47719
$865$	−32.8246	−1.11607
$866$	22.7440	0.772873
$867$	−14.3681	−0.487968
$868$	−0.575132	−0.0195212
$869$	4.53494	0.153837
$870$	−30.1840	−1.02333
$871$	−15.8044	−0.535513
$872$	−91.3365	−3.09304
$873$	−75.3919	−2.55163
$874$	1.13586	0.0384210
$875$	−15.2640	−0.516016
$876$	−33.8561	−1.14389
$877$	2.90897	0.0982288	0.0491144	−	0.998793i	$-0.484360\pi$
$877$	2.90897	0.0982288	0.0491144	+	0.998793i	$0.484360\pi$
$878$	2.03157	0.0685620
$879$	80.3625	2.71056
$880$	−70.3619	−2.37190
$881$	−22.7326	−0.765882	−0.382941	−	0.923773i	$-0.625089\pi$
$881$	−22.7326	−0.765882	−0.382941	+	0.923773i	$0.625089\pi$
$882$	70.3324	2.36822
$883$	0.716750	0.0241205	0.0120603	−	0.999927i	$-0.496161\pi$
$883$	0.716750	0.0241205	0.0120603	+	0.999927i	$0.496161\pi$
$884$	−29.3709	−0.987851
$885$	18.3833	0.617947
$886$	−29.0734	−0.976742
$887$	26.8965	0.903095	0.451548	−	0.892247i	$-0.350872\pi$
$887$	26.8965	0.903095	0.451548	+	0.892247i	$0.350872\pi$
$888$	193.608	6.49706
$889$	2.60874	0.0874942
$890$	5.45134	0.182729
$891$	14.5063	0.485978
$892$	−3.18148	−0.106524
$893$	3.12300	0.104507
$894$	−145.559	−4.86820
$895$	5.35765	0.179086
$896$	−11.4417	−0.382241
$897$	2.34457	0.0782828
$898$	−23.5858	−0.787070
$899$	−0.261926	−0.00873571
$900$	−65.8222	−2.19407
$901$	37.7673	1.25821
$902$	38.6869	1.28813
$903$	27.4481	0.913415
$904$	43.5882	1.44972
$905$	37.0789	1.23255
$906$	−116.732	−3.87816
$907$	−10.5602	−0.350645	−0.175323	−	0.984511i	$-0.556097\pi$
$907$	−10.5602	−0.350645	−0.175323	+	0.984511i	$0.556097\pi$
$908$	44.2928	1.46991
$909$	−4.55086	−0.150942
$910$	−9.33820	−0.309558
$911$	−30.8567	−1.02233	−0.511164	−	0.859483i	$-0.670785\pi$
$911$	−30.8567	−1.02233	−0.511164	+	0.859483i	$0.670785\pi$
$912$	−22.5073	−0.745291
$913$	−70.3830	−2.32934
$914$	68.5628	2.26786
$915$	3.26341	0.107885
$916$	4.88723	0.161479
$917$	5.72726	0.189131
$918$	55.9053	1.84515
$919$	−34.7982	−1.14789	−0.573944	−	0.818895i	$-0.694587\pi$
$919$	−34.7982	−1.14789	−0.573944	+	0.818895i	$0.694587\pi$
$920$	4.39544	0.144913
$921$	−26.1338	−0.861139
$922$	−16.3661	−0.538990
$923$	12.1797	0.400901
$924$	−103.249	−3.39664
$925$	28.1304	0.924921
$926$	−51.5719	−1.69476
$927$	89.9720	2.95507
$928$	18.9414	0.621781
$929$	25.3258	0.830911	0.415456	−	0.909613i	$-0.363622\pi$
$929$	25.3258	0.830911	0.415456	+	0.909613i	$0.363622\pi$
$930$	1.04899	0.0343978
$931$	5.27235	0.172794
$932$	107.854	3.53286
$933$	43.2879	1.41718
$934$	80.6791	2.63990
$935$	30.9834	1.01326
$936$	−63.8288	−2.08631
$937$	−1.07542	−0.0351324	−0.0175662	−	0.999846i	$-0.505592\pi$
$937$	−1.07542	−0.0351324	−0.0175662	+	0.999846i	$0.505592\pi$
$938$	−28.8151	−0.940848
$939$	−20.1884	−0.658822
$940$	21.4309	0.699000
$941$	−46.5173	−1.51642	−0.758210	−	0.652011i	$-0.773926\pi$
$941$	−46.5173	−1.51642	−0.758210	+	0.652011i	$0.773926\pi$
$942$	−41.8066	−1.36213
$943$	−1.11532	−0.0363199
$944$	−33.7307	−1.09784
$945$	12.3770	0.402625
$946$	111.970	3.64046
$947$	−40.5378	−1.31730	−0.658651	−	0.752448i	$-0.728873\pi$
$947$	−40.5378	−1.31730	−0.658651	+	0.752448i	$0.728873\pi$
$948$	9.95464	0.323312
$949$	−4.77017	−0.154846
$950$	−7.08603	−0.229901
$951$	−2.86321	−0.0928459
$952$	−30.1973	−0.978702
$953$	−1.92904	−0.0624879	−0.0312439	−	0.999512i	$-0.509947\pi$
$953$	−1.92904	−0.0624879	−0.0312439	+	0.999512i	$0.509947\pi$
$954$	145.548	4.71229
$955$	4.97467	0.160977
$956$	−50.5890	−1.63616
$957$	−47.0215	−1.51999
$958$	−24.2485	−0.783433
$959$	−8.48828	−0.274101
$960$	−8.50401	−0.274466
$961$	−30.9909	−0.999706
$962$	48.3738	1.55964
$963$	20.0882	0.647333
$964$	−68.9336	−2.22020
$965$	24.1991	0.778997
$966$	4.27469	0.137536
$967$	28.4008	0.913308	0.456654	−	0.889644i	$-0.349048\pi$
$967$	28.4008	0.913308	0.456654	+	0.889644i	$0.349048\pi$
$968$	−164.503	−5.28733
$969$	9.91092	0.318385
$970$	−55.6960	−1.78829
$971$	−35.4842	−1.13874	−0.569371	−	0.822081i	$-0.692813\pi$
$971$	−35.4842	−1.13874	−0.569371	+	0.822081i	$0.692813\pi$
$972$	−54.7435	−1.75590
$973$	9.06115	0.290487
$974$	−66.9022	−2.14368
$975$	−14.6265	−0.468424
$976$	−5.98789	−0.191668
$977$	32.7689	1.04837	0.524185	−	0.851604i	$-0.324370\pi$
$977$	32.7689	1.04837	0.524185	+	0.851604i	$0.324370\pi$
$978$	88.9429	2.84408
$979$	8.49225	0.271414
$980$	36.1804	1.15574
$981$	71.5315	2.28382
$982$	73.9552	2.36001
$983$	57.7029	1.84044	0.920218	−	0.391405i	$-0.128011\pi$
$983$	57.7029	1.84044	0.920218	+	0.391405i	$0.128011\pi$
$984$	47.8881	1.52662
$985$	−27.9612	−0.890917
$986$	−24.3877	−0.776661
$987$	11.7531	0.374106
$988$	−8.48509	−0.269947
$989$	−3.22803	−0.102645
$990$	119.404	3.79490
$991$	25.8703	0.821796	0.410898	−	0.911681i	$-0.365215\pi$
$991$	25.8703	0.821796	0.410898	+	0.911681i	$0.365215\pi$
$992$	−0.658274	−0.0209002
$993$	−61.0384	−1.93700
$994$	22.2065	0.704347
$995$	22.8370	0.723981
$996$	−154.498	−4.89545
$997$	−62.9735	−1.99439	−0.997195	−	0.0748476i	$-0.976153\pi$
$997$	−62.9735	−1.99439	−0.997195	+	0.0748476i	$0.976153\pi$
$998$	−75.3184	−2.38416
$999$	−64.1156	−2.02853

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.b.1.6	✓	99

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.b.1.6	✓	99	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.56636 q^{2} +2.86321 q^{3} +4.58620 q^{4} -1.49629 q^{5} -7.34803 q^{6} -1.31440 q^{7} -6.63713 q^{8} +5.19797 q^{9} +O(q^{10})\)	\(q-2.56636 q^{2} +2.86321 q^{3} +4.58620 q^{4} -1.49629 q^{5} -7.34803 q^{6} -1.31440 q^{7} -6.63713 q^{8} +5.19797 q^{9} +3.84001 q^{10} +5.98208 q^{11} +13.1313 q^{12} +1.85013 q^{13} +3.37322 q^{14} -4.28419 q^{15} +7.86086 q^{16} -3.46147 q^{17} -13.3399 q^{18} -1.00000 q^{19} -6.86228 q^{20} -3.76340 q^{21} -15.3522 q^{22} +0.442595 q^{23} -19.0035 q^{24} -2.76112 q^{25} -4.74811 q^{26} +6.29324 q^{27} -6.02810 q^{28} -2.74531 q^{29} +10.9948 q^{30} +0.0954084 q^{31} -6.89954 q^{32} +17.1279 q^{33} +8.88339 q^{34} +1.96672 q^{35} +23.8389 q^{36} -10.1880 q^{37} +2.56636 q^{38} +5.29732 q^{39} +9.93106 q^{40} -2.51996 q^{41} +9.65824 q^{42} -7.29343 q^{43} +27.4350 q^{44} -7.77765 q^{45} -1.13586 q^{46} -3.12300 q^{47} +22.5073 q^{48} -5.27235 q^{49} +7.08603 q^{50} -9.91092 q^{51} +8.48509 q^{52} -10.9108 q^{53} -16.1507 q^{54} -8.95091 q^{55} +8.72384 q^{56} -2.86321 q^{57} +7.04545 q^{58} -4.29096 q^{59} -19.6481 q^{60} -0.761735 q^{61} -0.244852 q^{62} -6.83220 q^{63} +1.98498 q^{64} -2.76833 q^{65} -43.9565 q^{66} -8.54232 q^{67} -15.8750 q^{68} +1.26724 q^{69} -5.04731 q^{70} +6.58317 q^{71} -34.4996 q^{72} -2.57828 q^{73} +26.1461 q^{74} -7.90567 q^{75} -4.58620 q^{76} -7.86284 q^{77} -13.5948 q^{78} +0.758087 q^{79} -11.7621 q^{80} +2.42495 q^{81} +6.46713 q^{82} -11.7656 q^{83} -17.2597 q^{84} +5.17936 q^{85} +18.7176 q^{86} -7.86040 q^{87} -39.7039 q^{88} +1.41961 q^{89} +19.9603 q^{90} -2.43181 q^{91} +2.02983 q^{92} +0.273174 q^{93} +8.01475 q^{94} +1.49629 q^{95} -19.7548 q^{96} -14.5041 q^{97} +13.5308 q^{98} +31.0946 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9}+O(q^{10}) \) 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9	\( 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9} - 6 q^{10} - 9 q^{11} - 27 q^{12} - 28 q^{13} - 13 q^{14} - 10 q^{15} + 38 q^{16} - 36 q^{17} - 14 q^{18} - 99 q^{19} - 34 q^{20} - 20 q^{21} - 53 q^{22} - 38 q^{23} - 25 q^{24} - 8 q^{25} - 3 q^{26} - 3 q^{27} - 63 q^{28} - 34 q^{29} - 30 q^{30} - 16 q^{31} - 43 q^{32} - 41 q^{33} - 14 q^{34} - 25 q^{35} - 16 q^{36} - 80 q^{37} + 4 q^{38} - 48 q^{39} - 10 q^{40} - 32 q^{41} - 37 q^{42} - 76 q^{43} - 21 q^{44} - 53 q^{45} - 23 q^{46} - 31 q^{47} - 74 q^{48} - 32 q^{49} - 29 q^{50} - 30 q^{51} - 71 q^{52} - 35 q^{53} - 80 q^{54} - 45 q^{55} - 33 q^{56} + 3 q^{57} - 91 q^{58} + 12 q^{59} - 56 q^{60} - 61 q^{61} - 46 q^{62} - 43 q^{63} - 30 q^{64} - 46 q^{65} - 75 q^{66} - 26 q^{67} - 55 q^{68} - 45 q^{69} - 76 q^{70} - 41 q^{71} - 77 q^{72} - 143 q^{73} - 64 q^{74} - 8 q^{75} - 80 q^{76} - 58 q^{77} - 34 q^{78} - 22 q^{79} - 36 q^{80} - 81 q^{81} - 109 q^{82} - 7 q^{83} - 6 q^{84} - 80 q^{85} + 32 q^{86} - 57 q^{87} - 120 q^{88} - 28 q^{89} - 12 q^{90} - 30 q^{91} - 107 q^{92} - 121 q^{93} + 8 q^{94} + 15 q^{95} + 4 q^{96} - 128 q^{97} + 54 q^{98} - 34 q^{99}+O(q^{100}) \) 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9 - 6 * q^10 - 9 * q^11 - 27 * q^12 - 28 * q^13 - 13 * q^14 - 10 * q^15 + 38 * q^16 - 36 * q^17 - 14 * q^18 - 99 * q^19 - 34 * q^20 - 20 * q^21 - 53 * q^22 - 38 * q^23 - 25 * q^24 - 8 * q^25 - 3 * q^26 - 3 * q^27 - 63 * q^28 - 34 * q^29 - 30 * q^30 - 16 * q^31 - 43 * q^32 - 41 * q^33 - 14 * q^34 - 25 * q^35 - 16 * q^36 - 80 * q^37 + 4 * q^38 - 48 * q^39 - 10 * q^40 - 32 * q^41 - 37 * q^42 - 76 * q^43 - 21 * q^44 - 53 * q^45 - 23 * q^46 - 31 * q^47 - 74 * q^48 - 32 * q^49 - 29 * q^50 - 30 * q^51 - 71 * q^52 - 35 * q^53 - 80 * q^54 - 45 * q^55 - 33 * q^56 + 3 * q^57 - 91 * q^58 + 12 * q^59 - 56 * q^60 - 61 * q^61 - 46 * q^62 - 43 * q^63 - 30 * q^64 - 46 * q^65 - 75 * q^66 - 26 * q^67 - 55 * q^68 - 45 * q^69 - 76 * q^70 - 41 * q^71 - 77 * q^72 - 143 * q^73 - 64 * q^74 - 8 * q^75 - 80 * q^76 - 58 * q^77 - 34 * q^78 - 22 * q^79 - 36 * q^80 - 81 * q^81 - 109 * q^82 - 7 * q^83 - 6 * q^84 - 80 * q^85 + 32 * q^86 - 57 * q^87 - 120 * q^88 - 28 * q^89 - 12 * q^90 - 30 * q^91 - 107 * q^92 - 121 * q^93 + 8 * q^94 + 15 * q^95 + 4 * q^96 - 128 * q^97 + 54 * q^98 - 34 * q^99

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