LMFDB - Embedded newform 6026.2.a.j.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$33$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.90551 q^{3} +1.00000 q^{4} +3.90912 q^{5} +1.90551 q^{6} +1.35086 q^{7} -1.00000 q^{8} +0.630974 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.90551 q^{3} +1.00000 q^{4} +3.90912 q^{5} +1.90551 q^{6} +1.35086 q^{7} -1.00000 q^{8} +0.630974 q^{9} -3.90912 q^{10} +4.12504 q^{11} -1.90551 q^{12} +0.627723 q^{13} -1.35086 q^{14} -7.44888 q^{15} +1.00000 q^{16} +5.89576 q^{17} -0.630974 q^{18} +6.12395 q^{19} +3.90912 q^{20} -2.57408 q^{21} -4.12504 q^{22} +1.00000 q^{23} +1.90551 q^{24} +10.2812 q^{25} -0.627723 q^{26} +4.51421 q^{27} +1.35086 q^{28} -2.99288 q^{29} +7.44888 q^{30} -0.570916 q^{31} -1.00000 q^{32} -7.86031 q^{33} -5.89576 q^{34} +5.28068 q^{35} +0.630974 q^{36} +5.63949 q^{37} -6.12395 q^{38} -1.19613 q^{39} -3.90912 q^{40} -0.123458 q^{41} +2.57408 q^{42} +9.95959 q^{43} +4.12504 q^{44} +2.46655 q^{45} -1.00000 q^{46} -2.45111 q^{47} -1.90551 q^{48} -5.17518 q^{49} -10.2812 q^{50} -11.2344 q^{51} +0.627723 q^{52} -1.69180 q^{53} -4.51421 q^{54} +16.1253 q^{55} -1.35086 q^{56} -11.6693 q^{57} +2.99288 q^{58} +0.881464 q^{59} -7.44888 q^{60} +3.92400 q^{61} +0.570916 q^{62} +0.852357 q^{63} +1.00000 q^{64} +2.45385 q^{65} +7.86031 q^{66} -9.11742 q^{67} +5.89576 q^{68} -1.90551 q^{69} -5.28068 q^{70} +9.58993 q^{71} -0.630974 q^{72} -0.290042 q^{73} -5.63949 q^{74} -19.5910 q^{75} +6.12395 q^{76} +5.57235 q^{77} +1.19613 q^{78} +4.59215 q^{79} +3.90912 q^{80} -10.4948 q^{81} +0.123458 q^{82} -1.08868 q^{83} -2.57408 q^{84} +23.0473 q^{85} -9.95959 q^{86} +5.70297 q^{87} -4.12504 q^{88} +11.3190 q^{89} -2.46655 q^{90} +0.847965 q^{91} +1.00000 q^{92} +1.08789 q^{93} +2.45111 q^{94} +23.9393 q^{95} +1.90551 q^{96} -12.6345 q^{97} +5.17518 q^{98} +2.60279 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9}+O(q^{10}) $ 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9	\( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9} + 4 q^{10} + 5 q^{11} + 3 q^{12} + 15 q^{13} - 11 q^{14} + 16 q^{15} + 33 q^{16} + 2 q^{17} - 44 q^{18} + 32 q^{19} - 4 q^{20} + 8 q^{21} - 5 q^{22} + 33 q^{23} - 3 q^{24} + 49 q^{25} - 15 q^{26} + 15 q^{27} + 11 q^{28} + 20 q^{29} - 16 q^{30} + 25 q^{31} - 33 q^{32} - 6 q^{33} - 2 q^{34} + 15 q^{35} + 44 q^{36} + 6 q^{37} - 32 q^{38} + 25 q^{39} + 4 q^{40} + 2 q^{41} - 8 q^{42} + 31 q^{43} + 5 q^{44} + 2 q^{45} - 33 q^{46} + 4 q^{47} + 3 q^{48} + 72 q^{49} - 49 q^{50} + 26 q^{51} + 15 q^{52} - 65 q^{53} - 15 q^{54} - 4 q^{55} - 11 q^{56} + 12 q^{57} - 20 q^{58} + 8 q^{59} + 16 q^{60} + 23 q^{61} - 25 q^{62} - 14 q^{63} + 33 q^{64} + 5 q^{65} + 6 q^{66} + 31 q^{67} + 2 q^{68} + 3 q^{69} - 15 q^{70} + 20 q^{71} - 44 q^{72} + 22 q^{73} - 6 q^{74} - 32 q^{75} + 32 q^{76} + 2 q^{77} - 25 q^{78} + 53 q^{79} - 4 q^{80} + 17 q^{81} - 2 q^{82} + 45 q^{83} + 8 q^{84} + 60 q^{85} - 31 q^{86} + 11 q^{87} - 5 q^{88} - 54 q^{89} - 2 q^{90} + 38 q^{91} + 33 q^{92} + 63 q^{93} - 4 q^{94} + 44 q^{95} - 3 q^{96} - 72 q^{98} + 43 q^{99}+O(q^{100}) \) 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9 + 4 * q^10 + 5 * q^11 + 3 * q^12 + 15 * q^13 - 11 * q^14 + 16 * q^15 + 33 * q^16 + 2 * q^17 - 44 * q^18 + 32 * q^19 - 4 * q^20 + 8 * q^21 - 5 * q^22 + 33 * q^23 - 3 * q^24 + 49 * q^25 - 15 * q^26 + 15 * q^27 + 11 * q^28 + 20 * q^29 - 16 * q^30 + 25 * q^31 - 33 * q^32 - 6 * q^33 - 2 * q^34 + 15 * q^35 + 44 * q^36 + 6 * q^37 - 32 * q^38 + 25 * q^39 + 4 * q^40 + 2 * q^41 - 8 * q^42 + 31 * q^43 + 5 * q^44 + 2 * q^45 - 33 * q^46 + 4 * q^47 + 3 * q^48 + 72 * q^49 - 49 * q^50 + 26 * q^51 + 15 * q^52 - 65 * q^53 - 15 * q^54 - 4 * q^55 - 11 * q^56 + 12 * q^57 - 20 * q^58 + 8 * q^59 + 16 * q^60 + 23 * q^61 - 25 * q^62 - 14 * q^63 + 33 * q^64 + 5 * q^65 + 6 * q^66 + 31 * q^67 + 2 * q^68 + 3 * q^69 - 15 * q^70 + 20 * q^71 - 44 * q^72 + 22 * q^73 - 6 * q^74 - 32 * q^75 + 32 * q^76 + 2 * q^77 - 25 * q^78 + 53 * q^79 - 4 * q^80 + 17 * q^81 - 2 * q^82 + 45 * q^83 + 8 * q^84 + 60 * q^85 - 31 * q^86 + 11 * q^87 - 5 * q^88 - 54 * q^89 - 2 * q^90 + 38 * q^91 + 33 * q^92 + 63 * q^93 - 4 * q^94 + 44 * q^95 - 3 * q^96 - 72 * q^98 + 43 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.90551	−1.10015	−0.550074	−	0.835116i	$-0.685400\pi$
$3$	−1.90551	−1.10015	−0.550074	+	0.835116i	$0.685400\pi$
$4$	1.00000	0.500000
$5$	3.90912	1.74821	0.874106	−	0.485734i	$-0.161448\pi$
$5$	3.90912	1.74821	0.874106	+	0.485734i	$0.161448\pi$
$6$	1.90551	0.777922
$7$	1.35086	0.510577	0.255288	−	0.966865i	$-0.417830\pi$
$7$	1.35086	0.510577	0.255288	+	0.966865i	$0.417830\pi$
$8$	−1.00000	−0.353553
$9$	0.630974	0.210325
$10$	−3.90912	−1.23617
$11$	4.12504	1.24375	0.621873	−	0.783118i	$-0.286372\pi$
$11$	4.12504	1.24375	0.621873	+	0.783118i	$0.286372\pi$
$12$	−1.90551	−0.550074
$13$	0.627723	0.174099	0.0870495	−	0.996204i	$-0.472256\pi$
$13$	0.627723	0.174099	0.0870495	+	0.996204i	$0.472256\pi$
$14$	−1.35086	−0.361032
$15$	−7.44888	−1.92329
$16$	1.00000	0.250000
$17$	5.89576	1.42993	0.714966	−	0.699159i	$-0.246442\pi$
$17$	5.89576	1.42993	0.714966	+	0.699159i	$0.246442\pi$
$18$	−0.630974	−0.148722
$19$	6.12395	1.40493	0.702465	−	0.711718i	$-0.252083\pi$
$19$	6.12395	1.40493	0.702465	+	0.711718i	$0.252083\pi$
$20$	3.90912	0.874106
$21$	−2.57408	−0.561710
$22$	−4.12504	−0.879462
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.90551	0.388961
$25$	10.2812	2.05625
$26$	−0.627723	−0.123107
$27$	4.51421	0.868759
$28$	1.35086	0.255288
$29$	−2.99288	−0.555765	−0.277882	−	0.960615i	$-0.589633\pi$
$29$	−2.99288	−0.555765	−0.277882	+	0.960615i	$0.589633\pi$
$30$	7.44888	1.35997
$31$	−0.570916	−0.102540	−0.0512698	−	0.998685i	$-0.516327\pi$
$31$	−0.570916	−0.102540	−0.0512698	+	0.998685i	$0.516327\pi$
$32$	−1.00000	−0.176777
$33$	−7.86031	−1.36830
$34$	−5.89576	−1.01112
$35$	5.28068	0.892597
$36$	0.630974	0.105162
$37$	5.63949	0.927126	0.463563	−	0.886064i	$-0.346571\pi$
$37$	5.63949	0.927126	0.463563	+	0.886064i	$0.346571\pi$
$38$	−6.12395	−0.993436
$39$	−1.19613	−0.191535
$40$	−3.90912	−0.618087
$41$	−0.123458	−0.0192809	−0.00964044	−	0.999954i	$-0.503069\pi$
$41$	−0.123458	−0.0192809	−0.00964044	+	0.999954i	$0.503069\pi$
$42$	2.57408	0.397189
$43$	9.95959	1.51882	0.759411	−	0.650611i	$-0.225487\pi$
$43$	9.95959	1.51882	0.759411	+	0.650611i	$0.225487\pi$
$44$	4.12504	0.621873
$45$	2.46655	0.367692
$46$	−1.00000	−0.147442
$47$	−2.45111	−0.357532	−0.178766	−	0.983892i	$-0.557210\pi$
$47$	−2.45111	−0.357532	−0.178766	+	0.983892i	$0.557210\pi$
$48$	−1.90551	−0.275037
$49$	−5.17518	−0.739311
$50$	−10.2812	−1.45399
$51$	−11.2344	−1.57314
$52$	0.627723	0.0870495
$53$	−1.69180	−0.232387	−0.116193	−	0.993227i	$-0.537069\pi$
$53$	−1.69180	−0.232387	−0.116193	+	0.993227i	$0.537069\pi$
$54$	−4.51421	−0.614306
$55$	16.1253	2.17433
$56$	−1.35086	−0.180516
$57$	−11.6693	−1.54563
$58$	2.99288	0.392985
$59$	0.881464	0.114757	0.0573784	−	0.998353i	$-0.481726\pi$
$59$	0.881464	0.114757	0.0573784	+	0.998353i	$0.481726\pi$
$60$	−7.44888	−0.961646
$61$	3.92400	0.502416	0.251208	−	0.967933i	$-0.419172\pi$
$61$	3.92400	0.502416	0.251208	+	0.967933i	$0.419172\pi$
$62$	0.570916	0.0725064
$63$	0.852357	0.107387
$64$	1.00000	0.125000
$65$	2.45385	0.304362
$66$	7.86031	0.967538
$67$	−9.11742	−1.11387	−0.556935	−	0.830556i	$-0.688023\pi$
$67$	−9.11742	−1.11387	−0.556935	+	0.830556i	$0.688023\pi$
$68$	5.89576	0.714966
$69$	−1.90551	−0.229397
$70$	−5.28068	−0.631161
$71$	9.58993	1.13812	0.569058	−	0.822298i	$-0.307308\pi$
$71$	9.58993	1.13812	0.569058	+	0.822298i	$0.307308\pi$
$72$	−0.630974	−0.0743610
$73$	−0.290042	−0.0339468	−0.0169734	−	0.999856i	$-0.505403\pi$
$73$	−0.290042	−0.0339468	−0.0169734	+	0.999856i	$0.505403\pi$
$74$	−5.63949	−0.655577
$75$	−19.5910	−2.26218
$76$	6.12395	0.702465
$77$	5.57235	0.635028
$78$	1.19613	0.135435
$79$	4.59215	0.516658	0.258329	−	0.966057i	$-0.416828\pi$
$79$	4.59215	0.516658	0.258329	+	0.966057i	$0.416828\pi$
$80$	3.90912	0.437053
$81$	−10.4948	−1.16609
$82$	0.123458	0.0136336
$83$	−1.08868	−0.119498	−0.0597491	−	0.998213i	$-0.519030\pi$
$83$	−1.08868	−0.119498	−0.0597491	+	0.998213i	$0.519030\pi$
$84$	−2.57408	−0.280855
$85$	23.0473	2.49983
$86$	−9.95959	−1.07397
$87$	5.70297	0.611423
$88$	−4.12504	−0.439731
$89$	11.3190	1.19981	0.599907	−	0.800070i	$-0.295204\pi$
$89$	11.3190	1.19981	0.599907	+	0.800070i	$0.295204\pi$
$90$	−2.46655	−0.259998
$91$	0.847965	0.0888909
$92$	1.00000	0.104257
$93$	1.08789	0.112809
$94$	2.45111	0.252813
$95$	23.9393	2.45612
$96$	1.90551	0.194480
$97$	−12.6345	−1.28284	−0.641418	−	0.767191i	$-0.721654\pi$
$97$	−12.6345	−1.28284	−0.641418	+	0.767191i	$0.721654\pi$
$98$	5.17518	0.522772
$99$	2.60279	0.261591
$100$	10.2812	1.02812
$101$	10.4233	1.03716	0.518579	−	0.855030i	$-0.326461\pi$
$101$	10.4233	1.03716	0.518579	+	0.855030i	$0.326461\pi$
$102$	11.2344	1.11238
$103$	3.50324	0.345184	0.172592	−	0.984993i	$-0.444786\pi$
$103$	3.50324	0.345184	0.172592	+	0.984993i	$0.444786\pi$
$104$	−0.627723	−0.0615533
$105$	−10.0624	−0.981989
$106$	1.69180	0.164322
$107$	−17.4415	−1.68613	−0.843067	−	0.537809i	$-0.819252\pi$
$107$	−17.4415	−1.68613	−0.843067	+	0.537809i	$0.819252\pi$
$108$	4.51421	0.434380
$109$	−12.6160	−1.20839	−0.604197	−	0.796835i	$-0.706506\pi$
$109$	−12.6160	−1.20839	−0.604197	+	0.796835i	$0.706506\pi$
$110$	−16.1253	−1.53749
$111$	−10.7461	−1.01998
$112$	1.35086	0.127644
$113$	−7.44359	−0.700234	−0.350117	−	0.936706i	$-0.613858\pi$
$113$	−7.44359	−0.700234	−0.350117	+	0.936706i	$0.613858\pi$
$114$	11.6693	1.09293
$115$	3.90912	0.364528
$116$	−2.99288	−0.277882
$117$	0.396077	0.0366173
$118$	−0.881464	−0.0811453
$119$	7.96435	0.730091
$120$	7.44888	0.679986
$121$	6.01597	0.546906
$122$	−3.92400	−0.355262
$123$	0.235250	0.0212118
$124$	−0.570916	−0.0512698
$125$	20.6450	1.84655
$126$	−0.852357	−0.0759340
$127$	15.4540	1.37132	0.685662	−	0.727920i	$-0.259513\pi$
$127$	15.4540	1.37132	0.685662	+	0.727920i	$0.259513\pi$
$128$	−1.00000	−0.0883883
$129$	−18.9781	−1.67093
$130$	−2.45385	−0.215217
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−7.86031	−0.684152
$133$	8.27260	0.717325
$134$	9.11742	0.787625
$135$	17.6466	1.51878
$136$	−5.89576	−0.505558
$137$	12.8883	1.10112	0.550560	−	0.834796i	$-0.314414\pi$
$137$	12.8883	1.10112	0.550560	+	0.834796i	$0.314414\pi$
$138$	1.90551	0.162208
$139$	−5.48357	−0.465110	−0.232555	−	0.972583i	$-0.574709\pi$
$139$	−5.48357	−0.465110	−0.232555	+	0.972583i	$0.574709\pi$
$140$	5.28068	0.446299
$141$	4.67063	0.393338
$142$	−9.58993	−0.804769
$143$	2.58938	0.216535
$144$	0.630974	0.0525812
$145$	−11.6996	−0.971595
$146$	0.290042	0.0240040
$147$	9.86136	0.813351
$148$	5.63949	0.463563
$149$	−9.64275	−0.789965	−0.394982	−	0.918689i	$-0.629249\pi$
$149$	−9.64275	−0.789965	−0.394982	+	0.918689i	$0.629249\pi$
$150$	19.5910	1.59960
$151$	−19.9241	−1.62140	−0.810701	−	0.585460i	$-0.800914\pi$
$151$	−19.9241	−1.62140	−0.810701	+	0.585460i	$0.800914\pi$
$152$	−6.12395	−0.496718
$153$	3.72007	0.300750
$154$	−5.57235	−0.449033
$155$	−2.23178	−0.179261
$156$	−1.19613	−0.0957673
$157$	−17.1798	−1.37110	−0.685548	−	0.728027i	$-0.740437\pi$
$157$	−17.1798	−1.37110	−0.685548	+	0.728027i	$0.740437\pi$
$158$	−4.59215	−0.365332
$159$	3.22375	0.255660
$160$	−3.90912	−0.309043
$161$	1.35086	0.106463
$162$	10.4948	0.824549
$163$	9.19505	0.720212	0.360106	−	0.932911i	$-0.382741\pi$
$163$	9.19505	0.720212	0.360106	+	0.932911i	$0.382741\pi$
$164$	−0.123458	−0.00964044
$165$	−30.7269	−2.39209
$166$	1.08868	0.0844980
$167$	−8.57176	−0.663302	−0.331651	−	0.943402i	$-0.607606\pi$
$167$	−8.57176	−0.663302	−0.331651	+	0.943402i	$0.607606\pi$
$168$	2.57408	0.198594
$169$	−12.6060	−0.969690
$170$	−23.0473	−1.76764
$171$	3.86405	0.295491
$172$	9.95959	0.759411
$173$	10.5549	0.802475	0.401237	−	0.915974i	$-0.368580\pi$
$173$	10.5549	0.802475	0.401237	+	0.915974i	$0.368580\pi$
$174$	−5.70297	−0.432341
$175$	13.8885	1.04987
$176$	4.12504	0.310937
$177$	−1.67964	−0.126249
$178$	−11.3190	−0.848397
$179$	−0.755210	−0.0564471	−0.0282235	−	0.999602i	$-0.508985\pi$
$179$	−0.755210	−0.0564471	−0.0282235	+	0.999602i	$0.508985\pi$
$180$	2.46655	0.183846
$181$	−5.17070	−0.384335	−0.192168	−	0.981362i	$-0.561552\pi$
$181$	−5.17070	−0.384335	−0.192168	+	0.981362i	$0.561552\pi$
$182$	−0.847965	−0.0628554
$183$	−7.47722	−0.552732
$184$	−1.00000	−0.0737210
$185$	22.0455	1.62081
$186$	−1.08789	−0.0797677
$187$	24.3203	1.77847
$188$	−2.45111	−0.178766
$189$	6.09806	0.443568
$190$	−23.9393	−1.73674
$191$	−25.6432	−1.85548	−0.927740	−	0.373228i	$-0.878251\pi$
$191$	−25.6432	−1.85548	−0.927740	+	0.373228i	$0.878251\pi$
$192$	−1.90551	−0.137518
$193$	−17.5619	−1.26413	−0.632067	−	0.774914i	$-0.717793\pi$
$193$	−17.5619	−1.26413	−0.632067	+	0.774914i	$0.717793\pi$
$194$	12.6345	0.907102
$195$	−4.67583	−0.334843
$196$	−5.17518	−0.369656
$197$	−22.8982	−1.63143	−0.815715	−	0.578454i	$-0.803656\pi$
$197$	−22.8982	−1.63143	−0.815715	+	0.578454i	$0.803656\pi$
$198$	−2.60279	−0.184972
$199$	18.8112	1.33349	0.666747	−	0.745284i	$-0.267686\pi$
$199$	18.8112	1.33349	0.666747	+	0.745284i	$0.267686\pi$
$200$	−10.2812	−0.726994
$201$	17.3733	1.22542
$202$	−10.4233	−0.733381
$203$	−4.04297	−0.283761
$204$	−11.2344	−0.786569
$205$	−0.482612	−0.0337071
$206$	−3.50324	−0.244082
$207$	0.630974	0.0438557
$208$	0.627723	0.0435247
$209$	25.2615	1.74738
$210$	10.0624	0.694371
$211$	−22.9957	−1.58309	−0.791545	−	0.611111i	$-0.790723\pi$
$211$	−22.9957	−1.58309	−0.791545	+	0.611111i	$0.790723\pi$
$212$	−1.69180	−0.116193
$213$	−18.2737	−1.25209
$214$	17.4415	1.19228
$215$	38.9332	2.65523
$216$	−4.51421	−0.307153
$217$	−0.771227	−0.0523543
$218$	12.6160	0.854464
$219$	0.552678	0.0373465
$220$	16.1253	1.08717
$221$	3.70091	0.248950
$222$	10.7461	0.721232
$223$	−11.1898	−0.749327	−0.374663	−	0.927161i	$-0.622242\pi$
$223$	−11.1898	−0.749327	−0.374663	+	0.927161i	$0.622242\pi$
$224$	−1.35086	−0.0902581
$225$	6.48719	0.432480
$226$	7.44359	0.495140
$227$	−7.88620	−0.523425	−0.261713	−	0.965146i	$-0.584287\pi$
$227$	−7.88620	−0.523425	−0.261713	+	0.965146i	$0.584287\pi$
$228$	−11.6693	−0.772815
$229$	−7.52730	−0.497418	−0.248709	−	0.968578i	$-0.580006\pi$
$229$	−7.52730	−0.497418	−0.248709	+	0.968578i	$0.580006\pi$
$230$	−3.90912	−0.257760
$231$	−10.6182	−0.698625
$232$	2.99288	0.196492
$233$	−19.7965	−1.29691	−0.648456	−	0.761252i	$-0.724585\pi$
$233$	−19.7965	−1.29691	−0.648456	+	0.761252i	$0.724585\pi$
$234$	−0.396077	−0.0258923
$235$	−9.58171	−0.625042
$236$	0.881464	0.0573784
$237$	−8.75040	−0.568399
$238$	−7.96435	−0.516252
$239$	21.4877	1.38992	0.694962	−	0.719047i	$-0.255421\pi$
$239$	21.4877	1.38992	0.694962	+	0.719047i	$0.255421\pi$
$240$	−7.44888	−0.480823
$241$	−9.15873	−0.589966	−0.294983	−	0.955503i	$-0.595314\pi$
$241$	−9.15873	−0.589966	−0.294983	+	0.955503i	$0.595314\pi$
$242$	−6.01597	−0.386721
$243$	6.45533	0.414110
$244$	3.92400	0.251208
$245$	−20.2304	−1.29247
$246$	−0.235250	−0.0149990
$247$	3.84414	0.244597
$248$	0.570916	0.0362532
$249$	2.07449	0.131466
$250$	−20.6450	−1.30571
$251$	−10.3799	−0.655176	−0.327588	−	0.944821i	$-0.606236\pi$
$251$	−10.3799	−0.655176	−0.327588	+	0.944821i	$0.606236\pi$
$252$	0.852357	0.0536934
$253$	4.12504	0.259339
$254$	−15.4540	−0.969672
$255$	−43.9168	−2.75018
$256$	1.00000	0.0625000
$257$	−22.9122	−1.42922	−0.714611	−	0.699522i	$-0.753396\pi$
$257$	−22.9122	−1.42922	−0.714611	+	0.699522i	$0.753396\pi$
$258$	18.9781	1.18153
$259$	7.61816	0.473369
$260$	2.45385	0.152181
$261$	−1.88843	−0.116891
$262$	1.00000	0.0617802
$263$	14.0072	0.863720	0.431860	−	0.901941i	$-0.357857\pi$
$263$	14.0072	0.863720	0.431860	+	0.901941i	$0.357857\pi$
$264$	7.86031	0.483769
$265$	−6.61346	−0.406261
$266$	−8.27260	−0.507225
$267$	−21.5685	−1.31997
$268$	−9.11742	−0.556935
$269$	21.7852	1.32827	0.664134	−	0.747614i	$-0.268801\pi$
$269$	21.7852	1.32827	0.664134	+	0.747614i	$0.268801\pi$
$270$	−17.6466	−1.07394
$271$	16.0004	0.971957	0.485978	−	0.873971i	$-0.338463\pi$
$271$	16.0004	0.971957	0.485978	+	0.873971i	$0.338463\pi$
$272$	5.89576	0.357483
$273$	−1.61581	−0.0977931
$274$	−12.8883	−0.778609
$275$	42.4105	2.55745
$276$	−1.90551	−0.114698
$277$	−22.8987	−1.37585	−0.687924	−	0.725782i	$-0.741478\pi$
$277$	−22.8987	−1.37585	−0.687924	+	0.725782i	$0.741478\pi$
$278$	5.48357	0.328883
$279$	−0.360233	−0.0215666
$280$	−5.28068	−0.315581
$281$	8.34364	0.497740	0.248870	−	0.968537i	$-0.419941\pi$
$281$	8.34364	0.497740	0.248870	+	0.968537i	$0.419941\pi$
$282$	−4.67063	−0.278132
$283$	6.14718	0.365412	0.182706	−	0.983168i	$-0.441514\pi$
$283$	6.14718	0.365412	0.182706	+	0.983168i	$0.441514\pi$
$284$	9.58993	0.569058
$285$	−45.6166	−2.70209
$286$	−2.58938	−0.153113
$287$	−0.166774	−0.00984437
$288$	−0.630974	−0.0371805
$289$	17.7600	1.04471
$290$	11.6996	0.687021
$291$	24.0751	1.41131
$292$	−0.290042	−0.0169734
$293$	−31.5660	−1.84411	−0.922053	−	0.387063i	$-0.873489\pi$
$293$	−31.5660	−1.84411	−0.922053	+	0.387063i	$0.873489\pi$
$294$	−9.86136	−0.575126
$295$	3.44575	0.200619
$296$	−5.63949	−0.327789
$297$	18.6213	1.08052
$298$	9.64275	0.558589
$299$	0.627723	0.0363021
$300$	−19.5910	−1.13109
$301$	13.4540	0.775476
$302$	19.9241	1.14650
$303$	−19.8617	−1.14103
$304$	6.12395	0.351233
$305$	15.3394	0.878331
$306$	−3.72007	−0.212662
$307$	−14.3547	−0.819264	−0.409632	−	0.912251i	$-0.634343\pi$
$307$	−14.3547	−0.819264	−0.409632	+	0.912251i	$0.634343\pi$
$308$	5.57235	0.317514
$309$	−6.67546	−0.379753
$310$	2.23178	0.126757
$311$	11.8093	0.669642	0.334821	−	0.942282i	$-0.391324\pi$
$311$	11.8093	0.669642	0.334821	+	0.942282i	$0.391324\pi$
$312$	1.19613	0.0677177
$313$	−34.1717	−1.93150	−0.965749	−	0.259478i	$-0.916449\pi$
$313$	−34.1717	−1.93150	−0.965749	+	0.259478i	$0.916449\pi$
$314$	17.1798	0.969511
$315$	3.33197	0.187735
$316$	4.59215	0.258329
$317$	−32.5727	−1.82947	−0.914733	−	0.404058i	$-0.867599\pi$
$317$	−32.5727	−1.82947	−0.914733	+	0.404058i	$0.867599\pi$
$318$	−3.22375	−0.180779
$319$	−12.3458	−0.691230
$320$	3.90912	0.218527
$321$	33.2350	1.85500
$322$	−1.35086	−0.0752805
$323$	36.1054	2.00896
$324$	−10.4948	−0.583044
$325$	6.45377	0.357991
$326$	−9.19505	−0.509267
$327$	24.0400	1.32941
$328$	0.123458	0.00681682
$329$	−3.31111	−0.182547
$330$	30.7269	1.69146
$331$	13.2828	0.730086	0.365043	−	0.930991i	$-0.381054\pi$
$331$	13.2828	0.730086	0.365043	+	0.930991i	$0.381054\pi$
$332$	−1.08868	−0.0597491
$333$	3.55837	0.194998
$334$	8.57176	0.469026
$335$	−35.6411	−1.94728
$336$	−2.57408	−0.140427
$337$	8.79553	0.479123	0.239561	−	0.970881i	$-0.422996\pi$
$337$	8.79553	0.479123	0.239561	+	0.970881i	$0.422996\pi$
$338$	12.6060	0.685674
$339$	14.1839	0.770361
$340$	23.0473	1.24991
$341$	−2.35505	−0.127533
$342$	−3.86405	−0.208944
$343$	−16.4470	−0.888052
$344$	−9.95959	−0.536985
$345$	−7.44888	−0.401034
$346$	−10.5549	−0.567435
$347$	26.5832	1.42706	0.713531	−	0.700624i	$-0.247095\pi$
$347$	26.5832	1.42706	0.713531	+	0.700624i	$0.247095\pi$
$348$	5.70297	0.305712
$349$	−11.6515	−0.623690	−0.311845	−	0.950133i	$-0.600947\pi$
$349$	−11.6515	−0.623690	−0.311845	+	0.950133i	$0.600947\pi$
$350$	−13.8885	−0.742372
$351$	2.83367	0.151250
$352$	−4.12504	−0.219865
$353$	−9.58739	−0.510285	−0.255143	−	0.966903i	$-0.582122\pi$
$353$	−9.58739	−0.510285	−0.255143	+	0.966903i	$0.582122\pi$
$354$	1.67964	0.0892718
$355$	37.4882	1.98967
$356$	11.3190	0.599907
$357$	−15.1762	−0.803207
$358$	0.755210	0.0399141
$359$	−5.20122	−0.274510	−0.137255	−	0.990536i	$-0.543828\pi$
$359$	−5.20122	−0.274510	−0.137255	+	0.990536i	$0.543828\pi$
$360$	−2.46655	−0.129999
$361$	18.5028	0.973830
$362$	5.17070	0.271766
$363$	−11.4635	−0.601677
$364$	0.847965	0.0444455
$365$	−1.13381	−0.0593462
$366$	7.47722	0.390841
$367$	14.1967	0.741064	0.370532	−	0.928820i	$-0.379175\pi$
$367$	14.1967	0.741064	0.370532	+	0.928820i	$0.379175\pi$
$368$	1.00000	0.0521286
$369$	−0.0778987	−0.00405524
$370$	−22.0455	−1.14609
$371$	−2.28539	−0.118651
$372$	1.08789	0.0564043
$373$	18.6368	0.964975	0.482487	−	0.875903i	$-0.339733\pi$
$373$	18.6368	0.964975	0.482487	+	0.875903i	$0.339733\pi$
$374$	−24.3203	−1.25757
$375$	−39.3393	−2.03147
$376$	2.45111	0.126407
$377$	−1.87870	−0.0967581
$378$	−6.09806	−0.313650
$379$	31.7092	1.62879	0.814395	−	0.580310i	$-0.197069\pi$
$379$	31.7092	1.62879	0.814395	+	0.580310i	$0.197069\pi$
$380$	23.9393	1.22806
$381$	−29.4478	−1.50866
$382$	25.6432	1.31202
$383$	25.6622	1.31128	0.655640	−	0.755074i	$-0.272399\pi$
$383$	25.6622	1.31128	0.655640	+	0.755074i	$0.272399\pi$
$384$	1.90551	0.0972402
$385$	21.7830	1.11016
$386$	17.5619	0.893878
$387$	6.28424	0.319446
$388$	−12.6345	−0.641418
$389$	29.0771	1.47427	0.737133	−	0.675747i	$-0.236179\pi$
$389$	29.0771	1.47427	0.737133	+	0.675747i	$0.236179\pi$
$390$	4.67583	0.236770
$391$	5.89576	0.298162
$392$	5.17518	0.261386
$393$	1.90551	0.0961203
$394$	22.8982	1.15360
$395$	17.9513	0.903227
$396$	2.60279	0.130795
$397$	−26.0030	−1.30505	−0.652527	−	0.757766i	$-0.726291\pi$
$397$	−26.0030	−1.30505	−0.652527	+	0.757766i	$0.726291\pi$
$398$	−18.8112	−0.942923
$399$	−15.7635	−0.789163
$400$	10.2812	0.514062
$401$	−28.9860	−1.44749	−0.723745	−	0.690068i	$-0.757581\pi$
$401$	−28.9860	−1.44749	−0.723745	+	0.690068i	$0.757581\pi$
$402$	−17.3733	−0.866503
$403$	−0.358377	−0.0178520
$404$	10.4233	0.518579
$405$	−41.0254	−2.03857
$406$	4.04297	0.200649
$407$	23.2631	1.15311
$408$	11.2344	0.556188
$409$	23.4628	1.16016	0.580081	−	0.814559i	$-0.303021\pi$
$409$	23.4628	1.16016	0.580081	+	0.814559i	$0.303021\pi$
$410$	0.482612	0.0238345
$411$	−24.5588	−1.21139
$412$	3.50324	0.172592
$413$	1.19073	0.0585922
$414$	−0.630974	−0.0310107
$415$	−4.25579	−0.208908
$416$	−0.627723	−0.0307766
$417$	10.4490	0.511690
$418$	−25.2615	−1.23558
$419$	12.0942	0.590841	0.295420	−	0.955367i	$-0.404540\pi$
$419$	12.0942	0.590841	0.295420	+	0.955367i	$0.404540\pi$
$420$	−10.0624	−0.490994
$421$	−5.37086	−0.261760	−0.130880	−	0.991398i	$-0.541780\pi$
$421$	−5.37086	−0.261760	−0.130880	+	0.991398i	$0.541780\pi$
$422$	22.9957	1.11941
$423$	−1.54659	−0.0751977
$424$	1.69180	0.0821611
$425$	60.6158	2.94030
$426$	18.2737	0.885365
$427$	5.30077	0.256522
$428$	−17.4415	−0.843067
$429$	−4.93410	−0.238221
$430$	−38.9332	−1.87753
$431$	−0.184747	−0.00889896	−0.00444948	−	0.999990i	$-0.501416\pi$
$431$	−0.184747	−0.00889896	−0.00444948	+	0.999990i	$0.501416\pi$
$432$	4.51421	0.217190
$433$	15.0616	0.723814	0.361907	−	0.932214i	$-0.382126\pi$
$433$	15.0616	0.723814	0.361907	+	0.932214i	$0.382126\pi$
$434$	0.771227	0.0370201
$435$	22.2936	1.06890
$436$	−12.6160	−0.604197
$437$	6.12395	0.292948
$438$	−0.552678	−0.0264080
$439$	−3.49267	−0.166696	−0.0833481	−	0.996520i	$-0.526561\pi$
$439$	−3.49267	−0.166696	−0.0833481	+	0.996520i	$0.526561\pi$
$440$	−16.1253	−0.768743
$441$	−3.26540	−0.155495
$442$	−3.70091	−0.176034
$443$	−9.46345	−0.449622	−0.224811	−	0.974402i	$-0.572176\pi$
$443$	−9.46345	−0.449622	−0.224811	+	0.974402i	$0.572176\pi$
$444$	−10.7461	−0.509988
$445$	44.2475	2.09753
$446$	11.1898	0.529854
$447$	18.3744	0.869078
$448$	1.35086	0.0638221
$449$	22.2102	1.04816	0.524081	−	0.851668i	$-0.324409\pi$
$449$	22.2102	1.04816	0.524081	+	0.851668i	$0.324409\pi$
$450$	−6.48719	−0.305809
$451$	−0.509269	−0.0239805
$452$	−7.44359	−0.350117
$453$	37.9657	1.78378
$454$	7.88620	0.370118
$455$	3.31480	0.155400
$456$	11.6693	0.546463
$457$	−0.623414	−0.0291621	−0.0145810	−	0.999894i	$-0.504641\pi$
$457$	−0.623414	−0.0291621	−0.0145810	+	0.999894i	$0.504641\pi$
$458$	7.52730	0.351728
$459$	26.6147	1.24227
$460$	3.90912	0.182264
$461$	1.64477	0.0766048	0.0383024	−	0.999266i	$-0.487805\pi$
$461$	1.64477	0.0766048	0.0383024	+	0.999266i	$0.487805\pi$
$462$	10.6182	0.494002
$463$	−9.95819	−0.462796	−0.231398	−	0.972859i	$-0.574330\pi$
$463$	−9.95819	−0.462796	−0.231398	+	0.972859i	$0.574330\pi$
$464$	−2.99288	−0.138941
$465$	4.25268	0.197213
$466$	19.7965	0.917056
$467$	−4.13588	−0.191386	−0.0956928	−	0.995411i	$-0.530507\pi$
$467$	−4.13588	−0.191386	−0.0956928	+	0.995411i	$0.530507\pi$
$468$	0.396077	0.0183087
$469$	−12.3163	−0.568716
$470$	9.58171	0.441971
$471$	32.7363	1.50841
$472$	−0.881464	−0.0405727
$473$	41.0837	1.88903
$474$	8.75040	0.401919
$475$	62.9618	2.88889
$476$	7.96435	0.365045
$477$	−1.06748	−0.0488766
$478$	−21.4877	−0.982824
$479$	−6.19574	−0.283091	−0.141545	−	0.989932i	$-0.545207\pi$
$479$	−6.19574	−0.283091	−0.141545	+	0.989932i	$0.545207\pi$
$480$	7.44888	0.339993
$481$	3.54004	0.161412
$482$	9.15873	0.417169
$483$	−2.57408	−0.117125
$484$	6.01597	0.273453
$485$	−49.3897	−2.24267
$486$	−6.45533	−0.292820
$487$	30.0026	1.35955	0.679773	−	0.733422i	$-0.262078\pi$
$487$	30.0026	1.35955	0.679773	+	0.733422i	$0.262078\pi$
$488$	−3.92400	−0.177631
$489$	−17.5213	−0.792339
$490$	20.2304	0.913917
$491$	−29.9727	−1.35265	−0.676325	−	0.736603i	$-0.736428\pi$
$491$	−29.9727	−1.35265	−0.676325	+	0.736603i	$0.736428\pi$
$492$	0.235250	0.0106059
$493$	−17.6453	−0.794706
$494$	−3.84414	−0.172956
$495$	10.1746	0.457316
$496$	−0.570916	−0.0256349
$497$	12.9547	0.581095
$498$	−2.07449	−0.0929603
$499$	24.3521	1.09015	0.545076	−	0.838387i	$-0.316501\pi$
$499$	24.3521	1.09015	0.545076	+	0.838387i	$0.316501\pi$
$500$	20.6450	0.923273
$501$	16.3336	0.729731
$502$	10.3799	0.463279
$503$	−38.0050	−1.69456	−0.847280	−	0.531147i	$-0.821761\pi$
$503$	−38.0050	−1.69456	−0.847280	+	0.531147i	$0.821761\pi$
$504$	−0.852357	−0.0379670
$505$	40.7460	1.81317
$506$	−4.12504	−0.183380
$507$	24.0208	1.06680
$508$	15.4540	0.685662
$509$	21.5470	0.955056	0.477528	−	0.878616i	$-0.341533\pi$
$509$	21.5470	0.955056	0.477528	+	0.878616i	$0.341533\pi$
$510$	43.9168	1.94467
$511$	−0.391806	−0.0173325
$512$	−1.00000	−0.0441942
$513$	27.6448	1.22055
$514$	22.9122	1.01061
$515$	13.6946	0.603455
$516$	−18.9781	−0.835464
$517$	−10.1109	−0.444679
$518$	−7.61816	−0.334723
$519$	−20.1125	−0.882841
$520$	−2.45385	−0.107608
$521$	−11.0519	−0.484194	−0.242097	−	0.970252i	$-0.577835\pi$
$521$	−11.0519	−0.484194	−0.242097	+	0.970252i	$0.577835\pi$
$522$	1.88843	0.0826544
$523$	22.1985	0.970673	0.485336	−	0.874327i	$-0.338697\pi$
$523$	22.1985	0.970673	0.485336	+	0.874327i	$0.338697\pi$
$524$	−1.00000	−0.0436852
$525$	−26.4647	−1.15502
$526$	−14.0072	−0.610743
$527$	−3.36599	−0.146625
$528$	−7.86031	−0.342076
$529$	1.00000	0.0434783
$530$	6.61346	0.287270
$531$	0.556181	0.0241362
$532$	8.27260	0.358663
$533$	−0.0774973	−0.00335678
$534$	21.5685	0.933362
$535$	−68.1810	−2.94772
$536$	9.11742	0.393812
$537$	1.43906	0.0621001
$538$	−21.7852	−0.939227
$539$	−21.3478	−0.919516
$540$	17.6466	0.759388
$541$	3.48787	0.149955	0.0749776	−	0.997185i	$-0.476111\pi$
$541$	3.48787	0.149955	0.0749776	+	0.997185i	$0.476111\pi$
$542$	−16.0004	−0.687277
$543$	9.85283	0.422825
$544$	−5.89576	−0.252779
$545$	−49.3175	−2.11253
$546$	1.61581	0.0691502
$547$	11.6591	0.498507	0.249254	−	0.968438i	$-0.419815\pi$
$547$	11.6591	0.498507	0.249254	+	0.968438i	$0.419815\pi$
$548$	12.8883	0.550560
$549$	2.47594	0.105671
$550$	−42.4105	−1.80839
$551$	−18.3283	−0.780811
$552$	1.90551	0.0811040
$553$	6.20335	0.263793
$554$	22.8987	0.972872
$555$	−42.0079	−1.78314
$556$	−5.48357	−0.232555
$557$	−13.1036	−0.555216	−0.277608	−	0.960694i	$-0.589542\pi$
$557$	−13.1036	−0.555216	−0.277608	+	0.960694i	$0.589542\pi$
$558$	0.360233	0.0152499
$559$	6.25186	0.264425
$560$	5.28068	0.223149
$561$	−46.3426	−1.95658
$562$	−8.34364	−0.351955
$563$	−17.5815	−0.740972	−0.370486	−	0.928838i	$-0.620809\pi$
$563$	−17.5815	−0.740972	−0.370486	+	0.928838i	$0.620809\pi$
$564$	4.67063	0.196669
$565$	−29.0979	−1.22416
$566$	−6.14718	−0.258385
$567$	−14.1770	−0.595378
$568$	−9.58993	−0.402385
$569$	−35.5767	−1.49145	−0.745727	−	0.666252i	$-0.767898\pi$
$569$	−35.5767	−1.49145	−0.745727	+	0.666252i	$0.767898\pi$
$570$	45.6166	1.91067
$571$	−35.4573	−1.48384	−0.741922	−	0.670487i	$-0.766085\pi$
$571$	−35.4573	−1.48384	−0.741922	+	0.670487i	$0.766085\pi$
$572$	2.58938	0.108268
$573$	48.8635	2.04130
$574$	0.166774	0.00696102
$575$	10.2812	0.428757
$576$	0.630974	0.0262906
$577$	47.3114	1.96960	0.984799	−	0.173698i	$-0.0555718\pi$
$577$	47.3114	1.96960	0.984799	+	0.173698i	$0.0555718\pi$
$578$	−17.7600	−0.738720
$579$	33.4644	1.39073
$580$	−11.6996	−0.485797
$581$	−1.47065	−0.0610130
$582$	−24.0751	−0.997946
$583$	−6.97875	−0.289030
$584$	0.290042	0.0120020
$585$	1.54831	0.0640148
$586$	31.5660	1.30398
$587$	−5.47905	−0.226145	−0.113072	−	0.993587i	$-0.536069\pi$
$587$	−5.47905	−0.226145	−0.113072	+	0.993587i	$0.536069\pi$
$588$	9.86136	0.406676
$589$	−3.49626	−0.144061
$590$	−3.44575	−0.141859
$591$	43.6328	1.79481
$592$	5.63949	0.231782
$593$	−13.0261	−0.534919	−0.267460	−	0.963569i	$-0.586184\pi$
$593$	−13.0261	−0.534919	−0.267460	+	0.963569i	$0.586184\pi$
$594$	−18.6213	−0.764041
$595$	31.1336	1.27635
$596$	−9.64275	−0.394982
$597$	−35.8450	−1.46704
$598$	−0.627723	−0.0256695
$599$	41.5922	1.69941	0.849707	−	0.527256i	$-0.176779\pi$
$599$	41.5922	1.69941	0.849707	+	0.527256i	$0.176779\pi$
$600$	19.5910	0.799800
$601$	6.29492	0.256775	0.128388	−	0.991724i	$-0.459020\pi$
$601$	6.29492	0.256775	0.128388	+	0.991724i	$0.459020\pi$
$602$	−13.4540	−0.548344
$603$	−5.75285	−0.234274
$604$	−19.9241	−0.810701
$605$	23.5172	0.956108
$606$	19.8617	0.806828
$607$	3.17752	0.128972	0.0644859	−	0.997919i	$-0.479459\pi$
$607$	3.17752	0.128972	0.0644859	+	0.997919i	$0.479459\pi$
$608$	−6.12395	−0.248359
$609$	7.70392	0.312178
$610$	−15.3394	−0.621073
$611$	−1.53862	−0.0622459
$612$	3.72007	0.150375
$613$	13.9515	0.563494	0.281747	−	0.959489i	$-0.409086\pi$
$613$	13.9515	0.563494	0.281747	+	0.959489i	$0.409086\pi$
$614$	14.3547	0.579307
$615$	0.919623	0.0370828
$616$	−5.57235	−0.224516
$617$	15.2908	0.615584	0.307792	−	0.951454i	$-0.400410\pi$
$617$	15.2908	0.615584	0.307792	+	0.951454i	$0.400410\pi$
$618$	6.67546	0.268526
$619$	27.0625	1.08773	0.543867	−	0.839172i	$-0.316960\pi$
$619$	27.0625	1.08773	0.543867	+	0.839172i	$0.316960\pi$
$620$	−2.23178	−0.0896305
$621$	4.51421	0.181149
$622$	−11.8093	−0.473509
$623$	15.2904	0.612598
$624$	−1.19613	−0.0478836
$625$	29.2977	1.17191
$626$	34.1717	1.36578
$627$	−48.1362	−1.92237
$628$	−17.1798	−0.685548
$629$	33.2491	1.32573
$630$	−3.33197	−0.132749
$631$	6.32060	0.251619	0.125810	−	0.992054i	$-0.459847\pi$
$631$	6.32060	0.251619	0.125810	+	0.992054i	$0.459847\pi$
$632$	−4.59215	−0.182666
$633$	43.8186	1.74163
$634$	32.5727	1.29363
$635$	60.4117	2.39737
$636$	3.22375	0.127830
$637$	−3.24858	−0.128713
$638$	12.3458	0.488774
$639$	6.05100	0.239374
$640$	−3.90912	−0.154522
$641$	−12.7648	−0.504179	−0.252090	−	0.967704i	$-0.581118\pi$
$641$	−12.7648	−0.504179	−0.252090	+	0.967704i	$0.581118\pi$
$642$	−33.2350	−1.31168
$643$	14.6464	0.577597	0.288798	−	0.957390i	$-0.406744\pi$
$643$	14.6464	0.577597	0.288798	+	0.957390i	$0.406744\pi$
$644$	1.35086	0.0532313
$645$	−74.1877	−2.92114
$646$	−36.1054	−1.42055
$647$	17.9792	0.706835	0.353417	−	0.935466i	$-0.385020\pi$
$647$	17.9792	0.706835	0.353417	+	0.935466i	$0.385020\pi$
$648$	10.4948	0.412274
$649$	3.63607	0.142728
$650$	−6.45377	−0.253138
$651$	1.46958	0.0575975
$652$	9.19505	0.360106
$653$	−15.2773	−0.597849	−0.298924	−	0.954277i	$-0.596628\pi$
$653$	−15.2773	−0.597849	−0.298924	+	0.954277i	$0.596628\pi$
$654$	−24.0400	−0.940037
$655$	−3.90912	−0.152742
$656$	−0.123458	−0.00482022
$657$	−0.183009	−0.00713985
$658$	3.31111	0.129081
$659$	−0.470451	−0.0183261	−0.00916307	−	0.999958i	$-0.502917\pi$
$659$	−0.470451	−0.0183261	−0.00916307	+	0.999958i	$0.502917\pi$
$660$	−30.7269	−1.19604
$661$	15.8773	0.617556	0.308778	−	0.951134i	$-0.400080\pi$
$661$	15.8773	0.617556	0.308778	+	0.951134i	$0.400080\pi$
$662$	−13.2828	−0.516249
$663$	−7.05212	−0.273882
$664$	1.08868	0.0422490
$665$	32.3386	1.25404
$666$	−3.55837	−0.137884
$667$	−2.99288	−0.115885
$668$	−8.57176	−0.331651
$669$	21.3224	0.824370
$670$	35.6411	1.37694
$671$	16.1866	0.624879
$672$	2.57408	0.0992972
$673$	32.5463	1.25457	0.627285	−	0.778790i	$-0.284166\pi$
$673$	32.5463	1.25457	0.627285	+	0.778790i	$0.284166\pi$
$674$	−8.79553	−0.338791
$675$	46.4116	1.78639
$676$	−12.6060	−0.484845
$677$	−12.6055	−0.484470	−0.242235	−	0.970218i	$-0.577880\pi$
$677$	−12.6055	−0.484470	−0.242235	+	0.970218i	$0.577880\pi$
$678$	−14.1839	−0.544727
$679$	−17.0674	−0.654987
$680$	−23.0473	−0.883822
$681$	15.0272	0.575845
$682$	2.35505	0.0901796
$683$	−13.5200	−0.517329	−0.258664	−	0.965967i	$-0.583282\pi$
$683$	−13.5200	−0.517329	−0.258664	+	0.965967i	$0.583282\pi$
$684$	3.86405	0.147746
$685$	50.3818	1.92499
$686$	16.4470	0.627948
$687$	14.3434	0.547233
$688$	9.95959	0.379706
$689$	−1.06198	−0.0404583
$690$	7.44888	0.283574
$691$	−7.77553	−0.295795	−0.147897	−	0.989003i	$-0.547251\pi$
$691$	−7.77553	−0.295795	−0.147897	+	0.989003i	$0.547251\pi$
$692$	10.5549	0.401237
$693$	3.51601	0.133562
$694$	−26.5832	−1.00908
$695$	−21.4360	−0.813112
$696$	−5.70297	−0.216171
$697$	−0.727879	−0.0275704
$698$	11.6515	0.441016
$699$	37.7225	1.42679
$700$	13.8885	0.524936
$701$	16.1761	0.610961	0.305481	−	0.952198i	$-0.401183\pi$
$701$	16.1761	0.610961	0.305481	+	0.952198i	$0.401183\pi$
$702$	−2.83367	−0.106950
$703$	34.5360	1.30255
$704$	4.12504	0.155468
$705$	18.2580	0.687638
$706$	9.58739	0.360826
$707$	14.0804	0.529549
$708$	−1.67964	−0.0631247
$709$	−16.2480	−0.610205	−0.305102	−	0.952320i	$-0.598691\pi$
$709$	−16.2480	−0.610205	−0.305102	+	0.952320i	$0.598691\pi$
$710$	−37.4882	−1.40691
$711$	2.89753	0.108666
$712$	−11.3190	−0.424199
$713$	−0.570916	−0.0213810
$714$	15.1762	0.567953
$715$	10.1222	0.378549
$716$	−0.755210	−0.0282235
$717$	−40.9450	−1.52912
$718$	5.20122	0.194108
$719$	−28.6131	−1.06709	−0.533544	−	0.845772i	$-0.679140\pi$
$719$	−28.6131	−1.06709	−0.533544	+	0.845772i	$0.679140\pi$
$720$	2.46655	0.0919231
$721$	4.73238	0.176243
$722$	−18.5028	−0.688602
$723$	17.4521	0.649050
$724$	−5.17070	−0.192168
$725$	−30.7706	−1.14279
$726$	11.4635	0.425450
$727$	10.1961	0.378152	0.189076	−	0.981962i	$-0.439451\pi$
$727$	10.1961	0.378152	0.189076	+	0.981962i	$0.439451\pi$
$728$	−0.847965	−0.0314277
$729$	19.1837	0.710506
$730$	1.13381	0.0419641
$731$	58.7194	2.17181
$732$	−7.47722	−0.276366
$733$	36.7819	1.35857	0.679284	−	0.733875i	$-0.262290\pi$
$733$	36.7819	1.35857	0.679284	+	0.733875i	$0.262290\pi$
$734$	−14.1967	−0.524011
$735$	38.5493	1.42191
$736$	−1.00000	−0.0368605
$737$	−37.6097	−1.38537
$738$	0.0778987	0.00286749
$739$	51.5236	1.89533	0.947664	−	0.319270i	$-0.103438\pi$
$739$	51.5236	1.89533	0.947664	+	0.319270i	$0.103438\pi$
$740$	22.0455	0.810407
$741$	−7.32506	−0.269093
$742$	2.28539	0.0838991
$743$	−16.3654	−0.600390	−0.300195	−	0.953878i	$-0.597052\pi$
$743$	−16.3654	−0.600390	−0.300195	+	0.953878i	$0.597052\pi$
$744$	−1.08789	−0.0398839
$745$	−37.6947	−1.38103
$746$	−18.6368	−0.682340
$747$	−0.686929	−0.0251334
$748$	24.3203	0.889237
$749$	−23.5610	−0.860901
$750$	39.3393	1.43647
$751$	−33.0319	−1.20535	−0.602676	−	0.797986i	$-0.705899\pi$
$751$	−33.0319	−1.20535	−0.602676	+	0.797986i	$0.705899\pi$
$752$	−2.45111	−0.0893829
$753$	19.7791	0.720790
$754$	1.87870	0.0684183
$755$	−77.8859	−2.83456
$756$	6.09806	0.221784
$757$	−7.51324	−0.273073	−0.136537	−	0.990635i	$-0.543597\pi$
$757$	−7.51324	−0.273073	−0.136537	+	0.990635i	$0.543597\pi$
$758$	−31.7092	−1.15173
$759$	−7.86031	−0.285311
$760$	−23.9393	−0.868369
$761$	29.9228	1.08470	0.542351	−	0.840152i	$-0.317534\pi$
$761$	29.9228	1.08470	0.542351	+	0.840152i	$0.317534\pi$
$762$	29.4478	1.06678
$763$	−17.0425	−0.616978
$764$	−25.6432	−0.927740
$765$	14.5422	0.525775
$766$	−25.6622	−0.927215
$767$	0.553315	0.0199790
$768$	−1.90551	−0.0687592
$769$	53.5018	1.92932	0.964662	−	0.263492i	$-0.0848742\pi$
$769$	53.5018	1.92932	0.964662	+	0.263492i	$0.0848742\pi$
$770$	−21.7830	−0.785005
$771$	43.6594	1.57236
$772$	−17.5619	−0.632067
$773$	15.0372	0.540852	0.270426	−	0.962741i	$-0.412835\pi$
$773$	15.0372	0.540852	0.270426	+	0.962741i	$0.412835\pi$
$774$	−6.28424	−0.225882
$775$	−5.86972	−0.210847
$776$	12.6345	0.453551
$777$	−14.5165	−0.520776
$778$	−29.0771	−1.04246
$779$	−0.756050	−0.0270883
$780$	−4.67583	−0.167422
$781$	39.5589	1.41553
$782$	−5.89576	−0.210832
$783$	−13.5105	−0.482826
$784$	−5.17518	−0.184828
$785$	−67.1579	−2.39697
$786$	−1.90551	−0.0679673
$787$	23.3203	0.831279	0.415640	−	0.909529i	$-0.363558\pi$
$787$	23.3203	0.831279	0.415640	+	0.909529i	$0.363558\pi$
$788$	−22.8982	−0.815715
$789$	−26.6909	−0.950220
$790$	−17.9513	−0.638678
$791$	−10.0552	−0.357523
$792$	−2.60279	−0.0924862
$793$	2.46318	0.0874702
$794$	26.0030	0.922812
$795$	12.6020	0.446948
$796$	18.8112	0.666747
$797$	−39.2309	−1.38963	−0.694816	−	0.719188i	$-0.744514\pi$
$797$	−39.2309	−1.38963	−0.694816	+	0.719188i	$0.744514\pi$
$798$	15.7635	0.558023
$799$	−14.4512	−0.511246
$800$	−10.2812	−0.363497
$801$	7.14201	0.252351
$802$	28.9860	1.02353
$803$	−1.19643	−0.0422212
$804$	17.3733	0.612710
$805$	5.28068	0.186119
$806$	0.358377	0.0126233
$807$	−41.5120	−1.46129
$808$	−10.4233	−0.366691
$809$	29.3362	1.03141	0.515703	−	0.856767i	$-0.327531\pi$
$809$	29.3362	1.03141	0.515703	+	0.856767i	$0.327531\pi$
$810$	41.0254	1.44149
$811$	−15.6924	−0.551036	−0.275518	−	0.961296i	$-0.588849\pi$
$811$	−15.6924	−0.551036	−0.275518	+	0.961296i	$0.588849\pi$
$812$	−4.04297	−0.141880
$813$	−30.4890	−1.06930
$814$	−23.2631	−0.815372
$815$	35.9446	1.25908
$816$	−11.2344	−0.393284
$817$	60.9920	2.13384
$818$	−23.4628	−0.820359
$819$	0.535044	0.0186960
$820$	−0.482612	−0.0168535
$821$	−31.8220	−1.11060	−0.555298	−	0.831651i	$-0.687396\pi$
$821$	−31.8220	−1.11060	−0.555298	+	0.831651i	$0.687396\pi$
$822$	24.5588	0.856585
$823$	−7.02874	−0.245007	−0.122503	−	0.992468i	$-0.539092\pi$
$823$	−7.02874	−0.245007	−0.122503	+	0.992468i	$0.539092\pi$
$824$	−3.50324	−0.122041
$825$	−80.8138	−2.81357
$826$	−1.19073	−0.0414309
$827$	−35.3054	−1.22769	−0.613845	−	0.789427i	$-0.710378\pi$
$827$	−35.3054	−1.22769	−0.613845	+	0.789427i	$0.710378\pi$
$828$	0.630974	0.0219279
$829$	−38.2760	−1.32938	−0.664689	−	0.747120i	$-0.731436\pi$
$829$	−38.2760	−1.32938	−0.664689	+	0.747120i	$0.731436\pi$
$830$	4.25579	0.147721
$831$	43.6337	1.51364
$832$	0.627723	0.0217624
$833$	−30.5116	−1.05717
$834$	−10.4490	−0.361820
$835$	−33.5081	−1.15959
$836$	25.2615	0.873689
$837$	−2.57723	−0.0890822
$838$	−12.0942	−0.417788
$839$	22.6329	0.781375	0.390687	−	0.920523i	$-0.372237\pi$
$839$	22.6329	0.781375	0.390687	+	0.920523i	$0.372237\pi$
$840$	10.0624	0.347185
$841$	−20.0426	−0.691126
$842$	5.37086	0.185092
$843$	−15.8989	−0.547587
$844$	−22.9957	−0.791545
$845$	−49.2783	−1.69522
$846$	1.54659	0.0531728
$847$	8.12673	0.279238
$848$	−1.69180	−0.0580967
$849$	−11.7135	−0.402007
$850$	−60.6158	−2.07910
$851$	5.63949	0.193319
$852$	−18.2737	−0.626047
$853$	−8.55894	−0.293053	−0.146526	−	0.989207i	$-0.546809\pi$
$853$	−8.55894	−0.293053	−0.146526	+	0.989207i	$0.546809\pi$
$854$	−5.30077	−0.181389
$855$	15.1051	0.516582
$856$	17.4415	0.596138
$857$	−39.8627	−1.36169	−0.680843	−	0.732430i	$-0.738386\pi$
$857$	−39.8627	−1.36169	−0.680843	+	0.732430i	$0.738386\pi$
$858$	4.93410	0.168447
$859$	5.95911	0.203322	0.101661	−	0.994819i	$-0.467584\pi$
$859$	5.95911	0.203322	0.101661	+	0.994819i	$0.467584\pi$
$860$	38.9332	1.32761
$861$	0.317790	0.0108303
$862$	0.184747	0.00629251
$863$	−58.0020	−1.97441	−0.987206	−	0.159451i	$-0.949028\pi$
$863$	−58.0020	−1.97441	−0.987206	+	0.159451i	$0.949028\pi$
$864$	−4.51421	−0.153576
$865$	41.2604	1.40290
$866$	−15.0616	−0.511814
$867$	−33.8419	−1.14933
$868$	−0.771227	−0.0261772
$869$	18.9428	0.642591
$870$	−22.2936	−0.755825
$871$	−5.72321	−0.193924
$872$	12.6160	0.427232
$873$	−7.97202	−0.269812
$874$	−6.12395	−0.207146
$875$	27.8885	0.942804
$876$	0.552678	0.0186732
$877$	11.4277	0.385884	0.192942	−	0.981210i	$-0.438197\pi$
$877$	11.4277	0.385884	0.192942	+	0.981210i	$0.438197\pi$
$878$	3.49267	0.117872
$879$	60.1494	2.02879
$880$	16.1253	0.543584
$881$	56.2958	1.89665	0.948326	−	0.317296i	$-0.102775\pi$
$881$	56.2958	1.89665	0.948326	+	0.317296i	$0.102775\pi$
$882$	3.26540	0.109952
$883$	36.0535	1.21330	0.606648	−	0.794971i	$-0.292514\pi$
$883$	36.0535	1.21330	0.606648	+	0.794971i	$0.292514\pi$
$884$	3.70091	0.124475
$885$	−6.56592	−0.220711
$886$	9.46345	0.317931
$887$	−10.2250	−0.343321	−0.171660	−	0.985156i	$-0.554913\pi$
$887$	−10.2250	−0.343321	−0.171660	+	0.985156i	$0.554913\pi$
$888$	10.7461	0.360616
$889$	20.8762	0.700166
$890$	−44.2475	−1.48318
$891$	−43.2915	−1.45032
$892$	−11.1898	−0.374663
$893$	−15.0105	−0.502307
$894$	−18.3744	−0.614531
$895$	−2.95221	−0.0986815
$896$	−1.35086	−0.0451290
$897$	−1.19613	−0.0399377
$898$	−22.2102	−0.741162
$899$	1.70868	0.0569878
$900$	6.48719	0.216240
$901$	−9.97446	−0.332297
$902$	0.509269	0.0169568
$903$	−25.6368	−0.853138
$904$	7.44359	0.247570
$905$	−20.2129	−0.671900
$906$	−37.9657	−1.26132
$907$	−24.1243	−0.801035	−0.400517	−	0.916289i	$-0.631170\pi$
$907$	−24.1243	−0.801035	−0.400517	+	0.916289i	$0.631170\pi$
$908$	−7.88620	−0.261713
$909$	6.57683	0.218140
$910$	−3.31480	−0.109885
$911$	13.3165	0.441197	0.220598	−	0.975365i	$-0.429199\pi$
$911$	13.3165	0.441197	0.220598	+	0.975365i	$0.429199\pi$
$912$	−11.6693	−0.386408
$913$	−4.49085	−0.148626
$914$	0.623414	0.0206207
$915$	−29.2294	−0.966293
$916$	−7.52730	−0.248709
$917$	−1.35086	−0.0446093
$918$	−26.6147	−0.878416
$919$	43.8757	1.44732	0.723662	−	0.690154i	$-0.242457\pi$
$919$	43.8757	1.44732	0.723662	+	0.690154i	$0.242457\pi$
$920$	−3.90912	−0.128880
$921$	27.3530	0.901312
$922$	−1.64477	−0.0541677
$923$	6.01982	0.198145
$924$	−10.6182	−0.349312
$925$	57.9810	1.90640
$926$	9.95819	0.327246
$927$	2.21045	0.0726007
$928$	2.99288	0.0982462
$929$	23.9819	0.786822	0.393411	−	0.919363i	$-0.371295\pi$
$929$	23.9819	0.786822	0.393411	+	0.919363i	$0.371295\pi$
$930$	−4.25268	−0.139451
$931$	−31.6925	−1.03868
$932$	−19.7965	−0.648456
$933$	−22.5027	−0.736705
$934$	4.13588	0.135330
$935$	95.0709	3.10915
$936$	−0.396077	−0.0129462
$937$	−5.11390	−0.167064	−0.0835319	−	0.996505i	$-0.526620\pi$
$937$	−5.11390	−0.167064	−0.0835319	+	0.996505i	$0.526620\pi$
$938$	12.3163	0.402143
$939$	65.1145	2.12493
$940$	−9.58171	−0.312521
$941$	18.7636	0.611677	0.305838	−	0.952083i	$-0.401063\pi$
$941$	18.7636	0.611677	0.305838	+	0.952083i	$0.401063\pi$
$942$	−32.7363	−1.06661
$943$	−0.123458	−0.00402034
$944$	0.881464	0.0286892
$945$	23.8381	0.775452
$946$	−41.0837	−1.33575
$947$	−49.4283	−1.60620	−0.803101	−	0.595842i	$-0.796818\pi$
$947$	−49.4283	−1.60620	−0.803101	+	0.595842i	$0.796818\pi$
$948$	−8.75040	−0.284200
$949$	−0.182066	−0.00591010
$950$	−62.9618	−2.04275
$951$	62.0677	2.01268
$952$	−7.96435	−0.258126
$953$	−0.279492	−0.00905363	−0.00452682	−	0.999990i	$-0.501441\pi$
$953$	−0.279492	−0.00905363	−0.00452682	+	0.999990i	$0.501441\pi$
$954$	1.06748	0.0345610
$955$	−100.243	−3.24377
$956$	21.4877	0.694962
$957$	23.5250	0.760455
$958$	6.19574	0.200175
$959$	17.4102	0.562206
$960$	−7.44888	−0.240412
$961$	−30.6741	−0.989486
$962$	−3.54004	−0.114135
$963$	−11.0051	−0.354635
$964$	−9.15873	−0.294983
$965$	−68.6517	−2.20998
$966$	2.57408	0.0828196
$967$	−17.3550	−0.558100	−0.279050	−	0.960277i	$-0.590020\pi$
$967$	−17.3550	−0.558100	−0.279050	+	0.960277i	$0.590020\pi$
$968$	−6.01597	−0.193360
$969$	−68.7992	−2.21015
$970$	49.3897	1.58581
$971$	−4.03730	−0.129563	−0.0647816	−	0.997899i	$-0.520635\pi$
$971$	−4.03730	−0.129563	−0.0647816	+	0.997899i	$0.520635\pi$
$972$	6.45533	0.207055
$973$	−7.40753	−0.237475
$974$	−30.0026	−0.961345
$975$	−12.2977	−0.393843
$976$	3.92400	0.125604
$977$	4.76461	0.152433	0.0762167	−	0.997091i	$-0.475716\pi$
$977$	4.76461	0.152433	0.0762167	+	0.997091i	$0.475716\pi$
$978$	17.5213	0.560268
$979$	46.6915	1.49227
$980$	−20.2304	−0.646237
$981$	−7.96037	−0.254155
$982$	29.9727	0.956468
$983$	15.9665	0.509253	0.254627	−	0.967039i	$-0.418047\pi$
$983$	15.9665	0.509253	0.254627	+	0.967039i	$0.418047\pi$
$984$	−0.235250	−0.00749951
$985$	−89.5119	−2.85209
$986$	17.6453	0.561942
$987$	6.30936	0.200829
$988$	3.84414	0.122298
$989$	9.95959	0.316696
$990$	−10.1746	−0.323371
$991$	−12.6243	−0.401024	−0.200512	−	0.979691i	$-0.564261\pi$
$991$	−12.6243	−0.401024	−0.200512	+	0.979691i	$0.564261\pi$
$992$	0.570916	0.0181266
$993$	−25.3105	−0.803203
$994$	−12.9547	−0.410897
$995$	73.5355	2.33123
$996$	2.07449	0.0657328
$997$	−47.7936	−1.51364	−0.756820	−	0.653623i	$-0.773248\pi$
$997$	−47.7936	−1.51364	−0.756820	+	0.653623i	$0.773248\pi$
$998$	−24.3521	−0.770853
$999$	25.4578	0.805450

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.j.1.7	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.j.1.7	✓	33	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.90551 q^{3} +1.00000 q^{4} +3.90912 q^{5} +1.90551 q^{6} +1.35086 q^{7} -1.00000 q^{8} +0.630974 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.90551 q^{3} +1.00000 q^{4} +3.90912 q^{5} +1.90551 q^{6} +1.35086 q^{7} -1.00000 q^{8} +0.630974 q^{9} -3.90912 q^{10} +4.12504 q^{11} -1.90551 q^{12} +0.627723 q^{13} -1.35086 q^{14} -7.44888 q^{15} +1.00000 q^{16} +5.89576 q^{17} -0.630974 q^{18} +6.12395 q^{19} +3.90912 q^{20} -2.57408 q^{21} -4.12504 q^{22} +1.00000 q^{23} +1.90551 q^{24} +10.2812 q^{25} -0.627723 q^{26} +4.51421 q^{27} +1.35086 q^{28} -2.99288 q^{29} +7.44888 q^{30} -0.570916 q^{31} -1.00000 q^{32} -7.86031 q^{33} -5.89576 q^{34} +5.28068 q^{35} +0.630974 q^{36} +5.63949 q^{37} -6.12395 q^{38} -1.19613 q^{39} -3.90912 q^{40} -0.123458 q^{41} +2.57408 q^{42} +9.95959 q^{43} +4.12504 q^{44} +2.46655 q^{45} -1.00000 q^{46} -2.45111 q^{47} -1.90551 q^{48} -5.17518 q^{49} -10.2812 q^{50} -11.2344 q^{51} +0.627723 q^{52} -1.69180 q^{53} -4.51421 q^{54} +16.1253 q^{55} -1.35086 q^{56} -11.6693 q^{57} +2.99288 q^{58} +0.881464 q^{59} -7.44888 q^{60} +3.92400 q^{61} +0.570916 q^{62} +0.852357 q^{63} +1.00000 q^{64} +2.45385 q^{65} +7.86031 q^{66} -9.11742 q^{67} +5.89576 q^{68} -1.90551 q^{69} -5.28068 q^{70} +9.58993 q^{71} -0.630974 q^{72} -0.290042 q^{73} -5.63949 q^{74} -19.5910 q^{75} +6.12395 q^{76} +5.57235 q^{77} +1.19613 q^{78} +4.59215 q^{79} +3.90912 q^{80} -10.4948 q^{81} +0.123458 q^{82} -1.08868 q^{83} -2.57408 q^{84} +23.0473 q^{85} -9.95959 q^{86} +5.70297 q^{87} -4.12504 q^{88} +11.3190 q^{89} -2.46655 q^{90} +0.847965 q^{91} +1.00000 q^{92} +1.08789 q^{93} +2.45111 q^{94} +23.9393 q^{95} +1.90551 q^{96} -12.6345 q^{97} +5.17518 q^{98} +2.60279 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9}+O(q^{10}) \) 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9	\( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9} + 4 q^{10} + 5 q^{11} + 3 q^{12} + 15 q^{13} - 11 q^{14} + 16 q^{15} + 33 q^{16} + 2 q^{17} - 44 q^{18} + 32 q^{19} - 4 q^{20} + 8 q^{21} - 5 q^{22} + 33 q^{23} - 3 q^{24} + 49 q^{25} - 15 q^{26} + 15 q^{27} + 11 q^{28} + 20 q^{29} - 16 q^{30} + 25 q^{31} - 33 q^{32} - 6 q^{33} - 2 q^{34} + 15 q^{35} + 44 q^{36} + 6 q^{37} - 32 q^{38} + 25 q^{39} + 4 q^{40} + 2 q^{41} - 8 q^{42} + 31 q^{43} + 5 q^{44} + 2 q^{45} - 33 q^{46} + 4 q^{47} + 3 q^{48} + 72 q^{49} - 49 q^{50} + 26 q^{51} + 15 q^{52} - 65 q^{53} - 15 q^{54} - 4 q^{55} - 11 q^{56} + 12 q^{57} - 20 q^{58} + 8 q^{59} + 16 q^{60} + 23 q^{61} - 25 q^{62} - 14 q^{63} + 33 q^{64} + 5 q^{65} + 6 q^{66} + 31 q^{67} + 2 q^{68} + 3 q^{69} - 15 q^{70} + 20 q^{71} - 44 q^{72} + 22 q^{73} - 6 q^{74} - 32 q^{75} + 32 q^{76} + 2 q^{77} - 25 q^{78} + 53 q^{79} - 4 q^{80} + 17 q^{81} - 2 q^{82} + 45 q^{83} + 8 q^{84} + 60 q^{85} - 31 q^{86} + 11 q^{87} - 5 q^{88} - 54 q^{89} - 2 q^{90} + 38 q^{91} + 33 q^{92} + 63 q^{93} - 4 q^{94} + 44 q^{95} - 3 q^{96} - 72 q^{98} + 43 q^{99}+O(q^{100}) \) 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9 + 4 * q^10 + 5 * q^11 + 3 * q^12 + 15 * q^13 - 11 * q^14 + 16 * q^15 + 33 * q^16 + 2 * q^17 - 44 * q^18 + 32 * q^19 - 4 * q^20 + 8 * q^21 - 5 * q^22 + 33 * q^23 - 3 * q^24 + 49 * q^25 - 15 * q^26 + 15 * q^27 + 11 * q^28 + 20 * q^29 - 16 * q^30 + 25 * q^31 - 33 * q^32 - 6 * q^33 - 2 * q^34 + 15 * q^35 + 44 * q^36 + 6 * q^37 - 32 * q^38 + 25 * q^39 + 4 * q^40 + 2 * q^41 - 8 * q^42 + 31 * q^43 + 5 * q^44 + 2 * q^45 - 33 * q^46 + 4 * q^47 + 3 * q^48 + 72 * q^49 - 49 * q^50 + 26 * q^51 + 15 * q^52 - 65 * q^53 - 15 * q^54 - 4 * q^55 - 11 * q^56 + 12 * q^57 - 20 * q^58 + 8 * q^59 + 16 * q^60 + 23 * q^61 - 25 * q^62 - 14 * q^63 + 33 * q^64 + 5 * q^65 + 6 * q^66 + 31 * q^67 + 2 * q^68 + 3 * q^69 - 15 * q^70 + 20 * q^71 - 44 * q^72 + 22 * q^73 - 6 * q^74 - 32 * q^75 + 32 * q^76 + 2 * q^77 - 25 * q^78 + 53 * q^79 - 4 * q^80 + 17 * q^81 - 2 * q^82 + 45 * q^83 + 8 * q^84 + 60 * q^85 - 31 * q^86 + 11 * q^87 - 5 * q^88 - 54 * q^89 - 2 * q^90 + 38 * q^91 + 33 * q^92 + 63 * q^93 - 4 * q^94 + 44 * q^95 - 3 * q^96 - 72 * q^98 + 43 * q^99

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