LMFDB - Embedded newform 6026.2.a.l.1.1

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:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q-1.00000 q^{2} -3.41962 q^{3} +1.00000 q^{4} -1.05998 q^{5} +3.41962 q^{6} -0.874431 q^{7} -1.00000 q^{8} +8.69383 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.41962 q^{3} +1.00000 q^{4} -1.05998 q^{5} +3.41962 q^{6} -0.874431 q^{7} -1.00000 q^{8} +8.69383 q^{9} +1.05998 q^{10} +1.91876 q^{11} -3.41962 q^{12} -4.30911 q^{13} +0.874431 q^{14} +3.62474 q^{15} +1.00000 q^{16} -2.56348 q^{17} -8.69383 q^{18} -2.73851 q^{19} -1.05998 q^{20} +2.99023 q^{21} -1.91876 q^{22} -1.00000 q^{23} +3.41962 q^{24} -3.87644 q^{25} +4.30911 q^{26} -19.4708 q^{27} -0.874431 q^{28} +6.92608 q^{29} -3.62474 q^{30} +5.58418 q^{31} -1.00000 q^{32} -6.56144 q^{33} +2.56348 q^{34} +0.926881 q^{35} +8.69383 q^{36} +0.420839 q^{37} +2.73851 q^{38} +14.7355 q^{39} +1.05998 q^{40} -6.84871 q^{41} -2.99023 q^{42} +6.86190 q^{43} +1.91876 q^{44} -9.21530 q^{45} +1.00000 q^{46} +2.60869 q^{47} -3.41962 q^{48} -6.23537 q^{49} +3.87644 q^{50} +8.76615 q^{51} -4.30911 q^{52} +10.2175 q^{53} +19.4708 q^{54} -2.03385 q^{55} +0.874431 q^{56} +9.36466 q^{57} -6.92608 q^{58} -10.0029 q^{59} +3.62474 q^{60} +2.54193 q^{61} -5.58418 q^{62} -7.60216 q^{63} +1.00000 q^{64} +4.56758 q^{65} +6.56144 q^{66} +11.1832 q^{67} -2.56348 q^{68} +3.41962 q^{69} -0.926881 q^{70} -1.04674 q^{71} -8.69383 q^{72} -12.5086 q^{73} -0.420839 q^{74} +13.2560 q^{75} -2.73851 q^{76} -1.67783 q^{77} -14.7355 q^{78} -4.80519 q^{79} -1.05998 q^{80} +40.5012 q^{81} +6.84871 q^{82} -5.69975 q^{83} +2.99023 q^{84} +2.71725 q^{85} -6.86190 q^{86} -23.6846 q^{87} -1.91876 q^{88} -0.816101 q^{89} +9.21530 q^{90} +3.76802 q^{91} -1.00000 q^{92} -19.0958 q^{93} -2.60869 q^{94} +2.90277 q^{95} +3.41962 q^{96} -9.44340 q^{97} +6.23537 q^{98} +16.6814 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9}+O(q^{10}) $ 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9} - q^{10} + 14 q^{11} + 4 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 36 q^{16} - 4 q^{17} - 46 q^{18} + 29 q^{19} + q^{20} + 24 q^{21} - 14 q^{22} - 36 q^{23} - 4 q^{24} + 49 q^{25} - 4 q^{26} + 19 q^{27} + 13 q^{28} - 13 q^{29} - 10 q^{30} + 21 q^{31} - 36 q^{32} - 5 q^{33} + 4 q^{34} + 30 q^{35} + 46 q^{36} + 13 q^{37} - 29 q^{38} + 30 q^{39} - q^{40} - 8 q^{41} - 24 q^{42} + 42 q^{43} + 14 q^{44} + 30 q^{45} + 36 q^{46} - 14 q^{47} + 4 q^{48} + 61 q^{49} - 49 q^{50} + 46 q^{51} + 4 q^{52} - 3 q^{53} - 19 q^{54} + 26 q^{55} - 13 q^{56} + 26 q^{57} + 13 q^{58} + 45 q^{59} + 10 q^{60} + 34 q^{61} - 21 q^{62} + 63 q^{63} + 36 q^{64} - 25 q^{65} + 5 q^{66} + 42 q^{67} - 4 q^{68} - 4 q^{69} - 30 q^{70} - 2 q^{71} - 46 q^{72} + 16 q^{73} - 13 q^{74} + 72 q^{75} + 29 q^{76} - 36 q^{77} - 30 q^{78} + 33 q^{79} + q^{80} + 96 q^{81} + 8 q^{82} + 8 q^{83} + 24 q^{84} + 18 q^{85} - 42 q^{86} + 11 q^{87} - 14 q^{88} + 21 q^{89} - 30 q^{90} + 60 q^{91} - 36 q^{92} - 27 q^{93} + 14 q^{94} - 44 q^{95} - 4 q^{96} + 20 q^{97} - 61 q^{98} + 76 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9 - q^10 + 14 * q^11 + 4 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 36 * q^16 - 4 * q^17 - 46 * q^18 + 29 * q^19 + q^20 + 24 * q^21 - 14 * q^22 - 36 * q^23 - 4 * q^24 + 49 * q^25 - 4 * q^26 + 19 * q^27 + 13 * q^28 - 13 * q^29 - 10 * q^30 + 21 * q^31 - 36 * q^32 - 5 * q^33 + 4 * q^34 + 30 * q^35 + 46 * q^36 + 13 * q^37 - 29 * q^38 + 30 * q^39 - q^40 - 8 * q^41 - 24 * q^42 + 42 * q^43 + 14 * q^44 + 30 * q^45 + 36 * q^46 - 14 * q^47 + 4 * q^48 + 61 * q^49 - 49 * q^50 + 46 * q^51 + 4 * q^52 - 3 * q^53 - 19 * q^54 + 26 * q^55 - 13 * q^56 + 26 * q^57 + 13 * q^58 + 45 * q^59 + 10 * q^60 + 34 * q^61 - 21 * q^62 + 63 * q^63 + 36 * q^64 - 25 * q^65 + 5 * q^66 + 42 * q^67 - 4 * q^68 - 4 * q^69 - 30 * q^70 - 2 * q^71 - 46 * q^72 + 16 * q^73 - 13 * q^74 + 72 * q^75 + 29 * q^76 - 36 * q^77 - 30 * q^78 + 33 * q^79 + q^80 + 96 * q^81 + 8 * q^82 + 8 * q^83 + 24 * q^84 + 18 * q^85 - 42 * q^86 + 11 * q^87 - 14 * q^88 + 21 * q^89 - 30 * q^90 + 60 * q^91 - 36 * q^92 - 27 * q^93 + 14 * q^94 - 44 * q^95 - 4 * q^96 + 20 * q^97 - 61 * q^98 + 76 * 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
$3$	−3.41962	−1.97432	−0.987160	−	0.159732i	$-0.948937\pi$
$3$	−3.41962	−1.97432	−0.987160	+	0.159732i	$0.948937\pi$
$4$	1.00000	0.500000
$5$	−1.05998	−0.474038	−0.237019	−	0.971505i	$-0.576170\pi$
$5$	−1.05998	−0.474038	−0.237019	+	0.971505i	$0.576170\pi$
$6$	3.41962	1.39606
$7$	−0.874431	−0.330504	−0.165252	−	0.986251i	$-0.552844\pi$
$7$	−0.874431	−0.330504	−0.165252	+	0.986251i	$0.552844\pi$
$8$	−1.00000	−0.353553
$9$	8.69383	2.89794
$10$	1.05998	0.335196
$11$	1.91876	0.578528	0.289264	−	0.957249i	$-0.406589\pi$
$11$	1.91876	0.578528	0.289264	+	0.957249i	$0.406589\pi$
$12$	−3.41962	−0.987160
$13$	−4.30911	−1.19513	−0.597566	−	0.801820i	$-0.703865\pi$
$13$	−4.30911	−1.19513	−0.597566	+	0.801820i	$0.703865\pi$
$14$	0.874431	0.233702
$15$	3.62474	0.935904
$16$	1.00000	0.250000
$17$	−2.56348	−0.621736	−0.310868	−	0.950453i	$-0.600620\pi$
$17$	−2.56348	−0.621736	−0.310868	+	0.950453i	$0.600620\pi$
$18$	−8.69383	−2.04916
$19$	−2.73851	−0.628256	−0.314128	−	0.949381i	$-0.601712\pi$
$19$	−2.73851	−0.628256	−0.314128	+	0.949381i	$0.601712\pi$
$20$	−1.05998	−0.237019
$21$	2.99023	0.652521
$22$	−1.91876	−0.409081
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	3.41962	0.698028
$25$	−3.87644	−0.775288
$26$	4.30911	0.845086
$27$	−19.4708	−3.74715
$28$	−0.874431	−0.165252
$29$	6.92608	1.28614	0.643070	−	0.765807i	$-0.277660\pi$
$29$	6.92608	1.28614	0.643070	+	0.765807i	$0.277660\pi$
$30$	−3.62474	−0.661784
$31$	5.58418	1.00295	0.501474	−	0.865172i	$-0.332791\pi$
$31$	5.58418	1.00295	0.501474	+	0.865172i	$0.332791\pi$
$32$	−1.00000	−0.176777
$33$	−6.56144	−1.14220
$34$	2.56348	0.439634
$35$	0.926881	0.156672
$36$	8.69383	1.44897
$37$	0.420839	0.0691855	0.0345928	−	0.999401i	$-0.488987\pi$
$37$	0.420839	0.0691855	0.0345928	+	0.999401i	$0.488987\pi$
$38$	2.73851	0.444244
$39$	14.7355	2.35957
$40$	1.05998	0.167598
$41$	−6.84871	−1.06959	−0.534794	−	0.844982i	$-0.679611\pi$
$41$	−6.84871	−1.06959	−0.534794	+	0.844982i	$0.679611\pi$
$42$	−2.99023	−0.461402
$43$	6.86190	1.04643	0.523215	−	0.852201i	$-0.324733\pi$
$43$	6.86190	1.04643	0.523215	+	0.852201i	$0.324733\pi$
$44$	1.91876	0.289264
$45$	−9.21530	−1.37374
$46$	1.00000	0.147442
$47$	2.60869	0.380516	0.190258	−	0.981734i	$-0.439068\pi$
$47$	2.60869	0.380516	0.190258	+	0.981734i	$0.439068\pi$
$48$	−3.41962	−0.493580
$49$	−6.23537	−0.890767
$50$	3.87644	0.548211
$51$	8.76615	1.22751
$52$	−4.30911	−0.597566
$53$	10.2175	1.40348	0.701742	−	0.712431i	$-0.252406\pi$
$53$	10.2175	1.40348	0.701742	+	0.712431i	$0.252406\pi$
$54$	19.4708	2.64963
$55$	−2.03385	−0.274245
$56$	0.874431	0.116851
$57$	9.36466	1.24038
$58$	−6.92608	−0.909439
$59$	−10.0029	−1.30226	−0.651132	−	0.758965i	$-0.725705\pi$
$59$	−10.0029	−1.30226	−0.651132	+	0.758965i	$0.725705\pi$
$60$	3.62474	0.467952
$61$	2.54193	0.325461	0.162731	−	0.986671i	$-0.447970\pi$
$61$	2.54193	0.325461	0.162731	+	0.986671i	$0.447970\pi$
$62$	−5.58418	−0.709192
$63$	−7.60216	−0.957782
$64$	1.00000	0.125000
$65$	4.56758	0.566538
$66$	6.56144	0.807658
$67$	11.1832	1.36625	0.683126	−	0.730301i	$-0.260620\pi$
$67$	11.1832	1.36625	0.683126	+	0.730301i	$0.260620\pi$
$68$	−2.56348	−0.310868
$69$	3.41962	0.411674
$70$	−0.926881	−0.110783
$71$	−1.04674	−0.124225	−0.0621124	−	0.998069i	$-0.519784\pi$
$71$	−1.04674	−0.124225	−0.0621124	+	0.998069i	$0.519784\pi$
$72$	−8.69383	−1.02458
$73$	−12.5086	−1.46402	−0.732012	−	0.681291i	$-0.761419\pi$
$73$	−12.5086	−1.46402	−0.732012	+	0.681291i	$0.761419\pi$
$74$	−0.420839	−0.0489215
$75$	13.2560	1.53067
$76$	−2.73851	−0.314128
$77$	−1.67783	−0.191206
$78$	−14.7355	−1.66847
$79$	−4.80519	−0.540626	−0.270313	−	0.962773i	$-0.587127\pi$
$79$	−4.80519	−0.540626	−0.270313	+	0.962773i	$0.587127\pi$
$80$	−1.05998	−0.118510
$81$	40.5012	4.50013
$82$	6.84871	0.756313
$83$	−5.69975	−0.625629	−0.312814	−	0.949814i	$-0.601272\pi$
$83$	−5.69975	−0.625629	−0.312814	+	0.949814i	$0.601272\pi$
$84$	2.99023	0.326260
$85$	2.71725	0.294727
$86$	−6.86190	−0.739938
$87$	−23.6846	−2.53926
$88$	−1.91876	−0.204541
$89$	−0.816101	−0.0865066	−0.0432533	−	0.999064i	$-0.513772\pi$
$89$	−0.816101	−0.0865066	−0.0432533	+	0.999064i	$0.513772\pi$
$90$	9.21530	0.971378
$91$	3.76802	0.394996
$92$	−1.00000	−0.104257
$93$	−19.0958	−1.98014
$94$	−2.60869	−0.269066
$95$	2.90277	0.297818
$96$	3.41962	0.349014
$97$	−9.44340	−0.958832	−0.479416	−	0.877588i	$-0.659151\pi$
$97$	−9.44340	−0.958832	−0.479416	+	0.877588i	$0.659151\pi$
$98$	6.23537	0.629867
$99$	16.6814	1.67654
$100$	−3.87644	−0.387644
$101$	−0.876350	−0.0872001	−0.0436001	−	0.999049i	$-0.513883\pi$
$101$	−0.876350	−0.0872001	−0.0436001	+	0.999049i	$0.513883\pi$
$102$	−8.76615	−0.867978
$103$	13.0825	1.28906	0.644529	−	0.764579i	$-0.277053\pi$
$103$	13.0825	1.28906	0.644529	+	0.764579i	$0.277053\pi$
$104$	4.30911	0.422543
$105$	−3.16959	−0.309320
$106$	−10.2175	−0.992413
$107$	−15.9843	−1.54526	−0.772630	−	0.634857i	$-0.781059\pi$
$107$	−15.9843	−1.54526	−0.772630	+	0.634857i	$0.781059\pi$
$108$	−19.4708	−1.87357
$109$	−6.78098	−0.649500	−0.324750	−	0.945800i	$-0.605280\pi$
$109$	−6.78098	−0.649500	−0.324750	+	0.945800i	$0.605280\pi$
$110$	2.03385	0.193920
$111$	−1.43911	−0.136594
$112$	−0.874431	−0.0826260
$113$	−6.80710	−0.640358	−0.320179	−	0.947357i	$-0.603743\pi$
$113$	−6.80710	−0.640358	−0.320179	+	0.947357i	$0.603743\pi$
$114$	−9.36466	−0.877081
$115$	1.05998	0.0988438
$116$	6.92608	0.643070
$117$	−37.4627	−3.46342
$118$	10.0029	0.920839
$119$	2.24159	0.205486
$120$	−3.62474	−0.330892
$121$	−7.31835	−0.665305
$122$	−2.54193	−0.230136
$123$	23.4200	2.11171
$124$	5.58418	0.501474
$125$	9.40886	0.841554
$126$	7.60216	0.677254
$127$	−8.47707	−0.752218	−0.376109	−	0.926575i	$-0.622738\pi$
$127$	−8.47707	−0.752218	−0.376109	+	0.926575i	$0.622738\pi$
$128$	−1.00000	−0.0883883
$129$	−23.4651	−2.06599
$130$	−4.56758	−0.400603
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−6.56144	−0.571100
$133$	2.39464	0.207641
$134$	−11.1832	−0.966085
$135$	20.6386	1.77629
$136$	2.56348	0.219817
$137$	−10.3041	−0.880341	−0.440170	−	0.897914i	$-0.645082\pi$
$137$	−10.3041	−0.880341	−0.440170	+	0.897914i	$0.645082\pi$
$138$	−3.41962	−0.291098
$139$	1.89503	0.160734	0.0803670	−	0.996765i	$-0.474391\pi$
$139$	1.89503	0.160734	0.0803670	+	0.996765i	$0.474391\pi$
$140$	0.926881	0.0783358
$141$	−8.92073	−0.751261
$142$	1.04674	0.0878402
$143$	−8.26815	−0.691418
$144$	8.69383	0.724486
$145$	−7.34152	−0.609680
$146$	12.5086	1.03522
$147$	21.3226	1.75866
$148$	0.420839	0.0345928
$149$	−0.0312994	−0.00256415	−0.00128207	−	0.999999i	$-0.500408\pi$
$149$	−0.0312994	−0.00256415	−0.00128207	+	0.999999i	$0.500408\pi$
$150$	−13.2560	−1.08234
$151$	−5.63995	−0.458973	−0.229486	−	0.973312i	$-0.573705\pi$
$151$	−5.63995	−0.458973	−0.229486	+	0.973312i	$0.573705\pi$
$152$	2.73851	0.222122
$153$	−22.2865	−1.80176
$154$	1.67783	0.135203
$155$	−5.91913	−0.475436
$156$	14.7355	1.17979
$157$	−21.2744	−1.69788	−0.848940	−	0.528489i	$-0.822759\pi$
$157$	−21.2744	−1.69788	−0.848940	+	0.528489i	$0.822759\pi$
$158$	4.80519	0.382280
$159$	−34.9401	−2.77093
$160$	1.05998	0.0837989
$161$	0.874431	0.0689148
$162$	−40.5012	−3.18207
$163$	−12.2253	−0.957560	−0.478780	−	0.877935i	$-0.658921\pi$
$163$	−12.2253	−0.957560	−0.478780	+	0.877935i	$0.658921\pi$
$164$	−6.84871	−0.534794
$165$	6.95501	0.541447
$166$	5.69975	0.442386
$167$	1.41279	0.109325	0.0546626	−	0.998505i	$-0.482592\pi$
$167$	1.41279	0.109325	0.0546626	+	0.998505i	$0.482592\pi$
$168$	−2.99023	−0.230701
$169$	5.56842	0.428340
$170$	−2.71725	−0.208403
$171$	−23.8081	−1.82065
$172$	6.86190	0.523215
$173$	−3.30464	−0.251247	−0.125624	−	0.992078i	$-0.540093\pi$
$173$	−3.30464	−0.251247	−0.125624	+	0.992078i	$0.540093\pi$
$174$	23.6846	1.79552
$175$	3.38968	0.256236
$176$	1.91876	0.144632
$177$	34.2061	2.57109
$178$	0.816101	0.0611694
$179$	11.8424	0.885141	0.442570	−	0.896734i	$-0.354067\pi$
$179$	11.8424	0.885141	0.442570	+	0.896734i	$0.354067\pi$
$180$	−9.21530	−0.686868
$181$	0.0335311	0.00249235	0.00124617	−	0.999999i	$-0.499603\pi$
$181$	0.0335311	0.00249235	0.00124617	+	0.999999i	$0.499603\pi$
$182$	−3.76802	−0.279304
$183$	−8.69246	−0.642565
$184$	1.00000	0.0737210
$185$	−0.446082	−0.0327966
$186$	19.0958	1.40017
$187$	−4.91871	−0.359692
$188$	2.60869	0.190258
$189$	17.0258	1.23845
$190$	−2.90277	−0.210589
$191$	−12.7557	−0.922970	−0.461485	−	0.887148i	$-0.652683\pi$
$191$	−12.7557	−0.922970	−0.461485	+	0.887148i	$0.652683\pi$
$192$	−3.41962	−0.246790
$193$	3.88736	0.279819	0.139909	−	0.990164i	$-0.455319\pi$
$193$	3.88736	0.279819	0.139909	+	0.990164i	$0.455319\pi$
$194$	9.44340	0.677996
$195$	−15.6194	−1.11853
$196$	−6.23537	−0.445384
$197$	−0.950352	−0.0677098	−0.0338549	−	0.999427i	$-0.510778\pi$
$197$	−0.950352	−0.0677098	−0.0338549	+	0.999427i	$0.510778\pi$
$198$	−16.6814	−1.18549
$199$	5.97567	0.423604	0.211802	−	0.977313i	$-0.432067\pi$
$199$	5.97567	0.423604	0.211802	+	0.977313i	$0.432067\pi$
$200$	3.87644	0.274106
$201$	−38.2425	−2.69742
$202$	0.876350	0.0616598
$203$	−6.05638	−0.425075
$204$	8.76615	0.613753
$205$	7.25950	0.507026
$206$	−13.0825	−0.911502
$207$	−8.69383	−0.604263
$208$	−4.30911	−0.298783
$209$	−5.25454	−0.363464
$210$	3.16959	0.218722
$211$	24.7055	1.70080	0.850398	−	0.526140i	$-0.176361\pi$
$211$	24.7055	1.70080	0.850398	+	0.526140i	$0.176361\pi$
$212$	10.2175	0.701742
$213$	3.57945	0.245260
$214$	15.9843	1.09266
$215$	−7.27349	−0.496048
$216$	19.4708	1.32482
$217$	−4.88298	−0.331479
$218$	6.78098	0.459266
$219$	42.7748	2.89045
$220$	−2.03385	−0.137122
$221$	11.0463	0.743056
$222$	1.43911	0.0965868
$223$	−7.76583	−0.520038	−0.260019	−	0.965603i	$-0.583729\pi$
$223$	−7.76583	−0.520038	−0.260019	+	0.965603i	$0.583729\pi$
$224$	0.874431	0.0584254
$225$	−33.7011	−2.24674
$226$	6.80710	0.452802
$227$	−5.14167	−0.341264	−0.170632	−	0.985335i	$-0.554581\pi$
$227$	−5.14167	−0.341264	−0.170632	+	0.985335i	$0.554581\pi$
$228$	9.36466	0.620190
$229$	21.7310	1.43602	0.718012	−	0.696030i	$-0.245052\pi$
$229$	21.7310	1.43602	0.718012	+	0.696030i	$0.245052\pi$
$230$	−1.05998	−0.0698931
$231$	5.73753	0.377502
$232$	−6.92608	−0.454720
$233$	6.77600	0.443911	0.221955	−	0.975057i	$-0.428756\pi$
$233$	6.77600	0.443911	0.221955	+	0.975057i	$0.428756\pi$
$234$	37.4627	2.44901
$235$	−2.76516	−0.180379
$236$	−10.0029	−0.651132
$237$	16.4319	1.06737
$238$	−2.24159	−0.145301
$239$	15.2694	0.987696	0.493848	−	0.869548i	$-0.335590\pi$
$239$	15.2694	0.987696	0.493848	+	0.869548i	$0.335590\pi$
$240$	3.62474	0.233976
$241$	3.57377	0.230207	0.115103	−	0.993354i	$-0.463280\pi$
$241$	3.57377	0.230207	0.115103	+	0.993354i	$0.463280\pi$
$242$	7.31835	0.470442
$243$	−80.0866	−5.13756
$244$	2.54193	0.162731
$245$	6.60938	0.422258
$246$	−23.4200	−1.49321
$247$	11.8005	0.750849
$248$	−5.58418	−0.354596
$249$	19.4910	1.23519
$250$	−9.40886	−0.595069
$251$	−7.32195	−0.462158	−0.231079	−	0.972935i	$-0.574226\pi$
$251$	−7.32195	−0.462158	−0.231079	+	0.972935i	$0.574226\pi$
$252$	−7.60216	−0.478891
$253$	−1.91876	−0.120632
$254$	8.47707	0.531899
$255$	−9.29196	−0.581885
$256$	1.00000	0.0625000
$257$	−4.82184	−0.300778	−0.150389	−	0.988627i	$-0.548053\pi$
$257$	−4.82184	−0.300778	−0.150389	+	0.988627i	$0.548053\pi$
$258$	23.4651	1.46087
$259$	−0.367995	−0.0228661
$260$	4.56758	0.283269
$261$	60.2142	3.72716
$262$	−1.00000	−0.0617802
$263$	18.6847	1.15215	0.576073	−	0.817398i	$-0.304584\pi$
$263$	18.6847	1.15215	0.576073	+	0.817398i	$0.304584\pi$
$264$	6.56144	0.403829
$265$	−10.8304	−0.665305
$266$	−2.39464	−0.146825
$267$	2.79076	0.170792
$268$	11.1832	0.683126
$269$	−5.54887	−0.338320	−0.169160	−	0.985589i	$-0.554106\pi$
$269$	−5.54887	−0.338320	−0.169160	+	0.985589i	$0.554106\pi$
$270$	−20.6386	−1.25603
$271$	20.9442	1.27227	0.636135	−	0.771578i	$-0.280532\pi$
$271$	20.9442	1.27227	0.636135	+	0.771578i	$0.280532\pi$
$272$	−2.56348	−0.155434
$273$	−12.8852	−0.779849
$274$	10.3041	0.622495
$275$	−7.43796	−0.448526
$276$	3.41962	0.205837
$277$	−14.9723	−0.899598	−0.449799	−	0.893130i	$-0.648504\pi$
$277$	−14.9723	−0.899598	−0.449799	+	0.893130i	$0.648504\pi$
$278$	−1.89503	−0.113656
$279$	48.5479	2.90649
$280$	−0.926881	−0.0553917
$281$	−14.6713	−0.875216	−0.437608	−	0.899166i	$-0.644174\pi$
$281$	−14.6713	−0.875216	−0.437608	+	0.899166i	$0.644174\pi$
$282$	8.92073	0.531222
$283$	8.76686	0.521136	0.260568	−	0.965456i	$-0.416090\pi$
$283$	8.76686	0.521136	0.260568	+	0.965456i	$0.416090\pi$
$284$	−1.04674	−0.0621124
$285$	−9.92637	−0.587987
$286$	8.26815	0.488906
$287$	5.98873	0.353503
$288$	−8.69383	−0.512289
$289$	−10.4286	−0.613444
$290$	7.34152	0.431109
$291$	32.2929	1.89304
$292$	−12.5086	−0.732012
$293$	−31.3940	−1.83406	−0.917029	−	0.398820i	$-0.869420\pi$
$293$	−31.3940	−1.83406	−0.917029	+	0.398820i	$0.869420\pi$
$294$	−21.3226	−1.24356
$295$	10.6029	0.617322
$296$	−0.420839	−0.0244608
$297$	−37.3597	−2.16783
$298$	0.0312994	0.00181313
$299$	4.30911	0.249202
$300$	13.2560	0.765333
$301$	−6.00026	−0.345849
$302$	5.63995	0.324543
$303$	2.99679	0.172161
$304$	−2.73851	−0.157064
$305$	−2.69440	−0.154281
$306$	22.2865	1.27403
$307$	24.9983	1.42673	0.713365	−	0.700793i	$-0.247170\pi$
$307$	24.9983	1.42673	0.713365	+	0.700793i	$0.247170\pi$
$308$	−1.67783	−0.0956030
$309$	−44.7373	−2.54502
$310$	5.91913	0.336184
$311$	7.07360	0.401107	0.200554	−	0.979683i	$-0.435726\pi$
$311$	7.07360	0.401107	0.200554	+	0.979683i	$0.435726\pi$
$312$	−14.7355	−0.834235
$313$	−30.9443	−1.74908	−0.874538	−	0.484956i	$-0.838835\pi$
$313$	−30.9443	−1.74908	−0.874538	+	0.484956i	$0.838835\pi$
$314$	21.2744	1.20058
$315$	8.05815	0.454025
$316$	−4.80519	−0.270313
$317$	1.38946	0.0780396	0.0390198	−	0.999238i	$-0.487576\pi$
$317$	1.38946	0.0780396	0.0390198	+	0.999238i	$0.487576\pi$
$318$	34.9401	1.95934
$319$	13.2895	0.744069
$320$	−1.05998	−0.0592548
$321$	54.6603	3.05084
$322$	−0.874431	−0.0487302
$323$	7.02011	0.390610
$324$	40.5012	2.25007
$325$	16.7040	0.926571
$326$	12.2253	0.677097
$327$	23.1884	1.28232
$328$	6.84871	0.378157
$329$	−2.28112	−0.125762
$330$	−6.95501	−0.382861
$331$	−2.21858	−0.121944	−0.0609721	−	0.998139i	$-0.519420\pi$
$331$	−2.21858	−0.121944	−0.0609721	+	0.998139i	$0.519420\pi$
$332$	−5.69975	−0.312814
$333$	3.65870	0.200496
$334$	−1.41279	−0.0773046
$335$	−11.8540	−0.647655
$336$	2.99023	0.163130
$337$	−6.77813	−0.369228	−0.184614	−	0.982811i	$-0.559104\pi$
$337$	−6.77813	−0.369228	−0.184614	+	0.982811i	$0.559104\pi$
$338$	−5.56842	−0.302882
$339$	23.2777	1.26427
$340$	2.71725	0.147363
$341$	10.7147	0.580234
$342$	23.8081	1.28739
$343$	11.5734	0.624906
$344$	−6.86190	−0.369969
$345$	−3.62474	−0.195149
$346$	3.30464	0.177659
$347$	27.8423	1.49466	0.747328	−	0.664456i	$-0.231337\pi$
$347$	27.8423	1.49466	0.747328	+	0.664456i	$0.231337\pi$
$348$	−23.6846	−1.26963
$349$	16.5224	0.884425	0.442213	−	0.896910i	$-0.354194\pi$
$349$	16.5224	0.884425	0.442213	+	0.896910i	$0.354194\pi$
$350$	−3.38968	−0.181186
$351$	83.9016	4.47834
$352$	−1.91876	−0.102270
$353$	−7.73235	−0.411551	−0.205776	−	0.978599i	$-0.565972\pi$
$353$	−7.73235	−0.411551	−0.205776	+	0.978599i	$0.565972\pi$
$354$	−34.2061	−1.81803
$355$	1.10952	0.0588873
$356$	−0.816101	−0.0432533
$357$	−7.66540	−0.405696
$358$	−11.8424	−0.625889
$359$	−25.5956	−1.35088	−0.675441	−	0.737414i	$-0.736047\pi$
$359$	−25.5956	−1.35088	−0.675441	+	0.737414i	$0.736047\pi$
$360$	9.21530	0.485689
$361$	−11.5006	−0.605294
$362$	−0.0335311	−0.00176236
$363$	25.0260	1.31353
$364$	3.76802	0.197498
$365$	13.2589	0.694004
$366$	8.69246	0.454362
$367$	17.3062	0.903376	0.451688	−	0.892176i	$-0.350822\pi$
$367$	17.3062	0.903376	0.451688	+	0.892176i	$0.350822\pi$
$368$	−1.00000	−0.0521286
$369$	−59.5415	−3.09961
$370$	0.446082	0.0231907
$371$	−8.93452	−0.463857
$372$	−19.0958	−0.990071
$373$	21.4787	1.11213	0.556063	−	0.831140i	$-0.312311\pi$
$373$	21.4787	1.11213	0.556063	+	0.831140i	$0.312311\pi$
$374$	4.91871	0.254341
$375$	−32.1748	−1.66150
$376$	−2.60869	−0.134533
$377$	−29.8452	−1.53711
$378$	−17.0258	−0.875715
$379$	−2.19062	−0.112525	−0.0562623	−	0.998416i	$-0.517918\pi$
$379$	−2.19062	−0.112525	−0.0562623	+	0.998416i	$0.517918\pi$
$380$	2.90277	0.148909
$381$	28.9884	1.48512
$382$	12.7557	0.652638
$383$	−22.1091	−1.12972	−0.564860	−	0.825187i	$-0.691070\pi$
$383$	−22.1091	−1.12972	−0.564860	+	0.825187i	$0.691070\pi$
$384$	3.41962	0.174507
$385$	1.77846	0.0906389
$386$	−3.88736	−0.197862
$387$	59.6562	3.03249
$388$	−9.44340	−0.479416
$389$	14.3035	0.725216	0.362608	−	0.931942i	$-0.381886\pi$
$389$	14.3035	0.725216	0.362608	+	0.931942i	$0.381886\pi$
$390$	15.6194	0.790919
$391$	2.56348	0.129641
$392$	6.23537	0.314934
$393$	−3.41962	−0.172497
$394$	0.950352	0.0478781
$395$	5.09341	0.256277
$396$	16.6814	0.838271
$397$	19.9912	1.00333	0.501664	−	0.865062i	$-0.332721\pi$
$397$	19.9912	1.00333	0.501664	+	0.865062i	$0.332721\pi$
$398$	−5.97567	−0.299533
$399$	−8.18875	−0.409950
$400$	−3.87644	−0.193822
$401$	−22.2833	−1.11277	−0.556387	−	0.830923i	$-0.687813\pi$
$401$	−22.2833	−1.11277	−0.556387	+	0.830923i	$0.687813\pi$
$402$	38.2425	1.90736
$403$	−24.0629	−1.19866
$404$	−0.876350	−0.0436001
$405$	−42.9305	−2.13323
$406$	6.05638	0.300573
$407$	0.807490	0.0400258
$408$	−8.76615	−0.433989
$409$	34.9529	1.72831	0.864156	−	0.503225i	$-0.167853\pi$
$409$	34.9529	1.72831	0.864156	+	0.503225i	$0.167853\pi$
$410$	−7.25950	−0.358521
$411$	35.2362	1.73808
$412$	13.0825	0.644529
$413$	8.74683	0.430403
$414$	8.69383	0.427278
$415$	6.04163	0.296572
$416$	4.30911	0.211271
$417$	−6.48028	−0.317341
$418$	5.25454	0.257008
$419$	0.593922	0.0290150	0.0145075	−	0.999895i	$-0.495382\pi$
$419$	0.593922	0.0290150	0.0145075	+	0.999895i	$0.495382\pi$
$420$	−3.16959	−0.154660
$421$	24.5387	1.19595	0.597973	−	0.801517i	$-0.295973\pi$
$421$	24.5387	1.19595	0.597973	+	0.801517i	$0.295973\pi$
$422$	−24.7055	−1.20264
$423$	22.6795	1.10271
$424$	−10.2175	−0.496206
$425$	9.93719	0.482024
$426$	−3.57945	−0.173425
$427$	−2.22275	−0.107566
$428$	−15.9843	−0.772630
$429$	28.2740	1.36508
$430$	7.27349	0.350759
$431$	−27.5218	−1.32568	−0.662840	−	0.748761i	$-0.730649\pi$
$431$	−27.5218	−1.32568	−0.662840	+	0.748761i	$0.730649\pi$
$432$	−19.4708	−0.936787
$433$	3.75532	0.180469	0.0902347	−	0.995921i	$-0.471238\pi$
$433$	3.75532	0.180469	0.0902347	+	0.995921i	$0.471238\pi$
$434$	4.88298	0.234391
$435$	25.1052	1.20370
$436$	−6.78098	−0.324750
$437$	2.73851	0.131001
$438$	−42.7748	−2.04386
$439$	11.1205	0.530752	0.265376	−	0.964145i	$-0.414504\pi$
$439$	11.1205	0.530752	0.265376	+	0.964145i	$0.414504\pi$
$440$	2.03385	0.0969601
$441$	−54.2092	−2.58139
$442$	−11.0463	−0.525420
$443$	−17.1795	−0.816224	−0.408112	−	0.912932i	$-0.633813\pi$
$443$	−17.1795	−0.816224	−0.408112	+	0.912932i	$0.633813\pi$
$444$	−1.43911	−0.0682972
$445$	0.865052	0.0410074
$446$	7.76583	0.367723
$447$	0.107032	0.00506245
$448$	−0.874431	−0.0413130
$449$	7.12319	0.336164	0.168082	−	0.985773i	$-0.446243\pi$
$449$	7.12319	0.336164	0.168082	+	0.985773i	$0.446243\pi$
$450$	33.7011	1.58869
$451$	−13.1410	−0.618787
$452$	−6.80710	−0.320179
$453$	19.2865	0.906160
$454$	5.14167	0.241310
$455$	−3.99403	−0.187243
$456$	−9.36466	−0.438540
$457$	−20.4743	−0.957748	−0.478874	−	0.877884i	$-0.658955\pi$
$457$	−20.4743	−0.957748	−0.478874	+	0.877884i	$0.658955\pi$
$458$	−21.7310	−1.01542
$459$	49.9130	2.32974
$460$	1.05998	0.0494219
$461$	13.2520	0.617207	0.308604	−	0.951191i	$-0.400138\pi$
$461$	13.2520	0.617207	0.308604	+	0.951191i	$0.400138\pi$
$462$	−5.73753	−0.266934
$463$	22.7338	1.05653	0.528264	−	0.849080i	$-0.322843\pi$
$463$	22.7338	1.05653	0.528264	+	0.849080i	$0.322843\pi$
$464$	6.92608	0.321535
$465$	20.2412	0.938663
$466$	−6.77600	−0.313892
$467$	16.5371	0.765245	0.382623	−	0.923905i	$-0.375021\pi$
$467$	16.5371	0.765245	0.382623	+	0.923905i	$0.375021\pi$
$468$	−37.4627	−1.73171
$469$	−9.77898	−0.451551
$470$	2.76516	0.127547
$471$	72.7504	3.35216
$472$	10.0029	0.460420
$473$	13.1663	0.605389
$474$	−16.4319	−0.754744
$475$	10.6157	0.487079
$476$	2.24159	0.102743
$477$	88.8294	4.06722
$478$	−15.2694	−0.698406
$479$	15.0493	0.687620	0.343810	−	0.939039i	$-0.388282\pi$
$479$	15.0493	0.687620	0.343810	+	0.939039i	$0.388282\pi$
$480$	−3.62474	−0.165446
$481$	−1.81344	−0.0826858
$482$	−3.57377	−0.162781
$483$	−2.99023	−0.136060
$484$	−7.31835	−0.332652
$485$	10.0098	0.454523
$486$	80.0866	3.63280
$487$	29.3400	1.32952	0.664762	−	0.747056i	$-0.268533\pi$
$487$	29.3400	1.32952	0.664762	+	0.747056i	$0.268533\pi$
$488$	−2.54193	−0.115068
$489$	41.8060	1.89053
$490$	−6.60938	−0.298581
$491$	1.94163	0.0876244	0.0438122	−	0.999040i	$-0.486050\pi$
$491$	1.94163	0.0876244	0.0438122	+	0.999040i	$0.486050\pi$
$492$	23.4200	1.05586
$493$	−17.7549	−0.799640
$494$	−11.8005	−0.530931
$495$	−17.6820	−0.794745
$496$	5.58418	0.250737
$497$	0.915299	0.0410568
$498$	−19.4910	−0.873412
$499$	12.2282	0.547411	0.273706	−	0.961814i	$-0.411751\pi$
$499$	12.2282	0.547411	0.273706	+	0.961814i	$0.411751\pi$
$500$	9.40886	0.420777
$501$	−4.83122	−0.215843
$502$	7.32195	0.326795
$503$	2.54852	0.113633	0.0568165	−	0.998385i	$-0.481905\pi$
$503$	2.54852	0.113633	0.0568165	+	0.998385i	$0.481905\pi$
$504$	7.60216	0.338627
$505$	0.928915	0.0413362
$506$	1.91876	0.0852994
$507$	−19.0419	−0.845680
$508$	−8.47707	−0.376109
$509$	9.96739	0.441797	0.220898	−	0.975297i	$-0.429101\pi$
$509$	9.96739	0.441797	0.220898	+	0.975297i	$0.429101\pi$
$510$	9.29196	0.411455
$511$	10.9379	0.483866
$512$	−1.00000	−0.0441942
$513$	53.3208	2.35417
$514$	4.82184	0.212682
$515$	−13.8672	−0.611063
$516$	−23.4651	−1.03299
$517$	5.00545	0.220139
$518$	0.367995	0.0161688
$519$	11.3006	0.496043
$520$	−4.56758	−0.200301
$521$	4.48483	0.196484	0.0982421	−	0.995163i	$-0.468678\pi$
$521$	4.48483	0.196484	0.0982421	+	0.995163i	$0.468678\pi$
$522$	−60.2142	−2.63550
$523$	−11.5013	−0.502919	−0.251459	−	0.967868i	$-0.580911\pi$
$523$	−11.5013	−0.502919	−0.251459	+	0.967868i	$0.580911\pi$
$524$	1.00000	0.0436852
$525$	−11.5914	−0.505892
$526$	−18.6847	−0.814690
$527$	−14.3150	−0.623569
$528$	−6.56144	−0.285550
$529$	1.00000	0.0434783
$530$	10.8304	0.470442
$531$	−86.9633	−3.77388
$532$	2.39464	0.103821
$533$	29.5118	1.27830
$534$	−2.79076	−0.120768
$535$	16.9431	0.732512
$536$	−11.1832	−0.483043
$537$	−40.4965	−1.74755
$538$	5.54887	0.239229
$539$	−11.9642	−0.515334
$540$	20.6386	0.888146
$541$	6.23819	0.268201	0.134100	−	0.990968i	$-0.457186\pi$
$541$	6.23819	0.268201	0.134100	+	0.990968i	$0.457186\pi$
$542$	−20.9442	−0.899630
$543$	−0.114664	−0.00492069
$544$	2.56348	0.109908
$545$	7.18771	0.307888
$546$	12.8852	0.551436
$547$	−14.8207	−0.633689	−0.316844	−	0.948478i	$-0.602623\pi$
$547$	−14.8207	−0.633689	−0.316844	+	0.948478i	$0.602623\pi$
$548$	−10.3041	−0.440170
$549$	22.0991	0.943168
$550$	7.43796	0.317156
$551$	−18.9671	−0.808026
$552$	−3.41962	−0.145549
$553$	4.20181	0.178679
$554$	14.9723	0.636112
$555$	1.52543	0.0647510
$556$	1.89503	0.0803670
$557$	11.2887	0.478317	0.239159	−	0.970980i	$-0.423128\pi$
$557$	11.2887	0.478317	0.239159	+	0.970980i	$0.423128\pi$
$558$	−48.5479	−2.05520
$559$	−29.5687	−1.25062
$560$	0.926881	0.0391679
$561$	16.8202	0.710147
$562$	14.6713	0.618872
$563$	−10.5201	−0.443369	−0.221685	−	0.975118i	$-0.571156\pi$
$563$	−10.5201	−0.443369	−0.221685	+	0.975118i	$0.571156\pi$
$564$	−8.92073	−0.375631
$565$	7.21540	0.303554
$566$	−8.76686	−0.368499
$567$	−35.4155	−1.48731
$568$	1.04674	0.0439201
$569$	−0.823047	−0.0345039	−0.0172520	−	0.999851i	$-0.505492\pi$
$569$	−0.823047	−0.0345039	−0.0172520	+	0.999851i	$0.505492\pi$
$570$	9.92637	0.415770
$571$	30.2801	1.26718	0.633591	−	0.773668i	$-0.281580\pi$
$571$	30.2801	1.26718	0.633591	+	0.773668i	$0.281580\pi$
$572$	−8.26815	−0.345709
$573$	43.6197	1.82224
$574$	−5.98873	−0.249965
$575$	3.87644	0.161659
$576$	8.69383	0.362243
$577$	−6.98864	−0.290941	−0.145471	−	0.989363i	$-0.546470\pi$
$577$	−6.98864	−0.290941	−0.145471	+	0.989363i	$0.546470\pi$
$578$	10.4286	0.433771
$579$	−13.2933	−0.552452
$580$	−7.34152	−0.304840
$581$	4.98404	0.206773
$582$	−32.2929	−1.33858
$583$	19.6050	0.811955
$584$	12.5086	0.517611
$585$	39.7097	1.64180
$586$	31.3940	1.29687
$587$	−34.1644	−1.41012	−0.705058	−	0.709150i	$-0.749079\pi$
$587$	−34.1644	−1.41012	−0.705058	+	0.709150i	$0.749079\pi$
$588$	21.3226	0.879330
$589$	−15.2923	−0.630109
$590$	−10.6029	−0.436513
$591$	3.24985	0.133681
$592$	0.420839	0.0172964
$593$	10.7084	0.439742	0.219871	−	0.975529i	$-0.429436\pi$
$593$	10.7084	0.439742	0.219871	+	0.975529i	$0.429436\pi$
$594$	37.3597	1.53289
$595$	−2.37604	−0.0974083
$596$	−0.0312994	−0.00128207
$597$	−20.4346	−0.836331
$598$	−4.30911	−0.176213
$599$	−25.7475	−1.05202	−0.526008	−	0.850480i	$-0.676312\pi$
$599$	−25.7475	−1.05202	−0.526008	+	0.850480i	$0.676312\pi$
$600$	−13.2560	−0.541172
$601$	−23.8127	−0.971342	−0.485671	−	0.874142i	$-0.661425\pi$
$601$	−23.8127	−0.971342	−0.485671	+	0.874142i	$0.661425\pi$
$602$	6.00026	0.244552
$603$	97.2252	3.95932
$604$	−5.63995	−0.229486
$605$	7.75732	0.315380
$606$	−2.99679	−0.121736
$607$	25.6292	1.04026	0.520128	−	0.854089i	$-0.325884\pi$
$607$	25.6292	1.04026	0.520128	+	0.854089i	$0.325884\pi$
$608$	2.73851	0.111061
$609$	20.7106	0.839234
$610$	2.69440	0.109093
$611$	−11.2411	−0.454767
$612$	−22.2865	−0.900878
$613$	20.0603	0.810228	0.405114	−	0.914266i	$-0.367232\pi$
$613$	20.0603	0.810228	0.405114	+	0.914266i	$0.367232\pi$
$614$	−24.9983	−1.00885
$615$	−24.8248	−1.00103
$616$	1.67783	0.0676015
$617$	35.2975	1.42102	0.710512	−	0.703685i	$-0.248463\pi$
$617$	35.2975	1.42102	0.710512	+	0.703685i	$0.248463\pi$
$618$	44.7373	1.79960
$619$	−19.5808	−0.787019	−0.393509	−	0.919321i	$-0.628739\pi$
$619$	−19.5808	−0.787019	−0.393509	+	0.919321i	$0.628739\pi$
$620$	−5.91913	−0.237718
$621$	19.4708	0.781335
$622$	−7.07360	−0.283626
$623$	0.713625	0.0285908
$624$	14.7355	0.589893
$625$	9.40897	0.376359
$626$	30.9443	1.23678
$627$	17.9686	0.717595
$628$	−21.2744	−0.848940
$629$	−1.07881	−0.0430151
$630$	−8.05815	−0.321044
$631$	−20.1785	−0.803293	−0.401647	−	0.915795i	$-0.631562\pi$
$631$	−20.1785	−0.803293	−0.401647	+	0.915795i	$0.631562\pi$
$632$	4.80519	0.191140
$633$	−84.4835	−3.35792
$634$	−1.38946	−0.0551823
$635$	8.98554	0.356580
$636$	−34.9401	−1.38546
$637$	26.8689	1.06458
$638$	−13.2895	−0.526136
$639$	−9.10015	−0.359996
$640$	1.05998	0.0418995
$641$	−43.6255	−1.72310	−0.861551	−	0.507671i	$-0.830507\pi$
$641$	−43.6255	−1.72310	−0.861551	+	0.507671i	$0.830507\pi$
$642$	−54.6603	−2.15727
$643$	22.2601	0.877853	0.438926	−	0.898523i	$-0.355359\pi$
$643$	22.2601	0.877853	0.438926	+	0.898523i	$0.355359\pi$
$644$	0.874431	0.0344574
$645$	24.8726	0.979357
$646$	−7.02011	−0.276203
$647$	37.9393	1.49155	0.745774	−	0.666199i	$-0.232080\pi$
$647$	37.9393	1.49155	0.745774	+	0.666199i	$0.232080\pi$
$648$	−40.5012	−1.59104
$649$	−19.1931	−0.753396
$650$	−16.7040	−0.655185
$651$	16.6980	0.654445
$652$	−12.2253	−0.478780
$653$	−44.3419	−1.73523	−0.867617	−	0.497233i	$-0.834350\pi$
$653$	−44.3419	−1.73523	−0.867617	+	0.497233i	$0.834350\pi$
$654$	−23.1884	−0.906738
$655$	−1.05998	−0.0414169
$656$	−6.84871	−0.267397
$657$	−108.748	−4.24266
$658$	2.28112	0.0889273
$659$	12.2990	0.479101	0.239550	−	0.970884i	$-0.423000\pi$
$659$	12.2990	0.479101	0.239550	+	0.970884i	$0.423000\pi$
$660$	6.95501	0.270723
$661$	−10.1666	−0.395435	−0.197718	−	0.980259i	$-0.563353\pi$
$661$	−10.1666	−0.395435	−0.197718	+	0.980259i	$0.563353\pi$
$662$	2.21858	0.0862275
$663$	−37.7743	−1.46703
$664$	5.69975	0.221193
$665$	−2.53827	−0.0984299
$666$	−3.65870	−0.141772
$667$	−6.92608	−0.268179
$668$	1.41279	0.0546626
$669$	26.5562	1.02672
$670$	11.8540	0.457961
$671$	4.87736	0.188289
$672$	−2.99023	−0.115351
$673$	15.2266	0.586942	0.293471	−	0.955968i	$-0.405190\pi$
$673$	15.2266	0.586942	0.293471	+	0.955968i	$0.405190\pi$
$674$	6.77813	0.261084
$675$	75.4772	2.90512
$676$	5.56842	0.214170
$677$	−28.5917	−1.09887	−0.549435	−	0.835537i	$-0.685157\pi$
$677$	−28.5917	−1.09887	−0.549435	+	0.835537i	$0.685157\pi$
$678$	−23.2777	−0.893976
$679$	8.25760	0.316898
$680$	−2.71725	−0.104202
$681$	17.5826	0.673766
$682$	−10.7147	−0.410288
$683$	27.9655	1.07007	0.535035	−	0.844830i	$-0.320298\pi$
$683$	27.9655	1.07007	0.535035	+	0.844830i	$0.320298\pi$
$684$	−23.8081	−0.910326
$685$	10.9222	0.417315
$686$	−11.5734	−0.441875
$687$	−74.3119	−2.83517
$688$	6.86190	0.261607
$689$	−44.0284	−1.67735
$690$	3.62474	0.137991
$691$	39.4747	1.50169	0.750845	−	0.660479i	$-0.229647\pi$
$691$	39.4747	1.50169	0.750845	+	0.660479i	$0.229647\pi$
$692$	−3.30464	−0.125624
$693$	−14.5867	−0.554104
$694$	−27.8423	−1.05688
$695$	−2.00869	−0.0761941
$696$	23.6846	0.897762
$697$	17.5565	0.665002
$698$	−16.5224	−0.625383
$699$	−23.1714	−0.876422
$700$	3.38968	0.128118
$701$	−41.3861	−1.56313	−0.781565	−	0.623824i	$-0.785578\pi$
$701$	−41.3861	−1.56313	−0.781565	+	0.623824i	$0.785578\pi$
$702$	−83.9016	−3.16666
$703$	−1.15247	−0.0434662
$704$	1.91876	0.0723160
$705$	9.45581	0.356126
$706$	7.73235	0.291011
$707$	0.766308	0.0288200
$708$	34.2061	1.28554
$709$	9.94917	0.373649	0.186824	−	0.982393i	$-0.440180\pi$
$709$	9.94917	0.373649	0.186824	+	0.982393i	$0.440180\pi$
$710$	−1.10952	−0.0416396
$711$	−41.7755	−1.56670
$712$	0.816101	0.0305847
$713$	−5.58418	−0.209129
$714$	7.66540	0.286870
$715$	8.76409	0.327758
$716$	11.8424	0.442570
$717$	−52.2156	−1.95003
$718$	25.5956	0.955218
$719$	18.7753	0.700199	0.350099	−	0.936713i	$-0.386148\pi$
$719$	18.7753	0.700199	0.350099	+	0.936713i	$0.386148\pi$
$720$	−9.21530	−0.343434
$721$	−11.4398	−0.426039
$722$	11.5006	0.428007
$723$	−12.2210	−0.454502
$724$	0.0335311	0.00124617
$725$	−26.8485	−0.997129
$726$	−25.0260	−0.928803
$727$	5.75073	0.213283	0.106641	−	0.994298i	$-0.465990\pi$
$727$	5.75073	0.213283	0.106641	+	0.994298i	$0.465990\pi$
$728$	−3.76802	−0.139652
$729$	152.362	5.64305
$730$	−13.2589	−0.490735
$731$	−17.5904	−0.650603
$732$	−8.69246	−0.321282
$733$	42.8238	1.58173	0.790866	−	0.611989i	$-0.209630\pi$
$733$	42.8238	1.58173	0.790866	+	0.611989i	$0.209630\pi$
$734$	−17.3062	−0.638783
$735$	−22.6016	−0.833672
$736$	1.00000	0.0368605
$737$	21.4580	0.790415
$738$	59.5415	2.19175
$739$	−3.32795	−0.122421	−0.0612104	−	0.998125i	$-0.519496\pi$
$739$	−3.32795	−0.122421	−0.0612104	+	0.998125i	$0.519496\pi$
$740$	−0.446082	−0.0163983
$741$	−40.3533	−1.48242
$742$	8.93452	0.327996
$743$	39.6246	1.45369	0.726843	−	0.686804i	$-0.240987\pi$
$743$	39.6246	1.45369	0.726843	+	0.686804i	$0.240987\pi$
$744$	19.0958	0.700086
$745$	0.0331768	0.00121550
$746$	−21.4787	−0.786392
$747$	−49.5526	−1.81304
$748$	−4.91871	−0.179846
$749$	13.9772	0.510715
$750$	32.1748	1.17486
$751$	23.8791	0.871360	0.435680	−	0.900102i	$-0.356508\pi$
$751$	23.8791	0.871360	0.435680	+	0.900102i	$0.356508\pi$
$752$	2.60869	0.0951291
$753$	25.0383	0.912448
$754$	29.8452	1.08690
$755$	5.97825	0.217571
$756$	17.0258	0.619224
$757$	40.0260	1.45477	0.727385	−	0.686229i	$-0.240735\pi$
$757$	40.0260	1.45477	0.727385	+	0.686229i	$0.240735\pi$
$758$	2.19062	0.0795669
$759$	6.56144	0.238165
$760$	−2.90277	−0.105294
$761$	45.7977	1.66016	0.830082	−	0.557641i	$-0.188294\pi$
$761$	45.7977	1.66016	0.830082	+	0.557641i	$0.188294\pi$
$762$	−28.9884	−1.05014
$763$	5.92950	0.214662
$764$	−12.7557	−0.461485
$765$	23.6233	0.854101
$766$	22.1091	0.798833
$767$	43.1035	1.55638
$768$	−3.41962	−0.123395
$769$	43.6308	1.57337	0.786684	−	0.617356i	$-0.211796\pi$
$769$	43.6308	1.57337	0.786684	+	0.617356i	$0.211796\pi$
$770$	−1.77846	−0.0640914
$771$	16.4889	0.593832
$772$	3.88736	0.139909
$773$	37.2804	1.34088	0.670442	−	0.741962i	$-0.266105\pi$
$773$	37.2804	1.34088	0.670442	+	0.741962i	$0.266105\pi$
$774$	−59.6562	−2.14430
$775$	−21.6467	−0.777574
$776$	9.44340	0.338998
$777$	1.25840	0.0451450
$778$	−14.3035	−0.512805
$779$	18.7552	0.671976
$780$	−15.6194	−0.559264
$781$	−2.00844	−0.0718675
$782$	−2.56348	−0.0916700
$783$	−134.856	−4.81936
$784$	−6.23537	−0.222692
$785$	22.5505	0.804860
$786$	3.41962	0.121974
$787$	−6.37265	−0.227160	−0.113580	−	0.993529i	$-0.536232\pi$
$787$	−6.37265	−0.227160	−0.113580	+	0.993529i	$0.536232\pi$
$788$	−0.950352	−0.0338549
$789$	−63.8945	−2.27471
$790$	−5.09341	−0.181215
$791$	5.95234	0.211641
$792$	−16.6814	−0.592747
$793$	−10.9535	−0.388969
$794$	−19.9912	−0.709460
$795$	37.0358	1.31353
$796$	5.97567	0.211802
$797$	−28.9386	−1.02506	−0.512529	−	0.858670i	$-0.671291\pi$
$797$	−28.9386	−1.02506	−0.512529	+	0.858670i	$0.671291\pi$
$798$	8.18875	0.289879
$799$	−6.68733	−0.236581
$800$	3.87644	0.137053
$801$	−7.09505	−0.250691
$802$	22.2833	0.786850
$803$	−24.0011	−0.846980
$804$	−38.2425	−1.34871
$805$	−0.926881	−0.0326683
$806$	24.0629	0.847578
$807$	18.9750	0.667953
$808$	0.876350	0.0308299
$809$	−13.9202	−0.489408	−0.244704	−	0.969598i	$-0.578691\pi$
$809$	−13.9202	−0.489408	−0.244704	+	0.969598i	$0.578691\pi$
$810$	42.9305	1.50842
$811$	39.3269	1.38096	0.690478	−	0.723354i	$-0.257400\pi$
$811$	39.3269	1.38096	0.690478	+	0.723354i	$0.257400\pi$
$812$	−6.05638	−0.212537
$813$	−71.6213	−2.51187
$814$	−0.807490	−0.0283025
$815$	12.9586	0.453920
$816$	8.76615	0.306877
$817$	−18.7914	−0.657426
$818$	−34.9529	−1.22210
$819$	32.7585	1.14468
$820$	7.25950	0.253513
$821$	24.4060	0.851774	0.425887	−	0.904776i	$-0.359962\pi$
$821$	24.4060	0.851774	0.425887	+	0.904776i	$0.359962\pi$
$822$	−35.2362	−1.22900
$823$	−23.6856	−0.825629	−0.412814	−	0.910815i	$-0.635454\pi$
$823$	−23.6856	−0.825629	−0.412814	+	0.910815i	$0.635454\pi$
$824$	−13.0825	−0.455751
$825$	25.4350	0.885534
$826$	−8.74683	−0.304341
$827$	54.3010	1.88823	0.944116	−	0.329614i	$-0.106919\pi$
$827$	54.3010	1.88823	0.944116	+	0.329614i	$0.106919\pi$
$828$	−8.69383	−0.302131
$829$	27.1696	0.943641	0.471820	−	0.881695i	$-0.343597\pi$
$829$	27.1696	0.943641	0.471820	+	0.881695i	$0.343597\pi$
$830$	−6.04163	−0.209708
$831$	51.1996	1.77610
$832$	−4.30911	−0.149391
$833$	15.9843	0.553822
$834$	6.48028	0.224394
$835$	−1.49753	−0.0518243
$836$	−5.25454	−0.181732
$837$	−108.728	−3.75820
$838$	−0.593922	−0.0205167
$839$	21.9269	0.757001	0.378500	−	0.925601i	$-0.376440\pi$
$839$	21.9269	0.757001	0.378500	+	0.925601i	$0.376440\pi$
$840$	3.16959	0.109361
$841$	18.9706	0.654159
$842$	−24.5387	−0.845661
$843$	50.1703	1.72796
$844$	24.7055	0.850398
$845$	−5.90242	−0.203049
$846$	−22.6795	−0.779737
$847$	6.39940	0.219886
$848$	10.2175	0.350871
$849$	−29.9794	−1.02889
$850$	−9.93719	−0.340843
$851$	−0.420839	−0.0144262
$852$	3.57945	0.122630
$853$	41.3248	1.41494	0.707468	−	0.706746i	$-0.249838\pi$
$853$	41.3248	1.41494	0.707468	+	0.706746i	$0.249838\pi$
$854$	2.22275	0.0760608
$855$	25.2362	0.863058
$856$	15.9843	0.546332
$857$	−13.4328	−0.458856	−0.229428	−	0.973326i	$-0.573686\pi$
$857$	−13.4328	−0.458856	−0.229428	+	0.973326i	$0.573686\pi$
$858$	−28.2740	−0.965258
$859$	28.8791	0.985344	0.492672	−	0.870215i	$-0.336020\pi$
$859$	28.8791	0.985344	0.492672	+	0.870215i	$0.336020\pi$
$860$	−7.27349	−0.248024
$861$	−20.4792	−0.697929
$862$	27.5218	0.937397
$863$	−15.1961	−0.517280	−0.258640	−	0.965974i	$-0.583274\pi$
$863$	−15.1961	−0.517280	−0.258640	+	0.965974i	$0.583274\pi$
$864$	19.4708	0.662409
$865$	3.50286	0.119101
$866$	−3.75532	−0.127611
$867$	35.6617	1.21114
$868$	−4.88298	−0.165739
$869$	−9.22001	−0.312767
$870$	−25.1052	−0.851147
$871$	−48.1898	−1.63285
$872$	6.78098	0.229633
$873$	−82.0993	−2.77864
$874$	−2.73851	−0.0926313
$875$	−8.22740	−0.278137
$876$	42.7748	1.44523
$877$	0.110808	0.00374172	0.00187086	−	0.999998i	$-0.499404\pi$
$877$	0.110808	0.00374172	0.00187086	+	0.999998i	$0.499404\pi$
$878$	−11.1205	−0.375298
$879$	107.356	3.62102
$880$	−2.03385	−0.0685611
$881$	−57.0614	−1.92245	−0.961224	−	0.275769i	$-0.911068\pi$
$881$	−57.0614	−1.92245	−0.961224	+	0.275769i	$0.911068\pi$
$882$	54.2092	1.82532
$883$	40.5551	1.36479	0.682393	−	0.730985i	$-0.260939\pi$
$883$	40.5551	1.36479	0.682393	+	0.730985i	$0.260939\pi$
$884$	11.0463	0.371528
$885$	−36.2578	−1.21879
$886$	17.1795	0.577157
$887$	−11.5555	−0.387997	−0.193998	−	0.981002i	$-0.562146\pi$
$887$	−11.5555	−0.387997	−0.193998	+	0.981002i	$0.562146\pi$
$888$	1.43911	0.0482934
$889$	7.41262	0.248611
$890$	−0.865052	−0.0289966
$891$	77.7121	2.60345
$892$	−7.76583	−0.260019
$893$	−7.14391	−0.239062
$894$	−0.107032	−0.00357969
$895$	−12.5527	−0.419590
$896$	0.874431	0.0292127
$897$	−14.7355	−0.492005
$898$	−7.12319	−0.237704
$899$	38.6765	1.28993
$900$	−33.7011	−1.12337
$901$	−26.1924	−0.872597
$902$	13.1410	0.437549
$903$	20.5186	0.682817
$904$	6.80710	0.226401
$905$	−0.0355424	−0.00118147
$906$	−19.2865	−0.640752
$907$	−4.11612	−0.136674	−0.0683368	−	0.997662i	$-0.521769\pi$
$907$	−4.11612	−0.136674	−0.0683368	+	0.997662i	$0.521769\pi$
$908$	−5.14167	−0.170632
$909$	−7.61884	−0.252701
$910$	3.99403	0.132401
$911$	−42.9356	−1.42252	−0.711259	−	0.702930i	$-0.751875\pi$
$911$	−42.9356	−1.42252	−0.711259	+	0.702930i	$0.751875\pi$
$912$	9.36466	0.310095
$913$	−10.9365	−0.361944
$914$	20.4743	0.677230
$915$	9.21384	0.304600
$916$	21.7310	0.718012
$917$	−0.874431	−0.0288763
$918$	−49.9130	−1.64737
$919$	−41.9472	−1.38371	−0.691855	−	0.722037i	$-0.743206\pi$
$919$	−41.9472	−1.38371	−0.691855	+	0.722037i	$0.743206\pi$
$920$	−1.05998	−0.0349466
$921$	−85.4848	−2.81682
$922$	−13.2520	−0.436432
$923$	4.51050	0.148465
$924$	5.73753	0.188751
$925$	−1.63136	−0.0536387
$926$	−22.7338	−0.747077
$927$	113.737	3.73562
$928$	−6.92608	−0.227360
$929$	19.7491	0.647948	0.323974	−	0.946066i	$-0.394981\pi$
$929$	19.7491	0.647948	0.323974	+	0.946066i	$0.394981\pi$
$930$	−20.2412	−0.663735
$931$	17.0756	0.559630
$932$	6.77600	0.221955
$933$	−24.1891	−0.791914
$934$	−16.5371	−0.541110
$935$	5.21375	0.170508
$936$	37.4627	1.22451
$937$	−6.27618	−0.205034	−0.102517	−	0.994731i	$-0.532690\pi$
$937$	−6.27618	−0.205034	−0.102517	+	0.994731i	$0.532690\pi$
$938$	9.77898	0.319295
$939$	105.818	3.45324
$940$	−2.76516	−0.0901896
$941$	30.1669	0.983413	0.491707	−	0.870761i	$-0.336373\pi$
$941$	30.1669	0.983413	0.491707	+	0.870761i	$0.336373\pi$
$942$	−72.7504	−2.37034
$943$	6.84871	0.223025
$944$	−10.0029	−0.325566
$945$	−18.0471	−0.587072
$946$	−13.1663	−0.428075
$947$	41.4146	1.34579	0.672896	−	0.739737i	$-0.265050\pi$
$947$	41.4146	1.34579	0.672896	+	0.739737i	$0.265050\pi$
$948$	16.4319	0.533684
$949$	53.9011	1.74970
$950$	−10.6157	−0.344417
$951$	−4.75141	−0.154075
$952$	−2.24159	−0.0726504
$953$	−41.6325	−1.34861	−0.674304	−	0.738454i	$-0.735556\pi$
$953$	−41.6325	−1.34861	−0.674304	+	0.738454i	$0.735556\pi$
$954$	−88.8294	−2.87596
$955$	13.5208	0.437523
$956$	15.2694	0.493848
$957$	−45.4451	−1.46903
$958$	−15.0493	−0.486221
$959$	9.01025	0.290956
$960$	3.62474	0.116988
$961$	0.183096	0.00590631
$962$	1.81344	0.0584677
$963$	−138.965	−4.47808
$964$	3.57377	0.115103
$965$	−4.12053	−0.132645
$966$	2.99023	0.0962090
$967$	22.6121	0.727155	0.363577	−	0.931564i	$-0.381555\pi$
$967$	22.6121	0.727155	0.363577	+	0.931564i	$0.381555\pi$
$968$	7.31835	0.235221
$969$	−24.0062	−0.771189
$970$	−10.0098	−0.321396
$971$	9.57950	0.307421	0.153710	−	0.988116i	$-0.450878\pi$
$971$	9.57950	0.307421	0.153710	+	0.988116i	$0.450878\pi$
$972$	−80.0866	−2.56878
$973$	−1.65707	−0.0531233
$974$	−29.3400	−0.940115
$975$	−57.1214	−1.82935
$976$	2.54193	0.0813653
$977$	−32.8955	−1.05242	−0.526210	−	0.850355i	$-0.676387\pi$
$977$	−32.8955	−1.05242	−0.526210	+	0.850355i	$0.676387\pi$
$978$	−41.8060	−1.33681
$979$	−1.56590	−0.0500465
$980$	6.60938	0.211129
$981$	−58.9527	−1.88221
$982$	−1.94163	−0.0619598
$983$	−40.1301	−1.27995	−0.639976	−	0.768395i	$-0.721056\pi$
$983$	−40.1301	−1.27995	−0.639976	+	0.768395i	$0.721056\pi$
$984$	−23.4200	−0.746603
$985$	1.00736	0.0320970
$986$	17.7549	0.565431
$987$	7.80057	0.248295
$988$	11.8005	0.375425
$989$	−6.86190	−0.218196
$990$	17.6820	0.561970
$991$	−38.5406	−1.22428	−0.612141	−	0.790749i	$-0.709692\pi$
$991$	−38.5406	−1.22428	−0.612141	+	0.790749i	$0.709692\pi$
$992$	−5.58418	−0.177298
$993$	7.58671	0.240757
$994$	−0.915299	−0.0290315
$995$	−6.33410	−0.200805
$996$	19.4910	0.617596
$997$	29.9068	0.947157	0.473579	−	0.880752i	$-0.342962\pi$
$997$	29.9068	0.947157	0.473579	+	0.880752i	$0.342962\pi$
$998$	−12.2282	−0.387078
$999$	−8.19406	−0.259248

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.l.1.1	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.l.1.1	✓	36	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.41962 q^{3} +1.00000 q^{4} -1.05998 q^{5} +3.41962 q^{6} -0.874431 q^{7} -1.00000 q^{8} +8.69383 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.41962 q^{3} +1.00000 q^{4} -1.05998 q^{5} +3.41962 q^{6} -0.874431 q^{7} -1.00000 q^{8} +8.69383 q^{9} +1.05998 q^{10} +1.91876 q^{11} -3.41962 q^{12} -4.30911 q^{13} +0.874431 q^{14} +3.62474 q^{15} +1.00000 q^{16} -2.56348 q^{17} -8.69383 q^{18} -2.73851 q^{19} -1.05998 q^{20} +2.99023 q^{21} -1.91876 q^{22} -1.00000 q^{23} +3.41962 q^{24} -3.87644 q^{25} +4.30911 q^{26} -19.4708 q^{27} -0.874431 q^{28} +6.92608 q^{29} -3.62474 q^{30} +5.58418 q^{31} -1.00000 q^{32} -6.56144 q^{33} +2.56348 q^{34} +0.926881 q^{35} +8.69383 q^{36} +0.420839 q^{37} +2.73851 q^{38} +14.7355 q^{39} +1.05998 q^{40} -6.84871 q^{41} -2.99023 q^{42} +6.86190 q^{43} +1.91876 q^{44} -9.21530 q^{45} +1.00000 q^{46} +2.60869 q^{47} -3.41962 q^{48} -6.23537 q^{49} +3.87644 q^{50} +8.76615 q^{51} -4.30911 q^{52} +10.2175 q^{53} +19.4708 q^{54} -2.03385 q^{55} +0.874431 q^{56} +9.36466 q^{57} -6.92608 q^{58} -10.0029 q^{59} +3.62474 q^{60} +2.54193 q^{61} -5.58418 q^{62} -7.60216 q^{63} +1.00000 q^{64} +4.56758 q^{65} +6.56144 q^{66} +11.1832 q^{67} -2.56348 q^{68} +3.41962 q^{69} -0.926881 q^{70} -1.04674 q^{71} -8.69383 q^{72} -12.5086 q^{73} -0.420839 q^{74} +13.2560 q^{75} -2.73851 q^{76} -1.67783 q^{77} -14.7355 q^{78} -4.80519 q^{79} -1.05998 q^{80} +40.5012 q^{81} +6.84871 q^{82} -5.69975 q^{83} +2.99023 q^{84} +2.71725 q^{85} -6.86190 q^{86} -23.6846 q^{87} -1.91876 q^{88} -0.816101 q^{89} +9.21530 q^{90} +3.76802 q^{91} -1.00000 q^{92} -19.0958 q^{93} -2.60869 q^{94} +2.90277 q^{95} +3.41962 q^{96} -9.44340 q^{97} +6.23537 q^{98} +16.6814 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9}+O(q^{10}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9} - q^{10} + 14 q^{11} + 4 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 36 q^{16} - 4 q^{17} - 46 q^{18} + 29 q^{19} + q^{20} + 24 q^{21} - 14 q^{22} - 36 q^{23} - 4 q^{24} + 49 q^{25} - 4 q^{26} + 19 q^{27} + 13 q^{28} - 13 q^{29} - 10 q^{30} + 21 q^{31} - 36 q^{32} - 5 q^{33} + 4 q^{34} + 30 q^{35} + 46 q^{36} + 13 q^{37} - 29 q^{38} + 30 q^{39} - q^{40} - 8 q^{41} - 24 q^{42} + 42 q^{43} + 14 q^{44} + 30 q^{45} + 36 q^{46} - 14 q^{47} + 4 q^{48} + 61 q^{49} - 49 q^{50} + 46 q^{51} + 4 q^{52} - 3 q^{53} - 19 q^{54} + 26 q^{55} - 13 q^{56} + 26 q^{57} + 13 q^{58} + 45 q^{59} + 10 q^{60} + 34 q^{61} - 21 q^{62} + 63 q^{63} + 36 q^{64} - 25 q^{65} + 5 q^{66} + 42 q^{67} - 4 q^{68} - 4 q^{69} - 30 q^{70} - 2 q^{71} - 46 q^{72} + 16 q^{73} - 13 q^{74} + 72 q^{75} + 29 q^{76} - 36 q^{77} - 30 q^{78} + 33 q^{79} + q^{80} + 96 q^{81} + 8 q^{82} + 8 q^{83} + 24 q^{84} + 18 q^{85} - 42 q^{86} + 11 q^{87} - 14 q^{88} + 21 q^{89} - 30 q^{90} + 60 q^{91} - 36 q^{92} - 27 q^{93} + 14 q^{94} - 44 q^{95} - 4 q^{96} + 20 q^{97} - 61 q^{98} + 76 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9 - q^10 + 14 * q^11 + 4 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 36 * q^16 - 4 * q^17 - 46 * q^18 + 29 * q^19 + q^20 + 24 * q^21 - 14 * q^22 - 36 * q^23 - 4 * q^24 + 49 * q^25 - 4 * q^26 + 19 * q^27 + 13 * q^28 - 13 * q^29 - 10 * q^30 + 21 * q^31 - 36 * q^32 - 5 * q^33 + 4 * q^34 + 30 * q^35 + 46 * q^36 + 13 * q^37 - 29 * q^38 + 30 * q^39 - q^40 - 8 * q^41 - 24 * q^42 + 42 * q^43 + 14 * q^44 + 30 * q^45 + 36 * q^46 - 14 * q^47 + 4 * q^48 + 61 * q^49 - 49 * q^50 + 46 * q^51 + 4 * q^52 - 3 * q^53 - 19 * q^54 + 26 * q^55 - 13 * q^56 + 26 * q^57 + 13 * q^58 + 45 * q^59 + 10 * q^60 + 34 * q^61 - 21 * q^62 + 63 * q^63 + 36 * q^64 - 25 * q^65 + 5 * q^66 + 42 * q^67 - 4 * q^68 - 4 * q^69 - 30 * q^70 - 2 * q^71 - 46 * q^72 + 16 * q^73 - 13 * q^74 + 72 * q^75 + 29 * q^76 - 36 * q^77 - 30 * q^78 + 33 * q^79 + q^80 + 96 * q^81 + 8 * q^82 + 8 * q^83 + 24 * q^84 + 18 * q^85 - 42 * q^86 + 11 * q^87 - 14 * q^88 + 21 * q^89 - 30 * q^90 + 60 * q^91 - 36 * q^92 - 27 * q^93 + 14 * q^94 - 44 * q^95 - 4 * q^96 + 20 * q^97 - 61 * q^98 + 76 * q^99

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