LMFDB - Embedded newform 6041.2.a.d.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, 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("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$1$
Dimension:	$101$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.79653 q^{2} +2.70133 q^{3} +1.22753 q^{4} +2.96874 q^{5} -4.85303 q^{6} -1.00000 q^{7} +1.38776 q^{8} +4.29718 q^{9} +O(q^{10})$	\(q-1.79653 q^{2} +2.70133 q^{3} +1.22753 q^{4} +2.96874 q^{5} -4.85303 q^{6} -1.00000 q^{7} +1.38776 q^{8} +4.29718 q^{9} -5.33345 q^{10} +1.75877 q^{11} +3.31598 q^{12} -5.00158 q^{13} +1.79653 q^{14} +8.01956 q^{15} -4.94823 q^{16} -5.72676 q^{17} -7.72004 q^{18} -6.05188 q^{19} +3.64424 q^{20} -2.70133 q^{21} -3.15968 q^{22} -8.81120 q^{23} +3.74880 q^{24} +3.81345 q^{25} +8.98550 q^{26} +3.50412 q^{27} -1.22753 q^{28} +4.27176 q^{29} -14.4074 q^{30} -10.4075 q^{31} +6.11414 q^{32} +4.75101 q^{33} +10.2883 q^{34} -2.96874 q^{35} +5.27494 q^{36} +11.4088 q^{37} +10.8724 q^{38} -13.5109 q^{39} +4.11991 q^{40} +6.81949 q^{41} +4.85303 q^{42} +8.24006 q^{43} +2.15895 q^{44} +12.7572 q^{45} +15.8296 q^{46} +3.70002 q^{47} -13.3668 q^{48} +1.00000 q^{49} -6.85099 q^{50} -15.4699 q^{51} -6.13961 q^{52} -6.24041 q^{53} -6.29527 q^{54} +5.22133 q^{55} -1.38776 q^{56} -16.3481 q^{57} -7.67437 q^{58} -11.3029 q^{59} +9.84429 q^{60} +8.68533 q^{61} +18.6974 q^{62} -4.29718 q^{63} -1.08780 q^{64} -14.8484 q^{65} -8.53535 q^{66} -13.1105 q^{67} -7.02979 q^{68} -23.8019 q^{69} +5.33345 q^{70} -5.02668 q^{71} +5.96346 q^{72} +4.81218 q^{73} -20.4962 q^{74} +10.3014 q^{75} -7.42890 q^{76} -1.75877 q^{77} +24.2728 q^{78} -4.37952 q^{79} -14.6900 q^{80} -3.42576 q^{81} -12.2515 q^{82} -11.0344 q^{83} -3.31598 q^{84} -17.0013 q^{85} -14.8035 q^{86} +11.5394 q^{87} +2.44075 q^{88} +0.180032 q^{89} -22.9188 q^{90} +5.00158 q^{91} -10.8160 q^{92} -28.1140 q^{93} -6.64721 q^{94} -17.9665 q^{95} +16.5163 q^{96} +3.19755 q^{97} -1.79653 q^{98} +7.55774 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9}+O(q^{10}) $ 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9	\( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9} - 23 q^{10} - 13 q^{11} - 31 q^{12} - 35 q^{13} - 3 q^{14} - 20 q^{15} + 45 q^{16} - 19 q^{17} + 3 q^{18} - 59 q^{19} - 31 q^{20} + 17 q^{21} - 13 q^{22} - 29 q^{23} - 59 q^{24} + 103 q^{25} - 18 q^{26} - 47 q^{27} - 85 q^{28} - 26 q^{29} - 8 q^{30} - 125 q^{31} + 12 q^{32} - 18 q^{33} - 66 q^{34} + 12 q^{35} + 40 q^{36} + 22 q^{37} - 31 q^{38} - 94 q^{39} - 79 q^{40} - 39 q^{41} + 17 q^{42} - 5 q^{43} - 53 q^{44} - 50 q^{45} - 37 q^{46} - 47 q^{47} - 81 q^{48} + 101 q^{49} + 2 q^{50} - 23 q^{51} - 56 q^{52} - 5 q^{53} - 77 q^{54} - 155 q^{55} + 3 q^{56} + 61 q^{57} - 31 q^{58} - 33 q^{59} - 48 q^{60} - 96 q^{61} - 38 q^{62} - 88 q^{63} - 33 q^{64} - 8 q^{65} - 91 q^{66} + 8 q^{67} - 41 q^{68} - 91 q^{69} + 23 q^{70} - 116 q^{71} - 5 q^{72} - 62 q^{73} - 23 q^{74} - 94 q^{75} - 112 q^{76} + 13 q^{77} + 17 q^{78} - 127 q^{79} - 87 q^{80} + 37 q^{81} - 118 q^{82} - 58 q^{83} + 31 q^{84} - 6 q^{85} - 26 q^{86} - 82 q^{87} - 40 q^{88} - 57 q^{89} - 123 q^{90} + 35 q^{91} - 28 q^{92} - 10 q^{93} - 107 q^{94} - 70 q^{95} - 76 q^{96} - 69 q^{97} + 3 q^{98} - 67 q^{99}+O(q^{100}) \) 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9 - 23 * q^10 - 13 * q^11 - 31 * q^12 - 35 * q^13 - 3 * q^14 - 20 * q^15 + 45 * q^16 - 19 * q^17 + 3 * q^18 - 59 * q^19 - 31 * q^20 + 17 * q^21 - 13 * q^22 - 29 * q^23 - 59 * q^24 + 103 * q^25 - 18 * q^26 - 47 * q^27 - 85 * q^28 - 26 * q^29 - 8 * q^30 - 125 * q^31 + 12 * q^32 - 18 * q^33 - 66 * q^34 + 12 * q^35 + 40 * q^36 + 22 * q^37 - 31 * q^38 - 94 * q^39 - 79 * q^40 - 39 * q^41 + 17 * q^42 - 5 * q^43 - 53 * q^44 - 50 * q^45 - 37 * q^46 - 47 * q^47 - 81 * q^48 + 101 * q^49 + 2 * q^50 - 23 * q^51 - 56 * q^52 - 5 * q^53 - 77 * q^54 - 155 * q^55 + 3 * q^56 + 61 * q^57 - 31 * q^58 - 33 * q^59 - 48 * q^60 - 96 * q^61 - 38 * q^62 - 88 * q^63 - 33 * q^64 - 8 * q^65 - 91 * q^66 + 8 * q^67 - 41 * q^68 - 91 * q^69 + 23 * q^70 - 116 * q^71 - 5 * q^72 - 62 * q^73 - 23 * q^74 - 94 * q^75 - 112 * q^76 + 13 * q^77 + 17 * q^78 - 127 * q^79 - 87 * q^80 + 37 * q^81 - 118 * q^82 - 58 * q^83 + 31 * q^84 - 6 * q^85 - 26 * q^86 - 82 * q^87 - 40 * q^88 - 57 * q^89 - 123 * q^90 + 35 * q^91 - 28 * q^92 - 10 * q^93 - 107 * q^94 - 70 * q^95 - 76 * q^96 - 69 * q^97 + 3 * q^98 - 67 * 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 $

$2$	−1.79653	−1.27034	−0.635171	−	0.772372i	$-0.719070\pi$
$2$	−1.79653	−1.27034	−0.635171	+	0.772372i	$0.719070\pi$
$3$	2.70133	1.55961	0.779807	−	0.626020i	$-0.215317\pi$
$3$	2.70133	1.55961	0.779807	+	0.626020i	$0.215317\pi$
$4$	1.22753	0.613767
$5$	2.96874	1.32766	0.663832	−	0.747882i	$-0.268929\pi$
$5$	2.96874	1.32766	0.663832	+	0.747882i	$0.268929\pi$
$6$	−4.85303	−1.98124
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.38776	0.490647
$9$	4.29718	1.43239
$10$	−5.33345	−1.68659
$11$	1.75877	0.530288	0.265144	−	0.964209i	$-0.414580\pi$
$11$	1.75877	0.530288	0.265144	+	0.964209i	$0.414580\pi$
$12$	3.31598	0.957240
$13$	−5.00158	−1.38719	−0.693594	−	0.720366i	$-0.743974\pi$
$13$	−5.00158	−1.38719	−0.693594	+	0.720366i	$0.743974\pi$
$14$	1.79653	0.480144
$15$	8.01956	2.07064
$16$	−4.94823	−1.23706
$17$	−5.72676	−1.38894	−0.694471	−	0.719520i	$-0.744362\pi$
$17$	−5.72676	−1.38894	−0.694471	+	0.719520i	$0.744362\pi$
$18$	−7.72004	−1.81963
$19$	−6.05188	−1.38840	−0.694199	−	0.719783i	$-0.744241\pi$
$19$	−6.05188	−1.38840	−0.694199	+	0.719783i	$0.744241\pi$
$20$	3.64424	0.814876
$21$	−2.70133	−0.589479
$22$	−3.15968	−0.673647
$23$	−8.81120	−1.83726	−0.918631	−	0.395117i	$-0.870704\pi$
$23$	−8.81120	−1.83726	−0.918631	+	0.395117i	$0.870704\pi$
$24$	3.74880	0.765220
$25$	3.81345	0.762689
$26$	8.98550	1.76220
$27$	3.50412	0.674368
$28$	−1.22753	−0.231982
$29$	4.27176	0.793247	0.396623	−	0.917981i	$-0.370182\pi$
$29$	4.27176	0.793247	0.396623	+	0.917981i	$0.370182\pi$
$30$	−14.4074	−2.63042
$31$	−10.4075	−1.86924	−0.934618	−	0.355653i	$-0.884258\pi$
$31$	−10.4075	−1.86924	−0.934618	+	0.355653i	$0.884258\pi$
$32$	6.11414	1.08084
$33$	4.75101	0.827045
$34$	10.2883	1.76443
$35$	−2.96874	−0.501809
$36$	5.27494	0.879157
$37$	11.4088	1.87559	0.937795	−	0.347189i	$-0.112864\pi$
$37$	11.4088	1.87559	0.937795	+	0.347189i	$0.112864\pi$
$38$	10.8724	1.76374
$39$	−13.5109	−2.16348
$40$	4.11991	0.651415
$41$	6.81949	1.06503	0.532513	−	0.846422i	$-0.321248\pi$
$41$	6.81949	1.06503	0.532513	+	0.846422i	$0.321248\pi$
$42$	4.85303	0.748839
$43$	8.24006	1.25660	0.628298	−	0.777972i	$-0.283752\pi$
$43$	8.24006	1.25660	0.628298	+	0.777972i	$0.283752\pi$
$44$	2.15895	0.325474
$45$	12.7572	1.90174
$46$	15.8296	2.33395
$47$	3.70002	0.539703	0.269852	−	0.962902i	$-0.413025\pi$
$47$	3.70002	0.539703	0.269852	+	0.962902i	$0.413025\pi$
$48$	−13.3668	−1.92933
$49$	1.00000	0.142857
$50$	−6.85099	−0.968876
$51$	−15.4699	−2.16621
$52$	−6.13961	−0.851410
$53$	−6.24041	−0.857186	−0.428593	−	0.903498i	$-0.640991\pi$
$53$	−6.24041	−0.857186	−0.428593	+	0.903498i	$0.640991\pi$
$54$	−6.29527	−0.856678
$55$	5.22133	0.704044
$56$	−1.38776	−0.185447
$57$	−16.3481	−2.16536
$58$	−7.67437	−1.00769
$59$	−11.3029	−1.47151	−0.735753	−	0.677250i	$-0.763172\pi$
$59$	−11.3029	−1.47151	−0.735753	+	0.677250i	$0.763172\pi$
$60$	9.84429	1.27089
$61$	8.68533	1.11204	0.556021	−	0.831168i	$-0.312327\pi$
$61$	8.68533	1.11204	0.556021	+	0.831168i	$0.312327\pi$
$62$	18.6974	2.37457
$63$	−4.29718	−0.541394
$64$	−1.08780	−0.135975
$65$	−14.8484	−1.84172
$66$	−8.53535	−1.05063
$67$	−13.1105	−1.60170	−0.800852	−	0.598863i	$-0.795619\pi$
$67$	−13.1105	−1.60170	−0.800852	+	0.598863i	$0.795619\pi$
$68$	−7.02979	−0.852488
$69$	−23.8019	−2.86542
$70$	5.33345	0.637469
$71$	−5.02668	−0.596558	−0.298279	−	0.954479i	$-0.596413\pi$
$71$	−5.02668	−0.596558	−0.298279	+	0.954479i	$0.596413\pi$
$72$	5.96346	0.702801
$73$	4.81218	0.563223	0.281611	−	0.959529i	$-0.409131\pi$
$73$	4.81218	0.563223	0.281611	+	0.959529i	$0.409131\pi$
$74$	−20.4962	−2.38264
$75$	10.3014	1.18950
$76$	−7.42890	−0.852153
$77$	−1.75877	−0.200430
$78$	24.2728	2.74835
$79$	−4.37952	−0.492735	−0.246367	−	0.969177i	$-0.579237\pi$
$79$	−4.37952	−0.492735	−0.246367	+	0.969177i	$0.579237\pi$
$80$	−14.6900	−1.64239
$81$	−3.42576	−0.380640
$82$	−12.2515	−1.35295
$83$	−11.0344	−1.21118	−0.605590	−	0.795777i	$-0.707063\pi$
$83$	−11.0344	−1.21118	−0.605590	+	0.795777i	$0.707063\pi$
$84$	−3.31598	−0.361803
$85$	−17.0013	−1.84405
$86$	−14.8035	−1.59631
$87$	11.5394	1.23716
$88$	2.44075	0.260185
$89$	0.180032	0.0190833	0.00954167	−	0.999954i	$-0.496963\pi$
$89$	0.180032	0.0190833	0.00954167	+	0.999954i	$0.496963\pi$
$90$	−22.9188	−2.41586
$91$	5.00158	0.524308
$92$	−10.8160	−1.12765
$93$	−28.1140	−2.91529
$94$	−6.64721	−0.685608
$95$	−17.9665	−1.84332
$96$	16.5163	1.68569
$97$	3.19755	0.324662	0.162331	−	0.986736i	$-0.448099\pi$
$97$	3.19755	0.324662	0.162331	+	0.986736i	$0.448099\pi$
$98$	−1.79653	−0.181477
$99$	7.55774	0.759582
$100$	4.68114	0.468114
$101$	7.85873	0.781973	0.390987	−	0.920396i	$-0.372134\pi$
$101$	7.85873	0.781973	0.390987	+	0.920396i	$0.372134\pi$
$102$	27.7921	2.75183
$103$	−8.35211	−0.822958	−0.411479	−	0.911419i	$-0.634988\pi$
$103$	−8.35211	−0.822958	−0.411479	+	0.911419i	$0.634988\pi$
$104$	−6.94099	−0.680620
$105$	−8.01956	−0.782629
$106$	11.2111	1.08892
$107$	5.26753	0.509231	0.254616	−	0.967042i	$-0.418051\pi$
$107$	5.26753	0.509231	0.254616	+	0.967042i	$0.418051\pi$
$108$	4.30143	0.413905
$109$	18.9208	1.81228	0.906141	−	0.422977i	$-0.139015\pi$
$109$	18.9208	1.81228	0.906141	+	0.422977i	$0.139015\pi$
$110$	−9.38030	−0.894376
$111$	30.8189	2.92520
$112$	4.94823	0.467564
$113$	−15.0317	−1.41406	−0.707031	−	0.707183i	$-0.749966\pi$
$113$	−15.0317	−1.41406	−0.707031	+	0.707183i	$0.749966\pi$
$114$	29.3700	2.75075
$115$	−26.1582	−2.43926
$116$	5.24374	0.486869
$117$	−21.4927	−1.98700
$118$	20.3060	1.86932
$119$	5.72676	0.524971
$120$	11.1292	1.01595
$121$	−7.90674	−0.718794
$122$	−15.6035	−1.41267
$123$	18.4217	1.66103
$124$	−12.7755	−1.14728
$125$	−3.52257	−0.315069
$126$	7.72004	0.687756
$127$	1.77044	0.157102	0.0785508	−	0.996910i	$-0.474971\pi$
$127$	1.77044	0.157102	0.0785508	+	0.996910i	$0.474971\pi$
$128$	−10.2740	−0.908102
$129$	22.2591	1.95981
$130$	26.6757	2.33961
$131$	−0.443639	−0.0387609	−0.0193805	−	0.999812i	$-0.506169\pi$
$131$	−0.443639	−0.0387609	−0.0193805	+	0.999812i	$0.506169\pi$
$132$	5.83203	0.507613
$133$	6.05188	0.524765
$134$	23.5535	2.03471
$135$	10.4028	0.895334
$136$	−7.94737	−0.681481
$137$	−9.08270	−0.775988	−0.387994	−	0.921662i	$-0.626832\pi$
$137$	−9.08270	−0.775988	−0.387994	+	0.921662i	$0.626832\pi$
$138$	42.7610	3.64006
$139$	−17.9418	−1.52180	−0.760900	−	0.648869i	$-0.775242\pi$
$139$	−17.9418	−1.52180	−0.760900	+	0.648869i	$0.775242\pi$
$140$	−3.64424	−0.307994
$141$	9.99497	0.841729
$142$	9.03061	0.757832
$143$	−8.79661	−0.735609
$144$	−21.2634	−1.77195
$145$	12.6818	1.05316
$146$	−8.64524	−0.715485
$147$	2.70133	0.222802
$148$	14.0047	1.15118
$149$	−2.71960	−0.222798	−0.111399	−	0.993776i	$-0.535533\pi$
$149$	−2.71960	−0.222798	−0.111399	+	0.993776i	$0.535533\pi$
$150$	−18.5068	−1.51107
$151$	−24.1219	−1.96301	−0.981507	−	0.191428i	$-0.938688\pi$
$151$	−24.1219	−1.96301	−0.981507	+	0.191428i	$0.938688\pi$
$152$	−8.39857	−0.681214
$153$	−24.6089	−1.98951
$154$	3.15968	0.254615
$155$	−30.8971	−2.48172
$156$	−16.5851	−1.32787
$157$	−8.40945	−0.671147	−0.335573	−	0.942014i	$-0.608930\pi$
$157$	−8.40945	−0.671147	−0.335573	+	0.942014i	$0.608930\pi$
$158$	7.86796	0.625941
$159$	−16.8574	−1.33688
$160$	18.1513	1.43499
$161$	8.81120	0.694419
$162$	6.15450	0.483543
$163$	16.5968	1.29996	0.649982	−	0.759950i	$-0.274776\pi$
$163$	16.5968	1.29996	0.649982	+	0.759950i	$0.274776\pi$
$164$	8.37116	0.653678
$165$	14.1045	1.09804
$166$	19.8236	1.53861
$167$	−5.18955	−0.401579	−0.200790	−	0.979634i	$-0.564351\pi$
$167$	−5.18955	−0.401579	−0.200790	+	0.979634i	$0.564351\pi$
$168$	−3.74880	−0.289226
$169$	12.0158	0.924289
$170$	30.5434	2.34257
$171$	−26.0061	−1.98873
$172$	10.1150	0.771258
$173$	14.5608	1.10704	0.553520	−	0.832836i	$-0.313284\pi$
$173$	14.5608	1.10704	0.553520	+	0.832836i	$0.313284\pi$
$174$	−20.7310	−1.57161
$175$	−3.81345	−0.288269
$176$	−8.70278	−0.655997
$177$	−30.5328	−2.29498
$178$	−0.323433	−0.0242424
$179$	15.8205	1.18248	0.591238	−	0.806497i	$-0.298639\pi$
$179$	15.8205	1.18248	0.591238	+	0.806497i	$0.298639\pi$
$180$	15.6600	1.16722
$181$	8.89911	0.661465	0.330733	−	0.943724i	$-0.392704\pi$
$181$	8.89911	0.661465	0.330733	+	0.943724i	$0.392704\pi$
$182$	−8.98550	−0.666050
$183$	23.4619	1.73436
$184$	−12.2278	−0.901448
$185$	33.8697	2.49015
$186$	50.5078	3.70341
$187$	−10.0720	−0.736540
$188$	4.54190	0.331252
$189$	−3.50412	−0.254887
$190$	32.2774	2.34165
$191$	−19.2435	−1.39241	−0.696204	−	0.717844i	$-0.745129\pi$
$191$	−19.2435	−1.39241	−0.696204	+	0.717844i	$0.745129\pi$
$192$	−2.93851	−0.212069
$193$	23.1485	1.66627	0.833134	−	0.553072i	$-0.186545\pi$
$193$	23.1485	1.66627	0.833134	+	0.553072i	$0.186545\pi$
$194$	−5.74451	−0.412432
$195$	−40.1104	−2.87237
$196$	1.22753	0.0876810
$197$	9.64176	0.686947	0.343473	−	0.939162i	$-0.388396\pi$
$197$	9.64176	0.686947	0.343473	+	0.939162i	$0.388396\pi$
$198$	−13.5777	−0.964928
$199$	−9.04497	−0.641181	−0.320591	−	0.947218i	$-0.603881\pi$
$199$	−9.04497	−0.641181	−0.320591	+	0.947218i	$0.603881\pi$
$200$	5.29215	0.374212
$201$	−35.4158	−2.49804
$202$	−14.1185	−0.993373
$203$	−4.27176	−0.299819
$204$	−18.9898	−1.32955
$205$	20.2453	1.41400
$206$	15.0049	1.04544
$207$	−37.8633	−2.63168
$208$	24.7489	1.71603
$209$	−10.6439	−0.736251
$210$	14.4074	0.994206
$211$	−8.89215	−0.612161	−0.306080	−	0.952006i	$-0.599018\pi$
$211$	−8.89215	−0.612161	−0.306080	+	0.952006i	$0.599018\pi$
$212$	−7.66032	−0.526113
$213$	−13.5787	−0.930399
$214$	−9.46330	−0.646898
$215$	24.4626	1.66834
$216$	4.86288	0.330877
$217$	10.4075	0.706505
$218$	−33.9918	−2.30222
$219$	12.9993	0.878410
$220$	6.40936	0.432119
$221$	28.6428	1.92672
$222$	−55.3671	−3.71600
$223$	−2.43015	−0.162735	−0.0813675	−	0.996684i	$-0.525929\pi$
$223$	−2.43015	−0.162735	−0.0813675	+	0.996684i	$0.525929\pi$
$224$	−6.11414	−0.408518
$225$	16.3871	1.09247
$226$	27.0049	1.79634
$227$	−21.2733	−1.41196	−0.705980	−	0.708231i	$-0.749493\pi$
$227$	−21.2733	−1.41196	−0.705980	+	0.708231i	$0.749493\pi$
$228$	−20.0679	−1.32903
$229$	−6.55546	−0.433197	−0.216599	−	0.976261i	$-0.569496\pi$
$229$	−6.55546	−0.433197	−0.216599	+	0.976261i	$0.569496\pi$
$230$	46.9941	3.09870
$231$	−4.75101	−0.312594
$232$	5.92819	0.389205
$233$	−16.5923	−1.08700	−0.543500	−	0.839409i	$-0.682901\pi$
$233$	−16.5923	−1.08700	−0.543500	+	0.839409i	$0.682901\pi$
$234$	38.6123	2.52417
$235$	10.9844	0.716544
$236$	−13.8746	−0.903163
$237$	−11.8305	−0.768476
$238$	−10.2883	−0.666892
$239$	−24.1481	−1.56201	−0.781005	−	0.624525i	$-0.785293\pi$
$239$	−24.1481	−1.56201	−0.781005	+	0.624525i	$0.785293\pi$
$240$	−39.6826	−2.56150
$241$	16.4566	1.06006	0.530032	−	0.847978i	$-0.322180\pi$
$241$	16.4566	1.06006	0.530032	+	0.847978i	$0.322180\pi$
$242$	14.2047	0.913114
$243$	−19.7665	−1.26802
$244$	10.6615	0.682535
$245$	2.96874	0.189666
$246$	−33.0952	−2.11007
$247$	30.2689	1.92597
$248$	−14.4431	−0.917136
$249$	−29.8075	−1.88897
$250$	6.32842	0.400245
$251$	8.96048	0.565581	0.282790	−	0.959182i	$-0.408740\pi$
$251$	8.96048	0.565581	0.282790	+	0.959182i	$0.408740\pi$
$252$	−5.27494	−0.332290
$253$	−15.4968	−0.974278
$254$	−3.18066	−0.199573
$255$	−45.9261	−2.87600
$256$	20.6332	1.28958
$257$	19.1874	1.19688	0.598440	−	0.801168i	$-0.295788\pi$
$257$	19.1874	1.19688	0.598440	+	0.801168i	$0.295788\pi$
$258$	−39.9893	−2.48962
$259$	−11.4088	−0.708907
$260$	−18.2269	−1.13039
$261$	18.3566	1.13624
$262$	0.797013	0.0492396
$263$	18.2860	1.12756	0.563781	−	0.825924i	$-0.309346\pi$
$263$	18.2860	1.12756	0.563781	+	0.825924i	$0.309346\pi$
$264$	6.59326	0.405787
$265$	−18.5262	−1.13805
$266$	−10.8724	−0.666631
$267$	0.486326	0.0297626
$268$	−16.0936	−0.983073
$269$	−23.3633	−1.42449	−0.712243	−	0.701933i	$-0.752320\pi$
$269$	−23.3633	−1.42449	−0.712243	+	0.701933i	$0.752320\pi$
$270$	−18.6891	−1.13738
$271$	−7.71305	−0.468534	−0.234267	−	0.972172i	$-0.575269\pi$
$271$	−7.71305	−0.468534	−0.234267	+	0.972172i	$0.575269\pi$
$272$	28.3373	1.71820
$273$	13.5109	0.817717
$274$	16.3174	0.985769
$275$	6.70696	0.404445
$276$	−29.2177	−1.75870
$277$	8.26957	0.496870	0.248435	−	0.968649i	$-0.420084\pi$
$277$	8.26957	0.496870	0.248435	+	0.968649i	$0.420084\pi$
$278$	32.2330	1.93321
$279$	−44.7228	−2.67748
$280$	−4.11991	−0.246212
$281$	−6.77317	−0.404053	−0.202027	−	0.979380i	$-0.564753\pi$
$281$	−6.77317	−0.404053	−0.202027	+	0.979380i	$0.564753\pi$
$282$	−17.9563	−1.06928
$283$	0.505427	0.0300445	0.0150223	−	0.999887i	$-0.495218\pi$
$283$	0.505427	0.0300445	0.0150223	+	0.999887i	$0.495218\pi$
$284$	−6.17043	−0.366147
$285$	−48.5334	−2.87487
$286$	15.8034	0.934475
$287$	−6.81949	−0.402542
$288$	26.2736	1.54819
$289$	15.7957	0.929162
$290$	−22.7832	−1.33788
$291$	8.63764	0.506347
$292$	5.90712	0.345688
$293$	−8.76560	−0.512092	−0.256046	−	0.966665i	$-0.582420\pi$
$293$	−8.76560	−0.512092	−0.256046	+	0.966665i	$0.582420\pi$
$294$	−4.85303	−0.283035
$295$	−33.5553	−1.95367
$296$	15.8326	0.920254
$297$	6.16293	0.357610
$298$	4.88585	0.283030
$299$	44.0699	2.54863
$300$	12.6453	0.730077
$301$	−8.24006	−0.474949
$302$	43.3358	2.49370
$303$	21.2290	1.21958
$304$	29.9461	1.71753
$305$	25.7845	1.47642
$306$	44.2108	2.52736
$307$	−6.04912	−0.345242	−0.172621	−	0.984988i	$-0.555224\pi$
$307$	−6.04912	−0.345242	−0.172621	+	0.984988i	$0.555224\pi$
$308$	−2.15895	−0.123017
$309$	−22.5618	−1.28350
$310$	55.5077	3.15263
$311$	1.39728	0.0792327	0.0396163	−	0.999215i	$-0.487386\pi$
$311$	1.39728	0.0792327	0.0396163	+	0.999215i	$0.487386\pi$
$312$	−18.7499	−1.06150
$313$	23.6539	1.33700	0.668500	−	0.743713i	$-0.266937\pi$
$313$	23.6539	1.33700	0.668500	+	0.743713i	$0.266937\pi$
$314$	15.1079	0.852586
$315$	−12.7572	−0.718789
$316$	−5.37601	−0.302424
$317$	4.96486	0.278854	0.139427	−	0.990232i	$-0.455474\pi$
$317$	4.96486	0.278854	0.139427	+	0.990232i	$0.455474\pi$
$318$	30.2849	1.69829
$319$	7.51304	0.420649
$320$	−3.22941	−0.180529
$321$	14.2293	0.794204
$322$	−15.8296	−0.882150
$323$	34.6577	1.92840
$324$	−4.20524	−0.233625
$325$	−19.0732	−1.05799
$326$	−29.8168	−1.65140
$327$	51.1112	2.82646
$328$	9.46383	0.522552
$329$	−3.70002	−0.203989
$330$	−25.3393	−1.39488
$331$	−10.1907	−0.560132	−0.280066	−	0.959981i	$-0.590356\pi$
$331$	−10.1907	−0.560132	−0.280066	+	0.959981i	$0.590356\pi$
$332$	−13.5451	−0.743383
$333$	49.0256	2.68659
$334$	9.32320	0.510143
$335$	−38.9217	−2.12652
$336$	13.3668	0.729219
$337$	−22.5720	−1.22958	−0.614788	−	0.788692i	$-0.710759\pi$
$337$	−22.5720	−1.22958	−0.614788	+	0.788692i	$0.710759\pi$
$338$	−21.5867	−1.17416
$339$	−40.6055	−2.20539
$340$	−20.8697	−1.13182
$341$	−18.3043	−0.991234
$342$	46.7208	2.52637
$343$	−1.00000	−0.0539949
$344$	11.4352	0.616546
$345$	−70.6619	−3.80431
$346$	−26.1590	−1.40632
$347$	−6.46497	−0.347058	−0.173529	−	0.984829i	$-0.555517\pi$
$347$	−6.46497	−0.347058	−0.173529	+	0.984829i	$0.555517\pi$
$348$	14.1651	0.759327
$349$	−16.8898	−0.904091	−0.452046	−	0.891995i	$-0.649306\pi$
$349$	−16.8898	−0.904091	−0.452046	+	0.891995i	$0.649306\pi$
$350$	6.85099	0.366201
$351$	−17.5261	−0.935475
$352$	10.7533	0.573155
$353$	5.25931	0.279925	0.139962	−	0.990157i	$-0.455302\pi$
$353$	5.25931	0.279925	0.139962	+	0.990157i	$0.455302\pi$
$354$	54.8531	2.91541
$355$	−14.9229	−0.792027
$356$	0.220995	0.0117127
$357$	15.4699	0.818752
$358$	−28.4220	−1.50215
$359$	33.1923	1.75182	0.875911	−	0.482472i	$-0.160261\pi$
$359$	33.1923	1.75182	0.875911	+	0.482472i	$0.160261\pi$
$360$	17.7040	0.933083
$361$	17.6253	0.927647
$362$	−15.9875	−0.840287
$363$	−21.3587	−1.12104
$364$	6.13961	0.321803
$365$	14.2861	0.747770
$366$	−42.1502	−2.20322
$367$	−4.55170	−0.237597	−0.118798	−	0.992918i	$-0.537904\pi$
$367$	−4.55170	−0.237597	−0.118798	+	0.992918i	$0.537904\pi$
$368$	43.5998	2.27280
$369$	29.3046	1.52554
$370$	−60.8481	−3.16334
$371$	6.24041	0.323986
$372$	−34.5109	−1.78931
$373$	32.3728	1.67620	0.838100	−	0.545516i	$-0.183666\pi$
$373$	32.3728	1.67620	0.838100	+	0.545516i	$0.183666\pi$
$374$	18.0947	0.935657
$375$	−9.51563	−0.491385
$376$	5.13474	0.264804
$377$	−21.3656	−1.10038
$378$	6.29527	0.323794
$379$	−17.3174	−0.889534	−0.444767	−	0.895646i	$-0.646714\pi$
$379$	−17.3174	−0.889534	−0.444767	+	0.895646i	$0.646714\pi$
$380$	−22.0545	−1.13137
$381$	4.78256	0.245018
$382$	34.5715	1.76883
$383$	8.88218	0.453858	0.226929	−	0.973911i	$-0.427131\pi$
$383$	8.88218	0.453858	0.226929	+	0.973911i	$0.427131\pi$
$384$	−27.7535	−1.41629
$385$	−5.22133	−0.266104
$386$	−41.5871	−2.11673
$387$	35.4090	1.79994
$388$	3.92510	0.199267
$389$	−9.95536	−0.504757	−0.252378	−	0.967629i	$-0.581213\pi$
$389$	−9.95536	−0.504757	−0.252378	+	0.967629i	$0.581213\pi$
$390$	72.0598	3.64889
$391$	50.4596	2.55185
$392$	1.38776	0.0700925
$393$	−1.19842	−0.0604521
$394$	−17.3217	−0.872657
$395$	−13.0017	−0.654186
$396$	9.27739	0.466207
$397$	−20.5242	−1.03008	−0.515039	−	0.857167i	$-0.672223\pi$
$397$	−20.5242	−1.03008	−0.515039	+	0.857167i	$0.672223\pi$
$398$	16.2496	0.814519
$399$	16.3481	0.818430
$400$	−18.8698	−0.943490
$401$	−15.4514	−0.771607	−0.385803	−	0.922581i	$-0.626076\pi$
$401$	−15.4514	−0.771607	−0.385803	+	0.922581i	$0.626076\pi$
$402$	63.6257	3.17336
$403$	52.0537	2.59298
$404$	9.64687	0.479950
$405$	−10.1702	−0.505362
$406$	7.67437	0.380873
$407$	20.0654	0.994604
$408$	−21.4685	−1.06285
$409$	−1.07424	−0.0531175	−0.0265588	−	0.999647i	$-0.508455\pi$
$409$	−1.07424	−0.0531175	−0.0265588	+	0.999647i	$0.508455\pi$
$410$	−36.3714	−1.79626
$411$	−24.5354	−1.21024
$412$	−10.2525	−0.505105
$413$	11.3029	0.556177
$414$	68.0228	3.34314
$415$	−32.7583	−1.60804
$416$	−30.5803	−1.49932
$417$	−48.4666	−2.37342
$418$	19.1220	0.935290
$419$	−14.9246	−0.729112	−0.364556	−	0.931181i	$-0.618779\pi$
$419$	−14.9246	−0.729112	−0.364556	+	0.931181i	$0.618779\pi$
$420$	−9.84429	−0.480352
$421$	−2.54679	−0.124123	−0.0620615	−	0.998072i	$-0.519768\pi$
$421$	−2.54679	−0.124123	−0.0620615	+	0.998072i	$0.519768\pi$
$422$	15.9750	0.777653
$423$	15.8997	0.773068
$424$	−8.66019	−0.420576
$425$	−21.8387	−1.05933
$426$	24.3947	1.18192
$427$	−8.68533	−0.420312
$428$	6.46608	0.312550
$429$	−23.7625	−1.14727
$430$	−43.9479	−2.11936
$431$	5.60938	0.270194	0.135097	−	0.990832i	$-0.456865\pi$
$431$	5.60938	0.270194	0.135097	+	0.990832i	$0.456865\pi$
$432$	−17.3392	−0.834232
$433$	−29.5321	−1.41922	−0.709610	−	0.704594i	$-0.751129\pi$
$433$	−29.5321	−1.41922	−0.709610	+	0.704594i	$0.751129\pi$
$434$	−18.6974	−0.897502
$435$	34.2577	1.64253
$436$	23.2259	1.11232
$437$	53.3243	2.55085
$438$	−23.3537	−1.11588
$439$	−27.1295	−1.29482	−0.647411	−	0.762141i	$-0.724148\pi$
$439$	−27.1295	−1.29482	−0.647411	+	0.762141i	$0.724148\pi$
$440$	7.24596	0.345437
$441$	4.29718	0.204628
$442$	−51.4578	−2.44760
$443$	38.5252	1.83039	0.915193	−	0.403016i	$-0.132038\pi$
$443$	38.5252	1.83039	0.915193	+	0.403016i	$0.132038\pi$
$444$	37.8312	1.79539
$445$	0.534469	0.0253363
$446$	4.36585	0.206729
$447$	−7.34653	−0.347479
$448$	1.08780	0.0513938
$449$	34.8656	1.64541	0.822706	−	0.568468i	$-0.192464\pi$
$449$	34.8656	1.64541	0.822706	+	0.568468i	$0.192464\pi$
$450$	−29.4399	−1.38781
$451$	11.9939	0.564771
$452$	−18.4519	−0.867905
$453$	−65.1612	−3.06154
$454$	38.2183	1.79367
$455$	14.8484	0.696104
$456$	−22.6873	−1.06243
$457$	20.4513	0.956672	0.478336	−	0.878177i	$-0.341240\pi$
$457$	20.4513	0.956672	0.478336	+	0.878177i	$0.341240\pi$
$458$	11.7771	0.550308
$459$	−20.0673	−0.936659
$460$	−32.1101	−1.49714
$461$	−34.0187	−1.58441	−0.792203	−	0.610257i	$-0.791066\pi$
$461$	−34.0187	−1.58441	−0.792203	+	0.610257i	$0.791066\pi$
$462$	8.53535	0.397100
$463$	9.40425	0.437053	0.218526	−	0.975831i	$-0.429875\pi$
$463$	9.40425	0.437053	0.218526	+	0.975831i	$0.429875\pi$
$464$	−21.1377	−0.981291
$465$	−83.4633	−3.87052
$466$	29.8087	1.38086
$467$	36.9410	1.70943	0.854714	−	0.519100i	$-0.173733\pi$
$467$	36.9410	1.70943	0.854714	+	0.519100i	$0.173733\pi$
$468$	−26.3830	−1.21956
$469$	13.1105	0.605387
$470$	−19.7339	−0.910256
$471$	−22.7167	−1.04673
$472$	−15.6857	−0.721991
$473$	14.4923	0.666359
$474$	21.2540	0.976226
$475$	−23.0785	−1.05892
$476$	7.02979	0.322210
$477$	−26.8162	−1.22783
$478$	43.3829	1.98429
$479$	−1.29551	−0.0591935	−0.0295968	−	0.999562i	$-0.509422\pi$
$479$	−1.29551	−0.0591935	−0.0295968	+	0.999562i	$0.509422\pi$
$480$	49.0327	2.23803
$481$	−57.0618	−2.60180
$482$	−29.5649	−1.34664
$483$	23.8019	1.08303
$484$	−9.70579	−0.441172
$485$	9.49271	0.431042
$486$	35.5112	1.61082
$487$	15.4103	0.698309	0.349154	−	0.937065i	$-0.386469\pi$
$487$	15.4103	0.698309	0.349154	+	0.937065i	$0.386469\pi$
$488$	12.0532	0.545621
$489$	44.8335	2.02744
$490$	−5.33345	−0.240941
$491$	−7.41214	−0.334505	−0.167253	−	0.985914i	$-0.553490\pi$
$491$	−7.41214	−0.334505	−0.167253	+	0.985914i	$0.553490\pi$
$492$	22.6133	1.01949
$493$	−24.4634	−1.10177
$494$	−54.3792	−2.44664
$495$	22.4370	1.00847
$496$	51.4985	2.31235
$497$	5.02668	0.225478
$498$	53.5502	2.39964
$499$	6.39007	0.286059	0.143029	−	0.989718i	$-0.454316\pi$
$499$	6.39007	0.286059	0.143029	+	0.989718i	$0.454316\pi$
$500$	−4.32408	−0.193379
$501$	−14.0187	−0.626309
$502$	−16.0978	−0.718481
$503$	25.9591	1.15746	0.578730	−	0.815519i	$-0.303548\pi$
$503$	25.9591	1.15746	0.578730	+	0.815519i	$0.303548\pi$
$504$	−5.96346	−0.265634
$505$	23.3306	1.03820
$506$	27.8406	1.23767
$507$	32.4585	1.44153
$508$	2.17328	0.0964238
$509$	29.6820	1.31563	0.657816	−	0.753178i	$-0.271480\pi$
$509$	29.6820	1.31563	0.657816	+	0.753178i	$0.271480\pi$
$510$	82.5078	3.65350
$511$	−4.81218	−0.212878
$512$	−16.5202	−0.730098
$513$	−21.2065	−0.936291
$514$	−34.4709	−1.52045
$515$	−24.7953	−1.09261
$516$	27.3238	1.20286
$517$	6.50747	0.286198
$518$	20.4962	0.900553
$519$	39.3336	1.72655
$520$	−20.6060	−0.903634
$521$	−34.5098	−1.51190	−0.755951	−	0.654628i	$-0.772825\pi$
$521$	−34.5098	−1.51190	−0.755951	+	0.654628i	$0.772825\pi$
$522$	−32.9782	−1.44342
$523$	28.7489	1.25710	0.628551	−	0.777768i	$-0.283648\pi$
$523$	28.7489	1.25710	0.628551	+	0.777768i	$0.283648\pi$
$524$	−0.544582	−0.0237902
$525$	−10.3014	−0.449589
$526$	−32.8514	−1.43239
$527$	59.6010	2.59626
$528$	−23.5091	−1.02310
$529$	54.6372	2.37553
$530$	33.2829	1.44572
$531$	−48.5705	−2.10778
$532$	7.42890	0.322083
$533$	−34.1082	−1.47739
$534$	−0.873701	−0.0378087
$535$	15.6380	0.676088
$536$	−18.1942	−0.785872
$537$	42.7363	1.84421
$538$	41.9730	1.80958
$539$	1.75877	0.0757555
$540$	12.7698	0.549527
$541$	−2.68637	−0.115496	−0.0577480	−	0.998331i	$-0.518392\pi$
$541$	−2.68637	−0.115496	−0.0577480	+	0.998331i	$0.518392\pi$
$542$	13.8568	0.595198
$543$	24.0394	1.03163
$544$	−35.0142	−1.50122
$545$	56.1709	2.40610
$546$	−24.2728	−1.03878
$547$	−0.183072	−0.00782759	−0.00391380	−	0.999992i	$-0.501246\pi$
$547$	−0.183072	−0.00782759	−0.00391380	+	0.999992i	$0.501246\pi$
$548$	−11.1493	−0.476276
$549$	37.3224	1.59288
$550$	−12.0493	−0.513783
$551$	−25.8522	−1.10134
$552$	−33.0314	−1.40591
$553$	4.37952	0.186236
$554$	−14.8566	−0.631195
$555$	91.4933	3.88368
$556$	−22.0241	−0.934031
$557$	−25.0484	−1.06133	−0.530667	−	0.847580i	$-0.678059\pi$
$557$	−25.0484	−1.06133	−0.530667	+	0.847580i	$0.678059\pi$
$558$	80.3460	3.40132
$559$	−41.2133	−1.74314
$560$	14.6900	0.620767
$561$	−27.2079	−1.14872
$562$	12.1682	0.513286
$563$	33.8198	1.42533	0.712667	−	0.701503i	$-0.247487\pi$
$563$	33.8198	1.42533	0.712667	+	0.701503i	$0.247487\pi$
$564$	12.2692	0.516625
$565$	−44.6252	−1.87740
$566$	−0.908017	−0.0381668
$567$	3.42576	0.143869
$568$	−6.97583	−0.292699
$569$	32.5140	1.36306	0.681529	−	0.731791i	$-0.261315\pi$
$569$	32.5140	1.36306	0.681529	+	0.731791i	$0.261315\pi$
$570$	87.1920	3.65207
$571$	−21.8738	−0.915392	−0.457696	−	0.889109i	$-0.651325\pi$
$571$	−21.8738	−0.915392	−0.457696	+	0.889109i	$0.651325\pi$
$572$	−10.7981	−0.451493
$573$	−51.9829	−2.17162
$574$	12.2515	0.511366
$575$	−33.6010	−1.40126
$576$	−4.67449	−0.194770
$577$	−12.5778	−0.523620	−0.261810	−	0.965119i	$-0.584319\pi$
$577$	−12.5778	−0.523620	−0.261810	+	0.965119i	$0.584319\pi$
$578$	−28.3776	−1.18035
$579$	62.5318	2.59873
$580$	15.5673	0.646398
$581$	11.0344	0.457783
$582$	−15.5178	−0.643234
$583$	−10.9754	−0.454556
$584$	6.67815	0.276344
$585$	−63.8063	−2.63807
$586$	15.7477	0.650532
$587$	11.5101	0.475072	0.237536	−	0.971379i	$-0.423660\pi$
$587$	11.5101	0.475072	0.237536	+	0.971379i	$0.423660\pi$
$588$	3.31598	0.136749
$589$	62.9848	2.59524
$590$	60.2832	2.48182
$591$	26.0456	1.07137
$592$	−56.4532	−2.32021
$593$	5.98681	0.245849	0.122924	−	0.992416i	$-0.460773\pi$
$593$	5.98681	0.245849	0.122924	+	0.992416i	$0.460773\pi$
$594$	−11.0719	−0.454286
$595$	17.0013	0.696985
$596$	−3.33840	−0.136746
$597$	−24.4335	−0.999995
$598$	−79.1730	−3.23762
$599$	6.71377	0.274317	0.137159	−	0.990549i	$-0.456203\pi$
$599$	6.71377	0.274317	0.137159	+	0.990549i	$0.456203\pi$
$600$	14.2958	0.583625
$601$	9.95878	0.406227	0.203114	−	0.979155i	$-0.434894\pi$
$601$	9.95878	0.406227	0.203114	+	0.979155i	$0.434894\pi$
$602$	14.8035	0.603347
$603$	−56.3383	−2.29427
$604$	−29.6105	−1.20483
$605$	−23.4731	−0.954317
$606$	−38.1387	−1.54928
$607$	1.92759	0.0782385	0.0391193	−	0.999235i	$-0.487545\pi$
$607$	1.92759	0.0782385	0.0391193	+	0.999235i	$0.487545\pi$
$608$	−37.0021	−1.50063
$609$	−11.5394	−0.467602
$610$	−46.3228	−1.87555
$611$	−18.5059	−0.748670
$612$	−30.2083	−1.22110
$613$	−5.58197	−0.225454	−0.112727	−	0.993626i	$-0.535958\pi$
$613$	−5.58197	−0.225454	−0.112727	+	0.993626i	$0.535958\pi$
$614$	10.8675	0.438575
$615$	54.6893	2.20529
$616$	−2.44075	−0.0983405
$617$	−9.31914	−0.375174	−0.187587	−	0.982248i	$-0.560067\pi$
$617$	−9.31914	−0.375174	−0.187587	+	0.982248i	$0.560067\pi$
$618$	40.5331	1.63048
$619$	38.0679	1.53008	0.765039	−	0.643984i	$-0.222720\pi$
$619$	38.0679	1.53008	0.765039	+	0.643984i	$0.222720\pi$
$620$	−37.9273	−1.52320
$621$	−30.8755	−1.23899
$622$	−2.51027	−0.100653
$623$	−0.180032	−0.00721283
$624$	66.8550	2.67634
$625$	−29.5249	−1.18099
$626$	−42.4951	−1.69845
$627$	−28.7526	−1.14827
$628$	−10.3229	−0.411928
$629$	−65.3353	−2.60509
$630$	22.9188	0.913108
$631$	6.61285	0.263253	0.131627	−	0.991299i	$-0.457980\pi$
$631$	6.61285	0.263253	0.131627	+	0.991299i	$0.457980\pi$
$632$	−6.07773	−0.241759
$633$	−24.0206	−0.954734
$634$	−8.91954	−0.354240
$635$	5.25600	0.208578
$636$	−20.6930	−0.820532
$637$	−5.00158	−0.198170
$638$	−13.4974	−0.534368
$639$	−21.6006	−0.854506
$640$	−30.5009	−1.20565
$641$	15.2700	0.603130	0.301565	−	0.953446i	$-0.402491\pi$
$641$	15.2700	0.603130	0.301565	+	0.953446i	$0.402491\pi$
$642$	−25.5635	−1.00891
$643$	−27.1075	−1.06902	−0.534509	−	0.845163i	$-0.679503\pi$
$643$	−27.1075	−1.06902	−0.534509	+	0.845163i	$0.679503\pi$
$644$	10.8160	0.426212
$645$	66.0816	2.60196
$646$	−62.2637	−2.44973
$647$	−11.8407	−0.465506	−0.232753	−	0.972536i	$-0.574773\pi$
$647$	−11.8407	−0.465506	−0.232753	+	0.972536i	$0.574773\pi$
$648$	−4.75414	−0.186760
$649$	−19.8791	−0.780323
$650$	34.2657	1.34401
$651$	28.1140	1.10187
$652$	20.3732	0.797875
$653$	6.12108	0.239536	0.119768	−	0.992802i	$-0.461785\pi$
$653$	6.12108	0.239536	0.119768	+	0.992802i	$0.461785\pi$
$654$	−91.8231	−3.59057
$655$	−1.31705	−0.0514615
$656$	−33.7444	−1.31750
$657$	20.6788	0.806757
$658$	6.64721	0.259135
$659$	24.7456	0.963953	0.481976	−	0.876184i	$-0.339919\pi$
$659$	24.7456	0.963953	0.481976	+	0.876184i	$0.339919\pi$
$660$	17.3138	0.673939
$661$	−25.7337	−1.00093	−0.500463	−	0.865758i	$-0.666837\pi$
$661$	−25.7337	−1.00093	−0.500463	+	0.865758i	$0.666837\pi$
$662$	18.3080	0.711559
$663$	77.3737	3.00494
$664$	−15.3131	−0.594263
$665$	17.9665	0.696711
$666$	−88.0761	−3.41288
$667$	−37.6394	−1.45740
$668$	−6.37035	−0.246476
$669$	−6.56464	−0.253804
$670$	69.9242	2.70141
$671$	15.2755	0.589703
$672$	−16.5163	−0.637130
$673$	47.2637	1.82188	0.910940	−	0.412538i	$-0.135358\pi$
$673$	47.2637	1.82188	0.910940	+	0.412538i	$0.135358\pi$
$674$	40.5514	1.56198
$675$	13.3628	0.514334
$676$	14.7498	0.567298
$677$	−48.4445	−1.86187	−0.930936	−	0.365182i	$-0.881007\pi$
$677$	−48.4445	−1.86187	−0.930936	+	0.365182i	$0.881007\pi$
$678$	72.9492	2.80160
$679$	−3.19755	−0.122711
$680$	−23.5937	−0.904777
$681$	−57.4663	−2.20211
$682$	32.8843	1.25921
$683$	−22.5828	−0.864105	−0.432053	−	0.901848i	$-0.642211\pi$
$683$	−22.5828	−0.864105	−0.432053	+	0.901848i	$0.642211\pi$
$684$	−31.9233	−1.22062
$685$	−26.9642	−1.03025
$686$	1.79653	0.0685920
$687$	−17.7085	−0.675620
$688$	−40.7737	−1.55448
$689$	31.2119	1.18908
$690$	126.947	4.83277
$691$	24.6750	0.938682	0.469341	−	0.883017i	$-0.344492\pi$
$691$	24.6750	0.938682	0.469341	+	0.883017i	$0.344492\pi$
$692$	17.8739	0.679465
$693$	−7.55774	−0.287095
$694$	11.6145	0.440882
$695$	−53.2645	−2.02044
$696$	16.0140	0.607009
$697$	−39.0536	−1.47926
$698$	30.3431	1.14850
$699$	−44.8214	−1.69530
$700$	−4.68114	−0.176930
$701$	43.1293	1.62897	0.814486	−	0.580184i	$-0.197019\pi$
$701$	43.1293	1.62897	0.814486	+	0.580184i	$0.197019\pi$
$702$	31.4863	1.18837
$703$	−69.0446	−2.60406
$704$	−1.91319	−0.0721061
$705$	29.6725	1.11753
$706$	−9.44852	−0.355600
$707$	−7.85873	−0.295558
$708$	−37.4800	−1.40858
$709$	−13.2677	−0.498279	−0.249140	−	0.968468i	$-0.580148\pi$
$709$	−13.2677	−0.498279	−0.249140	+	0.968468i	$0.580148\pi$
$710$	26.8096	1.00615
$711$	−18.8196	−0.705790
$712$	0.249841	0.00936320
$713$	91.7022	3.43428
$714$	−27.7921	−1.04009
$715$	−26.1149	−0.976641
$716$	19.4202	0.725766
$717$	−65.2319	−2.43613
$718$	−59.6311	−2.22541
$719$	−0.821993	−0.0306552	−0.0153276	−	0.999883i	$-0.504879\pi$
$719$	−0.821993	−0.0306552	−0.0153276	+	0.999883i	$0.504879\pi$
$720$	−63.1257	−2.35256
$721$	8.35211	0.311049
$722$	−31.6644	−1.17843
$723$	44.4548	1.65329
$724$	10.9240	0.405986
$725$	16.2901	0.605001
$726$	38.3716	1.42411
$727$	10.5376	0.390817	0.195409	−	0.980722i	$-0.437397\pi$
$727$	10.5376	0.390817	0.195409	+	0.980722i	$0.437397\pi$
$728$	6.94099	0.257250
$729$	−43.1185	−1.59698
$730$	−25.6655	−0.949924
$731$	−47.1888	−1.74534
$732$	28.8003	1.06449
$733$	2.19865	0.0812091	0.0406046	−	0.999175i	$-0.487072\pi$
$733$	2.19865	0.0812091	0.0406046	+	0.999175i	$0.487072\pi$
$734$	8.17729	0.301829
$735$	8.01956	0.295806
$736$	−53.8729	−1.98578
$737$	−23.0583	−0.849364
$738$	−52.6467	−1.93795
$739$	23.2207	0.854189	0.427094	−	0.904207i	$-0.359537\pi$
$739$	23.2207	0.854189	0.427094	+	0.904207i	$0.359537\pi$
$740$	41.5763	1.52837
$741$	81.7664	3.00376
$742$	−11.2111	−0.411573
$743$	−3.15925	−0.115902	−0.0579508	−	0.998319i	$-0.518457\pi$
$743$	−3.15925	−0.115902	−0.0579508	+	0.998319i	$0.518457\pi$
$744$	−39.0155	−1.43038
$745$	−8.07379	−0.295801
$746$	−58.1589	−2.12935
$747$	−47.4168	−1.73489
$748$	−12.3638	−0.452064
$749$	−5.26753	−0.192471
$750$	17.0952	0.624227
$751$	−26.7456	−0.975962	−0.487981	−	0.872854i	$-0.662266\pi$
$751$	−26.7456	−0.975962	−0.487981	+	0.872854i	$0.662266\pi$
$752$	−18.3085	−0.667644
$753$	24.2052	0.882087
$754$	38.3839	1.39786
$755$	−71.6118	−2.60622
$756$	−4.30143	−0.156441
$757$	−49.4122	−1.79592	−0.897959	−	0.440079i	$-0.854950\pi$
$757$	−49.4122	−1.79592	−0.897959	+	0.440079i	$0.854950\pi$
$758$	31.1113	1.13001
$759$	−41.8621	−1.51950
$760$	−24.9332	−0.904422
$761$	9.83302	0.356447	0.178223	−	0.983990i	$-0.442965\pi$
$761$	9.83302	0.356447	0.178223	+	0.983990i	$0.442965\pi$
$762$	−8.59202	−0.311256
$763$	−18.9208	−0.684978
$764$	−23.6220	−0.854614
$765$	−73.0576	−2.64140
$766$	−15.9571	−0.576555
$767$	56.5321	2.04126
$768$	55.7371	2.01124
$769$	−4.35797	−0.157152	−0.0785762	−	0.996908i	$-0.525037\pi$
$769$	−4.35797	−0.157152	−0.0785762	+	0.996908i	$0.525037\pi$
$770$	9.38030	0.338042
$771$	51.8316	1.86667
$772$	28.4156	1.02270
$773$	−11.2675	−0.405263	−0.202632	−	0.979255i	$-0.564949\pi$
$773$	−11.2675	−0.405263	−0.202632	+	0.979255i	$0.564949\pi$
$774$	−63.6135	−2.28654
$775$	−39.6883	−1.42565
$776$	4.43743	0.159295
$777$	−30.8189	−1.10562
$778$	17.8851	0.641213
$779$	−41.2708	−1.47868
$780$	−49.2369	−1.76297
$781$	−8.84076	−0.316347
$782$	−90.6523	−3.24172
$783$	14.9688	0.534941
$784$	−4.94823	−0.176722
$785$	−24.9655	−0.891057
$786$	2.15299	0.0767948
$787$	39.1392	1.39516	0.697581	−	0.716506i	$-0.254260\pi$
$787$	39.1392	1.39516	0.697581	+	0.716506i	$0.254260\pi$
$788$	11.8356	0.421626
$789$	49.3965	1.75856
$790$	23.3580	0.831039
$791$	15.0317	0.534465
$792$	10.4883	0.372687
$793$	−43.4403	−1.54261
$794$	36.8724	1.30855
$795$	−50.0453	−1.77492
$796$	−11.1030	−0.393536
$797$	9.31130	0.329823	0.164912	−	0.986308i	$-0.447266\pi$
$797$	9.31130	0.329823	0.164912	+	0.986308i	$0.447266\pi$
$798$	−29.3700	−1.03969
$799$	−21.1891	−0.749617
$800$	23.3159	0.824343
$801$	0.773630	0.0273349
$802$	27.7590	0.980204
$803$	8.46350	0.298670
$804$	−43.4741	−1.53321
$805$	26.1582	0.921955
$806$	−93.5163	−3.29397
$807$	−63.1120	−2.22165
$808$	10.9060	0.383673
$809$	−7.26121	−0.255290	−0.127645	−	0.991820i	$-0.540742\pi$
$809$	−7.26121	−0.255290	−0.127645	+	0.991820i	$0.540742\pi$
$810$	18.2711	0.641983
$811$	1.03116	0.0362088	0.0181044	−	0.999836i	$-0.494237\pi$
$811$	1.03116	0.0362088	0.0181044	+	0.999836i	$0.494237\pi$
$812$	−5.24374	−0.184019
$813$	−20.8355	−0.730732
$814$	−36.0481	−1.26349
$815$	49.2717	1.72591
$816$	76.5484	2.67973
$817$	−49.8679	−1.74466
$818$	1.92990	0.0674774
$819$	21.4927	0.751015
$820$	24.8519	0.867864
$821$	−17.0862	−0.596313	−0.298156	−	0.954517i	$-0.596372\pi$
$821$	−17.0862	−0.596313	−0.298156	+	0.954517i	$0.596372\pi$
$822$	44.0786	1.53742
$823$	−34.9793	−1.21930	−0.609652	−	0.792670i	$-0.708691\pi$
$823$	−34.9793	−1.21930	−0.609652	+	0.792670i	$0.708691\pi$
$824$	−11.5907	−0.403782
$825$	18.1177	0.630778
$826$	−20.3060	−0.706535
$827$	12.8007	0.445123	0.222561	−	0.974919i	$-0.428558\pi$
$827$	12.8007	0.445123	0.222561	+	0.974919i	$0.428558\pi$
$828$	−46.4785	−1.61524
$829$	18.2000	0.632113	0.316057	−	0.948740i	$-0.397641\pi$
$829$	18.2000	0.632113	0.316057	+	0.948740i	$0.397641\pi$
$830$	58.8513	2.04276
$831$	22.3388	0.774925
$832$	5.44073	0.188623
$833$	−5.72676	−0.198420
$834$	87.0719	3.01505
$835$	−15.4064	−0.533162
$836$	−13.0657	−0.451887
$837$	−36.4690	−1.26055
$838$	26.8125	0.926221
$839$	−24.1724	−0.834523	−0.417262	−	0.908786i	$-0.637010\pi$
$839$	−24.1724	−0.834523	−0.417262	+	0.908786i	$0.637010\pi$
$840$	−11.1292	−0.383995
$841$	−10.7520	−0.370760
$842$	4.57540	0.157679
$843$	−18.2966	−0.630167
$844$	−10.9154	−0.375724
$845$	35.6717	1.22714
$846$	−28.5643	−0.982060
$847$	7.90674	0.271679
$848$	30.8790	1.06039
$849$	1.36532	0.0468578
$850$	39.2339	1.34571
$851$	−100.525	−3.44595
$852$	−16.6684	−0.571049
$853$	41.3577	1.41606	0.708030	−	0.706182i	$-0.249584\pi$
$853$	41.3577	1.41606	0.708030	+	0.706182i	$0.249584\pi$
$854$	15.6035	0.533940
$855$	−77.2053	−2.64037
$856$	7.31007	0.249853
$857$	−0.593945	−0.0202888	−0.0101444	−	0.999949i	$-0.503229\pi$
$857$	−0.593945	−0.0202888	−0.0101444	+	0.999949i	$0.503229\pi$
$858$	42.6902	1.45742
$859$	43.7258	1.49191	0.745953	−	0.665999i	$-0.231994\pi$
$859$	43.7258	1.49191	0.745953	+	0.665999i	$0.231994\pi$
$860$	30.0287	1.02397
$861$	−18.4217	−0.627810
$862$	−10.0774	−0.343239
$863$	−1.00000	−0.0340404
$863$	−1.00000	−0.0340404
$864$	21.4247	0.728883
$865$	43.2274	1.46978
$866$	53.0554	1.80289
$867$	42.6695	1.44913
$868$	12.7755	0.433630
$869$	−7.70256	−0.261291
$870$	−61.5451	−2.08657
$871$	65.5732	2.22186
$872$	26.2575	0.889191
$873$	13.7405	0.465044
$874$	−95.7990	−3.24045
$875$	3.52257	0.119085
$876$	15.9571	0.539139
$877$	36.3103	1.22611	0.613056	−	0.790039i	$-0.289940\pi$
$877$	36.3103	1.22611	0.613056	+	0.790039i	$0.289940\pi$
$878$	48.7391	1.64487
$879$	−23.6788	−0.798666
$880$	−25.8363	−0.870943
$881$	38.0618	1.28233	0.641167	−	0.767402i	$-0.278451\pi$
$881$	38.0618	1.28233	0.641167	+	0.767402i	$0.278451\pi$
$882$	−7.72004	−0.259947
$883$	37.0453	1.24667	0.623337	−	0.781953i	$-0.285777\pi$
$883$	37.0453	1.24667	0.623337	+	0.781953i	$0.285777\pi$
$884$	35.1600	1.18256
$885$	−90.6440	−3.04696
$886$	−69.2118	−2.32521
$887$	−2.28499	−0.0767225	−0.0383613	−	0.999264i	$-0.512214\pi$
$887$	−2.28499	−0.0767225	−0.0383613	+	0.999264i	$0.512214\pi$
$888$	42.7692	1.43524
$889$	−1.77044	−0.0593788
$890$	−0.960192	−0.0321857
$891$	−6.02512	−0.201849
$892$	−2.98310	−0.0998815
$893$	−22.3921	−0.749323
$894$	13.1983	0.441417
$895$	46.9669	1.56993
$896$	10.2740	0.343230
$897$	119.047	3.97487
$898$	−62.6373	−2.09023
$899$	−44.4582	−1.48277
$900$	20.1157	0.670524
$901$	35.7373	1.19058
$902$	−21.5475	−0.717452
$903$	−22.2591	−0.740737
$904$	−20.8604	−0.693806
$905$	26.4192	0.878203
$906$	117.064	3.88920
$907$	−43.5750	−1.44689	−0.723443	−	0.690384i	$-0.757441\pi$
$907$	−43.5750	−1.44689	−0.723443	+	0.690384i	$0.757441\pi$
$908$	−26.1138	−0.866615
$909$	33.7704	1.12009
$910$	−26.6757	−0.884289
$911$	10.0166	0.331864	0.165932	−	0.986137i	$-0.446937\pi$
$911$	10.0166	0.331864	0.165932	+	0.986137i	$0.446937\pi$
$912$	80.8943	2.67868
$913$	−19.4069	−0.642275
$914$	−36.7415	−1.21530
$915$	69.6525	2.30264
$916$	−8.04705	−0.265882
$917$	0.443639	0.0146503
$918$	36.0515	1.18988
$919$	12.0052	0.396014	0.198007	−	0.980201i	$-0.436553\pi$
$919$	12.0052	0.396014	0.198007	+	0.980201i	$0.436553\pi$
$920$	−36.3013	−1.19682
$921$	−16.3407	−0.538443
$922$	61.1157	2.01274
$923$	25.1413	0.827537
$924$	−5.83203	−0.191860
$925$	43.5067	1.43049
$926$	−16.8951	−0.555206
$927$	−35.8906	−1.17880
$928$	26.1182	0.857371
$929$	−35.4126	−1.16185	−0.580925	−	0.813957i	$-0.697309\pi$
$929$	−35.4126	−1.16185	−0.580925	+	0.813957i	$0.697309\pi$
$930$	149.945	4.91688
$931$	−6.05188	−0.198342
$932$	−20.3677	−0.667165
$933$	3.77452	0.123572
$934$	−66.3658	−2.17156
$935$	−29.9013	−0.977877
$936$	−29.8267	−0.974916
$937$	−28.5095	−0.931364	−0.465682	−	0.884952i	$-0.654191\pi$
$937$	−28.5095	−0.931364	−0.465682	+	0.884952i	$0.654191\pi$
$938$	−23.5535	−0.769048
$939$	63.8971	2.08520
$940$	13.4837	0.439791
$941$	27.5661	0.898628	0.449314	−	0.893374i	$-0.351668\pi$
$941$	27.5661	0.898628	0.449314	+	0.893374i	$0.351668\pi$
$942$	40.8113	1.32970
$943$	−60.0879	−1.95673
$944$	55.9291	1.82034
$945$	−10.4028	−0.338404
$946$	−26.0360	−0.846503
$947$	7.65791	0.248849	0.124424	−	0.992229i	$-0.460292\pi$
$947$	7.65791	0.248849	0.124424	+	0.992229i	$0.460292\pi$
$948$	−14.5224	−0.471665
$949$	−24.0685	−0.781296
$950$	41.4614	1.34518
$951$	13.4117	0.434905
$952$	7.94737	0.257576
$953$	20.6843	0.670029	0.335014	−	0.942213i	$-0.391259\pi$
$953$	20.6843	0.670029	0.335014	+	0.942213i	$0.391259\pi$
$954$	48.1762	1.55976
$955$	−57.1289	−1.84865
$956$	−29.6426	−0.958710
$957$	20.2952	0.656051
$958$	2.32743	0.0751960
$959$	9.08270	0.293296
$960$	−8.72370	−0.281556
$961$	77.3154	2.49404
$962$	102.514	3.30517
$963$	22.6355	0.729420
$964$	20.2011	0.650632
$965$	68.7221	2.21224
$966$	−42.7610	−1.37581
$967$	−56.0542	−1.80258	−0.901290	−	0.433216i	$-0.857379\pi$
$967$	−56.0542	−1.80258	−0.901290	+	0.433216i	$0.857379\pi$
$968$	−10.9727	−0.352675
$969$	93.6218	3.00757
$970$	−17.0540	−0.547570
$971$	16.2605	0.521825	0.260912	−	0.965362i	$-0.415977\pi$
$971$	16.2605	0.521825	0.260912	+	0.965362i	$0.415977\pi$
$972$	−24.2640	−0.778269
$973$	17.9418	0.575187
$974$	−27.6852	−0.887090
$975$	−51.5231	−1.65006
$976$	−42.9770	−1.37566
$977$	31.1530	0.996672	0.498336	−	0.866984i	$-0.333945\pi$
$977$	31.1530	0.996672	0.498336	+	0.866984i	$0.333945\pi$
$978$	−80.5449	−2.57554
$979$	0.316634	0.0101197
$980$	3.64424	0.116411
$981$	81.3060	2.59590
$982$	13.3162	0.424936
$983$	19.0743	0.608376	0.304188	−	0.952612i	$-0.401615\pi$
$983$	19.0743	0.608376	0.304188	+	0.952612i	$0.401615\pi$
$984$	25.5649	0.814980
$985$	28.6239	0.912034
$986$	43.9493	1.39963
$987$	−9.99497	−0.318144
$988$	37.1562	1.18210
$989$	−72.6048	−2.30870
$990$	−40.3089	−1.28110
$991$	9.01213	0.286280	0.143140	−	0.989702i	$-0.454280\pi$
$991$	9.01213	0.286280	0.143140	+	0.989702i	$0.454280\pi$
$992$	−63.6327	−2.02034
$993$	−27.5285	−0.873590
$994$	−9.03061	−0.286433
$995$	−26.8522	−0.851273
$996$	−36.5897	−1.15939
$997$	−40.7245	−1.28976	−0.644879	−	0.764284i	$-0.723092\pi$
$997$	−40.7245	−1.28976	−0.644879	+	0.764284i	$0.723092\pi$
$998$	−11.4800	−0.363392
$999$	39.9777	1.26484

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.d.1.20	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.d.1.20	✓	101	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-1.79653 q^{2} +2.70133 q^{3} +1.22753 q^{4} +2.96874 q^{5} -4.85303 q^{6} -1.00000 q^{7} +1.38776 q^{8} +4.29718 q^{9} +O(q^{10})\)	\(q-1.79653 q^{2} +2.70133 q^{3} +1.22753 q^{4} +2.96874 q^{5} -4.85303 q^{6} -1.00000 q^{7} +1.38776 q^{8} +4.29718 q^{9} -5.33345 q^{10} +1.75877 q^{11} +3.31598 q^{12} -5.00158 q^{13} +1.79653 q^{14} +8.01956 q^{15} -4.94823 q^{16} -5.72676 q^{17} -7.72004 q^{18} -6.05188 q^{19} +3.64424 q^{20} -2.70133 q^{21} -3.15968 q^{22} -8.81120 q^{23} +3.74880 q^{24} +3.81345 q^{25} +8.98550 q^{26} +3.50412 q^{27} -1.22753 q^{28} +4.27176 q^{29} -14.4074 q^{30} -10.4075 q^{31} +6.11414 q^{32} +4.75101 q^{33} +10.2883 q^{34} -2.96874 q^{35} +5.27494 q^{36} +11.4088 q^{37} +10.8724 q^{38} -13.5109 q^{39} +4.11991 q^{40} +6.81949 q^{41} +4.85303 q^{42} +8.24006 q^{43} +2.15895 q^{44} +12.7572 q^{45} +15.8296 q^{46} +3.70002 q^{47} -13.3668 q^{48} +1.00000 q^{49} -6.85099 q^{50} -15.4699 q^{51} -6.13961 q^{52} -6.24041 q^{53} -6.29527 q^{54} +5.22133 q^{55} -1.38776 q^{56} -16.3481 q^{57} -7.67437 q^{58} -11.3029 q^{59} +9.84429 q^{60} +8.68533 q^{61} +18.6974 q^{62} -4.29718 q^{63} -1.08780 q^{64} -14.8484 q^{65} -8.53535 q^{66} -13.1105 q^{67} -7.02979 q^{68} -23.8019 q^{69} +5.33345 q^{70} -5.02668 q^{71} +5.96346 q^{72} +4.81218 q^{73} -20.4962 q^{74} +10.3014 q^{75} -7.42890 q^{76} -1.75877 q^{77} +24.2728 q^{78} -4.37952 q^{79} -14.6900 q^{80} -3.42576 q^{81} -12.2515 q^{82} -11.0344 q^{83} -3.31598 q^{84} -17.0013 q^{85} -14.8035 q^{86} +11.5394 q^{87} +2.44075 q^{88} +0.180032 q^{89} -22.9188 q^{90} +5.00158 q^{91} -10.8160 q^{92} -28.1140 q^{93} -6.64721 q^{94} -17.9665 q^{95} +16.5163 q^{96} +3.19755 q^{97} -1.79653 q^{98} +7.55774 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9}+O(q^{10}) \) 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9	\( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9} - 23 q^{10} - 13 q^{11} - 31 q^{12} - 35 q^{13} - 3 q^{14} - 20 q^{15} + 45 q^{16} - 19 q^{17} + 3 q^{18} - 59 q^{19} - 31 q^{20} + 17 q^{21} - 13 q^{22} - 29 q^{23} - 59 q^{24} + 103 q^{25} - 18 q^{26} - 47 q^{27} - 85 q^{28} - 26 q^{29} - 8 q^{30} - 125 q^{31} + 12 q^{32} - 18 q^{33} - 66 q^{34} + 12 q^{35} + 40 q^{36} + 22 q^{37} - 31 q^{38} - 94 q^{39} - 79 q^{40} - 39 q^{41} + 17 q^{42} - 5 q^{43} - 53 q^{44} - 50 q^{45} - 37 q^{46} - 47 q^{47} - 81 q^{48} + 101 q^{49} + 2 q^{50} - 23 q^{51} - 56 q^{52} - 5 q^{53} - 77 q^{54} - 155 q^{55} + 3 q^{56} + 61 q^{57} - 31 q^{58} - 33 q^{59} - 48 q^{60} - 96 q^{61} - 38 q^{62} - 88 q^{63} - 33 q^{64} - 8 q^{65} - 91 q^{66} + 8 q^{67} - 41 q^{68} - 91 q^{69} + 23 q^{70} - 116 q^{71} - 5 q^{72} - 62 q^{73} - 23 q^{74} - 94 q^{75} - 112 q^{76} + 13 q^{77} + 17 q^{78} - 127 q^{79} - 87 q^{80} + 37 q^{81} - 118 q^{82} - 58 q^{83} + 31 q^{84} - 6 q^{85} - 26 q^{86} - 82 q^{87} - 40 q^{88} - 57 q^{89} - 123 q^{90} + 35 q^{91} - 28 q^{92} - 10 q^{93} - 107 q^{94} - 70 q^{95} - 76 q^{96} - 69 q^{97} + 3 q^{98} - 67 q^{99}+O(q^{100}) \) 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9 - 23 * q^10 - 13 * q^11 - 31 * q^12 - 35 * q^13 - 3 * q^14 - 20 * q^15 + 45 * q^16 - 19 * q^17 + 3 * q^18 - 59 * q^19 - 31 * q^20 + 17 * q^21 - 13 * q^22 - 29 * q^23 - 59 * q^24 + 103 * q^25 - 18 * q^26 - 47 * q^27 - 85 * q^28 - 26 * q^29 - 8 * q^30 - 125 * q^31 + 12 * q^32 - 18 * q^33 - 66 * q^34 + 12 * q^35 + 40 * q^36 + 22 * q^37 - 31 * q^38 - 94 * q^39 - 79 * q^40 - 39 * q^41 + 17 * q^42 - 5 * q^43 - 53 * q^44 - 50 * q^45 - 37 * q^46 - 47 * q^47 - 81 * q^48 + 101 * q^49 + 2 * q^50 - 23 * q^51 - 56 * q^52 - 5 * q^53 - 77 * q^54 - 155 * q^55 + 3 * q^56 + 61 * q^57 - 31 * q^58 - 33 * q^59 - 48 * q^60 - 96 * q^61 - 38 * q^62 - 88 * q^63 - 33 * q^64 - 8 * q^65 - 91 * q^66 + 8 * q^67 - 41 * q^68 - 91 * q^69 + 23 * q^70 - 116 * q^71 - 5 * q^72 - 62 * q^73 - 23 * q^74 - 94 * q^75 - 112 * q^76 + 13 * q^77 + 17 * q^78 - 127 * q^79 - 87 * q^80 + 37 * q^81 - 118 * q^82 - 58 * q^83 + 31 * q^84 - 6 * q^85 - 26 * q^86 - 82 * q^87 - 40 * q^88 - 57 * q^89 - 123 * q^90 + 35 * q^91 - 28 * q^92 - 10 * q^93 - 107 * q^94 - 70 * q^95 - 76 * q^96 - 69 * q^97 + 3 * q^98 - 67 * q^99

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