LMFDB - Embedded newform 6041.2.a.d.1.18

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			1.18
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)

$f(q)$	$=$	$q-1.87092 q^{2} -1.43026 q^{3} +1.50033 q^{4} +1.61115 q^{5} +2.67590 q^{6} -1.00000 q^{7} +0.934843 q^{8} -0.954356 q^{9} +O(q^{10})$	\(q-1.87092 q^{2} -1.43026 q^{3} +1.50033 q^{4} +1.61115 q^{5} +2.67590 q^{6} -1.00000 q^{7} +0.934843 q^{8} -0.954356 q^{9} -3.01432 q^{10} -4.14183 q^{11} -2.14586 q^{12} +3.26058 q^{13} +1.87092 q^{14} -2.30436 q^{15} -4.74967 q^{16} -5.11903 q^{17} +1.78552 q^{18} -2.47072 q^{19} +2.41725 q^{20} +1.43026 q^{21} +7.74901 q^{22} -0.510532 q^{23} -1.33707 q^{24} -2.40421 q^{25} -6.10028 q^{26} +5.65576 q^{27} -1.50033 q^{28} +3.51681 q^{29} +4.31126 q^{30} +6.20713 q^{31} +7.01655 q^{32} +5.92389 q^{33} +9.57727 q^{34} -1.61115 q^{35} -1.43185 q^{36} +6.30318 q^{37} +4.62252 q^{38} -4.66348 q^{39} +1.50617 q^{40} +7.10314 q^{41} -2.67590 q^{42} -2.62321 q^{43} -6.21410 q^{44} -1.53761 q^{45} +0.955162 q^{46} -1.55230 q^{47} +6.79326 q^{48} +1.00000 q^{49} +4.49807 q^{50} +7.32154 q^{51} +4.89195 q^{52} -2.17150 q^{53} -10.5815 q^{54} -6.67309 q^{55} -0.934843 q^{56} +3.53378 q^{57} -6.57966 q^{58} +12.6137 q^{59} -3.45730 q^{60} -2.80930 q^{61} -11.6130 q^{62} +0.954356 q^{63} -3.62804 q^{64} +5.25328 q^{65} -11.0831 q^{66} -13.8186 q^{67} -7.68022 q^{68} +0.730193 q^{69} +3.01432 q^{70} +8.25353 q^{71} -0.892173 q^{72} +6.75117 q^{73} -11.7927 q^{74} +3.43864 q^{75} -3.70690 q^{76} +4.14183 q^{77} +8.72498 q^{78} -9.12911 q^{79} -7.65242 q^{80} -5.22614 q^{81} -13.2894 q^{82} +8.97474 q^{83} +2.14586 q^{84} -8.24750 q^{85} +4.90780 q^{86} -5.02995 q^{87} -3.87196 q^{88} +0.367182 q^{89} +2.87674 q^{90} -3.26058 q^{91} -0.765965 q^{92} -8.87782 q^{93} +2.90422 q^{94} -3.98070 q^{95} -10.0355 q^{96} +3.50684 q^{97} -1.87092 q^{98} +3.95278 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.87092	−1.32294	−0.661469	−	0.749973i	$-0.730067\pi$
$2$	−1.87092	−1.32294	−0.661469	+	0.749973i	$0.730067\pi$
$3$	−1.43026	−0.825761	−0.412881	−	0.910785i	$-0.635477\pi$
$3$	−1.43026	−0.825761	−0.412881	+	0.910785i	$0.635477\pi$
$4$	1.50033	0.750164
$5$	1.61115	0.720527	0.360263	−	0.932851i	$-0.382687\pi$
$5$	1.61115	0.720527	0.360263	+	0.932851i	$0.382687\pi$
$6$	2.67590	1.09243
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.934843	0.330517
$9$	−0.954356	−0.318119
$10$	−3.01432	−0.953212
$11$	−4.14183	−1.24881	−0.624404	−	0.781102i	$-0.714658\pi$
$11$	−4.14183	−1.24881	−0.624404	+	0.781102i	$0.714658\pi$
$12$	−2.14586	−0.619457
$13$	3.26058	0.904323	0.452161	−	0.891936i	$-0.350653\pi$
$13$	3.26058	0.904323	0.452161	+	0.891936i	$0.350653\pi$
$14$	1.87092	0.500023
$15$	−2.30436	−0.594983
$16$	−4.74967	−1.18742
$17$	−5.11903	−1.24155	−0.620773	−	0.783990i	$-0.713181\pi$
$17$	−5.11903	−1.24155	−0.620773	+	0.783990i	$0.713181\pi$
$18$	1.78552	0.420851
$19$	−2.47072	−0.566823	−0.283411	−	0.958998i	$-0.591466\pi$
$19$	−2.47072	−0.566823	−0.283411	+	0.958998i	$0.591466\pi$
$20$	2.41725	0.540513
$21$	1.43026	0.312108
$22$	7.74901	1.65210
$23$	−0.510532	−0.106453	−0.0532266	−	0.998582i	$-0.516951\pi$
$23$	−0.510532	−0.106453	−0.0532266	+	0.998582i	$0.516951\pi$
$24$	−1.33707	−0.272928
$25$	−2.40421	−0.480841
$26$	−6.10028	−1.19636
$27$	5.65576	1.08845
$28$	−1.50033	−0.283536
$29$	3.51681	0.653055	0.326528	−	0.945188i	$-0.394121\pi$
$29$	3.51681	0.653055	0.326528	+	0.945188i	$0.394121\pi$
$30$	4.31126	0.787125
$31$	6.20713	1.11483	0.557417	−	0.830233i	$-0.311792\pi$
$31$	6.20713	1.11483	0.557417	+	0.830233i	$0.311792\pi$
$32$	7.01655	1.24036
$33$	5.92389	1.03122
$34$	9.57727	1.64249
$35$	−1.61115	−0.272333
$36$	−1.43185	−0.238641
$37$	6.30318	1.03624	0.518118	−	0.855309i	$-0.326633\pi$
$37$	6.30318	1.03624	0.518118	+	0.855309i	$0.326633\pi$
$38$	4.62252	0.749871
$39$	−4.66348	−0.746755
$40$	1.50617	0.238146
$41$	7.10314	1.10932	0.554662	−	0.832076i	$-0.312848\pi$
$41$	7.10314	1.10932	0.554662	+	0.832076i	$0.312848\pi$
$42$	−2.67590	−0.412900
$43$	−2.62321	−0.400035	−0.200018	−	0.979792i	$-0.564100\pi$
$43$	−2.62321	−0.400035	−0.200018	+	0.979792i	$0.564100\pi$
$44$	−6.21410	−0.936811
$45$	−1.53761	−0.229213
$46$	0.955162	0.140831
$47$	−1.55230	−0.226426	−0.113213	−	0.993571i	$-0.536114\pi$
$47$	−1.55230	−0.226426	−0.113213	+	0.993571i	$0.536114\pi$
$48$	6.79326	0.980523
$49$	1.00000	0.142857
$50$	4.49807	0.636123
$51$	7.32154	1.02522
$52$	4.89195	0.678391
$53$	−2.17150	−0.298278	−0.149139	−	0.988816i	$-0.547650\pi$
$53$	−2.17150	−0.298278	−0.149139	+	0.988816i	$0.547650\pi$
$54$	−10.5815	−1.43995
$55$	−6.67309	−0.899799
$56$	−0.934843	−0.124924
$57$	3.53378	0.468060
$58$	−6.57966	−0.863952
$59$	12.6137	1.64216	0.821082	−	0.570811i	$-0.193371\pi$
$59$	12.6137	1.64216	0.821082	+	0.570811i	$0.193371\pi$
$60$	−3.45730	−0.446335
$61$	−2.80930	−0.359695	−0.179847	−	0.983695i	$-0.557560\pi$
$61$	−2.80930	−0.359695	−0.179847	+	0.983695i	$0.557560\pi$
$62$	−11.6130	−1.47486
$63$	0.954356	0.120238
$64$	−3.62804	−0.453505
$65$	5.25328	0.651589
$66$	−11.0831	−1.36424
$67$	−13.8186	−1.68821	−0.844105	−	0.536178i	$-0.819868\pi$
$67$	−13.8186	−1.68821	−0.844105	+	0.536178i	$0.819868\pi$
$68$	−7.68022	−0.931364
$69$	0.730193	0.0879049
$70$	3.01432	0.360280
$71$	8.25353	0.979514	0.489757	−	0.871859i	$-0.337086\pi$
$71$	8.25353	0.979514	0.489757	+	0.871859i	$0.337086\pi$
$72$	−0.892173	−0.105144
$73$	6.75117	0.790164	0.395082	−	0.918646i	$-0.370716\pi$
$73$	6.75117	0.790164	0.395082	+	0.918646i	$0.370716\pi$
$74$	−11.7927	−1.37088
$75$	3.43864	0.397060
$76$	−3.70690	−0.425210
$77$	4.14183	0.472005
$78$	8.72498	0.987910
$79$	−9.12911	−1.02711	−0.513553	−	0.858058i	$-0.671671\pi$
$79$	−9.12911	−1.02711	−0.513553	+	0.858058i	$0.671671\pi$
$80$	−7.65242	−0.855566
$81$	−5.22614	−0.580682
$82$	−13.2894	−1.46757
$83$	8.97474	0.985106	0.492553	−	0.870283i	$-0.336064\pi$
$83$	8.97474	0.985106	0.492553	+	0.870283i	$0.336064\pi$
$84$	2.14586	0.234133
$85$	−8.24750	−0.894567
$86$	4.90780	0.529222
$87$	−5.02995	−0.539268
$88$	−3.87196	−0.412752
$89$	0.367182	0.0389212	0.0194606	−	0.999811i	$-0.493805\pi$
$89$	0.367182	0.0389212	0.0194606	+	0.999811i	$0.493805\pi$
$90$	2.87674	0.303235
$91$	−3.26058	−0.341802
$92$	−0.765965	−0.0798574
$93$	−8.87782	−0.920587
$94$	2.90422	0.299548
$95$	−3.98070	−0.408411
$96$	−10.0355	−1.02424
$97$	3.50684	0.356066	0.178033	−	0.984025i	$-0.443027\pi$
$97$	3.50684	0.356066	0.178033	+	0.984025i	$0.443027\pi$
$98$	−1.87092	−0.188991
$99$	3.95278	0.397269
$100$	−3.60710	−0.360710
$101$	−12.2803	−1.22194	−0.610970	−	0.791654i	$-0.709220\pi$
$101$	−12.2803	−1.22194	−0.610970	+	0.791654i	$0.709220\pi$
$102$	−13.6980	−1.35630
$103$	1.13257	0.111595	0.0557975	−	0.998442i	$-0.482230\pi$
$103$	1.13257	0.111595	0.0557975	+	0.998442i	$0.482230\pi$
$104$	3.04813	0.298894
$105$	2.30436	0.224882
$106$	4.06269	0.394603
$107$	−11.9526	−1.15550	−0.577751	−	0.816213i	$-0.696070\pi$
$107$	−11.9526	−1.15550	−0.577751	+	0.816213i	$0.696070\pi$
$108$	8.48550	0.816517
$109$	0.118261	0.0113273	0.00566366	−	0.999984i	$-0.498197\pi$
$109$	0.118261	0.0113273	0.00566366	+	0.999984i	$0.498197\pi$
$110$	12.4848	1.19038
$111$	−9.01518	−0.855683
$112$	4.74967	0.448802
$113$	3.13905	0.295297	0.147649	−	0.989040i	$-0.452830\pi$
$113$	3.13905	0.295297	0.147649	+	0.989040i	$0.452830\pi$
$114$	−6.61140	−0.619214
$115$	−0.822541	−0.0767024
$116$	5.27637	0.489899
$117$	−3.11176	−0.287682
$118$	−23.5992	−2.17248
$119$	5.11903	0.469260
$120$	−2.15421	−0.196652
$121$	6.15473	0.559521
$122$	5.25597	0.475854
$123$	−10.1593	−0.916036
$124$	9.31274	0.836309
$125$	−11.9293	−1.06699
$126$	−1.78552	−0.159067
$127$	9.73882	0.864181	0.432090	−	0.901830i	$-0.357776\pi$
$127$	9.73882	0.864181	0.432090	+	0.901830i	$0.357776\pi$
$128$	−7.24534	−0.640404
$129$	3.75187	0.330333
$130$	−9.82844	−0.862011
$131$	8.03406	0.701939	0.350969	−	0.936387i	$-0.385852\pi$
$131$	8.03406	0.701939	0.350969	+	0.936387i	$0.385852\pi$
$132$	8.88778	0.773582
$133$	2.47072	0.214239
$134$	25.8534	2.23340
$135$	9.11225	0.784258
$136$	−4.78549	−0.410352
$137$	2.65393	0.226741	0.113370	−	0.993553i	$-0.463835\pi$
$137$	2.65393	0.226741	0.113370	+	0.993553i	$0.463835\pi$
$138$	−1.36613	−0.116293
$139$	10.9482	0.928614	0.464307	−	0.885674i	$-0.346304\pi$
$139$	10.9482	0.928614	0.464307	+	0.885674i	$0.346304\pi$
$140$	−2.41725	−0.204295
$141$	2.22019	0.186974
$142$	−15.4417	−1.29584
$143$	−13.5048	−1.12933
$144$	4.53288	0.377740
$145$	5.66610	0.470544
$146$	−12.6309	−1.04534
$147$	−1.43026	−0.117966
$148$	9.45684	0.777347
$149$	7.79165	0.638317	0.319159	−	0.947701i	$-0.396600\pi$
$149$	7.79165	0.638317	0.319159	+	0.947701i	$0.396600\pi$
$150$	−6.43341	−0.525286
$151$	−1.54391	−0.125642	−0.0628209	−	0.998025i	$-0.520010\pi$
$151$	−1.54391	−0.125642	−0.0628209	+	0.998025i	$0.520010\pi$
$152$	−2.30974	−0.187345
$153$	4.88538	0.394959
$154$	−7.74901	−0.624433
$155$	10.0006	0.803268
$156$	−6.99675	−0.560189
$157$	14.5635	1.16230	0.581148	−	0.813798i	$-0.302604\pi$
$157$	14.5635	1.16230	0.581148	+	0.813798i	$0.302604\pi$
$158$	17.0798	1.35880
$159$	3.10580	0.246306
$160$	11.3047	0.893715
$161$	0.510532	0.0402355
$162$	9.77766	0.768206
$163$	−15.9831	−1.25189	−0.625947	−	0.779866i	$-0.715287\pi$
$163$	−15.9831	−1.25189	−0.625947	+	0.779866i	$0.715287\pi$
$164$	10.6570	0.832175
$165$	9.54426	0.743019
$166$	−16.7910	−1.30323
$167$	−16.0121	−1.23906	−0.619529	−	0.784974i	$-0.712676\pi$
$167$	−16.0121	−1.23906	−0.619529	+	0.784974i	$0.712676\pi$
$168$	1.33707	0.103157
$169$	−2.36860	−0.182200
$170$	15.4304	1.18346
$171$	2.35795	0.180317
$172$	−3.93567	−0.300092
$173$	5.04285	0.383401	0.191700	−	0.981453i	$-0.438600\pi$
$173$	5.04285	0.383401	0.191700	+	0.981453i	$0.438600\pi$
$174$	9.41062	0.713418
$175$	2.40421	0.181741
$176$	19.6723	1.48286
$177$	−18.0409	−1.35603
$178$	−0.686967	−0.0514904
$179$	−3.70850	−0.277186	−0.138593	−	0.990349i	$-0.544258\pi$
$179$	−3.70850	−0.277186	−0.138593	+	0.990349i	$0.544258\pi$
$180$	−2.30692	−0.171947
$181$	−3.12298	−0.232129	−0.116065	−	0.993242i	$-0.537028\pi$
$181$	−3.12298	−0.232129	−0.116065	+	0.993242i	$0.537028\pi$
$182$	6.10028	0.452183
$183$	4.01804	0.297022
$184$	−0.477267	−0.0351846
$185$	10.1553	0.746636
$186$	16.6097	1.21788
$187$	21.2021	1.55045
$188$	−2.32896	−0.169857
$189$	−5.65576	−0.411396
$190$	7.44755	0.540302
$191$	−7.45262	−0.539253	−0.269626	−	0.962965i	$-0.586900\pi$
$191$	−7.45262	−0.539253	−0.269626	+	0.962965i	$0.586900\pi$
$192$	5.18904	0.374487
$193$	0.817451	0.0588414	0.0294207	−	0.999567i	$-0.490634\pi$
$193$	0.817451	0.0588414	0.0294207	+	0.999567i	$0.490634\pi$
$194$	−6.56101	−0.471053
$195$	−7.51355	−0.538057
$196$	1.50033	0.107166
$197$	14.8943	1.06117	0.530587	−	0.847630i	$-0.321971\pi$
$197$	14.8943	1.06117	0.530587	+	0.847630i	$0.321971\pi$
$198$	−7.39532	−0.525562
$199$	−2.00813	−0.142352	−0.0711761	−	0.997464i	$-0.522675\pi$
$199$	−2.00813	−0.142352	−0.0711761	+	0.997464i	$0.522675\pi$
$200$	−2.24756	−0.158926
$201$	19.7642	1.39406
$202$	22.9755	1.61655
$203$	−3.51681	−0.246832
$204$	10.9847	0.769084
$205$	11.4442	0.799297
$206$	−2.11894	−0.147633
$207$	0.487229	0.0338648
$208$	−15.4867	−1.07381
$209$	10.2333	0.707853
$210$	−4.31126	−0.297505
$211$	−15.2862	−1.05235	−0.526174	−	0.850377i	$-0.676374\pi$
$211$	−15.2862	−1.05235	−0.526174	+	0.850377i	$0.676374\pi$
$212$	−3.25796	−0.223758
$213$	−11.8047	−0.808844
$214$	22.3623	1.52866
$215$	−4.22637	−0.288236
$216$	5.28725	0.359751
$217$	−6.20713	−0.421368
$218$	−0.221256	−0.0149854
$219$	−9.65592	−0.652487
$220$	−10.0118	−0.674998
$221$	−16.6910	−1.12276
$222$	16.8667	1.13202
$223$	−18.1380	−1.21461	−0.607304	−	0.794469i	$-0.707749\pi$
$223$	−18.1380	−1.21461	−0.607304	+	0.794469i	$0.707749\pi$
$224$	−7.01655	−0.468813
$225$	2.29447	0.152965
$226$	−5.87291	−0.390660
$227$	9.48608	0.629613	0.314807	−	0.949156i	$-0.398060\pi$
$227$	9.48608	0.629613	0.314807	+	0.949156i	$0.398060\pi$
$228$	5.30183	0.351122
$229$	−1.12064	−0.0740539	−0.0370270	−	0.999314i	$-0.511789\pi$
$229$	−1.12064	−0.0740539	−0.0370270	+	0.999314i	$0.511789\pi$
$230$	1.53891	0.101472
$231$	−5.92389	−0.389763
$232$	3.28767	0.215846
$233$	7.79317	0.510547	0.255274	−	0.966869i	$-0.417834\pi$
$233$	7.79317	0.510547	0.255274	+	0.966869i	$0.417834\pi$
$234$	5.82184	0.380585
$235$	−2.50098	−0.163146
$236$	18.9247	1.23189
$237$	13.0570	0.848144
$238$	−9.57727	−0.620802
$239$	−15.4577	−0.999879	−0.499939	−	0.866060i	$-0.666644\pi$
$239$	−15.4577	−0.999879	−0.499939	+	0.866060i	$0.666644\pi$
$240$	10.9449	0.706493
$241$	8.50236	0.547685	0.273843	−	0.961775i	$-0.411705\pi$
$241$	8.50236	0.547685	0.273843	+	0.961775i	$0.411705\pi$
$242$	−11.5150	−0.740212
$243$	−9.49254	−0.608947
$244$	−4.21488	−0.269830
$245$	1.61115	0.102932
$246$	19.0073	1.21186
$247$	−8.05600	−0.512591
$248$	5.80270	0.368472
$249$	−12.8362	−0.813462
$250$	22.3187	1.41156
$251$	3.43233	0.216647	0.108323	−	0.994116i	$-0.465452\pi$
$251$	3.43233	0.216647	0.108323	+	0.994116i	$0.465452\pi$
$252$	1.43185	0.0901979
$253$	2.11453	0.132940
$254$	−18.2205	−1.14326
$255$	11.7961	0.738699
$256$	20.8115	1.30072
$257$	−18.5824	−1.15914	−0.579570	−	0.814923i	$-0.696779\pi$
$257$	−18.5824	−1.15914	−0.579570	+	0.814923i	$0.696779\pi$
$258$	−7.01943	−0.437011
$259$	−6.30318	−0.391660
$260$	7.88164	0.488799
$261$	−3.35629	−0.207749
$262$	−15.0311	−0.928622
$263$	−5.59437	−0.344964	−0.172482	−	0.985013i	$-0.555179\pi$
$263$	−5.59437	−0.344964	−0.172482	+	0.985013i	$0.555179\pi$
$264$	5.53791	0.340835
$265$	−3.49860	−0.214917
$266$	−4.62252	−0.283425
$267$	−0.525166	−0.0321396
$268$	−20.7324	−1.26644
$269$	16.0351	0.977677	0.488839	−	0.872374i	$-0.337421\pi$
$269$	16.0351	0.977677	0.488839	+	0.872374i	$0.337421\pi$
$270$	−17.0483	−1.03752
$271$	−15.2732	−0.927781	−0.463890	−	0.885893i	$-0.653547\pi$
$271$	−15.2732	−0.927781	−0.463890	+	0.885893i	$0.653547\pi$
$272$	24.3137	1.47423
$273$	4.66348	0.282247
$274$	−4.96528	−0.299964
$275$	9.95781	0.600478
$276$	1.09553	0.0659431
$277$	22.9646	1.37981	0.689905	−	0.723900i	$-0.257652\pi$
$277$	22.9646	1.37981	0.689905	+	0.723900i	$0.257652\pi$
$278$	−20.4832	−1.22850
$279$	−5.92382	−0.354650
$280$	−1.50617	−0.0900108
$281$	−0.825349	−0.0492362	−0.0246181	−	0.999697i	$-0.507837\pi$
$281$	−0.825349	−0.0492362	−0.0246181	+	0.999697i	$0.507837\pi$
$282$	−4.15380	−0.247355
$283$	9.85358	0.585734	0.292867	−	0.956153i	$-0.405391\pi$
$283$	9.85358	0.585734	0.292867	+	0.956153i	$0.405391\pi$
$284$	12.3830	0.734797
$285$	5.69343	0.337250
$286$	25.2663	1.49403
$287$	−7.10314	−0.419285
$288$	−6.69629	−0.394583
$289$	9.20444	0.541438
$290$	−10.6008	−0.622500
$291$	−5.01569	−0.294025
$292$	10.1290	0.592753
$293$	5.57948	0.325957	0.162978	−	0.986630i	$-0.447890\pi$
$293$	5.57948	0.325957	0.162978	+	0.986630i	$0.447890\pi$
$294$	2.67590	0.156061
$295$	20.3225	1.18322
$296$	5.89248	0.342494
$297$	−23.4252	−1.35927
$298$	−14.5775	−0.844454
$299$	−1.66463	−0.0962680
$300$	5.15909	0.297860
$301$	2.62321	0.151199
$302$	2.88853	0.166216
$303$	17.5641	1.00903
$304$	11.7351	0.673055
$305$	−4.52620	−0.259170
$306$	−9.14013	−0.522506
$307$	−27.0412	−1.54332	−0.771660	−	0.636035i	$-0.780573\pi$
$307$	−27.0412	−1.54332	−0.771660	+	0.636035i	$0.780573\pi$
$308$	6.21410	0.354081
$309$	−1.61986	−0.0921508
$310$	−18.7103	−1.06267
$311$	11.6601	0.661185	0.330592	−	0.943774i	$-0.392751\pi$
$311$	11.6601	0.661185	0.330592	+	0.943774i	$0.392751\pi$
$312$	−4.35962	−0.246815
$313$	16.1975	0.915535	0.457767	−	0.889072i	$-0.348649\pi$
$313$	16.1975	0.915535	0.457767	+	0.889072i	$0.348649\pi$
$314$	−27.2472	−1.53765
$315$	1.53761	0.0866344
$316$	−13.6967	−0.770498
$317$	0.910482	0.0511378	0.0255689	−	0.999673i	$-0.491860\pi$
$317$	0.910482	0.0511378	0.0255689	+	0.999673i	$0.491860\pi$
$318$	−5.81070	−0.325848
$319$	−14.5660	−0.815541
$320$	−5.84531	−0.326763
$321$	17.0953	0.954169
$322$	−0.955162	−0.0532291
$323$	12.6477	0.703737
$324$	−7.84092	−0.435607
$325$	−7.83911	−0.434836
$326$	29.9031	1.65618
$327$	−0.169144	−0.00935367
$328$	6.64032	0.366650
$329$	1.55230	0.0855811
$330$	−17.8565	−0.982968
$331$	−14.6081	−0.802936	−0.401468	−	0.915873i	$-0.631500\pi$
$331$	−14.6081	−0.802936	−0.401468	+	0.915873i	$0.631500\pi$
$332$	13.4651	0.738991
$333$	−6.01548	−0.329646
$334$	29.9574	1.63920
$335$	−22.2638	−1.21640
$336$	−6.79326	−0.370603
$337$	17.1880	0.936288	0.468144	−	0.883652i	$-0.344923\pi$
$337$	17.1880	0.936288	0.468144	+	0.883652i	$0.344923\pi$
$338$	4.43146	0.241040
$339$	−4.48966	−0.243845
$340$	−12.3740	−0.671073
$341$	−25.7089	−1.39221
$342$	−4.41153	−0.238548
$343$	−1.00000	−0.0539949
$344$	−2.45229	−0.132218
$345$	1.17645	0.0633378
$346$	−9.43475	−0.507215
$347$	−16.4559	−0.883397	−0.441699	−	0.897163i	$-0.645624\pi$
$347$	−16.4559	−0.883397	−0.441699	+	0.897163i	$0.645624\pi$
$348$	−7.54658	−0.404539
$349$	−4.59442	−0.245934	−0.122967	−	0.992411i	$-0.539241\pi$
$349$	−4.59442	−0.245934	−0.122967	+	0.992411i	$0.539241\pi$
$350$	−4.49807	−0.240432
$351$	18.4411	0.984311
$352$	−29.0613	−1.54897
$353$	15.6950	0.835362	0.417681	−	0.908594i	$-0.362843\pi$
$353$	15.6950	0.835362	0.417681	+	0.908594i	$0.362843\pi$
$354$	33.7530	1.79395
$355$	13.2976	0.705766
$356$	0.550894	0.0291973
$357$	−7.32154	−0.387497
$358$	6.93830	0.366700
$359$	7.61734	0.402028	0.201014	−	0.979588i	$-0.435576\pi$
$359$	7.61734	0.402028	0.201014	+	0.979588i	$0.435576\pi$
$360$	−1.43742	−0.0757588
$361$	−12.8955	−0.678712
$362$	5.84284	0.307093
$363$	−8.80287	−0.462031
$364$	−4.89195	−0.256408
$365$	10.8771	0.569334
$366$	−7.51741	−0.392941
$367$	−18.6998	−0.976123	−0.488061	−	0.872809i	$-0.662296\pi$
$367$	−18.6998	−0.976123	−0.488061	+	0.872809i	$0.662296\pi$
$368$	2.42486	0.126404
$369$	−6.77892	−0.352897
$370$	−18.9998	−0.987753
$371$	2.17150	0.112738
$372$	−13.3196	−0.690591
$373$	25.6724	1.32926	0.664632	−	0.747171i	$-0.268588\pi$
$373$	25.6724	1.32926	0.664632	+	0.747171i	$0.268588\pi$
$374$	−39.6674	−2.05115
$375$	17.0619	0.881075
$376$	−1.45116	−0.0748377
$377$	11.4668	0.590573
$378$	10.5815	0.544251
$379$	−1.69938	−0.0872913	−0.0436456	−	0.999047i	$-0.513897\pi$
$379$	−1.69938	−0.0872913	−0.0436456	+	0.999047i	$0.513897\pi$
$380$	−5.97235	−0.306375
$381$	−13.9290	−0.713607
$382$	13.9432	0.713398
$383$	29.5505	1.50996	0.754980	−	0.655748i	$-0.227647\pi$
$383$	29.5505	1.50996	0.754980	+	0.655748i	$0.227647\pi$
$384$	10.3627	0.528820
$385$	6.67309	0.340092
$386$	−1.52938	−0.0778436
$387$	2.50347	0.127259
$388$	5.26141	0.267108
$389$	−22.2829	−1.12979	−0.564895	−	0.825163i	$-0.691083\pi$
$389$	−22.2829	−1.12979	−0.564895	+	0.825163i	$0.691083\pi$
$390$	14.0572	0.711815
$391$	2.61343	0.132167
$392$	0.934843	0.0472167
$393$	−11.4908	−0.579634
$394$	−27.8660	−1.40387
$395$	−14.7083	−0.740057
$396$	5.93047	0.298017
$397$	−8.72631	−0.437961	−0.218980	−	0.975729i	$-0.570273\pi$
$397$	−8.72631	−0.437961	−0.218980	+	0.975729i	$0.570273\pi$
$398$	3.75704	0.188323
$399$	−3.53378	−0.176910
$400$	11.4192	0.570960
$401$	−4.28268	−0.213867	−0.106933	−	0.994266i	$-0.534103\pi$
$401$	−4.28268	−0.213867	−0.106933	+	0.994266i	$0.534103\pi$
$402$	−36.9771	−1.84425
$403$	20.2389	1.00817
$404$	−18.4246	−0.916656
$405$	−8.42007	−0.418397
$406$	6.57966	0.326543
$407$	−26.1067	−1.29406
$408$	6.84449	0.338853
$409$	20.1577	0.996734	0.498367	−	0.866966i	$-0.333933\pi$
$409$	20.1577	0.996734	0.498367	+	0.866966i	$0.333933\pi$
$410$	−21.4111	−1.05742
$411$	−3.79581	−0.187234
$412$	1.69922	0.0837146
$413$	−12.6137	−0.620679
$414$	−0.911565	−0.0448010
$415$	14.4596	0.709795
$416$	22.8780	1.12169
$417$	−15.6588	−0.766813
$418$	−19.1457	−0.936445
$419$	30.2698	1.47878	0.739388	−	0.673279i	$-0.235115\pi$
$419$	30.2698	1.47878	0.739388	+	0.673279i	$0.235115\pi$
$420$	3.45730	0.168699
$421$	7.43093	0.362161	0.181081	−	0.983468i	$-0.442040\pi$
$421$	7.43093	0.362161	0.181081	+	0.983468i	$0.442040\pi$
$422$	28.5993	1.39219
$423$	1.48145	0.0720304
$424$	−2.03001	−0.0985859
$425$	12.3072	0.596987
$426$	22.0856	1.07005
$427$	2.80930	0.135952
$428$	−17.9328	−0.866817
$429$	19.3153	0.932553
$430$	7.90718	0.381318
$431$	−17.4933	−0.842623	−0.421312	−	0.906916i	$-0.638430\pi$
$431$	−17.4933	−0.842623	−0.421312	+	0.906916i	$0.638430\pi$
$432$	−26.8630	−1.29245
$433$	−35.1702	−1.69017	−0.845086	−	0.534630i	$-0.820451\pi$
$433$	−35.1702	−1.69017	−0.845086	+	0.534630i	$0.820451\pi$
$434$	11.6130	0.557443
$435$	−8.10399	−0.388557
$436$	0.177430	0.00849736
$437$	1.26138	0.0603401
$438$	18.0654	0.863200
$439$	14.5415	0.694028	0.347014	−	0.937860i	$-0.387196\pi$
$439$	14.5415	0.694028	0.347014	+	0.937860i	$0.387196\pi$
$440$	−6.23829	−0.297399
$441$	−0.954356	−0.0454455
$442$	31.2275	1.48534
$443$	−40.7253	−1.93492	−0.967458	−	0.253030i	$-0.918573\pi$
$443$	−40.7253	−1.93492	−0.967458	+	0.253030i	$0.918573\pi$
$444$	−13.5257	−0.641903
$445$	0.591584	0.0280438
$446$	33.9346	1.60685
$447$	−11.1441	−0.527097
$448$	3.62804	0.171409
$449$	−20.8737	−0.985089	−0.492545	−	0.870287i	$-0.663933\pi$
$449$	−20.8737	−0.985089	−0.492545	+	0.870287i	$0.663933\pi$
$450$	−4.29276	−0.202363
$451$	−29.4200	−1.38533
$452$	4.70961	0.221522
$453$	2.20820	0.103750
$454$	−17.7477	−0.832939
$455$	−5.25328	−0.246277
$456$	3.30353	0.154702
$457$	−20.9614	−0.980534	−0.490267	−	0.871572i	$-0.663101\pi$
$457$	−20.9614	−0.980534	−0.490267	+	0.871572i	$0.663101\pi$
$458$	2.09662	0.0979687
$459$	−28.9520	−1.35136
$460$	−1.23408	−0.0575394
$461$	−36.4116	−1.69586	−0.847928	−	0.530112i	$-0.822150\pi$
$461$	−36.4116	−1.69586	−0.847928	+	0.530112i	$0.822150\pi$
$462$	11.0831	0.515633
$463$	−28.6430	−1.33115	−0.665576	−	0.746330i	$-0.731814\pi$
$463$	−28.6430	−1.33115	−0.665576	+	0.746330i	$0.731814\pi$
$464$	−16.7037	−0.775449
$465$	−14.3035	−0.663307
$466$	−14.5804	−0.675422
$467$	39.3939	1.82293	0.911466	−	0.411376i	$-0.134952\pi$
$467$	39.3939	1.82293	0.911466	+	0.411376i	$0.134952\pi$
$468$	−4.66866	−0.215809
$469$	13.8186	0.638083
$470$	4.67913	0.215832
$471$	−20.8296	−0.959779
$472$	11.7918	0.542763
$473$	10.8649	0.499567
$474$	−24.4286	−1.12204
$475$	5.94013	0.272552
$476$	7.68022	0.352023
$477$	2.07238	0.0948878
$478$	28.9202	1.32278
$479$	1.50023	0.0685474	0.0342737	−	0.999412i	$-0.489088\pi$
$479$	1.50023	0.0685474	0.0342737	+	0.999412i	$0.489088\pi$
$480$	−16.1687	−0.737995
$481$	20.5520	0.937092
$482$	−15.9072	−0.724553
$483$	−0.730193	−0.0332249
$484$	9.23412	0.419733
$485$	5.65004	0.256555
$486$	17.7597	0.805599
$487$	−4.15828	−0.188430	−0.0942149	−	0.995552i	$-0.530034\pi$
$487$	−4.15828	−0.188430	−0.0942149	+	0.995552i	$0.530034\pi$
$488$	−2.62626	−0.118885
$489$	22.8600	1.03376
$490$	−3.01432	−0.136173
$491$	−17.0295	−0.768531	−0.384265	−	0.923223i	$-0.625545\pi$
$491$	−17.0295	−0.768531	−0.384265	+	0.923223i	$0.625545\pi$
$492$	−15.2423	−0.687178
$493$	−18.0027	−0.810799
$494$	15.0721	0.678126
$495$	6.36851	0.286243
$496$	−29.4818	−1.32377
$497$	−8.25353	−0.370221
$498$	24.0155	1.07616
$499$	−13.1205	−0.587354	−0.293677	−	0.955905i	$-0.594879\pi$
$499$	−13.1205	−0.587354	−0.293677	+	0.955905i	$0.594879\pi$
$500$	−17.8978	−0.800415
$501$	22.9015	1.02317
$502$	−6.42160	−0.286610
$503$	6.83226	0.304635	0.152318	−	0.988332i	$-0.451326\pi$
$503$	6.83226	0.304635	0.152318	+	0.988332i	$0.451326\pi$
$504$	0.892173	0.0397405
$505$	−19.7854	−0.880441
$506$	−3.95612	−0.175871
$507$	3.38772	0.150454
$508$	14.6114	0.648278
$509$	−37.4240	−1.65879	−0.829394	−	0.558664i	$-0.811314\pi$
$509$	−37.4240	−1.65879	−0.829394	+	0.558664i	$0.811314\pi$
$510$	−22.0695	−0.977253
$511$	−6.75117	−0.298654
$512$	−24.4459	−1.08037
$513$	−13.9738	−0.616959
$514$	34.7662	1.53347
$515$	1.82473	0.0804072
$516$	5.62903	0.247804
$517$	6.42936	0.282763
$518$	11.7927	0.518142
$519$	−7.21259	−0.316597
$520$	4.91099	0.215361
$521$	−7.81315	−0.342300	−0.171150	−	0.985245i	$-0.554748\pi$
$521$	−7.81315	−0.342300	−0.171150	+	0.985245i	$0.554748\pi$
$522$	6.27934	0.274839
$523$	−3.15447	−0.137936	−0.0689678	−	0.997619i	$-0.521971\pi$
$523$	−3.15447	−0.137936	−0.0689678	+	0.997619i	$0.521971\pi$
$524$	12.0537	0.526570
$525$	−3.43864	−0.150075
$526$	10.4666	0.456366
$527$	−31.7745	−1.38412
$528$	−28.1365	−1.22449
$529$	−22.7394	−0.988668
$530$	6.54559	0.284322
$531$	−12.0380	−0.522403
$532$	3.70690	0.160714
$533$	23.1604	1.00319
$534$	0.982541	0.0425187
$535$	−19.2574	−0.832570
$536$	−12.9182	−0.557982
$537$	5.30412	0.228890
$538$	−30.0003	−1.29341
$539$	−4.14183	−0.178401
$540$	13.6714	0.588322
$541$	−22.5076	−0.967676	−0.483838	−	0.875158i	$-0.660758\pi$
$541$	−22.5076	−0.967676	−0.483838	+	0.875158i	$0.660758\pi$
$542$	28.5749	1.22740
$543$	4.46668	0.191683
$544$	−35.9179	−1.53997
$545$	0.190535	0.00816164
$546$	−8.72498	−0.373395
$547$	−38.2836	−1.63689	−0.818445	−	0.574585i	$-0.805163\pi$
$547$	−38.2836	−1.63689	−0.818445	+	0.574585i	$0.805163\pi$
$548$	3.98177	0.170093
$549$	2.68108	0.114426
$550$	−18.6302	−0.794396
$551$	−8.68907	−0.370167
$552$	0.682616	0.0290541
$553$	9.12911	0.388209
$554$	−42.9649	−1.82540
$555$	−14.5248	−0.616543
$556$	16.4259	0.696613
$557$	−15.3157	−0.648945	−0.324473	−	0.945895i	$-0.605187\pi$
$557$	−15.3157	−0.648945	−0.324473	+	0.945895i	$0.605187\pi$
$558$	11.0830	0.469179
$559$	−8.55318	−0.361761
$560$	7.65242	0.323374
$561$	−30.3246	−1.28030
$562$	1.54416	0.0651364
$563$	−13.3569	−0.562924	−0.281462	−	0.959572i	$-0.590819\pi$
$563$	−13.3569	−0.562924	−0.281462	+	0.959572i	$0.590819\pi$
$564$	3.33102	0.140261
$565$	5.05748	0.212770
$566$	−18.4352	−0.774890
$567$	5.22614	0.219477
$568$	7.71576	0.323746
$569$	−20.3568	−0.853403	−0.426701	−	0.904393i	$-0.640324\pi$
$569$	−20.3568	−0.853403	−0.426701	+	0.904393i	$0.640324\pi$
$570$	−10.6519	−0.446161
$571$	−37.7695	−1.58061	−0.790303	−	0.612716i	$-0.790077\pi$
$571$	−37.7695	−1.58061	−0.790303	+	0.612716i	$0.790077\pi$
$572$	−20.2616	−0.847180
$573$	10.6592	0.445294
$574$	13.2894	0.554688
$575$	1.22742	0.0511871
$576$	3.46244	0.144269
$577$	−12.0266	−0.500675	−0.250337	−	0.968159i	$-0.580542\pi$
$577$	−12.0266	−0.500675	−0.250337	+	0.968159i	$0.580542\pi$
$578$	−17.2207	−0.716289
$579$	−1.16917	−0.0485890
$580$	8.50101	0.352985
$581$	−8.97474	−0.372335
$582$	9.38395	0.388977
$583$	8.99396	0.372492
$584$	6.31128	0.261163
$585$	−5.01350	−0.207283
$586$	−10.4387	−0.431221
$587$	−19.9613	−0.823889	−0.411945	−	0.911209i	$-0.635150\pi$
$587$	−19.9613	−0.823889	−0.411945	+	0.911209i	$0.635150\pi$
$588$	−2.14586	−0.0884938
$589$	−15.3361	−0.631913
$590$	−38.0217	−1.56533
$591$	−21.3027	−0.876277
$592$	−29.9380	−1.23045
$593$	34.7256	1.42601	0.713005	−	0.701159i	$-0.247334\pi$
$593$	34.7256	1.42601	0.713005	+	0.701159i	$0.247334\pi$
$594$	43.8265	1.79822
$595$	8.24750	0.338115
$596$	11.6900	0.478843
$597$	2.87214	0.117549
$598$	3.11438	0.127357
$599$	3.64029	0.148738	0.0743690	−	0.997231i	$-0.476306\pi$
$599$	3.64029	0.148738	0.0743690	+	0.997231i	$0.476306\pi$
$600$	3.21459	0.131235
$601$	−18.6924	−0.762478	−0.381239	−	0.924477i	$-0.624502\pi$
$601$	−18.6924	−0.762478	−0.381239	+	0.924477i	$0.624502\pi$
$602$	−4.90780	−0.200027
$603$	13.1879	0.537051
$604$	−2.31638	−0.0942520
$605$	9.91618	0.403150
$606$	−32.8610	−1.33488
$607$	−5.32891	−0.216294	−0.108147	−	0.994135i	$-0.534492\pi$
$607$	−5.32891	−0.216294	−0.108147	+	0.994135i	$0.534492\pi$
$608$	−17.3360	−0.703066
$609$	5.02995	0.203824
$610$	8.46814	0.342865
$611$	−5.06140	−0.204762
$612$	7.32967	0.296284
$613$	−19.5046	−0.787784	−0.393892	−	0.919157i	$-0.628872\pi$
$613$	−19.5046	−0.787784	−0.393892	+	0.919157i	$0.628872\pi$
$614$	50.5917	2.04172
$615$	−16.3682	−0.660029
$616$	3.87196	0.156006
$617$	6.18153	0.248859	0.124430	−	0.992228i	$-0.460290\pi$
$617$	6.18153	0.248859	0.124430	+	0.992228i	$0.460290\pi$
$618$	3.03063	0.121910
$619$	29.1492	1.17161	0.585803	−	0.810454i	$-0.300779\pi$
$619$	29.1492	1.17161	0.585803	+	0.810454i	$0.300779\pi$
$620$	15.0042	0.602583
$621$	−2.88744	−0.115869
$622$	−21.8151	−0.874706
$623$	−0.367182	−0.0147108
$624$	22.1500	0.886710
$625$	−7.19876	−0.287950
$626$	−30.3041	−1.21120
$627$	−14.6363	−0.584517
$628$	21.8501	0.871914
$629$	−32.2661	−1.28654
$630$	−2.87674	−0.114612
$631$	−19.8188	−0.788972	−0.394486	−	0.918902i	$-0.629077\pi$
$631$	−19.8188	−0.788972	−0.394486	+	0.918902i	$0.629077\pi$
$632$	−8.53429	−0.339476
$633$	21.8633	0.868988
$634$	−1.70344	−0.0676521
$635$	15.6907	0.622665
$636$	4.65973	0.184770
$637$	3.26058	0.129189
$638$	27.2518	1.07891
$639$	−7.87681	−0.311602
$640$	−11.6733	−0.461428
$641$	34.5967	1.36649	0.683245	−	0.730190i	$-0.260568\pi$
$641$	34.5967	1.36649	0.683245	+	0.730190i	$0.260568\pi$
$642$	−31.9840	−1.26231
$643$	−38.4771	−1.51739	−0.758694	−	0.651448i	$-0.774162\pi$
$643$	−38.4771	−1.51739	−0.758694	+	0.651448i	$0.774162\pi$
$644$	0.765965	0.0301833
$645$	6.04481	0.238014
$646$	−23.6628	−0.931000
$647$	−0.506190	−0.0199004	−0.00995019	−	0.999950i	$-0.503167\pi$
$647$	−0.506190	−0.0199004	−0.00995019	+	0.999950i	$0.503167\pi$
$648$	−4.88562	−0.191925
$649$	−52.2437	−2.05075
$650$	14.6663	0.575261
$651$	8.87782	0.347949
$652$	−23.9799	−0.939126
$653$	30.4798	1.19277	0.596384	−	0.802700i	$-0.296604\pi$
$653$	30.4798	1.19277	0.596384	+	0.802700i	$0.296604\pi$
$654$	0.316454	0.0123743
$655$	12.9440	0.505766
$656$	−33.7376	−1.31723
$657$	−6.44302	−0.251366
$658$	−2.90422	−0.113218
$659$	6.94202	0.270423	0.135211	−	0.990817i	$-0.456829\pi$
$659$	6.94202	0.270423	0.135211	+	0.990817i	$0.456829\pi$
$660$	14.3195	0.557387
$661$	−35.9444	−1.39808	−0.699038	−	0.715084i	$-0.746388\pi$
$661$	−35.9444	−1.39808	−0.699038	+	0.715084i	$0.746388\pi$
$662$	27.3306	1.06223
$663$	23.8725	0.927130
$664$	8.38997	0.325594
$665$	3.98070	0.154365
$666$	11.2545	0.436101
$667$	−1.79544	−0.0695198
$668$	−24.0235	−0.929497
$669$	25.9420	1.00298
$670$	41.6537	1.60922
$671$	11.6357	0.449189
$672$	10.0355	0.387128
$673$	16.9237	0.652359	0.326180	−	0.945308i	$-0.394239\pi$
$673$	16.9237	0.652359	0.326180	+	0.945308i	$0.394239\pi$
$674$	−32.1572	−1.23865
$675$	−13.5976	−0.523372
$676$	−3.55369	−0.136680
$677$	25.8703	0.994276	0.497138	−	0.867672i	$-0.334384\pi$
$677$	25.8703	0.994276	0.497138	+	0.867672i	$0.334384\pi$
$678$	8.39979	0.322592
$679$	−3.50684	−0.134580
$680$	−7.71012	−0.295670
$681$	−13.5676	−0.519910
$682$	48.0992	1.84181
$683$	−29.3703	−1.12382	−0.561912	−	0.827197i	$-0.689934\pi$
$683$	−29.3703	−1.12382	−0.561912	+	0.827197i	$0.689934\pi$
$684$	3.53770	0.135267
$685$	4.27587	0.163373
$686$	1.87092	0.0714319
$687$	1.60281	0.0611508
$688$	12.4594	0.475009
$689$	−7.08034	−0.269740
$690$	−2.20104	−0.0837920
$691$	−30.1498	−1.14695	−0.573476	−	0.819222i	$-0.694406\pi$
$691$	−30.1498	−1.14695	−0.573476	+	0.819222i	$0.694406\pi$
$692$	7.56593	0.287614
$693$	−3.95278	−0.150154
$694$	30.7876	1.16868
$695$	17.6391	0.669091
$696$	−4.70222	−0.178237
$697$	−36.3612	−1.37728
$698$	8.59578	0.325355
$699$	−11.1463	−0.421590
$700$	3.60710	0.136336
$701$	18.1773	0.686548	0.343274	−	0.939235i	$-0.388464\pi$
$701$	18.1773	0.686548	0.343274	+	0.939235i	$0.388464\pi$
$702$	−34.5017	−1.30218
$703$	−15.5734	−0.587362
$704$	15.0267	0.566341
$705$	3.57706	0.134720
$706$	−29.3641	−1.10513
$707$	12.2803	0.461850
$708$	−27.0672	−1.01725
$709$	44.4849	1.67067	0.835333	−	0.549744i	$-0.185275\pi$
$709$	44.4849	1.67067	0.835333	+	0.549744i	$0.185275\pi$
$710$	−24.8788	−0.933684
$711$	8.71242	0.326741
$712$	0.343258	0.0128641
$713$	−3.16894	−0.118678
$714$	13.6980	0.512634
$715$	−21.7582	−0.813709
$716$	−5.56397	−0.207935
$717$	22.1086	0.825661
$718$	−14.2514	−0.531858
$719$	31.4411	1.17256	0.586278	−	0.810110i	$-0.300593\pi$
$719$	31.4411	1.17256	0.586278	+	0.810110i	$0.300593\pi$
$720$	7.30313	0.272172
$721$	−1.13257	−0.0421789
$722$	24.1265	0.897894
$723$	−12.1606	−0.452257
$724$	−4.68550	−0.174135
$725$	−8.45514	−0.314016
$726$	16.4694	0.611238
$727$	40.8412	1.51471	0.757357	−	0.653001i	$-0.226490\pi$
$727$	40.8412	1.51471	0.757357	+	0.653001i	$0.226490\pi$
$728$	−3.04813	−0.112971
$729$	29.2552	1.08353
$730$	−20.3502	−0.753194
$731$	13.4283	0.496662
$732$	6.02838	0.222815
$733$	−6.82856	−0.252219	−0.126109	−	0.992016i	$-0.540249\pi$
$733$	−6.82856	−0.252219	−0.126109	+	0.992016i	$0.540249\pi$
$734$	34.9858	1.29135
$735$	−2.30436	−0.0849976
$736$	−3.58217	−0.132041
$737$	57.2342	2.10825
$738$	12.6828	0.466860
$739$	−15.9275	−0.585902	−0.292951	−	0.956128i	$-0.594637\pi$
$739$	−15.9275	−0.585902	−0.292951	+	0.956128i	$0.594637\pi$
$740$	15.2364	0.560100
$741$	11.5222	0.423277
$742$	−4.06269	−0.149146
$743$	33.7840	1.23941	0.619707	−	0.784833i	$-0.287251\pi$
$743$	33.7840	1.23941	0.619707	+	0.784833i	$0.287251\pi$
$744$	−8.29936	−0.304269
$745$	12.5535	0.459924
$746$	−48.0308	−1.75853
$747$	−8.56510	−0.313380
$748$	31.8102	1.16309
$749$	11.9526	0.436739
$750$	−31.9215	−1.16561
$751$	15.2762	0.557438	0.278719	−	0.960373i	$-0.410090\pi$
$751$	15.2762	0.557438	0.278719	+	0.960373i	$0.410090\pi$
$752$	7.37292	0.268863
$753$	−4.90912	−0.178898
$754$	−21.4535	−0.781291
$755$	−2.48747	−0.0905283
$756$	−8.48550	−0.308615
$757$	−19.4744	−0.707811	−0.353905	−	0.935281i	$-0.615147\pi$
$757$	−19.4744	−0.707811	−0.353905	+	0.935281i	$0.615147\pi$
$758$	3.17940	0.115481
$759$	−3.02433	−0.109776
$760$	−3.72133	−0.134987
$761$	−11.2615	−0.408228	−0.204114	−	0.978947i	$-0.565431\pi$
$761$	−11.2615	−0.408228	−0.204114	+	0.978947i	$0.565431\pi$
$762$	26.0601	0.944057
$763$	−0.118261	−0.00428133
$764$	−11.1814	−0.404528
$765$	7.87106	0.284579
$766$	−55.2865	−1.99758
$767$	41.1280	1.48505
$768$	−29.7659	−1.07408
$769$	−7.45150	−0.268708	−0.134354	−	0.990933i	$-0.542896\pi$
$769$	−7.45150	−0.268708	−0.134354	+	0.990933i	$0.542896\pi$
$770$	−12.4848	−0.449921
$771$	26.5777	0.957172
$772$	1.22645	0.0441408
$773$	11.8794	0.427273	0.213636	−	0.976913i	$-0.431469\pi$
$773$	11.8794	0.427273	0.213636	+	0.976913i	$0.431469\pi$
$774$	−4.68379	−0.168355
$775$	−14.9232	−0.536058
$776$	3.27835	0.117686
$777$	9.01518	0.323418
$778$	41.6895	1.49464
$779$	−17.5499	−0.628790
$780$	−11.2728	−0.403631
$781$	−34.1847	−1.22322
$782$	−4.88950	−0.174848
$783$	19.8902	0.710819
$784$	−4.74967	−0.169631
$785$	23.4640	0.837466
$786$	21.4983	0.766820
$787$	−11.4685	−0.408808	−0.204404	−	0.978887i	$-0.565526\pi$
$787$	−11.4685	−0.408808	−0.204404	+	0.978887i	$0.565526\pi$
$788$	22.3463	0.796055
$789$	8.00141	0.284858
$790$	27.5181	0.979049
$791$	−3.13905	−0.111612
$792$	3.69523	0.131304
$793$	−9.15997	−0.325280
$794$	16.3262	0.579395
$795$	5.00391	0.177470
$796$	−3.01285	−0.106788
$797$	−0.370378	−0.0131195	−0.00655973	−	0.999978i	$-0.502088\pi$
$797$	−0.370378	−0.0131195	−0.00655973	+	0.999978i	$0.502088\pi$
$798$	6.61140	0.234041
$799$	7.94627	0.281119
$800$	−16.8692	−0.596418
$801$	−0.350422	−0.0123816
$802$	8.01253	0.282932
$803$	−27.9622	−0.986763
$804$	29.6528	1.04577
$805$	0.822541	0.0289908
$806$	−37.8652	−1.33375
$807$	−22.9344	−0.807328
$808$	−11.4802	−0.403872
$809$	−9.02079	−0.317154	−0.158577	−	0.987347i	$-0.550691\pi$
$809$	−9.02079	−0.317154	−0.158577	+	0.987347i	$0.550691\pi$
$810$	15.7533	0.553513
$811$	−48.5964	−1.70645	−0.853226	−	0.521542i	$-0.825357\pi$
$811$	−48.5964	−1.70645	−0.853226	+	0.521542i	$0.825357\pi$
$812$	−5.27637	−0.185164
$813$	21.8446	0.766125
$814$	48.8434	1.71196
$815$	−25.7511	−0.902022
$816$	−34.7749	−1.21737
$817$	6.48121	0.226749
$818$	−37.7134	−1.31862
$819$	3.11176	0.108734
$820$	17.1701	0.599604
$821$	−7.95166	−0.277515	−0.138757	−	0.990326i	$-0.544311\pi$
$821$	−7.95166	−0.277515	−0.138757	+	0.990326i	$0.544311\pi$
$822$	7.10164	0.247698
$823$	14.1334	0.492660	0.246330	−	0.969186i	$-0.420775\pi$
$823$	14.1334	0.492660	0.246330	+	0.969186i	$0.420775\pi$
$824$	1.05877	0.0368840
$825$	−14.2423	−0.495852
$826$	23.5992	0.821120
$827$	−4.50427	−0.156629	−0.0783143	−	0.996929i	$-0.524954\pi$
$827$	−4.50427	−0.156629	−0.0783143	+	0.996929i	$0.524954\pi$
$828$	0.731004	0.0254041
$829$	−51.7887	−1.79870	−0.899349	−	0.437232i	$-0.855959\pi$
$829$	−51.7887	−1.79870	−0.899349	+	0.437232i	$0.855959\pi$
$830$	−27.0527	−0.939014
$831$	−32.8454	−1.13939
$832$	−11.8295	−0.410115
$833$	−5.11903	−0.177364
$834$	29.2962	1.01445
$835$	−25.7979	−0.892774
$836$	15.3533	0.531006
$837$	35.1060	1.21344
$838$	−56.6323	−1.95633
$839$	−33.5312	−1.15763	−0.578813	−	0.815460i	$-0.696484\pi$
$839$	−33.5312	−1.15763	−0.578813	+	0.815460i	$0.696484\pi$
$840$	2.15421	0.0743274
$841$	−16.6320	−0.573519
$842$	−13.9026	−0.479117
$843$	1.18046	0.0406573
$844$	−22.9344	−0.789434
$845$	−3.81617	−0.131280
$846$	−2.77166	−0.0952918
$847$	−6.15473	−0.211479
$848$	10.3139	0.354181
$849$	−14.0932	−0.483677
$850$	−23.0257	−0.789776
$851$	−3.21797	−0.110311
$852$	−17.7109	−0.606766
$853$	8.38084	0.286954	0.143477	−	0.989654i	$-0.454172\pi$
$853$	8.38084	0.286954	0.143477	+	0.989654i	$0.454172\pi$
$854$	−5.25597	−0.179856
$855$	3.79900	0.129923
$856$	−11.1738	−0.381913
$857$	30.2962	1.03490	0.517449	−	0.855714i	$-0.326882\pi$
$857$	30.2962	1.03490	0.517449	+	0.855714i	$0.326882\pi$
$858$	−36.1374	−1.23371
$859$	−11.8309	−0.403664	−0.201832	−	0.979420i	$-0.564689\pi$
$859$	−11.8309	−0.403664	−0.201832	+	0.979420i	$0.564689\pi$
$860$	−6.34094	−0.216224
$861$	10.1593	0.346229
$862$	32.7285	1.11474
$863$	−1.00000	−0.0340404
$863$	−1.00000	−0.0340404
$864$	39.6839	1.35007
$865$	8.12477	0.276250
$866$	65.8005	2.23599
$867$	−13.1647	−0.447098
$868$	−9.31274	−0.316095
$869$	37.8112	1.28266
$870$	15.1619	0.514036
$871$	−45.0567	−1.52669
$872$	0.110555	0.00374387
$873$	−3.34678	−0.113271
$874$	−2.35994	−0.0798262
$875$	11.9293	0.403283
$876$	−14.4871	−0.489472
$877$	−10.8637	−0.366842	−0.183421	−	0.983034i	$-0.558717\pi$
$877$	−10.8637	−0.366842	−0.183421	+	0.983034i	$0.558717\pi$
$878$	−27.2060	−0.918156
$879$	−7.98011	−0.269163
$880$	31.6950	1.06844
$881$	−23.3806	−0.787711	−0.393856	−	0.919172i	$-0.628859\pi$
$881$	−23.3806	−0.787711	−0.393856	+	0.919172i	$0.628859\pi$
$882$	1.78552	0.0601216
$883$	−17.9771	−0.604977	−0.302489	−	0.953153i	$-0.597817\pi$
$883$	−17.9771	−0.604977	−0.302489	+	0.953153i	$0.597817\pi$
$884$	−25.0420	−0.842254
$885$	−29.0665	−0.977059
$886$	76.1936	2.55977
$887$	45.2511	1.51938	0.759691	−	0.650284i	$-0.225350\pi$
$887$	45.2511	1.51938	0.759691	+	0.650284i	$0.225350\pi$
$888$	−8.42778	−0.282818
$889$	−9.73882	−0.326630
$890$	−1.10680	−0.0371002
$891$	21.6458	0.725160
$892$	−27.2129	−0.911156
$893$	3.83530	0.128344
$894$	20.8497	0.697317
$895$	−5.97494	−0.199720
$896$	7.24534	0.242050
$897$	2.38085	0.0794944
$898$	39.0529	1.30321
$899$	21.8293	0.728048
$900$	3.44246	0.114749
$901$	11.1159	0.370326
$902$	55.0423	1.83271
$903$	−3.75187	−0.124854
$904$	2.93452	0.0976008
$905$	−5.03158	−0.167255
$906$	−4.13135	−0.137255
$907$	−0.353673	−0.0117435	−0.00587176	−	0.999983i	$-0.501869\pi$
$907$	−0.353673	−0.0117435	−0.00587176	+	0.999983i	$0.501869\pi$
$908$	14.2322	0.472313
$909$	11.7198	0.388722
$910$	9.82844	0.325810
$911$	−2.38166	−0.0789079	−0.0394539	−	0.999221i	$-0.512562\pi$
$911$	−2.38166	−0.0789079	−0.0394539	+	0.999221i	$0.512562\pi$
$912$	−16.7843	−0.555783
$913$	−37.1718	−1.23021
$914$	39.2171	1.29719
$915$	6.47364	0.214012
$916$	−1.68133	−0.0555526
$917$	−8.03406	−0.265308
$918$	54.1667	1.78777
$919$	−43.0354	−1.41961	−0.709804	−	0.704400i	$-0.751216\pi$
$919$	−43.0354	−1.41961	−0.709804	+	0.704400i	$0.751216\pi$
$920$	−0.768947	−0.0253514
$921$	38.6759	1.27441
$922$	68.1230	2.24351
$923$	26.9113	0.885797
$924$	−8.88778	−0.292387
$925$	−15.1541	−0.498265
$926$	53.5886	1.76103
$927$	−1.08087	−0.0355005
$928$	24.6759	0.810026
$929$	−54.4428	−1.78621	−0.893105	−	0.449848i	$-0.851478\pi$
$929$	−54.4428	−1.78621	−0.893105	+	0.449848i	$0.851478\pi$
$930$	26.7606	0.877514
$931$	−2.47072	−0.0809747
$932$	11.6923	0.382995
$933$	−16.6770	−0.545981
$934$	−73.7027	−2.41163
$935$	34.1597	1.11714
$936$	−2.90900	−0.0950838
$937$	−4.60281	−0.150367	−0.0751837	−	0.997170i	$-0.523954\pi$
$937$	−4.60281	−0.150367	−0.0751837	+	0.997170i	$0.523954\pi$
$938$	−25.8534	−0.844145
$939$	−23.1666	−0.756013
$940$	−3.75230	−0.122386
$941$	−27.0863	−0.882988	−0.441494	−	0.897264i	$-0.645551\pi$
$941$	−27.0863	−0.882988	−0.441494	+	0.897264i	$0.645551\pi$
$942$	38.9705	1.26973
$943$	−3.62638	−0.118091
$944$	−59.9109	−1.94993
$945$	−9.11225	−0.296422
$946$	−20.3273	−0.660896
$947$	−30.0848	−0.977624	−0.488812	−	0.872389i	$-0.662570\pi$
$947$	−30.0848	−0.977624	−0.488812	+	0.872389i	$0.662570\pi$
$948$	19.5898	0.636247
$949$	22.0127	0.714564
$950$	−11.1135	−0.360569
$951$	−1.30223	−0.0422276
$952$	4.78549	0.155099
$953$	52.3208	1.69484	0.847419	−	0.530925i	$-0.178155\pi$
$953$	52.3208	1.69484	0.847419	+	0.530925i	$0.178155\pi$
$954$	−3.87725	−0.125531
$955$	−12.0073	−0.388546
$956$	−23.1917	−0.750073
$957$	20.8332	0.673442
$958$	−2.80681	−0.0906839
$959$	−2.65393	−0.0856999
$960$	8.36031	0.269828
$961$	7.52851	0.242855
$962$	−38.4511	−1.23971
$963$	11.4070	0.367587
$964$	12.7563	0.410854
$965$	1.31703	0.0423968
$966$	1.36613	0.0439545
$967$	−17.8479	−0.573949	−0.286974	−	0.957938i	$-0.592649\pi$
$967$	−17.8479	−0.573949	−0.286974	+	0.957938i	$0.592649\pi$
$968$	5.75371	0.184931
$969$	−18.0895	−0.581118
$970$	−10.5707	−0.339406
$971$	−53.5407	−1.71820	−0.859102	−	0.511804i	$-0.828977\pi$
$971$	−53.5407	−1.71820	−0.859102	+	0.511804i	$0.828977\pi$
$972$	−14.2419	−0.456810
$973$	−10.9482	−0.350983
$974$	7.77980	0.249281
$975$	11.2120	0.359070
$976$	13.3433	0.427108
$977$	45.0465	1.44116	0.720582	−	0.693369i	$-0.243874\pi$
$977$	45.0465	1.44116	0.720582	+	0.693369i	$0.243874\pi$
$978$	−42.7691	−1.36761
$979$	−1.52080	−0.0486051
$980$	2.41725	0.0772162
$981$	−0.112863	−0.00360344
$982$	31.8608	1.01672
$983$	45.4373	1.44922	0.724612	−	0.689157i	$-0.242019\pi$
$983$	45.4373	1.44922	0.724612	+	0.689157i	$0.242019\pi$
$984$	−9.49738	−0.302765
$985$	23.9969	0.764605
$986$	33.6815	1.07264
$987$	−2.22019	−0.0706695
$988$	−12.0866	−0.384527
$989$	1.33923	0.0425850
$990$	−11.9149	−0.378682
$991$	40.9310	1.30022	0.650108	−	0.759842i	$-0.274724\pi$
$991$	40.9310	1.30022	0.650108	+	0.759842i	$0.274724\pi$
$992$	43.5527	1.38280
$993$	20.8934	0.663033
$994$	15.4417	0.489780
$995$	−3.23539	−0.102569
$996$	−19.2585	−0.610230
$997$	41.2751	1.30720	0.653598	−	0.756842i	$-0.273259\pi$
$997$	41.2751	1.30720	0.653598	+	0.756842i	$0.273259\pi$
$998$	24.5474	0.777033
$999$	35.6492	1.12789

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.d.1.18	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.d.1.18	✓	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)

\(f(q)\)	\(=\)	\(q-1.87092 q^{2} -1.43026 q^{3} +1.50033 q^{4} +1.61115 q^{5} +2.67590 q^{6} -1.00000 q^{7} +0.934843 q^{8} -0.954356 q^{9} +O(q^{10})\)	\(q-1.87092 q^{2} -1.43026 q^{3} +1.50033 q^{4} +1.61115 q^{5} +2.67590 q^{6} -1.00000 q^{7} +0.934843 q^{8} -0.954356 q^{9} -3.01432 q^{10} -4.14183 q^{11} -2.14586 q^{12} +3.26058 q^{13} +1.87092 q^{14} -2.30436 q^{15} -4.74967 q^{16} -5.11903 q^{17} +1.78552 q^{18} -2.47072 q^{19} +2.41725 q^{20} +1.43026 q^{21} +7.74901 q^{22} -0.510532 q^{23} -1.33707 q^{24} -2.40421 q^{25} -6.10028 q^{26} +5.65576 q^{27} -1.50033 q^{28} +3.51681 q^{29} +4.31126 q^{30} +6.20713 q^{31} +7.01655 q^{32} +5.92389 q^{33} +9.57727 q^{34} -1.61115 q^{35} -1.43185 q^{36} +6.30318 q^{37} +4.62252 q^{38} -4.66348 q^{39} +1.50617 q^{40} +7.10314 q^{41} -2.67590 q^{42} -2.62321 q^{43} -6.21410 q^{44} -1.53761 q^{45} +0.955162 q^{46} -1.55230 q^{47} +6.79326 q^{48} +1.00000 q^{49} +4.49807 q^{50} +7.32154 q^{51} +4.89195 q^{52} -2.17150 q^{53} -10.5815 q^{54} -6.67309 q^{55} -0.934843 q^{56} +3.53378 q^{57} -6.57966 q^{58} +12.6137 q^{59} -3.45730 q^{60} -2.80930 q^{61} -11.6130 q^{62} +0.954356 q^{63} -3.62804 q^{64} +5.25328 q^{65} -11.0831 q^{66} -13.8186 q^{67} -7.68022 q^{68} +0.730193 q^{69} +3.01432 q^{70} +8.25353 q^{71} -0.892173 q^{72} +6.75117 q^{73} -11.7927 q^{74} +3.43864 q^{75} -3.70690 q^{76} +4.14183 q^{77} +8.72498 q^{78} -9.12911 q^{79} -7.65242 q^{80} -5.22614 q^{81} -13.2894 q^{82} +8.97474 q^{83} +2.14586 q^{84} -8.24750 q^{85} +4.90780 q^{86} -5.02995 q^{87} -3.87196 q^{88} +0.367182 q^{89} +2.87674 q^{90} -3.26058 q^{91} -0.765965 q^{92} -8.87782 q^{93} +2.90422 q^{94} -3.98070 q^{95} -10.0355 q^{96} +3.50684 q^{97} -1.87092 q^{98} +3.95278 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9}+O(q^{10}) \) 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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