LMFDB - Embedded newform 6013.2.a.c.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6013,2,Mod(1,6013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6013, 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("6013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6013 = 7 \cdot 859 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6013.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:	$48.0140467354$
Analytic rank:	$1$
Dimension:	$104$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.37810 q^{2} +0.188335 q^{3} +3.65538 q^{4} +0.902654 q^{5} -0.447879 q^{6} -1.00000 q^{7} -3.93667 q^{8} -2.96453 q^{9} +O(q^{10})$	\(q-2.37810 q^{2} +0.188335 q^{3} +3.65538 q^{4} +0.902654 q^{5} -0.447879 q^{6} -1.00000 q^{7} -3.93667 q^{8} -2.96453 q^{9} -2.14661 q^{10} -3.00738 q^{11} +0.688435 q^{12} +6.41331 q^{13} +2.37810 q^{14} +0.170001 q^{15} +2.05104 q^{16} -6.94054 q^{17} +7.04996 q^{18} +5.90237 q^{19} +3.29954 q^{20} -0.188335 q^{21} +7.15186 q^{22} +8.24686 q^{23} -0.741410 q^{24} -4.18522 q^{25} -15.2515 q^{26} -1.12333 q^{27} -3.65538 q^{28} -4.36719 q^{29} -0.404280 q^{30} +1.63016 q^{31} +2.99574 q^{32} -0.566393 q^{33} +16.5053 q^{34} -0.902654 q^{35} -10.8365 q^{36} -6.07235 q^{37} -14.0364 q^{38} +1.20785 q^{39} -3.55345 q^{40} -9.42544 q^{41} +0.447879 q^{42} +4.08741 q^{43} -10.9931 q^{44} -2.67595 q^{45} -19.6119 q^{46} +6.08992 q^{47} +0.386282 q^{48} +1.00000 q^{49} +9.95288 q^{50} -1.30714 q^{51} +23.4431 q^{52} +4.41809 q^{53} +2.67139 q^{54} -2.71462 q^{55} +3.93667 q^{56} +1.11162 q^{57} +10.3856 q^{58} -14.1265 q^{59} +0.621418 q^{60} +11.4274 q^{61} -3.87668 q^{62} +2.96453 q^{63} -11.2263 q^{64} +5.78900 q^{65} +1.34694 q^{66} +9.78138 q^{67} -25.3703 q^{68} +1.55317 q^{69} +2.14661 q^{70} +4.26748 q^{71} +11.6704 q^{72} +6.00503 q^{73} +14.4407 q^{74} -0.788221 q^{75} +21.5754 q^{76} +3.00738 q^{77} -2.87239 q^{78} -10.3063 q^{79} +1.85138 q^{80} +8.68203 q^{81} +22.4147 q^{82} +5.48540 q^{83} -0.688435 q^{84} -6.26491 q^{85} -9.72028 q^{86} -0.822493 q^{87} +11.8390 q^{88} +5.47576 q^{89} +6.36368 q^{90} -6.41331 q^{91} +30.1454 q^{92} +0.307015 q^{93} -14.4825 q^{94} +5.32780 q^{95} +0.564202 q^{96} -8.25745 q^{97} -2.37810 q^{98} +8.91546 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 19 q^{2} - 26 q^{3} + 99 q^{4} + 2 q^{5} + 2 q^{6} - 104 q^{7} - 54 q^{8} + 90 q^{9}+O(q^{10}) $ 104 * q - 19 * q^2 - 26 * q^3 + 99 * q^4 + 2 * q^5 + 2 * q^6 - 104 * q^7 - 54 * q^8 + 90 * q^9	\( 104 q - 19 q^{2} - 26 q^{3} + 99 q^{4} + 2 q^{5} + 2 q^{6} - 104 q^{7} - 54 q^{8} + 90 q^{9} + 3 q^{10} - 54 q^{11} - 38 q^{12} + 7 q^{13} + 19 q^{14} - 33 q^{15} + 93 q^{16} - 7 q^{17} - 55 q^{18} - 12 q^{19} - 24 q^{20} + 26 q^{21} - 22 q^{22} - 69 q^{23} + 78 q^{25} - 11 q^{26} - 95 q^{27} - 99 q^{28} - 41 q^{29} - 26 q^{30} - 12 q^{31} - 127 q^{32} - 6 q^{33} - 17 q^{34} - 2 q^{35} + 71 q^{36} - 47 q^{37} - 32 q^{38} - 57 q^{39} + 6 q^{40} + 10 q^{41} - 2 q^{42} - 41 q^{43} - 120 q^{44} + 23 q^{45} - 31 q^{46} - 99 q^{47} - 84 q^{48} + 104 q^{49} - 104 q^{50} - 74 q^{51} + 14 q^{52} - 74 q^{53} + 19 q^{54} - 32 q^{55} + 54 q^{56} - 47 q^{57} - 36 q^{58} - 76 q^{59} - 99 q^{60} + 49 q^{61} - 55 q^{62} - 90 q^{63} + 86 q^{64} - 70 q^{65} + 61 q^{66} - 117 q^{67} - 30 q^{68} + 51 q^{69} - 3 q^{70} - 125 q^{71} - 147 q^{72} - 20 q^{73} - 75 q^{74} - 124 q^{75} + 4 q^{76} + 54 q^{77} - 70 q^{78} - 72 q^{79} - 69 q^{80} + 76 q^{81} - 37 q^{82} - 98 q^{83} + 38 q^{84} - 33 q^{85} - 64 q^{86} - 8 q^{87} - 62 q^{88} - 26 q^{89} + 11 q^{90} - 7 q^{91} - 162 q^{92} - 81 q^{93} + 31 q^{94} - 116 q^{95} + 20 q^{96} - 61 q^{97} - 19 q^{98} - 158 q^{99}+O(q^{100}) \) 104 * q - 19 * q^2 - 26 * q^3 + 99 * q^4 + 2 * q^5 + 2 * q^6 - 104 * q^7 - 54 * q^8 + 90 * q^9 + 3 * q^10 - 54 * q^11 - 38 * q^12 + 7 * q^13 + 19 * q^14 - 33 * q^15 + 93 * q^16 - 7 * q^17 - 55 * q^18 - 12 * q^19 - 24 * q^20 + 26 * q^21 - 22 * q^22 - 69 * q^23 + 78 * q^25 - 11 * q^26 - 95 * q^27 - 99 * q^28 - 41 * q^29 - 26 * q^30 - 12 * q^31 - 127 * q^32 - 6 * q^33 - 17 * q^34 - 2 * q^35 + 71 * q^36 - 47 * q^37 - 32 * q^38 - 57 * q^39 + 6 * q^40 + 10 * q^41 - 2 * q^42 - 41 * q^43 - 120 * q^44 + 23 * q^45 - 31 * q^46 - 99 * q^47 - 84 * q^48 + 104 * q^49 - 104 * q^50 - 74 * q^51 + 14 * q^52 - 74 * q^53 + 19 * q^54 - 32 * q^55 + 54 * q^56 - 47 * q^57 - 36 * q^58 - 76 * q^59 - 99 * q^60 + 49 * q^61 - 55 * q^62 - 90 * q^63 + 86 * q^64 - 70 * q^65 + 61 * q^66 - 117 * q^67 - 30 * q^68 + 51 * q^69 - 3 * q^70 - 125 * q^71 - 147 * q^72 - 20 * q^73 - 75 * q^74 - 124 * q^75 + 4 * q^76 + 54 * q^77 - 70 * q^78 - 72 * q^79 - 69 * q^80 + 76 * q^81 - 37 * q^82 - 98 * q^83 + 38 * q^84 - 33 * q^85 - 64 * q^86 - 8 * q^87 - 62 * q^88 - 26 * q^89 + 11 * q^90 - 7 * q^91 - 162 * q^92 - 81 * q^93 + 31 * q^94 - 116 * q^95 + 20 * q^96 - 61 * q^97 - 19 * q^98 - 158 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.37810	−1.68157	−0.840787	−	0.541366i	$-0.817907\pi$
$2$	−2.37810	−1.68157	−0.840787	+	0.541366i	$0.817907\pi$
$3$	0.188335	0.108735	0.0543675	−	0.998521i	$-0.482686\pi$
$3$	0.188335	0.108735	0.0543675	+	0.998521i	$0.482686\pi$
$4$	3.65538	1.82769
$5$	0.902654	0.403679	0.201840	−	0.979419i	$-0.435308\pi$
$5$	0.902654	0.403679	0.201840	+	0.979419i	$0.435308\pi$
$6$	−0.447879	−0.182846
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.93667	−1.39182
$9$	−2.96453	−0.988177
$10$	−2.14661	−0.678816
$11$	−3.00738	−0.906758	−0.453379	−	0.891318i	$-0.649782\pi$
$11$	−3.00738	−0.906758	−0.453379	+	0.891318i	$0.649782\pi$
$12$	0.688435	0.198734
$13$	6.41331	1.77873	0.889366	−	0.457195i	$-0.151146\pi$
$13$	6.41331	1.77873	0.889366	+	0.457195i	$0.151146\pi$
$14$	2.37810	0.635575
$15$	0.170001	0.0438941
$16$	2.05104	0.512760
$17$	−6.94054	−1.68333	−0.841664	−	0.540001i	$-0.818424\pi$
$17$	−6.94054	−1.68333	−0.841664	+	0.540001i	$0.818424\pi$
$18$	7.04996	1.66169
$19$	5.90237	1.35410	0.677048	−	0.735939i	$-0.263259\pi$
$19$	5.90237	1.35410	0.677048	+	0.735939i	$0.263259\pi$
$20$	3.29954	0.737800
$21$	−0.188335	−0.0410980
$22$	7.15186	1.52478
$23$	8.24686	1.71959	0.859795	−	0.510640i	$-0.170591\pi$
$23$	8.24686	1.71959	0.859795	+	0.510640i	$0.170591\pi$
$24$	−0.741410	−0.151340
$25$	−4.18522	−0.837043
$26$	−15.2515	−2.99107
$27$	−1.12333	−0.216184
$28$	−3.65538	−0.690802
$29$	−4.36719	−0.810967	−0.405484	−	0.914102i	$-0.632897\pi$
$29$	−4.36719	−0.810967	−0.405484	+	0.914102i	$0.632897\pi$
$30$	−0.404280	−0.0738111
$31$	1.63016	0.292785	0.146392	−	0.989227i	$-0.453234\pi$
$31$	1.63016	0.292785	0.146392	+	0.989227i	$0.453234\pi$
$32$	2.99574	0.529577
$33$	−0.566393	−0.0985964
$34$	16.5053	2.83064
$35$	−0.902654	−0.152576
$36$	−10.8365	−1.80608
$37$	−6.07235	−0.998288	−0.499144	−	0.866519i	$-0.666352\pi$
$37$	−6.07235	−0.998288	−0.499144	+	0.866519i	$0.666352\pi$
$38$	−14.0364	−2.27701
$39$	1.20785	0.193411
$40$	−3.55345	−0.561849
$41$	−9.42544	−1.47201	−0.736003	−	0.676978i	$-0.763289\pi$
$41$	−9.42544	−1.47201	−0.736003	+	0.676978i	$0.763289\pi$
$42$	0.447879	0.0691093
$43$	4.08741	0.623324	0.311662	−	0.950193i	$-0.399114\pi$
$43$	4.08741	0.623324	0.311662	+	0.950193i	$0.399114\pi$
$44$	−10.9931	−1.65727
$45$	−2.67595	−0.398906
$46$	−19.6119	−2.89162
$47$	6.08992	0.888305	0.444153	−	0.895951i	$-0.353505\pi$
$47$	6.08992	0.888305	0.444153	+	0.895951i	$0.353505\pi$
$48$	0.386282	0.0557550
$49$	1.00000	0.142857
$50$	9.95288	1.40755
$51$	−1.30714	−0.183037
$52$	23.4431	3.25097
$53$	4.41809	0.606872	0.303436	−	0.952852i	$-0.401866\pi$
$53$	4.41809	0.606872	0.303436	+	0.952852i	$0.401866\pi$
$54$	2.67139	0.363530
$55$	−2.71462	−0.366040
$56$	3.93667	0.526059
$57$	1.11162	0.147238
$58$	10.3856	1.36370
$59$	−14.1265	−1.83912	−0.919559	−	0.392951i	$-0.871454\pi$
$59$	−14.1265	−1.83912	−0.919559	+	0.392951i	$0.871454\pi$
$60$	0.621418	0.0802248
$61$	11.4274	1.46313	0.731567	−	0.681769i	$-0.238789\pi$
$61$	11.4274	1.46313	0.731567	+	0.681769i	$0.238789\pi$
$62$	−3.87668	−0.492339
$63$	2.96453	0.373496
$64$	−11.2263	−1.40328
$65$	5.78900	0.718037
$66$	1.34694	0.165797
$67$	9.78138	1.19499	0.597493	−	0.801874i	$-0.296164\pi$
$67$	9.78138	1.19499	0.597493	+	0.801874i	$0.296164\pi$
$68$	−25.3703	−3.07660
$69$	1.55317	0.186980
$70$	2.14661	0.256568
$71$	4.26748	0.506457	0.253229	−	0.967406i	$-0.418508\pi$
$71$	4.26748	0.506457	0.253229	+	0.967406i	$0.418508\pi$
$72$	11.6704	1.37537
$73$	6.00503	0.702835	0.351418	−	0.936219i	$-0.385700\pi$
$73$	6.00503	0.702835	0.351418	+	0.936219i	$0.385700\pi$
$74$	14.4407	1.67869
$75$	−0.788221	−0.0910159
$76$	21.5754	2.47487
$77$	3.00738	0.342722
$78$	−2.87239	−0.325234
$79$	−10.3063	−1.15955	−0.579777	−	0.814775i	$-0.696860\pi$
$79$	−10.3063	−1.15955	−0.579777	+	0.814775i	$0.696860\pi$
$80$	1.85138	0.206991
$81$	8.68203	0.964670
$82$	22.4147	2.47529
$83$	5.48540	0.602101	0.301050	−	0.953608i	$-0.402663\pi$
$83$	5.48540	0.602101	0.301050	+	0.953608i	$0.402663\pi$
$84$	−0.688435	−0.0751144
$85$	−6.26491	−0.679525
$86$	−9.72028	−1.04816
$87$	−0.822493	−0.0881806
$88$	11.8390	1.26205
$89$	5.47576	0.580429	0.290215	−	0.956962i	$-0.406273\pi$
$89$	5.47576	0.580429	0.290215	+	0.956962i	$0.406273\pi$
$90$	6.36368	0.670791
$91$	−6.41331	−0.672298
$92$	30.1454	3.14288
$93$	0.307015	0.0318359
$94$	−14.4825	−1.49375
$95$	5.32780	0.546621
$96$	0.564202	0.0575836
$97$	−8.25745	−0.838417	−0.419209	−	0.907890i	$-0.637692\pi$
$97$	−8.25745	−0.838417	−0.419209	+	0.907890i	$0.637692\pi$
$98$	−2.37810	−0.240225
$99$	8.91546	0.896037
$100$	−15.2986	−1.52986
$101$	1.00097	0.0996007	0.0498004	−	0.998759i	$-0.484141\pi$
$101$	1.00097	0.0996007	0.0498004	+	0.998759i	$0.484141\pi$
$102$	3.10853	0.307790
$103$	4.51823	0.445195	0.222597	−	0.974910i	$-0.428547\pi$
$103$	4.51823	0.445195	0.222597	+	0.974910i	$0.428547\pi$
$104$	−25.2471	−2.47568
$105$	−0.170001	−0.0165904
$106$	−10.5067	−1.02050
$107$	−17.8365	−1.72432	−0.862160	−	0.506636i	$-0.830889\pi$
$107$	−17.8365	−1.72432	−0.862160	+	0.506636i	$0.830889\pi$
$108$	−4.10619	−0.395118
$109$	−6.97063	−0.667666	−0.333833	−	0.942632i	$-0.608342\pi$
$109$	−6.97063	−0.667666	−0.333833	+	0.942632i	$0.608342\pi$
$110$	6.45565	0.615522
$111$	−1.14363	−0.108549
$112$	−2.05104	−0.193805
$113$	−11.9466	−1.12384	−0.561919	−	0.827192i	$-0.689937\pi$
$113$	−11.9466	−1.12384	−0.561919	+	0.827192i	$0.689937\pi$
$114$	−2.64355	−0.247591
$115$	7.44406	0.694163
$116$	−15.9637	−1.48220
$117$	−19.0125	−1.75770
$118$	33.5944	3.09261
$119$	6.94054	0.636239
$120$	−0.669237	−0.0610927
$121$	−1.95568	−0.177789
$122$	−27.1757	−2.46037
$123$	−1.77514	−0.160059
$124$	5.95884	0.535119
$125$	−8.29107	−0.741576
$126$	−7.04996	−0.628060
$127$	4.38675	0.389261	0.194630	−	0.980877i	$-0.437649\pi$
$127$	4.38675	0.389261	0.194630	+	0.980877i	$0.437649\pi$
$128$	20.7058	1.83015
$129$	0.769800	0.0677771
$130$	−13.7669	−1.20743
$131$	−10.6660	−0.931893	−0.465947	−	0.884813i	$-0.654286\pi$
$131$	−10.6660	−0.931893	−0.465947	+	0.884813i	$0.654286\pi$
$132$	−2.07038	−0.180204
$133$	−5.90237	−0.511800
$134$	−23.2611	−2.00946
$135$	−1.01398	−0.0872692
$136$	27.3226	2.34289
$137$	−6.87975	−0.587777	−0.293888	−	0.955840i	$-0.594949\pi$
$137$	−6.87975	−0.587777	−0.293888	+	0.955840i	$0.594949\pi$
$138$	−3.69360	−0.314420
$139$	15.7209	1.33343	0.666714	−	0.745313i	$-0.267700\pi$
$139$	15.7209	1.33343	0.666714	+	0.745313i	$0.267700\pi$
$140$	−3.29954	−0.278862
$141$	1.14694	0.0965899
$142$	−10.1485	−0.851645
$143$	−19.2872	−1.61288
$144$	−6.08037	−0.506698
$145$	−3.94206	−0.327371
$146$	−14.2806	−1.18187
$147$	0.188335	0.0155336
$148$	−22.1967	−1.82456
$149$	12.8795	1.05513	0.527563	−	0.849516i	$-0.323106\pi$
$149$	12.8795	1.05513	0.527563	+	0.849516i	$0.323106\pi$
$150$	1.87447	0.153050
$151$	1.68647	0.137243	0.0686213	−	0.997643i	$-0.478140\pi$
$151$	1.68647	0.137243	0.0686213	+	0.997643i	$0.478140\pi$
$152$	−23.2357	−1.88466
$153$	20.5754	1.66343
$154$	−7.15186	−0.576313
$155$	1.47147	0.118191
$156$	4.41515	0.353495
$157$	6.46819	0.516218	0.258109	−	0.966116i	$-0.416901\pi$
$157$	6.46819	0.516218	0.258109	+	0.966116i	$0.416901\pi$
$158$	24.5095	1.94987
$159$	0.832080	0.0659882
$160$	2.70412	0.213779
$161$	−8.24686	−0.649944
$162$	−20.6468	−1.62216
$163$	−9.36426	−0.733466	−0.366733	−	0.930326i	$-0.619524\pi$
$163$	−9.36426	−0.733466	−0.366733	+	0.930326i	$0.619524\pi$
$164$	−34.4536	−2.69037
$165$	−0.511257	−0.0398013
$166$	−13.0448	−1.01248
$167$	5.46231	0.422686	0.211343	−	0.977412i	$-0.432216\pi$
$167$	5.46231	0.422686	0.211343	+	0.977412i	$0.432216\pi$
$168$	0.741410	0.0572011
$169$	28.1306	2.16389
$170$	14.8986	1.14267
$171$	−17.4978	−1.33809
$172$	14.9410	1.13924
$173$	−16.8500	−1.28108	−0.640540	−	0.767925i	$-0.721290\pi$
$173$	−16.8500	−1.28108	−0.640540	+	0.767925i	$0.721290\pi$
$174$	1.95598	0.148282
$175$	4.18522	0.316373
$176$	−6.16825	−0.464950
$177$	−2.66052	−0.199977
$178$	−13.0219	−0.976034
$179$	0.185338	0.0138528	0.00692642	−	0.999976i	$-0.497795\pi$
$179$	0.185338	0.0138528	0.00692642	+	0.999976i	$0.497795\pi$
$180$	−9.78160	−0.729077
$181$	−9.09357	−0.675920	−0.337960	−	0.941161i	$-0.609737\pi$
$181$	−9.09357	−0.675920	−0.337960	+	0.941161i	$0.609737\pi$
$182$	15.2515	1.13052
$183$	2.15218	0.159094
$184$	−32.4651	−2.39336
$185$	−5.48123	−0.402988
$186$	−0.730113	−0.0535345
$187$	20.8728	1.52637
$188$	22.2610	1.62355
$189$	1.12333	0.0817101
$190$	−12.6701	−0.919183
$191$	19.2819	1.39519	0.697594	−	0.716493i	$-0.254254\pi$
$191$	19.2819	1.39519	0.697594	+	0.716493i	$0.254254\pi$
$192$	−2.11429	−0.152586
$193$	−7.88578	−0.567631	−0.283815	−	0.958879i	$-0.591600\pi$
$193$	−7.88578	−0.567631	−0.283815	+	0.958879i	$0.591600\pi$
$194$	19.6371	1.40986
$195$	1.09027	0.0780758
$196$	3.65538	0.261099
$197$	−15.5187	−1.10566	−0.552830	−	0.833294i	$-0.686452\pi$
$197$	−15.5187	−1.10566	−0.552830	+	0.833294i	$0.686452\pi$
$198$	−21.2019	−1.50675
$199$	−16.0166	−1.13539	−0.567693	−	0.823240i	$-0.692164\pi$
$199$	−16.0166	−1.13539	−0.567693	+	0.823240i	$0.692164\pi$
$200$	16.4758	1.16501
$201$	1.84217	0.129937
$202$	−2.38042	−0.167486
$203$	4.36719	0.306517
$204$	−4.77811	−0.334535
$205$	−8.50791	−0.594218
$206$	−10.7448	−0.748627
$207$	−24.4481	−1.69926
$208$	13.1540	0.912063
$209$	−17.7506	−1.22784
$210$	0.404280	0.0278980
$211$	−21.8462	−1.50395	−0.751977	−	0.659190i	$-0.770899\pi$
$211$	−21.8462	−1.50395	−0.751977	+	0.659190i	$0.770899\pi$
$212$	16.1498	1.10917
$213$	0.803715	0.0550696
$214$	42.4171	2.89957
$215$	3.68952	0.251623
$216$	4.42216	0.300890
$217$	−1.63016	−0.110662
$218$	16.5769	1.12273
$219$	1.13095	0.0764228
$220$	−9.92297	−0.669007
$221$	−44.5119	−2.99419
$222$	2.71968	0.182533
$223$	−18.2541	−1.22239	−0.611194	−	0.791481i	$-0.709310\pi$
$223$	−18.2541	−1.22239	−0.611194	+	0.791481i	$0.709310\pi$
$224$	−2.99574	−0.200161
$225$	12.4072	0.827146
$226$	28.4102	1.88982
$227$	23.4373	1.55559	0.777794	−	0.628519i	$-0.216339\pi$
$227$	23.4373	1.55559	0.777794	+	0.628519i	$0.216339\pi$
$228$	4.06339	0.269105
$229$	−11.1105	−0.734205	−0.367102	−	0.930181i	$-0.619650\pi$
$229$	−11.1105	−0.734205	−0.367102	+	0.930181i	$0.619650\pi$
$230$	−17.7028	−1.16729
$231$	0.566393	0.0372659
$232$	17.1922	1.12872
$233$	9.76893	0.639984	0.319992	−	0.947420i	$-0.396320\pi$
$233$	9.76893	0.639984	0.319992	+	0.947420i	$0.396320\pi$
$234$	45.2136	2.95571
$235$	5.49709	0.358590
$236$	−51.6379	−3.36134
$237$	−1.94104	−0.126084
$238$	−16.5053	−1.06988
$239$	−4.06862	−0.263177	−0.131589	−	0.991304i	$-0.542008\pi$
$239$	−4.06862	−0.263177	−0.131589	+	0.991304i	$0.542008\pi$
$240$	0.348679	0.0225071
$241$	−26.1290	−1.68311	−0.841557	−	0.540168i	$-0.818361\pi$
$241$	−26.1290	−1.68311	−0.841557	+	0.540168i	$0.818361\pi$
$242$	4.65082	0.298966
$243$	5.00511	0.321078
$244$	41.7717	2.67416
$245$	0.902654	0.0576685
$246$	4.22146	0.269150
$247$	37.8537	2.40858
$248$	−6.41738	−0.407504
$249$	1.03309	0.0654695
$250$	19.7170	1.24701
$251$	2.57774	0.162705	0.0813527	−	0.996685i	$-0.474076\pi$
$251$	2.57774	0.162705	0.0813527	+	0.996685i	$0.474076\pi$
$252$	10.8365	0.682634
$253$	−24.8014	−1.55925
$254$	−10.4321	−0.654570
$255$	−1.17990	−0.0738882
$256$	−26.7879	−1.67424
$257$	−8.37536	−0.522440	−0.261220	−	0.965279i	$-0.584125\pi$
$257$	−8.37536	−0.522440	−0.261220	+	0.965279i	$0.584125\pi$
$258$	−1.83067	−0.113972
$259$	6.07235	0.377317
$260$	21.1610	1.31235
$261$	12.9467	0.801379
$262$	25.3649	1.56705
$263$	−10.0769	−0.621367	−0.310683	−	0.950513i	$-0.600558\pi$
$263$	−10.0769	−0.621367	−0.310683	+	0.950513i	$0.600558\pi$
$264$	2.22970	0.137229
$265$	3.98801	0.244981
$266$	14.0364	0.860630
$267$	1.03127	0.0631130
$268$	35.7546	2.18406
$269$	9.75778	0.594943	0.297471	−	0.954731i	$-0.403857\pi$
$269$	9.75778	0.594943	0.297471	+	0.954731i	$0.403857\pi$
$270$	2.41134	0.146750
$271$	15.3603	0.933074	0.466537	−	0.884502i	$-0.345502\pi$
$271$	15.3603	0.933074	0.466537	+	0.884502i	$0.345502\pi$
$272$	−14.2353	−0.863144
$273$	−1.20785	−0.0731023
$274$	16.3608	0.988390
$275$	12.5865	0.758996
$276$	5.67742	0.341741
$277$	−19.7278	−1.18533	−0.592664	−	0.805450i	$-0.701924\pi$
$277$	−19.7278	−1.18533	−0.592664	+	0.805450i	$0.701924\pi$
$278$	−37.3859	−2.24226
$279$	−4.83265	−0.289323
$280$	3.55345	0.212359
$281$	−7.32050	−0.436704	−0.218352	−	0.975870i	$-0.570068\pi$
$281$	−7.32050	−0.436704	−0.218352	+	0.975870i	$0.570068\pi$
$282$	−2.72755	−0.162423
$283$	17.1486	1.01938	0.509690	−	0.860358i	$-0.329760\pi$
$283$	17.1486	1.01938	0.509690	+	0.860358i	$0.329760\pi$
$284$	15.5993	0.925646
$285$	1.00341	0.0594368
$286$	45.8671	2.71218
$287$	9.42544	0.556366
$288$	−8.88097	−0.523316
$289$	31.1711	1.83360
$290$	9.37464	0.550498
$291$	−1.55516	−0.0911654
$292$	21.9506	1.28456
$293$	5.10192	0.298057	0.149029	−	0.988833i	$-0.452385\pi$
$293$	5.10192	0.298057	0.149029	+	0.988833i	$0.452385\pi$
$294$	−0.447879	−0.0261209
$295$	−12.7514	−0.742414
$296$	23.9048	1.38944
$297$	3.37827	0.196027
$298$	−30.6287	−1.77427
$299$	52.8897	3.05869
$300$	−2.88125	−0.166349
$301$	−4.08741	−0.235594
$302$	−4.01059	−0.230784
$303$	0.188518	0.0108301
$304$	12.1060	0.694327
$305$	10.3150	0.590637
$306$	−48.9306	−2.79717
$307$	−9.80389	−0.559537	−0.279769	−	0.960067i	$-0.590258\pi$
$307$	−9.80389	−0.559537	−0.279769	+	0.960067i	$0.590258\pi$
$308$	10.9931	0.626390
$309$	0.850939	0.0484082
$310$	−3.49930	−0.198747
$311$	−31.6297	−1.79356	−0.896778	−	0.442480i	$-0.854099\pi$
$311$	−31.6297	−1.79356	−0.896778	+	0.442480i	$0.854099\pi$
$312$	−4.75490	−0.269193
$313$	14.0516	0.794244	0.397122	−	0.917766i	$-0.370009\pi$
$313$	14.0516	0.794244	0.397122	+	0.917766i	$0.370009\pi$
$314$	−15.3820	−0.868058
$315$	2.67595	0.150772
$316$	−37.6736	−2.11930
$317$	25.9673	1.45847	0.729236	−	0.684263i	$-0.239876\pi$
$317$	25.9673	1.45847	0.729236	+	0.684263i	$0.239876\pi$
$318$	−1.97877	−0.110964
$319$	13.1338	0.735351
$320$	−10.1334	−0.566476
$321$	−3.35923	−0.187494
$322$	19.6119	1.09293
$323$	−40.9656	−2.27939
$324$	31.7361	1.76312
$325$	−26.8411	−1.48888
$326$	22.2692	1.23338
$327$	−1.31281	−0.0725986
$328$	37.1048	2.04877
$329$	−6.08992	−0.335748
$330$	1.21582	0.0669289
$331$	11.3831	0.625670	0.312835	−	0.949808i	$-0.398721\pi$
$331$	11.3831	0.625670	0.312835	+	0.949808i	$0.398721\pi$
$332$	20.0512	1.10045
$333$	18.0017	0.986485
$334$	−12.9899	−0.710778
$335$	8.82920	0.482391
$336$	−0.386282	−0.0210734
$337$	−13.1158	−0.714464	−0.357232	−	0.934016i	$-0.616279\pi$
$337$	−13.1158	−0.714464	−0.357232	+	0.934016i	$0.616279\pi$
$338$	−66.8974	−3.63874
$339$	−2.24995	−0.122201
$340$	−22.9006	−1.24196
$341$	−4.90249	−0.265485
$342$	41.6115	2.25009
$343$	−1.00000	−0.0539949
$344$	−16.0908	−0.867555
$345$	1.40198	0.0754798
$346$	40.0710	2.15423
$347$	−10.7543	−0.577323	−0.288662	−	0.957431i	$-0.593210\pi$
$347$	−10.7543	−0.577323	−0.288662	+	0.957431i	$0.593210\pi$
$348$	−3.00653	−0.161167
$349$	8.67516	0.464371	0.232185	−	0.972672i	$-0.425412\pi$
$349$	8.67516	0.464371	0.232185	+	0.972672i	$0.425412\pi$
$350$	−9.95288	−0.532004
$351$	−7.20425	−0.384534
$352$	−9.00932	−0.480199
$353$	−19.3368	−1.02919	−0.514596	−	0.857433i	$-0.672058\pi$
$353$	−19.3368	−1.02919	−0.514596	+	0.857433i	$0.672058\pi$
$354$	6.32699	0.336275
$355$	3.85206	0.204446
$356$	20.0160	1.06084
$357$	1.30714	0.0691814
$358$	−0.440754	−0.0232946
$359$	27.7292	1.46349	0.731746	−	0.681577i	$-0.238706\pi$
$359$	27.7292	1.46349	0.731746	+	0.681577i	$0.238706\pi$
$360$	10.5343	0.555206
$361$	15.8380	0.833577
$362$	21.6255	1.13661
$363$	−0.368323	−0.0193319
$364$	−23.4431	−1.22875
$365$	5.42046	0.283720
$366$	−5.11812	−0.267528
$367$	−28.1018	−1.46690	−0.733451	−	0.679742i	$-0.762092\pi$
$367$	−28.1018	−1.46690	−0.733451	+	0.679742i	$0.762092\pi$
$368$	16.9146	0.881737
$369$	27.9420	1.45460
$370$	13.0349	0.677654
$371$	−4.41809	−0.229376
$372$	1.12226	0.0581862
$373$	5.52939	0.286301	0.143150	−	0.989701i	$-0.454277\pi$
$373$	5.52939	0.286301	0.143150	+	0.989701i	$0.454277\pi$
$374$	−49.6378	−2.56671
$375$	−1.56150	−0.0806353
$376$	−23.9740	−1.23636
$377$	−28.0082	−1.44249
$378$	−2.67139	−0.137401
$379$	28.7580	1.47720	0.738600	−	0.674144i	$-0.235487\pi$
$379$	28.7580	1.47720	0.738600	+	0.674144i	$0.235487\pi$
$380$	19.4751	0.999053
$381$	0.826176	0.0423263
$382$	−45.8543	−2.34611
$383$	−29.8821	−1.52690	−0.763452	−	0.645864i	$-0.776497\pi$
$383$	−29.8821	−1.52690	−0.763452	+	0.645864i	$0.776497\pi$
$384$	3.89961	0.199001
$385$	2.71462	0.138350
$386$	18.7532	0.954513
$387$	−12.1172	−0.615954
$388$	−30.1841	−1.53237
$389$	21.1370	1.07169	0.535844	−	0.844317i	$-0.319994\pi$
$389$	21.1370	1.07169	0.535844	+	0.844317i	$0.319994\pi$
$390$	−2.59278	−0.131290
$391$	−57.2377	−2.89463
$392$	−3.93667	−0.198832
$393$	−2.00878	−0.101329
$394$	36.9051	1.85925
$395$	−9.30306	−0.468088
$396$	32.5894	1.63768
$397$	11.6312	0.583751	0.291876	−	0.956456i	$-0.405721\pi$
$397$	11.6312	0.583751	0.291876	+	0.956456i	$0.405721\pi$
$398$	38.0891	1.90924
$399$	−1.11162	−0.0556506
$400$	−8.58405	−0.429202
$401$	30.2746	1.51184	0.755921	−	0.654663i	$-0.227189\pi$
$401$	30.2746	1.51184	0.755921	+	0.654663i	$0.227189\pi$
$402$	−4.38088	−0.218498
$403$	10.4547	0.520786
$404$	3.65894	0.182039
$405$	7.83687	0.389417
$406$	−10.3856	−0.515430
$407$	18.2618	0.905206
$408$	5.14579	0.254755
$409$	−17.8279	−0.881534	−0.440767	−	0.897621i	$-0.645294\pi$
$409$	−17.8279	−0.881534	−0.440767	+	0.897621i	$0.645294\pi$
$410$	20.2327	0.999222
$411$	−1.29569	−0.0639119
$412$	16.5158	0.813677
$413$	14.1265	0.695122
$414$	58.1400	2.85743
$415$	4.95142	0.243056
$416$	19.2126	0.941976
$417$	2.96079	0.144990
$418$	42.2129	2.06470
$419$	−28.7989	−1.40692	−0.703460	−	0.710735i	$-0.748363\pi$
$419$	−28.7989	−1.40692	−0.703460	+	0.710735i	$0.748363\pi$
$420$	−0.621418	−0.0303221
$421$	−9.34846	−0.455616	−0.227808	−	0.973706i	$-0.573156\pi$
$421$	−9.34846	−0.455616	−0.227808	+	0.973706i	$0.573156\pi$
$422$	51.9525	2.52901
$423$	−18.0537	−0.877803
$424$	−17.3925	−0.844657
$425$	29.0477	1.40902
$426$	−1.91132	−0.0926036
$427$	−11.4274	−0.553013
$428$	−65.1992	−3.15152
$429$	−3.63246	−0.175377
$430$	−8.77405	−0.423122
$431$	−11.5221	−0.555002	−0.277501	−	0.960725i	$-0.589506\pi$
$431$	−11.5221	−0.555002	−0.277501	+	0.960725i	$0.589506\pi$
$432$	−2.30399	−0.110851
$433$	−33.9755	−1.63276	−0.816379	−	0.577517i	$-0.804022\pi$
$433$	−33.9755	−1.63276	−0.816379	+	0.577517i	$0.804022\pi$
$434$	3.87668	0.186087
$435$	−0.742427	−0.0355967
$436$	−25.4803	−1.22029
$437$	48.6760	2.32849
$438$	−2.68953	−0.128511
$439$	−10.6224	−0.506979	−0.253490	−	0.967338i	$-0.581578\pi$
$439$	−10.6224	−0.506979	−0.253490	+	0.967338i	$0.581578\pi$
$440$	10.6866	0.509462
$441$	−2.96453	−0.141168
$442$	105.854	5.03495
$443$	11.8542	0.563211	0.281606	−	0.959530i	$-0.409133\pi$
$443$	11.8542	0.563211	0.281606	+	0.959530i	$0.409133\pi$
$444$	−4.18042	−0.198394
$445$	4.94272	0.234307
$446$	43.4103	2.05554
$447$	2.42565	0.114729
$448$	11.2263	0.530391
$449$	30.4976	1.43927	0.719636	−	0.694352i	$-0.244309\pi$
$449$	30.4976	1.43927	0.719636	+	0.694352i	$0.244309\pi$
$450$	−29.5056	−1.39091
$451$	28.3458	1.33475
$452$	−43.6693	−2.05403
$453$	0.317620	0.0149231
$454$	−55.7363	−2.61584
$455$	−5.78900	−0.271393
$456$	−4.37608	−0.204929
$457$	−3.80723	−0.178095	−0.0890473	−	0.996027i	$-0.528382\pi$
$457$	−3.80723	−0.178095	−0.0890473	+	0.996027i	$0.528382\pi$
$458$	26.4220	1.23462
$459$	7.79650	0.363910
$460$	27.2109	1.26871
$461$	−19.0557	−0.887514	−0.443757	−	0.896147i	$-0.646355\pi$
$461$	−19.0557	−0.887514	−0.443757	+	0.896147i	$0.646355\pi$
$462$	−1.34694	−0.0626654
$463$	−17.4947	−0.813046	−0.406523	−	0.913641i	$-0.633259\pi$
$463$	−17.4947	−0.813046	−0.406523	+	0.913641i	$0.633259\pi$
$464$	−8.95729	−0.415832
$465$	0.277128	0.0128515
$466$	−23.2315	−1.07618
$467$	−28.6157	−1.32418	−0.662089	−	0.749425i	$-0.730330\pi$
$467$	−28.6157	−1.32418	−0.662089	+	0.749425i	$0.730330\pi$
$468$	−69.4977	−3.21253
$469$	−9.78138	−0.451662
$470$	−13.0726	−0.602996
$471$	1.21818	0.0561310
$472$	55.6115	2.55972
$473$	−12.2924	−0.565204
$474$	4.61600	0.212020
$475$	−24.7027	−1.13344
$476$	25.3703	1.16285
$477$	−13.0976	−0.599696
$478$	9.67560	0.442552
$479$	−23.2415	−1.06193	−0.530967	−	0.847393i	$-0.678171\pi$
$479$	−23.2415	−1.06193	−0.530967	+	0.847393i	$0.678171\pi$
$480$	0.509279	0.0232453
$481$	−38.9439	−1.77569
$482$	62.1374	2.83028
$483$	−1.55317	−0.0706717
$484$	−7.14877	−0.324944
$485$	−7.45363	−0.338452
$486$	−11.9027	−0.539916
$487$	8.92678	0.404511	0.202255	−	0.979333i	$-0.435173\pi$
$487$	8.92678	0.404511	0.202255	+	0.979333i	$0.435173\pi$
$488$	−44.9860	−2.03642
$489$	−1.76362	−0.0797534
$490$	−2.14661	−0.0969738
$491$	−11.4525	−0.516843	−0.258421	−	0.966032i	$-0.583202\pi$
$491$	−11.4525	−0.516843	−0.258421	+	0.966032i	$0.583202\pi$
$492$	−6.48880	−0.292538
$493$	30.3107	1.36512
$494$	−90.0201	−4.05020
$495$	8.04758	0.361712
$496$	3.34352	0.150128
$497$	−4.26748	−0.191423
$498$	−2.45680	−0.110092
$499$	27.5933	1.23524	0.617622	−	0.786475i	$-0.288096\pi$
$499$	27.5933	1.23524	0.617622	+	0.786475i	$0.288096\pi$
$500$	−30.3070	−1.35537
$501$	1.02874	0.0459608
$502$	−6.13013	−0.273601
$503$	−8.68083	−0.387059	−0.193530	−	0.981094i	$-0.561994\pi$
$503$	−8.68083	−0.387059	−0.193530	+	0.981094i	$0.561994\pi$
$504$	−11.6704	−0.519839
$505$	0.903534	0.0402067
$506$	58.9804	2.62200
$507$	5.29796	0.235291
$508$	16.0352	0.711448
$509$	−39.2284	−1.73877	−0.869385	−	0.494136i	$-0.835485\pi$
$509$	−39.2284	−1.73877	−0.869385	+	0.494136i	$0.835485\pi$
$510$	2.80592	0.124248
$511$	−6.00503	−0.265647
$512$	22.2929	0.985217
$513$	−6.63029	−0.292735
$514$	19.9175	0.878522
$515$	4.07840	0.179716
$516$	2.81391	0.123876
$517$	−18.3147	−0.805478
$518$	−14.4407	−0.634487
$519$	−3.17344	−0.139298
$520$	−22.7894	−0.999380
$521$	−36.1071	−1.58188	−0.790941	−	0.611892i	$-0.790409\pi$
$521$	−36.1071	−1.58188	−0.790941	+	0.611892i	$0.790409\pi$
$522$	−30.7885	−1.34758
$523$	−15.7866	−0.690301	−0.345150	−	0.938547i	$-0.612172\pi$
$523$	−15.7866	−0.690301	−0.345150	+	0.938547i	$0.612172\pi$
$524$	−38.9883	−1.70321
$525$	0.788221	0.0344008
$526$	23.9639	1.04487
$527$	−11.3142	−0.492853
$528$	−1.16170	−0.0505563
$529$	45.0107	1.95699
$530$	−9.48390	−0.411954
$531$	41.8786	1.81737
$532$	−21.5754	−0.935412
$533$	−60.4483	−2.61831
$534$	−2.45248	−0.106129
$535$	−16.1002	−0.696072
$536$	−38.5060	−1.66321
$537$	0.0349056	0.00150629
$538$	−23.2050	−1.00044
$539$	−3.00738	−0.129537
$540$	−3.70647	−0.159501
$541$	−28.0937	−1.20784	−0.603922	−	0.797043i	$-0.706396\pi$
$541$	−28.0937	−1.20784	−0.603922	+	0.797043i	$0.706396\pi$
$542$	−36.5285	−1.56903
$543$	−1.71263	−0.0734962
$544$	−20.7921	−0.891453
$545$	−6.29207	−0.269523
$546$	2.87239	0.122927
$547$	19.4291	0.830727	0.415363	−	0.909656i	$-0.363654\pi$
$547$	19.4291	0.830727	0.415363	+	0.909656i	$0.363654\pi$
$548$	−25.1481	−1.07427
$549$	−33.8770	−1.44584
$550$	−29.9321	−1.27631
$551$	−25.7768	−1.09813
$552$	−6.11431	−0.260242
$553$	10.3063	0.438270
$554$	46.9147	1.99322
$555$	−1.03231	−0.0438189
$556$	57.4658	2.43709
$557$	−12.6661	−0.536680	−0.268340	−	0.963324i	$-0.586475\pi$
$557$	−12.6661	−0.536680	−0.268340	+	0.963324i	$0.586475\pi$
$558$	11.4925	0.486518
$559$	26.2138	1.10873
$560$	−1.85138	−0.0782351
$561$	3.93108	0.165970
$562$	17.4089	0.734350
$563$	−8.40890	−0.354393	−0.177196	−	0.984176i	$-0.556703\pi$
$563$	−8.40890	−0.354393	−0.177196	+	0.984176i	$0.556703\pi$
$564$	4.19251	0.176536
$565$	−10.7836	−0.453670
$566$	−40.7812	−1.71416
$567$	−8.68203	−0.364611
$568$	−16.7997	−0.704898
$569$	−22.4017	−0.939128	−0.469564	−	0.882898i	$-0.655589\pi$
$569$	−22.4017	−0.939128	−0.469564	+	0.882898i	$0.655589\pi$
$570$	−2.38621	−0.0999474
$571$	26.9069	1.12602	0.563010	−	0.826450i	$-0.309643\pi$
$571$	26.9069	1.12602	0.563010	+	0.826450i	$0.309643\pi$
$572$	−70.5022	−2.94785
$573$	3.63145	0.151706
$574$	−22.4147	−0.935570
$575$	−34.5149	−1.43937
$576$	33.2806	1.38669
$577$	−0.0487168	−0.00202811	−0.00101405	−	0.999999i	$-0.500323\pi$
$577$	−0.0487168	−0.00202811	−0.00101405	+	0.999999i	$0.500323\pi$
$578$	−74.1282	−3.08333
$579$	−1.48517	−0.0617214
$580$	−14.4097	−0.598332
$581$	−5.48540	−0.227573
$582$	3.69834	0.153301
$583$	−13.2869	−0.550286
$584$	−23.6398	−0.978221
$585$	−17.1617	−0.709548
$586$	−12.1329	−0.501205
$587$	25.2143	1.04071	0.520353	−	0.853951i	$-0.325800\pi$
$587$	25.2143	1.04071	0.520353	+	0.853951i	$0.325800\pi$
$588$	0.688435	0.0283906
$589$	9.62178	0.396459
$590$	30.3241	1.24842
$591$	−2.92271	−0.120224
$592$	−12.4546	−0.511882
$593$	−13.7718	−0.565540	−0.282770	−	0.959188i	$-0.591253\pi$
$593$	−13.7718	−0.565540	−0.282770	+	0.959188i	$0.591253\pi$
$594$	−8.03388	−0.329634
$595$	6.26491	0.256836
$596$	47.0793	1.92844
$597$	−3.01648	−0.123456
$598$	−125.777	−5.14341
$599$	−29.0244	−1.18590	−0.592952	−	0.805238i	$-0.702037\pi$
$599$	−29.0244	−1.18590	−0.592952	+	0.805238i	$0.702037\pi$
$600$	3.10296	0.126678
$601$	45.8563	1.87052	0.935259	−	0.353963i	$-0.115166\pi$
$601$	45.8563	1.87052	0.935259	+	0.353963i	$0.115166\pi$
$602$	9.72028	0.396169
$603$	−28.9972	−1.18086
$604$	6.16467	0.250837
$605$	−1.76531	−0.0717699
$606$	−0.448316	−0.0182116
$607$	−30.4351	−1.23532	−0.617661	−	0.786445i	$-0.711919\pi$
$607$	−30.4351	−1.23532	−0.617661	+	0.786445i	$0.711919\pi$
$608$	17.6820	0.717099
$609$	0.822493	0.0333291
$610$	−24.5302	−0.993200
$611$	39.0565	1.58006
$612$	75.2111	3.04023
$613$	27.0239	1.09148	0.545742	−	0.837953i	$-0.316248\pi$
$613$	27.0239	1.09148	0.545742	+	0.837953i	$0.316248\pi$
$614$	23.3147	0.940903
$615$	−1.60233	−0.0646124
$616$	−11.8390	−0.477008
$617$	−14.9267	−0.600925	−0.300462	−	0.953794i	$-0.597141\pi$
$617$	−14.9267	−0.600925	−0.300462	+	0.953794i	$0.597141\pi$
$618$	−2.02362	−0.0814020
$619$	0.183707	0.00738379	0.00369190	−	0.999993i	$-0.498825\pi$
$619$	0.183707	0.00738379	0.00369190	+	0.999993i	$0.498825\pi$
$620$	5.37877	0.216017
$621$	−9.26393	−0.371749
$622$	75.2188	3.01600
$623$	−5.47576	−0.219382
$624$	2.47735	0.0991733
$625$	13.4421	0.537684
$626$	−33.4162	−1.33558
$627$	−3.34306	−0.133509
$628$	23.6437	0.943486
$629$	42.1454	1.68045
$630$	−6.36368	−0.253535
$631$	−36.3884	−1.44860	−0.724299	−	0.689486i	$-0.757836\pi$
$631$	−36.3884	−1.44860	−0.724299	+	0.689486i	$0.757836\pi$
$632$	40.5726	1.61389
$633$	−4.11439	−0.163532
$634$	−61.7530	−2.45253
$635$	3.95971	0.157136
$636$	3.04157	0.120606
$637$	6.41331	0.254105
$638$	−31.2335	−1.23655
$639$	−12.6511	−0.500469
$640$	18.6901	0.738792
$641$	−13.0926	−0.517126	−0.258563	−	0.965994i	$-0.583249\pi$
$641$	−13.0926	−0.517126	−0.258563	+	0.965994i	$0.583249\pi$
$642$	7.98860	0.315285
$643$	−38.5196	−1.51907	−0.759533	−	0.650469i	$-0.774572\pi$
$643$	−38.5196	−1.51907	−0.759533	+	0.650469i	$0.774572\pi$
$644$	−30.1454	−1.18790
$645$	0.694863	0.0273602
$646$	97.4206	3.83296
$647$	−25.2996	−0.994629	−0.497315	−	0.867570i	$-0.665681\pi$
$647$	−25.2996	−0.994629	−0.497315	+	0.867570i	$0.665681\pi$
$648$	−34.1782	−1.34265
$649$	42.4838	1.66764
$650$	63.8309	2.50365
$651$	−0.307015	−0.0120329
$652$	−34.2299	−1.34055
$653$	24.2979	0.950849	0.475424	−	0.879757i	$-0.342295\pi$
$653$	24.2979	0.950849	0.475424	+	0.879757i	$0.342295\pi$
$654$	3.12200	0.122080
$655$	−9.62771	−0.376186
$656$	−19.3320	−0.754786
$657$	−17.8021	−0.694525
$658$	14.4825	0.564585
$659$	−20.9091	−0.814503	−0.407251	−	0.913316i	$-0.633513\pi$
$659$	−20.9091	−0.814503	−0.407251	+	0.913316i	$0.633513\pi$
$660$	−1.86884	−0.0727445
$661$	−28.5423	−1.11017	−0.555083	−	0.831795i	$-0.687313\pi$
$661$	−28.5423	−1.11017	−0.555083	+	0.831795i	$0.687313\pi$
$662$	−27.0701	−1.05211
$663$	−8.38313	−0.325574
$664$	−21.5942	−0.838017
$665$	−5.32780	−0.206603
$666$	−42.8098	−1.65885
$667$	−36.0156	−1.39453
$668$	19.9668	0.772539
$669$	−3.43789	−0.132916
$670$	−20.9968	−0.811176
$671$	−34.3666	−1.32671
$672$	−0.564202	−0.0217646
$673$	31.0623	1.19736	0.598681	−	0.800988i	$-0.295692\pi$
$673$	31.0623	1.19736	0.598681	+	0.800988i	$0.295692\pi$
$674$	31.1908	1.20142
$675$	4.70137	0.180956
$676$	102.828	3.95492
$677$	10.9672	0.421502	0.210751	−	0.977540i	$-0.432409\pi$
$677$	10.9672	0.421502	0.210751	+	0.977540i	$0.432409\pi$
$678$	5.35062	0.205489
$679$	8.25745	0.316892
$680$	24.6629	0.945777
$681$	4.41406	0.169147
$682$	11.6586	0.446432
$683$	−50.5230	−1.93321	−0.966604	−	0.256273i	$-0.917505\pi$
$683$	−50.5230	−1.93321	−0.966604	+	0.256273i	$0.917505\pi$
$684$	−63.9609	−2.44561
$685$	−6.21003	−0.237273
$686$	2.37810	0.0907964
$687$	−2.09250	−0.0798338
$688$	8.38344	0.319616
$689$	28.3346	1.07946
$690$	−3.33404	−0.126925
$691$	29.8062	1.13388	0.566941	−	0.823759i	$-0.308127\pi$
$691$	29.8062	1.13388	0.566941	+	0.823759i	$0.308127\pi$
$692$	−61.5931	−2.34142
$693$	−8.91546	−0.338670
$694$	25.5749	0.970811
$695$	14.1905	0.538277
$696$	3.23788	0.122732
$697$	65.4177	2.47787
$698$	−20.6304	−0.780874
$699$	1.83983	0.0695887
$700$	15.2986	0.578231
$701$	31.4647	1.18841	0.594204	−	0.804315i	$-0.297467\pi$
$701$	31.4647	1.18841	0.594204	+	0.804315i	$0.297467\pi$
$702$	17.1325	0.646623
$703$	−35.8412	−1.35178
$704$	33.7616	1.27244
$705$	1.03529	0.0389914
$706$	45.9849	1.73066
$707$	−1.00097	−0.0376455
$708$	−9.72520	−0.365495
$709$	12.5509	0.471358	0.235679	−	0.971831i	$-0.424269\pi$
$709$	12.5509	0.471358	0.235679	+	0.971831i	$0.424269\pi$
$710$	−9.16060	−0.343791
$711$	30.5534	1.14584
$712$	−21.5562	−0.807854
$713$	13.4437	0.503469
$714$	−3.10853	−0.116334
$715$	−17.4097	−0.651086
$716$	0.677482	0.0253187
$717$	−0.766262	−0.0286166
$718$	−65.9430	−2.46097
$719$	28.3661	1.05788	0.528939	−	0.848660i	$-0.322590\pi$
$719$	28.3661	1.05788	0.528939	+	0.848660i	$0.322590\pi$
$720$	−5.48847	−0.204543
$721$	−4.51823	−0.168268
$722$	−37.6643	−1.40172
$723$	−4.92099	−0.183013
$724$	−33.2405	−1.23537
$725$	18.2776	0.678814
$726$	0.875910	0.0325081
$727$	−2.67254	−0.0991190	−0.0495595	−	0.998771i	$-0.515782\pi$
$727$	−2.67254	−0.0991190	−0.0495595	+	0.998771i	$0.515782\pi$
$728$	25.2471	0.935718
$729$	−25.1035	−0.929757
$730$	−12.8904	−0.477096
$731$	−28.3688	−1.04926
$732$	7.86705	0.290775
$733$	20.6676	0.763374	0.381687	−	0.924292i	$-0.375343\pi$
$733$	20.6676	0.763374	0.381687	+	0.924292i	$0.375343\pi$
$734$	66.8290	2.46671
$735$	0.170001	0.00627058
$736$	24.7055	0.910655
$737$	−29.4163	−1.08356
$738$	−66.4490	−2.44602
$739$	−16.9623	−0.623969	−0.311985	−	0.950087i	$-0.600994\pi$
$739$	−16.9623	−0.623969	−0.311985	+	0.950087i	$0.600994\pi$
$740$	−20.0360	−0.736537
$741$	7.12917	0.261897
$742$	10.5067	0.385712
$743$	−7.17360	−0.263174	−0.131587	−	0.991305i	$-0.542007\pi$
$743$	−7.17360	−0.263174	−0.131587	+	0.991305i	$0.542007\pi$
$744$	−1.20861	−0.0443099
$745$	11.6257	0.425933
$746$	−13.1495	−0.481436
$747$	−16.2616	−0.594982
$748$	76.2981	2.78974
$749$	17.8365	0.651732
$750$	3.71340	0.135594
$751$	−51.3698	−1.87451	−0.937255	−	0.348645i	$-0.886642\pi$
$751$	−51.3698	−1.87451	−0.937255	+	0.348645i	$0.886642\pi$
$752$	12.4907	0.455488
$753$	0.485477	0.0176918
$754$	66.6063	2.42566
$755$	1.52230	0.0554020
$756$	4.10619	0.149341
$757$	24.5838	0.893515	0.446758	−	0.894655i	$-0.352579\pi$
$757$	24.5838	0.893515	0.446758	+	0.894655i	$0.352579\pi$
$758$	−68.3895	−2.48402
$759$	−4.67097	−0.169545
$760$	−20.9738	−0.760798
$761$	−21.1207	−0.765624	−0.382812	−	0.923826i	$-0.625044\pi$
$761$	−21.1207	−0.765624	−0.382812	+	0.923826i	$0.625044\pi$
$762$	−1.96473	−0.0711748
$763$	6.97063	0.252354
$764$	70.4826	2.54997
$765$	18.5725	0.671491
$766$	71.0628	2.56760
$767$	−90.5979	−3.27130
$768$	−5.04509	−0.182049
$769$	−35.6133	−1.28425	−0.642124	−	0.766601i	$-0.721947\pi$
$769$	−35.6133	−1.28425	−0.642124	+	0.766601i	$0.721947\pi$
$770$	−6.45565	−0.232646
$771$	−1.57737	−0.0568076
$772$	−28.8255	−1.03745
$773$	1.91262	0.0687922	0.0343961	−	0.999408i	$-0.489049\pi$
$773$	1.91262	0.0687922	0.0343961	+	0.999408i	$0.489049\pi$
$774$	28.8161	1.03577
$775$	−6.82255	−0.245073
$776$	32.5068	1.16693
$777$	1.14363	0.0410276
$778$	−50.2660	−1.80212
$779$	−55.6324	−1.99324
$780$	3.98535	0.142698
$781$	−12.8339	−0.459234
$782$	136.117	4.86754
$783$	4.90579	0.175319
$784$	2.05104	0.0732515
$785$	5.83854	0.208386
$786$	4.77708	0.170393
$787$	−2.60087	−0.0927108	−0.0463554	−	0.998925i	$-0.514761\pi$
$787$	−2.60087	−0.0927108	−0.0463554	+	0.998925i	$0.514761\pi$
$788$	−56.7267	−2.02080
$789$	−1.89782	−0.0675643
$790$	22.1236	0.787124
$791$	11.9466	0.424771
$792$	−35.0972	−1.24712
$793$	73.2878	2.60253
$794$	−27.6601	−0.981621
$795$	0.751080	0.0266381
$796$	−58.5467	−2.07513
$797$	0.683610	0.0242147	0.0121074	−	0.999927i	$-0.496146\pi$
$797$	0.683610	0.0242147	0.0121074	+	0.999927i	$0.496146\pi$
$798$	2.64355	0.0935806
$799$	−42.2673	−1.49531
$800$	−12.5378	−0.443279
$801$	−16.2331	−0.573567
$802$	−71.9962	−2.54227
$803$	−18.0594	−0.637302
$804$	6.73384	0.237484
$805$	−7.44406	−0.262369
$806$	−24.8624	−0.875739
$807$	1.83773	0.0646911
$808$	−3.94050	−0.138626
$809$	−7.35233	−0.258494	−0.129247	−	0.991612i	$-0.541256\pi$
$809$	−7.35233	−0.258494	−0.129247	+	0.991612i	$0.541256\pi$
$810$	−18.6369	−0.654834
$811$	52.1015	1.82953	0.914765	−	0.403986i	$-0.132375\pi$
$811$	52.1015	1.82953	0.914765	+	0.403986i	$0.132375\pi$
$812$	15.9637	0.560218
$813$	2.89288	0.101458
$814$	−43.4286	−1.52217
$815$	−8.45269	−0.296085
$816$	−2.68101	−0.0938540
$817$	24.1254	0.844040
$818$	42.3967	1.48237
$819$	19.0125	0.664349
$820$	−31.0996	−1.08605
$821$	0.256818	0.00896301	0.00448150	−	0.999990i	$-0.498573\pi$
$821$	0.256818	0.00896301	0.00448150	+	0.999990i	$0.498573\pi$
$822$	3.08130	0.107473
$823$	−7.59135	−0.264618	−0.132309	−	0.991209i	$-0.542239\pi$
$823$	−7.59135	−0.264618	−0.132309	+	0.991209i	$0.542239\pi$
$824$	−17.7868	−0.619631
$825$	2.37048	0.0825294
$826$	−33.5944	−1.16890
$827$	−39.1692	−1.36205	−0.681024	−	0.732261i	$-0.738465\pi$
$827$	−39.1692	−1.36205	−0.681024	+	0.732261i	$0.738465\pi$
$828$	−89.3670	−3.10572
$829$	−18.4567	−0.641029	−0.320514	−	0.947244i	$-0.603856\pi$
$829$	−18.4567	−0.641029	−0.320514	+	0.947244i	$0.603856\pi$
$830$	−11.7750	−0.408716
$831$	−3.71543	−0.128887
$832$	−71.9976	−2.49607
$833$	−6.94054	−0.240476
$834$	−7.04106	−0.243812
$835$	4.93058	0.170630
$836$	−64.8854	−2.24411
$837$	−1.83120	−0.0632955
$838$	68.4869	2.36584
$839$	5.50414	0.190024	0.0950121	−	0.995476i	$-0.469711\pi$
$839$	5.50414	0.190024	0.0950121	+	0.995476i	$0.469711\pi$
$840$	0.669237	0.0230909
$841$	−9.92764	−0.342332
$842$	22.2316	0.766152
$843$	−1.37870	−0.0474851
$844$	−79.8561	−2.74876
$845$	25.3922	0.873518
$846$	42.9337	1.47609
$847$	1.95568	0.0671981
$848$	9.06169	0.311180
$849$	3.22968	0.110842
$850$	−69.0784	−2.36937
$851$	−50.0778	−1.71665
$852$	2.93788	0.100650
$853$	−13.6636	−0.467833	−0.233916	−	0.972257i	$-0.575154\pi$
$853$	−13.6636	−0.467833	−0.233916	+	0.972257i	$0.575154\pi$
$854$	27.1757	0.929932
$855$	−15.7944	−0.540158
$856$	70.2164	2.39995
$857$	−30.3485	−1.03668	−0.518342	−	0.855174i	$-0.673450\pi$
$857$	−30.3485	−1.03668	−0.518342	+	0.855174i	$0.673450\pi$
$858$	8.63836	0.294909
$859$	−1.00000	−0.0341196
$859$	−1.00000	−0.0341196
$860$	13.4866	0.459889
$861$	1.77514	0.0604965
$862$	27.4008	0.933276
$863$	−1.66423	−0.0566511	−0.0283256	−	0.999599i	$-0.509018\pi$
$863$	−1.66423	−0.0566511	−0.0283256	+	0.999599i	$0.509018\pi$
$864$	−3.36520	−0.114486
$865$	−15.2097	−0.517146
$866$	80.7973	2.74560
$867$	5.87060	0.199376
$868$	−5.95884	−0.202256
$869$	30.9950	1.05143
$870$	1.76557	0.0598584
$871$	62.7310	2.12556
$872$	27.4410	0.929271
$873$	24.4795	0.828505
$874$	−115.757	−3.91553
$875$	8.29107	0.280289
$876$	4.13407	0.139677
$877$	−45.4634	−1.53519	−0.767595	−	0.640936i	$-0.778547\pi$
$877$	−45.4634	−1.53519	−0.767595	+	0.640936i	$0.778547\pi$
$878$	25.2612	0.852523
$879$	0.960868	0.0324093
$880$	−5.56780	−0.187690
$881$	−35.7310	−1.20381	−0.601905	−	0.798568i	$-0.705591\pi$
$881$	−35.7310	−1.20381	−0.601905	+	0.798568i	$0.705591\pi$
$882$	7.04996	0.237385
$883$	−52.1847	−1.75615	−0.878077	−	0.478520i	$-0.841174\pi$
$883$	−52.1847	−1.75615	−0.878077	+	0.478520i	$0.841174\pi$
$884$	−162.708	−5.47245
$885$	−2.40153	−0.0807264
$886$	−28.1906	−0.947081
$887$	−58.2288	−1.95513	−0.977566	−	0.210629i	$-0.932449\pi$
$887$	−58.2288	−1.95513	−0.977566	+	0.210629i	$0.932449\pi$
$888$	4.50210	0.151081
$889$	−4.38675	−0.147127
$890$	−11.7543	−0.394005
$891$	−26.1101	−0.874722
$892$	−66.7258	−2.23415
$893$	35.9449	1.20285
$894$	−5.76845	−0.192926
$895$	0.167296	0.00559210
$896$	−20.7058	−0.691731
$897$	9.96096	0.332587
$898$	−72.5265	−2.42024
$899$	−7.11920	−0.237439
$900$	45.3530	1.51177
$901$	−30.6640	−1.02156
$902$	−67.4094	−2.24449
$903$	−0.769800	−0.0256173
$904$	47.0297	1.56418
$905$	−8.20835	−0.272855
$906$	−0.755333	−0.0250943
$907$	−28.6126	−0.950065	−0.475032	−	0.879968i	$-0.657564\pi$
$907$	−28.6126	−0.950065	−0.475032	+	0.879968i	$0.657564\pi$
$908$	85.6722	2.84313
$909$	−2.96742	−0.0984231
$910$	13.7669	0.456367
$911$	−40.2842	−1.33468	−0.667338	−	0.744755i	$-0.732566\pi$
$911$	−40.2842	−1.33468	−0.667338	+	0.744755i	$0.732566\pi$
$912$	2.27998	0.0754976
$913$	−16.4967	−0.545960
$914$	9.05398	0.299479
$915$	1.94268	0.0642230
$916$	−40.6132	−1.34190
$917$	10.6660	0.352222
$918$	−18.5409	−0.611941
$919$	25.4520	0.839583	0.419792	−	0.907620i	$-0.362103\pi$
$919$	25.4520	0.839583	0.419792	+	0.907620i	$0.362103\pi$
$920$	−29.3048	−0.966150
$921$	−1.84641	−0.0608413
$922$	45.3165	1.49242
$923$	27.3687	0.900852
$924$	2.07038	0.0681106
$925$	25.4141	0.835610
$926$	41.6041	1.36720
$927$	−13.3944	−0.439931
$928$	−13.0830	−0.429470
$929$	34.8586	1.14367	0.571837	−	0.820367i	$-0.306231\pi$
$929$	34.8586	1.14367	0.571837	+	0.820367i	$0.306231\pi$
$930$	−0.659040	−0.0216108
$931$	5.90237	0.193442
$932$	35.7092	1.16969
$933$	−5.95697	−0.195022
$934$	68.0512	2.22670
$935$	18.8409	0.616165
$936$	74.8457	2.44641
$937$	−25.6442	−0.837759	−0.418880	−	0.908042i	$-0.637577\pi$
$937$	−25.6442	−0.837759	−0.418880	+	0.908042i	$0.637577\pi$
$938$	23.2611	0.759503
$939$	2.64641	0.0863622
$940$	20.0939	0.655392
$941$	−35.8960	−1.17018	−0.585088	−	0.810969i	$-0.698940\pi$
$941$	−35.8960	−1.17018	−0.585088	+	0.810969i	$0.698940\pi$
$942$	−2.89697	−0.0943883
$943$	−77.7303	−2.53125
$944$	−28.9741	−0.943027
$945$	1.01398	0.0329847
$946$	29.2325	0.950432
$947$	−41.0557	−1.33413	−0.667066	−	0.744999i	$-0.732450\pi$
$947$	−41.0557	−1.33413	−0.667066	+	0.744999i	$0.732450\pi$
$948$	−7.09524	−0.230443
$949$	38.5121	1.25016
$950$	58.7456	1.90596
$951$	4.89055	0.158587
$952$	−27.3226	−0.885530
$953$	34.4105	1.11466	0.557332	−	0.830290i	$-0.311825\pi$
$953$	34.4105	1.11466	0.557332	+	0.830290i	$0.311825\pi$
$954$	31.1474	1.00843
$955$	17.4049	0.563209
$956$	−14.8724	−0.481006
$957$	2.47355	0.0799584
$958$	55.2708	1.78572
$959$	6.87975	0.222159
$960$	−1.90848	−0.0615958
$961$	−28.3426	−0.914277
$962$	92.6126	2.98595
$963$	52.8769	1.70393
$964$	−95.5112	−3.07621
$965$	−7.11813	−0.229141
$966$	3.69360	0.118840
$967$	27.5814	0.886958	0.443479	−	0.896285i	$-0.353744\pi$
$967$	27.5814	0.886958	0.443479	+	0.896285i	$0.353744\pi$
$968$	7.69887	0.247451
$969$	−7.71525	−0.247850
$970$	17.7255	0.569132
$971$	47.0690	1.51052	0.755258	−	0.655428i	$-0.227512\pi$
$971$	47.0690	1.51052	0.755258	+	0.655428i	$0.227512\pi$
$972$	18.2956	0.586831
$973$	−15.7209	−0.503989
$974$	−21.2288	−0.680215
$975$	−5.05511	−0.161893
$976$	23.4382	0.750237
$977$	54.5064	1.74381	0.871907	−	0.489672i	$-0.162883\pi$
$977$	54.5064	1.74381	0.871907	+	0.489672i	$0.162883\pi$
$978$	4.19406	0.134111
$979$	−16.4677	−0.526309
$980$	3.29954	0.105400
$981$	20.6647	0.659772
$982$	27.2352	0.869109
$983$	2.91549	0.0929895	0.0464948	−	0.998919i	$-0.485195\pi$
$983$	2.91549	0.0929895	0.0464948	+	0.998919i	$0.485195\pi$
$984$	6.98812	0.222773
$985$	−14.0080	−0.446332
$986$	−72.0820	−2.29556
$987$	−1.14694	−0.0365076
$988$	138.370	4.40213
$989$	33.7083	1.07186
$990$	−19.1380	−0.608245
$991$	−51.5183	−1.63653	−0.818266	−	0.574840i	$-0.805064\pi$
$991$	−51.5183	−1.63653	−0.818266	+	0.574840i	$0.805064\pi$
$992$	4.88352	0.155052
$993$	2.14382	0.0680322
$994$	10.1485	0.321891
$995$	−14.4574	−0.458332
$996$	3.77634	0.119658
$997$	−2.12831	−0.0674044	−0.0337022	−	0.999432i	$-0.510730\pi$
$997$	−2.12831	−0.0674044	−0.0337022	+	0.999432i	$0.510730\pi$
$998$	−65.6197	−2.07715
$999$	6.82124	0.215814

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.c.1.15	✓	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.c.1.15	✓	104	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:	\( N \)	\(=\)	\( 6013 = 7 \cdot 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.37810 q^{2} +0.188335 q^{3} +3.65538 q^{4} +0.902654 q^{5} -0.447879 q^{6} -1.00000 q^{7} -3.93667 q^{8} -2.96453 q^{9} +O(q^{10})\)	\(q-2.37810 q^{2} +0.188335 q^{3} +3.65538 q^{4} +0.902654 q^{5} -0.447879 q^{6} -1.00000 q^{7} -3.93667 q^{8} -2.96453 q^{9} -2.14661 q^{10} -3.00738 q^{11} +0.688435 q^{12} +6.41331 q^{13} +2.37810 q^{14} +0.170001 q^{15} +2.05104 q^{16} -6.94054 q^{17} +7.04996 q^{18} +5.90237 q^{19} +3.29954 q^{20} -0.188335 q^{21} +7.15186 q^{22} +8.24686 q^{23} -0.741410 q^{24} -4.18522 q^{25} -15.2515 q^{26} -1.12333 q^{27} -3.65538 q^{28} -4.36719 q^{29} -0.404280 q^{30} +1.63016 q^{31} +2.99574 q^{32} -0.566393 q^{33} +16.5053 q^{34} -0.902654 q^{35} -10.8365 q^{36} -6.07235 q^{37} -14.0364 q^{38} +1.20785 q^{39} -3.55345 q^{40} -9.42544 q^{41} +0.447879 q^{42} +4.08741 q^{43} -10.9931 q^{44} -2.67595 q^{45} -19.6119 q^{46} +6.08992 q^{47} +0.386282 q^{48} +1.00000 q^{49} +9.95288 q^{50} -1.30714 q^{51} +23.4431 q^{52} +4.41809 q^{53} +2.67139 q^{54} -2.71462 q^{55} +3.93667 q^{56} +1.11162 q^{57} +10.3856 q^{58} -14.1265 q^{59} +0.621418 q^{60} +11.4274 q^{61} -3.87668 q^{62} +2.96453 q^{63} -11.2263 q^{64} +5.78900 q^{65} +1.34694 q^{66} +9.78138 q^{67} -25.3703 q^{68} +1.55317 q^{69} +2.14661 q^{70} +4.26748 q^{71} +11.6704 q^{72} +6.00503 q^{73} +14.4407 q^{74} -0.788221 q^{75} +21.5754 q^{76} +3.00738 q^{77} -2.87239 q^{78} -10.3063 q^{79} +1.85138 q^{80} +8.68203 q^{81} +22.4147 q^{82} +5.48540 q^{83} -0.688435 q^{84} -6.26491 q^{85} -9.72028 q^{86} -0.822493 q^{87} +11.8390 q^{88} +5.47576 q^{89} +6.36368 q^{90} -6.41331 q^{91} +30.1454 q^{92} +0.307015 q^{93} -14.4825 q^{94} +5.32780 q^{95} +0.564202 q^{96} -8.25745 q^{97} -2.37810 q^{98} +8.91546 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 19 q^{2} - 26 q^{3} + 99 q^{4} + 2 q^{5} + 2 q^{6} - 104 q^{7} - 54 q^{8} + 90 q^{9}+O(q^{10}) \) 104 * q - 19 * q^2 - 26 * q^3 + 99 * q^4 + 2 * q^5 + 2 * q^6 - 104 * q^7 - 54 * q^8 + 90 * q^9	\( 104 q - 19 q^{2} - 26 q^{3} + 99 q^{4} + 2 q^{5} + 2 q^{6} - 104 q^{7} - 54 q^{8} + 90 q^{9} + 3 q^{10} - 54 q^{11} - 38 q^{12} + 7 q^{13} + 19 q^{14} - 33 q^{15} + 93 q^{16} - 7 q^{17} - 55 q^{18} - 12 q^{19} - 24 q^{20} + 26 q^{21} - 22 q^{22} - 69 q^{23} + 78 q^{25} - 11 q^{26} - 95 q^{27} - 99 q^{28} - 41 q^{29} - 26 q^{30} - 12 q^{31} - 127 q^{32} - 6 q^{33} - 17 q^{34} - 2 q^{35} + 71 q^{36} - 47 q^{37} - 32 q^{38} - 57 q^{39} + 6 q^{40} + 10 q^{41} - 2 q^{42} - 41 q^{43} - 120 q^{44} + 23 q^{45} - 31 q^{46} - 99 q^{47} - 84 q^{48} + 104 q^{49} - 104 q^{50} - 74 q^{51} + 14 q^{52} - 74 q^{53} + 19 q^{54} - 32 q^{55} + 54 q^{56} - 47 q^{57} - 36 q^{58} - 76 q^{59} - 99 q^{60} + 49 q^{61} - 55 q^{62} - 90 q^{63} + 86 q^{64} - 70 q^{65} + 61 q^{66} - 117 q^{67} - 30 q^{68} + 51 q^{69} - 3 q^{70} - 125 q^{71} - 147 q^{72} - 20 q^{73} - 75 q^{74} - 124 q^{75} + 4 q^{76} + 54 q^{77} - 70 q^{78} - 72 q^{79} - 69 q^{80} + 76 q^{81} - 37 q^{82} - 98 q^{83} + 38 q^{84} - 33 q^{85} - 64 q^{86} - 8 q^{87} - 62 q^{88} - 26 q^{89} + 11 q^{90} - 7 q^{91} - 162 q^{92} - 81 q^{93} + 31 q^{94} - 116 q^{95} + 20 q^{96} - 61 q^{97} - 19 q^{98} - 158 q^{99}+O(q^{100}) \) 104 * q - 19 * q^2 - 26 * q^3 + 99 * q^4 + 2 * q^5 + 2 * q^6 - 104 * q^7 - 54 * q^8 + 90 * q^9 + 3 * q^10 - 54 * q^11 - 38 * q^12 + 7 * q^13 + 19 * q^14 - 33 * q^15 + 93 * q^16 - 7 * q^17 - 55 * q^18 - 12 * q^19 - 24 * q^20 + 26 * q^21 - 22 * q^22 - 69 * q^23 + 78 * q^25 - 11 * q^26 - 95 * q^27 - 99 * q^28 - 41 * q^29 - 26 * q^30 - 12 * q^31 - 127 * q^32 - 6 * q^33 - 17 * q^34 - 2 * q^35 + 71 * q^36 - 47 * q^37 - 32 * q^38 - 57 * q^39 + 6 * q^40 + 10 * q^41 - 2 * q^42 - 41 * q^43 - 120 * q^44 + 23 * q^45 - 31 * q^46 - 99 * q^47 - 84 * q^48 + 104 * q^49 - 104 * q^50 - 74 * q^51 + 14 * q^52 - 74 * q^53 + 19 * q^54 - 32 * q^55 + 54 * q^56 - 47 * q^57 - 36 * q^58 - 76 * q^59 - 99 * q^60 + 49 * q^61 - 55 * q^62 - 90 * q^63 + 86 * q^64 - 70 * q^65 + 61 * q^66 - 117 * q^67 - 30 * q^68 + 51 * q^69 - 3 * q^70 - 125 * q^71 - 147 * q^72 - 20 * q^73 - 75 * q^74 - 124 * q^75 + 4 * q^76 + 54 * q^77 - 70 * q^78 - 72 * q^79 - 69 * q^80 + 76 * q^81 - 37 * q^82 - 98 * q^83 + 38 * q^84 - 33 * q^85 - 64 * q^86 - 8 * q^87 - 62 * q^88 - 26 * q^89 + 11 * q^90 - 7 * q^91 - 162 * q^92 - 81 * q^93 + 31 * q^94 - 116 * q^95 + 20 * q^96 - 61 * q^97 - 19 * q^98 - 158 * q^99

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