LMFDB - Embedded newform 6041.2.a.c.1.7

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:	$83$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	$q-2.28673 q^{2} +0.00653898 q^{3} +3.22911 q^{4} +3.50344 q^{5} -0.0149528 q^{6} +1.00000 q^{7} -2.81064 q^{8} -2.99996 q^{9} +O(q^{10})$	\(q-2.28673 q^{2} +0.00653898 q^{3} +3.22911 q^{4} +3.50344 q^{5} -0.0149528 q^{6} +1.00000 q^{7} -2.81064 q^{8} -2.99996 q^{9} -8.01141 q^{10} +1.20275 q^{11} +0.0211151 q^{12} +1.80404 q^{13} -2.28673 q^{14} +0.0229089 q^{15} -0.0310544 q^{16} -3.77345 q^{17} +6.86008 q^{18} -6.46967 q^{19} +11.3130 q^{20} +0.00653898 q^{21} -2.75035 q^{22} -6.56428 q^{23} -0.0183787 q^{24} +7.27410 q^{25} -4.12535 q^{26} -0.0392336 q^{27} +3.22911 q^{28} +6.95736 q^{29} -0.0523864 q^{30} -2.29789 q^{31} +5.69230 q^{32} +0.00786474 q^{33} +8.62885 q^{34} +3.50344 q^{35} -9.68720 q^{36} -1.76108 q^{37} +14.7944 q^{38} +0.0117966 q^{39} -9.84693 q^{40} -6.77179 q^{41} -0.0149528 q^{42} +5.09815 q^{43} +3.88381 q^{44} -10.5102 q^{45} +15.0107 q^{46} -7.25908 q^{47} -0.000203064 q^{48} +1.00000 q^{49} -16.6339 q^{50} -0.0246745 q^{51} +5.82546 q^{52} +6.95675 q^{53} +0.0897164 q^{54} +4.21376 q^{55} -2.81064 q^{56} -0.0423050 q^{57} -15.9096 q^{58} +6.11304 q^{59} +0.0739755 q^{60} +8.60447 q^{61} +5.25465 q^{62} -2.99996 q^{63} -12.9546 q^{64} +6.32036 q^{65} -0.0179845 q^{66} +6.58044 q^{67} -12.1849 q^{68} -0.0429237 q^{69} -8.01141 q^{70} -4.16898 q^{71} +8.43181 q^{72} +1.33387 q^{73} +4.02710 q^{74} +0.0475652 q^{75} -20.8913 q^{76} +1.20275 q^{77} -0.0269756 q^{78} -14.6464 q^{79} -0.108797 q^{80} +8.99962 q^{81} +15.4852 q^{82} -5.83526 q^{83} +0.0211151 q^{84} -13.2201 q^{85} -11.6581 q^{86} +0.0454940 q^{87} -3.38050 q^{88} +11.2738 q^{89} +24.0339 q^{90} +1.80404 q^{91} -21.1968 q^{92} -0.0150259 q^{93} +16.5995 q^{94} -22.6661 q^{95} +0.0372218 q^{96} +4.68104 q^{97} -2.28673 q^{98} -3.60819 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9}+O(q^{10}) $ 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9} - 20 q^{10} - 26 q^{11} - 14 q^{12} - 22 q^{13} - 8 q^{14} - 37 q^{15} - 10 q^{16} - 9 q^{17} - 27 q^{18} - 42 q^{19} - 22 q^{20} - 12 q^{21} - 44 q^{22} - 46 q^{23} - 24 q^{24} - 20 q^{25} - 9 q^{26} - 39 q^{27} + 48 q^{28} - 36 q^{29} - 11 q^{30} - 107 q^{31} - 19 q^{32} - 25 q^{33} - 24 q^{34} - 11 q^{35} - 32 q^{36} - 75 q^{37} - 16 q^{38} - 78 q^{39} - 34 q^{40} - 17 q^{41} - 8 q^{42} - 87 q^{43} - 32 q^{44} - 17 q^{45} - 56 q^{46} - 39 q^{47} - 16 q^{48} + 83 q^{49} - 26 q^{50} - 71 q^{51} - 53 q^{52} - 28 q^{53} - 25 q^{54} - 94 q^{55} - 18 q^{56} - 79 q^{57} - 69 q^{58} - 26 q^{59} - 43 q^{60} - 56 q^{61} - 6 q^{62} + 39 q^{63} - 108 q^{64} - 26 q^{65} + 10 q^{66} - 123 q^{67} - 11 q^{68} + 2 q^{69} - 20 q^{70} - 96 q^{71} - 11 q^{72} - 53 q^{73} - 26 q^{74} - 27 q^{75} - 65 q^{76} - 26 q^{77} - 43 q^{78} - 160 q^{79} + 12 q^{80} - 53 q^{81} - 20 q^{82} - 2 q^{83} - 14 q^{84} - 110 q^{85} + 24 q^{86} - 52 q^{87} - 79 q^{88} - 5 q^{89} - 4 q^{90} - 22 q^{91} - 51 q^{92} - 30 q^{93} - 9 q^{94} - 76 q^{95} - 3 q^{96} - 44 q^{97} - 8 q^{98} - 82 q^{99}+O(q^{100}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9 - 20 * q^10 - 26 * q^11 - 14 * q^12 - 22 * q^13 - 8 * q^14 - 37 * q^15 - 10 * q^16 - 9 * q^17 - 27 * q^18 - 42 * q^19 - 22 * q^20 - 12 * q^21 - 44 * q^22 - 46 * q^23 - 24 * q^24 - 20 * q^25 - 9 * q^26 - 39 * q^27 + 48 * q^28 - 36 * q^29 - 11 * q^30 - 107 * q^31 - 19 * q^32 - 25 * q^33 - 24 * q^34 - 11 * q^35 - 32 * q^36 - 75 * q^37 - 16 * q^38 - 78 * q^39 - 34 * q^40 - 17 * q^41 - 8 * q^42 - 87 * q^43 - 32 * q^44 - 17 * q^45 - 56 * q^46 - 39 * q^47 - 16 * q^48 + 83 * q^49 - 26 * q^50 - 71 * q^51 - 53 * q^52 - 28 * q^53 - 25 * q^54 - 94 * q^55 - 18 * q^56 - 79 * q^57 - 69 * q^58 - 26 * q^59 - 43 * q^60 - 56 * q^61 - 6 * q^62 + 39 * q^63 - 108 * q^64 - 26 * q^65 + 10 * q^66 - 123 * q^67 - 11 * q^68 + 2 * q^69 - 20 * q^70 - 96 * q^71 - 11 * q^72 - 53 * q^73 - 26 * q^74 - 27 * q^75 - 65 * q^76 - 26 * q^77 - 43 * q^78 - 160 * q^79 + 12 * q^80 - 53 * q^81 - 20 * q^82 - 2 * q^83 - 14 * q^84 - 110 * q^85 + 24 * q^86 - 52 * q^87 - 79 * q^88 - 5 * q^89 - 4 * q^90 - 22 * q^91 - 51 * q^92 - 30 * q^93 - 9 * q^94 - 76 * q^95 - 3 * q^96 - 44 * q^97 - 8 * q^98 - 82 * 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 $

$2$	−2.28673	−1.61696	−0.808480	−	0.588524i	$-0.799709\pi$
$2$	−2.28673	−1.61696	−0.808480	+	0.588524i	$0.799709\pi$
$3$	0.00653898	0.00377528	0.00188764	−	0.999998i	$-0.499399\pi$
$3$	0.00653898	0.00377528	0.00188764	+	0.999998i	$0.499399\pi$
$4$	3.22911	1.61456
$5$	3.50344	1.56679	0.783393	−	0.621526i	$-0.213487\pi$
$5$	3.50344	1.56679	0.783393	+	0.621526i	$0.213487\pi$
$6$	−0.0149528	−0.00610447
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.81064	−0.993713
$9$	−2.99996	−0.999986
$10$	−8.01141	−2.53343
$11$	1.20275	0.362642	0.181321	−	0.983424i	$-0.441963\pi$
$11$	1.20275	0.362642	0.181321	+	0.983424i	$0.441963\pi$
$12$	0.0211151	0.00609540
$13$	1.80404	0.500352	0.250176	−	0.968200i	$-0.419512\pi$
$13$	1.80404	0.500352	0.250176	+	0.968200i	$0.419512\pi$
$14$	−2.28673	−0.611153
$15$	0.0229089	0.00591506
$16$	−0.0310544	−0.00776360
$17$	−3.77345	−0.915197	−0.457598	−	0.889159i	$-0.651290\pi$
$17$	−3.77345	−0.915197	−0.457598	+	0.889159i	$0.651290\pi$
$18$	6.86008	1.61694
$19$	−6.46967	−1.48424	−0.742122	−	0.670264i	$-0.766181\pi$
$19$	−6.46967	−1.48424	−0.742122	+	0.670264i	$0.766181\pi$
$20$	11.3130	2.52967
$21$	0.00653898	0.00142692
$22$	−2.75035	−0.586378
$23$	−6.56428	−1.36875	−0.684374	−	0.729131i	$-0.739924\pi$
$23$	−6.56428	−1.36875	−0.684374	+	0.729131i	$0.739924\pi$
$24$	−0.0183787	−0.00375154
$25$	7.27410	1.45482
$26$	−4.12535	−0.809048
$27$	−0.0392336	−0.00755050
$28$	3.22911	0.610245
$29$	6.95736	1.29195	0.645975	−	0.763359i	$-0.276451\pi$
$29$	6.95736	1.29195	0.645975	+	0.763359i	$0.276451\pi$
$30$	−0.0523864	−0.00956440
$31$	−2.29789	−0.412713	−0.206357	−	0.978477i	$-0.566161\pi$
$31$	−2.29789	−0.412713	−0.206357	+	0.978477i	$0.566161\pi$
$32$	5.69230	1.00627
$33$	0.00786474	0.00136908
$34$	8.62885	1.47984
$35$	3.50344	0.592190
$36$	−9.68720	−1.61453
$37$	−1.76108	−0.289519	−0.144760	−	0.989467i	$-0.546241\pi$
$37$	−1.76108	−0.289519	−0.144760	+	0.989467i	$0.546241\pi$
$38$	14.7944	2.39996
$39$	0.0117966	0.00188897
$40$	−9.84693	−1.55694
$41$	−6.77179	−1.05758	−0.528788	−	0.848754i	$-0.677353\pi$
$41$	−6.77179	−1.05758	−0.528788	+	0.848754i	$0.677353\pi$
$42$	−0.0149528	−0.00230727
$43$	5.09815	0.777460	0.388730	−	0.921352i	$-0.372914\pi$
$43$	5.09815	0.777460	0.388730	+	0.921352i	$0.372914\pi$
$44$	3.88381	0.585506
$45$	−10.5102	−1.56676
$46$	15.0107	2.21321
$47$	−7.25908	−1.05885	−0.529423	−	0.848358i	$-0.677591\pi$
$47$	−7.25908	−1.05885	−0.529423	+	0.848358i	$0.677591\pi$
$48$	−0.000203064 0	−2.93098e−5 0
$49$	1.00000	0.142857
$50$	−16.6339	−2.35238
$51$	−0.0246745	−0.00345512
$52$	5.82546	0.807846
$53$	6.95675	0.955583	0.477792	−	0.878473i	$-0.341437\pi$
$53$	6.95675	0.955583	0.477792	+	0.878473i	$0.341437\pi$
$54$	0.0897164	0.0122089
$55$	4.21376	0.568183
$56$	−2.81064	−0.375588
$57$	−0.0423050	−0.00560344
$58$	−15.9096	−2.08903
$59$	6.11304	0.795850	0.397925	−	0.917418i	$-0.369730\pi$
$59$	6.11304	0.795850	0.397925	+	0.917418i	$0.369730\pi$
$60$	0.0739755	0.00955019
$61$	8.60447	1.10169	0.550845	−	0.834608i	$-0.314306\pi$
$61$	8.60447	1.10169	0.550845	+	0.834608i	$0.314306\pi$
$62$	5.25465	0.667341
$63$	−2.99996	−0.377959
$64$	−12.9546	−1.61933
$65$	6.32036	0.783944
$66$	−0.0179845	−0.00221374
$67$	6.58044	0.803929	0.401965	−	0.915655i	$-0.368327\pi$
$67$	6.58044	0.803929	0.401965	+	0.915655i	$0.368327\pi$
$68$	−12.1849	−1.47764
$69$	−0.0429237	−0.00516740
$70$	−8.01141	−0.957546
$71$	−4.16898	−0.494767	−0.247384	−	0.968918i	$-0.579571\pi$
$71$	−4.16898	−0.494767	−0.247384	+	0.968918i	$0.579571\pi$
$72$	8.43181	0.993699
$73$	1.33387	0.156118	0.0780589	−	0.996949i	$-0.475128\pi$
$73$	1.33387	0.156118	0.0780589	+	0.996949i	$0.475128\pi$
$74$	4.02710	0.468141
$75$	0.0475652	0.00549235
$76$	−20.8913	−2.39640
$77$	1.20275	0.137066
$78$	−0.0269756	−0.00305438
$79$	−14.6464	−1.64785	−0.823926	−	0.566698i	$-0.808221\pi$
$79$	−14.6464	−1.64785	−0.823926	+	0.566698i	$0.808221\pi$
$80$	−0.108797	−0.0121639
$81$	8.99962	0.999957
$82$	15.4852	1.71006
$83$	−5.83526	−0.640503	−0.320252	−	0.947332i	$-0.603767\pi$
$83$	−5.83526	−0.640503	−0.320252	+	0.947332i	$0.603767\pi$
$84$	0.0211151	0.00230385
$85$	−13.2201	−1.43392
$86$	−11.6581	−1.25712
$87$	0.0454940	0.00487747
$88$	−3.38050	−0.360362
$89$	11.2738	1.19502	0.597508	−	0.801863i	$-0.296157\pi$
$89$	11.2738	1.19502	0.597508	+	0.801863i	$0.296157\pi$
$90$	24.0339	2.53339
$91$	1.80404	0.189115
$92$	−21.1968	−2.20992
$93$	−0.0150259	−0.00155811
$94$	16.5995	1.71211
$95$	−22.6661	−2.32549
$96$	0.0372218	0.00379894
$97$	4.68104	0.475287	0.237644	−	0.971352i	$-0.423625\pi$
$97$	4.68104	0.475287	0.237644	+	0.971352i	$0.423625\pi$
$98$	−2.28673	−0.230994
$99$	−3.60819	−0.362637
$100$	23.4889	2.34889
$101$	2.37131	0.235954	0.117977	−	0.993016i	$-0.462359\pi$
$101$	2.37131	0.235954	0.117977	+	0.993016i	$0.462359\pi$
$102$	0.0564238	0.00558679
$103$	−7.63557	−0.752356	−0.376178	−	0.926548i	$-0.622762\pi$
$103$	−7.63557	−0.752356	−0.376178	+	0.926548i	$0.622762\pi$
$104$	−5.07052	−0.497206
$105$	0.0229089	0.00223568
$106$	−15.9082	−1.54514
$107$	−16.9145	−1.63519	−0.817593	−	0.575797i	$-0.804692\pi$
$107$	−16.9145	−1.63519	−0.817593	+	0.575797i	$0.804692\pi$
$108$	−0.126690	−0.0121907
$109$	−3.59906	−0.344728	−0.172364	−	0.985033i	$-0.555140\pi$
$109$	−3.59906	−0.344728	−0.172364	+	0.985033i	$0.555140\pi$
$110$	−9.63571	−0.918728
$111$	−0.0115156	−0.00109302
$112$	−0.0310544	−0.00293436
$113$	−2.19393	−0.206388	−0.103194	−	0.994661i	$-0.532906\pi$
$113$	−2.19393	−0.206388	−0.103194	+	0.994661i	$0.532906\pi$
$114$	0.0967400	0.00906053
$115$	−22.9976	−2.14453
$116$	22.4661	2.08593
$117$	−5.41205	−0.500344
$118$	−13.9788	−1.28686
$119$	−3.77345	−0.345912
$120$	−0.0643888	−0.00587787
$121$	−9.55340	−0.868491
$122$	−19.6761	−1.78139
$123$	−0.0442806	−0.00399264
$124$	−7.42015	−0.666349
$125$	7.96718	0.712606
$126$	6.86008	0.611144
$127$	−17.3674	−1.54110	−0.770552	−	0.637377i	$-0.780019\pi$
$127$	−17.3674	−1.54110	−0.770552	+	0.637377i	$0.780019\pi$
$128$	18.2391	1.61212
$129$	0.0333367	0.00293513
$130$	−14.4529	−1.26761
$131$	−5.35526	−0.467891	−0.233945	−	0.972250i	$-0.575164\pi$
$131$	−5.35526	−0.467891	−0.233945	+	0.972250i	$0.575164\pi$
$132$	0.0253961	0.00221045
$133$	−6.46967	−0.560992
$134$	−15.0477	−1.29992
$135$	−0.137453	−0.0118300
$136$	10.6058	0.909443
$137$	−12.7998	−1.09356	−0.546778	−	0.837277i	$-0.684146\pi$
$137$	−12.7998	−1.09356	−0.546778	+	0.837277i	$0.684146\pi$
$138$	0.0981547	0.00835548
$139$	21.2473	1.80217	0.901085	−	0.433643i	$-0.142772\pi$
$139$	21.2473	1.80217	0.901085	+	0.433643i	$0.142772\pi$
$140$	11.3130	0.956124
$141$	−0.0474669	−0.00399744
$142$	9.53332	0.800018
$143$	2.16981	0.181449
$144$	0.0931619	0.00776349
$145$	24.3747	2.02421
$146$	−3.05020	−0.252436
$147$	0.00653898	0.000539326 0
$148$	−5.68672	−0.467445
$149$	−4.87910	−0.399711	−0.199856	−	0.979825i	$-0.564047\pi$
$149$	−4.87910	−0.399711	−0.199856	+	0.979825i	$0.564047\pi$
$150$	−0.108768	−0.00888091
$151$	1.72590	0.140452	0.0702258	−	0.997531i	$-0.477628\pi$
$151$	1.72590	0.140452	0.0702258	+	0.997531i	$0.477628\pi$
$152$	18.1840	1.47491
$153$	11.3202	0.915184
$154$	−2.75035	−0.221630
$155$	−8.05053	−0.646634
$156$	0.0380925	0.00304984
$157$	−16.8187	−1.34228	−0.671139	−	0.741331i	$-0.734195\pi$
$157$	−16.8187	−1.34228	−0.671139	+	0.741331i	$0.734195\pi$
$158$	33.4924	2.66451
$159$	0.0454900	0.00360759
$160$	19.9426	1.57660
$161$	−6.56428	−0.517338
$162$	−20.5796	−1.61689
$163$	13.4857	1.05628	0.528142	−	0.849156i	$-0.322889\pi$
$163$	13.4857	1.05628	0.528142	+	0.849156i	$0.322889\pi$
$164$	−21.8669	−1.70752
$165$	0.0275537	0.00214505
$166$	13.3436	1.03567
$167$	5.43596	0.420647	0.210324	−	0.977632i	$-0.432548\pi$
$167$	5.43596	0.420647	0.210324	+	0.977632i	$0.432548\pi$
$168$	−0.0183787	−0.00141795
$169$	−9.74543	−0.749648
$170$	30.2307	2.31859
$171$	19.4087	1.48422
$172$	16.4625	1.25525
$173$	−11.0227	−0.838042	−0.419021	−	0.907976i	$-0.637627\pi$
$173$	−11.0227	−0.838042	−0.419021	+	0.907976i	$0.637627\pi$
$174$	−0.104032	−0.00788667
$175$	7.27410	0.549870
$176$	−0.0373506	−0.00281541
$177$	0.0399730	0.00300455
$178$	−25.7800	−1.93229
$179$	−22.0037	−1.64464	−0.822319	−	0.569027i	$-0.807320\pi$
$179$	−22.0037	−1.64464	−0.822319	+	0.569027i	$0.807320\pi$
$180$	−33.9385	−2.52963
$181$	−12.2874	−0.913312	−0.456656	−	0.889643i	$-0.650953\pi$
$181$	−12.2874	−0.913312	−0.456656	+	0.889643i	$0.650953\pi$
$182$	−4.12535	−0.305791
$183$	0.0562644	0.00415918
$184$	18.4499	1.36014
$185$	−6.16983	−0.453615
$186$	0.0343600	0.00251940
$187$	−4.53851	−0.331889
$188$	−23.4404	−1.70957
$189$	−0.0392336	−0.00285382
$190$	51.8312	3.76023
$191$	−2.94203	−0.212878	−0.106439	−	0.994319i	$-0.533945\pi$
$191$	−2.94203	−0.212878	−0.106439	+	0.994319i	$0.533945\pi$
$192$	−0.0847100	−0.00611341
$193$	−9.46556	−0.681346	−0.340673	−	0.940182i	$-0.610655\pi$
$193$	−9.46556	−0.681346	−0.340673	+	0.940182i	$0.610655\pi$
$194$	−10.7042	−0.768520
$195$	0.0413287	0.00295961
$196$	3.22911	0.230651
$197$	−1.44923	−0.103253	−0.0516267	−	0.998666i	$-0.516441\pi$
$197$	−1.44923	−0.103253	−0.0516267	+	0.998666i	$0.516441\pi$
$198$	8.25095	0.586369
$199$	−10.1582	−0.720097	−0.360048	−	0.932934i	$-0.617240\pi$
$199$	−10.1582	−0.720097	−0.360048	+	0.932934i	$0.617240\pi$
$200$	−20.4449	−1.44567
$201$	0.0430294	0.00303506
$202$	−5.42254	−0.381529
$203$	6.95736	0.488311
$204$	−0.0796768	−0.00557849
$205$	−23.7246	−1.65700
$206$	17.4605	1.21653
$207$	19.6926	1.36873
$208$	−0.0560235	−0.00388453
$209$	−7.78139	−0.538250
$210$	−0.0523864	−0.00361501
$211$	−18.0656	−1.24368	−0.621842	−	0.783142i	$-0.713616\pi$
$211$	−18.0656	−1.24368	−0.621842	+	0.783142i	$0.713616\pi$
$212$	22.4641	1.54284
$213$	−0.0272609	−0.00186788
$214$	38.6788	2.64403
$215$	17.8611	1.21811
$216$	0.110272	0.00750303
$217$	−2.29789	−0.155991
$218$	8.23007	0.557410
$219$	0.00872215	0.000589388 0
$220$	13.6067	0.917363
$221$	−6.80747	−0.457920
$222$	0.0263331	0.00176736
$223$	−19.1815	−1.28449	−0.642243	−	0.766501i	$-0.721996\pi$
$223$	−19.1815	−1.28449	−0.642243	+	0.766501i	$0.721996\pi$
$224$	5.69230	0.380333
$225$	−21.8220	−1.45480
$226$	5.01692	0.333720
$227$	−15.7548	−1.04569	−0.522843	−	0.852429i	$-0.675129\pi$
$227$	−15.7548	−1.04569	−0.522843	+	0.852429i	$0.675129\pi$
$228$	−0.136608	−0.00904707
$229$	−1.38236	−0.0913489	−0.0456744	−	0.998956i	$-0.514544\pi$
$229$	−1.38236	−0.0913489	−0.0456744	+	0.998956i	$0.514544\pi$
$230$	52.5891	3.46763
$231$	0.00786474	0.000517462 0
$232$	−19.5547	−1.28383
$233$	23.6588	1.54994	0.774971	−	0.631997i	$-0.217764\pi$
$233$	23.6588	1.54994	0.774971	+	0.631997i	$0.217764\pi$
$234$	12.3759	0.809036
$235$	−25.4318	−1.65898
$236$	19.7397	1.28494
$237$	−0.0957726	−0.00622110
$238$	8.62885	0.559325
$239$	22.6447	1.46476	0.732381	−	0.680895i	$-0.238409\pi$
$239$	22.6447	1.46476	0.732381	+	0.680895i	$0.238409\pi$
$240$	−0.000711423 0	−4.59221e−5 0
$241$	−19.5623	−1.26012	−0.630060	−	0.776546i	$-0.716970\pi$
$241$	−19.5623	−1.26012	−0.630060	+	0.776546i	$0.716970\pi$
$242$	21.8460	1.40431
$243$	0.176549	0.0113256
$244$	27.7848	1.77874
$245$	3.50344	0.223827
$246$	0.101257	0.00645594
$247$	−11.6716	−0.742644
$248$	6.45855	0.410119
$249$	−0.0381566	−0.00241808
$250$	−18.2188	−1.15226
$251$	−2.48956	−0.157140	−0.0785698	−	0.996909i	$-0.525035\pi$
$251$	−2.48956	−0.157140	−0.0785698	+	0.996909i	$0.525035\pi$
$252$	−9.68720	−0.610236
$253$	−7.89518	−0.496365
$254$	39.7144	2.49190
$255$	−0.0864457	−0.00541344
$256$	−15.7985	−0.987405
$257$	13.1299	0.819021	0.409511	−	0.912305i	$-0.365699\pi$
$257$	13.1299	0.819021	0.409511	+	0.912305i	$0.365699\pi$
$258$	−0.0762318	−0.00474598
$259$	−1.76108	−0.109428
$260$	20.4092	1.26572
$261$	−20.8718	−1.29193
$262$	12.2460	0.756561
$263$	12.5736	0.775319	0.387660	−	0.921803i	$-0.373284\pi$
$263$	12.5736	0.775319	0.387660	+	0.921803i	$0.373284\pi$
$264$	−0.0221050	−0.00136047
$265$	24.3726	1.49719
$266$	14.7944	0.907101
$267$	0.0737189	0.00451152
$268$	21.2490	1.29799
$269$	18.6220	1.13540	0.567701	−	0.823235i	$-0.307833\pi$
$269$	18.6220	1.13540	0.567701	+	0.823235i	$0.307833\pi$
$270$	0.314316	0.0191287
$271$	−11.6140	−0.705500	−0.352750	−	0.935718i	$-0.614753\pi$
$271$	−11.6140	−0.705500	−0.352750	+	0.935718i	$0.614753\pi$
$272$	0.117182	0.00710522
$273$	0.0117966	0.000713962 0
$274$	29.2695	1.76824
$275$	8.74891	0.527579
$276$	−0.138605	−0.00834306
$277$	−12.2450	−0.735731	−0.367865	−	0.929879i	$-0.619911\pi$
$277$	−12.2450	−0.735731	−0.367865	+	0.929879i	$0.619911\pi$
$278$	−48.5867	−2.91403
$279$	6.89358	0.412708
$280$	−9.84693	−0.588466
$281$	−4.52781	−0.270107	−0.135053	−	0.990838i	$-0.543121\pi$
$281$	−4.52781	−0.270107	−0.135053	+	0.990838i	$0.543121\pi$
$282$	0.108544	0.00646369
$283$	21.6118	1.28469	0.642345	−	0.766416i	$-0.277962\pi$
$283$	21.6118	1.28469	0.642345	+	0.766416i	$0.277962\pi$
$284$	−13.4621	−0.798830
$285$	−0.148213	−0.00877939
$286$	−4.96176	−0.293395
$287$	−6.77179	−0.399726
$288$	−17.0767	−1.00625
$289$	−2.76105	−0.162415
$290$	−55.7382	−3.27306
$291$	0.0306092	0.00179434
$292$	4.30722	0.252061
$293$	−14.5356	−0.849179	−0.424590	−	0.905386i	$-0.639582\pi$
$293$	−14.5356	−0.849179	−0.424590	+	0.905386i	$0.639582\pi$
$294$	−0.0149528	−0.000872067 0
$295$	21.4167	1.24693
$296$	4.94976	0.287699
$297$	−0.0471881	−0.00273813
$298$	11.1572	0.646317
$299$	−11.8422	−0.684855
$300$	0.153593	0.00886771
$301$	5.09815	0.293852
$302$	−3.94665	−0.227104
$303$	0.0155060	0.000890794 0
$304$	0.200912	0.0115231
$305$	30.1452	1.72611
$306$	−25.8862	−1.47981
$307$	20.4359	1.16634	0.583169	−	0.812351i	$-0.301813\pi$
$307$	20.4359	1.16634	0.583169	+	0.812351i	$0.301813\pi$
$308$	3.88381	0.221301
$309$	−0.0499288	−0.00284035
$310$	18.4093	1.04558
$311$	2.65346	0.150464	0.0752319	−	0.997166i	$-0.476030\pi$
$311$	2.65346	0.150464	0.0752319	+	0.997166i	$0.476030\pi$
$312$	−0.0331560	−0.00187709
$313$	−3.88240	−0.219446	−0.109723	−	0.993962i	$-0.534996\pi$
$313$	−3.88240	−0.219446	−0.109723	+	0.993962i	$0.534996\pi$
$314$	38.4597	2.17041
$315$	−10.5102	−0.592181
$316$	−47.2950	−2.66055
$317$	6.88831	0.386886	0.193443	−	0.981112i	$-0.438035\pi$
$317$	6.88831	0.386886	0.193443	+	0.981112i	$0.438035\pi$
$318$	−0.104023	−0.00583333
$319$	8.36795	0.468515
$320$	−45.3858	−2.53714
$321$	−0.110603	−0.00617328
$322$	15.0107	0.836514
$323$	24.4130	1.35838
$324$	29.0608	1.61449
$325$	13.1228	0.727922
$326$	−30.8382	−1.70797
$327$	−0.0235342	−0.00130144
$328$	19.0331	1.05093
$329$	−7.25908	−0.400206
$330$	−0.0630076	−0.00346846
$331$	19.9654	1.09740	0.548698	−	0.836021i	$-0.315124\pi$
$331$	19.9654	1.09740	0.548698	+	0.836021i	$0.315124\pi$
$332$	−18.8427	−1.03413
$333$	5.28315	0.289515
$334$	−12.4305	−0.680169
$335$	23.0542	1.25959
$336$	−0.000203064 0	−1.10780e−5 0
$337$	27.1107	1.47682	0.738408	−	0.674354i	$-0.235578\pi$
$337$	27.1107	1.47682	0.738408	+	0.674354i	$0.235578\pi$
$338$	22.2851	1.21215
$339$	−0.0143461	−0.000779171 0
$340$	−42.6891	−2.31514
$341$	−2.76378	−0.149667
$342$	−44.3825	−2.39993
$343$	1.00000	0.0539949
$344$	−14.3291	−0.772572
$345$	−0.150381	−0.00809622
$346$	25.2059	1.35508
$347$	−25.6659	−1.37782	−0.688910	−	0.724847i	$-0.741910\pi$
$347$	−25.6659	−1.37782	−0.688910	+	0.724847i	$0.741910\pi$
$348$	0.146905	0.00787495
$349$	−30.1083	−1.61166	−0.805830	−	0.592147i	$-0.798281\pi$
$349$	−30.1083	−1.61166	−0.805830	+	0.592147i	$0.798281\pi$
$350$	−16.6339	−0.889118
$351$	−0.0707791	−0.00377791
$352$	6.84640	0.364915
$353$	18.9013	1.00602	0.503008	−	0.864282i	$-0.332227\pi$
$353$	18.9013	1.00602	0.503008	+	0.864282i	$0.332227\pi$
$354$	−0.0914073	−0.00485824
$355$	−14.6058	−0.775195
$356$	36.4043	1.92942
$357$	−0.0246745	−0.00130591
$358$	50.3165	2.65931
$359$	21.9909	1.16063	0.580317	−	0.814391i	$-0.302929\pi$
$359$	21.9909	1.16063	0.580317	+	0.814391i	$0.302929\pi$
$360$	29.5404	1.55691
$361$	22.8567	1.20298
$362$	28.0978	1.47679
$363$	−0.0624694	−0.00327879
$364$	5.82546	0.305337
$365$	4.67314	0.244603
$366$	−0.128661	−0.00672523
$367$	−4.82896	−0.252070	−0.126035	−	0.992026i	$-0.540225\pi$
$367$	−4.82896	−0.252070	−0.126035	+	0.992026i	$0.540225\pi$
$368$	0.203850	0.0106264
$369$	20.3151	1.05756
$370$	14.1087	0.733477
$371$	6.95675	0.361176
$372$	−0.0485202	−0.00251565
$373$	−19.4978	−1.00956	−0.504778	−	0.863249i	$-0.668426\pi$
$373$	−19.4978	−1.00956	−0.504778	+	0.863249i	$0.668426\pi$
$374$	10.3783	0.536651
$375$	0.0520972	0.00269029
$376$	20.4027	1.05219
$377$	12.5514	0.646429
$378$	0.0897164	0.00461451
$379$	−3.44006	−0.176704	−0.0883520	−	0.996089i	$-0.528160\pi$
$379$	−3.44006	−0.176704	−0.0883520	+	0.996089i	$0.528160\pi$
$380$	−73.1915	−3.75464
$381$	−0.113565	−0.00581810
$382$	6.72762	0.344215
$383$	−29.7133	−1.51828	−0.759140	−	0.650927i	$-0.774380\pi$
$383$	−29.7133	−1.51828	−0.759140	+	0.650927i	$0.774380\pi$
$384$	0.119265	0.00608620
$385$	4.21376	0.214753
$386$	21.6451	1.10171
$387$	−15.2942	−0.777449
$388$	15.1156	0.767378
$389$	−9.35628	−0.474382	−0.237191	−	0.971463i	$-0.576227\pi$
$389$	−9.35628	−0.474382	−0.237191	+	0.971463i	$0.576227\pi$
$390$	−0.0945073	−0.00478556
$391$	24.7700	1.25267
$392$	−2.81064	−0.141959
$393$	−0.0350179	−0.00176642
$394$	3.31399	0.166956
$395$	−51.3129	−2.58183
$396$	−11.6513	−0.585498
$397$	29.9878	1.50504	0.752522	−	0.658568i	$-0.228837\pi$
$397$	29.9878	1.50504	0.752522	+	0.658568i	$0.228837\pi$
$398$	23.2291	1.16437
$399$	−0.0423050	−0.00211790
$400$	−0.225893	−0.0112946
$401$	17.1868	0.858269	0.429135	−	0.903241i	$-0.358819\pi$
$401$	17.1868	0.858269	0.429135	+	0.903241i	$0.358819\pi$
$402$	−0.0983963	−0.00490756
$403$	−4.14549	−0.206502
$404$	7.65724	0.380962
$405$	31.5296	1.56672
$406$	−15.9096	−0.789579
$407$	−2.11813	−0.104992
$408$	0.0693513	0.00343340
$409$	7.69115	0.380303	0.190152	−	0.981755i	$-0.439102\pi$
$409$	7.69115	0.380303	0.190152	+	0.981755i	$0.439102\pi$
$410$	54.2516	2.67929
$411$	−0.0836973	−0.00412848
$412$	−24.6561	−1.21472
$413$	6.11304	0.300803
$414$	−45.0315	−2.21318
$415$	−20.4435	−1.00353
$416$	10.2692	0.503487
$417$	0.138935	0.00680369
$418$	17.7939	0.870328
$419$	−7.35456	−0.359294	−0.179647	−	0.983731i	$-0.557495\pi$
$419$	−7.35456	−0.359294	−0.179647	+	0.983731i	$0.557495\pi$
$420$	0.0739755	0.00360963
$421$	−30.8199	−1.50207	−0.751035	−	0.660262i	$-0.770445\pi$
$421$	−30.8199	−1.50207	−0.751035	+	0.660262i	$0.770445\pi$
$422$	41.3110	2.01099
$423$	21.7769	1.05883
$424$	−19.5530	−0.949575
$425$	−27.4485	−1.33145
$426$	0.0623381	0.00302029
$427$	8.60447	0.416399
$428$	−54.6188	−2.64010
$429$	0.0141883	0.000685019 0
$430$	−40.8433	−1.96964
$431$	−12.4645	−0.600395	−0.300198	−	0.953877i	$-0.597053\pi$
$431$	−12.4645	−0.600395	−0.300198	+	0.953877i	$0.597053\pi$
$432$	0.00121837	5.86191e−5 0
$433$	−4.26384	−0.204907	−0.102454	−	0.994738i	$-0.532669\pi$
$433$	−4.26384	−0.204907	−0.102454	+	0.994738i	$0.532669\pi$
$434$	5.25465	0.252231
$435$	0.159386	0.00764195
$436$	−11.6218	−0.556582
$437$	42.4688	2.03156
$438$	−0.0199452	−0.000953017 0
$439$	−32.8059	−1.56574	−0.782871	−	0.622185i	$-0.786245\pi$
$439$	−32.8059	−1.56574	−0.782871	+	0.622185i	$0.786245\pi$
$440$	−11.8434	−0.564611
$441$	−2.99996	−0.142855
$442$	15.5668	0.740438
$443$	−12.7146	−0.604087	−0.302044	−	0.953294i	$-0.597669\pi$
$443$	−12.7146	−0.604087	−0.302044	+	0.953294i	$0.597669\pi$
$444$	−0.0371853	−0.00176474
$445$	39.4970	1.87234
$446$	43.8627	2.07696
$447$	−0.0319043	−0.00150902
$448$	−12.9546	−0.612048
$449$	21.4953	1.01443	0.507214	−	0.861820i	$-0.330675\pi$
$449$	21.4953	1.01443	0.507214	+	0.861820i	$0.330675\pi$
$450$	49.9009	2.35235
$451$	−8.14475	−0.383522
$452$	−7.08445	−0.333225
$453$	0.0112856	0.000530244 0
$454$	36.0270	1.69083
$455$	6.32036	0.296303
$456$	0.118904	0.00556821
$457$	−21.7263	−1.01631	−0.508156	−	0.861265i	$-0.669673\pi$
$457$	−21.7263	−1.01631	−0.508156	+	0.861265i	$0.669673\pi$
$458$	3.16108	0.147707
$459$	0.148046	0.00691020
$460$	−74.2618	−3.46247
$461$	−18.6777	−0.869909	−0.434955	−	0.900452i	$-0.643236\pi$
$461$	−18.6777	−0.869909	−0.434955	+	0.900452i	$0.643236\pi$
$462$	−0.0179845	−0.000836715 0
$463$	−27.0097	−1.25525	−0.627623	−	0.778517i	$-0.715972\pi$
$463$	−27.0097	−1.25525	−0.627623	+	0.778517i	$0.715972\pi$
$464$	−0.216057	−0.0100302
$465$	−0.0526422	−0.00244122
$466$	−54.1013	−2.50619
$467$	7.21549	0.333893	0.166947	−	0.985966i	$-0.446609\pi$
$467$	7.21549	0.333893	0.166947	+	0.985966i	$0.446609\pi$
$468$	−17.4761	−0.807834
$469$	6.58044	0.303857
$470$	58.1554	2.68251
$471$	−0.109977	−0.00506747
$472$	−17.1816	−0.790846
$473$	6.13179	0.281940
$474$	0.219006	0.0100593
$475$	−47.0611	−2.15931
$476$	−12.1849	−0.558494
$477$	−20.8700	−0.955570
$478$	−51.7821	−2.36846
$479$	−15.3092	−0.699496	−0.349748	−	0.936844i	$-0.613733\pi$
$479$	−15.3092	−0.699496	−0.349748	+	0.936844i	$0.613733\pi$
$480$	0.130404	0.00595212
$481$	−3.17706	−0.144861
$482$	44.7337	2.03756
$483$	−0.0429237	−0.00195309
$484$	−30.8490	−1.40223
$485$	16.3997	0.744674
$486$	−0.403719	−0.0183131
$487$	11.1701	0.506164	0.253082	−	0.967445i	$-0.418556\pi$
$487$	11.1701	0.506164	0.253082	+	0.967445i	$0.418556\pi$
$488$	−24.1841	−1.09476
$489$	0.0881829	0.00398777
$490$	−8.01141	−0.361919
$491$	30.0074	1.35421	0.677107	−	0.735885i	$-0.263234\pi$
$491$	30.0074	1.35421	0.677107	+	0.735885i	$0.263234\pi$
$492$	−0.142987	−0.00644635
$493$	−26.2533	−1.18239
$494$	26.6897	1.20083
$495$	−12.6411	−0.568175
$496$	0.0713596	0.00320414
$497$	−4.16898	−0.187004
$498$	0.0872538	0.00390994
$499$	−4.16724	−0.186551	−0.0932756	−	0.995640i	$-0.529734\pi$
$499$	−4.16724	−0.186551	−0.0932756	+	0.995640i	$0.529734\pi$
$500$	25.7269	1.15054
$501$	0.0355456	0.00158806
$502$	5.69294	0.254088
$503$	10.3924	0.463372	0.231686	−	0.972791i	$-0.425576\pi$
$503$	10.3924	0.463372	0.231686	+	0.972791i	$0.425576\pi$
$504$	8.43181	0.375583
$505$	8.30776	0.369690
$506$	18.0541	0.802603
$507$	−0.0637251	−0.00283013
$508$	−56.0812	−2.48820
$509$	−43.3979	−1.92358	−0.961789	−	0.273793i	$-0.911722\pi$
$509$	−43.3979	−1.92358	−0.961789	+	0.273793i	$0.911722\pi$
$510$	0.197678	0.00875331
$511$	1.33387	0.0590070
$512$	−0.351337	−0.0155270
$513$	0.253828	0.0112068
$514$	−30.0245	−1.32432
$515$	−26.7508	−1.17878
$516$	0.107648	0.00473893
$517$	−8.73084	−0.383982
$518$	4.02710	0.176941
$519$	−0.0720773	−0.00316384
$520$	−17.7643	−0.779015
$521$	−12.5872	−0.551457	−0.275728	−	0.961236i	$-0.588919\pi$
$521$	−12.5872	−0.551457	−0.275728	+	0.961236i	$0.588919\pi$
$522$	47.7280	2.08900
$523$	13.3347	0.583086	0.291543	−	0.956558i	$-0.405831\pi$
$523$	13.3347	0.583086	0.291543	+	0.956558i	$0.405831\pi$
$524$	−17.2927	−0.755436
$525$	0.0475652	0.00207591
$526$	−28.7523	−1.25366
$527$	8.67098	0.377714
$528$	−0.000244235 0	−1.06290e−5 0
$529$	20.0898	0.873469
$530$	−55.7334	−2.42090
$531$	−18.3388	−0.795838
$532$	−20.8913	−0.905753
$533$	−12.2166	−0.529160
$534$	−0.168575	−0.00729495
$535$	−59.2589	−2.56199
$536$	−18.4953	−0.798875
$537$	−0.143882	−0.00620896
$538$	−42.5833	−1.83590
$539$	1.20275	0.0518060
$540$	−0.443850	−0.0191003
$541$	−3.91510	−0.168323	−0.0841616	−	0.996452i	$-0.526821\pi$
$541$	−3.91510	−0.168323	−0.0841616	+	0.996452i	$0.526821\pi$
$542$	26.5580	1.14077
$543$	−0.0803467	−0.00344801
$544$	−21.4796	−0.920932
$545$	−12.6091	−0.540115
$546$	−0.0269756	−0.00115445
$547$	21.7587	0.930334	0.465167	−	0.885223i	$-0.345994\pi$
$547$	21.7587	0.930334	0.465167	+	0.885223i	$0.345994\pi$
$548$	−41.3319	−1.76561
$549$	−25.8130	−1.10167
$550$	−20.0064	−0.853074
$551$	−45.0118	−1.91757
$552$	0.120643	0.00513491
$553$	−14.6464	−0.622829
$554$	28.0009	1.18965
$555$	−0.0403444	−0.00171252
$556$	68.6098	2.90971
$557$	10.1031	0.428082	0.214041	−	0.976825i	$-0.431337\pi$
$557$	10.1031	0.428082	0.214041	+	0.976825i	$0.431337\pi$
$558$	−15.7637	−0.667331
$559$	9.19728	0.389003
$560$	−0.108797	−0.00459752
$561$	−0.0296772	−0.00125297
$562$	10.3539	0.436751
$563$	23.3331	0.983373	0.491687	−	0.870772i	$-0.336381\pi$
$563$	23.3331	0.983373	0.491687	+	0.870772i	$0.336381\pi$
$564$	−0.153276	−0.00645409
$565$	−7.68631	−0.323365
$566$	−49.4203	−2.07729
$567$	8.99962	0.377948
$568$	11.7175	0.491657
$569$	−12.8250	−0.537653	−0.268826	−	0.963189i	$-0.586636\pi$
$569$	−12.8250	−0.537653	−0.268826	+	0.963189i	$0.586636\pi$
$570$	0.338923	0.0141959
$571$	−15.2487	−0.638137	−0.319068	−	0.947732i	$-0.603370\pi$
$571$	−15.2487	−0.638137	−0.319068	+	0.947732i	$0.603370\pi$
$572$	7.00656	0.292959
$573$	−0.0192379	−0.000803674 0
$574$	15.4852	0.646341
$575$	−47.7492	−1.99128
$576$	38.8633	1.61930
$577$	13.9144	0.579265	0.289632	−	0.957138i	$-0.406467\pi$
$577$	13.9144	0.579265	0.289632	+	0.957138i	$0.406467\pi$
$578$	6.31377	0.262618
$579$	−0.0618950	−0.00257227
$580$	78.7087	3.26820
$581$	−5.83526	−0.242088
$582$	−0.0699948	−0.00290138
$583$	8.36722	0.346535
$584$	−3.74904	−0.155136
$585$	−18.9608	−0.783933
$586$	33.2389	1.37309
$587$	−38.7184	−1.59808	−0.799040	−	0.601278i	$-0.794659\pi$
$587$	−38.7184	−1.59808	−0.799040	+	0.601278i	$0.794659\pi$
$588$	0.0211151	0.000870772 0
$589$	14.8666	0.612568
$590$	−48.9740	−2.01623
$591$	−0.00947648	−0.000389810 0
$592$	0.0546892	0.00224771
$593$	18.2686	0.750200	0.375100	−	0.926984i	$-0.377608\pi$
$593$	18.2686	0.750200	0.375100	+	0.926984i	$0.377608\pi$
$594$	0.107906	0.00442745
$595$	−13.2201	−0.541970
$596$	−15.7552	−0.645357
$597$	−0.0664243	−0.00271857
$598$	27.0800	1.10738
$599$	6.35738	0.259756	0.129878	−	0.991530i	$-0.458542\pi$
$599$	6.35738	0.259756	0.129878	+	0.991530i	$0.458542\pi$
$600$	−0.133689	−0.00545782
$601$	−21.5216	−0.877883	−0.438941	−	0.898516i	$-0.644646\pi$
$601$	−21.5216	−0.877883	−0.438941	+	0.898516i	$0.644646\pi$
$602$	−11.6581	−0.475147
$603$	−19.7410	−0.803918
$604$	5.57312	0.226767
$605$	−33.4698	−1.36074
$606$	−0.0354579	−0.00144038
$607$	11.4755	0.465778	0.232889	−	0.972503i	$-0.425182\pi$
$607$	11.4755	0.465778	0.232889	+	0.972503i	$0.425182\pi$
$608$	−36.8273	−1.49355
$609$	0.0454940	0.00184351
$610$	−68.9339	−2.79105
$611$	−13.0957	−0.529795
$612$	36.5542	1.47762
$613$	−41.6783	−1.68337	−0.841686	−	0.539967i	$-0.818437\pi$
$613$	−41.6783	−1.68337	−0.841686	+	0.539967i	$0.818437\pi$
$614$	−46.7313	−1.88592
$615$	−0.155134	−0.00625562
$616$	−3.38050	−0.136204
$617$	16.3654	0.658845	0.329423	−	0.944183i	$-0.393146\pi$
$617$	16.3654	0.658845	0.329423	+	0.944183i	$0.393146\pi$
$618$	0.114174	0.00459273
$619$	−14.4157	−0.579417	−0.289708	−	0.957115i	$-0.593558\pi$
$619$	−14.4157	−0.579417	−0.289708	+	0.957115i	$0.593558\pi$
$620$	−25.9961	−1.04403
$621$	0.257540	0.0103347
$622$	−6.06773	−0.243294
$623$	11.2738	0.451674
$624$	−0.000366336 0	−1.46652e−5 0
$625$	−8.45795	−0.338318
$626$	8.87798	0.354836
$627$	−0.0508823	−0.00203204
$628$	−54.3095	−2.16718
$629$	6.64534	0.264967
$630$	24.0339	0.957533
$631$	−39.4811	−1.57172	−0.785858	−	0.618407i	$-0.787778\pi$
$631$	−39.4811	−1.57172	−0.785858	+	0.618407i	$0.787778\pi$
$632$	41.1659	1.63749
$633$	−0.118130	−0.00469526
$634$	−15.7517	−0.625579
$635$	−60.8455	−2.41458
$636$	0.146892	0.00582466
$637$	1.80404	0.0714788
$638$	−19.1352	−0.757570
$639$	12.5068	0.494760
$640$	63.8995	2.52585
$641$	11.9198	0.470805	0.235403	−	0.971898i	$-0.424359\pi$
$641$	11.9198	0.470805	0.235403	+	0.971898i	$0.424359\pi$
$642$	0.252920	0.00998194
$643$	−9.38114	−0.369956	−0.184978	−	0.982743i	$-0.559221\pi$
$643$	−9.38114	−0.369956	−0.184978	+	0.982743i	$0.559221\pi$
$644$	−21.1968	−0.835271
$645$	0.116793	0.00459872
$646$	−55.8258	−2.19644
$647$	1.18806	0.0467074	0.0233537	−	0.999727i	$-0.492566\pi$
$647$	1.18806	0.0467074	0.0233537	+	0.999727i	$0.492566\pi$
$648$	−25.2947	−0.993670
$649$	7.35244	0.288609
$650$	−30.0082	−1.17702
$651$	−0.0150259	−0.000588910 0
$652$	43.5470	1.70543
$653$	24.1790	0.946197	0.473099	−	0.881009i	$-0.343135\pi$
$653$	24.1790	0.946197	0.473099	+	0.881009i	$0.343135\pi$
$654$	0.0538162	0.00210438
$655$	−18.7618	−0.733085
$656$	0.210294	0.00821059
$657$	−4.00156	−0.156116
$658$	16.5995	0.647117
$659$	35.5016	1.38295	0.691473	−	0.722403i	$-0.256962\pi$
$659$	35.5016	1.38295	0.691473	+	0.722403i	$0.256962\pi$
$660$	0.0889739	0.00346330
$661$	10.1564	0.395037	0.197519	−	0.980299i	$-0.436712\pi$
$661$	10.1564	0.395037	0.197519	+	0.980299i	$0.436712\pi$
$662$	−45.6553	−1.77444
$663$	−0.0445139	−0.00172878
$664$	16.4009	0.636477
$665$	−22.6661	−0.878954
$666$	−12.0811	−0.468134
$667$	−45.6701	−1.76835
$668$	17.5533	0.679159
$669$	−0.125427	−0.00484929
$670$	−52.7186	−2.03670
$671$	10.3490	0.399519
$672$	0.0372218	0.00143586
$673$	−36.4614	−1.40548	−0.702742	−	0.711445i	$-0.748041\pi$
$673$	−36.4614	−1.40548	−0.702742	+	0.711445i	$0.748041\pi$
$674$	−61.9948	−2.38795
$675$	−0.285389	−0.0109846
$676$	−31.4691	−1.21035
$677$	46.5466	1.78893	0.894465	−	0.447137i	$-0.147556\pi$
$677$	46.5466	1.78893	0.894465	+	0.447137i	$0.147556\pi$
$678$	0.0328055	0.00125989
$679$	4.68104	0.179642
$680$	37.1569	1.42490
$681$	−0.103021	−0.00394776
$682$	6.32002	0.242006
$683$	−5.16592	−0.197668	−0.0988342	−	0.995104i	$-0.531511\pi$
$683$	−5.16592	−0.197668	−0.0988342	+	0.995104i	$0.531511\pi$
$684$	62.6730	2.39636
$685$	−44.8432	−1.71337
$686$	−2.28673	−0.0873076
$687$	−0.00903921	−0.000344867 0
$688$	−0.158320	−0.00603589
$689$	12.5503	0.478128
$690$	0.343879	0.0130913
$691$	−43.3911	−1.65068	−0.825338	−	0.564638i	$-0.809016\pi$
$691$	−43.3911	−1.65068	−0.825338	+	0.564638i	$0.809016\pi$
$692$	−35.5936	−1.35307
$693$	−3.60819	−0.137064
$694$	58.6910	2.22788
$695$	74.4386	2.82362
$696$	−0.127867	−0.00484680
$697$	25.5530	0.967890
$698$	68.8494	2.60599
$699$	0.154705	0.00585146
$700$	23.4889	0.887797
$701$	18.2038	0.687547	0.343774	−	0.939053i	$-0.388295\pi$
$701$	18.2038	0.687547	0.343774	+	0.939053i	$0.388295\pi$
$702$	0.161852	0.00610872
$703$	11.3936	0.429717
$704$	−15.5811	−0.587237
$705$	−0.166298	−0.00626313
$706$	−43.2221	−1.62669
$707$	2.37131	0.0891824
$708$	0.129077	0.00485102
$709$	12.1097	0.454789	0.227395	−	0.973803i	$-0.426979\pi$
$709$	12.1097	0.454789	0.227395	+	0.973803i	$0.426979\pi$
$710$	33.3994	1.25346
$711$	43.9387	1.64783
$712$	−31.6865	−1.18750
$713$	15.0840	0.564900
$714$	0.0564238	0.00211161
$715$	7.60180	0.284291
$716$	−71.0526	−2.65536
$717$	0.148073	0.00552988
$718$	−50.2871	−1.87670
$719$	−27.6829	−1.03240	−0.516199	−	0.856469i	$-0.672654\pi$
$719$	−27.6829	−1.03240	−0.516199	+	0.856469i	$0.672654\pi$
$720$	0.326387	0.0121637
$721$	−7.63557	−0.284364
$722$	−52.2669	−1.94517
$723$	−0.127918	−0.00475731
$724$	−39.6773	−1.47459
$725$	50.6085	1.87955
$726$	0.142850	0.00530168
$727$	9.56596	0.354782	0.177391	−	0.984140i	$-0.443234\pi$
$727$	9.56596	0.354782	0.177391	+	0.984140i	$0.443234\pi$
$728$	−5.07052	−0.187926
$729$	−26.9977	−0.999914
$730$	−10.6862	−0.395514
$731$	−19.2376	−0.711529
$732$	0.181684	0.00671524
$733$	19.0039	0.701926	0.350963	−	0.936389i	$-0.385854\pi$
$733$	19.0039	0.701926	0.350963	+	0.936389i	$0.385854\pi$
$734$	11.0425	0.407586
$735$	0.0229089	0.000845008 0
$736$	−37.3659	−1.37732
$737$	7.91462	0.291539
$738$	−46.4550	−1.71003
$739$	−24.6156	−0.905501	−0.452750	−	0.891637i	$-0.649557\pi$
$739$	−24.6156	−0.905501	−0.452750	+	0.891637i	$0.649557\pi$
$740$	−19.9231	−0.732387
$741$	−0.0763201	−0.00280369
$742$	−15.9082	−0.584008
$743$	29.0730	1.06659	0.533293	−	0.845931i	$-0.320954\pi$
$743$	29.0730	1.06659	0.533293	+	0.845931i	$0.320954\pi$
$744$	0.0422323	0.00154831
$745$	−17.0936	−0.626262
$746$	44.5860	1.63241
$747$	17.5055	0.640494
$748$	−14.6554	−0.535854
$749$	−16.9145	−0.618042
$750$	−0.119132	−0.00435009
$751$	−49.9367	−1.82222	−0.911108	−	0.412169i	$-0.864771\pi$
$751$	−49.9367	−1.82222	−0.911108	+	0.412169i	$0.864771\pi$
$752$	0.225426	0.00822045
$753$	−0.0162792	−0.000593246 0
$754$	−28.7016	−1.04525
$755$	6.04658	0.220058
$756$	−0.126690	−0.00460766
$757$	0.875397	0.0318169	0.0159084	−	0.999873i	$-0.494936\pi$
$757$	0.875397	0.0318169	0.0159084	+	0.999873i	$0.494936\pi$
$758$	7.86648	0.285723
$759$	−0.0516264	−0.00187392
$760$	63.7064	2.31087
$761$	14.0800	0.510401	0.255201	−	0.966888i	$-0.417858\pi$
$761$	14.0800	0.510401	0.255201	+	0.966888i	$0.417858\pi$
$762$	0.259691	0.00940763
$763$	−3.59906	−0.130295
$764$	−9.50016	−0.343704
$765$	39.6597	1.43390
$766$	67.9462	2.45500
$767$	11.0282	0.398205
$768$	−0.103306	−0.00372773
$769$	−14.0166	−0.505450	−0.252725	−	0.967538i	$-0.581327\pi$
$769$	−14.0166	−0.505450	−0.252725	+	0.967538i	$0.581327\pi$
$770$	−9.63571	−0.347247
$771$	0.0858562	0.00309203
$772$	−30.5654	−1.10007
$773$	36.7046	1.32017	0.660087	−	0.751189i	$-0.270520\pi$
$773$	36.7046	1.32017	0.660087	+	0.751189i	$0.270520\pi$
$774$	34.9737	1.25710
$775$	−16.7151	−0.600424
$776$	−13.1567	−0.472299
$777$	−0.0115156	−0.000413121 0
$778$	21.3952	0.767056
$779$	43.8113	1.56970
$780$	0.133455	0.00477845
$781$	−5.01424	−0.179423
$782$	−56.6422	−2.02552
$783$	−0.272962	−0.00975487
$784$	−0.0310544	−0.00110909
$785$	−58.9233	−2.10306
$786$	0.0800763	0.00285623
$787$	36.1327	1.28799	0.643996	−	0.765029i	$-0.277275\pi$
$787$	36.1327	1.28799	0.643996	+	0.765029i	$0.277275\pi$
$788$	−4.67973	−0.166708
$789$	0.0822182	0.00292705
$790$	117.339	4.17472
$791$	−2.19393	−0.0780072
$792$	10.1413	0.360357
$793$	15.5228	0.551232
$794$	−68.5738	−2.43359
$795$	0.159372	0.00565233
$796$	−32.8020	−1.16264
$797$	−21.9405	−0.777173	−0.388587	−	0.921412i	$-0.627037\pi$
$797$	−21.9405	−0.777173	−0.388587	+	0.921412i	$0.627037\pi$
$798$	0.0967400	0.00342456
$799$	27.3918	0.969052
$800$	41.4064	1.46394
$801$	−33.8208	−1.19500
$802$	−39.3016	−1.38779
$803$	1.60431	0.0566149
$804$	0.138947	0.00490027
$805$	−22.9976	−0.810558
$806$	9.47961	0.333905
$807$	0.121769	0.00428646
$808$	−6.66492	−0.234471
$809$	−22.1224	−0.777781	−0.388890	−	0.921284i	$-0.627141\pi$
$809$	−22.1224	−0.777781	−0.388890	+	0.921284i	$0.627141\pi$
$810$	−72.0996	−2.53332
$811$	4.43385	0.155694	0.0778468	−	0.996965i	$-0.475196\pi$
$811$	4.43385	0.155694	0.0778468	+	0.996965i	$0.475196\pi$
$812$	22.4661	0.788406
$813$	−0.0759437	−0.00266346
$814$	4.84358	0.169768
$815$	47.2465	1.65497
$816$	0.000766252 0	2.68242e−5 0
$817$	−32.9834	−1.15394
$818$	−17.5876	−0.614935
$819$	−5.41205	−0.189112
$820$	−76.6093	−2.67531
$821$	23.5193	0.820828	0.410414	−	0.911899i	$-0.365384\pi$
$821$	23.5193	0.820828	0.410414	+	0.911899i	$0.365384\pi$
$822$	0.191393	0.00667559
$823$	52.0879	1.81567	0.907836	−	0.419326i	$-0.137734\pi$
$823$	52.0879	1.81567	0.907836	+	0.419326i	$0.137734\pi$
$824$	21.4609	0.747625
$825$	0.0572089	0.00199176
$826$	−13.9788	−0.486386
$827$	−11.2302	−0.390513	−0.195257	−	0.980752i	$-0.562554\pi$
$827$	−11.2302	−0.390513	−0.195257	+	0.980752i	$0.562554\pi$
$828$	63.5895	2.20989
$829$	−8.95990	−0.311190	−0.155595	−	0.987821i	$-0.549730\pi$
$829$	−8.95990	−0.311190	−0.155595	+	0.987821i	$0.549730\pi$
$830$	46.7487	1.62267
$831$	−0.0800697	−0.00277759
$832$	−23.3707	−0.810233
$833$	−3.77345	−0.130742
$834$	−0.317707	−0.0110013
$835$	19.0446	0.659064
$836$	−25.1270	−0.869035
$837$	0.0901545	0.00311619
$838$	16.8179	0.580963
$839$	0.352512	0.0121701	0.00608503	−	0.999981i	$-0.498063\pi$
$839$	0.352512	0.0121701	0.00608503	+	0.999981i	$0.498063\pi$
$840$	−0.0643888	−0.00222163
$841$	19.4048	0.669133
$842$	70.4767	2.42879
$843$	−0.0296072	−0.00101973
$844$	−58.3358	−2.00800
$845$	−34.1425	−1.17454
$846$	−49.7978	−1.71209
$847$	−9.55340	−0.328259
$848$	−0.216038	−0.00741876
$849$	0.141319	0.00485006
$850$	62.7671	2.15290
$851$	11.5602	0.396279
$852$	−0.0880285	−0.00301581
$853$	35.9447	1.23072	0.615361	−	0.788246i	$-0.289010\pi$
$853$	35.9447	1.23072	0.615361	+	0.788246i	$0.289010\pi$
$854$	−19.6761	−0.673301
$855$	67.9974	2.32546
$856$	47.5406	1.62490
$857$	6.03976	0.206314	0.103157	−	0.994665i	$-0.467106\pi$
$857$	6.03976	0.206314	0.103157	+	0.994665i	$0.467106\pi$
$858$	−0.0324448	−0.00110765
$859$	5.83933	0.199235	0.0996177	−	0.995026i	$-0.468238\pi$
$859$	5.83933	0.199235	0.0996177	+	0.995026i	$0.468238\pi$
$860$	57.6754	1.96671
$861$	−0.0442806	−0.00150908
$862$	28.5030	0.970815
$863$	1.00000	0.0340404
$863$	1.00000	0.0340404
$864$	−0.223329	−0.00759782
$865$	−38.6175	−1.31303
$866$	9.75023	0.331326
$867$	−0.0180544	−0.000613161 0
$868$	−7.42015	−0.251856
$869$	−17.6160	−0.597581
$870$	−0.364471	−0.0123567
$871$	11.8714	0.402247
$872$	10.1157	0.342560
$873$	−14.0429	−0.475280
$874$	−97.1144	−3.28494
$875$	7.96718	0.269340
$876$	0.0281648	0.000951601 0
$877$	−17.2721	−0.583238	−0.291619	−	0.956535i	$-0.594194\pi$
$877$	−17.2721	−0.583238	−0.291619	+	0.956535i	$0.594194\pi$
$878$	75.0181	2.53174
$879$	−0.0950480	−0.00320589
$880$	−0.130856	−0.00441114
$881$	12.3398	0.415738	0.207869	−	0.978157i	$-0.433347\pi$
$881$	12.3398	0.415738	0.207869	+	0.978157i	$0.433347\pi$
$882$	6.86008	0.230991
$883$	−25.6190	−0.862147	−0.431074	−	0.902317i	$-0.641865\pi$
$883$	−25.6190	−0.862147	−0.431074	+	0.902317i	$0.641865\pi$
$884$	−21.9821	−0.739338
$885$	0.140043	0.00470750
$886$	29.0747	0.976784
$887$	10.7416	0.360667	0.180334	−	0.983606i	$-0.442282\pi$
$887$	10.7416	0.360667	0.180334	+	0.983606i	$0.442282\pi$
$888$	0.0323664	0.00108614
$889$	−17.3674	−0.582483
$890$	−90.3187	−3.02749
$891$	10.8243	0.362627
$892$	−61.9391	−2.07387
$893$	46.9639	1.57159
$894$	0.0729564	0.00244003
$895$	−77.0888	−2.57680
$896$	18.2391	0.609324
$897$	−0.0774362	−0.00258552
$898$	−49.1539	−1.64029
$899$	−15.9873	−0.533205
$900$	−70.4657	−2.34886
$901$	−26.2510	−0.874547
$902$	18.6248	0.620139
$903$	0.0333367	0.00110937
$904$	6.16636	0.205090
$905$	−43.0480	−1.43096
$906$	−0.0258071	−0.000857382 0
$907$	6.51897	0.216459	0.108229	−	0.994126i	$-0.465482\pi$
$907$	6.51897	0.216459	0.108229	+	0.994126i	$0.465482\pi$
$908$	−50.8742	−1.68832
$909$	−7.11384	−0.235951
$910$	−14.4529	−0.479110
$911$	42.3740	1.40391	0.701957	−	0.712219i	$-0.252310\pi$
$911$	42.3740	1.40391	0.701957	+	0.712219i	$0.252310\pi$
$912$	0.00131376	4.35028e−5 0
$913$	−7.01835	−0.232274
$914$	49.6820	1.64334
$915$	0.197119	0.00651655
$916$	−4.46379	−0.147488
$917$	−5.35526	−0.176846
$918$	−0.338541	−0.0111735
$919$	39.4283	1.30062	0.650310	−	0.759669i	$-0.274639\pi$
$919$	39.4283	1.30062	0.650310	+	0.759669i	$0.274639\pi$
$920$	64.6380	2.13105
$921$	0.133630	0.00440325
$922$	42.7109	1.40661
$923$	−7.52103	−0.247558
$924$	0.0253961	0.000835471 0
$925$	−12.8102	−0.421198
$926$	61.7637	2.02968
$927$	22.9064	0.752345
$928$	39.6034	1.30004
$929$	8.74426	0.286890	0.143445	−	0.989658i	$-0.454182\pi$
$929$	8.74426	0.286890	0.143445	+	0.989658i	$0.454182\pi$
$930$	0.120378	0.00394736
$931$	−6.46967	−0.212035
$932$	76.3971	2.50247
$933$	0.0173509	0.000568043 0
$934$	−16.4998	−0.539891
$935$	−15.9004	−0.519999
$936$	15.2114	0.497199
$937$	20.0430	0.654776	0.327388	−	0.944890i	$-0.393832\pi$
$937$	20.0430	0.654776	0.327388	+	0.944890i	$0.393832\pi$
$938$	−15.0477	−0.491324
$939$	−0.0253869	−0.000828471 0
$940$	−82.1220	−2.67852
$941$	8.57336	0.279484	0.139742	−	0.990188i	$-0.455373\pi$
$941$	8.57336	0.279484	0.139742	+	0.990188i	$0.455373\pi$
$942$	0.251487	0.00819390
$943$	44.4519	1.44755
$944$	−0.189837	−0.00617866
$945$	−0.137453	−0.00447133
$946$	−14.0217	−0.455885
$947$	26.2863	0.854191	0.427095	−	0.904207i	$-0.359537\pi$
$947$	26.2863	0.854191	0.427095	+	0.904207i	$0.359537\pi$
$948$	−0.309261	−0.0100443
$949$	2.40636	0.0781138
$950$	107.616	3.49152
$951$	0.0450425	0.00146060
$952$	10.6058	0.343737
$953$	10.0620	0.325940	0.162970	−	0.986631i	$-0.447893\pi$
$953$	10.0620	0.325940	0.162970	+	0.986631i	$0.447893\pi$
$954$	47.7239	1.54512
$955$	−10.3072	−0.333534
$956$	73.1222	2.36494
$957$	0.0547178	0.00176878
$958$	35.0080	1.13106
$959$	−12.7998	−0.413326
$960$	−0.296776	−0.00957842
$961$	−25.7197	−0.829668
$962$	7.26506	0.234235
$963$	50.7427	1.63516
$964$	−63.1690	−2.03454
$965$	−33.1620	−1.06752
$966$	0.0981547	0.00315807
$967$	−13.8378	−0.444992	−0.222496	−	0.974934i	$-0.571420\pi$
$967$	−13.8378	−0.444992	−0.222496	+	0.974934i	$0.571420\pi$
$968$	26.8512	0.863030
$969$	0.159636	0.00512825
$970$	−37.5017	−1.20411
$971$	−21.2542	−0.682081	−0.341040	−	0.940049i	$-0.610779\pi$
$971$	−21.2542	−0.682081	−0.341040	+	0.940049i	$0.610779\pi$
$972$	0.570097	0.0182859
$973$	21.2473	0.681156
$974$	−25.5429	−0.818447
$975$	0.0858096	0.00274811
$976$	−0.267207	−0.00855307
$977$	−14.0867	−0.450675	−0.225337	−	0.974281i	$-0.572348\pi$
$977$	−14.0867	−0.450675	−0.225337	+	0.974281i	$0.572348\pi$
$978$	−0.201650	−0.00644806
$979$	13.5595	0.433364
$980$	11.3130	0.361381
$981$	10.7970	0.344723
$982$	−68.6186	−2.18971
$983$	28.0254	0.893870	0.446935	−	0.894566i	$-0.352515\pi$
$983$	28.0254	0.893870	0.446935	+	0.894566i	$0.352515\pi$
$984$	0.124457	0.00396754
$985$	−5.07729	−0.161776
$986$	60.0340	1.91187
$987$	−0.0474669	−0.00151089
$988$	−37.6888	−1.19904
$989$	−33.4657	−1.06415
$990$	28.9067	0.918715
$991$	−32.3588	−1.02791	−0.513955	−	0.857817i	$-0.671820\pi$
$991$	−32.3588	−1.02791	−0.513955	+	0.857817i	$0.671820\pi$
$992$	−13.0803	−0.415300
$993$	0.130553	0.00414298
$994$	9.53332	0.302379
$995$	−35.5887	−1.12824
$996$	−0.123212	−0.00390413
$997$	−32.7952	−1.03863	−0.519317	−	0.854582i	$-0.673813\pi$
$997$	−32.7952	−1.03863	−0.519317	+	0.854582i	$0.673813\pi$
$998$	9.52933	0.301646
$999$	0.0690933	0.00218602

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.c.1.7	✓	83

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.c.1.7	✓	83	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)

\(f(q)\)	\(=\)	\(q-2.28673 q^{2} +0.00653898 q^{3} +3.22911 q^{4} +3.50344 q^{5} -0.0149528 q^{6} +1.00000 q^{7} -2.81064 q^{8} -2.99996 q^{9} +O(q^{10})\)	\(q-2.28673 q^{2} +0.00653898 q^{3} +3.22911 q^{4} +3.50344 q^{5} -0.0149528 q^{6} +1.00000 q^{7} -2.81064 q^{8} -2.99996 q^{9} -8.01141 q^{10} +1.20275 q^{11} +0.0211151 q^{12} +1.80404 q^{13} -2.28673 q^{14} +0.0229089 q^{15} -0.0310544 q^{16} -3.77345 q^{17} +6.86008 q^{18} -6.46967 q^{19} +11.3130 q^{20} +0.00653898 q^{21} -2.75035 q^{22} -6.56428 q^{23} -0.0183787 q^{24} +7.27410 q^{25} -4.12535 q^{26} -0.0392336 q^{27} +3.22911 q^{28} +6.95736 q^{29} -0.0523864 q^{30} -2.29789 q^{31} +5.69230 q^{32} +0.00786474 q^{33} +8.62885 q^{34} +3.50344 q^{35} -9.68720 q^{36} -1.76108 q^{37} +14.7944 q^{38} +0.0117966 q^{39} -9.84693 q^{40} -6.77179 q^{41} -0.0149528 q^{42} +5.09815 q^{43} +3.88381 q^{44} -10.5102 q^{45} +15.0107 q^{46} -7.25908 q^{47} -0.000203064 q^{48} +1.00000 q^{49} -16.6339 q^{50} -0.0246745 q^{51} +5.82546 q^{52} +6.95675 q^{53} +0.0897164 q^{54} +4.21376 q^{55} -2.81064 q^{56} -0.0423050 q^{57} -15.9096 q^{58} +6.11304 q^{59} +0.0739755 q^{60} +8.60447 q^{61} +5.25465 q^{62} -2.99996 q^{63} -12.9546 q^{64} +6.32036 q^{65} -0.0179845 q^{66} +6.58044 q^{67} -12.1849 q^{68} -0.0429237 q^{69} -8.01141 q^{70} -4.16898 q^{71} +8.43181 q^{72} +1.33387 q^{73} +4.02710 q^{74} +0.0475652 q^{75} -20.8913 q^{76} +1.20275 q^{77} -0.0269756 q^{78} -14.6464 q^{79} -0.108797 q^{80} +8.99962 q^{81} +15.4852 q^{82} -5.83526 q^{83} +0.0211151 q^{84} -13.2201 q^{85} -11.6581 q^{86} +0.0454940 q^{87} -3.38050 q^{88} +11.2738 q^{89} +24.0339 q^{90} +1.80404 q^{91} -21.1968 q^{92} -0.0150259 q^{93} +16.5995 q^{94} -22.6661 q^{95} +0.0372218 q^{96} +4.68104 q^{97} -2.28673 q^{98} -3.60819 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9}+O(q^{10}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9} - 20 q^{10} - 26 q^{11} - 14 q^{12} - 22 q^{13} - 8 q^{14} - 37 q^{15} - 10 q^{16} - 9 q^{17} - 27 q^{18} - 42 q^{19} - 22 q^{20} - 12 q^{21} - 44 q^{22} - 46 q^{23} - 24 q^{24} - 20 q^{25} - 9 q^{26} - 39 q^{27} + 48 q^{28} - 36 q^{29} - 11 q^{30} - 107 q^{31} - 19 q^{32} - 25 q^{33} - 24 q^{34} - 11 q^{35} - 32 q^{36} - 75 q^{37} - 16 q^{38} - 78 q^{39} - 34 q^{40} - 17 q^{41} - 8 q^{42} - 87 q^{43} - 32 q^{44} - 17 q^{45} - 56 q^{46} - 39 q^{47} - 16 q^{48} + 83 q^{49} - 26 q^{50} - 71 q^{51} - 53 q^{52} - 28 q^{53} - 25 q^{54} - 94 q^{55} - 18 q^{56} - 79 q^{57} - 69 q^{58} - 26 q^{59} - 43 q^{60} - 56 q^{61} - 6 q^{62} + 39 q^{63} - 108 q^{64} - 26 q^{65} + 10 q^{66} - 123 q^{67} - 11 q^{68} + 2 q^{69} - 20 q^{70} - 96 q^{71} - 11 q^{72} - 53 q^{73} - 26 q^{74} - 27 q^{75} - 65 q^{76} - 26 q^{77} - 43 q^{78} - 160 q^{79} + 12 q^{80} - 53 q^{81} - 20 q^{82} - 2 q^{83} - 14 q^{84} - 110 q^{85} + 24 q^{86} - 52 q^{87} - 79 q^{88} - 5 q^{89} - 4 q^{90} - 22 q^{91} - 51 q^{92} - 30 q^{93} - 9 q^{94} - 76 q^{95} - 3 q^{96} - 44 q^{97} - 8 q^{98} - 82 q^{99}+O(q^{100}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9 - 20 * q^10 - 26 * q^11 - 14 * q^12 - 22 * q^13 - 8 * q^14 - 37 * q^15 - 10 * q^16 - 9 * q^17 - 27 * q^18 - 42 * q^19 - 22 * q^20 - 12 * q^21 - 44 * q^22 - 46 * q^23 - 24 * q^24 - 20 * q^25 - 9 * q^26 - 39 * q^27 + 48 * q^28 - 36 * q^29 - 11 * q^30 - 107 * q^31 - 19 * q^32 - 25 * q^33 - 24 * q^34 - 11 * q^35 - 32 * q^36 - 75 * q^37 - 16 * q^38 - 78 * q^39 - 34 * q^40 - 17 * q^41 - 8 * q^42 - 87 * q^43 - 32 * q^44 - 17 * q^45 - 56 * q^46 - 39 * q^47 - 16 * q^48 + 83 * q^49 - 26 * q^50 - 71 * q^51 - 53 * q^52 - 28 * q^53 - 25 * q^54 - 94 * q^55 - 18 * q^56 - 79 * q^57 - 69 * q^58 - 26 * q^59 - 43 * q^60 - 56 * q^61 - 6 * q^62 + 39 * q^63 - 108 * q^64 - 26 * q^65 + 10 * q^66 - 123 * q^67 - 11 * q^68 + 2 * q^69 - 20 * q^70 - 96 * q^71 - 11 * q^72 - 53 * q^73 - 26 * q^74 - 27 * q^75 - 65 * q^76 - 26 * q^77 - 43 * q^78 - 160 * q^79 + 12 * q^80 - 53 * q^81 - 20 * q^82 - 2 * q^83 - 14 * q^84 - 110 * q^85 + 24 * q^86 - 52 * q^87 - 79 * q^88 - 5 * q^89 - 4 * q^90 - 22 * q^91 - 51 * q^92 - 30 * q^93 - 9 * q^94 - 76 * q^95 - 3 * q^96 - 44 * q^97 - 8 * q^98 - 82 * q^99

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