LMFDB - Embedded newform 862.2.a.i.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [862,2,Mod(1,862)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(862, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("862.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 862 = 2 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	862.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:	$6.88310465423$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.11017801.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 6x^{4} + 13x^{3} + 3x^{2} - 10x - 1 $ x^6 - 2x^5 - 6x^4 + 13x^3 + 3x^2 - 10*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.0983884$ of defining polynomial
Character	$\chi$	$=$	862.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.0983884 q^{3} +1.00000 q^{4} -1.85330 q^{5} -0.0983884 q^{6} +3.35263 q^{7} -1.00000 q^{8} -2.99032 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.0983884 q^{3} +1.00000 q^{4} -1.85330 q^{5} -0.0983884 q^{6} +3.35263 q^{7} -1.00000 q^{8} -2.99032 q^{9} +1.85330 q^{10} -1.72856 q^{11} +0.0983884 q^{12} -0.453782 q^{13} -3.35263 q^{14} -0.182344 q^{15} +1.00000 q^{16} +0.953933 q^{17} +2.99032 q^{18} -2.88001 q^{19} -1.85330 q^{20} +0.329860 q^{21} +1.72856 q^{22} -2.84245 q^{23} -0.0983884 q^{24} -1.56526 q^{25} +0.453782 q^{26} -0.589378 q^{27} +3.35263 q^{28} +2.72246 q^{29} +0.182344 q^{30} -6.43524 q^{31} -1.00000 q^{32} -0.170070 q^{33} -0.953933 q^{34} -6.21345 q^{35} -2.99032 q^{36} +7.23942 q^{37} +2.88001 q^{38} -0.0446469 q^{39} +1.85330 q^{40} -3.42148 q^{41} -0.329860 q^{42} +3.00341 q^{43} -1.72856 q^{44} +5.54197 q^{45} +2.84245 q^{46} -10.3682 q^{47} +0.0983884 q^{48} +4.24016 q^{49} +1.56526 q^{50} +0.0938559 q^{51} -0.453782 q^{52} -12.4490 q^{53} +0.589378 q^{54} +3.20355 q^{55} -3.35263 q^{56} -0.283360 q^{57} -2.72246 q^{58} -5.49473 q^{59} -0.182344 q^{60} -8.52910 q^{61} +6.43524 q^{62} -10.0254 q^{63} +1.00000 q^{64} +0.840996 q^{65} +0.170070 q^{66} +3.09637 q^{67} +0.953933 q^{68} -0.279664 q^{69} +6.21345 q^{70} -7.28415 q^{71} +2.99032 q^{72} +6.74025 q^{73} -7.23942 q^{74} -0.154004 q^{75} -2.88001 q^{76} -5.79523 q^{77} +0.0446469 q^{78} -3.76326 q^{79} -1.85330 q^{80} +8.91297 q^{81} +3.42148 q^{82} +1.57672 q^{83} +0.329860 q^{84} -1.76793 q^{85} -3.00341 q^{86} +0.267859 q^{87} +1.72856 q^{88} -4.88785 q^{89} -5.54197 q^{90} -1.52137 q^{91} -2.84245 q^{92} -0.633153 q^{93} +10.3682 q^{94} +5.33753 q^{95} -0.0983884 q^{96} -2.75923 q^{97} -4.24016 q^{98} +5.16895 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 2 q^{5} + 2 q^{6} + 3 q^{7} - 6 q^{8} - 2 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 2 * q^5 + 2 * q^6 + 3 * q^7 - 6 * q^8 - 2 * q^9	\( 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 2 q^{5} + 2 q^{6} + 3 q^{7} - 6 q^{8} - 2 q^{9} + 2 q^{10} - 6 q^{11} - 2 q^{12} - 9 q^{13} - 3 q^{14} - 3 q^{15} + 6 q^{16} - 17 q^{17} + 2 q^{18} + q^{19} - 2 q^{20} - 8 q^{21} + 6 q^{22} - 20 q^{23} + 2 q^{24} + 10 q^{25} + 9 q^{26} + 7 q^{27} + 3 q^{28} + q^{29} + 3 q^{30} + 8 q^{31} - 6 q^{32} - 5 q^{33} + 17 q^{34} - 14 q^{35} - 2 q^{36} - 3 q^{37} - q^{38} - 13 q^{39} + 2 q^{40} - 19 q^{41} + 8 q^{42} - 21 q^{43} - 6 q^{44} - 16 q^{45} + 20 q^{46} - 10 q^{47} - 2 q^{48} - 7 q^{49} - 10 q^{50} - 2 q^{51} - 9 q^{52} - q^{53} - 7 q^{54} + 3 q^{55} - 3 q^{56} - 11 q^{57} - q^{58} + 11 q^{59} - 3 q^{60} - 2 q^{61} - 8 q^{62} + 6 q^{64} - 30 q^{65} + 5 q^{66} + 4 q^{67} - 17 q^{68} + 16 q^{69} + 14 q^{70} - 4 q^{71} + 2 q^{72} - 39 q^{73} + 3 q^{74} - 21 q^{75} + q^{76} - 33 q^{77} + 13 q^{78} - 16 q^{79} - 2 q^{80} - 22 q^{81} + 19 q^{82} - 20 q^{83} - 8 q^{84} - 16 q^{85} + 21 q^{86} + q^{87} + 6 q^{88} - 17 q^{89} + 16 q^{90} + 20 q^{91} - 20 q^{92} - 5 q^{93} + 10 q^{94} - 16 q^{95} + 2 q^{96} - 29 q^{97} + 7 q^{98} - 4 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 2 * q^5 + 2 * q^6 + 3 * q^7 - 6 * q^8 - 2 * q^9 + 2 * q^10 - 6 * q^11 - 2 * q^12 - 9 * q^13 - 3 * q^14 - 3 * q^15 + 6 * q^16 - 17 * q^17 + 2 * q^18 + q^19 - 2 * q^20 - 8 * q^21 + 6 * q^22 - 20 * q^23 + 2 * q^24 + 10 * q^25 + 9 * q^26 + 7 * q^27 + 3 * q^28 + q^29 + 3 * q^30 + 8 * q^31 - 6 * q^32 - 5 * q^33 + 17 * q^34 - 14 * q^35 - 2 * q^36 - 3 * q^37 - q^38 - 13 * q^39 + 2 * q^40 - 19 * q^41 + 8 * q^42 - 21 * q^43 - 6 * q^44 - 16 * q^45 + 20 * q^46 - 10 * q^47 - 2 * q^48 - 7 * q^49 - 10 * q^50 - 2 * q^51 - 9 * q^52 - q^53 - 7 * q^54 + 3 * q^55 - 3 * q^56 - 11 * q^57 - q^58 + 11 * q^59 - 3 * q^60 - 2 * q^61 - 8 * q^62 + 6 * q^64 - 30 * q^65 + 5 * q^66 + 4 * q^67 - 17 * q^68 + 16 * q^69 + 14 * q^70 - 4 * q^71 + 2 * q^72 - 39 * q^73 + 3 * q^74 - 21 * q^75 + q^76 - 33 * q^77 + 13 * q^78 - 16 * q^79 - 2 * q^80 - 22 * q^81 + 19 * q^82 - 20 * q^83 - 8 * q^84 - 16 * q^85 + 21 * q^86 + q^87 + 6 * q^88 - 17 * q^89 + 16 * q^90 + 20 * q^91 - 20 * q^92 - 5 * q^93 + 10 * q^94 - 16 * q^95 + 2 * q^96 - 29 * q^97 + 7 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.0983884	0.0568045	0.0284023	−	0.999597i	$-0.490958\pi$
$3$	0.0983884	0.0568045	0.0284023	+	0.999597i	$0.490958\pi$
$4$	1.00000	0.500000
$5$	−1.85330	−0.828823	−0.414411	−	0.910090i	$-0.636013\pi$
$5$	−1.85330	−0.828823	−0.414411	+	0.910090i	$0.636013\pi$
$6$	−0.0983884	−0.0401669
$7$	3.35263	1.26718	0.633588	−	0.773670i	$-0.281581\pi$
$7$	3.35263	1.26718	0.633588	+	0.773670i	$0.281581\pi$
$8$	−1.00000	−0.353553
$9$	−2.99032	−0.996773
$10$	1.85330	0.586066
$11$	−1.72856	−0.521181	−0.260590	−	0.965449i	$-0.583917\pi$
$11$	−1.72856	−0.521181	−0.260590	+	0.965449i	$0.583917\pi$
$12$	0.0983884	0.0284023
$13$	−0.453782	−0.125857	−0.0629283	−	0.998018i	$-0.520044\pi$
$13$	−0.453782	−0.125857	−0.0629283	+	0.998018i	$0.520044\pi$
$14$	−3.35263	−0.896029
$15$	−0.182344	−0.0470809
$16$	1.00000	0.250000
$17$	0.953933	0.231363	0.115681	−	0.993286i	$-0.463095\pi$
$17$	0.953933	0.231363	0.115681	+	0.993286i	$0.463095\pi$
$18$	2.99032	0.704825
$19$	−2.88001	−0.660720	−0.330360	−	0.943855i	$-0.607170\pi$
$19$	−2.88001	−0.660720	−0.330360	+	0.943855i	$0.607170\pi$
$20$	−1.85330	−0.414411
$21$	0.329860	0.0719814
$22$	1.72856	0.368531
$23$	−2.84245	−0.592692	−0.296346	−	0.955081i	$-0.595768\pi$
$23$	−2.84245	−0.592692	−0.296346	+	0.955081i	$0.595768\pi$
$24$	−0.0983884	−0.0200834
$25$	−1.56526	−0.313053
$26$	0.453782	0.0889940
$27$	−0.589378	−0.113426
$28$	3.35263	0.633588
$29$	2.72246	0.505548	0.252774	−	0.967525i	$-0.418657\pi$
$29$	2.72246	0.505548	0.252774	+	0.967525i	$0.418657\pi$
$30$	0.182344	0.0332912
$31$	−6.43524	−1.15580	−0.577902	−	0.816106i	$-0.696128\pi$
$31$	−6.43524	−1.15580	−0.577902	+	0.816106i	$0.696128\pi$
$32$	−1.00000	−0.176777
$33$	−0.170070	−0.0296054
$34$	−0.953933	−0.163598
$35$	−6.21345	−1.05026
$36$	−2.99032	−0.498387
$37$	7.23942	1.19015	0.595076	−	0.803669i	$-0.297122\pi$
$37$	7.23942	1.19015	0.595076	+	0.803669i	$0.297122\pi$
$38$	2.88001	0.467199
$39$	−0.0446469	−0.00714922
$40$	1.85330	0.293033
$41$	−3.42148	−0.534345	−0.267172	−	0.963649i	$-0.586089\pi$
$41$	−3.42148	−0.534345	−0.267172	+	0.963649i	$0.586089\pi$
$42$	−0.329860	−0.0508985
$43$	3.00341	0.458016	0.229008	−	0.973425i	$-0.426452\pi$
$43$	3.00341	0.458016	0.229008	+	0.973425i	$0.426452\pi$
$44$	−1.72856	−0.260590
$45$	5.54197	0.826148
$46$	2.84245	0.419097
$47$	−10.3682	−1.51236	−0.756182	−	0.654362i	$-0.772937\pi$
$47$	−10.3682	−1.51236	−0.756182	+	0.654362i	$0.772937\pi$
$48$	0.0983884	0.0142011
$49$	4.24016	0.605737
$50$	1.56526	0.221362
$51$	0.0938559	0.0131425
$52$	−0.453782	−0.0629283
$53$	−12.4490	−1.71000	−0.855002	−	0.518625i	$-0.826444\pi$
$53$	−12.4490	−1.71000	−0.855002	+	0.518625i	$0.826444\pi$
$54$	0.589378	0.0802042
$55$	3.20355	0.431967
$56$	−3.35263	−0.448015
$57$	−0.283360	−0.0375319
$58$	−2.72246	−0.357477
$59$	−5.49473	−0.715353	−0.357677	−	0.933846i	$-0.616431\pi$
$59$	−5.49473	−0.715353	−0.357677	+	0.933846i	$0.616431\pi$
$60$	−0.182344	−0.0235405
$61$	−8.52910	−1.09204	−0.546020	−	0.837772i	$-0.683858\pi$
$61$	−8.52910	−1.09204	−0.546020	+	0.837772i	$0.683858\pi$
$62$	6.43524	0.817277
$63$	−10.0254	−1.26309
$64$	1.00000	0.125000
$65$	0.840996	0.104313
$66$	0.170070	0.0209342
$67$	3.09637	0.378282	0.189141	−	0.981950i	$-0.439430\pi$
$67$	3.09637	0.378282	0.189141	+	0.981950i	$0.439430\pi$
$68$	0.953933	0.115681
$69$	−0.279664	−0.0336676
$70$	6.21345	0.742649
$71$	−7.28415	−0.864469	−0.432235	−	0.901761i	$-0.642275\pi$
$71$	−7.28415	−0.864469	−0.432235	+	0.901761i	$0.642275\pi$
$72$	2.99032	0.352413
$73$	6.74025	0.788887	0.394443	−	0.918920i	$-0.370937\pi$
$73$	6.74025	0.788887	0.394443	+	0.918920i	$0.370937\pi$
$74$	−7.23942	−0.841565
$75$	−0.154004	−0.0177828
$76$	−2.88001	−0.330360
$77$	−5.79523	−0.660428
$78$	0.0446469	0.00505526
$79$	−3.76326	−0.423399	−0.211700	−	0.977335i	$-0.567900\pi$
$79$	−3.76326	−0.423399	−0.211700	+	0.977335i	$0.567900\pi$
$80$	−1.85330	−0.207206
$81$	8.91297	0.990330
$82$	3.42148	0.377839
$83$	1.57672	0.173067	0.0865336	−	0.996249i	$-0.472421\pi$
$83$	1.57672	0.173067	0.0865336	+	0.996249i	$0.472421\pi$
$84$	0.329860	0.0359907
$85$	−1.76793	−0.191759
$86$	−3.00341	−0.323866
$87$	0.267859	0.0287174
$88$	1.72856	0.184265
$89$	−4.88785	−0.518111	−0.259056	−	0.965862i	$-0.583411\pi$
$89$	−4.88785	−0.518111	−0.259056	+	0.965862i	$0.583411\pi$
$90$	−5.54197	−0.584175
$91$	−1.52137	−0.159482
$92$	−2.84245	−0.296346
$93$	−0.633153	−0.0656549
$94$	10.3682	1.06940
$95$	5.33753	0.547620
$96$	−0.0983884	−0.0100417
$97$	−2.75923	−0.280158	−0.140079	−	0.990140i	$-0.544736\pi$
$97$	−2.75923	−0.280158	−0.140079	+	0.990140i	$0.544736\pi$
$98$	−4.24016	−0.428321
$99$	5.16895	0.519499
$100$	−1.56526	−0.156526
$101$	−16.8051	−1.67217	−0.836083	−	0.548602i	$-0.815160\pi$
$101$	−16.8051	−1.67217	−0.836083	+	0.548602i	$0.815160\pi$
$102$	−0.0938559	−0.00929312
$103$	−4.78556	−0.471536	−0.235768	−	0.971809i	$-0.575760\pi$
$103$	−4.78556	−0.471536	−0.235768	+	0.971809i	$0.575760\pi$
$104$	0.453782	0.0444970
$105$	−0.611331	−0.0596598
$106$	12.4490	1.20916
$107$	8.76565	0.847408	0.423704	−	0.905801i	$-0.360730\pi$
$107$	8.76565	0.847408	0.423704	+	0.905801i	$0.360730\pi$
$108$	−0.589378	−0.0567129
$109$	7.40928	0.709681	0.354840	−	0.934927i	$-0.384535\pi$
$109$	7.40928	0.709681	0.354840	+	0.934927i	$0.384535\pi$
$110$	−3.20355	−0.305446
$111$	0.712274	0.0676061
$112$	3.35263	0.316794
$113$	−5.48572	−0.516053	−0.258026	−	0.966138i	$-0.583072\pi$
$113$	−5.48572	−0.516053	−0.258026	+	0.966138i	$0.583072\pi$
$114$	0.283360	0.0265390
$115$	5.26793	0.491237
$116$	2.72246	0.252774
$117$	1.35695	0.125450
$118$	5.49473	0.505831
$119$	3.19819	0.293177
$120$	0.182344	0.0166456
$121$	−8.01208	−0.728370
$122$	8.52910	0.772188
$123$	−0.336633	−0.0303532
$124$	−6.43524	−0.577902
$125$	12.1674	1.08829
$126$	10.0254	0.893138
$127$	−3.61557	−0.320830	−0.160415	−	0.987050i	$-0.551283\pi$
$127$	−3.61557	−0.320830	−0.160415	+	0.987050i	$0.551283\pi$
$128$	−1.00000	−0.0883883
$129$	0.295501	0.0260174
$130$	−0.840996	−0.0737602
$131$	3.62395	0.316626	0.158313	−	0.987389i	$-0.449395\pi$
$131$	3.62395	0.316626	0.158313	+	0.987389i	$0.449395\pi$
$132$	−0.170070	−0.0148027
$133$	−9.65562	−0.837249
$134$	−3.09637	−0.267485
$135$	1.09230	0.0940099
$136$	−0.953933	−0.0817991
$137$	−9.56417	−0.817122	−0.408561	−	0.912731i	$-0.633969\pi$
$137$	−9.56417	−0.817122	−0.408561	+	0.912731i	$0.633969\pi$
$138$	0.279664	0.0238066
$139$	14.2810	1.21130	0.605650	−	0.795731i	$-0.292913\pi$
$139$	14.2810	1.21130	0.605650	+	0.795731i	$0.292913\pi$
$140$	−6.21345	−0.525132
$141$	−1.02011	−0.0859091
$142$	7.28415	0.611272
$143$	0.784390	0.0655940
$144$	−2.99032	−0.249193
$145$	−5.04555	−0.419010
$146$	−6.74025	−0.557827
$147$	0.417182	0.0344086
$148$	7.23942	0.595076
$149$	3.52730	0.288967	0.144484	−	0.989507i	$-0.453848\pi$
$149$	3.52730	0.288967	0.144484	+	0.989507i	$0.453848\pi$
$150$	0.154004	0.0125744
$151$	2.41835	0.196803	0.0984015	−	0.995147i	$-0.468627\pi$
$151$	2.41835	0.196803	0.0984015	+	0.995147i	$0.468627\pi$
$152$	2.88001	0.233600
$153$	−2.85256	−0.230616
$154$	5.79523	0.466993
$155$	11.9265	0.957956
$156$	−0.0446469	−0.00357461
$157$	−6.14868	−0.490718	−0.245359	−	0.969432i	$-0.578906\pi$
$157$	−6.14868	−0.490718	−0.245359	+	0.969432i	$0.578906\pi$
$158$	3.76326	0.299389
$159$	−1.22484	−0.0971360
$160$	1.85330	0.146517
$161$	−9.52970	−0.751045
$162$	−8.91297	−0.700269
$163$	−15.8786	−1.24371	−0.621856	−	0.783132i	$-0.713621\pi$
$163$	−15.8786	−1.24371	−0.621856	+	0.783132i	$0.713621\pi$
$164$	−3.42148	−0.267172
$165$	0.315192	0.0245377
$166$	−1.57672	−0.122377
$167$	14.7350	1.14023	0.570114	−	0.821566i	$-0.306899\pi$
$167$	14.7350	1.14023	0.570114	+	0.821566i	$0.306899\pi$
$168$	−0.329860	−0.0254493
$169$	−12.7941	−0.984160
$170$	1.76793	0.135594
$171$	8.61215	0.658588
$172$	3.00341	0.229008
$173$	14.3166	1.08847	0.544237	−	0.838932i	$-0.316819\pi$
$173$	14.3166	1.08847	0.544237	+	0.838932i	$0.316819\pi$
$174$	−0.267859	−0.0203063
$175$	−5.24776	−0.396693
$176$	−1.72856	−0.130295
$177$	−0.540618	−0.0406353
$178$	4.88785	0.366360
$179$	18.7933	1.40468	0.702339	−	0.711843i	$-0.252139\pi$
$179$	18.7933	1.40468	0.702339	+	0.711843i	$0.252139\pi$
$180$	5.54197	0.413074
$181$	17.4204	1.29485	0.647425	−	0.762130i	$-0.275846\pi$
$181$	17.4204	1.29485	0.647425	+	0.762130i	$0.275846\pi$
$182$	1.52137	0.112771
$183$	−0.839164	−0.0620328
$184$	2.84245	0.209548
$185$	−13.4168	−0.986426
$186$	0.633153	0.0464250
$187$	−1.64893	−0.120582
$188$	−10.3682	−0.756182
$189$	−1.97597	−0.143731
$190$	−5.33753	−0.387225
$191$	−1.15466	−0.0835481	−0.0417741	−	0.999127i	$-0.513301\pi$
$191$	−1.15466	−0.0835481	−0.0417741	+	0.999127i	$0.513301\pi$
$192$	0.0983884	0.00710057
$193$	−2.67281	−0.192393	−0.0961967	−	0.995362i	$-0.530668\pi$
$193$	−2.67281	−0.192393	−0.0961967	+	0.995362i	$0.530668\pi$
$194$	2.75923	0.198102
$195$	0.0827442	0.00592544
$196$	4.24016	0.302868
$197$	26.1733	1.86477	0.932385	−	0.361468i	$-0.117724\pi$
$197$	26.1733	1.86477	0.932385	+	0.361468i	$0.117724\pi$
$198$	−5.16895	−0.367341
$199$	17.0739	1.21034	0.605168	−	0.796098i	$-0.293106\pi$
$199$	17.0739	1.21034	0.605168	+	0.796098i	$0.293106\pi$
$200$	1.56526	0.110681
$201$	0.304647	0.0214881
$202$	16.8051	1.18240
$203$	9.12742	0.640619
$204$	0.0938559	0.00657123
$205$	6.34103	0.442877
$206$	4.78556	0.333426
$207$	8.49984	0.590779
$208$	−0.453782	−0.0314641
$209$	4.97827	0.344354
$210$	0.611331	0.0421859
$211$	14.8969	1.02554	0.512772	−	0.858525i	$-0.328618\pi$
$211$	14.8969	1.02554	0.512772	+	0.858525i	$0.328618\pi$
$212$	−12.4490	−0.855002
$213$	−0.716675	−0.0491058
$214$	−8.76565	−0.599208
$215$	−5.56624	−0.379614
$216$	0.589378	0.0401021
$217$	−21.5750	−1.46461
$218$	−7.40928	−0.501820
$219$	0.663162	0.0448123
$220$	3.20355	0.215983
$221$	−0.432878	−0.0291185
$222$	−0.712274	−0.0478047
$223$	0.998630	0.0668732	0.0334366	−	0.999441i	$-0.489355\pi$
$223$	0.998630	0.0668732	0.0334366	+	0.999441i	$0.489355\pi$
$224$	−3.35263	−0.224007
$225$	4.68064	0.312043
$226$	5.48572	0.364905
$227$	−8.31483	−0.551875	−0.275937	−	0.961176i	$-0.588988\pi$
$227$	−8.31483	−0.551875	−0.275937	+	0.961176i	$0.588988\pi$
$228$	−0.283360	−0.0187659
$229$	−1.90425	−0.125836	−0.0629181	−	0.998019i	$-0.520041\pi$
$229$	−1.90425	−0.125836	−0.0629181	+	0.998019i	$0.520041\pi$
$230$	−5.26793	−0.347357
$231$	−0.570184	−0.0375153
$232$	−2.72246	−0.178738
$233$	7.18901	0.470968	0.235484	−	0.971878i	$-0.424333\pi$
$233$	7.18901	0.470968	0.235484	+	0.971878i	$0.424333\pi$
$234$	−1.35695	−0.0887068
$235$	19.2155	1.25348
$236$	−5.49473	−0.357677
$237$	−0.370261	−0.0240510
$238$	−3.19819	−0.207308
$239$	18.5543	1.20018	0.600088	−	0.799934i	$-0.295132\pi$
$239$	18.5543	1.20018	0.600088	+	0.799934i	$0.295132\pi$
$240$	−0.182344	−0.0117702
$241$	14.8793	0.958457	0.479229	−	0.877690i	$-0.340916\pi$
$241$	14.8793	0.958457	0.479229	+	0.877690i	$0.340916\pi$
$242$	8.01208	0.515036
$243$	2.64507	0.169681
$244$	−8.52910	−0.546020
$245$	−7.85830	−0.502048
$246$	0.336633	0.0214630
$247$	1.30690	0.0831559
$248$	6.43524	0.408638
$249$	0.155131	0.00983101
$250$	−12.1674	−0.769536
$251$	14.4179	0.910048	0.455024	−	0.890479i	$-0.349631\pi$
$251$	14.4179	0.910048	0.455024	+	0.890479i	$0.349631\pi$
$252$	−10.0254	−0.631544
$253$	4.91335	0.308900
$254$	3.61557	0.226861
$255$	−0.173944	−0.0108928
$256$	1.00000	0.0625000
$257$	−28.2203	−1.76034	−0.880168	−	0.474662i	$-0.842570\pi$
$257$	−28.2203	−1.76034	−0.880168	+	0.474662i	$0.842570\pi$
$258$	−0.295501	−0.0183971
$259$	24.2711	1.50813
$260$	0.840996	0.0521564
$261$	−8.14103	−0.503917
$262$	−3.62395	−0.223888
$263$	13.1182	0.808903	0.404452	−	0.914559i	$-0.367462\pi$
$263$	13.1182	0.808903	0.404452	+	0.914559i	$0.367462\pi$
$264$	0.170070	0.0104671
$265$	23.0718	1.41729
$266$	9.65562	0.592024
$267$	−0.480908	−0.0294311
$268$	3.09637	0.189141
$269$	3.36226	0.205000	0.102500	−	0.994733i	$-0.467316\pi$
$269$	3.36226	0.205000	0.102500	+	0.994733i	$0.467316\pi$
$270$	−1.09230	−0.0664750
$271$	24.0369	1.46014	0.730070	−	0.683372i	$-0.239487\pi$
$271$	24.0369	1.46014	0.730070	+	0.683372i	$0.239487\pi$
$272$	0.953933	0.0578407
$273$	−0.149685	−0.00905933
$274$	9.56417	0.577793
$275$	2.70566	0.163157
$276$	−0.279664	−0.0168338
$277$	−7.12919	−0.428352	−0.214176	−	0.976795i	$-0.568707\pi$
$277$	−7.12919	−0.428352	−0.214176	+	0.976795i	$0.568707\pi$
$278$	−14.2810	−0.856519
$279$	19.2434	1.15207
$280$	6.21345	0.371325
$281$	−8.22449	−0.490632	−0.245316	−	0.969443i	$-0.578892\pi$
$281$	−8.22449	−0.490632	−0.245316	+	0.969443i	$0.578892\pi$
$282$	1.02011	0.0607469
$283$	8.89832	0.528950	0.264475	−	0.964393i	$-0.414801\pi$
$283$	8.89832	0.528950	0.264475	+	0.964393i	$0.414801\pi$
$284$	−7.28415	−0.432235
$285$	0.525151	0.0311073
$286$	−0.784390	−0.0463820
$287$	−11.4710	−0.677109
$288$	2.99032	0.176206
$289$	−16.0900	−0.946471
$290$	5.04555	0.296285
$291$	−0.271477	−0.0159142
$292$	6.74025	0.394443
$293$	−3.04378	−0.177820	−0.0889099	−	0.996040i	$-0.528338\pi$
$293$	−3.04378	−0.177820	−0.0889099	+	0.996040i	$0.528338\pi$
$294$	−0.417182	−0.0243306
$295$	10.1834	0.592901
$296$	−7.23942	−0.420783
$297$	1.01878	0.0591154
$298$	−3.52730	−0.204331
$299$	1.28985	0.0745941
$300$	−0.154004	−0.00889141
$301$	10.0693	0.580388
$302$	−2.41835	−0.139161
$303$	−1.65342	−0.0949867
$304$	−2.88001	−0.165180
$305$	15.8070	0.905107
$306$	2.85256	0.163070
$307$	−14.7210	−0.840170	−0.420085	−	0.907485i	$-0.638000\pi$
$307$	−14.7210	−0.840170	−0.420085	+	0.907485i	$0.638000\pi$
$308$	−5.79523	−0.330214
$309$	−0.470844	−0.0267854
$310$	−11.9265	−0.677377
$311$	−3.72117	−0.211008	−0.105504	−	0.994419i	$-0.533646\pi$
$311$	−3.72117	−0.211008	−0.105504	+	0.994419i	$0.533646\pi$
$312$	0.0446469	0.00252763
$313$	−19.7704	−1.11749	−0.558746	−	0.829339i	$-0.688717\pi$
$313$	−19.7704	−1.11749	−0.558746	+	0.829339i	$0.688717\pi$
$314$	6.14868	0.346990
$315$	18.5802	1.04688
$316$	−3.76326	−0.211700
$317$	1.26563	0.0710850	0.0355425	−	0.999368i	$-0.488684\pi$
$317$	1.26563	0.0710850	0.0355425	+	0.999368i	$0.488684\pi$
$318$	1.22484	0.0686855
$319$	−4.70594	−0.263482
$320$	−1.85330	−0.103603
$321$	0.862438	0.0481366
$322$	9.52970	0.531069
$323$	−2.74734	−0.152866
$324$	8.91297	0.495165
$325$	0.710289	0.0393997
$326$	15.8786	0.879437
$327$	0.728987	0.0403131
$328$	3.42148	0.188919
$329$	−34.7609	−1.91643
$330$	−0.315192	−0.0173508
$331$	−23.4879	−1.29101	−0.645505	−	0.763756i	$-0.723353\pi$
$331$	−23.4879	−1.29101	−0.645505	+	0.763756i	$0.723353\pi$
$332$	1.57672	0.0865336
$333$	−21.6482	−1.18631
$334$	−14.7350	−0.806263
$335$	−5.73851	−0.313528
$336$	0.329860	0.0179953
$337$	−19.3475	−1.05392	−0.526962	−	0.849889i	$-0.676669\pi$
$337$	−19.3475	−1.05392	−0.526962	+	0.849889i	$0.676669\pi$
$338$	12.7941	0.695906
$339$	−0.539731	−0.0293142
$340$	−1.76793	−0.0958794
$341$	11.1237	0.602383
$342$	−8.61215	−0.465692
$343$	−9.25274	−0.499601
$344$	−3.00341	−0.161933
$345$	0.518303	0.0279045
$346$	−14.3166	−0.769667
$347$	−18.2428	−0.979327	−0.489663	−	0.871912i	$-0.662880\pi$
$347$	−18.2428	−0.979327	−0.489663	+	0.871912i	$0.662880\pi$
$348$	0.267859	0.0143587
$349$	13.0613	0.699156	0.349578	−	0.936907i	$-0.386325\pi$
$349$	13.0613	0.699156	0.349578	+	0.936907i	$0.386325\pi$
$350$	5.24776	0.280505
$351$	0.267449	0.0142754
$352$	1.72856	0.0921326
$353$	13.3400	0.710015	0.355008	−	0.934863i	$-0.384478\pi$
$353$	13.3400	0.710015	0.355008	+	0.934863i	$0.384478\pi$
$354$	0.540618	0.0287335
$355$	13.4997	0.716492
$356$	−4.88785	−0.259056
$357$	0.314665	0.0166538
$358$	−18.7933	−0.993257
$359$	−16.4888	−0.870246	−0.435123	−	0.900371i	$-0.643295\pi$
$359$	−16.4888	−0.870246	−0.435123	+	0.900371i	$0.643295\pi$
$360$	−5.54197	−0.292088
$361$	−10.7055	−0.563449
$362$	−17.4204	−0.915597
$363$	−0.788295	−0.0413748
$364$	−1.52137	−0.0797412
$365$	−12.4917	−0.653847
$366$	0.839164	0.0438638
$367$	−29.5918	−1.54468	−0.772340	−	0.635210i	$-0.780914\pi$
$367$	−29.5918	−1.54468	−0.772340	+	0.635210i	$0.780914\pi$
$368$	−2.84245	−0.148173
$369$	10.2313	0.532620
$370$	13.4168	0.697508
$371$	−41.7370	−2.16688
$372$	−0.633153	−0.0328275
$373$	−6.39951	−0.331354	−0.165677	−	0.986180i	$-0.552981\pi$
$373$	−6.39951	−0.331354	−0.165677	+	0.986180i	$0.552981\pi$
$374$	1.64893	0.0852642
$375$	1.19713	0.0618197
$376$	10.3682	0.534701
$377$	−1.23540	−0.0636265
$378$	1.97597	0.101633
$379$	3.16882	0.162771	0.0813856	−	0.996683i	$-0.474065\pi$
$379$	3.16882	0.162771	0.0813856	+	0.996683i	$0.474065\pi$
$380$	5.33753	0.273810
$381$	−0.355730	−0.0182246
$382$	1.15466	0.0590774
$383$	6.87426	0.351258	0.175629	−	0.984456i	$-0.443804\pi$
$383$	6.87426	0.351258	0.175629	+	0.984456i	$0.443804\pi$
$384$	−0.0983884	−0.00502086
$385$	10.7403	0.547378
$386$	2.67281	0.136043
$387$	−8.98117	−0.456538
$388$	−2.75923	−0.140079
$389$	−2.00256	−0.101534	−0.0507669	−	0.998711i	$-0.516167\pi$
$389$	−2.00256	−0.101534	−0.0507669	+	0.998711i	$0.516167\pi$
$390$	−0.0827442	−0.00418992
$391$	−2.71151	−0.137127
$392$	−4.24016	−0.214160
$393$	0.356554	0.0179858
$394$	−26.1733	−1.31859
$395$	6.97446	0.350923
$396$	5.16895	0.259750
$397$	−34.3295	−1.72295	−0.861475	−	0.507800i	$-0.830459\pi$
$397$	−34.3295	−1.72295	−0.861475	+	0.507800i	$0.830459\pi$
$398$	−17.0739	−0.855837
$399$	−0.950001	−0.0475595
$400$	−1.56526	−0.0782632
$401$	−23.5130	−1.17418	−0.587091	−	0.809521i	$-0.699727\pi$
$401$	−23.5130	−1.17418	−0.587091	+	0.809521i	$0.699727\pi$
$402$	−0.304647	−0.0151944
$403$	2.92020	0.145465
$404$	−16.8051	−0.836083
$405$	−16.5184	−0.820808
$406$	−9.12742	−0.452986
$407$	−12.5138	−0.620285
$408$	−0.0938559	−0.00464656
$409$	19.5976	0.969040	0.484520	−	0.874780i	$-0.338994\pi$
$409$	19.5976	0.969040	0.484520	+	0.874780i	$0.338994\pi$
$410$	−6.34103	−0.313161
$411$	−0.941003	−0.0464163
$412$	−4.78556	−0.235768
$413$	−18.4218	−0.906479
$414$	−8.49984	−0.417744
$415$	−2.92214	−0.143442
$416$	0.453782	0.0222485
$417$	1.40509	0.0688074
$418$	−4.97827	−0.243495
$419$	−22.4975	−1.09907	−0.549536	−	0.835470i	$-0.685196\pi$
$419$	−22.4975	−1.09907	−0.549536	+	0.835470i	$0.685196\pi$
$420$	−0.611331	−0.0298299
$421$	−10.3793	−0.505856	−0.252928	−	0.967485i	$-0.581394\pi$
$421$	−10.3793	−0.505856	−0.252928	+	0.967485i	$0.581394\pi$
$422$	−14.8969	−0.725170
$423$	31.0044	1.50748
$424$	12.4490	0.604578
$425$	−1.49316	−0.0724288
$426$	0.716675	0.0347230
$427$	−28.5949	−1.38381
$428$	8.76565	0.423704
$429$	0.0771749	0.00372604
$430$	5.56624	0.268428
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	−0.589378	−0.0283565
$433$	−6.65327	−0.319736	−0.159868	−	0.987138i	$-0.551107\pi$
$433$	−6.65327	−0.319736	−0.159868	+	0.987138i	$0.551107\pi$
$434$	21.5750	1.03563
$435$	−0.496423	−0.0238017
$436$	7.40928	0.354840
$437$	8.18629	0.391603
$438$	−0.663162	−0.0316871
$439$	18.3124	0.874001	0.437001	−	0.899461i	$-0.356041\pi$
$439$	18.3124	0.874001	0.437001	+	0.899461i	$0.356041\pi$
$440$	−3.20355	−0.152723
$441$	−12.6794	−0.603782
$442$	0.432878	0.0205899
$443$	30.1293	1.43148	0.715742	−	0.698365i	$-0.246089\pi$
$443$	30.1293	1.43148	0.715742	+	0.698365i	$0.246089\pi$
$444$	0.712274	0.0338031
$445$	9.05867	0.429422
$446$	−0.998630	−0.0472865
$447$	0.347045	0.0164147
$448$	3.35263	0.158397
$449$	30.0145	1.41647	0.708236	−	0.705975i	$-0.249491\pi$
$449$	30.0145	1.41647	0.708236	+	0.705975i	$0.249491\pi$
$450$	−4.68064	−0.220648
$451$	5.91423	0.278490
$452$	−5.48572	−0.258026
$453$	0.237938	0.0111793
$454$	8.31483	0.390234
$455$	2.81955	0.132183
$456$	0.283360	0.0132695
$457$	12.7375	0.595834	0.297917	−	0.954592i	$-0.403708\pi$
$457$	12.7375	0.595834	0.297917	+	0.954592i	$0.403708\pi$
$458$	1.90425	0.0889796
$459$	−0.562227	−0.0262425
$460$	5.26793	0.245618
$461$	16.6200	0.774072	0.387036	−	0.922065i	$-0.373499\pi$
$461$	16.6200	0.774072	0.387036	+	0.922065i	$0.373499\pi$
$462$	0.570184	0.0265273
$463$	−24.4727	−1.13734	−0.568672	−	0.822565i	$-0.692542\pi$
$463$	−24.4727	−1.13734	−0.568672	+	0.822565i	$0.692542\pi$
$464$	2.72246	0.126387
$465$	1.17342	0.0544163
$466$	−7.18901	−0.333024
$467$	5.57689	0.258068	0.129034	−	0.991640i	$-0.458812\pi$
$467$	5.57689	0.258068	0.129034	+	0.991640i	$0.458812\pi$
$468$	1.35695	0.0627252
$469$	10.3810	0.479350
$470$	−19.2155	−0.886345
$471$	−0.604959	−0.0278750
$472$	5.49473	0.252916
$473$	−5.19159	−0.238709
$474$	0.370261	0.0170066
$475$	4.50798	0.206840
$476$	3.19819	0.146589
$477$	37.2265	1.70449
$478$	−18.5543	−0.848653
$479$	−4.30728	−0.196805	−0.0984023	−	0.995147i	$-0.531373\pi$
$479$	−4.30728	−0.196805	−0.0984023	+	0.995147i	$0.531373\pi$
$480$	0.182344	0.00832281
$481$	−3.28512	−0.149788
$482$	−14.8793	−0.677732
$483$	−0.937611	−0.0426628
$484$	−8.01208	−0.364185
$485$	5.11370	0.232201
$486$	−2.64507	−0.119983
$487$	26.9995	1.22347	0.611733	−	0.791064i	$-0.290473\pi$
$487$	26.9995	1.22347	0.611733	+	0.791064i	$0.290473\pi$
$488$	8.52910	0.386094
$489$	−1.56227	−0.0706485
$490$	7.85830	0.355002
$491$	7.17504	0.323805	0.161903	−	0.986807i	$-0.448237\pi$
$491$	7.17504	0.323805	0.161903	+	0.986807i	$0.448237\pi$
$492$	−0.336633	−0.0151766
$493$	2.59705	0.116965
$494$	−1.30690	−0.0588001
$495$	−9.57964	−0.430573
$496$	−6.43524	−0.288951
$497$	−24.4211	−1.09543
$498$	−0.155131	−0.00695157
$499$	25.3594	1.13524	0.567620	−	0.823290i	$-0.307864\pi$
$499$	25.3594	1.13524	0.567620	+	0.823290i	$0.307864\pi$
$500$	12.1674	0.544144
$501$	1.44975	0.0647701
$502$	−14.4179	−0.643501
$503$	−3.45864	−0.154213	−0.0771066	−	0.997023i	$-0.524568\pi$
$503$	−3.45864	−0.154213	−0.0771066	+	0.997023i	$0.524568\pi$
$504$	10.0254	0.446569
$505$	31.1449	1.38593
$506$	−4.91335	−0.218425
$507$	−1.25879	−0.0559048
$508$	−3.61557	−0.160415
$509$	−11.8413	−0.524857	−0.262429	−	0.964951i	$-0.584523\pi$
$509$	−11.8413	−0.524857	−0.262429	+	0.964951i	$0.584523\pi$
$510$	0.173944	0.00770235
$511$	22.5976	0.999659
$512$	−1.00000	−0.0441942
$513$	1.69741	0.0749427
$514$	28.2203	1.24475
$515$	8.86910	0.390819
$516$	0.295501	0.0130087
$517$	17.9221	0.788215
$518$	−24.2711	−1.06641
$519$	1.40859	0.0618303
$520$	−0.840996	−0.0368801
$521$	−7.81262	−0.342277	−0.171139	−	0.985247i	$-0.554745\pi$
$521$	−7.81262	−0.342277	−0.171139	+	0.985247i	$0.554745\pi$
$522$	8.14103	0.356323
$523$	−18.6990	−0.817650	−0.408825	−	0.912613i	$-0.634061\pi$
$523$	−18.6990	−0.817650	−0.408825	+	0.912613i	$0.634061\pi$
$524$	3.62395	0.158313
$525$	−0.516318	−0.0225340
$526$	−13.1182	−0.571981
$527$	−6.13879	−0.267410
$528$	−0.170070	−0.00740136
$529$	−14.9205	−0.648716
$530$	−23.0718	−1.00218
$531$	16.4310	0.713045
$532$	−9.65562	−0.418624
$533$	1.55260	0.0672508
$534$	0.480908	0.0208109
$535$	−16.2454	−0.702351
$536$	−3.09637	−0.133743
$537$	1.84904	0.0797921
$538$	−3.36226	−0.144957
$539$	−7.32937	−0.315698
$540$	1.09230	0.0470049
$541$	11.8021	0.507413	0.253707	−	0.967281i	$-0.418350\pi$
$541$	11.8021	0.507413	0.253707	+	0.967281i	$0.418350\pi$
$542$	−24.0369	−1.03248
$543$	1.71397	0.0735533
$544$	−0.953933	−0.0408995
$545$	−13.7317	−0.588199
$546$	0.149685	0.00640591
$547$	−13.5327	−0.578618	−0.289309	−	0.957236i	$-0.593425\pi$
$547$	−13.5327	−0.578618	−0.289309	+	0.957236i	$0.593425\pi$
$548$	−9.56417	−0.408561
$549$	25.5047	1.08852
$550$	−2.70566	−0.115370
$551$	−7.84072	−0.334026
$552$	0.279664	0.0119033
$553$	−12.6168	−0.536522
$554$	7.12919	0.302890
$555$	−1.32006	−0.0560335
$556$	14.2810	0.605650
$557$	22.1124	0.936933	0.468467	−	0.883481i	$-0.344807\pi$
$557$	22.1124	0.936933	0.468467	+	0.883481i	$0.344807\pi$
$558$	−19.2434	−0.814639
$559$	−1.36290	−0.0576443
$560$	−6.21345	−0.262566
$561$	−0.162236	−0.00684960
$562$	8.22449	0.346929
$563$	−23.1622	−0.976172	−0.488086	−	0.872795i	$-0.662305\pi$
$563$	−23.1622	−0.976172	−0.488086	+	0.872795i	$0.662305\pi$
$564$	−1.02011	−0.0429546
$565$	10.1667	0.427716
$566$	−8.89832	−0.374024
$567$	29.8819	1.25492
$568$	7.28415	0.305636
$569$	4.53872	0.190273	0.0951366	−	0.995464i	$-0.469671\pi$
$569$	4.53872	0.190273	0.0951366	+	0.995464i	$0.469671\pi$
$570$	−0.525151	−0.0219962
$571$	−3.28990	−0.137678	−0.0688390	−	0.997628i	$-0.521929\pi$
$571$	−3.28990	−0.137678	−0.0688390	+	0.997628i	$0.521929\pi$
$572$	0.784390	0.0327970
$573$	−0.113605	−0.00474591
$574$	11.4710	0.478788
$575$	4.44919	0.185544
$576$	−2.99032	−0.124597
$577$	−23.7966	−0.990667	−0.495334	−	0.868703i	$-0.664954\pi$
$577$	−23.7966	−0.990667	−0.495334	+	0.868703i	$0.664954\pi$
$578$	16.0900	0.669256
$579$	−0.262974	−0.0109288
$580$	−5.04555	−0.209505
$581$	5.28616	0.219307
$582$	0.271477	0.0112531
$583$	21.5189	0.891221
$584$	−6.74025	−0.278914
$585$	−2.51485	−0.103976
$586$	3.04378	0.125738
$587$	−36.9800	−1.52633	−0.763165	−	0.646204i	$-0.776356\pi$
$587$	−36.9800	−1.52633	−0.763165	+	0.646204i	$0.776356\pi$
$588$	0.417182	0.0172043
$589$	18.5336	0.763662
$590$	−10.1834	−0.419244
$591$	2.57515	0.105927
$592$	7.23942	0.297538
$593$	−23.2675	−0.955480	−0.477740	−	0.878501i	$-0.658544\pi$
$593$	−23.2675	−0.955480	−0.477740	+	0.878501i	$0.658544\pi$
$594$	−1.01878	−0.0418009
$595$	−5.92722	−0.242992
$596$	3.52730	0.144484
$597$	1.67987	0.0687526
$598$	−1.28985	−0.0527460
$599$	45.5755	1.86216	0.931082	−	0.364811i	$-0.118866\pi$
$599$	45.5755	1.86216	0.931082	+	0.364811i	$0.118866\pi$
$600$	0.154004	0.00628718
$601$	2.87379	0.117224	0.0586122	−	0.998281i	$-0.481332\pi$
$601$	2.87379	0.117224	0.0586122	+	0.998281i	$0.481332\pi$
$602$	−10.0693	−0.410396
$603$	−9.25913	−0.377061
$604$	2.41835	0.0984015
$605$	14.8488	0.603690
$606$	1.65342	0.0671657
$607$	−13.9216	−0.565059	−0.282530	−	0.959259i	$-0.591174\pi$
$607$	−13.9216	−0.565059	−0.282530	+	0.959259i	$0.591174\pi$
$608$	2.88001	0.116800
$609$	0.898032	0.0363901
$610$	−15.8070	−0.640007
$611$	4.70492	0.190341
$612$	−2.85256	−0.115308
$613$	−15.2140	−0.614487	−0.307244	−	0.951631i	$-0.599407\pi$
$613$	−15.2140	−0.614487	−0.307244	+	0.951631i	$0.599407\pi$
$614$	14.7210	0.594090
$615$	0.623884	0.0251574
$616$	5.79523	0.233497
$617$	−17.6625	−0.711064	−0.355532	−	0.934664i	$-0.615700\pi$
$617$	−17.6625	−0.711064	−0.355532	+	0.934664i	$0.615700\pi$
$618$	0.470844	0.0189401
$619$	−7.49036	−0.301063	−0.150532	−	0.988605i	$-0.548099\pi$
$619$	−7.49036	−0.301063	−0.150532	+	0.988605i	$0.548099\pi$
$620$	11.9265	0.478978
$621$	1.67528	0.0672266
$622$	3.72117	0.149205
$623$	−16.3872	−0.656538
$624$	−0.0446469	−0.00178731
$625$	−14.7236	−0.588945
$626$	19.7704	0.790186
$627$	0.489804	0.0195609
$628$	−6.14868	−0.245359
$629$	6.90592	0.275357
$630$	−18.5802	−0.740253
$631$	−23.7876	−0.946970	−0.473485	−	0.880802i	$-0.657004\pi$
$631$	−23.7876	−0.946970	−0.473485	+	0.880802i	$0.657004\pi$
$632$	3.76326	0.149694
$633$	1.46568	0.0582556
$634$	−1.26563	−0.0502647
$635$	6.70076	0.265911
$636$	−1.22484	−0.0485680
$637$	−1.92411	−0.0762359
$638$	4.70594	0.186310
$639$	21.7819	0.861680
$640$	1.85330	0.0732583
$641$	15.4918	0.611889	0.305945	−	0.952049i	$-0.401028\pi$
$641$	15.4918	0.611889	0.305945	+	0.952049i	$0.401028\pi$
$642$	−0.862438	−0.0340377
$643$	19.9453	0.786566	0.393283	−	0.919418i	$-0.371339\pi$
$643$	19.9453	0.786566	0.393283	+	0.919418i	$0.371339\pi$
$644$	−9.52970	−0.375523
$645$	−0.547653	−0.0215638
$646$	2.74734	0.108093
$647$	−14.9930	−0.589435	−0.294717	−	0.955584i	$-0.595225\pi$
$647$	−14.9930	−0.589435	−0.294717	+	0.955584i	$0.595225\pi$
$648$	−8.91297	−0.350135
$649$	9.49798	0.372828
$650$	−0.710289	−0.0278598
$651$	−2.12273	−0.0831964
$652$	−15.8786	−0.621856
$653$	10.0109	0.391757	0.195879	−	0.980628i	$-0.437244\pi$
$653$	10.0109	0.391757	0.195879	+	0.980628i	$0.437244\pi$
$654$	−0.728987	−0.0285057
$655$	−6.71628	−0.262427
$656$	−3.42148	−0.133586
$657$	−20.1555	−0.786341
$658$	34.7609	1.35512
$659$	18.9046	0.736419	0.368210	−	0.929743i	$-0.379971\pi$
$659$	18.9046	0.736419	0.368210	+	0.929743i	$0.379971\pi$
$660$	0.315192	0.0122688
$661$	−49.7430	−1.93478	−0.967390	−	0.253293i	$-0.918486\pi$
$661$	−49.7430	−1.93478	−0.967390	+	0.253293i	$0.918486\pi$
$662$	23.4879	0.912881
$663$	−0.0425901	−0.00165406
$664$	−1.57672	−0.0611885
$665$	17.8948	0.693931
$666$	21.6482	0.838850
$667$	−7.73846	−0.299634
$668$	14.7350	0.570114
$669$	0.0982536	0.00379870
$670$	5.73851	0.221698
$671$	14.7431	0.569150
$672$	−0.329860	−0.0127246
$673$	−32.6130	−1.25714	−0.628569	−	0.777754i	$-0.716359\pi$
$673$	−32.6130	−1.25714	−0.628569	+	0.777754i	$0.716359\pi$
$674$	19.3475	0.745237
$675$	0.922532	0.0355083
$676$	−12.7941	−0.492080
$677$	−14.2492	−0.547642	−0.273821	−	0.961781i	$-0.588288\pi$
$677$	−14.2492	−0.547642	−0.273821	+	0.961781i	$0.588288\pi$
$678$	0.539731	0.0207282
$679$	−9.25071	−0.355009
$680$	1.76793	0.0677969
$681$	−0.818083	−0.0313490
$682$	−11.1237	−0.425949
$683$	−3.85572	−0.147535	−0.0737675	−	0.997275i	$-0.523502\pi$
$683$	−3.85572	−0.147535	−0.0737675	+	0.997275i	$0.523502\pi$
$684$	8.61215	0.329294
$685$	17.7253	0.677250
$686$	9.25274	0.353271
$687$	−0.187356	−0.00714807
$688$	3.00341	0.114504
$689$	5.64914	0.215215
$690$	−0.518303	−0.0197314
$691$	−10.2860	−0.391297	−0.195649	−	0.980674i	$-0.562681\pi$
$691$	−10.2860	−0.391297	−0.195649	+	0.980674i	$0.562681\pi$
$692$	14.3166	0.544237
$693$	17.3296	0.658297
$694$	18.2428	0.692489
$695$	−26.4671	−1.00395
$696$	−0.267859	−0.0101532
$697$	−3.26386	−0.123627
$698$	−13.0613	−0.494378
$699$	0.707315	0.0267531
$700$	−5.24776	−0.198347
$701$	−18.5294	−0.699846	−0.349923	−	0.936778i	$-0.613792\pi$
$701$	−18.5294	−0.699846	−0.349923	+	0.936778i	$0.613792\pi$
$702$	−0.267449	−0.0100942
$703$	−20.8496	−0.786358
$704$	−1.72856	−0.0651476
$705$	1.89058	0.0712034
$706$	−13.3400	−0.502056
$707$	−56.3413	−2.11893
$708$	−0.540618	−0.0203177
$709$	44.4251	1.66842	0.834211	−	0.551446i	$-0.185924\pi$
$709$	44.4251	1.66842	0.834211	+	0.551446i	$0.185924\pi$
$710$	−13.4997	−0.506636
$711$	11.2533	0.422033
$712$	4.88785	0.183180
$713$	18.2919	0.685036
$714$	−0.314665	−0.0117760
$715$	−1.45371	−0.0543658
$716$	18.7933	0.702339
$717$	1.82552	0.0681754
$718$	16.4888	0.615357
$719$	14.1491	0.527671	0.263835	−	0.964568i	$-0.415012\pi$
$719$	14.1491	0.527671	0.263835	+	0.964568i	$0.415012\pi$
$720$	5.54197	0.206537
$721$	−16.0442	−0.597519
$722$	10.7055	0.398419
$723$	1.46395	0.0544447
$724$	17.4204	0.647425
$725$	−4.26137	−0.158263
$726$	0.788295	0.0292564
$727$	33.1499	1.22946	0.614731	−	0.788737i	$-0.289265\pi$
$727$	33.1499	1.22946	0.614731	+	0.788737i	$0.289265\pi$
$728$	1.52137	0.0563856
$729$	−26.4787	−0.980691
$730$	12.4917	0.462340
$731$	2.86506	0.105968
$732$	−0.839164	−0.0310164
$733$	18.2369	0.673594	0.336797	−	0.941577i	$-0.390656\pi$
$733$	18.2369	0.673594	0.336797	+	0.941577i	$0.390656\pi$
$734$	29.5918	1.09225
$735$	−0.773165	−0.0285186
$736$	2.84245	0.104774
$737$	−5.35226	−0.197153
$738$	−10.2313	−0.376620
$739$	40.2718	1.48142	0.740712	−	0.671823i	$-0.234488\pi$
$739$	40.2718	1.48142	0.740712	+	0.671823i	$0.234488\pi$
$740$	−13.4168	−0.493213
$741$	0.128583	0.00472363
$742$	41.7370	1.53221
$743$	43.4499	1.59402	0.797012	−	0.603963i	$-0.206413\pi$
$743$	43.4499	1.59402	0.797012	+	0.603963i	$0.206413\pi$
$744$	0.633153	0.0232125
$745$	−6.53715	−0.239503
$746$	6.39951	0.234303
$747$	−4.71489	−0.172509
$748$	−1.64893	−0.0602909
$749$	29.3880	1.07382
$750$	−1.19713	−0.0437131
$751$	−6.25477	−0.228240	−0.114120	−	0.993467i	$-0.536405\pi$
$751$	−6.25477	−0.228240	−0.114120	+	0.993467i	$0.536405\pi$
$752$	−10.3682	−0.378091
$753$	1.41855	0.0516949
$754$	1.23540	0.0449908
$755$	−4.48195	−0.163115
$756$	−1.97597	−0.0718653
$757$	20.0001	0.726918	0.363459	−	0.931610i	$-0.381596\pi$
$757$	20.0001	0.726918	0.363459	+	0.931610i	$0.381596\pi$
$758$	−3.16882	−0.115097
$759$	0.483417	0.0175469
$760$	−5.33753	−0.193613
$761$	−43.9438	−1.59296	−0.796482	−	0.604663i	$-0.793308\pi$
$761$	−43.9438	−1.59296	−0.796482	+	0.604663i	$0.793308\pi$
$762$	0.355730	0.0128868
$763$	24.8406	0.899291
$764$	−1.15466	−0.0417741
$765$	5.28667	0.191140
$766$	−6.87426	−0.248377
$767$	2.49341	0.0900318
$768$	0.0983884	0.00355028
$769$	6.79043	0.244869	0.122435	−	0.992477i	$-0.460930\pi$
$769$	6.79043	0.244869	0.122435	+	0.992477i	$0.460930\pi$
$770$	−10.7403	−0.387055
$771$	−2.77655	−0.0999951
$772$	−2.67281	−0.0961967
$773$	−8.42743	−0.303113	−0.151557	−	0.988449i	$-0.548429\pi$
$773$	−8.42743	−0.303113	−0.151557	+	0.988449i	$0.548429\pi$
$774$	8.98117	0.322821
$775$	10.0729	0.361828
$776$	2.75923	0.0990508
$777$	2.38800	0.0856689
$778$	2.00256	0.0717952
$779$	9.85388	0.353052
$780$	0.0827442	0.00296272
$781$	12.5911	0.450545
$782$	2.71151	0.0969633
$783$	−1.60456	−0.0573422
$784$	4.24016	0.151434
$785$	11.3954	0.406718
$786$	−0.356554	−0.0127179
$787$	−30.0787	−1.07219	−0.536095	−	0.844158i	$-0.680101\pi$
$787$	−30.0787	−1.07219	−0.536095	+	0.844158i	$0.680101\pi$
$788$	26.1733	0.932385
$789$	1.29068	0.0459494
$790$	−6.97446	−0.248140
$791$	−18.3916	−0.653930
$792$	−5.16895	−0.183671
$793$	3.87035	0.137440
$794$	34.3295	1.21831
$795$	2.27000	0.0805085
$796$	17.0739	0.605168
$797$	26.9636	0.955100	0.477550	−	0.878605i	$-0.341525\pi$
$797$	26.9636	0.955100	0.477550	+	0.878605i	$0.341525\pi$
$798$	0.950001	0.0336297
$799$	−9.89061	−0.349905
$800$	1.56526	0.0553405
$801$	14.6162	0.516439
$802$	23.5130	0.830273
$803$	−11.6509	−0.411153
$804$	0.304647	0.0107441
$805$	17.6614	0.622484
$806$	−2.92020	−0.102860
$807$	0.330807	0.0116450
$808$	16.8051	0.591200
$809$	17.2324	0.605859	0.302929	−	0.953013i	$-0.402035\pi$
$809$	17.2324	0.605859	0.302929	+	0.953013i	$0.402035\pi$
$810$	16.5184	0.580399
$811$	41.1069	1.44346	0.721729	−	0.692176i	$-0.243348\pi$
$811$	41.1069	1.44346	0.721729	+	0.692176i	$0.243348\pi$
$812$	9.12742	0.320310
$813$	2.36496	0.0829426
$814$	12.5138	0.438608
$815$	29.4280	1.03082
$816$	0.0938559	0.00328561
$817$	−8.64986	−0.302620
$818$	−19.5976	−0.685215
$819$	4.54937	0.158968
$820$	6.34103	0.221439
$821$	−20.3684	−0.710862	−0.355431	−	0.934702i	$-0.615666\pi$
$821$	−20.3684	−0.710862	−0.355431	+	0.934702i	$0.615666\pi$
$822$	0.941003	0.0328213
$823$	18.4780	0.644102	0.322051	−	0.946722i	$-0.395628\pi$
$823$	18.4780	0.644102	0.322051	+	0.946722i	$0.395628\pi$
$824$	4.78556	0.166713
$825$	0.266205	0.00926807
$826$	18.4218	0.640977
$827$	−13.2403	−0.460410	−0.230205	−	0.973142i	$-0.573940\pi$
$827$	−13.2403	−0.460410	−0.230205	+	0.973142i	$0.573940\pi$
$828$	8.49984	0.295390
$829$	−50.3415	−1.74843	−0.874217	−	0.485536i	$-0.838624\pi$
$829$	−50.3415	−1.74843	−0.874217	+	0.485536i	$0.838624\pi$
$830$	2.92214	0.101429
$831$	−0.701429	−0.0243323
$832$	−0.453782	−0.0157321
$833$	4.04483	0.140145
$834$	−1.40509	−0.0486542
$835$	−27.3084	−0.945047
$836$	4.97827	0.172177
$837$	3.79279	0.131098
$838$	22.4975	0.777162
$839$	−3.37964	−0.116678	−0.0583391	−	0.998297i	$-0.518580\pi$
$839$	−3.37964	−0.116678	−0.0583391	+	0.998297i	$0.518580\pi$
$840$	0.611331	0.0210929
$841$	−21.5882	−0.744421
$842$	10.3793	0.357695
$843$	−0.809194	−0.0278701
$844$	14.8969	0.512772
$845$	23.7113	0.815694
$846$	−31.0044	−1.06595
$847$	−26.8616	−0.922974
$848$	−12.4490	−0.427501
$849$	0.875491	0.0300468
$850$	1.49316	0.0512149
$851$	−20.5777	−0.705394
$852$	−0.716675	−0.0245529
$853$	−34.5525	−1.18305	−0.591527	−	0.806285i	$-0.701475\pi$
$853$	−34.5525	−1.18305	−0.591527	+	0.806285i	$0.701475\pi$
$854$	28.5949	0.978499
$855$	−15.9609	−0.545852
$856$	−8.76565	−0.299604
$857$	48.2756	1.64906	0.824532	−	0.565815i	$-0.191438\pi$
$857$	48.2756	1.64906	0.824532	+	0.565815i	$0.191438\pi$
$858$	−0.0771749	−0.00263471
$859$	−22.8291	−0.778920	−0.389460	−	0.921043i	$-0.627338\pi$
$859$	−22.8291	−0.778920	−0.389460	+	0.921043i	$0.627338\pi$
$860$	−5.56624	−0.189807
$861$	−1.12861	−0.0384629
$862$	1.00000	0.0340601
$863$	42.0247	1.43054	0.715268	−	0.698850i	$-0.246305\pi$
$863$	42.0247	1.43054	0.715268	+	0.698850i	$0.246305\pi$
$864$	0.589378	0.0200510
$865$	−26.5331	−0.902152
$866$	6.65327	0.226087
$867$	−1.58307	−0.0537639
$868$	−21.5750	−0.732304
$869$	6.50502	0.220668
$870$	0.496423	0.0168303
$871$	−1.40508	−0.0476092
$872$	−7.40928	−0.250910
$873$	8.25099	0.279254
$874$	−8.18629	−0.276905
$875$	40.7929	1.37905
$876$	0.663162	0.0224062
$877$	25.9154	0.875102	0.437551	−	0.899194i	$-0.355846\pi$
$877$	25.9154	0.875102	0.437551	+	0.899194i	$0.355846\pi$
$878$	−18.3124	−0.618012
$879$	−0.299473	−0.0101010
$880$	3.20355	0.107992
$881$	−37.1438	−1.25141	−0.625704	−	0.780061i	$-0.715188\pi$
$881$	−37.1438	−1.25141	−0.625704	+	0.780061i	$0.715188\pi$
$882$	12.6794	0.426938
$883$	17.4917	0.588642	0.294321	−	0.955707i	$-0.404906\pi$
$883$	17.4917	0.588642	0.294321	+	0.955707i	$0.404906\pi$
$884$	−0.432878	−0.0145593
$885$	1.00193	0.0336795
$886$	−30.1293	−1.01221
$887$	−51.8307	−1.74030	−0.870152	−	0.492783i	$-0.835980\pi$
$887$	−51.8307	−1.74030	−0.870152	+	0.492783i	$0.835980\pi$
$888$	−0.712274	−0.0239024
$889$	−12.1217	−0.406549
$890$	−9.05867	−0.303647
$891$	−15.4066	−0.516141
$892$	0.998630	0.0334366
$893$	29.8606	0.999248
$894$	−0.347045	−0.0116069
$895$	−34.8297	−1.16423
$896$	−3.35263	−0.112004
$897$	0.126907	0.00423729
$898$	−30.0145	−1.00160
$899$	−17.5197	−0.584315
$900$	4.68064	0.156021
$901$	−11.8755	−0.395631
$902$	−5.91423	−0.196922
$903$	0.990707	0.0329687
$904$	5.48572	0.182452
$905$	−32.2853	−1.07320
$906$	−0.237938	−0.00790496
$907$	11.4031	0.378634	0.189317	−	0.981916i	$-0.439373\pi$
$907$	11.4031	0.378634	0.189317	+	0.981916i	$0.439373\pi$
$908$	−8.31483	−0.275937
$909$	50.2525	1.66677
$910$	−2.81955	−0.0934673
$911$	−33.9343	−1.12429	−0.562146	−	0.827038i	$-0.690024\pi$
$911$	−33.9343	−1.12429	−0.562146	+	0.827038i	$0.690024\pi$
$912$	−0.283360	−0.00938297
$913$	−2.72545	−0.0901993
$914$	−12.7375	−0.421318
$915$	1.55523	0.0514142
$916$	−1.90425	−0.0629181
$917$	12.1498	0.401221
$918$	0.562227	0.0185563
$919$	14.5598	0.480285	0.240142	−	0.970738i	$-0.422806\pi$
$919$	14.5598	0.480285	0.240142	+	0.970738i	$0.422806\pi$
$920$	−5.26793	−0.173678
$921$	−1.44837	−0.0477255
$922$	−16.6200	−0.547352
$923$	3.30541	0.108799
$924$	−0.570184	−0.0187577
$925$	−11.3316	−0.372581
$926$	24.4727	0.804223
$927$	14.3104	0.470014
$928$	−2.72246	−0.0893692
$929$	6.23173	0.204456	0.102228	−	0.994761i	$-0.467403\pi$
$929$	6.23173	0.204456	0.102228	+	0.994761i	$0.467403\pi$
$930$	−1.17342	−0.0384781
$931$	−12.2117	−0.400222
$932$	7.18901	0.235484
$933$	−0.366120	−0.0119862
$934$	−5.57689	−0.182481
$935$	3.05597	0.0999410
$936$	−1.35695	−0.0443534
$937$	−5.40535	−0.176585	−0.0882926	−	0.996095i	$-0.528141\pi$
$937$	−5.40535	−0.176585	−0.0882926	+	0.996095i	$0.528141\pi$
$938$	−10.3810	−0.338951
$939$	−1.94518	−0.0634786
$940$	19.2155	0.626741
$941$	3.86470	0.125986	0.0629928	−	0.998014i	$-0.479935\pi$
$941$	3.86470	0.125986	0.0629928	+	0.998014i	$0.479935\pi$
$942$	0.604959	0.0197106
$943$	9.72538	0.316702
$944$	−5.49473	−0.178838
$945$	3.66207	0.119127
$946$	5.19159	0.168793
$947$	8.62771	0.280363	0.140181	−	0.990126i	$-0.455231\pi$
$947$	8.62771	0.280363	0.140181	+	0.990126i	$0.455231\pi$
$948$	−0.370261	−0.0120255
$949$	−3.05860	−0.0992865
$950$	−4.50798	−0.146258
$951$	0.124523	0.00403795
$952$	−3.19819	−0.103654
$953$	−27.2350	−0.882228	−0.441114	−	0.897451i	$-0.645417\pi$
$953$	−27.2350	−0.882228	−0.441114	+	0.897451i	$0.645417\pi$
$954$	−37.2265	−1.20525
$955$	2.13993	0.0692466
$956$	18.5543	0.600088
$957$	−0.463010	−0.0149670
$958$	4.30728	0.139162
$959$	−32.0652	−1.03544
$960$	−0.182344	−0.00588511
$961$	10.4123	0.335882
$962$	3.28512	0.105916
$963$	−26.2121	−0.844673
$964$	14.8793	0.479229
$965$	4.95354	0.159460
$966$	0.937611	0.0301672
$967$	48.0459	1.54505	0.772525	−	0.634984i	$-0.218993\pi$
$967$	48.0459	1.54505	0.772525	+	0.634984i	$0.218993\pi$
$968$	8.01208	0.257518
$969$	−0.270306	−0.00868348
$970$	−5.11370	−0.164191
$971$	20.4718	0.656970	0.328485	−	0.944509i	$-0.393462\pi$
$971$	20.4718	0.656970	0.328485	+	0.944509i	$0.393462\pi$
$972$	2.64507	0.0848405
$973$	47.8791	1.53493
$974$	−26.9995	−0.865121
$975$	0.0698842	0.00223808
$976$	−8.52910	−0.273010
$977$	57.2543	1.83173	0.915864	−	0.401489i	$-0.131507\pi$
$977$	57.2543	1.83173	0.915864	+	0.401489i	$0.131507\pi$
$978$	1.56227	0.0499560
$979$	8.44895	0.270030
$980$	−7.85830	−0.251024
$981$	−22.1561	−0.707391
$982$	−7.17504	−0.228965
$983$	32.4037	1.03352	0.516759	−	0.856131i	$-0.327138\pi$
$983$	32.4037	1.03352	0.516759	+	0.856131i	$0.327138\pi$
$984$	0.336633	0.0107315
$985$	−48.5070	−1.54556
$986$	−2.59705	−0.0827068
$987$	−3.42007	−0.108862
$988$	1.30690	0.0415779
$989$	−8.53706	−0.271463
$990$	9.57964	0.304461
$991$	16.2478	0.516129	0.258065	−	0.966128i	$-0.416915\pi$
$991$	16.2478	0.516129	0.258065	+	0.966128i	$0.416915\pi$
$992$	6.43524	0.204319
$993$	−2.31093	−0.0733352
$994$	24.4211	0.774590
$995$	−31.6431	−1.00315
$996$	0.155131	0.00491550
$997$	−26.5413	−0.840570	−0.420285	−	0.907392i	$-0.638070\pi$
$997$	−26.5413	−0.840570	−0.420285	+	0.907392i	$0.638070\pi$
$998$	−25.3594	−0.802736
$999$	−4.26675	−0.134994

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	862.2.a.i.1.4	✓	6
3.2	odd	2		7758.2.a.t.1.4		6
4.3	odd	2		6896.2.a.q.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
862.2.a.i.1.4	✓	6	1.1	even	1	trivial
6896.2.a.q.1.3		6	4.3	odd	2
7758.2.a.t.1.4		6	3.2	odd	2

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:	\( N \)	\(=\)	\( 862 = 2 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	862.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.0983884 q^{3} +1.00000 q^{4} -1.85330 q^{5} -0.0983884 q^{6} +3.35263 q^{7} -1.00000 q^{8} -2.99032 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.0983884 q^{3} +1.00000 q^{4} -1.85330 q^{5} -0.0983884 q^{6} +3.35263 q^{7} -1.00000 q^{8} -2.99032 q^{9} +1.85330 q^{10} -1.72856 q^{11} +0.0983884 q^{12} -0.453782 q^{13} -3.35263 q^{14} -0.182344 q^{15} +1.00000 q^{16} +0.953933 q^{17} +2.99032 q^{18} -2.88001 q^{19} -1.85330 q^{20} +0.329860 q^{21} +1.72856 q^{22} -2.84245 q^{23} -0.0983884 q^{24} -1.56526 q^{25} +0.453782 q^{26} -0.589378 q^{27} +3.35263 q^{28} +2.72246 q^{29} +0.182344 q^{30} -6.43524 q^{31} -1.00000 q^{32} -0.170070 q^{33} -0.953933 q^{34} -6.21345 q^{35} -2.99032 q^{36} +7.23942 q^{37} +2.88001 q^{38} -0.0446469 q^{39} +1.85330 q^{40} -3.42148 q^{41} -0.329860 q^{42} +3.00341 q^{43} -1.72856 q^{44} +5.54197 q^{45} +2.84245 q^{46} -10.3682 q^{47} +0.0983884 q^{48} +4.24016 q^{49} +1.56526 q^{50} +0.0938559 q^{51} -0.453782 q^{52} -12.4490 q^{53} +0.589378 q^{54} +3.20355 q^{55} -3.35263 q^{56} -0.283360 q^{57} -2.72246 q^{58} -5.49473 q^{59} -0.182344 q^{60} -8.52910 q^{61} +6.43524 q^{62} -10.0254 q^{63} +1.00000 q^{64} +0.840996 q^{65} +0.170070 q^{66} +3.09637 q^{67} +0.953933 q^{68} -0.279664 q^{69} +6.21345 q^{70} -7.28415 q^{71} +2.99032 q^{72} +6.74025 q^{73} -7.23942 q^{74} -0.154004 q^{75} -2.88001 q^{76} -5.79523 q^{77} +0.0446469 q^{78} -3.76326 q^{79} -1.85330 q^{80} +8.91297 q^{81} +3.42148 q^{82} +1.57672 q^{83} +0.329860 q^{84} -1.76793 q^{85} -3.00341 q^{86} +0.267859 q^{87} +1.72856 q^{88} -4.88785 q^{89} -5.54197 q^{90} -1.52137 q^{91} -2.84245 q^{92} -0.633153 q^{93} +10.3682 q^{94} +5.33753 q^{95} -0.0983884 q^{96} -2.75923 q^{97} -4.24016 q^{98} +5.16895 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 2 q^{5} + 2 q^{6} + 3 q^{7} - 6 q^{8} - 2 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 2 * q^5 + 2 * q^6 + 3 * q^7 - 6 * q^8 - 2 * q^9	\( 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 2 q^{5} + 2 q^{6} + 3 q^{7} - 6 q^{8} - 2 q^{9} + 2 q^{10} - 6 q^{11} - 2 q^{12} - 9 q^{13} - 3 q^{14} - 3 q^{15} + 6 q^{16} - 17 q^{17} + 2 q^{18} + q^{19} - 2 q^{20} - 8 q^{21} + 6 q^{22} - 20 q^{23} + 2 q^{24} + 10 q^{25} + 9 q^{26} + 7 q^{27} + 3 q^{28} + q^{29} + 3 q^{30} + 8 q^{31} - 6 q^{32} - 5 q^{33} + 17 q^{34} - 14 q^{35} - 2 q^{36} - 3 q^{37} - q^{38} - 13 q^{39} + 2 q^{40} - 19 q^{41} + 8 q^{42} - 21 q^{43} - 6 q^{44} - 16 q^{45} + 20 q^{46} - 10 q^{47} - 2 q^{48} - 7 q^{49} - 10 q^{50} - 2 q^{51} - 9 q^{52} - q^{53} - 7 q^{54} + 3 q^{55} - 3 q^{56} - 11 q^{57} - q^{58} + 11 q^{59} - 3 q^{60} - 2 q^{61} - 8 q^{62} + 6 q^{64} - 30 q^{65} + 5 q^{66} + 4 q^{67} - 17 q^{68} + 16 q^{69} + 14 q^{70} - 4 q^{71} + 2 q^{72} - 39 q^{73} + 3 q^{74} - 21 q^{75} + q^{76} - 33 q^{77} + 13 q^{78} - 16 q^{79} - 2 q^{80} - 22 q^{81} + 19 q^{82} - 20 q^{83} - 8 q^{84} - 16 q^{85} + 21 q^{86} + q^{87} + 6 q^{88} - 17 q^{89} + 16 q^{90} + 20 q^{91} - 20 q^{92} - 5 q^{93} + 10 q^{94} - 16 q^{95} + 2 q^{96} - 29 q^{97} + 7 q^{98} - 4 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 2 * q^5 + 2 * q^6 + 3 * q^7 - 6 * q^8 - 2 * q^9 + 2 * q^10 - 6 * q^11 - 2 * q^12 - 9 * q^13 - 3 * q^14 - 3 * q^15 + 6 * q^16 - 17 * q^17 + 2 * q^18 + q^19 - 2 * q^20 - 8 * q^21 + 6 * q^22 - 20 * q^23 + 2 * q^24 + 10 * q^25 + 9 * q^26 + 7 * q^27 + 3 * q^28 + q^29 + 3 * q^30 + 8 * q^31 - 6 * q^32 - 5 * q^33 + 17 * q^34 - 14 * q^35 - 2 * q^36 - 3 * q^37 - q^38 - 13 * q^39 + 2 * q^40 - 19 * q^41 + 8 * q^42 - 21 * q^43 - 6 * q^44 - 16 * q^45 + 20 * q^46 - 10 * q^47 - 2 * q^48 - 7 * q^49 - 10 * q^50 - 2 * q^51 - 9 * q^52 - q^53 - 7 * q^54 + 3 * q^55 - 3 * q^56 - 11 * q^57 - q^58 + 11 * q^59 - 3 * q^60 - 2 * q^61 - 8 * q^62 + 6 * q^64 - 30 * q^65 + 5 * q^66 + 4 * q^67 - 17 * q^68 + 16 * q^69 + 14 * q^70 - 4 * q^71 + 2 * q^72 - 39 * q^73 + 3 * q^74 - 21 * q^75 + q^76 - 33 * q^77 + 13 * q^78 - 16 * q^79 - 2 * q^80 - 22 * q^81 + 19 * q^82 - 20 * q^83 - 8 * q^84 - 16 * q^85 + 21 * q^86 + q^87 + 6 * q^88 - 17 * q^89 + 16 * q^90 + 20 * q^91 - 20 * q^92 - 5 * q^93 + 10 * q^94 - 16 * q^95 + 2 * q^96 - 29 * q^97 + 7 * q^98 - 4 * q^99

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