LMFDB - Embedded newform 8022.2.a.p.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8022,2,Mod(1,8022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8022, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8022 = 2 \cdot 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8022.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:	$64.0559925015$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 17x^{7} - 12x^{6} + 72x^{5} + 81x^{4} - 67x^{3} - 105x^{2} - 17x + 6 $ x^9 - 17x^7 - 12x^6 + 72x^5 + 81x^4 - 67x^3 - 105x^2 - 17*x + 6
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$3.74341$ of defining polynomial
Character	$\chi$	$=$	8022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.149044 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.149044 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.149044 q^{10} +5.38262 q^{11} -1.00000 q^{12} -0.241172 q^{13} +1.00000 q^{14} +0.149044 q^{15} +1.00000 q^{16} -2.19200 q^{17} +1.00000 q^{18} -2.35387 q^{19} -0.149044 q^{20} -1.00000 q^{21} +5.38262 q^{22} -4.56424 q^{23} -1.00000 q^{24} -4.97779 q^{25} -0.241172 q^{26} -1.00000 q^{27} +1.00000 q^{28} -4.38930 q^{29} +0.149044 q^{30} -3.59376 q^{31} +1.00000 q^{32} -5.38262 q^{33} -2.19200 q^{34} -0.149044 q^{35} +1.00000 q^{36} -8.04663 q^{37} -2.35387 q^{38} +0.241172 q^{39} -0.149044 q^{40} -11.6921 q^{41} -1.00000 q^{42} -2.04976 q^{43} +5.38262 q^{44} -0.149044 q^{45} -4.56424 q^{46} +1.11989 q^{47} -1.00000 q^{48} +1.00000 q^{49} -4.97779 q^{50} +2.19200 q^{51} -0.241172 q^{52} +4.80541 q^{53} -1.00000 q^{54} -0.802249 q^{55} +1.00000 q^{56} +2.35387 q^{57} -4.38930 q^{58} +5.36709 q^{59} +0.149044 q^{60} -13.7297 q^{61} -3.59376 q^{62} +1.00000 q^{63} +1.00000 q^{64} +0.0359454 q^{65} -5.38262 q^{66} +2.91103 q^{67} -2.19200 q^{68} +4.56424 q^{69} -0.149044 q^{70} -4.13586 q^{71} +1.00000 q^{72} +8.72885 q^{73} -8.04663 q^{74} +4.97779 q^{75} -2.35387 q^{76} +5.38262 q^{77} +0.241172 q^{78} -9.14730 q^{79} -0.149044 q^{80} +1.00000 q^{81} -11.6921 q^{82} -4.71645 q^{83} -1.00000 q^{84} +0.326705 q^{85} -2.04976 q^{86} +4.38930 q^{87} +5.38262 q^{88} -2.06493 q^{89} -0.149044 q^{90} -0.241172 q^{91} -4.56424 q^{92} +3.59376 q^{93} +1.11989 q^{94} +0.350832 q^{95} -1.00000 q^{96} -8.66261 q^{97} +1.00000 q^{98} +5.38262 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 4 q^{5} - 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 4 * q^5 - 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 4 q^{5} - 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9} - 4 q^{10} - 3 q^{11} - 9 q^{12} - 9 q^{13} + 9 q^{14} + 4 q^{15} + 9 q^{16} - 12 q^{17} + 9 q^{18} - 18 q^{19} - 4 q^{20} - 9 q^{21} - 3 q^{22} + q^{23} - 9 q^{24} + 9 q^{25} - 9 q^{26} - 9 q^{27} + 9 q^{28} - 11 q^{29} + 4 q^{30} - 22 q^{31} + 9 q^{32} + 3 q^{33} - 12 q^{34} - 4 q^{35} + 9 q^{36} + 8 q^{37} - 18 q^{38} + 9 q^{39} - 4 q^{40} - 22 q^{41} - 9 q^{42} - 3 q^{43} - 3 q^{44} - 4 q^{45} + q^{46} - 49 q^{47} - 9 q^{48} + 9 q^{49} + 9 q^{50} + 12 q^{51} - 9 q^{52} + 8 q^{53} - 9 q^{54} - 19 q^{55} + 9 q^{56} + 18 q^{57} - 11 q^{58} - 18 q^{59} + 4 q^{60} + 3 q^{61} - 22 q^{62} + 9 q^{63} + 9 q^{64} - 32 q^{65} + 3 q^{66} - 11 q^{67} - 12 q^{68} - q^{69} - 4 q^{70} - 7 q^{71} + 9 q^{72} - 23 q^{73} + 8 q^{74} - 9 q^{75} - 18 q^{76} - 3 q^{77} + 9 q^{78} - 17 q^{79} - 4 q^{80} + 9 q^{81} - 22 q^{82} - 30 q^{83} - 9 q^{84} + 18 q^{85} - 3 q^{86} + 11 q^{87} - 3 q^{88} + 23 q^{89} - 4 q^{90} - 9 q^{91} + q^{92} + 22 q^{93} - 49 q^{94} - 30 q^{95} - 9 q^{96} - 46 q^{97} + 9 q^{98} - 3 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 4 * q^5 - 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9 - 4 * q^10 - 3 * q^11 - 9 * q^12 - 9 * q^13 + 9 * q^14 + 4 * q^15 + 9 * q^16 - 12 * q^17 + 9 * q^18 - 18 * q^19 - 4 * q^20 - 9 * q^21 - 3 * q^22 + q^23 - 9 * q^24 + 9 * q^25 - 9 * q^26 - 9 * q^27 + 9 * q^28 - 11 * q^29 + 4 * q^30 - 22 * q^31 + 9 * q^32 + 3 * q^33 - 12 * q^34 - 4 * q^35 + 9 * q^36 + 8 * q^37 - 18 * q^38 + 9 * q^39 - 4 * q^40 - 22 * q^41 - 9 * q^42 - 3 * q^43 - 3 * q^44 - 4 * q^45 + q^46 - 49 * q^47 - 9 * q^48 + 9 * q^49 + 9 * q^50 + 12 * q^51 - 9 * q^52 + 8 * q^53 - 9 * q^54 - 19 * q^55 + 9 * q^56 + 18 * q^57 - 11 * q^58 - 18 * q^59 + 4 * q^60 + 3 * q^61 - 22 * q^62 + 9 * q^63 + 9 * q^64 - 32 * q^65 + 3 * q^66 - 11 * q^67 - 12 * q^68 - q^69 - 4 * q^70 - 7 * q^71 + 9 * q^72 - 23 * q^73 + 8 * q^74 - 9 * q^75 - 18 * q^76 - 3 * q^77 + 9 * q^78 - 17 * q^79 - 4 * q^80 + 9 * q^81 - 22 * q^82 - 30 * q^83 - 9 * q^84 + 18 * q^85 - 3 * q^86 + 11 * q^87 - 3 * q^88 + 23 * q^89 - 4 * q^90 - 9 * q^91 + q^92 + 22 * q^93 - 49 * q^94 - 30 * q^95 - 9 * q^96 - 46 * q^97 + 9 * q^98 - 3 * 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−0.149044	−0.0666547	−0.0333273	−	0.999444i	$-0.510610\pi$
$5$	−0.149044	−0.0666547	−0.0333273	+	0.999444i	$0.510610\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.149044	−0.0471320
$11$	5.38262	1.62292	0.811460	−	0.584408i	$-0.198673\pi$
$11$	5.38262	1.62292	0.811460	+	0.584408i	$0.198673\pi$
$12$	−1.00000	−0.288675
$13$	−0.241172	−0.0668891	−0.0334446	−	0.999441i	$-0.510648\pi$
$13$	−0.241172	−0.0668891	−0.0334446	+	0.999441i	$0.510648\pi$
$14$	1.00000	0.267261
$15$	0.149044	0.0384831
$16$	1.00000	0.250000
$17$	−2.19200	−0.531637	−0.265819	−	0.964023i	$-0.585642\pi$
$17$	−2.19200	−0.531637	−0.265819	+	0.964023i	$0.585642\pi$
$18$	1.00000	0.235702
$19$	−2.35387	−0.540015	−0.270008	−	0.962858i	$-0.587026\pi$
$19$	−2.35387	−0.540015	−0.270008	+	0.962858i	$0.587026\pi$
$20$	−0.149044	−0.0333273
$21$	−1.00000	−0.218218
$22$	5.38262	1.14758
$23$	−4.56424	−0.951710	−0.475855	−	0.879524i	$-0.657861\pi$
$23$	−4.56424	−0.951710	−0.475855	+	0.879524i	$0.657861\pi$
$24$	−1.00000	−0.204124
$25$	−4.97779	−0.995557
$26$	−0.241172	−0.0472978
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	−4.38930	−0.815073	−0.407537	−	0.913189i	$-0.633612\pi$
$29$	−4.38930	−0.815073	−0.407537	+	0.913189i	$0.633612\pi$
$30$	0.149044	0.0272117
$31$	−3.59376	−0.645459	−0.322730	−	0.946491i	$-0.604600\pi$
$31$	−3.59376	−0.645459	−0.322730	+	0.946491i	$0.604600\pi$
$32$	1.00000	0.176777
$33$	−5.38262	−0.936994
$34$	−2.19200	−0.375924
$35$	−0.149044	−0.0251931
$36$	1.00000	0.166667
$37$	−8.04663	−1.32286	−0.661429	−	0.750008i	$-0.730050\pi$
$37$	−8.04663	−1.32286	−0.661429	+	0.750008i	$0.730050\pi$
$38$	−2.35387	−0.381849
$39$	0.241172	0.0386185
$40$	−0.149044	−0.0235660
$41$	−11.6921	−1.82600	−0.913000	−	0.407959i	$-0.866241\pi$
$41$	−11.6921	−1.82600	−0.913000	+	0.407959i	$0.866241\pi$
$42$	−1.00000	−0.154303
$43$	−2.04976	−0.312586	−0.156293	−	0.987711i	$-0.549954\pi$
$43$	−2.04976	−0.312586	−0.156293	+	0.987711i	$0.549954\pi$
$44$	5.38262	0.811460
$45$	−0.149044	−0.0222182
$46$	−4.56424	−0.672961
$47$	1.11989	0.163353	0.0816764	−	0.996659i	$-0.473973\pi$
$47$	1.11989	0.163353	0.0816764	+	0.996659i	$0.473973\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−4.97779	−0.703965
$51$	2.19200	0.306941
$52$	−0.241172	−0.0334446
$53$	4.80541	0.660074	0.330037	−	0.943968i	$-0.392939\pi$
$53$	4.80541	0.660074	0.330037	+	0.943968i	$0.392939\pi$
$54$	−1.00000	−0.136083
$55$	−0.802249	−0.108175
$56$	1.00000	0.133631
$57$	2.35387	0.311778
$58$	−4.38930	−0.576344
$59$	5.36709	0.698736	0.349368	−	0.936986i	$-0.386396\pi$
$59$	5.36709	0.698736	0.349368	+	0.936986i	$0.386396\pi$
$60$	0.149044	0.0192415
$61$	−13.7297	−1.75791	−0.878956	−	0.476904i	$-0.841759\pi$
$61$	−13.7297	−1.75791	−0.878956	+	0.476904i	$0.841759\pi$
$62$	−3.59376	−0.456409
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	0.0359454	0.00445847
$66$	−5.38262	−0.662555
$67$	2.91103	0.355639	0.177819	−	0.984063i	$-0.443096\pi$
$67$	2.91103	0.355639	0.177819	+	0.984063i	$0.443096\pi$
$68$	−2.19200	−0.265819
$69$	4.56424	0.549470
$70$	−0.149044	−0.0178142
$71$	−4.13586	−0.490836	−0.245418	−	0.969417i	$-0.578925\pi$
$71$	−4.13586	−0.490836	−0.245418	+	0.969417i	$0.578925\pi$
$72$	1.00000	0.117851
$73$	8.72885	1.02164	0.510818	−	0.859689i	$-0.329343\pi$
$73$	8.72885	1.02164	0.510818	+	0.859689i	$0.329343\pi$
$74$	−8.04663	−0.935402
$75$	4.97779	0.574785
$76$	−2.35387	−0.270008
$77$	5.38262	0.613406
$78$	0.241172	0.0273074
$79$	−9.14730	−1.02915	−0.514576	−	0.857445i	$-0.672051\pi$
$79$	−9.14730	−1.02915	−0.514576	+	0.857445i	$0.672051\pi$
$80$	−0.149044	−0.0166637
$81$	1.00000	0.111111
$82$	−11.6921	−1.29118
$83$	−4.71645	−0.517698	−0.258849	−	0.965918i	$-0.583343\pi$
$83$	−4.71645	−0.517698	−0.258849	+	0.965918i	$0.583343\pi$
$84$	−1.00000	−0.109109
$85$	0.326705	0.0354361
$86$	−2.04976	−0.221031
$87$	4.38930	0.470583
$88$	5.38262	0.573789
$89$	−2.06493	−0.218882	−0.109441	−	0.993993i	$-0.534906\pi$
$89$	−2.06493	−0.218882	−0.109441	+	0.993993i	$0.534906\pi$
$90$	−0.149044	−0.0157107
$91$	−0.241172	−0.0252817
$92$	−4.56424	−0.475855
$93$	3.59376	0.372656
$94$	1.11989	0.115508
$95$	0.350832	0.0359946
$96$	−1.00000	−0.102062
$97$	−8.66261	−0.879554	−0.439777	−	0.898107i	$-0.644943\pi$
$97$	−8.66261	−0.879554	−0.439777	+	0.898107i	$0.644943\pi$
$98$	1.00000	0.101015
$99$	5.38262	0.540974
$100$	−4.97779	−0.497779
$101$	−18.0401	−1.79506	−0.897530	−	0.440952i	$-0.854641\pi$
$101$	−18.0401	−1.79506	−0.897530	+	0.440952i	$0.854641\pi$
$102$	2.19200	0.217040
$103$	4.84365	0.477259	0.238629	−	0.971111i	$-0.423302\pi$
$103$	4.84365	0.477259	0.238629	+	0.971111i	$0.423302\pi$
$104$	−0.241172	−0.0236489
$105$	0.149044	0.0145452
$106$	4.80541	0.466743
$107$	−7.37693	−0.713155	−0.356577	−	0.934266i	$-0.616056\pi$
$107$	−7.37693	−0.713155	−0.356577	+	0.934266i	$0.616056\pi$
$108$	−1.00000	−0.0962250
$109$	11.1278	1.06585	0.532925	−	0.846163i	$-0.321093\pi$
$109$	11.1278	1.06585	0.532925	+	0.846163i	$0.321093\pi$
$110$	−0.802249	−0.0764914
$111$	8.04663	0.763752
$112$	1.00000	0.0944911
$113$	7.60259	0.715192	0.357596	−	0.933876i	$-0.383597\pi$
$113$	7.60259	0.715192	0.357596	+	0.933876i	$0.383597\pi$
$114$	2.35387	0.220460
$115$	0.680274	0.0634359
$116$	−4.38930	−0.407537
$117$	−0.241172	−0.0222964
$118$	5.36709	0.494081
$119$	−2.19200	−0.200940
$120$	0.149044	0.0136058
$121$	17.9726	1.63387
$122$	−13.7297	−1.24303
$123$	11.6921	1.05424
$124$	−3.59376	−0.322730
$125$	1.48713	0.133013
$126$	1.00000	0.0890871
$127$	4.00778	0.355633	0.177817	−	0.984064i	$-0.443097\pi$
$127$	4.00778	0.355633	0.177817	+	0.984064i	$0.443097\pi$
$128$	1.00000	0.0883883
$129$	2.04976	0.180471
$130$	0.0359454	0.00315262
$131$	20.9732	1.83244	0.916219	−	0.400677i	$-0.131225\pi$
$131$	20.9732	1.83244	0.916219	+	0.400677i	$0.131225\pi$
$132$	−5.38262	−0.468497
$133$	−2.35387	−0.204107
$134$	2.91103	0.251474
$135$	0.149044	0.0128277
$136$	−2.19200	−0.187962
$137$	3.73452	0.319061	0.159531	−	0.987193i	$-0.449002\pi$
$137$	3.73452	0.319061	0.159531	+	0.987193i	$0.449002\pi$
$138$	4.56424	0.388534
$139$	−18.1969	−1.54344	−0.771720	−	0.635962i	$-0.780604\pi$
$139$	−18.1969	−1.54344	−0.771720	+	0.635962i	$0.780604\pi$
$140$	−0.149044	−0.0125965
$141$	−1.11989	−0.0943118
$142$	−4.13586	−0.347074
$143$	−1.29814	−0.108556
$144$	1.00000	0.0833333
$145$	0.654201	0.0543284
$146$	8.72885	0.722405
$147$	−1.00000	−0.0824786
$148$	−8.04663	−0.661429
$149$	8.30284	0.680195	0.340098	−	0.940390i	$-0.389540\pi$
$149$	8.30284	0.680195	0.340098	+	0.940390i	$0.389540\pi$
$150$	4.97779	0.406435
$151$	23.2265	1.89014	0.945071	−	0.326864i	$-0.105992\pi$
$151$	23.2265	1.89014	0.945071	+	0.326864i	$0.105992\pi$
$152$	−2.35387	−0.190924
$153$	−2.19200	−0.177212
$154$	5.38262	0.433744
$155$	0.535630	0.0430229
$156$	0.241172	0.0193092
$157$	−6.57682	−0.524887	−0.262444	−	0.964947i	$-0.584528\pi$
$157$	−6.57682	−0.524887	−0.262444	+	0.964947i	$0.584528\pi$
$158$	−9.14730	−0.727720
$159$	−4.80541	−0.381094
$160$	−0.149044	−0.0117830
$161$	−4.56424	−0.359713
$162$	1.00000	0.0785674
$163$	21.4909	1.68330	0.841650	−	0.540024i	$-0.181585\pi$
$163$	21.4909	1.68330	0.841650	+	0.540024i	$0.181585\pi$
$164$	−11.6921	−0.913000
$165$	0.802249	0.0624550
$166$	−4.71645	−0.366068
$167$	4.99816	0.386769	0.193385	−	0.981123i	$-0.438053\pi$
$167$	4.99816	0.386769	0.193385	+	0.981123i	$0.438053\pi$
$168$	−1.00000	−0.0771517
$169$	−12.9418	−0.995526
$170$	0.326705	0.0250571
$171$	−2.35387	−0.180005
$172$	−2.04976	−0.156293
$173$	10.6612	0.810553	0.405276	−	0.914194i	$-0.367175\pi$
$173$	10.6612	0.810553	0.405276	+	0.914194i	$0.367175\pi$
$174$	4.38930	0.332752
$175$	−4.97779	−0.376285
$176$	5.38262	0.405730
$177$	−5.36709	−0.403415
$178$	−2.06493	−0.154773
$179$	−22.1134	−1.65283	−0.826417	−	0.563058i	$-0.809625\pi$
$179$	−22.1134	−1.65283	−0.826417	+	0.563058i	$0.809625\pi$
$180$	−0.149044	−0.0111091
$181$	−7.84398	−0.583038	−0.291519	−	0.956565i	$-0.594161\pi$
$181$	−7.84398	−0.583038	−0.291519	+	0.956565i	$0.594161\pi$
$182$	−0.241172	−0.0178769
$183$	13.7297	1.01493
$184$	−4.56424	−0.336480
$185$	1.19930	0.0881747
$186$	3.59376	0.263508
$187$	−11.7987	−0.862805
$188$	1.11989	0.0816764
$189$	−1.00000	−0.0727393
$190$	0.350832	0.0254520
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	−1.00000	−0.0721688
$193$	−26.9331	−1.93868	−0.969342	−	0.245717i	$-0.920977\pi$
$193$	−26.9331	−1.93868	−0.969342	+	0.245717i	$0.920977\pi$
$194$	−8.66261	−0.621939
$195$	−0.0359454	−0.00257410
$196$	1.00000	0.0714286
$197$	12.6355	0.900242	0.450121	−	0.892968i	$-0.351381\pi$
$197$	12.6355	0.900242	0.450121	+	0.892968i	$0.351381\pi$
$198$	5.38262	0.382526
$199$	25.4772	1.80603	0.903017	−	0.429605i	$-0.141347\pi$
$199$	25.4772	1.80603	0.903017	+	0.429605i	$0.141347\pi$
$200$	−4.97779	−0.351983
$201$	−2.91103	−0.205328
$202$	−18.0401	−1.26930
$203$	−4.38930	−0.308069
$204$	2.19200	0.153470
$205$	1.74264	0.121711
$206$	4.84365	0.337473
$207$	−4.56424	−0.317237
$208$	−0.241172	−0.0167223
$209$	−12.6700	−0.876402
$210$	0.149044	0.0102850
$211$	−7.88401	−0.542757	−0.271379	−	0.962473i	$-0.587480\pi$
$211$	−7.88401	−0.542757	−0.271379	+	0.962473i	$0.587480\pi$
$212$	4.80541	0.330037
$213$	4.13586	0.283384
$214$	−7.37693	−0.504277
$215$	0.305505	0.0208353
$216$	−1.00000	−0.0680414
$217$	−3.59376	−0.243961
$218$	11.1278	0.753669
$219$	−8.72885	−0.589841
$220$	−0.802249	−0.0540876
$221$	0.528648	0.0355607
$222$	8.04663	0.540054
$223$	−13.3901	−0.896667	−0.448333	−	0.893866i	$-0.647982\pi$
$223$	−13.3901	−0.896667	−0.448333	+	0.893866i	$0.647982\pi$
$224$	1.00000	0.0668153
$225$	−4.97779	−0.331852
$226$	7.60259	0.505717
$227$	−23.4319	−1.55523	−0.777616	−	0.628739i	$-0.783571\pi$
$227$	−23.4319	−1.55523	−0.777616	+	0.628739i	$0.783571\pi$
$228$	2.35387	0.155889
$229$	−14.1791	−0.936981	−0.468490	−	0.883469i	$-0.655202\pi$
$229$	−14.1791	−0.936981	−0.468490	+	0.883469i	$0.655202\pi$
$230$	0.680274	0.0448560
$231$	−5.38262	−0.354150
$232$	−4.38930	−0.288172
$233$	9.94436	0.651477	0.325738	−	0.945460i	$-0.394387\pi$
$233$	9.94436	0.651477	0.325738	+	0.945460i	$0.394387\pi$
$234$	−0.241172	−0.0157659
$235$	−0.166913	−0.0108882
$236$	5.36709	0.349368
$237$	9.14730	0.594181
$238$	−2.19200	−0.142086
$239$	24.4592	1.58214	0.791069	−	0.611728i	$-0.209525\pi$
$239$	24.4592	1.58214	0.791069	+	0.611728i	$0.209525\pi$
$240$	0.149044	0.00962077
$241$	6.07097	0.391066	0.195533	−	0.980697i	$-0.437356\pi$
$241$	6.07097	0.391066	0.195533	+	0.980697i	$0.437356\pi$
$242$	17.9726	1.15532
$243$	−1.00000	−0.0641500
$244$	−13.7297	−0.878956
$245$	−0.149044	−0.00952210
$246$	11.6921	0.745462
$247$	0.567689	0.0361212
$248$	−3.59376	−0.228204
$249$	4.71645	0.298893
$250$	1.48713	0.0940545
$251$	−26.7804	−1.69036	−0.845182	−	0.534478i	$-0.820508\pi$
$251$	−26.7804	−1.69036	−0.845182	+	0.534478i	$0.820508\pi$
$252$	1.00000	0.0629941
$253$	−24.5676	−1.54455
$254$	4.00778	0.251471
$255$	−0.326705	−0.0204590
$256$	1.00000	0.0625000
$257$	−2.78863	−0.173950	−0.0869748	−	0.996211i	$-0.527720\pi$
$257$	−2.78863	−0.173950	−0.0869748	+	0.996211i	$0.527720\pi$
$258$	2.04976	0.127613
$259$	−8.04663	−0.499993
$260$	0.0359454	0.00222924
$261$	−4.38930	−0.271691
$262$	20.9732	1.29573
$263$	−15.9297	−0.982265	−0.491133	−	0.871085i	$-0.663417\pi$
$263$	−15.9297	−0.982265	−0.491133	+	0.871085i	$0.663417\pi$
$264$	−5.38262	−0.331277
$265$	−0.716220	−0.0439970
$266$	−2.35387	−0.144325
$267$	2.06493	0.126371
$268$	2.91103	0.177819
$269$	−27.2386	−1.66076	−0.830382	−	0.557194i	$-0.811878\pi$
$269$	−27.2386	−1.66076	−0.830382	+	0.557194i	$0.811878\pi$
$270$	0.149044	0.00907055
$271$	11.3625	0.690220	0.345110	−	0.938562i	$-0.387842\pi$
$271$	11.3625	0.690220	0.345110	+	0.938562i	$0.387842\pi$
$272$	−2.19200	−0.132909
$273$	0.241172	0.0145964
$274$	3.73452	0.225610
$275$	−26.7935	−1.61571
$276$	4.56424	0.274735
$277$	29.6739	1.78293	0.891466	−	0.453087i	$-0.149677\pi$
$277$	29.6739	1.78293	0.891466	+	0.453087i	$0.149677\pi$
$278$	−18.1969	−1.09138
$279$	−3.59376	−0.215153
$280$	−0.149044	−0.00890711
$281$	19.3026	1.15150	0.575748	−	0.817627i	$-0.304711\pi$
$281$	19.3026	1.15150	0.575748	+	0.817627i	$0.304711\pi$
$282$	−1.11989	−0.0666885
$283$	−18.6867	−1.11081	−0.555404	−	0.831580i	$-0.687437\pi$
$283$	−18.6867	−1.11081	−0.555404	+	0.831580i	$0.687437\pi$
$284$	−4.13586	−0.245418
$285$	−0.350832	−0.0207815
$286$	−1.29814	−0.0767605
$287$	−11.6921	−0.690163
$288$	1.00000	0.0589256
$289$	−12.1952	−0.717362
$290$	0.654201	0.0384160
$291$	8.66261	0.507811
$292$	8.72885	0.510818
$293$	−31.4553	−1.83764	−0.918820	−	0.394678i	$-0.870856\pi$
$293$	−31.4553	−1.83764	−0.918820	+	0.394678i	$0.870856\pi$
$294$	−1.00000	−0.0583212
$295$	−0.799935	−0.0465740
$296$	−8.04663	−0.467701
$297$	−5.38262	−0.312331
$298$	8.30284	0.480971
$299$	1.10077	0.0636591
$300$	4.97779	0.287393
$301$	−2.04976	−0.118146
$302$	23.2265	1.33653
$303$	18.0401	1.03638
$304$	−2.35387	−0.135004
$305$	2.04634	0.117173
$306$	−2.19200	−0.125308
$307$	0.178914	0.0102112	0.00510558	−	0.999987i	$-0.498375\pi$
$307$	0.178914	0.0102112	0.00510558	+	0.999987i	$0.498375\pi$
$308$	5.38262	0.306703
$309$	−4.84365	−0.275545
$310$	0.535630	0.0304218
$311$	18.1631	1.02993	0.514967	−	0.857210i	$-0.327804\pi$
$311$	18.1631	1.02993	0.514967	+	0.857210i	$0.327804\pi$
$312$	0.241172	0.0136537
$313$	10.8426	0.612863	0.306431	−	0.951893i	$-0.400865\pi$
$313$	10.8426	0.612863	0.306431	+	0.951893i	$0.400865\pi$
$314$	−6.57682	−0.371151
$315$	−0.149044	−0.00839770
$316$	−9.14730	−0.514576
$317$	16.2577	0.913121	0.456561	−	0.889692i	$-0.349081\pi$
$317$	16.2577	0.913121	0.456561	+	0.889692i	$0.349081\pi$
$318$	−4.80541	−0.269474
$319$	−23.6259	−1.32280
$320$	−0.149044	−0.00833183
$321$	7.37693	0.411740
$322$	−4.56424	−0.254355
$323$	5.15968	0.287092
$324$	1.00000	0.0555556
$325$	1.20050	0.0665920
$326$	21.4909	1.19027
$327$	−11.1278	−0.615369
$328$	−11.6921	−0.645589
$329$	1.11989	0.0617415
$330$	0.802249	0.0441624
$331$	−22.2162	−1.22111	−0.610556	−	0.791973i	$-0.709054\pi$
$331$	−22.2162	−1.22111	−0.610556	+	0.791973i	$0.709054\pi$
$332$	−4.71645	−0.258849
$333$	−8.04663	−0.440953
$334$	4.99816	0.273487
$335$	−0.433872	−0.0237050
$336$	−1.00000	−0.0545545
$337$	10.7577	0.586009	0.293005	−	0.956111i	$-0.405345\pi$
$337$	10.7577	0.586009	0.293005	+	0.956111i	$0.405345\pi$
$338$	−12.9418	−0.703943
$339$	−7.60259	−0.412916
$340$	0.326705	0.0177180
$341$	−19.3439	−1.04753
$342$	−2.35387	−0.127283
$343$	1.00000	0.0539949
$344$	−2.04976	−0.110516
$345$	−0.680274	−0.0366247
$346$	10.6612	0.573147
$347$	3.34030	0.179317	0.0896584	−	0.995973i	$-0.471422\pi$
$347$	3.34030	0.179317	0.0896584	+	0.995973i	$0.471422\pi$
$348$	4.38930	0.235291
$349$	−1.45223	−0.0777361	−0.0388681	−	0.999244i	$-0.512375\pi$
$349$	−1.45223	−0.0777361	−0.0388681	+	0.999244i	$0.512375\pi$
$350$	−4.97779	−0.266074
$351$	0.241172	0.0128728
$352$	5.38262	0.286895
$353$	−23.2614	−1.23808	−0.619041	−	0.785359i	$-0.712478\pi$
$353$	−23.2614	−1.23808	−0.619041	+	0.785359i	$0.712478\pi$
$354$	−5.36709	−0.285258
$355$	0.616427	0.0327165
$356$	−2.06493	−0.109441
$357$	2.19200	0.116013
$358$	−22.1134	−1.16873
$359$	−6.21587	−0.328061	−0.164030	−	0.986455i	$-0.552450\pi$
$359$	−6.21587	−0.328061	−0.164030	+	0.986455i	$0.552450\pi$
$360$	−0.149044	−0.00785533
$361$	−13.4593	−0.708383
$362$	−7.84398	−0.412270
$363$	−17.9726	−0.943316
$364$	−0.241172	−0.0126409
$365$	−1.30099	−0.0680967
$366$	13.7297	0.717664
$367$	22.4879	1.17386	0.586929	−	0.809638i	$-0.300337\pi$
$367$	22.4879	1.17386	0.586929	+	0.809638i	$0.300337\pi$
$368$	−4.56424	−0.237927
$369$	−11.6921	−0.608667
$370$	1.19930	0.0623489
$371$	4.80541	0.249485
$372$	3.59376	0.186328
$373$	−4.96744	−0.257204	−0.128602	−	0.991696i	$-0.541049\pi$
$373$	−4.96744	−0.257204	−0.128602	+	0.991696i	$0.541049\pi$
$374$	−11.7987	−0.610095
$375$	−1.48713	−0.0767952
$376$	1.11989	0.0577539
$377$	1.05858	0.0545195
$378$	−1.00000	−0.0514344
$379$	26.0914	1.34023	0.670113	−	0.742259i	$-0.266246\pi$
$379$	26.0914	1.34023	0.670113	+	0.742259i	$0.266246\pi$
$380$	0.350832	0.0179973
$381$	−4.00778	−0.205325
$382$	−1.00000	−0.0511645
$383$	−31.6821	−1.61888	−0.809440	−	0.587203i	$-0.800229\pi$
$383$	−31.6821	−1.61888	−0.809440	+	0.587203i	$0.800229\pi$
$384$	−1.00000	−0.0510310
$385$	−0.802249	−0.0408864
$386$	−26.9331	−1.37086
$387$	−2.04976	−0.104195
$388$	−8.66261	−0.439777
$389$	31.5413	1.59921	0.799605	−	0.600527i	$-0.205042\pi$
$389$	31.5413	1.59921	0.799605	+	0.600527i	$0.205042\pi$
$390$	−0.0359454	−0.00182016
$391$	10.0048	0.505964
$392$	1.00000	0.0505076
$393$	−20.9732	−1.05796
$394$	12.6355	0.636567
$395$	1.36335	0.0685978
$396$	5.38262	0.270487
$397$	14.9561	0.750627	0.375313	−	0.926898i	$-0.377535\pi$
$397$	14.9561	0.750627	0.375313	+	0.926898i	$0.377535\pi$
$398$	25.4772	1.27706
$399$	2.35387	0.117841
$400$	−4.97779	−0.248889
$401$	18.7629	0.936974	0.468487	−	0.883471i	$-0.344799\pi$
$401$	18.7629	0.936974	0.468487	+	0.883471i	$0.344799\pi$
$402$	−2.91103	−0.145189
$403$	0.866716	0.0431742
$404$	−18.0401	−0.897530
$405$	−0.149044	−0.00740607
$406$	−4.38930	−0.217837
$407$	−43.3119	−2.14689
$408$	2.19200	0.108520
$409$	30.0917	1.48794	0.743970	−	0.668213i	$-0.232940\pi$
$409$	30.0917	1.48794	0.743970	+	0.668213i	$0.232940\pi$
$410$	1.74264	0.0860630
$411$	−3.73452	−0.184210
$412$	4.84365	0.238629
$413$	5.36709	0.264097
$414$	−4.56424	−0.224320
$415$	0.702961	0.0345070
$416$	−0.241172	−0.0118244
$417$	18.1969	0.891106
$418$	−12.6700	−0.619710
$419$	20.5206	1.00250	0.501249	−	0.865303i	$-0.332874\pi$
$419$	20.5206	1.00250	0.501249	+	0.865303i	$0.332874\pi$
$420$	0.149044	0.00727262
$421$	10.0621	0.490398	0.245199	−	0.969473i	$-0.421147\pi$
$421$	10.0621	0.490398	0.245199	+	0.969473i	$0.421147\pi$
$422$	−7.88401	−0.383787
$423$	1.11989	0.0544509
$424$	4.80541	0.233371
$425$	10.9113	0.529275
$426$	4.13586	0.200383
$427$	−13.7297	−0.664428
$428$	−7.37693	−0.356577
$429$	1.29814	0.0626747
$430$	0.305505	0.0147328
$431$	−32.7423	−1.57714	−0.788571	−	0.614944i	$-0.789179\pi$
$431$	−32.7423	−1.57714	−0.788571	+	0.614944i	$0.789179\pi$
$432$	−1.00000	−0.0481125
$433$	21.6827	1.04201	0.521003	−	0.853555i	$-0.325558\pi$
$433$	21.6827	1.04201	0.521003	+	0.853555i	$0.325558\pi$
$434$	−3.59376	−0.172506
$435$	−0.654201	−0.0313665
$436$	11.1278	0.532925
$437$	10.7436	0.513938
$438$	−8.72885	−0.417081
$439$	−11.1714	−0.533182	−0.266591	−	0.963810i	$-0.585897\pi$
$439$	−11.1714	−0.533182	−0.266591	+	0.963810i	$0.585897\pi$
$440$	−0.802249	−0.0382457
$441$	1.00000	0.0476190
$442$	0.528648	0.0251452
$443$	−24.5605	−1.16690	−0.583452	−	0.812148i	$-0.698298\pi$
$443$	−24.5605	−1.16690	−0.583452	+	0.812148i	$0.698298\pi$
$444$	8.04663	0.381876
$445$	0.307766	0.0145895
$446$	−13.3901	−0.634039
$447$	−8.30284	−0.392711
$448$	1.00000	0.0472456
$449$	−22.9754	−1.08428	−0.542138	−	0.840289i	$-0.682385\pi$
$449$	−22.9754	−1.08428	−0.542138	+	0.840289i	$0.682385\pi$
$450$	−4.97779	−0.234655
$451$	−62.9342	−2.96345
$452$	7.60259	0.357596
$453$	−23.2265	−1.09127
$454$	−23.4319	−1.09972
$455$	0.0359454	0.00168514
$456$	2.35387	0.110230
$457$	−9.29965	−0.435019	−0.217510	−	0.976058i	$-0.569793\pi$
$457$	−9.29965	−0.435019	−0.217510	+	0.976058i	$0.569793\pi$
$458$	−14.1791	−0.662545
$459$	2.19200	0.102314
$460$	0.680274	0.0317180
$461$	10.3162	0.480474	0.240237	−	0.970714i	$-0.422775\pi$
$461$	10.3162	0.480474	0.240237	+	0.970714i	$0.422775\pi$
$462$	−5.38262	−0.250422
$463$	19.1808	0.891409	0.445704	−	0.895180i	$-0.352953\pi$
$463$	19.1808	0.891409	0.445704	+	0.895180i	$0.352953\pi$
$464$	−4.38930	−0.203768
$465$	−0.535630	−0.0248393
$466$	9.94436	0.460664
$467$	8.26269	0.382352	0.191176	−	0.981556i	$-0.438770\pi$
$467$	8.26269	0.382352	0.191176	+	0.981556i	$0.438770\pi$
$468$	−0.241172	−0.0111482
$469$	2.91103	0.134419
$470$	−0.166913	−0.00769914
$471$	6.57682	0.303044
$472$	5.36709	0.247041
$473$	−11.0331	−0.507302
$474$	9.14730	0.420150
$475$	11.7171	0.537616
$476$	−2.19200	−0.100470
$477$	4.80541	0.220025
$478$	24.4592	1.11874
$479$	1.24196	0.0567465	0.0283733	−	0.999597i	$-0.490967\pi$
$479$	1.24196	0.0567465	0.0283733	+	0.999597i	$0.490967\pi$
$480$	0.149044	0.00680291
$481$	1.94062	0.0884848
$482$	6.07097	0.276525
$483$	4.56424	0.207680
$484$	17.9726	0.816936
$485$	1.29111	0.0586264
$486$	−1.00000	−0.0453609
$487$	−28.6981	−1.30044	−0.650218	−	0.759748i	$-0.725322\pi$
$487$	−28.6981	−1.30044	−0.650218	+	0.759748i	$0.725322\pi$
$488$	−13.7297	−0.621515
$489$	−21.4909	−0.971853
$490$	−0.149044	−0.00673314
$491$	−6.84088	−0.308725	−0.154362	−	0.988014i	$-0.549332\pi$
$491$	−6.84088	−0.308725	−0.154362	+	0.988014i	$0.549332\pi$
$492$	11.6921	0.527121
$493$	9.62133	0.433323
$494$	0.567689	0.0255415
$495$	−0.802249	−0.0360584
$496$	−3.59376	−0.161365
$497$	−4.13586	−0.185519
$498$	4.71645	0.211349
$499$	−6.59084	−0.295046	−0.147523	−	0.989059i	$-0.547130\pi$
$499$	−6.59084	−0.295046	−0.147523	+	0.989059i	$0.547130\pi$
$500$	1.48713	0.0665066
$501$	−4.99816	−0.223301
$502$	−26.7804	−1.19527
$503$	−5.17639	−0.230804	−0.115402	−	0.993319i	$-0.536816\pi$
$503$	−5.17639	−0.230804	−0.115402	+	0.993319i	$0.536816\pi$
$504$	1.00000	0.0445435
$505$	2.68878	0.119649
$506$	−24.5676	−1.09216
$507$	12.9418	0.574767
$508$	4.00778	0.177817
$509$	1.97878	0.0877081	0.0438540	−	0.999038i	$-0.486036\pi$
$509$	1.97878	0.0877081	0.0438540	+	0.999038i	$0.486036\pi$
$510$	−0.326705	−0.0144667
$511$	8.72885	0.386142
$512$	1.00000	0.0441942
$513$	2.35387	0.103926
$514$	−2.78863	−0.123001
$515$	−0.721918	−0.0318115
$516$	2.04976	0.0902357
$517$	6.02794	0.265109
$518$	−8.04663	−0.353549
$519$	−10.6612	−0.467973
$520$	0.0359454	0.00157631
$521$	−29.6382	−1.29847	−0.649236	−	0.760587i	$-0.724911\pi$
$521$	−29.6382	−1.29847	−0.649236	+	0.760587i	$0.724911\pi$
$522$	−4.38930	−0.192115
$523$	4.37673	0.191381	0.0956906	−	0.995411i	$-0.469494\pi$
$523$	4.37673	0.191381	0.0956906	+	0.995411i	$0.469494\pi$
$524$	20.9732	0.916219
$525$	4.97779	0.217248
$526$	−15.9297	−0.694566
$527$	7.87752	0.343150
$528$	−5.38262	−0.234248
$529$	−2.16771	−0.0942482
$530$	−0.716220	−0.0311106
$531$	5.36709	0.232912
$532$	−2.35387	−0.102053
$533$	2.81981	0.122140
$534$	2.06493	0.0893581
$535$	1.09949	0.0475351
$536$	2.91103	0.125737
$537$	22.1134	0.954265
$538$	−27.2386	−1.17434
$539$	5.38262	0.231846
$540$	0.149044	0.00641385
$541$	12.9215	0.555537	0.277769	−	0.960648i	$-0.410405\pi$
$541$	12.9215	0.555537	0.277769	+	0.960648i	$0.410405\pi$
$542$	11.3625	0.488059
$543$	7.84398	0.336617
$544$	−2.19200	−0.0939810
$545$	−1.65854	−0.0710439
$546$	0.241172	0.0103212
$547$	−4.36536	−0.186649	−0.0933247	−	0.995636i	$-0.529749\pi$
$547$	−4.36536	−0.186649	−0.0933247	+	0.995636i	$0.529749\pi$
$548$	3.73452	0.159531
$549$	−13.7297	−0.585970
$550$	−26.7935	−1.14248
$551$	10.3319	0.440152
$552$	4.56424	0.194267
$553$	−9.14730	−0.388983
$554$	29.6739	1.26072
$555$	−1.19930	−0.0509077
$556$	−18.1969	−0.771720
$557$	−3.82383	−0.162021	−0.0810105	−	0.996713i	$-0.525815\pi$
$557$	−3.82383	−0.162021	−0.0810105	+	0.996713i	$0.525815\pi$
$558$	−3.59376	−0.152136
$559$	0.494346	0.0209086
$560$	−0.149044	−0.00629827
$561$	11.7987	0.498141
$562$	19.3026	0.814230
$563$	−0.300273	−0.0126550	−0.00632750	−	0.999980i	$-0.502014\pi$
$563$	−0.300273	−0.0126550	−0.00632750	+	0.999980i	$0.502014\pi$
$564$	−1.11989	−0.0471559
$565$	−1.13312	−0.0476709
$566$	−18.6867	−0.785461
$567$	1.00000	0.0419961
$568$	−4.13586	−0.173537
$569$	−34.1230	−1.43051	−0.715255	−	0.698864i	$-0.753689\pi$
$569$	−34.1230	−1.43051	−0.715255	+	0.698864i	$0.753689\pi$
$570$	−0.350832	−0.0146947
$571$	29.1835	1.22129	0.610647	−	0.791903i	$-0.290910\pi$
$571$	29.1835	1.22129	0.610647	+	0.791903i	$0.290910\pi$
$572$	−1.29814	−0.0542779
$573$	1.00000	0.0417756
$574$	−11.6921	−0.488019
$575$	22.7198	0.947482
$576$	1.00000	0.0416667
$577$	−35.6385	−1.48365	−0.741825	−	0.670593i	$-0.766040\pi$
$577$	−35.6385	−1.48365	−0.741825	+	0.670593i	$0.766040\pi$
$578$	−12.1952	−0.507252
$579$	26.9331	1.11930
$580$	0.654201	0.0271642
$581$	−4.71645	−0.195671
$582$	8.66261	0.359077
$583$	25.8657	1.07125
$584$	8.72885	0.361203
$585$	0.0359454	0.00148616
$586$	−31.4553	−1.29941
$587$	−9.35043	−0.385933	−0.192967	−	0.981205i	$-0.561811\pi$
$587$	−9.35043	−0.385933	−0.192967	+	0.981205i	$0.561811\pi$
$588$	−1.00000	−0.0412393
$589$	8.45927	0.348558
$590$	−0.799935	−0.0329328
$591$	−12.6355	−0.519755
$592$	−8.04663	−0.330714
$593$	12.3626	0.507671	0.253835	−	0.967247i	$-0.418308\pi$
$593$	12.3626	0.507671	0.253835	+	0.967247i	$0.418308\pi$
$594$	−5.38262	−0.220852
$595$	0.326705	0.0133936
$596$	8.30284	0.340098
$597$	−25.4772	−1.04271
$598$	1.10077	0.0450137
$599$	20.4719	0.836460	0.418230	−	0.908341i	$-0.362651\pi$
$599$	20.4719	0.836460	0.418230	+	0.908341i	$0.362651\pi$
$600$	4.97779	0.203217
$601$	28.8605	1.17724	0.588621	−	0.808409i	$-0.299671\pi$
$601$	28.8605	1.17724	0.588621	+	0.808409i	$0.299671\pi$
$602$	−2.04976	−0.0835420
$603$	2.91103	0.118546
$604$	23.2265	0.945071
$605$	−2.67871	−0.108905
$606$	18.0401	0.732831
$607$	−23.7318	−0.963244	−0.481622	−	0.876379i	$-0.659952\pi$
$607$	−23.7318	−0.963244	−0.481622	+	0.876379i	$0.659952\pi$
$608$	−2.35387	−0.0954621
$609$	4.38930	0.177864
$610$	2.04634	0.0828538
$611$	−0.270086	−0.0109265
$612$	−2.19200	−0.0886062
$613$	−8.95680	−0.361762	−0.180881	−	0.983505i	$-0.557895\pi$
$613$	−8.95680	−0.361762	−0.180881	+	0.983505i	$0.557895\pi$
$614$	0.178914	0.00722038
$615$	−1.74264	−0.0702701
$616$	5.38262	0.216872
$617$	4.36101	0.175568	0.0877839	−	0.996140i	$-0.472022\pi$
$617$	4.36101	0.175568	0.0877839	+	0.996140i	$0.472022\pi$
$618$	−4.84365	−0.194840
$619$	40.1298	1.61295	0.806477	−	0.591265i	$-0.201371\pi$
$619$	40.1298	1.61295	0.806477	+	0.591265i	$0.201371\pi$
$620$	0.535630	0.0215114
$621$	4.56424	0.183157
$622$	18.1631	0.728273
$623$	−2.06493	−0.0827295
$624$	0.241172	0.00965461
$625$	24.6673	0.986691
$626$	10.8426	0.433359
$627$	12.6700	0.505991
$628$	−6.57682	−0.262444
$629$	17.6382	0.703280
$630$	−0.149044	−0.00593807
$631$	23.0114	0.916069	0.458034	−	0.888934i	$-0.348554\pi$
$631$	23.0114	0.916069	0.458034	+	0.888934i	$0.348554\pi$
$632$	−9.14730	−0.363860
$633$	7.88401	0.313361
$634$	16.2577	0.645674
$635$	−0.597337	−0.0237046
$636$	−4.80541	−0.190547
$637$	−0.241172	−0.00955559
$638$	−23.6259	−0.935360
$639$	−4.13586	−0.163612
$640$	−0.149044	−0.00589150
$641$	−21.0825	−0.832709	−0.416354	−	0.909202i	$-0.636692\pi$
$641$	−21.0825	−0.832709	−0.416354	+	0.909202i	$0.636692\pi$
$642$	7.37693	0.291144
$643$	−3.10699	−0.122528	−0.0612638	−	0.998122i	$-0.519513\pi$
$643$	−3.10699	−0.122528	−0.0612638	+	0.998122i	$0.519513\pi$
$644$	−4.56424	−0.179856
$645$	−0.305505	−0.0120293
$646$	5.15968	0.203005
$647$	−38.6120	−1.51799	−0.758997	−	0.651095i	$-0.774310\pi$
$647$	−38.6120	−1.51799	−0.758997	+	0.651095i	$0.774310\pi$
$648$	1.00000	0.0392837
$649$	28.8890	1.13399
$650$	1.20050	0.0470876
$651$	3.59376	0.140851
$652$	21.4909	0.841650
$653$	−26.1819	−1.02458	−0.512288	−	0.858814i	$-0.671202\pi$
$653$	−26.1819	−1.02458	−0.512288	+	0.858814i	$0.671202\pi$
$654$	−11.1278	−0.435131
$655$	−3.12594	−0.122141
$656$	−11.6921	−0.456500
$657$	8.72885	0.340545
$658$	1.11989	0.0436579
$659$	49.1227	1.91355	0.956775	−	0.290831i	$-0.0939316\pi$
$659$	49.1227	1.91355	0.956775	+	0.290831i	$0.0939316\pi$
$660$	0.802249	0.0312275
$661$	14.4676	0.562723	0.281362	−	0.959602i	$-0.409214\pi$
$661$	14.4676	0.562723	0.281362	+	0.959602i	$0.409214\pi$
$662$	−22.2162	−0.863457
$663$	−0.528648	−0.0205310
$664$	−4.71645	−0.183034
$665$	0.350832	0.0136047
$666$	−8.04663	−0.311801
$667$	20.0338	0.775713
$668$	4.99816	0.193385
$669$	13.3901	0.517691
$670$	−0.433872	−0.0167619
$671$	−73.9019	−2.85295
$672$	−1.00000	−0.0385758
$673$	31.2039	1.20282	0.601411	−	0.798940i	$-0.294605\pi$
$673$	31.2039	1.20282	0.601411	+	0.798940i	$0.294605\pi$
$674$	10.7577	0.414371
$675$	4.97779	0.191595
$676$	−12.9418	−0.497763
$677$	2.69620	0.103623	0.0518117	−	0.998657i	$-0.483500\pi$
$677$	2.69620	0.103623	0.0518117	+	0.998657i	$0.483500\pi$
$678$	−7.60259	−0.291976
$679$	−8.66261	−0.332440
$680$	0.326705	0.0125286
$681$	23.4319	0.897914
$682$	−19.3439	−0.740715
$683$	−27.1544	−1.03903	−0.519517	−	0.854460i	$-0.673888\pi$
$683$	−27.1544	−1.03903	−0.519517	+	0.854460i	$0.673888\pi$
$684$	−2.35387	−0.0900026
$685$	−0.556609	−0.0212669
$686$	1.00000	0.0381802
$687$	14.1791	0.540966
$688$	−2.04976	−0.0781464
$689$	−1.15893	−0.0441518
$690$	−0.680274	−0.0258976
$691$	17.3821	0.661244	0.330622	−	0.943763i	$-0.392741\pi$
$691$	17.3821	0.661244	0.330622	+	0.943763i	$0.392741\pi$
$692$	10.6612	0.405276
$693$	5.38262	0.204469
$694$	3.34030	0.126796
$695$	2.71215	0.102878
$696$	4.38930	0.166376
$697$	25.6290	0.970769
$698$	−1.45223	−0.0549677
$699$	−9.94436	−0.376130
$700$	−4.97779	−0.188143
$701$	48.8536	1.84518	0.922588	−	0.385787i	$-0.126070\pi$
$701$	48.8536	1.84518	0.922588	+	0.385787i	$0.126070\pi$
$702$	0.241172	0.00910246
$703$	18.9407	0.714364
$704$	5.38262	0.202865
$705$	0.166913	0.00628632
$706$	−23.2614	−0.875456
$707$	−18.0401	−0.678469
$708$	−5.36709	−0.201708
$709$	3.27587	0.123028	0.0615139	−	0.998106i	$-0.480407\pi$
$709$	3.27587	0.123028	0.0615139	+	0.998106i	$0.480407\pi$
$710$	0.616427	0.0231341
$711$	−9.14730	−0.343051
$712$	−2.06493	−0.0773864
$713$	16.4028	0.614290
$714$	2.19200	0.0820334
$715$	0.193480	0.00723575
$716$	−22.1134	−0.826417
$717$	−24.4592	−0.913447
$718$	−6.21587	−0.231974
$719$	4.48605	0.167302	0.0836508	−	0.996495i	$-0.473342\pi$
$719$	4.48605	0.167302	0.0836508	+	0.996495i	$0.473342\pi$
$720$	−0.149044	−0.00555456
$721$	4.84365	0.180387
$722$	−13.4593	−0.500903
$723$	−6.07097	−0.225782
$724$	−7.84398	−0.291519
$725$	21.8490	0.811452
$726$	−17.9726	−0.667025
$727$	32.3121	1.19839	0.599194	−	0.800604i	$-0.295488\pi$
$727$	32.3121	1.19839	0.599194	+	0.800604i	$0.295488\pi$
$728$	−0.241172	−0.00893844
$729$	1.00000	0.0370370
$730$	−1.30099	−0.0481517
$731$	4.49307	0.166182
$732$	13.7297	0.507465
$733$	−28.4996	−1.05266	−0.526328	−	0.850282i	$-0.676432\pi$
$733$	−28.4996	−1.05266	−0.526328	+	0.850282i	$0.676432\pi$
$734$	22.4879	0.830043
$735$	0.149044	0.00549758
$736$	−4.56424	−0.168240
$737$	15.6689	0.577173
$738$	−11.6921	−0.430392
$739$	−50.2706	−1.84924	−0.924618	−	0.380897i	$-0.875615\pi$
$739$	−50.2706	−1.84924	−0.924618	+	0.380897i	$0.875615\pi$
$740$	1.19930	0.0440873
$741$	−0.567689	−0.0208546
$742$	4.80541	0.176412
$743$	−42.5579	−1.56130	−0.780649	−	0.624969i	$-0.785111\pi$
$743$	−42.5579	−1.56130	−0.780649	+	0.624969i	$0.785111\pi$
$744$	3.59376	0.131754
$745$	−1.23749	−0.0453382
$746$	−4.96744	−0.181871
$747$	−4.71645	−0.172566
$748$	−11.7987	−0.431402
$749$	−7.37693	−0.269547
$750$	−1.48713	−0.0543024
$751$	14.2109	0.518563	0.259282	−	0.965802i	$-0.416514\pi$
$751$	14.2109	0.518563	0.259282	+	0.965802i	$0.416514\pi$
$752$	1.11989	0.0408382
$753$	26.7804	0.975932
$754$	1.05858	0.0385511
$755$	−3.46177	−0.125987
$756$	−1.00000	−0.0363696
$757$	−28.3632	−1.03088	−0.515438	−	0.856927i	$-0.672371\pi$
$757$	−28.3632	−1.03088	−0.515438	+	0.856927i	$0.672371\pi$
$758$	26.0914	0.947683
$759$	24.5676	0.891746
$760$	0.350832	0.0127260
$761$	5.73156	0.207769	0.103884	−	0.994589i	$-0.466873\pi$
$761$	5.73156	0.207769	0.103884	+	0.994589i	$0.466873\pi$
$762$	−4.00778	−0.145187
$763$	11.1278	0.402853
$764$	−1.00000	−0.0361787
$765$	0.326705	0.0118120
$766$	−31.6821	−1.14472
$767$	−1.29439	−0.0467379
$768$	−1.00000	−0.0360844
$769$	5.41308	0.195201	0.0976003	−	0.995226i	$-0.468883\pi$
$769$	5.41308	0.195201	0.0976003	+	0.995226i	$0.468883\pi$
$770$	−0.802249	−0.0289110
$771$	2.78863	0.100430
$772$	−26.9331	−0.969342
$773$	−18.4137	−0.662294	−0.331147	−	0.943579i	$-0.607436\pi$
$773$	−18.4137	−0.662294	−0.331147	+	0.943579i	$0.607436\pi$
$774$	−2.04976	−0.0736772
$775$	17.8890	0.642592
$776$	−8.66261	−0.310969
$777$	8.04663	0.288671
$778$	31.5413	1.13081
$779$	27.5217	0.986068
$780$	−0.0359454	−0.00128705
$781$	−22.2618	−0.796588
$782$	10.0048	0.357771
$783$	4.38930	0.156861
$784$	1.00000	0.0357143
$785$	0.980238	0.0349862
$786$	−20.9732	−0.748090
$787$	−52.6856	−1.87804	−0.939020	−	0.343863i	$-0.888264\pi$
$787$	−52.6856	−1.87804	−0.939020	+	0.343863i	$0.888264\pi$
$788$	12.6355	0.450121
$789$	15.9297	0.567111
$790$	1.36335	0.0485060
$791$	7.60259	0.270317
$792$	5.38262	0.191263
$793$	3.31123	0.117585
$794$	14.9561	0.530773
$795$	0.716220	0.0254017
$796$	25.4772	0.903017
$797$	−19.3905	−0.686845	−0.343423	−	0.939181i	$-0.611586\pi$
$797$	−19.3905	−0.686845	−0.343423	+	0.939181i	$0.611586\pi$
$798$	2.35387	0.0833262
$799$	−2.45479	−0.0868444
$800$	−4.97779	−0.175991
$801$	−2.06493	−0.0729606
$802$	18.7629	0.662540
$803$	46.9841	1.65803
$804$	−2.91103	−0.102664
$805$	0.680274	0.0239765
$806$	0.866716	0.0305288
$807$	27.2386	0.958843
$808$	−18.0401	−0.634650
$809$	23.3496	0.820929	0.410464	−	0.911877i	$-0.365367\pi$
$809$	23.3496	0.820929	0.410464	+	0.911877i	$0.365367\pi$
$810$	−0.149044	−0.00523689
$811$	5.04779	0.177252	0.0886259	−	0.996065i	$-0.471752\pi$
$811$	5.04779	0.177252	0.0886259	+	0.996065i	$0.471752\pi$
$812$	−4.38930	−0.154034
$813$	−11.3625	−0.398499
$814$	−43.3119	−1.51808
$815$	−3.20310	−0.112200
$816$	2.19200	0.0767352
$817$	4.82488	0.168801
$818$	30.0917	1.05213
$819$	−0.241172	−0.00842724
$820$	1.74264	0.0608557
$821$	39.1644	1.36685	0.683424	−	0.730021i	$-0.260490\pi$
$821$	39.1644	1.36685	0.683424	+	0.730021i	$0.260490\pi$
$822$	−3.73452	−0.130256
$823$	1.00148	0.0349094	0.0174547	−	0.999848i	$-0.494444\pi$
$823$	1.00148	0.0349094	0.0174547	+	0.999848i	$0.494444\pi$
$824$	4.84365	0.168736
$825$	26.7935	0.932831
$826$	5.36709	0.186745
$827$	−31.2029	−1.08503	−0.542515	−	0.840046i	$-0.682528\pi$
$827$	−31.2029	−1.08503	−0.542515	+	0.840046i	$0.682528\pi$
$828$	−4.56424	−0.158618
$829$	21.1072	0.733084	0.366542	−	0.930402i	$-0.380542\pi$
$829$	21.1072	0.733084	0.366542	+	0.930402i	$0.380542\pi$
$830$	0.702961	0.0244001
$831$	−29.6739	−1.02938
$832$	−0.241172	−0.00836114
$833$	−2.19200	−0.0759481
$834$	18.1969	0.630107
$835$	−0.744948	−0.0257800
$836$	−12.6700	−0.438201
$837$	3.59376	0.124219
$838$	20.5206	0.708873
$839$	19.6429	0.678147	0.339073	−	0.940760i	$-0.389887\pi$
$839$	19.6429	0.678147	0.339073	+	0.940760i	$0.389887\pi$
$840$	0.149044	0.00514252
$841$	−9.73401	−0.335656
$842$	10.0621	0.346764
$843$	−19.3026	−0.664816
$844$	−7.88401	−0.271379
$845$	1.92891	0.0663565
$846$	1.11989	0.0385026
$847$	17.9726	0.617545
$848$	4.80541	0.165019
$849$	18.6867	0.641326
$850$	10.9113	0.374254
$851$	36.7268	1.25898
$852$	4.13586	0.141692
$853$	−49.1221	−1.68191	−0.840955	−	0.541105i	$-0.818006\pi$
$853$	−49.1221	−1.68191	−0.840955	+	0.541105i	$0.818006\pi$
$854$	−13.7297	−0.469822
$855$	0.350832	0.0119982
$856$	−7.37693	−0.252138
$857$	−24.6080	−0.840593	−0.420297	−	0.907387i	$-0.638074\pi$
$857$	−24.6080	−0.840593	−0.420297	+	0.907387i	$0.638074\pi$
$858$	1.29814	0.0443177
$859$	47.4122	1.61768	0.808842	−	0.588026i	$-0.200095\pi$
$859$	47.4122	1.61768	0.808842	+	0.588026i	$0.200095\pi$
$860$	0.305505	0.0104176
$861$	11.6921	0.398466
$862$	−32.7423	−1.11521
$863$	−45.6782	−1.55490	−0.777452	−	0.628942i	$-0.783488\pi$
$863$	−45.6782	−1.55490	−0.777452	+	0.628942i	$0.783488\pi$
$864$	−1.00000	−0.0340207
$865$	−1.58899	−0.0540271
$866$	21.6827	0.736810
$867$	12.1952	0.414169
$868$	−3.59376	−0.121980
$869$	−49.2365	−1.67023
$870$	−0.654201	−0.0221795
$871$	−0.702059	−0.0237884
$872$	11.1278	0.376835
$873$	−8.66261	−0.293185
$874$	10.7436	0.363409
$875$	1.48713	0.0502743
$876$	−8.72885	−0.294921
$877$	47.7511	1.61244	0.806221	−	0.591615i	$-0.201509\pi$
$877$	47.7511	1.61244	0.806221	+	0.591615i	$0.201509\pi$
$878$	−11.1714	−0.377017
$879$	31.4553	1.06096
$880$	−0.802249	−0.0270438
$881$	−0.393073	−0.0132430	−0.00662148	−	0.999978i	$-0.502108\pi$
$881$	−0.393073	−0.0132430	−0.00662148	+	0.999978i	$0.502108\pi$
$882$	1.00000	0.0336718
$883$	−33.2123	−1.11768	−0.558841	−	0.829275i	$-0.688754\pi$
$883$	−33.2123	−1.11768	−0.558841	+	0.829275i	$0.688754\pi$
$884$	0.528648	0.0177804
$885$	0.799935	0.0268895
$886$	−24.5605	−0.825125
$887$	−41.9661	−1.40908	−0.704541	−	0.709663i	$-0.748847\pi$
$887$	−41.9661	−1.40908	−0.704541	+	0.709663i	$0.748847\pi$
$888$	8.04663	0.270027
$889$	4.00778	0.134417
$890$	0.307766	0.0103163
$891$	5.38262	0.180325
$892$	−13.3901	−0.448333
$893$	−2.63608	−0.0882130
$894$	−8.30284	−0.277689
$895$	3.29588	0.110169
$896$	1.00000	0.0334077
$897$	−1.10077	−0.0367536
$898$	−22.9754	−0.766699
$899$	15.7741	0.526097
$900$	−4.97779	−0.165926
$901$	−10.5334	−0.350920
$902$	−62.9342	−2.09548
$903$	2.04976	0.0682118
$904$	7.60259	0.252858
$905$	1.16910	0.0388622
$906$	−23.2265	−0.771647
$907$	52.2075	1.73352	0.866761	−	0.498725i	$-0.166198\pi$
$907$	52.2075	1.73352	0.866761	+	0.498725i	$0.166198\pi$
$908$	−23.4319	−0.777616
$909$	−18.0401	−0.598354
$910$	0.0359454	0.00119158
$911$	35.6546	1.18129	0.590645	−	0.806932i	$-0.298873\pi$
$911$	35.6546	1.18129	0.590645	+	0.806932i	$0.298873\pi$
$912$	2.35387	0.0779445
$913$	−25.3869	−0.840183
$914$	−9.29965	−0.307605
$915$	−2.04634	−0.0676499
$916$	−14.1791	−0.468490
$917$	20.9732	0.692597
$918$	2.19200	0.0723466
$919$	17.8683	0.589421	0.294711	−	0.955587i	$-0.404777\pi$
$919$	17.8683	0.589421	0.294711	+	0.955587i	$0.404777\pi$
$920$	0.680274	0.0224280
$921$	−0.178914	−0.00589542
$922$	10.3162	0.339746
$923$	0.997454	0.0328316
$924$	−5.38262	−0.177075
$925$	40.0544	1.31698
$926$	19.1808	0.630321
$927$	4.84365	0.159086
$928$	−4.38930	−0.144086
$929$	55.5679	1.82312	0.911561	−	0.411164i	$-0.134878\pi$
$929$	55.5679	1.82312	0.911561	+	0.411164i	$0.134878\pi$
$930$	−0.535630	−0.0175640
$931$	−2.35387	−0.0771451
$932$	9.94436	0.325738
$933$	−18.1631	−0.594632
$934$	8.26269	0.270363
$935$	1.75853	0.0575100
$936$	−0.241172	−0.00788296
$937$	32.1839	1.05140	0.525701	−	0.850670i	$-0.323803\pi$
$937$	32.1839	1.05140	0.525701	+	0.850670i	$0.323803\pi$
$938$	2.91103	0.0950484
$939$	−10.8426	−0.353837
$940$	−0.166913	−0.00544411
$941$	52.8453	1.72271	0.861353	−	0.508006i	$-0.169617\pi$
$941$	52.8453	1.72271	0.861353	+	0.508006i	$0.169617\pi$
$942$	6.57682	0.214284
$943$	53.3656	1.73782
$944$	5.36709	0.174684
$945$	0.149044	0.00484841
$946$	−11.0331	−0.358717
$947$	16.6505	0.541068	0.270534	−	0.962710i	$-0.412800\pi$
$947$	16.6505	0.541068	0.270534	+	0.962710i	$0.412800\pi$
$948$	9.14730	0.297091
$949$	−2.10516	−0.0683363
$950$	11.7171	0.380152
$951$	−16.2577	−0.527191
$952$	−2.19200	−0.0710430
$953$	−45.6496	−1.47874	−0.739368	−	0.673301i	$-0.764876\pi$
$953$	−45.6496	−1.47874	−0.739368	+	0.673301i	$0.764876\pi$
$954$	4.80541	0.155581
$955$	0.149044	0.00482296
$956$	24.4592	0.791069
$957$	23.6259	0.763718
$958$	1.24196	0.0401259
$959$	3.73452	0.120594
$960$	0.149044	0.00481039
$961$	−18.0849	−0.583382
$962$	1.94062	0.0625682
$963$	−7.37693	−0.237718
$964$	6.07097	0.195533
$965$	4.01422	0.129222
$966$	4.56424	0.146852
$967$	−23.2441	−0.747479	−0.373740	−	0.927534i	$-0.621925\pi$
$967$	−23.2441	−0.747479	−0.373740	+	0.927534i	$0.621925\pi$
$968$	17.9726	0.577661
$969$	−5.15968	−0.165753
$970$	1.29111	0.0414551
$971$	−41.9222	−1.34535	−0.672674	−	0.739939i	$-0.734854\pi$
$971$	−41.9222	−1.34535	−0.672674	+	0.739939i	$0.734854\pi$
$972$	−1.00000	−0.0320750
$973$	−18.1969	−0.583366
$974$	−28.6981	−0.919547
$975$	−1.20050	−0.0384469
$976$	−13.7297	−0.439478
$977$	−25.5615	−0.817784	−0.408892	−	0.912583i	$-0.634085\pi$
$977$	−25.5615	−0.817784	−0.408892	+	0.912583i	$0.634085\pi$
$978$	−21.4909	−0.687204
$979$	−11.1147	−0.355228
$980$	−0.149044	−0.00476105
$981$	11.1278	0.355283
$982$	−6.84088	−0.218301
$983$	25.8170	0.823435	0.411718	−	0.911312i	$-0.364929\pi$
$983$	25.8170	0.823435	0.411718	+	0.911312i	$0.364929\pi$
$984$	11.6921	0.372731
$985$	−1.88325	−0.0600054
$986$	9.62133	0.306406
$987$	−1.11989	−0.0356465
$988$	0.567689	0.0180606
$989$	9.35561	0.297491
$990$	−0.802249	−0.0254971
$991$	9.68272	0.307582	0.153791	−	0.988103i	$-0.450852\pi$
$991$	9.68272	0.307582	0.153791	+	0.988103i	$0.450852\pi$
$992$	−3.59376	−0.114102
$993$	22.2162	0.705009
$994$	−4.13586	−0.131181
$995$	−3.79724	−0.120381
$996$	4.71645	0.149447
$997$	36.0359	1.14127	0.570634	−	0.821204i	$-0.306697\pi$
$997$	36.0359	1.14127	0.570634	+	0.821204i	$0.306697\pi$
$998$	−6.59084	−0.208629
$999$	8.04663	0.254584

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8022.2.a.p.1.5	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8022.2.a.p.1.5	✓	9	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:	\( N \)	\(=\)	\( 8022 = 2 \cdot 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.149044 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.149044 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.149044 q^{10} +5.38262 q^{11} -1.00000 q^{12} -0.241172 q^{13} +1.00000 q^{14} +0.149044 q^{15} +1.00000 q^{16} -2.19200 q^{17} +1.00000 q^{18} -2.35387 q^{19} -0.149044 q^{20} -1.00000 q^{21} +5.38262 q^{22} -4.56424 q^{23} -1.00000 q^{24} -4.97779 q^{25} -0.241172 q^{26} -1.00000 q^{27} +1.00000 q^{28} -4.38930 q^{29} +0.149044 q^{30} -3.59376 q^{31} +1.00000 q^{32} -5.38262 q^{33} -2.19200 q^{34} -0.149044 q^{35} +1.00000 q^{36} -8.04663 q^{37} -2.35387 q^{38} +0.241172 q^{39} -0.149044 q^{40} -11.6921 q^{41} -1.00000 q^{42} -2.04976 q^{43} +5.38262 q^{44} -0.149044 q^{45} -4.56424 q^{46} +1.11989 q^{47} -1.00000 q^{48} +1.00000 q^{49} -4.97779 q^{50} +2.19200 q^{51} -0.241172 q^{52} +4.80541 q^{53} -1.00000 q^{54} -0.802249 q^{55} +1.00000 q^{56} +2.35387 q^{57} -4.38930 q^{58} +5.36709 q^{59} +0.149044 q^{60} -13.7297 q^{61} -3.59376 q^{62} +1.00000 q^{63} +1.00000 q^{64} +0.0359454 q^{65} -5.38262 q^{66} +2.91103 q^{67} -2.19200 q^{68} +4.56424 q^{69} -0.149044 q^{70} -4.13586 q^{71} +1.00000 q^{72} +8.72885 q^{73} -8.04663 q^{74} +4.97779 q^{75} -2.35387 q^{76} +5.38262 q^{77} +0.241172 q^{78} -9.14730 q^{79} -0.149044 q^{80} +1.00000 q^{81} -11.6921 q^{82} -4.71645 q^{83} -1.00000 q^{84} +0.326705 q^{85} -2.04976 q^{86} +4.38930 q^{87} +5.38262 q^{88} -2.06493 q^{89} -0.149044 q^{90} -0.241172 q^{91} -4.56424 q^{92} +3.59376 q^{93} +1.11989 q^{94} +0.350832 q^{95} -1.00000 q^{96} -8.66261 q^{97} +1.00000 q^{98} +5.38262 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 4 q^{5} - 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 4 * q^5 - 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 4 q^{5} - 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9} - 4 q^{10} - 3 q^{11} - 9 q^{12} - 9 q^{13} + 9 q^{14} + 4 q^{15} + 9 q^{16} - 12 q^{17} + 9 q^{18} - 18 q^{19} - 4 q^{20} - 9 q^{21} - 3 q^{22} + q^{23} - 9 q^{24} + 9 q^{25} - 9 q^{26} - 9 q^{27} + 9 q^{28} - 11 q^{29} + 4 q^{30} - 22 q^{31} + 9 q^{32} + 3 q^{33} - 12 q^{34} - 4 q^{35} + 9 q^{36} + 8 q^{37} - 18 q^{38} + 9 q^{39} - 4 q^{40} - 22 q^{41} - 9 q^{42} - 3 q^{43} - 3 q^{44} - 4 q^{45} + q^{46} - 49 q^{47} - 9 q^{48} + 9 q^{49} + 9 q^{50} + 12 q^{51} - 9 q^{52} + 8 q^{53} - 9 q^{54} - 19 q^{55} + 9 q^{56} + 18 q^{57} - 11 q^{58} - 18 q^{59} + 4 q^{60} + 3 q^{61} - 22 q^{62} + 9 q^{63} + 9 q^{64} - 32 q^{65} + 3 q^{66} - 11 q^{67} - 12 q^{68} - q^{69} - 4 q^{70} - 7 q^{71} + 9 q^{72} - 23 q^{73} + 8 q^{74} - 9 q^{75} - 18 q^{76} - 3 q^{77} + 9 q^{78} - 17 q^{79} - 4 q^{80} + 9 q^{81} - 22 q^{82} - 30 q^{83} - 9 q^{84} + 18 q^{85} - 3 q^{86} + 11 q^{87} - 3 q^{88} + 23 q^{89} - 4 q^{90} - 9 q^{91} + q^{92} + 22 q^{93} - 49 q^{94} - 30 q^{95} - 9 q^{96} - 46 q^{97} + 9 q^{98} - 3 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 4 * q^5 - 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9 - 4 * q^10 - 3 * q^11 - 9 * q^12 - 9 * q^13 + 9 * q^14 + 4 * q^15 + 9 * q^16 - 12 * q^17 + 9 * q^18 - 18 * q^19 - 4 * q^20 - 9 * q^21 - 3 * q^22 + q^23 - 9 * q^24 + 9 * q^25 - 9 * q^26 - 9 * q^27 + 9 * q^28 - 11 * q^29 + 4 * q^30 - 22 * q^31 + 9 * q^32 + 3 * q^33 - 12 * q^34 - 4 * q^35 + 9 * q^36 + 8 * q^37 - 18 * q^38 + 9 * q^39 - 4 * q^40 - 22 * q^41 - 9 * q^42 - 3 * q^43 - 3 * q^44 - 4 * q^45 + q^46 - 49 * q^47 - 9 * q^48 + 9 * q^49 + 9 * q^50 + 12 * q^51 - 9 * q^52 + 8 * q^53 - 9 * q^54 - 19 * q^55 + 9 * q^56 + 18 * q^57 - 11 * q^58 - 18 * q^59 + 4 * q^60 + 3 * q^61 - 22 * q^62 + 9 * q^63 + 9 * q^64 - 32 * q^65 + 3 * q^66 - 11 * q^67 - 12 * q^68 - q^69 - 4 * q^70 - 7 * q^71 + 9 * q^72 - 23 * q^73 + 8 * q^74 - 9 * q^75 - 18 * q^76 - 3 * q^77 + 9 * q^78 - 17 * q^79 - 4 * q^80 + 9 * q^81 - 22 * q^82 - 30 * q^83 - 9 * q^84 + 18 * q^85 - 3 * q^86 + 11 * q^87 - 3 * q^88 + 23 * q^89 - 4 * q^90 - 9 * q^91 + q^92 + 22 * q^93 - 49 * q^94 - 30 * q^95 - 9 * q^96 - 46 * q^97 + 9 * q^98 - 3 * q^99

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