LMFDB - Embedded newform 2006.2.a.u.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2006,2,Mod(1,2006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2006, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2006 = 2 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2006.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:	$16.0179906455$
Analytic rank:	$0$
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} - x^{8} - 23x^{7} + 18x^{6} + 185x^{5} - 91x^{4} - 615x^{3} + 126x^{2} + 668x - 44 $ x^9 - x^8 - 23x^7 + 18x^6 + 185x^5 - 91x^4 - 615x^3 + 126x^2 + 668*x - 44
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.0653222$ of defining polynomial
Character	$\chi$	$=$	2006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.0653222 q^{3} +1.00000 q^{4} +0.997627 q^{5} +0.0653222 q^{6} +0.699368 q^{7} -1.00000 q^{8} -2.99573 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.0653222 q^{3} +1.00000 q^{4} +0.997627 q^{5} +0.0653222 q^{6} +0.699368 q^{7} -1.00000 q^{8} -2.99573 q^{9} -0.997627 q^{10} +5.54539 q^{11} -0.0653222 q^{12} +4.90594 q^{13} -0.699368 q^{14} -0.0651671 q^{15} +1.00000 q^{16} +1.00000 q^{17} +2.99573 q^{18} +1.04668 q^{19} +0.997627 q^{20} -0.0456843 q^{21} -5.54539 q^{22} +4.54424 q^{23} +0.0653222 q^{24} -4.00474 q^{25} -4.90594 q^{26} +0.391654 q^{27} +0.699368 q^{28} -5.51073 q^{29} +0.0651671 q^{30} -1.65806 q^{31} -1.00000 q^{32} -0.362237 q^{33} -1.00000 q^{34} +0.697708 q^{35} -2.99573 q^{36} -1.27827 q^{37} -1.04668 q^{38} -0.320466 q^{39} -0.997627 q^{40} -1.72647 q^{41} +0.0456843 q^{42} +12.8832 q^{43} +5.54539 q^{44} -2.98862 q^{45} -4.54424 q^{46} +2.04833 q^{47} -0.0653222 q^{48} -6.51088 q^{49} +4.00474 q^{50} -0.0653222 q^{51} +4.90594 q^{52} -0.548484 q^{53} -0.391654 q^{54} +5.53223 q^{55} -0.699368 q^{56} -0.0683712 q^{57} +5.51073 q^{58} -1.00000 q^{59} -0.0651671 q^{60} +8.29044 q^{61} +1.65806 q^{62} -2.09512 q^{63} +1.00000 q^{64} +4.89429 q^{65} +0.362237 q^{66} -3.27138 q^{67} +1.00000 q^{68} -0.296840 q^{69} -0.697708 q^{70} +6.00583 q^{71} +2.99573 q^{72} +6.00711 q^{73} +1.27827 q^{74} +0.261598 q^{75} +1.04668 q^{76} +3.87827 q^{77} +0.320466 q^{78} -4.26303 q^{79} +0.997627 q^{80} +8.96162 q^{81} +1.72647 q^{82} -15.6611 q^{83} -0.0456843 q^{84} +0.997627 q^{85} -12.8832 q^{86} +0.359973 q^{87} -5.54539 q^{88} +13.9946 q^{89} +2.98862 q^{90} +3.43106 q^{91} +4.54424 q^{92} +0.108308 q^{93} -2.04833 q^{94} +1.04419 q^{95} +0.0653222 q^{96} +7.47333 q^{97} +6.51088 q^{98} -16.6125 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} - q^{3} + 9 q^{4} + 7 q^{5} + q^{6} - 9 q^{8} + 20 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 - q^3 + 9 * q^4 + 7 * q^5 + q^6 - 9 * q^8 + 20 * q^9	\( 9 q - 9 q^{2} - q^{3} + 9 q^{4} + 7 q^{5} + q^{6} - 9 q^{8} + 20 q^{9} - 7 q^{10} + 5 q^{11} - q^{12} + 25 q^{13} - 5 q^{15} + 9 q^{16} + 9 q^{17} - 20 q^{18} + 14 q^{19} + 7 q^{20} - 7 q^{21} - 5 q^{22} + 2 q^{23} + q^{24} + 20 q^{25} - 25 q^{26} - 10 q^{27} + 18 q^{29} + 5 q^{30} + 6 q^{31} - 9 q^{32} - 9 q^{33} - 9 q^{34} - 17 q^{35} + 20 q^{36} + 11 q^{37} - 14 q^{38} - 8 q^{39} - 7 q^{40} + 18 q^{41} + 7 q^{42} - 10 q^{43} + 5 q^{44} + 27 q^{45} - 2 q^{46} - 20 q^{47} - q^{48} + 13 q^{49} - 20 q^{50} - q^{51} + 25 q^{52} - 7 q^{53} + 10 q^{54} + 29 q^{55} + 17 q^{57} - 18 q^{58} - 9 q^{59} - 5 q^{60} + 30 q^{61} - 6 q^{62} - 47 q^{63} + 9 q^{64} + 8 q^{65} + 9 q^{66} + 6 q^{67} + 9 q^{68} + 20 q^{69} + 17 q^{70} + 30 q^{71} - 20 q^{72} - 11 q^{74} - 7 q^{75} + 14 q^{76} - 3 q^{77} + 8 q^{78} + 29 q^{79} + 7 q^{80} - 3 q^{81} - 18 q^{82} + 9 q^{83} - 7 q^{84} + 7 q^{85} + 10 q^{86} + 44 q^{87} - 5 q^{88} + 8 q^{89} - 27 q^{90} + 13 q^{91} + 2 q^{92} + 7 q^{93} + 20 q^{94} + 27 q^{95} + q^{96} - 13 q^{97} - 13 q^{98} - 19 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - q^3 + 9 * q^4 + 7 * q^5 + q^6 - 9 * q^8 + 20 * q^9 - 7 * q^10 + 5 * q^11 - q^12 + 25 * q^13 - 5 * q^15 + 9 * q^16 + 9 * q^17 - 20 * q^18 + 14 * q^19 + 7 * q^20 - 7 * q^21 - 5 * q^22 + 2 * q^23 + q^24 + 20 * q^25 - 25 * q^26 - 10 * q^27 + 18 * q^29 + 5 * q^30 + 6 * q^31 - 9 * q^32 - 9 * q^33 - 9 * q^34 - 17 * q^35 + 20 * q^36 + 11 * q^37 - 14 * q^38 - 8 * q^39 - 7 * q^40 + 18 * q^41 + 7 * q^42 - 10 * q^43 + 5 * q^44 + 27 * q^45 - 2 * q^46 - 20 * q^47 - q^48 + 13 * q^49 - 20 * q^50 - q^51 + 25 * q^52 - 7 * q^53 + 10 * q^54 + 29 * q^55 + 17 * q^57 - 18 * q^58 - 9 * q^59 - 5 * q^60 + 30 * q^61 - 6 * q^62 - 47 * q^63 + 9 * q^64 + 8 * q^65 + 9 * q^66 + 6 * q^67 + 9 * q^68 + 20 * q^69 + 17 * q^70 + 30 * q^71 - 20 * q^72 - 11 * q^74 - 7 * q^75 + 14 * q^76 - 3 * q^77 + 8 * q^78 + 29 * q^79 + 7 * q^80 - 3 * q^81 - 18 * q^82 + 9 * q^83 - 7 * q^84 + 7 * q^85 + 10 * q^86 + 44 * q^87 - 5 * q^88 + 8 * q^89 - 27 * q^90 + 13 * q^91 + 2 * q^92 + 7 * q^93 + 20 * q^94 + 27 * q^95 + q^96 - 13 * q^97 - 13 * q^98 - 19 * 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
$3$	−0.0653222	−0.0377138	−0.0188569	−	0.999822i	$-0.506003\pi$
$3$	−0.0653222	−0.0377138	−0.0188569	+	0.999822i	$0.506003\pi$
$4$	1.00000	0.500000
$5$	0.997627	0.446152	0.223076	−	0.974801i	$-0.428390\pi$
$5$	0.997627	0.446152	0.223076	+	0.974801i	$0.428390\pi$
$6$	0.0653222	0.0266677
$7$	0.699368	0.264336	0.132168	−	0.991227i	$-0.457806\pi$
$7$	0.699368	0.264336	0.132168	+	0.991227i	$0.457806\pi$
$8$	−1.00000	−0.353553
$9$	−2.99573	−0.998578
$10$	−0.997627	−0.315477
$11$	5.54539	1.67200	0.835999	−	0.548731i	$-0.184889\pi$
$11$	5.54539	1.67200	0.835999	+	0.548731i	$0.184889\pi$
$12$	−0.0653222	−0.0188569
$13$	4.90594	1.36066	0.680331	−	0.732905i	$-0.261836\pi$
$13$	4.90594	1.36066	0.680331	+	0.732905i	$0.261836\pi$
$14$	−0.699368	−0.186914
$15$	−0.0651671	−0.0168261
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	2.99573	0.706101
$19$	1.04668	0.240124	0.120062	−	0.992766i	$-0.461691\pi$
$19$	1.04668	0.240124	0.120062	+	0.992766i	$0.461691\pi$
$20$	0.997627	0.223076
$21$	−0.0456843	−0.00996912
$22$	−5.54539	−1.18228
$23$	4.54424	0.947540	0.473770	−	0.880649i	$-0.342893\pi$
$23$	4.54424	0.947540	0.473770	+	0.880649i	$0.342893\pi$
$24$	0.0653222	0.0133338
$25$	−4.00474	−0.800948
$26$	−4.90594	−0.962133
$27$	0.391654	0.0753739
$28$	0.699368	0.132168
$29$	−5.51073	−1.02332	−0.511658	−	0.859189i	$-0.670969\pi$
$29$	−5.51073	−1.02332	−0.511658	+	0.859189i	$0.670969\pi$
$30$	0.0651671	0.0118978
$31$	−1.65806	−0.297796	−0.148898	−	0.988853i	$-0.547573\pi$
$31$	−1.65806	−0.297796	−0.148898	+	0.988853i	$0.547573\pi$
$32$	−1.00000	−0.176777
$33$	−0.362237	−0.0630574
$34$	−1.00000	−0.171499
$35$	0.697708	0.117934
$36$	−2.99573	−0.499289
$37$	−1.27827	−0.210147	−0.105074	−	0.994464i	$-0.533508\pi$
$37$	−1.27827	−0.210147	−0.105074	+	0.994464i	$0.533508\pi$
$38$	−1.04668	−0.169793
$39$	−0.320466	−0.0513157
$40$	−0.997627	−0.157739
$41$	−1.72647	−0.269629	−0.134814	−	0.990871i	$-0.543044\pi$
$41$	−1.72647	−0.269629	−0.134814	+	0.990871i	$0.543044\pi$
$42$	0.0456843	0.00704923
$43$	12.8832	1.96467	0.982333	−	0.187143i	$-0.0599227\pi$
$43$	12.8832	1.96467	0.982333	+	0.187143i	$0.0599227\pi$
$44$	5.54539	0.835999
$45$	−2.98862	−0.445518
$46$	−4.54424	−0.670012
$47$	2.04833	0.298780	0.149390	−	0.988778i	$-0.452269\pi$
$47$	2.04833	0.298780	0.149390	+	0.988778i	$0.452269\pi$
$48$	−0.0653222	−0.00942844
$49$	−6.51088	−0.930126
$50$	4.00474	0.566356
$51$	−0.0653222	−0.00914693
$52$	4.90594	0.680331
$53$	−0.548484	−0.0753400	−0.0376700	−	0.999290i	$-0.511994\pi$
$53$	−0.548484	−0.0753400	−0.0376700	+	0.999290i	$0.511994\pi$
$54$	−0.391654	−0.0532974
$55$	5.53223	0.745966
$56$	−0.699368	−0.0934570
$57$	−0.0683712	−0.00905598
$58$	5.51073	0.723594
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−0.0651671	−0.00841304
$61$	8.29044	1.06148	0.530741	−	0.847534i	$-0.321914\pi$
$61$	8.29044	1.06148	0.530741	+	0.847534i	$0.321914\pi$
$62$	1.65806	0.210574
$63$	−2.09512	−0.263960
$64$	1.00000	0.125000
$65$	4.89429	0.607062
$66$	0.362237	0.0445883
$67$	−3.27138	−0.399662	−0.199831	−	0.979830i	$-0.564039\pi$
$67$	−3.27138	−0.399662	−0.199831	+	0.979830i	$0.564039\pi$
$68$	1.00000	0.121268
$69$	−0.296840	−0.0357353
$70$	−0.697708	−0.0833921
$71$	6.00583	0.712761	0.356380	−	0.934341i	$-0.384011\pi$
$71$	6.00583	0.712761	0.356380	+	0.934341i	$0.384011\pi$
$72$	2.99573	0.353051
$73$	6.00711	0.703080	0.351540	−	0.936173i	$-0.385658\pi$
$73$	6.00711	0.703080	0.351540	+	0.936173i	$0.385658\pi$
$74$	1.27827	0.148596
$75$	0.261598	0.0302068
$76$	1.04668	0.120062
$77$	3.87827	0.441970
$78$	0.320466	0.0362857
$79$	−4.26303	−0.479629	−0.239814	−	0.970819i	$-0.577087\pi$
$79$	−4.26303	−0.479629	−0.239814	+	0.970819i	$0.577087\pi$
$80$	0.997627	0.111538
$81$	8.96162	0.995735
$82$	1.72647	0.190656
$83$	−15.6611	−1.71902	−0.859512	−	0.511116i	$-0.829232\pi$
$83$	−15.6611	−1.71902	−0.859512	+	0.511116i	$0.829232\pi$
$84$	−0.0456843	−0.00498456
$85$	0.997627	0.108208
$86$	−12.8832	−1.38923
$87$	0.359973	0.0385931
$88$	−5.54539	−0.591141
$89$	13.9946	1.48342	0.741711	−	0.670720i	$-0.234015\pi$
$89$	13.9946	1.48342	0.741711	+	0.670720i	$0.234015\pi$
$90$	2.98862	0.315029
$91$	3.43106	0.359672
$92$	4.54424	0.473770
$93$	0.108308	0.0112310
$94$	−2.04833	−0.211269
$95$	1.04419	0.107132
$96$	0.0653222	0.00666692
$97$	7.47333	0.758801	0.379401	−	0.925232i	$-0.376130\pi$
$97$	7.47333	0.758801	0.379401	+	0.925232i	$0.376130\pi$
$98$	6.51088	0.657699
$99$	−16.6125	−1.66962
$100$	−4.00474	−0.400474
$101$	2.77807	0.276428	0.138214	−	0.990402i	$-0.455864\pi$
$101$	2.77807	0.276428	0.138214	+	0.990402i	$0.455864\pi$
$102$	0.0653222	0.00646786
$103$	−5.13382	−0.505850	−0.252925	−	0.967486i	$-0.581393\pi$
$103$	−5.13382	−0.505850	−0.252925	+	0.967486i	$0.581393\pi$
$104$	−4.90594	−0.481067
$105$	−0.0455758	−0.00444775
$106$	0.548484	0.0532734
$107$	−15.1880	−1.46828	−0.734142	−	0.678996i	$-0.762415\pi$
$107$	−15.1880	−1.46828	−0.734142	+	0.678996i	$0.762415\pi$
$108$	0.391654	0.0376870
$109$	−2.45626	−0.235267	−0.117633	−	0.993057i	$-0.537531\pi$
$109$	−2.45626	−0.235267	−0.117633	+	0.993057i	$0.537531\pi$
$110$	−5.53223	−0.527477
$111$	0.0834997	0.00792544
$112$	0.699368	0.0660841
$113$	15.9702	1.50235	0.751175	−	0.660103i	$-0.229487\pi$
$113$	15.9702	1.50235	0.751175	+	0.660103i	$0.229487\pi$
$114$	0.0683712	0.00640355
$115$	4.53346	0.422747
$116$	−5.51073	−0.511658
$117$	−14.6969	−1.35873
$118$	1.00000	0.0920575
$119$	0.699368	0.0641110
$120$	0.0651671	0.00594892
$121$	19.7514	1.79558
$122$	−8.29044	−0.750581
$123$	0.112777	0.0101687
$124$	−1.65806	−0.148898
$125$	−8.98337	−0.803497
$126$	2.09512	0.186648
$127$	8.55475	0.759111	0.379556	−	0.925169i	$-0.376077\pi$
$127$	8.55475	0.759111	0.379556	+	0.925169i	$0.376077\pi$
$128$	−1.00000	−0.0883883
$129$	−0.841557	−0.0740950
$130$	−4.89429	−0.429258
$131$	1.27519	0.111414	0.0557068	−	0.998447i	$-0.482259\pi$
$131$	1.27519	0.111414	0.0557068	+	0.998447i	$0.482259\pi$
$132$	−0.362237	−0.0315287
$133$	0.732012	0.0634735
$134$	3.27138	0.282604
$135$	0.390725	0.0336282
$136$	−1.00000	−0.0857493
$137$	−5.59323	−0.477862	−0.238931	−	0.971037i	$-0.576797\pi$
$137$	−5.59323	−0.477862	−0.238931	+	0.971037i	$0.576797\pi$
$138$	0.296840	0.0252687
$139$	−0.433083	−0.0367336	−0.0183668	−	0.999831i	$-0.505847\pi$
$139$	−0.433083	−0.0367336	−0.0183668	+	0.999831i	$0.505847\pi$
$140$	0.697708	0.0589671
$141$	−0.133801	−0.0112681
$142$	−6.00583	−0.503998
$143$	27.2053	2.27502
$144$	−2.99573	−0.249644
$145$	−5.49765	−0.456555
$146$	−6.00711	−0.497152
$147$	0.425305	0.0350786
$148$	−1.27827	−0.105074
$149$	−6.86086	−0.562064	−0.281032	−	0.959698i	$-0.590677\pi$
$149$	−6.86086	−0.562064	−0.281032	+	0.959698i	$0.590677\pi$
$150$	−0.261598	−0.0213594
$151$	12.6134	1.02647	0.513233	−	0.858249i	$-0.328448\pi$
$151$	12.6134	1.02647	0.513233	+	0.858249i	$0.328448\pi$
$152$	−1.04668	−0.0848966
$153$	−2.99573	−0.242191
$154$	−3.87827	−0.312520
$155$	−1.65412	−0.132862
$156$	−0.320466	−0.0256579
$157$	15.6014	1.24513	0.622565	−	0.782568i	$-0.286091\pi$
$157$	15.6014	1.24513	0.622565	+	0.782568i	$0.286091\pi$
$158$	4.26303	0.339149
$159$	0.0358281	0.00284136
$160$	−0.997627	−0.0788693
$161$	3.17810	0.250469
$162$	−8.96162	−0.704091
$163$	12.0982	0.947601	0.473801	−	0.880632i	$-0.342882\pi$
$163$	12.0982	0.947601	0.473801	+	0.880632i	$0.342882\pi$
$164$	−1.72647	−0.134814
$165$	−0.361377	−0.0281332
$166$	15.6611	1.21553
$167$	−8.31642	−0.643544	−0.321772	−	0.946817i	$-0.604278\pi$
$167$	−8.31642	−0.643544	−0.321772	+	0.946817i	$0.604278\pi$
$168$	0.0456843	0.00352462
$169$	11.0682	0.851401
$170$	−0.997627	−0.0765145
$171$	−3.13556	−0.239782
$172$	12.8832	0.982333
$173$	7.89027	0.599886	0.299943	−	0.953957i	$-0.403032\pi$
$173$	7.89027	0.599886	0.299943	+	0.953957i	$0.403032\pi$
$174$	−0.359973	−0.0272895
$175$	−2.80079	−0.211720
$176$	5.54539	0.418000
$177$	0.0653222	0.00490992
$178$	−13.9946	−1.04894
$179$	14.3478	1.07240	0.536202	−	0.844090i	$-0.319859\pi$
$179$	14.3478	1.07240	0.536202	+	0.844090i	$0.319859\pi$
$180$	−2.98862	−0.222759
$181$	−9.34336	−0.694486	−0.347243	−	0.937775i	$-0.612882\pi$
$181$	−9.34336	−0.694486	−0.347243	+	0.937775i	$0.612882\pi$
$182$	−3.43106	−0.254327
$183$	−0.541550	−0.0400325
$184$	−4.54424	−0.335006
$185$	−1.27524	−0.0937576
$186$	−0.108308	−0.00794152
$187$	5.54539	0.405519
$188$	2.04833	0.149390
$189$	0.273911	0.0199241
$190$	−1.04419	−0.0757537
$191$	6.43591	0.465686	0.232843	−	0.972514i	$-0.425197\pi$
$191$	6.43591	0.465686	0.232843	+	0.972514i	$0.425197\pi$
$192$	−0.0653222	−0.00471422
$193$	12.4005	0.892607	0.446304	−	0.894882i	$-0.352740\pi$
$193$	12.4005	0.892607	0.446304	+	0.894882i	$0.352740\pi$
$194$	−7.47333	−0.536554
$195$	−0.319706	−0.0228946
$196$	−6.51088	−0.465063
$197$	−12.8542	−0.915827	−0.457913	−	0.888997i	$-0.651403\pi$
$197$	−12.8542	−0.915827	−0.457913	+	0.888997i	$0.651403\pi$
$198$	16.6125	1.18060
$199$	0.573079	0.0406245	0.0203122	−	0.999794i	$-0.493534\pi$
$199$	0.573079	0.0406245	0.0203122	+	0.999794i	$0.493534\pi$
$200$	4.00474	0.283178
$201$	0.213694	0.0150728
$202$	−2.77807	−0.195464
$203$	−3.85403	−0.270500
$204$	−0.0653222	−0.00457347
$205$	−1.72237	−0.120295
$206$	5.13382	0.357690
$207$	−13.6133	−0.946193
$208$	4.90594	0.340166
$209$	5.80423	0.401487
$210$	0.0455758	0.00314503
$211$	20.6056	1.41855	0.709273	−	0.704934i	$-0.249023\pi$
$211$	20.6056	1.41855	0.709273	+	0.704934i	$0.249023\pi$
$212$	−0.548484	−0.0376700
$213$	−0.392314	−0.0268809
$214$	15.1880	1.03823
$215$	12.8526	0.876540
$216$	−0.391654	−0.0266487
$217$	−1.15959	−0.0787183
$218$	2.45626	0.166359
$219$	−0.392398	−0.0265158
$220$	5.53223	0.372983
$221$	4.90594	0.330009
$222$	−0.0834997	−0.00560413
$223$	19.7928	1.32543	0.662713	−	0.748873i	$-0.269405\pi$
$223$	19.7928	1.32543	0.662713	+	0.748873i	$0.269405\pi$
$224$	−0.699368	−0.0467285
$225$	11.9971	0.799809
$226$	−15.9702	−1.06232
$227$	−16.7422	−1.11122	−0.555610	−	0.831443i	$-0.687515\pi$
$227$	−16.7422	−1.11122	−0.555610	+	0.831443i	$0.687515\pi$
$228$	−0.0683712	−0.00452799
$229$	16.0183	1.05852	0.529261	−	0.848459i	$-0.322469\pi$
$229$	16.0183	1.05852	0.529261	+	0.848459i	$0.322469\pi$
$230$	−4.53346	−0.298927
$231$	−0.253337	−0.0166684
$232$	5.51073	0.361797
$233$	−14.1372	−0.926157	−0.463079	−	0.886317i	$-0.653255\pi$
$233$	−14.1372	−0.926157	−0.463079	+	0.886317i	$0.653255\pi$
$234$	14.6969	0.960765
$235$	2.04347	0.133301
$236$	−1.00000	−0.0650945
$237$	0.278471	0.0180886
$238$	−0.699368	−0.0453333
$239$	5.46427	0.353454	0.176727	−	0.984260i	$-0.443449\pi$
$239$	5.46427	0.353454	0.176727	+	0.984260i	$0.443449\pi$
$240$	−0.0651671	−0.00420652
$241$	−3.66099	−0.235825	−0.117913	−	0.993024i	$-0.537620\pi$
$241$	−3.66099	−0.235825	−0.117913	+	0.993024i	$0.537620\pi$
$242$	−19.7514	−1.26967
$243$	−1.76036	−0.112927
$244$	8.29044	0.530741
$245$	−6.49543	−0.414978
$246$	−0.112777	−0.00719037
$247$	5.13493	0.326728
$248$	1.65806	0.105287
$249$	1.02301	0.0648309
$250$	8.98337	0.568158
$251$	−11.3799	−0.718295	−0.359147	−	0.933281i	$-0.616932\pi$
$251$	−11.3799	−0.718295	−0.359147	+	0.933281i	$0.616932\pi$
$252$	−2.09512	−0.131980
$253$	25.1996	1.58429
$254$	−8.55475	−0.536773
$255$	−0.0651671	−0.00408093
$256$	1.00000	0.0625000
$257$	13.1963	0.823164	0.411582	−	0.911373i	$-0.364976\pi$
$257$	13.1963	0.823164	0.411582	+	0.911373i	$0.364976\pi$
$258$	0.841557	0.0523930
$259$	−0.893985	−0.0555495
$260$	4.89429	0.303531
$261$	16.5087	1.02186
$262$	−1.27519	−0.0787814
$263$	−31.1206	−1.91898	−0.959490	−	0.281742i	$-0.909088\pi$
$263$	−31.1206	−1.91898	−0.959490	+	0.281742i	$0.909088\pi$
$264$	0.362237	0.0222941
$265$	−0.547182	−0.0336131
$266$	−0.732012	−0.0448825
$267$	−0.914156	−0.0559454
$268$	−3.27138	−0.199831
$269$	26.5162	1.61672	0.808360	−	0.588688i	$-0.200355\pi$
$269$	26.5162	1.61672	0.808360	+	0.588688i	$0.200355\pi$
$270$	−0.390725	−0.0237788
$271$	−1.25409	−0.0761805	−0.0380903	−	0.999274i	$-0.512127\pi$
$271$	−1.25409	−0.0761805	−0.0380903	+	0.999274i	$0.512127\pi$
$272$	1.00000	0.0606339
$273$	−0.224124	−0.0135646
$274$	5.59323	0.337899
$275$	−22.2079	−1.33918
$276$	−0.296840	−0.0178677
$277$	−28.3492	−1.70334	−0.851670	−	0.524078i	$-0.824410\pi$
$277$	−28.3492	−1.70334	−0.851670	+	0.524078i	$0.824410\pi$
$278$	0.433083	0.0259746
$279$	4.96710	0.297372
$280$	−0.697708	−0.0416961
$281$	24.1839	1.44269	0.721346	−	0.692575i	$-0.243524\pi$
$281$	24.1839	1.44269	0.721346	+	0.692575i	$0.243524\pi$
$282$	0.133801	0.00796776
$283$	−21.1999	−1.26020	−0.630102	−	0.776513i	$-0.716987\pi$
$283$	−21.1999	−1.26020	−0.630102	+	0.776513i	$0.716987\pi$
$284$	6.00583	0.356380
$285$	−0.0682089	−0.00404035
$286$	−27.2053	−1.60869
$287$	−1.20744	−0.0712727
$288$	2.99573	0.176525
$289$	1.00000	0.0588235
$290$	5.49765	0.322833
$291$	−0.488174	−0.0286173
$292$	6.00711	0.351540
$293$	−4.99255	−0.291668	−0.145834	−	0.989309i	$-0.546587\pi$
$293$	−4.99255	−0.291668	−0.145834	+	0.989309i	$0.546587\pi$
$294$	−0.425305	−0.0248043
$295$	−0.997627	−0.0580841
$296$	1.27827	0.0742982
$297$	2.17188	0.126025
$298$	6.86086	0.397439
$299$	22.2938	1.28928
$300$	0.261598	0.0151034
$301$	9.01008	0.519332
$302$	−12.6134	−0.725821
$303$	−0.181470	−0.0104252
$304$	1.04668	0.0600310
$305$	8.27077	0.473583
$306$	2.99573	0.171255
$307$	15.6992	0.896001	0.448000	−	0.894033i	$-0.352136\pi$
$307$	15.6992	0.896001	0.448000	+	0.894033i	$0.352136\pi$
$308$	3.87827	0.220985
$309$	0.335352	0.0190775
$310$	1.65412	0.0939478
$311$	−18.5270	−1.05057	−0.525284	−	0.850927i	$-0.676041\pi$
$311$	−18.5270	−1.05057	−0.525284	+	0.850927i	$0.676041\pi$
$312$	0.320466	0.0181428
$313$	−18.6303	−1.05305	−0.526523	−	0.850161i	$-0.676504\pi$
$313$	−18.6303	−1.05305	−0.526523	+	0.850161i	$0.676504\pi$
$314$	−15.6014	−0.880440
$315$	−2.09015	−0.117767
$316$	−4.26303	−0.239814
$317$	−4.27972	−0.240373	−0.120186	−	0.992751i	$-0.538349\pi$
$317$	−4.27972	−0.240373	−0.120186	+	0.992751i	$0.538349\pi$
$318$	−0.0358281	−0.00200914
$319$	−30.5591	−1.71098
$320$	0.997627	0.0557690
$321$	0.992116	0.0553745
$322$	−3.17810	−0.177109
$323$	1.04668	0.0582386
$324$	8.96162	0.497868
$325$	−19.6470	−1.08982
$326$	−12.0982	−0.670055
$327$	0.160448	0.00887280
$328$	1.72647	0.0953282
$329$	1.43254	0.0789783
$330$	0.361377	0.0198932
$331$	−4.33494	−0.238270	−0.119135	−	0.992878i	$-0.538012\pi$
$331$	−4.33494	−0.238270	−0.119135	+	0.992878i	$0.538012\pi$
$332$	−15.6611	−0.859512
$333$	3.82937	0.209848
$334$	8.31642	0.455054
$335$	−3.26361	−0.178310
$336$	−0.0456843	−0.00249228
$337$	9.05768	0.493403	0.246702	−	0.969092i	$-0.420653\pi$
$337$	9.05768	0.493403	0.246702	+	0.969092i	$0.420653\pi$
$338$	−11.0682	−0.602032
$339$	−1.04321	−0.0566593
$340$	0.997627	0.0541039
$341$	−9.19458	−0.497914
$342$	3.13556	0.169552
$343$	−9.44908	−0.510203
$344$	−12.8832	−0.694614
$345$	−0.296135	−0.0159434
$346$	−7.89027	−0.424183
$347$	−20.4633	−1.09853	−0.549263	−	0.835650i	$-0.685091\pi$
$347$	−20.4633	−1.09853	−0.549263	+	0.835650i	$0.685091\pi$
$348$	0.359973	0.0192966
$349$	31.4661	1.68434	0.842172	−	0.539210i	$-0.181277\pi$
$349$	31.4661	1.68434	0.842172	+	0.539210i	$0.181277\pi$
$350$	2.80079	0.149708
$351$	1.92143	0.102558
$352$	−5.54539	−0.295570
$353$	−26.1599	−1.39235	−0.696175	−	0.717872i	$-0.745116\pi$
$353$	−26.1599	−1.39235	−0.696175	+	0.717872i	$0.745116\pi$
$354$	−0.0653222	−0.00347183
$355$	5.99157	0.318000
$356$	13.9946	0.741711
$357$	−0.0456843	−0.00241787
$358$	−14.3478	−0.758304
$359$	−19.3646	−1.02203	−0.511013	−	0.859573i	$-0.670729\pi$
$359$	−19.3646	−1.02203	−0.511013	+	0.859573i	$0.670729\pi$
$360$	2.98862	0.157514
$361$	−17.9045	−0.942340
$362$	9.34336	0.491076
$363$	−1.29020	−0.0677180
$364$	3.43106	0.179836
$365$	5.99286	0.313681
$366$	0.541550	0.0283073
$367$	−12.6816	−0.661976	−0.330988	−	0.943635i	$-0.607382\pi$
$367$	−12.6816	−0.661976	−0.330988	+	0.943635i	$0.607382\pi$
$368$	4.54424	0.236885
$369$	5.17203	0.269245
$370$	1.27524	0.0662966
$371$	−0.383592	−0.0199151
$372$	0.108308	0.00561550
$373$	−3.45305	−0.178792	−0.0893960	−	0.995996i	$-0.528494\pi$
$373$	−3.45305	−0.178792	−0.0893960	+	0.995996i	$0.528494\pi$
$374$	−5.54539	−0.286745
$375$	0.586813	0.0303029
$376$	−2.04833	−0.105635
$377$	−27.0353	−1.39239
$378$	−0.273911	−0.0140884
$379$	31.8083	1.63388	0.816941	−	0.576722i	$-0.195668\pi$
$379$	31.8083	1.63388	0.816941	+	0.576722i	$0.195668\pi$
$380$	1.04419	0.0535659
$381$	−0.558815	−0.0286290
$382$	−6.43591	−0.329290
$383$	3.30274	0.168762	0.0843812	−	0.996434i	$-0.473109\pi$
$383$	3.30274	0.168762	0.0843812	+	0.996434i	$0.473109\pi$
$384$	0.0653222	0.00333346
$385$	3.86907	0.197186
$386$	−12.4005	−0.631169
$387$	−38.5945	−1.96187
$388$	7.47333	0.379401
$389$	−28.7646	−1.45842	−0.729212	−	0.684288i	$-0.760113\pi$
$389$	−28.7646	−1.45842	−0.729212	+	0.684288i	$0.760113\pi$
$390$	0.319706	0.0161889
$391$	4.54424	0.229812
$392$	6.51088	0.328849
$393$	−0.0832980	−0.00420183
$394$	12.8542	0.647587
$395$	−4.25291	−0.213987
$396$	−16.6125	−0.834810
$397$	−16.2200	−0.814058	−0.407029	−	0.913415i	$-0.633435\pi$
$397$	−16.2200	−0.814058	−0.407029	+	0.913415i	$0.633435\pi$
$398$	−0.573079	−0.0287258
$399$	−0.0478166	−0.00239382
$400$	−4.00474	−0.200237
$401$	8.14074	0.406529	0.203265	−	0.979124i	$-0.434845\pi$
$401$	8.14074	0.406529	0.203265	+	0.979124i	$0.434845\pi$
$402$	−0.213694	−0.0106581
$403$	−8.13433	−0.405200
$404$	2.77807	0.138214
$405$	8.94035	0.444249
$406$	3.85403	0.191272
$407$	−7.08853	−0.351366
$408$	0.0653222	0.00323393
$409$	4.23967	0.209638	0.104819	−	0.994491i	$-0.466574\pi$
$409$	4.23967	0.209638	0.104819	+	0.994491i	$0.466574\pi$
$410$	1.72237	0.0850617
$411$	0.365362	0.0180220
$412$	−5.13382	−0.252925
$413$	−0.699368	−0.0344137
$414$	13.6133	0.669059
$415$	−15.6239	−0.766946
$416$	−4.90594	−0.240533
$417$	0.0282899	0.00138536
$418$	−5.80423	−0.283894
$419$	−34.6458	−1.69256	−0.846279	−	0.532741i	$-0.821162\pi$
$419$	−34.6458	−1.69256	−0.846279	+	0.532741i	$0.821162\pi$
$420$	−0.0455758	−0.00222387
$421$	−3.47529	−0.169375	−0.0846876	−	0.996408i	$-0.526989\pi$
$421$	−3.47529	−0.169375	−0.0846876	+	0.996408i	$0.526989\pi$
$422$	−20.6056	−1.00306
$423$	−6.13625	−0.298355
$424$	0.548484	0.0266367
$425$	−4.00474	−0.194258
$426$	0.392314	0.0190077
$427$	5.79807	0.280588
$428$	−15.1880	−0.734142
$429$	−1.77711	−0.0857998
$430$	−12.8526	−0.619807
$431$	−26.4559	−1.27434	−0.637168	−	0.770725i	$-0.719894\pi$
$431$	−26.4559	−1.27434	−0.637168	+	0.770725i	$0.719894\pi$
$432$	0.391654	0.0188435
$433$	−39.5546	−1.90087	−0.950437	−	0.310918i	$-0.899364\pi$
$433$	−39.5546	−1.90087	−0.950437	+	0.310918i	$0.899364\pi$
$434$	1.15959	0.0556622
$435$	0.359118	0.0172184
$436$	−2.45626	−0.117633
$437$	4.75635	0.227527
$438$	0.392398	0.0187495
$439$	−25.6543	−1.22441	−0.612205	−	0.790699i	$-0.709717\pi$
$439$	−25.6543	−1.22441	−0.612205	+	0.790699i	$0.709717\pi$
$440$	−5.53223	−0.263739
$441$	19.5049	0.928803
$442$	−4.90594	−0.233352
$443$	21.8018	1.03583	0.517916	−	0.855431i	$-0.326708\pi$
$443$	21.8018	1.03583	0.517916	+	0.855431i	$0.326708\pi$
$444$	0.0834997	0.00396272
$445$	13.9614	0.661832
$446$	−19.7928	−0.937218
$447$	0.448167	0.0211976
$448$	0.699368	0.0330420
$449$	27.4258	1.29431	0.647153	−	0.762360i	$-0.275960\pi$
$449$	27.4258	1.29431	0.647153	+	0.762360i	$0.275960\pi$
$450$	−11.9971	−0.565550
$451$	−9.57393	−0.450819
$452$	15.9702	0.751175
$453$	−0.823937	−0.0387119
$454$	16.7422	0.785751
$455$	3.42291	0.160469
$456$	0.0683712	0.00320177
$457$	17.4384	0.815734	0.407867	−	0.913041i	$-0.366273\pi$
$457$	17.4384	0.815734	0.407867	+	0.913041i	$0.366273\pi$
$458$	−16.0183	−0.748487
$459$	0.391654	0.0182809
$460$	4.53346	0.211374
$461$	6.89281	0.321030	0.160515	−	0.987033i	$-0.448684\pi$
$461$	6.89281	0.321030	0.160515	+	0.987033i	$0.448684\pi$
$462$	0.253337	0.0117863
$463$	16.0034	0.743743	0.371871	−	0.928284i	$-0.378716\pi$
$463$	16.0034	0.743743	0.371871	+	0.928284i	$0.378716\pi$
$464$	−5.51073	−0.255829
$465$	0.108051	0.00501074
$466$	14.1372	0.654892
$467$	−13.9944	−0.647584	−0.323792	−	0.946128i	$-0.604958\pi$
$467$	−13.9944	−0.647584	−0.323792	+	0.946128i	$0.604958\pi$
$468$	−14.6969	−0.679363
$469$	−2.28790	−0.105645
$470$	−2.04347	−0.0942582
$471$	−1.01912	−0.0469585
$472$	1.00000	0.0460287
$473$	71.4422	3.28492
$474$	−0.278471	−0.0127906
$475$	−4.19167	−0.192327
$476$	0.699368	0.0320555
$477$	1.64311	0.0752329
$478$	−5.46427	−0.249930
$479$	13.1405	0.600406	0.300203	−	0.953875i	$-0.402946\pi$
$479$	13.1405	0.600406	0.300203	+	0.953875i	$0.402946\pi$
$480$	0.0651671	0.00297446
$481$	−6.27113	−0.285939
$482$	3.66099	0.166754
$483$	−0.207600	−0.00944615
$484$	19.7514	0.897789
$485$	7.45559	0.338541
$486$	1.76036	0.0798513
$487$	22.7101	1.02909	0.514547	−	0.857462i	$-0.327960\pi$
$487$	22.7101	1.02909	0.514547	+	0.857462i	$0.327960\pi$
$488$	−8.29044	−0.375291
$489$	−0.790278	−0.0357376
$490$	6.49543	0.293434
$491$	−4.47150	−0.201796	−0.100898	−	0.994897i	$-0.532172\pi$
$491$	−4.47150	−0.201796	−0.100898	+	0.994897i	$0.532172\pi$
$492$	0.112777	0.00508436
$493$	−5.51073	−0.248191
$494$	−5.13493	−0.231031
$495$	−16.5731	−0.744905
$496$	−1.65806	−0.0744490
$497$	4.20029	0.188409
$498$	−1.02301	−0.0458424
$499$	1.21751	0.0545033	0.0272516	−	0.999629i	$-0.491324\pi$
$499$	1.21751	0.0545033	0.0272516	+	0.999629i	$0.491324\pi$
$500$	−8.98337	−0.401749
$501$	0.543246	0.0242705
$502$	11.3799	0.507911
$503$	10.6658	0.475564	0.237782	−	0.971319i	$-0.423580\pi$
$503$	10.6658	0.475564	0.237782	+	0.971319i	$0.423580\pi$
$504$	2.09512	0.0933241
$505$	2.77148	0.123329
$506$	−25.1996	−1.12026
$507$	−0.723000	−0.0321096
$508$	8.55475	0.379556
$509$	6.57555	0.291456	0.145728	−	0.989325i	$-0.453448\pi$
$509$	6.57555	0.291456	0.145728	+	0.989325i	$0.453448\pi$
$510$	0.0651671	0.00288565
$511$	4.20118	0.185849
$512$	−1.00000	−0.0441942
$513$	0.409935	0.0180991
$514$	−13.1963	−0.582065
$515$	−5.12164	−0.225686
$516$	−0.841557	−0.0370475
$517$	11.3588	0.499559
$518$	0.893985	0.0392794
$519$	−0.515409	−0.0226240
$520$	−4.89429	−0.214629
$521$	−10.4106	−0.456097	−0.228048	−	0.973650i	$-0.573234\pi$
$521$	−10.4106	−0.456097	−0.228048	+	0.973650i	$0.573234\pi$
$522$	−16.5087	−0.722565
$523$	11.9137	0.520948	0.260474	−	0.965481i	$-0.416121\pi$
$523$	11.9137	0.520948	0.260474	+	0.965481i	$0.416121\pi$
$524$	1.27519	0.0557068
$525$	0.182954	0.00798475
$526$	31.1206	1.35692
$527$	−1.65806	−0.0722261
$528$	−0.362237	−0.0157643
$529$	−2.34984	−0.102167
$530$	0.547182	0.0237681
$531$	2.99573	0.130004
$532$	0.732012	0.0317367
$533$	−8.46994	−0.366874
$534$	0.914156	0.0395594
$535$	−15.1520	−0.655078
$536$	3.27138	0.141302
$537$	−0.937228	−0.0404444
$538$	−26.5162	−1.14319
$539$	−36.1054	−1.55517
$540$	0.390725	0.0168141
$541$	−26.0870	−1.12157	−0.560783	−	0.827963i	$-0.689500\pi$
$541$	−26.0870	−1.12157	−0.560783	+	0.827963i	$0.689500\pi$
$542$	1.25409	0.0538678
$543$	0.610329	0.0261917
$544$	−1.00000	−0.0428746
$545$	−2.45043	−0.104965
$546$	0.224124	0.00959162
$547$	−15.8269	−0.676711	−0.338355	−	0.941018i	$-0.609871\pi$
$547$	−15.8269	−0.676711	−0.338355	+	0.941018i	$0.609871\pi$
$548$	−5.59323	−0.238931
$549$	−24.8360	−1.05997
$550$	22.2079	0.946946
$551$	−5.76795	−0.245723
$552$	0.296840	0.0126343
$553$	−2.98143	−0.126783
$554$	28.3492	1.20444
$555$	0.0833015	0.00353595
$556$	−0.433083	−0.0183668
$557$	−10.8524	−0.459833	−0.229916	−	0.973210i	$-0.573845\pi$
$557$	−10.8524	−0.459833	−0.229916	+	0.973210i	$0.573845\pi$
$558$	−4.96710	−0.210274
$559$	63.2040	2.67325
$560$	0.697708	0.0294836
$561$	−0.362237	−0.0152937
$562$	−24.1839	−1.02014
$563$	−18.8234	−0.793310	−0.396655	−	0.917968i	$-0.629829\pi$
$563$	−18.8234	−0.793310	−0.396655	+	0.917968i	$0.629829\pi$
$564$	−0.133801	−0.00563405
$565$	15.9323	0.670277
$566$	21.1999	0.891099
$567$	6.26747	0.263209
$568$	−6.00583	−0.251999
$569$	−18.5733	−0.778635	−0.389317	−	0.921104i	$-0.627289\pi$
$569$	−18.5733	−0.778635	−0.389317	+	0.921104i	$0.627289\pi$
$570$	0.0682089	0.00285696
$571$	32.6352	1.36574	0.682870	−	0.730540i	$-0.260732\pi$
$571$	32.6352	1.36574	0.682870	+	0.730540i	$0.260732\pi$
$572$	27.2053	1.13751
$573$	−0.420408	−0.0175628
$574$	1.20744	0.0503974
$575$	−18.1985	−0.758931
$576$	−2.99573	−0.124822
$577$	−5.49881	−0.228918	−0.114459	−	0.993428i	$-0.536514\pi$
$577$	−5.49881	−0.228918	−0.114459	+	0.993428i	$0.536514\pi$
$578$	−1.00000	−0.0415945
$579$	−0.810028	−0.0336636
$580$	−5.49765	−0.228278
$581$	−10.9528	−0.454400
$582$	0.488174	0.0202355
$583$	−3.04156	−0.125968
$584$	−6.00711	−0.248576
$585$	−14.6620	−0.606199
$586$	4.99255	0.206240
$587$	−22.1802	−0.915473	−0.457736	−	0.889088i	$-0.651340\pi$
$587$	−22.1802	−0.915473	−0.457736	+	0.889088i	$0.651340\pi$
$588$	0.425305	0.0175393
$589$	−1.73545	−0.0715079
$590$	0.997627	0.0410716
$591$	0.839667	0.0345393
$592$	−1.27827	−0.0525368
$593$	10.2322	0.420185	0.210092	−	0.977682i	$-0.432624\pi$
$593$	10.2322	0.420185	0.210092	+	0.977682i	$0.432624\pi$
$594$	−2.17188	−0.0891132
$595$	0.697708	0.0286033
$596$	−6.86086	−0.281032
$597$	−0.0374347	−0.00153210
$598$	−22.2938	−0.911660
$599$	−25.6551	−1.04824	−0.524119	−	0.851645i	$-0.675605\pi$
$599$	−25.6551	−1.04824	−0.524119	+	0.851645i	$0.675605\pi$
$600$	−0.261598	−0.0106797
$601$	11.0187	0.449462	0.224731	−	0.974421i	$-0.427850\pi$
$601$	11.0187	0.449462	0.224731	+	0.974421i	$0.427850\pi$
$602$	−9.01008	−0.367224
$603$	9.80017	0.399094
$604$	12.6134	0.513233
$605$	19.7045	0.801101
$606$	0.181470	0.00737170
$607$	1.72615	0.0700622	0.0350311	−	0.999386i	$-0.488847\pi$
$607$	1.72615	0.0700622	0.0350311	+	0.999386i	$0.488847\pi$
$608$	−1.04668	−0.0424483
$609$	0.251754	0.0102016
$610$	−8.27077	−0.334874
$611$	10.0490	0.406538
$612$	−2.99573	−0.121095
$613$	11.1187	0.449079	0.224540	−	0.974465i	$-0.427912\pi$
$613$	11.1187	0.449079	0.224540	+	0.974465i	$0.427912\pi$
$614$	−15.6992	−0.633568
$615$	0.112509	0.00453680
$616$	−3.87827	−0.156260
$617$	2.55000	0.102659	0.0513295	−	0.998682i	$-0.483654\pi$
$617$	2.55000	0.102659	0.0513295	+	0.998682i	$0.483654\pi$
$618$	−0.335352	−0.0134898
$619$	−25.4065	−1.02118	−0.510588	−	0.859826i	$-0.670572\pi$
$619$	−25.4065	−1.02118	−0.510588	+	0.859826i	$0.670572\pi$
$620$	−1.65412	−0.0664312
$621$	1.77977	0.0714198
$622$	18.5270	0.742864
$623$	9.78736	0.392122
$624$	−0.320466	−0.0128289
$625$	11.0617	0.442466
$626$	18.6303	0.744616
$627$	−0.379145	−0.0151416
$628$	15.6014	0.622565
$629$	−1.27827	−0.0509681
$630$	2.09015	0.0832735
$631$	−24.8093	−0.987644	−0.493822	−	0.869563i	$-0.664401\pi$
$631$	−24.8093	−0.987644	−0.493822	+	0.869563i	$0.664401\pi$
$632$	4.26303	0.169574
$633$	−1.34600	−0.0534987
$634$	4.27972	0.169969
$635$	8.53445	0.338679
$636$	0.0358281	0.00142068
$637$	−31.9420	−1.26559
$638$	30.5591	1.20985
$639$	−17.9919	−0.711747
$640$	−0.997627	−0.0394347
$641$	23.6987	0.936044	0.468022	−	0.883717i	$-0.344967\pi$
$641$	23.6987	0.936044	0.468022	+	0.883717i	$0.344967\pi$
$642$	−0.992116	−0.0391557
$643$	−22.0352	−0.868982	−0.434491	−	0.900676i	$-0.643072\pi$
$643$	−22.0352	−0.868982	−0.434491	+	0.900676i	$0.643072\pi$
$644$	3.17810	0.125235
$645$	−0.839560	−0.0330576
$646$	−1.04668	−0.0411809
$647$	−49.1777	−1.93337	−0.966687	−	0.255961i	$-0.917608\pi$
$647$	−49.1777	−1.93337	−0.966687	+	0.255961i	$0.917608\pi$
$648$	−8.96162	−0.352045
$649$	−5.54539	−0.217676
$650$	19.6470	0.770619
$651$	0.0757471	0.00296876
$652$	12.0982	0.473801
$653$	−39.8409	−1.55910	−0.779548	−	0.626342i	$-0.784551\pi$
$653$	−39.8409	−1.55910	−0.779548	+	0.626342i	$0.784551\pi$
$654$	−0.160448	−0.00627402
$655$	1.27216	0.0497075
$656$	−1.72647	−0.0674072
$657$	−17.9957	−0.702080
$658$	−1.43254	−0.0558461
$659$	−37.3328	−1.45428	−0.727139	−	0.686490i	$-0.759150\pi$
$659$	−37.3328	−1.45428	−0.727139	+	0.686490i	$0.759150\pi$
$660$	−0.361377	−0.0140666
$661$	−16.1662	−0.628794	−0.314397	−	0.949292i	$-0.601802\pi$
$661$	−16.1662	−0.628794	−0.314397	+	0.949292i	$0.601802\pi$
$662$	4.33494	0.168482
$663$	−0.320466	−0.0124459
$664$	15.6611	0.607767
$665$	0.730275	0.0283188
$666$	−3.82937	−0.148385
$667$	−25.0421	−0.969634
$668$	−8.31642	−0.321772
$669$	−1.29291	−0.0499868
$670$	3.26361	0.126084
$671$	45.9738	1.77480
$672$	0.0456843	0.00176231
$673$	6.95722	0.268181	0.134091	−	0.990969i	$-0.457189\pi$
$673$	6.95722	0.268181	0.134091	+	0.990969i	$0.457189\pi$
$674$	−9.05768	−0.348889
$675$	−1.56847	−0.0603706
$676$	11.0682	0.425701
$677$	49.2521	1.89291	0.946456	−	0.322833i	$-0.104635\pi$
$677$	49.2521	1.89291	0.946456	+	0.322833i	$0.104635\pi$
$678$	1.04321	0.0400642
$679$	5.22661	0.200579
$680$	−0.997627	−0.0382572
$681$	1.09364	0.0419083
$682$	9.19458	0.352079
$683$	−38.4691	−1.47198	−0.735989	−	0.676993i	$-0.763283\pi$
$683$	−38.4691	−1.47198	−0.735989	+	0.676993i	$0.763283\pi$
$684$	−3.13556	−0.119891
$685$	−5.57995	−0.213199
$686$	9.44908	0.360768
$687$	−1.04635	−0.0399208
$688$	12.8832	0.491166
$689$	−2.69083	−0.102512
$690$	0.296135	0.0112737
$691$	−31.7444	−1.20762	−0.603808	−	0.797130i	$-0.706351\pi$
$691$	−31.7444	−1.20762	−0.603808	+	0.797130i	$0.706351\pi$
$692$	7.89027	0.299943
$693$	−11.6183	−0.441341
$694$	20.4633	0.776775
$695$	−0.432055	−0.0163888
$696$	−0.359973	−0.0136447
$697$	−1.72647	−0.0653946
$698$	−31.4661	−1.19101
$699$	0.923471	0.0349289
$700$	−2.80079	−0.105860
$701$	−5.43307	−0.205204	−0.102602	−	0.994722i	$-0.532717\pi$
$701$	−5.43307	−0.205204	−0.102602	+	0.994722i	$0.532717\pi$
$702$	−1.92143	−0.0725198
$703$	−1.33794	−0.0504613
$704$	5.54539	0.209000
$705$	−0.133484	−0.00502729
$706$	26.1599	0.984540
$707$	1.94290	0.0730701
$708$	0.0653222	0.00245496
$709$	6.59542	0.247696	0.123848	−	0.992301i	$-0.460476\pi$
$709$	6.59542	0.247696	0.123848	+	0.992301i	$0.460476\pi$
$710$	−5.99157	−0.224860
$711$	12.7709	0.478946
$712$	−13.9946	−0.524469
$713$	−7.53462	−0.282174
$714$	0.0456843	0.00170969
$715$	27.1408	1.01501
$716$	14.3478	0.536202
$717$	−0.356938	−0.0133301
$718$	19.3646	0.722681
$719$	−32.0987	−1.19708	−0.598540	−	0.801093i	$-0.704252\pi$
$719$	−32.0987	−1.19708	−0.598540	+	0.801093i	$0.704252\pi$
$720$	−2.98862	−0.111379
$721$	−3.59043	−0.133715
$722$	17.9045	0.666335
$723$	0.239144	0.00889387
$724$	−9.34336	−0.347243
$725$	22.0690	0.819624
$726$	1.29020	0.0478839
$727$	−17.1508	−0.636089	−0.318045	−	0.948076i	$-0.603026\pi$
$727$	−17.1508	−0.636089	−0.318045	+	0.948076i	$0.603026\pi$
$728$	−3.43106	−0.127163
$729$	−26.7699	−0.991476
$730$	−5.99286	−0.221806
$731$	12.8832	0.476501
$732$	−0.541550	−0.0200163
$733$	37.2003	1.37402	0.687012	−	0.726646i	$-0.258922\pi$
$733$	37.2003	1.37402	0.687012	+	0.726646i	$0.258922\pi$
$734$	12.6816	0.468087
$735$	0.424296	0.0156504
$736$	−4.54424	−0.167503
$737$	−18.1411	−0.668235
$738$	−5.17203	−0.190385
$739$	−6.87427	−0.252874	−0.126437	−	0.991975i	$-0.540354\pi$
$739$	−6.87427	−0.252874	−0.126437	+	0.991975i	$0.540354\pi$
$740$	−1.27524	−0.0468788
$741$	−0.335425	−0.0123221
$742$	0.383592	0.0140821
$743$	−44.8336	−1.64478	−0.822392	−	0.568921i	$-0.807361\pi$
$743$	−44.8336	−1.64478	−0.822392	+	0.568921i	$0.807361\pi$
$744$	−0.108308	−0.00397076
$745$	−6.84458	−0.250766
$746$	3.45305	0.126425
$747$	46.9163	1.71658
$748$	5.54539	0.202760
$749$	−10.6220	−0.388121
$750$	−0.586813	−0.0214274
$751$	−36.0436	−1.31525	−0.657625	−	0.753345i	$-0.728439\pi$
$751$	−36.0436	−1.31525	−0.657625	+	0.753345i	$0.728439\pi$
$752$	2.04833	0.0746949
$753$	0.743362	0.0270896
$754$	27.0353	0.984567
$755$	12.5835	0.457960
$756$	0.273911	0.00996203
$757$	24.9443	0.906617	0.453309	−	0.891354i	$-0.350244\pi$
$757$	24.9443	0.906617	0.453309	+	0.891354i	$0.350244\pi$
$758$	−31.8083	−1.15533
$759$	−1.64609	−0.0597494
$760$	−1.04419	−0.0378768
$761$	−26.5172	−0.961247	−0.480624	−	0.876927i	$-0.659590\pi$
$761$	−26.5172	−0.961247	−0.480624	+	0.876927i	$0.659590\pi$
$762$	0.558815	0.0202437
$763$	−1.71783	−0.0621896
$764$	6.43591	0.232843
$765$	−2.98862	−0.108054
$766$	−3.30274	−0.119333
$767$	−4.90594	−0.177143
$768$	−0.0653222	−0.00235711
$769$	−15.7870	−0.569293	−0.284647	−	0.958633i	$-0.591876\pi$
$769$	−15.7870	−0.569293	−0.284647	+	0.958633i	$0.591876\pi$
$770$	−3.86907	−0.139431
$771$	−0.862013	−0.0310446
$772$	12.4005	0.446304
$773$	−23.6409	−0.850302	−0.425151	−	0.905122i	$-0.639779\pi$
$773$	−23.6409	−0.850302	−0.425151	+	0.905122i	$0.639779\pi$
$774$	38.5945	1.38725
$775$	6.64009	0.238519
$776$	−7.47333	−0.268277
$777$	0.0583970	0.00209498
$778$	28.7646	1.03126
$779$	−1.80705	−0.0647443
$780$	−0.319706	−0.0114473
$781$	33.3047	1.19173
$782$	−4.54424	−0.162502
$783$	−2.15830	−0.0771314
$784$	−6.51088	−0.232532
$785$	15.5644	0.555517
$786$	0.0832980	0.00297114
$787$	47.5051	1.69337	0.846687	−	0.532091i	$-0.178593\pi$
$787$	47.5051	1.69337	0.846687	+	0.532091i	$0.178593\pi$
$788$	−12.8542	−0.457913
$789$	2.03287	0.0723720
$790$	4.25291	0.151312
$791$	11.1690	0.397126
$792$	16.6125	0.590300
$793$	40.6724	1.44432
$794$	16.2200	0.575626
$795$	0.0357431	0.00126768
$796$	0.573079	0.0203122
$797$	−47.0884	−1.66796	−0.833979	−	0.551797i	$-0.813942\pi$
$797$	−47.0884	−1.66796	−0.833979	+	0.551797i	$0.813942\pi$
$798$	0.0478166	0.00169269
$799$	2.04833	0.0724647
$800$	4.00474	0.141589
$801$	−41.9240	−1.48131
$802$	−8.14074	−0.287460
$803$	33.3118	1.17555
$804$	0.213694	0.00753639
$805$	3.17056	0.111747
$806$	8.13433	0.286519
$807$	−1.73210	−0.0609726
$808$	−2.77807	−0.0977322
$809$	46.1748	1.62342	0.811709	−	0.584062i	$-0.198538\pi$
$809$	46.1748	1.62342	0.811709	+	0.584062i	$0.198538\pi$
$810$	−8.94035	−0.314132
$811$	−26.7575	−0.939583	−0.469791	−	0.882778i	$-0.655671\pi$
$811$	−26.7575	−0.939583	−0.469791	+	0.882778i	$0.655671\pi$
$812$	−3.85403	−0.135250
$813$	0.0819199	0.00287306
$814$	7.08853	0.248453
$815$	12.0695	0.422774
$816$	−0.0653222	−0.00228673
$817$	13.4845	0.471763
$818$	−4.23967	−0.148236
$819$	−10.2785	−0.359161
$820$	−1.72237	−0.0601477
$821$	34.4671	1.20291	0.601455	−	0.798906i	$-0.294588\pi$
$821$	34.4671	1.20291	0.601455	+	0.798906i	$0.294588\pi$
$822$	−0.365362	−0.0127435
$823$	48.2216	1.68090	0.840450	−	0.541890i	$-0.182291\pi$
$823$	48.2216	1.68090	0.840450	+	0.541890i	$0.182291\pi$
$824$	5.13382	0.178845
$825$	1.45067	0.0505057
$826$	0.699368	0.0243341
$827$	8.54472	0.297129	0.148564	−	0.988903i	$-0.452535\pi$
$827$	8.54472	0.297129	0.148564	+	0.988903i	$0.452535\pi$
$828$	−13.6133	−0.473096
$829$	48.6444	1.68949	0.844745	−	0.535169i	$-0.179752\pi$
$829$	48.6444	1.68949	0.844745	+	0.535169i	$0.179752\pi$
$830$	15.6239	0.542313
$831$	1.85183	0.0642394
$832$	4.90594	0.170083
$833$	−6.51088	−0.225589
$834$	−0.0282899	−0.000979600 0
$835$	−8.29668	−0.287118
$836$	5.80423	0.200743
$837$	−0.649385	−0.0224460
$838$	34.6458	1.19682
$839$	14.7291	0.508504	0.254252	−	0.967138i	$-0.418171\pi$
$839$	14.7291	0.508504	0.254252	+	0.967138i	$0.418171\pi$
$840$	0.0455758	0.00157252
$841$	1.36813	0.0471771
$842$	3.47529	0.119766
$843$	−1.57975	−0.0544094
$844$	20.6056	0.709273
$845$	11.0419	0.379855
$846$	6.13625	0.210969
$847$	13.8135	0.474637
$848$	−0.548484	−0.0188350
$849$	1.38482	0.0475270
$850$	4.00474	0.137361
$851$	−5.80879	−0.199123
$852$	−0.392314	−0.0134404
$853$	10.7166	0.366929	0.183465	−	0.983026i	$-0.441269\pi$
$853$	10.7166	0.366929	0.183465	+	0.983026i	$0.441269\pi$
$854$	−5.79807	−0.198406
$855$	−3.12812	−0.106979
$856$	15.1880	0.519116
$857$	−8.31810	−0.284141	−0.142070	−	0.989857i	$-0.545376\pi$
$857$	−8.31810	−0.284141	−0.142070	+	0.989857i	$0.545376\pi$
$858$	1.77711	0.0606696
$859$	12.0206	0.410139	0.205069	−	0.978747i	$-0.434258\pi$
$859$	12.0206	0.410139	0.205069	+	0.978747i	$0.434258\pi$
$860$	12.8526	0.438270
$861$	0.0788723	0.00268796
$862$	26.4559	0.901091
$863$	−24.4132	−0.831033	−0.415517	−	0.909586i	$-0.636399\pi$
$863$	−24.4132	−0.831033	−0.415517	+	0.909586i	$0.636399\pi$
$864$	−0.391654	−0.0133244
$865$	7.87154	0.267640
$866$	39.5546	1.34412
$867$	−0.0653222	−0.00221846
$868$	−1.15959	−0.0393591
$869$	−23.6402	−0.801938
$870$	−0.359118	−0.0121753
$871$	−16.0492	−0.543806
$872$	2.45626	0.0831794
$873$	−22.3881	−0.757722
$874$	−4.75635	−0.160886
$875$	−6.28268	−0.212393
$876$	−0.392398	−0.0132579
$877$	19.3513	0.653446	0.326723	−	0.945120i	$-0.394056\pi$
$877$	19.3513	0.653446	0.326723	+	0.945120i	$0.394056\pi$
$878$	25.6543	0.865789
$879$	0.326124	0.0109999
$880$	5.53223	0.186491
$881$	39.2496	1.32235	0.661176	−	0.750230i	$-0.270057\pi$
$881$	39.2496	1.32235	0.661176	+	0.750230i	$0.270057\pi$
$882$	−19.5049	−0.656763
$883$	−5.89995	−0.198549	−0.0992745	−	0.995060i	$-0.531652\pi$
$883$	−5.89995	−0.198549	−0.0992745	+	0.995060i	$0.531652\pi$
$884$	4.90594	0.165005
$885$	0.0651671	0.00219057
$886$	−21.8018	−0.732444
$887$	54.2731	1.82231	0.911156	−	0.412062i	$-0.135191\pi$
$887$	54.2731	1.82231	0.911156	+	0.412062i	$0.135191\pi$
$888$	−0.0834997	−0.00280207
$889$	5.98292	0.200661
$890$	−13.9614	−0.467986
$891$	49.6957	1.66487
$892$	19.7928	0.662713
$893$	2.14394	0.0717442
$894$	−0.448167	−0.0149889
$895$	14.3137	0.478455
$896$	−0.699368	−0.0233643
$897$	−1.45628	−0.0486237
$898$	−27.4258	−0.915212
$899$	9.13711	0.304740
$900$	11.9971	0.399904
$901$	−0.548484	−0.0182726
$902$	9.57393	0.318777
$903$	−0.588558	−0.0195860
$904$	−15.9702	−0.531161
$905$	−9.32119	−0.309847
$906$	0.823937	0.0273735
$907$	−0.904179	−0.0300228	−0.0150114	−	0.999887i	$-0.504778\pi$
$907$	−0.904179	−0.0300228	−0.0150114	+	0.999887i	$0.504778\pi$
$908$	−16.7422	−0.555610
$909$	−8.32236	−0.276035
$910$	−3.42291	−0.113468
$911$	48.0562	1.59217	0.796086	−	0.605184i	$-0.206900\pi$
$911$	48.0562	1.59217	0.796086	+	0.605184i	$0.206900\pi$
$912$	−0.0683712	−0.00226400
$913$	−86.8467	−2.87420
$914$	−17.4384	−0.576811
$915$	−0.540265	−0.0178606
$916$	16.0183	0.529261
$917$	0.891826	0.0294507
$918$	−0.391654	−0.0129265
$919$	22.1966	0.732197	0.366099	−	0.930576i	$-0.380693\pi$
$919$	22.1966	0.732197	0.366099	+	0.930576i	$0.380693\pi$
$920$	−4.53346	−0.149464
$921$	−1.02551	−0.0337916
$922$	−6.89281	−0.227003
$923$	29.4642	0.969826
$924$	−0.253337	−0.00833418
$925$	5.11916	0.168317
$926$	−16.0034	−0.525905
$927$	15.3796	0.505131
$928$	5.51073	0.180899
$929$	2.49414	0.0818300	0.0409150	−	0.999163i	$-0.486973\pi$
$929$	2.49414	0.0818300	0.0409150	+	0.999163i	$0.486973\pi$
$930$	−0.108051	−0.00354313
$931$	−6.81479	−0.223346
$932$	−14.1372	−0.463079
$933$	1.21022	0.0396209
$934$	13.9944	0.457911
$935$	5.53223	0.180923
$936$	14.6969	0.480382
$937$	−3.75325	−0.122613	−0.0613067	−	0.998119i	$-0.519527\pi$
$937$	−3.75325	−0.122613	−0.0613067	+	0.998119i	$0.519527\pi$
$938$	2.28790	0.0747025
$939$	1.21697	0.0397143
$940$	2.04347	0.0666506
$941$	19.0974	0.622559	0.311279	−	0.950318i	$-0.399242\pi$
$941$	19.0974	0.622559	0.311279	+	0.950318i	$0.399242\pi$
$942$	1.01912	0.0332047
$943$	−7.84548	−0.255484
$944$	−1.00000	−0.0325472
$945$	0.273261	0.00888917
$946$	−71.4422	−2.32279
$947$	−47.0630	−1.52934	−0.764671	−	0.644421i	$-0.777098\pi$
$947$	−47.0630	−1.52934	−0.764671	+	0.644421i	$0.777098\pi$
$948$	0.278471	0.00904430
$949$	29.4705	0.956654
$950$	4.19167	0.135996
$951$	0.279560	0.00906537
$952$	−0.699368	−0.0226667
$953$	−33.7054	−1.09183	−0.545913	−	0.837842i	$-0.683817\pi$
$953$	−33.7054	−1.09183	−0.545913	+	0.837842i	$0.683817\pi$
$954$	−1.64311	−0.0531977
$955$	6.42063	0.207767
$956$	5.46427	0.176727
$957$	1.99619	0.0645277
$958$	−13.1405	−0.424551
$959$	−3.91172	−0.126316
$960$	−0.0651671	−0.00210326
$961$	−28.2508	−0.911318
$962$	6.27113	0.202189
$963$	45.4993	1.46619
$964$	−3.66099	−0.117913
$965$	12.3711	0.398239
$966$	0.207600	0.00667943
$967$	−1.94098	−0.0624178	−0.0312089	−	0.999513i	$-0.509936\pi$
$967$	−1.94098	−0.0624178	−0.0312089	+	0.999513i	$0.509936\pi$
$968$	−19.7514	−0.634833
$969$	−0.0683712	−0.00219640
$970$	−7.45559	−0.239385
$971$	1.63015	0.0523139	0.0261570	−	0.999658i	$-0.491673\pi$
$971$	1.63015	0.0523139	0.0261570	+	0.999658i	$0.491673\pi$
$972$	−1.76036	−0.0564634
$973$	−0.302884	−0.00971003
$974$	−22.7101	−0.727680
$975$	1.28339	0.0411012
$976$	8.29044	0.265371
$977$	−22.9790	−0.735165	−0.367582	−	0.929991i	$-0.619814\pi$
$977$	−22.9790	−0.735165	−0.367582	+	0.929991i	$0.619814\pi$
$978$	0.790278	0.0252703
$979$	77.6054	2.48028
$980$	−6.49543	−0.207489
$981$	7.35829	0.234932
$982$	4.47150	0.142691
$983$	6.87438	0.219259	0.109629	−	0.993973i	$-0.465034\pi$
$983$	6.87438	0.219259	0.109629	+	0.993973i	$0.465034\pi$
$984$	−0.112777	−0.00359518
$985$	−12.8237	−0.408598
$986$	5.51073	0.175497
$987$	−0.0935764	−0.00297857
$988$	5.13493	0.163364
$989$	58.5443	1.86160
$990$	16.5731	0.526727
$991$	−5.55424	−0.176436	−0.0882181	−	0.996101i	$-0.528117\pi$
$991$	−5.55424	−0.176436	−0.0882181	+	0.996101i	$0.528117\pi$
$992$	1.65806	0.0526434
$993$	0.283168	0.00898606
$994$	−4.20029	−0.133225
$995$	0.571718	0.0181247
$996$	1.02301	0.0324154
$997$	−17.8010	−0.563763	−0.281882	−	0.959449i	$-0.590959\pi$
$997$	−17.8010	−0.563763	−0.281882	+	0.959449i	$0.590959\pi$
$998$	−1.21751	−0.0385396
$999$	−0.500642	−0.0158396

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2006.2.a.u.1.5	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2006.2.a.u.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:	\( N \)	\(=\)	\( 2006 = 2 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2006.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.0653222 q^{3} +1.00000 q^{4} +0.997627 q^{5} +0.0653222 q^{6} +0.699368 q^{7} -1.00000 q^{8} -2.99573 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.0653222 q^{3} +1.00000 q^{4} +0.997627 q^{5} +0.0653222 q^{6} +0.699368 q^{7} -1.00000 q^{8} -2.99573 q^{9} -0.997627 q^{10} +5.54539 q^{11} -0.0653222 q^{12} +4.90594 q^{13} -0.699368 q^{14} -0.0651671 q^{15} +1.00000 q^{16} +1.00000 q^{17} +2.99573 q^{18} +1.04668 q^{19} +0.997627 q^{20} -0.0456843 q^{21} -5.54539 q^{22} +4.54424 q^{23} +0.0653222 q^{24} -4.00474 q^{25} -4.90594 q^{26} +0.391654 q^{27} +0.699368 q^{28} -5.51073 q^{29} +0.0651671 q^{30} -1.65806 q^{31} -1.00000 q^{32} -0.362237 q^{33} -1.00000 q^{34} +0.697708 q^{35} -2.99573 q^{36} -1.27827 q^{37} -1.04668 q^{38} -0.320466 q^{39} -0.997627 q^{40} -1.72647 q^{41} +0.0456843 q^{42} +12.8832 q^{43} +5.54539 q^{44} -2.98862 q^{45} -4.54424 q^{46} +2.04833 q^{47} -0.0653222 q^{48} -6.51088 q^{49} +4.00474 q^{50} -0.0653222 q^{51} +4.90594 q^{52} -0.548484 q^{53} -0.391654 q^{54} +5.53223 q^{55} -0.699368 q^{56} -0.0683712 q^{57} +5.51073 q^{58} -1.00000 q^{59} -0.0651671 q^{60} +8.29044 q^{61} +1.65806 q^{62} -2.09512 q^{63} +1.00000 q^{64} +4.89429 q^{65} +0.362237 q^{66} -3.27138 q^{67} +1.00000 q^{68} -0.296840 q^{69} -0.697708 q^{70} +6.00583 q^{71} +2.99573 q^{72} +6.00711 q^{73} +1.27827 q^{74} +0.261598 q^{75} +1.04668 q^{76} +3.87827 q^{77} +0.320466 q^{78} -4.26303 q^{79} +0.997627 q^{80} +8.96162 q^{81} +1.72647 q^{82} -15.6611 q^{83} -0.0456843 q^{84} +0.997627 q^{85} -12.8832 q^{86} +0.359973 q^{87} -5.54539 q^{88} +13.9946 q^{89} +2.98862 q^{90} +3.43106 q^{91} +4.54424 q^{92} +0.108308 q^{93} -2.04833 q^{94} +1.04419 q^{95} +0.0653222 q^{96} +7.47333 q^{97} +6.51088 q^{98} -16.6125 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - q^{3} + 9 q^{4} + 7 q^{5} + q^{6} - 9 q^{8} + 20 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 - q^3 + 9 * q^4 + 7 * q^5 + q^6 - 9 * q^8 + 20 * q^9	\( 9 q - 9 q^{2} - q^{3} + 9 q^{4} + 7 q^{5} + q^{6} - 9 q^{8} + 20 q^{9} - 7 q^{10} + 5 q^{11} - q^{12} + 25 q^{13} - 5 q^{15} + 9 q^{16} + 9 q^{17} - 20 q^{18} + 14 q^{19} + 7 q^{20} - 7 q^{21} - 5 q^{22} + 2 q^{23} + q^{24} + 20 q^{25} - 25 q^{26} - 10 q^{27} + 18 q^{29} + 5 q^{30} + 6 q^{31} - 9 q^{32} - 9 q^{33} - 9 q^{34} - 17 q^{35} + 20 q^{36} + 11 q^{37} - 14 q^{38} - 8 q^{39} - 7 q^{40} + 18 q^{41} + 7 q^{42} - 10 q^{43} + 5 q^{44} + 27 q^{45} - 2 q^{46} - 20 q^{47} - q^{48} + 13 q^{49} - 20 q^{50} - q^{51} + 25 q^{52} - 7 q^{53} + 10 q^{54} + 29 q^{55} + 17 q^{57} - 18 q^{58} - 9 q^{59} - 5 q^{60} + 30 q^{61} - 6 q^{62} - 47 q^{63} + 9 q^{64} + 8 q^{65} + 9 q^{66} + 6 q^{67} + 9 q^{68} + 20 q^{69} + 17 q^{70} + 30 q^{71} - 20 q^{72} - 11 q^{74} - 7 q^{75} + 14 q^{76} - 3 q^{77} + 8 q^{78} + 29 q^{79} + 7 q^{80} - 3 q^{81} - 18 q^{82} + 9 q^{83} - 7 q^{84} + 7 q^{85} + 10 q^{86} + 44 q^{87} - 5 q^{88} + 8 q^{89} - 27 q^{90} + 13 q^{91} + 2 q^{92} + 7 q^{93} + 20 q^{94} + 27 q^{95} + q^{96} - 13 q^{97} - 13 q^{98} - 19 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - q^3 + 9 * q^4 + 7 * q^5 + q^6 - 9 * q^8 + 20 * q^9 - 7 * q^10 + 5 * q^11 - q^12 + 25 * q^13 - 5 * q^15 + 9 * q^16 + 9 * q^17 - 20 * q^18 + 14 * q^19 + 7 * q^20 - 7 * q^21 - 5 * q^22 + 2 * q^23 + q^24 + 20 * q^25 - 25 * q^26 - 10 * q^27 + 18 * q^29 + 5 * q^30 + 6 * q^31 - 9 * q^32 - 9 * q^33 - 9 * q^34 - 17 * q^35 + 20 * q^36 + 11 * q^37 - 14 * q^38 - 8 * q^39 - 7 * q^40 + 18 * q^41 + 7 * q^42 - 10 * q^43 + 5 * q^44 + 27 * q^45 - 2 * q^46 - 20 * q^47 - q^48 + 13 * q^49 - 20 * q^50 - q^51 + 25 * q^52 - 7 * q^53 + 10 * q^54 + 29 * q^55 + 17 * q^57 - 18 * q^58 - 9 * q^59 - 5 * q^60 + 30 * q^61 - 6 * q^62 - 47 * q^63 + 9 * q^64 + 8 * q^65 + 9 * q^66 + 6 * q^67 + 9 * q^68 + 20 * q^69 + 17 * q^70 + 30 * q^71 - 20 * q^72 - 11 * q^74 - 7 * q^75 + 14 * q^76 - 3 * q^77 + 8 * q^78 + 29 * q^79 + 7 * q^80 - 3 * q^81 - 18 * q^82 + 9 * q^83 - 7 * q^84 + 7 * q^85 + 10 * q^86 + 44 * q^87 - 5 * q^88 + 8 * q^89 - 27 * q^90 + 13 * q^91 + 2 * q^92 + 7 * q^93 + 20 * q^94 + 27 * q^95 + q^96 - 13 * q^97 - 13 * q^98 - 19 * q^99

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