LMFDB - Embedded newform 2006.2.a.w.1.9

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:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 6 x^{12} - 9 x^{11} + 91 x^{10} + 14 x^{9} - 517 x^{8} + 70 x^{7} + 1296 x^{6} - 300 x^{5} + \cdots + 16 $ x^13 - 6x^12 - 9x^11 + 91x^10 + 14x^9 - 517x^8 + 70x^7 + 1296x^6 - 300x^5 - 1312x^4 + 472x^3 + 368x^2 - 176x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-0.723365$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.72336 q^{3} +1.00000 q^{4} -0.202404 q^{5} +1.72336 q^{6} +3.37958 q^{7} +1.00000 q^{8} -0.0300134 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.72336 q^{3} +1.00000 q^{4} -0.202404 q^{5} +1.72336 q^{6} +3.37958 q^{7} +1.00000 q^{8} -0.0300134 q^{9} -0.202404 q^{10} -1.77032 q^{11} +1.72336 q^{12} +6.73067 q^{13} +3.37958 q^{14} -0.348815 q^{15} +1.00000 q^{16} +1.00000 q^{17} -0.0300134 q^{18} -0.233780 q^{19} -0.202404 q^{20} +5.82424 q^{21} -1.77032 q^{22} -0.809138 q^{23} +1.72336 q^{24} -4.95903 q^{25} +6.73067 q^{26} -5.22182 q^{27} +3.37958 q^{28} -2.41052 q^{29} -0.348815 q^{30} +10.3073 q^{31} +1.00000 q^{32} -3.05091 q^{33} +1.00000 q^{34} -0.684039 q^{35} -0.0300134 q^{36} -6.77314 q^{37} -0.233780 q^{38} +11.5994 q^{39} -0.202404 q^{40} -4.20752 q^{41} +5.82424 q^{42} +0.745875 q^{43} -1.77032 q^{44} +0.00607483 q^{45} -0.809138 q^{46} -12.4215 q^{47} +1.72336 q^{48} +4.42153 q^{49} -4.95903 q^{50} +1.72336 q^{51} +6.73067 q^{52} +13.5803 q^{53} -5.22182 q^{54} +0.358319 q^{55} +3.37958 q^{56} -0.402888 q^{57} -2.41052 q^{58} +1.00000 q^{59} -0.348815 q^{60} +13.3292 q^{61} +10.3073 q^{62} -0.101433 q^{63} +1.00000 q^{64} -1.36231 q^{65} -3.05091 q^{66} -5.61566 q^{67} +1.00000 q^{68} -1.39444 q^{69} -0.684039 q^{70} +4.68873 q^{71} -0.0300134 q^{72} -10.1965 q^{73} -6.77314 q^{74} -8.54622 q^{75} -0.233780 q^{76} -5.98293 q^{77} +11.5994 q^{78} +17.0967 q^{79} -0.202404 q^{80} -8.90906 q^{81} -4.20752 q^{82} +2.05930 q^{83} +5.82424 q^{84} -0.202404 q^{85} +0.745875 q^{86} -4.15421 q^{87} -1.77032 q^{88} -4.78948 q^{89} +0.00607483 q^{90} +22.7468 q^{91} -0.809138 q^{92} +17.7633 q^{93} -12.4215 q^{94} +0.0473180 q^{95} +1.72336 q^{96} +0.818602 q^{97} +4.42153 q^{98} +0.0531334 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 13 q^{2} + 7 q^{3} + 13 q^{4} + q^{5} + 7 q^{6} + 8 q^{7} + 13 q^{8} + 16 q^{9}+O(q^{10}) $ 13 * q + 13 * q^2 + 7 * q^3 + 13 * q^4 + q^5 + 7 * q^6 + 8 * q^7 + 13 * q^8 + 16 * q^9	\( 13 q + 13 q^{2} + 7 q^{3} + 13 q^{4} + q^{5} + 7 q^{6} + 8 q^{7} + 13 q^{8} + 16 q^{9} + q^{10} + 13 q^{11} + 7 q^{12} + 9 q^{13} + 8 q^{14} - 9 q^{15} + 13 q^{16} + 13 q^{17} + 16 q^{18} + 16 q^{19} + q^{20} - 3 q^{21} + 13 q^{22} + 18 q^{23} + 7 q^{24} + 14 q^{25} + 9 q^{26} + 10 q^{27} + 8 q^{28} + 8 q^{29} - 9 q^{30} + 32 q^{31} + 13 q^{32} + 13 q^{33} + 13 q^{34} - q^{35} + 16 q^{36} - 3 q^{37} + 16 q^{38} + 20 q^{39} + q^{40} + 24 q^{41} - 3 q^{42} - 2 q^{43} + 13 q^{44} - 3 q^{45} + 18 q^{46} + 26 q^{47} + 7 q^{48} + 23 q^{49} + 14 q^{50} + 7 q^{51} + 9 q^{52} - 27 q^{53} + 10 q^{54} - 7 q^{55} + 8 q^{56} - 21 q^{57} + 8 q^{58} + 13 q^{59} - 9 q^{60} + 20 q^{61} + 32 q^{62} - 3 q^{63} + 13 q^{64} + 16 q^{65} + 13 q^{66} + 4 q^{67} + 13 q^{68} - 2 q^{69} - q^{70} - 8 q^{71} + 16 q^{72} + 10 q^{73} - 3 q^{74} + 39 q^{75} + 16 q^{76} - 15 q^{77} + 20 q^{78} + 35 q^{79} + q^{80} + 29 q^{81} + 24 q^{82} - q^{83} - 3 q^{84} + q^{85} - 2 q^{86} - 32 q^{87} + 13 q^{88} - 20 q^{89} - 3 q^{90} - 15 q^{91} + 18 q^{92} - 7 q^{93} + 26 q^{94} - 3 q^{95} + 7 q^{96} - 3 q^{97} + 23 q^{98} + 65 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 7 * q^3 + 13 * q^4 + q^5 + 7 * q^6 + 8 * q^7 + 13 * q^8 + 16 * q^9 + q^10 + 13 * q^11 + 7 * q^12 + 9 * q^13 + 8 * q^14 - 9 * q^15 + 13 * q^16 + 13 * q^17 + 16 * q^18 + 16 * q^19 + q^20 - 3 * q^21 + 13 * q^22 + 18 * q^23 + 7 * q^24 + 14 * q^25 + 9 * q^26 + 10 * q^27 + 8 * q^28 + 8 * q^29 - 9 * q^30 + 32 * q^31 + 13 * q^32 + 13 * q^33 + 13 * q^34 - q^35 + 16 * q^36 - 3 * q^37 + 16 * q^38 + 20 * q^39 + q^40 + 24 * q^41 - 3 * q^42 - 2 * q^43 + 13 * q^44 - 3 * q^45 + 18 * q^46 + 26 * q^47 + 7 * q^48 + 23 * q^49 + 14 * q^50 + 7 * q^51 + 9 * q^52 - 27 * q^53 + 10 * q^54 - 7 * q^55 + 8 * q^56 - 21 * q^57 + 8 * q^58 + 13 * q^59 - 9 * q^60 + 20 * q^61 + 32 * q^62 - 3 * q^63 + 13 * q^64 + 16 * q^65 + 13 * q^66 + 4 * q^67 + 13 * q^68 - 2 * q^69 - q^70 - 8 * q^71 + 16 * q^72 + 10 * q^73 - 3 * q^74 + 39 * q^75 + 16 * q^76 - 15 * q^77 + 20 * q^78 + 35 * q^79 + q^80 + 29 * q^81 + 24 * q^82 - q^83 - 3 * q^84 + q^85 - 2 * q^86 - 32 * q^87 + 13 * q^88 - 20 * q^89 - 3 * q^90 - 15 * q^91 + 18 * q^92 - 7 * q^93 + 26 * q^94 - 3 * q^95 + 7 * q^96 - 3 * q^97 + 23 * q^98 + 65 * 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
$3$	1.72336	0.994985	0.497493	−	0.867468i	$-0.334254\pi$
$3$	1.72336	0.994985	0.497493	+	0.867468i	$0.334254\pi$
$4$	1.00000	0.500000
$5$	−0.202404	−0.0905177	−0.0452588	−	0.998975i	$-0.514411\pi$
$5$	−0.202404	−0.0905177	−0.0452588	+	0.998975i	$0.514411\pi$
$6$	1.72336	0.703561
$7$	3.37958	1.27736	0.638680	−	0.769473i	$-0.279481\pi$
$7$	3.37958	1.27736	0.638680	+	0.769473i	$0.279481\pi$
$8$	1.00000	0.353553
$9$	−0.0300134	−0.0100045
$10$	−0.202404	−0.0640057
$11$	−1.77032	−0.533771	−0.266886	−	0.963728i	$-0.585995\pi$
$11$	−1.77032	−0.533771	−0.266886	+	0.963728i	$0.585995\pi$
$12$	1.72336	0.497493
$13$	6.73067	1.86675	0.933376	−	0.358900i	$-0.116848\pi$
$13$	6.73067	1.86675	0.933376	+	0.358900i	$0.116848\pi$
$14$	3.37958	0.903229
$15$	−0.348815	−0.0900638
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.0300134	−0.00707424
$19$	−0.233780	−0.0536328	−0.0268164	−	0.999640i	$-0.508537\pi$
$19$	−0.233780	−0.0536328	−0.0268164	+	0.999640i	$0.508537\pi$
$20$	−0.202404	−0.0452588
$21$	5.82424	1.27095
$22$	−1.77032	−0.377433
$23$	−0.809138	−0.168717	−0.0843584	−	0.996435i	$-0.526884\pi$
$23$	−0.809138	−0.168717	−0.0843584	+	0.996435i	$0.526884\pi$
$24$	1.72336	0.351780
$25$	−4.95903	−0.991807
$26$	6.73067	1.31999
$27$	−5.22182	−1.00494
$28$	3.37958	0.638680
$29$	−2.41052	−0.447623	−0.223812	−	0.974632i	$-0.571850\pi$
$29$	−2.41052	−0.447623	−0.223812	+	0.974632i	$0.571850\pi$
$30$	−0.348815	−0.0636847
$31$	10.3073	1.85125	0.925624	−	0.378445i	$-0.123541\pi$
$31$	10.3073	1.85125	0.925624	+	0.378445i	$0.123541\pi$
$32$	1.00000	0.176777
$33$	−3.05091	−0.531094
$34$	1.00000	0.171499
$35$	−0.684039	−0.115624
$36$	−0.0300134	−0.00500224
$37$	−6.77314	−1.11350	−0.556749	−	0.830681i	$-0.687951\pi$
$37$	−6.77314	−1.11350	−0.556749	+	0.830681i	$0.687951\pi$
$38$	−0.233780	−0.0379241
$39$	11.5994	1.85739
$40$	−0.202404	−0.0320028
$41$	−4.20752	−0.657104	−0.328552	−	0.944486i	$-0.606561\pi$
$41$	−4.20752	−0.657104	−0.328552	+	0.944486i	$0.606561\pi$
$42$	5.82424	0.898700
$43$	0.745875	0.113745	0.0568724	−	0.998381i	$-0.481887\pi$
$43$	0.745875	0.113745	0.0568724	+	0.998381i	$0.481887\pi$
$44$	−1.77032	−0.266886
$45$	0.00607483	0.000905583 0
$46$	−0.809138	−0.119301
$47$	−12.4215	−1.81186	−0.905928	−	0.423432i	$-0.860825\pi$
$47$	−12.4215	−1.81186	−0.905928	+	0.423432i	$0.860825\pi$
$48$	1.72336	0.248746
$49$	4.42153	0.631647
$50$	−4.95903	−0.701313
$51$	1.72336	0.241319
$52$	6.73067	0.933376
$53$	13.5803	1.86540	0.932698	−	0.360659i	$-0.117448\pi$
$53$	13.5803	1.86540	0.932698	+	0.360659i	$0.117448\pi$
$54$	−5.22182	−0.710600
$55$	0.358319	0.0483157
$56$	3.37958	0.451615
$57$	−0.402888	−0.0533639
$58$	−2.41052	−0.316517
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−0.348815	−0.0450319
$61$	13.3292	1.70663	0.853317	−	0.521392i	$-0.174587\pi$
$61$	13.3292	1.70663	0.853317	+	0.521392i	$0.174587\pi$
$62$	10.3073	1.30903
$63$	−0.101433	−0.0127793
$64$	1.00000	0.125000
$65$	−1.36231	−0.168974
$66$	−3.05091	−0.375541
$67$	−5.61566	−0.686063	−0.343031	−	0.939324i	$-0.611454\pi$
$67$	−5.61566	−0.686063	−0.343031	+	0.939324i	$0.611454\pi$
$68$	1.00000	0.121268
$69$	−1.39444	−0.167871
$70$	−0.684039	−0.0817582
$71$	4.68873	0.556450	0.278225	−	0.960516i	$-0.410254\pi$
$71$	4.68873	0.556450	0.278225	+	0.960516i	$0.410254\pi$
$72$	−0.0300134	−0.00353712
$73$	−10.1965	−1.19341	−0.596705	−	0.802461i	$-0.703524\pi$
$73$	−10.1965	−1.19341	−0.596705	+	0.802461i	$0.703524\pi$
$74$	−6.77314	−0.787362
$75$	−8.54622	−0.986833
$76$	−0.233780	−0.0268164
$77$	−5.98293	−0.681818
$78$	11.5994	1.31337
$79$	17.0967	1.92353	0.961765	−	0.273877i	$-0.0883061\pi$
$79$	17.0967	1.92353	0.961765	+	0.273877i	$0.0883061\pi$
$80$	−0.202404	−0.0226294
$81$	−8.90906	−0.989895
$82$	−4.20752	−0.464643
$83$	2.05930	0.226038	0.113019	−	0.993593i	$-0.463948\pi$
$83$	2.05930	0.226038	0.113019	+	0.993593i	$0.463948\pi$
$84$	5.82424	0.635477
$85$	−0.202404	−0.0219538
$86$	0.745875	0.0804298
$87$	−4.15421	−0.445378
$88$	−1.77032	−0.188717
$89$	−4.78948	−0.507684	−0.253842	−	0.967246i	$-0.581694\pi$
$89$	−4.78948	−0.507684	−0.253842	+	0.967246i	$0.581694\pi$
$90$	0.00607483	0.000640344 0
$91$	22.7468	2.38451
$92$	−0.809138	−0.0843584
$93$	17.7633	1.84196
$94$	−12.4215	−1.28118
$95$	0.0473180	0.00485472
$96$	1.72336	0.175890
$97$	0.818602	0.0831165	0.0415582	−	0.999136i	$-0.486768\pi$
$97$	0.818602	0.0831165	0.0415582	+	0.999136i	$0.486768\pi$
$98$	4.42153	0.446642
$99$	0.0531334	0.00534010
$100$	−4.95903	−0.495903
$101$	−3.80112	−0.378225	−0.189113	−	0.981955i	$-0.560561\pi$
$101$	−3.80112	−0.378225	−0.189113	+	0.981955i	$0.560561\pi$
$102$	1.72336	0.170639
$103$	−6.17395	−0.608337	−0.304169	−	0.952618i	$-0.598379\pi$
$103$	−6.17395	−0.608337	−0.304169	+	0.952618i	$0.598379\pi$
$104$	6.73067	0.659996
$105$	−1.17885	−0.115044
$106$	13.5803	1.31903
$107$	−12.2110	−1.18048	−0.590240	−	0.807228i	$-0.700967\pi$
$107$	−12.2110	−1.18048	−0.590240	+	0.807228i	$0.700967\pi$
$108$	−5.22182	−0.502470
$109$	−8.05526	−0.771554	−0.385777	−	0.922592i	$-0.626067\pi$
$109$	−8.05526	−0.771554	−0.385777	+	0.922592i	$0.626067\pi$
$110$	0.358319	0.0341644
$111$	−11.6726	−1.10791
$112$	3.37958	0.319340
$113$	11.4258	1.07485	0.537425	−	0.843312i	$-0.319397\pi$
$113$	11.4258	1.07485	0.537425	+	0.843312i	$0.319397\pi$
$114$	−0.402888	−0.0377340
$115$	0.163772	0.0152719
$116$	−2.41052	−0.223812
$117$	−0.202011	−0.0186759
$118$	1.00000	0.0920575
$119$	3.37958	0.309805
$120$	−0.348815	−0.0318424
$121$	−7.86597	−0.715088
$122$	13.3292	1.20677
$123$	−7.25109	−0.653809
$124$	10.3073	0.925624
$125$	2.01575	0.180294
$126$	−0.101433	−0.00903634
$127$	9.37371	0.831782	0.415891	−	0.909414i	$-0.363470\pi$
$127$	9.37371	0.831782	0.415891	+	0.909414i	$0.363470\pi$
$128$	1.00000	0.0883883
$129$	1.28541	0.113174
$130$	−1.36231	−0.119483
$131$	−21.2005	−1.85230	−0.926148	−	0.377160i	$-0.876901\pi$
$131$	−21.2005	−1.85230	−0.926148	+	0.377160i	$0.876901\pi$
$132$	−3.05091	−0.265547
$133$	−0.790077	−0.0685084
$134$	−5.61566	−0.485120
$135$	1.05692	0.0909648
$136$	1.00000	0.0857493
$137$	−10.6167	−0.907044	−0.453522	−	0.891245i	$-0.649833\pi$
$137$	−10.6167	−0.907044	−0.453522	+	0.891245i	$0.649833\pi$
$138$	−1.39444	−0.118703
$139$	−9.39808	−0.797134	−0.398567	−	0.917139i	$-0.630492\pi$
$139$	−9.39808	−0.797134	−0.398567	+	0.917139i	$0.630492\pi$
$140$	−0.684039	−0.0578118
$141$	−21.4067	−1.80277
$142$	4.68873	0.393470
$143$	−11.9154	−0.996418
$144$	−0.0300134	−0.00250112
$145$	0.487899	0.0405178
$146$	−10.1965	−0.843868
$147$	7.61991	0.628479
$148$	−6.77314	−0.556749
$149$	9.52791	0.780557	0.390278	−	0.920697i	$-0.372379\pi$
$149$	9.52791	0.780557	0.390278	+	0.920697i	$0.372379\pi$
$150$	−8.54622	−0.697796
$151$	2.64460	0.215215	0.107607	−	0.994193i	$-0.465681\pi$
$151$	2.64460	0.215215	0.107607	+	0.994193i	$0.465681\pi$
$152$	−0.233780	−0.0189621
$153$	−0.0300134	−0.00242644
$154$	−5.98293	−0.482118
$155$	−2.08624	−0.167571
$156$	11.5994	0.928695
$157$	3.29974	0.263348	0.131674	−	0.991293i	$-0.457965\pi$
$157$	3.29974	0.263348	0.131674	+	0.991293i	$0.457965\pi$
$158$	17.0967	1.36014
$159$	23.4038	1.85604
$160$	−0.202404	−0.0160014
$161$	−2.73454	−0.215512
$162$	−8.90906	−0.699962
$163$	4.14267	0.324479	0.162239	−	0.986751i	$-0.448128\pi$
$163$	4.14267	0.324479	0.162239	+	0.986751i	$0.448128\pi$
$164$	−4.20752	−0.328552
$165$	0.617515	0.0480735
$166$	2.05930	0.159833
$167$	4.85066	0.375356	0.187678	−	0.982231i	$-0.439904\pi$
$167$	4.85066	0.375356	0.187678	+	0.982231i	$0.439904\pi$
$168$	5.82424	0.449350
$169$	32.3019	2.48476
$170$	−0.202404	−0.0155237
$171$	0.00701655	0.000536569 0
$172$	0.745875	0.0568724
$173$	−4.44497	−0.337945	−0.168972	−	0.985621i	$-0.554045\pi$
$173$	−4.44497	−0.337945	−0.168972	+	0.985621i	$0.554045\pi$
$174$	−4.15421	−0.314930
$175$	−16.7594	−1.26689
$176$	−1.77032	−0.133443
$177$	1.72336	0.129536
$178$	−4.78948	−0.358987
$179$	−4.68196	−0.349946	−0.174973	−	0.984573i	$-0.555984\pi$
$179$	−4.68196	−0.349946	−0.174973	+	0.984573i	$0.555984\pi$
$180$	0.00607483	0.000452791 0
$181$	12.9820	0.964944	0.482472	−	0.875911i	$-0.339739\pi$
$181$	12.9820	0.964944	0.482472	+	0.875911i	$0.339739\pi$
$182$	22.7468	1.68611
$183$	22.9711	1.69808
$184$	−0.809138	−0.0596504
$185$	1.37091	0.100791
$186$	17.7633	1.30247
$187$	−1.77032	−0.129459
$188$	−12.4215	−0.905928
$189$	−17.6475	−1.28367
$190$	0.0473180	0.00343281
$191$	−16.7659	−1.21314	−0.606570	−	0.795030i	$-0.707455\pi$
$191$	−16.7659	−1.21314	−0.606570	+	0.795030i	$0.707455\pi$
$192$	1.72336	0.124373
$193$	−23.8996	−1.72033	−0.860164	−	0.510017i	$-0.829639\pi$
$193$	−23.8996	−1.72033	−0.860164	+	0.510017i	$0.829639\pi$
$194$	0.818602	0.0587722
$195$	−2.34776	−0.168127
$196$	4.42153	0.315823
$197$	−0.679540	−0.0484153	−0.0242076	−	0.999707i	$-0.507706\pi$
$197$	−0.679540	−0.0484153	−0.0242076	+	0.999707i	$0.507706\pi$
$198$	0.0531334	0.00377602
$199$	−18.7667	−1.33034	−0.665170	−	0.746692i	$-0.731641\pi$
$199$	−18.7667	−1.33034	−0.665170	+	0.746692i	$0.731641\pi$
$200$	−4.95903	−0.350657
$201$	−9.67784	−0.682622
$202$	−3.80112	−0.267446
$203$	−8.14655	−0.571775
$204$	1.72336	0.120660
$205$	0.851617	0.0594795
$206$	−6.17395	−0.430159
$207$	0.0242850	0.00168792
$208$	6.73067	0.466688
$209$	0.413865	0.0286277
$210$	−1.17885	−0.0813482
$211$	25.9499	1.78647	0.893233	−	0.449594i	$-0.148431\pi$
$211$	25.9499	1.78647	0.893233	+	0.449594i	$0.148431\pi$
$212$	13.5803	0.932698
$213$	8.08040	0.553660
$214$	−12.2110	−0.834726
$215$	−0.150968	−0.0102959
$216$	−5.22182	−0.355300
$217$	34.8343	2.36471
$218$	−8.05526	−0.545571
$219$	−17.5723	−1.18742
$220$	0.358319	0.0241579
$221$	6.73067	0.452754
$222$	−11.6726	−0.783413
$223$	−0.876370	−0.0586861	−0.0293430	−	0.999569i	$-0.509342\pi$
$223$	−0.876370	−0.0586861	−0.0293430	+	0.999569i	$0.509342\pi$
$224$	3.37958	0.225807
$225$	0.148838	0.00992251
$226$	11.4258	0.760034
$227$	−10.1582	−0.674221	−0.337111	−	0.941465i	$-0.609450\pi$
$227$	−10.1582	−0.674221	−0.337111	+	0.941465i	$0.609450\pi$
$228$	−0.402888	−0.0266819
$229$	−7.20036	−0.475813	−0.237907	−	0.971288i	$-0.576461\pi$
$229$	−7.20036	−0.475813	−0.237907	+	0.971288i	$0.576461\pi$
$230$	0.163772	0.0107988
$231$	−10.3108	−0.678399
$232$	−2.41052	−0.158259
$233$	−0.298971	−0.0195863	−0.00979313	−	0.999952i	$-0.503117\pi$
$233$	−0.298971	−0.0195863	−0.00979313	+	0.999952i	$0.503117\pi$
$234$	−0.202011	−0.0132058
$235$	2.51415	0.164005
$236$	1.00000	0.0650945
$237$	29.4639	1.91388
$238$	3.37958	0.219065
$239$	−4.40063	−0.284653	−0.142327	−	0.989820i	$-0.545458\pi$
$239$	−4.40063	−0.284653	−0.142327	+	0.989820i	$0.545458\pi$
$240$	−0.348815	−0.0225159
$241$	−9.32096	−0.600416	−0.300208	−	0.953874i	$-0.597056\pi$
$241$	−9.32096	−0.600416	−0.300208	+	0.953874i	$0.597056\pi$
$242$	−7.86597	−0.505644
$243$	0.311897	0.0200082
$244$	13.3292	0.853317
$245$	−0.894934	−0.0571752
$246$	−7.25109	−0.462312
$247$	−1.57350	−0.100119
$248$	10.3073	0.654515
$249$	3.54893	0.224904
$250$	2.01575	0.127487
$251$	−17.7295	−1.11908	−0.559538	−	0.828805i	$-0.689021\pi$
$251$	−17.7295	−1.11908	−0.559538	+	0.828805i	$0.689021\pi$
$252$	−0.101433	−0.00638966
$253$	1.43243	0.0900562
$254$	9.37371	0.588159
$255$	−0.348815	−0.0218437
$256$	1.00000	0.0625000
$257$	6.94855	0.433439	0.216719	−	0.976234i	$-0.430464\pi$
$257$	6.94855	0.433439	0.216719	+	0.976234i	$0.430464\pi$
$258$	1.28541	0.0800264
$259$	−22.8903	−1.42234
$260$	−1.36231	−0.0844870
$261$	0.0723481	0.00447824
$262$	−21.2005	−1.30977
$263$	−1.21462	−0.0748966	−0.0374483	−	0.999299i	$-0.511923\pi$
$263$	−1.21462	−0.0748966	−0.0374483	+	0.999299i	$0.511923\pi$
$264$	−3.05091	−0.187770
$265$	−2.74870	−0.168851
$266$	−0.790077	−0.0484428
$267$	−8.25403	−0.505138
$268$	−5.61566	−0.343031
$269$	−22.8965	−1.39602	−0.698012	−	0.716086i	$-0.745932\pi$
$269$	−22.8965	−1.39602	−0.698012	+	0.716086i	$0.745932\pi$
$270$	1.05692	0.0643218
$271$	−8.09194	−0.491550	−0.245775	−	0.969327i	$-0.579042\pi$
$271$	−8.09194	−0.491550	−0.245775	+	0.969327i	$0.579042\pi$
$272$	1.00000	0.0606339
$273$	39.2010	2.37255
$274$	−10.6167	−0.641377
$275$	8.77907	0.529398
$276$	−1.39444	−0.0839354
$277$	21.4575	1.28925	0.644627	−	0.764497i	$-0.277013\pi$
$277$	21.4575	1.28925	0.644627	+	0.764497i	$0.277013\pi$
$278$	−9.39808	−0.563659
$279$	−0.309358	−0.0185208
$280$	−0.684039	−0.0408791
$281$	−2.96913	−0.177123	−0.0885617	−	0.996071i	$-0.528227\pi$
$281$	−2.96913	−0.177123	−0.0885617	+	0.996071i	$0.528227\pi$
$282$	−21.4067	−1.27475
$283$	−1.85751	−0.110418	−0.0552088	−	0.998475i	$-0.517582\pi$
$283$	−1.85751	−0.110418	−0.0552088	+	0.998475i	$0.517582\pi$
$284$	4.68873	0.278225
$285$	0.0815461	0.00483038
$286$	−11.9154	−0.704574
$287$	−14.2196	−0.839358
$288$	−0.0300134	−0.00176856
$289$	1.00000	0.0588235
$290$	0.487899	0.0286504
$291$	1.41075	0.0826997
$292$	−10.1965	−0.596705
$293$	6.87977	0.401920	0.200960	−	0.979599i	$-0.435594\pi$
$293$	6.87977	0.401920	0.200960	+	0.979599i	$0.435594\pi$
$294$	7.61991	0.444402
$295$	−0.202404	−0.0117844
$296$	−6.77314	−0.393681
$297$	9.24428	0.536408
$298$	9.52791	0.551937
$299$	−5.44604	−0.314952
$300$	−8.54622	−0.493416
$301$	2.52074	0.145293
$302$	2.64460	0.152180
$303$	−6.55072	−0.376329
$304$	−0.233780	−0.0134082
$305$	−2.69789	−0.154481
$306$	−0.0300134	−0.00171575
$307$	−29.8065	−1.70115	−0.850574	−	0.525855i	$-0.823745\pi$
$307$	−29.8065	−1.70115	−0.850574	+	0.525855i	$0.823745\pi$
$308$	−5.98293	−0.340909
$309$	−10.6400	−0.605286
$310$	−2.08624	−0.118490
$311$	−10.7925	−0.611989	−0.305995	−	0.952033i	$-0.598989\pi$
$311$	−10.7925	−0.611989	−0.305995	+	0.952033i	$0.598989\pi$
$312$	11.5994	0.656687
$313$	−1.41103	−0.0797559	−0.0398779	−	0.999205i	$-0.512697\pi$
$313$	−1.41103	−0.0797559	−0.0398779	+	0.999205i	$0.512697\pi$
$314$	3.29974	0.186215
$315$	0.0205304	0.00115675
$316$	17.0967	0.961765
$317$	9.87268	0.554505	0.277253	−	0.960797i	$-0.410576\pi$
$317$	9.87268	0.554505	0.277253	+	0.960797i	$0.410576\pi$
$318$	23.4038	1.31242
$319$	4.26740	0.238928
$320$	−0.202404	−0.0113147
$321$	−21.0440	−1.17456
$322$	−2.73454	−0.152390
$323$	−0.233780	−0.0130079
$324$	−8.90906	−0.494948
$325$	−33.3776	−1.85146
$326$	4.14267	0.229441
$327$	−13.8822	−0.767685
$328$	−4.20752	−0.232321
$329$	−41.9793	−2.31439
$330$	0.617515	0.0339931
$331$	−10.2731	−0.564662	−0.282331	−	0.959317i	$-0.591108\pi$
$331$	−10.2731	−0.564662	−0.282331	+	0.959317i	$0.591108\pi$
$332$	2.05930	0.113019
$333$	0.203285	0.0111400
$334$	4.85066	0.265417
$335$	1.13663	0.0621008
$336$	5.82424	0.317738
$337$	21.1608	1.15270	0.576351	−	0.817203i	$-0.304476\pi$
$337$	21.1608	1.15270	0.576351	+	0.817203i	$0.304476\pi$
$338$	32.3019	1.75699
$339$	19.6908	1.06946
$340$	−0.202404	−0.0109769
$341$	−18.2472	−0.988143
$342$	0.00701655	0.000379411 0
$343$	−8.71414	−0.470519
$344$	0.745875	0.0402149
$345$	0.282240	0.0151953
$346$	−4.44497	−0.238963
$347$	−6.44928	−0.346215	−0.173108	−	0.984903i	$-0.555381\pi$
$347$	−6.44928	−0.346215	−0.173108	+	0.984903i	$0.555381\pi$
$348$	−4.15421	−0.222689
$349$	16.0643	0.859904	0.429952	−	0.902852i	$-0.358530\pi$
$349$	16.0643	0.859904	0.429952	+	0.902852i	$0.358530\pi$
$350$	−16.7594	−0.895829
$351$	−35.1463	−1.87597
$352$	−1.77032	−0.0943583
$353$	27.4287	1.45988	0.729942	−	0.683509i	$-0.239547\pi$
$353$	27.4287	1.45988	0.729942	+	0.683509i	$0.239547\pi$
$354$	1.72336	0.0915958
$355$	−0.949017	−0.0503686
$356$	−4.78948	−0.253842
$357$	5.82424	0.308252
$358$	−4.68196	−0.247449
$359$	30.4418	1.60666	0.803328	−	0.595537i	$-0.203061\pi$
$359$	30.4418	1.60666	0.803328	+	0.595537i	$0.203061\pi$
$360$	0.00607483	0.000320172 0
$361$	−18.9453	−0.997124
$362$	12.9820	0.682318
$363$	−13.5559	−0.711502
$364$	22.7468	1.19226
$365$	2.06381	0.108025
$366$	22.9711	1.20072
$367$	29.8549	1.55841	0.779207	−	0.626767i	$-0.215622\pi$
$367$	29.8549	1.55841	0.779207	+	0.626767i	$0.215622\pi$
$368$	−0.809138	−0.0421792
$369$	0.126282	0.00657398
$370$	1.37091	0.0712702
$371$	45.8956	2.38278
$372$	17.7633	0.920982
$373$	−25.9234	−1.34226	−0.671131	−	0.741338i	$-0.734191\pi$
$373$	−25.9234	−1.34226	−0.671131	+	0.741338i	$0.734191\pi$
$374$	−1.77032	−0.0915410
$375$	3.47386	0.179390
$376$	−12.4215	−0.640588
$377$	−16.2244	−0.835601
$378$	−17.6475	−0.907691
$379$	−5.29048	−0.271754	−0.135877	−	0.990726i	$-0.543385\pi$
$379$	−5.29048	−0.271754	−0.135877	+	0.990726i	$0.543385\pi$
$380$	0.0473180	0.00242736
$381$	16.1543	0.827611
$382$	−16.7659	−0.857820
$383$	27.9237	1.42684	0.713418	−	0.700738i	$-0.247146\pi$
$383$	27.9237	1.42684	0.713418	+	0.700738i	$0.247146\pi$
$384$	1.72336	0.0879451
$385$	1.21097	0.0617166
$386$	−23.8996	−1.21646
$387$	−0.0223863	−0.00113796
$388$	0.818602	0.0415582
$389$	−16.5097	−0.837073	−0.418536	−	0.908200i	$-0.637457\pi$
$389$	−16.5097	−0.837073	−0.418536	+	0.908200i	$0.637457\pi$
$390$	−2.34776	−0.118884
$391$	−0.809138	−0.0409198
$392$	4.42153	0.223321
$393$	−36.5362	−1.84301
$394$	−0.679540	−0.0342348
$395$	−3.46044	−0.174113
$396$	0.0531334	0.00267005
$397$	−23.5991	−1.18441	−0.592203	−	0.805788i	$-0.701742\pi$
$397$	−23.5991	−1.18441	−0.592203	+	0.805788i	$0.701742\pi$
$398$	−18.7667	−0.940692
$399$	−1.36159	−0.0681649
$400$	−4.95903	−0.247952
$401$	16.3761	0.817781	0.408891	−	0.912583i	$-0.365916\pi$
$401$	16.3761	0.817781	0.408891	+	0.912583i	$0.365916\pi$
$402$	−9.67784	−0.482687
$403$	69.3751	3.45582
$404$	−3.80112	−0.189113
$405$	1.80323	0.0896031
$406$	−8.14655	−0.404306
$407$	11.9906	0.594353
$408$	1.72336	0.0853193
$409$	−11.2194	−0.554762	−0.277381	−	0.960760i	$-0.589466\pi$
$409$	−11.2194	−0.554762	−0.277381	+	0.960760i	$0.589466\pi$
$410$	0.851617	0.0420584
$411$	−18.2964	−0.902495
$412$	−6.17395	−0.304169
$413$	3.37958	0.166298
$414$	0.0242850	0.00119354
$415$	−0.416810	−0.0204604
$416$	6.73067	0.329998
$417$	−16.1963	−0.793137
$418$	0.413865	0.0202428
$419$	30.0900	1.46999	0.734997	−	0.678070i	$-0.237184\pi$
$419$	30.0900	1.46999	0.734997	+	0.678070i	$0.237184\pi$
$420$	−1.17885	−0.0575219
$421$	15.6995	0.765144	0.382572	−	0.923926i	$-0.375038\pi$
$421$	15.6995	0.765144	0.382572	+	0.923926i	$0.375038\pi$
$422$	25.9499	1.26322
$423$	0.372811	0.0181267
$424$	13.5803	0.659517
$425$	−4.95903	−0.240548
$426$	8.08040	0.391496
$427$	45.0472	2.17998
$428$	−12.2110	−0.590240
$429$	−20.5346	−0.991422
$430$	−0.150968	−0.00728032
$431$	−14.4725	−0.697117	−0.348559	−	0.937287i	$-0.613329\pi$
$431$	−14.4725	−0.697117	−0.348559	+	0.937287i	$0.613329\pi$
$432$	−5.22182	−0.251235
$433$	8.12502	0.390463	0.195232	−	0.980757i	$-0.437454\pi$
$433$	8.12502	0.390463	0.195232	+	0.980757i	$0.437454\pi$
$434$	34.8343	1.67210
$435$	0.840828	0.0403146
$436$	−8.05526	−0.385777
$437$	0.189160	0.00904876
$438$	−17.5723	−0.839636
$439$	7.01469	0.334793	0.167396	−	0.985890i	$-0.446464\pi$
$439$	7.01469	0.334793	0.167396	+	0.985890i	$0.446464\pi$
$440$	0.358319	0.0170822
$441$	−0.132705	−0.00631930
$442$	6.73067	0.320145
$443$	20.0117	0.950783	0.475391	−	0.879774i	$-0.342306\pi$
$443$	20.0117	0.950783	0.475391	+	0.879774i	$0.342306\pi$
$444$	−11.6726	−0.553957
$445$	0.969409	0.0459544
$446$	−0.876370	−0.0414973
$447$	16.4201	0.776643
$448$	3.37958	0.159670
$449$	−19.6816	−0.928832	−0.464416	−	0.885617i	$-0.653736\pi$
$449$	−19.6816	−0.928832	−0.464416	+	0.885617i	$0.653736\pi$
$450$	0.148838	0.00701627
$451$	7.44865	0.350743
$452$	11.4258	0.537425
$453$	4.55762	0.214136
$454$	−10.1582	−0.476747
$455$	−4.60404	−0.215841
$456$	−0.402888	−0.0188670
$457$	−28.1126	−1.31505	−0.657525	−	0.753432i	$-0.728397\pi$
$457$	−28.1126	−1.31505	−0.657525	+	0.753432i	$0.728397\pi$
$458$	−7.20036	−0.336451
$459$	−5.22182	−0.243734
$460$	0.163772	0.00763593
$461$	15.2111	0.708451	0.354226	−	0.935160i	$-0.384745\pi$
$461$	15.2111	0.708451	0.354226	+	0.935160i	$0.384745\pi$
$462$	−10.3108	−0.479700
$463$	12.5389	0.582734	0.291367	−	0.956611i	$-0.405890\pi$
$463$	12.5389	0.582734	0.291367	+	0.956611i	$0.405890\pi$
$464$	−2.41052	−0.111906
$465$	−3.59535	−0.166730
$466$	−0.298971	−0.0138496
$467$	35.4609	1.64093	0.820467	−	0.571694i	$-0.193713\pi$
$467$	35.4609	1.64093	0.820467	+	0.571694i	$0.193713\pi$
$468$	−0.202011	−0.00933794
$469$	−18.9786	−0.876348
$470$	2.51415	0.115969
$471$	5.68666	0.262027
$472$	1.00000	0.0460287
$473$	−1.32044	−0.0607138
$474$	29.4639	1.35332
$475$	1.15932	0.0531934
$476$	3.37958	0.154903
$477$	−0.407591	−0.0186623
$478$	−4.40063	−0.201280
$479$	19.7843	0.903969	0.451985	−	0.892026i	$-0.350716\pi$
$479$	19.7843	0.903969	0.451985	+	0.892026i	$0.350716\pi$
$480$	−0.348815	−0.0159212
$481$	−45.5878	−2.07862
$482$	−9.32096	−0.424558
$483$	−4.71261	−0.214431
$484$	−7.86597	−0.357544
$485$	−0.165688	−0.00752351
$486$	0.311897	0.0141479
$487$	21.0468	0.953721	0.476860	−	0.878979i	$-0.341775\pi$
$487$	21.0468	0.953721	0.476860	+	0.878979i	$0.341775\pi$
$488$	13.3292	0.603386
$489$	7.13933	0.322851
$490$	−0.894934	−0.0404290
$491$	12.3112	0.555595	0.277798	−	0.960640i	$-0.410396\pi$
$491$	12.3112	0.555595	0.277798	+	0.960640i	$0.410396\pi$
$492$	−7.25109	−0.326904
$493$	−2.41052	−0.108565
$494$	−1.57350	−0.0707950
$495$	−0.0107544	−0.000483374 0
$496$	10.3073	0.462812
$497$	15.8459	0.710787
$498$	3.54893	0.159031
$499$	20.1986	0.904213	0.452106	−	0.891964i	$-0.350673\pi$
$499$	20.1986	0.904213	0.452106	+	0.891964i	$0.350673\pi$
$500$	2.01575	0.0901469
$501$	8.35946	0.373473
$502$	−17.7295	−0.791306
$503$	−7.89025	−0.351809	−0.175905	−	0.984407i	$-0.556285\pi$
$503$	−7.89025	−0.351809	−0.175905	+	0.984407i	$0.556285\pi$
$504$	−0.101433	−0.00451817
$505$	0.769361	0.0342361
$506$	1.43243	0.0636794
$507$	55.6680	2.47230
$508$	9.37371	0.415891
$509$	−23.9453	−1.06136	−0.530679	−	0.847573i	$-0.678063\pi$
$509$	−23.9453	−1.06136	−0.530679	+	0.847573i	$0.678063\pi$
$510$	−0.348815	−0.0154458
$511$	−34.4598	−1.52441
$512$	1.00000	0.0441942
$513$	1.22076	0.0538978
$514$	6.94855	0.306487
$515$	1.24963	0.0550653
$516$	1.28541	0.0565872
$517$	21.9899	0.967117
$518$	−22.8903	−1.00574
$519$	−7.66030	−0.336250
$520$	−1.36231	−0.0597414
$521$	14.1344	0.619241	0.309620	−	0.950860i	$-0.399798\pi$
$521$	14.1344	0.619241	0.309620	+	0.950860i	$0.399798\pi$
$522$	0.0723481	0.00316659
$523$	−34.8344	−1.52320	−0.761601	−	0.648047i	$-0.775586\pi$
$523$	−34.8344	−1.52320	−0.761601	+	0.648047i	$0.775586\pi$
$524$	−21.2005	−0.926148
$525$	−28.8826	−1.26054
$526$	−1.21462	−0.0529599
$527$	10.3073	0.448994
$528$	−3.05091	−0.132774
$529$	−22.3453	−0.971535
$530$	−2.74870	−0.119396
$531$	−0.0300134	−0.00130247
$532$	−0.790077	−0.0342542
$533$	−28.3194	−1.22665
$534$	−8.25403	−0.357187
$535$	2.47155	0.106854
$536$	−5.61566	−0.242560
$537$	−8.06872	−0.348191
$538$	−22.8965	−0.987138
$539$	−7.82752	−0.337155
$540$	1.05692	0.0454824
$541$	−31.5795	−1.35771	−0.678855	−	0.734272i	$-0.737523\pi$
$541$	−31.5795	−1.35771	−0.678855	+	0.734272i	$0.737523\pi$
$542$	−8.09194	−0.347579
$543$	22.3727	0.960105
$544$	1.00000	0.0428746
$545$	1.63042	0.0698393
$546$	39.2010	1.67765
$547$	−14.6890	−0.628056	−0.314028	−	0.949414i	$-0.601679\pi$
$547$	−14.6890	−0.628056	−0.314028	+	0.949414i	$0.601679\pi$
$548$	−10.6167	−0.453522
$549$	−0.400056	−0.0170740
$550$	8.77907	0.374341
$551$	0.563533	0.0240073
$552$	−1.39444	−0.0593513
$553$	57.7796	2.45704
$554$	21.4575	0.911640
$555$	2.36258	0.100286
$556$	−9.39808	−0.398567
$557$	17.6113	0.746216	0.373108	−	0.927788i	$-0.378292\pi$
$557$	17.6113	0.746216	0.373108	+	0.927788i	$0.378292\pi$
$558$	−0.309358	−0.0130962
$559$	5.02024	0.212333
$560$	−0.684039	−0.0289059
$561$	−3.05091	−0.128809
$562$	−2.96913	−0.125245
$563$	−24.0254	−1.01255	−0.506275	−	0.862372i	$-0.668978\pi$
$563$	−24.0254	−1.01255	−0.506275	+	0.862372i	$0.668978\pi$
$564$	−21.4067	−0.901385
$565$	−2.31263	−0.0972929
$566$	−1.85751	−0.0780771
$567$	−30.1088	−1.26445
$568$	4.68873	0.196735
$569$	−30.8196	−1.29203	−0.646013	−	0.763327i	$-0.723565\pi$
$569$	−30.8196	−1.29203	−0.646013	+	0.763327i	$0.723565\pi$
$570$	0.0815461	0.00341559
$571$	6.84776	0.286570	0.143285	−	0.989681i	$-0.454233\pi$
$571$	6.84776	0.286570	0.143285	+	0.989681i	$0.454233\pi$
$572$	−11.9154	−0.498209
$573$	−28.8938	−1.20706
$574$	−14.2196	−0.593516
$575$	4.01254	0.167334
$576$	−0.0300134	−0.00125056
$577$	44.0690	1.83462	0.917308	−	0.398177i	$-0.130357\pi$
$577$	44.0690	1.83462	0.917308	+	0.398177i	$0.130357\pi$
$578$	1.00000	0.0415945
$579$	−41.1877	−1.71170
$580$	0.487899	0.0202589
$581$	6.95956	0.288731
$582$	1.41075	0.0584775
$583$	−24.0414	−0.995695
$584$	−10.1965	−0.421934
$585$	0.0408877	0.00169050
$586$	6.87977	0.284201
$587$	−26.6671	−1.10067	−0.550335	−	0.834944i	$-0.685500\pi$
$587$	−26.6671	−1.10067	−0.550335	+	0.834944i	$0.685500\pi$
$588$	7.61991	0.314240
$589$	−2.40964	−0.0992877
$590$	−0.202404	−0.00833283
$591$	−1.17110	−0.0481725
$592$	−6.77314	−0.278374
$593$	−9.12916	−0.374890	−0.187445	−	0.982275i	$-0.560021\pi$
$593$	−9.12916	−0.374890	−0.187445	+	0.982275i	$0.560021\pi$
$594$	9.24428	0.379298
$595$	−0.684039	−0.0280428
$596$	9.52791	0.390278
$597$	−32.3419	−1.32367
$598$	−5.44604	−0.222705
$599$	1.26541	0.0517031	0.0258516	−	0.999666i	$-0.491770\pi$
$599$	1.26541	0.0517031	0.0258516	+	0.999666i	$0.491770\pi$
$600$	−8.54622	−0.348898
$601$	−26.5303	−1.08219	−0.541097	−	0.840960i	$-0.681991\pi$
$601$	−26.5303	−1.08219	−0.541097	+	0.840960i	$0.681991\pi$
$602$	2.52074	0.102738
$603$	0.168545	0.00686370
$604$	2.64460	0.107607
$605$	1.59210	0.0647281
$606$	−6.55072	−0.266105
$607$	−5.64144	−0.228979	−0.114490	−	0.993424i	$-0.536523\pi$
$607$	−5.64144	−0.228979	−0.114490	+	0.993424i	$0.536523\pi$
$608$	−0.233780	−0.00948104
$609$	−14.0395	−0.568908
$610$	−2.69789	−0.109234
$611$	−83.6047	−3.38229
$612$	−0.0300134	−0.00121322
$613$	−14.1684	−0.572257	−0.286128	−	0.958191i	$-0.592368\pi$
$613$	−14.1684	−0.572257	−0.286128	+	0.958191i	$0.592368\pi$
$614$	−29.8065	−1.20289
$615$	1.46765	0.0591812
$616$	−5.98293	−0.241059
$617$	−45.9749	−1.85088	−0.925439	−	0.378897i	$-0.876304\pi$
$617$	−45.9749	−1.85088	−0.925439	+	0.378897i	$0.876304\pi$
$618$	−10.6400	−0.428002
$619$	45.2383	1.81828	0.909141	−	0.416489i	$-0.136740\pi$
$619$	45.2383	1.81828	0.909141	+	0.416489i	$0.136740\pi$
$620$	−2.08624	−0.0837853
$621$	4.22517	0.169550
$622$	−10.7925	−0.432742
$623$	−16.1864	−0.648495
$624$	11.5994	0.464348
$625$	24.3872	0.975487
$626$	−1.41103	−0.0563959
$627$	0.713241	0.0284841
$628$	3.29974	0.131674
$629$	−6.77314	−0.270063
$630$	0.0205304	0.000817949 0
$631$	−36.6968	−1.46088	−0.730439	−	0.682978i	$-0.760685\pi$
$631$	−36.6968	−1.46088	−0.730439	+	0.682978i	$0.760685\pi$
$632$	17.0967	0.680070
$633$	44.7212	1.77751
$634$	9.87268	0.392094
$635$	−1.89727	−0.0752910
$636$	23.4038	0.928021
$637$	29.7598	1.17913
$638$	4.26740	0.168948
$639$	−0.140725	−0.00556700
$640$	−0.202404	−0.00800071
$641$	−23.1127	−0.912898	−0.456449	−	0.889749i	$-0.650879\pi$
$641$	−23.1127	−0.912898	−0.456449	+	0.889749i	$0.650879\pi$
$642$	−21.0440	−0.830540
$643$	−3.57303	−0.140907	−0.0704533	−	0.997515i	$-0.522445\pi$
$643$	−3.57303	−0.140907	−0.0704533	+	0.997515i	$0.522445\pi$
$644$	−2.73454	−0.107756
$645$	−0.260173	−0.0102443
$646$	−0.233780	−0.00919796
$647$	46.0469	1.81029	0.905145	−	0.425102i	$-0.139762\pi$
$647$	46.0469	1.81029	0.905145	+	0.425102i	$0.139762\pi$
$648$	−8.90906	−0.349981
$649$	−1.77032	−0.0694911
$650$	−33.3776	−1.30918
$651$	60.0323	2.35285
$652$	4.14267	0.162239
$653$	−32.2144	−1.26065	−0.630323	−	0.776333i	$-0.717078\pi$
$653$	−32.2144	−1.26065	−0.630323	+	0.776333i	$0.717078\pi$
$654$	−13.8822	−0.542835
$655$	4.29106	0.167666
$656$	−4.20752	−0.164276
$657$	0.306032	0.0119394
$658$	−41.9793	−1.63652
$659$	−9.47180	−0.368969	−0.184484	−	0.982835i	$-0.559062\pi$
$659$	−9.47180	−0.368969	−0.184484	+	0.982835i	$0.559062\pi$
$660$	0.617515	0.0240367
$661$	−26.1953	−1.01888	−0.509440	−	0.860506i	$-0.670148\pi$
$661$	−26.1953	−1.01888	−0.509440	+	0.860506i	$0.670148\pi$
$662$	−10.2731	−0.399276
$663$	11.5994	0.450483
$664$	2.05930	0.0799164
$665$	0.159915	0.00620122
$666$	0.203285	0.00787715
$667$	1.95045	0.0755215
$668$	4.85066	0.187678
$669$	−1.51031	−0.0583918
$670$	1.13663	0.0439119
$671$	−23.5970	−0.910952
$672$	5.82424	0.224675
$673$	49.8700	1.92235	0.961173	−	0.275945i	$-0.0889908\pi$
$673$	49.8700	1.92235	0.961173	+	0.275945i	$0.0889908\pi$
$674$	21.1608	0.815083
$675$	25.8952	0.996706
$676$	32.3019	1.24238
$677$	6.28037	0.241374	0.120687	−	0.992691i	$-0.461490\pi$
$677$	6.28037	0.241374	0.120687	+	0.992691i	$0.461490\pi$
$678$	19.6908	0.756222
$679$	2.76653	0.106170
$680$	−0.202404	−0.00776183
$681$	−17.5062	−0.670840
$682$	−18.2472	−0.698723
$683$	18.8923	0.722892	0.361446	−	0.932393i	$-0.382283\pi$
$683$	18.8923	0.722892	0.361446	+	0.932393i	$0.382283\pi$
$684$	0.00701655	0.000268284 0
$685$	2.14886	0.0821035
$686$	−8.71414	−0.332707
$687$	−12.4089	−0.473427
$688$	0.745875	0.0284362
$689$	91.4044	3.48223
$690$	0.282240	0.0107447
$691$	23.8282	0.906469	0.453235	−	0.891391i	$-0.350270\pi$
$691$	23.8282	0.906469	0.453235	+	0.891391i	$0.350270\pi$
$692$	−4.44497	−0.168972
$693$	0.179568	0.00682123
$694$	−6.44928	−0.244811
$695$	1.90221	0.0721548
$696$	−4.15421	−0.157465
$697$	−4.20752	−0.159371
$698$	16.0643	0.608044
$699$	−0.515237	−0.0194880
$700$	−16.7594	−0.633447
$701$	24.8544	0.938739	0.469370	−	0.883002i	$-0.344481\pi$
$701$	24.8544	0.938739	0.469370	+	0.883002i	$0.344481\pi$
$702$	−35.1463	−1.32651
$703$	1.58343	0.0597200
$704$	−1.77032	−0.0667214
$705$	4.33280	0.163183
$706$	27.4287	1.03229
$707$	−12.8462	−0.483130
$708$	1.72336	0.0647680
$709$	9.59007	0.360163	0.180081	−	0.983652i	$-0.442364\pi$
$709$	9.59007	0.360163	0.180081	+	0.983652i	$0.442364\pi$
$710$	−0.949017	−0.0356160
$711$	−0.513131	−0.0192439
$712$	−4.78948	−0.179493
$713$	−8.34003	−0.312337
$714$	5.82424	0.217967
$715$	2.41173	0.0901935
$716$	−4.68196	−0.174973
$717$	−7.58389	−0.283226
$718$	30.4418	1.13608
$719$	24.2369	0.903883	0.451942	−	0.892047i	$-0.350731\pi$
$719$	24.2369	0.903883	0.451942	+	0.892047i	$0.350731\pi$
$720$	0.00607483	0.000226396 0
$721$	−20.8653	−0.777065
$722$	−18.9453	−0.705073
$723$	−16.0634	−0.597405
$724$	12.9820	0.482472
$725$	11.9539	0.443955
$726$	−13.5559	−0.503108
$727$	11.7747	0.436701	0.218350	−	0.975870i	$-0.429932\pi$
$727$	11.7747	0.436701	0.218350	+	0.975870i	$0.429932\pi$
$728$	22.7468	0.843053
$729$	27.2647	1.00980
$730$	2.06381	0.0763850
$731$	0.745875	0.0275872
$732$	22.9711	0.849038
$733$	−21.5566	−0.796213	−0.398106	−	0.917339i	$-0.630333\pi$
$733$	−21.5566	−0.796213	−0.398106	+	0.917339i	$0.630333\pi$
$734$	29.8549	1.10197
$735$	−1.54230	−0.0568885
$736$	−0.809138	−0.0298252
$737$	9.94152	0.366201
$738$	0.126282	0.00464851
$739$	30.3723	1.11726	0.558632	−	0.829416i	$-0.311326\pi$
$739$	30.3723	1.11726	0.558632	+	0.829416i	$0.311326\pi$
$740$	1.37091	0.0503956
$741$	−2.71171	−0.0996171
$742$	45.8956	1.68488
$743$	23.5036	0.862265	0.431133	−	0.902289i	$-0.358114\pi$
$743$	23.5036	0.862265	0.431133	+	0.902289i	$0.358114\pi$
$744$	17.7633	0.651233
$745$	−1.92848	−0.0706542
$746$	−25.9234	−0.949123
$747$	−0.0618067	−0.00226139
$748$	−1.77032	−0.0647293
$749$	−41.2679	−1.50790
$750$	3.47386	0.126848
$751$	52.0493	1.89930	0.949652	−	0.313306i	$-0.101436\pi$
$751$	52.0493	1.89930	0.949652	+	0.313306i	$0.101436\pi$
$752$	−12.4215	−0.452964
$753$	−30.5544	−1.11346
$754$	−16.2244	−0.590859
$755$	−0.535278	−0.0194807
$756$	−17.6475	−0.641834
$757$	−33.0106	−1.19979	−0.599895	−	0.800079i	$-0.704791\pi$
$757$	−33.0106	−1.19979	−0.599895	+	0.800079i	$0.704791\pi$
$758$	−5.29048	−0.192159
$759$	2.46860	0.0896046
$760$	0.0473180	0.00171640
$761$	−15.7714	−0.571713	−0.285857	−	0.958272i	$-0.592278\pi$
$761$	−15.7714	−0.571713	−0.285857	+	0.958272i	$0.592278\pi$
$762$	16.1543	0.585209
$763$	−27.2234	−0.985552
$764$	−16.7659	−0.606570
$765$	0.00607483	0.000219636 0
$766$	27.9237	1.00893
$767$	6.73067	0.243030
$768$	1.72336	0.0621866
$769$	2.50296	0.0902590	0.0451295	−	0.998981i	$-0.485630\pi$
$769$	2.50296	0.0902590	0.0451295	+	0.998981i	$0.485630\pi$
$770$	1.21097	0.0436402
$771$	11.9749	0.431265
$772$	−23.8996	−0.860164
$773$	3.23205	0.116249	0.0581243	−	0.998309i	$-0.481488\pi$
$773$	3.23205	0.116249	0.0581243	+	0.998309i	$0.481488\pi$
$774$	−0.0223863	−0.000804658 0
$775$	−51.1143	−1.83608
$776$	0.818602	0.0293861
$777$	−39.4484	−1.41520
$778$	−16.5097	−0.591900
$779$	0.983634	0.0352423
$780$	−2.34776	−0.0840633
$781$	−8.30055	−0.297017
$782$	−0.809138	−0.0289347
$783$	12.5873	0.449834
$784$	4.42153	0.157912
$785$	−0.667880	−0.0238377
$786$	−36.5362	−1.30320
$787$	1.95366	0.0696404	0.0348202	−	0.999394i	$-0.488914\pi$
$787$	1.95366	0.0696404	0.0348202	+	0.999394i	$0.488914\pi$
$788$	−0.679540	−0.0242076
$789$	−2.09323	−0.0745210
$790$	−3.46044	−0.123117
$791$	38.6144	1.37297
$792$	0.0531334	0.00188801
$793$	89.7147	3.18586
$794$	−23.5991	−0.837502
$795$	−4.73701	−0.168005
$796$	−18.7667	−0.665170
$797$	−30.9883	−1.09766	−0.548831	−	0.835933i	$-0.684927\pi$
$797$	−30.9883	−1.09766	−0.548831	+	0.835933i	$0.684927\pi$
$798$	−1.36159	−0.0481998
$799$	−12.4215	−0.439440
$800$	−4.95903	−0.175328
$801$	0.143749	0.00507912
$802$	16.3761	0.578259
$803$	18.0510	0.637007
$804$	−9.67784	−0.341311
$805$	0.553481	0.0195077
$806$	69.3751	2.44363
$807$	−39.4590	−1.38902
$808$	−3.80112	−0.133723
$809$	−3.34464	−0.117591	−0.0587956	−	0.998270i	$-0.518726\pi$
$809$	−3.34464	−0.117591	−0.0587956	+	0.998270i	$0.518726\pi$
$810$	1.80323	0.0633589
$811$	33.6301	1.18091	0.590456	−	0.807070i	$-0.298948\pi$
$811$	33.6301	1.18091	0.590456	+	0.807070i	$0.298948\pi$
$812$	−8.14655	−0.285888
$813$	−13.9454	−0.489085
$814$	11.9906	0.420271
$815$	−0.838491	−0.0293711
$816$	1.72336	0.0603298
$817$	−0.174371	−0.00610046
$818$	−11.2194	−0.392276
$819$	−0.682710	−0.0238558
$820$	0.851617	0.0297398
$821$	38.9255	1.35851	0.679255	−	0.733902i	$-0.262303\pi$
$821$	38.9255	1.35851	0.679255	+	0.733902i	$0.262303\pi$
$822$	−18.2964	−0.638161
$823$	23.6392	0.824011	0.412005	−	0.911181i	$-0.364828\pi$
$823$	23.6392	0.824011	0.412005	+	0.911181i	$0.364828\pi$
$824$	−6.17395	−0.215080
$825$	15.1295	0.526743
$826$	3.37958	0.117590
$827$	27.7773	0.965911	0.482956	−	0.875645i	$-0.339563\pi$
$827$	27.7773	0.965911	0.482956	+	0.875645i	$0.339563\pi$
$828$	0.0242850	0.000843962 0
$829$	40.8501	1.41878	0.709391	−	0.704815i	$-0.248970\pi$
$829$	40.8501	1.41878	0.709391	+	0.704815i	$0.248970\pi$
$830$	−0.416810	−0.0144677
$831$	36.9790	1.28279
$832$	6.73067	0.233344
$833$	4.42153	0.153197
$834$	−16.1963	−0.560832
$835$	−0.981792	−0.0339763
$836$	0.413865	0.0143138
$837$	−53.8229	−1.86039
$838$	30.0900	1.03944
$839$	31.7309	1.09547	0.547736	−	0.836651i	$-0.315490\pi$
$839$	31.7309	1.09547	0.547736	+	0.836651i	$0.315490\pi$
$840$	−1.17885	−0.0406741
$841$	−23.1894	−0.799634
$842$	15.6995	0.541039
$843$	−5.11689	−0.176235
$844$	25.9499	0.893233
$845$	−6.53803	−0.224915
$846$	0.372811	0.0128175
$847$	−26.5836	−0.913425
$848$	13.5803	0.466349
$849$	−3.20117	−0.109864
$850$	−4.95903	−0.170093
$851$	5.48040	0.187866
$852$	8.08040	0.276830
$853$	6.21788	0.212896	0.106448	−	0.994318i	$-0.466052\pi$
$853$	6.21788	0.212896	0.106448	+	0.994318i	$0.466052\pi$
$854$	45.0472	1.54148
$855$	−0.00142018	−4.85690e−5 0
$856$	−12.2110	−0.417363
$857$	26.7456	0.913611	0.456805	−	0.889567i	$-0.348994\pi$
$857$	26.7456	0.913611	0.456805	+	0.889567i	$0.348994\pi$
$858$	−20.5346	−0.701041
$859$	53.0348	1.80952	0.904762	−	0.425918i	$-0.140049\pi$
$859$	53.0348	1.80952	0.904762	+	0.425918i	$0.140049\pi$
$860$	−0.150968	−0.00514796
$861$	−24.5056	−0.835148
$862$	−14.4725	−0.492936
$863$	−6.05178	−0.206005	−0.103003	−	0.994681i	$-0.532845\pi$
$863$	−6.05178	−0.206005	−0.103003	+	0.994681i	$0.532845\pi$
$864$	−5.22182	−0.177650
$865$	0.899678	0.0305900
$866$	8.12502	0.276099
$867$	1.72336	0.0585285
$868$	34.8343	1.18235
$869$	−30.2666	−1.02672
$870$	0.840828	0.0285067
$871$	−37.7972	−1.28071
$872$	−8.05526	−0.272786
$873$	−0.0245691	−0.000831537 0
$874$	0.189160	0.00639844
$875$	6.81236	0.230300
$876$	−17.5723	−0.593712
$877$	−3.05602	−0.103194	−0.0515972	−	0.998668i	$-0.516431\pi$
$877$	−3.05602	−0.103194	−0.0515972	+	0.998668i	$0.516431\pi$
$878$	7.01469	0.236734
$879$	11.8564	0.399905
$880$	0.358319	0.0120789
$881$	58.1892	1.96044	0.980222	−	0.197902i	$-0.0634127\pi$
$881$	58.1892	1.96044	0.980222	+	0.197902i	$0.0634127\pi$
$882$	−0.132705	−0.00446842
$883$	18.7059	0.629504	0.314752	−	0.949174i	$-0.398079\pi$
$883$	18.7059	0.629504	0.314752	+	0.949174i	$0.398079\pi$
$884$	6.73067	0.226377
$885$	−0.348815	−0.0117253
$886$	20.0117	0.672305
$887$	−20.9574	−0.703681	−0.351840	−	0.936060i	$-0.614444\pi$
$887$	−20.9574	−0.703681	−0.351840	+	0.936060i	$0.614444\pi$
$888$	−11.6726	−0.391707
$889$	31.6792	1.06248
$890$	0.969409	0.0324947
$891$	15.7719	0.528378
$892$	−0.876370	−0.0293430
$893$	2.90389	0.0971750
$894$	16.4201	0.549169
$895$	0.947646	0.0316763
$896$	3.37958	0.112904
$897$	−9.38551	−0.313373
$898$	−19.6816	−0.656783
$899$	−24.8460	−0.828661
$900$	0.148838	0.00496126
$901$	13.5803	0.452425
$902$	7.44865	0.248013
$903$	4.34416	0.144564
$904$	11.4258	0.380017
$905$	−2.62760	−0.0873445
$906$	4.55762	0.151417
$907$	−31.5377	−1.04719	−0.523596	−	0.851967i	$-0.675410\pi$
$907$	−31.5377	−1.04719	−0.523596	+	0.851967i	$0.675410\pi$
$908$	−10.1582	−0.337111
$909$	0.114085	0.00378395
$910$	−4.60404	−0.152622
$911$	54.5154	1.80617	0.903087	−	0.429457i	$-0.141295\pi$
$911$	54.5154	1.80617	0.903087	+	0.429457i	$0.141295\pi$
$912$	−0.402888	−0.0133410
$913$	−3.64562	−0.120652
$914$	−28.1126	−0.929881
$915$	−4.64944	−0.153706
$916$	−7.20036	−0.237907
$917$	−71.6487	−2.36605
$918$	−5.22182	−0.172346
$919$	−12.3705	−0.408066	−0.204033	−	0.978964i	$-0.565405\pi$
$919$	−12.3705	−0.408066	−0.204033	+	0.978964i	$0.565405\pi$
$920$	0.163772	0.00539942
$921$	−51.3675	−1.69262
$922$	15.2111	0.500951
$923$	31.5583	1.03875
$924$	−10.3108	−0.339199
$925$	33.5882	1.10437
$926$	12.5389	0.412055
$927$	0.185301	0.00608610
$928$	−2.41052	−0.0791293
$929$	47.7317	1.56603	0.783013	−	0.622006i	$-0.213682\pi$
$929$	47.7317	1.56603	0.783013	+	0.622006i	$0.213682\pi$
$930$	−3.59535	−0.117896
$931$	−1.03367	−0.0338770
$932$	−0.298971	−0.00979313
$933$	−18.5995	−0.608920
$934$	35.4609	1.16032
$935$	0.358319	0.0117183
$936$	−0.202011	−0.00660292
$937$	−18.4115	−0.601477	−0.300738	−	0.953707i	$-0.597233\pi$
$937$	−18.4115	−0.601477	−0.300738	+	0.953707i	$0.597233\pi$
$938$	−18.9786	−0.619672
$939$	−2.43171	−0.0793559
$940$	2.51415	0.0820025
$941$	37.3574	1.21782	0.608908	−	0.793241i	$-0.291608\pi$
$941$	37.3574	1.21782	0.608908	+	0.793241i	$0.291608\pi$
$942$	5.68666	0.185281
$943$	3.40446	0.110864
$944$	1.00000	0.0325472
$945$	3.57193	0.116195
$946$	−1.32044	−0.0429311
$947$	−18.3432	−0.596075	−0.298037	−	0.954554i	$-0.596332\pi$
$947$	−18.3432	−0.596075	−0.298037	+	0.954554i	$0.596332\pi$
$948$	29.4639	0.956942
$949$	−68.6292	−2.22780
$950$	1.15932	0.0376134
$951$	17.0142	0.551724
$952$	3.37958	0.109533
$953$	−43.1143	−1.39661	−0.698304	−	0.715801i	$-0.746062\pi$
$953$	−43.1143	−1.39661	−0.698304	+	0.715801i	$0.746062\pi$
$954$	−0.407591	−0.0131963
$955$	3.39349	0.109811
$956$	−4.40063	−0.142327
$957$	7.35428	0.237730
$958$	19.7843	0.639203
$959$	−35.8799	−1.15862
$960$	−0.348815	−0.0112580
$961$	75.2407	2.42712
$962$	−45.5878	−1.46981
$963$	0.366494	0.0118101
$964$	−9.32096	−0.300208
$965$	4.83736	0.155720
$966$	−4.71261	−0.151626
$967$	46.7680	1.50396	0.751979	−	0.659187i	$-0.229099\pi$
$967$	46.7680	1.50396	0.751979	+	0.659187i	$0.229099\pi$
$968$	−7.86597	−0.252822
$969$	−0.402888	−0.0129426
$970$	−0.165688	−0.00531993
$971$	−15.6264	−0.501475	−0.250738	−	0.968055i	$-0.580673\pi$
$971$	−15.6264	−0.501475	−0.250738	+	0.968055i	$0.580673\pi$
$972$	0.311897	0.0100041
$973$	−31.7615	−1.01823
$974$	21.0468	0.674382
$975$	−57.5218	−1.84217
$976$	13.3292	0.426659
$977$	−22.3408	−0.714746	−0.357373	−	0.933962i	$-0.616327\pi$
$977$	−22.3408	−0.714746	−0.357373	+	0.933962i	$0.616327\pi$
$978$	7.13933	0.228290
$979$	8.47891	0.270987
$980$	−0.894934	−0.0285876
$981$	0.241766	0.00771900
$982$	12.3112	0.392865
$983$	35.5356	1.13341	0.566705	−	0.823921i	$-0.308218\pi$
$983$	35.5356	1.13341	0.566705	+	0.823921i	$0.308218\pi$
$984$	−7.25109	−0.231156
$985$	0.137542	0.00438244
$986$	−2.41052	−0.0767667
$987$	−72.3456	−2.30279
$988$	−1.57350	−0.0500596
$989$	−0.603516	−0.0191907
$990$	−0.0107544	−0.000341797 0
$991$	−7.88341	−0.250425	−0.125212	−	0.992130i	$-0.539961\pi$
$991$	−7.88341	−0.250425	−0.125212	+	0.992130i	$0.539961\pi$
$992$	10.3073	0.327257
$993$	−17.7043	−0.561830
$994$	15.8459	0.502602
$995$	3.79846	0.120419
$996$	3.54893	0.112452
$997$	−56.8225	−1.79959	−0.899793	−	0.436316i	$-0.856283\pi$
$997$	−56.8225	−1.79959	−0.899793	+	0.436316i	$0.856283\pi$
$998$	20.1986	0.639375
$999$	35.3681	1.11900

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2006.2.a.w.1.9	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2006.2.a.w.1.9	✓	13	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.72336 q^{3} +1.00000 q^{4} -0.202404 q^{5} +1.72336 q^{6} +3.37958 q^{7} +1.00000 q^{8} -0.0300134 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.72336 q^{3} +1.00000 q^{4} -0.202404 q^{5} +1.72336 q^{6} +3.37958 q^{7} +1.00000 q^{8} -0.0300134 q^{9} -0.202404 q^{10} -1.77032 q^{11} +1.72336 q^{12} +6.73067 q^{13} +3.37958 q^{14} -0.348815 q^{15} +1.00000 q^{16} +1.00000 q^{17} -0.0300134 q^{18} -0.233780 q^{19} -0.202404 q^{20} +5.82424 q^{21} -1.77032 q^{22} -0.809138 q^{23} +1.72336 q^{24} -4.95903 q^{25} +6.73067 q^{26} -5.22182 q^{27} +3.37958 q^{28} -2.41052 q^{29} -0.348815 q^{30} +10.3073 q^{31} +1.00000 q^{32} -3.05091 q^{33} +1.00000 q^{34} -0.684039 q^{35} -0.0300134 q^{36} -6.77314 q^{37} -0.233780 q^{38} +11.5994 q^{39} -0.202404 q^{40} -4.20752 q^{41} +5.82424 q^{42} +0.745875 q^{43} -1.77032 q^{44} +0.00607483 q^{45} -0.809138 q^{46} -12.4215 q^{47} +1.72336 q^{48} +4.42153 q^{49} -4.95903 q^{50} +1.72336 q^{51} +6.73067 q^{52} +13.5803 q^{53} -5.22182 q^{54} +0.358319 q^{55} +3.37958 q^{56} -0.402888 q^{57} -2.41052 q^{58} +1.00000 q^{59} -0.348815 q^{60} +13.3292 q^{61} +10.3073 q^{62} -0.101433 q^{63} +1.00000 q^{64} -1.36231 q^{65} -3.05091 q^{66} -5.61566 q^{67} +1.00000 q^{68} -1.39444 q^{69} -0.684039 q^{70} +4.68873 q^{71} -0.0300134 q^{72} -10.1965 q^{73} -6.77314 q^{74} -8.54622 q^{75} -0.233780 q^{76} -5.98293 q^{77} +11.5994 q^{78} +17.0967 q^{79} -0.202404 q^{80} -8.90906 q^{81} -4.20752 q^{82} +2.05930 q^{83} +5.82424 q^{84} -0.202404 q^{85} +0.745875 q^{86} -4.15421 q^{87} -1.77032 q^{88} -4.78948 q^{89} +0.00607483 q^{90} +22.7468 q^{91} -0.809138 q^{92} +17.7633 q^{93} -12.4215 q^{94} +0.0473180 q^{95} +1.72336 q^{96} +0.818602 q^{97} +4.42153 q^{98} +0.0531334 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} + 7 q^{3} + 13 q^{4} + q^{5} + 7 q^{6} + 8 q^{7} + 13 q^{8} + 16 q^{9}+O(q^{10}) \) 13 * q + 13 * q^2 + 7 * q^3 + 13 * q^4 + q^5 + 7 * q^6 + 8 * q^7 + 13 * q^8 + 16 * q^9	\( 13 q + 13 q^{2} + 7 q^{3} + 13 q^{4} + q^{5} + 7 q^{6} + 8 q^{7} + 13 q^{8} + 16 q^{9} + q^{10} + 13 q^{11} + 7 q^{12} + 9 q^{13} + 8 q^{14} - 9 q^{15} + 13 q^{16} + 13 q^{17} + 16 q^{18} + 16 q^{19} + q^{20} - 3 q^{21} + 13 q^{22} + 18 q^{23} + 7 q^{24} + 14 q^{25} + 9 q^{26} + 10 q^{27} + 8 q^{28} + 8 q^{29} - 9 q^{30} + 32 q^{31} + 13 q^{32} + 13 q^{33} + 13 q^{34} - q^{35} + 16 q^{36} - 3 q^{37} + 16 q^{38} + 20 q^{39} + q^{40} + 24 q^{41} - 3 q^{42} - 2 q^{43} + 13 q^{44} - 3 q^{45} + 18 q^{46} + 26 q^{47} + 7 q^{48} + 23 q^{49} + 14 q^{50} + 7 q^{51} + 9 q^{52} - 27 q^{53} + 10 q^{54} - 7 q^{55} + 8 q^{56} - 21 q^{57} + 8 q^{58} + 13 q^{59} - 9 q^{60} + 20 q^{61} + 32 q^{62} - 3 q^{63} + 13 q^{64} + 16 q^{65} + 13 q^{66} + 4 q^{67} + 13 q^{68} - 2 q^{69} - q^{70} - 8 q^{71} + 16 q^{72} + 10 q^{73} - 3 q^{74} + 39 q^{75} + 16 q^{76} - 15 q^{77} + 20 q^{78} + 35 q^{79} + q^{80} + 29 q^{81} + 24 q^{82} - q^{83} - 3 q^{84} + q^{85} - 2 q^{86} - 32 q^{87} + 13 q^{88} - 20 q^{89} - 3 q^{90} - 15 q^{91} + 18 q^{92} - 7 q^{93} + 26 q^{94} - 3 q^{95} + 7 q^{96} - 3 q^{97} + 23 q^{98} + 65 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 7 * q^3 + 13 * q^4 + q^5 + 7 * q^6 + 8 * q^7 + 13 * q^8 + 16 * q^9 + q^10 + 13 * q^11 + 7 * q^12 + 9 * q^13 + 8 * q^14 - 9 * q^15 + 13 * q^16 + 13 * q^17 + 16 * q^18 + 16 * q^19 + q^20 - 3 * q^21 + 13 * q^22 + 18 * q^23 + 7 * q^24 + 14 * q^25 + 9 * q^26 + 10 * q^27 + 8 * q^28 + 8 * q^29 - 9 * q^30 + 32 * q^31 + 13 * q^32 + 13 * q^33 + 13 * q^34 - q^35 + 16 * q^36 - 3 * q^37 + 16 * q^38 + 20 * q^39 + q^40 + 24 * q^41 - 3 * q^42 - 2 * q^43 + 13 * q^44 - 3 * q^45 + 18 * q^46 + 26 * q^47 + 7 * q^48 + 23 * q^49 + 14 * q^50 + 7 * q^51 + 9 * q^52 - 27 * q^53 + 10 * q^54 - 7 * q^55 + 8 * q^56 - 21 * q^57 + 8 * q^58 + 13 * q^59 - 9 * q^60 + 20 * q^61 + 32 * q^62 - 3 * q^63 + 13 * q^64 + 16 * q^65 + 13 * q^66 + 4 * q^67 + 13 * q^68 - 2 * q^69 - q^70 - 8 * q^71 + 16 * q^72 + 10 * q^73 - 3 * q^74 + 39 * q^75 + 16 * q^76 - 15 * q^77 + 20 * q^78 + 35 * q^79 + q^80 + 29 * q^81 + 24 * q^82 - q^83 - 3 * q^84 + q^85 - 2 * q^86 - 32 * q^87 + 13 * q^88 - 20 * q^89 - 3 * q^90 - 15 * q^91 + 18 * q^92 - 7 * q^93 + 26 * q^94 - 3 * q^95 + 7 * q^96 - 3 * q^97 + 23 * q^98 + 65 * q^99

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