LMFDB - Embedded newform 2006.2.a.v.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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 21 x^{10} + 62 x^{9} + 144 x^{8} - 418 x^{7} - 370 x^{6} + 1042 x^{5} + 417 x^{4} + \cdots + 62 $ x^12 - 3x^11 - 21x^10 + 62x^9 + 144x^8 - 418x^7 - 370x^6 + 1042x^5 + 417x^4 - 935x^3 - 233x^2 + 228*x + 62
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.09998$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.09998 q^{3} +1.00000 q^{4} -3.08354 q^{5} +1.09998 q^{6} +3.13875 q^{7} -1.00000 q^{8} -1.79003 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.09998 q^{3} +1.00000 q^{4} -3.08354 q^{5} +1.09998 q^{6} +3.13875 q^{7} -1.00000 q^{8} -1.79003 q^{9} +3.08354 q^{10} -2.44808 q^{11} -1.09998 q^{12} -0.162900 q^{13} -3.13875 q^{14} +3.39185 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.79003 q^{18} +3.47858 q^{19} -3.08354 q^{20} -3.45257 q^{21} +2.44808 q^{22} -5.13080 q^{23} +1.09998 q^{24} +4.50824 q^{25} +0.162900 q^{26} +5.26896 q^{27} +3.13875 q^{28} -6.96215 q^{29} -3.39185 q^{30} -0.948053 q^{31} -1.00000 q^{32} +2.69285 q^{33} +1.00000 q^{34} -9.67846 q^{35} -1.79003 q^{36} -0.764713 q^{37} -3.47858 q^{38} +0.179187 q^{39} +3.08354 q^{40} -10.0701 q^{41} +3.45257 q^{42} +9.93350 q^{43} -2.44808 q^{44} +5.51965 q^{45} +5.13080 q^{46} +3.67818 q^{47} -1.09998 q^{48} +2.85173 q^{49} -4.50824 q^{50} +1.09998 q^{51} -0.162900 q^{52} +4.34667 q^{53} -5.26896 q^{54} +7.54875 q^{55} -3.13875 q^{56} -3.82638 q^{57} +6.96215 q^{58} +1.00000 q^{59} +3.39185 q^{60} +2.93424 q^{61} +0.948053 q^{62} -5.61847 q^{63} +1.00000 q^{64} +0.502308 q^{65} -2.69285 q^{66} -10.0501 q^{67} -1.00000 q^{68} +5.64379 q^{69} +9.67846 q^{70} +10.4200 q^{71} +1.79003 q^{72} -14.2944 q^{73} +0.764713 q^{74} -4.95899 q^{75} +3.47858 q^{76} -7.68389 q^{77} -0.179187 q^{78} -2.43256 q^{79} -3.08354 q^{80} -0.425671 q^{81} +10.0701 q^{82} +13.3939 q^{83} -3.45257 q^{84} +3.08354 q^{85} -9.93350 q^{86} +7.65825 q^{87} +2.44808 q^{88} +5.99560 q^{89} -5.51965 q^{90} -0.511301 q^{91} -5.13080 q^{92} +1.04284 q^{93} -3.67818 q^{94} -10.7263 q^{95} +1.09998 q^{96} -7.05472 q^{97} -2.85173 q^{98} +4.38214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} - 3 q^{3} + 12 q^{4} - q^{5} + 3 q^{6} + 4 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 - 3 * q^3 + 12 * q^4 - q^5 + 3 * q^6 + 4 * q^7 - 12 * q^8 + 15 * q^9	\( 12 q - 12 q^{2} - 3 q^{3} + 12 q^{4} - q^{5} + 3 q^{6} + 4 q^{7} - 12 q^{8} + 15 q^{9} + q^{10} - 3 q^{11} - 3 q^{12} + 15 q^{13} - 4 q^{14} - 3 q^{15} + 12 q^{16} - 12 q^{17} - 15 q^{18} + 16 q^{19} - q^{20} + 15 q^{21} + 3 q^{22} - 14 q^{23} + 3 q^{24} + 19 q^{25} - 15 q^{26} - 12 q^{27} + 4 q^{28} + 14 q^{29} + 3 q^{30} + 26 q^{31} - 12 q^{32} + 13 q^{33} + 12 q^{34} - 5 q^{35} + 15 q^{36} + 15 q^{37} - 16 q^{38} + 4 q^{39} + q^{40} - 2 q^{41} - 15 q^{42} + 8 q^{43} - 3 q^{44} - 17 q^{45} + 14 q^{46} - 6 q^{47} - 3 q^{48} + 30 q^{49} - 19 q^{50} + 3 q^{51} + 15 q^{52} + q^{53} + 12 q^{54} + q^{55} - 4 q^{56} + 3 q^{57} - 14 q^{58} + 12 q^{59} - 3 q^{60} + 30 q^{61} - 26 q^{62} + q^{63} + 12 q^{64} - 4 q^{65} - 13 q^{66} + 10 q^{67} - 12 q^{68} + 8 q^{69} + 5 q^{70} + 6 q^{71} - 15 q^{72} + 26 q^{73} - 15 q^{74} + 7 q^{75} + 16 q^{76} + 45 q^{77} - 4 q^{78} - 11 q^{79} - q^{80} + 48 q^{81} + 2 q^{82} - 21 q^{83} + 15 q^{84} + q^{85} - 8 q^{86} + 2 q^{87} + 3 q^{88} - 2 q^{89} + 17 q^{90} + 31 q^{91} - 14 q^{92} + 41 q^{93} + 6 q^{94} - 29 q^{95} + 3 q^{96} + 27 q^{97} - 30 q^{98} + 9 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 3 * q^3 + 12 * q^4 - q^5 + 3 * q^6 + 4 * q^7 - 12 * q^8 + 15 * q^9 + q^10 - 3 * q^11 - 3 * q^12 + 15 * q^13 - 4 * q^14 - 3 * q^15 + 12 * q^16 - 12 * q^17 - 15 * q^18 + 16 * q^19 - q^20 + 15 * q^21 + 3 * q^22 - 14 * q^23 + 3 * q^24 + 19 * q^25 - 15 * q^26 - 12 * q^27 + 4 * q^28 + 14 * q^29 + 3 * q^30 + 26 * q^31 - 12 * q^32 + 13 * q^33 + 12 * q^34 - 5 * q^35 + 15 * q^36 + 15 * q^37 - 16 * q^38 + 4 * q^39 + q^40 - 2 * q^41 - 15 * q^42 + 8 * q^43 - 3 * q^44 - 17 * q^45 + 14 * q^46 - 6 * q^47 - 3 * q^48 + 30 * q^49 - 19 * q^50 + 3 * q^51 + 15 * q^52 + q^53 + 12 * q^54 + q^55 - 4 * q^56 + 3 * q^57 - 14 * q^58 + 12 * q^59 - 3 * q^60 + 30 * q^61 - 26 * q^62 + q^63 + 12 * q^64 - 4 * q^65 - 13 * q^66 + 10 * q^67 - 12 * q^68 + 8 * q^69 + 5 * q^70 + 6 * q^71 - 15 * q^72 + 26 * q^73 - 15 * q^74 + 7 * q^75 + 16 * q^76 + 45 * q^77 - 4 * q^78 - 11 * q^79 - q^80 + 48 * q^81 + 2 * q^82 - 21 * q^83 + 15 * q^84 + q^85 - 8 * q^86 + 2 * q^87 + 3 * q^88 - 2 * q^89 + 17 * q^90 + 31 * q^91 - 14 * q^92 + 41 * q^93 + 6 * q^94 - 29 * q^95 + 3 * q^96 + 27 * q^97 - 30 * q^98 + 9 * 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
$3$	−1.09998	−0.635076	−0.317538	−	0.948246i	$-0.602856\pi$
$3$	−1.09998	−0.635076	−0.317538	+	0.948246i	$0.602856\pi$
$4$	1.00000	0.500000
$5$	−3.08354	−1.37900	−0.689501	−	0.724285i	$-0.742170\pi$
$5$	−3.08354	−1.37900	−0.689501	+	0.724285i	$0.742170\pi$
$6$	1.09998	0.449067
$7$	3.13875	1.18633	0.593167	−	0.805079i	$-0.297877\pi$
$7$	3.13875	1.18633	0.593167	+	0.805079i	$0.297877\pi$
$8$	−1.00000	−0.353553
$9$	−1.79003	−0.596678
$10$	3.08354	0.975102
$11$	−2.44808	−0.738123	−0.369061	−	0.929405i	$-0.620321\pi$
$11$	−2.44808	−0.738123	−0.369061	+	0.929405i	$0.620321\pi$
$12$	−1.09998	−0.317538
$13$	−0.162900	−0.0451802	−0.0225901	−	0.999745i	$-0.507191\pi$
$13$	−0.162900	−0.0451802	−0.0225901	+	0.999745i	$0.507191\pi$
$14$	−3.13875	−0.838866
$15$	3.39185	0.875772
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.79003	0.421915
$19$	3.47858	0.798040	0.399020	−	0.916942i	$-0.369350\pi$
$19$	3.47858	0.798040	0.399020	+	0.916942i	$0.369350\pi$
$20$	−3.08354	−0.689501
$21$	−3.45257	−0.753413
$22$	2.44808	0.521932
$23$	−5.13080	−1.06984	−0.534922	−	0.844901i	$-0.679659\pi$
$23$	−5.13080	−1.06984	−0.534922	+	0.844901i	$0.679659\pi$
$24$	1.09998	0.224533
$25$	4.50824	0.901648
$26$	0.162900	0.0319472
$27$	5.26896	1.01401
$28$	3.13875	0.593167
$29$	−6.96215	−1.29284	−0.646419	−	0.762982i	$-0.723734\pi$
$29$	−6.96215	−1.29284	−0.646419	+	0.762982i	$0.723734\pi$
$30$	−3.39185	−0.619264
$31$	−0.948053	−0.170275	−0.0851377	−	0.996369i	$-0.527133\pi$
$31$	−0.948053	−0.170275	−0.0851377	+	0.996369i	$0.527133\pi$
$32$	−1.00000	−0.176777
$33$	2.69285	0.468764
$34$	1.00000	0.171499
$35$	−9.67846	−1.63596
$36$	−1.79003	−0.298339
$37$	−0.764713	−0.125718	−0.0628591	−	0.998022i	$-0.520022\pi$
$37$	−0.764713	−0.125718	−0.0628591	+	0.998022i	$0.520022\pi$
$38$	−3.47858	−0.564300
$39$	0.179187	0.0286929
$40$	3.08354	0.487551
$41$	−10.0701	−1.57269	−0.786346	−	0.617787i	$-0.788029\pi$
$41$	−10.0701	−1.57269	−0.786346	+	0.617787i	$0.788029\pi$
$42$	3.45257	0.532743
$43$	9.93350	1.51484	0.757422	−	0.652926i	$-0.226459\pi$
$43$	9.93350	1.51484	0.757422	+	0.652926i	$0.226459\pi$
$44$	−2.44808	−0.369061
$45$	5.51965	0.822821
$46$	5.13080	0.756495
$47$	3.67818	0.536518	0.268259	−	0.963347i	$-0.413552\pi$
$47$	3.67818	0.536518	0.268259	+	0.963347i	$0.413552\pi$
$48$	−1.09998	−0.158769
$49$	2.85173	0.407391
$50$	−4.50824	−0.637561
$51$	1.09998	0.154029
$52$	−0.162900	−0.0225901
$53$	4.34667	0.597061	0.298531	−	0.954400i	$-0.403503\pi$
$53$	4.34667	0.597061	0.298531	+	0.954400i	$0.403503\pi$
$54$	−5.26896	−0.717015
$55$	7.54875	1.01787
$56$	−3.13875	−0.419433
$57$	−3.82638	−0.506816
$58$	6.96215	0.914175
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	3.39185	0.437886
$61$	2.93424	0.375691	0.187845	−	0.982199i	$-0.439850\pi$
$61$	2.93424	0.375691	0.187845	+	0.982199i	$0.439850\pi$
$62$	0.948053	0.120403
$63$	−5.61847	−0.707860
$64$	1.00000	0.125000
$65$	0.502308	0.0623036
$66$	−2.69285	−0.331466
$67$	−10.0501	−1.22781	−0.613907	−	0.789379i	$-0.710403\pi$
$67$	−10.0501	−1.22781	−0.613907	+	0.789379i	$0.710403\pi$
$68$	−1.00000	−0.121268
$69$	5.64379	0.679433
$70$	9.67846	1.15680
$71$	10.4200	1.23662	0.618312	−	0.785933i	$-0.287817\pi$
$71$	10.4200	1.23662	0.618312	+	0.785933i	$0.287817\pi$
$72$	1.79003	0.210958
$73$	−14.2944	−1.67303	−0.836514	−	0.547945i	$-0.815410\pi$
$73$	−14.2944	−1.67303	−0.836514	+	0.547945i	$0.815410\pi$
$74$	0.764713	0.0888961
$75$	−4.95899	−0.572615
$76$	3.47858	0.399020
$77$	−7.68389	−0.875661
$78$	−0.179187	−0.0202889
$79$	−2.43256	−0.273684	−0.136842	−	0.990593i	$-0.543695\pi$
$79$	−2.43256	−0.273684	−0.136842	+	0.990593i	$0.543695\pi$
$80$	−3.08354	−0.344751
$81$	−0.425671	−0.0472967
$82$	10.0701	1.11206
$83$	13.3939	1.47018	0.735088	−	0.677972i	$-0.237141\pi$
$83$	13.3939	1.47018	0.735088	+	0.677972i	$0.237141\pi$
$84$	−3.45257	−0.376707
$85$	3.08354	0.334457
$86$	−9.93350	−1.07116
$87$	7.65825	0.821051
$88$	2.44808	0.260966
$89$	5.99560	0.635532	0.317766	−	0.948169i	$-0.397067\pi$
$89$	5.99560	0.635532	0.317766	+	0.948169i	$0.397067\pi$
$90$	−5.51965	−0.581822
$91$	−0.511301	−0.0535989
$92$	−5.13080	−0.534922
$93$	1.04284	0.108138
$94$	−3.67818	−0.379376
$95$	−10.7263	−1.10050
$96$	1.09998	0.112267
$97$	−7.05472	−0.716298	−0.358149	−	0.933664i	$-0.616592\pi$
$97$	−7.05472	−0.716298	−0.358149	+	0.933664i	$0.616592\pi$
$98$	−2.85173	−0.288069
$99$	4.38214	0.440422
$100$	4.50824	0.450824
$101$	0.982587	0.0977711	0.0488855	−	0.998804i	$-0.484433\pi$
$101$	0.982587	0.0977711	0.0488855	+	0.998804i	$0.484433\pi$
$102$	−1.09998	−0.108915
$103$	−13.0188	−1.28278	−0.641388	−	0.767217i	$-0.721641\pi$
$103$	−13.0188	−1.28278	−0.641388	+	0.767217i	$0.721641\pi$
$104$	0.162900	0.0159736
$105$	10.6462	1.03896
$106$	−4.34667	−0.422186
$107$	15.5873	1.50688	0.753441	−	0.657516i	$-0.228393\pi$
$107$	15.5873	1.50688	0.753441	+	0.657516i	$0.228393\pi$
$108$	5.26896	0.507006
$109$	17.6096	1.68669	0.843346	−	0.537371i	$-0.180583\pi$
$109$	17.6096	1.68669	0.843346	+	0.537371i	$0.180583\pi$
$110$	−7.54875	−0.719745
$111$	0.841173	0.0798406
$112$	3.13875	0.296584
$113$	9.87674	0.929125	0.464563	−	0.885540i	$-0.346212\pi$
$113$	9.87674	0.929125	0.464563	+	0.885540i	$0.346212\pi$
$114$	3.82638	0.358373
$115$	15.8210	1.47532
$116$	−6.96215	−0.646419
$117$	0.291596	0.0269581
$118$	−1.00000	−0.0920575
$119$	−3.13875	−0.287728
$120$	−3.39185	−0.309632
$121$	−5.00692	−0.455175
$122$	−2.93424	−0.265653
$123$	11.0770	0.998779
$124$	−0.948053	−0.0851377
$125$	1.51637	0.135628
$126$	5.61847	0.500533
$127$	22.0827	1.95952	0.979761	−	0.200171i	$-0.0641499\pi$
$127$	22.0827	1.95952	0.979761	+	0.200171i	$0.0641499\pi$
$128$	−1.00000	−0.0883883
$129$	−10.9267	−0.962041
$130$	−0.502308	−0.0440553
$131$	11.4864	1.00357	0.501785	−	0.864992i	$-0.332677\pi$
$131$	11.4864	1.00357	0.501785	+	0.864992i	$0.332677\pi$
$132$	2.69285	0.234382
$133$	10.9184	0.946743
$134$	10.0501	0.868195
$135$	−16.2471	−1.39833
$136$	1.00000	0.0857493
$137$	10.7293	0.916664	0.458332	−	0.888781i	$-0.348447\pi$
$137$	10.7293	0.916664	0.458332	+	0.888781i	$0.348447\pi$
$138$	−5.64379	−0.480432
$139$	4.65512	0.394842	0.197421	−	0.980319i	$-0.436743\pi$
$139$	4.65512	0.394842	0.197421	+	0.980319i	$0.436743\pi$
$140$	−9.67846	−0.817979
$141$	−4.04594	−0.340730
$142$	−10.4200	−0.874425
$143$	0.398791	0.0333485
$144$	−1.79003	−0.149170
$145$	21.4681	1.78283
$146$	14.2944	1.18301
$147$	−3.13686	−0.258724
$148$	−0.764713	−0.0628591
$149$	11.3156	0.927006	0.463503	−	0.886095i	$-0.346592\pi$
$149$	11.3156	0.927006	0.463503	+	0.886095i	$0.346592\pi$
$150$	4.95899	0.404900
$151$	0.775744	0.0631291	0.0315646	−	0.999502i	$-0.489951\pi$
$151$	0.775744	0.0631291	0.0315646	+	0.999502i	$0.489951\pi$
$152$	−3.47858	−0.282150
$153$	1.79003	0.144716
$154$	7.68389	0.619186
$155$	2.92336	0.234810
$156$	0.179187	0.0143464
$157$	−7.88695	−0.629447	−0.314723	−	0.949183i	$-0.601912\pi$
$157$	−7.88695	−0.629447	−0.314723	+	0.949183i	$0.601912\pi$
$158$	2.43256	0.193524
$159$	−4.78127	−0.379179
$160$	3.08354	0.243775
$161$	−16.1043	−1.26919
$162$	0.425671	0.0334438
$163$	−3.56730	−0.279413	−0.139706	−	0.990193i	$-0.544616\pi$
$163$	−3.56730	−0.279413	−0.139706	+	0.990193i	$0.544616\pi$
$164$	−10.0701	−0.786346
$165$	−8.30350	−0.646427
$166$	−13.3939	−1.03957
$167$	4.77647	0.369614	0.184807	−	0.982775i	$-0.440834\pi$
$167$	4.77647	0.369614	0.184807	+	0.982775i	$0.440834\pi$
$168$	3.45257	0.266372
$169$	−12.9735	−0.997959
$170$	−3.08354	−0.236497
$171$	−6.22677	−0.476173
$172$	9.93350	0.757422
$173$	17.5161	1.33172	0.665861	−	0.746076i	$-0.268065\pi$
$173$	17.5161	1.33172	0.665861	+	0.746076i	$0.268065\pi$
$174$	−7.65825	−0.580571
$175$	14.1502	1.06966
$176$	−2.44808	−0.184531
$177$	−1.09998	−0.0826799
$178$	−5.99560	−0.449389
$179$	15.5972	1.16579	0.582894	−	0.812548i	$-0.301920\pi$
$179$	15.5972	1.16579	0.582894	+	0.812548i	$0.301920\pi$
$180$	5.51965	0.411410
$181$	5.03258	0.374069	0.187034	−	0.982353i	$-0.440112\pi$
$181$	5.03258	0.374069	0.187034	+	0.982353i	$0.440112\pi$
$182$	0.511301	0.0379001
$183$	−3.22761	−0.238592
$184$	5.13080	0.378247
$185$	2.35803	0.173366
$186$	−1.04284	−0.0764650
$187$	2.44808	0.179021
$188$	3.67818	0.268259
$189$	16.5379	1.20296
$190$	10.7263	0.778171
$191$	−16.4471	−1.19007	−0.595035	−	0.803699i	$-0.702862\pi$
$191$	−16.4471	−1.19007	−0.595035	+	0.803699i	$0.702862\pi$
$192$	−1.09998	−0.0793845
$193$	−5.45721	−0.392819	−0.196409	−	0.980522i	$-0.562928\pi$
$193$	−5.45721	−0.392819	−0.196409	+	0.980522i	$0.562928\pi$
$194$	7.05472	0.506499
$195$	−0.552531	−0.0395675
$196$	2.85173	0.203695
$197$	−2.18455	−0.155643	−0.0778215	−	0.996967i	$-0.524796\pi$
$197$	−2.18455	−0.155643	−0.0778215	+	0.996967i	$0.524796\pi$
$198$	−4.38214	−0.311425
$199$	7.88556	0.558992	0.279496	−	0.960147i	$-0.409833\pi$
$199$	7.88556	0.558992	0.279496	+	0.960147i	$0.409833\pi$
$200$	−4.50824	−0.318781
$201$	11.0549	0.779755
$202$	−0.982587	−0.0691346
$203$	−21.8524	−1.53374
$204$	1.09998	0.0770143
$205$	31.0517	2.16874
$206$	13.0188	0.907059
$207$	9.18430	0.638353
$208$	−0.162900	−0.0112951
$209$	−8.51582	−0.589052
$210$	−10.6462	−0.734655
$211$	6.08150	0.418668	0.209334	−	0.977844i	$-0.432870\pi$
$211$	6.08150	0.418668	0.209334	+	0.977844i	$0.432870\pi$
$212$	4.34667	0.298531
$213$	−11.4618	−0.785351
$214$	−15.5873	−1.06553
$215$	−30.6304	−2.08897
$216$	−5.26896	−0.358507
$217$	−2.97570	−0.202004
$218$	−17.6096	−1.19267
$219$	15.7236	1.06250
$220$	7.54875	0.508937
$221$	0.162900	0.0109578
$222$	−0.841173	−0.0564558
$223$	22.9668	1.53797	0.768986	−	0.639266i	$-0.220762\pi$
$223$	22.9668	1.53797	0.768986	+	0.639266i	$0.220762\pi$
$224$	−3.13875	−0.209716
$225$	−8.06991	−0.537994
$226$	−9.87674	−0.656991
$227$	−4.49427	−0.298295	−0.149148	−	0.988815i	$-0.547653\pi$
$227$	−4.49427	−0.298295	−0.149148	+	0.988815i	$0.547653\pi$
$228$	−3.82638	−0.253408
$229$	21.8693	1.44516	0.722581	−	0.691286i	$-0.242956\pi$
$229$	21.8693	1.44516	0.722581	+	0.691286i	$0.242956\pi$
$230$	−15.8210	−1.04321
$231$	8.45216	0.556111
$232$	6.96215	0.457087
$233$	19.4539	1.27447	0.637234	−	0.770670i	$-0.280078\pi$
$233$	19.4539	1.27447	0.637234	+	0.770670i	$0.280078\pi$
$234$	−0.291596	−0.0190622
$235$	−11.3418	−0.739860
$236$	1.00000	0.0650945
$237$	2.67578	0.173810
$238$	3.13875	0.203455
$239$	25.4009	1.64305	0.821524	−	0.570174i	$-0.193124\pi$
$239$	25.4009	1.64305	0.821524	+	0.570174i	$0.193124\pi$
$240$	3.39185	0.218943
$241$	6.83971	0.440584	0.220292	−	0.975434i	$-0.429299\pi$
$241$	6.83971	0.440584	0.220292	+	0.975434i	$0.429299\pi$
$242$	5.00692	0.321857
$243$	−15.3387	−0.983975
$244$	2.93424	0.187845
$245$	−8.79345	−0.561793
$246$	−11.0770	−0.706243
$247$	−0.566659	−0.0360556
$248$	0.948053	0.0602014
$249$	−14.7331	−0.933674
$250$	−1.51637	−0.0959034
$251$	6.44345	0.406707	0.203354	−	0.979105i	$-0.434816\pi$
$251$	6.44345	0.406707	0.203354	+	0.979105i	$0.434816\pi$
$252$	−5.61847	−0.353930
$253$	12.5606	0.789677
$254$	−22.0827	−1.38559
$255$	−3.39185	−0.212406
$256$	1.00000	0.0625000
$257$	6.59071	0.411117	0.205558	−	0.978645i	$-0.434099\pi$
$257$	6.59071	0.411117	0.205558	+	0.978645i	$0.434099\pi$
$258$	10.9267	0.680266
$259$	−2.40024	−0.149144
$260$	0.502308	0.0311518
$261$	12.4625	0.771409
$262$	−11.4864	−0.709632
$263$	−18.9728	−1.16992	−0.584958	−	0.811064i	$-0.698889\pi$
$263$	−18.9728	−1.16992	−0.584958	+	0.811064i	$0.698889\pi$
$264$	−2.69285	−0.165733
$265$	−13.4032	−0.823349
$266$	−10.9184	−0.669449
$267$	−6.59507	−0.403612
$268$	−10.0501	−0.613907
$269$	−10.1552	−0.619174	−0.309587	−	0.950871i	$-0.600191\pi$
$269$	−10.1552	−0.619174	−0.309587	+	0.950871i	$0.600191\pi$
$270$	16.2471	0.988765
$271$	−16.4447	−0.998942	−0.499471	−	0.866331i	$-0.666472\pi$
$271$	−16.4447	−0.998942	−0.499471	+	0.866331i	$0.666472\pi$
$272$	−1.00000	−0.0606339
$273$	0.562423	0.0340394
$274$	−10.7293	−0.648179
$275$	−11.0365	−0.665527
$276$	5.64379	0.339716
$277$	−14.3853	−0.864332	−0.432166	−	0.901794i	$-0.642250\pi$
$277$	−14.3853	−0.864332	−0.432166	+	0.901794i	$0.642250\pi$
$278$	−4.65512	−0.279196
$279$	1.69705	0.101600
$280$	9.67846	0.578399
$281$	−6.17596	−0.368427	−0.184213	−	0.982886i	$-0.558974\pi$
$281$	−6.17596	−0.368427	−0.184213	+	0.982886i	$0.558974\pi$
$282$	4.04594	0.240932
$283$	−5.13961	−0.305518	−0.152759	−	0.988263i	$-0.548816\pi$
$283$	−5.13961	−0.305518	−0.152759	+	0.988263i	$0.548816\pi$
$284$	10.4200	0.618312
$285$	11.7988	0.698901
$286$	−0.398791	−0.0235810
$287$	−31.6076	−1.86574
$288$	1.79003	0.105479
$289$	1.00000	0.0588235
$290$	−21.4681	−1.26065
$291$	7.76008	0.454904
$292$	−14.2944	−0.836514
$293$	−18.0581	−1.05496	−0.527482	−	0.849566i	$-0.676864\pi$
$293$	−18.0581	−1.05496	−0.527482	+	0.849566i	$0.676864\pi$
$294$	3.13686	0.182946
$295$	−3.08354	−0.179531
$296$	0.764713	0.0444481
$297$	−12.8988	−0.748466
$298$	−11.3156	−0.655493
$299$	0.835804	0.0483358
$300$	−4.95899	−0.286308
$301$	31.1787	1.79711
$302$	−0.775744	−0.0446390
$303$	−1.08083	−0.0620921
$304$	3.47858	0.199510
$305$	−9.04785	−0.518078
$306$	−1.79003	−0.102329
$307$	−15.2740	−0.871732	−0.435866	−	0.900012i	$-0.643558\pi$
$307$	−15.2740	−0.871732	−0.435866	+	0.900012i	$0.643558\pi$
$308$	−7.68389	−0.437830
$309$	14.3204	0.814660
$310$	−2.92336	−0.166036
$311$	−7.15974	−0.405992	−0.202996	−	0.979180i	$-0.565068\pi$
$311$	−7.15974	−0.405992	−0.202996	+	0.979180i	$0.565068\pi$
$312$	−0.179187	−0.0101445
$313$	19.8840	1.12391	0.561955	−	0.827168i	$-0.310049\pi$
$313$	19.8840	1.12391	0.561955	+	0.827168i	$0.310049\pi$
$314$	7.88695	0.445086
$315$	17.3248	0.976141
$316$	−2.43256	−0.136842
$317$	−15.2623	−0.857217	−0.428609	−	0.903490i	$-0.640996\pi$
$317$	−15.2623	−0.857217	−0.428609	+	0.903490i	$0.640996\pi$
$318$	4.78127	0.268120
$319$	17.0439	0.954274
$320$	−3.08354	−0.172375
$321$	−17.1458	−0.956984
$322$	16.1043	0.897456
$323$	−3.47858	−0.193553
$324$	−0.425671	−0.0236484
$325$	−0.734390	−0.0407366
$326$	3.56730	0.197575
$327$	−19.3703	−1.07118
$328$	10.0701	0.556030
$329$	11.5449	0.636490
$330$	8.30350	0.457093
$331$	3.26200	0.179296	0.0896478	−	0.995974i	$-0.471426\pi$
$331$	3.26200	0.179296	0.0896478	+	0.995974i	$0.471426\pi$
$332$	13.3939	0.735088
$333$	1.36886	0.0750133
$334$	−4.77647	−0.261357
$335$	30.9899	1.69316
$336$	−3.45257	−0.188353
$337$	−5.61751	−0.306006	−0.153003	−	0.988226i	$-0.548894\pi$
$337$	−5.61751	−0.306006	−0.153003	+	0.988226i	$0.548894\pi$
$338$	12.9735	0.705663
$339$	−10.8643	−0.590065
$340$	3.08354	0.167229
$341$	2.32091	0.125684
$342$	6.22677	0.336705
$343$	−13.0204	−0.703033
$344$	−9.93350	−0.535578
$345$	−17.4029	−0.936940
$346$	−17.5161	−0.941669
$347$	14.9687	0.803564	0.401782	−	0.915735i	$-0.368391\pi$
$347$	14.9687	0.803564	0.401782	+	0.915735i	$0.368391\pi$
$348$	7.65825	0.410525
$349$	26.8670	1.43816	0.719078	−	0.694930i	$-0.244565\pi$
$349$	26.8670	1.43816	0.719078	+	0.694930i	$0.244565\pi$
$350$	−14.1502	−0.756361
$351$	−0.858312	−0.0458133
$352$	2.44808	0.130483
$353$	28.8753	1.53688	0.768440	−	0.639922i	$-0.221033\pi$
$353$	28.8753	1.53688	0.768440	+	0.639922i	$0.221033\pi$
$354$	1.09998	0.0584635
$355$	−32.1305	−1.70531
$356$	5.99560	0.317766
$357$	3.45257	0.182730
$358$	−15.5972	−0.824336
$359$	7.28887	0.384692	0.192346	−	0.981327i	$-0.438390\pi$
$359$	7.28887	0.384692	0.192346	+	0.981327i	$0.438390\pi$
$360$	−5.51965	−0.290911
$361$	−6.89950	−0.363132
$362$	−5.03258	−0.264507
$363$	5.50753	0.289071
$364$	−0.511301	−0.0267994
$365$	44.0773	2.30711
$366$	3.22761	0.168710
$367$	−19.3232	−1.00867	−0.504333	−	0.863509i	$-0.668261\pi$
$367$	−19.3232	−1.00867	−0.504333	+	0.863509i	$0.668261\pi$
$368$	−5.13080	−0.267461
$369$	18.0259	0.938391
$370$	−2.35803	−0.122588
$371$	13.6431	0.708315
$372$	1.04284	0.0540689
$373$	−38.2536	−1.98070	−0.990348	−	0.138605i	$-0.955738\pi$
$373$	−38.2536	−1.98070	−0.990348	+	0.138605i	$0.955738\pi$
$374$	−2.44808	−0.126587
$375$	−1.66798	−0.0861340
$376$	−3.67818	−0.189688
$377$	1.13413	0.0584107
$378$	−16.5379	−0.850620
$379$	20.6926	1.06291	0.531453	−	0.847088i	$-0.321646\pi$
$379$	20.6926	1.06291	0.531453	+	0.847088i	$0.321646\pi$
$380$	−10.7263	−0.550250
$381$	−24.2906	−1.24445
$382$	16.4471	0.841507
$383$	−9.16970	−0.468550	−0.234275	−	0.972170i	$-0.575272\pi$
$383$	−9.16970	−0.468550	−0.234275	+	0.972170i	$0.575272\pi$
$384$	1.09998	0.0561333
$385$	23.6936	1.20754
$386$	5.45721	0.277765
$387$	−17.7813	−0.903874
$388$	−7.05472	−0.358149
$389$	6.50804	0.329971	0.164985	−	0.986296i	$-0.447242\pi$
$389$	6.50804	0.329971	0.164985	+	0.986296i	$0.447242\pi$
$390$	0.552531	0.0279785
$391$	5.13080	0.259475
$392$	−2.85173	−0.144034
$393$	−12.6349	−0.637344
$394$	2.18455	0.110056
$395$	7.50090	0.377411
$396$	4.38214	0.220211
$397$	4.93066	0.247463	0.123731	−	0.992316i	$-0.460514\pi$
$397$	4.93066	0.247463	0.123731	+	0.992316i	$0.460514\pi$
$398$	−7.88556	−0.395267
$399$	−12.0100	−0.601254
$400$	4.50824	0.225412
$401$	−16.9918	−0.848529	−0.424265	−	0.905538i	$-0.639467\pi$
$401$	−16.9918	−0.848529	−0.424265	+	0.905538i	$0.639467\pi$
$402$	−11.0549	−0.551370
$403$	0.154437	0.00769308
$404$	0.982587	0.0488855
$405$	1.31257	0.0652223
$406$	21.8524	1.08452
$407$	1.87208	0.0927954
$408$	−1.09998	−0.0544573
$409$	20.5287	1.01508	0.507539	−	0.861629i	$-0.330555\pi$
$409$	20.5287	1.01508	0.507539	+	0.861629i	$0.330555\pi$
$410$	−31.0517	−1.53353
$411$	−11.8020	−0.582151
$412$	−13.0188	−0.641388
$413$	3.13875	0.154448
$414$	−9.18430	−0.451384
$415$	−41.3008	−2.02738
$416$	0.162900	0.00798681
$417$	−5.12056	−0.250755
$418$	8.51582	0.416523
$419$	6.48784	0.316952	0.158476	−	0.987363i	$-0.449342\pi$
$419$	6.48784	0.316952	0.158476	+	0.987363i	$0.449342\pi$
$420$	10.6462	0.519479
$421$	28.2089	1.37482	0.687410	−	0.726270i	$-0.258748\pi$
$421$	28.2089	1.37482	0.687410	+	0.726270i	$0.258748\pi$
$422$	−6.08150	−0.296043
$423$	−6.58408	−0.320129
$424$	−4.34667	−0.211093
$425$	−4.50824	−0.218682
$426$	11.4618	0.555327
$427$	9.20983	0.445695
$428$	15.5873	0.753441
$429$	−0.438663	−0.0211789
$430$	30.6304	1.47713
$431$	2.55970	0.123297	0.0616483	−	0.998098i	$-0.480364\pi$
$431$	2.55970	0.123297	0.0616483	+	0.998098i	$0.480364\pi$
$432$	5.26896	0.253503
$433$	22.0289	1.05864	0.529320	−	0.848422i	$-0.322447\pi$
$433$	22.0289	1.05864	0.529320	+	0.848422i	$0.322447\pi$
$434$	2.97570	0.142838
$435$	−23.6146	−1.13223
$436$	17.6096	0.843346
$437$	−17.8479	−0.853779
$438$	−15.7236	−0.751301
$439$	−25.1827	−1.20191	−0.600953	−	0.799284i	$-0.705212\pi$
$439$	−25.1827	−1.20191	−0.600953	+	0.799284i	$0.705212\pi$
$440$	−7.54875	−0.359873
$441$	−5.10470	−0.243081
$442$	−0.162900	−0.00774834
$443$	−1.57459	−0.0748112	−0.0374056	−	0.999300i	$-0.511909\pi$
$443$	−1.57459	−0.0748112	−0.0374056	+	0.999300i	$0.511909\pi$
$444$	0.841173	0.0399203
$445$	−18.4877	−0.876401
$446$	−22.9668	−1.08751
$447$	−12.4469	−0.588720
$448$	3.13875	0.148292
$449$	−0.149370	−0.00704920	−0.00352460	−	0.999994i	$-0.501122\pi$
$449$	−0.149370	−0.00704920	−0.00352460	+	0.999994i	$0.501122\pi$
$450$	8.06991	0.380419
$451$	24.6525	1.16084
$452$	9.87674	0.464563
$453$	−0.853306	−0.0400918
$454$	4.49427	0.210927
$455$	1.57662	0.0739130
$456$	3.82638	0.179187
$457$	−17.3054	−0.809511	−0.404756	−	0.914425i	$-0.632643\pi$
$457$	−17.3054	−0.809511	−0.404756	+	0.914425i	$0.632643\pi$
$458$	−21.8693	−1.02188
$459$	−5.26896	−0.245934
$460$	15.8210	0.737659
$461$	14.5565	0.677963	0.338982	−	0.940793i	$-0.389918\pi$
$461$	14.5565	0.677963	0.338982	+	0.940793i	$0.389918\pi$
$462$	−8.45216	−0.393230
$463$	−28.7122	−1.33437	−0.667185	−	0.744892i	$-0.732501\pi$
$463$	−28.7122	−1.33437	−0.667185	+	0.744892i	$0.732501\pi$
$464$	−6.96215	−0.323210
$465$	−3.21565	−0.149122
$466$	−19.4539	−0.901186
$467$	−30.9558	−1.43247	−0.716233	−	0.697861i	$-0.754135\pi$
$467$	−30.9558	−1.43247	−0.716233	+	0.697861i	$0.754135\pi$
$468$	0.291596	0.0134790
$469$	−31.5447	−1.45660
$470$	11.3418	0.523160
$471$	8.67551	0.399747
$472$	−1.00000	−0.0460287
$473$	−24.3180	−1.11814
$474$	−2.67578	−0.122902
$475$	15.6823	0.719551
$476$	−3.13875	−0.143864
$477$	−7.78069	−0.356254
$478$	−25.4009	−1.16181
$479$	−32.9336	−1.50478	−0.752388	−	0.658721i	$-0.771098\pi$
$479$	−32.9336	−1.50478	−0.752388	+	0.658721i	$0.771098\pi$
$480$	−3.39185	−0.154816
$481$	0.124572	0.00567997
$482$	−6.83971	−0.311540
$483$	17.7144	0.806035
$484$	−5.00692	−0.227587
$485$	21.7535	0.987777
$486$	15.3387	0.695776
$487$	−34.5771	−1.56684	−0.783418	−	0.621495i	$-0.786526\pi$
$487$	−34.5771	−1.56684	−0.783418	+	0.621495i	$0.786526\pi$
$488$	−2.93424	−0.132827
$489$	3.92398	0.177448
$490$	8.79345	0.397247
$491$	−20.7017	−0.934254	−0.467127	−	0.884190i	$-0.654711\pi$
$491$	−20.7017	−0.934254	−0.467127	+	0.884190i	$0.654711\pi$
$492$	11.0770	0.499389
$493$	6.96215	0.313559
$494$	0.566659	0.0254952
$495$	−13.5125	−0.607343
$496$	−0.948053	−0.0425688
$497$	32.7057	1.46705
$498$	14.7331	0.660207
$499$	10.4728	0.468828	0.234414	−	0.972137i	$-0.424683\pi$
$499$	10.4728	0.468828	0.234414	+	0.972137i	$0.424683\pi$
$500$	1.51637	0.0678140
$501$	−5.25404	−0.234733
$502$	−6.44345	−0.287585
$503$	18.8072	0.838572	0.419286	−	0.907854i	$-0.362280\pi$
$503$	18.8072	0.838572	0.419286	+	0.907854i	$0.362280\pi$
$504$	5.61847	0.250266
$505$	−3.02985	−0.134827
$506$	−12.5606	−0.558386
$507$	14.2706	0.633780
$508$	22.0827	0.979761
$509$	−17.7618	−0.787279	−0.393639	−	0.919265i	$-0.628784\pi$
$509$	−17.7618	−0.787279	−0.393639	+	0.919265i	$0.628784\pi$
$510$	3.39185	0.150194
$511$	−44.8664	−1.98477
$512$	−1.00000	−0.0441942
$513$	18.3285	0.809223
$514$	−6.59071	−0.290704
$515$	40.1439	1.76895
$516$	−10.9267	−0.481021
$517$	−9.00447	−0.396016
$518$	2.40024	0.105461
$519$	−19.2674	−0.845744
$520$	−0.502308	−0.0220277
$521$	21.7652	0.953551	0.476776	−	0.879025i	$-0.341805\pi$
$521$	21.7652	0.953551	0.476776	+	0.879025i	$0.341805\pi$
$522$	−12.4625	−0.545468
$523$	32.2021	1.40810	0.704050	−	0.710151i	$-0.251373\pi$
$523$	32.2021	1.40810	0.704050	+	0.710151i	$0.251373\pi$
$524$	11.4864	0.501785
$525$	−15.5650	−0.679313
$526$	18.9728	0.827255
$527$	0.948053	0.0412979
$528$	2.69285	0.117191
$529$	3.32506	0.144568
$530$	13.4032	0.582196
$531$	−1.79003	−0.0776809
$532$	10.9184	0.473372
$533$	1.64042	0.0710545
$534$	6.59507	0.285396
$535$	−48.0641	−2.07799
$536$	10.0501	0.434097
$537$	−17.1566	−0.740364
$538$	10.1552	0.437822
$539$	−6.98127	−0.300704
$540$	−16.2471	−0.699163
$541$	−24.8231	−1.06723	−0.533614	−	0.845728i	$-0.679166\pi$
$541$	−24.8231	−1.06723	−0.533614	+	0.845728i	$0.679166\pi$
$542$	16.4447	0.706359
$543$	−5.53576	−0.237562
$544$	1.00000	0.0428746
$545$	−54.2999	−2.32595
$546$	−0.562423	−0.0240695
$547$	−35.4718	−1.51666	−0.758331	−	0.651869i	$-0.773985\pi$
$547$	−35.4718	−1.51666	−0.758331	+	0.651869i	$0.773985\pi$
$548$	10.7293	0.458332
$549$	−5.25239	−0.224166
$550$	11.0365	0.470599
$551$	−24.2184	−1.03174
$552$	−5.64379	−0.240216
$553$	−7.63519	−0.324681
$554$	14.3853	0.611175
$555$	−2.59379	−0.110100
$556$	4.65512	0.197421
$557$	−20.8163	−0.882014	−0.441007	−	0.897504i	$-0.645379\pi$
$557$	−20.8163	−0.882014	−0.441007	+	0.897504i	$0.645379\pi$
$558$	−1.69705	−0.0718418
$559$	−1.61816	−0.0684410
$560$	−9.67846	−0.408990
$561$	−2.69285	−0.113692
$562$	6.17596	0.260517
$563$	−6.68211	−0.281617	−0.140809	−	0.990037i	$-0.544970\pi$
$563$	−6.68211	−0.281617	−0.140809	+	0.990037i	$0.544970\pi$
$564$	−4.04594	−0.170365
$565$	−30.4553	−1.28127
$566$	5.13961	0.216034
$567$	−1.33607	−0.0561098
$568$	−10.4200	−0.437213
$569$	−7.57360	−0.317502	−0.158751	−	0.987319i	$-0.550747\pi$
$569$	−7.57360	−0.317502	−0.158751	+	0.987319i	$0.550747\pi$
$570$	−11.7988	−0.494198
$571$	−20.5726	−0.860936	−0.430468	−	0.902606i	$-0.641651\pi$
$571$	−20.5726	−0.860936	−0.430468	+	0.902606i	$0.641651\pi$
$572$	0.398791	0.0166743
$573$	18.0916	0.755786
$574$	31.6076	1.31928
$575$	−23.1309	−0.964623
$576$	−1.79003	−0.0745848
$577$	21.1235	0.879384	0.439692	−	0.898149i	$-0.355088\pi$
$577$	21.1235	0.879384	0.439692	+	0.898149i	$0.355088\pi$
$578$	−1.00000	−0.0415945
$579$	6.00285	0.249470
$580$	21.4681	0.891414
$581$	42.0402	1.74412
$582$	−7.76008	−0.321666
$583$	−10.6410	−0.440705
$584$	14.2944	0.591505
$585$	−0.899149	−0.0371752
$586$	18.0581	0.745972
$587$	−27.6604	−1.14167	−0.570834	−	0.821065i	$-0.693380\pi$
$587$	−27.6604	−1.14167	−0.570834	+	0.821065i	$0.693380\pi$
$588$	−3.13686	−0.129362
$589$	−3.29788	−0.135887
$590$	3.08354	0.126947
$591$	2.40298	0.0988452
$592$	−0.764713	−0.0314295
$593$	6.51742	0.267638	0.133819	−	0.991006i	$-0.457276\pi$
$593$	6.51742	0.267638	0.133819	+	0.991006i	$0.457276\pi$
$594$	12.8988	0.529245
$595$	9.67846	0.396778
$596$	11.3156	0.463503
$597$	−8.67399	−0.355003
$598$	−0.835804	−0.0341786
$599$	−1.41092	−0.0576485	−0.0288242	−	0.999584i	$-0.509176\pi$
$599$	−1.41092	−0.0576485	−0.0288242	+	0.999584i	$0.509176\pi$
$600$	4.95899	0.202450
$601$	30.0589	1.22613	0.613064	−	0.790034i	$-0.289937\pi$
$601$	30.0589	1.22613	0.613064	+	0.790034i	$0.289937\pi$
$602$	−31.1787	−1.27075
$603$	17.9900	0.732609
$604$	0.775744	0.0315646
$605$	15.4391	0.627687
$606$	1.08083	0.0439057
$607$	21.4741	0.871606	0.435803	−	0.900042i	$-0.356464\pi$
$607$	21.4741	0.871606	0.435803	+	0.900042i	$0.356464\pi$
$608$	−3.47858	−0.141075
$609$	24.0373	0.974041
$610$	9.04785	0.366337
$611$	−0.599174	−0.0242400
$612$	1.79003	0.0723579
$613$	6.17309	0.249329	0.124664	−	0.992199i	$-0.460215\pi$
$613$	6.17309	0.249329	0.124664	+	0.992199i	$0.460215\pi$
$614$	15.2740	0.616407
$615$	−34.1564	−1.37732
$616$	7.68389	0.309593
$617$	−1.37095	−0.0551925	−0.0275962	−	0.999619i	$-0.508785\pi$
$617$	−1.37095	−0.0551925	−0.0275962	+	0.999619i	$0.508785\pi$
$618$	−14.3204	−0.576052
$619$	46.3120	1.86144	0.930718	−	0.365738i	$-0.119183\pi$
$619$	46.3120	1.86144	0.930718	+	0.365738i	$0.119183\pi$
$620$	2.92336	0.117405
$621$	−27.0340	−1.08484
$622$	7.15974	0.287080
$623$	18.8187	0.753954
$624$	0.179187	0.00717322
$625$	−27.2170	−1.08868
$626$	−19.8840	−0.794725
$627$	9.36727	0.374093
$628$	−7.88695	−0.314723
$629$	0.764713	0.0304911
$630$	−17.3248	−0.690236
$631$	34.1919	1.36116	0.680579	−	0.732675i	$-0.261728\pi$
$631$	34.1919	1.36116	0.680579	+	0.732675i	$0.261728\pi$
$632$	2.43256	0.0967620
$633$	−6.68956	−0.265886
$634$	15.2623	0.606144
$635$	−68.0929	−2.70219
$636$	−4.78127	−0.189590
$637$	−0.464546	−0.0184060
$638$	−17.0439	−0.674773
$639$	−18.6521	−0.737867
$640$	3.08354	0.121888
$641$	−24.2439	−0.957578	−0.478789	−	0.877930i	$-0.658924\pi$
$641$	−24.2439	−0.957578	−0.478789	+	0.877930i	$0.658924\pi$
$642$	17.1458	0.676690
$643$	−27.8240	−1.09727	−0.548635	−	0.836062i	$-0.684852\pi$
$643$	−27.8240	−1.09727	−0.548635	+	0.836062i	$0.684852\pi$
$644$	−16.1043	−0.634597
$645$	33.6929	1.32666
$646$	3.47858	0.136863
$647$	41.3065	1.62393	0.811963	−	0.583709i	$-0.198399\pi$
$647$	41.3065	1.62393	0.811963	+	0.583709i	$0.198399\pi$
$648$	0.425671	0.0167219
$649$	−2.44808	−0.0960954
$650$	0.734390	0.0288052
$651$	3.27322	0.128288
$652$	−3.56730	−0.139706
$653$	19.3894	0.758764	0.379382	−	0.925240i	$-0.376137\pi$
$653$	19.3894	0.758764	0.379382	+	0.925240i	$0.376137\pi$
$654$	19.3703	0.757437
$655$	−35.4188	−1.38393
$656$	−10.0701	−0.393173
$657$	25.5874	0.998260
$658$	−11.5449	−0.450067
$659$	−5.24266	−0.204225	−0.102112	−	0.994773i	$-0.532560\pi$
$659$	−5.24266	−0.204225	−0.102112	+	0.994773i	$0.532560\pi$
$660$	−8.30350	−0.323213
$661$	41.1713	1.60138	0.800688	−	0.599081i	$-0.204467\pi$
$661$	41.1713	1.60138	0.800688	+	0.599081i	$0.204467\pi$
$662$	−3.26200	−0.126781
$663$	−0.179187	−0.00695905
$664$	−13.3939	−0.519786
$665$	−33.6673	−1.30556
$666$	−1.36886	−0.0530424
$667$	35.7214	1.38314
$668$	4.77647	0.184807
$669$	−25.2631	−0.976729
$670$	−30.9899	−1.19724
$671$	−7.18324	−0.277306
$672$	3.45257	0.133186
$673$	−7.94029	−0.306076	−0.153038	−	0.988220i	$-0.548906\pi$
$673$	−7.94029	−0.306076	−0.153038	+	0.988220i	$0.548906\pi$
$674$	5.61751	0.216379
$675$	23.7537	0.914282
$676$	−12.9735	−0.498979
$677$	−11.1366	−0.428015	−0.214008	−	0.976832i	$-0.568652\pi$
$677$	−11.1366	−0.428015	−0.214008	+	0.976832i	$0.568652\pi$
$678$	10.8643	0.417239
$679$	−22.1430	−0.849770
$680$	−3.08354	−0.118248
$681$	4.94363	0.189440
$682$	−2.32091	−0.0888721
$683$	14.6841	0.561872	0.280936	−	0.959726i	$-0.409355\pi$
$683$	14.6841	0.561872	0.280936	+	0.959726i	$0.409355\pi$
$684$	−6.22677	−0.238087
$685$	−33.0842	−1.26408
$686$	13.0204	0.497120
$687$	−24.0558	−0.917788
$688$	9.93350	0.378711
$689$	−0.708071	−0.0269754
$690$	17.4029	0.662516
$691$	−33.6866	−1.28150	−0.640750	−	0.767750i	$-0.721377\pi$
$691$	−33.6866	−1.28150	−0.640750	+	0.767750i	$0.721377\pi$
$692$	17.5161	0.665861
$693$	13.7544	0.522488
$694$	−14.9687	−0.568205
$695$	−14.3543	−0.544488
$696$	−7.65825	−0.290285
$697$	10.0701	0.381434
$698$	−26.8670	−1.01693
$699$	−21.3990	−0.809385
$700$	14.1502	0.534828
$701$	−8.97644	−0.339036	−0.169518	−	0.985527i	$-0.554221\pi$
$701$	−8.97644	−0.339036	−0.169518	+	0.985527i	$0.554221\pi$
$702$	0.858312	0.0323949
$703$	−2.66011	−0.100328
$704$	−2.44808	−0.0922654
$705$	12.4758	0.469867
$706$	−28.8753	−1.08674
$707$	3.08409	0.115989
$708$	−1.09998	−0.0413399
$709$	35.4393	1.33095	0.665475	−	0.746420i	$-0.268229\pi$
$709$	35.4393	1.33095	0.665475	+	0.746420i	$0.268229\pi$
$710$	32.1305	1.20583
$711$	4.35437	0.163301
$712$	−5.99560	−0.224695
$713$	4.86427	0.182168
$714$	−3.45257	−0.129209
$715$	−1.22969	−0.0459877
$716$	15.5972	0.582894
$717$	−27.9406	−1.04346
$718$	−7.28887	−0.272018
$719$	−22.7317	−0.847750	−0.423875	−	0.905721i	$-0.639330\pi$
$719$	−22.7317	−0.847750	−0.423875	+	0.905721i	$0.639330\pi$
$720$	5.51965	0.205705
$721$	−40.8626	−1.52180
$722$	6.89950	0.256773
$723$	−7.52357	−0.279805
$724$	5.03258	0.187034
$725$	−31.3870	−1.16569
$726$	−5.50753	−0.204404
$727$	24.4704	0.907558	0.453779	−	0.891114i	$-0.350076\pi$
$727$	24.4704	0.907558	0.453779	+	0.891114i	$0.350076\pi$
$728$	0.511301	0.0189501
$729$	18.1493	0.672196
$730$	−44.0773	−1.63137
$731$	−9.93350	−0.367404
$732$	−3.22761	−0.119296
$733$	1.55889	0.0575790	0.0287895	−	0.999585i	$-0.490835\pi$
$733$	1.55889	0.0575790	0.0287895	+	0.999585i	$0.490835\pi$
$734$	19.3232	0.713234
$735$	9.67265	0.356781
$736$	5.13080	0.189124
$737$	24.6034	0.906277
$738$	−18.0259	−0.663542
$739$	−0.598059	−0.0220000	−0.0110000	−	0.999939i	$-0.503501\pi$
$739$	−0.598059	−0.0220000	−0.0110000	+	0.999939i	$0.503501\pi$
$740$	2.35803	0.0866828
$741$	0.623316	0.0228981
$742$	−13.6431	−0.500854
$743$	−24.2629	−0.890118	−0.445059	−	0.895501i	$-0.646817\pi$
$743$	−24.2629	−0.890118	−0.445059	+	0.895501i	$0.646817\pi$
$744$	−1.04284	−0.0382325
$745$	−34.8920	−1.27834
$746$	38.2536	1.40056
$747$	−23.9756	−0.877222
$748$	2.44808	0.0895105
$749$	48.9246	1.78767
$750$	1.66798	0.0609060
$751$	19.1424	0.698518	0.349259	−	0.937026i	$-0.386433\pi$
$751$	19.1424	0.698518	0.349259	+	0.937026i	$0.386433\pi$
$752$	3.67818	0.134130
$753$	−7.08770	−0.258290
$754$	−1.13413	−0.0413026
$755$	−2.39204	−0.0870552
$756$	16.5379	0.601479
$757$	41.8679	1.52172	0.760858	−	0.648918i	$-0.224778\pi$
$757$	41.8679	1.52172	0.760858	+	0.648918i	$0.224778\pi$
$758$	−20.6926	−0.751588
$759$	−13.8164	−0.501505
$760$	10.7263	0.389085
$761$	43.5315	1.57802	0.789008	−	0.614383i	$-0.210595\pi$
$761$	43.5315	1.57802	0.789008	+	0.614383i	$0.210595\pi$
$762$	24.2906	0.879956
$763$	55.2720	2.00098
$764$	−16.4471	−0.595035
$765$	−5.51965	−0.199563
$766$	9.16970	0.331315
$767$	−0.162900	−0.00588196
$768$	−1.09998	−0.0396923
$769$	54.1241	1.95177	0.975883	−	0.218296i	$-0.0700499\pi$
$769$	54.1241	1.95177	0.975883	+	0.218296i	$0.0700499\pi$
$770$	−23.6936	−0.853859
$771$	−7.24967	−0.261091
$772$	−5.45721	−0.196409
$773$	48.2493	1.73541	0.867704	−	0.497082i	$-0.165595\pi$
$773$	48.2493	1.73541	0.867704	+	0.497082i	$0.165595\pi$
$774$	17.7813	0.639136
$775$	−4.27405	−0.153528
$776$	7.05472	0.253250
$777$	2.64023	0.0947177
$778$	−6.50804	−0.233324
$779$	−35.0298	−1.25507
$780$	−0.552531	−0.0197838
$781$	−25.5089	−0.912781
$782$	−5.13080	−0.183477
$783$	−36.6833	−1.31095
$784$	2.85173	0.101848
$785$	24.3197	0.868009
$786$	12.6349	0.450670
$787$	−22.2587	−0.793436	−0.396718	−	0.917941i	$-0.629851\pi$
$787$	−22.2587	−0.793436	−0.396718	+	0.917941i	$0.629851\pi$
$788$	−2.18455	−0.0778215
$789$	20.8698	0.742986
$790$	−7.50090	−0.266870
$791$	31.0006	1.10225
$792$	−4.38214	−0.155713
$793$	−0.477986	−0.0169738
$794$	−4.93066	−0.174982
$795$	14.7433	0.522889
$796$	7.88556	0.279496
$797$	51.5933	1.82753	0.913765	−	0.406244i	$-0.133162\pi$
$797$	51.5933	1.82753	0.913765	+	0.406244i	$0.133162\pi$
$798$	12.0100	0.425151
$799$	−3.67818	−0.130125
$800$	−4.50824	−0.159390
$801$	−10.7323	−0.379208
$802$	16.9918	0.600001
$803$	34.9937	1.23490
$804$	11.0549	0.389877
$805$	49.6582	1.75022
$806$	−0.154437	−0.00543983
$807$	11.1706	0.393222
$808$	−0.982587	−0.0345673
$809$	3.44114	0.120984	0.0604920	−	0.998169i	$-0.480733\pi$
$809$	3.44114	0.120984	0.0604920	+	0.998169i	$0.480733\pi$
$810$	−1.31257	−0.0461191
$811$	4.67847	0.164283	0.0821416	−	0.996621i	$-0.473824\pi$
$811$	4.67847	0.164283	0.0821416	+	0.996621i	$0.473824\pi$
$812$	−21.8524	−0.766870
$813$	18.0889	0.634404
$814$	−1.87208	−0.0656163
$815$	10.9999	0.385311
$816$	1.09998	0.0385071
$817$	34.5544	1.20891
$818$	−20.5287	−0.717768
$819$	0.915246	0.0319813
$820$	31.0517	1.08437
$821$	−4.00417	−0.139746	−0.0698732	−	0.997556i	$-0.522259\pi$
$821$	−4.00417	−0.139746	−0.0698732	+	0.997556i	$0.522259\pi$
$822$	11.8020	0.411643
$823$	8.93567	0.311478	0.155739	−	0.987798i	$-0.450224\pi$
$823$	8.93567	0.311478	0.155739	+	0.987798i	$0.450224\pi$
$824$	13.0188	0.453530
$825$	12.1400	0.422660
$826$	−3.13875	−0.109211
$827$	−9.08675	−0.315977	−0.157989	−	0.987441i	$-0.550501\pi$
$827$	−9.08675	−0.315977	−0.157989	+	0.987441i	$0.550501\pi$
$828$	9.18430	0.319177
$829$	40.1518	1.39453	0.697265	−	0.716814i	$-0.254400\pi$
$829$	40.1518	1.39453	0.697265	+	0.716814i	$0.254400\pi$
$830$	41.3008	1.43357
$831$	15.8237	0.548916
$832$	−0.162900	−0.00564753
$833$	−2.85173	−0.0988068
$834$	5.12056	0.177310
$835$	−14.7284	−0.509699
$836$	−8.51582	−0.294526
$837$	−4.99526	−0.172661
$838$	−6.48784	−0.224119
$839$	2.03279	0.0701796	0.0350898	−	0.999384i	$-0.488828\pi$
$839$	2.03279	0.0701796	0.0350898	+	0.999384i	$0.488828\pi$
$840$	−10.6462	−0.367327
$841$	19.4715	0.671431
$842$	−28.2089	−0.972144
$843$	6.79345	0.233979
$844$	6.08150	0.209334
$845$	40.0042	1.37619
$846$	6.58408	0.226365
$847$	−15.7155	−0.539990
$848$	4.34667	0.149265
$849$	5.65349	0.194027
$850$	4.50824	0.154631
$851$	3.92359	0.134499
$852$	−11.4618	−0.392675
$853$	−7.13512	−0.244302	−0.122151	−	0.992512i	$-0.538979\pi$
$853$	−7.13512	−0.244302	−0.122151	+	0.992512i	$0.538979\pi$
$854$	−9.20983	−0.315154
$855$	19.2005	0.656644
$856$	−15.5873	−0.532763
$857$	−37.0703	−1.26630	−0.633149	−	0.774030i	$-0.718238\pi$
$857$	−37.0703	−1.26630	−0.633149	+	0.774030i	$0.718238\pi$
$858$	0.438663	0.0149757
$859$	−52.4233	−1.78866	−0.894330	−	0.447407i	$-0.852348\pi$
$859$	−52.4233	−1.78866	−0.894330	+	0.447407i	$0.852348\pi$
$860$	−30.6304	−1.04449
$861$	34.7679	1.18489
$862$	−2.55970	−0.0871838
$863$	−32.4480	−1.10454	−0.552272	−	0.833664i	$-0.686239\pi$
$863$	−32.4480	−1.10454	−0.552272	+	0.833664i	$0.686239\pi$
$864$	−5.26896	−0.179254
$865$	−54.0115	−1.83645
$866$	−22.0289	−0.748572
$867$	−1.09998	−0.0373574
$868$	−2.97570	−0.101002
$869$	5.95509	0.202013
$870$	23.6146	0.800608
$871$	1.63715	0.0554729
$872$	−17.6096	−0.596336
$873$	12.6282	0.427400
$874$	17.8479	0.603713
$875$	4.75949	0.160900
$876$	15.7236	0.531250
$877$	−37.5572	−1.26822	−0.634109	−	0.773244i	$-0.718633\pi$
$877$	−37.5572	−1.26822	−0.634109	+	0.773244i	$0.718633\pi$
$878$	25.1827	0.849876
$879$	19.8636	0.669983
$880$	7.54875	0.254468
$881$	30.9688	1.04337	0.521683	−	0.853140i	$-0.325304\pi$
$881$	30.9688	1.04337	0.521683	+	0.853140i	$0.325304\pi$
$882$	5.10470	0.171884
$883$	28.8740	0.971689	0.485844	−	0.874045i	$-0.338512\pi$
$883$	28.8740	0.971689	0.485844	+	0.874045i	$0.338512\pi$
$884$	0.162900	0.00547891
$885$	3.39185	0.114016
$886$	1.57459	0.0528995
$887$	51.9537	1.74443	0.872217	−	0.489120i	$-0.162682\pi$
$887$	51.9537	1.74443	0.872217	+	0.489120i	$0.162682\pi$
$888$	−0.841173	−0.0282279
$889$	69.3120	2.32465
$890$	18.4877	0.619709
$891$	1.04207	0.0349108
$892$	22.9668	0.768986
$893$	12.7948	0.428163
$894$	12.4469	0.416288
$895$	−48.0946	−1.60762
$896$	−3.13875	−0.104858
$897$	−0.919372	−0.0306969
$898$	0.149370	0.00498454
$899$	6.60049	0.220139
$900$	−8.06991	−0.268997
$901$	−4.34667	−0.144809
$902$	−24.6525	−0.820837
$903$	−34.2961	−1.14130
$904$	−9.87674	−0.328495
$905$	−15.5182	−0.515842
$906$	0.853306	0.0283492
$907$	19.6548	0.652626	0.326313	−	0.945262i	$-0.394194\pi$
$907$	19.6548	0.652626	0.326313	+	0.945262i	$0.394194\pi$
$908$	−4.49427	−0.149148
$909$	−1.75887	−0.0583379
$910$	−1.57662	−0.0522644
$911$	31.5415	1.04502	0.522509	−	0.852634i	$-0.324996\pi$
$911$	31.5415	1.04502	0.522509	+	0.852634i	$0.324996\pi$
$912$	−3.82638	−0.126704
$913$	−32.7894	−1.08517
$914$	17.3054	0.572411
$915$	9.95249	0.329019
$916$	21.8693	0.722581
$917$	36.0529	1.19057
$918$	5.26896	0.173902
$919$	29.5492	0.974737	0.487368	−	0.873196i	$-0.337957\pi$
$919$	29.5492	0.974737	0.487368	+	0.873196i	$0.337957\pi$
$920$	−15.8210	−0.521604
$921$	16.8011	0.553616
$922$	−14.5565	−0.479393
$923$	−1.69741	−0.0558710
$924$	8.45216	0.278056
$925$	−3.44751	−0.113353
$926$	28.7122	0.943542
$927$	23.3040	0.765404
$928$	6.96215	0.228544
$929$	7.97723	0.261724	0.130862	−	0.991401i	$-0.458225\pi$
$929$	7.97723	0.261724	0.130862	+	0.991401i	$0.458225\pi$
$930$	3.21565	0.105445
$931$	9.91998	0.325114
$932$	19.4539	0.637234
$933$	7.87561	0.257836
$934$	30.9558	1.01291
$935$	−7.54875	−0.246871
$936$	−0.291596	−0.00953111
$937$	−57.2253	−1.86947	−0.934735	−	0.355345i	$-0.884363\pi$
$937$	−57.2253	−1.86947	−0.934735	+	0.355345i	$0.884363\pi$
$938$	31.5447	1.02997
$939$	−21.8721	−0.713769
$940$	−11.3418	−0.369930
$941$	−12.9793	−0.423112	−0.211556	−	0.977366i	$-0.567853\pi$
$941$	−12.9793	−0.423112	−0.211556	+	0.977366i	$0.567853\pi$
$942$	−8.67551	−0.282664
$943$	51.6678	1.68254
$944$	1.00000	0.0325472
$945$	−50.9955	−1.65888
$946$	24.3180	0.790645
$947$	−54.2055	−1.76144	−0.880722	−	0.473634i	$-0.842942\pi$
$947$	−54.2055	−1.76144	−0.880722	+	0.473634i	$0.842942\pi$
$948$	2.67578	0.0869052
$949$	2.32855	0.0755878
$950$	−15.6823	−0.508800
$951$	16.7883	0.544398
$952$	3.13875	0.101727
$953$	−33.9252	−1.09895	−0.549473	−	0.835512i	$-0.685171\pi$
$953$	−33.9252	−1.09895	−0.549473	+	0.835512i	$0.685171\pi$
$954$	7.78069	0.251909
$955$	50.7154	1.64111
$956$	25.4009	0.821524
$957$	−18.7480	−0.606036
$958$	32.9336	1.06404
$959$	33.6765	1.08747
$960$	3.39185	0.109471
$961$	−30.1012	−0.971006
$962$	−0.124572	−0.00401635
$963$	−27.9018	−0.899123
$964$	6.83971	0.220292
$965$	16.8275	0.541698
$966$	−17.7144	−0.569953
$967$	18.4673	0.593869	0.296934	−	0.954898i	$-0.404036\pi$
$967$	18.4673	0.593869	0.296934	+	0.954898i	$0.404036\pi$
$968$	5.00692	0.160929
$969$	3.82638	0.122921
$970$	−21.7535	−0.698464
$971$	53.7936	1.72632	0.863159	−	0.504933i	$-0.168483\pi$
$971$	53.7936	1.72632	0.863159	+	0.504933i	$0.168483\pi$
$972$	−15.3387	−0.491988
$973$	14.6112	0.468415
$974$	34.5771	1.10792
$975$	0.807818	0.0258709
$976$	2.93424	0.0939226
$977$	12.3876	0.396313	0.198157	−	0.980170i	$-0.436505\pi$
$977$	12.3876	0.396313	0.198157	+	0.980170i	$0.436505\pi$
$978$	−3.92398	−0.125475
$979$	−14.6777	−0.469101
$980$	−8.79345	−0.280896
$981$	−31.5218	−1.00641
$982$	20.7017	0.660617
$983$	−9.98275	−0.318400	−0.159200	−	0.987246i	$-0.550891\pi$
$983$	−9.98275	−0.318400	−0.159200	+	0.987246i	$0.550891\pi$
$984$	−11.0770	−0.353122
$985$	6.73617	0.214632
$986$	−6.96215	−0.221720
$987$	−12.6992	−0.404220
$988$	−0.566659	−0.0180278
$989$	−50.9667	−1.62065
$990$	13.5125	0.429456
$991$	12.3280	0.391611	0.195805	−	0.980643i	$-0.437268\pi$
$991$	12.3280	0.391611	0.195805	+	0.980643i	$0.437268\pi$
$992$	0.948053	0.0301007
$993$	−3.58815	−0.113866
$994$	−32.7057	−1.03736
$995$	−24.3155	−0.770852
$996$	−14.7331	−0.466837
$997$	19.0026	0.601818	0.300909	−	0.953653i	$-0.402710\pi$
$997$	19.0026	0.601818	0.300909	+	0.953653i	$0.402710\pi$
$998$	−10.4728	−0.331511
$999$	−4.02925	−0.127480

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2006.2.a.v.1.5	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2006.2.a.v.1.5	✓	12	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.09998 q^{3} +1.00000 q^{4} -3.08354 q^{5} +1.09998 q^{6} +3.13875 q^{7} -1.00000 q^{8} -1.79003 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.09998 q^{3} +1.00000 q^{4} -3.08354 q^{5} +1.09998 q^{6} +3.13875 q^{7} -1.00000 q^{8} -1.79003 q^{9} +3.08354 q^{10} -2.44808 q^{11} -1.09998 q^{12} -0.162900 q^{13} -3.13875 q^{14} +3.39185 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.79003 q^{18} +3.47858 q^{19} -3.08354 q^{20} -3.45257 q^{21} +2.44808 q^{22} -5.13080 q^{23} +1.09998 q^{24} +4.50824 q^{25} +0.162900 q^{26} +5.26896 q^{27} +3.13875 q^{28} -6.96215 q^{29} -3.39185 q^{30} -0.948053 q^{31} -1.00000 q^{32} +2.69285 q^{33} +1.00000 q^{34} -9.67846 q^{35} -1.79003 q^{36} -0.764713 q^{37} -3.47858 q^{38} +0.179187 q^{39} +3.08354 q^{40} -10.0701 q^{41} +3.45257 q^{42} +9.93350 q^{43} -2.44808 q^{44} +5.51965 q^{45} +5.13080 q^{46} +3.67818 q^{47} -1.09998 q^{48} +2.85173 q^{49} -4.50824 q^{50} +1.09998 q^{51} -0.162900 q^{52} +4.34667 q^{53} -5.26896 q^{54} +7.54875 q^{55} -3.13875 q^{56} -3.82638 q^{57} +6.96215 q^{58} +1.00000 q^{59} +3.39185 q^{60} +2.93424 q^{61} +0.948053 q^{62} -5.61847 q^{63} +1.00000 q^{64} +0.502308 q^{65} -2.69285 q^{66} -10.0501 q^{67} -1.00000 q^{68} +5.64379 q^{69} +9.67846 q^{70} +10.4200 q^{71} +1.79003 q^{72} -14.2944 q^{73} +0.764713 q^{74} -4.95899 q^{75} +3.47858 q^{76} -7.68389 q^{77} -0.179187 q^{78} -2.43256 q^{79} -3.08354 q^{80} -0.425671 q^{81} +10.0701 q^{82} +13.3939 q^{83} -3.45257 q^{84} +3.08354 q^{85} -9.93350 q^{86} +7.65825 q^{87} +2.44808 q^{88} +5.99560 q^{89} -5.51965 q^{90} -0.511301 q^{91} -5.13080 q^{92} +1.04284 q^{93} -3.67818 q^{94} -10.7263 q^{95} +1.09998 q^{96} -7.05472 q^{97} -2.85173 q^{98} +4.38214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} - 3 q^{3} + 12 q^{4} - q^{5} + 3 q^{6} + 4 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 - 3 * q^3 + 12 * q^4 - q^5 + 3 * q^6 + 4 * q^7 - 12 * q^8 + 15 * q^9	\( 12 q - 12 q^{2} - 3 q^{3} + 12 q^{4} - q^{5} + 3 q^{6} + 4 q^{7} - 12 q^{8} + 15 q^{9} + q^{10} - 3 q^{11} - 3 q^{12} + 15 q^{13} - 4 q^{14} - 3 q^{15} + 12 q^{16} - 12 q^{17} - 15 q^{18} + 16 q^{19} - q^{20} + 15 q^{21} + 3 q^{22} - 14 q^{23} + 3 q^{24} + 19 q^{25} - 15 q^{26} - 12 q^{27} + 4 q^{28} + 14 q^{29} + 3 q^{30} + 26 q^{31} - 12 q^{32} + 13 q^{33} + 12 q^{34} - 5 q^{35} + 15 q^{36} + 15 q^{37} - 16 q^{38} + 4 q^{39} + q^{40} - 2 q^{41} - 15 q^{42} + 8 q^{43} - 3 q^{44} - 17 q^{45} + 14 q^{46} - 6 q^{47} - 3 q^{48} + 30 q^{49} - 19 q^{50} + 3 q^{51} + 15 q^{52} + q^{53} + 12 q^{54} + q^{55} - 4 q^{56} + 3 q^{57} - 14 q^{58} + 12 q^{59} - 3 q^{60} + 30 q^{61} - 26 q^{62} + q^{63} + 12 q^{64} - 4 q^{65} - 13 q^{66} + 10 q^{67} - 12 q^{68} + 8 q^{69} + 5 q^{70} + 6 q^{71} - 15 q^{72} + 26 q^{73} - 15 q^{74} + 7 q^{75} + 16 q^{76} + 45 q^{77} - 4 q^{78} - 11 q^{79} - q^{80} + 48 q^{81} + 2 q^{82} - 21 q^{83} + 15 q^{84} + q^{85} - 8 q^{86} + 2 q^{87} + 3 q^{88} - 2 q^{89} + 17 q^{90} + 31 q^{91} - 14 q^{92} + 41 q^{93} + 6 q^{94} - 29 q^{95} + 3 q^{96} + 27 q^{97} - 30 q^{98} + 9 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 3 * q^3 + 12 * q^4 - q^5 + 3 * q^6 + 4 * q^7 - 12 * q^8 + 15 * q^9 + q^10 - 3 * q^11 - 3 * q^12 + 15 * q^13 - 4 * q^14 - 3 * q^15 + 12 * q^16 - 12 * q^17 - 15 * q^18 + 16 * q^19 - q^20 + 15 * q^21 + 3 * q^22 - 14 * q^23 + 3 * q^24 + 19 * q^25 - 15 * q^26 - 12 * q^27 + 4 * q^28 + 14 * q^29 + 3 * q^30 + 26 * q^31 - 12 * q^32 + 13 * q^33 + 12 * q^34 - 5 * q^35 + 15 * q^36 + 15 * q^37 - 16 * q^38 + 4 * q^39 + q^40 - 2 * q^41 - 15 * q^42 + 8 * q^43 - 3 * q^44 - 17 * q^45 + 14 * q^46 - 6 * q^47 - 3 * q^48 + 30 * q^49 - 19 * q^50 + 3 * q^51 + 15 * q^52 + q^53 + 12 * q^54 + q^55 - 4 * q^56 + 3 * q^57 - 14 * q^58 + 12 * q^59 - 3 * q^60 + 30 * q^61 - 26 * q^62 + q^63 + 12 * q^64 - 4 * q^65 - 13 * q^66 + 10 * q^67 - 12 * q^68 + 8 * q^69 + 5 * q^70 + 6 * q^71 - 15 * q^72 + 26 * q^73 - 15 * q^74 + 7 * q^75 + 16 * q^76 + 45 * q^77 - 4 * q^78 - 11 * q^79 - q^80 + 48 * q^81 + 2 * q^82 - 21 * q^83 + 15 * q^84 + q^85 - 8 * q^86 + 2 * q^87 + 3 * q^88 - 2 * q^89 + 17 * q^90 + 31 * q^91 - 14 * q^92 + 41 * q^93 + 6 * q^94 - 29 * q^95 + 3 * q^96 + 27 * q^97 - 30 * q^98 + 9 * q^99

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