LMFDB - Embedded newform 637.2.g.h.263.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(263,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("637.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.g (of order $3$, degree $2$, not minimal)

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:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.1485512441856.7
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 24x^{6} + 455x^{4} + 2904x^{2} + 14641 $ x^8 + 24x^6 + 455x^4 + 2904*x^2 + 14641
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			263.4
Root			$-2.04914 - 3.54921i$ of defining polynomial
Character	$\chi$	$=$	637.263
Dual form			637.2.g.h.373.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +1.41421 q^{3} +(0.500000 + 0.866025i) q^{4} +(1.34203 + 2.32446i) q^{5} +(-0.707107 + 1.22474i) q^{6} -3.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +1.41421 q^{3} +(0.500000 + 0.866025i) q^{4} +(1.34203 + 2.32446i) q^{5} +(-0.707107 + 1.22474i) q^{6} -3.00000 q^{8} -1.00000 q^{9} -2.68406 q^{10} +5.79583 q^{11} +(0.707107 + 1.22474i) q^{12} +(2.75624 + 2.32446i) q^{13} +(1.89792 + 3.28729i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-2.75624 - 4.77395i) q^{17} +(0.500000 - 0.866025i) q^{18} -2.82843 q^{19} +(-1.34203 + 2.32446i) q^{20} +(-2.89792 + 5.01934i) q^{22} +(-0.897916 + 1.55524i) q^{23} -4.24264 q^{24} +(-1.10208 + 1.90887i) q^{25} +(-3.39116 + 1.22474i) q^{26} -5.65685 q^{27} +(4.39792 + 7.61741i) q^{29} -3.79583 q^{30} +(0.707107 - 1.22474i) q^{31} +(-2.50000 - 4.33013i) q^{32} +8.19654 q^{33} +5.51249 q^{34} +(-0.500000 - 0.866025i) q^{36} +(3.39792 - 5.88536i) q^{37} +(1.41421 - 2.44949i) q^{38} +(3.89792 + 3.28729i) q^{39} +(-4.02609 - 6.97339i) q^{40} +(-4.87756 - 8.44819i) q^{41} +(0.897916 - 1.55524i) q^{43} +(2.89792 + 5.01934i) q^{44} +(-1.34203 - 2.32446i) q^{45} +(-0.897916 - 1.55524i) q^{46} +(-1.41421 - 2.44949i) q^{47} +(0.707107 - 1.22474i) q^{48} +(-1.10208 - 1.90887i) q^{50} +(-3.89792 - 6.75139i) q^{51} +(-0.634922 + 3.54921i) q^{52} +(-3.29583 + 5.70855i) q^{53} +(2.82843 - 4.89898i) q^{54} +(7.77817 + 13.4722i) q^{55} -4.00000 q^{57} -8.79583 q^{58} +(-0.562738 - 0.974691i) q^{59} +(-1.89792 + 3.28729i) q^{60} +1.55858 q^{61} +(0.707107 + 1.22474i) q^{62} +7.00000 q^{64} +(-1.70417 + 9.52628i) q^{65} +(-4.09827 + 7.09841i) q^{66} +5.79583 q^{67} +(2.75624 - 4.77395i) q^{68} +(-1.26984 + 2.19944i) q^{69} +(-3.00000 + 5.19615i) q^{71} +3.00000 q^{72} +(2.90061 - 5.02401i) q^{73} +(3.39792 + 5.88536i) q^{74} +(-1.55858 + 2.69954i) q^{75} +(-1.41421 - 2.44949i) q^{76} +(-4.79583 + 1.73205i) q^{78} +(5.89792 + 10.2155i) q^{79} +2.68406 q^{80} -5.00000 q^{81} +9.75513 q^{82} -9.89949 q^{83} +(7.39792 - 12.8136i) q^{85} +(0.897916 + 1.55524i) q^{86} +(6.21959 + 10.7726i) q^{87} -17.3875 q^{88} +(-6.07522 + 10.5226i) q^{89} +2.68406 q^{90} -1.79583 q^{92} +(1.00000 - 1.73205i) q^{93} +2.82843 q^{94} +(-3.79583 - 6.57457i) q^{95} +(-3.53553 - 6.12372i) q^{96} +(2.12132 - 3.67423i) q^{97} -5.79583 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 4 q^{4} - 24 q^{8} - 8 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + 4 * q^4 - 24 * q^8 - 8 * q^9	$ 8 q - 4 q^{2} + 4 q^{4} - 24 q^{8} - 8 q^{9} + 8 q^{11} - 4 q^{15} + 4 q^{16} + 4 q^{18} - 4 q^{22} + 12 q^{23} - 28 q^{25} + 16 q^{29} + 8 q^{30} - 20 q^{32} - 4 q^{36} + 8 q^{37} + 12 q^{39} - 12 q^{43} + 4 q^{44} + 12 q^{46} - 28 q^{50} - 12 q^{51} + 12 q^{53} - 32 q^{57} - 32 q^{58} + 4 q^{60} + 56 q^{64} - 52 q^{65} + 8 q^{67} - 24 q^{71} + 24 q^{72} + 8 q^{74} + 28 q^{79} - 40 q^{81} + 40 q^{85} - 12 q^{86} - 24 q^{88} + 24 q^{92} + 8 q^{93} + 8 q^{95} - 8 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 + 4 * q^4 - 24 * q^8 - 8 * q^9 + 8 * q^11 - 4 * q^15 + 4 * q^16 + 4 * q^18 - 4 * q^22 + 12 * q^23 - 28 * q^25 + 16 * q^29 + 8 * q^30 - 20 * q^32 - 4 * q^36 + 8 * q^37 + 12 * q^39 - 12 * q^43 + 4 * q^44 + 12 * q^46 - 28 * q^50 - 12 * q^51 + 12 * q^53 - 32 * q^57 - 32 * q^58 + 4 * q^60 + 56 * q^64 - 52 * q^65 + 8 * q^67 - 24 * q^71 + 24 * q^72 + 8 * q^74 + 28 * q^79 - 40 * q^81 + 40 * q^85 - 12 * q^86 - 24 * q^88 + 24 * q^92 + 8 * q^93 + 8 * q^95 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i	−0.986869	−	0.161521i	$-0.948360\pi$
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i	0.633316	+	0.773893i	$0.281693\pi$
$3$	1.41421			0.816497			0.408248	−	0.912871i	$-0.366140\pi$
$3$	1.41421			0.816497			0.408248	+	0.912871i	$0.366140\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.34203	+	2.32446i	0.600174	+	1.03953i	0.992794	+	0.119831i	$0.0382352\pi$
$5$	1.34203	+	2.32446i	0.600174	+	1.03953i	−0.392621	+	0.919700i	$0.628431\pi$
$6$	−0.707107	+	1.22474i	−0.288675	+	0.500000i
$7$		0			0
$7$		0			0
$8$	−3.00000			−1.06066
$9$	−1.00000			−0.333333
$10$	−2.68406			−0.848774
$11$	5.79583			1.74751			0.873754	−	0.486367i	$-0.161678\pi$
$11$	5.79583			1.74751			0.873754	+	0.486367i	$0.161678\pi$
$12$	0.707107	+	1.22474i	0.204124	+	0.353553i
$13$	2.75624	+	2.32446i	0.764444	+	0.644690i
$13$	2.75624	+	2.32446i	0.764444	+	0.644690i
$14$		0			0
$15$	1.89792	+	3.28729i	0.490040	+	0.848774i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−2.75624	−	4.77395i	−0.668487	−	1.15785i	−0.978327	−	0.207065i	$-0.933609\pi$
$17$	−2.75624	−	4.77395i	−0.668487	−	1.15785i	0.309840	−	0.950789i	$-0.399724\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−2.82843			−0.648886			−0.324443	−	0.945905i	$-0.605177\pi$
$19$	−2.82843			−0.648886			−0.324443	+	0.945905i	$0.605177\pi$
$20$	−1.34203	+	2.32446i	−0.300087	+	0.519766i
$21$		0			0
$22$	−2.89792	+	5.01934i	−0.617838	+	1.07013i
$23$	−0.897916	+	1.55524i	−0.187228	+	0.324289i	−0.944325	−	0.329014i	$-0.893284\pi$
$23$	−0.897916	+	1.55524i	−0.187228	+	0.324289i	0.757097	+	0.653303i	$0.226617\pi$
$24$	−4.24264			−0.866025
$25$	−1.10208	+	1.90887i	−0.220417	+	0.381773i
$26$	−3.39116	+	1.22474i	−0.665062	+	0.240192i
$27$	−5.65685			−1.08866
$28$		0			0
$29$	4.39792	+	7.61741i	0.816672	+	1.41452i	0.908121	+	0.418708i	$0.137517\pi$
$29$	4.39792	+	7.61741i	0.816672	+	1.41452i	−0.0914483	+	0.995810i	$0.529150\pi$
$30$	−3.79583			−0.693021
$31$	0.707107	−	1.22474i	0.127000	−	0.219971i	−0.795513	−	0.605937i	$-0.792798\pi$
$31$	0.707107	−	1.22474i	0.127000	−	0.219971i	0.922513	+	0.385966i	$0.126132\pi$
$32$	−2.50000	−	4.33013i	−0.441942	−	0.765466i
$33$	8.19654			1.42684
$34$	5.51249			0.945383
$35$		0			0
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	3.39792	−	5.88536i	0.558614	−	0.967548i	−0.438999	−	0.898488i	$-0.644667\pi$
$37$	3.39792	−	5.88536i	0.558614	−	0.967548i	0.997613	−	0.0690599i	$-0.0220000\pi$
$38$	1.41421	−	2.44949i	0.229416	−	0.397360i
$39$	3.89792	+	3.28729i	0.624166	+	0.526387i
$40$	−4.02609	−	6.97339i	−0.636580	−	1.10259i
$41$	−4.87756	−	8.44819i	−0.761747	−	1.31939i	−0.941949	−	0.335755i	$-0.891008\pi$
$41$	−4.87756	−	8.44819i	−0.761747	−	1.31939i	0.180202	−	0.983630i	$-0.442325\pi$
$42$		0			0
$43$	0.897916	−	1.55524i	0.136931	−	0.237171i	−0.789403	−	0.613876i	$-0.789610\pi$
$43$	0.897916	−	1.55524i	0.136931	−	0.237171i	0.926333	+	0.376705i	$0.122943\pi$
$44$	2.89792	+	5.01934i	0.436877	+	0.756694i
$45$	−1.34203	−	2.32446i	−0.200058	−	0.346510i
$46$	−0.897916	−	1.55524i	−0.132390	−	0.229307i
$47$	−1.41421	−	2.44949i	−0.206284	−	0.357295i	0.744257	−	0.667893i	$-0.232804\pi$
$47$	−1.41421	−	2.44949i	−0.206284	−	0.357295i	−0.950541	+	0.310599i	$0.899470\pi$
$48$	0.707107	−	1.22474i	0.102062	−	0.176777i
$49$		0			0
$50$	−1.10208	−	1.90887i	−0.155858	−	0.269954i
$51$	−3.89792	−	6.75139i	−0.545817	−	0.945383i
$52$	−0.634922	+	3.54921i	−0.0880479	+	0.492187i
$53$	−3.29583	+	5.70855i	−0.452717	+	0.784129i	−0.998554	−	0.0537624i	$-0.982879\pi$
$53$	−3.29583	+	5.70855i	−0.452717	+	0.784129i	0.545836	+	0.837892i	$0.316212\pi$
$54$	2.82843	−	4.89898i	0.384900	−	0.666667i
$55$	7.77817	+	13.4722i	1.04881	+	1.81659i
$56$		0			0
$57$	−4.00000			−0.529813
$58$	−8.79583			−1.15495
$59$	−0.562738	−	0.974691i	−0.0732622	−	0.126894i	0.827067	−	0.562103i	$-0.190008\pi$
$59$	−0.562738	−	0.974691i	−0.0732622	−	0.126894i	−0.900329	+	0.435209i	$0.856674\pi$
$60$	−1.89792	+	3.28729i	−0.245020	+	0.424387i
$61$	1.55858			0.199556			0.0997780	−	0.995010i	$-0.468187\pi$
$61$	1.55858			0.199556			0.0997780	+	0.995010i	$0.468187\pi$
$62$	0.707107	+	1.22474i	0.0898027	+	0.155543i
$63$		0			0
$64$	7.00000			0.875000
$65$	−1.70417	+	9.52628i	−0.211376	+	1.18159i
$66$	−4.09827	+	7.09841i	−0.504462	+	0.873754i
$67$	5.79583			0.708074			0.354037	−	0.935232i	$-0.384809\pi$
$67$	5.79583			0.708074			0.354037	+	0.935232i	$0.384809\pi$
$68$	2.75624	−	4.77395i	0.334244	−	0.578927i
$69$	−1.26984	+	2.19944i	−0.152871	+	0.264781i
$70$		0			0
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$	3.00000			0.353553
$73$	2.90061	−	5.02401i	0.339491	−	0.588015i	−0.644846	−	0.764312i	$-0.723079\pi$
$73$	2.90061	−	5.02401i	0.339491	−	0.588015i	0.984337	+	0.176297i	$0.0564119\pi$
$74$	3.39792	+	5.88536i	0.395000	+	0.684160i
$75$	−1.55858	+	2.69954i	−0.179970	+	0.311716i
$76$	−1.41421	−	2.44949i	−0.162221	−	0.280976i
$77$		0			0
$78$	−4.79583	+	1.73205i	−0.543021	+	0.196116i
$79$	5.89792	+	10.2155i	0.663567	+	1.14933i	0.979672	+	0.200608i	$0.0642917\pi$
$79$	5.89792	+	10.2155i	0.663567	+	1.14933i	−0.316104	+	0.948724i	$0.602375\pi$
$80$	2.68406			0.300087
$81$	−5.00000			−0.555556
$82$	9.75513			1.07727
$83$	−9.89949			−1.08661			−0.543305	−	0.839535i	$-0.682827\pi$
$83$	−9.89949			−1.08661			−0.543305	+	0.839535i	$0.682827\pi$
$84$		0			0
$85$	7.39792	−	12.8136i	0.802417	−	1.38983i
$86$	0.897916	+	1.55524i	0.0968247	+	0.167705i
$87$	6.21959	+	10.7726i	0.666810	+	1.15495i
$88$	−17.3875			−1.85351
$89$	−6.07522	+	10.5226i	−0.643972	+	1.11539i	0.340565	+	0.940221i	$0.389382\pi$
$89$	−6.07522	+	10.5226i	−0.643972	+	1.11539i	−0.984538	+	0.175172i	$0.943952\pi$
$90$	2.68406			0.282925
$91$		0			0
$92$	−1.79583			−0.187228
$93$	1.00000	−	1.73205i	0.103695	−	0.179605i
$94$	2.82843			0.291730
$95$	−3.79583	−	6.57457i	−0.389444	−	0.674537i
$96$	−3.53553	−	6.12372i	−0.360844	−	0.625000i
$97$	2.12132	−	3.67423i	0.215387	−	0.373062i	−0.738005	−	0.674795i	$-0.764232\pi$
$97$	2.12132	−	3.67423i	0.215387	−	0.373062i	0.953392	+	0.301733i	$0.0975652\pi$
$98$		0			0
$99$	−5.79583			−0.582503
$100$	−2.20417			−0.220417
$101$	−2.97280			−0.295804			−0.147902	−	0.989002i	$-0.547252\pi$
$101$	−2.97280			−0.295804			−0.147902	+	0.989002i	$0.547252\pi$
$102$	7.79583			0.771902
$103$	4.09827	+	7.09841i	0.403815	+	0.699428i	0.994183	−	0.107707i	$-0.0343507\pi$
$103$	4.09827	+	7.09841i	0.403815	+	0.699428i	−0.590368	+	0.807134i	$0.701017\pi$
$104$	−8.26873	−	6.97339i	−0.810815	−	0.683797i
$105$		0			0
$106$	−3.29583	−	5.70855i	−0.320119	−	0.554463i
$107$	3.00000	−	5.19615i	0.290021	−	0.502331i	−0.683793	−	0.729676i	$-0.739671\pi$
$107$	3.00000	−	5.19615i	0.290021	−	0.502331i	0.973814	+	0.227345i	$0.0730044\pi$
$108$	−2.82843	−	4.89898i	−0.272166	−	0.471405i
$109$	8.79583	−	15.2348i	0.842488	−	1.45923i	−0.0452972	−	0.998974i	$-0.514423\pi$
$109$	8.79583	−	15.2348i	0.842488	−	1.45923i	0.887785	−	0.460258i	$-0.152243\pi$
$110$	−15.5563			−1.48324
$111$	4.80538	−	8.32316i	0.456106	−	0.789999i
$112$		0			0
$113$	8.29583	−	14.3688i	0.780406	−	1.35170i	−0.151299	−	0.988488i	$-0.548346\pi$
$113$	8.29583	−	14.3688i	0.780406	−	1.35170i	0.931705	−	0.363215i	$-0.118321\pi$
$114$	2.00000	−	3.46410i	0.187317	−	0.324443i
$115$	−4.82012			−0.449478
$116$	−4.39792	+	7.61741i	−0.408336	+	0.707259i
$117$	−2.75624	−	2.32446i	−0.254815	−	0.214897i
$118$	1.12548			0.103608
$119$		0			0
$120$	−5.69375	−	9.86186i	−0.519766	−	0.900260i
$121$	22.5917			2.05379
$122$	−0.779291	+	1.34977i	−0.0705537	+	0.122203i
$123$	−6.89792	−	11.9475i	−0.621964	−	1.07727i
$124$	1.41421			0.127000
$125$	7.50417			0.671194
$126$		0			0
$127$	−3.79583	−	6.57457i	−0.336826	−	0.583399i	0.647008	−	0.762483i	$-0.276020\pi$
$127$	−3.79583	−	6.57457i	−0.336826	−	0.583399i	−0.983834	+	0.179084i	$0.942687\pi$
$128$	1.50000	−	2.59808i	0.132583	−	0.229640i
$129$	1.26984	−	2.19944i	0.111804	−	0.193649i
$130$	−7.39792	−	6.23899i	−0.648840	−	0.547196i
$131$	4.09827	+	7.09841i	0.358068	+	0.620191i	0.987638	−	0.156752i	$-0.0501024\pi$
$131$	4.09827	+	7.09841i	0.358068	+	0.620191i	−0.629570	+	0.776944i	$0.716769\pi$
$132$	4.09827	+	7.09841i	0.356709	+	0.617838i
$133$		0			0
$134$	−2.89792	+	5.01934i	−0.250342	+	0.433605i
$135$	−7.59166	−	13.1491i	−0.653386	−	1.13170i
$136$	8.26873	+	14.3219i	0.709038	+	1.22809i
$137$	4.60208	+	7.97104i	0.393183	+	0.681012i	0.992867	−	0.119224i	$-0.0380407\pi$
$137$	4.60208	+	7.97104i	0.393183	+	0.681012i	−0.599685	+	0.800236i	$0.704707\pi$
$138$	−1.26984	−	2.19944i	−0.108096	−	0.187228i
$139$	7.63381	−	13.2221i	0.647491	−	1.12149i	−0.336229	−	0.941780i	$-0.609152\pi$
$139$	7.63381	−	13.2221i	0.647491	−	1.12149i	0.983720	−	0.179707i	$-0.0575150\pi$
$140$		0			0
$141$	−2.00000	−	3.46410i	−0.168430	−	0.291730i
$142$	−3.00000	−	5.19615i	−0.251754	−	0.436051i
$143$	15.9747	+	13.4722i	1.33587	+	1.12660i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−11.8043	+	20.4456i	−0.980291	+	1.69791i
$146$	2.90061	+	5.02401i	0.240056	+	0.415790i
$147$		0			0
$148$	6.79583			0.558614
$149$	4.59166			0.376164			0.188082	−	0.982153i	$-0.439773\pi$
$149$	4.59166			0.376164			0.188082	+	0.982153i	$0.439773\pi$
$150$	−1.55858	−	2.69954i	−0.127258	−	0.220417i
$151$	8.79583	−	15.2348i	0.715795	−	1.23979i	−0.246858	−	0.969052i	$-0.579398\pi$
$151$	8.79583	−	15.2348i	0.715795	−	1.23979i	0.962652	−	0.270741i	$-0.0872687\pi$
$152$	8.48528			0.688247
$153$	2.75624	+	4.77395i	0.222829	+	0.385951i
$154$		0			0
$155$	3.79583			0.304889
$156$	−0.897916	+	5.01934i	−0.0718908	+	0.401869i
$157$	3.46335	−	5.99870i	0.276405	−	0.478748i	−0.694083	−	0.719895i	$-0.744190\pi$
$157$	3.46335	−	5.99870i	0.276405	−	0.478748i	0.970489	+	0.241146i	$0.0775234\pi$
$158$	−11.7958			−0.938426
$159$	−4.66101	+	8.07311i	−0.369642	+	0.640239i
$160$	6.71015	−	11.6223i	0.530484	−	0.918825i
$161$		0			0
$162$	2.50000	−	4.33013i	0.196419	−	0.340207i
$163$	−13.3875			−1.04859			−0.524295	−	0.851537i	$-0.675671\pi$
$163$	−13.3875			−1.04859			−0.524295	+	0.851537i	$0.675671\pi$
$164$	4.87756	−	8.44819i	0.380874	−	0.659693i
$165$	11.0000	+	19.0526i	0.856349	+	1.48324i
$166$	4.94975	−	8.57321i	0.384175	−	0.665410i
$167$	−7.63381	−	13.2221i	−0.590722	−	1.02316i	−0.994135	−	0.108142i	$-0.965510\pi$
$167$	−7.63381	−	13.2221i	−0.590722	−	1.02316i	0.403414	−	0.915018i	$-0.367824\pi$
$168$		0			0
$169$	2.19375	+	12.8136i	0.168750	+	0.985659i
$170$	7.39792	+	12.8136i	0.567394	+	0.982756i
$171$	2.82843			0.216295
$172$	1.79583			0.136931
$173$	9.32202			0.708740			0.354370	−	0.935105i	$-0.384695\pi$
$173$	9.32202			0.708740			0.354370	+	0.935105i	$0.384695\pi$
$174$	−12.4392			−0.943012
$175$		0			0
$176$	2.89792	−	5.01934i	0.218439	−	0.378347i
$177$	−0.795832	−	1.37842i	−0.0598184	−	0.103608i
$178$	−6.07522	−	10.5226i	−0.455357	−	0.788702i
$179$	−0.408337			−0.0305205			−0.0152603	−	0.999884i	$-0.504858\pi$
$179$	−0.408337			−0.0305205			−0.0152603	+	0.999884i	$0.504858\pi$
$180$	1.34203	−	2.32446i	0.100029	−	0.173255i
$181$	−16.5375			−1.22922			−0.614610	−	0.788831i	$-0.710686\pi$
$181$	−16.5375			−1.22922			−0.614610	+	0.788831i	$0.710686\pi$
$182$		0			0
$183$	2.20417			0.162937
$184$	2.69375	−	4.66571i	0.198586	−	0.343960i
$185$	18.2404			1.34106
$186$	1.00000	+	1.73205i	0.0733236	+	0.127000i
$187$	−15.9747	−	27.6690i	−1.16819	−	2.02336i
$188$	1.41421	−	2.44949i	0.103142	−	0.178647i
$189$		0			0
$190$	7.59166			0.550757
$191$	−25.7958			−1.86652			−0.933260	−	0.359200i	$-0.883049\pi$
$191$	−25.7958			−1.86652			−0.933260	+	0.359200i	$0.883049\pi$
$192$	9.89949			0.714435
$193$	3.40834			0.245337			0.122669	−	0.992448i	$-0.460855\pi$
$193$	3.40834			0.245337			0.122669	+	0.992448i	$0.460855\pi$
$194$	2.12132	+	3.67423i	0.152302	+	0.263795i
$195$	−2.41006	+	13.4722i	−0.172588	+	0.964764i
$196$		0			0
$197$	4.00000	+	6.92820i	0.284988	+	0.493614i	0.972606	−	0.232458i	$-0.0746770\pi$
$197$	4.00000	+	6.92820i	0.284988	+	0.493614i	−0.687618	+	0.726073i	$0.741344\pi$
$198$	2.89792	−	5.01934i	0.205946	−	0.356709i
$199$	11.0250	+	19.0958i	0.781539	+	1.35367i	0.931045	+	0.364905i	$0.118899\pi$
$199$	11.0250	+	19.0958i	0.781539	+	1.35367i	−0.149505	+	0.988761i	$0.547768\pi$
$200$	3.30625	−	5.72660i	0.233787	−	0.404932i
$201$	8.19654			0.578140
$202$	1.48640	−	2.57452i	0.104583	−	0.181142i
$203$		0			0
$204$	3.89792	−	6.75139i	0.272909	−	0.472692i
$205$	13.0917	−	22.6754i	0.914361	−	1.58372i
$206$	−8.19654			−0.571080
$207$	0.897916	−	1.55524i	0.0624095	−	0.108096i
$208$	3.39116	−	1.22474i	0.235135	−	0.0849208i
$209$	−16.3931			−1.13393
$210$		0			0
$211$	0.897916	+	1.55524i	0.0618151	+	0.107067i	0.895277	−	0.445510i	$-0.146978\pi$
$211$	0.897916	+	1.55524i	0.0618151	+	0.107067i	−0.833462	+	0.552577i	$0.813644\pi$
$212$	−6.59166			−0.452717
$213$	−4.24264	+	7.34847i	−0.290701	+	0.503509i
$214$	3.00000	+	5.19615i	0.205076	+	0.355202i
$215$	4.82012			0.328729
$216$	16.9706			1.15470
$217$		0			0
$218$	8.79583	+	15.2348i	0.595729	+	1.03183i
$219$	4.10208	−	7.10502i	0.277193	−	0.480113i
$220$	−7.77817	+	13.4722i	−0.524404	+	0.908295i
$221$	3.50000	−	19.5650i	0.235435	−	1.31608i
$222$	4.80538	+	8.32316i	0.322516	+	0.558614i
$223$	2.82843	+	4.89898i	0.189405	+	0.328060i	0.945052	−	0.326920i	$-0.106011\pi$
$223$	2.82843	+	4.89898i	0.189405	+	0.328060i	−0.755647	+	0.654979i	$0.772677\pi$
$224$		0			0
$225$	1.10208	−	1.90887i	0.0734723	−	0.127258i
$226$	8.29583	+	14.3688i	0.551831	+	0.955798i
$227$	−10.4622	−	18.1211i	−0.694403	−	1.20274i	−0.970382	−	0.241577i	$-0.922335\pi$
$227$	−10.4622	−	18.1211i	−0.694403	−	1.20274i	0.275979	−	0.961164i	$-0.410998\pi$
$228$	−2.00000	−	3.46410i	−0.132453	−	0.229416i
$229$	−6.36396	−	11.0227i	−0.420542	−	0.728401i	0.575450	−	0.817837i	$-0.304827\pi$
$229$	−6.36396	−	11.0227i	−0.420542	−	0.728401i	−0.995993	+	0.0894361i	$0.971494\pi$
$230$	2.41006	−	4.17434i	0.158915	−	0.275248i
$231$		0			0
$232$	−13.1937	−	22.8522i	−0.866212	−	1.50032i
$233$	10.5917	+	18.3453i	0.693883	+	1.20184i	0.970556	+	0.240876i	$0.0774348\pi$
$233$	10.5917	+	18.3453i	0.693883	+	1.20184i	−0.276673	+	0.960964i	$0.589232\pi$
$234$	3.39116	−	1.22474i	0.221687	−	0.0800641i
$235$	3.79583	−	6.57457i	0.247613	−	0.428878i
$236$	0.562738	−	0.974691i	0.0366311	−	0.0634470i
$237$	8.34091	+	14.4469i	0.541800	+	0.938426i
$238$		0			0
$239$	−19.7958			−1.28049			−0.640243	−	0.768172i	$-0.721166\pi$
$239$	−19.7958			−1.28049			−0.640243	+	0.768172i	$0.721166\pi$
$240$	3.79583			0.245020
$241$	−2.19350	−	3.79926i	−0.141296	−	0.244732i	0.786689	−	0.617350i	$-0.211794\pi$
$241$	−2.19350	−	3.79926i	−0.141296	−	0.244732i	−0.927985	+	0.372618i	$0.878460\pi$
$242$	−11.2958	+	19.5650i	−0.726124	+	1.25768i
$243$	9.89949			0.635053
$244$	0.779291	+	1.34977i	0.0498890	+	0.0864103i
$245$		0			0
$246$	13.7958			0.879590
$247$	−7.79583	−	6.57457i	−0.496037	−	0.418330i
$248$	−2.12132	+	3.67423i	−0.134704	+	0.233314i
$249$	−14.0000			−0.887214
$250$	−3.75209	+	6.49881i	−0.237303	+	0.411021i
$251$	1.55858	−	2.69954i	0.0983769	−	0.170394i	−0.812636	−	0.582771i	$-0.801968\pi$
$251$	1.55858	−	2.69954i	0.0983769	−	0.170394i	0.911013	+	0.412378i	$0.135302\pi$
$252$		0			0
$253$	−5.20417	+	9.01388i	−0.327183	+	0.566698i
$254$	7.59166			0.476343
$255$	10.4622	−	18.1211i	0.655170	−	1.13479i
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	−7.70599	+	13.3472i	−0.480686	+	0.832573i	−0.999754	−	0.0221596i	$-0.992946\pi$
$257$	−7.70599	+	13.3472i	−0.480686	+	0.832573i	0.519068	+	0.854733i	$0.326279\pi$
$258$	1.26984	+	2.19944i	0.0790571	+	0.136931i
$259$		0			0
$260$	−9.10208	+	3.28729i	−0.564487	+	0.203869i
$261$	−4.39792	−	7.61741i	−0.272224	−	0.471506i
$262$	−8.19654			−0.506384
$263$	−25.3875			−1.56546			−0.782730	−	0.622361i	$-0.786173\pi$
$263$	−25.3875			−1.56546			−0.782730	+	0.622361i	$0.786173\pi$
$264$	−24.5896			−1.51339
$265$	−17.6924			−1.08684
$266$		0			0
$267$	−8.59166	+	14.8812i	−0.525801	+	0.910714i
$268$	2.89792	+	5.01934i	0.177018	+	0.306605i
$269$	0.562738	+	0.974691i	0.0343107	+	0.0594279i	0.882671	−	0.469992i	$-0.155743\pi$
$269$	0.562738	+	0.974691i	0.0343107	+	0.0594279i	−0.848360	+	0.529420i	$0.822410\pi$
$270$	15.1833			0.924028
$271$	11.5877	−	20.0705i	0.703903	−	1.21920i	−0.263183	−	0.964746i	$-0.584772\pi$
$271$	11.5877	−	20.0705i	0.703903	−	1.21920i	0.967086	−	0.254450i	$-0.0818944\pi$
$272$	−5.51249			−0.334244
$273$		0			0
$274$	−9.20417			−0.556044
$275$	−6.38749	+	11.0635i	−0.385180	+	0.667152i
$276$	−2.53969			−0.152871
$277$	3.09166	+	5.35492i	0.185760	+	0.321746i	0.943832	−	0.330425i	$-0.107192\pi$
$277$	3.09166	+	5.35492i	0.185760	+	0.321746i	−0.758072	+	0.652170i	$0.773859\pi$
$278$	7.63381	+	13.2221i	0.457845	+	0.793011i
$279$	−0.707107	+	1.22474i	−0.0423334	+	0.0733236i
$280$		0			0
$281$	15.2042			0.907005			0.453502	−	0.891255i	$-0.350174\pi$
$281$	15.2042			0.907005			0.453502	+	0.891255i	$0.350174\pi$
$282$	4.00000			0.238197
$283$	−29.4097			−1.74823			−0.874114	−	0.485721i	$-0.838557\pi$
$283$	−29.4097			−1.74823			−0.874114	+	0.485721i	$0.838557\pi$
$284$	−6.00000			−0.356034
$285$	−5.36812	−	9.29785i	−0.317980	−	0.550757i
$286$	−19.6546	+	7.09841i	−1.16220	+	0.419738i
$287$		0			0
$288$	2.50000	+	4.33013i	0.147314	+	0.255155i
$289$	−6.69375	+	11.5939i	−0.393750	+	0.681995i
$290$	−11.8043	−	20.4456i	−0.693170	−	1.20061i
$291$	3.00000	−	5.19615i	0.175863	−	0.304604i
$292$	5.80122			0.339491
$293$	4.87756	−	8.44819i	0.284950	−	0.493548i	−0.687647	−	0.726045i	$-0.741356\pi$
$293$	4.87756	−	8.44819i	0.284950	−	0.493548i	0.972597	+	0.232497i	$0.0746896\pi$
$294$		0			0
$295$	1.51042	−	2.61613i	0.0879401	−	0.152317i
$296$	−10.1937	+	17.6561i	−0.592500	+	1.02624i
$297$	−32.7862			−1.90245
$298$	−2.29583	+	3.97650i	−0.132994	+	0.230352i
$299$	−6.08996	+	2.19944i	−0.352192	+	0.127197i
$300$	−3.11716			−0.179970
$301$		0			0
$302$	8.79583	+	15.2348i	0.506143	+	0.876666i
$303$	−4.20417			−0.241523
$304$	−1.41421	+	2.44949i	−0.0811107	+	0.140488i
$305$	2.09166	+	3.62287i	0.119768	+	0.207445i
$306$	−5.51249			−0.315128
$307$	34.2004			1.95192			0.975960	−	0.217951i	$-0.0699374\pi$
$307$	34.2004			1.95192			0.975960	+	0.217951i	$0.0699374\pi$
$308$		0			0
$309$	5.79583	+	10.0387i	0.329713	+	0.571080i
$310$	−1.89792	+	3.28729i	−0.107794	+	0.186705i
$311$	−5.93085	+	10.2725i	−0.336308	+	0.582502i	−0.983735	−	0.179625i	$-0.942512\pi$
$311$	−5.93085	+	10.2725i	−0.336308	+	0.582502i	0.647427	+	0.762127i	$0.275845\pi$
$312$	−11.6937	−	9.86186i	−0.662028	−	0.558318i
$313$	−0.851476	−	1.47480i	−0.0481283	−	0.0833606i	0.840958	−	0.541101i	$-0.181992\pi$
$313$	−0.851476	−	1.47480i	−0.0481283	−	0.0833606i	−0.889086	+	0.457740i	$0.848659\pi$
$314$	3.46335	+	5.99870i	0.195448	+	0.338526i
$315$		0			0
$316$	−5.89792	+	10.2155i	−0.331784	+	0.574666i
$317$	6.29583	+	10.9047i	0.353609	+	0.612469i	0.986879	−	0.161462i	$-0.0516210\pi$
$317$	6.29583	+	10.9047i	0.353609	+	0.612469i	−0.633270	+	0.773931i	$0.718288\pi$
$318$	−4.66101	−	8.07311i	−0.261376	−	0.452717i
$319$	25.4896	+	44.1492i	1.42714	+	2.47188i
$320$	9.39420	+	16.2712i	0.525152	+	0.909590i
$321$	4.24264	−	7.34847i	0.236801	−	0.410152i
$322$		0			0
$323$	7.79583	+	13.5028i	0.433772	+	0.751315i
$324$	−2.50000	−	4.33013i	−0.138889	−	0.240563i
$325$	−7.47470	+	2.69954i	−0.414622	+	0.149744i
$326$	6.69375	−	11.5939i	0.370732	−	0.642127i
$327$	12.4392	−	21.5453i	0.687888	−	1.19146i
$328$	14.6327	+	25.3446i	0.807955	+	1.39942i
$329$		0			0
$330$	−22.0000			−1.21106
$331$	0.612505			0.0336663			0.0168332	−	0.999858i	$-0.494642\pi$
$331$	0.612505			0.0336663			0.0168332	+	0.999858i	$0.494642\pi$
$332$	−4.94975	−	8.57321i	−0.271653	−	0.470516i
$333$	−3.39792	+	5.88536i	−0.186205	+	0.322516i
$334$	15.2676			0.835407
$335$	7.77817	+	13.4722i	0.424967	+	0.736065i
$336$		0			0
$337$	−29.9792			−1.63307			−0.816534	−	0.577297i	$-0.804108\pi$
$337$	−29.9792			−1.63307			−0.816534	+	0.577297i	$0.804108\pi$
$338$	−12.1937	−	4.50694i	−0.663252	−	0.245145i
$339$	11.7321	−	20.3206i	0.637199	−	1.10366i
$340$	14.7958			0.802417
$341$	4.09827	−	7.09841i	0.221934	−	0.384401i
$342$	−1.41421	+	2.44949i	−0.0764719	+	0.132453i
$343$		0			0
$344$	−2.69375	+	4.66571i	−0.145237	+	0.251558i
$345$	−6.81667			−0.366997
$346$	−4.66101	+	8.07311i	−0.250577	+	0.434013i
$347$	−7.48958	−	12.9723i	−0.402062	−	0.696391i	0.591913	−	0.806002i	$-0.298373\pi$
$347$	−7.48958	−	12.9723i	−0.402062	−	0.696391i	−0.993975	+	0.109611i	$0.965040\pi$
$348$	−6.21959	+	10.7726i	−0.333405	+	0.577475i
$349$	−6.50833	−	11.2728i	−0.348383	−	0.603417i	0.637579	−	0.770385i	$-0.279936\pi$
$349$	−6.50833	−	11.2728i	−0.348383	−	0.603417i	−0.985962	+	0.166968i	$0.946602\pi$
$350$		0			0
$351$	−15.5917	−	13.1491i	−0.832221	−	0.701849i
$352$	−14.4896	−	25.0967i	−0.772297	−	1.33766i
$353$	−15.1232			−0.804929			−0.402464	−	0.915436i	$-0.631846\pi$
$353$	−15.1232			−0.804929			−0.402464	+	0.915436i	$0.631846\pi$
$354$	1.59166			0.0845959
$355$	−16.1043			−0.854730
$356$	−12.1504			−0.643972
$357$		0			0
$358$	0.204168	−	0.353630i	0.0107906	−	0.0186899i
$359$	2.00000	+	3.46410i	0.105556	+	0.182828i	0.913965	−	0.405793i	$-0.133004\pi$
$359$	2.00000	+	3.46410i	0.105556	+	0.182828i	−0.808409	+	0.588621i	$0.799671\pi$
$360$	4.02609	+	6.97339i	0.212193	+	0.367530i
$361$	−11.0000			−0.578947
$362$	8.26873	−	14.3219i	0.434595	−	0.752740i
$363$	31.9494			1.67691
$364$		0			0
$365$	15.5708			0.815014
$366$	−1.10208	+	1.90887i	−0.0576069	+	0.0997780i
$367$	21.2132			1.10732			0.553660	−	0.832743i	$-0.313231\pi$
$367$	21.2132			1.10732			0.553660	+	0.832743i	$0.313231\pi$
$368$	0.897916	+	1.55524i	0.0468071	+	0.0810723i
$369$	4.87756	+	8.44819i	0.253916	+	0.439795i
$370$	−9.12020	+	15.7967i	−0.474137	+	0.821229i
$371$		0			0
$372$	2.00000			0.103695
$373$	−12.5917			−0.651972			−0.325986	−	0.945375i	$-0.605696\pi$
$373$	−12.5917			−0.651972			−0.325986	+	0.945375i	$0.605696\pi$
$374$	31.9494			1.65207
$375$	10.6125			0.548027
$376$	4.24264	+	7.34847i	0.218797	+	0.378968i
$377$	−5.58467	+	31.2182i	−0.287625	+	1.60782i
$378$		0			0
$379$	1.69375	+	2.93366i	0.0870020	+	0.150692i	0.906243	−	0.422758i	$-0.138938\pi$
$379$	1.69375	+	2.93366i	0.0870020	+	0.150692i	−0.819241	+	0.573450i	$0.805605\pi$
$380$	3.79583	−	6.57457i	0.194722	−	0.337268i
$381$	−5.36812	−	9.29785i	−0.275017	−	0.476343i
$382$	12.8979	−	22.3398i	0.659915	−	1.14301i
$383$	−14.9789			−0.765385			−0.382692	−	0.923876i	$-0.625003\pi$
$383$	−14.9789			−0.765385			−0.382692	+	0.923876i	$0.625003\pi$
$384$	2.12132	−	3.67423i	0.108253	−	0.187500i
$385$		0			0
$386$	−1.70417	+	2.95171i	−0.0867399	+	0.150238i
$387$	−0.897916	+	1.55524i	−0.0456436	+	0.0790571i
$388$	4.24264			0.215387
$389$	−14.1937	+	24.5843i	−0.719652	+	1.24647i	0.241486	+	0.970404i	$0.422365\pi$
$389$	−14.1937	+	24.5843i	−0.719652	+	1.24647i	−0.961138	+	0.276069i	$0.910968\pi$
$390$	−10.4622	−	8.82327i	−0.529776	−	0.446784i
$391$	9.89949			0.500639
$392$		0			0
$393$	5.79583	+	10.0387i	0.292361	+	0.506384i
$394$	−8.00000			−0.403034
$395$	−15.8303	+	27.4190i	−0.796511	+	1.37960i
$396$	−2.89792	−	5.01934i	−0.145626	−	0.252231i
$397$	7.07107			0.354887			0.177443	−	0.984131i	$-0.443217\pi$
$397$	7.07107			0.354887			0.177443	+	0.984131i	$0.443217\pi$
$398$	−22.0499			−1.10526
$399$		0			0
$400$	1.10208	+	1.90887i	0.0551042	+	0.0954433i
$401$	−12.1937	+	21.1202i	−0.608927	+	1.05469i	0.382491	+	0.923959i	$0.375066\pi$
$401$	−12.1937	+	21.1202i	−0.608927	+	1.05469i	−0.991418	+	0.130733i	$0.958267\pi$
$402$	−4.09827	+	7.09841i	−0.204403	+	0.354037i
$403$	4.79583	−	1.73205i	0.238897	−	0.0862796i
$404$	−1.48640	−	2.57452i	−0.0739511	−	0.128087i
$405$	−6.71015	−	11.6223i	−0.333430	−	0.577517i
$406$		0			0
$407$	19.6937	−	34.1106i	0.976183	−	1.69080i
$408$	11.6937	+	20.2542i	0.578927	+	1.00273i
$409$	14.3440	+	24.8445i	0.709263	+	1.22848i	0.965131	+	0.261767i	$0.0843053\pi$
$409$	14.3440	+	24.8445i	0.709263	+	1.22848i	−0.255868	+	0.966712i	$0.582361\pi$
$410$	13.0917	+	22.6754i	0.646551	+	1.11986i
$411$	6.50833	+	11.2728i	0.321032	+	0.556044i
$412$	−4.09827	+	7.09841i	−0.201907	+	0.349714i
$413$		0			0
$414$	0.897916	+	1.55524i	0.0441302	+	0.0764357i
$415$	−13.2854	−	23.0110i	−0.652155	−	1.12957i
$416$	3.17461	−	17.7460i	0.155648	−	0.870071i
$417$	10.7958	−	18.6989i	0.528674	−	0.915690i
$418$	8.19654	−	14.1968i	0.400906	−	0.694390i
$419$	−14.2718	−	24.7194i	−0.697221	−	1.20762i	−0.969426	−	0.245384i	$-0.921086\pi$
$419$	−14.2718	−	24.7194i	−0.697221	−	1.20762i	0.272205	−	0.962239i	$-0.412247\pi$
$420$		0			0
$421$	−6.59166			−0.321258			−0.160629	−	0.987015i	$-0.551352\pi$
$421$	−6.59166			−0.321258			−0.160629	+	0.987015i	$0.551352\pi$
$422$	−1.79583			−0.0874197
$423$	1.41421	+	2.44949i	0.0687614	+	0.119098i
$424$	9.88749	−	17.1256i	0.480179	−	0.831695i
$425$	12.1504			0.589383
$426$	−4.24264	−	7.34847i	−0.205557	−	0.356034i
$427$		0			0
$428$	6.00000			0.290021
$429$	22.5917	+	19.0526i	1.09074	+	0.919866i
$430$	−2.41006	+	4.17434i	−0.116223	+	0.201305i
$431$	−5.18333			−0.249672			−0.124836	−	0.992177i	$-0.539840\pi$
$431$	−5.18333			−0.249672			−0.124836	+	0.992177i	$0.539840\pi$
$432$	−2.82843	+	4.89898i	−0.136083	+	0.235702i
$433$	−6.71015	+	11.6223i	−0.322469	+	0.558533i	−0.980997	−	0.194024i	$-0.937846\pi$
$433$	−6.71015	+	11.6223i	−0.322469	+	0.558533i	0.658528	+	0.752556i	$0.271179\pi$
$434$		0			0
$435$	−16.6937	+	28.9144i	−0.800404	+	1.38634i
$436$	17.5917			0.842488
$437$	2.53969	−	4.39887i	0.121490	−	0.210427i
$438$	4.10208	+	7.10502i	0.196005	+	0.339491i
$439$	−17.1002	+	29.6184i	−0.816148	+	1.41361i	0.0923531	+	0.995726i	$0.470561\pi$
$439$	−17.1002	+	29.6184i	−0.816148	+	1.41361i	−0.908501	+	0.417883i	$0.862772\pi$
$440$	−23.3345	−	40.4166i	−1.11243	−	1.92678i
$441$		0			0
$442$	15.1937	+	12.8136i	0.722693	+	0.609479i
$443$	−5.00000	−	8.66025i	−0.237557	−	0.411461i	0.722456	−	0.691417i	$-0.243013\pi$
$443$	−5.00000	−	8.66025i	−0.237557	−	0.411461i	−0.960013	+	0.279956i	$0.909680\pi$
$444$	9.61076			0.456106
$445$	−32.6125			−1.54598
$446$	−5.65685			−0.267860
$447$	6.49359			0.307136
$448$		0			0
$449$	−2.20417	+	3.81773i	−0.104021	+	0.180170i	−0.913338	−	0.407203i	$-0.866504\pi$
$449$	−2.20417	+	3.81773i	−0.104021	+	0.180170i	0.809317	+	0.587372i	$0.199838\pi$
$450$	1.10208	+	1.90887i	0.0519527	+	0.0899848i
$451$	−28.2695	−	48.9643i	−1.33116	−	2.30564i
$452$	16.5917			0.780406
$453$	12.4392	−	21.5453i	0.584444	−	1.01229i
$454$	20.9245			0.982034
$455$		0			0
$456$	12.0000			0.561951
$457$	7.29583	−	12.6368i	0.341285	−	0.591122i	−0.643387	−	0.765541i	$-0.722471\pi$
$457$	7.29583	−	12.6368i	0.341285	−	0.591122i	0.984672	+	0.174419i	$0.0558047\pi$
$458$	12.7279			0.594737
$459$	15.5917	+	27.0056i	0.727757	+	1.26051i
$460$	−2.41006	−	4.17434i	−0.112370	−	0.194630i
$461$	−15.4842	+	26.8194i	−0.721169	+	1.24910i	0.239362	+	0.970930i	$0.423062\pi$
$461$	−15.4842	+	26.8194i	−0.721169	+	1.24910i	−0.960531	+	0.278172i	$0.910272\pi$
$462$		0			0
$463$	11.3875			0.529222			0.264611	−	0.964355i	$-0.414756\pi$
$463$	11.3875			0.529222			0.264611	+	0.964355i	$0.414756\pi$
$464$	8.79583			0.408336
$465$	5.36812			0.248940
$466$	−21.1833			−0.981299
$467$	2.41006	+	4.17434i	0.111524	+	0.193166i	0.916385	−	0.400298i	$-0.131093\pi$
$467$	2.41006	+	4.17434i	0.111524	+	0.193166i	−0.804861	+	0.593464i	$0.797760\pi$
$468$	0.634922	−	3.54921i	0.0293493	−	0.164062i
$469$		0			0
$470$	3.79583	+	6.57457i	0.175089	+	0.303262i
$471$	4.89792	−	8.48344i	0.225684	−	0.390896i
$472$	1.68821	+	2.92407i	0.0777063	+	0.134591i
$473$	5.20417	−	9.01388i	0.239288	−	0.414459i
$474$	−16.6818			−0.766222
$475$	3.11716	−	5.39909i	0.143025	−	0.247727i
$476$		0			0
$477$	3.29583	−	5.70855i	0.150906	−	0.261376i
$478$	9.89792	−	17.1437i	0.452720	−	0.784134i
$479$	−7.35981			−0.336278			−0.168139	−	0.985763i	$-0.553776\pi$
$479$	−7.35981			−0.336278			−0.168139	+	0.985763i	$0.553776\pi$
$480$	9.48958	−	16.4364i	0.433138	−	0.750217i
$481$	23.0458	−	8.32316i	1.05080	−	0.379503i
$482$	4.38701			0.199823
$483$		0			0
$484$	11.2958	+	19.5650i	0.513447	+	0.889316i
$485$	11.3875			0.517079
$486$	−4.94975	+	8.57321i	−0.224525	+	0.388889i
$487$	−9.79583	−	16.9669i	−0.443891	−	0.768843i	0.554083	−	0.832462i	$-0.313069\pi$
$487$	−9.79583	−	16.9669i	−0.443891	−	0.768843i	−0.997974	+	0.0636190i	$0.979736\pi$
$488$	−4.67575			−0.211661
$489$	−18.9328			−0.856170
$490$		0			0
$491$	4.79583	+	8.30662i	0.216433	+	0.374873i	0.953715	−	0.300712i	$-0.0972244\pi$
$491$	4.79583	+	8.30662i	0.216433	+	0.374873i	−0.737282	+	0.675585i	$0.763891\pi$
$492$	6.89792	−	11.9475i	0.310982	−	0.538637i
$493$	24.2434	−	41.9909i	1.09187	−	1.89117i
$494$	9.59166	−	3.46410i	0.431549	−	0.155857i
$495$	−7.77817	−	13.4722i	−0.349603	−	0.605530i
$496$	−0.707107	−	1.22474i	−0.0317500	−	0.0549927i
$497$		0			0
$498$	7.00000	−	12.1244i	0.313678	−	0.543305i
$499$	−8.10208	−	14.0332i	−0.362699	−	0.628213i	0.625705	−	0.780060i	$-0.284811\pi$
$499$	−8.10208	−	14.0332i	−0.362699	−	0.628213i	−0.988404	+	0.151847i	$0.951478\pi$
$500$	3.75209	+	6.49881i	0.167798	+	0.290635i
$501$	−10.7958	−	18.6989i	−0.482322	−	0.835407i
$502$	1.55858	+	2.69954i	0.0695629	+	0.120487i
$503$	14.2718	−	24.7194i	0.636347	−	1.10218i	−0.349881	−	0.936794i	$-0.613778\pi$
$503$	14.2718	−	24.7194i	0.636347	−	1.10218i	0.986228	−	0.165391i	$-0.0528885\pi$
$504$		0			0
$505$	−3.98958	−	6.91015i	−0.177534	−	0.307498i
$506$	−5.20417	−	9.01388i	−0.231354	−	0.400716i
$507$	3.10243	+	18.1211i	0.137784	+	0.804787i
$508$	3.79583	−	6.57457i	0.168413	−	0.291700i
$509$	−13.2185	+	22.8951i	−0.585899	+	1.01481i	0.408864	+	0.912595i	$0.365925\pi$
$509$	−13.2185	+	22.8951i	−0.585899	+	1.01481i	−0.994763	+	0.102211i	$0.967408\pi$
$510$	10.4622	+	18.1211i	0.463275	+	0.802417i
$511$		0			0
$512$	−11.0000			−0.486136
$513$	16.0000			0.706417
$514$	−7.70599	−	13.3472i	−0.339897	−	0.588718i
$515$	−11.0000	+	19.0526i	−0.484718	+	0.839556i
$516$	2.53969			0.111804
$517$	−8.19654	−	14.1968i	−0.360484	−	0.624376i
$518$		0			0
$519$	13.1833			0.578684
$520$	5.11251	−	28.5788i	0.224198	−	1.25326i
$521$	−12.5114	+	21.6703i	−0.548133	+	0.949394i	0.450269	+	0.892893i	$0.351328\pi$
$521$	−12.5114	+	21.6703i	−0.548133	+	0.949394i	−0.998403	+	0.0565015i	$0.982005\pi$
$522$	8.79583			0.384983
$523$	−14.2865	+	24.7450i	−0.624705	+	1.08202i	0.363893	+	0.931441i	$0.381448\pi$
$523$	−14.2865	+	24.7450i	−0.624705	+	1.08202i	−0.988598	+	0.150580i	$0.951886\pi$
$524$	−4.09827	+	7.09841i	−0.179034	+	0.310096i
$525$		0			0
$526$	12.6937	−	21.9862i	0.553474	−	0.958645i
$527$	−7.79583			−0.339592
$528$	4.09827	−	7.09841i	0.178354	−	0.308919i
$529$	9.88749	+	17.1256i	0.429891	+	0.744593i
$530$	8.84620	−	15.3221i	0.384255	−	0.665548i
$531$	0.562738	+	0.974691i	0.0244207	+	0.0422980i
$532$		0			0
$533$	6.19375	−	34.6230i	0.268281	−	1.49969i
$534$	−8.59166	−	14.8812i	−0.371798	−	0.643972i
$535$	16.1043			0.696252
$536$	−17.3875			−0.751025
$537$	−0.577476			−0.0249199
$538$	−1.12548			−0.0485227
$539$		0			0
$540$	7.59166	−	13.1491i	0.326693	−	0.565849i
$541$	6.29583	+	10.9047i	0.270679	+	0.468830i	0.969036	−	0.246920i	$-0.0794185\pi$
$541$	6.29583	+	10.9047i	0.270679	+	0.468830i	−0.698357	+	0.715750i	$0.746085\pi$
$542$	11.5877	+	20.0705i	0.497735	+	0.862102i
$543$	−23.3875			−1.00365
$544$	−13.7812	+	23.8698i	−0.590865	+	1.02341i
$545$	47.2170			2.02256
$546$		0			0
$547$	−36.9792			−1.58111			−0.790557	−	0.612388i	$-0.790209\pi$
$547$	−36.9792			−1.58111			−0.790557	+	0.612388i	$0.790209\pi$
$548$	−4.60208	+	7.97104i	−0.196591	+	0.340506i
$549$	−1.55858			−0.0665187
$550$	−6.38749	−	11.0635i	−0.272364	−	0.471748i
$551$	−12.4392	−	21.5453i	−0.529927	−	0.917861i
$552$	3.80953	−	6.59831i	0.162145	−	0.280843i
$553$		0			0
$554$	−6.18333			−0.262704
$555$	25.7958			1.09497
$556$	15.2676			0.647491
$557$	20.5917			0.872497			0.436248	−	0.899826i	$-0.356307\pi$
$557$	20.5917			0.872497			0.436248	+	0.899826i	$0.356307\pi$
$558$	−0.707107	−	1.22474i	−0.0299342	−	0.0518476i
$559$	6.08996	−	2.19944i	0.257578	−	0.0930262i
$560$		0			0
$561$	−22.5917	−	39.1299i	−0.953821	−	1.65207i
$562$	−7.60208	+	13.1672i	−0.320675	+	0.555425i
$563$	0.562738	+	0.974691i	0.0237166	+	0.0410783i	0.877640	−	0.479320i	$-0.159117\pi$
$563$	0.562738	+	0.974691i	0.0237166	+	0.0410783i	−0.853924	+	0.520399i	$0.825783\pi$
$564$	2.00000	−	3.46410i	0.0842152	−	0.145865i
$565$	44.5330			1.87352
$566$	14.7049	−	25.4696i	0.618092	−	1.07057i
$567$		0			0
$568$	9.00000	−	15.5885i	0.377632	−	0.654077i
$569$	−3.20417	+	5.54978i	−0.134326	+	0.232659i	−0.925340	−	0.379139i	$-0.876220\pi$
$569$	−3.20417	+	5.54978i	−0.134326	+	0.232659i	0.791014	+	0.611798i	$0.209554\pi$
$570$	10.7362			0.449691
$571$	−7.59166	+	13.1491i	−0.317701	+	0.550275i	−0.980008	−	0.198958i	$-0.936244\pi$
$571$	−7.59166	+	13.1491i	−0.317701	+	0.550275i	0.662307	+	0.749233i	$0.269578\pi$
$572$	−3.67990	+	20.5706i	−0.153864	+	0.860100i
$573$	−36.4808			−1.52401
$574$		0			0
$575$	−1.97916	−	3.42800i	−0.0825366	−	0.142958i
$576$	−7.00000			−0.291667
$577$	4.58883	−	7.94808i	0.191035	−	0.330883i	−0.754558	−	0.656233i	$-0.772149\pi$
$577$	4.58883	−	7.94808i	0.191035	−	0.330883i	0.945594	+	0.325350i	$0.105482\pi$
$578$	−6.69375	−	11.5939i	−0.278423	−	0.482243i
$579$	4.82012			0.200317
$580$	−23.6085			−0.980291
$581$		0			0
$582$	3.00000	+	5.19615i	0.124354	+	0.215387i
$583$	−19.1021	+	33.0858i	−0.791127	+	1.37027i
$584$	−8.70183	+	15.0720i	−0.360084	+	0.623685i
$585$	1.70417	−	9.52628i	0.0704587	−	0.393863i
$586$	4.87756	+	8.44819i	0.201490	+	0.348991i
$587$	−1.55858	−	2.69954i	−0.0643296	−	0.111422i	0.832067	−	0.554675i	$-0.187158\pi$
$587$	−1.55858	−	2.69954i	−0.0643296	−	0.111422i	−0.896396	+	0.443253i	$0.853824\pi$
$588$		0			0
$589$	−2.00000	+	3.46410i	−0.0824086	+	0.142736i
$590$	1.51042	+	2.61613i	0.0621831	+	0.107704i
$591$	5.65685	+	9.79796i	0.232692	+	0.403034i
$592$	−3.39792	−	5.88536i	−0.139653	−	0.241887i
$593$	0.779291	+	1.34977i	0.0320017	+	0.0554285i	0.881583	−	0.472030i	$-0.156478\pi$
$593$	0.779291	+	1.34977i	0.0320017	+	0.0554285i	−0.849581	+	0.527458i	$0.823145\pi$
$594$	16.3931	−	28.3937i	0.672617	−	1.16501i
$595$		0			0
$596$	2.29583	+	3.97650i	0.0940409	+	0.162884i
$597$	15.5917	+	27.0056i	0.638124	+	1.10526i
$598$	1.14021	−	6.37378i	0.0466268	−	0.260643i
$599$	7.20417	−	12.4780i	0.294354	−	0.509837i	−0.680480	−	0.732767i	$-0.738229\pi$
$599$	7.20417	−	12.4780i	0.294354	−	0.509837i	0.974834	+	0.222930i	$0.0715621\pi$
$600$	4.67575	−	8.09863i	0.190887	−	0.330625i
$601$	15.4842	+	26.8194i	0.631612	+	1.09398i	0.987222	+	0.159350i	$0.0509398\pi$
$601$	15.4842	+	26.8194i	0.631612	+	1.09398i	−0.355610	+	0.934634i	$0.615727\pi$
$602$		0			0
$603$	−5.79583			−0.236025
$604$	17.5917			0.715795
$605$	30.3187	+	52.5135i	1.23263	+	2.13498i
$606$	2.10208	−	3.64092i	0.0853913	−	0.147902i
$607$	−35.9033			−1.45727			−0.728636	−	0.684901i	$-0.759845\pi$
$607$	−35.9033			−1.45727			−0.728636	+	0.684901i	$0.759845\pi$
$608$	7.07107	+	12.2474i	0.286770	+	0.496700i
$609$		0			0
$610$	−4.18333			−0.169378
$611$	1.79583	−	10.0387i	0.0726516	−	0.406121i
$612$	−2.75624	+	4.77395i	−0.111415	+	0.192976i
$613$	−5.97916			−0.241496			−0.120748	−	0.992683i	$-0.538529\pi$
$613$	−5.97916			−0.241496			−0.120748	+	0.992683i	$0.538529\pi$
$614$	−17.1002	+	29.6184i	−0.690108	+	1.19530i
$615$	18.5144	−	32.0679i	0.746573	−	1.29310i
$616$		0			0
$617$	12.1937	−	21.1202i	0.490902	−	0.850267i	−0.509043	−	0.860741i	$-0.670001\pi$
$617$	12.1937	−	21.1202i	0.490902	−	0.850267i	0.999945	+	0.0104740i	$0.00333405\pi$
$618$	−11.5917			−0.466285
$619$	−16.9558	+	29.3684i	−0.681512	+	1.18041i	0.293007	+	0.956110i	$0.405344\pi$
$619$	−16.9558	+	29.3684i	−0.681512	+	1.18041i	−0.974519	+	0.224303i	$0.927989\pi$
$620$	1.89792	+	3.28729i	0.0762221	+	0.132021i
$621$	5.07938	−	8.79774i	0.203828	−	0.353041i
$622$	−5.93085	−	10.2725i	−0.237806	−	0.411891i
$623$		0			0
$624$	4.79583	−	1.73205i	0.191987	−	0.0693375i
$625$	15.5812	+	26.9875i	0.623250	+	1.07950i
$626$	1.70295			0.0680636
$627$	−23.1833			−0.925853
$628$	6.92670			0.276405
$629$	−37.4619			−1.49370
$630$		0			0
$631$	10.2042	−	17.6741i	0.406222	−	0.703596i	−0.588241	−	0.808685i	$-0.700179\pi$
$631$	10.2042	−	17.6741i	0.406222	−	0.703596i	0.994463	+	0.105089i	$0.0335128\pi$
$632$	−17.6937	−	30.6465i	−0.703819	−	1.21905i
$633$	1.26984	+	2.19944i	0.0504718	+	0.0874197i
$634$	−12.5917			−0.500079
$635$	10.1882	−	17.6465i	0.404308	−	0.700281i
$636$	−9.32202			−0.369642
$637$		0			0
$638$	−50.9792			−2.01828
$639$	3.00000	−	5.19615i	0.118678	−	0.205557i
$640$	8.05217			0.318290
$641$	−2.39792	−	4.15331i	−0.0947120	−	0.164046i	0.814776	−	0.579775i	$-0.196860\pi$
$641$	−2.39792	−	4.15331i	−0.0947120	−	0.164046i	−0.909488	+	0.415729i	$0.863526\pi$
$642$	4.24264	+	7.34847i	0.167444	+	0.290021i
$643$	−2.82843	+	4.89898i	−0.111542	+	0.193197i	−0.916392	−	0.400281i	$-0.868912\pi$
$643$	−2.82843	+	4.89898i	−0.111542	+	0.193197i	0.804850	+	0.593478i	$0.202246\pi$
$644$		0			0
$645$	6.81667			0.268406
$646$	−15.5917			−0.613446
$647$	−1.96221			−0.0771426			−0.0385713	−	0.999256i	$-0.512281\pi$
$647$	−1.96221			−0.0771426			−0.0385713	+	0.999256i	$0.512281\pi$
$648$	15.0000			0.589256
$649$	−3.26153	−	5.64914i	−0.128026	−	0.221748i
$650$	1.39948	−	7.82305i	0.0548920	−	0.306845i
$651$		0			0
$652$	−6.69375	−	11.5939i	−0.262147	−	0.454053i
$653$	−12.5917	+	21.8094i	−0.492750	+	0.853468i	−0.999965	−	0.00835161i	$-0.997342\pi$
$653$	−12.5917	+	21.8094i	−0.492750	+	0.853468i	0.507215	+	0.861819i	$0.330675\pi$
$654$	12.4392	+	21.5453i	0.486411	+	0.842488i
$655$	−11.0000	+	19.0526i	−0.429806	+	0.744445i
$656$	−9.75513			−0.380874
$657$	−2.90061	+	5.02401i	−0.113164	+	0.196005i
$658$		0			0
$659$	18.7958	−	32.5553i	0.732182	−	1.26818i	−0.223767	−	0.974643i	$-0.571836\pi$
$659$	18.7958	−	32.5553i	0.732182	−	1.26818i	0.955949	−	0.293533i	$-0.0948311\pi$
$660$	−11.0000	+	19.0526i	−0.428174	+	0.741620i
$661$	27.8512			1.08328			0.541642	−	0.840609i	$-0.317803\pi$
$661$	27.8512			1.08328			0.541642	+	0.840609i	$0.317803\pi$
$662$	−0.306253	+	0.530445i	−0.0119028	+	0.0206163i
$663$	4.94975	−	27.6690i	0.192232	−	1.07458i
$664$	29.6985			1.15252
$665$		0			0
$666$	−3.39792	−	5.88536i	−0.131667	−	0.228053i
$667$	−15.7958			−0.611617
$668$	7.63381	−	13.2221i	0.295361	−	0.511580i
$669$	4.00000	+	6.92820i	0.154649	+	0.267860i
$670$	−15.5563			−0.600994
$671$	9.03328			0.348726
$672$		0			0
$673$	−11.9896	−	20.7666i	−0.462164	−	0.800492i	0.536904	−	0.843643i	$-0.319594\pi$
$673$	−11.9896	−	20.7666i	−0.462164	−	0.800492i	−0.999069	+	0.0431511i	$0.986260\pi$
$674$	14.9896	−	25.9627i	0.577377	−	1.00005i
$675$	6.23433	−	10.7982i	0.239959	−	0.415622i
$676$	−10.0000	+	8.30662i	−0.384615	+	0.319486i
$677$	−17.3889	−	30.1185i	−0.668311	−	1.15755i	−0.978376	−	0.206833i	$-0.933684\pi$
$677$	−17.3889	−	30.1185i	−0.668311	−	1.15755i	0.310065	−	0.950715i	$-0.399649\pi$
$678$	11.7321	+	20.3206i	0.450568	+	0.780406i
$679$		0			0
$680$	−22.1937	+	38.4407i	−0.851091	+	1.47413i
$681$	−14.7958	−	25.6271i	−0.566977	−	0.982034i
$682$	4.09827	+	7.09841i	0.156931	+	0.271812i
$683$	−25.3875	−	43.9724i	−0.971425	−	1.68256i	−0.691259	−	0.722607i	$-0.742944\pi$
$683$	−25.3875	−	43.9724i	−0.971425	−	1.68256i	−0.280166	−	0.959952i	$-0.590390\pi$
$684$	1.41421	+	2.44949i	0.0540738	+	0.0936586i
$685$	−12.3523	+	21.3947i	−0.471956	+	0.817451i
$686$		0			0
$687$	−9.00000	−	15.5885i	−0.343371	−	0.594737i
$688$	−0.897916	−	1.55524i	−0.0342327	−	0.0592928i
$689$	−22.3534	+	8.07311i	−0.851597	+	0.307561i
$690$	3.40834	−	5.90341i	0.129753	−	0.224739i
$691$	−5.51249	+	9.54790i	−0.209705	+	0.363219i	−0.951622	−	0.307273i	$-0.900584\pi$
$691$	−5.51249	+	9.54790i	−0.209705	+	0.363219i	0.741917	+	0.670492i	$0.233917\pi$
$692$	4.66101	+	8.07311i	0.177185	+	0.306893i
$693$		0			0
$694$	14.9792			0.568601
$695$	40.9792			1.55443
$696$	−18.6588	−	32.3179i	−0.707259	−	1.22501i
$697$	−26.8875	+	46.5705i	−1.01844	+	1.76398i
$698$	13.0167			0.492688
$699$	14.9789	+	25.9442i	0.566553	+	0.981299i
$700$		0			0
$701$	−10.4083			−0.393117			−0.196559	−	0.980492i	$-0.562977\pi$
$701$	−10.4083			−0.393117			−0.196559	+	0.980492i	$0.562977\pi$
$702$	19.1833	−	6.92820i	0.724028	−	0.261488i
$703$	−9.61076	+	16.6463i	−0.362477	+	0.627828i
$704$	40.5708			1.52907
$705$	5.36812	−	9.29785i	0.202175	−	0.350177i
$706$	7.56162	−	13.0971i	0.284585	−	0.492916i
$707$		0			0
$708$	0.795832	−	1.37842i	0.0299092	−	0.0518042i
$709$	−18.7958			−0.705892			−0.352946	−	0.935644i	$-0.614820\pi$
$709$	−18.7958			−0.705892			−0.352946	+	0.935644i	$0.614820\pi$
$710$	8.05217	−	13.9468i	0.302193	−	0.523413i
$711$	−5.89792	−	10.2155i	−0.221189	−	0.383111i
$712$	18.2257	−	31.5678i	0.683036	−	1.18305i
$713$	1.26984	+	2.19944i	0.0475561	+	0.0823695i
$714$		0			0
$715$	−9.87707	+	55.2127i	−0.369382	+	2.06484i
$716$	−0.204168	−	0.353630i	−0.00763013	−	0.0132158i
$717$	−27.9955			−1.04551
$718$	−4.00000			−0.149279
$719$	29.1210			1.08603			0.543015	−	0.839723i	$-0.317283\pi$
$719$	29.1210			1.08603			0.543015	+	0.839723i	$0.317283\pi$
$720$	−2.68406			−0.100029
$721$		0			0
$722$	5.50000	−	9.52628i	0.204689	−	0.354531i
$723$	−3.10208	−	5.37297i	−0.115368	−	0.199823i
$724$	−8.26873	−	14.3219i	−0.307305	−	0.532268i
$725$	−19.3875			−0.720033
$726$	−15.9747	+	27.6690i	−0.592877	+	1.02689i
$727$	−35.3259			−1.31016			−0.655082	−	0.755558i	$-0.727366\pi$
$727$	−35.3259			−1.31016			−0.655082	+	0.755558i	$0.727366\pi$
$728$		0			0
$729$	29.0000			1.07407
$730$	−7.78541	+	13.4847i	−0.288151	+	0.499092i
$731$	−9.89949			−0.366146
$732$	1.10208	+	1.90887i	0.0407342	+	0.0705537i
$733$	−0.346184	−	0.599609i	−0.0127866	−	0.0221471i	0.859561	−	0.511033i	$-0.170737\pi$
$733$	−0.346184	−	0.599609i	−0.0127866	−	0.0221471i	−0.872348	+	0.488886i	$0.837404\pi$
$734$	−10.6066	+	18.3712i	−0.391497	+	0.678092i
$735$		0			0
$736$	8.97916			0.330976
$737$	33.5917			1.23736
$738$	−9.75513			−0.359091
$739$	15.1833			0.558528			0.279264	−	0.960214i	$-0.409910\pi$
$739$	15.1833			0.558528			0.279264	+	0.960214i	$0.409910\pi$
$740$	9.12020	+	15.7967i	0.335265	+	0.580697i
$741$	−11.0250	−	9.29785i	−0.405012	−	0.341565i
$742$		0			0
$743$	−4.59166	−	7.95299i	−0.168452	−	0.291767i	0.769424	−	0.638738i	$-0.220543\pi$
$743$	−4.59166	−	7.95299i	−0.168452	−	0.291767i	−0.937876	+	0.346971i	$0.887210\pi$
$744$	−3.00000	+	5.19615i	−0.109985	+	0.190500i
$745$	6.16215	+	10.6731i	0.225764	+	0.391034i
$746$	6.29583	−	10.9047i	0.230507	−	0.399249i
$747$	9.89949			0.362204
$748$	15.9747	−	27.6690i	0.584094	−	1.01168i
$749$		0			0
$750$	−5.30625	+	9.19070i	−0.193757	+	0.335597i
$751$	−0.897916	+	1.55524i	−0.0327654	+	0.0567514i	−0.881943	−	0.471356i	$-0.843765\pi$
$751$	−0.897916	+	1.55524i	−0.0327654	+	0.0567514i	0.849178	+	0.528107i	$0.177098\pi$
$752$	−2.82843			−0.103142
$753$	2.20417	−	3.81773i	0.0803244	−	0.139126i
$754$	−24.2434	−	20.4456i	−0.882894	−	0.744584i
$755$	47.2170			1.71840
$756$		0			0
$757$	12.5917	+	21.8094i	0.457652	+	0.792676i	0.998836	−	0.0482277i	$-0.0153573\pi$
$757$	12.5917	+	21.8094i	0.457652	+	0.792676i	−0.541185	+	0.840904i	$0.682024\pi$
$758$	−3.38749			−0.123039
$759$	−7.35981	+	12.7476i	−0.267144	+	0.462707i
$760$	11.3875	+	19.7237i	0.413068	+	0.715454i
$761$	9.32202			0.337923			0.168961	−	0.985623i	$-0.445959\pi$
$761$	9.32202			0.337923			0.168961	+	0.985623i	$0.445959\pi$
$762$	10.7362			0.388933
$763$		0			0
$764$	−12.8979	−	22.3398i	−0.466630	−	0.808227i
$765$	−7.39792	+	12.8136i	−0.267472	+	0.463275i
$766$	7.48944	−	12.9721i	0.270604	−	0.468700i
$767$	0.714590	−	3.99455i	0.0258023	−	0.144235i
$768$	12.0208	+	20.8207i	0.433764	+	0.751301i
$769$	−2.12132	−	3.67423i	−0.0764968	−	0.132496i	0.825239	−	0.564783i	$-0.191040\pi$
$769$	−2.12132	−	3.67423i	−0.0764968	−	0.132496i	−0.901736	+	0.432287i	$0.857707\pi$
$770$		0			0
$771$	−10.8979	+	18.8757i	−0.392479	+	0.679793i
$772$	1.70417	+	2.95171i	0.0613344	+	0.106234i
$773$	−3.82427	−	6.62383i	−0.137549	−	0.238243i	0.789019	−	0.614369i	$-0.210589\pi$
$773$	−3.82427	−	6.62383i	−0.137549	−	0.238243i	−0.926568	+	0.376126i	$0.877256\pi$
$774$	−0.897916	−	1.55524i	−0.0322749	−	0.0559018i
$775$	1.55858	+	2.69954i	0.0559859	+	0.0969705i
$776$	−6.36396	+	11.0227i	−0.228453	+	0.395692i
$777$		0			0
$778$	−14.1937	−	24.5843i	−0.508870	−	0.881390i
$779$	13.7958	+	23.8951i	0.494287	+	0.856130i
$780$	−12.8723	+	4.64893i	−0.460902	+	0.166458i
$781$	−17.3875	+	30.1160i	−0.622173	+	1.07764i
$782$	−4.94975	+	8.57321i	−0.177003	+	0.306578i
$783$	−24.8784	−	43.0906i	−0.889080	−	1.53993i
$784$		0			0
$785$	18.5917			0.663565
$786$	−11.5917			−0.413461
$787$	−12.7132	−	22.0199i	−0.453176	−	0.784924i	0.545405	−	0.838173i	$-0.316376\pi$
$787$	−12.7132	−	22.0199i	−0.453176	−	0.784924i	−0.998581	+	0.0532485i	$0.983042\pi$
$788$	−4.00000	+	6.92820i	−0.142494	+	0.246807i
$789$	−35.9033			−1.27819
$790$	−15.8303	−	27.4190i	−0.563219	−	0.975523i
$791$		0			0
$792$	17.3875			0.617838
$793$	4.29583	+	3.62287i	0.152549	+	0.128652i
$794$	−3.53553	+	6.12372i	−0.125471	+	0.217323i
$795$	−25.0208			−0.887398
$796$	−11.0250	+	19.0958i	−0.390770	+	0.676833i
$797$	13.1463	−	22.7700i	0.465666	−	0.806556i	−0.533566	−	0.845759i	$-0.679148\pi$
$797$	13.1463	−	22.7700i	0.465666	−	0.806556i	0.999231	+	0.0392022i	$0.0124817\pi$
$798$		0			0
$799$	−7.79583	+	13.5028i	−0.275797	+	0.477694i
$800$	11.0208			0.389646
$801$	6.07522	−	10.5226i	0.214657	−	0.371798i
$802$	−12.1937	−	21.1202i	−0.430576	−	0.745780i
$803$	16.8115	−	29.1183i	0.593263	−	1.02756i
$804$	4.09827	+	7.09841i	0.144535	+	0.250342i
$805$		0			0
$806$	−0.897916	+	5.01934i	−0.0316277	+	0.176799i
$807$	0.795832	+	1.37842i	0.0280146	+	0.0485227i
$808$	8.91839			0.313748
$809$	39.3667			1.38406			0.692029	−	0.721870i	$-0.256717\pi$
$809$	39.3667			1.38406			0.692029	+	0.721870i	$0.256717\pi$
$810$	13.4203			0.471541
$811$	−38.4725			−1.35095			−0.675476	−	0.737382i	$-0.736062\pi$
$811$	−38.4725			−1.35095			−0.675476	+	0.737382i	$0.736062\pi$
$812$		0			0
$813$	16.3875	−	28.3840i	0.574735	−	0.995469i
$814$	19.6937	+	34.1106i	0.690265	+	1.19557i
$815$	−17.9664	−	31.1187i	−0.629336	−	1.09004i
$816$	−7.79583			−0.272909
$817$	−2.53969	+	4.39887i	−0.0888525	+	0.153897i
$818$	−28.6879			−1.00305
$819$		0			0
$820$	26.1833			0.914361
$821$	20.1833	−	34.9585i	0.704403	−	1.22006i	−0.262504	−	0.964931i	$-0.584548\pi$
$821$	20.1833	−	34.9585i	0.704403	−	1.22006i	0.966907	−	0.255131i	$-0.0821185\pi$
$822$	−13.0167			−0.454008
$823$	−18.3875	−	31.8481i	−0.640948	−	1.11015i	−0.985222	−	0.171285i	$-0.945208\pi$
$823$	−18.3875	−	31.8481i	−0.640948	−	1.11015i	0.344274	−	0.938869i	$-0.388125\pi$
$824$	−12.2948	−	21.2952i	−0.428310	−	0.741855i
$825$	−9.03328	+	15.6461i	−0.314498	+	0.544727i
$826$		0			0
$827$	26.9792			0.938157			0.469079	−	0.883156i	$-0.344586\pi$
$827$	26.9792			0.938157			0.469079	+	0.883156i	$0.344586\pi$
$828$	1.79583			0.0624095
$829$	20.2026			0.701666			0.350833	−	0.936438i	$-0.385898\pi$
$829$	20.2026			0.701666			0.350833	+	0.936438i	$0.385898\pi$
$830$	26.5708			0.922287
$831$	4.37227	+	7.57300i	0.151672	+	0.262704i
$832$	19.2937	+	16.2712i	0.668889	+	0.564104i
$833$		0			0
$834$	10.7958	+	18.6989i	0.373829	+	0.647491i
$835$	20.4896	−	35.4890i	0.709071	−	1.22815i
$836$	−8.19654	−	14.1968i	−0.283483	−	0.491008i
$837$	−4.00000	+	6.92820i	−0.138260	+	0.239474i
$838$	28.5435			0.986020
$839$	−2.82843	+	4.89898i	−0.0976481	+	0.169132i	−0.910711	−	0.413045i	$-0.864465\pi$
$839$	−2.82843	+	4.89898i	−0.0976481	+	0.169132i	0.813063	+	0.582176i	$0.197799\pi$
$840$		0			0
$841$	−24.1833	+	41.8867i	−0.833908	+	1.44437i
$842$	3.29583	−	5.70855i	0.113582	−	0.196730i
$843$	21.5019			0.740566
$844$	−0.897916	+	1.55524i	−0.0309075	+	0.0535334i
$845$	−26.8406	+	22.2955i	−0.923344	+	0.766987i
$846$	−2.82843			−0.0972433
$847$		0			0
$848$	3.29583	+	5.70855i	0.113179	+	0.196032i
$849$	−41.5917			−1.42742
$850$	−6.07522	+	10.5226i	−0.208378	+	0.360922i
$851$	6.10208	+	10.5691i	0.209177	+	0.362305i
$852$	−8.48528			−0.290701
$853$	−13.1610			−0.450625			−0.225313	−	0.974287i	$-0.572340\pi$
$853$	−13.1610			−0.450625			−0.225313	+	0.974287i	$0.572340\pi$
$854$		0			0
$855$	3.79583	+	6.57457i	0.129815	+	0.224846i
$856$	−9.00000	+	15.5885i	−0.307614	+	0.532803i
$857$	18.8753	−	32.6930i	0.644769	−	1.11677i	−0.339586	−	0.940575i	$-0.610287\pi$
$857$	18.8753	−	32.6930i	0.644769	−	1.11677i	0.984355	−	0.176198i	$-0.0563798\pi$
$858$	−27.7958	+	10.0387i	−0.948934	+	0.342715i
$859$	−11.8764	−	20.5706i	−0.405219	−	0.701860i	0.589128	−	0.808040i	$-0.299471\pi$
$859$	−11.8764	−	20.5706i	−0.405219	−	0.701860i	−0.994347	+	0.106180i	$0.966138\pi$
$860$	2.41006	+	4.17434i	0.0821823	+	0.142344i
$861$		0			0
$862$	2.59166	−	4.48889i	0.0882724	−	0.152892i
$863$	−8.89792	−	15.4116i	−0.302889	−	0.524618i	0.673900	−	0.738822i	$-0.264618\pi$
$863$	−8.89792	−	15.4116i	−0.302889	−	0.524618i	−0.976789	+	0.214204i	$0.931284\pi$
$864$	14.1421	+	24.4949i	0.481125	+	0.833333i
$865$	12.5104	+	21.6687i	0.425367	+	0.736757i
$866$	−6.71015	−	11.6223i	−0.228020	−	0.394942i
$867$	−9.46639	+	16.3963i	−0.321495	+	0.556846i
$868$		0			0
$869$	34.1833	+	59.2073i	1.15959	+	2.00847i
$870$	−16.6937	−	28.9144i	−0.565971	−	0.980291i
$871$	15.9747	+	13.4722i	0.541283	+	0.456488i
$872$	−26.3875	+	45.7045i	−0.893593	+	1.54775i
$873$	−2.12132	+	3.67423i	−0.0717958	+	0.124354i
$874$	2.53969	+	4.39887i	0.0859063	+	0.148794i
$875$		0			0
$876$	8.20417			0.277193
$877$	−4.79583			−0.161944			−0.0809719	−	0.996716i	$-0.525802\pi$
$877$	−4.79583			−0.161944			−0.0809719	+	0.996716i	$0.525802\pi$
$878$	−17.1002	−	29.6184i	−0.577104	−	0.999573i
$879$	6.89792	−	11.9475i	0.232661	−	0.402981i
$880$	15.5563			0.524404
$881$	11.6599	+	20.1955i	0.392832	+	0.680405i	0.992822	−	0.119603i	$-0.0381621\pi$
$881$	11.6599	+	20.1955i	0.392832	+	0.680405i	−0.599990	+	0.800007i	$0.704829\pi$
$882$		0			0
$883$	−16.6125			−0.559055			−0.279528	−	0.960138i	$-0.590178\pi$
$883$	−16.6125			−0.559055			−0.279528	+	0.960138i	$0.590178\pi$
$884$	18.6937	−	6.75139i	0.628739	−	0.227074i
$885$	2.13606	−	3.69976i	0.0718028	−	0.124366i
$886$	10.0000			0.335957
$887$	14.2865	−	24.7450i	0.479694	−	0.830854i	−0.520035	−	0.854145i	$-0.674081\pi$
$887$	14.2865	−	24.7450i	0.479694	−	0.830854i	0.999729	+	0.0232909i	$0.00741439\pi$
$888$	−14.4161	+	24.9695i	−0.483774	+	0.837921i
$889$		0			0
$890$	16.3063	−	28.2433i	0.546587	−	0.946716i
$891$	−28.9792			−0.970838
$892$	−2.82843	+	4.89898i	−0.0947027	+	0.164030i
$893$	4.00000	+	6.92820i	0.133855	+	0.231843i
$894$	−3.24680	+	5.62362i	−0.108589	+	0.188082i
$895$	−0.548000	−	0.949164i	−0.0183176	−	0.0317271i
$896$		0			0
$897$	−8.61251	+	3.11047i	−0.287563	+	0.103856i
$898$	−2.20417	−	3.81773i	−0.0735541	−	0.127399i
$899$	12.4392			0.414870
$900$	2.20417			0.0734723
$901$	36.3364			1.21054
$902$	56.5391			1.88255
$903$		0			0
$904$	−24.8875	+	43.1064i	−0.827746	+	1.43370i
$905$	−22.1937	−	38.4407i	−0.737745	−	1.27781i
$906$	12.4392	+	21.5453i	0.413264	+	0.715795i
$907$	49.3875			1.63988			0.819942	−	0.572446i	$-0.194005\pi$
$907$	49.3875			1.63988			0.819942	+	0.572446i	$0.194005\pi$
$908$	10.4622	−	18.1211i	0.347201	−	0.601370i
$909$	2.97280			0.0986014
$910$		0			0
$911$	−43.1833			−1.43073			−0.715364	−	0.698752i	$-0.753739\pi$
$911$	−43.1833			−1.43073			−0.715364	+	0.698752i	$0.753739\pi$
$912$	−2.00000	+	3.46410i	−0.0662266	+	0.114708i
$913$	−57.3758			−1.89886
$914$	7.29583	+	12.6368i	0.241325	+	0.417987i
$915$	2.95806	+	5.12351i	0.0977904	+	0.169378i
$916$	6.36396	−	11.0227i	0.210271	−	0.364200i
$917$		0			0
$918$	−31.1833			−1.02920
$919$	10.0000			0.329870			0.164935	−	0.986304i	$-0.447259\pi$
$919$	10.0000			0.329870			0.164935	+	0.986304i	$0.447259\pi$
$920$	14.4603			0.476744
$921$	48.3667			1.59374
$922$	−15.4842	−	26.8194i	−0.509944	−	0.883249i
$923$	−20.3470	+	7.34847i	−0.669729	+	0.241878i
$924$		0			0
$925$	7.48958	+	12.9723i	0.246256	+	0.426528i
$926$	−5.69375	+	9.86186i	−0.187108	+	0.324081i
$927$	−4.09827	−	7.09841i	−0.134605	−	0.233143i
$928$	21.9896	−	38.0871i	0.721843	−	1.25027i
$929$	−28.1399			−0.923240			−0.461620	−	0.887078i	$-0.652732\pi$
$929$	−28.1399			−0.923240			−0.461620	+	0.887078i	$0.652732\pi$
$930$	−2.68406	+	4.64893i	−0.0880137	+	0.152444i
$931$		0			0
$932$	−10.5917	+	18.3453i	−0.346941	+	0.600920i
$933$	−8.38749	+	14.5276i	−0.274594	+	0.475611i
$934$	−4.82012			−0.157719
$935$	42.8771	−	74.2653i	1.40223	−	2.42873i
$936$	8.26873	+	6.97339i	0.270272	+	0.227932i
$937$	6.63796			0.216853			0.108426	−	0.994104i	$-0.465419\pi$
$937$	6.63796			0.216853			0.108426	+	0.994104i	$0.465419\pi$
$938$		0			0
$939$	−1.20417	−	2.08568i	−0.0392966	−	0.0680636i
$940$	7.59166			0.247613
$941$	11.7321	−	20.3206i	0.382455	−	0.662431i	−0.608958	−	0.793203i	$-0.708412\pi$
$941$	11.7321	−	20.3206i	0.382455	−	0.662431i	0.991413	+	0.130772i	$0.0417454\pi$
$942$	4.89792	+	8.48344i	0.159583	+	0.276405i
$943$	17.5186			0.570483
$944$	−1.12548			−0.0366311
$945$		0			0
$946$	5.20417	+	9.01388i	0.169202	+	0.293067i
$947$	−14.1021	+	24.4255i	−0.458256	+	0.793723i	−0.998869	−	0.0475486i	$-0.984859\pi$
$947$	−14.1021	+	24.4255i	−0.458256	+	0.793723i	0.540613	+	0.841272i	$0.318192\pi$
$948$	−8.34091	+	14.4469i	−0.270900	+	0.469213i
$949$	19.6729	−	7.10502i	0.638610	−	0.230639i
$950$	3.11716	+	5.39909i	0.101134	+	0.175170i
$951$	8.90365	+	15.4216i	0.288721	+	0.500079i
$952$		0			0
$953$	2.40834	−	4.17136i	0.0780137	−	0.135124i	−0.824379	−	0.566038i	$-0.808476\pi$
$953$	2.40834	−	4.17136i	0.0780137	−	0.135124i	0.902393	+	0.430914i	$0.141809\pi$
$954$	3.29583	+	5.70855i	0.106706	+	0.184821i
$955$	−34.6188	−	59.9614i	−1.12024	−	1.94031i
$956$	−9.89792	−	17.1437i	−0.320121	−	0.554467i
$957$	36.0477	+	62.4365i	1.16526	+	2.01828i
$958$	3.67990	−	6.37378i	0.118892	−	0.205927i
$959$		0			0
$960$	13.2854	+	23.0110i	0.428785	+	0.742677i
$961$	14.5000	+	25.1147i	0.467742	+	0.810153i
$962$	−4.31483	+	24.1198i	−0.139116	+	0.777654i
$963$	−3.00000	+	5.19615i	−0.0966736	+	0.167444i
$964$	2.19350	−	3.79926i	0.0706480	−	0.122366i
$965$	4.57409	+	7.92255i	0.147245	+	0.255036i
$966$		0			0
$967$	11.3875			0.366197			0.183099	−	0.983095i	$-0.441387\pi$
$967$	11.3875			0.366197			0.183099	+	0.983095i	$0.441387\pi$
$968$	−67.7750			−2.17837
$969$	11.0250	+	19.0958i	0.354173	+	0.613446i
$970$	−5.69375	+	9.86186i	−0.182815	+	0.316645i
$971$	−22.6274			−0.726148			−0.363074	−	0.931760i	$-0.618273\pi$
$971$	−22.6274			−0.726148			−0.363074	+	0.931760i	$0.618273\pi$
$972$	4.94975	+	8.57321i	0.158763	+	0.274986i
$973$		0			0
$974$	19.5917			0.627757
$975$	−10.5708	+	3.81773i	−0.338537	+	0.122265i
$976$	0.779291	−	1.34977i	0.0249445	−	0.0432051i
$977$	0.387495			0.0123970			0.00619852	−	0.999981i	$-0.498027\pi$
$977$	0.387495			0.0123970			0.00619852	+	0.999981i	$0.498027\pi$
$978$	9.46639	−	16.3963i	0.302702	−	0.524295i
$979$	−35.2110	+	60.9872i	−1.12535	+	1.94916i
$980$		0			0
$981$	−8.79583	+	15.2348i	−0.280829	+	0.486411i
$982$	−9.59166			−0.306082
$983$	−20.7801	+	35.9922i	−0.662782	+	1.14797i	0.317099	+	0.948392i	$0.397291\pi$
$983$	−20.7801	+	35.9922i	−0.662782	+	1.14797i	−0.979882	+	0.199580i	$0.936042\pi$
$984$	20.6937	+	35.8426i	0.659693	+	1.14262i
$985$	−10.7362	+	18.5957i	−0.342085	+	0.592508i
$986$	24.2434	+	41.9909i	0.772069	+	1.33726i
$987$		0			0
$988$	1.79583	−	10.0387i	0.0571330	−	0.319373i
$989$	1.61251	+	2.79294i	0.0512747	+	0.0888104i
$990$	15.5563			0.494413
$991$	18.2042			0.578274			0.289137	−	0.957288i	$-0.406632\pi$
$991$	18.2042			0.578274			0.289137	+	0.957288i	$0.406632\pi$
$992$	−7.07107			−0.224507
$993$	0.866213			0.0274885
$994$		0			0
$995$	−29.5917	+	51.2543i	−0.938119	+	1.62487i
$996$	−7.00000	−	12.1244i	−0.221803	−	0.384175i
$997$	2.75624	+	4.77395i	0.0872911	+	0.151193i	0.906365	−	0.422495i	$-0.138846\pi$
$997$	2.75624	+	4.77395i	0.0872911	+	0.151193i	−0.819074	+	0.573688i	$0.805512\pi$
$998$	16.2042			0.512934
$999$	−19.2215	+	33.2926i	−0.608142	+	1.05333i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.g.h.263.4		8
7.2	even	3		637.2.h.k.471.2		8
7.3	odd	6		637.2.f.g.393.4	yes	8
7.4	even	3		637.2.f.g.393.1	yes	8
7.5	odd	6		637.2.h.k.471.3		8
7.6	odd	2	inner	637.2.g.h.263.1		8
13.9	even	3		637.2.h.k.165.2		8
91.3	odd	6		8281.2.a.bv.1.2		4
91.9	even	3	inner	637.2.g.h.373.4		8
91.10	odd	6		8281.2.a.bn.1.1		4
91.48	odd	6		637.2.h.k.165.3		8
91.61	odd	6	inner	637.2.g.h.373.1		8
91.74	even	3		637.2.f.g.295.1	✓	8
91.81	even	3		8281.2.a.bv.1.3		4
91.87	odd	6		637.2.f.g.295.4	yes	8
91.88	even	6		8281.2.a.bn.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.f.g.295.1	✓	8	91.74	even	3
637.2.f.g.295.4	yes	8	91.87	odd	6
637.2.f.g.393.1	yes	8	7.4	even	3
637.2.f.g.393.4	yes	8	7.3	odd	6
637.2.g.h.263.1		8	7.6	odd	2	inner
637.2.g.h.263.4		8	1.1	even	1	trivial
637.2.g.h.373.1		8	91.61	odd	6	inner
637.2.g.h.373.4		8	91.9	even	3	inner
637.2.h.k.165.2		8	13.9	even	3
637.2.h.k.165.3		8	91.48	odd	6
637.2.h.k.471.2		8	7.2	even	3
637.2.h.k.471.3		8	7.5	odd	6
8281.2.a.bn.1.1		4	91.10	odd	6
8281.2.a.bn.1.4		4	91.88	even	6
8281.2.a.bv.1.2		4	91.3	odd	6
8281.2.a.bv.1.3		4	91.81	even	3

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +1.41421 q^{3} +(0.500000 + 0.866025i) q^{4} +(1.34203 + 2.32446i) q^{5} +(-0.707107 + 1.22474i) q^{6} -3.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +1.41421 q^{3} +(0.500000 + 0.866025i) q^{4} +(1.34203 + 2.32446i) q^{5} +(-0.707107 + 1.22474i) q^{6} -3.00000 q^{8} -1.00000 q^{9} -2.68406 q^{10} +5.79583 q^{11} +(0.707107 + 1.22474i) q^{12} +(2.75624 + 2.32446i) q^{13} +(1.89792 + 3.28729i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-2.75624 - 4.77395i) q^{17} +(0.500000 - 0.866025i) q^{18} -2.82843 q^{19} +(-1.34203 + 2.32446i) q^{20} +(-2.89792 + 5.01934i) q^{22} +(-0.897916 + 1.55524i) q^{23} -4.24264 q^{24} +(-1.10208 + 1.90887i) q^{25} +(-3.39116 + 1.22474i) q^{26} -5.65685 q^{27} +(4.39792 + 7.61741i) q^{29} -3.79583 q^{30} +(0.707107 - 1.22474i) q^{31} +(-2.50000 - 4.33013i) q^{32} +8.19654 q^{33} +5.51249 q^{34} +(-0.500000 - 0.866025i) q^{36} +(3.39792 - 5.88536i) q^{37} +(1.41421 - 2.44949i) q^{38} +(3.89792 + 3.28729i) q^{39} +(-4.02609 - 6.97339i) q^{40} +(-4.87756 - 8.44819i) q^{41} +(0.897916 - 1.55524i) q^{43} +(2.89792 + 5.01934i) q^{44} +(-1.34203 - 2.32446i) q^{45} +(-0.897916 - 1.55524i) q^{46} +(-1.41421 - 2.44949i) q^{47} +(0.707107 - 1.22474i) q^{48} +(-1.10208 - 1.90887i) q^{50} +(-3.89792 - 6.75139i) q^{51} +(-0.634922 + 3.54921i) q^{52} +(-3.29583 + 5.70855i) q^{53} +(2.82843 - 4.89898i) q^{54} +(7.77817 + 13.4722i) q^{55} -4.00000 q^{57} -8.79583 q^{58} +(-0.562738 - 0.974691i) q^{59} +(-1.89792 + 3.28729i) q^{60} +1.55858 q^{61} +(0.707107 + 1.22474i) q^{62} +7.00000 q^{64} +(-1.70417 + 9.52628i) q^{65} +(-4.09827 + 7.09841i) q^{66} +5.79583 q^{67} +(2.75624 - 4.77395i) q^{68} +(-1.26984 + 2.19944i) q^{69} +(-3.00000 + 5.19615i) q^{71} +3.00000 q^{72} +(2.90061 - 5.02401i) q^{73} +(3.39792 + 5.88536i) q^{74} +(-1.55858 + 2.69954i) q^{75} +(-1.41421 - 2.44949i) q^{76} +(-4.79583 + 1.73205i) q^{78} +(5.89792 + 10.2155i) q^{79} +2.68406 q^{80} -5.00000 q^{81} +9.75513 q^{82} -9.89949 q^{83} +(7.39792 - 12.8136i) q^{85} +(0.897916 + 1.55524i) q^{86} +(6.21959 + 10.7726i) q^{87} -17.3875 q^{88} +(-6.07522 + 10.5226i) q^{89} +2.68406 q^{90} -1.79583 q^{92} +(1.00000 - 1.73205i) q^{93} +2.82843 q^{94} +(-3.79583 - 6.57457i) q^{95} +(-3.53553 - 6.12372i) q^{96} +(2.12132 - 3.67423i) q^{97} -5.79583 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 4 q^{4} - 24 q^{8} - 8 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + 4 * q^4 - 24 * q^8 - 8 * q^9	\( 8 q - 4 q^{2} + 4 q^{4} - 24 q^{8} - 8 q^{9} + 8 q^{11} - 4 q^{15} + 4 q^{16} + 4 q^{18} - 4 q^{22} + 12 q^{23} - 28 q^{25} + 16 q^{29} + 8 q^{30} - 20 q^{32} - 4 q^{36} + 8 q^{37} + 12 q^{39} - 12 q^{43} + 4 q^{44} + 12 q^{46} - 28 q^{50} - 12 q^{51} + 12 q^{53} - 32 q^{57} - 32 q^{58} + 4 q^{60} + 56 q^{64} - 52 q^{65} + 8 q^{67} - 24 q^{71} + 24 q^{72} + 8 q^{74} + 28 q^{79} - 40 q^{81} + 40 q^{85} - 12 q^{86} - 24 q^{88} + 24 q^{92} + 8 q^{93} + 8 q^{95} - 8 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 4 * q^4 - 24 * q^8 - 8 * q^9 + 8 * q^11 - 4 * q^15 + 4 * q^16 + 4 * q^18 - 4 * q^22 + 12 * q^23 - 28 * q^25 + 16 * q^29 + 8 * q^30 - 20 * q^32 - 4 * q^36 + 8 * q^37 + 12 * q^39 - 12 * q^43 + 4 * q^44 + 12 * q^46 - 28 * q^50 - 12 * q^51 + 12 * q^53 - 32 * q^57 - 32 * q^58 + 4 * q^60 + 56 * q^64 - 52 * q^65 + 8 * q^67 - 24 * q^71 + 24 * q^72 + 8 * q^74 + 28 * q^79 - 40 * q^81 + 40 * q^85 - 12 * q^86 - 24 * q^88 + 24 * q^92 + 8 * q^93 + 8 * q^95 - 8 * q^99

Introduction

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