LMFDB - Embedded newform 637.2.e.o.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(79,637)]

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([2, 0]))

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

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

chi := DirichletCharacter("637.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.e (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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
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} - 2 x^{11} + 9 x^{10} - 6 x^{9} + 34 x^{8} - 18 x^{7} + 85 x^{6} - 2 x^{5} + 92 x^{4} - 26 x^{3} + \cdots + 1 $ x^12 - 2x^11 + 9x^10 - 6x^9 + 34x^8 - 18x^7 + 85x^6 - 2x^5 + 92x^4 - 26x^3 + 43x^2 + 6*x + 1
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			79.1
Root			$0.379209 - 0.656810i$ of defining polynomial
Character	$\chi$	$=$	637.79
Dual form			637.2.e.o.508.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09161 + 1.89072i) q^{2} +(0.879209 + 1.52284i) q^{3} +(-1.38322 - 2.39581i) q^{4} +(1.05533 - 1.82788i) q^{5} -3.83901 q^{6} +1.67333 q^{8} +(-0.0460183 + 0.0797060i) q^{9} +O(q^{10})$	\(q+(-1.09161 + 1.89072i) q^{2} +(0.879209 + 1.52284i) q^{3} +(-1.38322 - 2.39581i) q^{4} +(1.05533 - 1.82788i) q^{5} -3.83901 q^{6} +1.67333 q^{8} +(-0.0460183 + 0.0797060i) q^{9} +(2.30401 + 3.99066i) q^{10} +(2.88445 + 4.99601i) q^{11} +(2.43229 - 4.21285i) q^{12} -1.00000 q^{13} +3.71141 q^{15} +(0.939830 - 1.62783i) q^{16} +(0.820411 + 1.42099i) q^{17} +(-0.100468 - 0.174016i) q^{18} +(-1.33538 + 2.31295i) q^{19} -5.83901 q^{20} -12.5948 q^{22} +(-3.21234 + 5.56394i) q^{23} +(1.47120 + 2.54820i) q^{24} +(0.272571 + 0.472106i) q^{25} +(1.09161 - 1.89072i) q^{26} +5.11342 q^{27} -6.04973 q^{29} +(-4.05142 + 7.01726i) q^{30} +(2.56101 + 4.43580i) q^{31} +(3.72518 + 6.45220i) q^{32} +(-5.07207 + 8.78508i) q^{33} -3.58227 q^{34} +0.254614 q^{36} +(-2.87386 + 4.97767i) q^{37} +(-2.91544 - 5.04968i) q^{38} +(-0.879209 - 1.52284i) q^{39} +(1.76591 - 3.05864i) q^{40} +7.14100 q^{41} -4.47061 q^{43} +(7.97967 - 13.8212i) q^{44} +(0.0971286 + 0.168232i) q^{45} +(-7.01325 - 12.1473i) q^{46} +(5.89550 - 10.2113i) q^{47} +3.30523 q^{48} -1.19016 q^{50} +(-1.44263 + 2.49870i) q^{51} +(1.38322 + 2.39581i) q^{52} +(-1.72480 - 2.98744i) q^{53} +(-5.58186 + 9.66806i) q^{54} +12.1761 q^{55} -4.69633 q^{57} +(6.60395 - 11.4384i) q^{58} +(6.59027 + 11.4147i) q^{59} +(-5.13372 - 8.89186i) q^{60} +(3.12333 - 5.40976i) q^{61} -11.1825 q^{62} -12.5065 q^{64} +(-1.05533 + 1.82788i) q^{65} +(-11.0734 - 19.1798i) q^{66} +(-3.87108 - 6.70491i) q^{67} +(2.26962 - 3.93111i) q^{68} -11.2973 q^{69} +13.6372 q^{71} +(-0.0770035 + 0.133374i) q^{72} +(-7.75204 - 13.4269i) q^{73} +(-6.27427 - 10.8673i) q^{74} +(-0.479293 + 0.830160i) q^{75} +7.38854 q^{76} +3.83901 q^{78} +(-0.561071 + 0.971803i) q^{79} +(-1.98366 - 3.43579i) q^{80} +(4.63382 + 8.02601i) q^{81} +(-7.79519 + 13.5017i) q^{82} -4.96925 q^{83} +3.46321 q^{85} +(4.88016 - 8.45269i) q^{86} +(-5.31898 - 9.21275i) q^{87} +(4.82662 + 8.35995i) q^{88} +(0.573148 - 0.992721i) q^{89} -0.424106 q^{90} +17.7736 q^{92} +(-4.50333 + 7.79999i) q^{93} +(12.8712 + 22.2935i) q^{94} +(2.81853 + 4.88184i) q^{95} +(-6.55043 + 11.3457i) q^{96} +6.97223 q^{97} -0.530949 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{3} - 4 q^{4} + 6 q^{5} - 8 q^{6} - 6 q^{9}+O(q^{10}) $ 12 * q + 8 * q^3 - 4 * q^4 + 6 * q^5 - 8 * q^6 - 6 * q^9	$ 12 q + 8 q^{3} - 4 q^{4} + 6 q^{5} - 8 q^{6} - 6 q^{9} + 4 q^{10} - 4 q^{11} - 4 q^{12} - 12 q^{13} + 24 q^{15} + 16 q^{17} + 4 q^{18} + 2 q^{19} - 32 q^{20} - 24 q^{22} + 6 q^{23} + 12 q^{24} + 4 q^{25} - 40 q^{27} - 12 q^{29} + 6 q^{31} + 20 q^{32} + 4 q^{33} - 48 q^{36} + 8 q^{38} - 8 q^{39} + 4 q^{40} + 16 q^{41} + 4 q^{43} + 4 q^{44} + 14 q^{45} - 8 q^{46} + 30 q^{47} + 16 q^{48} + 16 q^{50} + 4 q^{51} + 4 q^{52} + 14 q^{53} - 48 q^{54} + 16 q^{55} + 8 q^{57} + 8 q^{58} + 24 q^{59} - 12 q^{60} - 56 q^{62} - 40 q^{64} - 6 q^{65} - 4 q^{66} - 16 q^{67} + 28 q^{68} + 40 q^{69} + 16 q^{71} - 28 q^{72} - 6 q^{73} + 12 q^{74} + 12 q^{75} + 32 q^{76} + 8 q^{78} + 22 q^{79} - 28 q^{80} - 46 q^{81} - 40 q^{82} - 100 q^{83} - 16 q^{85} + 16 q^{86} - 16 q^{87} + 44 q^{88} + 26 q^{89} + 80 q^{90} + 40 q^{92} - 16 q^{93} - 32 q^{94} + 6 q^{95} - 20 q^{96} + 28 q^{97} + 24 q^{99}+O(q^{100}) $ 12 * q + 8 * q^3 - 4 * q^4 + 6 * q^5 - 8 * q^6 - 6 * q^9 + 4 * q^10 - 4 * q^11 - 4 * q^12 - 12 * q^13 + 24 * q^15 + 16 * q^17 + 4 * q^18 + 2 * q^19 - 32 * q^20 - 24 * q^22 + 6 * q^23 + 12 * q^24 + 4 * q^25 - 40 * q^27 - 12 * q^29 + 6 * q^31 + 20 * q^32 + 4 * q^33 - 48 * q^36 + 8 * q^38 - 8 * q^39 + 4 * q^40 + 16 * q^41 + 4 * q^43 + 4 * q^44 + 14 * q^45 - 8 * q^46 + 30 * q^47 + 16 * q^48 + 16 * q^50 + 4 * q^51 + 4 * q^52 + 14 * q^53 - 48 * q^54 + 16 * q^55 + 8 * q^57 + 8 * q^58 + 24 * q^59 - 12 * q^60 - 56 * q^62 - 40 * q^64 - 6 * q^65 - 4 * q^66 - 16 * q^67 + 28 * q^68 + 40 * q^69 + 16 * q^71 - 28 * q^72 - 6 * q^73 + 12 * q^74 + 12 * q^75 + 32 * q^76 + 8 * q^78 + 22 * q^79 - 28 * q^80 - 46 * q^81 - 40 * q^82 - 100 * q^83 - 16 * q^85 + 16 * q^86 - 16 * q^87 + 44 * q^88 + 26 * q^89 + 80 * q^90 + 40 * q^92 - 16 * q^93 - 32 * q^94 + 6 * q^95 - 20 * q^96 + 28 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.09161	+	1.89072i	−0.771885	+	1.33694i	0.164644	+	0.986353i	$0.447352\pi$
$2$	−1.09161	+	1.89072i	−0.771885	+	1.33694i	−0.936529	+	0.350591i	$0.885981\pi$
$3$	0.879209	+	1.52284i	0.507612	+	0.879209i	0.999961	+	0.00881173i	$0.00280490\pi$
$3$	0.879209	+	1.52284i	0.507612	+	0.879209i	−0.492349	+	0.870398i	$0.663862\pi$
$4$	−1.38322	−	2.39581i	−0.691612	−	1.19791i
$5$	1.05533	−	1.82788i	0.471957	−	0.817453i	−0.527529	−	0.849537i	$-0.676881\pi$
$5$	1.05533	−	1.82788i	0.471957	−	0.817453i	0.999485	+	0.0320846i	$0.0102146\pi$
$6$	−3.83901			−1.56727
$7$		0			0
$7$		0			0
$8$	1.67333			0.591610
$9$	−0.0460183	+	0.0797060i	−0.0153394	+	0.0265687i
$10$	2.30401	+	3.99066i	0.728592	+	1.26196i
$11$	2.88445	+	4.99601i	0.869694	+	1.50635i	0.862310	+	0.506381i	$0.169017\pi$
$11$	2.88445	+	4.99601i	0.869694	+	1.50635i	0.00738342	+	0.999973i	$0.497650\pi$
$12$	2.43229	−	4.21285i	0.702141	−	1.21614i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$		0			0
$15$	3.71141			0.958283
$16$	0.939830	−	1.62783i	0.234957	−	0.406958i
$17$	0.820411	+	1.42099i	0.198979	+	0.344642i	0.948198	−	0.317681i	$-0.102904\pi$
$17$	0.820411	+	1.42099i	0.198979	+	0.344642i	−0.749219	+	0.662323i	$0.769571\pi$
$18$	−0.100468	−	0.174016i	−0.0236805	−	0.0410159i
$19$	−1.33538	+	2.31295i	−0.306358	+	0.530628i	−0.977563	−	0.210644i	$-0.932444\pi$
$19$	−1.33538	+	2.31295i	−0.306358	+	0.530628i	0.671205	+	0.741272i	$0.265777\pi$
$20$	−5.83901			−1.30564
$21$		0			0
$22$	−12.5948			−2.68521
$23$	−3.21234	+	5.56394i	−0.669820	+	1.16016i	0.308134	+	0.951343i	$0.400295\pi$
$23$	−3.21234	+	5.56394i	−0.669820	+	1.16016i	−0.977954	+	0.208820i	$0.933038\pi$
$24$	1.47120	+	2.54820i	0.300308	+	0.520149i
$25$	0.272571	+	0.472106i	0.0545141	+	0.0944212i
$26$	1.09161	−	1.89072i	0.214082	−	0.370801i
$27$	5.11342			0.984078
$28$		0			0
$29$	−6.04973			−1.12341			−0.561704	−	0.827338i	$-0.689854\pi$
$29$	−6.04973			−1.12341			−0.561704	+	0.827338i	$0.689854\pi$
$30$	−4.05142	+	7.01726i	−0.739684	+	1.28117i
$31$	2.56101	+	4.43580i	0.459971	+	0.796693i	0.998959	−	0.0456207i	$-0.0145266\pi$
$31$	2.56101	+	4.43580i	0.459971	+	0.796693i	−0.538988	+	0.842313i	$0.681193\pi$
$32$	3.72518	+	6.45220i	0.658525	+	1.14060i
$33$	−5.07207	+	8.78508i	−0.882933	+	1.52929i
$34$	−3.58227			−0.614355
$35$		0			0
$36$	0.254614			0.0424357
$37$	−2.87386	+	4.97767i	−0.472460	+	0.818324i	−0.999503	−	0.0315141i	$-0.989967\pi$
$37$	−2.87386	+	4.97767i	−0.472460	+	0.818324i	0.527044	+	0.849838i	$0.323300\pi$
$38$	−2.91544	−	5.04968i	−0.472946	−	0.819167i
$39$	−0.879209	−	1.52284i	−0.140786	−	0.243849i
$40$	1.76591	−	3.05864i	0.279214	−	0.483613i
$41$	7.14100			1.11524			0.557619	−	0.830097i	$-0.311715\pi$
$41$	7.14100			1.11524			0.557619	+	0.830097i	$0.311715\pi$
$42$		0			0
$43$	−4.47061			−0.681761			−0.340881	−	0.940107i	$-0.610725\pi$
$43$	−4.47061			−0.681761			−0.340881	+	0.940107i	$0.610725\pi$
$44$	7.97967	−	13.8212i	1.20298	−	2.08362i
$45$	0.0971286	+	0.168232i	0.0144791	+	0.0250785i
$46$	−7.01325	−	12.1473i	−1.03405	−	1.79102i
$47$	5.89550	−	10.2113i	0.859947	−	1.48947i	−0.0120319	−	0.999928i	$-0.503830\pi$
$47$	5.89550	−	10.2113i	0.859947	−	1.48947i	0.871979	−	0.489544i	$-0.162837\pi$
$48$	3.30523			0.477069
$49$		0			0
$50$	−1.19016			−0.168314
$51$	−1.44263	+	2.49870i	−0.202008	+	0.349888i
$52$	1.38322	+	2.39581i	0.191819	+	0.332240i
$53$	−1.72480	−	2.98744i	−0.236919	−	0.410356i	0.722910	−	0.690943i	$-0.242804\pi$
$53$	−1.72480	−	2.98744i	−0.236919	−	0.410356i	−0.959829	+	0.280587i	$0.909471\pi$
$54$	−5.58186	+	9.66806i	−0.759595	+	1.31566i
$55$	12.1761			1.64183
$56$		0			0
$57$	−4.69633			−0.622044
$58$	6.60395	−	11.4384i	0.867141	−	1.50193i
$59$	6.59027	+	11.4147i	0.857981	+	1.48607i	0.873852	+	0.486192i	$0.161614\pi$
$59$	6.59027	+	11.4147i	0.857981	+	1.48607i	−0.0158712	+	0.999874i	$0.505052\pi$
$60$	−5.13372	−	8.89186i	−0.662760	−	1.14793i
$61$	3.12333	−	5.40976i	0.399901	−	0.692649i	−0.593812	−	0.804604i	$-0.702378\pi$
$61$	3.12333	−	5.40976i	0.399901	−	0.692649i	0.993713	+	0.111954i	$0.0357111\pi$
$62$	−11.1825			−1.42018
$63$		0			0
$64$	−12.5065			−1.56331
$65$	−1.05533	+	1.82788i	−0.130897	+	0.226721i
$66$	−11.0734	−	19.1798i	−1.36305	−	2.36086i
$67$	−3.87108	−	6.70491i	−0.472928	−	0.819135i	0.526592	−	0.850118i	$-0.323470\pi$
$67$	−3.87108	−	6.70491i	−0.472928	−	0.819135i	−0.999520	+	0.0309831i	$0.990136\pi$
$68$	2.26962	−	3.93111i	0.275232	−	0.476717i
$69$	−11.2973			−1.36003
$70$		0			0
$71$	13.6372			1.61844			0.809221	−	0.587504i	$-0.199889\pi$
$71$	13.6372			1.61844			0.809221	+	0.587504i	$0.199889\pi$
$72$	−0.0770035	+	0.133374i	−0.00907495	+	0.0157183i
$73$	−7.75204	−	13.4269i	−0.907308	−	1.57150i	−0.817789	−	0.575518i	$-0.804800\pi$
$73$	−7.75204	−	13.4269i	−0.907308	−	1.57150i	−0.0895192	−	0.995985i	$-0.528533\pi$
$74$	−6.27427	−	10.8673i	−0.729369	−	1.26330i
$75$	−0.479293	+	0.830160i	−0.0553440	+	0.0958586i
$76$	7.38854			0.847524
$77$		0			0
$78$	3.83901			0.434683
$79$	−0.561071	+	0.971803i	−0.0631254	+	0.109336i	−0.895861	−	0.444335i	$-0.853440\pi$
$79$	−0.561071	+	0.971803i	−0.0631254	+	0.109336i	0.832735	+	0.553671i	$0.186773\pi$
$80$	−1.98366	−	3.43579i	−0.221779	−	0.384133i
$81$	4.63382	+	8.02601i	0.514869	+	0.891779i
$82$	−7.79519	+	13.5017i	−0.860835	+	1.49101i
$83$	−4.96925			−0.545446			−0.272723	−	0.962093i	$-0.587924\pi$
$83$	−4.96925			−0.545446			−0.272723	+	0.962093i	$0.587924\pi$
$84$		0			0
$85$	3.46321			0.375638
$86$	4.88016	−	8.45269i	0.526241	−	0.911476i
$87$	−5.31898	−	9.21275i	−0.570255	−	0.987710i
$88$	4.82662	+	8.35995i	0.514519	+	0.891174i
$89$	0.573148	−	0.992721i	0.0607535	−	0.105228i	−0.834049	−	0.551691i	$-0.813983\pi$
$89$	0.573148	−	0.992721i	0.0607535	−	0.105228i	0.894802	+	0.446462i	$0.147316\pi$
$90$	−0.424106			−0.0447047
$91$		0			0
$92$	17.7736			1.85302
$93$	−4.50333	+	7.79999i	−0.466973	+	0.808821i
$94$	12.8712	+	22.2935i	1.32756	+	2.29940i
$95$	2.81853	+	4.88184i	0.289175	+	0.500866i
$96$	−6.55043	+	11.3457i	−0.668550	+	1.15796i
$97$	6.97223			0.707923			0.353961	−	0.935260i	$-0.384834\pi$
$97$	6.97223			0.707923			0.353961	+	0.935260i	$0.384834\pi$
$98$		0			0
$99$	−0.530949			−0.0533624
$100$	0.754052	−	1.30606i	0.0754052	−	0.130606i
$101$	−3.24960	−	5.62847i	−0.323347	−	0.560053i	0.657829	−	0.753167i	$-0.271475\pi$
$101$	−3.24960	−	5.62847i	−0.323347	−	0.560053i	−0.981176	+	0.193113i	$0.938141\pi$
$102$	−3.14957	−	5.45521i	−0.311854	−	0.540147i
$103$	−0.289024	+	0.500604i	−0.0284784	+	0.0493260i	−0.879913	−	0.475134i	$-0.842400\pi$
$103$	−0.289024	+	0.500604i	−0.0284784	+	0.0493260i	0.851435	+	0.524460i	$0.175733\pi$
$104$	−1.67333			−0.164083
$105$		0			0
$106$	7.53122			0.731497
$107$	8.12863	−	14.0792i	0.785824	−	1.36109i	−0.142681	−	0.989769i	$-0.545572\pi$
$107$	8.12863	−	14.0792i	0.785824	−	1.36109i	0.928505	−	0.371319i	$-0.121094\pi$
$108$	−7.07300	−	12.2508i	−0.680600	−	1.17883i
$109$	−0.890953	−	1.54318i	−0.0853378	−	0.147809i	0.820197	−	0.572081i	$-0.193864\pi$
$109$	−0.890953	−	1.54318i	−0.0853378	−	0.147809i	−0.905535	+	0.424271i	$0.860530\pi$
$110$	−13.2916	+	23.0217i	−1.26730	+	2.19503i
$111$	−10.1069			−0.959304
$112$		0			0
$113$	−7.52215			−0.707624			−0.353812	−	0.935316i	$-0.615115\pi$
$113$	−7.52215			−0.707624			−0.353812	+	0.935316i	$0.615115\pi$
$114$	5.12656	−	8.87946i	0.480146	−	0.831638i
$115$	6.78015	+	11.7436i	0.632252	+	1.09509i
$116$	8.36814	+	14.4940i	0.776962	+	1.34574i
$117$	0.0460183	−	0.0797060i	0.00425439	−	0.00736882i
$118$	−28.7760			−2.64905
$119$		0			0
$120$	6.21040			0.566930
$121$	−11.1401	+	19.2952i	−1.01273	+	1.75411i
$122$	6.81891	+	11.8107i	0.617355	+	1.06929i
$123$	6.27844	+	10.8746i	0.566108	+	0.980527i
$124$	7.08490	−	12.2714i	0.636243	−	1.10200i
$125$	11.7039			1.04683
$126$		0			0
$127$	−19.3056			−1.71310			−0.856549	−	0.516067i	$-0.827396\pi$
$127$	−19.3056			−1.71310			−0.856549	+	0.516067i	$0.827396\pi$
$128$	6.20181	−	10.7418i	0.548168	−	0.949454i
$129$	−3.93060	−	6.80800i	−0.346070	−	0.599411i
$130$	−2.30401	−	3.99066i	−0.202075	−	0.350004i
$131$	4.84852	−	8.39788i	0.423617	−	0.733726i	−0.572673	−	0.819784i	$-0.694094\pi$
$131$	4.84852	−	8.39788i	0.423617	−	0.733726i	0.996290	+	0.0860579i	$0.0274270\pi$
$132$	28.0632			2.44259
$133$		0			0
$134$	16.9028			1.46018
$135$	5.39633	−	9.34671i	0.464442	−	0.804437i
$136$	1.37281	+	2.37778i	0.117718	+	0.203893i
$137$	7.72467	+	13.3795i	0.659963	+	1.14309i	0.980625	+	0.195895i	$0.0627613\pi$
$137$	7.72467	+	13.3795i	0.659963	+	1.14309i	−0.320662	+	0.947194i	$0.603905\pi$
$138$	12.3322	−	21.3601i	1.04979	−	1.81829i
$139$	−3.84912			−0.326478			−0.163239	−	0.986587i	$-0.552194\pi$
$139$	−3.84912			−0.326478			−0.163239	+	0.986587i	$0.552194\pi$
$140$		0			0
$141$	20.7335			1.74608
$142$	−14.8865	+	25.7842i	−1.24925	+	2.16377i
$143$	−2.88445	−	4.99601i	−0.241210	−	0.417787i
$144$	0.0864987	+	0.149820i	0.00720822	+	0.0124850i
$145$	−6.38445	+	11.0582i	−0.530199	+	0.918332i
$146$	33.8488			2.80135
$147$		0			0
$148$	15.9008			1.30704
$149$	0.520140	−	0.900909i	0.0426115	−	0.0738054i	−0.843933	−	0.536449i	$-0.819766\pi$
$149$	0.520140	−	0.900909i	0.0426115	−	0.0738054i	0.886545	+	0.462643i	$0.153099\pi$
$150$	−1.04640	−	1.81242i	−0.0854384	−	0.147984i
$151$	2.17168	+	3.76146i	0.176729	+	0.306104i	0.940758	−	0.339078i	$-0.110115\pi$
$151$	2.17168	+	3.76146i	0.176729	+	0.306104i	−0.764029	+	0.645182i	$0.776782\pi$
$152$	−2.23453	+	3.87032i	−0.181244	+	0.313925i
$153$	−0.151016			−0.0122089
$154$		0			0
$155$	10.8108			0.868345
$156$	−2.43229	+	4.21285i	−0.194739	+	0.337298i
$157$	0.168000	+	0.290985i	0.0134079	+	0.0232231i	0.872651	−	0.488343i	$-0.162399\pi$
$157$	0.168000	+	0.290985i	0.0134079	+	0.0232231i	−0.859244	+	0.511567i	$0.829065\pi$
$158$	−1.22494	−	2.12166i	−0.0974511	−	0.168790i
$159$	3.03291	−	5.25316i	0.240526	−	0.416603i
$160$	15.7251			1.24318
$161$		0			0
$162$	−20.2333			−1.58968
$163$	−3.39959	+	5.88827i	−0.266277	+	0.461205i	−0.967897	−	0.251346i	$-0.919127\pi$
$163$	−3.39959	+	5.88827i	−0.266277	+	0.461205i	0.701621	+	0.712551i	$0.252460\pi$
$164$	−9.87761	−	17.1085i	−0.771312	−	1.33595i
$165$	10.7054	+	18.5423i	0.833412	+	1.44351i
$166$	5.42448	−	9.39548i	0.421022	−	0.729231i
$167$	−0.668649			−0.0517416			−0.0258708	−	0.999665i	$-0.508236\pi$
$167$	−0.668649			−0.0517416			−0.0258708	+	0.999665i	$0.508236\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	−3.78047	+	6.54797i	−0.289949	+	0.502206i
$171$	−0.122904	−	0.212876i	−0.00939871	−	0.0162790i
$172$	6.18385	+	10.7107i	0.471514	+	0.816687i
$173$	12.5589	−	21.7527i	0.954837	−	1.65383i	0.220095	−	0.975478i	$-0.429363\pi$
$173$	12.5589	−	21.7527i	0.954837	−	1.65383i	0.734741	−	0.678347i	$-0.237303\pi$
$174$	23.2250			1.76068
$175$		0			0
$176$	10.8436			0.817364
$177$	−11.5885	+	20.0718i	−0.871042	+	1.50869i
$178$	1.25131	+	2.16733i	0.0937895	+	0.162448i
$179$	0.947633	+	1.64135i	0.0708294	+	0.122680i	0.899265	−	0.437404i	$-0.144102\pi$
$179$	0.947633	+	1.64135i	0.0708294	+	0.122680i	−0.828436	+	0.560084i	$0.810769\pi$
$180$	0.268701	−	0.465404i	0.0200278	−	0.0346892i
$181$	−11.3595			−0.844347			−0.422174	−	0.906515i	$-0.638733\pi$
$181$	−11.3595			−0.844347			−0.422174	+	0.906515i	$0.638733\pi$
$182$		0			0
$183$	10.9842			0.811978
$184$	−5.37530	+	9.31029i	−0.396272	+	0.686364i
$185$	6.06572	+	10.5061i	0.445961	+	0.772427i
$186$	−9.83175	−	17.0291i	−0.720899	−	1.24863i
$187$	−4.73286	+	8.19756i	−0.346101	+	0.599465i
$188$	−32.6192			−2.37900
$189$		0			0
$190$	−12.3070			−0.892840
$191$	11.7203	−	20.3002i	0.848055	−	1.46887i	−0.0348873	−	0.999391i	$-0.511107\pi$
$191$	11.7203	−	20.3002i	0.848055	−	1.46887i	0.882942	−	0.469482i	$-0.155559\pi$
$192$	−10.9958	−	19.0453i	−0.793553	−	1.37447i
$193$	0.926048	+	1.60396i	0.0666584	+	0.115456i	0.897428	−	0.441160i	$-0.145433\pi$
$193$	0.926048	+	1.60396i	0.0666584	+	0.115456i	−0.830770	+	0.556616i	$0.812100\pi$
$194$	−7.61095	+	13.1826i	−0.546435	+	0.946453i
$195$	−3.71141			−0.265780
$196$		0			0
$197$	−9.87082			−0.703267			−0.351634	−	0.936138i	$-0.614374\pi$
$197$	−9.87082			−0.703267			−0.351634	+	0.936138i	$0.614374\pi$
$198$	0.579589	−	1.00388i	0.0411896	−	0.0713425i
$199$	6.12461	+	10.6081i	0.434162	+	0.751991i	0.997227	−	0.0744219i	$-0.0237111\pi$
$199$	6.12461	+	10.6081i	0.434162	+	0.751991i	−0.563065	+	0.826413i	$0.690378\pi$
$200$	0.456099	+	0.789987i	0.0322511	+	0.0558605i
$201$	6.80698	−	11.7900i	0.480127	−	0.831605i
$202$	14.1892			0.998347
$203$		0			0
$204$	7.98190			0.558845
$205$	7.53609	−	13.0529i	0.526343	−	0.911654i
$206$	−0.631003	−	1.09293i	−0.0439640	−	0.0761480i
$207$	−0.295653	−	0.512086i	−0.0205493	−	0.0355924i
$208$	−0.939830	+	1.62783i	−0.0651655	+	0.112870i
$209$	−15.4074			−1.06575
$210$		0			0
$211$	−0.739899			−0.0509368			−0.0254684	−	0.999676i	$-0.508108\pi$
$211$	−0.739899			−0.0509368			−0.0254684	+	0.999676i	$0.508108\pi$
$212$	−4.77156	+	8.26459i	−0.327712	+	0.567614i
$213$	11.9900	+	20.7673i	0.821540	+	1.42295i
$214$	17.7466	+	30.7380i	1.21313	+	2.10121i
$215$	−4.71795	+	8.17173i	−0.321762	+	0.557308i
$216$	8.55641			0.582190
$217$		0			0
$218$	3.89029			0.263484
$219$	13.6313	−	23.6102i	0.921120	−	1.59543i
$220$	−16.8423	−	29.1718i	−1.13551	−	1.96676i
$221$	−0.820411	−	1.42099i	−0.0551868	−	0.0955864i
$222$	11.0328	−	19.1094i	0.740472	−	1.28254i
$223$	−8.30577			−0.556196			−0.278098	−	0.960553i	$-0.589704\pi$
$223$	−8.30577			−0.556196			−0.278098	+	0.960553i	$0.589704\pi$
$224$		0			0
$225$	−0.0501729			−0.00334486
$226$	8.21125	−	14.2223i	0.546205	−	0.946054i
$227$	6.64583	+	11.5109i	0.441099	+	0.764006i	0.997771	−	0.0667264i	$-0.0212555\pi$
$227$	6.64583	+	11.5109i	0.441099	+	0.764006i	−0.556672	+	0.830732i	$0.687922\pi$
$228$	6.49607	+	11.2515i	0.430213	+	0.745151i
$229$	8.96033	−	15.5197i	0.592115	−	1.02557i	−0.401832	−	0.915714i	$-0.631626\pi$
$229$	8.96033	−	15.5197i	0.592115	−	1.02557i	0.993947	−	0.109860i	$-0.0350404\pi$
$230$	−29.6051			−1.95210
$231$		0			0
$232$	−10.1232			−0.664619
$233$	−3.14984	+	5.45568i	−0.206353	+	0.357413i	−0.950563	−	0.310532i	$-0.899493\pi$
$233$	−3.14984	+	5.45568i	−0.206353	+	0.357413i	0.744210	+	0.667946i	$0.232826\pi$
$234$	0.100468	+	0.174016i	0.00656780	+	0.0113758i
$235$	−12.4434	−	21.5525i	−0.811715	−	1.40593i
$236$	18.2317	−	31.5782i	1.18678	−	2.05556i
$237$	−1.97320			−0.128173
$238$		0			0
$239$	9.41783			0.609189			0.304594	−	0.952482i	$-0.401479\pi$
$239$	9.41783			0.609189			0.304594	+	0.952482i	$0.401479\pi$
$240$	3.48810	−	6.04156i	0.225156	−	0.389981i
$241$	−9.97465	−	17.2766i	−0.642524	−	1.11288i	−0.984867	−	0.173309i	$-0.944554\pi$
$241$	−9.97465	−	17.2766i	−0.642524	−	1.11288i	0.342344	−	0.939575i	$-0.388779\pi$
$242$	−24.3212	−	42.1256i	−1.56343	−	2.70794i
$243$	−0.478069	+	0.828039i	−0.0306681	+	0.0531187i
$244$	−17.2811			−1.10631
$245$		0			0
$246$	−27.4144			−1.74788
$247$	1.33538	−	2.31295i	0.0849684	−	0.147170i
$248$	4.28540	+	7.42253i	0.272123	+	0.471331i
$249$	−4.36901	−	7.56735i	−0.276875	−	0.479561i
$250$	−12.7761	+	22.1288i	−0.808029	+	1.39955i
$251$	−1.22202			−0.0771330			−0.0385665	−	0.999256i	$-0.512279\pi$
$251$	−1.22202			−0.0771330			−0.0385665	+	0.999256i	$0.512279\pi$
$252$		0			0
$253$	−37.0633			−2.33015
$254$	21.0742	−	36.5016i	1.32231	−	2.29031i
$255$	3.04488	+	5.27389i	0.190678	+	0.330264i
$256$	1.03346	+	1.79000i	0.0645911	+	0.111875i
$257$	−11.2120	+	19.4198i	−0.699386	+	1.21137i	0.269294	+	0.963058i	$0.413210\pi$
$257$	−11.2120	+	19.4198i	−0.699386	+	1.21137i	−0.968680	+	0.248313i	$0.920124\pi$
$258$	17.1627			1.06850
$259$		0			0
$260$	5.83901			0.362120
$261$	0.278398	−	0.482200i	0.0172324	−	0.0298474i
$262$	10.5854	+	18.3344i	0.653967	+	1.13270i
$263$	−4.49524	−	7.78598i	−0.277188	−	0.480104i	0.693497	−	0.720460i	$-0.256069\pi$
$263$	−4.49524	−	7.78598i	−0.277188	−	0.480104i	−0.970685	+	0.240356i	$0.922736\pi$
$264$	−8.48722	+	14.7003i	−0.522352	+	0.904740i
$265$	−7.28090			−0.447262
$266$		0			0
$267$	2.01567			0.123357
$268$	−10.7091	+	18.5488i	−0.654165	+	1.13305i
$269$	−11.1027	−	19.2305i	−0.676945	−	1.17250i	−0.975896	−	0.218235i	$-0.929970\pi$
$269$	−11.1027	−	19.2305i	−0.676945	−	1.17250i	0.298951	−	0.954268i	$-0.403363\pi$
$270$	11.7814	+	20.4059i	0.716991	+	1.24187i
$271$	−5.42116	+	9.38972i	−0.329312	+	0.570385i	−0.982375	−	0.186918i	$-0.940150\pi$
$271$	−5.42116	+	9.38972i	−0.329312	+	0.570385i	0.653064	+	0.757303i	$0.273483\pi$
$272$	3.08419			0.187006
$273$		0			0
$274$	−33.7293			−2.03766
$275$	−1.57243	+	2.72353i	−0.0948211	+	0.164235i
$276$	15.6267	+	27.0662i	0.940616	+	1.62920i
$277$	−2.94414	−	5.09940i	−0.176896	−	0.306393i	0.763920	−	0.645311i	$-0.223272\pi$
$277$	−2.94414	−	5.09940i	−0.176896	−	0.306393i	−0.940816	+	0.338918i	$0.889939\pi$
$278$	4.20173	−	7.27762i	0.252003	−	0.436482i
$279$	−0.471413			−0.0282227
$280$		0			0
$281$	26.9071			1.60514			0.802572	−	0.596556i	$-0.203465\pi$
$281$	26.9071			1.60514			0.802572	+	0.596556i	$0.203465\pi$
$282$	−22.6329	+	39.2013i	−1.34777	+	2.33441i
$283$	−1.74859	−	3.02864i	−0.103943	−	0.180034i	0.809363	−	0.587309i	$-0.199813\pi$
$283$	−1.74859	−	3.02864i	−0.103943	−	0.180034i	−0.913306	+	0.407275i	$0.866479\pi$
$284$	−18.8634	−	32.6723i	−1.11933	−	1.93874i
$285$	−4.95616	+	8.58432i	−0.293578	+	0.508491i
$286$	12.5948			0.744744
$287$		0			0
$288$	−0.685705			−0.0404056
$289$	7.15385	−	12.3908i	0.420815	−	0.728873i
$290$	−13.9387	−	24.1425i	−0.818506	−	1.41769i
$291$	6.13005	+	10.6176i	0.359350	+	0.622412i
$292$	−21.4456	+	37.1449i	−1.25501	+	2.17374i
$293$	−1.00509			−0.0587179			−0.0293589	−	0.999569i	$-0.509347\pi$
$293$	−1.00509			−0.0587179			−0.0293589	+	0.999569i	$0.509347\pi$
$294$		0			0
$295$	27.8196			1.61972
$296$	−4.80890	+	8.32926i	−0.279512	+	0.484129i
$297$	14.7494	+	25.5467i	0.855846	+	1.48237i
$298$	1.13558	+	1.96688i	0.0657824	+	0.113938i
$299$	3.21234	−	5.56394i	0.185775	−	0.321771i
$300$	2.65188			0.153106
$301$		0			0
$302$	−9.48252			−0.545657
$303$	5.71415	−	9.89720i	0.328270	−	0.568579i
$304$	2.51007	+	4.34756i	0.143962	+	0.249350i
$305$	−6.59227	−	11.4181i	−0.377472	−	0.653801i
$306$	0.164850	−	0.285529i	0.00942385	−	0.0163226i
$307$	−4.25772			−0.243001			−0.121501	−	0.992591i	$-0.538771\pi$
$307$	−4.25772			−0.243001			−0.121501	+	0.992591i	$0.538771\pi$
$308$		0			0
$309$	−1.01645			−0.0578238
$310$	−11.8012	+	20.4402i	−0.670262	+	1.16093i
$311$	−3.47022	−	6.01059i	−0.196778	−	0.340829i	0.750704	−	0.660639i	$-0.229714\pi$
$311$	−3.47022	−	6.01059i	−0.196778	−	0.340829i	−0.947482	+	0.319809i	$0.896381\pi$
$312$	−1.47120	−	2.54820i	−0.0832905	−	0.144263i
$313$	−4.98150	+	8.62820i	−0.281571	+	0.487695i	−0.971772	−	0.235923i	$-0.924189\pi$
$313$	−4.98150	+	8.62820i	−0.281571	+	0.487695i	0.690201	+	0.723618i	$0.257522\pi$
$314$	−0.733563			−0.0413973
$315$		0			0
$316$	3.10435			0.174633
$317$	−1.87673	+	3.25058i	−0.105407	+	0.182571i	−0.913905	−	0.405929i	$-0.866948\pi$
$317$	−1.87673	+	3.25058i	−0.105407	+	0.182571i	0.808497	+	0.588500i	$0.200281\pi$
$318$	6.62152	+	11.4688i	0.371316	+	0.643139i
$319$	−17.4501	−	30.2245i	−0.977020	−	1.69225i
$320$	−13.1984	+	22.8603i	−0.737813	+	1.27793i
$321$	28.5871			1.59557
$322$		0			0
$323$	−4.38225			−0.243835
$324$	12.8192	−	22.2035i	0.712179	−	1.23353i
$325$	−0.272571	−	0.472106i	−0.0151195	−	0.0261877i
$326$	−7.42206	−	12.8554i	−0.411070	−	0.711994i
$327$	1.56667	−	2.71355i	0.0866370	−	0.150060i
$328$	11.9492			0.659785
$329$		0			0
$330$	−46.7444			−2.57319
$331$	9.99061	−	17.3043i	0.549134	−	0.951128i	−0.449200	−	0.893431i	$-0.648291\pi$
$331$	9.99061	−	17.3043i	0.549134	−	0.951128i	0.998334	−	0.0576966i	$-0.0183756\pi$
$332$	6.87359	+	11.9054i	0.377237	+	0.653394i
$333$	−0.264500	−	0.458128i	−0.0144945	−	0.0251052i
$334$	0.729904	−	1.26423i	0.0399385	−	0.0691756i
$335$	−16.3410			−0.892805
$336$		0			0
$337$	18.4887			1.00714			0.503571	−	0.863954i	$-0.332019\pi$
$337$	18.4887			1.00714			0.503571	+	0.863954i	$0.332019\pi$
$338$	−1.09161	+	1.89072i	−0.0593757	+	0.102842i
$339$	−6.61355	−	11.4550i	−0.359198	−	0.622150i
$340$	−4.79039	−	8.29720i	−0.259795	−	0.449979i
$341$	−14.7742	+	25.5896i	−0.800067	+	1.38576i
$342$	0.536653			0.0290189
$343$		0			0
$344$	−7.48078			−0.403337
$345$	−11.9223	+	20.6501i	−0.641877	+	1.11176i
$346$	27.4189	+	47.4909i	1.47405	+	2.55313i
$347$	0.398050	+	0.689443i	0.0213684	+	0.0370112i	0.876512	−	0.481380i	$-0.159864\pi$
$347$	0.398050	+	0.689443i	0.0213684	+	0.0370112i	−0.855143	+	0.518391i	$0.826531\pi$
$348$	−14.7147	+	25.4866i	−0.788790	+	1.36622i
$349$	11.3725			0.608754			0.304377	−	0.952552i	$-0.401552\pi$
$349$	11.3725			0.608754			0.304377	+	0.952552i	$0.401552\pi$
$350$		0			0
$351$	−5.11342			−0.272934
$352$	−21.4902	+	37.2221i	−1.14543	+	1.98394i
$353$	12.0534	+	20.8771i	0.641537	+	1.11117i	0.985090	+	0.172041i	$0.0550361\pi$
$353$	12.0534	+	20.8771i	0.641537	+	1.11117i	−0.343553	+	0.939133i	$0.611631\pi$
$354$	−25.3002	−	43.8212i	−1.34469	−	2.32907i
$355$	14.3917	−	24.9272i	0.763834	−	1.32300i
$356$	−3.17117			−0.168072
$357$		0			0
$358$	−4.13778			−0.218689
$359$	−4.53591	+	7.85642i	−0.239396	+	0.414646i	−0.960541	−	0.278138i	$-0.910283\pi$
$359$	−4.53591	+	7.85642i	−0.239396	+	0.414646i	0.721145	+	0.692784i	$0.243616\pi$
$360$	0.162528	+	0.281506i	0.00856597	+	0.0148367i
$361$	5.93350	+	10.2771i	0.312289	+	0.540901i
$362$	12.4002	−	21.4777i	0.651739	−	1.12884i
$363$	−39.1778			−2.05630
$364$		0			0
$365$	−32.7238			−1.71284
$366$	−11.9905	+	20.7682i	−0.626754	+	1.08557i
$367$	−15.7754	−	27.3237i	−0.823467	−	1.42629i	−0.903085	−	0.429462i	$-0.858703\pi$
$367$	−15.7754	−	27.3237i	−0.823467	−	1.42629i	0.0796176	−	0.996825i	$-0.474630\pi$
$368$	6.03811	+	10.4583i	0.314758	+	0.545178i
$369$	−0.328617	+	0.569181i	−0.0171071	+	0.0296304i
$370$	−26.4856			−1.37692
$371$		0			0
$372$	24.9164			1.29186
$373$	8.02905	−	13.9067i	0.415728	−	0.720063i	−0.579776	−	0.814776i	$-0.696860\pi$
$373$	8.02905	−	13.9067i	0.415728	−	0.720063i	0.995505	+	0.0947130i	$0.0301933\pi$
$374$	−10.3329	−	17.8971i	−0.534301	−	0.925436i
$375$	10.2902	+	17.8231i	0.531381	+	0.920379i
$376$	9.86509	−	17.0868i	0.508753	−	0.881186i
$377$	6.04973			0.311577
$378$		0			0
$379$	−5.36895			−0.275785			−0.137892	−	0.990447i	$-0.544033\pi$
$379$	−5.36895			−0.275785			−0.137892	+	0.990447i	$0.544033\pi$
$380$	7.79733	−	13.5054i	0.399994	−	0.692811i
$381$	−16.9737	−	29.3993i	−0.869588	−	1.50617i
$382$	25.5881	+	44.3199i	1.30920	+	2.26760i
$383$	17.2537	−	29.8843i	0.881625	−	1.52702i	0.0320905	−	0.999485i	$-0.489784\pi$
$383$	17.2537	−	29.8843i	0.881625	−	1.52702i	0.849534	−	0.527534i	$-0.176883\pi$
$384$	21.8108			1.11303
$385$		0			0
$386$	−4.04353			−0.205810
$387$	0.205730	−	0.356334i	0.0104578	−	0.0181135i
$388$	−9.64416	−	16.7042i	−0.489608	−	0.848026i
$389$	−11.4605	−	19.8501i	−0.581070	−	1.00644i	−0.995353	−	0.0962942i	$-0.969301\pi$
$389$	−11.4605	−	19.8501i	−0.581070	−	1.00644i	0.414283	−	0.910148i	$-0.364032\pi$
$390$	4.05142	−	7.01726i	0.205151	−	0.355333i
$391$	−10.5418			−0.533120
$392$		0			0
$393$	17.0514			0.860131
$394$	10.7751	−	18.6630i	0.542841	−	0.940228i
$395$	1.18423	+	2.05114i	0.0595849	+	0.103204i
$396$	0.734421	+	1.27206i	0.0369061	+	0.0639232i
$397$	5.41468	−	9.37850i	0.271755	−	0.470694i	−0.697556	−	0.716530i	$-0.745729\pi$
$397$	5.41468	−	9.37850i	0.271755	−	0.470694i	0.969311	+	0.245836i	$0.0790626\pi$
$398$	−26.7427			−1.34049
$399$		0			0
$400$	1.02468			0.0512340
$401$	−18.7708	+	32.5119i	−0.937367	+	1.62357i	−0.167010	+	0.985955i	$0.553411\pi$
$401$	−18.7708	+	32.5119i	−0.937367	+	1.62357i	−0.770357	+	0.637613i	$0.779922\pi$
$402$	14.8611	+	25.7402i	0.741206	+	1.28381i
$403$	−2.56101	−	4.43580i	−0.127573	−	0.220963i
$404$	−8.98984	+	15.5709i	−0.447261	+	0.774680i
$405$	19.5608			0.971983
$406$		0			0
$407$	−33.1580			−1.64358
$408$	−2.41398	+	4.18114i	−0.119510	+	0.206997i
$409$	−10.2363	−	17.7299i	−0.506155	−	0.876686i	−0.999975	−	0.00712174i	$-0.997733\pi$
$409$	−10.2363	−	17.7299i	−0.506155	−	0.876686i	0.493820	−	0.869564i	$-0.335600\pi$
$410$	16.4529	+	28.4973i	0.812553	+	1.40738i
$411$	−13.5832	+	23.5268i	−0.670010	+	1.16049i
$412$	1.59914			0.0787840
$413$		0			0
$414$	1.29095			0.0634468
$415$	−5.24418	+	9.08319i	−0.257427	+	0.445876i
$416$	−3.72518	−	6.45220i	−0.182642	−	0.316345i
$417$	−3.38418	−	5.86157i	−0.165724	−	0.287042i
$418$	16.8188	−	29.1311i	0.822637	−	1.42485i
$419$	15.4980			0.757127			0.378564	−	0.925575i	$-0.376418\pi$
$419$	15.4980			0.757127			0.378564	+	0.925575i	$0.376418\pi$
$420$		0			0
$421$	17.9390			0.874293			0.437147	−	0.899390i	$-0.355989\pi$
$421$	17.9390			0.874293			0.437147	+	0.899390i	$0.355989\pi$
$422$	0.807681	−	1.39894i	0.0393173	−	0.0680996i
$423$	0.542601	+	0.939813i	0.0263822	+	0.0456953i
$424$	−2.88615	−	4.99895i	−0.140164	−	0.242771i
$425$	−0.447240	+	0.774642i	−0.0216943	+	0.0375757i
$426$	−52.3535			−2.53654
$427$		0			0
$428$	−44.9749			−2.17394
$429$	5.07207	−	8.78508i	0.244882	−	0.424147i
$430$	−10.3003	−	17.8407i	−0.496726	−	0.860354i
$431$	−10.7219	−	18.5709i	−0.516456	−	0.894529i	−0.999817	−	0.0191077i	$-0.993917\pi$
$431$	−10.7219	−	18.5709i	−0.516456	−	0.894529i	0.483361	−	0.875421i	$-0.339416\pi$
$432$	4.80574	−	8.32379i	0.231216	−	0.400479i
$433$	14.9365			0.717800			0.358900	−	0.933376i	$-0.383152\pi$
$433$	14.9365			0.717800			0.358900	+	0.933376i	$0.383152\pi$
$434$		0			0
$435$	−22.4531			−1.07654
$436$	−2.46478	+	4.26912i	−0.118041	+	0.204454i
$437$	−8.57943	−	14.8600i	−0.410410	−	0.710850i
$438$	29.7602	+	51.5462i	1.42200	+	2.46297i
$439$	−1.79661	+	3.11182i	−0.0857476	+	0.148519i	−0.905710	−	0.423899i	$-0.860661\pi$
$439$	−1.79661	+	3.11182i	−0.0857476	+	0.148519i	0.819962	+	0.572418i	$0.193995\pi$
$440$	20.3746			0.971323
$441$		0			0
$442$	3.58227			0.170391
$443$	6.82672	−	11.8242i	0.324347	−	0.561786i	−0.657033	−	0.753862i	$-0.728189\pi$
$443$	6.82672	−	11.8242i	0.324347	−	0.561786i	0.981380	+	0.192076i	$0.0615221\pi$
$444$	13.9801	+	24.2143i	0.663466	+	1.14916i
$445$	−1.20972	−	2.09529i	−0.0573461	−	0.0993263i
$446$	9.06666	−	15.7039i	0.429319	−	0.743602i
$447$	1.82925			0.0865205
$448$		0			0
$449$	−8.72412			−0.411717			−0.205858	−	0.978582i	$-0.565999\pi$
$449$	−8.72412			−0.411717			−0.205858	+	0.978582i	$0.565999\pi$
$450$	0.0547692	−	0.0948631i	0.00258185	−	0.00447189i
$451$	20.5978	+	35.6765i	0.969915	+	1.67994i
$452$	10.4048	+	18.0217i	0.489402	+	0.847668i
$453$	−3.81873	+	6.61423i	−0.179419	+	0.310763i
$454$	−29.0186			−1.36191
$455$		0			0
$456$	−7.85848			−0.368007
$457$	15.2330	−	26.3843i	0.712568	−	1.23420i	−0.251322	−	0.967904i	$-0.580865\pi$
$457$	15.2330	−	26.3843i	0.712568	−	1.23420i	0.963890	−	0.266300i	$-0.0858013\pi$
$458$	19.5624	+	33.8830i	0.914090	+	1.58325i
$459$	4.19510	+	7.26613i	0.195811	+	0.339154i
$460$	18.7569	−	32.4879i	0.874546	−	1.51476i
$461$	−5.22253			−0.243237			−0.121619	−	0.992577i	$-0.538809\pi$
$461$	−5.22253			−0.243237			−0.121619	+	0.992577i	$0.538809\pi$
$462$		0			0
$463$	20.6220			0.958386			0.479193	−	0.877709i	$-0.340929\pi$
$463$	20.6220			0.958386			0.479193	+	0.877709i	$0.340929\pi$
$464$	−5.68572	+	9.84796i	−0.263953	+	0.457180i
$465$	9.50496	+	16.4631i	0.440782	+	0.763457i
$466$	−6.87679	−	11.9109i	−0.318561	−	0.551764i
$467$	0.835745	−	1.44755i	0.0386737	−	0.0669848i	−0.846041	−	0.533118i	$-0.821020\pi$
$467$	0.835745	−	1.44755i	0.0386737	−	0.0669848i	0.884714	+	0.466134i	$0.154353\pi$
$468$	−0.254614			−0.0117696
$469$		0			0
$470$	54.3332			2.50620
$471$	−0.295415	+	0.511673i	−0.0136120	+	0.0235767i
$472$	11.0277	+	19.1005i	0.507590	+	0.879171i
$473$	−12.8952	−	22.3352i	−0.592923	−	1.02697i
$474$	2.15396	−	3.73077i	0.0989346	−	0.171360i
$475$	−1.45595			−0.0668034
$476$		0			0
$477$	0.317489			0.0145368
$478$	−10.2806	+	17.8065i	−0.470224	+	0.814451i
$479$	5.32196	+	9.21790i	0.243166	+	0.421177i	0.961614	−	0.274404i	$-0.0884806\pi$
$479$	5.32196	+	9.21790i	0.243166	+	0.421177i	−0.718448	+	0.695581i	$0.755147\pi$
$480$	13.8257	+	23.9468i	0.631053	+	1.09302i
$481$	2.87386	−	4.97767i	0.131037	−	0.226962i
$482$	43.5537			1.98382
$483$		0			0
$484$	61.6369			2.80168
$485$	7.35798	−	12.7444i	0.334109	−	0.578693i
$486$	−1.04373	−	1.80779i	−0.0473445	−	0.0820031i
$487$	15.9156	+	27.5667i	0.721206	+	1.24916i	0.960517	+	0.278222i	$0.0897450\pi$
$487$	15.9156	+	27.5667i	0.721206	+	1.24916i	−0.239311	+	0.970943i	$0.576922\pi$
$488$	5.22635	−	9.05230i	0.236586	−	0.409778i
$489$	−11.9558			−0.540661
$490$		0			0
$491$	6.87077			0.310074			0.155037	−	0.987909i	$-0.450450\pi$
$491$	6.87077			0.310074			0.155037	+	0.987909i	$0.450450\pi$
$492$	17.3690	−	30.0839i	0.783054	−	1.35629i
$493$	−4.96327	−	8.59663i	−0.223534	−	0.387173i
$494$	2.91544	+	5.04968i	0.131172	+	0.227196i
$495$	−0.560325	+	0.970511i	−0.0251847	+	0.0436212i
$496$	9.62765			0.432294
$497$		0			0
$498$	19.0770			0.854862
$499$	−0.172167	+	0.298203i	−0.00770727	+	0.0133494i	−0.869853	−	0.493310i	$-0.835787\pi$
$499$	−0.172167	+	0.298203i	−0.00770727	+	0.0133494i	0.862146	+	0.506660i	$0.169120\pi$
$500$	−16.1891	−	28.0403i	−0.723998	−	1.25400i
$501$	−0.587882	−	1.01824i	−0.0262646	−	0.0454917i
$502$	1.33397	−	2.31050i	0.0595378	−	0.103122i
$503$	−30.0808			−1.34123			−0.670617	−	0.741803i	$-0.733971\pi$
$503$	−30.0808			−1.34123			−0.670617	+	0.741803i	$0.733971\pi$
$504$		0			0
$505$	−13.7175			−0.610423
$506$	40.4587	−	70.0766i	1.79861	−	3.11528i
$507$	0.879209	+	1.52284i	0.0390471	+	0.0676315i
$508$	26.7040	+	46.2527i	1.18480	+	2.05213i
$509$	16.6553	−	28.8478i	0.738232	−	1.27865i	−0.215059	−	0.976601i	$-0.568994\pi$
$509$	16.6553	−	28.8478i	0.738232	−	1.27865i	0.953291	−	0.302054i	$-0.0976722\pi$
$510$	−13.2953			−0.588726
$511$		0			0
$512$	20.2947			0.896908
$513$	−6.82838	+	11.8271i	−0.301480	+	0.522179i
$514$	−24.4783	−	42.3976i	−1.07969	−	1.87008i
$515$	0.610029	+	1.05660i	0.0268811	+	0.0465594i
$516$	−10.8738	+	18.8340i	−0.478693	+	0.829120i
$517$	68.0210			2.99156
$518$		0			0
$519$	44.1677			1.93875
$520$	−1.76591	+	3.05864i	−0.0774401	+	0.134130i
$521$	16.3863	+	28.3819i	0.717897	+	1.24343i	0.961831	+	0.273643i	$0.0882286\pi$
$521$	16.3863	+	28.3819i	0.717897	+	1.24343i	−0.243934	+	0.969792i	$0.578438\pi$
$522$	0.607805	+	1.05275i	0.0266029	+	0.0460775i
$523$	12.6308	−	21.8772i	0.552307	−	0.956623i	−0.445801	−	0.895132i	$-0.647081\pi$
$523$	12.6308	−	21.8772i	0.552307	−	0.956623i	0.998108	−	0.0614909i	$-0.0195855\pi$
$524$	−26.8263			−1.17191
$525$		0			0
$526$	19.6282			0.855830
$527$	−4.20216	+	7.27835i	−0.183049	+	0.317050i
$528$	9.53376	+	16.5130i	0.414904	+	0.718634i
$529$	−9.13831	−	15.8280i	−0.397318	−	0.688175i
$530$	7.94790	−	13.7662i	0.345235	−	0.597964i
$531$	−1.21309			−0.0526437
$532$		0			0
$533$	−7.14100			−0.309311
$534$	−2.20032	+	3.81107i	−0.0952173	+	0.164921i
$535$	−17.1567	−	29.7163i	−0.741750	−	1.28475i
$536$	−6.47758	−	11.2195i	−0.279789	−	0.484608i
$537$	−1.66634	+	2.88618i	−0.0719077	+	0.124548i
$538$	48.4794			2.09009
$539$		0			0
$540$	−29.8573			−1.28485
$541$	−6.58148	+	11.3995i	−0.282960	+	0.490101i	−0.972112	−	0.234515i	$-0.924650\pi$
$541$	−6.58148	+	11.3995i	−0.282960	+	0.490101i	0.689152	+	0.724616i	$0.257983\pi$
$542$	−11.8356	−	20.4998i	−0.508382	−	0.880543i
$543$	−9.98740	−	17.2987i	−0.428601	−	0.742358i
$544$	−6.11236	+	10.5869i	−0.262065	+	0.453910i
$545$	−3.76099			−0.161103
$546$		0			0
$547$	−2.79349			−0.119441			−0.0597204	−	0.998215i	$-0.519021\pi$
$547$	−2.79349			−0.119441			−0.0597204	+	0.998215i	$0.519021\pi$
$548$	21.3699	−	37.0137i	0.912877	−	1.58115i
$549$	0.287460	+	0.497896i	0.0122685	+	0.0212497i
$550$	−3.43296	−	5.94606i	−0.146382	−	0.253541i
$551$	8.07872	−	13.9927i	0.344165	−	0.596111i
$552$	−18.9040			−0.804610
$553$		0			0
$554$	12.8554			0.546174
$555$	−10.6661	+	18.4742i	−0.452750	+	0.784186i
$556$	5.32419	+	9.22177i	0.225796	+	0.391090i
$557$	2.30642	+	3.99484i	0.0977262	+	0.169267i	0.910743	−	0.412973i	$-0.135510\pi$
$557$	2.30642	+	3.99484i	0.0977262	+	0.169267i	−0.813017	+	0.582240i	$0.802176\pi$
$558$	0.514599	−	0.891311i	0.0217847	−	0.0377322i
$559$	4.47061			0.189087
$560$		0			0
$561$	−16.6447			−0.702740
$562$	−29.3721	+	50.8739i	−1.23899	+	2.14599i
$563$	20.1403	+	34.8840i	0.848811	+	1.47018i	0.882270	+	0.470743i	$0.156014\pi$
$563$	20.1403	+	34.8840i	0.848811	+	1.47018i	−0.0334593	+	0.999440i	$0.510652\pi$
$564$	−28.6791	−	49.6736i	−1.20761	−	2.09164i
$565$	−7.93833	+	13.7496i	−0.333968	+	0.578449i
$566$	7.63510			0.320927
$567$		0			0
$568$	22.8195			0.957486
$569$	−3.59934	+	6.23425i	−0.150892	+	0.261353i	−0.931556	−	0.363598i	$-0.881548\pi$
$569$	−3.59934	+	6.23425i	−0.150892	+	0.261353i	0.780663	+	0.624952i	$0.214881\pi$
$570$	−10.8204	−	18.7415i	−0.453216	−	0.784993i
$571$	−5.69101	−	9.85712i	−0.238161	−	0.412508i	0.722025	−	0.691867i	$-0.243211\pi$
$571$	−5.69101	−	9.85712i	−0.238161	−	0.412508i	−0.960187	+	0.279359i	$0.909878\pi$
$572$	−7.97967	+	13.8212i	−0.333647	+	0.577893i
$573$	41.2186			1.72193
$574$		0			0
$575$	−3.50236			−0.146059
$576$	0.575525	−	0.996839i	0.0239802	−	0.0415350i
$577$	−17.8129	−	30.8528i	−0.741560	−	1.28442i	−0.951785	−	0.306766i	$-0.900753\pi$
$577$	−17.8129	−	30.8528i	−0.741560	−	1.28442i	0.210225	−	0.977653i	$-0.432580\pi$
$578$	15.6184	+	27.0519i	0.649641	+	1.12521i
$579$	−1.62838	+	2.82044i	−0.0676732	+	0.117213i
$580$	35.3245			1.46677
$581$		0			0
$582$	−26.7665			−1.10951
$583$	9.95017	−	17.2342i	0.412094	−	0.713768i
$584$	−12.9717	−	22.4676i	−0.536772	−	0.929717i
$585$	−0.0971286	−	0.168232i	−0.00401577	−	0.00695552i
$586$	1.09716	−	1.90034i	0.0453234	−	0.0785025i
$587$	−4.14755			−0.171188			−0.0855938	−	0.996330i	$-0.527279\pi$
$587$	−4.14755			−0.171188			−0.0855938	+	0.996330i	$0.527279\pi$
$588$		0			0
$589$	−13.6797			−0.563663
$590$	−30.3681	+	52.5991i	−1.25024	+	2.16547i
$591$	−8.67852	−	15.0316i	−0.356987	−	0.618319i
$592$	5.40188	+	9.35633i	0.222016	+	0.384543i
$593$	−12.0656	+	20.8983i	−0.495476	+	0.858190i	−0.999986	−	0.00521562i	$-0.998340\pi$
$593$	−12.0656	+	20.8983i	−0.495476	+	0.858190i	0.504510	+	0.863406i	$0.331673\pi$
$594$	−64.4023			−2.64246
$595$		0			0
$596$	−2.87788			−0.117883
$597$	−10.7696	+	18.6535i	−0.440772	+	0.763439i
$598$	7.01325	+	12.1473i	0.286793	+	0.496741i
$599$	24.2803	+	42.0548i	0.992068	+	1.71831i	0.604896	+	0.796305i	$0.293215\pi$
$599$	24.2803	+	42.0548i	0.992068	+	1.71831i	0.387172	+	0.922007i	$0.373452\pi$
$600$	−0.802014	+	1.38913i	−0.0327421	+	0.0567109i
$601$	33.2069			1.35454			0.677270	−	0.735735i	$-0.263163\pi$
$601$	33.2069			1.35454			0.677270	+	0.735735i	$0.263163\pi$
$602$		0			0
$603$	0.712562			0.0290178
$604$	6.00785	−	10.4059i	0.244456	−	0.423410i
$605$	23.5128	+	40.7254i	0.955932	+	1.65572i
$606$	12.4753	+	21.6078i	0.506772	+	0.877756i
$607$	−10.8973	+	18.8747i	−0.442308	+	0.766100i	−0.997860	−	0.0653815i	$-0.979174\pi$
$607$	−10.8973	+	18.8747i	−0.442308	+	0.766100i	0.555552	+	0.831482i	$0.312507\pi$
$608$	−19.8982			−0.806978
$609$		0			0
$610$	28.7847			1.16546
$611$	−5.89550	+	10.2113i	−0.238506	+	0.413105i
$612$	0.208888	+	0.361805i	0.00844381	+	0.0146251i
$613$	11.3995	+	19.7446i	0.460423	+	0.797476i	0.998982	−	0.0451115i	$-0.0143643\pi$
$613$	11.3995	+	19.7446i	0.460423	+	0.797476i	−0.538559	+	0.842588i	$0.681031\pi$
$614$	4.64777	−	8.05018i	0.187569	−	0.324879i
$615$	26.5032			1.06871
$616$		0			0
$617$	−42.5433			−1.71273			−0.856364	−	0.516373i	$-0.827282\pi$
$617$	−42.5433			−1.71273			−0.856364	+	0.516373i	$0.827282\pi$
$618$	1.10957	−	1.92183i	0.0446333	−	0.0773072i
$619$	−22.0642	−	38.2164i	−0.886836	−	1.53605i	−0.843594	−	0.536981i	$-0.819565\pi$
$619$	−22.0642	−	38.2164i	−0.886836	−	1.53605i	−0.0432419	−	0.999065i	$-0.513769\pi$
$620$	−14.9538	−	25.9007i	−0.600558	−	1.04020i
$621$	−16.4261	+	28.4508i	−0.659155	+	1.14169i
$622$	15.1525			0.607559
$623$		0			0
$624$	−3.30523			−0.132315
$625$	10.9886	−	19.0327i	0.439542	−	0.761310i
$626$	−10.8757	−	18.8373i	−0.434680	−	0.752889i
$627$	−13.5463	−	23.4629i	−0.540987	−	0.937018i
$628$	0.464764	−	0.804995i	0.0185461	−	0.0321228i
$629$	−9.43098			−0.376038
$630$		0			0
$631$	9.09226			0.361957			0.180979	−	0.983487i	$-0.442074\pi$
$631$	9.09226			0.361957			0.180979	+	0.983487i	$0.442074\pi$
$632$	−0.938854	+	1.62614i	−0.0373456	+	0.0646845i
$633$	−0.650526	−	1.12674i	−0.0258561	−	0.0447841i
$634$	−4.09730	−	7.09674i	−0.162725	−	0.281847i
$635$	−20.3737	+	35.2884i	−0.808507	+	1.40038i
$636$	−16.7808			−0.665402
$637$		0			0
$638$	76.1950			3.01659
$639$	−0.627562	+	1.08697i	−0.0248260	+	0.0429998i
$640$	−13.0899	−	22.6723i	−0.517423	−	0.896202i
$641$	11.3321	+	19.6278i	0.447591	+	0.775250i	0.998229	−	0.0594943i	$-0.0189488\pi$
$641$	11.3321	+	19.6278i	0.447591	+	0.775250i	−0.550638	+	0.834744i	$0.685615\pi$
$642$	−31.2059	+	54.0503i	−1.23160	+	2.13319i
$643$	−24.3792			−0.961422			−0.480711	−	0.876879i	$-0.659621\pi$
$643$	−24.3792			−0.961422			−0.480711	+	0.876879i	$0.659621\pi$
$644$		0			0
$645$	−16.5923			−0.653320
$646$	4.78371	−	8.28563i	0.188213	−	0.325994i
$647$	−18.5182	−	32.0745i	−0.728026	−	1.26098i	−0.957716	−	0.287715i	$-0.907105\pi$
$647$	−18.5182	−	32.0745i	−0.728026	−	1.26098i	0.229690	−	0.973264i	$-0.426229\pi$
$648$	7.75389	+	13.4301i	0.304601	+	0.527585i
$649$	−38.0186	+	65.8501i	−1.49236	+	2.58484i
$650$	1.19016			0.0466820
$651$		0			0
$652$	18.8096			0.736641
$653$	−9.36705	+	16.2242i	−0.366561	+	0.634902i	−0.989025	−	0.147746i	$-0.952798\pi$
$653$	−9.36705	+	16.2242i	−0.366561	+	0.634902i	0.622464	+	0.782648i	$0.286132\pi$
$654$	3.42038	+	5.92428i	0.133748	+	0.231658i
$655$	−10.2335	−	17.7250i	−0.399857	−	0.692573i
$656$	6.71133	−	11.6244i	0.262033	−	0.453855i
$657$	1.42694			0.0556703
$658$		0			0
$659$	−28.5206			−1.11100			−0.555502	−	0.831515i	$-0.687474\pi$
$659$	−28.5206			−1.11100			−0.555502	+	0.831515i	$0.687474\pi$
$660$	29.6159	−	51.2962i	1.15280	−	1.99670i
$661$	−9.98790	−	17.2995i	−0.388484	−	0.672874i	0.603762	−	0.797165i	$-0.293668\pi$
$661$	−9.98790	−	17.2995i	−0.388484	−	0.672874i	−0.992246	+	0.124291i	$0.960335\pi$
$662$	21.8117	+	37.7790i	0.847736	+	1.46832i
$663$	1.44263	−	2.49870i	0.0560270	−	0.0970415i
$664$	−8.31517			−0.322691
$665$		0			0
$666$	1.15492			0.0447524
$667$	19.4338	−	33.6604i	0.752481	−	1.30334i
$668$	0.924891	+	1.60196i	0.0357851	+	0.0619816i
$669$	−7.30251	−	12.6483i	−0.282331	−	0.489012i
$670$	17.8380	−	30.8964i	0.689143	−	1.19363i
$671$	36.0363			1.39117
$672$		0			0
$673$	−4.18849			−0.161454			−0.0807272	−	0.996736i	$-0.525724\pi$
$673$	−4.18849			−0.161454			−0.0807272	+	0.996736i	$0.525724\pi$
$674$	−20.1824	+	34.9570i	−0.777398	+	1.34649i
$675$	1.39377	+	2.41408i	0.0536461	+	0.0929178i
$676$	−1.38322	−	2.39581i	−0.0532009	−	0.0921467i
$677$	−19.1698	+	33.2031i	−0.736755	+	1.27610i	0.217194	+	0.976129i	$0.430310\pi$
$677$	−19.1698	+	33.2031i	−0.736755	+	1.27610i	−0.953949	+	0.299969i	$0.903024\pi$
$678$	28.8776			1.10904
$679$		0			0
$680$	5.79507			0.222231
$681$	−11.6861	+	20.2410i	−0.447814	+	0.775637i
$682$	−32.2553	−	55.8678i	−1.23512	−	2.13929i
$683$	1.30604	+	2.26212i	0.0499741	+	0.0865577i	0.889930	−	0.456096i	$-0.150753\pi$
$683$	1.30604	+	2.26212i	0.0499741	+	0.0865577i	−0.839956	+	0.542654i	$0.817419\pi$
$684$	−0.340008	+	0.588911i	−0.0130005	+	0.0225176i
$685$	32.6082			1.24589
$686$		0			0
$687$	31.5120			1.20226
$688$	−4.20161	+	7.27740i	−0.160185	+	0.277448i
$689$	1.72480	+	2.98744i	0.0657095	+	0.113812i
$690$	−26.0291	−	45.0837i	−0.990910	−	1.71631i
$691$	−20.4592	+	35.4365i	−0.778307	+	1.34807i	0.154611	+	0.987975i	$0.450588\pi$
$691$	−20.4592	+	35.4365i	−0.778307	+	1.34807i	−0.932917	+	0.360091i	$0.882746\pi$
$692$	−69.4872			−2.64151
$693$		0			0
$694$	−1.73806			−0.0659759
$695$	−4.06208	+	7.03572i	−0.154083	+	0.266880i
$696$	−8.90039	−	15.4159i	−0.337368	−	0.584339i
$697$	5.85856	+	10.1473i	0.221909	+	0.384357i
$698$	−12.4143	+	21.5022i	−0.469888	+	0.813870i
$699$	−11.0775			−0.418988
$700$		0			0
$701$	−0.762896			−0.0288142			−0.0144071	−	0.999896i	$-0.504586\pi$
$701$	−0.762896			−0.0288142			−0.0144071	+	0.999896i	$0.504586\pi$
$702$	5.58186	−	9.66806i	0.210674	−	0.364897i
$703$	−7.67541	−	13.2942i	−0.289484	−	0.501400i
$704$	−36.0742	−	62.4824i	−1.35960	−	2.35489i
$705$	21.8806	−	37.8984i	0.824072	−	1.42733i
$706$	−52.6304			−1.98077
$707$		0			0
$708$	64.1178			2.40969
$709$	−1.32641	+	2.29740i	−0.0498142	+	0.0862807i	−0.889857	−	0.456239i	$-0.849196\pi$
$709$	−1.32641	+	2.29740i	−0.0498142	+	0.0862807i	0.840043	+	0.542520i	$0.182530\pi$
$710$	31.4203	+	54.4216i	1.17918	+	2.04241i
$711$	−0.0516390	−	0.0894414i	−0.00193661	−	0.00335432i
$712$	0.959063	−	1.66115i	0.0359424	−	0.0622541i
$713$	−32.9074			−1.23239
$714$		0			0
$715$	−12.1761			−0.455362
$716$	2.62158	−	4.54070i	0.0979729	−	0.169694i
$717$	8.28025	+	14.3418i	0.309231	+	0.535605i
$718$	−9.90288	−	17.1523i	−0.369572	−	0.640118i
$719$	5.52216	−	9.56465i	0.205942	−	0.356701i	−0.744491	−	0.667633i	$-0.767308\pi$
$719$	5.52216	−	9.56465i	0.205942	−	0.356701i	0.950432	+	0.310931i	$0.100641\pi$
$720$	0.365138			0.0136079
$721$		0			0
$722$	−25.9083			−0.964206
$723$	17.5396	−	30.3795i	0.652305	−	1.12983i
$724$	15.7128	+	27.2153i	0.583961	+	1.01145i
$725$	−1.64898	−	2.85612i	−0.0612416	−	0.106074i
$726$	42.7669	−	74.0744i	1.58723	−	2.74916i
$727$	−3.46566			−0.128534			−0.0642672	−	0.997933i	$-0.520471\pi$
$727$	−3.46566			−0.128534			−0.0642672	+	0.997933i	$0.520471\pi$
$728$		0			0
$729$	26.1216			0.967468
$730$	35.7216	−	61.8716i	1.32211	−	2.28997i
$731$	−3.66774	−	6.35270i	−0.135656	−	0.234963i
$732$	−15.1937	−	26.3162i	−0.561574	−	0.972675i
$733$	−14.5166	+	25.1435i	−0.536182	+	0.928695i	0.462923	+	0.886398i	$0.346801\pi$
$733$	−14.5166	+	25.1435i	−0.536182	+	0.928695i	−0.999105	+	0.0422961i	$0.986533\pi$
$734$	68.8822			2.54249
$735$		0			0
$736$	−47.8663			−1.76437
$737$	22.3319	−	38.6799i	0.822605	−	1.42479i
$738$	−0.717442	−	1.24265i	−0.0264094	−	0.0457424i
$739$	−23.7761	−	41.1814i	−0.874618	−	1.51488i	−0.857169	−	0.515034i	$-0.827779\pi$
$739$	−23.7761	−	41.1814i	−0.874618	−	1.51488i	−0.0174482	−	0.999848i	$-0.505554\pi$
$740$	16.7805	−	29.0647i	0.616864	−	1.06844i
$741$	4.69633			0.172524
$742$		0			0
$743$	12.6122			0.462697			0.231349	−	0.972871i	$-0.425686\pi$
$743$	12.6122			0.462697			0.231349	+	0.972871i	$0.425686\pi$
$744$	−7.53553	+	13.0519i	−0.276266	+	0.478507i
$745$	−1.09784	−	1.90151i	−0.0402216	−	0.0696658i
$746$	17.5292	+	30.3614i	0.641789	+	1.11161i
$747$	0.228676	−	0.396079i	0.00836683	−	0.0144918i
$748$	26.1864			0.957471
$749$		0			0
$750$	−44.9313			−1.64066
$751$	3.85390	−	6.67516i	0.140631	−	0.243580i	−0.787103	−	0.616821i	$-0.788420\pi$
$751$	3.85390	−	6.67516i	0.140631	−	0.243580i	0.927734	+	0.373241i	$0.121754\pi$
$752$	−11.0815	−	19.1938i	−0.404102	−	0.699925i
$753$	−1.07441	−	1.86093i	−0.0391536	−	0.0678161i
$754$	−6.60395	+	11.4384i	−0.240502	+	0.416561i
$755$	9.16734			0.333633
$756$		0			0
$757$	2.39454			0.0870311			0.0435156	−	0.999053i	$-0.486144\pi$
$757$	2.39454			0.0870311			0.0435156	+	0.999053i	$0.486144\pi$
$758$	5.86080	−	10.1512i	0.212874	−	0.368708i
$759$	−32.5864	−	56.4414i	−1.18281	−	2.04869i
$760$	4.71632	+	8.16891i	0.171079	+	0.296318i
$761$	−20.6648	+	35.7925i	−0.749098	+	1.29748i	0.199158	+	0.979967i	$0.436179\pi$
$761$	−20.6648	+	35.7925i	−0.749098	+	1.29748i	−0.948255	+	0.317508i	$0.897154\pi$
$762$	74.1146			2.68489
$763$		0			0
$764$	−64.8475			−2.34610
$765$	−0.159371	+	0.276038i	−0.00576206	+	0.00998018i
$766$	37.6687	+	65.2441i	1.36103	+	2.35736i
$767$	−6.59027	−	11.4147i	−0.237961	−	0.412161i
$768$	−1.81725	+	3.14757i	−0.0655744	+	0.113578i
$769$	−36.7414			−1.32493			−0.662464	−	0.749094i	$-0.730489\pi$
$769$	−36.7414			−1.32493			−0.662464	+	0.749094i	$0.730489\pi$
$770$		0			0
$771$	−39.4308			−1.42007
$772$	2.56186	−	4.43728i	0.0922035	−	0.159701i
$773$	−11.9836	−	20.7562i	−0.431020	−	0.746548i	0.565942	−	0.824445i	$-0.308513\pi$
$773$	−11.9836	−	20.7562i	−0.431020	−	0.746548i	−0.996961	+	0.0778972i	$0.975179\pi$
$774$	0.449153	+	0.777956i	0.0161445	+	0.0279630i
$775$	−1.39611	+	2.41814i	−0.0501498	+	0.0868620i
$776$	11.6668			0.418814

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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.09161 + 1.89072i) q^{2} +(0.879209 + 1.52284i) q^{3} +(-1.38322 - 2.39581i) q^{4} +(1.05533 - 1.82788i) q^{5} -3.83901 q^{6} +1.67333 q^{8} +(-0.0460183 + 0.0797060i) q^{9} +O(q^{10})\)	\(q+(-1.09161 + 1.89072i) q^{2} +(0.879209 + 1.52284i) q^{3} +(-1.38322 - 2.39581i) q^{4} +(1.05533 - 1.82788i) q^{5} -3.83901 q^{6} +1.67333 q^{8} +(-0.0460183 + 0.0797060i) q^{9} +(2.30401 + 3.99066i) q^{10} +(2.88445 + 4.99601i) q^{11} +(2.43229 - 4.21285i) q^{12} -1.00000 q^{13} +3.71141 q^{15} +(0.939830 - 1.62783i) q^{16} +(0.820411 + 1.42099i) q^{17} +(-0.100468 - 0.174016i) q^{18} +(-1.33538 + 2.31295i) q^{19} -5.83901 q^{20} -12.5948 q^{22} +(-3.21234 + 5.56394i) q^{23} +(1.47120 + 2.54820i) q^{24} +(0.272571 + 0.472106i) q^{25} +(1.09161 - 1.89072i) q^{26} +5.11342 q^{27} -6.04973 q^{29} +(-4.05142 + 7.01726i) q^{30} +(2.56101 + 4.43580i) q^{31} +(3.72518 + 6.45220i) q^{32} +(-5.07207 + 8.78508i) q^{33} -3.58227 q^{34} +0.254614 q^{36} +(-2.87386 + 4.97767i) q^{37} +(-2.91544 - 5.04968i) q^{38} +(-0.879209 - 1.52284i) q^{39} +(1.76591 - 3.05864i) q^{40} +7.14100 q^{41} -4.47061 q^{43} +(7.97967 - 13.8212i) q^{44} +(0.0971286 + 0.168232i) q^{45} +(-7.01325 - 12.1473i) q^{46} +(5.89550 - 10.2113i) q^{47} +3.30523 q^{48} -1.19016 q^{50} +(-1.44263 + 2.49870i) q^{51} +(1.38322 + 2.39581i) q^{52} +(-1.72480 - 2.98744i) q^{53} +(-5.58186 + 9.66806i) q^{54} +12.1761 q^{55} -4.69633 q^{57} +(6.60395 - 11.4384i) q^{58} +(6.59027 + 11.4147i) q^{59} +(-5.13372 - 8.89186i) q^{60} +(3.12333 - 5.40976i) q^{61} -11.1825 q^{62} -12.5065 q^{64} +(-1.05533 + 1.82788i) q^{65} +(-11.0734 - 19.1798i) q^{66} +(-3.87108 - 6.70491i) q^{67} +(2.26962 - 3.93111i) q^{68} -11.2973 q^{69} +13.6372 q^{71} +(-0.0770035 + 0.133374i) q^{72} +(-7.75204 - 13.4269i) q^{73} +(-6.27427 - 10.8673i) q^{74} +(-0.479293 + 0.830160i) q^{75} +7.38854 q^{76} +3.83901 q^{78} +(-0.561071 + 0.971803i) q^{79} +(-1.98366 - 3.43579i) q^{80} +(4.63382 + 8.02601i) q^{81} +(-7.79519 + 13.5017i) q^{82} -4.96925 q^{83} +3.46321 q^{85} +(4.88016 - 8.45269i) q^{86} +(-5.31898 - 9.21275i) q^{87} +(4.82662 + 8.35995i) q^{88} +(0.573148 - 0.992721i) q^{89} -0.424106 q^{90} +17.7736 q^{92} +(-4.50333 + 7.79999i) q^{93} +(12.8712 + 22.2935i) q^{94} +(2.81853 + 4.88184i) q^{95} +(-6.55043 + 11.3457i) q^{96} +6.97223 q^{97} -0.530949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{3} - 4 q^{4} + 6 q^{5} - 8 q^{6} - 6 q^{9}+O(q^{10}) \) 12 * q + 8 * q^3 - 4 * q^4 + 6 * q^5 - 8 * q^6 - 6 * q^9	\( 12 q + 8 q^{3} - 4 q^{4} + 6 q^{5} - 8 q^{6} - 6 q^{9} + 4 q^{10} - 4 q^{11} - 4 q^{12} - 12 q^{13} + 24 q^{15} + 16 q^{17} + 4 q^{18} + 2 q^{19} - 32 q^{20} - 24 q^{22} + 6 q^{23} + 12 q^{24} + 4 q^{25} - 40 q^{27} - 12 q^{29} + 6 q^{31} + 20 q^{32} + 4 q^{33} - 48 q^{36} + 8 q^{38} - 8 q^{39} + 4 q^{40} + 16 q^{41} + 4 q^{43} + 4 q^{44} + 14 q^{45} - 8 q^{46} + 30 q^{47} + 16 q^{48} + 16 q^{50} + 4 q^{51} + 4 q^{52} + 14 q^{53} - 48 q^{54} + 16 q^{55} + 8 q^{57} + 8 q^{58} + 24 q^{59} - 12 q^{60} - 56 q^{62} - 40 q^{64} - 6 q^{65} - 4 q^{66} - 16 q^{67} + 28 q^{68} + 40 q^{69} + 16 q^{71} - 28 q^{72} - 6 q^{73} + 12 q^{74} + 12 q^{75} + 32 q^{76} + 8 q^{78} + 22 q^{79} - 28 q^{80} - 46 q^{81} - 40 q^{82} - 100 q^{83} - 16 q^{85} + 16 q^{86} - 16 q^{87} + 44 q^{88} + 26 q^{89} + 80 q^{90} + 40 q^{92} - 16 q^{93} - 32 q^{94} + 6 q^{95} - 20 q^{96} + 28 q^{97} + 24 q^{99}+O(q^{100}) \) 12 * q + 8 * q^3 - 4 * q^4 + 6 * q^5 - 8 * q^6 - 6 * q^9 + 4 * q^10 - 4 * q^11 - 4 * q^12 - 12 * q^13 + 24 * q^15 + 16 * q^17 + 4 * q^18 + 2 * q^19 - 32 * q^20 - 24 * q^22 + 6 * q^23 + 12 * q^24 + 4 * q^25 - 40 * q^27 - 12 * q^29 + 6 * q^31 + 20 * q^32 + 4 * q^33 - 48 * q^36 + 8 * q^38 - 8 * q^39 + 4 * q^40 + 16 * q^41 + 4 * q^43 + 4 * q^44 + 14 * q^45 - 8 * q^46 + 30 * q^47 + 16 * q^48 + 16 * q^50 + 4 * q^51 + 4 * q^52 + 14 * q^53 - 48 * q^54 + 16 * q^55 + 8 * q^57 + 8 * q^58 + 24 * q^59 - 12 * q^60 - 56 * q^62 - 40 * q^64 - 6 * q^65 - 4 * q^66 - 16 * q^67 + 28 * q^68 + 40 * q^69 + 16 * q^71 - 28 * q^72 - 6 * q^73 + 12 * q^74 + 12 * q^75 + 32 * q^76 + 8 * q^78 + 22 * q^79 - 28 * q^80 - 46 * q^81 - 40 * q^82 - 100 * q^83 - 16 * q^85 + 16 * q^86 - 16 * q^87 + 44 * q^88 + 26 * q^89 + 80 * q^90 + 40 * q^92 - 16 * q^93 - 32 * q^94 + 6 * q^95 - 20 * q^96 + 28 * q^97 + 24 * q^99

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