LMFDB - Embedded newform 114.2.l.a.71.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,2,Mod(29,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 17]))

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

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

chi := DirichletCharacter("114.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	114.l (of order $18$, degree $6$, 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:	$0.910294583043$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + \cdots + 19683 $ x^18 - x^15 - 18x^14 + 36x^13 + 10x^12 + 18x^11 + 90x^10 - 567x^9 + 270x^8 + 162x^7 + 270x^6 + 2916x^5 - 4374x^4 - 729x^3 + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			71.1
Root			$-0.363139 + 1.69356i$ of defining polynomial
Character	$\chi$	$=$	114.71
Dual form			114.2.l.a.53.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.939693 - 0.342020i) q^{2} +(-1.64823 + 0.532290i) q^{3} +(0.766044 - 0.642788i) q^{4} +(2.20556 - 2.62849i) q^{5} +(-1.36678 + 1.06392i) q^{6} +(1.68651 + 2.92113i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.43333 - 1.75467i) q^{9} +(1.17355 - 3.22432i) q^{10} +(-2.33635 - 1.34889i) q^{11} +(-0.920469 + 1.46722i) q^{12} +(-5.05419 + 0.891189i) q^{13} +(2.58389 + 2.16814i) q^{14} +(-2.23616 + 5.50635i) q^{15} +(0.173648 - 0.984808i) q^{16} +(1.44531 + 3.97095i) q^{17} +(1.68645 - 2.48110i) q^{18} +(-2.73048 + 3.39772i) q^{19} -3.43124i q^{20} +(-4.33465 - 3.91698i) q^{21} +(-2.65680 - 0.468466i) q^{22} +(-1.69398 - 2.01881i) q^{23} +(-0.363139 + 1.69356i) q^{24} +(-1.17620 - 6.67054i) q^{25} +(-4.44458 + 2.56608i) q^{26} +(-3.07670 + 4.18735i) q^{27} +(3.16961 + 1.15364i) q^{28} +(-3.54249 - 1.28936i) q^{29} +(-0.218019 + 5.93909i) q^{30} +(4.78254 - 2.76120i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(4.56886 + 0.979673i) q^{33} +(2.71629 + 3.23715i) q^{34} +(11.3979 + 2.00975i) q^{35} +(0.736160 - 2.90828i) q^{36} +5.17636i q^{37} +(-1.40372 + 4.12669i) q^{38} +(7.85610 - 4.15918i) q^{39} +(-1.17355 - 3.22432i) q^{40} +(-0.289735 + 1.64317i) q^{41} +(-5.41293 - 2.19822i) q^{42} +(1.85806 + 1.55910i) q^{43} +(-2.65680 + 0.468466i) q^{44} +(0.754733 - 10.2660i) q^{45} +(-2.28230 - 1.31768i) q^{46} +(-0.0440069 + 0.120908i) q^{47} +(0.237991 + 1.71562i) q^{48} +(-2.18866 + 3.79087i) q^{49} +(-3.38672 - 5.86597i) q^{50} +(-4.49590 - 5.77572i) q^{51} +(-3.29889 + 3.93146i) q^{52} +(6.53342 - 5.48219i) q^{53} +(-1.45900 + 4.98712i) q^{54} +(-8.69853 + 3.16600i) q^{55} +3.37303 q^{56} +(2.69188 - 7.05363i) q^{57} -3.76983 q^{58} +(-3.87665 + 1.41099i) q^{59} +(1.82642 + 5.65549i) q^{60} +(3.53369 - 2.96512i) q^{61} +(3.54973 - 4.23041i) q^{62} +(9.22948 + 4.14880i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-8.80484 + 15.2504i) q^{65} +(4.62839 - 0.642049i) q^{66} +(3.81629 - 10.4852i) q^{67} +(3.65965 + 2.11290i) q^{68} +(3.86667 + 2.42578i) q^{69} +(11.3979 - 2.00975i) q^{70} +(-9.91131 - 8.31658i) q^{71} +(-0.302925 - 2.98467i) q^{72} +(-0.414656 + 2.35163i) q^{73} +(1.77042 + 4.86419i) q^{74} +(5.48930 + 10.3685i) q^{75} +(0.0923461 + 4.35792i) q^{76} -9.09972i q^{77} +(5.95979 - 6.59529i) q^{78} +(2.22246 + 0.391880i) q^{79} +(-2.20556 - 2.62849i) q^{80} +(2.84224 - 8.53942i) q^{81} +(0.289735 + 1.64317i) q^{82} +(-6.27861 + 3.62496i) q^{83} +(-5.83832 - 0.214320i) q^{84} +(13.6253 + 4.95920i) q^{85} +(2.27924 + 0.829577i) q^{86} +(6.52515 + 0.239533i) q^{87} +(-2.33635 + 1.34889i) q^{88} +(-0.209662 - 1.18905i) q^{89} +(-2.80197 - 9.90505i) q^{90} +(-11.1272 - 13.2609i) q^{91} +(-2.59533 - 0.457627i) q^{92} +(-6.41298 + 7.09680i) q^{93} +0.128667i q^{94} +(2.90863 + 14.6709i) q^{95} +(0.810416 + 1.53076i) q^{96} +(3.13271 + 8.60706i) q^{97} +(-0.760113 + 4.31081i) q^{98} +(-8.05200 + 0.817228i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{6} + 9 q^{8} - 12 q^{13} + 12 q^{14} - 24 q^{15} - 6 q^{17} - 6 q^{19} - 24 q^{22} - 18 q^{25} - 18 q^{26} - 3 q^{27} + 6 q^{28} + 6 q^{29} - 27 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} - 3 q^{38}+ \cdots - 30 q^{99}+O(q^{100}) $ 18 * q + 3 * q^6 + 9 * q^8 - 12 * q^13 + 12 * q^14 - 24 * q^15 - 6 * q^17 - 6 * q^19 - 24 * q^22 - 18 * q^25 - 18 * q^26 - 3 * q^27 + 6 * q^28 + 6 * q^29 - 27 * q^33 - 6 * q^34 + 24 * q^35 - 3 * q^36 - 3 * q^38 + 6 * q^39 - 3 * q^41 - 6 * q^43 - 24 * q^44 + 54 * q^45 + 18 * q^46 - 30 * q^47 + 6 * q^48 + 21 * q^49 - 3 * q^50 - 33 * q^51 - 6 * q^52 + 60 * q^53 + 30 * q^55 + 12 * q^57 + 12 * q^58 - 3 * q^59 + 18 * q^60 + 54 * q^61 - 6 * q^62 + 84 * q^63 - 9 * q^64 - 24 * q^65 + 30 * q^66 - 15 * q^67 + 27 * q^68 + 24 * q^69 + 24 * q^70 - 36 * q^71 - 42 * q^73 - 6 * q^74 - 18 * q^78 - 6 * q^79 + 3 * q^82 - 36 * q^83 - 24 * q^84 + 6 * q^86 - 54 * q^87 + 60 * q^89 - 12 * q^90 - 18 * q^91 - 84 * q^93 - 6 * q^95 + 9 * q^97 - 12 * q^98 - 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$

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 $

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	−1.64823	+	0.532290i	−0.951607	+	0.307318i
$3$	−1.64823	+	0.532290i	−0.951607	+	0.307318i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	2.20556	−	2.62849i	0.986357	−	1.17549i	0.00187711	−	0.999998i	$-0.499402\pi$
$5$	2.20556	−	2.62849i	0.986357	−	1.17549i	0.984480	−	0.175496i	$-0.0561531\pi$
$6$	−1.36678	+	1.06392i	−0.557984	+	0.434342i
$7$	1.68651	+	2.92113i	0.637442	+	1.10408i	0.985992	+	0.166792i	$0.0533409\pi$
$7$	1.68651	+	2.92113i	0.637442	+	1.10408i	−0.348550	+	0.937290i	$0.613326\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	2.43333	−	1.75467i	0.811112	−	0.584891i
$10$	1.17355	−	3.22432i	0.371111	−	1.01962i
$11$	−2.33635	−	1.34889i	−0.704437	−	0.406707i	0.104561	−	0.994519i	$-0.466656\pi$
$11$	−2.33635	−	1.34889i	−0.704437	−	0.406707i	−0.808998	+	0.587811i	$0.799990\pi$
$12$	−0.920469	+	1.46722i	−0.265717	+	0.423550i
$13$	−5.05419	+	0.891189i	−1.40178	+	0.247171i	−0.822874	−	0.568224i	$-0.807631\pi$
$13$	−5.05419	+	0.891189i	−1.40178	+	0.247171i	−0.578905	+	0.815395i	$0.696520\pi$
$14$	2.58389	+	2.16814i	0.690573	+	0.579460i
$15$	−2.23616	+	5.50635i	−0.577374	+	1.42173i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	1.44531	+	3.97095i	0.350538	+	0.963096i	0.982198	+	0.187850i	$0.0601520\pi$
$17$	1.44531	+	3.97095i	0.350538	+	0.963096i	−0.631659	+	0.775246i	$0.717626\pi$
$18$	1.68645	−	2.48110i	0.397501	−	0.584802i
$19$	−2.73048	+	3.39772i	−0.626414	+	0.779490i
$19$	−2.73048	+	3.39772i	−0.626414	+	0.779490i
$20$		−	3.43124i		−	0.767250i
$21$	−4.33465	−	3.91698i	−0.945899	−	0.854755i
$22$	−2.65680	−	0.468466i	−0.566433	−	0.0998773i
$23$	−1.69398	−	2.01881i	−0.353220	−	0.420951i	0.559952	−	0.828525i	$-0.310819\pi$
$23$	−1.69398	−	2.01881i	−0.353220	−	0.420951i	−0.913172	+	0.407574i	$0.866375\pi$
$24$	−0.363139	+	1.69356i	−0.0741255	+	0.345696i
$25$	−1.17620	−	6.67054i	−0.235239	−	1.33411i
$26$	−4.44458	+	2.56608i	−0.871653	+	0.503249i
$27$	−3.07670	+	4.18735i	−0.592112	+	0.805856i
$28$	3.16961	+	1.15364i	0.599000	+	0.218018i
$29$	−3.54249	−	1.28936i	−0.657823	−	0.239428i	−0.00852691	−	0.999964i	$-0.502714\pi$
$29$	−3.54249	−	1.28936i	−0.657823	−	0.239428i	−0.649296	+	0.760536i	$0.724936\pi$
$30$	−0.218019	+	5.93909i	−0.0398047	+	1.08432i
$31$	4.78254	−	2.76120i	0.858970	−	0.495927i	−0.00469717	−	0.999989i	$-0.501495\pi$
$31$	4.78254	−	2.76120i	0.858970	−	0.495927i	0.863667	+	0.504062i	$0.168162\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	4.56886	+	0.979673i	0.795336	+	0.170539i
$34$	2.71629	+	3.23715i	0.465840	+	0.555166i
$35$	11.3979	+	2.00975i	1.92659	+	0.339710i
$36$	0.736160	−	2.90828i	0.122693	−	0.484713i
$37$			5.17636i			0.850989i	0.904961	+	0.425494i	$0.139900\pi$
$37$			5.17636i			0.850989i	−0.904961	+	0.425494i	$0.860100\pi$
$38$	−1.40372	+	4.12669i	−0.227713	+	0.669438i
$39$	7.85610	−	4.15918i	1.25798	−	0.666002i
$40$	−1.17355	−	3.22432i	−0.185555	−	0.509809i
$41$	−0.289735	+	1.64317i	−0.0452490	+	0.256620i	−0.999038	−	0.0438581i	$-0.986035\pi$
$41$	−0.289735	+	1.64317i	−0.0452490	+	0.256620i	0.953789	+	0.300478i	$0.0971462\pi$
$42$	−5.41293	−	2.19822i	−0.835233	−	0.339193i
$43$	1.85806	+	1.55910i	0.283351	+	0.237760i	0.773374	−	0.633950i	$-0.218567\pi$
$43$	1.85806	+	1.55910i	0.283351	+	0.237760i	−0.490023	+	0.871709i	$0.663012\pi$
$44$	−2.65680	+	0.468466i	−0.400528	+	0.0706240i
$45$	0.754733	−	10.2660i	0.112509	−	1.53037i
$46$	−2.28230	−	1.31768i	−0.336506	−	0.194282i
$47$	−0.0440069	+	0.120908i	−0.00641906	+	0.0176362i	−0.942861	−	0.333187i	$-0.891876\pi$
$47$	−0.0440069	+	0.120908i	−0.00641906	+	0.0176362i	0.936442	+	0.350823i	$0.114098\pi$
$48$	0.237991	+	1.71562i	0.0343510	+	0.247629i
$49$	−2.18866	+	3.79087i	−0.312665	+	0.541552i
$50$	−3.38672	−	5.86597i	−0.478955	−	0.829574i
$51$	−4.49590	−	5.77572i	−0.629551	−	0.808763i
$52$	−3.29889	+	3.93146i	−0.457473	+	0.545195i
$53$	6.53342	−	5.48219i	0.897434	−	0.753036i	−0.0722533	−	0.997386i	$-0.523019\pi$
$53$	6.53342	−	5.48219i	0.897434	−	0.753036i	0.969687	+	0.244350i	$0.0785746\pi$
$54$	−1.45900	+	4.98712i	−0.198544	+	0.678661i
$55$	−8.69853	+	3.16600i	−1.17291	+	0.426904i
$56$	3.37303			0.450740
$57$	2.69188	−	7.05363i	0.356549	−	0.934277i
$58$	−3.76983			−0.495004
$59$	−3.87665	+	1.41099i	−0.504697	+	0.183695i	−0.581805	−	0.813328i	$-0.697653\pi$
$59$	−3.87665	+	1.41099i	−0.504697	+	0.183695i	0.0771085	+	0.997023i	$0.475431\pi$
$60$	1.82642	+	5.65549i	0.235789	+	0.730120i
$61$	3.53369	−	2.96512i	0.452443	−	0.379645i	−0.387898	−	0.921702i	$-0.626799\pi$
$61$	3.53369	−	2.96512i	0.452443	−	0.379645i	0.840342	+	0.542057i	$0.182354\pi$
$62$	3.54973	−	4.23041i	0.450817	−	0.537262i
$63$	9.22948	+	4.14880i	1.16281	+	0.522700i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−8.80484	+	15.2504i	−1.09211	+	1.89158i
$66$	4.62839	−	0.642049i	0.569715	−	0.0790308i
$67$	3.81629	−	10.4852i	0.466234	−	1.28097i	−0.454490	−	0.890752i	$-0.650179\pi$
$67$	3.81629	−	10.4852i	0.466234	−	1.28097i	0.920724	−	0.390215i	$-0.127599\pi$
$68$	3.65965	+	2.11290i	0.443797	+	0.256226i
$69$	3.86667	+	2.42578i	0.465492	+	0.292029i
$70$	11.3979	−	2.00975i	1.36230	−	0.240211i
$71$	−9.91131	−	8.31658i	−1.17626	−	0.986996i	−0.999996	−	0.00265261i	$-0.999156\pi$
$71$	−9.91131	−	8.31658i	−1.17626	−	0.986996i	−0.176260	−	0.984344i	$-0.556400\pi$
$72$	−0.302925	−	2.98467i	−0.0357001	−	0.351746i
$73$	−0.414656	+	2.35163i	−0.0485318	+	0.275238i	−0.999411	−	0.0343255i	$-0.989072\pi$
$73$	−0.414656	+	2.35163i	−0.0485318	+	0.275238i	0.950879	+	0.309563i	$0.100183\pi$
$74$	1.77042	+	4.86419i	0.205807	+	0.565450i
$75$	5.48930	+	10.3685i	0.633850	+	1.19725i
$76$	0.0923461	+	4.35792i	0.0105928	+	0.499888i
$77$		−	9.09972i		−	1.03701i
$78$	5.95979	−	6.59529i	0.674814	−	0.746770i
$79$	2.22246	+	0.391880i	0.250046	+	0.0440899i	0.297266	−	0.954795i	$-0.403925\pi$
$79$	2.22246	+	0.391880i	0.250046	+	0.0440899i	−0.0472200	+	0.998885i	$0.515036\pi$
$80$	−2.20556	−	2.62849i	−0.246589	−	0.293874i
$81$	2.84224	−	8.53942i	0.315804	−	0.948824i
$82$	0.289735	+	1.64317i	0.0319959	+	0.181458i
$83$	−6.27861	+	3.62496i	−0.689167	+	0.397891i	−0.803300	−	0.595575i	$-0.796924\pi$
$83$	−6.27861	+	3.62496i	−0.689167	+	0.397891i	0.114133	+	0.993465i	$0.463591\pi$
$84$	−5.83832	−	0.214320i	−0.637013	−	0.0233843i
$85$	13.6253	+	4.95920i	1.47787	+	0.537901i
$86$	2.27924	+	0.829577i	0.245777	+	0.0894556i
$87$	6.52515	+	0.239533i	0.699570	+	0.0256807i
$88$	−2.33635	+	1.34889i	−0.249056	+	0.143793i
$89$	−0.209662	−	1.18905i	−0.0222241	−	0.126039i	0.971677	−	0.236312i	$-0.0759387\pi$
$89$	−0.209662	−	1.18905i	−0.0222241	−	0.126039i	−0.993901	+	0.110273i	$0.964828\pi$
$90$	−2.80197	−	9.90505i	−0.295354	−	1.04408i
$91$	−11.1272	−	13.2609i	−1.16645	−	1.39012i
$92$	−2.59533	−	0.457627i	−0.270582	−	0.0477109i
$93$	−6.41298	+	7.09680i	−0.664995	+	0.735904i
$94$			0.128667i			0.0132710i
$95$	2.90863	+	14.6709i	0.298419	+	1.50520i
$96$	0.810416	+	1.53076i	0.0827127	+	0.156233i
$97$	3.13271	+	8.60706i	0.318079	+	0.873914i	0.990959	+	0.134163i	$0.0428346\pi$
$97$	3.13271	+	8.60706i	0.318079	+	0.873914i	−0.672880	+	0.739751i	$0.734943\pi$
$98$	−0.760113	+	4.31081i	−0.0767830	+	0.435458i
$99$	−8.05200	+	0.817228i	−0.809257	+	0.0821345i
$100$	−5.18876	−	4.35388i	−0.518876	−	0.435388i
$101$	−5.56915	+	0.981991i	−0.554151	+	0.0977117i	−0.443709	−	0.896171i	$-0.646338\pi$
$101$	−5.56915	+	0.981991i	−0.554151	+	0.0977117i	−0.110442	+	0.993883i	$0.535227\pi$
$102$	−6.20017	−	3.88971i	−0.613909	−	0.385139i
$103$	3.35680	+	1.93805i	0.330755	+	0.190961i	0.656176	−	0.754608i	$-0.272173\pi$
$103$	3.35680	+	1.93805i	0.330755	+	0.190961i	−0.325421	+	0.945569i	$0.605506\pi$
$104$	−1.75530	+	4.82265i	−0.172121	+	0.472900i
$105$	−19.8561	+	2.75443i	−1.93775	+	0.268805i
$106$	4.26438	−	7.38613i	0.414194	−	0.717404i
$107$	3.48940	+	6.04382i	0.337333	+	0.584278i	0.983930	−	0.178554i	$-0.0571419\pi$
$107$	3.48940	+	6.04382i	0.337333	+	0.584278i	−0.646597	+	0.762832i	$0.723809\pi$
$108$	0.334684	+	5.18536i	0.0322050	+	0.498962i
$109$	3.68457	−	4.39110i	0.352918	−	0.420591i	−0.560155	−	0.828388i	$-0.689258\pi$
$109$	3.68457	−	4.39110i	0.352918	−	0.420591i	0.913073	+	0.407797i	$0.133703\pi$
$110$	−7.09110	+	5.95014i	−0.676110	+	0.567324i
$111$	−2.75533	−	8.53184i	−0.261524	−	0.809807i
$112$	3.16961	−	1.15364i	0.299500	−	0.109009i
$113$	16.8907			1.58895			0.794474	−	0.607298i	$-0.207747\pi$
$113$	16.8907			1.58895			0.794474	+	0.607298i	$0.207747\pi$
$114$	0.117059	−	7.54893i	0.0109636	−	0.707022i
$115$	−9.04260			−0.843227
$116$	−3.54249	+	1.28936i	−0.328912	+	0.119714i
$117$	−10.7348	+	11.0370i	−0.992431	+	1.02037i
$118$	−3.16027	+	2.65178i	−0.290927	+	0.244117i
$119$	−9.16212	+	10.9190i	−0.839890	+	1.00094i
$120$	3.65056	+	4.68975i	0.333249	+	0.428113i
$121$	−1.86097	−	3.22329i	−0.169179	−	0.293026i
$122$	2.30645	−	3.99490i	0.208817	−	0.361681i
$123$	−0.397092	−	2.86255i	−0.0358046	−	0.258107i
$124$	1.88877	−	5.18936i	0.169617	−	0.466019i
$125$	−5.26986	−	3.04256i	−0.471351	−	0.272134i
$126$	10.0918	+	0.741928i	0.899053	+	0.0660962i
$127$	5.44679	−	0.960416i	0.483324	−	0.0852231i	0.0733234	−	0.997308i	$-0.476639\pi$
$127$	5.44679	−	0.960416i	0.483324	−	0.0852231i	0.410001	+	0.912085i	$0.365528\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	−3.89240	−	1.58072i	−0.342707	−	0.139175i
$130$	−3.05789	+	17.3422i	−0.268195	+	1.52101i
$131$	−5.04199	−	13.8528i	−0.440521	−	1.21032i	−0.939150	−	0.343506i	$-0.888385\pi$
$131$	−5.04199	−	13.8528i	−0.440521	−	1.21032i	0.498629	−	0.866815i	$-0.333837\pi$
$132$	4.12967	−	2.18633i	0.359442	−	0.190296i
$133$	−14.5302	−	2.24577i	−1.25992	−	0.194733i
$134$		−	11.1581i		−	0.963911i
$135$	4.22053	+	17.3225i	0.363245	+	1.49089i
$136$	4.16160	+	0.733802i	0.356854	+	0.0629230i
$137$	−12.8171	−	15.2748i	−1.09503	−	1.30501i	−0.948840	−	0.315756i	$-0.897742\pi$
$137$	−12.8171	−	15.2748i	−1.09503	−	1.30501i	−0.146195	−	0.989256i	$-0.546703\pi$
$138$	4.46315	+	0.957006i	0.379928	+	0.0814658i
$139$	−0.280984	−	1.59354i	−0.0238328	−	0.135162i	0.970570	−	0.240820i	$-0.0774164\pi$
$139$	−0.280984	−	1.59354i	−0.0238328	−	0.135162i	−0.994403	+	0.105658i	$0.966305\pi$
$140$	10.0231	−	5.78684i	0.847107	−	0.489077i
$141$	0.00817546	−	0.222709i	0.000688498	−	0.0187554i
$142$	−12.1580	−	4.42516i	−1.02028	−	0.371351i
$143$	13.0105	+	4.73543i	1.08799	+	0.395997i
$144$	−1.30547	−	2.70106i	−0.108789	−	0.225089i
$145$	−11.2022	+	6.46761i	−0.930295	+	0.537106i
$146$	0.414656	+	2.35163i	0.0343172	+	0.194622i
$147$	1.58957	−	7.41322i	0.131106	−	0.611432i
$148$	3.32730	+	3.96532i	0.273502	+	0.325948i
$149$	23.7332	+	4.18480i	1.94430	+	0.342832i	0.999902	+	0.0140170i	$0.00446189\pi$
$149$	23.7332	+	4.18480i	1.94430	+	0.342832i	0.944394	+	0.328815i	$0.106649\pi$
$150$	8.70450	+	7.86576i	0.710719	+	0.642237i
$151$			14.7053i			1.19670i	0.801235	+	0.598349i	$0.204176\pi$
$151$			14.7053i			1.19670i	−0.801235	+	0.598349i	$0.795824\pi$
$152$	1.57727	+	4.06352i	0.127934	+	0.329595i
$153$	10.4846	+	7.12660i	0.847633	+	0.576152i
$154$	−3.11229	−	8.55094i	−0.250795	−	0.689054i
$155$	3.29041	−	18.6609i	0.264292	−	1.49888i
$156$	3.34465	−	8.23592i	0.267786	−	0.659401i
$157$	11.7536	+	9.86243i	0.938038	+	0.787108i	0.977243	−	0.212124i	$-0.0680380\pi$
$157$	11.7536	+	9.86243i	0.938038	+	0.787108i	−0.0392046	+	0.999231i	$0.512482\pi$
$158$	2.22246	−	0.391880i	0.176810	−	0.0311763i
$159$	−7.85047	+	12.5136i	−0.622583	+	0.992392i
$160$	−2.97155	−	1.71562i	−0.234921	−	0.135632i
$161$	3.04028	−	8.35309i	0.239607	−	0.658316i
$162$	−0.249825	−	8.99653i	−0.0196281	−	0.706834i
$163$	5.96235	−	10.3271i	0.467007	−	0.808880i	−0.532283	−	0.846567i	$-0.678666\pi$
$163$	5.96235	−	10.3271i	0.467007	−	0.808880i	0.999290	+	0.0376868i	$0.0119989\pi$
$164$	0.834259	+	1.44498i	0.0651447	+	0.112834i
$165$	12.6520	−	9.84845i	0.984953	−	0.766701i
$166$	−4.66016	+	5.55376i	−0.361698	+	0.431055i
$167$	1.37759	−	1.15593i	0.106601	−	0.0894489i	−0.587929	−	0.808912i	$-0.700057\pi$
$167$	1.37759	−	1.15593i	0.106601	−	0.0894489i	0.694530	+	0.719463i	$0.255612\pi$
$168$	−5.55953	+	1.79543i	−0.428927	+	0.138520i
$169$	12.5346	−	4.56221i	0.964198	−	0.350939i
$170$	14.4997			1.11208
$171$	−0.682271	+	13.0589i	−0.0521746	+	0.998638i
$172$	2.42552			0.184944
$173$	−6.36766	+	2.31764i	−0.484124	+	0.176207i	−0.572540	−	0.819877i	$-0.694042\pi$
$173$	−6.36766	+	2.31764i	−0.484124	+	0.176207i	0.0884156	+	0.996084i	$0.471820\pi$
$174$	6.21356	−	2.00665i	0.471049	−	0.152123i
$175$	17.5018	−	14.6858i	1.32301	−	1.11014i
$176$	−1.73411	+	2.06663i	−0.130713	+	0.155778i
$177$	5.63856	−	4.38913i	0.423820	−	0.329907i
$178$	−0.603697	−	1.04563i	−0.0452490	−	0.0783735i
$179$	7.17879	−	12.4340i	0.536568	−	0.929363i	−0.462518	−	0.886610i	$-0.653054\pi$
$179$	7.17879	−	12.4340i	0.536568	−	0.929363i	0.999086	−	0.0427531i	$-0.0136129\pi$
$180$	−6.02072	−	8.34937i	−0.448758	−	0.622325i
$181$	−4.09139	+	11.2410i	−0.304111	+	0.835537i	0.689664	+	0.724129i	$0.257758\pi$
$181$	−4.09139	+	11.2410i	−0.304111	+	0.835537i	−0.993775	+	0.111408i	$0.964464\pi$
$182$	−14.9917	−	8.65545i	−1.11126	−	0.641585i
$183$	−4.24604	+	6.76816i	−0.313876	+	0.500316i
$184$	−2.59533	+	0.457627i	−0.191330	+	0.0337367i
$185$	13.6060	+	11.4168i	1.00033	+	0.839379i
$186$	−3.59898	+	8.86218i	−0.263890	+	0.649807i
$187$	1.97964	−	11.2271i	0.144766	−	0.821008i
$188$	0.0440069	+	0.120908i	0.00320953	+	0.00881811i
$189$	−17.4207	−	1.92542i	−1.26717	−	0.140054i
$190$	7.75096	+	12.7913i	0.562314	+	0.927980i
$191$			10.1652i			0.735526i	0.929919	+	0.367763i	$0.119876\pi$
$191$			10.1652i			0.735526i	−0.929919	+	0.367763i	$0.880124\pi$
$192$	1.28509	+	1.16127i	0.0927436	+	0.0838071i
$193$	−12.3371	−	2.17537i	−0.888046	−	0.156587i	−0.289027	−	0.957321i	$-0.593332\pi$
$193$	−12.3371	−	2.17537i	−0.888046	−	0.156587i	−0.599019	+	0.800734i	$0.704443\pi$
$194$	5.88758	+	7.01654i	0.422703	+	0.503758i
$195$	6.39477	−	29.8230i	0.457939	−	2.13567i
$196$	0.760113	+	4.31081i	0.0542938	+	0.307915i
$197$	−19.9041	+	11.4916i	−1.41811	+	0.818744i	−0.996132	−	0.0878643i	$-0.971996\pi$
$197$	−19.9041	+	11.4916i	−1.41811	+	0.818744i	−0.421974	+	0.906608i	$0.638662\pi$
$198$	−7.28690	+	3.52189i	−0.517857	+	0.250290i
$199$	−23.8117	−	8.66676i	−1.68797	−	0.614370i	−0.693601	−	0.720360i	$-0.743977\pi$
$199$	−23.8117	−	8.66676i	−1.68797	−	0.614370i	−0.994367	+	0.105990i	$0.966199\pi$
$200$	−6.36495	−	2.31665i	−0.450070	−	0.163812i
$201$	−0.708978	+	19.3133i	−0.0500075	+	1.36226i
$202$	−4.89743	+	2.82753i	−0.344582	+	0.198944i
$203$	−2.20807	−	12.5226i	−0.154976	−	0.878913i
$204$	−7.15662	−	1.53455i	−0.501063	−	0.107440i
$205$	3.68002	+	4.38567i	0.257024	+	0.306309i
$206$	3.81721	+	0.673077i	0.265957	+	0.0468955i
$207$	−7.66438	−	1.94005i	−0.532711	−	0.134843i
$208$			5.13216i			0.355851i
$209$	10.9625	−	4.25515i	0.758294	−	0.294335i
$210$	−17.7165	+	9.37949i	−1.22256	+	0.647247i
$211$	−4.07273	−	11.1897i	−0.280378	−	0.770333i	−0.997317	−	0.0731972i	$-0.976680\pi$
$211$	−4.07273	−	11.1897i	−0.280378	−	0.770333i	0.716939	−	0.697136i	$-0.245542\pi$
$212$	1.48101	−	8.39920i	0.101716	−	0.576859i
$213$	20.7630	+	8.43196i	1.42266	+	0.577748i
$214$	5.34607	+	4.48588i	0.365450	+	0.306649i
$215$	8.19612	−	1.44520i	0.558971	−	0.0985616i
$216$	2.08800	+	4.75818i	0.142070	+	0.323753i
$217$	16.1316	+	9.31361i	1.09509	+	0.632249i
$218$	1.96052	−	5.38648i	0.132783	−	0.364818i
$219$	−0.568301	−	4.09675i	−0.0384022	−	0.276833i
$220$	−4.62839	+	8.01660i	−0.312046	+	0.540479i
$221$	−10.8437	−	18.7819i	−0.729427	−	1.26341i
$222$	−5.50722	−	7.07493i	−0.369620	−	0.474838i
$223$	8.14222	−	9.70352i	0.545243	−	0.649796i	−0.421111	−	0.907009i	$-0.638360\pi$
$223$	8.14222	−	9.70352i	0.545243	−	0.649796i	0.966355	+	0.257213i	$0.0828043\pi$
$224$	2.58389	−	2.16814i	0.172643	−	0.144865i
$225$	−14.5667	−	14.1678i	−0.971113	−	0.944521i
$226$	15.8721	−	5.77698i	1.05580	−	0.384279i
$227$	3.77953			0.250857			0.125428	−	0.992103i	$-0.459970\pi$
$227$	3.77953			0.250857			0.125428	+	0.992103i	$0.459970\pi$
$228$	−2.47189	−	7.13371i	−0.163705	−	0.472441i
$229$	15.3222			1.01252			0.506259	−	0.862381i	$-0.331028\pi$
$229$	15.3222			1.01252			0.506259	+	0.862381i	$0.331028\pi$
$230$	−8.49726	+	3.09275i	−0.560293	+	0.203930i
$231$	4.84369	+	14.9984i	0.318691	+	0.986825i
$232$	−2.88786	+	2.42320i	−0.189597	+	0.159091i
$233$	−15.6260	+	18.6223i	−1.02369	+	1.21999i	−0.0484572	+	0.998825i	$0.515430\pi$
$233$	−15.6260	+	18.6223i	−1.02369	+	1.21999i	−0.975236	+	0.221165i	$0.929014\pi$
$234$	−6.31251	+	14.0429i	−0.412662	+	0.918014i
$235$	0.220745	+	0.382341i	0.0143998	+	0.0249412i
$236$	−2.06272	+	3.57274i	−0.134272	+	0.232566i
$237$	−3.87172	+	0.537085i	−0.251496	+	0.0348874i
$238$	−4.87506	+	13.3941i	−0.316003	+	0.868212i
$239$	11.5689	+	6.67933i	0.748332	+	0.432050i	0.825091	−	0.565000i	$-0.191124\pi$
$239$	11.5689	+	6.67933i	0.748332	+	0.432050i	−0.0767587	+	0.997050i	$0.524457\pi$
$240$	5.03439	+	3.15836i	0.324969	+	0.203871i
$241$	−21.6352	+	3.81487i	−1.39365	+	0.245737i	−0.819530	−	0.573037i	$-0.805765\pi$
$241$	−21.6352	+	3.81487i	−1.39365	+	0.245737i	−0.574116	+	0.818774i	$0.694654\pi$
$242$	−2.85116	−	2.39241i	−0.183280	−	0.153790i
$243$	−0.139216	+	15.5878i	−0.00893073	+	0.999960i
$244$	0.801023	−	4.54283i	0.0512803	−	0.290825i
$245$	5.13702	+	14.1138i	0.328192	+	0.901700i
$246$	−1.35219	−	2.55410i	−0.0862126	−	0.162843i
$247$	10.7723	−	19.6061i	0.685427	−	1.24751i
$248$		−	5.52241i		−	0.350673i
$249$	8.41908	−	9.31681i	0.533537	−	0.590429i
$250$	−5.99267	−	1.05667i	−0.379009	−	0.0668296i
$251$	4.35873	+	5.19453i	0.275121	+	0.327876i	0.885857	−	0.463958i	$-0.153571\pi$
$251$	4.35873	+	5.19453i	0.275121	+	0.327876i	−0.610737	+	0.791834i	$0.709127\pi$
$252$	9.73699	−	2.75443i	0.613373	−	0.173513i
$253$	1.23458	+	7.00166i	0.0776175	+	0.440191i
$254$	4.78983	−	2.76541i	0.300540	−	0.173517i
$255$	−25.0974	−	0.921305i	−1.57166	−	0.0576944i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−16.7251	−	6.08743i	−1.04328	−	0.379724i	−0.237158	−	0.971471i	$-0.576216\pi$
$257$	−16.7251	−	6.08743i	−1.04328	−	0.379724i	−0.806123	+	0.591747i	$0.798438\pi$
$258$	−4.19830	−	0.154116i	−0.261375	−	0.00959486i
$259$	−15.1208	+	8.73000i	−0.939561	+	0.542456i
$260$	3.05789	+	17.3422i	0.189642	+	1.07551i
$261$	−10.8825	+	3.07847i	−0.673607	+	0.190552i
$262$	−9.47585	−	11.2929i	−0.585420	−	0.697676i
$263$	−3.78041	−	0.666587i	−0.233110	−	0.0411035i	0.0558728	−	0.998438i	$-0.482206\pi$
$263$	−3.78041	−	0.666587i	−0.233110	−	0.0411035i	−0.288983	+	0.957334i	$0.593317\pi$
$264$	3.13285	−	3.46691i	0.192814	−	0.213374i
$265$		−	29.2643i		−	1.79769i
$266$	−14.4220	+	2.85928i	−0.884268	+	0.175313i
$267$	0.978490	+	1.84823i	0.0598826	+	0.113110i
$268$	−3.81629	−	10.4852i	−0.233117	−	0.640483i
$269$	−0.457985	+	2.59736i	−0.0279239	+	0.158364i	−0.995581	−	0.0939040i	$-0.970065\pi$
$269$	−0.457985	+	2.59736i	−0.0279239	+	0.158364i	0.967657	+	0.252268i	$0.0811765\pi$
$270$	9.89065	+	14.8343i	0.601926	+	0.902790i
$271$	10.7222	+	8.99702i	0.651329	+	0.546530i	0.907474	−	0.420108i	$-0.138008\pi$
$271$	10.7222	+	8.99702i	0.651329	+	0.546530i	−0.256145	+	0.966638i	$0.582452\pi$
$272$	4.16160	−	0.733802i	0.252334	−	0.0444933i
$273$	25.3989	+	15.9342i	1.53721	+	0.964379i
$274$	−17.2684	−	9.96990i	−1.04322	−	0.602304i
$275$	−6.24984	+	17.1713i	−0.376880	+	1.03547i
$276$	4.52130	−	0.627194i	0.272150	−	0.0377526i
$277$	−0.166629	+	0.288609i	−0.0100117	+	0.0173408i	−0.870988	−	0.491305i	$-0.836520\pi$
$277$	−0.166629	+	0.288609i	−0.0100117	+	0.0173408i	0.860976	+	0.508645i	$0.169854\pi$
$278$	−0.809062	−	1.40134i	−0.0485243	−	0.0840466i
$279$	6.79252	−	15.1107i	0.406657	−	0.904656i
$280$	7.43942	−	8.86596i	0.444590	−	0.529842i
$281$	−1.92247	+	1.61315i	−0.114685	+	0.0962323i	−0.698327	−	0.715779i	$-0.746072\pi$
$281$	−1.92247	+	1.61315i	−0.114685	+	0.0962323i	0.583642	+	0.812011i	$0.301627\pi$
$282$	−0.0684884	−	0.212074i	−0.00407842	−	0.0126288i
$283$	−24.7578	+	9.01110i	−1.47170	+	0.535655i	−0.948561	−	0.316594i	$-0.897461\pi$
$283$	−24.7578	+	9.01110i	−1.47170	+	0.535655i	−0.523138	+	0.852248i	$0.675239\pi$
$284$	−12.9383			−0.767747
$285$	−12.6033	−	22.6328i	−0.746553	−	1.34065i
$286$	13.8455			0.818700
$287$	−5.28855	+	1.92487i	−0.312173	+	0.113622i
$288$	−2.15056	−	2.09167i	−0.126723	−	0.123253i
$289$	−0.656761	+	0.551088i	−0.0386330	+	0.0324169i
$290$	−8.31460	+	9.90896i	−0.488250	+	0.581874i
$291$	−9.74489	−	12.5189i	−0.571255	−	0.733872i
$292$	1.19395	+	2.06799i	0.0698709	+	0.121020i
$293$	6.53329	−	11.3160i	0.381679	−	0.661087i	−0.609624	−	0.792691i	$-0.708679\pi$
$293$	6.53329	−	11.3160i	0.381679	−	0.661087i	0.991302	+	0.131604i	$0.0420127\pi$
$294$	−1.04176	−	7.50982i	−0.0607567	−	0.437981i
$295$	−4.84144	+	13.3017i	−0.281879	+	0.774457i
$296$	4.48286	+	2.58818i	0.260561	+	0.150435i
$297$	12.8366	−	5.63298i	0.744853	−	0.326859i
$298$	23.7332	−	4.18480i	1.37482	−	0.242419i
$299$	10.3608	+	8.69378i	0.599183	+	0.502775i
$300$	10.8698	+	4.41429i	0.627568	+	0.254859i
$301$	−1.42068	+	8.05706i	−0.0818864	+	0.464401i
$302$	5.02950	+	13.8184i	0.289415	+	0.795162i
$303$	8.65654	−	4.58295i	0.497305	−	0.263284i
$304$	2.87196	+	3.27900i	0.164718	+	0.188064i
$305$		−	15.8280i		−	0.906310i
$306$	12.2898	+	3.11086i	0.702560	+	0.177836i
$307$	7.06477	+	1.24571i	0.403208	+	0.0710964i	0.371575	−	0.928403i	$-0.378818\pi$
$307$	7.06477	+	1.24571i	0.403208	+	0.0710964i	0.0316333	+	0.999500i	$0.489929\pi$
$308$	−5.84919	−	6.97079i	−0.333288	−	0.397198i
$309$	−6.56438	−	1.40756i	−0.373435	−	0.0800734i
$310$	−3.29041	−	18.6609i	−0.186883	−	1.05987i
$311$	9.96292	−	5.75210i	0.564945	−	0.326171i	−0.190183	−	0.981749i	$-0.560908\pi$
$311$	9.96292	−	5.75210i	0.564945	−	0.326171i	0.755128	+	0.655577i	$0.227575\pi$
$312$	0.326094	−	8.88317i	0.0184615	−	0.502911i
$313$	16.6644	+	6.06533i	0.941925	+	0.342833i	0.766926	−	0.641736i	$-0.221785\pi$
$313$	16.6644	+	6.06533i	0.941925	+	0.342833i	0.174999	+	0.984569i	$0.444008\pi$
$314$	14.4179	+	5.24769i	0.813650	+	0.296144i
$315$	31.2612	−	15.1091i	1.76137	−	0.851303i
$316$	1.95440	−	1.12837i	0.109944	−	0.0634759i
$317$	5.91797	+	33.5625i	0.332386	+	1.88506i	0.451653	+	0.892194i	$0.350835\pi$
$317$	5.91797	+	33.5625i	0.332386	+	1.88506i	−0.119267	+	0.992862i	$0.538054\pi$
$318$	−3.09713	+	14.4439i	−0.173678	+	0.809976i
$319$	6.53729	+	7.79084i	0.366018	+	0.436203i
$320$	−3.37912	−	0.595829i	−0.188898	−	0.0333079i
$321$	−8.96840	−	8.10424i	−0.500567	−	0.452334i
$322$		−	8.88918i		−	0.495374i
$323$	−17.4385	−	5.93183i	−0.970307	−	0.330056i
$324$	−3.31175	−	8.36853i	−0.183986	−	0.464918i
$325$	11.8894	+	32.6659i	0.659507	+	1.81198i
$326$	2.07070	−	11.7435i	0.114686	−	0.650414i
$327$	−3.73569	+	9.19881i	−0.206584	+	0.508695i
$328$	1.27816	+	1.07250i	0.0705745	+	0.0592190i
$329$	−0.427405	+	0.0753631i	−0.0235636	+	0.00415490i
$330$	8.52058	−	13.5817i	0.469042	−	0.747650i
$331$	18.0961	+	10.4478i	0.994652	+	0.574263i	0.906662	−	0.421858i	$-0.138622\pi$
$331$	18.0961	+	10.4478i	0.994652	+	0.574263i	0.0879907	+	0.996121i	$0.471955\pi$
$332$	−2.47962	+	6.81269i	−0.136087	+	0.373895i
$333$	9.08283	+	12.5958i	0.497736	+	0.690247i
$334$	0.899158	−	1.55739i	0.0491997	−	0.0852164i
$335$	−19.1430	−	33.1567i	−1.04590	−	1.81155i
$336$	−4.61018	+	3.58862i	−0.251506	+	0.195775i
$337$	−19.1366	+	22.8061i	−1.04244	+	1.24233i	−0.0729092	+	0.997339i	$0.523228\pi$
$337$	−19.1366	+	22.8061i	−1.04244	+	1.24233i	−0.969526	+	0.244988i	$0.921216\pi$
$338$	10.2183	−	8.57416i	0.555801	−	0.466373i
$339$	−27.8399	+	8.99077i	−1.51205	+	0.488312i
$340$	13.6253	−	4.95920i	0.738935	−	0.268950i
$341$	−14.8983			−0.806788
$342$	3.82528	+	12.5047i	0.206847	+	0.676176i
$343$	8.84639			0.477660
$344$	2.27924	−	0.829577i	0.122889	−	0.0447278i
$345$	14.9043	−	4.81329i	0.802420	−	0.259139i
$346$	−5.19097	+	4.35574i	−0.279068	+	0.234166i
$347$	−3.49226	+	4.16191i	−0.187474	+	0.223423i	−0.851592	−	0.524204i	$-0.824363\pi$
$347$	−3.49226	+	4.16191i	−0.187474	+	0.223423i	0.664118	+	0.747628i	$0.268807\pi$
$348$	5.15252	−	4.01079i	0.276204	−	0.215001i
$349$	−8.07643	−	13.9888i	−0.432322	−	0.748803i	0.564751	−	0.825261i	$-0.308972\pi$
$349$	−8.07643	−	13.9888i	−0.432322	−	0.748803i	−0.997073	+	0.0764582i	$0.975639\pi$
$350$	11.4235	−	19.7861i	0.610612	−	1.05761i
$351$	11.8185	−	23.9056i	0.630826	−	1.27598i
$352$	−0.922698	+	2.53509i	−0.0491800	+	0.135121i
$353$	−18.1153	−	10.4589i	−0.964180	−	0.556670i	−0.0667232	−	0.997772i	$-0.521254\pi$
$353$	−18.1153	−	10.4589i	−0.964180	−	0.556670i	−0.897457	+	0.441102i	$0.854588\pi$
$354$	3.79735	−	6.05294i	0.201827	−	0.321710i
$355$	−43.7200	+	7.70902i	−2.32042	+	0.409152i
$356$	−0.924917	−	0.776097i	−0.0490205	−	0.0411331i
$357$	9.28922	−	22.8739i	0.491638	−	1.21062i
$358$	2.49317	−	14.1395i	0.131768	−	0.747294i
$359$	−8.05343	−	22.1266i	−0.425044	−	1.16780i	−0.948785	−	0.315921i	$-0.897686\pi$
$359$	−8.05343	−	22.1266i	−0.425044	−	1.16780i	0.523741	−	0.851877i	$-0.324536\pi$
$360$	−8.51328	−	5.78663i	−0.448689	−	0.304982i
$361$	−4.08900	−	18.5548i	−0.215211	−	0.976568i
$362$			11.9624i			0.628731i
$363$	4.78302	+	4.32215i	0.251044	+	0.226854i
$364$	−17.0479	−	3.00601i	−0.893553	−	0.157558i
$365$	5.26668	+	6.27659i	0.275671	+	0.328532i
$366$	−1.67513	+	7.81222i	−0.0875603	+	0.408351i
$367$	3.11469	+	17.6643i	0.162586	+	0.922069i	0.951519	+	0.307590i	$0.0995226\pi$
$367$	3.11469	+	17.6643i	0.162586	+	0.922069i	−0.788933	+	0.614479i	$0.789366\pi$
$368$	−2.28230	+	1.31768i	−0.118973	+	0.0686891i
$369$	2.17820	+	4.50677i	0.113393	+	0.234613i
$370$	16.6902	+	6.07474i	0.867683	+	0.315811i
$371$	27.0329	+	9.83916i	1.40348	+	0.510824i
$372$	−0.350891	+	9.55865i	−0.0181928	+	0.495593i
$373$	12.2615	−	7.07917i	0.634876	−	0.366546i	−0.147762	−	0.989023i	$-0.547207\pi$
$373$	12.2615	−	7.07917i	0.634876	−	0.366546i	0.782638	+	0.622477i	$0.213874\pi$
$374$	−1.97964	−	11.2271i	−0.102365	−	0.580540i
$375$	10.3055	+	2.20974i	0.532172	+	0.114111i
$376$	0.0827058	+	0.0985650i	0.00426523	+	0.00508310i
$377$	19.0534	+	3.35964i	0.981303	+	0.173030i
$378$	−17.0286	+	4.14892i	−0.875858	+	0.213397i
$379$		−	1.25595i		−	0.0645137i	−0.999480	−	0.0322569i	$-0.989731\pi$
$379$		−	1.25595i		−	0.0645137i	0.999480	−	0.0322569i	$-0.0102695\pi$
$380$	11.6584	+	9.36893i	0.598064	+	0.480616i
$381$	−8.46635	+	4.48226i	−0.433744	+	0.229633i
$382$	3.47670	+	9.55214i	0.177883	+	0.488730i
$383$	−0.465296	+	2.63882i	−0.0237755	+	0.134838i	−0.994385	−	0.105822i	$-0.966253\pi$
$383$	−0.465296	+	2.63882i	−0.0237755	+	0.134838i	0.970610	+	0.240660i	$0.0773637\pi$
$384$	1.60477	+	0.651705i	0.0818930	+	0.0332572i
$385$	−23.9185	−	20.0700i	−1.21900	−	1.02286i
$386$	−12.3371	+	2.17537i	−0.627944	+	0.110723i
$387$	7.25698	+	0.533515i	0.368893	+	0.0271201i
$388$	7.93231	+	4.57972i	0.402702	+	0.232500i
$389$	−11.2472	+	30.9013i	−0.570253	+	1.56676i	0.233852	+	0.972272i	$0.424867\pi$
$389$	−11.2472	+	30.9013i	−0.570253	+	1.56676i	−0.804106	+	0.594486i	$0.797355\pi$
$390$	−4.19094	−	30.2116i	−0.212217	−	1.52982i
$391$	5.56827	−	9.64452i	0.281599	−	0.487744i
$392$	2.18866	+	3.79087i	0.110544	+	0.191468i
$393$	15.6841	+	20.1488i	0.791156	+	1.01637i
$394$	−14.7733	+	17.6062i	−0.744270	+	0.886987i
$395$	5.93183	−	4.97739i	0.298463	−	0.250440i
$396$	−5.64289	+	5.80176i	−0.283566	+	0.291549i
$397$	−2.19998	+	0.800726i	−0.110414	+	0.0401873i	−0.396636	−	0.917976i	$-0.629823\pi$
$397$	−2.19998	+	0.800726i	−0.110414	+	0.0401873i	0.286223	+	0.958163i	$0.407600\pi$
$398$	−25.3399			−1.27017
$399$	25.1445	−	4.03271i	1.25880	−	0.201888i
$400$	−6.77344			−0.338672
$401$	−12.8782	+	4.68726i	−0.643104	+	0.234071i	−0.642925	−	0.765929i	$-0.722279\pi$
$401$	−12.8782	+	4.68726i	−0.643104	+	0.234071i	−0.000179351		1.00000i	$0.500057\pi$
$402$	5.93933	+	18.3911i	0.296227	+	0.917264i
$403$	−21.7111	+	18.2178i	−1.08151	+	0.907492i
$404$	−3.63500	+	4.33203i	−0.180848	+	0.215526i
$405$	−16.1770	−	26.3050i	−0.803843	−	1.30711i
$406$	−6.35788	−	11.0122i	−0.315536	−	0.546525i
$407$	6.98237	−	12.0938i	0.346103	−	0.599468i
$408$	−7.24987	+	1.00570i	−0.358922	+	0.0497896i
$409$	7.27394	−	19.9850i	0.359673	−	0.988194i	−0.619470	−	0.785020i	$-0.712652\pi$
$409$	7.27394	−	19.9850i	0.359673	−	0.988194i	0.979143	−	0.203173i	$-0.0651254\pi$
$410$	4.95807	+	2.86255i	0.244862	+	0.141371i
$411$	29.2561	+	18.3540i	1.44310	+	0.905335i
$412$	3.81721	−	0.673077i	0.188060	−	0.0331601i
$413$	−10.6597	−	8.94454i	−0.524529	−	0.440132i
$414$	−7.86570	+	0.798320i	−0.386578	+	0.0392353i
$415$	−4.31971	+	24.4983i	−0.212046	+	1.20257i
$416$	1.75530	+	4.82265i	0.0860607	+	0.236450i
$417$	1.31135	+	2.47696i	0.0642173	+	0.121297i
$418$	8.84606	−	7.74794i	0.432675	−	0.378964i
$419$			29.1990i			1.42646i	0.700928	+	0.713232i	$0.252770\pi$
$419$			29.1990i			1.42646i	−0.700928	+	0.713232i	$0.747230\pi$
$420$	−13.4401	+	14.8733i	−0.655811	+	0.725740i
$421$	7.45681	+	1.31484i	0.363423	+	0.0640812i	0.352378	−	0.935858i	$-0.385373\pi$
$421$	7.45681	+	1.31484i	0.363423	+	0.0640812i	0.0110448	+	0.999939i	$0.496484\pi$
$422$	−7.65423	−	9.12195i	−0.372602	−	0.444050i
$423$	0.105070	+	0.371427i	0.00510870	+	0.0180594i
$424$	−1.48101	−	8.39920i	−0.0719240	−	0.407901i
$425$	24.7884	−	14.3116i	1.20241	−	0.694214i
$426$	22.3947	+	0.822092i	1.08503	+	0.0398305i
$427$	14.6211	+	5.32165i	0.707565	+	0.257533i
$428$	6.55793	+	2.38689i	0.316989	+	0.115375i
$429$	−23.9649	−	0.879734i	−1.15704	−	0.0424740i
$430$	7.20755	−	4.16128i	0.347579	−	0.200675i
$431$	4.16028	+	23.5941i	0.200394	+	1.13649i	0.904526	+	0.426419i	$0.140225\pi$
$431$	4.16028	+	23.5941i	0.200394	+	1.13649i	−0.704132	+	0.710069i	$0.748664\pi$
$432$	3.58947	+	3.75709i	0.172698	+	0.180763i
$433$	−9.89407	−	11.7913i	−0.475479	−	0.566654i	0.473984	−	0.880534i	$-0.342816\pi$
$433$	−9.89407	−	11.7913i	−0.475479	−	0.566654i	−0.949463	+	0.313880i	$0.898371\pi$
$434$	18.3442	+	3.23458i	0.880551	+	0.155265i
$435$	15.0212	−	16.6230i	0.720213	−	0.797010i
$436$		−	5.73217i		−	0.274521i
$437$	11.4847	−	0.243366i	0.549389	−	0.0116418i
$438$	−1.93520	−	3.65532i	−0.0924674	−	0.174658i
$439$	−7.60564	−	20.8963i	−0.362997	−	0.997327i	−0.977964	−	0.208774i	$-0.933053\pi$
$439$	−7.60564	−	20.8963i	−0.362997	−	0.997327i	0.614967	−	0.788553i	$-0.289169\pi$
$440$	−1.60742	+	9.11615i	−0.0766309	+	0.434595i
$441$	1.32600	+	13.0648i	0.0631428	+	0.622134i
$442$	−16.6135	−	13.9404i	−0.790225	−	0.663078i
$443$	−30.8547	+	5.44051i	−1.46595	+	0.258486i	−0.848948	−	0.528476i	$-0.822764\pi$
$443$	−30.8547	+	5.44051i	−1.46595	+	0.258486i	−0.617001	+	0.786963i	$0.711652\pi$
$444$	−7.59486	−	4.76468i	−0.360436	−	0.226122i
$445$	−3.58782	−	2.07143i	−0.170079	−	0.0981952i
$446$	4.33238	−	11.9031i	0.205144	−	0.563629i
$447$	−41.3453	+	5.73541i	−1.95556	+	0.271276i
$448$	1.68651	−	2.92113i	0.0796803	−	0.138010i
$449$	6.15216	+	10.6559i	0.290338	+	0.502881i	0.973890	−	0.227022i	$-0.0728988\pi$
$449$	6.15216	+	10.6559i	0.290338	+	0.502881i	−0.683551	+	0.729902i	$0.739565\pi$
$450$	−18.5339	−	8.33128i	−0.873696	−	0.392740i
$451$	2.89339	−	3.44820i	0.136244	−	0.162370i
$452$	12.9391	−	10.8572i	0.608602	−	0.510678i
$453$	−7.82747	−	24.2377i	−0.367767	−	1.13879i
$454$	3.55160	−	1.29268i	0.166685	−	0.0606683i
$455$	−59.3979			−2.78462
$456$	−4.76268	−	5.85806i	−0.223033	−	0.274329i
$457$	−37.8216			−1.76922			−0.884609	−	0.466334i	$-0.845575\pi$
$457$	−37.8216			−1.76922			−0.884609	+	0.466334i	$0.845575\pi$
$458$	14.3981	−	5.24049i	0.672781	−	0.244872i
$459$	−21.0745	−	6.16543i	−0.983675	−	0.287777i
$460$	−6.92703	+	5.81247i	−0.322975	+	0.271008i
$461$	24.9818	−	29.7722i	1.16352	−	1.38663i	0.255970	−	0.966685i	$-0.417605\pi$
$461$	24.9818	−	29.7722i	1.16352	−	1.38663i	0.907550	−	0.419945i	$-0.137950\pi$
$462$	9.68135	+	12.4373i	0.450417	+	0.578635i
$463$	12.3259	+	21.3492i	0.572835	+	0.992180i	0.996273	+	0.0862548i	$0.0274899\pi$
$463$	12.3259	+	21.3492i	0.572835	+	0.992180i	−0.423438	+	0.905925i	$0.639177\pi$
$464$	−1.88492	+	3.26477i	−0.0875051	+	0.151563i
$465$	4.50962	+	32.5089i	0.209129	+	1.50756i
$466$	−8.31442	+	22.8437i	−0.385158	+	1.05821i
$467$	−3.17931	−	1.83558i	−0.147121	−	0.0849404i	0.424632	−	0.905366i	$-0.360403\pi$
$467$	−3.17931	−	1.83558i	−0.147121	−	0.0849404i	−0.571754	+	0.820425i	$0.693737\pi$
$468$	−1.12886	+	15.3550i	−0.0521817	+	0.709786i
$469$	37.0647	−	6.53551i	1.71149	−	0.301782i
$470$	0.338201	+	0.283784i	0.0156000	+	0.0130900i
$471$	−24.6223	−	9.99925i	−1.13454	−	0.460741i
$472$	−0.716376	+	4.06277i	−0.0329739	+	0.187004i
$473$	−2.23803	−	6.14892i	−0.102905	−	0.282728i
$474$	−3.45454	+	1.82890i	−0.158672	+	0.0840043i
$475$	25.8762	+	14.2174i	1.18728	+	0.652337i
$476$			14.2537i			0.653318i
$477$	6.27854	−	24.8040i	0.287474	−	1.13570i
$478$	13.1557	+	2.31971i	0.601728	+	0.106101i
$479$	16.6874	+	19.8872i	0.762465	+	0.908670i	0.998001	−	0.0631952i	$-0.0201291\pi$
$479$	16.6874	+	19.8872i	0.762465	+	0.908670i	−0.235536	+	0.971866i	$0.575685\pi$
$480$	5.81100	+	1.24602i	0.265235	+	0.0568727i
$481$	−4.61312	−	26.1623i	−0.210340	−	1.19290i
$482$	−19.0257	+	10.9845i	−0.866596	+	0.500329i
$483$	−0.564813	+	15.3861i	−0.0256999	+	0.700094i
$484$	−3.49747	−	1.27298i	−0.158976	−	0.0578625i
$485$	29.5329	+	10.7491i	1.34102	+	0.488092i
$486$	5.20053	+	14.6954i	0.235901	+	0.666596i
$487$	8.59327	−	4.96133i	0.389398	−	0.224819i	−0.292501	−	0.956265i	$-0.594488\pi$
$487$	8.59327	−	4.96133i	0.389398	−	0.224819i	0.681899	+	0.731446i	$0.261154\pi$
$488$	−0.801023	−	4.54283i	−0.0362606	−	0.205644i
$489$	−4.33032	+	20.1951i	−0.195824	+	0.913255i
$490$	9.65444	+	11.5057i	0.436143	+	0.519775i
$491$	−14.8971	−	2.62676i	−0.672296	−	0.118544i	−0.172929	−	0.984934i	$-0.555323\pi$
$491$	−14.8971	−	2.62676i	−0.672296	−	0.118544i	−0.499367	+	0.866391i	$0.666434\pi$
$492$	−2.14420	−	1.93759i	−0.0966679	−	0.0873534i
$493$		−	15.9305i		−	0.717476i
$494$	3.41700	−	22.1080i	0.153738	−	0.994688i
$495$	−15.6111	+	22.9670i	−0.701668	+	1.03229i
$496$	−1.88877	−	5.18936i	−0.0848084	−	0.233009i
$497$	7.57822	−	42.9782i	0.339930	−	1.92784i
$498$	4.72481	−	11.6344i	0.211724	−	0.521351i
$499$	16.3136	+	13.6887i	0.730296	+	0.612791i	0.930212	−	0.367022i	$-0.119623\pi$
$499$	16.3136	+	13.6887i	0.730296	+	0.612791i	−0.199917	+	0.979813i	$0.564067\pi$
$500$	−5.99267	+	1.05667i	−0.268000	+	0.0472557i
$501$	−1.65529	+	2.63853i	−0.0739531	+	0.117881i
$502$	5.87250	+	3.39049i	0.262103	+	0.151325i
$503$	1.99181	−	5.47245i	0.0888104	−	0.244004i	−0.887334	−	0.461128i	$-0.847445\pi$
$503$	1.99181	−	5.47245i	0.0888104	−	0.244004i	0.976144	+	0.217123i	$0.0696673\pi$
$504$	8.20770	−	5.91856i	0.365600	−	0.263634i
$505$	−9.70195	+	16.8043i	−0.431731	+	0.747780i
$506$	3.55484	+	6.15716i	0.158032	+	0.273719i
$507$	−18.2315	+	14.1916i	−0.809688	+	0.630272i
$508$	3.55514	−	4.23685i	0.157734	−	0.187980i
$509$	10.9586	−	9.19535i	0.485731	−	0.407577i	−0.366763	−	0.930315i	$-0.619534\pi$
$509$	10.9586	−	9.19535i	0.485731	−	0.407577i	0.852493	+	0.522738i	$0.175089\pi$
$510$	−23.8989	+	7.71806i	−1.05826	+	0.341762i
$511$	−7.56874	+	2.75480i	−0.334821	+	0.121865i
$512$	−1.00000			−0.0441942
$513$	−5.82657	−	21.8872i	−0.257249	−	0.966345i
$514$	−17.7985			−0.785056
$515$	12.4977	−	4.54881i	0.550717	−	0.200444i
$516$	−3.99782	+	1.29108i	−0.175994	+	0.0568367i
$517$	0.265908	−	0.223123i	0.0116946	−	0.00981294i
$518$	−11.2231	+	13.3751i	−0.493114	+	0.587670i
$519$	9.26173	−	7.20945i	0.406545	−	0.316460i
$520$	8.80484	+	15.2504i	0.386118	+	0.668776i
$521$	5.93133	−	10.2734i	0.259856	−	0.450084i	−0.706347	−	0.707866i	$-0.749658\pi$
$521$	5.93133	−	10.2734i	0.259856	−	0.450084i	0.966203	+	0.257781i	$0.0829914\pi$
$522$	−9.17327	+	6.61483i	−0.401503	+	0.289523i
$523$	10.6971	−	29.3899i	0.467750	−	1.28513i	−0.451787	−	0.892126i	$-0.649213\pi$
$523$	10.6971	−	29.3899i	0.467750	−	1.28513i	0.919536	−	0.393005i	$-0.128565\pi$
$524$	−12.7668	−	7.37090i	−0.557719	−	0.321999i
$525$	−21.0300	+	33.5216i	−0.917823	+	1.46300i
$526$	−3.78041	+	0.666587i	−0.164834	+	0.0290646i
$527$	17.8768	+	15.0004i	0.778727	+	0.653430i
$528$	1.75816	−	4.32933i	0.0765142	−	0.188410i
$529$	2.78789	−	15.8109i	0.121213	−	0.687431i
$530$	−10.0090	−	27.4994i	−0.434762	−	1.19450i
$531$	−6.95737	+	10.2357i	−0.301924	+	0.444190i
$532$	−12.5743	+	7.61945i	−0.545165	+	0.330345i
$533$		−	8.56309i		−	0.370909i
$534$	1.55161	+	1.40210i	0.0671448	+	0.0606750i
$535$	23.5822	+	4.15817i	1.01955	+	0.179774i
$536$	−7.17227	−	8.54758i	−0.309795	−	0.369199i
$537$	−5.21380	+	24.3154i	−0.224992	+	1.04929i
$538$	0.457985	+	2.59736i	0.0197451	+	0.111980i
$539$	10.2270	−	5.90454i	0.440506	−	0.254326i
$540$	14.3678	+	10.5569i	0.618293	+	0.454298i
$541$	−26.2388	−	9.55016i	−1.12810	−	0.410593i	−0.290495	−	0.956876i	$-0.593820\pi$
$541$	−26.2388	−	9.55016i	−1.12810	−	0.410593i	−0.837601	+	0.546283i	$0.816042\pi$
$542$	13.1528	+	4.78721i	0.564960	+	0.205628i
$543$	0.760086	−	20.7056i	0.0326184	−	0.888561i
$544$	3.65965	−	2.11290i	0.156906	−	0.0905897i
$545$	−3.41540	−	19.3697i	−0.146300	−	0.829706i
$546$	29.3170	+	6.28627i	1.25465	+	0.269027i
$547$	12.0859	+	14.4034i	0.516757	+	0.615847i	0.959811	−	0.280648i	$-0.0905494\pi$
$547$	12.0859	+	14.4034i	0.516757	+	0.615847i	−0.443054	+	0.896495i	$0.646105\pi$
$548$	−19.6369	−	3.46251i	−0.838845	−	0.147911i
$549$	3.39584	−	13.4156i	0.144931	−	0.572564i
$550$			18.2733i			0.779177i
$551$	14.0536	−	8.51581i	0.598702	−	0.362786i
$552$	4.03412	−	2.13575i	0.171704	−	0.0909034i
$553$	2.60348	+	7.15300i	0.110711	+	0.304177i
$554$	−0.0578695	+	0.328194i	−0.00245864	+	0.0139436i
$555$	−28.5029	−	11.5752i	−1.20988	−	0.491339i
$556$	−1.23956	−	1.04011i	−0.0525689	−	0.0441105i
$557$	22.6372	−	3.99155i	0.959170	−	0.169128i	0.327919	−	0.944706i	$-0.393653\pi$
$557$	22.6372	−	3.99155i	0.959170	−	0.169128i	0.631251	+	0.775578i	$0.282542\pi$
$558$	1.21470	−	16.5226i	0.0514225	−	0.699458i
$559$	−10.7804	−	6.22408i	−0.455963	−	0.263250i
$560$	3.95843	−	10.8757i	0.167274	−	0.459582i
$561$	2.71317	+	19.5586i	0.114550	+	0.825766i
$562$	−1.25481	+	2.17339i	−0.0529308	+	0.0916788i
$563$	−6.45057	−	11.1727i	−0.271859	−	0.470874i	0.697479	−	0.716605i	$-0.254305\pi$
$563$	−6.45057	−	11.1727i	−0.271859	−	0.470874i	−0.969338	+	0.245732i	$0.920972\pi$
$564$	−0.136892	−	0.175860i	−0.00576417	−	0.00740503i
$565$	37.2536	−	44.3971i	1.56727	−	1.86780i
$566$	−20.1827	+	16.9353i	−0.848344	+	0.711845i
$567$	29.7382	−	6.09931i	1.24889	−	0.256147i
$568$	−12.1580	+	4.42516i	−0.510139	+	0.185676i
$569$	37.8380			1.58625			0.793125	−	0.609059i	$-0.208453\pi$
$569$	37.8380			1.58625			0.793125	+	0.609059i	$0.208453\pi$
$570$	−19.5841	−	16.9573i	−0.820286	−	0.710264i
$571$	20.7087			0.866632			0.433316	−	0.901242i	$-0.357343\pi$
$571$	20.7087			0.866632			0.433316	+	0.901242i	$0.357343\pi$
$572$	13.0105	−	4.73543i	0.543996	−	0.197998i
$573$	−5.41082	−	16.7546i	−0.226040	−	0.699932i
$574$	−4.31126	+	3.61758i	−0.179949	+	0.150995i
$575$	−11.4741	+	13.6743i	−0.478503	+	0.570258i
$576$	−2.73626	−	1.22999i	−0.114011	−	0.0512497i
$577$	−8.69281	−	15.0564i	−0.361886	−	0.626805i	0.626385	−	0.779514i	$-0.284534\pi$
$577$	−8.69281	−	15.0564i	−0.361886	−	0.626805i	−0.988271	+	0.152708i	$0.951200\pi$
$578$	−0.428670	+	0.742479i	−0.0178303	+	0.0308830i
$579$	21.4924	−	2.98142i	0.893193	−	0.123904i
$580$	−4.42411	+	12.1551i	−0.183701	+	0.504715i
$581$	−21.1779	−	12.2271i	−0.878608	−	0.507265i
$582$	−13.4389	−	8.43098i	−0.557061	−	0.349476i
$583$	−22.6593	+	3.99544i	−0.938451	+	0.165474i
$584$	1.82924	+	1.53492i	0.0756947	+	0.0635154i
$585$	5.33441	+	52.5590i	0.220551	+	2.17305i
$586$	2.26899	−	12.8681i	0.0937310	−	0.531575i
$587$	10.0782	+	27.6896i	0.415971	+	1.14287i	0.953964	+	0.299922i	$0.0969607\pi$
$587$	10.0782	+	27.6896i	0.415971	+	1.14287i	−0.537992	+	0.842950i	$0.680817\pi$
$588$	−3.54744	−	6.70062i	−0.146294	−	0.276329i
$589$	−3.67683	+	23.7891i	−0.151501	+	0.980214i
$590$			14.1554i			0.582769i
$591$	26.6896	−	29.5356i	1.09786	−	1.21493i
$592$	5.09772	+	0.898866i	0.209515	+	0.0369432i
$593$	8.16230	+	9.72745i	0.335185	+	0.399458i	0.907141	−	0.420826i	$-0.138260\pi$
$593$	8.16230	+	9.72745i	0.335185	+	0.399458i	−0.571956	+	0.820284i	$0.693815\pi$
$594$	10.1358	−	9.68364i	0.415878	−	0.397324i
$595$	8.49279	+	48.1650i	0.348170	+	1.97457i
$596$	20.8706	−	12.0496i	0.854893	−	0.493573i
$597$	43.8604	+	1.61008i	1.79509	+	0.0658963i
$598$	12.7095	+	4.62587i	0.519729	+	0.189166i
$599$	16.8817	+	6.14443i	0.689767	+	0.251055i	0.663035	−	0.748588i	$-0.269268\pi$
$599$	16.8817	+	6.14443i	0.689767	+	0.251055i	0.0267313	+	0.999643i	$0.491490\pi$
$600$	11.7240	+	0.430381i	0.478632	+	0.0175702i
$601$	8.14038	−	4.69985i	0.332053	−	0.191711i	−0.324699	−	0.945817i	$-0.605263\pi$
$601$	8.14038	−	4.69985i	0.332053	−	0.191711i	0.656752	+	0.754106i	$0.271930\pi$
$602$	1.42068	+	8.05706i	0.0579025	+	0.328381i
$603$	−9.11174	−	32.2102i	−0.371059	−	1.31170i
$604$	9.45237	+	11.2649i	0.384611	+	0.458362i
$605$	−12.5768	−	2.21764i	−0.511321	−	0.0901597i
$606$	6.56703	−	7.26728i	0.266767	−	0.295213i
$607$		−	9.88885i		−	0.401376i	−0.979655	−	0.200688i	$-0.935682\pi$
$607$		−	9.88885i		−	0.401376i	0.979655	−	0.200688i	$-0.0643177\pi$
$608$	3.82024	+	2.09899i	0.154931	+	0.0851251i
$609$	10.3050	+	19.4648i	0.417582	+	0.788752i
$610$	−5.41350	−	14.8735i	−0.219186	−	0.602209i
$611$	0.114667	−	0.650309i	0.00463893	−	0.0263087i
$612$	12.6126	−	1.28010i	0.509834	−	0.0517449i
$613$	−24.8777	−	20.8749i	−1.00480	−	0.843129i	−0.0171592	−	0.999853i	$-0.505462\pi$
$613$	−24.8777	−	20.8749i	−1.00480	−	0.843129i	−0.987642	+	0.156724i	$0.949907\pi$
$614$	7.06477	−	1.24571i	0.285111	−	0.0502728i
$615$	−8.39997	−	5.26977i	−0.338720	−	0.212498i
$616$	−7.88059	−	4.54986i	−0.317518	−	0.183319i
$617$	−7.64721	+	21.0105i	−0.307865	+	0.845852i	0.685207	+	0.728348i	$0.259712\pi$
$617$	−7.64721	+	21.0105i	−0.307865	+	0.845852i	−0.993072	+	0.117504i	$0.962511\pi$
$618$	−6.64991	+	0.922475i	−0.267499	+	0.0371074i
$619$	−9.39662	+	16.2754i	−0.377682	+	0.654164i	−0.990725	−	0.135886i	$-0.956612\pi$
$619$	−9.39662	+	16.2754i	−0.377682	+	0.654164i	0.613043	+	0.790050i	$0.289945\pi$
$620$	−9.47436	−	16.4101i	−0.380500	−	0.659045i
$621$	13.6653	−	0.882017i	0.548372	−	0.0353941i
$622$	7.39475	−	8.81272i	0.296503	−	0.353358i
$623$	3.11977	−	2.61780i	0.124991	−	0.104880i
$624$	−2.73179	−	8.45898i	−0.109359	−	0.338630i
$625$	12.2044	−	4.44205i	0.488178	−	0.177682i
$626$	17.7338			0.708787
$627$	−15.8038	+	12.8487i	−0.631143	+	0.513128i
$628$	15.3432			0.612261
$629$	−20.5551	+	7.48143i	−0.819584	+	0.298304i
$630$	24.2083	−	24.8899i	0.964483	−	0.991638i
$631$	−22.1517	+	18.5875i	−0.881846	+	0.739956i	−0.966558	−	0.256449i	$-0.917447\pi$
$631$	−22.1517	+	18.5875i	−0.881846	+	0.739956i	0.0847122	+	0.996405i	$0.473003\pi$
$632$	1.45061	−	1.72877i	0.0577021	−	0.0687667i
$633$	12.6690	+	16.2754i	0.503547	+	0.646889i
$634$	17.0401	+	29.5143i	0.676749	+	1.17216i
$635$	9.48879	−	16.4351i	0.376551	−	0.652206i
$636$	2.02977	+	14.6321i	0.0804856	+	0.580202i
$637$	7.68350	−	21.1102i	0.304431	−	0.836418i
$638$	8.80767	+	5.08511i	0.348699	+	0.201321i
$639$	−38.7104	−	2.84590i	−1.53136	−	0.112582i
$640$	−3.37912	+	0.595829i	−0.133571	+	0.0235522i
$641$	−18.2950	−	15.3513i	−0.722609	−	0.606341i	0.205497	−	0.978658i	$-0.434119\pi$
$641$	−18.2950	−	15.3513i	−0.722609	−	0.606341i	−0.928106	+	0.372317i	$0.878563\pi$
$642$	−11.1994	−	4.54812i	−0.442003	−	0.179500i
$643$	6.83453	−	38.7606i	0.269528	−	1.52857i	−0.486297	−	0.873793i	$-0.661653\pi$
$643$	6.83453	−	38.7606i	0.269528	−	1.52857i	0.755825	−	0.654774i	$-0.227236\pi$
$644$	−3.04028	−	8.35309i	−0.119804	−	0.329158i
$645$	−12.7398	+	6.74473i	−0.501631	+	0.265574i
$646$	−18.4157	+	0.390236i	−0.724555	+	0.0153536i
$647$		−	24.3840i		−	0.958633i	−0.877642	−	0.479317i	$-0.840885\pi$
$647$		−	24.3840i		−	0.958633i	0.877642	−	0.479317i	$-0.159115\pi$
$648$	−5.97424	−	6.73116i	−0.234690	−	0.264425i
$649$	10.9605	+	1.93263i	0.430237	+	0.0758624i
$650$	22.3448	+	26.6295i	0.876436	+	1.04450i
$651$	−31.5462	−	6.76427i	−1.23639	−	0.265113i
$652$	−2.07070	−	11.7435i	−0.0810949	−	0.459912i
$653$	−20.0643	+	11.5841i	−0.785178	+	0.453323i	−0.838262	−	0.545268i	$-0.816428\pi$
$653$	−20.0643	+	11.5841i	−0.785178	+	0.453323i	0.0530845	+	0.998590i	$0.483095\pi$
$654$	−0.364219	+	9.92173i	−0.0142421	+	0.387970i
$655$	−47.5322	−	17.3003i	−1.85724	−	0.675979i
$656$	1.56789	+	0.570666i	0.0612159	+	0.0222808i
$657$	3.11735	+	6.44989i	0.121619	+	0.251634i
$658$	−0.375854	+	0.216999i	−0.0146523	+	0.00845952i
$659$	−3.15401	−	17.8873i	−0.122863	−	0.696790i	−0.982554	−	0.185976i	$-0.940455\pi$
$659$	−3.15401	−	17.8873i	−0.122863	−	0.696790i	0.859691	−	0.510814i	$-0.170656\pi$
$660$	3.36150	−	15.6769i	0.130846	−	0.610221i
$661$	22.4662	+	26.7742i	0.873835	+	1.04140i	0.998787	+	0.0492336i	$0.0156779\pi$
$661$	22.4662	+	26.7742i	0.873835	+	1.04140i	−0.124952	+	0.992163i	$0.539878\pi$
$662$	20.5781	+	3.62848i	0.799792	+	0.141025i
$663$	27.8704	+	25.1849i	1.08240	+	0.978099i
$664$			7.24992i			0.281351i
$665$	−37.9501	+	33.2391i	−1.47164	+	1.28896i
$666$	12.8431	+	8.72969i	0.497660	+	0.338269i
$667$	3.39794	+	9.33576i	0.131569	+	0.361482i
$668$	0.312274	−	1.77099i	0.0120823	−	0.0685218i
$669$	−8.25518	+	20.3277i	−0.319164	+	0.785913i
$670$	−29.3288	−	24.6098i	−1.13307	−	0.950760i
$671$	−12.2556	+	2.16099i	−0.473122	+	0.0834242i
$672$	−3.10477	+	4.94898i	−0.119769	+	0.190911i
$673$	−8.97335	−	5.18077i	−0.345897	−	0.199704i	0.316980	−	0.948432i	$-0.397331\pi$
$673$	−8.97335	−	5.18077i	−0.345897	−	0.199704i	−0.662877	+	0.748729i	$0.730665\pi$
$674$	−10.1824	+	27.9758i	−0.392210	+	1.07759i
$675$	31.5507	+	15.5981i	1.21439	+	0.600372i
$676$	6.66951	−	11.5519i	0.256520	−	0.444305i
$677$	−2.66151	−	4.60988i	−0.102290	−	0.177172i	0.810338	−	0.585963i	$-0.199284\pi$
$677$	−2.66151	−	4.60988i	−0.102290	−	0.177172i	−0.912628	+	0.408791i	$0.865950\pi$
$678$	−23.0859	+	17.9704i	−0.886608	+	0.690147i
$679$	−19.8590	+	23.6670i	−0.762117	+	0.908255i
$680$	11.1074	−	9.32025i	0.425951	−	0.357415i
$681$	−6.22955	+	2.01181i	−0.238717	+	0.0770927i
$682$	−13.9998	+	5.09551i	−0.536080	+	0.195117i
$683$	−29.5958			−1.13245			−0.566226	−	0.824250i	$-0.691597\pi$
$683$	−29.5958			−1.13245			−0.566226	+	0.824250i	$0.691597\pi$
$684$	7.87144	+	10.4422i	0.300972	+	0.399269i
$685$	−68.4183			−2.61413
$686$	8.31289	−	3.02564i	0.317388	−	0.115520i
$687$	−25.2545	+	8.15584i	−0.963519	+	0.311165i
$688$	1.85806	−	1.55910i	0.0708378	−	0.0594400i
$689$	−28.1354	+	33.5305i	−1.07187	+	1.27741i
$690$	12.3592	−	9.62058i	0.470507	−	0.366249i
$691$	9.35680	+	16.2065i	0.355950	+	0.616523i	0.987280	−	0.158991i	$-0.0508241\pi$
$691$	9.35680	+	16.2065i	0.355950	+	0.616523i	−0.631330	+	0.775514i	$0.717491\pi$
$692$	−3.38816	+	5.86847i	−0.128799	+	0.223086i
$693$	−15.9670	−	22.1427i	−0.606538	−	0.841130i
$694$	−1.85819	+	5.10534i	−0.0705361	+	0.193796i
$695$	−4.80833	−	2.77609i	−0.182390	−	0.105303i
$696$	3.47002	−	5.53118i	0.131531	−	0.209659i
$697$	−6.94369	+	1.22436i	−0.263011	+	0.0463760i
$698$	−12.3738	−	10.3829i	−0.468356	−	0.392997i
$699$	15.8428	−	39.0115i	0.599229	−	1.47555i
$700$	3.96734	−	22.4999i	0.149951	−	0.850417i
$701$	9.40339	+	25.8356i	0.355161	+	0.975798i	0.980685	+	0.195593i	$0.0626630\pi$
$701$	9.40339	+	25.8356i	0.355161	+	0.975798i	−0.625524	+	0.780205i	$0.715115\pi$
$702$	2.92958	−	26.5061i	0.110570	−	1.00041i
$703$	−17.5878	−	14.1339i	−0.663337	−	0.533071i
$704$			2.69779i			0.101677i
$705$	−0.567355	−	0.512687i	−0.0213678	−	0.0193089i
$706$	−20.6000	−	3.63233i	−0.775290	−	0.136705i
$707$	−12.2610	−	14.6120i	−0.461121	−	0.549543i
$708$	1.49811	−	6.98667i	0.0563024	−	0.262575i
$709$	7.22305	+	40.9640i	0.271267	+	1.53843i	0.750574	+	0.660786i	$0.229777\pi$
$709$	7.22305	+	40.9640i	0.271267	+	1.53843i	−0.479307	+	0.877647i	$0.659112\pi$
$710$	−38.4467	+	22.1972i	−1.44288	+	0.833047i
$711$	6.09561	−	2.94612i	0.228603	−	0.110488i
$712$	−1.13458	−	0.412953i	−0.0425201	−	0.0154761i
$713$	−13.6759	−	4.97762i	−0.512166	−	0.186413i
$714$	0.905674	−	24.6716i	0.0338940	−	0.923310i
$715$	41.1425	−	23.7536i	1.53864	−	0.888335i
$716$	−2.49317	−	14.1395i	−0.0931741	−	0.528416i
$717$	−22.6236	−	4.85105i	−0.844895	−	0.181166i
$718$	−15.1355	−	18.0378i	−0.564852	−	0.673164i
$719$	−26.6001	−	4.69031i	−0.992015	−	0.174919i	−0.345992	−	0.938237i	$-0.612458\pi$
$719$	−26.6001	−	4.69031i	−0.992015	−	0.174919i	−0.646022	+	0.763318i	$0.723569\pi$
$720$	−9.97901	−	2.52594i	−0.371896	−	0.0941364i
$721$			13.0742i			0.486908i
$722$	−10.1885	−	16.0373i	−0.379177	−	0.596846i
$723$	33.6292	−	17.8040i	1.25068	−	0.662137i
$724$	4.09139	+	11.2410i	0.152055	+	0.417768i
$725$	−4.43406	+	25.1468i	−0.164677	+	0.933930i
$726$	5.97283	+	2.42560i	0.221673	+	0.0900225i
$727$	23.4708	+	19.6943i	0.870483	+	0.730422i	0.964200	−	0.265177i	$-0.0854303\pi$
$727$	23.4708	+	19.6943i	0.870483	+	0.730422i	−0.0937165	+	0.995599i	$0.529875\pi$
$728$	−17.0479	+	3.00601i	−0.631838	+	0.111410i
$729$	−8.06779	−	25.7665i	−0.298807	−	0.954314i
$730$	7.09578	+	4.09675i	0.262627	+	0.151628i
$731$	−3.50562	+	9.63162i	−0.129660	+	0.356238i
$732$	1.09783	+	7.91401i	0.0405770	+	0.292510i
$733$	−24.9658	+	43.2420i	−0.922132	+	1.59718i	−0.126023	+	0.992027i	$0.540221\pi$
$733$	−24.9658	+	43.2420i	−0.922132	+	1.59718i	−0.796110	+	0.605152i	$0.793112\pi$
$734$	8.96840	+	15.5337i	0.331030	+	0.573361i
$735$	−15.9797	−	20.5285i	−0.589418	−	0.757205i
$736$	−1.69398	+	2.01881i	−0.0624410	+	0.0744143i
$737$	−23.0596	+	19.3493i	−0.849410	+	0.712740i
$738$	3.58825	+	3.48999i	0.132085	+	0.128468i
$739$	32.2619	−	11.7424i	1.18677	−	0.431950i	0.328183	−	0.944614i	$-0.393564\pi$
$739$	32.2619	−	11.7424i	1.18677	−	0.431950i	0.858589	+	0.512664i	$0.171341\pi$
$740$	17.7614			0.652921
$741$	−7.31916	+	38.0494i	−0.268876	+	1.39778i
$742$	28.7678			1.05610
$743$	27.6540	−	10.0652i	1.01453	−	0.369257i	0.219357	−	0.975645i	$-0.429604\pi$
$743$	27.6540	−	10.0652i	1.01453	−	0.369257i	0.795169	+	0.606387i	$0.207382\pi$
$744$	2.93952	+	9.10220i	0.107768	+	0.333703i
$745$	63.3446	−	53.1525i	2.32077	−	1.94736i
$746$	9.10081	−	10.8459i	0.333204	−	0.397097i
$747$	−8.91734	+	19.8377i	−0.326269	+	0.725822i
$748$	−5.70015	−	9.87295i	−0.208418	−	0.360991i
$749$	−11.7698	+	20.3860i	−0.430061	+	0.744887i
$750$	10.4398	−	1.44820i	0.381206	−	0.0528808i
$751$	0.559448	−	1.53707i	0.0204145	−	0.0560885i	−0.929067	−	0.369912i	$-0.879388\pi$
$751$	0.559448	−	1.53707i	0.0204145	−	0.0560885i	0.949481	+	0.313824i	$0.101610\pi$
$752$	0.111429	+	0.0643337i	0.00406341	+	0.00234601i
$753$	−9.94920	−	6.24169i	−0.362569	−	0.227460i
$754$	19.0534	−	3.35964i	0.693886	−	0.122351i
$755$	38.6526	+	32.4334i	1.40671	+	1.18037i
$756$	−14.5827	+	9.72284i	−0.530366	+	0.353616i
$757$	4.17165	−	23.6586i	0.151621	−	0.859887i	−0.810189	−	0.586169i	$-0.800635\pi$
$757$	4.17165	−	23.6586i	0.151621	−	0.859887i	0.961810	−	0.273718i	$-0.0882534\pi$
$758$	−0.429560	−	1.18021i	−0.0156023	−	0.0428670i
$759$	−5.76179	−	10.8832i	−0.209140	−	0.395035i
$760$	14.1597	+	4.81651i	0.513626	+	0.174713i
$761$			12.8974i			0.467530i	0.972293	+	0.233765i	$0.0751047\pi$
$761$			12.8974i			0.467530i	−0.972293	+	0.233765i	$0.924895\pi$
$762$	−6.42274	+	7.10761i	−0.232671	+	0.257481i
$763$	19.0410	+	3.35745i	0.689332	+	0.121548i
$764$	6.53405	+	7.78698i	0.236394	+	0.281723i
$765$	41.8567	−	11.8406i	1.51333	−	0.428096i
$766$	0.465296	+	2.63882i	0.0168118	+	0.0953446i
$767$	18.3359	−	10.5862i	0.662069	−	0.382246i
$768$	1.73088	+	0.0635395i	0.0624579	+	0.00229278i
$769$	21.8210	+	7.94220i	0.786886	+	0.286403i	0.704041	−	0.710159i	$-0.251377\pi$
$769$	21.8210	+	7.94220i	0.786886	+	0.286403i	0.0828452	+	0.996562i	$0.473599\pi$
$770$	−29.3404	−	10.6790i	−1.05735	−	0.384845i
$771$	30.8071	+	1.13090i	1.10949	+	0.0407285i
$772$	−10.8491	+	6.26373i	−0.390467	+	0.225436i
$773$	−6.98308	−	39.6030i	−0.251164	−	1.42442i	−0.805730	−	0.592283i	$-0.798227\pi$
$773$	−6.98308	−	39.6030i	−0.251164	−	1.42442i	0.554566	−	0.832140i	$-0.312884\pi$
$774$	7.00180	−	1.98069i	0.251675	−	0.0711945i
$775$	−24.0439	−	28.6544i	−0.863683	−	1.02930i
$776$	9.02029	+	1.59052i	0.323809	+	0.0570964i
$777$	20.2757	−	22.4377i	0.727387	−	0.804949i
$778$			32.8845i			1.17897i
$779$	−4.79191	−	5.47107i	−0.171688	−	0.196021i
$780$	−14.2712	−	26.9562i	−0.510990	−	0.965187i
$781$	11.9381	+	32.7998i	0.427181	+	1.17367i
$782$	1.93384	−	10.9673i	0.0691539	−	0.392191i
$783$	16.2982	−	10.8666i	0.582449	−	0.388342i
$784$	3.35322	+	2.81368i	0.119758	+	0.100489i
$785$	51.8465	−	9.14194i	1.85048	−	0.326290i
$786$	21.6295	+	13.5694i	0.771498	+	0.484004i
$787$	−40.4947	−	23.3796i	−1.44348	−	0.833393i	−0.445400	−	0.895332i	$-0.646938\pi$
$787$	−40.4947	−	23.3796i	−1.44348	−	0.833393i	−0.998080	+	0.0619383i	$0.980272\pi$
$788$	−7.86073	+	21.5972i	−0.280027	+	0.769368i
$789$	6.58580	−	0.913581i	0.234461	−	0.0325244i
$790$	3.87172	−	6.70602i	0.137750	−	0.238590i
$791$	28.4865	+	49.3400i	1.01286	+	1.75433i
$792$	−3.31826	+	7.38185i	−0.117909	+	0.262303i
$793$	−15.2175	+	18.1355i	−0.540388	+	0.644009i
$794$	−1.79344	+	1.50487i	−0.0636467	+	0.0534059i
$795$	15.5771	+	48.2343i	0.552463	+	1.71070i
$796$	−23.8117	+	8.66676i	−0.843984	+	0.307185i
$797$	6.73284			0.238489			0.119245	−	0.992865i	$-0.461953\pi$
$797$	6.73284			0.238489			0.119245	+	0.992865i	$0.461953\pi$
$798$	22.2488	−	12.3894i	0.787599	−	0.438581i
$799$	−0.543722			−0.0192355
$800$	−6.36495	+	2.31665i	−0.225035	+	0.0819061i
$801$	−2.59657	−	2.52547i	−0.0917454	−	0.0892331i
$802$	−10.4984	+	8.80918i	−0.370710	+	0.311063i
$803$	4.14089	−	4.93492i	0.146129	−	0.174149i
$804$	11.8713	+	15.2506i	0.418667	+	0.537847i
$805$	−15.2505	−	26.4146i	−0.537508	−	0.930992i
$806$	−14.1709	+	24.5448i	−0.499149	+	0.864552i
$807$	−0.627685	−	4.52484i	−0.0220955	−	0.159282i
$808$	−1.93414	+	5.31402i	−0.0680430	+	0.186947i
$809$	7.36554	+	4.25250i	0.258959	+	0.149510i	0.623859	−	0.781537i	$-0.285564\pi$
$809$	7.36554	+	4.25250i	0.258959	+	0.149510i	−0.364901	+	0.931046i	$0.618897\pi$
$810$	−24.1983	−	19.1857i	−0.850240	−	0.674118i
$811$	28.9589	−	5.10623i	1.01688	−	0.179304i	0.359727	−	0.933058i	$-0.382870\pi$
$811$	28.9589	−	5.10623i	1.01688	−	0.179304i	0.657157	+	0.753753i	$0.271759\pi$
$812$	−9.74083	−	8.17353i	−0.341836	−	0.286835i
$813$	−22.4617	−	9.12184i	−0.787768	−	0.319917i
$814$	2.42495	−	13.7526i	0.0849945	−	0.482028i
$815$	−13.9943	−	38.4490i	−0.490198	−	1.34681i
$816$	−6.46868	+	3.42465i	−0.226449	+	0.119887i
$817$	−10.3708	+	2.05609i	−0.362827	+	0.0719333i
$818$		−	21.2676i		−	0.743603i
$819$	−50.3449	−	12.7436i	−1.75919	−	0.445297i
$820$	5.63811	+	0.994152i	0.196891	+	0.0347173i
$821$	6.42410	+	7.65594i	0.224203	+	0.267194i	0.866406	−	0.499340i	$-0.166424\pi$
$821$	6.42410	+	7.65594i	0.224203	+	0.267194i	−0.642204	+	0.766534i	$0.721980\pi$
$822$	33.7692	+	7.24092i	1.17783	+	0.252556i
$823$	−8.07641	−	45.8036i	−0.281526	−	1.59661i	−0.717437	−	0.696623i	$-0.754685\pi$
$823$	−8.07641	−	45.8036i	−0.281526	−	1.59661i	0.435911	−	0.899990i	$-0.356426\pi$
$824$	3.35680	−	1.93805i	0.116940	−	0.0675151i
$825$	1.16108	−	31.6290i	0.0404235	−	1.10118i
$826$	−13.0760	−	4.75929i	−0.454974	−	0.165597i
$827$	−46.9782	−	17.0987i	−1.63359	−	0.594579i	−0.647690	−	0.761904i	$-0.724265\pi$
$827$	−46.9782	−	17.0987i	−1.63359	−	0.594579i	−0.985902	+	0.167325i	$0.946487\pi$
$828$	−7.11830	+	3.44040i	−0.247378	+	0.119562i
$829$	16.9994	−	9.81460i	0.590413	−	0.340875i	−0.174848	−	0.984595i	$-0.555943\pi$
$829$	16.9994	−	9.81460i	0.590413	−	0.340875i	0.765261	+	0.643720i	$0.222610\pi$
$830$	4.31971	+	24.4983i	0.149939	+	0.850349i
$831$	0.121019	−	0.564389i	0.00419809	−	0.0195785i
$832$	3.29889	+	3.93146i	0.114368	+	0.136299i
$833$	−18.2166	−	3.21208i	−0.631168	−	0.111292i
$834$	2.07944	+	1.87907i	0.0720051	+	0.0650669i
$835$		−	6.17046i		−	0.213538i
$836$	5.66262	−	10.3062i	0.195846	−	0.356448i
$837$	−3.15235	+	28.5216i	−0.108961	+	0.985850i
$838$	9.98665	+	27.4381i	0.344983	+	0.947833i
$839$	−2.71691	+	15.4084i	−0.0937982	+	0.531956i	0.901311	+	0.433173i	$0.142606\pi$
$839$	−2.71691	+	15.4084i	−0.0937982	+	0.531956i	−0.995109	+	0.0987829i	$0.968505\pi$
$840$	−7.54263	+	18.5731i	−0.260245	+	0.640832i
$841$	−11.3285	−	9.50576i	−0.390639	−	0.327785i
$842$	7.45681	−	1.31484i	0.256979	−	0.0453123i
$843$	2.31002	−	3.68215i	0.0795613	−	0.126820i
$844$	−10.3125	−	5.95393i	−0.354971	−	0.204943i
$845$	15.6541	−	43.0092i	0.538516	−	1.47956i
$846$	0.225769	+	0.313091i	0.00776211	+	0.0107643i
$847$	6.27709	−	10.8722i	0.215683	−	0.373574i
$848$	−4.26438	−	7.38613i	−0.146440	−	0.253641i
$849$	36.0101	−	28.0307i	1.23586	−	0.962012i
$850$	18.3986	−	21.9266i	0.631067	−	0.752077i
$851$	10.4501	−	8.76867i	0.358225	−	0.300586i
$852$	21.3253	−	6.88693i	0.730593	−	0.235942i
$853$	6.82954	−	2.48575i	0.233839	−	0.0851104i	−0.222443	−	0.974946i	$-0.571403\pi$
$853$	6.82954	−	2.48575i	0.233839	−	0.0851104i	0.456282	+	0.889835i	$0.349181\pi$
$854$	15.5595			0.532434
$855$	32.8203	+	30.5955i	1.12243	+	1.04634i
$856$	6.97880			0.238530
$857$	−10.7658	+	3.91845i	−0.367754	+	0.133852i	−0.519285	−	0.854601i	$-0.673802\pi$
$857$	−10.7658	+	3.91845i	−0.367754	+	0.133852i	0.151531	+	0.988452i	$0.451580\pi$
$858$	−22.8206	+	7.36981i	−0.779081	+	0.251601i
$859$	−38.6125	+	32.3998i	−1.31744	+	1.10547i	−0.330602	+	0.943770i	$0.607252\pi$
$859$	−38.6125	+	32.3998i	−1.31744	+	1.10547i	−0.986841	+	0.161695i	$0.948304\pi$
$860$	5.34964	−	6.37545i	0.182421	−	0.217401i
$861$	7.69216	−	5.98768i	0.262148	−	0.204060i
$862$	11.9790	+	20.7483i	0.408008	+	0.706690i
$863$	13.4511	−	23.2980i	0.457882	−	0.793075i	−0.540967	−	0.841044i	$-0.681942\pi$
$863$	13.4511	−	23.2980i	0.457882	−	0.793075i	0.998849	+	0.0479693i	$0.0152749\pi$
$864$	4.65800	+	2.30284i	0.158468	+	0.0783441i
$865$	−7.95239	+	21.8490i	−0.270389	+	0.742889i
$866$	−13.3303	−	7.69622i	−0.452980	−	0.261528i
$867$	0.789156	−	1.25791i	0.0268011	−	0.0427208i
$868$	18.3442	−	3.23458i	0.622644	−	0.109789i
$869$	−4.66385	−	3.91344i	−0.158210	−	0.132754i
$870$	8.42995	−	20.7580i	0.285802	−	0.703763i
$871$	−9.94396	+	56.3950i	−0.336938	+	1.91087i
$872$	−1.96052	−	5.38648i	−0.0663915	−	0.182409i
$873$	22.7255	+	15.4470i	0.769143	+	0.522801i
$874$	10.7089	−	4.15670i	0.362233	−	0.140602i
$875$		−	20.5252i		−	0.693880i
$876$	−3.06868	−	2.77300i	−0.103681	−	0.0936909i
$877$	3.93346	+	0.693575i	0.132823	+	0.0234204i	0.239665	−	0.970856i	$-0.422963\pi$
$877$	3.93346	+	0.693575i	0.132823	+	0.0234204i	−0.106841	+	0.994276i	$0.534074\pi$
$878$	−14.2939	−	17.0348i	−0.482397	−	0.574898i
$879$	−4.74499	+	22.1290i	−0.160044	+	0.746392i
$880$	1.60742	+	9.11615i	0.0541862	+	0.307305i
$881$	27.5291	−	15.8939i	0.927479	−	0.535480i	0.0414655	−	0.999140i	$-0.486797\pi$
$881$	27.5291	−	15.8939i	0.927479	−	0.535480i	0.886013	+	0.463660i	$0.153464\pi$
$882$	5.71446	+	11.8234i	0.192416	+	0.398115i
$883$	14.7726	+	5.37678i	0.497136	+	0.180943i	0.578406	−	0.815749i	$-0.303675\pi$
$883$	14.7726	+	5.37678i	0.497136	+	0.180943i	−0.0812691	+	0.996692i	$0.525897\pi$
$884$	−20.3795	−	7.41754i	−0.685438	−	0.249479i
$885$	0.899427	−	24.5014i	0.0302339	−	0.823605i
$886$	−27.1331	+	15.6653i	−0.911555	+	0.526287i
$887$	7.99628	+	45.3492i	0.268489	+	1.52268i	0.758913	+	0.651192i	$0.225731\pi$
$887$	7.99628	+	45.3492i	0.268489	+	1.52268i	−0.490424	+	0.871484i	$0.663158\pi$
$888$	−8.76645	−	1.87974i	−0.294183	−	0.0630799i
$889$	11.9916	+	14.2910i	0.402185	+	0.479305i
$890$	−4.07992	−	0.719400i	−0.136759	−	0.0241144i
$891$	−18.1593	+	16.1172i	−0.608358	+	0.539948i
$892$		−	12.6670i		−	0.424124i
$893$	−0.290651	−	0.479659i	−0.00972628	−	0.0160512i
$894$	−36.8902	+	19.5304i	−1.23379	+	0.653195i
$895$	−16.8494	−	46.2934i	−0.563214	−	1.54742i
$896$	0.585720	−	3.32178i	0.0195675	−	0.110973i
$897$	−21.7047	−	8.81439i	−0.724699	−	0.294304i
$898$	9.42566	+	7.90907i	0.314538	+	0.263929i
$899$	−20.5023	+	3.61510i	−0.683789	+	0.120570i
$900$	−20.2656	−	1.48988i	−0.675521	−	0.0496626i
$901$	31.2123	+	18.0204i	1.03983	+	0.600347i
$902$	1.53954	−	4.22985i	0.0512610	−	0.140838i
$903$	−1.94709	−	14.0361i	−0.0647950	−	0.467093i
$904$	8.44537	−	14.6278i	0.280889	−	0.486514i
$905$	20.5230	+	35.5469i	0.682208	+	1.18162i
$906$	−15.6452	−	20.0988i	−0.519777	−	0.667739i
$907$	−0.695285	+	0.828609i	−0.0230866	+	0.0275135i	−0.777464	−	0.628927i	$-0.783494\pi$
$907$	−0.695285	+	0.828609i	−0.0230866	+	0.0275135i	0.754378	+	0.656441i	$0.227939\pi$
$908$	2.89529	−	2.42944i	0.0960836	−	0.0806237i
$909$	−11.8285	+	12.1616i	−0.392327	+	0.403373i
$910$	−55.8158	+	20.3153i	−1.85028	+	0.673445i
$911$	45.4512			1.50587			0.752933	−	0.658098i	$-0.228639\pi$
$911$	45.4512			1.50587			0.752933	+	0.658098i	$0.228639\pi$
$912$	−6.47903	−	3.87584i	−0.214542	−	0.128342i
$913$	19.5587			0.647300
$914$	−35.5406	+	12.9357i	−1.17558	+	0.427876i
$915$	8.42510	+	26.0882i	0.278525	+	0.862451i
$916$	11.7375	−	9.84891i	0.387817	−	0.325417i
$917$	31.9623	−	38.0912i	1.05549	−	1.25788i
$918$	−21.9123	+	1.41431i	−0.723213	+	0.0466791i
$919$	−10.4915	−	18.1717i	−0.346081	−	0.599430i	0.639468	−	0.768817i	$-0.279155\pi$
$919$	−10.4915	−	18.1717i	−0.346081	−	0.599430i	−0.985550	+	0.169387i	$0.945821\pi$
$920$	−4.52130	+	7.83112i	−0.149063	+	0.258184i
$921$	−12.3075	+	1.70729i	−0.405545	+	0.0562571i
$922$	13.2926	−	36.5210i	0.437767	−	1.20276i
$923$	57.5053	+	33.2007i	1.89281	+	1.09281i
$924$	13.3513	+	8.37601i	0.439225	+	0.275551i
$925$	34.5291	−	6.08841i	1.13531	−	0.200186i
$926$	18.8844	+	15.8459i	0.620581	+	0.520730i
$927$	11.5688	−	1.17417i	0.379971	−	0.0385647i
$928$	−0.654625	+	3.71256i	−0.0214891	+	0.121871i
$929$	−10.4843	−	28.8055i	−0.343980	−	0.945077i	−0.984227	−	0.176908i	$-0.943390\pi$
$929$	−10.4843	−	28.8055i	−0.343980	−	0.945077i	0.640247	−	0.768169i	$-0.278832\pi$
$930$	15.3563	+	29.0060i	0.503554	+	0.951143i
$931$	−6.90422	−	17.7873i	−0.226277	−	0.582956i
$932$			24.3097i			0.796292i
$933$	−13.3594	+	14.7839i	−0.437368	+	0.484005i
$934$	−3.61538	−	0.637489i	−0.118299	−	0.0208593i
$935$	−25.1441	−	29.9655i	−0.822299	−	0.979978i
$936$	4.19094	+	14.8151i	0.136985	+	0.484247i
$937$	−0.894500	−	5.07296i	−0.0292221	−	0.165726i	0.966704	−	0.255896i	$-0.0823703\pi$
$937$	−0.894500	−	5.07296i	−0.0292221	−	0.165726i	−0.995926	+	0.0901691i	$0.971259\pi$
$938$	32.5942	−	18.8182i	1.06424	−	0.614438i
$939$	−30.6952	−	1.12680i	−1.00170	−	0.0367717i
$940$	0.414864	+	0.150998i	0.0135314	+	0.00492502i
$941$	−23.0587	−	8.39267i	−0.751691	−	0.273593i	−0.0623740	−	0.998053i	$-0.519867\pi$
$941$	−23.0587	−	8.39267i	−0.751691	−	0.273593i	−0.689317	+	0.724460i	$0.742089\pi$
$942$	−26.5573	−	0.974900i	−0.865285	−	0.0317639i
$943$	3.80805	−	2.19858i	0.124007	−	0.0715956i
$944$	0.716376	+	4.06277i	0.0233161	+	0.132232i
$945$	−43.4833	+	41.5434i	−1.41451	+	1.35141i
$946$	−4.20611	−	5.01265i	−0.136752	−	0.162975i
$947$	23.9834	+	4.22892i	0.779357	+	0.137422i	0.549154	−	0.835721i	$-0.314950\pi$
$947$	23.9834	+	4.22892i	0.779357	+	0.137422i	0.230203	+	0.973143i	$0.426061\pi$
$948$	−2.62068	+	2.90013i	−0.0851158	+	0.0941918i
$949$		−	12.2551i		−	0.397818i
$950$	29.1783	+	4.50977i	0.946669	+	0.146316i
$951$	−27.6191	−	52.1686i	−0.895612	−	1.69168i
$952$	4.87506	+	13.3941i	0.158002	+	0.434106i
$953$	−0.495016	+	2.80737i	−0.0160351	+	0.0909398i	−0.991775	−	0.127993i	$-0.959146\pi$
$953$	−0.495016	+	2.80737i	−0.0160351	+	0.0909398i	0.975740	+	0.218933i	$0.0702576\pi$
$954$	−2.58358	−	25.4555i	−0.0836464	−	0.824153i
$955$	26.7190	+	22.4199i	0.864607	+	0.725492i
$956$	13.1557	−	2.31971i	0.425486	−	0.0750247i
$957$	−14.9220	−	9.36138i	−0.482358	−	0.302610i
$958$	22.4828	+	12.9805i	0.726387	+	0.419380i
$959$	23.0034	−	63.2014i	0.742819	−	2.04088i
$960$	5.88672	−	0.816605i	0.189993	−	0.0263558i
$961$	−0.251521	+	0.435647i	−0.00811358	+	0.0140531i
$962$	−13.2829	−	23.0067i	−0.428259	−	0.741767i
$963$	19.0958	+	8.58387i	0.615354	+	0.276611i
$964$	−14.1214	+	16.8292i	−0.454819	+	0.542032i
$965$	−32.9282	+	27.6301i	−1.06000	+	0.889444i
$966$	4.73162	+	14.6514i	0.152237	+	0.471402i
$967$	−24.1580	+	8.79281i	−0.776870	+	0.282758i	−0.699867	−	0.714273i	$-0.746757\pi$
$967$	−24.1580	+	8.79281i	−0.776870	+	0.282758i	−0.0770033	+	0.997031i	$0.524535\pi$
$968$	−3.72193			−0.119627
$969$	31.9002	+	0.494669i	1.02478	+	0.0158911i
$970$	31.4283			1.00910
$971$	−8.94724	+	3.25653i	−0.287131	+	0.104507i	−0.481570	−	0.876407i	$-0.659933\pi$
$971$	−8.94724	+	3.25653i	−0.287131	+	0.104507i	0.194440	+	0.980914i	$0.437711\pi$
$972$	9.91302	+	12.0305i	0.317960	+	0.385877i
$973$	4.18105	−	3.50832i	0.134038	−	0.112472i
$974$	6.37816	−	7.60120i	0.204369	−	0.243558i
$975$	−36.9843	−	47.5124i	−1.18444	−	1.52161i
$976$	−2.30645	−	3.99490i	−0.0738278	−	0.127874i
$977$	−11.2275	+	19.4466i	−0.359199	+	0.622151i	−0.987827	−	0.155555i	$-0.950283\pi$
$977$	−11.2275	+	19.4466i	−0.359199	+	0.622151i	0.628628	+	0.777706i	$0.283617\pi$
$978$	2.83797	+	20.4583i	0.0907482	+	0.654183i
$979$	−1.11406	+	3.06085i	−0.0356055	+	0.0978253i
$980$	13.0074	+	7.50982i	0.415506	+	0.239892i
$981$	1.26084	−	17.1502i	0.0402556	−	0.547565i
$982$	−14.8971	+	2.62676i	−0.475385	+	0.0838232i
$983$	−15.1924	−	12.7479i	−0.484561	−	0.406595i	0.367511	−	0.930019i	$-0.380210\pi$
$983$	−15.1924	−	12.7479i	−0.484561	−	0.406595i	−0.852072	+	0.523424i	$0.824654\pi$
$984$	−2.67758	−	1.08738i	−0.0853582	−	0.0346644i
$985$	−13.6941	+	77.6630i	−0.436330	+	2.47455i
$986$	−5.44857	−	14.9698i	−0.173518	−	0.476736i
$987$	0.664348	−	0.351719i	0.0211464	−	0.0111954i
$988$	−4.35047	−	21.9434i	−0.138407	−	0.698114i
$989$		−	6.39215i		−	0.203258i
$990$	−6.81447	+	26.9213i	−0.216578	+	0.855614i
$991$	11.0355	+	1.94586i	0.350556	+	0.0618124i	0.346154	−	0.938178i	$-0.387488\pi$
$991$	11.0355	+	1.94586i	0.350556	+	0.0618124i	0.00440221	+	0.999990i	$0.498599\pi$
$992$	−3.54973	−	4.23041i	−0.112704	−	0.134316i
$993$	−35.3878	−	7.58801i	−1.12300	−	0.240798i
$994$	−7.57822	−	42.9782i	−0.240367	−	1.36319i
$995$	−75.2987	+	43.4737i	−2.38713	+	1.37821i
$996$	0.460656	−	12.5488i	0.0145964	−	0.397623i
$997$	−6.92900	−	2.52195i	−0.219444	−	0.0798710i	0.229959	−	0.973200i	$-0.426141\pi$
$997$	−6.92900	−	2.52195i	−0.219444	−	0.0798710i	−0.449402	+	0.893329i	$0.648363\pi$
$998$	20.0116	+	7.28361i	0.633455	+	0.230559i
$999$	−21.6752	−	15.9261i	−0.685774	−	0.503880i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.2.l.a.71.1	yes	18
3.2	odd	2		114.2.l.b.71.1	yes	18
4.3	odd	2		912.2.cc.d.641.3		18
12.11	even	2		912.2.cc.c.641.3		18
19.15	odd	18		114.2.l.b.53.1	yes	18
57.53	even	18	inner	114.2.l.a.53.1	✓	18
76.15	even	18		912.2.cc.c.737.3		18
228.167	odd	18		912.2.cc.d.737.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.l.a.53.1	✓	18	57.53	even	18	inner
114.2.l.a.71.1	yes	18	1.1	even	1	trivial
114.2.l.b.53.1	yes	18	19.15	odd	18
114.2.l.b.71.1	yes	18	3.2	odd	2
912.2.cc.c.641.3		18	12.11	even	2
912.2.cc.c.737.3		18	76.15	even	18
912.2.cc.d.641.3		18	4.3	odd	2
912.2.cc.d.737.3		18	228.167	odd	18

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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.l (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(-1.64823 + 0.532290i) q^{3} +(0.766044 - 0.642788i) q^{4} +(2.20556 - 2.62849i) q^{5} +(-1.36678 + 1.06392i) q^{6} +(1.68651 + 2.92113i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.43333 - 1.75467i) q^{9} +(1.17355 - 3.22432i) q^{10} +(-2.33635 - 1.34889i) q^{11} +(-0.920469 + 1.46722i) q^{12} +(-5.05419 + 0.891189i) q^{13} +(2.58389 + 2.16814i) q^{14} +(-2.23616 + 5.50635i) q^{15} +(0.173648 - 0.984808i) q^{16} +(1.44531 + 3.97095i) q^{17} +(1.68645 - 2.48110i) q^{18} +(-2.73048 + 3.39772i) q^{19} -3.43124i q^{20} +(-4.33465 - 3.91698i) q^{21} +(-2.65680 - 0.468466i) q^{22} +(-1.69398 - 2.01881i) q^{23} +(-0.363139 + 1.69356i) q^{24} +(-1.17620 - 6.67054i) q^{25} +(-4.44458 + 2.56608i) q^{26} +(-3.07670 + 4.18735i) q^{27} +(3.16961 + 1.15364i) q^{28} +(-3.54249 - 1.28936i) q^{29} +(-0.218019 + 5.93909i) q^{30} +(4.78254 - 2.76120i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(4.56886 + 0.979673i) q^{33} +(2.71629 + 3.23715i) q^{34} +(11.3979 + 2.00975i) q^{35} +(0.736160 - 2.90828i) q^{36} +5.17636i q^{37} +(-1.40372 + 4.12669i) q^{38} +(7.85610 - 4.15918i) q^{39} +(-1.17355 - 3.22432i) q^{40} +(-0.289735 + 1.64317i) q^{41} +(-5.41293 - 2.19822i) q^{42} +(1.85806 + 1.55910i) q^{43} +(-2.65680 + 0.468466i) q^{44} +(0.754733 - 10.2660i) q^{45} +(-2.28230 - 1.31768i) q^{46} +(-0.0440069 + 0.120908i) q^{47} +(0.237991 + 1.71562i) q^{48} +(-2.18866 + 3.79087i) q^{49} +(-3.38672 - 5.86597i) q^{50} +(-4.49590 - 5.77572i) q^{51} +(-3.29889 + 3.93146i) q^{52} +(6.53342 - 5.48219i) q^{53} +(-1.45900 + 4.98712i) q^{54} +(-8.69853 + 3.16600i) q^{55} +3.37303 q^{56} +(2.69188 - 7.05363i) q^{57} -3.76983 q^{58} +(-3.87665 + 1.41099i) q^{59} +(1.82642 + 5.65549i) q^{60} +(3.53369 - 2.96512i) q^{61} +(3.54973 - 4.23041i) q^{62} +(9.22948 + 4.14880i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-8.80484 + 15.2504i) q^{65} +(4.62839 - 0.642049i) q^{66} +(3.81629 - 10.4852i) q^{67} +(3.65965 + 2.11290i) q^{68} +(3.86667 + 2.42578i) q^{69} +(11.3979 - 2.00975i) q^{70} +(-9.91131 - 8.31658i) q^{71} +(-0.302925 - 2.98467i) q^{72} +(-0.414656 + 2.35163i) q^{73} +(1.77042 + 4.86419i) q^{74} +(5.48930 + 10.3685i) q^{75} +(0.0923461 + 4.35792i) q^{76} -9.09972i q^{77} +(5.95979 - 6.59529i) q^{78} +(2.22246 + 0.391880i) q^{79} +(-2.20556 - 2.62849i) q^{80} +(2.84224 - 8.53942i) q^{81} +(0.289735 + 1.64317i) q^{82} +(-6.27861 + 3.62496i) q^{83} +(-5.83832 - 0.214320i) q^{84} +(13.6253 + 4.95920i) q^{85} +(2.27924 + 0.829577i) q^{86} +(6.52515 + 0.239533i) q^{87} +(-2.33635 + 1.34889i) q^{88} +(-0.209662 - 1.18905i) q^{89} +(-2.80197 - 9.90505i) q^{90} +(-11.1272 - 13.2609i) q^{91} +(-2.59533 - 0.457627i) q^{92} +(-6.41298 + 7.09680i) q^{93} +0.128667i q^{94} +(2.90863 + 14.6709i) q^{95} +(0.810416 + 1.53076i) q^{96} +(3.13271 + 8.60706i) q^{97} +(-0.760113 + 4.31081i) q^{98} +(-8.05200 + 0.817228i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{6} + 9 q^{8} - 12 q^{13} + 12 q^{14} - 24 q^{15} - 6 q^{17} - 6 q^{19} - 24 q^{22} - 18 q^{25} - 18 q^{26} - 3 q^{27} + 6 q^{28} + 6 q^{29} - 27 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} - 3 q^{38}+ \cdots - 30 q^{99}+O(q^{100}) \) 18 * q + 3 * q^6 + 9 * q^8 - 12 * q^13 + 12 * q^14 - 24 * q^15 - 6 * q^17 - 6 * q^19 - 24 * q^22 - 18 * q^25 - 18 * q^26 - 3 * q^27 + 6 * q^28 + 6 * q^29 - 27 * q^33 - 6 * q^34 + 24 * q^35 - 3 * q^36 - 3 * q^38 + 6 * q^39 - 3 * q^41 - 6 * q^43 - 24 * q^44 + 54 * q^45 + 18 * q^46 - 30 * q^47 + 6 * q^48 + 21 * q^49 - 3 * q^50 - 33 * q^51 - 6 * q^52 + 60 * q^53 + 30 * q^55 + 12 * q^57 + 12 * q^58 - 3 * q^59 + 18 * q^60 + 54 * q^61 - 6 * q^62 + 84 * q^63 - 9 * q^64 - 24 * q^65 + 30 * q^66 - 15 * q^67 + 27 * q^68 + 24 * q^69 + 24 * q^70 - 36 * q^71 - 42 * q^73 - 6 * q^74 - 18 * q^78 - 6 * q^79 + 3 * q^82 - 36 * q^83 - 24 * q^84 + 6 * q^86 - 54 * q^87 + 60 * q^89 - 12 * q^90 - 18 * q^91 - 84 * q^93 - 6 * q^95 + 9 * q^97 - 12 * q^98 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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