LMFDB - Embedded newform 114.2.l.b.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.b.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} +(-1.36678 - 1.06392i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-2.20556 + 2.62849i) q^{5} +(1.64823 + 0.532290i) q^{6} +(1.68651 + 2.92113i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.736160 + 2.90828i) q^{9} +(1.17355 - 3.22432i) q^{10} +(2.33635 + 1.34889i) q^{11} +(-1.73088 + 0.0635395i) q^{12} +(-5.05419 + 0.891189i) q^{13} +(-2.58389 - 2.16814i) q^{14} +(5.81100 - 1.24602i) 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} +(0.802750 - 5.78684i) q^{21} +(-2.65680 - 0.468466i) q^{22} +(1.69398 + 2.01881i) q^{23} +(1.60477 - 0.651705i) q^{24} +(-1.17620 - 6.67054i) q^{25} +(4.44458 - 2.56608i) q^{26} +(2.08800 - 4.75818i) q^{27} +(3.16961 + 1.15364i) q^{28} +(3.54249 + 1.28936i) q^{29} +(-5.03439 + 3.15836i) q^{30} +(4.78254 - 2.76120i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-1.75816 - 4.32933i) q^{33} +(2.71629 + 3.23715i) q^{34} +(-11.3979 - 2.00975i) q^{35} +(2.43333 + 1.75467i) 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} +(1.22488 + 5.71241i) q^{42} +(1.85806 + 1.55910i) q^{43} +(2.65680 - 0.468466i) q^{44} +(-9.26801 - 4.47940i) q^{45} +(-2.28230 - 1.31768i) q^{46} +(0.0440069 - 0.120908i) q^{47} +(-1.28509 + 1.16127i) q^{48} +(-2.18866 + 3.79087i) q^{49} +(3.38672 + 5.86597i) q^{50} +(-2.24935 + 6.96509i) q^{51} +(-3.29889 + 3.93146i) q^{52} +(-6.53342 + 5.48219i) q^{53} +(-0.334684 + 5.18536i) q^{54} +(-8.69853 + 3.16600i) q^{55} -3.37303 q^{56} +(7.34685 - 1.73892i) q^{57} -3.76983 q^{58} +(3.87665 - 1.41099i) q^{59} +(3.65056 - 4.68975i) q^{60} +(3.53369 - 2.96512i) q^{61} +(-3.54973 + 4.23041i) q^{62} +(-7.25390 + 7.05526i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(8.80484 - 15.2504i) q^{65} +(3.13285 + 3.46691i) q^{66} +(3.81629 - 10.4852i) q^{67} +(-3.65965 - 2.11290i) q^{68} +(-0.167450 - 4.56152i) q^{69} +(11.3979 - 2.00975i) q^{70} +(9.91131 + 8.31658i) q^{71} +(-2.88672 - 0.816605i) 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} +(-8.80484 - 1.22141i) q^{78} +(2.22246 + 0.391880i) q^{79} +(2.20556 + 2.62849i) q^{80} +(-7.91614 + 4.28191i) q^{81} +(0.289735 + 1.64317i) q^{82} +(6.27861 - 3.62496i) q^{83} +(-3.10477 - 4.94898i) q^{84} +(13.6253 + 4.95920i) q^{85} +(-2.27924 - 0.829577i) q^{86} +(-3.47002 - 5.53118i) q^{87} +(-2.33635 + 1.34889i) q^{88} +(0.209662 + 1.18905i) q^{89} +(10.2411 + 1.03941i) q^{90} +(-11.1272 - 13.2609i) q^{91} +(2.59533 + 0.457627i) q^{92} +(-9.47436 - 1.31428i) 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} +(-2.20303 + 7.78777i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{3} - 9 q^{8} - 3 q^{9} - 12 q^{13} - 12 q^{14} + 18 q^{15} + 6 q^{17} - 6 q^{19} - 24 q^{22} + 3 q^{24} - 18 q^{25} + 18 q^{26} - 6 q^{27} + 6 q^{28} - 6 q^{29} - 24 q^{33} - 6 q^{34} - 24 q^{35}+ \cdots - 102 q^{99}+O(q^{100}) $ 18 * q + 3 * q^3 - 9 * q^8 - 3 * q^9 - 12 * q^13 - 12 * q^14 + 18 * q^15 + 6 * q^17 - 6 * q^19 - 24 * q^22 + 3 * q^24 - 18 * q^25 + 18 * q^26 - 6 * q^27 + 6 * q^28 - 6 * q^29 - 24 * q^33 - 6 * q^34 - 24 * q^35 + 3 * q^38 + 6 * q^39 + 3 * q^41 - 6 * q^43 + 24 * q^44 - 54 * q^45 + 18 * q^46 + 30 * q^47 + 21 * q^49 + 3 * q^50 + 42 * q^51 - 6 * q^52 - 60 * q^53 + 54 * q^54 + 30 * q^55 + 12 * q^57 + 12 * q^58 + 3 * q^59 + 24 * q^60 + 54 * q^61 + 6 * q^62 - 18 * q^63 - 9 * q^64 + 24 * q^65 - 27 * q^66 - 15 * q^67 - 27 * q^68 + 30 * q^69 + 24 * q^70 + 36 * q^71 + 6 * q^72 - 42 * q^73 + 6 * q^74 - 24 * q^78 - 6 * q^79 - 3 * q^81 + 3 * q^82 + 36 * q^83 - 30 * q^84 - 6 * q^86 - 60 * q^89 - 18 * q^91 - 66 * q^93 + 6 * q^95 + 9 * q^97 + 12 * q^98 - 102 * 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
$3$	−1.36678	−	1.06392i	−0.789109	−	0.614253i
$3$	−1.36678	−	1.06392i	−0.789109	−	0.614253i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−2.20556	+	2.62849i	−0.986357	+	1.17549i	−0.00187711	+	0.999998i	$0.500598\pi$
$5$	−2.20556	+	2.62849i	−0.986357	+	1.17549i	−0.984480	+	0.175496i	$0.943847\pi$
$6$	1.64823	+	0.532290i	0.672888	+	0.217306i
$7$	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
$9$	0.736160	+	2.90828i	0.245387	+	0.969425i
$10$	1.17355	−	3.22432i	0.371111	−	1.01962i
$11$	2.33635	+	1.34889i	0.704437	+	0.406707i	0.808998	−	0.587811i	$-0.200010\pi$
$11$	2.33635	+	1.34889i	0.704437	+	0.406707i	−0.104561	+	0.994519i	$0.533344\pi$
$12$	−1.73088	+	0.0635395i	−0.499663	+	0.0183423i
$13$	−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
$15$	5.81100	−	1.24602i	1.50039	−	0.321721i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−1.44531	−	3.97095i	−0.350538	−	0.963096i	−0.982198	−	0.187850i	$-0.939848\pi$
$17$	−1.44531	−	3.97095i	−0.350538	−	0.963096i	0.631659	−	0.775246i	$-0.282374\pi$
$18$	−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
$21$	0.802750	−	5.78684i	0.175174	−	1.26279i
$22$	−2.65680	−	0.468466i	−0.566433	−	0.0998773i
$23$	1.69398	+	2.01881i	0.353220	+	0.420951i	0.913172	−	0.407574i	$-0.133625\pi$
$23$	1.69398	+	2.01881i	0.353220	+	0.420951i	−0.559952	+	0.828525i	$0.689181\pi$
$24$	1.60477	−	0.651705i	0.327572	−	0.133029i
$25$	−1.17620	−	6.67054i	−0.235239	−	1.33411i
$26$	4.44458	−	2.56608i	0.871653	−	0.503249i
$27$	2.08800	−	4.75818i	0.401836	−	0.915712i
$28$	3.16961	+	1.15364i	0.599000	+	0.218018i
$29$	3.54249	+	1.28936i	0.657823	+	0.239428i	0.649296	−	0.760536i	$-0.275064\pi$
$29$	3.54249	+	1.28936i	0.657823	+	0.239428i	0.00852691	+	0.999964i	$0.497286\pi$
$30$	−5.03439	+	3.15836i	−0.919150	+	0.576634i
$31$	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
$33$	−1.75816	−	4.32933i	−0.306057	−	0.753639i
$34$	2.71629	+	3.23715i	0.465840	+	0.555166i
$35$	−11.3979	−	2.00975i	−1.92659	−	0.339710i
$36$	2.43333	+	1.75467i	0.405556	+	0.292446i
$37$			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	−0.953789	−	0.300478i	$-0.902854\pi$
$41$	0.289735	−	1.64317i	0.0452490	−	0.256620i	0.999038	+	0.0438581i	$0.0139649\pi$
$42$	1.22488	+	5.71241i	0.189003	+	0.881444i
$43$	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
$45$	−9.26801	−	4.47940i	−1.38159	−	0.667749i
$46$	−2.28230	−	1.31768i	−0.336506	−	0.194282i
$47$	0.0440069	−	0.120908i	0.00641906	−	0.0176362i	−0.936442	−	0.350823i	$-0.885902\pi$
$47$	0.0440069	−	0.120908i	0.00641906	−	0.0176362i	0.942861	+	0.333187i	$0.108124\pi$
$48$	−1.28509	+	1.16127i	−0.185487	+	0.167614i
$49$	−2.18866	+	3.79087i	−0.312665	+	0.541552i
$50$	3.38672	+	5.86597i	0.478955	+	0.829574i
$51$	−2.24935	+	6.96509i	−0.314972	+	0.975307i
$52$	−3.29889	+	3.93146i	−0.457473	+	0.545195i
$53$	−6.53342	+	5.48219i	−0.897434	+	0.753036i	−0.969687	−	0.244350i	$-0.921425\pi$
$53$	−6.53342	+	5.48219i	−0.897434	+	0.753036i	0.0722533	+	0.997386i	$0.476981\pi$
$54$	−0.334684	+	5.18536i	−0.0455448	+	0.705638i
$55$	−8.69853	+	3.16600i	−1.17291	+	0.426904i
$56$	−3.37303			−0.450740
$57$	7.34685	−	1.73892i	0.973113	−	0.230326i
$58$	−3.76983			−0.495004
$59$	3.87665	−	1.41099i	0.504697	−	0.183695i	−0.0771085	−	0.997023i	$-0.524569\pi$
$59$	3.87665	−	1.41099i	0.504697	−	0.183695i	0.581805	+	0.813328i	$0.302347\pi$
$60$	3.65056	−	4.68975i	0.471285	−	0.605444i
$61$	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
$63$	−7.25390	+	7.05526i	−0.913906	+	0.888880i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	8.80484	−	15.2504i	1.09211	−	1.89158i
$66$	3.13285	+	3.46691i	0.385627	+	0.426747i
$67$	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
$69$	−0.167450	−	4.56152i	−0.0201586	−	0.549143i
$70$	11.3979	−	2.00975i	1.36230	−	0.240211i
$71$	9.91131	+	8.31658i	1.17626	+	0.986996i	0.999996	+	0.00265261i	$0.000844352\pi$
$71$	9.91131	+	8.31658i	1.17626	+	0.986996i	0.176260	+	0.984344i	$0.443600\pi$
$72$	−2.88672	−	0.816605i	−0.340203	−	0.0962378i
$73$	−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
$78$	−8.80484	−	1.22141i	−0.996952	−	0.138297i
$79$	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
$81$	−7.91614	+	4.28191i	−0.879571	+	0.475768i
$82$	0.289735	+	1.64317i	0.0319959	+	0.181458i
$83$	6.27861	−	3.62496i	0.689167	−	0.397891i	−0.114133	−	0.993465i	$-0.536409\pi$
$83$	6.27861	−	3.62496i	0.689167	−	0.397891i	0.803300	+	0.595575i	$0.203076\pi$
$84$	−3.10477	−	4.94898i	−0.338758	−	0.539977i
$85$	13.6253	+	4.95920i	1.47787	+	0.537901i
$86$	−2.27924	−	0.829577i	−0.245777	−	0.0894556i
$87$	−3.47002	−	5.53118i	−0.372025	−	0.593005i
$88$	−2.33635	+	1.34889i	−0.249056	+	0.143793i
$89$	0.209662	+	1.18905i	0.0222241	+	0.126039i	0.993901	−	0.110273i	$-0.0351724\pi$
$89$	0.209662	+	1.18905i	0.0222241	+	0.126039i	−0.971677	+	0.236312i	$0.924061\pi$
$90$	10.2411	+	1.03941i	1.07951	+	0.109563i
$91$	−11.1272	−	13.2609i	−1.16645	−	1.39012i
$92$	2.59533	+	0.457627i	0.270582	+	0.0477109i
$93$	−9.47436	−	1.31428i	−0.982446	−	0.136285i
$94$			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
$99$	−2.20303	+	7.78777i	−0.221413	+	0.782700i
$100$	−5.18876	−	4.35388i	−0.518876	−	0.435388i
$101$	5.56915	−	0.981991i	0.554151	−	0.0977117i	0.110442	−	0.993883i	$-0.464773\pi$
$101$	5.56915	−	0.981991i	0.554151	−	0.0977117i	0.443709	+	0.896171i	$0.353662\pi$
$102$	−0.268505	−	7.31436i	−0.0265859	−	0.724230i
$103$	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
$105$	13.4401	+	14.8733i	1.31162	+	1.45148i
$106$	4.26438	−	7.38613i	0.414194	−	0.717404i
$107$	−3.48940	−	6.04382i	−0.337333	−	0.584278i	0.646597	−	0.762832i	$-0.276191\pi$
$107$	−3.48940	−	6.04382i	−0.337333	−	0.584278i	−0.983930	+	0.178554i	$0.942858\pi$
$108$	−1.45900	−	4.98712i	−0.140392	−	0.479885i
$109$	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
$111$	5.50722	−	7.07493i	0.522722	−	0.671523i
$112$	3.16961	−	1.15364i	0.299500	−	0.109009i
$113$	−16.8907			−1.58895			−0.794474	−	0.607298i	$-0.792253\pi$
$113$	−16.8907			−1.58895			−0.794474	+	0.607298i	$0.792253\pi$
$114$	−6.30903	+	4.14682i	−0.590895	+	0.388386i
$115$	−9.04260			−0.843227
$116$	3.54249	−	1.28936i	0.328912	−	0.119714i
$117$	−6.31251	−	14.0429i	−0.583592	−	1.29827i
$118$	−3.16027	+	2.65178i	−0.290927	+	0.244117i
$119$	9.16212	−	10.9190i	0.839890	−	1.00094i
$120$	−1.82642	+	5.65549i	−0.166728	+	0.516273i
$121$	−1.86097	−	3.22329i	−0.169179	−	0.293026i
$122$	−2.30645	+	3.99490i	−0.208817	+	0.361681i
$123$	−2.14420	+	1.93759i	−0.193336	+	0.174707i
$124$	1.88877	−	5.18936i	0.169617	−	0.466019i
$125$	5.26986	+	3.04256i	0.471351	+	0.272134i
$126$	4.40340	−	9.11076i	0.392286	−	0.811651i
$127$	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
$129$	−0.880802	−	4.10776i	−0.0775503	−	0.361668i
$130$	−3.05789	+	17.3422i	−0.268195	+	1.52101i
$131$	5.04199	+	13.8528i	0.440521	+	1.21032i	0.939150	+	0.343506i	$0.111615\pi$
$131$	5.04199	+	13.8528i	0.440521	+	1.21032i	−0.498629	+	0.866815i	$0.666163\pi$
$132$	−4.12967	−	2.18633i	−0.359442	−	0.190296i
$133$	−14.5302	−	2.24577i	−1.25992	−	0.194733i
$134$			11.1581i			0.963911i
$135$	7.90159	+	15.9827i	0.680061	+	1.37557i
$136$	4.16160	+	0.733802i	0.356854	+	0.0629230i
$137$	12.8171	+	15.2748i	1.09503	+	1.30501i	0.948840	+	0.315756i	$0.102258\pi$
$137$	12.8171	+	15.2748i	1.09503	+	1.30501i	0.146195	+	0.989256i	$0.453297\pi$
$138$	1.71748	+	4.22916i	0.146202	+	0.360010i
$139$	−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
$141$	−0.188784	+	0.118434i	−0.0158984	+	0.00997398i
$142$	−12.1580	−	4.42516i	−1.02028	−	0.371351i
$143$	−13.0105	−	4.73543i	−1.08799	−	0.395997i
$144$	2.99193	−	0.219959i	0.249327	−	0.0183299i
$145$	−11.2022	+	6.46761i	−0.930295	+	0.537106i
$146$	−0.414656	−	2.35163i	−0.0343172	−	0.194622i
$147$	7.02457	−	2.85272i	0.579377	−	0.235288i
$148$	3.32730	+	3.96532i	0.273502	+	0.325948i
$149$	−23.7332	−	4.18480i	−1.94430	−	0.342832i	−0.999902	−	0.0140170i	$-0.995538\pi$
$149$	−23.7332	−	4.18480i	−1.94430	−	0.342832i	−0.944394	−	0.328815i	$-0.893351\pi$
$150$	1.61202	−	11.6207i	0.131621	−	0.948824i
$151$			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
$156$	8.69159	−	1.86369i	0.695884	−	0.149214i
$157$	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
$159$	14.7623	−	0.541913i	1.17073	−	0.0429765i
$160$	−2.97155	−	1.71562i	−0.234921	−	0.135632i
$161$	−3.04028	+	8.35309i	−0.239607	+	0.658316i
$162$	5.97424	−	6.73116i	0.469380	−	0.528850i
$163$	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
$165$	15.2573	+	4.92729i	1.18778	+	0.383589i
$166$	−4.66016	+	5.55376i	−0.361698	+	0.431055i
$167$	−1.37759	+	1.15593i	−0.106601	+	0.0894489i	−0.694530	−	0.719463i	$-0.744388\pi$
$167$	−1.37759	+	1.15593i	−0.106601	+	0.0894489i	0.587929	+	0.808912i	$0.299943\pi$
$168$	4.61018	+	3.58862i	0.355683	+	0.276868i
$169$	12.5346	−	4.56221i	0.964198	−	0.350939i
$170$	−14.4997			−1.11208
$171$	−11.8916	−	5.43971i	−0.909371	−	0.415985i
$172$	2.42552			0.184944
$173$	6.36766	−	2.31764i	0.484124	−	0.176207i	−0.0884156	−	0.996084i	$-0.528180\pi$
$173$	6.36766	−	2.31764i	0.484124	−	0.176207i	0.572540	+	0.819877i	$0.305958\pi$
$174$	5.15252	+	4.01079i	0.390612	+	0.304057i
$175$	17.5018	−	14.6858i	1.32301	−	1.11014i
$176$	1.73411	−	2.06663i	0.130713	−	0.155778i
$177$	−6.79969	−	2.19593i	−0.511096	−	0.165056i
$178$	−0.603697	−	1.04563i	−0.0452490	−	0.0783735i
$179$	−7.17879	+	12.4340i	−0.536568	+	0.929363i	0.462518	+	0.886610i	$0.346946\pi$
$179$	−7.17879	+	12.4340i	−0.536568	+	0.929363i	−0.999086	+	0.0427531i	$0.986387\pi$
$180$	−9.97901	+	2.52594i	−0.743791	+	0.188273i
$181$	−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
$183$	−7.98441	+	0.293102i	−0.590225	+	0.0216667i
$184$	−2.59533	+	0.457627i	−0.191330	+	0.0337367i
$185$	−13.6060	−	11.4168i	−1.00033	−	0.839379i
$186$	9.35250	−	2.00540i	0.685759	−	0.147043i
$187$	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	$-0.880124\pi$
$191$		−	10.1652i		−	0.735526i	0.929919	−	0.367763i	$-0.119876\pi$
$192$	−0.237991	+	1.71562i	−0.0171755	+	0.123814i
$193$	−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
$195$	−28.2595	+	11.4763i	−2.02370	+	0.821836i
$196$	0.760113	+	4.31081i	0.0542938	+	0.307915i
$197$	19.9041	−	11.4916i	1.41811	−	0.818744i	0.421974	−	0.906608i	$-0.361338\pi$
$197$	19.9041	−	11.4916i	1.41811	−	0.818744i	0.996132	+	0.0878643i	$0.0280042\pi$
$198$	−0.593403	−	8.07159i	−0.0421713	−	0.573623i
$199$	−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
$201$	−16.3714	+	10.2707i	−1.15475	+	0.724437i
$202$	−4.89743	+	2.82753i	−0.344582	+	0.198944i
$203$	2.20807	+	12.5226i	0.154976	+	0.878913i
$204$	2.75397	+	6.78142i	0.192817	+	0.474794i
$205$	3.68002	+	4.38567i	0.257024	+	0.306309i
$206$	−3.81721	−	0.673077i	−0.265957	−	0.0468955i
$207$	−4.62422	+	6.41274i	−0.321405	+	0.445716i
$208$			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
$213$	−4.69840	−	21.9117i	−0.321929	−	1.50137i
$214$	5.34607	+	4.48588i	0.365450	+	0.306649i
$215$	−8.19612	+	1.44520i	−0.558971	+	0.0985616i
$216$	3.07670	+	4.18735i	0.209343	+	0.284913i
$217$	16.1316	+	9.31361i	1.09509	+	0.632249i
$218$	−1.96052	+	5.38648i	−0.132783	+	0.364818i
$219$	3.06868	−	2.77300i	0.207362	−	0.187382i
$220$	−4.62839	+	8.01660i	−0.312046	+	0.540479i
$221$	10.8437	+	18.7819i	0.729427	+	1.26341i
$222$	−2.75533	+	8.53184i	−0.184925	+	0.572620i
$223$	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
$225$	18.5339	−	8.33128i	1.23559	−	0.555419i
$226$	15.8721	−	5.77698i	1.05580	−	0.384279i
$227$	−3.77953			−0.250857			−0.125428	−	0.992103i	$-0.540030\pi$
$227$	−3.77953			−0.250857			−0.125428	+	0.992103i	$0.540030\pi$
$228$	4.51025	−	6.05456i	0.298699	−	0.400973i
$229$	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
$231$	9.68135	−	12.4373i	0.636986	−	0.818313i
$232$	−2.88786	+	2.42320i	−0.189597	+	0.159091i
$233$	15.6260	−	18.6223i	1.02369	−	1.21999i	0.0484572	−	0.998825i	$-0.484570\pi$
$233$	15.6260	−	18.6223i	1.02369	−	1.21999i	0.975236	−	0.221165i	$-0.0709860\pi$
$234$	10.7348	+	11.0370i	0.701755	+	0.721512i
$235$	0.220745	+	0.382341i	0.0143998	+	0.0249412i
$236$	2.06272	−	3.57274i	0.134272	−	0.232566i
$237$	−2.62068	−	2.90013i	−0.170232	−	0.188384i
$238$	−4.87506	+	13.3941i	−0.316003	+	0.868212i
$239$	−11.5689	−	6.67933i	−0.748332	−	0.432050i	0.0767587	−	0.997050i	$-0.475543\pi$
$239$	−11.5689	−	6.67933i	−0.748332	−	0.432050i	−0.825091	+	0.565000i	$0.808876\pi$
$240$	−0.218019	−	5.93909i	−0.0140731	−	0.383367i
$241$	−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
$243$	15.3752	+	2.56970i	0.986319	+	0.164846i
$244$	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
$249$	−12.4381	−	1.72541i	−0.788234	−	0.109344i
$250$	−5.99267	−	1.05667i	−0.379009	−	0.0668296i
$251$	−4.35873	−	5.19453i	−0.275121	−	0.327876i	0.610737	−	0.791834i	$-0.290873\pi$
$251$	−4.35873	−	5.19453i	−0.275121	−	0.327876i	−0.885857	+	0.463958i	$0.846429\pi$
$252$	−1.02177	+	10.0674i	−0.0643658	+	0.634184i
$253$	1.23458	+	7.00166i	0.0776175	+	0.440191i
$254$	−4.78983	+	2.76541i	−0.300540	+	0.173517i
$255$	−13.3466	−	21.2743i	−0.835794	−	1.33225i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	16.7251	+	6.08743i	1.04328	+	0.379724i	0.806123	−	0.591747i	$-0.201562\pi$
$257$	16.7251	+	6.08743i	1.04328	+	0.379724i	0.237158	+	0.971471i	$0.423784\pi$
$258$	2.23262	+	3.55878i	0.138997	+	0.221560i
$259$	−15.1208	+	8.73000i	−0.939561	+	0.542456i
$260$	−3.05789	−	17.3422i	−0.189642	−	1.07551i
$261$	−1.14198	+	11.2517i	−0.0706866	+	0.696463i
$262$	−9.47585	−	11.2929i	−0.585420	−	0.697676i
$263$	3.78041	+	0.666587i	0.233110	+	0.0411035i	0.288983	−	0.957334i	$-0.406683\pi$
$263$	3.78041	+	0.666587i	0.233110	+	0.0411035i	−0.0558728	+	0.998438i	$0.517794\pi$
$264$	4.62839	+	0.642049i	0.284858	+	0.0395154i
$265$		−	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	−0.967657	−	0.252268i	$-0.918824\pi$
$269$	0.457985	−	2.59736i	0.0279239	−	0.158364i	0.995581	+	0.0939040i	$0.0299347\pi$
$270$	−12.8915	−	12.3164i	−0.784551	−	0.749549i
$271$	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
$273$	1.09993	+	29.9632i	0.0665705	+	1.81345i
$274$	−17.2684	−	9.96990i	−1.04322	−	0.602304i
$275$	6.24984	−	17.1713i	0.376880	−	1.03547i
$276$	−3.06036	−	3.38669i	−0.184212	−	0.203855i
$277$	−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
$279$	11.5511	+	11.8763i	0.691544	+	0.711014i
$280$	7.43942	−	8.86596i	0.444590	−	0.529842i
$281$	1.92247	−	1.61315i	0.114685	−	0.0962323i	−0.583642	−	0.812011i	$-0.698373\pi$
$281$	1.92247	−	1.61315i	0.114685	−	0.0962323i	0.698327	+	0.715779i	$0.253928\pi$
$282$	0.136892	−	0.175860i	0.00815177	−	0.0104723i
$283$	−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
$285$	−11.6332	+	23.1464i	−0.689090	+	1.37107i
$286$	13.8455			0.818700
$287$	5.28855	−	1.92487i	0.312173	−	0.113622i
$288$	−2.73626	+	1.22999i	−0.161236	+	0.0724780i
$289$	−0.656761	+	0.551088i	−0.0386330	+	0.0324169i
$290$	8.31460	−	9.90896i	0.488250	−	0.581874i
$291$	4.87548	−	15.0969i	0.285806	−	0.884995i
$292$	1.19395	+	2.06799i	0.0698709	+	0.121020i
$293$	−6.53329	+	11.3160i	−0.381679	+	0.661087i	−0.991302	−	0.131604i	$-0.957987\pi$
$293$	−6.53329	+	11.3160i	−0.381679	+	0.661087i	0.609624	+	0.792691i	$0.291321\pi$
$294$	−5.62525	+	5.08322i	−0.328071	+	0.296460i
$295$	−4.84144	+	13.3017i	−0.281879	+	0.774457i
$296$	−4.48286	−	2.58818i	−0.260561	−	0.150435i
$297$	11.2966	−	8.30030i	0.655495	−	0.481632i
$298$	23.7332	−	4.18480i	1.37482	−	0.242419i
$299$	−10.3608	−	8.69378i	−0.599183	−	0.502775i
$300$	2.45970	+	11.4712i	0.142011	+	0.662290i
$301$	−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
$306$	−7.41489	+	10.2828i	−0.423881	+	0.587827i
$307$	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
$309$	−2.52607	−	6.22023i	−0.143703	−	0.353857i
$310$	−3.29041	−	18.6609i	−0.186883	−	1.05987i
$311$	−9.96292	+	5.75210i	−0.564945	+	0.326171i	−0.755128	−	0.655577i	$-0.772425\pi$
$311$	−9.96292	+	5.75210i	−0.564945	+	0.326171i	0.190183	+	0.981749i	$0.439092\pi$
$312$	−7.53000	+	4.72399i	−0.426303	+	0.267443i
$313$	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
$315$	−2.54574	−	34.6276i	−0.143436	−	1.95104i
$316$	1.95440	−	1.12837i	0.109944	−	0.0634759i
$317$	−5.91797	−	33.5625i	−0.332386	−	1.88506i	−0.451653	−	0.892194i	$-0.649165\pi$
$317$	−5.91797	−	33.5625i	−0.332386	−	1.88506i	0.119267	−	0.992862i	$-0.461946\pi$
$318$	−13.6867	+	5.55824i	−0.767512	+	0.311691i
$319$	6.53729	+	7.79084i	0.366018	+	0.436203i
$320$	3.37912	+	0.595829i	0.188898	+	0.0333079i
$321$	−1.66089	+	11.9730i	−0.0927019	+	0.668267i
$322$		−	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
$327$	−9.70775	+	2.08158i	−0.536840	+	0.115111i
$328$	1.27816	+	1.07250i	0.0705745	+	0.0592190i
$329$	0.427405	−	0.0753631i	0.0235636	−	0.00415490i
$330$	−16.0224	+	0.588171i	−0.882005	+	0.0323777i
$331$	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
$333$	−15.0543	+	3.81063i	−0.824970	+	0.208821i
$334$	0.899158	−	1.55739i	0.0491997	−	0.0852164i
$335$	19.1430	+	33.1567i	1.04590	+	1.81155i
$336$	−5.55953	−	1.79543i	−0.303297	−	0.0979487i
$337$	−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
$339$	23.0859	+	17.9704i	1.25385	+	0.976016i
$340$	13.6253	−	4.95920i	0.738935	−	0.268950i
$341$	14.8983			0.806788
$342$	13.0349	+	1.04450i	0.704847	+	0.0564802i
$343$	8.84639			0.477660
$344$	−2.27924	+	0.829577i	−0.122889	+	0.0447278i
$345$	12.3592	+	9.62058i	0.665398	+	0.517955i
$346$	−5.19097	+	4.35574i	−0.279068	+	0.234166i
$347$	3.49226	−	4.16191i	0.187474	−	0.223423i	−0.664118	−	0.747628i	$-0.731193\pi$
$347$	3.49226	−	4.16191i	0.187474	−	0.223423i	0.851592	+	0.524204i	$0.175637\pi$
$348$	−6.21356	−	2.00665i	−0.333082	−	0.107567i
$349$	−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
$351$	−6.31270	+	25.9095i	−0.336947	+	1.38295i
$352$	−0.922698	+	2.53509i	−0.0491800	+	0.135121i
$353$	18.1153	+	10.4589i	0.964180	+	0.556670i	0.897457	−	0.441102i	$-0.145412\pi$
$353$	18.1153	+	10.4589i	0.964180	+	0.556670i	0.0667232	+	0.997772i	$0.478746\pi$
$354$	7.14067	−	0.262129i	0.379522	−	0.0139320i
$355$	−43.7200	+	7.70902i	−2.32042	+	0.409152i
$356$	0.924917	+	0.776097i	0.0490205	+	0.0411331i
$357$	−24.1395	+	5.17608i	−1.27760	+	0.273947i
$358$	2.49317	−	14.1395i	0.131768	−	0.747294i
$359$	8.05343	+	22.1266i	0.425044	+	1.16780i	0.948785	+	0.315921i	$0.102314\pi$
$359$	8.05343	+	22.1266i	0.425044	+	1.16780i	−0.523741	+	0.851877i	$0.675464\pi$
$360$	8.51328	−	5.78663i	0.448689	−	0.304982i
$361$	−4.08900	−	18.5548i	−0.215211	−	0.976568i
$362$		−	11.9624i		−	0.628731i
$363$	−0.885785	+	6.38543i	−0.0464917	+	0.335148i
$364$	−17.0479	−	3.00601i	−0.893553	−	0.157558i
$365$	−5.26668	−	6.27659i	−0.275671	−	0.328532i
$366$	7.40265	−	3.00626i	0.386943	−	0.157140i
$367$	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
$369$	4.99208	−	0.367005i	0.259877	−	0.0191055i
$370$	16.6902	+	6.07474i	0.867683	+	0.315811i
$371$	−27.0329	−	9.83916i	−1.40348	−	0.510824i
$372$	−8.10259	+	5.08320i	−0.420100	+	0.263552i
$373$	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
$375$	−3.96570	−	9.76519i	−0.204788	−	0.504272i
$376$	0.0827058	+	0.0985650i	0.00426523	+	0.00508310i
$377$	−19.0534	−	3.35964i	−0.981303	−	0.173030i
$378$	−15.7116	+	7.76753i	−0.808115	+	0.399519i
$379$		−	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	−0.970610	−	0.240660i	$-0.922636\pi$
$383$	0.465296	−	2.63882i	0.0237755	−	0.134838i	0.994385	+	0.105822i	$0.0337474\pi$
$384$	−0.363139	−	1.69356i	−0.0185314	−	0.0864239i
$385$	−23.9185	−	20.0700i	−1.21900	−	1.02286i
$386$	12.3371	−	2.17537i	0.627944	−	0.110723i
$387$	−3.16645	+	6.55149i	−0.160960	+	0.333031i
$388$	7.93231	+	4.57972i	0.402702	+	0.232500i
$389$	11.2472	−	30.9013i	0.570253	−	1.56676i	−0.233852	−	0.972272i	$-0.575133\pi$
$389$	11.2472	−	30.9013i	0.570253	−	1.56676i	0.804106	−	0.594486i	$-0.202645\pi$
$390$	22.6301	−	20.4495i	1.14592	−	1.03550i
$391$	5.56827	−	9.64452i	0.281599	−	0.487744i
$392$	−2.18866	−	3.79087i	−0.110544	−	0.191468i
$393$	7.84692	−	24.2979i	0.395825	−	1.22567i
$394$	−14.7733	+	17.6062i	−0.744270	+	0.886987i
$395$	−5.93183	+	4.97739i	−0.298463	+	0.250440i
$396$	3.31826	+	7.38185i	0.166749	+	0.370952i
$397$	−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
$399$	17.4702	+	18.5284i	0.874603	+	0.927578i
$400$	−6.77344			−0.338672
$401$	12.8782	−	4.68726i	0.643104	−	0.234071i	0.000179351	−	1.00000i	$-0.499943\pi$
$401$	12.8782	−	4.68726i	0.643104	−	0.234071i	0.642925	+	0.765929i	$0.277721\pi$
$402$	11.8713	−	15.2506i	0.592085	−	0.760631i
$403$	−21.7111	+	18.2178i	−1.08151	+	0.907492i
$404$	3.63500	−	4.33203i	0.180848	−	0.215526i
$405$	6.20459	−	30.2515i	0.308308	−	1.50321i
$406$	−6.35788	−	11.0122i	−0.315536	−	0.546525i
$407$	−6.98237	+	12.0938i	−0.346103	+	0.599468i
$408$	−4.90727	−	5.43054i	−0.242946	−	0.268852i
$409$	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
$411$	−1.26696	−	34.5135i	−0.0624947	−	1.70243i
$412$	3.81721	−	0.673077i	0.188060	−	0.0331601i
$413$	10.6597	+	8.94454i	0.524529	+	0.440132i
$414$	2.15206	−	7.60758i	0.105768	−	0.373892i
$415$	−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	$-0.747230\pi$
$419$		−	29.1990i		−	1.42646i	0.700928	−	0.713232i	$-0.252770\pi$
$420$	19.8561	+	2.75443i	0.968877	+	0.134402i
$421$	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
$423$	0.384029	+	0.0389766i	0.0186722	+	0.00189511i
$424$	−1.48101	−	8.39920i	−0.0719240	−	0.407901i
$425$	−24.7884	+	14.3116i	−1.20241	+	0.694214i
$426$	11.9093	+	18.9833i	0.577008	+	0.919746i
$427$	14.6211	+	5.32165i	0.707565	+	0.257533i
$428$	−6.55793	−	2.38689i	−0.316989	−	0.115375i
$429$	12.7443	+	20.3144i	0.615302	+	0.980787i
$430$	7.20755	−	4.16128i	0.347579	−	0.200675i
$431$	−4.16028	−	23.5941i	−0.200394	−	1.13649i	−0.904526	−	0.426419i	$-0.859775\pi$
$431$	−4.16028	−	23.5941i	−0.200394	−	1.13649i	0.704132	−	0.710069i	$-0.251336\pi$
$432$	−4.32331	−	2.88253i	−0.208006	−	0.138686i
$433$	−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
$435$	22.1920	+	3.07847i	1.06402	+	0.147601i
$436$		−	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
$441$	−12.6361	−	3.57454i	−0.601718	−	0.170216i
$442$	−16.6135	−	13.9404i	−0.790225	−	0.663078i
$443$	30.8547	−	5.44051i	1.46595	−	0.258486i	0.617001	−	0.786963i	$-0.288348\pi$
$443$	30.8547	−	5.44051i	1.46595	−	0.258486i	0.848948	+	0.528476i	$0.177236\pi$
$444$	−0.328903	−	8.95969i	−0.0156091	−	0.425208i
$445$	−3.58782	−	2.07143i	−0.170079	−	0.0981952i
$446$	−4.33238	+	11.9031i	−0.205144	+	0.563629i
$447$	27.9857	+	30.9698i	1.32368	+	1.46482i
$448$	1.68651	−	2.92113i	0.0796803	−	0.138010i
$449$	−6.15216	−	10.6559i	−0.290338	−	0.502881i	0.683551	−	0.729902i	$-0.260435\pi$
$449$	−6.15216	−	10.6559i	−0.290338	−	0.502881i	−0.973890	+	0.227022i	$0.927101\pi$
$450$	−14.5667	+	14.1678i	−0.686681	+	0.667877i
$451$	2.89339	−	3.44820i	0.136244	−	0.162370i
$452$	−12.9391	+	10.8572i	−0.608602	+	0.510678i
$453$	15.6452	−	20.0988i	0.735076	−	0.944326i
$454$	3.55160	−	1.29268i	0.166685	−	0.0606683i
$455$	59.3979			2.78462
$456$	−2.16747	+	7.23202i	−0.101501	+	0.338670i
$457$	−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
$459$	−21.9123	−	1.41431i	−1.02278	−	0.0660142i
$460$	−6.92703	+	5.81247i	−0.322975	+	0.271008i
$461$	−24.9818	+	29.7722i	−1.16352	+	1.38663i	−0.255970	+	0.966685i	$0.582395\pi$
$461$	−24.9818	+	29.7722i	−1.16352	+	1.38663i	−0.907550	+	0.419945i	$0.862050\pi$
$462$	−4.84369	+	14.9984i	−0.225349	+	0.697791i
$463$	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
$465$	24.3509	−	22.0045i	1.12924	−	1.02043i
$466$	−8.31442	+	22.8437i	−0.385158	+	1.05821i
$467$	3.17931	+	1.83558i	0.147121	+	0.0849404i	0.571754	−	0.820425i	$-0.306263\pi$
$467$	3.17931	+	1.83558i	0.147121	+	0.0849404i	−0.424632	+	0.905366i	$0.639597\pi$
$468$	−13.8623	−	6.69989i	−0.640784	−	0.309702i
$469$	37.0647	−	6.53551i	1.71149	−	0.301782i
$470$	−0.338201	−	0.283784i	−0.0156000	−	0.0130900i
$471$	−5.57172	−	25.9846i	−0.256731	−	1.19731i
$472$	−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
$477$	−20.7534	−	14.9652i	−0.950231	−	0.685210i
$478$	13.1557	+	2.31971i	0.601728	+	0.106101i
$479$	−16.6874	−	19.8872i	−0.762465	−	0.908670i	0.235536	−	0.971866i	$-0.424315\pi$
$479$	−16.6874	−	19.8872i	−0.762465	−	0.908670i	−0.998001	+	0.0631952i	$0.979871\pi$
$480$	2.23616	+	5.50635i	0.102066	+	0.251329i
$481$	−4.61312	−	26.1623i	−0.210340	−	1.19290i
$482$	19.0257	−	10.9845i	0.866596	−	0.500329i
$483$	13.0424	−	8.18221i	0.593449	−	0.372304i
$484$	−3.49747	−	1.27298i	−0.158976	−	0.0578625i
$485$	−29.5329	−	10.7491i	−1.34102	−	0.488092i
$486$	−15.3268	+	2.84390i	−0.695240	+	0.129002i
$487$	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
$489$	−19.1364	+	7.77138i	−0.865376	+	0.351434i
$490$	9.65444	+	11.5057i	0.436143	+	0.519775i
$491$	14.8971	+	2.62676i	0.672296	+	0.118544i	0.499367	−	0.866391i	$-0.333566\pi$
$491$	14.8971	+	2.62676i	0.672296	+	0.118544i	0.172929	+	0.984934i	$0.444677\pi$
$492$	−0.397092	+	2.86255i	−0.0179023	+	0.129054i
$493$		−	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
$498$	12.2781	−	2.63273i	0.550196	−	0.117975i
$499$	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
$501$	3.11268	−	0.114264i	0.139064	−	0.00510494i
$502$	5.87250	+	3.39049i	0.262103	+	0.151325i
$503$	−1.99181	+	5.47245i	−0.0888104	+	0.244004i	−0.976144	−	0.217123i	$-0.930333\pi$
$503$	−1.99181	+	5.47245i	−0.0888104	+	0.244004i	0.887334	+	0.461128i	$0.152555\pi$
$504$	−2.48309	−	9.80969i	−0.110605	−	0.436959i
$505$	−9.70195	+	16.8043i	−0.431731	+	0.747780i
$506$	−3.55484	−	6.15716i	−0.158032	−	0.273719i
$507$	−21.9858	−	7.10023i	−0.976423	−	0.315332i
$508$	3.55514	−	4.23685i	0.157734	−	0.187980i
$509$	−10.9586	+	9.19535i	−0.485731	+	0.407577i	−0.852493	−	0.522738i	$-0.824911\pi$
$509$	−10.9586	+	9.19535i	−0.485731	+	0.407577i	0.366763	+	0.930315i	$0.380466\pi$
$510$	19.8179	+	15.4265i	0.877552	+	0.683098i
$511$	−7.56874	+	2.75480i	−0.334821	+	0.121865i
$512$	1.00000			0.0441942
$513$	10.4657	+	20.0865i	0.462073	+	0.886842i
$514$	−17.7985			−0.785056
$515$	−12.4977	+	4.54881i	−0.550717	+	0.200444i
$516$	−3.31515	−	2.58055i	−0.145941	−	0.113603i
$517$	0.265908	−	0.223123i	0.0116946	−	0.00981294i
$518$	11.2231	−	13.3751i	0.493114	−	0.587670i
$519$	−11.1690	−	3.60697i	−0.490263	−	0.158328i
$520$	8.80484	+	15.2504i	0.386118	+	0.668776i
$521$	−5.93133	+	10.2734i	−0.259856	+	0.450084i	−0.966203	−	0.257781i	$-0.917009\pi$
$521$	−5.93133	+	10.2734i	−0.259856	+	0.450084i	0.706347	+	0.707866i	$0.250342\pi$
$522$	−2.77520	−	10.9637i	−0.121467	−	0.479869i
$523$	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
$525$	−39.5455	+	1.45169i	−1.72591	+	0.0633568i
$526$	−3.78041	+	0.666587i	−0.164834	+	0.0290646i
$527$	−17.8768	−	15.0004i	−0.778727	−	0.653430i
$528$	−4.56886	+	0.979673i	−0.198834	+	0.0426348i
$529$	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
$534$	−0.287349	+	2.07143i	−0.0124348	+	0.0896396i
$535$	23.5822	+	4.15817i	1.01955	+	0.179774i
$536$	7.17227	+	8.54758i	0.309795	+	0.369199i
$537$	23.0406	−	9.35691i	0.994275	−	0.403780i
$538$	0.457985	+	2.59736i	0.0197451	+	0.111980i
$539$	−10.2270	+	5.90454i	−0.440506	+	0.254326i
$540$	16.3265	+	7.16444i	0.702580	+	0.308308i
$541$	−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
$543$	17.5515	−	11.0110i	0.753207	−	0.472529i
$544$	3.65965	−	2.11290i	0.156906	−	0.0905897i
$545$	3.41540	+	19.3697i	0.146300	+	0.829706i
$546$	−11.2816	−	27.7800i	−0.482808	−	1.18887i
$547$	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
$549$	11.2248	+	8.09415i	0.479061	+	0.345450i
$550$			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
$555$	6.44985	+	30.0799i	0.273781	+	1.27682i
$556$	−1.23956	−	1.04011i	−0.0525689	−	0.0441105i
$557$	−22.6372	+	3.99155i	−0.959170	+	0.169128i	−0.631251	−	0.775578i	$-0.717458\pi$
$557$	−22.6372	+	3.99155i	−0.959170	+	0.169128i	−0.327919	+	0.944706i	$0.606347\pi$
$558$	−14.9164	−	7.20935i	−0.631460	−	0.305196i
$559$	−10.7804	−	6.22408i	−0.455963	−	0.263250i
$560$	−3.95843	+	10.8757i	−0.167274	+	0.459582i
$561$	−14.6504	+	13.2388i	−0.618542	+	0.558942i
$562$	−1.25481	+	2.17339i	−0.0529308	+	0.0916788i
$563$	6.45057	+	11.1727i	0.271859	+	0.470874i	0.969338	−	0.245732i	$-0.0790282\pi$
$563$	6.45057	+	11.1727i	0.271859	+	0.470874i	−0.697479	+	0.716605i	$0.745695\pi$
$564$	−0.0684884	+	0.212074i	−0.00288388	+	0.00892992i
$565$	37.2536	−	44.3971i	1.56727	−	1.86780i
$566$	20.1827	−	16.9353i	0.848344	−	0.711845i
$567$	−25.8587	−	15.9025i	−1.08596	−	0.667844i
$568$	−12.1580	+	4.42516i	−0.510139	+	0.185676i
$569$	−37.8380			−1.58625			−0.793125	−	0.609059i	$-0.791547\pi$
$569$	−37.8380			−1.58625			−0.793125	+	0.609059i	$0.791547\pi$
$570$	3.01508	−	25.7293i	0.126288	−	1.07768i
$571$	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
$573$	−10.8149	+	13.8935i	−0.451799	+	0.580411i
$574$	−4.31126	+	3.61758i	−0.179949	+	0.150995i
$575$	11.4741	−	13.6743i	0.478503	−	0.570258i
$576$	2.15056	−	2.09167i	0.0896067	−	0.0871530i
$577$	−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
$579$	14.5477	+	16.0989i	0.604582	+	0.669049i
$580$	−4.42411	+	12.1551i	−0.183701	+	0.504715i
$581$	21.1779	+	12.2271i	0.878608	+	0.507265i
$582$	0.581986	+	15.8539i	0.0241241	+	0.657167i
$583$	−22.6593	+	3.99544i	−0.938451	+	0.165474i
$584$	−1.82924	−	1.53492i	−0.0756947	−	0.0635154i
$585$	50.8342	+	14.3802i	2.10174	+	0.594546i
$586$	2.26899	−	12.8681i	0.0937310	−	0.531575i
$587$	−10.0782	−	27.6896i	−0.415971	−	1.14287i	−0.953964	−	0.299922i	$-0.903039\pi$
$587$	−10.0782	−	27.6896i	−0.415971	−	1.14287i	0.537992	−	0.842950i	$-0.319183\pi$
$588$	3.54744	−	6.70062i	0.146294	−	0.276329i
$589$	−3.67683	+	23.7891i	−0.151501	+	0.980214i
$590$		−	14.1554i		−	0.582769i
$591$	−39.4306	−	5.46980i	−1.62196	−	0.224998i
$592$	5.09772	+	0.898866i	0.209515	+	0.0369432i
$593$	−8.16230	−	9.72745i	−0.335185	−	0.399458i	0.571956	−	0.820284i	$-0.306185\pi$
$593$	−8.16230	−	9.72745i	−0.335185	−	0.399458i	−0.907141	+	0.420826i	$0.861740\pi$
$594$	−7.77645	+	11.6634i	−0.319072	+	0.478555i
$595$	8.49279	+	48.1650i	0.348170	+	1.97457i
$596$	−20.8706	+	12.0496i	−0.854893	+	0.493573i
$597$	23.3246	+	37.1792i	0.954612	+	1.52164i
$598$	12.7095	+	4.62587i	0.519729	+	0.189166i
$599$	−16.8817	−	6.14443i	−0.689767	−	0.251055i	−0.0267313	−	0.999643i	$-0.508510\pi$
$599$	−16.8817	−	6.14443i	−0.689767	−	0.251055i	−0.663035	+	0.748588i	$0.730732\pi$
$600$	−6.23474	−	9.93813i	−0.254532	−	0.405723i
$601$	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
$603$	33.3031	+	3.38006i	1.35621	+	0.137647i
$604$	9.45237	+	11.2649i	0.384611	+	0.458362i
$605$	12.5768	+	2.21764i	0.511321	+	0.0901597i
$606$	9.70195	+	1.34585i	0.394115	+	0.0546715i
$607$		−	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
$612$	3.45080	−	12.1987i	0.139491	−	0.493103i
$613$	−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
$615$	−0.363769	−	9.90947i	−0.0146686	−	0.399589i
$616$	−7.88059	−	4.54986i	−0.317518	−	0.183319i
$617$	7.64721	−	21.0105i	0.307865	−	0.845852i	−0.685207	−	0.728348i	$-0.740288\pi$
$617$	7.64721	−	21.0105i	0.307865	−	0.845852i	0.993072	−	0.117504i	$-0.0374893\pi$
$618$	4.50117	+	4.98114i	0.181064	+	0.200371i
$619$	−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
$621$	13.1429	−	3.84500i	0.527406	−	0.154295i
$622$	7.39475	−	8.81272i	0.296503	−	0.353358i
$623$	−3.11977	+	2.61780i	−0.124991	+	0.104880i
$624$	5.46019	−	7.01451i	0.218583	−	0.280805i
$625$	12.2044	−	4.44205i	0.488178	−	0.177682i
$626$	−17.7338			−0.708787
$627$	19.5105	+	5.84738i	0.779173	+	0.233522i
$628$	15.3432			0.612261
$629$	20.5551	−	7.48143i	0.819584	−	0.298304i
$630$	14.2355	+	31.6686i	0.567158	+	1.26171i
$631$	−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
$633$	−6.33844	+	19.6269i	−0.251930	+	0.780100i
$634$	17.0401	+	29.5143i	0.676749	+	1.17216i
$635$	−9.48879	+	16.4351i	−0.376551	+	0.652206i
$636$	10.9603	−	9.90417i	0.434602	−	0.392726i
$637$	7.68350	−	21.1102i	0.304431	−	0.836418i
$638$	−8.80767	−	5.08511i	−0.348699	−	0.201321i
$639$	−16.8906	+	34.9472i	−0.668182	+	1.38249i
$640$	−3.37912	+	0.595829i	−0.133571	+	0.0235522i
$641$	18.2950	+	15.3513i	0.722609	+	0.606341i	0.928106	−	0.372317i	$-0.121437\pi$
$641$	18.2950	+	15.3513i	0.722609	+	0.606341i	−0.205497	+	0.978658i	$0.565881\pi$
$642$	−2.53427	−	11.8190i	−0.100020	−	0.466458i
$643$	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	$0.159115\pi$
$647$			24.3840i			0.958633i	−0.877642	+	0.479317i	$0.840885\pi$
$648$	0.249825	−	8.99653i	0.00981406	−	0.353417i
$649$	10.9605	+	1.93263i	0.430237	+	0.0758624i
$650$	−22.3448	−	26.6295i	−0.876436	−	1.04450i
$651$	−12.1395	−	29.8924i	−0.475783	−	1.17157i
$652$	−2.07070	−	11.7435i	−0.0810949	−	0.459912i
$653$	20.0643	−	11.5841i	0.785178	−	0.453323i	−0.0530845	−	0.998590i	$-0.516905\pi$
$653$	20.0643	−	11.5841i	0.785178	−	0.453323i	0.838262	+	0.545268i	$0.183572\pi$
$654$	8.41036	−	5.27629i	0.328871	−	0.206319i
$655$	−47.5322	−	17.3003i	−1.85724	−	0.675979i
$656$	−1.56789	−	0.570666i	−0.0612159	−	0.0222808i
$657$	−7.14445	+	0.525242i	−0.278731	+	0.0204916i
$658$	−0.375854	+	0.216999i	−0.0146523	+	0.00845952i
$659$	3.15401	+	17.8873i	0.122863	+	0.696790i	0.982554	+	0.185976i	$0.0595448\pi$
$659$	3.15401	+	17.8873i	0.122863	+	0.696790i	−0.859691	+	0.510814i	$0.829344\pi$
$660$	14.8550	−	6.03269i	0.578229	−	0.234822i
$661$	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
$663$	5.16141	−	37.2074i	0.200453	−	1.44502i
$664$			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
$669$	−21.4523	+	4.59990i	−0.829395	+	0.177842i
$670$	−29.3288	−	24.6098i	−1.13307	−	0.950760i
$671$	12.2556	−	2.16099i	0.473122	−	0.0834242i
$672$	5.83832	−	0.214320i	0.225218	−	0.00826759i
$673$	−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
$675$	−34.1955	−	8.33153i	−1.31619	−	0.320681i
$676$	6.66951	−	11.5519i	0.256520	−	0.444305i
$677$	2.66151	+	4.60988i	0.102290	+	0.177172i	0.912628	−	0.408791i	$-0.134050\pi$
$677$	2.66151	+	4.60988i	0.102290	+	0.177172i	−0.810338	+	0.585963i	$0.800716\pi$
$678$	−27.8399	−	8.99077i	−1.06918	−	0.345289i
$679$	−19.8590	+	23.6670i	−0.762117	+	0.908255i
$680$	−11.1074	+	9.32025i	−0.425951	+	0.357415i
$681$	5.16578	+	4.02111i	0.197953	+	0.154089i
$682$	−13.9998	+	5.09551i	−0.536080	+	0.195117i
$683$	29.5958			1.13245			0.566226	−	0.824250i	$-0.308403\pi$
$683$	29.5958			1.13245			0.566226	+	0.824250i	$0.308403\pi$
$684$	−12.6061	+	3.47669i	−0.482005	+	0.132935i
$685$	−68.4183			−2.61413
$686$	−8.31289	+	3.02564i	−0.317388	+	0.115520i
$687$	−20.9420	−	16.3015i	−0.798987	−	0.621942i
$688$	1.85806	−	1.55910i	0.0708378	−	0.0594400i
$689$	28.1354	−	33.5305i	1.07187	−	1.27741i
$690$	−14.9043	−	4.81329i	−0.567397	−	0.183239i
$691$	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
$693$	−26.4645	+	6.69885i	−1.00530	+	0.254468i
$694$	−1.85819	+	5.10534i	−0.0705361	+	0.193796i
$695$	4.80833	+	2.77609i	0.182390	+	0.105303i
$696$	6.52515	−	0.239533i	0.247335	−	0.00907948i
$697$	−6.94369	+	1.22436i	−0.263011	+	0.0463760i
$698$	12.3738	+	10.3829i	0.468356	+	0.392997i
$699$	−41.1699	+	8.82782i	−1.55719	+	0.333899i
$700$	3.96734	−	22.4999i	0.149951	−	0.850417i
$701$	−9.40339	−	25.8356i	−0.355161	−	0.975798i	−0.980685	−	0.195593i	$-0.937337\pi$
$701$	−9.40339	−	25.8356i	−0.355161	−	0.975798i	0.625524	−	0.780205i	$-0.284885\pi$
$702$	−2.92958	−	26.5061i	−0.110570	−	1.00041i
$703$	−17.5878	−	14.1339i	−0.663337	−	0.533071i
$704$		−	2.69779i		−	0.101677i
$705$	0.105070	−	0.757429i	0.00395718	−	0.0285264i
$706$	−20.6000	−	3.63233i	−0.775290	−	0.136705i
$707$	12.2610	+	14.6120i	0.461121	+	0.549543i
$708$	−6.62038	+	2.68857i	−0.248809	+	0.101043i
$709$	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
$711$	0.496392	+	6.75202i	0.0186161	+	0.253220i
$712$	−1.13458	−	0.412953i	−0.0425201	−	0.0154761i
$713$	13.6759	+	4.97762i	0.512166	+	0.186413i
$714$	20.9134	−	13.1201i	0.782663	−	0.491008i
$715$	41.1425	−	23.7536i	1.53864	−	0.888335i
$716$	2.49317	+	14.1395i	0.0931741	+	0.528416i
$717$	8.70590	+	21.4375i	0.325128	+	0.800600i
$718$	−15.1355	−	18.0378i	−0.564852	−	0.673164i
$719$	26.6001	+	4.69031i	0.992015	+	0.174919i	0.646022	−	0.763318i	$-0.276431\pi$
$719$	26.6001	+	4.69031i	0.992015	+	0.174919i	0.345992	+	0.938237i	$0.387542\pi$
$720$	−6.02072	+	8.34937i	−0.224379	+	0.311163i
$721$			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
$726$	−1.35158	−	6.30329i	−0.0501618	−	0.233937i
$727$	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
$729$	−18.2805	−	19.8701i	−0.677056	−	0.735931i
$730$	7.09578	+	4.09675i	0.262627	+	0.151628i
$731$	3.50562	−	9.63162i	0.129660	−	0.356238i
$732$	−5.92801	+	5.35681i	−0.219106	+	0.197993i
$733$	−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
$735$	−7.99480	+	24.7558i	−0.294893	+	0.913133i
$736$	−1.69398	+	2.01881i	−0.0624410	+	0.0744143i
$737$	23.0596	−	19.3493i	0.849410	−	0.712740i
$738$	−4.56550	+	2.05226i	−0.168058	+	0.0755449i
$739$	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
$741$	−35.5826	+	15.3363i	−1.30716	+	0.563392i
$742$	28.7678			1.05610
$743$	−27.6540	+	10.0652i	−1.01453	+	0.369257i	−0.795169	−	0.606387i	$-0.792618\pi$
$743$	−27.6540	+	10.0652i	−1.01453	+	0.369257i	−0.219357	+	0.975645i	$0.570396\pi$
$744$	5.87538	−	7.54790i	0.215402	−	0.276719i
$745$	63.3446	−	53.1525i	2.32077	−	1.94736i
$746$	−9.10081	+	10.8459i	−0.333204	+	0.397097i
$747$	15.1644	+	15.5914i	0.554838	+	0.570459i
$748$	−5.70015	−	9.87295i	−0.208418	−	0.360991i
$749$	11.7698	−	20.3860i	0.430061	−	0.744887i
$750$	7.06643	+	7.81993i	0.258030	+	0.285544i
$751$	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
$753$	0.430860	+	11.7371i	0.0157014	+	0.427724i
$754$	19.0534	−	3.35964i	0.693886	−	0.122351i
$755$	−38.6526	−	32.4334i	−1.40671	−	1.18037i
$756$	12.1074	−	12.6728i	0.440341	−	0.460904i
$757$	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	$-0.924895\pi$
$761$		−	12.8974i		−	0.467530i	0.972293	−	0.233765i	$-0.0751047\pi$
$762$	9.48879	+	1.31628i	0.343743	+	0.0476839i
$763$	19.0410	+	3.35745i	0.689332	+	0.121548i
$764$	−6.53405	−	7.78698i	−0.236394	−	0.281723i
$765$	−4.39233	+	43.2769i	−0.158805	+	1.56468i
$766$	0.465296	+	2.63882i	0.0168118	+	0.0953446i
$767$	−18.3359	+	10.5862i	−0.662069	+	0.382246i
$768$	0.920469	+	1.46722i	0.0332146	+	0.0529438i
$769$	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
$771$	−16.3829	−	26.1143i	−0.590017	−	0.940482i
$772$	−10.8491	+	6.26373i	−0.390467	+	0.225436i
$773$	6.98308	+	39.6030i	0.251164	+	1.42442i	0.805730	+	0.592283i	$0.201773\pi$
$773$	6.98308	+	39.6030i	0.251164	+	1.42442i	−0.554566	+	0.832140i	$0.687116\pi$
$774$	0.734751	−	7.23937i	0.0264101	−	0.260214i
$775$	−24.0439	−	28.6544i	−0.863683	−	1.02930i
$776$	−9.02029	−	1.59052i	−0.323809	−	0.0570964i
$777$	29.9548	+	4.15532i	1.07462	+	0.149071i
$778$			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
$783$	13.5317	−	14.1636i	0.483584	−	0.506166i
$784$	3.35322	+	2.81368i	0.119758	+	0.100489i
$785$	−51.8465	+	9.14194i	−1.85048	+	0.326290i
$786$	0.936686	+	25.5164i	0.0334105	+	0.910139i
$787$	−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
$789$	−4.45778	−	4.93312i	−0.158701	−	0.175624i
$790$	3.87172	−	6.70602i	0.137750	−	0.238590i
$791$	−28.4865	−	49.3400i	−1.01286	−	1.75433i
$792$	−5.64289	−	5.80176i	−0.200511	−	0.206157i
$793$	−15.2175	+	18.1355i	−0.540388	+	0.644009i
$794$	1.79344	−	1.50487i	0.0636467	−	0.0534059i
$795$	−31.1348	+	39.9978i	−1.10424	+	1.41857i
$796$	−23.8117	+	8.66676i	−0.843984	+	0.307185i
$797$	−6.73284			−0.238489			−0.119245	−	0.992865i	$-0.538047\pi$
$797$	−6.73284			−0.238489			−0.119245	+	0.992865i	$0.538047\pi$
$798$	−22.7537	−	11.4358i	−0.805471	−	0.404823i
$799$	−0.543722			−0.0192355
$800$	6.36495	−	2.31665i	0.225035	−	0.0819061i
$801$	−3.30374	+	1.48508i	−0.116732	+	0.0524729i
$802$	−10.4984	+	8.80918i	−0.370710	+	0.311063i
$803$	−4.14089	+	4.93492i	−0.146129	+	0.174149i
$804$	−5.93933	+	18.3911i	−0.209464	+	0.648604i
$805$	−15.2505	−	26.4146i	−0.537508	−	0.930992i
$806$	14.1709	−	24.5448i	0.499149	−	0.864552i
$807$	−3.38934	+	3.06276i	−0.119311	+	0.107814i
$808$	−1.93414	+	5.31402i	−0.0680430	+	0.186947i
$809$	−7.36554	−	4.25250i	−0.258959	−	0.149510i	0.364901	−	0.931046i	$-0.381103\pi$
$809$	−7.36554	−	4.25250i	−0.258959	−	0.149510i	−0.623859	+	0.781537i	$0.714436\pi$
$810$	4.51621	+	30.5492i	0.158683	+	1.07339i
$811$	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
$813$	−5.08282	−	23.7045i	−0.178262	−	0.831353i
$814$	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
$819$	30.3750	−	42.1232i	1.06139	−	1.47190i
$820$	5.63811	+	0.994152i	0.196891	+	0.0347173i
$821$	−6.42410	−	7.65594i	−0.224203	−	0.267194i	0.642204	−	0.766534i	$-0.278020\pi$
$821$	−6.42410	−	7.65594i	−0.224203	−	0.267194i	−0.866406	+	0.499340i	$0.833576\pi$
$822$	12.9949	+	31.9988i	0.453248	+	1.11608i
$823$	−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
$825$	−26.8110	+	16.8200i	−0.933439	+	0.585598i
$826$	−13.0760	−	4.75929i	−0.454974	−	0.165597i
$827$	46.9782	+	17.0987i	1.63359	+	0.594579i	0.985902	−	0.167325i	$-0.0535131\pi$
$827$	46.9782	+	17.0987i	1.63359	+	0.594579i	0.647690	+	0.761904i	$0.275735\pi$
$828$	0.579673	+	7.88483i	0.0201450	+	0.274017i
$829$	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
$831$	0.534800	−	0.217185i	0.0185520	−	0.00753408i
$832$	3.29889	+	3.93146i	0.114368	+	0.136299i
$833$	18.2166	+	3.21208i	0.631168	+	0.111292i
$834$	0.385099	−	2.77609i	0.0133349	−	0.0961282i
$835$		−	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	$-0.857394\pi$
$839$	2.71691	−	15.4084i	0.0937982	−	0.531956i	0.995109	−	0.0987829i	$-0.0314949\pi$
$840$	−19.6007	+	4.20286i	−0.676287	+	0.145012i
$841$	−11.3285	−	9.50576i	−0.390639	−	0.327785i
$842$	−7.45681	+	1.31484i	−0.256979	+	0.0453123i
$843$	−4.34385	+	0.159459i	−0.149610	+	0.00549207i
$844$	−10.3125	−	5.95393i	−0.354971	−	0.204943i
$845$	−15.6541	+	43.0092i	−0.538516	+	1.47956i
$846$	−0.374200	+	0.0947198i	−0.0128653	+	0.00325653i
$847$	6.27709	−	10.8722i	0.215683	−	0.373574i
$848$	4.26438	+	7.38613i	0.146440	+	0.253641i
$849$	43.4255	+	14.0241i	1.49036	+	0.481305i
$850$	18.3986	−	21.9266i	0.631067	−	0.752077i
$851$	−10.4501	+	8.76867i	−0.358225	+	0.300586i
$852$	−17.6838	−	13.7653i	−0.605836	−	0.471591i
$853$	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
$855$	40.5258	−	19.2592i	1.38595	−	0.658651i
$856$	6.97880			0.238530
$857$	10.7658	−	3.91845i	0.367754	−	0.133852i	−0.151531	−	0.988452i	$-0.548420\pi$
$857$	10.7658	−	3.91845i	0.367754	−	0.133852i	0.519285	+	0.854601i	$0.326198\pi$
$858$	−18.9237	−	14.7304i	−0.646044	−	0.502889i
$859$	−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
$861$	−9.27617	−	2.99570i	−0.316131	−	0.102093i
$862$	11.9790	+	20.7483i	0.408008	+	0.706690i
$863$	−13.4511	+	23.2980i	−0.457882	+	0.793075i	−0.998849	−	0.0479693i	$-0.984725\pi$
$863$	−13.4511	+	23.2980i	−0.457882	+	0.793075i	0.540967	+	0.841044i	$0.318058\pi$
$864$	5.04847	+	1.23003i	0.171752	+	0.0418464i
$865$	−7.95239	+	21.8490i	−0.270389	+	0.742889i
$866$	13.3303	+	7.69622i	0.452980	+	0.261528i
$867$	1.48396	−	0.0544750i	0.0503979	−	0.00185007i
$868$	18.3442	−	3.23458i	0.622644	−	0.109789i
$869$	4.66385	+	3.91344i	0.158210	+	0.132754i
$870$	−21.9065	+	4.69729i	−0.742701	+	0.159253i
$871$	−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
$876$	0.568301	−	4.09675i	0.0192011	−	0.138416i
$877$	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
$879$	20.9688	−	8.51555i	0.707261	−	0.287223i
$880$	1.60742	+	9.11615i	0.0541862	+	0.307305i
$881$	−27.5291	+	15.8939i	−0.927479	+	0.535480i	−0.886013	−	0.463660i	$-0.846536\pi$
$881$	−27.5291	+	15.8939i	−0.927479	+	0.535480i	−0.0414655	+	0.999140i	$0.513203\pi$
$882$	13.0966	−	0.962829i	0.440985	−	0.0324202i
$883$	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
$885$	20.7691	−	13.0296i	0.698146	−	0.437986i
$886$	−27.1331	+	15.6653i	−0.911555	+	0.526287i
$887$	−7.99628	−	45.3492i	−0.268489	−	1.52268i	−0.758913	−	0.651192i	$-0.774269\pi$
$887$	−7.99628	−	45.3492i	−0.268489	−	1.52268i	0.490424	−	0.871484i	$-0.336842\pi$
$888$	3.37346	+	8.30686i	0.113206	+	0.278760i
$889$	11.9916	+	14.2910i	0.402185	+	0.479305i
$890$	4.07992	+	0.719400i	0.136759	+	0.0241144i
$891$	−24.2708	−	0.673976i	−0.813101	−	0.0225790i
$892$		−	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
$897$	4.91150	+	22.9056i	0.163990	+	0.764794i
$898$	9.42566	+	7.90907i	0.314538	+	0.263929i
$899$	20.5023	−	3.61510i	0.683789	−	0.120570i
$900$	8.84254	−	18.2955i	0.294751	−	0.609850i
$901$	31.2123	+	18.0204i	1.03983	+	0.600347i
$902$	−1.53954	+	4.22985i	−0.0512610	+	0.140838i
$903$	10.5138	−	9.50072i	0.349877	−	0.316164i
$904$	8.44537	−	14.6278i	0.280889	−	0.486514i
$905$	−20.5230	−	35.5469i	−0.682208	−	1.18162i
$906$	−7.82747	+	24.2377i	−0.260050	+	0.805244i
$907$	−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
$909$	6.95568	+	15.4737i	0.230705	+	0.513231i
$910$	−55.8158	+	20.3153i	−1.85028	+	0.673445i
$911$	−45.4512			−1.50587			−0.752933	−	0.658098i	$-0.771361\pi$
$911$	−45.4512			−1.50587			−0.752933	+	0.658098i	$0.771361\pi$
$912$	−0.436740	−	7.53719i	−0.0144619	−	0.249581i
$913$	19.5587			0.647300
$914$	35.5406	−	12.9357i	1.17558	−	0.427876i
$915$	16.8397	−	21.6334i	0.556704	−	0.715177i
$916$	11.7375	−	9.84891i	0.387817	−	0.325417i
$917$	−31.9623	+	38.0912i	−1.05549	+	1.25788i
$918$	21.0745	−	6.16543i	0.695563	−	0.203489i
$919$	−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
$921$	−8.33064	−	9.21894i	−0.274504	−	0.303774i
$922$	13.2926	−	36.5210i	0.437767	−	1.20276i
$923$	−57.5053	−	33.2007i	−1.89281	−	1.09281i
$924$	−0.578191	−	15.7506i	−0.0190211	−	0.518156i
$925$	34.5291	−	6.08841i	1.13531	−	0.200186i
$926$	−18.8844	−	15.8459i	−0.620581	−	0.520730i
$927$	−3.16524	+	11.1892i	−0.103960	+	0.367502i
$928$	−0.654625	+	3.71256i	−0.0214891	+	0.121871i
$929$	10.4843	+	28.8055i	0.343980	+	0.945077i	0.984227	+	0.176908i	$0.0566096\pi$
$929$	10.4843	+	28.8055i	0.343980	+	0.945077i	−0.640247	+	0.768169i	$0.721168\pi$
$930$	−15.3563	+	29.0060i	−0.503554	+	0.951143i
$931$	−6.90422	−	17.7873i	−0.226277	−	0.582956i
$932$		−	24.3097i		−	0.796292i
$933$	19.7368	+	2.73789i	0.646155	+	0.0896346i
$934$	−3.61538	−	0.637489i	−0.118299	−	0.0208593i
$935$	25.1441	+	29.9655i	0.822299	+	0.979978i
$936$	15.3178	+	1.55466i	0.500677	+	0.0508156i
$937$	−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
$939$	−16.3235	−	26.0195i	−0.532696	−	0.849113i
$940$	0.414864	+	0.150998i	0.0135314	+	0.00492502i
$941$	23.0587	+	8.39267i	0.751691	+	0.273593i	0.689317	−	0.724460i	$-0.257911\pi$
$941$	23.0587	+	8.39267i	0.751691	+	0.273593i	0.0623740	+	0.998053i	$0.480133\pi$
$942$	14.1230	+	22.5119i	0.460151	+	0.733477i
$943$	3.80805	−	2.19858i	0.124007	−	0.0715956i
$944$	−0.716376	−	4.06277i	−0.0233161	−	0.132232i
$945$	−33.3614	+	50.0367i	−1.08525	+	1.62769i
$946$	−4.20611	−	5.01265i	−0.136752	−	0.162975i
$947$	−23.9834	−	4.22892i	−0.779357	−	0.137422i	−0.230203	−	0.973143i	$-0.573939\pi$
$947$	−23.9834	−	4.22892i	−0.779357	−	0.137422i	−0.549154	+	0.835721i	$0.685050\pi$
$948$	−3.87172	−	0.537085i	−0.125748	−	0.0174437i
$949$		−	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	−0.975740	−	0.218933i	$-0.929742\pi$
$953$	0.495016	−	2.80737i	0.0160351	−	0.0909398i	0.991775	+	0.127993i	$0.0408535\pi$
$954$	24.6202	+	6.96464i	0.797108	+	0.225488i
$955$	26.7190	+	22.4199i	0.864607	+	0.725492i
$956$	−13.1557	+	2.31971i	−0.425486	+	0.0750247i
$957$	−0.646210	−	17.6035i	−0.0208890	−	0.569040i
$958$	22.4828	+	12.9805i	0.726387	+	0.419380i
$959$	−23.0034	+	63.2014i	−0.742819	+	2.04088i
$960$	−3.98459	−	4.40947i	−0.128602	−	0.142315i
$961$	−0.251521	+	0.435647i	−0.00811358	+	0.0140531i
$962$	13.2829	+	23.0067i	0.428259	+	0.741767i
$963$	15.0083	−	14.5973i	0.483637	−	0.470393i
$964$	−14.1214	+	16.8292i	−0.454819	+	0.542032i
$965$	32.9282	−	27.6301i	1.06000	−	0.889444i
$966$	−9.45735	+	12.1495i	−0.304285	+	0.390904i
$967$	−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
$969$	−17.5236	−	26.6607i	−0.562940	−	0.856464i
$970$	31.4283			1.00910
$971$	8.94724	−	3.25653i	0.287131	−	0.104507i	−0.194440	−	0.980914i	$-0.562289\pi$
$971$	8.94724	−	3.25653i	0.287131	−	0.104507i	0.481570	+	0.876407i	$0.340067\pi$
$972$	13.4299	−	7.91448i	0.430763	−	0.253857i
$973$	4.18105	−	3.50832i	0.134038	−	0.112472i
$974$	−6.37816	+	7.60120i	−0.204369	+	0.243558i
$975$	18.5037	−	57.2964i	0.592591	−	1.83495i
$976$	−2.30645	−	3.99490i	−0.0738278	−	0.127874i
$977$	11.2275	−	19.4466i	0.359199	−	0.622151i	−0.628628	−	0.777706i	$-0.716383\pi$
$977$	11.2275	−	19.4466i	0.359199	−	0.622151i	0.987827	+	0.155555i	$0.0497166\pi$
$978$	15.3243	−	13.8477i	0.490018	−	0.442802i
$979$	−1.11406	+	3.06085i	−0.0356055	+	0.0978253i
$980$	−13.0074	−	7.50982i	−0.415506	−	0.239892i
$981$	15.4830	+	7.48319i	0.494333	+	0.238920i
$982$	−14.8971	+	2.62676i	−0.475385	+	0.0838232i
$983$	15.1924	+	12.7479i	0.484561	+	0.406595i	0.852072	−	0.523424i	$-0.175346\pi$
$983$	15.1924	+	12.7479i	0.484561	+	0.406595i	−0.367511	+	0.930019i	$0.619790\pi$
$984$	−0.605904	−	2.82573i	−0.0193155	−	0.0900809i
$985$	−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
$990$	22.5248	+	16.2426i	0.715886	+	0.516225i
$991$	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
$993$	−13.6178	−	33.5326i	−0.432147	−	1.06412i
$994$	−7.57822	−	42.9782i	−0.240367	−	1.36319i
$995$	75.2987	−	43.4737i	2.38713	−	1.37821i
$996$	−10.6372	+	6.67332i	−0.337053	+	0.211452i
$997$	−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
$999$	24.6300	+	10.8082i	0.779260	+	0.341957i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.l.a.53.1	✓	18	19.15	odd	18
114.2.l.a.71.1	yes	18	3.2	odd	2
114.2.l.b.53.1	yes	18	57.53	even	18	inner
114.2.l.b.71.1	yes	18	1.1	even	1	trivial
912.2.cc.c.641.3		18	4.3	odd	2
912.2.cc.c.737.3		18	228.167	odd	18
912.2.cc.d.641.3		18	12.11	even	2
912.2.cc.d.737.3		18	76.15	even	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} +(-1.36678 - 1.06392i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-2.20556 + 2.62849i) q^{5} +(1.64823 + 0.532290i) q^{6} +(1.68651 + 2.92113i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.736160 + 2.90828i) q^{9} +(1.17355 - 3.22432i) q^{10} +(2.33635 + 1.34889i) q^{11} +(-1.73088 + 0.0635395i) q^{12} +(-5.05419 + 0.891189i) q^{13} +(-2.58389 - 2.16814i) q^{14} +(5.81100 - 1.24602i) 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} +(0.802750 - 5.78684i) q^{21} +(-2.65680 - 0.468466i) q^{22} +(1.69398 + 2.01881i) q^{23} +(1.60477 - 0.651705i) q^{24} +(-1.17620 - 6.67054i) q^{25} +(4.44458 - 2.56608i) q^{26} +(2.08800 - 4.75818i) q^{27} +(3.16961 + 1.15364i) q^{28} +(3.54249 + 1.28936i) q^{29} +(-5.03439 + 3.15836i) q^{30} +(4.78254 - 2.76120i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-1.75816 - 4.32933i) q^{33} +(2.71629 + 3.23715i) q^{34} +(-11.3979 - 2.00975i) q^{35} +(2.43333 + 1.75467i) 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} +(1.22488 + 5.71241i) q^{42} +(1.85806 + 1.55910i) q^{43} +(2.65680 - 0.468466i) q^{44} +(-9.26801 - 4.47940i) q^{45} +(-2.28230 - 1.31768i) q^{46} +(0.0440069 - 0.120908i) q^{47} +(-1.28509 + 1.16127i) q^{48} +(-2.18866 + 3.79087i) q^{49} +(3.38672 + 5.86597i) q^{50} +(-2.24935 + 6.96509i) q^{51} +(-3.29889 + 3.93146i) q^{52} +(-6.53342 + 5.48219i) q^{53} +(-0.334684 + 5.18536i) q^{54} +(-8.69853 + 3.16600i) q^{55} -3.37303 q^{56} +(7.34685 - 1.73892i) q^{57} -3.76983 q^{58} +(3.87665 - 1.41099i) q^{59} +(3.65056 - 4.68975i) q^{60} +(3.53369 - 2.96512i) q^{61} +(-3.54973 + 4.23041i) q^{62} +(-7.25390 + 7.05526i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(8.80484 - 15.2504i) q^{65} +(3.13285 + 3.46691i) q^{66} +(3.81629 - 10.4852i) q^{67} +(-3.65965 - 2.11290i) q^{68} +(-0.167450 - 4.56152i) q^{69} +(11.3979 - 2.00975i) q^{70} +(9.91131 + 8.31658i) q^{71} +(-2.88672 - 0.816605i) 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} +(-8.80484 - 1.22141i) q^{78} +(2.22246 + 0.391880i) q^{79} +(2.20556 + 2.62849i) q^{80} +(-7.91614 + 4.28191i) q^{81} +(0.289735 + 1.64317i) q^{82} +(6.27861 - 3.62496i) q^{83} +(-3.10477 - 4.94898i) q^{84} +(13.6253 + 4.95920i) q^{85} +(-2.27924 - 0.829577i) q^{86} +(-3.47002 - 5.53118i) q^{87} +(-2.33635 + 1.34889i) q^{88} +(0.209662 + 1.18905i) q^{89} +(10.2411 + 1.03941i) q^{90} +(-11.1272 - 13.2609i) q^{91} +(2.59533 + 0.457627i) q^{92} +(-9.47436 - 1.31428i) 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} +(-2.20303 + 7.78777i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} - 9 q^{8} - 3 q^{9} - 12 q^{13} - 12 q^{14} + 18 q^{15} + 6 q^{17} - 6 q^{19} - 24 q^{22} + 3 q^{24} - 18 q^{25} + 18 q^{26} - 6 q^{27} + 6 q^{28} - 6 q^{29} - 24 q^{33} - 6 q^{34} - 24 q^{35}+ \cdots - 102 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 - 9 * q^8 - 3 * q^9 - 12 * q^13 - 12 * q^14 + 18 * q^15 + 6 * q^17 - 6 * q^19 - 24 * q^22 + 3 * q^24 - 18 * q^25 + 18 * q^26 - 6 * q^27 + 6 * q^28 - 6 * q^29 - 24 * q^33 - 6 * q^34 - 24 * q^35 + 3 * q^38 + 6 * q^39 + 3 * q^41 - 6 * q^43 + 24 * q^44 - 54 * q^45 + 18 * q^46 + 30 * q^47 + 21 * q^49 + 3 * q^50 + 42 * q^51 - 6 * q^52 - 60 * q^53 + 54 * q^54 + 30 * q^55 + 12 * q^57 + 12 * q^58 + 3 * q^59 + 24 * q^60 + 54 * q^61 + 6 * q^62 - 18 * q^63 - 9 * q^64 + 24 * q^65 - 27 * q^66 - 15 * q^67 - 27 * q^68 + 30 * q^69 + 24 * q^70 + 36 * q^71 + 6 * q^72 - 42 * q^73 + 6 * q^74 - 24 * q^78 - 6 * q^79 - 3 * q^81 + 3 * q^82 + 36 * q^83 - 30 * q^84 - 6 * q^86 - 60 * q^89 - 18 * q^91 - 66 * q^93 + 6 * q^95 + 9 * q^97 + 12 * q^98 - 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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