LMFDB - Embedded newform 185.2.z.a.113.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [185,2,Mod(17,185)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("185.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(185, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([9, 7])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$185 = 5 \cdot 37$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	185.z (of order $36$ , degree $12$ , minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$17$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			113.11
Character	$\chi$	$=$	185.113
Dual form			185.2.z.a.167.11

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.253046 - 0.212330i) q^{2} +(2.89010 - 0.252851i) q^{3} +(-0.328349 + 1.86216i) q^{4} +(-2.16715 + 0.550872i) q^{5} +(0.677638 - 0.677638i) q^{6} +(0.0428415 - 0.0918740i) q^{7} +(0.642633 + 1.11307i) q^{8} +(5.33430 - 0.940582i) q^{9} +(-0.431421 + 0.599548i) q^{10} +(1.69513 - 0.978686i) q^{11} +(-0.478111 + 5.46484i) q^{12} +(0.445624 - 2.52726i) q^{13} +(-0.00866678 - 0.0323449i) q^{14} +(-6.12399 + 2.14004i) q^{15} +(-3.15474 - 1.14823i) q^{16} +(-4.59416 + 0.810075i) q^{17} +(1.15011 - 1.37065i) q^{18} +(-0.633002 - 7.23525i) q^{19} +(-0.314230 - 4.21645i) q^{20} +(0.100586 - 0.276357i) q^{21} +(0.221141 - 0.607581i) q^{22} +(-2.18217 + 3.77963i) q^{23} +(2.13871 + 3.05440i) q^{24} +(4.39308 - 2.38765i) q^{25} +(-0.423851 - 0.734131i) q^{26} +(6.77198 - 1.81455i) q^{27} +(0.157017 + 0.109944i) q^{28} +(-5.98245 - 1.60299i) q^{29} +(-1.09525 + 1.84184i) q^{30} +(7.10437 + 7.10437i) q^{31} +(-3.45761 + 1.25847i) q^{32} +(4.65164 - 3.25711i) q^{33} +(-0.990529 + 1.18047i) q^{34} +(-0.0422332 + 0.222705i) q^{35} +10.2422i q^{36} +(-4.09326 - 4.49947i) q^{37} +(-1.69644 - 1.69644i) q^{38} +(0.648877 - 7.41670i) q^{39} +(-2.00584 - 2.05819i) q^{40} +(1.74713 + 0.308067i) q^{41} +(-0.0332263 - 0.0912884i) q^{42} +2.69621 q^{43} +(1.26587 + 3.47796i) q^{44} +(-11.0421 + 4.97690i) q^{45} +(0.250342 + 1.41976i) q^{46} +(0.359543 + 1.34183i) q^{47} +(-9.40785 - 2.52083i) q^{48} +(4.49291 + 5.35444i) q^{49} +(0.604679 - 1.53697i) q^{50} +(-13.0727 + 3.50283i) q^{51} +(4.55983 + 1.65964i) q^{52} +(-2.88753 - 6.19232i) q^{53} +(1.32834 - 1.89706i) q^{54} +(-3.13448 + 3.05476i) q^{55} +(0.129794 - 0.0113555i) q^{56} +(-3.65887 - 20.7505i) q^{57} +(-1.85420 + 0.864626i) q^{58} +(3.29687 + 7.07015i) q^{59} +(-1.97429 - 12.1065i) q^{60} +(-7.68948 + 5.38424i) q^{61} +(3.30620 + 0.289255i) q^{62} +(0.142115 - 0.530380i) q^{63} +(2.74949 - 4.76225i) q^{64} +(0.426463 + 5.72243i) q^{65} +(0.485493 - 1.81188i) q^{66} +(0.547995 + 0.255534i) q^{67} -8.82104i q^{68} +(-5.35101 + 11.4753i) q^{69} +(0.0366001 + 0.0653219i) q^{70} +(2.97761 + 2.49851i) q^{71} +(4.47494 + 5.33302i) q^{72} +(-0.534900 + 0.534900i) q^{73} +(-1.99116 - 0.269446i) q^{74} +(12.0927 - 8.01132i) q^{75} +(13.6810 + 1.19693i) q^{76} +(-0.0172936 - 0.197667i) q^{77} +(-1.41060 - 2.01454i) q^{78} +(-2.44197 - 1.13871i) q^{79} +(7.46933 + 0.750532i) q^{80} +(3.84308 - 1.39877i) q^{81} +(0.507516 - 0.293015i) q^{82} +(-3.38710 + 4.83728i) q^{83} +(0.481593 + 0.278048i) q^{84} +(9.50999 - 4.28635i) q^{85} +(0.682263 - 0.572487i) q^{86} +(-17.6952 - 3.12014i) q^{87} +(2.17870 + 1.25787i) q^{88} +(5.67316 - 2.64544i) q^{89} +(-1.73741 + 3.60396i) q^{90} +(-0.213098 - 0.149213i) q^{91} +(-6.32176 - 5.30459i) q^{92} +(22.3287 + 18.7360i) q^{93} +(0.375893 + 0.263203i) q^{94} +(5.35751 + 15.3312i) q^{95} +(-9.67462 + 4.51135i) q^{96} +(12.6773 + 7.31926i) q^{97} +(2.27382 + 0.400936i) q^{98} +(8.12183 - 6.81502i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$204 q - 12 q^{2} - 6 q^{3} - 12 q^{5} - 24 q^{6} - 12 q^{7} - 24 q^{8} - 6 q^{10} - 36 q^{11} + 36 q^{12} - 12 q^{13} - 24 q^{14} - 12 q^{15} - 24 q^{16} - 30 q^{17} - 90 q^{18} + 42 q^{20} - 24 q^{21}+ \cdots + 192 q^{99}+O(q^{100})$ 204 * q - 12 * q^2 - 6 * q^3 - 12 * q^5 - 24 * q^6 - 12 * q^7 - 24 * q^8 - 6 * q^10 - 36 * q^11 + 36 * q^12 - 12 * q^13 - 24 * q^14 - 12 * q^15 - 24 * q^16 - 30 * q^17 - 90 * q^18 + 42 * q^20 - 24 * q^21 - 24 * q^22 - 6 * q^23 + 36 * q^24 - 18 * q^25 - 12 * q^26 - 42 * q^27 + 36 * q^30 - 12 * q^31 + 12 * q^32 - 24 * q^33 + 36 * q^35 - 36 * q^37 + 60 * q^38 + 24 * q^39 + 66 * q^40 - 18 * q^41 - 42 * q^42 - 24 * q^43 - 180 * q^44 + 72 * q^45 - 24 * q^46 - 6 * q^47 - 6 * q^48 + 36 * q^49 + 90 * q^50 - 24 * q^51 + 60 * q^52 - 90 * q^53 - 42 * q^55 - 24 * q^56 - 36 * q^57 - 90 * q^60 + 60 * q^61 - 96 * q^62 - 6 * q^63 - 18 * q^64 + 6 * q^65 + 120 * q^66 + 30 * q^67 + 132 * q^69 - 132 * q^70 + 24 * q^71 + 216 * q^72 + 90 * q^73 - 66 * q^74 - 120 * q^75 + 36 * q^76 + 24 * q^77 - 138 * q^78 - 96 * q^79 + 108 * q^80 + 132 * q^81 - 18 * q^82 - 72 * q^83 - 18 * q^85 + 96 * q^86 - 114 * q^87 + 198 * q^88 - 12 * q^89 + 36 * q^90 - 96 * q^91 - 54 * q^92 + 42 * q^93 + 72 * q^94 + 30 * q^95 + 60 * q^96 + 54 * q^97 - 60 * q^98 + 192 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$ .

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{3}{4}\right)$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	0.253046	−	0.212330i	0.178930	−	0.150140i	−0.548924	−	0.835872i	$-0.684962\pi$
$2$	0.253046	−	0.212330i	0.178930	−	0.150140i	0.727854	+	0.685732i	$0.240518\pi$
$3$	2.89010	−	0.252851i	1.66860	−	0.145983i	0.786672	−	0.617371i	$-0.211802\pi$
$3$	2.89010	−	0.252851i	1.66860	−	0.145983i	0.881926	+	0.471387i	$0.156247\pi$
$4$	−0.328349	+	1.86216i	−0.164174	+	0.931078i
$5$	−2.16715	+	0.550872i	−0.969179	+	0.246358i
$5$	−2.16715	+	0.550872i	−0.969179	+	0.246358i
$6$	0.677638	−	0.677638i	0.276645	−	0.276645i
$7$	0.0428415	−	0.0918740i	0.0161926	−	0.0347251i	−0.898045	−	0.439903i	$-0.855013\pi$
$7$	0.0428415	−	0.0918740i	0.0161926	−	0.0347251i	0.914238	+	0.405178i	$0.132791\pi$
$8$	0.642633	+	1.11307i	0.227205	+	0.393531i
$9$	5.33430	−	0.940582i	1.77810	−	0.313527i
$10$	−0.431421	+	0.599548i	−0.136427	+	0.189594i
$11$	1.69513	−	0.978686i	0.511102	−	0.295085i	−0.222184	−	0.975005i	$-0.571319\pi$
$11$	1.69513	−	0.978686i	0.511102	−	0.295085i	0.733287	+	0.679920i	$0.237985\pi$
$12$	−0.478111	+	5.46484i	−0.138019	+	1.57756i
$13$	0.445624	−	2.52726i	0.123594	−	0.700935i	−0.858539	−	0.512748i	$-0.828628\pi$
$13$	0.445624	−	2.52726i	0.123594	−	0.700935i	0.982133	−	0.188188i	$-0.0602613\pi$
$14$	−0.00866678	−	0.0323449i	−0.00231629	−	0.00864453i
$15$	−6.12399	+	2.14004i	−1.58121	+	0.552556i
$16$	−3.15474	−	1.14823i	−0.788686	−	0.287058i
$17$	−4.59416	+	0.810075i	−1.11425	+	0.196472i	−0.700314	−	0.713835i	$-0.746957\pi$
$17$	−4.59416	+	0.810075i	−1.11425	+	0.196472i	−0.413934	+	0.910307i	$0.635846\pi$
$18$	1.15011	−	1.37065i	0.271083	−	0.323064i
$19$	−0.633002	−	7.23525i	−0.145221	−	1.65988i	−0.623613	−	0.781733i	$-0.714336\pi$
$19$	−0.633002	−	7.23525i	−0.145221	−	1.65988i	0.478392	−	0.878146i	$-0.341220\pi$
$20$	−0.314230	−	4.21645i	−0.0702641	−	0.942827i
$21$	0.100586	−	0.276357i	0.0219496	−	0.0603061i
$22$	0.221141	−	0.607581i	0.0471475	−	0.129537i
$23$	−2.18217	+	3.77963i	−0.455015	+	0.788108i	−0.998689	−	0.0511879i	$-0.983699\pi$
$23$	−2.18217	+	3.77963i	−0.455015	+	0.788108i	0.543675	+	0.839296i	$0.317033\pi$
$24$	2.13871	+	3.05440i	0.436563	+	0.623477i
$25$	4.39308	−	2.38765i	0.878616	−	0.477529i
$26$	−0.423851	−	0.734131i	−0.0831240	−	0.143975i
$27$	6.77198	−	1.81455i	1.30327	−	0.349210i
$28$	0.157017	+	0.109944i	0.0296734	+	0.0207775i
$29$	−5.98245	−	1.60299i	−1.11091	−	0.297668i	−0.343712	−	0.939075i	$-0.611684\pi$
$29$	−5.98245	−	1.60299i	−1.11091	−	0.297668i	−0.767201	+	0.641407i	$0.778351\pi$
$30$	−1.09525	+	1.84184i	−0.199965	+	0.336272i
$31$	7.10437	+	7.10437i	1.27598	+	1.27598i	0.942897	+	0.333086i	$0.108090\pi$
$31$	7.10437	+	7.10437i	1.27598	+	1.27598i	0.333086	+	0.942897i	$0.391910\pi$
$32$	−3.45761	+	1.25847i	−0.611225	+	0.222468i
$33$	4.65164	−	3.25711i	0.809747	−	0.566991i
$34$	−0.990529	+	1.18047i	−0.169874	+	0.202448i
$35$	−0.0422332	+	0.222705i	−0.00713871	+	0.0376440i
$36$			10.2422i			1.70703i
$37$	−4.09326	−	4.49947i	−0.672928	−	0.739708i
$37$	−4.09326	−	4.49947i	−0.672928	−	0.739708i
$38$	−1.69644	−	1.69644i	−0.275199	−	0.275199i
$39$	0.648877	−	7.41670i	0.103903	−	1.18762i
$40$	−2.00584	−	2.05819i	−0.317152	−	0.325428i
$41$	1.74713	+	0.308067i	0.272856	+	0.0481119i	0.308402	−	0.951256i	$-0.400206\pi$
$41$	1.74713	+	0.308067i	0.272856	+	0.0481119i	−0.0355456	+	0.999368i	$0.511317\pi$
$42$	−0.0332263	−	0.0912884i	−0.00512692	−	0.0140861i
$43$	2.69621			0.411168			0.205584	−	0.978639i	$-0.434091\pi$
$43$	2.69621			0.411168			0.205584	+	0.978639i	$0.434091\pi$
$44$	1.26587	+	3.47796i	0.190837	+	0.524322i
$45$	−11.0421	+	4.97690i	−1.64606	+	0.741913i
$46$	0.250342	+	1.41976i	0.0369110	+	0.209332i
$47$	0.359543	+	1.34183i	0.0524447	+	0.195726i	0.987178	−	0.159624i	$-0.0510282\pi$
$47$	0.359543	+	1.34183i	0.0524447	+	0.195726i	−0.934733	+	0.355350i	$0.884362\pi$
$48$	−9.40785	−	2.52083i	−1.35791	−	0.363850i
$49$	4.49291	+	5.35444i	0.641844	+	0.764920i
$50$	0.604679	−	1.53697i	0.0855145	−	0.217360i
$51$	−13.0727	+	3.50283i	−1.83055	+	0.490494i
$52$	4.55983	+	1.65964i	0.632335	+	0.230151i
$53$	−2.88753	−	6.19232i	−0.396632	−	0.850581i	−0.998642	−	0.0520923i	$-0.983411\pi$
$53$	−2.88753	−	6.19232i	−0.396632	−	0.850581i	0.602010	−	0.798489i	$-0.294367\pi$
$54$	1.32834	−	1.89706i	0.180764	−	0.258157i
$55$	−3.13448	+	3.05476i	−0.422653	+	0.411904i
$56$	0.129794	−	0.0113555i	0.0173444	−	0.00151744i
$57$	−3.65887	−	20.7505i	−0.484630	−	2.74847i
$58$	−1.85420	+	0.864626i	−0.243468	+	0.113531i
$59$	3.29687	+	7.07015i	0.429215	+	0.920455i	0.995366	+	0.0961538i	$0.0306541\pi$
$59$	3.29687	+	7.07015i	0.429215	+	0.920455i	−0.566151	+	0.824301i	$0.691568\pi$
$60$	−1.97429	−	12.1065i	−0.254880	−	1.56294i
$61$	−7.68948	+	5.38424i	−0.984538	+	0.689381i	−0.950721	−	0.310047i	$-0.899655\pi$
$61$	−7.68948	+	5.38424i	−0.984538	+	0.689381i	−0.0338165	+	0.999428i	$0.510766\pi$
$62$	3.30620	+	0.289255i	0.419888	+	0.0367355i
$63$	0.142115	−	0.530380i	0.0179048	−	0.0668216i
$64$	2.74949	−	4.76225i	0.343686	−	0.595281i
$65$	0.426463	+	5.72243i	0.0528962	+	0.709780i
$66$	0.485493	−	1.81188i	0.0597600	−	0.223027i
$67$	0.547995	+	0.255534i	0.0669483	+	0.0312185i	0.455804	−	0.890080i	$-0.349352\pi$
$67$	0.547995	+	0.255534i	0.0669483	+	0.0312185i	−0.388856	+	0.921299i	$0.627130\pi$
$68$		−	8.82104i		−	1.06971i
$69$	−5.35101	+	11.4753i	−0.644186	+	1.38146i
$70$	0.0366001	+	0.0653219i	0.00437455	+	0.00780746i
$71$	2.97761	+	2.49851i	0.353377	+	0.296519i	0.802145	−	0.597130i	$-0.203692\pi$
$71$	2.97761	+	2.49851i	0.353377	+	0.296519i	−0.448767	+	0.893649i	$0.648137\pi$
$72$	4.47494	+	5.33302i	0.527376	+	0.628503i
$73$	−0.534900	+	0.534900i	−0.0626053	+	0.0626053i	−0.737716	−	0.675111i	$-0.764096\pi$
$73$	−0.534900	+	0.534900i	−0.0626053	+	0.0626053i	0.675111	+	0.737716i	$0.264096\pi$
$74$	−1.99116	−	0.269446i	−0.231467	−	0.0313225i
$75$	12.0927	−	8.01132i	1.39635	−	0.925068i
$76$	13.6810	+	1.19693i	1.56932	+	0.137298i
$77$	−0.0172936	−	0.197667i	−0.00197079	−	0.0225263i
$78$	−1.41060	−	2.01454i	−0.159718	−	0.228102i
$79$	−2.44197	−	1.13871i	−0.274743	−	0.128115i	0.280364	−	0.959894i	$-0.409545\pi$
$79$	−2.44197	−	1.13871i	−0.274743	−	0.128115i	−0.555107	+	0.831779i	$0.687323\pi$
$80$	7.46933	+	0.750532i	0.835097	+	0.0839120i
$81$	3.84308	−	1.39877i	0.427009	−	0.155418i
$82$	0.507516	−	0.293015i	0.0560458	−	0.0323581i
$83$	−3.38710	+	4.83728i	−0.371782	+	0.530960i	−0.960830	−	0.277138i	$-0.910614\pi$
$83$	−3.38710	+	4.83728i	−0.371782	+	0.530960i	0.589048	+	0.808098i	$0.299503\pi$
$84$	0.481593	+	0.278048i	0.0525461	+	0.0303375i
$85$	9.50999	−	4.28635i	1.03150	−	0.464920i
$86$	0.682263	−	0.572487i	0.0735703	−	0.0617329i
$87$	−17.6952	−	3.12014i	−1.89712	−	0.334514i
$88$	2.17870	+	1.25787i	0.232250	+	0.134090i
$89$	5.67316	−	2.64544i	0.601353	−	0.280416i	−0.0980060	−	0.995186i	$-0.531246\pi$
$89$	5.67316	−	2.64544i	0.601353	−	0.280416i	0.699359	+	0.714770i	$0.253469\pi$
$90$	−1.73741	+	3.60396i	−0.183139	+	0.379890i
$91$	−0.213098	−	0.149213i	−0.0223387	−	0.0156418i
$92$	−6.32176	−	5.30459i	−0.659089	−	0.553041i
$93$	22.3287	+	18.7360i	2.31537	+	1.94283i
$94$	0.375893	+	0.263203i	0.0387704	+	0.0271473i
$95$	5.35751	+	15.3312i	0.549669	+	1.57294i
$96$	−9.67462	+	4.51135i	−0.987412	+	0.460438i
$97$	12.6773	+	7.31926i	1.28719	+	0.743158i	0.978152	−	0.207892i	$-0.0666602\pi$
$97$	12.6773	+	7.31926i	1.28719	+	0.743158i	0.309036	+	0.951050i	$0.399994\pi$
$98$	2.27382	+	0.400936i	0.229691	+	0.0405006i
$99$	8.12183	−	6.81502i	0.816275	−	0.684936i
$100$	3.00371	+	8.96458i	0.300371	+	0.896458i
$101$	5.56082	+	3.21054i	0.553322	+	0.319461i	0.750461	−	0.660915i	$-0.229832\pi$
$101$	5.56082	+	3.21054i	0.553322	+	0.319461i	−0.197139	+	0.980376i	$0.563165\pi$
$102$	−2.56424	+	3.66212i	−0.253898	+	0.362604i
$103$	4.42314	−	2.55370i	0.435825	−	0.251624i	−0.266000	−	0.963973i	$-0.585702\pi$
$103$	4.42314	−	2.55370i	0.435825	−	0.251624i	0.701825	+	0.712349i	$0.252369\pi$
$104$	3.09940	−	1.12809i	0.303921	−	0.110618i
$105$	−0.0657470	+	0.654318i	−0.00641625	+	0.0638549i
$106$	−2.04549	−	0.953830i	−0.198676	−	0.0926441i
$107$	−1.12310	−	1.60395i	−0.108574	−	0.155060i	0.761188	−	0.648531i	$-0.224616\pi$
$107$	−1.12310	−	1.60395i	−0.108574	−	0.155060i	−0.869762	+	0.493472i	$0.835728\pi$
$108$	1.15540	+	13.2063i	0.111179	+	1.27078i
$109$	11.8020	+	1.03254i	1.13043	+	0.0988997i	0.636984	−	0.770877i	$-0.280182\pi$
$109$	11.8020	+	1.03254i	1.13043	+	0.0988997i	0.493445	+	0.869777i	$0.335737\pi$
$110$	−0.144547	+	1.43854i	−0.0137820	+	0.137159i
$111$	−12.9676	−	11.9689i	−1.23083	−	1.13604i
$112$	−0.240647	+	0.240647i	−0.0227390	+	0.0227390i
$113$	−12.7158	−	15.1541i	−1.19621	−	1.42558i	−0.878733	−	0.477314i	$-0.841610\pi$
$113$	−12.7158	−	15.1541i	−1.19621	−	1.42558i	−0.317472	−	0.948268i	$-0.602834\pi$
$114$	−5.33183	−	4.47393i	−0.499371	−	0.419022i
$115$	2.64700	−	9.39313i	0.246834	−	0.875914i
$116$	4.94935	−	10.6139i	0.459536	−	0.985478i
$117$		−	13.9003i		−	1.28508i
$118$	2.33547	+	1.08905i	0.214997	+	0.100255i
$119$	−0.122396	+	0.456789i	−0.0112200	+	0.0418738i
$120$	−6.31750	−	5.44118i	−0.576706	−	0.496710i
$121$	−3.58435	+	6.20827i	−0.325850	+	0.564388i
$122$	−0.802553	+	2.99517i	−0.0726597	+	0.271170i
$123$	5.12728	+	0.448579i	0.462311	+	0.0404470i
$124$	−15.5622	+	10.8967i	−1.39752	+	0.978556i
$125$	−8.20517	+	7.59441i	−0.733893	+	0.679265i
$126$	−0.0766542	−	0.164386i	−0.00682890	−	0.0146446i
$127$	−15.5960	+	7.27251i	−1.38392	+	0.645331i	−0.964893	−	0.262644i	$-0.915406\pi$
$127$	−15.5960	+	7.27251i	−1.38392	+	0.645331i	−0.419024	+	0.907975i	$0.637628\pi$
$128$	−1.59331	−	9.03609i	−0.140830	−	0.798685i
$129$	7.79230	−	0.681738i	0.686074	−	0.0600237i
$130$	1.32296	+	1.35748i	0.116031	+	0.119059i
$131$	10.6954	−	15.2746i	0.934460	−	1.33455i	−0.00790841	−	0.999969i	$-0.502517\pi$
$131$	10.6954	−	15.2746i	0.934460	−	1.33455i	0.942368	−	0.334578i	$-0.108594\pi$
$132$	4.53790	+	9.73156i	0.394973	+	0.847023i
$133$	−0.691850	−	0.251813i	−0.0599910	−	0.0218349i
$134$	0.192925	−	0.0516942i	0.0166662	−	0.00446570i
$135$	−13.6763	+	7.66290i	−1.17707	+	0.659517i
$136$	−3.85403	−	4.59306i	−0.330480	−	0.393851i
$137$	−7.19303	−	1.92737i	−0.614542	−	0.164666i	−0.0618965	−	0.998083i	$-0.519715\pi$
$137$	−7.19303	−	1.92737i	−0.614542	−	0.164666i	−0.552645	+	0.833417i	$0.686382\pi$
$138$	1.08250	+	4.03995i	0.0921486	+	0.343903i
$139$	−3.16681	−	17.9599i	−0.268605	−	1.52334i	−0.758569	−	0.651593i	$-0.774101\pi$
$139$	−3.16681	−	17.9599i	−0.268605	−	1.52334i	0.489964	−	0.871743i	$-0.337010\pi$
$140$	−0.400844	−	0.151770i	−0.0338775	−	0.0128269i
$141$	1.37840	+	3.78712i	0.116082	+	0.318933i
$142$	1.28398			0.107749
$143$	−1.71800	−	4.72017i	−0.143666	−	0.394720i
$144$	−17.9084	−	3.15773i	−1.49236	−	0.263144i
$145$	13.8479	+	0.178359i	1.15001	+	0.0148119i
$146$	−0.0217785	+	0.248929i	−0.00180240	+	0.0206015i
$147$	14.3388	+	14.3388i	1.18265	+	1.18265i
$148$	9.72273	−	6.14490i	0.799204	−	0.505108i
$149$			23.0978i			1.89224i	0.323811	+	0.946122i	$0.395036\pi$
$149$			23.0978i			1.89224i	−0.323811	+	0.946122i	$0.604964\pi$
$150$	1.35896	−	4.59488i	0.110958	−	0.375170i
$151$	1.97273	−	2.35101i	0.160539	−	0.191322i	−0.679779	−	0.733417i	$-0.737924\pi$
$151$	1.97273	−	2.35101i	0.160539	−	0.191322i	0.840317	+	0.542095i	$0.182369\pi$
$152$	7.64657	−	5.35419i	0.620219	−	0.434282i
$153$	−23.7447	+	8.64237i	−1.91965	+	0.698694i
$154$	−0.0463468	−	0.0463468i	−0.00373473	−	0.00373473i
$155$	−19.3098	−	11.4826i	−1.55100	−	0.922307i
$156$	13.5980	+	3.64357i	1.08871	+	0.291719i
$157$	15.6805	+	10.9796i	1.25144	+	0.876267i	0.995894	−	0.0905296i	$-0.0288560\pi$
$157$	15.6805	+	10.9796i	1.25144	+	0.876267i	0.255546	+	0.966797i	$0.417745\pi$
$158$	−0.859711	+	0.230359i	−0.0683949	+	0.0183264i
$159$	−9.91097	−	17.1663i	−0.785991	−	1.36138i
$160$	6.79990	−	4.63199i	0.537579	−	0.366191i
$161$	0.253762	+	0.362410i	0.0199993	+	0.0285619i
$162$	0.675473	−	1.16995i	0.0530702	−	0.0919203i
$163$	0.634829	−	1.74418i	0.0497236	−	0.136615i	−0.912345	−	0.409423i	$-0.865730\pi$
$163$	0.634829	−	1.74418i	0.0497236	−	0.136615i	0.962068	+	0.272808i	$0.0879524\pi$
$164$	−1.14734	+	3.15228i	−0.0895920	+	0.246152i
$165$	−8.28655	+	9.62112i	−0.645107	+	0.749003i
$166$	0.170011	+	1.94323i	0.0131954	+	0.150824i
$167$	−0.872617	+	1.03994i	−0.0675251	+	0.0804733i	−0.798750	−	0.601664i	$-0.794505\pi$
$167$	−0.872617	+	1.03994i	−0.0675251	+	0.0804733i	0.731224	+	0.682137i	$0.238949\pi$
$168$	0.372246	−	0.0656369i	0.0287194	−	0.00506400i
$169$	6.02755	+	2.19385i	0.463658	+	0.168758i
$170$	1.49634	−	3.10390i	0.114764	−	0.238058i
$171$	−10.1820	−	37.9996i	−0.778634	−	2.90590i
$172$	−0.885296	+	5.02076i	−0.0675032	+	0.382829i
$173$	−1.04875	+	11.9872i	−0.0797348	+	0.911373i	0.845996	+	0.533190i	$0.179007\pi$
$173$	−1.04875	+	11.9872i	−0.0797348	+	0.911373i	−0.925731	+	0.378184i	$0.876549\pi$
$174$	−5.14019	+	2.96769i	−0.389676	+	0.224980i
$175$	−0.0311563	−	0.505900i	−0.00235520	−	0.0382425i
$176$	−6.47148	+	1.14110i	−0.487806	+	0.0860133i
$177$	11.3160	+	19.5998i	0.850559	+	1.47321i
$178$	0.873860	−	1.87400i	0.0654986	−	0.140462i
$179$	−12.5624	+	12.5624i	−0.938955	+	0.938955i	−0.998241	−	0.0592860i	$-0.981118\pi$
$179$	−12.5624	+	12.5624i	−0.938955	+	0.938955i	0.0592860	+	0.998241i	$0.481118\pi$
$180$	−5.64212	−	22.1963i	−0.420539	−	1.65441i
$181$	2.19810	−	12.4660i	0.163383	−	0.926593i	−0.787332	−	0.616529i	$-0.788538\pi$
$181$	2.19810	−	12.4660i	0.163383	−	0.926593i	0.950716	−	0.310064i	$-0.100351\pi$
$182$	−0.0856060	+	0.00748955i	−0.00634554	+	0.000555162i
$183$	−20.8619	+	17.5053i	−1.54216	+	1.29403i
$184$	−5.60935			−0.413526
$185$	11.3493	+	7.49616i	0.834420	+	0.551128i
$186$	9.62838			0.705987
$187$	−6.99491	+	5.86943i	−0.511519	+	0.429215i
$188$	−2.61676	+	0.228937i	−0.190847	+	0.0166969i
$189$	0.123413	−	0.699907i	0.00897694	−	0.0509108i
$190$	4.61097	+	2.74192i	0.334515	+	0.198920i
$191$	0.270743	−	0.270743i	0.0195903	−	0.0195903i	−0.697244	−	0.716834i	$-0.745591\pi$
$191$	0.270743	−	0.270743i	0.0195903	−	0.0195903i	0.716834	+	0.697244i	$0.245591\pi$
$192$	6.74215	−	14.4586i	0.486572	−	1.04346i
$193$	−0.623835	−	1.08051i	−0.0449046	−	0.0777771i	0.842700	−	0.538384i	$-0.180965\pi$
$193$	−0.623835	−	1.08051i	−0.0449046	−	0.0777771i	−0.887604	+	0.460607i	$0.847632\pi$
$194$	4.76204	−	0.839677i	0.341895	−	0.0602853i
$195$	2.67944	+	16.4305i	0.191879	+	1.17662i
$196$	−11.4460	+	6.60838i	−0.817575	+	0.472027i
$197$	1.63580	−	18.6973i	0.116546	−	1.33213i	−0.682513	−	0.730874i	$-0.739113\pi$
$197$	1.63580	−	18.6973i	0.116546	−	1.33213i	0.799059	−	0.601253i	$-0.205332\pi$
$198$	0.608156	−	3.44902i	0.0432198	−	0.245111i
$199$	0.517447	+	1.93114i	0.0366808	+	0.136895i	0.981838	−	0.189721i	$-0.0607584\pi$
$199$	0.517447	+	1.93114i	0.0366808	+	0.136895i	−0.945157	+	0.326616i	$0.894092\pi$
$200$	5.48076	+	3.35544i	0.387548	+	0.237265i
$201$	1.64837	+	0.599958i	0.116267	+	0.0423178i
$202$	2.08884	−	0.368318i	0.146970	−	0.0259148i
$203$	−0.403571	+	0.480957i	−0.0283251	+	0.0337565i
$204$	−2.23041	−	25.4937i	−0.156160	−	1.78491i
$205$	−3.95601	+	0.294821i	−0.276299	+	0.0205912i
$206$	0.577027	−	1.58537i	0.0402034	−	0.110458i
$207$	−8.08532	+	22.2142i	−0.561969	+	1.54400i
$208$	−4.30771	+	7.46117i	−0.298686	+	0.517339i
$209$	−8.15406	−	11.6452i	−0.564028	−	0.805516i
$210$	0.122295	+	0.179532i	0.00843913	+	0.0123889i
$211$	−1.42157	−	2.46222i	−0.0978646	−	0.169506i	0.812936	−	0.582353i	$-0.197868\pi$
$211$	−1.42157	−	2.46222i	−0.0978646	−	0.169506i	−0.910801	+	0.412847i	$0.864535\pi$
$212$	12.4792	−	3.34379i	0.857074	−	0.229652i
$213$	9.23734	+	6.46805i	0.632932	+	0.443184i
$214$	−0.624762	−	0.167404i	−0.0427078	−	0.0114435i
$215$	−5.84309	+	1.48527i	−0.398495	+	0.101294i
$216$	6.37162	+	6.37162i	0.433534	+	0.433534i
$217$	0.957069	−	0.348345i	0.0649701	−	0.0236472i
$218$	3.20569	−	2.24465i	0.217117	−	0.152027i
$219$	−1.41066	+	1.68116i	−0.0953237	+	0.113602i
$220$	−4.65925	−	6.83992i	−0.314126	−	0.461147i
$221$			11.9716i			0.805298i
$222$	−5.82276	−	0.275261i	−0.390798	−	0.0184743i
$223$	−18.5657	−	18.5657i	−1.24325	−	1.24325i	−0.958643	−	0.284611i	$-0.908136\pi$
$223$	−18.5657	−	18.5657i	−1.24325	−	1.24325i	−0.284611	−	0.958643i	$-0.591864\pi$
$224$	−0.0325089	+	0.371579i	−0.00217210	+	0.0248272i
$225$	21.1882	−	16.8685i	1.41255	−	1.12457i
$226$	−6.43537	−	1.13473i	−0.428074	−	0.0754811i
$227$	1.78086	+	4.89287i	0.118200	+	0.324751i	0.984657	−	0.174500i	$-0.0558308\pi$
$227$	1.78086	+	4.89287i	0.118200	+	0.324751i	−0.866457	+	0.499251i	$0.833609\pi$
$228$	39.8421			2.63861
$229$	1.15257	+	3.16665i	0.0761637	+	0.209258i	0.971931	−	0.235264i	$-0.0755956\pi$
$229$	1.15257	+	3.16665i	0.0761637	+	0.209258i	−0.895768	+	0.444522i	$0.853373\pi$
$230$	−1.32464	−	2.93893i	−0.0873440	−	0.193787i
$231$	−0.0999606	−	0.566905i	−0.00657692	−	0.0372996i
$232$	−2.06027	−	7.68904i	−0.135263	−	0.504810i
$233$	15.2109	+	4.07575i	0.996500	+	0.267011i	0.719978	−	0.693996i	$-0.244152\pi$
$233$	15.2109	+	4.07575i	0.996500	+	0.267011i	0.276521	+	0.961008i	$0.410818\pi$
$234$	−2.95146	−	3.51741i	−0.192943	−	0.229940i
$235$	−1.51836	−	2.70989i	−0.0990470	−	0.176774i
$236$	−14.2483	+	3.81781i	−0.927482	+	0.248518i
$237$	−7.34544	−	2.67352i	−0.477138	−	0.173664i
$238$	0.0660183	+	0.141577i	0.00427933	+	0.00917706i
$239$	−5.81151	+	8.29970i	−0.375915	+	0.536863i	−0.961879	−	0.273474i	$-0.911827\pi$
$239$	−5.81151	+	8.29970i	−0.375915	+	0.536863i	0.585964	+	0.810337i	$0.300716\pi$
$240$	21.7769	+	0.280483i	1.40569	+	0.0181051i
$241$	−0.962344	+	0.0841942i	−0.0619900	+	0.00542342i	−0.118109	−	0.993001i	$-0.537683\pi$
$241$	−0.962344	+	0.0841942i	−0.0619900	+	0.00542342i	0.0561185	+	0.998424i	$0.482128\pi$
$242$	0.411202	+	2.33204i	0.0264330	+	0.149909i
$243$	−8.30884	+	3.87447i	−0.533012	+	0.248548i
$244$	−7.50146	−	16.0869i	−0.480232	−	1.02986i
$245$	−12.6864	−	9.12885i	−0.810506	−	0.583221i
$246$	1.39268	−	0.975167i	0.0887942	−	0.0621744i
$247$	−18.5674	−	1.62444i	−1.18142	−	0.103361i
$248$	−3.34218	+	12.4732i	−0.212229	+	0.792048i
$249$	−8.56593	+	14.8366i	−0.542844	+	0.940233i
$250$	−0.463757	+	3.66394i	−0.0293306	+	0.231728i
$251$	−1.00731	+	3.75934i	−0.0635810	+	0.237287i	−0.990402	−	0.138216i	$-0.955863\pi$
$251$	−1.00731	+	3.75934i	−0.0635810	+	0.237287i	0.926821	+	0.375503i	$0.122530\pi$
$252$	0.940987	+	0.438790i	0.0592766	+	0.0276411i
$253$			8.54265i			0.537072i
$254$	−2.40231	+	5.15177i	−0.150734	+	0.323251i
$255$	26.4010	−	14.7926i	1.65329	−	0.926347i
$256$	6.10310	+	5.12111i	0.381444	+	0.320069i
$257$	6.92868	+	8.25728i	0.432199	+	0.515075i	0.937555	−	0.347836i	$-0.113083\pi$
$257$	6.92868	+	8.25728i	0.432199	+	0.515075i	−0.505356	+	0.862911i	$0.668639\pi$
$258$	1.82705	−	1.82705i	0.113747	−	0.113747i
$259$	−0.588746	+	0.183300i	−0.0365829	+	0.0113897i
$260$	−10.7961	−	1.08481i	−0.669545	−	0.0672771i
$261$	−33.4200	−	2.92387i	−2.06864	−	0.180983i
$262$	−0.536841	−	6.13612i	−0.0331661	−	0.379091i
$263$	−11.9689	−	17.0934i	−0.738035	−	1.05402i	−0.996129	−	0.0879036i	$-0.971983\pi$
$263$	−11.9689	−	17.0934i	−0.738035	−	1.05402i	0.258094	−	0.966120i	$-0.416906\pi$
$264$	6.61470	+	3.08449i	0.407107	+	0.189837i
$265$	9.66888	+	11.8290i	0.593955	+	0.726652i
$266$	−0.228537	+	0.0831807i	−0.0140125	+	0.00510013i
$267$	15.7271	−	9.08003i	0.962481	−	0.555689i
$268$	−0.655778	+	0.936549i	−0.0400580	+	0.0572088i
$269$	16.3279	+	9.42690i	0.995527	+	0.574768i	0.906922	−	0.421299i	$-0.138426\pi$
$269$	16.3279	+	9.42690i	0.995527	+	0.574768i	0.0886055	+	0.996067i	$0.471759\pi$
$270$	−1.83367	+	4.84296i	−0.111593	+	0.294733i
$271$	10.8451	−	9.10009i	0.658791	−	0.552791i	−0.250933	−	0.968004i	$-0.580737\pi$
$271$	10.8451	−	9.10009i	0.658791	−	0.552791i	0.909724	+	0.415213i	$0.136293\pi$
$272$	15.4236	+	2.71959i	0.935191	+	0.164899i
$273$	−0.653603	−	0.377358i	−0.0395578	−	0.0228387i
$274$	−2.22940	+	1.03959i	−0.134683	+	0.0628038i
$275$	5.11010	−	8.34683i	0.308151	−	0.503333i
$276$	−19.6118	−	13.7323i	−1.18049	−	0.826588i
$277$	−21.4363	−	17.9872i	−1.28798	−	1.08075i	−0.992090	−	0.125525i	$-0.959938\pi$
$277$	−21.4363	−	17.9872i	−1.28798	−	1.08075i	−0.295893	−	0.955221i	$-0.595617\pi$
$278$	−4.61477	−	3.87225i	−0.276776	−	0.232242i
$279$	44.5791	+	31.2146i	2.66888	+	1.86877i
$280$	−0.275027	+	0.0961089i	−0.0164360	+	0.00574360i
$281$	17.8007	−	8.30060i	1.06190	−	0.495173i	0.188449	−	0.982083i	$-0.439654\pi$
$281$	17.8007	−	8.30060i	1.06190	−	0.495173i	0.873452	+	0.486910i	$0.161876\pi$
$282$	1.15292	+	0.665637i	0.0686552	+	0.0396381i
$283$	−13.6438	−	2.40578i	−0.811042	−	0.143009i	−0.247278	−	0.968945i	$-0.579536\pi$
$283$	−13.6438	−	2.40578i	−0.811042	−	0.143009i	−0.563764	+	0.825936i	$0.690647\pi$
$284$	−5.63032	+	4.72440i	−0.334098	+	0.280341i
$285$	19.3602	+	42.9539i	1.14680	+	2.54437i
$286$	−1.43697	−	0.829634i	−0.0849697	−	0.0490573i
$287$	0.103153	−	0.147318i	0.00608894	−	0.00869591i
$288$	−17.2602	+	9.96521i	−1.01707	+	0.587206i
$289$	4.47532	−	1.62888i	0.263254	−	0.0958167i
$290$	3.54202	−	2.89520i	0.207995	−	0.170012i
$291$	38.4894	+	17.9479i	2.25629	+	1.05212i
$292$	−0.820434	−	1.17170i	−0.0480122	−	0.0685686i
$293$	0.0441606	+	0.504758i	0.00257989	+	0.0294883i	0.997376	−	0.0724021i	$-0.0230665\pi$
$293$	0.0441606	+	0.504758i	0.00257989	+	0.0294883i	−0.994796	+	0.101890i	$0.967511\pi$
$294$	6.67294	+	0.583807i	0.389174	+	0.0340483i
$295$	−11.0396	−	13.5059i	−0.642748	−	0.786345i
$296$	2.37777	−	7.44761i	0.138205	−	0.432883i
$297$	9.70355	−	9.70355i	0.563057	−	0.563057i
$298$	4.90436	+	5.84479i	0.284102	+	0.338580i
$299$	8.57968	+	7.19921i	0.496176	+	0.416341i
$300$	10.9477	+	25.1490i	0.632067	+	1.45198i
$301$	0.115510	−	0.247711i	0.00665787	−	0.0142778i
$302$		−	1.01378i		−	0.0583367i
$303$	16.8831	+	7.87272i	0.969908	+	0.452276i
$304$	−6.31079	+	23.5522i	−0.361949	+	1.35081i
$305$	13.6982	−	15.9044i	0.784359	−	0.910682i
$306$	−4.17346	+	7.22864i	−0.238581	+	0.413234i
$307$	−2.00005	+	7.46427i	−0.114149	+	0.426008i	−0.999222	−	0.0394434i	$-0.987442\pi$
$307$	−2.00005	+	7.46427i	−0.114149	+	0.426008i	0.885073	+	0.465452i	$0.154108\pi$
$308$	0.373766	+	0.0327003i	0.0212973	+	0.00186327i
$309$	12.1376	−	8.49883i	0.690484	−	0.483482i
$310$	−7.32438	+	1.19444i	−0.415997	+	0.0678394i
$311$	1.78516	+	3.82830i	0.101227	+	0.217083i	0.950398	−	0.311035i	$-0.100676\pi$
$311$	1.78516	+	3.82830i	0.101227	+	0.217083i	−0.849171	+	0.528118i	$0.822898\pi$
$312$	8.67232	−	4.04397i	0.490973	−	0.228945i
$313$	0.697674	+	3.95670i	0.0394348	+	0.223646i	0.998156	−	0.0607021i	$-0.0193339\pi$
$313$	0.697674	+	3.95670i	0.0394348	+	0.223646i	−0.958721	+	0.284348i	$0.908223\pi$
$314$	6.29918	−	0.551107i	0.355483	−	0.0311008i
$315$	−0.0158126	+	1.22770i	−0.000890938	+	0.0691730i
$316$	2.92227	−	4.17343i	0.164390	−	0.234774i
$317$	−12.0947	−	25.9372i	−0.679306	−	1.45678i	−0.878953	−	0.476908i	$-0.841757\pi$
$317$	−12.0947	−	25.9372i	−0.679306	−	1.45678i	0.199647	−	0.979868i	$-0.436020\pi$
$318$	−6.15285	−	2.23946i	−0.345035	−	0.125582i
$319$	−11.7099	+	3.13765i	−0.655628	+	0.175675i
$320$	−3.33516	+	11.8351i	−0.186441	+	0.661604i
$321$	−3.65142	−	4.35159i	−0.203802	−	0.242882i
$322$	0.141164	+	0.0378248i	0.00786677	+	0.00210790i
$323$	8.76920	+	32.7271i	0.487931	+	1.82099i
$324$	1.34285	+	7.61570i	0.0746029	+	0.423094i
$325$	−4.07654	−	12.1664i	−0.226126	−	0.674873i
$326$	−0.209701	−	0.576150i	−0.0116143	−	0.0319100i
$327$	34.3701			1.90067
$328$	0.779865	+	2.14266i	0.0430608	+	0.118309i
$329$	0.138683	+	0.0244535i	0.00764584	+	0.00134817i
$330$	−0.0540189	+	4.19407i	−0.00297364	+	0.230876i
$331$	0.307643	−	3.51638i	0.0169096	−	0.193278i	−0.983041	−	0.183384i	$-0.941295\pi$
$331$	0.307643	−	3.51638i	0.0169096	−	0.193278i	0.999951	−	0.00989417i	$-0.00314946\pi$
$332$	−7.89562	−	7.89562i	−0.433328	−	0.433328i
$333$	−26.0668	−	20.1515i	−1.42845	−	1.10429i
$334$			0.448436i			0.0245373i
$335$	−1.32835	−	0.251906i	−0.0725758	−	0.0137631i
$336$	−0.634645	+	0.756340i	−0.0346227	+	0.0412618i
$337$	−15.2035	+	10.6456i	−0.828185	+	0.579901i	−0.908985	−	0.416829i	$-0.863141\pi$
$337$	−15.2035	+	10.6456i	−0.828185	+	0.579901i	0.0807998	+	0.996730i	$0.474253\pi$
$338$	1.99107	−	0.724689i	0.108300	−	0.0394179i
$339$	−40.5817	−	40.5817i	−2.20410	−	2.20410i
$340$	4.85927	+	19.1165i	0.263531	+	1.03674i
$341$	18.9958	+	5.08991i	1.02868	+	0.275634i
$342$	−10.6450	−	7.45369i	−0.575614	−	0.403050i
$343$	1.36984	−	0.367047i	0.0739644	−	0.0198187i
$344$	1.73267	+	3.00108i	0.0934194	+	0.161807i
$345$	5.27503	−	27.8164i	0.283998	−	1.49758i
$346$	2.27988	+	3.25600i	0.122567	+	0.175044i
$347$	11.4460	−	19.8251i	0.614454	−	1.06427i	−0.376026	−	0.926609i	$-0.622710\pi$
$347$	11.4460	−	19.8251i	0.614454	−	1.06427i	0.990480	−	0.137657i	$-0.0439571\pi$
$348$	11.6204	−	31.9267i	0.622917	−	1.71145i
$349$	7.51453	−	20.6460i	0.402244	−	1.10516i	−0.558931	−	0.829214i	$-0.688788\pi$
$349$	7.51453	−	20.6460i	0.402244	−	1.10516i	0.961175	−	0.275941i	$-0.0889894\pi$
$350$	−0.115302	−	0.121400i	−0.00616315	−	0.00648912i
$351$	−1.56807	−	17.9232i	−0.0836976	−	0.956667i
$352$	−4.62947	+	5.51718i	−0.246751	+	0.294067i
$353$	−27.8911	+	4.91796i	−1.48450	+	0.261757i	−0.856373	−	0.516357i	$-0.827288\pi$
$353$	−27.8911	+	4.91796i	−1.48450	+	0.261757i	−0.628123	+	0.778114i	$0.716177\pi$
$354$	7.02509	+	2.55692i	0.373379	+	0.135899i
$355$	−7.82929	−	3.77437i	−0.415536	−	0.200323i
$356$	3.06345	+	11.4329i	0.162362	+	0.605944i
$357$	−0.238237	+	1.35111i	−0.0126089	+	0.0715084i
$358$	−0.511478	+	5.84622i	−0.0270325	+	0.308982i
$359$	29.7418	−	17.1715i	1.56971	−	0.906275i	0.573513	−	0.819196i	$-0.305580\pi$
$359$	29.7418	−	17.1715i	1.56971	−	0.906275i	0.996201	−	0.0870790i	$-0.0277533\pi$
$360$	−12.6357	−	9.09234i	−0.665958	−	0.479208i
$361$	−33.2367	+	5.86054i	−1.74930	+	0.308449i
$362$	−2.09070	−	3.62120i	−0.109885	−	0.190326i
$363$	−8.78934	+	18.8488i	−0.461321	+	0.989306i
$364$	0.347828	−	0.347828i	0.0182312	−	0.0182312i
$365$	0.864546	−	1.45387i	0.0452524	−	0.0760990i
$366$	−1.56213	+	8.85925i	−0.0816536	+	0.463081i
$367$	4.00229	−	0.350155i	0.208918	−	0.0182780i	0.0177837	−	0.999842i	$-0.494339\pi$
$367$	4.00229	−	0.350155i	0.208918	−	0.0182780i	0.191134	+	0.981564i	$0.438783\pi$
$368$	11.2241	−	9.41814i	0.585097	−	0.490954i
$369$	9.60951			0.500251
$370$	4.46356	−	0.512942i	0.232050	−	0.0266666i
$371$	−0.692619			−0.0359590
$372$	−42.2209	+	35.4275i	−2.18905	+	1.83683i
$373$	15.8261	−	1.38460i	0.819445	−	0.0716921i	0.330279	−	0.943883i	$-0.392857\pi$
$373$	15.8261	−	1.38460i	0.819445	−	0.0716921i	0.489165	+	0.872191i	$0.337302\pi$
$374$	−0.523773	+	2.97047i	−0.0270837	+	0.153599i
$375$	−21.7935	+	24.0233i	−1.12541	+	1.24056i
$376$	−1.26250	+	1.26250i	−0.0651087	+	0.0651087i
$377$	−6.71710	+	14.4049i	−0.345948	+	0.741888i
$378$	−0.117383	−	0.203313i	−0.00603751	−	0.0104573i
$379$	−28.9230	+	5.09991i	−1.48568	+	0.261965i	−0.856844	−	0.515576i	$-0.827578\pi$
$379$	−28.9230	+	5.09991i	−1.48568	+	0.261965i	−0.628833	+	0.777541i	$0.716467\pi$
$380$	−30.3082	+	4.94256i	−1.55478	+	0.253548i
$381$	−43.2350	+	24.9617i	−2.21499	+	1.27883i
$382$	0.0110233	−	0.125997i	0.000564002	−	0.00644658i
$383$	4.26806	−	24.2054i	0.218088	−	1.23684i	−0.657379	−	0.753560i	$-0.728335\pi$
$383$	4.26806	−	24.2054i	0.218088	−	1.23684i	0.875467	−	0.483278i	$-0.160554\pi$
$384$	−6.88959	−	25.7123i	−0.351583	−	1.31213i
$385$	0.146367	+	0.418848i	0.00745957	+	0.0213465i
$386$	−0.387285	−	0.140960i	−0.0197123	−	0.00717468i
$387$	14.3824	−	2.53600i	0.731098	−	0.128912i
$388$	−17.7922	+	21.2039i	−0.903262	+	1.07647i
$389$	−1.30480	−	14.9139i	−0.0661558	−	0.756165i	−0.954738	−	0.297448i	$-0.903865\pi$
$389$	−1.30480	−	14.9139i	−0.0661558	−	0.756165i	0.888582	−	0.458717i	$-0.151691\pi$
$390$	4.16673	+	3.58875i	0.210990	+	0.181723i
$391$	6.96347	−	19.1320i	0.352158	−	0.967546i
$392$	−3.07259	+	8.44187i	−0.155189	+	0.426379i
$393$	27.0485	−	46.8494i	1.36442	−	2.36324i
$394$	−3.55607	−	5.07860i	−0.179152	−	0.255856i
$395$	5.91939	+	1.12254i	0.297837	+	0.0564810i
$396$	10.0239	+	17.3618i	0.503718	+	0.872464i
$397$	−22.8691	+	6.12775i	−1.14777	+	0.307543i	−0.782069	−	0.623192i	$-0.785836\pi$
$397$	−22.8691	+	6.12775i	−1.14777	+	0.307543i	−0.365696	+	0.930734i	$0.619169\pi$
$398$	0.540977	+	0.378796i	0.0271167	+	0.0189873i
$399$	−2.06318	−	0.552828i	−0.103288	−	0.0276760i
$400$	−16.6006	+	2.48814i	−0.830031	+	0.124407i
$401$	−1.82258	−	1.82258i	−0.0910155	−	0.0910155i	0.660133	−	0.751149i	$-0.270500\pi$
$401$	−1.82258	−	1.82258i	−0.0910155	−	0.0910155i	−0.751149	+	0.660133i	$0.770500\pi$
$402$	0.544502	−	0.198183i	0.0271573	−	0.00988445i
$403$	21.1204	−	14.7887i	1.05208	−	0.736677i
$404$	−7.80442	+	9.30094i	−0.388284	+	0.462739i
$405$	−7.55799	+	5.14838i	−0.375559	+	0.255825i
$406$			0.207394i			0.0102928i
$407$	−11.3422	−	3.62118i	−0.562212	−	0.179495i
$408$	−12.2999	−	12.2999i	−0.608935	−	0.608935i
$409$	0.220894	−	2.52483i	0.0109225	−	0.124845i	−0.988776	−	0.149407i	$-0.952264\pi$
$409$	0.220894	−	2.52483i	0.0109225	−	0.124845i	0.999698	+	0.0245620i	$0.00781910\pi$
$410$	−0.938450	+	0.914584i	−0.0463468	+	0.0451681i
$411$	−21.2759	−	3.75151i	−1.04946	−	0.185048i
$412$	3.30306	+	9.07508i	0.162730	+	0.447097i
$413$	0.790806			0.0389130
$414$	2.67080	+	7.33797i	0.131263	+	0.360642i
$415$	4.67563	−	12.3490i	0.229517	−	0.606187i
$416$	1.63968	+	9.29907i	0.0803918	+	0.455925i
$417$	−13.6935	−	51.1050i	−0.670576	−	2.50262i
$418$	−4.53598	−	1.21541i	−0.221862	−	0.0594477i
$419$	2.76444	+	3.29453i	0.135052	+	0.160948i	0.829332	−	0.558757i	$-0.188721\pi$
$419$	2.76444	+	3.29453i	0.135052	+	0.160948i	−0.694280	+	0.719705i	$0.744277\pi$
$420$	−1.19685	−	0.337275i	−0.0584005	−	0.0164574i
$421$	8.79491	−	2.35659i	0.428638	−	0.114853i	−0.0380489	−	0.999276i	$-0.512114\pi$
$421$	8.79491	−	2.35659i	0.428638	−	0.114853i	0.466687	+	0.884423i	$0.345448\pi$
$422$	−0.882526	−	0.321213i	−0.0429607	−	0.0156364i
$423$	3.18002	+	6.81957i	0.154618	+	0.331579i
$424$	5.03689	−	7.19342i	0.244613	−	0.349343i
$425$	−18.2483	+	14.5280i	−0.885175	+	0.704709i
$426$	3.71083	−	0.324656i	0.179790	−	0.0157296i
$427$	0.165242	+	0.937132i	0.00799661	+	0.0453510i
$428$	3.35557	−	1.56473i	0.162198	−	0.0756340i
$429$	−6.15869	−	13.2073i	−0.297344	−	0.637657i
$430$	−1.16320	+	1.61651i	−0.0560945	+	0.0779548i
$431$	−1.03542	+	0.725011i	−0.0498746	+	0.0349225i	−0.598248	−	0.801311i	$-0.704136\pi$
$431$	−1.03542	+	0.725011i	−0.0498746	+	0.0349225i	0.548373	+	0.836234i	$0.315247\pi$
$432$	−23.4474	−	2.05138i	−1.12811	−	0.0986972i
$433$	−0.905545	+	3.37954i	−0.0435177	+	0.162410i	−0.984265	−	0.176698i	$-0.943459\pi$
$433$	−0.905545	+	3.37954i	−0.0435177	+	0.162410i	0.940747	+	0.339108i	$0.110125\pi$
$434$	0.168218	−	0.291362i	0.00807471	−	0.0139858i
$435$	40.0669	−	2.98598i	1.92106	−	0.143167i
$436$	−5.79794	+	21.6382i	−0.277671	+	1.03628i
$437$	28.7279	+	13.3960i	1.37424	+	0.640820i
$438$			0.724937i			0.0346388i
$439$	−4.69096	+	10.0598i	−0.223887	+	0.480128i	−0.985879	−	0.167459i	$-0.946444\pi$
$439$	−4.69096	+	10.0598i	−0.223887	+	0.480128i	0.761992	+	0.647587i	$0.224222\pi$
$440$	−5.41449	−	1.52581i	−0.258126	−	0.0727403i
$441$	29.0028	+	24.3363i	1.38109	+	1.15887i
$442$	2.54194	+	3.02937i	0.120908	+	0.144092i
$443$	−17.5241	+	17.5241i	−0.832593	+	0.832593i	−0.987871	−	0.155278i	$-0.950373\pi$
$443$	−17.5241	+	17.5241i	−0.832593	+	0.832593i	0.155278	+	0.987871i	$0.450373\pi$
$444$	26.5459	−	20.2178i	1.25981	−	0.959493i
$445$	−10.8373	+	8.85824i	−0.513737	+	0.419921i
$446$	−8.64005	−	0.755906i	−0.409118	−	0.0357932i
$447$	5.84029	+	66.7548i	0.276236	+	3.15739i
$448$	−0.319735	−	0.456628i	−0.0151060	−	0.0215737i
$449$	31.0163	+	14.4631i	1.46375	+	0.682557i	0.981144	−	0.193280i	$-0.0619127\pi$
$449$	31.0163	+	14.4631i	1.46375	+	0.682557i	0.482606	+	0.875838i	$0.339690\pi$
$450$	1.77990	−	8.76740i	0.0839052	−	0.413299i
$451$	3.26313	−	1.18768i	0.153655	−	0.0559257i
$452$	32.3946	−	18.7030i	1.52371	−	0.879717i
$453$	5.10693	−	7.29345i	0.239944	−	0.342676i
$454$	1.48954	+	0.859989i	0.0699078	+	0.0403613i
$455$	0.544013	+	0.205977i	0.0255037	+	0.00965634i
$456$	20.7455	−	17.4076i	0.971498	−	0.815183i
$457$	32.8288	+	5.78860i	1.53566	+	0.270779i	0.876567	−	0.481279i	$-0.159828\pi$
$457$	32.8288	+	5.78860i	1.53566	+	0.270779i	0.659097	+	0.752058i	$0.270939\pi$
$458$	0.964027	+	0.556581i	0.0450460	+	0.0260073i
$459$	−29.6417	+	13.8221i	−1.38355	+	0.645162i
$460$	16.6224	+	8.01335i	0.775021	+	0.373624i
$461$	10.6516	+	7.45832i	0.496094	+	0.347369i	0.794695	−	0.607009i	$-0.207631\pi$
$461$	10.6516	+	7.45832i	0.496094	+	0.347369i	−0.298601	+	0.954378i	$0.596520\pi$
$462$	−0.145666	−	0.122228i	−0.00677698	−	0.00568656i
$463$	23.2956	+	19.5473i	1.08264	+	0.908442i	0.996137	−	0.0878100i	$-0.0279868\pi$
$463$	23.2956	+	19.5473i	1.08264	+	0.908442i	0.0865014	+	0.996252i	$0.472431\pi$
$464$	17.0325	+	11.9263i	0.790713	+	0.553663i
$465$	−58.7107	−	28.3034i	−2.72264	−	1.31254i
$466$	4.71446	−	2.19839i	0.218393	−	0.101838i
$467$	3.97301	+	2.29382i	0.183849	+	0.106145i	0.589100	−	0.808060i	$-0.299482\pi$
$467$	3.97301	+	2.29382i	0.183849	+	0.106145i	−0.405251	+	0.914206i	$0.632816\pi$
$468$	25.8846	+	4.56415i	1.19651	+	0.210978i
$469$	0.0469539	−	0.0393990i	0.00216813	−	0.00181928i
$470$	−0.959607	−	0.363331i	−0.0442634	−	0.0167592i
$471$	48.0943	+	27.7673i	2.21607	+	1.27945i
$472$	−5.75092	+	8.21316i	−0.264708	+	0.378042i
$473$	4.57043	−	2.63874i	0.210149	−	0.121329i
$474$	−2.42640	+	0.883138i	−0.111448	+	0.0405639i
$475$	−20.0560	−	30.2736i	−0.920234	−	1.38905i
$476$	−0.810424	−	0.377907i	−0.0371457	−	0.0173213i
$477$	−21.2273	−	30.3158i	−0.971933	−	1.38806i
$478$	0.291701	+	3.33416i	0.0133421	+	0.152501i
$479$	−25.0861	−	2.19475i	−1.14621	−	0.100281i	−0.501818	−	0.864973i	$-0.667335\pi$
$479$	−25.0861	−	2.19475i	−1.14621	−	0.100281i	−0.644396	+	0.764692i	$0.722891\pi$
$480$	18.4812	−	15.1063i	0.843546	−	0.689503i
$481$	−13.1954	+	8.33966i	−0.601657	+	0.380256i
$482$	−0.225640	+	0.225640i	−0.0102776	+	0.0102776i
$483$	0.825034	+	0.983237i	0.0375403	+	0.0447388i
$484$	−10.3839	−	8.71309i	−0.471994	−	0.396050i
$485$	−31.5057	−	8.87835i	−1.43060	−	0.403145i
$486$	−1.27985	+	2.74464i	−0.0580550	+	0.124499i
$487$			2.34534i			0.106278i	0.998587	+	0.0531388i	$0.0169226\pi$
$487$			2.34534i			0.106278i	−0.998587	+	0.0531388i	$0.983077\pi$
$488$	−10.9346	−	5.09887i	−0.494984	−	0.230815i
$489$	1.39370	−	5.20136i	0.0630253	−	0.235214i
$490$	−5.14858	+	0.383697i	−0.232589	+	0.0173337i
$491$	19.8792	−	34.4318i	0.897137	−	1.55389i	0.0659990	−	0.997820i	$-0.478977\pi$
$491$	19.8792	−	34.4318i	0.897137	−	1.55389i	0.831138	−	0.556067i	$-0.187690\pi$
$492$	−2.51886	+	9.40051i	−0.113559	+	0.423808i
$493$	28.7829	+	2.51818i	1.29632	+	0.113413i
$494$	−5.04332	+	3.53137i	−0.226910	+	0.158884i
$495$	−13.8470	+	19.2433i	−0.622377	+	0.864921i
$496$	−14.2550	−	30.5699i	−0.640068	−	1.37263i
$497$	0.357114	−	0.166525i	0.0160187	−	0.00746966i
$498$	0.982697	+	5.57315i	0.0440357	+	0.249739i
$499$	−0.962102	+	0.0841730i	−0.0430696	+	0.00376810i	−0.108670	−	0.994078i	$-0.534659\pi$
$499$	−0.962102	+	0.0841730i	−0.0430696	+	0.00376810i	0.0656006	+	0.997846i	$0.479104\pi$
$500$	−11.4478	−	17.7729i	−0.511963	−	0.794830i
$501$	−2.25900	+	3.22618i	−0.100925	+	0.144135i
$502$	0.543326	+	1.16517i	0.0242498	+	0.0520040i
$503$	19.5117	+	7.10167i	0.869982	+	0.316648i	0.738160	−	0.674626i	$-0.235695\pi$
$503$	19.5117	+	7.10167i	0.869982	+	0.316648i	0.131822	+	0.991273i	$0.457917\pi$
$504$	0.681679	−	0.182655i	0.0303644	−	0.00813612i
$505$	−13.8197	−	3.89442i	−0.614970	−	0.173299i
$506$	1.81386	+	2.16168i	0.0806361	+	0.0960984i
$507$	17.9749	+	4.81637i	0.798294	+	0.213902i
$508$	−8.42165	−	31.4300i	−0.373650	−	1.39448i
$509$	−2.09443	−	11.8781i	−0.0928338	−	0.526487i	−0.995390	−	0.0959138i	$-0.969423\pi$
$509$	−2.09443	−	11.8781i	−0.0928338	−	0.526487i	0.902556	−	0.430573i	$-0.141688\pi$
$510$	3.53974	−	9.34893i	0.156742	−	0.413978i
$511$	0.0262274	+	0.0720593i	0.00116023	+	0.00318771i
$512$	20.9827			0.927313
$513$	−17.4154	−	47.8484i	−0.768908	−	2.11256i
$514$	3.50654	+	0.618298i	0.154667	+	0.0272720i
$515$	−8.17884	+	7.97084i	−0.360403	+	0.351237i
$516$	−1.28909	+	14.7343i	−0.0567489	+	0.648643i
$517$	1.92271	+	1.92271i	0.0845606	+	0.0845606i
$518$	−0.110059	+	0.171392i	−0.00483573	+	0.00753053i
$519$			34.9095i			1.53236i
$520$	−6.09542	+	4.15211i	−0.267302	+	0.182082i
$521$	9.73599	−	11.6029i	0.426541	−	0.508332i	−0.509380	−	0.860542i	$-0.670125\pi$
$521$	9.73599	−	11.6029i	0.426541	−	0.508332i	0.935921	+	0.352210i	$0.114570\pi$
$522$	−9.07760	+	6.35620i	−0.397316	+	0.278203i
$523$	22.0510	−	8.02589i	0.964221	−	0.350948i	0.188535	−	0.982067i	$-0.439626\pi$
$523$	22.0510	−	8.02589i	0.964221	−	0.350948i	0.775686	+	0.631119i	$0.217404\pi$
$524$	24.9319	+	24.9319i	1.08915	+	1.08915i
$525$	−0.217962	−	1.45422i	−0.00951264	−	0.0634675i
$526$	−6.65813	−	1.78404i	−0.290308	−	0.0777878i
$527$	−38.3937	−	26.8835i	−1.67246	−	1.17107i
$528$	−18.4147	+	4.93419i	−0.801395	+	0.214733i
$529$	1.97624	+	3.42295i	0.0859235	+	0.148824i
$530$	4.95833	+	0.940286i	0.215376	+	0.0408434i
$531$	24.2365	+	34.6134i	1.05178	+	1.50209i
$532$	0.696083	−	1.20565i	0.0301790	−	0.0522716i
$533$	1.55713	−	4.27818i	0.0674467	−	0.185308i
$534$	2.05170	−	5.63700i	0.0887857	−	0.243937i
$535$	3.31749	+	2.85731i	0.143428	+	0.123532i
$536$	0.0677314	+	0.774173i	0.00292555	+	0.0334392i
$537$	−33.1300	+	39.4829i	−1.42967	+	1.70381i
$538$	6.13331	−	1.08147i	0.264426	−	0.0466254i
$539$	12.8564	+	4.67935i	0.553764	+	0.201554i
$540$	−9.77892	−	27.9836i	−0.420818	−	1.20422i
$541$	1.31659	+	4.91358i	0.0566046	+	0.211251i	0.988436	−	0.151641i	$-0.0484559\pi$
$541$	1.31659	+	4.91358i	0.0566046	+	0.211251i	−0.931831	+	0.362893i	$0.881789\pi$
$542$	0.812070	−	4.60548i	0.0348814	−	0.197822i
$543$	3.20067	−	36.5838i	0.137354	−	1.56996i
$544$	14.8654	−	8.58252i	0.637347	−	0.367972i
$545$	−26.1456	+	4.26373i	−1.11995	+	0.182638i
$546$	−0.245516	+	0.0432911i	−0.0105071	+	0.00185269i
$547$	2.61135	+	4.52299i	0.111653	+	0.193389i	0.916437	−	0.400179i	$-0.131052\pi$
$547$	2.61135	+	4.52299i	0.111653	+	0.193389i	−0.804784	+	0.593568i	$0.797719\pi$
$548$	5.95088	−	12.7617i	0.254209	−	0.545153i
$549$	−35.9537	+	35.9537i	−1.53447	+	1.53447i
$550$	−0.479197	−	3.19716i	−0.0204330	−	0.136327i
$551$	−7.81114	+	44.2992i	−0.332766	+	1.88721i
$552$	−16.2116	+	1.41833i	−0.690010	+	0.0603680i
$553$	−0.209235	+	0.175569i	−0.00889759	+	0.00746596i
$554$	−9.24360			−0.392723
$555$	34.6961	+	18.7949i	1.47277	+	0.797800i
$556$	34.4839			1.46244
$557$	5.60274	−	4.70126i	0.237396	−	0.199199i	−0.516326	−	0.856392i	$-0.672701\pi$
$557$	5.60274	−	4.70126i	0.237396	−	0.199199i	0.753722	+	0.657193i	$0.228256\pi$
$558$	17.9084	−	1.56678i	0.758121	−	0.0663270i
$559$	1.20149	−	6.81401i	0.0508178	−	0.288202i
$560$	0.388952	−	0.654084i	0.0164362	−	0.0276401i
$561$	−18.7319	+	18.7319i	−0.790861	+	0.790861i
$562$	2.74192	−	5.88006i	0.115661	−	0.248035i
$563$	10.0337	+	17.3788i	0.422869	+	0.732431i	0.996219	−	0.0868799i	$-0.0276896\pi$
$563$	10.0337	+	17.3788i	0.422869	+	0.732431i	−0.573350	+	0.819311i	$0.694356\pi$
$564$	−7.50480	+	1.32330i	−0.316009	+	0.0557209i
$565$	35.9051	+	25.8365i	1.51054	+	1.08695i
$566$	−3.96333	+	2.28823i	−0.166591	+	0.0961815i
$567$	0.0361332	−	0.413004i	0.00151745	−	0.0173445i
$568$	−0.867516	+	4.91993i	−0.0364001	+	0.206435i
$569$	1.55423	+	5.80048i	0.0651569	+	0.243169i	0.990822	−	0.135176i	$-0.0431600\pi$
$569$	1.55423	+	5.80048i	0.0651569	+	0.243169i	−0.925665	+	0.378345i	$0.876493\pi$
$570$	14.0194	+	6.75853i	0.587210	+	0.283084i
$571$	−36.0810	−	13.1324i	−1.50994	−	0.549574i	−0.551330	−	0.834287i	$-0.685879\pi$
$571$	−36.0810	−	13.1324i	−1.50994	−	0.549574i	−0.958613	+	0.284713i	$0.908102\pi$
$572$	9.35380	−	1.64933i	0.391102	−	0.0689618i
$573$	0.714015	−	0.850930i	0.0298284	−	0.0355481i
$574$	−0.00517764	−	0.0591807i	−0.000216111	−	0.00247016i
$575$	−0.562028	+	21.8145i	−0.0234382	+	0.909727i
$576$	10.1873	−	27.9894i	0.424471	−	1.16623i
$577$	2.44703	−	6.72316i	0.101871	−	0.279889i	−0.878278	−	0.478150i	$-0.841307\pi$
$577$	2.44703	−	6.72316i	0.101871	−	0.279889i	0.980149	+	0.198262i	$0.0635296\pi$
$578$	0.786599	−	1.36243i	0.0327182	−	0.0566696i
$579$	−2.07615	−	2.96505i	−0.0862819	−	0.123223i
$580$	−4.87907	+	25.7284i	−0.202592	+	1.06831i
$581$	0.299311	+	0.518422i	0.0124175	+	0.0215078i
$582$	13.5505	−	3.63083i	0.561685	−	0.150503i
$583$	−10.9551	−	7.67084i	−0.453713	−	0.317694i
$584$	−0.939126	−	0.251638i	−0.0388613	−	0.0104129i
$585$	7.65730	+	30.1241i	0.316590	+	1.24548i
$586$	0.118350	+	0.118350i	0.00488900	+	0.00488900i
$587$	27.2458	−	9.91664i	1.12455	−	0.409304i	0.288241	−	0.957558i	$-0.406930\pi$
$587$	27.2458	−	9.91664i	1.12455	−	0.409304i	0.836312	+	0.548254i	$0.184707\pi$
$588$	−31.4093	+	21.9930i	−1.29530	+	0.906976i
$589$	46.9048	−	55.8989i	1.93268	−	2.30328i
$590$	−5.66123	−	1.07358i	−0.233069	−	0.0441986i
$591$		−	54.4506i		−	2.23980i
$592$	7.74676	+	18.8947i	0.318390	+	0.776567i
$593$	23.4877	+	23.4877i	0.964525	+	0.964525i	0.999392	−	0.0348666i	$-0.0111006\pi$
$593$	23.4877	+	23.4877i	0.964525	+	0.964525i	−0.0348666	+	0.999392i	$0.511101\pi$
$594$	0.395081	−	4.51580i	0.0162104	−	0.185285i
$595$	0.0136186	−	1.05735i	0.000558306	−	0.0433473i
$596$	−43.0117	−	7.58412i	−1.76183	−	0.310658i
$597$	1.98376	+	5.45034i	0.0811899	+	0.223067i
$598$	3.69966			0.151290
$599$	−8.71614	−	23.9474i	−0.356132	−	0.978464i	−0.980359	−	0.197221i	$-0.936808\pi$
$599$	−8.71614	−	23.9474i	−0.356132	−	0.978464i	0.624227	−	0.781243i	$-0.285414\pi$
$600$	16.6884	+	8.31172i	0.681299	+	0.339325i
$601$	2.09852	+	11.9013i	0.0856005	+	0.485465i	0.997225	+	0.0744415i	$0.0237174\pi$
$601$	2.09852	+	11.9013i	0.0856005	+	0.485465i	−0.911625	+	0.411023i	$0.865171\pi$
$602$	−0.0233674	−	0.0872085i	−0.000952386	−	0.00355435i
$603$	3.16352	+	0.847664i	0.128829	+	0.0345195i
$604$	3.73020	+	4.44548i	0.151780	+	0.180884i
$605$	4.34785	−	15.4288i	0.176765	−	0.627269i
$606$	5.94381	−	1.59264i	0.241451	−	0.0646965i
$607$	−24.2152	−	8.81360i	−0.982863	−	0.357733i	−0.199910	−	0.979814i	$-0.564065\pi$
$607$	−24.2152	−	8.81360i	−0.982863	−	0.357733i	−0.782953	+	0.622081i	$0.786287\pi$
$608$	11.2940	+	24.2200i	0.458032	+	0.982252i
$609$	−1.04475	+	1.49205i	−0.0423353	+	0.0604611i
$610$	0.0892970	−	6.93308i	0.00361553	−	0.280712i
$611$	3.55138	−	0.310705i	0.143673	−	0.0125698i
$612$	−8.29691	−	47.0541i	−0.335383	−	1.90205i
$613$	−0.871736	+	0.406497i	−0.0352091	+	0.0164183i	−0.440143	−	0.897928i	$-0.645072\pi$
$613$	−0.871736	+	0.406497i	−0.0352091	+	0.0164183i	0.404934	+	0.914346i	$0.367295\pi$
$614$	1.07879	+	2.31347i	0.0435364	+	0.0933641i
$615$	−11.3587	+	1.85234i	−0.458027	+	0.0746935i
$616$	0.208905	−	0.146277i	0.00841700	−	0.00589365i
$617$	−12.3397	−	1.07959i	−0.496779	−	0.0434625i	−0.163986	−	0.986463i	$-0.552435\pi$
$617$	−12.3397	−	1.07959i	−0.496779	−	0.0434625i	−0.332792	+	0.943000i	$0.607991\pi$
$618$	1.26680	−	4.72777i	0.0509583	−	0.190179i
$619$	3.30679	−	5.72754i	0.132911	−	0.230209i	−0.791886	−	0.610669i	$-0.790901\pi$
$619$	3.30679	−	5.72754i	0.132911	−	0.230209i	0.924798	+	0.380459i	$0.124234\pi$
$620$	27.7228	−	32.1876i	1.11338	−	1.29269i
$621$	−7.91931	+	29.5553i	−0.317791	+	1.18601i
$622$	1.26459	+	0.589689i	0.0507055	+	0.0236444i
$623$		−	0.634550i		−	0.0254227i
$624$	−10.5631	+	22.6527i	−0.422864	+	0.906835i
$625$	13.5983	−	20.9782i	0.543932	−	0.839130i
$626$	1.01667	+	0.853089i	0.0406344	+	0.0340963i
$627$	−26.5105	−	31.5940i	−1.05873	−	1.26174i
$628$	−25.5944	+	25.5944i	−1.02133	+	1.02133i
$629$	22.4500	+	17.3554i	0.895140	+	0.692006i
$630$	0.256677	+	0.314021i	0.0102262	+	0.0125109i
$631$	−17.1248	−	1.49822i	−0.681726	−	0.0596433i	−0.258968	−	0.965886i	$-0.583382\pi$
$631$	−17.1248	−	1.49822i	−0.681726	−	0.0596433i	−0.422758	+	0.906243i	$0.638938\pi$
$632$	−0.301823	−	3.44986i	−0.0120059	−	0.137228i
$633$	−4.73104	−	6.75662i	−0.188042	−	0.268552i
$634$	−8.56776	−	3.99521i	−0.340269	−	0.158670i
$635$	29.7925	−	24.3520i	1.18228	−	0.966380i
$636$	35.2206	−	12.8192i	1.39659	−	0.508316i
$637$	15.5342	−	8.96867i	0.615487	−	0.355352i
$638$	−2.29691	+	3.28033i	−0.0909357	+	0.129870i
$639$	18.2335	+	10.5271i	0.721308	+	0.416447i
$640$	8.43066	+	18.7048i	0.333251	+	0.739374i
$641$	−20.4391	+	17.1504i	−0.807296	+	0.677401i	−0.949961	−	0.312370i	$-0.898877\pi$
$641$	−20.4391	+	17.1504i	−0.807296	+	0.677401i	0.142665	+	0.989771i	$0.454433\pi$
$642$	−1.84795	−	0.325844i	−0.0729328	−	0.0128600i
$643$	6.80050	+	3.92627i	0.268186	+	0.154837i	0.628063	−	0.778163i	$-0.283848\pi$
$643$	6.80050	+	3.92627i	0.268186	+	0.154837i	−0.359877	+	0.933000i	$0.617181\pi$
$644$	−0.758187	+	0.353549i	−0.0298768	+	0.0139318i
$645$	−16.5115	+	5.76999i	−0.650141	+	0.227193i
$646$	9.16797	+	6.41948i	0.360709	+	0.252571i
$647$	14.1199	+	11.8480i	0.555109	+	0.465792i	0.876667	−	0.481098i	$-0.159762\pi$
$647$	14.1199	+	11.8480i	0.555109	+	0.465792i	−0.321558	+	0.946890i	$0.604206\pi$
$648$	4.02662	+	3.37873i	0.158180	+	0.132729i
$649$	12.5081	+	8.75826i	0.490985	+	0.343792i
$650$	−3.61485	−	2.21309i	−0.141786	−	0.0868045i
$651$	2.67794	−	1.24874i	0.104957	−	0.0489422i
$652$	3.03949	+	1.75485i	0.119036	+	0.0687252i
$653$	−6.81243	−	1.20121i	−0.266591	−	0.0470072i	0.0387548	−	0.999249i	$-0.487661\pi$
$653$	−6.81243	−	1.20121i	−0.266591	−	0.0470072i	−0.305346	+	0.952242i	$0.598772\pi$
$654$	8.69720	−	7.29781i	0.340087	−	0.285367i
$655$	−14.7641	+	38.9941i	−0.576883	+	1.52363i
$656$	−5.15803	−	2.97799i	−0.201387	−	0.116271i
$657$	−2.35020	+	3.35643i	−0.0916901	+	0.130947i
$658$	0.0402853	−	0.0232587i	0.00157049	−	0.000906720i
$659$	−1.15352	+	0.419847i	−0.0449348	+	0.0163549i	−0.364390	−	0.931247i	$-0.618722\pi$
$659$	−1.15352	+	0.419847i	−0.0449348	+	0.0163549i	0.319455	+	0.947601i	$0.396500\pi$
$660$	−15.1952	−	18.5899i	−0.591471	−	0.723612i
$661$	3.30512	+	1.54120i	0.128554	+	0.0599458i	0.485831	−	0.874053i	$-0.338517\pi$
$661$	3.30512	+	1.54120i	0.128554	+	0.0599458i	−0.357277	+	0.933998i	$0.616295\pi$
$662$	−0.668787	−	0.955126i	−0.0259931	−	0.0371220i
$663$	3.02703	+	34.5991i	0.117560	+	1.34372i
$664$	−7.56090	−	0.661493i	−0.293420	−	0.0256709i
$665$	1.63806	+	0.164595i	0.0635212	+	0.00638272i
$666$	−10.8749	+	0.435536i	−0.421393	+	0.0168767i
$667$	19.1135	−	19.1135i	0.740076	−	0.740076i
$668$	−1.65002	−	1.96641i	−0.0638411	−	0.0760828i
$669$	−58.3512	−	48.9624i	−2.25599	−	1.89300i
$670$	−0.389622	+	0.218306i	−0.0150524	+	0.00843391i
$671$	−7.76523	+	16.6526i	−0.299773	+	0.642866i
$672$			1.08212i			0.0417437i
$673$	−30.7784	−	14.3522i	−1.18642	−	0.553237i	−0.273698	−	0.961816i	$-0.588247\pi$
$673$	−30.7784	−	14.3522i	−1.18642	−	0.553237i	−0.912723	+	0.408579i	$0.866025\pi$
$674$	−1.58679	+	5.92197i	−0.0611208	+	0.228106i
$675$	25.4174	−	24.1406i	0.978315	−	0.929170i
$676$	−6.06443	+	10.5039i	−0.233247	+	0.403996i
$677$	−2.90830	+	10.8539i	−0.111775	+	0.417151i	−0.999025	−	0.0441377i	$-0.985946\pi$
$677$	−2.90830	+	10.8539i	−0.111775	+	0.417151i	0.887250	+	0.461288i	$0.152613\pi$
$678$	−18.8858	−	1.65229i	−0.725303	−	0.0634558i
$679$	1.21557	−	0.851149i	0.0466491	−	0.0326641i
$680$	10.8825	+	7.83076i	0.417323	+	0.300296i
$681$	6.38402	+	13.6906i	0.244636	+	0.524624i
$682$	5.88755	−	2.74541i	0.225446	−	0.105127i
$683$	−4.88006	−	27.6762i	−0.186730	−	1.05900i	−0.923712	−	0.383087i	$-0.874861\pi$
$683$	−4.88006	−	27.6762i	−0.186730	−	1.05900i	0.736982	−	0.675912i	$-0.236250\pi$
$684$	74.1045	−	6.48330i	2.83346	−	0.247895i
$685$	16.6501	+	0.214451i	0.636168	+	0.00819374i
$686$	0.268696	−	0.383738i	0.0102589	−	0.0146512i
$687$	4.13172	+	8.86049i	0.157635	+	0.338049i
$688$	−8.50585	−	3.09587i	−0.324282	−	0.118029i
$689$	−16.9363	+	4.53808i	−0.645223	+	0.172887i
$690$	−4.57144	−	8.15886i	−0.174032	−	0.310602i
$691$	20.4649	+	24.3892i	0.778523	+	0.927807i	0.998866	−	0.0476151i	$-0.0151621\pi$
$691$	20.4649	+	24.3892i	0.778523	+	0.927807i	−0.220343	+	0.975422i	$0.570718\pi$
$692$	−21.9778	−	5.88893i	−0.835470	−	0.223863i
$693$	−0.278172	−	1.03815i	−0.0105669	−	0.0394361i
$694$	−1.31310	−	7.44698i	−0.0498448	−	0.282684i
$695$	16.7565	+	37.1772i	0.635612	+	1.41021i
$696$	−7.89856	−	21.7011i	−0.299394	−	0.822579i
$697$	−8.27617			−0.313482
$698$	−2.48226	−	6.81994i	−0.0939548	−	0.258139i
$699$	44.9916	+	7.93323i	1.70174	+	0.300062i
$700$	0.952296	+	0.108094i	0.0359934	+	0.00408555i
$701$	2.57780	−	29.4644i	0.0973623	−	1.11286i	−0.777631	−	0.628721i	$-0.783579\pi$
$701$	2.57780	−	29.4644i	0.0973623	−	1.11286i	0.874993	−	0.484135i	$-0.160866\pi$
$702$	−4.20243	−	4.20243i	−0.158610	−	0.158610i
$703$	−29.9637	+	32.4639i	−1.13010	+	1.22440i
$704$		−	10.7635i		−	0.405666i
$705$	−5.07341	−	7.44793i	−0.191076	−	0.280505i
$706$	−6.01350	+	7.16661i	−0.226321	+	0.269719i
$707$	0.533199	−	0.373350i	0.0200530	−	0.0140413i
$708$	−40.2135	+	14.6365i	−1.51132	+	0.550074i
$709$	−14.3219	−	14.3219i	−0.537869	−	0.537869i	0.385034	−	0.922903i	$-0.374190\pi$
$709$	−14.3219	−	14.3219i	−0.537869	−	0.537869i	−0.922903	+	0.385034i	$0.874190\pi$
$710$	−2.78258	+	0.707310i	−0.104428	+	0.0265449i
$711$	−14.0972	−	3.77734i	−0.528688	−	0.141661i
$712$	6.59032	+	4.61459i	0.246983	+	0.172939i
$713$	−42.3549	+	11.3490i	−1.58620	+	0.425022i
$714$	0.226597	+	0.392478i	0.00848019	+	0.0146881i
$715$	6.32338	+	9.28291i	0.236481	+	0.347161i
$716$	−19.2683	−	27.5179i	−0.720089	−	1.02839i
$717$	−14.6972	+	25.4564i	−0.548879	+	0.950686i
$718$	3.88002	−	10.6603i	0.144801	−	0.397837i
$719$	−0.678470	+	1.86408i	−0.0253027	+	0.0695185i	−0.951701	−	0.307027i	$-0.900666\pi$
$719$	−0.678470	+	1.86408i	−0.0253027	+	0.0695185i	0.926398	+	0.376545i	$0.122888\pi$
$720$	40.5496	−	3.02196i	1.51120	−	0.112622i
$721$	−0.0451245	−	0.515776i	−0.00168053	−	0.0192085i
$722$	−7.16604	+	8.54016i	−0.266692	+	0.317832i
$723$	−2.75998	+	0.486659i	−0.102645	+	0.0180990i
$724$	22.4920	+	8.18641i	0.835907	+	0.304245i
$725$	−30.1088	+	7.24190i	−1.11821	+	0.268957i
$726$	1.77807	+	6.63585i	0.0659904	+	0.246280i
$727$	4.35110	−	24.6763i	0.161373	−	0.915194i	−0.791352	−	0.611361i	$-0.790622\pi$
$727$	4.35110	−	24.6763i	0.161373	−	0.915194i	0.952725	−	0.303833i	$-0.0982665\pi$
$728$	0.0291410	−	0.333083i	0.00108004	−	0.0123449i
$729$	−33.6591	+	19.4331i	−1.24663	+	0.719744i
$730$	−0.0899311	−	0.551465i	−0.00332850	−	0.0204106i
$731$	−12.3868	+	2.18413i	−0.458143	+	0.0807829i
$732$	−25.7475	−	44.5960i	−0.951657	−	1.64832i
$733$	1.68928	−	3.62267i	0.0623949	−	0.133806i	−0.872638	−	0.488368i	$-0.837592\pi$
$733$	1.68928	−	3.62267i	0.0623949	−	0.133806i	0.935032	+	0.354562i	$0.115370\pi$
$734$	0.938414	−	0.938414i	0.0346375	−	0.0346375i
$735$	−38.9732	−	23.1755i	−1.43755	−	0.854841i
$736$	2.78856	−	15.8147i	0.102788	−	0.582937i
$737$	1.17901	−	0.103150i	0.0434295	−	0.00379959i
$738$	2.43164	−	2.04039i	0.0895100	−	0.0751078i
$739$	−15.5384			−0.571590			−0.285795	−	0.958291i	$-0.592258\pi$
$739$	−15.5384			−0.571590			−0.285795	+	0.958291i	$0.592258\pi$
$740$	−17.6856	+	18.6729i	−0.650134	+	0.686430i
$741$	−54.0724			−1.98640
$742$	−0.175264	+	0.147064i	−0.00643415	+	0.00539890i
$743$	−1.24013	+	0.108497i	−0.0454959	+	0.00398038i	−0.109881	−	0.993945i	$-0.535047\pi$
$743$	−1.24013	+	0.108497i	−0.0454959	+	0.00398038i	0.0643851	+	0.997925i	$0.479491\pi$
$744$	−6.50537	+	36.8938i	−0.238498	+	1.35259i
$745$	−12.7239	−	50.0564i	−0.466169	−	1.83392i
$746$	3.71073	−	3.71073i	0.135860	−	0.135860i
$747$	−13.5180	+	28.9893i	−0.494596	+	1.06066i
$748$	−8.63303	−	14.9528i	−0.315655	−	0.546730i
$749$	−0.195476	+	0.0344677i	−0.00714255	+	0.00125942i
$750$	−0.413874	+	10.7064i	−0.0151125	+	0.390943i
$751$	−19.5393	+	11.2810i	−0.712999	+	0.411650i	−0.812170	−	0.583420i	$-0.801714\pi$
$751$	−19.5393	+	11.2810i	−0.712999	+	0.411650i	0.0991716	+	0.995070i	$0.468381\pi$
$752$	0.406470	−	4.64598i	0.0148225	−	0.169421i
$753$	−1.96068	+	11.1196i	−0.0714511	+	0.405219i
$754$	1.35886	+	5.07133i	0.0494867	+	0.184687i
$755$	−2.98010	+	6.18171i	−0.108457	+	0.224976i
$756$	1.26281	+	0.459627i	0.0459281	+	0.0167165i
$757$	34.7890	−	6.13424i	1.26443	−	0.222953i	0.499073	−	0.866560i	$-0.333674\pi$
$757$	34.7890	−	6.13424i	1.26443	−	0.222953i	0.765356	+	0.643607i	$0.222563\pi$
$758$	−6.23598	+	7.43175i	−0.226501	+	0.269933i
$759$	2.16002	+	24.6891i	0.0784036	+	0.896157i
$760$	−13.6218	+	15.8156i	−0.494114	+	0.573692i
$761$	5.92922	−	16.2904i	0.214934	−	0.590527i	−0.784633	−	0.619961i	$-0.787148\pi$
$761$	5.92922	−	16.2904i	0.214934	−	0.590527i	0.999567	+	0.0294343i	$0.00937057\pi$
$762$	−5.64028	+	15.4965i	−0.204326	+	0.561381i
$763$	0.600481	−	1.04006i	0.0217389	−	0.0376528i
$764$	0.415267	+	0.593063i	0.0150238	+	0.0214563i
$765$	46.6975	−	31.8096i	1.68835	−	1.15008i
$766$	−4.05953	−	7.03131i	−0.146677	−	0.254051i
$767$	19.3373	−	5.18140i	0.698228	−	0.187090i
$768$	18.9334	+	13.2573i	0.683201	+	0.478383i
$769$	0.817445	+	0.219034i	0.0294778	+	0.00789856i	0.273528	−	0.961864i	$-0.411809\pi$
$769$	0.817445	+	0.219034i	0.0294778	+	0.00789856i	−0.244050	+	0.969763i	$0.578476\pi$
$770$	0.125972	+	0.0749094i	0.00453971	+	0.00269955i
$771$	22.1124	+	22.1124i	0.796359	+	0.796359i
$772$	2.21692	−	0.806893i	0.0797887	−	0.0290407i
$773$	24.7001	−	17.2952i	0.888400	−	0.622065i	−0.0377218	−	0.999288i	$-0.512010\pi$
$773$	24.7001	−	17.2952i	0.888400	−	0.622065i	0.926122	+	0.377224i	$0.123121\pi$
$774$	3.10093	−	3.69554i	0.111461	−	0.132834i
$775$	48.1728	+	14.2473i	1.73042	+	0.511779i
$776$			18.8144i			0.675397i
$777$	−1.65518	+	0.678620i	−0.0593794	+	0.0243454i
$778$	−3.49685	−	3.49685i	−0.125368	−	0.125368i
$779$	1.12300	−	12.8359i	0.0402356	−	0.459896i
$780$	−31.4760	−	0.405407i	−1.12702	−	0.0145159i
$781$	7.49271	+	1.32117i	0.268110	+	0.0472751i
$782$	−2.30023	−	6.31982i	−0.0822559	−	0.225996i
$783$	−43.4218			−1.55177
$784$	−8.02583	−	22.0508i	−0.286637	−	0.787528i
$785$	−40.0303	−	15.1565i	−1.42874	−	0.540958i
$786$	−3.10305	−	17.5982i	−0.110682	−	0.627709i
$787$	−3.44980	−	12.8748i	−0.122972	−	0.458939i	0.876787	−	0.480879i	$-0.159682\pi$
$787$	−3.44980	−	12.8748i	−0.122972	−	0.458939i	−0.999759	+	0.0219403i	$0.993016\pi$
$788$	34.2802	+	9.18535i	1.22118	+	0.327214i
$789$	−38.9134	−	46.3752i	−1.38535	−	1.65100i
$790$	1.73622	−	0.972813i	0.0617721	−	0.0346111i
$791$	−1.93704	+	0.519028i	−0.0688731	+	0.0184545i
$792$	12.8050	+	4.66063i	0.455005	+	0.165608i
$793$	10.1807	+	21.8327i	0.361529	+	0.775300i
$794$	−4.48581	+	6.40640i	−0.159195	+	0.227354i
$795$	30.9350	+	31.7423i	1.09715	+	1.12578i
$796$	−3.76598	+	0.329481i	−0.133482	+	0.0116781i
$797$	−3.79401	−	21.5169i	−0.134391	−	0.762168i	−0.975282	−	0.220964i	$-0.929080\pi$
$797$	−3.79401	−	21.5169i	−0.134391	−	0.762168i	0.840891	−	0.541204i	$-0.182031\pi$
$798$	−0.639462	+	0.298186i	−0.0226367	+	0.0105557i
$799$	−2.73878	−	5.87334i	−0.0968912	−	0.207784i
$800$	−12.1848	+	13.7841i	−0.430797	+	0.487341i
$801$	27.7741	−	19.4476i	0.981350	−	0.687148i
$802$	−0.848187	−	0.0742067i	−0.0299505	−	0.00262033i
$803$	−0.383228	+	1.43023i	−0.0135238	+	0.0504716i
$804$	−1.65846	+	2.87253i	−0.0584893	+	0.101306i
$805$	−0.749583	−	0.645607i	−0.0264193	−	0.0227546i
$806$	2.20435	−	8.22673i	0.0776447	−	0.289774i
$807$	49.5727	+	23.1161i	1.74504	+	0.813726i
$808$			8.25280i			0.290332i
$809$	−16.4285	+	35.2311i	−0.577596	+	1.23866i	0.372885	+	0.927878i	$0.378369\pi$
$809$	−16.4285	+	35.2311i	−0.577596	+	1.23866i	−0.950481	+	0.310782i	$0.899409\pi$
$810$	−0.819357	+	2.90757i	−0.0287893	+	0.102161i
$811$	−24.0031	−	20.1410i	−0.842863	−	0.707246i	0.115343	−	0.993326i	$-0.463203\pi$
$811$	−24.0031	−	20.1410i	−0.842863	−	0.707246i	−0.958206	+	0.286080i	$0.907648\pi$
$812$	−0.763105	−	0.909433i	−0.0267797	−	0.0319149i
$813$	29.0423	−	29.0423i	1.01856	−	1.01856i
$814$	−3.63898	+	1.49197i	−0.127546	+	0.0522935i
$815$	−0.414950	+	4.12961i	−0.0145351	+	0.144654i
$816$	45.2632	+	3.96002i	1.58453	+	0.138628i
$817$	−1.70670	−	19.5077i	−0.0597100	−	0.682489i
$818$	−0.480203	−	0.685801i	−0.0167899	−	0.0239785i
$819$	−1.27708	−	0.595511i	−0.0446247	−	0.0208088i
$820$	0.749946	−	7.46351i	0.0261893	−	0.260637i
$821$	33.7124	−	12.2703i	1.17657	−	0.428237i	0.321581	−	0.946882i	$-0.395786\pi$
$821$	33.7124	−	12.2703i	1.17657	−	0.428237i	0.854990	+	0.518645i	$0.173563\pi$
$822$	−6.18033	+	3.56821i	−0.215564	+	0.124456i
$823$	−12.3515	+	17.6398i	−0.430546	+	0.614884i	−0.974542	−	0.224204i	$-0.928022\pi$
$823$	−12.3515	+	17.6398i	−0.430546	+	0.614884i	0.543996	+	0.839088i	$0.316911\pi$
$824$	5.68491	+	3.28218i	0.198043	+	0.114340i
$825$	12.6582	−	25.4152i	0.440702	−	0.884845i
$826$	0.200110	−	0.167912i	0.00696271	−	0.00584241i
$827$	−38.8525	−	6.85074i	−1.35103	−	0.238224i	−0.549160	−	0.835717i	$-0.685052\pi$
$827$	−38.8525	−	6.85074i	−1.35103	−	0.238224i	−0.801874	+	0.597494i	$0.796163\pi$
$828$	−38.7116	−	22.3501i	−1.34532	−	0.776721i
$829$	2.21117	−	1.03109i	0.0767972	−	0.0358111i	−0.383840	−	0.923400i	$-0.625399\pi$
$829$	2.21117	−	1.03109i	0.0767972	−	0.0358111i	0.460637	+	0.887588i	$0.347621\pi$
$830$	−1.43891	−	4.11763i	−0.0499454	−	0.142925i
$831$	−66.5011	−	46.5646i	−2.30690	−	1.61531i
$832$	−10.8102	−	9.07084i	−0.374776	−	0.314475i
$833$	−24.9786	−	20.9596i	−0.865459	−	0.726206i
$834$	−14.3162	−	10.0243i	−0.495731	−	0.347114i
$835$	1.31821	−	2.73442i	0.0456187	−	0.0946283i
$836$	24.3626	−	11.3605i	0.842597	−	0.392909i
$837$	61.0019	+	35.2195i	2.10853	+	1.21736i
$838$	1.39906	+	0.246691i	0.0483296	+	0.00852181i
$839$	−1.23595	+	1.03709i	−0.0426698	+	0.0358042i	−0.663873	−	0.747845i	$-0.731089\pi$
$839$	−1.23595	+	1.03709i	−0.0426698	+	0.0358042i	0.621203	+	0.783649i	$0.286644\pi$
$840$	−0.770554	+	0.347305i	−0.0265867	+	0.0119832i
$841$	8.10537	+	4.67964i	0.279496	+	0.161367i
$842$	1.72514	−	2.46375i	0.0594522	−	0.0849065i
$843$	49.3470	−	28.4905i	1.69960	−	0.981264i
$844$	5.05181	−	1.83871i	0.173891	−	0.0632910i
$845$	−14.2711	−	1.43399i	−0.490942	−	0.0493307i
$846$	2.25269	+	1.05045i	0.0774491	+	0.0361151i
$847$	0.416820	+	0.595280i	0.0143221	+	0.0204541i
$848$	1.99918	+	22.8507i	0.0686522	+	0.784698i
$849$	−40.0403	−	3.50307i	−1.37418	−	0.120225i
$850$	−1.53293	+	7.55091i	−0.0525792	+	0.258994i
$851$	25.9385	−	5.65242i	0.889162	−	0.193762i
$852$	−15.0776	+	15.0776i	−0.516550	+	0.516550i
$853$	31.4820	+	37.5188i	1.07792	+	1.28462i	0.956410	+	0.292028i	$0.0943300\pi$
$853$	31.4820	+	37.5188i	1.07792	+	1.28462i	0.121512	+	0.992590i	$0.461226\pi$
$854$	0.240795	+	0.202051i	0.00823985	+	0.00691406i
$855$	42.9988	+	76.7419i	1.47053	+	2.62452i
$856$	1.06357	−	2.28084i	0.0363522	−	0.0779575i
$857$			42.1640i			1.44030i	0.693821	+	0.720148i	$0.255926\pi$
$857$			42.1640i			1.44030i	−0.693821	+	0.720148i	$0.744074\pi$
$858$	−4.36275	−	2.03438i	−0.148942	−	0.0694527i
$859$	−11.6268	+	43.3919i	−0.396702	+	1.48051i	0.422160	+	0.906521i	$0.361272\pi$
$859$	−11.6268	+	43.3919i	−0.396702	+	1.48051i	−0.818862	+	0.573991i	$0.805395\pi$
$860$	−0.847230	−	11.3684i	−0.0288903	−	0.387660i
$861$	0.260873	−	0.451846i	0.00889054	−	0.0153989i
$862$	−0.108067	+	0.403313i	−0.00368079	+	0.0137369i
$863$	1.02836	+	0.0899694i	0.0350056	+	0.00306260i	0.104645	−	0.994510i	$-0.466629\pi$
$863$	1.02836	+	0.0899694i	0.0350056	+	0.00306260i	−0.0696395	+	0.997572i	$0.522185\pi$
$864$	−21.1313	+	14.7963i	−0.718902	+	0.503381i
$865$	−4.33065	−	26.5559i	−0.147246	−	0.902927i
$866$	0.488435	+	1.04745i	0.0165977	+	0.0355939i
$867$	12.5223	−	5.83922i	0.425278	−	0.198310i
$868$	0.334420	+	1.89659i	0.0113510	+	0.0643745i
$869$	−5.25390	+	0.459657i	−0.178226	+	0.0155928i
$870$	9.50474	−	9.26301i	0.322241	−	0.314045i
$871$	0.890001	−	1.27105i	0.0301565	−	0.0430680i
$872$	6.43507	+	13.8001i	0.217919	+	0.467329i
$873$	74.5091	+	27.1191i	2.52175	+	0.917843i
$874$	10.1139	−	2.71000i	0.342106	−	0.0916671i
$875$	0.346207	+	1.07920i	0.0117039	+	0.0364836i
$876$	−2.66740	−	3.17888i	−0.0901230	−	0.107404i
$877$	25.6828	+	6.88167i	0.867245	+	0.232378i	0.664896	−	0.746936i	$-0.268476\pi$
$877$	25.6828	+	6.88167i	0.867245	+	0.232378i	0.202349	+	0.979314i	$0.435143\pi$
$878$	0.948974	+	3.54162i	0.0320263	+	0.119524i
$879$	0.255257	+	1.44763i	0.00860959	+	0.0488274i
$880$	13.3961	−	6.03788i	0.451581	−	0.203537i
$881$	−3.80556	−	10.4557i	−0.128212	−	0.352261i	0.858932	−	0.512089i	$-0.171128\pi$
$881$	−3.80556	−	10.4557i	−0.128212	−	0.352261i	−0.987145	+	0.159828i	$0.948906\pi$
$882$	12.5064			0.421111
$883$	15.7117	+	43.1675i	0.528741	+	1.45270i	0.860554	+	0.509359i	$0.170117\pi$
$883$	15.7117	+	43.1675i	0.528741	+	1.45270i	−0.331814	+	0.943345i	$0.607660\pi$
$884$	−22.2930	−	3.93086i	−0.749796	−	0.132209i
$885$	−35.3204	−	36.2421i	−1.18728	−	1.21826i
$886$	−0.713494	+	8.15527i	−0.0239703	+	0.273982i
$887$	−2.16043	−	2.16043i	−0.0725402	−	0.0725402i	0.669906	−	0.742446i	$-0.266334\pi$
$887$	−2.16043	−	2.16043i	−0.0725402	−	0.0725402i	−0.742446	+	0.669906i	$0.766334\pi$
$888$	4.98886	−	22.1255i	0.167415	−	0.742484i
$889$			1.74443i			0.0585062i
$890$	−0.861452	+	4.54262i	−0.0288759	+	0.152269i
$891$	5.14558	−	6.13226i	0.172383	−	0.205439i
$892$	40.6684	−	28.4763i	1.36168	−	0.953457i
$893$	9.48090	−	3.45077i	0.317266	−	0.115475i
$894$	15.6519	+	15.6519i	0.523479	+	0.523479i
$895$	20.3043	−	34.1448i	0.678697	−	1.14133i
$896$	−0.898441	−	0.240737i	−0.0300148	−	0.00804244i
$897$	26.6164	+	18.6370i	0.888697	+	0.622273i
$898$	10.9195	−	2.92587i	0.364388	−	0.0976376i
$899$	−31.1133	−	53.8898i	−1.03769	−	1.79732i
$900$	24.4546	+	44.9946i	0.815155	+	1.49982i
$901$	18.2820	+	26.1094i	0.609062	+	0.869831i
$902$	0.573539	−	0.993399i	0.0190968	−	0.0330766i
$903$	0.271200	−	0.745116i	0.00902498	−	0.0247959i
$904$	8.69605	−	23.8922i	0.289226	−	0.794643i
$905$	2.10359	+	28.2266i	0.0699255	+	0.938285i
$906$	−0.256336	−	2.92993i	−0.00851619	−	0.0973404i
$907$	−30.6044	+	36.4729i	−1.01620	+	1.21106i	−0.0388941	+	0.999243i	$0.512384\pi$
$907$	−30.6044	+	36.4729i	−1.01620	+	1.21106i	−0.977309	+	0.211820i	$0.932061\pi$
$908$	−9.69604	+	1.70967i	−0.321774	+	0.0567375i
$909$	32.6829	+	11.8956i	1.08402	+	0.394552i
$910$	0.181395	−	0.0633889i	0.00601319	−	0.00210132i
$911$	−8.85548	−	33.0491i	−0.293395	−	1.09497i	−0.942484	−	0.334253i	$-0.891516\pi$
$911$	−8.85548	−	33.0491i	−0.293395	−	1.09497i	0.649088	−	0.760713i	$-0.275151\pi$
$912$	−12.2836	+	69.6638i	−0.406751	+	2.30680i
$913$	−1.00741	+	11.5147i	−0.0333404	+	0.381082i
$914$	9.53627	−	5.50577i	0.315432	−	0.182115i
$915$	35.5678	−	49.4288i	1.17584	−	1.63407i
$916$	−6.27524	+	1.10649i	−0.207340	+	0.0365596i
$917$	−0.945130	−	1.63701i	−0.0312110	−	0.0540590i
$918$	−4.56583	+	9.79146i	−0.150695	+	0.323166i
$919$	−28.7199	+	28.7199i	−0.947382	+	0.947382i	−0.998683	−	0.0513008i	$-0.983663\pi$
$919$	−28.7199	+	28.7199i	−0.947382	+	0.947382i	0.0513008	+	0.998683i	$0.483663\pi$
$920$	12.1563	−	3.09003i	0.400781	−	0.101875i
$921$	−3.89298	+	22.0782i	−0.128278	+	0.727501i
$922$	4.27897	−	0.374361i	0.140920	−	0.0123289i
$923$	7.64128	−	6.41180i	0.251516	−	0.211047i
$924$	1.08849			0.0358086
$925$	−28.7252	−	9.99326i	−0.944477	−	0.328576i
$926$	10.0453			0.330110
$927$	21.1924	−	17.7825i	0.696050	−	0.584055i
$928$	22.7023	−	1.98619i	0.745239	−	0.0652000i
$929$	4.45772	−	25.2810i	0.146253	−	0.829442i	−0.820100	−	0.572221i	$-0.806082\pi$
$929$	4.45772	−	25.2810i	0.146253	−	0.829442i	0.966353	−	0.257221i	$-0.0828069\pi$
$930$	−20.8662	+	5.30401i	−0.684228	+	0.173925i
$931$	35.8967	−	35.8967i	1.17647	−	1.17647i
$932$	−12.5842	+	26.9868i	−0.412208	+	0.883983i
$933$	6.12728	+	10.6128i	0.200598	+	0.347446i
$934$	1.49240	−	0.263150i	0.0488328	−	0.00861054i
$935$	11.9257	−	16.5732i	0.390013	−	0.542003i
$936$	15.4721	−	8.93280i	0.505720	−	0.291978i
$937$	−3.92038	+	44.8102i	−0.128073	+	1.46389i	0.611732	+	0.791065i	$0.290473\pi$
$937$	−3.92038	+	44.8102i	−0.128073	+	1.46389i	−0.739806	+	0.672821i	$0.765083\pi$
$938$	0.00351587	−	0.0199395i	0.000114797	−	0.000651047i
$939$	3.01680	+	11.2589i	0.0984495	+	0.367419i
$940$	5.54479	−	1.93764i	0.180851	−	0.0631989i
$941$	−30.4369	−	11.0781i	−0.992214	−	0.361136i	−0.205637	−	0.978628i	$-0.565927\pi$
$941$	−30.4369	−	11.0781i	−0.992214	−	0.361136i	−0.786577	+	0.617492i	$0.788149\pi$
$942$	18.0659	−	3.18551i	0.588619	−	0.103789i
$943$	−4.97693	+	5.93127i	−0.162071	+	0.193149i
$944$	−2.28259	−	26.0901i	−0.0742919	−	0.849160i
$945$	0.118106	+	1.58479i	0.00384199	+	0.0515532i
$946$	0.596243	−	1.63816i	0.0193855	−	0.0532613i
$947$	−15.1169	+	41.5333i	−0.491233	+	1.34965i	0.408319	+	0.912839i	$0.366115\pi$
$947$	−15.1169	+	41.5333i	−0.491233	+	1.34965i	−0.899552	+	0.436813i	$0.856107\pi$
$948$	7.39038	−	12.8005i	0.240029	−	0.415742i
$949$	1.11347	+	1.59019i	0.0361446	+	0.0516199i
$950$	−11.5031	−	3.40210i	−0.373210	−	0.110379i
$951$	−41.5131	−	71.9028i	−1.34615	−	2.33161i
$952$	−0.587095	+	0.157312i	−0.0190279	+	0.00509850i
$953$	−31.2957	−	21.9135i	−1.01377	−	0.709847i	−0.0563065	−	0.998414i	$-0.517932\pi$
$953$	−31.2957	−	21.9135i	−1.01377	−	0.709847i	−0.957460	+	0.288567i	$0.906821\pi$
$954$	−11.8084	−	3.16406i	−0.382313	−	0.102440i
$955$	−0.437595	+	0.735885i	−0.0141603	+	0.0238127i
$956$	−13.5471	−	13.5471i	−0.438146	−	0.438146i
$957$	−33.0493	+	12.0290i	−1.06833	+	0.388842i
$958$	−6.81394	+	4.77117i	−0.220148	+	0.154150i
$959$	−0.485235	+	0.578281i	−0.0156691	+	0.0186737i
$960$	−6.64641	+	35.0480i	−0.214512	+	1.13117i
$961$			69.9441i			2.25626i
$962$	−1.56827	+	4.91209i	−0.0505630	+	0.158372i
$963$	−7.49959	−	7.49959i	−0.241671	−	0.241671i
$964$	0.159201	−	1.81968i	0.00512753	−	0.0586080i
$965$	1.94717	+	1.99798i	0.0626816	+	0.0643173i
$966$	0.417542	+	0.0736240i	0.0134342	+	0.00236881i
$967$	4.66672	+	12.8217i	0.150072	+	0.412318i	0.991835	−	0.127528i	$-0.0407044\pi$
$967$	4.66672	+	12.8217i	0.150072	+	0.412318i	−0.841763	+	0.539847i	$0.818482\pi$
$968$	−9.21368			−0.296139
$969$	33.6189	+	92.3672i	1.08000	+	2.96726i
$970$	−9.85751	+	4.44299i	−0.316506	+	0.142656i
$971$	0.726948	+	4.12273i	0.0233289	+	0.132305i	0.994248	−	0.107104i	$-0.0341577\pi$
$971$	0.726948	+	4.12273i	0.0233289	+	0.132305i	−0.970919	+	0.239408i	$0.923047\pi$
$972$	−4.48669	−	16.7445i	−0.143911	−	0.537081i
$973$	−1.78571	−	0.478481i	−0.0572474	−	0.0153394i
$974$	0.497987	+	0.593478i	0.0159565	+	0.0190163i
$975$	−14.8579	−	34.1314i	−0.475833	−	1.09308i
$976$	30.4407	−	8.15656i	0.974384	−	0.261085i
$977$	−7.63428	−	2.77865i	−0.244242	−	0.0888969i	0.216999	−	0.976172i	$-0.430373\pi$
$977$	−7.63428	−	2.77865i	−0.244242	−	0.0888969i	−0.461241	+	0.887275i	$0.652596\pi$
$978$	−0.751738	−	1.61211i	−0.0240379	−	0.0515495i
$979$	7.02771	−	10.0366i	0.224607	−	0.320772i
$980$	21.1649	−	20.6267i	0.676089	−	0.658894i
$981$	63.9268	−	5.59287i	2.04103	−	0.178567i
$982$	−2.28057	−	12.9338i	−0.0727761	−	0.412734i
$983$	−40.4733	+	18.8730i	−1.29090	+	0.601955i	−0.942128	−	0.335253i	$-0.891178\pi$
$983$	−40.4733	+	18.8730i	−1.29090	+	0.601955i	−0.348770	+	0.937209i	$0.613400\pi$
$984$	2.79566	+	5.99531i	0.0891223	+	0.191123i
$985$	6.75480	+	41.4210i	0.215226	+	1.31978i
$986$	7.81806	−	5.47427i	0.248978	−	0.174336i
$987$	0.406990	+	0.0356070i	0.0129546	+	0.00113338i
$988$	9.12154	−	34.0421i	0.290195	−	1.08302i
$989$	−5.88359	+	10.1907i	−0.187087	+	0.324045i
$990$	0.582007	+	7.80957i	0.0184974	+	0.248204i
$991$	10.5994	−	39.5576i	0.336702	−	1.25659i	−0.565310	−	0.824879i	$-0.691243\pi$
$991$	10.5994	−	39.5576i	0.336702	−	1.25659i	0.902012	−	0.431711i	$-0.142090\pi$
$992$	−33.5047	−	15.6235i	−1.06378	−	0.496047i
$993$		−	10.2405i		−	0.324971i
$994$	0.0550078	−	0.117965i	0.00174474	−	0.00374161i
$995$	−2.18520	−	3.90002i	−0.0692753	−	0.123639i
$996$	−24.8155	−	20.8227i	−0.786310	−	0.659792i
$997$	30.5633	+	36.4239i	0.967949	+	1.15356i	0.988108	+	0.153759i	$0.0491381\pi$
$997$	30.5633	+	36.4239i	0.967949	+	1.15356i	−0.0201598	+	0.999797i	$0.506418\pi$
$998$	−0.225583	+	0.225583i	−0.00714071	+	0.00714071i
$999$	−35.8840	−	23.0429i	−1.13532	−	0.729045i

Display

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a_n

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instead) (See

a_n

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a_n

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)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.z.a.113.11	✓	204
5.2	odd	4		185.2.bc.a.2.11	yes	204
5.3	odd	4		925.2.bq.b.557.7		204
5.4	even	2		925.2.bn.b.668.7		204
37.19	odd	36		185.2.bc.a.93.11	yes	204
185.19	odd	36		925.2.bq.b.93.7		204
185.93	even	36		925.2.bn.b.907.7		204
185.167	even	36	inner	185.2.z.a.167.11	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.z.a.113.11	✓	204	1.1	even	1	trivial
185.2.z.a.167.11	yes	204	185.167	even	36	inner
185.2.bc.a.2.11	yes	204	5.2	odd	4
185.2.bc.a.93.11	yes	204	37.19	odd	36
925.2.bn.b.668.7		204	5.4	even	2
925.2.bn.b.907.7		204	185.93	even	36
925.2.bq.b.93.7		204	185.19	odd	36
925.2.bq.b.557.7		204	5.3	odd	4

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	185.2.z.a.113.11

Level	$185$
Weight	$2$
Character	185.113
Analytic conductor	$1.477$
Analytic rank	$0$
Dimension	$204$
Inner twists	$2$