LMFDB - Embedded newform 357.2.bl.a.10.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [357,2,Mod(10,357)] 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("357.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(357, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([0, 8, 9])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$357 = 3 \cdot 7 \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	357.bl (of order $48$ , degree $16$ , 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:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$24$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			10.13
Character	$\chi$	$=$	357.10
Dual form			357.2.bl.a.250.13

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0808615 - 0.0106456i) q^{2} +(0.442289 + 0.896873i) q^{3} +(-1.92543 + 0.515916i) q^{4} +(0.199390 - 0.174860i) q^{5} +(0.0453119 + 0.0678141i) q^{6} +(-2.58704 - 0.554286i) q^{7} +(-0.300903 + 0.124638i) q^{8} +(-0.608761 + 0.793353i) q^{9} +(0.0142615 - 0.0162621i) q^{10} +(-6.03304 + 0.395426i) q^{11} +(-1.31431 - 1.49868i) q^{12} +(-1.97467 - 1.97467i) q^{13} +(-0.215093 - 0.0172797i) q^{14} +(0.245015 + 0.101489i) q^{15} +(3.42958 - 1.98007i) q^{16} +(3.81928 + 1.55342i) q^{17} +(-0.0407796 + 0.0706324i) q^{18} +(0.124184 + 0.943275i) q^{19} +(-0.293697 + 0.439548i) q^{20} +(-0.647094 - 2.56540i) q^{21} +(-0.483631 + 0.0962002i) q^{22} +(-5.23560 - 2.58191i) q^{23} +(-0.244870 - 0.214745i) q^{24} +(-0.643451 + 4.88749i) q^{25} +(-0.180696 - 0.138653i) q^{26} +(-0.980785 - 0.195090i) q^{27} +(5.26712 - 0.267460i) q^{28} +(-0.808749 - 4.06585i) q^{29} +(0.0208927 + 0.00559818i) q^{30} +(-6.53981 + 3.22508i) q^{31} +(0.773023 - 0.593162i) q^{32} +(-3.02299 - 5.23598i) q^{33} +(0.325370 + 0.0849534i) q^{34} +(-0.612751 + 0.341851i) q^{35} +(0.762821 - 1.84161i) q^{36} +(-0.141667 + 2.16142i) q^{37} +(0.0200835 + 0.0749526i) q^{38} +(0.897652 - 2.64440i) q^{39} +(-0.0382027 + 0.0774673i) q^{40} +(-0.435830 + 2.19107i) q^{41} +(-0.0796353 - 0.200553i) q^{42} +(4.25459 + 10.2715i) q^{43} +(11.4122 - 3.87391i) q^{44} +(0.0173451 + 0.264634i) q^{45} +(-0.450845 - 0.153041i) q^{46} +(1.94519 - 7.25956i) q^{47} +(3.29273 + 2.20013i) q^{48} +(6.38554 + 2.86792i) q^{49} +0.402060i q^{50} +(0.296003 + 4.11247i) q^{51} +(4.82084 + 2.78331i) q^{52} +(-1.17932 - 1.53691i) q^{53} +(-0.0813847 - 0.00533423i) q^{54} +(-1.13378 + 1.13378i) q^{55} +(0.847531 - 0.155657i) q^{56} +(-0.791072 + 0.528577i) q^{57} +(-0.108680 - 0.320162i) q^{58} +(-10.4642 - 1.37764i) q^{59} +(-0.524118 - 0.0690014i) q^{60} +(2.64239 + 7.78423i) q^{61} +(-0.494486 + 0.330405i) q^{62} +(2.01463 - 1.71501i) q^{63} +(-5.54428 + 5.54428i) q^{64} +(-0.739018 - 0.0484378i) q^{65} +(-0.300184 - 0.391207i) q^{66} +(2.89693 + 1.67254i) q^{67} +(-8.15517 - 1.02057i) q^{68} -5.83762i q^{69} +(-0.0459088 + 0.0341657i) q^{70} +(4.95492 + 3.31077i) q^{71} +(0.0842960 - 0.314597i) q^{72} +(3.65497 + 1.24070i) q^{73} +(0.0115542 + 0.176284i) q^{74} +(-4.66805 + 1.58459i) q^{75} +(-0.725759 - 1.75214i) q^{76} +(15.8269 + 2.32104i) q^{77} +(0.0444343 - 0.223386i) q^{78} +(7.03631 - 14.2682i) q^{79} +(0.337587 - 0.994500i) q^{80} +(-0.258819 - 0.965926i) q^{81} +(-0.0119166 + 0.181813i) q^{82} +(1.65021 - 3.98395i) q^{83} +(2.56946 + 4.60564i) q^{84} +(1.03316 - 0.358103i) q^{85} +(0.453379 + 0.785276i) q^{86} +(3.28885 - 2.52363i) q^{87} +(1.76607 - 0.870930i) q^{88} +(-1.34788 - 0.361165i) q^{89} +(0.00421975 + 0.0212141i) q^{90} +(4.01401 + 6.20307i) q^{91} +(11.4128 + 2.27015i) q^{92} +(-5.78497 - 4.43896i) q^{93} +(0.0800087 - 0.607727i) q^{94} +(0.189702 + 0.166364i) q^{95} +(0.873890 + 0.430955i) q^{96} +(-14.5554 + 2.89526i) q^{97} +(0.546875 + 0.163926i) q^{98} +(3.35897 - 5.02705i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$384 q - 16 q^{11} + 32 q^{14} - 64 q^{22} - 16 q^{25} - 48 q^{28} - 64 q^{30} - 64 q^{35} - 32 q^{37} - 48 q^{42} - 64 q^{44} + 32 q^{46} - 64 q^{49} + 80 q^{56} - 32 q^{58} - 288 q^{61} - 528 q^{68} + 176 q^{70}+ \cdots + 32 q^{99}+O(q^{100})$ 384 * q - 16 * q^11 + 32 * q^14 - 64 * q^22 - 16 * q^25 - 48 * q^28 - 64 * q^30 - 64 * q^35 - 32 * q^37 - 48 * q^42 - 64 * q^44 + 32 * q^46 - 64 * q^49 + 80 * q^56 - 32 * q^58 - 288 * q^61 - 528 * q^68 + 176 * q^70 + 64 * q^71 - 48 * q^73 - 128 * q^74 + 96 * q^77 + 128 * q^78 - 480 * q^80 - 240 * q^82 + 32 * q^85 - 144 * q^87 - 96 * q^88 - 64 * q^91 + 320 * q^92 - 192 * q^94 - 64 * q^95 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$ .

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{16}\right)$	$1$

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

)

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

$2$	0.0808615	−	0.0106456i	0.0571777	−	0.00752759i	−0.101883	−	0.994796i	$-0.532487\pi$
$2$	0.0808615	−	0.0106456i	0.0571777	−	0.00752759i	0.159061	+	0.987269i	$0.449153\pi$
$3$	0.442289	+	0.896873i	0.255355	+	0.517810i
$3$	0.442289	+	0.896873i	0.255355	+	0.517810i
$4$	−1.92543	+	0.515916i	−0.962713	+	0.257958i
$5$	0.199390	−	0.174860i	0.0891697	−	0.0781998i	−0.613601	−	0.789617i	$-0.710279\pi$
$5$	0.199390	−	0.174860i	0.0891697	−	0.0781998i	0.702770	+	0.711417i	$0.251946\pi$
$6$	0.0453119	+	0.0678141i	0.0184985	+	0.0276850i
$7$	−2.58704	−	0.554286i	−0.977809	−	0.209500i
$7$	−2.58704	−	0.554286i	−0.977809	−	0.209500i
$8$	−0.300903	+	0.124638i	−0.106385	+	0.0440662i
$9$	−0.608761	+	0.793353i	−0.202920	+	0.264451i
$10$	0.0142615	−	0.0162621i	0.00450987	−	0.00514252i
$11$	−6.03304	+	0.395426i	−1.81903	+	0.119225i	−0.936420	−	0.350881i	$-0.885882\pi$
$11$	−6.03304	+	0.395426i	−1.81903	+	0.119225i	−0.882610	+	0.470107i	$0.844215\pi$
$12$	−1.31431	−	1.49868i	−0.379407	−	0.432631i
$13$	−1.97467	−	1.97467i	−0.547674	−	0.547674i	0.378093	−	0.925767i	$-0.376580\pi$
$13$	−1.97467	−	1.97467i	−0.547674	−	0.547674i	−0.925767	+	0.378093i	$0.876580\pi$
$14$	−0.215093	−	0.0172797i	−0.0574859	−	0.00461821i
$15$	0.245015	+	0.101489i	0.0632626	+	0.0262042i
$16$	3.42958	−	1.98007i	0.857394	−	0.495017i
$17$	3.81928	+	1.55342i	0.926311	+	0.376760i
$17$	3.81928	+	1.55342i	0.926311	+	0.376760i
$18$	−0.0407796	+	0.0706324i	−0.00961185	+	0.0166482i
$19$	0.124184	+	0.943275i	0.0284899	+	0.216402i	0.999768	−	0.0215455i	$-0.00685868\pi$
$19$	0.124184	+	0.943275i	0.0284899	+	0.216402i	−0.971278	+	0.237948i	$0.923525\pi$
$20$	−0.293697	+	0.439548i	−0.0656726	+	0.0982860i
$21$	−0.647094	−	2.56540i	−0.141208	−	0.559816i
$22$	−0.483631	+	0.0962002i	−0.103111	+	0.0205100i
$23$	−5.23560	−	2.58191i	−1.09170	−	0.538366i	−0.194908	−	0.980822i	$-0.562441\pi$
$23$	−5.23560	−	2.58191i	−1.09170	−	0.538366i	−0.896790	+	0.442456i	$0.854107\pi$
$24$	−0.244870	−	0.214745i	−0.0499839	−	0.0438347i
$25$	−0.643451	+	4.88749i	−0.128690	+	0.977499i
$26$	−0.180696	−	0.138653i	−0.0354374	−	0.0271921i
$27$	−0.980785	−	0.195090i	−0.188752	−	0.0375451i
$28$	5.26712	−	0.267460i	0.995392	−	0.0505451i
$29$	−0.808749	−	4.06585i	−0.150181	−	0.755010i	−0.980314	−	0.197445i	$-0.936736\pi$
$29$	−0.808749	−	4.06585i	−0.150181	−	0.755010i	0.830133	−	0.557565i	$-0.188264\pi$
$30$	0.0208927	+	0.00559818i	0.00381447	+	0.00102208i
$31$	−6.53981	+	3.22508i	−1.17458	+	0.579241i	−0.921566	−	0.388221i	$-0.873090\pi$
$31$	−6.53981	+	3.22508i	−1.17458	+	0.579241i	−0.253018	+	0.967462i	$0.581423\pi$
$32$	0.773023	−	0.593162i	0.136653	−	0.104857i
$33$	−3.02299	−	5.23598i	−0.526235	−	0.911466i
$34$	0.325370	+	0.0849534i	0.0558005	+	0.0145694i
$35$	−0.612751	+	0.341851i	−0.103574	+	0.0577833i
$36$	0.762821	−	1.84161i	0.127137	−	0.306936i
$37$	−0.141667	+	2.16142i	−0.0232899	+	0.355335i	0.970270	+	0.242025i	$0.0778118\pi$
$37$	−0.141667	+	2.16142i	−0.0232899	+	0.355335i	−0.993560	+	0.113309i	$0.963855\pi$
$38$	0.0200835	+	0.0749526i	0.00325797	+	0.0121589i
$39$	0.897652	−	2.64440i	0.143739	−	0.423442i
$40$	−0.0382027	+	0.0774673i	−0.00604037	+	0.0122487i
$41$	−0.435830	+	2.19107i	−0.0680652	+	0.342187i	−0.999779	−	0.0210055i	$-0.993313\pi$
$41$	−0.435830	+	2.19107i	−0.0680652	+	0.342187i	0.931714	+	0.363192i	$0.118313\pi$
$42$	−0.0796353	−	0.200553i	−0.0122880	−	0.0309460i
$43$	4.25459	+	10.2715i	0.648820	+	1.56639i	0.814471	+	0.580204i	$0.197027\pi$
$43$	4.25459	+	10.2715i	0.648820	+	1.56639i	−0.165651	+	0.986184i	$0.552973\pi$
$44$	11.4122	−	3.87391i	1.72045	−	0.584014i
$45$	0.0173451	+	0.264634i	0.00258565	+	0.0394494i
$46$	−0.450845	−	0.153041i	−0.0664734	−	0.0225647i
$47$	1.94519	−	7.25956i	0.283735	−	1.05892i	−0.666023	−	0.745931i	$-0.732005\pi$
$47$	1.94519	−	7.25956i	0.283735	−	1.05892i	0.949758	−	0.312984i	$-0.101329\pi$
$48$	3.29273	+	2.20013i	0.475265	+	0.317562i
$49$	6.38554	+	2.86792i	0.912219	+	0.409702i
$50$			0.402060i			0.0568599i
$51$	0.296003	+	4.11247i	0.0414487	+	0.575861i
$52$	4.82084	+	2.78331i	0.668530	+	0.385976i
$53$	−1.17932	−	1.53691i	−0.161991	−	0.211111i	0.705304	−	0.708905i	$-0.250810\pi$
$53$	−1.17932	−	1.53691i	−0.161991	−	0.211111i	−0.867296	+	0.497793i	$0.834144\pi$
$54$	−0.0813847	−	0.00533423i	−0.0110750	−	0.000725897i
$55$	−1.13378	+	1.13378i	−0.152879	+	0.152879i
$56$	0.847531	−	0.155657i	0.113256	−	0.0208006i
$57$	−0.791072	+	0.528577i	−0.104780	+	0.0700118i
$58$	−0.108680	−	0.320162i	−0.0142704	−	0.0420393i
$59$	−10.4642	−	1.37764i	−1.36232	−	0.179353i	−0.586317	−	0.810082i	$-0.699423\pi$
$59$	−10.4642	−	1.37764i	−1.36232	−	0.179353i	−0.776003	+	0.630729i	$0.782756\pi$
$60$	−0.524118	−	0.0690014i	−0.0676633	−	0.00890804i
$61$	2.64239	+	7.78423i	0.338323	+	0.996669i	0.974357	+	0.225007i	$0.0722406\pi$
$61$	2.64239	+	7.78423i	0.338323	+	0.996669i	−0.636034	+	0.771661i	$0.719426\pi$
$62$	−0.494486	+	0.330405i	−0.0627998	+	0.0419615i
$63$	2.01463	−	1.71501i	0.253820	−	0.216071i
$64$	−5.54428	+	5.54428i	−0.693035	+	0.693035i
$65$	−0.739018	−	0.0484378i	−0.0916639	−	0.00600797i
$66$	−0.300184	−	0.391207i	−0.0369501	−	0.0481543i
$67$	2.89693	+	1.67254i	0.353916	+	0.204334i	0.666409	−	0.745587i	$-0.267831\pi$
$67$	2.89693	+	1.67254i	0.353916	+	0.204334i	−0.312492	+	0.949920i	$0.601164\pi$
$68$	−8.15517	−	1.02057i	−0.988960	−	0.123762i
$69$		−	5.83762i		−	0.702767i
$70$	−0.0459088	+	0.0341657i	−0.00548715	+	0.00408358i
$71$	4.95492	+	3.31077i	0.588040	+	0.392916i	0.813696	−	0.581291i	$-0.197452\pi$
$71$	4.95492	+	3.31077i	0.588040	+	0.392916i	−0.225655	+	0.974207i	$0.572452\pi$
$72$	0.0842960	−	0.314597i	0.00993437	−	0.0370756i
$73$	3.65497	+	1.24070i	0.427782	+	0.145213i	0.527023	−	0.849851i	$-0.323308\pi$
$73$	3.65497	+	1.24070i	0.427782	+	0.145213i	−0.0992409	+	0.995063i	$0.531641\pi$
$74$	0.0115542	+	0.176284i	0.00134315	+	0.0204926i
$75$	−4.66805	+	1.58459i	−0.539020	+	0.182973i
$76$	−0.725759	−	1.75214i	−0.0832503	−	0.200984i
$77$	15.8269	+	2.32104i	1.80364	+	0.264507i
$78$	0.0444343	−	0.223386i	0.00503119	−	0.0252935i
$79$	7.03631	−	14.2682i	0.791647	−	1.60530i	−0.00434163	−	0.999991i	$-0.501382\pi$
$79$	7.03631	−	14.2682i	0.791647	−	1.60530i	0.795989	−	0.605311i	$-0.206951\pi$
$80$	0.337587	−	0.994500i	0.0377434	−	0.111188i
$81$	−0.258819	−	0.965926i	−0.0287577	−	0.107325i
$82$	−0.0119166	+	0.181813i	−0.00131597	+	0.0200778i
$83$	1.65021	−	3.98395i	0.181134	−	0.437295i	−0.807067	−	0.590460i	$-0.798946\pi$
$83$	1.65021	−	3.98395i	0.181134	−	0.437295i	0.988201	+	0.153165i	$0.0489464\pi$
$84$	2.56946	+	4.60564i	0.280351	+	0.502516i
$85$	1.03316	−	0.358103i	0.112061	−	0.0388417i
$86$	0.453379	+	0.785276i	0.0488892	+	0.0846785i
$87$	3.28885	−	2.52363i	0.352602	−	0.270561i
$88$	1.76607	−	0.870930i	0.188264	−	0.0928415i
$89$	−1.34788	−	0.361165i	−0.142875	−	0.0382834i	0.186672	−	0.982422i	$-0.440230\pi$
$89$	−1.34788	−	0.361165i	−0.142875	−	0.0382834i	−0.329548	+	0.944139i	$0.606896\pi$
$90$	0.00421975	+	0.0212141i	0.000444800	+	0.00223616i
$91$	4.01401	+	6.20307i	0.420783	+	0.650258i
$92$	11.4128	+	2.27015i	1.18987	+	0.236679i
$93$	−5.78497	−	4.43896i	−0.599873	−	0.460299i
$94$	0.0800087	−	0.607727i	0.00825227	−	0.0626822i
$95$	0.189702	+	0.166364i	0.0194630	+	0.0170686i
$96$	0.873890	+	0.430955i	0.0891910	+	0.0439842i
$97$	−14.5554	+	2.89526i	−1.47788	+	0.293969i	−0.867221	−	0.497924i	$-0.834096\pi$
$97$	−14.5554	+	2.89526i	−1.47788	+	0.293969i	−0.610660	+	0.791893i	$0.709096\pi$
$98$	0.546875	+	0.163926i	0.0552427	+	0.0165590i
$99$	3.35897	−	5.02705i	0.337589	−	0.505238i
$100$	−1.28262	−	9.74248i	−0.128262	−	0.974248i
$101$	−6.90666	+	11.9627i	−0.687238	+	1.19033i	0.285490	+	0.958382i	$0.407844\pi$
$101$	−6.90666	+	11.9627i	−0.687238	+	1.19033i	−0.972728	+	0.231949i	$0.925490\pi$
$102$	0.0677150	+	0.329389i	0.00670479	+	0.0326144i
$103$	−2.72391	+	1.57265i	−0.268394	+	0.154958i	−0.628158	−	0.778086i	$-0.716191\pi$
$103$	−2.72391	+	1.57265i	−0.268394	+	0.154958i	0.359763	+	0.933044i	$0.382857\pi$
$104$	0.840301	+	0.348064i	0.0823983	+	0.0341305i
$105$	−0.577609	−	0.398363i	−0.0563689	−	0.0388762i
$106$	−0.111723	−	0.111723i	−0.0108515	−	0.0108515i
$107$	3.36960	+	3.84229i	0.325752	+	0.371449i	0.891415	−	0.453188i	$-0.149713\pi$
$107$	3.36960	+	3.84229i	0.325752	+	0.371449i	−0.565664	+	0.824636i	$0.691380\pi$
$108$	1.98908	−	0.130371i	0.191399	−	0.0125450i
$109$	4.69632	−	5.35513i	0.449826	−	0.512928i	−0.481833	−	0.876263i	$-0.660029\pi$
$109$	4.69632	−	5.35513i	0.449826	−	0.512928i	0.931659	+	0.363335i	$0.118362\pi$
$110$	−0.0796095	+	0.103749i	−0.00759046	+	0.00989208i
$111$	−2.00117	+	0.828913i	−0.189943	+	0.0786770i
$112$	−9.96997	+	3.22154i	−0.942073	+	0.304407i
$113$	−3.85130	−	5.76387i	−0.362300	−	0.542220i	0.604879	−	0.796317i	$-0.293221\pi$
$113$	−3.85130	−	5.76387i	−0.362300	−	0.542220i	−0.967179	+	0.254098i	$0.918221\pi$
$114$	−0.0583403	+	0.0511630i	−0.00546407	+	0.00479186i
$115$	−1.49540	+	0.400691i	−0.139447	+	0.0373646i
$116$	3.65483	+	7.41126i	0.339342	+	0.688118i
$117$	2.76871	−	0.364507i	0.255967	−	0.0336987i
$118$	−0.860815			−0.0792445
$119$	−9.01958	−	6.13573i	−0.826824	−	0.562461i
$120$	−0.0863749			−0.00788492
$121$	25.3353	−	3.33546i	2.30321	−	0.303223i
$122$	0.296536	+	0.601315i	0.0268471	+	0.0544405i
$123$	−2.15787	+	0.578200i	−0.194569	+	0.0521345i
$124$	10.9280	−	9.58364i	0.981368	−	0.860636i
$125$	1.46302	+	2.18957i	0.130857	+	0.195841i
$126$	0.144649	−	0.160125i	0.0128864	−	0.0142651i
$127$	−14.7655	+	6.11605i	−1.31022	+	0.542712i	−0.924949	−	0.380091i	$-0.875893\pi$
$127$	−14.7655	+	6.11605i	−1.31022	+	0.542712i	−0.385273	+	0.922803i	$0.625893\pi$
$128$	−1.57562	+	2.05339i	−0.139266	+	0.181496i
$129$	−7.33047	+	8.35880i	−0.645412	+	0.735951i
$130$	−0.0602738	+	0.00395055i	−0.00528636	+	0.000346486i
$131$	−11.6037	−	13.2315i	−1.01382	−	1.15604i	−0.987696	−	0.156385i	$-0.950016\pi$
$131$	−11.6037	−	13.2315i	−1.01382	−	1.15604i	−0.0261265	−	0.999659i	$-0.508317\pi$
$132$	8.52187	+	8.52187i	0.741734	+	0.741734i
$133$	0.201574	−	2.50912i	0.0174786	−	0.217568i
$134$	0.252055	+	0.104405i	0.0217743	+	0.00901920i
$135$	−0.229672	+	0.132601i	−0.0197670	+	0.0114125i
$136$	−1.34285	+	0.00859872i	−0.115148	+	0.000737334i
$137$	7.93778	−	13.7486i	0.678170	−	1.17463i	−0.297361	−	0.954765i	$-0.596106\pi$
$137$	7.93778	−	13.7486i	0.678170	−	1.17463i	0.975531	−	0.219861i	$-0.0705602\pi$
$138$	−0.0621451	−	0.472039i	−0.00529014	−	0.0401826i
$139$	−0.127721	+	0.191148i	−0.0108332	+	0.0162130i	−0.836847	−	0.547437i	$-0.815603\pi$
$139$	−0.127721	+	0.191148i	−0.0108332	+	0.0162130i	0.826014	+	0.563650i	$0.190603\pi$
$140$	1.00344	−	0.974337i	0.0848062	−	0.0823465i
$141$	7.37124	−	1.46623i	0.620770	−	0.123479i
$142$	0.435907	+	0.214966i	0.0365805	+	0.0180395i
$143$	12.6941	+	11.1324i	1.06153	+	0.930938i
$144$	−0.516901	+	3.92625i	−0.0430751	+	0.327188i
$145$	−0.872211	−	0.669271i	−0.0724332	−	0.0555799i
$146$	0.308755	+	0.0614151i	0.0255527	+	0.00508275i
$147$	0.252094	+	6.99546i	0.0207924	+	0.576976i
$148$	−0.842342	−	4.23474i	−0.0692400	−	0.348093i
$149$	−12.8617	−	3.44628i	−1.05367	−	0.282330i	−0.309902	−	0.950768i	$-0.600296\pi$
$149$	−12.8617	−	3.44628i	−1.05367	−	0.282330i	−0.743767	+	0.668438i	$0.766963\pi$
$150$	−0.360597	+	0.177827i	−0.0294426	+	0.0145195i
$151$	−4.92401	+	3.77833i	−0.400710	+	0.307476i	−0.789384	−	0.613900i	$-0.789600\pi$
$151$	−4.92401	+	3.77833i	−0.400710	+	0.307476i	0.388674	+	0.921375i	$0.372933\pi$
$152$	−0.154935	−	0.268356i	−0.0125669	−	0.0217665i
$153$	−3.55744	+	2.08437i	−0.287602	+	0.168512i
$154$	1.30449	+	0.0191961i	0.105119	+	0.00154687i
$155$	−0.740033	+	1.78660i	−0.0594409	+	0.143503i
$156$	−0.364075	+	5.55471i	−0.0291493	+	0.444732i
$157$	1.09219	+	4.07611i	0.0871662	+	0.325309i	0.995716	−	0.0924688i	$-0.0294758\pi$
$157$	1.09219	+	4.07611i	0.0871662	+	0.325309i	−0.908549	+	0.417777i	$0.862809\pi$
$158$	0.417073	−	1.22866i	0.0331805	−	0.0977467i
$159$	0.856818	−	1.73745i	0.0679501	−	0.137789i
$160$	0.0504126	−	0.253441i	0.00398546	−	0.0200363i
$161$	12.1136	+	9.58152i	0.954684	+	0.755130i
$162$	−0.0312114	−	0.0753509i	−0.00245220	−	0.00592013i
$163$	4.87713	−	1.65556i	0.382006	−	0.129674i	−0.123829	−	0.992304i	$-0.539518\pi$
$163$	4.87713	−	1.65556i	0.382006	−	0.129674i	0.505836	+	0.862630i	$0.331184\pi$
$164$	−0.291248	−	4.44359i	−0.0227427	−	0.346986i
$165$	−1.51832	−	0.515399i	−0.118201	−	0.0401237i
$166$	0.0910265	−	0.339716i	0.00706503	−	0.0263671i
$167$	−2.31278	−	1.54535i	−0.178968	−	0.119583i	0.462859	−	0.886432i	$-0.346823\pi$
$167$	−2.31278	−	1.54535i	−0.178968	−	0.119583i	−0.641827	+	0.766849i	$0.721823\pi$
$168$	0.514458	+	0.691282i	0.0396913	+	0.0533336i
$169$		−	5.20138i		−	0.400106i
$170$	0.0797303	−	0.0399553i	0.00611503	−	0.00306443i
$171$	−0.823949	−	0.475707i	−0.0630089	−	0.0363782i
$172$	−13.4911	−	17.5820i	−1.02869	−	1.34061i
$173$	−25.6948	−	1.68413i	−1.95354	−	0.128042i	−0.963394	−	0.268090i	$-0.913607\pi$
$173$	−25.6948	−	1.68413i	−1.95354	−	0.128042i	−0.990145	+	0.140049i	$0.955274\pi$
$174$	0.239076	−	0.239076i	0.0181243	−	0.0181243i
$175$	4.37370	−	12.2875i	0.330621	−	0.928846i
$176$	−19.9078	+	13.3020i	−1.50061	+	1.00267i
$177$	−3.39262	−	9.99435i	−0.255005	−	0.751221i
$178$	−0.112837	−	0.0148552i	−0.00845748	−	0.00111345i
$179$	8.16783	+	1.07531i	0.610492	+	0.0803728i	0.429432	−	0.903099i	$-0.358714\pi$
$179$	8.16783	+	1.07531i	0.610492	+	0.0803728i	0.181060	+	0.983472i	$0.442047\pi$
$180$	−0.169926	−	0.500585i	−0.0126655	−	0.0373114i
$181$	−17.2188	+	11.5052i	−1.27986	+	0.855178i	−0.994652	−	0.103286i	$-0.967064\pi$
$181$	−17.2188	+	11.5052i	−1.27986	+	0.855178i	−0.285213	+	0.958464i	$0.592064\pi$
$182$	0.390614	+	0.458858i	0.0289543	+	0.0340128i
$183$	−5.81276	+	5.81276i	−0.429692	+	0.429692i
$184$	1.89721	+	0.124350i	0.139864	+	0.00916718i
$185$	0.349698	+	0.455736i	0.0257103	+	0.0335064i
$186$	−0.515037	−	0.297357i	−0.0377643	−	0.0218032i
$187$	−23.6561	−	7.86160i	−1.72991	−	0.574897i
$188$			14.9813i			1.09262i
$189$	2.42919	+	1.04834i	0.176698	+	0.0762556i
$190$	0.0171107	+	0.0114330i	0.00124134	+	0.000829435i
$191$	−2.77556	+	10.3585i	−0.200832	+	0.749516i	0.789847	+	0.613303i	$0.210160\pi$
$191$	−2.77556	+	10.3585i	−0.200832	+	0.749516i	−0.990680	+	0.136213i	$0.956507\pi$
$192$	−7.42469	−	2.52034i	−0.535831	−	0.181890i
$193$	1.38533	+	21.1361i	0.0997184	+	1.52141i	0.695654	+	0.718377i	$0.255115\pi$
$193$	1.38533	+	21.1361i	0.0997184	+	1.52141i	−0.595936	+	0.803032i	$0.703219\pi$
$194$	−1.14615	+	0.389067i	−0.0822890	+	0.0279334i
$195$	−0.283417	−	0.684229i	−0.0202959	−	0.0489986i
$196$	−13.7745	−	2.22756i	−0.983892	−	0.159111i
$197$	2.86945	−	14.4257i	0.204440	−	1.02779i	−0.733155	−	0.680061i	$-0.761953\pi$
$197$	2.86945	−	14.4257i	0.204440	−	1.02779i	0.937595	−	0.347728i	$-0.113047\pi$
$198$	0.218095	−	0.442253i	0.0154994	−	0.0314296i
$199$	5.62127	−	16.5597i	0.398481	−	1.17389i	−0.543843	−	0.839187i	$-0.683031\pi$
$199$	5.62127	−	16.5597i	0.398481	−	1.17389i	0.942324	−	0.334701i	$-0.108635\pi$
$200$	−0.415551	−	1.55086i	−0.0293839	−	0.109662i
$201$	−0.218779	+	3.33793i	−0.0154315	+	0.235439i
$202$	−0.431133	+	1.04085i	−0.0303344	+	0.0732337i
$203$	−0.161380	+	10.9668i	−0.0113267	+	0.769718i
$204$	−2.69162	−	7.76554i	−0.188451	−	0.543696i
$205$	0.296230	+	0.513085i	0.0206896	+	0.0358354i
$206$	−0.203517	+	0.156164i	−0.0141797	+	0.0108805i
$207$	5.23560	−	2.58191i	0.363899	−	0.179455i
$208$	−10.6822	−	2.86230i	−0.740680	−	0.198465i
$209$	−1.12221	−	5.64171i	−0.0776246	−	0.390245i
$210$	−0.0509472	−	0.0260632i	−0.00351569	−	0.00179853i
$211$	−12.8159	−	2.54925i	−0.882286	−	0.175498i	−0.266900	−	0.963724i	$-0.586000\pi$
$211$	−12.8159	−	2.54925i	−0.882286	−	0.175498i	−0.615385	+	0.788227i	$0.711000\pi$
$212$	3.06360	+	2.35079i	0.210409	+	0.161453i
$213$	−0.777835	+	5.90825i	−0.0532964	+	0.404826i
$214$	0.313375	+	0.274822i	0.0214219	+	0.0187865i
$215$	2.64440	+	1.30407i	0.180346	+	0.0889370i
$216$	0.319436	−	0.0635399i	0.0217349	−	0.00432334i
$217$	18.7063	−	4.71848i	1.26987	−	0.320311i
$218$	0.322743	−	0.483019i	0.0218589	−	0.0327142i
$219$	0.503807	+	3.82679i	0.0340441	+	0.258591i
$220$	1.59808	−	2.76795i	0.107742	−	0.186615i
$221$	−4.47431	−	10.6093i	−0.300975	−	0.713658i
$222$	−0.152994	+	0.0883309i	−0.0102683	+	0.00592838i
$223$	−20.1097	−	8.32970i	−1.34664	−	0.557798i	−0.411287	−	0.911506i	$-0.634921\pi$
$223$	−20.1097	−	8.32970i	−1.34664	−	0.557798i	−0.935356	+	0.353708i	$0.884921\pi$
$224$	−2.32862	+	1.10606i	−0.155588	+	0.0739015i
$225$	−3.48580	−	3.48580i	−0.232387	−	0.232387i
$226$	−0.372782	−	0.425076i	−0.0247971	−	0.0282756i
$227$	−19.9503	+	1.30761i	−1.32415	+	0.0867892i	−0.711007	−	0.703185i	$-0.751761\pi$
$227$	−19.9503	+	1.30761i	−1.32415	+	0.0867892i	−0.613140	+	0.789974i	$0.710094\pi$
$228$	1.25045	−	1.42586i	0.0828130	−	0.0944301i
$229$	6.05783	−	7.89472i	0.400313	−	0.521698i	−0.549088	−	0.835764i	$-0.685025\pi$
$229$	6.05783	−	7.89472i	0.400313	−	0.521698i	0.949401	+	0.314067i	$0.101692\pi$
$230$	−0.116655	+	0.0483199i	−0.00769197	+	0.00318612i
$231$	4.91837	+	15.2213i	0.323605	+	1.00149i
$232$	0.750114	+	1.12263i	0.0492474	+	0.0737040i
$233$	−2.76336	+	2.42340i	−0.181034	+	0.158762i	−0.745067	−	0.666990i	$-0.767582\pi$
$233$	−2.76336	+	2.42340i	−0.181034	+	0.158762i	0.564033	+	0.825752i	$0.309249\pi$
$234$	0.220002	−	0.0589493i	0.0143820	−	0.00385363i
$235$	−0.881555	−	1.78762i	−0.0575063	−	0.116611i
$236$	20.8588	−	2.74611i	1.35779	−	0.178756i
$237$	15.9089			1.03339
$238$	−0.794656	−	0.400125i	−0.0515099	−	0.0259363i
$239$	18.9807			1.22776			0.613881	−	0.789399i	$-0.289607\pi$
$239$	18.9807			1.22776			0.613881	+	0.789399i	$0.289607\pi$
$240$	1.04125	−	0.137083i	0.0672125	−	0.00884869i
$241$	−0.182685	−	0.370448i	−0.0117677	−	0.0238626i	0.890910	−	0.454181i	$-0.150068\pi$
$241$	−0.182685	−	0.370448i	−0.0117677	−	0.0238626i	−0.902677	+	0.430318i	$0.858401\pi$
$242$	2.01314	−	0.539420i	0.129410	−	0.0346752i
$243$	0.751840	−	0.659346i	0.0482305	−	0.0422971i
$244$	−9.10374	−	13.6247i	−0.582807	−	0.872233i
$245$	1.77469	−	0.544742i	0.113381	−	0.0348023i
$246$	−0.168333	+	0.0697260i	−0.0107325	+	0.00444557i
$247$	1.61743	−	2.10788i	0.102915	−	0.134121i
$248$	1.56588	−	1.78554i	0.0994334	−	0.113382i
$249$	4.30296	−	0.282031i	0.272689	−	0.0178730i
$250$	0.141612	+	0.161477i	0.00895630	+	0.0102127i
$251$	6.94955	+	6.94955i	0.438652	+	0.438652i	0.891558	−	0.452906i	$-0.149613\pi$
$251$	6.94955	+	6.94955i	0.438652	+	0.438652i	−0.452906	+	0.891558i	$0.649613\pi$
$252$	−2.99423	+	4.34150i	−0.188619	+	0.273489i
$253$	32.6075	+	13.5065i	2.05002	+	0.849145i
$254$	−1.12885	+	0.651741i	−0.0708302	+	0.0408939i
$255$	0.778126	+	0.768224i	0.0487281	+	0.0481081i
$256$	7.73525	−	13.3978i	0.483453	−	0.837365i
$257$	2.63176	+	19.9902i	0.164165	+	1.24695i	0.852952	+	0.521990i	$0.174810\pi$
$257$	2.63176	+	19.9902i	0.164165	+	1.24695i	−0.688787	+	0.724964i	$0.741857\pi$
$258$	−0.503768	+	0.753943i	−0.0313632	+	0.0469384i
$259$	1.56454	−	5.51314i	0.0972157	−	0.342570i
$260$	1.44791	−	0.288008i	0.0897959	−	0.0178615i
$261$	3.71799	+	1.83351i	0.230138	+	0.113492i
$262$	−1.07915	−	0.946392i	−0.0666703	−	0.0584683i
$263$	−2.80080	+	21.2742i	−0.172705	+	1.31182i	0.657114	+	0.753791i	$0.271777\pi$
$263$	−2.80080	+	21.2742i	−0.172705	+	1.31182i	−0.829819	+	0.558032i	$0.811557\pi$
$264$	1.56223	+	1.19874i	0.0961484	+	0.0737773i
$265$	−0.503888	−	0.100230i	−0.0309536	−	0.00615705i
$266$	−0.0104116	−	0.205037i	−0.000638377	−	0.0125716i
$267$	−0.272235	−	1.36862i	−0.0166605	−	0.0837582i
$268$	−6.44072	−	1.72579i	−0.393430	−	0.105419i
$269$	3.26356	−	1.60941i	0.198983	−	0.0981274i	−0.340068	−	0.940401i	$-0.610450\pi$
$269$	3.26356	−	1.60941i	0.198983	−	0.0981274i	0.539050	+	0.842274i	$0.318783\pi$
$270$	−0.0171600	+	0.0131673i	−0.00104432	+	0.000801338i
$271$	2.81704	+	4.87926i	0.171123	+	0.296394i	0.938813	−	0.344428i	$-0.111927\pi$
$271$	2.81704	+	4.87926i	0.171123	+	0.296394i	−0.767690	+	0.640822i	$0.778594\pi$
$272$	16.1744	−	2.23485i	0.980716	−	0.135508i
$273$	−3.78801	+	6.34360i	−0.229261	+	0.383932i
$274$	0.495498	−	1.19624i	0.0299341	−	0.0722674i
$275$	1.94932	−	29.7409i	0.117548	−	1.79344i
$276$	3.01172	+	11.2399i	0.181284	+	0.676563i
$277$	−1.40334	+	4.13410i	−0.0843185	+	0.248394i	−0.980909	−	0.194466i	$-0.937703\pi$
$277$	−1.40334	+	4.13410i	−0.0843185	+	0.248394i	0.896591	+	0.442860i	$0.146036\pi$
$278$	−0.00829284	+	0.0168162i	−0.000497372	+	0.00100857i
$279$	1.42256	−	7.15168i	0.0851663	−	0.428160i
$280$	0.141771	−	0.179236i	0.00847242	−	0.0107114i
$281$	−6.60887	−	15.9552i	−0.394252	−	0.951809i	−0.989003	−	0.147899i	$-0.952749\pi$
$281$	−6.60887	−	15.9552i	−0.394252	−	0.951809i	0.594750	−	0.803910i	$-0.297251\pi$
$282$	0.580440	−	0.197033i	0.0345647	−	0.0117331i
$283$	1.38872	+	21.1878i	0.0825508	+	1.25948i	0.815323	+	0.579007i	$0.196560\pi$
$283$	1.38872	+	21.1878i	0.0825508	+	1.25948i	−0.732772	+	0.680474i	$0.761774\pi$
$284$	−11.2484	−	3.81832i	−0.667470	−	0.226576i
$285$	−0.0653045	+	0.243720i	−0.00386830	+	0.0144367i
$286$	1.14497	+	0.765047i	0.0677037	+	0.0452382i
$287$	2.34199	−	5.42680i	0.138243	−	0.320334i
$288$			0.974375i			0.0574156i
$289$	12.1738	+	11.8659i	0.716104	+	0.697993i
$290$	−0.0776531	−	0.0448331i	−0.00455995	−	0.00263269i
$291$	−9.03439	−	11.7738i	−0.529605	−	0.690195i
$292$	−7.67748	−	0.503209i	−0.449290	−	0.0294481i
$293$	12.3523	−	12.3523i	0.721629	−	0.721629i	−0.247308	−	0.968937i	$-0.579546\pi$
$293$	12.3523	−	12.3523i	0.721629	−	0.721629i	0.968937	+	0.247308i	$0.0795459\pi$
$294$	0.0948557	+	0.562980i	0.00553210	+	0.0328336i
$295$	−2.32734	+	1.55508i	−0.135503	+	0.0905403i
$296$	−0.226767	−	0.668033i	−0.0131805	−	0.0388286i
$297$	5.99426	+	0.789159i	0.347822	+	0.0457917i
$298$	−1.07670	−	0.141751i	−0.0623717	−	0.00821139i
$299$	5.24015	+	15.4370i	0.303046	+	0.892744i
$300$	8.17047	−	5.45934i	0.471722	−	0.315195i
$301$	−5.31345	−	28.9310i	−0.306262	−	1.66756i
$302$	−0.357940	+	0.357940i	−0.0205972	+	0.0205972i
$303$	−13.7837	−	0.903434i	−0.791855	−	0.0519009i
$304$	2.29365	+	2.98914i	0.131550	+	0.171439i
$305$	1.88802	+	1.09005i	0.108107	+	0.0624159i
$306$	−0.265471	+	0.206417i	−0.0151759	+	0.0118001i
$307$		−	7.69191i		−	0.439001i	−0.975612	−	0.219500i	$-0.929557\pi$
$307$		−	7.69191i		−	0.439001i	0.975612	−	0.219500i	$-0.0704427\pi$
$308$	−31.6710	+	3.69635i	−1.80462	+	0.210619i
$309$	−2.61522	−	1.74743i	−0.148775	−	0.0994080i
$310$	−0.0408207	+	0.152345i	−0.00231846	+	0.00865262i
$311$	15.1374	+	5.13846i	0.858364	+	0.291375i	0.715710	−	0.698397i	$-0.246103\pi$
$311$	15.1374	+	5.13846i	0.858364	+	0.291375i	0.142654	+	0.989773i	$0.454436\pi$
$312$	0.0594864	+	0.907587i	0.00336776	+	0.0513820i
$313$	14.1782	−	4.81285i	0.801400	−	0.272039i	0.109458	−	0.993991i	$-0.465089\pi$
$313$	14.1782	−	4.81285i	0.801400	−	0.272039i	0.691942	+	0.721953i	$0.256755\pi$
$314$	0.131709	+	0.317973i	0.00743276	+	0.0179443i
$315$	0.101811	−	0.694233i	0.00573638	−	0.0391156i
$316$	−6.18669	+	31.1026i	−0.348028	+	1.74966i
$317$	2.59571	−	5.26357i	0.145789	−	0.295632i	−0.811713	−	0.584056i	$-0.801465\pi$
$317$	2.59571	−	5.26357i	0.145789	−	0.295632i	0.957503	+	0.288425i	$0.0931314\pi$
$318$	0.0507873	−	0.149615i	0.00284801	−	0.00838997i
$319$	6.48696	+	24.2097i	0.363200	+	1.35548i
$320$	−0.135999	+	2.07494i	−0.00760258	+	0.115993i
$321$	−1.95571	+	4.72151i	−0.109157	+	0.263529i
$322$	1.08152	+	0.645820i	0.0602710	+	0.0359901i
$323$	−0.991007	+	3.79554i	−0.0551411	+	0.211189i
$324$	0.996674	+	1.72629i	0.0553708	+	0.0959050i
$325$	10.9218	−	8.38057i	0.605831	−	0.464870i
$326$	0.376748	−	0.185791i	0.0208661	−	0.0102900i
$327$	6.88000	+	1.84349i	0.380465	+	0.101945i
$328$	−0.141948	−	0.713618i	−0.00783774	−	0.0394030i
$329$	−9.05615	+	17.7026i	−0.499282	+	0.975974i
$330$	−0.128260	−	0.0255125i	−0.00706048	−	0.00140442i
$331$	5.49759	+	4.21845i	0.302175	+	0.231867i	0.748708	−	0.662900i	$-0.230675\pi$
$331$	5.49759	+	4.21845i	0.302175	+	0.231867i	−0.446533	+	0.894767i	$0.647341\pi$
$332$	−1.12196	+	8.52217i	−0.0615758	+	0.467715i
$333$	−1.62853	−	1.42818i	−0.0892427	−	0.0782637i
$334$	−0.203466	−	0.100338i	−0.0111332	−	0.00549027i
$335$	0.870079	−	0.173069i	0.0475375	−	0.00945579i
$336$	−7.29892	−	7.51694i	−0.398189	−	0.410083i
$337$	3.70068	−	5.53846i	0.201589	−	0.301699i	−0.716877	−	0.697200i	$-0.754429\pi$
$337$	3.70068	−	5.53846i	0.201589	−	0.301699i	0.918466	+	0.395501i	$0.129429\pi$
$338$	−0.0553720	−	0.420592i	−0.00301184	−	0.0228772i
$339$	3.46608	−	6.00342i	0.188251	−	0.326061i
$340$	−1.80451	+	1.22252i	−0.0978635	+	0.0663006i
$341$	38.1796	−	22.0430i	2.06754	−	1.19370i
$342$	−0.0716900	−	0.0296950i	−0.00387655	−	0.00160572i
$343$	−14.9300	−	10.9588i	−0.806143	−	0.591721i
$344$	−2.56044	−	2.56044i	−0.138049	−	0.138049i
$345$	−1.02077	−	1.16396i	−0.0549562	−	0.0626655i
$346$	−2.09565	+	0.137356i	−0.112663	+	0.00738431i
$347$	−13.1042	+	14.9425i	−0.703471	+	0.802155i	−0.987660	−	0.156613i	$-0.949942\pi$
$347$	−13.1042	+	14.9425i	−0.703471	+	0.802155i	0.284189	+	0.958768i	$0.408276\pi$
$348$	−5.03046	+	6.55583i	−0.269661	+	0.351429i
$349$	30.2642	−	12.5359i	1.62001	−	0.671029i	0.625947	−	0.779866i	$-0.284713\pi$
$349$	30.2642	−	12.5359i	1.62001	−	0.671029i	0.994060	+	0.108837i	$0.0347126\pi$
$350$	0.222856	−	1.04015i	0.0119122	−	0.0555981i
$351$	1.55149	+	2.32196i	0.0828122	+	0.123937i
$352$	−4.42913	+	3.88424i	−0.236073	+	0.207031i
$353$	5.50959	−	1.47629i	0.293246	−	0.0785749i	−0.109197	−	0.994020i	$-0.534828\pi$
$353$	5.50959	−	1.47629i	0.293246	−	0.0785749i	0.402443	+	0.915445i	$0.368161\pi$
$354$	−0.380729	−	0.772042i	−0.0202355	−	0.0410336i
$355$	1.56688	−	0.206284i	0.0831613	−	0.0109484i
$356$	2.78158			0.147424
$357$	1.51371	−	10.8032i	0.0801140	−	0.571765i
$358$	0.671910			0.0355116
$359$	3.26837	−	0.430289i	0.172498	−	0.0227098i	−0.0437824	−	0.999041i	$-0.513941\pi$
$359$	3.26837	−	0.430289i	0.172498	−	0.0227098i	0.216280	+	0.976331i	$0.430607\pi$
$360$	−0.0382027	−	0.0774673i	−0.00201346	−	0.00408289i
$361$	17.4782	−	4.68328i	0.919908	−	0.246489i
$362$	−1.26986	+	1.11364i	−0.0667423	+	0.0585315i
$363$	14.1970	+	21.2473i	0.745149	+	1.11519i
$364$	−10.9289	−	9.87266i	−0.572832	−	0.517468i
$365$	0.945712	−	0.391727i	0.0495008	−	0.0205039i
$366$	−0.408149	+	0.531910i	−0.0213343	+	0.0278034i
$367$	−3.58936	+	4.09288i	−0.187363	+	0.213647i	−0.837894	−	0.545833i	$-0.816213\pi$
$367$	−3.58936	+	4.09288i	−0.187363	+	0.213647i	0.650531	+	0.759480i	$0.274547\pi$
$368$	−23.0682	+	1.51197i	−1.20252	+	0.0788170i
$369$	−1.47297	−	1.67960i	−0.0766799	−	0.0874367i
$370$	0.0331287	+	0.0331287i	0.00172228	+	0.00172228i
$371$	2.19904	+	4.62973i	0.114169	+	0.240364i
$372$	13.4287	+	5.56233i	0.696244	+	0.288394i
$373$	−9.06711	+	5.23490i	−0.469477	+	0.271053i	−0.716021	−	0.698079i	$-0.754038\pi$
$373$	−9.06711	+	5.23490i	−0.469477	+	0.271053i	0.246544	+	0.969132i	$0.420705\pi$
$374$	−1.99656	−	0.383867i	−0.103240	−	0.0198493i
$375$	−1.31669	+	2.28057i	−0.0679933	+	0.117768i
$376$	0.319503	+	2.42686i	0.0164771	+	0.125156i
$377$	−6.43170	+	9.62572i	−0.331249	+	0.495750i
$378$	0.207589	+	0.0589102i	0.0106772	+	0.00303001i
$379$	−25.9429	+	5.16037i	−1.33260	+	0.265071i	−0.809459	−	0.587176i	$-0.800240\pi$
$379$	−25.9429	+	5.16037i	−1.33260	+	0.265071i	−0.523140	+	0.852247i	$0.675240\pi$
$380$	−0.451087	−	0.222452i	−0.0231403	−	0.0114115i
$381$	−12.0159	−	10.5377i	−0.615594	−	0.539861i
$382$	−0.114163	+	0.867153i	−0.00584108	+	0.0443674i
$383$	28.4274	+	21.8131i	1.45257	+	1.11460i	0.971253	+	0.238051i	$0.0765085\pi$
$383$	28.4274	+	21.8131i	1.45257	+	1.11460i	0.481318	+	0.876546i	$0.340158\pi$
$384$	−2.53851	−	0.504940i	−0.129543	−	0.0257676i
$385$	3.56157	−	2.30470i	0.181515	−	0.117458i
$386$	0.337027	+	1.69435i	0.0171542	+	0.0862401i
$387$	−10.7390	−	2.87750i	−0.545892	−	0.146271i
$388$	26.5317	−	13.0840i	1.34694	−	0.664239i
$389$	4.73661	−	3.63453i	0.240156	−	0.184278i	−0.481670	−	0.876352i	$-0.659970\pi$
$389$	4.73661	−	3.63453i	0.240156	−	0.184278i	0.721826	+	0.692075i	$0.243303\pi$
$390$	−0.0302016	−	0.0523106i	−0.00152932	−	0.00264885i
$391$	−15.9854	−	17.9941i	−0.808417	−	0.910002i
$392$	−2.27888	−	0.0670835i	−0.115101	−	0.00338823i
$393$	6.73479	−	16.2592i	0.339725	−	0.820169i
$394$	0.0784576	−	1.19703i	0.00395264	−	0.0603056i
$395$	−1.09198	−	4.07531i	−0.0549432	−	0.205051i
$396$	−3.87391	+	11.4122i	−0.194671	+	0.573483i
$397$	−5.71179	+	11.5824i	−0.286666	+	0.581302i	−0.991804	−	0.127768i	$-0.959219\pi$
$397$	−5.71179	+	11.5824i	−0.286666	+	0.581302i	0.705138	+	0.709071i	$0.250885\pi$
$398$	0.278256	−	1.39889i	0.0139477	−	0.0701199i
$399$	2.33952	−	0.928970i	0.117122	−	0.0465067i
$400$	7.47080	+	18.0361i	0.373540	+	0.901805i
$401$	−20.7398	+	7.04023i	−1.03570	+	0.351572i	−0.786964	−	0.616999i	$-0.788348\pi$
$401$	−20.7398	+	7.04023i	−1.03570	+	0.351572i	−0.248735	+	0.968572i	$0.580015\pi$
$402$	0.0178435	+	0.272239i	0.000889951	+	0.0135780i
$403$	19.2824	+	6.54549i	0.960524	+	0.326054i
$404$	7.12651	−	26.5965i	0.354557	−	1.32323i
$405$	−0.220508	−	0.147338i	−0.0109571	−	0.00732131i
$406$	0.103699	+	0.888510i	0.00514649	+	0.0440960i
$407$		−	13.0959i		−	0.649141i
$408$	−0.601637	−	1.20056i	−0.0297855	−	0.0594365i
$409$	−23.7902	−	13.7353i	−1.17635	−	0.679167i	−0.221184	−	0.975232i	$-0.570992\pi$
$409$	−23.7902	−	13.7353i	−1.17635	−	0.679167i	−0.955168	+	0.296066i	$0.904325\pi$
$410$	0.0294157	+	0.0383353i	0.00145274	+	0.00189325i
$411$	15.8416	+	1.03831i	0.781407	+	0.0512161i
$412$	4.43333	−	4.43333i	0.218414	−	0.218414i
$413$	26.3076	+	9.36414i	1.29451	+	0.460779i
$414$	0.395873	−	0.264514i	0.0194561	−	0.0130001i
$415$	−0.367599	−	1.08291i	−0.0180447	−	0.0531581i
$416$	−2.69776	−	0.355167i	−0.132269	−	0.0174135i
$417$	−0.227925	−	0.0300070i	−0.0111616	−	0.00146945i
$418$	−0.150803	−	0.444250i	−0.00737600	−	0.0217290i
$419$	2.64970	−	1.77047i	0.129446	−	0.0864933i	−0.489161	−	0.872193i	$-0.662697\pi$
$419$	2.64970	−	1.77047i	0.129446	−	0.0864933i	0.618608	+	0.785700i	$0.287697\pi$
$420$	1.31767	+	0.469020i	0.0642955	+	0.0228858i
$421$	14.5909	−	14.5909i	0.711115	−	0.711115i	−0.255653	−	0.966768i	$-0.582291\pi$
$421$	14.5909	−	14.5909i	0.711115	−	0.711115i	0.966768	+	0.255653i	$0.0822906\pi$
$422$	−1.06345	−	0.0697025i	−0.0517682	−	0.00339306i
$423$	4.57524	+	5.96256i	0.222456	+	0.289910i
$424$	0.546417	+	0.315474i	0.0265363	+	0.0153208i
$425$	−10.0498	+	17.6671i	−0.487489	+	0.856983i
$426$			0.486030i			0.0235482i
$427$	−2.52128	−	21.6027i	−0.122013	−	1.04543i
$428$	−8.47022	−	5.65962i	−0.409424	−	0.273568i
$429$	−4.36990	+	16.3087i	−0.210981	+	0.787392i
$430$	0.227713	+	0.0772980i	0.0109813	+	0.00372764i
$431$	1.01645	+	15.5080i	0.0489605	+	0.746993i	0.949803	+	0.312847i	$0.101283\pi$
$431$	1.01645	+	15.5080i	0.0489605	+	0.746993i	−0.900843	+	0.434145i	$0.857050\pi$
$432$	−3.74997	+	1.27294i	−0.180420	+	0.0612445i
$433$	−1.63321	−	3.94293i	−0.0784873	−	0.189485i	0.879765	−	0.475408i	$-0.157700\pi$
$433$	−1.63321	−	3.94293i	−0.0784873	−	0.189485i	−0.958252	+	0.285923i	$0.907700\pi$
$434$	1.46239	−	0.580684i	0.0701971	−	0.0278737i
$435$	0.214482	−	1.07827i	0.0102836	−	0.0516993i
$436$	−6.27962	+	12.7338i	−0.300739	+	0.609839i
$437$	1.78527	−	5.25924i	0.0854012	−	0.251584i
$438$	0.0814772	+	0.304077i	0.00389313	+	0.0145294i
$439$	−1.53664	+	23.4446i	−0.0733398	+	1.11895i	0.789593	+	0.613631i	$0.210292\pi$
$439$	−1.53664	+	23.4446i	−0.0733398	+	1.11895i	−0.862933	+	0.505318i	$0.831375\pi$
$440$	0.199845	−	0.482470i	0.00952726	−	0.0230008i
$441$	−6.16254	+	3.32011i	−0.293454	+	0.158100i
$442$	−0.474742	−	0.810251i	−0.0225812	−	0.0385397i
$443$	12.5921	+	21.8102i	0.598270	+	1.03623i	0.993076	+	0.117470i	$0.0374784\pi$
$443$	12.5921	+	21.8102i	0.598270	+	1.03623i	−0.394806	+	0.918764i	$0.629188\pi$
$444$	3.42546	−	2.62845i	0.162565	−	0.124741i
$445$	−0.331907	+	0.163679i	−0.0157339	+	0.00775911i
$446$	−1.71477	−	0.459472i	−0.0811969	−	0.0217566i
$447$	−2.59770	−	13.0595i	−0.122867	−	0.617695i
$448$	17.4164	−	11.2702i	0.822847	−	0.532465i
$449$	32.4493	+	6.45457i	1.53138	+	0.304610i	0.887605	−	0.460606i	$-0.152368\pi$
$449$	32.4493	+	6.45457i	1.53138	+	0.304610i	0.643773	+	0.765216i	$0.277368\pi$
$450$	−0.318976	−	0.244759i	−0.0150367	−	0.0115380i
$451$	1.76297	−	13.3911i	0.0830152	−	0.630563i
$452$	10.3891	+	9.11097i	0.488661	+	0.428544i
$453$	−5.56651	−	2.74510i	−0.261538	−	0.128976i
$454$	−1.59929	+	0.318119i	−0.0750584	+	0.0149301i
$455$	1.88502	+	0.534938i	0.0883711	+	0.0250783i
$456$	0.172155	−	0.257648i	0.00806189	−	0.0120655i
$457$	4.19209	+	31.8421i	0.196098	+	1.48951i	0.752497	+	0.658596i	$0.228849\pi$
$457$	4.19209	+	31.8421i	0.196098	+	1.48951i	−0.556399	+	0.830915i	$0.687817\pi$
$458$	0.405801	−	0.702868i	0.0189618	−	0.0328429i
$459$	−3.44283	−	2.26868i	−0.160698	−	0.105893i
$460$	2.67255	−	1.54300i	0.124609	−	0.0719428i
$461$	−11.9181	−	4.93666i	−0.555083	−	0.229923i	0.0874659	−	0.996168i	$-0.472123\pi$
$461$	−11.9181	−	4.93666i	−0.555083	−	0.229923i	−0.642549	+	0.766245i	$0.722123\pi$
$462$	0.559747	+	1.17846i	0.0260418	+	0.0548267i
$463$	13.0283	+	13.0283i	0.605477	+	0.605477i	0.941761	−	0.336284i	$-0.109170\pi$
$463$	13.0283	+	13.0283i	0.605477	+	0.605477i	−0.336284	+	0.941761i	$0.609170\pi$
$464$	−10.8243	−	12.3428i	−0.502507	−	0.572999i
$465$	−1.92966	+	0.126477i	−0.0894858	+	0.00586521i
$466$	−0.197651	+	0.225378i	−0.00915600	+	0.0104404i
$467$	−7.80463	+	10.1712i	−0.361155	+	0.470667i	−0.938224	−	0.346029i	$-0.887530\pi$
$467$	−7.80463	+	10.1712i	−0.361155	+	0.470667i	0.577068	+	0.816696i	$0.304197\pi$
$468$	−5.14289	+	2.13026i	−0.237730	+	0.0984711i
$469$	−6.56740	−	5.93266i	−0.303255	−	0.273945i
$470$	−0.0903142	−	0.135165i	−0.00416588	−	0.00623468i
$471$	−3.17269	+	2.78237i	−0.146190	+	0.128205i
$472$	3.32040	−	0.889700i	0.152834	−	0.0409517i
$473$	−29.7297	−	60.2860i	−1.36698	−	2.77195i
$474$	1.28642	−	0.169360i	0.0590870	−	0.00777896i
$475$	−4.69016			−0.215199
$476$	20.5321	+	7.16054i	0.941086	+	0.328203i
$477$	1.93724			0.0887000
$478$	1.53481	−	0.202062i	0.0702006	−	0.00924209i
$479$	−16.9963	−	34.4650i	−0.776579	−	1.57475i	−0.817735	−	0.575595i	$-0.804771\pi$
$479$	−16.9963	−	34.4650i	−0.776579	−	1.57475i	0.0411556	−	0.999153i	$-0.486896\pi$
$480$	0.249601	−	0.0668805i	0.0113927	−	0.00305266i
$481$	4.54782	−	3.98833i	0.207363	−	0.181852i
$482$	−0.0187158	−	0.0280102i	−0.000852481	−	0.00127583i
$483$	−3.23571	+	15.1021i	−0.147230	+	0.687171i
$484$	−47.0604	+	19.4931i	−2.13911	+	0.886049i
$485$	−2.39594	+	3.12245i	−0.108794	+	0.141783i
$486$	0.0537758	−	0.0613195i	0.00243932	−	0.00278151i
$487$	−2.22883	+	0.146085i	−0.100998	+	0.00661976i	−0.115818	−	0.993270i	$-0.536949\pi$
$487$	−2.22883	+	0.146085i	−0.100998	+	0.00661976i	0.0148203	+	0.999890i	$0.495282\pi$
$488$	−1.76531	−	2.01295i	−0.0799119	−	0.0911221i
$489$	3.64193	+	3.64193i	0.164694	+	0.164694i
$490$	0.137705	−	0.0629414i	0.00622089	−	0.00284340i
$491$	−38.9649	−	16.1398i	−1.75846	−	0.728379i	−0.996758	−	0.0804550i	$-0.974363\pi$
$491$	−38.9649	−	16.1398i	−1.75846	−	0.728379i	−0.761705	−	0.647924i	$-0.775637\pi$
$492$	3.85652	−	2.22656i	0.173865	−	0.100381i
$493$	3.22714	−	16.7850i	0.145343	−	0.755956i
$494$	0.108348	−	0.187665i	0.00487482	−	0.00844343i
$495$	−0.209287	−	1.58969i	−0.00940674	−	0.0714513i
$496$	−16.0429	+	24.0099i	−0.720347	+	1.07808i
$497$	−10.9834	−	11.3115i	−0.492675	−	0.507391i
$498$	0.344942	−	0.0686132i	0.0154572	−	0.00307463i
$499$	−1.37888	−	0.679989i	−0.0617272	−	0.0304405i	0.411163	−	0.911562i	$-0.365123\pi$
$499$	−1.37888	−	0.679989i	−0.0617272	−	0.0304405i	−0.472890	+	0.881121i	$0.656789\pi$
$500$	−3.94657	−	3.46105i	−0.176496	−	0.154783i
$501$	0.363066	−	2.75776i	0.0162206	−	0.123207i
$502$	0.635933	+	0.487969i	0.0283831	+	0.0217791i
$503$	−1.06772	−	0.212383i	−0.0476074	−	0.00946970i	0.171229	−	0.985231i	$-0.445226\pi$
$503$	−1.06772	−	0.212383i	−0.0476074	−	0.00946970i	−0.218837	+	0.975762i	$0.570226\pi$
$504$	−0.392453	+	0.767150i	−0.0174813	+	0.0341716i
$505$	0.714679	+	3.59293i	0.0318028	+	0.159883i
$506$	2.78048	+	0.745027i	0.123607	+	0.0331205i
$507$	4.66498	−	2.30051i	0.207179	−	0.102169i
$508$	25.2744	−	19.3937i	1.12137	−	0.860459i
$509$	−0.900613	−	1.55991i	−0.0399190	−	0.0691417i	0.845376	−	0.534172i	$-0.179377\pi$
$509$	−0.900613	−	1.55991i	−0.0399190	−	0.0691417i	−0.885295	+	0.465031i	$0.846043\pi$
$510$	0.0710987	+	0.0538361i	0.00314830	+	0.00238390i
$511$	−8.76786	−	5.23563i	−0.387867	−	0.231611i
$512$	2.46381	−	5.94816i	0.108886	−	0.262874i
$513$	0.0622255	−	0.949377i	0.00274732	−	0.0419160i
$514$	0.425616	+	1.58842i	0.0187731	+	0.0700622i
$515$	−0.268125	+	0.789872i	−0.0118150	+	0.0348059i
$516$	9.80184	−	19.8762i	0.431502	−	0.874999i
$517$	−8.86480	+	44.5664i	−0.389873	+	1.96003i
$518$	0.0678202	−	0.462457i	0.00297985	−	0.0203192i
$519$	−9.85407	−	23.7898i	−0.432546	−	1.04426i
$520$	0.228410	−	0.0775346i	0.0100164	−	0.00340012i
$521$	−2.75339	−	42.0086i	−0.120628	−	1.84043i	−0.446224	−	0.894921i	$-0.647232\pi$
$521$	−2.75339	−	42.0086i	−0.120628	−	1.84043i	0.325596	−	0.945509i	$-0.394435\pi$
$522$	0.320162	+	0.108680i	0.0140131	+	0.00475680i
$523$	−9.46892	+	35.3385i	−0.414047	+	1.54524i	0.372690	+	0.927956i	$0.378435\pi$
$523$	−9.46892	+	35.3385i	−0.414047	+	1.54524i	−0.786737	+	0.617288i	$0.788231\pi$
$524$	29.1685	+	19.4898i	1.27423	+	0.851414i
$525$	12.9547	−	1.51196i	0.565391	−	0.0659874i
$526$			1.75008i			0.0763071i
$527$	−29.9872	+	2.15839i	−1.30626	+	0.0940211i
$528$	−20.7352	−	11.9714i	−0.902382	−	0.520990i
$529$	6.74373	+	8.78860i	0.293206	+	0.382113i
$530$	−0.0418121	−	0.00274051i	−0.00181620	−	0.000119040i
$531$	7.46314	−	7.46314i	0.323873	−	0.323873i
$532$	0.906382	+	4.93512i	0.0392966	+	0.213965i
$533$	5.18724	−	3.46601i	0.224684	−	0.150129i
$534$	−0.0365832	−	0.107771i	−0.00158311	−	0.00466369i
$535$	1.34373	+	0.176905i	0.0580944	+	0.00764827i
$536$	−1.08016	−	0.142205i	−0.0466556	−	0.00614233i
$537$	2.64812	+	7.80110i	0.114275	+	0.336642i
$538$	0.246763	−	0.164882i	0.0106387	−	0.00710856i
$539$	−39.6582	−	14.7772i	−1.70820	−	0.636501i
$540$	0.373805	−	0.373805i	0.0160860	−	0.0160860i
$541$	−18.2494	−	1.19613i	−0.784601	−	0.0514255i	−0.332164	−	0.943222i	$-0.607779\pi$
$541$	−18.2494	−	1.19613i	−0.784601	−	0.0514255i	−0.452437	+	0.891796i	$0.649445\pi$
$542$	0.279733	+	0.364556i	0.0120156	+	0.0156590i
$543$	−17.9344	−	10.3544i	−0.769640	−	0.444352i
$544$	3.87382	−	1.06462i	0.166089	−	0.0456452i
$545$		−	1.88896i		−	0.0809140i
$546$	−0.238773	+	0.553279i	−0.0102185	+	0.0236782i
$547$	15.6051	+	10.4270i	0.667225	+	0.445825i	0.842502	−	0.538694i	$-0.181082\pi$
$547$	15.6051	+	10.4270i	0.667225	+	0.445825i	−0.175277	+	0.984519i	$0.556082\pi$
$548$	−8.19046	+	30.5672i	−0.349879	+	1.30577i
$549$	−7.78423	−	2.64239i	−0.332223	−	0.112774i
$550$	−0.158985	−	2.42564i	−0.00677915	−	0.103430i
$551$	3.73478	−	1.26779i	0.159107	−	0.0540096i
$552$	0.727589	+	1.75655i	0.0309682	+	0.0747639i
$553$	−26.1119	+	33.0123i	−1.11039	+	1.40383i
$554$	−0.0694661	+	0.349229i	−0.00295133	+	0.0148373i
$555$	−0.254069	+	0.515202i	−0.0107846	+	0.0218691i
$556$	0.147301	−	0.433936i	0.00624697	−	0.0184030i
$557$	1.03613	+	3.86691i	0.0439024	+	0.163846i	0.984397	−	0.175963i	$-0.0563041\pi$
$557$	1.03613	+	3.86691i	0.0439024	+	0.163846i	−0.940494	+	0.339810i	$0.889637\pi$
$558$	0.0388961	−	0.593440i	0.00164660	−	0.0251223i
$559$	11.8814	−	28.6842i	0.502529	−	1.21321i
$560$	−1.42459	+	2.38569i	−0.0601998	+	0.100814i
$561$	−3.41198	−	24.6936i	−0.144054	−	1.04257i
$562$	−0.704257	−	1.21981i	−0.0297073	−	0.0514545i
$563$	−1.16368	+	0.892925i	−0.0490433	+	0.0376323i	−0.632992	−	0.774158i	$-0.718174\pi$
$563$	−1.16368	+	0.892925i	−0.0490433	+	0.0376323i	0.583949	+	0.811790i	$0.301507\pi$
$564$	−13.4363	+	6.62606i	−0.565771	+	0.279007i
$565$	−1.77578	−	0.475819i	−0.0747076	−	0.0200178i
$566$	0.337851	+	1.69849i	0.0142009	+	0.0713929i
$567$	0.134176	+	2.64235i	0.00563487	+	0.110968i
$568$	−1.90359	−	0.378648i	−0.0798730	−	0.0158877i
$569$	16.3420	+	12.5397i	0.685093	+	0.525691i	0.891639	−	0.452746i	$-0.149556\pi$
$569$	16.3420	+	12.5397i	0.685093	+	0.525691i	−0.206546	+	0.978437i	$0.566222\pi$
$570$	−0.00268607	+	0.0204028i	−0.000112507	+	0.000854577i
$571$	10.1952	+	8.94097i	0.426657	+	0.374168i	0.845576	−	0.533856i	$-0.179257\pi$
$571$	10.1952	+	8.94097i	0.426657	+	0.374168i	−0.418919	+	0.908024i	$0.637591\pi$
$572$	−30.1849	−	14.8855i	−1.26209	−	0.622396i
$573$	−10.5179	+	2.09213i	−0.439390	+	0.0874002i
$574$	0.131605	−	0.463751i	0.00549308	−	0.0193566i
$575$	15.9879	−	23.9276i	0.666743	−	0.997851i
$576$	−1.02343	−	7.77372i	−0.0426429	−	0.323905i
$577$	−14.9368	+	25.8713i	−0.621828	+	1.07704i	0.367317	+	0.930096i	$0.380276\pi$
$577$	−14.9368	+	25.8713i	−0.621828	+	1.07704i	−0.989145	+	0.146942i	$0.953057\pi$
$578$	1.11071	+	0.829897i	0.0461994	+	0.0345191i
$579$	−18.3437	+	10.5907i	−0.762337	+	0.440135i
$580$	2.02467	+	0.838644i	0.0840697	+	0.0348228i
$581$	−6.47739	+	9.39194i	−0.268727	+	0.389643i
$582$	−0.855874	−	0.855874i	−0.0354771	−	0.0354771i
$583$	7.72259	+	8.80593i	0.319837	+	0.364704i
$584$	−1.25443	+	0.0822196i	−0.0519086	+	0.00340227i
$585$	0.488314	−	0.556815i	0.0201893	−	0.0230215i
$586$	0.867328	−	1.13032i	0.0358290	−	0.0466932i
$587$	−28.6386	+	11.8625i	−1.18204	+	0.489618i	−0.885156	−	0.465295i	$-0.845948\pi$
$587$	−28.6386	+	11.8625i	−1.18204	+	0.489618i	−0.296886	+	0.954913i	$0.595948\pi$
$588$	−4.09446	−	13.3392i	−0.168853	−	0.550099i
$589$	−3.85428	−	5.76833i	−0.158813	−	0.237680i
$590$	−0.171638	+	0.150522i	−0.00706621	+	0.00619690i
$591$	14.2072	−	3.80680i	0.584404	−	0.156591i
$592$	3.79389	+	7.69325i	0.155928	+	0.316191i
$593$	−12.5631	+	1.65397i	−0.515905	+	0.0679202i	−0.383984	−	0.923340i	$-0.625448\pi$
$593$	−12.5631	+	1.65397i	−0.515905	+	0.0679202i	−0.131922	+	0.991260i	$0.542115\pi$
$594$	0.493106			0.0202324
$595$	−2.87130	+	0.353763i	−0.117712	+	0.0145029i
$596$	26.5422			1.08721
$597$	17.3382	−	2.28262i	0.709605	−	0.0934213i
$598$	0.588063	+	1.19247i	0.0240477	+	0.0487639i
$599$	29.9704	−	8.03053i	1.22456	−	0.328119i	0.412098	−	0.911139i	$-0.364796\pi$
$599$	29.9704	−	8.03053i	1.22456	−	0.328119i	0.812457	+	0.583021i	$0.198129\pi$
$600$	1.20713	−	1.05862i	0.0492808	−	0.0432181i
$601$	9.04836	+	13.5418i	0.369090	+	0.552383i	0.968803	−	0.247833i	$-0.0797183\pi$
$601$	9.04836	+	13.5418i	0.369090	+	0.552383i	−0.599712	+	0.800216i	$0.704718\pi$
$602$	−0.737643	−	2.28284i	−0.0300641	−	0.0930417i
$603$	−3.09046	+	1.28011i	−0.125853	+	0.0521301i
$604$	7.53152	−	9.81527i	0.306453	−	0.399378i
$605$	4.46836	−	5.09518i	0.181665	−	0.207149i
$606$	−1.12419	+	0.0736834i	−0.0456672	+	0.00299318i
$607$	5.80996	+	6.62499i	0.235819	+	0.268900i	0.857630	−	0.514267i	$-0.171936\pi$
$607$	5.80996	+	6.62499i	0.235819	+	0.268900i	−0.621811	+	0.783167i	$0.713603\pi$
$608$	0.655512	+	0.655512i	0.0265845	+	0.0265845i
$609$	−9.90720	+	4.70575i	−0.401460	+	0.190687i
$610$	0.164272	+	0.0680437i	0.00665118	+	0.00275501i
$611$	−18.1763	+	10.4941i	−0.735335	+	0.424546i
$612$	5.77423	−	5.84865i	0.233409	−	0.236418i
$613$	−11.0901	+	19.2086i	−0.447924	+	0.775827i	−0.998251	−	0.0591226i	$-0.981170\pi$
$613$	−11.0901	+	19.2086i	−0.447924	+	0.775827i	0.550327	+	0.834949i	$0.314503\pi$
$614$	−0.0818852	−	0.621980i	−0.00330462	−	0.0251011i
$615$	−0.329153	+	0.492612i	−0.0132727	+	0.0198640i
$616$	−5.05164	+	1.27422i	−0.203536	+	0.0513399i
$617$	−25.5278	+	5.07780i	−1.02771	+	0.204425i	−0.680027	−	0.733187i	$-0.738032\pi$
$617$	−25.5278	+	5.07780i	−1.02771	+	0.204425i	−0.347685	+	0.937612i	$0.613032\pi$
$618$	−0.230073	−	0.113459i	−0.00925489	−	0.00456401i
$619$	−6.41829	−	5.62869i	−0.257973	−	0.226236i	0.520584	−	0.853811i	$-0.325714\pi$
$619$	−6.41829	−	5.62869i	−0.257973	−	0.226236i	−0.778556	+	0.627575i	$0.784048\pi$
$620$	0.503144	−	3.82176i	0.0202067	−	0.153485i
$621$	4.63129	+	3.55372i	0.185847	+	0.142606i
$622$	1.27874	+	0.254357i	0.0512727	+	0.0101988i
$623$	3.28684	+	1.68146i	0.131684	+	0.0673663i
$624$	−2.15752	−	10.8466i	−0.0863698	−	0.434210i
$625$	−23.1339	−	6.19871i	−0.925356	−	0.247948i
$626$	1.09524	−	0.540111i	0.0437744	−	0.0215872i
$627$	4.56355	−	3.50174i	0.182251	−	0.139846i
$628$	−4.20586	−	7.28476i	−0.167832	−	0.290694i
$629$	−3.89865	+	8.03498i	−0.155449	+	0.320376i
$630$	0.000842022	−	0.0572206i	3.35470e−5	−	0.00227972i
$631$	1.96148	−	4.73544i	0.0780855	−	0.188515i	−0.880016	−	0.474944i	$-0.842468\pi$
$631$	1.96148	−	4.73544i	0.0780855	−	0.188515i	0.958101	+	0.286429i	$0.0924683\pi$
$632$	−0.338882	+	5.17034i	−0.0134800	+	0.205665i
$633$	−3.38199	−	12.6218i	−0.134422	−	0.501670i
$634$	0.153859	−	0.453253i	0.00611051	−	0.0180010i
$635$	−1.87463	+	3.80136i	−0.0743922	+	0.150853i
$636$	−0.753358	+	3.78739i	−0.0298726	+	0.150180i
$637$	−6.94613	−	18.2725i	−0.275215	−	0.723982i
$638$	0.782272	+	1.88857i	0.0309704	+	0.0747693i
$639$	−5.64297	+	1.91553i	−0.223233	+	0.0757772i
$640$	0.0448932	+	0.684937i	0.00177456	+	0.0270745i
$641$	17.3276	+	5.88193i	0.684399	+	0.232322i	0.641916	−	0.766775i	$-0.278140\pi$
$641$	17.3276	+	5.88193i	0.684399	+	0.232322i	0.0424830	+	0.999097i	$0.486473\pi$
$642$	−0.107878	+	0.402608i	−0.00425762	+	0.0158897i
$643$	−9.68112	−	6.46871i	−0.381786	−	0.255101i	0.349837	−	0.936811i	$-0.386237\pi$
$643$	−9.68112	−	6.46871i	−0.381786	−	0.255101i	−0.731623	+	0.681709i	$0.761237\pi$
$644$	−28.2671	−	12.1989i	−1.11388	−	0.480705i
$645$			2.94846i			0.116096i
$646$	−0.0397285	+	0.317463i	−0.00156310	+	0.0124904i
$647$	36.2048	+	20.9028i	1.42336	+	0.821775i	0.996584	−	0.0825840i	$-0.0263173\pi$
$647$	36.2048	+	20.9028i	1.42336	+	0.821775i	0.426772	+	0.904359i	$0.359651\pi$
$648$	0.198270	+	0.258391i	0.00778879	+	0.0101506i
$649$	63.6755	+	4.17352i	2.49948	+	0.163825i
$650$	0.793935	−	0.793935i	0.0311407	−	0.0311407i
$651$	12.5055	+	14.6903i	0.490128	+	0.575758i
$652$	−8.53643	+	5.70386i	−0.334312	+	0.223380i
$653$	−1.79804	−	5.29686i	−0.0703629	−	0.207282i	0.906060	−	0.423150i	$-0.139075\pi$
$653$	−1.79804	−	5.29686i	−0.0703629	−	0.207282i	−0.976423	+	0.215867i	$0.930742\pi$
$654$	0.575952	+	0.0758256i	0.0225215	+	0.00296501i
$655$	−4.62733	−	0.609199i	−0.180805	−	0.0238034i
$656$	2.84374	+	8.37740i	0.111030	+	0.327082i
$657$	−3.20932	+	2.14440i	−0.125207	+	0.0836609i
$658$	−0.543840	+	1.52786i	−0.0212011	+	0.0595624i
$659$	8.59117	−	8.59117i	0.334665	−	0.334665i	−0.519690	−	0.854355i	$-0.673953\pi$
$659$	8.59117	−	8.59117i	0.334665	−	0.334665i	0.854355	+	0.519690i	$0.173953\pi$
$660$	3.18931	+	0.209038i	0.124144	+	0.00813680i
$661$	−6.92612	−	9.02629i	−0.269395	−	0.351082i	0.638992	−	0.769214i	$-0.279352\pi$
$661$	−6.92612	−	9.02629i	−0.269395	−	0.351082i	−0.908386	+	0.418132i	$0.862685\pi$
$662$	0.489452	+	0.282585i	0.0190231	+	0.0109830i
$663$	7.53624	−	8.70526i	0.292683	−	0.338084i
$664$			1.40446i			0.0545036i
$665$	−0.398553	−	0.535540i	−0.0154552	−	0.0207673i
$666$	−0.146889	−	0.0981481i	−0.00569183	−	0.00380316i
$667$	−6.26339	+	23.3753i	−0.242520	+	0.905095i
$668$	5.25035	+	1.78225i	0.203142	+	0.0689575i
$669$	−1.42360	−	21.7199i	−0.0550396	−	0.839741i
$670$	0.0685135	−	0.0232572i	0.00264691	−	0.000898504i
$671$	−19.0197	−	45.9177i	−0.734249	−	1.77263i
$672$	−2.02192	−	1.59928i	−0.0779971	−	0.0616936i
$673$	−4.54380	+	22.8432i	−0.175151	+	0.880541i	0.788839	+	0.614600i	$0.210683\pi$
$673$	−4.54380	+	22.8432i	−0.175151	+	0.880541i	−0.963989	+	0.265941i	$0.914317\pi$
$674$	0.240282	−	0.487245i	0.00925534	−	0.0187680i
$675$	1.58459	−	4.66805i	0.0609909	−	0.179673i
$676$	2.68348	+	10.0149i	0.103211	+	0.385188i
$677$	−1.47211	+	22.4600i	−0.0565777	+	0.863208i	0.871400	+	0.490573i	$0.163212\pi$
$677$	−1.47211	+	22.4600i	−0.0565777	+	0.863208i	−0.927978	+	0.372635i	$0.878454\pi$
$678$	0.216362	−	0.522344i	0.00830933	−	0.0200605i
$679$	39.2603	+	0.577729i	1.50667	+	0.0221712i
$680$	−0.266246	+	0.236524i	−0.0102101	+	0.00907030i
$681$	−9.99655	−	17.3145i	−0.383069	−	0.663494i
$682$	2.85260	−	2.18888i	0.109232	−	0.0838165i
$683$	−26.1920	+	12.9165i	−1.00221	+	0.494236i	−0.867919	−	0.496706i	$-0.834543\pi$
$683$	−26.1920	+	12.9165i	−1.00221	+	0.494236i	−0.134292	+	0.990942i	$0.542876\pi$
$684$	1.83188	+	0.490850i	0.0700436	+	0.0187681i
$685$	−0.821376	−	4.12934i	−0.0313832	−	0.157774i
$686$	−1.32392	−	0.727208i	−0.0505477	−	0.0277649i
$687$	9.75987	+	1.94136i	0.372362	+	0.0740674i
$688$	34.9297	+	26.8025i	1.33168	+	1.02184i
$689$	−0.706137	+	5.36365i	−0.0269017	+	0.204339i
$690$	−0.0949318	−	0.0832529i	−0.00361399	−	0.00316938i
$691$	21.3543	+	10.5308i	0.812356	+	0.400610i	0.800509	−	0.599320i	$-0.204562\pi$
$691$	21.3543	+	10.5308i	0.812356	+	0.400610i	0.0118465	+	0.999930i	$0.496229\pi$
$692$	50.3423	−	10.0137i	1.91373	−	0.380664i
$693$	−11.4762	+	11.1433i	−0.435945	+	0.423301i
$694$	−0.900555	+	1.34778i	−0.0341846	+	0.0511609i
$695$	0.00795791	+	0.0604463i	0.000301861	+	0.00229286i
$696$	−0.675085	+	1.16928i	−0.0255890	+	0.0443215i
$697$	−5.06820	+	7.69126i	−0.191972	+	0.291327i
$698$	2.31376	−	1.33585i	0.0875771	−	0.0505626i
$699$	−3.39568	−	1.40654i	−0.128437	−	0.0532002i
$700$	−2.08192	+	25.9151i	−0.0786893	+	0.979499i
$701$	−13.0941	−	13.0941i	−0.494556	−	0.494556i	0.415182	−	0.909738i	$-0.363718\pi$
$701$	−13.0941	−	13.0941i	−0.494556	−	0.494556i	−0.909738	+	0.415182i	$0.863718\pi$
$702$	0.150174	+	0.171241i	0.00566796	+	0.00646307i
$703$	−2.05640	+	0.134784i	−0.0775587	+	0.00508346i
$704$	31.2565	−	35.6412i	1.17802	−	1.34328i
$705$	1.21336	−	1.58128i	0.0456979	−	0.0595546i
$706$	0.429798	−	0.178028i	0.0161756	−	0.00670017i
$707$	24.4985	−	27.1197i	0.921362	−	1.01994i
$708$	11.6885	+	17.4931i	0.439281	+	0.657430i
$709$	−4.54994	+	3.99019i	−0.170877	+	0.149855i	−0.740513	−	0.672042i	$-0.765417\pi$
$709$	−4.54994	+	3.99019i	−0.170877	+	0.149855i	0.569636	+	0.821897i	$0.307084\pi$
$710$	0.124504	−	0.0333608i	0.00467256	−	0.00125201i
$711$	7.03631	+	14.2682i	0.263882	+	0.535101i
$712$	0.450597	−	0.0593222i	0.0168868	−	0.00222319i
$713$	42.5667			1.59413
$714$	0.00739429	−	0.889676i	0.000276724	−	0.0332953i
$715$	4.47768			0.167456
$716$	−16.2813	+	2.14348i	−0.608462	+	0.0801055i
$717$	8.39497	+	17.0233i	0.313516	+	0.635747i
$718$	0.259705	−	0.0695877i	0.00969209	−	0.00259699i
$719$	24.8476	−	21.7908i	0.926659	−	0.812658i	−0.0559328	−	0.998435i	$-0.517813\pi$
$719$	24.8476	−	21.7908i	0.926659	−	0.812658i	0.982592	+	0.185776i	$0.0594799\pi$
$720$	0.583480	+	0.873239i	0.0217450	+	0.0325437i
$721$	7.91855	−	2.55868i	0.294902	−	0.0952902i
$722$	1.36346	−	0.564764i	0.0507428	−	0.0210183i
$723$	0.251445	−	0.327690i	0.00935134	−	0.0121869i
$724$	27.2178	−	31.0360i	1.01154	−	1.15344i
$725$	20.3922	−	1.33658i	0.757348	−	0.0496392i
$726$	1.37418	+	1.56695i	0.0510007	+	0.0581551i
$727$	−32.1996	−	32.1996i	−1.19422	−	1.19422i	−0.975871	−	0.218347i	$-0.929934\pi$
$727$	−32.1996	−	32.1996i	−1.19422	−	1.19422i	−0.218347	−	0.975871i	$-0.570066\pi$
$728$	−1.98096	−	1.36622i	−0.0734194	−	0.0506355i
$729$	0.923880	+	0.382683i	0.0342178	+	0.0141735i
$730$	0.0723015	−	0.0417433i	0.00267600	−	0.00154499i
$731$	0.293523	+	45.8389i	0.0108563	+	1.69541i
$732$	8.19315	−	14.1910i	0.302828	−	0.524513i
$733$	0.501252	+	3.80739i	0.0185142	+	0.140629i	0.998205	−	0.0598830i	$-0.0190728\pi$
$733$	0.501252	+	3.80739i	0.0185142	+	0.140629i	−0.979691	+	0.200512i	$0.935739\pi$
$734$	−0.246670	+	0.369168i	−0.00910476	+	0.0136262i
$735$	1.27349	+	1.35074i	0.0469734	+	0.0498228i
$736$	−5.57873	+	1.10968i	−0.205635	+	0.0409033i
$737$	−18.1387	−	8.94500i	−0.668146	−	0.329493i
$738$	−0.136987	−	0.120135i	−0.00504257	−	0.00442222i
$739$	0.747072	−	5.67457i	0.0274815	−	0.208743i	−0.972195	−	0.234172i	$-0.924762\pi$
$739$	0.747072	−	5.67457i	0.0274815	−	0.208743i	0.999677	+	0.0254296i	$0.00809538\pi$
$740$	−0.908440	−	0.697071i	−0.0333949	−	0.0256248i
$741$	2.60587	+	0.518339i	0.0957289	+	0.0190417i
$742$	0.227104	+	0.350957i	0.00833727	+	0.0128840i
$743$	7.02584	+	35.3213i	0.257753	+	1.29581i	0.865190	+	0.501444i	$0.167198\pi$
$743$	7.02584	+	35.3213i	0.257753	+	1.29581i	−0.607437	+	0.794368i	$0.707802\pi$
$744$	2.29397	+	0.614668i	0.0841012	+	0.0225348i
$745$	−3.16710	+	1.56184i	−0.116034	+	0.0572214i
$746$	−0.677452	+	0.519827i	−0.0248033	+	0.0190322i
$747$	2.15610	+	3.73447i	0.0788875	+	0.136637i
$748$	49.6040	+	2.93236i	1.81370	+	0.107218i
$749$	−6.58756	−	11.8079i	−0.240704	−	0.431451i
$750$	−0.0821911	+	0.198427i	−0.00300120	+	0.00724553i
$751$	2.34180	−	35.7289i	0.0854533	−	1.30377i	−0.712767	−	0.701401i	$-0.752558\pi$
$751$	2.34180	−	35.7289i	0.0854533	−	1.30377i	0.798221	−	0.602365i	$-0.205775\pi$
$752$	−7.70322	−	28.7488i	−0.280908	−	1.04836i
$753$	−3.15915	+	9.30657i	−0.115126	+	0.339150i
$754$	−0.417605	+	0.846819i	−0.0152083	+	0.0308393i
$755$	−0.321118	+	1.61437i	−0.0116867	+	0.0587530i
$756$	−5.21809	−	0.765243i	−0.189780	−	0.0278316i
$757$	−8.98037	−	21.6805i	−0.326397	−	0.787993i	−0.998854	−	0.0478564i	$-0.984761\pi$
$757$	−8.98037	−	21.6805i	−0.326397	−	0.787993i	0.672457	−	0.740136i	$-0.265239\pi$
$758$	−2.04285	+	0.693454i	−0.0741997	+	0.0251874i
$759$	2.30835	+	35.2186i	0.0837877	+	1.27835i
$760$	−0.0778171	−	0.0264154i	−0.00282272	−	0.000958186i
$761$	−8.10118	+	30.2340i	−0.293668	+	1.09598i	0.648602	+	0.761128i	$0.275354\pi$
$761$	−8.10118	+	30.2340i	−0.293668	+	1.09598i	−0.942270	+	0.334855i	$0.891313\pi$
$762$	−1.08381	−	0.724176i	−0.0392621	−	0.0262341i
$763$	−15.1178	+	11.2508i	−0.547302	+	0.407307i
$764$		−	21.3765i		−	0.773375i
$765$	−0.344843	+	1.03766i	−0.0124678	+	0.0375166i
$766$	2.53089	+	1.46121i	0.0914449	+	0.0527958i
$767$	17.9429	+	23.3836i	0.647880	+	0.844334i
$768$	15.4374	+	1.01182i	0.557048	+	0.0365109i
$769$	19.9907	−	19.9907i	0.720885	−	0.720885i	−0.247901	−	0.968785i	$-0.579741\pi$
$769$	19.9907	−	19.9907i	0.720885	−	0.720885i	0.968785	+	0.247901i	$0.0797407\pi$
$770$	0.263459	−	0.224276i	0.00949441	−	0.00808236i
$771$	−16.7647	+	11.2018i	−0.603764	+	0.403422i
$772$	−13.5718	−	39.9813i	−0.488460	−	1.43896i
$773$	−24.0712	−	3.16903i	−0.865781	−	0.113982i	−0.315463	−	0.948938i	$-0.602160\pi$
$773$	−24.0712	−	3.16903i	−0.865781	−	0.113982i	−0.550317	+	0.834956i	$0.685493\pi$
$774$	−0.899002	−	0.118356i	−0.0323139	−	0.00425421i
$775$	−11.5545	−	34.0384i	−0.415050	−	1.22270i
$776$	4.01891	−	2.68535i	0.144271	−	0.0963985i
$777$	5.63657	−	1.03521i	0.202211	−	0.0371379i
$778$	0.344318	−	0.344318i	0.0123444	−	0.0123444i
$779$	−2.12090	−	0.139011i	−0.0759891	−	0.00498059i
$780$	0.898703	+	1.17121i	0.0321787	+	0.0419361i
$781$	−31.2024	−	18.0147i	−1.11651	−	0.644616i
$782$	−1.48416	−	1.28486i	−0.0530736	−	0.0459464i
$783$			4.14551i			0.148148i
$784$	27.5783	−	2.80805i	0.984941	−	0.100287i
$785$	0.930519	+	0.621753i	0.0332116	+	0.0221913i
$786$	0.371496	−	1.38644i	0.0132508	−	0.0494527i
$787$	−10.8506	−	3.68328i	−0.386782	−	0.131295i	0.121274	−	0.992619i	$-0.461302\pi$
$787$	−10.8506	−	3.68328i	−0.386782	−	0.131295i	−0.508055	+	0.861324i	$0.669635\pi$
$788$	1.91754	+	29.2560i	0.0683096	+	1.04220i
$789$	−20.3190	+	6.89737i	−0.723376	+	0.245553i
$790$	−0.131683	−	0.317911i	−0.00468507	−	0.0113108i
$791$	6.76862	+	17.0461i	0.240664	+	0.606089i
$792$	−0.384161	+	1.93131i	−0.0136506	+	0.0686260i
$793$	10.1534	−	20.5891i	0.360559	−	0.731140i
$794$	−0.338562	+	0.997373i	−0.0120151	+	0.0353954i
$795$	−0.132971	−	0.496254i	−0.00471599	−	0.0176003i
$796$	−2.27991	+	34.7846i	−0.0808091	+	1.23291i
$797$	−12.8332	+	30.9822i	−0.454576	+	1.09744i	0.515987	+	0.856597i	$0.327425\pi$
$797$	−12.8332	+	30.9822i	−0.454576	+	1.09744i	−0.970563	+	0.240848i	$0.922575\pi$
$798$	0.179287	−	0.100024i	0.00634671	−	0.00354080i
$799$	18.7064	−	24.7046i	0.661784	−	0.873985i
$800$	2.40167	+	4.15982i	0.0849119	+	0.147072i
$801$	1.10707	−	0.849486i	0.0391164	−	0.0300151i
$802$	−1.60211	+	0.790072i	−0.0565724	+	0.0278984i
$803$	−22.5412	−	6.03990i	−0.795462	−	0.213143i
$804$	−1.30085	−	6.53980i	−0.0458773	−	0.230641i
$805$	4.09075	−	0.207725i	0.144180	−	0.00732133i
$806$	1.62888	+	0.324005i	0.0573750	+	0.0114126i
$807$	2.88687	+	2.21517i	0.101623	+	0.0779778i
$808$	0.587227	−	4.46043i	0.0206586	−	0.156917i
$809$	−8.70467	−	7.63379i	−0.306040	−	0.268390i	0.492525	−	0.870298i	$-0.336074\pi$
$809$	−8.70467	−	7.63379i	−0.306040	−	0.268390i	−0.798565	+	0.601908i	$0.794407\pi$
$810$	−0.0193991	−	0.00956657i	−0.000681615	−	0.000336135i
$811$	−31.1104	+	6.18825i	−1.09243	+	0.217299i	−0.708253	−	0.705959i	$-0.750516\pi$
$811$	−31.1104	+	6.18825i	−1.09243	+	0.217299i	−0.384182	+	0.923257i	$0.625516\pi$
$812$	−5.34723	−	21.1990i	−0.187651	−	0.743940i
$813$	−3.13013	+	4.68457i	−0.109779	+	0.164295i
$814$	−0.139414	−	1.05896i	−0.00488647	−	0.0371164i
$815$	0.682958	−	1.18292i	0.0239230	−	0.0414358i
$816$	9.15812	+	13.5179i	0.320598	+	0.473221i
$817$	−9.16049	+	5.28881i	−0.320485	+	0.185032i
$818$	−2.06994	−	0.857395i	−0.0723736	−	0.0299781i
$819$	−7.36480	−	0.591661i	−0.257347	−	0.0206743i
$820$	−0.835078	−	0.835078i	−0.0291622	−	0.0291622i
$821$	4.78317	+	5.45416i	0.166934	+	0.190351i	0.829258	−	0.558866i	$-0.188763\pi$
$821$	4.78317	+	5.45416i	0.166934	+	0.190351i	−0.662324	+	0.749217i	$0.730430\pi$
$822$	1.29203	−	0.0846839i	0.0450646	−	0.00295369i
$823$	11.8297	−	13.4892i	0.412359	−	0.470205i	−0.507956	−	0.861383i	$-0.669599\pi$
$823$	11.8297	−	13.4892i	0.412359	−	0.470205i	0.920315	+	0.391178i	$0.127932\pi$
$824$	0.623619	−	0.812716i	0.0217248	−	0.0283123i
$825$	27.5359	−	11.4058i	0.958678	−	0.397098i
$826$	2.22696	+	0.477137i	0.0774859	+	0.0166017i
$827$	4.49248	+	6.72347i	0.156219	+	0.233798i	0.901320	−	0.433153i	$-0.142599\pi$
$827$	4.49248	+	6.72347i	0.156219	+	0.233798i	−0.745102	+	0.666951i	$0.767599\pi$
$828$	−8.74871	+	7.67241i	−0.304039	+	0.266635i
$829$	−30.0919	+	8.06311i	−1.04514	+	0.280043i	−0.740240	−	0.672342i	$-0.765288\pi$
$829$	−30.0919	+	8.06311i	−1.04514	+	0.280043i	−0.304896	+	0.952386i	$0.598622\pi$
$830$	−0.0412529	−	0.0836527i	−0.00143191	−	0.00290363i
$831$	−4.32845	+	0.569851i	−0.150152	+	0.0197679i
$832$	21.8962			0.759115
$833$	19.9331	+	20.8728i	0.690639	+	0.723199i
$834$	−0.0187498			−0.000649254
$835$	−0.731363	+	0.0962858i	−0.0253099	+	0.00333211i
$836$	5.07137	+	10.2837i	0.175397	+	0.355670i
$837$	7.04333	−	1.88725i	0.243453	−	0.0652330i
$838$	0.195411	−	0.171371i	0.00675036	−	0.00591991i
$839$	−14.9129	−	22.3187i	−0.514850	−	0.770527i	0.479402	−	0.877595i	$-0.340854\pi$
$839$	−14.9129	−	22.3187i	−0.514850	−	0.770527i	−0.994252	+	0.107069i	$0.965854\pi$
$840$	0.223455	+	0.0478764i	0.00770994	+	0.00165189i
$841$	10.9154	−	4.52131i	0.376394	−	0.155907i
$842$	1.02451	−	1.33517i	0.0353070	−	0.0460129i
$843$	11.3868	−	12.9841i	0.392181	−	0.447197i
$844$	25.9913	−	1.70356i	0.894659	−	0.0586391i
$845$	−0.909514	−	1.03710i	−0.0312882	−	0.0356774i
$846$	0.433436	+	0.433436i	0.0149018	+	0.0149018i
$847$	−67.3922	−	5.41404i	−2.31562	−	0.186029i
$848$	−7.08774	−	2.93584i	−0.243394	−	0.100817i
$849$	−18.3885	+	10.6166i	−0.631092	+	0.364361i
$850$	−0.624568	+	1.53558i	−0.0214225	+	0.0526699i
$851$	6.32230	−	10.9505i	0.216726	−	0.375380i
$852$	−1.55050	−	11.7772i	−0.0531191	−	0.403480i
$853$	−10.7793	+	16.1324i	−0.369077	+	0.552363i	−0.968800	−	0.247845i	$-0.920278\pi$
$853$	−10.7793	+	16.1324i	−0.369077	+	0.552363i	0.599722	+	0.800208i	$0.295278\pi$
$854$	−0.433849	−	1.71999i	−0.0148460	−	0.0588568i
$855$	−0.247469	+	0.0492246i	−0.00846326	+	0.00168345i
$856$	−1.49282	−	0.736176i	−0.0510234	−	0.0251620i
$857$	5.76847	+	5.05881i	0.197047	+	0.172806i	0.752184	−	0.658954i	$-0.229001\pi$
$857$	5.76847	+	5.05881i	0.197047	+	0.172806i	−0.555136	+	0.831759i	$0.687334\pi$
$858$	−0.179741	+	1.36527i	−0.00613625	+	0.0466095i
$859$	−4.17690	−	3.20505i	−0.142514	−	0.109355i	0.535044	−	0.844824i	$-0.320295\pi$
$859$	−4.17690	−	3.20505i	−0.142514	−	0.109355i	−0.677558	+	0.735469i	$0.736962\pi$
$860$	−5.76438	−	1.14661i	−0.196564	−	0.0390990i
$861$	5.90298	−	0.299748i	0.201173	−	0.0102154i
$862$	0.247283	+	1.24318i	0.00842251	+	0.0423428i
$863$	34.7666	+	9.31568i	1.18347	+	0.317109i	0.796301	−	0.604900i	$-0.206787\pi$
$863$	34.7666	+	9.31568i	1.18347	+	0.317109i	0.387167	+	0.922010i	$0.373454\pi$
$864$	−0.873890	+	0.430955i	−0.0297303	+	0.0146614i
$865$	−5.41776	+	4.15719i	−0.184209	+	0.141349i
$866$	−0.174039	−	0.301445i	−0.00591409	−	0.0102435i
$867$	−5.25787	+	16.1665i	−0.178567	+	0.549042i
$868$	−33.5834	+	18.7360i	−1.13989	+	0.635941i
$869$	−36.8083	+	88.8632i	−1.24864	+	3.01448i
$870$	0.00586445	−	0.0894741i	0.000198823	−	0.00303346i
$871$	−2.41776	−	9.02319i	−0.0819225	−	0.305739i
$872$	−0.745683	+	2.19671i	−0.0252520	+	0.0743900i
$873$	6.56383	−	13.3101i	0.222152	−	0.450480i
$874$	0.0883719	−	0.444276i	0.00298923	−	0.0150279i
$875$	−2.57125	−	6.47543i	−0.0869241	−	0.218909i
$876$	−2.94435	−	7.10828i	−0.0994803	−	0.240167i
$877$	14.0103	−	4.75587i	0.473096	−	0.160594i	−0.0747006	−	0.997206i	$-0.523800\pi$
$877$	14.0103	−	4.75587i	0.473096	−	0.160594i	0.547797	+	0.836612i	$0.315467\pi$
$878$	0.125327	+	1.91212i	0.00422959	+	0.0645310i
$879$	16.5417	+	5.61516i	0.557938	+	0.189395i
$880$	−1.64343	+	6.13335i	−0.0553999	+	0.206755i
$881$	27.2393	+	18.2007i	0.917715	+	0.613198i	0.922167	−	0.386793i	$-0.126417\pi$
$881$	27.2393	+	18.2007i	0.917715	+	0.613198i	−0.00445182	+	0.999990i	$0.501417\pi$
$882$	−0.462968	+	0.334073i	−0.0155889	+	0.0112488i
$883$		−	49.6475i		−	1.67077i	−0.549665	−	0.835385i	$-0.685245\pi$
$883$		−	49.6475i		−	1.67077i	0.549665	−	0.835385i	$-0.314755\pi$
$884$	14.0885	+	18.1190i	0.473846	+	0.609409i
$885$	−2.42407	−	1.39953i	−0.0814841	−	0.0470449i
$886$	1.25040	+	1.62956i	0.0420081	+	0.0547460i
$887$	49.2933	+	3.23086i	1.65511	+	0.108482i	0.864099	−	0.503322i	$-0.167889\pi$
$887$	49.2933	+	3.23086i	1.65511	+	0.108482i	0.791010	+	0.611804i	$0.209556\pi$
$888$	0.498844	−	0.498844i	0.0167401	−	0.0167401i
$889$	41.5888	−	7.63818i	1.39484	−	0.256176i
$890$	−0.0250961	+	0.0167687i	−0.000841222	+	0.000562087i
$891$	1.94342	+	5.72512i	0.0651069	+	0.191799i
$892$	43.0171	+	5.66331i	1.44032	+	0.189622i
$893$	7.08932	+	0.933327i	0.237235	+	0.0312326i
$894$	−0.349081	−	1.02836i	−0.0116750	−	0.0343935i
$895$	1.81661	−	1.21382i	0.0607226	−	0.0405735i
$896$	5.21435	−	4.43885i	0.174199	−	0.148292i
$897$	−11.5274	+	11.5274i	−0.384887	+	0.384887i
$898$	2.69261	+	0.176483i	0.0898537	+	0.00588932i
$899$	18.4018	+	23.9816i	0.613733	+	0.799832i
$900$	8.51004	+	4.91327i	0.283668	+	0.163776i
$901$	−2.11666	−	7.70187i	−0.0705162	−	0.256587i
$902$		−	1.10159i		−	0.0366791i
$903$	23.5974	−	17.5614i	0.785271	−	0.584405i
$904$	1.87726	+	1.25435i	0.0624368	+	0.0417189i
$905$	−1.42145	+	5.30491i	−0.0472505	+	0.176341i
$906$	−0.479340	−	0.162714i	−0.0159250	−	0.00540581i
$907$	−1.20470	−	18.3801i	−0.0400013	−	0.610302i	−0.970056	−	0.242881i	$-0.921908\pi$
$907$	−1.20470	−	18.3801i	−0.0400013	−	0.610302i	0.930055	−	0.367421i	$-0.119759\pi$
$908$	37.7382	−	12.8104i	1.25239	−	0.425128i
$909$	−5.28613	−	12.7618i	−0.175330	−	0.423283i
$910$	0.158120	+	0.0231887i	0.00524164	+	0.000768697i
$911$	10.2406	−	51.4830i	0.339286	−	1.70571i	−0.314691	−	0.949194i	$-0.601901\pi$
$911$	10.2406	−	51.4830i	0.339286	−	1.70571i	0.653978	−	0.756514i	$-0.273099\pi$
$912$	−1.66642	+	3.37917i	−0.0551808	+	0.111896i
$913$	−8.38040	+	24.6879i	−0.277351	+	0.817049i
$914$	0.677958	+	2.53018i	0.0224249	+	0.0836908i
$915$	−0.142585	+	2.17542i	−0.00471371	+	0.0719173i
$916$	−7.59089	+	18.3260i	−0.250810	+	0.605509i
$917$	22.6853	+	40.6622i	0.749133	+	1.34279i
$918$	−0.302544	−	0.146797i	−0.00998545	−	0.00484504i
$919$	8.48736	+	14.7005i	0.279972	+	0.484926i	0.971378	−	0.237541i	$-0.0763414\pi$
$919$	8.48736	+	14.7005i	0.279972	+	0.484926i	−0.691405	+	0.722467i	$0.743008\pi$
$920$	0.400028	−	0.306952i	0.0131885	−	0.0101199i
$921$	6.89867	−	3.40205i	0.227319	−	0.112101i
$922$	−1.01627	−	0.272310i	−0.0334692	−	0.00896804i
$923$	−3.24664	−	16.3220i	−0.106865	−	0.537244i
$924$	−17.3229	−	26.7700i	−0.569880	−	0.880667i
$925$	−10.4728	−	2.08316i	−0.344342	−	0.0684939i
$926$	1.19218	+	0.914795i	0.0391776	+	0.0300620i
$927$	0.410543	−	3.11839i	0.0134840	−	0.102421i
$928$	−3.03689	−	2.66328i	−0.0996908	−	0.0874265i
$929$	−41.1441	−	20.2900i	−1.34989	−	0.665694i	−0.383687	−	0.923463i	$-0.625346\pi$
$929$	−41.1441	−	20.2900i	−1.34989	−	0.665694i	−0.966206	+	0.257770i	$0.917012\pi$
$930$	−0.154689	+	0.0307695i	−0.00507244	+	0.00100897i
$931$	−1.91225	+	6.37946i	−0.0626714	+	0.209078i
$932$	4.07037	−	6.09174i	0.133329	−	0.199542i
$933$	2.08656	+	15.8490i	0.0683110	+	0.518874i
$934$	−0.522816	+	0.905544i	−0.0171071	+	0.0296303i
$935$	−6.09146	+	2.56899i	−0.199212	+	0.0840148i
$936$	−0.787680	+	0.454767i	−0.0257461	+	0.0148645i
$937$	−25.0551	−	10.3782i	−0.818516	−	0.339040i	−0.0661696	−	0.997808i	$-0.521078\pi$
$937$	−25.0551	−	10.3782i	−0.818516	−	0.339040i	−0.752346	+	0.658768i	$0.771078\pi$
$938$	−0.594207	−	0.409810i	−0.0194016	−	0.0133808i
$939$	10.5874	+	10.5874i	0.345506	+	0.345506i
$940$	2.61963	+	2.98712i	0.0854429	+	0.0974290i
$941$	2.96688	−	0.194460i	0.0967175	−	0.00633920i	−0.0169675	−	0.999856i	$-0.505401\pi$
$941$	2.96688	−	0.194460i	0.0967175	−	0.00633920i	0.113685	+	0.993517i	$0.463735\pi$
$942$	−0.226928	+	0.258762i	−0.00739372	+	0.00843092i
$943$	7.93897	−	10.3463i	0.258529	−	0.336921i
$944$	−38.6155	+	15.9951i	−1.25683	+	0.520595i
$945$	0.667669	−	0.215740i	0.0217193	−	0.00701803i
$946$	−3.04577	−	4.55832i	−0.0990267	−	0.148204i
$947$	21.2401	−	18.6271i	0.690211	−	0.605299i	−0.240676	−	0.970605i	$-0.577369\pi$
$947$	21.2401	−	18.6271i	0.690211	−	0.605299i	0.930887	+	0.365307i	$0.119036\pi$
$948$	−30.6314	+	8.20765i	−0.994860	+	0.266572i
$949$	−4.76739	−	9.66732i	−0.154756	−	0.313814i
$950$	−0.379253	+	0.0499296i	−0.0123046	+	0.00161993i
$951$	5.86881			0.190309
$952$	3.47876	+	0.722075i	0.112747	+	0.0234026i
$953$	−21.6867			−0.702500			−0.351250	−	0.936282i	$-0.614243\pi$
$953$	−21.6867			−0.702500			−0.351250	+	0.936282i	$0.614243\pi$
$954$	0.156648	−	0.0206231i	0.00507166	−	0.000667697i
$955$	1.25787	+	2.55071i	0.0407038	+	0.0825392i
$956$	−36.5460	+	9.79248i	−1.18198	+	0.316711i
$957$	−18.8439	+	16.5256i	−0.609136	+	0.534198i
$958$	−1.74125	−	2.60596i	−0.0562571	−	0.0841947i
$959$	−28.1560	+	31.1685i	−0.909205	+	1.00648i
$960$	−1.92111	+	0.795751i	−0.0620036	+	0.0256827i
$961$	13.4964	−	17.5888i	0.435367	−	0.567381i
$962$	0.325286	−	0.370917i	0.0104876	−	0.0119588i
$963$	−5.09958	+	0.334244i	−0.164332	+	0.0107709i
$964$	0.542866	+	0.619020i	0.0174845	+	0.0199373i
$965$	3.97208	+	3.97208i	0.127866	+	0.127866i
$966$	−0.100873	+	1.25563i	−0.00324552	+	0.0403992i
$967$	−5.88610	−	2.43810i	−0.189284	−	0.0784041i	0.286028	−	0.958221i	$-0.407665\pi$
$967$	−5.88610	−	2.43810i	−0.189284	−	0.0784041i	−0.475312	+	0.879817i	$0.657665\pi$
$968$	−7.20773	+	4.16139i	−0.231665	+	0.133752i
$969$	−3.84243	+	0.789917i	−0.123437	+	0.0253758i
$970$	−0.160499	+	0.277992i	−0.00515331	+	0.00892579i
$971$	1.98924	+	15.1098i	0.0638378	+	0.484896i	0.993263	+	0.115885i	$0.0369704\pi$
$971$	1.98924	+	15.1098i	0.0638378	+	0.484896i	−0.929425	+	0.369011i	$0.879696\pi$
$972$	−1.10744	+	1.65741i	−0.0355213	+	0.0531614i
$973$	0.436371	−	0.423714i	0.0139894	−	0.0135837i
$974$	−0.178672	+	0.0355400i	−0.00572501	+	0.00113878i
$975$	12.3469	+	6.08881i	0.395417	+	0.194998i
$976$	24.4756	+	21.4645i	0.783444	+	0.687062i
$977$	4.58539	−	34.8295i	0.146700	−	1.11429i	−0.746741	−	0.665114i	$-0.768383\pi$
$977$	4.58539	−	34.8295i	0.146700	−	1.11429i	0.893441	−	0.449180i	$-0.148284\pi$
$978$	0.333263	+	0.255721i	0.0106566	+	0.00817707i
$979$	8.27465	+	1.64593i	0.264459	+	0.0526042i
$980$	−3.13600	+	1.96445i	−0.100176	+	0.0627522i
$981$	1.38957	+	6.98584i	0.0443655	+	0.223041i
$982$	−3.32258	−	0.890283i	−0.106028	−	0.0284101i
$983$	−31.7982	+	15.6811i	−1.01421	+	0.500151i	−0.871906	−	0.489673i	$-0.837116\pi$
$983$	−31.7982	+	15.6811i	−1.01421	+	0.500151i	−0.142299	+	0.989824i	$0.545450\pi$
$984$	0.577243	−	0.442934i	0.0184018	−	0.0141202i
$985$	−1.95034	−	3.37809i	−0.0621430	−	0.107635i
$986$	0.0822656	−	1.39161i	0.00261987	−	0.0443180i
$987$	−19.8824	−	0.292576i	−0.632863	−	0.00931281i
$988$	−2.02675	+	4.89302i	−0.0644797	+	0.155668i
$989$	4.24476	−	64.7625i	0.134975	−	2.05933i
$990$	−0.0338465	−	0.126317i	−0.00107571	−	0.00401461i
$991$	−10.4770	+	30.8644i	−0.332814	+	0.980440i	0.643754	+	0.765233i	$0.277376\pi$
$991$	−10.4770	+	30.8644i	−0.332814	+	0.980440i	−0.976568	+	0.215207i	$0.930957\pi$
$992$	−3.14243	+	6.37222i	−0.0997723	+	0.202318i
$993$	−1.35189	+	6.79641i	−0.0429009	+	0.215678i
$994$	−1.00856	−	0.797742i	−0.0319895	−	0.0253028i
$995$	−1.77481	−	4.28477i	−0.0562653	−	0.135836i
$996$	−8.13953	+	2.76300i	−0.257911	+	0.0875490i
$997$	1.37657	+	21.0023i	0.0435963	+	0.665151i	0.962604	+	0.270912i	$0.0873252\pi$
$997$	1.37657	+	21.0023i	0.0435963	+	0.665151i	−0.919008	+	0.394239i	$0.871008\pi$
$998$	−0.118737	−	0.0403059i	−0.00375857	−	0.00127586i
$999$	0.560616	−	2.09225i	0.0177371	−	0.0661958i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.bl.a.10.13	✓	384
7.5	odd	6	inner	357.2.bl.a.61.12	yes	384
17.12	odd	16	inner	357.2.bl.a.199.12	yes	384
119.12	even	48	inner	357.2.bl.a.250.13	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bl.a.10.13	✓	384	1.1	even	1	trivial
357.2.bl.a.61.12	yes	384	7.5	odd	6	inner
357.2.bl.a.199.12	yes	384	17.12	odd	16	inner
357.2.bl.a.250.13	yes	384	119.12	even	48	inner

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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

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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	357.2.bl.a.10.13

Level	$357$
Weight	$2$
Character	357.10
Analytic conductor	$2.851$
Analytic rank	$0$
Dimension	$384$
Inner twists	$4$