LMFDB - Embedded newform 153.3.i.a.50.28

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,3,Mod(50,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.50"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	153.i (of order $6$, degree $2$, 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:	$4.16894804471$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			50.28
Character	$\chi$	$=$	153.50
Dual form			153.3.i.a.101.28

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.91245 - 1.10416i) q^{2} +(1.04331 - 2.81274i) q^{3} +(0.438319 - 0.759190i) q^{4} +(1.77620 - 3.07647i) q^{5} +(-1.11042 - 6.53121i) q^{6} +(3.82505 - 2.20839i) q^{7} +6.89736i q^{8} +(-6.82301 - 5.86911i) q^{9} -7.84480i q^{10} +(-0.708179 - 1.22660i) q^{11} +(-1.67810 - 2.02495i) q^{12} +(-1.55468 + 2.69278i) q^{13} +(4.87682 - 8.44690i) q^{14} +(-6.80018 - 8.20569i) q^{15} +(9.36903 + 16.2276i) q^{16} +(-16.9994 - 0.139826i) q^{17} +(-19.5291 - 3.69074i) q^{18} +21.5252 q^{19} +(-1.55708 - 2.69694i) q^{20} +(-2.22093 - 13.0629i) q^{21} +(-2.70872 - 1.56388i) q^{22} +(0.883809 - 1.53080i) q^{23} +(19.4005 + 7.19607i) q^{24} +(6.19024 + 10.7218i) q^{25} +6.86643i q^{26} +(-23.6268 + 13.0681i) q^{27} -3.87192i q^{28} +(17.1717 + 29.7423i) q^{29} +(-22.0654 - 8.18455i) q^{30} +(-5.35110 - 3.08946i) q^{31} +(11.9425 + 6.89502i) q^{32} +(-4.18896 + 0.712198i) q^{33} +(-32.6650 + 18.5026i) q^{34} -15.6902i q^{35} +(-7.44643 + 2.60742i) q^{36} +7.71265i q^{37} +(41.1659 - 23.7671i) q^{38} +(5.95209 + 7.18231i) q^{39} +(21.2195 + 12.2511i) q^{40} +(9.30986 - 16.1252i) q^{41} +(-18.6709 - 22.5299i) q^{42} +(22.6064 + 39.1554i) q^{43} -1.24163 q^{44} +(-30.1752 + 10.5661i) q^{45} -3.90345i q^{46} +(27.3169 - 15.7714i) q^{47} +(55.4189 - 9.42221i) q^{48} +(-14.7460 + 25.5408i) q^{49} +(23.6771 + 13.6700i) q^{50} +(-18.1289 + 47.6691i) q^{51} +(1.36289 + 2.36059i) q^{52} -55.4075i q^{53} +(-30.7560 + 51.0797i) q^{54} -5.03146 q^{55} +(15.2321 + 26.3827i) q^{56} +(22.4574 - 60.5447i) q^{57} +(65.6802 + 37.9205i) q^{58} +(-49.6000 - 28.6366i) q^{59} +(-9.21032 + 1.56592i) q^{60} +(13.7839 - 7.95816i) q^{61} -13.6450 q^{62} +(-39.0597 - 7.38175i) q^{63} -44.4995 q^{64} +(5.52284 + 9.56584i) q^{65} +(-7.22481 + 5.98731i) q^{66} +(-52.9793 + 91.7628i) q^{67} +(-7.55732 + 12.8445i) q^{68} +(-3.38366 - 4.08302i) q^{69} +(-17.3244 - 30.0067i) q^{70} -100.875 q^{71} +(40.4814 - 47.0608i) q^{72} -44.3391i q^{73} +(8.51597 + 14.7501i) q^{74} +(36.6160 - 6.22537i) q^{75} +(9.43489 - 16.3417i) q^{76} +(-5.41764 - 3.12787i) q^{77} +(19.3135 + 7.16381i) q^{78} +(-68.3530 + 39.4636i) q^{79} +66.5650 q^{80} +(12.1070 + 80.0901i) q^{81} -41.1181i q^{82} +(73.2711 - 42.3031i) q^{83} +(-10.8907 - 4.03961i) q^{84} +(-30.6245 + 52.0498i) q^{85} +(86.4674 + 49.9220i) q^{86} +(101.573 - 17.2692i) q^{87} +(8.46031 - 4.88456i) q^{88} -150.514i q^{89} +(-46.0420 + 53.5252i) q^{90} +13.7334i q^{91} +(-0.774780 - 1.34196i) q^{92} +(-14.2727 + 11.8280i) q^{93} +(34.8282 - 60.3242i) q^{94} +(38.2330 - 66.2215i) q^{95} +(31.8536 - 26.3976i) q^{96} +(-96.3476 + 55.6263i) q^{97} +65.1275i q^{98} +(-2.36715 + 12.5255i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 6 q^{2} + 62 q^{4} - 8 q^{9} - 2 q^{13} - 106 q^{16} - 2 q^{18} - 32 q^{19} - 28 q^{21} - 132 q^{25} + 180 q^{30} - 98 q^{33} - 27 q^{34} + 158 q^{36} - 102 q^{38} + 110 q^{42} + 58 q^{43} - 312 q^{47}+ \cdots - 18 q^{94}+O(q^{100}) $ 68 * q - 6 * q^2 + 62 * q^4 - 8 * q^9 - 2 * q^13 - 106 * q^16 - 2 * q^18 - 32 * q^19 - 28 * q^21 - 132 * q^25 + 180 * q^30 - 98 * q^33 - 27 * q^34 + 158 * q^36 - 102 * q^38 + 110 * q^42 + 58 * q^43 - 312 * q^47 + 152 * q^49 - 90 * q^50 - 17 * q^51 + 70 * q^52 + 92 * q^55 - 258 * q^59 - 126 * q^60 - 16 * q^64 + 400 * q^66 + 82 * q^67 - 333 * q^68 + 404 * q^69 + 204 * q^70 + 474 * q^72 + 34 * q^76 - 60 * q^77 - 88 * q^81 - 690 * q^83 - 200 * q^84 - 44 * q^85 - 1248 * q^86 + 114 * q^87 + 50 * q^93 - 18 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	1.91245	−	1.10416i	0.956227	−	0.552078i	0.0612170	−	0.998124i	$-0.480502\pi$
$2$	1.91245	−	1.10416i	0.956227	−	0.552078i	0.895010	+	0.446047i	$0.147168\pi$
$3$	1.04331	−	2.81274i	0.347770	−	0.937580i
$3$	1.04331	−	2.81274i	0.347770	−	0.937580i
$4$	0.438319	−	0.759190i	0.109580	−	0.189798i
$5$	1.77620	−	3.07647i	0.355240	−	0.615293i	−0.631919	−	0.775034i	$-0.717733\pi$
$5$	1.77620	−	3.07647i	0.355240	−	0.615293i	0.987159	+	0.159741i	$0.0510659\pi$
$6$	−1.11042	−	6.53121i	−0.185070	−	1.08853i
$7$	3.82505	−	2.20839i	0.546436	−	0.315485i	−0.201248	−	0.979540i	$-0.564500\pi$
$7$	3.82505	−	2.20839i	0.546436	−	0.315485i	0.747683	+	0.664056i	$0.231166\pi$
$8$			6.89736i			0.862169i
$9$	−6.82301	−	5.86911i	−0.758113	−	0.652124i
$10$		−	7.84480i		−	0.784480i
$11$	−0.708179	−	1.22660i	−0.0643799	−	0.111509i	0.832039	−	0.554717i	$-0.187174\pi$
$11$	−0.708179	−	1.22660i	−0.0643799	−	0.111509i	−0.896419	+	0.443208i	$0.853840\pi$
$12$	−1.67810	−	2.02495i	−0.139842	−	0.168746i
$13$	−1.55468	+	2.69278i	−0.119591	+	0.207137i	−0.919606	−	0.392843i	$-0.871492\pi$
$13$	−1.55468	+	2.69278i	−0.119591	+	0.207137i	0.800015	+	0.599980i	$0.204825\pi$
$14$	4.87682	−	8.44690i	0.348344	−	0.603350i
$15$	−6.80018	−	8.20569i	−0.453345	−	0.547046i
$16$	9.36903	+	16.2276i	0.585564	+	1.01423i
$17$	−16.9994	−	0.139826i	−0.999966	−	0.00822508i
$17$	−16.9994	−	0.139826i	−0.999966	−	0.00822508i
$18$	−19.5291	−	3.69074i	−1.08495	−	0.205041i
$19$	21.5252			1.13290			0.566452	−	0.824095i	$-0.308316\pi$
$19$	21.5252			1.13290			0.566452	+	0.824095i	$0.308316\pi$
$20$	−1.55708	−	2.69694i	−0.0778541	−	0.134847i
$21$	−2.22093	−	13.0629i	−0.105758	−	0.622043i
$22$	−2.70872	−	1.56388i	−0.123124	−	0.0710854i
$23$	0.883809	−	1.53080i	0.0384265	−	0.0665566i	−0.846173	−	0.532909i	$-0.821099\pi$
$23$	0.883809	−	1.53080i	0.0384265	−	0.0665566i	0.884599	+	0.466352i	$0.154432\pi$
$24$	19.4005	+	7.19607i	0.808353	+	0.299836i
$25$	6.19024	+	10.7218i	0.247610	+	0.428872i
$26$			6.86643i			0.264093i
$27$	−23.6268	+	13.0681i	−0.875067	+	0.484002i
$28$		−	3.87192i		−	0.138283i
$29$	17.1717	+	29.7423i	0.592128	+	1.02560i	0.993945	+	0.109876i	$0.0350454\pi$
$29$	17.1717	+	29.7423i	0.592128	+	1.02560i	−0.401817	+	0.915720i	$0.631621\pi$
$30$	−22.0654	−	8.18455i	−0.735512	−	0.272818i
$31$	−5.35110	−	3.08946i	−0.172616	−	0.0996600i	0.411203	−	0.911544i	$-0.365109\pi$
$31$	−5.35110	−	3.08946i	−0.172616	−	0.0996600i	−0.583819	+	0.811884i	$0.698442\pi$
$32$	11.9425	+	6.89502i	0.373204	+	0.215469i
$33$	−4.18896	+	0.712198i	−0.126938	+	0.0215818i
$34$	−32.6650	+	18.5026i	−0.960735	+	0.544194i
$35$		−	15.6902i		−	0.448291i
$36$	−7.44643	+	2.60742i	−0.206845	+	0.0724284i
$37$			7.71265i			0.208450i	0.994554	+	0.104225i	$0.0332362\pi$
$37$			7.71265i			0.208450i	−0.994554	+	0.104225i	$0.966764\pi$
$38$	41.1659	−	23.7671i	1.08331	−	0.625451i
$39$	5.95209	+	7.18231i	0.152618	+	0.184162i
$40$	21.2195	+	12.2511i	0.530487	+	0.306277i
$41$	9.30986	−	16.1252i	0.227070	−	0.393296i	−0.729869	−	0.683587i	$-0.760419\pi$
$41$	9.30986	−	16.1252i	0.227070	−	0.393296i	0.956938	+	0.290291i	$0.0937521\pi$
$42$	−18.6709	−	22.5299i	−0.444545	−	0.536427i
$43$	22.6064	+	39.1554i	0.525730	+	0.910591i	0.999551	+	0.0299700i	$0.00954118\pi$
$43$	22.6064	+	39.1554i	0.525730	+	0.910591i	−0.473821	+	0.880621i	$0.657125\pi$
$44$	−1.24163			−0.0282189
$45$	−30.1752	+	10.5661i	−0.670559	+	0.234801i
$46$		−	3.90345i		−	0.0848576i
$47$	27.3169	−	15.7714i	0.581211	−	0.335562i	−0.180404	−	0.983593i	$-0.557740\pi$
$47$	27.3169	−	15.7714i	0.581211	−	0.335562i	0.761614	+	0.648030i	$0.224407\pi$
$48$	55.4189	−	9.42221i	1.15456	−	0.196296i
$49$	−14.7460	+	25.5408i	−0.300939	+	0.521241i
$50$	23.6771	+	13.6700i	0.473542	+	0.273399i
$51$	−18.1289	+	47.6691i	−0.355470	+	0.934688i
$52$	1.36289	+	2.36059i	0.0262094	+	0.0453961i
$53$		−	55.4075i		−	1.04542i	−0.852509	−	0.522712i	$-0.824920\pi$
$53$		−	55.4075i		−	1.04542i	0.852509	−	0.522712i	$-0.175080\pi$
$54$	−30.7560	+	51.0797i	−0.569555	+	0.945921i
$55$	−5.03146			−0.0914811
$56$	15.2321	+	26.3827i	0.272001	+	0.471120i
$57$	22.4574	−	60.5447i	0.393990	−	1.06219i
$58$	65.6802	+	37.9205i	1.13242	+	0.653802i
$59$	−49.6000	−	28.6366i	−0.840677	−	0.485365i	0.0168170	−	0.999859i	$-0.494647\pi$
$59$	−49.6000	−	28.6366i	−0.840677	−	0.485365i	−0.857494	+	0.514493i	$0.827980\pi$
$60$	−9.21032	+	1.56592i	−0.153505	+	0.0260987i
$61$	13.7839	−	7.95816i	0.225966	−	0.130462i	−0.382744	−	0.923855i	$-0.625021\pi$
$61$	13.7839	−	7.95816i	0.225966	−	0.130462i	0.608710	+	0.793393i	$0.291687\pi$
$62$	−13.6450			−0.220080
$63$	−39.0597	−	7.38175i	−0.619995	−	0.117171i
$64$	−44.4995			−0.695305
$65$	5.52284	+	9.56584i	0.0849667	+	0.147167i
$66$	−7.22481	+	5.98731i	−0.109467	+	0.0907168i
$67$	−52.9793	+	91.7628i	−0.790736	+	1.36959i	0.134776	+	0.990876i	$0.456969\pi$
$67$	−52.9793	+	91.7628i	−0.790736	+	1.36959i	−0.925512	+	0.378719i	$0.876365\pi$
$68$	−7.55732	+	12.8445i	−0.111137	+	0.188890i
$69$	−3.38366	−	4.08302i	−0.0490386	−	0.0591743i
$70$	−17.3244	−	30.0067i	−0.247491	−	0.428668i
$71$	−100.875			−1.42078			−0.710388	−	0.703810i	$-0.751481\pi$
$71$	−100.875			−1.42078			−0.710388	+	0.703810i	$0.751481\pi$
$72$	40.4814	−	47.0608i	0.562241	−	0.653622i
$73$		−	44.3391i		−	0.607385i	−0.952770	−	0.303692i	$-0.901780\pi$
$73$		−	44.3391i		−	0.607385i	0.952770	−	0.303692i	$-0.0982195\pi$
$74$	8.51597	+	14.7501i	0.115081	+	0.199326i
$75$	36.6160	−	6.22537i	0.488213	−	0.0830050i
$76$	9.43489	−	16.3417i	0.124143	−	0.215022i
$77$	−5.41764	−	3.12787i	−0.0703589	−	0.0406217i
$78$	19.3135	+	7.16381i	0.247609	+	0.0918437i
$79$	−68.3530	+	39.4636i	−0.865228	+	0.499540i	−0.865760	−	0.500460i	$-0.833164\pi$
$79$	−68.3530	+	39.4636i	−0.865228	+	0.499540i	0.000531310		1.00000i	$0.499831\pi$
$80$	66.5650			0.832063
$81$	12.1070	+	80.0901i	0.149469	+	0.988766i
$82$		−	41.1181i		−	0.501441i
$83$	73.2711	−	42.3031i	0.882784	−	0.509675i	0.0112086	−	0.999937i	$-0.496432\pi$
$83$	73.2711	−	42.3031i	0.882784	−	0.509675i	0.871575	+	0.490262i	$0.163099\pi$
$84$	−10.8907	−	4.03961i	−0.129651	−	0.0480906i
$85$	−30.6245	+	52.0498i	−0.360288	+	0.612350i
$86$	86.4674	+	49.9220i	1.00543	+	0.580488i
$87$	101.573	−	17.2692i	1.16750	−	0.198496i
$88$	8.46031	−	4.88456i	0.0961398	−	0.0555064i
$89$		−	150.514i		−	1.69117i	−0.533840	−	0.845585i	$-0.679252\pi$
$89$		−	150.514i		−	1.69117i	0.533840	−	0.845585i	$-0.320748\pi$
$90$	−46.0420	+	53.5252i	−0.511578	+	0.594724i
$91$			13.7334i			0.150916i
$92$	−0.774780	−	1.34196i	−0.00842152	−	0.0145865i
$93$	−14.2727	+	11.8280i	−0.153470	+	0.127183i
$94$	34.8282	−	60.3242i	0.370513	−	0.641747i
$95$	38.2330	−	66.2215i	0.402452	−	0.697068i
$96$	31.8536	−	26.3976i	0.331809	−	0.274975i
$97$	−96.3476	+	55.6263i	−0.993274	+	0.573467i	−0.906251	−	0.422739i	$-0.861069\pi$
$97$	−96.3476	+	55.6263i	−0.993274	+	0.573467i	−0.0870227	+	0.996206i	$0.527735\pi$
$98$			65.1275i			0.664566i
$99$	−2.36715	+	12.5255i	−0.0239106	+	0.126520i
$100$	10.8532			0.108532
$101$	−81.4139	+	47.0043i	−0.806078	+	0.465389i	−0.845592	−	0.533830i	$-0.820752\pi$
$101$	−81.4139	+	47.0043i	−0.806078	+	0.465389i	0.0395141	+	0.999219i	$0.487419\pi$
$102$	17.9633	+	111.182i	0.176111	+	1.09002i
$103$	17.7283	−	30.7063i	0.172120	−	0.298120i	−0.767041	−	0.641598i	$-0.778272\pi$
$103$	17.7283	−	30.7063i	0.172120	−	0.298120i	0.939161	+	0.343478i	$0.111605\pi$
$104$	−18.5731	−	10.7232i	−0.178587	−	0.103107i
$105$	−44.1324	−	16.3697i	−0.420308	−	0.155902i
$106$	−61.1785	−	105.964i	−0.577156	−	0.999663i
$107$	−148.903			−1.39161			−0.695807	−	0.718229i	$-0.744953\pi$
$107$	−148.903			−1.39161			−0.695807	+	0.718229i	$0.744953\pi$
$108$	−0.434921	+	23.6652i	−0.00402704	+	0.219122i
$109$		−	203.589i		−	1.86779i	−0.357544	−	0.933896i	$-0.616386\pi$
$109$		−	203.589i		−	1.86779i	0.357544	−	0.933896i	$-0.383614\pi$
$110$	−9.62244	+	5.55552i	−0.0874767	+	0.0505047i
$111$	21.6937	+	8.04668i	0.195439	+	0.0724926i
$112$	71.6740	+	41.3810i	0.639946	+	0.369473i
$113$	62.6190	−	108.459i	0.554150	−	0.959816i	−0.443819	−	0.896116i	$-0.646377\pi$
$113$	62.6190	−	108.459i	0.554150	−	0.959816i	0.997969	−	0.0636997i	$-0.0202900\pi$
$114$	−23.9020	−	140.585i	−0.209667	−	1.23321i
$115$	−3.13964	−	5.43802i	−0.0273012	−	0.0472871i
$116$	30.1067			0.259541
$117$	26.4118	−	9.24831i	0.225742	−	0.0790454i
$118$	−126.477			−1.07184
$119$	−65.3324	+	37.0066i	−0.549012	+	0.310980i
$120$	56.5976	−	46.9032i	0.471646	−	0.390860i
$121$	59.4970	−	103.052i	0.491710	−	0.851668i
$122$	17.5741	−	30.4392i	0.144050	−	0.249502i
$123$	−35.6428	−	43.0097i	−0.289779	−	0.349673i
$124$	−4.69098	+	2.70834i	−0.0378305	+	0.0218414i
$125$	132.790			1.06232
$126$	−82.8504	+	29.0107i	−0.657543	+	0.230244i
$127$	76.3604			0.601263			0.300631	−	0.953740i	$-0.402803\pi$
$127$	76.3604			0.601263			0.300631	+	0.953740i	$0.402803\pi$
$128$	−132.873	+	76.7145i	−1.03807	+	0.599332i
$129$	133.720	−	22.7347i	1.03659	−	0.176238i
$130$	21.1243	+	12.1961i	0.162495	+	0.0938165i
$131$	7.14440	−	12.3745i	0.0545374	−	0.0944615i	−0.837468	−	0.546487i	$-0.815965\pi$
$131$	7.14440	−	12.3745i	0.0545374	−	0.0944615i	0.892005	+	0.452025i	$0.149298\pi$
$132$	−1.29541	+	3.49239i	−0.00981368	+	0.0264575i
$133$	82.3349	−	47.5361i	0.619059	−	0.357414i
$134$			233.990i			1.74619i
$135$	−1.76243	+	95.8985i	−0.0130550	+	0.710359i
$136$	0.964432	−	117.251i	0.00709141	−	0.862140i
$137$	−81.9500	+	47.3139i	−0.598175	+	0.345357i	−0.768323	−	0.640062i	$-0.778909\pi$
$137$	−81.9500	+	47.3139i	−0.598175	+	0.345357i	0.170148	+	0.985419i	$0.445575\pi$
$138$	−10.9794	−	4.07250i	−0.0795608	−	0.0295109i
$139$	72.1283	+	41.6433i	0.518909	+	0.299592i	0.736488	−	0.676451i	$-0.236483\pi$
$139$	72.1283	+	41.6433i	0.518909	+	0.299592i	−0.217579	+	0.976043i	$0.569816\pi$
$140$	−11.9118	−	6.87730i	−0.0850845	−	0.0491236i
$141$	−15.8609	−	93.2898i	−0.112489	−	0.661630i
$142$	−192.919	+	111.382i	−1.35858	+	0.784379i
$143$	4.40396			0.0307969
$144$	31.3168	−	165.709i	0.217478	−	1.15076i
$145$	122.002			0.841390
$146$	−48.9573	−	84.7964i	−0.335324	−	0.580798i
$147$	56.4551	+	68.1236i	0.384048	+	0.463426i
$148$	5.85537	+	3.38060i	0.0395633	+	0.0228419i
$149$	−175.664	−	101.420i	−1.17895	−	0.680668i	−0.223180	−	0.974777i	$-0.571644\pi$
$149$	−175.664	−	101.420i	−1.17895	−	0.680668i	−0.955772	+	0.294109i	$0.904977\pi$
$150$	63.1526	−	52.3355i	0.421017	−	0.348903i
$151$	12.4662	+	21.5922i	0.0825579	+	0.142994i	0.904348	−	0.426796i	$-0.140358\pi$
$151$	12.4662	+	21.5922i	0.0825579	+	0.142994i	−0.821790	+	0.569790i	$0.807024\pi$
$152$			148.467i			0.976755i
$153$	115.167	+	100.726i	0.752723	+	0.658337i
$154$	−13.8146			−0.0897054
$155$	−19.0092	+	10.9750i	−0.122640	+	0.0708064i
$156$	8.06165	−	1.37063i	0.0516773	−	0.00878606i
$157$	127.288	−	220.468i	0.810748	−	1.40426i	−0.101592	−	0.994826i	$-0.532394\pi$
$157$	127.288	−	220.468i	0.810748	−	1.40426i	0.912341	−	0.409431i	$-0.134273\pi$
$158$	−87.1480	+	150.945i	−0.551570	+	0.955347i
$159$	−155.847	−	57.8072i	−0.980169	−	0.363567i
$160$	42.4246	−	24.4938i	0.265154	−	0.153086i
$161$		−	7.80719i		−	0.0484919i
$162$	111.586	+	139.801i	0.688803	+	0.862966i
$163$			80.6427i			0.494740i	0.968921	+	0.247370i	$0.0795664\pi$
$163$			80.6427i			0.494740i	−0.968921	+	0.247370i	$0.920434\pi$
$164$	−8.16137	−	14.1359i	−0.0497645	−	0.0861946i
$165$	−5.24937	+	14.1522i	−0.0318144	+	0.0857709i
$166$	93.4183	−	161.805i	0.562761	−	0.974731i
$167$	−130.070	+	225.288i	−0.778862	+	1.34903i	0.153736	+	0.988112i	$0.450869\pi$
$167$	−130.070	+	225.288i	−0.778862	+	1.34903i	−0.932598	+	0.360917i	$0.882464\pi$
$168$	90.0995	−	15.3185i	0.536307	−	0.0911817i
$169$	79.6659	+	137.985i	0.471396	+	0.816482i
$170$	−1.09691	+	133.357i	−0.00645241	+	0.784453i
$171$	−146.867	−	126.334i	−0.858869	−	0.738794i
$172$	39.6352			0.230437
$173$	65.8536	+	114.062i	0.380657	+	0.659317i	0.991156	−	0.132700i	$-0.0423646\pi$
$173$	65.8536	+	114.062i	0.380657	+	0.659317i	−0.610500	+	0.792017i	$0.709031\pi$
$174$	175.185	−	145.179i	1.00681	−	0.834360i
$175$	47.3559	+	27.3410i	0.270605	+	0.156234i
$176$	13.2699	−	22.9841i	0.0753971	−	0.130592i
$177$	−132.295	+	109.635i	−0.747431	+	0.619407i
$178$	−166.191	−	287.851i	−0.933658	−	1.61714i
$179$			115.487i			0.645179i	0.946539	+	0.322589i	$0.104553\pi$
$179$			115.487i			0.645179i	−0.946539	+	0.322589i	$0.895447\pi$
$180$	−5.20468	+	27.5400i	−0.0289149	+	0.153000i
$181$			199.995i			1.10495i	0.833530	+	0.552474i	$0.186316\pi$
$181$			199.995i			1.10495i	−0.833530	+	0.552474i	$0.813684\pi$
$182$	15.1638	+	26.2644i	0.0833175	+	0.144310i
$183$	−8.00333	−	47.0734i	−0.0437340	−	0.257232i
$184$	10.5585	+	6.09595i	0.0573831	+	0.0331301i
$185$	23.7277	+	13.6992i	0.128258	+	0.0740498i
$186$	−14.2359	+	38.3798i	−0.0765373	+	0.206343i
$187$	11.8671	+	20.9505i	0.0634605	+	0.112035i
$188$		−	27.6516i		−	0.147083i
$189$	−61.5142	+	102.163i	−0.325472	+	0.540546i
$190$		−	168.861i		−	0.888740i
$191$	53.6891	−	30.9974i	0.281095	−	0.162290i	−0.352824	−	0.935690i	$-0.614779\pi$
$191$	53.6891	−	30.9974i	0.281095	−	0.162290i	0.633919	+	0.773399i	$0.281445\pi$
$192$	−46.4268	+	125.166i	−0.241806	+	0.651904i
$193$	143.537	+	82.8710i	0.743714	+	0.429384i	0.823418	−	0.567435i	$-0.192064\pi$
$193$	143.537	+	82.8710i	0.743714	+	0.429384i	−0.0797040	+	0.996819i	$0.525398\pi$
$194$	−122.840	+	212.765i	−0.633197	+	1.09673i
$195$	32.6682	−	5.55419i	0.167529	−	0.0284830i
$196$	12.9269	+	22.3900i	0.0659535	+	0.114235i
$197$	33.9096			0.172130			0.0860649	−	0.996290i	$-0.472571\pi$
$197$	33.9096			0.172130			0.0860649	+	0.996290i	$0.472571\pi$
$198$	9.30303	+	26.5681i	0.0469850	+	0.134182i
$199$			216.086i			1.08586i	0.839778	+	0.542929i	$0.182685\pi$
$199$			216.086i			1.08586i	−0.839778	+	0.542929i	$0.817315\pi$
$200$	−73.9521	+	42.6963i	−0.369761	+	0.213481i
$201$	202.831	+	244.754i	1.00911	+	1.21768i
$202$	−103.800	+	179.787i	−0.513862	+	0.890035i
$203$	131.365	+	75.8438i	0.647120	+	0.373615i
$204$	28.2436	+	34.6576i	0.138449	+	0.169890i
$205$	−33.0723	−	57.2829i	−0.161328	−	0.279429i
$206$		−	78.2993i		−	0.380094i
$207$	−15.0147	+	5.25751i	−0.0725348	+	0.0253986i
$208$	−58.2633			−0.280112
$209$	−15.2437	−	26.4028i	−0.0729362	−	0.126329i
$210$	−102.476	+	17.4227i	−0.487980	+	0.0829654i
$211$	−68.8378	−	39.7435i	−0.326245	−	0.188358i	0.327927	−	0.944703i	$-0.393650\pi$
$211$	−68.8378	−	39.7435i	−0.326245	−	0.188358i	−0.654173	+	0.756345i	$0.726983\pi$
$212$	−42.0648	−	24.2862i	−0.198419	−	0.114557i
$213$	−105.244	+	283.735i	−0.494103	+	1.33209i
$214$	−284.769	+	164.412i	−1.33070	+	0.768279i
$215$	160.614			0.747041
$216$	−90.1351	−	162.962i	−0.417292	−	0.754456i
$217$	−27.2910			−0.125765
$218$	−224.794	−	389.355i	−1.03117	−	1.78603i
$219$	−124.714	−	46.2594i	−0.569472	−	0.211230i
$220$	−2.20538	+	3.81984i	−0.0100245	+	0.0173629i
$221$	26.8052	−	45.5584i	0.121290	−	0.206147i
$222$	50.3730	−	8.56431i	0.226905	−	0.0385780i
$223$	−5.57705	−	9.65974i	−0.0250092	−	0.0433172i	0.853250	−	0.521502i	$-0.174628\pi$
$223$	−5.57705	−	9.65974i	−0.0250092	−	0.0433172i	−0.878259	+	0.478185i	$0.841295\pi$
$224$	60.9076			0.271909
$225$	20.6914	−	109.486i	0.0919619	−	0.486606i
$226$		−	276.564i		−	1.22374i
$227$	−9.08769	−	15.7403i	−0.0400339	−	0.0693407i	0.845314	−	0.534270i	$-0.179413\pi$
$227$	−9.08769	−	15.7403i	−0.0400339	−	0.0693407i	−0.885348	+	0.464929i	$0.846080\pi$
$228$	−36.1215	−	43.5873i	−0.158427	−	0.191173i
$229$	−29.0162	+	50.2575i	−0.126708	+	0.219465i	−0.922399	−	0.386237i	$-0.873775\pi$
$229$	−29.0162	+	50.2575i	−0.126708	+	0.219465i	0.795691	+	0.605703i	$0.207108\pi$
$230$	−12.0088	−	6.93330i	−0.0522123	−	0.0301448i
$231$	−14.4502	+	11.9751i	−0.0625548	+	0.0518401i
$232$	−205.143	+	118.439i	−0.884238	+	0.510515i
$233$	393.043			1.68688			0.843439	−	0.537224i	$-0.180527\pi$
$233$	393.043			1.68688			0.843439	+	0.537224i	$0.180527\pi$
$234$	40.2999	−	46.8497i	0.172222	−	0.200213i
$235$		−	112.053i		−	0.476820i
$236$	−43.4812	+	25.1039i	−0.184242	+	0.106372i
$237$	39.6876	+	233.432i	0.167458	+	0.984946i
$238$	−84.0842	+	142.910i	−0.353295	+	0.600464i
$239$	−134.761	−	77.8044i	−0.563854	−	0.325541i	0.190837	−	0.981622i	$-0.438880\pi$
$239$	−134.761	−	77.8044i	−0.563854	−	0.325541i	−0.754691	+	0.656080i	$0.772213\pi$
$240$	69.4479	−	187.230i	0.289366	−	0.780125i
$241$	118.785	−	68.5806i	0.492884	−	0.284567i	−0.232886	−	0.972504i	$-0.574817\pi$
$241$	118.785	−	68.5806i	0.492884	−	0.284567i	0.725770	+	0.687937i	$0.241484\pi$
$242$		−	262.776i		−	1.08585i
$243$	237.904	+	49.5048i	0.979028	+	0.203723i
$244$		−	13.9528i		−	0.0571838i
$245$	52.3836	+	90.7311i	0.213811	+	0.370331i
$246$	−115.655	−	42.8989i	−0.470141	−	0.174386i
$247$	−33.4647	+	57.9626i	−0.135485	+	0.234667i
$248$	21.3091	−	36.9085i	0.0859238	−	0.148824i
$249$	−42.5432	−	250.228i	−0.170856	−	1.00493i
$250$	253.955	−	146.621i	1.01582	−	0.586484i
$251$		−	234.999i		−	0.936250i	−0.883662	−	0.468125i	$-0.844930\pi$
$251$		−	234.999i		−	0.936250i	0.883662	−	0.468125i	$-0.155070\pi$
$252$	−22.7247	+	26.4182i	−0.0901775	+	0.104834i
$253$	−2.50358			−0.00989557
$254$	146.036	−	84.3137i	0.574944	−	0.331944i
$255$	114.452	+	140.443i	0.448830	+	0.550756i
$256$	−80.4103	+	139.275i	−0.314103	+	0.544042i
$257$	82.7205	+	47.7587i	0.321870	+	0.185832i	0.652226	−	0.758025i	$-0.273835\pi$
$257$	82.7205	+	47.7587i	0.321870	+	0.185832i	−0.330356	+	0.943856i	$0.607169\pi$
$258$	230.630	−	191.126i	0.893913	−	0.740799i
$259$	17.0326	+	29.5013i	0.0657628	+	0.113905i
$260$	9.68305			0.0372425
$261$	57.3980	−	303.715i	0.219916	−	1.16366i
$262$		−	31.5541i		−	0.120436i
$263$	313.310	−	180.890i	1.19129	−	0.687793i	0.232693	−	0.972550i	$-0.425246\pi$
$263$	313.310	−	180.890i	1.19129	−	0.687793i	0.958600	+	0.284757i	$0.0919130\pi$
$264$	−4.91229	−	28.8927i	−0.0186071	−	0.109442i
$265$	−170.459	−	98.4147i	−0.643243	−	0.371376i
$266$	104.974	−	181.821i	0.394641	−	0.683537i
$267$	−423.357	−	157.033i	−1.58561	−	0.588138i
$268$	46.4436	+	80.4427i	0.173297	+	0.300159i
$269$	−420.642			−1.56373			−0.781863	−	0.623450i	$-0.785730\pi$
$269$	−420.642			−1.56373			−0.781863	+	0.623450i	$0.785730\pi$
$270$	102.516	+	185.347i	0.379690	+	0.686472i
$271$	−100.068			−0.369253			−0.184627	−	0.982809i	$-0.559108\pi$
$271$	−100.068			−0.369253			−0.184627	+	0.982809i	$0.559108\pi$
$272$	−156.999	−	277.170i	−0.577202	−	1.01901i
$273$	38.6284	+	14.3281i	0.141496	+	0.0524841i
$274$	−104.484	+	180.971i	−0.381328	+	0.660479i
$275$	8.76759	−	15.1859i	0.0318821	−	0.0552215i
$276$	−4.58292	+	0.779178i	−0.0166048	+	0.00282311i
$277$	473.610	−	273.439i	1.70978	−	0.987143i	0.774972	−	0.631996i	$-0.217764\pi$
$277$	473.610	−	273.439i	1.70978	−	0.987143i	0.934810	−	0.355147i	$-0.115569\pi$
$278$	183.923			0.661592
$279$	18.3783	+	52.4857i	0.0658719	+	0.188121i
$280$	108.221			0.386503
$281$	133.786	−	77.2417i	0.476109	−	0.274881i	−0.242685	−	0.970105i	$-0.578028\pi$
$281$	133.786	−	77.2417i	0.476109	−	0.274881i	0.718793	+	0.695224i	$0.244695\pi$
$282$	−133.340	−	160.899i	−0.472836	−	0.570566i
$283$	−276.014	−	159.357i	−0.975314	−	0.563098i	−0.0744622	−	0.997224i	$-0.523724\pi$
$283$	−276.014	−	159.357i	−0.975314	−	0.563098i	−0.900852	+	0.434126i	$0.857057\pi$
$284$	−44.2154	+	76.5834i	−0.155688	+	0.269660i
$285$	−146.375	−	176.629i	−0.513596	−	0.619751i
$286$	8.42237	−	4.86266i	0.0294489	−	0.0170023i
$287$		−	82.2393i		−	0.286548i
$288$	−41.0163	−	117.137i	−0.142418	−	0.406725i
$289$	288.961	+	4.75393i	0.999865	+	0.0164496i
$290$	233.322	−	134.709i	0.804559	−	0.464513i
$291$	55.9420	+	329.036i	0.192241	+	1.13071i
$292$	−33.6618	−	19.4347i	−0.115280	−	0.0665570i
$293$	87.7848	+	50.6826i	0.299607	+	0.172978i	0.642266	−	0.766482i	$-0.277994\pi$
$293$	87.7848	+	50.6826i	0.299607	+	0.172978i	−0.342659	+	0.939460i	$0.611328\pi$
$294$	183.187	+	67.9481i	0.623084	+	0.231116i
$295$	−176.199	+	101.728i	−0.597284	+	0.344842i
$296$	−53.1969			−0.179719
$297$	32.7613	+	19.7261i	0.110307	+	0.0664180i
$298$	−447.932			−1.50313
$299$	2.74808	+	4.75981i	0.00919090	+	0.0159191i
$300$	11.3232	−	30.5272i	0.0377441	−	0.101757i
$301$	172.941	+	99.8476i	0.574555	+	0.331720i
$302$	47.6822	+	27.5293i	0.157888	+	0.0911567i
$303$	47.2711	+	278.036i	0.156010	+	0.917611i
$304$	201.670	+	349.303i	0.663388	+	1.14902i
$305$		−	56.5411i		−	0.185381i
$306$	331.468	+	65.4711i	1.08323	+	0.213958i
$307$	−114.755			−0.373794			−0.186897	−	0.982380i	$-0.559843\pi$
$307$	−114.755			−0.373794			−0.186897	+	0.982380i	$0.559843\pi$
$308$	−4.74930	+	2.74201i	−0.0154198	+	0.00890263i
$309$	−67.8729	−	81.9013i	−0.219653	−	0.265053i
$310$	−24.2362	+	41.9783i	−0.0781813	+	0.135414i
$311$	49.0382	−	84.9367i	0.157679	−	0.273108i	−0.776352	−	0.630299i	$-0.782932\pi$
$311$	49.0382	−	84.9367i	0.157679	−	0.273108i	0.934031	+	0.357191i	$0.116265\pi$
$312$	−49.5390	+	41.0537i	−0.158779	+	0.131582i
$313$	276.012	−	159.356i	0.881829	−	0.509124i	0.0105678	−	0.999944i	$-0.496636\pi$
$313$	276.012	−	159.356i	0.881829	−	0.509124i	0.871261	+	0.490820i	$0.163303\pi$
$314$		−	562.181i		−	1.79038i
$315$	−92.0874	+	107.054i	−0.292341	+	0.339855i
$316$			69.1906i			0.218958i
$317$	−84.7398	−	146.774i	−0.267318	−	0.463008i	0.700850	−	0.713308i	$-0.252804\pi$
$317$	−84.7398	−	146.774i	−0.267318	−	0.463008i	−0.968168	+	0.250300i	$0.919471\pi$
$318$	−361.878	+	61.5258i	−1.13798	+	0.193477i
$319$	24.3213	−	42.1257i	0.0762423	−	0.132055i
$320$	−79.0400	+	136.901i	−0.247000	+	0.427817i
$321$	−155.351	+	418.824i	−0.483961	+	1.30475i
$322$	−8.62035	−	14.9309i	−0.0267713	−	0.0463692i
$323$	−365.916	−	3.00979i	−1.13287	−	0.00931822i
$324$	66.1103	+	25.9134i	0.204044	+	0.0799798i
$325$	−38.4953			−0.118447
$326$	89.0421	+	154.225i	0.273135	+	0.473084i
$327$	−572.644	−	212.407i	−1.75120	−	0.649561i
$328$	111.221	+	64.2134i	0.339088	+	0.195773i
$329$	69.6590	−	120.653i	0.211729	−	0.366726i
$330$	5.58705	+	32.8615i	0.0169305	+	0.0995804i
$331$	−148.453	−	257.128i	−0.448498	−	0.776821i	0.549790	−	0.835303i	$-0.314708\pi$
$331$	−148.453	−	257.128i	−0.448498	−	0.776821i	−0.998289	+	0.0584812i	$0.981374\pi$
$332$		−	74.1689i		−	0.223400i
$333$	45.2664	−	52.6235i	0.135935	−	0.158029i
$334$			574.470i			1.71997i
$335$	188.204	+	325.978i	0.561802	+	0.973069i
$336$	191.172	−	158.427i	0.568965	−	0.471509i
$337$	−454.800	−	262.579i	−1.34955	−	0.779166i	−0.361368	−	0.932423i	$-0.617690\pi$
$337$	−454.800	−	262.579i	−1.34955	−	0.779166i	−0.988186	+	0.153257i	$0.951024\pi$
$338$	304.715	+	175.927i	0.901523	+	0.520495i
$339$	−239.737	−	289.287i	−0.707188	−	0.853355i
$340$	26.0924	+	46.0642i	0.0767423	+	0.135483i
$341$			8.75156i			0.0256644i
$342$	−420.368	−	79.4438i	−1.22914	−	0.232292i
$343$			346.682i			1.01074i
$344$	−270.069	+	155.924i	−0.785084	+	0.453269i
$345$	−18.5713	+	3.15746i	−0.0538300	+	0.00915206i
$346$	251.884	+	145.425i	0.727988	+	0.420304i
$347$	−209.954	+	363.652i	−0.605056	+	1.04799i	0.386987	+	0.922085i	$0.373516\pi$
$347$	−209.954	+	363.652i	−0.605056	+	1.04799i	−0.992043	+	0.125902i	$0.959818\pi$
$348$	31.4106	−	84.6824i	0.0902604	−	0.243340i
$349$	274.372	+	475.226i	0.786166	+	1.36168i	0.928300	+	0.371831i	$0.121270\pi$
$349$	274.372	+	475.226i	0.786166	+	1.36168i	−0.142135	+	0.989847i	$0.545397\pi$
$350$	120.755			0.345013
$351$	1.54263	−	83.9385i	0.00439495	−	0.239141i
$352$		−	19.5316i		−	0.0554875i
$353$	400.248	−	231.083i	1.13385	−	0.654627i	0.188947	−	0.981987i	$-0.439492\pi$
$353$	400.248	−	231.083i	1.13385	−	0.654627i	0.944900	+	0.327360i	$0.106159\pi$
$354$	−131.954	+	355.746i	−0.372753	+	1.00493i
$355$	−179.174	+	310.339i	−0.504716	+	0.874194i
$356$	−114.269	−	65.9732i	−0.320980	−	0.185318i
$357$	35.9280	+	222.372i	0.100639	+	0.622892i
$358$	127.516	+	220.864i	0.356189	+	0.616937i
$359$			377.149i			1.05055i	0.850931	+	0.525277i	$0.176038\pi$
$359$			377.149i			1.05055i	−0.850931	+	0.525277i	$0.823962\pi$
$360$	−72.8779	−	208.129i	−0.202439	−	0.578135i
$361$	102.333			0.283472
$362$	220.826	+	382.482i	0.610017	+	1.05658i
$363$	−227.784	−	274.864i	−0.627504	−	0.757202i
$364$	10.4262	+	6.01959i	0.0286435	+	0.0165373i
$365$	−136.408	−	78.7550i	−0.373720	−	0.215767i
$366$	−67.2824	−	81.1888i	−0.183832	−	0.221827i
$367$	−481.665	+	278.090i	−1.31244	+	0.757737i	−0.982500	−	0.186265i	$-0.940362\pi$
$367$	−481.665	+	278.090i	−1.31244	+	0.757737i	−0.329940	+	0.944002i	$0.607028\pi$
$368$	33.1217			0.0900047
$369$	−158.162	+	55.3815i	−0.428622	+	0.150085i
$370$	60.5042			0.163525
$371$	−122.362	−	211.936i	−0.329816	−	0.571257i
$372$	2.72371	+	16.0201i	0.00732180	+	0.0430649i
$373$	182.405	−	315.935i	0.489022	−	0.847010i	−0.510899	−	0.859641i	$-0.670687\pi$
$373$	182.405	−	315.935i	0.489022	−	0.847010i	0.999920	+	0.0126306i	$0.00402055\pi$
$374$	45.8280	+	26.9638i	0.122535	+	0.0720957i
$375$	138.541	−	373.505i	0.369443	−	0.996012i
$376$	108.781	+	188.414i	0.289311	+	0.501102i
$377$	−106.786			−0.283252
$378$	−4.83901	+	263.304i	−0.0128016	+	0.696571i
$379$		−	555.368i		−	1.46535i	−0.680579	−	0.732675i	$-0.738272\pi$
$379$		−	555.368i		−	1.46535i	0.680579	−	0.732675i	$-0.261728\pi$
$380$	−33.5165	−	58.0522i	−0.0882012	−	0.152769i
$381$	79.6675	−	214.782i	0.209101	−	0.563732i
$382$	68.4520	−	118.562i	0.179194	−	0.310373i
$383$	446.221	+	257.626i	1.16507	+	0.672652i	0.952513	−	0.304498i	$-0.0984886\pi$
$383$	446.221	+	257.626i	1.16507	+	0.672652i	0.212554	+	0.977149i	$0.431822\pi$
$384$	77.1499	+	453.775i	0.200911	+	1.18171i
$385$	−19.2456	+	11.1114i	−0.0499885	+	0.0288609i
$386$	366.010			0.948213
$387$	75.5639	−	399.838i	0.195256	−	1.03317i
$388$			97.5282i			0.251361i
$389$	−560.338	+	323.511i	−1.44046	+	0.831649i	−0.997880	−	0.0650808i	$-0.979269\pi$
$389$	−560.338	+	323.511i	−1.44046	+	0.831649i	−0.442578	+	0.896730i	$0.645936\pi$
$390$	56.3438	−	46.6929i	0.144471	−	0.119725i
$391$	−15.2383	+	25.8992i	−0.0389726	+	0.0662383i
$392$	−176.164	−	101.708i	−0.449398	−	0.259460i
$393$	−27.3523	−	33.0057i	−0.0695988	−	0.0839840i
$394$	64.8505	−	37.4414i	0.164595	−	0.0950291i
$395$			280.381i			0.709825i
$396$	8.47167	+	7.28728i	0.0213931	+	0.0184022i
$397$			687.340i			1.73134i	0.500619	+	0.865668i	$0.333106\pi$
$397$			687.340i			1.73134i	−0.500619	+	0.865668i	$0.666894\pi$
$398$	238.592	+	413.254i	0.599479	+	1.03833i
$399$	−47.8059	−	281.181i	−0.119814	−	0.704715i
$400$	−115.993	+	200.906i	−0.289983	+	0.502265i
$401$	120.496	−	208.705i	0.300489	−	0.520462i	−0.675758	−	0.737124i	$-0.736183\pi$
$401$	120.496	−	208.705i	0.300489	−	0.520462i	0.976247	+	0.216662i	$0.0695168\pi$
$402$	658.152	+	244.123i	1.63719	+	0.607272i
$403$	16.6385	−	9.60624i	0.0412866	−	0.0238368i
$404$			82.4115i			0.203989i
$405$	267.899	+	105.009i	0.661479	+	0.259282i
$406$	334.973			0.825058
$407$	9.46035	−	5.46194i	0.0232441	−	0.0134200i
$408$	−328.791	−	125.042i	−0.805859	−	0.306475i
$409$	288.068	−	498.948i	0.704322	−	1.21992i	−0.262614	−	0.964901i	$-0.584585\pi$
$409$	288.068	−	498.948i	0.704322	−	1.21992i	0.966936	−	0.255020i	$-0.0820820\pi$
$410$	−126.499	−	73.0340i	−0.308533	−	0.178132i
$411$	47.5824	+	279.867i	0.115772	+	0.680942i
$412$	−15.5413	−	26.9183i	−0.0377216	−	0.0653357i
$413$	−252.963			−0.612501
$414$	−22.9098	+	26.6333i	−0.0553377	+	0.0643316i
$415$		−	300.555i		−	0.724228i
$416$	−37.1336	+	21.4391i	−0.0892634	+	0.0515362i
$417$	192.384	−	159.431i	0.461352	−	0.382329i
$418$	−58.3056	−	33.6628i	−0.139487	−	0.0805329i
$419$	398.013	−	689.378i	0.949911	−	1.64529i	0.204304	−	0.978908i	$-0.434507\pi$
$419$	398.013	−	689.378i	0.949911	−	1.64529i	0.745607	−	0.666386i	$-0.232160\pi$
$420$	−31.7718	+	26.3297i	−0.0756471	+	0.0626898i
$421$	−52.6204	−	91.1413i	−0.124989	−	0.216488i	0.796740	−	0.604323i	$-0.206556\pi$
$421$	−52.6204	−	91.1413i	−0.124989	−	0.216488i	−0.921729	+	0.387835i	$0.873223\pi$
$422$	−175.532			−0.415953
$423$	−278.948	−	52.7174i	−0.659451	−	0.124627i
$424$	382.165			0.901333
$425$	−103.731	−	183.130i	−0.244074	−	0.430894i
$426$	112.014	+	658.836i	0.262944	+	1.54656i
$427$	35.1495	−	60.8807i	0.0823173	−	0.142578i
$428$	−65.2668	+	113.045i	−0.152493	+	0.264125i
$429$	4.59469	−	12.3872i	0.0107102	−	0.0288746i
$430$	307.166	−	177.343i	0.714340	−	0.412425i
$431$	251.529			0.583594			0.291797	−	0.956480i	$-0.405747\pi$
$431$	251.529			0.583594			0.291797	+	0.956480i	$0.405747\pi$
$432$	−433.424	−	260.972i	−1.00330	−	0.604102i
$433$	247.092			0.570651			0.285325	−	0.958431i	$-0.407898\pi$
$433$	247.092			0.570651			0.285325	+	0.958431i	$0.407898\pi$
$434$	−52.1927	+	30.1335i	−0.120260	+	0.0694320i
$435$	127.285	−	343.159i	0.292610	−	0.788870i
$436$	−154.563	−	89.2370i	−0.354502	−	0.204672i
$437$	19.0241	−	32.9508i	0.0435335	−	0.0754023i
$438$	−289.588	+	49.2351i	−0.661160	+	0.112409i
$439$	536.953	−	310.010i	1.22313	−	0.706173i	0.257544	−	0.966267i	$-0.417087\pi$
$439$	536.953	−	310.010i	1.22313	−	0.706173i	0.965583	+	0.260094i	$0.0837535\pi$
$440$		−	34.7038i		−	0.0788722i
$441$	250.514	−	87.7194i	0.568059	−	0.198910i
$442$	0.960108	−	116.725i	0.00217219	−	0.264085i
$443$	321.142	−	185.411i	0.724925	−	0.418536i	−0.0916378	−	0.995792i	$-0.529210\pi$
$443$	321.142	−	185.411i	0.724925	−	0.418536i	0.816563	+	0.577257i	$0.195877\pi$
$444$	15.6177	−	12.9426i	0.0351750	−	0.0291501i
$445$	−463.052	−	267.343i	−1.04057	−	0.600771i
$446$	−21.3317	−	12.3159i	−0.0478289	−	0.0276140i
$447$	−468.539	+	388.285i	−1.04818	+	0.868646i
$448$	−170.213	+	98.2725i	−0.379940	+	0.219358i
$449$	−454.217			−1.01162			−0.505810	−	0.862645i	$-0.668806\pi$
$449$	−454.217			−1.01162			−0.505810	+	0.862645i	$0.668806\pi$
$450$	−81.3185	−	232.234i	−0.180708	−	0.516075i
$451$	−26.3722			−0.0584749
$452$	−54.8941	−	95.0794i	−0.121447	−	0.210353i
$453$	73.7393	−	12.5370i	0.162780	−	0.0276755i
$454$	−34.7596	−	20.0685i	−0.0765629	−	0.0442036i
$455$	42.2503	+	24.3932i	0.0928577	+	0.0536114i
$456$	417.599	+	154.897i	0.915786	+	0.339686i
$457$	−412.915	−	715.190i	−0.903534	−	1.56497i	−0.822873	−	0.568226i	$-0.807630\pi$
$457$	−412.915	−	715.190i	−0.903534	−	1.56497i	−0.0806614	−	0.996742i	$-0.525703\pi$
$458$			128.154i			0.279811i
$459$	403.469	−	218.846i	0.879018	−	0.476789i
$460$	−5.50465			−0.0119666
$461$	−373.424	+	215.597i	−0.810031	+	0.467672i	−0.846967	−	0.531646i	$-0.821574\pi$
$461$	−373.424	+	215.597i	−0.810031	+	0.467672i	0.0369358	+	0.999318i	$0.488240\pi$
$462$	−14.4129	+	38.8570i	−0.0311968	+	0.0841060i
$463$	−257.345	+	445.734i	−0.555821	+	0.962709i	0.442019	+	0.897006i	$0.354263\pi$
$463$	−257.345	+	445.734i	−0.555821	+	0.962709i	−0.997839	+	0.0657036i	$0.979071\pi$
$464$	−321.765	+	557.313i	−0.693458	+	1.20110i
$465$	11.0373	+	64.9184i	0.0237361	+	0.139609i
$466$	751.676	−	433.980i	1.61304	−	0.931288i
$467$			453.857i			0.971858i	0.873998	+	0.485929i	$0.161519\pi$
$467$			453.857i			0.971858i	−0.873998	+	0.485929i	$0.838481\pi$
$468$	4.55558	−	24.1053i	0.00973415	−	0.0515071i
$469$			467.996i			0.997860i
$470$	−123.724	−	214.296i	−0.263242	−	0.455948i
$471$	−487.320	−	588.043i	−1.03465	−	1.24850i
$472$	197.517	−	342.109i	0.418467	−	0.724806i
$473$	32.0187	−	55.4581i	0.0676929	−	0.117248i
$474$	333.646	+	402.607i	0.703895	+	0.849381i
$475$	133.246	+	230.789i	0.280518	+	0.485871i
$476$	−0.541396	+	65.8204i	−0.00113739	+	0.138278i
$477$	−325.193	+	378.046i	−0.681746	+	0.792550i
$478$	−343.632			−0.718896
$479$	233.447	+	404.343i	0.487364	+	0.844139i	0.999894	−	0.0145299i	$-0.00462518\pi$
$479$	233.447	+	404.343i	0.487364	+	0.844139i	−0.512530	+	0.858669i	$0.671292\pi$
$480$	−24.6329	−	144.884i	−0.0513185	−	0.301841i
$481$	−20.7685	−	11.9907i	−0.0431778	−	0.0249287i
$482$	151.447	−	262.315i	0.314206	−	0.544221i
$483$	−21.9596	−	8.14531i	−0.0454650	−	0.0168640i
$484$	−52.1573	−	90.3390i	−0.107763	−	0.186651i
$485$			395.213i			0.814873i
$486$	509.641	−	168.007i	1.04864	−	0.345694i
$487$			610.782i			1.25417i	0.778950	+	0.627086i	$0.215752\pi$
$487$			610.782i			1.25417i	−0.778950	+	0.627086i	$0.784248\pi$
$488$	54.8902	+	95.0727i	0.112480	+	0.194821i
$489$	226.827	+	84.1352i	0.463859	+	0.172056i
$490$	200.363	+	115.679i	0.408903	+	0.236080i
$491$	−157.490	−	90.9272i	−0.320755	−	0.185188i	0.330974	−	0.943640i	$-0.392623\pi$
$491$	−157.490	−	90.9272i	−0.320755	−	0.185188i	−0.651729	+	0.758452i	$0.725956\pi$
$492$	−48.2755	+	8.20770i	−0.0981209	+	0.0166823i
$493$	−287.751	−	508.003i	−0.583673	−	1.03043i
$494$			147.801i			0.299193i
$495$	34.3297	+	29.5302i	0.0693530	+	0.0596570i
$496$		−	115.781i		−	0.233429i
$497$	−385.852	+	222.772i	−0.776363	+	0.448233i
$498$	−357.652	−	431.574i	−0.718177	−	0.866615i
$499$	−633.250	−	365.607i	−1.26904	−	0.732679i	−0.294232	−	0.955734i	$-0.595064\pi$
$499$	−633.250	−	365.607i	−1.26904	−	0.732679i	−0.974806	+	0.223055i	$0.928397\pi$
$500$	58.2045	−	100.813i	0.116409	−	0.201626i
$501$	497.973	+	600.898i	0.993958	+	1.19940i
$502$	−259.475	−	449.424i	−0.516883	−	0.895267i
$503$	−489.996			−0.974147			−0.487073	−	0.873361i	$-0.661936\pi$
$503$	−489.996			−0.974147			−0.487073	+	0.873361i	$0.661936\pi$
$504$	50.9146	−	269.408i	0.101021	−	0.534541i
$505$			333.956i			0.661299i
$506$	−4.78798	+	2.76434i	−0.00946241	+	0.00546312i
$507$	471.233	−	80.1181i	0.929454	−	0.158024i
$508$	33.4702	−	57.9721i	0.0658862	−	0.114118i
$509$	−501.158	−	289.344i	−0.984593	−	0.568455i	−0.0809394	−	0.996719i	$-0.525792\pi$
$509$	−501.158	−	289.344i	−0.984593	−	0.568455i	−0.903654	+	0.428264i	$0.859125\pi$
$510$	373.954	+	142.218i	0.733244	+	0.278859i
$511$	−97.9181	−	169.599i	−0.191621	−	0.331897i
$512$		−	258.574i		−	0.505027i
$513$	−508.571	+	281.292i	−0.991367	+	0.548328i
$514$	210.932			0.410374
$515$	−62.9780	−	109.081i	−0.122287	−	0.211808i
$516$	41.3518	−	111.484i	0.0801391	−	0.216053i
$517$	−38.6905	−	22.3380i	−0.0748365	−	0.0432069i
$518$	65.1480	+	37.6132i	0.125768	+	0.0726124i
$519$	389.532	−	66.2274i	0.750543	−	0.127606i
$520$	−65.9790	+	38.0930i	−0.126883	+	0.0732557i
$521$	353.079			0.677695			0.338848	−	0.940841i	$-0.389963\pi$
$521$	353.079			0.677695			0.338848	+	0.940841i	$0.389963\pi$
$522$	−225.577	−	644.217i	−0.432140	−	1.23413i
$523$	−584.015			−1.11666			−0.558332	−	0.829618i	$-0.688559\pi$
$523$	−584.015			−1.11666			−0.558332	+	0.829618i	$0.688559\pi$
$524$	−6.26305	−	10.8479i	−0.0119524	−	0.0207021i
$525$	126.310	−	104.675i	0.240590	−	0.199381i
$526$	399.460	−	691.886i	0.759430	−	1.31537i
$527$	90.5337	+	53.2673i	0.171791	+	0.101076i
$528$	−50.8038	−	61.3043i	−0.0962193	−	0.116107i
$529$	262.938	+	455.422i	0.497047	+	0.860910i
$530$	−434.661			−0.820115
$531$	170.350	+	486.495i	0.320810	+	0.916187i
$532$		−	83.3438i		−	0.156661i
$533$	28.9477	+	50.1389i	0.0543109	+	0.0940692i
$534$	−983.040	+	167.134i	−1.84090	+	0.312986i
$535$	−264.481	+	458.094i	−0.494356	+	0.856250i
$536$	−632.921	−	365.417i	−1.18082	−	0.681748i
$537$	324.835	+	120.489i	0.604907	+	0.224374i
$538$	−804.459	+	464.454i	−1.49528	+	0.863298i
$539$	41.7712			0.0774976
$540$	72.0327	+	43.3721i	0.133394	+	0.0803188i
$541$		−	203.117i		−	0.375448i	−0.982222	−	0.187724i	$-0.939889\pi$
$541$		−	203.117i		−	0.375448i	0.982222	−	0.187724i	$-0.0601110\pi$
$542$	−191.375	+	110.490i	−0.353090	+	0.203856i
$543$	562.535	+	208.657i	1.03598	+	0.384267i
$544$	−202.052	−	118.881i	−0.371419	−	0.218532i
$545$	−626.336	−	361.615i	−1.14924	−	0.663514i
$546$	89.6955	−	15.2498i	0.164278	−	0.0279301i
$547$	632.756	−	365.322i	1.15677	−	0.667864i	0.206246	−	0.978500i	$-0.433875\pi$
$547$	632.756	−	365.322i	1.15677	−	0.667864i	0.950529	+	0.310636i	$0.100542\pi$
$548$			82.9542i			0.151376i
$549$	−140.755	−	26.6009i	−0.256385	−	0.0484533i
$550$		−	38.7231i		−	0.0704057i
$551$	369.624	+	640.208i	0.670824	+	1.16190i
$552$	28.1621	−	23.3383i	0.0510183	−	0.0422796i
$553$	−174.302	+	301.901i	−0.315194	+	0.545933i
$554$	603.838	−	1045.88i	1.08996	−	1.88787i
$555$	63.2876	−	52.4474i	0.114032	−	0.0944998i
$556$	63.2304	−	36.5061i	0.113724	−	0.0656584i
$557$		−	274.409i		−	0.492654i	−0.969187	−	0.246327i	$-0.920776\pi$
$557$		−	274.409i		−	0.492654i	0.969187	−	0.246327i	$-0.0792238\pi$
$558$	93.0999	+	80.0839i	0.166846	+	0.143520i
$559$	−140.583			−0.251490
$560$	254.614	−	147.002i	0.454669	−	0.262503i
$561$	71.3095	−	11.5212i	0.127111	−	0.0205370i
$562$	170.574	−	295.442i	0.303512	−	0.525698i
$563$	838.226	+	483.950i	1.48886	+	0.859592i	0.999919	−	0.0127273i	$-0.00405134\pi$
$563$	838.226	+	483.950i	1.48886	+	0.859592i	0.488937	+	0.872319i	$0.337385\pi$
$564$	−77.7769	−	28.8492i	−0.137902	−	0.0511511i
$565$	−222.447	−	385.290i	−0.393712	−	0.681930i
$566$	−703.819			−1.24350
$567$	223.180	+	279.611i	0.393616	+	0.493142i
$568$		−	695.771i		−	1.22495i
$569$	−350.531	+	202.379i	−0.616048	+	0.355675i	−0.775329	−	0.631558i	$-0.782416\pi$
$569$	−350.531	+	202.379i	−0.616048	+	0.355675i	0.159281	+	0.987233i	$0.449082\pi$
$570$	−474.961	−	176.174i	−0.833265	−	0.309077i
$571$	539.740	+	311.619i	0.945253	+	0.545742i	0.891603	−	0.452818i	$-0.149581\pi$
$571$	539.740	+	311.619i	0.945253	+	0.545742i	0.0536499	+	0.998560i	$0.482914\pi$
$572$	1.93034	−	3.34345i	0.00337472	−	0.00584518i
$573$	−31.1734	−	183.353i	−0.0544038	−	0.319989i
$574$	−90.8050	−	157.279i	−0.158197	−	0.274005i
$575$	21.8840			0.0380591
$576$	303.621	+	261.173i	0.527120	+	0.453425i
$577$	−116.940			−0.202669			−0.101335	−	0.994852i	$-0.532311\pi$
$577$	−116.940			−0.202669			−0.101335	+	0.994852i	$0.532311\pi$
$578$	557.873	−	309.966i	0.965179	−	0.536274i
$579$	382.848	−	317.272i	0.661223	−	0.547965i
$580$	53.4755	−	92.6224i	0.0921992	−	0.159694i
$581$	186.844	−	323.623i	0.321590	−	0.557010i
$582$	470.294	+	567.498i	0.808065	+	0.975082i
$583$	−67.9629	+	39.2384i	−0.116574	+	0.0673043i
$584$	305.822			0.523669
$585$	18.4606	−	97.6820i	0.0315565	−	0.166978i
$586$	223.846			0.381989
$587$	164.072	−	94.7270i	0.279509	−	0.161375i	−0.353692	−	0.935362i	$-0.615074\pi$
$587$	164.072	−	94.7270i	0.279509	−	0.161375i	0.633201	+	0.773987i	$0.281741\pi$
$588$	76.4641	−	13.0003i	0.130041	−	0.0221093i
$589$	−115.183	−	66.5012i	−0.195558	−	0.112905i
$590$	−224.648	+	389.102i	−0.380759	+	0.659494i
$591$	35.3782	−	95.3788i	0.0598615	−	0.161386i
$592$	−125.158	+	72.2601i	−0.211416	+	0.122061i
$593$		−	436.488i		−	0.736068i	−0.929812	−	0.368034i	$-0.880031\pi$
$593$		−	436.488i		−	0.736068i	0.929812	−	0.368034i	$-0.119969\pi$
$594$	84.4352	+	1.55175i	0.142147	+	0.00261238i
$595$	−2.19390	+	266.724i	−0.00368723	+	0.448276i
$596$	−153.994	+	88.9082i	−0.258378	+	0.149175i
$597$	607.794	+	225.444i	1.01808	+	0.377629i
$598$	10.5111	+	6.06861i	0.0175772	+	0.0101482i
$599$	205.367	+	118.569i	0.342850	+	0.197944i	0.661531	−	0.749917i	$-0.269907\pi$
$599$	205.367	+	118.569i	0.342850	+	0.197944i	−0.318682	+	0.947862i	$0.603240\pi$
$600$	42.9386	+	252.554i	0.0715644	+	0.420923i
$601$	167.618	−	96.7745i	0.278899	−	0.161022i	−0.354026	−	0.935236i	$-0.615188\pi$
$601$	167.618	−	96.7745i	0.278899	−	0.161022i	0.632925	+	0.774213i	$0.281854\pi$
$602$	440.989			0.732540
$603$	900.045	−	315.158i	1.49261	−	0.522649i
$604$	21.8567			0.0361867
$605$	−211.357	−	366.081i	−0.349350	−	0.605092i
$606$	397.399	+	479.536i	0.655774	+	0.791314i
$607$	127.850	+	73.8140i	0.210625	+	0.121605i	0.601602	−	0.798796i	$-0.294529\pi$
$607$	127.850	+	73.8140i	0.210625	+	0.121605i	−0.390977	+	0.920401i	$0.627863\pi$
$608$	257.065	+	148.416i	0.422804	+	0.244106i
$609$	350.383	−	290.368i	0.575342	−	0.476795i
$610$	−62.4301	−	108.132i	−0.102344	−	0.177266i
$611$			98.0780i			0.160520i
$612$	126.950	−	43.2835i	0.207434	−	0.0707247i
$613$	−980.994			−1.60032			−0.800158	−	0.599789i	$-0.795251\pi$
$613$	−980.994			−1.60032			−0.800158	+	0.599789i	$0.795251\pi$
$614$	−219.463	+	126.707i	−0.357432	+	0.206363i
$615$	−195.627	+	33.2600i	−0.318092	+	0.0540814i
$616$	21.5741	−	37.3674i	0.0350228	−	0.0606613i
$617$	−378.719	+	655.961i	−0.613808	+	1.06315i	0.376785	+	0.926301i	$0.377030\pi$
$617$	−378.719	+	655.961i	−0.613808	+	1.06315i	−0.990592	+	0.136845i	$0.956304\pi$
$618$	−220.235	−	81.6903i	−0.356368	−	0.132185i
$619$	842.718	−	486.544i	1.36142	−	0.786016i	0.371606	−	0.928390i	$-0.378807\pi$
$619$	842.718	−	486.544i	1.36142	−	0.786016i	0.989813	+	0.142375i	$0.0454738\pi$
$620$			19.2422i			0.0310358i
$621$	−0.876957	+	47.7176i	−0.00141217	+	0.0768400i
$622$		−	216.583i		−	0.348205i
$623$	−332.394	−	575.724i	−0.533539	−	0.924116i
$624$	−60.7867	+	163.880i	−0.0974145	+	0.262628i
$625$	81.1059	−	140.480i	0.129769	−	0.224767i
$626$	351.907	−	609.521i	0.562152	−	0.973676i
$627$	−90.1681	+	15.3302i	−0.143809	+	0.0244501i
$628$	−111.585	−	193.271i	−0.177683	−	0.307756i
$629$	1.07843	−	131.111i	0.00171452	−	0.208443i
$630$	−57.9083	+	306.415i	−0.0919180	+	0.486373i
$631$	−850.171			−1.34734			−0.673669	−	0.739033i	$-0.735283\pi$
$631$	−850.171			−1.34734			−0.673669	+	0.739033i	$0.735283\pi$
$632$	−272.195	−	471.455i	−0.430688	−	0.745973i
$633$	−183.607	+	152.158i	−0.290059	+	0.240376i
$634$	−324.122	−	187.132i	−0.511233	−	0.295161i
$635$	135.631	−	234.920i	0.213592	−	0.369953i
$636$	−112.197	+	92.9795i	−0.176411	+	0.146194i
$637$	−45.8506	−	79.4156i	−0.0719790	−	0.124671i
$638$		−	107.418i		−	0.168367i
$639$	688.272	+	592.047i	1.07711	+	0.926522i
$640$			545.041i			0.851626i
$641$	472.888	+	819.066i	0.737735	+	1.27779i	0.953513	+	0.301351i	$0.0974377\pi$
$641$	472.888	+	819.066i	0.737735	+	1.27779i	−0.215779	+	0.976442i	$0.569229\pi$
$642$	165.345	+	972.514i	0.257547	+	1.51482i
$643$	−670.084	−	386.873i	−1.04212	−	0.601669i	−0.121688	−	0.992568i	$-0.538831\pi$
$643$	−670.084	−	386.873i	−1.04212	−	0.601669i	−0.920433	+	0.390900i	$0.872164\pi$
$644$	−5.92714	−	3.42204i	−0.00920364	−	0.00531372i
$645$	167.570	−	451.765i	0.259798	−	0.700411i
$646$	−703.120	+	398.272i	−1.08842	+	0.616520i
$647$			329.359i			0.509056i	0.967065	+	0.254528i	$0.0819200\pi$
$647$			329.359i			0.509056i	−0.967065	+	0.254528i	$0.918080\pi$
$648$	−552.410	+	83.5064i	−0.852484	+	0.128868i
$649$			81.1192i			0.124991i
$650$	−73.6205	+	42.5048i	−0.113262	+	0.0653921i
$651$	−28.4729	+	76.7624i	−0.0437372	+	0.117915i
$652$	61.2231	+	35.3472i	0.0939005	+	0.0542135i
$653$	−469.925	+	813.934i	−0.719640	+	1.24645i	0.241503	+	0.970400i	$0.422360\pi$
$653$	−469.925	+	813.934i	−0.719640	+	1.24645i	−0.961143	+	0.276052i	$0.910974\pi$
$654$	−1329.68	+	226.070i	−2.03316	+	0.345673i
$655$	−25.3797	−	43.9590i	−0.0387477	−	0.0671130i
$656$	348.897			0.531856
$657$	−260.231	+	302.526i	−0.396090	+	0.460466i
$658$		−	307.657i		−	0.467565i
$659$	−257.584	+	148.716i	−0.390871	+	0.225669i	−0.682537	−	0.730851i	$-0.739124\pi$
$659$	−257.584	+	148.716i	−0.390871	+	0.225669i	0.291667	+	0.956520i	$0.405790\pi$
$660$	8.44331	+	10.1884i	0.0127929	+	0.0154370i
$661$	165.831	−	287.228i	0.250879	−	0.434535i	−0.712889	−	0.701277i	$-0.752614\pi$
$661$	165.831	−	287.228i	0.250879	−	0.434535i	0.963768	+	0.266742i	$0.0859471\pi$
$662$	−567.818	−	327.830i	−0.857732	−	0.495212i
$663$	−100.178	−	122.927i	−0.151098	−	0.185411i
$664$	291.779	+	505.377i	0.439427	+	0.761109i
$665$		−	337.734i		−	0.507870i
$666$	28.4654	−	150.621i	0.0427408	−	0.226158i
$667$	60.7061			0.0910136
$668$	114.024	+	197.496i	0.170695	+	0.295652i
$669$	−32.9889	+	5.60871i	−0.0493108	+	0.00838372i
$670$	719.861	+	415.612i	1.07442	+	0.620316i
$671$	−19.5230	−	11.2716i	−0.0290953	−	0.0167982i
$672$	63.5455	−	171.317i	0.0945617	−	0.254936i
$673$	−505.629	+	291.925i	−0.751307	+	0.433767i	−0.826166	−	0.563427i	$-0.809483\pi$
$673$	−505.629	+	291.925i	−0.751307	+	0.433767i	0.0748591	+	0.997194i	$0.476149\pi$
$674$	−1159.71			−1.72064
$675$	−286.369	−	172.428i	−0.424250	−	0.255448i
$676$	139.676			0.206622
$677$	66.8519	+	115.791i	0.0987473	+	0.171035i	0.911166	−	0.412039i	$-0.135183\pi$
$677$	66.8519	+	115.791i	0.0987473	+	0.171035i	−0.812419	+	0.583074i	$0.801850\pi$
$678$	−777.903	−	288.542i	−1.14735	−	0.425578i
$679$	−245.689	+	425.547i	−0.361840	+	0.626726i
$680$	−359.006	−	211.228i	−0.527950	−	0.310630i
$681$	−53.7548	+	9.13928i	−0.0789350	+	0.0134204i
$682$	9.66308	+	16.7370i	0.0141687	+	0.0245410i
$683$	867.670			1.27038			0.635190	−	0.772356i	$-0.280922\pi$
$683$	867.670			1.27038			0.635190	+	0.772356i	$0.280922\pi$
$684$	−160.286	+	56.1252i	−0.234336	+	0.0820544i
$685$			336.155i			0.490738i
$686$	382.791	+	663.014i	0.558005	+	0.966493i
$687$	111.088	+	134.049i	0.161701	+	0.195122i
$688$	−423.600	+	733.697i	−0.615698	+	1.06642i
$689$	149.200	+	86.1409i	0.216546	+	0.125023i
$690$	−32.0305	+	26.5442i	−0.0464210	+	0.0384698i
$691$	−157.602	+	90.9914i	−0.228078	+	0.131681i	−0.609685	−	0.792644i	$-0.708704\pi$
$691$	−157.602	+	90.9914i	−0.228078	+	0.131681i	0.381607	+	0.924325i	$0.375371\pi$
$692$	115.459			0.166849
$693$	18.6068	+	53.1382i	0.0268496	+	0.0766786i
$694$			927.289i			1.33615i
$695$	256.228	−	147.933i	0.368674	−	0.212854i
$696$	119.112	+	700.583i	0.171138	+	1.00659i
$697$	−160.517	+	272.817i	−0.230297	+	0.391415i
$698$	1049.45	+	605.898i	1.50351	+	0.868049i
$699$	410.065	−	1105.53i	0.586645	−	1.58158i
$700$	41.5140	−	23.9681i	0.0593057	−	0.0342402i
$701$		−	637.468i		−	0.909369i	−0.890653	−	0.454684i	$-0.849752\pi$
$701$		−	637.468i		−	0.909369i	0.890653	−	0.454684i	$-0.150248\pi$
$702$	−89.7310	−	162.232i	−0.127822	−	0.231099i
$703$			166.016i			0.236154i
$704$	31.5136	+	54.5832i	0.0447637	+	0.0775330i
$705$	−315.175	−	116.906i	−0.447057	−	0.165824i
$706$	510.304	−	883.872i	0.722810	−	1.25194i
$707$	−207.608	+	359.588i	−0.293646	+	0.508611i
$708$	25.2464	+	148.492i	0.0356587	+	0.209735i
$709$	675.791	−	390.168i	0.953160	−	0.550307i	0.0590992	−	0.998252i	$-0.481177\pi$
$709$	675.791	−	390.168i	0.953160	−	0.550307i	0.894061	+	0.447945i	$0.147844\pi$
$710$			791.345i			1.11457i
$711$	697.990	+	131.911i	0.981702	+	0.185528i
$712$	1038.15			1.45808
$713$	−9.45871	+	5.46099i	−0.0132661	+	0.00765917i
$714$	314.244	+	385.607i	0.440118	+	0.540066i
$715$	7.82231	−	13.5486i	0.0109403	−	0.0189491i
$716$	87.6766	+	50.6201i	0.122453	+	0.0706985i
$717$	−359.441	+	297.874i	−0.501312	+	0.415445i
$718$	416.431	+	721.279i	0.579987	+	1.00457i
$719$	942.607			1.31100			0.655498	−	0.755197i	$-0.272459\pi$
$719$	942.607			1.31100			0.655498	+	0.755197i	$0.272459\pi$
$720$	−454.174	−	390.678i	−0.630797	−	0.542608i
$721$		−	156.604i		−	0.217204i
$722$	195.708	−	112.992i	0.271063	−	0.156498i
$723$	−68.9699	−	405.662i	−0.0953941	−	0.561082i
$724$	151.835	+	87.6617i	0.209716	+	0.121080i
$725$	−212.594	+	368.224i	−0.293233	+	0.507895i
$726$	−739.119	−	274.156i	−1.01807	−	0.377626i
$727$	498.869	+	864.067i	0.686202	+	1.18854i	0.973057	+	0.230563i	$0.0740569\pi$
$727$	498.869	+	864.067i	0.686202	+	1.18854i	−0.286855	+	0.957974i	$0.592610\pi$
$728$	−94.7240			−0.130115
$729$	387.451	−	617.513i	0.531483	−	0.847069i
$730$	−347.831			−0.476481
$731$	−378.821	−	668.781i	−0.518223	−	0.914885i
$732$	−39.2457	−	14.5571i	−0.0536143	−	0.0198868i
$733$	416.123	−	720.746i	0.567698	−	0.983283i	−0.429095	−	0.903260i	$-0.641167\pi$
$733$	416.123	−	720.746i	0.567698	−	0.983283i	0.996793	−	0.0800230i	$-0.0254994\pi$
$734$	−614.108	+	1063.67i	−0.836660	+	1.44914i
$735$	309.855	−	52.6810i	0.421572	−	0.0716748i
$736$	21.1098	−	12.1878i	0.0286818	−	0.0165595i
$737$	150.075			0.203630
$738$	−241.327	+	280.550i	−0.327001	+	0.380149i
$739$	587.105			0.794458			0.397229	−	0.917719i	$-0.369972\pi$
$739$	587.105			0.794458			0.397229	+	0.917719i	$0.369972\pi$
$740$	20.8006	−	12.0092i	0.0281089	−	0.0162287i
$741$	128.120	+	154.601i	0.172901	+	0.208638i
$742$	−468.022	−	270.212i	−0.630757	−	0.364168i
$743$	−271.448	+	470.162i	−0.365341	+	0.632789i	−0.988831	−	0.149042i	$-0.952381\pi$
$743$	−271.448	+	470.162i	−0.365341	+	0.632789i	0.623490	+	0.781831i	$0.285714\pi$
$744$	−81.5819	−	98.4439i	−0.109653	−	0.132317i
$745$	−624.028	+	360.283i	−0.837621	+	0.483601i
$746$		−	805.614i		−	1.07991i
$747$	−748.211	−	141.402i	−1.00162	−	0.189293i
$748$	21.1070	+	0.173613i	0.0282179	+	0.000232103i
$749$	−569.560	+	328.836i	−0.760427	+	0.439033i
$750$	−147.453	−	867.281i	−0.196604	−	1.15637i
$751$	324.334	+	187.254i	0.431869	+	0.249340i	0.700143	−	0.714003i	$-0.253120\pi$
$751$	324.334	+	187.254i	0.431869	+	0.249340i	−0.268273	+	0.963343i	$0.586453\pi$
$752$	511.866	+	295.526i	0.680673	+	0.392986i
$753$	−660.990	−	245.176i	−0.877809	−	0.325599i
$754$	−204.223	+	117.908i	−0.270853	+	0.156377i
$755$	88.5700			0.117311
$756$	50.5985	+	91.4811i	0.0669292	+	0.121007i
$757$	1006.50			1.32959			0.664795	−	0.747026i	$-0.268519\pi$
$757$	1006.50			1.32959			0.664795	+	0.747026i	$0.268519\pi$
$758$	−613.212	−	1062.11i	−0.808987	−	1.40121i
$759$	−2.61201	+	7.04192i	−0.00344138	+	0.00927789i
$760$	456.753	+	263.707i	0.600991	+	0.346982i
$761$	2.45474	+	1.41725i	0.00322568	+	0.00186235i	0.501612	−	0.865093i	$-0.332741\pi$
$761$	2.45474	+	1.41725i	0.00322568	+	0.00186235i	−0.498386	+	0.866955i	$0.666074\pi$
$762$	−84.7923	−	498.726i	−0.111276	−	0.654496i
$763$	−449.605	−	778.739i	−0.589260	−	1.02063i
$764$		−	54.3470i		−	0.0711348i
$765$	514.438	−	175.398i	0.672468	−	0.229278i
$766$	1137.83			1.48542
$767$	154.224	−	89.0413i	0.201074	−	0.116090i
$768$	307.851	+	371.480i	0.400848	+	0.483698i
$769$	−121.604	+	210.625i	−0.158133	+	0.273895i	−0.934195	−	0.356762i	$-0.883881\pi$
$769$	−121.604	+	210.625i	−0.158133	+	0.273895i	0.776062	+	0.630656i	$0.217214\pi$
$770$	−24.5375	+	42.5002i	−0.0318669	+	0.0551951i
$771$	220.636	−	182.844i	0.286169	−	0.237152i
$772$	125.830	−	72.6478i	0.162992	−	0.0941034i
$773$			1414.57i			1.82997i	0.403485	+	0.914986i	$0.367799\pi$
$773$			1414.57i			1.82997i	−0.403485	+	0.914986i	$0.632201\pi$
$774$	−296.970	−	848.105i	−0.383683	−	1.09574i
$775$		−	76.4980i		−	0.0987071i
$776$	−383.674	−	664.544i	−0.494426	−	0.856371i
$777$	100.750	−	17.1293i	0.129665	−	0.0220454i
$778$	−714.414	+	1237.40i	−0.918270	+	1.59049i
$779$	200.396	−	347.097i	0.257248	−	0.445567i
$780$	10.1024	−	27.2359i	0.0129518	−	0.0349178i
$781$	71.4376	+	123.734i	0.0914694	+	0.158430i
$782$	−0.545805	+	66.3564i	−0.000697960	+	0.0848548i
$783$	−794.387	−	478.314i	−1.01454	−	0.610873i
$784$	−552.623			−0.704876
$785$	−452.176	−	783.191i	−0.576020	−	0.997696i
$786$	−88.7535	−	32.9207i	−0.112918	−	0.0418838i
$787$	940.172	+	542.809i	1.19463	+	0.689719i	0.959353	−	0.282210i	$-0.0910674\pi$
$787$	940.172	+	542.809i	1.19463	+	0.689719i	0.235276	+	0.971929i	$0.424401\pi$
$788$	14.8632	−	25.7438i	0.0188619	−	0.0326698i
$789$	−181.916	−	1069.98i	−0.230566	−	1.35613i
$790$	309.584	+	536.216i	0.391879	+	0.678754i
$791$		−	553.149i		−	0.699304i
$792$	−86.3928	−	16.3271i	−0.109082	−	0.0206150i
$793$			49.4895i			0.0624080i
$794$	758.930	+	1314.51i	0.955832	+	1.65555i
$795$	−454.657	+	376.781i	−0.571895	+	0.473938i
$796$	164.050	+	94.7145i	0.206093	+	0.118988i
$797$	−326.560	−	188.539i	−0.409736	−	0.236561i	0.280940	−	0.959725i	$-0.409354\pi$
$797$	−326.560	−	188.539i	−0.409736	−	0.236561i	−0.690676	+	0.723164i	$0.742687\pi$
$798$	−401.894	−	484.961i	−0.503627	−	0.607721i
$799$	−466.577	+	264.286i	−0.583951	+	0.330770i
$800$			170.727i			0.213409i
$801$	−883.385	+	1026.96i	−1.10285	+	1.28210i
$802$		−	532.186i		−	0.663573i
$803$	−54.3864	+	31.4000i	−0.0677290	+	0.0391034i
$804$	274.720	−	46.7073i	0.341691	−	0.0580936i
$805$	−24.0186	−	13.8671i	−0.0298367	−	0.0172262i
$806$	21.2136	−	36.7430i	0.0263196	−	0.0455868i
$807$	−438.860	+	1183.16i	−0.543816	+	1.46612i
$808$	−324.206	−	561.540i	−0.401244	−	0.694976i
$809$	−335.596			−0.414828			−0.207414	−	0.978253i	$-0.566505\pi$
$809$	−335.596			−0.414828			−0.207414	+	0.978253i	$0.566505\pi$
$810$	628.290	−	94.9771i	0.775667	−	0.117256i
$811$		−	1601.45i		−	1.97466i	−0.158674	−	0.987331i	$-0.550722\pi$
$811$		−	1601.45i		−	1.97466i	0.158674	−	0.987331i	$-0.449278\pi$
$812$	115.160	−	66.4875i	0.141822	−	0.0818812i
$813$	−104.401	+	281.464i	−0.128415	+	0.346204i
$814$	12.0617	−	20.8914i	0.0148178	−	0.0256651i
$815$	248.094	+	143.237i	0.304410	+	0.175751i
$816$	−943.407	+	152.423i	−1.15614	+	0.186793i
$817$	486.607	+	842.828i	0.595602	+	1.03161i
$818$		−	1272.29i		−	1.55536i
$819$	80.6027	−	93.7030i	0.0984160	−	0.114411i
$820$	−57.9849			−0.0707133
$821$	−89.3883	−	154.825i	−0.108877	−	0.188581i	0.806438	−	0.591318i	$-0.201392\pi$
$821$	−89.3883	−	154.825i	−0.108877	−	0.188581i	−0.915316	+	0.402737i	$0.868059\pi$
$822$	400.016	+	482.694i	0.486637	+	0.587219i
$823$	447.254	+	258.222i	0.543444	+	0.313758i	0.746474	−	0.665415i	$-0.231745\pi$
$823$	447.254	+	258.222i	0.543444	+	0.313758i	−0.203030	+	0.979173i	$0.565079\pi$
$824$	211.793	+	122.279i	0.257030	+	0.148396i
$825$	−33.5667	−	40.5045i	−0.0406869	−	0.0490964i
$826$	−483.780	+	279.311i	−0.585690	+	0.338148i
$827$	602.569			0.728620			0.364310	−	0.931278i	$-0.381305\pi$
$827$	602.569			0.728620			0.364310	+	0.931278i	$0.381305\pi$
$828$	−2.58977	+	13.7035i	−0.00312774	+	0.0165501i
$829$	667.735			0.805471			0.402735	−	0.915316i	$-0.368060\pi$
$829$	667.735			0.805471			0.402735	+	0.915316i	$0.368060\pi$
$830$	−331.859	−	574.797i	−0.399830	−	0.692526i
$831$	−274.991	−	1617.42i	−0.330915	−	1.94636i
$832$	69.1825	−	119.828i	0.0831521	−	0.144024i
$833$	254.245	−	432.117i	0.305216	−	0.518748i
$834$	191.888	−	517.327i	0.230082	−	0.620296i
$835$	462.060	+	800.312i	0.553365	+	0.958457i
$836$	−26.7263			−0.0319693
$837$	166.803	+	3.06551i	0.199286	+	0.00366250i
$838$		−	1757.87i		−	2.09770i
$839$	−607.384	−	1052.02i	−0.723938	−	1.25390i	−0.959409	−	0.282017i	$-0.908997\pi$
$839$	−607.384	−	1052.02i	−0.723938	−	1.25390i	0.235471	−	0.971881i	$-0.424337\pi$
$840$	112.908	−	304.397i	0.134414	−	0.362377i
$841$	−169.236	+	293.125i	−0.201232	+	0.348543i
$842$	−201.268	−	116.202i	−0.239036	−	0.138007i
$843$	−77.6801	−	456.894i	−0.0921472	−	0.541985i
$844$	−60.3458	+	34.8407i	−0.0714997	+	0.0412804i
$845$	566.010			0.669834
$846$	−591.683	+	207.182i	−0.699389	+	0.244896i
$847$		−	525.571i		−	0.620509i
$848$	899.133	−	519.115i	1.06030	−	0.612163i
$849$	−736.197	+	610.097i	−0.867134	+	0.718607i
$850$	−400.585	−	235.692i	−0.471277	−	0.277285i
$851$	11.8065	+	6.81651i	0.0138737	+	0.00801001i
$852$	169.279	+	204.267i	0.198684	+	0.239750i
$853$	−131.958	+	76.1857i	−0.154698	+	0.0893150i	−0.575351	−	0.817907i	$-0.695134\pi$
$853$	−131.958	+	76.1857i	−0.154698	+	0.0893150i	0.420653	+	0.907222i	$0.361801\pi$
$854$		−	155.242i		−	0.181782i
$855$	−649.525	+	227.436i	−0.759679	+	0.266007i
$856$		−	1027.03i		−	1.19981i
$857$	291.231	+	504.426i	0.339826	+	0.588596i	0.984400	−	0.175946i	$-0.0562986\pi$
$857$	291.231	+	504.426i	0.339826	+	0.588596i	−0.644574	+	0.764542i	$0.722965\pi$
$858$	−4.89026	−	28.7632i	−0.00569960	−	0.0335235i
$859$	−219.907	+	380.890i	−0.256004	+	0.443412i	−0.965168	−	0.261632i	$-0.915739\pi$
$859$	−219.907	+	380.890i	−0.256004	+	0.443412i	0.709164	+	0.705044i	$0.249073\pi$
$860$	70.4000	−	121.936i	0.0818605	−	0.141787i
$861$	−231.318	−	85.8010i	−0.268662	−	0.0996528i
$862$	481.037	−	277.727i	0.558048	−	0.322189i
$863$			1284.95i			1.48893i	0.667659	+	0.744467i	$0.267297\pi$
$863$			1284.95i			1.48893i	−0.667659	+	0.744467i	$0.732703\pi$
$864$	−372.268	−	6.84156i	−0.430866	−	0.00791847i
$865$	467.876			0.540897
$866$	472.552	−	272.828i	0.545672	−	0.315044i
$867$	314.847	−	807.812i	0.363145	−	0.931732i
$868$	−11.9621	+	20.7190i	−0.0137813	+	0.0238699i
$869$	96.8123	+	55.8946i	0.111407	+	0.0643206i
$870$	−135.473	−	796.817i	−0.155716	−	0.915882i
$871$	−164.732	−	285.324i	−0.189129	−	0.327582i
$872$	1404.23			1.61035
$873$	983.858	+	185.936i	1.12699	+	0.212985i
$874$		−	84.0225i		−	0.0961356i
$875$	507.929	−	293.253i	0.580491	−	0.335146i
$876$	−89.7843	+	74.4056i	−0.102493	+	0.0849379i
$877$	−1065.73	−	615.297i	−1.21519	−	0.701593i	−0.251308	−	0.967907i	$-0.580861\pi$
$877$	−1065.73	−	615.297i	−1.21519	−	0.701593i	−0.963886	+	0.266315i	$0.914194\pi$
$878$	684.598	−	1185.76i	0.779725	−	1.35052i
$879$	234.144	−	194.038i	0.266375	−	0.220749i
$880$	−47.1399	−	81.6487i	−0.0535681	−	0.0927826i
$881$	168.980			0.191804			0.0959022	−	0.995391i	$-0.469426\pi$
$881$	168.980			0.191804			0.0959022	+	0.995391i	$0.469426\pi$
$882$	382.241	−	444.366i	0.433380	−	0.503816i
$883$	−1721.94			−1.95011			−0.975053	−	0.221971i	$-0.928751\pi$
$883$	−1721.94			−1.95011			−0.975053	+	0.221971i	$0.928751\pi$
$884$	−22.8383	−	40.3193i	−0.0258352	−	0.0456101i
$885$	102.306	+	601.735i	0.115600	+	0.679927i
$886$	409.446	−	709.181i	0.462128	−	0.800430i
$887$	47.2929	−	81.9137i	0.0533178	−	0.0923492i	−0.838135	−	0.545463i	$-0.816354\pi$
$887$	47.2929	−	81.9137i	0.0533178	−	0.0923492i	0.891452	+	0.453114i	$0.149687\pi$
$888$	−55.5008	+	149.629i	−0.0625009	+	0.168501i
$889$	292.082	−	168.634i	0.328551	−	0.189689i
$890$	−1180.75			−1.32669
$891$	89.6647	−	71.5686i	0.100634	−	0.0803239i
$892$	−9.77810			−0.0109620
$893$	588.001	−	339.483i	0.658456	−	0.380160i
$894$	−467.331	+	1259.92i	−0.522742	+	1.40930i
$895$	355.292	+	205.128i	0.396974	+	0.229193i
$896$	−338.831	+	586.873i	−0.378160	+	0.654993i
$897$	16.2552	−	2.76368i	0.0181218	−	0.00308102i
$898$	−868.669	+	501.526i	−0.967338	+	0.558493i
$899$		−	212.205i		−	0.236046i
$900$	−74.0515	−	63.6986i	−0.0822794	−	0.0707762i
$901$	−7.74743	+	941.896i	−0.00859870	+	1.04539i
$902$	−50.4356	+	29.1190i	−0.0559153	+	0.0322827i
$903$	461.276	−	382.267i	0.510827	−	0.423330i
$904$	748.082	+	431.905i	0.827524	+	0.477771i
$905$	615.279	+	355.232i	0.679866	+	0.392521i
$906$	127.180	−	105.396i	0.140375	−	0.116331i
$907$	−336.689	+	194.387i	−0.371212	+	0.214319i	−0.673988	−	0.738743i	$-0.735420\pi$
$907$	−336.689	+	194.387i	−0.371212	+	0.214319i	0.302776	+	0.953062i	$0.402087\pi$
$908$	−15.9332			−0.0175476
$909$	831.362	+	157.116i	0.914589	+	0.172845i
$910$	107.736			0.118391
$911$	−10.7455	−	18.6118i	−0.0117953	−	0.0204301i	0.860067	−	0.510180i	$-0.170421\pi$
$911$	−10.7455	−	18.6118i	−0.0117953	−	0.0204301i	−0.871863	+	0.489750i	$0.837088\pi$
$912$	1192.90	−	202.815i	1.30801	−	0.222385i
$913$	−103.778	−	59.9162i	−0.113667	−	0.0656257i
$914$	−1579.36	−	911.845i	−1.72797	−	0.997642i
$915$	−159.035	−	58.9898i	−0.173809	−	0.0644697i
$916$	25.4367	+	44.0576i	0.0277693	+	0.0480978i
$917$		−	63.1106i		−	0.0688229i
$918$	529.976	−	864.025i	0.577316	−	0.941204i
$919$	−987.516			−1.07456			−0.537278	−	0.843406i	$-0.680547\pi$
$919$	−987.516			−1.07456			−0.537278	+	0.843406i	$0.680547\pi$
$920$	37.5079	−	21.6552i	0.0407695	−	0.0235383i
$921$	−119.725	+	322.775i	−0.129994	+	0.350462i
$922$	−476.104	+	824.637i	−0.516382	+	0.894400i
$923$	156.828	−	271.635i	0.169912	−	0.294296i
$924$	2.75757	+	16.2193i	0.00298439	+	0.0175534i
$925$	−82.6936	+	47.7432i	−0.0893985	+	0.0516142i
$926$			1136.60i			1.22742i
$927$	−301.180	+	105.460i	−0.324897	+	0.113765i
$928$			473.597i			0.510342i
$929$	−360.372	−	624.183i	−0.387914	−	0.671887i	0.604254	−	0.796791i	$-0.293471\pi$
$929$	−360.372	−	624.183i	−0.387914	−	0.671887i	−0.992169	+	0.124904i	$0.960138\pi$
$930$	92.7883	+	111.966i	0.0997723	+	0.120394i
$931$	−317.410	+	549.771i	−0.340935	+	0.590516i
$932$	172.278	−	298.394i	0.184848	−	0.320165i
$933$	−187.743	−	226.547i	−0.201225	−	0.242816i
$934$	501.129	+	867.981i	0.536541	+	0.929316i
$935$	85.5320	+	0.703531i	0.0914780	+	0.000752439i
$936$	63.7889	+	182.172i	0.0681505	+	0.194628i
$937$	726.411			0.775251			0.387626	−	0.921817i	$-0.373295\pi$
$937$	726.411			0.775251			0.387626	+	0.921817i	$0.373295\pi$
$938$	516.741	+	895.021i	0.550896	+	0.954181i
$939$	−160.260	−	942.609i	−0.170671	−	1.00384i
$940$	−85.0693	−	49.1148i	−0.0904993	−	0.0522498i
$941$	−699.817	+	1212.12i	−0.743695	+	1.28812i	0.207108	+	0.978318i	$0.433595\pi$
$941$	−699.817	+	1212.12i	−0.743695	+	1.28812i	−0.950802	+	0.309799i	$0.899738\pi$
$942$	−1581.27	−	586.528i	−1.67863	−	0.622641i
$943$	−16.4563	−	28.5031i	−0.0174510	−	0.0302260i
$944$		−	1073.19i		−	1.13685i
$945$	205.040	+	370.709i	0.216974	+	0.392284i
$946$		−	141.415i		−	0.149487i
$947$	−777.033	−	1345.86i	−0.820520	−	1.42118i	−0.905295	−	0.424783i	$-0.860350\pi$
$947$	−777.033	−	1345.86i	−0.820520	−	1.42118i	0.0847748	−	0.996400i	$-0.472983\pi$
$948$	194.615	+	72.1872i	0.205290	+	0.0761468i
$949$	119.396	+	68.9331i	0.125812	+	0.0726376i
$950$	509.653	+	294.249i	0.536477	+	0.309735i
$951$	−501.246	+	85.2208i	−0.527072	+	0.0896117i
$952$	−255.247	−	450.621i	−0.268117	−	0.473341i
$953$		−	770.289i		−	0.808278i	−0.914698	−	0.404139i	$-0.867571\pi$
$953$		−	770.289i		−	0.808278i	0.914698	−	0.404139i	$-0.132429\pi$
$954$	−204.495	+	1082.06i	−0.214355	+	1.13423i
$955$		−	220.230i		−	0.230608i
$956$	−118.137	+	68.2062i	−0.123574	+	0.0713454i
$957$	−93.1140	−	112.360i	−0.0972978	−	0.117408i
$958$	892.914	+	515.524i	0.932061	+	0.538126i
$959$	−208.975	+	361.956i	−0.217910	+	0.377430i
$960$	302.605	+	365.149i	0.315213	+	0.380364i
$961$	−461.410	−	799.186i	−0.480136	−	0.831620i
$962$	−52.9584			−0.0550503
$963$	1015.96	+	873.926i	1.05500	+	0.907504i
$964$		−	120.241i		−	0.124731i
$965$	509.900	−	294.391i	0.528394	−	0.305068i
$966$	−50.9904	+	8.66928i	−0.0527851	+	0.00897441i
$967$	−65.1526	+	112.848i	−0.0673760	+	0.116699i	−0.897745	−	0.440515i	$-0.854796\pi$
$967$	−65.1526	+	112.848i	−0.0673760	+	0.116699i	0.830369	+	0.557213i	$0.188129\pi$
$968$	710.785	+	410.372i	0.734282	+	0.423938i
$969$	−390.229	+	1026.09i	−0.402713	+	1.05891i
$970$	436.377	+	755.827i	0.449873	+	0.779203i
$971$		−	643.927i		−	0.663158i	−0.943427	−	0.331579i	$-0.892419\pi$
$971$		−	643.927i		−	0.663158i	0.943427	−	0.331579i	$-0.107581\pi$
$972$	141.861	−	158.915i	0.145948	−	0.163493i
$973$	367.859			0.378067
$974$	674.398	+	1168.09i	0.692400	+	1.19927i
$975$	−40.1625	+	108.277i	−0.0411923	+	0.111054i
$976$	258.284	+	149.120i	0.264635	+	0.152787i
$977$	−417.532	−	241.062i	−0.427362	−	0.246737i	0.270860	−	0.962619i	$-0.412692\pi$
$977$	−417.532	−	241.062i	−0.427362	−	0.246737i	−0.698222	+	0.715881i	$0.746025\pi$
$978$	526.694	−	89.5475i	0.538542	−	0.0915618i
$979$	−184.621	+	106.591i	−0.188581	+	0.108877i
$980$	91.8429			0.0937173
$981$	−1194.89	+	1389.09i	−1.21803	+	1.41600i
$982$	−401.591			−0.408952
$983$	806.156	+	1396.30i	0.820097	+	1.42045i	0.905609	+	0.424113i	$0.139414\pi$
$983$	806.156	+	1396.30i	0.820097	+	1.42045i	−0.0855119	+	0.996337i	$0.527253\pi$
$984$	296.653	−	245.841i	0.301477	−	0.249839i
$985$	60.2301	−	104.322i	0.0611474	−	0.105910i
$986$	−1111.22	−	653.810i	−1.12700	−	0.663094i
$987$	−266.689	−	321.811i	−0.270202	−	0.326050i
$988$	29.3364	+	50.8122i	0.0296928	+	0.0514294i
$989$	79.9190			0.0808079
$990$	98.2600	+	18.5698i	0.0992525	+	0.0187574i
$991$			1219.44i			1.23051i	0.788327	+	0.615257i	$0.210948\pi$
$991$			1219.44i			1.23051i	−0.788327	+	0.615257i	$0.789052\pi$
$992$	−42.6038	−	73.7919i	−0.0429473	−	0.0743870i
$993$	−878.116	+	149.295i	−0.884306	+	0.150348i
$994$	−491.950	+	852.082i	−0.494919	+	0.857225i
$995$	664.781	+	383.811i	0.668122	+	0.385740i
$996$	−208.618	−	77.3811i	−0.209456	−	0.0776918i
$997$	−563.615	+	325.403i	−0.565311	+	0.326383i	−0.755274	−	0.655409i	$-0.772496\pi$
$997$	−563.615	+	325.403i	−0.565311	+	0.326383i	0.189963	+	0.981791i	$0.439163\pi$
$998$	−1614.75			−1.61798
$999$	−100.789	−	182.225i	−0.100890	−	0.182408i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.3.i.a.50.28	yes	68
3.2	odd	2		459.3.i.a.152.8		68
9.2	odd	6	inner	153.3.i.a.101.27	yes	68
9.7	even	3		459.3.i.a.305.7		68
17.16	even	2	inner	153.3.i.a.50.27	✓	68
51.50	odd	2		459.3.i.a.152.7		68
153.16	even	6		459.3.i.a.305.8		68
153.101	odd	6	inner	153.3.i.a.101.28	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.i.a.50.27	✓	68	17.16	even	2	inner
153.3.i.a.50.28	yes	68	1.1	even	1	trivial
153.3.i.a.101.27	yes	68	9.2	odd	6	inner
153.3.i.a.101.28	yes	68	153.101	odd	6	inner
459.3.i.a.152.7		68	51.50	odd	2
459.3.i.a.152.8		68	3.2	odd	2
459.3.i.a.305.7		68	9.7	even	3
459.3.i.a.305.8		68	153.16	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	153.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.91245 - 1.10416i) q^{2} +(1.04331 - 2.81274i) q^{3} +(0.438319 - 0.759190i) q^{4} +(1.77620 - 3.07647i) q^{5} +(-1.11042 - 6.53121i) q^{6} +(3.82505 - 2.20839i) q^{7} +6.89736i q^{8} +(-6.82301 - 5.86911i) q^{9} -7.84480i q^{10} +(-0.708179 - 1.22660i) q^{11} +(-1.67810 - 2.02495i) q^{12} +(-1.55468 + 2.69278i) q^{13} +(4.87682 - 8.44690i) q^{14} +(-6.80018 - 8.20569i) q^{15} +(9.36903 + 16.2276i) q^{16} +(-16.9994 - 0.139826i) q^{17} +(-19.5291 - 3.69074i) q^{18} +21.5252 q^{19} +(-1.55708 - 2.69694i) q^{20} +(-2.22093 - 13.0629i) q^{21} +(-2.70872 - 1.56388i) q^{22} +(0.883809 - 1.53080i) q^{23} +(19.4005 + 7.19607i) q^{24} +(6.19024 + 10.7218i) q^{25} +6.86643i q^{26} +(-23.6268 + 13.0681i) q^{27} -3.87192i q^{28} +(17.1717 + 29.7423i) q^{29} +(-22.0654 - 8.18455i) q^{30} +(-5.35110 - 3.08946i) q^{31} +(11.9425 + 6.89502i) q^{32} +(-4.18896 + 0.712198i) q^{33} +(-32.6650 + 18.5026i) q^{34} -15.6902i q^{35} +(-7.44643 + 2.60742i) q^{36} +7.71265i q^{37} +(41.1659 - 23.7671i) q^{38} +(5.95209 + 7.18231i) q^{39} +(21.2195 + 12.2511i) q^{40} +(9.30986 - 16.1252i) q^{41} +(-18.6709 - 22.5299i) q^{42} +(22.6064 + 39.1554i) q^{43} -1.24163 q^{44} +(-30.1752 + 10.5661i) q^{45} -3.90345i q^{46} +(27.3169 - 15.7714i) q^{47} +(55.4189 - 9.42221i) q^{48} +(-14.7460 + 25.5408i) q^{49} +(23.6771 + 13.6700i) q^{50} +(-18.1289 + 47.6691i) q^{51} +(1.36289 + 2.36059i) q^{52} -55.4075i q^{53} +(-30.7560 + 51.0797i) q^{54} -5.03146 q^{55} +(15.2321 + 26.3827i) q^{56} +(22.4574 - 60.5447i) q^{57} +(65.6802 + 37.9205i) q^{58} +(-49.6000 - 28.6366i) q^{59} +(-9.21032 + 1.56592i) q^{60} +(13.7839 - 7.95816i) q^{61} -13.6450 q^{62} +(-39.0597 - 7.38175i) q^{63} -44.4995 q^{64} +(5.52284 + 9.56584i) q^{65} +(-7.22481 + 5.98731i) q^{66} +(-52.9793 + 91.7628i) q^{67} +(-7.55732 + 12.8445i) q^{68} +(-3.38366 - 4.08302i) q^{69} +(-17.3244 - 30.0067i) q^{70} -100.875 q^{71} +(40.4814 - 47.0608i) q^{72} -44.3391i q^{73} +(8.51597 + 14.7501i) q^{74} +(36.6160 - 6.22537i) q^{75} +(9.43489 - 16.3417i) q^{76} +(-5.41764 - 3.12787i) q^{77} +(19.3135 + 7.16381i) q^{78} +(-68.3530 + 39.4636i) q^{79} +66.5650 q^{80} +(12.1070 + 80.0901i) q^{81} -41.1181i q^{82} +(73.2711 - 42.3031i) q^{83} +(-10.8907 - 4.03961i) q^{84} +(-30.6245 + 52.0498i) q^{85} +(86.4674 + 49.9220i) q^{86} +(101.573 - 17.2692i) q^{87} +(8.46031 - 4.88456i) q^{88} -150.514i q^{89} +(-46.0420 + 53.5252i) q^{90} +13.7334i q^{91} +(-0.774780 - 1.34196i) q^{92} +(-14.2727 + 11.8280i) q^{93} +(34.8282 - 60.3242i) q^{94} +(38.2330 - 66.2215i) q^{95} +(31.8536 - 26.3976i) q^{96} +(-96.3476 + 55.6263i) q^{97} +65.1275i q^{98} +(-2.36715 + 12.5255i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 6 q^{2} + 62 q^{4} - 8 q^{9} - 2 q^{13} - 106 q^{16} - 2 q^{18} - 32 q^{19} - 28 q^{21} - 132 q^{25} + 180 q^{30} - 98 q^{33} - 27 q^{34} + 158 q^{36} - 102 q^{38} + 110 q^{42} + 58 q^{43} - 312 q^{47}+ \cdots - 18 q^{94}+O(q^{100}) \) 68 * q - 6 * q^2 + 62 * q^4 - 8 * q^9 - 2 * q^13 - 106 * q^16 - 2 * q^18 - 32 * q^19 - 28 * q^21 - 132 * q^25 + 180 * q^30 - 98 * q^33 - 27 * q^34 + 158 * q^36 - 102 * q^38 + 110 * q^42 + 58 * q^43 - 312 * q^47 + 152 * q^49 - 90 * q^50 - 17 * q^51 + 70 * q^52 + 92 * q^55 - 258 * q^59 - 126 * q^60 - 16 * q^64 + 400 * q^66 + 82 * q^67 - 333 * q^68 + 404 * q^69 + 204 * q^70 + 474 * q^72 + 34 * q^76 - 60 * q^77 - 88 * q^81 - 690 * q^83 - 200 * q^84 - 44 * q^85 - 1248 * q^86 + 114 * q^87 + 50 * q^93 - 18 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more