LMFDB - Embedded newform 153.3.i.a.101.28

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			101.28
Character	$\chi$	$=$	153.101
Dual form			153.3.i.a.50.28

$q$-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 $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

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

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	0.895010	−	0.446047i	$-0.147168\pi$
$2$	1.91245	+	1.10416i	0.956227	+	0.552078i	0.0612170	+	0.998124i	$0.480502\pi$
$3$	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	0.987159	−	0.159741i	$-0.0510659\pi$
$5$	1.77620	+	3.07647i	0.355240	+	0.615293i	−0.631919	+	0.775034i	$0.717733\pi$
$6$	−1.11042	+	6.53121i	−0.185070	+	1.08853i
$7$	3.82505	+	2.20839i	0.546436	+	0.315485i	0.747683	−	0.664056i	$-0.231166\pi$
$7$	3.82505	+	2.20839i	0.546436	+	0.315485i	−0.201248	+	0.979540i	$0.564500\pi$
$8$		−	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	−0.896419	−	0.443208i	$-0.853840\pi$
$11$	−0.708179	+	1.22660i	−0.0643799	+	0.111509i	0.832039	+	0.554717i	$0.187174\pi$
$12$	−1.67810	+	2.02495i	−0.139842	+	0.168746i
$13$	−1.55468	−	2.69278i	−0.119591	−	0.207137i	0.800015	−	0.599980i	$-0.204825\pi$
$13$	−1.55468	−	2.69278i	−0.119591	−	0.207137i	−0.919606	+	0.392843i	$0.871492\pi$
$14$	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	0.884599	−	0.466352i	$-0.154432\pi$
$23$	0.883809	+	1.53080i	0.0384265	+	0.0665566i	−0.846173	+	0.532909i	$0.821099\pi$
$24$	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	−0.401817	−	0.915720i	$-0.631621\pi$
$29$	17.1717	−	29.7423i	0.592128	−	1.02560i	0.993945	−	0.109876i	$-0.0350454\pi$
$30$	−22.0654	+	8.18455i	−0.735512	+	0.272818i
$31$	−5.35110	+	3.08946i	−0.172616	+	0.0996600i	−0.583819	−	0.811884i	$-0.698442\pi$
$31$	−5.35110	+	3.08946i	−0.172616	+	0.0996600i	0.411203	+	0.911544i	$0.365109\pi$
$32$	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	$-0.966764\pi$
$37$		−	7.71265i		−	0.208450i	0.994554	−	0.104225i	$-0.0332362\pi$
$38$	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	0.956938	−	0.290291i	$-0.0937521\pi$
$41$	9.30986	+	16.1252i	0.227070	+	0.393296i	−0.729869	+	0.683587i	$0.760419\pi$
$42$	−18.6709	+	22.5299i	−0.444545	+	0.536427i
$43$	22.6064	−	39.1554i	0.525730	−	0.910591i	−0.473821	−	0.880621i	$-0.657125\pi$
$43$	22.6064	−	39.1554i	0.525730	−	0.910591i	0.999551	−	0.0299700i	$-0.00954118\pi$
$44$	−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	0.761614	−	0.648030i	$-0.224407\pi$
$47$	27.3169	+	15.7714i	0.581211	+	0.335562i	−0.180404	+	0.983593i	$0.557740\pi$
$48$	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	$0.175080\pi$
$53$			55.4075i			1.04542i	−0.852509	+	0.522712i	$0.824920\pi$
$54$	−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	−0.857494	−	0.514493i	$-0.827980\pi$
$59$	−49.6000	+	28.6366i	−0.840677	+	0.485365i	0.0168170	+	0.999859i	$0.494647\pi$
$60$	−9.21032	−	1.56592i	−0.153505	−	0.0260987i
$61$	13.7839	+	7.95816i	0.225966	+	0.130462i	0.608710	−	0.793393i	$-0.291687\pi$
$61$	13.7839	+	7.95816i	0.225966	+	0.130462i	−0.382744	+	0.923855i	$0.625021\pi$
$62$	−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	−0.925512	−	0.378719i	$-0.876365\pi$
$67$	−52.9793	−	91.7628i	−0.790736	−	1.36959i	0.134776	−	0.990876i	$-0.456969\pi$
$68$	−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	$0.0982195\pi$
$73$			44.3391i			0.607385i	−0.952770	+	0.303692i	$0.901780\pi$
$74$	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	0.000531310	−	1.00000i	$-0.499831\pi$
$79$	−68.3530	−	39.4636i	−0.865228	−	0.499540i	−0.865760	+	0.500460i	$0.833164\pi$
$80$	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	0.871575	−	0.490262i	$-0.163099\pi$
$83$	73.2711	+	42.3031i	0.882784	+	0.509675i	0.0112086	+	0.999937i	$0.496432\pi$
$84$	−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	$0.320748\pi$
$89$			150.514i			1.69117i	−0.533840	+	0.845585i	$0.679252\pi$
$90$	−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	−0.0870227	−	0.996206i	$-0.527735\pi$
$97$	−96.3476	−	55.6263i	−0.993274	−	0.573467i	−0.906251	+	0.422739i	$0.861069\pi$
$98$		−	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	0.0395141	−	0.999219i	$-0.487419\pi$
$101$	−81.4139	−	47.0043i	−0.806078	−	0.465389i	−0.845592	+	0.533830i	$0.820752\pi$
$102$	17.9633	−	111.182i	0.176111	−	1.09002i
$103$	17.7283	+	30.7063i	0.172120	+	0.298120i	0.939161	−	0.343478i	$-0.111605\pi$
$103$	17.7283	+	30.7063i	0.172120	+	0.298120i	−0.767041	+	0.641598i	$0.778272\pi$
$104$	−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	$0.383614\pi$
$109$			203.589i			1.86779i	−0.357544	+	0.933896i	$0.616386\pi$
$110$	−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	0.997969	+	0.0636997i	$0.0202900\pi$
$113$	62.6190	+	108.459i	0.554150	+	0.959816i	−0.443819	+	0.896116i	$0.646377\pi$
$114$	−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	0.892005	−	0.452025i	$-0.149298\pi$
$131$	7.14440	+	12.3745i	0.0545374	+	0.0944615i	−0.837468	+	0.546487i	$0.815965\pi$
$132$	−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	0.170148	−	0.985419i	$-0.445575\pi$
$137$	−81.9500	−	47.3139i	−0.598175	−	0.345357i	−0.768323	+	0.640062i	$0.778909\pi$
$138$	−10.9794	+	4.07250i	−0.0795608	+	0.0295109i
$139$	72.1283	−	41.6433i	0.518909	−	0.299592i	−0.217579	−	0.976043i	$-0.569816\pi$
$139$	72.1283	−	41.6433i	0.518909	−	0.299592i	0.736488	+	0.676451i	$0.236483\pi$
$140$	−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	−0.955772	−	0.294109i	$-0.904977\pi$
$149$	−175.664	+	101.420i	−1.17895	+	0.680668i	−0.223180	+	0.974777i	$0.571644\pi$
$150$	63.1526	+	52.3355i	0.421017	+	0.348903i
$151$	12.4662	−	21.5922i	0.0825579	−	0.142994i	−0.821790	−	0.569790i	$-0.807024\pi$
$151$	12.4662	−	21.5922i	0.0825579	−	0.142994i	0.904348	+	0.426796i	$0.140358\pi$
$152$		−	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	0.912341	+	0.409431i	$0.134273\pi$
$157$	127.288	+	220.468i	0.810748	+	1.40426i	−0.101592	+	0.994826i	$0.532394\pi$
$158$	−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	$-0.920434\pi$
$163$		−	80.6427i		−	0.494740i	0.968921	−	0.247370i	$-0.0795664\pi$
$164$	−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	−0.932598	−	0.360917i	$-0.882464\pi$
$167$	−130.070	−	225.288i	−0.778862	−	1.34903i	0.153736	−	0.988112i	$-0.450869\pi$
$168$	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	−0.610500	−	0.792017i	$-0.709031\pi$
$173$	65.8536	−	114.062i	0.380657	−	0.659317i	0.991156	+	0.132700i	$0.0423646\pi$
$174$	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	$-0.895447\pi$
$179$		−	115.487i		−	0.645179i	0.946539	−	0.322589i	$-0.104553\pi$
$180$	−5.20468	−	27.5400i	−0.0289149	−	0.153000i
$181$		−	199.995i		−	1.10495i	−0.833530	−	0.552474i	$-0.813684\pi$
$181$		−	199.995i		−	1.10495i	0.833530	−	0.552474i	$-0.186316\pi$
$182$	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	0.633919	−	0.773399i	$-0.281445\pi$
$191$	53.6891	+	30.9974i	0.281095	+	0.162290i	−0.352824	+	0.935690i	$0.614779\pi$
$192$	−46.4268	−	125.166i	−0.241806	−	0.651904i
$193$	143.537	−	82.8710i	0.743714	−	0.429384i	−0.0797040	−	0.996819i	$-0.525398\pi$
$193$	143.537	−	82.8710i	0.743714	−	0.429384i	0.823418	+	0.567435i	$0.192064\pi$
$194$	−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	$-0.817315\pi$
$199$		−	216.086i		−	1.08586i	0.839778	−	0.542929i	$-0.182685\pi$
$200$	−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	−0.654173	−	0.756345i	$-0.726983\pi$
$211$	−68.8378	+	39.7435i	−0.326245	+	0.188358i	0.327927	+	0.944703i	$0.393650\pi$
$212$	−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	−0.878259	−	0.478185i	$-0.841295\pi$
$223$	−5.57705	+	9.65974i	−0.0250092	+	0.0433172i	0.853250	+	0.521502i	$0.174628\pi$
$224$	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	−0.885348	−	0.464929i	$-0.846080\pi$
$227$	−9.08769	+	15.7403i	−0.0400339	+	0.0693407i	0.845314	+	0.534270i	$0.179413\pi$
$228$	−36.1215	+	43.5873i	−0.158427	+	0.191173i
$229$	−29.0162	−	50.2575i	−0.126708	−	0.219465i	0.795691	−	0.605703i	$-0.207108\pi$
$229$	−29.0162	−	50.2575i	−0.126708	−	0.219465i	−0.922399	+	0.386237i	$0.873775\pi$
$230$	−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	−0.754691	−	0.656080i	$-0.772213\pi$
$239$	−134.761	+	77.8044i	−0.563854	+	0.325541i	0.190837	+	0.981622i	$0.438880\pi$
$240$	69.4479	+	187.230i	0.289366	+	0.780125i
$241$	118.785	+	68.5806i	0.492884	+	0.284567i	0.725770	−	0.687937i	$-0.241484\pi$
$241$	118.785	+	68.5806i	0.492884	+	0.284567i	−0.232886	+	0.972504i	$0.574817\pi$
$242$			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	$0.155070\pi$
$251$			234.999i			0.936250i	−0.883662	+	0.468125i	$0.844930\pi$
$252$	−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	−0.330356	−	0.943856i	$-0.607169\pi$
$257$	82.7205	−	47.7587i	0.321870	−	0.185832i	0.652226	+	0.758025i	$0.273835\pi$
$258$	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	0.958600	−	0.284757i	$-0.0919130\pi$
$263$	313.310	+	180.890i	1.19129	+	0.687793i	0.232693	+	0.972550i	$0.425246\pi$
$264$	−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	0.934810	+	0.355147i	$0.115569\pi$
$277$	473.610	+	273.439i	1.70978	+	0.987143i	0.774972	+	0.631996i	$0.217764\pi$
$278$	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	0.718793	−	0.695224i	$-0.244695\pi$
$281$	133.786	+	77.2417i	0.476109	+	0.274881i	−0.242685	+	0.970105i	$0.578028\pi$
$282$	−133.340	+	160.899i	−0.472836	+	0.570566i
$283$	−276.014	+	159.357i	−0.975314	+	0.563098i	−0.900852	−	0.434126i	$-0.857057\pi$
$283$	−276.014	+	159.357i	−0.975314	+	0.563098i	−0.0744622	+	0.997224i	$0.523724\pi$
$284$	−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	−0.342659	−	0.939460i	$-0.611328\pi$
$293$	87.7848	−	50.6826i	0.299607	−	0.172978i	0.642266	+	0.766482i	$0.277994\pi$
$294$	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	0.934031	−	0.357191i	$-0.116265\pi$
$311$	49.0382	+	84.9367i	0.157679	+	0.273108i	−0.776352	+	0.630299i	$0.782932\pi$
$312$	−49.5390	−	41.0537i	−0.158779	−	0.131582i
$313$	276.012	+	159.356i	0.881829	+	0.509124i	0.871261	−	0.490820i	$-0.163303\pi$
$313$	276.012	+	159.356i	0.881829	+	0.509124i	0.0105678	+	0.999944i	$0.496636\pi$
$314$			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	−0.968168	−	0.250300i	$-0.919471\pi$
$317$	−84.7398	+	146.774i	−0.267318	+	0.463008i	0.700850	+	0.713308i	$0.252804\pi$
$318$	−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	−0.998289	−	0.0584812i	$-0.981374\pi$
$331$	−148.453	+	257.128i	−0.448498	+	0.776821i	0.549790	+	0.835303i	$0.314708\pi$
$332$			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	−0.988186	−	0.153257i	$-0.951024\pi$
$337$	−454.800	+	262.579i	−1.34955	+	0.779166i	−0.361368	+	0.932423i	$0.617690\pi$
$338$	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	−0.992043	−	0.125902i	$-0.959818\pi$
$347$	−209.954	−	363.652i	−0.605056	−	1.04799i	0.386987	−	0.922085i	$-0.373516\pi$
$348$	31.4106	+	84.6824i	0.0902604	+	0.243340i
$349$	274.372	−	475.226i	0.786166	−	1.36168i	−0.142135	−	0.989847i	$-0.545397\pi$
$349$	274.372	−	475.226i	0.786166	−	1.36168i	0.928300	−	0.371831i	$-0.121270\pi$
$350$	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	0.944900	−	0.327360i	$-0.106159\pi$
$353$	400.248	+	231.083i	1.13385	+	0.654627i	0.188947	+	0.981987i	$0.439492\pi$
$354$	−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	$-0.823962\pi$
$359$		−	377.149i		−	1.05055i	0.850931	−	0.525277i	$-0.176038\pi$
$360$	−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	−0.329940	−	0.944002i	$-0.607028\pi$
$367$	−481.665	−	278.090i	−1.31244	−	0.757737i	−0.982500	+	0.186265i	$0.940362\pi$
$368$	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	0.999920	−	0.0126306i	$-0.00402055\pi$
$373$	182.405	+	315.935i	0.489022	+	0.847010i	−0.510899	+	0.859641i	$0.670687\pi$
$374$	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	$0.261728\pi$
$379$			555.368i			1.46535i	−0.680579	+	0.732675i	$0.738272\pi$
$380$	−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	0.212554	−	0.977149i	$-0.431822\pi$
$383$	446.221	−	257.626i	1.16507	−	0.672652i	0.952513	+	0.304498i	$0.0984886\pi$
$384$	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	−0.442578	−	0.896730i	$-0.645936\pi$
$389$	−560.338	−	323.511i	−1.44046	−	0.831649i	−0.997880	+	0.0650808i	$0.979269\pi$
$390$	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	$-0.666894\pi$
$397$		−	687.340i		−	1.73134i	0.500619	−	0.865668i	$-0.333106\pi$
$398$	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	0.976247	−	0.216662i	$-0.0695168\pi$
$401$	120.496	+	208.705i	0.300489	+	0.520462i	−0.675758	+	0.737124i	$0.736183\pi$
$402$	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	0.966936	+	0.255020i	$0.0820820\pi$
$409$	288.068	+	498.948i	0.704322	+	1.21992i	−0.262614	+	0.964901i	$0.584585\pi$
$410$	−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	0.745607	+	0.666386i	$0.232160\pi$
$419$	398.013	+	689.378i	0.949911	+	1.64529i	0.204304	+	0.978908i	$0.434507\pi$
$420$	−31.7718	−	26.3297i	−0.0756471	−	0.0626898i
$421$	−52.6204	+	91.1413i	−0.124989	+	0.216488i	−0.921729	−	0.387835i	$-0.873223\pi$
$421$	−52.6204	+	91.1413i	−0.124989	+	0.216488i	0.796740	+	0.604323i	$0.206556\pi$
$422$	−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	0.965583	−	0.260094i	$-0.0837535\pi$
$439$	536.953	+	310.010i	1.22313	+	0.706173i	0.257544	+	0.966267i	$0.417087\pi$
$440$			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	0.816563	−	0.577257i	$-0.195877\pi$
$443$	321.142	+	185.411i	0.724925	+	0.418536i	−0.0916378	+	0.995792i	$0.529210\pi$
$444$	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	−0.0806614	+	0.996742i	$0.525703\pi$
$457$	−412.915	+	715.190i	−0.903534	+	1.56497i	−0.822873	+	0.568226i	$0.807630\pi$
$458$		−	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	0.0369358	−	0.999318i	$-0.488240\pi$
$461$	−373.424	−	215.597i	−0.810031	−	0.467672i	−0.846967	+	0.531646i	$0.821574\pi$
$462$	−14.4129	−	38.8570i	−0.0311968	−	0.0841060i
$463$	−257.345	−	445.734i	−0.555821	−	0.962709i	−0.997839	−	0.0657036i	$-0.979071\pi$
$463$	−257.345	−	445.734i	−0.555821	−	0.962709i	0.442019	−	0.897006i	$-0.354263\pi$
$464$	−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	$-0.838481\pi$
$467$		−	453.857i		−	0.971858i	0.873998	−	0.485929i	$-0.161519\pi$
$468$	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	−0.512530	−	0.858669i	$-0.671292\pi$
$479$	233.447	−	404.343i	0.487364	−	0.844139i	0.999894	+	0.0145299i	$0.00462518\pi$
$480$	−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	$-0.784248\pi$
$487$		−	610.782i		−	1.25417i	0.778950	−	0.627086i	$-0.215752\pi$
$488$	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	−0.651729	−	0.758452i	$-0.725956\pi$
$491$	−157.490	+	90.9272i	−0.320755	+	0.185188i	0.330974	+	0.943640i	$0.392623\pi$
$492$	−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	−0.974806	−	0.223055i	$-0.928397\pi$
$499$	−633.250	+	365.607i	−1.26904	+	0.732679i	−0.294232	+	0.955734i	$0.595064\pi$
$500$	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	−0.903654	−	0.428264i	$-0.859125\pi$
$509$	−501.158	+	289.344i	−0.984593	+	0.568455i	−0.0809394	+	0.996719i	$0.525792\pi$
$510$	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	$0.0601110\pi$
$541$			203.117i			0.375448i	−0.982222	+	0.187724i	$0.939889\pi$
$542$	−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	0.950529	−	0.310636i	$-0.100542\pi$
$547$	632.756	+	365.322i	1.15677	+	0.667864i	0.206246	+	0.978500i	$0.433875\pi$
$548$		−	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	$0.0792238\pi$
$557$			274.409i			0.492654i	−0.969187	+	0.246327i	$0.920776\pi$
$558$	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	0.488937	−	0.872319i	$-0.337385\pi$
$563$	838.226	−	483.950i	1.48886	−	0.859592i	0.999919	+	0.0127273i	$0.00405134\pi$
$564$	−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	0.159281	−	0.987233i	$-0.449082\pi$
$569$	−350.531	−	202.379i	−0.616048	−	0.355675i	−0.775329	+	0.631558i	$0.782416\pi$
$570$	−474.961	+	176.174i	−0.833265	+	0.309077i
$571$	539.740	−	311.619i	0.945253	−	0.545742i	0.0536499	−	0.998560i	$-0.482914\pi$
$571$	539.740	−	311.619i	0.945253	−	0.545742i	0.891603	+	0.452818i	$0.149581\pi$
$572$	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	0.633201	−	0.773987i	$-0.281741\pi$
$587$	164.072	+	94.7270i	0.279509	+	0.161375i	−0.353692	+	0.935362i	$0.615074\pi$
$588$	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	$0.119969\pi$
$593$			436.488i			0.736068i	−0.929812	+	0.368034i	$0.880031\pi$
$594$	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	−0.318682	−	0.947862i	$-0.603240\pi$
$599$	205.367	−	118.569i	0.342850	−	0.197944i	0.661531	+	0.749917i	$0.269907\pi$
$600$	42.9386	−	252.554i	0.0715644	−	0.420923i
$601$	167.618	+	96.7745i	0.278899	+	0.161022i	0.632925	−	0.774213i	$-0.281854\pi$
$601$	167.618	+	96.7745i	0.278899	+	0.161022i	−0.354026	+	0.935236i	$0.615188\pi$
$602$	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	−0.390977	−	0.920401i	$-0.627863\pi$
$607$	127.850	−	73.8140i	0.210625	−	0.121605i	0.601602	+	0.798796i	$0.294529\pi$
$608$	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	−0.990592	−	0.136845i	$-0.956304\pi$
$617$	−378.719	−	655.961i	−0.613808	−	1.06315i	0.376785	−	0.926301i	$-0.377030\pi$
$618$	−220.235	+	81.6903i	−0.356368	+	0.132185i
$619$	842.718	+	486.544i	1.36142	+	0.786016i	0.989813	−	0.142375i	$-0.0454738\pi$
$619$	842.718	+	486.544i	1.36142	+	0.786016i	0.371606	+	0.928390i	$0.378807\pi$
$620$		−	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	−0.215779	−	0.976442i	$-0.569229\pi$
$641$	472.888	−	819.066i	0.737735	−	1.27779i	0.953513	−	0.301351i	$-0.0974377\pi$
$642$	165.345	−	972.514i	0.257547	−	1.51482i
$643$	−670.084	+	386.873i	−1.04212	+	0.601669i	−0.920433	−	0.390900i	$-0.872164\pi$
$643$	−670.084	+	386.873i	−1.04212	+	0.601669i	−0.121688	+	0.992568i	$0.538831\pi$
$644$	−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	$-0.918080\pi$
$647$		−	329.359i		−	0.509056i	0.967065	−	0.254528i	$-0.0819200\pi$
$648$	−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	−0.961143	−	0.276052i	$-0.910974\pi$
$653$	−469.925	−	813.934i	−0.719640	−	1.24645i	0.241503	−	0.970400i	$-0.422360\pi$
$654$	−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	0.291667	−	0.956520i	$-0.405790\pi$
$659$	−257.584	−	148.716i	−0.390871	−	0.225669i	−0.682537	+	0.730851i	$0.739124\pi$
$660$	8.44331	−	10.1884i	0.0127929	−	0.0154370i
$661$	165.831	+	287.228i	0.250879	+	0.434535i	0.963768	−	0.266742i	$-0.0859471\pi$
$661$	165.831	+	287.228i	0.250879	+	0.434535i	−0.712889	+	0.701277i	$0.752614\pi$
$662$	−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	0.0748591	−	0.997194i	$-0.476149\pi$
$673$	−505.629	−	291.925i	−0.751307	−	0.433767i	−0.826166	+	0.563427i	$0.809483\pi$
$674$	−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	−0.812419	−	0.583074i	$-0.801850\pi$
$677$	66.8519	−	115.791i	0.0987473	−	0.171035i	0.911166	+	0.412039i	$0.135183\pi$
$678$	−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	0.381607	−	0.924325i	$-0.375371\pi$
$691$	−157.602	−	90.9914i	−0.228078	−	0.131681i	−0.609685	+	0.792644i	$0.708704\pi$
$692$	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	$0.150248\pi$
$701$			637.468i			0.909369i	−0.890653	+	0.454684i	$0.849752\pi$
$702$	−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	0.894061	−	0.447945i	$-0.147844\pi$
$709$	675.791	+	390.168i	0.953160	+	0.550307i	0.0590992	+	0.998252i	$0.481177\pi$
$710$		−	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	−0.286855	−	0.957974i	$-0.592610\pi$
$727$	498.869	−	864.067i	0.686202	−	1.18854i	0.973057	−	0.230563i	$-0.0740569\pi$
$728$	−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	0.996793	+	0.0800230i	$0.0254994\pi$
$733$	416.123	+	720.746i	0.567698	+	0.983283i	−0.429095	+	0.903260i	$0.641167\pi$
$734$	−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	0.623490	−	0.781831i	$-0.285714\pi$
$743$	−271.448	−	470.162i	−0.365341	−	0.632789i	−0.988831	+	0.149042i	$0.952381\pi$
$744$	−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	−0.268273	−	0.963343i	$-0.586453\pi$
$751$	324.334	−	187.254i	0.431869	−	0.249340i	0.700143	+	0.714003i	$0.253120\pi$
$752$	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	−0.498386	−	0.866955i	$-0.666074\pi$
$761$	2.45474	−	1.41725i	0.00322568	−	0.00186235i	0.501612	+	0.865093i	$0.332741\pi$
$762$	−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	0.776062	−	0.630656i	$-0.217214\pi$
$769$	−121.604	−	210.625i	−0.158133	−	0.273895i	−0.934195	+	0.356762i	$0.883881\pi$
$770$	−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	$-0.632201\pi$
$773$		−	1414.57i		−	1.82997i	0.403485	−	0.914986i	$-0.367799\pi$
$774$	−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	0.235276	−	0.971929i	$-0.424401\pi$
$787$	940.172	−	542.809i	1.19463	−	0.689719i	0.959353	+	0.282210i	$0.0910674\pi$
$788$	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	−0.690676	−	0.723164i	$-0.742687\pi$
$797$	−326.560	+	188.539i	−0.409736	+	0.236561i	0.280940	+	0.959725i	$0.409354\pi$
$798$	−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	$0.449278\pi$
$811$			1601.45i			1.97466i	−0.158674	+	0.987331i	$0.550722\pi$
$812$	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	−0.915316	−	0.402737i	$-0.868059\pi$
$821$	−89.3883	+	154.825i	−0.108877	+	0.188581i	0.806438	+	0.591318i	$0.201392\pi$
$822$	400.016	−	482.694i	0.486637	−	0.587219i
$823$	447.254	−	258.222i	0.543444	−	0.313758i	−0.203030	−	0.979173i	$-0.565079\pi$
$823$	447.254	−	258.222i	0.543444	−	0.313758i	0.746474	+	0.665415i	$0.231745\pi$
$824$	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	0.235471	+	0.971881i	$0.424337\pi$
$839$	−607.384	+	1052.02i	−0.723938	+	1.25390i	−0.959409	+	0.282017i	$0.908997\pi$
$840$	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	0.420653	−	0.907222i	$-0.361801\pi$
$853$	−131.958	−	76.1857i	−0.154698	−	0.0893150i	−0.575351	+	0.817907i	$0.695134\pi$
$854$			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	−0.644574	−	0.764542i	$-0.722965\pi$
$857$	291.231	−	504.426i	0.339826	−	0.588596i	0.984400	+	0.175946i	$0.0562986\pi$
$858$	−4.89026	+	28.7632i	−0.00569960	+	0.0335235i
$859$	−219.907	−	380.890i	−0.256004	−	0.443412i	0.709164	−	0.705044i	$-0.249073\pi$
$859$	−219.907	−	380.890i	−0.256004	−	0.443412i	−0.965168	+	0.261632i	$0.915739\pi$
$860$	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	$-0.732703\pi$
$863$		−	1284.95i		−	1.48893i	0.667659	−	0.744467i	$-0.267297\pi$
$864$	−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	−0.963886	−	0.266315i	$-0.914194\pi$
$877$	−1065.73	+	615.297i	−1.21519	+	0.701593i	−0.251308	+	0.967907i	$0.580861\pi$
$878$	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	0.891452	−	0.453114i	$-0.149687\pi$
$887$	47.2929	+	81.9137i	0.0533178	+	0.0923492i	−0.838135	+	0.545463i	$0.816354\pi$
$888$	−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	0.302776	−	0.953062i	$-0.402087\pi$
$907$	−336.689	−	194.387i	−0.371212	−	0.214319i	−0.673988	+	0.738743i	$0.735420\pi$
$908$	−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	−0.871863	−	0.489750i	$-0.837088\pi$
$911$	−10.7455	+	18.6118i	−0.0117953	+	0.0204301i	0.860067	+	0.510180i	$0.170421\pi$
$912$	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	−0.992169	−	0.124904i	$-0.960138\pi$
$929$	−360.372	+	624.183i	−0.387914	+	0.671887i	0.604254	+	0.796791i	$0.293471\pi$
$930$	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	−0.950802	−	0.309799i	$-0.899738\pi$
$941$	−699.817	−	1212.12i	−0.743695	−	1.28812i	0.207108	−	0.978318i	$-0.433595\pi$
$942$	−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	0.0847748	+	0.996400i	$0.472983\pi$
$947$	−777.033	+	1345.86i	−0.820520	+	1.42118i	−0.905295	+	0.424783i	$0.860350\pi$
$948$	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	$0.132429\pi$
$953$			770.289i			0.808278i	−0.914698	+	0.404139i	$0.867571\pi$
$954$	−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	0.830369	−	0.557213i	$-0.188129\pi$
$967$	−65.1526	−	112.848i	−0.0673760	−	0.116699i	−0.897745	+	0.440515i	$0.854796\pi$
$968$	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	$0.107581\pi$
$971$			643.927i			0.663158i	−0.943427	+	0.331579i	$0.892419\pi$
$972$	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	−0.698222	−	0.715881i	$-0.746025\pi$
$977$	−417.532	+	241.062i	−0.427362	+	0.246737i	0.270860	+	0.962619i	$0.412692\pi$
$978$	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	−0.0855119	−	0.996337i	$-0.527253\pi$
$983$	806.156	−	1396.30i	0.820097	−	1.42045i	0.905609	−	0.424113i	$-0.139414\pi$
$984$	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	$-0.789052\pi$
$991$		−	1219.44i		−	1.23051i	0.788327	−	0.615257i	$-0.210948\pi$
$992$	−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	0.189963	−	0.981791i	$-0.439163\pi$
$997$	−563.615	−	325.403i	−0.565311	−	0.326383i	−0.755274	+	0.655409i	$0.772496\pi$
$998$	−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.101.28	yes	68
3.2	odd	2		459.3.i.a.305.8		68
9.4	even	3		459.3.i.a.152.7		68
9.5	odd	6	inner	153.3.i.a.50.27	✓	68
17.16	even	2	inner	153.3.i.a.101.27	yes	68
51.50	odd	2		459.3.i.a.305.7		68
153.50	odd	6	inner	153.3.i.a.50.28	yes	68
153.67	even	6		459.3.i.a.152.8		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.i.a.50.27	✓	68	9.5	odd	6	inner
153.3.i.a.50.28	yes	68	153.50	odd	6	inner
153.3.i.a.101.27	yes	68	17.16	even	2	inner
153.3.i.a.101.28	yes	68	1.1	even	1	trivial
459.3.i.a.152.7		68	9.4	even	3
459.3.i.a.152.8		68	153.67	even	6
459.3.i.a.305.7		68	51.50	odd	2
459.3.i.a.305.8		68	3.2	odd	2

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

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