LMFDB - Embedded newform 153.3.i.a.101.34

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			101.34
Character	$\chi$	$=$	153.101
Dual form			153.3.i.a.50.34

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.19506 + 1.84467i) q^{2} +(1.40405 - 2.65116i) q^{3} +(4.80561 + 8.32355i) q^{4} +(2.19271 + 3.79789i) q^{5} +(9.37654 - 5.88060i) q^{6} +(-6.88722 - 3.97634i) q^{7} +20.7016i q^{8} +(-5.05728 - 7.44472i) q^{9} +16.1793i q^{10} +(1.03936 - 1.80023i) q^{11} +(28.8144 - 1.05373i) q^{12} +(-9.18814 - 15.9143i) q^{13} +(-14.6700 - 25.4093i) q^{14} +(13.1475 - 0.480799i) q^{15} +(-18.9653 + 32.8488i) q^{16} +(-9.71863 + 13.9481i) q^{17} +(-2.42528 - 33.1153i) q^{18} +21.4499 q^{19} +(-21.0746 + 36.5023i) q^{20} +(-20.2119 + 12.6761i) q^{21} +(6.64164 - 3.83455i) q^{22} +(10.9542 + 18.9732i) q^{23} +(54.8834 + 29.0662i) q^{24} +(2.88404 - 4.99530i) q^{25} -67.7963i q^{26} +(-26.8378 + 2.95489i) q^{27} -76.4348i q^{28} +(16.2309 - 28.1127i) q^{29} +(42.8939 + 22.7166i) q^{30} +(-41.8857 + 24.1827i) q^{31} +(-49.4777 + 28.5660i) q^{32} +(-3.31337 - 5.28312i) q^{33} +(-56.7811 + 26.6372i) q^{34} -34.8758i q^{35} +(37.6632 - 77.8710i) q^{36} -24.0602i q^{37} +(68.5337 + 39.5680i) q^{38} +(-55.0920 + 2.01469i) q^{39} +(-78.6225 + 45.3927i) q^{40} +(17.7716 + 30.7814i) q^{41} +(-87.9615 + 3.21672i) q^{42} +(-28.7393 + 49.7779i) q^{43} +19.9790 q^{44} +(17.1851 - 35.5311i) q^{45} +80.8274i q^{46} +(-30.6916 - 17.7198i) q^{47} +(60.4592 + 96.4013i) q^{48} +(7.12251 + 12.3365i) q^{49} +(18.4294 - 10.6402i) q^{50} +(23.3331 + 45.3494i) q^{51} +(88.3091 - 152.956i) q^{52} -32.6500i q^{53} +(-91.1992 - 40.0658i) q^{54} +9.11607 q^{55} +(82.3167 - 142.577i) q^{56} +(30.1167 - 56.8671i) q^{57} +(103.717 - 59.8811i) q^{58} +(-30.3262 + 17.5088i) q^{59} +(67.1835 + 107.123i) q^{60} +(40.3133 + 23.2749i) q^{61} -178.437 q^{62} +(5.22788 + 71.3829i) q^{63} -59.0568 q^{64} +(40.2939 - 69.7910i) q^{65} +(-0.840807 - 22.9919i) q^{66} +(13.0587 + 22.6183i) q^{67} +(-162.801 - 13.8647i) q^{68} +(65.6812 - 2.40194i) q^{69} +(64.3343 - 111.430i) q^{70} +119.707 q^{71} +(154.118 - 104.694i) q^{72} +106.970i q^{73} +(44.3831 - 76.8737i) q^{74} +(-9.19400 - 14.6597i) q^{75} +(103.080 + 178.539i) q^{76} +(-14.3166 + 8.26569i) q^{77} +(-179.739 - 95.1894i) q^{78} +(74.5942 + 43.0670i) q^{79} -166.341 q^{80} +(-29.8478 + 75.3001i) q^{81} +131.131i q^{82} +(-5.09082 - 2.93919i) q^{83} +(-202.641 - 107.318i) q^{84} +(-74.2833 - 6.32621i) q^{85} +(-183.647 + 106.029i) q^{86} +(-51.7422 - 82.5022i) q^{87} +(37.2676 + 21.5165i) q^{88} -83.7512i q^{89} +(120.450 - 81.8233i) q^{90} +146.141i q^{91} +(-105.283 + 182.356i) q^{92} +(5.30258 + 144.999i) q^{93} +(-65.3744 - 113.232i) q^{94} +(47.0334 + 81.4643i) q^{95} +(6.26370 + 171.281i) q^{96} +(-89.0451 - 51.4102i) q^{97} +52.5547i q^{98} +(-18.6585 + 1.36650i) 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 $

$2$	3.19506	+	1.84467i	1.59753	+	0.922334i	0.991961	+	0.126541i	$0.0403876\pi$
$2$	3.19506	+	1.84467i	1.59753	+	0.922334i	0.605569	+	0.795793i	$0.292946\pi$
$3$	1.40405	−	2.65116i	0.468017	−	0.883720i
$3$	1.40405	−	2.65116i	0.468017	−	0.883720i
$4$	4.80561	+	8.32355i	1.20140	+	2.08089i
$5$	2.19271	+	3.79789i	0.438542	+	0.759577i	0.997577	−	0.0695667i	$-0.0221617\pi$
$5$	2.19271	+	3.79789i	0.438542	+	0.759577i	−0.559035	+	0.829144i	$0.688828\pi$
$6$	9.37654	−	5.88060i	1.56276	−	0.980100i
$7$	−6.88722	−	3.97634i	−0.983888	−	0.568048i	−0.0804464	−	0.996759i	$-0.525635\pi$
$7$	−6.88722	−	3.97634i	−0.983888	−	0.568048i	−0.903442	+	0.428711i	$0.858968\pi$
$8$			20.7016i			2.58771i
$9$	−5.05728	−	7.44472i	−0.561920	−	0.827191i
$10$			16.1793i			1.61793i
$11$	1.03936	−	1.80023i	0.0944873	−	0.163657i	−0.814907	−	0.579591i	$-0.803212\pi$
$11$	1.03936	−	1.80023i	0.0944873	−	0.163657i	0.909395	+	0.415935i	$0.136545\pi$
$12$	28.8144	−	1.05373i	2.40120	−	0.0878109i
$13$	−9.18814	−	15.9143i	−0.706780	−	1.22418i	−0.966045	−	0.258372i	$-0.916814\pi$
$13$	−9.18814	−	15.9143i	−0.706780	−	1.22418i	0.259266	−	0.965806i	$-0.416519\pi$
$14$	−14.6700	−	25.4093i	−1.04786	−	1.81495i
$15$	13.1475	−	0.480799i	0.876498	−	0.0320532i
$16$	−18.9653	+	32.8488i	−1.18533	+	2.05305i
$17$	−9.71863	+	13.9481i	−0.571684	+	0.820474i
$17$	−9.71863	+	13.9481i	−0.571684	+	0.820474i
$18$	−2.42528	−	33.1153i	−0.134738	−	1.83974i
$19$	21.4499			1.12894			0.564471	−	0.825453i	$-0.309080\pi$
$19$	21.4499			1.12894			0.564471	+	0.825453i	$0.309080\pi$
$20$	−21.0746	+	36.5023i	−1.05373	+	1.82511i
$21$	−20.2119	+	12.6761i	−0.962471	+	0.603625i
$22$	6.64164	−	3.83455i	0.301893	−	0.174298i
$23$	10.9542	+	18.9732i	0.476269	+	0.824922i	0.999630	−	0.0271886i	$-0.00865547\pi$
$23$	10.9542	+	18.9732i	0.476269	+	0.824922i	−0.523361	+	0.852111i	$0.675322\pi$
$24$	54.8834	+	29.0662i	2.28681	+	1.21109i
$25$	2.88404	−	4.99530i	0.115362	−	0.199812i
$26$		−	67.7963i		−	2.60755i
$27$	−26.8378	+	2.95489i	−0.993993	+	0.109440i
$28$		−	76.4348i		−	2.72981i
$29$	16.2309	−	28.1127i	0.559685	−	0.969403i	−0.437838	−	0.899054i	$-0.644256\pi$
$29$	16.2309	−	28.1127i	0.559685	−	0.969403i	0.997522	−	0.0703485i	$-0.0224111\pi$
$30$	42.8939	+	22.7166i	1.42980	+	0.757219i
$31$	−41.8857	+	24.1827i	−1.35115	+	0.780088i	−0.988411	−	0.151801i	$-0.951493\pi$
$31$	−41.8857	+	24.1827i	−1.35115	+	0.780088i	−0.362742	+	0.931890i	$0.618159\pi$
$32$	−49.4777	+	28.5660i	−1.54618	+	0.892686i
$33$	−3.31337	−	5.28312i	−0.100405	−	0.160094i
$34$	−56.7811	+	26.6372i	−1.67003	+	0.783447i
$35$		−	34.8758i		−	0.996452i
$36$	37.6632	−	77.8710i	1.04620	−	2.16308i
$37$		−	24.0602i		−	0.650275i	−0.945667	−	0.325138i	$-0.894589\pi$
$37$		−	24.0602i		−	0.650275i	0.945667	−	0.325138i	$-0.105411\pi$
$38$	68.5337	+	39.5680i	1.80352	+	1.04126i
$39$	−55.0920	+	2.01469i	−1.41262	+	0.0516588i
$40$	−78.6225	+	45.3927i	−1.96556	+	1.13482i
$41$	17.7716	+	30.7814i	0.433454	+	0.750765i	0.997168	−	0.0752052i	$-0.0239612\pi$
$41$	17.7716	+	30.7814i	0.433454	+	0.750765i	−0.563714	+	0.825970i	$0.690628\pi$
$42$	−87.9615	+	3.21672i	−2.09432	+	0.0765886i
$43$	−28.7393	+	49.7779i	−0.668355	+	1.15763i	0.310009	+	0.950734i	$0.399668\pi$
$43$	−28.7393	+	49.7779i	−0.668355	+	1.15763i	−0.978364	+	0.206891i	$0.933665\pi$
$44$	19.9790			0.454069
$45$	17.1851	−	35.5311i	0.381890	−	0.789580i
$46$			80.8274i			1.75712i
$47$	−30.6916	−	17.7198i	−0.653014	−	0.377018i	0.136596	−	0.990627i	$-0.456384\pi$
$47$	−30.6916	−	17.7198i	−0.653014	−	0.377018i	−0.789610	+	0.613609i	$0.789717\pi$
$48$	60.4592	+	96.4013i	1.25957	+	2.00836i
$49$	7.12251	+	12.3365i	0.145357	+	0.251766i
$50$	18.4294	−	10.6402i	0.368587	−	0.212804i
$51$	23.3331	+	45.3494i	0.457511	+	0.889204i
$52$	88.3091	−	152.956i	1.69825	−	2.94146i
$53$		−	32.6500i		−	0.616037i	−0.951380	−	0.308019i	$-0.900334\pi$
$53$		−	32.6500i		−	0.616037i	0.951380	−	0.308019i	$-0.0996659\pi$
$54$	−91.1992	−	40.0658i	−1.68887	−	0.741960i
$55$	9.11607			0.165747
$56$	82.3167	−	142.577i	1.46994	−	2.54601i
$57$	30.1167	−	56.8671i	0.528364	−	0.997668i
$58$	103.717	−	59.8811i	1.78823	−	1.03243i
$59$	−30.3262	+	17.5088i	−0.514003	+	0.296760i	−0.734478	−	0.678633i	$-0.762573\pi$
$59$	−30.3262	+	17.5088i	−0.514003	+	0.296760i	0.220475	+	0.975393i	$0.429239\pi$
$60$	67.1835	+	107.123i	1.11973	+	1.78539i
$61$	40.3133	+	23.2749i	0.660873	+	0.381555i	0.792610	−	0.609729i	$-0.208722\pi$
$61$	40.3133	+	23.2749i	0.660873	+	0.381555i	−0.131736	+	0.991285i	$0.542055\pi$
$62$	−178.437			−2.87801
$63$	5.22788	+	71.3829i	0.0829823	+	1.13306i
$64$	−59.0568			−0.922763
$65$	40.2939	−	69.7910i	0.619905	−	1.07371i
$66$	−0.840807	−	22.9919i	−0.0127395	−	0.348363i
$67$	13.0587	+	22.6183i	0.194906	+	0.337587i	0.946870	−	0.321617i	$-0.104226\pi$
$67$	13.0587	+	22.6183i	0.194906	+	0.337587i	−0.751964	+	0.659205i	$0.770893\pi$
$68$	−162.801	−	13.8647i	−2.39414	−	0.203893i
$69$	65.6812	−	2.40194i	0.951902	−	0.0348107i
$70$	64.3343	−	111.430i	0.919062	−	1.59186i
$71$	119.707			1.68601			0.843006	−	0.537905i	$-0.180784\pi$
$71$	119.707			1.68601			0.843006	+	0.537905i	$0.180784\pi$
$72$	154.118	−	104.694i	2.14053	−	1.45408i
$73$			106.970i			1.46534i	0.680585	+	0.732669i	$0.261726\pi$
$73$			106.970i			1.46534i	−0.680585	+	0.732669i	$0.738274\pi$
$74$	44.3831	−	76.8737i	0.599771	−	1.03883i
$75$	−9.19400	−	14.6597i	−0.122587	−	0.195463i
$76$	103.080	+	178.539i	1.35631	+	2.34920i
$77$	−14.3166	+	8.26569i	−0.185930	+	0.107347i
$78$	−179.739	−	95.1894i	−2.30434	−	1.22038i
$79$	74.5942	+	43.0670i	0.944230	+	0.545151i	0.891284	−	0.453446i	$-0.149805\pi$
$79$	74.5942	+	43.0670i	0.944230	+	0.545151i	0.0529462	+	0.998597i	$0.483139\pi$
$80$	−166.341			−2.07927
$81$	−29.8478	+	75.3001i	−0.368491	+	0.929631i
$82$			131.131i			1.59916i
$83$	−5.09082	−	2.93919i	−0.0613352	−	0.0354119i	0.469019	−	0.883188i	$-0.344608\pi$
$83$	−5.09082	−	2.93919i	−0.0613352	−	0.0354119i	−0.530354	+	0.847776i	$0.677941\pi$
$84$	−202.641	−	107.318i	−2.41239	−	1.27760i
$85$	−74.2833	−	6.32621i	−0.873921	−	0.0744260i
$86$	−183.647	+	106.029i	−2.13543	+	1.23289i
$87$	−51.7422	−	82.5022i	−0.594738	−	0.948301i
$88$	37.2676	+	21.5165i	0.423496	+	0.244505i
$89$		−	83.7512i		−	0.941025i	−0.882393	−	0.470512i	$-0.844069\pi$
$89$		−	83.7512i		−	0.941025i	0.882393	−	0.470512i	$-0.155931\pi$
$90$	120.450	−	81.8233i	1.33834	−	0.909148i
$91$			146.141i			1.60594i
$92$	−105.283	+	182.356i	−1.14438	+	1.98213i
$93$	5.30258	+	144.999i	0.0570170	+	1.55913i
$94$	−65.3744	−	113.232i	−0.695473	−	1.20459i
$95$	47.0334	+	81.4643i	0.495089	+	0.857519i
$96$	6.26370	+	171.281i	0.0652468	+	1.78418i
$97$	−89.0451	−	51.4102i	−0.917991	−	0.530002i	−0.0349972	−	0.999387i	$-0.511142\pi$
$97$	−89.0451	−	51.4102i	−0.917991	−	0.530002i	−0.882994	+	0.469385i	$0.844476\pi$
$98$			52.5547i			0.536272i
$99$	−18.6585	+	1.36650i	−0.188470	+	0.0138030i
$100$	55.4382			0.554382
$101$	−67.3879	−	38.9064i	−0.667207	−	0.385212i	0.127810	−	0.991799i	$-0.459205\pi$
$101$	−67.3879	−	38.9064i	−0.667207	−	0.385212i	−0.795018	+	0.606586i	$0.792538\pi$
$102$	−9.10414	+	187.936i	−0.0892563	+	1.84251i
$103$	54.5327	+	94.4534i	0.529444	+	0.917024i	0.999410	+	0.0343393i	$0.0109327\pi$
$103$	54.5327	+	94.4534i	0.529444	+	0.917024i	−0.469966	+	0.882684i	$0.655734\pi$
$104$	329.453	−	190.210i	3.16781	−	1.82894i
$105$	−92.4613	−	48.9674i	−0.880584	−	0.466356i
$106$	60.2284	−	104.319i	0.568192	−	0.984138i
$107$	−49.2826			−0.460585			−0.230293	−	0.973121i	$-0.573968\pi$
$107$	−49.2826			−0.460585			−0.230293	+	0.973121i	$0.573968\pi$
$108$	−153.567	−	209.186i	−1.42192	−	1.93691i
$109$		−	168.680i		−	1.54752i	−0.633479	−	0.773760i	$-0.718374\pi$
$109$		−	168.680i		−	1.54752i	0.633479	−	0.773760i	$-0.281626\pi$
$110$	29.1264	+	16.8161i	0.264785	+	0.152874i
$111$	−63.7874	−	33.7817i	−0.574661	−	0.304340i
$112$	261.236	−	150.825i	2.33246	−	1.34665i
$113$	6.12807	+	10.6141i	0.0542307	+	0.0939303i	0.891866	−	0.452299i	$-0.149396\pi$
$113$	6.12807	+	10.6141i	0.0542307	+	0.0939303i	−0.837636	+	0.546229i	$0.816063\pi$
$114$	201.126	−	126.138i	1.76426	−	1.10648i
$115$	−48.0387	+	83.2055i	−0.417728	+	0.723526i
$116$	311.996			2.68962
$117$	−72.0107	+	148.886i	−0.615476	+	1.27253i
$118$	−129.192			−1.09485
$119$	122.396	−	57.4187i	1.02854	−	0.482510i
$120$	9.95332	+	272.174i	0.0829444	+	2.26812i
$121$	58.3395	+	101.047i	0.482144	+	0.835098i
$122$	85.8689	+	148.729i	0.703843	+	1.21909i
$123$	106.559	−	3.89681i	0.866330	−	0.0316814i
$124$	−402.573	−	232.425i	−3.24655	−	1.87440i
$125$	134.931			1.07945
$126$	−114.974	+	237.716i	−0.912495	+	1.88664i
$127$	−149.806			−1.17958			−0.589788	−	0.807558i	$-0.700789\pi$
$127$	−149.806			−1.17958			−0.589788	+	0.807558i	$0.700789\pi$
$128$	9.22070	+	5.32357i	0.0720367	+	0.0415904i
$129$	91.6177	+	146.083i	0.710214	+	1.13243i
$130$	257.483	−	148.658i	1.98064	−	1.14352i
$131$	−63.5692	−	110.105i	−0.485261	−	0.840497i	0.514595	−	0.857433i	$-0.327942\pi$
$131$	−63.5692	−	110.105i	−0.485261	−	0.840497i	−0.999857	+	0.0169360i	$0.994609\pi$
$132$	28.0516	−	52.9676i	0.212512	−	0.401269i
$133$	−147.730	−	85.2920i	−1.11075	−	0.641293i
$134$			96.3560i			0.719074i
$135$	−70.0699	−	95.4478i	−0.519036	−	0.707021i
$136$	−288.748	−	201.192i	−2.12315	−	1.47935i
$137$	172.816	+	99.7751i	1.26143	+	0.728285i	0.973351	−	0.229322i	$-0.0736509\pi$
$137$	172.816	+	99.7751i	1.26143	+	0.728285i	0.288077	+	0.957607i	$0.406984\pi$
$138$	214.286	+	113.486i	1.55280	+	0.822361i
$139$	−57.5376	+	33.2194i	−0.413940	+	0.238988i	−0.692481	−	0.721436i	$-0.743482\pi$
$139$	−57.5376	+	33.2194i	−0.413940	+	0.238988i	0.278541	+	0.960424i	$0.410149\pi$
$140$	290.291	−	167.599i	2.07351	−	1.19714i
$141$	−90.0707	+	56.4889i	−0.638799	+	0.400630i
$142$	382.470	+	220.819i	2.69345	+	1.55507i
$143$	−38.1991			−0.267127
$144$	340.463	−	24.9346i	2.36433	−	0.173157i
$145$	142.358			0.981782
$146$	−197.324	+	341.775i	−1.35153	+	2.34092i
$147$	42.7065	−	1.56176i	0.290520	−	0.0106242i
$148$	200.266	−	115.624i	1.35315	−	0.781242i
$149$	−64.0964	+	37.0061i	−0.430177	+	0.248363i	−0.699422	−	0.714709i	$-0.746559\pi$
$149$	−64.0964	+	37.0061i	−0.430177	+	0.248363i	0.269245	+	0.963072i	$0.413226\pi$
$150$	−2.33309	−	63.7985i	−0.0155539	−	0.425323i
$151$	93.7875	−	162.445i	0.621109	−	1.07579i	−0.368170	−	0.929758i	$-0.620016\pi$
$151$	93.7875	−	162.445i	0.621109	−	1.07579i	0.989279	−	0.146034i	$-0.0466510\pi$
$152$			444.048i			2.92137i
$153$	152.989	+	1.81325i	0.999930	+	0.0118513i
$154$	−60.9899			−0.396038
$155$	−183.687	−	106.051i	−1.18507	−	0.684203i
$156$	−281.520	−	448.879i	−1.80461	−	2.87743i
$157$	16.1956	+	28.0516i	0.103157	+	0.178672i	0.912984	−	0.407996i	$-0.133772\pi$
$157$	16.1956	+	28.0516i	0.103157	+	0.178672i	−0.809827	+	0.586669i	$0.800439\pi$
$158$	158.889	+	275.203i	1.00562	+	1.74179i
$159$	−86.5603	−	45.8422i	−0.544404	−	0.288316i
$160$	−216.981	−	125.274i	−1.35613	−	0.782961i
$161$		−	174.230i		−	1.08218i
$162$	−234.269	+	185.529i	−1.44611	+	1.14524i
$163$		−	48.0877i		−	0.295016i	−0.989061	−	0.147508i	$-0.952875\pi$
$163$		−	48.0877i		−	0.295016i	0.989061	−	0.147508i	$-0.0471253\pi$
$164$	−170.807	+	295.846i	−1.04151	+	1.80394i
$165$	12.7994	−	24.1681i	0.0775723	−	0.146474i
$166$	−10.8436	−	18.7818i	−0.0653232	−	0.113143i
$167$	0.203918	+	0.353196i	0.00122106	+	0.00211494i	0.866635	−	0.498942i	$-0.166278\pi$
$167$	0.203918	+	0.353196i	0.00122106	+	0.00211494i	−0.865414	+	0.501057i	$0.832945\pi$
$168$	−262.417	−	418.420i	−1.56200	−	2.49059i
$169$	−84.3437	+	146.088i	−0.499075	+	0.864424i
$170$	−225.670	−	157.241i	−1.32747	−	0.924945i
$171$	−108.478	−	159.689i	−0.634375	−	0.933851i
$172$	−552.438			−3.21185
$173$	153.817	−	266.419i	0.889116	−	1.53999i	0.0481945	−	0.998838i	$-0.484653\pi$
$173$	153.817	−	266.419i	0.889116	−	1.53999i	0.840922	−	0.541157i	$-0.182013\pi$
$174$	−13.1302	−	359.047i	−0.0754610	−	2.06349i
$175$	−39.7260	+	22.9358i	−0.227006	+	0.131062i
$176$	39.4235	+	68.2835i	0.223997	+	0.387974i
$177$	3.83918	+	104.983i	0.0216903	+	0.593123i
$178$	154.493	−	267.590i	0.867939	−	1.50331i
$179$		−	118.710i		−	0.663186i	−0.943423	−	0.331593i	$-0.892414\pi$
$179$		−	118.710i		−	0.663186i	0.943423	−	0.331593i	$-0.107586\pi$
$180$	378.330	−	27.7078i	2.10183	−	0.153932i
$181$		−	221.600i		−	1.22431i	−0.790739	−	0.612154i	$-0.790303\pi$
$181$		−	221.600i		−	1.22431i	0.790739	−	0.612154i	$-0.209697\pi$
$182$	−269.581	+	466.928i	−1.48121	+	2.56554i
$183$	118.307	−	74.1978i	0.646488	−	0.405452i
$184$	−392.777	+	226.770i	−2.13466	+	1.23244i
$185$	91.3779	−	52.7570i	0.493934	−	0.285173i
$186$	−250.534	+	473.064i	−1.34696	+	2.54335i
$187$	15.0085	+	31.9928i	0.0802592	+	0.171084i
$188$		−	340.618i		−	1.81180i
$189$	196.588	+	86.3652i	1.04015	+	0.456959i
$190$			347.044i			1.82655i
$191$	122.967	+	70.9950i	0.643806	+	0.371702i	0.786079	−	0.618126i	$-0.212108\pi$
$191$	122.967	+	70.9950i	0.643806	+	0.371702i	−0.142273	+	0.989827i	$0.545441\pi$
$192$	−82.9188	+	156.569i	−0.431869	+	0.815464i
$193$	−143.902	+	83.0821i	−0.745608	+	0.430477i	−0.824105	−	0.566437i	$-0.808321\pi$
$193$	−143.902	+	83.0821i	−0.745608	+	0.430477i	0.0784966	+	0.996914i	$0.474988\pi$
$194$	−189.670	−	328.517i	−0.977678	−	1.69339i
$195$	−128.452	−	204.816i	−0.658730	−	1.05034i
$196$	−68.4559	+	118.569i	−0.349265	+	0.604944i
$197$	−34.8165			−0.176733			−0.0883667	−	0.996088i	$-0.528165\pi$
$197$	−34.8165			−0.176733			−0.0883667	+	0.996088i	$0.528165\pi$
$198$	−62.1358	−	30.0527i	−0.313817	−	0.151782i
$199$		−	38.8025i		−	0.194987i	−0.995236	−	0.0974937i	$-0.968917\pi$
$199$		−	38.8025i		−	0.194987i	0.995236	−	0.0974937i	$-0.0310826\pi$
$200$	103.411	+	59.7044i	0.517055	+	0.298522i
$201$	78.2999	−	2.86340i	0.389552	−	0.0142458i
$202$	−143.539	−	248.617i	−0.710589	−	1.23078i
$203$	−223.571	+	129.079i	−1.10133	+	0.635856i
$204$	−265.339	+	412.145i	−1.30068	+	2.02032i
$205$	−77.9361	+	134.989i	−0.380176	+	0.658484i
$206$			402.379i			1.95330i
$207$	85.8519	−	177.504i	0.414743	−	0.857506i
$208$	697.022			3.35107
$209$	22.2942	−	38.6146i	0.106671	−	0.184759i
$210$	−205.091	−	327.014i	−0.976623	−	1.55721i
$211$	−60.3426	+	34.8388i	−0.285984	+	0.165113i	−0.636129	−	0.771582i	$-0.719466\pi$
$211$	−60.3426	+	34.8388i	−0.285984	+	0.165113i	0.350145	+	0.936695i	$0.386132\pi$
$212$	271.764	−	156.903i	1.28190	−	0.740108i
$213$	168.074	−	317.362i	0.789082	−	1.48996i
$214$	−157.461	−	90.9101i	−0.735799	−	0.424814i
$215$	−252.068			−1.17241
$216$	−61.1711	−	555.587i	−0.283200	−	2.57216i
$217$	384.635			1.77251
$218$	311.158	−	538.942i	1.42733	−	2.47221i
$219$	283.594	+	150.191i	1.29495	+	0.685803i
$220$	43.8082	+	75.8781i	0.199128	+	0.344900i
$221$	311.270	+	26.5088i	1.40846	+	0.119949i
$222$	−141.488	−	225.601i	−0.637335	−	1.01622i
$223$	101.651	−	176.064i	0.455832	−	0.789525i	−0.542903	−	0.839795i	$-0.682675\pi$
$223$	101.651	−	176.064i	0.455832	−	0.789525i	0.998736	+	0.0502706i	$0.0160084\pi$
$224$	454.352			2.02835
$225$	−51.7740	+	3.79179i	−0.230107	+	0.0168524i
$226$			45.2170i			0.200075i
$227$	−124.328	+	215.342i	−0.547699	+	0.948642i	0.450733	+	0.892659i	$0.351163\pi$
$227$	−124.328	+	215.342i	−0.547699	+	0.948642i	−0.998432	+	0.0559830i	$0.982171\pi$
$228$	618.065	−	22.6024i	2.71081	−	0.0991335i
$229$	−215.212	−	372.758i	−0.939790	−	1.62776i	−0.765862	−	0.643005i	$-0.777687\pi$
$229$	−215.212	−	372.758i	−0.939790	−	1.62776i	−0.173928	−	0.984758i	$-0.555646\pi$
$230$	−306.973	+	177.231i	−1.33467	+	0.770570i
$231$	1.81243	+	49.5610i	0.00784602	+	0.214550i
$232$	581.979	+	336.006i	2.50853	+	1.44830i
$233$	−335.764			−1.44105			−0.720524	−	0.693430i	$-0.756098\pi$
$233$	−335.764			−1.44105			−0.720524	+	0.693430i	$0.756098\pi$
$234$	−504.724	+	342.865i	−2.15694	+	1.46523i
$235$		−	155.418i		−	0.661353i
$236$	−291.471	−	168.281i	−1.23505	−	0.713055i
$237$	218.911	−	137.293i	0.923676	−	0.579294i
$238$	496.983	+	42.3247i	2.08816	+	0.177835i
$239$	−113.974	+	65.8029i	−0.476878	+	0.275326i	−0.719115	−	0.694891i	$-0.755452\pi$
$239$	−113.974	+	65.8029i	−0.476878	+	0.275326i	0.242236	+	0.970217i	$0.422119\pi$
$240$	−233.552	+	440.997i	−0.973132	+	1.83749i
$241$	−30.3066	−	17.4975i	−0.125753	−	0.0726038i	0.435804	−	0.900042i	$-0.356464\pi$
$241$	−30.3066	−	17.4975i	−0.125753	−	0.0726038i	−0.561557	+	0.827438i	$0.689798\pi$
$242$			430.468i			1.77879i
$243$	157.725	+	184.856i	0.649073	+	0.760726i
$244$			447.400i			1.83360i
$245$	−31.2352	+	54.1009i	−0.127491	+	0.220820i
$246$	347.649	+	184.115i	1.41321	+	0.748434i
$247$	−197.085	−	341.361i	−0.797913	−	1.38203i
$248$	−500.623	−	867.104i	−2.01864	−	3.49639i
$249$	−14.9400	+	9.36980i	−0.0600001	+	0.0376297i
$250$	431.113	+	248.903i	1.72445	+	0.995612i
$251$			39.0034i			0.155392i	0.996977	+	0.0776960i	$0.0247563\pi$
$251$			39.0034i			0.155392i	−0.996977	+	0.0776960i	$0.975244\pi$
$252$	−569.036	+	386.553i	−2.25808	+	1.53394i
$253$	45.5414			0.180006
$254$	−478.640	−	276.343i	−1.88441	−	1.08796i
$255$	−121.069	+	188.054i	−0.474781	+	0.737468i
$256$	137.754	+	238.597i	0.538102	+	0.932020i
$257$	−176.596	+	101.958i	−0.687144	+	0.396723i	−0.802541	−	0.596596i	$-0.796519\pi$
$257$	−176.596	+	101.958i	−0.687144	+	0.396723i	0.115397	+	0.993319i	$0.463186\pi$
$258$	23.2491	+	635.748i	0.0901127	+	2.46414i
$259$	−95.6714	+	165.708i	−0.369388	+	0.639798i
$260$	774.545			2.97902
$261$	−291.375	+	21.3395i	−1.11638	+	0.0817606i
$262$		−	469.057i		−	1.79029i
$263$	158.320	+	91.4059i	0.601976	+	0.347551i	0.769818	−	0.638263i	$-0.220347\pi$
$263$	158.320	+	91.4059i	0.601976	+	0.347551i	−0.167843	+	0.985814i	$0.553680\pi$
$264$	109.369	−	68.5922i	0.414277	−	0.259819i
$265$	124.001	−	71.5919i	0.467928	−	0.270158i
$266$	−314.671	−	545.026i	−1.18297	−	2.04897i
$267$	−222.038	−	117.591i	−0.831602	−	0.440415i
$268$	−125.510	+	217.390i	−0.468321	+	0.811156i
$269$	407.942			1.51651			0.758257	−	0.651956i	$-0.226051\pi$
$269$	407.942			1.51651			0.758257	+	0.651956i	$0.226051\pi$
$270$	−47.8081	−	434.217i	−0.177067	−	1.60821i
$271$	−108.406			−0.400023			−0.200011	−	0.979794i	$-0.564098\pi$
$271$	−108.406			−0.400023			−0.200011	+	0.979794i	$0.564098\pi$
$272$	−273.860	−	583.774i	−1.00684	−	2.14623i
$273$	387.442	+	205.189i	1.41920	+	0.751607i
$274$	368.104	+	637.575i	1.34345	+	2.32692i
$275$	−5.99511	−	10.3838i	−0.0218004	−	0.0377594i
$276$	335.631	+	535.158i	1.21605	+	1.93898i
$277$	132.028	+	76.2265i	0.476636	+	0.275186i	0.719014	−	0.694996i	$-0.244594\pi$
$277$	132.028	+	76.2265i	0.476636	+	0.275186i	−0.242378	+	0.970182i	$0.577927\pi$
$278$	−245.115			−0.881708
$279$	391.862	+	189.529i	1.40452	+	0.679314i
$280$	721.987			2.57853
$281$	−154.824	−	89.3876i	−0.550975	−	0.318105i	0.198540	−	0.980093i	$-0.436380\pi$
$281$	−154.824	−	89.3876i	−0.550975	−	0.318105i	−0.749515	+	0.661987i	$0.769713\pi$
$282$	−391.985	+	14.3347i	−1.39002	+	0.0508324i
$283$	−141.536	+	81.7156i	−0.500126	+	0.288748i	−0.728766	−	0.684763i	$-0.759906\pi$
$283$	−141.536	+	81.7156i	−0.500126	+	0.288748i	0.228640	+	0.973511i	$0.426572\pi$
$284$	575.264	+	996.386i	2.02558	+	3.50840i
$285$	282.012	−	10.3131i	0.989516	−	0.0361862i
$286$	−122.049	−	70.4648i	−0.426743	−	0.246380i
$287$		−	282.664i		−	0.984892i
$288$	462.888	+	223.882i	1.60725	+	0.777366i
$289$	−100.096	−	271.112i	−0.346354	−	0.938104i
$290$	454.843	+	262.604i	1.56843	+	0.905531i
$291$	−261.320	+	163.890i	−0.898008	+	0.563196i
$292$	−890.368	+	514.054i	−3.04920	+	1.76046i
$293$	155.957	−	90.0416i	0.532275	−	0.307309i	−0.209667	−	0.977773i	$-0.567238\pi$
$293$	155.957	−	90.0416i	0.532275	−	0.307309i	0.741942	+	0.670464i	$0.233905\pi$
$294$	139.331	+	73.7894i	0.473914	+	0.250984i
$295$	−132.993	−	76.7836i	−0.450824	−	0.260283i
$296$	498.086			1.68272
$297$	−22.5747	+	51.3853i	−0.0760091	+	0.173015i
$298$	−273.056			−0.916295
$299$	201.297	−	348.657i	0.673235	−	1.16608i
$300$	77.8381	−	146.975i	0.259460	−	0.489918i
$301$	395.867	−	228.554i	1.31517	−	0.759316i
$302$	599.313	−	346.014i	1.98448	−	1.14574i
$303$	−197.763	+	124.030i	−0.652684	+	0.409338i
$304$	−406.803	+	704.603i	−1.33817	+	2.31777i
$305$			204.140i			0.669313i
$306$	485.465	+	288.008i	1.58649	+	0.941202i
$307$	−172.053			−0.560433			−0.280216	−	0.959937i	$-0.590406\pi$
$307$	−172.053			−0.560433			−0.280216	+	0.959937i	$0.590406\pi$
$308$	−137.600	−	79.4433i	−0.446753	−	0.257933i
$309$	326.978	−	11.9575i	1.05818	−	0.0386973i
$310$	−391.260	−	677.682i	−1.26213	−	2.18607i
$311$	−223.867	−	387.748i	−0.719829	−	1.24678i	−0.961067	−	0.276314i	$-0.910887\pi$
$311$	−223.867	−	387.748i	−0.719829	−	1.24678i	0.241239	−	0.970466i	$-0.422446\pi$
$312$	−41.7075	−	1140.50i	−0.133678	−	3.65543i
$313$	−160.210	−	92.4973i	−0.511853	−	0.295518i	0.221742	−	0.975105i	$-0.428826\pi$
$313$	−160.210	−	92.4973i	−0.511853	−	0.295518i	−0.733595	+	0.679587i	$0.762159\pi$
$314$			119.502i			0.380579i
$315$	−259.641	+	176.377i	−0.824257	+	0.559927i
$316$			827.851i			2.61978i
$317$	−75.9882	+	131.615i	−0.239710	+	0.415191i	−0.960631	−	0.277827i	$-0.910386\pi$
$317$	−75.9882	+	131.615i	−0.239710	+	0.415191i	0.720921	+	0.693017i	$0.243719\pi$
$318$	−192.001	−	306.144i	−0.603778	−	0.962716i
$319$	−33.7394	−	58.4384i	−0.105766	−	0.183192i
$320$	−129.495	−	224.291i	−0.404670	−	0.700910i
$321$	−69.1953	+	130.656i	−0.215562	+	0.407028i
$322$	321.397	−	556.676i	0.998127	−	1.72881i
$323$	−208.464	+	299.184i	−0.645398	+	0.926267i
$324$	−770.201	+	113.423i	−2.37716	+	0.350072i
$325$	−105.996			−0.326141
$326$	88.7058	−	153.643i	0.272104	−	0.471297i
$327$	−447.197	−	236.835i	−1.36757	−	0.724266i
$328$	−637.225	+	367.902i	−1.94276	+	1.12165i
$329$	140.920	+	244.081i	0.428328	+	0.741886i
$330$	85.4771	−	53.6080i	0.259022	−	0.162448i
$331$	−32.3863	+	56.0948i	−0.0978440	+	0.169471i	−0.910792	−	0.412866i	$-0.864528\pi$
$331$	−32.3863	+	56.0948i	−0.0978440	+	0.169471i	0.812948	+	0.582336i	$0.197861\pi$
$332$		−	56.4983i		−	0.170176i
$333$	−179.121	+	121.679i	−0.537902	+	0.365403i
$334$			1.50464i			0.00450491i
$335$	−57.2679	+	99.1910i	−0.170949	+	0.296092i
$336$	−33.0715	−	904.343i	−0.0984271	−	2.69150i
$337$	275.905	−	159.294i	0.818708	−	0.472681i	−0.0312627	−	0.999511i	$-0.509953\pi$
$337$	275.905	−	159.294i	0.818708	−	0.472681i	0.849971	+	0.526830i	$0.176619\pi$
$338$	−538.967	+	311.172i	−1.59458	+	0.920629i
$339$	36.7438	−	1.34371i	0.108389	−	0.00396374i
$340$	−304.320	−	648.702i	−0.895058	−	1.90795i
$341$			100.538i			0.294834i
$342$	−52.0219	−	710.321i	−0.152111	−	2.07696i
$343$			276.395i			0.805816i
$344$	−1030.48	−	594.950i	−2.99559	−	1.72951i
$345$	153.142	+	244.183i	0.443891	+	0.707777i
$346$	982.910	−	567.483i	2.84078	−	1.64012i
$347$	2.31115	+	4.00302i	0.00666036	+	0.0115361i	0.869336	−	0.494221i	$-0.164547\pi$
$347$	2.31115	+	4.00302i	0.00666036	+	0.0115361i	−0.862676	+	0.505757i	$0.831213\pi$
$348$	438.059	−	827.152i	1.25879	−	2.37687i
$349$	−343.796	+	595.472i	−0.985089	+	1.70622i	−0.343550	+	0.939134i	$0.611630\pi$
$349$	−343.796	+	595.472i	−0.985089	+	1.70622i	−0.641539	+	0.767090i	$0.721704\pi$
$350$	−169.236			−0.483531
$351$	293.615	+	399.956i	0.836509	+	1.13947i
$352$			118.761i			0.337390i
$353$	203.050	+	117.231i	0.575213	+	0.332100i	0.759229	−	0.650824i	$-0.225576\pi$
$353$	203.050	+	117.231i	0.575213	+	0.332100i	−0.184015	+	0.982923i	$0.558910\pi$
$354$	−181.392	+	342.508i	−0.512407	+	0.967538i
$355$	262.482	+	454.633i	0.739387	+	1.28066i
$356$	697.107	−	402.475i	1.95817	−	1.13055i
$357$	19.6247	−	405.111i	0.0549712	−	1.13477i
$358$	218.981	−	379.286i	0.611679	−	1.05946i
$359$		−	292.062i		−	0.813544i	−0.913530	−	0.406772i	$-0.866654\pi$
$359$		−	292.062i		−	0.813544i	0.913530	−	0.406772i	$-0.133346\pi$
$360$	735.553	+	355.759i	2.04320	+	0.988219i
$361$	99.0981			0.274510
$362$	408.778	−	708.024i	1.12922	−	1.95587i
$363$	349.803	−	12.7922i	0.963644	−	0.0352401i
$364$	−1216.41	+	702.294i	−3.34178	+	1.92938i
$365$	−406.259	+	234.554i	−1.11304	+	0.642612i
$366$	514.869	−	18.8286i	1.40675	−	0.0514442i
$367$	48.8824	+	28.2223i	0.133195	+	0.0768999i	0.565117	−	0.825011i	$-0.308831\pi$
$367$	48.8824	+	28.2223i	0.133195	+	0.0768999i	−0.431922	+	0.901911i	$0.642164\pi$
$368$	−830.996			−2.25814
$369$	139.283	−	287.975i	0.377459	−	0.780420i
$370$	389.277			1.05210
$371$	−129.827	+	224.867i	−0.349939	+	0.606112i
$372$	−1181.43	+	740.947i	−3.17588	+	1.99179i
$373$	−259.782	−	449.955i	−0.696466	−	1.20631i	−0.969684	−	0.244362i	$-0.921422\pi$
$373$	−259.782	−	449.955i	−0.696466	−	1.20631i	0.273219	−	0.961952i	$-0.411912\pi$
$374$	−11.0631	+	129.905i	−0.0295805	+	0.347338i
$375$	189.450	−	357.723i	0.505200	−	0.953929i
$376$	366.830	−	635.368i	0.975611	−	1.68981i
$377$	−596.525			−1.58230
$378$	468.794	+	638.581i	1.24020	+	1.68937i
$379$		−	46.3947i		−	0.122413i	−0.998125	−	0.0612067i	$-0.980505\pi$
$379$		−	46.3947i		−	0.122413i	0.998125	−	0.0612067i	$-0.0194949\pi$
$380$	−452.048	+	782.970i	−1.18960	+	2.06045i
$381$	−210.335	+	397.160i	−0.552062	+	1.04241i
$382$	261.925	+	453.667i	0.685667	+	1.18761i
$383$	−267.702	+	154.558i	−0.698960	+	0.403545i	−0.806960	−	0.590606i	$-0.798889\pi$
$383$	−267.702	+	154.558i	−0.698960	+	0.403545i	0.108000	+	0.994151i	$0.465555\pi$
$384$	27.0600	−	16.9710i	0.0704686	−	0.0441952i
$385$	−62.7843	−	36.2486i	−0.163076	−	0.0941521i
$386$	−613.036			−1.58818
$387$	515.925	−	37.7849i	1.33314	−	0.0976355i
$388$		−	988.229i		−	2.54698i
$389$	591.711	+	341.625i	1.52111	+	0.878213i	0.999690	+	0.0249119i	$0.00793053\pi$
$389$	591.711	+	341.625i	1.52111	+	0.878213i	0.521419	+	0.853301i	$0.325403\pi$
$390$	−32.5964	−	891.350i	−0.0835804	−	2.28551i
$391$	−371.099	−	31.6040i	−0.949103	−	0.0808287i
$392$	−255.387	+	147.448i	−0.651497	+	0.376142i
$393$	−381.161	+	13.9389i	−0.969874	+	0.0354680i
$394$	−111.241	−	64.2249i	−0.282337	−	0.163007i
$395$			377.734i			0.956287i
$396$	−101.040	−	148.738i	−0.255150	−	0.375602i
$397$			7.45136i			0.0187692i	0.999956	+	0.00938458i	$0.00298725\pi$
$397$			7.45136i			0.0187692i	−0.999956	+	0.00938458i	$0.997013\pi$
$398$	71.5778	−	123.976i	0.179844	−	0.311498i
$399$	−433.543	+	271.902i	−1.08657	+	0.681458i
$400$	109.393	+	189.474i	0.273483	+	0.473686i
$401$	−54.6818	−	94.7117i	−0.136364	−	0.236189i	0.789754	−	0.613424i	$-0.210208\pi$
$401$	−54.6818	−	94.7117i	−0.136364	−	0.236189i	−0.926118	+	0.377235i	$0.876875\pi$
$402$	255.455	+	135.289i	0.635460	+	0.336539i
$403$	769.704	+	444.389i	1.90993	+	1.10270i
$404$		−	747.876i		−	1.85118i
$405$	−351.429	+	51.7529i	−0.867726	+	0.127785i
$406$	−952.430			−2.34589
$407$	−43.3138	−	25.0072i	−0.106422	−	0.0614428i
$408$	−938.808	+	483.033i	−2.30100	+	1.18390i
$409$	296.591	+	513.710i	0.725160	+	1.25601i	0.958908	+	0.283717i	$0.0915677\pi$
$409$	296.591	+	513.710i	0.725160	+	1.25601i	−0.233748	+	0.972297i	$0.575099\pi$
$410$	−498.021	+	287.533i	−1.21469	+	0.701299i
$411$	507.161	−	318.072i	1.23397	−	0.773898i
$412$	−524.125	+	907.812i	−1.27215	+	2.20343i
$413$	278.484			0.674295
$414$	601.738	−	408.767i	1.45347	−	0.987360i
$415$		−	25.7791i		−	0.0621184i
$416$	909.216	+	524.936i	2.18561	+	1.26187i
$417$	7.28405	+	199.183i	0.0174678	+	0.477657i
$418$	142.462	−	82.2507i	0.340819	−	0.196772i
$419$	119.514	+	207.004i	0.285235	+	0.494042i	0.972666	−	0.232208i	$-0.0745949\pi$
$419$	119.514	+	207.004i	0.285235	+	0.494042i	−0.687431	+	0.726250i	$0.741262\pi$
$420$	−36.7497	−	1004.92i	−0.0874994	−	2.39268i
$421$	80.2921	−	139.070i	0.190718	−	0.330333i	−0.754771	−	0.655989i	$-0.772252\pi$
$421$	80.2921	−	139.070i	0.190718	−	0.330333i	0.945488	+	0.325656i	$0.105585\pi$
$422$	−257.065			−0.609158
$423$	23.2971	+	318.105i	0.0550760	+	0.752021i
$424$	675.908			1.59412
$425$	41.6458	+	88.7742i	0.0979902	+	0.208881i
$426$	1122.43	−	703.948i	2.63482	−	1.65246i
$427$	−185.098	−	320.598i	−0.433484	−	0.750816i
$428$	−236.833	−	410.206i	−0.553348	−	0.958426i
$429$	−53.6335	+	101.272i	−0.125020	+	0.236065i
$430$	−805.371	−	464.981i	−1.87296	−	1.08135i
$431$	−353.987			−0.821315			−0.410658	−	0.911790i	$-0.634701\pi$
$431$	−353.987			−0.821315			−0.410658	+	0.911790i	$0.634701\pi$
$432$	411.922	−	937.631i	0.953523	−	2.17044i
$433$	−237.294			−0.548022			−0.274011	−	0.961726i	$-0.588351\pi$
$433$	−237.294			−0.548022			−0.274011	+	0.961726i	$0.588351\pi$
$434$	1228.93	+	709.524i	2.83164	+	1.63485i
$435$	199.878	−	377.414i	0.459490	−	0.867619i
$436$	1404.01	−	810.608i	3.22022	−	1.85919i
$437$	234.966	+	406.974i	0.537680	+	0.931290i
$438$	629.046	+	1003.00i	1.43618	+	2.28997i
$439$	−392.321	−	226.506i	−0.893669	−	0.515960i	−0.0185280	−	0.999828i	$-0.505898\pi$
$439$	−392.321	−	226.506i	−0.893669	−	0.515960i	−0.875141	+	0.483868i	$0.839231\pi$
$440$			188.718i			0.428904i
$441$	55.8216	−	115.414i	0.126580	−	0.261711i
$442$	945.626	+	658.887i	2.13943	+	1.49069i
$443$	500.801	+	289.138i	1.13048	+	0.652681i	0.944055	−	0.329789i	$-0.106978\pi$
$443$	500.801	+	289.138i	1.13048	+	0.652681i	0.186421	+	0.982470i	$0.440311\pi$
$444$	−25.3530	−	693.279i	−0.0571013	−	1.56144i
$445$	318.078	−	183.642i	0.714781	−	0.412679i
$446$	649.559	−	375.023i	1.45641	−	0.840859i
$447$	8.11437	+	221.888i	0.0181530	+	0.496394i
$448$	406.737	+	234.830i	0.907895	+	0.524174i
$449$	436.088			0.971244			0.485622	−	0.874169i	$-0.338593\pi$
$449$	436.088			0.971244			0.485622	+	0.874169i	$0.338593\pi$
$450$	−172.416	−	83.3910i	−0.383146	−	0.185313i
$451$	73.8845			0.163824
$452$	−58.8981	+	102.015i	−0.130306	+	0.225696i
$453$	−298.984	−	476.726i	−0.660010	−	1.05238i
$454$	−794.468	+	458.686i	−1.74993	+	1.01032i
$455$	−555.025	+	320.444i	−1.21984	+	0.704272i
$456$	1177.24	+	623.466i	2.58167	+	1.36725i
$457$	−28.7310	+	49.7636i	−0.0628687	+	0.108892i	−0.895747	−	0.444565i	$-0.853358\pi$
$457$	−28.7310	+	49.7636i	−0.0628687	+	0.108892i	0.832878	+	0.553457i	$0.186692\pi$
$458$		−	1587.98i		−	3.46720i
$459$	219.612	−	403.053i	0.478457	−	0.878111i
$460$	−923.421			−2.00744
$461$	−58.0300	−	33.5036i	−0.125879	−	0.0726760i	0.435739	−	0.900073i	$-0.356487\pi$
$461$	−58.0300	−	33.5036i	−0.125879	−	0.0726760i	−0.561617	+	0.827397i	$0.689821\pi$
$462$	−85.6329	+	161.694i	−0.185353	+	0.349987i
$463$	223.471	+	387.064i	0.482660	+	0.835991i	0.999802	−	0.0199084i	$-0.00633746\pi$
$463$	223.471	+	387.064i	0.482660	+	0.835991i	−0.517142	+	0.855900i	$0.673004\pi$
$464$	615.645	+	1066.33i	1.32682	+	2.29812i
$465$	−539.065	+	338.081i	−1.15928	+	0.727055i
$466$	−1072.79	−	619.373i	−2.30212	−	1.32913i
$467$		−	469.650i		−	1.00568i	−0.864381	−	0.502838i	$-0.832289\pi$
$467$		−	469.650i		−	1.00568i	0.864381	−	0.502838i	$-0.167711\pi$
$468$	−1585.32	+	116.104i	−3.38743	+	0.248086i
$469$		−	207.703i		−	0.442864i
$470$	286.694	−	496.569i	0.609988	−	1.05653i
$471$	97.1086	−	3.55123i	0.206175	−	0.00753976i
$472$	−362.462	−	627.802i	−0.767927	−	1.33009i
$473$	59.7409	+	103.474i	0.126302	+	0.218762i
$474$	952.694	−	34.8397i	2.00990	−	0.0735015i
$475$	61.8623	−	107.149i	0.130237	−	0.225576i
$476$	1066.12	+	742.842i	2.23974	+	1.56059i
$477$	−243.070	+	165.120i	−0.509581	+	0.346164i
$478$	−485.538			−1.01577
$479$	−267.493	+	463.311i	−0.558440	+	0.967246i	0.439187	+	0.898396i	$0.355267\pi$
$479$	−267.493	+	463.311i	−0.558440	+	0.967246i	−0.997627	+	0.0688507i	$0.978067\pi$
$480$	−636.772	+	399.359i	−1.32661	+	0.831998i
$481$	−382.901	+	221.068i	−0.796053	+	0.459601i
$482$	−64.5542	−	111.811i	−0.133930	−	0.231973i
$483$	−461.912	−	244.628i	−0.956339	−	0.506476i
$484$	−560.713	+	971.183i	−1.15850	+	2.00658i
$485$		−	450.911i		−	0.929713i
$486$	162.941	+	881.577i	0.335270	+	1.81395i
$487$			718.176i			1.47469i	0.675515	+	0.737347i	$0.263921\pi$
$487$			718.176i			1.47469i	−0.675515	+	0.737347i	$0.736079\pi$
$488$	−481.828	+	834.551i	−0.987353	+	1.71015i
$489$	−127.488	−	67.5175i	−0.260712	−	0.138073i
$490$	−199.597	+	115.237i	−0.407340	+	0.235178i
$491$	−557.334	+	321.777i	−1.13510	+	0.655351i	−0.945213	−	0.326455i	$-0.894146\pi$
$491$	−557.334	+	321.777i	−1.13510	+	0.655351i	−0.189888	+	0.981806i	$0.560812\pi$
$492$	544.514	+	868.219i	1.10674	+	1.76467i
$493$	234.375	+	499.606i	0.475406	+	1.01340i
$494$		−	1454.22i		−	2.94377i
$495$	−46.1025	−	67.8666i	−0.0931364	−	0.137104i
$496$		−	1834.53i		−	3.69865i
$497$	−824.447	−	475.994i	−1.65885	−	0.957735i
$498$	−65.0184	+	2.37770i	−0.130559	+	0.00477450i
$499$	455.759	−	263.133i	0.913345	−	0.527320i	0.0318393	−	0.999493i	$-0.489864\pi$
$499$	455.759	−	263.133i	0.913345	−	0.527320i	0.881506	+	0.472173i	$0.156530\pi$
$500$	648.425	+	1123.11i	1.29685	+	2.24621i
$501$	1.22269	−	0.0447133i	0.00244049	−	8.92480e-5i
$502$	−71.9483	+	124.618i	−0.143323	+	0.248243i
$503$	97.0865			0.193015			0.0965074	−	0.995332i	$-0.469233\pi$
$503$	97.0865			0.193015			0.0965074	+	0.995332i	$0.469233\pi$
$504$	−1477.74	+	108.226i	−2.93203	+	0.214734i
$505$		−	341.242i		−	0.675727i
$506$	145.508	+	84.0088i	0.287564	+	0.166025i
$507$	268.879	+	428.723i	0.530332	+	0.845608i
$508$	−719.909	−	1246.92i	−1.41714	−	2.45457i
$509$	457.008	−	263.854i	0.897855	−	0.518377i	0.0213514	−	0.999772i	$-0.493203\pi$
$509$	457.008	−	263.854i	0.897855	−	0.518377i	0.876504	+	0.481395i	$0.159870\pi$
$510$	−733.722	+	377.512i	−1.43867	+	0.740220i
$511$	425.347	−	736.723i	0.832382	−	1.44173i
$512$			973.854i			1.90206i
$513$	−575.669	+	63.3821i	−1.12216	+	0.123552i
$514$	−752.314			−1.46365
$515$	−239.149	+	414.218i	−0.464367	+	0.804307i
$516$	−775.652	+	1464.60i	−1.50320	+	2.83838i
$517$	−63.7994	+	36.8346i	−0.123403	+	0.0712468i
$518$	−611.352	+	352.964i	−1.18022	+	0.681398i
$519$	−490.352	−	781.859i	−0.944802	−	1.50647i
$520$	1444.79	+	834.149i	2.77844	+	1.60413i
$521$	122.591			0.235300			0.117650	−	0.993055i	$-0.462464\pi$
$521$	122.591			0.235300			0.117650	+	0.993055i	$0.462464\pi$
$522$	−970.325	−	469.310i	−1.85886	−	0.899060i
$523$	425.010			0.812639			0.406319	−	0.913731i	$-0.366812\pi$
$523$	425.010			0.812639			0.406319	+	0.913731i	$0.366812\pi$
$524$	610.977	−	1058.24i	1.16599	−	2.01955i
$525$	5.02917	+	137.523i	0.00957937	+	0.261949i
$526$	337.227	+	584.095i	0.641116	+	1.11045i
$527$	69.7698	−	819.248i	0.132391	−	1.55455i
$528$	236.383	−	8.64444i	0.447695	−	0.0163720i
$529$	24.5114	−	42.4550i	0.0463354	−	0.0802553i
$530$	528.254			0.996705
$531$	283.716	+	137.223i	0.534306	+	0.258424i
$532$		−	1639.52i		−	3.08180i
$533$	326.576	−	565.647i	0.612714	−	1.06125i
$534$	−492.507	−	785.296i	−0.922299	−	1.47059i
$535$	−108.063	−	187.170i	−0.201986	−	0.349850i
$536$	−468.237	+	270.337i	−0.873577	+	0.504360i
$537$	−314.720	−	166.675i	−0.586070	−	0.310382i
$538$	1303.40	+	752.518i	2.42268	+	1.39873i
$539$	29.6114			0.0549377
$540$	457.736	−	1041.92i	0.847660	−	1.92947i
$541$		−	123.415i		−	0.228123i	−0.993474	−	0.114062i	$-0.963614\pi$
$541$		−	123.415i		−	0.228123i	0.993474	−	0.114062i	$-0.0363861\pi$
$542$	−346.364	−	199.974i	−0.639049	−	0.368955i
$543$	−587.496	−	311.137i	−1.08194	−	0.572997i
$544$	82.4159	−	967.740i	0.151500	−	1.77893i
$545$	640.626	−	369.866i	1.17546	−	0.678653i
$546$	859.394	+	1370.29i	1.57398	+	2.50969i
$547$	104.563	+	60.3695i	0.191157	+	0.110365i	0.592524	−	0.805553i	$-0.298131\pi$
$547$	104.563	+	60.3695i	0.191157	+	0.110365i	−0.401367	+	0.915917i	$0.631465\pi$
$548$			1917.92i			3.49985i
$549$	−30.6006	−	417.829i	−0.0557389	−	0.761073i
$550$		−	44.2360i		−	0.0804291i
$551$	348.150	−	603.014i	0.631852	−	1.09440i
$552$	49.7241	+	1359.71i	0.0900799	+	2.46324i
$553$	−342.497	−	593.223i	−0.619344	−	1.07274i
$554$	281.225	+	487.096i	0.507627	+	0.879235i
$555$	−11.5681	−	316.331i	−0.0208434	−	0.569965i
$556$	−553.006	−	319.278i	−0.994616	−	0.574242i
$557$		−	333.930i		−	0.599516i	−0.954015	−	0.299758i	$-0.903094\pi$
$557$		−	333.930i		−	0.599516i	0.954015	−	0.299758i	$-0.0969059\pi$
$558$	902.404	+	1328.41i	1.61721	+	2.38066i
$559$	1056.24			1.88952
$560$	1145.63	+	661.429i	2.04577	+	1.18112i
$561$	105.891	+	5.12964i	0.188753	+	0.00914374i
$562$	−329.781	−	571.198i	−0.586799	−	1.01637i
$563$	590.128	−	340.711i	1.04818	−	0.605170i	0.126044	−	0.992025i	$-0.459772\pi$
$563$	590.128	−	340.711i	1.04818	−	0.605170i	0.922141	+	0.386855i	$0.126439\pi$
$564$	−903.032	−	478.245i	−1.60112	−	0.847952i
$565$	−26.8742	+	46.5474i	−0.0475649	+	0.0823848i
$566$	−602.953			−1.06529
$567$	504.987	−	399.924i	0.890629	−	0.705333i
$568$			2478.13i			4.36290i
$569$	144.350	+	83.3404i	0.253690	+	0.146468i	0.621453	−	0.783452i	$-0.286543\pi$
$569$	144.350	+	83.3404i	0.253690	+	0.146468i	−0.367763	+	0.929920i	$0.619876\pi$
$570$	920.070	+	487.268i	1.61416	+	0.854856i
$571$	145.543	−	84.0296i	0.254892	−	0.147162i	−0.367110	−	0.930178i	$-0.619653\pi$
$571$	145.543	−	84.0296i	0.254892	−	0.147162i	0.622002	+	0.783015i	$0.286319\pi$
$572$	−183.570	−	317.953i	−0.320927	−	0.555861i
$573$	360.871	−	226.324i	0.629792	−	0.394981i
$574$	521.421	−	903.128i	0.908399	−	1.57339i
$575$	126.369			0.219773
$576$	298.667	+	439.662i	0.518519	+	0.763301i
$577$	−674.718			−1.16935			−0.584677	−	0.811266i	$-0.698779\pi$
$577$	−674.718			−1.16935			−0.584677	+	0.811266i	$0.698779\pi$
$578$	180.298	−	1050.86i	0.311934	−	1.81810i
$579$	18.2175	+	498.160i	0.0314638	+	0.860379i
$580$	684.118	+	1184.93i	1.17951	+	2.04298i
$581$	23.3744	+	40.4856i	0.0402313	+	0.0696827i
$582$	−1137.26	+	41.5891i	−1.95405	+	0.0714589i
$583$	−58.7773	−	33.9351i	−0.100819	−	0.0582077i
$584$	−2214.45			−3.79186
$585$	−723.352	+	52.9763i	−1.23650	+	0.0905578i
$586$	664.388			1.13377
$587$	−413.333	−	238.638i	−0.704144	−	0.406538i	0.104745	−	0.994499i	$-0.466597\pi$
$587$	−413.333	−	238.638i	−0.704144	−	0.406538i	−0.808889	+	0.587961i	$0.799931\pi$
$588$	218.230	+	347.965i	0.371139	+	0.591776i
$589$	−898.445	+	518.717i	−1.52537	+	0.880674i
$590$	−283.281	−	490.656i	−0.480137	−	0.831621i
$591$	−48.8841	+	92.3040i	−0.0827142	+	0.156183i
$592$	790.348	+	456.308i	1.33505	+	0.770790i
$593$			181.237i			0.305628i	0.988255	+	0.152814i	$0.0488335\pi$
$593$			181.237i			0.305628i	−0.988255	+	0.152814i	$0.951166\pi$
$594$	−166.916	+	122.536i	−0.281004	+	0.206290i
$595$	486.450	+	338.945i	0.817563	+	0.569656i
$596$	−616.044	−	355.673i	−1.03363	−	0.596767i
$597$	−102.872	−	54.4807i	−0.172314	−	0.0912574i
$598$	1286.31	−	742.653i	2.15103	−	1.24190i
$599$	54.6446	−	31.5491i	0.0912263	−	0.0526695i	−0.453693	−	0.891158i	$-0.649894\pi$
$599$	54.6446	−	31.5491i	0.0912263	−	0.0526695i	0.544919	+	0.838489i	$0.316560\pi$
$600$	303.480	−	190.331i	0.505800	−	0.317218i
$601$	656.668	+	379.127i	1.09263	+	0.630828i	0.934274	−	0.356555i	$-0.116049\pi$
$601$	656.668	+	379.127i	1.09263	+	0.630828i	0.158351	+	0.987383i	$0.449382\pi$
$602$	1686.43			2.80137
$603$	102.346	−	211.606i	0.169728	−	0.350922i
$604$	1802.82			2.98481
$605$	−255.843	+	443.133i	−0.422881	+	0.732452i
$606$	−860.659	+	31.4740i	−1.42023	+	0.0519373i
$607$	−848.506	+	489.885i	−1.39787	+	0.807060i	−0.994169	−	0.107832i	$-0.965609\pi$
$607$	−848.506	+	489.885i	−1.39787	+	0.807060i	−0.403699	+	0.914892i	$0.632276\pi$
$608$	−1061.29	+	612.737i	−1.74555	+	1.00779i
$609$	28.3033	+	773.955i	0.0464750	+	1.27086i
$610$	−376.571	+	652.241i	−0.617330	+	1.06925i
$611$			651.249i			1.06587i
$612$	720.113	+	1282.13i	1.17666	+	2.09498i
$613$	211.062			0.344310			0.172155	−	0.985070i	$-0.444927\pi$
$613$	211.062			0.344310			0.172155	+	0.985070i	$0.444927\pi$
$614$	−549.719	−	317.381i	−0.895308	−	0.516906i
$615$	248.452	+	396.153i	0.403987	+	0.644151i
$616$	−171.114	−	296.377i	−0.277782	−	0.481132i
$617$	−153.576	−	266.002i	−0.248908	−	0.431121i	0.714315	−	0.699824i	$-0.246738\pi$
$617$	−153.576	−	266.002i	−0.248908	−	0.431121i	−0.963223	+	0.268703i	$0.913405\pi$
$618$	1066.77	+	564.961i	1.72617	+	0.914176i
$619$	672.948	+	388.527i	1.08715	+	0.627668i	0.932817	−	0.360350i	$-0.117343\pi$
$619$	672.948	+	388.527i	1.08715	+	0.627668i	0.154336	+	0.988018i	$0.450676\pi$
$620$		−	2038.57i		−	3.28801i
$621$	−350.050	−	476.831i	−0.563688	−	0.767844i
$622$		−	1651.84i		−	2.65569i
$623$	−333.023	+	576.813i	−0.534547	+	0.925863i
$624$	978.654	−	1847.92i	1.56836	−	2.96140i
$625$	223.764	+	387.570i	0.358022	+	0.620112i
$626$	−341.254	−	591.069i	−0.545134	−	0.944199i
$627$	−71.0714	−	113.322i	−0.113352	−	0.180737i
$628$	−155.659	+	269.610i	−0.247865	+	0.429315i
$629$	335.593	+	233.832i	0.533534	+	0.371752i
$630$	−1154.92	+	84.5835i	−1.83321	+	0.134260i
$631$	1.79220			0.00284025			0.00142012	−	0.999999i	$-0.499548\pi$
$631$	1.79220			0.00284025			0.00142012	+	0.999999i	$0.499548\pi$
$632$	−891.557	+	1544.22i	−1.41069	+	2.44339i
$633$	7.63916	+	208.893i	0.0120682	+	0.330005i
$634$	−485.574	+	280.346i	−0.765889	+	0.442186i
$635$	−328.482	−	568.947i	−0.517294	−	0.895979i
$636$	−34.4043	−	940.788i	−0.0540948	−	1.47923i
$637$	130.885	−	226.700i	0.205471	−	0.355887i
$638$		−	248.952i		−	0.390207i
$639$	−605.391	−	891.184i	−0.947404	−	1.39465i
$640$			46.6922i			0.0729566i
$641$	427.808	−	740.985i	0.667407	−	1.15598i	−0.311219	−	0.950338i	$-0.600737\pi$
$641$	427.808	−	740.985i	0.667407	−	1.15598i	0.978627	−	0.205645i	$-0.0659293\pi$
$642$	−462.100	+	289.811i	−0.719782	+	0.451420i
$643$	−399.040	+	230.386i	−0.620591	+	0.358298i	−0.777099	−	0.629378i	$-0.783310\pi$
$643$	−399.040	+	230.386i	−0.620591	+	0.358298i	0.156508	+	0.987677i	$0.449976\pi$
$644$	1450.21	−	837.282i	2.25189	−	1.30013i
$645$	−353.916	+	668.271i	−0.548707	+	1.03608i
$646$	−1217.95	+	571.366i	−1.88537	+	0.884467i
$647$			695.709i			1.07529i	0.843173	+	0.537643i	$0.180685\pi$
$647$			695.709i			1.07529i	−0.843173	+	0.537643i	$0.819315\pi$
$648$	−1558.84	−	617.898i	−2.40561	−	0.953547i
$649$			72.7919i			0.112160i
$650$	−338.663	−	195.527i	−0.521020	−	0.300811i
$651$	540.047	−	1019.73i	0.829565	−	1.56640i
$652$	400.260	−	231.090i	0.613896	−	0.354433i
$653$	396.734	+	687.164i	0.607557	+	1.05232i	0.991642	+	0.129021i	$0.0411835\pi$
$653$	396.734	+	687.164i	0.607557	+	1.05232i	−0.384085	+	0.923298i	$0.625483\pi$
$654$	−991.938	−	1581.63i	−1.51673	−	2.41840i
$655$	278.778	−	482.857i	0.425615	−	0.737187i
$656$	−1348.17			−2.05514
$657$	796.359	−	540.976i	1.21211	−	0.823403i
$658$			1039.80i			1.58025i
$659$	636.913	+	367.722i	0.966484	+	0.558000i	0.898163	−	0.439664i	$-0.144902\pi$
$659$	636.913	+	367.722i	0.966484	+	0.558000i	0.0683215	+	0.997663i	$0.478236\pi$
$660$	262.674	−	9.60589i	0.397991	−	0.0145544i
$661$	−138.419	−	239.749i	−0.209409	−	0.362707i	0.742120	−	0.670267i	$-0.233821\pi$
$661$	−138.419	−	239.749i	−0.209409	−	0.362707i	−0.951528	+	0.307561i	$0.900487\pi$
$662$	−206.953	+	119.484i	−0.312617	+	0.180490i
$663$	507.318	−	788.006i	0.765185	−	1.18855i
$664$	60.8460	−	105.388i	0.0916355	−	0.158717i
$665$		−	748.083i		−	1.12494i
$666$	−796.761	+	58.3526i	−1.19634	+	0.0876165i
$667$	711.184			1.06624
$668$	−1.95989	+	3.39464i	−0.00293397	+	0.00508179i
$669$	−324.051	−	516.695i	−0.484381	−	0.772339i
$670$	−365.949	+	211.281i	−0.546193	+	0.315344i
$671$	83.8001	−	48.3820i	0.124888	−	0.0721043i
$672$	637.933	−	1204.56i	0.949304	−	1.79250i
$673$	−491.306	−	283.656i	−0.730023	−	0.421479i	0.0884073	−	0.996084i	$-0.471822\pi$
$673$	−491.306	−	283.656i	−0.730023	−	0.421479i	−0.818431	+	0.574605i	$0.805156\pi$
$674$	1175.38			1.74388
$675$	−62.6407	+	142.585i	−0.0928011	+	0.211237i
$676$	−1621.29			−2.39836
$677$	−35.9444	+	62.2575i	−0.0530936	+	0.0919609i	−0.891351	−	0.453314i	$-0.850242\pi$
$677$	−35.9444	+	62.2575i	−0.0530936	+	0.0919609i	0.838257	+	0.545275i	$0.183575\pi$
$678$	119.877	+	63.4870i	0.176810	+	0.0936386i
$679$	408.849	+	708.147i	0.602133	+	1.04293i
$680$	130.963	−	1537.79i	0.192593	−	2.26145i
$681$	396.343	+	631.963i	0.582001	+	0.927992i
$682$	−185.460	+	321.226i	−0.271935	+	0.471006i
$683$	−663.026			−0.970755			−0.485378	−	0.874305i	$-0.661318\pi$
$683$	−663.026			−0.970755			−0.485378	+	0.874305i	$0.661318\pi$
$684$	807.872	−	1670.32i	1.18110	−	2.44199i
$685$			875.112i			1.27754i
$686$	−509.857	+	883.099i	−0.743232	+	1.28732i
$687$	−1290.41	+	47.1898i	−1.87832	+	0.0686896i
$688$	−1090.10	−	1888.10i	−1.58444	−	2.74433i
$689$	−519.602	+	299.992i	−0.754139	+	0.435403i
$690$	38.8617	+	1062.68i	0.0563213	+	1.54011i
$691$	787.191	+	454.485i	1.13921	+	0.657720i	0.946234	−	0.323484i	$-0.104854\pi$
$691$	787.191	+	454.485i	1.13921	+	0.657720i	0.192971	+	0.981204i	$0.438188\pi$
$692$	2956.74			4.27274
$693$	133.939	+	64.7812i	0.193274	+	0.0934793i
$694$			17.0532i			0.0245723i
$695$	−252.327	−	145.681i	−0.363060	−	0.209613i
$696$	1707.93	−	1071.15i	2.45392	−	1.53901i
$697$	−602.056	−	51.2731i	−0.863782	−	0.0735625i
$698$	−2196.90	+	1268.38i	−3.14742	+	1.81716i
$699$	−471.430	+	890.164i	−0.674434	+	1.27348i
$700$	−381.815	−	220.441i	−0.545450	−	0.314916i
$701$			357.642i			0.510188i	0.966916	+	0.255094i	$0.0821064\pi$
$701$			357.642i			0.510188i	−0.966916	+	0.255094i	$0.917894\pi$
$702$	200.331	+	1819.50i	0.285371	+	2.59189i
$703$		−	516.089i		−	0.734123i
$704$	−61.3813	+	106.316i	−0.0871894	+	0.151016i
$705$	−412.037	−	218.215i	−0.584450	−	0.309524i
$706$	432.505	+	749.121i	0.612614	+	1.06108i
$707$	309.410	+	535.914i	0.437638	+	0.758012i
$708$	−855.380	+	536.462i	−1.20816	+	0.757714i
$709$	−265.277	−	153.158i	−0.374157	−	0.216019i	0.301116	−	0.953587i	$-0.402641\pi$
$709$	−265.277	−	153.158i	−0.374157	−	0.216019i	−0.675273	+	0.737568i	$0.735974\pi$
$710$			1936.77i			2.72785i
$711$	−56.6222	−	773.135i	−0.0796375	−	1.08739i
$712$	1733.79			2.43510
$713$	−917.649	−	529.805i	−1.28702	−	0.743064i
$714$	809.998	−	1258.15i	1.13445	−	1.76212i
$715$	−83.7597	−	145.076i	−0.117146	−	0.202904i
$716$	988.091	−	570.475i	1.38002	−	0.796752i
$717$	14.4287	+	394.554i	0.0201237	+	0.550284i
$718$	538.758	−	933.157i	0.750360	−	1.29966i
$719$	−729.214			−1.01421			−0.507103	−	0.861885i	$-0.669284\pi$
$719$	−729.214			−1.01421			−0.507103	+	0.861885i	$0.669284\pi$
$720$	841.235	+	1238.37i	1.16838	+	1.71995i
$721$		−	867.362i		−	1.20300i
$722$	316.624	+	182.803i	0.438538	+	0.253190i
$723$	−88.9407	+	55.7802i	−0.123016	+	0.0771510i
$724$	1844.50	−	1064.92i	2.54765	−	1.47089i
$725$	−93.6209	−	162.156i	−0.129132	−	0.223664i
$726$	1141.24	+	604.399i	1.57195	+	0.832505i
$727$	8.98580	−	15.5639i	0.0123601	−	0.0214083i	−0.859779	−	0.510666i	$-0.829399\pi$
$727$	8.98580	−	15.5639i	0.0123601	−	0.0214083i	0.872139	+	0.489258i	$0.162732\pi$
$728$	−3025.35			−4.15570
$729$	711.537	−	158.606i	0.976046	−	0.217566i
$730$	−1730.69			−2.37081
$731$	−414.998	−	884.630i	−0.567713	−	1.21016i
$732$	1186.13	+	628.172i	1.62039	+	0.858158i
$733$	−502.060	−	869.594i	−0.684939	−	1.18635i	−0.973456	−	0.228875i	$-0.926495\pi$
$733$	−502.060	−	869.594i	−0.684939	−	1.18635i	0.288517	−	0.957475i	$-0.406838\pi$
$734$	104.121	+	180.344i	0.141855	+	0.245700i
$735$	99.5744	+	158.770i	0.135475	+	0.216013i
$736$	−1083.98	−	625.834i	−1.47279	−	0.850318i
$737$	54.2908			0.0736646
$738$	976.234	−	663.167i	1.32281	−	0.898600i
$739$	−116.839			−0.158104			−0.0790518	−	0.996871i	$-0.525189\pi$
$739$	−116.839			−0.158104			−0.0790518	+	0.996871i	$0.525189\pi$
$740$	878.252	+	507.059i	1.18683	+	0.685215i
$741$	−1181.72	+	43.2150i	−1.59476	+	0.0583198i
$742$	−829.612	+	478.977i	−1.11808	+	0.645521i
$743$	196.721	+	340.731i	0.264766	+	0.458588i	0.967502	−	0.252862i	$-0.0813719\pi$
$743$	196.721	+	340.731i	0.264766	+	0.458588i	−0.702736	+	0.711450i	$0.748039\pi$
$744$	−3001.73	+	109.772i	−4.03458	+	0.147543i
$745$	−281.090	−	162.287i	−0.377302	−	0.217835i
$746$		−	1916.84i		−	2.56950i
$747$	3.86429	+	52.7640i	0.00517308	+	0.0706346i
$748$	−194.169	+	278.669i	−0.259584	+	0.372552i
$749$	339.420	+	195.964i	0.453164	+	0.261635i
$750$	1265.19	−	793.475i	1.68691	−	1.05797i
$751$	178.598	−	103.114i	0.237814	−	0.137302i	−0.376358	−	0.926475i	$-0.622824\pi$
$751$	178.598	−	103.114i	0.237814	−	0.137302i	0.614172	+	0.789172i	$0.289490\pi$
$752$	1164.15	−	672.123i	1.54807	−	0.893780i
$753$	103.404	+	54.7627i	0.137323	+	0.0727261i
$754$	−1905.93	−	1100.39i	−2.52776	−	1.45941i
$755$	822.596			1.08953
$756$	225.857	+	2051.34i	0.298752	+	2.71342i
$757$	−133.014			−0.175712			−0.0878558	−	0.996133i	$-0.528001\pi$
$757$	−133.014			−0.175712			−0.0878558	+	0.996133i	$0.528001\pi$
$758$	85.5829	−	148.234i	0.112906	−	0.195559i
$759$	63.9425	−	120.737i	0.0842457	−	0.159074i
$760$	−1686.44	+	973.669i	−2.21901	+	1.28114i
$761$	874.074	−	504.647i	1.14859	−	0.663137i	0.200044	−	0.979787i	$-0.435891\pi$
$761$	874.074	−	504.647i	1.14859	−	0.663137i	0.948542	+	0.316650i	$0.102558\pi$
$762$	−1404.66	+	880.951i	−1.84339	+	1.15610i
$763$	−670.727	+	1161.73i	−0.879066	+	1.52259i
$764$			1364.70i			1.78625i
$765$	328.575	+	585.012i	0.429509	+	0.764721i
$766$	−1140.43			−1.48881
$767$	557.282	+	321.747i	0.726574	+	0.419488i
$768$	825.972	−	30.2055i	1.07548	−	0.0393301i
$769$	−7.11279	−	12.3197i	−0.00924941	−	0.0160204i	0.861364	−	0.507989i	$-0.169611\pi$
$769$	−7.11279	−	12.3197i	−0.00924941	−	0.0160204i	−0.870613	+	0.491968i	$0.836278\pi$
$770$	−133.733	−	231.633i	−0.173679	−	0.300822i
$771$	22.3564	+	611.338i	0.0289967	+	0.792916i
$772$	−1383.08	−	798.519i	−1.79155	−	1.03435i
$773$			196.684i			0.254442i	0.991874	+	0.127221i	$0.0406057\pi$
$773$			196.684i			0.254442i	−0.991874	+	0.127221i	$0.959394\pi$
$774$	1718.11	+	830.986i	2.21978	+	1.07363i
$775$			278.976i			0.359969i
$776$	1064.28	−	1843.38i	1.37149	−	2.37549i
$777$	304.990	+	486.302i	0.392522	+	0.625871i
$778$	1260.37	+	2183.02i	1.62001	+	2.80594i
$779$	381.200	+	660.257i	0.489345	+	0.847570i
$780$	1087.50	−	2053.44i	1.39423	−	2.63262i
$781$	124.419	−	215.499i	0.159307	−	0.275927i
$782$	−1127.39	−	785.532i	−1.44167	−	1.00452i
$783$	−352.531	+	802.443i	−0.450231	+	1.02483i
$784$	−540.321			−0.689185
$785$	−71.0244	+	123.018i	−0.0904770	+	0.156711i
$786$	−1243.54	−	658.579i	−1.58212	−	0.837887i
$787$	590.306	−	340.814i	0.750072	−	0.433054i	−0.0756481	−	0.997135i	$-0.524103\pi$
$787$	590.306	−	340.814i	0.750072	−	0.433054i	0.825720	+	0.564080i	$0.190769\pi$
$788$	−167.314	−	289.797i	−0.212328	−	0.367762i
$789$	464.620	−	291.392i	0.588872	−	0.369318i
$790$	−696.793	+	1206.88i	−0.882017	+	1.52770i
$791$		−	97.4690i		−	0.123223i
$792$	−28.2888	−	386.262i	−0.0357181	−	0.487705i
$793$		−	855.411i		−	1.07870i
$794$	−13.7453	+	23.8075i	−0.0173114	+	0.0299843i
$795$	−15.6981	−	429.265i	−0.0197460	−	0.539956i
$796$	322.975	−	186.469i	0.405747	−	0.234258i
$797$	599.475	−	346.107i	0.752164	−	0.434262i	−0.0743113	−	0.997235i	$-0.523676\pi$
$797$	599.475	−	346.107i	0.752164	−	0.434262i	0.826475	+	0.562973i	$0.190343\pi$
$798$	−1886.76	+	68.9983i	−2.36437	+	0.0864641i
$799$	545.438	−	255.876i	0.682651	−	0.320246i
$800$			329.541i			0.411927i
$801$	−623.504	+	423.553i	−0.778407	+	0.528781i
$802$		−	403.479i		−	0.503091i
$803$	192.569	+	111.180i	0.239813	+	0.138456i
$804$	400.112	+	637.973i	0.497652	+	0.793499i
$805$	661.706	−	382.036i	0.821996	−	0.474579i
$806$	1639.50	+	2839.70i	2.03412	+	3.52320i
$807$	572.772	−	1081.52i	0.709754	−	1.34017i
$808$	805.428	−	1395.04i	0.996816	−	1.72654i
$809$	798.159			0.986599			0.493299	−	0.869860i	$-0.335791\pi$
$809$	798.159			0.986599			0.493299	+	0.869860i	$0.335791\pi$
$810$	−1218.30	−	482.916i	−1.50408	−	0.596193i
$811$			1154.48i			1.42352i	0.702422	+	0.711761i	$0.252102\pi$
$811$			1154.48i			1.42352i	−0.702422	+	0.711761i	$0.747898\pi$
$812$	−2148.79	−	1240.60i	−2.64629	−	1.52784i
$813$	−152.208	+	287.402i	−0.187218	+	0.353508i
$814$	−92.2600	−	159.799i	−0.113342	−	0.196313i
$815$	182.631	−	105.442i	0.224088	−	0.129377i
$816$	−1932.19	−	93.6008i	−2.36788	−	0.114707i
$817$	−616.454	+	1067.73i	−0.754534	+	1.30689i
$818$			2188.45i			2.67536i
$819$	1087.98	−	739.074i	1.32842	−	0.902410i
$820$	−1498.12			−1.82698
$821$	−375.955	+	651.174i	−0.457924	+	0.793147i	−0.998851	−	0.0479221i	$-0.984740\pi$
$821$	−375.955	+	651.174i	−0.457924	+	0.793147i	0.540927	+	0.841069i	$0.318073\pi$
$822$	2207.15	−	80.7146i	2.68510	−	0.0981930i
$823$	518.448	−	299.326i	0.629949	−	0.363701i	−0.150783	−	0.988567i	$-0.548180\pi$
$823$	518.448	−	299.326i	0.629949	−	0.363701i	0.780732	+	0.624865i	$0.214846\pi$
$824$	−1955.34	+	1128.92i	−2.37299	+	1.37004i
$825$	−35.9466	+	1.31456i	−0.0435717	+	0.00159340i
$826$	889.773	+	513.711i	1.07721	+	0.621926i
$827$	−33.0840			−0.0400049			−0.0200024	−	0.999800i	$-0.506367\pi$
$827$	−33.0840			−0.0400049			−0.0200024	+	0.999800i	$0.506367\pi$
$828$	1890.03	−	138.421i	2.28265	−	0.167175i
$829$	−1422.44			−1.71585			−0.857923	−	0.513778i	$-0.828245\pi$
$829$	−1422.44			−1.71585			−0.857923	+	0.513778i	$0.828245\pi$
$830$	47.5540	−	82.3659i	0.0572939	−	0.0992360i
$831$	387.463	−	243.002i	0.466261	−	0.292421i
$832$	542.622	+	939.849i	0.652190	+	1.12963i
$833$	−241.292	−	20.5492i	−0.289666	−	0.0246689i
$834$	−344.154	+	649.839i	−0.412654	+	0.779183i
$835$	−0.894264	+	1.54891i	−0.00107098	+	0.00185498i
$836$	428.548			0.512617
$837$	1052.66	−	772.780i	1.25766	−	0.923273i
$838$			881.852i			1.05233i
$839$	−411.373	+	712.519i	−0.490314	+	0.849248i	−0.999938	−	0.0111488i	$-0.996451\pi$
$839$	−411.373	+	712.519i	−0.490314	+	0.849248i	0.509624	+	0.860397i	$0.329784\pi$
$840$	1013.71	−	1914.10i	1.20679	−	2.27869i
$841$	−106.382	−	184.258i	−0.126494	−	0.219094i
$842$	513.076	−	296.225i	0.609354	−	0.351811i
$843$	−454.361	+	284.958i	−0.538981	+	0.338028i
$844$	−579.966	−	334.843i	−0.687163	−	0.396734i
$845$	−739.766			−0.875462
$846$	−512.363	+	1059.34i	−0.605630	+	1.25217i
$847$		−	927.909i		−	1.09552i
$848$	1072.51	+	619.215i	1.26476	+	0.730207i
$849$	17.9179	+	489.966i	0.0211047	+	0.577110i
$850$	−30.6981	+	360.462i	−0.0361154	+	0.424073i
$851$	456.499	−	263.560i	0.536427	−	0.309706i
$852$	3449.28	−	126.139i	4.04845	−	0.148050i
$853$	−375.231	−	216.640i	−0.439896	−	0.253974i	0.263658	−	0.964616i	$-0.415071\pi$
$853$	−375.231	−	216.640i	−0.439896	−	0.253974i	−0.703553	+	0.710642i	$0.748404\pi$
$854$		−	1365.77i		−	1.59927i
$855$	368.618	−	762.139i	0.431132	−	0.891390i
$856$		−	1020.23i		−	1.19186i
$857$	−316.535	+	548.254i	−0.369352	+	0.639736i	−0.989464	−	0.144777i	$-0.953754\pi$
$857$	−316.535	+	548.254i	−0.369352	+	0.639736i	0.620112	+	0.784513i	$0.287087\pi$
$858$	−358.176	+	224.634i	−0.417454	+	0.261811i
$859$	724.169	+	1254.30i	0.843037	+	1.46018i	0.887315	+	0.461164i	$0.152568\pi$
$859$	724.169	+	1254.30i	0.843037	+	1.46018i	−0.0442773	+	0.999019i	$0.514099\pi$
$860$	−1211.34	−	2098.10i	−1.40853	−	2.43965i
$861$	−749.387	−	396.875i	−0.870368	−	0.460946i
$862$	−1131.01	−	652.988i	−1.31208	−	0.757527i
$863$			564.570i			0.654195i	0.944991	+	0.327098i	$0.106071\pi$
$863$			564.570i			0.654195i	−0.944991	+	0.327098i	$0.893929\pi$
$864$	1243.46	−	912.849i	1.43919	−	1.05654i
$865$	1349.11			1.55966
$866$	−758.168	−	437.728i	−0.875482	−	0.505460i
$867$	−859.301	−	115.284i	−0.991120	−	0.132968i
$868$	1848.40	+	3201.53i	2.12950	+	3.68840i
$869$	155.060	−	89.5242i	0.178436	−	0.103020i
$870$	1334.83	−	837.153i	1.53428	−	0.962244i
$871$	239.970	−	415.641i	0.275511	−	0.477200i
$872$	3491.95			4.00453
$873$	67.5915	+	922.912i	0.0774244	+	1.05717i
$874$			1733.74i			1.98368i
$875$	−929.299	−	536.531i	−1.06206	−	0.613178i
$876$	112.717	+	3082.26i	0.128673	+	3.51857i
$877$	−789.612	+	455.883i	−0.900356	+	0.519821i	−0.877316	−	0.479914i	$-0.840668\pi$
$877$	−789.612	+	455.883i	−0.900356	+	0.519821i	−0.0230400	+	0.999735i	$0.507335\pi$
$878$	−835.659	−	1447.40i	−0.951775	−	1.64852i
$879$	−19.7435	−	539.889i	−0.0224614	−	0.614208i
$880$	−172.889	+	299.452i	−0.196464	+	0.340286i
$881$	1529.75			1.73638			0.868188	−	0.496236i	$-0.165285\pi$
$881$	1529.75			1.73638			0.868188	+	0.496236i	$0.165285\pi$
$882$	391.255	−	265.784i	0.443600	−	0.301342i
$883$	229.642			0.260070			0.130035	−	0.991509i	$-0.458491\pi$
$883$	229.642			0.260070			0.130035	+	0.991509i	$0.458491\pi$
$884$	1275.19	+	2718.26i	1.44253	+	3.07496i
$885$	−390.295	+	244.778i	−0.441011	+	0.276585i
$886$	1066.73	+	1847.62i	1.20398	+	2.08535i
$887$	−197.974	−	342.901i	−0.223195	−	0.386586i	0.732581	−	0.680680i	$-0.238315\pi$
$887$	−197.974	−	342.901i	−0.223195	−	0.386586i	−0.955776	+	0.294094i	$0.904982\pi$
$888$	699.337	−	1320.50i	0.787542	−	1.48705i
$889$	1031.75	+	595.680i	1.16057	+	0.670056i
$890$	1355.04			1.52251
$891$	104.535	+	131.997i	0.117323	+	0.148144i
$892$	1953.97			2.19055
$893$	−658.333	−	380.089i	−0.737215	−	0.425631i
$894$	−383.384	+	723.914i	−0.428841	+	0.809748i
$895$	450.848	−	260.297i	0.503741	−	0.290835i
$896$	−42.3366	−	73.3292i	−0.0472507	−	0.0818406i
$897$	−641.713	−	1023.20i	−0.715400	−	1.14069i
$898$	1393.33	+	804.439i	1.55159	+	0.895811i
$899$			1570.03i			1.74641i
$900$	−280.367	−	412.722i	−0.311519	−	0.458580i
$901$	455.404	+	317.313i	0.505442	+	0.352179i
$902$	236.065	+	136.292i	0.261713	+	0.151100i
$903$	−50.1153	−	1370.41i	−0.0554987	−	1.51762i
$904$	−219.730	+	126.861i	−0.243064	+	0.140333i
$905$	841.611	−	485.904i	0.929957	−	0.536911i
$906$	−75.8709	−	2074.70i	−0.0837427	−	2.28995i
$907$	−715.022	−	412.818i	−0.788337	−	0.455147i	0.0510394	−	0.998697i	$-0.483747\pi$
$907$	−715.022	−	412.818i	−0.788337	−	0.455147i	−0.839377	+	0.543550i	$0.817080\pi$
$908$	−2389.88			−2.63202
$909$	51.1522	+	698.445i	0.0562731	+	0.768367i
$910$	−2364.45			−2.59830
$911$	620.749	−	1075.17i	0.681393	−	1.18021i	−0.293162	−	0.956063i	$-0.594708\pi$
$911$	620.749	−	1075.17i	0.681393	−	1.18021i	0.974556	−	0.224145i	$-0.0719591\pi$
$912$	1296.84	+	2067.80i	1.42198	+	2.26732i
$913$	−10.5824	+	6.10975i	−0.0115908	+	0.00669195i
$914$	−183.595	+	105.998i	−0.200869	+	0.115972i
$915$	541.208	+	286.623i	0.591485	+	0.313250i
$916$	2068.45	−	3582.65i	2.25813	−	3.91119i
$917$			1011.09i			1.10261i
$918$	1445.17	−	882.667i	1.57426	−	0.961511i
$919$	754.747			0.821269			0.410635	−	0.911800i	$-0.365307\pi$
$919$	754.747			0.821269			0.410635	+	0.911800i	$0.365307\pi$
$920$	−1722.49	−	994.481i	−1.87227	−	1.08096i
$921$	−241.571	+	456.139i	−0.262292	+	0.495265i
$922$	−123.606	−	214.092i	−0.134063	−	0.232204i
$923$	−1099.88	−	1905.05i	−1.19164	−	2.06398i
$924$	−403.814	+	253.257i	−0.437028	+	0.274087i
$925$	−120.188	−	69.3905i	−0.129933	−	0.0750168i
$926$			1648.92i			1.78069i
$927$	427.392	−	883.659i	0.461049	−	0.953246i
$928$			1854.60i			1.99849i
$929$	−556.423	+	963.752i	−0.598948	+	1.03741i	0.394029	+	0.919098i	$0.371081\pi$
$929$	−556.423	+	963.752i	−0.598948	+	1.03741i	−0.992977	+	0.118310i	$0.962252\pi$
$930$	−2345.99	+	85.7920i	−2.52257	+	0.0922495i
$931$	152.777	+	264.618i	0.164100	+	0.284229i
$932$	−1613.55	−	2794.75i	−1.73128	−	2.99866i
$933$	−1342.30	+	49.0875i	−1.43870	+	0.0526126i
$934$	866.349	−	1500.56i	0.927569	−	1.60660i
$935$	−88.5957	+	127.151i	−0.0947548	+	0.135991i
$936$	−3082.19	−	1490.74i	−3.29294	−	1.59267i
$937$	−1172.18			−1.25099			−0.625496	−	0.780228i	$-0.715103\pi$
$937$	−1172.18			−1.25099			−0.625496	+	0.780228i	$0.715103\pi$
$938$	383.144	−	663.624i	0.408469	−	0.707489i
$939$	−470.168	+	294.871i	−0.500711	+	0.314027i
$940$	1293.63	−	746.877i	1.37620	−	0.794550i
$941$	−194.242	−	336.437i	−0.206421	−	0.357531i	0.744164	−	0.667997i	$-0.232848\pi$
$941$	−194.242	−	336.437i	−0.206421	−	0.357531i	−0.950584	+	0.310466i	$0.899515\pi$
$942$	316.819	+	167.787i	0.336325	+	0.178118i
$943$	−389.348	+	674.370i	−0.412882	+	0.715132i
$944$		−	1328.24i		−	1.40703i
$945$	103.054	+	935.991i	0.109052	+	0.990467i
$946$			440.809i			0.465971i
$947$	153.874	−	266.517i	0.162485	−	0.281433i	−0.773274	−	0.634072i	$-0.781382\pi$
$947$	153.874	−	266.517i	0.162485	−	0.281433i	0.935759	+	0.352639i	$0.114716\pi$
$948$	2194.76	+	1162.35i	2.31515	+	1.22610i
$949$	1702.35	−	982.852i	1.79384	−	1.03567i
$950$	395.308	−	228.231i	0.416113	−	0.240243i
$951$	242.242	+	386.251i	0.254723	+	0.406153i
$952$	1188.66	+	2533.81i	1.24859	+	2.66156i
$953$		−	1076.46i		−	1.12955i	−0.825244	−	0.564777i	$-0.808962\pi$
$953$		−	1076.46i		−	1.12955i	0.825244	−	0.564777i	$-0.191038\pi$
$954$	−1081.22	+	79.1852i	−1.13335	+	0.0830034i
$955$			622.686i			0.652027i
$956$	−1095.43	−	632.445i	−1.14584	−	0.661554i
$957$	−202.301	+	7.39809i	−0.211391	+	0.00773050i
$958$	−1709.31	+	986.871i	−1.78425	+	1.03014i
$959$	−793.479	−	1374.35i	−0.827402	−	1.43310i
$960$	−776.448	+	28.3944i	−0.808800	+	0.0295775i
$961$	689.110	−	1193.57i	0.717075	−	1.24201i
$962$	−1631.19			−1.69562
$963$	249.236	+	366.895i	0.258812	+	0.380992i
$964$		−	336.345i		−	0.348905i
$965$	−631.073	−	364.350i	−0.653961	−	0.377565i
$966$	−1024.58	−	1633.68i	−1.06064	−	1.69118i
$967$	−484.747	−	839.607i	−0.501290	−	0.868260i	−0.999999	−	0.00149021i	$-0.999526\pi$
$967$	−484.747	−	839.607i	−0.501290	−	0.868260i	0.498709	−	0.866770i	$-0.333808\pi$
$968$	−2091.84	+	1207.72i	−2.16099	+	1.24765i
$969$	500.492	+	972.740i	0.516503	+	1.00386i
$970$	831.781	−	1440.69i	0.857506	−	1.48524i
$971$			936.089i			0.964047i	0.876158	+	0.482023i	$0.160098\pi$
$971$			936.089i			0.964047i	−0.876158	+	0.482023i	$0.839902\pi$
$972$	−780.699	+	2201.18i	−0.803188	+	2.26459i
$973$	528.366			0.543027
$974$	−1324.80	+	2294.61i	−1.36016	+	2.35587i
$975$	−148.823	+	281.012i	−0.152639	+	0.288217i
$976$	−1529.10	+	882.829i	−1.56670	+	0.904538i
$977$	−855.704	+	494.041i	−0.875848	+	0.505671i	−0.869287	−	0.494307i	$-0.835422\pi$
$977$	−855.704	+	494.041i	−0.875848	+	0.505671i	−0.00656104	+	0.999978i	$0.502088\pi$
$978$	−282.784	−	450.896i	−0.289146	−	0.461039i
$979$	−150.771	−	87.0477i	−0.154005	−	0.0889149i
$980$	−600.416			−0.612669
$981$	−1255.77	+	853.061i	−1.28010	+	0.869583i
$982$	−2374.29			−2.41781
$983$	−368.129	+	637.617i	−0.374495	+	0.648644i	−0.990251	−	0.139292i	$-0.955517\pi$
$983$	−368.129	+	637.617i	−0.374495	+	0.648644i	0.615756	+	0.787937i	$0.288851\pi$
$984$	80.6704	+	2205.94i	0.0819821	+	2.24181i
$985$	−76.3425	−	132.229i	−0.0775051	−	0.134243i
$986$	−172.764	+	2028.61i	−0.175217	+	2.05742i
$987$	844.955	−	30.8997i	0.856084	−	0.0313067i
$988$	1894.22	−	3280.89i	1.91723	−	3.32074i
$989$	−1259.26			−1.27327
$990$	−22.1090	−	301.882i	−0.0223323	−	0.304931i
$991$			1950.49i			1.96820i	0.177608	+	0.984101i	$0.443164\pi$
$991$			1950.49i			1.96820i	−0.177608	+	0.984101i	$0.556836\pi$
$992$	1381.61	−	2393.01i	1.39275	−	2.41231i
$993$	103.244	+	164.621i	0.103972	+	0.165782i
$994$	−1756.10	−	3041.66i	−1.76670	−	3.06002i
$995$	147.367	−	85.0827i	0.148108	−	0.0855102i
$996$	−149.786	−	79.3264i	−0.150387	−	0.0796450i
$997$	−531.571	−	306.903i	−0.533171	−	0.307826i	0.209136	−	0.977887i	$-0.432935\pi$
$997$	−531.571	−	306.903i	−0.533171	−	0.307826i	−0.742307	+	0.670060i	$0.766268\pi$
$998$	1941.57			1.94546
$999$	71.0952	+	645.723i	0.0711664	+	0.646369i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.3.i.a.101.34	yes	68
3.2	odd	2		459.3.i.a.305.2		68
9.4	even	3		459.3.i.a.152.1		68
9.5	odd	6	inner	153.3.i.a.50.33	✓	68
17.16	even	2	inner	153.3.i.a.101.33	yes	68
51.50	odd	2		459.3.i.a.305.1		68
153.50	odd	6	inner	153.3.i.a.50.34	yes	68
153.67	even	6		459.3.i.a.152.2		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.i.a.50.33	✓	68	9.5	odd	6	inner
153.3.i.a.50.34	yes	68	153.50	odd	6	inner
153.3.i.a.101.33	yes	68	17.16	even	2	inner
153.3.i.a.101.34	yes	68	1.1	even	1	trivial
459.3.i.a.152.1		68	9.4	even	3
459.3.i.a.152.2		68	153.67	even	6
459.3.i.a.305.1		68	51.50	odd	2
459.3.i.a.305.2		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+(3.19506 + 1.84467i) q^{2} +(1.40405 - 2.65116i) q^{3} +(4.80561 + 8.32355i) q^{4} +(2.19271 + 3.79789i) q^{5} +(9.37654 - 5.88060i) q^{6} +(-6.88722 - 3.97634i) q^{7} +20.7016i q^{8} +(-5.05728 - 7.44472i) q^{9} +16.1793i q^{10} +(1.03936 - 1.80023i) q^{11} +(28.8144 - 1.05373i) q^{12} +(-9.18814 - 15.9143i) q^{13} +(-14.6700 - 25.4093i) q^{14} +(13.1475 - 0.480799i) q^{15} +(-18.9653 + 32.8488i) q^{16} +(-9.71863 + 13.9481i) q^{17} +(-2.42528 - 33.1153i) q^{18} +21.4499 q^{19} +(-21.0746 + 36.5023i) q^{20} +(-20.2119 + 12.6761i) q^{21} +(6.64164 - 3.83455i) q^{22} +(10.9542 + 18.9732i) q^{23} +(54.8834 + 29.0662i) q^{24} +(2.88404 - 4.99530i) q^{25} -67.7963i q^{26} +(-26.8378 + 2.95489i) q^{27} -76.4348i q^{28} +(16.2309 - 28.1127i) q^{29} +(42.8939 + 22.7166i) q^{30} +(-41.8857 + 24.1827i) q^{31} +(-49.4777 + 28.5660i) q^{32} +(-3.31337 - 5.28312i) q^{33} +(-56.7811 + 26.6372i) q^{34} -34.8758i q^{35} +(37.6632 - 77.8710i) q^{36} -24.0602i q^{37} +(68.5337 + 39.5680i) q^{38} +(-55.0920 + 2.01469i) q^{39} +(-78.6225 + 45.3927i) q^{40} +(17.7716 + 30.7814i) q^{41} +(-87.9615 + 3.21672i) q^{42} +(-28.7393 + 49.7779i) q^{43} +19.9790 q^{44} +(17.1851 - 35.5311i) q^{45} +80.8274i q^{46} +(-30.6916 - 17.7198i) q^{47} +(60.4592 + 96.4013i) q^{48} +(7.12251 + 12.3365i) q^{49} +(18.4294 - 10.6402i) q^{50} +(23.3331 + 45.3494i) q^{51} +(88.3091 - 152.956i) q^{52} -32.6500i q^{53} +(-91.1992 - 40.0658i) q^{54} +9.11607 q^{55} +(82.3167 - 142.577i) q^{56} +(30.1167 - 56.8671i) q^{57} +(103.717 - 59.8811i) q^{58} +(-30.3262 + 17.5088i) q^{59} +(67.1835 + 107.123i) q^{60} +(40.3133 + 23.2749i) q^{61} -178.437 q^{62} +(5.22788 + 71.3829i) q^{63} -59.0568 q^{64} +(40.2939 - 69.7910i) q^{65} +(-0.840807 - 22.9919i) q^{66} +(13.0587 + 22.6183i) q^{67} +(-162.801 - 13.8647i) q^{68} +(65.6812 - 2.40194i) q^{69} +(64.3343 - 111.430i) q^{70} +119.707 q^{71} +(154.118 - 104.694i) q^{72} +106.970i q^{73} +(44.3831 - 76.8737i) q^{74} +(-9.19400 - 14.6597i) q^{75} +(103.080 + 178.539i) q^{76} +(-14.3166 + 8.26569i) q^{77} +(-179.739 - 95.1894i) q^{78} +(74.5942 + 43.0670i) q^{79} -166.341 q^{80} +(-29.8478 + 75.3001i) q^{81} +131.131i q^{82} +(-5.09082 - 2.93919i) q^{83} +(-202.641 - 107.318i) q^{84} +(-74.2833 - 6.32621i) q^{85} +(-183.647 + 106.029i) q^{86} +(-51.7422 - 82.5022i) q^{87} +(37.2676 + 21.5165i) q^{88} -83.7512i q^{89} +(120.450 - 81.8233i) q^{90} +146.141i q^{91} +(-105.283 + 182.356i) q^{92} +(5.30258 + 144.999i) q^{93} +(-65.3744 - 113.232i) q^{94} +(47.0334 + 81.4643i) q^{95} +(6.26370 + 171.281i) q^{96} +(-89.0451 - 51.4102i) q^{97} +52.5547i q^{98} +(-18.6585 + 1.36650i) 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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