LMFDB - Embedded newform 60.3.l.a.23.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,3,Mod(23,60)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("60.23");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	60.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.63488158616$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.20
Character	$\chi$	$=$	60.23
Dual form			60.3.l.a.47.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.99497 + 0.141758i) q^{2} +(-2.17477 + 2.06649i) q^{3} +(3.95981 + 0.565605i) q^{4} +(3.07600 + 3.94185i) q^{5} +(-4.63154 + 3.81429i) q^{6} +(-5.18766 - 5.18766i) q^{7} +(7.81952 + 1.68970i) q^{8} +(0.459255 - 8.98827i) q^{9} +O(q^{10})$	\(q+(1.99497 + 0.141758i) q^{2} +(-2.17477 + 2.06649i) q^{3} +(3.95981 + 0.565605i) q^{4} +(3.07600 + 3.94185i) q^{5} +(-4.63154 + 3.81429i) q^{6} +(-5.18766 - 5.18766i) q^{7} +(7.81952 + 1.68970i) q^{8} +(0.459255 - 8.98827i) q^{9} +(5.57774 + 8.29993i) q^{10} +7.14796 q^{11} +(-9.78049 + 6.95284i) q^{12} +(-7.93751 - 7.93751i) q^{13} +(-9.61384 - 11.0846i) q^{14} +(-14.8354 - 2.21611i) q^{15} +(15.3602 + 4.47938i) q^{16} +(-16.5858 - 16.5858i) q^{17} +(2.19036 - 17.8662i) q^{18} -12.1545 q^{19} +(9.95085 + 17.3488i) q^{20} +(22.0022 + 0.561734i) q^{21} +(14.2600 + 1.01328i) q^{22} +(11.0852 + 11.0852i) q^{23} +(-20.4974 + 12.4842i) q^{24} +(-6.07643 + 24.2503i) q^{25} +(-14.7099 - 16.9603i) q^{26} +(17.5754 + 20.4965i) q^{27} +(-17.6080 - 23.4763i) q^{28} +26.1010 q^{29} +(-29.2820 - 6.52411i) q^{30} -8.74184i q^{31} +(30.0081 + 11.1137i) q^{32} +(-15.5452 + 14.7712i) q^{33} +(-30.7369 - 35.4392i) q^{34} +(4.49175 - 36.4063i) q^{35} +(6.90238 - 35.3321i) q^{36} +(-26.7167 + 26.7167i) q^{37} +(-24.2478 - 1.72299i) q^{38} +(33.6650 + 0.859495i) q^{39} +(17.3923 + 36.0209i) q^{40} +35.4164i q^{41} +(43.8141 + 4.23963i) q^{42} +(24.6907 - 24.6907i) q^{43} +(28.3045 + 4.04292i) q^{44} +(36.8431 - 25.8376i) q^{45} +(20.5431 + 23.6860i) q^{46} +(-58.6014 + 58.6014i) q^{47} +(-42.6615 + 22.0000i) q^{48} +4.82369i q^{49} +(-15.5600 + 47.5172i) q^{50} +(70.3445 + 1.79595i) q^{51} +(-26.9415 - 35.9205i) q^{52} +(-20.4453 + 20.4453i) q^{53} +(32.1568 + 43.3813i) q^{54} +(21.9871 + 28.1762i) q^{55} +(-31.7994 - 49.3306i) q^{56} +(26.4332 - 25.1171i) q^{57} +(52.0707 + 3.70002i) q^{58} -59.4125i q^{59} +(-57.4919 - 17.1663i) q^{60} +7.42905 q^{61} +(1.23923 - 17.4397i) q^{62} +(-49.0106 + 44.2457i) q^{63} +(58.2898 + 26.4253i) q^{64} +(6.87272 - 55.7043i) q^{65} +(-33.1061 + 27.2644i) q^{66} +(-35.8479 - 35.8479i) q^{67} +(-56.2954 - 75.0574i) q^{68} +(-47.0150 - 1.20033i) q^{69} +(14.1218 - 71.9927i) q^{70} -46.2359 q^{71} +(18.7786 - 69.5080i) q^{72} +(10.6280 + 10.6280i) q^{73} +(-57.0864 + 49.5118i) q^{74} +(-36.8981 - 65.2957i) q^{75} +(-48.1294 - 6.87464i) q^{76} +(-37.0812 - 37.0812i) q^{77} +(67.0389 + 6.48695i) q^{78} -68.3530 q^{79} +(29.5909 + 74.3262i) q^{80} +(-80.5782 - 8.25582i) q^{81} +(-5.02056 + 70.6547i) q^{82} +(76.6461 + 76.6461i) q^{83} +(86.8069 + 14.6689i) q^{84} +(14.3608 - 116.396i) q^{85} +(52.7574 - 45.7572i) q^{86} +(-56.7637 + 53.9374i) q^{87} +(55.8936 + 12.0779i) q^{88} +41.0916 q^{89} +(77.1636 - 46.3225i) q^{90} +82.3543i q^{91} +(37.6253 + 50.1649i) q^{92} +(18.0649 + 19.0115i) q^{93} +(-125.215 + 108.601i) q^{94} +(-37.3872 - 47.9112i) q^{95} +(-88.2270 + 37.8418i) q^{96} +(81.7315 - 81.7315i) q^{97} +(-0.683795 + 9.62311i) q^{98} +(3.28274 - 64.2478i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{6}+O(q^{10}) $ 40 * q - 4 * q^6	$ 40 q - 4 q^{6} - 12 q^{10} - 20 q^{12} - 8 q^{13} - 36 q^{16} - 24 q^{18} - 24 q^{21} - 76 q^{22} - 8 q^{25} - 84 q^{28} + 68 q^{30} - 40 q^{33} + 172 q^{36} - 40 q^{37} + 104 q^{40} + 236 q^{42} - 104 q^{45} + 240 q^{46} + 196 q^{48} + 304 q^{52} - 72 q^{57} + 180 q^{58} - 284 q^{60} + 48 q^{61} - 552 q^{66} - 372 q^{70} - 600 q^{72} + 104 q^{73} - 736 q^{76} - 408 q^{78} + 72 q^{81} - 720 q^{82} + 216 q^{85} - 580 q^{88} + 528 q^{90} + 368 q^{93} + 884 q^{96} + 72 q^{97}+O(q^{100}) $ 40 * q - 4 * q^6 - 12 * q^10 - 20 * q^12 - 8 * q^13 - 36 * q^16 - 24 * q^18 - 24 * q^21 - 76 * q^22 - 8 * q^25 - 84 * q^28 + 68 * q^30 - 40 * q^33 + 172 * q^36 - 40 * q^37 + 104 * q^40 + 236 * q^42 - 104 * q^45 + 240 * q^46 + 196 * q^48 + 304 * q^52 - 72 * q^57 + 180 * q^58 - 284 * q^60 + 48 * q^61 - 552 * q^66 - 372 * q^70 - 600 * q^72 + 104 * q^73 - 736 * q^76 - 408 * q^78 + 72 * q^81 - 720 * q^82 + 216 * q^85 - 580 * q^88 + 528 * q^90 + 368 * q^93 + 884 * q^96 + 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.99497	+	0.141758i	0.997485	+	0.0708789i
$2$	1.99497	+	0.141758i	0.997485	+	0.0708789i
$3$	−2.17477	+	2.06649i	−0.724924	+	0.688829i
$3$	−2.17477	+	2.06649i	−0.724924	+	0.688829i
$4$	3.95981	+	0.565605i	0.989952	+	0.141401i
$5$	3.07600	+	3.94185i	0.615200	+	0.788371i
$5$	3.07600	+	3.94185i	0.615200	+	0.788371i
$6$	−4.63154	+	3.81429i	−0.771924	+	0.635715i
$7$	−5.18766	−	5.18766i	−0.741095	−	0.741095i	0.231694	−	0.972789i	$-0.425573\pi$
$7$	−5.18766	−	5.18766i	−0.741095	−	0.741095i	−0.972789	+	0.231694i	$0.925573\pi$
$8$	7.81952	+	1.68970i	0.977440	+	0.211212i
$9$	0.459255	−	8.98827i	0.0510283	−	0.998697i
$10$	5.57774	+	8.29993i	0.557774	+	0.829993i
$11$	7.14796			0.649814			0.324907	−	0.945746i	$-0.394667\pi$
$11$	7.14796			0.649814			0.324907	+	0.945746i	$0.394667\pi$
$12$	−9.78049	+	6.95284i	−0.815041	+	0.579403i
$13$	−7.93751	−	7.93751i	−0.610578	−	0.610578i	0.332519	−	0.943097i	$-0.392102\pi$
$13$	−7.93751	−	7.93751i	−0.610578	−	0.610578i	−0.943097	+	0.332519i	$0.892102\pi$
$14$	−9.61384	−	11.0846i	−0.686703	−	0.791759i
$15$	−14.8354	−	2.21611i	−0.989026	−	0.147741i
$16$	15.3602	+	4.47938i	0.960011	+	0.279961i
$17$	−16.5858	−	16.5858i	−0.975633	−	0.975633i	0.0240774	−	0.999710i	$-0.492335\pi$
$17$	−16.5858	−	16.5858i	−0.975633	−	0.975633i	−0.999710	+	0.0240774i	$0.992335\pi$
$18$	2.19036	−	17.8662i	0.121687	−	0.992569i
$19$	−12.1545			−0.639709			−0.319855	−	0.947467i	$-0.603634\pi$
$19$	−12.1545			−0.639709			−0.319855	+	0.947467i	$0.603634\pi$
$20$	9.95085	+	17.3488i	0.497542	+	0.867440i
$21$	22.0022	+	0.561734i	1.04772	+	0.0267492i
$22$	14.2600	+	1.01328i	0.648180	+	0.0460581i
$23$	11.0852	+	11.0852i	0.481963	+	0.481963i	0.905758	−	0.423795i	$-0.139302\pi$
$23$	11.0852	+	11.0852i	0.481963	+	0.481963i	−0.423795	+	0.905758i	$0.639302\pi$
$24$	−20.4974	+	12.4842i	−0.854059	+	0.520177i
$25$	−6.07643	+	24.2503i	−0.243057	+	0.970012i
$26$	−14.7099	−	16.9603i	−0.565765	−	0.652319i
$27$	17.5754	+	20.4965i	0.650940	+	0.759129i
$28$	−17.6080	−	23.4763i	−0.628857	−	0.838440i
$29$	26.1010			0.900034			0.450017	−	0.893020i	$-0.351418\pi$
$29$	26.1010			0.900034			0.450017	+	0.893020i	$0.351418\pi$
$30$	−29.2820	−	6.52411i	−0.976067	−	0.217470i
$31$		−	8.74184i		−	0.281995i	−0.990010	−	0.140997i	$-0.954969\pi$
$31$		−	8.74184i		−	0.281995i	0.990010	−	0.140997i	$-0.0450309\pi$
$32$	30.0081	+	11.1137i	0.937753	+	0.347302i
$33$	−15.5452	+	14.7712i	−0.471066	+	0.447611i
$34$	−30.7369	−	35.4392i	−0.904027	−	1.04233i
$35$	4.49175	−	36.4063i	0.128336	−	1.04018i
$36$	6.90238	−	35.3321i	0.191733	−	0.981447i
$37$	−26.7167	+	26.7167i	−0.722074	+	0.722074i	−0.969027	−	0.246953i	$-0.920571\pi$
$37$	−26.7167	+	26.7167i	−0.722074	+	0.722074i	0.246953	+	0.969027i	$0.420571\pi$
$38$	−24.2478	−	1.72299i	−0.638100	−	0.0453419i
$39$	33.6650	+	0.859495i	0.863206	+	0.0220383i
$40$	17.3923	+	36.0209i	0.434808	+	0.900523i
$41$			35.4164i			0.863815i	0.901918	+	0.431908i	$0.142159\pi$
$41$			35.4164i			0.863815i	−0.901918	+	0.431908i	$0.857841\pi$
$42$	43.8141	+	4.23963i	1.04319	+	0.100944i
$43$	24.6907	−	24.6907i	0.574203	−	0.574203i	−0.359097	−	0.933300i	$-0.616915\pi$
$43$	24.6907	−	24.6907i	0.574203	−	0.574203i	0.933300	+	0.359097i	$0.116915\pi$
$44$	28.3045	+	4.04292i	0.643285	+	0.0918846i
$45$	36.8431	−	25.8376i	0.818736	−	0.574170i
$46$	20.5431	+	23.6860i	0.446590	+	0.514912i
$47$	−58.6014	+	58.6014i	−1.24684	+	1.24684i	−0.289728	+	0.957109i	$0.593565\pi$
$47$	−58.6014	+	58.6014i	−1.24684	+	1.24684i	−0.957109	+	0.289728i	$0.906435\pi$
$48$	−42.6615	+	22.0000i	−0.888780	+	0.458334i
$49$			4.82369i			0.0984426i
$50$	−15.5600	+	47.5172i	−0.311199	+	0.950345i
$51$	70.3445	+	1.79595i	1.37930	+	0.0352147i
$52$	−26.9415	−	35.9205i	−0.518106	−	0.690779i
$53$	−20.4453	+	20.4453i	−0.385761	+	0.385761i	−0.873172	−	0.487411i	$-0.837941\pi$
$53$	−20.4453	+	20.4453i	−0.385761	+	0.385761i	0.487411	+	0.873172i	$0.337941\pi$
$54$	32.1568	+	43.3813i	0.595497	+	0.803358i
$55$	21.9871	+	28.1762i	0.399766	+	0.512295i
$56$	−31.7994	−	49.3306i	−0.567847	−	0.880904i
$57$	26.4332	−	25.1171i	0.463740	−	0.440651i
$58$	52.0707	+	3.70002i	0.897771	+	0.0637935i
$59$		−	59.4125i		−	1.00699i	−0.863998	−	0.503496i	$-0.832047\pi$
$59$		−	59.4125i		−	1.00699i	0.863998	−	0.503496i	$-0.167953\pi$
$60$	−57.4919	−	17.1663i	−0.958198	−	0.286106i
$61$	7.42905			0.121788			0.0608939	−	0.998144i	$-0.480605\pi$
$61$	7.42905			0.121788			0.0608939	+	0.998144i	$0.480605\pi$
$62$	1.23923	−	17.4397i	0.0199875	−	0.281286i
$63$	−49.0106	+	44.2457i	−0.777946	+	0.702312i
$64$	58.2898	+	26.4253i	0.910779	+	0.412895i
$65$	6.87272	−	55.7043i	0.105734	−	0.856989i
$66$	−33.1061	+	27.2644i	−0.501607	+	0.413097i
$67$	−35.8479	−	35.8479i	−0.535044	−	0.535044i	0.387025	−	0.922069i	$-0.373503\pi$
$67$	−35.8479	−	35.8479i	−0.535044	−	0.535044i	−0.922069	+	0.387025i	$0.873503\pi$
$68$	−56.2954	−	75.0574i	−0.827874	−	1.10379i
$69$	−47.0150	−	1.20033i	−0.681377	−	0.0173961i
$70$	14.1218	−	71.9927i	0.201740	−	1.02847i
$71$	−46.2359			−0.651210			−0.325605	−	0.945506i	$-0.605568\pi$
$71$	−46.2359			−0.651210			−0.325605	+	0.945506i	$0.605568\pi$
$72$	18.7786	−	69.5080i	0.260814	−	0.965389i
$73$	10.6280	+	10.6280i	0.145589	+	0.145589i	0.776144	−	0.630555i	$-0.217173\pi$
$73$	10.6280	+	10.6280i	0.145589	+	0.145589i	−0.630555	+	0.776144i	$0.717173\pi$
$74$	−57.0864	+	49.5118i	−0.771438	+	0.669078i
$75$	−36.8981	−	65.2957i	−0.491975	−	0.870609i
$76$	−48.1294	−	6.87464i	−0.633282	−	0.0904558i
$77$	−37.0812	−	37.0812i	−0.481574	−	0.481574i
$78$	67.0389	+	6.48695i	0.859473	+	0.0831660i
$79$	−68.3530			−0.865228			−0.432614	−	0.901579i	$-0.642409\pi$
$79$	−68.3530			−0.865228			−0.432614	+	0.901579i	$0.642409\pi$
$80$	29.5909	+	74.3262i	0.369886	+	0.929077i
$81$	−80.5782	−	8.25582i	−0.994792	−	0.101924i
$82$	−5.02056	+	70.6547i	−0.0612263	+	0.861643i
$83$	76.6461	+	76.6461i	0.923447	+	0.923447i	0.997271	−	0.0738244i	$-0.0235204\pi$
$83$	76.6461	+	76.6461i	0.923447	+	0.923447i	−0.0738244	+	0.997271i	$0.523520\pi$
$84$	86.8069	+	14.6689i	1.03342	+	0.174630i
$85$	14.3608	−	116.396i	0.168951	−	1.36937i
$86$	52.7574	−	45.7572i	0.613458	−	0.532060i
$87$	−56.7637	+	53.9374i	−0.652456	+	0.619970i
$88$	55.8936	+	12.0779i	0.635155	+	0.137249i
$89$	41.0916			0.461703			0.230852	−	0.972989i	$-0.425849\pi$
$89$	41.0916			0.461703			0.230852	+	0.972989i	$0.425849\pi$
$90$	77.1636	−	46.3225i	0.857374	−	0.514694i
$91$			82.3543i			0.904992i
$92$	37.6253	+	50.1649i	0.408970	+	0.545271i
$93$	18.0649	+	19.0115i	0.194246	+	0.204425i
$94$	−125.215	+	108.601i	−1.33208	+	1.15533i
$95$	−37.3872	−	47.9112i	−0.393549	−	0.504328i
$96$	−88.2270	+	37.8418i	−0.919031	+	0.394185i
$97$	81.7315	−	81.7315i	0.842593	−	0.842593i	−0.146602	−	0.989196i	$-0.546834\pi$
$97$	81.7315	−	81.7315i	0.842593	−	0.842593i	0.989196	+	0.146602i	$0.0468338\pi$
$98$	−0.683795	+	9.62311i	−0.00697750	+	0.0981950i
$99$	3.28274	−	64.2478i	0.0331589	−	0.648968i
$100$	−37.7776	+	92.5897i	−0.377776	+	0.925897i
$101$			125.873i			1.24626i	0.782117	+	0.623132i	$0.214140\pi$
$101$			125.873i			1.24626i	−0.782117	+	0.623132i	$0.785860\pi$
$102$	140.081	+	13.5548i	1.37334	+	0.132890i
$103$	46.2904	−	46.2904i	0.449421	−	0.449421i	−0.445741	−	0.895162i	$-0.647060\pi$
$103$	46.2904	−	46.2904i	0.449421	−	0.449421i	0.895162	+	0.445741i	$0.147060\pi$
$104$	−48.6555	−	75.4796i	−0.467842	−	0.725765i
$105$	65.4646	+	88.4574i	0.623472	+	0.842452i
$106$	−43.6861	+	37.8895i	−0.412133	+	0.357448i
$107$	107.270	−	107.270i	1.00252	−	1.00252i	0.00252770	−	0.999997i	$-0.499195\pi$
$107$	107.270	−	107.270i	1.00252	−	1.00252i	0.999997	−	0.00252770i	$-0.000804591\pi$
$108$	58.0023	+	91.1029i	0.537058	+	0.843545i
$109$			22.8980i			0.210073i	0.994468	+	0.105037i	$0.0334960\pi$
$109$			22.8980i			0.210073i	−0.994468	+	0.105037i	$0.966504\pi$
$110$	39.8695	+	59.3275i	0.362450	+	0.539341i
$111$	2.89296	−	113.313i	0.0260627	−	1.02083i
$112$	−56.4459	−	102.921i	−0.503982	−	0.918937i
$113$	85.7431	−	85.7431i	0.758788	−	0.758788i	−0.217314	−	0.976102i	$-0.569729\pi$
$113$	85.7431	−	85.7431i	0.758788	−	0.758788i	0.976102	+	0.217314i	$0.0697294\pi$
$114$	56.2940	−	46.3607i	0.493807	−	0.406673i
$115$	−9.59812	+	77.7940i	−0.0834619	+	0.676470i
$116$	103.355	+	14.7629i	0.890991	+	0.127266i
$117$	−74.9899	+	67.6992i	−0.640939	+	0.578626i
$118$	8.42219	−	118.526i	0.0713745	−	1.00446i
$119$			172.083i			1.44607i
$120$	−112.261	−	42.3963i	−0.935509	−	0.353302i
$121$	−69.9067			−0.577741
$122$	14.8207	+	1.05313i	0.121481	+	0.00863219i
$123$	−73.1876	−	77.0226i	−0.595021	−	0.626200i
$124$	4.94443	−	34.6160i	0.0398745	−	0.279162i
$125$	−114.282	+	50.6415i	−0.914258	+	0.405132i
$126$	−104.047	+	81.3212i	−0.825769	+	0.645406i
$127$	77.5158	+	77.5158i	0.610361	+	0.610361i	0.943040	−	0.332679i	$-0.107953\pi$
$127$	77.5158	+	77.5158i	0.610361	+	0.610361i	−0.332679	+	0.943040i	$0.607953\pi$
$128$	112.540	+	60.9807i	0.879222	+	0.476412i
$129$	−2.67358	+	104.720i	−0.0207254	+	0.811781i
$130$	21.6074	−	110.154i	0.166211	−	0.847340i
$131$	20.0258			0.152869			0.0764345	−	0.997075i	$-0.475646\pi$
$131$	20.0258			0.152869			0.0764345	+	0.997075i	$0.475646\pi$
$132$	−69.9106	+	49.6986i	−0.529625	+	0.376504i
$133$	63.0533	+	63.0533i	0.474085	+	0.474085i
$134$	−66.4338	−	76.5972i	−0.495775	−	0.571621i
$135$	−26.7322	+	132.327i	−0.198017	+	0.980199i
$136$	−101.668	−	157.718i	−0.747557	−	1.15969i
$137$	−8.45410	−	8.45410i	−0.0617088	−	0.0617088i	0.675579	−	0.737288i	$-0.263894\pi$
$137$	−8.45410	−	8.45410i	−0.0617088	−	0.0617088i	−0.737288	+	0.675579i	$0.763894\pi$
$138$	−93.6234	−	9.05937i	−0.678430	−	0.0656476i
$139$	165.614			1.19147			0.595734	−	0.803182i	$-0.296861\pi$
$139$	165.614			1.19147			0.595734	+	0.803182i	$0.296861\pi$
$140$	38.3781	−	141.621i	0.274129	−	1.01158i
$141$	6.34551	−	248.543i	0.0450036	−	1.76272i
$142$	−92.2392	−	6.55430i	−0.649572	−	0.0461571i
$143$	−56.7370	−	56.7370i	−0.396762	−	0.396762i
$144$	47.3161	−	136.004i	0.328584	−	0.944475i
$145$	80.2867	+	102.886i	0.553701	+	0.709561i
$146$	19.6960	+	22.7092i	0.134904	+	0.155542i
$147$	−9.96809	−	10.4904i	−0.0678101	−	0.0713633i
$148$	−120.904	+	90.6821i	−0.816921	+	0.612717i
$149$	26.8277			0.180052			0.0900259	−	0.995939i	$-0.471305\pi$
$149$	26.8277			0.180052			0.0900259	+	0.995939i	$0.471305\pi$
$150$	−64.3544	−	135.494i	−0.429029	−	0.903290i
$151$			6.88363i			0.0455870i	0.999740	+	0.0227935i	$0.00725602\pi$
$151$			6.88363i			0.0455870i	−0.999740	+	0.0227935i	$0.992744\pi$
$152$	−95.0422	−	20.5374i	−0.625278	−	0.135115i
$153$	−156.694	+	141.460i	−1.02415	+	0.924577i
$154$	−68.7193	−	79.2324i	−0.446229	−	0.514496i
$155$	34.4591	−	26.8899i	0.222317	−	0.173483i
$156$	132.821	+	22.4446i	0.851417	+	0.143875i
$157$	−33.6577	+	33.6577i	−0.214380	+	0.214380i	−0.806125	−	0.591745i	$-0.798439\pi$
$157$	−33.6577	+	33.6577i	−0.214380	+	0.214380i	0.591745	+	0.806125i	$0.298439\pi$
$158$	−136.362	−	9.68957i	−0.863051	−	0.0613264i
$159$	2.21388	−	86.7139i	0.0139237	−	0.545371i
$160$	48.4966	+	152.473i	0.303104	+	0.952958i
$161$		−	115.012i		−	0.714361i
$162$	−159.581	−	27.8927i	−0.985066	−	0.172177i
$163$	1.81560	−	1.81560i	0.0111386	−	0.0111386i	−0.701516	−	0.712654i	$-0.747493\pi$
$163$	1.81560	−	1.81560i	0.0111386	−	0.0111386i	0.712654	+	0.701516i	$0.247493\pi$
$164$	−20.0317	+	140.242i	−0.122145	+	0.855136i
$165$	−106.043	−	15.8407i	−0.642683	−	0.0960040i
$166$	142.041	+	163.772i	0.855671	+	0.986577i
$167$	110.613	−	110.613i	0.662355	−	0.662355i	−0.293579	−	0.955935i	$-0.594847\pi$
$167$	110.613	−	110.613i	0.662355	−	0.662355i	0.955935	+	0.293579i	$0.0948465\pi$
$168$	171.098	+	41.5696i	1.01844	+	0.247438i
$169$		−	42.9918i		−	0.254389i
$170$	45.1495	−	230.172i	0.265585	−	1.35395i
$171$	−5.58200	+	109.248i	−0.0326433	+	0.638876i
$172$	111.736	−	83.8054i	0.649627	−	0.487241i
$173$	58.8176	−	58.8176i	0.339986	−	0.339986i	−0.516376	−	0.856362i	$-0.672719\pi$
$173$	58.8176	−	58.8176i	0.339986	−	0.339986i	0.856362	+	0.516376i	$0.172719\pi$
$174$	−120.888	+	99.5568i	−0.694758	+	0.572165i
$175$	157.325	−	94.2799i	0.898999	−	0.538742i
$176$	109.794	+	32.0184i	0.623829	+	0.181923i
$177$	122.775	+	129.209i	0.693646	+	0.729992i
$178$	81.9764	+	5.82505i	0.460542	+	0.0327250i
$179$			221.072i			1.23504i	0.786555	+	0.617520i	$0.211862\pi$
$179$			221.072i			1.23504i	−0.786555	+	0.617520i	$0.788138\pi$
$180$	160.506	−	81.4734i	0.891698	−	0.452630i
$181$	184.455			1.01909			0.509545	−	0.860444i	$-0.329814\pi$
$181$	184.455			1.01909			0.509545	+	0.860444i	$0.329814\pi$
$182$	−11.6744	+	164.294i	−0.0641449	+	0.902716i
$183$	−16.1565	+	15.3520i	−0.0882868	+	0.0838910i
$184$	67.9500	+	105.411i	0.369294	+	0.572887i
$185$	−187.494	−	23.1328i	−1.01348	−	0.125042i
$186$	33.3439	+	40.4882i	0.179268	+	0.217679i
$187$	−118.554	−	118.554i	−0.633980	−	0.633980i
$188$	−265.195	+	198.905i	−1.41061	+	1.05801i
$189$	15.1537	−	197.504i	0.0801780	−	1.04499i
$190$	−67.7945	−	100.881i	−0.356813	−	0.530954i
$191$	−247.515			−1.29589			−0.647944	−	0.761688i	$-0.724371\pi$
$191$	−247.515			−1.29589			−0.647944	+	0.761688i	$0.724371\pi$
$192$	−181.375	+	62.9863i	−0.944659	+	0.328054i
$193$	−218.501	−	218.501i	−1.13213	−	1.13213i	−0.989823	−	0.142305i	$-0.954549\pi$
$193$	−218.501	−	218.501i	−1.13213	−	1.13213i	−0.142305	−	0.989823i	$-0.545451\pi$
$194$	174.638	−	151.466i	0.900196	−	0.780752i
$195$	100.166	+	135.346i	0.513670	+	0.694085i
$196$	−2.72830	+	19.1009i	−0.0139199	+	0.0974534i
$197$	199.518	+	199.518i	1.01278	+	1.01278i	0.999917	+	0.0128655i	$0.00409532\pi$
$197$	199.518	+	199.518i	1.01278	+	1.01278i	0.0128655	+	0.999917i	$0.495905\pi$
$198$	15.6566	−	127.707i	0.0790737	−	0.644985i
$199$	−278.384			−1.39891			−0.699457	−	0.714674i	$-0.746575\pi$
$199$	−278.384			−1.39891			−0.699457	+	0.714674i	$0.746575\pi$
$200$	−88.4905	+	179.358i	−0.442453	+	0.896792i
$201$	152.040	+	3.88171i	0.756419	+	0.0193120i
$202$	−17.8434	+	251.112i	−0.0883338	+	1.24313i
$203$	−135.403	−	135.403i	−0.667011	−	0.667011i
$204$	277.535	+	46.8988i	1.36047	+	0.229896i
$205$	−139.606	+	108.941i	−0.681007	+	0.531419i
$206$	98.9099	−	85.7859i	0.480145	−	0.416436i
$207$	104.727	−	94.5455i	0.505929	−	0.456742i
$208$	−86.3665	−	157.477i	−0.415224	−	0.757100i
$209$	−86.8797			−0.415692
$210$	118.060	+	185.750i	0.562192	+	0.884524i
$211$		−	85.1758i		−	0.403677i	−0.979419	−	0.201838i	$-0.935308\pi$
$211$		−	85.1758i		−	0.403677i	0.979419	−	0.201838i	$-0.0646916\pi$
$212$	−92.5236	+	69.3956i	−0.436432	+	0.327338i
$213$	100.552	−	95.5459i	0.472077	−	0.448572i
$214$	229.207	−	198.794i	1.07106	−	0.928945i
$215$	173.276	+	21.3786i	0.805935	+	0.0994351i
$216$	102.798	+	189.970i	0.475918	+	0.879490i
$217$	−45.3497	+	45.3497i	−0.208985	+	0.208985i
$218$	−3.24597	+	45.6808i	−0.0148898	+	0.209545i
$219$	−45.0762	−	1.15083i	−0.205827	−	0.00525494i
$220$	71.1282	+	124.008i	0.323310	+	0.563675i
$221$			263.299i			1.19140i
$222$	21.8343	−	225.645i	0.0983528	−	1.01642i
$223$	−222.212	+	222.212i	−0.996466	+	0.996466i	−0.999994	−	0.00352781i	$-0.998877\pi$
$223$	−222.212	+	222.212i	−0.996466	+	0.996466i	0.00352781	+	0.999994i	$0.498877\pi$
$224$	−98.0181	−	213.326i	−0.437581	−	0.952347i
$225$	215.178	+	65.7537i	0.956345	+	0.292239i
$226$	183.210	−	158.900i	0.810662	−	0.703098i
$227$	−33.6138	+	33.6138i	−0.148078	+	0.148078i	−0.777259	−	0.629181i	$-0.783391\pi$
$227$	−33.6138	+	33.6138i	−0.148078	+	0.148078i	0.629181	+	0.777259i	$0.283391\pi$
$228$	118.877	−	84.5081i	0.521389	−	0.370650i
$229$		−	127.633i		−	0.557349i	−0.960386	−	0.278675i	$-0.910105\pi$
$229$		−	127.633i		−	0.557349i	0.960386	−	0.278675i	$-0.0898951\pi$
$230$	−30.1759	+	153.836i	−0.131199	+	0.668853i
$231$	157.271	+	4.01525i	0.680827	+	0.0173820i
$232$	204.097	+	44.1029i	0.879730	+	0.190098i
$233$	190.936	−	190.936i	0.819467	−	0.819467i	−0.166564	−	0.986031i	$-0.553267\pi$
$233$	190.936	−	190.936i	0.819467	−	0.819467i	0.986031	+	0.166564i	$0.0532671\pi$
$234$	−159.199	+	124.427i	−0.680339	+	0.531741i
$235$	−411.256	−	50.7402i	−1.75002	−	0.215916i
$236$	33.6040	−	235.262i	0.142390	−	0.996874i
$237$	148.652	−	141.251i	0.627224	−	0.595994i
$238$	−24.3941	+	343.300i	−0.102496	+	1.44244i
$239$		−	164.867i		−	0.689820i	−0.938636	−	0.344910i	$-0.887910\pi$
$239$		−	164.867i		−	0.689820i	0.938636	−	0.344910i	$-0.112090\pi$
$240$	−217.948	−	100.493i	−0.908115	−	0.418722i
$241$	−20.3865			−0.0845915			−0.0422957	−	0.999105i	$-0.513467\pi$
$241$	−20.3865			−0.0845915			−0.0422957	+	0.999105i	$0.513467\pi$
$242$	−139.462	−	9.90982i	−0.576288	−	0.0409497i
$243$	192.300	−	148.559i	0.791356	−	0.611355i
$244$	29.4176	+	4.20191i	0.120564	+	0.0172209i
$245$	−19.0143	+	14.8377i	−0.0776092	+	0.0605619i
$246$	−135.089	−	164.033i	−0.549140	−	0.666800i
$247$	96.4763	+	96.4763i	0.390592	+	0.390592i
$248$	14.7711	−	68.3570i	0.0595609	−	0.275633i
$249$	−325.076	−	8.29945i	−1.30553	−	0.0333311i
$250$	−235.168	+	84.8279i	−0.940674	+	0.339312i
$251$	−425.326			−1.69452			−0.847262	−	0.531175i	$-0.821751\pi$
$251$	−425.326			−1.69452			−0.847262	+	0.531175i	$0.821751\pi$
$252$	−219.098	+	147.484i	−0.869437	+	0.585253i
$253$	79.2362	+	79.2362i	0.313187	+	0.313187i
$254$	143.653	+	165.630i	0.565564	+	0.652087i
$255$	209.300	+	282.812i	0.820786	+	1.10907i
$256$	215.870	+	137.608i	0.843243	+	0.537532i
$257$	−162.977	−	162.977i	−0.634150	−	0.634150i	0.314956	−	0.949106i	$-0.398010\pi$
$257$	−162.977	−	162.977i	−0.634150	−	0.634150i	−0.949106	+	0.314956i	$0.898010\pi$
$258$	−20.1786	+	208.534i	−0.0782115	+	0.808271i
$259$	277.195			1.07025
$260$	58.7213	−	216.691i	0.225851	−	0.833428i
$261$	11.9870	−	234.603i	0.0459273	−	0.898862i
$262$	39.9510	+	2.83882i	0.152485	+	0.0108352i
$263$	216.217	+	216.217i	0.822117	+	0.822117i	0.986411	−	0.164294i	$-0.0525346\pi$
$263$	216.217	+	216.217i	0.822117	+	0.822117i	−0.164294	+	0.986411i	$0.552535\pi$
$264$	−146.515	+	89.2368i	−0.554980	+	0.338018i
$265$	−143.482	−	17.7027i	−0.541443	−	0.0668025i
$266$	116.851	+	134.728i	0.439290	+	0.506495i
$267$	−89.3647	+	84.9152i	−0.334699	+	0.318035i
$268$	−121.675	−	162.227i	−0.454012	−	0.605324i
$269$	−90.1584			−0.335161			−0.167581	−	0.985858i	$-0.553595\pi$
$269$	−90.1584			−0.335161			−0.167581	+	0.985858i	$0.553595\pi$
$270$	−72.0884	+	260.199i	−0.266994	+	0.963698i
$271$		−	406.310i		−	1.49930i	−0.661836	−	0.749649i	$-0.730223\pi$
$271$		−	406.310i		−	1.49930i	0.661836	−	0.749649i	$-0.269777\pi$
$272$	−180.466	−	329.054i	−0.663479	−	1.20976i
$273$	−170.184	−	179.102i	−0.623385	−	0.656050i
$274$	−15.6672	−	18.0641i	−0.0571797	−	0.0659274i
$275$	−43.4341	+	173.340i	−0.157942	+	0.630328i
$276$	−185.492	−	31.3450i	−0.672071	−	0.113569i
$277$	−190.299	+	190.299i	−0.687001	+	0.687001i	−0.961568	−	0.274567i	$-0.911466\pi$
$277$	−190.299	+	190.299i	−0.687001	+	0.687001i	0.274567	+	0.961568i	$0.411466\pi$
$278$	330.395	+	23.4771i	1.18847	+	0.0844500i
$279$	−78.5741	−	4.01474i	−0.281628	−	0.0143897i
$280$	96.6390	−	277.090i	0.345139	−	0.989607i
$281$		−	150.443i		−	0.535385i	−0.963504	−	0.267692i	$-0.913739\pi$
$281$		−	150.443i		−	0.535385i	0.963504	−	0.267692i	$-0.0862611\pi$
$282$	47.8921	−	494.937i	0.169830	−	1.75510i
$283$	152.489	−	152.489i	0.538830	−	0.538830i	−0.384355	−	0.923185i	$-0.625576\pi$
$283$	152.489	−	152.489i	0.538830	−	0.538830i	0.923185	+	0.384355i	$0.125576\pi$
$284$	−183.085	−	26.1513i	−0.644667	−	0.0920819i
$285$	180.316	+	26.9357i	0.632689	+	0.0945111i
$286$	−105.146	−	121.232i	−0.367642	−	0.423886i
$287$	183.728	−	183.728i	0.640169	−	0.640169i
$288$	113.674	−	264.617i	0.394701	−	0.918810i
$289$			261.175i			0.903718i
$290$	145.585	+	216.636i	0.502016	+	0.747022i
$291$	−8.85011	+	346.645i	−0.0304128	+	1.19122i
$292$	36.0737	+	48.0962i	0.123540	+	0.164713i
$293$	−132.745	+	132.745i	−0.453054	+	0.453054i	−0.896367	−	0.443313i	$-0.853803\pi$
$293$	−132.745	+	132.745i	−0.453054	+	0.453054i	0.443313	+	0.896367i	$0.353803\pi$
$294$	−18.3989	−	22.3411i	−0.0625814	−	0.0759902i
$295$	234.196	−	182.753i	0.793883	−	0.619502i
$296$	−254.055	+	163.769i	−0.858295	+	0.553273i
$297$	125.628	+	146.508i	0.422990	+	0.493293i
$298$	53.5205	+	3.80304i	0.179599	+	0.0127619i
$299$		−	175.977i		−	0.588552i
$300$	−109.178	−	279.428i	−0.363926	−	0.931428i
$301$	−256.174			−0.851078
$302$	−0.975809	+	13.7326i	−0.00323115	+	0.0454723i
$303$	−260.114	−	273.744i	−0.858463	−	0.903446i
$304$	−186.695	−	54.4445i	−0.614128	−	0.179094i
$305$	22.8518	+	29.2842i	0.0749239	+	0.0960139i
$306$	−332.654	+	259.996i	−1.08710	+	0.849661i
$307$	88.3919	+	88.3919i	0.287922	+	0.287922i	0.836258	−	0.548336i	$-0.184739\pi$
$307$	88.3919	+	88.3919i	0.287922	+	0.287922i	−0.548336	+	0.836258i	$0.684739\pi$
$308$	−125.861	−	167.808i	−0.408640	−	0.544830i
$309$	−5.01245	+	196.329i	−0.0162215	+	0.635370i
$310$	72.5567	−	48.7597i	0.234054	−	0.157289i
$311$	514.733			1.65509			0.827545	−	0.561399i	$-0.189737\pi$
$311$	514.733			1.65509			0.827545	+	0.561399i	$0.189737\pi$
$312$	261.792	+	63.6047i	0.839078	+	0.203861i
$313$	387.047	+	387.047i	1.23657	+	1.23657i	0.961393	+	0.275179i	$0.0887372\pi$
$313$	387.047	+	387.047i	1.23657	+	1.23657i	0.275179	+	0.961393i	$0.411263\pi$
$314$	−71.9174	+	62.3749i	−0.229036	+	0.198646i
$315$	−325.167	−	57.0929i	−1.03228	−	0.181247i
$316$	−270.665	−	38.6608i	−0.856534	−	0.122344i
$317$	−3.71813	−	3.71813i	−0.0117291	−	0.0117291i	0.701218	−	0.712947i	$-0.252640\pi$
$317$	−3.71813	−	3.71813i	−0.0117291	−	0.0117291i	−0.712947	+	0.701218i	$0.752640\pi$
$318$	16.7090	−	172.678i	0.0525440	−	0.543012i
$319$	186.569			0.584855
$320$	75.1350	+	311.054i	0.234797	+	0.972044i
$321$	−11.6155	+	454.960i	−0.0361854	+	1.41732i
$322$	16.3039	−	229.446i	0.0506331	−	0.712564i
$323$	201.591	+	201.591i	0.624121	+	0.624121i
$324$	−314.405	−	78.2669i	−0.970385	−	0.241565i
$325$	240.719	−	144.255i	0.740673	−	0.443862i
$326$	3.87944	−	3.36469i	0.0119001	−	0.0103211i
$327$	−47.3184	−	49.7978i	−0.144705	−	0.152287i
$328$	−59.8431	+	276.939i	−0.182449	+	0.844328i
$329$	608.008			1.84805
$330$	−209.307	−	46.6340i	−0.634262	−	0.141315i
$331$			573.217i			1.73177i	0.500241	+	0.865886i	$0.333245\pi$
$331$			573.217i			1.73177i	−0.500241	+	0.865886i	$0.666755\pi$
$332$	260.152	+	346.855i	0.783592	+	1.04474i
$333$	227.868	+	252.407i	0.684287	+	0.757980i
$334$	236.351	−	204.990i	0.707636	−	0.613742i
$335$	31.0390	−	251.576i	0.0926538	−	0.750972i
$336$	335.442	+	107.185i	0.998339	+	0.319002i
$337$	143.969	−	143.969i	0.427209	−	0.427209i	−0.460468	−	0.887676i	$-0.652318\pi$
$337$	143.969	−	143.969i	0.427209	−	0.427209i	0.887676	+	0.460468i	$0.152318\pi$
$338$	6.09443	−	85.7674i	0.0180309	−	0.253750i
$339$	−9.28449	+	363.659i	−0.0273879	+	1.07274i
$340$	122.701	−	452.785i	0.360884	−	1.33172i
$341$		−	62.4863i		−	0.183244i
$342$	−26.6227	+	217.155i	−0.0778440	+	0.634955i
$343$	−229.172	+	229.172i	−0.668139	+	0.668139i
$344$	234.790	−	151.350i	0.682528	−	0.439970i
$345$	−139.887	−	189.019i	−0.405469	−	0.547880i
$346$	125.677	−	109.002i	0.363229	−	0.315033i
$347$	−358.220	+	358.220i	−1.03233	+	1.03233i	−0.0328744	+	0.999459i	$0.510466\pi$
$347$	−358.220	+	358.220i	−1.03233	+	1.03233i	−0.999459	+	0.0328744i	$0.989534\pi$
$348$	−255.281	+	181.476i	−0.733565	+	0.521483i
$349$			153.076i			0.438613i	0.975656	+	0.219307i	$0.0703795\pi$
$349$			153.076i			0.438613i	−0.975656	+	0.219307i	$0.929621\pi$
$350$	327.223	−	165.783i	0.934924	−	0.473667i
$351$	23.1862	−	302.196i	0.0660576	−	0.860957i
$352$	214.497	+	79.4399i	0.609366	+	0.225682i
$353$	−199.291	+	199.291i	−0.564563	+	0.564563i	−0.930600	−	0.366037i	$-0.880714\pi$
$353$	−199.291	+	199.291i	−0.564563	+	0.564563i	0.366037	+	0.930600i	$0.380714\pi$
$354$	226.617	+	275.172i	0.640160	+	0.777321i
$355$	−142.222	−	182.255i	−0.400624	−	0.513395i
$356$	162.715	+	23.2416i	0.457064	+	0.0652854i
$357$	−355.607	−	374.240i	−0.996097	−	1.04829i
$358$	−31.3387	+	441.032i	−0.0875383	+	1.23193i
$359$		−	54.0713i		−	0.150616i	−0.997160	−	0.0753082i	$-0.976006\pi$
$359$		−	54.0713i		−	0.150616i	0.997160	−	0.0753082i	$-0.0239941\pi$
$360$	331.754	−	139.784i	0.921538	−	0.388289i
$361$	−213.269			−0.590772
$362$	367.983	+	26.1480i	1.01653	+	0.0722321i
$363$	152.031	−	144.461i	0.418818	−	0.397965i
$364$	−46.5800	+	326.107i	−0.127967	+	0.895899i
$365$	−9.20231	+	74.5859i	−0.0252118	+	0.204345i
$366$	−34.4080	+	28.3366i	−0.0940109	+	0.0774223i
$367$	−8.93510	−	8.93510i	−0.0243463	−	0.0243463i	0.694829	−	0.719175i	$-0.255480\pi$
$367$	−8.93510	−	8.93510i	−0.0243463	−	0.0243463i	−0.719175	+	0.694829i	$0.755480\pi$
$368$	120.615	+	219.925i	0.327759	+	0.597621i
$369$	318.333	+	16.2652i	0.862690	+	0.0440791i
$370$	−370.766	−	72.7280i	−1.00207	−	0.196562i
$371$	212.127			0.571771
$372$	60.7806	+	85.4996i	0.163389	+	0.229838i
$373$	−409.810	−	409.810i	−1.09869	−	1.09869i	−0.994565	−	0.104121i	$-0.966797\pi$
$373$	−409.810	−	409.810i	−1.09869	−	1.09869i	−0.104121	−	0.994565i	$-0.533203\pi$
$374$	−219.706	−	253.318i	−0.587450	−	0.677321i
$375$	143.888	−	346.297i	0.383700	−	0.923458i
$376$	−557.253	+	359.216i	−1.48206	+	0.955361i
$377$	−207.177	−	207.177i	−0.549541	−	0.549541i
$378$	58.2288	−	391.866i	0.154045	−	1.03668i
$379$	−5.84018			−0.0154095			−0.00770473	−	0.999970i	$-0.502453\pi$
$379$	−5.84018			−0.0154095			−0.00770473	+	0.999970i	$0.502453\pi$
$380$	−120.947	−	210.866i	−0.318282	−	0.554909i
$381$	−328.765	−	8.39362i	−0.862899	−	0.0220305i
$382$	−493.784	−	35.0872i	−1.29263	−	0.0918512i
$383$	−137.693	−	137.693i	−0.359513	−	0.359513i	0.504121	−	0.863633i	$-0.331817\pi$
$383$	−137.693	−	137.693i	−0.359513	−	0.359513i	−0.863633	+	0.504121i	$0.831817\pi$
$384$	−370.766	+	99.9445i	−0.965535	+	0.260272i
$385$	32.1069	−	260.230i	0.0833945	−	0.675923i
$386$	−404.928	−	466.876i	−1.04904	−	1.20952i
$387$	−210.588	−	233.266i	−0.544155	−	0.602756i
$388$	369.869	−	277.414i	0.953271	−	0.714983i
$389$	−34.5568			−0.0888349			−0.0444174	−	0.999013i	$-0.514143\pi$
$389$	−34.5568			−0.0888349			−0.0444174	+	0.999013i	$0.514143\pi$
$390$	180.641	+	284.211i	0.463182	+	0.728747i
$391$		−	367.711i		−	0.940438i
$392$	−8.15058	+	37.7189i	−0.0207923	+	0.0962217i
$393$	−43.5516	+	41.3832i	−0.110818	+	0.105301i
$394$	369.750	+	426.316i	0.938451	+	1.08202i
$395$	−210.254	−	269.437i	−0.532288	−	0.682120i
$396$	49.3379	−	252.552i	0.124591	−	0.637758i
$397$	446.029	−	446.029i	1.12350	−	1.12350i	0.132286	−	0.991212i	$-0.457768\pi$
$397$	446.029	−	446.029i	1.12350	−	1.12350i	0.991212	−	0.132286i	$-0.0422318\pi$
$398$	−555.368	−	39.4631i	−1.39540	−	0.0991536i
$399$	−267.425	−	6.82759i	−0.670239	−	0.0171117i
$400$	−201.961	+	345.270i	−0.504903	+	0.863176i
$401$		−	103.887i		−	0.259071i	−0.991575	−	0.129535i	$-0.958651\pi$
$401$		−	103.887i		−	0.259071i	0.991575	−	0.129535i	$-0.0413486\pi$
$402$	302.766	+	29.2968i	0.753148	+	0.0728776i
$403$	−69.3885	+	69.3885i	−0.172180	+	0.172180i
$404$	−71.1942	+	498.432i	−0.176223	+	1.23374i
$405$	−215.315	−	343.022i	−0.531643	−	0.846969i
$406$	−250.931	−	289.320i	−0.618056	−	0.712610i
$407$	−190.970	+	190.970i	−0.469214	+	0.469214i
$408$	547.026	+	132.905i	1.34075	+	0.325746i
$409$		−	583.243i		−	1.42602i	−0.701153	−	0.713011i	$-0.747331\pi$
$409$		−	583.243i		−	1.42602i	0.701153	−	0.713011i	$-0.252669\pi$
$410$	−293.954	+	197.544i	−0.716960	+	0.481814i
$411$	35.8560	+	0.915433i	0.0872409	+	0.00222733i
$412$	209.483	−	157.119i	0.508454	−	0.381357i
$413$	−308.212	+	308.212i	−0.746276	+	0.746276i
$414$	222.330	−	173.770i	0.537030	−	0.419733i
$415$	−66.3643	+	537.891i	−0.159914	+	1.29612i
$416$	−149.975	−	326.404i	−0.360517	−	0.784626i
$417$	−360.173	+	342.240i	−0.863724	+	0.820719i
$418$	−173.322	−	12.3159i	−0.414647	−	0.0294638i
$419$			231.688i			0.552954i	0.961021	+	0.276477i	$0.0891669\pi$
$419$			231.688i			0.552954i	−0.961021	+	0.276477i	$0.910833\pi$
$420$	209.195	+	387.302i	0.498084	+	0.922147i
$421$	252.861			0.600620			0.300310	−	0.953842i	$-0.402910\pi$
$421$	252.861			0.600620			0.300310	+	0.953842i	$0.402910\pi$
$422$	12.0743	−	169.923i	0.0286122	−	0.402662i
$423$	499.812	+	553.638i	1.18159	+	1.30884i
$424$	−194.419	+	125.326i	−0.458536	+	0.295581i
$425$	502.992	−	301.427i	1.18351	−	0.709241i
$426$	214.144	−	176.357i	0.502684	−	0.413984i
$427$	−38.5394	−	38.5394i	−0.0902562	−	0.0902562i
$428$	485.442	−	364.097i	1.13421	−	0.850693i
$429$	240.636	+	6.14364i	0.560924	+	0.0143208i
$430$	342.650	+	67.2128i	0.796860	+	0.156309i
$431$	122.832			0.284993			0.142496	−	0.989795i	$-0.454487\pi$
$431$	122.832			0.284993			0.142496	+	0.989795i	$0.454487\pi$
$432$	178.150	+	393.556i	0.412383	+	0.911010i
$433$	317.452	+	317.452i	0.733145	+	0.733145i	0.971241	−	0.238097i	$-0.0765235\pi$
$433$	317.452	+	317.452i	0.733145	+	0.733145i	−0.238097	+	0.971241i	$0.576523\pi$
$434$	−96.9000	+	84.0427i	−0.223272	+	0.193647i
$435$	−387.219	−	57.8427i	−0.890158	−	0.132972i
$436$	−12.9512	+	90.6716i	−0.0297046	+	0.207962i
$437$	−134.734	−	134.734i	−0.308316	−	0.308316i
$438$	−89.7625	−	8.68578i	−0.204937	−	0.0198305i
$439$	−238.776			−0.543908			−0.271954	−	0.962310i	$-0.587670\pi$
$439$	−238.776			−0.543908			−0.271954	+	0.962310i	$0.587670\pi$
$440$	124.319	+	257.476i	0.282544	+	0.585173i
$441$	43.3566	+	2.21530i	0.0983143	+	0.00502336i
$442$	−37.3247	+	525.274i	−0.0844451	+	1.18840i
$443$	−228.090	−	228.090i	−0.514875	−	0.514875i	0.401141	−	0.916016i	$-0.368614\pi$
$443$	−228.090	−	228.090i	−0.514875	−	0.514875i	−0.916016	+	0.401141i	$0.868614\pi$
$444$	75.5458	−	447.060i	0.170148	−	1.00689i
$445$	126.398	+	161.977i	0.284040	+	0.363993i
$446$	−474.806	+	411.806i	−1.06459	+	0.923331i
$447$	−58.3442	+	55.4392i	−0.130524	+	0.124025i
$448$	−165.303	−	439.473i	−0.368979	−	0.980967i
$449$	−483.206			−1.07618			−0.538091	−	0.842887i	$-0.680854\pi$
$449$	−483.206			−1.07618			−0.538091	+	0.842887i	$0.680854\pi$
$450$	419.952	+	161.680i	0.933227	+	0.359288i
$451$			253.155i			0.561320i
$452$	388.023	−	291.030i	0.858458	−	0.643871i
$453$	−14.2249	−	14.9703i	−0.0314016	−	0.0330471i
$454$	−71.8235	+	62.2934i	−0.158202	+	0.137210i
$455$	−324.629	+	253.322i	−0.713469	+	0.556751i
$456$	249.135	−	151.739i	0.546349	−	0.332762i
$457$	48.6424	−	48.6424i	0.106438	−	0.106438i	−0.651882	−	0.758320i	$-0.726020\pi$
$457$	48.6424	−	48.6424i	0.106438	−	0.106438i	0.758320	+	0.651882i	$0.226020\pi$
$458$	18.0930	−	254.624i	0.0395043	−	0.555947i
$459$	48.4486	−	631.451i	0.105552	−	1.37571i
$460$	−82.0074	+	302.621i	−0.178277	+	0.657871i
$461$			436.442i			0.946728i	0.880867	+	0.473364i	$0.156960\pi$
$461$			436.442i			0.946728i	−0.880867	+	0.473364i	$0.843040\pi$
$462$	313.182	+	30.3047i	0.677882	+	0.0655946i
$463$	−31.1103	+	31.1103i	−0.0671929	+	0.0671929i	−0.739905	−	0.672712i	$-0.765129\pi$
$463$	−31.1103	+	31.1103i	−0.0671929	+	0.0671929i	0.672712	+	0.739905i	$0.265129\pi$
$464$	400.916	+	116.916i	0.864043	+	0.251975i
$465$	−19.3729	+	129.689i	−0.0416621	+	0.278900i
$466$	407.978	−	353.845i	0.875489	−	0.759323i
$467$	−228.219	+	228.219i	−0.488693	+	0.488693i	−0.907894	−	0.419201i	$-0.862310\pi$
$467$	−228.219	+	228.219i	−0.488693	+	0.488693i	0.419201	+	0.907894i	$0.362310\pi$
$468$	−335.237	+	225.661i	−0.716318	+	0.482182i
$469$			371.934i			0.793036i
$470$	−813.250	−	159.524i	−1.73032	−	0.339412i
$471$	3.64455	−	142.751i	0.00773790	−	0.303081i
$472$	100.389	−	464.577i	0.212689	−	0.984274i
$473$	176.488	−	176.488i	0.373125	−	0.373125i
$474$	316.580	−	260.718i	0.667890	−	0.550038i
$475$	73.8559	−	294.750i	0.155486	−	0.620526i
$476$	−97.3308	+	681.414i	−0.204477	+	1.43154i
$477$	174.379	+	193.158i	0.365574	+	0.404943i
$478$	23.3712	−	328.904i	0.0488937	−	0.688085i
$479$		−	698.050i		−	1.45731i	−0.684883	−	0.728653i	$-0.740147\pi$
$479$		−	698.050i		−	1.45731i	0.684883	−	0.728653i	$-0.259853\pi$
$480$	−420.553	−	231.377i	−0.876152	−	0.482035i
$481$	424.129			0.881765
$482$	−40.6705	−	2.88995i	−0.0843787	−	0.00599575i
$483$	237.671	+	250.125i	0.492073	+	0.517857i
$484$	−276.817	−	39.5396i	−0.571936	−	0.0816934i
$485$	573.580	+	70.7675i	1.18264	+	0.145912i
$486$	404.691	−	269.111i	0.832698	−	0.553727i
$487$	521.267	+	521.267i	1.07036	+	1.07036i	0.997329	+	0.0730343i	$0.0232683\pi$
$487$	521.267	+	521.267i	1.07036	+	1.07036i	0.0730343	+	0.997329i	$0.476732\pi$
$488$	58.0916	+	12.5529i	0.119040	+	0.0257231i
$489$	−0.196598	+	7.70043i	−0.000402041	+	0.0157473i
$490$	−40.0362	+	26.9053i	−0.0817066	+	0.0549087i
$491$	423.603			0.862736			0.431368	−	0.902176i	$-0.358031\pi$
$491$	423.603			0.862736			0.431368	+	0.902176i	$0.358031\pi$
$492$	−246.245	−	346.390i	−0.500497	−	0.704045i
$493$	−432.905	−	432.905i	−0.878103	−	0.878103i
$494$	178.791	+	206.144i	0.361925	+	0.417295i
$495$	263.353	−	184.686i	0.532027	−	0.373104i
$496$	39.1580	−	134.276i	0.0789476	−	0.270718i
$497$	239.856	+	239.856i	0.482608	+	0.482608i
$498$	−647.340	−	62.6392i	−1.29988	−	0.125782i
$499$	422.547			0.846787			0.423393	−	0.905946i	$-0.360839\pi$
$499$	422.547			0.846787			0.423393	+	0.905946i	$0.360839\pi$
$500$	−481.179	+	135.892i	−0.962358	+	0.271784i
$501$	−11.9775	+	469.140i	−0.0239072	+	0.936407i
$502$	−848.512	−	60.2933i	−1.69026	−	0.120106i
$503$	71.8560	+	71.8560i	0.142855	+	0.142855i	0.774917	−	0.632063i	$-0.217791\pi$
$503$	71.8560	+	71.8560i	0.142855	+	0.142855i	−0.632063	+	0.774917i	$0.717791\pi$
$504$	−458.001	+	263.167i	−0.908733	+	0.522156i
$505$	−496.172	+	387.184i	−0.982518	+	0.766702i
$506$	146.842	+	169.306i	0.290201	+	0.334597i
$507$	88.8421	+	93.4973i	0.175231	+	0.184413i
$508$	263.104	+	350.791i	0.517922	+	0.690534i
$509$	−196.155			−0.385374			−0.192687	−	0.981260i	$-0.561720\pi$
$509$	−196.155			−0.385374			−0.192687	+	0.981260i	$0.561720\pi$
$510$	377.457	+	593.871i	0.740112	+	1.16445i
$511$		−	110.269i		−	0.215791i
$512$	411.148	+	305.125i	0.803023	+	0.595948i
$513$	−213.620	−	249.124i	−0.416413	−	0.485622i
$514$	−302.030	−	348.237i	−0.587608	−	0.677503i
$515$	324.859	+	40.0807i	0.630795	+	0.0778265i
$516$	−69.8170	+	413.158i	−0.135304	+	0.800694i
$517$	−418.880	+	418.880i	−0.810213	+	0.810213i
$518$	552.995	+	39.2946i	1.06756	+	0.0758582i
$519$	−6.36893	+	249.461i	−0.0122715	+	0.480657i
$520$	147.865	−	423.968i	0.284356	−	0.815324i
$521$			22.8866i			0.0439282i	0.999759	+	0.0219641i	$0.00699195\pi$
$521$			22.8866i			0.0439282i	−0.999759	+	0.0219641i	$0.993008\pi$
$522$	57.1705	−	466.327i	0.109522	−	0.893346i
$523$	665.171	−	665.171i	1.27184	−	1.27184i	0.326715	−	0.945123i	$-0.394058\pi$
$523$	665.171	−	665.171i	1.27184	−	1.27184i	0.945123	−	0.326715i	$-0.105942\pi$
$524$	79.2985	+	11.3267i	0.151333	+	0.0216159i
$525$	−147.317	+	530.147i	−0.280604	+	1.00980i
$526$	400.696	+	461.997i	0.761779	+	0.878320i
$527$	−144.990	+	144.990i	−0.275124	+	0.275124i
$528$	−304.942	+	157.255i	−0.577542	+	0.297832i
$529$		−	283.239i		−	0.535423i
$530$	−283.734	−	55.6560i	−0.535346	−	0.105011i
$531$	−534.016	−	27.2855i	−1.00568	−	0.0513851i
$532$	214.016	+	285.342i	0.402285	+	0.536358i
$533$	281.118	−	281.118i	0.527426	−	0.527426i
$534$	−190.317	+	156.735i	−0.356400	+	0.293512i
$535$	752.806	+	92.8802i	1.40711	+	0.173608i
$536$	−219.741	−	340.886i	−0.409965	−	0.635981i
$537$	−456.843	−	480.781i	−0.850731	−	0.895309i
$538$	−179.863	−	12.7807i	−0.334318	−	0.0237559i
$539$			34.4795i			0.0639694i
$540$	−180.699	+	508.869i	−0.334628	+	0.942350i
$541$	197.624			0.365294			0.182647	−	0.983179i	$-0.441533\pi$
$541$	197.624			0.365294			0.182647	+	0.983179i	$0.441533\pi$
$542$	57.5976	−	810.575i	0.106269	−	1.49553i
$543$	−401.148	+	381.175i	−0.738763	+	0.701979i
$544$	−313.379	−	682.036i	−0.576064	−	1.25374i
$545$	−90.2605	+	70.4342i	−0.165616	+	0.129237i
$546$	−314.123	−	381.427i	−0.575317	−	0.698585i
$547$	−547.610	−	547.610i	−1.00111	−	1.00111i	−0.999999	−	0.00111506i	$-0.999645\pi$
$547$	−547.610	−	547.610i	−1.00111	−	1.00111i	−0.00111506	−	0.999999i	$-0.500355\pi$
$548$	−28.6949	−	38.2583i	−0.0523630	−	0.0698144i
$549$	3.41183	−	66.7744i	0.00621463	−	0.121629i
$550$	−111.222	+	339.651i	−0.202222	+	0.617548i
$551$	−317.244			−0.575760
$552$	−365.607	−	88.8273i	−0.662331	−	0.160919i
$553$	354.592	+	354.592i	0.641216	+	0.641216i
$554$	−406.618	+	352.665i	−0.733967	+	0.636579i
$555$	455.561	−	337.146i	0.820830	−	0.607471i
$556$	655.800	+	93.6722i	1.17950	+	0.168475i
$557$	−13.7649	−	13.7649i	−0.0247126	−	0.0247126i	0.694643	−	0.719355i	$-0.255563\pi$
$557$	−13.7649	−	13.7649i	−0.0247126	−	0.0247126i	−0.719355	+	0.694643i	$0.755563\pi$
$558$	−156.184	−	19.1478i	−0.279899	−	0.0343150i
$559$	−391.966			−0.701192
$560$	232.072	−	539.087i	0.414414	−	0.962655i
$561$	502.819	+	12.8374i	0.896291	+	0.0228830i
$562$	21.3265	−	300.130i	0.0379475	−	0.534038i
$563$	−50.4772	−	50.4772i	−0.0896575	−	0.0896575i	0.660856	−	0.750513i	$-0.270194\pi$
$563$	−50.4772	−	50.4772i	−0.0896575	−	0.0896575i	−0.750513	+	0.660856i	$0.770194\pi$
$564$	165.705	−	980.596i	0.293802	−	1.73865i
$565$	601.733	+	74.2409i	1.06501	+	0.131400i
$566$	325.827	−	282.594i	0.575667	−	0.499283i
$567$	375.184	+	460.841i	0.661700	+	0.812770i
$568$	−361.543	−	78.1248i	−0.636519	−	0.137544i
$569$	−981.959			−1.72576			−0.862882	−	0.505406i	$-0.831343\pi$
$569$	−981.959			−1.72576			−0.862882	+	0.505406i	$0.831343\pi$
$570$	355.908	+	79.2971i	0.624399	+	0.139118i
$571$			721.470i			1.26352i	0.775164	+	0.631760i	$0.217667\pi$
$571$			721.470i			1.26352i	−0.775164	+	0.631760i	$0.782333\pi$
$572$	−192.577	−	256.758i	−0.336673	−	0.448878i
$573$	538.288	−	511.486i	0.939420	−	0.892646i
$574$	392.578	−	340.488i	0.683933	−	0.593184i
$575$	−336.177	+	201.460i	−0.584655	+	0.350365i
$576$	264.288	−	511.789i	0.458833	−	0.888523i
$577$	−581.890	+	581.890i	−1.00847	+	1.00847i	−0.00851059	+	0.999964i	$0.502709\pi$
$577$	−581.890	+	581.890i	−1.00847	+	1.00847i	−0.999964	+	0.00851059i	$0.997291\pi$
$578$	−37.0236	+	521.035i	−0.0640546	+	0.901445i
$579$	926.718	+	23.6598i	1.60055	+	0.0408633i
$580$	259.727	+	452.821i	0.447805	+	0.780726i
$581$		−	795.228i		−	1.36872i
$582$	−66.7953	+	690.291i	−0.114769	+	1.18607i
$583$	−146.142	+	146.142i	−0.250673	+	0.250673i
$584$	65.1479	+	101.064i	0.111555	+	0.173055i
$585$	−497.529	−	87.3564i	−0.850477	−	0.149327i
$586$	−283.640	+	246.005i	−0.484027	+	0.419803i
$587$	681.614	−	681.614i	1.16118	−	1.16118i	0.176965	−	0.984217i	$-0.443372\pi$
$587$	681.614	−	681.614i	1.16118	−	1.16118i	0.984217	−	0.176965i	$-0.0566280\pi$
$588$	−33.5383	−	47.1780i	−0.0570379	−	0.0802347i
$589$			106.253i			0.180395i
$590$	493.120	−	331.388i	0.835796	−	0.561674i
$591$	−846.208	−	21.6044i	−1.43182	−	0.0365556i
$592$	−530.048	+	290.700i	−0.895352	+	0.491047i
$593$	−428.337	+	428.337i	−0.722322	+	0.722322i	−0.969078	−	0.246756i	$-0.920635\pi$
$593$	−428.337	+	428.337i	−0.722322	+	0.722322i	0.246756	+	0.969078i	$0.420635\pi$
$594$	229.856	+	310.088i	0.386962	+	0.522033i
$595$	−678.325	+	529.326i	−1.14004	+	0.889624i
$596$	106.233	+	15.1739i	0.178243	+	0.0254596i
$597$	605.422	−	575.277i	1.01411	−	0.963614i
$598$	24.9461	−	351.069i	0.0417159	−	0.587072i
$599$			798.031i			1.33227i	0.745830	+	0.666136i	$0.232053\pi$
$599$			798.031i			1.33227i	−0.745830	+	0.666136i	$0.767947\pi$
$600$	−178.195	−	572.928i	−0.296992	−	0.954880i
$601$	−20.9629			−0.0348801			−0.0174400	−	0.999848i	$-0.505552\pi$
$601$	−20.9629			−0.0348801			−0.0174400	+	0.999848i	$0.505552\pi$
$602$	−511.060	−	36.3147i	−0.848937	−	0.0603235i
$603$	−338.674	+	305.748i	−0.561649	+	0.507044i
$604$	−3.89342	+	27.2579i	−0.00644606	+	0.0451289i
$605$	−215.033	−	275.562i	−0.355427	−	0.455474i
$606$	−480.115	−	582.984i	−0.792269	−	0.962021i
$607$	−648.167	−	648.167i	−1.06782	−	1.06782i	−0.997526	−	0.0702937i	$-0.977606\pi$
$607$	−648.167	−	648.167i	−1.06782	−	1.06782i	−0.0702937	−	0.997526i	$-0.522394\pi$
$608$	−364.733	−	135.081i	−0.599890	−	0.222172i
$609$	574.280	+	14.6618i	0.942988	+	0.0240752i
$610$	41.4373	+	61.6606i	0.0679300	+	0.101083i
$611$	930.298			1.52258
$612$	−700.491	+	471.528i	−1.14459	+	0.770471i
$613$	−394.049	−	394.049i	−0.642821	−	0.642821i	0.308427	−	0.951248i	$-0.400197\pi$
$613$	−394.049	−	394.049i	−0.642821	−	0.642821i	−0.951248	+	0.308427i	$0.900197\pi$
$614$	163.809	+	188.870i	0.266790	+	0.307605i
$615$	78.4867	−	525.417i	0.127621	−	0.854336i
$616$	−227.301	−	352.613i	−0.368995	−	0.572424i
$617$	597.558	+	597.558i	0.968489	+	0.968489i	0.999518	−	0.0310296i	$-0.00987863\pi$
$617$	597.558	+	597.558i	0.968489	+	0.968489i	−0.0310296	+	0.999518i	$0.509879\pi$
$618$	−37.8309	+	390.961i	−0.0612151	+	0.632623i
$619$	−541.863			−0.875384			−0.437692	−	0.899125i	$-0.644204\pi$
$619$	−541.863			−0.875384			−0.437692	+	0.899125i	$0.644204\pi$
$620$	151.660	−	86.9887i	0.244614	−	0.140304i
$621$	−32.3808	+	422.033i	−0.0521430	+	0.679602i
$622$	1026.88	+	72.9675i	1.65093	+	0.117311i
$623$	−213.169	−	213.169i	−0.342166	−	0.342166i
$624$	513.251	+	164.000i	0.822518	+	0.262821i
$625$	−551.154	−	294.711i	−0.881846	−	0.471537i
$626$	717.280	+	827.014i	1.14582	+	1.32111i
$627$	188.943	−	179.536i	0.301345	−	0.286341i
$628$	−152.315	+	114.241i	−0.242540	+	0.181913i
$629$	886.235			1.40896
$630$	−640.604	−	159.994i	−1.01683	−	0.253958i
$631$		−	941.798i		−	1.49255i	−0.665638	−	0.746274i	$-0.731841\pi$
$631$		−	941.798i		−	1.49255i	0.665638	−	0.746274i	$-0.268159\pi$
$632$	−534.488	−	115.496i	−0.845708	−	0.182747i
$633$	176.015	+	185.238i	0.278064	+	0.292635i
$634$	−6.89048	−	7.94463i	−0.0108683	−	0.0125310i
$635$	−67.1173	+	543.995i	−0.105697	+	0.856685i
$636$	57.8124	−	342.118i	0.0909000	−	0.537922i
$637$	38.2881	−	38.2881i	0.0601068	−	0.0601068i
$638$	372.199	+	26.4476i	0.583384	+	0.0414539i
$639$	−21.2341	+	415.581i	−0.0332302	+	0.650361i
$640$	105.798	+	631.195i	0.165309	+	0.986242i
$641$		−	563.904i		−	0.879726i	−0.898065	−	0.439863i	$-0.855027\pi$
$641$		−	563.904i		−	0.879726i	0.898065	−	0.439863i	$-0.144973\pi$
$642$	−87.6668	+	905.986i	−0.136553	+	1.41119i
$643$	41.5913	−	41.5913i	0.0646832	−	0.0646832i	−0.674025	−	0.738708i	$-0.735436\pi$
$643$	41.5913	−	41.5913i	0.0646832	−	0.0646832i	0.738708	+	0.674025i	$0.235436\pi$
$644$	65.0514	−	455.426i	0.101012	−	0.707183i
$645$	−421.014	+	311.579i	−0.652735	+	0.483069i
$646$	373.591	+	430.745i	0.578315	+	0.666789i
$647$	−28.6494	+	28.6494i	−0.0442804	+	0.0442804i	−0.728900	−	0.684620i	$-0.759968\pi$
$647$	−28.6494	+	28.6494i	−0.0442804	+	0.0442804i	0.684620	+	0.728900i	$0.259968\pi$
$648$	−616.133	−	200.709i	−0.950822	−	0.309737i
$649$		−	424.678i		−	0.654358i
$650$	500.676	−	253.661i	0.770271	−	0.390248i
$651$	4.91059	−	192.340i	0.00754315	−	0.295453i
$652$	8.21634	−	6.16252i	0.0126018	−	0.00945171i
$653$	−386.414	+	386.414i	−0.591753	+	0.591753i	−0.938105	−	0.346352i	$-0.887420\pi$
$653$	−386.414	+	386.414i	−0.591753	+	0.591753i	0.346352	+	0.938105i	$0.387420\pi$
$654$	−87.3395	−	106.053i	−0.133547	−	0.162160i
$655$	61.5995	+	78.9390i	0.0940451	+	0.120517i
$656$	−158.644	+	544.003i	−0.241835	+	0.829272i
$657$	100.409	−	90.6466i	0.152829	−	0.137970i
$658$	1212.96	+	86.1899i	1.84340	+	0.130988i
$659$		−	851.849i		−	1.29264i	−0.763067	−	0.646320i	$-0.776307\pi$
$659$		−	851.849i		−	1.29264i	0.763067	−	0.646320i	$-0.223693\pi$
$660$	−410.950	−	122.704i	−0.622651	−	0.185916i
$661$	−523.764			−0.792381			−0.396191	−	0.918168i	$-0.629668\pi$
$661$	−523.764			−0.792381			−0.396191	+	0.918168i	$0.629668\pi$
$662$	−81.2580	+	1143.55i	−0.122746	+	1.72742i
$663$	−544.105	−	572.616i	−0.820671	−	0.863673i
$664$	469.827	+	728.845i	0.707571	+	1.09766i
$665$	−54.5949	+	442.499i	−0.0820976	+	0.665412i
$666$	418.808	+	535.847i	0.628841	+	0.804575i
$667$	289.334	+	289.334i	0.433784	+	0.433784i
$668$	500.571	−	375.444i	0.749358	−	0.562042i
$669$	24.0617	−	942.458i	0.0359667	−	1.40876i
$670$	97.5847	−	497.486i	0.145649	−	0.742516i
$671$	53.1026			0.0791394
$672$	654.002	+	261.382i	0.973217	+	0.388961i
$673$	−319.629	−	319.629i	−0.474931	−	0.474931i	0.428575	−	0.903506i	$-0.359016\pi$
$673$	−319.629	−	319.629i	−0.474931	−	0.474931i	−0.903506	+	0.428575i	$0.859016\pi$
$674$	307.623	−	266.806i	0.456414	−	0.395854i
$675$	−603.841	+	301.663i	−0.894580	+	0.446908i
$676$	24.3164	−	170.239i	0.0359710	−	0.251833i
$677$	509.574	+	509.574i	0.752694	+	0.752694i	0.974981	−	0.222288i	$-0.0713524\pi$
$677$	509.574	+	509.574i	0.752694	+	0.752694i	−0.222288	+	0.974981i	$0.571352\pi$
$678$	−70.0737	+	724.172i	−0.103354	+	1.06810i
$679$	−847.991			−1.24888
$680$	308.970	−	885.899i	0.454367	−	1.30279i
$681$	3.63979	−	142.565i	0.00534477	−	0.209346i
$682$	8.85793	−	124.658i	0.0129882	−	0.182784i
$683$	−278.938	−	278.938i	−0.408402	−	0.408402i	0.472779	−	0.881181i	$-0.343251\pi$
$683$	−278.938	−	278.938i	−0.408402	−	0.408402i	−0.881181	+	0.472779i	$0.843251\pi$
$684$	−83.8948	+	429.443i	−0.122653	+	0.627841i
$685$	7.32001	−	59.3297i	0.0106861	−	0.0866126i
$686$	−489.678	+	424.704i	−0.713816	+	0.619102i
$687$	263.752	+	277.572i	0.383918	+	0.404035i
$688$	489.853	−	268.655i	0.711996	−	0.390487i
$689$	324.570			0.471074
$690$	−252.275	−	396.916i	−0.365616	−	0.575241i
$691$		−	108.692i		−	0.157297i	−0.996902	−	0.0786483i	$-0.974940\pi$
$691$		−	108.692i		−	0.157297i	0.996902	−	0.0786483i	$-0.0250604\pi$
$692$	266.174	−	199.639i	0.384645	−	0.288496i
$693$	−350.326	+	316.266i	−0.505520	+	0.456373i
$694$	−765.418	+	663.857i	−1.10291	+	0.956567i
$695$	509.429	+	652.827i	0.732992	+	0.939319i
$696$	−535.003	+	325.851i	−0.768682	+	0.468177i
$697$	587.408	−	587.408i	0.842766	−	0.842766i
$698$	−21.6997	+	305.382i	−0.0310884	+	0.437510i
$699$	−20.6751	+	809.808i	−0.0295780	+	1.15852i
$700$	676.302	−	284.347i	0.966145	−	0.406209i
$701$		−	1299.56i		−	1.85387i	−0.375224	−	0.926934i	$-0.622434\pi$
$701$		−	1299.56i		−	1.85387i	0.375224	−	0.926934i	$-0.377566\pi$
$702$	89.0945	−	599.585i	0.126915	−	0.854110i
$703$	324.728	−	324.728i	0.461918	−	0.461918i
$704$	416.653	+	188.887i	0.591837	+	0.268305i
$705$	999.241	−	739.507i	1.41736	−	1.04895i
$706$	−425.830	+	369.328i	−0.603158	+	0.523127i
$707$	652.985	−	652.985i	0.923599	−	0.923599i
$708$	413.086	+	581.084i	0.583454	+	0.820740i
$709$			1025.36i			1.44620i	0.690743	+	0.723100i	$0.257283\pi$
$709$			1025.36i			1.44620i	−0.690743	+	0.723100i	$0.742717\pi$
$710$	−257.892	−	383.755i	−0.363228	−	0.540499i
$711$	−31.3914	+	614.375i	−0.0441511	+	0.864100i
$712$	321.316	+	69.4324i	0.451287	+	0.0975174i
$713$	96.9047	−	96.9047i	0.135911	−	0.135911i
$714$	−656.373	−	797.008i	−0.919290	−	1.11626i
$715$	49.1259	−	398.172i	0.0687076	−	0.556884i
$716$	−125.040	+	875.403i	−0.174636	+	1.22263i
$717$	340.695	+	358.548i	0.475168	+	0.500066i
$718$	7.66503	−	107.871i	0.0106755	−	0.150238i
$719$			873.333i			1.21465i	0.794454	+	0.607325i	$0.207757\pi$
$719$			873.333i			1.21465i	−0.794454	+	0.607325i	$0.792243\pi$
$720$	681.654	−	231.836i	0.946741	−	0.321995i
$721$	−480.278			−0.666127
$722$	−425.465	−	30.2325i	−0.589286	−	0.0418733i
$723$	44.3361	−	42.1285i	0.0613224	−	0.0582691i
$724$	730.408	+	104.329i	1.00885	+	0.144101i
$725$	−158.601	+	632.957i	−0.218760	+	0.873044i
$726$	323.776	−	266.644i	0.445972	−	0.367279i
$727$	−165.684	−	165.684i	−0.227901	−	0.227901i	0.583914	−	0.811815i	$-0.301520\pi$
$727$	−165.684	−	165.684i	−0.227901	−	0.227901i	−0.811815	+	0.583914i	$0.801520\pi$
$728$	−139.154	+	643.971i	−0.191146	+	0.884575i
$729$	−111.212	+	720.467i	−0.152554	+	0.988295i
$730$	−28.9315	+	147.492i	−0.0396321	+	0.202044i
$731$	−819.029			−1.12042
$732$	−72.6598	+	51.6530i	−0.0992620	+	0.0705642i
$733$	896.646	+	896.646i	1.22325	+	1.22325i	0.966468	+	0.256786i	$0.0826637\pi$
$733$	896.646	+	896.646i	1.22325	+	1.22325i	0.256786	+	0.966468i	$0.417336\pi$
$734$	−16.5586	−	19.0919i	−0.0225594	−	0.0260107i
$735$	10.6898	−	71.5613i	0.0145440	−	0.0973623i
$736$	209.448	+	455.841i	0.284576	+	0.619349i
$737$	−256.239	−	256.239i	−0.347679	−	0.347679i
$738$	632.758	+	77.5747i	0.857396	+	0.105115i
$739$	135.132			0.182858			0.0914290	−	0.995812i	$-0.470857\pi$
$739$	135.132			0.182858			0.0914290	+	0.995812i	$0.470857\pi$
$740$	−729.358	−	197.649i	−0.985618	−	0.267093i
$741$	−409.181	−	10.4467i	−0.552201	−	0.0140981i
$742$	423.187	+	30.0707i	0.570333	+	0.0405265i
$743$	−472.574	−	472.574i	−0.636035	−	0.636035i	0.313540	−	0.949575i	$-0.398485\pi$
$743$	−472.574	−	472.574i	−0.636035	−	0.636035i	−0.949575	+	0.313540i	$0.898485\pi$
$744$	109.135	+	179.185i	0.146687	+	0.240840i
$745$	82.5221	+	105.751i	0.110768	+	0.141948i
$746$	−759.465	−	875.652i	−1.01805	−	1.17380i
$747$	724.116	−	653.716i	0.969366	−	0.875122i
$748$	−402.397	−	536.507i	−0.537964	−	0.717256i
$749$	−1112.96			−1.48593
$750$	336.142	−	670.454i	0.448189	−	0.893939i
$751$			643.372i			0.856687i	0.903616	+	0.428344i	$0.140903\pi$
$751$			643.372i			0.856687i	−0.903616	+	0.428344i	$0.859097\pi$
$752$	−1162.63	+	637.630i	−1.54604	+	0.847912i
$753$	924.986	−	878.930i	1.22840	−	1.16724i
$754$	−383.943	−	442.681i	−0.509208	−	0.587110i
$755$	−27.1343	+	21.1741i	−0.0359394	+	0.0280451i
$756$	171.715	−	773.507i	0.227136	−	1.02316i
$757$	205.600	−	205.600i	0.271598	−	0.271598i	−0.558145	−	0.829743i	$-0.688487\pi$
$757$	205.600	−	205.600i	0.271598	−	0.271598i	0.829743	+	0.558145i	$0.188487\pi$
$758$	−11.6510	−	0.827892i	−0.0153707	−	0.00109221i
$759$	−336.061	−	8.57991i	−0.442768	−	0.0113042i
$760$	−211.394	−	437.816i	−0.278151	−	0.576073i
$761$			477.527i			0.627499i	0.949506	+	0.313750i	$0.101585\pi$
$761$			477.527i			0.627499i	−0.949506	+	0.313750i	$0.898415\pi$
$762$	−654.686	−	63.3500i	−0.859167	−	0.0831365i
$763$	118.787	−	118.787i	0.155684	−	0.155684i
$764$	−980.111	−	139.996i	−1.28287	−	0.183240i
$765$	−1039.61	−	182.535i	−1.35896	−	0.238607i
$766$	−255.175	−	294.213i	−0.333126	−	0.384090i
$767$	−471.588	+	471.588i	−0.614847	+	0.614847i
$768$	−753.834	+	146.827i	−0.981555	+	0.191181i
$769$			743.814i			0.967249i	0.875276	+	0.483624i	$0.160680\pi$
$769$			743.814i			0.967249i	−0.875276	+	0.483624i	$0.839320\pi$
$770$	100.942	−	514.601i	0.131093	−	0.668312i
$771$	691.226	+	17.6476i	0.896532	+	0.0228892i
$772$	−741.636	−	988.806i	−0.960668	−	1.28084i
$773$	357.445	−	357.445i	0.462412	−	0.462412i	−0.437033	−	0.899445i	$-0.643971\pi$
$773$	357.445	−	357.445i	0.462412	−	0.462412i	0.899445	+	0.437033i	$0.143971\pi$
$774$	−387.049	−	495.212i	−0.500063	−	0.639809i
$775$	211.992	+	53.1192i	0.273538	+	0.0685409i
$776$	777.203	−	501.000i	1.00155	−	0.645618i
$777$	−602.835	+	572.820i	−0.775850	+	0.737220i
$778$	−68.9397	−	4.89869i	−0.0886114	−	0.00629652i
$779$		−	430.468i		−	0.552591i
$780$	320.084	+	592.601i	0.410365	+	0.759744i
$781$	−330.492			−0.423165
$782$	52.1260	−	733.573i	0.0666573	−	0.938073i
$783$	458.735	+	534.979i	0.585869	+	0.683242i
$784$	−21.6071	+	74.0927i	−0.0275601	+	0.0945060i
$785$	−236.205	−	29.1426i	−0.300898	−	0.0371244i
$786$	−92.7506	+	76.3844i	−0.118003	+	0.0971811i
$787$	−188.018	−	188.018i	−0.238905	−	0.238905i	0.577492	−	0.816396i	$-0.304032\pi$
$787$	−188.018	−	188.018i	−0.238905	−	0.238905i	−0.816396	+	0.577492i	$0.804032\pi$
$788$	677.205	+	902.903i	0.859398	+	1.14582i
$789$	−917.032	−	23.4126i	−1.16227	−	0.0296737i
$790$	−381.255	−	567.325i	−0.482602	−	0.718133i
$791$	−889.612			−1.12467
$792$	134.229	−	496.840i	0.169481	−	0.627324i
$793$	−58.9682	−	58.9682i	−0.0743609	−	0.0743609i
$794$	953.042	−	826.586i	1.20030	−	1.04104i
$795$	348.624	−	258.005i	0.438520	−	0.324535i
$796$	−1102.35	−	157.456i	−1.38486	−	0.197808i
$797$	−651.365	−	651.365i	−0.817271	−	0.817271i	0.168441	−	0.985712i	$-0.446127\pi$
$797$	−651.365	−	651.365i	−0.817271	−	0.817271i	−0.985712	+	0.168441i	$0.946127\pi$
$798$	−532.538	−	51.5305i	−0.667341	−	0.0645746i
$799$	1943.90			2.43291
$800$	−451.852	+	660.174i	−0.564815	+	0.825218i
$801$	18.8715	−	369.342i	0.0235599	−	0.461102i
$802$	14.7269	−	207.252i	0.0183627	−	0.258419i
$803$	75.9686	+	75.9686i	0.0946060	+	0.0946060i
$804$	599.855	+	101.366i	0.746088	+	0.126077i
$805$	453.361	−	353.777i	0.563181	−	0.439475i
$806$	−148.264	+	128.592i	−0.183951	+	0.159543i
$807$	196.074	−	186.311i	0.242966	−	0.230869i
$808$	−212.687	+	984.264i	−0.263226	+	1.21815i
$809$	735.550			0.909209			0.454604	−	0.890694i	$-0.349781\pi$
$809$	735.550			0.909209			0.454604	+	0.890694i	$0.349781\pi$
$810$	−380.921	−	714.842i	−0.470273	−	0.882521i
$811$			92.4709i			0.114021i	0.998374	+	0.0570104i	$0.0181568\pi$
$811$			92.4709i			0.114021i	−0.998374	+	0.0570104i	$0.981843\pi$
$812$	−459.586	−	612.756i	−0.565993	−	0.754625i
$813$	839.634	+	883.630i	1.03276	+	1.08688i
$814$	−408.051	+	353.908i	−0.501291	+	0.434777i
$815$	12.7416	+	1.57204i	0.0156339	+	0.00192889i
$816$	1072.46	+	342.686i	1.31429	+	0.419958i
$817$	−300.103	+	300.103i	−0.367323	+	0.367323i
$818$	82.6793	−	1163.55i	0.101075	−	1.42244i
$819$	740.223	+	37.8216i	0.903813	+	0.0461802i
$820$	−614.432	+	352.423i	−0.749308	+	0.429785i
$821$			593.249i			0.722593i	0.932451	+	0.361296i	$0.117666\pi$
$821$			593.249i			0.722593i	−0.932451	+	0.361296i	$0.882334\pi$
$822$	71.4019	+	6.90913i	0.0868636	+	0.00840527i
$823$	−468.289	+	468.289i	−0.569003	+	0.569003i	−0.931849	−	0.362846i	$-0.881805\pi$
$823$	−468.289	+	468.289i	−0.569003	+	0.569003i	0.362846	+	0.931849i	$0.381805\pi$
$824$	440.185	−	283.752i	0.534206	−	0.344359i
$825$	−263.746	−	466.731i	−0.319692	−	0.565735i
$826$	−658.565	+	571.182i	−0.797295	+	0.691504i
$827$	−337.326	+	337.326i	−0.407891	+	0.407891i	−0.881003	−	0.473111i	$-0.843131\pi$
$827$	−337.326	+	337.326i	−0.407891	+	0.407891i	0.473111	+	0.881003i	$0.343131\pi$
$828$	468.176	−	315.148i	0.565430	−	0.380613i
$829$		−	483.086i		−	0.582733i	−0.956611	−	0.291367i	$-0.905890\pi$
$829$		−	483.086i		−	0.582733i	0.956611	−	0.291367i	$-0.0941099\pi$
$830$	−208.645	+	1063.67i	−0.251379	+	1.28153i
$831$	20.6061	−	807.109i	0.0247968	−	0.971250i
$832$	−252.925	−	672.427i	−0.303997	−	0.808206i
$833$	80.0045	−	80.0045i	0.0960438	−	0.0960438i
$834$	−767.049	+	631.700i	−0.919723	+	0.757435i
$835$	776.268	+	95.7749i	0.929663	+	0.114700i
$836$	−344.027	−	49.1396i	−0.411516	−	0.0587794i
$837$	179.177	−	153.641i	0.214071	−	0.183562i
$838$	−32.8435	+	462.210i	−0.0391928	+	0.551563i
$839$		−	835.860i		−	0.996257i	−0.867103	−	0.498129i	$-0.834021\pi$
$839$		−	835.860i		−	0.996257i	0.867103	−	0.498129i	$-0.165979\pi$
$840$	362.435	+	802.310i	0.431470	+	0.955131i
$841$	−159.738			−0.189938
$842$	504.450	+	35.8451i	0.599110	+	0.0425713i
$843$	310.889	+	327.179i	0.368789	+	0.388113i
$844$	48.1759	−	337.280i	0.0570804	−	0.399621i
$845$	169.467	−	132.243i	0.200553	−	0.156500i
$846$	918.628	+	1175.34i	1.08585	+	1.38929i
$847$	362.652	+	362.652i	0.428161	+	0.428161i
$848$	−405.626	+	222.462i	−0.478333	+	0.262337i
$849$	−16.5119	+	646.745i	−0.0194487	+	0.761773i
$850$	1046.18	−	530.035i	1.23080	−	0.623571i
$851$	−592.319			−0.696026
$852$	452.210	−	321.471i	0.530763	−	0.377313i
$853$	−306.961	−	306.961i	−0.359861	−	0.359861i	0.503901	−	0.863762i	$-0.331898\pi$
$853$	−306.961	−	306.961i	−0.359861	−	0.359861i	−0.863762	+	0.503901i	$0.831898\pi$
$854$	−71.4217	−	82.3482i	−0.0836320	−	0.0964265i
$855$	−447.809	+	314.043i	−0.523753	+	0.367302i
$856$	1020.06	−	657.547i	1.19165	−	0.768162i
$857$	861.944	+	861.944i	1.00577	+	1.00577i	0.999983	+	0.00578611i	$0.00184179\pi$
$857$	861.944	+	861.944i	1.00577	+	1.00577i	0.00578611	+	0.999983i	$0.498158\pi$
$858$	479.191	+	46.3685i	0.558498	+	0.0540425i
$859$	−518.926			−0.604104			−0.302052	−	0.953291i	$-0.597672\pi$
$859$	−518.926			−0.604104			−0.302052	+	0.953291i	$0.597672\pi$
$860$	674.048	+	182.661i	0.783777	+	0.212396i
$861$	−19.8946	+	779.240i	−0.0231064	+	0.905041i
$862$	245.046	+	17.4124i	0.284276	+	0.0202000i
$863$	284.726	+	284.726i	0.329926	+	0.329926i	0.852558	−	0.522633i	$-0.175050\pi$
$863$	284.726	+	284.726i	0.329926	+	0.329926i	−0.522633	+	0.852558i	$0.675050\pi$
$864$	299.613	+	810.387i	0.346775	+	0.937948i
$865$	412.774	+	50.9274i	0.477195	+	0.0588756i
$866$	588.305	+	678.308i	0.679336	+	0.783266i
$867$	−539.714	−	567.995i	−0.622508	−	0.655127i
$868$	−205.226	+	153.926i	−0.236436	+	0.177334i
$869$	−488.584			−0.562237
$870$	−764.290	−	170.286i	−0.878494	−	0.195731i
$871$			569.087i			0.653372i
$872$	−38.6907	+	179.051i	−0.0443701	+	0.205334i
$873$	−697.090	−	772.161i	−0.798499	−	0.884492i
$874$	−249.691	−	287.890i	−0.285688	−	0.329394i
$875$	855.569	+	330.147i	0.977793	+	0.377310i
$876$	−177.842	−	30.0524i	−0.203016	−	0.0343064i
$877$	−127.814	+	127.814i	−0.145740	+	0.145740i	−0.776212	−	0.630472i	$-0.782861\pi$
$877$	−127.814	+	127.814i	−0.145740	+	0.145740i	0.630472	+	0.776212i	$0.282861\pi$
$878$	−476.350	−	33.8483i	−0.542540	−	0.0385516i
$879$	14.3740	−	563.006i	0.0163527	−	0.640507i
$880$	211.514	+	531.280i	0.240357	+	0.603728i
$881$			833.425i			0.945999i	0.881063	+	0.472999i	$0.156829\pi$
$881$			833.425i			0.945999i	−0.881063	+	0.472999i	$0.843171\pi$
$882$	86.1811	+	10.5656i	0.0977110	+	0.0119791i
$883$	314.080	−	314.080i	0.355696	−	0.355696i	−0.506527	−	0.862224i	$-0.669071\pi$
$883$	314.080	−	314.080i	0.355696	−	0.355696i	0.862224	+	0.506527i	$0.169071\pi$
$884$	−148.923	+	1042.61i	−0.168465	+	1.17943i
$885$	−131.665	+	881.408i	−0.148774	+	0.995941i
$886$	−422.698	−	487.365i	−0.477086	−	0.550074i
$887$	341.814	−	341.814i	0.385359	−	0.385359i	−0.487669	−	0.873029i	$-0.662153\pi$
$887$	341.814	−	341.814i	0.385359	−	0.385359i	0.873029	+	0.487669i	$0.162153\pi$
$888$	214.086	−	881.162i	0.241088	−	0.992300i
$889$		−	804.252i		−	0.904670i
$890$	229.198	+	341.057i	0.257526	+	0.383210i
$891$	−575.969	−	59.0123i	−0.646430	−	0.0662315i
$892$	−1005.60	+	754.233i	−1.12736	+	0.845552i
$893$	712.269	−	712.269i	0.797613	−	0.797613i
$894$	−124.254	+	102.329i	−0.138986	+	0.114462i
$895$	−871.434	+	680.018i	−0.973669	+	0.759797i
$896$	−267.475	−	900.169i	−0.298521	−	1.00465i
$897$	363.655	+	382.710i	0.405412	+	0.426655i
$898$	−963.981	−	68.4982i	−1.07348	−	0.0762787i
$899$		−	228.171i		−	0.253805i
$900$	814.872	+	382.078i	0.905413	+	0.424531i
$901$	678.202			0.752722
$902$	−35.8867	+	505.037i	−0.0397857	+	0.559908i
$903$	557.121	−	529.381i	0.616966	−	0.586247i
$904$	815.350	−	525.590i	0.901936	−	0.581405i
$905$	567.385	+	727.096i	0.626945	+	0.803421i
$906$	−26.2562	−	31.8818i	−0.0289803	−	0.0351897i
$907$	542.622	+	542.622i	0.598261	+	0.598261i	0.939850	−	0.341589i	$-0.110965\pi$
$907$	542.622	+	542.622i	0.598261	+	0.598261i	−0.341589	+	0.939850i	$0.610965\pi$
$908$	−152.116	+	114.092i	−0.167529	+	0.125652i
$909$	1131.38	+	57.8076i	1.24464	+	0.0635948i
$910$	−683.534	+	459.351i	−0.751137	+	0.504781i
$911$	695.346			0.763277			0.381639	−	0.924312i	$-0.375360\pi$
$911$	695.346			0.763277			0.381639	+	0.924312i	$0.375360\pi$
$912$	518.528	−	267.399i	0.568561	−	0.293200i
$913$	547.863	+	547.863i	0.600069	+	0.600069i
$914$	103.935	−	90.1446i	0.113715	−	0.0986265i
$915$	−110.213	−	16.4636i	−0.120451	−	0.0179930i
$916$	72.1899	−	505.402i	0.0788099	−	0.551749i
$917$	−103.887	−	103.887i	−0.113290	−	0.113290i
$918$	186.167	−	1252.86i	0.202796	−	1.36477i
$919$	−718.456			−0.781780			−0.390890	−	0.920437i	$-0.627833\pi$
$919$	−718.456			−0.781780			−0.390890	+	0.920437i	$0.627833\pi$
$920$	−206.501	+	592.094i	−0.224458	+	0.643580i
$921$	−374.893	−	9.57132i	−0.407050	−	0.0103923i
$922$	−61.8690	+	870.688i	−0.0671031	+	0.944347i
$923$	366.998	+	366.998i	0.397614	+	0.397614i
$924$	620.492	+	104.853i	0.671528	+	0.113477i
$925$	−485.547	−	810.232i	−0.524915	−	0.875926i
$926$	−66.4743	+	57.6540i	−0.0717865	+	0.0622613i
$927$	−394.812	−	437.330i	−0.425902	−	0.471769i
$928$	783.242	+	290.077i	0.844010	+	0.312583i
$929$	−832.286			−0.895895			−0.447947	−	0.894060i	$-0.647845\pi$
$929$	−832.286			−0.895895			−0.447947	+	0.894060i	$0.647845\pi$
$930$	−57.0327	+	255.979i	−0.0613255	+	0.275246i
$931$		−	58.6294i		−	0.0629746i
$932$	864.064	−	648.075i	0.927107	−	0.695360i
$933$	−1119.43	+	1063.69i	−1.19981	+	1.14008i
$934$	−487.643	+	422.939i	−0.522102	+	0.452826i
$935$	102.651	−	831.997i	0.109787	−	0.889836i
$936$	−700.776	+	402.665i	−0.748693	+	0.430198i
$937$	1098.42	−	1098.42i	1.17227	−	1.17227i	0.190603	−	0.981667i	$-0.438956\pi$
$937$	1098.42	−	1098.42i	1.17227	−	1.17227i	0.981667	−	0.190603i	$-0.0610442\pi$
$938$	−52.7245	+	741.997i	−0.0562095	+	0.791041i
$939$	−1641.57	−	41.9105i	−1.74821	−	0.0446331i
$940$	−1599.80	−	433.530i	−1.70191	−	0.461202i
$941$		−	1235.22i		−	1.31267i	−0.754470	−	0.656334i	$-0.772106\pi$
$941$		−	1235.22i		−	1.31267i	0.754470	−	0.656334i	$-0.227894\pi$
$942$	27.5069	−	284.268i	0.0292005	−	0.301770i
$943$	−392.597	+	392.597i	−0.416327	+	0.416327i
$944$	266.131	−	912.587i	0.281919	−	0.966724i
$945$	825.145	−	547.789i	0.873169	−	0.579671i
$946$	377.108	−	327.070i	0.398634	−	0.345740i
$947$	−1168.65	+	1168.65i	−1.23405	+	1.23405i	−0.271656	+	0.962394i	$0.587571\pi$
$947$	−1168.65	+	1168.65i	−1.23405	+	1.23405i	−0.962394	+	0.271656i	$0.912429\pi$
$948$	668.526	−	475.247i	0.705196	−	0.501315i
$949$		−	168.720i		−	0.177787i
$950$	189.123	−	577.547i	0.199077	−	0.607944i
$951$	15.7696	+	0.402609i	0.0165821	+	0.000423354i
$952$	−290.768	+	1345.60i	−0.305428	+	1.41345i
$953$	−756.942	+	756.942i	−0.794273	+	0.794273i	−0.982186	−	0.187913i	$-0.939828\pi$
$953$	−756.942	+	756.942i	−0.794273	+	0.794273i	0.187913	+	0.982186i	$0.439828\pi$
$954$	320.498	+	410.064i	0.335952	+	0.429836i
$955$	−761.356	−	975.667i	−0.797231	−	1.02164i
$956$	93.2496	−	652.841i	0.0975414	−	0.682888i
$957$	−405.744	+	385.542i	−0.423975	+	0.402865i
$958$	98.9541	−	1392.59i	0.103292	−	1.45364i
$959$			87.7140i			0.0914641i
$960$	−806.191	−	521.206i	−0.839782	−	0.542923i
$961$	884.580			0.920479
$962$	846.124	+	60.1236i	0.879547	+	0.0624986i
$963$	−914.909	−	1013.44i	−0.950061	−	1.05238i
$964$	−80.7268	−	11.5307i	−0.0837415	−	0.0119613i
$965$	189.189	−	1533.41i	0.196051	−	1.58902i
$966$	438.689	+	532.683i	0.454130	+	0.551432i
$967$	366.482	+	366.482i	0.378989	+	0.378989i	0.870737	−	0.491749i	$-0.163642\pi$
$967$	366.482	+	366.482i	0.378989	+	0.378989i	−0.491749	+	0.870737i	$0.663642\pi$
$968$	−546.637	−	118.121i	−0.564708	−	0.122026i
$969$	−855.000	−	21.8288i	−0.882353	−	0.0225272i
$970$	1134.24	+	222.489i	1.16932	+	0.229370i
$971$	1773.80			1.82678			0.913390	−	0.407086i	$-0.133455\pi$
$971$	1773.80			1.82678			0.913390	+	0.407086i	$0.133455\pi$
$972$	845.496	−	479.501i	0.869852	−	0.493314i
$973$	−859.150	−	859.150i	−0.882991	−	0.882991i
$974$	966.018	+	1113.81i	0.991805	+	1.14354i
$975$	−225.406	+	811.165i	−0.231186	+	0.831964i
$976$	114.112	+	33.2775i	0.116918	+	0.0340958i
$977$	−887.249	−	887.249i	−0.908136	−	0.908136i	0.0879854	−	0.996122i	$-0.471957\pi$
$977$	−887.249	−	887.249i	−0.908136	−	0.908136i	−0.996122	+	0.0879854i	$0.971957\pi$
$978$	−1.48380	+	15.3343i	−0.00151718	+	0.0156792i
$979$	293.721			0.300021
$980$	−83.6851	+	47.9997i	−0.0853930	+	0.0489793i
$981$	205.813	+	10.5160i	0.209799	+	0.0107197i
$982$	845.076	+	60.0491i	0.860566	+	0.0611498i
$983$	297.097	+	297.097i	0.302235	+	0.302235i	0.841888	−	0.539653i	$-0.181444\pi$
$983$	297.097	+	297.097i	0.302235	+	0.302235i	−0.539653	+	0.841888i	$0.681444\pi$
$984$	−442.147	−	725.945i	−0.449336	−	0.737749i
$985$	−172.753	+	1400.19i	−0.175384	+	1.42151i
$986$	−802.264	−	925.000i	−0.813656	−	0.938134i
$987$	−1322.28	+	1256.44i	−1.33969	+	1.27299i
$988$	327.460	+	436.595i	0.331438	+	0.441898i
$989$	547.401			0.553490
$990$	551.562	−	331.111i	0.557134	−	0.334456i
$991$		−	1518.20i		−	1.53198i	−0.642850	−	0.765992i	$-0.722248\pi$
$991$		−	1518.20i		−	1.53198i	0.642850	−	0.765992i	$-0.277752\pi$
$992$	97.1538	−	262.326i	0.0979373	−	0.264442i
$993$	−1184.55	−	1246.61i	−1.19290	−	1.25540i
$994$	444.504	+	512.507i	0.447188	+	0.515601i
$995$	−856.310	−	1097.35i	−0.860613	−	1.10286i
$996$	−1282.54	−	216.729i	−1.28770	−	0.217599i
$997$	−566.238	+	566.238i	−0.567942	+	0.567942i	−0.931551	−	0.363610i	$-0.881544\pi$
$997$	−566.238	+	566.238i	−0.567942	+	0.567942i	0.363610	+	0.931551i	$0.381544\pi$
$998$	842.968	+	59.8993i	0.844657	+	0.0600193i
$999$	−1017.16	−	78.0421i	−1.01817	−	0.0781203i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.3.l.a.23.20	yes	40
3.2	odd	2	inner	60.3.l.a.23.1	✓	40
4.3	odd	2	inner	60.3.l.a.23.11	yes	40
5.2	odd	4	inner	60.3.l.a.47.10	yes	40
5.3	odd	4		300.3.l.g.107.11		40
5.4	even	2		300.3.l.g.143.1		40
12.11	even	2	inner	60.3.l.a.23.10	yes	40
15.2	even	4	inner	60.3.l.a.47.11	yes	40
15.8	even	4		300.3.l.g.107.10		40
15.14	odd	2		300.3.l.g.143.20		40
20.3	even	4		300.3.l.g.107.20		40
20.7	even	4	inner	60.3.l.a.47.1	yes	40
20.19	odd	2		300.3.l.g.143.10		40
60.23	odd	4		300.3.l.g.107.1		40
60.47	odd	4	inner	60.3.l.a.47.20	yes	40
60.59	even	2		300.3.l.g.143.11		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.l.a.23.1	✓	40	3.2	odd	2	inner
60.3.l.a.23.10	yes	40	12.11	even	2	inner
60.3.l.a.23.11	yes	40	4.3	odd	2	inner
60.3.l.a.23.20	yes	40	1.1	even	1	trivial
60.3.l.a.47.1	yes	40	20.7	even	4	inner
60.3.l.a.47.10	yes	40	5.2	odd	4	inner
60.3.l.a.47.11	yes	40	15.2	even	4	inner
60.3.l.a.47.20	yes	40	60.47	odd	4	inner
300.3.l.g.107.1		40	60.23	odd	4
300.3.l.g.107.10		40	15.8	even	4
300.3.l.g.107.11		40	5.3	odd	4
300.3.l.g.107.20		40	20.3	even	4
300.3.l.g.143.1		40	5.4	even	2
300.3.l.g.143.10		40	20.19	odd	2
300.3.l.g.143.11		40	60.59	even	2
300.3.l.g.143.20		40	15.14	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	60.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.99497 + 0.141758i) q^{2} +(-2.17477 + 2.06649i) q^{3} +(3.95981 + 0.565605i) q^{4} +(3.07600 + 3.94185i) q^{5} +(-4.63154 + 3.81429i) q^{6} +(-5.18766 - 5.18766i) q^{7} +(7.81952 + 1.68970i) q^{8} +(0.459255 - 8.98827i) q^{9} +O(q^{10})\)	\(q+(1.99497 + 0.141758i) q^{2} +(-2.17477 + 2.06649i) q^{3} +(3.95981 + 0.565605i) q^{4} +(3.07600 + 3.94185i) q^{5} +(-4.63154 + 3.81429i) q^{6} +(-5.18766 - 5.18766i) q^{7} +(7.81952 + 1.68970i) q^{8} +(0.459255 - 8.98827i) q^{9} +(5.57774 + 8.29993i) q^{10} +7.14796 q^{11} +(-9.78049 + 6.95284i) q^{12} +(-7.93751 - 7.93751i) q^{13} +(-9.61384 - 11.0846i) q^{14} +(-14.8354 - 2.21611i) q^{15} +(15.3602 + 4.47938i) q^{16} +(-16.5858 - 16.5858i) q^{17} +(2.19036 - 17.8662i) q^{18} -12.1545 q^{19} +(9.95085 + 17.3488i) q^{20} +(22.0022 + 0.561734i) q^{21} +(14.2600 + 1.01328i) q^{22} +(11.0852 + 11.0852i) q^{23} +(-20.4974 + 12.4842i) q^{24} +(-6.07643 + 24.2503i) q^{25} +(-14.7099 - 16.9603i) q^{26} +(17.5754 + 20.4965i) q^{27} +(-17.6080 - 23.4763i) q^{28} +26.1010 q^{29} +(-29.2820 - 6.52411i) q^{30} -8.74184i q^{31} +(30.0081 + 11.1137i) q^{32} +(-15.5452 + 14.7712i) q^{33} +(-30.7369 - 35.4392i) q^{34} +(4.49175 - 36.4063i) q^{35} +(6.90238 - 35.3321i) q^{36} +(-26.7167 + 26.7167i) q^{37} +(-24.2478 - 1.72299i) q^{38} +(33.6650 + 0.859495i) q^{39} +(17.3923 + 36.0209i) q^{40} +35.4164i q^{41} +(43.8141 + 4.23963i) q^{42} +(24.6907 - 24.6907i) q^{43} +(28.3045 + 4.04292i) q^{44} +(36.8431 - 25.8376i) q^{45} +(20.5431 + 23.6860i) q^{46} +(-58.6014 + 58.6014i) q^{47} +(-42.6615 + 22.0000i) q^{48} +4.82369i q^{49} +(-15.5600 + 47.5172i) q^{50} +(70.3445 + 1.79595i) q^{51} +(-26.9415 - 35.9205i) q^{52} +(-20.4453 + 20.4453i) q^{53} +(32.1568 + 43.3813i) q^{54} +(21.9871 + 28.1762i) q^{55} +(-31.7994 - 49.3306i) q^{56} +(26.4332 - 25.1171i) q^{57} +(52.0707 + 3.70002i) q^{58} -59.4125i q^{59} +(-57.4919 - 17.1663i) q^{60} +7.42905 q^{61} +(1.23923 - 17.4397i) q^{62} +(-49.0106 + 44.2457i) q^{63} +(58.2898 + 26.4253i) q^{64} +(6.87272 - 55.7043i) q^{65} +(-33.1061 + 27.2644i) q^{66} +(-35.8479 - 35.8479i) q^{67} +(-56.2954 - 75.0574i) q^{68} +(-47.0150 - 1.20033i) q^{69} +(14.1218 - 71.9927i) q^{70} -46.2359 q^{71} +(18.7786 - 69.5080i) q^{72} +(10.6280 + 10.6280i) q^{73} +(-57.0864 + 49.5118i) q^{74} +(-36.8981 - 65.2957i) q^{75} +(-48.1294 - 6.87464i) q^{76} +(-37.0812 - 37.0812i) q^{77} +(67.0389 + 6.48695i) q^{78} -68.3530 q^{79} +(29.5909 + 74.3262i) q^{80} +(-80.5782 - 8.25582i) q^{81} +(-5.02056 + 70.6547i) q^{82} +(76.6461 + 76.6461i) q^{83} +(86.8069 + 14.6689i) q^{84} +(14.3608 - 116.396i) q^{85} +(52.7574 - 45.7572i) q^{86} +(-56.7637 + 53.9374i) q^{87} +(55.8936 + 12.0779i) q^{88} +41.0916 q^{89} +(77.1636 - 46.3225i) q^{90} +82.3543i q^{91} +(37.6253 + 50.1649i) q^{92} +(18.0649 + 19.0115i) q^{93} +(-125.215 + 108.601i) q^{94} +(-37.3872 - 47.9112i) q^{95} +(-88.2270 + 37.8418i) q^{96} +(81.7315 - 81.7315i) q^{97} +(-0.683795 + 9.62311i) q^{98} +(3.28274 - 64.2478i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{6}+O(q^{10}) \) 40 * q - 4 * q^6	\( 40 q - 4 q^{6} - 12 q^{10} - 20 q^{12} - 8 q^{13} - 36 q^{16} - 24 q^{18} - 24 q^{21} - 76 q^{22} - 8 q^{25} - 84 q^{28} + 68 q^{30} - 40 q^{33} + 172 q^{36} - 40 q^{37} + 104 q^{40} + 236 q^{42} - 104 q^{45} + 240 q^{46} + 196 q^{48} + 304 q^{52} - 72 q^{57} + 180 q^{58} - 284 q^{60} + 48 q^{61} - 552 q^{66} - 372 q^{70} - 600 q^{72} + 104 q^{73} - 736 q^{76} - 408 q^{78} + 72 q^{81} - 720 q^{82} + 216 q^{85} - 580 q^{88} + 528 q^{90} + 368 q^{93} + 884 q^{96} + 72 q^{97}+O(q^{100}) \) 40 * q - 4 * q^6 - 12 * q^10 - 20 * q^12 - 8 * q^13 - 36 * q^16 - 24 * q^18 - 24 * q^21 - 76 * q^22 - 8 * q^25 - 84 * q^28 + 68 * q^30 - 40 * q^33 + 172 * q^36 - 40 * q^37 + 104 * q^40 + 236 * q^42 - 104 * q^45 + 240 * q^46 + 196 * q^48 + 304 * q^52 - 72 * q^57 + 180 * q^58 - 284 * q^60 + 48 * q^61 - 552 * q^66 - 372 * q^70 - 600 * q^72 + 104 * q^73 - 736 * q^76 - 408 * q^78 + 72 * q^81 - 720 * q^82 + 216 * q^85 - 580 * q^88 + 528 * q^90 + 368 * q^93 + 884 * q^96 + 72 * q^97

Introduction

L-functions

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