LMFDB - Embedded newform 60.4.j.a.7.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,4,Mod(7,60)]

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, 0, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("60.7");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	60.j (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:	$3.54011460034$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.157351936.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{4} + 16 $ x^8 + x^4 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.4
Root			$1.28897 + 0.581861i$ of defining polynomial
Character	$\chi$	$=$	60.7
Dual form			60.4.j.a.43.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.57794 + 1.16372i) q^{2} +(2.12132 + 2.12132i) q^{3} +(5.29150 + 6.00000i) q^{4} +(-8.61249 + 7.12917i) q^{5} +(3.00000 + 7.93725i) q^{6} +(8.98612 - 8.98612i) q^{7} +(6.65882 + 21.6255i) q^{8} +9.00000i q^{9} +O(q^{10})$	\(q+(2.57794 + 1.16372i) q^{2} +(2.12132 + 2.12132i) q^{3} +(5.29150 + 6.00000i) q^{4} +(-8.61249 + 7.12917i) q^{5} +(3.00000 + 7.93725i) q^{6} +(8.98612 - 8.98612i) q^{7} +(6.65882 + 21.6255i) q^{8} +9.00000i q^{9} +(-30.4988 + 8.35600i) q^{10} -38.8201i q^{11} +(-1.50295 + 23.9529i) q^{12} +(28.7750 - 28.7750i) q^{13} +(33.6230 - 12.7083i) q^{14} +(-33.3931 - 3.14659i) q^{15} +(-8.00000 + 63.4980i) q^{16} +(11.2917 + 11.2917i) q^{17} +(-10.4735 + 23.2014i) q^{18} +15.7801 q^{19} +(-88.3480 - 13.9509i) q^{20} +38.1249 q^{21} +(45.1758 - 100.076i) q^{22} +(-106.243 - 106.243i) q^{23} +(-31.7490 + 60.0000i) q^{24} +(23.3498 - 122.800i) q^{25} +(107.666 - 40.6940i) q^{26} +(-19.0919 + 19.0919i) q^{27} +(101.467 + 6.36664i) q^{28} +208.958i q^{29} +(-82.4235 - 46.9720i) q^{30} -243.881i q^{31} +(-94.5175 + 154.384i) q^{32} +(82.3498 - 82.3498i) q^{33} +(15.9689 + 42.2497i) q^{34} +(-13.3292 + 141.456i) q^{35} +(-54.0000 + 47.6235i) q^{36} +(-203.475 - 203.475i) q^{37} +(40.6801 + 18.3637i) q^{38} +122.082 q^{39} +(-211.521 - 138.777i) q^{40} +25.7503 q^{41} +(98.2834 + 44.3667i) q^{42} +(253.557 + 253.557i) q^{43} +(232.921 - 205.417i) q^{44} +(-64.1625 - 77.5124i) q^{45} +(-150.250 - 397.523i) q^{46} +(-366.988 + 366.988i) q^{47} +(-151.670 + 117.729i) q^{48} +181.499i q^{49} +(203.099 - 289.397i) q^{50} +47.9067i q^{51} +(324.913 + 20.3870i) q^{52} +(-501.716 + 501.716i) q^{53} +(-71.4353 + 27.0000i) q^{54} +(276.755 + 334.337i) q^{55} +(254.166 + 134.492i) q^{56} +(33.4747 + 33.4747i) q^{57} +(-243.169 + 538.680i) q^{58} +646.366 q^{59} +(-157.820 - 217.009i) q^{60} +527.249 q^{61} +(283.810 - 628.710i) q^{62} +(80.8750 + 80.8750i) q^{63} +(-423.320 + 288.000i) q^{64} +(-42.6824 + 452.967i) q^{65} +(308.125 - 116.460i) q^{66} +(-392.384 + 392.384i) q^{67} +(-8.00015 + 127.500i) q^{68} -450.749i q^{69} +(-198.978 + 349.154i) q^{70} -611.293i q^{71} +(-194.629 + 59.9294i) q^{72} +(144.800 - 144.800i) q^{73} +(-287.757 - 761.333i) q^{74} +(310.030 - 210.965i) q^{75} +(83.5006 + 94.6807i) q^{76} +(-348.842 - 348.842i) q^{77} +(314.720 + 142.070i) q^{78} -551.355 q^{79} +(-383.788 - 603.909i) q^{80} -81.0000 q^{81} +(66.3826 + 29.9662i) q^{82} +(-494.620 - 494.620i) q^{83} +(201.738 + 228.749i) q^{84} +(-177.750 - 16.7492i) q^{85} +(358.583 + 948.723i) q^{86} +(-443.267 + 443.267i) q^{87} +(839.502 - 258.496i) q^{88} -740.166i q^{89} +(-75.2040 - 274.489i) q^{90} -517.151i q^{91} +(75.2726 - 1199.64i) q^{92} +(517.350 - 517.350i) q^{93} +(-1373.14 + 518.999i) q^{94} +(-135.906 + 112.499i) q^{95} +(-528.000 + 126.996i) q^{96} +(84.7998 + 84.7998i) q^{97} +(-211.215 + 467.894i) q^{98} +349.381 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 24 q^{5} + 24 q^{6}+O(q^{10}) $ 8 * q - 24 * q^5 + 24 * q^6	$ 8 q - 24 q^{5} + 24 q^{6} - 56 q^{10} + 320 q^{13} - 64 q^{16} + 240 q^{17} - 432 q^{20} - 144 q^{21} - 40 q^{22} - 352 q^{25} - 336 q^{26} + 560 q^{28} - 72 q^{30} + 120 q^{33} - 432 q^{36} - 640 q^{37} - 240 q^{38} + 448 q^{40} + 1104 q^{41} + 840 q^{42} - 648 q^{45} - 304 q^{46} + 2352 q^{50} + 1920 q^{52} - 1200 q^{53} - 960 q^{56} - 720 q^{57} - 1960 q^{58} - 336 q^{60} - 272 q^{61} - 1200 q^{62} + 2592 q^{65} + 2016 q^{66} - 1440 q^{68} - 712 q^{70} + 440 q^{73} + 2464 q^{76} - 3120 q^{77} + 960 q^{78} + 192 q^{80} - 648 q^{81} - 1680 q^{82} - 2320 q^{85} + 3168 q^{86} + 800 q^{88} + 1008 q^{90} - 3360 q^{92} + 3600 q^{93} - 4224 q^{96} - 40 q^{97} - 3360 q^{98}+O(q^{100}) $ 8 * q - 24 * q^5 + 24 * q^6 - 56 * q^10 + 320 * q^13 - 64 * q^16 + 240 * q^17 - 432 * q^20 - 144 * q^21 - 40 * q^22 - 352 * q^25 - 336 * q^26 + 560 * q^28 - 72 * q^30 + 120 * q^33 - 432 * q^36 - 640 * q^37 - 240 * q^38 + 448 * q^40 + 1104 * q^41 + 840 * q^42 - 648 * q^45 - 304 * q^46 + 2352 * q^50 + 1920 * q^52 - 1200 * q^53 - 960 * q^56 - 720 * q^57 - 1960 * q^58 - 336 * q^60 - 272 * q^61 - 1200 * q^62 + 2592 * q^65 + 2016 * q^66 - 1440 * q^68 - 712 * q^70 + 440 * q^73 + 2464 * q^76 - 3120 * q^77 + 960 * q^78 + 192 * q^80 - 648 * q^81 - 1680 * q^82 - 2320 * q^85 + 3168 * q^86 + 800 * q^88 + 1008 * q^90 - 3360 * q^92 + 3600 * q^93 - 4224 * q^96 - 40 * q^97 - 3360 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	2.57794	+	1.16372i	0.911438	+	0.411438i
$2$	2.57794	+	1.16372i	0.911438	+	0.411438i
$3$	2.12132	+	2.12132i	0.408248	+	0.408248i
$3$	2.12132	+	2.12132i	0.408248	+	0.408248i
$4$	5.29150	+	6.00000i	0.661438	+	0.750000i
$5$	−8.61249	+	7.12917i	−0.770324	+	0.637652i
$5$	−8.61249	+	7.12917i	−0.770324	+	0.637652i
$6$	3.00000	+	7.93725i	0.204124	+	0.540062i
$7$	8.98612	−	8.98612i	0.485205	−	0.485205i	−0.421584	−	0.906789i	$-0.638526\pi$
$7$	8.98612	−	8.98612i	0.485205	−	0.485205i	0.906789	+	0.421584i	$0.138526\pi$
$8$	6.65882	+	21.6255i	0.294281	+	0.955719i
$9$			9.00000i			0.333333i
$10$	−30.4988	+	8.35600i	−0.964457	+	0.264240i
$11$		−	38.8201i		−	1.06406i	−0.846724	−	0.532032i	$-0.821429\pi$
$11$		−	38.8201i		−	1.06406i	0.846724	−	0.532032i	$-0.178571\pi$
$12$	−1.50295	+	23.9529i	−0.0361554	+	0.576217i
$13$	28.7750	−	28.7750i	0.613904	−	0.613904i	−0.330057	−	0.943961i	$-0.607068\pi$
$13$	28.7750	−	28.7750i	0.613904	−	0.613904i	0.943961	+	0.330057i	$0.107068\pi$
$14$	33.6230	−	12.7083i	0.641865	−	0.242602i
$15$	−33.3931	−	3.14659i	−0.574804	−	0.0541630i
$16$	−8.00000	+	63.4980i	−0.125000	+	0.992157i
$17$	11.2917	+	11.2917i	0.161097	+	0.161097i	0.783052	−	0.621956i	$-0.213662\pi$
$17$	11.2917	+	11.2917i	0.161097	+	0.161097i	−0.621956	+	0.783052i	$0.713662\pi$
$18$	−10.4735	+	23.2014i	−0.137146	+	0.303813i
$19$	15.7801			0.190537			0.0952686	−	0.995452i	$-0.469629\pi$
$19$	15.7801			0.190537			0.0952686	+	0.995452i	$0.469629\pi$
$20$	−88.3480	−	13.9509i	−0.987761	−	0.155976i
$21$	38.1249			0.396168
$22$	45.1758	−	100.076i	0.437796	−	0.969827i
$23$	−106.243	−	106.243i	−0.963179	−	0.963179i	0.0361669	−	0.999346i	$-0.488485\pi$
$23$	−106.243	−	106.243i	−0.963179	−	0.963179i	−0.999346	+	0.0361669i	$0.988485\pi$
$24$	−31.7490	+	60.0000i	−0.270031	+	0.510310i
$25$	23.3498	−	122.800i	0.186799	−	0.982398i
$26$	107.666	−	40.6940i	0.812119	−	0.306952i
$27$	−19.0919	+	19.0919i	−0.136083	+	0.136083i
$28$	101.467	+	6.36664i	0.684836	+	0.0429708i
$29$			208.958i			1.33802i	0.743254	+	0.669009i	$0.233281\pi$
$29$			208.958i			1.33802i	−0.743254	+	0.669009i	$0.766719\pi$
$30$	−82.4235	−	46.9720i	−0.501613	−	0.285862i
$31$		−	243.881i		−	1.41298i	−0.707724	−	0.706489i	$-0.750278\pi$
$31$		−	243.881i		−	1.41298i	0.707724	−	0.706489i	$-0.249722\pi$
$32$	−94.5175	+	154.384i	−0.522141	+	0.852859i
$33$	82.3498	−	82.3498i	0.434402	−	0.434402i
$34$	15.9689	+	42.2497i	0.0805483	+	0.213111i
$35$	−13.3292	+	141.456i	−0.0643729	+	0.683157i
$36$	−54.0000	+	47.6235i	−0.250000	+	0.220479i
$37$	−203.475	−	203.475i	−0.904082	−	0.904082i	0.0917043	−	0.995786i	$-0.470769\pi$
$37$	−203.475	−	203.475i	−0.904082	−	0.904082i	−0.995786	+	0.0917043i	$0.970769\pi$
$38$	40.6801	+	18.3637i	0.173663	+	0.0783942i
$39$	122.082			0.501251
$40$	−211.521	−	138.777i	−0.836108	−	0.548564i
$41$	25.7503			0.0980858			0.0490429	−	0.998797i	$-0.484383\pi$
$41$	25.7503			0.0980858			0.0490429	+	0.998797i	$0.484383\pi$
$42$	98.2834	+	44.3667i	0.361082	+	0.162998i
$43$	253.557	+	253.557i	0.899234	+	0.899234i	0.995368	−	0.0961347i	$-0.0306480\pi$
$43$	253.557	+	253.557i	0.899234	+	0.899234i	−0.0961347	+	0.995368i	$0.530648\pi$
$44$	232.921	−	205.417i	0.798047	−	0.703812i
$45$	−64.1625	−	77.5124i	−0.212551	−	0.256775i
$46$	−150.250	−	397.523i	−0.481589	−	1.27417i
$47$	−366.988	+	366.988i	−1.13895	+	1.13895i	−0.150311	+	0.988639i	$0.548028\pi$
$47$	−366.988	+	366.988i	−1.13895	+	1.13895i	−0.988639	+	0.150311i	$0.951972\pi$
$48$	−151.670	+	117.729i	−0.456077	+	0.354015i
$49$			181.499i			0.529153i
$50$	203.099	−	289.397i	0.574451	−	0.818539i
$51$			47.9067i			0.131535i
$52$	324.913	+	20.3870i	0.866488	+	0.0543687i
$53$	−501.716	+	501.716i	−1.30030	+	1.30030i	−0.372114	+	0.928187i	$0.621367\pi$
$53$	−501.716	+	501.716i	−1.30030	+	1.30030i	−0.928187	+	0.372114i	$0.878633\pi$
$54$	−71.4353	+	27.0000i	−0.180021	+	0.0680414i
$55$	276.755	+	334.337i	0.678503	+	0.819674i
$56$	254.166	+	134.492i	0.606506	+	0.320933i
$57$	33.4747	+	33.4747i	0.0777865	+	0.0777865i
$58$	−243.169	+	538.680i	−0.550511	+	1.21952i
$59$	646.366			1.42626			0.713132	−	0.701029i	$-0.247276\pi$
$59$	646.366			1.42626			0.713132	+	0.701029i	$0.247276\pi$
$60$	−157.820	−	217.009i	−0.339575	−	0.466928i
$61$	527.249			1.10668			0.553338	−	0.832957i	$-0.313354\pi$
$61$	527.249			1.10668			0.553338	+	0.832957i	$0.313354\pi$
$62$	283.810	−	628.710i	0.581353	−	1.28784i
$63$	80.8750	+	80.8750i	0.161735	+	0.161735i
$64$	−423.320	+	288.000i	−0.826797	+	0.562500i
$65$	−42.6824	+	452.967i	−0.0814477	+	0.864363i
$66$	308.125	−	116.460i	0.574660	−	0.217201i
$67$	−392.384	+	392.384i	−0.715483	+	0.715483i	−0.967677	−	0.252194i	$-0.918848\pi$
$67$	−392.384	+	392.384i	−0.715483	+	0.715483i	0.252194	+	0.967677i	$0.418848\pi$
$68$	−8.00015	+	127.500i	−0.0142671	+	0.227378i
$69$		−	450.749i		−	0.786432i
$70$	−198.978	+	349.154i	−0.339748	+	0.596170i
$71$		−	611.293i		−	1.02179i	−0.859643	−	0.510896i	$-0.829314\pi$
$71$		−	611.293i		−	1.02179i	0.859643	−	0.510896i	$-0.170686\pi$
$72$	−194.629	+	59.9294i	−0.318573	+	0.0980937i
$73$	144.800	−	144.800i	0.232158	−	0.232158i	−0.581435	−	0.813593i	$-0.697509\pi$
$73$	144.800	−	144.800i	0.232158	−	0.232158i	0.813593	+	0.581435i	$0.197509\pi$
$74$	−287.757	−	761.333i	−0.452041	−	1.19599i
$75$	310.030	−	210.965i	0.477323	−	0.324802i
$76$	83.5006	+	94.6807i	0.126029	+	0.142903i
$77$	−348.842	−	348.842i	−0.516288	−	0.516288i
$78$	314.720	+	142.070i	0.456859	+	0.206234i
$79$	−551.355			−0.785218			−0.392609	−	0.919705i	$-0.628427\pi$
$79$	−551.355			−0.785218			−0.392609	+	0.919705i	$0.628427\pi$
$80$	−383.788	−	603.909i	−0.536361	−	0.843989i
$81$	−81.0000			−0.111111
$82$	66.3826	+	29.9662i	0.0893991	+	0.0403562i
$83$	−494.620	−	494.620i	−0.654116	−	0.654116i	0.299866	−	0.953981i	$-0.403058\pi$
$83$	−494.620	−	494.620i	−0.654116	−	0.654116i	−0.953981	+	0.299866i	$0.903058\pi$
$84$	201.738	+	228.749i	0.262040	+	0.297126i
$85$	−177.750	−	16.7492i	−0.226820	−	0.0213730i
$86$	358.583	+	948.723i	0.449617	+	1.18957i
$87$	−443.267	+	443.267i	−0.546244	+	0.546244i
$88$	839.502	−	258.496i	1.01695	−	0.313134i
$89$		−	740.166i		−	0.881544i	−0.897619	−	0.440772i	$-0.854705\pi$
$89$		−	740.166i		−	0.881544i	0.897619	−	0.440772i	$-0.145295\pi$
$90$	−75.2040	−	274.489i	−0.0880800	−	0.321486i
$91$		−	517.151i		−	0.595739i
$92$	75.2726	−	1199.64i	0.0853012	−	1.35947i
$93$	517.350	−	517.350i	0.576846	−	0.576846i
$94$	−1373.14	+	518.999i	−1.50669	+	0.569475i
$95$	−135.906	+	112.499i	−0.146775	+	0.121497i
$96$	−528.000	+	126.996i	−0.561341	+	0.135015i
$97$	84.7998	+	84.7998i	0.0887641	+	0.0887641i	0.750095	−	0.661331i	$-0.230008\pi$
$97$	84.7998	+	84.7998i	0.0887641	+	0.0887641i	−0.661331	+	0.750095i	$0.730008\pi$
$98$	−211.215	+	467.894i	−0.217714	+	0.482290i
$99$	349.381			0.354688
$100$	860.354	−	509.696i	0.860354	−	0.509696i
$101$	573.126			0.564635			0.282318	−	0.959321i	$-0.408897\pi$
$101$	573.126			0.564635			0.282318	+	0.959321i	$0.408897\pi$
$102$	−55.7501	+	123.500i	−0.0541184	+	0.119886i
$103$	−1298.81	−	1298.81i	−1.24248	−	1.24248i	−0.958970	−	0.283508i	$-0.908502\pi$
$103$	−1298.81	−	1298.81i	−1.24248	−	1.24248i	−0.283508	−	0.958970i	$-0.591498\pi$
$104$	813.881	+	430.665i	0.767380	+	0.406060i
$105$	−328.350	+	271.799i	−0.305178	+	0.252617i
$106$	−1877.25	+	709.533i	−1.72014	+	0.650151i
$107$	364.866	−	364.866i	0.329653	−	0.329653i	−0.522801	−	0.852455i	$-0.675113\pi$
$107$	364.866	−	364.866i	0.329653	−	0.329653i	0.852455	+	0.522801i	$0.175113\pi$
$108$	−215.576	−	13.5265i	−0.192072	−	0.0120518i
$109$			1210.25i			1.06349i	0.846903	+	0.531747i	$0.178464\pi$
$109$			1210.25i			1.06349i	−0.846903	+	0.531747i	$0.821536\pi$
$110$	324.381	+	1183.97i	0.281168	+	1.02624i
$111$		−	863.270i		−	0.738180i
$112$	498.712	+	642.490i	0.420748	+	0.542050i
$113$	564.456	−	564.456i	0.469908	−	0.469908i	−0.431977	−	0.901885i	$-0.642184\pi$
$113$	564.456	−	564.456i	0.469908	−	0.469908i	0.901885	+	0.431977i	$0.142184\pi$
$114$	47.3404	+	125.251i	0.0388933	+	0.102902i
$115$	1672.43	+	157.591i	1.35613	+	0.127787i
$116$	−1253.75	+	1105.70i	−1.00351	+	0.885016i
$117$	258.975	+	258.975i	0.204635	+	0.204635i
$118$	1666.29	+	752.190i	1.29995	+	0.586819i
$119$	202.937			0.156330
$120$	−154.312	−	743.093i	−0.117389	−	0.565290i
$121$	−175.999			−0.132231
$122$	1359.21	+	613.571i	1.00867	+	0.455329i
$123$	54.6246	+	54.6246i	0.0400434	+	0.0400434i
$124$	1463.29	−	1290.50i	1.05973	−	0.934597i
$125$	674.361	+	1224.08i	0.482533	+	0.875878i
$126$	114.375	+	302.607i	0.0808674	+	0.213955i
$127$	−190.770	+	190.770i	−0.133292	+	0.133292i	−0.770605	−	0.637313i	$-0.780046\pi$
$127$	−190.770	+	190.770i	−0.133292	+	0.133292i	0.637313	+	0.770605i	$0.280046\pi$
$128$	−1426.44	+	249.818i	−0.985008	+	0.172508i
$129$			1075.75i			0.734221i
$130$	−637.160	+	1118.05i	−0.429866	+	0.754302i
$131$			1711.34i			1.14138i	0.821166	+	0.570689i	$0.193324\pi$
$131$			1711.34i			1.14138i	−0.821166	+	0.570689i	$0.806676\pi$
$132$	929.853	+	58.3446i	0.613131	+	0.0384716i
$133$	141.802	−	141.802i	0.0924496	−	0.0924496i
$134$	−1468.17	+	554.915i	−0.946495	+	0.357741i
$135$	28.3193	−	300.538i	0.0180543	−	0.191601i
$136$	−168.999	+	319.378i	−0.106555	+	0.201371i
$137$	122.540	+	122.540i	0.0764184	+	0.0764184i	0.744283	−	0.667864i	$-0.232791\pi$
$137$	122.540	+	122.540i	0.0764184	+	0.0764184i	−0.667864	+	0.744283i	$0.732791\pi$
$138$	524.547	−	1162.00i	0.323568	−	0.716784i
$139$	799.394			0.487797			0.243898	−	0.969801i	$-0.421574\pi$
$139$	799.394			0.487797			0.243898	+	0.969801i	$0.421574\pi$
$140$	−919.270	+	668.541i	−0.554946	+	0.403586i
$141$	−1557.00			−0.929949
$142$	711.376	−	1575.87i	0.420404	−	0.931299i
$143$	−1117.05	−	1117.05i	−0.653233	−	0.653233i
$144$	−571.482	−	72.0000i	−0.330719	−	0.0416667i
$145$	−1489.70	−	1799.65i	−0.853191	−	1.03071i
$146$	541.791	−	204.778i	0.307116	−	0.116079i
$147$	−385.018	+	385.018i	−0.216026	+	0.216026i
$148$	144.161	−	2297.54i	0.0800675	−	1.27606i
$149$		−	2446.79i		−	1.34529i	−0.739964	−	0.672647i	$-0.765157\pi$
$149$		−	2446.79i		−	1.34529i	0.739964	−	0.672647i	$-0.234843\pi$
$150$	1044.74	−	183.066i	0.568686	−	0.0996484i
$151$			905.413i			0.487957i	0.969781	+	0.243978i	$0.0784526\pi$
$151$			905.413i			0.487957i	−0.969781	+	0.243978i	$0.921547\pi$
$152$	105.077	+	341.252i	0.0560715	+	0.182100i
$153$	−101.625	+	101.625i	−0.0536989	+	0.0536989i
$154$	−493.337	−	1305.25i	−0.258144	−	0.682985i
$155$	1738.67	+	2100.42i	0.900989	+	1.08845i
$156$	645.998	+	732.493i	0.331546	+	0.375938i
$157$	−30.2239	−	30.2239i	−0.0153639	−	0.0153639i	0.699383	−	0.714747i	$-0.253458\pi$
$157$	−30.2239	−	30.2239i	−0.0153639	−	0.0153639i	−0.714747	+	0.699383i	$0.753458\pi$
$158$	−1421.36	−	641.623i	−0.715677	−	0.323068i
$159$	−2128.60			−1.06169
$160$	−286.599	−	2003.46i	−0.141610	−	0.989922i
$161$	−1909.42			−0.934678
$162$	−208.813	−	94.2615i	−0.101271	−	0.0457153i
$163$	955.533	+	955.533i	0.459160	+	0.459160i	0.898380	−	0.439219i	$-0.144745\pi$
$163$	955.533	+	955.533i	0.459160	+	0.459160i	−0.439219	+	0.898380i	$0.644745\pi$
$164$	136.258	+	154.502i	0.0648777	+	0.0735644i
$165$	−122.151	+	1296.32i	−0.0576329	+	0.611628i
$166$	−699.498	−	1850.70i	−0.327058	−	0.865314i
$167$	−173.415	+	173.415i	−0.0803550	+	0.0803550i	−0.746142	−	0.665787i	$-0.768096\pi$
$167$	−173.415	+	173.415i	−0.0803550	+	0.0803550i	0.665787	+	0.746142i	$0.268096\pi$
$168$	253.867	+	824.467i	0.116585	+	0.378625i
$169$			540.996i			0.246243i
$170$	−438.737	−	250.030i	−0.197939	−	0.112803i
$171$			142.021i			0.0635124i
$172$	−179.644	+	2863.04i	−0.0796381	+	1.26921i
$173$	1289.00	−	1289.00i	0.566480	−	0.566480i	−0.364660	−	0.931141i	$-0.618815\pi$
$173$	1289.00	−	1289.00i	0.566480	−	0.566480i	0.931141	+	0.364660i	$0.118815\pi$
$174$	−1658.55	+	626.874i	−0.722612	+	0.273122i
$175$	−893.669	−	1313.32i	−0.386029	−	0.567300i
$176$	2465.00	+	310.561i	1.05572	+	0.133008i
$177$	1371.15	+	1371.15i	0.582270	+	0.582270i
$178$	861.347	−	1908.10i	0.362701	−	0.803473i
$179$	826.182			0.344982			0.172491	−	0.985011i	$-0.444818\pi$
$179$	826.182			0.344982			0.172491	+	0.985011i	$0.444818\pi$
$180$	125.558	−	795.132i	0.0519919	−	0.329254i
$181$	1414.74			0.580979			0.290489	−	0.956878i	$-0.406182\pi$
$181$	1414.74			0.580979			0.290489	+	0.956878i	$0.406182\pi$
$182$	601.820	−	1333.18i	0.245109	−	0.542979i
$183$	1118.46	+	1118.46i	0.451799	+	0.451799i
$184$	1590.09	−	3004.99i	0.637083	−	1.20397i
$185$	3203.03	+	301.817i	1.27293	+	0.119946i
$186$	1935.75	−	731.643i	0.763096	−	0.288423i
$187$	438.345	−	438.345i	0.171417	−	0.171417i
$188$	−4143.84	−	260.010i	−1.60756	−	0.100868i
$189$			343.124i			0.132056i
$190$	−481.275	+	131.859i	−0.183765	+	0.0503476i
$191$		−	932.465i		−	0.353250i	−0.984278	−	0.176625i	$-0.943482\pi$
$191$		−	932.465i		−	0.353250i	0.984278	−	0.176625i	$-0.0565180\pi$
$192$	−1508.94	−	287.058i	−0.567178	−	0.107899i
$193$	−2205.49	+	2205.49i	−0.822565	+	0.822565i	−0.986475	−	0.163910i	$-0.947589\pi$
$193$	−2205.49	+	2205.49i	−0.822565	+	0.822565i	0.163910	+	0.986475i	$0.447589\pi$
$194$	119.925	+	317.292i	0.0443820	+	0.117424i
$195$	−1051.43	+	870.344i	−0.386126	+	0.319624i
$196$	−1089.00	+	960.405i	−0.396865	+	0.350002i
$197$	−1852.98	−	1852.98i	−0.670150	−	0.670150i	0.287600	−	0.957751i	$-0.407143\pi$
$197$	−1852.98	−	1852.98i	−0.670150	−	0.670150i	−0.957751	+	0.287600i	$0.907143\pi$
$198$	900.681	+	406.582i	0.323276	+	0.145932i
$199$	−1633.75			−0.581978			−0.290989	−	0.956726i	$-0.593984\pi$
$199$	−1633.75			−0.581978			−0.290989	+	0.956726i	$0.593984\pi$
$200$	2811.08	−	312.751i	0.993868	−	0.110574i
$201$	−1664.74			−0.584189
$202$	1477.48	+	666.959i	0.514630	+	0.232312i
$203$	1877.72	+	1877.72i	0.649213	+	0.649213i
$204$	−287.440	+	253.498i	−0.0986511	+	0.0870021i
$205$	−221.774	+	183.578i	−0.0755579	+	0.0625447i
$206$	−1836.79	−	4859.69i	−0.621239	−	1.64364i
$207$	956.183	−	956.183i	0.321060	−	0.321060i
$208$	1596.96	+	2057.36i	0.532351	+	0.685827i
$209$		−	612.586i		−	0.202744i
$210$	−1162.76	+	318.572i	−0.382087	+	0.104683i
$211$			4234.33i			1.38153i	0.723078	+	0.690766i	$0.242726\pi$
$211$			4234.33i			1.38153i	−0.723078	+	0.690766i	$0.757274\pi$
$212$	−5665.13	−	355.464i	−1.83529	−	0.115158i
$213$	1296.75	−	1296.75i	0.417145	−	0.417145i
$214$	1365.20	−	515.998i	0.436090	−	0.164827i
$215$	−3991.40	−	376.105i	−1.26610	−	0.119303i
$216$	−540.000	−	285.741i	−0.170103	−	0.0900103i
$217$	−2191.54	−	2191.54i	−0.685584	−	0.685584i
$218$	−1408.39	+	3119.95i	−0.437562	+	0.969309i
$219$	614.333			0.189556
$220$	−541.575	+	3429.68i	−0.165968	+	1.05104i
$221$	649.839			0.197796
$222$	1004.61	−	2225.45i	0.303715	−	0.672805i
$223$	487.697	+	487.697i	0.146451	+	0.146451i	0.776531	−	0.630080i	$-0.216978\pi$
$223$	487.697	+	487.697i	0.146451	+	0.146451i	−0.630080	+	0.776531i	$0.716978\pi$
$224$	537.967	+	2236.66i	0.160466	+	0.667156i
$225$	1105.20	+	210.148i	0.327466	+	0.0622662i
$226$	2112.00	−	798.262i	0.621630	−	0.234954i
$227$	2178.24	−	2178.24i	0.636892	−	0.636892i	−0.312895	−	0.949788i	$-0.601299\pi$
$227$	2178.24	−	2178.24i	0.636892	−	0.636892i	0.949788	+	0.312895i	$0.101299\pi$
$228$	−23.7167	+	377.980i	−0.00688894	+	0.109791i
$229$			3797.50i			1.09583i	0.836533	+	0.547916i	$0.184579\pi$
$229$			3797.50i			1.09583i	−0.836533	+	0.547916i	$0.815421\pi$
$230$	4128.04	+	2352.51i	1.18345	+	0.674434i
$231$		−	1480.01i		−	0.421548i
$232$	−4518.81	+	1391.41i	−1.27877	+	0.393753i
$233$	−2072.14	+	2072.14i	−0.582620	+	0.582620i	−0.935622	−	0.353003i	$-0.885161\pi$
$233$	−2072.14	+	2072.14i	−0.582620	+	0.582620i	0.353003	+	0.935622i	$0.385161\pi$
$234$	366.246	+	968.997i	0.102317	+	0.270706i
$235$	544.358	−	5776.99i	0.151106	−	1.60361i
$236$	3420.25	+	3878.19i	0.943386	+	1.06970i
$237$	−1169.60	−	1169.60i	−0.320564	−	0.320564i
$238$	523.159	+	236.163i	0.142485	+	0.0643199i
$239$	1188.51			0.321665			0.160833	−	0.986982i	$-0.448582\pi$
$239$	1188.51			0.321665			0.160833	+	0.986982i	$0.448582\pi$
$240$	466.947	−	2095.22i	0.125589	−	0.563525i
$241$	6989.98			1.86832			0.934159	−	0.356858i	$-0.116152\pi$
$241$	6989.98			1.86832			0.934159	+	0.356858i	$0.116152\pi$
$242$	−453.714	−	204.814i	−0.120520	−	0.0544047i
$243$	−171.827	−	171.827i	−0.0453609	−	0.0453609i
$244$	2789.94	+	3163.49i	0.731998	+	0.830007i
$245$	−1293.94	−	1563.16i	−0.337416	−	0.407619i
$246$	77.2508	+	204.386i	0.0200217	+	0.0529724i
$247$	454.073	−	454.073i	0.116972	−	0.116972i
$248$	5274.04	−	1623.96i	1.35041	−	0.415813i
$249$		−	2098.49i		−	0.534083i
$250$	313.974	+	3940.36i	0.0794297	+	0.996840i
$251$		−	3950.18i		−	0.993359i	−0.867934	−	0.496679i	$-0.834552\pi$
$251$		−	3950.18i		−	0.993359i	0.867934	−	0.496679i	$-0.165448\pi$
$252$	−57.2998	+	913.201i	−0.0143236	+	0.228279i
$253$	−4124.35	+	4124.35i	−1.02488	+	1.02488i
$254$	−713.794	+	269.789i	−0.176329	+	0.0666459i
$255$	−341.535	−	412.596i	−0.0838735	−	0.101324i
$256$	−3968.00	−	1015.97i	−0.968750	−	0.248039i
$257$	4166.19	+	4166.19i	1.01121	+	1.01121i	0.999936	+	0.0112693i	$0.00358721\pi$
$257$	4166.19	+	4166.19i	1.01121	+	1.01121i	0.0112693	+	0.999936i	$0.496413\pi$
$258$	−1251.87	+	2773.21i	−0.302086	+	0.669197i
$259$	−3656.89			−0.877330
$260$	−2943.65	+	2140.78i	−0.702145	+	0.510637i
$261$	−1880.62			−0.446006
$262$	−1991.52	+	4411.72i	−0.469606	+	1.04029i
$263$	2028.86	+	2028.86i	0.475684	+	0.475684i	0.903748	−	0.428064i	$-0.140804\pi$
$263$	2028.86	+	2028.86i	0.475684	+	0.475684i	−0.428064	+	0.903748i	$0.640804\pi$
$264$	2329.21	+	1232.50i	0.543002	+	0.287330i
$265$	744.202	−	7897.84i	0.172513	−	1.83079i
$266$	530.575	−	200.538i	0.122299	−	0.0462248i
$267$	1570.13	−	1570.13i	0.359889	−	0.359889i
$268$	−4430.61	−	278.003i	−1.00986	−	0.0633647i
$269$		−	391.791i		−	0.0888027i	−0.999014	−	0.0444014i	$-0.985862\pi$
$269$		−	391.791i		−	0.0888027i	0.999014	−	0.0444014i	$-0.0141380\pi$
$270$	422.748	−	741.812i	0.0952874	−	0.167204i
$271$		−	2030.42i		−	0.455127i	−0.973763	−	0.227563i	$-0.926924\pi$
$271$		−	2030.42i		−	0.455127i	0.973763	−	0.227563i	$-0.0730759\pi$
$272$	−807.335	+	626.668i	−0.179970	+	0.139696i
$273$	1097.04	−	1097.04i	0.243209	−	0.243209i
$274$	173.298	+	458.504i	0.0382092	+	0.101092i
$275$	−4767.10	−	906.442i	−1.04533	−	0.198766i
$276$	2704.49	−	2385.14i	0.589824	−	0.520176i
$277$	4588.12	+	4588.12i	0.995210	+	0.995210i	0.999989	−	0.00477858i	$-0.00152108\pi$
$277$	4588.12	+	4588.12i	0.995210	+	0.995210i	−0.00477858	+	0.999989i	$0.501521\pi$
$278$	2060.79	+	930.273i	0.444596	+	0.200698i
$279$	2194.93			0.470993
$280$	−3147.81	+	653.682i	−0.671850	+	0.139518i
$281$	−2401.75			−0.509880			−0.254940	−	0.966957i	$-0.582056\pi$
$281$	−2401.75			−0.509880			−0.254940	+	0.966957i	$0.582056\pi$
$282$	−4013.84	−	1811.91i	−0.847590	−	0.382616i
$283$	−1874.48	−	1874.48i	−0.393732	−	0.393732i	0.482283	−	0.876015i	$-0.339808\pi$
$283$	−1874.48	−	1874.48i	−0.393732	−	0.393732i	−0.876015	+	0.482283i	$0.839808\pi$
$284$	3667.76	−	3234.66i	0.766343	−	0.675851i
$285$	−526.947	−	49.6535i	−0.109522	−	0.0103201i
$286$	−1579.75	−	4179.61i	−0.326617	−	0.864146i
$287$	231.395	−	231.395i	0.0475917	−	0.0475917i
$288$	−1389.46	−	850.658i	−0.284286	−	0.174047i
$289$		−	4657.99i		−	0.948096i
$290$	−1746.05	−	6372.97i	−0.353558	−	1.29046i
$291$			359.775i			0.0724755i
$292$	1635.01	+	102.590i	0.327677	+	0.0205604i
$293$	919.438	−	919.438i	0.183325	−	0.183325i	−0.609478	−	0.792803i	$-0.708621\pi$
$293$	919.438	−	919.438i	0.183325	−	0.183325i	0.792803	+	0.609478i	$0.208621\pi$
$294$	−1440.61	+	544.498i	−0.285775	+	0.108013i
$295$	−5566.81	+	4608.05i	−1.09869	+	0.909461i
$296$	3045.33	−	5755.13i	0.597994	−	1.13010i
$297$	741.148	+	741.148i	0.144801	+	0.144801i
$298$	2847.38	−	6307.66i	0.553504	−	1.22615i
$299$	−6114.27			−1.18260
$300$	2906.32	+	743.858i	0.559321	+	0.143156i
$301$	4556.98			0.872625
$302$	−1053.65	+	2334.10i	−0.200764	+	0.444742i
$303$	1215.78	+	1215.78i	0.230511	+	0.230511i
$304$	−126.241	+	1002.01i	−0.0238172	+	0.189043i
$305$	−4540.92	+	3758.85i	−0.852500	+	0.705675i
$306$	−380.247	+	143.720i	−0.0710369	+	0.0268494i
$307$	2004.00	−	2004.00i	0.372555	−	0.372555i	−0.495852	−	0.868407i	$-0.665144\pi$
$307$	2004.00	−	2004.00i	0.372555	−	0.372555i	0.868407	+	0.495852i	$0.165144\pi$
$308$	247.153	−	3938.95i	0.0457236	−	0.728709i
$309$		−	5510.37i		−	1.01448i
$310$	2037.87	+	7438.08i	0.373366	+	1.36276i
$311$			3829.04i			0.698151i	0.937095	+	0.349075i	$0.113504\pi$
$311$			3829.04i			0.698151i	−0.937095	+	0.349075i	$0.886496\pi$
$312$	812.923	+	2640.08i	0.147509	+	0.479055i
$313$	706.908	−	706.908i	0.127657	−	0.127657i	−0.640391	−	0.768049i	$-0.721228\pi$
$313$	706.908	−	706.908i	0.127657	−	0.127657i	0.768049	+	0.640391i	$0.221228\pi$
$314$	−42.7430	−	113.087i	−0.00768193	−	0.0203245i
$315$	−1273.11	−	119.963i	−0.227719	−	0.0214576i
$316$	−2917.49	−	3308.13i	−0.519373	−	0.588914i
$317$	742.045	+	742.045i	0.131475	+	0.131475i	0.769782	−	0.638307i	$-0.220365\pi$
$317$	742.045	+	742.045i	0.131475	+	0.131475i	−0.638307	+	0.769782i	$0.720365\pi$
$318$	−5487.39	−	2477.10i	−0.967666	−	0.436820i
$319$	8111.77			1.42374
$320$	1592.64	−	5498.32i	0.278222	−	0.960517i
$321$	1547.99			0.269161
$322$	−4922.35	−	2222.03i	−0.851901	−	0.384562i
$323$	178.185	+	178.185i	0.0306949	+	0.0306949i
$324$	−428.612	−	486.000i	−0.0734931	−	0.0833333i
$325$	−2861.67	−	4205.46i	−0.488422	−	0.717775i
$326$	1351.33	+	3575.28i	0.229580	+	0.607412i
$327$	−2567.33	+	2567.33i	−0.434170	+	0.434170i
$328$	171.466	+	556.861i	0.0288648	+	0.0937425i
$329$			6595.59i			1.10525i
$330$	−1823.46	+	3199.69i	−0.304176	+	0.533748i
$331$			7332.79i			1.21766i	0.793299	+	0.608832i	$0.208362\pi$
$331$			7332.79i			1.21766i	−0.793299	+	0.608832i	$0.791638\pi$
$332$	350.437	−	5585.00i	0.0579299	−	0.923244i
$333$	1831.27	−	1831.27i	0.301361	−	0.301361i
$334$	−648.861	+	245.246i	−0.106300	+	0.0401775i
$335$	582.029	−	6176.78i	0.0949243	−	1.00738i
$336$	−304.999	+	2420.85i	−0.0495210	+	0.393061i
$337$	−5725.79	−	5725.79i	−0.925530	−	0.925530i	0.0718830	−	0.997413i	$-0.477099\pi$
$337$	−5725.79	−	5725.79i	−0.925530	−	0.925530i	−0.997413	+	0.0718830i	$0.977099\pi$
$338$	−629.568	+	1394.65i	−0.101314	+	0.224435i
$339$	2394.79			0.383678
$340$	−840.071	−	1155.13i	−0.133998	−	0.184252i
$341$	−9467.48			−1.50350
$342$	−165.273	+	366.121i	−0.0261314	+	0.0578876i
$343$	4713.21	+	4713.21i	0.741952	+	0.741952i
$344$	−3794.89	+	7171.67i	−0.594787	+	1.12404i
$345$	3213.47	+	3882.07i	0.501470	+	0.605808i
$346$	4823.01	−	1822.93i	0.749383	−	0.283240i
$347$	1944.55	−	1944.55i	0.300832	−	0.300832i	−0.540507	−	0.841339i	$-0.681768\pi$
$347$	1944.55	−	1944.55i	0.300832	−	0.300832i	0.841339	+	0.540507i	$0.181768\pi$
$348$	−5005.15	−	314.053i	−0.770989	−	0.0483765i
$349$			9581.22i			1.46954i	0.678314	+	0.734772i	$0.262711\pi$
$349$			9581.22i			1.46954i	−0.678314	+	0.734772i	$0.737289\pi$
$350$	−775.484	−	4425.63i	−0.118432	−	0.675885i
$351$			1098.74i			0.167084i
$352$	5993.20	+	3669.18i	0.907496	+	0.555591i
$353$	−346.439	+	346.439i	−0.0522354	+	0.0522354i	−0.732742	−	0.680507i	$-0.761760\pi$
$353$	−346.439	+	346.439i	−0.0522354	+	0.0522354i	0.680507	+	0.732742i	$0.261760\pi$
$354$	1939.10	+	5130.37i	0.291135	+	0.770271i
$355$	4358.02	+	5264.76i	0.651548	+	0.787111i
$356$	4440.99	−	3916.59i	0.661158	−	0.583087i
$357$	430.495	+	430.495i	0.0638213	+	0.0638213i
$358$	2129.84	+	961.446i	0.314430	+	0.141939i
$359$	2196.06			0.322852			0.161426	−	0.986885i	$-0.448391\pi$
$359$	2196.06			0.322852			0.161426	+	0.986885i	$0.448391\pi$
$360$	1248.99	−	1903.68i	0.182855	−	0.278703i
$361$	−6609.99			−0.963696
$362$	3647.12	+	1646.37i	0.529526	+	0.239037i
$363$	−373.350	−	373.350i	−0.0539829	−	0.0539829i
$364$	3102.91	−	2736.51i	0.446804	−	0.394044i
$365$	−214.784	+	2279.39i	−0.0308008	+	0.326873i
$366$	1581.75	+	4184.91i	0.225899	+	0.597674i
$367$	5063.03	−	5063.03i	0.720130	−	0.720130i	−0.248501	−	0.968632i	$-0.579938\pi$
$367$	5063.03	−	5063.03i	0.720130	−	0.720130i	0.968632	+	0.248501i	$0.0799380\pi$
$368$	7596.14	−	5896.25i	1.07602	−	0.835227i
$369$			231.753i			0.0326953i
$370$	7905.97	+	4505.50i	1.11084	+	0.633053i
$371$			9016.95i			1.26182i
$372$	5841.66	+	366.541i	0.814182	+	0.0510867i
$373$	−700.635	+	700.635i	−0.0972588	+	0.0972588i	−0.754062	−	0.656803i	$-0.771908\pi$
$373$	−700.635	+	700.635i	−0.0972588	+	0.0972588i	0.656803	+	0.754062i	$0.271908\pi$
$374$	1640.14	−	619.914i	0.226763	−	0.0857085i
$375$	−1166.12	+	4027.19i	−0.160582	+	0.554569i
$376$	−10380.0	−	5492.57i	−1.42369	−	0.753345i
$377$	6012.77	+	6012.77i	0.821415	+	0.821415i
$378$	−399.301	+	884.551i	−0.0543328	+	0.120361i
$379$	−7182.07			−0.973398			−0.486699	−	0.873570i	$-0.661799\pi$
$379$	−7182.07			−0.973398			−0.486699	+	0.873570i	$0.661799\pi$
$380$	−1394.14	−	220.147i	−0.188205	−	0.0297192i
$381$	−809.367			−0.108832
$382$	1085.13	−	2403.83i	0.145340	−	0.321966i
$383$	6705.49	+	6705.49i	0.894608	+	0.894608i	0.994953	−	0.100345i	$-0.0319947\pi$
$383$	6705.49	+	6705.49i	0.894608	+	0.894608i	−0.100345	+	0.994953i	$0.531995\pi$
$384$	−3555.89	−	2496.00i	−0.472554	−	0.331702i
$385$	5491.35	+	517.442i	0.726922	+	0.0684969i
$386$	−8252.21	+	3119.04i	−1.08815	+	0.411282i
$387$	−2282.01	+	2282.01i	−0.299745	+	0.299745i
$388$	−60.0804	+	957.517i	−0.00786114	+	0.125285i
$389$			1204.96i			0.157053i	0.996912	+	0.0785267i	$0.0250216\pi$
$389$			1204.96i			0.157053i	−0.996912	+	0.0785267i	$0.974978\pi$
$390$	−3723.36	+	1020.12i	−0.483435	+	0.132451i
$391$		−	2399.32i		−	0.310330i
$392$	−3925.01	+	1208.57i	−0.505721	+	0.155720i
$393$	−3630.30	+	3630.30i	−0.465965	+	0.465965i
$394$	−2620.51	−	6933.23i	−0.335075	−	0.886526i
$395$	4748.53	−	3930.70i	0.604872	−	0.500696i
$396$	1848.75	+	2096.28i	0.234604	+	0.266016i
$397$	−7705.96	−	7705.96i	−0.974184	−	0.974184i	0.0254910	−	0.999675i	$-0.491885\pi$
$397$	−7705.96	−	7705.96i	−0.974184	−	0.974184i	−0.999675	+	0.0254910i	$0.991885\pi$
$398$	−4211.71	−	1901.23i	−0.530437	−	0.239448i
$399$	601.615			0.0754848
$400$	7610.75	+	2465.07i	0.951343	+	0.308133i
$401$	−2779.99			−0.346200			−0.173100	−	0.984904i	$-0.555378\pi$
$401$	−2779.99			−0.346200			−0.173100	+	0.984904i	$0.555378\pi$
$402$	−4291.60	−	1937.30i	−0.532452	−	0.240358i
$403$	−7017.68	−	7017.68i	−0.867434	−	0.867434i
$404$	3032.70	+	3438.76i	0.373471	+	0.423476i
$405$	697.611	−	577.463i	0.0855916	−	0.0708503i
$406$	2655.50	+	7025.79i	0.324606	+	0.858828i
$407$	−7898.90	+	7898.90i	−0.962000	+	0.962000i
$408$	−1036.00	+	319.002i	−0.125710	+	0.0387082i
$409$		−	10322.0i		−	1.24790i	−0.781465	−	0.623949i	$-0.785527\pi$
$409$		−	10322.0i		−	1.24790i	0.781465	−	0.623949i	$-0.214473\pi$
$410$	−785.353	+	215.169i	−0.0945995	+	0.0259182i
$411$			519.895i			0.0623954i
$412$	920.201	−	14665.5i	0.110037	−	1.75368i
$413$	5808.32	−	5808.32i	0.692030	−	0.692030i
$414$	3577.71	−	1352.25i	0.424722	−	0.160530i
$415$	7786.14	+	733.677i	0.920980	+	0.0867826i
$416$	1722.66	+	7162.15i	0.203030	+	0.844119i
$417$	1695.77	+	1695.77i	0.199142	+	0.199142i
$418$	712.879	−	1579.21i	0.0834164	−	0.184788i
$419$	−10705.0			−1.24815			−0.624075	−	0.781365i	$-0.714524\pi$
$419$	−10705.0			−1.24815			−0.624075	+	0.781365i	$0.714524\pi$
$420$	−3368.26	−	531.876i	−0.391319	−	0.0617926i
$421$	14290.0			1.65428			0.827140	−	0.561996i	$-0.189966\pi$
$421$	14290.0			1.65428			0.827140	+	0.561996i	$0.189966\pi$
$422$	−4927.58	+	10915.8i	−0.568414	+	1.25918i
$423$	−3302.89	−	3302.89i	−0.379650	−	0.379650i
$424$	−14190.7	−	7508.99i	−1.62538	−	0.860068i
$425$	1650.28	−	1122.96i	0.188354	−	0.128168i
$426$	4851.99	−	1833.88i	0.551830	−	0.208572i
$427$	4737.92	−	4737.92i	0.536965	−	0.536965i
$428$	4119.88	+	258.506i	0.465285	+	0.0291948i
$429$		−	4739.24i		−	0.533363i
$430$	−9851.90	−	5614.46i	−1.10489	−	0.629659i
$431$		−	15321.0i		−	1.71227i	−0.516756	−	0.856133i	$-0.672860\pi$
$431$		−	15321.0i		−	1.71227i	0.516756	−	0.856133i	$-0.327140\pi$
$432$	−1059.56	−	1365.03i	−0.118005	−	0.152026i
$433$	−192.550	+	192.550i	−0.0213704	+	0.0213704i	−0.717711	−	0.696341i	$-0.754810\pi$
$433$	−192.550	+	192.550i	−0.0213704	+	0.0213704i	0.696341	+	0.717711i	$0.254810\pi$
$434$	−3099.31	−	8200.00i	−0.342792	−	0.906942i
$435$	657.504	−	6977.76i	0.0724711	−	0.769098i
$436$	−7261.50	+	6404.04i	−0.797621	+	0.703435i
$437$	−1676.52	−	1676.52i	−0.183521	−	0.183521i
$438$	1583.71	+	714.913i	0.172769	+	0.0779906i
$439$	−5728.97			−0.622845			−0.311423	−	0.950272i	$-0.600805\pi$
$439$	−5728.97			−0.622845			−0.311423	+	0.950272i	$0.600805\pi$
$440$	−5387.34	+	8211.25i	−0.583707	+	0.889672i
$441$	−1633.49			−0.176384
$442$	1675.24	+	756.232i	0.180279	+	0.0813807i
$443$	−11245.1	−	11245.1i	−1.20603	−	1.20603i	−0.972302	−	0.233729i	$-0.924907\pi$
$443$	−11245.1	−	11245.1i	−1.20603	−	1.20603i	−0.233729	−	0.972302i	$-0.575093\pi$
$444$	5179.62	−	4568.00i	0.553635	−	0.488260i
$445$	5276.77	+	6374.67i	0.562119	+	0.679075i
$446$	689.707	+	1824.79i	0.0732255	+	0.193737i
$447$	5190.42	−	5190.42i	0.549214	−	0.549214i
$448$	−1216.00	+	6392.01i	−0.128238	+	0.674094i
$449$		−	4654.40i		−	0.489209i	−0.969623	−	0.244604i	$-0.921342\pi$
$449$		−	4654.40i		−	0.489209i	0.969623	−	0.244604i	$-0.0786581\pi$
$450$	2604.57	+	1827.89i	0.272846	+	0.191484i
$451$		−	999.628i		−	0.104369i
$452$	6373.56	+	399.916i	0.663246	+	0.0416161i
$453$	−1920.67	+	1920.67i	−0.199208	+	0.199208i
$454$	8150.21	−	3080.49i	0.842530	−	0.318446i
$455$	3686.86	+	4453.96i	0.379874	+	0.458912i
$456$	−501.003	+	946.807i	−0.0514509	+	0.0972331i
$457$	−105.211	−	105.211i	−0.0107693	−	0.0107693i	0.701702	−	0.712471i	$-0.252424\pi$
$457$	−105.211	−	105.211i	−0.0107693	−	0.0107693i	−0.712471	+	0.701702i	$0.752424\pi$
$458$	−4419.23	+	9789.70i	−0.450867	+	0.998783i
$459$	−431.160			−0.0438449
$460$	7904.14	+	10868.5i	0.801158	+	1.10162i
$461$	5834.36			0.589443			0.294721	−	0.955583i	$-0.404773\pi$
$461$	5834.36			0.589443			0.294721	+	0.955583i	$0.404773\pi$
$462$	1722.32	−	3815.37i	0.173441	−	0.384215i
$463$	−3513.45	−	3513.45i	−0.352665	−	0.352665i	0.508436	−	0.861100i	$-0.330224\pi$
$463$	−3513.45	−	3513.45i	−0.352665	−	0.352665i	−0.861100	+	0.508436i	$0.830224\pi$
$464$	−13268.4	−	1671.66i	−1.32752	−	0.167252i
$465$	−767.393	+	8143.94i	−0.0765311	+	0.812186i
$466$	−7753.24	+	2930.45i	−0.770733	+	0.291310i
$467$	−8879.48	+	8879.48i	−0.879857	+	0.879857i	−0.993519	−	0.113662i	$-0.963742\pi$
$467$	−8879.48	+	8879.48i	−0.879857	+	0.879857i	0.113662	+	0.993519i	$0.463742\pi$
$468$	−183.483	+	2924.22i	−0.0181229	+	0.288829i
$469$			7052.02i			0.694311i
$470$	8126.13	−	14259.2i	0.797512	−	1.39942i
$471$		−	128.229i		−	0.0125445i
$472$	4304.03	+	13977.9i	0.419723	+	1.36311i
$473$	9843.10	−	9843.10i	0.956841	−	0.956841i
$474$	−1654.06	−	4376.24i	−0.160282	−	0.424066i
$475$	368.463	−	1937.80i	0.0355921	−	0.187183i
$476$	1073.84	+	1217.62i	0.103402	+	0.117247i
$477$	−4515.44	−	4515.44i	−0.433434	−	0.433434i
$478$	3063.89	+	1383.09i	0.293178	+	0.132345i
$479$	14862.9			1.41775			0.708875	−	0.705335i	$-0.249203\pi$
$479$	14862.9			1.41775			0.708875	+	0.705335i	$0.249203\pi$
$480$	3642.02	−	4857.95i	0.346322	−	0.461946i
$481$	−11710.0			−1.11004
$482$	18019.7	+	8134.40i	1.70286	+	0.768696i
$483$	−4050.48	−	4050.48i	−0.381581	−	0.381581i
$484$	−931.299	−	1055.99i	−0.0874623	−	0.0991729i
$485$	−1334.89	−	125.785i	−0.124978	−	0.0117765i
$486$	−243.000	−	642.918i	−0.0226805	−	0.0600069i
$487$	−5063.44	+	5063.44i	−0.471142	+	0.471142i	−0.902284	−	0.431142i	$-0.858111\pi$
$487$	−5063.44	+	5063.44i	−0.471142	+	0.471142i	0.431142	+	0.902284i	$0.358111\pi$
$488$	3510.85	+	11402.0i	0.325674	+	1.05767i
$489$			4053.98i			0.374903i
$490$	−1516.61	−	5535.52i	−0.139823	−	0.510345i
$491$		−	11014.1i		−	1.01234i	−0.862434	−	0.506169i	$-0.831061\pi$
$491$		−	11014.1i		−	1.01234i	0.862434	−	0.506169i	$-0.168939\pi$
$492$	−38.7014	+	616.794i	−0.00354633	+	0.0565187i
$493$	−2359.49	+	2359.49i	−0.215550	+	0.215550i
$494$	1698.99	−	642.157i	0.154739	−	0.0584858i
$495$	−3009.04	+	2490.80i	−0.273225	+	0.226168i
$496$	15486.0	+	1951.05i	1.40190	+	0.176622i
$497$	−5493.15	−	5493.15i	−0.495778	−	0.495778i
$498$	2442.06	−	5409.78i	0.219742	−	0.486784i
$499$	−3339.95			−0.299633			−0.149816	−	0.988714i	$-0.547868\pi$
$499$	−3339.95			−0.299633			−0.149816	+	0.988714i	$0.547868\pi$
$500$	−3776.08	+	10523.4i	−0.337743	+	0.941238i
$501$	−735.739			−0.0656096
$502$	4596.91	−	10183.3i	0.408705	−	0.905385i
$503$	8101.33	+	8101.33i	0.718132	+	0.718132i	0.968222	−	0.250091i	$-0.0804604\pi$
$503$	8101.33	+	8101.33i	0.718132	+	0.718132i	−0.250091	+	0.968222i	$0.580460\pi$
$504$	−1210.43	+	2287.49i	−0.106978	+	0.202169i
$505$	−4936.04	+	4085.91i	−0.434952	+	0.360041i
$506$	−15431.9	+	5832.71i	−1.35579	+	0.512442i
$507$	−1147.62	+	1147.62i	−0.100528	+	0.100528i
$508$	−2154.08	−	135.160i	−0.188133	−	0.0118046i
$509$		−	14083.0i		−	1.22637i	−0.789941	−	0.613183i	$-0.789889\pi$
$509$		−	14083.0i		−	1.22637i	0.789941	−	0.613183i	$-0.210111\pi$
$510$	−400.308	−	1461.10i	−0.0347568	−	0.126860i
$511$		−	2602.38i		−	0.225288i
$512$	−9046.94	−	7236.75i	−0.780903	−	0.624653i
$513$	−301.272	+	301.272i	−0.0259288	+	0.0259288i
$514$	5891.88	+	15588.5i	0.505603	+	1.33770i
$515$	20445.4	+	1926.54i	1.74938	+	0.164842i
$516$	−6454.50	+	5692.34i	−0.550666	+	0.485642i
$517$	14246.5	+	14246.5i	1.21191	+	1.21191i
$518$	−9427.24	−	4255.61i	−0.799631	−	0.360967i
$519$	5468.78			0.462529
$520$	−10079.8	+	2093.20i	−0.850057	+	0.176525i
$521$	9152.23			0.769610			0.384805	−	0.922998i	$-0.374269\pi$
$521$	9152.23			0.769610			0.384805	+	0.922998i	$0.374269\pi$
$522$	−4848.12	−	2188.52i	−0.406507	−	0.183504i
$523$	−10888.3	−	10888.3i	−0.910348	−	0.910348i	0.0859510	−	0.996299i	$-0.472607\pi$
$523$	−10888.3	−	10888.3i	−0.910348	−	0.910348i	−0.996299	+	0.0859510i	$0.972607\pi$
$524$	−10268.0	+	9055.56i	−0.856033	+	0.754950i
$525$	890.209	−	4681.72i	0.0740036	−	0.389195i
$526$	2869.24	+	7591.30i	0.237842	+	0.629271i
$527$	2753.83	−	2753.83i	0.227626	−	0.227626i
$528$	4570.25	+	5887.85i	0.376695	+	0.485295i
$529$			10408.0i			0.855427i
$530$	11109.4	−	19494.1i	0.910493	−	1.59768i
$531$			5817.29i			0.475422i
$532$	1601.16	+	100.466i	0.130487	+	0.00818753i
$533$	740.965	−	740.965i	0.0602153	−	0.0602153i
$534$	5874.88	−	2220.50i	0.476088	−	0.179944i
$535$	−541.210	+	5743.59i	−0.0437356	+	0.464144i
$536$	−11098.3	−	5872.67i	−0.894353	−	0.473247i
$537$	1752.60	+	1752.60i	0.140838	+	0.140838i
$538$	455.936	−	1010.01i	0.0365368	−	0.0809381i
$539$	7045.82			0.563052
$540$	1953.08	−	1420.38i	0.155643	−	0.113192i
$541$	−9855.75			−0.783238			−0.391619	−	0.920127i	$-0.628085\pi$
$541$	−9855.75			−0.783238			−0.391619	+	0.920127i	$0.628085\pi$
$542$	2362.85	−	5234.29i	0.187256	−	0.414820i
$543$	3001.13	+	3001.13i	0.237184	+	0.237184i
$544$	−2810.53	+	675.996i	−0.221508	+	0.0532777i
$545$	−8628.08	−	10423.3i	−0.678140	−	0.819236i
$546$	4104.76	−	1551.45i	0.321736	−	0.121605i
$547$	−17375.0	+	17375.0i	−1.35813	+	1.35813i	−0.481918	+	0.876216i	$0.660060\pi$
$547$	−17375.0	+	17375.0i	−1.35813	+	1.35813i	−0.876216	+	0.481918i	$0.839940\pi$
$548$	−86.8195	+	1383.66i	−0.00676778	+	0.107860i
$549$			4745.24i			0.368892i
$550$	−11234.4	−	7884.33i	−0.870977	−	0.611252i
$551$			3297.38i			0.254942i
$552$	9747.65	−	3001.46i	0.751608	−	0.231432i
$553$	−4954.54	+	4954.54i	−0.380991	+	0.380991i
$554$	6488.58	+	17167.2i	0.497605	+	1.31654i
$555$	6154.40	+	7434.90i	0.470702	+	0.568638i
$556$	4230.00	+	4796.37i	0.322647	+	0.365848i
$557$	139.313	+	139.313i	0.0105976	+	0.0105976i	0.712386	−	0.701788i	$-0.247615\pi$
$557$	139.313	+	139.313i	0.0105976	+	0.0105976i	−0.701788	+	0.712386i	$0.747615\pi$
$558$	5658.39	+	2554.29i	0.429281	+	0.193784i
$559$	14592.2			1.10409
$560$	−8875.57	−	1978.03i	−0.669752	−	0.149263i
$561$	1859.74			0.139961
$562$	−6191.56	−	2794.97i	−0.464724	−	0.209784i
$563$	−1963.98	−	1963.98i	−0.147020	−	0.147020i	0.629766	−	0.776785i	$-0.283151\pi$
$563$	−1963.98	−	1963.98i	−0.147020	−	0.147020i	−0.776785	+	0.629766i	$0.783151\pi$
$564$	−8238.85	−	9341.98i	−0.615103	−	0.697462i
$565$	−837.266	+	8885.48i	−0.0623435	+	0.661619i
$566$	−2650.91	−	7013.65i	−0.196866	−	0.520858i
$567$	−727.875	+	727.875i	−0.0539116	+	0.0539116i
$568$	13219.5	−	4070.49i	0.976545	−	0.300694i
$569$			15432.8i			1.13704i	0.822668	+	0.568522i	$0.192484\pi$
$569$			15432.8i			1.13704i	−0.822668	+	0.568522i	$0.807516\pi$
$570$	−1300.65	−	741.223i	−0.0955761	−	0.0544674i
$571$		−	7847.00i		−	0.575108i	−0.957764	−	0.287554i	$-0.907158\pi$
$571$		−	7847.00i		−	0.575108i	0.957764	−	0.287554i	$-0.0928421\pi$
$572$	791.426	−	12613.2i	0.0578517	−	0.921998i
$573$	1978.06	−	1978.06i	0.144214	−	0.144214i
$574$	865.801	−	327.242i	0.0629579	−	0.0237958i
$575$	−15527.3	+	10565.8i	−1.12615	+	0.766305i
$576$	−2592.00	−	3809.88i	−0.187500	−	0.275599i
$577$	−9726.14	−	9726.14i	−0.701741	−	0.701741i	0.263043	−	0.964784i	$-0.415274\pi$
$577$	−9726.14	−	9726.14i	−0.701741	−	0.701741i	−0.964784	+	0.263043i	$0.915274\pi$
$578$	5420.61	−	12008.0i	0.390082	−	0.864130i
$579$	−9357.12			−0.671621
$580$	2915.15	−	18461.0i	0.208698	−	1.32164i
$581$	−8889.43			−0.634760
$582$	−418.678	+	927.477i	−0.0298192	+	0.0660570i
$583$	19476.6	+	19476.6i	1.38360	+	1.38360i
$584$	4095.56	+	2167.16i	0.290197	+	0.153558i
$585$	−4076.70	−	384.142i	−0.288121	−	0.0271492i
$586$	3440.22	−	1300.28i	0.242516	−	0.0916624i
$587$	5740.65	−	5740.65i	0.403649	−	0.403649i	−0.475868	−	0.879517i	$-0.657866\pi$
$587$	5740.65	−	5740.65i	0.403649	−	0.403649i	0.879517	+	0.475868i	$0.157866\pi$
$588$	−4347.44	−	272.785i	−0.304907	−	0.0191317i
$589$		−	3848.47i		−	0.269225i
$590$	−19713.4	+	5401.03i	−1.37557	+	0.376876i
$591$		−	7861.54i		−	0.547176i
$592$	14548.0	−	11292.4i	1.01000	−	0.783981i
$593$	8362.60	−	8362.60i	0.579107	−	0.579107i	−0.355550	−	0.934657i	$-0.615706\pi$
$593$	8362.60	−	8362.60i	0.579107	−	0.579107i	0.934657	+	0.355550i	$0.115706\pi$
$594$	1048.14	+	2773.12i	0.0724003	+	0.191553i
$595$	−1747.79	+	1446.77i	−0.120425	+	0.0996840i
$596$	14680.7	−	12947.2i	1.00897	−	0.889828i
$597$	−3465.71	−	3465.71i	−0.237592	−	0.237592i
$598$	−15762.2	−	7115.31i	−1.07787	−	0.486566i
$599$	6073.61			0.414292			0.207146	−	0.978310i	$-0.433583\pi$
$599$	6073.61			0.414292			0.207146	+	0.978310i	$0.433583\pi$
$600$	6626.65	+	5299.76i	0.450887	+	0.360603i
$601$	26636.5			1.80786			0.903931	−	0.427679i	$-0.140669\pi$
$601$	26636.5			1.80786			0.903931	+	0.427679i	$0.140669\pi$
$602$	11747.6	+	5303.06i	0.795343	+	0.359031i
$603$	−3531.46	−	3531.46i	−0.238494	−	0.238494i
$604$	−5432.48	+	4791.00i	−0.365968	+	0.322753i
$605$	1515.79	−	1254.73i	0.101860	−	0.0843171i
$606$	1719.38	+	4549.05i	0.115256	+	0.304938i
$607$	−17791.7	+	17791.7i	−1.18969	+	1.18969i	−0.212538	+	0.977153i	$0.568173\pi$
$607$	−17791.7	+	17791.7i	−1.18969	+	1.18969i	−0.977153	+	0.212538i	$0.931827\pi$
$608$	−1491.50	+	2436.20i	−0.0994872	+	0.162502i
$609$			7966.49i			0.530080i
$610$	−16080.5	+	4405.69i	−1.06734	+	0.292428i
$611$			21120.2i			1.39841i
$612$	−1147.50	−	72.0013i	−0.0757926	−	0.00475569i
$613$	626.573	−	626.573i	0.0412839	−	0.0412839i	−0.686163	−	0.727447i	$-0.740707\pi$
$613$	626.573	−	626.573i	0.0412839	−	0.0412839i	0.727447	+	0.686163i	$0.240707\pi$
$614$	7498.28	−	2834.08i	0.492844	−	0.186277i
$615$	−859.882	−	81.0255i	−0.0563801	−	0.00531262i
$616$	5220.99	−	9866.74i	0.341493	−	0.645361i
$617$	−6326.92	−	6326.92i	−0.412824	−	0.412824i	0.469897	−	0.882721i	$-0.344291\pi$
$617$	−6326.92	−	6326.92i	−0.412824	−	0.412824i	−0.882721	+	0.469897i	$0.844291\pi$
$618$	6412.54	−	14205.4i	0.417395	−	0.924635i
$619$	19250.8			1.25001			0.625005	−	0.780621i	$-0.285097\pi$
$619$	19250.8			1.25001			0.625005	+	0.780621i	$0.285097\pi$
$620$	−3402.36	+	21546.4i	−0.220390	+	1.39568i
$621$	4056.74			0.262144
$622$	−4455.94	+	9871.01i	−0.287246	+	0.636321i
$623$	−6651.22	−	6651.22i	−0.427729	−	0.427729i
$624$	−976.657	+	7751.97i	−0.0626564	+	0.497319i
$625$	−14534.6	−	5734.71i	−0.930213	−	0.367021i
$626$	2645.01	−	999.718i	0.168875	−	0.0638287i
$627$	1299.49	−	1299.49i	0.0827698	−	0.0827698i
$628$	21.4135	−	341.273i	0.00136066	−	0.0216851i
$629$		−	4595.16i		−	0.291289i
$630$	−3142.38	−	1790.80i	−0.198723	−	0.113249i
$631$		−	13031.7i		−	0.822161i	−0.911599	−	0.411081i	$-0.865151\pi$
$631$		−	13031.7i		−	0.822161i	0.911599	−	0.411081i	$-0.134849\pi$
$632$	−3671.37	−	11923.3i	−0.231075	−	0.750448i
$633$	−8982.37	+	8982.37i	−0.564008	+	0.564008i
$634$	1049.41	+	2776.48i	0.0657373	+	0.173924i
$635$	282.971	−	3003.03i	0.0176841	−	0.187672i
$636$	−11263.5	−	12771.6i	−0.702243	−	0.796269i
$637$	5222.65	+	5222.65i	0.324849	+	0.324849i
$638$	20911.6	+	9439.84i	1.29765	+	0.585779i
$639$	5501.64			0.340597
$640$	10504.2	−	12320.9i	0.648775	−	0.760980i
$641$	20195.0			1.24439			0.622195	−	0.782863i	$-0.286241\pi$
$641$	20195.0			1.24439			0.622195	+	0.782863i	$0.286241\pi$
$642$	3990.63	+	1801.43i	0.245323	+	0.110743i
$643$	−4730.31	−	4730.31i	−0.290117	−	0.290117i	0.547010	−	0.837126i	$-0.315766\pi$
$643$	−4730.31	−	4730.31i	−0.290117	−	0.290117i	−0.837126	+	0.547010i	$0.815766\pi$
$644$	−10103.7	−	11456.5i	−0.618231	−	0.701008i
$645$	−7669.21	−	9264.88i	−0.468178	−	0.565588i
$646$	251.991	+	666.706i	0.0153475	+	0.0406056i
$647$	−7268.71	+	7268.71i	−0.441673	+	0.441673i	−0.892574	−	0.450901i	$-0.851103\pi$
$647$	−7268.71	+	7268.71i	−0.441673	+	0.441673i	0.450901	+	0.892574i	$0.351103\pi$
$648$	−539.364	−	1751.66i	−0.0326979	−	0.106191i
$649$		−	25092.0i		−	1.51764i
$650$	−2483.23	−	14171.6i	−0.149847	−	0.855163i
$651$		−	9297.93i		−	0.559777i
$652$	−676.993	+	10789.4i	−0.0406642	+	0.648076i
$653$	−20647.8	+	20647.8i	−1.23738	+	1.23738i	−0.276313	+	0.961068i	$0.589113\pi$
$653$	−20647.8	+	20647.8i	−1.23738	+	1.23738i	−0.961068	+	0.276313i	$0.910887\pi$
$654$	−9606.06	+	3630.75i	−0.574353	+	0.217085i
$655$	−12200.4	−	14738.9i	−0.727802	−	0.879231i
$656$	−206.002	+	1635.09i	−0.0122607	+	0.0973165i
$657$	1303.20	+	1303.20i	0.0773860	+	0.0773860i
$658$	−7675.43	+	17003.0i	−0.454741	+	1.00736i
$659$	−24317.2			−1.43742			−0.718712	−	0.695307i	$-0.755268\pi$
$659$	−24317.2			−1.43742			−0.718712	+	0.695307i	$0.755268\pi$
$660$	−8424.30	+	6126.59i	−0.496841	+	0.361329i
$661$	−14423.7			−0.848742			−0.424371	−	0.905488i	$-0.639505\pi$
$661$	−14423.7			−0.848742			−0.424371	+	0.905488i	$0.639505\pi$
$662$	−8533.33	+	18903.5i	−0.500993	+	1.10982i
$663$	1378.52	+	1378.52i	0.0807498	+	0.0807498i
$664$	7402.79	−	13990.0i	0.432657	−	0.817645i
$665$	−210.337	+	2232.20i	−0.0122654	+	0.130167i
$666$	6851.99	−	2589.81i	0.398663	−	0.150680i
$667$	22200.2	−	22200.2i	1.28875	−	1.28875i
$668$	−1958.12	−	122.864i	−0.113416	−	0.00711641i
$669$			2069.12i			0.119577i
$670$	8688.48	−	15246.0i	0.500993	−	0.879112i
$671$		−	20467.8i		−	1.17757i
$672$	−3603.47	+	5885.87i	−0.206855	+	0.337876i
$673$	22481.9	−	22481.9i	1.28769	−	1.28769i	0.351502	−	0.936187i	$-0.385671\pi$
$673$	22481.9	−	22481.9i	1.28769	−	1.28769i	0.936187	−	0.351502i	$-0.114329\pi$
$674$	−8097.49	−	21423.9i	−0.462765	−	1.22436i
$675$	1898.69	+	2790.27i	0.108267	+	0.159108i
$676$	−3245.97	+	2862.68i	−0.184682	+	0.162874i
$677$	−7006.79	−	7006.79i	−0.397774	−	0.397774i	0.479673	−	0.877447i	$-0.340755\pi$
$677$	−7006.79	−	7006.79i	−0.397774	−	0.397774i	−0.877447	+	0.479673i	$0.840755\pi$
$678$	6173.60	+	2786.86i	0.349699	+	0.157860i
$679$	1524.04			0.0861375
$680$	−821.399	−	3955.46i	−0.0463224	−	0.223066i
$681$	9241.47			0.520021
$682$	−24406.6	−	11017.5i	−1.37035	−	0.618596i
$683$	8104.50	+	8104.50i	0.454041	+	0.454041i	0.896693	−	0.442652i	$-0.145962\pi$
$683$	8104.50	+	8104.50i	0.454041	+	0.454041i	−0.442652	+	0.896693i	$0.645962\pi$
$684$	−852.127	+	751.505i	−0.0476343	+	0.0420095i
$685$	−1928.99	−	181.766i	−0.107595	−	0.0101386i
$686$	6665.49	+	17635.2i	0.370976	+	0.981510i
$687$	−8055.71	+	8055.71i	−0.447372	+	0.447372i
$688$	−18128.8	+	14071.9i	−1.00458	+	0.779776i
$689$			28873.8i			1.59652i
$690$	3766.46	+	13747.3i	0.207807	+	0.758480i
$691$			17999.5i			0.990928i	0.868628	+	0.495464i	$0.165002\pi$
$691$			17999.5i			0.990928i	−0.868628	+	0.495464i	$0.834998\pi$
$692$	14554.8	+	913.255i	0.799552	+	0.0501687i
$693$	3139.58	−	3139.58i	0.172096	−	0.172096i
$694$	7275.83	−	2750.01i	0.397964	−	0.150416i
$695$	−6884.77	+	5699.02i	−0.375762	+	0.311045i
$696$	−12537.5	−	6634.21i	−0.682805	−	0.361306i
$697$	290.765	+	290.765i	0.0158013	+	0.0158013i
$698$	−11149.9	+	24699.8i	−0.604626	+	1.33940i
$699$	−8791.34			−0.475707
$700$	3151.05	−	12311.4i	0.170141	−	0.664755i
$701$	18730.1			1.00917			0.504584	−	0.863362i	$-0.331646\pi$
$701$	18730.1			1.00917			0.504584	+	0.863362i	$0.331646\pi$
$702$	−1278.63	+	2832.48i	−0.0687445	+	0.152286i
$703$	−3210.86	−	3210.86i	−0.172261	−	0.172261i
$704$	11180.2	+	16433.3i	0.598536	+	0.879765i
$705$	13409.6	−	11100.1i	0.716362	−	0.592984i
$706$	−1296.26	+	489.939i	−0.0691009	+	0.0261177i
$707$	5150.18	−	5150.18i	0.273964	−	0.273964i
$708$	−971.455	+	15482.3i	−0.0515671	+	0.821838i
$709$		−	6597.00i		−	0.349443i	−0.984618	−	0.174722i	$-0.944097\pi$
$709$		−	6597.00i		−	0.349443i	0.984618	−	0.174722i	$-0.0559026\pi$
$710$	5107.97	+	18643.7i	0.269998	+	0.985474i
$711$		−	4962.19i		−	0.261739i
$712$	16006.4	−	4928.63i	0.842508	−	0.259422i
$713$	−25910.6	+	25910.6i	−1.36095	+	1.36095i
$714$	608.812	+	1610.76i	0.0319107	+	0.0844277i
$715$	17584.2	+	1656.94i	0.919737	+	0.0866655i
$716$	4371.75	+	4957.09i	0.228184	+	0.258736i
$717$	2521.20	+	2521.20i	0.131319	+	0.131319i
$718$	5661.31	+	2555.61i	0.294259	+	0.132833i
$719$	2093.70			0.108598			0.0542989	−	0.998525i	$-0.482708\pi$
$719$	2093.70			0.108598			0.0542989	+	0.998525i	$0.482708\pi$
$720$	5435.18	−	3454.10i	0.281330	−	0.178787i
$721$	−23342.5			−1.20571
$722$	−17040.1	−	7692.19i	−0.878349	−	0.396501i
$723$	14828.0	+	14828.0i	0.762737	+	0.762737i
$724$	7486.13	+	8488.47i	0.384281	+	0.435734i
$725$	25660.0	+	4879.13i	1.31447	+	0.249940i
$726$	−527.997	−	1396.95i	−0.0269915	−	0.0714127i
$727$	1214.94	−	1214.94i	0.0619801	−	0.0619801i	−0.675437	−	0.737417i	$-0.736045\pi$
$727$	1214.94	−	1214.94i	0.0619801	−	0.0619801i	0.737417	+	0.675437i	$0.236045\pi$
$728$	11183.6	−	3443.62i	0.569359	−	0.175315i
$729$		−	729.000i		−	0.0370370i
$730$	−3206.27	+	5626.17i	−0.162561	+	0.285252i
$731$			5726.18i			0.289727i
$732$	−792.428	+	12629.1i	−0.0400123	+	0.637686i
$733$	1538.15	−	1538.15i	0.0775074	−	0.0775074i	−0.667290	−	0.744798i	$-0.732546\pi$
$733$	1538.15	−	1538.15i	0.0775074	−	0.0775074i	0.744798	+	0.667290i	$0.232546\pi$
$734$	18944.1	−	7160.20i	0.952643	−	0.360065i
$735$	571.104	−	6060.83i	0.0286605	−	0.304159i
$736$	26444.0	−	6360.37i	1.32437	−	0.318541i
$737$	15232.4	+	15232.4i	0.761319	+	0.761319i
$738$	−269.695	+	597.443i	−0.0134521	+	0.0297997i
$739$	7751.58			0.385854			0.192927	−	0.981213i	$-0.438202\pi$
$739$	7751.58			0.385854			0.192927	+	0.981213i	$0.438202\pi$
$740$	15137.9	+	20815.2i	0.752002	+	1.03403i
$741$	1926.47			0.0955070
$742$	−10493.2	+	23245.1i	−0.519162	+	1.15007i
$743$	−15280.2	−	15280.2i	−0.754477	−	0.754477i	0.220834	−	0.975311i	$-0.429122\pi$
$743$	−15280.2	−	15280.2i	−0.754477	−	0.754477i	−0.975311	+	0.220834i	$0.929122\pi$
$744$	14632.9	+	7742.98i	0.721058	+	0.381548i
$745$	17443.6	+	21072.9i	0.857829	+	1.03631i
$746$	−2621.54	+	990.848i	−0.128661	+	0.0486294i
$747$	4451.58	−	4451.58i	0.218039	−	0.218039i
$748$	4949.58	+	310.566i	0.241944	+	0.0151811i
$749$		−	6557.45i		−	0.319898i
$750$	−7692.72	+	9024.80i	−0.374531	+	0.439385i
$751$		−	39607.5i		−	1.92450i	−0.272171	−	0.962249i	$-0.587742\pi$
$751$		−	39607.5i		−	1.92450i	0.272171	−	0.962249i	$-0.412258\pi$
$752$	−20367.1	−	26238.9i	−0.987648	−	1.27239i
$753$	8379.59	−	8379.59i	0.405537	−	0.405537i
$754$	8503.34	+	22497.7i	0.410708	+	1.08663i
$755$	−6454.85	−	7797.86i	−0.311147	−	0.375885i
$756$	−2058.74	+	1815.64i	−0.0990420	+	0.0873468i
$757$	5309.98	+	5309.98i	0.254946	+	0.254946i	0.822995	−	0.568049i	$-0.192301\pi$
$757$	5309.98	+	5309.98i	0.254946	+	0.254946i	−0.568049	+	0.822995i	$0.692301\pi$
$758$	−18514.9	−	8357.93i	−0.887192	−	0.400493i
$759$	−17498.1			−0.836814
$760$	−3337.82	−	2189.92i	−0.159310	−	0.104522i
$761$	−22046.7			−1.05019			−0.525094	−	0.851044i	$-0.675970\pi$
$761$	−22046.7			−1.05019			−0.525094	+	0.851044i	$0.675970\pi$
$762$	−2086.50	−	941.878i	−0.0991939	−	0.0447777i
$763$	10875.4	+	10875.4i	0.516012	+	0.516012i
$764$	5594.79	−	4934.14i	0.264938	−	0.233653i
$765$	150.742	−	1599.75i	0.00712432	−	0.0756068i
$766$	9483.00	+	25089.7i	0.447304	+	1.18345i
$767$	18599.2	−	18599.2i	0.875590	−	0.875590i
$768$	−6262.20	−	10572.6i	−0.294229	−	0.496752i
$769$		−	9309.49i		−	0.436552i	−0.975887	−	0.218276i	$-0.929957\pi$
$769$		−	9309.49i		−	0.436552i	0.975887	−	0.218276i	$-0.0700433\pi$
$770$	13554.2	+	7724.33i	0.634362	+	0.361514i
$771$			17675.7i			0.825646i
$772$	−24903.4	−	1562.59i	−1.16100	−	0.0728481i
$773$	−13668.6	+	13668.6i	−0.635999	+	0.635999i	−0.949566	−	0.313567i	$-0.898476\pi$
$773$	−13668.6	+	13668.6i	−0.635999	+	0.635999i	0.313567	+	0.949566i	$0.398476\pi$
$774$	−8538.50	+	3227.25i	−0.396525	+	0.149872i
$775$	−29948.5	−	5694.58i	−1.38811	−	0.263942i
$776$	−1269.17	+	2398.50i	−0.0587119	+	0.110955i
$777$	−7757.44	−	7757.44i	−0.358168	−	0.358168i
$778$	−1402.24	+	3106.30i	−0.0646177	+	0.143144i
$779$	406.343			0.0186890
$780$	−10785.7	−	1703.15i	−0.495116	−	0.0781829i
$781$	−23730.5			−1.08725
$782$	2792.14	−	6185.30i	0.127681	−	0.282846i
$783$	−3989.40	−	3989.40i	−0.182081	−	0.182081i
$784$	−11524.9	−	1452.00i	−0.525003	−	0.0661441i
$785$	475.774	+	44.8315i	0.0216320	+	0.00203835i
$786$	−13583.3	+	5134.02i	−0.616414	+	0.232983i
$787$	−1953.67	+	1953.67i	−0.0884888	+	0.0884888i	−0.749966	−	0.661477i	$-0.769930\pi$
$787$	−1953.67	+	1953.67i	−0.0884888	+	0.0884888i	0.661477	+	0.749966i	$0.269930\pi$
$788$	1312.83	−	20923.0i	0.0593500	−	0.945876i
$789$			8607.73i			0.388394i
$790$	16815.7	−	4607.12i	0.757309	−	0.207486i
$791$		−	10144.5i		−	0.456003i
$792$	2326.46	+	7555.52i	0.104378	+	0.338982i
$793$	15171.6	−	15171.6i	0.679394	−	0.679394i
$794$	−10897.9	−	28833.1i	−0.487092	−	1.28872i
$795$	18332.5	−	15175.2i	0.817847	−	0.676990i
$796$	−8645.01	−	9802.52i	−0.384942	−	0.436484i
$797$	−18631.1	−	18631.1i	−0.828037	−	0.828037i	0.159208	−	0.987245i	$-0.449106\pi$
$797$	−18631.1	−	18631.1i	−0.828037	−	0.828037i	−0.987245	+	0.159208i	$0.949106\pi$
$798$	1550.92	+	700.113i	0.0687997	+	0.0310573i
$799$	−8287.84			−0.366962
$800$	16751.4	+	15211.6i	0.740312	+	0.672263i
$801$	6661.49			0.293848
$802$	−7166.63	−	3235.13i	−0.315539	−	0.142440i
$803$	−5621.14	−	5621.14i	−0.247031	−	0.247031i
$804$	−8809.00	−	9988.47i	−0.386405	−	0.438142i
$805$	16444.8	−	13612.6i	0.720005	−	0.596000i
$806$	−9924.50	−	26257.8i	−0.433717	−	1.14751i
$807$	831.115	−	831.115i	0.0362536	−	0.0362536i
$808$	3816.34	+	12394.1i	0.166161	+	0.539633i
$809$		−	17520.6i		−	0.761425i	−0.924693	−	0.380712i	$-0.875679\pi$
$809$		−	17520.6i		−	0.761425i	0.924693	−	0.380712i	$-0.124321\pi$
$810$	2470.40	−	676.836i	0.107162	−	0.0293600i
$811$			39421.8i			1.70689i	0.521183	+	0.853445i	$0.325491\pi$
$811$			39421.8i			1.70689i	−0.521183	+	0.853445i	$0.674509\pi$
$812$	−1330.36	+	21202.3i	−0.0574957	+	0.916323i
$813$	4307.17	−	4307.17i	0.185805	−	0.185805i
$814$	−29555.0	+	11170.7i	−1.27261	+	0.481000i
$815$	−15041.7	−	1417.36i	−0.646487	−	0.0609176i
$816$	−3041.98	−	383.253i	−0.130503	−	0.0164419i
$817$	4001.16	+	4001.16i	0.171338	+	0.171338i
$818$	12011.9	−	26609.5i	0.513432	−	1.13738i
$819$	4654.36			0.198580
$820$	−2274.99	−	359.239i	−0.0968853	−	0.0152990i
$821$	−1985.12			−0.0843864			−0.0421932	−	0.999109i	$-0.513434\pi$
$821$	−1985.12			−0.0843864			−0.0421932	+	0.999109i	$0.513434\pi$
$822$	−605.013	+	1340.25i	−0.0256718	+	0.0568695i
$823$	11773.8	+	11773.8i	0.498674	+	0.498674i	0.911025	−	0.412351i	$-0.135292\pi$
$823$	11773.8	+	11773.8i	0.498674	+	0.498674i	−0.412351	+	0.911025i	$0.635292\pi$
$824$	19438.8	−	36735.8i	0.821822	−	1.55310i
$825$	−8189.69	−	12035.4i	−0.345610	−	0.507901i
$826$	21732.7	−	8214.20i	0.915470	−	0.346015i
$827$	14710.3	−	14710.3i	0.618534	−	0.618534i	−0.326622	−	0.945155i	$-0.605910\pi$
$827$	14710.3	−	14710.3i	0.618534	−	0.618534i	0.945155	+	0.326622i	$0.105910\pi$
$828$	10796.7	+	677.453i	0.453156	+	0.0284337i
$829$		−	514.236i		−	0.0215442i	−0.999942	−	0.0107721i	$-0.996571\pi$
$829$		−	514.236i		−	0.0215442i	0.999942	−	0.0107721i	$-0.00342894\pi$
$830$	19218.4	+	10952.3i	0.803710	+	0.458023i
$831$			19465.7i			0.812586i
$832$	−3893.84	+	20468.3i	−0.162253	+	0.852896i
$833$	−2049.44	+	2049.44i	−0.0852447	+	0.0852447i
$834$	2398.18	+	6345.00i	0.0995711	+	0.263440i
$835$	257.230	−	2729.85i	0.0106608	−	0.113138i
$836$	3675.51	−	3241.50i	0.152058	−	0.134102i
$837$	4656.15	+	4656.15i	0.192282	+	0.192282i
$838$	−27596.9	−	12457.7i	−1.13761	−	0.513536i
$839$	−27918.0			−1.14879			−0.574396	−	0.818577i	$-0.694763\pi$
$839$	−27918.0			−1.14879			−0.574396	+	0.818577i	$0.694763\pi$
$840$	−8064.19	−	5290.85i	−0.331239	−	0.217324i
$841$	−19274.4			−0.790293
$842$	36838.7	+	16629.6i	1.50777	+	0.680633i
$843$	−5094.88	−	5094.88i	−0.208158	−	0.208158i
$844$	−25406.0	+	22406.0i	−1.03615	+	0.913797i
$845$	−3856.85	−	4659.32i	−0.157017	−	0.189687i
$846$	−4670.99	−	12358.3i	−0.189825	−	0.502230i
$847$	−1581.55	+	1581.55i	−0.0641589	+	0.0641589i
$848$	−27844.2	−	35871.7i	−1.12756	−	1.45264i
$849$		−	7952.73i		−	0.321481i
$850$	5561.13	−	974.453i	0.224406	−	0.0393217i
$851$			43235.4i			1.74159i
$852$	14642.2	+	918.743i	0.588774	+	0.0369432i
$853$	25357.8	−	25357.8i	1.01786	−	1.01786i	0.0180228	−	0.999838i	$-0.494263\pi$
$853$	25357.8	−	25357.8i	1.01786	−	1.01786i	0.999838	−	0.0180228i	$-0.00573714\pi$
$854$	17727.7	−	6700.43i	0.710337	−	0.268482i
$855$	−1012.49	−	1223.15i	−0.0404989	−	0.0489252i
$856$	10320.0	+	5460.81i	0.412066	+	0.218045i
$857$	−5121.17	−	5121.17i	−0.204126	−	0.204126i	0.597639	−	0.801765i	$-0.296105\pi$
$857$	−5121.17	−	5121.17i	−0.204126	−	0.204126i	−0.801765	+	0.597639i	$0.796105\pi$
$858$	5515.15	−	12217.4i	0.219446	−	0.486127i
$859$	−47092.3			−1.87051			−0.935255	−	0.353975i	$-0.884830\pi$
$859$	−47092.3			−1.87051			−0.935255	+	0.353975i	$0.884830\pi$
$860$	−18863.9	−	25938.6i	−0.747969	−	1.02849i
$861$	981.726			0.0388584
$862$	17829.4	−	39496.5i	0.704491	−	1.56062i
$863$	7615.70	+	7615.70i	0.300396	+	0.300396i	0.841169	−	0.540773i	$-0.181868\pi$
$863$	7615.70	+	7615.70i	0.300396	+	0.300396i	−0.540773	+	0.841169i	$0.681868\pi$
$864$	−1142.96	−	4752.00i	−0.0450051	−	0.187114i
$865$	−1912.00	+	20291.0i	−0.0751559	+	0.797591i
$866$	−720.456	+	272.307i	−0.0282703	+	0.0106852i
$867$	9881.10	−	9881.10i	0.387058	−	0.387058i
$868$	1552.70	−	24745.8i	0.0607168	−	0.967659i
$869$			21403.6i			0.835522i
$870$	9815.17	−	17223.1i	0.382489	−	0.671168i
$871$			22581.7i			0.878476i
$872$	−26172.2	+	8058.84i	−1.01640	+	0.312966i
$873$	−763.198	+	763.198i	−0.0295880	+	0.0295880i
$874$	−2370.96	−	6272.97i	−0.0917607	−	0.242776i
$875$	17059.6	+	4939.81i	0.659107	+	0.190853i
$876$	3250.75	+	3686.00i	0.125380	+	0.142167i
$877$	34347.4	+	34347.4i	1.32250	+	1.32250i	0.911749	+	0.410749i	$0.134733\pi$
$877$	34347.4	+	34347.4i	1.32250	+	1.32250i	0.410749	+	0.911749i	$0.365267\pi$
$878$	−14768.9	−	6666.93i	−0.567685	−	0.256262i
$879$	3900.85			0.149684
$880$	−23443.8	+	14898.7i	−0.898058	+	0.570722i
$881$	4007.97			0.153271			0.0766355	−	0.997059i	$-0.475582\pi$
$881$	4007.97			0.153271			0.0766355	+	0.997059i	$0.475582\pi$
$882$	−4211.04	−	1900.93i	−0.160763	−	0.0725712i
$883$	18107.5	+	18107.5i	0.690108	+	0.690108i	0.962255	−	0.272148i	$-0.0877340\pi$
$883$	18107.5	+	18107.5i	0.690108	+	0.690108i	−0.272148	+	0.962255i	$0.587734\pi$
$884$	3438.62	+	3899.03i	0.130830	+	0.148347i
$885$	−21584.1	−	2033.84i	−0.819823	−	0.0772508i
$886$	−15903.0	−	42075.4i	−0.603016	−	1.59543i
$887$	−8295.62	+	8295.62i	−0.314024	+	0.314024i	−0.846466	−	0.532442i	$-0.821274\pi$
$887$	−8295.62	+	8295.62i	−0.314024	+	0.314024i	0.532442	+	0.846466i	$0.321274\pi$
$888$	18668.6	−	5748.36i	0.705492	−	0.217232i
$889$			3428.56i			0.129348i
$890$	6184.83	+	22574.2i	0.232939	+	0.850211i
$891$			3144.43i			0.118229i
$892$	−345.532	+	5506.83i	−0.0129700	+	0.206707i
$893$	−5791.11	+	5791.11i	−0.217012	+	0.217012i
$894$	19420.8	−	7340.36i	0.726541	−	0.274607i
$895$	−7115.48	+	5890.00i	−0.265748	+	0.219979i
$896$	−10573.3	+	15063.1i	−0.394229	+	0.561632i
$897$	−12970.3	−	12970.3i	−0.482794	−	0.482794i
$898$	5416.43	−	11998.7i	0.201279	−	0.445883i
$899$	50960.9			1.89059
$900$	4587.27	+	7743.19i	0.169899	+	0.286785i
$901$	−11330.5			−0.418948
$902$	1163.29	−	2576.98i	0.0429416	−	0.0951263i
$903$	9666.82	+	9666.82i	0.356248	+	0.356248i
$904$	15965.2	+	8448.01i	0.587385	+	0.310815i
$905$	−12184.5	+	10086.0i	−0.447542	+	0.370463i
$906$	−7186.49	+	2716.24i	−0.263527	+	0.0996038i
$907$	36466.7	−	36466.7i	1.33501	−	1.33501i	0.434195	−	0.900819i	$-0.357033\pi$
$907$	36466.7	−	36466.7i	1.33501	−	1.33501i	0.900819	−	0.434195i	$-0.142967\pi$
$908$	24595.6	+	1543.27i	0.898934	+	0.0564046i
$909$			5158.13i			0.188212i
$910$	4321.32	+	15772.5i	0.157418	+	0.574564i
$911$			36350.5i			1.32200i	0.750385	+	0.661002i	$0.229868\pi$
$911$			36350.5i			1.32200i	−0.750385	+	0.661002i	$0.770132\pi$
$912$	−2393.37	+	1857.78i	−0.0868997	+	0.0674531i
$913$	−19201.2	+	19201.2i	−0.696020	+	0.696020i
$914$	−148.791	−	393.665i	−0.00538466	−	0.0142465i
$915$	−17606.5	−	1659.03i	−0.636122	−	0.0599409i
$916$	−22785.0	+	20094.5i	−0.821874	+	0.724825i
$917$	15378.3	+	15378.3i	0.553802	+	0.553802i
$918$	−1111.50	−	501.750i	−0.0399619	−	0.0180395i
$919$	1636.73			0.0587495			0.0293748	−	0.999568i	$-0.490648\pi$
$919$	1636.73			0.0587495			0.0293748	+	0.999568i	$0.490648\pi$
$920$	7728.46	+	37216.5i	0.276956	+	1.33369i
$921$	8502.25			0.304190
$922$	15040.6	+	6789.57i	0.537240	+	0.242519i
$923$	−17590.0	−	17590.0i	−0.627282	−	0.627282i
$924$	8880.06	−	7831.48i	0.316161	−	0.278828i
$925$	−29737.7	+	20235.5i	−1.05705	+	0.719287i
$926$	−4968.76	−	13146.1i	−0.176332	−	0.466531i
$927$	11689.3	−	11689.3i	0.414159	−	0.414159i
$928$	−32259.8	−	19750.2i	−1.14114	−	0.698634i
$929$		−	12094.4i		−	0.427131i	−0.976929	−	0.213565i	$-0.931492\pi$
$929$		−	12094.4i		−	0.427131i	0.976929	−	0.213565i	$-0.0685076\pi$
$930$	−11455.6	+	20101.5i	−0.403917	+	0.708769i
$931$			2864.08i			0.100823i
$932$	−23397.6	−	1468.11i	−0.822332	−	0.0515981i
$933$	−8122.62	+	8122.62i	−0.285019	+	0.285019i
$934$	−33224.0	+	12557.5i	−1.16394	+	0.439929i
$935$	−650.204	+	6900.28i	−0.0227422	+	0.241351i
$936$	−3875.99	+	7324.93i	−0.135353	+	0.255793i
$937$	12301.6	+	12301.6i	0.428896	+	0.428896i	0.888252	−	0.459356i	$-0.151920\pi$
$937$	12301.6	+	12301.6i	0.428896	+	0.428896i	−0.459356	+	0.888252i	$0.651920\pi$
$938$	−8206.59	+	18179.6i	−0.285666	+	0.632821i
$939$	2999.16			0.104232
$940$	37542.4	−	27302.8i	1.30266	−	0.947362i
$941$	25713.6			0.890797			0.445398	−	0.895332i	$-0.353062\pi$
$941$	25713.6			0.890797			0.445398	+	0.895332i	$0.353062\pi$
$942$	149.223	−	330.566i	0.00516130	−	0.0114336i
$943$	−2735.78	−	2735.78i	−0.0944742	−	0.0944742i
$944$	−5170.92	+	41042.9i	−0.178283	+	1.41508i
$945$	−2446.19	−	2955.15i	−0.0842058	−	0.101726i
$946$	36829.5	−	13920.2i	1.26578	−	0.478421i
$947$	11717.1	−	11717.1i	0.402064	−	0.402064i	−0.476896	−	0.878960i	$-0.658238\pi$
$947$	11717.1	−	11717.1i	0.402064	−	0.402064i	0.878960	+	0.476896i	$0.158238\pi$
$948$	828.658	−	13206.5i	0.0283898	−	0.452456i
$949$		−	8333.24i		−	0.285046i
$950$	3204.93	−	4566.72i	0.109454	−	0.155962i
$951$			3148.23i			0.107348i
$952$	1351.32	+	4388.61i	0.0460049	+	0.149407i
$953$	13039.5	−	13039.5i	0.443222	−	0.443222i	−0.449872	−	0.893093i	$-0.648530\pi$
$953$	13039.5	−	13039.5i	0.443222	−	0.443222i	0.893093	+	0.449872i	$0.148530\pi$
$954$	−6385.80	−	16895.2i	−0.216717	−	0.573379i
$955$	6647.70	+	8030.84i	0.225251	+	0.272117i
$956$	6288.98	+	7131.03i	0.212762	+	0.241249i
$957$	17207.7	+	17207.7i	0.581238	+	0.581238i
$958$	38315.5	+	17296.2i	1.29219	+	0.583316i
$959$	2202.32			0.0741572
$960$	15042.2	−	8285.20i	0.505713	−	0.278545i
$961$	−29687.0			−0.996508
$962$	−30187.6	−	13627.2i	−1.01173	−	0.456712i
$963$	3283.79	+	3283.79i	0.109884	+	0.109884i
$964$	36987.5	+	41939.9i	1.23578	+	1.40124i
$965$	3271.44	−	34718.1i	0.109131	−	1.15815i
$966$	−5728.25	−	15155.5i	−0.190790	−	0.504784i
$967$	−4219.47	+	4219.47i	−0.140319	+	0.140319i	−0.773777	−	0.633458i	$-0.781635\pi$
$967$	−4219.47	+	4219.47i	−0.140319	+	0.140319i	0.633458	+	0.773777i	$0.281635\pi$
$968$	−1171.95	−	3806.06i	−0.0389130	−	0.126375i
$969$			755.973i			0.0250623i
$970$	−3294.88	−	1877.70i	−0.109064	−	0.0621541i
$971$			33342.1i			1.10195i	0.834520	+	0.550977i	$0.185745\pi$
$971$			33342.1i			1.10195i	−0.834520	+	0.550977i	$0.814255\pi$
$972$	121.739	−	1940.18i	0.00401726	−	0.0640241i
$973$	7183.45	−	7183.45i	0.236681	−	0.236681i
$974$	−18945.7	+	7160.79i	−0.623263	+	0.235571i
$975$	2850.60	−	14991.7i	0.0936330	−	0.492428i
$976$	−4217.99	+	33479.2i	−0.138335	+	1.09800i
$977$	4301.21	+	4301.21i	0.140847	+	0.140847i	0.774015	−	0.633167i	$-0.218246\pi$
$977$	4301.21	+	4301.21i	0.140847	+	0.140847i	−0.633167	+	0.774015i	$0.718246\pi$
$978$	−4717.71	+	10450.9i	−0.154249	+	0.341701i
$979$	−28733.3			−0.938019
$980$	2532.08	−	16035.1i	0.0825350	−	0.522677i
$981$	−10892.2			−0.354498
$982$	12817.3	−	28393.6i	0.416514	−	0.922683i
$983$	8362.60	+	8362.60i	0.271338	+	0.271338i	0.829639	−	0.558301i	$-0.188546\pi$
$983$	8362.60	+	8362.60i	0.271338	+	0.271338i	−0.558301	+	0.829639i	$0.688546\pi$
$984$	−817.546	+	1545.02i	−0.0264862	+	0.0500542i
$985$	29169.0	+	2748.56i	0.943556	+	0.0889100i
$986$	−8828.42	+	3336.83i	−0.285146	+	0.107775i
$987$	−13991.4	+	13991.4i	−0.451215	+	0.451215i
$988$	5127.17	+	321.710i	0.165098	+	0.0103593i
$989$		−	53877.1i		−	1.73225i
$990$	−10655.7	+	2919.43i	−0.342081	+	0.0937227i
$991$		−	35928.9i		−	1.15168i	−0.817561	−	0.575842i	$-0.804674\pi$
$991$		−	35928.9i		−	1.15168i	0.817561	−	0.575842i	$-0.195326\pi$
$992$	37651.3	+	23051.0i	1.20507	+	0.737773i
$993$	−15555.2	+	15555.2i	−0.497109	+	0.497109i
$994$	−7768.49	−	20553.5i	−0.247889	−	0.655852i
$995$	14070.7	−	11647.3i	0.448312	−	0.371100i
$996$	12591.0	−	11104.2i	0.400562	−	0.353263i
$997$	−31189.1	−	31189.1i	−0.990740	−	0.990740i	0.00921702	−	0.999958i	$-0.497066\pi$
$997$	−31189.1	−	31189.1i	−0.990740	−	0.990740i	−0.999958	+	0.00921702i	$0.997066\pi$
$998$	−8610.18	−	3886.78i	−0.273097	−	0.123280i
$999$	7769.43			0.246060

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.4.j.a.7.4	yes	8
3.2	odd	2		180.4.k.d.127.1		8
4.3	odd	2	inner	60.4.j.a.7.3	✓	8
5.3	odd	4	inner	60.4.j.a.43.3	yes	8
12.11	even	2		180.4.k.d.127.2		8
15.8	even	4		180.4.k.d.163.2		8
20.3	even	4	inner	60.4.j.a.43.4	yes	8
60.23	odd	4		180.4.k.d.163.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.4.j.a.7.3	✓	8	4.3	odd	2	inner
60.4.j.a.7.4	yes	8	1.1	even	1	trivial
60.4.j.a.43.3	yes	8	5.3	odd	4	inner
60.4.j.a.43.4	yes	8	20.3	even	4	inner
180.4.k.d.127.1		8	3.2	odd	2
180.4.k.d.127.2		8	12.11	even	2
180.4.k.d.163.1		8	60.23	odd	4
180.4.k.d.163.2		8	15.8	even	4

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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	60.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.57794 + 1.16372i) q^{2} +(2.12132 + 2.12132i) q^{3} +(5.29150 + 6.00000i) q^{4} +(-8.61249 + 7.12917i) q^{5} +(3.00000 + 7.93725i) q^{6} +(8.98612 - 8.98612i) q^{7} +(6.65882 + 21.6255i) q^{8} +9.00000i q^{9} +O(q^{10})\)	\(q+(2.57794 + 1.16372i) q^{2} +(2.12132 + 2.12132i) q^{3} +(5.29150 + 6.00000i) q^{4} +(-8.61249 + 7.12917i) q^{5} +(3.00000 + 7.93725i) q^{6} +(8.98612 - 8.98612i) q^{7} +(6.65882 + 21.6255i) q^{8} +9.00000i q^{9} +(-30.4988 + 8.35600i) q^{10} -38.8201i q^{11} +(-1.50295 + 23.9529i) q^{12} +(28.7750 - 28.7750i) q^{13} +(33.6230 - 12.7083i) q^{14} +(-33.3931 - 3.14659i) q^{15} +(-8.00000 + 63.4980i) q^{16} +(11.2917 + 11.2917i) q^{17} +(-10.4735 + 23.2014i) q^{18} +15.7801 q^{19} +(-88.3480 - 13.9509i) q^{20} +38.1249 q^{21} +(45.1758 - 100.076i) q^{22} +(-106.243 - 106.243i) q^{23} +(-31.7490 + 60.0000i) q^{24} +(23.3498 - 122.800i) q^{25} +(107.666 - 40.6940i) q^{26} +(-19.0919 + 19.0919i) q^{27} +(101.467 + 6.36664i) q^{28} +208.958i q^{29} +(-82.4235 - 46.9720i) q^{30} -243.881i q^{31} +(-94.5175 + 154.384i) q^{32} +(82.3498 - 82.3498i) q^{33} +(15.9689 + 42.2497i) q^{34} +(-13.3292 + 141.456i) q^{35} +(-54.0000 + 47.6235i) q^{36} +(-203.475 - 203.475i) q^{37} +(40.6801 + 18.3637i) q^{38} +122.082 q^{39} +(-211.521 - 138.777i) q^{40} +25.7503 q^{41} +(98.2834 + 44.3667i) q^{42} +(253.557 + 253.557i) q^{43} +(232.921 - 205.417i) q^{44} +(-64.1625 - 77.5124i) q^{45} +(-150.250 - 397.523i) q^{46} +(-366.988 + 366.988i) q^{47} +(-151.670 + 117.729i) q^{48} +181.499i q^{49} +(203.099 - 289.397i) q^{50} +47.9067i q^{51} +(324.913 + 20.3870i) q^{52} +(-501.716 + 501.716i) q^{53} +(-71.4353 + 27.0000i) q^{54} +(276.755 + 334.337i) q^{55} +(254.166 + 134.492i) q^{56} +(33.4747 + 33.4747i) q^{57} +(-243.169 + 538.680i) q^{58} +646.366 q^{59} +(-157.820 - 217.009i) q^{60} +527.249 q^{61} +(283.810 - 628.710i) q^{62} +(80.8750 + 80.8750i) q^{63} +(-423.320 + 288.000i) q^{64} +(-42.6824 + 452.967i) q^{65} +(308.125 - 116.460i) q^{66} +(-392.384 + 392.384i) q^{67} +(-8.00015 + 127.500i) q^{68} -450.749i q^{69} +(-198.978 + 349.154i) q^{70} -611.293i q^{71} +(-194.629 + 59.9294i) q^{72} +(144.800 - 144.800i) q^{73} +(-287.757 - 761.333i) q^{74} +(310.030 - 210.965i) q^{75} +(83.5006 + 94.6807i) q^{76} +(-348.842 - 348.842i) q^{77} +(314.720 + 142.070i) q^{78} -551.355 q^{79} +(-383.788 - 603.909i) q^{80} -81.0000 q^{81} +(66.3826 + 29.9662i) q^{82} +(-494.620 - 494.620i) q^{83} +(201.738 + 228.749i) q^{84} +(-177.750 - 16.7492i) q^{85} +(358.583 + 948.723i) q^{86} +(-443.267 + 443.267i) q^{87} +(839.502 - 258.496i) q^{88} -740.166i q^{89} +(-75.2040 - 274.489i) q^{90} -517.151i q^{91} +(75.2726 - 1199.64i) q^{92} +(517.350 - 517.350i) q^{93} +(-1373.14 + 518.999i) q^{94} +(-135.906 + 112.499i) q^{95} +(-528.000 + 126.996i) q^{96} +(84.7998 + 84.7998i) q^{97} +(-211.215 + 467.894i) q^{98} +349.381 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 24 q^{5} + 24 q^{6}+O(q^{10}) \) 8 * q - 24 * q^5 + 24 * q^6	\( 8 q - 24 q^{5} + 24 q^{6} - 56 q^{10} + 320 q^{13} - 64 q^{16} + 240 q^{17} - 432 q^{20} - 144 q^{21} - 40 q^{22} - 352 q^{25} - 336 q^{26} + 560 q^{28} - 72 q^{30} + 120 q^{33} - 432 q^{36} - 640 q^{37} - 240 q^{38} + 448 q^{40} + 1104 q^{41} + 840 q^{42} - 648 q^{45} - 304 q^{46} + 2352 q^{50} + 1920 q^{52} - 1200 q^{53} - 960 q^{56} - 720 q^{57} - 1960 q^{58} - 336 q^{60} - 272 q^{61} - 1200 q^{62} + 2592 q^{65} + 2016 q^{66} - 1440 q^{68} - 712 q^{70} + 440 q^{73} + 2464 q^{76} - 3120 q^{77} + 960 q^{78} + 192 q^{80} - 648 q^{81} - 1680 q^{82} - 2320 q^{85} + 3168 q^{86} + 800 q^{88} + 1008 q^{90} - 3360 q^{92} + 3600 q^{93} - 4224 q^{96} - 40 q^{97} - 3360 q^{98}+O(q^{100}) \) 8 * q - 24 * q^5 + 24 * q^6 - 56 * q^10 + 320 * q^13 - 64 * q^16 + 240 * q^17 - 432 * q^20 - 144 * q^21 - 40 * q^22 - 352 * q^25 - 336 * q^26 + 560 * q^28 - 72 * q^30 + 120 * q^33 - 432 * q^36 - 640 * q^37 - 240 * q^38 + 448 * q^40 + 1104 * q^41 + 840 * q^42 - 648 * q^45 - 304 * q^46 + 2352 * q^50 + 1920 * q^52 - 1200 * q^53 - 960 * q^56 - 720 * q^57 - 1960 * q^58 - 336 * q^60 - 272 * q^61 - 1200 * q^62 + 2592 * q^65 + 2016 * q^66 - 1440 * q^68 - 712 * q^70 + 440 * q^73 + 2464 * q^76 - 3120 * q^77 + 960 * q^78 + 192 * q^80 - 648 * q^81 - 1680 * q^82 - 2320 * q^85 + 3168 * q^86 + 800 * q^88 + 1008 * q^90 - 3360 * q^92 + 3600 * q^93 - 4224 * q^96 - 40 * q^97 - 3360 * q^98

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